Properties

Label 3240.2.q.bd.1081.2
Level $3240$
Weight $2$
Character 3240.1081
Analytic conductor $25.872$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3240.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.8715302549\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1081.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 3240.1081
Dual form 3240.2.q.bd.2161.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{5} +(1.18614 + 2.05446i) q^{7} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{5} +(1.18614 + 2.05446i) q^{7} +(-1.68614 - 2.92048i) q^{11} +(-1.18614 + 2.05446i) q^{13} -4.74456 q^{17} +1.00000 q^{19} +(-0.186141 + 0.322405i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.68614 - 2.92048i) q^{29} +(3.05842 - 5.29734i) q^{31} +2.37228 q^{35} +6.00000 q^{37} +(5.87228 - 10.1711i) q^{41} +(-3.37228 - 5.84096i) q^{43} +(-1.81386 - 3.14170i) q^{47} +(0.686141 - 1.18843i) q^{49} +7.11684 q^{53} -3.37228 q^{55} +(2.50000 - 4.33013i) q^{59} +(-0.627719 - 1.08724i) q^{61} +(1.18614 + 2.05446i) q^{65} +(-5.37228 + 9.30506i) q^{67} -1.37228 q^{71} +3.25544 q^{73} +(4.00000 - 6.92820i) q^{77} +(-4.37228 - 7.57301i) q^{79} +(-5.00000 - 8.66025i) q^{83} +(-2.37228 + 4.10891i) q^{85} -1.37228 q^{89} -5.62772 q^{91} +(0.500000 - 0.866025i) q^{95} +(-3.37228 - 5.84096i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5} - q^{7} + O(q^{10}) \) \( 4 q + 2 q^{5} - q^{7} - q^{11} + q^{13} + 4 q^{17} + 4 q^{19} + 5 q^{23} - 2 q^{25} - q^{29} - 5 q^{31} - 2 q^{35} + 24 q^{37} + 12 q^{41} - 2 q^{43} - 13 q^{47} - 3 q^{49} - 6 q^{53} - 2 q^{55} + 10 q^{59} - 14 q^{61} - q^{65} - 10 q^{67} + 6 q^{71} + 36 q^{73} + 16 q^{77} - 6 q^{79} - 20 q^{83} + 2 q^{85} + 6 q^{89} - 34 q^{91} + 2 q^{95} - 2 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).

\(n\) \(1297\) \(1621\) \(2431\) \(3161\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 1.18614 + 2.05446i 0.448319 + 0.776511i 0.998277 0.0586811i \(-0.0186895\pi\)
−0.549958 + 0.835192i \(0.685356\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.68614 2.92048i −0.508391 0.880558i −0.999953 0.00971581i \(-0.996907\pi\)
0.491562 0.870842i \(-0.336426\pi\)
\(12\) 0 0
\(13\) −1.18614 + 2.05446i −0.328976 + 0.569804i −0.982309 0.187267i \(-0.940037\pi\)
0.653333 + 0.757071i \(0.273370\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.74456 −1.15073 −0.575363 0.817898i \(-0.695139\pi\)
−0.575363 + 0.817898i \(0.695139\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.186141 + 0.322405i −0.0388130 + 0.0672261i −0.884779 0.466010i \(-0.845691\pi\)
0.845966 + 0.533236i \(0.179024\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.68614 2.92048i −0.313108 0.542320i 0.665925 0.746019i \(-0.268037\pi\)
−0.979034 + 0.203699i \(0.934704\pi\)
\(30\) 0 0
\(31\) 3.05842 5.29734i 0.549309 0.951431i −0.449013 0.893525i \(-0.648224\pi\)
0.998322 0.0579057i \(-0.0184423\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.37228 0.400989
\(36\) 0 0
\(37\) 6.00000 0.986394 0.493197 0.869918i \(-0.335828\pi\)
0.493197 + 0.869918i \(0.335828\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.87228 10.1711i 0.917096 1.58846i 0.113293 0.993562i \(-0.463860\pi\)
0.803803 0.594896i \(-0.202807\pi\)
\(42\) 0 0
\(43\) −3.37228 5.84096i −0.514268 0.890738i −0.999863 0.0165545i \(-0.994730\pi\)
0.485595 0.874184i \(-0.338603\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.81386 3.14170i −0.264579 0.458264i 0.702875 0.711314i \(-0.251900\pi\)
−0.967453 + 0.253050i \(0.918566\pi\)
\(48\) 0 0
\(49\) 0.686141 1.18843i 0.0980201 0.169776i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.11684 0.977574 0.488787 0.872403i \(-0.337440\pi\)
