Properties

Label 819.2.et.c.514.8
Level $819$
Weight $2$
Character 819.514
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 514.8
Character \(\chi\) \(=\) 819.514
Dual form 819.2.et.c.145.8

$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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 0.997357 0.0726530i \(-0.0231466\pi\)
−0.0726530 + 0.997357i \(0.523147\pi\)
\(3\) 0 0
\(4\) 1.42031i 0.710156i
\(5\) 0.0744995 + 0.0199621i 0.0333172 + 0.00892732i 0.275439 0.961319i \(-0.411177\pi\)
−0.242122 + 0.970246i \(0.577843\pi\)
\(6\) 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 0.155988 0.987759i \(-0.450144\pi\)
−0.358790 + 0.933418i \(0.616811\pi\)
\(12\) 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 −0.904496 0.426482i \(-0.859753\pi\)
0.570076 0.821592i \(-0.306914\pi\)
\(20\) −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 \(0.278949\pi\)
−0.639965 + 0.768404i \(0.721051\pi\)
\(24\) 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 −0.984903 0.173105i \(-0.944620\pi\)
0.642365 + 0.766399i \(0.277953\pi\)
\(30\) 0 0
\(31\) 2.34941 + 8.76813i 0.421967 + 1.57480i 0.770458 + 0.637491i \(0.220028\pi\)
−0.348491 + 0.937312i \(0.613306\pi\)
\(32\) 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 −0.386811 0.922159i \(-0.626423\pi\)
0.922159 + 0.386811i \(0.126423\pi\)
\(38\) 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 0.981663 0.190622i \(-0.0610506\pi\)
−0.945457 + 0.325748i \(0.894384\pi\)
\(42\) 0 0
\(43\) −2.14988 + 1.24124i −0.327854 + 0.189287i −0.654888 0.755726i \(-0.727284\pi\)
0.327034 + 0.945013i \(0.393951\pi\)
\(44\) 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 −0.973383 0.229184i \(-0.926394\pi\)
0.957566 + 0.288213i \(0.0930611\pi\)
\(48\) 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 0.135544 + 0.990771i \(0.456722\pi\)
−0.925805 + 0.378001i \(0.876612\pi\)
\(54\) 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 −0.935172 0.354193i \(-0.884756\pi\)
−0.354193 0.935172i \(-0.615244\pi\)
\(60\) 0 0
\(61\) 5.63177 + 3.25150i 0.721074 + 0.416312i 0.815148 0.579253i \(-0.196656\pi\)
−0.0940739 + 0.995565i \(0.529989\pi\)
\(62\) −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 −0.991037 0.133590i \(-0.957349\pi\)
0.925058 + 0.379826i \(0.124016\pi\)
\(68\) 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 −0.972645 0.232296i \(-0.925376\pi\)
0.958483 + 0.285148i \(0.0920428\pi\)
\(72\) 0 0
\(73\) −4.91231 + 1.31625i −0.574942 + 0.154055i −0.534562 0.845129i \(-0.679524\pi\)
−0.0403800 + 0.999184i \(0.512857\pi\)
\(74\) 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 0.989130 0.147043i \(-0.0469754\pi\)
−0.621908 + 0.783091i \(0.713642\pi\)
\(80\) 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 0.0485904 0.998819i \(-0.484527\pi\)
0.998819 0.0485904i \(-0.0154729\pi\)
\(84\) 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 0.520378 0.853936i \(-0.325791\pi\)
−0.853936 + 0.520378i \(0.825791\pi\)
\(90\) 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 −0.647569 0.762007i \(-0.724214\pi\)
−0.941815 + 0.336132i \(0.890881\pi\)
\(98\) 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 −0.999990 0.00445781i \(-0.998581\pi\)
0.496134 0.868246i \(-0.334752\pi\)
\(102\) 0 0
\(103\) 1.47339 + 2.55198i 0.145177 + 0.251454i 0.929439 0.368976i \(-0.120291\pi\)
−0.784262 + 0.620430i \(0.786958\pi\)
