Properties

Label 825.2.k.h.518.2
Level $825$
Weight $2$
Character 825.518
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
Defining polynomial: \(x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 518.2
Root \(0.707107 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 825.518
Dual form 825.2.k.h.782.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.70711 + 1.70711i) q^{2} +(0.292893 - 1.70711i) q^{3} +3.82843i q^{4} +(3.41421 - 2.41421i) q^{6} +(3.41421 - 3.41421i) q^{7} +(-3.12132 + 3.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} +O(q^{10})\) \(q+(1.70711 + 1.70711i) q^{2} +(0.292893 - 1.70711i) q^{3} +3.82843i q^{4} +(3.41421 - 2.41421i) q^{6} +(3.41421 - 3.41421i) q^{7} +(-3.12132 + 3.12132i) q^{8} +(-2.82843 - 1.00000i) q^{9} -1.00000i q^{11} +(6.53553 + 1.12132i) q^{12} +(0.585786 + 0.585786i) q^{13} +11.6569 q^{14} -3.00000 q^{16} +(-2.00000 - 2.00000i) q^{17} +(-3.12132 - 6.53553i) q^{18} +4.82843i q^{19} +(-4.82843 - 6.82843i) q^{21} +(1.70711 - 1.70711i) q^{22} +(4.82843 - 4.82843i) q^{23} +(4.41421 + 6.24264i) q^{24} +2.00000i q^{26} +(-2.53553 + 4.53553i) q^{27} +(13.0711 + 13.0711i) q^{28} -3.17157 q^{29} +4.00000 q^{31} +(1.12132 + 1.12132i) q^{32} +(-1.70711 - 0.292893i) q^{33} -6.82843i q^{34} +(3.82843 - 10.8284i) q^{36} +(-5.65685 + 5.65685i) q^{37} +(-8.24264 + 8.24264i) q^{38} +(1.17157 - 0.828427i) q^{39} -0.828427i q^{41} +(3.41421 - 19.8995i) q^{42} +(7.41421 + 7.41421i) q^{43} +3.82843 q^{44} +16.4853 q^{46} +(0.828427 + 0.828427i) q^{47} +(-0.878680 + 5.12132i) q^{48} -16.3137i q^{49} +(-4.00000 + 2.82843i) q^{51} +(-2.24264 + 2.24264i) q^{52} +(-8.48528 + 8.48528i) q^{53} +(-12.0711 + 3.41421i) q^{54} +21.3137i q^{56} +(8.24264 + 1.41421i) q^{57} +(-5.41421 - 5.41421i) q^{58} -13.6569 q^{59} -6.00000 q^{61} +(6.82843 + 6.82843i) q^{62} +(-13.0711 + 6.24264i) q^{63} +9.82843i q^{64} +(-2.41421 - 3.41421i) q^{66} +(-5.41421 + 5.41421i) q^{67} +(7.65685 - 7.65685i) q^{68} +(-6.82843 - 9.65685i) q^{69} -1.65685i q^{71} +(11.9497 - 5.70711i) q^{72} +(7.41421 + 7.41421i) q^{73} -19.3137 q^{74} -18.4853 q^{76} +(-3.41421 - 3.41421i) q^{77} +(3.41421 + 0.585786i) q^{78} -0.828427i q^{79} +(7.00000 + 5.65685i) q^{81} +(1.41421 - 1.41421i) q^{82} +(4.24264 - 4.24264i) q^{83} +(26.1421 - 18.4853i) q^{84} +25.3137i q^{86} +(-0.928932 + 5.41421i) q^{87} +(3.12132 + 3.12132i) q^{88} +7.31371 q^{89} +4.00000 q^{91} +(18.4853 + 18.4853i) q^{92} +(1.17157 - 6.82843i) q^{93} +2.82843i q^{94} +(2.24264 - 1.58579i) q^{96} +(9.65685 - 9.65685i) q^{97} +(27.8492 - 27.8492i) q^{98} +(-1.00000 + 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{7} - 4 q^{8} + O(q^{10}) \) \( 4 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{7} - 4 q^{8} + 12 q^{12} + 8 q^{13} + 24 q^{14} - 12 q^{16} - 8 q^{17} - 4 q^{18} - 8 q^{21} + 4 q^{22} + 8 q^{23} + 12 q^{24} + 4 q^{27} + 24 q^{28} - 24 q^{29} + 16 q^{31} - 4 q^{32} - 4 q^{33} + 4 q^{36} - 16 q^{38} + 16 q^{39} + 8 q^{42} + 24 q^{43} + 4 q^{44} + 32 q^{46} - 8 q^{47} - 12 q^{48} - 16 q^{51} + 8 q^{52} - 20 q^{54} + 16 q^{57} - 16 q^{58} - 32 q^{59} - 24 q^{61} + 16 q^{62} - 24 q^{63} - 4 q^{66} - 16 q^{67} + 8 q^{68} - 16 q^{69} + 28 q^{72} + 24 q^{73} - 32 q^{74} - 40 q^{76} - 8 q^{77} + 8 q^{78} + 28 q^{81} + 48 q^{84} - 32 q^{87} + 4 q^{88} - 16 q^{89} + 16 q^{91} + 40 q^{92} + 16 q^{93} - 8 q^{96} + 16 q^{97} + 52 q^{98} - 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.70711 + 1.70711i 1.20711 + 1.20711i 0.971960 + 0.235147i \(0.0755571\pi\)
0.235147 + 0.971960i \(0.424443\pi\)
\(3\) 0.292893 1.70711i 0.169102 0.985599i
\(4\) 3.82843i 1.91421i
\(5\) 0 0
\(6\) 3.41421 2.41421i 1.39385 0.985599i
\(7\) 3.41421 3.41421i 1.29045 1.29045i 0.355944 0.934507i \(-0.384159\pi\)
0.934507 0.355944i \(-0.115841\pi\)
\(8\) −3.12132 + 3.12132i −1.10355 + 1.10355i
\(9\) −2.82843 1.00000i −0.942809 0.333333i
\(10\) 0 0
\(11\) 1.00000i 0.301511i
\(12\) 6.53553 + 1.12132i 1.88665 + 0.323697i
\(13\) 0.585786 + 0.585786i 0.162468 + 0.162468i 0.783659 0.621191i \(-0.213351\pi\)
−0.621191 + 0.783659i \(0.713351\pi\)
\(14\) 11.6569 3.11543
\(15\) 0 0
\(16\) −3.00000 −0.750000
\(17\) −2.00000 2.00000i −0.485071 0.485071i 0.421676 0.906747i \(-0.361442\pi\)
−0.906747 + 0.421676i \(0.861442\pi\)
\(18\) −3.12132 6.53553i −0.735702 1.54044i
\(19\) 4.82843i 1.10772i 0.832611 + 0.553859i \(0.186845\pi\)
−0.832611 + 0.553859i \(0.813155\pi\)
\(20\) 0 0
\(21\) −4.82843 6.82843i −1.05365 1.49008i
\(22\) 1.70711 1.70711i 0.363956 0.363956i
\(23\) 4.82843 4.82843i 1.00680 1.00680i 0.00681991 0.999977i \(-0.497829\pi\)
0.999977 0.00681991i \(-0.00217086\pi\)
\(24\) 4.41421 + 6.24264i 0.901048 + 1.27427i
\(25\) 0 0
\(26\) 2.00000i 0.392232i
\(27\) −2.53553 + 4.53553i −0.487964 + 0.872864i
\(28\) 13.0711 + 13.0711i 2.47020 + 2.47020i
\(29\) −3.17157 −0.588946 −0.294473 0.955660i \(-0.595144\pi\)
−0.294473 + 0.955660i \(0.595144\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.12132 + 1.12132i 0.198223 + 0.198223i
