Properties

Label 819.2.et.c.145.8
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 145.8
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.30773 - 1.30773i) q^{2} -1.42031i q^{4} +(0.0744995 - 0.0199621i) q^{5} +(2.55141 + 0.700217i) q^{7} +(0.758075 + 0.758075i) q^{8} +O(q^{10})\) \(q+(1.30773 - 1.30773i) q^{2} -1.42031i q^{4} +(0.0744995 - 0.0199621i) q^{5} +(2.55141 + 0.700217i) q^{7} +(0.758075 + 0.758075i) q^{8} +(0.0713202 - 0.123530i) q^{10} +(-0.672618 + 0.180227i) q^{11} +(2.39818 + 2.69235i) q^{13} +(4.25225 - 2.42086i) q^{14} +4.82334 q^{16} +1.23731 q^{17} +(-1.45771 + 5.44023i) q^{19} +(-0.0283524 - 0.105813i) q^{20} +(-0.643914 + 1.11529i) q^{22} -7.37027i q^{23} +(-4.32498 + 2.49703i) q^{25} +(6.65703 + 0.384694i) q^{26} +(0.994527 - 3.62380i) q^{28} +(-1.84462 - 3.19498i) q^{29} +(2.34941 - 8.76813i) q^{31} +(4.79147 - 4.79147i) q^{32} +(1.61806 - 1.61806i) q^{34} +(0.204057 + 0.00123434i) q^{35} +(3.25640 + 3.25640i) q^{37} +(5.20806 + 9.02063i) q^{38} +(0.0716090 + 0.0413434i) q^{40} +(0.231836 - 0.865225i) q^{41} +(-2.14988 - 1.24124i) q^{43} +(0.255979 + 0.955327i) q^{44} +(-9.63832 - 9.63832i) q^{46} +(-0.108435 - 0.404685i) q^{47} +(6.01939 + 3.57308i) q^{49} +(-2.39046 + 8.92133i) q^{50} +(3.82397 - 3.40616i) q^{52} +(-5.75319 - 9.96481i) q^{53} +(-0.0465120 + 0.0268537i) q^{55} +(1.40334 + 2.46498i) q^{56} +(-6.59044 - 1.76590i) q^{58} +(-9.90380 + 9.90380i) q^{59} +(5.63177 - 3.25150i) q^{61} +(-8.39395 - 14.5387i) q^{62} -2.88522i q^{64} +(0.232408 + 0.152706i) q^{65} +(-0.540059 - 2.01553i) q^{67} -1.75736i q^{68} +(0.268465 - 0.265237i) q^{70} +(-0.119329 - 0.445340i) q^{71} +(-4.91231 - 1.31625i) q^{73} +8.51697 q^{74} +(7.72682 + 2.07040i) q^{76} +(-1.84232 - 0.0111443i) q^{77} +(3.26395 - 5.65332i) q^{79} +(0.359336 - 0.0962839i) q^{80} +(-0.828301 - 1.43466i) q^{82} +(9.54235 + 9.54235i) q^{83} +(0.0921787 - 0.0246992i) q^{85} +(-4.43466 + 1.18826i) q^{86} +(-0.646521 - 0.373269i) q^{88} +(-3.14679 + 3.14679i) q^{89} +(4.23351 + 8.54853i) q^{91} -10.4681 q^{92} +(-0.671022 - 0.387414i) q^{94} +0.434393i q^{95} +(-15.6536 + 4.19437i) q^{97} +(12.5444 - 3.19911i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30773 1.30773i 0.924704 0.924704i −0.0726530 0.997357i \(-0.523147\pi\)
0.997357 + 0.0726530i \(0.0231466\pi\)
\(3\) 0 0
\(4\) 1.42031i 0.710156i
\(5\) 0.0744995 0.0199621i 0.0333172 0.00892732i −0.242122 0.970246i \(-0.577843\pi\)
0.275439 + 0.961319i \(0.411177\pi\)
\(6\) 0 0
\(7\) 2.55141 + 0.700217i 0.964343 + 0.264657i
\(8\) 0.758075 + 0.758075i 0.268020 + 0.268020i
\(9\) 0 0
\(10\) 0.0713202 0.123530i 0.0225534 0.0390637i
\(11\) −0.672618 + 0.180227i −0.202802 + 0.0543406i −0.358790 0.933418i \(-0.616811\pi\)
0.155988 + 0.987759i \(0.450144\pi\)
\(12\) 0 0
\(13\) 2.39818 + 2.69235i 0.665135 + 0.746723i
\(14\) 4.25225 2.42086i 1.13646 0.647002i
\(15\) 0 0
\(16\) 4.82334 1.20583
\(17\) 1.23731 0.300091 0.150045 0.988679i \(-0.452058\pi\)
0.150045 + 0.988679i \(0.452058\pi\)
\(18\) 0 0
\(19\) −1.45771 + 5.44023i −0.334420 + 1.24807i 0.570076 + 0.821592i \(0.306914\pi\)
−0.904496 + 0.426482i \(0.859753\pi\)
\(20\) −0.0283524 0.105813i −0.00633979 0.0236604i
\(21\) 0 0
\(22\) −0.643914 + 1.11529i −0.137283 + 0.237781i
\(23\) 7.37027i 1.53681i −0.639965 0.768404i \(-0.721051\pi\)
0.639965 0.768404i \(-0.278949\pi\)
\(24\) 0 0
\(25\) −4.32498 + 2.49703i −0.864995 + 0.499405i
\(26\) 6.65703 + 0.384694i 1.30555 + 0.0754446i
\(27\) 0 0
\(28\) 0.994527 3.62380i 0.187948 0.684834i
\(29\) −1.84462 3.19498i −0.342538 0.593293i 0.642365 0.766399i \(-0.277953\pi\)
−0.984903 + 0.173105i \(0.944620\pi\)
\(30\) 0 0
\(31\) 2.34941 8.76813i 0.421967 1.57480i −0.348491 0.937312i \(-0.613306\pi\)
0.770458 0.637491i \(-0.220028\pi\)
\(32\) 4.79147 4.79147i 0.847020 0.847020i
\(33\) 0 0
\(34\) 1.61806 1.61806i 0.277495 0.277495i
\(35\) 0.204057 + 0.00123434i 0.0344919 + 0.000208642i
\(36\) 0 0
\(37\) 3.25640 + 3.25640i 0.535348 + 0.535348i 0.922159 0.386811i \(-0.126423\pi\)
−0.386811 + 0.922159i \(0.626423\pi\)
\(38\) 5.20806 + 9.02063i 0.844860 + 1.46334i
\(39\) 0 0
\(40\) 0.0716090 + 0.0413434i 0.0113224 + 0.00653697i
\(41\) 0.231836 0.865225i 0.0362067 0.135125i −0.945457 0.325748i \(-0.894384\pi\)
0.981663 + 0.190622i \(0.0610506\pi\)
\(42\) 0 0
\(43\) −2.14988 1.24124i −0.327854 0.189287i 0.327034 0.945013i \(-0.393951\pi\)
−0.654888 + 0.755726i \(0.727284\pi\)
\(44\) 0.255979 + 0.955327i 0.0385903 + 0.144021i
\(45\) 0 0
\(46\) −9.63832 9.63832i −1.42109 1.42109i
\(47\) −0.108435 0.404685i −0.0158169 0.0590293i 0.957566 0.288213i \(-0.0930611\pi\)
−0.973383 + 0.229184i \(0.926394\pi\)
\(48\) 0 0
\(49\) 6.01939 + 3.57308i 0.859913 + 0.510440i
\(50\) −2.39046 + 8.92133i −0.338063 + 1.26167i
\(51\) 0 0
\(52\) 3.82397 3.40616i 0.530290 0.472350i
\(53\) −5.75319 9.96481i −0.790261 1.36877i −0.925805 0.378001i \(-0.876612\pi\)
0.135544 0.990771i \(-0.456722\pi\)
