Properties

Label 2268.2.t.b.2105.3
Level $2268$
Weight $2$
Character 2268.2105
Analytic conductor $18.110$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{6} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 2105.3
Root \(-0.268067 - 1.71118i\) of defining polynomial
Character \(\chi\) \(=\) 2268.2105
Dual form 2268.2.t.b.1781.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.842869 + 1.45989i) q^{5} +(2.30301 - 1.30235i) q^{7} +O(q^{10})\) \(q+(-0.842869 + 1.45989i) q^{5} +(2.30301 - 1.30235i) q^{7} +(-3.38216 + 1.95269i) q^{11} +6.05515i q^{13} +(-0.201244 - 0.348565i) q^{17} +(-0.145617 - 0.0840718i) q^{19} +(-7.69373 - 4.44198i) q^{23} +(1.07914 + 1.86913i) q^{25} -7.10580i q^{29} +(-5.44527 + 3.14383i) q^{31} +(-0.0398441 + 4.45986i) q^{35} +(3.13257 - 5.42578i) q^{37} -3.29414 q^{41} -3.60947 q^{43} +(-4.38482 + 7.59474i) q^{47} +(3.60775 - 5.99868i) q^{49} +(4.94628 - 2.85574i) q^{53} -6.58345i q^{55} +(-2.25163 - 3.89994i) q^{59} +(-4.43678 - 2.56157i) q^{61} +(-8.83986 - 5.10369i) q^{65} +(2.95521 + 5.11857i) q^{67} +11.4308i q^{71} +(-6.05559 + 3.49620i) q^{73} +(-5.24607 + 8.90184i) q^{77} +(-0.603968 + 1.04610i) q^{79} -0.362701 q^{83} +0.678488 q^{85} +(-1.38526 + 2.39934i) q^{89} +(7.88594 + 13.9451i) q^{91} +(0.245471 - 0.141723i) q^{95} -0.587643i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{7} + O(q^{10}) \) \( 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(5\) −0.842869 + 1.45989i −0.376942 + 0.652883i −0.990616 0.136677i \(-0.956358\pi\)
0.613673 + 0.789560i \(0.289691\pi\)
\(6\) 0 0
\(7\) 2.30301 1.30235i 0.870458 0.492243i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.38216 + 1.95269i −1.01976 + 0.588758i −0.914034 0.405637i \(-0.867050\pi\)
−0.105725 + 0.994395i \(0.533716\pi\)
\(12\) 0 0
\(13\) 6.05515i 1.67940i 0.543054 + 0.839698i \(0.317268\pi\)
−0.543054 + 0.839698i \(0.682732\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.201244 0.348565i −0.0488088 0.0845393i 0.840589 0.541674i \(-0.182209\pi\)
−0.889398 + 0.457134i \(0.848876\pi\)
\(18\) 0 0
\(19\) −0.145617 0.0840718i −0.0334067 0.0192874i 0.483204 0.875508i \(-0.339473\pi\)
−0.516610 + 0.856221i \(0.672806\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.69373 4.44198i −1.60425 0.926216i −0.990623 0.136623i \(-0.956375\pi\)
−0.613630 0.789593i \(-0.710291\pi\)
\(24\) 0 0
\(25\) 1.07914 + 1.86913i 0.215829 + 0.373827i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.10580i 1.31951i −0.751479 0.659757i \(-0.770659\pi\)
0.751479 0.659757i \(-0.229341\pi\)
\(30\) 0 0
\(31\) −5.44527 + 3.14383i −0.978000 + 0.564649i −0.901666 0.432434i \(-0.857655\pi\)
−0.0763342 + 0.997082i \(0.524322\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.0398441 + 4.45986i −0.00673488 + 0.753855i
\(36\) 0 0
\(37\) 3.13257 5.42578i 0.514992 0.891992i −0.484857 0.874594i \(-0.661128\pi\)
0.999849 0.0173987i \(-0.00553846\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.29414 −0.514458 −0.257229 0.966350i \(-0.582810\pi\)
−0.257229 + 0.966350i \(0.582810\pi\)
\(42\) 0 0
\(43\) −3.60947 −0.550439 −0.275220 0.961381i \(-0.588751\pi\)
−0.275220 + 0.961381i \(0.588751\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.38482 + 7.59474i −0.639592 + 1.10781i 0.345930 + 0.938260i \(0.387563\pi\)
−0.985522 + 0.169546i \(0.945770\pi\)
\(48\) 0 0
\(49\) 3.60775 5.99868i 0.515393 0.856954i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.94628 2.85574i 0.679424 0.392266i −0.120214 0.992748i \(-0.538358\pi\)
0.799638 + 0.600482i \(0.205025\pi\)
\(54\) 0 0
\(55\) 6.58345i 0.887712i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.25163 3.89994i −0.293138 0.507729i 0.681412 0.731900i \(-0.261366\pi\)
−0.974550 + 0.224171i \(0.928033\pi\)
