Properties

Label 546.2.e.h.545.6
Level $546$
Weight $2$
Character 546.545
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.10070523904.11
Defining polynomial: \(x^{8} - 10 x^{4} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 545.6
Root \(0.420861 + 1.68014i\) of defining polynomial
Character \(\chi\) \(=\) 546.545
Dual form 546.2.e.h.545.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(0.420861 + 1.68014i) q^{3} +1.00000 q^{4} +3.36028i q^{5} +(0.420861 + 1.68014i) q^{6} +(2.37608 - 1.16372i) q^{7} +1.00000 q^{8} +(-2.64575 + 1.41421i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(0.420861 + 1.68014i) q^{3} +1.00000 q^{4} +3.36028i q^{5} +(0.420861 + 1.68014i) q^{6} +(2.37608 - 1.16372i) q^{7} +1.00000 q^{8} +(-2.64575 + 1.41421i) q^{9} +3.36028i q^{10} +(0.420861 + 1.68014i) q^{12} +(-2.79694 - 2.27533i) q^{13} +(2.37608 - 1.16372i) q^{14} +(-5.64575 + 1.41421i) q^{15} +1.00000 q^{16} +7.82087 q^{17} +(-2.64575 + 1.41421i) q^{18} -5.59388 q^{19} +3.36028i q^{20} +(2.95522 + 3.50238i) q^{21} -0.500983i q^{23} +(0.420861 + 1.68014i) q^{24} -6.29150 q^{25} +(-2.79694 - 2.27533i) q^{26} +(-3.48957 - 3.85005i) q^{27} +(2.37608 - 1.16372i) q^{28} -5.15587i q^{29} +(-5.64575 + 1.41421i) q^{30} -3.06871 q^{31} +1.00000 q^{32} +7.82087 q^{34} +(3.91044 + 7.98430i) q^{35} +(-2.64575 + 1.41421i) q^{36} -2.32744i q^{37} -5.59388 q^{38} +(2.64575 - 5.65685i) q^{39} +3.36028i q^{40} +9.87000i q^{41} +(2.95522 + 3.50238i) q^{42} +8.00000 q^{43} +(-4.75216 - 8.89047i) q^{45} -0.500983i q^{46} +4.33981i q^{47} +(0.420861 + 1.68014i) q^{48} +(4.29150 - 5.53019i) q^{49} -6.29150 q^{50} +(3.29150 + 13.1402i) q^{51} +(-2.79694 - 2.27533i) q^{52} -0.500983i q^{53} +(-3.48957 - 3.85005i) q^{54} +(2.37608 - 1.16372i) q^{56} +(-2.35425 - 9.39851i) q^{57} -5.15587i q^{58} -2.16991i q^{59} +(-5.64575 + 1.41421i) q^{60} +4.55066i q^{61} -3.06871 q^{62} +(-4.64076 + 6.43920i) q^{63} +1.00000 q^{64} +(7.64575 - 9.39851i) q^{65} -13.1402i q^{67} +7.82087 q^{68} +(0.841723 - 0.210845i) q^{69} +(3.91044 + 7.98430i) q^{70} +6.58301 q^{71} +(-2.64575 + 1.41421i) q^{72} +12.5730 q^{73} -2.32744i q^{74} +(-2.64785 - 10.5706i) q^{75} -5.59388 q^{76} +(2.64575 - 5.65685i) q^{78} -0.708497 q^{79} +3.36028i q^{80} +(5.00000 - 7.48331i) q^{81} +9.87000i q^{82} -11.2712i q^{83} +(2.95522 + 3.50238i) q^{84} +26.2803i q^{85} +8.00000 q^{86} +(8.66259 - 2.16991i) q^{87} -3.14944i q^{89} +(-4.75216 - 8.89047i) q^{90} +(-9.29360 - 2.15150i) q^{91} -0.500983i q^{92} +(-1.29150 - 5.15587i) q^{93} +4.33981i q^{94} -18.7970i q^{95} +(0.420861 + 1.68014i) q^{96} -10.8896 q^{97} +(4.29150 - 5.53019i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} + 8q^{4} + 8q^{8} + O(q^{10}) \) \( 8q + 8q^{2} + 8q^{4} + 8q^{8} - 24q^{15} + 8q^{16} + 8q^{21} - 8q^{25} - 24q^{30} + 8q^{32} + 8q^{42} + 64q^{43} - 8q^{49} - 8q^{50} - 16q^{51} - 40q^{57} - 24q^{60} - 8q^{63} + 8q^{64} + 40q^{65} - 32q^{71} - 48q^{79} + 40q^{81} + 8q^{84} + 64q^{86} - 32q^{91} + 32q^{93} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0.420861 + 1.68014i 0.242984 + 0.970030i
\(4\) 1.00000 0.500000
\(5\) 3.36028i 1.50276i 0.659867 + 0.751382i \(0.270612\pi\)
−0.659867 + 0.751382i \(0.729388\pi\)
\(6\) 0.420861 + 1.68014i 0.171816 + 0.685915i
\(7\) 2.37608 1.16372i 0.898073 0.439846i
\(8\) 1.00000 0.353553
\(9\) −2.64575 + 1.41421i −0.881917 + 0.471405i
\(10\) 3.36028i 1.06261i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0.420861 + 1.68014i 0.121492 + 0.485015i
\(13\) −2.79694 2.27533i −0.775732 0.631063i
\(14\) 2.37608 1.16372i 0.635034 0.311018i
\(15\) −5.64575 + 1.41421i −1.45773 + 0.365148i
\(16\) 1.00000 0.250000
\(17\) 7.82087 1.89684 0.948420 0.317017i \(-0.102681\pi\)
0.948420 + 0.317017i \(0.102681\pi\)
\(18\) −2.64575 + 1.41421i −0.623610 + 0.333333i
\(19\) −5.59388 −1.28332 −0.641662 0.766987i \(-0.721755\pi\)
−0.641662 + 0.766987i \(0.721755\pi\)
\(20\) 3.36028i 0.751382i
\(21\) 2.95522 + 3.50238i 0.644881 + 0.764283i
\(22\) 0 0
\(23\) 0.500983i 0.104462i −0.998635 0.0522311i \(-0.983367\pi\)
0.998635 0.0522311i \(-0.0166333\pi\)
\(24\) 0.420861 + 1.68014i 0.0859080 + 0.342957i
\(25\) −6.29150 −1.25830
\(26\) −2.79694 2.27533i −0.548525 0.446229i
\(27\) −3.48957 3.85005i −0.671569 0.740942i
\(28\) 2.37608 1.16372i 0.449037 0.219923i
\(29\) 5.15587i 0.957421i −0.877973 0.478711i \(-0.841104\pi\)
0.877973 0.478711i \(-0.158896\pi\)
\(30\) −5.64575 + 1.41421i −1.03077 + 0.258199i
\(31\) −3.06871 −0.551157 −0.275578 0.961279i \(-0.588869\pi\)
−0.275578 + 0.961279i \(0.588869\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 7.82087 1.34127
\(35\) 3.91044 + 7.98430i 0.660984 + 1.34959i
\(36\) −2.64575 + 1.41421i −0.440959 + 0.235702i
\(37\) 2.32744i 0.382629i −0.981529 0.191315i \(-0.938725\pi\)
0.981529 0.191315i \(-0.0612751\pi\)
\(38\) −5.59388 −0.907447
\(39\) 2.64575 5.65685i 0.423659 0.905822i
\(40\) 3.36028i 0.531307i