0.488787 + 0.872403i \(0.337440\pi\)
\(54\) 0 0
\(55\) −3.37228 −0.454718
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.50000 4.33013i 0.325472 0.563735i −0.656136 0.754643i \(-0.727810\pi\)
0.981608 + 0.190909i \(0.0611434\pi\)
\(60\) 0 0
\(61\) −0.627719 1.08724i −0.0803711 0.139207i 0.823038 0.567986i \(-0.192277\pi\)
−0.903409 + 0.428779i \(0.858944\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.18614 + 2.05446i 0.147123 + 0.254824i
\(66\) 0 0
\(67\) −5.37228 + 9.30506i −0.656329 + 1.13679i 0.325230 + 0.945635i \(0.394558\pi\)
−0.981559 + 0.191160i \(0.938775\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.37228 −0.162860 −0.0814299 0.996679i \(-0.525949\pi\)
−0.0814299 + 0.996679i \(0.525949\pi\)
\(72\) 0 0
\(73\) 3.25544 0.381020 0.190510 0.981685i \(-0.438986\pi\)
0.190510 + 0.981685i \(0.438986\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.00000 6.92820i 0.455842 0.789542i
\(78\) 0 0
\(79\) −4.37228 7.57301i −0.491920 0.852031i 0.508037 0.861335i \(-0.330371\pi\)
−0.999957 + 0.00930489i \(0.997038\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.00000 8.66025i −0.548821 0.950586i −0.998356 0.0573233i \(-0.981743\pi\)
0.449534 0.893263i \(-0.351590\pi\)
\(84\) 0 0
\(85\) −2.37228 + 4.10891i −0.257310 + 0.445674i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.37228 −0.145462 −0.0727308 0.997352i \(-0.523171\pi\)
−0.0727308 + 0.997352i \(0.523171\pi\)
\(90\) 0 0
\(91\) −5.62772 −0.589945
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 0 0
\(97\) −3.37228 5.84096i −0.342403 0.593060i 0.642475 0.766306i \(-0.277908\pi\)
−0.984878 + 0.173247i \(0.944574\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.43070 + 11.1383i 0.639879 + 1.10830i 0.985459 + 0.169913i \(0.0543488\pi\)
−0.345580 + 0.938389i \(0.612318\pi\)
\(102\) 0 0
\(103\) −8.55842 + 14.8236i −0.843286 + 1.46061i 0.0438147 + 0.999040i \(0.486049\pi\)
−0.887101 + 0.461575i \(0.847284\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 0 0
\(109\) 18.1168 1.73528 0.867639 0.497194i \(-0.165636\pi\)
0.867639 + 0.497194i \(0.165636\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.62772 2.81929i 0.153123 0.265217i −0.779251 0.626712i \(-0.784400\pi\)
0.932374 + 0.361495i \(0.117734\pi\)
\(114\) 0 0
\(115\) 0.186141 + 0.322405i 0.0173577 + 0.0300644i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.62772 9.74749i −0.515892 0.893551i
\(120\) 0 0
\(121\) −0.186141 + 0.322405i −0.0169219 + 0.0293096i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 15.8614 1.40747 0.703736 0.710461i \(-0.251514\pi\)
0.703736 + 0.710461i \(0.251514\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 8.87228 15.3672i 0.775175 1.34264i −0.159521 0.987194i \(-0.550995\pi\)
0.934696 0.355448i \(-0.115672\pi\)
\(132\) 0 0
\(133\) 1.18614 + 2.05446i 0.102851 + 0.178144i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.37228 14.5012i −0.715292 1.23892i −0.962847 0.270049i \(-0.912960\pi\)
0.247554 0.968874i \(-0.420373\pi\)
\(138\) 0 0
\(139\) −7.50000 + 12.9904i −0.636142 + 1.10183i 0.350130 + 0.936701i \(0.386137\pi\)
−0.986272 + 0.165129i \(0.947196\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) −3.37228 −0.280053
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.74456 + 3.02167i −0.142920 + 0.247545i −0.928595 0.371095i \(-0.878983\pi\)
0.785675 + 0.618640i \(0.212316\pi\)
\(150\) 0 0
\(151\) −9.31386 16.1321i −0.757951 1.31281i −0.943894 0.330249i \(-0.892867\pi\)
0.185943 0.982561i \(-0.440466\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.05842 5.29734i −0.245658 0.425493i
\(156\) 0 0
