Properties

Label 28.2.f.a.19.2
Level $28$
Weight $2$
Character 28.19
Analytic conductor $0.224$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 28 = 2^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 28.f (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.223581125660\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 28.19
Dual form 28.2.f.a.3.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 + 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.73205 - 1.73205i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(0.366025 + 1.36603i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.73205 - 1.73205i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.633975 - 2.36603i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(3.00000 + 1.73205i) q^{12} +3.46410i q^{13} +(-2.09808 + 3.09808i) q^{14} +3.00000i q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.50000 + 0.866025i) q^{17} +(2.59808 - 4.50000i) q^{19} +3.46410 q^{20} +(1.50000 - 4.33013i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.26795 + 4.73205i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-4.73205 + 1.26795i) q^{26} -5.19615 q^{27} +(-5.00000 - 1.73205i) q^{28} +4.00000 q^{29} +(-4.09808 + 1.09808i) q^{30} +(0.866025 + 1.50000i) q^{31} +(5.46410 + 1.46410i) q^{32} +(1.50000 + 0.866025i) q^{33} +(-1.73205 - 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(7.09808 + 1.90192i) q^{38} +(5.19615 - 3.00000i) q^{39} +(1.26795 + 4.73205i) q^{40} -3.46410i q^{41} +(6.46410 + 0.464102i) q^{42} +2.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(0.366025 - 1.36603i) q^{46} +(-4.33013 + 7.50000i) q^{47} -6.92820 q^{48} +(-1.00000 + 6.92820i) q^{49} +(2.00000 - 2.00000i) q^{50} +(2.59808 + 1.50000i) q^{51} +(-3.46410 - 6.00000i) q^{52} +(0.500000 + 0.866025i) q^{53} +(-1.90192 - 7.09808i) q^{54} +1.73205 q^{55} +(0.535898 - 7.46410i) q^{56} -9.00000 q^{57} +(1.46410 + 5.46410i) q^{58} +(2.59808 + 4.50000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(-4.50000 - 2.59808i) q^{61} +(-1.73205 + 1.73205i) q^{62} +8.00000i q^{64} +(3.00000 - 5.19615i) q^{65} +(-0.633975 + 2.36603i) q^{66} +(-2.59808 + 1.50000i) q^{67} +(1.73205 - 3.00000i) q^{68} +1.73205i q^{69} +(5.83013 - 2.83013i) q^{70} -14.0000i q^{71} +(7.50000 - 4.33013i) q^{73} +(-4.09808 - 1.09808i) q^{74} +(-1.73205 + 3.00000i) q^{75} +10.3923i q^{76} +(-2.50000 - 0.866025i) q^{77} +(6.00000 + 6.00000i) q^{78} +(-7.79423 - 4.50000i) q^{79} +(-6.00000 + 3.46410i) q^{80} +(4.50000 + 7.79423i) q^{81} +(4.73205 - 1.26795i) q^{82} +13.8564 q^{83} +(1.73205 + 9.00000i) q^{84} +3.00000 q^{85} +(-2.73205 + 0.732051i) q^{86} +(-3.46410 - 6.00000i) q^{87} +(2.73205 + 0.732051i) q^{88} +(13.5000 + 7.79423i) q^{89} +(-6.92820 + 6.00000i) q^{91} +2.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(-11.8301 - 3.16987i) q^{94} +(-7.79423 + 4.50000i) q^{95} +(-2.53590 - 9.46410i) q^{96} -17.3205i q^{97} +(-9.83013 + 1.16987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 6 q^{5} - 8 q^{8} + O(q^{10}) \) \( 4 q - 2 q^{2} - 6 q^{5} - 8 q^{8} + 6 q^{10} + 12 q^{12} + 2 q^{14} + 8 q^{16} - 6 q^{17} + 6 q^{21} - 4 q^{22} - 12 q^{24} - 4 q^{25} - 12 q^{26} - 20 q^{28} + 16 q^{29} - 6 q^{30} + 8 q^{32} + 6 q^{33} - 6 q^{37} + 18 q^{38} + 12 q^{40} + 12 q^{42} + 4 q^{44} - 2 q^{46} - 4 q^{49} + 8 q^{50} + 2 q^{53} - 18 q^{54} + 16 q^{56} - 36 q^{57} - 8 q^{58} - 12 q^{60} - 18 q^{61} + 12 q^{65} - 6 q^{66} + 6 q^{70} + 30 q^{73} - 6 q^{74} - 10 q^{77} + 24 q^{78} - 24 q^{80} + 18 q^{81} + 12 q^{82} + 12 q^{85} - 4 q^{86} + 4 q^{88} + 54 q^{89} + 8 q^{92} + 6 q^{93} - 30 q^{94} - 24 q^{96} - 22 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 + 1.36603i 0.258819 + 0.965926i
\(3\) −0.866025 1.50000i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(4\) −1.73205 + 1.00000i −0.866025 + 0.500000i
\(5\) −1.50000 0.866025i −0.670820 0.387298i 0.125567 0.992085i \(-0.459925\pi\)
−0.796387 + 0.604787i \(0.793258\pi\)
\(6\) 1.73205 1.73205i 0.707107 0.707107i
\(7\) 1.73205 + 2.00000i 0.654654 + 0.755929i
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 0 0
\(10\) 0.633975 2.36603i 0.200480 0.748203i
\(11\) −0.866025 + 0.500000i −0.261116 + 0.150756i −0.624844 0.780750i \(-0.714837\pi\)
0.363727 + 0.931505i \(0.381504\pi\)
\(12\) 3.00000 + 1.73205i 0.866025 + 0.500000i
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) −2.09808 + 3.09808i −0.560734 + 0.827996i
\(15\) 3.00000i 0.774597i
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −1.50000 + 0.866025i −0.363803 + 0.210042i −0.670748 0.741685i \(-0.734027\pi\)
0.306944 + 0.951727i \(0.400693\pi\)
\(18\) 0 0
\(19\) 2.59808 4.50000i 0.596040 1.03237i −0.397360 0.917663i \(-0.630073\pi\)
0.993399 0.114708i \(-0.0365932\pi\)
\(20\) 3.46410 0.774597
\(21\) 1.50000 4.33013i 0.327327 0.944911i
\(22\) −1.00000 1.00000i −0.213201 0.213201i
\(23\) −0.866025 0.500000i −0.180579 0.104257i 0.406986 0.913434i \(-0.366580\pi\)
−0.587565 + 0.809177i \(0.699913\pi\)
\(24\) −1.26795 + 4.73205i −0.258819 + 0.965926i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) −4.73205 + 1.26795i −0.928032 + 0.248665i
\(27\) −5.19615 −1.00000
\(28\) −5.00000 1.73205i −0.944911 0.327327i
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) −4.09808 + 1.09808i −0.748203 + 0.200480i
\(31\) 0.866025 + 1.50000i 0.155543 + 0.269408i 0.933257 0.359211i \(-0.116954\pi\)
−0.777714 + 0.628619i \(0.783621\pi\)
\(32\) 5.46410 + 1.46410i 0.965926 + 0.258819i
\(33\) 1.50000 + 0.866025i 0.261116 + 0.150756i