\(33\) −1.70711 0.292893i −0.297169 0.0509862i
\(34\) 6.82843i 1.17107i
\(35\) 0 0
\(36\) 3.82843 10.8284i 0.638071 1.80474i
\(37\) −5.65685 + 5.65685i −0.929981 + 0.929981i −0.997704 0.0677230i \(-0.978427\pi\)
0.0677230 + 0.997704i \(0.478427\pi\)
\(38\) −8.24264 + 8.24264i −1.33713 + 1.33713i
\(39\) 1.17157 0.828427i 0.187602 0.132655i
\(40\) 0 0
\(41\) 0.828427i 0.129379i −0.997905 0.0646893i \(-0.979394\pi\)
0.997905 0.0646893i \(-0.0206056\pi\)
\(42\) 3.41421 19.8995i 0.526825 3.07056i
\(43\) 7.41421 + 7.41421i 1.13066 + 1.13066i 0.990068 + 0.140589i \(0.0448996\pi\)
0.140589 + 0.990068i \(0.455100\pi\)
\(44\) 3.82843 0.577157
\(45\) 0 0
\(46\) 16.4853 2.43062
\(47\) 0.828427 + 0.828427i 0.120839 + 0.120839i 0.764940 0.644102i \(-0.222769\pi\)
−0.644102 + 0.764940i \(0.722769\pi\)
\(48\) −0.878680 + 5.12132i −0.126826 + 0.739199i
\(49\) 16.3137i 2.33053i
\(50\) 0 0
\(51\) −4.00000 + 2.82843i −0.560112 + 0.396059i
\(52\) −2.24264 + 2.24264i −0.310998 + 0.310998i
\(53\) −8.48528 + 8.48528i −1.16554 + 1.16554i −0.182300 + 0.983243i \(0.558354\pi\)
−0.983243 + 0.182300i \(0.941646\pi\)
\(54\) −12.0711 + 3.41421i −1.64266 + 0.464616i
\(55\) 0 0
\(56\) 21.3137i 2.84816i
\(57\) 8.24264 + 1.41421i 1.09176 + 0.187317i
\(58\) −5.41421 5.41421i −0.710921 0.710921i
\(59\) −13.6569 −1.77797 −0.888985 0.457935i \(-0.848589\pi\)
−0.888985 + 0.457935i \(0.848589\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 6.82843 + 6.82843i 0.867211 + 0.867211i
\(63\) −13.0711 + 6.24264i −1.64680 + 0.786499i
\(64\) 9.82843i 1.22855i
\(65\) 0 0
\(66\) −2.41421 3.41421i −0.297169 0.420261i
\(67\) −5.41421 + 5.41421i −0.661451 + 0.661451i −0.955722 0.294271i \(-0.904923\pi\)
0.294271 + 0.955722i \(0.404923\pi\)
\(68\) 7.65685 7.65685i 0.928530 0.928530i
\(69\) −6.82843 9.65685i −0.822046 1.16255i
\(70\) 0 0
\(71\) 1.65685i 0.196632i −0.995155 0.0983162i \(-0.968654\pi\)
0.995155 0.0983162i \(-0.0313457\pi\)
\(72\) 11.9497 5.70711i 1.40829 0.672589i
\(73\) 7.41421 + 7.41421i 0.867768 + 0.867768i 0.992225 0.124457i \(-0.0397189\pi\)
−0.124457 + 0.992225i \(0.539719\pi\)
\(74\) −19.3137 −2.24517
\(75\) 0 0
\(76\) −18.4853 −2.12041
\(77\) −3.41421 3.41421i −0.389086 0.389086i
\(78\) 3.41421 + 0.585786i 0.386584 + 0.0663273i
\(79\) 0.828427i 0.0932053i −0.998914 0.0466027i \(-0.985161\pi\)
0.998914 0.0466027i \(-0.0148395\pi\)
\(80\) 0 0
\(81\) 7.00000 + 5.65685i 0.777778 + 0.628539i
\(82\) 1.41421 1.41421i 0.156174 0.156174i
\(83\) 4.24264 4.24264i 0.465690 0.465690i −0.434825 0.900515i \(-0.643190\pi\)
0.900515 + 0.434825i \(0.143190\pi\)
\(84\) 26.1421 18.4853i 2.85234 2.01691i
\(85\) 0 0
\(86\) 25.3137i 2.72965i
\(87\) −0.928932 + 5.41421i −0.0995920 + 0.580465i
\(88\) 3.12132 + 3.12132i 0.332734 + 0.332734i
\(89\) 7.31371 0.775252 0.387626 0.921817i \(-0.373295\pi\)
0.387626 + 0.921817i \(0.373295\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) 18.4853 + 18.4853i 1.92722 + 1.92722i
\(93\) 1.17157 6.82843i 0.121486 0.708075i
\(94\) 2.82843i 0.291730i
\(95\) 0 0
\(96\) 2.24264 1.58579i 0.228889 0.161849i
\(97\) 9.65685 9.65685i 0.980505 0.980505i −0.0193086 0.999814i \(-0.506146\pi\)
0.999814 + 0.0193086i \(0.00614649\pi\)
\(98\) 27.8492 27.8492i 2.81320 2.81320i
\(99\) −1.00000 + 2.82843i −0.100504 + 0.284268i
\(100\) 0 0
\(101\) 4.82843i 0.480446i −0.970718 0.240223i \(-0.922779\pi\)
0.970718 0.240223i \(-0.0772206\pi\)
\(102\) −11.6569 2.00000i −1.15420 0.198030i
\(103\) −4.24264 4.24264i −0.418040 0.418040i 0.466488 0.884528i \(-0.345519\pi\)
−0.884528 + 0.466488i \(0.845519\pi\)
\(104\) −3.65685 −0.358584
\(105\) 0 0
\(106\) −28.9706 −2.81387
\(107\) −5.89949 5.89949i −0.570326 0.570326i 0.361894 0.932219i \(-0.382130\pi\)
−0.932219 + 0.361894i \(0.882130\pi\)
\(108\) −17.3640 9.70711i −1.67085 0.934067i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) 0 0
\(111\) 8.00000 + 11.3137i 0.759326 + 1.07385i
\(112\) −10.2426 + 10.2426i −0.967839 + 0.967839i
\(113\) −8.48528 + 8.48528i −0.798228 + 0.798228i −0.982816 0.184588i \(-0.940905\pi\)
0.184588 + 0.982816i \(0.440905\pi\)
\(114\) 11.6569 + 16.4853i 1.09176 + 1.54399i
\(115\) 0 0
\(116\) 12.1421i 1.12737i
\(117\) −1.07107 2.24264i −0.0990203 0.207332i
\(118\) −23.3137 23.3137i −2.14620 2.14620i
\(119\) −13.6569 −1.25192
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −10.2426 10.2426i −0.927325 0.927325i
\(123\) −1.41421 0.242641i −0.127515 0.0218782i
\(124\) 15.3137i 1.37521i
\(125\) 0 0
\(126\) −32.9706 11.6569i −2.93725 1.03848i
\(127\) −1.75736 + 1.75736i −0.155940 + 0.155940i −0.780765 0.624825i \(-0.785170\pi\)
0.624825 + 0.780765i \(0.285170\pi\)
\(128\) −14.5355 + 14.5355i −1.28477 + 1.28477i
\(129\) 14.8284 10.4853i 1.30557 0.923178i
\(130\) 0 0
\(131\) 6.34315i 0.554203i 0.960841 + 0.277102i \(0.0893739\pi\)
−0.960841 + 0.277102i \(0.910626\pi\)
\(132\) 1.12132 6.53553i 0.0975984 0.568845i
\(133\) 16.4853 + 16.4853i 1.42946 + 1.42946i
\(134\) −18.4853 −1.59689
\(135\) 0 0
\(136\) 12.4853 1.07060
\(137\) −9.65685 9.65685i −0.825041 0.825041i 0.161785 0.986826i \(-0.448275\pi\)