\(41\) 9.87000i 1.54144i 0.637177 + 0.770718i \(0.280102\pi\)
−0.637177 + 0.770718i \(0.719898\pi\)
\(42\) 2.95522 + 3.50238i 0.456000 + 0.540429i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −4.75216 8.89047i −0.708410 1.32531i
\(46\) 0.500983i 0.0738660i
\(47\) 4.33981i 0.633027i 0.948588 + 0.316513i \(0.102512\pi\)
−0.948588 + 0.316513i \(0.897488\pi\)
\(48\) 0.420861 + 1.68014i 0.0607461 + 0.242508i
\(49\) 4.29150 5.53019i 0.613072 0.790027i
\(50\) −6.29150 −0.889753
\(51\) 3.29150 + 13.1402i 0.460903 + 1.83999i
\(52\) −2.79694 2.27533i −0.387866 0.315531i
\(53\) 0.500983i 0.0688153i −0.999408 0.0344077i \(-0.989046\pi\)
0.999408 0.0344077i \(-0.0109545\pi\)
\(54\) −3.48957 3.85005i −0.474871 0.523925i
\(55\) 0 0
\(56\) 2.37608 1.16372i 0.317517 0.155509i
\(57\) −2.35425 9.39851i −0.311828 1.24486i
\(58\) 5.15587i 0.676999i
\(59\) 2.16991i 0.282498i −0.989974 0.141249i \(-0.954888\pi\)
0.989974 0.141249i \(-0.0451118\pi\)
\(60\) −5.64575 + 1.41421i −0.728863 + 0.182574i
\(61\) 4.55066i 0.582652i 0.956624 + 0.291326i \(0.0940965\pi\)
−0.956624 + 0.291326i \(0.905904\pi\)
\(62\) −3.06871 −0.389727
\(63\) −4.64076 + 6.43920i −0.584681 + 0.811263i
\(64\) 1.00000 0.125000
\(65\) 7.64575 9.39851i 0.948339 1.16574i
\(66\) 0 0
\(67\) 13.1402i 1.60533i −0.596432 0.802664i \(-0.703415\pi\)
0.596432 0.802664i \(-0.296585\pi\)
\(68\) 7.82087 0.948420
\(69\) 0.841723 0.210845i 0.101332 0.0253827i
\(70\) 3.91044 + 7.98430i 0.467386 + 0.954306i
\(71\) 6.58301 0.781259 0.390629 0.920548i \(-0.372257\pi\)
0.390629 + 0.920548i \(0.372257\pi\)
\(72\) −2.64575 + 1.41421i −0.311805 + 0.166667i
\(73\) 12.5730 1.47156 0.735781 0.677220i \(-0.236815\pi\)
0.735781 + 0.677220i \(0.236815\pi\)
\(74\) 2.32744i 0.270560i
\(75\) −2.64785 10.5706i −0.305747 1.22059i
\(76\) −5.59388 −0.641662
\(77\) 0 0
\(78\) 2.64575 5.65685i 0.299572 0.640513i
\(79\) −0.708497 −0.0797122 −0.0398561 0.999205i \(-0.512690\pi\)
−0.0398561 + 0.999205i \(0.512690\pi\)
\(80\) 3.36028i 0.375691i
\(81\) 5.00000 7.48331i 0.555556 0.831479i
\(82\) 9.87000i 1.08996i
\(83\) 11.2712i 1.23718i −0.785715 0.618589i \(-0.787705\pi\)
0.785715 0.618589i \(-0.212295\pi\)
\(84\) 2.95522 + 3.50238i 0.322441 + 0.382141i
\(85\) 26.2803i 2.85050i
\(86\) 8.00000 0.862662
\(87\) 8.66259 2.16991i 0.928727 0.232638i
\(88\) 0 0
\(89\) 3.14944i 0.333840i −0.985970 0.166920i \(-0.946618\pi\)
0.985970 0.166920i \(-0.0533821\pi\)
\(90\) −4.75216 8.89047i −0.500921 0.937138i
\(91\) −9.29360 2.15150i −0.974234 0.225539i
\(92\) 0.500983i 0.0522311i
\(93\) −1.29150 5.15587i −0.133923 0.534639i
\(94\) 4.33981i 0.447618i
\(95\) 18.7970i 1.92853i
\(96\) 0.420861 + 1.68014i 0.0429540 + 0.171479i
\(97\) −10.8896 −1.10567 −0.552835 0.833291i \(-0.686454\pi\)
−0.552835 + 0.833291i \(0.686454\pi\)
\(98\) 4.29150 5.53019i 0.433507 0.558634i
\(99\) 0 0
\(100\) −6.29150 −0.629150
\(101\) −10.3460 −1.02947 −0.514735 0.857350i \(-0.672110\pi\)
−0.514735 + 0.857350i \(0.672110\pi\)
\(102\) 3.29150 + 13.1402i 0.325907 + 1.30107i
\(103\) 16.5906i 1.63472i −0.576129 0.817359i \(-0.695437\pi\)
0.576129 0.817359i \(-0.304563\pi\)
\(104\) −2.79694 2.27533i −0.274263 0.223114i
\(105\) −11.7690 + 9.93037i −1.14854 + 0.969105i
\(106\) 0.500983i 0.0486598i
\(107\) 5.65685i 0.546869i 0.961891 + 0.273434i \(0.0881596\pi\)
−0.961891 + 0.273434i \(0.911840\pi\)
\(108\) −3.48957 3.85005i −0.335784 0.370471i
\(109\) 6.98233i 0.668786i 0.942434 + 0.334393i \(0.108531\pi\)
−0.942434 + 0.334393i \(0.891469\pi\)
\(110\) 0 0
\(111\) 3.91044 0.979531i 0.371162 0.0929730i
\(112\) 2.37608 1.16372i 0.224518 0.109961i
\(113\) 14.1421i 1.33038i 0.746674 + 0.665190i \(0.231650\pi\)
−0.746674 + 0.665190i \(0.768350\pi\)
\(114\) −2.35425 9.39851i −0.220496 0.880251i
\(115\) 1.68345 0.156982
\(116\) 5.15587i 0.478711i
\(117\) 10.6178 + 2.06448i 0.981617 + 0.190862i
\(118\) 2.16991i 0.199756i
\(119\) 18.5830 9.10132i 1.70350 0.834316i
\(120\) −5.64575 + 1.41421i −0.515384 + 0.129099i
\(121\) −11.0000 −1.00000
\(122\) 4.55066i 0.411997i
\(123\) −16.5830 + 4.15390i −1.49524 + 0.374545i
\(124\) −3.06871 −0.275578
\(125\) 4.33981i 0.388165i
\(126\) −4.64076 + 6.43920i −0.413432 + 0.573650i
\(127\) 14.5830 1.29403 0.647016 0.762476i \(-0.276017\pi\)
0.647016 + 0.762476i \(0.276017\pi\)
\(128\) 1.00000 0.0883883
\(129\) 3.36689 + 13.4411i 0.296438 + 1.18343i
\(130\) 7.64575 9.39851i 0.670577 0.824304i
\(131\) −18.1669 −1.58725 −0.793625 0.608407i \(-0.791809\pi\)
−0.793625 + 0.608407i \(0.791809\pi\)
\(132\) 0 0
\(133\) −13.2915 + 6.50972i −1.15252 + 0.564464i
\(134\) 13.1402i 1.13514i
\(135\) 12.9373 11.7260i 1.11346 1.00921i
\(136\) 7.82087 0.670634
\(137\) −9.29150 −0.793827 −0.396913 0.917856i \(-0.629919\pi\)
−0.396913 + 0.917856i \(0.629919\pi\)
\(138\) 0.841723 0.210845i 0.0716522 0.0179483i
\(139\) 0.979531i 0.0830828i −0.999137 0.0415414i \(-0.986773\pi\)
0.999137 0.0415414i \(-0.0132268\pi\)
\(140\) 3.91044 + 7.98430i 0.330492 + 0.674796i
