Properties

Label 140.2.q.b.9.1
Level $140$
Weight $2$
Character 140.9
Analytic conductor $1.118$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 140.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.11790562830\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-19})\)
Defining polynomial: \(x^{4} - x^{3} - 4 x^{2} - 5 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 9.1
Root \(-1.63746 - 1.52274i\) of defining polynomial
Character \(\chi\) \(=\) 140.9
Dual form 140.2.q.b.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(-1.13746 - 2.38876i) q^{7} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +(-0.500000 - 2.17945i) q^{5} +(-1.13746 - 2.38876i) q^{7} +(2.63746 + 4.56821i) q^{11} +2.62685i q^{13} +(-2.63746 - 2.83616i) q^{15} +(-0.362541 + 0.209313i) q^{17} +(1.63746 - 2.83616i) q^{19} +(-3.77492 - 2.59808i) q^{21} +(6.77492 + 3.91150i) q^{23} +(-4.50000 + 2.17945i) q^{25} +5.19615i q^{27} -4.27492 q^{29} +(-1.63746 - 2.83616i) q^{31} +(7.91238 + 4.56821i) q^{33} +(-4.63746 + 3.67341i) q^{35} +(-8.63746 - 4.98684i) q^{37} +(2.27492 + 3.94027i) q^{39} -3.72508 q^{41} -2.15068i q^{43} +(5.63746 + 3.25479i) q^{47} +(-4.41238 + 5.43424i) q^{49} +(-0.362541 + 0.627940i) q^{51} +(-4.91238 + 2.83616i) q^{53} +(8.63746 - 8.03231i) q^{55} -5.67232i q^{57} +(-1.63746 - 2.83616i) q^{59} +(6.77492 - 11.7345i) q^{61} +(5.72508 - 1.31342i) q^{65} +(-3.04983 + 1.76082i) q^{67} +13.5498 q^{69} -4.54983 q^{71} +(5.63746 - 3.25479i) q^{73} +(-4.86254 + 7.16629i) q^{75} +(7.91238 - 11.4964i) q^{77} +(3.63746 - 6.30026i) q^{79} +(4.50000 + 7.79423i) q^{81} -7.40437i q^{83} +(0.637459 + 0.685484i) q^{85} +(-6.41238 + 3.70219i) q^{87} +(-3.50000 + 6.06218i) q^{89} +(6.27492 - 2.98793i) q^{91} +(-4.91238 - 2.83616i) q^{93} +(-7.00000 - 2.15068i) q^{95} +6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + O(q^{10}) \) \( 4 q + 6 q^{3} - 2 q^{5} + 3 q^{7} + 3 q^{11} - 3 q^{15} - 9 q^{17} - q^{19} + 12 q^{23} - 18 q^{25} - 2 q^{29} + q^{31} + 9 q^{33} - 11 q^{35} - 27 q^{37} - 6 q^{39} - 30 q^{41} + 15 q^{47} + 5 q^{49} - 9 q^{51} + 3 q^{53} + 27 q^{55} + q^{59} + 12 q^{61} + 38 q^{65} + 18 q^{67} + 24 q^{69} + 12 q^{71} + 15 q^{73} - 27 q^{75} + 9 q^{77} + 7 q^{79} + 18 q^{81} - 5 q^{85} - 3 q^{87} - 14 q^{89} + 10 q^{91} + 3 q^{93} - 28 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/140\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(101\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.50000 0.866025i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) 0 0
\(5\) −0.500000 2.17945i −0.223607 0.974679i
\(6\) 0 0
\(7\) −1.13746 2.38876i −0.429919 0.902867i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.63746 + 4.56821i 0.795224 + 1.37737i 0.922697 + 0.385526i \(0.125980\pi\)
−0.127473 + 0.991842i \(0.540687\pi\)
\(12\) 0 0
\(13\) 2.62685i 0.728557i 0.931290 + 0.364278i \(0.118684\pi\)
−0.931290 + 0.364278i \(0.881316\pi\)
\(14\) 0 0
\(15\) −2.63746 2.83616i −0.680989 0.732294i
\(16\) 0 0
\(17\) −0.362541 + 0.209313i −0.0879292 + 0.0507659i −0.543320 0.839526i \(-0.682833\pi\)
0.455391 + 0.890292i \(0.349500\pi\)
\(18\) 0 0
\(19\) 1.63746 2.83616i 0.375659 0.650660i −0.614767 0.788709i \(-0.710750\pi\)
0.990425 + 0.138049i \(0.0440831\pi\)
\(20\) 0 0
\(21\) −3.77492 2.59808i −0.823754 0.566947i
\(22\) 0 0
\(23\) 6.77492 + 3.91150i 1.41267 + 0.815604i 0.995639 0.0932891i \(-0.0297381\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −4.50000 + 2.17945i −0.900000 + 0.435890i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −4.27492 −0.793832 −0.396916 0.917855i \(-0.629920\pi\)
−0.396916 + 0.917855i \(0.629920\pi\)
\(30\) 0 0
\(31\) −1.63746 2.83616i −0.294096 0.509390i 0.680678 0.732583i \(-0.261685\pi\)
−0.974774 + 0.223193i \(0.928352\pi\)
\(32\) 0 0
\(33\) 7.91238 + 4.56821i 1.37737 + 0.795224i
\(34\) 0 0
\(35\) −4.63746 + 3.67341i −0.783874 + 0.620920i
\(36\) 0 0
\(37\) −8.63746 4.98684i −1.41999 0.819831i −0.423692 0.905806i \(-0.639266\pi\)
−0.996297 + 0.0859750i \(0.972599\pi\)
\(38\) 0 0
\(39\) 2.27492 + 3.94027i 0.364278 + 0.630949i
\(40\) 0 0
\(41\) −3.72508 −0.581760 −0.290880 0.956760i \(-0.593948\pi\)