−0.986826 + 0.161785i \(0.948275\pi\)
\(138\) 4.82843 28.1421i 0.411023 2.39562i
\(139\) 11.1716i 0.947560i −0.880643 0.473780i \(-0.842889\pi\)
0.880643 0.473780i \(-0.157111\pi\)
\(140\) 0 0
\(141\) 1.65685 1.17157i 0.139532 0.0986642i
\(142\) 2.82843 2.82843i 0.237356 0.237356i
\(143\) 0.585786 0.585786i 0.0489859 0.0489859i
\(144\) 8.48528 + 3.00000i 0.707107 + 0.250000i
\(145\) 0 0
\(146\) 25.3137i 2.09498i
\(147\) −27.8492 4.77817i −2.29697 0.394097i
\(148\) −21.6569 21.6569i −1.78018 1.78018i
\(149\) −21.7990 −1.78584 −0.892921 0.450213i \(-0.851348\pi\)
−0.892921 + 0.450213i \(0.851348\pi\)
\(150\) 0 0
\(151\) −2.48528 −0.202249 −0.101125 0.994874i \(-0.532244\pi\)
−0.101125 + 0.994874i \(0.532244\pi\)
\(152\) −15.0711 15.0711i −1.22243 1.22243i
\(153\) 3.65685 + 7.65685i 0.295639 + 0.619020i
\(154\) 11.6569i 0.939336i
\(155\) 0 0
\(156\) 3.17157 + 4.48528i 0.253929 + 0.359110i
\(157\) 7.31371 7.31371i 0.583697 0.583697i −0.352220 0.935917i \(-0.614573\pi\)
0.935917 + 0.352220i \(0.114573\pi\)
\(158\) 1.41421 1.41421i 0.112509 0.112509i
\(159\) 12.0000 + 16.9706i 0.951662 + 1.34585i
\(160\) 0 0
\(161\) 32.9706i 2.59844i
\(162\) 2.29289 + 21.6066i 0.180147 + 1.69757i
\(163\) 9.89949 + 9.89949i 0.775388 + 0.775388i 0.979043 0.203655i \(-0.0652819\pi\)
−0.203655 + 0.979043i \(0.565282\pi\)
\(164\) 3.17157 0.247658
\(165\) 0 0
\(166\) 14.4853 1.12428
\(167\) −0.242641 0.242641i −0.0187761 0.0187761i 0.697656 0.716433i \(-0.254226\pi\)
−0.716433 + 0.697656i \(0.754226\pi\)
\(168\) 36.3848 + 6.24264i 2.80715 + 0.481630i
\(169\) 12.3137i 0.947208i
\(170\) 0 0
\(171\) 4.82843 13.6569i 0.369239 1.04437i
\(172\) −28.3848 + 28.3848i −2.16432 + 2.16432i
\(173\) 0.828427 0.828427i 0.0629841 0.0629841i −0.674913 0.737897i \(-0.735819\pi\)
0.737897 + 0.674913i \(0.235819\pi\)
\(174\) −10.8284 + 7.65685i −0.820901 + 0.580465i
\(175\) 0 0
\(176\) 3.00000i 0.226134i
\(177\) −4.00000 + 23.3137i −0.300658 + 1.75237i
\(178\) 12.4853 + 12.4853i 0.935811 + 0.935811i
\(179\) 3.31371 0.247678 0.123839 0.992302i \(-0.460479\pi\)
0.123839 + 0.992302i \(0.460479\pi\)
\(180\) 0 0
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 6.82843 + 6.82843i 0.506157 + 0.506157i
\(183\) −1.75736 + 10.2426i −0.129908 + 0.757158i
\(184\) 30.1421i 2.22211i
\(185\) 0 0
\(186\) 13.6569 9.65685i 1.00137 0.708075i
\(187\) −2.00000 + 2.00000i −0.146254 + 0.146254i
\(188\) −3.17157 + 3.17157i −0.231311 + 0.231311i
\(189\) 6.82843 + 24.1421i 0.496695 + 1.75608i
\(190\) 0 0
\(191\) 11.3137i 0.818631i 0.912393 + 0.409316i \(0.134232\pi\)
−0.912393 + 0.409316i \(0.865768\pi\)
\(192\) 16.7782 + 2.87868i 1.21086 + 0.207751i
\(193\) −5.07107 5.07107i −0.365023 0.365023i 0.500635 0.865658i \(-0.333100\pi\)
−0.865658 + 0.500635i \(0.833100\pi\)
\(194\) 32.9706 2.36715
\(195\) 0 0
\(196\) 62.4558 4.46113
\(197\) 2.48528 + 2.48528i 0.177069 + 0.177069i 0.790077 0.613008i \(-0.210041\pi\)
−0.613008 + 0.790077i \(0.710041\pi\)
\(198\) −6.53553 + 3.12132i −0.464460 + 0.221823i
\(199\) 20.9706i 1.48656i 0.668978 + 0.743282i \(0.266732\pi\)
−0.668978 + 0.743282i \(0.733268\pi\)
\(200\) 0 0
\(201\) 7.65685 + 10.8284i 0.540073 + 0.763778i
\(202\) 8.24264 8.24264i 0.579950 0.579950i
\(203\) −10.8284 + 10.8284i −0.760007 + 0.760007i
\(204\) −10.8284 15.3137i −0.758142 1.07217i
\(205\) 0 0
\(206\) 14.4853i 1.00924i
\(207\) −18.4853 + 8.82843i −1.28482 + 0.613618i
\(208\) −1.75736 1.75736i −0.121851 0.121851i
\(209\) 4.82843 0.333989
\(210\) 0 0
\(211\) 6.48528 0.446465 0.223233 0.974765i \(-0.428339\pi\)
0.223233 + 0.974765i \(0.428339\pi\)
\(212\) −32.4853 32.4853i −2.23110 2.23110i
\(213\) −2.82843 0.485281i −0.193801 0.0332509i
\(214\) 20.1421i 1.37689i
\(215\) 0 0
\(216\) −6.24264 22.0711i −0.424758 1.50175i
\(217\) 13.6569 13.6569i 0.927088 0.927088i
\(218\) 3.41421 3.41421i 0.231240 0.231240i
\(219\) 14.8284 10.4853i 1.00201 0.708530i
\(220\) 0 0
\(221\) 2.34315i 0.157617i
\(222\) −5.65685 + 32.9706i −0.379663 + 2.21284i
\(223\) −7.75736 7.75736i −0.519471 0.519471i 0.397940 0.917411i \(-0.369725\pi\)
−0.917411 + 0.397940i \(0.869725\pi\)
\(224\) 7.65685 0.511595
\(225\) 0 0
\(226\) −28.9706 −1.92709
\(227\) 11.7574 + 11.7574i 0.780363 + 0.780363i 0.979892 0.199529i \(-0.0639411\pi\)
−0.199529 + 0.979892i \(0.563941\pi\)
\(228\) −5.41421 + 31.5563i −0.358565 + 2.08987i
\(229\) 18.0000i 1.18947i 0.803921 + 0.594737i \(0.202744\pi\)
−0.803921 + 0.594737i \(0.797256\pi\)
\(230\) 0 0
\(231\) −6.82843 + 4.82843i −0.449278 + 0.317687i
\(232\) 9.89949 9.89949i 0.649934 0.649934i
\(233\) −10.0000 + 10.0000i −0.655122 + 0.655122i −0.954222 0.299100i \(-0.903314\pi\)
0.299100 + 0.954222i \(0.403314\pi\)
\(234\) 2.00000 5.65685i 0.130744 0.369800i
\(235\) 0 0
\(236\) 52.2843i 3.40342i
\(237\) −1.41421 0.242641i −0.0918630 0.0157612i
\(238\) −23.3137 23.3137i −1.51120 1.51120i
\(239\) 13.6569 0.883388 0.441694 0.897166i \(-0.354378\pi\)
0.441694 + 0.897166i \(0.354378\pi\)
\(240\) 0 0
\(241\) 6.97056 0.449013 0.224507 0.974473i \(-0.427923\pi\)
