Properties

Label 147.2.e.e.67.2
Level $147$
Weight $2$
Character 147.67
Analytic conductor $1.174$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.17380090971\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.2.e.e.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.20711 + 2.09077i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.292893 + 0.507306i) q^{5} +2.41421 q^{6} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.20711 + 2.09077i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.91421 + 3.31552i) q^{4} +(0.292893 + 0.507306i) q^{5} +2.41421 q^{6} -4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.707107 + 1.22474i) q^{10} +(1.00000 - 1.73205i) q^{11} +(1.91421 + 3.31552i) q^{12} -5.41421 q^{13} +0.585786 q^{15} +(-1.50000 - 2.59808i) q^{16} +(3.12132 - 5.40629i) q^{17} +(1.20711 - 2.09077i) q^{18} +(1.41421 + 2.44949i) q^{19} -2.24264 q^{20} +4.82843 q^{22} +(-1.82843 - 3.16693i) q^{23} +(-2.20711 + 3.82282i) q^{24} +(2.32843 - 4.03295i) q^{25} +(-6.53553 - 11.3199i) q^{26} -1.00000 q^{27} -1.17157 q^{29} +(0.707107 + 1.22474i) q^{30} +(-3.41421 + 5.91359i) q^{31} +(-0.792893 + 1.37333i) q^{32} +(-1.00000 - 1.73205i) q^{33} +15.0711 q^{34} +3.82843 q^{36} +(2.00000 + 3.46410i) q^{37} +(-3.41421 + 5.91359i) q^{38} +(-2.70711 + 4.68885i) q^{39} +(-1.29289 - 2.23936i) q^{40} +2.24264 q^{41} -5.65685 q^{43} +(3.82843 + 6.63103i) q^{44} +(0.292893 - 0.507306i) q^{45} +(4.41421 - 7.64564i) q^{46} +(1.41421 + 2.44949i) q^{47} -3.00000 q^{48} +11.2426 q^{50} +(-3.12132 - 5.40629i) q^{51} +(10.3640 - 17.9509i) q^{52} +(1.00000 - 1.73205i) q^{53} +(-1.20711 - 2.09077i) q^{54} +1.17157 q^{55} +2.82843 q^{57} +(-1.41421 - 2.44949i) q^{58} +(-3.41421 + 5.91359i) q^{59} +(-1.12132 + 1.94218i) q^{60} +(1.87868 + 3.25397i) q^{61} -16.4853 q^{62} -9.82843 q^{64} +(-1.58579 - 2.74666i) q^{65} +(2.41421 - 4.18154i) q^{66} +(-2.82843 + 4.89898i) q^{67} +(11.9497 + 20.6976i) q^{68} -3.65685 q^{69} -13.3137 q^{71} +(2.20711 + 3.82282i) q^{72} +(-2.94975 + 5.10911i) q^{73} +(-4.82843 + 8.36308i) q^{74} +(-2.32843 - 4.03295i) q^{75} -10.8284 q^{76} -13.0711 q^{78} +(-1.17157 - 2.02922i) q^{79} +(0.878680 - 1.52192i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.70711 + 4.68885i) q^{82} +15.3137 q^{83} +3.65685 q^{85} +(-6.82843 - 11.8272i) q^{86} +(-0.585786 + 1.01461i) q^{87} +(-4.41421 + 7.64564i) q^{88} +(-2.87868 - 4.98602i) q^{89} +1.41421 q^{90} +14.0000 q^{92} +(3.41421 + 5.91359i) q^{93} +(-3.41421 + 5.91359i) q^{94} +(-0.828427 + 1.43488i) q^{95} +(0.792893 + 1.37333i) q^{96} -5.41421 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 2q^{3} - 2q^{4} + 4q^{5} + 4q^{6} - 12q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} + 2q^{3} - 2q^{4} + 4q^{5} + 4q^{6} - 12q^{8} - 2q^{9} + 4q^{11} + 2q^{12} - 16q^{13} + 8q^{15} - 6q^{16} + 4q^{17} + 2q^{18} + 8q^{20} + 8q^{22} + 4q^{23} - 6q^{24} - 2q^{25} - 12q^{26} - 4q^{27} - 16q^{29} - 8q^{31} - 6q^{32} - 4q^{33} + 32q^{34} + 4q^{36} + 8q^{37} - 8q^{38} - 8q^{39} - 8q^{40} - 8q^{41} + 4q^{44} + 4q^{45} + 12q^{46} - 12q^{48} + 28q^{50} - 4q^{51} + 16q^{52} + 4q^{53} - 2q^{54} + 16q^{55} - 8q^{59} + 4q^{60} + 16q^{61} - 32q^{62} - 28q^{64} - 12q^{65} + 4q^{66} + 28q^{68} + 8q^{69} - 8q^{71} + 6q^{72} + 8q^{73} - 8q^{74} + 2q^{75} - 32q^{76} - 24q^{78} - 16q^{79} + 12q^{80} - 2q^{81} + 8q^{82} + 16q^{83} - 8q^{85} - 16q^{86} - 8q^{87} - 12q^{88} - 20q^{89} + 56q^{92} + 8q^{93} - 8q^{94} + 8q^{95} + 6q^{96} - 16q^{97} - 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20711 + 2.09077i 0.853553 + 1.47840i 0.877981 + 0.478696i \(0.158890\pi\)
−0.0244272 + 0.999702i \(0.507776\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −1.91421 + 3.31552i −0.957107 + 1.65776i
\(5\) 0.292893 + 0.507306i 0.130986 + 0.226874i 0.924057 0.382255i \(-0.124852\pi\)
−0.793071 + 0.609129i \(0.791519\pi\)
\(6\) 2.41421 0.985599
\(7\) 0 0
\(8\) −4.41421 −1.56066
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.707107 + 1.22474i −0.223607 + 0.387298i
\(11\) 1.00000 1.73205i 0.301511 0.522233i −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 1.91421 + 3.31552i 0.552586 + 0.957107i
\(13\) −5.41421 −1.50163 −0.750816 0.660511i \(-0.770340\pi\)
−0.750816 + 0.660511i \(0.770340\pi\)
\(14\) 0 0
\(15\) 0.585786 0.151249
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) 3.12132 5.40629i 0.757031 1.31122i −0.187327 0.982298i \(-0.559982\pi\)
0.944358 0.328919i \(-0.106684\pi\)
\(18\) 1.20711 2.09077i 0.284518 0.492799i
\(19\) 1.41421 + 2.44949i 0.324443 + 0.561951i 0.981399 0.191977i \(-0.0614899\pi\)
−0.656957 + 0.753928i \(0.728157\pi\)
\(20\) −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 \(-0.291174\pi\)
−0.991242 + 0.132060i \(0.957841\pi\)
\(24\) −2.20711 + 3.82282i −0.450524 + 0.780330i
\(25\) 2.32843 4.03295i 0.465685 0.806591i