\(60\) 0 0
\(61\) −4.43678 2.56157i −0.568071 0.327976i 0.188308 0.982110i \(-0.439700\pi\)
−0.756379 + 0.654134i \(0.773033\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.83986 5.10369i −1.09645 0.633035i
\(66\) 0 0
\(67\) 2.95521 + 5.11857i 0.361036 + 0.625332i 0.988132 0.153610i \(-0.0490899\pi\)
−0.627096 + 0.778942i \(0.715757\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.4308i 1.35658i 0.734792 + 0.678292i \(0.237280\pi\)
−0.734792 + 0.678292i \(0.762720\pi\)
\(72\) 0 0
\(73\) −6.05559 + 3.49620i −0.708753 + 0.409199i −0.810599 0.585601i \(-0.800858\pi\)
0.101846 + 0.994800i \(0.467525\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.24607 + 8.90184i −0.597845 + 1.01446i
\(78\) 0 0
\(79\) −0.603968 + 1.04610i −0.0679517 + 0.117696i −0.898000 0.439996i \(-0.854980\pi\)
0.830048 + 0.557692i \(0.188313\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.362701 −0.0398116 −0.0199058 0.999802i \(-0.506337\pi\)
−0.0199058 + 0.999802i \(0.506337\pi\)
\(84\) 0 0
\(85\) 0.678488 0.0735924
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.38526 + 2.39934i −0.146837 + 0.254329i −0.930057 0.367416i \(-0.880243\pi\)
0.783220 + 0.621745i \(0.213576\pi\)
\(90\) 0 0
\(91\) 7.88594 + 13.9451i 0.826671 + 1.46184i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.245471 0.141723i 0.0251848 0.0145405i
\(96\) 0 0
\(97\) 0.587643i 0.0596661i −0.999555 0.0298330i \(-0.990502\pi\)
0.999555 0.0298330i \(-0.00949756\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.92329 + 11.9915i 0.688893 + 1.19320i 0.972196 + 0.234167i \(0.0752364\pi\)
−0.283303 + 0.959030i \(0.591430\pi\)
\(102\) 0 0
\(103\) −10.4610 6.03967i −1.03075 0.595106i −0.113554 0.993532i \(-0.536223\pi\)
−0.917201 + 0.398425i \(0.869557\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −15.9299 9.19711i −1.54000 0.889118i −0.998838 0.0481978i \(-0.984652\pi\)
−0.541159 0.840920i \(-0.682014\pi\)
\(108\) 0 0
\(109\) −5.51036 9.54422i −0.527796 0.914170i −0.999475 0.0323997i \(-0.989685\pi\)
0.471679 0.881771i \(-0.343648\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.50796i 0.800361i 0.916436 + 0.400181i \(0.131053\pi\)
−0.916436 + 0.400181i \(0.868947\pi\)
\(114\) 0 0
\(115\) 12.9696 7.48801i 1.20942 0.698260i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.917422 0.540659i −0.0840999 0.0495621i
\(120\) 0 0
\(121\) 2.12600 3.68234i 0.193273 0.334758i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0670 −1.07930
\(126\) 0 0
\(127\) −10.6312 −0.943365 −0.471682 0.881769i \(-0.656353\pi\)
−0.471682 + 0.881769i \(0.656353\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.16740 5.48610i 0.276737 0.479322i −0.693835 0.720134i \(-0.744080\pi\)
0.970572 + 0.240812i \(0.0774136\pi\)
\(132\) 0 0
\(133\) −0.444848 0.00397424i −0.0385732 0.000344611i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.4158 + 8.32296i −1.23162 + 0.711078i −0.967368 0.253375i \(-0.918459\pi\)
−0.264255 + 0.964453i \(0.585126\pi\)
\(138\) 0 0
\(139\) 4.89601i 0.415274i −0.978206 0.207637i \(-0.933423\pi\)
0.978206 0.207637i \(-0.0665773\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −11.8238 20.4795i −0.988758 1.71258i
\(144\) 0 0
\(145\) 10.3737 + 5.98926i 0.861489 + 0.497381i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.57864 + 2.64348i 0.375097 + 0.216562i 0.675683 0.737192i \(-0.263849\pi\)
−0.300586 + 0.953755i \(0.597182\pi\)
\(150\) 0 0
\(151\) 7.29163 + 12.6295i 0.593385 + 1.02777i 0.993773 + 0.111427i \(0.0355421\pi\)
−0.400388 + 0.916346i \(0.631125\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10.5993i 0.851360i
\(156\) 0 0
\(157\) 15.4160 8.90044i 1.23033 0.710332i 0.263232 0.964732i \(-0.415211\pi\)