\(54\) 0 0
\(55\) −0.0465120 + 0.0268537i −0.00627168 + 0.00362095i
\(56\) 1.40334 + 2.46498i 0.187530 + 0.329396i
\(57\) 0 0
\(58\) −6.59044 1.76590i −0.865367 0.231875i
\(59\) −9.90380 + 9.90380i −1.28937 + 1.28937i −0.354193 + 0.935172i \(0.615244\pi\)
−0.935172 + 0.354193i \(0.884756\pi\)
\(60\) 0 0
\(61\) 5.63177 3.25150i 0.721074 0.416312i −0.0940739 0.995565i \(-0.529989\pi\)
0.815148 + 0.579253i \(0.196656\pi\)
\(62\) −8.39395 14.5387i −1.06603 1.84642i
\(63\) 0 0
\(64\) 2.88522i 0.360652i
\(65\) 0.232408 + 0.152706i 0.0288267 + 0.0189408i
\(66\) 0 0
\(67\) −0.540059 2.01553i −0.0659787 0.246236i 0.925058 0.379826i \(-0.124016\pi\)
−0.991037 + 0.133590i \(0.957349\pi\)
\(68\) 1.75736i 0.213111i
\(69\) 0 0
\(70\) 0.268465 0.265237i 0.0320877 0.0317018i
\(71\) −0.119329 0.445340i −0.0141617 0.0528522i 0.958483 0.285148i \(-0.0920428\pi\)
−0.972645 + 0.232296i \(0.925376\pi\)
\(72\) 0 0
\(73\) −4.91231 1.31625i −0.574942 0.154055i −0.0403800 0.999184i \(-0.512857\pi\)
−0.534562 + 0.845129i \(0.679524\pi\)
\(74\) 8.51697 0.990078
\(75\) 0 0
\(76\) 7.72682 + 2.07040i 0.886328 + 0.237491i
\(77\) −1.84232 0.0111443i −0.209952 0.00127001i
\(78\) 0 0
\(79\) 3.26395 5.65332i 0.367223 0.636048i −0.621908 0.783091i \(-0.713642\pi\)
0.989130 + 0.147043i \(0.0469754\pi\)
\(80\) 0.359336 0.0962839i 0.0401750 0.0107649i
\(81\) 0 0
\(82\) −0.828301 1.43466i −0.0914705 0.158432i
\(83\) 9.54235 + 9.54235i 1.04741 + 1.04741i 0.998819 + 0.0485904i \(0.0154729\pi\)
0.0485904 + 0.998819i \(0.484527\pi\)
\(84\) 0 0
\(85\) 0.0921787 0.0246992i 0.00999818 0.00267900i
\(86\) −4.43466 + 1.18826i −0.478202 + 0.128134i
\(87\) 0 0
\(88\) −0.646521 0.373269i −0.0689193 0.0397906i
\(89\) −3.14679 + 3.14679i −0.333559 + 0.333559i −0.853936 0.520378i \(-0.825791\pi\)
0.520378 + 0.853936i \(0.325791\pi\)
\(90\) 0 0
\(91\) 4.23351 + 8.54853i 0.443793 + 0.896130i
\(92\) −10.4681 −1.09137
\(93\) 0 0
\(94\) −0.671022 0.387414i −0.0692106 0.0399588i
\(95\) 0.434393i 0.0445678i
\(96\) 0 0
\(97\) −15.6536 + 4.19437i −1.58938 + 0.425874i −0.941815 0.336132i \(-0.890881\pi\)
−0.647569 + 0.762007i \(0.724214\pi\)
\(98\) 12.5444 3.19911i 1.26717 0.323159i
\(99\) 0 0
\(100\) 3.54656 + 6.14282i 0.354656 + 0.614282i
\(101\) −5.06369 + 8.77056i −0.503856 + 0.872704i 0.496134 + 0.868246i \(0.334752\pi\)
−0.999990 + 0.00445781i \(0.998581\pi\)
\(102\) 0 0
\(103\) 1.47339 2.55198i 0.145177 0.251454i −0.784262 0.620430i \(-0.786958\pi\)
0.929439 + 0.368976i \(0.120291\pi\)
\(104\) −0.223002 + 3.85900i −0.0218672 + 0.378406i
\(105\) 0 0
\(106\) −20.5549 5.50767i −1.99647 0.534952i
\(107\) −16.8417 −1.62815 −0.814075 0.580760i \(-0.802755\pi\)
−0.814075 + 0.580760i \(0.802755\pi\)
\(108\) 0 0
\(109\) −10.8967 2.91975i −1.04371 0.279662i −0.304061 0.952653i \(-0.598343\pi\)
−0.739651 + 0.672991i \(0.765009\pi\)
\(110\) −0.0257077 + 0.0959425i −0.00245113 + 0.00914776i
\(111\) 0 0
\(112\) 12.3063 + 3.37738i 1.16284 + 0.319133i
\(113\) 5.69946 9.87175i 0.536160 0.928656i −0.462946 0.886386i \(-0.653208\pi\)
0.999106 0.0422699i \(-0.0134589\pi\)
\(114\) 0 0
\(115\) −0.147126 0.549082i −0.0137196 0.0512021i
\(116\) −4.53787 + 2.61994i −0.421331 + 0.243256i
\(117\) 0 0
\(118\) 25.9030i 2.38456i
\(119\) 3.15688 + 0.866382i 0.289390 + 0.0794211i
\(120\) 0 0
\(121\) −9.10635 + 5.25755i −0.827850 + 0.477959i
\(122\) 3.11274 11.6169i 0.281814 1.05175i
\(123\) 0 0
\(124\) −12.4535 3.33690i −1.11836 0.299663i
\(125\) −0.545050 + 0.545050i −0.0487507 + 0.0487507i
\(126\) 0 0
\(127\) −11.9564 + 6.90305i −1.06096 + 0.612547i −0.925698 0.378263i \(-0.876522\pi\)
−0.135264 + 0.990810i \(0.543188\pi\)
\(128\) 5.80986 + 5.80986i 0.513524 + 0.513524i
\(129\) 0 0
\(130\) 0.503625 0.104229i 0.0441708 0.00914147i
\(131\) 12.3717 + 7.14282i 1.08092 + 0.624071i 0.931145 0.364648i \(-0.118811\pi\)
0.149778 + 0.988720i \(0.452144\pi\)
\(132\) 0 0
\(133\) −7.52855 + 12.8596i −0.652808 + 1.11506i
\(134\) −3.34201 1.92951i −0.288706 0.166685i
\(135\) 0 0
\(136\) 0.937970 + 0.937970i 0.0804303 + 0.0804303i
\(137\) 2.98739 + 2.98739i 0.255230 + 0.255230i 0.823111 0.567881i \(-0.192236\pi\)
−0.567881 + 0.823111i \(0.692236\pi\)
\(138\) 0 0
\(139\) 8.52594 + 4.92246i 0.723161 + 0.417517i 0.815915 0.578172i \(-0.196234\pi\)
−0.0927539 + 0.995689i \(0.529567\pi\)
\(140\) 0.00175315 0.289824i 0.000148169 0.0244946i
\(141\) 0 0
\(142\) −0.738434 0.426335i −0.0619680 0.0357772i
\(143\) −2.09829 1.37870i −0.175468 0.115293i
\(144\) 0 0
\(145\) −0.201202 0.201202i −0.0167089 0.0167089i
\(146\) −8.14527 + 4.70267i −0.674107 + 0.389196i
\(147\) 0 0
\(148\) 4.62510 4.62510i 0.380181 0.380181i
\(149\) −3.39107 0.908635i −0.277807 0.0744383i 0.117225 0.993105i \(-0.462600\pi\)
−0.395033 + 0.918667i \(0.629267\pi\)
\(150\) 0 0
\(151\) 5.00350 18.6733i 0.407179 1.51961i −0.392821 0.919615i \(-0.628501\pi\)
0.800001 0.599999i \(-0.204832\pi\)
\(152\) −5.22915 + 3.01905i −0.424140 + 0.244877i