−0.290880 + 0.956760i \(0.593948\pi\)
\(42\) 0 0
\(43\) 2.15068i 0.327975i −0.986462 0.163988i \(-0.947564\pi\)
0.986462 0.163988i \(-0.0524357\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.63746 + 3.25479i 0.822308 + 0.474760i 0.851212 0.524823i \(-0.175868\pi\)
−0.0289038 + 0.999582i \(0.509202\pi\)
\(48\) 0 0
\(49\) −4.41238 + 5.43424i −0.630339 + 0.776320i
\(50\) 0 0
\(51\) −0.362541 + 0.627940i −0.0507659 + 0.0879292i
\(52\) 0 0
\(53\) −4.91238 + 2.83616i −0.674767 + 0.389577i −0.797880 0.602816i \(-0.794045\pi\)
0.123114 + 0.992393i \(0.460712\pi\)
\(54\) 0 0
\(55\) 8.63746 8.03231i 1.16467 1.08308i
\(56\) 0 0
\(57\) 5.67232i 0.751318i
\(58\) 0 0
\(59\) −1.63746 2.83616i −0.213179 0.369237i 0.739529 0.673125i \(-0.235048\pi\)
−0.952708 + 0.303888i \(0.901715\pi\)
\(60\) 0 0
\(61\) 6.77492 11.7345i 0.867439 1.50245i 0.00283468 0.999996i \(-0.499098\pi\)
0.864605 0.502453i \(-0.167569\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.72508 1.31342i 0.710109 0.162910i
\(66\) 0 0
\(67\) −3.04983 + 1.76082i −0.372597 + 0.215119i −0.674592 0.738191i \(-0.735681\pi\)
0.301996 + 0.953309i \(0.402347\pi\)
\(68\) 0 0
\(69\) 13.5498 1.63121
\(70\) 0 0
\(71\) −4.54983 −0.539966 −0.269983 0.962865i \(-0.587018\pi\)
−0.269983 + 0.962865i \(0.587018\pi\)
\(72\) 0 0
\(73\) 5.63746 3.25479i 0.659815 0.380944i −0.132392 0.991197i \(-0.542266\pi\)
0.792206 + 0.610253i \(0.208932\pi\)
\(74\) 0 0
\(75\) −4.86254 + 7.16629i −0.561478 + 0.827492i
\(76\) 0 0
\(77\) 7.91238 11.4964i 0.901699 1.31014i
\(78\) 0 0
\(79\) 3.63746 6.30026i 0.409246 0.708835i −0.585559 0.810630i \(-0.699125\pi\)
0.994805 + 0.101795i \(0.0324584\pi\)
\(80\) 0 0
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) 0 0
\(83\) 7.40437i 0.812736i −0.913710 0.406368i \(-0.866795\pi\)
0.913710 0.406368i \(-0.133205\pi\)
\(84\) 0 0
\(85\) 0.637459 + 0.685484i 0.0691421 + 0.0743512i
\(86\) 0 0
\(87\) −6.41238 + 3.70219i −0.687479 + 0.396916i
\(88\) 0 0
\(89\) −3.50000 + 6.06218i −0.370999 + 0.642590i −0.989720 0.143022i \(-0.954318\pi\)
0.618720 + 0.785611i \(0.287651\pi\)
\(90\) 0 0
\(91\) 6.27492 2.98793i 0.657790 0.313220i
\(92\) 0 0
\(93\) −4.91238 2.83616i −0.509390 0.294096i
\(94\) 0 0
\(95\) −7.00000 2.15068i −0.718185 0.220655i
\(96\) 0 0
\(97\) 6.92820i 0.703452i 0.936103 + 0.351726i \(0.114405\pi\)
−0.936103 + 0.351726i \(0.885595\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.77492 + 11.7345i 0.674129 + 1.16763i 0.976723 + 0.214507i \(0.0688144\pi\)
−0.302593 + 0.953120i \(0.597852\pi\)
\(102\) 0 0
\(103\) −9.77492 5.64355i −0.963151 0.556076i −0.0660098 0.997819i \(-0.521027\pi\)
−0.897141 + 0.441743i \(0.854360\pi\)
\(104\) 0 0
\(105\) −3.77492 + 9.52628i −0.368394 + 0.929670i
\(106\) 0 0
\(107\) 3.04983 + 1.76082i 0.294839 + 0.170225i 0.640122 0.768273i \(-0.278884\pi\)
−0.345283 + 0.938499i \(0.612217\pi\)
\(108\) 0 0
\(109\) −5.77492 10.0025i −0.553137 0.958061i −0.998046 0.0624852i \(-0.980097\pi\)
0.444909 0.895576i \(-0.353236\pi\)
\(110\) 0 0
\(111\) −17.2749 −1.63966
\(112\) 0 0
\(113\) 4.30136i 0.404637i 0.979320 + 0.202319i \(0.0648477\pi\)
−0.979320 + 0.202319i \(0.935152\pi\)
\(114\) 0 0
\(115\) 5.13746 16.7213i 0.479070 1.55927i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.912376 + 0.627940i 0.0836374 + 0.0575632i
\(120\) 0 0
\(121\) −8.41238 + 14.5707i −0.764761 + 1.32461i
\(122\) 0 0
\(123\) −5.58762 + 3.22602i −0.503819 + 0.290880i
\(124\) 0 0
\(125\) 7.00000 + 8.71780i 0.626099 + 0.779744i
\(126\) 0 0
\(127\) 15.6460i 1.38836i 0.719802 + 0.694179i \(0.244232\pi\)
−0.719802 + 0.694179i \(0.755768\pi\)
\(128\) 0 0
\(129\) −1.86254 3.22602i −0.163988 0.284035i
\(130\) 0 0
\(131\) 5.36254 9.28819i 0.468527 0.811513i −0.530826 0.847481i \(-0.678118\pi\)
0.999353 + 0.0359678i \(0.0114514\pi\)
\(132\) 0 0
\(133\) −8.63746 0.685484i −0.748963 0.0594390i
\(134\) 0 0
\(135\) 11.3248 2.59808i 0.974679 0.223607i
\(136\) 0 0
\(137\) 18.4622 10.6592i 1.57733 0.910674i 0.582103 0.813115i \(-0.302230\pi\)
0.995230 0.0975588i \(-0.0311034\pi\)
\(138\) 0 0
\(139\) −13.0997 −1.11110 −0.555550 0.831483i \(-0.687492\pi\)
