Properties

Label 441.2.e.f.226.1
Level $441$
Weight $2$
Character 441.226
Analytic conductor $3.521$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.2.e.f.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(-0.292893 + 0.507306i) q^{5} +4.41421 q^{8} +O(q^{10})\) \(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(-0.292893 + 0.507306i) q^{5} +4.41421 q^{8} +(-0.707107 - 1.22474i) q^{10} +(-1.00000 - 1.73205i) q^{11} -5.41421 q^{13} +(-1.50000 + 2.59808i) q^{16} +(-3.12132 - 5.40629i) q^{17} +(1.41421 - 2.44949i) q^{19} +2.24264 q^{20} +4.82843 q^{22} +(1.82843 - 3.16693i) q^{23} +(2.32843 + 4.03295i) q^{25} +(6.53553 - 11.3199i) q^{26} +1.17157 q^{29} +(-3.41421 - 5.91359i) q^{31} +(0.792893 + 1.37333i) q^{32} +15.0711 q^{34} +(2.00000 - 3.46410i) q^{37} +(3.41421 + 5.91359i) q^{38} +(-1.29289 + 2.23936i) q^{40} -2.24264 q^{41} -5.65685 q^{43} +(-3.82843 + 6.63103i) q^{44} +(4.41421 + 7.64564i) q^{46} +(-1.41421 + 2.44949i) q^{47} -11.2426 q^{50} +(10.3640 + 17.9509i) q^{52} +(-1.00000 - 1.73205i) q^{53} +1.17157 q^{55} +(-1.41421 + 2.44949i) q^{58} +(3.41421 + 5.91359i) q^{59} +(1.87868 - 3.25397i) q^{61} +16.4853 q^{62} -9.82843 q^{64} +(1.58579 - 2.74666i) q^{65} +(-2.82843 - 4.89898i) q^{67} +(-11.9497 + 20.6976i) q^{68} +13.3137 q^{71} +(-2.94975 - 5.10911i) q^{73} +(4.82843 + 8.36308i) q^{74} -10.8284 q^{76} +(-1.17157 + 2.02922i) q^{79} +(-0.878680 - 1.52192i) q^{80} +(2.70711 - 4.68885i) q^{82} -15.3137 q^{83} +3.65685 q^{85} +(6.82843 - 11.8272i) q^{86} +(-4.41421 - 7.64564i) q^{88} +(2.87868 - 4.98602i) q^{89} -14.0000 q^{92} +(-3.41421 - 5.91359i) q^{94} +(0.828427 + 1.43488i) q^{95} -5.41421 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} - 4q^{5} + 12q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} - 4q^{5} + 12q^{8} - 4q^{11} - 16q^{13} - 6q^{16} - 4q^{17} - 8q^{20} + 8q^{22} - 4q^{23} - 2q^{25} + 12q^{26} + 16q^{29} - 8q^{31} + 6q^{32} + 32q^{34} + 8q^{37} + 8q^{38} - 8q^{40} + 8q^{41} - 4q^{44} + 12q^{46} - 28q^{50} + 16q^{52} - 4q^{53} + 16q^{55} + 8q^{59} + 16q^{61} + 32q^{62} - 28q^{64} + 12q^{65} - 28q^{68} + 8q^{71} + 8q^{73} + 8q^{74} - 32q^{76} - 16q^{79} - 12q^{80} + 8q^{82} - 16q^{83} - 8q^{85} + 16q^{86} - 12q^{88} + 20q^{89} - 56q^{92} - 8q^{94} - 8q^{95} - 16q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.20711 + 2.09077i −0.853553 + 1.47840i 0.0244272 + 0.999702i \(0.492224\pi\)
−0.877981 + 0.478696i \(0.841110\pi\)
\(3\) 0 0
\(4\) −1.91421 3.31552i −0.957107 1.65776i
\(5\) −0.292893 + 0.507306i −0.130986 + 0.226874i −0.924057 0.382255i \(-0.875148\pi\)
0.793071 + 0.609129i \(0.208481\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 4.41421 1.56066
\(9\) 0 0
\(10\) −0.707107 1.22474i −0.223607 0.387298i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 0 0
\(13\) −5.41421 −1.50163 −0.750816 0.660511i \(-0.770340\pi\)
−0.750816 + 0.660511i \(0.770340\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) −3.12132 5.40629i −0.757031 1.31122i −0.944358 0.328919i \(-0.893316\pi\)
0.187327 0.982298i \(-0.440018\pi\)
\(18\) 0 0
\(19\) 1.41421 2.44949i 0.324443 0.561951i −0.656957 0.753928i \(-0.728157\pi\)
0.981399 + 0.191977i \(0.0614899\pi\)
\(20\) 2.24264 0.501470
\(21\) 0 0
\(22\) 4.82843 1.02942
\(23\) 1.82843 3.16693i 0.381253 0.660350i −0.609988 0.792410i \(-0.708826\pi\)
0.991242 + 0.132060i \(0.0421592\pi\)
\(24\) 0 0
\(25\) 2.32843 + 4.03295i 0.465685 + 0.806591i
\(26\) 6.53553 11.3199i 1.28172 2.22001i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.17157 0.217556 0.108778 0.994066i \(-0.465306\pi\)
0.108778 + 0.994066i \(0.465306\pi\)
\(30\) 0 0
\(31\) −3.41421 5.91359i −0.613211 1.06211i −0.990696 0.136097i \(-0.956544\pi\)
0.377485 0.926016i \(-0.376789\pi\)
\(32\) 0.792893 + 1.37333i 0.140165 + 0.242773i
\(33\) 0 0
\(34\) 15.0711 2.58467
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 3.41421 + 5.91359i 0.553859 + 0.959311i
\(39\) 0 0
\(40\) −1.29289 + 2.23936i −0.204424 + 0.354073i
\(41\) −2.24264 −0.350242 −0.175121 0.984547i \(-0.556032\pi\)
−0.175121 + 0.984547i \(0.556032\pi\)
\(42\) 0 0
\(43\) −5.65685 −0.862662 −0.431331 0.902194i \(-0.641956\pi\)
−0.431331 + 0.902194i \(0.641956\pi\)
\(44\) −3.82843 + 6.63103i −0.577157 + 0.999665i
\(45\) 0 0
\(46\) 4.41421 + 7.64564i 0.650840 + 1.12729i
