Properties

Label 1260.2.bm.b.109.1
Level $1260$
Weight $2$
Character 1260.109
Analytic conductor $10.061$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.0611506547\)
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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.1
Root \(2.13746 - 0.656712i\) of defining polynomial
Character \(\chi\) \(=\) 1260.109
Dual form 1260.2.bm.b.289.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 2.17945i) q^{5} +(-1.13746 + 2.38876i) q^{7} +O(q^{10})\) \(q+(0.500000 - 2.17945i) q^{5} +(-1.13746 + 2.38876i) q^{7} +(-2.63746 + 4.56821i) q^{11} -2.62685i q^{13} +(0.362541 + 0.209313i) q^{17} +(1.63746 + 2.83616i) q^{19} +(-6.77492 + 3.91150i) q^{23} +(-4.50000 - 2.17945i) q^{25} +4.27492 q^{29} +(-1.63746 + 2.83616i) q^{31} +(4.63746 + 3.67341i) q^{35} +(-8.63746 + 4.98684i) q^{37} +3.72508 q^{41} +2.15068i q^{43} +(-5.63746 + 3.25479i) q^{47} +(-4.41238 - 5.43424i) q^{49} +(4.91238 + 2.83616i) q^{53} +(8.63746 + 8.03231i) q^{55} +(1.63746 - 2.83616i) q^{59} +(6.77492 + 11.7345i) q^{61} +(-5.72508 - 1.31342i) q^{65} +(-3.04983 - 1.76082i) q^{67} +4.54983 q^{71} +(5.63746 + 3.25479i) q^{73} +(-7.91238 - 11.4964i) q^{77} +(3.63746 + 6.30026i) q^{79} -7.40437i q^{83} +(0.637459 - 0.685484i) q^{85} +(3.50000 + 6.06218i) q^{89} +(6.27492 + 2.98793i) q^{91} +(7.00000 - 2.15068i) q^{95} -6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5} + 3 q^{7} + O(q^{10}) \) \( 4 q + 2 q^{5} + 3 q^{7} - 3 q^{11} + 9 q^{17} - q^{19} - 12 q^{23} - 18 q^{25} + 2 q^{29} + q^{31} + 11 q^{35} - 27 q^{37} + 30 q^{41} - 15 q^{47} + 5 q^{49} - 3 q^{53} + 27 q^{55} - q^{59} + 12 q^{61} - 38 q^{65} + 18 q^{67} - 12 q^{71} + 15 q^{73} - 9 q^{77} + 7 q^{79} - 5 q^{85} + 14 q^{89} + 10 q^{91} + 28 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(757\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0 0
\(4\) 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 0.127473 + 0.991842i \(0.459313\pi\)
−0.922697 + 0.385526i \(0.874020\pi\)
\(12\) 0 0
\(13\) 2.62685i 0.728557i −0.931290 0.364278i \(-0.881316\pi\)
0.931290 0.364278i \(-0.118684\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.362541 + 0.209313i 0.0879292 + 0.0507659i 0.543320 0.839526i \(-0.317167\pi\)
−0.455391 + 0.890292i \(0.650500\pi\)
\(18\) 0 0
\(19\) 1.63746 + 2.83616i 0.375659 + 0.650660i 0.990425 0.138049i \(-0.0440831\pi\)
−0.614767 + 0.788709i \(0.710750\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.77492 + 3.91150i −1.41267 + 0.815604i −0.995639 0.0932891i \(-0.970262\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −4.50000 2.17945i −0.900000 0.435890i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.27492 0.793832 0.396916 0.917855i \(-0.370080\pi\)
0.396916 + 0.917855i \(0.370080\pi\)
\(30\) 0 0
\(31\) −1.63746 + 2.83616i −0.294096 + 0.509390i −0.974774 0.223193i \(-0.928352\pi\)
0.680678 + 0.732583i \(0.261685\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.63746 + 3.67341i 0.783874 + 0.620920i
\(36\) 0 0
\(37\) −8.63746 + 4.98684i −1.41999 + 0.819831i −0.996297 0.0859750i \(-0.972599\pi\)
−0.423692 + 0.905806i \(0.639266\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.72508 0.581760 0.290880 0.956760i \(-0.406052\pi\)
0.290880 + 0.956760i \(0.406052\pi\)
\(42\) 0 0
\(43\) 2.15068i 0.327975i 0.986462 + 0.163988i \(0.0524357\pi\)
−0.986462 + 0.163988i \(0.947564\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.63746 + 3.25479i −0.822308 + 0.474760i −0.851212 0.524823i \(-0.824132\pi\)
0.0289038 + 0.999582i \(0.490798\pi\)
\(48\) 0 0