0.224507 + 0.974473i \(0.427923\pi\)
\(242\) −1.70711 1.70711i −0.109737 0.109737i
\(243\) 11.7071 10.2929i 0.751011 0.660289i
\(244\) 22.9706i 1.47054i
\(245\) 0 0
\(246\) −2.00000 2.82843i −0.127515 0.180334i
\(247\) −2.82843 + 2.82843i −0.179969 + 0.179969i
\(248\) −12.4853 + 12.4853i −0.792816 + 0.792816i
\(249\) −6.00000 8.48528i −0.380235 0.537733i
\(250\) 0 0
\(251\) 9.65685i 0.609535i −0.952427 0.304768i \(-0.901421\pi\)
0.952427 0.304768i \(-0.0985788\pi\)
\(252\) −23.8995 50.0416i −1.50553 3.15233i
\(253\) −4.82843 4.82843i −0.303561 0.303561i
\(254\) −6.00000 −0.376473
\(255\) 0 0
\(256\) −29.9706 −1.87316
\(257\) 16.0000 + 16.0000i 0.998053 + 0.998053i 0.999998 0.00194553i \(-0.000619281\pi\)
−0.00194553 + 0.999998i \(0.500619\pi\)
\(258\) 43.2132 + 7.41421i 2.69034 + 0.461589i
\(259\) 38.6274i 2.40019i
\(260\) 0 0
\(261\) 8.97056 + 3.17157i 0.555264 + 0.196315i
\(262\) −10.8284 + 10.8284i −0.668982 + 0.668982i
\(263\) 7.75736 7.75736i 0.478339 0.478339i −0.426261 0.904600i \(-0.640169\pi\)
0.904600 + 0.426261i \(0.140169\pi\)
\(264\) 6.24264 4.41421i 0.384208 0.271676i
\(265\) 0 0
\(266\) 56.2843i 3.45101i
\(267\) 2.14214 12.4853i 0.131097 0.764087i
\(268\) −20.7279 20.7279i −1.26616 1.26616i
\(269\) −2.34315 −0.142864 −0.0714321 0.997445i \(-0.522757\pi\)
−0.0714321 + 0.997445i \(0.522757\pi\)
\(270\) 0 0
\(271\) −26.4853 −1.60887 −0.804433 0.594043i \(-0.797531\pi\)
−0.804433 + 0.594043i \(0.797531\pi\)
\(272\) 6.00000 + 6.00000i 0.363803 + 0.363803i
\(273\) 1.17157 6.82843i 0.0709068 0.413275i
\(274\) 32.9706i 1.99182i
\(275\) 0 0
\(276\) 36.9706 26.1421i 2.22537 1.57357i
\(277\) 2.92893 2.92893i 0.175982 0.175982i −0.613619 0.789602i \(-0.710287\pi\)
0.789602 + 0.613619i \(0.210287\pi\)
\(278\) 19.0711 19.0711i 1.14381 1.14381i
\(279\) −11.3137 4.00000i −0.677334 0.239474i
\(280\) 0 0
\(281\) 20.1421i 1.20158i 0.799407 + 0.600790i \(0.205147\pi\)
−0.799407 + 0.600790i \(0.794853\pi\)
\(282\) 4.82843 + 0.828427i 0.287529 + 0.0493321i
\(283\) 7.41421 + 7.41421i 0.440729 + 0.440729i 0.892257 0.451528i \(-0.149121\pi\)
−0.451528 + 0.892257i \(0.649121\pi\)
\(284\) 6.34315 0.376396
\(285\) 0 0
\(286\) 2.00000 0.118262
\(287\) −2.82843 2.82843i −0.166957 0.166957i
\(288\) −2.05025 4.29289i −0.120812 0.252961i
\(289\) 9.00000i 0.529412i
\(290\) 0 0
\(291\) −13.6569 19.3137i −0.800579 1.13219i
\(292\) −28.3848 + 28.3848i −1.66109 + 1.66109i
\(293\) 14.4853 14.4853i 0.846239 0.846239i −0.143422 0.989662i \(-0.545811\pi\)
0.989662 + 0.143422i \(0.0458107\pi\)
\(294\) −39.3848 55.6985i −2.29697 3.24840i
\(295\) 0 0
\(296\) 35.3137i 2.05257i
\(297\) 4.53553 + 2.53553i 0.263178 + 0.147127i
\(298\) −37.2132 37.2132i −2.15570 2.15570i
\(299\) 5.65685 0.327144
\(300\) 0 0
\(301\) 50.6274 2.91812
\(302\) −4.24264 4.24264i −0.244137 0.244137i
\(303\) −8.24264 1.41421i −0.473527 0.0812444i
\(304\) 14.4853i 0.830788i
\(305\) 0 0
\(306\) −6.82843 + 19.3137i −0.390355 + 1.10409i
\(307\) 6.72792 6.72792i 0.383983 0.383983i −0.488552 0.872535i \(-0.662475\pi\)
0.872535 + 0.488552i \(0.162475\pi\)
\(308\) 13.0711 13.0711i 0.744793 0.744793i
\(309\) −8.48528 + 6.00000i −0.482711 + 0.341328i
\(310\) 0 0
\(311\) 21.6569i 1.22805i −0.789288 0.614024i \(-0.789550\pi\)
0.789288 0.614024i \(-0.210450\pi\)
\(312\) −1.07107 + 6.24264i −0.0606373 + 0.353420i
\(313\) 13.1716 + 13.1716i 0.744501 + 0.744501i 0.973441 0.228939i \(-0.0735258\pi\)
−0.228939 + 0.973441i \(0.573526\pi\)
\(314\) 24.9706 1.40917
\(315\) 0 0
\(316\) 3.17157 0.178415
\(317\) 10.1421 + 10.1421i 0.569639 + 0.569639i 0.932027 0.362388i \(-0.118039\pi\)
−0.362388 + 0.932027i \(0.618039\pi\)
\(318\) −8.48528 + 49.4558i −0.475831 + 2.77335i
\(319\) 3.17157i 0.177574i
\(320\) 0 0
\(321\) −11.7990 + 8.34315i −0.658555 + 0.465669i
\(322\) 56.2843 56.2843i 3.13660 3.13660i
\(323\) 9.65685 9.65685i 0.537322 0.537322i
\(324\) −21.6569 + 26.7990i −1.20316 + 1.48883i
\(325\) 0 0
\(326\) 33.7990i 1.87195i
\(327\) −3.41421 0.585786i −0.188806 0.0323941i
\(328\) 2.58579 + 2.58579i 0.142776 + 0.142776i
\(329\) 5.65685 0.311872
\(330\) 0 0
\(331\) −9.65685 −0.530789 −0.265394 0.964140i \(-0.585502\pi\)
−0.265394 + 0.964140i \(0.585502\pi\)
\(332\) 16.2426 + 16.2426i 0.891431 + 0.891431i
\(333\) 21.6569 10.3431i 1.18679 0.566801i
\(334\) 0.828427i 0.0453295i
\(335\) 0 0
\(336\) 14.4853 + 20.4853i 0.790237 + 1.11756i
\(337\) −3.89949 + 3.89949i −0.212419 + 0.212419i −0.805294 0.592875i \(-0.797993\pi\)
0.592875 + 0.805294i \(0.297993\pi\)
\(338\) 21.0208 21.0208i 1.14338 1.14338i
\(339\) 12.0000 + 16.9706i 0.651751 + 0.921714i
\(340\) 0 0
\(341\) 4.00000i 0.216612i
\(342\) 31.5563 15.0711i 1.70637 0.814950i
\(343\) −31.7990 31.7990i −1.71698 1.71698i
\(344\) −46.2843 −2.49548
\(345\) 0 0
\(346\) 2.82843 0.152057
\(347\) −16.2426 16.2426i −0.871951 0.871951i 0.120734 0.992685i \(-0.461475\pi\)
−0.992685 + 0.120734i \(0.961475\pi\)
\(348\) −20.7279 3.55635i −1.11113 0.190640i
\(349\) 22.9706i 1.22959i 0.788688 + 0.614793i \(0.210760\pi\)
