Properties

Label 729.2.i.a.685.24
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.24
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.24

$q$-expansion

\(f(q)\) \(=\) \(q+(2.24894 + 0.626034i) q^{2} +(2.95346 + 1.78242i) q^{4} +(0.812747 - 0.0315383i) q^{5} +(1.20842 + 0.188994i) q^{7} +(2.32230 + 2.46149i) q^{8} +O(q^{10})\) \(q+(2.24894 + 0.626034i) q^{2} +(2.95346 + 1.78242i) q^{4} +(0.812747 - 0.0315383i) q^{5} +(1.20842 + 0.188994i) q^{7} +(2.32230 + 2.46149i) q^{8} +(1.84756 + 0.437879i) q^{10} +(0.262100 + 1.91892i) q^{11} +(-1.56973 + 2.28872i) q^{13} +(2.59935 + 1.18155i) q^{14} +(0.466363 + 0.885368i) q^{16} +(3.40839 - 1.71176i) q^{17} +(-0.0225985 - 0.388002i) q^{19} +(2.45663 + 1.35551i) q^{20} +(-0.611859 + 4.47960i) q^{22} +(1.72522 - 4.46842i) q^{23} +(-4.32540 + 0.336197i) q^{25} +(-4.96303 + 4.16448i) q^{26} +(3.23216 + 2.71210i) q^{28} +(5.20543 + 3.72061i) q^{29} +(-3.58945 + 4.11306i) q^{31} +(-0.938296 - 4.33166i) q^{32} +(8.73687 - 1.71587i) q^{34} +(0.988102 + 0.115493i) q^{35} +(-5.86331 - 7.87579i) q^{37} +(0.192080 - 0.886739i) q^{38} +(1.96507 + 1.92733i) q^{40} +(0.617630 - 2.39779i) q^{41} +(0.752751 + 0.683085i) q^{43} +(-2.64621 + 6.13461i) q^{44} +(6.67729 - 8.96915i) q^{46} +(-1.84929 - 2.11906i) q^{47} +(-5.24117 - 1.68051i) q^{49} +(-9.93802 - 1.95176i) q^{50} +(-8.71559 + 3.96172i) q^{52} +(-1.44784 + 8.21109i) q^{53} +(0.273541 + 1.55133i) q^{55} +(2.34111 + 3.41342i) q^{56} +(9.37743 + 11.6262i) q^{58} +(0.578998 - 0.236547i) q^{59} +(10.0154 - 6.04435i) q^{61} +(-10.6474 + 7.00288i) q^{62} +(0.717966 - 12.3270i) q^{64} +(-1.20361 + 1.90965i) q^{65} +(-7.98108 + 5.70453i) q^{67} +(13.1176 + 1.01958i) q^{68} +(2.14988 + 0.878321i) q^{70} +(-2.59953 - 8.68305i) q^{71} +(-13.5233 + 3.20508i) q^{73} +(-8.25569 - 21.3828i) q^{74} +(0.624839 - 1.18623i) q^{76} +(-0.0459350 + 2.36840i) q^{77} +(-5.21181 + 5.11171i) q^{79} +(0.406958 + 0.704872i) q^{80} +(2.89011 - 5.00581i) q^{82} +(0.514050 + 1.99566i) q^{83} +(2.71617 - 1.49872i) q^{85} +(1.26525 + 2.00746i) q^{86} +(-4.11472 + 5.10145i) q^{88} +(1.84629 - 6.16704i) q^{89} +(-2.32945 + 2.46907i) q^{91} +(13.0600 - 10.1222i) q^{92} +(-2.83234 - 5.92334i) q^{94} +(-0.0306038 - 0.314635i) q^{95} +(5.74213 + 0.222821i) q^{97} +(-10.7350 - 7.06051i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24894 + 0.626034i 1.59024 + 0.442673i 0.946535 0.322602i \(-0.104558\pi\)
0.643703 + 0.765275i \(0.277397\pi\)
\(3\) 0 0
\(4\) 2.95346 + 1.78242i 1.47673 + 0.891211i
\(5\) 0.812747 0.0315383i 0.363471 0.0141043i 0.143607 0.989635i \(-0.454130\pi\)
0.219864 + 0.975530i \(0.429439\pi\)
\(6\) 0 0
\(7\) 1.20842 + 0.188994i 0.456741 + 0.0714330i 0.378705 0.925518i \(-0.376370\pi\)
0.0780362 + 0.996951i \(0.475135\pi\)
\(8\) 2.32230 + 2.46149i 0.821056 + 0.870268i
\(9\) 0 0
\(10\) 1.84756 + 0.437879i 0.584249 + 0.138470i
\(11\) 0.262100 + 1.91892i 0.0790263 + 0.578575i 0.987141 + 0.159853i \(0.0511020\pi\)
−0.908115 + 0.418722i \(0.862478\pi\)
\(12\) 0 0
\(13\) −1.56973 + 2.28872i −0.435364 + 0.634776i −0.978835 0.204652i \(-0.934394\pi\)
0.543471 + 0.839428i \(0.317110\pi\)
\(14\) 2.59935 + 1.18155i 0.694705 + 0.315782i
\(15\) 0 0
\(16\) 0.466363 + 0.885368i 0.116591 + 0.221342i
\(17\) 3.40839 1.71176i 0.826656 0.415162i 0.0154201 0.999881i \(-0.495091\pi\)
0.811236 + 0.584719i \(0.198795\pi\)
\(18\) 0 0
\(19\) −0.0225985 0.388002i −0.00518446 0.0890137i 0.994723 0.102594i \(-0.0327142\pi\)
−0.999908 + 0.0135801i \(0.995677\pi\)
\(20\) 2.45663 + 1.35551i 0.549319 + 0.303101i
\(21\) 0 0
\(22\) −0.611859 + 4.47960i −0.130449 + 0.955054i
\(23\) 1.72522 4.46842i 0.359733 0.931731i −0.628367 0.777917i \(-0.716276\pi\)
0.988100 0.153814i \(-0.0491557\pi\)
\(24\) 0 0
\(25\) −4.32540 + 0.336197i −0.865080 + 0.0672394i
\(26\) −4.96303 + 4.16448i −0.973330 + 0.816721i
\(27\) 0 0
\(28\) 3.23216 + 2.71210i 0.610821 + 0.512540i
\(29\) 5.20543 + 3.72061i 0.966623 + 0.690901i 0.951069 0.308978i \(-0.0999871\pi\)
0.0155541 + 0.999879i \(0.495049\pi\)
\(30\) 0 0
\(31\) −3.58945 + 4.11306i −0.644685 + 0.738727i −0.979028 0.203725i \(-0.934695\pi\)
0.334344 + 0.942451i \(0.391485\pi\)
\(32\) −0.938296 4.33166i −0.165869 0.765736i
\(33\) 0 0
\(34\) 8.73687 1.71587i 1.49836 0.294268i
\(35\) 0.988102 + 0.115493i 0.167020 + 0.0195218i
\(36\) 0 0
\(37\) −5.86331 7.87579i −0.963922 1.29477i −0.955557 0.294807i \(-0.904745\pi\)
−0.00836474 0.999965i \(-0.502663\pi\)
\(38\) 0.192080 0.886739i 0.0311594 0.143848i
\(39\) 0 0
\(40\) 1.96507 + 1.92733i 0.310705 + 0.304737i
\(41\) 0.617630 2.39779i 0.0964576 0.374471i −0.901888 0.431970i \(-0.857819\pi\)
0.998346 + 0.0574986i \(0.0183125\pi\)
\(42\) 0 0
\(43\) 0.752751 + 0.683085i 0.114793 + 0.104169i 0.727383 0.686232i \(-0.240736\pi\)
−0.612590 + 0.790401i \(0.709872\pi\)
\(44\) −2.64621 + 6.13461i −0.398932 + 0.924827i
\(45\) 0 0
\(46\) 6.67729 8.96915i 0.984512 1.32243i
\(47\) −1.84929 2.11906i −0.269747 0.309096i 0.602541 0.798088i \(-0.294155\pi\)
−0.872288 + 0.488992i \(0.837365\pi\)
\(48\) 0 0
\(49\) −5.24117 1.68051i −0.748738 0.240073i