\(34\) −1.73205 1.73205i −0.297044 0.297044i
\(35\) −0.866025 4.50000i −0.146385 0.760639i
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) 7.09808 + 1.90192i 1.15146 + 0.308533i
\(39\) 5.19615 3.00000i 0.832050 0.480384i
\(40\) 1.26795 + 4.73205i 0.200480 + 0.748203i
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) 6.46410 + 0.464102i 0.997433 + 0.0716124i
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) 0 0
\(46\) 0.366025 1.36603i 0.0539675 0.201409i
\(47\) −4.33013 + 7.50000i −0.631614 + 1.09399i 0.355608 + 0.934635i \(0.384274\pi\)
−0.987222 + 0.159352i \(0.949059\pi\)
\(48\) −6.92820 −1.00000
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) 2.00000 2.00000i 0.282843 0.282843i
\(51\) 2.59808 + 1.50000i 0.363803 + 0.210042i
\(52\) −3.46410 6.00000i −0.480384 0.832050i
\(53\) 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) −1.90192 7.09808i −0.258819 0.965926i
\(55\) 1.73205 0.233550
\(56\) 0.535898 7.46410i 0.0716124 0.997433i
\(57\) −9.00000 −1.19208
\(58\) 1.46410 + 5.46410i 0.192246 + 0.717472i
\(59\) 2.59808 + 4.50000i 0.338241 + 0.585850i 0.984102 0.177605i \(-0.0568349\pi\)
−0.645861 + 0.763455i \(0.723502\pi\)
\(60\) −3.00000 5.19615i −0.387298 0.670820i
\(61\) −4.50000 2.59808i −0.576166 0.332650i 0.183442 0.983030i \(-0.441276\pi\)
−0.759608 + 0.650381i \(0.774609\pi\)
\(62\) −1.73205 + 1.73205i −0.219971 + 0.219971i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) −0.633975 + 2.36603i −0.0780369 + 0.291238i
\(67\) −2.59808 + 1.50000i −0.317406 + 0.183254i −0.650236 0.759733i \(-0.725330\pi\)
0.332830 + 0.942987i \(0.391996\pi\)
\(68\) 1.73205 3.00000i 0.210042 0.363803i
\(69\) 1.73205i 0.208514i
\(70\) 5.83013 2.83013i 0.696833 0.338265i
\(71\) 14.0000i 1.66149i −0.556650 0.830747i \(-0.687914\pi\)
0.556650 0.830747i \(-0.312086\pi\)
\(72\) 0 0
\(73\) 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i \(-0.497494\pi\)
0.869935 + 0.493166i \(0.164160\pi\)
\(74\) −4.09808 1.09808i −0.476392 0.127649i
\(75\) −1.73205 + 3.00000i −0.200000 + 0.346410i
\(76\) 10.3923i 1.19208i
\(77\) −2.50000 0.866025i −0.284901 0.0986928i
\(78\) 6.00000 + 6.00000i 0.679366 + 0.679366i
\(79\) −7.79423 4.50000i −0.876919 0.506290i −0.00727784 0.999974i \(-0.502317\pi\)
−0.869641 + 0.493684i \(0.835650\pi\)
\(80\) −6.00000 + 3.46410i −0.670820 + 0.387298i
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) 4.73205 1.26795i 0.522568 0.140022i
\(83\) 13.8564 1.52094 0.760469 0.649374i \(-0.224969\pi\)
0.760469 + 0.649374i \(0.224969\pi\)
\(84\) 1.73205 + 9.00000i 0.188982 + 0.981981i
\(85\) 3.00000 0.325396
\(86\) −2.73205 + 0.732051i −0.294605 + 0.0789391i
\(87\) −3.46410 6.00000i −0.371391 0.643268i
\(88\) 2.73205 + 0.732051i 0.291238 + 0.0780369i
\(89\) 13.5000 + 7.79423i 1.43100 + 0.826187i 0.997197 0.0748225i \(-0.0238390\pi\)
0.433800 + 0.901009i \(0.357172\pi\)
\(90\) 0 0
\(91\) −6.92820 + 6.00000i −0.726273 + 0.628971i
\(92\) 2.00000 0.208514
\(93\) 1.50000 2.59808i 0.155543 0.269408i
\(94\) −11.8301 3.16987i −1.22018 0.326947i
\(95\) −7.79423 + 4.50000i −0.799671 + 0.461690i
\(96\) −2.53590 9.46410i −0.258819 0.965926i
\(97\) 17.3205i 1.75863i −0.476240 0.879316i \(-0.658000\pi\)
0.476240 0.879316i \(-0.342000\pi\)
\(98\) −9.83013 + 1.16987i −0.992993 + 0.118175i
\(99\) 0 0
\(100\) 3.46410 + 2.00000i 0.346410 + 0.200000i
\(101\) −7.50000 + 4.33013i −0.746278 + 0.430864i −0.824347 0.566084i \(-0.808458\pi\)
0.0780696 + 0.996948i \(0.475124\pi\)
\(102\) −1.09808 + 4.09808i −0.108726 + 0.405770i
\(103\) 4.33013 7.50000i 0.426660 0.738997i −0.569914 0.821705i \(-0.693023\pi\)
0.996574 + 0.0827075i \(0.0263567\pi\)
\(104\) 6.92820 6.92820i 0.679366 0.679366i
\(105\) −6.00000 + 5.19615i −0.585540 + 0.507093i
\(106\) −1.00000 + 1.00000i −0.0971286 + 0.0971286i
\(107\) 11.2583 + 6.50000i 1.08838 + 0.628379i 0.933146 0.359498i \(-0.117052\pi\)
0.155238 + 0.987877i \(0.450386\pi\)
\(108\) 9.00000 5.19615i 0.866025 0.500000i
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) 0.633975 + 2.36603i 0.0604471 + 0.225592i
\(111\) 5.19615 0.493197
\(112\) 10.3923 2.00000i 0.981981 0.188982i
\(113\) −16.0000 −1.50515 −0.752577 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) −3.29423 12.2942i −0.308533 1.15146i
\(115\) 0.866025 + 1.50000i 0.0807573 + 0.139876i
\(116\) −6.92820 + 4.00000i −0.643268 + 0.371391i
\(117\) 0 0
\(118\) −5.19615 + 5.19615i −0.478345 + 0.478345i
\(119\) −4.33013 1.50000i −0.396942 0.137505i
\(120\) 6.00000 6.00000i 0.547723 0.547723i
\(121\) −5.00000 + 8.66025i −0.454545 + 0.787296i
\(122\) 1.90192 7.09808i 0.172192 0.642630i
\(123\) −5.19615 + 3.00000i −0.468521 + 0.270501i
\(124\) −3.00000 1.73205i −0.269408 0.155543i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 6.00000i 0.532414i 0.963916 + 0.266207i \(0.0857705\pi\)
−0.963916 + 0.266207i \(0.914230\pi\)
\(128\) −10.9282 + 2.92820i −0.965926 + 0.258819i
\(129\) 3.00000 1.73205i 0.264135 0.152499i
\(130\) 8.19615 + 2.19615i 0.718850 + 0.192615i
\(131\) −2.59808 + 4.50000i −0.226995 + 0.393167i −0.956916 0.290365i \(-0.906223\pi\)
0.729921 + 0.683531i \(0.239557\pi\)
\(132\) −3.46410 −0.301511
\(133\) 13.5000 2.59808i 1.17060 0.225282i
\(134\) −3.00000 3.00000i −0.259161 0.259161i
\(135\) 7.79423 + 4.50000i 0.670820 + 0.387298i
\(136\) 4.73205 + 1.26795i 0.405770 + 0.108726i
\(137\) −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i \(-0.180268\pi\)
−0.886594 + 0.462549i \(0.846935\pi\)
\(138\) −2.36603 + 0.633975i −0.201409 + 0.0539675i