\(157\) 2.93070 5.07613i 0.233896 0.405119i −0.725056 0.688690i \(-0.758186\pi\)
0.958951 + 0.283571i \(0.0915193\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.883156 −0.0696024
\(162\) 0 0
\(163\) −13.4891 −1.05655 −0.528275 0.849073i \(-0.677161\pi\)
−0.528275 + 0.849073i \(0.677161\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 + 10.3923i −0.464294 + 0.804181i −0.999169 0.0407502i \(-0.987025\pi\)
0.534875 + 0.844931i \(0.320359\pi\)
\(168\) 0 0
\(169\) 3.68614 + 6.38458i 0.283549 + 0.491122i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −6.93070 12.0043i −0.526932 0.912672i −0.999507 0.0313823i \(-0.990009\pi\)
0.472576 0.881290i \(-0.343324\pi\)
\(174\) 0 0
\(175\) 1.18614 2.05446i 0.0896638 0.155302i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 15.7446 1.17680 0.588402 0.808569i \(-0.299757\pi\)
0.588402 + 0.808569i \(0.299757\pi\)
\(180\) 0 0
\(181\) 14.8614 1.10464 0.552320 0.833632i \(-0.313743\pi\)
0.552320 + 0.833632i \(0.313743\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) 0 0
\(187\) 8.00000 + 13.8564i 0.585018 + 1.01328i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.68614 9.84868i −0.411435 0.712626i 0.583612 0.812033i \(-0.301639\pi\)
−0.995047 + 0.0994067i \(0.968306\pi\)
\(192\) 0 0
\(193\) 5.37228 9.30506i 0.386705 0.669793i −0.605299 0.795998i \(-0.706946\pi\)
0.992004 + 0.126205i \(0.0402797\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.37228 0.454006 0.227003 0.973894i \(-0.427107\pi\)
0.227003 + 0.973894i \(0.427107\pi\)
\(198\) 0 0
\(199\) −9.48913 −0.672666 −0.336333 0.941743i \(-0.609187\pi\)
−0.336333 + 0.941743i \(0.609187\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.00000 6.92820i 0.280745 0.486265i
\(204\) 0 0
\(205\) −5.87228 10.1711i −0.410138 0.710380i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.68614 2.92048i −0.116633 0.202014i
\(210\) 0 0
\(211\) −8.50000 + 14.7224i −0.585164 + 1.01353i 0.409691 + 0.912224i \(0.365637\pi\)
−0.994855 + 0.101310i \(0.967697\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.74456 −0.459975
\(216\) 0 0
\(217\) 14.5109 0.985062
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.62772 9.74749i 0.378561 0.655687i
\(222\) 0 0
\(223\) −1.25544 2.17448i −0.0840703 0.145614i 0.820924 0.571037i \(-0.193459\pi\)
−0.904995 + 0.425423i \(0.860125\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.74456 + 4.75372i 0.182163 + 0.315516i 0.942617 0.333876i \(-0.108357\pi\)
−0.760454 + 0.649392i \(0.775023\pi\)
\(228\) 0 0
\(229\) 2.62772 4.55134i 0.173645 0.300761i −0.766047 0.642785i \(-0.777779\pi\)
0.939691 + 0.342024i \(0.111112\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −20.2337 −1.32555 −0.662776 0.748817i \(-0.730622\pi\)
−0.662776 + 0.748817i \(0.730622\pi\)
\(234\) 0 0
\(235\) −3.62772 −0.236646
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.11684 12.3267i 0.460350 0.797350i −0.538628 0.842544i \(-0.681057\pi\)
0.998978 + 0.0451935i \(0.0143905\pi\)
\(240\) 0 0
\(241\) −14.8030 25.6395i −0.953544 1.65159i −0.737665 0.675167i \(-0.764072\pi\)
−0.215879 0.976420i \(-0.569262\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −0.686141 1.18843i −0.0438359 0.0759260i
\(246\) 0 0
\(247\) −1.18614 + 2.05446i −0.0754723 + 0.130722i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −15.8614 −1.00116 −0.500582 0.865689i \(-0.666880\pi\)
−0.500582 + 0.865689i \(0.666880\pi\)
\(252\) 0 0
\(253\) 1.25544 0.0789287
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.7446 20.3422i 0.732606 1.26891i −0.223160 0.974782i \(-0.571637\pi\)
0.955766 0.294128i \(-0.0950294\pi\)
\(258\) 0 0