\(141\) −7.29150 + 1.82646i −0.614055 + 0.153816i
\(142\) 6.58301 0.552434
\(143\) 0 0
\(144\) −2.64575 + 1.41421i −0.220479 + 0.117851i
\(145\) 17.3252 1.43878
\(146\) 12.5730 1.04055
\(147\) 11.0976 + 4.88289i 0.915317 + 0.402734i
\(148\) 2.32744i 0.191315i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) −2.64785 10.5706i −0.216196 0.863087i
\(151\) 6.15784i 0.501118i −0.968101 0.250559i \(-0.919386\pi\)
0.968101 0.250559i \(-0.0806144\pi\)
\(152\) −5.59388 −0.453724
\(153\) −20.6921 + 11.0604i −1.67286 + 0.894179i
\(154\) 0 0
\(155\) 10.3117i 0.828259i
\(156\) 2.64575 5.65685i 0.211830 0.452911i
\(157\) 17.5701i 1.40225i −0.713040 0.701123i \(-0.752682\pi\)
0.713040 0.701123i \(-0.247318\pi\)
\(158\) −0.708497 −0.0563650
\(159\) 0.841723 0.210845i 0.0667530 0.0167211i
\(160\) 3.36028i 0.265654i
\(161\) −0.583005 1.19038i −0.0459472 0.0938148i
\(162\) 5.00000 7.48331i 0.392837 0.587945i
\(163\) 8.48528i 0.664619i 0.943170 + 0.332309i \(0.107828\pi\)
−0.943170 + 0.332309i \(0.892172\pi\)
\(164\) 9.87000i 0.770718i
\(165\) 0 0
\(166\) 11.2712i 0.874817i
\(167\) 6.72057i 0.520053i −0.965601 0.260027i \(-0.916269\pi\)
0.965601 0.260027i \(-0.0837313\pi\)
\(168\) 2.95522 + 3.50238i 0.228000 + 0.270215i
\(169\) 2.64575 + 12.7279i 0.203519 + 0.979071i
\(170\) 26.2803i 2.01561i
\(171\) 14.8000 7.91094i 1.13179 0.604965i
\(172\) 8.00000 0.609994
\(173\) 5.29570 0.402625 0.201312 0.979527i \(-0.435479\pi\)
0.201312 + 0.979527i \(0.435479\pi\)
\(174\) 8.66259 2.16991i 0.656709 0.164500i
\(175\) −14.9491 + 7.32156i −1.13005 + 0.553458i
\(176\) 0 0
\(177\) 3.64575 0.913230i 0.274031 0.0686426i
\(178\) 3.14944i 0.236060i
\(179\) 11.3137i 0.845626i −0.906217 0.422813i \(-0.861043\pi\)
0.906217 0.422813i \(-0.138957\pi\)
\(180\) −4.75216 8.89047i −0.354205 0.662657i
\(181\) 24.7124i 1.83686i 0.395589 + 0.918428i \(0.370540\pi\)
−0.395589 + 0.918428i \(0.629460\pi\)
\(182\) −9.29360 2.15150i −0.688888 0.159480i
\(183\) −7.64575 + 1.91520i −0.565190 + 0.141575i
\(184\) 0.500983i 0.0369330i
\(185\) 7.82087 0.575002
\(186\) −1.29150 5.15587i −0.0946976 0.378047i
\(187\) 0 0
\(188\) 4.33981i 0.316513i
\(189\) −12.7719 5.08713i −0.929018 0.370034i
\(190\) 18.7970i 1.36368i
\(191\) 7.98430i 0.577724i 0.957371 + 0.288862i \(0.0932768\pi\)
−0.957371 + 0.288862i \(0.906723\pi\)
\(192\) 0.420861 + 1.68014i 0.0303731 + 0.121254i
\(193\) 8.48528i 0.610784i −0.952227 0.305392i \(-0.901213\pi\)
0.952227 0.305392i \(-0.0987875\pi\)
\(194\) −10.8896 −0.781826
\(195\) 19.0086 + 8.89047i 1.36124 + 0.636660i
\(196\) 4.29150 5.53019i 0.306536 0.395014i
\(197\) −12.5830 −0.896502 −0.448251 0.893908i \(-0.647953\pi\)
−0.448251 + 0.893908i \(0.647953\pi\)
\(198\) 0 0
\(199\) 12.6724i 0.898326i −0.893450 0.449163i \(-0.851722\pi\)
0.893450 0.449163i \(-0.148278\pi\)
\(200\) −6.29150 −0.444876
\(201\) 22.0773 5.53019i 1.55722 0.390070i
\(202\) −10.3460 −0.727945
\(203\) −6.00000 12.2508i −0.421117 0.859835i
\(204\) 3.29150 + 13.1402i 0.230451 + 0.919996i
\(205\) −33.1660 −2.31641
\(206\) 16.5906i 1.15592i
\(207\) 0.708497 + 1.32548i 0.0492440 + 0.0921270i
\(208\) −2.79694 2.27533i −0.193933 0.157766i
\(209\) 0 0
\(210\) −11.7690 + 9.93037i −0.812138 + 0.685260i
\(211\) −10.5830 −0.728564 −0.364282 0.931289i \(-0.618686\pi\)
−0.364282 + 0.931289i \(0.618686\pi\)
\(212\) 0.500983i 0.0344077i
\(213\) 2.77053 + 11.0604i 0.189834 + 0.757845i
\(214\) 5.65685i 0.386695i
\(215\) 26.8823i 1.83336i
\(216\) −3.48957 3.85005i −0.237435 0.261963i
\(217\) −7.29150 + 3.57113i −0.494979 + 0.242424i
\(218\) 6.98233i 0.472903i
\(219\) 5.29150 + 21.1245i 0.357567 + 1.42746i
\(220\) 0 0
\(221\) −21.8745 17.7951i −1.47144 1.19703i
\(222\) 3.91044 0.979531i 0.262451 0.0657418i
\(223\) −8.11905 −0.543692 −0.271846 0.962341i \(-0.587634\pi\)
−0.271846 + 0.962341i \(0.587634\pi\)
\(224\) 2.37608 1.16372i 0.158758 0.0777544i
\(225\) 16.6458 8.89753i 1.10972 0.593169i
\(226\) 14.1421i 0.940721i
\(227\) 17.9918i 1.19416i 0.802183 + 0.597079i \(0.203672\pi\)
−0.802183 + 0.597079i \(0.796328\pi\)
\(228\) −2.35425 9.39851i −0.155914 0.622432i
\(229\) −16.1853 −1.06955 −0.534777 0.844993i \(-0.679604\pi\)
−0.534777 + 0.844993i \(0.679604\pi\)
\(230\) 1.68345 0.111003
\(231\) 0 0
\(232\) 5.15587i 0.338500i
\(233\) 22.6274i 1.48237i 0.671300 + 0.741186i \(0.265736\pi\)
−0.671300 + 0.741186i \(0.734264\pi\)
\(234\) 10.6178 + 2.06448i 0.694108 + 0.134960i
\(235\) −14.5830 −0.951290
\(236\) 2.16991i 0.141249i
\(237\) −0.298179 1.19038i −0.0193688 0.0773232i
\(238\) 18.5830 9.10132i 1.20456 0.589951i
\(239\) 9.87451 0.638729 0.319364 0.947632i \(-0.396531\pi\)
0.319364 + 0.947632i \(0.396531\pi\)
\(240\) −5.64575 + 1.41421i −0.364432 + 0.0912871i
\(241\) 1.98162 0.127648 0.0638238 0.997961i \(-0.479670\pi\)
0.0638238 + 0.997961i \(0.479670\pi\)
\(242\) −11.0000 −0.707107
\(243\) 14.6773 + 5.25127i 0.941551 + 0.336869i
\(244\) 4.55066i 0.291326i
\(245\) 18.5830 + 14.4207i 1.18722 + 0.921302i