\(49\) −4.41238 5.43424i −0.630339 0.776320i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.91238 + 2.83616i 0.674767 + 0.389577i 0.797880 0.602816i \(-0.205955\pi\)
−0.123114 + 0.992393i \(0.539288\pi\)
\(54\) 0 0
\(55\) 8.63746 + 8.03231i 1.16467 + 1.08308i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.63746 2.83616i 0.213179 0.369237i −0.739529 0.673125i \(-0.764952\pi\)
0.952708 + 0.303888i \(0.0982849\pi\)
\(60\) 0 0
\(61\) 6.77492 + 11.7345i 0.867439 + 1.50245i 0.864605 + 0.502453i \(0.167569\pi\)
0.00283468 + 0.999996i \(0.499098\pi\)
\(62\) 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 0.301996 0.953309i \(-0.402347\pi\)
−0.674592 + 0.738191i \(0.735681\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.54983 0.539966 0.269983 0.962865i \(-0.412982\pi\)
0.269983 + 0.962865i \(0.412982\pi\)
\(72\) 0 0
\(73\) 5.63746 + 3.25479i 0.659815 + 0.380944i 0.792206 0.610253i \(-0.208932\pi\)
−0.132392 + 0.991197i \(0.542266\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.91238 11.4964i −0.901699 1.31014i
\(78\) 0 0
\(79\) 3.63746 + 6.30026i 0.409246 + 0.708835i 0.994805 0.101795i \(-0.0324584\pi\)
−0.585559 + 0.810630i \(0.699125\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 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
\(87\) 0 0
\(88\) 0 0
\(89\) 3.50000 + 6.06218i 0.370999 + 0.642590i 0.989720 0.143022i \(-0.0456819\pi\)
−0.618720 + 0.785611i \(0.712349\pi\)
\(90\) 0 0
\(91\) 6.27492 + 2.98793i 0.657790 + 0.313220i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.00000 2.15068i 0.718185 0.220655i
\(96\) 0 0
\(97\) 6.92820i 0.703452i −0.936103 0.351726i \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.77492 + 11.7345i −0.674129 + 1.16763i 0.302593 + 0.953120i \(0.402148\pi\)
−0.976723 + 0.214507i \(0.931186\pi\)
\(102\) 0 0
\(103\) −9.77492 + 5.64355i −0.963151 + 0.556076i −0.897141 0.441743i \(-0.854360\pi\)
−0.0660098 + 0.997819i \(0.521027\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.04983 + 1.76082i −0.294839 + 0.170225i −0.640122 0.768273i \(-0.721116\pi\)
0.345283 + 0.938499i \(0.387783\pi\)
\(108\) 0 0
\(109\) −5.77492 + 10.0025i −0.553137 + 0.958061i 0.444909 + 0.895576i \(0.353236\pi\)
−0.998046 + 0.0624852i \(0.980097\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 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
\(123\) 0 0
\(124\) 0 0
\(125\) −7.00000 + 8.71780i −0.626099 + 0.779744i
\(126\) 0 0
\(127\) 15.6460i 1.38836i −0.719802 0.694179i \(-0.755768\pi\)
0.719802 0.694179i \(-0.244232\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.36254 9.28819i −0.468527 0.811513i 0.530826 0.847481i \(-0.321882\pi\)
−0.999353 + 0.0359678i \(0.988549\pi\)
\(132\) 0 0
\(133\) −8.63746 + 0.685484i −0.748963 + 0.0594390i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −18.4622 10.6592i −1.57733 0.910674i −0.995230 0.0975588i \(-0.968897\pi\)
−0.582103 0.813115i \(-0.697770\pi\)
\(138\) 0 0
\(139\) −13.0997 −1.11110 −0.555550 0.831483i \(-0.687492\pi\)
−0.555550 + 0.831483i \(0.687492\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 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
\(147\) 0 0
\(148\) 0 0
\(149\) 3.77492 + 6.53835i 0.309253 + 0.535642i 0.978199 0.207669i \(-0.0665876\pi\)
−0.668946 + 0.743311i \(0.733254\pi\)
\(150\) 0 0
\(151\) 6.36254 11.0202i 0.517776 0.896815i −0.482011 0.876165i \(-0.660093\pi\)
0.999787 0.0206494i \(-0.00657337\pi\)
\(152\) 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 0.574367 0.818598i \(-0.305248\pi\)
