Properties

Label 819.2.et.c.145.5
Level $819$
Weight $2$
Character 819.145
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.5
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.111217 + 0.111217i) q^{2} +1.97526i q^{4} +(2.13060 - 0.570893i) q^{5} +(-0.399954 - 2.61535i) q^{7} +(-0.442117 - 0.442117i) q^{8} +O(q^{10})\) \(q+(-0.111217 + 0.111217i) q^{2} +1.97526i q^{4} +(2.13060 - 0.570893i) q^{5} +(-0.399954 - 2.61535i) q^{7} +(-0.442117 - 0.442117i) q^{8} +(-0.173466 + 0.300452i) q^{10} +(5.42348 - 1.45322i) q^{11} +(-1.34030 + 3.34718i) q^{13} +(0.335353 + 0.246390i) q^{14} -3.85218 q^{16} +3.59112 q^{17} +(1.24688 - 4.65341i) q^{19} +(1.12766 + 4.20850i) q^{20} +(-0.441561 + 0.764807i) q^{22} -4.45466i q^{23} +(-0.116582 + 0.0673085i) q^{25} +(-0.223198 - 0.521328i) q^{26} +(5.16599 - 0.790013i) q^{28} +(-1.02264 - 1.77127i) q^{29} +(0.643610 - 2.40198i) q^{31} +(1.31266 - 1.31266i) q^{32} +(-0.399394 + 0.399394i) q^{34} +(-2.34523 - 5.34393i) q^{35} +(7.22320 + 7.22320i) q^{37} +(0.378865 + 0.656213i) q^{38} +(-1.19438 - 0.689574i) q^{40} +(-1.34422 + 5.01671i) q^{41} +(4.12300 + 2.38042i) q^{43} +(2.87049 + 10.7128i) q^{44} +(0.495434 + 0.495434i) q^{46} +(1.22397 + 4.56791i) q^{47} +(-6.68007 + 2.09204i) q^{49} +(0.00548003 - 0.0204517i) q^{50} +(-6.61155 - 2.64745i) q^{52} +(-0.201475 - 0.348965i) q^{53} +(10.7257 - 6.19246i) q^{55} +(-0.979463 + 1.33312i) q^{56} +(0.310731 + 0.0832601i) q^{58} +(1.93268 - 1.93268i) q^{59} +(1.61092 - 0.930065i) q^{61} +(0.195561 + 0.338722i) q^{62} -7.41238i q^{64} +(-0.944776 + 7.89667i) q^{65} +(1.78441 + 6.65951i) q^{67} +7.09340i q^{68} +(0.855166 + 0.333507i) q^{70} +(3.63562 + 13.5683i) q^{71} +(-4.45744 - 1.19437i) q^{73} -1.60669 q^{74} +(9.19171 + 2.46291i) q^{76} +(-5.96981 - 13.6031i) q^{77} +(-2.45889 + 4.25893i) q^{79} +(-8.20746 + 2.19918i) q^{80} +(-0.408443 - 0.707445i) q^{82} +(-10.3390 - 10.3390i) q^{83} +(7.65124 - 2.05014i) q^{85} +(-0.723291 + 0.193805i) q^{86} +(-3.04031 - 1.75532i) q^{88} +(12.7764 - 12.7764i) q^{89} +(9.29008 + 2.16664i) q^{91} +8.79911 q^{92} +(-0.644155 - 0.371903i) q^{94} -10.6264i q^{95} +(-3.52628 + 0.944864i) q^{97} +(0.510268 - 0.975608i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.111217 + 0.111217i −0.0786424 + 0.0786424i −0.745334 0.666691i \(-0.767710\pi\)
0.666691 + 0.745334i \(0.267710\pi\)
\(3\) 0 0
\(4\) 1.97526i 0.987631i
\(5\) 2.13060 0.570893i 0.952834 0.255311i 0.251270 0.967917i \(-0.419152\pi\)
0.701564 + 0.712606i \(0.252485\pi\)
\(6\) 0 0
\(7\) −0.399954 2.61535i −0.151168 0.988508i
\(8\) −0.442117 0.442117i −0.156312 0.156312i
\(9\) 0 0
\(10\) −0.173466 + 0.300452i −0.0548548 + 0.0950114i
\(11\) 5.42348 1.45322i 1.63524 0.438162i 0.679814 0.733385i \(-0.262061\pi\)
0.955428 + 0.295223i \(0.0953940\pi\)
\(12\) 0 0
\(13\) −1.34030 + 3.34718i −0.371734 + 0.928339i
\(14\) 0.335353 + 0.246390i 0.0896268 + 0.0658504i
\(15\) 0 0
\(16\) −3.85218 −0.963045
\(17\) 3.59112 0.870974 0.435487 0.900195i \(-0.356576\pi\)
0.435487 + 0.900195i \(0.356576\pi\)
\(18\) 0 0
\(19\) 1.24688 4.65341i 0.286053 1.06757i −0.662013 0.749493i \(-0.730298\pi\)
0.948066 0.318073i \(-0.103036\pi\)
\(20\) 1.12766 + 4.20850i 0.252153 + 0.941048i
\(21\) 0 0
\(22\) −0.441561 + 0.764807i −0.0941412 + 0.163057i
\(23\) 4.45466i 0.928860i −0.885610 0.464430i \(-0.846259\pi\)
0.885610 0.464430i \(-0.153741\pi\)
\(24\) 0 0
\(25\) −0.116582 + 0.0673085i −0.0233164 + 0.0134617i
\(26\) −0.223198 0.521328i −0.0437728 0.102241i
\(27\) 0 0
\(28\) 5.16599 0.790013i 0.976281 0.149298i
\(29\) −1.02264 1.77127i −0.189900 0.328917i 0.755317 0.655360i \(-0.227483\pi\)
−0.945217 + 0.326443i \(0.894150\pi\)
\(30\) 0 0
\(31\) 0.643610 2.40198i 0.115596 0.431409i −0.883735 0.467988i \(-0.844979\pi\)
0.999331 + 0.0365784i \(0.0116459\pi\)
\(32\) 1.31266 1.31266i 0.232048 0.232048i
\(33\) 0 0
\(34\) −0.399394 + 0.399394i −0.0684955 + 0.0684955i
\(35\) −2.34523 5.34393i −0.396415 0.903289i
\(36\) 0 0
\(37\) 7.22320 + 7.22320i 1.18749 + 1.18749i 0.977760 + 0.209727i \(0.0672574\pi\)
0.209727 + 0.977760i \(0.432743\pi\)
\(38\) 0.378865 + 0.656213i 0.0614600 + 0.106452i
\(39\) 0 0
\(40\) −1.19438 0.689574i −0.188848 0.109031i
\(41\) −1.34422 + 5.01671i −0.209932 + 0.783479i 0.777957 + 0.628318i \(0.216256\pi\)
−0.987889 + 0.155161i \(0.950410\pi\)
\(42\) 0 0
\(43\) 4.12300 + 2.38042i 0.628752 + 0.363010i 0.780268 0.625445i \(-0.215082\pi\)
−0.151517 + 0.988455i \(0.548416\pi\)
\(44\) 2.87049 + 10.7128i 0.432742 + 1.61502i
\(45\) 0 0
\(46\) 0.495434 + 0.495434i 0.0730477 + 0.0730477i
\(47\) 1.22397 + 4.56791i 0.178534 + 0.666298i 0.995923 + 0.0902113i \(0.0287542\pi\)
−0.817389 + 0.576087i \(0.804579\pi\)
\(48\) 0 0
\(49\) −6.68007 + 2.09204i −0.954296 + 0.298862i
\(50\) 0.00548003 0.0204517i 0.000774993 0.00289231i
\(51\) 0 0
\(52\) −6.61155 2.64745i −0.916857 0.367136i
\(53\) −0.201475 0.348965i −0.0276747 0.0479340i 0.851856 0.523776i \(-0.175477\pi\)
