Properties

Label 3240.2.q.bd.2161.2
Level $3240$
Weight $2$
Character 3240.2161
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 2161.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 3240.2161
Dual form 3240.2.q.bd.1081.2

$q$-expansion

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

Character values

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

\(n\) \(1297\) \(1621\) \(2431\) \(3161\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 1.18614 2.05446i 0.448319 0.776511i −0.549958 0.835192i \(-0.685356\pi\)
0.998277 + 0.0586811i \(0.0186895\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.68614 + 2.92048i −0.508391 + 0.880558i 0.491562 + 0.870842i \(0.336426\pi\)
−0.999953 + 0.00971581i \(0.996907\pi\)
\(12\) 0 0
\(13\) −1.18614 2.05446i −0.328976 0.569804i 0.653333 0.757071i \(-0.273370\pi\)
−0.982309 + 0.187267i \(0.940037\pi\)
\(14\) 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 0.845966 0.533236i \(-0.179024\pi\)
−0.884779 + 0.466010i \(0.845691\pi\)
\(24\) 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 −0.979034 0.203699i \(-0.934704\pi\)
0.665925 + 0.746019i \(0.268037\pi\)
\(30\) 0 0
\(31\) 3.05842 + 5.29734i 0.549309 + 0.951431i 0.998322 + 0.0579057i \(0.0184423\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) 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 0.803803 + 0.594896i \(0.202807\pi\)
0.113293 + 0.993562i \(0.463860\pi\)
\(42\) 0 0
\(43\) −3.37228 + 5.84096i −0.514268 + 0.890738i 0.485595 + 0.874184i \(0.338603\pi\)
−0.999863 + 0.0165545i \(0.994730\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.81386 + 3.14170i −0.264579 + 0.458264i −0.967453 0.253050i \(-0.918566\pi\)
0.702875 + 0.711314i \(0.251900\pi\)
\(48\) 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 0.981608 0.190909i \(-0.0611434\pi\)
−0.656136 + 0.754643i \(0.727810\pi\)
\(60\) 0 0
\(61\) −0.627719 + 1.08724i −0.0803711 + 0.139207i −0.903409 0.428779i \(-0.858944\pi\)
0.823038 + 0.567986i \(0.192277\pi\)
\(62\) 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 −0.981559 0.191160i \(-0.938775\pi\)
0.325230 0.945635i \(-0.394558\pi\)
\(68\) 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 −0.999957 0.00930489i \(-0.997038\pi\)
0.508037 + 0.861335i \(0.330371\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −5.00000 + 8.66025i −0.548821 + 0.950586i 0.449534 + 0.893263i \(0.351590\pi\)
−0.998356 + 0.0573233i \(0.981743\pi\)
\(84\) 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 −0.984878 0.173247i \(-0.944574\pi\)
0.642475 + 0.766306i \(0.277908\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 6.43070 11.1383i 0.639879 1.10830i −0.345580 0.938389i \(-0.612318\pi\)
0.985459 0.169913i \(-0.0543488\pi\)
\(102\) 0 0
\(103\) −8.55842 14.8236i −0.843286 1.46061i −0.887101 0.461575i \(-0.847284\pi\)
0.0438147 0.999040i \(-0.486049\pi\)
\(104\) 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 0.932374 0.361495i \(-0.117734\pi\)
−0.779251 + 0.626712i \(0.784400\pi\)
\(114\) 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 0.934696 + 0.355448i \(0.115672\pi\)
−0.159521 + 0.987194i \(0.550995\pi\)
\(132\) 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 0.247554 + 0.968874i \(0.420373\pi\)
−0.962847 + 0.270049i \(0.912960\pi\)
\(138\) 0 0
\(139\) −7.50000 12.9904i −0.636142 1.10183i −0.986272 0.165129i \(-0.947196\pi\)
0.350130 0.936701i \(-0.386137\pi\)
\(140\) 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 0.785675 0.618640i \(-0.212316\pi\)
−0.928595 + 0.371095i \(0.878983\pi\)
\(150\) 0 0
\(151\) −9.31386 + 16.1321i −0.757951 + 1.31281i 0.185943 + 0.982561i \(0.440466\pi\)
−0.943894 + 0.330249i \(0.892867\pi\)
\(152\) 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 0.958951 0.283571i \(-0.0915193\pi\)
−0.725056 + 0.688690i \(0.758186\pi\)
\(158\) 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 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 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 0.472576 + 0.881290i \(0.343324\pi\)
−0.999507 + 0.0313823i \(0.990009\pi\)
\(174\) 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 −0.995047 0.0994067i \(-0.968306\pi\)
0.583612 + 0.812033i \(0.301639\pi\)
\(192\) 0 0
\(193\) 5.37228 + 9.30506i 0.386705 + 0.669793i 0.992004 0.126205i \(-0.0402797\pi\)
−0.605299 + 0.795998i \(0.706946\pi\)
\(194\) 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 −0.994855 0.101310i \(-0.967697\pi\)
