Properties

Label 450.2.h.e.91.1
Level $450$
Weight $2$
Character 450.91
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \(x^{8} - 3 x^{7} + 4 x^{6} - 7 x^{5} + 11 x^{4} + 5 x^{3} - 10 x^{2} - 25 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.1
Root \(1.66637 + 0.917186i\) of defining polynomial
Character \(\chi\) \(=\) 450.91
Dual form 450.2.h.e.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-2.02373 + 0.951057i) q^{5} -2.77447 q^{7} +(-0.309017 + 0.951057i) q^{8} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{4} +(-2.02373 + 0.951057i) q^{5} -2.77447 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.19625 - 0.420099i) q^{10} +(2.24459 + 1.63079i) q^{11} +(-4.59343 + 3.33732i) q^{13} +(-2.24459 - 1.63079i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-1.59343 + 4.90406i) q^{17} +(0.436451 - 1.34326i) q^{19} +(-1.52988 - 1.63079i) q^{20} +(0.857358 + 2.63868i) q^{22} +(-0.529876 - 0.384978i) q^{23} +(3.19098 - 3.84937i) q^{25} -5.67779 q^{26} +(-0.857358 - 2.63868i) q^{28} +(-1.26594 - 3.89618i) q^{29} +(-2.20239 + 6.77827i) q^{31} -1.00000 q^{32} +(-4.17164 + 3.03088i) q^{34} +(5.61478 - 2.63868i) q^{35} +(0.847416 - 0.615684i) q^{37} +(1.14264 - 0.830178i) q^{38} +(-0.279141 - 2.21858i) q^{40} +(7.36789 - 5.35309i) q^{41} +9.24660 q^{43} +(-0.857358 + 2.63868i) q^{44} +(-0.202395 - 0.622907i) q^{46} +(0.857358 + 2.63868i) q^{47} +0.697669 q^{49} +(4.84416 - 1.23859i) q^{50} +(-4.59343 - 3.33732i) q^{52} +(0.162577 + 0.500362i) q^{53} +(-6.09343 - 1.16555i) q^{55} +(0.857358 - 2.63868i) q^{56} +(1.26594 - 3.89618i) q^{58} +(-3.05975 + 2.22304i) q^{59} +(8.76365 + 6.36716i) q^{61} +(-5.76594 + 4.18920i) q^{62} +(-0.809017 - 0.587785i) q^{64} +(6.12188 - 11.1224i) q^{65} +(-1.33600 + 4.11180i) q^{67} -5.15643 q^{68} +(6.09343 + 1.16555i) q^{70} +(4.09343 + 12.5983i) q^{71} +(-3.40859 - 2.47648i) q^{73} +1.04746 q^{74} +1.41238 q^{76} +(-6.22754 - 4.52458i) q^{77} +(-3.05975 - 9.41695i) q^{79} +(1.07822 - 1.95894i) q^{80} +9.10722 q^{82} +(-1.44497 + 4.44717i) q^{83} +(-1.43937 - 11.4399i) q^{85} +(7.48066 + 5.43502i) q^{86} +(-2.24459 + 1.63079i) q^{88} +(-7.43002 - 5.39823i) q^{89} +(12.7443 - 9.25928i) q^{91} +(0.202395 - 0.622907i) q^{92} +(-0.857358 + 2.63868i) q^{94} +(0.394254 + 3.13348i) q^{95} +(-0.0278640 - 0.0857567i) q^{97} +(0.564426 + 0.410079i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} - q^{11} - 13q^{13} + q^{14} - 2q^{16} + 11q^{17} + 20q^{19} - 5q^{20} + q^{22} + 3q^{23} + 30q^{25} - 22q^{26} - q^{28} + 15q^{29} - 9q^{31} - 8q^{32} - q^{34} + 15q^{35} - 6q^{37} + 15q^{38} - 5q^{40} + 9q^{41} + 12q^{43} - q^{44} + 7q^{46} + q^{47} - 4q^{49} + 5q^{50} - 13q^{52} - 7q^{53} - 25q^{55} + q^{56} - 15q^{58} - 10q^{59} + 6q^{61} - 21q^{62} - 2q^{64} + 10q^{65} - 11q^{67} - 24q^{68} + 25q^{70} + 9q^{71} - 8q^{73} - 24q^{74} - 10q^{76} - 33q^{77} - 10q^{79} + 26q^{82} - 27q^{83} + 5q^{85} + 23q^{86} + q^{88} + 15q^{89} + q^{91} - 7q^{92} - q^{94} + 30q^{95} - 36q^{97} + 19q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.572061 + 0.415627i
\(3\) 0 0
\(4\) 0.309017 + 0.951057i 0.154508 + 0.475528i
\(5\) −2.02373 + 0.951057i −0.905040 + 0.425325i
\(6\) 0 0
\(7\) −2.77447 −1.04865 −0.524325 0.851518i \(-0.675682\pi\)
−0.524325 + 0.851518i \(0.675682\pi\)
\(8\) −0.309017 + 0.951057i −0.109254 + 0.336249i
\(9\) 0 0
\(10\) −2.19625 0.420099i −0.694515 0.132847i
\(11\) 2.24459 + 1.63079i 0.676770 + 0.491702i 0.872284 0.488999i \(-0.162638\pi\)
−0.195515 + 0.980701i \(0.562638\pi\)
\(12\) 0 0
\(13\) −4.59343 + 3.33732i −1.27399 + 0.925606i −0.999354 0.0359433i \(-0.988556\pi\)
−0.274633 + 0.961549i \(0.588556\pi\)
\(14\) −2.24459 1.63079i −0.599892 0.435847i
\(15\) 0 0
\(16\) −0.809017 + 0.587785i −0.202254 + 0.146946i
\(17\) −1.59343 + 4.90406i −0.386462 + 1.18941i 0.548951 + 0.835854i \(0.315027\pi\)
−0.935414 + 0.353555i \(0.884973\pi\)
\(18\) 0 0
\(19\) 0.436451 1.34326i 0.100129 0.308164i −0.888428 0.459017i \(-0.848202\pi\)
0.988556 + 0.150852i \(0.0482018\pi\)
\(20\) −1.52988 1.63079i −0.342091 0.364656i
\(21\) 0 0
\(22\) 0.857358 + 2.63868i 0.182789 + 0.562567i
\(23\) −0.529876 0.384978i −0.110487 0.0802734i 0.531170 0.847265i \(-0.321753\pi\)
−0.641657 + 0.766992i \(0.721753\pi\)
\(24\) 0 0
\(25\) 3.19098 3.84937i 0.638197 0.769873i
\(26\) −5.67779 −1.11351
\(27\) 0 0
\(28\) −0.857358 2.63868i −0.162025 0.498663i
\(29\) −1.26594 3.89618i −0.235080 0.723502i −0.997111 0.0759609i \(-0.975798\pi\)
0.762031 0.647541i \(-0.224202\pi\)
\(30\) 0 0
\(31\) −2.20239 + 6.77827i −0.395562 + 1.21741i 0.532961 + 0.846140i \(0.321079\pi\)
−0.928523 + 0.371274i \(0.878921\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −4.17164 + 3.03088i −0.715431 + 0.519791i
\(35\) 5.61478 2.63868i 0.949071 0.446018i
\(36\) 0 0
\(37\) 0.847416 0.615684i 0.139314 0.101218i −0.515945 0.856622i \(-0.672559\pi\)
0.655260 + 0.755404i \(0.272559\pi\)
\(38\) 1.14264 0.830178i 0.185361 0.134673i