\(26\) −6.53553 11.3199i −1.28172 2.22001i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −1.17157 −0.217556 −0.108778 0.994066i \(-0.534694\pi\)
−0.108778 + 0.994066i \(0.534694\pi\)
\(30\) 0.707107 + 1.22474i 0.129099 + 0.223607i
\(31\) −3.41421 + 5.91359i −0.613211 + 1.06211i 0.377485 + 0.926016i \(0.376789\pi\)
−0.990696 + 0.136097i \(0.956544\pi\)
\(32\) −0.792893 + 1.37333i −0.140165 + 0.242773i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) 15.0711 2.58467
\(35\) 0 0
\(36\) 3.82843 0.638071
\(37\) 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) −3.41421 + 5.91359i −0.553859 + 0.959311i
\(39\) −2.70711 + 4.68885i −0.433484 + 0.750816i
\(40\) −1.29289 2.23936i −0.204424 0.354073i
\(41\) 2.24264 0.350242 0.175121 0.984547i \(-0.443968\pi\)
0.175121 + 0.984547i \(0.443968\pi\)
\(42\) 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
\(45\) 0.292893 0.507306i 0.0436619 0.0756247i
\(46\) 4.41421 7.64564i 0.650840 1.12729i
\(47\) 1.41421 + 2.44949i 0.206284 + 0.357295i 0.950541 0.310599i \(-0.100530\pi\)
−0.744257 + 0.667893i \(0.767196\pi\)
\(48\) −3.00000 −0.433013
\(49\) 0 0
\(50\) 11.2426 1.58995
\(51\) −3.12132 5.40629i −0.437072 0.757031i
\(52\) 10.3640 17.9509i 1.43722 2.48934i
\(53\) 1.00000 1.73205i 0.137361 0.237915i −0.789136 0.614218i \(-0.789471\pi\)
0.926497 + 0.376303i \(0.122805\pi\)
\(54\) −1.20711 2.09077i −0.164266 0.284518i
\(55\) 1.17157 0.157975
\(56\) 0 0
\(57\) 2.82843 0.374634
\(58\) −1.41421 2.44949i −0.185695 0.321634i
\(59\) −3.41421 + 5.91359i −0.444493 + 0.769884i −0.998017 0.0629492i \(-0.979949\pi\)
0.553524 + 0.832833i \(0.313283\pi\)
\(60\) −1.12132 + 1.94218i −0.144762 + 0.250735i
\(61\) 1.87868 + 3.25397i 0.240540 + 0.416628i 0.960868 0.277006i \(-0.0893421\pi\)
−0.720328 + 0.693634i \(0.756009\pi\)
\(62\) −16.4853 −2.09363
\(63\) 0 0
\(64\) −9.82843 −1.22855
\(65\) −1.58579 2.74666i −0.196693 0.340682i
\(66\) 2.41421 4.18154i 0.297169 0.514712i
\(67\) −2.82843 + 4.89898i −0.345547 + 0.598506i −0.985453 0.169948i \(-0.945640\pi\)
0.639906 + 0.768453i \(0.278973\pi\)
\(68\) 11.9497 + 20.6976i 1.44912 + 2.50995i
\(69\) −3.65685 −0.440234
\(70\) 0 0
\(71\) −13.3137 −1.58005 −0.790023 0.613077i \(-0.789932\pi\)
−0.790023 + 0.613077i \(0.789932\pi\)
\(72\) 2.20711 + 3.82282i 0.260110 + 0.450524i
\(73\) −2.94975 + 5.10911i −0.345242 + 0.597976i −0.985398 0.170269i \(-0.945536\pi\)
0.640156 + 0.768245i \(0.278870\pi\)
\(74\) −4.82843 + 8.36308i −0.561293 + 0.972188i
\(75\) −2.32843 4.03295i −0.268864 0.465685i
\(76\) −10.8284 −1.24211
\(77\) 0 0
\(78\) −13.0711 −1.48001
\(79\) −1.17157 2.02922i −0.131812 0.228306i 0.792563 0.609790i \(-0.208746\pi\)
−0.924375 + 0.381485i \(0.875413\pi\)
\(80\) 0.878680 1.52192i 0.0982394 0.170156i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.70711 + 4.68885i 0.298950 + 0.517796i
\(83\) 15.3137 1.68090 0.840449 0.541891i \(-0.182291\pi\)
0.840449 + 0.541891i \(0.182291\pi\)
\(84\) 0 0
\(85\) 3.65685 0.396642
\(86\) −6.82843 11.8272i −0.736328 1.27536i
\(87\) −0.585786 + 1.01461i −0.0628029 + 0.108778i
\(88\) −4.41421 + 7.64564i −0.470557 + 0.815028i
\(89\) −2.87868 4.98602i −0.305139 0.528517i 0.672153 0.740412i \(-0.265370\pi\)
−0.977292 + 0.211895i \(0.932036\pi\)
\(90\) 1.41421 0.149071
\(91\) 0 0
\(92\) 14.0000 1.45960
\(93\) 3.41421 + 5.91359i 0.354037 + 0.613211i
\(94\) −3.41421 + 5.91359i −0.352149 + 0.609940i
\(95\) −0.828427 + 1.43488i −0.0849948 + 0.147215i
\(96\) 0.792893 + 1.37333i 0.0809243 + 0.140165i
\(97\) −5.41421 −0.549730 −0.274865 0.961483i \(-0.588633\pi\)
−0.274865 + 0.961483i \(0.588633\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 8.91421 + 15.4399i 0.891421 + 1.54399i
\(101\) 8.53553 14.7840i 0.849317 1.47106i −0.0325010 0.999472i \(-0.510347\pi\)
0.881818 0.471589i \(-0.156319\pi\)
\(102\) 7.53553 13.0519i 0.746129 1.29233i
\(103\) −6.24264 10.8126i −0.615106 1.06539i −0.990366 0.138475i \(-0.955780\pi\)
0.375260 0.926919i \(-0.377553\pi\)
\(104\) 23.8995 2.34354
\(105\) 0 0
\(106\) 4.82843 0.468978
\(107\) 5.82843 + 10.0951i 0.563455 + 0.975933i 0.997192 + 0.0748933i \(0.0238616\pi\)
−0.433736 + 0.901040i \(0.642805\pi\)
\(108\) 1.91421 3.31552i 0.184195 0.319036i
\(109\) −2.82843 + 4.89898i −0.270914 + 0.469237i −0.969096 0.246683i \(-0.920659\pi\)
0.698182 + 0.715920i \(0.253993\pi\)
\(110\) 1.41421 + 2.44949i 0.134840 + 0.233550i
\(111\) 4.00000 0.379663
\(112\) 0 0
\(113\) 17.3137 1.62874 0.814368 0.580348i \(-0.197084\pi\)
0.814368 + 0.580348i \(0.197084\pi\)
\(114\) 3.41421 + 5.91359i 0.319770 + 0.553859i
\(115\) 1.07107 1.85514i 0.0998776 0.172993i
\(116\) 2.24264 3.88437i 0.208224 0.360654i
\(117\) 2.70711 + 4.68885i 0.250272 + 0.433484i
\(118\) −16.4853 −1.51759
\(119\) 0 0
\(120\) −2.58579 −0.236049
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −4.53553 + 7.85578i −0.410628 + 0.711228i
\(123\) 1.12132 1.94218i 0.101106 0.175121i