\(153\) 0 0
\(154\) −2.42383 + 2.39469i −0.195318 + 0.192969i
\(155\) 0.700121i 0.0562351i
\(156\) 0 0
\(157\) 2.19466 1.26709i 0.175153 0.101125i −0.409860 0.912148i \(-0.634423\pi\)
0.585013 + 0.811024i \(0.301089\pi\)
\(158\) −3.12465 11.6614i −0.248584 0.927729i
\(159\) 0 0
\(160\) 0.261314 0.452610i 0.0206587 0.0357820i
\(161\) 5.16079 18.8046i 0.406727 1.48201i
\(162\) 0 0
\(163\) 3.66969 13.6955i 0.287432 1.07271i −0.659611 0.751607i \(-0.729279\pi\)
0.947044 0.321105i \(-0.104054\pi\)
\(164\) −1.22889 0.329280i −0.0959601 0.0257124i
\(165\) 0 0
\(166\) 24.9576 1.93709
\(167\) 3.12094 + 0.836254i 0.241506 + 0.0647113i 0.377542 0.925993i \(-0.376770\pi\)
−0.136036 + 0.990704i \(0.543436\pi\)
\(168\) 0 0
\(169\) −1.49748 + 12.9135i −0.115190 + 0.993343i
\(170\) 0.0882449 0.152845i 0.00676807 0.0117226i
\(171\) 0 0
\(172\) −1.76294 + 3.05350i −0.134423 + 0.232828i
\(173\) 0.319180 + 0.552836i 0.0242668 + 0.0420314i 0.877904 0.478837i \(-0.158942\pi\)
−0.853637 + 0.520868i \(0.825608\pi\)
\(174\) 0 0
\(175\) −12.7832 + 3.34252i −0.966323 + 0.252671i
\(176\) −3.24426 + 0.869298i −0.244546 + 0.0655258i
\(177\) 0 0
\(178\) 8.23029i 0.616886i
\(179\) −6.77885 3.91377i −0.506675 0.292529i 0.224791 0.974407i \(-0.427830\pi\)
−0.731466 + 0.681878i \(0.761163\pi\)
\(180\) 0 0
\(181\) 7.74072 0.575363 0.287682 0.957726i \(-0.407115\pi\)
0.287682 + 0.957726i \(0.407115\pi\)
\(182\) 16.7155 + 5.64288i 1.23903 + 0.418278i
\(183\) 0 0
\(184\) 5.58722 5.58722i 0.411895 0.411895i
\(185\) 0.307604 + 0.177595i 0.0226155 + 0.0130571i
\(186\) 0 0
\(187\) −0.832234 + 0.222996i −0.0608590 + 0.0163071i
\(188\) −0.574779 + 0.154011i −0.0419200 + 0.0112324i
\(189\) 0 0
\(190\) 0.568069 + 0.568069i 0.0412120 + 0.0412120i
\(191\) 6.77349 + 11.7320i 0.490112 + 0.848899i 0.999935 0.0113800i \(-0.00362244\pi\)
−0.509823 + 0.860279i \(0.670289\pi\)
\(192\) 0 0
\(193\) 15.0008 4.01944i 1.07978 0.289326i 0.325273 0.945620i \(-0.394544\pi\)
0.754505 + 0.656295i \(0.227877\pi\)
\(194\) −14.9856 + 25.9558i −1.07590 + 1.86352i
\(195\) 0 0
\(196\) 5.07489 8.54942i 0.362492 0.610673i
\(197\) −12.9524 3.47059i −0.922822 0.247269i −0.234031 0.972229i \(-0.575192\pi\)
−0.688791 + 0.724960i \(0.741858\pi\)
\(198\) 0 0
\(199\) −3.28625 −0.232956 −0.116478 0.993193i \(-0.537160\pi\)
−0.116478 + 0.993193i \(0.537160\pi\)
\(200\) −5.17159 1.38572i −0.365686 0.0979854i
\(201\) 0 0
\(202\) 4.84759 + 18.0915i 0.341075 + 1.27291i
\(203\) −2.46921 9.44335i −0.173305 0.662793i
\(204\) 0 0
\(205\) 0.0690867i 0.00482523i
\(206\) −1.41051 5.26409i −0.0982748 0.366767i
\(207\) 0 0
\(208\) 11.5672 + 12.9861i 0.802043 + 0.900424i
\(209\) 3.92191i 0.271285i
\(210\) 0 0
\(211\) −6.31298 10.9344i −0.434604 0.752756i 0.562660 0.826689i \(-0.309778\pi\)
−0.997263 + 0.0739331i \(0.976445\pi\)
\(212\) −14.1531 + 8.17132i −0.972042 + 0.561209i
\(213\) 0 0
\(214\) −22.0244 + 22.0244i −1.50556 + 1.50556i
\(215\) −0.184943 0.0495553i −0.0126130 0.00337964i
\(216\) 0 0
\(217\) 12.1339 20.7260i 0.823704 1.40697i
\(218\) −18.0681 + 10.4316i −1.22373 + 0.706520i
\(219\) 0 0
\(220\) 0.0381407 + 0.0660616i 0.00257144 + 0.00445387i
\(221\) 2.96728 + 3.33126i 0.199601 + 0.224085i
\(222\) 0 0
\(223\) 5.22617 19.5043i 0.349971 1.30611i −0.536726 0.843756i \(-0.680339\pi\)
0.886697 0.462351i \(-0.152994\pi\)
\(224\) 15.5801 8.86994i 1.04099 0.592648i
\(225\) 0 0
\(226\) −5.45623 20.3629i −0.362943 1.35452i
\(227\) −9.03303 9.03303i −0.599543 0.599543i 0.340648 0.940191i \(-0.389354\pi\)
−0.940191 + 0.340648i \(0.889354\pi\)
\(228\) 0 0
\(229\) 3.18409 + 11.8832i 0.210410 + 0.785262i 0.987732 + 0.156159i \(0.0499112\pi\)
−0.777322 + 0.629104i \(0.783422\pi\)
\(230\) −0.910452 0.525649i −0.0600334 0.0346603i
\(231\) 0 0
\(232\) 1.02367 3.82040i 0.0672074 0.250821i
\(233\) 0.0361142 + 0.0208505i 0.00236592 + 0.00136596i 0.501182 0.865342i \(-0.332899\pi\)
−0.498817 + 0.866708i \(0.666232\pi\)
\(234\) 0 0
\(235\) −0.0161567 0.0279842i −0.00105395 0.00182549i
\(236\) 14.0665 + 14.0665i 0.915651 + 0.915651i
\(237\) 0 0
\(238\) 5.26133 2.99534i 0.341042 0.194159i
\(239\) −1.45212 + 1.45212i −0.0939296 + 0.0939296i −0.752510 0.658581i \(-0.771157\pi\)
0.658581 + 0.752510i \(0.271157\pi\)
\(240\) 0 0
\(241\) −1.95322 + 1.95322i −0.125818 + 0.125818i −0.767212 0.641394i \(-0.778356\pi\)
0.641394 + 0.767212i \(0.278356\pi\)
\(242\) −5.03318 + 18.7841i −0.323545 + 1.20749i
\(243\) 0 0
\(244\) −4.61815 7.99887i −0.295647 0.512075i
\(245\) 0.519768 + 0.146033i 0.0332068 + 0.00932972i
\(246\) 0 0
\(247\) −18.1428 + 9.12199i −1.15440 + 0.580419i
\(248\) 8.42793 4.86587i 0.535174 0.308983i
\(249\) 0 0
\(250\) 1.42556i 0.0901600i
\(251\) −11.9299 + 20.6631i −0.753006 + 1.30424i 0.193353 + 0.981129i \(0.438064\pi\)
−0.946359 + 0.323116i \(0.895270\pi\)
\(252\) 0 0
\(253\) 1.32833 + 4.95738i 0.0835111 + 0.311668i
\(254\) −6.60846 + 24.6631i −0.414652 + 1.54750i
\(255\) 0 0
\(256\) 20.9659 1.31037
