Properties

Label 819.2.fm.e.370.8
Level $819$
Weight $2$
Character 819.370
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
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.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 370.8
Character \(\chi\) \(=\) 819.370
Dual form 819.2.fm.e.622.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.706652 + 2.63726i) q^{2} +(-4.72373 + 2.72725i) q^{4} +(2.18431 + 2.18431i) q^{5} +(0.666364 + 2.56046i) q^{7} +(-6.66928 - 6.66928i) q^{8} +O(q^{10})\) \(q+(0.706652 + 2.63726i) q^{2} +(-4.72373 + 2.72725i) q^{4} +(2.18431 + 2.18431i) q^{5} +(0.666364 + 2.56046i) q^{7} +(-6.66928 - 6.66928i) q^{8} +(-4.21705 + 7.30414i) q^{10} +(0.456585 - 0.122342i) q^{11} +(-2.45314 - 2.64236i) q^{13} +(-6.28171 + 3.56673i) q^{14} +(7.42128 - 12.8540i) q^{16} +(1.14138 + 1.97693i) q^{17} +(-1.51851 + 5.66717i) q^{19} +(-16.2753 - 4.36094i) q^{20} +(0.645294 + 1.11768i) q^{22} +(-0.481898 - 0.278224i) q^{23} +4.54242i q^{25} +(5.23509 - 8.33681i) q^{26} +(-10.1307 - 10.2776i) q^{28} +(3.64605 - 6.31515i) q^{29} +(2.74924 + 2.74924i) q^{31} +(20.9229 + 5.60626i) q^{32} +(-4.40713 + 4.40713i) q^{34} +(-4.13729 + 7.04838i) q^{35} +(-6.41041 + 1.71767i) q^{37} -16.0189 q^{38} -29.1356i q^{40} +(1.49535 - 0.400678i) q^{41} +(5.08624 - 2.93654i) q^{43} +(-1.82313 + 1.82313i) q^{44} +(0.393215 - 1.46750i) q^{46} +(6.55220 - 6.55220i) q^{47} +(-6.11192 + 3.41240i) q^{49} +(-11.9795 + 3.20991i) q^{50} +(18.7944 + 5.79150i) q^{52} -4.17698 q^{53} +(1.26456 + 0.730092i) q^{55} +(12.6323 - 21.5206i) q^{56} +(19.2312 + 5.15298i) q^{58} +(14.2781 + 3.82579i) q^{59} +(0.553719 - 0.319690i) q^{61} +(-5.30771 + 9.19322i) q^{62} +29.4556i q^{64} +(0.413319 - 11.1302i) q^{65} +(-2.17304 - 8.10989i) q^{67} +(-10.7832 - 6.22567i) q^{68} +(-21.5120 - 5.93037i) q^{70} +(2.13591 + 0.572316i) q^{71} +(-2.43968 + 2.43968i) q^{73} +(-9.05986 - 15.6921i) q^{74} +(-8.28273 - 30.9116i) q^{76} +(0.617503 + 1.08755i) q^{77} -11.8014 q^{79} +(44.2876 - 11.8668i) q^{80} +(2.11339 + 3.66049i) q^{82} +(1.80810 + 1.80810i) q^{83} +(-1.82510 + 6.81137i) q^{85} +(11.3386 + 11.3386i) q^{86} +(-3.86103 - 2.22917i) q^{88} +(0.363443 + 1.35639i) q^{89} +(5.13099 - 8.04195i) q^{91} +3.03514 q^{92} +(21.9100 + 12.6497i) q^{94} +(-15.6957 + 9.06194i) q^{95} +(-3.25005 + 12.1294i) q^{97} +(-13.3184 - 13.7073i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.706652 + 2.63726i 0.499678 + 1.86482i 0.502069 + 0.864828i \(0.332572\pi\)
−0.00239085 + 0.999997i \(0.500761\pi\)
\(3\) 0 0
\(4\) −4.72373 + 2.72725i −2.36187 + 1.36362i
\(5\) 2.18431 + 2.18431i 0.976853 + 0.976853i 0.999738 0.0228851i \(-0.00728519\pi\)
−0.0228851 + 0.999738i \(0.507285\pi\)
\(6\) 0 0
\(7\) 0.666364 + 2.56046i 0.251862 + 0.967763i
\(8\) −6.66928 6.66928i −2.35795 2.35795i
\(9\) 0 0
\(10\) −4.21705 + 7.30414i −1.33355 + 2.30977i
\(11\) 0.456585 0.122342i 0.137666 0.0368874i −0.189328 0.981914i \(-0.560631\pi\)
0.326994 + 0.945026i \(0.393964\pi\)
\(12\) 0 0
\(13\) −2.45314 2.64236i −0.680379 0.732860i
\(14\) −6.28171 + 3.56673i −1.67886 + 0.953248i
\(15\) 0 0
\(16\) 7.42128 12.8540i 1.85532 3.21351i
\(17\) 1.14138 + 1.97693i 0.276826 + 0.479477i 0.970594 0.240722i \(-0.0773841\pi\)
−0.693768 + 0.720198i \(0.744051\pi\)
\(18\) 0 0
\(19\) −1.51851 + 5.66717i −0.348371 + 1.30014i 0.540254 + 0.841502i \(0.318328\pi\)
−0.888625 + 0.458635i \(0.848339\pi\)
\(20\) −16.2753 4.36094i −3.63926 0.975136i
\(21\) 0 0
\(22\) 0.645294 + 1.11768i 0.137577 + 0.238291i
\(23\) −0.481898 0.278224i −0.100483 0.0580137i 0.448917 0.893574i \(-0.351810\pi\)
−0.549399 + 0.835560i \(0.685143\pi\)
\(24\) 0 0
\(25\) 4.54242i 0.908484i
\(26\) 5.23509 8.33681i 1.02668 1.63498i
\(27\) 0 0
\(28\) −10.1307 10.2776i −1.91453 1.94228i
\(29\) 3.64605 6.31515i 0.677055 1.17269i −0.298809 0.954313i \(-0.596589\pi\)
0.975864 0.218381i \(-0.0700774\pi\)
\(30\) 0 0
\(31\) 2.74924 + 2.74924i 0.493778 + 0.493778i 0.909494 0.415716i \(-0.136469\pi\)
−0.415716 + 0.909494i \(0.636469\pi\)
\(32\) 20.9229 + 5.60626i 3.69867 + 0.991057i
\(33\) 0 0
\(34\) −4.40713 + 4.40713i −0.755816 + 0.755816i
\(35\) −4.13729 + 7.04838i −0.699330 + 1.19139i
\(36\) 0 0
\(37\) −6.41041 + 1.71767i −1.05387 + 0.282382i −0.743848 0.668348i \(-0.767002\pi\)
−0.310017 + 0.950731i \(0.600335\pi\)
\(38\) −16.0189 −2.59860
\(39\) 0 0
\(40\) 29.1356i 4.60674i
\(41\) 1.49535 0.400678i 0.233535 0.0625755i −0.140154 0.990130i \(-0.544760\pi\)
0.373688 + 0.927554i \(0.378093\pi\)
\(42\) 0 0
\(43\) 5.08624 2.93654i 0.775644 0.447818i −0.0592406 0.998244i \(-0.518868\pi\)
0.834884 + 0.550426i \(0.185535\pi\)
\(44\) −1.82313 + 1.82313i −0.274848 + 0.274848i
\(45\) 0 0
\(46\) 0.393215 1.46750i 0.0579763 0.216371i
\(47\) 6.55220 6.55220i 0.955736 0.955736i −0.0433248 0.999061i \(-0.513795\pi\)
0.999061 + 0.0433248i \(0.0137950\pi\)
\(48\) 0 0