\(47\) −1.41421 + 2.44949i −0.206284 + 0.357295i −0.950541 0.310599i \(-0.899470\pi\)
0.744257 + 0.667893i \(0.232804\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −11.2426 −1.58995
\(51\) 0 0
\(52\) 10.3640 + 17.9509i 1.43722 + 2.48934i
\(53\) −1.00000 1.73205i −0.137361 0.237915i 0.789136 0.614218i \(-0.210529\pi\)
−0.926497 + 0.376303i \(0.877195\pi\)
\(54\) 0 0
\(55\) 1.17157 0.157975
\(56\) 0 0
\(57\) 0 0
\(58\) −1.41421 + 2.44949i −0.185695 + 0.321634i
\(59\) 3.41421 + 5.91359i 0.444493 + 0.769884i 0.998017 0.0629492i \(-0.0200506\pi\)
−0.553524 + 0.832833i \(0.686717\pi\)
\(60\) 0 0
\(61\) 1.87868 3.25397i 0.240540 0.416628i −0.720328 0.693634i \(-0.756009\pi\)
0.960868 + 0.277006i \(0.0893421\pi\)
\(62\) 16.4853 2.09363
\(63\) 0 0
\(64\) −9.82843 −1.22855
\(65\) 1.58579 2.74666i 0.196693 0.340682i
\(66\) 0 0
\(67\) −2.82843 4.89898i −0.345547 0.598506i 0.639906 0.768453i \(-0.278973\pi\)
−0.985453 + 0.169948i \(0.945640\pi\)
\(68\) −11.9497 + 20.6976i −1.44912 + 2.50995i
\(69\) 0 0
\(70\) 0 0
\(71\) 13.3137 1.58005 0.790023 0.613077i \(-0.210068\pi\)
0.790023 + 0.613077i \(0.210068\pi\)
\(72\) 0 0
\(73\) −2.94975 5.10911i −0.345242 0.597976i 0.640156 0.768245i \(-0.278870\pi\)
−0.985398 + 0.170269i \(0.945536\pi\)
\(74\) 4.82843 + 8.36308i 0.561293 + 0.972188i
\(75\) 0 0
\(76\) −10.8284 −1.24211
\(77\) 0 0
\(78\) 0 0
\(79\) −1.17157 + 2.02922i −0.131812 + 0.228306i −0.924375 0.381485i \(-0.875413\pi\)
0.792563 + 0.609790i \(0.208746\pi\)
\(80\) −0.878680 1.52192i −0.0982394 0.170156i
\(81\) 0 0
\(82\) 2.70711 4.68885i 0.298950 0.517796i
\(83\) −15.3137 −1.68090 −0.840449 0.541891i \(-0.817709\pi\)
−0.840449 + 0.541891i \(0.817709\pi\)
\(84\) 0 0
\(85\) 3.65685 0.396642
\(86\) 6.82843 11.8272i 0.736328 1.27536i
\(87\) 0 0
\(88\) −4.41421 7.64564i −0.470557 0.815028i
\(89\) 2.87868 4.98602i 0.305139 0.528517i −0.672153 0.740412i \(-0.734630\pi\)
0.977292 + 0.211895i \(0.0679636\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −14.0000 −1.45960
\(93\) 0 0
\(94\) −3.41421 5.91359i −0.352149 0.609940i
\(95\) 0.828427 + 1.43488i 0.0849948 + 0.147215i
\(96\) 0 0
\(97\) −5.41421 −0.549730 −0.274865 0.961483i \(-0.588633\pi\)
−0.274865 + 0.961483i \(0.588633\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.91421 15.4399i 0.891421 1.54399i
\(101\) −8.53553 14.7840i −0.849317 1.47106i −0.881818 0.471589i \(-0.843681\pi\)
0.0325010 0.999472i \(-0.489653\pi\)
\(102\) 0 0
\(103\) −6.24264 + 10.8126i −0.615106 + 1.06539i 0.375260 + 0.926919i \(0.377553\pi\)
−0.990366 + 0.138475i \(0.955780\pi\)
\(104\) −23.8995 −2.34354
\(105\) 0 0
\(106\) 4.82843 0.468978
\(107\) −5.82843 + 10.0951i −0.563455 + 0.975933i 0.433736 + 0.901040i \(0.357195\pi\)
−0.997192 + 0.0748933i \(0.976138\pi\)
\(108\) 0 0
\(109\) −2.82843 4.89898i −0.270914 0.469237i 0.698182 0.715920i \(-0.253993\pi\)
−0.969096 + 0.246683i \(0.920659\pi\)
\(110\) −1.41421 + 2.44949i −0.134840 + 0.233550i
\(111\) 0 0
\(112\) 0 0
\(113\) −17.3137 −1.62874 −0.814368 0.580348i \(-0.802916\pi\)
−0.814368 + 0.580348i \(0.802916\pi\)
\(114\) 0 0
\(115\) 1.07107 + 1.85514i 0.0998776 + 0.172993i
\(116\) −2.24264 3.88437i −0.208224 0.360654i
\(117\) 0 0
\(118\) −16.4853 −1.51759
\(119\) 0 0
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 4.53553 + 7.85578i 0.410628 + 0.711228i
\(123\) 0 0
\(124\) −13.0711 + 22.6398i −1.17382 + 2.03311i
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) 9.65685 0.856907 0.428454 0.903564i \(-0.359059\pi\)
0.428454 + 0.903564i \(0.359059\pi\)
\(128\) 10.2782 17.8023i 0.908471 1.57352i
\(129\) 0 0
\(130\) 3.82843 + 6.63103i 0.335775 + 0.581580i
\(131\) −3.65685 + 6.33386i −0.319501 + 0.553392i −0.980384 0.197097i \(-0.936849\pi\)
0.660883 + 0.750489i \(0.270182\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 13.6569 1.17977
\(135\) 0 0
\(136\) −13.7782 23.8645i −1.18147 2.04636i
\(137\) −7.07107 12.2474i −0.604122 1.04637i −0.992190 0.124739i \(-0.960191\pi\)
0.388067 0.921631i \(-0.373143\pi\)
\(138\) 0 0
\(139\) 6.34315 0.538019 0.269009 0.963138i \(-0.413304\pi\)
0.269009 + 0.963138i \(0.413304\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −16.0711 + 27.8359i −1.34865 + 2.33594i
\(143\) 5.41421 + 9.37769i 0.452759 + 0.784202i
\(144\) 0 0
\(145\) −0.343146 + 0.594346i −0.0284967 + 0.0493577i
\(146\) 14.2426 1.17873