\(124\) −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
\(129\) −2.82843 + 4.89898i −0.249029 + 0.431331i
\(130\) 3.82843 6.63103i 0.335775 0.581580i
\(131\) 3.65685 + 6.33386i 0.319501 + 0.553392i 0.980384 0.197097i \(-0.0631514\pi\)
−0.660883 + 0.750489i \(0.729818\pi\)
\(132\) 7.65685 0.666444
\(133\) 0 0
\(134\) −13.6569 −1.17977
\(135\) −0.292893 0.507306i −0.0252082 0.0436619i
\(136\) −13.7782 + 23.8645i −1.18147 + 2.04636i
\(137\) 7.07107 12.2474i 0.604122 1.04637i −0.388067 0.921631i \(-0.626857\pi\)
0.992190 0.124739i \(-0.0398094\pi\)
\(138\) −4.41421 7.64564i −0.375763 0.650840i
\(139\) 6.34315 0.538019 0.269009 0.963138i \(-0.413304\pi\)
0.269009 + 0.963138i \(0.413304\pi\)
\(140\) 0 0
\(141\) 2.82843 0.238197
\(142\) −16.0711 27.8359i −1.34865 2.33594i
\(143\) −5.41421 + 9.37769i −0.452759 + 0.784202i
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) −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 \(-0.0968249\pi\)
−0.736434 + 0.676510i \(0.763492\pi\)
\(150\) 5.62132 9.73641i 0.458979 0.794975i
\(151\) −6.00000 + 10.3923i −0.488273 + 0.845714i −0.999909 0.0134886i \(-0.995706\pi\)
0.511636 + 0.859202i \(0.329040\pi\)
\(152\) −6.24264 10.8126i −0.506345 0.877015i
\(153\) −6.24264 −0.504688
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) −10.3640 17.9509i −0.829781 1.43722i
\(157\) 10.1213 17.5306i 0.807769 1.39910i −0.106636 0.994298i \(-0.534008\pi\)
0.914406 0.404799i \(-0.132659\pi\)
\(158\) 2.82843 4.89898i 0.225018 0.389742i
\(159\) −1.00000 1.73205i −0.0793052 0.137361i
\(160\) −0.928932 −0.0734385
\(161\) 0 0
\(162\) −2.41421 −0.189679
\(163\) −5.65685 9.79796i −0.443079 0.767435i 0.554837 0.831959i \(-0.312781\pi\)
−0.997916 + 0.0645236i \(0.979447\pi\)
\(164\) −4.29289 + 7.43551i −0.335219 + 0.580616i
\(165\) 0.585786 1.01461i 0.0456034 0.0789874i
\(166\) 18.4853 + 32.0174i 1.43474 + 2.48504i
\(167\) −19.7990 −1.53209 −0.766046 0.642786i \(-0.777779\pi\)
−0.766046 + 0.642786i \(0.777779\pi\)
\(168\) 0 0
\(169\) 16.3137 1.25490
\(170\) 4.41421 + 7.64564i 0.338555 + 0.586394i
\(171\) 1.41421 2.44949i 0.108148 0.187317i
\(172\) 10.8284 18.7554i 0.825660 1.43008i
\(173\) 3.46447 + 6.00063i 0.263398 + 0.456220i 0.967143 0.254234i \(-0.0818233\pi\)
−0.703744 + 0.710453i \(0.748490\pi\)
\(174\) −2.82843 −0.214423
\(175\) 0 0
\(176\) −6.00000 −0.452267
\(177\) 3.41421 + 5.91359i 0.256628 + 0.444493i
\(178\) 6.94975 12.0373i 0.520906 0.902235i
\(179\) 4.17157 7.22538i 0.311798 0.540050i −0.666954 0.745099i \(-0.732402\pi\)
0.978752 + 0.205049i \(0.0657354\pi\)
\(180\) 1.12132 + 1.94218i 0.0835783 + 0.144762i
\(181\) 5.41421 0.402435 0.201218 0.979547i \(-0.435510\pi\)
0.201218 + 0.979547i \(0.435510\pi\)
\(182\) 0 0
\(183\) 3.75736 0.277752
\(184\) 8.07107 + 13.9795i 0.595007 + 1.03058i
\(185\) −1.17157 + 2.02922i −0.0861358 + 0.149191i
\(186\) −8.24264 + 14.2767i −0.604380 + 1.04682i
\(187\) −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 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) −4.91421 + 8.51167i −0.354653 + 0.614277i
\(193\) 8.65685 14.9941i 0.623134 1.07930i −0.365765 0.930707i \(-0.619192\pi\)
0.988899 0.148592i \(-0.0474742\pi\)
\(194\) −6.53553 11.3199i −0.469224 0.812720i
\(195\) −3.17157 −0.227121
\(196\) 0 0
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −2.41421 4.18154i −0.171571 0.297169i
\(199\) 5.17157 8.95743i 0.366603 0.634975i −0.622429 0.782676i \(-0.713854\pi\)
0.989032 + 0.147701i \(0.0471874\pi\)
\(200\) −10.2782 + 17.8023i −0.726777 + 1.25881i
\(201\) 2.82843 + 4.89898i 0.199502 + 0.345547i
\(202\) 41.2132 2.89975
\(203\) 0 0
\(204\) 23.8995 1.67330
\(205\) 0.656854 + 1.13770i 0.0458767 + 0.0794608i
\(206\) 15.0711 26.1039i 1.05005 1.81874i
\(207\) −1.82843 + 3.16693i −0.127084 + 0.220117i
\(208\) 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
\(213\) −6.65685 + 11.5300i −0.456120 + 0.790023i
\(214\) −14.0711 + 24.3718i −0.961878 + 1.66602i
\(215\) −1.65685 2.86976i −0.112997 0.195716i
\(216\) 4.41421 0.300349
\(217\) 0 0
\(218\) −13.6569 −0.924959
\(219\) 2.94975 + 5.10911i 0.199325 + 0.345242i
\(220\) −2.24264 + 3.88437i −0.151199 + 0.261884i
\(221\) −16.8995 + 29.2708i −1.13678 + 1.96897i
\(222\) 4.82843 + 8.36308i 0.324063 + 0.561293i
\(223\) 8.97056 0.600713 0.300357 0.953827i \(-0.402894\pi\)
0.300357 + 0.953827i \(0.402894\pi\)
\(224\) 0 0
\(225\) −4.65685 −0.310457
\(226\) 20.8995 + 36.1990i 1.39021 + 2.40792i
\(227\) −7.89949 + 13.6823i −0.524308 + 0.908128i 0.475292 + 0.879828i \(0.342343\pi\)
−0.999599 + 0.0282996i \(0.990991\pi\)
\(228\) −5.41421 + 9.37769i −0.358565 + 0.621053i
\(229\) 4.12132 + 7.13834i 0.272345 + 0.471715i 0.969462 0.245243i \(-0.0788676\pi\)
−0.697117 + 0.716957i \(0.745534\pi\)
\(230\) 5.17157 0.341003
\(231\) 0 0
\(232\) 5.17157 0.339530
\(233\) −11.0711 19.1757i −0.725290 1.25624i −0.958855 0.283898i \(-0.908372\pi\)