−0.421743 + 0.906715i \(0.638582\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.63746 20.6328i −0.129050 1.62610i
\(162\) 0 0
\(163\) −4.91238 + 2.83616i −0.384767 + 0.222145i −0.679890 0.733314i \(-0.737973\pi\)
0.295123 + 0.955459i \(0.404639\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 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 \(-0.382610\pi\)
0.988041 + 0.154190i \(0.0492769\pi\)
\(174\) 0 0
\(175\) 10.3248 8.27040i 0.780478 0.625183i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.63746 6.30026i 0.271876 0.470904i −0.697466 0.716618i \(-0.745689\pi\)
0.969342 + 0.245714i \(0.0790225\pi\)
\(180\) 0 0
\(181\) −24.2749 −1.80434 −0.902170 0.431380i \(-0.858027\pi\)
−0.902170 + 0.431380i \(0.858027\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 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
\(189\) 0 0
\(190\) 0 0
\(191\) 0.0876242 + 0.151770i 0.00634026 + 0.0109817i 0.869178 0.494499i \(-0.164648\pi\)
−0.862838 + 0.505481i \(0.831315\pi\)
\(192\) 0 0
\(193\) 18.4622 + 10.6592i 1.32894 + 0.767263i 0.985136 0.171778i \(-0.0549513\pi\)
0.343803 + 0.939042i \(0.388285\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 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 −0.378560 0.925577i \(-0.623581\pi\)
0.990853 0.134946i \(-0.0430861\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 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
\(213\) 0 0
\(214\) 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
\(219\) 0 0
\(220\) 0 0
\(221\) 0.549834 0.952341i 0.0369859 0.0640614i
\(222\) 0 0
\(223\) 8.71780i 0.583787i 0.956451 + 0.291893i \(0.0942853\pi\)
−0.956451 + 0.291893i \(0.905715\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.9124 9.76436i −1.12251 0.648084i −0.180472 0.983580i \(-0.557763\pi\)
−0.942041 + 0.335496i \(0.891096\pi\)
\(228\) 0 0
\(229\) 1.63746 + 2.83616i 0.108206 + 0.187419i 0.915044 0.403355i \(-0.132156\pi\)
−0.806837 + 0.590774i \(0.798823\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.3625 7.13752i 0.809897 0.467594i −0.0370231 0.999314i \(-0.511788\pi\)
0.846920 + 0.531720i \(0.178454\pi\)
\(234\) 0 0
\(235\) 4.27492 + 13.9140i 0.278865 + 0.907646i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.549834 0.0355658 0.0177829 0.999842i \(-0.494339\pi\)
0.0177829 + 0.999842i \(0.494339\pi\)
\(240\) 0 0
\(241\) −4.91238 + 8.50848i −0.316434 + 0.548080i −0.979741 0.200267i \(-0.935819\pi\)
0.663307 + 0.748347i \(0.269152\pi\)
\(242\) 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
\(249\) 0 0
\(250\) 0 0
\(251\) 20.5498 1.29709 0.648547 0.761175i \(-0.275377\pi\)
0.648547 + 0.761175i \(0.275377\pi\)
\(252\) 0 0
\(253\) 41.2657i 2.59435i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.0876 5.82409i 0.629249 0.363297i −0.151212 0.988501i \(-0.548318\pi\)
0.780461 + 0.625204i \(0.214984\pi\)
\(258\) 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 \(-0.340986\pi\)
−0.520674 + 0.853755i \(0.674319\pi\)
\(264\) 0 0
\(265\) 8.63746 9.28819i 0.530595 0.570569i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 7.22508 12.5142i 0.440521 0.763005i −0.557207 0.830374i \(-0.688127\pi\)
0.997728 + 0.0673687i \(0.0214604\pi\)
\(270\) 0 0
\(271\) −4.91238 8.50848i −0.298406 0.516854i 0.677366 0.735646i \(-0.263121\pi\)
−0.975771 + 0.218793i \(0.929788\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 21.8248 14.8087i 1.31608 0.893001i
\(276\) 0 0
\(277\) −12.3625 7.13752i −0.742793 0.428852i 0.0802909 0.996771i \(-0.474415\pi\)