\(246\) −16.5830 + 4.15390i −1.05729 + 0.264843i
\(247\) 15.6458 + 12.7279i 0.995515 + 0.809858i
\(248\) −3.06871 −0.194863
\(249\) 18.9373 4.74362i 1.20010 0.300615i
\(250\) 4.33981i 0.274474i
\(251\) 10.3460 0.653036 0.326518 0.945191i \(-0.394125\pi\)
0.326518 + 0.945191i \(0.394125\pi\)
\(252\) −4.64076 + 6.43920i −0.292341 + 0.405632i
\(253\) 0 0
\(254\) 14.5830 0.915019
\(255\) −44.1547 + 11.0604i −2.76507 + 0.692628i
\(256\) 1.00000 0.0625000
\(257\) 12.8712 0.802884 0.401442 0.915884i \(-0.368509\pi\)
0.401442 + 0.915884i \(0.368509\pi\)
\(258\) 3.36689 + 13.4411i 0.209614 + 0.836808i
\(259\) −2.70850 5.53019i −0.168298 0.343629i
\(260\) 7.64575 9.39851i 0.474169 0.582871i
\(261\) 7.29150 + 13.6412i 0.451333 + 0.844366i
\(262\) −18.1669 −1.12236
\(263\) 8.98626i 0.554117i −0.960853 0.277058i \(-0.910640\pi\)
0.960853 0.277058i \(-0.0893596\pi\)
\(264\) 0 0
\(265\) 1.68345 0.103413
\(266\) −13.2915 + 6.50972i −0.814954 + 0.399137i
\(267\) 5.29150 1.32548i 0.323835 0.0811179i
\(268\) 13.1402i 0.802664i
\(269\) −20.9374 −1.27658 −0.638289 0.769797i \(-0.720358\pi\)
−0.638289 + 0.769797i \(0.720358\pi\)
\(270\) 12.9373 11.7260i 0.787336 0.713619i
\(271\) 7.52269 0.456971 0.228485 0.973547i \(-0.426623\pi\)
0.228485 + 0.973547i \(0.426623\pi\)
\(272\) 7.82087 0.474210
\(273\) −0.296491 16.5201i −0.0179445 0.999839i
\(274\) −9.29150 −0.561320
\(275\) 0 0
\(276\) 0.841723 0.210845i 0.0506658 0.0126914i
\(277\) −11.1660 −0.670901 −0.335450 0.942058i \(-0.608888\pi\)
−0.335450 + 0.942058i \(0.608888\pi\)
\(278\) 0.979531i 0.0587484i
\(279\) 8.11905 4.33981i 0.486075 0.259818i
\(280\) 3.91044 + 7.98430i 0.233693 + 0.477153i
\(281\) 2.70850 0.161575 0.0807877 0.996731i \(-0.474256\pi\)
0.0807877 + 0.996731i \(0.474256\pi\)
\(282\) −7.29150 + 1.82646i −0.434203 + 0.108764i
\(283\) 12.0399i 0.715698i 0.933779 + 0.357849i \(0.116490\pi\)
−0.933779 + 0.357849i \(0.883510\pi\)
\(284\) 6.58301 0.390629
\(285\) 31.5817 7.91094i 1.87074 0.468604i
\(286\) 0 0
\(287\) 11.4859 + 23.4519i 0.677994 + 1.38432i
\(288\) −2.64575 + 1.41421i −0.155902 + 0.0833333i
\(289\) 44.1660 2.59800
\(290\) 17.3252 1.01737
\(291\) −4.58301 18.2960i −0.268661 1.07253i
\(292\) 12.5730 0.735781
\(293\) 18.7605i 1.09600i −0.836479 0.547999i \(-0.815390\pi\)
0.836479 0.547999i \(-0.184610\pi\)
\(294\) 11.0976 + 4.88289i 0.647227 + 0.284776i
\(295\) 7.29150 0.424528
\(296\) 2.32744i 0.135280i
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −1.13990 + 1.40122i −0.0659222 + 0.0810347i
\(300\) −2.64785 10.5706i −0.152874 0.610295i
\(301\) 19.0086 9.30978i 1.09564 0.536607i
\(302\) 6.15784i 0.354344i
\(303\) −4.35425 17.3828i −0.250145 0.998616i
\(304\) −5.59388 −0.320831
\(305\) −15.2915 −0.875589
\(306\) −20.6921 + 11.0604i −1.18289 + 0.632280i
\(307\) 2.22699 0.127101 0.0635505 0.997979i \(-0.479758\pi\)
0.0635505 + 0.997979i \(0.479758\pi\)
\(308\) 0 0
\(309\) 27.8745 6.98233i 1.58573 0.397211i
\(310\) 10.3117i 0.585668i
\(311\) −28.5129 −1.61682 −0.808410 0.588619i \(-0.799672\pi\)
−0.808410 + 0.588619i \(0.799672\pi\)
\(312\) 2.64575 5.65685i 0.149786 0.320256i
\(313\) 27.3040i 1.54331i 0.636041 + 0.771655i \(0.280571\pi\)
−0.636041 + 0.771655i \(0.719429\pi\)
\(314\) 17.5701i 0.991538i
\(315\) −21.6375 15.5943i −1.21914 0.878638i
\(316\) −0.708497 −0.0398561
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0.841723 0.210845i 0.0472015 0.0118236i
\(319\) 0 0
\(320\) 3.36028i 0.187846i
\(321\) −9.50432 + 2.38075i −0.530479 + 0.132881i
\(322\) −0.583005 1.19038i −0.0324896 0.0663371i
\(323\) −43.7490 −2.43426
\(324\) 5.00000 7.48331i 0.277778 0.415740i
\(325\) 17.5970 + 14.3152i 0.976104 + 0.794067i
\(326\) 8.48528i 0.469956i
\(327\) −11.7313 + 2.93859i −0.648743 + 0.162505i
\(328\) 9.87000i 0.544980i
\(329\) 5.05034 + 10.3117i 0.278434 + 0.568505i
\(330\) 0 0
\(331\) 8.48528i 0.466393i 0.972430 + 0.233197i \(0.0749186\pi\)
−0.972430 + 0.233197i \(0.925081\pi\)
\(332\) 11.2712i 0.618589i
\(333\) 3.29150 + 6.15784i 0.180373 + 0.337447i
\(334\) 6.72057i 0.367733i
\(335\) 44.1547 2.41243
\(336\) 2.95522 + 3.50238i 0.161220 + 0.191071i
\(337\) −19.8745 −1.08263 −0.541317 0.840819i \(-0.682074\pi\)
−0.541317 + 0.840819i \(0.682074\pi\)
\(338\) 2.64575 + 12.7279i 0.143910 + 0.692308i
\(339\) −23.7608 + 5.95188i −1.29051 + 0.323262i
\(340\) 26.2803i 1.42525i
\(341\) 0 0
\(342\) 14.8000 7.91094i 0.800293 0.427775i
\(343\) 3.76135 18.1343i 0.203094 0.979159i
\(344\) 8.00000 0.431331
\(345\) 0.708497 + 2.82843i 0.0381442 + 0.152277i
\(346\) 5.29570 0.284699
\(347\) 31.9372i 1.71448i 0.514918 + 0.857239i \(0.327822\pi\)
−0.514918 + 0.857239i \(0.672178\pi\)
\(348\) 8.66259 2.16991i 0.464364 0.116319i
\(349\) −0.543544 −0.0290952 −0.0145476 0.999894i \(-0.504631\pi\)
−0.0145476 + 0.999894i \(0.504631\pi\)
\(350\) −14.9491 + 7.32156i −0.799063 + 0.391354i
\(351\) 1.00000 + 18.7083i 0.0533761 + 0.998574i
\(352\) 0 0