0.409691 0.912224i \(-0.365637\pi\)
\(212\) 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 −0.904995 0.425423i \(-0.860125\pi\)
0.820924 + 0.571037i \(0.193459\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 2.74456 4.75372i 0.182163 0.315516i −0.760454 0.649392i \(-0.775023\pi\)
0.942617 + 0.333876i \(0.108357\pi\)
\(228\) 0 0
\(229\) 2.62772 + 4.55134i 0.173645 + 0.300761i 0.939691 0.342024i \(-0.111112\pi\)
−0.766047 + 0.642785i \(0.777779\pi\)
\(230\) 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 0.998978 0.0451935i \(-0.0143905\pi\)
−0.538628 + 0.842544i \(0.681057\pi\)
\(240\) 0 0
\(241\) −14.8030 + 25.6395i −0.953544 + 1.65159i −0.215879 + 0.976420i \(0.569262\pi\)
−0.737665 + 0.675167i \(0.764072\pi\)
\(242\) 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 0.955766 + 0.294128i \(0.0950294\pi\)
−0.223160 + 0.974782i \(0.571637\pi\)
\(258\) 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 −0.994253 0.107060i \(-0.965856\pi\)
0.589843 + 0.807518i \(0.299190\pi\)
\(264\) 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 −0.485638 0.874160i \(-0.661413\pi\)
0.999864 0.0165051i \(-0.00525398\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5.81386 10.0699i 0.346826 0.600720i −0.638858 0.769325i \(-0.720593\pi\)
0.985684 + 0.168605i \(0.0539262\pi\)
\(282\) 0 0
\(283\) −2.62772 4.55134i −0.156202 0.270549i 0.777294 0.629137i \(-0.216592\pi\)
−0.933496 + 0.358588i \(0.883258\pi\)
\(284\) 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 0.994309 0.106531i \(-0.0339744\pi\)
−0.589413 + 0.807832i \(0.700641\pi\)
\(294\) 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 0.669966 0.742392i \(-0.266309\pi\)
−0.977913 + 0.209012i \(0.932975\pi\)
\(312\) 0 0
\(313\) 2.00000 3.46410i 0.113047 0.195803i −0.803951 0.594696i \(-0.797272\pi\)
0.916997 + 0.398894i \(0.130606\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −8.18614 + 14.1788i −0.459779 + 0.796361i −0.998949 0.0458359i \(-0.985405\pi\)
0.539170 + 0.842197i \(0.318738\pi\)
\(318\) 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 0.466886 + 0.884318i \(0.345376\pi\)
−0.999284 + 0.0378236i \(0.987957\pi\)
\(332\) 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 0.855708 0.517460i \(-0.173122\pi\)
−0.875987 + 0.482335i \(0.839789\pi\)
\(338\) 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 −0.911804 0.410626i \(-0.865310\pi\)
0.100289 0.994958i \(-0.468023\pi\)
\(348\) 0 0
\(349\) 12.6861 21.9730i 0.679074 1.17619i −0.296187 0.955130i \(-0.595715\pi\)
0.975260 0.221060i \(-0.0709516\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 12.4891 21.6318i 0.664729 1.15134i −0.314630 0.949215i \(-0.601880\pi\)
0.979359 0.202130i \(-0.0647864\pi\)
\(354\) 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 −0.915971 0.401244i \(-0.868578\pi\)
0.805473 + 0.592633i \(0.201911\pi\)
\(368\) 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 0.856226 0.516601i \(-0.172803\pi\)
−0.875502 + 0.483214i \(0.839469\pi\)
\(374\) 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 0.637753 0.770241i \(-0.279864\pi\)
−0.985925 + 0.167190i \(0.946531\pi\)
\(384\) 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 −0.724532 0.689241i \(-0.757944\pi\)
0.959166 + 0.282842i \(0.0912773\pi\)
\(390\) 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 0.608245 0.793749i \(-0.291874\pi\)
−0.991530 + 0.129881i \(0.958540\pi\)
\(402\) 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 0.991958 0.126565i \(-0.0403953\pi\)
−0.605588 + 0.795778i \(0.707062\pi\)
\(410\) 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 0.700226 0.713922i \(-0.253083\pi\)
−0.968387 + 0.249452i \(0.919749\pi\)
\(420\) 0 0
\(421\) −11.3139 + 19.5962i −0.551404 + 0.955059i 0.446770 + 0.894649i \(0.352574\pi\)
−0.998174 + 0.0604104i \(0.980759\pi\)
\(422\) 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 0.209519 + 0.977805i \(0.432810\pi\)
−0.951563 + 0.307453i \(0.900523\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 8.48913 14.7036i 0.403331 0.698589i −0.590795 0.806822i \(-0.701186\pi\)
0.994126 + 0.108233i \(0.0345192\pi\)
\(444\) 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 0.177508 0.984119i \(-0.443197\pi\)
0.763519 0.645786i \(-0.223470\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 6.94158 12.0232i 0.323302 0.559975i −0.657866 0.753135i \(-0.728541\pi\)
0.981167 + 0.193161i \(0.0618739\pi\)
\(462\) 0 0