\(104\) −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 −0.739651 0.672991i \(-0.765009\pi\)
−0.304061 + 0.952653i \(0.598343\pi\)
\(110\) −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 0.999106 + 0.0422699i \(0.0134589\pi\)
−0.462946 + 0.886386i \(0.653208\pi\)
\(114\) 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 −0.135264 0.990810i \(-0.543188\pi\)
−0.925698 + 0.378263i \(0.876522\pi\)
\(128\) 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 0.149778 0.988720i \(-0.452144\pi\)
0.931145 + 0.364648i \(0.118811\pi\)
\(132\) 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 −0.567881 0.823111i \(-0.692236\pi\)
0.823111 + 0.567881i \(0.192236\pi\)
\(138\) 0 0
\(139\) 8.52594 4.92246i 0.723161 0.417517i −0.0927539 0.995689i \(-0.529567\pi\)
0.815915 + 0.578172i \(0.196234\pi\)
\(140\) 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 −0.395033 0.918667i \(-0.629267\pi\)
0.117225 + 0.993105i \(0.462600\pi\)
\(150\) 0 0
\(151\) 5.00350 + 18.6733i 0.407179 + 1.51961i 0.800001 + 0.599999i \(0.204832\pi\)
−0.392821 + 0.919615i \(0.628501\pi\)
\(152\) −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 0.585013 0.811024i \(-0.301089\pi\)
−0.409860 + 0.912148i \(0.634423\pi\)
\(158\) −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 0.947044 + 0.321105i \(0.104054\pi\)
−0.659611 + 0.751607i \(0.729279\pi\)
\(164\) −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 −0.136036 0.990704i \(-0.543436\pi\)
0.377542 + 0.925993i \(0.376770\pi\)
\(168\) 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 −0.853637 0.520868i \(-0.825608\pi\)
0.877904 + 0.478837i \(0.158942\pi\)
\(174\) 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 −0.731466 0.681878i \(-0.761163\pi\)
0.224791 + 0.974407i \(0.427830\pi\)
\(180\) 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 −0.509823 0.860279i \(-0.670289\pi\)
0.999935 + 0.0113800i \(0.00362244\pi\)
\(192\) 0 0
\(193\) 15.0008 + 4.01944i 1.07978 + 0.289326i 0.754505 0.656295i \(-0.227877\pi\)
0.325273 + 0.945620i \(0.394544\pi\)
\(194\) −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 −0.688791 0.724960i \(-0.741858\pi\)
−0.234031 + 0.972229i \(0.575192\pi\)
\(198\) 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 −0.997263 0.0739331i \(-0.976445\pi\)
0.562660 + 0.826689i \(0.309778\pi\)
\(212\) −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 0.886697 + 0.462351i \(0.152994\pi\)
−0.536726 + 0.843756i \(0.680339\pi\)
\(224\) 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 −0.940191 0.340648i \(-0.889354\pi\)
0.340648 + 0.940191i \(0.389354\pi\)
\(228\) 0 0
\(229\) 3.18409 11.8832i 0.210410 0.785262i −0.777322 0.629104i \(-0.783422\pi\)
0.987732 0.156159i \(-0.0499112\pi\)
\(230\) −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 −0.498817 0.866708i \(-0.666232\pi\)
0.501182 + 0.865342i \(0.332899\pi\)
\(234\) 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 0.658581 0.752510i \(-0.271157\pi\)
−0.752510 + 0.658581i \(0.771157\pi\)
\(240\) 0 0
\(241\) −1.95322 1.95322i −0.125818 0.125818i 0.641394 0.767212i \(-0.278356\pi\)
−0.767212 + 0.641394i \(0.778356\pi\)
\(242\) −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 −0.946359 0.323116i \(-0.895270\pi\)
0.193353 0.981129i \(-0.438064\pi\)
\(252\) 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 0.999646 0.0265886i \(-0.00846440\pi\)
−0.522850 + 0.852425i \(0.675131\pi\)