\(353\) 30.0317i 1.59843i 0.601048 + 0.799213i \(0.294750\pi\)
−0.601048 + 0.799213i \(0.705250\pi\)
\(354\) 3.64575 0.913230i 0.193769 0.0485376i
\(355\) 22.1208i 1.17405i
\(356\) 3.14944i 0.166920i
\(357\) 23.1124 + 27.3917i 1.22324 + 1.44972i
\(358\) 11.3137i 0.597948i
\(359\) −27.2915 −1.44039 −0.720195 0.693771i \(-0.755948\pi\)
−0.720195 + 0.693771i \(0.755948\pi\)
\(360\) −4.75216 8.89047i −0.250461 0.468569i
\(361\) 12.2915 0.646921
\(362\) 24.7124i 1.29885i
\(363\) −4.62948 18.4816i −0.242984 0.970030i
\(364\) −9.29360 2.15150i −0.487117 0.112769i
\(365\) 42.2489i 2.21141i
\(366\) −7.64575 + 1.91520i −0.399650 + 0.100109i
\(367\) 14.6315i 0.763759i −0.924212 0.381879i \(-0.875277\pi\)
0.924212 0.381879i \(-0.124723\pi\)
\(368\) 0.500983i 0.0261156i
\(369\) −13.9583 26.1136i −0.726640 1.35942i
\(370\) 7.82087 0.406588
\(371\) −0.583005 1.19038i −0.0302681 0.0618012i
\(372\) −1.29150 5.15587i −0.0669613 0.267319i
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) 7.29150 1.82646i 0.376532 0.0943180i
\(376\) 4.33981i 0.223809i
\(377\) −11.7313 + 14.4207i −0.604193 + 0.742702i
\(378\) −12.7719 5.08713i −0.656915 0.261654i
\(379\) 30.1107i 1.54668i −0.633989 0.773342i \(-0.718583\pi\)
0.633989 0.773342i \(-0.281417\pi\)
\(380\) 18.7970i 0.964267i
\(381\) 6.13742 + 24.5015i 0.314430 + 1.25525i
\(382\) 7.98430i 0.408512i
\(383\) 21.6991i 1.10877i −0.832260 0.554385i \(-0.812953\pi\)
0.832260 0.554385i \(-0.187047\pi\)
\(384\) 0.420861 + 1.68014i 0.0214770 + 0.0857394i
\(385\) 0 0
\(386\) 8.48528i 0.431889i
\(387\) −21.1660 + 11.3137i −1.07593 + 0.575108i
\(388\) −10.8896 −0.552835
\(389\) 9.81076i 0.497425i −0.968577 0.248713i \(-0.919993\pi\)
0.968577 0.248713i \(-0.0800075\pi\)
\(390\) 19.0086 + 8.89047i 0.962539 + 0.450187i
\(391\) 3.91813i 0.198148i
\(392\) 4.29150 5.53019i 0.216754 0.279317i
\(393\) −7.64575 30.5230i −0.385677 1.53968i
\(394\) −12.5830 −0.633923
\(395\) 2.38075i 0.119789i
\(396\) 0 0
\(397\) −26.2860 −1.31925 −0.659627 0.751593i \(-0.729286\pi\)
−0.659627 + 0.751593i \(0.729286\pi\)
\(398\) 12.6724i 0.635212i
\(399\) −16.5311 19.5919i −0.827592 0.980823i
\(400\) −6.29150 −0.314575
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) 22.0773 5.53019i 1.10112 0.275821i
\(403\) 8.58301 + 6.98233i 0.427550 + 0.347815i
\(404\) −10.3460 −0.514735
\(405\) 25.1461 + 16.8014i 1.24952 + 0.834869i
\(406\) −6.00000 12.2508i −0.297775 0.607995i
\(407\) 0 0
\(408\) 3.29150 + 13.1402i 0.162954 + 0.650535i
\(409\) 4.75216 0.234979 0.117490 0.993074i \(-0.462515\pi\)
0.117490 + 0.993074i \(0.462515\pi\)
\(410\) −33.1660 −1.63795
\(411\) −3.91044 15.6110i −0.192888 0.770036i
\(412\) 16.5906i 0.817359i
\(413\) −2.52517 5.15587i −0.124255 0.253704i
\(414\) 0.708497 + 1.32548i 0.0348207 + 0.0651437i
\(415\) 37.8745 1.85919
\(416\) −2.79694 2.27533i −0.137131 0.111557i
\(417\) 1.64575 0.412247i 0.0805928 0.0201878i
\(418\) 0 0
\(419\) 15.3964 0.752162 0.376081 0.926587i \(-0.377271\pi\)
0.376081 + 0.926587i \(0.377271\pi\)
\(420\) −11.7690 + 9.93037i −0.574268 + 0.484552i
\(421\) 19.2980i 0.940527i 0.882526 + 0.470264i \(0.155841\pi\)
−0.882526 + 0.470264i \(0.844159\pi\)
\(422\) −10.5830 −0.515173
\(423\) −6.13742 11.4821i −0.298412 0.558277i
\(424\) 0.500983i 0.0243299i
\(425\) −49.2050 −2.38679
\(426\) 2.77053 + 11.0604i 0.134233 + 0.535877i
\(427\) 5.29570 + 10.8127i 0.256277 + 0.523264i
\(428\) 5.65685i 0.273434i
\(429\) 0 0
\(430\) 26.8823i 1.29638i
\(431\) −3.29150 −0.158546 −0.0792731 0.996853i \(-0.525260\pi\)
−0.0792731 + 0.996853i \(0.525260\pi\)
\(432\) −3.48957 3.85005i −0.167892 0.185236i
\(433\) 1.95906i 0.0941465i 0.998891 + 0.0470733i \(0.0149894\pi\)
−0.998891 + 0.0470733i \(0.985011\pi\)
\(434\) −7.29150 + 3.57113i −0.350003 + 0.171420i
\(435\) 7.29150 + 29.1088i 0.349601 + 1.39566i
\(436\) 6.98233i 0.334393i
\(437\) 2.80244i 0.134059i
\(438\) 5.29150 + 21.1245i 0.252838 + 1.00937i
\(439\) 14.6315i 0.698324i −0.937062 0.349162i \(-0.886466\pi\)
0.937062 0.349162i \(-0.113534\pi\)
\(440\) 0 0
\(441\) −3.53338 + 20.7006i −0.168256 + 0.985743i
\(442\) −21.8745 17.7951i −1.04046 0.846425i
\(443\) 5.65685i 0.268765i 0.990930 + 0.134383i \(0.0429051\pi\)
−0.990930 + 0.134383i \(0.957095\pi\)
\(444\) 3.91044 0.979531i 0.185581 0.0464865i
\(445\) 10.5830 0.501683
\(446\) −8.11905 −0.384448
\(447\) 2.52517 + 10.0808i 0.119436 + 0.476808i
\(448\) 2.37608 1.16372i 0.112259 0.0549807i
\(449\) 22.4575 1.05984 0.529918 0.848049i \(-0.322223\pi\)
0.529918 + 0.848049i \(0.322223\pi\)
\(450\) 16.6458 8.89753i 0.784688 0.419434i
\(451\) 0 0
\(452\) 14.1421i 0.665190i
\(453\) 10.3460 2.59160i 0.486099 0.121764i
\(454\) 17.9918i 0.844397i
\(455\) 7.22966 31.2291i 0.338931 1.46404i
\(456\) −2.35425 9.39851i −0.110248 0.440126i
\(457\) 17.7951i 0.832418i −0.909269 0.416209i \(-0.863359\pi\)
0.909269 0.416209i \(-0.136641\pi\)
\(458\) −16.1853 −0.756289
\(459\) −27.2915 30.1107i −1.27386 1.40545i