\(39\) 0 0
\(40\) −0.279141 2.21858i −0.0441361 0.350788i
\(41\) 7.36789 5.35309i 1.15067 0.836012i 0.162101 0.986774i \(-0.448173\pi\)
0.988570 + 0.150762i \(0.0481728\pi\)
\(42\) 0 0
\(43\) 9.24660 1.41009 0.705047 0.709161i \(-0.250926\pi\)
0.705047 + 0.709161i \(0.250926\pi\)
\(44\) −0.857358 + 2.63868i −0.129252 + 0.397795i
\(45\) 0 0
\(46\) −0.202395 0.622907i −0.0298415 0.0918426i
\(47\) 0.857358 + 2.63868i 0.125058 + 0.384890i 0.993912 0.110179i \(-0.0351425\pi\)
−0.868853 + 0.495070i \(0.835143\pi\)
\(48\) 0 0
\(49\) 0.697669 0.0996670
\(50\) 4.84416 1.23859i 0.685068 0.175163i
\(51\) 0 0
\(52\) −4.59343 3.33732i −0.636994 0.462803i
\(53\) 0.162577 + 0.500362i 0.0223317 + 0.0687299i 0.961601 0.274450i \(-0.0884959\pi\)
−0.939270 + 0.343180i \(0.888496\pi\)
\(54\) 0 0
\(55\) −6.09343 1.16555i −0.821637 0.157163i
\(56\) 0.857358 2.63868i 0.114569 0.352608i
\(57\) 0 0
\(58\) 1.26594 3.89618i 0.166227 0.511593i
\(59\) −3.05975 + 2.22304i −0.398346 + 0.289415i −0.768867 0.639409i \(-0.779179\pi\)
0.370521 + 0.928824i \(0.379179\pi\)
\(60\) 0 0
\(61\) 8.76365 + 6.36716i 1.12207 + 0.815232i 0.984522 0.175263i \(-0.0560776\pi\)
0.137549 + 0.990495i \(0.456078\pi\)
\(62\) −5.76594 + 4.18920i −0.732276 + 0.532029i
\(63\) 0 0
\(64\) −0.809017 0.587785i −0.101127 0.0734732i
\(65\) 6.12188 11.1224i 0.759326 1.37957i
\(66\) 0 0
\(67\) −1.33600 + 4.11180i −0.163219 + 0.502336i −0.998901 0.0468778i \(-0.985073\pi\)
0.835682 + 0.549214i \(0.185073\pi\)
\(68\) −5.15643 −0.625309
\(69\) 0 0
\(70\) 6.09343 + 1.16555i 0.728304 + 0.139310i
\(71\) 4.09343 + 12.5983i 0.485800 + 1.49514i 0.830819 + 0.556543i \(0.187873\pi\)
−0.345018 + 0.938596i \(0.612127\pi\)
\(72\) 0 0
\(73\) −3.40859 2.47648i −0.398945 0.289850i 0.370166 0.928966i \(-0.379301\pi\)
−0.769111 + 0.639115i \(0.779301\pi\)
\(74\) 1.04746 0.121765
\(75\) 0 0
\(76\) 1.41238 0.162012
\(77\) −6.22754 4.52458i −0.709695 0.515623i
\(78\) 0 0
\(79\) −3.05975 9.41695i −0.344249 1.05949i −0.961985 0.273104i \(-0.911950\pi\)
0.617736 0.786386i \(-0.288050\pi\)
\(80\) 1.07822 1.95894i 0.120548 0.219016i
\(81\) 0 0
\(82\) 9.10722 1.00572
\(83\) −1.44497 + 4.44717i −0.158606 + 0.488141i −0.998508 0.0545976i \(-0.982612\pi\)
0.839902 + 0.542738i \(0.182612\pi\)
\(84\) 0 0
\(85\) −1.43937 11.4399i −0.156122 1.24084i
\(86\) 7.48066 + 5.43502i 0.806660 + 0.586073i
\(87\) 0 0
\(88\) −2.24459 + 1.63079i −0.239274 + 0.173843i
\(89\) −7.43002 5.39823i −0.787581 0.572211i 0.119664 0.992814i \(-0.461818\pi\)
−0.907245 + 0.420603i \(0.861818\pi\)
\(90\) 0 0
\(91\) 12.7443 9.25928i 1.33597 0.970637i
\(92\) 0.202395 0.622907i 0.0211011 0.0649425i
\(93\) 0 0
\(94\) −0.857358 + 2.63868i −0.0884297 + 0.272159i
\(95\) 0.394254 + 3.13348i 0.0404496 + 0.321488i
\(96\) 0 0
\(97\) −0.0278640 0.0857567i −0.00282917 0.00870727i 0.949632 0.313367i \(-0.101457\pi\)
−0.952461 + 0.304660i \(0.901457\pi\)
\(98\) 0.564426 + 0.410079i 0.0570156 + 0.0414243i
\(99\) 0 0
\(100\) 4.64703 + 1.84529i 0.464703 + 0.184529i
\(101\) 7.90632 0.786709 0.393354 0.919387i \(-0.371315\pi\)
0.393354 + 0.919387i \(0.371315\pi\)
\(102\) 0 0
\(103\) 2.42091 + 7.45079i 0.238539 + 0.734148i 0.996632 + 0.0820014i \(0.0261312\pi\)
−0.758093 + 0.652146i \(0.773869\pi\)
\(104\) −1.75453 5.39990i −0.172046 0.529503i
\(105\) 0 0
\(106\) −0.162577 + 0.500362i −0.0157909 + 0.0485994i
\(107\) 10.2220 0.988194 0.494097 0.869407i \(-0.335499\pi\)
0.494097 + 0.869407i \(0.335499\pi\)
\(108\) 0 0
\(109\) −3.16400 + 2.29878i −0.303056 + 0.220183i −0.728911 0.684608i \(-0.759973\pi\)
0.425855 + 0.904791i \(0.359973\pi\)
\(110\) −4.24459 4.52458i −0.404706 0.431401i
\(111\) 0 0
\(112\) 2.24459 1.63079i 0.212094 0.154095i
\(113\) −5.15785 + 3.74740i −0.485210 + 0.352526i −0.803339 0.595522i \(-0.796945\pi\)
0.318129 + 0.948047i \(0.396945\pi\)
\(114\) 0 0
\(115\) 1.43846 + 0.275149i 0.134137 + 0.0256578i
\(116\) 3.31428 2.40797i 0.307724 0.223574i
\(117\) 0 0
\(118\) −3.78206 −0.348167
\(119\) 4.42091 13.6062i 0.405264 1.24727i
\(120\) 0 0
\(121\) −1.02048 3.14070i −0.0927706 0.285519i
\(122\) 3.34742 + 10.3023i 0.303061 + 0.932725i
\(123\) 0 0
\(124\) −7.12710 −0.640032
\(125\) −2.79673 + 10.8249i −0.250147 + 0.968208i
\(126\) 0 0
\(127\) −7.72525 5.61272i −0.685505 0.498049i 0.189674 0.981847i \(-0.439257\pi\)
−0.875179 + 0.483798i \(0.839257\pi\)
\(128\) −0.309017 0.951057i −0.0273135 0.0840623i
\(129\) 0 0
\(130\) 11.4903 5.39990i 1.00777 0.473602i
\(131\) −1.73026 + 5.32519i −0.151173 + 0.465264i −0.997753 0.0669981i \(-0.978658\pi\)
0.846580 + 0.532262i \(0.178658\pi\)
\(132\) 0 0
\(133\) −1.21092 + 3.72682i −0.105000 + 0.323156i
\(134\) −3.49771 + 2.54123i −0.302156 + 0.219529i
\(135\) 0 0
\(136\) −4.17164 3.03088i −0.357715 0.259895i
\(137\) 6.45931 4.69296i 0.551856 0.400947i −0.276613 0.960981i \(-0.589212\pi\)
0.828469 + 0.560035i \(0.189212\pi\)
\(138\) 0 0
\(139\) 17.8699 + 12.9832i 1.51571 + 1.10122i 0.963565 + 0.267473i \(0.0861887\pi\)