\(147\) 0 0
\(148\) −15.3137 −1.25878
\(149\) −2.65685 + 4.60181i −0.217658 + 0.376995i −0.954092 0.299515i \(-0.903175\pi\)
0.736434 + 0.676510i \(0.236508\pi\)
\(150\) 0 0
\(151\) −6.00000 10.3923i −0.488273 0.845714i 0.511636 0.859202i \(-0.329040\pi\)
−0.999909 + 0.0134886i \(0.995706\pi\)
\(152\) 6.24264 10.8126i 0.506345 0.877015i
\(153\) 0 0
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) 10.1213 + 17.5306i 0.807769 + 1.39910i 0.914406 + 0.404799i \(0.132659\pi\)
−0.106636 + 0.994298i \(0.534008\pi\)
\(158\) −2.82843 4.89898i −0.225018 0.389742i
\(159\) 0 0
\(160\) −0.928932 −0.0734385
\(161\) 0 0
\(162\) 0 0
\(163\) −5.65685 + 9.79796i −0.443079 + 0.767435i −0.997916 0.0645236i \(-0.979447\pi\)
0.554837 + 0.831959i \(0.312781\pi\)
\(164\) 4.29289 + 7.43551i 0.335219 + 0.580616i
\(165\) 0 0
\(166\) 18.4853 32.0174i 1.43474 2.48504i
\(167\) 19.7990 1.53209 0.766046 0.642786i \(-0.222221\pi\)
0.766046 + 0.642786i \(0.222221\pi\)
\(168\) 0 0
\(169\) 16.3137 1.25490
\(170\) −4.41421 + 7.64564i −0.338555 + 0.586394i
\(171\) 0 0
\(172\) 10.8284 + 18.7554i 0.825660 + 1.43008i
\(173\) −3.46447 + 6.00063i −0.263398 + 0.456220i −0.967143 0.254234i \(-0.918177\pi\)
0.703744 + 0.710453i \(0.251510\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) 0 0
\(178\) 6.94975 + 12.0373i 0.520906 + 0.902235i
\(179\) −4.17157 7.22538i −0.311798 0.540050i 0.666954 0.745099i \(-0.267598\pi\)
−0.978752 + 0.205049i \(0.934265\pi\)
\(180\) 0 0
\(181\) 5.41421 0.402435 0.201218 0.979547i \(-0.435510\pi\)
0.201218 + 0.979547i \(0.435510\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 8.07107 13.9795i 0.595007 1.03058i
\(185\) 1.17157 + 2.02922i 0.0861358 + 0.149191i
\(186\) 0 0
\(187\) −6.24264 + 10.8126i −0.456507 + 0.790693i
\(188\) 10.8284 0.789744
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) 0 0
\(193\) 8.65685 + 14.9941i 0.623134 + 1.07930i 0.988899 + 0.148592i \(0.0474742\pi\)
−0.365765 + 0.930707i \(0.619192\pi\)
\(194\) 6.53553 11.3199i 0.469224 0.812720i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 5.17157 + 8.95743i 0.366603 + 0.634975i 0.989032 0.147701i \(-0.0471874\pi\)
−0.622429 + 0.782676i \(0.713854\pi\)
\(200\) 10.2782 + 17.8023i 0.726777 + 1.25881i
\(201\) 0 0
\(202\) 41.2132 2.89975
\(203\) 0 0
\(204\) 0 0
\(205\) 0.656854 1.13770i 0.0458767 0.0794608i
\(206\) −15.0711 26.1039i −1.05005 1.81874i
\(207\) 0 0
\(208\) 8.12132 14.0665i 0.563112 0.975339i
\(209\) −5.65685 −0.391293
\(210\) 0 0
\(211\) −20.9706 −1.44367 −0.721837 0.692064i \(-0.756702\pi\)
−0.721837 + 0.692064i \(0.756702\pi\)
\(212\) −3.82843 + 6.63103i −0.262937 + 0.455421i
\(213\) 0 0
\(214\) −14.0711 24.3718i −0.961878 1.66602i
\(215\) 1.65685 2.86976i 0.112997 0.195716i
\(216\) 0 0
\(217\) 0 0
\(218\) 13.6569 0.924959
\(219\) 0 0
\(220\) −2.24264 3.88437i −0.151199 0.261884i
\(221\) 16.8995 + 29.2708i 1.13678 + 1.96897i
\(222\) 0 0
\(223\) 8.97056 0.600713 0.300357 0.953827i \(-0.402894\pi\)
0.300357 + 0.953827i \(0.402894\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 20.8995 36.1990i 1.39021 2.40792i
\(227\) 7.89949 + 13.6823i 0.524308 + 0.908128i 0.999599 + 0.0282996i \(0.00900924\pi\)
−0.475292 + 0.879828i \(0.657657\pi\)
\(228\) 0 0
\(229\) 4.12132 7.13834i 0.272345 0.471715i −0.697117 0.716957i \(-0.745534\pi\)
0.969462 + 0.245243i \(0.0788676\pi\)
\(230\) −5.17157 −0.341003
\(231\) 0 0
\(232\) 5.17157 0.339530
\(233\) 11.0711 19.1757i 0.725290 1.25624i −0.233565 0.972341i \(-0.575039\pi\)
0.958855 0.283898i \(-0.0916275\pi\)
\(234\) 0 0
\(235\) −0.828427 1.43488i −0.0540406 0.0936011i
\(236\) 13.0711 22.6398i 0.850854 1.47372i
\(237\) 0 0
\(238\) 0 0
\(239\) 4.34315 0.280935 0.140467 0.990085i \(-0.455139\pi\)
0.140467 + 0.990085i \(0.455139\pi\)
\(240\) 0 0
\(241\) −3.87868 6.71807i −0.249848 0.432749i 0.713636 0.700517i \(-0.247047\pi\)
−0.963483 + 0.267768i \(0.913714\pi\)
\(242\) 8.44975 + 14.6354i 0.543170 + 0.940799i
\(243\) 0 0
\(244\) −14.3848 −0.920891
\(245\) 0 0
\(246\) 0 0
\(247\) −7.65685 + 13.2621i −0.487194 + 0.843845i
\(248\) −15.0711 26.1039i −0.957014 1.65760i
\(249\) 0 0
\(250\) 6.82843 11.8272i 0.431868 0.748017i
\(251\) 4.48528 0.283108 0.141554 0.989931i \(-0.454790\pi\)
0.141554 + 0.989931i \(0.454790\pi\)
\(252\) 0 0
\(253\) −7.31371 −0.459809
\(254\) −11.6569 + 20.1903i −0.731416 + 1.26685i