−0.879531 + 0.475841i \(0.842144\pi\)
\(54\) 0 0
\(55\) 10.7257 6.19246i 1.44625 0.834991i
\(56\) −0.979463 + 1.33312i −0.130886 + 0.178145i
\(57\) 0 0
\(58\) 0.310731 + 0.0832601i 0.0408010 + 0.0109326i
\(59\) 1.93268 1.93268i 0.251614 0.251614i −0.570018 0.821632i \(-0.693064\pi\)
0.821632 + 0.570018i \(0.193064\pi\)
\(60\) 0 0
\(61\) 1.61092 0.930065i 0.206257 0.119083i −0.393314 0.919404i \(-0.628671\pi\)
0.599571 + 0.800322i \(0.295338\pi\)
\(62\) 0.195561 + 0.338722i 0.0248363 + 0.0430178i
\(63\) 0 0
\(64\) 7.41238i 0.926548i
\(65\) −0.944776 + 7.89667i −0.117185 + 0.979461i
\(66\) 0 0
\(67\) 1.78441 + 6.65951i 0.218000 + 0.813589i 0.985089 + 0.172047i \(0.0550381\pi\)
−0.767088 + 0.641542i \(0.778295\pi\)
\(68\) 7.09340i 0.860201i
\(69\) 0 0
\(70\) 0.855166 + 0.333507i 0.102212 + 0.0398617i
\(71\) 3.63562 + 13.5683i 0.431469 + 1.61026i 0.749378 + 0.662142i \(0.230353\pi\)
−0.317909 + 0.948121i \(0.602981\pi\)
\(72\) 0 0
\(73\) −4.45744 1.19437i −0.521704 0.139790i −0.0116493 0.999932i \(-0.503708\pi\)
−0.510055 + 0.860142i \(0.670375\pi\)
\(74\) −1.60669 −0.186773
\(75\) 0 0
\(76\) 9.19171 + 2.46291i 1.05436 + 0.282515i
\(77\) −5.96981 13.6031i −0.680323 1.55021i
\(78\) 0 0
\(79\) −2.45889 + 4.25893i −0.276647 + 0.479167i −0.970549 0.240902i \(-0.922557\pi\)
0.693902 + 0.720069i \(0.255890\pi\)
\(80\) −8.20746 + 2.19918i −0.917622 + 0.245876i
\(81\) 0 0
\(82\) −0.408443 0.707445i −0.0451050 0.0781242i
\(83\) −10.3390 10.3390i −1.13485 1.13485i −0.989359 0.145496i \(-0.953522\pi\)
−0.145496 0.989359i \(-0.546478\pi\)
\(84\) 0 0
\(85\) 7.65124 2.05014i 0.829894 0.222369i
\(86\) −0.723291 + 0.193805i −0.0779945 + 0.0208986i
\(87\) 0 0
\(88\) −3.04031 1.75532i −0.324098 0.187118i
\(89\) 12.7764 12.7764i 1.35430 1.35430i 0.473513 0.880787i \(-0.342986\pi\)
0.880787 0.473513i \(-0.157014\pi\)
\(90\) 0 0
\(91\) 9.29008 + 2.16664i 0.973865 + 0.227126i
\(92\) 8.79911 0.917371
\(93\) 0 0
\(94\) −0.644155 0.371903i −0.0664396 0.0383589i
\(95\) 10.6264i 1.09025i
\(96\) 0 0
\(97\) −3.52628 + 0.944864i −0.358040 + 0.0959365i −0.433355 0.901223i \(-0.642670\pi\)
0.0753153 + 0.997160i \(0.476004\pi\)
\(98\) 0.510268 0.975608i 0.0515449 0.0985513i
\(99\) 0 0
\(100\) −0.132952 0.230280i −0.0132952 0.0230280i
\(101\) 4.85620 8.41119i 0.483210 0.836945i −0.516604 0.856225i \(-0.672804\pi\)
0.999814 + 0.0192798i \(0.00613733\pi\)
\(102\) 0 0
\(103\) −3.12086 + 5.40548i −0.307507 + 0.532618i −0.977816 0.209464i \(-0.932828\pi\)
0.670309 + 0.742082i \(0.266161\pi\)
\(104\) 2.07241 0.887272i 0.203217 0.0870042i
\(105\) 0 0
\(106\) 0.0612184 + 0.0164034i 0.00594605 + 0.00159324i
\(107\) 4.47949 0.433049 0.216525 0.976277i \(-0.430528\pi\)
0.216525 + 0.976277i \(0.430528\pi\)
\(108\) 0 0
\(109\) −13.4448 3.60252i −1.28778 0.345059i −0.450961 0.892544i \(-0.648919\pi\)
−0.836815 + 0.547485i \(0.815585\pi\)
\(110\) −0.504169 + 1.88158i −0.0480706 + 0.179402i
\(111\) 0 0
\(112\) 1.54069 + 10.0748i 0.145582 + 0.951978i
\(113\) −4.28714 + 7.42555i −0.403301 + 0.698537i −0.994122 0.108265i \(-0.965470\pi\)
0.590821 + 0.806802i \(0.298804\pi\)
\(114\) 0 0
\(115\) −2.54313 9.49110i −0.237148 0.885049i
\(116\) 3.49872 2.01999i 0.324848 0.187551i
\(117\) 0 0
\(118\) 0.429895i 0.0395750i
\(119\) −1.43628 9.39202i −0.131664 0.860965i
\(120\) 0 0
\(121\) 17.7761 10.2630i 1.61601 0.933001i
\(122\) −0.0757227 + 0.282601i −0.00685561 + 0.0255855i
\(123\) 0 0
\(124\) 4.74455 + 1.27130i 0.426073 + 0.114166i
\(125\) −8.00851 + 8.00851i −0.716303 + 0.716303i
\(126\) 0 0
\(127\) −8.25421 + 4.76557i −0.732443 + 0.422876i −0.819315 0.573344i \(-0.805646\pi\)
0.0868725 + 0.996219i \(0.472313\pi\)
\(128\) 3.44971 + 3.44971i 0.304914 + 0.304914i
\(129\) 0 0
\(130\) −0.773169 0.983320i −0.0678114 0.0862428i
\(131\) −3.05542 1.76405i −0.266954 0.154126i 0.360549 0.932740i \(-0.382589\pi\)
−0.627502 + 0.778615i \(0.715923\pi\)
\(132\) 0 0
\(133\) −12.6690 1.39987i −1.09854 0.121384i
\(134\) −0.939108 0.542194i −0.0811266 0.0468385i
\(135\) 0 0
\(136\) −1.58769 1.58769i −0.136144 0.136144i
\(137\) −7.14511 7.14511i −0.610448 0.610448i 0.332615 0.943063i \(-0.392069\pi\)
−0.943063 + 0.332615i \(0.892069\pi\)
\(138\) 0 0
\(139\) −9.05971 5.23063i −0.768435 0.443656i 0.0638813 0.997958i \(-0.479652\pi\)
−0.832316 + 0.554302i \(0.812985\pi\)
\(140\) 10.5557 4.63243i 0.892116 0.391512i
\(141\) 0 0
\(142\) −1.91337 1.10469i −0.160567 0.0927032i
\(143\) −2.40494 + 20.1011i −0.201111 + 1.68094i
\(144\) 0 0
\(145\) −3.19005 3.19005i −0.264919 0.264919i
\(146\) 0.628578 0.362909i 0.0520214 0.0300346i
\(147\) 0 0
\(148\) −14.2677 + 14.2677i −1.17280 + 1.17280i
\(149\) −0.428100 0.114709i −0.0350713 0.00939732i 0.241241 0.970465i \(-0.422446\pi\)
−0.276312 + 0.961068i \(0.589112\pi\)
\(150\) 0 0
\(151\) 2.55428 9.53270i 0.207864 0.775760i −0.780693 0.624915i \(-0.785134\pi\)
0.988557 0.150845i \(-0.0481996\pi\)