\(49\) −6.11192 + 3.41240i −0.873131 + 0.487485i
\(50\) −11.9795 + 3.20991i −1.69416 + 0.453949i
\(51\) 0 0
\(52\) 18.7944 + 5.79150i 2.60631 + 0.803136i
\(53\) −4.17698 −0.573753 −0.286876 0.957968i \(-0.592617\pi\)
−0.286876 + 0.957968i \(0.592617\pi\)
\(54\) 0 0
\(55\) 1.26456 + 0.730092i 0.170513 + 0.0984456i
\(56\) 12.6323 21.5206i 1.68806 2.87581i
\(57\) 0 0
\(58\) 19.2312 + 5.15298i 2.52518 + 0.676619i
\(59\) 14.2781 + 3.82579i 1.85884 + 0.498076i 0.999902 0.0139966i \(-0.00445541\pi\)
0.858942 + 0.512072i \(0.171122\pi\)
\(60\) 0 0
\(61\) 0.553719 0.319690i 0.0708965 0.0409321i −0.464133 0.885766i \(-0.653634\pi\)
0.535029 + 0.844834i \(0.320301\pi\)
\(62\) −5.30771 + 9.19322i −0.674079 + 1.16754i
\(63\) 0 0
\(64\) 29.4556i 3.68195i
\(65\) 0.413319 11.1302i 0.0512659 1.38053i
\(66\) 0 0
\(67\) −2.17304 8.10989i −0.265479 0.990780i −0.961957 0.273202i \(-0.911917\pi\)
0.696478 0.717578i \(-0.254749\pi\)
\(68\) −10.7832 6.22567i −1.30765 0.754973i
\(69\) 0 0
\(70\) −21.5120 5.93037i −2.57118 0.708815i
\(71\) 2.13591 + 0.572316i 0.253486 + 0.0679214i 0.383324 0.923614i \(-0.374779\pi\)
−0.129838 + 0.991535i \(0.541446\pi\)
\(72\) 0 0
\(73\) −2.43968 + 2.43968i −0.285543 + 0.285543i −0.835315 0.549772i \(-0.814715\pi\)
0.549772 + 0.835315i \(0.314715\pi\)
\(74\) −9.05986 15.6921i −1.05319 1.82417i
\(75\) 0 0
\(76\) −8.28273 30.9116i −0.950094 3.54580i
\(77\) 0.617503 + 1.08755i 0.0703710 + 0.123937i
\(78\) 0 0
\(79\) −11.8014 −1.32776 −0.663878 0.747841i \(-0.731091\pi\)
−0.663878 + 0.747841i \(0.731091\pi\)
\(80\) 44.2876 11.8668i 4.95150 1.32675i
\(81\) 0 0
\(82\) 2.11339 + 3.66049i 0.233384 + 0.404234i
\(83\) 1.80810 + 1.80810i 0.198465 + 0.198465i 0.799342 0.600877i \(-0.205182\pi\)
−0.600877 + 0.799342i \(0.705182\pi\)
\(84\) 0 0
\(85\) −1.82510 + 6.81137i −0.197960 + 0.738796i
\(86\) 11.3386 + 11.3386i 1.22267 + 1.22267i
\(87\) 0 0
\(88\) −3.86103 2.22917i −0.411587 0.237630i
\(89\) 0.363443 + 1.35639i 0.0385248 + 0.143777i 0.982509 0.186213i \(-0.0596214\pi\)
−0.943985 + 0.329990i \(0.892955\pi\)
\(90\) 0 0
\(91\) 5.13099 8.04195i 0.537873 0.843026i
\(92\) 3.03514 0.316436
\(93\) 0 0
\(94\) 21.9100 + 12.6497i 2.25984 + 1.30472i
\(95\) −15.6957 + 9.06194i −1.61035 + 0.929736i
\(96\) 0 0
\(97\) −3.25005 + 12.1294i −0.329993 + 1.23155i 0.579204 + 0.815183i \(0.303364\pi\)
−0.909197 + 0.416367i \(0.863303\pi\)
\(98\) −13.3184 13.7073i −1.34536 1.38465i
\(99\) 0 0
\(100\) −12.3883 21.4572i −1.23883 2.14572i
\(101\) −3.23413 + 5.60168i −0.321808 + 0.557388i −0.980861 0.194708i \(-0.937624\pi\)
0.659053 + 0.752096i \(0.270957\pi\)
\(102\) 0 0
\(103\) 8.52900 0.840388 0.420194 0.907434i \(-0.361962\pi\)
0.420194 + 0.907434i \(0.361962\pi\)
\(104\) −1.26197 + 33.9834i −0.123747 + 3.33235i
\(105\) 0 0
\(106\) −2.95167 11.0158i −0.286692 1.06995i
\(107\) −2.34420 + 4.06027i −0.226622 + 0.392521i −0.956805 0.290731i \(-0.906102\pi\)
0.730183 + 0.683252i \(0.239435\pi\)
\(108\) 0 0
\(109\) 3.66100 3.66100i 0.350661 0.350661i −0.509695 0.860355i \(-0.670242\pi\)
0.860355 + 0.509695i \(0.170242\pi\)
\(110\) −1.03184 + 3.85088i −0.0983822 + 0.367167i
\(111\) 0 0
\(112\) 37.8575 + 10.4364i 3.57720 + 0.986150i
\(113\) 4.41169 + 7.64128i 0.415017 + 0.718831i 0.995430 0.0954914i \(-0.0304422\pi\)
−0.580413 + 0.814322i \(0.697109\pi\)
\(114\) 0 0
\(115\) −0.444887 1.66034i −0.0414859 0.154828i
\(116\) 39.7748i 3.69300i
\(117\) 0 0
\(118\) 40.3584i 3.71530i
\(119\) −4.30128 + 4.23982i −0.394298 + 0.388664i
\(120\) 0 0
\(121\) −9.33278 + 5.38828i −0.848434 + 0.489844i
\(122\) 1.23439 + 1.23439i 0.111757 + 0.111757i
\(123\) 0 0
\(124\) −20.4845 5.48882i −1.83957 0.492910i
\(125\) 0.999502 0.999502i 0.0893982 0.0893982i
\(126\) 0 0
\(127\) 8.32452 + 4.80617i 0.738682 + 0.426478i 0.821590 0.570079i \(-0.193087\pi\)
−0.0829079 + 0.996557i \(0.526421\pi\)
\(128\) −35.8364 + 9.60232i −3.16752 + 0.848734i
\(129\) 0 0
\(130\) 29.6452 6.77512i 2.60006 0.594218i
\(131\) 15.6056i 1.36346i 0.731602 + 0.681732i \(0.238773\pi\)
−0.731602 + 0.681732i \(0.761227\pi\)
\(132\) 0 0
\(133\) −15.5224 0.111698i −1.34597 0.00968549i
\(134\) 19.8523 11.4617i 1.71498 0.990143i
\(135\) 0 0
\(136\) 5.57252 20.7969i 0.477840 1.78332i
\(137\) −5.03398 + 18.7871i −0.430082 + 1.60509i 0.322488 + 0.946574i \(0.395481\pi\)
−0.752569 + 0.658513i \(0.771186\pi\)
\(138\) 0 0
\(139\) 4.85118 2.80083i 0.411472 0.237564i −0.279950 0.960015i \(-0.590318\pi\)
0.691422 + 0.722451i \(0.256985\pi\)
\(140\) 0.320781 44.5781i 0.0271110 3.76754i
\(141\) 0 0
\(142\) 6.03739i 0.506646i
\(143\) −1.44334 0.906344i −0.120698 0.0757923i
\(144\) 0 0
\(145\) 21.7583 5.83013i 1.80693 0.484166i
\(146\) −8.15808 4.71007i −0.675168 0.389808i
\(147\) 0 0
\(148\) 25.5966 25.5966i 2.10403 2.10403i
\(149\) 19.1586 + 5.13354i 1.56954 + 0.420556i 0.935667 0.352885i \(-0.114799\pi\)
0.633869 + 0.773440i \(0.281466\pi\)
\(150\) 0 0