−0.823084 + 0.567920i \(0.807748\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 9.46221 + 5.46301i 0.562470 + 0.324742i 0.754136 0.656718i \(-0.228056\pi\)
−0.191666 + 0.981460i \(0.561389\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 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
\(291\) 0 0
\(292\) 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
\(297\) 0 0
\(298\) 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
\(303\) 0 0
\(304\) 0 0
\(305\) 28.9622 8.89834i 1.65837 0.509517i
\(306\) 0 0
\(307\) 26.5145i 1.51326i 0.653843 + 0.756631i \(0.273156\pi\)
−0.653843 + 0.756631i \(0.726844\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.91238 + 8.50848i −0.278555 + 0.482472i −0.971026 0.238974i \(-0.923189\pi\)
0.692471 + 0.721446i \(0.256522\pi\)
\(312\) 0 0
\(313\) 29.0120 16.7501i 1.63986 0.946772i 0.658977 0.752163i \(-0.270990\pi\)
0.980881 0.194609i \(-0.0623438\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −22.1873 + 12.8098i −1.24616 + 0.719472i −0.970342 0.241737i \(-0.922283\pi\)
−0.275821 + 0.961209i \(0.588950\pi\)
\(318\) 0 0
\(319\) −11.2749 + 19.5287i −0.631274 + 1.09340i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.37097i 0.0762827i
\(324\) 0 0
\(325\) −5.72508 + 11.8208i −0.317570 + 0.655701i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.36254 17.1687i −0.0751193 0.946543i
\(330\) 0 0
\(331\) −8.91238 15.4367i −0.489868 0.848477i 0.510064 0.860137i \(-0.329622\pi\)
−0.999932 + 0.0116596i \(0.996289\pi\)
\(332\) 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 \(-0.962623\pi\)
0.993114 0.117155i \(-0.0373774\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 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
\(345\) 0 0
\(346\) 0 0
\(347\) 10.5000 + 6.06218i 0.563670 + 0.325435i 0.754617 0.656165i \(-0.227823\pi\)
−0.190947 + 0.981600i \(0.561156\pi\)
\(348\) 0 0
\(349\) 3.72508 0.199399 0.0996996 0.995018i \(-0.468212\pi\)
0.0996996 + 0.995018i \(0.468212\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7.08762 4.09204i −0.377236 0.217797i 0.299379 0.954134i \(-0.403221\pi\)
−0.676615 + 0.736337i \(0.736554\pi\)
\(354\) 0 0
\(355\) 2.27492 9.91613i 0.120740 0.526294i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −18.1873 31.5013i −0.959889 1.66258i −0.722762 0.691097i \(-0.757128\pi\)
−0.237127 0.971479i \(-0.576206\pi\)
\(360\) 0 0
\(361\) 4.13746 7.16629i 0.217761 0.377173i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.91238 10.6592i 0.518837 0.557926i
\(366\) 0 0
\(367\) 5.22508 + 3.01670i 0.272747 + 0.157471i 0.630135 0.776485i \(-0.282999\pi\)
−0.357388 + 0.933956i \(0.616333\pi\)
\(368\) 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 −0.706660 0.707553i \(-0.749799\pi\)
0.259429 + 0.965762i \(0.416466\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) 0 0
\(383\) −5.32475 + 3.07425i −0.272082 + 0.157087i −0.629833 0.776730i \(-0.716877\pi\)
0.357751 + 0.933817i \(0.383544\pi\)
\(384\) 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 0.0844123 + 0.996431i \(0.473099\pi\)
−0.905141 + 0.425112i \(0.860235\pi\)
\(390\) 0 0
\(391\) −3.27492 −0.165620
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 15.5498 4.77753i 0.782397 0.240383i
\(396\) 0 0
\(397\) 9.36254 5.40547i 0.469892 0.271293i −0.246302 0.969193i \(-0.579216\pi\)
0.716195 + 0.697901i \(0.245882\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i \(-0.142801\pi\)
−0.826139 + 0.563466i \(0.809468\pi\)
\(402\) 0 0
\(403\) 7.45017 + 4.30136i 0.371119 + 0.214266i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 52.6103i 2.60780i