0.233565 0.972341i \(-0.424961\pi\)
\(234\) −6.53553 + 11.3199i −0.427241 + 0.740003i
\(235\) −0.828427 + 1.43488i −0.0540406 + 0.0936011i
\(236\) −13.0711 22.6398i −0.850854 1.47372i
\(237\) −2.34315 −0.152204
\(238\) 0 0
\(239\) −4.34315 −0.280935 −0.140467 0.990085i \(-0.544861\pi\)
−0.140467 + 0.990085i \(0.544861\pi\)
\(240\) −0.878680 1.52192i −0.0567185 0.0982394i
\(241\) −3.87868 + 6.71807i −0.249848 + 0.432749i −0.963483 0.267768i \(-0.913714\pi\)
0.713636 + 0.700517i \(0.247047\pi\)
\(242\) −8.44975 + 14.6354i −0.543170 + 0.940799i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −14.3848 −0.920891
\(245\) 0 0
\(246\) 5.41421 0.345198
\(247\) −7.65685 13.2621i −0.487194 0.843845i
\(248\) 15.0711 26.1039i 0.957014 1.65760i
\(249\) 7.65685 13.2621i 0.485233 0.840449i
\(250\) 6.82843 + 11.8272i 0.431868 + 0.748017i
\(251\) −4.48528 −0.283108 −0.141554 0.989931i \(-0.545210\pi\)
−0.141554 + 0.989931i \(0.545210\pi\)
\(252\) 0 0
\(253\) −7.31371 −0.459809
\(254\) 11.6569 + 20.1903i 0.731416 + 1.26685i
\(255\) 1.82843 3.16693i 0.114501 0.198321i
\(256\) 14.9853 25.9553i 0.936580 1.62220i
\(257\) −9.60660 16.6391i −0.599243 1.03792i −0.992933 0.118677i \(-0.962135\pi\)
0.393690 0.919243i \(-0.371198\pi\)
\(258\) −13.6569 −0.850239
\(259\) 0 0
\(260\) 12.1421 0.753023
\(261\) 0.585786 + 1.01461i 0.0362593 + 0.0628029i
\(262\) −8.82843 + 15.2913i −0.545422 + 0.944699i
\(263\) 8.65685 14.9941i 0.533805 0.924577i −0.465416 0.885092i \(-0.654095\pi\)
0.999220 0.0394843i \(-0.0125715\pi\)
\(264\) 4.41421 + 7.64564i 0.271676 + 0.470557i
\(265\) 1.17157 0.0719691
\(266\) 0 0
\(267\) −5.75736 −0.352345
\(268\) −10.8284 18.7554i −0.661451 1.14567i
\(269\) 5.36396 9.29065i 0.327046 0.566461i −0.654878 0.755735i \(-0.727280\pi\)
0.981924 + 0.189274i \(0.0606133\pi\)
\(270\) 0.707107 1.22474i 0.0430331 0.0745356i
\(271\) 9.07107 + 15.7116i 0.551028 + 0.954409i 0.998201 + 0.0599610i \(0.0190976\pi\)
−0.447173 + 0.894448i \(0.647569\pi\)
\(272\) −18.7279 −1.13555
\(273\) 0 0
\(274\) 34.1421 2.06260
\(275\) −4.65685 8.06591i −0.280819 0.486393i
\(276\) 7.00000 12.1244i 0.421350 0.729800i
\(277\) −6.65685 + 11.5300i −0.399972 + 0.692771i −0.993722 0.111878i \(-0.964313\pi\)
0.593750 + 0.804649i \(0.297647\pi\)
\(278\) 7.65685 + 13.2621i 0.459228 + 0.795406i
\(279\) 6.82843 0.408807
\(280\) 0 0
\(281\) −16.4853 −0.983429 −0.491715 0.870756i \(-0.663630\pi\)
−0.491715 + 0.870756i \(0.663630\pi\)
\(282\) 3.41421 + 5.91359i 0.203313 + 0.352149i
\(283\) 4.24264 7.34847i 0.252199 0.436821i −0.711932 0.702248i \(-0.752180\pi\)
0.964131 + 0.265427i \(0.0855130\pi\)
\(284\) 25.4853 44.1418i 1.51227 2.61933i
\(285\) 0.828427 + 1.43488i 0.0490718 + 0.0849948i
\(286\) −26.1421 −1.54582
\(287\) 0 0
\(288\) 1.58579 0.0934434
\(289\) −10.9853 19.0271i −0.646193 1.11924i
\(290\) 0.828427 1.43488i 0.0486469 0.0842589i
\(291\) −2.70711 + 4.68885i −0.158693 + 0.274865i
\(292\) −11.2929 19.5599i −0.660867 1.14465i
\(293\) −19.4142 −1.13419 −0.567095 0.823652i \(-0.691933\pi\)
−0.567095 + 0.823652i \(0.691933\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) −8.82843 15.2913i −0.513142 0.888788i
\(297\) −1.00000 + 1.73205i −0.0580259 + 0.100504i
\(298\) −6.41421 + 11.1097i −0.371565 + 0.643570i
\(299\) 9.89949 + 17.1464i 0.572503 + 0.991604i
\(300\) 17.8284 1.02932
\(301\) 0 0
\(302\) −28.9706 −1.66707
\(303\) −8.53553 14.7840i −0.490354 0.849317i
\(304\) 4.24264 7.34847i 0.243332 0.421464i
\(305\) −1.10051 + 1.90613i −0.0630147 + 0.109145i
\(306\) −7.53553 13.0519i −0.430778 0.746129i
\(307\) −1.85786 −0.106034 −0.0530170 0.998594i \(-0.516884\pi\)
−0.0530170 + 0.998594i \(0.516884\pi\)
\(308\) 0 0
\(309\) −12.4853 −0.710263
\(310\) −4.82843 8.36308i −0.274236 0.474991i
\(311\) −11.0711 + 19.1757i −0.627783 + 1.08735i 0.360213 + 0.932870i \(0.382704\pi\)
−0.987996 + 0.154481i \(0.950629\pi\)
\(312\) 11.9497 20.6976i 0.676521 1.17177i
\(313\) −8.94975 15.5014i −0.505870 0.876192i −0.999977 0.00679098i \(-0.997838\pi\)
0.494107 0.869401i \(-0.335495\pi\)
\(314\) 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 \(-0.257276\pi\)
−0.971589 + 0.236675i \(0.923942\pi\)
\(318\) 2.41421 4.18154i 0.135382 0.234489i
\(319\) −1.17157 + 2.02922i −0.0655955 + 0.113615i
\(320\) −2.87868 4.98602i −0.160923 0.278727i
\(321\) 11.6569 0.650622
\(322\) 0 0
\(323\) 17.6569 0.982454
\(324\) −1.91421 3.31552i −0.106345 0.184195i
\(325\) −12.6066 + 21.8353i −0.699288 + 1.21120i
\(326\) 13.6569 23.6544i 0.756383 1.31009i
\(327\) 2.82843 + 4.89898i 0.156412 + 0.270914i
\(328\) −9.89949 −0.546608
\(329\) 0 0
\(330\) 2.82843 0.155700
\(331\) 2.00000 + 3.46410i 0.109930 + 0.190404i 0.915742 0.401768i \(-0.131604\pi\)
−0.805812 + 0.592172i \(0.798271\pi\)
\(332\) −29.3137 + 50.7728i −1.60880 + 2.78652i
\(333\) 2.00000 3.46410i 0.109599 0.189832i
\(334\) −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