0.552140 + 0.833751i \(0.313811\pi\)
\(140\) 4.24459 + 4.52458i 0.358733 + 0.382396i
\(141\) 0 0
\(142\) −4.09343 + 12.5983i −0.343513 + 1.05722i
\(143\) −15.7528 −1.31732
\(144\) 0 0
\(145\) 6.26741 + 6.68083i 0.520480 + 0.554813i
\(146\) −1.30196 4.00703i −0.107751 0.331624i
\(147\) 0 0
\(148\) 0.847416 + 0.615684i 0.0696572 + 0.0506089i
\(149\) −4.18401 −0.342768 −0.171384 0.985204i \(-0.554824\pi\)
−0.171384 + 0.985204i \(0.554824\pi\)
\(150\) 0 0
\(151\) −0.331561 −0.0269821 −0.0134910 0.999909i \(-0.504294\pi\)
−0.0134910 + 0.999909i \(0.504294\pi\)
\(152\) 1.14264 + 0.830178i 0.0926805 + 0.0673364i
\(153\) 0 0
\(154\) −2.37871 7.32092i −0.191682 0.589936i
\(155\) −1.98946 15.8120i −0.159798 1.27005i
\(156\) 0 0
\(157\) 3.60750 0.287910 0.143955 0.989584i \(-0.454018\pi\)
0.143955 + 0.989584i \(0.454018\pi\)
\(158\) 3.05975 9.41695i 0.243421 0.749172i
\(159\) 0 0
\(160\) 2.02373 0.951057i 0.159990 0.0751876i
\(161\) 1.47012 + 1.06811i 0.115862 + 0.0841787i
\(162\) 0 0
\(163\) −4.12101 + 2.99409i −0.322782 + 0.234515i −0.737362 0.675498i \(-0.763929\pi\)
0.414580 + 0.910013i \(0.363929\pi\)
\(164\) 7.36789 + 5.35309i 0.575336 + 0.418006i
\(165\) 0 0
\(166\) −3.78299 + 2.74850i −0.293617 + 0.213325i
\(167\) −6.44699 + 19.8418i −0.498883 + 1.53540i 0.311934 + 0.950104i \(0.399023\pi\)
−0.810817 + 0.585300i \(0.800977\pi\)
\(168\) 0 0
\(169\) 5.94464 18.2957i 0.457280 1.40736i
\(170\) 5.55975 10.1011i 0.426414 0.774723i
\(171\) 0 0
\(172\) 2.85736 + 8.79404i 0.217871 + 0.670539i
\(173\) −9.69826 7.04620i −0.737345 0.535713i 0.154533 0.987988i \(-0.450613\pi\)
−0.891879 + 0.452275i \(0.850613\pi\)
\(174\) 0 0
\(175\) −8.85328 + 10.6799i −0.669245 + 0.807328i
\(176\) −2.77447 −0.209133
\(177\) 0 0
\(178\) −2.83802 8.73452i −0.212718 0.654680i
\(179\) 2.63942 + 8.12330i 0.197279 + 0.607164i 0.999942 + 0.0107309i \(0.00341581\pi\)
−0.802663 + 0.596433i \(0.796584\pi\)
\(180\) 0 0
\(181\) 2.41912 7.44529i 0.179812 0.553404i −0.820009 0.572351i \(-0.806031\pi\)
0.999820 + 0.0189471i \(0.00603140\pi\)
\(182\) 15.7528 1.16768
\(183\) 0 0
\(184\) 0.529876 0.384978i 0.0390630 0.0283809i
\(185\) −1.12939 + 2.05192i −0.0830346 + 0.150860i
\(186\) 0 0
\(187\) −11.5741 + 8.40906i −0.846381 + 0.614932i
\(188\) −2.24459 + 1.63079i −0.163704 + 0.118938i
\(189\) 0 0
\(190\) −1.52286 + 2.76678i −0.110480 + 0.200723i
\(191\) 2.72324 1.97855i 0.197047 0.143163i −0.484887 0.874577i \(-0.661139\pi\)
0.681934 + 0.731414i \(0.261139\pi\)
\(192\) 0 0
\(193\) −15.4211 −1.11004 −0.555018 0.831839i \(-0.687288\pi\)
−0.555018 + 0.831839i \(0.687288\pi\)
\(194\) 0.0278640 0.0857567i 0.00200052 0.00615697i
\(195\) 0 0
\(196\) 0.215591 + 0.663522i 0.0153994 + 0.0473945i
\(197\) −2.72086 8.37394i −0.193853 0.596619i −0.999988 0.00488692i \(-0.998444\pi\)
0.806135 0.591732i \(-0.201556\pi\)
\(198\) 0 0
\(199\) −17.6222 −1.24920 −0.624601 0.780944i \(-0.714738\pi\)
−0.624601 + 0.780944i \(0.714738\pi\)
\(200\) 2.67490 + 4.22433i 0.189144 + 0.298705i
\(201\) 0 0
\(202\) 6.39635 + 4.64722i 0.450046 + 0.326977i
\(203\) 3.51232 + 10.8098i 0.246517 + 0.758700i
\(204\) 0 0
\(205\) −9.81955 + 17.8405i −0.685827 + 1.24603i
\(206\) −2.42091 + 7.45079i −0.168673 + 0.519121i
\(207\) 0 0
\(208\) 1.75453 5.39990i 0.121655 0.374415i
\(209\) 3.17022 2.30330i 0.219289 0.159323i
\(210\) 0 0
\(211\) −4.93617 3.58634i −0.339820 0.246894i 0.404766 0.914420i \(-0.367353\pi\)
−0.744586 + 0.667527i \(0.767353\pi\)
\(212\) −0.425633 + 0.309240i −0.0292326 + 0.0212387i
\(213\) 0 0
\(214\) 8.26974 + 6.00832i 0.565308 + 0.410720i
\(215\) −18.7126 + 8.79404i −1.27619 + 0.599749i
\(216\) 0 0
\(217\) 6.11047 18.8061i 0.414806 1.27664i
\(218\) −3.91091 −0.264880
\(219\) 0 0
\(220\) −0.774467 6.15537i −0.0522146 0.414995i
\(221\) −9.04713 27.8442i −0.608576 1.87300i
\(222\) 0 0
\(223\) 4.06828 + 2.95578i 0.272432 + 0.197933i 0.715610 0.698500i \(-0.246149\pi\)
−0.443178 + 0.896434i \(0.646149\pi\)
\(224\) 2.77447 0.185377
\(225\) 0 0
\(226\) −6.37545 −0.424089
\(227\) −14.4314 10.4851i −0.957848 0.695918i −0.00519840 0.999986i \(-0.501655\pi\)
−0.952650 + 0.304069i \(0.901655\pi\)
\(228\) 0 0
\(229\) −6.66137 20.5016i −0.440195 1.35478i −0.887668 0.460485i \(-0.847676\pi\)
0.447472 0.894298i \(-0.352324\pi\)
\(230\) 1.00201 + 1.06811i 0.0660707 + 0.0704289i
\(231\) 0 0
\(232\) 4.09668 0.268960
\(233\) −4.54454 + 13.9867i −0.297723 + 0.916297i 0.684570 + 0.728947i \(0.259990\pi\)
−0.982293 + 0.187350i \(0.940010\pi\)
\(234\) 0 0
\(235\) −4.24459 4.52458i −0.276887 0.295151i
\(236\) −3.05975 2.22304i −0.199173 0.144708i
\(237\) 0 0
\(238\) 11.5741 8.40906i 0.750236 0.545079i
\(239\) 5.61478 + 4.07938i 0.363190 + 0.263873i 0.754381 0.656436i \(-0.227937\pi\)
−0.391192 + 0.920309i \(0.627937\pi\)
\(240\) 0 0
\(241\) −2.67787 + 1.94559i −0.172497 + 0.125326i −0.670684 0.741743i \(-0.733999\pi\)
0.498187 + 0.867070i \(0.333999\pi\)
\(242\) 1.02048 3.14070i 0.0655987 0.201892i
