Properties

Label 666.2.x.g.379.2
Level $666$
Weight $2$
Character 666.379
Analytic conductor $5.318$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.x (of order \(9\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 24x^{10} + 264x^{8} - 1687x^{6} + 6600x^{4} - 15000x^{2} + 15625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 74)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 379.2
Root \(2.14169 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 666.379
Dual form 666.2.x.g.181.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(0.773586 + 0.649116i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\) \(q+(-0.173648 - 0.984808i) q^{2} +(-0.939693 + 0.342020i) q^{4} +(-0.266044 - 0.223238i) q^{5} +(0.773586 + 0.649116i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.173648 + 0.300767i) q^{10} +(-2.73237 - 4.73261i) q^{11} +(-5.97892 + 2.17615i) q^{13} +(0.504922 - 0.874551i) q^{14} +(0.766044 - 0.642788i) q^{16} +(0.490749 + 0.178618i) q^{17} +(0.869950 - 4.93373i) q^{19} +(0.326352 + 0.118782i) q^{20} +(-4.18624 + 3.51267i) q^{22} +(0.721492 - 1.24966i) q^{23} +(-0.847296 - 4.80526i) q^{25} +(3.18132 + 5.51020i) q^{26} +(-0.948944 - 0.345387i) q^{28} +(-3.16714 - 5.48565i) q^{29} +3.30777 q^{31} +(-0.766044 - 0.642788i) q^{32} +(0.0906868 - 0.514310i) q^{34} +(-0.0609011 - 0.345387i) q^{35} +(-5.88521 + 1.53765i) q^{37} -5.00984 q^{38} +(0.0603074 - 0.342020i) q^{40} +(-1.03412 + 0.376390i) q^{41} -6.27037 q^{43} +(4.18624 + 3.51267i) q^{44} +(-1.35596 - 0.493529i) q^{46} +(-5.71910 + 9.90577i) q^{47} +(-1.03845 - 5.88936i) q^{49} +(-4.58512 + 1.66885i) q^{50} +(4.87406 - 4.08982i) q^{52} +(-0.0706817 + 0.0593090i) q^{53} +(-0.329565 + 1.86905i) q^{55} +(-0.175358 + 0.994503i) q^{56} +(-4.85235 + 4.07160i) q^{58} +(-2.29059 + 1.92203i) q^{59} +(-3.58571 + 1.30509i) q^{61} +(-0.574388 - 3.25751i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(2.07646 + 0.755769i) q^{65} +(-0.892251 - 0.748687i) q^{67} -0.522244 q^{68} +(-0.329565 + 0.119952i) q^{70} +(-0.0543332 + 0.308139i) q^{71} +13.2325 q^{73} +(2.53624 + 5.52879i) q^{74} +(0.869950 + 4.93373i) q^{76} +(0.958285 - 5.43471i) q^{77} +(7.12939 + 5.98227i) q^{79} -0.347296 q^{80} +(0.550245 + 0.953052i) q^{82} +(8.89395 + 3.23713i) q^{83} +(-0.0906868 - 0.157074i) q^{85} +(1.08884 + 6.17511i) q^{86} +(2.73237 - 4.73261i) q^{88} +(12.0788 - 10.1354i) q^{89} +(-6.03778 - 2.19757i) q^{91} +(-0.250571 + 1.42106i) q^{92} +(10.7484 + 3.91209i) q^{94} +(-1.33284 + 1.11839i) q^{95} +(0.464564 - 0.804648i) q^{97} +(-5.61956 + 2.04535i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{5} + 6 q^{7} + 6 q^{8} - 3 q^{11} - 6 q^{13} - 3 q^{14} + 3 q^{17} - 3 q^{19} + 6 q^{20} - 3 q^{22} + 21 q^{23} - 6 q^{25} - 3 q^{28} - 6 q^{29} + 42 q^{31} - 3 q^{34} + 9 q^{35} - 3 q^{37} - 42 q^{38} + 12 q^{40} + 21 q^{41} + 36 q^{43} + 3 q^{44} + 3 q^{46} - 9 q^{47} - 12 q^{49} - 12 q^{50} + 3 q^{52} + 6 q^{53} + 3 q^{56} - 3 q^{58} + 6 q^{59} - 18 q^{61} + 33 q^{62} - 6 q^{64} - 3 q^{65} - 27 q^{67} - 6 q^{68} + 18 q^{71} + 54 q^{73} - 3 q^{74} - 3 q^{76} - 51 q^{77} - 12 q^{79} - 18 q^{82} + 6 q^{83} + 3 q^{85} + 3 q^{88} + 15 q^{89} - 51 q^{91} + 6 q^{92} - 12 q^{94} + 15 q^{95} - 42 q^{97} - 51 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.173648 0.984808i −0.122788 0.696364i
\(3\) 0 0
\(4\) −0.939693 + 0.342020i −0.469846 + 0.171010i
\(5\) −0.266044 0.223238i −0.118979 0.0998350i 0.581357 0.813649i \(-0.302522\pi\)
−0.700336 + 0.713814i \(0.746966\pi\)
\(6\) 0 0
\(7\) 0.773586 + 0.649116i 0.292388 + 0.245343i 0.777168 0.629294i \(-0.216656\pi\)
−0.484780 + 0.874636i \(0.661100\pi\)
\(8\) 0.500000 + 0.866025i 0.176777 + 0.306186i
\(9\) 0 0
\(10\) −0.173648 + 0.300767i −0.0549124 + 0.0951110i
\(11\) −2.73237 4.73261i −0.823842 1.42694i −0.902801 0.430058i \(-0.858493\pi\)
0.0789595 0.996878i \(-0.474840\pi\)
\(12\) 0 0
\(13\) −5.97892 + 2.17615i −1.65825 + 0.603555i −0.990087 0.140456i \(-0.955143\pi\)
−0.668167 + 0.744011i \(0.732921\pi\)
\(14\) 0.504922 0.874551i 0.134946 0.233734i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) 0.490749 + 0.178618i 0.119024 + 0.0433212i 0.400846 0.916146i \(-0.368716\pi\)
−0.281821 + 0.959467i \(0.590939\pi\)
\(18\) 0 0
\(19\) 0.869950 4.93373i 0.199580 1.13188i −0.706163 0.708049i \(-0.749575\pi\)
0.905743 0.423827i \(-0.139313\pi\)
\(20\) 0.326352 + 0.118782i 0.0729745 + 0.0265605i
\(21\) 0 0
\(22\) −4.18624 + 3.51267i −0.892509 + 0.748904i
\(23\) 0.721492 1.24966i 0.150441 0.260572i −0.780948 0.624596i \(-0.785264\pi\)
0.931390 + 0.364023i \(0.118597\pi\)
\(24\) 0 0
\(25\) −0.847296 4.80526i −0.169459 0.961051i
\(26\) 3.18132 + 5.51020i 0.623908 + 1.08064i
\(27\) 0 0
\(28\) −0.948944 0.345387i −0.179333 0.0652720i
\(29\) −3.16714 5.48565i −0.588124 1.01866i −0.994478 0.104945i \(-0.966533\pi\)
0.406354 0.913716i \(-0.366800\pi\)
\(30\) 0 0
\(31\) 3.30777 0.594092 0.297046 0.954863i \(-0.403998\pi\)
0.297046 + 0.954863i \(0.403998\pi\)
\(32\) −0.766044 0.642788i −0.135419 0.113630i
\(33\) 0 0