\(152\) −2.60862 + 1.50609i −0.211587 + 0.122160i
\(153\) 0 0
\(154\) 2.17684 + 0.848949i 0.175415 + 0.0684102i
\(155\) 5.48511i 0.440574i
\(156\) 0 0
\(157\) −19.2252 + 11.0997i −1.53434 + 0.885852i −0.535186 + 0.844734i \(0.679759\pi\)
−0.999154 + 0.0411178i \(0.986908\pi\)
\(158\) −0.200195 0.747137i −0.0159266 0.0594390i
\(159\) 0 0
\(160\) 2.04737 3.54615i 0.161859 0.280348i
\(161\) −11.6505 + 1.78166i −0.918185 + 0.140414i
\(162\) 0 0
\(163\) −0.722700 + 2.69715i −0.0566062 + 0.211257i −0.988436 0.151638i \(-0.951545\pi\)
0.931830 + 0.362895i \(0.118212\pi\)
\(164\) −9.90932 2.65519i −0.773788 0.207336i
\(165\) 0 0
\(166\) 2.29975 0.178495
\(167\) −2.34772 0.629070i −0.181672 0.0486789i 0.166836 0.985985i \(-0.446645\pi\)
−0.348508 + 0.937306i \(0.613312\pi\)
\(168\) 0 0
\(169\) −9.40717 8.97247i −0.723628 0.690190i
\(170\) −0.622938 + 1.07896i −0.0477772 + 0.0827525i
\(171\) 0 0
\(172\) −4.70194 + 8.14400i −0.358520 + 0.620974i
\(173\) −5.37379 9.30768i −0.408562 0.707650i 0.586167 0.810190i \(-0.300636\pi\)
−0.994729 + 0.102540i \(0.967303\pi\)
\(174\) 0 0
\(175\) 0.222662 + 0.277981i 0.0168317 + 0.0210134i
\(176\) −20.8922 + 5.59806i −1.57481 + 0.421970i
\(177\) 0 0
\(178\) 2.84192i 0.213011i
\(179\) −16.5020 9.52742i −1.23342 0.712113i −0.265675 0.964063i \(-0.585595\pi\)
−0.967740 + 0.251950i \(0.918928\pi\)
\(180\) 0 0
\(181\) −20.5472 −1.52726 −0.763632 0.645652i \(-0.776586\pi\)
−0.763632 + 0.645652i \(0.776586\pi\)
\(182\) −1.27418 + 0.792248i −0.0944488 + 0.0587253i
\(183\) 0 0
\(184\) −1.96948 + 1.96948i −0.145192 + 0.145192i
\(185\) 19.5134 + 11.2661i 1.43466 + 0.828299i
\(186\) 0 0
\(187\) 19.4764 5.21868i 1.42425 0.381628i
\(188\) −9.02281 + 2.41766i −0.658056 + 0.176326i
\(189\) 0 0
\(190\) 1.18184 + 1.18184i 0.0857395 + 0.0857395i
\(191\) 9.70429 + 16.8083i 0.702178 + 1.21621i 0.967700 + 0.252103i \(0.0811222\pi\)
−0.265522 + 0.964105i \(0.585544\pi\)
\(192\) 0 0
\(193\) −17.4662 + 4.68005i −1.25724 + 0.336877i −0.825130 0.564943i \(-0.808898\pi\)
−0.432112 + 0.901820i \(0.642232\pi\)
\(194\) 0.287098 0.497268i 0.0206124 0.0357018i
\(195\) 0 0
\(196\) −4.13232 13.1949i −0.295165 0.942492i
\(197\) 12.0770 + 3.23603i 0.860453 + 0.230558i 0.661955 0.749544i \(-0.269727\pi\)
0.198498 + 0.980101i \(0.436394\pi\)
\(198\) 0 0
\(199\) 20.9422 1.48455 0.742276 0.670094i \(-0.233746\pi\)
0.742276 + 0.670094i \(0.233746\pi\)
\(200\) 0.0813010 + 0.0217845i 0.00574885 + 0.00154040i
\(201\) 0 0
\(202\) 0.395375 + 1.47556i 0.0278185 + 0.103820i
\(203\) −4.22348 + 3.38299i −0.296430 + 0.237440i
\(204\) 0 0
\(205\) 11.4560i 0.800123i
\(206\) −0.254089 0.948274i −0.0177032 0.0660694i
\(207\) 0 0
\(208\) 5.16310 12.8939i 0.357996 0.894033i
\(209\) 27.0497i 1.87107i
\(210\) 0 0
\(211\) 8.85575 + 15.3386i 0.609655 + 1.05595i 0.991297 + 0.131643i \(0.0420253\pi\)
−0.381642 + 0.924310i \(0.624641\pi\)
\(212\) 0.689297 0.397966i 0.0473411 0.0273324i
\(213\) 0 0
\(214\) −0.498196 + 0.498196i −0.0340560 + 0.0340560i
\(215\) 10.1434 + 2.71792i 0.691776 + 0.185361i
\(216\) 0 0
\(217\) −6.53944 0.722580i −0.443926 0.0490519i
\(218\) 1.89595 1.09463i 0.128410 0.0741375i
\(219\) 0 0
\(220\) 12.2317 + 21.1860i 0.824663 + 1.42836i
\(221\) −4.81319 + 12.0201i −0.323770 + 0.808560i
\(222\) 0 0
\(223\) 3.51328 13.1117i 0.235267 0.878027i −0.742762 0.669556i \(-0.766485\pi\)
0.978029 0.208471i \(-0.0668487\pi\)
\(224\) −3.95807 2.90806i −0.264460 0.194303i
\(225\) 0 0
\(226\) −0.349045 1.30265i −0.0232181 0.0866511i
\(227\) 5.69257 + 5.69257i 0.377829 + 0.377829i 0.870319 0.492489i \(-0.163913\pi\)
−0.492489 + 0.870319i \(0.663913\pi\)
\(228\) 0 0
\(229\) 0.157795 + 0.588900i 0.0104274 + 0.0389156i 0.970944 0.239309i \(-0.0769208\pi\)
−0.960516 + 0.278224i \(0.910254\pi\)
\(230\) 1.33841 + 0.772732i 0.0882523 + 0.0509525i
\(231\) 0 0
\(232\) −0.330981 + 1.23524i −0.0217299 + 0.0810973i
\(233\) −20.5734 11.8780i −1.34781 0.778157i −0.359868 0.933003i \(-0.617178\pi\)
−0.987939 + 0.154846i \(0.950512\pi\)
\(234\) 0 0
\(235\) 5.21557 + 9.03364i 0.340227 + 0.589290i
\(236\) 3.81755 + 3.81755i 0.248502 + 0.248502i
\(237\) 0 0
\(238\) 1.20429 + 0.884814i 0.0780627 + 0.0573540i
\(239\) −8.02410 + 8.02410i −0.519036 + 0.519036i −0.917280 0.398244i \(-0.869620\pi\)
0.398244 + 0.917280i \(0.369620\pi\)
\(240\) 0 0
\(241\) 9.76834 9.76834i 0.629234 0.629234i −0.318641 0.947875i \(-0.603227\pi\)
0.947875 + 0.318641i \(0.103227\pi\)
\(242\) −0.835579 + 3.11842i −0.0537131 + 0.200460i
\(243\) 0 0
\(244\) 1.83712 + 3.18199i 0.117610 + 0.203706i
\(245\) −13.0382 + 8.27090i −0.832983 + 0.528409i
\(246\) 0 0
\(247\) 13.9046 + 10.4105i 0.884728 + 0.662405i
\(248\) −1.34651 + 0.777407i −0.0855034 + 0.0493654i
\(249\) 0 0
\(250\) 1.78137i 0.112663i
\(251\) 10.1546 17.5882i 0.640950 1.11016i −0.344271 0.938870i \(-0.611874\pi\)
0.985221 0.171287i \(-0.0547927\pi\)
\(252\) 0 0
\(253\) −6.47359 24.1598i −0.406991 1.51891i
\(254\) 0.387996 1.44802i 0.0243450 0.0908570i