0.967099 + 0.254400i \(0.0818781\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −23.5038 0.209981i −1.85236 0.0165488i
\(162\) 0 0
\(163\) 0.0482228 0.0835243i 0.00377710 0.00654213i −0.864131 0.503267i \(-0.832131\pi\)
0.867908 + 0.496725i \(0.165464\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.95745 −0.383619 −0.191809 0.981432i \(-0.561436\pi\)
−0.191809 + 0.981432i \(0.561436\pi\)
\(168\) 0 0
\(169\) −23.6648 −1.82037
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 7.40033 12.8177i 0.562637 0.974515i −0.434629 0.900610i \(-0.643120\pi\)
0.997265 0.0739055i \(-0.0235463\pi\)
\(174\) 0 0
\(175\) 4.91956 + 2.89921i 0.371884 + 0.219160i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −0.592751 + 0.342225i −0.0443043 + 0.0255791i −0.521989 0.852952i \(-0.674810\pi\)
0.477684 + 0.878532i \(0.341476\pi\)
\(180\) 0 0
\(181\) 7.84745i 0.583297i 0.956526 + 0.291648i \(0.0942037\pi\)
−0.956526 + 0.291648i \(0.905796\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.28070 + 9.14644i 0.388245 + 0.672459i
\(186\) 0 0
\(187\) 1.36128 + 0.785934i 0.0995464 + 0.0574732i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −16.9694 9.79729i −1.22786 0.708907i −0.261281 0.965263i \(-0.584145\pi\)
−0.966582 + 0.256356i \(0.917478\pi\)
\(192\) 0 0
\(193\) −9.18116 15.9022i −0.660875 1.14467i −0.980386 0.197086i \(-0.936852\pi\)
0.319512 0.947582i \(-0.396481\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.92313i 0.422006i 0.977485 + 0.211003i \(0.0676730\pi\)
−0.977485 + 0.211003i \(0.932327\pi\)
\(198\) 0 0
\(199\) −13.6268 + 7.86741i −0.965975 + 0.557706i −0.898007 0.439982i \(-0.854985\pi\)
−0.0679681 + 0.997687i \(0.521652\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −9.25426 16.3648i −0.649522 1.14858i
\(204\) 0 0
\(205\) 2.77653 4.80909i 0.193921 0.335881i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.656665 0.0454225
\(210\) 0 0
\(211\) −10.1324 −0.697541 −0.348771 0.937208i \(-0.613401\pi\)
−0.348771 + 0.937208i \(0.613401\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3.04231 5.26944i 0.207484 0.359373i
\(216\) 0 0
\(217\) −8.44616 + 14.3320i −0.573363 + 0.972917i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.11061 1.21856i 0.141975 0.0819693i
\(222\) 0 0
\(223\) 15.4665i 1.03571i 0.855467 + 0.517857i \(0.173270\pi\)
−0.855467 + 0.517857i \(0.826730\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 14.0360 + 24.3110i 0.931600 + 1.61358i 0.780588 + 0.625046i \(0.214920\pi\)
0.151011 + 0.988532i \(0.451747\pi\)
\(228\) 0 0
\(229\) 14.7453 + 8.51319i 0.974396 + 0.562568i 0.900573 0.434704i \(-0.143147\pi\)
0.0738222 + 0.997271i \(0.476480\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 16.0015 + 9.23847i 1.04829 + 0.605233i 0.922171 0.386782i \(-0.126413\pi\)
0.126122 + 0.992015i \(0.459747\pi\)
\(234\) 0 0
\(235\) −7.39166 12.8027i −0.482179 0.835158i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.00506i 0.453120i 0.973997 + 0.226560i \(0.0727479\pi\)
−0.973997 + 0.226560i \(0.927252\pi\)
\(240\) 0 0
\(241\) −5.38459 + 3.10879i −0.346852 + 0.200255i −0.663298 0.748355i \(-0.730844\pi\)
0.316446 + 0.948611i \(0.397510\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 5.71656 + 10.3230i 0.365217 + 0.659514i
\(246\) 0 0
\(247\) 0.509067 0.881730i 0.0323912 0.0561031i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 9.81844 0.619734 0.309867 0.950780i \(-0.399715\pi\)
0.309867 + 0.950780i \(0.399715\pi\)
\(252\) 0 0
\(253\) 34.6952 2.18127
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −0.667904 + 1.15684i −0.0416627 + 0.0721619i −0.886105 0.463485i \(-0.846599\pi\)
0.844442 + 0.535647i \(0.179932\pi\)
\(258\) 0 0
\(259\) 0.148083 16.5754i 0.00920144 1.02994i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −17.6238 + 10.1751i −1.08673 + 0.627424i −0.932704 0.360643i \(-0.882557\pi\)