−0.555550 + 0.831483i \(0.687492\pi\)
\(140\) 0 0
\(141\) 11.2749 0.949519
\(142\) 0 0
\(143\) −12.0000 + 6.92820i −1.00349 + 0.579365i
\(144\) 0 0
\(145\) 2.13746 + 9.31697i 0.177506 + 0.773732i
\(146\) 0 0
\(147\) −1.91238 + 11.9726i −0.157730 + 0.987482i
\(148\) 0 0
\(149\) −3.77492 + 6.53835i −0.309253 + 0.535642i −0.978199 0.207669i \(-0.933412\pi\)
0.668946 + 0.743311i \(0.266746\pi\)
\(150\) 0 0
\(151\) 6.36254 + 11.0202i 0.517776 + 0.896815i 0.999787 + 0.0206494i \(0.00657337\pi\)
−0.482011 + 0.876165i \(0.660093\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.36254 + 4.98684i −0.430730 + 0.400553i
\(156\) 0 0
\(157\) 1.91238 1.10411i 0.152624 0.0881176i −0.421743 0.906715i \(-0.638582\pi\)
0.574367 + 0.818598i \(0.305248\pi\)
\(158\) 0 0
\(159\) −4.91238 + 8.50848i −0.389577 + 0.674767i
\(160\) 0 0
\(161\) 1.63746 20.6328i 0.129050 1.62610i
\(162\) 0 0
\(163\) −4.91238 2.83616i −0.384767 0.222145i 0.295123 0.955459i \(-0.404639\pi\)
−0.679890 + 0.733314i \(0.737973\pi\)
\(164\) 0 0
\(165\) 6.00000 19.5287i 0.467099 1.52031i
\(166\) 0 0
\(167\) 0.476171i 0.0368472i 0.999830 + 0.0184236i \(0.00586474\pi\)
−0.999830 + 0.0184236i \(0.994135\pi\)
\(168\) 0 0
\(169\) 6.09967 0.469205
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −17.7371 10.2405i −1.34853 0.778573i −0.360488 0.932764i \(-0.617390\pi\)
−0.988041 + 0.154190i \(0.950723\pi\)
\(174\) 0 0
\(175\) 10.3248 + 8.27040i 0.780478 + 0.625183i
\(176\) 0 0
\(177\) −4.91238 2.83616i −0.369237 0.213179i
\(178\) 0 0
\(179\) −3.63746 6.30026i −0.271876 0.470904i 0.697466 0.716618i \(-0.254311\pi\)
−0.969342 + 0.245714i \(0.920978\pi\)
\(180\) 0 0
\(181\) −24.2749 −1.80434 −0.902170 0.431380i \(-0.858027\pi\)
−0.902170 + 0.431380i \(0.858027\pi\)
\(182\) 0 0
\(183\) 23.4690i 1.73488i
\(184\) 0 0
\(185\) −6.54983 + 21.3183i −0.481553 + 1.56735i
\(186\) 0 0
\(187\) −1.91238 1.10411i −0.139847 0.0807406i
\(188\) 0 0
\(189\) 12.4124 5.91041i 0.902867 0.429919i
\(190\) 0 0
\(191\) −0.0876242 + 0.151770i −0.00634026 + 0.0109817i −0.869178 0.494499i \(-0.835352\pi\)
0.862838 + 0.505481i \(0.168685\pi\)
\(192\) 0 0
\(193\) 18.4622 10.6592i 1.32894 0.767263i 0.343803 0.939042i \(-0.388285\pi\)
0.985136 + 0.171778i \(0.0549513\pi\)
\(194\) 0 0
\(195\) 7.45017 6.92820i 0.533517 0.496139i
\(196\) 0 0
\(197\) 8.60271i 0.612918i −0.951884 0.306459i \(-0.900856\pi\)
0.951884 0.306459i \(-0.0991442\pi\)
\(198\) 0 0
\(199\) 8.63746 + 14.9605i 0.612293 + 1.06052i 0.990853 + 0.134946i \(0.0430861\pi\)
−0.378560 + 0.925577i \(0.623581\pi\)
\(200\) 0 0
\(201\) −3.04983 + 5.28247i −0.215119 + 0.372597i
\(202\) 0 0
\(203\) 4.86254 + 10.2118i 0.341284 + 0.716725i
\(204\) 0 0
\(205\) 1.86254 + 8.11863i 0.130086 + 0.567030i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 17.2749 1.19493
\(210\) 0 0
\(211\) 25.6495 1.76578 0.882892 0.469576i \(-0.155593\pi\)
0.882892 + 0.469576i \(0.155593\pi\)
\(212\) 0 0
\(213\) −6.82475 + 3.94027i −0.467624 + 0.269983i
\(214\) 0 0
\(215\) −4.68729 + 1.07534i −0.319671 + 0.0733375i
\(216\) 0 0
\(217\) −4.91238 + 7.13752i −0.333474 + 0.484526i
\(218\) 0 0
\(219\) 5.63746 9.76436i 0.380944 0.659815i
\(220\) 0 0
\(221\) −0.549834 0.952341i −0.0369859 0.0640614i
\(222\) 0 0
\(223\) 8.71780i 0.583787i −0.956451 0.291893i \(-0.905715\pi\)
0.956451 0.291893i \(-0.0942853\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 16.9124 9.76436i 1.12251 0.648084i 0.180472 0.983580i \(-0.442237\pi\)
0.942041 + 0.335496i \(0.108904\pi\)
\(228\) 0 0
\(229\) 1.63746 2.83616i 0.108206 0.187419i −0.806837 0.590774i \(-0.798823\pi\)
0.915044 + 0.403355i \(0.132156\pi\)
\(230\) 0 0
\(231\) 1.91238 24.0969i 0.125825 1.58546i
\(232\) 0 0
\(233\) −12.3625 7.13752i −0.809897 0.467594i 0.0370231 0.999314i \(-0.488212\pi\)
−0.846920 + 0.531720i \(0.821546\pi\)
\(234\) 0 0
\(235\) 4.27492 13.9140i 0.278865 0.907646i
\(236\) 0 0
\(237\) 12.6005i 0.818492i
\(238\) 0 0
\(239\) −0.549834 −0.0355658 −0.0177829 0.999842i \(-0.505661\pi\)
−0.0177829 + 0.999842i \(0.505661\pi\)
\(240\) 0 0
\(241\) −4.91238 8.50848i −0.316434 0.548080i 0.663307 0.748347i \(-0.269152\pi\)