\(255\) 0 0
\(256\) 14.9853 + 25.9553i 0.936580 + 1.62220i
\(257\) 9.60660 16.6391i 0.599243 1.03792i −0.393690 0.919243i \(-0.628802\pi\)
0.992933 0.118677i \(-0.0378651\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −12.1421 −0.753023
\(261\) 0 0
\(262\) −8.82843 15.2913i −0.545422 0.944699i
\(263\) −8.65685 14.9941i −0.533805 0.924577i −0.999220 0.0394843i \(-0.987428\pi\)
0.465416 0.885092i \(-0.345905\pi\)
\(264\) 0 0
\(265\) 1.17157 0.0719691
\(266\) 0 0
\(267\) 0 0
\(268\) −10.8284 + 18.7554i −0.661451 + 1.14567i
\(269\) −5.36396 9.29065i −0.327046 0.566461i 0.654878 0.755735i \(-0.272720\pi\)
−0.981924 + 0.189274i \(0.939387\pi\)
\(270\) 0 0
\(271\) 9.07107 15.7116i 0.551028 0.954409i −0.447173 0.894448i \(-0.647569\pi\)
0.998201 0.0599610i \(-0.0190976\pi\)
\(272\) 18.7279 1.13555
\(273\) 0 0
\(274\) 34.1421 2.06260
\(275\) 4.65685 8.06591i 0.280819 0.486393i
\(276\) 0 0
\(277\) −6.65685 11.5300i −0.399972 0.692771i 0.593750 0.804649i \(-0.297647\pi\)
−0.993722 + 0.111878i \(0.964313\pi\)
\(278\) −7.65685 + 13.2621i −0.459228 + 0.795406i
\(279\) 0 0
\(280\) 0 0
\(281\) 16.4853 0.983429 0.491715 0.870756i \(-0.336370\pi\)
0.491715 + 0.870756i \(0.336370\pi\)
\(282\) 0 0
\(283\) 4.24264 + 7.34847i 0.252199 + 0.436821i 0.964131 0.265427i \(-0.0855130\pi\)
−0.711932 + 0.702248i \(0.752180\pi\)
\(284\) −25.4853 44.1418i −1.51227 2.61933i
\(285\) 0 0
\(286\) −26.1421 −1.54582
\(287\) 0 0
\(288\) 0 0
\(289\) −10.9853 + 19.0271i −0.646193 + 1.11924i
\(290\) −0.828427 1.43488i −0.0486469 0.0842589i
\(291\) 0 0
\(292\) −11.2929 + 19.5599i −0.660867 + 1.14465i
\(293\) 19.4142 1.13419 0.567095 0.823652i \(-0.308067\pi\)
0.567095 + 0.823652i \(0.308067\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 8.82843 15.2913i 0.513142 0.888788i
\(297\) 0 0
\(298\) −6.41421 11.1097i −0.371565 0.643570i
\(299\) −9.89949 + 17.1464i −0.572503 + 0.991604i
\(300\) 0 0
\(301\) 0 0
\(302\) 28.9706 1.66707
\(303\) 0 0
\(304\) 4.24264 + 7.34847i 0.243332 + 0.421464i
\(305\) 1.10051 + 1.90613i 0.0630147 + 0.109145i
\(306\) 0 0
\(307\) −1.85786 −0.106034 −0.0530170 0.998594i \(-0.516884\pi\)
−0.0530170 + 0.998594i \(0.516884\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.82843 + 8.36308i −0.274236 + 0.474991i
\(311\) 11.0711 + 19.1757i 0.627783 + 1.08735i 0.987996 + 0.154481i \(0.0493707\pi\)
−0.360213 + 0.932870i \(0.617296\pi\)
\(312\) 0 0
\(313\) −8.94975 + 15.5014i −0.505870 + 0.876192i 0.494107 + 0.869401i \(0.335495\pi\)
−0.999977 + 0.00679098i \(0.997838\pi\)
\(314\) −48.8701 −2.75790
\(315\) 0 0
\(316\) 8.97056 0.504634
\(317\) 5.00000 8.66025i 0.280828 0.486408i −0.690761 0.723083i \(-0.742724\pi\)
0.971589 + 0.236675i \(0.0760576\pi\)
\(318\) 0 0
\(319\) −1.17157 2.02922i −0.0655955 0.113615i
\(320\) 2.87868 4.98602i 0.160923 0.278727i
\(321\) 0 0
\(322\) 0 0
\(323\) −17.6569 −0.982454
\(324\) 0 0
\(325\) −12.6066 21.8353i −0.699288 1.21120i
\(326\) −13.6569 23.6544i −0.756383 1.31009i
\(327\) 0 0
\(328\) −9.89949 −0.546608
\(329\) 0 0
\(330\) 0 0
\(331\) 2.00000 3.46410i 0.109930 0.190404i −0.805812 0.592172i \(-0.798271\pi\)
0.915742 + 0.401768i \(0.131604\pi\)
\(332\) 29.3137 + 50.7728i 1.60880 + 2.78652i
\(333\) 0 0
\(334\) −23.8995 + 41.3951i −1.30772 + 2.26504i
\(335\) 3.31371 0.181047
\(336\) 0 0
\(337\) −18.3431 −0.999215 −0.499607 0.866252i \(-0.666522\pi\)
−0.499607 + 0.866252i \(0.666522\pi\)
\(338\) −19.6924 + 34.1082i −1.07112 + 1.85524i
\(339\) 0 0
\(340\) −7.00000 12.1244i −0.379628 0.657536i
\(341\) −6.82843 + 11.8272i −0.369780 + 0.640478i
\(342\) 0 0
\(343\) 0 0
\(344\) −24.9706 −1.34632
\(345\) 0 0
\(346\) −8.36396 14.4868i −0.449649 0.778815i
\(347\) 5.34315 + 9.25460i 0.286835 + 0.496813i 0.973053 0.230584i \(-0.0740635\pi\)
−0.686217 + 0.727396i \(0.740730\pi\)
\(348\) 0 0
\(349\) −9.89949 −0.529908 −0.264954 0.964261i \(-0.585357\pi\)
−0.264954 + 0.964261i \(0.585357\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.58579 2.74666i 0.0845227 0.146398i
\(353\) −5.36396 9.29065i −0.285495 0.494492i 0.687234 0.726436i \(-0.258825\pi\)
−0.972729 + 0.231944i \(0.925491\pi\)
\(354\) 0 0
\(355\) −3.89949 + 6.75412i −0.206964 + 0.358472i
\(356\) −22.0416 −1.16820
\(357\) 0 0
\(358\) 20.1421 1.06454
\(359\) −5.82843 + 10.0951i −0.307613 + 0.532801i −0.977840 0.209355i \(-0.932863\pi\)