\(257\) −6.71724 −0.419010 −0.209505 0.977808i \(-0.567185\pi\)
−0.209505 + 0.977808i \(0.567185\pi\)
\(258\) 0 0
\(259\) 6.02822 + 10.5886i 0.374575 + 0.657943i
\(260\) 0.216890 0.330092i 0.0134510 0.0204714i
\(261\) 0 0
\(262\) 25.5198 6.83800i 1.57662 0.422453i
\(263\) 7.73235 13.3928i 0.476797 0.825836i −0.522850 0.852425i \(-0.675131\pi\)
0.999646 + 0.0265886i \(0.00846440\pi\)
\(264\) 0 0
\(265\) −0.627528 0.627528i −0.0385487 0.0385487i
\(266\) 6.97151 + 26.6621i 0.427451 + 1.63476i
\(267\) 0 0
\(268\) −2.86268 + 0.767052i −0.174866 + 0.0468552i
\(269\) 0.350892i 0.0213943i −0.999943 0.0106971i \(-0.996595\pi\)
0.999943 0.0106971i \(-0.00340507\pi\)
\(270\) 0 0
\(271\) 7.06051 7.06051i 0.428895 0.428895i −0.459357 0.888252i \(-0.651920\pi\)
0.888252 + 0.459357i \(0.151920\pi\)
\(272\) 5.96794 0.361860
\(273\) 0 0
\(274\) 7.81340 0.472025
\(275\) 2.45902 2.45902i 0.148285 0.148285i
\(276\) 0 0
\(277\) 9.69499i 0.582516i −0.956645 0.291258i \(-0.905926\pi\)
0.956645 0.291258i \(-0.0940738\pi\)
\(278\) 17.5869 4.71239i 1.05479 0.282630i
\(279\) 0 0
\(280\) 0.153754 + 0.155626i 0.00918859 + 0.00930043i
\(281\) 22.0548 + 22.0548i 1.31568 + 1.31568i 0.917161 + 0.398518i \(0.130475\pi\)
0.398518 + 0.917161i \(0.369525\pi\)
\(282\) 0 0
\(283\) 2.07530 3.59453i 0.123364 0.213673i −0.797728 0.603017i \(-0.793965\pi\)
0.921092 + 0.389344i \(0.127298\pi\)
\(284\) −0.632522 + 0.169484i −0.0375333 + 0.0100570i
\(285\) 0 0
\(286\) −4.54697 + 0.941028i −0.268868 + 0.0556441i
\(287\) 1.19735 2.04521i 0.0706776 0.120725i
\(288\) 0 0
\(289\) −15.4691 −0.909946
\(290\) −0.526236 −0.0309016
\(291\) 0 0
\(292\) −1.86949 + 6.97701i −0.109403 + 0.408299i
\(293\) −4.12495 15.3945i −0.240982 0.899357i −0.975361 0.220617i \(-0.929193\pi\)
0.734379 0.678740i \(-0.237474\pi\)
\(294\) 0 0
\(295\) −0.540128 + 0.935529i −0.0314475 + 0.0544686i
\(296\) 4.93718i 0.286968i
\(297\) 0 0
\(298\) −5.62285 + 3.24635i −0.325723 + 0.188056i
\(299\) 19.8433 17.6752i 1.14757 1.02219i
\(300\) 0 0
\(301\) −4.61610 4.67228i −0.266068 0.269306i
\(302\) −17.8764 30.9629i −1.02867 1.78171i
\(303\) 0 0
\(304\) −7.03100 + 26.2401i −0.403256 + 1.50497i
\(305\) 0.354657 0.354657i 0.0203076 0.0203076i
\(306\) 0 0
\(307\) 5.87701 5.87701i 0.335419 0.335419i −0.519221 0.854640i \(-0.673778\pi\)
0.854640 + 0.519221i \(0.173778\pi\)
\(308\) −0.0158283 + 2.61667i −0.000901902 + 0.149099i
\(309\) 0 0
\(310\) −0.915569 0.915569i −0.0520008 0.0520008i
\(311\) −12.8619 22.2775i −0.729331 1.26324i −0.957166 0.289539i \(-0.906498\pi\)
0.227835 0.973700i \(-0.426835\pi\)
\(312\) 0 0
\(313\) −19.5449 11.2842i −1.10474 0.637823i −0.167280 0.985909i \(-0.553498\pi\)
−0.937463 + 0.348086i \(0.886832\pi\)
\(314\) 1.21301 4.52703i 0.0684543 0.255475i
\(315\) 0 0
\(316\) −8.02948 4.63582i −0.451693 0.260785i
\(317\) 2.81372 + 10.5010i 0.158034 + 0.589792i 0.998826 + 0.0484339i \(0.0154230\pi\)
−0.840792 + 0.541358i \(0.817910\pi\)
\(318\) 0 0
\(319\) 1.81655 + 1.81655i 0.101707 + 0.101707i
\(320\) −0.0575950 0.214947i −0.00321966 0.0120159i
\(321\) 0 0
\(322\) −17.8424 31.3402i −0.994318 1.74652i
\(323\) −1.80363 + 6.73123i −0.100356 + 0.374536i
\(324\) 0 0
\(325\) −17.0949 5.65602i −0.948256 0.313740i
\(326\) −13.1110 22.7089i −0.726152 1.25773i
\(327\) 0 0
\(328\) 0.831654 0.480156i 0.0459204 0.0265122i
\(329\) 0.00670501 1.10844i 0.000369659 0.0611105i
\(330\) 0 0
\(331\) 20.9107 + 5.60302i 1.14936 + 0.307970i 0.782708 0.622389i \(-0.213838\pi\)
0.366650 + 0.930359i \(0.380505\pi\)
\(332\) 13.5531 13.5531i 0.743824 0.743824i
\(333\) 0 0
\(334\) 5.17494 2.98775i 0.283160 0.163483i
\(335\) −0.0804682 0.139375i −0.00439645 0.00761487i
\(336\) 0 0
\(337\) 15.6989i 0.855172i 0.903975 + 0.427586i \(0.140636\pi\)
−0.903975 + 0.427586i \(0.859364\pi\)
\(338\) 14.9290 + 18.8456i 0.812032 + 1.02507i
\(339\) 0 0
\(340\) −0.0350806 0.130923i −0.00190251 0.00710027i
\(341\) 6.32103i 0.342303i
\(342\) 0 0
\(343\) 12.8560 + 13.3313i 0.694159 + 0.719821i
\(344\) −0.688822 2.57072i −0.0371388 0.138604i
\(345\) 0 0
\(346\) 1.14036 + 0.305559i 0.0613062 + 0.0164270i
\(347\) 20.2272 1.08585 0.542927 0.839780i \(-0.317316\pi\)
0.542927 + 0.839780i \(0.317316\pi\)
\(348\) 0 0
\(349\) −22.3749 5.99533i −1.19770 0.320923i −0.395775 0.918348i \(-0.629524\pi\)
−0.801925 + 0.597425i \(0.796191\pi\)
\(350\) −12.3459 + 21.0881i −0.659917 + 1.12721i
\(351\) 0 0
\(352\) −2.35927 + 4.08638i −0.125750 + 0.217805i
\(353\) −12.3710 + 3.31480i −0.658442 + 0.176429i −0.572543 0.819875i \(-0.694043\pi\)
−0.0858994 + 0.996304i \(0.527376\pi\)
\(354\) 0 0
\(355\) −0.0177798 0.0307956i −0.000943656 0.00163446i
\(356\) 4.46942 + 4.46942i 0.236879 + 0.236879i
\(357\) 0 0
\(358\) −13.9830 + 3.74675i −0.739027 + 0.198022i
\(359\) 26.0068 6.96850i 1.37259 0.367783i 0.504163 0.863608i \(-0.331801\pi\)
0.868423 + 0.495825i \(0.165134\pi\)
\(360\) 0 0
\(361\) −11.0167 6.36050i −0.579827 0.334763i