\(460\) 1.68345 0.0784911
\(461\) 25.9027i 1.20641i −0.797586 0.603205i \(-0.793890\pi\)
0.797586 0.603205i \(-0.206110\pi\)
\(462\) 0 0
\(463\) 11.6372i 0.540827i 0.962744 + 0.270414i \(0.0871605\pi\)
−0.962744 + 0.270414i \(0.912840\pi\)
\(464\) 5.15587i 0.239355i
\(465\) 17.3252 4.33981i 0.803436 0.201254i
\(466\) 22.6274i 1.04819i
\(467\) −33.8086 −1.56448 −0.782239 0.622979i \(-0.785922\pi\)
−0.782239 + 0.622979i \(0.785922\pi\)
\(468\) 10.6178 + 2.06448i 0.490808 + 0.0954309i
\(469\) −15.2915 31.2221i −0.706096 1.44170i
\(470\) −14.5830 −0.672664
\(471\) 29.5203 7.39458i 1.36022 0.340724i
\(472\) 2.16991i 0.0998781i
\(473\) 0 0
\(474\) −0.298179 1.19038i −0.0136958 0.0546758i
\(475\) 35.1939 1.61481
\(476\) 18.5830 9.10132i 0.851751 0.417158i
\(477\) 0.708497 + 1.32548i 0.0324399 + 0.0606894i
\(478\) 9.87451 0.451649
\(479\) 35.9836i 1.64413i −0.569392 0.822066i \(-0.692821\pi\)
0.569392 0.822066i \(-0.307179\pi\)
\(480\) −5.64575 + 1.41421i −0.257692 + 0.0645497i
\(481\) −5.29570 + 6.50972i −0.241463 + 0.296818i
\(482\) 1.98162 0.0902605
\(483\) 1.75464 1.48051i 0.0798387 0.0673657i
\(484\) −11.0000 −0.500000
\(485\) 36.5921i 1.66156i
\(486\) 14.6773 + 5.25127i 0.665777 + 0.238202i
\(487\) 20.1225i 0.911838i −0.890021 0.455919i \(-0.849311\pi\)
0.890021 0.455919i \(-0.150689\pi\)
\(488\) 4.55066i 0.205999i
\(489\) −14.2565 + 3.57113i −0.644700 + 0.161492i
\(490\) 18.5830 + 14.4207i 0.839495 + 0.651459i
\(491\) 3.65292i 0.164854i −0.996597 0.0824270i \(-0.973733\pi\)
0.996597 0.0824270i \(-0.0262671\pi\)
\(492\) −16.5830 + 4.15390i −0.747620 + 0.187272i
\(493\) 40.3234i 1.81607i
\(494\) 15.6458 + 12.7279i 0.703936 + 0.572656i
\(495\) 0 0
\(496\) −3.06871 −0.137789
\(497\) 15.6417 7.66079i 0.701628 0.343633i
\(498\) 18.9373 4.74362i 0.848599 0.212567i
\(499\) 3.83039i 0.171472i −0.996318 0.0857360i \(-0.972676\pi\)
0.996318 0.0857360i \(-0.0273242\pi\)
\(500\) 4.33981i 0.194082i
\(501\) 11.2915 2.82843i 0.504467 0.126365i
\(502\) 10.3460 0.461766
\(503\) −15.6417 −0.697431 −0.348715 0.937229i \(-0.613382\pi\)
−0.348715 + 0.937229i \(0.613382\pi\)
\(504\) −4.64076 + 6.43920i −0.206716 + 0.286825i
\(505\) 34.7656i 1.54705i
\(506\) 0 0
\(507\) −20.2712 + 9.80193i −0.900276 + 0.435319i
\(508\) 14.5830 0.647016
\(509\) 25.9027i 1.14812i −0.818814 0.574059i \(-0.805368\pi\)
0.818814 0.574059i \(-0.194632\pi\)
\(510\) −44.1547 + 11.0604i −1.95520 + 0.489762i
\(511\) 29.8745 14.6315i 1.32157 0.647260i
\(512\) 1.00000 0.0441942
\(513\) 19.5203 + 21.5367i 0.861840 + 0.950869i
\(514\) 12.8712 0.567725
\(515\) 55.7490 2.45660
\(516\) 3.36689 + 13.4411i 0.148219 + 0.591713i
\(517\) 0 0
\(518\) −2.70850 5.53019i −0.119005 0.242983i
\(519\) 2.22876 + 8.89753i 0.0978316 + 0.390558i
\(520\) 7.64575 9.39851i 0.335288 0.412152i
\(521\) 36.3338 1.59181 0.795907 0.605419i \(-0.206995\pi\)
0.795907 + 0.605419i \(0.206995\pi\)
\(522\) 7.29150 + 13.6412i 0.319140 + 0.597057i
\(523\) 13.9990i 0.612132i 0.952010 + 0.306066i \(0.0990129\pi\)
−0.952010 + 0.306066i \(0.900987\pi\)
\(524\) −18.1669 −0.793625
\(525\) −18.5928 22.0353i −0.811455 0.961697i
\(526\) 8.98626i 0.391820i
\(527\) −24.0000 −1.04546
\(528\) 0 0
\(529\) 22.7490 0.989088
\(530\) 1.68345 0.0731242
\(531\) 3.06871 + 5.74103i 0.133171 + 0.249140i
\(532\) −13.2915 + 6.50972i −0.576260 + 0.282232i
\(533\) 22.4575 27.6058i 0.972743 1.19574i
\(534\) 5.29150 1.32548i 0.228986 0.0573590i
\(535\) −19.0086 −0.821815
\(536\) 13.1402i 0.567569i
\(537\) 19.0086 4.76150i 0.820283 0.205474i
\(538\) −20.9374 −0.902677
\(539\) 0 0
\(540\) 12.9373 11.7260i 0.556731 0.504605i
\(541\) 37.9176i 1.63020i 0.579318 + 0.815102i \(0.303319\pi\)
−0.579318 + 0.815102i \(0.696681\pi\)
\(542\) 7.52269 0.323127
\(543\) −41.5203 + 10.4005i −1.78180 + 0.446327i
\(544\) 7.82087 0.335317
\(545\) −23.4626 −1.00503
\(546\) −0.296491 16.5201i −0.0126887 0.706993i
\(547\) 14.5830 0.623524 0.311762 0.950160i \(-0.399081\pi\)
0.311762 + 0.950160i \(0.399081\pi\)
\(548\) −9.29150 −0.396913
\(549\) −6.43560 12.0399i −0.274665 0.513851i
\(550\) 0 0
\(551\) 28.8413i 1.22868i
\(552\) 0.841723 0.210845i 0.0358261 0.00897414i
\(553\) −1.68345 + 0.824494i −0.0715874 + 0.0350610i
\(554\) −11.1660 −0.474398
\(555\) 3.29150 + 13.1402i 0.139717 + 0.557769i
\(556\) 0.979531i 0.0415414i
\(557\) 19.1660 0.812090 0.406045 0.913853i \(-0.366908\pi\)
0.406045 + 0.913853i \(0.366908\pi\)
\(558\) 8.11905 4.33981i 0.343707 0.183719i
\(559\) −22.3755 18.2026i −0.946384 0.769889i
\(560\) 3.91044 + 7.98430i 0.165246 + 0.337398i
\(561\) 0 0
\(562\) 2.70850 0.114251
\(563\) −33.8086 −1.42486 −0.712432 0.701741i \(-0.752406\pi\)
−0.712432 + 0.701741i \(0.752406\pi\)
\(564\) −7.29150 + 1.82646i −0.307028 + 0.0769079i
\(565\) −47.5216 −1.99925
\(566\) 12.0399i 0.506075i
\(567\) 3.17190 23.5996i 0.133207 0.991088i
\(568\) 6.58301 0.276217
\(569\) 15.1441i 0.634874i −0.948279 0.317437i \(-0.897178\pi\)
0.948279 0.317437i \(-0.102822\pi\)