\(408\) 0 0
\(409\) −10.0498 + 17.4068i −0.496932 + 0.860712i −0.999994 0.00353862i \(-0.998874\pi\)
0.503061 + 0.864251i \(0.332207\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 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
\(417\) 0 0
\(418\) 0 0
\(419\) −13.0997 −0.639961 −0.319980 0.947424i \(-0.603676\pi\)
−0.319980 + 0.947424i \(0.603676\pi\)
\(420\) 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
\(429\) 0 0
\(430\) 0 0
\(431\) −9.18729 + 15.9129i −0.442536 + 0.766495i −0.997877 0.0651276i \(-0.979255\pi\)
0.555341 + 0.831623i \(0.312588\pi\)
\(432\) 0 0
\(433\) 18.1578i 0.872606i 0.899800 + 0.436303i \(0.143712\pi\)
−0.899800 + 0.436303i \(0.856288\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −22.1873 12.8098i −1.06136 0.612778i
\(438\) 0 0
\(439\) 11.9124 + 20.6328i 0.568547 + 0.984752i 0.996710 + 0.0810504i \(0.0258275\pi\)
−0.428163 + 0.903701i \(0.640839\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −10.5000 + 6.06218i −0.498870 + 0.288023i −0.728247 0.685315i \(-0.759665\pi\)
0.229377 + 0.973338i \(0.426331\pi\)
\(444\) 0 0
\(445\) 14.9622 4.59698i 0.709277 0.217918i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.17525 −0.149849 −0.0749246 0.997189i \(-0.523872\pi\)
−0.0749246 + 0.997189i \(0.523872\pi\)
\(450\) 0 0
\(451\) −9.82475 + 17.0170i −0.462629 + 0.801298i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9.64950 12.1819i 0.452376 0.571096i
\(456\) 0 0
\(457\) −1.18729 + 0.685484i −0.0555392 + 0.0320656i −0.527512 0.849547i \(-0.676875\pi\)
0.471973 + 0.881613i \(0.343542\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 2.15068i 0.0999505i −0.998750 0.0499752i \(-0.984086\pi\)
0.998750 0.0499752i \(-0.0159142\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13.5997 + 7.85177i −0.629318 + 0.363337i −0.780488 0.625171i \(-0.785029\pi\)
0.151170 + 0.988508i \(0.451696\pi\)
\(468\) 0 0
\(469\) 7.67525 5.28247i 0.354410 0.243922i
\(470\) 0 0
\(471\) 0 0
\(472\) 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 \(-0.905393\pi\)
0.731703 + 0.681624i \(0.238726\pi\)
\(480\) 0 0
\(481\) 13.0997 + 22.6893i 0.597293 + 1.03454i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −15.0997 3.46410i −0.685641 0.157297i
\(486\) 0 0
\(487\) −2.53779 1.46519i −0.114998 0.0663943i 0.441398 0.897312i \(-0.354483\pi\)
−0.556396 + 0.830917i \(0.687816\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 28.5498 1.28844 0.644218 0.764842i \(-0.277183\pi\)
0.644218 + 0.764842i \(0.277183\pi\)
\(492\) 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 0.883643 0.468161i \(-0.155083\pi\)
−0.847261 + 0.531177i \(0.821750\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 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
\(507\) 0 0
\(508\) 0 0
\(509\) 7.22508 + 12.5142i 0.320246 + 0.554683i 0.980539 0.196326i \(-0.0629010\pi\)
−0.660293 + 0.751008i \(0.729568\pi\)
\(510\) 0 0
\(511\) −14.1873 + 9.76436i −0.627609 + 0.431950i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 7.41238 + 24.1257i 0.326628 + 1.06311i
\(516\) 0 0
\(517\) 34.3375i 1.51016i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 4.91238 8.50848i 0.215215 0.372763i −0.738124 0.674665i \(-0.764288\pi\)
0.953339 + 0.301902i \(0.0976214\pi\)
\(522\) 0 0
\(523\) −6.36254 + 3.67341i −0.278215 + 0.160627i −0.632615 0.774467i \(-0.718018\pi\)
0.354400 + 0.935094i \(0.384685\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 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
\(537\) 0 0
\(538\) 0 0
\(539\) 36.4622 5.82409i 1.57054 0.250861i