\(139\) −6.92820 −0.587643 −0.293821 0.955860i \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) 6.00000 + 6.92820i 0.507093 + 0.585540i
\(141\) 15.0000 1.26323
\(142\) 19.1244 5.12436i 1.60488 0.430026i
\(143\) −1.73205 3.00000i −0.144841 0.250873i
\(144\) 0 0
\(145\) −6.00000 3.46410i −0.498273 0.287678i
\(146\) 8.66025 + 8.66025i 0.716728 + 0.716728i
\(147\) 11.2583 4.50000i 0.928571 0.371154i
\(148\) 6.00000i 0.493197i
\(149\) −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i \(-0.846375\pi\)
0.844818 + 0.535054i \(0.179709\pi\)
\(150\) −4.73205 1.26795i −0.386370 0.103528i
\(151\) 6.06218 3.50000i 0.493333 0.284826i −0.232623 0.972567i \(-0.574731\pi\)
0.725956 + 0.687741i \(0.241398\pi\)
\(152\) −14.1962 + 3.80385i −1.15146 + 0.308533i
\(153\) 0 0
\(154\) 0.267949 3.73205i 0.0215920 0.300737i
\(155\) 3.00000i 0.240966i
\(156\) −6.00000 + 10.3923i −0.480384 + 0.832050i
\(157\) 1.50000 0.866025i 0.119713 0.0691164i −0.438948 0.898513i \(-0.644649\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 3.29423 12.2942i 0.262075 0.978076i
\(159\) 0.866025 1.50000i 0.0686803 0.118958i
\(160\) −6.92820 6.92820i −0.547723 0.547723i
\(161\) −0.500000 2.59808i −0.0394055 0.204757i
\(162\) −9.00000 + 9.00000i −0.707107 + 0.707107i
\(163\) −18.1865 10.5000i −1.42448 0.822423i −0.427802 0.903873i \(-0.640712\pi\)
−0.996678 + 0.0814491i \(0.974045\pi\)
\(164\) 3.46410 + 6.00000i 0.270501 + 0.468521i
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) 5.07180 + 18.9282i 0.393648 + 1.46911i
\(167\) −17.3205 −1.34030 −0.670151 0.742225i \(-0.733770\pi\)
−0.670151 + 0.742225i \(0.733770\pi\)
\(168\) −11.6603 + 5.66025i −0.899608 + 0.436698i
\(169\) 1.00000 0.0769231
\(170\) 1.09808 + 4.09808i 0.0842186 + 0.314308i
\(171\) 0 0
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) −10.5000 6.06218i −0.798300 0.460899i 0.0445762 0.999006i \(-0.485806\pi\)
−0.842876 + 0.538107i \(0.819140\pi\)
\(174\) 6.92820 6.92820i 0.525226 0.525226i
\(175\) 1.73205 5.00000i 0.130931 0.377964i
\(176\) 4.00000i 0.301511i
\(177\) 4.50000 7.79423i 0.338241 0.585850i
\(178\) −5.70577 + 21.2942i −0.427666 + 1.59607i
\(179\) 16.4545 9.50000i 1.22987 0.710063i 0.262864 0.964833i \(-0.415333\pi\)
0.967002 + 0.254770i \(0.0819996\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) −10.7321 7.26795i −0.795513 0.538736i
\(183\) 9.00000i 0.665299i
\(184\) 0.732051 + 2.73205i 0.0539675 + 0.201409i
\(185\) 4.50000 2.59808i 0.330847 0.191014i
\(186\) 4.09808 + 1.09808i 0.300486 + 0.0805149i
\(187\) 0.866025 1.50000i 0.0633300 0.109691i
\(188\) 17.3205i 1.26323i
\(189\) −9.00000 10.3923i −0.654654 0.755929i
\(190\) −9.00000 9.00000i −0.652929 0.652929i
\(191\) 0.866025 + 0.500000i 0.0626634 + 0.0361787i 0.531004 0.847369i \(-0.321815\pi\)
−0.468341 + 0.883548i \(0.655148\pi\)
\(192\) 12.0000 6.92820i 0.866025 0.500000i
\(193\) 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i \(0.0148568\pi\)
−0.459049 + 0.888411i \(0.651810\pi\)
\(194\) 23.6603 6.33975i 1.69871 0.455167i
\(195\) −10.3923 −0.744208
\(196\) −5.19615 13.0000i −0.371154 0.928571i
\(197\) 16.0000 1.13995 0.569976 0.821661i \(-0.306952\pi\)
0.569976 + 0.821661i \(0.306952\pi\)
\(198\) 0 0
\(199\) 11.2583 + 19.5000i 0.798082 + 1.38232i 0.920864 + 0.389885i \(0.127485\pi\)
−0.122782 + 0.992434i \(0.539182\pi\)
\(200\) −1.46410 + 5.46410i −0.103528 + 0.386370i
\(201\) 4.50000 + 2.59808i 0.317406 + 0.183254i
\(202\) −8.66025 8.66025i −0.609333 0.609333i
\(203\) 6.92820 + 8.00000i 0.486265 + 0.561490i
\(204\) −6.00000 −0.420084
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) 11.8301 + 3.16987i 0.824244 + 0.220856i
\(207\) 0 0
\(208\) 12.0000 + 6.92820i 0.832050 + 0.480384i
\(209\) 5.19615i 0.359425i
\(210\) −9.29423 6.29423i −0.641363 0.434343i
\(211\) 10.0000i 0.688428i 0.938891 + 0.344214i \(0.111855\pi\)
−0.938891 + 0.344214i \(0.888145\pi\)
\(212\) −1.73205 1.00000i −0.118958 0.0686803i
\(213\) −21.0000 + 12.1244i −1.43890 + 0.830747i
\(214\) −4.75833 + 17.7583i −0.325273 + 1.21393i
\(215\) 1.73205 3.00000i 0.118125 0.204598i
\(216\) 10.3923 + 10.3923i 0.707107 + 0.707107i
\(217\) −1.50000 + 4.33013i −0.101827 + 0.293948i
\(218\) 9.00000 9.00000i 0.609557 0.609557i
\(219\) −12.9904 7.50000i −0.877809 0.506803i
\(220\) −3.00000 + 1.73205i −0.202260 + 0.116775i
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) 1.90192 + 7.09808i 0.127649 + 0.476392i
\(223\) 6.92820 0.463947 0.231973 0.972722i \(-0.425482\pi\)
0.231973 + 0.972722i \(0.425482\pi\)
\(224\) 6.53590 + 13.4641i 0.436698 + 0.899608i
\(225\) 0 0
\(226\) −5.85641 21.8564i −0.389562 1.45387i
\(227\) −9.52628 16.5000i −0.632281 1.09514i −0.987084 0.160202i \(-0.948785\pi\)
0.354803 0.934941i \(-0.384548\pi\)
\(228\) 15.5885 9.00000i 1.03237 0.596040i
\(229\) −13.5000 7.79423i −0.892105 0.515057i −0.0174746 0.999847i \(-0.505563\pi\)
−0.874630 + 0.484790i \(0.838896\pi\)
\(230\) −1.73205 + 1.73205i −0.114208 + 0.114208i
\(231\) 0.866025 + 4.50000i 0.0569803 + 0.296078i
\(232\) −8.00000 8.00000i −0.525226 0.525226i
\(233\) 3.50000 6.06218i 0.229293 0.397146i −0.728306 0.685252i \(-0.759692\pi\)
0.957599 + 0.288106i \(0.0930254\pi\)
\(234\) 0 0
\(235\) 12.9904 7.50000i 0.847399 0.489246i
\(236\) −9.00000 5.19615i −0.585850 0.338241i
\(237\) 15.5885i 1.01258i
\(238\) 0.464102 6.46410i 0.0300832 0.419005i
\(239\) 20.0000i 1.29369i 0.762620 + 0.646846i \(0.223912\pi\)
−0.762620 + 0.646846i \(0.776088\pi\)
\(240\) 10.3923 + 6.00000i 0.670820 + 0.387298i