−0.154026 + 0.988067i \(0.549224\pi\)
\(264\) 0 0
\(265\) 9.62805i 0.591446i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 13.3614 + 23.1426i 0.814659 + 1.41103i 0.909572 + 0.415546i \(0.136409\pi\)
−0.0949131 + 0.995486i \(0.530257\pi\)
\(270\) 0 0
\(271\) 3.76517 + 2.17382i 0.228718 + 0.132050i 0.609980 0.792417i \(-0.291177\pi\)
−0.381263 + 0.924467i \(0.624511\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −7.29968 4.21447i −0.440187 0.254142i
\(276\) 0 0
\(277\) 2.19901 + 3.80880i 0.132126 + 0.228849i 0.924496 0.381192i \(-0.124486\pi\)
−0.792370 + 0.610041i \(0.791153\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.33787i 0.318430i 0.987244 + 0.159215i \(0.0508964\pi\)
−0.987244 + 0.159215i \(0.949104\pi\)
\(282\) 0 0
\(283\) 15.5431 8.97381i 0.923941 0.533437i 0.0390505 0.999237i \(-0.487567\pi\)
0.884890 + 0.465800i \(0.154233\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −7.58645 + 4.29014i −0.447814 + 0.253239i
\(288\) 0 0
\(289\) 8.41900 14.5821i 0.495235 0.857773i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 26.2253 1.53210 0.766048 0.642783i \(-0.222220\pi\)
0.766048 + 0.642783i \(0.222220\pi\)
\(294\) 0 0
\(295\) 7.59132 0.441984
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 26.8968 46.5867i 1.55548 2.69418i
\(300\) 0 0
\(301\) −8.31267 + 4.70081i −0.479134 + 0.270950i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.47924 4.31814i 0.428260 0.247256i
\(306\) 0 0
\(307\) 7.19520i 0.410652i 0.978694 + 0.205326i \(0.0658254\pi\)
−0.978694 + 0.205326i \(0.934175\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.08721 1.88311i −0.0616503 0.106781i 0.833553 0.552440i \(-0.186303\pi\)
−0.895203 + 0.445658i \(0.852970\pi\)
\(312\) 0 0
\(313\) 10.2870 + 5.93922i 0.581457 + 0.335704i 0.761712 0.647916i \(-0.224359\pi\)
−0.180255 + 0.983620i \(0.557692\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 7.09969 + 4.09901i 0.398758 + 0.230223i 0.685948 0.727651i \(-0.259388\pi\)
−0.287190 + 0.957874i \(0.592721\pi\)
\(318\) 0 0
\(319\) 13.8754 + 24.0329i 0.776875 + 1.34559i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.0676757i 0.00376558i
\(324\) 0 0
\(325\) −11.3179 + 6.53438i −0.627803 + 0.362462i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.207279 + 23.2014i −0.0114277 + 1.27913i
\(330\) 0 0
\(331\) −8.58540 + 14.8704i −0.471897 + 0.817349i −0.999483 0.0321526i \(-0.989764\pi\)
0.527586 + 0.849501i \(0.323097\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −9.96340 −0.544359
\(336\) 0 0
\(337\) −7.90797 −0.430775 −0.215387 0.976529i \(-0.569101\pi\)
−0.215387 + 0.976529i \(0.569101\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 12.2779 21.2659i 0.664883 1.15161i
\(342\) 0 0
\(343\) 0.496303 18.5136i 0.0267979 0.999641i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.443850 + 0.256257i −0.0238271 + 0.0137566i −0.511866 0.859065i \(-0.671046\pi\)
0.488039 + 0.872822i \(0.337712\pi\)
\(348\) 0 0
\(349\) 6.63505i 0.355166i 0.984106 + 0.177583i \(0.0568278\pi\)
−0.984106 + 0.177583i \(0.943172\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.03437 + 15.6480i 0.480851 + 0.832858i 0.999759 0.0219721i \(-0.00699449\pi\)
−0.518908 + 0.854830i \(0.673661\pi\)
\(354\) 0 0
\(355\) −16.6877 9.63465i −0.885691 0.511354i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.52677 + 0.881479i 0.0805796 + 0.0465227i 0.539748 0.841826i \(-0.318519\pi\)
−0.459169 + 0.888349i \(0.651853\pi\)
\(360\) 0 0
\(361\) −9.48586 16.4300i −0.499256 0.864737i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11.7873i 0.616977i
\(366\) 0 0
\(367\) 28.9614 16.7209i 1.51177 0.872822i 0.511867 0.859065i \(-0.328954\pi\)