\(259\) 7.11684 + 12.3267i 0.442219 + 0.765946i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.55842 11.3595i −0.404410 0.700458i 0.589843 0.807518i \(-0.299190\pi\)
−0.994253 + 0.107060i \(0.965856\pi\)
\(264\) 0 0
\(265\) 3.55842 6.16337i 0.218592 0.378613i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −12.1168 −0.738777 −0.369389 0.929275i \(-0.620433\pi\)
−0.369389 + 0.929275i \(0.620433\pi\)
\(270\) 0 0
\(271\) −20.7446 −1.26014 −0.630071 0.776537i \(-0.716974\pi\)
−0.630071 + 0.776537i \(0.716974\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.68614 + 2.92048i −0.101678 + 0.176112i
\(276\) 0 0
\(277\) 8.55842 + 14.8236i 0.514226 + 0.890665i 0.999864 + 0.0165051i \(0.00525398\pi\)
−0.485638 + 0.874160i \(0.661413\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.81386 + 10.0699i 0.346826 + 0.600720i 0.985684 0.168605i \(-0.0539262\pi\)
−0.638858 + 0.769325i \(0.720593\pi\)
\(282\) 0 0
\(283\) −2.62772 + 4.55134i −0.156202 + 0.270549i −0.933496 0.358588i \(-0.883258\pi\)
0.777294 + 0.629137i \(0.216592\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 27.8614 1.64461
\(288\) 0 0
\(289\) 5.51087 0.324169
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 6.93070 12.0043i 0.404896 0.701300i −0.589413 0.807832i \(-0.700641\pi\)
0.994309 + 0.106531i \(0.0339744\pi\)
\(294\) 0 0
\(295\) −2.50000 4.33013i −0.145556 0.252110i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.441578 0.764836i −0.0255371 0.0442316i
\(300\) 0 0
\(301\) 8.00000 13.8564i 0.461112 0.798670i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.25544 −0.0718861
\(306\) 0 0
\(307\) −10.7446 −0.613225 −0.306612 0.951834i \(-0.599195\pi\)
−0.306612 + 0.951834i \(0.599195\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.43070 + 9.40625i −0.307947 + 0.533380i −0.977913 0.209012i \(-0.932975\pi\)
0.669966 + 0.742392i \(0.266309\pi\)
\(312\) 0 0
\(313\) 2.00000 + 3.46410i 0.113047 + 0.195803i 0.916997 0.398894i \(-0.130606\pi\)
−0.803951 + 0.594696i \(0.797272\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.18614 14.1788i −0.459779 0.796361i 0.539170 0.842197i \(-0.318738\pi\)
−0.998949 + 0.0458359i \(0.985405\pi\)
\(318\) 0 0
\(319\) −5.68614 + 9.84868i −0.318363 + 0.551420i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.74456 −0.263995
\(324\) 0 0
\(325\) 2.37228 0.131590
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.30298 7.45299i 0.237231 0.410897i
\(330\) 0 0
\(331\) −9.68614 16.7769i −0.532398 0.922141i −0.999284 0.0378236i \(-0.987957\pi\)
0.466886 0.884318i \(-0.345376\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.37228 + 9.30506i 0.293519 + 0.508390i
\(336\) 0 0
\(337\) −0.372281 + 0.644810i −0.0202795 + 0.0351250i −0.875987 0.482335i \(-0.839789\pi\)
0.855708 + 0.517460i \(0.173122\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −20.6277 −1.11705
\(342\) 0 0
\(343\) 19.8614 1.07242
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −15.1168 + 26.1831i −0.811515 + 1.40558i 0.100289 + 0.994958i \(0.468023\pi\)
−0.911804 + 0.410626i \(0.865310\pi\)
\(348\) 0 0
\(349\) 12.6861 + 21.9730i 0.679074 + 1.17619i 0.975260 + 0.221060i \(0.0709516\pi\)
−0.296187 + 0.955130i \(0.595715\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.4891 + 21.6318i 0.664729 + 1.15134i 0.979359 + 0.202130i \(0.0647864\pi\)
−0.314630 + 0.949215i \(0.601880\pi\)
\(354\) 0 0
\(355\) −0.686141 + 1.18843i −0.0364166 + 0.0630753i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.6277 0.560910 0.280455 0.959867i \(-0.409515\pi\)
0.280455 + 0.959867i \(0.409515\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.62772 2.81929i 0.0851987 0.147568i
\(366\) 0 0