\(243\) 0 0
\(244\) −3.34742 + 10.3023i −0.214296 + 0.659536i
\(245\) −1.41189 + 0.663522i −0.0902026 + 0.0423909i
\(246\) 0 0
\(247\) 2.47807 + 7.62672i 0.157676 + 0.485277i
\(248\) −5.76594 4.18920i −0.366138 0.266015i
\(249\) 0 0
\(250\) −8.62531 + 7.11365i −0.545513 + 0.449906i
\(251\) 9.46454 0.597397 0.298698 0.954348i \(-0.403448\pi\)
0.298698 + 0.954348i \(0.403448\pi\)
\(252\) 0 0
\(253\) −0.561537 1.72823i −0.0353036 0.108653i
\(254\) −2.95078 9.08158i −0.185149 0.569829i
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.0193136 0.0594410i
\(257\) 7.07963 0.441615 0.220808 0.975317i \(-0.429131\pi\)
0.220808 + 0.975317i \(0.429131\pi\)
\(258\) 0 0
\(259\) −2.35113 + 1.70820i −0.146092 + 0.106142i
\(260\) 12.4698 + 2.38523i 0.773347 + 0.147926i
\(261\) 0 0
\(262\) −4.52988 + 3.29115i −0.279857 + 0.203328i
\(263\) 1.15969 0.842563i 0.0715095 0.0519547i −0.551456 0.834204i \(-0.685928\pi\)
0.622966 + 0.782249i \(0.285928\pi\)
\(264\) 0 0
\(265\) −0.804885 0.857977i −0.0494437 0.0527051i
\(266\) −3.17022 + 2.30330i −0.194379 + 0.141225i
\(267\) 0 0
\(268\) −4.32340 −0.264094
\(269\) 4.41368 13.5839i 0.269107 0.828226i −0.721612 0.692298i \(-0.756598\pi\)
0.990719 0.135928i \(-0.0434015\pi\)
\(270\) 0 0
\(271\) 9.51325 + 29.2788i 0.577889 + 1.77856i 0.626125 + 0.779723i \(0.284640\pi\)
−0.0482363 + 0.998836i \(0.515360\pi\)
\(272\) −1.59343 4.90406i −0.0966156 0.297352i
\(273\) 0 0
\(274\) 7.98414 0.482340
\(275\) 13.4400 3.43643i 0.810460 0.207224i
\(276\) 0 0
\(277\) −2.58051 1.87485i −0.155048 0.112649i 0.507556 0.861619i \(-0.330549\pi\)
−0.662604 + 0.748970i \(0.730549\pi\)
\(278\) 6.82570 + 21.0073i 0.409378 + 1.25994i
\(279\) 0 0
\(280\) 0.774467 + 6.15537i 0.0462833 + 0.367854i
\(281\) −6.30053 + 19.3910i −0.375858 + 1.15677i 0.567040 + 0.823690i \(0.308088\pi\)
−0.942898 + 0.333081i \(0.891912\pi\)
\(282\) 0 0
\(283\) −4.10897 + 12.6461i −0.244253 + 0.751733i 0.751506 + 0.659727i \(0.229328\pi\)
−0.995758 + 0.0920063i \(0.970672\pi\)
\(284\) −10.7167 + 7.78616i −0.635921 + 0.462023i
\(285\) 0 0
\(286\) −12.7443 9.25928i −0.753587 0.547513i
\(287\) −20.4420 + 14.8520i −1.20665 + 0.876684i
\(288\) 0 0
\(289\) −7.75751 5.63616i −0.456324 0.331539i
\(290\) 1.14355 + 9.08880i 0.0671516 + 0.533713i
\(291\) 0 0
\(292\) 1.30196 4.00703i 0.0761917 0.234494i
\(293\) 26.0420 1.52139 0.760696 0.649108i \(-0.224858\pi\)
0.760696 + 0.649108i \(0.224858\pi\)
\(294\) 0 0
\(295\) 4.07788 7.40883i 0.237423 0.431359i
\(296\) 0.323684 + 0.996198i 0.0188138 + 0.0579028i
\(297\) 0 0
\(298\) −3.38494 2.45930i −0.196084 0.142464i
\(299\) 3.71874 0.215060
\(300\) 0 0
\(301\) −25.6544 −1.47869
\(302\) −0.268239 0.194887i −0.0154354 0.0112145i
\(303\) 0 0
\(304\) 0.436451 + 1.34326i 0.0250322 + 0.0770411i
\(305\) −23.7908 4.55071i −1.36226 0.260573i
\(306\) 0 0
\(307\) 25.1000 1.43253 0.716267 0.697826i \(-0.245849\pi\)
0.716267 + 0.697826i \(0.245849\pi\)
\(308\) 2.37871 7.32092i 0.135540 0.417148i
\(309\) 0 0
\(310\) 7.68456 13.9616i 0.436453 0.792964i
\(311\) 0.585185 + 0.425162i 0.0331828 + 0.0241087i 0.604253 0.796792i \(-0.293472\pi\)
−0.571070 + 0.820901i \(0.693472\pi\)
\(312\) 0 0
\(313\) −17.4879 + 12.7057i −0.988477 + 0.718170i −0.959587 0.281412i \(-0.909197\pi\)
−0.0288898 + 0.999583i \(0.509197\pi\)
\(314\) 2.91853 + 2.12043i 0.164702 + 0.119663i
\(315\) 0 0
\(316\) 8.01054 5.81999i 0.450628 0.327400i
\(317\) 5.81992 17.9119i 0.326879 1.00603i −0.643706 0.765273i \(-0.722604\pi\)
0.970585 0.240758i \(-0.0773960\pi\)
\(318\) 0 0
\(319\) 3.51232 10.8098i 0.196652 0.605233i
\(320\) 2.19625 + 0.420099i 0.122774 + 0.0234842i
\(321\) 0 0
\(322\) 0.561537 + 1.72823i 0.0312933 + 0.0963107i
\(323\) 5.89196 + 4.28076i 0.327837 + 0.238188i
\(324\) 0 0
\(325\) −1.81098 + 28.3311i −0.100455 + 1.57153i
\(326\) −5.09385 −0.282122
\(327\) 0 0
\(328\) 2.81428 + 8.66148i 0.155393 + 0.478250i
\(329\) −2.37871 7.32092i −0.131143 0.403615i
\(330\) 0 0
\(331\) 5.21494 16.0499i 0.286639 0.882185i −0.699263 0.714864i \(-0.746489\pi\)
0.985903 0.167320i \(-0.0535115\pi\)
\(332\) −4.67603 −0.256631
\(333\) 0 0
\(334\) −16.8784 + 12.2629i −0.923546 + 0.670996i
\(335\) −1.20684 9.59180i −0.0659366 0.524056i
\(336\) 0 0
\(337\) −15.6562 + 11.3749i −0.852845 + 0.619628i −0.925929 0.377698i \(-0.876716\pi\)
0.0730841 + 0.997326i \(0.476716\pi\)
\(338\) 15.5633 11.3074i 0.846530 0.615040i
\(339\) 0 0
\(340\) 10.4352 4.90406i 0.565930 0.265960i
\(341\) −15.9974 + 11.6228i −0.866309 + 0.629410i
\(342\) 0 0
\(343\) 17.4856 0.944134
\(344\) −2.85736 + 8.79404i −0.154058 + 0.474143i
\(345\) 0 0
\(346\) −3.70441 11.4010i −0.199150 0.612921i
\(347\) 2.79311 + 8.59630i 0.149942 + 0.461473i 0.997613 0.0690480i \(-0.0219962\pi\)
−0.847672 + 0.530521i \(0.821996\pi\)
\(348\) 0 0
\(349\) 36.7305 1.96614 0.983068 0.183240i \(-0.0586584\pi\)
0.983068 + 0.183240i \(0.0586584\pi\)
\(350\) −13.4400 + 3.43643i −0.718396 + 0.183685i
\(351\) 0 0