\(34\) 0.0906868 0.514310i 0.0155527 0.0882035i
\(35\) −0.0609011 0.345387i −0.0102942 0.0583811i
\(36\) 0 0
\(37\) −5.88521 + 1.53765i −0.967522 + 0.252787i
\(38\) −5.00984 −0.812704
\(39\) 0 0
\(40\) 0.0603074 0.342020i 0.00953543 0.0540781i
\(41\) −1.03412 + 0.376390i −0.161503 + 0.0587822i −0.421506 0.906825i \(-0.638498\pi\)
0.260004 + 0.965608i \(0.416276\pi\)
\(42\) 0 0
\(43\) −6.27037 −0.956222 −0.478111 0.878299i \(-0.658678\pi\)
−0.478111 + 0.878299i \(0.658678\pi\)
\(44\) 4.18624 + 3.51267i 0.631099 + 0.529555i
\(45\) 0 0
\(46\) −1.35596 0.493529i −0.199926 0.0727670i
\(47\) −5.71910 + 9.90577i −0.834216 + 1.44491i 0.0604506 + 0.998171i \(0.480746\pi\)
−0.894667 + 0.446734i \(0.852587\pi\)
\(48\) 0 0
\(49\) −1.03845 5.88936i −0.148350 0.841337i
\(50\) −4.58512 + 1.66885i −0.648434 + 0.236011i
\(51\) 0 0
\(52\) 4.87406 4.08982i 0.675911 0.567156i
\(53\) −0.0706817 + 0.0593090i −0.00970887 + 0.00814671i −0.647629 0.761956i \(-0.724239\pi\)
0.637920 + 0.770102i \(0.279795\pi\)
\(54\) 0 0
\(55\) −0.329565 + 1.86905i −0.0444385 + 0.252023i
\(56\) −0.175358 + 0.994503i −0.0234332 + 0.132896i
\(57\) 0 0
\(58\) −4.85235 + 4.07160i −0.637144 + 0.534628i
\(59\) −2.29059 + 1.92203i −0.298210 + 0.250228i −0.779599 0.626279i \(-0.784577\pi\)
0.481389 + 0.876507i \(0.340132\pi\)
\(60\) 0 0
\(61\) −3.58571 + 1.30509i −0.459103 + 0.167100i −0.561210 0.827674i \(-0.689664\pi\)
0.102107 + 0.994773i \(0.467442\pi\)
\(62\) −0.574388 3.25751i −0.0729473 0.413705i
\(63\) 0 0
\(64\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(65\) 2.07646 + 0.755769i 0.257553 + 0.0937416i
\(66\) 0 0
\(67\) −0.892251 0.748687i −0.109006 0.0914667i 0.586656 0.809836i \(-0.300444\pi\)
−0.695662 + 0.718370i \(0.744889\pi\)
\(68\) −0.522244 −0.0633314
\(69\) 0 0
\(70\) −0.329565 + 0.119952i −0.0393905 + 0.0143370i
\(71\) −0.0543332 + 0.308139i −0.00644816 + 0.0365693i −0.987862 0.155334i \(-0.950355\pi\)
0.981414 + 0.191903i \(0.0614659\pi\)
\(72\) 0 0
\(73\) 13.2325 1.54875 0.774376 0.632726i \(-0.218064\pi\)
0.774376 + 0.632726i \(0.218064\pi\)
\(74\) 2.53624 + 5.52879i 0.294832 + 0.642708i
\(75\) 0 0
\(76\) 0.869950 + 4.93373i 0.0997902 + 0.565938i
\(77\) 0.958285 5.43471i 0.109207 0.619342i
\(78\) 0 0
\(79\) 7.12939 + 5.98227i 0.802119 + 0.673058i 0.948713 0.316139i \(-0.102387\pi\)
−0.146594 + 0.989197i \(0.546831\pi\)
\(80\) −0.347296 −0.0388289
\(81\) 0 0
\(82\) 0.550245 + 0.953052i 0.0607644 + 0.105247i
\(83\) 8.89395 + 3.23713i 0.976238 + 0.355322i 0.780377 0.625310i \(-0.215027\pi\)
0.195862 + 0.980632i \(0.437250\pi\)
\(84\) 0 0
\(85\) −0.0906868 0.157074i −0.00983636 0.0170371i
\(86\) 1.08884 + 6.17511i 0.117412 + 0.665879i
\(87\) 0 0
\(88\) 2.73237 4.73261i 0.291272 0.504498i
\(89\) 12.0788 10.1354i 1.28035 1.07435i 0.287160 0.957883i \(-0.407289\pi\)
0.993195 0.116463i \(-0.0371555\pi\)
\(90\) 0 0
\(91\) −6.03778 2.19757i −0.632931 0.230368i
\(92\) −0.250571 + 1.42106i −0.0261239 + 0.148156i
\(93\) 0 0
\(94\) 10.7484 + 3.91209i 1.10861 + 0.403502i
\(95\) −1.33284 + 1.11839i −0.136747 + 0.114744i
\(96\) 0 0
\(97\) 0.464564 0.804648i 0.0471693 0.0816997i −0.841477 0.540293i \(-0.818313\pi\)
0.888646 + 0.458594i \(0.151647\pi\)
\(98\) −5.61956 + 2.04535i −0.567662 + 0.206612i
\(99\) 0 0
\(100\) 2.43969 + 4.22567i 0.243969 + 0.422567i
\(101\) 4.28093 7.41479i 0.425969 0.737799i −0.570542 0.821269i \(-0.693267\pi\)
0.996510 + 0.0834694i \(0.0266001\pi\)
\(102\) 0 0
\(103\) −2.47956 4.29473i −0.244319 0.423172i 0.717621 0.696434i \(-0.245231\pi\)
−0.961940 + 0.273261i \(0.911898\pi\)
\(104\) −4.87406 4.08982i −0.477941 0.401040i
\(105\) 0 0
\(106\) 0.0706817 + 0.0593090i 0.00686521 + 0.00576059i
\(107\) −3.35307 + 1.22042i −0.324153 + 0.117982i −0.498971 0.866619i \(-0.666289\pi\)
0.174818 + 0.984601i \(0.444066\pi\)
\(108\) 0 0
\(109\) −0.169947 0.963819i −0.0162780 0.0923171i 0.975586 0.219616i \(-0.0704804\pi\)
−0.991864 + 0.127299i \(0.959369\pi\)
\(110\) 1.89789 0.180956
\(111\) 0 0
\(112\) 1.00984 0.0954213
\(113\) −1.60399 9.09669i −0.150891 0.855745i −0.962447 0.271470i \(-0.912490\pi\)
0.811556 0.584275i \(-0.198621\pi\)
\(114\) 0 0
\(115\) −0.470920 + 0.171401i −0.0439136 + 0.0159832i
\(116\) 4.85235 + 4.07160i 0.450529 + 0.378039i
\(117\) 0 0
\(118\) 2.29059 + 1.92203i 0.210866 + 0.176938i
\(119\) 0.263693 + 0.456729i 0.0241727 + 0.0418683i
\(120\) 0 0
\(121\) −9.43174 + 16.3362i −0.857430 + 1.48511i
\(122\) 1.90792 + 3.30461i 0.172735 + 0.299185i
\(123\) 0 0
\(124\) −3.10828 + 1.13132i −0.279132 + 0.101596i
\(125\) −1.71554 + 2.97140i −0.153442 + 0.265770i
\(126\) 0 0
\(127\) 5.18728 4.35264i 0.460296 0.386235i −0.382944 0.923772i \(-0.625090\pi\)
0.843240 + 0.537537i \(0.180645\pi\)
\(128\) 0.939693 + 0.342020i 0.0830579 + 0.0302306i
\(129\) 0 0
\(130\) 0.383714 2.17615i 0.0336539 0.190861i
\(131\) −14.2349 5.18108i −1.24371 0.452673i −0.365438 0.930836i \(-0.619081\pi\)
−0.878271 + 0.478163i \(0.841303\pi\)
\(132\) 0 0
\(133\) 3.87554 3.25197i 0.336052 0.281981i
\(134\) −0.582375 + 1.00870i −0.0503096 + 0.0871387i
\(135\) 0 0