\(362\) 10.1228 10.1228i 0.532041 0.532041i
\(363\) 0 0
\(364\) 12.1416 6.01291i 0.636392 0.315162i
\(365\) −0.392240 −0.0205308
\(366\) 0 0
\(367\) −21.5194 12.4242i −1.12330 0.648540i −0.181062 0.983472i \(-0.557953\pi\)
−0.942242 + 0.334932i \(0.891287\pi\)
\(368\) 35.5493i 1.85314i
\(369\) 0 0
\(370\) 0.634510 0.170016i 0.0329866 0.00883874i
\(371\) −7.70121 29.4528i −0.399827 1.52911i
\(372\) 0 0
\(373\) 16.7470 + 29.0067i 0.867129 + 1.50191i 0.864918 + 0.501914i \(0.167371\pi\)
0.00221133 + 0.999998i \(0.499296\pi\)
\(374\) −0.796718 + 1.37996i −0.0411973 + 0.0713558i
\(375\) 0 0
\(376\) 0.224579 0.388983i 0.0115818 0.0200603i
\(377\) 4.17827 12.6285i 0.215192 0.650401i
\(378\) 0 0
\(379\) 2.63846 + 0.706973i 0.135529 + 0.0363148i 0.325946 0.945389i \(-0.394317\pi\)
−0.190417 + 0.981703i \(0.560984\pi\)
\(380\) 0.616974 0.0316501
\(381\) 0 0
\(382\) 24.2002 + 6.48442i 1.23819 + 0.331772i
\(383\) −5.37033 + 20.0424i −0.274411 + 1.02412i 0.681824 + 0.731516i \(0.261187\pi\)
−0.956235 + 0.292600i \(0.905480\pi\)
\(384\) 0 0
\(385\) −0.137475 + 0.0359464i −0.00700636 + 0.00183200i
\(386\) 14.3606 24.8733i 0.730935 1.26602i
\(387\) 0 0
\(388\) 5.95732 + 22.2330i 0.302437 + 1.12871i
\(389\) −29.3050 + 16.9193i −1.48582 + 0.857841i −0.999870 0.0161427i \(-0.994861\pi\)
−0.485955 + 0.873984i \(0.661528\pi\)
\(390\) 0 0
\(391\) 9.11928i 0.461182i
\(392\) 1.85449 + 7.27181i 0.0936657 + 0.367282i
\(393\) 0 0
\(394\) −21.4769 + 12.3997i −1.08199 + 0.624686i
\(395\) 0.130310 0.486325i 0.00655662 0.0244697i
\(396\) 0 0
\(397\) −4.02654 1.07891i −0.202086 0.0541488i 0.156356 0.987701i \(-0.450025\pi\)
−0.358442 + 0.933552i \(0.616692\pi\)
\(398\) −4.29752 + 4.29752i −0.215415 + 0.215415i
\(399\) 0 0
\(400\) −20.8608 + 12.0440i −1.04304 + 0.602200i
\(401\) −26.9224 26.9224i −1.34444 1.34444i −0.891584 0.452856i \(-0.850405\pi\)
−0.452856 0.891584i \(-0.649595\pi\)
\(402\) 0 0
\(403\) 29.2412 14.7021i 1.45661 0.732364i
\(404\) 12.4569 + 7.19202i 0.619756 + 0.357816i
\(405\) 0 0
\(406\) −15.5784 9.12028i −0.773143 0.452632i
\(407\) −2.77720 1.60342i −0.137661 0.0794785i
\(408\) 0 0
\(409\) 13.5134 + 13.5134i 0.668194 + 0.668194i 0.957298 0.289104i \(-0.0933573\pi\)
−0.289104 + 0.957298i \(0.593357\pi\)
\(410\) −0.0903468 0.0903468i −0.00446191 0.00446191i
\(411\) 0 0
\(412\) −3.62461 2.09267i −0.178572 0.103098i
\(413\) −32.2035 + 18.3339i −1.58463 + 0.902150i
\(414\) 0 0
\(415\) 0.901386 + 0.520415i 0.0442473 + 0.0255462i
\(416\) 24.3911 + 1.40950i 1.19587 + 0.0691066i
\(417\) 0 0
\(418\) −5.12880 5.12880i −0.250858 0.250858i
\(419\) 29.2306 16.8763i 1.42801 0.824460i 0.431043 0.902331i \(-0.358146\pi\)
0.996963 + 0.0778716i \(0.0248124\pi\)
\(420\) 0 0
\(421\) 20.2556 20.2556i 0.987197 0.987197i −0.0127222 0.999919i \(-0.504050\pi\)
0.999919 + 0.0127222i \(0.00404970\pi\)
\(422\) −22.5549 6.04357i −1.09796 0.294196i
\(423\) 0 0
\(424\) 3.19273 11.9154i 0.155053 0.578664i
\(425\) −5.35132 + 3.08958i −0.259577 + 0.149867i
\(426\) 0 0
\(427\) 16.6457 4.35246i 0.805542 0.210630i
\(428\) 23.9205i 1.15624i
\(429\) 0 0
\(430\) −0.306660 + 0.177050i −0.0147885 + 0.00853812i
\(431\) −4.52853 16.9007i −0.218132 0.814079i −0.985041 0.172323i \(-0.944873\pi\)
0.766909 0.641756i \(-0.221794\pi\)
\(432\) 0 0
\(433\) 6.74582 11.6841i 0.324184 0.561502i −0.657163 0.753748i \(-0.728244\pi\)
0.981347 + 0.192246i \(0.0615771\pi\)
\(434\) −11.2361 42.9719i −0.539352 2.06272i
\(435\) 0 0
\(436\) −4.14696 + 15.4767i −0.198603 + 0.741198i
\(437\) 40.0960 + 10.7437i 1.91805 + 0.513940i
\(438\) 0 0
\(439\) −23.7377 −1.13294 −0.566470 0.824082i \(-0.691691\pi\)
−0.566470 + 0.824082i \(0.691691\pi\)
\(440\) −0.0556167 0.0149024i −0.00265142 0.000710446i
\(441\) 0 0
\(442\) 8.23678 + 0.475984i 0.391784 + 0.0226402i
\(443\) −17.9783 + 31.1393i −0.854173 + 1.47947i 0.0232374 + 0.999730i \(0.492603\pi\)
−0.877410 + 0.479741i \(0.840731\pi\)
\(444\) 0 0
\(445\) −0.171618 + 0.297250i −0.00813545 + 0.0140910i
\(446\) −18.6720 32.3408i −0.884144 1.53138i
\(447\) 0 0
\(448\) 2.02028 7.36138i 0.0954492 0.347792i
\(449\) −27.2216 + 7.29399i −1.28466 + 0.344225i −0.835632 0.549290i \(-0.814898\pi\)
−0.449033 + 0.893515i \(0.648231\pi\)
\(450\) 0 0
\(451\) 0.623749i 0.0293712i
\(452\) −14.0210 8.09501i −0.659491 0.380757i
\(453\) 0 0
\(454\) −23.6255 −1.10880
\(455\) 0.486041 + 0.552352i 0.0227860 + 0.0258946i
\(456\) 0 0
\(457\) 0.0883512 0.0883512i 0.00413290 0.00413290i −0.705037 0.709170i \(-0.749070\pi\)
0.709170 + 0.705037i \(0.249070\pi\)
\(458\) 19.7039 + 11.3761i 0.920703 + 0.531568i
\(459\) 0 0
\(460\) −0.779868 + 0.208965i −0.0363615 + 0.00974304i
\(461\) 16.8148 4.50551i 0.783143 0.209843i 0.154973 0.987919i \(-0.450471\pi\)
0.628170 + 0.778076i \(0.283804\pi\)
\(462\) 0 0
\(463\) −1.07038 1.07038i −0.0497447 0.0497447i 0.681797 0.731542i \(-0.261199\pi\)
−0.731542 + 0.681797i \(0.761199\pi\)
\(464\) −8.89725 15.4105i −0.413044 0.715414i