−0.788688 + 0.614793i \(0.789240\pi\)
\(350\) 0 0
\(351\) −4.14214 + 1.17157i −0.221091 + 0.0625339i
\(352\) 1.12132 1.12132i 0.0597666 0.0597666i
\(353\) −4.48528 + 4.48528i −0.238727 + 0.238727i −0.816323 0.577596i \(-0.803991\pi\)
0.577596 + 0.816323i \(0.303991\pi\)
\(354\) −46.6274 + 32.9706i −2.47822 + 1.75237i
\(355\) 0 0
\(356\) 28.0000i 1.48400i
\(357\) −4.00000 + 23.3137i −0.211702 + 1.23389i
\(358\) 5.65685 + 5.65685i 0.298974 + 0.298974i
\(359\) 16.9706 0.895672 0.447836 0.894116i \(-0.352195\pi\)
0.447836 + 0.894116i \(0.352195\pi\)
\(360\) 0 0
\(361\) −4.31371 −0.227037
\(362\) −10.2426 10.2426i −0.538341 0.538341i
\(363\) −0.292893 + 1.70711i −0.0153729 + 0.0895999i
\(364\) 15.3137i 0.802656i
\(365\) 0 0
\(366\) −20.4853 + 14.4853i −1.07078 + 0.757158i
\(367\) 16.2426 16.2426i 0.847859 0.847859i −0.142007 0.989866i \(-0.545355\pi\)
0.989866 + 0.142007i \(0.0453555\pi\)
\(368\) −14.4853 + 14.4853i −0.755097 + 0.755097i
\(369\) −0.828427 + 2.34315i −0.0431262 + 0.121979i
\(370\) 0 0
\(371\) 57.9411i 3.00815i
\(372\) 26.1421 + 4.48528i 1.35541 + 0.232551i
\(373\) 3.89949 + 3.89949i 0.201908 + 0.201908i 0.800817 0.598909i \(-0.204399\pi\)
−0.598909 + 0.800817i \(0.704399\pi\)
\(374\) −6.82843 −0.353090
\(375\) 0 0
\(376\) −5.17157 −0.266704
\(377\) −1.85786 1.85786i −0.0956849 0.0956849i
\(378\) −29.5563 + 52.8701i −1.52021 + 2.71934i
\(379\) 26.6274i 1.36776i −0.729595 0.683879i \(-0.760291\pi\)
0.729595 0.683879i \(-0.239709\pi\)
\(380\) 0 0
\(381\) 2.48528 + 3.51472i 0.127325 + 0.180064i
\(382\) −19.3137 + 19.3137i −0.988175 + 0.988175i
\(383\) 13.3137 13.3137i 0.680299 0.680299i −0.279769 0.960067i \(-0.590258\pi\)
0.960067 + 0.279769i \(0.0902578\pi\)
\(384\) 20.5563 + 29.0711i 1.04901 + 1.48353i
\(385\) 0 0
\(386\) 17.3137i 0.881245i
\(387\) −13.5563 28.3848i −0.689108 1.44288i
\(388\) 36.9706 + 36.9706i 1.87690 + 1.87690i
\(389\) 12.0000 0.608424 0.304212 0.952604i \(-0.401607\pi\)
0.304212 + 0.952604i \(0.401607\pi\)
\(390\) 0 0
\(391\) −19.3137 −0.976736
\(392\) 50.9203 + 50.9203i 2.57186 + 2.57186i
\(393\) 10.8284 + 1.85786i 0.546222 + 0.0937169i
\(394\) 8.48528i 0.427482i
\(395\) 0 0
\(396\) −10.8284 3.82843i −0.544149 0.192386i
\(397\) 17.1716 17.1716i 0.861817 0.861817i −0.129732 0.991549i \(-0.541412\pi\)
0.991549 + 0.129732i \(0.0414119\pi\)
\(398\) −35.7990 + 35.7990i −1.79444 + 1.79444i
\(399\) 32.9706 23.3137i 1.65059 1.16715i
\(400\) 0 0
\(401\) 36.2843i 1.81195i 0.423331 + 0.905975i \(0.360861\pi\)
−0.423331 + 0.905975i \(0.639139\pi\)
\(402\) −5.41421 + 31.5563i −0.270036 + 1.57389i
\(403\) 2.34315 + 2.34315i 0.116720 + 0.116720i
\(404\) 18.4853 0.919677
\(405\) 0 0
\(406\) −36.9706 −1.83482
\(407\) 5.65685 + 5.65685i 0.280400 + 0.280400i
\(408\) 3.65685 21.3137i 0.181041 1.05519i
\(409\) 27.6569i 1.36754i −0.729696 0.683772i \(-0.760338\pi\)
0.729696 0.683772i \(-0.239662\pi\)
\(410\) 0 0
\(411\) −19.3137 + 13.6569i −0.952675 + 0.673643i
\(412\) 16.2426 16.2426i 0.800217 0.800217i
\(413\) −46.6274 + 46.6274i −2.29439 + 2.29439i
\(414\) −46.6274 16.4853i −2.29161 0.810207i
\(415\) 0 0
\(416\) 1.31371i 0.0644099i
\(417\) −19.0711 3.27208i −0.933914 0.160234i
\(418\) 8.24264 + 8.24264i 0.403161 + 0.403161i
\(419\) 12.6863 0.619766 0.309883 0.950775i \(-0.399710\pi\)
0.309883 + 0.950775i \(0.399710\pi\)
\(420\) 0 0
\(421\) −9.31371 −0.453922 −0.226961 0.973904i \(-0.572879\pi\)
−0.226961 + 0.973904i \(0.572879\pi\)
\(422\) 11.0711 + 11.0711i 0.538931 + 0.538931i
\(423\) −1.51472 3.17157i −0.0736481 0.154207i
\(424\) 52.9706i 2.57248i
\(425\) 0 0
\(426\) −4.00000 5.65685i −0.193801 0.274075i
\(427\) −20.4853 + 20.4853i −0.991352 + 0.991352i
\(428\) 22.5858 22.5858i 1.09173 1.09173i
\(429\) −0.828427 1.17157i −0.0399968 0.0565641i
\(430\) 0 0
\(431\) 5.65685i 0.272481i −0.990676 0.136241i \(-0.956498\pi\)
0.990676 0.136241i \(-0.0435020\pi\)
\(432\) 7.60660 13.6066i 0.365973 0.654648i
\(433\) 15.3137 + 15.3137i 0.735930 + 0.735930i 0.971788 0.235858i \(-0.0757899\pi\)
−0.235858 + 0.971788i \(0.575790\pi\)
\(434\) 46.6274 2.23819
\(435\) 0 0
\(436\) 7.65685 0.366697
\(437\) 23.3137 + 23.3137i 1.11525 + 1.11525i
\(438\) 43.2132 + 7.41421i 2.06481 + 0.354265i
\(439\) 4.14214i 0.197693i 0.995103 + 0.0988467i \(0.0315153\pi\)
−0.995103 + 0.0988467i \(0.968485\pi\)
\(440\) 0 0
\(441\) −16.3137 + 46.1421i −0.776843 + 2.19724i
\(442\) 4.00000 4.00000i 0.190261 0.190261i
\(443\) −9.31371 + 9.31371i −0.442508 + 0.442508i −0.892854 0.450346i \(-0.851301\pi\)
0.450346 + 0.892854i \(0.351301\pi\)
\(444\) −43.3137 + 30.6274i −2.05558 + 1.45351i
\(445\) 0 0
\(446\) 26.4853i 1.25411i
\(447\) −6.38478 + 37.2132i −0.301990 + 1.76012i
\(448\) 33.5563 + 33.5563i 1.58539 + 1.58539i
\(449\) −25.6569 −1.21082 −0.605411 0.795913i \(-0.706991\pi\)
−0.605411 + 0.795913i \(0.706991\pi\)
\(450\) 0 0
\(451\) −0.828427 −0.0390091
\(452\) −32.4853 32.4853i −1.52798 1.52798i
\(453\) −0.727922 + 4.24264i −0.0342008 + 0.199337i
\(454\) 40.1421i 1.88396i
\(455\) 0 0
\(456\) −30.1421 + 21.3137i −1.41153 + 0.998106i