\(136\) 0.0906868 + 0.514310i 0.00777633 + 0.0441017i
\(137\) −4.24086 7.34539i −0.362321 0.627559i 0.626021 0.779806i \(-0.284682\pi\)
−0.988342 + 0.152247i \(0.951349\pi\)
\(138\) 0 0
\(139\) 17.2324 + 6.27209i 1.46164 + 0.531992i 0.945815 0.324705i \(-0.105265\pi\)
0.515820 + 0.856697i \(0.327487\pi\)
\(140\) 0.175358 + 0.303728i 0.0148204 + 0.0256697i
\(141\) 0 0
\(142\) 0.312892 0.0262573
\(143\) 26.6355 + 22.3499i 2.22737 + 1.86899i
\(144\) 0 0
\(145\) −0.382004 + 2.16645i −0.0317237 + 0.179914i
\(146\) −2.29781 13.0315i −0.190168 1.07850i
\(147\) 0 0
\(148\) 5.00438 3.45777i 0.411357 0.284227i
\(149\) −5.45291 −0.446720 −0.223360 0.974736i \(-0.571703\pi\)
−0.223360 + 0.974736i \(0.571703\pi\)
\(150\) 0 0
\(151\) −2.70116 + 15.3190i −0.219817 + 1.24665i 0.652531 + 0.757762i \(0.273707\pi\)
−0.872349 + 0.488884i \(0.837404\pi\)
\(152\) 4.70771 1.71347i 0.381846 0.138981i
\(153\) 0 0
\(154\) −5.51855 −0.444697
\(155\) −0.880013 0.738419i −0.0706843 0.0593112i
\(156\) 0 0
\(157\) 3.76650 + 1.37089i 0.300599 + 0.109409i 0.487916 0.872890i \(-0.337757\pi\)
−0.187317 + 0.982299i \(0.559979\pi\)
\(158\) 4.65338 8.05989i 0.370203 0.641211i
\(159\) 0 0
\(160\) 0.0603074 + 0.342020i 0.00476772 + 0.0270391i
\(161\) 1.36931 0.498388i 0.107917 0.0392785i
\(162\) 0 0
\(163\) 3.59446 3.01611i 0.281540 0.236240i −0.491072 0.871119i \(-0.663395\pi\)
0.772611 + 0.634879i \(0.218950\pi\)
\(164\) 0.843024 0.707381i 0.0658291 0.0552372i
\(165\) 0 0
\(166\) 1.64354 9.32096i 0.127563 0.723447i
\(167\) 0.134923 0.765189i 0.0104407 0.0592121i −0.979142 0.203176i \(-0.934874\pi\)
0.989583 + 0.143964i \(0.0459848\pi\)
\(168\) 0 0
\(169\) 21.0533 17.6658i 1.61948 1.35891i
\(170\) −0.138940 + 0.116585i −0.0106562 + 0.00894164i
\(171\) 0 0
\(172\) 5.89222 2.14459i 0.449277 0.163524i
\(173\) −1.86383 10.5703i −0.141704 0.803644i −0.969955 0.243286i \(-0.921775\pi\)
0.828251 0.560358i \(-0.189336\pi\)
\(174\) 0 0
\(175\) 2.46371 4.26727i 0.186239 0.322575i
\(176\) −5.13518 1.86905i −0.387079 0.140885i
\(177\) 0 0
\(178\) −12.0788 10.1354i −0.905348 0.759677i
\(179\) 11.8976 0.889267 0.444633 0.895713i \(-0.353334\pi\)
0.444633 + 0.895713i \(0.353334\pi\)
\(180\) 0 0
\(181\) −4.12213 + 1.50033i −0.306395 + 0.111519i −0.490642 0.871361i \(-0.663238\pi\)
0.184247 + 0.982880i \(0.441015\pi\)
\(182\) −1.11574 + 6.32766i −0.0827039 + 0.469037i
\(183\) 0 0
\(184\) 1.44298 0.106378
\(185\) 1.90899 + 0.904718i 0.140352 + 0.0665162i
\(186\) 0 0
\(187\) −0.495580 2.81058i −0.0362404 0.205530i
\(188\) 1.98622 11.2644i 0.144860 0.821543i
\(189\) 0 0
\(190\) 1.33284 + 1.11839i 0.0966945 + 0.0811363i
\(191\) 10.4903 0.759053 0.379527 0.925181i \(-0.376087\pi\)
0.379527 + 0.925181i \(0.376087\pi\)
\(192\) 0 0
\(193\) −4.91474 8.51259i −0.353771 0.612749i 0.633136 0.774041i \(-0.281767\pi\)
−0.986907 + 0.161291i \(0.948434\pi\)
\(194\) −0.873095 0.317780i −0.0626845 0.0228153i
\(195\) 0 0
\(196\) 2.99011 + 5.17902i 0.213579 + 0.369930i
\(197\) 2.09473 + 11.8798i 0.149244 + 0.846402i 0.963861 + 0.266404i \(0.0858356\pi\)
−0.814618 + 0.579998i \(0.803053\pi\)
\(198\) 0 0
\(199\) 4.64995 8.05395i 0.329626 0.570929i −0.652811 0.757520i \(-0.726411\pi\)
0.982438 + 0.186591i \(0.0597439\pi\)
\(200\) 3.73783 3.13641i 0.264304 0.221778i
\(201\) 0 0
\(202\) −8.04552 2.92833i −0.566081 0.206037i
\(203\) 1.11077 6.29947i 0.0779605 0.442136i
\(204\) 0 0
\(205\) 0.359147 + 0.130719i 0.0250839 + 0.00912980i
\(206\) −3.79891 + 3.18767i −0.264683 + 0.222095i
\(207\) 0 0
\(208\) −3.18132 + 5.51020i −0.220585 + 0.382064i
\(209\) −25.7265 + 9.36367i −1.77954 + 0.647699i
\(210\) 0 0
\(211\) 2.20002 + 3.81054i 0.151455 + 0.262329i 0.931763 0.363068i \(-0.118271\pi\)
−0.780307 + 0.625396i \(0.784937\pi\)
\(212\) 0.0461342 0.0799067i 0.00316851 0.00548802i
\(213\) 0 0
\(214\) 1.78413 + 3.09020i 0.121961 + 0.211242i
\(215\) 1.66820 + 1.39978i 0.113770 + 0.0954644i
\(216\) 0 0
\(217\) 2.55884 + 2.14712i 0.173705 + 0.145756i
\(218\) −0.919666 + 0.334731i −0.0622876 + 0.0226708i
\(219\) 0 0
\(220\) −0.329565 1.86905i −0.0222192 0.126012i
\(221\) −3.32285 −0.223519
\(222\) 0 0
\(223\) 11.2311 0.752092 0.376046 0.926601i \(-0.377283\pi\)
0.376046 + 0.926601i \(0.377283\pi\)
\(224\) −0.175358 0.994503i −0.0117166 0.0664480i
\(225\) 0 0
\(226\) −8.67996 + 3.15925i −0.577382 + 0.210150i
\(227\) 11.6086 + 9.74076i 0.770489 + 0.646517i 0.940834 0.338868i \(-0.110044\pi\)
−0.170345 + 0.985384i \(0.554488\pi\)
\(228\) 0 0
\(229\) −11.9210 10.0029i −0.787759 0.661008i 0.157431 0.987530i \(-0.449679\pi\)
−0.945190 + 0.326522i \(0.894123\pi\)
\(230\) 0.250571 + 0.434003i 0.0165222 + 0.0286173i
\(231\) 0 0
\(232\) 3.16714 5.48565i 0.207933 0.360151i
\(233\) 6.79356 + 11.7668i 0.445061 + 0.770868i 0.998056 0.0623159i \(-0.0198486\pi\)
−0.552995 + 0.833184i \(0.686515\pi\)
\(234\) 0 0
\(235\) 3.73288 1.35866i 0.243506 0.0886289i
\(236\) 1.49508 2.58955i 0.0973213 0.168565i
\(237\) 0 0
\(238\) 0.404001 0.338997i 0.0261875 0.0219739i
\(239\) −18.3188 6.66750i −1.18494 0.431285i −0.326999 0.945025i \(-0.606037\pi\)