\(241\) −4.50000 + 2.59808i −0.289870 + 0.167357i −0.637883 0.770133i \(-0.720190\pi\)
0.348013 + 0.937490i \(0.386857\pi\)
\(242\) −13.6603 3.66025i −0.878114 0.235290i
\(243\) 0 0
\(244\) 10.3923 0.665299
\(245\) 7.50000 9.52628i 0.479157 0.608612i
\(246\) −6.00000 6.00000i −0.382546 0.382546i
\(247\) 15.5885 + 9.00000i 0.991870 + 0.572656i
\(248\) 1.26795 4.73205i 0.0805149 0.300486i
\(249\) −12.0000 20.7846i −0.760469 1.31717i
\(250\) −16.5622 + 4.43782i −1.04748 + 0.280673i
\(251\) −3.46410 −0.218652 −0.109326 0.994006i \(-0.534869\pi\)
−0.109326 + 0.994006i \(0.534869\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) −8.19615 + 2.19615i −0.514272 + 0.137799i
\(255\) −2.59808 4.50000i −0.162698 0.281801i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 4.50000 + 2.59808i 0.280702 + 0.162064i 0.633741 0.773545i \(-0.281518\pi\)
−0.353039 + 0.935609i \(0.614852\pi\)
\(258\) 3.46410 + 3.46410i 0.215666 + 0.215666i
\(259\) −7.79423 + 1.50000i −0.484310 + 0.0932055i
\(260\) 12.0000i 0.744208i
\(261\) 0 0
\(262\) −7.09808 1.90192i −0.438521 0.117501i
\(263\) −19.9186 + 11.5000i −1.22823 + 0.709120i −0.966660 0.256063i \(-0.917574\pi\)
−0.261573 + 0.965184i \(0.584241\pi\)
\(264\) −1.26795 4.73205i −0.0780369 0.291238i
\(265\) 1.73205i 0.106399i
\(266\) 8.49038 + 17.4904i 0.520579 + 1.07240i
\(267\) 27.0000i 1.65237i
\(268\) 3.00000 5.19615i 0.183254 0.317406i
\(269\) 19.5000 11.2583i 1.18894 0.686433i 0.230871 0.972984i \(-0.425842\pi\)
0.958065 + 0.286552i \(0.0925091\pi\)
\(270\) −3.29423 + 12.2942i −0.200480 + 0.748203i
\(271\) 7.79423 13.5000i 0.473466 0.820067i −0.526073 0.850439i \(-0.676336\pi\)
0.999539 + 0.0303728i \(0.00966946\pi\)
\(272\) 6.92820i 0.420084i
\(273\) 15.0000 + 5.19615i 0.907841 + 0.314485i
\(274\) 1.00000 1.00000i 0.0604122 0.0604122i
\(275\) 1.73205 + 1.00000i 0.104447 + 0.0603023i
\(276\) −1.73205 3.00000i −0.104257 0.180579i
\(277\) 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i \(-0.0389525\pi\)
−0.601975 + 0.798515i \(0.705619\pi\)
\(278\) −2.53590 9.46410i −0.152093 0.567619i
\(279\) 0 0
\(280\) −7.26795 + 10.7321i −0.434343 + 0.641363i
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 5.49038 + 20.4904i 0.326947 + 1.22018i
\(283\) −6.06218 10.5000i −0.360359 0.624160i 0.627661 0.778487i \(-0.284012\pi\)
−0.988020 + 0.154327i \(0.950679\pi\)
\(284\) 14.0000 + 24.2487i 0.830747 + 1.43890i
\(285\) 13.5000 + 7.79423i 0.799671 + 0.461690i
\(286\) 3.46410 3.46410i 0.204837 0.204837i
\(287\) 6.92820 6.00000i 0.408959 0.354169i
\(288\) 0 0
\(289\) −7.00000 + 12.1244i −0.411765 + 0.713197i
\(290\) 2.53590 9.46410i 0.148913 0.555751i
\(291\) −25.9808 + 15.0000i −1.52302 + 0.879316i
\(292\) −8.66025 + 15.0000i −0.506803 + 0.877809i
\(293\) 20.7846i 1.21425i −0.794606 0.607125i \(-0.792323\pi\)
0.794606 0.607125i \(-0.207677\pi\)
\(294\) 10.2679 + 13.7321i 0.598839 + 0.800869i
\(295\) 9.00000i 0.524000i
\(296\) 8.19615 2.19615i 0.476392 0.127649i
\(297\) 4.50000 2.59808i 0.261116 0.150756i
\(298\) −1.36603 0.366025i −0.0791317 0.0212033i
\(299\) 1.73205 3.00000i 0.100167 0.173494i
\(300\) 6.92820i 0.400000i
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) 7.00000 + 7.00000i 0.402805 + 0.402805i
\(303\) 12.9904 + 7.50000i 0.746278 + 0.430864i
\(304\) −10.3923 18.0000i −0.596040 1.03237i
\(305\) 4.50000 + 7.79423i 0.257669 + 0.446296i
\(306\) 0 0
\(307\) 20.7846 1.18624 0.593120 0.805114i \(-0.297896\pi\)
0.593120 + 0.805114i \(0.297896\pi\)
\(308\) 5.19615 1.00000i 0.296078 0.0569803i
\(309\) −15.0000 −0.853320
\(310\) 4.09808 1.09808i 0.232755 0.0623665i
\(311\) −4.33013 7.50000i −0.245539 0.425286i 0.716744 0.697336i \(-0.245632\pi\)
−0.962283 + 0.272050i \(0.912298\pi\)
\(312\) −16.3923 4.39230i −0.928032 0.248665i
\(313\) 1.50000 + 0.866025i 0.0847850 + 0.0489506i 0.541793 0.840512i \(-0.317746\pi\)
−0.457008 + 0.889463i \(0.651079\pi\)
\(314\) 1.73205 + 1.73205i 0.0977453 + 0.0977453i
\(315\) 0 0
\(316\) 18.0000 1.01258
\(317\) −5.50000 + 9.52628i −0.308911 + 0.535049i −0.978124 0.208021i \(-0.933298\pi\)
0.669214 + 0.743070i \(0.266631\pi\)
\(318\) 2.36603 + 0.633975i 0.132680 + 0.0355515i
\(319\) −3.46410 + 2.00000i −0.193952 + 0.111979i
\(320\) 6.92820 12.0000i 0.387298 0.670820i
\(321\) 22.5167i 1.25676i
\(322\) 3.36603 1.63397i 0.187581 0.0910578i
\(323\) 9.00000i 0.500773i
\(324\) −15.5885 9.00000i −0.866025 0.500000i
\(325\) 6.00000 3.46410i 0.332820 0.192154i
\(326\) 7.68653 28.6865i 0.425718 1.58880i
\(327\) −7.79423 + 13.5000i −0.431022 + 0.746552i
\(328\) −6.92820 + 6.92820i −0.382546 + 0.382546i
\(329\) −22.5000 + 4.33013i −1.24047 + 0.238728i
\(330\) 3.00000 3.00000i 0.165145 0.165145i
\(331\) 6.06218 + 3.50000i 0.333207 + 0.192377i 0.657264 0.753660i \(-0.271714\pi\)
−0.324057 + 0.946038i \(0.605047\pi\)
\(332\) −24.0000 + 13.8564i −1.31717 + 0.760469i
\(333\) 0 0
\(334\) −6.33975 23.6603i −0.346895 1.29463i
\(335\) 5.19615 0.283896
\(336\) −12.0000 13.8564i −0.654654 0.755929i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0.366025 + 1.36603i 0.0199092 + 0.0743020i
\(339\) 13.8564 + 24.0000i 0.752577 + 1.30350i
\(340\) −5.19615 + 3.00000i −0.281801 + 0.162698i
\(341\) −1.50000 0.866025i −0.0812296 0.0468979i
\(342\) 0 0
\(343\) −15.5885 + 10.0000i −0.841698 + 0.539949i
\(344\) 4.00000 4.00000i 0.215666 0.215666i
\(345\) 1.50000 2.59808i 0.0807573 0.139876i
\(346\) 4.43782 16.5622i 0.238579 0.890388i
\(347\) 11.2583 6.50000i 0.604379 0.348938i −0.166383 0.986061i \(-0.553209\pi\)