\(457\) 16.5858 16.5858i 0.775850 0.775850i −0.203272 0.979122i \(-0.565158\pi\)
0.979122 + 0.203272i \(0.0651576\pi\)
\(458\) −30.7279 + 30.7279i −1.43582 + 1.43582i
\(459\) 14.1421 4.00000i 0.660098 0.186704i
\(460\) 0 0
\(461\) 28.8284i 1.34267i −0.741152 0.671337i \(-0.765720\pi\)
0.741152 0.671337i \(-0.234280\pi\)
\(462\) −19.8995 3.41421i −0.925808 0.158844i
\(463\) 14.3848 + 14.3848i 0.668517 + 0.668517i 0.957373 0.288855i \(-0.0932747\pi\)
−0.288855 + 0.957373i \(0.593275\pi\)
\(464\) 9.51472 0.441710
\(465\) 0 0
\(466\) −34.1421 −1.58160
\(467\) −7.17157 7.17157i −0.331861 0.331861i 0.521432 0.853293i \(-0.325398\pi\)
−0.853293 + 0.521432i \(0.825398\pi\)
\(468\) 8.58579 4.10051i 0.396878 0.189546i
\(469\) 36.9706i 1.70714i
\(470\) 0 0
\(471\) −10.3431 14.6274i −0.476587 0.673996i
\(472\) 42.6274 42.6274i 1.96209 1.96209i
\(473\) 7.41421 7.41421i 0.340906 0.340906i
\(474\) −2.00000 2.82843i −0.0918630 0.129914i
\(475\) 0 0
\(476\) 52.2843i 2.39645i
\(477\) 32.4853 15.5147i 1.48740 0.710370i
\(478\) 23.3137 + 23.3137i 1.06634 + 1.06634i
\(479\) −37.6569 −1.72059 −0.860293 0.509800i \(-0.829719\pi\)
−0.860293 + 0.509800i \(0.829719\pi\)
\(480\) 0 0
\(481\) −6.62742 −0.302184
\(482\) 11.8995 + 11.8995i 0.542007 + 0.542007i
\(483\) −56.2843 9.65685i −2.56102 0.439402i
\(484\) 3.82843i 0.174019i
\(485\) 0 0
\(486\) 37.5563 + 2.41421i 1.70359 + 0.109511i
\(487\) −13.4142 + 13.4142i −0.607856 + 0.607856i −0.942385 0.334529i \(-0.891423\pi\)
0.334529 + 0.942385i \(0.391423\pi\)
\(488\) 18.7279 18.7279i 0.847773 0.847773i
\(489\) 19.7990 14.0000i 0.895341 0.633102i
\(490\) 0 0
\(491\) 26.6274i 1.20168i −0.799370 0.600839i \(-0.794833\pi\)
0.799370 0.600839i \(-0.205167\pi\)
\(492\) 0.928932 5.41421i 0.0418795 0.244092i
\(493\) 6.34315 + 6.34315i 0.285681 + 0.285681i
\(494\) −9.65685 −0.434482
\(495\) 0 0
\(496\) −12.0000 −0.538816
\(497\) −5.65685 5.65685i −0.253745 0.253745i
\(498\) 4.24264 24.7279i 0.190117 1.10808i
\(499\) 13.6569i 0.611365i −0.952134 0.305682i \(-0.901115\pi\)
0.952134 0.305682i \(-0.0988846\pi\)
\(500\) 0 0
\(501\) −0.485281 + 0.343146i −0.0216808 + 0.0153306i
\(502\) 16.4853 16.4853i 0.735774 0.735774i
\(503\) 10.3848 10.3848i 0.463034 0.463034i −0.436614 0.899649i \(-0.643823\pi\)
0.899649 + 0.436614i \(0.143823\pi\)
\(504\) 21.3137 60.2843i 0.949388 2.68527i
\(505\) 0 0
\(506\) 16.4853i 0.732860i
\(507\) −21.0208 3.60660i −0.933567 0.160175i
\(508\) −6.72792 6.72792i −0.298503 0.298503i
\(509\) 12.6863 0.562310 0.281155 0.959662i \(-0.409282\pi\)
0.281155 + 0.959662i \(0.409282\pi\)
\(510\) 0 0
\(511\) 50.6274 2.23963
\(512\) −22.0919 22.0919i −0.976333 0.976333i
\(513\) −21.8995 12.2426i −0.966886 0.540526i
\(514\) 54.6274i 2.40951i
\(515\) 0 0
\(516\) 40.1421 + 56.7696i 1.76716 + 2.49914i
\(517\) 0.828427 0.828427i 0.0364342 0.0364342i
\(518\) −65.9411 + 65.9411i −2.89729 + 2.89729i
\(519\) −1.17157 1.65685i −0.0514263 0.0727278i
\(520\) 0 0
\(521\) 7.02944i 0.307965i −0.988074 0.153983i \(-0.950790\pi\)
0.988074 0.153983i \(-0.0492100\pi\)
\(522\) 9.89949 + 20.7279i 0.433289 + 0.907237i
\(523\) −17.0711 17.0711i −0.746466 0.746466i 0.227348 0.973814i \(-0.426995\pi\)
−0.973814 + 0.227348i \(0.926995\pi\)
\(524\) −24.2843 −1.06086
\(525\) 0 0
\(526\) 26.4853 1.15481
\(527\) −8.00000 8.00000i −0.348485 0.348485i
\(528\) 5.12132 + 0.878680i 0.222877 + 0.0382396i
\(529\) 23.6274i 1.02728i
\(530\) 0 0
\(531\) 38.6274 + 13.6569i 1.67629 + 0.592657i
\(532\) −63.1127 + 63.1127i −2.73628 + 2.73628i
\(533\) 0.485281 0.485281i 0.0210199 0.0210199i
\(534\) 24.9706 17.6569i 1.08058 0.764087i
\(535\) 0 0
\(536\) 33.7990i 1.45989i
\(537\) 0.970563 5.65685i 0.0418829 0.244111i
\(538\) −4.00000 4.00000i −0.172452 0.172452i
\(539\) −16.3137 −0.702681
\(540\) 0 0
\(541\) −1.02944 −0.0442590 −0.0221295 0.999755i \(-0.507045\pi\)
−0.0221295 + 0.999755i \(0.507045\pi\)
\(542\) −45.2132 45.2132i −1.94207 1.94207i
\(543\) −1.75736 + 10.2426i −0.0754155 + 0.439554i
\(544\) 4.48528i 0.192305i
\(545\) 0 0
\(546\) 13.6569 9.65685i 0.584459 0.413275i
\(547\) −18.7279 + 18.7279i −0.800748 + 0.800748i −0.983212 0.182464i \(-0.941593\pi\)
0.182464 + 0.983212i \(0.441593\pi\)
\(548\) 36.9706 36.9706i 1.57930 1.57930i
\(549\) 16.9706 + 6.00000i 0.724286 + 0.256074i
\(550\) 0 0
\(551\) 15.3137i 0.652386i
\(552\) 51.4558 + 8.82843i 2.19011 + 0.375763i
\(553\) −2.82843 2.82843i −0.120277 0.120277i
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) 42.7696 1.81383
\(557\) −31.4558 31.4558i −1.33283 1.33283i −0.902831 0.429996i \(-0.858515\pi\)
−0.429996 0.902831i \(-0.641485\pi\)
\(558\) −12.4853 26.1421i −0.528544 1.10668i
\(559\) 8.68629i 0.367391i
\(560\) 0 0
\(561\) 2.82843 + 4.00000i 0.119416 + 0.168880i
\(562\) −34.3848 + 34.3848i −1.45043 + 1.45043i
\(563\) 8.24264 8.24264i 0.347386 0.347386i −0.511749 0.859135i \(-0.671002\pi\)
0.859135 + 0.511749i \(0.171002\pi\)
\(564\) 4.48528 + 6.34315i 0.188864 + 0.267095i
\(565\) 0 0
\(566\) 25.3137i 1.06401i
\(567\) 43.2132 4.58579i 1.81478 0.192585i