−0.857946 + 0.513740i \(0.828260\pi\)
\(240\) 0 0
\(241\) 0.250684 1.42170i 0.0161480 0.0915797i −0.975669 0.219250i \(-0.929639\pi\)
0.991817 + 0.127671i \(0.0407500\pi\)
\(242\) 17.7259 + 6.45169i 1.13946 + 0.414730i
\(243\) 0 0
\(244\) 2.92310 2.45277i 0.187132 0.157022i
\(245\) −1.03845 + 1.79865i −0.0663443 + 0.114912i
\(246\) 0 0
\(247\) 5.53518 + 31.3915i 0.352195 + 1.99740i
\(248\) 1.65388 + 2.86461i 0.105022 + 0.181903i
\(249\) 0 0
\(250\) 3.22416 + 1.17350i 0.203913 + 0.0742184i
\(251\) 5.03646 + 8.72340i 0.317898 + 0.550616i 0.980049 0.198754i \(-0.0636895\pi\)
−0.662151 + 0.749371i \(0.730356\pi\)
\(252\) 0 0
\(253\) −7.88554 −0.495760
\(254\) −5.18728 4.35264i −0.325479 0.273109i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) 1.21293 + 6.87888i 0.0756607 + 0.429093i 0.998984 + 0.0450692i \(0.0143508\pi\)
−0.923323 + 0.384024i \(0.874538\pi\)
\(258\) 0 0
\(259\) −5.55082 2.63068i −0.344911 0.163462i
\(260\) −2.20972 −0.137041
\(261\) 0 0
\(262\) −2.63050 + 14.9183i −0.162513 + 0.921657i
\(263\) 2.50225 0.910746i 0.154296 0.0561590i −0.263718 0.964600i \(-0.584949\pi\)
0.418013 + 0.908441i \(0.362727\pi\)
\(264\) 0 0
\(265\) 0.0320445 0.00196848
\(266\) −3.87554 3.25197i −0.237625 0.199391i
\(267\) 0 0
\(268\) 1.09451 + 0.398368i 0.0668577 + 0.0243342i
\(269\) 1.20752 2.09148i 0.0736236 0.127520i −0.826863 0.562403i \(-0.809877\pi\)
0.900487 + 0.434883i \(0.143210\pi\)
\(270\) 0 0
\(271\) −4.38472 24.8670i −0.266353 1.51056i −0.765156 0.643845i \(-0.777338\pi\)
0.498803 0.866715i \(-0.333773\pi\)
\(272\) 0.490749 0.178618i 0.0297560 0.0108303i
\(273\) 0 0
\(274\) −6.49738 + 5.45195i −0.392521 + 0.329364i
\(275\) −20.4263 + 17.1397i −1.23175 + 1.03356i
\(276\) 0 0
\(277\) −3.07913 + 17.4626i −0.185007 + 1.04923i 0.740940 + 0.671571i \(0.234380\pi\)
−0.925947 + 0.377654i \(0.876731\pi\)
\(278\) 3.18442 18.0598i 0.190989 1.08315i
\(279\) 0 0
\(280\) 0.268664 0.225435i 0.0160557 0.0134723i
\(281\) −15.1288 + 12.6946i −0.902511 + 0.757297i −0.970680 0.240377i \(-0.922729\pi\)
0.0681682 + 0.997674i \(0.478285\pi\)
\(282\) 0 0
\(283\) −22.8810 + 8.32799i −1.36013 + 0.495047i −0.916095 0.400961i \(-0.868676\pi\)
−0.444037 + 0.896009i \(0.646454\pi\)
\(284\) −0.0543332 0.308139i −0.00322408 0.0182847i
\(285\) 0 0
\(286\) 17.3851 30.1119i 1.02800 1.78055i
\(287\) −1.04430 0.380095i −0.0616432 0.0224363i
\(288\) 0 0
\(289\) −12.8138 10.7521i −0.753754 0.632475i
\(290\) 2.19988 0.129181
\(291\) 0 0
\(292\) −12.4345 + 4.52580i −0.727675 + 0.264852i
\(293\) 4.03707 22.8954i 0.235848 1.33756i −0.604972 0.796247i \(-0.706816\pi\)
0.840820 0.541315i \(-0.182073\pi\)
\(294\) 0 0
\(295\) 1.03847 0.0604621
\(296\) −4.27424 4.32791i −0.248435 0.251555i
\(297\) 0 0
\(298\) 0.946888 + 5.37007i 0.0548518 + 0.311080i
\(299\) −1.59429 + 9.04170i −0.0922005 + 0.522895i
\(300\) 0 0
\(301\) −4.85067 4.07019i −0.279588 0.234602i
\(302\) 15.5554 0.895111
\(303\) 0 0
\(304\) −2.50492 4.33865i −0.143667 0.248839i
\(305\) 1.24530 + 0.453253i 0.0713059 + 0.0259532i
\(306\) 0 0
\(307\) 5.33508 + 9.24063i 0.304489 + 0.527391i 0.977147 0.212563i \(-0.0681809\pi\)
−0.672658 + 0.739953i \(0.734848\pi\)
\(308\) 0.958285 + 5.43471i 0.0546034 + 0.309671i
\(309\) 0 0
\(310\) −0.574388 + 0.994869i −0.0326230 + 0.0565047i
\(311\) −13.0382 + 10.9403i −0.739326 + 0.620368i −0.932657 0.360765i \(-0.882516\pi\)
0.193330 + 0.981134i \(0.438071\pi\)
\(312\) 0 0
\(313\) −10.2525 3.73159i −0.579503 0.210922i 0.0356035 0.999366i \(-0.488665\pi\)
−0.615106 + 0.788444i \(0.710887\pi\)
\(314\) 0.696020 3.94733i 0.0392787 0.222761i
\(315\) 0 0
\(316\) −8.74550 3.18310i −0.491973 0.179063i
\(317\) 22.0930 18.5382i 1.24086 1.04121i 0.243409 0.969924i \(-0.421734\pi\)
0.997456 0.0712854i \(-0.0227101\pi\)
\(318\) 0 0
\(319\) −17.3076 + 29.9777i −0.969042 + 1.67843i
\(320\) 0.326352 0.118782i 0.0182436 0.00664014i
\(321\) 0 0
\(322\) −0.728595 1.26196i −0.0406030 0.0703264i
\(323\) 1.30818 2.26584i 0.0727892 0.126075i
\(324\) 0 0
\(325\) 15.5229 + 26.8864i 0.861054 + 1.49139i
\(326\) −3.59446 3.01611i −0.199079 0.167047i
\(327\) 0 0
\(328\) −0.843024 0.707381i −0.0465482 0.0390586i
\(329\) −10.8542 + 3.95061i −0.598412 + 0.217804i
\(330\) 0 0
\(331\) 0.687569 + 3.89939i 0.0377922 + 0.214330i 0.997856 0.0654519i \(-0.0208489\pi\)
−0.960064 + 0.279782i \(0.909738\pi\)
\(332\) −9.46475 −0.519446
\(333\) 0 0
\(334\) −0.776993 −0.0425152
\(335\) 0.0702431 + 0.398368i 0.00383779 + 0.0217652i
\(336\) 0 0
\(337\) 4.01886 1.46274i 0.218921 0.0796807i −0.230231 0.973136i \(-0.573948\pi\)
0.449152 + 0.893455i \(0.351726\pi\)
\(338\) −21.0533 17.6658i −1.14515 0.960893i
\(339\) 0 0
\(340\) 0.138940 + 0.116585i 0.00753509 + 0.00632269i
\(341\) −9.03806 15.6544i −0.489438 0.847732i
\(342\) 0 0
\(343\) 6.55400 11.3519i 0.353883 0.612943i
\(344\) −3.13518 5.43030i −0.169038 0.292782i
\(345\) 0 0
\(346\) −10.0860 + 3.67102i −0.542229 + 0.197355i
\(347\) −5.06401 + 8.77113i −0.271850 + 0.470859i −0.969336 0.245740i \(-0.920969\pi\)
0.697485 + 0.716599i \(0.254302\pi\)
\(348\) 0 0