\(50\) −9.93802 1.95176i −1.40545 0.276021i
\(51\) 0 0
\(52\) −8.71559 + 3.96172i −1.20863 + 0.549392i
\(53\) −1.44784 + 8.21109i −0.198876 + 1.12788i 0.707915 + 0.706298i \(0.249636\pi\)
−0.906790 + 0.421582i \(0.861475\pi\)
\(54\) 0 0
\(55\) 0.273541 + 1.55133i 0.0368842 + 0.209181i
\(56\) 2.34111 + 3.41342i 0.312844 + 0.456138i
\(57\) 0 0
\(58\) 9.37743 + 11.6262i 1.23132 + 1.52659i
\(59\) 0.578998 0.236547i 0.0753792 0.0307958i −0.340197 0.940354i \(-0.610494\pi\)
0.415576 + 0.909559i \(0.363580\pi\)
\(60\) 0 0
\(61\) 10.0154 6.04435i 1.28234 0.773899i 0.298757 0.954329i \(-0.403428\pi\)
0.983588 + 0.180430i \(0.0577489\pi\)
\(62\) −10.6474 + 7.00288i −1.35222 + 0.889367i
\(63\) 0 0
\(64\) 0.717966 12.3270i 0.0897458 1.54088i
\(65\) −1.20361 + 1.90965i −0.149289 + 0.236863i
\(66\) 0 0
\(67\) −7.98108 + 5.70453i −0.975044 + 0.696920i −0.953042 0.302838i \(-0.902066\pi\)
−0.0220023 + 0.999758i \(0.507004\pi\)
\(68\) 13.1176 + 1.01958i 1.59074 + 0.123642i
\(69\) 0 0
\(70\) 2.14988 + 0.878321i 0.256959 + 0.104979i
\(71\) −2.59953 8.68305i −0.308508 1.03049i −0.961885 0.273455i \(-0.911833\pi\)
0.653377 0.757033i \(-0.273352\pi\)
\(72\) 0 0
\(73\) −13.5233 + 3.20508i −1.58278 + 0.375127i −0.925570 0.378577i \(-0.876414\pi\)
−0.657214 + 0.753704i \(0.728265\pi\)
\(74\) −8.25569 21.3828i −0.959704 2.48570i
\(75\) 0 0
\(76\) 0.624839 1.18623i 0.0716740 0.136070i
\(77\) −0.0459350 + 2.36840i −0.00523478 + 0.269904i
\(78\) 0 0
\(79\) −5.21181 + 5.11171i −0.586374 + 0.575112i −0.931635 0.363395i \(-0.881618\pi\)
0.345261 + 0.938507i \(0.387790\pi\)
\(80\) 0.406958 + 0.704872i 0.0454993 + 0.0788070i
\(81\) 0 0
\(82\) 2.89011 5.00581i 0.319159 0.552799i
\(83\) 0.514050 + 1.99566i 0.0564243 + 0.219053i 0.990388 0.138314i \(-0.0441684\pi\)
−0.933964 + 0.357367i \(0.883675\pi\)
\(84\) 0 0
\(85\) 2.71617 1.49872i 0.294610 0.162559i
\(86\) 1.26525 + 2.00746i 0.136436 + 0.216470i
\(87\) 0 0
\(88\) −4.11472 + 5.10145i −0.438630 + 0.543816i
\(89\) 1.84629 6.16704i 0.195706 0.653705i −0.802653 0.596446i \(-0.796579\pi\)
0.998359 0.0572586i \(-0.0182360\pi\)
\(90\) 0 0
\(91\) −2.32945 + 2.46907i −0.244193 + 0.258829i
\(92\) 13.0600 10.1222i 1.36160 1.05532i
\(93\) 0 0
\(94\) −2.83234 5.92334i −0.292134 0.610946i
\(95\) −0.0306038 0.314635i −0.00313988 0.0322808i
\(96\) 0 0
\(97\) 5.74213 + 0.222821i 0.583025 + 0.0226240i 0.328601 0.944469i \(-0.393423\pi\)
0.254424 + 0.967093i \(0.418114\pi\)
\(98\) −10.7350 7.06051i −1.08440 0.713220i
\(99\) 0 0
\(100\) −13.3741 6.71675i −1.33741 0.671675i
\(101\) −0.203754 10.5055i −0.0202743 1.04534i −0.862453 0.506137i \(-0.831073\pi\)
0.842179 0.539199i \(-0.181273\pi\)
\(102\) 0 0
\(103\) 9.24977 + 7.16912i 0.911407 + 0.706394i 0.956235 0.292601i \(-0.0945207\pi\)
−0.0448273 + 0.998995i \(0.514274\pi\)
\(104\) −9.27903 + 1.45121i −0.909884 + 0.142303i
\(105\) 0 0
\(106\) −8.39651 + 17.5598i −0.815541 + 1.70556i
\(107\) −5.22484 1.90168i −0.505104 0.183843i 0.0768843 0.997040i \(-0.475503\pi\)
−0.581988 + 0.813197i \(0.697725\pi\)
\(108\) 0 0
\(109\) −9.12963 + 3.32291i −0.874460 + 0.318277i −0.739972 0.672638i \(-0.765161\pi\)
−0.134488 + 0.990915i \(0.542939\pi\)
\(110\) −0.356007 + 3.66008i −0.0339440 + 0.348975i
\(111\) 0 0
\(112\) 0.396234 + 1.15804i 0.0374406 + 0.109424i
\(113\) 14.1772 12.8651i 1.33368 1.21025i 0.374569 0.927199i \(-0.377791\pi\)
0.959106 0.283047i \(-0.0913452\pi\)
\(114\) 0 0
\(115\) 1.26124 3.68611i 0.117611 0.343731i
\(116\) 8.74231 + 20.2669i 0.811703 + 1.88174i
\(117\) 0 0
\(118\) 1.45022 0.169506i 0.133503 0.0156043i
\(119\) 4.44229 1.42436i 0.407224 0.130571i
\(120\) 0 0
\(121\) 6.98354 1.94400i 0.634867 0.176727i
\(122\) 26.3080 7.32334i 2.38182 0.663024i
\(123\) 0 0
\(124\) −17.9325 + 5.74982i −1.61039 + 0.516349i
\(125\) −7.54415 + 0.881784i −0.674769 + 0.0788692i
\(126\) 0 0
\(127\) −6.58900 15.2750i −0.584679 1.35544i −0.911869 0.410480i \(-0.865361\pi\)
0.327190 0.944958i \(-0.393898\pi\)
\(128\) 6.46213 18.8863i 0.571177 1.66933i
\(129\) 0 0
\(130\) −3.90235 + 3.54119i −0.342258 + 0.310583i
\(131\) 2.87785 + 8.41085i 0.251439 + 0.734859i 0.997609 + 0.0691038i \(0.0220140\pi\)
−0.746170 + 0.665755i \(0.768109\pi\)
\(132\) 0 0
\(133\) 0.0460214 0.473141i 0.00399056 0.0410266i
\(134\) −21.5202 + 7.83270i −1.85906 + 0.676642i
\(135\) 0 0
\(136\) 12.1288 + 4.41451i 1.04003 + 0.378541i
\(137\) −6.37384 + 13.3298i −0.544554 + 1.13884i 0.427486 + 0.904022i \(0.359399\pi\)
−0.972040 + 0.234816i \(0.924551\pi\)
\(138\) 0 0
\(139\) 22.5519 3.52705i 1.91282 0.299160i 0.917658 0.397371i \(-0.130077\pi\)
0.995166 + 0.0982109i \(0.0313120\pi\)
\(140\) 2.71246 + 2.10232i 0.229245 + 0.177678i
\(141\) 0 0
\(142\) −0.410301 21.1550i −0.0344317 1.77529i
\(143\) −4.80328 2.41230i −0.401671 0.201727i
\(144\) 0 0
\(145\) 4.34803 + 2.85975i 0.361085 + 0.237489i
\(146\) −32.4196 1.25803i −2.68306 0.104115i
\(147\) 0 0
\(148\) −3.27906 33.7117i −0.269537 2.77108i
\(149\) 3.78360 + 7.91273i 0.309965 + 0.648236i 0.996917 0.0784666i \(-0.0250024\pi\)
−0.686952 + 0.726703i \(0.741052\pi\)