\(568\) 5.17157 + 5.17157i 0.216994 + 0.216994i
\(569\) −7.17157 −0.300648 −0.150324 0.988637i \(-0.548032\pi\)
−0.150324 + 0.988637i \(0.548032\pi\)
\(570\) 0 0
\(571\) −38.4853 −1.61056 −0.805279 0.592895i \(-0.797985\pi\)
−0.805279 + 0.592895i \(0.797985\pi\)
\(572\) 2.24264 + 2.24264i 0.0937695 + 0.0937695i
\(573\) 19.3137 + 3.31371i 0.806842 + 0.138432i
\(574\) 9.65685i 0.403069i
\(575\) 0 0
\(576\) 9.82843 27.7990i 0.409518 1.15829i
\(577\) 20.4853 20.4853i 0.852813 0.852813i −0.137665 0.990479i \(-0.543960\pi\)
0.990479 + 0.137665i \(0.0439599\pi\)
\(578\) 15.3640 15.3640i 0.639057 0.639057i
\(579\) −10.1421 + 7.17157i −0.421493 + 0.298040i
\(580\) 0 0
\(581\) 28.9706i 1.20190i
\(582\) 9.65685 56.2843i 0.400289 2.33306i
\(583\) 8.48528 + 8.48528i 0.351424 + 0.351424i
\(584\) −46.2843 −1.91526
\(585\) 0 0
\(586\) 49.4558 2.04300
\(587\) 5.51472 + 5.51472i 0.227617 + 0.227617i 0.811696 0.584080i \(-0.198544\pi\)
−0.584080 + 0.811696i \(0.698544\pi\)
\(588\) 18.2929 106.619i 0.754386 4.39689i
\(589\) 19.3137i 0.795807i
\(590\) 0 0
\(591\) 4.97056 3.51472i 0.204462 0.144576i
\(592\) 16.9706 16.9706i 0.697486 0.697486i
\(593\) 8.34315 8.34315i 0.342612 0.342612i −0.514737 0.857348i \(-0.672110\pi\)
0.857348 + 0.514737i \(0.172110\pi\)
\(594\) 3.41421 + 12.0711i 0.140087 + 0.495282i
\(595\) 0 0
\(596\) 83.4558i 3.41848i
\(597\) 35.7990 + 6.14214i 1.46516 + 0.251381i
\(598\) 9.65685 + 9.65685i 0.394898 + 0.394898i
\(599\) 0.686292 0.0280411 0.0140206 0.999902i \(-0.495537\pi\)
0.0140206 + 0.999902i \(0.495537\pi\)
\(600\) 0 0
\(601\) −10.9706 −0.447499 −0.223749 0.974647i \(-0.571830\pi\)
−0.223749 + 0.974647i \(0.571830\pi\)
\(602\) 86.4264 + 86.4264i 3.52248 + 3.52248i
\(603\) 20.7279 9.89949i 0.844106 0.403139i
\(604\) 9.51472i 0.387148i
\(605\) 0 0
\(606\) −11.6569 16.4853i −0.473527 0.669669i
\(607\) −27.8995 + 27.8995i −1.13241 + 1.13241i −0.142629 + 0.989776i \(0.545556\pi\)
−0.989776 + 0.142629i \(0.954444\pi\)
\(608\) −5.41421 + 5.41421i −0.219575 + 0.219575i
\(609\) 15.3137 + 21.6569i 0.620543 + 0.877580i
\(610\) 0 0
\(611\) 0.970563i 0.0392648i
\(612\) −29.3137 + 14.0000i −1.18494 + 0.565916i
\(613\) −30.0416 30.0416i −1.21337 1.21337i −0.969911 0.243459i \(-0.921718\pi\)
−0.243459 0.969911i \(-0.578282\pi\)
\(614\) 22.9706 0.927016
\(615\) 0 0
\(616\) 21.3137 0.858754
\(617\) 24.4853 + 24.4853i 0.985740 + 0.985740i 0.999900 0.0141594i \(-0.00450724\pi\)
−0.0141594 + 0.999900i \(0.504507\pi\)
\(618\) −24.7279 4.24264i −0.994703 0.170664i
\(619\) 28.9706i 1.16443i −0.813037 0.582213i \(-0.802187\pi\)
0.813037 0.582213i \(-0.197813\pi\)
\(620\) 0 0
\(621\) 9.65685 + 34.1421i 0.387516 + 1.37008i
\(622\) 36.9706 36.9706i 1.48238 1.48238i
\(623\) 24.9706 24.9706i 1.00042 1.00042i
\(624\) −3.51472 + 2.48528i −0.140701 + 0.0994909i
\(625\) 0 0
\(626\) 44.9706i 1.79739i
\(627\) 1.41421 8.24264i 0.0564782 0.329179i
\(628\) 28.0000 + 28.0000i 1.11732 + 1.11732i
\(629\) 22.6274 0.902214
\(630\) 0 0
\(631\) −9.65685 −0.384433 −0.192217 0.981353i \(-0.561568\pi\)
−0.192217 + 0.981353i \(0.561568\pi\)
\(632\) 2.58579 + 2.58579i 0.102857 + 0.102857i
\(633\) 1.89949 11.0711i 0.0754981 0.440035i
\(634\) 34.6274i 1.37523i
\(635\) 0 0
\(636\) −64.9706 + 45.9411i −2.57625 + 1.82168i
\(637\) 9.55635 9.55635i 0.378636 0.378636i
\(638\) −5.41421 + 5.41421i −0.214351 + 0.214351i
\(639\) −1.65685 + 4.68629i −0.0655441 + 0.185387i
\(640\) 0 0
\(641\) 17.6569i 0.697404i 0.937234 + 0.348702i \(0.113377\pi\)
−0.937234 + 0.348702i \(0.886623\pi\)
\(642\) −34.3848 5.89949i −1.35706 0.232834i
\(643\) −1.41421 1.41421i −0.0557711 0.0557711i 0.678671 0.734442i \(-0.262556\pi\)
−0.734442 + 0.678671i \(0.762556\pi\)
\(644\) 126.225 4.97398
\(645\) 0 0
\(646\) 32.9706 1.29721
\(647\) −6.00000 6.00000i −0.235884 0.235884i 0.579259 0.815143i \(-0.303342\pi\)
−0.815143 + 0.579259i \(0.803342\pi\)
\(648\) −39.5061 + 4.19239i −1.55195 + 0.164693i
\(649\) 13.6569i 0.536078i
\(650\) 0 0
\(651\) −19.3137 27.3137i −0.756964 1.07051i
\(652\) −37.8995 + 37.8995i −1.48426 + 1.48426i
\(653\) −4.00000 + 4.00000i −0.156532 + 0.156532i −0.781028 0.624496i \(-0.785304\pi\)
0.624496 + 0.781028i \(0.285304\pi\)
\(654\) −4.82843 6.82843i −0.188806 0.267013i
\(655\) 0 0
\(656\) 2.48528i 0.0970339i
\(657\) −13.5563 28.3848i −0.528884 1.10740i
\(658\) 9.65685 + 9.65685i 0.376463 + 0.376463i
\(659\) −41.6569 −1.62272 −0.811360 0.584546i \(-0.801273\pi\)
−0.811360 + 0.584546i \(0.801273\pi\)
\(660\) 0 0
\(661\) 0.627417 0.0244037 0.0122018 0.999926i \(-0.496116\pi\)
0.0122018 + 0.999926i \(0.496116\pi\)
\(662\) −16.4853 16.4853i −0.640719 0.640719i
\(663\) −4.00000 0.686292i −0.155347 0.0266534i
\(664\) 26.4853i 1.02783i
\(665\) 0 0
\(666\) 54.6274 + 19.3137i 2.11677 + 0.748391i
\(667\) −15.3137 + 15.3137i −0.592949 + 0.592949i
\(668\) 0.928932 0.928932i 0.0359415 0.0359415i
\(669\) −15.5147 + 10.9706i −0.599834 + 0.424146i
\(670\) 0 0
\(671\) 6.00000i 0.231627i
\(672\) 2.24264 13.0711i 0.0865117 0.504227i