0.670227 + 0.742156i \(0.266197\pi\)
\(360\) 0 0
\(361\) 5.50000 + 9.52628i 0.289474 + 0.501383i
\(362\) −6.53553 + 11.3199i −0.343500 + 0.594960i
\(363\) 0 0
\(364\) 0 0
\(365\) 3.45584 0.180887
\(366\) 0 0
\(367\) 9.65685 + 16.7262i 0.504084 + 0.873099i 0.999989 + 0.00472187i \(0.00150302\pi\)
−0.495905 + 0.868377i \(0.665164\pi\)
\(368\) 5.48528 + 9.50079i 0.285940 + 0.495263i
\(369\) 0 0
\(370\) −5.65685 −0.294086
\(371\) 0 0
\(372\) 0 0
\(373\) 16.6569 28.8505i 0.862459 1.49382i −0.00708885 0.999975i \(-0.502256\pi\)
0.869548 0.493848i \(-0.164410\pi\)
\(374\) −15.0711 26.1039i −0.779306 1.34980i
\(375\) 0 0
\(376\) −6.24264 + 10.8126i −0.321940 + 0.557616i
\(377\) −6.34315 −0.326689
\(378\) 0 0
\(379\) 31.3137 1.60848 0.804239 0.594307i \(-0.202573\pi\)
0.804239 + 0.594307i \(0.202573\pi\)
\(380\) 3.17157 5.49333i 0.162698 0.281802i
\(381\) 0 0
\(382\) −21.7279 37.6339i −1.11170 1.92552i
\(383\) 14.8284 25.6836i 0.757697 1.31237i −0.186325 0.982488i \(-0.559658\pi\)
0.944022 0.329882i \(-0.107009\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −41.7990 −2.12751
\(387\) 0 0
\(388\) 10.3640 + 17.9509i 0.526150 + 0.911319i
\(389\) 5.07107 + 8.78335i 0.257113 + 0.445333i 0.965467 0.260524i \(-0.0838953\pi\)
−0.708354 + 0.705857i \(0.750562\pi\)
\(390\) 0 0
\(391\) −22.8284 −1.15448
\(392\) 0 0
\(393\) 0 0
\(394\) 2.41421 4.18154i 0.121626 0.210663i
\(395\) −0.686292 1.18869i −0.0345311 0.0598096i
\(396\) 0 0
\(397\) 17.1924 29.7781i 0.862861 1.49452i −0.00629405 0.999980i \(-0.502003\pi\)
0.869155 0.494539i \(-0.164663\pi\)
\(398\) −24.9706 −1.25166
\(399\) 0 0
\(400\) −13.9706 −0.698528
\(401\) 11.0711 19.1757i 0.552863 0.957586i −0.445204 0.895429i \(-0.646869\pi\)
0.998066 0.0621570i \(-0.0197980\pi\)
\(402\) 0 0
\(403\) 18.4853 + 32.0174i 0.920817 + 1.59490i
\(404\) −32.6777 + 56.5994i −1.62577 + 2.81592i
\(405\) 0 0
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) −9.29289 16.0958i −0.459504 0.795884i 0.539431 0.842030i \(-0.318639\pi\)
−0.998935 + 0.0461457i \(0.985306\pi\)
\(410\) 1.58579 + 2.74666i 0.0783164 + 0.135648i
\(411\) 0 0
\(412\) 47.7990 2.35489
\(413\) 0 0
\(414\) 0 0
\(415\) 4.48528 7.76874i 0.220174 0.381352i
\(416\) −4.29289 7.43551i −0.210476 0.364556i
\(417\) 0 0
\(418\) 6.82843 11.8272i 0.333989 0.578486i
\(419\) 38.8284 1.89689 0.948446 0.316938i \(-0.102655\pi\)
0.948446 + 0.316938i \(0.102655\pi\)
\(420\) 0 0
\(421\) −28.6274 −1.39521 −0.697607 0.716480i \(-0.745752\pi\)
−0.697607 + 0.716480i \(0.745752\pi\)
\(422\) 25.3137 43.8446i 1.23225 2.13432i
\(423\) 0 0
\(424\) −4.41421 7.64564i −0.214373 0.371305i
\(425\) 14.5355 25.1763i 0.705077 1.22123i
\(426\) 0 0
\(427\) 0 0
\(428\) 44.6274 2.15715
\(429\) 0 0
\(430\) 4.00000 + 6.92820i 0.192897 + 0.334108i
\(431\) 3.48528 + 6.03668i 0.167880 + 0.290777i 0.937674 0.347515i \(-0.112975\pi\)
−0.769794 + 0.638292i \(0.779641\pi\)
\(432\) 0 0
\(433\) 11.7574 0.565023 0.282511 0.959264i \(-0.408833\pi\)
0.282511 + 0.959264i \(0.408833\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −10.8284 + 18.7554i −0.518588 + 0.898220i
\(437\) −5.17157 8.95743i −0.247390 0.428492i
\(438\) 0 0
\(439\) 17.6569 30.5826i 0.842716 1.45963i −0.0448746 0.998993i \(-0.514289\pi\)
0.887590 0.460634i \(-0.152378\pi\)
\(440\) 5.17157 0.246545
\(441\) 0 0
\(442\) −81.5980 −3.88122
\(443\) 0.514719 0.891519i 0.0244550 0.0423573i −0.853539 0.521029i \(-0.825548\pi\)
0.877994 + 0.478672i \(0.158882\pi\)
\(444\) 0 0
\(445\) 1.68629 + 2.92074i 0.0799379 + 0.138456i
\(446\) −10.8284 + 18.7554i −0.512741 + 0.888093i
\(447\) 0 0
\(448\) 0 0
\(449\) −17.3137 −0.817084 −0.408542 0.912739i \(-0.633963\pi\)
−0.408542 + 0.912739i \(0.633963\pi\)
\(450\) 0 0
\(451\) 2.24264 + 3.88437i 0.105602 + 0.182908i
\(452\) 33.1421 + 57.4039i 1.55887 + 2.70005i
\(453\) 0 0
\(454\) −38.1421 −1.79010
\(455\) 0 0
\(456\) 0 0
\(457\) 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i \(-0.695012\pi\)
0.996038 + 0.0889312i \(0.0283451\pi\)
\(458\) 9.94975 + 17.2335i 0.464921 + 0.805267i
\(459\) 0 0
\(460\) 4.10051 7.10228i 0.191187 0.331146i
\(461\) −19.4142 −0.904210 −0.452105 0.891965i \(-0.649327\pi\)
−0.452105 + 0.891965i \(0.649327\pi\)
\(462\) 0 0
\(463\) 18.6274 0.865689 0.432845 0.901468i \(-0.357510\pi\)
0.432845 + 0.901468i \(0.357510\pi\)