\(255\) 0 0
\(256\) 14.0574 0.878589
\(257\) 24.6914 1.54021 0.770105 0.637917i \(-0.220204\pi\)
0.770105 + 0.637917i \(0.220204\pi\)
\(258\) 0 0
\(259\) 16.0022 21.7801i 0.994330 1.35335i
\(260\) −15.5980 1.86618i −0.967346 0.115736i
\(261\) 0 0
\(262\) 0.536008 0.143623i 0.0331147 0.00887305i
\(263\) −15.1818 + 26.2956i −0.936148 + 1.62146i −0.163575 + 0.986531i \(0.552302\pi\)
−0.772573 + 0.634925i \(0.781031\pi\)
\(264\) 0 0
\(265\) −0.628485 0.628485i −0.0386075 0.0386075i
\(266\) 1.56470 1.25332i 0.0959377 0.0768458i
\(267\) 0 0
\(268\) −13.1543 + 3.52468i −0.803525 + 0.215304i
\(269\) 5.95292i 0.362956i −0.983395 0.181478i \(-0.941912\pi\)
0.983395 0.181478i \(-0.0580882\pi\)
\(270\) 0 0
\(271\) −9.55925 + 9.55925i −0.580683 + 0.580683i −0.935091 0.354408i \(-0.884683\pi\)
0.354408 + 0.935091i \(0.384683\pi\)
\(272\) −13.8336 −0.838788
\(273\) 0 0
\(274\) 1.58932 0.0960141
\(275\) −0.534466 + 0.534466i −0.0322295 + 0.0322295i
\(276\) 0 0
\(277\) 11.5559i 0.694326i −0.937805 0.347163i \(-0.887145\pi\)
0.937805 0.347163i \(-0.112855\pi\)
\(278\) 1.58933 0.425860i 0.0953216 0.0255414i
\(279\) 0 0
\(280\) −1.32578 + 3.39951i −0.0792304 + 0.203159i
\(281\) −22.1034 22.1034i −1.31858 1.31858i −0.914904 0.403672i \(-0.867734\pi\)
−0.403672 0.914904i \(-0.632266\pi\)
\(282\) 0 0
\(283\) 11.2897 19.5544i 0.671105 1.16239i −0.306486 0.951875i \(-0.599153\pi\)
0.977591 0.210513i \(-0.0675136\pi\)
\(284\) −26.8010 + 7.18130i −1.59035 + 0.426132i
\(285\) 0 0
\(286\) −1.96812 2.50306i −0.116377 0.148009i
\(287\) 13.6581 + 1.50916i 0.806210 + 0.0890828i
\(288\) 0 0
\(289\) −4.10387 −0.241404
\(290\) 0.709577 0.0416678
\(291\) 0 0
\(292\) 2.35919 8.80461i 0.138061 0.515251i
\(293\) 0.143904 + 0.537058i 0.00840697 + 0.0313752i 0.970002 0.243097i \(-0.0781634\pi\)
−0.961595 + 0.274473i \(0.911497\pi\)
\(294\) 0 0
\(295\) 3.01442 5.22113i 0.175506 0.303986i
\(296\) 6.38700i 0.371237i
\(297\) 0 0
\(298\) 0.0603696 0.0348544i 0.00349712 0.00201906i
\(299\) 14.9105 + 5.97059i 0.862297 + 0.345288i
\(300\) 0 0
\(301\) 4.57660 11.7351i 0.263791 0.676402i
\(302\) 0.776119 + 1.34428i 0.0446607 + 0.0773545i
\(303\) 0 0
\(304\) −4.80320 + 17.9258i −0.275482 + 1.02811i
\(305\) 2.90126 2.90126i 0.166126 0.166126i
\(306\) 0 0
\(307\) −5.01312 + 5.01312i −0.286114 + 0.286114i −0.835541 0.549427i \(-0.814846\pi\)
0.549427 + 0.835541i \(0.314846\pi\)
\(308\) 26.8696 11.7919i 1.53104 0.671908i
\(309\) 0 0
\(310\) 0.610037 + 0.610037i 0.0346478 + 0.0346478i
\(311\) −0.404846 0.701214i −0.0229567 0.0397622i 0.854319 0.519749i \(-0.173975\pi\)
−0.877276 + 0.479987i \(0.840641\pi\)
\(312\) 0 0
\(313\) 0.914764 + 0.528139i 0.0517055 + 0.0298522i 0.525630 0.850713i \(-0.323830\pi\)
−0.473924 + 0.880566i \(0.657163\pi\)
\(314\) 0.903699 3.37265i 0.0509987 0.190330i
\(315\) 0 0
\(316\) −8.41250 4.85696i −0.473240 0.273225i
\(317\) 8.45663 + 31.5606i 0.474972 + 1.77262i 0.621503 + 0.783412i \(0.286522\pi\)
−0.146531 + 0.989206i \(0.546811\pi\)
\(318\) 0 0
\(319\) −8.12033 8.12033i −0.454651 0.454651i
\(320\) −4.23168 15.7928i −0.236558 0.882846i
\(321\) 0 0
\(322\) 1.09758 1.49388i 0.0611658 0.0832508i
\(323\) 4.47769 16.7110i 0.249145 0.929822i
\(324\) 0 0
\(325\) −0.0690384 0.480434i −0.00382956 0.0266497i
\(326\) −0.219593 0.380346i −0.0121621 0.0210654i
\(327\) 0 0
\(328\) 2.81228 1.62367i 0.155282 0.0896521i
\(329\) 11.4571 5.02805i 0.631652 0.277205i
\(330\) 0 0
\(331\) −23.2335 6.22540i −1.27703 0.342179i −0.444309 0.895874i \(-0.646551\pi\)
−0.832720 + 0.553695i \(0.813217\pi\)
\(332\) 20.4223 20.4223i 1.12082 1.12082i
\(333\) 0 0
\(334\) 0.331070 0.191143i 0.0181153 0.0104589i
\(335\) 7.60374 + 13.1701i 0.415436 + 0.719557i
\(336\) 0 0
\(337\) 26.8501i 1.46262i 0.682046 + 0.731310i \(0.261091\pi\)
−0.682046 + 0.731310i \(0.738909\pi\)
\(338\) 2.04413 0.0483460i 0.111186 0.00262968i
\(339\) 0 0
\(340\) 4.04957 + 15.1132i 0.219619 + 0.819629i
\(341\) 13.9624i 0.756108i
\(342\) 0 0
\(343\) 8.14312 + 16.6340i 0.439687 + 0.898151i
\(344\) −0.770426 2.87527i −0.0415386 0.155024i
\(345\) 0 0
\(346\) 1.63283 + 0.437516i 0.0877815 + 0.0235210i
\(347\) −23.0516 −1.23747 −0.618737 0.785598i \(-0.712355\pi\)
−0.618737 + 0.785598i \(0.712355\pi\)
\(348\) 0 0
\(349\) 5.97543 + 1.60111i 0.319858 + 0.0857056i 0.415176 0.909741i \(-0.363720\pi\)
−0.0953181 + 0.995447i \(0.530387\pi\)
\(350\) −0.0556802 0.00615242i −0.00297623 0.000328861i
\(351\) 0 0
\(352\) 5.21162 9.02679i 0.277780 0.481129i
\(353\) −27.1270 + 7.26865i −1.44382 + 0.386871i −0.893871 0.448325i \(-0.852021\pi\)
−0.549952 + 0.835196i \(0.685354\pi\)
\(354\) 0 0
\(355\) 15.4921 + 26.8331i 0.822236 + 1.42416i
\(356\) 25.2368 + 25.2368i 1.33755 + 1.33755i
\(357\) 0 0
\(358\) 2.89491 0.775689i 0.153001 0.0409965i
\(359\) 7.64083 2.04735i 0.403268 0.108055i −0.0514834 0.998674i \(-0.516395\pi\)
0.454751 + 0.890619i \(0.349728\pi\)
\(360\) 0 0