0.999905 0.0137576i \(-0.00437931\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7.67218 13.0186i 0.398320 0.675893i
\(372\) 0 0
\(373\) −12.7844 + 22.1433i −0.661952 + 1.14653i 0.318150 + 0.948040i \(0.396938\pi\)
−0.980102 + 0.198494i \(0.936395\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 43.0267 2.21599
\(378\) 0 0
\(379\) 25.7920 1.32485 0.662423 0.749130i \(-0.269528\pi\)
0.662423 + 0.749130i \(0.269528\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 16.4158 28.4330i 0.838808 1.45286i −0.0520838 0.998643i \(-0.516586\pi\)
0.890892 0.454215i \(-0.150080\pi\)
\(384\) 0 0
\(385\) −8.57397 15.1618i −0.436970 0.772715i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 17.4542 10.0772i 0.884965 0.510935i 0.0126730 0.999920i \(-0.495966\pi\)
0.872292 + 0.488985i \(0.162633\pi\)
\(390\) 0 0
\(391\) 3.57568i 0.180830i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.01813 1.76346i −0.0512278 0.0887291i
\(396\) 0 0
\(397\) −30.2125 17.4432i −1.51632 0.875449i −0.999816 0.0191652i \(-0.993899\pi\)
−0.516506 0.856284i \(-0.672768\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8.36793 4.83122i −0.417874 0.241260i 0.276293 0.961073i \(-0.410894\pi\)
−0.694167 + 0.719814i \(0.744227\pi\)
\(402\) 0 0
\(403\) −19.0364 32.9719i −0.948268 1.64245i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 24.4678i 1.21282i
\(408\) 0 0
\(409\) −32.1202 + 18.5446i −1.58824 + 0.916973i −0.594647 + 0.803987i \(0.702708\pi\)
−0.993597 + 0.112986i \(0.963958\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.2646 6.04920i −0.505090 0.297662i
\(414\) 0 0
\(415\) 0.305709 0.529504i 0.0150067 0.0259923i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.68386 −0.179968 −0.0899841 0.995943i \(-0.528682\pi\)
−0.0899841 + 0.995943i \(0.528682\pi\)
\(420\) 0 0
\(421\) 17.1028 0.833539 0.416769 0.909012i \(-0.363162\pi\)
0.416769 + 0.909012i \(0.363162\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.434342 0.752303i 0.0210687 0.0364921i
\(426\) 0 0
\(427\) −13.5540 0.121091i −0.655926 0.00585999i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.3242 15.7756i 1.31616 0.759885i 0.333051 0.942909i \(-0.391922\pi\)
0.983108 + 0.183024i \(0.0585887\pi\)
\(432\) 0 0
\(433\) 10.0692i 0.483893i 0.970290 + 0.241947i \(0.0777859\pi\)
−0.970290 + 0.241947i \(0.922214\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.746890 + 1.29365i 0.0357286 + 0.0618837i
\(438\) 0 0
\(439\) −24.1966 13.9699i −1.15484 0.666748i −0.204779 0.978808i \(-0.565648\pi\)
−0.950062 + 0.312060i \(0.898981\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −30.1930 17.4319i −1.43451 0.828215i −0.437050 0.899437i \(-0.643977\pi\)
−0.997460 + 0.0712223i \(0.977310\pi\)
\(444\) 0 0
\(445\) −2.33518 4.04466i −0.110698 0.191735i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 23.2411i 1.09682i 0.836211 + 0.548408i \(0.184766\pi\)
−0.836211 + 0.548408i \(0.815234\pi\)
\(450\) 0 0
\(451\) 11.1413 6.43244i 0.524624 0.302892i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −27.0051 0.241262i −1.26602 0.0113105i
\(456\) 0 0
\(457\) 3.10938 5.38560i 0.145451 0.251928i −0.784090 0.620647i \(-0.786870\pi\)
0.929541 + 0.368719i \(0.120203\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.34329 0.202287 0.101144 0.994872i \(-0.467750\pi\)
0.101144 + 0.994872i \(0.467750\pi\)
\(462\) 0 0
\(463\) −7.14903 −0.332243 −0.166122 0.986105i \(-0.553124\pi\)
−0.166122 + 0.986105i \(0.553124\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0.944451 1.63584i 0.0437040 0.0756975i −0.843346 0.537371i \(-0.819417\pi\)
0.887050 + 0.461673i \(0.152751\pi\)
\(468\) 0 0
\(469\) 13.4721 + 7.93941i 0.622082 + 0.366608i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.2078 7.04818i 0.561316 0.324076i