\(465\) 0 0
\(466\) 0.0744944 0.0199607i 0.00345089 0.000924663i
\(467\) 14.6317 25.3429i 0.677075 1.17273i −0.298782 0.954321i \(-0.596580\pi\)
0.975858 0.218408i \(-0.0700862\pi\)
\(468\) 0 0
\(469\) 0.0333942 5.52059i 0.00154200 0.254917i
\(470\) −0.0577244 0.0154672i −0.00266263 0.000713449i
\(471\) 0 0
\(472\) −15.0156 −0.691151
\(473\) 1.66975 + 0.447409i 0.0767754 + 0.0205719i
\(474\) 0 0
\(475\) −7.27985 27.1688i −0.334023 1.24659i
\(476\) 1.23053 4.48375i 0.0564014 0.205512i
\(477\) 0 0
\(478\) 3.79795i 0.173714i
\(479\) 0.884245 + 3.30005i 0.0404022 + 0.150783i 0.983180 0.182638i \(-0.0584636\pi\)
−0.942778 + 0.333421i \(0.891797\pi\)
\(480\) 0 0
\(481\) −0.957931 + 16.5768i −0.0436779 + 0.755836i
\(482\) 5.10857i 0.232689i
\(483\) 0 0
\(484\) 7.46736 + 12.9339i 0.339426 + 0.587903i
\(485\) −1.08246 + 0.624958i −0.0491519 + 0.0283779i
\(486\) 0 0
\(487\) −4.37510 + 4.37510i −0.198255 + 0.198255i −0.799251 0.600997i \(-0.794770\pi\)
0.600997 + 0.799251i \(0.294770\pi\)
\(488\) 6.73418 + 1.80442i 0.304842 + 0.0816822i
\(489\) 0 0
\(490\) 0.870688 0.488744i 0.0393337 0.0220792i
\(491\) 33.1219 19.1229i 1.49477 0.863006i 0.494788 0.869014i \(-0.335246\pi\)
0.999982 + 0.00600745i \(0.00191224\pi\)
\(492\) 0 0
\(493\) −2.28236 3.95317i −0.102793 0.178042i
\(494\) −11.7968 + 35.6550i −0.530764 + 1.60419i
\(495\) 0 0
\(496\) 11.3320 42.2917i 0.508823 1.89895i
\(497\) 0.00737861 1.21980i 0.000330976 0.0547156i
\(498\) 0 0
\(499\) −1.07153 3.99901i −0.0479684 0.179020i 0.937785 0.347216i \(-0.112873\pi\)
−0.985754 + 0.168195i \(0.946206\pi\)
\(500\) 0.774141 + 0.774141i 0.0346206 + 0.0346206i
\(501\) 0 0
\(502\) 11.4207 + 42.6228i 0.509733 + 1.90235i
\(503\) 20.9643 + 12.1038i 0.934752 + 0.539680i 0.888311 0.459241i \(-0.151879\pi\)
0.0464410 + 0.998921i \(0.485212\pi\)
\(504\) 0 0
\(505\) −0.202163 + 0.754484i −0.00899616 + 0.0335741i
\(506\) 8.22000 + 4.74582i 0.365424 + 0.210977i
\(507\) 0 0
\(508\) 9.80449 + 16.9819i 0.435004 + 0.753449i
\(509\) 16.4577 + 16.4577i 0.729476 + 0.729476i 0.970515 0.241039i \(-0.0774883\pi\)
−0.241039 + 0.970515i \(0.577488\pi\)
\(510\) 0 0
\(511\) −11.6117 6.79797i −0.513670 0.300725i
\(512\) 15.7980 15.7980i 0.698179 0.698179i
\(513\) 0 0
\(514\) −8.78434 + 8.78434i −0.387460 + 0.387460i
\(515\) 0.0588237 0.219533i 0.00259208 0.00967379i
\(516\) 0 0
\(517\) 0.145871 + 0.252655i 0.00641538 + 0.0111118i
\(518\) 21.7303 + 5.96373i 0.954774 + 0.262031i
\(519\) 0 0
\(520\) 0.0604201 + 0.291945i 0.00264960 + 0.0128026i
\(521\) −29.3950 + 16.9712i −1.28782 + 0.743522i −0.978265 0.207360i \(-0.933513\pi\)
−0.309553 + 0.950882i \(0.600179\pi\)
\(522\) 0 0
\(523\) 7.59842i 0.332256i 0.986104 + 0.166128i \(0.0531264\pi\)
−0.986104 + 0.166128i \(0.946874\pi\)
\(524\) 10.1450 17.5717i 0.443188 0.767624i
\(525\) 0 0
\(526\) −7.40236 27.6260i −0.322758 1.20455i
\(527\) 2.90694 10.8489i 0.126628 0.472584i
\(528\) 0 0
\(529\) −31.3209 −1.36178
\(530\) −1.64127 −0.0712924
\(531\) 0 0
\(532\) 18.2646 + 10.6929i 0.791870 + 0.463595i
\(533\) 2.88547 1.45078i 0.124984 0.0628402i
\(534\) 0 0
\(535\) −1.25470 + 0.336196i −0.0542454 + 0.0145350i
\(536\) 1.11851 1.93732i 0.0483125 0.0836797i
\(537\) 0 0
\(538\) −0.458872 0.458872i −0.0197834 0.0197834i
\(539\) −4.69272 1.31846i −0.202130 0.0567901i
\(540\) 0 0
\(541\) −22.5943 + 6.05411i −0.971403 + 0.260287i −0.709420 0.704786i \(-0.751043\pi\)
−0.261983 + 0.965073i \(0.584376\pi\)
\(542\) 18.4665i 0.793203i
\(543\) 0 0
\(544\) 5.92851 5.92851i 0.254183 0.254183i
\(545\) −0.870081 −0.0372702
\(546\) 0 0
\(547\) 39.6600 1.69574 0.847870 0.530204i \(-0.177885\pi\)
0.847870 + 0.530204i \(0.177885\pi\)
\(548\) 4.24303 4.24303i 0.181253 0.181253i
\(549\) 0 0
\(550\) 6.43147i 0.274239i
\(551\) 20.0704 5.37784i 0.855026 0.229104i
\(552\) 0 0
\(553\) 12.2862 12.1385i 0.522463 0.516180i
\(554\) −12.6784 12.6784i −0.538655 0.538655i
\(555\) 0 0
\(556\) 6.99142 12.1095i 0.296502 0.513557i
\(557\) 11.3970 3.05383i 0.482908 0.129395i −0.00914829 0.999958i \(-0.502912\pi\)
0.492056 + 0.870563i \(0.336245\pi\)
\(558\) 0 0
\(559\) −1.81397 8.76494i −0.0767226 0.370717i
\(560\) 0.984234 + 0.00595366i 0.0415915 + 0.000251588i
\(561\) 0 0
\(562\) 57.6834 2.43323
\(563\) −18.3834 −0.774770 −0.387385 0.921918i \(-0.626622\pi\)
−0.387385 + 0.921918i \(0.626622\pi\)
\(564\) 0 0
\(565\) 0.227546 0.849214i 0.00957294 0.0357267i
\(566\) −1.98674 7.41460i −0.0835088 0.311659i
\(567\) 0 0
\(568\) 0.247141 0.428061i 0.0103698 0.0179610i
\(569\) 13.5278i 0.567116i −0.958955 0.283558i \(-0.908485\pi\)
0.958955 0.283558i \(-0.0915149\pi\)
\(570\) 0 0
\(571\) −12.8299 + 7.40732i −0.536913 + 0.309987i −0.743827 0.668372i \(-0.766991\pi\)
0.206914 + 0.978359i \(0.433658\pi\)
\(572\) −1.95819 + 2.98023i −0.0818760 + 0.124610i
\(573\) 0 0
\(574\) −1.10876 4.24039i −0.0462789 0.176991i
\(575\) 18.4038 + 31.8763i 0.767490 + 1.32933i
\(576\) 0 0