\(150\) 0 0
\(151\) −6.63152 + 5.13981i −0.539665 + 0.418272i −0.845629 0.533771i \(-0.820774\pi\)
0.305964 + 0.952043i \(0.401021\pi\)
\(152\) 0.902582 0.956681i 0.0732091 0.0775971i
\(153\) 0 0
\(154\) −1.58600 + 5.29761i −0.127804 + 0.426894i
\(155\) −2.78760 + 3.45608i −0.223905 + 0.277599i
\(156\) 0 0
\(157\) −3.29632 5.22996i −0.263075 0.417397i 0.688303 0.725423i \(-0.258356\pi\)
−0.951378 + 0.308027i \(0.900331\pi\)
\(158\) −14.9211 + 8.23313i −1.18706 + 0.654992i
\(159\) 0 0
\(160\) −0.899210 3.49095i −0.0710888 0.275984i
\(161\) 2.92930 5.07369i 0.230861 0.399863i
\(162\) 0 0
\(163\) −1.12503 1.94861i −0.0881191 0.152627i 0.818597 0.574368i \(-0.194752\pi\)
−0.906716 + 0.421742i \(0.861419\pi\)
\(164\) 6.09801 5.98089i 0.476175 0.467029i
\(165\) 0 0
\(166\) −0.0932885 + 4.80993i −0.00724059 + 0.373323i
\(167\) −11.2371 + 21.3330i −0.869550 + 1.65080i −0.116154 + 0.993231i \(0.537057\pi\)
−0.753395 + 0.657568i \(0.771585\pi\)
\(168\) 0 0
\(169\) 1.90812 + 4.94216i 0.146779 + 0.380166i
\(170\) 7.04675 1.67011i 0.540461 0.128092i
\(171\) 0 0
\(172\) 1.00567 + 3.35918i 0.0766819 + 0.256135i
\(173\) 18.9667 + 7.74875i 1.44201 + 0.589126i 0.958214 0.286054i \(-0.0923436\pi\)
0.483797 + 0.875180i \(0.339257\pi\)
\(174\) 0 0
\(175\) −5.29046 0.411207i −0.399921 0.0310843i
\(176\) −1.57671 + 1.12697i −0.118849 + 0.0849483i
\(177\) 0 0
\(178\) 8.01297 12.7134i 0.600597 0.952912i
\(179\) 0.974992 16.7400i 0.0728743 1.25120i −0.741536 0.670914i \(-0.765902\pi\)
0.814410 0.580290i \(-0.197061\pi\)
\(180\) 0 0
\(181\) 8.99829 5.91827i 0.668837 0.439901i −0.169150 0.985590i \(-0.554102\pi\)
0.837988 + 0.545689i \(0.183732\pi\)
\(182\) −6.78450 + 4.09447i −0.502901 + 0.303502i
\(183\) 0 0
\(184\) 15.0054 6.13040i 1.10622 0.451939i
\(185\) −5.01377 6.21610i −0.368620 0.457017i
\(186\) 0 0
\(187\) 4.17806 + 6.09176i 0.305530 + 0.445474i
\(188\) −1.68476 9.55477i −0.122874 0.696853i
\(189\) 0 0
\(190\) 0.128146 0.726752i 0.00929668 0.0527241i
\(191\) −21.6491 + 9.84070i −1.56647 + 0.712048i −0.994153 0.107984i \(-0.965561\pi\)
−0.572318 + 0.820032i \(0.693956\pi\)
\(192\) 0 0
\(193\) −3.79909 0.746116i −0.273464 0.0537066i 0.0541000 0.998536i \(-0.482771\pi\)
−0.327564 + 0.944829i \(0.606228\pi\)
\(194\) 12.7742 + 4.09588i 0.917133 + 0.294067i
\(195\) 0 0
\(196\) −12.4842 14.3053i −0.891728 1.02181i
\(197\) 0.668486 0.897932i 0.0476276 0.0639750i −0.777671 0.628671i \(-0.783599\pi\)
0.825299 + 0.564696i \(0.191007\pi\)
\(198\) 0 0
\(199\) −8.85993 + 20.5396i −0.628064 + 1.45602i 0.245544 + 0.969385i \(0.421033\pi\)
−0.873608 + 0.486630i \(0.838226\pi\)
\(200\) −10.8724 9.86619i −0.768796 0.697645i
\(201\) 0 0
\(202\) 6.11857 23.7537i 0.430501 1.67131i
\(203\) 5.58718 + 5.47987i 0.392143 + 0.384611i
\(204\) 0 0
\(205\) 0.426355 1.96827i 0.0297779 0.137470i
\(206\) 16.3140 + 21.9136i 1.13665 + 1.52679i
\(207\) 0 0
\(208\) −2.75842 0.322413i −0.191262 0.0223553i
\(209\) 0.738620 0.145060i 0.0510914 0.0100340i
\(210\) 0 0
\(211\) 2.07197 + 9.56528i 0.142640 + 0.658501i 0.991524 + 0.129922i \(0.0414726\pi\)
−0.848884 + 0.528579i \(0.822725\pi\)
\(212\) −18.9117 + 21.6705i −1.29886 + 1.48833i
\(213\) 0 0
\(214\) −10.5598 7.54769i −0.721853 0.515950i
\(215\) 0.633339 + 0.531434i 0.0431934 + 0.0362435i
\(216\) 0 0
\(217\) −5.11492 + 4.29193i −0.347223 + 0.291355i
\(218\) −22.6122 + 1.75756i −1.53149 + 0.119037i
\(219\) 0 0
\(220\) −1.95723 + 5.06934i −0.131956 + 0.341775i
\(221\) −1.43251 + 10.4878i −0.0963611 + 0.705488i
\(222\) 0 0
\(223\) 13.5939 + 7.50082i 0.910318 + 0.502292i 0.867862 0.496806i \(-0.165494\pi\)
0.0424564 + 0.999098i \(0.486482\pi\)
\(224\) −0.315202 5.41181i −0.0210603 0.361591i
\(225\) 0 0
\(226\) 39.9375 20.0574i 2.65660 1.33420i
\(227\) 5.64784 + 10.7222i 0.374861 + 0.711655i 0.997486 0.0708648i \(-0.0225759\pi\)
−0.622625 + 0.782520i \(0.713934\pi\)
\(228\) 0 0
\(229\) −6.33592 2.88003i −0.418689 0.190318i 0.193376 0.981125i \(-0.438056\pi\)
−0.612065 + 0.790807i \(0.709661\pi\)
\(230\) 5.14407 7.50024i 0.339190 0.494551i
\(231\) 0 0
\(232\) 2.93028 + 21.4535i 0.192383 + 1.40849i
\(233\) −8.53758 2.02344i −0.559315 0.132560i −0.0587716 0.998271i \(-0.518718\pi\)
−0.500544 + 0.865711i \(0.666867\pi\)
\(234\) 0 0
\(235\) −1.56984 1.66393i −0.102405 0.108543i
\(236\) 2.13167 + 0.333388i 0.138760 + 0.0217017i
\(237\) 0 0
\(238\) 10.8821 0.422276i 0.705383 0.0273721i
\(239\) 7.81731 + 4.71777i 0.505660 + 0.305167i 0.746486 0.665401i \(-0.231739\pi\)
−0.240826 + 0.970568i \(0.577418\pi\)
\(240\) 0 0
\(241\) 13.9241 + 3.87605i 0.896933 + 0.249678i 0.685810 0.727781i \(-0.259448\pi\)
0.211124 + 0.977459i \(0.432288\pi\)
\(242\) 16.9225 1.08782
\(243\) 0 0
\(244\) 40.3537 2.58338
\(245\) −4.31274 1.20053i −0.275531 0.0766993i
\(246\) 0 0
\(247\) 0.923501 + 0.557335i 0.0587609 + 0.0354624i
\(248\) −18.4600 + 0.716333i −1.17221 + 0.0454872i
\(249\) 0 0
\(250\) −17.5183 2.73982i −1.10796 0.173281i
\(251\) 14.0757 + 14.9194i 0.888451 + 0.941703i 0.998636 0.0522083i \(-0.0166260\pi\)
−0.110186 + 0.993911i \(0.535145\pi\)