\(151\) 0.637052 + 0.637052i 0.0518426 + 0.0518426i 0.732553 0.680710i \(-0.238329\pi\)
−0.680710 + 0.732553i \(0.738329\pi\)
\(152\) 47.9233 27.6686i 3.88710 2.24422i
\(153\) 0 0
\(154\) −2.43178 + 2.39703i −0.195958 + 0.193158i
\(155\) 12.0104i 0.964697i
\(156\) 0 0
\(157\) 0.106383i 0.00849030i −0.999991 0.00424515i \(-0.998649\pi\)
0.999991 0.00424515i \(-0.00135128\pi\)
\(158\) −8.33945 31.1232i −0.663451 2.47603i
\(159\) 0 0
\(160\) 33.4562 + 57.9478i 2.64494 + 4.58118i
\(161\) 0.391262 1.41928i 0.0308358 0.111855i
\(162\) 0 0
\(163\) 3.70956 13.8443i 0.290555 1.08437i −0.654128 0.756383i \(-0.726964\pi\)
0.944684 0.327983i \(-0.106369\pi\)
\(164\) −5.97090 + 5.97090i −0.466249 + 0.466249i
\(165\) 0 0
\(166\) −3.49074 + 6.04613i −0.270934 + 0.469271i
\(167\) −3.66050 13.6612i −0.283258 1.05713i −0.950103 0.311936i \(-0.899023\pi\)
0.666845 0.745196i \(-0.267644\pi\)
\(168\) 0 0
\(169\) −0.964180 + 12.9642i −0.0741677 + 0.997246i
\(170\) −19.2531 −1.47664
\(171\) 0 0
\(172\) −16.0173 + 27.7429i −1.22131 + 2.11537i
\(173\) −0.208401 0.360961i −0.0158444 0.0274434i 0.857994 0.513659i \(-0.171710\pi\)
−0.873839 + 0.486216i \(0.838377\pi\)
\(174\) 0 0
\(175\) −11.6307 + 3.02690i −0.879197 + 0.228812i
\(176\) 1.81586 6.77690i 0.136876 0.510828i
\(177\) 0 0
\(178\) −3.32032 + 1.91699i −0.248868 + 0.143684i
\(179\) −8.99794 5.19496i −0.672537 0.388290i 0.124500 0.992220i \(-0.460267\pi\)
−0.797037 + 0.603930i \(0.793601\pi\)
\(180\) 0 0
\(181\) −21.4482 −1.59423 −0.797117 0.603825i \(-0.793643\pi\)
−0.797117 + 0.603825i \(0.793643\pi\)
\(182\) 24.8345 + 7.84888i 1.84086 + 0.581798i
\(183\) 0 0
\(184\) 1.35836 + 5.06947i 0.100140 + 0.373726i
\(185\) −17.7542 10.2504i −1.30532 0.753626i
\(186\) 0 0
\(187\) 0.763000 + 0.763000i 0.0557961 + 0.0557961i
\(188\) −13.0814 + 48.8203i −0.954057 + 3.56059i
\(189\) 0 0
\(190\) −34.9901 34.9901i −2.53845 2.53845i
\(191\) −0.111216 0.192631i −0.00804729 0.0139383i 0.861974 0.506953i \(-0.169228\pi\)
−0.870021 + 0.493015i \(0.835895\pi\)
\(192\) 0 0
\(193\) −1.98209 + 0.531099i −0.142674 + 0.0382293i −0.329449 0.944173i \(-0.606863\pi\)
0.186775 + 0.982403i \(0.440196\pi\)
\(194\) −34.2849 −2.46152
\(195\) 0 0
\(196\) 19.5646 32.7880i 1.39747 2.34200i
\(197\) −3.40878 12.7217i −0.242865 0.906386i −0.974444 0.224629i \(-0.927883\pi\)
0.731579 0.681757i \(-0.238784\pi\)
\(198\) 0 0
\(199\) −1.49318 2.58626i −0.105849 0.183335i 0.808236 0.588859i \(-0.200423\pi\)
−0.914085 + 0.405523i \(0.867089\pi\)
\(200\) 30.2947 30.2947i 2.14216 2.14216i
\(201\) 0 0
\(202\) −17.0585 4.57081i −1.20023 0.321601i
\(203\) 18.5993 + 5.12739i 1.30541 + 0.359872i
\(204\) 0 0
\(205\) 4.14152 + 2.39111i 0.289256 + 0.167002i
\(206\) 6.02704 + 22.4932i 0.419923 + 1.56718i
\(207\) 0 0
\(208\) −52.1705 + 11.9231i −3.61737 + 0.826715i
\(209\) 2.77332i 0.191835i
\(210\) 0 0
\(211\) 3.61160 6.25548i 0.248633 0.430645i −0.714514 0.699621i \(-0.753352\pi\)
0.963147 + 0.268976i \(0.0866853\pi\)
\(212\) 19.7310 11.3917i 1.35513 0.782384i
\(213\) 0 0
\(214\) −12.3645 3.31306i −0.845222 0.226476i
\(215\) 17.5242 + 4.69560i 1.19514 + 0.320237i
\(216\) 0 0
\(217\) −5.20733 + 8.87132i −0.353496 + 0.602224i
\(218\) 12.2421 + 7.06797i 0.829138 + 0.478703i
\(219\) 0 0
\(220\) −7.96457 −0.536971
\(221\) 2.42380 7.86565i 0.163043 0.529101i
\(222\) 0 0
\(223\) 18.5687 4.97547i 1.24345 0.333182i 0.423649 0.905827i \(-0.360749\pi\)
0.819804 + 0.572644i \(0.194082\pi\)
\(224\) −0.412385 + 57.3080i −0.0275536 + 3.82905i
\(225\) 0 0
\(226\) −17.0345 + 17.0345i −1.13312 + 1.13312i
\(227\) 3.99587 14.9128i 0.265215 0.989797i −0.696903 0.717165i \(-0.745439\pi\)
0.962118 0.272632i \(-0.0878941\pi\)
\(228\) 0 0
\(229\) −8.38486 + 8.38486i −0.554087 + 0.554087i −0.927618 0.373531i \(-0.878147\pi\)
0.373531 + 0.927618i \(0.378147\pi\)
\(230\) 4.06437 2.34657i 0.267997 0.154728i
\(231\) 0 0
\(232\) −66.4341 + 17.8010i −4.36161 + 1.16869i
\(233\) 19.9540i 1.30723i −0.756828 0.653614i \(-0.773252\pi\)
0.756828 0.653614i \(-0.226748\pi\)
\(234\) 0 0
\(235\) 28.6241 1.86723
\(236\) −77.8796 + 20.8678i −5.06953 + 1.35838i
\(237\) 0 0
\(238\) −14.2210 8.34753i −0.921812 0.541090i
\(239\) 5.27726 5.27726i 0.341357 0.341357i −0.515520 0.856877i \(-0.672401\pi\)
0.856877 + 0.515520i \(0.172401\pi\)
\(240\) 0 0
\(241\) 8.35123 + 2.23771i 0.537950 + 0.144143i 0.517557 0.855649i \(-0.326842\pi\)
0.0203932 + 0.999792i \(0.493508\pi\)
\(242\) −20.8053 20.8053i −1.33742 1.33742i
\(243\) 0 0
\(244\) −1.74375 + 3.02026i −0.111632 + 0.193352i
\(245\) −20.8041 5.89659i −1.32912 0.376720i
\(246\) 0 0
\(247\) 18.6998 9.88990i 1.18984 0.629280i
\(248\) 36.6709i 2.32861i
\(249\) 0 0
\(250\) 3.34225 + 1.92965i 0.211382 + 0.122042i
\(251\) −8.48610 14.6984i −0.535638 0.927752i −0.999132 0.0416520i \(-0.986738\pi\)
0.463494 0.886100i \(-0.346595\pi\)
\(252\) 0 0