\(673\) −5.27208 5.27208i −0.203224 0.203224i 0.598156 0.801380i \(-0.295900\pi\)
−0.801380 + 0.598156i \(0.795900\pi\)
\(674\) −13.3137 −0.512825
\(675\) 0 0
\(676\) 47.1421 1.81316
\(677\) 2.48528 + 2.48528i 0.0955171 + 0.0955171i 0.753251 0.657734i \(-0.228485\pi\)
−0.657734 + 0.753251i \(0.728485\pi\)
\(678\) −8.48528 + 49.4558i −0.325875 + 1.89934i
\(679\) 65.9411i 2.53059i
\(680\) 0 0
\(681\) 23.5147 16.6274i 0.901086 0.637164i
\(682\) 6.82843 6.82843i 0.261474 0.261474i
\(683\) −6.48528 + 6.48528i −0.248152 + 0.248152i −0.820212 0.572060i \(-0.806145\pi\)
0.572060 + 0.820212i \(0.306145\pi\)
\(684\) 52.2843 + 18.4853i 1.99914 + 0.706802i
\(685\) 0 0
\(686\) 108.569i 4.14517i
\(687\) 30.7279 + 5.27208i 1.17234 + 0.201142i
\(688\) −22.2426 22.2426i −0.847993 0.847993i
\(689\) −9.94113 −0.378727
\(690\) 0 0
\(691\) −37.9411 −1.44335 −0.721674 0.692233i \(-0.756627\pi\)
−0.721674 + 0.692233i \(0.756627\pi\)
\(692\) 3.17157 + 3.17157i 0.120565 + 0.120565i
\(693\) 6.24264 + 13.0711i 0.237138 + 0.496529i
\(694\) 55.4558i 2.10508i
\(695\) 0 0
\(696\) −14.0000 19.7990i −0.530669 0.750479i
\(697\) −1.65685 + 1.65685i −0.0627578 + 0.0627578i
\(698\) −39.2132 + 39.2132i −1.48424 + 1.48424i
\(699\) 14.1421 + 20.0000i 0.534905 + 0.756469i
\(700\) 0 0
\(701\) 50.4853i 1.90680i −0.301705 0.953401i \(-0.597556\pi\)
0.301705 0.953401i \(-0.402444\pi\)
\(702\) −9.07107 5.07107i −0.342365 0.191395i
\(703\) −27.3137 27.3137i −1.03016 1.03016i
\(704\) 9.82843 0.370423
\(705\) 0 0
\(706\) −15.3137 −0.576339
\(707\) −16.4853 16.4853i −0.619993 0.619993i
\(708\) −89.2548 15.3137i −3.35440 0.575524i
\(709\) 10.0000i 0.375558i −0.982211 0.187779i \(-0.939871\pi\)
0.982211 0.187779i \(-0.0601289\pi\)
\(710\) 0 0
\(711\) −0.828427 + 2.34315i −0.0310684 + 0.0878748i
\(712\) −22.8284 + 22.8284i −0.855531 + 0.855531i
\(713\) 19.3137 19.3137i 0.723304 0.723304i
\(714\) −46.6274 + 32.9706i −1.74499 + 1.23389i
\(715\) 0 0
\(716\) 12.6863i 0.474109i
\(717\) 4.00000 23.3137i 0.149383 0.870666i
\(718\) 28.9706 + 28.9706i 1.08117 + 1.08117i
\(719\) −27.3137 −1.01863 −0.509315 0.860580i \(-0.670101\pi\)
−0.509315 + 0.860580i \(0.670101\pi\)
\(720\) 0 0
\(721\) −28.9706 −1.07892
\(722\) −7.36396 7.36396i −0.274058 0.274058i
\(723\) 2.04163 11.8995i 0.0759291 0.442547i
\(724\) 22.9706i 0.853694i
\(725\) 0 0
\(726\) −3.41421 + 2.41421i −0.126713 + 0.0895999i
\(727\) 9.89949 9.89949i 0.367152 0.367152i −0.499286 0.866437i \(-0.666404\pi\)
0.866437 + 0.499286i \(0.166404\pi\)
\(728\) −12.4853 + 12.4853i −0.462735 + 0.462735i
\(729\) −14.1421 23.0000i −0.523783 0.851852i
\(730\) 0 0
\(731\) 29.6569i 1.09690i
\(732\) −39.2132 6.72792i −1.44936 0.248671i
\(733\) 11.8995 + 11.8995i 0.439518 + 0.439518i 0.891850 0.452332i \(-0.149408\pi\)
−0.452332 + 0.891850i \(0.649408\pi\)
\(734\) 55.4558 2.04691
\(735\) 0 0
\(736\) 10.8284 0.399141
\(737\) 5.41421 + 5.41421i 0.199435 + 0.199435i
\(738\) −5.41421 + 2.58579i −0.199300 + 0.0951841i
\(739\) 22.4853i 0.827134i 0.910474 + 0.413567i \(0.135717\pi\)
−0.910474 + 0.413567i \(0.864283\pi\)
\(740\) 0 0
\(741\) 4.00000 + 5.65685i 0.146944 + 0.207810i
\(742\) −98.9117 + 98.9117i −3.63116 + 3.63116i
\(743\) 8.72792 8.72792i 0.320196 0.320196i −0.528646 0.848842i \(-0.677300\pi\)
0.848842 + 0.528646i \(0.177300\pi\)
\(744\) 17.6569 + 24.9706i 0.647332 + 0.915465i
\(745\) 0 0
\(746\) 13.3137i 0.487450i
\(747\) −16.2426 + 7.75736i −0.594287 + 0.283827i
\(748\) −7.65685 7.65685i −0.279962 0.279962i
\(749\) −40.2843 −1.47196
\(750\) 0 0
\(751\) 24.2843 0.886146 0.443073 0.896486i \(-0.353888\pi\)
0.443073 + 0.896486i \(0.353888\pi\)
\(752\) −2.48528 2.48528i −0.0906289 0.0906289i
\(753\) −16.4853 2.82843i −0.600757 0.103074i
\(754\) 6.34315i 0.231004i
\(755\) 0 0
\(756\) −92.4264 + 26.1421i −3.36152 + 0.950780i
\(757\) 23.3137 23.3137i 0.847351 0.847351i −0.142451 0.989802i \(-0.545498\pi\)
0.989802 + 0.142451i \(0.0454983\pi\)
\(758\) 45.4558 45.4558i 1.65103 1.65103i
\(759\) −9.65685 + 6.82843i −0.350522 + 0.247856i
\(760\) 0 0
\(761\) 25.7990i 0.935213i −0.883937 0.467606i \(-0.845117\pi\)
0.883937 0.467606i \(-0.154883\pi\)
\(762\) −1.75736 + 10.2426i −0.0636624 + 0.371052i
\(763\) −6.82843 6.82843i −0.247206 0.247206i
\(764\) −43.3137 −1.56703
\(765\) 0 0
\(766\) 45.4558 1.64239
\(767\) −8.00000 8.00000i −0.288863 0.288863i
\(768\) −8.77817 + 51.1630i −0.316755 + 1.84618i
\(769\) 21.3137i 0.768592i 0.923210 + 0.384296i \(0.125556\pi\)
−0.923210 + 0.384296i \(0.874444\pi\)
\(770\) 0 0
\(771\) 32.0000 22.6274i 1.15245 0.814907i
\(772\) 19.4142 19.4142i 0.698733 0.698733i
\(773\) 28.9706 28.9706i 1.04200 1.04200i 0.0429202 0.999079i \(-0.486334\pi\)
0.999079 0.0429202i \(-0.0136661\pi\)
\(774\) 25.3137 71.5980i 0.909882 2.57354i
\(775\) 0 0
\(776\) 60.2843i 2.16408i
\(777\) 65.9411 + 11.3137i 2.36562 + 0.405877i
\(778\) 20.4853 + 20.4853i 0.734433 + 0.734433i
\(779\) 4.00000 0.143315
\(780\) 0 0
\(781\) −1.65685 −0.0592869
\(782\) −32.9706 32.9706i −1.17902 1.17902i
\(783\) 8.04163 14.3848i 0.287384 0.514070i