\(252\) 0 0
\(253\) 9.02671 + 2.13937i 0.567504 + 0.134501i
\(254\) −5.25556 38.4775i −0.329763 2.41429i
\(255\) 0 0
\(256\) 12.3883 18.0625i 0.774267 1.12891i
\(257\) −20.8559 9.48017i −1.30096 0.591357i −0.360972 0.932577i \(-0.617555\pi\)
−0.939983 + 0.341220i \(0.889160\pi\)
\(258\) 0 0
\(259\) −5.59688 10.6254i −0.347773 0.660231i
\(260\) −6.95862 + 3.49475i −0.431555 + 0.216735i
\(261\) 0 0
\(262\) 1.20663 + 20.7171i 0.0745460 + 1.27991i
\(263\) 21.7733 + 12.0140i 1.34260 + 0.740816i 0.981455 0.191693i \(-0.0613979\pi\)
0.361146 + 0.932509i \(0.382386\pi\)
\(264\) 0 0
\(265\) −0.917761 + 6.71920i −0.0563776 + 0.412757i
\(266\) 0.399702 1.03525i 0.0245073 0.0634755i
\(267\) 0 0
\(268\) −33.7397 + 2.62246i −2.06098 + 0.160192i
\(269\) 17.5142 14.6961i 1.06786 0.896039i 0.0730012 0.997332i \(-0.476742\pi\)
0.994857 + 0.101293i \(0.0322979\pi\)
\(270\) 0 0
\(271\) 2.94493 + 2.47109i 0.178892 + 0.150108i 0.727837 0.685750i \(-0.240526\pi\)
−0.548945 + 0.835859i \(0.684970\pi\)
\(272\) 3.10508 + 2.21938i 0.188273 + 0.134570i
\(273\) 0 0
\(274\) −22.6792 + 25.9875i −1.37010 + 1.56996i
\(275\) −1.77882 8.21196i −0.107267 0.495200i
\(276\) 0 0
\(277\) 13.3314 2.61819i 0.801004 0.157312i 0.224572 0.974457i \(-0.427901\pi\)
0.576432 + 0.817145i \(0.304445\pi\)
\(278\) 52.9257 + 6.18613i 3.17427 + 0.371019i
\(279\) 0 0
\(280\) 2.01038 + 2.70041i 0.120143 + 0.161380i
\(281\) −1.97291 + 9.10797i −0.117694 + 0.543336i 0.879970 + 0.475029i \(0.157562\pi\)
−0.997664 + 0.0683073i \(0.978240\pi\)
\(282\) 0 0
\(283\) 20.0443 + 19.6593i 1.19151 + 1.16862i 0.981610 + 0.190898i \(0.0611401\pi\)
0.209897 + 0.977723i \(0.432687\pi\)
\(284\) 7.79924 30.2785i 0.462799 1.79670i
\(285\) 0 0
\(286\) −9.29209 8.43212i −0.549453 0.498602i
\(287\) 1.19953 2.78081i 0.0708058 0.164146i
\(288\) 0 0
\(289\) −1.46469 + 1.96741i −0.0861580 + 0.115730i
\(290\) 7.98815 + 9.15340i 0.469080 + 0.537506i
\(291\) 0 0
\(292\) −45.6534 14.6382i −2.67166 0.856634i
\(293\) 17.0419 + 3.34693i 0.995601 + 0.195530i 0.663873 0.747845i \(-0.268912\pi\)
0.331728 + 0.943375i \(0.392368\pi\)
\(294\) 0 0
\(295\) 0.463119 0.210513i 0.0269638 0.0122566i
\(296\) 5.76984 32.7224i 0.335365 1.90195i
\(297\) 0 0
\(298\) 3.55544 + 20.1639i 0.205961 + 1.16806i
\(299\) 7.51884 + 10.9627i 0.434826 + 0.633992i
\(300\) 0 0
\(301\) 0.780542 + 0.967721i 0.0449897 + 0.0557785i
\(302\) −18.1316 + 7.40756i −1.04335 + 0.426257i
\(303\) 0 0
\(304\) 0.332985 0.200958i 0.0190980 0.0115257i
\(305\) 7.94938 5.22839i 0.455180 0.299377i
\(306\) 0 0
\(307\) 0.0490107 0.841481i 0.00279719 0.0480258i −0.996621 0.0821409i \(-0.973824\pi\)
0.999418 + 0.0341151i \(0.0108613\pi\)
\(308\) −4.35715 + 6.91309i −0.248272 + 0.393910i
\(309\) 0 0
\(310\) −8.43275 + 6.02737i −0.478948 + 0.342331i
\(311\) 1.14875 + 0.0892880i 0.0651397 + 0.00506306i 0.110021 0.993929i \(-0.464908\pi\)
−0.0448812 + 0.998992i \(0.514291\pi\)
\(312\) 0 0
\(313\) −9.93266 4.05794i −0.561427 0.229368i 0.0796789 0.996821i \(-0.474610\pi\)
−0.641106 + 0.767452i \(0.721524\pi\)
\(314\) −4.13907 13.8255i −0.233581 0.780216i
\(315\) 0 0
\(316\) −24.5041 + 5.80757i −1.37846 + 0.326701i
\(317\) −9.98259 25.8556i −0.560678 1.45219i −0.866049 0.499960i \(-0.833348\pi\)
0.305371 0.952234i \(-0.401220\pi\)
\(318\) 0 0
\(319\) −5.77520 + 10.9639i −0.323349 + 0.613863i
\(320\) 0.194752 10.0414i 0.0108870 0.561330i
\(321\) 0 0
\(322\) 9.76410 9.57657i 0.544132 0.533681i
\(323\) −0.741190 1.28378i −0.0412409 0.0714314i
\(324\) 0 0
\(325\) 6.02024 10.4274i 0.333943 0.578406i
\(326\) −1.31022 5.08660i −0.0725666 0.281721i
\(327\) 0 0
\(328\) 7.33645 4.04808i 0.405088 0.223518i
\(329\) −1.83424 2.91022i −0.101125 0.160446i
\(330\) 0 0
\(331\) −16.6070 + 20.5895i −0.912805 + 1.13170i 0.0780738 + 0.996948i \(0.475123\pi\)
−0.990879 + 0.134754i \(0.956976\pi\)
\(332\) −2.03889 + 6.81036i −0.111899 + 0.373767i
\(333\) 0 0
\(334\) −38.6266 + 40.9418i −2.11355 + 2.24024i
\(335\) −6.30669 + 4.88805i −0.344571 + 0.267063i
\(336\) 0 0
\(337\) −5.74555 12.0158i −0.312980 0.654542i 0.684224 0.729272i \(-0.260141\pi\)
−0.997204 + 0.0747299i \(0.976191\pi\)
\(338\) 1.19728 + 12.3092i 0.0651236 + 0.669530i
\(339\) 0 0
\(340\) 10.6935 + 0.414955i 0.579934 + 0.0225041i
\(341\) −8.83340 5.80982i −0.478356 0.314619i
\(342\) 0 0
\(343\) −13.6670 6.86384i −0.737951 0.370613i
\(344\) 0.0667035 + 3.43921i 0.00359641 + 0.185430i
\(345\) 0 0
\(346\) 37.8039 + 29.3002i 2.03235 + 1.57519i
\(347\) −7.27949 + 1.13849i −0.390784 + 0.0611175i −0.346859 0.937917i \(-0.612752\pi\)
−0.0439250 + 0.999035i \(0.513986\pi\)
\(348\) 0 0
\(349\) −6.86066 + 14.3479i −0.367243 + 0.768023i −0.999980 0.00634366i \(-0.997981\pi\)
0.632737 + 0.774367i \(0.281931\pi\)
\(350\) −11.6405 4.23678i −0.622209 0.226466i
\(351\) 0 0
\(352\) 8.06615 2.93584i 0.429927 0.156481i
\(353\) −1.95223 + 20.0707i −0.103907 + 1.06825i 0.787890 + 0.615816i \(0.211174\pi\)
−0.891796 + 0.452437i \(0.850555\pi\)
\(354\) 0 0
\(355\) −2.38661 6.97513i −0.126668 0.370202i
\(356\) 16.4452 14.9232i 0.871594 0.790930i