−0.979741 + 0.200267i \(0.935819\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 14.0498 + 6.89943i 0.897611 + 0.440788i
\(246\) 0 0
\(247\) 7.45017 + 4.30136i 0.474043 + 0.273689i
\(248\) 0 0
\(249\) −6.41238 11.1066i −0.406368 0.703850i
\(250\) 0 0
\(251\) −20.5498 −1.29709 −0.648547 0.761175i \(-0.724623\pi\)
−0.648547 + 0.761175i \(0.724623\pi\)
\(252\) 0 0
\(253\) 41.2657i 2.59435i
\(254\) 0 0
\(255\) 1.54983 + 0.476171i 0.0970544 + 0.0298190i
\(256\) 0 0
\(257\) −10.0876 5.82409i −0.629249 0.363297i 0.151212 0.988501i \(-0.451682\pi\)
−0.780461 + 0.625204i \(0.785016\pi\)
\(258\) 0 0
\(259\) −2.08762 + 26.3052i −0.129719 + 1.63452i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.675248 0.389855i 0.0416376 0.0240395i −0.479037 0.877795i \(-0.659014\pi\)
0.520674 + 0.853755i \(0.325681\pi\)
\(264\) 0 0
\(265\) 8.63746 + 9.28819i 0.530595 + 0.570569i
\(266\) 0 0
\(267\) 12.1244i 0.741999i
\(268\) 0 0
\(269\) −7.22508 12.5142i −0.440521 0.763005i 0.557207 0.830374i \(-0.311873\pi\)
−0.997728 + 0.0673687i \(0.978540\pi\)
\(270\) 0 0
\(271\) −4.91238 + 8.50848i −0.298406 + 0.516854i −0.975771 0.218793i \(-0.929788\pi\)
0.677366 + 0.735646i \(0.263121\pi\)
\(272\) 0 0
\(273\) 6.82475 9.91613i 0.413053 0.600152i
\(274\) 0 0
\(275\) −21.8248 14.8087i −1.31608 0.893001i
\(276\) 0 0
\(277\) −12.3625 + 7.13752i −0.742793 + 0.428852i −0.823084 0.567920i \(-0.807748\pi\)
0.0802909 + 0.996771i \(0.474415\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 9.46221 5.46301i 0.562470 0.324742i −0.191666 0.981460i \(-0.561389\pi\)
0.754136 + 0.656718i \(0.228056\pi\)
\(284\) 0 0
\(285\) −12.3625 + 2.83616i −0.732294 + 0.168000i
\(286\) 0 0
\(287\) 4.23713 + 8.89834i 0.250110 + 0.525252i
\(288\) 0 0
\(289\) −8.41238 + 14.5707i −0.494846 + 0.857098i
\(290\) 0 0
\(291\) 6.00000 + 10.3923i 0.351726 + 0.609208i
\(292\) 0 0
\(293\) 6.92820i 0.404750i 0.979308 + 0.202375i \(0.0648660\pi\)
−0.979308 + 0.202375i \(0.935134\pi\)
\(294\) 0 0
\(295\) −5.36254 + 4.98684i −0.312219 + 0.290345i
\(296\) 0 0
\(297\) −23.7371 + 13.7046i −1.37737 + 0.795224i
\(298\) 0 0
\(299\) −10.2749 + 17.7967i −0.594214 + 1.02921i
\(300\) 0 0
\(301\) −5.13746 + 2.44631i −0.296118 + 0.141003i
\(302\) 0 0
\(303\) 20.3248 + 11.7345i 1.16763 + 0.674129i
\(304\) 0 0
\(305\) −28.9622 8.89834i −1.65837 0.509517i
\(306\) 0 0
\(307\) 26.5145i 1.51326i −0.653843 0.756631i \(-0.726844\pi\)
0.653843 0.756631i \(-0.273156\pi\)
\(308\) 0 0
\(309\) −19.5498 −1.11215
\(310\) 0 0
\(311\) 4.91238 + 8.50848i 0.278555 + 0.482472i 0.971026 0.238974i \(-0.0768111\pi\)
−0.692471 + 0.721446i \(0.743478\pi\)
\(312\) 0 0
\(313\) 29.0120 + 16.7501i 1.63986 + 0.946772i 0.980881 + 0.194609i \(0.0623438\pi\)
0.658977 + 0.752163i \(0.270990\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.1873 + 12.8098i 1.24616 + 0.719472i 0.970342 0.241737i \(-0.0777171\pi\)
0.275821 + 0.961209i \(0.411050\pi\)
\(318\) 0 0
\(319\) −11.2749 19.5287i −0.631274 1.09340i
\(320\) 0 0
\(321\) 6.09967 0.340450
\(322\) 0 0
\(323\) 1.37097i 0.0762827i
\(324\) 0 0
\(325\) −5.72508 11.8208i −0.317570 0.655701i
\(326\) 0 0
\(327\) −17.3248 10.0025i −0.958061 0.553137i
\(328\) 0 0
\(329\) 1.36254 17.1687i 0.0751193 0.946543i
\(330\) 0 0
\(331\) −8.91238 + 15.4367i −0.489868 + 0.848477i −0.999932 0.0116596i \(-0.996289\pi\)
0.510064 + 0.860137i \(0.329622\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.36254 + 5.76655i 0.292987 + 0.315060i
\(336\) 0 0
\(337\) 4.30136i 0.234310i 0.993114 + 0.117155i \(0.0373774\pi\)
−0.993114 + 0.117155i \(0.962623\pi\)
\(338\) 0 0
\(339\) 3.72508 + 6.45203i 0.202319 + 0.350426i
\(340\) 0 0
\(341\) 8.63746 14.9605i 0.467745 0.810157i
\(342\) 0 0
\(343\) 18.0000 + 4.35890i 0.971909 + 0.235358i
\(344\) 0 0
\(345\) −6.77492 29.5312i −0.364749 1.58991i
\(346\) 0 0
\(347\) −10.5000 + 6.06218i −0.563670 + 0.325435i −0.754617 0.656165i \(-0.772177\pi\)
0.190947 + 0.981600i \(0.438844\pi\)
\(348\) 0 0
\(349\) 3.72508 0.199399 0.0996996 0.995018i \(-0.468212\pi\)
0.0996996 + 0.995018i \(0.468212\pi\)
\(350\) 0 0
\(351\) −13.6495 −0.728557
\(352\) 0 0
\(353\) 7.08762 4.09204i 0.377236 0.217797i −0.299379 0.954134i \(-0.596779\pi\)