\(361\) −3.64506 2.10447i −0.191845 0.110762i
\(362\) 2.28520 2.28520i 0.120108 0.120108i
\(363\) 0 0
\(364\) −4.27969 + 18.3503i −0.224317 + 0.961819i
\(365\) −10.1789 −0.532787
\(366\) 0 0
\(367\) −7.92031 4.57279i −0.413437 0.238698i 0.278829 0.960341i \(-0.410054\pi\)
−0.692265 + 0.721643i \(0.743387\pi\)
\(368\) 17.1601i 0.894534i
\(369\) 0 0
\(370\) −3.42321 + 0.917246i −0.177964 + 0.0476854i
\(371\) −0.832084 + 0.666497i −0.0431996 + 0.0346028i
\(372\) 0 0
\(373\) 16.4024 + 28.4099i 0.849286 + 1.47101i 0.881846 + 0.471537i \(0.156301\pi\)
−0.0325601 + 0.999470i \(0.510366\pi\)
\(374\) −1.58570 + 2.74651i −0.0819946 + 0.142019i
\(375\) 0 0
\(376\) 1.47841 2.56069i 0.0762433 0.132057i
\(377\) 7.29941 1.04893i 0.375939 0.0540224i
\(378\) 0 0
\(379\) −16.9754 4.54854i −0.871967 0.233643i −0.205029 0.978756i \(-0.565729\pi\)
−0.666938 + 0.745113i \(0.732395\pi\)
\(380\) 20.9899 1.07676
\(381\) 0 0
\(382\) −2.94866 0.790090i −0.150866 0.0404245i
\(383\) 7.96025 29.7081i 0.406750 1.51801i −0.394056 0.919087i \(-0.628928\pi\)
0.800806 0.598924i \(-0.204405\pi\)
\(384\) 0 0
\(385\) −20.4852 25.5746i −1.04402 1.30340i
\(386\) 1.42204 2.46304i 0.0723797 0.125365i
\(387\) 0 0
\(388\) −1.86635 6.96533i −0.0947498 0.353611i
\(389\) 13.1147 7.57176i 0.664940 0.383903i −0.129217 0.991616i \(-0.541246\pi\)
0.794157 + 0.607713i \(0.207913\pi\)
\(390\) 0 0
\(391\) 15.9972i 0.809013i
\(392\) 3.87830 + 2.02845i 0.195884 + 0.102452i
\(393\) 0 0
\(394\) −1.70307 + 0.983270i −0.0857996 + 0.0495364i
\(395\) −2.80753 + 10.4778i −0.141262 + 0.527198i
\(396\) 0 0
\(397\) 7.79662 + 2.08910i 0.391301 + 0.104849i 0.449105 0.893479i \(-0.351743\pi\)
−0.0578036 + 0.998328i \(0.518410\pi\)
\(398\) −2.32913 + 2.32913i −0.116749 + 0.116749i
\(399\) 0 0
\(400\) 0.449094 0.259285i 0.0224547 0.0129642i
\(401\) 12.1510 + 12.1510i 0.606791 + 0.606791i 0.942106 0.335315i \(-0.108843\pi\)
−0.335315 + 0.942106i \(0.608843\pi\)
\(402\) 0 0
\(403\) 7.17723 + 5.37367i 0.357523 + 0.267681i
\(404\) 16.6143 + 9.59227i 0.826592 + 0.477233i
\(405\) 0 0
\(406\) 0.0934760 0.845969i 0.00463914 0.0419848i
\(407\) 49.6718 + 28.6780i 2.46214 + 1.42152i
\(408\) 0 0
\(409\) 21.6885 + 21.6885i 1.07243 + 1.07243i 0.997164 + 0.0752633i \(0.0239797\pi\)
0.0752633 + 0.997164i \(0.476020\pi\)
\(410\) −1.27411 1.27411i −0.0629236 0.0629236i
\(411\) 0 0
\(412\) −10.6772 6.16451i −0.526030 0.303703i
\(413\) −5.82762 4.28165i −0.286758 0.210686i
\(414\) 0 0
\(415\) −27.9308 16.1259i −1.37107 0.791587i
\(416\) 2.63434 + 6.15308i 0.129159 + 0.301679i
\(417\) 0 0
\(418\) 3.00839 + 3.00839i 0.147145 + 0.147145i
\(419\) 15.2013 8.77646i 0.742631 0.428758i −0.0803942 0.996763i \(-0.525618\pi\)
0.823025 + 0.568005i \(0.192285\pi\)
\(420\) 0 0
\(421\) 15.5736 15.5736i 0.759010 0.759010i −0.217132 0.976142i \(-0.569670\pi\)
0.976142 + 0.217132i \(0.0696702\pi\)
\(422\) −2.69083 0.721005i −0.130987 0.0350980i
\(423\) 0 0
\(424\) −0.0652078 + 0.243359i −0.00316677 + 0.0118186i
\(425\) −0.418659 + 0.241713i −0.0203079 + 0.0117248i
\(426\) 0 0
\(427\) −3.07674 3.84113i −0.148894 0.185885i
\(428\) 8.84817i 0.427693i
\(429\) 0 0
\(430\) −1.43040 + 0.825843i −0.0689801 + 0.0398257i
\(431\) −1.12224 4.18826i −0.0540564 0.201741i 0.933616 0.358275i \(-0.116635\pi\)
−0.987673 + 0.156533i \(0.949968\pi\)
\(432\) 0 0
\(433\) −14.6114 + 25.3077i −0.702181 + 1.21621i 0.265519 + 0.964106i \(0.414457\pi\)
−0.967699 + 0.252107i \(0.918876\pi\)
\(434\) 0.807660 0.646934i 0.0387689 0.0310538i
\(435\) 0 0
\(436\) 7.11591 26.5570i 0.340791 1.27185i
\(437\) −20.7293 5.55441i −0.991619 0.265704i
\(438\) 0 0
\(439\) −0.0638652 −0.00304812 −0.00152406 0.999999i \(-0.500485\pi\)
−0.00152406 + 0.999999i \(0.500485\pi\)
\(440\) −7.47978 2.00420i −0.356585 0.0955466i
\(441\) 0 0
\(442\) −0.801532 1.87215i −0.0381250 0.0890491i
\(443\) −8.77423 + 15.1974i −0.416876 + 0.722051i −0.995623 0.0934562i \(-0.970208\pi\)
0.578747 + 0.815507i \(0.303542\pi\)
\(444\) 0 0
\(445\) 19.9275 34.5155i 0.944655 1.63619i
\(446\) 1.06751 + 1.84899i 0.0505482 + 0.0875520i
\(447\) 0 0
\(448\) −19.3859 + 2.96461i −0.915900 + 0.140065i
\(449\) 1.21603 0.325835i 0.0573881 0.0153771i −0.230011 0.973188i \(-0.573876\pi\)
0.287399 + 0.957811i \(0.407209\pi\)
\(450\) 0 0
\(451\) 29.1615i 1.37316i
\(452\) −14.6674 8.46823i −0.689897 0.398312i
\(453\) 0 0
\(454\) −1.26622 −0.0594268
\(455\) 21.0304 0.687386i 0.985920 0.0322252i
\(456\) 0 0
\(457\) −5.23927 + 5.23927i −0.245083 + 0.245083i −0.818949 0.573866i \(-0.805443\pi\)
0.573866 + 0.818949i \(0.305443\pi\)
\(458\) −0.0830452 0.0479462i −0.00388045 0.00224038i
\(459\) 0 0
\(460\) 18.7474 5.02335i 0.874102 0.234215i
\(461\) −17.9390 + 4.80674i −0.835502 + 0.223872i −0.651113 0.758981i \(-0.725697\pi\)
−0.184390 + 0.982853i \(0.559031\pi\)
\(462\) 0 0
\(463\) 10.9354 + 10.9354i 0.508209 + 0.508209i 0.913976 0.405767i \(-0.132996\pi\)
−0.405767 + 0.913976i \(0.632996\pi\)