\(357\) 0 0
\(358\) 12.6725 37.0367i 0.669761 1.95745i
\(359\) 4.03608 + 9.35668i 0.213016 + 0.493827i 0.990903 0.134577i \(-0.0429677\pi\)
−0.777887 + 0.628404i \(0.783708\pi\)
\(360\) 0 0
\(361\) 18.7215 2.18823i 0.985342 0.115170i
\(362\) 23.9416 7.67657i 1.25834 0.403471i
\(363\) 0 0
\(364\) −11.2809 + 3.14024i −0.591277 + 0.164593i
\(365\) −10.8899 + 3.03142i −0.570006 + 0.158672i
\(366\) 0 0
\(367\) 0.836497 0.268212i 0.0436648 0.0140006i −0.283413 0.958998i \(-0.591467\pi\)
0.327078 + 0.944997i \(0.393936\pi\)
\(368\) 4.76078 0.556455i 0.248173 0.0290072i
\(369\) 0 0
\(370\) −7.38416 17.1184i −0.383884 0.889943i
\(371\) −3.30145 + 9.64884i −0.171403 + 0.500943i
\(372\) 0 0
\(373\) 7.26335 6.59114i 0.376082 0.341276i −0.461941 0.886910i \(-0.652847\pi\)
0.838024 + 0.545634i \(0.183711\pi\)
\(374\) 5.58254 + 16.3156i 0.288666 + 0.843659i
\(375\) 0 0
\(376\) 0.921427 9.47310i 0.0475190 0.488538i
\(377\) −16.6865 + 6.07340i −0.859400 + 0.312796i
\(378\) 0 0
\(379\) −26.4212 9.61652i −1.35716 0.493967i −0.441988 0.897021i \(-0.645727\pi\)
−0.915176 + 0.403054i \(0.867949\pi\)
\(380\) 0.470424 0.983809i 0.0241323 0.0504683i
\(381\) 0 0
\(382\) −54.8479 + 8.57806i −2.80626 + 0.438892i
\(383\) −10.5854 8.20428i −0.540887 0.419219i 0.305181 0.952294i \(-0.401283\pi\)
−0.846068 + 0.533076i \(0.821036\pi\)
\(384\) 0 0
\(385\) 0.0373616 + 1.92636i 0.00190412 + 0.0981761i
\(386\) −8.07681 4.05632i −0.411099 0.206461i
\(387\) 0 0
\(388\) 16.5620 + 10.8930i 0.840808 + 0.553008i
\(389\) −24.9296 0.967381i −1.26398 0.0490481i −0.601955 0.798530i \(-0.705611\pi\)
−0.662024 + 0.749482i \(0.730303\pi\)
\(390\) 0 0
\(391\) −1.76865 18.1833i −0.0894444 0.919569i
\(392\) −8.03498 16.8037i −0.405828 0.848717i
\(393\) 0 0
\(394\) 2.06552 1.60090i 0.104059 0.0806520i
\(395\) −4.07467 + 4.31889i −0.205019 + 0.217307i
\(396\) 0 0
\(397\) −5.45169 + 18.2099i −0.273613 + 0.913930i 0.705172 + 0.709037i \(0.250870\pi\)
−0.978784 + 0.204893i \(0.934315\pi\)
\(398\) −32.7839 + 40.6457i −1.64331 + 2.03738i
\(399\) 0 0
\(400\) −2.31487 3.67278i −0.115743 0.183639i
\(401\) 29.9203 16.5093i 1.49415 0.824436i 0.495134 0.868817i \(-0.335119\pi\)
0.999015 + 0.0443805i \(0.0141314\pi\)
\(402\) 0 0
\(403\) −3.77917 14.6716i −0.188254 0.730846i
\(404\) 18.1234 31.3907i 0.901675 1.56175i
\(405\) 0 0
\(406\) 9.13463 + 15.8216i 0.453344 + 0.785215i
\(407\) 13.5762 13.3154i 0.672947 0.660022i
\(408\) 0 0
\(409\) 0.446182 23.0051i 0.0220623 1.13753i −0.811241 0.584711i \(-0.801208\pi\)
0.833304 0.552815i \(-0.186447\pi\)
\(410\) 2.19105 4.15960i 0.108208 0.205428i
\(411\) 0 0
\(412\) 14.5404 + 37.6607i 0.716356 + 1.85541i
\(413\) 0.744381 0.176421i 0.0366286 0.00868113i
\(414\) 0 0
\(415\) 0.480732 + 1.60576i 0.0235982 + 0.0788235i
\(416\) 11.3868 + 4.65202i 0.558284 + 0.228084i
\(417\) 0 0
\(418\) 1.75192 + 0.136170i 0.0856892 + 0.00666029i
\(419\) −13.2396 + 9.46309i −0.646796 + 0.462302i −0.856973 0.515361i \(-0.827658\pi\)
0.210177 + 0.977663i \(0.432596\pi\)
\(420\) 0 0
\(421\) 7.47157 11.8545i 0.364142 0.577751i −0.613067 0.790031i \(-0.710064\pi\)
0.977209 + 0.212280i \(0.0680890\pi\)
\(422\) −1.32846 + 22.8088i −0.0646686 + 1.11032i
\(423\) 0 0
\(424\) −23.5738 + 15.5047i −1.14485 + 0.752977i
\(425\) −14.1672 + 8.54993i −0.687209 + 0.414733i
\(426\) 0 0
\(427\) 13.2452 5.41127i 0.640981 0.261870i
\(428\) −12.0417 14.9294i −0.582059 0.721640i
\(429\) 0 0
\(430\) 1.09164 + 1.59165i 0.0526437 + 0.0767563i
\(431\) 0.922395 + 5.23116i 0.0444302 + 0.251976i 0.998931 0.0462332i \(-0.0147217\pi\)
−0.954500 + 0.298209i \(0.903611\pi\)
\(432\) 0 0
\(433\) 2.81395 15.9587i 0.135230 0.766926i −0.839470 0.543406i \(-0.817134\pi\)
0.974700 0.223519i \(-0.0717546\pi\)
\(434\) −14.1900 + 6.45015i −0.681143 + 0.309617i
\(435\) 0 0
\(436\) −32.8868 6.45876i −1.57499 0.309318i
\(437\) −1.77274 0.568408i −0.0848019 0.0271906i
\(438\) 0 0
\(439\) 11.4686 + 13.1415i 0.547364 + 0.627210i 0.958750 0.284252i \(-0.0917451\pi\)
−0.411385 + 0.911462i \(0.634955\pi\)
\(440\) −3.18333 + 4.27595i −0.151759 + 0.203848i
\(441\) 0 0
\(442\) −9.78737 + 22.6897i −0.465538 + 1.07924i
\(443\) 3.32472 + 3.01702i 0.157962 + 0.143343i 0.747156 0.664649i \(-0.231419\pi\)
−0.589194 + 0.807992i \(0.700555\pi\)
\(444\) 0 0
\(445\) 1.30607 5.07047i 0.0619136 0.240363i
\(446\) 25.8761 + 25.3791i 1.22527 + 1.20174i
\(447\) 0 0
\(448\) 3.19734 14.7605i 0.151060 0.697370i
\(449\) −8.69914 11.6850i −0.410538 0.551448i 0.547976 0.836494i \(-0.315399\pi\)
−0.958514 + 0.285046i \(0.907991\pi\)
\(450\) 0 0
\(451\) 4.76303 + 0.556718i 0.224282 + 0.0262148i
\(452\) 64.8027 12.7268i 3.04806 0.598620i
\(453\) 0 0
\(454\) 5.98920 + 27.6492i 0.281087 + 1.29764i
\(455\) −1.81538 + 2.08020i −0.0851064 + 0.0975211i
\(456\) 0 0
\(457\) 28.1791 + 20.1412i 1.31816 + 0.942167i 0.999983 0.00586262i \(-0.00186614\pi\)
0.318181 + 0.948030i \(0.396928\pi\)
\(458\) −12.4461 10.4435i −0.581567 0.487992i
\(459\) 0 0
\(460\) 10.2952 8.63871i 0.480017 0.402782i
\(461\) 14.3824 1.11789i 0.669857 0.0520654i 0.261940 0.965084i \(-0.415638\pi\)