\(253\) −0.254066 0.0680768i −0.0159730 0.00427995i
\(254\) −6.79257 + 25.3502i −0.426204 + 1.59061i
\(255\) 0 0
\(256\) −21.1921 36.7057i −1.32450 2.29411i
\(257\) −3.36830 + 5.83406i −0.210109 + 0.363919i −0.951748 0.306880i \(-0.900715\pi\)
0.741640 + 0.670798i \(0.234048\pi\)
\(258\) 0 0
\(259\) −8.66968 15.2690i −0.538708 0.948771i
\(260\) 28.4023 + 53.7032i 1.76144 + 3.33053i
\(261\) 0 0
\(262\) −41.1559 + 11.0277i −2.54262 + 0.681294i
\(263\) 2.64276 4.57739i 0.162960 0.282254i −0.772969 0.634443i \(-0.781229\pi\)
0.935929 + 0.352189i \(0.114563\pi\)
\(264\) 0 0
\(265\) −9.12383 9.12383i −0.560472 0.560472i
\(266\) −10.6744 41.0156i −0.654488 2.51483i
\(267\) 0 0
\(268\) 32.3825 + 32.3825i 1.97808 + 1.97808i
\(269\) −2.83734 + 1.63814i −0.172995 + 0.0998789i −0.583997 0.811755i \(-0.698512\pi\)
0.411002 + 0.911634i \(0.365179\pi\)
\(270\) 0 0
\(271\) 3.01677 + 11.2587i 0.183256 + 0.683919i 0.994997 + 0.0999024i \(0.0318531\pi\)
−0.811742 + 0.584017i \(0.801480\pi\)
\(272\) 33.8821 2.05440
\(273\) 0 0
\(274\) −53.1036 −3.20811
\(275\) 0.555727 + 2.07400i 0.0335116 + 0.125067i
\(276\) 0 0
\(277\) 3.66204 2.11428i 0.220031 0.127035i −0.385934 0.922526i \(-0.626121\pi\)
0.605964 + 0.795492i \(0.292787\pi\)
\(278\) 10.8146 + 10.8146i 0.648618 + 0.648618i
\(279\) 0 0
\(280\) 74.6005 19.4149i 4.45823 1.16026i
\(281\) −18.2360 18.2360i −1.08787 1.08787i −0.995748 0.0921208i \(-0.970635\pi\)
−0.0921208 0.995748i \(-0.529365\pi\)
\(282\) 0 0
\(283\) 1.92179 3.32864i 0.114239 0.197867i −0.803236 0.595660i \(-0.796890\pi\)
0.917475 + 0.397793i \(0.130224\pi\)
\(284\) −11.6503 + 3.12170i −0.691320 + 0.185239i
\(285\) 0 0
\(286\) 1.37032 4.44693i 0.0810290 0.262953i
\(287\) 2.02237 + 3.56179i 0.119377 + 0.210246i
\(288\) 0 0
\(289\) 5.89449 10.2096i 0.346735 0.600562i
\(290\) 30.7512 + 53.2626i 1.80577 + 3.12768i
\(291\) 0 0
\(292\) 4.87079 18.1780i 0.285041 1.06379i
\(293\) 28.6306 + 7.67154i 1.67262 + 0.448176i 0.965814 0.259236i \(-0.0834707\pi\)
0.706802 + 0.707412i \(0.250137\pi\)
\(294\) 0 0
\(295\) 22.8310 + 39.5444i 1.32927 + 2.30236i
\(296\) 54.2085 + 31.2973i 3.15080 + 1.81912i
\(297\) 0 0
\(298\) 54.1539i 3.13705i
\(299\) 0.446995 + 1.95587i 0.0258504 + 0.113111i
\(300\) 0 0
\(301\) 10.9082 + 11.0663i 0.628737 + 0.637851i
\(302\) −1.22990 + 2.13025i −0.0707727 + 0.122582i
\(303\) 0 0
\(304\) 61.5766 + 61.5766i 3.53166 + 3.53166i
\(305\) 1.90780 + 0.511192i 0.109240 + 0.0292708i
\(306\) 0 0
\(307\) 20.2018 20.2018i 1.15298 1.15298i 0.167023 0.985953i \(-0.446584\pi\)
0.985953 0.167023i \(-0.0534155\pi\)
\(308\) −5.88293 3.45319i −0.335211 0.196764i
\(309\) 0 0
\(310\) −31.6745 + 8.48716i −1.79899 + 0.482038i
\(311\) 24.6309 1.39669 0.698345 0.715762i \(-0.253920\pi\)
0.698345 + 0.715762i \(0.253920\pi\)
\(312\) 0 0
\(313\) 8.19304i 0.463098i −0.972823 0.231549i \(-0.925621\pi\)
0.972823 0.231549i \(-0.0743794\pi\)
\(314\) 0.280560 0.0751759i 0.0158329 0.00424242i
\(315\) 0 0
\(316\) 55.7465 32.1852i 3.13598 1.81056i
\(317\) −6.24432 + 6.24432i −0.350716 + 0.350716i −0.860376 0.509660i \(-0.829771\pi\)
0.509660 + 0.860376i \(0.329771\pi\)
\(318\) 0 0
\(319\) 0.892129 3.32947i 0.0499496 0.186414i
\(320\) −64.3402 + 64.3402i −3.59672 + 3.59672i
\(321\) 0 0
\(322\) 4.01949 + 0.0289240i 0.223998 + 0.00161187i
\(323\) −12.9368 + 3.46641i −0.719823 + 0.192876i
\(324\) 0 0
\(325\) 12.0027 11.1432i 0.665791 0.618113i
\(326\) 39.1323 2.16734
\(327\) 0 0
\(328\) −12.6452 7.30069i −0.698213 0.403113i
\(329\) 21.1428 + 12.4105i 1.16564 + 0.684213i
\(330\) 0 0
\(331\) −28.6185 7.66830i −1.57301 0.421488i −0.636260 0.771475i \(-0.719519\pi\)
−0.936755 + 0.349987i \(0.886186\pi\)
\(332\) −13.4721 3.60985i −0.739379 0.198116i
\(333\) 0 0
\(334\) 33.4413 19.3074i 1.82983 1.05645i
\(335\) 12.9679 22.4611i 0.708513 1.22718i
\(336\) 0 0
\(337\) 24.6356i 1.34198i −0.741464 0.670992i \(-0.765868\pi\)
0.741464 0.670992i \(-0.234132\pi\)
\(338\) −34.8713 + 6.61838i −1.89675 + 0.359992i
\(339\) 0 0
\(340\) −9.95501 37.1526i −0.539886 2.01488i
\(341\) 1.59161 + 0.918916i 0.0861905 + 0.0497621i
\(342\) 0 0
\(343\) −12.8101 13.3754i −0.691679 0.722205i
\(344\) −53.5062 14.3369i −2.88486 0.772996i
\(345\) 0 0
\(346\) 0.804681 0.804681i 0.0432599 0.0432599i
\(347\) 6.69623 + 11.5982i 0.359472 + 0.622624i 0.987873 0.155266i \(-0.0496234\pi\)
−0.628401 + 0.777890i \(0.716290\pi\)
\(348\) 0 0
\(349\) −2.72247 10.1604i −0.145730 0.543874i −0.999722 0.0235863i \(-0.992492\pi\)
0.853991 0.520287i \(-0.174175\pi\)
\(350\) −16.2016 28.5342i −0.866010 1.52522i
\(351\) 0 0
\(352\) 10.2390 0.545738
\(353\) 14.9904 4.01667i 0.797859 0.213786i 0.163215 0.986590i \(-0.447813\pi\)
0.634644 + 0.772805i \(0.281147\pi\)
\(354\) 0 0
\(355\) 3.41538 + 5.91561i 0.181270 + 0.313968i
\(356\) −5.41601 5.41601i −0.287048 0.287048i
\(357\) 0 0
\(358\) 7.34206 27.4009i 0.388040 1.44818i