\(464\) −1.75736 + 3.04384i −0.0815834 + 0.141307i
\(465\) 0 0
\(466\) 26.7279 + 46.2941i 1.23815 + 2.14453i
\(467\) −19.8995 + 34.4669i −0.920839 + 1.59494i −0.122718 + 0.992442i \(0.539161\pi\)
−0.798120 + 0.602498i \(0.794172\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 4.00000 0.184506
\(471\) 0 0
\(472\) 15.0711 + 26.1039i 0.693702 + 1.20153i
\(473\) 5.65685 + 9.79796i 0.260102 + 0.450511i
\(474\) 0 0
\(475\) 13.1716 0.604353
\(476\) 0 0
\(477\) 0 0
\(478\) −5.24264 + 9.08052i −0.239793 + 0.415333i
\(479\) −15.0711 26.1039i −0.688615 1.19272i −0.972286 0.233794i \(-0.924886\pi\)
0.283671 0.958922i \(-0.408447\pi\)
\(480\) 0 0
\(481\) −10.8284 + 18.7554i −0.493734 + 0.855172i
\(482\) 18.7279 0.853033
\(483\) 0 0
\(484\) −26.7990 −1.21814
\(485\) 1.58579 2.74666i 0.0720069 0.124720i
\(486\) 0 0
\(487\) 9.31371 + 16.1318i 0.422044 + 0.731002i 0.996139 0.0877864i \(-0.0279793\pi\)
−0.574095 + 0.818789i \(0.694646\pi\)
\(488\) 8.29289 14.3637i 0.375402 0.650215i
\(489\) 0 0
\(490\) 0 0
\(491\) −38.9706 −1.75872 −0.879358 0.476160i \(-0.842028\pi\)
−0.879358 + 0.476160i \(0.842028\pi\)
\(492\) 0 0
\(493\) −3.65685 6.33386i −0.164696 0.285263i
\(494\) −18.4853 32.0174i −0.831692 1.44053i
\(495\) 0 0
\(496\) 20.4853 0.919816
\(497\) 0 0
\(498\) 0 0
\(499\) 9.65685 16.7262i 0.432300 0.748766i −0.564771 0.825248i \(-0.691035\pi\)
0.997071 + 0.0764820i \(0.0243688\pi\)
\(500\) 10.8284 + 18.7554i 0.484262 + 0.838766i
\(501\) 0 0
\(502\) −5.41421 + 9.37769i −0.241648 + 0.418547i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 8.82843 15.2913i 0.392471 0.679781i
\(507\) 0 0
\(508\) −18.4853 32.0174i −0.820152 1.42054i
\(509\) 12.7782 22.1324i 0.566383 0.981003i −0.430537 0.902573i \(-0.641676\pi\)
0.996920 0.0784305i \(-0.0249909\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −31.2426 −1.38074
\(513\) 0 0
\(514\) 23.1924 + 40.1704i 1.02297 + 1.77184i
\(515\) −3.65685 6.33386i −0.161140 0.279103i
\(516\) 0 0
\(517\) 5.65685 0.248788
\(518\) 0 0
\(519\) 0 0
\(520\) 7.00000 12.1244i 0.306970 0.531688i
\(521\) 16.2929 + 28.2201i 0.713805 + 1.23635i 0.963419 + 0.268000i \(0.0863629\pi\)
−0.249614 + 0.968345i \(0.580304\pi\)
\(522\) 0 0
\(523\) −7.17157 + 12.4215i −0.313591 + 0.543156i −0.979137 0.203201i \(-0.934865\pi\)
0.665546 + 0.746357i \(0.268199\pi\)
\(524\) 28.0000 1.22319
\(525\) 0 0
\(526\) 41.7990 1.82252
\(527\) −21.3137 + 36.9164i −0.928440 + 1.60810i
\(528\) 0 0
\(529\) 4.81371 + 8.33759i 0.209292 + 0.362504i
\(530\) −1.41421 + 2.44949i −0.0614295 + 0.106399i
\(531\) 0 0
\(532\) 0 0
\(533\) 12.1421 0.525934
\(534\) 0 0
\(535\) −3.41421 5.91359i −0.147609 0.255667i
\(536\) −12.4853 21.6251i −0.539282 0.934064i
\(537\) 0 0
\(538\) 25.8995 1.11661
\(539\) 0 0
\(540\) 0 0
\(541\) 2.65685 4.60181i 0.114227 0.197847i −0.803243 0.595651i \(-0.796894\pi\)
0.917471 + 0.397804i \(0.130228\pi\)
\(542\) 21.8995 + 37.9310i 0.940664 + 1.62928i
\(543\) 0 0
\(544\) 4.94975 8.57321i 0.212219 0.367574i
\(545\) 3.31371 0.141944
\(546\) 0 0
\(547\) −3.02944 −0.129529 −0.0647647 0.997901i \(-0.520630\pi\)
−0.0647647 + 0.997901i \(0.520630\pi\)
\(548\) −27.0711 + 46.8885i −1.15642 + 2.00298i
\(549\) 0 0
\(550\) 11.2426 + 19.4728i 0.479388 + 0.830324i
\(551\) 1.65685 2.86976i 0.0705844 0.122256i
\(552\) 0 0
\(553\) 0 0
\(554\) 32.1421 1.36559
\(555\) 0 0
\(556\) −12.1421 21.0308i −0.514941 0.891904i
\(557\) 13.0000 + 22.5167i 0.550828 + 0.954062i 0.998215 + 0.0597213i \(0.0190212\pi\)
−0.447387 + 0.894340i \(0.647645\pi\)
\(558\) 0 0
\(559\) 30.6274 1.29540
\(560\) 0 0
\(561\) 0 0
\(562\) −19.8995 + 34.4669i −0.839410 + 1.45390i
\(563\) 3.41421 + 5.91359i 0.143892 + 0.249228i 0.928959 0.370183i \(-0.120705\pi\)
−0.785067 + 0.619411i \(0.787372\pi\)
\(564\) 0 0
\(565\) 5.07107 8.78335i 0.213341 0.369518i
\(566\) −20.4853 −0.861061
\(567\) 0 0
\(568\) 58.7696 2.46592
\(569\) 0.242641 0.420266i 0.0101720 0.0176185i −0.860895 0.508783i \(-0.830095\pi\)
0.871067 + 0.491165i \(0.163429\pi\)
\(570\) 0 0
\(571\) −16.8284 29.1477i −0.704248 1.21979i −0.966962 0.254919i \(-0.917951\pi\)
0.262715 0.964874i \(-0.415382\pi\)
\(572\) 20.7279 35.9018i 0.866678 1.50113i
\(573\) 0 0
\(574\) 0 0
\(575\) 17.0294 0.710177
\(576\) 0 0
\(577\) −7.05025 12.2114i −0.293506 0.508367i 0.681130 0.732162i \(-0.261489\pi\)
−0.974636 + 0.223795i \(0.928155\pi\)