0.407917 + 0.913019i \(0.366255\pi\)
\(462\) 0 0
\(463\) 1.22936 3.18413i 0.0571333 0.147979i −0.901378 0.433033i \(-0.857444\pi\)
0.958512 + 0.285054i \(0.0920114\pi\)
\(464\) −0.866496 + 6.34387i −0.0402261 + 0.294507i
\(465\) 0 0
\(466\) −17.9337 9.89541i −0.830763 0.458396i
\(467\) −1.36945 23.5126i −0.0633707 1.08803i −0.868743 0.495263i \(-0.835072\pi\)
0.805372 0.592770i \(-0.201965\pi\)
\(468\) 0 0
\(469\) −10.7226 + 5.38512i −0.495126 + 0.248662i
\(470\) −2.48879 4.72485i −0.114799 0.217941i
\(471\) 0 0
\(472\) 1.92686 + 0.875867i 0.0886911 + 0.0403150i
\(473\) −1.11349 + 1.62350i −0.0511981 + 0.0746487i
\(474\) 0 0
\(475\) 0.228193 + 1.67067i 0.0104702 + 0.0766555i
\(476\) 15.6589 + 3.71124i 0.717726 + 0.170104i
\(477\) 0 0
\(478\) 14.6271 + 15.5039i 0.669030 + 0.709130i
\(479\) 36.6453 + 5.73122i 1.67437 + 0.261866i 0.919236 0.393708i \(-0.128808\pi\)
0.755131 + 0.655574i \(0.227573\pi\)
\(480\) 0 0
\(481\) 27.2293 1.05662i 1.24155 0.0481777i
\(482\) 28.8880 + 17.4340i 1.31581 + 0.794096i
\(483\) 0 0
\(484\) 24.0906 + 6.70609i 1.09503 + 0.304822i
\(485\) 4.67393 0.212232
\(486\) 0 0
\(487\) 2.68562 0.121697 0.0608486 0.998147i \(-0.480619\pi\)
0.0608486 + 0.998147i \(0.480619\pi\)
\(488\) 38.1369 + 10.6161i 1.72638 + 0.480570i
\(489\) 0 0
\(490\) −8.94750 5.39985i −0.404207 0.243940i
\(491\) −17.8796 + 0.693811i −0.806896 + 0.0313112i −0.438922 0.898525i \(-0.644640\pi\)
−0.367974 + 0.929836i \(0.619948\pi\)
\(492\) 0 0
\(493\) 24.1109 + 3.77088i 1.08590 + 0.169832i
\(494\) 1.72798 + 1.83155i 0.0777456 + 0.0824055i
\(495\) 0 0
\(496\) −5.31556 1.25981i −0.238676 0.0565671i
\(497\) −1.50029 10.9841i −0.0672974 0.492704i
\(498\) 0 0
\(499\) −14.7926 + 21.5682i −0.662209 + 0.965524i 0.337498 + 0.941326i \(0.390419\pi\)
−0.999707 + 0.0241979i \(0.992297\pi\)
\(500\) −23.8530 10.8425i −1.06674 0.484893i
\(501\) 0 0
\(502\) 22.3153 + 42.3646i 0.995981 + 1.89082i
\(503\) −27.0288 + 13.5744i −1.20515 + 0.605250i −0.933996 0.357285i \(-0.883703\pi\)
−0.271157 + 0.962535i \(0.587406\pi\)
\(504\) 0 0
\(505\) −0.496925 8.53188i −0.0221129 0.379664i
\(506\) 18.9612 + 10.4623i 0.842927 + 0.465107i
\(507\) 0 0
\(508\) 7.76618 56.8585i 0.344569 2.52269i
\(509\) 0.703671 1.82255i 0.0311897 0.0807833i −0.916414 0.400232i \(-0.868930\pi\)
0.947604 + 0.319448i \(0.103498\pi\)
\(510\) 0 0
\(511\) −16.9476 + 1.31727i −0.749719 + 0.0582728i
\(512\) 8.58579 7.20433i 0.379442 0.318389i
\(513\) 0 0
\(514\) −40.9687 34.3768i −1.80705 1.51630i
\(515\) 7.74382 + 5.53495i 0.341234 + 0.243899i
\(516\) 0 0
\(517\) 3.58159 4.10405i 0.157518 0.180496i
\(518\) −5.93515 27.3997i −0.260776 1.20387i
\(519\) 0 0
\(520\) −7.49573 + 1.47211i −0.328710 + 0.0645564i
\(521\) 19.2337 + 2.24809i 0.842642 + 0.0984907i 0.526452 0.850205i \(-0.323522\pi\)
0.316190 + 0.948696i \(0.397596\pi\)
\(522\) 0 0
\(523\) 9.62812 + 12.9328i 0.421008 + 0.565512i 0.961138 0.276070i \(-0.0890321\pi\)
−0.540129 + 0.841582i \(0.681625\pi\)
\(524\) −6.49205 + 29.9706i −0.283606 + 1.30927i
\(525\) 0 0
\(526\) 41.4456 + 40.6496i 1.80712 + 1.77241i
\(527\) −5.19370 + 20.1632i −0.226241 + 0.878322i
\(528\) 0 0
\(529\) 0.0420672 + 0.0381740i 0.00182901 + 0.00165974i
\(530\) −6.27043 + 14.5365i −0.272370 + 0.631425i
\(531\) 0 0
\(532\) 0.979260 1.31537i 0.0424563 0.0570287i
\(533\) 4.51835 + 5.17745i 0.195711 + 0.224260i
\(534\) 0 0
\(535\) −4.30644 1.38081i −0.186184 0.0596974i
\(536\) −32.5761 6.39774i −1.40707 0.276340i
\(537\) 0 0
\(538\) 48.5885 22.0862i 2.09480 0.952203i
\(539\) 1.85105 10.4978i 0.0797303 0.452173i
\(540\) 0 0
\(541\) −3.83719 21.7618i −0.164974 0.935612i −0.949092 0.315000i \(-0.897995\pi\)
0.784118 0.620612i \(-0.213116\pi\)
\(542\) 5.07597 + 7.40095i 0.218032 + 0.317898i
\(543\) 0 0
\(544\) −10.6128 13.1578i −0.455021 0.564138i
\(545\) −7.31527 + 2.98862i −0.313352 + 0.128018i
\(546\) 0 0
\(547\) 18.0787 10.9106i 0.772990 0.466502i −0.0745603 0.997217i \(-0.523755\pi\)
0.847551 + 0.530714i \(0.178076\pi\)
\(548\) −42.5841 + 28.0080i −1.81910 + 1.19644i
\(549\) 0 0
\(550\) 1.14051 19.5818i 0.0486315 0.834970i
\(551\) 1.32597 2.10380i 0.0564882 0.0896247i
\(552\) 0 0
\(553\) −7.26415 + 5.19210i −0.308903 + 0.220791i
\(554\) 31.6205 + 2.45774i 1.34342 + 0.104419i
\(555\) 0 0
\(556\) 72.8927 + 29.7799i 3.09134 + 1.26295i
\(557\) 3.03735 + 10.1455i 0.128697 + 0.429877i 0.997914 0.0645527i \(-0.0205621\pi\)
−0.869218 + 0.494430i \(0.835377\pi\)
\(558\) 0 0
\(559\) −2.74500 + 0.650577i −0.116101 + 0.0275165i
\(560\) 0.358561 + 0.928696i 0.0151520 + 0.0392446i
\(561\) 0 0
\(562\) −10.1388 + 19.2481i −0.427682 + 0.811933i
\(563\) 0.0673809 3.47414i 0.00283977 0.146418i −0.995708 0.0925481i \(-0.970499\pi\)
0.998548 0.0538695i \(-0.0171555\pi\)
\(564\) 0 0
\(565\) 11.1167 10.9032i 0.467683 0.458700i
\(566\) 32.7709 + 56.7608i 1.37746 + 2.38583i
\(567\) 0 0
\(568\) 15.3363 26.5633i 0.643499 1.11457i
\(569\) −9.72314 37.7476i −0.407615 1.58246i −0.762139 0.647413i \(-0.775851\pi\)
0.354524 0.935047i \(-0.384643\pi\)
\(570\) 0 0