\(352\) −2.24459 1.63079i −0.119637 0.0869214i
\(353\) −5.67779 17.4744i −0.302198 0.930070i −0.980708 0.195479i \(-0.937374\pi\)
0.678510 0.734591i \(-0.262626\pi\)
\(354\) 0 0
\(355\) −20.2657 21.6024i −1.07559 1.14654i
\(356\) 2.83802 8.73452i 0.150415 0.462928i
\(357\) 0 0
\(358\) −2.63942 + 8.12330i −0.139498 + 0.429330i
\(359\) −19.7609 + 14.3572i −1.04294 + 0.757742i −0.970858 0.239657i \(-0.922965\pi\)
−0.0720846 + 0.997399i \(0.522965\pi\)
\(360\) 0 0
\(361\) 13.7575 + 9.99539i 0.724078 + 0.526073i
\(362\) 6.33334 4.60144i 0.332873 0.241846i
\(363\) 0 0
\(364\) 12.7443 + 9.25928i 0.667983 + 0.485318i
\(365\) 9.25334 + 1.76998i 0.484342 + 0.0926450i
\(366\) 0 0
\(367\) 4.48768 13.8117i 0.234255 0.720963i −0.762964 0.646441i \(-0.776257\pi\)
0.997219 0.0745221i \(-0.0237431\pi\)
\(368\) 0.654963 0.0341423
\(369\) 0 0
\(370\) −2.11979 + 0.996198i −0.110202 + 0.0517898i
\(371\) −0.451065 1.38824i −0.0234182 0.0720737i
\(372\) 0 0
\(373\) 18.8410 + 13.6888i 0.975549 + 0.708778i 0.956710 0.291044i \(-0.0940027\pi\)
0.0188399 + 0.999823i \(0.494003\pi\)
\(374\) −14.3064 −0.739764
\(375\) 0 0
\(376\) −2.77447 −0.143082
\(377\) 18.8178 + 13.6719i 0.969166 + 0.704140i
\(378\) 0 0
\(379\) 8.84332 + 27.2169i 0.454251 + 1.39804i 0.872013 + 0.489483i \(0.162815\pi\)
−0.417762 + 0.908556i \(0.637185\pi\)
\(380\) −2.85829 + 1.34326i −0.146627 + 0.0689076i
\(381\) 0 0
\(382\) 3.36611 0.172225
\(383\) 5.13454 15.8025i 0.262363 0.807469i −0.729927 0.683526i \(-0.760446\pi\)
0.992289 0.123944i \(-0.0395542\pi\)
\(384\) 0 0
\(385\) 16.9060 + 3.23378i 0.861610 + 0.164809i
\(386\) −12.4759 9.06430i −0.635008 0.461361i
\(387\) 0 0
\(388\) 0.0729490 0.0530006i 0.00370343 0.00269070i
\(389\) 21.3392 + 15.5039i 1.08194 + 0.786077i 0.978021 0.208508i \(-0.0668609\pi\)
0.103922 + 0.994585i \(0.466861\pi\)
\(390\) 0 0
\(391\) 2.73227 1.98511i 0.138177 0.100391i
\(392\) −0.215591 + 0.663522i −0.0108890 + 0.0335129i
\(393\) 0 0
\(394\) 2.72086 8.37394i 0.137075 0.421873i
\(395\) 15.1482 + 16.1474i 0.762187 + 0.812463i
\(396\) 0 0
\(397\) −5.53406 17.0321i −0.277747 0.854816i −0.988480 0.151354i \(-0.951637\pi\)
0.710733 0.703462i \(-0.248363\pi\)
\(398\) −14.2566 10.3580i −0.714620 0.519202i
\(399\) 0 0
\(400\) −0.318958 + 4.98982i −0.0159479 + 0.249491i
\(401\) −32.0164 −1.59882 −0.799411 0.600785i \(-0.794855\pi\)
−0.799411 + 0.600785i \(0.794855\pi\)
\(402\) 0 0
\(403\) −12.5047 38.4856i −0.622905 1.91710i
\(404\) 2.44319 + 7.51936i 0.121553 + 0.374102i
\(405\) 0 0
\(406\) −3.51232 + 10.8098i −0.174314 + 0.536482i
\(407\) 2.90615 0.144053
\(408\) 0 0
\(409\) −14.5901 + 10.6003i −0.721435 + 0.524153i −0.886842 0.462072i \(-0.847106\pi\)
0.165407 + 0.986225i \(0.447106\pi\)
\(410\) −18.4306 + 8.66148i −0.910221 + 0.427760i
\(411\) 0 0
\(412\) −6.33802 + 4.60484i −0.312252 + 0.226864i
\(413\) 8.48918 6.16775i 0.417725 0.303495i
\(414\) 0 0
\(415\) −1.30527 10.3741i −0.0640733 0.509246i
\(416\) 4.59343 3.33732i 0.225211 0.163626i
\(417\) 0 0
\(418\) 3.91861 0.191666
\(419\) 6.03511 18.5742i 0.294834 0.907407i −0.688443 0.725291i \(-0.741705\pi\)
0.983277 0.182116i \(-0.0582947\pi\)
\(420\) 0 0
\(421\) −6.04242 18.5967i −0.294490 0.906346i −0.983392 0.181492i \(-0.941907\pi\)
0.688903 0.724854i \(-0.258093\pi\)
\(422\) −1.88545 5.80281i −0.0917822 0.282477i
\(423\) 0 0
\(424\) −0.526111 −0.0255502
\(425\) 13.7929 + 21.7825i 0.669055 + 1.05660i
\(426\) 0 0
\(427\) −24.3145 17.6655i −1.17666 0.854893i
\(428\) 3.15876 + 9.72166i 0.152684 + 0.469914i
\(429\) 0 0
\(430\) −20.3079 3.88449i −0.979332 0.187327i
\(431\) 6.55002 20.1589i 0.315503 0.971019i −0.660044 0.751227i \(-0.729462\pi\)
0.975547 0.219792i \(-0.0705378\pi\)
\(432\) 0 0
\(433\) 2.64199 8.13122i 0.126966 0.390761i −0.867288 0.497807i \(-0.834139\pi\)
0.994254 + 0.107045i \(0.0341389\pi\)
\(434\) 15.9974 11.6228i 0.767901 0.557913i
\(435\) 0 0
\(436\) −3.16400 2.29878i −0.151528 0.110091i
\(437\) −0.748388 + 0.543736i −0.0358003 + 0.0260104i
\(438\) 0 0
\(439\) 22.7102 + 16.4999i 1.08390 + 0.787499i 0.978359 0.206916i \(-0.0663427\pi\)
0.105541 + 0.994415i \(0.466343\pi\)
\(440\) 2.99148 5.43502i 0.142613 0.259104i
\(441\) 0 0
\(442\) 9.04713 27.8442i 0.430328 1.32441i
\(443\) 33.0546 1.57047 0.785236 0.619197i \(-0.212542\pi\)
0.785236 + 0.619197i \(0.212542\pi\)
\(444\) 0 0
\(445\) 20.1704 + 3.85820i 0.956169 + 0.182896i
\(446\) 1.55394 + 4.78254i 0.0735813 + 0.226460i
\(447\) 0 0
\(448\) 2.24459 + 1.63079i 0.106047 + 0.0770476i
\(449\) 37.1628 1.75382 0.876911 0.480652i \(-0.159600\pi\)
0.876911 + 0.480652i \(0.159600\pi\)
\(450\) 0 0
\(451\) 25.2677 1.18981
\(452\) −5.15785 3.74740i −0.242605 0.176263i
\(453\) 0 0
\(454\) −5.51232 16.9652i −0.258706 0.796215i
\(455\) −16.9850 + 30.8589i −0.796267 + 1.44669i
\(456\) 0 0
\(457\) 29.3139 1.37125 0.685624 0.727956i \(-0.259529\pi\)
0.685624 + 0.727956i \(0.259529\pi\)
\(458\) 6.66137 20.5016i 0.311265 0.957976i
\(459\) 0 0