0.676615 + 0.736337i \(0.263446\pi\)
\(354\) 0 0
\(355\) 2.27492 + 9.91613i 0.120740 + 0.526294i
\(356\) 0 0
\(357\) 1.91238 + 0.151770i 0.101214 + 0.00803249i
\(358\) 0 0
\(359\) 18.1873 31.5013i 0.959889 1.66258i 0.237127 0.971479i \(-0.423794\pi\)
0.722762 0.691097i \(-0.242872\pi\)
\(360\) 0 0
\(361\) 4.13746 + 7.16629i 0.217761 + 0.377173i
\(362\) 0 0
\(363\) 29.1413i 1.52952i
\(364\) 0 0
\(365\) −9.91238 10.6592i −0.518837 0.557926i
\(366\) 0 0
\(367\) 5.22508 3.01670i 0.272747 0.157471i −0.357388 0.933956i \(-0.616333\pi\)
0.630135 + 0.776485i \(0.282999\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.3625 + 8.50848i 0.641831 + 0.441739i
\(372\) 0 0
\(373\) −8.63746 4.98684i −0.447231 0.258209i 0.259429 0.965762i \(-0.416466\pi\)
−0.706660 + 0.707553i \(0.749799\pi\)
\(374\) 0 0
\(375\) 18.0498 + 7.01452i 0.932089 + 0.362228i
\(376\) 0 0
\(377\) 11.2296i 0.578352i
\(378\) 0 0
\(379\) 21.6495 1.11206 0.556030 0.831162i \(-0.312324\pi\)
0.556030 + 0.831162i \(0.312324\pi\)
\(380\) 0 0
\(381\) 13.5498 + 23.4690i 0.694179 + 1.20235i
\(382\) 0 0
\(383\) 5.32475 + 3.07425i 0.272082 + 0.157087i 0.629833 0.776730i \(-0.283123\pi\)
−0.357751 + 0.933817i \(0.616456\pi\)
\(384\) 0 0
\(385\) −29.0120 11.4964i −1.47859 0.585912i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 16.1873 + 28.0372i 0.820728 + 1.42154i 0.905141 + 0.425112i \(0.139765\pi\)
−0.0844123 + 0.996431i \(0.526901\pi\)
\(390\) 0 0
\(391\) −3.27492 −0.165620
\(392\) 0 0
\(393\) 18.5764i 0.937055i
\(394\) 0 0
\(395\) −15.5498 4.77753i −0.782397 0.240383i
\(396\) 0 0
\(397\) 9.36254 + 5.40547i 0.469892 + 0.271293i 0.716195 0.697901i \(-0.245882\pi\)
−0.246302 + 0.969193i \(0.579216\pi\)
\(398\) 0 0
\(399\) −13.5498 + 6.45203i −0.678340 + 0.323006i
\(400\) 0 0
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) 7.45017 4.30136i 0.371119 0.214266i
\(404\) 0 0
\(405\) 14.7371 13.7046i 0.732294 0.680989i
\(406\) 0 0
\(407\) 52.6103i 2.60780i
\(408\) 0 0
\(409\) −10.0498 17.4068i −0.496932 0.860712i 0.503061 0.864251i \(-0.332207\pi\)
−0.999994 + 0.00353862i \(0.998874\pi\)
\(410\) 0 0
\(411\) 18.4622 31.9775i 0.910674 1.57733i
\(412\) 0 0
\(413\) −4.91238 + 7.13752i −0.241722 + 0.351214i
\(414\) 0 0
\(415\) −16.1375 + 3.70219i −0.792157 + 0.181733i
\(416\) 0 0
\(417\) −19.6495 + 11.3446i −0.962240 + 0.555550i
\(418\) 0 0
\(419\) 13.0997 0.639961 0.319980 0.947424i \(-0.396324\pi\)
0.319980 + 0.947424i \(0.396324\pi\)
\(420\) 0 0
\(421\) −4.27492 −0.208347 −0.104173 0.994559i \(-0.533220\pi\)
−0.104173 + 0.994559i \(0.533220\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.17525 1.73205i 0.0570079 0.0840168i
\(426\) 0 0
\(427\) −35.7371 2.83616i −1.72944 0.137251i
\(428\) 0 0
\(429\) −12.0000 + 20.7846i −0.579365 + 1.00349i
\(430\) 0 0
\(431\) 9.18729 + 15.9129i 0.442536 + 0.766495i 0.997877 0.0651276i \(-0.0207454\pi\)
−0.555341 + 0.831623i \(0.687412\pi\)
\(432\) 0 0
\(433\) 18.1578i 0.872606i −0.899800 0.436303i \(-0.856288\pi\)
0.899800 0.436303i \(-0.143712\pi\)
\(434\) 0 0
\(435\) 11.2749 + 12.1244i 0.540591 + 0.581318i
\(436\) 0 0
\(437\) 22.1873 12.8098i 1.06136 0.612778i
\(438\) 0 0
\(439\) 11.9124 20.6328i 0.568547 0.984752i −0.428163 0.903701i \(-0.640839\pi\)
0.996710 0.0810504i \(-0.0258275\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 10.5000 + 6.06218i 0.498870 + 0.288023i 0.728247 0.685315i \(-0.240335\pi\)
−0.229377 + 0.973338i \(0.573669\pi\)
\(444\) 0 0
\(445\) 14.9622 + 4.59698i 0.709277 + 0.217918i
\(446\) 0 0
\(447\) 13.0767i 0.618507i
\(448\) 0 0
\(449\) 3.17525 0.149849 0.0749246 0.997189i \(-0.476128\pi\)
0.0749246 + 0.997189i \(0.476128\pi\)
\(450\) 0 0
\(451\) −9.82475 17.0170i −0.462629 0.801298i
\(452\) 0 0
\(453\) 19.0876 + 11.0202i 0.896815 + 0.517776i
\(454\) 0 0
\(455\) −9.64950 12.1819i −0.452376 0.571096i
\(456\) 0 0
\(457\) −1.18729 0.685484i −0.0555392 0.0320656i 0.471973 0.881613i \(-0.343542\pi\)
−0.527512 + 0.849547i \(0.676875\pi\)
\(458\) 0 0
\(459\) −1.08762 1.88382i −0.0507659 0.0879292i
\(460\) 0 0
\(461\) −14.0000 −0.652045 −0.326023 0.945362i \(-0.605709\pi\)
−0.326023 + 0.945362i \(0.605709\pi\)