\(339\) 8.65685 14.9941i 0.470176 0.814368i
\(340\) −7.00000 + 12.1244i −0.379628 + 0.657536i
\(341\) 6.82843 + 11.8272i 0.369780 + 0.640478i
\(342\) 6.82843 0.369239
\(343\) 0 0
\(344\) 24.9706 1.34632
\(345\) −1.07107 1.85514i −0.0576644 0.0998776i
\(346\) −8.36396 + 14.4868i −0.449649 + 0.778815i
\(347\) −5.34315 + 9.25460i −0.286835 + 0.496813i −0.973053 0.230584i \(-0.925937\pi\)
0.686217 + 0.727396i \(0.259270\pi\)
\(348\) −2.24264 3.88437i −0.120218 0.208224i
\(349\) −9.89949 −0.529908 −0.264954 0.964261i \(-0.585357\pi\)
−0.264954 + 0.964261i \(0.585357\pi\)
\(350\) 0 0
\(351\) 5.41421 0.288989
\(352\) 1.58579 + 2.74666i 0.0845227 + 0.146398i
\(353\) 5.36396 9.29065i 0.285495 0.494492i −0.687234 0.726436i \(-0.741175\pi\)
0.972729 + 0.231944i \(0.0745087\pi\)
\(354\) −8.24264 + 14.2767i −0.438091 + 0.758797i
\(355\) −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 \(-0.0671366\pi\)
−0.670227 + 0.742156i \(0.733803\pi\)
\(360\) −1.29289 + 2.23936i −0.0681415 + 0.118024i
\(361\) 5.50000 9.52628i 0.289474 0.501383i
\(362\) 6.53553 + 11.3199i 0.343500 + 0.594960i
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −3.45584 −0.180887
\(366\) 4.53553 + 7.85578i 0.237076 + 0.410628i
\(367\) 9.65685 16.7262i 0.504084 0.873099i −0.495905 0.868377i \(-0.665164\pi\)
0.999989 0.00472187i \(-0.00150302\pi\)
\(368\) −5.48528 + 9.50079i −0.285940 + 0.495263i
\(369\) −1.12132 1.94218i −0.0583736 0.101106i
\(370\) −5.65685 −0.294086
\(371\) 0 0
\(372\) −26.1421 −1.35541
\(373\) 16.6569 + 28.8505i 0.862459 + 1.49382i 0.869548 + 0.493848i \(0.164410\pi\)
−0.00708885 + 0.999975i \(0.502256\pi\)
\(374\) 15.0711 26.1039i 0.779306 1.34980i
\(375\) 2.82843 4.89898i 0.146059 0.252982i
\(376\) −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
\(381\) 4.82843 8.36308i 0.247368 0.428454i
\(382\) −21.7279 + 37.6339i −1.11170 + 1.92552i
\(383\) −14.8284 25.6836i −0.757697 1.31237i −0.944022 0.329882i \(-0.892991\pi\)
0.186325 0.982488i \(-0.440342\pi\)
\(384\) −20.5563 −1.04901
\(385\) 0 0
\(386\) 41.7990 2.12751
\(387\) 2.82843 + 4.89898i 0.143777 + 0.249029i
\(388\) 10.3640 17.9509i 0.526150 0.911319i
\(389\) −5.07107 + 8.78335i −0.257113 + 0.445333i −0.965467 0.260524i \(-0.916105\pi\)
0.708354 + 0.705857i \(0.249438\pi\)
\(390\) −3.82843 6.63103i −0.193860 0.335775i
\(391\) −22.8284 −1.15448
\(392\) 0 0
\(393\) 7.31371 0.368928
\(394\) 2.41421 + 4.18154i 0.121626 + 0.210663i
\(395\) 0.686292 1.18869i 0.0345311 0.0598096i
\(396\) 3.82843 6.63103i 0.192386 0.333222i
\(397\) 17.1924 + 29.7781i 0.862861 + 1.49452i 0.869155 + 0.494539i \(0.164663\pi\)
−0.00629405 + 0.999980i \(0.502003\pi\)
\(398\) 24.9706 1.25166
\(399\) 0 0
\(400\) −13.9706 −0.698528
\(401\) −11.0711 19.1757i −0.552863 0.957586i −0.998066 0.0621570i \(-0.980202\pi\)
0.445204 0.895429i \(-0.353131\pi\)
\(402\) −6.82843 + 11.8272i −0.340571 + 0.589886i
\(403\) 18.4853 32.0174i 0.920817 1.59490i
\(404\) 32.6777 + 56.5994i 1.62577 + 2.81592i
\(405\) −0.585786 −0.0291080
\(406\) 0 0
\(407\) 8.00000 0.396545
\(408\) 13.7782 + 23.8645i 0.682121 + 1.18147i
\(409\) −9.29289 + 16.0958i −0.459504 + 0.795884i −0.998935 0.0461457i \(-0.985306\pi\)
0.539431 + 0.842030i \(0.318639\pi\)
\(410\) −1.58579 + 2.74666i −0.0783164 + 0.135648i
\(411\) −7.07107 12.2474i −0.348790 0.604122i
\(412\) 47.7990 2.35489
\(413\) 0 0
\(414\) −8.82843 −0.433894
\(415\) 4.48528 + 7.76874i 0.220174 + 0.381352i
\(416\) 4.29289 7.43551i 0.210476 0.364556i
\(417\) 3.17157 5.49333i 0.155313 0.269009i
\(418\) 6.82843 + 11.8272i 0.333989 + 0.578486i
\(419\) −38.8284 −1.89689 −0.948446 0.316938i \(-0.897345\pi\)
−0.948446 + 0.316938i \(0.897345\pi\)
\(420\) 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
\(423\) 1.41421 2.44949i 0.0687614 0.119098i
\(424\) −4.41421 + 7.64564i −0.214373 + 0.371305i
\(425\) −14.5355 25.1763i −0.705077 1.22123i
\(426\) −32.1421 −1.55729
\(427\) 0 0
\(428\) −44.6274 −2.15715
\(429\) 5.41421 + 9.37769i 0.261401 + 0.452759i
\(430\) 4.00000 6.92820i 0.192897 0.334108i
\(431\) −3.48528 + 6.03668i −0.167880 + 0.290777i −0.937674 0.347515i \(-0.887025\pi\)
0.769794 + 0.638292i \(0.220359\pi\)
\(432\) 1.50000 + 2.59808i 0.0721688 + 0.125000i
\(433\) 11.7574 0.565023 0.282511 0.959264i \(-0.408833\pi\)
0.282511 + 0.959264i \(0.408833\pi\)
\(434\) 0 0
\(435\) −0.686292 −0.0329052
\(436\) −10.8284 18.7554i −0.518588 0.898220i
\(437\) 5.17157 8.95743i 0.247390 0.428492i
\(438\) −7.12132 + 12.3345i −0.340270 + 0.589365i
\(439\) 17.6569 + 30.5826i 0.842716 + 1.45963i 0.887590 + 0.460634i \(0.152378\pi\)
−0.0448746 + 0.998993i \(0.514289\pi\)
\(440\) −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 \(-0.174452\pi\)
−0.877994 + 0.478672i \(0.841118\pi\)
\(444\) −7.65685 + 13.2621i −0.363378 + 0.629390i
\(445\) 1.68629 2.92074i 0.0799379 0.138456i
\(446\) 10.8284 + 18.7554i 0.512741 + 0.888093i