\(474\) 0 0
\(475\) 0.362903i 0.0166511i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.22491 9.04981i −0.238732 0.413497i 0.721618 0.692291i \(-0.243399\pi\)
−0.960351 + 0.278794i \(0.910065\pi\)
\(480\) 0 0
\(481\) 32.8539 + 18.9682i 1.49801 + 0.864875i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.857895 + 0.495306i 0.0389550 + 0.0224907i
\(486\) 0 0
\(487\) −11.8298 20.4898i −0.536060 0.928483i −0.999111 0.0421513i \(-0.986579\pi\)
0.463052 0.886331i \(-0.346754\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 13.4830i 0.608481i 0.952595 + 0.304241i \(0.0984027\pi\)
−0.952595 + 0.304241i \(0.901597\pi\)
\(492\) 0 0
\(493\) −2.47683 + 1.43000i −0.111551 + 0.0644039i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 14.8869 + 26.3253i 0.667770 + 1.18085i
\(498\) 0 0
\(499\) 6.04035 10.4622i 0.270403 0.468352i −0.698562 0.715550i \(-0.746176\pi\)
0.968965 + 0.247197i \(0.0795096\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 20.5283 0.915310 0.457655 0.889130i \(-0.348690\pi\)
0.457655 + 0.889130i \(0.348690\pi\)
\(504\) 0 0
\(505\) −23.3417 −1.03869
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.09043 7.08483i 0.181305 0.314029i −0.761020 0.648728i \(-0.775301\pi\)
0.942325 + 0.334699i \(0.108635\pi\)
\(510\) 0 0
\(511\) −9.39282 + 15.9383i −0.415514 + 0.705069i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 17.6345 10.1813i 0.777070 0.448642i
\(516\) 0 0
\(517\) 34.2488i 1.50626i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.8746 + 24.0314i 0.607856 + 1.05284i 0.991593 + 0.129395i \(0.0413034\pi\)
−0.383738 + 0.923442i \(0.625363\pi\)
\(522\) 0 0
\(523\) 19.8843 + 11.4802i 0.869478 + 0.501993i 0.867175 0.498004i \(-0.165934\pi\)
0.00230311 + 0.999997i \(0.499267\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.19166 + 1.26535i 0.0954700 + 0.0551196i
\(528\) 0 0
\(529\) 27.9623 + 48.4322i 1.21575 + 2.10575i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 19.9465i 0.863979i
\(534\) 0 0
\(535\) 26.8536 15.5039i 1.16098 0.670292i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.488426 + 27.3333i −0.0210380 + 1.17733i
\(540\) 0 0
\(541\) −2.60405 + 4.51035i −0.111957 + 0.193915i −0.916559 0.399899i \(-0.869045\pi\)
0.804602 + 0.593814i \(0.202379\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.5780 0.795795
\(546\) 0 0
\(547\) −21.2448 −0.908361 −0.454181 0.890910i \(-0.650068\pi\)
−0.454181 + 0.890910i \(0.650068\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.597397 + 1.03472i −0.0254500 + 0.0440807i
\(552\) 0 0
\(553\) −0.0285508 + 3.19577i −0.00121410 + 0.135898i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 11.0945 6.40543i 0.470090 0.271407i −0.246187 0.969222i \(-0.579178\pi\)
0.716277 + 0.697816i \(0.245844\pi\)
\(558\) 0 0
\(559\) 21.8559i 0.924406i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 18.7396 + 32.4580i 0.789781 + 1.36794i 0.926101 + 0.377277i \(0.123139\pi\)
−0.136319 + 0.990665i \(0.543527\pi\)
\(564\) 0 0
\(565\) −12.4207 7.17109i −0.522542 0.301690i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.94906 + 3.43469i 0.249397 + 0.143990i 0.619488 0.785006i \(-0.287340\pi\)
−0.370091 + 0.928996i \(0.620673\pi\)
\(570\) 0 0
\(571\) −0.0847909 0.146862i −0.00354839 0.00614599i 0.864246 0.503070i \(-0.167796\pi\)
−0.867794 + 0.496924i \(0.834463\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 19.1741i 0.799617i
\(576\) 0 0
\(577\) −5.41193 + 3.12458i −0.225302 + 0.130078i −0.608403 0.793628i \(-0.708189\pi\)
0.383101 + 0.923706i \(0.374856\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.835305 + 0.472365i −0.0346543 + 0.0195970i
\(582\) 0 0