\(349\) −5.50852 + 4.62220i −0.294864 + 0.247421i −0.778203 0.628013i \(-0.783869\pi\)
0.483338 + 0.875434i \(0.339424\pi\)
\(350\) −4.63026 1.68528i −0.247498 0.0900819i
\(351\) 0 0
\(352\) −0.948944 + 5.38173i −0.0505789 + 0.286847i
\(353\) −32.0012 11.6475i −1.70325 0.619933i −0.707064 0.707150i \(-0.749981\pi\)
−0.996189 + 0.0872167i \(0.972203\pi\)
\(354\) 0 0
\(355\) 0.0832432 0.0698494i 0.00441809 0.00370722i
\(356\) −7.88391 + 13.6553i −0.417846 + 0.723731i
\(357\) 0 0
\(358\) −2.06599 11.7168i −0.109191 0.619254i
\(359\) 4.93976 + 8.55592i 0.260711 + 0.451564i 0.966431 0.256926i \(-0.0827098\pi\)
−0.705720 + 0.708491i \(0.749376\pi\)
\(360\) 0 0
\(361\) −5.73076 2.08582i −0.301619 0.109780i
\(362\) 2.19334 + 3.79897i 0.115279 + 0.199670i
\(363\) 0 0
\(364\) 6.42527 0.336776
\(365\) −3.52044 2.95400i −0.184268 0.154620i
\(366\) 0 0
\(367\) −5.88735 + 33.3888i −0.307317 + 1.74288i 0.305074 + 0.952329i \(0.401319\pi\)
−0.612391 + 0.790555i \(0.709792\pi\)
\(368\) −0.250571 1.42106i −0.0130619 0.0740780i
\(369\) 0 0
\(370\) 0.559481 2.03709i 0.0290860 0.105903i
\(371\) −0.0931767 −0.00483749
\(372\) 0 0
\(373\) 5.44457 30.8777i 0.281909 1.59879i −0.434212 0.900811i \(-0.642973\pi\)
0.716121 0.697976i \(-0.245916\pi\)
\(374\) −2.68182 + 0.976103i −0.138674 + 0.0504731i
\(375\) 0 0
\(376\) −11.4382 −0.589880
\(377\) 30.8737 + 25.9061i 1.59008 + 1.33423i
\(378\) 0 0
\(379\) −10.0119 3.64403i −0.514276 0.187181i 0.0718279 0.997417i \(-0.477117\pi\)
−0.586104 + 0.810236i \(0.699339\pi\)
\(380\) 0.869950 1.50680i 0.0446275 0.0772971i
\(381\) 0 0
\(382\) −1.82163 10.3310i −0.0932025 0.528577i
\(383\) 18.2315 6.63571i 0.931585 0.339069i 0.168747 0.985659i \(-0.446028\pi\)
0.762838 + 0.646590i \(0.223806\pi\)
\(384\) 0 0
\(385\) −1.46818 + 1.23195i −0.0748253 + 0.0627859i
\(386\) −7.52982 + 6.31827i −0.383258 + 0.321592i
\(387\) 0 0
\(388\) −0.161341 + 0.915012i −0.00819087 + 0.0464527i
\(389\) −3.24705 + 18.4149i −0.164632 + 0.933674i 0.784811 + 0.619735i \(0.212760\pi\)
−0.949443 + 0.313939i \(0.898351\pi\)
\(390\) 0 0
\(391\) 0.577283 0.484398i 0.0291945 0.0244971i
\(392\) 4.58111 3.84401i 0.231381 0.194152i
\(393\) 0 0
\(394\) 11.3356 4.12582i 0.571079 0.207856i
\(395\) −0.561266 3.18310i −0.0282404 0.160159i
\(396\) 0 0
\(397\) 11.9316 20.6661i 0.598829 1.03720i −0.394165 0.919040i \(-0.628966\pi\)
0.992994 0.118163i \(-0.0377005\pi\)
\(398\) −8.73905 3.18075i −0.438049 0.159437i
\(399\) 0 0
\(400\) −3.73783 3.13641i −0.186891 0.156820i
\(401\) −17.8350 −0.890638 −0.445319 0.895372i \(-0.646910\pi\)
−0.445319 + 0.895372i \(0.646910\pi\)
\(402\) 0 0
\(403\) −19.7769 + 7.19819i −0.985156 + 0.358568i
\(404\) −1.48675 + 8.43179i −0.0739687 + 0.419497i
\(405\) 0 0
\(406\) −6.39665 −0.317460
\(407\) 23.3577 + 23.6510i 1.15780 + 1.17233i
\(408\) 0 0
\(409\) −1.73417 9.83496i −0.0857492 0.486308i −0.997192 0.0748818i \(-0.976142\pi\)
0.911443 0.411426i \(-0.134969\pi\)
\(410\) 0.0663677 0.376390i 0.00327767 0.0185886i
\(411\) 0 0
\(412\) 3.79891 + 3.18767i 0.187159 + 0.157045i
\(413\) −3.01959 −0.148584
\(414\) 0 0
\(415\) −1.64354 2.84669i −0.0806780 0.139738i
\(416\) 5.97892 + 2.17615i 0.293141 + 0.106694i
\(417\) 0 0
\(418\) 13.6888 + 23.7096i 0.669540 + 1.15968i
\(419\) −6.25638 35.4817i −0.305644 1.73340i −0.620456 0.784241i \(-0.713052\pi\)
0.314812 0.949154i \(-0.398059\pi\)
\(420\) 0 0
\(421\) −11.1668 + 19.3414i −0.544235 + 0.942643i 0.454419 + 0.890788i \(0.349847\pi\)
−0.998655 + 0.0518555i \(0.983486\pi\)
\(422\) 3.37062 2.82829i 0.164079 0.137679i
\(423\) 0 0
\(424\) −0.0867039 0.0315576i −0.00421071 0.00153257i
\(425\) 0.442496 2.50952i 0.0214642 0.121729i
\(426\) 0 0
\(427\) −3.62101 1.31794i −0.175233 0.0637796i
\(428\) 2.73344 2.29363i 0.132126 0.110867i
\(429\) 0 0
\(430\) 1.08884 1.88592i 0.0525084 0.0909472i
\(431\) 29.3710 10.6902i 1.41475 0.514928i 0.482231 0.876044i \(-0.339827\pi\)
0.932521 + 0.361116i \(0.117604\pi\)
\(432\) 0 0
\(433\) −2.71093 4.69547i −0.130279 0.225650i 0.793505 0.608564i \(-0.208254\pi\)
−0.923784 + 0.382914i \(0.874921\pi\)
\(434\) 1.67017 2.89281i 0.0801705 0.138859i
\(435\) 0 0
\(436\) 0.489344 + 0.847568i 0.0234353 + 0.0405912i
\(437\) −5.53783 4.64679i −0.264910 0.222286i
\(438\) 0 0
\(439\) −11.8195 9.91772i −0.564113 0.473347i 0.315573 0.948901i \(-0.397803\pi\)
−0.879687 + 0.475554i \(0.842248\pi\)
\(440\) −1.78343 + 0.649116i −0.0850217 + 0.0309454i
\(441\) 0 0
\(442\) 0.577007 + 3.27237i 0.0274454 + 0.155651i
\(443\) 8.45523 0.401720 0.200860 0.979620i \(-0.435626\pi\)
0.200860 + 0.979620i \(0.435626\pi\)
\(444\) 0 0
\(445\) −5.47610 −0.259592
\(446\) −1.95027 11.0605i −0.0923478 0.523730i
\(447\) 0 0
\(448\) −0.948944 + 0.345387i −0.0448334 + 0.0163180i
\(449\) −27.8798 23.3939i −1.31573 1.10403i −0.987192 0.159538i \(-0.949000\pi\)
−0.328538 0.944491i \(-0.606556\pi\)
\(450\) 0 0
\(451\) 4.60691 + 3.86566i 0.216931 + 0.182027i
\(452\) 4.61851 + 7.99950i 0.217236 + 0.376265i
\(453\) 0 0
\(454\) 7.57697 13.1237i 0.355605 0.615925i
\(455\) 1.11574 + 1.93251i 0.0523066 + 0.0905976i
\(456\) 0 0