\(264\) 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 \(0.00340507\pi\)
−0.999943 + 0.0106971i \(0.996595\pi\)
\(270\) 0 0
\(271\) 7.06051 + 7.06051i 0.428895 + 0.428895i 0.888252 0.459357i \(-0.151920\pi\)
−0.459357 + 0.888252i \(0.651920\pi\)
\(272\) 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 \(0.0940738\pi\)
−0.956645 + 0.291258i \(0.905926\pi\)
\(278\) 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 0.398518 0.917161i \(-0.369525\pi\)
0.917161 0.398518i \(-0.130475\pi\)
\(282\) 0 0
\(283\) 2.07530 + 3.59453i 0.123364 + 0.213673i 0.921092 0.389344i \(-0.127298\pi\)
−0.797728 + 0.603017i \(0.793965\pi\)
\(284\) −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 0.734379 + 0.678740i \(0.237474\pi\)
−0.975361 + 0.220617i \(0.929193\pi\)
\(294\) 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 0.854640 0.519221i \(-0.173778\pi\)
−0.519221 + 0.854640i \(0.673778\pi\)
\(308\) −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 0.227835 + 0.973700i \(0.426835\pi\)
−0.957166 + 0.289539i \(0.906498\pi\)
\(312\) 0 0
\(313\) −19.5449 + 11.2842i −1.10474 + 0.637823i −0.937463 0.348086i \(-0.886832\pi\)
−0.167280 + 0.985909i \(0.553498\pi\)
\(314\) 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 −0.840792 0.541358i \(-0.817910\pi\)
0.998826 0.0484339i \(-0.0154230\pi\)
\(318\) 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 0.366650 0.930359i \(-0.380505\pi\)
0.782708 + 0.622389i \(0.213838\pi\)
\(332\) 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 \(-0.859364\pi\)
0.903975 0.427586i \(-0.140636\pi\)
\(338\) 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 −0.801925 0.597425i \(-0.796191\pi\)
−0.395775 + 0.918348i \(0.629524\pi\)
\(350\) −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 −0.0858994 0.996304i \(-0.527376\pi\)
−0.572543 + 0.819875i \(0.694043\pi\)
\(354\) 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 0.868423 0.495825i \(-0.165134\pi\)
0.504163 + 0.863608i \(0.331801\pi\)
\(360\) 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 −0.942242 0.334932i \(-0.891287\pi\)
−0.181062 + 0.983472i \(0.557953\pi\)
\(368\) 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 0.00221133 0.999998i \(-0.499296\pi\)
0.864918 0.501914i \(-0.167371\pi\)
\(374\) −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 −0.190417 0.981703i \(-0.560984\pi\)
0.325946 + 0.945389i \(0.394317\pi\)
\(380\) 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 −0.956235 0.292600i \(-0.905480\pi\)
0.681824 0.731516i \(-0.261187\pi\)
\(384\) 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 −0.485955 0.873984i \(-0.661528\pi\)
−0.999870 + 0.0161427i \(0.994861\pi\)
\(390\) 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 −0.358442 0.933552i \(-0.616692\pi\)
0.156356 + 0.987701i \(0.450025\pi\)
\(398\) −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 −0.452856 + 0.891584i \(0.649595\pi\)
−0.891584 + 0.452856i \(0.850405\pi\)
\(402\) 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 −0.289104 0.957298i \(-0.593357\pi\)
0.957298 + 0.289104i \(0.0933573\pi\)
\(410\) −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 0.996963 0.0778716i \(-0.0248124\pi\)
0.431043 + 0.902331i \(0.358146\pi\)
\(420\) 0 0
\(421\) 20.2556 + 20.2556i 0.987197 + 0.987197i 0.999919 0.0127222i \(-0.00404970\pi\)
−0.0127222 + 0.999919i \(0.504050\pi\)
\(422\) −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 0.766909 + 0.641756i \(0.221794\pi\)