\(583\) −11.1527 + 19.3171i −0.461900 + 0.800033i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.5762 0.890545 0.445273 0.895395i \(-0.353107\pi\)
0.445273 + 0.895395i \(0.353107\pi\)
\(588\) 0 0
\(589\) 1.05723 0.0435624
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4.13036 + 7.15399i −0.169613 + 0.293779i −0.938284 0.345866i \(-0.887585\pi\)
0.768671 + 0.639645i \(0.220919\pi\)
\(594\) 0 0
\(595\) 1.56257 0.883632i 0.0640591 0.0362254i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 30.7618 17.7603i 1.25689 0.725667i 0.284422 0.958699i \(-0.408198\pi\)
0.972469 + 0.233033i \(0.0748649\pi\)
\(600\) 0 0
\(601\) 41.4516i 1.69085i −0.534098 0.845423i \(-0.679349\pi\)
0.534098 0.845423i \(-0.320651\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.58388 + 6.20746i 0.145705 + 0.252369i
\(606\) 0 0
\(607\) 2.09569 + 1.20995i 0.0850616 + 0.0491103i 0.541927 0.840425i \(-0.317695\pi\)
−0.456866 + 0.889536i \(0.651028\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −45.9873 26.5508i −1.86045 1.07413i
\(612\) 0 0
\(613\) 21.3228 + 36.9321i 0.861219 + 1.49168i 0.870753 + 0.491720i \(0.163632\pi\)
−0.00953416 + 0.999955i \(0.503035\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.3039i 0.616110i −0.951369 0.308055i \(-0.900322\pi\)
0.951369 0.308055i \(-0.0996781\pi\)
\(618\) 0 0
\(619\) −23.9177 + 13.8089i −0.961334 + 0.555026i −0.896583 0.442875i \(-0.853958\pi\)
−0.0647505 + 0.997901i \(0.520625\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.0654840 + 7.32981i −0.00262356 + 0.293663i
\(624\) 0 0
\(625\) 4.77517 8.27084i 0.191007 0.330834i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.52164 −0.100545
\(630\) 0 0
\(631\) 8.28775 0.329930 0.164965 0.986299i \(-0.447249\pi\)
0.164965 + 0.986299i \(0.447249\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 8.96069 15.5204i 0.355594 0.615907i
\(636\) 0 0
\(637\) 36.3229 + 21.8455i 1.43916 + 0.865549i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.58307 4.95544i 0.339011 0.195728i −0.320824 0.947139i \(-0.603960\pi\)
0.659835 + 0.751411i \(0.270626\pi\)
\(642\) 0 0
\(643\) 7.89432i 0.311321i 0.987811 + 0.155661i \(0.0497507\pi\)
−0.987811 + 0.155661i \(0.950249\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.15966 3.74063i −0.0849049 0.147060i 0.820446 0.571724i \(-0.193725\pi\)
−0.905351 + 0.424665i \(0.860392\pi\)
\(648\) 0 0
\(649\) 15.2308 + 8.79348i 0.597859 + 0.345174i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −37.5853 21.6999i −1.47082 0.849181i −0.471361 0.881940i \(-0.656237\pi\)
−0.999463 + 0.0327591i \(0.989571\pi\)
\(654\) 0 0
\(655\) 5.33940 + 9.24812i 0.208628 + 0.361354i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10.7952i 0.420522i −0.977645 0.210261i \(-0.932569\pi\)
0.977645 0.210261i \(-0.0674314\pi\)
\(660\) 0 0
\(661\) −3.39495 + 1.96008i −0.132048 + 0.0762381i −0.564569 0.825386i \(-0.690958\pi\)
0.432521 + 0.901624i \(0.357624\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.380751 0.646081i 0.0147649 0.0250539i
\(666\) 0 0
\(667\) −31.5638 + 54.6701i −1.22216 + 2.11683i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 20.0078 0.772394
\(672\) 0 0
\(673\) 24.6808 0.951375 0.475687 0.879614i \(-0.342199\pi\)
0.475687 + 0.879614i \(0.342199\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −7.36327 + 12.7536i −0.282994 + 0.490159i −0.972121 0.234481i \(-0.924661\pi\)
0.689127 + 0.724641i \(0.257994\pi\)
\(678\) 0 0
\(679\) −0.765319 1.35335i −0.0293702 0.0519368i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.60128 0.924499i 0.0612712 0.0353750i −0.469051 0.883171i \(-0.655404\pi\)
0.530323 + 0.847796i \(0.322071\pi\)
\(684\) 0 0
\(685\) 28.0606i 1.07214i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 17.2919 + 29.9505i 0.658769 + 1.14102i