\(457\) −12.2550 + 4.46044i −0.573263 + 0.208651i −0.612352 0.790585i \(-0.709777\pi\)
0.0390893 + 0.999236i \(0.487554\pi\)
\(458\) −7.78085 + 13.4768i −0.363575 + 0.629731i
\(459\) 0 0
\(460\) 0.383898 0.322128i 0.0178993 0.0150193i
\(461\) 16.5840 + 6.03608i 0.772393 + 0.281128i 0.697997 0.716101i \(-0.254075\pi\)
0.0743962 + 0.997229i \(0.476297\pi\)
\(462\) 0 0
\(463\) 4.60063 26.0915i 0.213809 1.21257i −0.669151 0.743126i \(-0.733342\pi\)
0.882961 0.469447i \(-0.155547\pi\)
\(464\) −5.95228 2.16645i −0.276328 0.100575i
\(465\) 0 0
\(466\) 10.4083 8.73363i 0.482157 0.404578i
\(467\) −9.54875 + 16.5389i −0.441864 + 0.765330i −0.997828 0.0658760i \(-0.979016\pi\)
0.555964 + 0.831206i \(0.312349\pi\)
\(468\) 0 0
\(469\) −0.204248 1.15835i −0.00943129 0.0534875i
\(470\) −1.98622 3.44024i −0.0916176 0.158686i
\(471\) 0 0
\(472\) −2.80983 1.02269i −0.129333 0.0470733i
\(473\) 17.1330 + 29.6752i 0.787776 + 1.36447i
\(474\) 0 0
\(475\) −24.4450 −1.12161
\(476\) −0.404001 0.338997i −0.0185173 0.0155379i
\(477\) 0 0
\(478\) −3.38518 + 19.1983i −0.154834 + 0.878110i
\(479\) −3.33101 18.8911i −0.152198 0.863156i −0.961303 0.275492i \(-0.911159\pi\)
0.809106 0.587663i \(-0.199952\pi\)
\(480\) 0 0
\(481\) 31.8410 22.0006i 1.45183 1.00314i
\(482\) −1.44363 −0.0657556
\(483\) 0 0
\(484\) 3.27561 18.5769i 0.148891 0.844404i
\(485\) −0.303223 + 0.110364i −0.0137686 + 0.00501137i
\(486\) 0 0
\(487\) −35.7577 −1.62034 −0.810168 0.586197i \(-0.800624\pi\)
−0.810168 + 0.586197i \(0.800624\pi\)
\(488\) −2.92310 2.45277i −0.132322 0.111032i
\(489\) 0 0
\(490\) 1.95165 + 0.710344i 0.0881667 + 0.0320901i
\(491\) 14.8866 25.7843i 0.671822 1.16363i −0.305565 0.952171i \(-0.598845\pi\)
0.977387 0.211459i \(-0.0678214\pi\)
\(492\) 0 0
\(493\) −0.574436 3.25779i −0.0258713 0.146723i
\(494\) 29.9535 10.9022i 1.34767 0.490512i
\(495\) 0 0
\(496\) 2.53390 2.12619i 0.113775 0.0954688i
\(497\) −0.242049 + 0.203103i −0.0108574 + 0.00911043i
\(498\) 0 0
\(499\) 4.30958 24.4409i 0.192923 1.09412i −0.722422 0.691453i \(-0.756971\pi\)
0.915345 0.402670i \(-0.131918\pi\)
\(500\) 0.595800 3.37895i 0.0266450 0.151111i
\(501\) 0 0
\(502\) 7.71630 6.47475i 0.344395 0.288982i
\(503\) −10.4375 + 8.75811i −0.465386 + 0.390505i −0.845108 0.534596i \(-0.820464\pi\)
0.379722 + 0.925100i \(0.376019\pi\)
\(504\) 0 0
\(505\) −2.79418 + 1.01700i −0.124339 + 0.0452558i
\(506\) 1.36931 + 7.76574i 0.0608733 + 0.345229i
\(507\) 0 0
\(508\) −3.38575 + 5.86430i −0.150219 + 0.260186i
\(509\) 19.8285 + 7.21697i 0.878881 + 0.319886i 0.741758 0.670668i \(-0.233992\pi\)
0.137123 + 0.990554i \(0.456215\pi\)
\(510\) 0 0
\(511\) 10.2365 + 8.58945i 0.452836 + 0.379975i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.56375 2.38901i 0.289515 0.105375i
\(515\) −0.299072 + 1.69612i −0.0131787 + 0.0747400i
\(516\) 0 0
\(517\) 62.5069 2.74905
\(518\) −1.62682 + 5.92330i −0.0714784 + 0.260255i
\(519\) 0 0
\(520\) 0.383714 + 2.17615i 0.0168270 + 0.0954305i
\(521\) −0.510798 + 2.89688i −0.0223784 + 0.126914i −0.993950 0.109830i \(-0.964969\pi\)
0.971572 + 0.236745i \(0.0760804\pi\)
\(522\) 0 0
\(523\) 8.30708 + 6.97047i 0.363243 + 0.304797i 0.806082 0.591804i \(-0.201584\pi\)
−0.442839 + 0.896601i \(0.646029\pi\)
\(524\) 15.1485 0.661764
\(525\) 0 0
\(526\) −1.33142 2.30609i −0.0580527 0.100550i
\(527\) 1.62328 + 0.590827i 0.0707113 + 0.0257368i
\(528\) 0 0
\(529\) 10.4589 + 18.1153i 0.454735 + 0.787624i
\(530\) −0.00556446 0.0315576i −0.000241705 0.00137078i
\(531\) 0 0
\(532\) −2.52958 + 4.38137i −0.109671 + 0.189956i
\(533\) 5.36386 4.50081i 0.232334 0.194952i
\(534\) 0 0
\(535\) 1.16451 + 0.423846i 0.0503461 + 0.0183245i
\(536\) 0.202257 1.14706i 0.00873616 0.0495452i
\(537\) 0 0
\(538\) −2.26939 0.825991i −0.0978404 0.0356110i
\(539\) −25.0346 + 21.0065i −1.07832 + 0.904815i
\(540\) 0 0
\(541\) −4.43868 + 7.68801i −0.190834 + 0.330534i −0.945527 0.325544i \(-0.894452\pi\)
0.754693 + 0.656078i \(0.227786\pi\)
\(542\) −23.7278 + 8.63621i −1.01920 + 0.370957i
\(543\) 0 0
\(544\) −0.261122 0.452277i −0.0111955 0.0193912i
\(545\) −0.169947 + 0.294357i −0.00727974 + 0.0126089i
\(546\) 0 0
\(547\) 18.2649 + 31.6358i 0.780952 + 1.35265i 0.931388 + 0.364028i \(0.118599\pi\)
−0.150436 + 0.988620i \(0.548068\pi\)
\(548\) 6.49738 + 5.45195i 0.277554 + 0.232896i
\(549\) 0 0
\(550\) 20.4263 + 17.1397i 0.870979 + 0.730838i
\(551\) −29.8200 + 10.8536i −1.27038 + 0.462379i
\(552\) 0 0
\(553\) 1.63201 + 9.25560i 0.0694002 + 0.393588i
\(554\) 17.7320 0.753360
\(555\) 0 0
\(556\) −18.3384 −0.777720
\(557\) −6.37699 36.1657i −0.270202 1.53239i −0.753803 0.657101i \(-0.771783\pi\)
0.483601 0.875288i \(-0.339329\pi\)
\(558\) 0 0
\(559\) 37.4900 13.6453i 1.58566 0.577133i
\(560\) −0.268664 0.225435i −0.0113531 0.00952639i
\(561\) 0 0
\(562\) 15.1288 + 12.6946i 0.638172 + 0.535490i
\(563\) 0.238456 + 0.413018i 0.0100497 + 0.0174066i 0.871007 0.491271i \(-0.163468\pi\)
−0.860957 + 0.508678i \(0.830134\pi\)
\(564\) 0 0
\(565\) −1.60399 + 2.77820i −0.0674805 + 0.116880i
\(566\) 12.1747 + 21.0872i 0.511741 + 0.886361i