0.770762 + 0.637123i \(0.219876\pi\)
\(348\) 12.0000 + 6.92820i 0.643268 + 0.371391i
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) 7.46410 + 0.535898i 0.398973 + 0.0286450i
\(351\) 18.0000i 0.960769i
\(352\) −5.46410 + 1.46410i −0.291238 + 0.0780369i
\(353\) −25.5000 + 14.7224i −1.35723 + 0.783596i −0.989249 0.146238i \(-0.953283\pi\)
−0.367979 + 0.929834i \(0.619950\pi\)
\(354\) 12.2942 + 3.29423i 0.653431 + 0.175086i
\(355\) −12.1244 + 21.0000i −0.643494 + 1.11456i
\(356\) −31.1769 −1.65237
\(357\) 1.50000 + 7.79423i 0.0793884 + 0.412514i
\(358\) 19.0000 + 19.0000i 1.00418 + 1.00418i
\(359\) −19.9186 11.5000i −1.05126 0.606947i −0.128260 0.991741i \(-0.540939\pi\)
−0.923003 + 0.384794i \(0.874273\pi\)
\(360\) 0 0
\(361\) −4.00000 6.92820i −0.210526 0.364642i
\(362\) −9.46410 + 2.53590i −0.497422 + 0.133284i
\(363\) 17.3205 0.909091
\(364\) 6.00000 17.3205i 0.314485 0.907841i
\(365\) −15.0000 −0.785136
\(366\) −12.2942 + 3.29423i −0.642630 + 0.172192i
\(367\) −0.866025 1.50000i −0.0452062 0.0782994i 0.842537 0.538639i \(-0.181061\pi\)
−0.887743 + 0.460339i \(0.847728\pi\)
\(368\) −3.46410 + 2.00000i −0.180579 + 0.104257i
\(369\) 0 0
\(370\) 5.19615 + 5.19615i 0.270135 + 0.270135i
\(371\) −0.866025 + 2.50000i −0.0449618 + 0.129794i
\(372\) 6.00000i 0.311086i
\(373\) 14.5000 25.1147i 0.750782 1.30039i −0.196663 0.980471i \(-0.563010\pi\)
0.947444 0.319921i \(-0.103656\pi\)
\(374\) 2.36603 + 0.633975i 0.122344 + 0.0327820i
\(375\) 18.1865 10.5000i 0.939149 0.542218i
\(376\) 23.6603 6.33975i 1.22018 0.326947i
\(377\) 13.8564i 0.713641i
\(378\) 10.9019 16.0981i 0.560734 0.827996i
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) 9.00000 15.5885i 0.461690 0.799671i
\(381\) 9.00000 5.19615i 0.461084 0.266207i
\(382\) −0.366025 + 1.36603i −0.0187275 + 0.0698919i
\(383\) 2.59808 4.50000i 0.132755 0.229939i −0.791982 0.610544i \(-0.790951\pi\)
0.924738 + 0.380605i \(0.124284\pi\)
\(384\) 13.8564 + 13.8564i 0.707107 + 0.707107i
\(385\) 3.00000 + 3.46410i 0.152894 + 0.176547i
\(386\) −15.0000 + 15.0000i −0.763480 + 0.763480i
\(387\) 0 0
\(388\) 17.3205 + 30.0000i 0.879316 + 1.52302i
\(389\) 9.50000 + 16.4545i 0.481669 + 0.834275i 0.999779 0.0210389i \(-0.00669738\pi\)
−0.518110 + 0.855314i \(0.673364\pi\)
\(390\) −3.80385 14.1962i −0.192615 0.718850i
\(391\) 1.73205 0.0875936
\(392\) 15.8564 11.8564i 0.800869 0.598839i
\(393\) 9.00000 0.453990
\(394\) 5.85641 + 21.8564i 0.295041 + 1.10111i
\(395\) 7.79423 + 13.5000i 0.392170 + 0.679259i
\(396\) 0 0
\(397\) 16.5000 + 9.52628i 0.828111 + 0.478110i 0.853206 0.521575i \(-0.174655\pi\)
−0.0250943 + 0.999685i \(0.507989\pi\)
\(398\) −22.5167 + 22.5167i −1.12866 + 1.12866i
\(399\) −15.5885 18.0000i −0.780399 0.901127i
\(400\) −8.00000 −0.400000
\(401\) 11.5000 19.9186i 0.574283 0.994687i −0.421837 0.906672i \(-0.638614\pi\)
0.996119 0.0880147i \(-0.0280523\pi\)
\(402\) −1.90192 + 7.09808i −0.0948593 + 0.354020i
\(403\) −5.19615 + 3.00000i −0.258839 + 0.149441i
\(404\) 8.66025 15.0000i 0.430864 0.746278i
\(405\) 15.5885i 0.774597i
\(406\) −8.39230 + 12.3923i −0.416503 + 0.615020i
\(407\) 3.00000i 0.148704i
\(408\) −2.19615 8.19615i −0.108726 0.405770i
\(409\) 22.5000 12.9904i 1.11255 0.642333i 0.173064 0.984911i \(-0.444633\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) −8.19615 2.19615i −0.404779 0.108460i
\(411\) −0.866025 + 1.50000i −0.0427179 + 0.0739895i
\(412\) 17.3205i 0.853320i
\(413\) −4.50000 + 12.9904i −0.221431 + 0.639215i
\(414\) 0 0
\(415\) −20.7846 12.0000i −1.02028 0.589057i
\(416\) −5.07180 + 18.9282i −0.248665 + 0.928032i
\(417\) 6.00000 + 10.3923i 0.293821 + 0.508913i
\(418\) −7.09808 + 1.90192i −0.347178 + 0.0930261i
\(419\) −20.7846 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(420\) 5.19615 15.0000i 0.253546 0.731925i
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −13.6603 + 3.66025i −0.664971 + 0.178178i
\(423\) 0 0
\(424\) 0.732051 2.73205i 0.0355515 0.132680i
\(425\) 3.00000 + 1.73205i 0.145521 + 0.0840168i
\(426\) −24.2487 24.2487i −1.17485 1.17485i
\(427\) −2.59808 13.5000i −0.125730 0.653311i
\(428\) −26.0000 −1.25676
\(429\) −3.00000 + 5.19615i −0.144841 + 0.250873i
\(430\) 4.73205 + 1.26795i 0.228200 + 0.0611459i
\(431\) 19.9186 11.5000i 0.959444 0.553936i 0.0634424 0.997985i \(-0.479792\pi\)
0.896002 + 0.444050i \(0.146459\pi\)
\(432\) −10.3923 + 18.0000i −0.500000 + 0.866025i
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) −6.46410 0.464102i −0.310287 0.0222776i
\(435\) 12.0000i 0.575356i
\(436\) 15.5885 + 9.00000i 0.746552 + 0.431022i
\(437\) −4.50000 + 2.59808i −0.215264 + 0.124283i
\(438\) 5.49038 20.4904i 0.262341 0.979068i
\(439\) −11.2583 + 19.5000i −0.537331 + 0.930684i 0.461716 + 0.887028i \(0.347234\pi\)
−0.999047 + 0.0436563i \(0.986099\pi\)
\(440\) −3.46410 3.46410i −0.165145 0.165145i
\(441\) 0 0
\(442\) 6.00000 6.00000i 0.285391 0.285391i
\(443\) 14.7224 + 8.50000i 0.699484 + 0.403847i 0.807155 0.590339i \(-0.201006\pi\)
−0.107671 + 0.994187i \(0.534339\pi\)
\(444\) −9.00000 + 5.19615i −0.427121 + 0.246598i
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) 2.53590 + 9.46410i 0.120078 + 0.448138i
\(447\) 1.73205 0.0819232
\(448\) −16.0000 + 13.8564i −0.755929 + 0.654654i
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) 0 0
\(451\) 1.73205 + 3.00000i 0.0815591 + 0.141264i
\(452\) 27.7128 16.0000i 1.30350 0.752577i
\(453\) −10.5000 6.06218i −0.493333 0.284826i
\(454\) 19.0526 19.0526i 0.894181 0.894181i
\(455\) 15.5885 3.00000i 0.730798 0.140642i