\(460\) 0.182827 + 1.45309i 0.00852435 + 0.0677504i
\(461\) 7.20624 + 5.23564i 0.335628 + 0.243848i 0.742815 0.669497i \(-0.233490\pi\)
−0.407187 + 0.913345i \(0.633490\pi\)
\(462\) 0 0
\(463\) 14.7865 10.7430i 0.687187 0.499271i −0.188547 0.982064i \(-0.560378\pi\)
0.875734 + 0.482793i \(0.160378\pi\)
\(464\) 3.31428 + 2.40797i 0.153862 + 0.111787i
\(465\) 0 0
\(466\) −11.8978 + 8.64424i −0.551154 + 0.400436i
\(467\) 11.3360 34.8886i 0.524568 1.61445i −0.240601 0.970624i \(-0.577345\pi\)
0.765169 0.643829i \(-0.222655\pi\)
\(468\) 0 0
\(469\) 3.70670 11.4081i 0.171160 0.526775i
\(470\) −0.774467 6.15537i −0.0357235 0.283926i
\(471\) 0 0
\(472\) −1.16872 3.59695i −0.0537948 0.165563i
\(473\) 20.7548 + 15.0793i 0.954309 + 0.693346i
\(474\) 0 0
\(475\) −3.77798 5.96637i −0.173346 0.273756i
\(476\) 14.3064 0.655731
\(477\) 0 0
\(478\) 2.14465 + 6.60057i 0.0980942 + 0.301903i
\(479\) 3.89046 + 11.9736i 0.177760 + 0.547088i 0.999749 0.0224155i \(-0.00713568\pi\)
−0.821989 + 0.569503i \(0.807136\pi\)
\(480\) 0 0
\(481\) −1.83781 + 5.65620i −0.0837969 + 0.257900i
\(482\) −3.31003 −0.150768
\(483\) 0 0
\(484\) 2.67164 1.94106i 0.121438 0.0882301i
\(485\) 0.137949 + 0.147048i 0.00626393 + 0.00667712i
\(486\) 0 0
\(487\) 14.8257 10.7715i 0.671816 0.488103i −0.198816 0.980037i \(-0.563710\pi\)
0.870633 + 0.491934i \(0.163710\pi\)
\(488\) −8.76365 + 6.36716i −0.396712 + 0.288228i
\(489\) 0 0
\(490\) −1.53226 0.293090i −0.0692202 0.0132405i
\(491\) 17.5595 12.7577i 0.792448 0.575747i −0.116241 0.993221i \(-0.537085\pi\)
0.908689 + 0.417474i \(0.137085\pi\)
\(492\) 0 0
\(493\) 21.1243 0.951389
\(494\) −2.47807 + 7.62672i −0.111494 + 0.343143i
\(495\) 0 0
\(496\) −2.20239 6.77827i −0.0988904 0.304353i
\(497\) −11.3571 34.9535i −0.509434 1.56788i
\(498\) 0 0
\(499\) 15.8391 0.709055 0.354527 0.935046i \(-0.384642\pi\)
0.354527 + 0.935046i \(0.384642\pi\)
\(500\) −11.1593 + 0.685229i −0.499060 + 0.0306444i
\(501\) 0 0
\(502\) 7.65697 + 5.56312i 0.341748 + 0.248294i
\(503\) −8.51433 26.2044i −0.379635 1.16840i −0.940298 0.340353i \(-0.889453\pi\)
0.560662 0.828044i \(-0.310547\pi\)
\(504\) 0 0
\(505\) −16.0003 + 7.51936i −0.712003 + 0.334607i
\(506\) 0.561537 1.72823i 0.0249634 0.0768294i
\(507\) 0 0
\(508\) 2.95078 9.08158i 0.130920 0.402930i
\(509\) −22.3386 + 16.2300i −0.990142 + 0.719380i −0.959952 0.280164i \(-0.909611\pi\)
−0.0301894 + 0.999544i \(0.509611\pi\)
\(510\) 0 0
\(511\) 9.45701 + 6.87092i 0.418354 + 0.303952i
\(512\) 0.809017 0.587785i 0.0357538 0.0259767i
\(513\) 0 0
\(514\) 5.72754 + 4.16130i 0.252631 + 0.183547i
\(515\) −11.9854 12.7760i −0.528139 0.562977i
\(516\) 0 0
\(517\) −2.37871 + 7.32092i −0.104616 + 0.321974i
\(518\) −2.90615 −0.127689
\(519\) 0 0
\(520\) 8.68631 + 9.25928i 0.380920 + 0.406046i
\(521\) −5.28084 16.2527i −0.231358 0.712046i −0.997584 0.0694747i \(-0.977868\pi\)
0.766226 0.642571i \(-0.222132\pi\)
\(522\) 0 0
\(523\) −29.3796 21.3456i −1.28468 0.933376i −0.284999 0.958528i \(-0.591993\pi\)
−0.999684 + 0.0251516i \(0.991993\pi\)
\(524\) −5.59923 −0.244604
\(525\) 0 0
\(526\) 1.43345 0.0625016
\(527\) −29.7317 21.6013i −1.29513 0.940970i
\(528\) 0 0
\(529\) −6.97483 21.4663i −0.303253 0.933318i
\(530\) −0.146859 1.16722i −0.00637915 0.0507007i
\(531\) 0 0
\(532\) −3.91861 −0.169893
\(533\) −15.9789 + 49.1780i −0.692123 + 2.13014i
\(534\) 0 0
\(535\) −20.6865 + 9.72166i −0.894356 + 0.420304i
\(536\) −3.49771 2.54123i −0.151078 0.109764i
\(537\) 0 0
\(538\) 11.5552 8.39532i 0.498178 0.361948i
\(539\) 1.56598 + 1.13775i 0.0674516 + 0.0490064i
\(540\) 0 0
\(541\) −20.1742 + 14.6574i −0.867355 + 0.630170i −0.929876 0.367873i \(-0.880086\pi\)
0.0625209 + 0.998044i \(0.480086\pi\)
\(542\) −9.51325 + 29.2788i −0.408629 + 1.25763i
\(543\) 0 0
\(544\) 1.59343 4.90406i 0.0683176 0.210260i
\(545\) 4.21681 7.66125i 0.180628 0.328172i
\(546\) 0 0
\(547\) 2.06176 + 6.34546i 0.0881547 + 0.271312i 0.985409 0.170201i \(-0.0544418\pi\)
−0.897255 + 0.441513i \(0.854442\pi\)
\(548\) 6.45931 + 4.69296i 0.275928 + 0.200473i
\(549\) 0 0
\(550\) 12.8930 + 5.11968i 0.549761 + 0.218304i
\(551\) −5.78609 −0.246496
\(552\) 0 0
\(553\) 8.48918 + 26.1270i 0.360997 + 1.11103i
\(554\) −0.985668 3.03357i −0.0418770 0.128884i
\(555\) 0 0
\(556\) −6.82570 + 21.0073i −0.289474 + 0.890909i
\(557\) 20.4328 0.865765 0.432882 0.901450i \(-0.357497\pi\)
0.432882 + 0.901450i \(0.357497\pi\)
\(558\) 0 0
\(559\) −42.4736 + 30.8589i −1.79644 + 1.30519i
\(560\) −2.99148 + 5.43502i −0.126413 + 0.229671i
\(561\) 0 0
\(562\) −16.4950 + 11.9843i −0.695799 + 0.505528i
\(563\) −0.487680 + 0.354320i −0.0205532 + 0.0149328i −0.598014 0.801485i \(-0.704043\pi\)
0.577461 + 0.816418i \(0.304043\pi\)
\(564\) 0 0
\(565\) 6.87412 12.4891i 0.289196 0.525422i
\(566\) −10.7574 + 7.81572i −0.452168 + 0.328519i
\(567\) 0 0
\(568\) −13.2466 −0.555815
\(569\) −10.4688 + 32.2195i −0.438873 + 1.35071i 0.450192 + 0.892932i \(0.351356\pi\)
−0.889065 + 0.457781i \(0.848644\pi\)
\(570\) 0 0