\(367\) −2.11684 3.66648i −0.110498 0.191389i 0.805473 0.592633i \(-0.201911\pi\)
−0.915971 + 0.401244i \(0.868578\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.44158 + 14.6212i 0.438265 + 0.759097i
\(372\) 0 0
\(373\) −0.372281 + 0.644810i −0.0192760 + 0.0333870i −0.875502 0.483214i \(-0.839469\pi\)
0.856226 + 0.516601i \(0.172803\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) 25.3505 1.30217 0.651085 0.759005i \(-0.274314\pi\)
0.651085 + 0.759005i \(0.274314\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.81386 + 11.8020i −0.348172 + 0.603052i −0.985925 0.167190i \(-0.946531\pi\)
0.637753 + 0.770241i \(0.279864\pi\)
\(384\) 0 0
\(385\) −4.00000 6.92820i −0.203859 0.353094i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 4.62772 + 8.01544i 0.234635 + 0.406399i 0.959166 0.282842i \(-0.0912773\pi\)
−0.724532 + 0.689241i \(0.757944\pi\)
\(390\) 0 0
\(391\) 0.883156 1.52967i 0.0446631 0.0773588i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.74456 −0.439987
\(396\) 0 0
\(397\) 34.0000 1.70641 0.853206 0.521575i \(-0.174655\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −7.67527 + 13.2940i −0.383284 + 0.663868i −0.991530 0.129881i \(-0.958540\pi\)
0.608245 + 0.793749i \(0.291874\pi\)
\(402\) 0 0
\(403\) 7.25544 + 12.5668i 0.361419 + 0.625996i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −10.1168 17.5229i −0.501473 0.868577i
\(408\) 0 0
\(409\) 7.81386 13.5340i 0.386370 0.669213i −0.605588 0.795778i \(-0.707062\pi\)
0.991958 + 0.126565i \(0.0403953\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 11.8614 0.583662
\(414\) 0 0
\(415\) −10.0000 −0.490881
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.48913 + 9.50744i −0.268161 + 0.464469i −0.968387 0.249452i \(-0.919749\pi\)
0.700226 + 0.713922i \(0.253083\pi\)
\(420\) 0 0
\(421\) −11.3139 19.5962i −0.551404 0.955059i −0.998174 0.0604104i \(-0.980759\pi\)
0.446770 0.894649i \(-0.352574\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.37228 + 4.10891i 0.115073 + 0.199311i
\(426\) 0 0
\(427\) 1.48913 2.57924i 0.0720638 0.124818i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.3723 −0.740457 −0.370228 0.928941i \(-0.620721\pi\)
−0.370228 + 0.928941i \(0.620721\pi\)
\(432\) 0 0
\(433\) 39.2119 1.88441 0.942203 0.335043i \(-0.108751\pi\)
0.942203 + 0.335043i \(0.108751\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.186141 + 0.322405i −0.00890432 + 0.0154227i
\(438\) 0 0
\(439\) −15.5475 26.9291i −0.742044 1.28526i −0.951563 0.307453i \(-0.900523\pi\)
0.209519 0.977805i \(-0.432810\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.48913 + 14.7036i 0.403331 + 0.698589i 0.994126 0.108233i \(-0.0345192\pi\)
−0.590795 + 0.806822i \(0.701186\pi\)
\(444\) 0 0
\(445\) −0.686141 + 1.18843i −0.0325262 + 0.0563370i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.7228 1.07236 0.536178 0.844105i \(-0.319868\pi\)
0.536178 + 0.844105i \(0.319868\pi\)
\(450\) 0 0
\(451\) −39.6060 −1.86497
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.81386 + 4.87375i −0.131916 + 0.228485i
\(456\) 0 0
\(457\) 20.1168 + 34.8434i 0.941026 + 1.62991i 0.763519 + 0.645786i \(0.223470\pi\)
0.177508 + 0.984119i \(0.443197\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.94158 + 12.0232i 0.323302 + 0.559975i 0.981167 0.193161i \(-0.0618739\pi\)
−0.657866 + 0.753135i \(0.728541\pi\)
\(462\) 0 0
\(463\) 10.9307 18.9325i 0.507993 0.879869i −0.491964 0.870615i \(-0.663721\pi\)
0.999957 0.00925409i \(-0.00294571\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.2337 0.843754 0.421877 0.906653i \(-0.361371\pi\)
0.421877 + 0.906653i \(0.361371\pi\)
\(468\) 0 0
\(469\) −25.4891 −1.17698