\(447\) 5.31371 0.251330
\(448\) 0 0
\(449\) 17.3137 0.817084 0.408542 0.912739i \(-0.366037\pi\)
0.408542 + 0.912739i \(0.366037\pi\)
\(450\) −5.62132 9.73641i −0.264992 0.458979i
\(451\) 2.24264 3.88437i 0.105602 0.182908i
\(452\) −33.1421 + 57.4039i −1.55887 + 2.70005i
\(453\) 6.00000 + 10.3923i 0.281905 + 0.488273i
\(454\) −38.1421 −1.79010
\(455\) 0 0
\(456\) −12.4853 −0.584677
\(457\) 9.00000 + 15.5885i 0.421002 + 0.729197i 0.996038 0.0889312i \(-0.0283451\pi\)
−0.575036 + 0.818128i \(0.695012\pi\)
\(458\) −9.94975 + 17.2335i −0.464921 + 0.805267i
\(459\) −3.12132 + 5.40629i −0.145691 + 0.252344i
\(460\) 4.10051 + 7.10228i 0.191187 + 0.331146i
\(461\) 19.4142 0.904210 0.452105 0.891965i \(-0.350673\pi\)
0.452105 + 0.891965i \(0.350673\pi\)
\(462\) 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
\(465\) −2.00000 + 3.46410i −0.0927478 + 0.160644i
\(466\) 26.7279 46.2941i 1.23815 2.14453i
\(467\) 19.8995 + 34.4669i 0.920839 + 1.59494i 0.798120 + 0.602498i \(0.205828\pi\)
0.122718 + 0.992442i \(0.460839\pi\)
\(468\) −20.7279 −0.958149
\(469\) 0 0
\(470\) −4.00000 −0.184506
\(471\) −10.1213 17.5306i −0.466366 0.807769i
\(472\) 15.0711 26.1039i 0.693702 1.20153i
\(473\) −5.65685 + 9.79796i −0.260102 + 0.450511i
\(474\) −2.82843 4.89898i −0.129914 0.225018i
\(475\) 13.1716 0.604353
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) −5.24264 9.08052i −0.239793 0.415333i
\(479\) 15.0711 26.1039i 0.688615 1.19272i −0.283671 0.958922i \(-0.591553\pi\)
0.972286 0.233794i \(-0.0751142\pi\)
\(480\) −0.464466 + 0.804479i −0.0211999 + 0.0367193i
\(481\) −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
\(486\) −1.20711 + 2.09077i −0.0547555 + 0.0948393i
\(487\) 9.31371 16.1318i 0.422044 0.731002i −0.574095 0.818789i \(-0.694646\pi\)
0.996139 + 0.0877864i \(0.0279793\pi\)
\(488\) −8.29289 14.3637i −0.375402 0.650215i
\(489\) −11.3137 −0.511624
\(490\) 0 0
\(491\) 38.9706 1.75872 0.879358 0.476160i \(-0.157972\pi\)
0.879358 + 0.476160i \(0.157972\pi\)
\(492\) 4.29289 + 7.43551i 0.193539 + 0.335219i
\(493\) −3.65685 + 6.33386i −0.164696 + 0.285263i
\(494\) 18.4853 32.0174i 0.831692 1.44053i
\(495\) −0.585786 1.01461i −0.0263291 0.0456034i
\(496\) 20.4853 0.919816
\(497\) 0 0
\(498\) 36.9706 1.65669
\(499\) 9.65685 + 16.7262i 0.432300 + 0.748766i 0.997071 0.0764820i \(-0.0243688\pi\)
−0.564771 + 0.825248i \(0.691035\pi\)
\(500\) −10.8284 + 18.7554i −0.484262 + 0.838766i
\(501\) −9.89949 + 17.1464i −0.442277 + 0.766046i
\(502\) −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
\(507\) 8.15685 14.1281i 0.362259 0.627450i
\(508\) −18.4853 + 32.0174i −0.820152 + 1.42054i
\(509\) −12.7782 22.1324i −0.566383 0.981003i −0.996920 0.0784305i \(-0.975009\pi\)
0.430537 0.902573i \(-0.358324\pi\)
\(510\) 8.82843 0.390929
\(511\) 0 0
\(512\) 31.2426 1.38074
\(513\) −1.41421 2.44949i −0.0624391 0.108148i
\(514\) 23.1924 40.1704i 1.02297 1.77184i
\(515\) 3.65685 6.33386i 0.161140 0.279103i
\(516\) −10.8284 18.7554i −0.476695 0.825660i
\(517\) 5.65685 0.248788
\(518\) 0 0
\(519\) 6.92893 0.304146
\(520\) 7.00000 + 12.1244i 0.306970 + 0.531688i
\(521\) −16.2929 + 28.2201i −0.713805 + 1.23635i 0.249614 + 0.968345i \(0.419696\pi\)
−0.963419 + 0.268000i \(0.913637\pi\)
\(522\) −1.41421 + 2.44949i −0.0618984 + 0.107211i
\(523\) −7.17157 12.4215i −0.313591 0.543156i 0.665546 0.746357i \(-0.268199\pi\)
−0.979137 + 0.203201i \(0.934865\pi\)
\(524\) −28.0000 −1.22319
\(525\) 0 0
\(526\) 41.7990 1.82252
\(527\) 21.3137 + 36.9164i 0.928440 + 1.60810i
\(528\) −3.00000 + 5.19615i −0.130558 + 0.226134i
\(529\) 4.81371 8.33759i 0.209292 0.362504i
\(530\) 1.41421 + 2.44949i 0.0614295 + 0.106399i
\(531\) 6.82843 0.296328
\(532\) 0 0
\(533\) −12.1421 −0.525934
\(534\) −6.94975 12.0373i −0.300745 0.520906i
\(535\) −3.41421 + 5.91359i −0.147609 + 0.255667i
\(536\) 12.4853 21.6251i 0.539282 0.934064i
\(537\) −4.17157 7.22538i −0.180017 0.311798i
\(538\) 25.8995 1.11661
\(539\) 0 0
\(540\) 2.24264 0.0965079
\(541\) 2.65685 + 4.60181i 0.114227 + 0.197847i 0.917471 0.397804i \(-0.130228\pi\)
−0.803243 + 0.595651i \(0.796894\pi\)
\(542\) −21.8995 + 37.9310i −0.940664 + 1.62928i
\(543\) 2.70711 4.68885i 0.116173 0.201218i
\(544\) 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
\(549\) 1.87868 3.25397i 0.0801801 0.138876i
\(550\) 11.2426 19.4728i 0.479388 0.830324i
\(551\) −1.65685 2.86976i −0.0705844 0.122256i
\(552\) 16.1421 0.687055
\(553\) 0 0
\(554\) −32.1421 −1.36559
\(555\) 1.17157 + 2.02922i 0.0497305 + 0.0861358i
\(556\) −12.1421 + 21.0308i −0.514941 + 0.891904i
\(557\) −13.0000 + 22.5167i −0.550828 + 0.954062i 0.447387 + 0.894340i \(0.352355\pi\)
−0.998215 + 0.0597213i \(0.980979\pi\)
\(558\) 8.24264 + 14.2767i 0.348939 + 0.604380i
\(559\) 30.6274 1.29540
\(560\) 0 0
\(561\) −12.4853 −0.527129
\(562\) −19.8995 34.4669i −0.839410 1.45390i