\(359\) 7.20920 + 7.20920i 0.380487 + 0.380487i 0.871278 0.490791i \(-0.163292\pi\)
−0.490791 + 0.871278i \(0.663292\pi\)
\(360\) 0 0
\(361\) −13.3564 7.71133i −0.702969 0.405859i
\(362\) −15.1564 56.5645i −0.796604 2.97297i
\(363\) 0 0
\(364\) −2.30500 + 51.9815i −0.120815 + 2.72457i
\(365\) −10.6580 −0.557868
\(366\) 0 0
\(367\) 13.1818 + 7.61053i 0.688085 + 0.397266i 0.802894 0.596121i \(-0.203292\pi\)
−0.114809 + 0.993388i \(0.536626\pi\)
\(368\) −7.15260 + 4.12955i −0.372855 + 0.215268i
\(369\) 0 0
\(370\) 14.4870 54.0660i 0.753141 2.81076i
\(371\) −2.78339 10.6950i −0.144506 0.555257i
\(372\) 0 0
\(373\) 16.3260 + 28.2774i 0.845326 + 1.46415i 0.885338 + 0.464948i \(0.153927\pi\)
−0.0400122 + 0.999199i \(0.512740\pi\)
\(374\) −1.47305 + 2.55141i −0.0761698 + 0.131930i
\(375\) 0 0
\(376\) −87.3969 −4.50715
\(377\) −25.6312 + 5.85776i −1.32007 + 0.301690i
\(378\) 0 0
\(379\) 6.47610 + 24.1691i 0.332655 + 1.24149i 0.906389 + 0.422444i \(0.138828\pi\)
−0.573734 + 0.819042i \(0.694506\pi\)
\(380\) 49.4284 85.6124i 2.53562 4.39183i
\(381\) 0 0
\(382\) 0.429428 0.429428i 0.0219714 0.0219714i
\(383\) 4.70967 17.5767i 0.240653 0.898129i −0.734866 0.678213i \(-0.762755\pi\)
0.975519 0.219917i \(-0.0705785\pi\)
\(384\) 0 0
\(385\) −1.02672 + 3.72435i −0.0523264 + 0.189811i
\(386\) −2.80129 4.85198i −0.142582 0.246959i
\(387\) 0 0
\(388\) −17.7274 66.1596i −0.899973 3.35874i
\(389\) 6.12739i 0.310671i 0.987862 + 0.155336i \(0.0496459\pi\)
−0.987862 + 0.155336i \(0.950354\pi\)
\(390\) 0 0
\(391\) 1.27024i 0.0642388i
\(392\) 63.5204 + 18.0039i 3.20826 + 0.909334i
\(393\) 0 0
\(394\) 31.1417 17.9797i 1.56890 0.905803i
\(395\) −25.7778 25.7778i −1.29702 1.29702i
\(396\) 0 0
\(397\) 12.7566 + 3.41813i 0.640237 + 0.171551i 0.564311 0.825563i \(-0.309142\pi\)
0.0759261 + 0.997113i \(0.475809\pi\)
\(398\) 5.76549 5.76549i 0.288998 0.288998i
\(399\) 0 0
\(400\) 58.3884 + 33.7105i 2.91942 + 1.68553i
\(401\) 4.95448 1.32755i 0.247415 0.0662946i −0.132980 0.991119i \(-0.542455\pi\)
0.380395 + 0.924824i \(0.375788\pi\)
\(402\) 0 0
\(403\) 0.520216 14.0088i 0.0259138 0.697827i
\(404\) 35.2811i 1.75530i
\(405\) 0 0
\(406\) −0.379042 + 52.6744i −0.0188115 + 2.61419i
\(407\) −2.71676 + 1.56852i −0.134665 + 0.0777488i
\(408\) 0 0
\(409\) −4.13326 + 15.4255i −0.204377 + 0.762744i 0.785262 + 0.619164i \(0.212528\pi\)
−0.989639 + 0.143580i \(0.954138\pi\)
\(410\) −3.37936 + 12.6119i −0.166895 + 0.622859i
\(411\) 0 0
\(412\) −40.2887 + 23.2607i −1.98488 + 1.14597i
\(413\) −0.281417 + 39.1078i −0.0138476 + 1.92437i
\(414\) 0 0
\(415\) 7.89891i 0.387742i
\(416\) −36.5130 69.0388i −1.79020 3.38491i
\(417\) 0 0
\(418\) −7.31398 + 1.95977i −0.357738 + 0.0958557i
\(419\) −12.6468 7.30162i −0.617836 0.356708i 0.158190 0.987409i \(-0.449434\pi\)
−0.776026 + 0.630701i \(0.782767\pi\)
\(420\) 0 0
\(421\) 2.04328 2.04328i 0.0995835 0.0995835i −0.655560 0.755143i \(-0.727567\pi\)
0.755143 + 0.655560i \(0.227567\pi\)
\(422\) 19.0495 + 5.10429i 0.927314 + 0.248473i
\(423\) 0 0
\(424\) 27.8575 + 27.8575i 1.35288 + 1.35288i
\(425\) −8.98005 + 5.18464i −0.435597 + 0.251492i
\(426\) 0 0
\(427\) 1.18753 + 1.20475i 0.0574687 + 0.0583018i
\(428\) 25.5729i 1.23611i
\(429\) 0 0
\(430\) 49.5341i 2.38875i
\(431\) −2.83206 10.5694i −0.136416 0.509110i −0.999988 0.00488525i \(-0.998445\pi\)
0.863572 0.504225i \(-0.168222\pi\)
\(432\) 0 0
\(433\) −17.9201 31.0385i −0.861184 1.49161i −0.870787 0.491660i \(-0.836390\pi\)
0.00960365 0.999954i \(-0.496943\pi\)
\(434\) −27.0757 7.46415i −1.29968 0.358291i
\(435\) 0 0
\(436\) −7.30914 + 27.2781i −0.350044 + 1.30638i
\(437\) 2.30851 2.30851i 0.110431 0.110431i
\(438\) 0 0
\(439\) 0.772225 1.33753i 0.0368563 0.0638369i −0.847009 0.531579i \(-0.821599\pi\)
0.883865 + 0.467742i \(0.154932\pi\)
\(440\) −3.56449 13.3029i −0.169931 0.634190i
\(441\) 0 0
\(442\) 22.4565 + 0.833923i 1.06815 + 0.0396657i
\(443\) 16.1657 0.768055 0.384027 0.923322i \(-0.374537\pi\)
0.384027 + 0.923322i \(0.374537\pi\)
\(444\) 0 0
\(445\) −2.16890 + 3.75664i −0.102816 + 0.178082i
\(446\) 26.2432 + 45.4546i 1.24265 + 2.15234i
\(447\) 0 0
\(448\) −75.4199 + 19.6281i −3.56326 + 0.927343i
\(449\) 3.96795 14.8086i 0.187259 0.698861i −0.806876 0.590720i \(-0.798844\pi\)
0.994136 0.108140i \(-0.0344896\pi\)
\(450\) 0 0
\(451\) 0.633736 0.365888i 0.0298415 0.0172290i
\(452\) −41.6793 24.0636i −1.96043 1.13186i
\(453\) 0 0
\(454\) 42.1526 1.97832
\(455\) 28.7738 6.35845i 1.34894 0.298089i
\(456\) 0 0
\(457\) −7.14198 26.6542i −0.334088 1.24683i −0.904855 0.425720i \(-0.860021\pi\)
0.570767 0.821112i \(-0.306646\pi\)
\(458\) −28.0382 16.1879i −1.31014 0.756410i
\(459\) 0 0
\(460\) 6.62969 + 6.62969i 0.309111 + 0.309111i
\(461\) 0.630674 2.35371i 0.0293734 0.109623i −0.949683 0.313214i \(-0.898594\pi\)
0.979056 + 0.203590i \(0.0652611\pi\)
\(462\) 0 0
\(463\) −15.9059 15.9059i −0.739208 0.739208i 0.233216 0.972425i \(-0.425075\pi\)