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −11.3723 + 19.6974i −0.522898 + 0.905686i
\(474\) 0 0
\(475\) −0.500000 0.866025i −0.0229416 0.0397360i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.0584 20.8858i −0.550963 0.954297i −0.998205 0.0598836i \(-0.980927\pi\)
0.447242 0.894413i \(-0.352406\pi\)
\(480\) 0 0
\(481\) −7.11684 + 12.3267i −0.324500 + 0.562051i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.74456 −0.306255
\(486\) 0 0
\(487\) −20.6060 −0.933746 −0.466873 0.884324i \(-0.654619\pi\)
−0.466873 + 0.884324i \(0.654619\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 9.98913 17.3017i 0.450803 0.780814i −0.547633 0.836719i \(-0.684471\pi\)
0.998436 + 0.0559050i \(0.0178044\pi\)
\(492\) 0 0
\(493\) 8.00000 + 13.8564i 0.360302 + 0.624061i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.62772 2.81929i −0.0730132 0.126463i
\(498\) 0 0
\(499\) −4.12772 + 7.14942i −0.184782 + 0.320052i −0.943503 0.331364i \(-0.892491\pi\)
0.758721 + 0.651416i \(0.225825\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 34.9783 1.55960 0.779802 0.626027i \(-0.215320\pi\)
0.779802 + 0.626027i \(0.215320\pi\)
\(504\) 0 0
\(505\) 12.8614 0.572325
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −19.0000 + 32.9090i −0.842160 + 1.45866i 0.0459045 + 0.998946i \(0.485383\pi\)
−0.888065 + 0.459718i \(0.847950\pi\)
\(510\) 0 0
\(511\) 3.86141 + 6.68815i 0.170819 + 0.295866i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.55842 + 14.8236i 0.377129 + 0.653207i
\(516\) 0 0
\(517\) −6.11684 + 10.5947i −0.269018 + 0.465954i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −17.1168 −0.749903 −0.374951 0.927045i \(-0.622341\pi\)
−0.374951 + 0.927045i \(0.622341\pi\)
\(522\) 0 0
\(523\) −5.76631 −0.252143 −0.126072 0.992021i \(-0.540237\pi\)
−0.126072 + 0.992021i \(0.540237\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −14.5109 + 25.1336i −0.632104 + 1.09484i
\(528\) 0 0
\(529\) 11.4307 + 19.7986i 0.496987 + 0.860807i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 13.9307 + 24.1287i 0.603406 + 1.04513i
\(534\) 0 0
\(535\) 3.00000 5.19615i 0.129701 0.224649i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.62772 −0.199330
\(540\) 0 0
\(541\) −38.3505 −1.64882 −0.824409 0.565994i \(-0.808492\pi\)
−0.824409 + 0.565994i \(0.808492\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.05842 15.6896i 0.388020 0.672071i
\(546\) 0 0
\(547\) 20.0000 + 34.6410i 0.855138 + 1.48114i 0.876517 + 0.481371i \(0.159861\pi\)
−0.0213785 + 0.999771i \(0.506805\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.68614 2.92048i −0.0718320 0.124417i
\(552\) 0 0
\(553\) 10.3723 17.9653i 0.441074 0.763963i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.60597 −0.364647 −0.182323 0.983239i \(-0.558362\pi\)
−0.182323 + 0.983239i \(0.558362\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12.1168 20.9870i 0.510664 0.884496i −0.489260 0.872138i \(-0.662733\pi\)
0.999924 0.0123579i \(-0.00393375\pi\)
\(564\) 0 0
\(565\) −1.62772 2.81929i −0.0684786 0.118608i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 21.6168 + 37.4415i 0.906225 + 1.56963i 0.819264 + 0.573416i \(0.194382\pi\)
0.0869612 + 0.996212i \(0.472284\pi\)
\(570\) 0 0
\(571\) −7.05842 + 12.2255i −0.295386 + 0.511623i −0.975075 0.221877i \(-0.928782\pi\)
0.679689 + 0.733501i \(0.262115\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.372281 0.0155252
\(576\) 0 0
\(577\) 13.4891 0.561560 0.280780 0.959772i \(-0.409407\pi\)
0.280780 + 0.959772i \(0.409407\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11.8614 20.5446i 0.492094 0.852332i
\(582\) 0 0