\(570\) 31.5817 7.91094i 1.32281 0.331353i
\(571\) −22.5830 −0.945069 −0.472535 0.881312i \(-0.656661\pi\)
−0.472535 + 0.881312i \(0.656661\pi\)
\(572\) 0 0
\(573\) −13.4148 + 3.36028i −0.560409 + 0.140378i
\(574\) 11.4859 + 23.4519i 0.479414 + 0.978864i
\(575\) 3.15194i 0.131445i
\(576\) −2.64575 + 1.41421i −0.110240 + 0.0589256i
\(577\) −3.06871 −0.127752 −0.0638761 0.997958i \(-0.520346\pi\)
−0.0638761 + 0.997958i \(0.520346\pi\)
\(578\) 44.1660 1.83706
\(579\) 14.2565 3.57113i 0.592479 0.148411i
\(580\) 17.3252 0.719389
\(581\) −13.1166 26.7813i −0.544167 1.11108i
\(582\) −4.58301 18.2960i −0.189972 0.758395i
\(583\) 0 0
\(584\) 12.5730 0.520276
\(585\) −6.93725 + 35.6788i −0.286820 + 1.47514i
\(586\) 18.7605i 0.774988i
\(587\) 19.9509i 0.823460i 0.911306 + 0.411730i \(0.135075\pi\)
−0.911306 + 0.411730i \(0.864925\pi\)
\(588\) 11.0976 + 4.88289i 0.457659 + 0.201367i
\(589\) 17.1660 0.707313
\(590\) 7.29150 0.300186
\(591\) −5.29570 21.1412i −0.217836 0.869634i
\(592\) 2.32744i 0.0956574i
\(593\) 3.99282i 0.163965i 0.996634 + 0.0819827i \(0.0261252\pi\)
−0.996634 + 0.0819827i \(0.973875\pi\)
\(594\) 0 0
\(595\) 30.5830 + 62.4442i 1.25378 + 2.55996i
\(596\) 6.00000 0.245770
\(597\) 21.2915 5.33334i 0.871403 0.218279i
\(598\) −1.13990 + 1.40122i −0.0466141 + 0.0573002i
\(599\) 43.5744i 1.78040i 0.455568 + 0.890201i \(0.349436\pi\)
−0.455568 + 0.890201i \(0.650564\pi\)
\(600\) −2.64785 10.5706i −0.108098 0.431544i
\(601\) 18.2026i 0.742501i −0.928533 0.371251i \(-0.878929\pi\)
0.928533 0.371251i \(-0.121071\pi\)
\(602\) 19.0086 9.30978i 0.774734 0.379438i
\(603\) 18.5830 + 34.7656i 0.756758 + 1.41577i
\(604\) 6.15784i 0.250559i
\(605\) 36.9631i 1.50276i
\(606\) −4.35425 17.3828i −0.176879 0.706128i
\(607\) 18.5496i 0.752906i −0.926436 0.376453i \(-0.877144\pi\)
0.926436 0.376453i \(-0.122856\pi\)
\(608\) −5.59388 −0.226862
\(609\) 18.0578 15.2367i 0.731740 0.617423i
\(610\) −15.2915 −0.619135
\(611\) 9.87451 12.1382i 0.399480 0.491059i
\(612\) −20.6921 + 11.0604i −0.836428 + 0.447089i
\(613\) 9.98823i 0.403421i 0.979445 + 0.201710i \(0.0646500\pi\)
−0.979445 + 0.201710i \(0.935350\pi\)
\(614\) 2.22699 0.0898740
\(615\) −13.9583 55.7236i −0.562853 2.24699i
\(616\) 0 0
\(617\) −31.1660 −1.25470 −0.627348 0.778739i \(-0.715860\pi\)
−0.627348 + 0.778739i \(0.715860\pi\)
\(618\) 27.8745 6.98233i 1.12128 0.280871i
\(619\) 33.5105 1.34690 0.673450 0.739233i \(-0.264812\pi\)
0.673450 + 0.739233i \(0.264812\pi\)
\(620\) 10.3117i 0.414130i
\(621\) −1.92881 + 1.74822i −0.0774005 + 0.0701536i
\(622\) −28.5129 −1.14327
\(623\) −3.66507 7.48331i −0.146838 0.299813i
\(624\) 2.64575 5.65685i 0.105915 0.226455i
\(625\) −16.8745 −0.674980
\(626\) 27.3040i 1.09129i
\(627\) 0 0
\(628\) 17.5701i 0.701123i
\(629\) 18.2026i 0.725787i
\(630\) −21.6375 15.5943i −0.862060 0.621291i
\(631\) 33.2627i 1.32417i −0.749431 0.662083i \(-0.769673\pi\)
0.749431 0.662083i \(-0.230327\pi\)
\(632\) −0.708497 −0.0281825
\(633\) −4.45398 17.7809i −0.177030 0.706729i
\(634\) −6.00000 −0.238290
\(635\) 49.0030i 1.94463i
\(636\) 0.841723 0.210845i 0.0333765 0.00836053i
\(637\) −24.5861 + 5.70303i −0.974136 + 0.225962i
\(638\) 0 0
\(639\) −17.4170 + 9.30978i −0.689006 + 0.368289i
\(640\) 3.36028i 0.132827i
\(641\) 1.82646i 0.0721409i 0.999349 + 0.0360704i \(0.0114841\pi\)
−0.999349 + 0.0360704i \(0.988516\pi\)
\(642\) −9.50432 + 2.38075i −0.375105 + 0.0939608i
\(643\) −5.59388 −0.220601 −0.110301 0.993898i \(-0.535181\pi\)
−0.110301 + 0.993898i \(0.535181\pi\)
\(644\) −0.583005 1.19038i −0.0229736 0.0469074i
\(645\) −45.1660 + 11.3137i −1.77841 + 0.445477i
\(646\) −43.7490 −1.72128
\(647\) 36.3338 1.42843 0.714215 0.699926i \(-0.246784\pi\)
0.714215 + 0.699926i \(0.246784\pi\)
\(648\) 5.00000 7.48331i 0.196419 0.293972i
\(649\) 0 0
\(650\) 17.5970 + 14.3152i 0.690209 + 0.561490i
\(651\) −9.06871 10.7478i −0.355431 0.421240i
\(652\) 8.48528i 0.332309i
\(653\) 35.0891i 1.37314i 0.727062 + 0.686572i \(0.240885\pi\)
−0.727062 + 0.686572i \(0.759115\pi\)
\(654\) −11.7313 + 2.93859i −0.458730 + 0.114908i
\(655\) 61.0460i 2.38526i
\(656\) 9.87000i 0.385359i
\(657\) −33.2651 + 17.7809i −1.29780 + 0.693701i
\(658\) 5.05034 + 10.3117i 0.196883 + 0.401994i
\(659\) 15.9686i 0.622048i −0.950402 0.311024i \(-0.899328\pi\)
0.950402 0.311024i \(-0.100672\pi\)
\(660\) 0 0
\(661\) 12.3277 0.479491 0.239745 0.970836i \(-0.422936\pi\)
0.239745 + 0.970836i \(0.422936\pi\)
\(662\) 8.48528i 0.329790i
\(663\) 20.6921 44.2415i 0.803614 1.71820i
\(664\) 11.2712i 0.437408i
\(665\) −21.8745 44.6632i −0.848257 1.73197i
\(666\) 3.29150 + 6.15784i 0.127543 + 0.238611i
\(667\) −2.58301 −0.100014
\(668\) 6.72057i 0.260027i
\(669\) −3.41699 13.6412i −0.132109 0.527397i
\(670\) 44.1547 1.70584
\(671\) 0 0
\(672\) 2.95522 + 3.50238i 0.114000 + 0.135107i
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) −19.8745 −0.765537
\(675\) 21.9547 + 24.2226i 0.845035 + 0.932328i