−0.972425 + 0.233216i \(0.925075\pi\)
\(464\) −54.1167 93.7330i −2.51231 4.35144i
\(465\) 0 0
\(466\) 52.6238 14.1005i 2.43775 0.653193i
\(467\) 6.66294 0.308324 0.154162 0.988046i \(-0.450732\pi\)
0.154162 + 0.988046i \(0.450732\pi\)
\(468\) 0 0
\(469\) 19.3170 10.9681i 0.891977 0.506460i
\(470\) 20.2272 + 75.4891i 0.933013 + 3.48205i
\(471\) 0 0
\(472\) −69.7091 120.740i −3.20862 5.55750i
\(473\) 1.96304 1.96304i 0.0902607 0.0902607i
\(474\) 0 0
\(475\) −25.7426 6.89772i −1.18115 0.316489i
\(476\) 8.75507 31.7585i 0.401288 1.45565i
\(477\) 0 0
\(478\) 17.6467 + 10.1883i 0.807140 + 0.466003i
\(479\) 5.91010 + 22.0568i 0.270039 + 1.00780i 0.959093 + 0.283090i \(0.0913596\pi\)
−0.689054 + 0.724710i \(0.741974\pi\)
\(480\) 0 0
\(481\) 20.2644 + 12.7250i 0.923975 + 0.580209i
\(482\) 23.6057i 1.07521i
\(483\) 0 0
\(484\) 29.3904 50.9056i 1.33593 2.31389i
\(485\) −33.5934 + 19.3952i −1.52540 + 0.880689i
\(486\) 0 0
\(487\) 12.0330 + 3.22424i 0.545269 + 0.146104i 0.520930 0.853600i \(-0.325585\pi\)
0.0243387 + 0.999704i \(0.492252\pi\)
\(488\) −5.82501 1.56081i −0.263686 0.0706544i
\(489\) 0 0
\(490\) 0.849633 59.0325i 0.0383825 2.66682i
\(491\) 16.7889 + 9.69310i 0.757674 + 0.437443i 0.828460 0.560048i \(-0.189217\pi\)
−0.0707859 + 0.997492i \(0.522551\pi\)
\(492\) 0 0
\(493\) 16.6462 0.749706
\(494\) 39.2965 + 42.3276i 1.76803 + 1.90441i
\(495\) 0 0
\(496\) 55.7417 14.9359i 2.50288 0.670644i
\(497\) −0.0420983 + 5.85029i −0.00188837 + 0.262421i
\(498\) 0 0
\(499\) −24.6585 + 24.6585i −1.10386 + 1.10386i −0.109925 + 0.993940i \(0.535061\pi\)
−0.993940 + 0.109925i \(0.964939\pi\)
\(500\) −1.99549 + 7.44727i −0.0892410 + 0.333052i
\(501\) 0 0
\(502\) 32.7667 32.7667i 1.46245 1.46245i
\(503\) −27.3019 + 15.7627i −1.21733 + 0.702826i −0.964346 0.264644i \(-0.914745\pi\)
−0.252984 + 0.967470i \(0.581412\pi\)
\(504\) 0 0
\(505\) −19.3001 + 5.17146i −0.858845 + 0.230127i
\(506\) 0.718145i 0.0319254i
\(507\) 0 0
\(508\) −52.4305 −2.32623
\(509\) 3.80510 1.01957i 0.168658 0.0451918i −0.173502 0.984834i \(-0.555508\pi\)
0.342160 + 0.939642i \(0.388842\pi\)
\(510\) 0 0
\(511\) −7.87243 4.62100i −0.348256 0.204421i
\(512\) 29.3590 29.3590i 1.29750 1.29750i
\(513\) 0 0
\(514\) −17.7662 4.76043i −0.783632 0.209973i
\(515\) 18.6300 + 18.6300i 0.820935 + 0.820935i
\(516\) 0 0
\(517\) 2.19003 3.79325i 0.0963175 0.166827i
\(518\) 34.1419 33.6541i 1.50011 1.47868i
\(519\) 0 0
\(520\) −76.9868 + 71.4737i −3.37609 + 3.13433i
\(521\) 7.46834i 0.327194i 0.986527 + 0.163597i \(0.0523097\pi\)
−0.986527 + 0.163597i \(0.947690\pi\)
\(522\) 0 0
\(523\) 10.8561 + 6.26775i 0.474703 + 0.274070i 0.718206 0.695830i \(-0.244963\pi\)
−0.243504 + 0.969900i \(0.578297\pi\)
\(524\) −42.5603 73.7166i −1.85925 3.22032i
\(525\) 0 0
\(526\) 13.9393 + 3.73502i 0.607782 + 0.162855i
\(527\) −2.29713 + 8.57300i −0.100064 + 0.373446i
\(528\) 0 0
\(529\) −11.3452 19.6504i −0.493269 0.854367i
\(530\) 17.6145 30.5093i 0.765127 1.32524i
\(531\) 0 0
\(532\) 73.6285 41.8059i 3.19220 1.81252i
\(533\) −4.72705 2.96834i −0.204751 0.128573i
\(534\) 0 0
\(535\) −13.9893 + 3.74843i −0.604812 + 0.162059i
\(536\) −39.5945 + 68.5797i −1.71022 + 2.96219i
\(537\) 0 0
\(538\) −6.32520 6.32520i −0.272699 0.272699i
\(539\) −2.37314 + 2.30579i −0.102218 + 0.0993175i
\(540\) 0 0
\(541\) −2.43106 2.43106i −0.104519 0.104519i 0.652913 0.757433i \(-0.273547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(542\) −27.5604 + 15.9120i −1.18382 + 0.683479i
\(543\) 0 0
\(544\) 12.7978 + 47.7620i 0.548701 + 2.04778i
\(545\) 15.9935 0.685088
\(546\) 0 0
\(547\) 28.6604 1.22543 0.612716 0.790303i \(-0.290077\pi\)
0.612716 + 0.790303i \(0.290077\pi\)
\(548\) −27.4578 102.474i −1.17294 4.37747i
\(549\) 0 0
\(550\) −5.07698 + 2.93119i −0.216483 + 0.124987i
\(551\) 30.2524 + 30.2524i 1.28880 + 1.28880i
\(552\) 0 0
\(553\) −7.86399 30.2169i −0.334411 1.28495i
\(554\) 8.16369 + 8.16369i 0.346842 + 0.346842i
\(555\) 0 0
\(556\) −15.2771 + 26.4608i −0.647895 + 1.12219i
\(557\) 40.3737 10.8181i 1.71069 0.458378i 0.735097 0.677962i \(-0.237137\pi\)
0.975594 + 0.219584i \(0.0704701\pi\)
\(558\) 0 0
\(559\) −20.2367 6.23594i −0.855920 0.263752i
\(560\) 59.8961 + 105.489i 2.53107 + 4.45772i
\(561\) 0 0
\(562\) 35.2066 60.9796i 1.48510 2.57227i
\(563\) −12.8281 22.2190i −0.540641 0.936418i −0.998867 0.0475822i \(-0.984848\pi\)
0.458226 0.888836i \(-0.348485\pi\)
\(564\) 0 0
\(565\) −7.05441 + 26.3274i −0.296781 + 1.10760i
\(566\) 10.1365 + 2.71608i 0.426070 + 0.114165i
\(567\) 0 0
\(568\) −10.4281 18.0620i −0.437552 0.757863i
\(569\) −20.8100 12.0147i −0.872401 0.503681i −0.00425579 0.999991i \(-0.501355\pi\)
−0.868145 + 0.496310i \(0.834688\pi\)
\(570\) 0 0
\(571\) 9.57728i 0.400797i −0.979714 0.200398i \(-0.935776\pi\)
0.979714 0.200398i \(-0.0642236\pi\)
\(572\) 9.28978 + 0.344976i 0.388425 + 0.0144242i
\(573\) 0 0