\(583\) −12.0000 20.7846i −0.496989 0.860811i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 15.0000 + 25.9808i 0.619116 + 1.07234i 0.989647 + 0.143521i \(0.0458424\pi\)
−0.370531 + 0.928820i \(0.620824\pi\)
\(588\) 0 0
\(589\) 3.05842 5.29734i 0.126020 0.218273i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −16.9783 −0.697213 −0.348607 0.937269i \(-0.613345\pi\)
−0.348607 + 0.937269i \(0.613345\pi\)
\(594\) 0 0
\(595\) −11.2554 −0.461428
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18.1753 + 31.4805i −0.742621 + 1.28626i 0.208677 + 0.977985i \(0.433084\pi\)
−0.951298 + 0.308273i \(0.900249\pi\)
\(600\) 0 0
\(601\) −6.50000 11.2583i −0.265141 0.459237i 0.702460 0.711723i \(-0.252085\pi\)
−0.967600 + 0.252486i \(0.918752\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.186141 + 0.322405i 0.00756769 + 0.0131076i
\(606\) 0 0
\(607\) 16.6277 28.8001i 0.674898 1.16896i −0.301600 0.953434i \(-0.597521\pi\)
0.976499 0.215524i \(-0.0691458\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8.60597 0.348160
\(612\) 0 0
\(613\) −33.3505 −1.34702 −0.673508 0.739180i \(-0.735213\pi\)
−0.673508 + 0.739180i \(0.735213\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −21.8614 + 37.8651i −0.880107 + 1.52439i −0.0288861 + 0.999583i \(0.509196\pi\)
−0.851221 + 0.524807i \(0.824137\pi\)
\(618\) 0 0
\(619\) 19.1861 + 33.2314i 0.771156 + 1.33568i 0.936930 + 0.349518i \(0.113655\pi\)
−0.165774 + 0.986164i \(0.553012\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.62772 2.81929i −0.0652132 0.112953i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −28.4674 −1.13507
\(630\) 0 0
\(631\) −36.6277 −1.45813 −0.729063 0.684446i \(-0.760044\pi\)
−0.729063 + 0.684446i \(0.760044\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 7.93070 13.7364i 0.314720 0.545112i
\(636\) 0 0
\(637\) 1.62772 + 2.81929i 0.0644926 + 0.111704i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.19702 + 2.07329i 0.0472793 + 0.0818901i 0.888697 0.458496i \(-0.151612\pi\)
−0.841417 + 0.540386i \(0.818278\pi\)
\(642\) 0 0
\(643\) −10.6277 + 18.4077i −0.419116 + 0.725931i −0.995851 0.0910009i \(-0.970993\pi\)
0.576734 + 0.816932i \(0.304327\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25.7228 −1.01127 −0.505634 0.862748i \(-0.668741\pi\)
−0.505634 + 0.862748i \(0.668741\pi\)
\(648\) 0 0
\(649\) −16.8614 −0.661868
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −12.3723 + 21.4294i −0.484165 + 0.838598i −0.999835 0.0181894i \(-0.994210\pi\)
0.515670 + 0.856787i \(0.327543\pi\)
\(654\) 0 0
\(655\) −8.87228 15.3672i −0.346669 0.600448i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −23.7921 41.2091i −0.926809 1.60528i −0.788626 0.614874i \(-0.789207\pi\)
−0.138183 0.990407i \(-0.544126\pi\)
\(660\) 0 0
\(661\) 22.5475 39.0535i 0.876998 1.51901i 0.0223789 0.999750i \(-0.492876\pi\)
0.854619 0.519255i \(-0.173791\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.37228 0.0919931
\(666\) 0 0
\(667\) 1.25544 0.0486107
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.11684 + 3.66648i −0.0817199 + 0.141543i
\(672\) 0 0
\(673\) 0.255437 + 0.442430i 0.00984639 + 0.0170544i 0.870907 0.491449i \(-0.163532\pi\)
−0.861060 + 0.508503i \(0.830199\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.5584 18.2877i −0.405793 0.702854i 0.588620 0.808410i \(-0.299671\pi\)
−0.994413 + 0.105555i \(0.966338\pi\)
\(678\) 0 0
\(679\) 8.00000 13.8564i 0.307012 0.531760i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −38.2337 −1.46297 −0.731486 0.681857i \(-0.761173\pi\)
−0.731486 + 0.681857i \(0.761173\pi\)
\(684\) 0 0
\(685\) −16.7446 −0.639777