\(540\) 0 0
\(541\) 8.77492 + 15.1986i 0.377263 + 0.653439i 0.990663 0.136334i \(-0.0435319\pi\)
−0.613400 + 0.789773i \(0.710199\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.9124 + 17.5874i 0.810117 + 0.753360i
\(546\) 0 0
\(547\) 20.5386i 0.878168i −0.898446 0.439084i \(-0.855303\pi\)
0.898446 0.439084i \(-0.144697\pi\)
\(548\) 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
\(555\) 0 0
\(556\) 0 0
\(557\) 8.63746 + 4.98684i 0.365981 + 0.211299i 0.671701 0.740822i \(-0.265564\pi\)
−0.305720 + 0.952121i \(0.598897\pi\)
\(558\) 0 0
\(559\) 5.64950 0.238949
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 19.5997 + 11.3159i 0.826028 + 0.476907i 0.852491 0.522743i \(-0.175091\pi\)
−0.0264630 + 0.999650i \(0.508424\pi\)
\(564\) 0 0
\(565\) 9.37459 + 2.15068i 0.394392 + 0.0904797i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.18729 7.25260i −0.175540 0.304045i 0.764808 0.644259i \(-0.222834\pi\)
−0.940348 + 0.340214i \(0.889501\pi\)
\(570\) 0 0
\(571\) −3.63746 + 6.30026i −0.152223 + 0.263658i −0.932044 0.362344i \(-0.881976\pi\)
0.779821 + 0.626002i \(0.215310\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 39.0120 2.83616i 1.62691 0.118276i
\(576\) 0 0
\(577\) 3.36254 + 1.94136i 0.139984 + 0.0808200i 0.568357 0.822782i \(-0.307579\pi\)
−0.428372 + 0.903602i \(0.640913\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 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
\(591\) 0 0
\(592\) 0 0
\(593\) 28.9124 16.6926i 1.18729 0.685482i 0.229600 0.973285i \(-0.426258\pi\)
0.957689 + 0.287804i \(0.0929250\pi\)
\(594\) 0 0
\(595\) 0.912376 + 2.30245i 0.0374038 + 0.0943911i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −2.63746 + 4.56821i −0.107764 + 0.186652i −0.914864 0.403762i \(-0.867702\pi\)
0.807100 + 0.590414i \(0.201036\pi\)
\(600\) 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 −0.286031 0.958220i \(-0.592336\pi\)
0.686828 + 0.726820i \(0.259003\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8.54983 + 14.8087i 0.345889 + 0.599098i
\(612\) 0 0
\(613\) −24.5619 14.1808i −0.992045 0.572757i −0.0861600 0.996281i \(-0.527460\pi\)
−0.905885 + 0.423524i \(0.860793\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 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 −0.941659 0.336570i \(-0.890733\pi\)
0.762307 + 0.647215i \(0.224067\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 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
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 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 \(-0.846536\pi\)
0.844548 + 0.535481i \(0.179869\pi\)
\(642\) 0 0
\(643\) 31.4071i 1.23857i 0.785164 + 0.619287i \(0.212578\pi\)
−0.785164 + 0.619287i \(0.787422\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.3248 + 13.4666i 0.916991 + 0.529425i 0.882674 0.469986i \(-0.155741\pi\)
0.0343169 + 0.999411i \(0.489074\pi\)
\(648\) 0 0
\(649\) 8.63746 + 14.9605i 0.339050 + 0.587252i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 24.5619 14.1808i 0.961181 0.554938i 0.0646444 0.997908i \(-0.479409\pi\)
0.896536 + 0.442970i \(0.146075\pi\)
\(654\) 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 \(-0.789815\pi\)
−0.789799 + 0.613366i \(0.789815\pi\)
\(660\) 0 0
\(661\) 0.225083 0.389855i 0.00875471 0.0151636i −0.861615 0.507563i \(-0.830547\pi\)
0.870370 + 0.492399i \(0.163880\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 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
\(669\) 0 0
\(670\) 0 0
\(671\) −71.4743 −2.75923
\(672\) 0 0