\(574\) −7.96426 + 7.85046i −0.332422 + 0.327672i
\(575\) 1.26381 2.18898i 0.0527045 0.0912868i
\(576\) 0 0
\(577\) −31.4027 31.4027i −1.30731 1.30731i −0.923347 0.383966i \(-0.874558\pi\)
−0.383966 0.923347i \(-0.625442\pi\)
\(578\) 31.0906 + 8.33071i 1.29320 + 0.346512i
\(579\) 0 0
\(580\) −86.8804 + 86.8804i −3.60751 + 3.60751i
\(581\) −3.42472 + 5.83443i −0.142081 + 0.242053i
\(582\) 0 0
\(583\) −1.90715 + 0.511019i −0.0789861 + 0.0211643i
\(584\) 32.5419 1.34659
\(585\) 0 0
\(586\) 80.9274i 3.34308i
\(587\) −6.09066 + 1.63199i −0.251388 + 0.0673593i −0.382312 0.924033i \(-0.624872\pi\)
0.130924 + 0.991392i \(0.458206\pi\)
\(588\) 0 0
\(589\) −19.7552 + 11.4056i −0.813997 + 0.469961i
\(590\) −88.1553 + 88.1553i −3.62930 + 3.62930i
\(591\) 0 0
\(592\) −25.4945 + 95.1470i −1.04782 + 3.91052i
\(593\) −27.7021 + 27.7021i −1.13759 + 1.13759i −0.148708 + 0.988881i \(0.547511\pi\)
−0.988881 + 0.148708i \(0.952489\pi\)
\(594\) 0 0
\(595\) −18.6564 0.134250i −0.764839 0.00550373i
\(596\) −104.501 + 28.0009i −4.28052 + 1.14696i
\(597\) 0 0
\(598\) −4.84227 + 2.56096i −0.198015 + 0.104726i
\(599\) −3.79502 −0.155060 −0.0775301 0.996990i \(-0.524703\pi\)
−0.0775301 + 0.996990i \(0.524703\pi\)
\(600\) 0 0
\(601\) 28.0748 + 16.2090i 1.14520 + 0.661180i 0.947712 0.319126i \(-0.103389\pi\)
0.197485 + 0.980306i \(0.436723\pi\)
\(602\) −21.4764 + 36.5877i −0.875314 + 1.49120i
\(603\) 0 0
\(604\) −4.74667 1.27187i −0.193139 0.0517515i
\(605\) −32.1553 8.61600i −1.30730 0.350290i
\(606\) 0 0
\(607\) 7.81574 4.51242i 0.317231 0.183154i −0.332927 0.942953i \(-0.608036\pi\)
0.650158 + 0.759799i \(0.274703\pi\)
\(608\) −63.5433 + 110.060i −2.57702 + 4.46353i
\(609\) 0 0
\(610\) 5.39259i 0.218340i
\(611\) −33.3868 1.23982i −1.35068 0.0501576i
\(612\) 0 0
\(613\) −6.48271 24.1938i −0.261834 0.977179i −0.964160 0.265323i \(-0.914521\pi\)
0.702325 0.711856i \(-0.252145\pi\)
\(614\) 67.5530 + 39.0017i 2.72622 + 1.57398i
\(615\) 0 0
\(616\) 3.13484 11.3715i 0.126306 0.458169i
\(617\) −22.1083 5.92389i −0.890045 0.238487i −0.215309 0.976546i \(-0.569076\pi\)
−0.674736 + 0.738059i \(0.735743\pi\)
\(618\) 0 0
\(619\) 27.9275 27.9275i 1.12250 1.12250i 0.131135 0.991365i \(-0.458138\pi\)
0.991365 0.131135i \(-0.0418620\pi\)
\(620\) −32.7553 56.7339i −1.31549 2.27849i
\(621\) 0 0
\(622\) 17.4055 + 64.9581i 0.697895 + 2.60458i
\(623\) −3.23079 + 1.83443i −0.129439 + 0.0734948i
\(624\) 0 0
\(625\) 27.0785 1.08314
\(626\) 21.6072 5.78963i 0.863597 0.231400i
\(627\) 0 0
\(628\) 0.290133 + 0.502526i 0.0115776 + 0.0200530i
\(629\) −10.7124 10.7124i −0.427133 0.427133i
\(630\) 0 0
\(631\) −12.1764 + 45.4430i −0.484736 + 1.80906i 0.0965126 + 0.995332i \(0.469231\pi\)
−0.581248 + 0.813726i \(0.697435\pi\)
\(632\) 78.7066 + 78.7066i 3.13078 + 3.13078i
\(633\) 0 0
\(634\) −20.8805 12.0553i −0.829269 0.478779i
\(635\) 7.68518 + 28.6815i 0.304977 + 1.13819i
\(636\) 0 0
\(637\) 24.0102 + 7.77882i 0.951319 + 0.308208i
\(638\) 9.41110 0.372589
\(639\) 0 0
\(640\) −99.2522 57.3033i −3.92329 2.26511i
\(641\) 2.21029 1.27611i 0.0873011 0.0504033i −0.455714 0.890126i \(-0.650616\pi\)
0.543015 + 0.839723i \(0.317283\pi\)
\(642\) 0 0
\(643\) −7.09734 + 26.4876i −0.279892 + 1.04457i 0.672600 + 0.740006i \(0.265177\pi\)
−0.952492 + 0.304564i \(0.901489\pi\)
\(644\) 2.02251 + 7.77136i 0.0796980 + 0.306235i
\(645\) 0 0
\(646\) −18.2836 31.6682i −0.719360 1.24597i
\(647\) 2.97944 5.16054i 0.117134 0.202882i −0.801497 0.597999i \(-0.795963\pi\)
0.918631 + 0.395117i \(0.129296\pi\)
\(648\) 0 0
\(649\) 6.98721 0.274272
\(650\) 37.8693 + 23.7799i 1.48535 + 0.932726i
\(651\) 0 0
\(652\) 20.2338 + 75.5135i 0.792416 + 2.95734i
\(653\) 9.88229 17.1166i 0.386724 0.669825i −0.605283 0.796010i \(-0.706940\pi\)
0.992007 + 0.126185i \(0.0402733\pi\)
\(654\) 0 0
\(655\) −34.0874 + 34.0874i −1.33190 + 1.33190i
\(656\) 5.94709 22.1949i 0.232195 0.866563i
\(657\) 0 0
\(658\) −17.7891 + 64.5289i −0.693492 + 2.51560i
\(659\) −0.623376 1.07972i −0.0242833 0.0420599i 0.853628 0.520882i \(-0.174397\pi\)
−0.877912 + 0.478823i \(0.841064\pi\)
\(660\) 0 0
\(661\) −6.22445 23.2300i −0.242103 0.903541i −0.974817 0.223004i \(-0.928414\pi\)
0.732714 0.680536i \(-0.238253\pi\)
\(662\) 80.8932i 3.14400i
\(663\) 0 0
\(664\) 24.1175i 0.935940i
\(665\) −33.6618 34.1498i −1.30535 1.32427i
\(666\) 0 0
\(667\) −3.51405 + 2.02884i −0.136065 + 0.0785569i
\(668\) 54.5486 + 54.5486i 2.11055 + 2.11055i
\(669\) 0 0
\(670\) 68.3995 + 18.3276i 2.64250 + 0.708057i
\(671\) 0.213709 0.213709i 0.00825013 0.00825013i
\(672\) 0 0
\(673\) −43.6649 25.2100i −1.68316 0.971772i −0.959540 0.281573i \(-0.909144\pi\)
−0.723619 0.690199i \(-0.757523\pi\)
\(674\) 64.9704 17.4088i 2.50257 0.670561i
\(675\) 0 0
\(676\) −30.8021 63.8690i −1.18469 2.45650i
\(677\) 30.3365i 1.16593i −0.812498 0.582964i \(-0.801893\pi\)
0.812498 0.582964i \(-0.198107\pi\)