\(563\) −3.41421 + 5.91359i −0.143892 + 0.249228i −0.928959 0.370183i \(-0.879295\pi\)
0.785067 + 0.619411i \(0.212628\pi\)
\(564\) −5.41421 + 9.37769i −0.227980 + 0.394872i
\(565\) 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 \(-0.169905\pi\)
−0.871067 + 0.491165i \(0.836571\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) −16.8284 + 29.1477i −0.704248 + 1.21979i 0.262715 + 0.964874i \(0.415382\pi\)
−0.966962 + 0.254919i \(0.917951\pi\)
\(572\) −20.7279 35.9018i −0.866678 1.50113i
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) −17.0294 −0.710177
\(576\) 4.91421 + 8.51167i 0.204759 + 0.354653i
\(577\) −7.05025 + 12.2114i −0.293506 + 0.508367i −0.974636 0.223795i \(-0.928155\pi\)
0.681130 + 0.732162i \(0.261489\pi\)
\(578\) 26.5208 45.9354i 1.10312 1.91066i
\(579\) −8.65685 14.9941i −0.359767 0.623134i
\(580\) 2.62742 0.109098
\(581\) 0 0
\(582\) −13.0711 −0.541813
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 13.0208 22.5527i 0.538805 0.933238i
\(585\) −1.58579 + 2.74666i −0.0655642 + 0.113561i
\(586\) −23.4350 40.5907i −0.968092 1.67678i
\(587\) 17.1716 0.708747 0.354373 0.935104i \(-0.384694\pi\)
0.354373 + 0.935104i \(0.384694\pi\)
\(588\) 0 0
\(589\) −19.3137 −0.795807
\(590\) −4.82843 8.36308i −0.198783 0.344303i
\(591\) 1.00000 1.73205i 0.0411345 0.0712470i
\(592\) 6.00000 10.3923i 0.246598 0.427121i
\(593\) −10.5355 18.2481i −0.432643 0.749359i 0.564457 0.825462i \(-0.309085\pi\)
−0.997100 + 0.0761034i \(0.975752\pi\)
\(594\) −4.82843 −0.198113
\(595\) 0 0
\(596\) −20.3431 −0.833288
\(597\) −5.17157 8.95743i −0.211658 0.366603i
\(598\) −23.8995 + 41.3951i −0.977323 + 1.69277i
\(599\) 1.00000 1.73205i 0.0408589 0.0707697i −0.844873 0.534967i \(-0.820324\pi\)
0.885732 + 0.464198i \(0.153657\pi\)
\(600\) 10.2782 + 17.8023i 0.419605 + 0.726777i
\(601\) 0.928932 0.0378919 0.0189460 0.999821i \(-0.493969\pi\)
0.0189460 + 0.999821i \(0.493969\pi\)
\(602\) 0 0
\(603\) 5.65685 0.230365
\(604\) −22.9706 39.7862i −0.934659 1.61888i
\(605\) −2.05025 + 3.55114i −0.0833546 + 0.144374i
\(606\) 20.6066 35.6917i 0.837086 1.44988i
\(607\) −14.8284 25.6836i −0.601867 1.04246i −0.992538 0.121934i \(-0.961090\pi\)
0.390671 0.920530i \(-0.372243\pi\)
\(608\) −4.48528 −0.181902
\(609\) 0 0
\(610\) −5.31371 −0.215146
\(611\) −7.65685 13.2621i −0.309763 0.536526i
\(612\) 11.9497 20.6976i 0.483040 0.836650i
\(613\) −13.6569 + 23.6544i −0.551595 + 0.955391i 0.446565 + 0.894751i \(0.352647\pi\)
−0.998160 + 0.0606394i \(0.980686\pi\)
\(614\) −2.24264 3.88437i −0.0905056 0.156760i
\(615\) 1.31371 0.0529738
\(616\) 0 0
\(617\) −7.51472 −0.302531 −0.151266 0.988493i \(-0.548335\pi\)
−0.151266 + 0.988493i \(0.548335\pi\)
\(618\) −15.0711 26.1039i −0.606247 1.05005i
\(619\) −2.48528 + 4.30463i −0.0998919 + 0.173018i −0.911640 0.410990i \(-0.865183\pi\)
0.811748 + 0.584008i \(0.198516\pi\)
\(620\) 7.65685 13.2621i 0.307507 0.532617i
\(621\) 1.82843 + 3.16693i 0.0733723 + 0.127084i
\(622\) −53.4558 −2.14338
\(623\) 0 0
\(624\) 16.2426 0.650226
\(625\) −9.98528 17.2950i −0.399411 0.691801i
\(626\) 21.6066 37.4237i 0.863573 1.49575i
\(627\) 2.82843 4.89898i 0.112956 0.195646i
\(628\) 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
\(633\) −10.4853 + 18.1610i −0.416753 + 0.721837i
\(634\) 12.0711 20.9077i 0.479403 0.830351i
\(635\) 2.82843 + 4.89898i 0.112243 + 0.194410i
\(636\) 7.65685 0.303614
\(637\) 0 0
\(638\) −5.65685 −0.223957
\(639\) 6.65685 + 11.5300i 0.263341 + 0.456120i
\(640\) 6.02082 10.4284i 0.237994 0.412217i
\(641\) 2.58579 4.47871i 0.102132 0.176899i −0.810431 0.585835i \(-0.800767\pi\)
0.912563 + 0.408936i \(0.134100\pi\)
\(642\) 14.0711 + 24.3718i 0.555341 + 0.961878i
\(643\) −50.4264 −1.98862 −0.994312 0.106510i \(-0.966033\pi\)
−0.994312 + 0.106510i \(0.966033\pi\)
\(644\) 0 0
\(645\) −3.31371 −0.130477
\(646\) 21.3137 + 36.9164i 0.838577 + 1.45246i
\(647\) 10.5858 18.3351i 0.416170 0.720828i −0.579380 0.815057i \(-0.696705\pi\)
0.995551 + 0.0942294i \(0.0300387\pi\)
\(648\) 2.20711 3.82282i 0.0867033 0.150175i
\(649\) 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 \(-0.291374\pi\)
−0.991325 + 0.131436i \(0.958041\pi\)
\(654\) −6.82843 + 11.8272i −0.267013 + 0.462479i
\(655\) −2.14214 + 3.71029i −0.0837002 + 0.144973i
\(656\) −3.36396 5.82655i −0.131341 0.227489i
\(657\) 5.89949 0.230161
\(658\) 0 0
\(659\) −13.3137 −0.518628 −0.259314 0.965793i \(-0.583497\pi\)
−0.259314 + 0.965793i \(0.583497\pi\)
\(660\) 2.24264 + 3.88437i 0.0872947 + 0.151199i
\(661\) 3.77817 6.54399i 0.146954 0.254532i −0.783146 0.621838i \(-0.786386\pi\)
0.930100 + 0.367306i \(0.119720\pi\)
\(662\) −4.82843 + 8.36308i −0.187662 + 0.325040i
\(663\) 16.8995 + 29.2708i 0.656322 + 1.13678i
\(664\) −67.5980 −2.62331
\(665\) 0 0
\(666\) 9.65685 0.374196
\(667\) 2.14214 + 3.71029i 0.0829438 + 0.143663i
\(668\) 37.8995 65.6439i 1.46638 2.53984i