\(571\) 9.78465 5.39894i 0.409475 0.225939i −0.264981 0.964254i \(-0.585366\pi\)
0.674456 + 0.738315i \(0.264378\pi\)
\(572\) −9.88656 15.6861i −0.413378 0.655869i
\(573\) 0 0
\(574\) 4.43854 5.50292i 0.185261 0.229688i
\(575\) −5.95999 + 19.9077i −0.248549 + 0.830210i
\(576\) 0 0
\(577\) −17.8279 + 18.8965i −0.742185 + 0.786670i −0.982942 0.183915i \(-0.941123\pi\)
0.240757 + 0.970585i \(0.422604\pi\)
\(578\) −4.52565 + 3.50765i −0.188242 + 0.145899i
\(579\) 0 0
\(580\) 7.74446 + 16.1962i 0.321571 + 0.672509i
\(581\) 0.244021 + 2.50876i 0.0101237 + 0.104081i
\(582\) 0 0
\(583\) −16.1359 0.626145i −0.668279 0.0259323i
\(584\) −39.2944 25.8444i −1.62602 1.06945i
\(585\) 0 0
\(586\) 36.2310 + 18.1959i 1.49669 + 0.751664i
\(587\) −0.627955 32.3772i −0.0259185 1.33635i −0.756710 0.653750i \(-0.773195\pi\)
0.730792 0.682600i \(-0.239151\pi\)
\(588\) 0 0
\(589\) 1.67699 + 1.29977i 0.0690992 + 0.0535559i
\(590\) 1.17331 0.183503i 0.0483045 0.00755469i
\(591\) 0 0
\(592\) 4.23854 8.86416i 0.174203 0.364315i
\(593\) 6.96329 + 2.53443i 0.285948 + 0.104077i 0.481012 0.876714i \(-0.340269\pi\)
−0.195064 + 0.980790i \(0.562492\pi\)
\(594\) 0 0
\(595\) 3.56553 1.29775i 0.146173 0.0532025i
\(596\) −2.92911 + 30.1139i −0.119981 + 1.23351i
\(597\) 0 0
\(598\) 10.0463 + 29.3616i 0.410826 + 1.20068i
\(599\) −2.31541 + 2.10112i −0.0946051 + 0.0858496i −0.717938 0.696107i \(-0.754914\pi\)
0.623333 + 0.781957i \(0.285778\pi\)
\(600\) 0 0
\(601\) −2.05783 + 6.01424i −0.0839407 + 0.245326i −0.980134 0.198339i \(-0.936445\pi\)
0.896193 + 0.443665i \(0.146322\pi\)
\(602\) 1.14956 + 2.66499i 0.0468527 + 0.108617i
\(603\) 0 0
\(604\) −28.7472 + 3.36007i −1.16971 + 0.136719i
\(605\) 5.61454 1.80023i 0.228263 0.0731897i
\(606\) 0 0
\(607\) −39.9301 + 11.1153i −1.62071 + 0.451156i −0.955378 0.295388i \(-0.904551\pi\)
−0.665336 + 0.746544i \(0.731712\pi\)
\(608\) −1.65949 + 0.461950i −0.0673011 + 0.0187345i
\(609\) 0 0
\(610\) 21.1508 6.78173i 0.856371 0.274584i
\(611\) 7.75281 0.906174i 0.313645 0.0366599i
\(612\) 0 0
\(613\) −14.1462 32.7946i −0.571361 1.32456i −0.921687 0.387935i \(-0.873188\pi\)
0.350326 0.936628i \(-0.386071\pi\)
\(614\) 0.637017 1.86175i 0.0257079 0.0751343i
\(615\) 0 0
\(616\) −5.93646 + 5.38705i −0.239187 + 0.217050i
\(617\) −3.78004 11.0476i −0.152178 0.444758i 0.843554 0.537044i \(-0.180459\pi\)
−0.995733 + 0.0922858i \(0.970583\pi\)
\(618\) 0 0
\(619\) 0.0269366 0.276933i 0.00108268 0.0111309i −0.994746 0.102375i \(-0.967356\pi\)
0.995829 + 0.0912439i \(0.0290843\pi\)
\(620\) −14.3932 + 5.23871i −0.578046 + 0.210392i
\(621\) 0 0
\(622\) 2.52757 + 0.919960i 0.101346 + 0.0368870i
\(623\) 3.39663 7.10346i 0.136083 0.284594i
\(624\) 0 0
\(625\) 15.3280 2.39726i 0.613122 0.0958905i
\(626\) −19.7975 15.3442i −0.791267 0.613278i
\(627\) 0 0
\(628\) −0.413538 21.3219i −0.0165020 0.850837i
\(629\) −33.4659 16.8072i −1.33437 0.670147i
\(630\) 0 0
\(631\) −16.1228 10.6042i −0.641840 0.422145i 0.186434 0.982467i \(-0.440307\pi\)
−0.828274 + 0.560323i \(0.810677\pi\)
\(632\) −24.6858 0.957921i −0.981947 0.0381040i
\(633\) 0 0
\(634\) −6.26375 64.3969i −0.248765 2.55753i
\(635\) −5.83694 12.2069i −0.231632 0.484417i
\(636\) 0 0
\(637\) 12.0734 9.35761i 0.478366 0.370762i
\(638\) −19.8519 + 21.0417i −0.785942 + 0.833050i
\(639\) 0 0
\(640\) 4.65643 15.5536i 0.184062 0.614809i
\(641\) −3.84742 + 4.77005i −0.151964 + 0.188406i −0.848625 0.528994i \(-0.822569\pi\)
0.696661 + 0.717400i \(0.254668\pi\)
\(642\) 0 0
\(643\) −15.1504 24.0377i −0.597473 0.947955i −0.999478 0.0323175i \(-0.989711\pi\)
0.402005 0.915637i \(-0.368313\pi\)
\(644\) 17.6950 9.76370i 0.697281 0.384744i
\(645\) 0 0
\(646\) −0.863199 3.35115i −0.0339621 0.131849i
\(647\) 4.69966 8.14006i 0.184763 0.320019i −0.758734 0.651401i \(-0.774182\pi\)
0.943497 + 0.331382i \(0.107515\pi\)
\(648\) 0 0
\(649\) 0.605669 + 1.04905i 0.0237746 + 0.0411788i
\(650\) 20.0670 19.6816i 0.787093 0.771976i
\(651\) 0 0
\(652\) 0.150513 7.76041i 0.00589454 0.303921i
\(653\) 11.8873 22.5674i 0.465185 0.883131i −0.534104 0.845419i \(-0.679351\pi\)
0.999289 0.0377124i \(-0.0120071\pi\)
\(654\) 0 0
\(655\) 2.60423 + 6.74512i 0.101756 + 0.263554i
\(656\) 2.41096 0.571409i 0.0941323 0.0223098i
\(657\) 0 0
\(658\) −2.30319 7.69320i −0.0897878 0.299912i
\(659\) 16.2922 + 6.65609i 0.634654 + 0.259285i 0.672613 0.739995i \(-0.265172\pi\)
−0.0379589 + 0.999279i \(0.512086\pi\)
\(660\) 0 0
\(661\) −25.6983 1.99743i −0.999547 0.0776909i −0.432720 0.901528i \(-0.642446\pi\)
−0.566826 + 0.823837i \(0.691829\pi\)
\(662\) −50.2379 + 35.9079i −1.95255 + 1.39560i
\(663\) 0 0
\(664\) −3.71853 + 5.89985i −0.144307 + 0.228959i
\(665\) 0.0224817 0.385996i 0.000871802 0.0149683i
\(666\) 0 0
\(667\) 25.6058 16.8412i 0.991460 0.652093i
\(668\) −71.2126 + 42.9770i −2.75530 + 1.66283i
\(669\) 0 0
\(670\) −17.2434 + 7.04471i −0.666171 + 0.272161i
\(671\) 14.2236 + 17.6345i 0.549097 + 0.680774i
\(672\) 0 0
\(673\) −19.0594 27.7893i −0.734686 1.07120i −0.994417 0.105518i \(-0.966350\pi\)
0.259731 0.965681i \(-0.416366\pi\)
\(674\) −5.39907 30.6197i −0.207965 1.17943i