\(464\) 3.93941 + 6.82326i 0.182882 + 0.316762i
\(465\) 0 0
\(466\) 3.60915 0.967070i 0.167191 0.0447986i
\(467\) 8.85362 15.3349i 0.409697 0.709616i −0.585159 0.810919i \(-0.698968\pi\)
0.994856 + 0.101303i \(0.0323011\pi\)
\(468\) 0 0
\(469\) 16.7032 7.33035i 0.771284 0.338484i
\(470\) −1.58476 0.424634i −0.0730993 0.0195869i
\(471\) 0 0
\(472\) −1.70894 −0.0786605
\(473\) 25.8203 + 6.91853i 1.18722 + 0.318114i
\(474\) 0 0
\(475\) 0.167851 + 0.626429i 0.00770153 + 0.0287425i
\(476\) 18.5517 2.83703i 0.850316 0.130035i
\(477\) 0 0
\(478\) 1.78483i 0.0816364i
\(479\) −4.37332 16.3215i −0.199822 0.745747i −0.990966 0.134116i \(-0.957181\pi\)
0.791143 0.611631i \(-0.209486\pi\)
\(480\) 0 0
\(481\) −33.8586 + 14.4960i −1.54382 + 0.660962i
\(482\) 2.17281i 0.0989689i
\(483\) 0 0
\(484\) 20.2721 + 35.1124i 0.921461 + 1.59602i
\(485\) −6.97369 + 4.02626i −0.316659 + 0.182823i
\(486\) 0 0
\(487\) −1.58169 + 1.58169i −0.0716733 + 0.0716733i −0.742035 0.670361i \(-0.766139\pi\)
0.670361 + 0.742035i \(0.266139\pi\)
\(488\) −1.12341 0.301017i −0.0508545 0.0136264i
\(489\) 0 0
\(490\) 0.530210 2.36994i 0.0239525 0.107063i
\(491\) 28.4705 16.4375i 1.28486 0.741812i 0.307124 0.951669i \(-0.400633\pi\)
0.977732 + 0.209858i \(0.0673000\pi\)
\(492\) 0 0
\(493\) −3.67243 6.36084i −0.165398 0.286478i
\(494\) −2.70425 + 0.388602i −0.121670 + 0.0174840i
\(495\) 0 0
\(496\) −2.47930 + 9.25288i −0.111324 + 0.415467i
\(497\) 34.0318 14.9351i 1.52653 0.669931i
\(498\) 0 0
\(499\) 7.97619 + 29.7675i 0.357063 + 1.33258i 0.877868 + 0.478902i \(0.158965\pi\)
−0.520805 + 0.853676i \(0.674368\pi\)
\(500\) −15.8189 15.8189i −0.707443 0.707443i
\(501\) 0 0
\(502\) 0.826749 + 3.08547i 0.0368996 + 0.137711i
\(503\) 9.25091 + 5.34101i 0.412478 + 0.238144i 0.691854 0.722038i \(-0.256794\pi\)
−0.279376 + 0.960182i \(0.590128\pi\)
\(504\) 0 0
\(505\) 5.54475 20.6933i 0.246738 0.920838i
\(506\) 3.40695 + 1.96700i 0.151457 + 0.0874440i
\(507\) 0 0
\(508\) −9.41325 16.3042i −0.417645 0.723383i
\(509\) 16.6654 + 16.6654i 0.738681 + 0.738681i 0.972323 0.233641i \(-0.0750642\pi\)
−0.233641 + 0.972323i \(0.575064\pi\)
\(510\) 0 0
\(511\) −1.34091 + 12.1354i −0.0593186 + 0.536840i
\(512\) −8.46284 + 8.46284i −0.374008 + 0.374008i
\(513\) 0 0
\(514\) −2.74611 + 2.74611i −0.121126 + 0.121126i
\(515\) −3.56335 + 13.2986i −0.157020 + 0.586006i
\(516\) 0 0
\(517\) 13.2763 + 22.9953i 0.583893 + 1.01133i
\(518\) 0.642600 + 4.20204i 0.0282342 + 0.184627i
\(519\) 0 0
\(520\) 3.90895 3.07355i 0.171419 0.134784i
\(521\) −27.2035 + 15.7059i −1.19180 + 0.688089i −0.958716 0.284367i \(-0.908217\pi\)
−0.233089 + 0.972455i \(0.574883\pi\)
\(522\) 0 0
\(523\) 7.66261i 0.335062i −0.985867 0.167531i \(-0.946420\pi\)
0.985867 0.167531i \(-0.0535795\pi\)
\(524\) 3.48446 6.03526i 0.152219 0.263652i
\(525\) 0 0
\(526\) −1.23605 4.61299i −0.0538942 0.201136i
\(527\) 2.31128 8.62581i 0.100681 0.375746i
\(528\) 0 0
\(529\) 3.15604 0.137219
\(530\) 0.139797 0.00607237
\(531\) 0 0
\(532\) 2.76511 25.0245i 0.119883 1.08495i
\(533\) −14.9901 11.2233i −0.649295 0.486134i
\(534\) 0 0
\(535\) 9.54402 2.55731i 0.412624 0.110562i
\(536\) 2.15536 3.73320i 0.0930976 0.161250i
\(537\) 0 0
\(538\) 0.662067 + 0.662067i 0.0285437 + 0.0285437i
\(539\) −33.1891 + 21.0537i −1.42956 + 0.906848i
\(540\) 0 0
\(541\) 21.5302 5.76899i 0.925654 0.248028i 0.235654 0.971837i \(-0.424277\pi\)
0.690001 + 0.723809i \(0.257610\pi\)
\(542\) 2.12630i 0.0913326i
\(543\) 0 0
\(544\) 4.71393 4.71393i 0.202108 0.202108i
\(545\) −30.7021 −1.31513
\(546\) 0 0
\(547\) 18.1017 0.773971 0.386986 0.922086i \(-0.373516\pi\)
0.386986 + 0.922086i \(0.373516\pi\)
\(548\) 14.1135 14.1135i 0.602897 0.602897i
\(549\) 0 0
\(550\) 0.118883i 0.00506920i
\(551\) −9.51756 + 2.55022i −0.405462 + 0.108643i
\(552\) 0 0
\(553\) 12.1220 + 4.72749i 0.515481 + 0.201033i
\(554\) 1.28521 + 1.28521i 0.0546035 + 0.0546035i
\(555\) 0 0
\(556\) 10.3319 17.8953i 0.438168 0.758930i
\(557\) −0.603665 + 0.161752i −0.0255781 + 0.00685364i −0.271585 0.962414i \(-0.587548\pi\)
0.246007 + 0.969268i \(0.420881\pi\)
\(558\) 0 0
\(559\) −13.4937 + 10.6099i −0.570724 + 0.448752i
\(560\) 9.03423 + 20.5858i 0.381766 + 0.869908i
\(561\) 0 0
\(562\) 4.91654 0.207392
\(563\) 6.32497 0.266566 0.133283 0.991078i \(-0.457448\pi\)
0.133283 + 0.991078i \(0.457448\pi\)
\(564\) 0 0
\(565\) −4.89500 + 18.2684i −0.205934 + 0.768557i
\(566\) 0.919172 + 3.43040i 0.0386357 + 0.144190i
\(567\) 0 0
\(568\) 4.39142 7.60615i 0.184260 0.319147i
\(569\) 7.32323i 0.307006i −0.988148 0.153503i \(-0.950945\pi\)
0.988148 0.153503i \(-0.0490554\pi\)
\(570\) 0 0
\(571\) 24.3352 14.0500i 1.01840 0.587972i 0.104758 0.994498i \(-0.466593\pi\)
0.913639 + 0.406526i \(0.133260\pi\)
\(572\) −39.7049 4.75039i −1.66015 0.198624i
\(573\) 0 0
\(574\) −1.68685 + 1.35117i −0.0704079 + 0.0563966i
\(575\) 0.299836 + 0.519332i 0.0125040 + 0.0216576i
\(576\) 0 0