\(567\) 0 0
\(568\) −0.294023 + 0.107015i −0.0123369 + 0.00449027i
\(569\) 4.54906 7.87920i 0.190706 0.330313i −0.754778 0.655980i \(-0.772255\pi\)
0.945485 + 0.325667i \(0.105589\pi\)
\(570\) 0 0
\(571\) 19.6081 16.4532i 0.820574 0.688543i −0.132532 0.991179i \(-0.542311\pi\)
0.953106 + 0.302635i \(0.0978664\pi\)
\(572\) −32.6733 11.8921i −1.36614 0.497234i
\(573\) 0 0
\(574\) −0.192979 + 1.09444i −0.00805480 + 0.0456811i
\(575\) −6.61626 2.40812i −0.275917 0.100426i
\(576\) 0 0
\(577\) 11.8194 9.91764i 0.492048 0.412877i −0.362712 0.931901i \(-0.618149\pi\)
0.854759 + 0.519024i \(0.173705\pi\)
\(578\) −8.36363 + 14.4862i −0.347881 + 0.602548i
\(579\) 0 0
\(580\) −0.382004 2.16645i −0.0158619 0.0899571i
\(581\) 4.77896 + 8.27741i 0.198265 + 0.343405i
\(582\) 0 0
\(583\) 0.473815 + 0.172455i 0.0196234 + 0.00714234i
\(584\) 6.61627 + 11.4597i 0.273783 + 0.474207i
\(585\) 0 0
\(586\) −23.2486 −0.960390
\(587\) −12.4394 10.4379i −0.513430 0.430819i 0.348904 0.937158i \(-0.386554\pi\)
−0.862334 + 0.506340i \(0.830998\pi\)
\(588\) 0 0
\(589\) 2.87759 16.3196i 0.118569 0.672439i
\(590\) −0.180328 1.02269i −0.00742400 0.0421036i
\(591\) 0 0
\(592\) −3.51995 + 4.96084i −0.144669 + 0.203889i
\(593\) 27.0626 1.11133 0.555663 0.831407i \(-0.312464\pi\)
0.555663 + 0.831407i \(0.312464\pi\)
\(594\) 0 0
\(595\) 0.0318052 0.180376i 0.00130389 0.00739472i
\(596\) 5.12406 1.86501i 0.209890 0.0763936i
\(597\) 0 0
\(598\) 9.18118 0.375446
\(599\) 30.5258 + 25.6142i 1.24725 + 1.04657i 0.996922 + 0.0784059i \(0.0249830\pi\)
0.250328 + 0.968161i \(0.419461\pi\)
\(600\) 0 0
\(601\) −33.5222 12.2011i −1.36740 0.497692i −0.449065 0.893499i \(-0.648243\pi\)
−0.918334 + 0.395807i \(0.870465\pi\)
\(602\) −3.16605 + 5.48376i −0.129038 + 0.223501i
\(603\) 0 0
\(604\) −2.70116 15.3190i −0.109909 0.623323i
\(605\) 6.15613 2.24065i 0.250282 0.0910953i
\(606\) 0 0
\(607\) −9.76538 + 8.19413i −0.396365 + 0.332589i −0.819086 0.573670i \(-0.805519\pi\)
0.422722 + 0.906259i \(0.361075\pi\)
\(608\) −3.83776 + 3.22027i −0.155642 + 0.130599i
\(609\) 0 0
\(610\) 0.230123 1.30509i 0.00931740 0.0528416i
\(611\) 12.6376 71.6714i 0.511263 2.89952i
\(612\) 0 0
\(613\) −3.13519 + 2.63074i −0.126629 + 0.106255i −0.703903 0.710296i \(-0.748561\pi\)
0.577274 + 0.816551i \(0.304117\pi\)
\(614\) 8.17382 6.85865i 0.329868 0.276792i
\(615\) 0 0
\(616\) 5.18574 1.88745i 0.208939 0.0760477i
\(617\) −8.20856 46.5531i −0.330464 1.87416i −0.468104 0.883673i \(-0.655063\pi\)
0.137640 0.990482i \(-0.456048\pi\)
\(618\) 0 0
\(619\) 10.5169 18.2157i 0.422708 0.732152i −0.573495 0.819209i \(-0.694413\pi\)
0.996203 + 0.0870571i \(0.0277463\pi\)
\(620\) 1.07950 + 0.392904i 0.0433536 + 0.0157794i
\(621\) 0 0
\(622\) 13.0382 + 10.9403i 0.522783 + 0.438667i
\(623\) 15.9230 0.637943
\(624\) 0 0
\(625\) −21.8059 + 7.93669i −0.872235 + 0.317468i
\(626\) −1.89458 + 10.7447i −0.0757225 + 0.429444i
\(627\) 0 0
\(628\) −4.00822 −0.159945
\(629\) −3.16281 0.296606i −0.126110 0.0118264i
\(630\) 0 0
\(631\) −5.68830 32.2599i −0.226448 1.28425i −0.859898 0.510465i \(-0.829473\pi\)
0.633451 0.773783i \(-0.281638\pi\)
\(632\) −1.61610 + 9.16537i −0.0642851 + 0.364579i
\(633\) 0 0
\(634\) −22.0930 18.5382i −0.877424 0.736246i
\(635\) −2.35172 −0.0933252
\(636\) 0 0
\(637\) 19.0250 + 32.9522i 0.753796 + 1.30561i
\(638\) 32.5277 + 11.8391i 1.28779 + 0.468716i
\(639\) 0 0
\(640\) −0.173648 0.300767i −0.00686405 0.0118889i
\(641\) −3.47857 19.7280i −0.137395 0.779208i −0.973162 0.230123i \(-0.926087\pi\)
0.835766 0.549085i \(-0.185024\pi\)
\(642\) 0 0
\(643\) 6.69618 11.5981i 0.264071 0.457385i −0.703249 0.710944i \(-0.748268\pi\)
0.967320 + 0.253559i \(0.0816012\pi\)
\(644\) −1.11627 + 0.936663i −0.0439873 + 0.0369097i
\(645\) 0 0
\(646\) −2.45858 0.894849i −0.0967314 0.0352074i
\(647\) −2.56647 + 14.5551i −0.100898 + 0.572222i 0.891881 + 0.452269i \(0.149385\pi\)
−0.992780 + 0.119953i \(0.961726\pi\)
\(648\) 0 0
\(649\) 15.3550 + 5.58876i 0.602736 + 0.219378i
\(650\) 23.7824 19.9558i 0.932823 0.782732i
\(651\) 0 0
\(652\) −2.34612 + 4.06359i −0.0918810 + 0.159143i
\(653\) −25.4991 + 9.28092i −0.997857 + 0.363190i −0.788758 0.614704i \(-0.789275\pi\)
−0.209099 + 0.977894i \(0.567053\pi\)
\(654\) 0 0
\(655\) 2.63050 + 4.55617i 0.102782 + 0.178024i
\(656\) −0.550245 + 0.953052i −0.0214835 + 0.0372104i
\(657\) 0 0
\(658\) 5.77540 + 10.0033i 0.225149 + 0.389969i
\(659\) −24.2414 20.3409i −0.944311 0.792371i 0.0340197 0.999421i \(-0.489169\pi\)
−0.978330 + 0.207050i \(0.933614\pi\)
\(660\) 0 0
\(661\) 26.0376 + 21.8481i 1.01274 + 0.849793i 0.988698 0.149918i \(-0.0479009\pi\)
0.0240454 + 0.999711i \(0.492345\pi\)
\(662\) 3.72076 1.35425i 0.144611 0.0526343i
\(663\) 0 0
\(664\) 1.64354 + 9.32096i 0.0637816 + 0.361723i
\(665\) −1.75703 −0.0681347
\(666\) 0 0
\(667\) −9.14028 −0.353913
\(668\) 0.134923 + 0.765189i 0.00522035 + 0.0296060i
\(669\) 0 0
\(670\) 0.380118 0.138352i 0.0146853 0.00534500i
\(671\) 15.9740 + 13.4038i 0.616669 + 0.517447i
\(672\) 0 0
\(673\) 30.3717 + 25.4849i 1.17074 + 0.982372i 0.999996 0.00294292i \(-0.000936763\pi\)