\(462\) 0 0
\(463\) 2.15068i 0.0999505i 0.998750 + 0.0499752i \(0.0159142\pi\)
−0.998750 + 0.0499752i \(0.984086\pi\)
\(464\) 0 0
\(465\) −3.72508 + 12.1244i −0.172747 + 0.562254i
\(466\) 0 0
\(467\) 13.5997 + 7.85177i 0.629318 + 0.363337i 0.780488 0.625171i \(-0.214971\pi\)
−0.151170 + 0.988508i \(0.548304\pi\)
\(468\) 0 0
\(469\) 7.67525 + 5.28247i 0.354410 + 0.243922i
\(470\) 0 0
\(471\) 1.91238 3.31233i 0.0881176 0.152624i
\(472\) 0 0
\(473\) 9.82475 5.67232i 0.451743 0.260814i
\(474\) 0 0
\(475\) −1.18729 + 16.3315i −0.0544767 + 0.749340i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.91238 + 8.50848i 0.224452 + 0.388763i 0.956155 0.292861i \(-0.0946074\pi\)
−0.731703 + 0.681624i \(0.761274\pi\)
\(480\) 0 0
\(481\) 13.0997 22.6893i 0.597293 1.03454i
\(482\) 0 0
\(483\) −15.4124 32.3673i −0.701287 1.47277i
\(484\) 0 0
\(485\) 15.0997 3.46410i 0.685641 0.157297i
\(486\) 0 0
\(487\) −2.53779 + 1.46519i −0.114998 + 0.0663943i −0.556396 0.830917i \(-0.687816\pi\)
0.441398 + 0.897312i \(0.354483\pi\)
\(488\) 0 0
\(489\) −9.82475 −0.444291
\(490\) 0 0
\(491\) −28.5498 −1.28844 −0.644218 0.764842i \(-0.722817\pi\)
−0.644218 + 0.764842i \(0.722817\pi\)
\(492\) 0 0
\(493\) 1.54983 0.894797i 0.0698010 0.0402996i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.17525 + 10.8685i 0.232142 + 0.487518i
\(498\) 0 0
\(499\) 0.812707 1.40765i 0.0363818 0.0630151i −0.847261 0.531177i \(-0.821750\pi\)
0.883643 + 0.468161i \(0.155083\pi\)
\(500\) 0 0
\(501\) 0.412376 + 0.714256i 0.0184236 + 0.0319106i
\(502\) 0 0
\(503\) 31.7682i 1.41647i 0.705975 + 0.708236i \(0.250509\pi\)
−0.705975 + 0.708236i \(0.749491\pi\)
\(504\) 0 0
\(505\) 22.1873 20.6328i 0.987322 0.918149i
\(506\) 0 0
\(507\) 9.14950 5.28247i 0.406344 0.234603i
\(508\) 0 0
\(509\) −7.22508 + 12.5142i −0.320246 + 0.554683i −0.980539 0.196326i \(-0.937099\pi\)
0.660293 + 0.751008i \(0.270432\pi\)
\(510\) 0 0
\(511\) −14.1873 9.76436i −0.627609 0.431950i
\(512\) 0 0
\(513\) 14.7371 + 8.50848i 0.650660 + 0.375659i
\(514\) 0 0
\(515\) −7.41238 + 24.1257i −0.326628 + 1.06311i
\(516\) 0 0
\(517\) 34.3375i 1.51016i
\(518\) 0 0
\(519\) −35.4743 −1.55715
\(520\) 0 0
\(521\) −4.91238 8.50848i −0.215215 0.372763i 0.738124 0.674665i \(-0.235712\pi\)
−0.953339 + 0.301902i \(0.902379\pi\)
\(522\) 0 0
\(523\) −6.36254 3.67341i −0.278215 0.160627i 0.354400 0.935094i \(-0.384685\pi\)
−0.632615 + 0.774467i \(0.718018\pi\)
\(524\) 0 0
\(525\) 22.6495 + 3.46410i 0.988505 + 0.151186i
\(526\) 0 0
\(527\) 1.18729 + 0.685484i 0.0517193 + 0.0298602i
\(528\) 0 0
\(529\) 19.0997 + 33.0816i 0.830420 + 1.43833i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9.78523i 0.423845i
\(534\) 0 0
\(535\) 2.31271 7.52737i 0.0999870 0.325437i
\(536\) 0 0
\(537\) −10.9124 6.30026i −0.470904 0.271876i
\(538\) 0 0
\(539\) −36.4622 5.82409i −1.57054 0.250861i
\(540\) 0 0
\(541\) 8.77492 15.1986i 0.377263 0.653439i −0.613400 0.789773i \(-0.710199\pi\)
0.990663 + 0.136334i \(0.0435319\pi\)
\(542\) 0 0
\(543\) −36.4124 + 21.0227i −1.56260 + 0.902170i
\(544\) 0 0
\(545\) −18.9124 + 17.5874i −0.810117 + 0.753360i
\(546\) 0 0
\(547\) 20.5386i 0.878168i 0.898446 + 0.439084i \(0.144697\pi\)
−0.898446 + 0.439084i \(0.855303\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.00000 + 12.1244i −0.298210 + 0.516515i
\(552\) 0 0
\(553\) −19.1873 1.52274i −0.815927 0.0647534i
\(554\) 0 0
\(555\) 8.63746 + 37.6498i 0.366640 + 1.59815i
\(556\) 0 0
\(557\) −8.63746 + 4.98684i −0.365981 + 0.211299i −0.671701 0.740822i \(-0.734436\pi\)
0.305720 + 0.952121i \(0.401103\pi\)
\(558\) 0 0
\(559\) 5.64950 0.238949
\(560\) 0 0
\(561\) −3.82475 −0.161481
\(562\) 0 0
\(563\) −19.5997 + 11.3159i −0.826028 + 0.476907i −0.852491 0.522743i \(-0.824909\pi\)
0.0264630 + 0.999650i \(0.491576\pi\)
\(564\) 0 0
\(565\) 9.37459 2.15068i 0.394392 0.0904797i
\(566\) 0 0
\(567\) 13.5000 19.6150i 0.566947 0.823754i
\(568\) 0 0
\(569\) 4.18729 7.25260i 0.175540 0.304045i −0.764808 0.644259i \(-0.777166\pi\)
0.940348 + 0.340214i \(0.110499\pi\)
\(570\) 0 0
\(571\) −3.63746 6.30026i −0.152223 0.263658i 0.779821 0.626002i \(-0.215310\pi\)
−0.932044 + 0.362344i \(0.881976\pi\)