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −8.44158 + 14.6212i −0.321599 + 0.557025i
\(690\) 0 0
\(691\) −20.6753 35.8106i −0.786524 1.36230i −0.928084 0.372370i \(-0.878545\pi\)
0.141560 0.989930i \(-0.454788\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7.50000 + 12.9904i 0.284491 + 0.492753i
\(696\) 0 0
\(697\) −27.8614 + 48.2574i −1.05533 + 1.82788i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 8.11684 0.306569 0.153284 0.988182i \(-0.451015\pi\)
0.153284 + 0.988182i \(0.451015\pi\)
\(702\) 0 0
\(703\) 6.00000 0.226294
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −15.2554 + 26.4232i −0.573740 + 0.993746i
\(708\) 0 0
\(709\) −9.23369 15.9932i −0.346778 0.600638i 0.638897 0.769292i \(-0.279391\pi\)
−0.985675 + 0.168655i \(0.946058\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.13859 + 1.97210i 0.0426407 + 0.0738558i
\(714\) 0 0
\(715\) 4.00000 6.92820i 0.149592 0.259100i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10.3940 0.387632 0.193816 0.981038i \(-0.437914\pi\)
0.193816 + 0.981038i \(0.437914\pi\)
\(720\) 0 0
\(721\) −40.6060 −1.51225
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.68614 + 2.92048i −0.0626217 + 0.108464i
\(726\) 0 0
\(727\) 23.5584 + 40.8044i 0.873734 + 1.51335i 0.858106 + 0.513473i \(0.171641\pi\)
0.0156277 + 0.999878i \(0.495025\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16.0000 + 27.7128i 0.591781 + 1.02500i
\(732\) 0 0
\(733\) 14.4891 25.0959i 0.535168 0.926938i −0.463987 0.885842i \(-0.653582\pi\)
0.999155 0.0410963i \(-0.0130851\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 36.2337 1.33469
\(738\) 0 0
\(739\) −12.8614 −0.473114 −0.236557 0.971618i \(-0.576019\pi\)
−0.236557 + 0.971618i \(0.576019\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −14.7446 + 25.5383i −0.540926 + 0.936911i 0.457926 + 0.888991i \(0.348593\pi\)
−0.998851 + 0.0479200i \(0.984741\pi\)
\(744\) 0 0
\(745\) 1.74456 + 3.02167i 0.0639158 + 0.110705i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7.11684 + 12.3267i 0.260044 + 0.450409i
\(750\) 0 0
\(751\) 19.1168 33.1113i 0.697584 1.20825i −0.271718 0.962377i \(-0.587592\pi\)
0.969302 0.245873i \(-0.0790747\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −18.6277 −0.677932
\(756\) 0 0
\(757\) 27.1168 0.985578 0.492789 0.870149i \(-0.335977\pi\)
0.492789 + 0.870149i \(0.335977\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.61684 + 14.9248i −0.312360 + 0.541024i −0.978873 0.204470i \(-0.934453\pi\)
0.666513 + 0.745494i \(0.267786\pi\)
\(762\) 0 0
\(763\) 21.4891 + 37.2203i 0.777959 + 1.34746i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.93070 + 10.2723i 0.214145 + 0.370911i
\(768\) 0 0
\(769\) 16.1753 28.0164i 0.583295 1.01030i −0.411791 0.911278i \(-0.635096\pi\)
0.995086 0.0990181i \(-0.0315702\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) −6.11684 −0.219724
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.87228 10.1711i 0.210396 0.364417i
\(780\) 0 0
\(781\) 2.31386 + 4.00772i 0.0827964 + 0.143408i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.93070 5.07613i −0.104601 0.181175i
\(786\) 0 0
\(787\) −7.86141 + 13.6164i −0.280229 + 0.485371i −0.971441 0.237281i \(-0.923744\pi\)
0.691212 + 0.722652i \(0.257077\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 7.72281 0.274592
\(792\) 0 0
\(793\) 2.97825 0.105761
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 7.11684 12.3267i 0.252092 0.436635i −0.712010 0.702169i \(-0.752215\pi\)
0.964101 + 0.265534i \(0.0855483\pi\)
\(798\) 0 0
\(799\) 8.60597 + 14.9060i 0.304457 + 0.527336i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −5.48913 9.50744i −0.193707 0.335510i
\(804\) 0 0