\(577\) −5.26970 + 19.6668i −0.219381 + 0.818740i 0.765198 + 0.643795i \(0.222641\pi\)
−0.984578 + 0.174944i \(0.944025\pi\)
\(578\) −20.2294 + 20.2294i −0.841431 + 0.841431i
\(579\) 0 0
\(580\) −0.285770 + 0.285770i −0.0118659 + 0.0118659i
\(581\) 17.6647 + 31.0282i 0.732857 + 1.28727i
\(582\) 0 0
\(583\) 5.66563 + 5.66563i 0.234646 + 0.234646i
\(584\) −2.72608 4.72171i −0.112806 0.195386i
\(585\) 0 0
\(586\) −25.5262 14.7375i −1.05448 0.608802i
\(587\) 7.64015 28.5134i 0.315343 1.17688i −0.608327 0.793686i \(-0.708159\pi\)
0.923670 0.383189i \(-0.125174\pi\)
\(588\) 0 0
\(589\) 44.2759 + 25.5627i 1.82436 + 1.05329i
\(590\) 0.517078 + 1.92976i 0.0212877 + 0.0794470i
\(591\) 0 0
\(592\) 15.7067 + 15.7067i 0.645541 + 0.645541i
\(593\) 9.26744 + 34.5866i 0.380568 + 1.42030i 0.845036 + 0.534710i \(0.179579\pi\)
−0.464467 + 0.885590i \(0.653754\pi\)
\(594\) 0 0
\(595\) 0.252480 + 0.00152726i 0.0103507 + 6.26116e-5i
\(596\) −1.29055 + 4.81638i −0.0528628 + 0.197287i
\(597\) 0 0
\(598\) 2.83530 49.0641i 0.115944 2.00638i
\(599\) −3.11170 5.38963i −0.127141 0.220214i 0.795427 0.606049i \(-0.207247\pi\)
−0.922568 + 0.385835i \(0.873913\pi\)
\(600\) 0 0
\(601\) 0.0256568 0.0148129i 0.00104656 0.000604232i −0.499477 0.866327i \(-0.666474\pi\)
0.500523 + 0.865723i \(0.333141\pi\)
\(602\) −12.1467 0.0734756i −0.495062 0.00299464i
\(603\) 0 0
\(604\) −26.5220 7.10654i −1.07916 0.289161i
\(605\) −0.573467 + 0.573467i −0.0233147 + 0.0233147i
\(606\) 0 0
\(607\) 22.7071 13.1100i 0.921653 0.532117i 0.0374913 0.999297i \(-0.488063\pi\)
0.884162 + 0.467180i \(0.154730\pi\)
\(608\) 19.0822 + 33.0513i 0.773883 + 1.34041i
\(609\) 0 0
\(610\) 0.927591i 0.0375571i
\(611\) 0.829506 1.26245i 0.0335582 0.0510733i
\(612\) 0 0
\(613\) 7.02053 + 26.2010i 0.283556 + 1.05825i 0.949888 + 0.312591i \(0.101197\pi\)
−0.666331 + 0.745656i \(0.732136\pi\)
\(614\) 15.3711i 0.620326i
\(615\) 0 0
\(616\) −1.38817 1.40507i −0.0559310 0.0566117i
\(617\) 10.0810 + 37.6229i 0.405847 + 1.51464i 0.802488 + 0.596668i \(0.203509\pi\)
−0.396641 + 0.917974i \(0.629824\pi\)
\(618\) 0 0
\(619\) 28.5176 + 7.64126i 1.14622 + 0.307128i 0.781448 0.623970i \(-0.214481\pi\)
0.364769 + 0.931098i \(0.381148\pi\)
\(620\) −0.994390 −0.0399357
\(621\) 0 0
\(622\) −45.9528 12.3130i −1.84254 0.493707i
\(623\) −10.2322 + 5.82531i −0.409943 + 0.233386i
\(624\) 0 0
\(625\) 12.4554 21.5734i 0.498216 0.862936i
\(626\) −40.3162 + 10.8027i −1.61136 + 0.431762i
\(627\) 0 0
\(628\) −1.79966 3.11710i −0.0718142 0.124386i
\(629\) 4.02916 + 4.02916i 0.160653 + 0.160653i
\(630\) 0 0
\(631\) 36.5172 9.78475i 1.45373 0.389525i 0.556408 0.830909i \(-0.312179\pi\)
0.897318 + 0.441384i \(0.145512\pi\)
\(632\) 6.75995 1.81132i 0.268896 0.0720506i
\(633\) 0 0
\(634\) 17.4120 + 10.0528i 0.691518 + 0.399248i
\(635\) −0.752949 + 0.752949i −0.0298799 + 0.0298799i
\(636\) 0 0
\(637\) 4.81560 + 24.7752i 0.190801 + 0.981629i
\(638\) 4.75111 0.188098
\(639\) 0 0
\(640\) 0.548808 + 0.316855i 0.0216936 + 0.0125248i
\(641\) 4.14733i 0.163810i −0.996640 0.0819049i \(-0.973900\pi\)
0.996640 0.0819049i \(-0.0261004\pi\)
\(642\) 0 0
\(643\) 39.3048 10.5317i 1.55003 0.415330i 0.620541 0.784174i \(-0.286913\pi\)
0.929491 + 0.368845i \(0.120247\pi\)
\(644\) −26.7084 7.32993i −1.05246 0.288840i
\(645\) 0 0
\(646\) 6.44397 + 11.1613i 0.253535 + 0.439135i
\(647\) −17.8485 + 30.9146i −0.701698 + 1.21538i 0.266172 + 0.963926i \(0.414241\pi\)
−0.967870 + 0.251451i \(0.919092\pi\)
\(648\) 0 0
\(649\) 4.87654 8.44641i 0.191421 0.331551i
\(650\) −29.7521 + 14.9590i −1.16697 + 0.586740i
\(651\) 0 0
\(652\) −19.4518 5.21211i −0.761793 0.204122i
\(653\) −35.3648 −1.38393 −0.691966 0.721930i \(-0.743255\pi\)
−0.691966 + 0.721930i \(0.743255\pi\)
\(654\) 0 0
\(655\) 1.06427 + 0.285171i 0.0415846 + 0.0111426i
\(656\) 1.11822 4.17327i 0.0436593 0.162939i
\(657\) 0 0
\(658\) −1.44078 1.45831i −0.0561674 0.0568510i
\(659\) 1.02268 1.77133i 0.0398378 0.0690011i −0.845419 0.534104i \(-0.820649\pi\)
0.885257 + 0.465103i \(0.153983\pi\)
\(660\) 0 0
\(661\) −5.33936 19.9268i −0.207677 0.775061i −0.988617 0.150455i \(-0.951926\pi\)
0.780940 0.624606i \(-0.214740\pi\)
\(662\) 34.6728 20.0184i 1.34760 0.778036i
\(663\) 0 0
\(664\) 14.4676i 0.561453i
\(665\) −0.304170 + 1.10832i −0.0117952 + 0.0429786i
\(666\) 0 0
\(667\) −23.5479 + 13.5954i −0.911778 + 0.526415i
\(668\) 1.18774 4.43271i 0.0459551 0.171507i
\(669\) 0 0
\(670\) −0.287496 0.0770342i −0.0111069 0.00297609i
\(671\) −3.20202 + 3.20202i −0.123613 + 0.123613i
\(672\) 0 0
\(673\) 17.7096 10.2246i 0.682655 0.394131i −0.118199 0.992990i \(-0.537712\pi\)
0.800855 + 0.598859i \(0.204379\pi\)
\(674\) 20.5299 + 20.5299i 0.790781 + 0.790781i
\(675\) 0 0
\(676\) 18.3412 + 2.12688i 0.705429 + 0.0818032i
\(677\) 38.1123 + 22.0042i 1.46478 + 0.845689i 0.999226 0.0393333i \(-0.0125234\pi\)
0.465549 + 0.885022i \(0.345857\pi\)
\(678\) 0 0
\(679\) −42.8758 0.259357i −1.64542 0.00995319i