\(571\) −1.92521 5.92520i −0.0805677 0.247962i 0.902657 0.430361i \(-0.141614\pi\)
−0.983225 + 0.182399i \(0.941614\pi\)
\(572\) −4.86789 14.9818i −0.203537 0.626422i
\(573\) 0 0
\(574\) −25.2677 −1.05465
\(575\) −3.17275 + 0.811231i −0.132313 + 0.0338307i
\(576\) 0 0
\(577\) −3.05893 2.22244i −0.127345 0.0925214i 0.522290 0.852768i \(-0.325078\pi\)
−0.649634 + 0.760247i \(0.725078\pi\)
\(578\) −2.96310 9.11949i −0.123249 0.379321i
\(579\) 0 0
\(580\) −4.41711 + 8.02516i −0.183410 + 0.333226i
\(581\) 4.00903 12.3385i 0.166323 0.511889i
\(582\) 0 0
\(583\) −0.451065 + 1.38824i −0.0186812 + 0.0574949i
\(584\) 3.40859 2.47648i 0.141048 0.102478i
\(585\) 0 0
\(586\) 21.0684 + 15.3071i 0.870330 + 0.632332i
\(587\) 13.2296 9.61184i 0.546042 0.396723i −0.280282 0.959918i \(-0.590428\pi\)
0.826324 + 0.563195i \(0.190428\pi\)
\(588\) 0 0
\(589\) 8.14373 + 5.91676i 0.335556 + 0.243796i
\(590\) 7.65388 3.59695i 0.315105 0.148084i
\(591\) 0 0
\(592\) −0.323684 + 0.996198i −0.0133033 + 0.0409435i
\(593\) −9.53314 −0.391479 −0.195740 0.980656i \(-0.562711\pi\)
−0.195740 + 0.980656i \(0.562711\pi\)
\(594\) 0 0
\(595\) 3.99349 + 31.7397i 0.163717 + 1.30120i
\(596\) −1.29293 3.97923i −0.0529605 0.162996i
\(597\) 0 0
\(598\) 3.00852 + 2.18582i 0.123028 + 0.0893848i
\(599\) 16.0682 0.656528 0.328264 0.944586i \(-0.393536\pi\)
0.328264 + 0.944586i \(0.393536\pi\)
\(600\) 0 0
\(601\) 15.0380 0.613413 0.306707 0.951804i \(-0.400773\pi\)
0.306707 + 0.951804i \(0.400773\pi\)
\(602\) −20.7548 15.0793i −0.845904 0.614585i
\(603\) 0 0
\(604\) −0.102458 0.315333i −0.00416896 0.0128307i
\(605\) 5.05216 + 5.38541i 0.205399 + 0.218948i
\(606\) 0 0
\(607\) −44.8348 −1.81979 −0.909894 0.414840i \(-0.863837\pi\)
−0.909894 + 0.414840i \(0.863837\pi\)
\(608\) −0.436451 + 1.34326i −0.0177004 + 0.0544763i
\(609\) 0 0
\(610\) −16.5723 17.6655i −0.670994 0.715255i
\(611\) −12.7443 9.25928i −0.515580 0.374590i
\(612\) 0 0
\(613\) 12.5793 9.13937i 0.508072 0.369136i −0.304020 0.952666i \(-0.598329\pi\)
0.812092 + 0.583530i \(0.198329\pi\)
\(614\) 20.3064 + 14.7534i 0.819498 + 0.595400i
\(615\) 0 0
\(616\) 6.22754 4.52458i 0.250915 0.182300i
\(617\) −5.43852 + 16.7380i −0.218946 + 0.673848i 0.779903 + 0.625900i \(0.215268\pi\)
−0.998850 + 0.0479478i \(0.984732\pi\)
\(618\) 0 0
\(619\) −11.5229 + 35.4637i −0.463143 + 1.42541i 0.398161 + 0.917316i \(0.369649\pi\)
−0.861303 + 0.508091i \(0.830351\pi\)
\(620\) 14.4233 6.77827i 0.579255 0.272222i
\(621\) 0 0
\(622\) 0.223521 + 0.687926i 0.00896236 + 0.0275833i
\(623\) 20.6144 + 14.9772i 0.825897 + 0.600049i
\(624\) 0 0
\(625\) −4.63525 24.5665i −0.185410 0.982661i
\(626\) −21.6163 −0.863960
\(627\) 0 0
\(628\) 1.11478 + 3.43094i 0.0444845 + 0.136909i
\(629\) 1.66906 + 5.13683i 0.0665496 + 0.204819i
\(630\) 0 0
\(631\) 2.64380 8.13677i 0.105248 0.323920i −0.884541 0.466463i \(-0.845528\pi\)
0.989789 + 0.142543i \(0.0455280\pi\)
\(632\) 9.90157 0.393863
\(633\) 0 0
\(634\) 15.2367 11.0701i 0.605129 0.439652i
\(635\) 20.9719 + 4.01150i 0.832243 + 0.159191i
\(636\) 0 0
\(637\) −3.20469 + 2.32834i −0.126974 + 0.0922523i
\(638\) 9.19537 6.68083i 0.364048 0.264497i
\(639\) 0 0
\(640\) 1.52988 + 1.63079i 0.0604737 + 0.0644627i
\(641\) −18.4582 + 13.4107i −0.729055 + 0.529690i −0.889264 0.457394i \(-0.848783\pi\)
0.160209 + 0.987083i \(0.448783\pi\)
\(642\) 0 0
\(643\) 34.7745 1.37137 0.685686 0.727898i \(-0.259503\pi\)
0.685686 + 0.727898i \(0.259503\pi\)
\(644\) −0.561537 + 1.72823i −0.0221277 + 0.0681020i
\(645\) 0 0
\(646\) 2.25053 + 6.92641i 0.0885459 + 0.272516i
\(647\) 5.08583 + 15.6526i 0.199945 + 0.615366i 0.999883 + 0.0152844i \(0.00486537\pi\)
−0.799939 + 0.600082i \(0.795135\pi\)
\(648\) 0 0
\(649\) −10.4932 −0.411894
\(650\) −18.1177 + 21.8559i −0.710635 + 0.857258i
\(651\) 0 0
\(652\) −4.12101 2.99409i −0.161391 0.117257i
\(653\) −9.33515 28.7306i −0.365313 1.12432i −0.949785 0.312903i \(-0.898699\pi\)
0.584473 0.811414i \(-0.301301\pi\)
\(654\) 0 0
\(655\) −1.56298 12.4223i −0.0610705 0.485381i
\(656\) −2.81428 + 8.66148i −0.109879 + 0.338174i
\(657\) 0 0
\(658\) 2.37871 7.32092i 0.0927318 0.285399i
\(659\) −23.0523 + 16.7485i −0.897991 + 0.652428i −0.937949 0.346773i \(-0.887277\pi\)
0.0399585 + 0.999201i \(0.487277\pi\)
\(660\) 0 0
\(661\) −41.0448 29.8208i −1.59646 1.15990i −0.893897 0.448273i \(-0.852039\pi\)
−0.702562 0.711622i \(-0.747961\pi\)
\(662\) 13.6529 9.91941i 0.530635 0.385529i
\(663\) 0 0
\(664\) −3.78299 2.74850i −0.146809 0.106663i
\(665\) −1.09385 8.69374i −0.0424175 0.337129i
\(666\) 0 0
\(667\) −0.829146 + 2.55185i −0.0321047 + 0.0988080i
\(668\) −20.8629 −0.807209
\(669\) 0 0
\(670\) 4.66156 8.46929i 0.180092 0.327197i
\(671\) 9.28730 + 28.5834i 0.358532 + 1.10345i
\(672\) 0 0
\(673\) 16.5401 + 12.0171i 0.637573 + 0.463224i 0.859016 0.511949i \(-0.171077\pi\)
−0.221442 + 0.975173i \(0.571077\pi\)
\(674\) −19.3521 −0.745414
\(675\) 0 0
\(676\) 19.2373 0.739894