\(456\) 18.0000 + 18.0000i 0.842927 + 0.842927i
\(457\) −7.50000 + 12.9904i −0.350835 + 0.607664i −0.986396 0.164386i \(-0.947436\pi\)
0.635561 + 0.772051i \(0.280769\pi\)
\(458\) 5.70577 21.2942i 0.266613 0.995014i
\(459\) 7.79423 4.50000i 0.363803 0.210042i
\(460\) −3.00000 1.73205i −0.139876 0.0807573i
\(461\) 17.3205i 0.806696i −0.915047 0.403348i \(-0.867846\pi\)
0.915047 0.403348i \(-0.132154\pi\)
\(462\) −5.83013 + 2.83013i −0.271242 + 0.131669i
\(463\) 30.0000i 1.39422i −0.716965 0.697109i \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) 8.00000 13.8564i 0.371391 0.643268i
\(465\) −4.50000 + 2.59808i −0.208683 + 0.120483i
\(466\) 9.56218 + 2.56218i 0.442959 + 0.118691i
\(467\) 4.33013 7.50000i 0.200374 0.347059i −0.748275 0.663389i \(-0.769117\pi\)
0.948649 + 0.316330i \(0.102451\pi\)
\(468\) 0 0
\(469\) −7.50000 2.59808i −0.346318 0.119968i
\(470\) 15.0000 + 15.0000i 0.691898 + 0.691898i
\(471\) −2.59808 1.50000i −0.119713 0.0691164i
\(472\) 3.80385 14.1962i 0.175086 0.653431i
\(473\) −1.00000 1.73205i −0.0459800 0.0796398i
\(474\) −21.2942 + 5.70577i −0.978076 + 0.262075i
\(475\) −10.3923 −0.476832
\(476\) 9.00000 1.73205i 0.412514 0.0793884i
\(477\) 0 0
\(478\) −27.3205 + 7.32051i −1.24961 + 0.334832i
\(479\) 6.06218 + 10.5000i 0.276988 + 0.479757i 0.970635 0.240558i \(-0.0773304\pi\)
−0.693647 + 0.720315i \(0.743997\pi\)
\(480\) −4.39230 + 16.3923i −0.200480 + 0.748203i
\(481\) −9.00000 5.19615i −0.410365 0.236924i
\(482\) −5.19615 5.19615i −0.236678 0.236678i
\(483\) −3.46410 + 3.00000i −0.157622 + 0.136505i
\(484\) 20.0000i 0.909091i
\(485\) −15.0000 + 25.9808i −0.681115 + 1.17973i
\(486\) 0 0
\(487\) −26.8468 + 15.5000i −1.21654 + 0.702372i −0.964177 0.265260i \(-0.914542\pi\)
−0.252367 + 0.967632i \(0.581209\pi\)
\(488\) 3.80385 + 14.1962i 0.172192 + 0.642630i
\(489\) 36.3731i 1.64485i
\(490\) 15.7583 + 6.75833i 0.711889 + 0.305310i
\(491\) 32.0000i 1.44414i 0.691820 + 0.722070i \(0.256809\pi\)
−0.691820 + 0.722070i \(0.743191\pi\)
\(492\) 6.00000 10.3923i 0.270501 0.468521i
\(493\) −6.00000 + 3.46410i −0.270226 + 0.156015i
\(494\) −6.58846 + 24.5885i −0.296429 + 1.10629i
\(495\) 0 0
\(496\) 6.92820 0.311086
\(497\) 28.0000 24.2487i 1.25597 1.08770i
\(498\) 24.0000 24.0000i 1.07547 1.07547i
\(499\) 30.3109 + 17.5000i 1.35690 + 0.783408i 0.989205 0.146538i \(-0.0468131\pi\)
0.367697 + 0.929946i \(0.380146\pi\)
\(500\) −12.1244 21.0000i −0.542218 0.939149i
\(501\) 15.0000 + 25.9808i 0.670151 + 1.16073i
\(502\) −1.26795 4.73205i −0.0565913 0.211202i
\(503\) −6.92820 −0.308913 −0.154457 0.988000i \(-0.549363\pi\)
−0.154457 + 0.988000i \(0.549363\pi\)
\(504\) 0 0
\(505\) 15.0000 0.667491
\(506\) 0.366025 + 1.36603i 0.0162718 + 0.0607272i
\(507\) −0.866025 1.50000i −0.0384615 0.0666173i
\(508\) −6.00000 10.3923i −0.266207 0.461084i
\(509\) 10.5000 + 6.06218i 0.465404 + 0.268701i 0.714314 0.699825i \(-0.246739\pi\)
−0.248910 + 0.968527i \(0.580072\pi\)
\(510\) 5.19615 5.19615i 0.230089 0.230089i
\(511\) 21.6506 + 7.50000i 0.957768 + 0.331780i
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) −13.5000 + 23.3827i −0.596040 + 1.03237i
\(514\) −1.90192 + 7.09808i −0.0838903 + 0.313083i
\(515\) −12.9904 + 7.50000i −0.572425 + 0.330489i
\(516\) −3.46410 + 6.00000i −0.152499 + 0.264135i
\(517\) 8.66025i 0.380878i
\(518\) −4.90192 10.0981i −0.215378 0.443684i
\(519\) 21.0000i 0.921798i
\(520\) −16.3923 + 4.39230i −0.718850 + 0.192615i
\(521\) 1.50000 0.866025i 0.0657162 0.0379413i −0.466782 0.884372i \(-0.654587\pi\)
0.532498 + 0.846431i \(0.321253\pi\)
\(522\) 0 0
\(523\) 12.9904 22.5000i 0.568030 0.983856i −0.428731 0.903432i \(-0.641039\pi\)
0.996761 0.0804241i \(-0.0256275\pi\)
\(524\) 10.3923i 0.453990i
\(525\) −9.00000 + 1.73205i −0.392792 + 0.0755929i
\(526\) −23.0000 23.0000i −1.00285 1.00285i
\(527\) −2.59808 1.50000i −0.113174 0.0653410i
\(528\) 6.00000 3.46410i 0.261116 0.150756i
\(529\) −11.0000 19.0526i −0.478261 0.828372i
\(530\) 2.36603 0.633975i 0.102774 0.0275381i
\(531\) 0 0
\(532\) −20.7846 + 18.0000i −0.901127 + 0.780399i
\(533\) 12.0000 0.519778
\(534\) 36.8827 9.88269i 1.59607 0.427666i
\(535\) −11.2583 19.5000i −0.486740 0.843059i
\(536\) 8.19615 + 2.19615i 0.354020 + 0.0948593i
\(537\) −28.5000 16.4545i −1.22987 0.710063i
\(538\) 22.5167 + 22.5167i 0.970762 + 0.970762i
\(539\) −2.59808 6.50000i −0.111907 0.279975i
\(540\) −18.0000 −0.774597
\(541\) 9.50000 16.4545i 0.408437 0.707433i −0.586278 0.810110i \(-0.699407\pi\)
0.994715 + 0.102677i \(0.0327407\pi\)
\(542\) 21.2942 + 5.70577i 0.914665 + 0.245084i
\(543\) 10.3923 6.00000i 0.445976 0.257485i
\(544\) −9.46410 + 2.53590i −0.405770 + 0.108726i
\(545\) 15.5885i 0.667736i
\(546\) −1.60770 + 22.3923i −0.0688030 + 0.958302i
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 1.73205 + 1.00000i 0.0739895 + 0.0427179i
\(549\) 0 0
\(550\) −0.732051 + 2.73205i −0.0312148 + 0.116495i
\(551\) 10.3923 18.0000i 0.442727 0.766826i
\(552\) 3.46410 3.46410i 0.147442 0.147442i
\(553\) −4.50000 23.3827i −0.191359 0.994333i
\(554\) −13.0000 + 13.0000i −0.552317 + 0.552317i
\(555\) −7.79423 4.50000i −0.330847 0.191014i
\(556\) 12.0000 6.92820i 0.508913 0.293821i
\(557\) −18.5000 32.0429i −0.783870 1.35770i −0.929672 0.368389i \(-0.879909\pi\)
0.145802 0.989314i \(-0.453424\pi\)
\(558\) 0 0
\(559\) −6.92820 −0.293032
\(560\) −17.3205 6.00000i −0.731925 0.253546i
\(561\) −3.00000 −0.126660
\(562\) −1.46410 5.46410i −0.0617594 0.230489i