\(675\) 0 0
\(676\) −3.17345 + 17.9975i −0.122056 + 0.692213i
\(677\) −9.41787 + 4.28095i −0.361958 + 0.164530i −0.586530 0.809927i \(-0.699507\pi\)
0.224572 + 0.974457i \(0.427902\pi\)
\(678\) 0 0
\(679\) 6.89681 + 1.35449i 0.264675 + 0.0519805i
\(680\) 9.99684 + 3.20536i 0.383361 + 0.122920i
\(681\) 0 0
\(682\) −16.2286 18.5959i −0.621426 0.712075i
\(683\) 16.9417 22.7566i 0.648255 0.870757i −0.349554 0.936916i \(-0.613667\pi\)
0.997809 + 0.0661589i \(0.0210744\pi\)
\(684\) 0 0
\(685\) −4.75992 + 11.0347i −0.181867 + 0.421615i
\(686\) −26.4393 23.9924i −1.00946 0.916033i
\(687\) 0 0
\(688\) −0.253727 + 0.985027i −0.00967323 + 0.0375538i
\(689\) −16.5202 16.2029i −0.629368 0.617280i
\(690\) 0 0
\(691\) −3.06411 + 14.1455i −0.116564 + 0.538120i 0.881286 + 0.472583i \(0.156678\pi\)
−0.997850 + 0.0655367i \(0.979124\pi\)
\(692\) 42.2058 + 56.6922i 1.60442 + 2.15512i
\(693\) 0 0
\(694\) −17.0838 1.99682i −0.648494 0.0757981i
\(695\) 18.2177 3.57784i 0.691037 0.135715i
\(696\) 0 0
\(697\) −1.99931 9.22983i −0.0757291 0.349605i
\(698\) −24.4114 + 27.9724i −0.923986 + 1.05877i
\(699\) 0 0
\(700\) −14.8922 10.6443i −0.562872 0.402317i
\(701\) 26.7077 + 22.4104i 1.00874 + 0.846431i 0.988171 0.153358i \(-0.0490086\pi\)
0.0205663 + 0.999788i \(0.493453\pi\)
\(702\) 0 0
\(703\) −2.92332 + 2.45296i −0.110255 + 0.0925150i
\(704\) 23.8427 1.85320i 0.898604 0.0698450i
\(705\) 0 0
\(706\) −16.9553 + 43.9155i −0.638123 + 1.65278i
\(707\) 1.73925 12.7336i 0.0654114 0.478896i
\(708\) 0 0
\(709\) −38.1099 21.0282i −1.43125 0.789729i −0.437272 0.899329i \(-0.644055\pi\)
−0.993976 + 0.109601i \(0.965043\pi\)
\(710\) −1.00066 17.1807i −0.0375542 0.644781i
\(711\) 0 0
\(712\) 19.4677 9.77707i 0.729585 0.366411i
\(713\) 12.1863 + 23.1351i 0.456380 + 0.866417i
\(714\) 0 0
\(715\) −3.97993 1.80910i −0.148841 0.0676565i
\(716\) 32.7173 47.7029i 1.22270 1.78274i
\(717\) 0 0
\(718\) 3.21928 + 23.5693i 0.120142 + 0.879598i
\(719\) −0.820677 0.194504i −0.0306061 0.00725377i 0.215284 0.976551i \(-0.430932\pi\)
−0.245890 + 0.969298i \(0.579080\pi\)
\(720\) 0 0
\(721\) 9.82272 + 10.4115i 0.365817 + 0.387744i
\(722\) 43.4733 + 6.79911i 1.61791 + 0.253037i
\(723\) 0 0
\(724\) 37.1249 1.44062i 1.37974 0.0535401i
\(725\) −23.7664 14.3431i −0.882663 0.532690i
\(726\) 0 0
\(727\) −33.6113 9.35634i −1.24657 0.347008i −0.418805 0.908076i \(-0.637551\pi\)
−0.827769 + 0.561069i \(0.810390\pi\)
\(728\) −11.4873 −0.425746
\(729\) 0 0
\(730\) −26.3886 −0.976684
\(731\) 3.73494 + 1.03969i 0.138142 + 0.0384544i
\(732\) 0 0
\(733\) −22.0139 13.2855i −0.813104 0.490711i 0.0481778 0.998839i \(-0.484659\pi\)
−0.861281 + 0.508128i \(0.830338\pi\)
\(734\) 2.04914 0.0795159i 0.0756351 0.00293498i
\(735\) 0 0
\(736\) −20.9744 3.28034i −0.773128 0.120915i
\(737\) −13.0384 13.8199i −0.480274 0.509061i
\(738\) 0 0
\(739\) −14.1298 3.34881i −0.519771 0.123188i −0.0376474 0.999291i \(-0.511986\pi\)
−0.482124 + 0.876103i \(0.660135\pi\)
\(740\) −3.72825 27.2957i −0.137053 1.00341i
\(741\) 0 0
\(742\) −13.4652 + 19.6328i −0.494324 + 0.720743i
\(743\) −2.97450 1.35208i −0.109124 0.0496029i 0.358505 0.933528i \(-0.383287\pi\)
−0.467629 + 0.883925i \(0.654892\pi\)
\(744\) 0 0
\(745\) 3.32466 + 6.31172i 0.121806 + 0.231243i
\(746\) 20.4611 10.2759i 0.749134 0.376229i
\(747\) 0 0
\(748\) 1.48164 + 25.4388i 0.0541742 + 0.930135i
\(749\) −5.95440 3.28550i −0.217569 0.120050i
\(750\) 0 0
\(751\) 2.46802 18.0691i 0.0900592 0.659350i −0.889315 0.457295i \(-0.848818\pi\)
0.979374 0.202055i \(-0.0647620\pi\)
\(752\) 1.01370 2.62556i 0.0369659 0.0957442i
\(753\) 0 0
\(754\) −41.3291 + 3.21235i −1.50512 + 0.116987i
\(755\) −5.22764 + 4.38651i −0.190253 + 0.159642i
\(756\) 0 0
\(757\) −20.5966 17.2826i −0.748597 0.628147i 0.186535 0.982448i \(-0.440274\pi\)
−0.935131 + 0.354301i \(0.884719\pi\)
\(758\) −53.3992 38.1675i −1.93955 1.38631i
\(759\) 0 0
\(760\) 0.703399 0.806005i 0.0255150 0.0292369i
\(761\) −5.95279 27.4811i −0.215788 0.996190i −0.948776 0.315948i \(-0.897677\pi\)
0.732988 0.680242i \(-0.238125\pi\)
\(762\) 0 0
\(763\) −11.6605 + 2.29004i −0.422137 + 0.0829050i
\(764\) −81.4799 9.52363i −2.94784 0.344553i
\(765\) 0 0
\(766\) −18.6696 25.0777i −0.674562 0.906094i
\(767\) −0.367480 + 1.69648i −0.0132689 + 0.0612563i
\(768\) 0 0
\(769\) 22.7067 + 22.2706i 0.818824 + 0.803097i 0.983052 0.183325i \(-0.0586862\pi\)
−0.164228 + 0.986422i \(0.552513\pi\)
\(770\) −1.12194 + 4.35564i −0.0404319 + 0.156966i
\(771\) 0 0
\(772\) −9.89055 8.97520i −0.355969 0.323024i
\(773\) 11.0897 25.7088i 0.398868 0.924681i −0.593889 0.804547i \(-0.702408\pi\)
0.992758 0.120134i \(-0.0383325\pi\)
\(774\) 0 0
\(775\) 14.1430 18.9974i 0.508033 0.682406i
\(776\) 12.7865 + 14.6517i 0.459007 + 0.525964i
\(777\) 0 0
\(778\) −55.4594 17.7823i −1.98831 0.637527i
\(779\) −0.944303 0.185455i −0.0338332 0.00664462i
\(780\) 0 0
\(781\) 15.9807 7.26412i 0.571834 0.259931i
\(782\) 7.40578 42.0003i 0.264830 1.50193i
\(783\) 0 0
\(784\) −0.956414 5.42409i −0.0341576 0.193718i
\(785\) −2.84401 4.14668i −0.101507 0.148001i
\(786\) 0 0