\(677\) 6.90383 + 5.01592i 0.265336 + 0.192778i 0.712496 0.701676i \(-0.247565\pi\)
−0.447160 + 0.894454i \(0.647565\pi\)
\(678\) 0 0
\(679\) 0.0773079 + 0.237929i 0.00296680 + 0.00913088i
\(680\) 11.3248 + 2.16621i 0.434287 + 0.0830705i
\(681\) 0 0
\(682\) −19.7739 −0.757182
\(683\) 15.0085 46.1913i 0.574283 1.76746i −0.0643246 0.997929i \(-0.520489\pi\)
0.638608 0.769532i \(-0.279511\pi\)
\(684\) 0 0
\(685\) −8.60863 + 15.6405i −0.328919 + 0.597591i
\(686\) 14.1462 + 10.2778i 0.540103 + 0.392408i
\(687\) 0 0
\(688\) −7.48066 + 5.43502i −0.285197 + 0.207208i
\(689\) −2.41665 1.75580i −0.0920671 0.0668907i
\(690\) 0 0
\(691\) −36.2501 + 26.3373i −1.37902 + 1.00192i −0.382048 + 0.924142i \(0.624781\pi\)
−0.996971 + 0.0777740i \(0.975219\pi\)
\(692\) 3.70441 11.4010i 0.140820 0.433401i
\(693\) 0 0
\(694\) −2.79311 + 8.59630i −0.106025 + 0.326311i
\(695\) −48.5117 9.27932i −1.84015 0.351985i
\(696\) 0 0
\(697\) 14.5117 + 44.6623i 0.549669 + 1.69171i
\(698\) 29.7156 + 21.5896i 1.12475 + 0.817179i
\(699\) 0 0
\(700\) −12.8930 5.11968i −0.487311 0.193506i
\(701\) −2.21913 −0.0838152 −0.0419076 0.999121i \(-0.513344\pi\)
−0.0419076 + 0.999121i \(0.513344\pi\)
\(702\) 0 0
\(703\) −0.457166 1.40701i −0.0172424 0.0530665i
\(704\) −0.857358 2.63868i −0.0323129 0.0994488i
\(705\) 0 0
\(706\) 5.67779 17.4744i 0.213686 0.657659i
\(707\) −21.9358 −0.824982
\(708\) 0 0
\(709\) −27.7968 + 20.1955i −1.04393 + 0.758459i −0.971049 0.238882i \(-0.923219\pi\)
−0.0728805 + 0.997341i \(0.523219\pi\)
\(710\) −3.69767 29.3886i −0.138771 1.10293i
\(711\) 0 0
\(712\) 7.43002 5.39823i 0.278452 0.202307i
\(713\) 3.77648 2.74377i 0.141430 0.102755i
\(714\) 0 0
\(715\) 31.8795 14.9818i 1.19223 0.560289i
\(716\) −6.91009 + 5.02047i −0.258242 + 0.187624i
\(717\) 0 0
\(718\) −24.4259 −0.911565
\(719\) −3.70511 + 11.4032i −0.138177 + 0.425266i −0.996071 0.0885618i \(-0.971773\pi\)
0.857893 + 0.513828i \(0.171773\pi\)
\(720\) 0 0
\(721\) −6.71673 20.6720i −0.250144 0.769864i
\(722\) 5.25489 + 16.1729i 0.195567 + 0.601892i
\(723\) 0 0
\(724\) 7.82844 0.290942
\(725\) −19.0374 7.55955i −0.707032 0.280754i
\(726\) 0 0
\(727\) −34.1265 24.7944i −1.26568 0.919573i −0.266661 0.963790i \(-0.585920\pi\)
−0.999022 + 0.0442177i \(0.985920\pi\)
\(728\) 4.86789 + 14.9818i 0.180416 + 0.555264i
\(729\) 0 0
\(730\) 6.44574 + 6.87092i 0.238568 + 0.254304i
\(731\) −14.7338 + 45.3459i −0.544948 + 1.67718i
\(732\) 0 0
\(733\) −0.0996219 + 0.306605i −0.00367962 + 0.0113247i −0.952879 0.303349i \(-0.901895\pi\)
0.949200 + 0.314674i \(0.101895\pi\)
\(734\) 11.7489 8.53607i 0.433660 0.315072i
\(735\) 0 0
\(736\) 0.529876 + 0.384978i 0.0195315 + 0.0141905i
\(737\) −9.70427 + 7.05056i −0.357461 + 0.259711i
\(738\) 0 0
\(739\) 4.44942 + 3.23269i 0.163674 + 0.118916i 0.666607 0.745409i \(-0.267746\pi\)
−0.502933 + 0.864325i \(0.667746\pi\)
\(740\) −2.30049 0.440039i −0.0845678 0.0161761i
\(741\) 0 0
\(742\) 0.451065 1.38824i 0.0165591 0.0509638i
\(743\) 6.03812 0.221517 0.110759 0.993847i \(-0.464672\pi\)
0.110759 + 0.993847i \(0.464672\pi\)
\(744\) 0 0
\(745\) 8.46733 3.97923i 0.310219 0.145788i
\(746\) 7.19662 + 22.1489i 0.263487 + 0.810929i
\(747\) 0 0
\(748\) −11.5741 8.40906i −0.423190 0.307466i
\(749\) −28.3605 −1.03627
\(750\) 0 0
\(751\) −13.5719 −0.495244 −0.247622 0.968857i \(-0.579649\pi\)
−0.247622 + 0.968857i \(0.579649\pi\)
\(752\) −2.24459 1.63079i −0.0818518 0.0594688i
\(753\) 0 0
\(754\) 7.18776 + 22.1216i 0.261763 + 0.805623i
\(755\) 0.670991 0.315333i 0.0244199 0.0114762i
\(756\) 0 0
\(757\) 33.0661 1.20181 0.600904 0.799321i \(-0.294807\pi\)
0.600904 + 0.799321i \(0.294807\pi\)
\(758\) −8.84332 + 27.2169i −0.321204 + 0.988563i
\(759\) 0 0
\(760\) −3.10195 0.593341i −0.112520 0.0215227i
\(761\) 4.19767 + 3.04978i 0.152165 + 0.110555i 0.661263 0.750154i \(-0.270021\pi\)
−0.509098 + 0.860709i \(0.670021\pi\)
\(762\) 0 0
\(763\) 8.77840 6.37788i 0.317799 0.230895i
\(764\) 2.72324 + 1.97855i 0.0985233 + 0.0715814i
\(765\) 0 0
\(766\) 13.4424 9.76647i 0.485694 0.352877i
\(767\) 6.63575 20.4227i 0.239603 0.737422i
\(768\) 0 0
\(769\) 10.2191 31.4512i 0.368511 1.13416i −0.579242 0.815156i \(-0.696651\pi\)
0.947753 0.319005i \(-0.103349\pi\)
\(770\) 11.7765 + 12.5533i 0.424395 + 0.452389i
\(771\) 0 0
\(772\) −4.76538 14.6663i −0.171510 0.527853i
\(773\) −0.914961 0.664758i −0.0329088 0.0239097i 0.571209 0.820804i \(-0.306474\pi\)
−0.604118 + 0.796895i \(0.706474\pi\)
\(774\) 0 0
\(775\) 19.0643 + 30.1072i 0.684808 + 1.08148i
\(776\) 0.0901699 0.00323691
\(777\) 0 0
\(778\) 8.15086 + 25.0858i 0.292223 + 0.899369i
\(779\) −3.97485 12.2333i −0.142414 0.438305i
\(780\) 0 0
\(781\) −11.3571 + 34.9535i −0.406388 + 1.25073i
\(782\) 3.37727 0.120771
\(783\) 0 0
\(784\) −0.564426 + 0.410079i −0.0201581 + 0.0146457i
\(785\) −7.30061 + 3.43094i −0.260570 + 0.122455i
\(786\) 0 0
\(787\) −12.7509 + 9.26408i −0.454521 + 0.330229i −0.791378 0.611327i \(-0.790636\pi\)
0.336857 + 0.941556i \(0.390636\pi\)