\(563\) −11.2583 19.5000i −0.474482 0.821827i 0.525091 0.851046i \(-0.324031\pi\)
−0.999573 + 0.0292191i \(0.990698\pi\)
\(564\) −25.9808 + 15.0000i −1.09399 + 0.631614i
\(565\) 24.0000 + 13.8564i 1.00969 + 0.582943i
\(566\) 12.1244 12.1244i 0.509625 0.509625i
\(567\) −7.79423 + 22.5000i −0.327327 + 0.944911i
\(568\) −28.0000 + 28.0000i −1.17485 + 1.17485i
\(569\) 6.50000 11.2583i 0.272494 0.471974i −0.697006 0.717066i \(-0.745485\pi\)
0.969500 + 0.245092i \(0.0788181\pi\)
\(570\) −5.70577 + 21.2942i −0.238988 + 0.891917i
\(571\) −18.1865 + 10.5000i −0.761083 + 0.439411i −0.829684 0.558233i \(-0.811480\pi\)
0.0686016 + 0.997644i \(0.478146\pi\)
\(572\) 6.00000 + 3.46410i 0.250873 + 0.144841i
\(573\) 1.73205i 0.0723575i
\(574\) 10.7321 + 7.26795i 0.447947 + 0.303358i
\(575\) 2.00000i 0.0834058i
\(576\) 0 0
\(577\) −28.5000 + 16.4545i −1.18647 + 0.685009i −0.957503 0.288425i \(-0.906868\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) −19.1244 5.12436i −0.795468 0.213145i
\(579\) 12.9904 22.5000i 0.539862 0.935068i
\(580\) 13.8564 0.575356
\(581\) 24.0000 + 27.7128i 0.995688 + 1.14972i
\(582\) −30.0000 30.0000i −1.24354 1.24354i
\(583\) −0.866025 0.500000i −0.0358671 0.0207079i
\(584\) −23.6603 6.33975i −0.979068 0.262341i
\(585\) 0 0
\(586\) 28.3923 7.60770i 1.17288 0.314271i
\(587\) 6.92820 0.285958 0.142979 0.989726i \(-0.454332\pi\)
0.142979 + 0.989726i \(0.454332\pi\)
\(588\) −15.0000 + 19.0526i −0.618590 + 0.785714i
\(589\) 9.00000 0.370839
\(590\) 12.2942 3.29423i 0.506145 0.135621i
\(591\) −13.8564 24.0000i −0.569976 0.987228i
\(592\) 6.00000 + 10.3923i 0.246598 + 0.427121i
\(593\) −13.5000 7.79423i −0.554379 0.320071i 0.196508 0.980502i \(-0.437040\pi\)
−0.750886 + 0.660432i \(0.770373\pi\)
\(594\) 5.19615 + 5.19615i 0.213201 + 0.213201i
\(595\) 5.19615 + 6.00000i 0.213021 + 0.245976i
\(596\) 2.00000i 0.0819232i
\(597\) 19.5000 33.7750i 0.798082 1.38232i
\(598\) 4.73205 + 1.26795i 0.193508 + 0.0518503i
\(599\) 14.7224 8.50000i 0.601542 0.347301i −0.168106 0.985769i \(-0.553765\pi\)
0.769648 + 0.638468i \(0.220432\pi\)
\(600\) 9.46410 2.53590i 0.386370 0.103528i
\(601\) 38.1051i 1.55434i 0.629291 + 0.777170i \(0.283346\pi\)
−0.629291 + 0.777170i \(0.716654\pi\)
\(602\) −6.19615 4.19615i −0.252536 0.171022i
\(603\) 0 0
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) 15.0000 8.66025i 0.609837 0.352089i
\(606\) −5.49038 + 20.4904i −0.223031 + 0.832365i
\(607\) −7.79423 + 13.5000i −0.316358 + 0.547948i −0.979725 0.200346i \(-0.935793\pi\)
0.663367 + 0.748294i \(0.269127\pi\)
\(608\) 20.7846 20.7846i 0.842927 0.842927i
\(609\) 6.00000 17.3205i 0.243132 0.701862i
\(610\) −9.00000 + 9.00000i −0.364399 + 0.364399i
\(611\) −25.9808 15.0000i −1.05107 0.606835i
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) 7.60770 + 28.3923i 0.307022 + 1.14582i
\(615\) 10.3923 0.419058
\(616\) 3.26795 + 6.73205i 0.131669 + 0.271242i
\(617\) 20.0000 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(618\) −5.49038 20.4904i −0.220856 0.824244i
\(619\) −7.79423 13.5000i −0.313276 0.542611i 0.665793 0.746136i \(-0.268093\pi\)
−0.979070 + 0.203526i \(0.934760\pi\)
\(620\) 3.00000 + 5.19615i 0.120483 + 0.208683i
\(621\) 4.50000 + 2.59808i 0.180579 + 0.104257i
\(622\) 8.66025 8.66025i 0.347245 0.347245i
\(623\) 7.79423 + 40.5000i 0.312269 + 1.62260i
\(624\) 24.0000i 0.960769i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) −0.633975 + 2.36603i −0.0253387 + 0.0945654i
\(627\) 7.79423 4.50000i 0.311272 0.179713i
\(628\) −1.73205 + 3.00000i −0.0691164 + 0.119713i
\(629\) 5.19615i 0.207184i
\(630\) 0 0
\(631\) 30.0000i 1.19428i 0.802137 + 0.597141i \(0.203697\pi\)
−0.802137 + 0.597141i \(0.796303\pi\)
\(632\) 6.58846 + 24.5885i 0.262075 + 0.978076i
\(633\) 15.0000 8.66025i 0.596196 0.344214i
\(634\) −15.0263 4.02628i −0.596770 0.159904i
\(635\) 5.19615 9.00000i 0.206203 0.357154i
\(636\) 3.46410i 0.137361i
\(637\) −24.0000 3.46410i −0.950915 0.137253i
\(638\) −4.00000 4.00000i −0.158362 0.158362i
\(639\) 0 0
\(640\) 18.9282 + 5.07180i 0.748203 + 0.200480i
\(641\) 6.50000 + 11.2583i 0.256735 + 0.444677i 0.965365 0.260902i \(-0.0840201\pi\)
−0.708631 + 0.705580i \(0.750687\pi\)
\(642\) 30.7583 8.24167i 1.21393 0.325273i
\(643\) −13.8564 −0.546443 −0.273222 0.961951i \(-0.588089\pi\)
−0.273222 + 0.961951i \(0.588089\pi\)
\(644\) 3.46410 + 4.00000i 0.136505 + 0.157622i
\(645\) −6.00000 −0.236250
\(646\) −12.2942 + 3.29423i −0.483710 + 0.129610i
\(647\) 16.4545 + 28.5000i 0.646892 + 1.12045i 0.983861 + 0.178935i \(0.0572651\pi\)
−0.336968 + 0.941516i \(0.609402\pi\)
\(648\) 6.58846 24.5885i 0.258819 0.965926i
\(649\) −4.50000 2.59808i −0.176640 0.101983i
\(650\) 6.92820 + 6.92820i 0.271746 + 0.271746i
\(651\) 7.79423 1.50000i 0.305480 0.0587896i
\(652\) 42.0000 1.64485
\(653\) −15.5000 + 26.8468i −0.606562 + 1.05060i 0.385241 + 0.922816i \(0.374118\pi\)
−0.991803 + 0.127780i \(0.959215\pi\)
\(654\) −21.2942 5.70577i −0.832670 0.223113i
\(655\) 7.79423 4.50000i 0.304546 0.175830i
\(656\) −12.0000 6.92820i −0.468521 0.270501i
\(657\) 0 0
\(658\) −14.1506 29.1506i −0.551649 1.13641i
\(659\) 38.0000i 1.48027i −0.672458 0.740135i \(-0.734762\pi\)
0.672458 0.740135i \(-0.265238\pi\)
\(660\) 5.19615 + 3.00000i 0.202260 + 0.116775i
\(661\) −34.5000 + 19.9186i −1.34189 + 0.774743i −0.987085 0.160196i \(-0.948788\pi\)
−0.354809 + 0.934939i \(0.615454\pi\)
\(662\) −2.56218 + 9.56218i −0.0995819 + 0.371645i
\(663\) −5.19615 + 9.00000i −0.201802 + 0.349531i
\(664\) −27.7128 27.7128i −1.07547 1.07547i