0.170749 + 0.985315i \(0.445381\pi\)
\(674\) −2.13839 3.70380i −0.0823676 0.142665i
\(675\) 0 0
\(676\) −13.7416 + 23.8011i −0.528522 + 0.915426i
\(677\) 9.65303 + 16.7195i 0.370996 + 0.642584i 0.989719 0.143025i \(-0.0456830\pi\)
−0.618723 + 0.785609i \(0.712350\pi\)
\(678\) 0 0
\(679\) 0.881690 0.320909i 0.0338362 0.0123154i
\(680\) 0.0906868 0.157074i 0.00347768 0.00602352i
\(681\) 0 0
\(682\) −13.8471 + 11.6191i −0.530233 + 0.444918i
\(683\) 1.90109 + 0.691940i 0.0727432 + 0.0264764i 0.378135 0.925750i \(-0.376565\pi\)
−0.305392 + 0.952227i \(0.598788\pi\)
\(684\) 0 0
\(685\) −0.511511 + 2.90092i −0.0195438 + 0.110838i
\(686\) −12.3175 4.48320i −0.470284 0.171169i
\(687\) 0 0
\(688\) −4.80338 + 4.03051i −0.183127 + 0.153662i
\(689\) 0.293535 0.508417i 0.0111828 0.0193692i
\(690\) 0 0
\(691\) −0.242292 1.37410i −0.00921721 0.0522734i 0.979852 0.199724i \(-0.0640045\pi\)
−0.989069 + 0.147450i \(0.952893\pi\)
\(692\) 5.36667 + 9.29535i 0.204010 + 0.353356i
\(693\) 0 0
\(694\) 9.51723 + 3.46399i 0.361269 + 0.131491i
\(695\) −3.18442 5.51559i −0.120792 0.209218i
\(696\) 0 0
\(697\) −0.574725 −0.0217692
\(698\) 5.50852 + 4.62220i 0.208501 + 0.174953i
\(699\) 0 0
\(700\) −0.855638 + 4.85256i −0.0323401 + 0.183410i
\(701\) 7.84895 + 44.5136i 0.296451 + 1.68126i 0.661247 + 0.750168i \(0.270027\pi\)
−0.364797 + 0.931087i \(0.618862\pi\)
\(702\) 0 0
\(703\) 2.46650 + 30.3737i 0.0930258 + 1.14557i
\(704\) 5.46475 0.205960
\(705\) 0 0
\(706\) −5.91359 + 33.5376i −0.222561 + 1.26220i
\(707\) 8.12472 2.95716i 0.305562 0.111215i
\(708\) 0 0
\(709\) −28.5445 −1.07201 −0.536005 0.844215i \(-0.680067\pi\)
−0.536005 + 0.844215i \(0.680067\pi\)
\(710\) −0.0832432 0.0698494i −0.00312406 0.00262140i
\(711\) 0 0
\(712\) 14.8169 + 5.39291i 0.555287 + 0.202108i
\(713\) 2.38653 4.13359i 0.0893761 0.154804i
\(714\) 0 0
\(715\) −2.09690 11.8921i −0.0784196 0.444740i
\(716\) −11.1801 + 4.06921i −0.417819 + 0.152074i
\(717\) 0 0
\(718\) 7.56816 6.35044i 0.282441 0.236996i
\(719\) 13.6923 11.4892i 0.510637 0.428475i −0.350717 0.936482i \(-0.614062\pi\)
0.861353 + 0.508007i \(0.169617\pi\)
\(720\) 0 0
\(721\) 0.869621 4.93187i 0.0323864 0.183672i
\(722\) −1.05900 + 6.00589i −0.0394119 + 0.223516i
\(723\) 0 0
\(724\) 3.36039 2.81970i 0.124888 0.104793i
\(725\) −23.6765 + 19.8669i −0.879322 + 0.737839i
\(726\) 0 0
\(727\) 16.3955 5.96747i 0.608075 0.221321i −0.0195860 0.999808i \(-0.506235\pi\)
0.627661 + 0.778487i \(0.284013\pi\)
\(728\) −1.11574 6.32766i −0.0413520 0.234519i
\(729\) 0 0
\(730\) −2.29781 + 3.97992i −0.0850457 + 0.147303i
\(731\) −3.07718 1.12000i −0.113813 0.0414247i
\(732\) 0 0
\(733\) −33.6087 28.2011i −1.24137 1.04163i −0.997416 0.0718424i \(-0.977112\pi\)
−0.243950 0.969788i \(-0.578443\pi\)
\(734\) 33.9039 1.25142
\(735\) 0 0
\(736\) −1.35596 + 0.493529i −0.0499814 + 0.0181917i
\(737\) −1.10528 + 6.26837i −0.0407136 + 0.230898i
\(738\) 0 0
\(739\) 39.5017 1.45309 0.726546 0.687118i \(-0.241124\pi\)
0.726546 + 0.687118i \(0.241124\pi\)
\(740\) −2.10329 0.197245i −0.0773186 0.00725087i
\(741\) 0 0
\(742\) 0.0161800 + 0.0917611i 0.000593985 + 0.00336866i
\(743\) −3.45404 + 19.5888i −0.126716 + 0.718644i 0.853557 + 0.520999i \(0.174440\pi\)
−0.980274 + 0.197645i \(0.936671\pi\)
\(744\) 0 0
\(745\) 1.45072 + 1.21730i 0.0531502 + 0.0445983i
\(746\) −31.3540 −1.14795
\(747\) 0 0
\(748\) 1.42697 + 2.47158i 0.0521751 + 0.0903699i
\(749\) −3.38608 1.23243i −0.123725 0.0450320i
\(750\) 0 0
\(751\) 16.6184 + 28.7839i 0.606413 + 1.05034i 0.991826 + 0.127594i \(0.0407255\pi\)
−0.385413 + 0.922744i \(0.625941\pi\)
\(752\) 1.98622 + 11.2644i 0.0724301 + 0.410771i
\(753\) 0 0
\(754\) 20.1514 34.9032i 0.733870 1.27110i
\(755\) 4.13842 3.47255i 0.150612 0.126379i
\(756\) 0 0
\(757\) −40.7915 14.8469i −1.48259 0.539620i −0.531105 0.847306i \(-0.678223\pi\)
−0.951488 + 0.307686i \(0.900445\pi\)
\(758\) −1.85012 + 10.4926i −0.0671994 + 0.381107i
\(759\) 0 0
\(760\) −1.63497 0.595081i −0.0593067 0.0215859i
\(761\) −19.3702 + 16.2536i −0.702171 + 0.589191i −0.922390 0.386259i \(-0.873767\pi\)
0.220220 + 0.975450i \(0.429323\pi\)
\(762\) 0 0
\(763\) 0.494161 0.855912i 0.0178898 0.0309861i
\(764\) −9.85768 + 3.58790i −0.356638 + 0.129806i
\(765\) 0 0
\(766\) −9.70076 16.8022i −0.350503 0.607089i
\(767\) 9.51263 16.4764i 0.343481 0.594927i
\(768\) 0 0
\(769\) −13.8992 24.0740i −0.501216 0.868132i −0.999999 0.00140492i \(-0.999553\pi\)
0.498783 0.866727i \(-0.333781\pi\)
\(770\) 1.46818 + 1.23195i 0.0529095 + 0.0443963i
\(771\) 0 0
\(772\) 7.52982 + 6.31827i 0.271004 + 0.227400i
\(773\) −0.927201 + 0.337474i −0.0333491 + 0.0121381i −0.358641 0.933476i \(-0.616760\pi\)
0.325292 + 0.945614i \(0.394537\pi\)
\(774\) 0 0
\(775\) −2.80266 15.8947i −0.100674 0.570953i
\(776\) 0.929128 0.0333538
\(777\) 0 0
\(778\) 18.6990 0.670392
\(779\) 0.957372 + 5.42952i 0.0343014 + 0.194533i
\(780\) 0 0
\(781\) 1.60676 0.584812i 0.0574944 0.0209262i
\(782\) −0.577283 0.484398i −0.0206436 0.0173220i
\(783\) 0 0
\(784\) −4.58111 3.84401i −0.163611 0.137286i