\(690\) 0 0
\(691\) 33.7613 + 19.4921i 1.28434 + 0.741514i 0.977639 0.210292i \(-0.0674415\pi\)
0.306701 + 0.951806i \(0.400775\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7.14764 + 4.12669i 0.271126 + 0.156534i
\(696\) 0 0
\(697\) 0.662926 + 1.14822i 0.0251101 + 0.0434920i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 25.4389i 0.960813i −0.877046 0.480406i \(-0.840489\pi\)
0.877046 0.480406i \(-0.159511\pi\)
\(702\) 0 0
\(703\) −0.912310 + 0.526722i −0.0344084 + 0.0198657i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 31.5616 + 18.6000i 1.18700 + 0.699525i
\(708\) 0 0
\(709\) 7.14517 12.3758i 0.268342 0.464783i −0.700092 0.714053i \(-0.746857\pi\)
0.968434 + 0.249270i \(0.0801908\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 55.8593 2.09195
\(714\) 0 0
\(715\) 39.8637 1.49082
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 16.7344 28.9848i 0.624088 1.08095i −0.364629 0.931153i \(-0.618804\pi\)
0.988716 0.149799i \(-0.0478626\pi\)
\(720\) 0 0
\(721\) −31.9577 0.285507i −1.19017 0.0106329i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 13.2817 7.66819i 0.493269 0.284789i
\(726\) 0 0
\(727\) 14.0127i 0.519703i −0.965649 0.259851i \(-0.916326\pi\)
0.965649 0.259851i \(-0.0836736\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.726384 + 1.25813i 0.0268663 + 0.0465338i
\(732\) 0 0
\(733\) −23.6491 13.6538i −0.873501 0.504316i −0.00499085 0.999988i \(-0.501589\pi\)
−0.868510 + 0.495672i \(0.834922\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −19.9899 11.5412i −0.736339 0.425126i
\(738\) 0 0
\(739\) 26.3157 + 45.5801i 0.968039 + 1.67669i 0.701220 + 0.712945i \(0.252639\pi\)
0.266819 + 0.963747i \(0.414027\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 35.7407i 1.31120i 0.755109 + 0.655599i \(0.227584\pi\)
−0.755109 + 0.655599i \(0.772416\pi\)
\(744\) 0 0
\(745\) −7.71839 + 4.45621i −0.282780 + 0.163263i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −48.6646 0.434766i −1.77816 0.0158860i
\(750\) 0 0
\(751\) 16.5641 28.6899i 0.604433 1.04691i −0.387708 0.921782i \(-0.626733\pi\)
0.992141 0.125126i \(-0.0399336\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −24.5836 −0.894687
\(756\) 0 0
\(757\) −13.6903 −0.497584 −0.248792 0.968557i \(-0.580034\pi\)
−0.248792 + 0.968557i \(0.580034\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.51737 + 11.2884i −0.236255 + 0.409205i −0.959637 0.281243i \(-0.909253\pi\)
0.723382 + 0.690448i \(0.242587\pi\)
\(762\) 0 0
\(763\) −25.1204 14.8040i −0.909419 0.535942i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 23.6147 13.6340i 0.852678 0.492294i
\(768\) 0 0
\(769\) 21.3464i 0.769772i −0.922964 0.384886i \(-0.874241\pi\)
0.922964 0.384886i \(-0.125759\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5.73940 + 9.94093i 0.206432 + 0.357550i 0.950588 0.310455i \(-0.100482\pi\)
−0.744156 + 0.668006i \(0.767148\pi\)
\(774\) 0 0
\(775\) −11.7525 6.78529i −0.422161 0.243735i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.479682 + 0.276944i 0.0171864 + 0.00992256i
\(780\) 0 0
\(781\) −22.3208 38.6607i −0.798701 1.38339i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 30.0076i 1.07102i
\(786\) 0 0
\(787\) −35.6808 + 20.6003i −1.27188 + 0.734322i −0.975342 0.220698i \(-0.929166\pi\)
−0.296541 + 0.955020i \(0.595833\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 11.0804 + 19.5939i 0.393972 + 0.696681i
\(792\) 0 0
\(793\) 15.5107 26.8653i 0.550801 0.954016i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 50.0132 1.77156 0.885779 0.464108i \(-0.153625\pi\)
0.885779 + 0.464108i \(0.153625\pi\)
\(798\) 0 0
\(799\) 3.52967 0.124871
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 13.6540 23.6494i 0.481838 0.834568i