\(665\) −22.5000 7.79423i −0.872513 0.302247i
\(666\) 0 0
\(667\) −3.46410 2.00000i −0.134131 0.0774403i
\(668\) 30.0000 17.3205i 1.16073 0.670151i
\(669\) −6.00000 10.3923i −0.231973 0.401790i
\(670\) 1.90192 + 7.09808i 0.0734777 + 0.274223i
\(671\) 5.19615 0.200595
\(672\) 14.5359 21.4641i 0.560734 0.827996i
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) 5.19615 + 9.00000i 0.200000 + 0.346410i
\(676\) −1.73205 + 1.00000i −0.0666173 + 0.0384615i
\(677\) −37.5000 21.6506i −1.44124 0.832102i −0.443309 0.896369i \(-0.646196\pi\)
−0.997933 + 0.0642672i \(0.979529\pi\)
\(678\) −27.7128 + 27.7128i −1.06430 + 1.06430i
\(679\) 34.6410 30.0000i 1.32940 1.15129i
\(680\) −6.00000 6.00000i −0.230089 0.230089i
\(681\) −16.5000 + 28.5788i −0.632281 + 1.09514i
\(682\) 0.633975 2.36603i 0.0242761 0.0905998i
\(683\) −21.6506 + 12.5000i −0.828439 + 0.478299i −0.853318 0.521391i \(-0.825413\pi\)
0.0248792 + 0.999690i \(0.492080\pi\)
\(684\) 0 0
\(685\) 1.73205i 0.0661783i
\(686\) −19.3660 17.6340i −0.739398 0.673268i
\(687\) 27.0000i 1.03011i
\(688\) 6.92820 + 4.00000i 0.264135 + 0.152499i
\(689\) −3.00000 + 1.73205i −0.114291 + 0.0659859i
\(690\) 4.09808 + 1.09808i 0.156011 + 0.0418030i
\(691\) −6.06218 + 10.5000i −0.230616 + 0.399439i −0.957990 0.286803i \(-0.907407\pi\)
0.727373 + 0.686242i \(0.240741\pi\)
\(692\) 24.2487 0.921798
\(693\) 0 0
\(694\) 13.0000 + 13.0000i 0.493473 + 0.493473i
\(695\) 10.3923 + 6.00000i 0.394203 + 0.227593i
\(696\) −5.07180 + 18.9282i −0.192246 + 0.717472i
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) −14.1962 + 3.80385i −0.537332 + 0.143978i
\(699\) −12.1244 −0.458585
\(700\) 2.00000 + 10.3923i 0.0755929 + 0.392792i
\(701\) −26.0000 −0.982006 −0.491003 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(702\) 24.5885 6.58846i 0.928032 0.248665i
\(703\) 7.79423 + 13.5000i 0.293965 + 0.509162i
\(704\) −4.00000 6.92820i −0.150756 0.261116i
\(705\) −22.5000 12.9904i −0.847399 0.489246i
\(706\) −29.4449 29.4449i −1.10817 1.10817i
\(707\) −21.6506 7.50000i −0.814256 0.282067i
\(708\) 18.0000i 0.676481i
\(709\) 4.50000 7.79423i 0.169001 0.292718i −0.769068 0.639167i \(-0.779279\pi\)
0.938069 + 0.346449i \(0.112613\pi\)
\(710\) −33.1244 8.87564i −1.24313 0.333097i
\(711\) 0 0
\(712\) −11.4115 42.5885i −0.427666 1.59607i
\(713\) 1.73205i 0.0648658i
\(714\) −10.0981 + 4.90192i −0.377911 + 0.183450i
\(715\) 6.00000i 0.224387i
\(716\) −19.0000 + 32.9090i −0.710063 + 1.22987i
\(717\) 30.0000 17.3205i 1.12037 0.646846i
\(718\) 8.41858 31.4186i 0.314179 1.17253i
\(719\) −12.9904 + 22.5000i −0.484459 + 0.839108i −0.999841 0.0178527i \(-0.994317\pi\)
0.515381 + 0.856961i \(0.327650\pi\)
\(720\) 0 0
\(721\) 22.5000 4.33013i 0.837944 0.161262i
\(722\) 8.00000 8.00000i 0.297729 0.297729i
\(723\) 7.79423 + 4.50000i 0.289870 + 0.167357i
\(724\) −6.92820 12.0000i −0.257485 0.445976i
\(725\) −4.00000 6.92820i −0.148556 0.257307i
\(726\) 6.33975 + 23.6603i 0.235290 + 0.878114i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 25.8564 + 1.85641i 0.958302 + 0.0688030i
\(729\) 27.0000 1.00000
\(730\) −5.49038 20.4904i −0.203208 0.758383i
\(731\) −1.73205 3.00000i −0.0640622 0.110959i
\(732\) −9.00000 15.5885i −0.332650 0.576166i
\(733\) 37.5000 + 21.6506i 1.38509 + 0.799684i 0.992757 0.120137i \(-0.0383334\pi\)
0.392337 + 0.919822i \(0.371667\pi\)
\(734\) 1.73205 1.73205i 0.0639312 0.0639312i
\(735\) −20.7846 3.00000i −0.766652 0.110657i
\(736\) −4.00000 4.00000i −0.147442 0.147442i
\(737\) 1.50000 2.59808i 0.0552532 0.0957014i
\(738\) 0 0
\(739\) 44.1673 25.5000i 1.62472 0.938033i 0.639087 0.769135i \(-0.279313\pi\)
0.985634 0.168898i \(-0.0540208\pi\)
\(740\) −5.19615 + 9.00000i −0.191014 + 0.330847i
\(741\) 31.1769i 1.14531i
\(742\) −3.73205 0.267949i −0.137008 0.00983672i
\(743\) 34.0000i 1.24734i −0.781688 0.623670i \(-0.785641\pi\)
0.781688 0.623670i \(-0.214359\pi\)
\(744\) −8.19615 + 2.19615i −0.300486 + 0.0805149i
\(745\) 1.50000 0.866025i 0.0549557 0.0317287i
\(746\) 39.6147 + 10.6147i 1.45040 + 0.388633i
\(747\) 0 0
\(748\) 3.46410i 0.126660i
\(749\) 6.50000 + 33.7750i 0.237505 + 1.23411i
\(750\) 21.0000 + 21.0000i 0.766812 + 0.766812i
\(751\) 21.6506 + 12.5000i 0.790043 + 0.456131i 0.839978 0.542621i \(-0.182568\pi\)
−0.0499348 + 0.998752i \(0.515901\pi\)
\(752\) 17.3205 + 30.0000i 0.631614 + 1.09399i
\(753\) 3.00000 + 5.19615i 0.109326 + 0.189358i
\(754\) −18.9282 + 5.07180i −0.689325 + 0.184704i
\(755\) −12.1244 −0.441250
\(756\) 25.9808 + 9.00000i 0.944911 + 0.327327i
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) 10.9282 2.92820i 0.396930 0.106357i
\(759\) −0.866025 1.50000i −0.0314347 0.0544466i
\(760\) 24.5885 + 6.58846i 0.891917 + 0.238988i
\(761\) 16.5000 + 9.52628i 0.598125 + 0.345327i 0.768303 0.640086i \(-0.221101\pi\)
−0.170179 + 0.985413i \(0.554435\pi\)
\(762\) 10.3923 + 10.3923i 0.376473 + 0.376473i
\(763\) 7.79423 22.5000i 0.282170 0.814555i
\(764\) −2.00000 −0.0723575
\(765\) 0 0
\(766\) 7.09808 + 1.90192i 0.256464 + 0.0687193i
\(767\) −15.5885 + 9.00000i −0.562867 + 0.324971i
\(768\) −13.8564 + 24.0000i −0.500000 + 0.866025i
\(769\) 3.46410i 0.124919i −0.998048 0.0624593i \(-0.980106\pi\)
0.998048 0.0624593i \(-0.0198944\pi\)
\(770\) −3.63397 + 5.36603i −0.130959 + 0.193378i
\(771\) 9.00000i 0.324127i
\(772\) −25.9808 15.0000i −0.935068 0.539862i
\(773\) 22.5000 12.9904i 0.809269 0.467232i −0.0374331 0.999299i \(-0.511918\pi\)
0.846702 + 0.532068i \(0.178585\pi\)
\(774\) 0 0
\(775\) 1.73205 3.00000i 0.0622171 0.107763i