\(676\) 2.64575 + 12.7279i 0.101760 + 0.489535i
\(677\) 15.8871 0.610591 0.305296 0.952258i \(-0.401245\pi\)
0.305296 + 0.952258i \(0.401245\pi\)
\(678\) −23.7608 + 5.95188i −0.912528 + 0.228581i
\(679\) −25.8745 + 12.6724i −0.992972 + 0.486324i
\(680\) 26.2803i 1.00780i
\(681\) −30.2288 + 7.57205i −1.15837 + 0.290162i
\(682\) 0 0
\(683\) 29.4170 1.12561 0.562805 0.826590i \(-0.309722\pi\)
0.562805 + 0.826590i \(0.309722\pi\)
\(684\) 14.8000 7.91094i 0.565893 0.302482i
\(685\) 31.2221i 1.19293i
\(686\) 3.76135 18.1343i 0.143609 0.692370i
\(687\) −6.81176 27.1936i −0.259885 1.03750i
\(688\) 8.00000 0.304997
\(689\) −1.13990 + 1.40122i −0.0434268 + 0.0533822i
\(690\) 0.708497 + 2.82843i 0.0269720 + 0.107676i
\(691\) −0.543544 −0.0206774 −0.0103387 0.999947i \(-0.503291\pi\)
−0.0103387 + 0.999947i \(0.503291\pi\)
\(692\) 5.29570 0.201312
\(693\) 0 0
\(694\) 31.9372i 1.21232i
\(695\) 3.29150 0.124854
\(696\) 8.66259 2.16991i 0.328355 0.0822501i
\(697\) 77.1920i 2.92386i
\(698\) −0.543544 −0.0205734
\(699\) −38.0173 + 9.52301i −1.43794 + 0.360193i
\(700\) −14.9491 + 7.32156i −0.565023 + 0.276729i
\(701\) 16.4696i 0.622047i 0.950402 + 0.311024i \(0.100672\pi\)
−0.950402 + 0.311024i \(0.899328\pi\)
\(702\) 1.00000 + 18.7083i 0.0377426 + 0.706099i
\(703\) 13.0194i 0.491038i
\(704\) 0 0
\(705\) −6.13742 24.5015i −0.231149 0.922780i
\(706\) 30.0317i 1.13026i
\(707\) −24.5830 + 12.0399i −0.924539 + 0.452807i
\(708\) 3.64575 0.913230i 0.137016 0.0343213i
\(709\) 36.2686i 1.36209i −0.732239 0.681047i \(-0.761525\pi\)
0.732239 0.681047i \(-0.238475\pi\)
\(710\) 22.1208i 0.830177i
\(711\) 1.87451 1.00197i 0.0702995 0.0375767i
\(712\) 3.14944i 0.118030i
\(713\) 1.53737i 0.0575751i
\(714\) 23.1124 + 27.3917i 0.864959 + 1.02511i
\(715\) 0 0
\(716\) 11.3137i 0.422813i
\(717\) 4.15580 + 16.5906i 0.155201 + 0.619586i
\(718\) −27.2915 −1.01851
\(719\) −33.5633 −1.25170 −0.625850 0.779944i \(-0.715248\pi\)
−0.625850 + 0.779944i \(0.715248\pi\)
\(720\) −4.75216 8.89047i −0.177102 0.331328i
\(721\) −19.3068 39.4205i −0.719023 1.46810i
\(722\) 12.2915 0.457442
\(723\) 0.833990 + 3.32941i 0.0310164 + 0.123822i
\(724\) 24.7124i 0.918428i
\(725\) 32.4382i 1.20472i
\(726\) −4.62948 18.4816i −0.171816 0.685915i
\(727\) 34.7932i 1.29041i 0.764010 + 0.645204i \(0.223228\pi\)
−0.764010 + 0.645204i \(0.776772\pi\)
\(728\) −9.29360 2.15150i −0.344444 0.0797400i
\(729\) −2.64575 + 26.8701i −0.0979908 + 0.995187i
\(730\) 42.2489i 1.56370i
\(731\) 62.5670 2.31412
\(732\) −7.64575 + 1.91520i −0.282595 + 0.0707877i
\(733\) 46.3817 1.71315 0.856573 0.516026i \(-0.172589\pi\)
0.856573 + 0.516026i \(0.172589\pi\)
\(734\) 14.6315i 0.540059i
\(735\) −16.4079 + 37.2912i −0.605214 + 1.37551i
\(736\) 0.500983i 0.0184665i
\(737\) 0 0
\(738\) −13.9583 26.1136i −0.513812 0.961254i
\(739\) 3.83039i 0.140903i 0.997515 + 0.0704517i \(0.0224441\pi\)
−0.997515 + 0.0704517i \(0.977556\pi\)
\(740\) 7.82087 0.287501
\(741\) −14.8000 + 31.6438i −0.543692 + 1.16246i
\(742\) −0.583005 1.19038i −0.0214028 0.0437001i
\(743\) 3.29150 0.120754 0.0603768 0.998176i \(-0.480770\pi\)
0.0603768 + 0.998176i \(0.480770\pi\)
\(744\) −1.29150 5.15587i −0.0473488 0.189023i
\(745\) 20.1617i 0.738667i
\(746\) −22.0000 −0.805477
\(747\) 15.9399 + 29.8209i 0.583211 + 1.09109i
\(748\) 0 0
\(749\) 6.58301 + 13.4411i 0.240538 + 0.491128i
\(750\) 7.29150 1.82646i 0.266248 0.0666929i
\(751\) −29.1660 −1.06428 −0.532141 0.846655i \(-0.678613\pi\)
−0.532141 + 0.846655i \(0.678613\pi\)
\(752\) 4.33981i 0.158257i
\(753\) 4.35425 + 17.3828i 0.158678 + 0.633465i
\(754\) −11.7313 + 14.4207i −0.427229 + 0.525170i
\(755\) 20.6921 0.753062
\(756\) −12.7719 5.08713i −0.464509 0.185017i
\(757\) −16.5830 −0.602720 −0.301360 0.953511i \(-0.597441\pi\)
−0.301360 + 0.953511i \(0.597441\pi\)
\(758\) 30.1107i 1.09367i
\(759\) 0 0
\(760\) 18.7970i 0.681840i
\(761\) 28.0726i 1.01763i 0.860875 + 0.508816i \(0.169917\pi\)
−0.860875 + 0.508816i \(0.830083\pi\)
\(762\) 6.13742 + 24.5015i 0.222335 + 0.887596i
\(763\) 8.12549 + 16.5906i 0.294163 + 0.600619i
\(764\) 7.98430i 0.288862i
\(765\) −37.1660 69.5312i −1.34374 2.51391i
\(766\) 21.6991i 0.784019i
\(767\) −4.93725 + 6.06910i −0.178274 + 0.219143i
\(768\) 0.420861 + 1.68014i 0.0151865 + 0.0606269i
\(769\) −36.6320 −1.32098 −0.660492 0.750833i \(-0.729652\pi\)
−0.660492 + 0.750833i \(0.729652\pi\)
\(770\) 0 0
\(771\) 5.41699 + 21.6255i 0.195088 + 0.778822i
\(772\) 8.48528i 0.305392i
\(773\) 5.74103i 0.206491i −0.994656 0.103245i \(-0.967077\pi\)
0.994656 0.103245i \(-0.0329227\pi\)
\(774\) −21.1660 + 11.3137i −0.760797 + 0.406663i
\(775\) 19.3068 0.693521
\(776\) −10.8896 −0.390913
\(777\) 8.15160 6.87810i 0.292437 0.246751i
\(778\) 9.81076i 0.351733i
\(779\) 55.2116i 1.97816i
\(780\) 19.0086 + 8.89047i 0.680618 + 0.318330i
\(781\) 0 0
\(782\) 3.91813i 0.140112i
\(783\) −19.8504 + 17.9918i −0.709394 + 0.642974i
\(784\) 4.29150 5.53019i 0.153268 0.197507i
\(785\) 59.0405