\(463\) 10.9307 + 18.9325i 0.507993 + 0.879869i 0.999957 + 0.00925409i \(0.00294571\pi\)
−0.491964 + 0.870615i \(0.663721\pi\)
\(464\) 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 0.447242 + 0.894413i \(0.352406\pi\)
−0.998205 + 0.0598836i \(0.980927\pi\)
\(480\) 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 0.998436 0.0559050i \(-0.0178044\pi\)
−0.547633 + 0.836719i \(0.684471\pi\)
\(492\) 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 0.758721 0.651416i \(-0.225825\pi\)
−0.943503 + 0.331364i \(0.892491\pi\)
\(500\) 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 −0.888065 0.459718i \(-0.847950\pi\)
0.0459045 0.998946i \(-0.485383\pi\)
\(510\) 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 −0.0213785 0.999771i \(-0.506805\pi\)
0.876517 0.481371i \(-0.159861\pi\)
\(548\) 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 0.999924 + 0.0123579i \(0.00393375\pi\)
−0.489260 + 0.872138i \(0.662733\pi\)
\(564\) 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 0.0869612 0.996212i \(-0.472284\pi\)
0.819264 0.573416i \(-0.194382\pi\)
\(570\) 0 0
\(571\) −7.05842 12.2255i −0.295386 0.511623i 0.679689 0.733501i \(-0.262115\pi\)
−0.975075 + 0.221877i \(0.928782\pi\)
\(572\) 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 −0.370531 0.928820i \(-0.620824\pi\)
0.989647 0.143521i \(-0.0458424\pi\)
\(588\) 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 −0.951298 0.308273i \(-0.900249\pi\)
0.208677 0.977985i \(-0.433084\pi\)
\(600\) 0 0
\(601\) −6.50000 + 11.2583i −0.265141 + 0.459237i −0.967600 0.252486i \(-0.918752\pi\)
0.702460 + 0.711723i \(0.252085\pi\)
\(602\) 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 0.976499 + 0.215524i \(0.0691458\pi\)
−0.301600 + 0.953434i \(0.597521\pi\)
\(608\) 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 −0.851221 0.524807i \(-0.824137\pi\)
−0.0288861 0.999583i \(-0.509196\pi\)
\(618\) 0 0
\(619\) 19.1861 33.2314i 0.771156 1.33568i −0.165774 0.986164i \(-0.553012\pi\)
0.936930 0.349518i \(-0.113655\pi\)
\(620\) 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 −0.841417 0.540386i \(-0.818278\pi\)
0.888697 + 0.458496i \(0.151612\pi\)
\(642\) 0 0
\(643\) −10.6277 18.4077i −0.419116 0.725931i 0.576734 0.816932i \(-0.304327\pi\)
−0.995851 + 0.0910009i \(0.970993\pi\)
\(644\) 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 0.515670 0.856787i \(-0.327543\pi\)
−0.999835 + 0.0181894i \(0.994210\pi\)
\(654\) 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 −0.138183 + 0.990407i \(0.544126\pi\)
−0.788626 + 0.614874i \(0.789207\pi\)
\(660\) 0 0
\(661\) 22.5475 + 39.0535i 0.876998 + 1.51901i 0.854619 + 0.519255i \(0.173791\pi\)
0.0223789 + 0.999750i \(0.492876\pi\)
\(662\) 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 −0.861060 0.508503i \(-0.830199\pi\)
0.870907 + 0.491449i \(0.163532\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.5584 + 18.2877i −0.405793 + 0.702854i −0.994413 0.105555i \(-0.966338\pi\)
0.588620 + 0.808410i \(0.299671\pi\)
\(678\) 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 0.141560 + 0.989930i \(0.454788\pi\)
−0.928084 + 0.372370i \(0.878545\pi\)
\(692\) 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 −0.985675 0.168655i \(-0.946058\pi\)
0.638897 + 0.769292i \(0.279391\pi\)
\(710\) 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 0.0156277 0.999878i \(-0.495025\pi\)
0.858106 0.513473i \(-0.171641\pi\)
\(728\) 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 0.999155 + 0.0410963i \(0.0130851\pi\)
−0.463987 + 0.885842i \(0.653582\pi\)
\(734\) 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 −0.998851 0.0479200i \(-0.984741\pi\)
0.457926 0.888991i \(-0.348593\pi\)
\(744\) 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 0.969302 + 0.245873i \(0.0790747\pi\)
−0.271718 + 0.962377i \(0.587592\pi\)
\(752\) 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 0.666513 0.745494i \(-0.267786\pi\)
−0.978873 + 0.204470i \(0.934453\pi\)
\(762\) 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 0.995086 + 0.0990181i \(0.0315702\pi\)
−0.411791 + 0.911278i \(0.635096\pi\)
\(770\) 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 0.691212 0.722652i \(-0.257077\pi\)
−0.971441 + 0.237281i \(0.923744\pi\)
\(788\) 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 0.964101 0.265534i \(-0.0855483\pi\)
−0.712010 + 0.702169i \(0.752215\pi\)
\(798\) 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
\(805\) −0.44157