\(577\) −9.18425 + 34.2761i −0.382345 + 1.42693i 0.459964 + 0.887938i \(0.347862\pi\)
−0.842309 + 0.538995i \(0.818804\pi\)
\(578\) 0.456420 0.456420i 0.0189846 0.0189846i
\(579\) 0 0
\(580\) 6.30119 6.30119i 0.261643 0.261643i
\(581\) −22.9050 + 31.1753i −0.950259 + 1.29337i
\(582\) 0 0
\(583\) −1.59982 1.59982i −0.0662578 0.0662578i
\(584\) 1.44266 + 2.49876i 0.0596977 + 0.103399i
\(585\) 0 0
\(586\) −0.0757346 0.0437254i −0.00312857 0.00180628i
\(587\) 4.40846 16.4526i 0.181957 0.679071i −0.813305 0.581838i \(-0.802334\pi\)
0.995262 0.0972337i \(-0.0309994\pi\)
\(588\) 0 0
\(589\) −10.3749 5.98996i −0.427491 0.246812i
\(590\) 0.245424 + 0.915934i 0.0101039 + 0.0377084i
\(591\) 0 0
\(592\) −27.8251 27.8251i −1.14360 1.14360i
\(593\) 3.60164 + 13.4415i 0.147901 + 0.551976i 0.999609 + 0.0279585i \(0.00890063\pi\)
−0.851708 + 0.524017i \(0.824433\pi\)
\(594\) 0 0
\(595\) −8.42198 19.1907i −0.345268 0.786742i
\(596\) 0.226580 0.845609i 0.00928109 0.0346375i
\(597\) 0 0
\(598\) −2.32234 + 0.994272i −0.0949674 + 0.0406588i
\(599\) 8.84405 + 15.3183i 0.361358 + 0.625890i 0.988185 0.153268i \(-0.0489799\pi\)
−0.626827 + 0.779159i \(0.715647\pi\)
\(600\) 0 0
\(601\) 23.8753 13.7844i 0.973894 0.562278i 0.0734732 0.997297i \(-0.476592\pi\)
0.900421 + 0.435019i \(0.143258\pi\)
\(602\) 0.796151 + 1.81414i 0.0324487 + 0.0739389i
\(603\) 0 0
\(604\) 18.8296 + 5.04537i 0.766164 + 0.205293i
\(605\) 32.0146 32.0146i 1.30158 1.30158i
\(606\) 0 0
\(607\) 17.6565 10.1940i 0.716657 0.413762i −0.0968642 0.995298i \(-0.530881\pi\)
0.813521 + 0.581536i \(0.197548\pi\)
\(608\) −4.47163 7.74509i −0.181348 0.314105i
\(609\) 0 0
\(610\) 0.645339i 0.0261290i
\(611\) −16.9301 2.02555i −0.684918 0.0819451i
\(612\) 0 0
\(613\) 5.69586 + 21.2573i 0.230054 + 0.858572i 0.980316 + 0.197433i \(0.0632603\pi\)
−0.750263 + 0.661140i \(0.770073\pi\)
\(614\) 1.11509i 0.0450014i
\(615\) 0 0
\(616\) −3.37479 + 8.65350i −0.135974 + 0.348660i
\(617\) −2.77212 10.3457i −0.111602 0.416503i 0.887409 0.460984i \(-0.152503\pi\)
−0.999010 + 0.0444809i \(0.985837\pi\)
\(618\) 0 0
\(619\) −46.3466 12.4185i −1.86283 0.499143i −0.862849 0.505462i \(-0.831322\pi\)
−0.999980 + 0.00631894i \(0.997989\pi\)
\(620\) 10.8345 0.435125
\(621\) 0 0
\(622\) 0.123013 + 0.0329612i 0.00493236 + 0.00132162i
\(623\) −38.5248 28.3048i −1.54346 1.13401i
\(624\) 0 0
\(625\) −12.1544 + 21.0520i −0.486176 + 0.842081i
\(626\) −0.160476 + 0.0429993i −0.00641389 + 0.00171860i
\(627\) 0 0
\(628\) −21.9248 37.9749i −0.874895 1.51536i
\(629\) 25.9394 + 25.9394i 1.03427 + 1.03427i
\(630\) 0 0
\(631\) −28.4576 + 7.62520i −1.13288 + 0.303554i −0.776085 0.630628i \(-0.782797\pi\)
−0.356795 + 0.934183i \(0.616131\pi\)
\(632\) 2.97006 0.795826i 0.118143 0.0316563i
\(633\) 0 0
\(634\) −4.45060 2.56955i −0.176756 0.102050i
\(635\) −14.8658 + 14.8658i −0.589931 + 0.589931i
\(636\) 0 0
\(637\) 1.95092 25.1633i 0.0772984 0.997008i
\(638\) 1.80624 0.0715097
\(639\) 0 0
\(640\) 9.31937 + 5.38054i 0.368380 + 0.212685i
\(641\) 3.78962i 0.149681i −0.997196 0.0748405i \(-0.976155\pi\)
0.997196 0.0748405i \(-0.0238448\pi\)
\(642\) 0 0
\(643\) −9.08002 + 2.43298i −0.358081 + 0.0959475i −0.433375 0.901214i \(-0.642677\pi\)
0.0752936 + 0.997161i \(0.476011\pi\)
\(644\) −3.51924 23.0127i −0.138677 0.906828i
\(645\) 0 0
\(646\) 1.36055 + 2.35654i 0.0535301 + 0.0927168i
\(647\) −14.8089 + 25.6498i −0.582199 + 1.00840i 0.413020 + 0.910722i \(0.364474\pi\)
−0.995218 + 0.0976755i \(0.968859\pi\)
\(648\) 0 0
\(649\) 7.67327 13.2905i 0.301202 0.521697i
\(650\) 0.0611107 + 0.0457542i 0.00239696 + 0.00179463i
\(651\) 0 0
\(652\) −5.32758 1.42752i −0.208644 0.0559060i
\(653\) −42.5984 −1.66700 −0.833502 0.552516i \(-0.813668\pi\)
−0.833502 + 0.552516i \(0.813668\pi\)
\(654\) 0 0
\(655\) −7.51697 2.01417i −0.293712 0.0787000i
\(656\) 5.17819 19.3253i 0.202174 0.754525i
\(657\) 0 0
\(658\) −0.715024 + 1.83343i −0.0278745 + 0.0714747i
\(659\) −0.832186 + 1.44139i −0.0324173 + 0.0561485i −0.881779 0.471663i \(-0.843654\pi\)
0.849362 + 0.527811i \(0.176987\pi\)
\(660\) 0 0
\(661\) −2.43629 9.09235i −0.0947606 0.353651i 0.902222 0.431271i \(-0.141935\pi\)
−0.996983 + 0.0776197i \(0.975268\pi\)
\(662\) 3.27633 1.89159i 0.127338 0.0735188i
\(663\) 0 0
\(664\) 9.14211i 0.354783i
\(665\) −27.7917 + 4.25007i −1.07772 + 0.164811i
\(666\) 0 0
\(667\) −7.89040 + 4.55552i −0.305518 + 0.176391i
\(668\) 1.24258 4.63736i 0.0480768 0.179425i
\(669\) 0 0
\(670\) −2.31040 0.619070i −0.0892586 0.0239168i
\(671\) 7.38521 7.38521i 0.285103 0.285103i
\(672\) 0 0
\(673\) 2.15591 1.24472i 0.0831043 0.0479803i −0.457872 0.889018i \(-0.651388\pi\)
0.540976 + 0.841038i \(0.318055\pi\)
\(674\) −2.98619 2.98619i −0.115024 0.115024i
\(675\) 0 0
\(676\) 17.7230 18.5816i 0.681653 0.714678i
\(677\) −18.2860 10.5574i −0.702789 0.405756i 0.105596 0.994409i \(-0.466325\pi\)
−0.808385 + 0.588654i \(0.799658\pi\)
\(678\) 0 0
\(679\) 3.88150 + 8.84455i 0.148958 + 0.339423i