\(572\) 0 0
\(573\) 0.303539i 0.0126805i
\(574\) 0 0
\(575\) −39.0120 2.83616i −1.62691 0.118276i
\(576\) 0 0
\(577\) 3.36254 1.94136i 0.139984 0.0808200i −0.428372 0.903602i \(-0.640913\pi\)
0.568357 + 0.822782i \(0.307579\pi\)
\(578\) 0 0
\(579\) 18.4622 31.9775i 0.767263 1.32894i
\(580\) 0 0
\(581\) −17.6873 + 8.42217i −0.733793 + 0.349410i
\(582\) 0 0
\(583\) −25.9124 14.9605i −1.07318 0.619601i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 20.8997i 0.862623i −0.902203 0.431311i \(-0.858051\pi\)
0.902203 0.431311i \(-0.141949\pi\)
\(588\) 0 0
\(589\) −10.7251 −0.441919
\(590\) 0 0
\(591\) −7.45017 12.9041i −0.306459 0.530802i
\(592\) 0 0
\(593\) −28.9124 16.6926i −1.18729 0.685482i −0.229600 0.973285i \(-0.573742\pi\)
−0.957689 + 0.287804i \(0.907075\pi\)
\(594\) 0 0
\(595\) 0.912376 2.30245i 0.0374038 0.0943911i
\(596\) 0 0
\(597\) 25.9124 + 14.9605i 1.06052 + 0.612293i
\(598\) 0 0
\(599\) 2.63746 + 4.56821i 0.107764 + 0.186652i 0.914864 0.403762i \(-0.132298\pi\)
−0.807100 + 0.590414i \(0.798964\pi\)
\(600\) 0 0
\(601\) 14.0000 0.571072 0.285536 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 35.9622 + 11.0490i 1.46207 + 0.449206i
\(606\) 0 0
\(607\) 9.87459 + 5.70109i 0.400797 + 0.231400i 0.686828 0.726820i \(-0.259003\pi\)
−0.286031 + 0.958220i \(0.592336\pi\)
\(608\) 0 0
\(609\) 16.1375 + 11.1066i 0.653923 + 0.450061i
\(610\) 0 0
\(611\) −8.54983 + 14.8087i −0.345889 + 0.599098i
\(612\) 0 0
\(613\) −24.5619 + 14.1808i −0.992045 + 0.572757i −0.905885 0.423524i \(-0.860793\pi\)
−0.0861600 + 0.996281i \(0.527460\pi\)
\(614\) 0 0
\(615\) 9.82475 + 10.5649i 0.396172 + 0.426019i
\(616\) 0 0
\(617\) 31.2920i 1.25977i 0.776689 + 0.629884i \(0.216898\pi\)
−0.776689 + 0.629884i \(0.783102\pi\)
\(618\) 0 0
\(619\) −4.46221 7.72877i −0.179351 0.310646i 0.762307 0.647215i \(-0.224067\pi\)
−0.941659 + 0.336570i \(0.890733\pi\)
\(620\) 0 0
\(621\) −20.3248 + 35.2035i −0.815604 + 1.41267i
\(622\) 0 0
\(623\) 18.4622 + 1.46519i 0.739673 + 0.0587017i
\(624\) 0 0
\(625\) 15.5000 19.6150i 0.620000 0.784602i
\(626\) 0 0
\(627\) 25.9124 14.9605i 1.03484 0.597466i
\(628\) 0 0
\(629\) 4.17525 0.166478
\(630\) 0 0
\(631\) 33.0997 1.31768 0.658839 0.752284i \(-0.271048\pi\)
0.658839 + 0.752284i \(0.271048\pi\)
\(632\) 0 0
\(633\) 38.4743 22.2131i 1.52921 0.882892i
\(634\) 0 0
\(635\) 34.0997 7.82300i 1.35320 0.310446i
\(636\) 0 0
\(637\) −14.2749 11.5906i −0.565593 0.459238i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.04983 + 1.81837i 0.0414660 + 0.0718212i 0.886014 0.463659i \(-0.153464\pi\)
−0.844548 + 0.535481i \(0.820131\pi\)
\(642\) 0 0
\(643\) 31.4071i 1.23857i −0.785164 0.619287i \(-0.787422\pi\)
0.785164 0.619287i \(-0.212578\pi\)
\(644\) 0 0
\(645\) −6.09967 + 5.67232i −0.240174 + 0.223348i
\(646\) 0 0
\(647\) −23.3248 + 13.4666i −0.916991 + 0.529425i −0.882674 0.469986i \(-0.844259\pi\)
−0.0343169 + 0.999411i \(0.510926\pi\)
\(648\) 0 0
\(649\) 8.63746 14.9605i 0.339050 0.587252i
\(650\) 0 0
\(651\) −1.18729 + 14.9605i −0.0465337 + 0.586349i
\(652\) 0 0
\(653\) −24.5619 14.1808i −0.961181 0.554938i −0.0646444 0.997908i \(-0.520591\pi\)
−0.896536 + 0.442970i \(0.853925\pi\)
\(654\) 0 0
\(655\) −22.9244 7.04329i −0.895731 0.275204i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 40.5498 1.57960 0.789799 0.613366i \(-0.210185\pi\)
0.789799 + 0.613366i \(0.210185\pi\)
\(660\) 0 0
\(661\) 0.225083 + 0.389855i 0.00875471 + 0.0151636i 0.870370 0.492399i \(-0.163880\pi\)
−0.861615 + 0.507563i \(0.830547\pi\)
\(662\) 0 0
\(663\) −1.64950 0.952341i −0.0640614 0.0369859i
\(664\) 0 0
\(665\) 2.82475 + 19.1676i 0.109539 + 0.743289i
\(666\) 0 0
\(667\) −28.9622 16.7213i −1.12142 0.647453i
\(668\) 0 0
\(669\) −7.54983 13.0767i −0.291893 0.505574i
\(670\) 0 0
\(671\) 71.4743 2.75923
\(672\) 0 0
\(673\) 31.2920i 1.20622i −0.797659 0.603109i \(-0.793928\pi\)
0.797659 0.603109i \(-0.206072\pi\)
\(674\) 0 0
\(675\) −11.3248 23.3827i −0.435890 0.900000i
\(676\) 0 0
\(677\) 40.1873 + 23.2021i 1.54452 + 0.891731i 0.998545 + 0.0539317i \(0.0171753\pi\)
0.545979 + 0.837799i \(0.316158\pi\)
\(678\) 0 0
\(679\) 16.5498 7.88054i 0.635124 0.302428i