−0.985041 + 0.172323i \(0.944873\pi\)
\(432\) 0 0
\(433\) 6.74582 + 11.6841i 0.324184 + 0.561502i 0.981347 0.192246i \(-0.0615771\pi\)
−0.657163 + 0.753748i \(0.728244\pi\)
\(434\) −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 −0.877410 0.479741i \(-0.840731\pi\)
0.0232374 0.999730i \(-0.492603\pi\)
\(444\) 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 −0.449033 0.893515i \(-0.648231\pi\)
−0.835632 + 0.549290i \(0.814898\pi\)
\(450\) 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 0.709170 0.705037i \(-0.249070\pi\)
−0.705037 + 0.709170i \(0.749070\pi\)
\(458\) 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 0.628170 0.778076i \(-0.283804\pi\)
0.154973 + 0.987919i \(0.450471\pi\)
\(462\) 0 0
\(463\) −1.07038 + 1.07038i −0.0497447 + 0.0497447i −0.731542 0.681797i \(-0.761199\pi\)
0.681797 + 0.731542i \(0.261199\pi\)
\(464\) −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 0.975858 + 0.218408i \(0.0700862\pi\)
−0.298782 + 0.954321i \(0.596580\pi\)
\(468\) 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 −0.942778 0.333421i \(-0.891797\pi\)
0.983180 + 0.182638i \(0.0584636\pi\)
\(480\) 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 0.600997 0.799251i \(-0.294770\pi\)
−0.799251 + 0.600997i \(0.794770\pi\)
\(488\) 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 0.999982 0.00600745i \(-0.00191224\pi\)
0.494788 + 0.869014i \(0.335246\pi\)
\(492\) 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 −0.985754 0.168195i \(-0.946206\pi\)
0.937785 + 0.347216i \(0.112873\pi\)
\(500\) 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 0.0464410 0.998921i \(-0.485212\pi\)
0.888311 + 0.459241i \(0.151879\pi\)
\(504\) 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 −0.241039 0.970515i \(-0.577488\pi\)
0.970515 + 0.241039i \(0.0774883\pi\)
\(510\) 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 −0.309553 0.950882i \(-0.600179\pi\)
−0.978265 + 0.207360i \(0.933513\pi\)
\(522\) 0 0
\(523\) 7.59842i 0.332256i −0.986104 0.166128i \(-0.946874\pi\)
0.986104 0.166128i \(-0.0531264\pi\)
\(524\) 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 −0.261983 0.965073i \(-0.584376\pi\)
−0.709420 + 0.704786i \(0.751043\pi\)
\(542\) 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 0.492056 0.870563i \(-0.336245\pi\)
−0.00914829 + 0.999958i \(0.502912\pi\)
\(558\) 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 \(0.0915149\pi\)
−0.958955 + 0.283558i \(0.908485\pi\)
\(570\) 0 0
\(571\) −12.8299 7.40732i −0.536913 0.309987i 0.206914 0.978359i \(-0.433658\pi\)
−0.743827 + 0.668372i \(0.766991\pi\)
\(572\) −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 −0.984578 0.174944i \(-0.944025\pi\)
0.765198 0.643795i \(-0.222641\pi\)
\(578\) −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 0.923670 + 0.383189i \(0.125174\pi\)
−0.608327 + 0.793686i \(0.708159\pi\)
\(588\) 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 −0.464467 0.885590i \(-0.653754\pi\)
0.845036 0.534710i \(-0.179579\pi\)
\(594\) 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 −0.922568 0.385835i \(-0.873913\pi\)
0.795427 + 0.606049i \(0.207247\pi\)
\(600\) 0 0
\(601\) 0.0256568 + 0.0148129i 0.00104656 + 0.000604232i 0.500523 0.865723i \(-0.333141\pi\)
−0.499477 + 0.866327i \(0.666474\pi\)
\(602\) −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 0.884162 0.467180i \(-0.154730\pi\)