\(669\) 4.48528 7.76874i 0.173411 0.300357i
\(670\) −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
\(675\) −2.32843 + 4.03295i −0.0896212 + 0.155228i
\(676\) −31.2279 + 54.0883i −1.20107 + 2.08032i
\(677\) 14.2929 + 24.7560i 0.549321 + 0.951451i 0.998321 + 0.0579196i \(0.0184467\pi\)
−0.449001 + 0.893531i \(0.648220\pi\)
\(678\) 41.7990 1.60528
\(679\) 0 0
\(680\) −16.1421 −0.619023
\(681\) 7.89949 + 13.6823i 0.302709 + 0.524308i
\(682\) −16.4853 + 28.5533i −0.631254 + 1.09336i
\(683\) 4.17157 7.22538i 0.159621 0.276471i −0.775111 0.631825i \(-0.782306\pi\)
0.934732 + 0.355354i \(0.115640\pi\)
\(684\) 5.41421 + 9.37769i 0.207018 + 0.358565i
\(685\) 8.28427 0.316526
\(686\) 0 0
\(687\) 8.24264 0.314476
\(688\) 8.48528 + 14.6969i 0.323498 + 0.560316i
\(689\) −5.41421 + 9.37769i −0.206265 + 0.357262i
\(690\) 2.58579 4.47871i 0.0984392 0.170502i
\(691\) −11.6569 20.1903i −0.443448 0.768074i 0.554495 0.832187i \(-0.312911\pi\)
−0.997943 + 0.0641132i \(0.979578\pi\)
\(692\) −26.5269 −1.00840
\(693\) 0 0
\(694\) −25.7990 −0.979316
\(695\) 1.85786 + 3.21792i 0.0704728 + 0.122062i
\(696\) 2.58579 4.47871i 0.0980140 0.169765i
\(697\) 7.00000 12.1244i 0.265144 0.459243i
\(698\) −11.9497 20.6976i −0.452305 0.783415i
\(699\) −22.1421 −0.837492
\(700\) 0 0
\(701\) −22.8284 −0.862218 −0.431109 0.902300i \(-0.641878\pi\)
−0.431109 + 0.902300i \(0.641878\pi\)
\(702\) 6.53553 + 11.3199i 0.246668 + 0.427241i
\(703\) −5.65685 + 9.79796i −0.213352 + 0.369537i
\(704\) −9.82843 + 17.0233i −0.370423 + 0.641591i
\(705\) 0.828427 + 1.43488i 0.0312004 + 0.0540406i
\(706\) 25.8995 0.974740
\(707\) 0 0
\(708\) −26.1421 −0.982482
\(709\) −10.1421 17.5667i −0.380896 0.659731i 0.610295 0.792174i \(-0.291051\pi\)
−0.991191 + 0.132443i \(0.957718\pi\)
\(710\) 9.41421 16.3059i 0.353309 0.611949i
\(711\) −1.17157 + 2.02922i −0.0439374 + 0.0761018i
\(712\) 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
\(717\) −2.17157 + 3.76127i −0.0810989 + 0.140467i
\(718\) −14.0711 + 24.3718i −0.525128 + 0.909548i
\(719\) −12.9706 22.4657i −0.483720 0.837828i 0.516105 0.856525i \(-0.327381\pi\)
−0.999825 + 0.0186972i \(0.994048\pi\)
\(720\) −1.75736 −0.0654929
\(721\) 0 0
\(722\) 26.5563 0.988325
\(723\) 3.87868 + 6.71807i 0.144250 + 0.249848i
\(724\) −10.3640 + 17.9509i −0.385174 + 0.667140i
\(725\) −2.72792 + 4.72490i −0.101312 + 0.175478i
\(726\) 8.44975 + 14.6354i 0.313600 + 0.543170i
\(727\) 4.48528 0.166350 0.0831749 0.996535i \(-0.473494\pi\)
0.0831749 + 0.996535i \(0.473494\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −4.17157 7.22538i −0.154397 0.267423i
\(731\) −17.6569 + 30.5826i −0.653062 + 1.13114i
\(732\) −7.19239 + 12.4576i −0.265838 + 0.460445i
\(733\) −4.84924 8.39913i −0.179111 0.310229i 0.762465 0.647029i \(-0.223989\pi\)
−0.941576 + 0.336800i \(0.890655\pi\)
\(734\) 46.6274 1.72105
\(735\) 0 0
\(736\) 5.79899 0.213754
\(737\) 5.65685 + 9.79796i 0.208373 + 0.360912i
\(738\) 2.70711 4.68885i 0.0996500 0.172599i
\(739\) −13.6569 + 23.6544i −0.502376 + 0.870140i 0.497621 + 0.867395i \(0.334207\pi\)
−0.999996 + 0.00274517i \(0.999126\pi\)
\(740\) −4.48528 7.76874i −0.164882 0.285584i
\(741\) −15.3137 −0.562563
\(742\) 0 0
\(743\) −17.0294 −0.624749 −0.312375 0.949959i \(-0.601124\pi\)
−0.312375 + 0.949959i \(0.601124\pi\)
\(744\) −15.0711 26.1039i −0.552532 0.957014i
\(745\) −1.55635 + 2.69568i −0.0570202 + 0.0987619i
\(746\) −40.2132 + 69.6513i −1.47231 + 2.55012i
\(747\) −7.65685 13.2621i −0.280150 0.485233i
\(748\) 47.7990 1.74770
\(749\) 0 0
\(750\) 13.6569 0.498678
\(751\) −1.17157 2.02922i −0.0427513 0.0740474i 0.843858 0.536567i \(-0.180279\pi\)
−0.886609 + 0.462519i \(0.846946\pi\)
\(752\) 4.24264 7.34847i 0.154713 0.267971i
\(753\) −2.24264 + 3.88437i −0.0817264 + 0.141554i
\(754\) 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
\(759\) −3.65685 + 6.33386i −0.132735 + 0.229904i
\(760\) 3.65685 6.33386i 0.132648 0.229753i
\(761\) 23.2635 + 40.2935i 0.843300 + 1.46064i 0.887090 + 0.461597i \(0.152723\pi\)
−0.0437901 + 0.999041i \(0.513943\pi\)
\(762\) 23.3137 0.844567
\(763\) 0 0
\(764\) −68.9117 −2.49314
\(765\) −1.82843 3.16693i −0.0661069 0.114501i
\(766\) 35.7990 62.0057i 1.29347 2.24036i
\(767\) 18.4853 32.0174i 0.667465 1.15608i
\(768\) −14.9853 25.9553i −0.540735 0.936580i
\(769\) 29.6985 1.07095 0.535477 0.844550i \(-0.320132\pi\)
0.535477 + 0.844550i \(0.320132\pi\)
\(770\) 0 0
\(771\) −19.2132 −0.691947
\(772\) 33.1421 + 57.4039i 1.19281 + 2.06601i
\(773\) 10.7782 18.6683i 0.387664 0.671454i −0.604471 0.796627i \(-0.706615\pi\)
0.992135 + 0.125174i \(0.0399488\pi\)
\(774\) −6.82843 + 11.8272i −0.245443 + 0.425119i
\(775\) 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
\(780\) 6.07107 10.5154i 0.217379 0.376512i
\(781\) −13.3137 + 23.0600i −0.476402 + 0.825152i
\(782\) −27.5563 47.7290i −0.985413 1.70679i
\(783\) 1.17157 0.0418686
\(784\) 0