\(680\) 0 0
\(681\) 16.9124 29.2931i 0.648084 1.12251i
\(682\) 0 0
\(683\) 16.5997 9.58382i 0.635169 0.366715i −0.147582 0.989050i \(-0.547149\pi\)
0.782751 + 0.622335i \(0.213816\pi\)
\(684\) 0 0
\(685\) −32.4622 34.9079i −1.24032 1.33376i
\(686\) 0 0
\(687\) 5.67232i 0.216413i
\(688\) 0 0
\(689\) −7.45017 12.9041i −0.283829 0.491606i
\(690\) 0 0
\(691\) −15.1873 + 26.3052i −0.577752 + 1.00070i 0.417985 + 0.908454i \(0.362737\pi\)
−0.995737 + 0.0922416i \(0.970597\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.54983 + 28.5501i 0.248449 + 1.08297i
\(696\) 0 0
\(697\) 1.35050 0.779710i 0.0511537 0.0295336i
\(698\) 0 0
\(699\) −24.7251 −0.935189
\(700\) 0 0
\(701\) 8.82475 0.333306 0.166653 0.986016i \(-0.446704\pi\)
0.166653 + 0.986016i \(0.446704\pi\)
\(702\) 0 0
\(703\) −28.2870 + 16.3315i −1.06686 + 0.615954i
\(704\) 0 0
\(705\) −5.63746 24.5731i −0.212319 0.925477i
\(706\) 0 0
\(707\) 20.3248 29.5312i 0.764391 1.11063i
\(708\) 0 0
\(709\) −5.22508 + 9.05011i −0.196232 + 0.339884i −0.947304 0.320337i \(-0.896204\pi\)
0.751072 + 0.660221i \(0.229537\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 25.6197i 0.959465i
\(714\) 0 0
\(715\) 21.0997 + 22.6893i 0.789083 + 0.848531i
\(716\) 0 0
\(717\) −0.824752 + 0.476171i −0.0308009 + 0.0177829i
\(718\) 0 0
\(719\) −15.1873 + 26.3052i −0.566390 + 0.981017i 0.430528 + 0.902577i \(0.358327\pi\)
−0.996919 + 0.0784400i \(0.975006\pi\)
\(720\) 0 0
\(721\) −2.36254 + 29.7693i −0.0879856 + 1.10867i
\(722\) 0 0
\(723\) −14.7371 8.50848i −0.548080 0.316434i
\(724\) 0 0
\(725\) 19.2371 9.31697i 0.714449 0.346023i
\(726\) 0 0
\(727\) 3.10302i 0.115085i −0.998343 0.0575423i \(-0.981674\pi\)
0.998343 0.0575423i \(-0.0183264\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 0.450166 + 0.779710i 0.0166500 + 0.0288386i
\(732\) 0 0
\(733\) −32.6375 18.8432i −1.20549 0.695991i −0.243721 0.969845i \(-0.578368\pi\)
−0.961771 + 0.273854i \(0.911701\pi\)
\(734\) 0 0
\(735\) 27.0498 1.81837i 0.997748 0.0670715i
\(736\) 0 0
\(737\) −16.0876 9.28819i −0.592595 0.342135i
\(738\) 0 0
\(739\) −10.4622 18.1211i −0.384859 0.666595i 0.606891 0.794785i \(-0.292416\pi\)
−0.991750 + 0.128190i \(0.959083\pi\)
\(740\) 0 0
\(741\) 14.9003 0.547377
\(742\) 0 0
\(743\) 6.45203i 0.236702i −0.992972 0.118351i \(-0.962239\pi\)
0.992972 0.118351i \(-0.0377608\pi\)
\(744\) 0 0
\(745\) 16.1375 + 4.95807i 0.591231 + 0.181650i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.737127 9.28819i 0.0269341 0.339383i
\(750\) 0 0
\(751\) 7.36254 12.7523i 0.268663 0.465338i −0.699854 0.714286i \(-0.746752\pi\)
0.968517 + 0.248948i \(0.0800849\pi\)
\(752\) 0 0
\(753\) −30.8248 + 17.7967i −1.12332 + 0.648547i
\(754\) 0 0
\(755\) 20.8368 19.3770i 0.758329 0.705200i
\(756\) 0 0
\(757\) 35.5934i 1.29366i −0.762633 0.646831i \(-0.776094\pi\)
0.762633 0.646831i \(-0.223906\pi\)
\(758\) 0 0
\(759\) 35.7371 + 61.8985i 1.29718 + 2.24677i
\(760\) 0 0
\(761\) −11.4622 + 19.8531i −0.415505 + 0.719675i −0.995481 0.0949578i \(-0.969728\pi\)
0.579977 + 0.814633i \(0.303062\pi\)
\(762\) 0 0
\(763\) −17.3248 + 25.1723i −0.627198 + 0.911298i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7.45017 4.30136i 0.269010 0.155313i
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −20.1752 −0.726594
\(772\) 0 0
\(773\) −34.9124 + 20.1567i −1.25571 + 0.724985i −0.972238 0.233995i \(-0.924820\pi\)
−0.283473 + 0.958980i \(0.591487\pi\)
\(774\) 0 0
\(775\) 13.5498 + 9.19397i 0.486724 + 0.330257i
\(776\) 0 0
\(777\) 19.6495 + 41.2657i 0.704922 + 1.48040i
\(778\) 0 0
\(779\) −6.09967 + 10.5649i −0.218543 + 0.378528i
\(780\) 0 0
\(781\) −12.0000 20.7846i −0.429394 0.743732i
\(782\) 0 0
\(783\) 22.2131i 0.793832i
\(784\) 0 0
\(785\) −3.36254 3.61587i −0.120014 0.129056i
\(786\) 0 0
\(787\) 1.50000 0.866025i 0.0534692 0.0308705i −0.473027 0.881048i \(-0.656839\pi\)
0.526496 + 0.850177i \(0.323505\pi\)
\(788\) 0 0
\(789\) 0.675248 1.16956i 0.0240395 0.0416376i
\(790\) 0 0
\(791\) 10.2749 4.89261i 0.365334 0.173961i
\(792\) 0 0
\(793\) 30.8248 + 17.7967i 1.09462 + 0.631979i
\(794\) 0 0
\(795\) 21.0000 + 6.45203i 0.744793 + 0.228830i
\(796\) 0 0