0.0374913 + 0.999297i \(0.488063\pi\)
\(608\) 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 −0.666331 0.745656i \(-0.732136\pi\)
0.949888 0.312591i \(-0.101197\pi\)
\(614\) 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 −0.396641 0.917974i \(-0.629824\pi\)
0.802488 0.596668i \(-0.203509\pi\)
\(618\) 0 0
\(619\) 28.5176 7.64126i 1.14622 0.307128i 0.364769 0.931098i \(-0.381148\pi\)
0.781448 + 0.623970i \(0.214481\pi\)
\(620\) −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 0.897318 0.441384i \(-0.145512\pi\)
0.556408 + 0.830909i \(0.312179\pi\)
\(632\) 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 \(0.0261004\pi\)
−0.996640 + 0.0819049i \(0.973900\pi\)
\(642\) 0 0
\(643\) 39.3048 + 10.5317i 1.55003 + 0.415330i 0.929491 0.368845i \(-0.120247\pi\)
0.620541 + 0.784174i \(0.286913\pi\)
\(644\) −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 −0.967870 0.251451i \(-0.919092\pi\)
0.266172 0.963926i \(-0.414241\pi\)
\(648\) 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 0.885257 0.465103i \(-0.153983\pi\)
−0.845419 + 0.534104i \(0.820649\pi\)
\(660\) 0 0
\(661\) −5.33936 + 19.9268i −0.207677 + 0.775061i 0.780940 + 0.624606i \(0.214740\pi\)
−0.988617 + 0.150455i \(0.951926\pi\)
\(662\) 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 0.800855 0.598859i \(-0.204379\pi\)
−0.118199 + 0.992990i \(0.537712\pi\)
\(674\) 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 0.465549 0.885022i \(-0.345857\pi\)
0.999226 + 0.0393333i \(0.0125234\pi\)
\(678\) 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 −0.638422 0.769687i \(-0.720412\pi\)
0.769687 + 0.638422i \(0.220412\pi\)
\(684\) 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 0.290511 0.956872i \(-0.406175\pi\)
0.956872 0.290511i \(-0.0938254\pi\)
\(692\) 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 \(-0.897285\pi\)
0.948386 0.317118i \(-0.102715\pi\)
\(702\) 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 0.924441 0.381326i \(-0.124532\pi\)
−0.991252 + 0.131983i \(0.957866\pi\)
\(710\) −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 0.268355 + 0.963320i \(0.413520\pi\)
−0.968437 + 0.249258i \(0.919813\pi\)
\(720\) 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 −0.0797732 0.996813i \(-0.525420\pi\)
−0.567492 + 0.823379i \(0.692086\pi\)
\(734\) −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 0.0710811 0.997471i \(-0.477355\pi\)
−0.437177 + 0.899375i \(0.644022\pi\)
\(740\) 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 0.511520 0.859271i \(-0.329082\pi\)
0.872625 + 0.488390i \(0.162416\pi\)
\(744\) 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 \(-0.801345\pi\)
0.811493 0.584362i \(-0.198655\pi\)
\(752\) −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 −0.803999 0.594630i \(-0.797299\pi\)
0.916964 + 0.398969i \(0.130632\pi\)
\(758\) 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 −0.712698 0.701471i \(-0.752527\pi\)
−0.266479 + 0.963841i \(0.585860\pi\)
\(762\) 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 −0.952054 0.305929i \(-0.901033\pi\)
0.671539 0.740969i \(-0.265634\pi\)
\(770\) −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 −0.518295 0.855202i \(-0.673433\pi\)
0.855202 + 0.518295i \(0.173433\pi\)
\(774\) 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 0.188820 0.982012i \(-0.439534\pi\)
−0.982012 + 0.188820i \(0.939534\pi\)
\(788\) −4.92932