\(680\) −4.28915 2.47634i −0.164481 0.0949633i
\(681\) 0 0
\(682\) 1.55286 + 1.55286i 0.0594621 + 0.0594621i
\(683\) −3.90071 3.90071i −0.149257 0.149257i 0.628529 0.777786i \(-0.283657\pi\)
−0.777786 + 0.628529i \(0.783657\pi\)
\(684\) 0 0
\(685\) −19.3025 11.1443i −0.737510 0.425801i
\(686\) −2.75564 0.944330i −0.105211 0.0360547i
\(687\) 0 0
\(688\) −15.8825 9.16979i −0.605516 0.349595i
\(689\) 1.43809 0.206653i 0.0547867 0.00787285i
\(690\) 0 0
\(691\) −11.4634 11.4634i −0.436089 0.436089i 0.454604 0.890694i \(-0.349781\pi\)
−0.890694 + 0.454604i \(0.849781\pi\)
\(692\) 18.3851 10.6146i 0.698897 0.403508i
\(693\) 0 0
\(694\) 2.56373 2.56373i 0.0973179 0.0973179i
\(695\) −22.2888 5.97226i −0.845461 0.226541i
\(696\) 0 0
\(697\) −4.82727 + 18.0156i −0.182846 + 0.682390i
\(698\) −0.842641 + 0.486499i −0.0318944 + 0.0184143i
\(699\) 0 0
\(700\) −0.549086 + 0.439817i −0.0207535 + 0.0166235i
\(701\) 11.5049i 0.434534i 0.976112 + 0.217267i \(0.0697142\pi\)
−0.976112 + 0.217267i \(0.930286\pi\)
\(702\) 0 0
\(703\) 42.6190 24.6061i 1.60741 0.928036i
\(704\) −10.7718 40.2009i −0.405978 1.51513i
\(705\) 0 0
\(706\) 2.20858 3.82538i 0.0831212 0.143970i
\(707\) −23.9404 9.33657i −0.900373 0.351138i
\(708\) 0 0
\(709\) −0.0992239 + 0.370309i −0.00372643 + 0.0139072i −0.967764 0.251859i \(-0.918958\pi\)
0.964038 + 0.265766i \(0.0856248\pi\)
\(710\) −4.70729 1.26132i −0.176662 0.0473363i
\(711\) 0 0
\(712\) −11.2974 −0.423387
\(713\) −10.7000 2.86706i −0.400719 0.107372i
\(714\) 0 0
\(715\) 6.35161 + 44.2004i 0.237537 + 1.65300i
\(716\) 18.8191 32.5957i 0.703304 1.21816i
\(717\) 0 0
\(718\) −0.622090 + 1.07749i −0.0232162 + 0.0402116i
\(719\) 11.9136 + 20.6350i 0.444304 + 0.769557i 0.998003 0.0631593i \(-0.0201176\pi\)
−0.553699 + 0.832717i \(0.686784\pi\)
\(720\) 0 0
\(721\) 15.3854 + 6.00018i 0.572982 + 0.223458i
\(722\) 0.639446 0.171339i 0.0237977 0.00637658i
\(723\) 0 0
\(724\) 40.5862i 1.50837i
\(725\) 0.238443 + 0.137665i 0.00885556 + 0.00511276i
\(726\) 0 0
\(727\) −0.135408 −0.00502200 −0.00251100 0.999997i \(-0.500799\pi\)
−0.00251100 + 0.999997i \(0.500799\pi\)
\(728\) −3.14939 5.06521i −0.116724 0.187729i
\(729\) 0 0
\(730\) 1.13207 1.13207i 0.0418996 0.0418996i
\(731\) 14.8062 + 8.54835i 0.547626 + 0.316172i
\(732\) 0 0
\(733\) −37.2352 + 9.97714i −1.37531 + 0.368514i −0.869417 0.494080i \(-0.835505\pi\)
−0.505897 + 0.862594i \(0.668838\pi\)
\(734\) 1.38945 0.372301i 0.0512854 0.0137419i
\(735\) 0 0
\(736\) −5.84746 5.84746i −0.215540 0.215540i
\(737\) 19.3554 + 33.5246i 0.712967 + 1.23489i
\(738\) 0 0
\(739\) −39.9013 + 10.6915i −1.46779 + 0.393294i −0.902174 0.431372i \(-0.858030\pi\)
−0.565620 + 0.824666i \(0.691363\pi\)
\(740\) −22.2535 + 38.5441i −0.818054 + 1.41691i
\(741\) 0 0
\(742\) 0.0184161 0.166668i 0.000676076 0.00611857i
\(743\) 29.7830 + 7.98032i 1.09263 + 0.292769i 0.759760 0.650203i \(-0.225316\pi\)
0.332870 + 0.942973i \(0.391983\pi\)
\(744\) 0 0
\(745\) −0.977597 −0.0358164
\(746\) −4.98389 1.33543i −0.182473 0.0488936i
\(747\) 0 0
\(748\) 10.3083 + 38.4709i 0.376907 + 1.40664i
\(749\) −1.79159 11.7154i −0.0654633 0.428072i
\(750\) 0 0
\(751\) 32.6954i 1.19307i −0.802586 0.596536i \(-0.796543\pi\)
0.802586 0.596536i \(-0.203457\pi\)
\(752\) −4.71494 17.5964i −0.171936 0.641675i
\(753\) 0 0
\(754\) −0.695160 + 0.928477i −0.0253162 + 0.0338131i
\(755\) 21.7686i 0.792241i
\(756\) 0 0
\(757\) 4.04055 + 6.99844i 0.146856 + 0.254363i 0.930064 0.367398i \(-0.119751\pi\)
−0.783208 + 0.621760i \(0.786418\pi\)
\(758\) 2.39383 1.38208i 0.0869477 0.0501993i
\(759\) 0 0
\(760\) −4.69811 + 4.69811i −0.170418 + 0.170418i
\(761\) 13.8024 + 3.69833i 0.500335 + 0.134064i 0.500155 0.865936i \(-0.333276\pi\)
0.000179461 1.00000i \(0.499943\pi\)
\(762\) 0 0
\(763\) −4.04454 + 36.6036i −0.146422 + 1.32514i
\(764\) −33.2008 + 19.1685i −1.20116 + 0.693493i
\(765\) 0 0
\(766\) 2.41873 + 4.18936i 0.0873922 + 0.151368i
\(767\) 3.87865 + 9.05941i 0.140050 + 0.327116i
\(768\) 0 0
\(769\) 0.992641 3.70459i 0.0357955 0.133591i −0.945716 0.324995i \(-0.894637\pi\)
0.981511 + 0.191404i \(0.0613041\pi\)
\(770\) 5.12264 + 0.566029i 0.184607 + 0.0203983i
\(771\) 0 0
\(772\) −9.24431 34.5003i −0.332710 1.24169i
\(773\) 0.986845 + 0.986845i 0.0354943 + 0.0354943i 0.724631 0.689137i \(-0.242010\pi\)
−0.689137 + 0.724631i \(0.742010\pi\)
\(774\) 0 0
\(775\) 0.0866409 + 0.323348i 0.00311223 + 0.0116150i
\(776\) 1.97677 + 1.14129i 0.0709619 + 0.0409699i
\(777\) 0 0
\(778\) −0.616466 + 2.30068i −0.0221014 + 0.0824835i
\(779\) 21.6687 + 12.5105i 0.776363 + 0.448234i
\(780\) 0 0
\(781\) 39.4355 + 68.3042i 1.41111 + 2.44412i
\(782\) 1.77916 + 1.77916i 0.0636227 + 0.0636227i
\(783\) 0 0
\(784\) 25.7329 8.05890i 0.919031 0.287818i
\(785\) −34.6246 + 34.6246i −1.23580 + 1.23580i
\(786\) 0 0
\(787\) −23.6123 + 23.6123i −0.841686 + 0.841686i −0.989078 0.147392i \(-0.952912\pi\)
0.147392 + 0.989078i \(0.452912\pi\)
\(788\) −6.39201