\(673\) 31.2920i 1.20622i 0.797659 + 0.603109i \(0.206072\pi\)
−0.797659 + 0.603109i \(0.793928\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −40.1873 + 23.2021i −1.54452 + 0.891731i −0.545979 + 0.837799i \(0.683842\pi\)
−0.998545 + 0.0539317i \(0.982825\pi\)
\(678\) 0 0
\(679\) 16.5498 + 7.88054i 0.635124 + 0.302428i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −16.5997 9.58382i −0.635169 0.366715i 0.147582 0.989050i \(-0.452851\pi\)
−0.782751 + 0.622335i \(0.786184\pi\)
\(684\) 0 0
\(685\) −32.4622 + 34.9079i −1.24032 + 1.33376i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 7.45017 12.9041i 0.283829 0.491606i
\(690\) 0 0
\(691\) −15.1873 26.3052i −0.577752 1.00070i −0.995737 0.0922416i \(-0.970597\pi\)
0.417985 0.908454i \(-0.362737\pi\)
\(692\) 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
\(699\) 0 0
\(700\) 0 0
\(701\) −8.82475 −0.333306 −0.166653 0.986016i \(-0.553296\pi\)
−0.166653 + 0.986016i \(0.553296\pi\)
\(702\) 0 0
\(703\) −28.2870 16.3315i −1.06686 0.615954i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.3248 29.5312i −0.764391 1.11063i
\(708\) 0 0
\(709\) −5.22508 9.05011i −0.196232 0.339884i 0.751072 0.660221i \(-0.229537\pi\)
−0.947304 + 0.320337i \(0.896204\pi\)
\(710\) 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 0
\(718\) 0 0
\(719\) 15.1873 + 26.3052i 0.566390 + 0.981017i 0.996919 + 0.0784400i \(0.0249939\pi\)
−0.430528 + 0.902577i \(0.641673\pi\)
\(720\) 0 0
\(721\) −2.36254 29.7693i −0.0879856 1.10867i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −19.2371 9.31697i −0.714449 0.346023i
\(726\) 0 0
\(727\) 3.10302i 0.115085i 0.998343 + 0.0575423i \(0.0183264\pi\)
−0.998343 + 0.0575423i \(0.981674\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.450166 + 0.779710i −0.0166500 + 0.0288386i
\(732\) 0 0
\(733\) −32.6375 + 18.8432i −1.20549 + 0.695991i −0.961771 0.273854i \(-0.911701\pi\)
−0.243721 + 0.969845i \(0.578368\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.0876 9.28819i 0.592595 0.342135i
\(738\) 0 0
\(739\) −10.4622 + 18.1211i −0.384859 + 0.666595i −0.991750 0.128190i \(-0.959083\pi\)
0.606891 + 0.794785i \(0.292416\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 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 0.968517 0.248948i \(-0.0800849\pi\)
−0.699854 + 0.714286i \(0.746752\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −20.8368 19.3770i −0.758329 0.705200i
\(756\) 0 0
\(757\) 35.5934i 1.29366i 0.762633 + 0.646831i \(0.223906\pi\)
−0.762633 + 0.646831i \(0.776094\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.4622 + 19.8531i 0.415505 + 0.719675i 0.995481 0.0949578i \(-0.0302716\pi\)
−0.579977 + 0.814633i \(0.696938\pi\)
\(762\) 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
\(771\) 0 0
\(772\) 0 0
\(773\) 34.9124 + 20.1567i 1.25571 + 0.724985i 0.972238 0.233995i \(-0.0751800\pi\)
0.283473 + 0.958980i \(0.408513\pi\)
\(774\) 0 0
\(775\) 13.5498 9.19397i 0.486724 0.330257i
\(776\) 0 0
\(777\) 0 0
\(778\) 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
\(783\) 0 0
\(784\) 0 0
\(785\) 3.36254 3.61587i 0.120014 0.129056i
\(786\) 0 0
\(787\) 1.50000 + 0.866025i 0.0534692 + 0.0308705i 0.526496 0.850177i \(-0.323505\pi\)
−0.473027 + 0.881048i \(0.656839\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 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
\(795\) 0 0
\(796\) 0 0
\(797\) 46.8229i 1.65855i 0.558839 + 0.829276i \(0.311247\pi\)
−0.558839 + 0.829276i \(0.688753\pi\)
\(798\) 0 0
\(799\) −2.72508 −0.0964065
\(800\) 0 0
\(801\) 0 0
\(802\) 0