\(578\) −26.5208 45.9354i −1.10312 1.91066i
\(579\) 0 0
\(580\) 2.62742 0.109098
\(581\) 0 0
\(582\) 0 0
\(583\) −2.00000 + 3.46410i −0.0828315 + 0.143468i
\(584\) −13.0208 22.5527i −0.538805 0.933238i
\(585\) 0 0
\(586\) −23.4350 + 40.5907i −0.968092 + 1.67678i
\(587\) −17.1716 −0.708747 −0.354373 0.935104i \(-0.615306\pi\)
−0.354373 + 0.935104i \(0.615306\pi\)
\(588\) 0 0
\(589\) −19.3137 −0.795807
\(590\) 4.82843 8.36308i 0.198783 0.344303i
\(591\) 0 0
\(592\) 6.00000 + 10.3923i 0.246598 + 0.427121i
\(593\) 10.5355 18.2481i 0.432643 0.749359i −0.564457 0.825462i \(-0.690915\pi\)
0.997100 + 0.0761034i \(0.0242479\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 20.3431 0.833288
\(597\) 0 0
\(598\) −23.8995 41.3951i −0.977323 1.69277i
\(599\) −1.00000 1.73205i −0.0408589 0.0707697i 0.844873 0.534967i \(-0.179676\pi\)
−0.885732 + 0.464198i \(0.846343\pi\)
\(600\) 0 0
\(601\) 0.928932 0.0378919 0.0189460 0.999821i \(-0.493969\pi\)
0.0189460 + 0.999821i \(0.493969\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −22.9706 + 39.7862i −0.934659 + 1.61888i
\(605\) 2.05025 + 3.55114i 0.0833546 + 0.144374i
\(606\) 0 0
\(607\) −14.8284 + 25.6836i −0.601867 + 1.04246i 0.390671 + 0.920530i \(0.372243\pi\)
−0.992538 + 0.121934i \(0.961090\pi\)
\(608\) 4.48528 0.181902
\(609\) 0 0
\(610\) −5.31371 −0.215146
\(611\) 7.65685 13.2621i 0.309763 0.536526i
\(612\) 0 0
\(613\) −13.6569 23.6544i −0.551595 0.955391i −0.998160 0.0606394i \(-0.980686\pi\)
0.446565 0.894751i \(-0.352647\pi\)
\(614\) 2.24264 3.88437i 0.0905056 0.156760i
\(615\) 0 0
\(616\) 0 0
\(617\) 7.51472 0.302531 0.151266 0.988493i \(-0.451665\pi\)
0.151266 + 0.988493i \(0.451665\pi\)
\(618\) 0 0
\(619\) −2.48528 4.30463i −0.0998919 0.173018i 0.811748 0.584008i \(-0.198516\pi\)
−0.911640 + 0.410990i \(0.865183\pi\)
\(620\) −7.65685 13.2621i −0.307507 0.532617i
\(621\) 0 0
\(622\) −53.4558 −2.14338
\(623\) 0 0
\(624\) 0 0
\(625\) −9.98528 + 17.2950i −0.399411 + 0.691801i
\(626\) −21.6066 37.4237i −0.863573 1.49575i
\(627\) 0 0
\(628\) 38.7487 67.1148i 1.54624 2.67817i
\(629\) −24.9706 −0.995642
\(630\) 0 0
\(631\) 0.686292 0.0273208 0.0136604 0.999907i \(-0.495652\pi\)
0.0136604 + 0.999907i \(0.495652\pi\)
\(632\) −5.17157 + 8.95743i −0.205714 + 0.356307i
\(633\) 0 0
\(634\) 12.0711 + 20.9077i 0.479403 + 0.830351i
\(635\) −2.82843 + 4.89898i −0.112243 + 0.194410i
\(636\) 0 0
\(637\) 0 0
\(638\) 5.65685 0.223957
\(639\) 0 0
\(640\) 6.02082 + 10.4284i 0.237994 + 0.412217i
\(641\) −2.58579 4.47871i −0.102132 0.176899i 0.810431 0.585835i \(-0.199233\pi\)
−0.912563 + 0.408936i \(0.865900\pi\)
\(642\) 0 0
\(643\) −50.4264 −1.98862 −0.994312 0.106510i \(-0.966033\pi\)
−0.994312 + 0.106510i \(0.966033\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 21.3137 36.9164i 0.838577 1.45246i
\(647\) −10.5858 18.3351i −0.416170 0.720828i 0.579380 0.815057i \(-0.303295\pi\)
−0.995551 + 0.0942294i \(0.969961\pi\)
\(648\) 0 0
\(649\) 6.82843 11.8272i 0.268039 0.464258i
\(650\) 60.8701 2.38752
\(651\) 0 0
\(652\) 43.3137 1.69630
\(653\) 9.75736 16.9002i 0.381835 0.661358i −0.609490 0.792794i \(-0.708626\pi\)
0.991325 + 0.131436i \(0.0419589\pi\)
\(654\) 0 0
\(655\) −2.14214 3.71029i −0.0837002 0.144973i
\(656\) 3.36396 5.82655i 0.131341 0.227489i
\(657\) 0 0
\(658\) 0 0
\(659\) 13.3137 0.518628 0.259314 0.965793i \(-0.416503\pi\)
0.259314 + 0.965793i \(0.416503\pi\)
\(660\) 0 0
\(661\) 3.77817 + 6.54399i 0.146954 + 0.254532i 0.930100 0.367306i \(-0.119720\pi\)
−0.783146 + 0.621838i \(0.786386\pi\)
\(662\) 4.82843 + 8.36308i 0.187662 + 0.325040i
\(663\) 0 0
\(664\) −67.5980 −2.62331
\(665\) 0 0
\(666\) 0 0
\(667\) 2.14214 3.71029i 0.0829438 0.143663i
\(668\) −37.8995 65.6439i −1.46638 2.53984i
\(669\) 0 0
\(670\) −4.00000 + 6.92820i −0.154533 + 0.267660i
\(671\) −7.51472 −0.290102
\(672\) 0 0
\(673\) 0.686292 0.0264546 0.0132273 0.999913i \(-0.495789\pi\)
0.0132273 + 0.999913i \(0.495789\pi\)
\(674\) 22.1421 38.3513i 0.852883 1.47724i
\(675\) 0 0
\(676\) −31.2279 54.0883i −1.20107 2.08032i
\(677\) −14.2929 + 24.7560i −0.549321 + 0.951451i 0.449001 + 0.893531i \(0.351780\pi\)
−0.998321 + 0.0579196i \(0.981553\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 16.1421 0.619023
\(681\) 0 0
\(682\) −16.4853 28.5533i −0.631254 1.09336i