\(680\) 0.0886022 + 0.0511545i 0.00339774 + 0.00196169i
\(681\) 0 0
\(682\) 8.26620 + 8.26620i 0.316529 + 0.316529i
\(683\) 3.43053 + 3.43053i 0.131265 + 0.131265i 0.769687 0.638422i \(-0.220412\pi\)
−0.638422 + 0.769687i \(0.720412\pi\)
\(684\) 0 0
\(685\) 0.282194 + 0.162925i 0.0107821 + 0.00622504i
\(686\) 34.2459 + 0.621523i 1.30751 + 0.0237299i
\(687\) 0 0
\(688\) −10.3696 5.98690i −0.395338 0.228248i
\(689\) 13.0316 39.3870i 0.496463 1.50052i
\(690\) 0 0
\(691\) 32.7898 + 32.7898i 1.24738 + 1.24738i 0.956872 + 0.290511i \(0.0938254\pi\)
0.290511 + 0.956872i \(0.406175\pi\)
\(692\) 0.785200 0.453336i 0.0298488 0.0172332i
\(693\) 0 0
\(694\) 26.4517 26.4517i 1.00409 1.00409i
\(695\) 0.733441 + 0.196525i 0.0278210 + 0.00745462i
\(696\) 0 0
\(697\) 0.286852 1.07055i 0.0108653 0.0405499i
\(698\) −37.1006 + 21.4200i −1.40428 + 0.810760i
\(699\) 0 0
\(700\) 4.74742 + 18.1562i 0.179436 + 0.686240i
\(701\) 16.7923i 0.634236i 0.948386 + 0.317118i \(0.102715\pi\)
−0.948386 + 0.317118i \(0.897285\pi\)
\(702\) 0 0
\(703\) −22.4624 + 12.9687i −0.847186 + 0.489123i
\(704\) 0.519996 + 1.94065i 0.0195981 + 0.0731410i
\(705\) 0 0
\(706\) −11.8431 + 20.5128i −0.445720 + 0.772009i
\(707\) −19.0608 + 18.8316i −0.716857 + 0.708236i
\(708\) 0 0
\(709\) −1.77899 + 6.63927i −0.0668113 + 0.249343i −0.991252 0.131983i \(-0.957866\pi\)
0.924441 + 0.381326i \(0.124532\pi\)
\(710\) −0.0635235 0.0170211i −0.00238399 0.000638789i
\(711\) 0 0
\(712\) −4.77100 −0.178801
\(713\) −64.6235 17.3158i −2.42017 0.648483i
\(714\) 0 0
\(715\) −0.183844 0.0608265i −0.00687536 0.00227478i
\(716\) −5.55877 + 9.62808i −0.207741 + 0.359818i
\(717\) 0 0
\(718\) 24.8969 43.1228i 0.929145 1.60933i
\(719\) −18.7721 32.5143i −0.700082 1.21258i −0.968437 0.249258i \(-0.919813\pi\)
0.268355 0.963320i \(-0.413520\pi\)
\(720\) 0 0
\(721\) 5.54615 5.47946i 0.206550 0.204066i
\(722\) −22.7247 + 6.08906i −0.845725 + 0.226611i
\(723\) 0 0
\(724\) 10.9942i 0.408598i
\(725\) 15.9559 + 9.21215i 0.592588 + 0.342131i
\(726\) 0 0
\(727\) −23.0678 −0.855536 −0.427768 0.903888i \(-0.640700\pi\)
−0.427768 + 0.903888i \(0.640700\pi\)
\(728\) −3.27111 + 9.68974i −0.121235 + 0.359126i
\(729\) 0 0
\(730\) −0.512943 + 0.512943i −0.0189849 + 0.0189849i
\(731\) −2.66006 1.53579i −0.0983859 0.0568032i
\(732\) 0 0
\(733\) −17.5240 + 4.69555i −0.647265 + 0.173434i −0.567492 0.823379i \(-0.692086\pi\)
−0.0797732 + 0.996813i \(0.525420\pi\)
\(734\) −44.3891 + 11.8940i −1.63843 + 0.439017i
\(735\) 0 0
\(736\) −35.3145 35.3145i −1.30171 1.30171i
\(737\) 0.726506 + 1.25835i 0.0267612 + 0.0463518i
\(738\) 0 0
\(739\) −9.95216 + 2.66667i −0.366096 + 0.0980952i −0.437177 0.899375i \(-0.644022\pi\)
0.0710811 + 0.997471i \(0.477355\pi\)
\(740\) 0.252241 0.436894i 0.00927256 0.0160606i
\(741\) 0 0
\(742\) −48.5874 28.4452i −1.78370 1.04426i
\(743\) 37.7291 + 10.1095i 1.38415 + 0.370881i 0.872625 0.488390i \(-0.162416\pi\)
0.511520 + 0.859271i \(0.329082\pi\)
\(744\) 0 0
\(745\) −0.270771 −0.00992030
\(746\) 59.8335 + 16.0324i 2.19066 + 0.586986i
\(747\) 0 0
\(748\) 0.316725 + 1.18203i 0.0115806 + 0.0432194i
\(749\) −42.9701 11.7928i −1.57009 0.430901i
\(750\) 0 0
\(751\) 32.0282i 1.16872i 0.811493 + 0.584362i \(0.198655\pi\)
−0.811493 + 0.584362i \(0.801345\pi\)
\(752\) −0.523018 1.95193i −0.0190725 0.0711796i
\(753\) 0 0
\(754\) −11.0506 21.9787i −0.402440 0.800418i
\(755\) 1.49103i 0.0542643i
\(756\) 0 0
\(757\) 3.10808 + 5.38335i 0.112965 + 0.195661i 0.916964 0.398969i \(-0.130632\pi\)
−0.803999 + 0.594630i \(0.797299\pi\)
\(758\) 4.37492 2.52586i 0.158904 0.0917435i
\(759\) 0 0
\(760\) −0.329303 + 0.329303i −0.0119451 + 0.0119451i
\(761\) −27.0118 7.23779i −0.979177 0.262370i −0.266479 0.963841i \(-0.585860\pi\)
−0.712698 + 0.701471i \(0.752527\pi\)
\(762\) 0 0
\(763\) −25.7574 15.0795i −0.932481 0.545915i
\(764\) 16.6631 9.62047i 0.602851 0.348056i
\(765\) 0 0
\(766\) 19.1870 + 33.2329i 0.693256 + 1.20075i
\(767\) −50.4156 2.91339i −1.82040 0.105197i
\(768\) 0 0
\(769\) −7.77893 + 29.0314i −0.280515 + 1.04690i 0.671539 + 0.740969i \(0.265634\pi\)
−0.952054 + 0.305929i \(0.901033\pi\)
\(770\) −0.132771 + 0.226788i −0.00478475 + 0.00817286i
\(771\) 0 0
\(772\) −5.70886 21.3058i −0.205466 0.766811i
\(773\) 9.36696 + 9.36696i 0.336906 + 0.336906i 0.855202 0.518295i \(-0.173433\pi\)
−0.518295 + 0.855202i \(0.673433\pi\)
\(774\) 0 0
\(775\) 11.7331 + 43.7885i 0.421465 + 1.57293i
\(776\) −15.0463 8.68696i −0.540129 0.311844i
\(777\) 0 0
\(778\) −16.1972 + 60.4489i −0.580699 + 2.16720i
\(779\) 4.36907 + 2.52248i 0.156538 + 0.0903774i
\(780\) 0 0
\(781\) 0.160525 + 0.278038i 0.00574404 + 0.00994897i
\(782\) −11.9256 11.9256i −0.426457 0.426457i
\(783\) 0 0
\(784\) 29.0336 + 17.2342i 1.03691 + 0.615506i
\(785\) 0.138207 0.138207i 0.00493283 0.00493283i
\(786\) 0 0
\(787\) −22.2518 + 22.2518i −0.793192 + 0.793192i −0.982012 0.188820i \(-0.939534\pi\)
0.188820 + 0.982012i \(0.439534\pi\)
\(788\) −4.92932 +