\(678\) 0 0
\(679\) −33.2225 0.239067i −1.27496 0.00917454i
\(680\) 57.5991 33.2548i 2.20882 1.27526i
\(681\) 0 0
\(682\) −1.29871 + 4.84684i −0.0497301 + 0.185595i
\(683\) 6.38263 23.8203i 0.244224 0.911458i −0.729547 0.683930i \(-0.760269\pi\)
0.973772 0.227528i \(-0.0730642\pi\)
\(684\) 0 0
\(685\) −52.0325 + 30.0410i −1.98806 + 1.14781i
\(686\) 26.2222 43.2353i 1.00117 1.65073i
\(687\) 0 0
\(688\) 87.1715i 3.32338i
\(689\) 10.2467 + 11.0371i 0.390370 + 0.420481i
\(690\) 0 0
\(691\) 40.1209 10.7504i 1.52627 0.408963i 0.604470 0.796628i \(-0.293385\pi\)
0.921800 + 0.387666i \(0.126718\pi\)
\(692\) 1.96886 + 1.13672i 0.0748449 + 0.0432117i
\(693\) 0 0
\(694\) −25.8556 + 25.8556i −0.981464 + 0.981464i
\(695\) 16.7144 + 4.47860i 0.634012 + 0.169883i
\(696\) 0 0
\(697\) 2.49888 + 2.49888i 0.0946519 + 0.0946519i
\(698\) 24.8718 14.3597i 0.941411 0.543524i
\(699\) 0 0
\(700\) 46.6851 46.0181i 1.76453 1.73932i
\(701\) 1.87133i 0.0706790i −0.999375 0.0353395i \(-0.988749\pi\)
0.999375 0.0353395i \(-0.0112513\pi\)
\(702\) 0 0
\(703\) 38.9372i 1.46854i
\(704\) 3.60365 + 13.4490i 0.135818 + 0.506878i
\(705\) 0 0
\(706\) 21.1860 + 36.6952i 0.797346 + 1.38104i
\(707\) −16.4980 4.54811i −0.620471 0.171049i
\(708\) 0 0
\(709\) −1.15519 + 4.31123i −0.0433841 + 0.161912i −0.984219 0.176953i \(-0.943376\pi\)
0.940835 + 0.338864i \(0.110043\pi\)
\(710\) −13.1875 + 13.1875i −0.494919 + 0.494919i
\(711\) 0 0
\(712\) 6.62222 11.4700i 0.248178 0.429858i
\(713\) −0.559949 2.08976i −0.0209702 0.0782620i
\(714\) 0 0
\(715\) −1.17297 5.13244i −0.0438665 0.191942i
\(716\) 56.6718 2.11793
\(717\) 0 0
\(718\) −13.9181 + 24.1069i −0.519421 + 0.899663i
\(719\) −9.74009 16.8703i −0.363244 0.629157i 0.625249 0.780426i \(-0.284998\pi\)
−0.988493 + 0.151269i \(0.951664\pi\)
\(720\) 0 0
\(721\) 5.68342 + 21.8382i 0.211662 + 0.813296i
\(722\) 10.8984 40.6736i 0.405598 1.51371i
\(723\) 0 0
\(724\) 101.316 58.4946i 3.76537 2.17394i
\(725\) 28.6860 + 16.5619i 1.06537 + 0.615093i
\(726\) 0 0
\(727\) −36.9369 −1.36991 −0.684957 0.728583i \(-0.740179\pi\)
−0.684957 + 0.728583i \(0.740179\pi\)
\(728\) −87.8541 + 19.4141i −3.25609 + 0.719533i
\(729\) 0 0
\(730\) −7.53153 28.1080i −0.278754 1.04033i
\(731\) 11.6107 + 6.70343i 0.429437 + 0.247935i
\(732\) 0 0
\(733\) 7.39416 + 7.39416i 0.273109 + 0.273109i 0.830351 0.557241i \(-0.188140\pi\)
−0.557241 + 0.830351i \(0.688140\pi\)
\(734\) −10.7560 + 40.1419i −0.397011 + 1.48166i
\(735\) 0 0
\(736\) −8.52289 8.52289i −0.314158 0.314158i
\(737\) −1.98435 3.43700i −0.0730946 0.126604i
\(738\) 0 0
\(739\) −40.7446 + 10.9175i −1.49882 + 0.401606i −0.912703 0.408623i \(-0.866009\pi\)
−0.586112 + 0.810230i \(0.699342\pi\)
\(740\) 111.822 4.11065
\(741\) 0 0
\(742\) 26.2386 14.8982i 0.963250 0.546929i
\(743\) 0.209458 + 0.781707i 0.00768426 + 0.0286780i 0.969662 0.244452i \(-0.0786079\pi\)
−0.961977 + 0.273130i \(0.911941\pi\)
\(744\) 0 0
\(745\) 30.6351 + 53.0616i 1.12238 + 1.94403i
\(746\) −63.0380 + 63.0380i −2.30799 + 2.30799i
\(747\) 0 0
\(748\) −5.68510 1.52332i −0.207868 0.0556980i
\(749\) −11.9583 3.29661i −0.436945 0.120456i
\(750\) 0 0
\(751\) 41.4868 + 23.9524i 1.51387 + 0.874035i 0.999868 + 0.0162488i \(0.00517239\pi\)
0.514006 + 0.857787i \(0.328161\pi\)
\(752\) −35.5965 132.848i −1.29807 4.84446i
\(753\) 0 0
\(754\) −33.5608 63.4568i −1.22221 2.31096i
\(755\) 2.78304i 0.101285i
\(756\) 0 0
\(757\) 1.02223 1.77055i 0.0371534 0.0643516i −0.846851 0.531831i \(-0.821504\pi\)
0.884004 + 0.467479i \(0.154838\pi\)
\(758\) −59.1640 + 34.1583i −2.14893 + 1.24069i
\(759\) 0 0
\(760\) 165.116 + 44.2427i 5.98939 + 1.60485i
\(761\) −13.8918 3.72230i −0.503578 0.134933i −0.00191784 0.999998i \(-0.500610\pi\)
−0.501660 + 0.865065i \(0.667277\pi\)
\(762\) 0 0
\(763\) 11.8134 + 6.93430i 0.427674 + 0.251038i
\(764\) 1.05071 + 0.606626i 0.0380132 + 0.0219470i
\(765\) 0 0
\(766\) 49.6825 1.79510
\(767\) −24.9170 47.1130i −0.899700 1.70115i
\(768\) 0 0
\(769\) −9.09993 + 2.43832i −0.328152 + 0.0879280i −0.419134 0.907925i \(-0.637666\pi\)
0.0909818 + 0.995853i \(0.470999\pi\)
\(770\) −10.5476 0.0759000i −0.380110 0.00273525i
\(771\) 0 0
\(772\) 7.91442 7.91442i 0.284846 0.284846i
\(773\) 6.89949 25.7493i 0.248157 0.926136i −0.723613 0.690206i \(-0.757520\pi\)
0.971770 0.235930i \(-0.0758136\pi\)
\(774\) 0 0
\(775\) −12.4882 + 12.4882i −0.448589 + 0.448589i
\(776\) 102.570 59.2186i 3.68204 2.12583i
\(777\) 0 0
\(778\) −16.1595 + 4.32993i −0.579347 + 0.155236i
\(779\) 9.08284i 0.325427i
\(780\) 0 0
\(781\) 1.04525 0.0374018
\(782\) 3.34995 0.897617i 0.119794 0.0320987i
\(783\) 0 0
\(784\) −1.49521 + 103.887i −0.0534003 + 3.71026i
\(785\) 0.232374 0.232374i 0.00829378 0.00829378i
\(786\) 0 0
\(787\) −42.0566 11.2690i −1.49916 0.401698i −0.586339 0.810066i \(-0.699431\pi\)
−0.912817 + 0.408368i \(0.866098\pi\)
\(788\) 50.7975 + 50.7975i 1.80959 + 1.80959i