\(683\) −4.17157 7.22538i −0.159621 0.276471i 0.775111 0.631825i \(-0.217694\pi\)
−0.934732 + 0.355354i \(0.884360\pi\)
\(684\) 0 0
\(685\) 8.28427 0.316526
\(686\) 0 0
\(687\) 0 0
\(688\) 8.48528 14.6969i 0.323498 0.560316i
\(689\) 5.41421 + 9.37769i 0.206265 + 0.357262i
\(690\) 0 0
\(691\) −11.6569 + 20.1903i −0.443448 + 0.768074i −0.997943 0.0641132i \(-0.979578\pi\)
0.554495 + 0.832187i \(0.312911\pi\)
\(692\) 26.5269 1.00840
\(693\) 0 0
\(694\) −25.7990 −0.979316
\(695\) −1.85786 + 3.21792i −0.0704728 + 0.122062i
\(696\) 0 0
\(697\) 7.00000 + 12.1244i 0.265144 + 0.459243i
\(698\) 11.9497 20.6976i 0.452305 0.783415i
\(699\) 0 0
\(700\) 0 0
\(701\) 22.8284 0.862218 0.431109 0.902300i \(-0.358122\pi\)
0.431109 + 0.902300i \(0.358122\pi\)
\(702\) 0 0
\(703\) −5.65685 9.79796i −0.213352 0.369537i
\(704\) 9.82843 + 17.0233i 0.370423 + 0.641591i
\(705\) 0 0
\(706\) 25.8995 0.974740
\(707\) 0 0
\(708\) 0 0
\(709\) −10.1421 + 17.5667i −0.380896 + 0.659731i −0.991191 0.132443i \(-0.957718\pi\)
0.610295 + 0.792174i \(0.291051\pi\)
\(710\) −9.41421 16.3059i −0.353309 0.611949i
\(711\) 0 0
\(712\) 12.7071 22.0094i 0.476219 0.824835i
\(713\) −24.9706 −0.935155
\(714\) 0 0
\(715\) −6.34315 −0.237220
\(716\) −15.9706 + 27.6618i −0.596848 + 1.03377i
\(717\) 0 0
\(718\) −14.0711 24.3718i −0.525128 0.909548i
\(719\) 12.9706 22.4657i 0.483720 0.837828i −0.516105 0.856525i \(-0.672619\pi\)
0.999825 + 0.0186972i \(0.00595184\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −26.5563 −0.988325
\(723\) 0 0
\(724\) −10.3640 17.9509i −0.385174 0.667140i
\(725\) 2.72792 + 4.72490i 0.101312 + 0.175478i
\(726\) 0 0
\(727\) 4.48528 0.166350 0.0831749 0.996535i \(-0.473494\pi\)
0.0831749 + 0.996535i \(0.473494\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −4.17157 + 7.22538i −0.154397 + 0.267423i
\(731\) 17.6569 + 30.5826i 0.653062 + 1.13114i
\(732\) 0 0
\(733\) −4.84924 + 8.39913i −0.179111 + 0.310229i −0.941576 0.336800i \(-0.890655\pi\)
0.762465 + 0.647029i \(0.223989\pi\)
\(734\) −46.6274 −1.72105
\(735\) 0 0
\(736\) 5.79899 0.213754
\(737\) −5.65685 + 9.79796i −0.208373 + 0.360912i
\(738\) 0 0
\(739\) −13.6569 23.6544i −0.502376 0.870140i −0.999996 0.00274517i \(-0.999126\pi\)
0.497621 0.867395i \(-0.334207\pi\)
\(740\) 4.48528 7.76874i 0.164882 0.285584i
\(741\) 0 0
\(742\) 0 0
\(743\) 17.0294 0.624749 0.312375 0.949959i \(-0.398876\pi\)
0.312375 + 0.949959i \(0.398876\pi\)
\(744\) 0 0
\(745\) −1.55635 2.69568i −0.0570202 0.0987619i
\(746\) 40.2132 + 69.6513i 1.47231 + 2.55012i
\(747\) 0 0
\(748\) 47.7990 1.74770
\(749\) 0 0
\(750\) 0 0
\(751\) −1.17157 + 2.02922i −0.0427513 + 0.0740474i −0.886609 0.462519i \(-0.846946\pi\)
0.843858 + 0.536567i \(0.180279\pi\)
\(752\) −4.24264 7.34847i −0.154713 0.267971i
\(753\) 0 0
\(754\) 7.65685 13.2621i 0.278846 0.482976i
\(755\) 7.02944 0.255827
\(756\) 0 0
\(757\) 37.6569 1.36866 0.684331 0.729172i \(-0.260094\pi\)
0.684331 + 0.729172i \(0.260094\pi\)
\(758\) −37.7990 + 65.4698i −1.37292 + 2.37797i
\(759\) 0 0
\(760\) 3.65685 + 6.33386i 0.132648 + 0.229753i
\(761\) −23.2635 + 40.2935i −0.843300 + 1.46064i 0.0437901 + 0.999041i \(0.486057\pi\)
−0.887090 + 0.461597i \(0.847277\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 68.9117 2.49314
\(765\) 0 0
\(766\) 35.7990 + 62.0057i 1.29347 + 2.24036i
\(767\) −18.4853 32.0174i −0.667465 1.15608i
\(768\) 0 0
\(769\) 29.6985 1.07095 0.535477 0.844550i \(-0.320132\pi\)
0.535477 + 0.844550i \(0.320132\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 33.1421 57.4039i 1.19281 2.06601i
\(773\) −10.7782 18.6683i −0.387664 0.671454i 0.604471 0.796627i \(-0.293385\pi\)
−0.992135 + 0.125174i \(0.960051\pi\)
\(774\) 0 0
\(775\) 15.8995 27.5387i 0.571127 0.989220i
\(776\) −23.8995 −0.857942
\(777\) 0 0
\(778\) −24.4853 −0.877840
\(779\) −3.17157 + 5.49333i −0.113633 + 0.196819i
\(780\) 0 0
\(781\) −13.3137 23.0600i −0.476402 0.825152i
\(782\) 27.5563 47.7290i 0.985413 1.70679i
\(783\) 0 0
\(784\) 0 0
\(785\) −11.8579 −0.423225
\(786\) 0 0
\(787\) 23.6569 + 40.9749i 0.843276 + 1.46060i 0.887110 + 0.461558i \(0.152709\pi\)
−0.0438344 + 0.999039i \(0.513957\pi\)
\(788\) 3.82843 + 6.63103i 0.136382 + 0.236221i
\(789\) 0 0
\(790\) 3.31371 0.117896
\(791\) 0 0
\(792\) 0 0
\(793\) −10.1716 + 17.6177i −0.361203 + 0.625622i
\(794\) 41.5061 + 71.8907i 1.47300 +