Properties

Label 28.2.f.a.3.2
Level $28$
Weight $2$
Character 28.3
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: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
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 3.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 28.3
Dual form 28.2.f.a.19.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 6 q^{5} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 6 q^{5} - 8 q^{8} + 6 q^{10} + 12 q^{12} + 2 q^{14} + 8 q^{16} - 6 q^{17} + 6 q^{21} - 4 q^{22} - 12 q^{24} - 4 q^{25} - 12 q^{26} - 20 q^{28} + 16 q^{29} - 6 q^{30} + 8 q^{32} + 6 q^{33} - 6 q^{37} + 18 q^{38} + 12 q^{40} + 12 q^{42} + 4 q^{44} - 2 q^{46} - 4 q^{49} + 8 q^{50} + 2 q^{53} - 18 q^{54} + 16 q^{56} - 36 q^{57} - 8 q^{58} - 12 q^{60} - 18 q^{61} + 12 q^{65} - 6 q^{66} + 6 q^{70} + 30 q^{73} - 6 q^{74} - 10 q^{77} + 24 q^{78} - 24 q^{80} + 18 q^{81} + 12 q^{82} + 12 q^{85} - 4 q^{86} + 4 q^{88} + 54 q^{89} + 8 q^{92} + 6 q^{93} - 30 q^{94} - 24 q^{96} - 22 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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 −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) 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 0.363727 0.931505i \(-0.381504\pi\)
−0.624844 + 0.780750i \(0.714837\pi\)
\(12\) 3.00000 1.73205i 0.866025 0.500000i
\(13\) 3.46410i 0.960769i −0.877058 0.480384i \(-0.840497\pi\)
0.877058 0.480384i \(-0.159503\pi\)
\(14\) −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 0.306944 0.951727i \(-0.400693\pi\)
−0.670748 + 0.741685i \(0.734027\pi\)
\(18\) 0 0
\(19\) 2.59808 + 4.50000i 0.596040 + 1.03237i 0.993399 + 0.114708i \(0.0365932\pi\)
−0.397360 + 0.917663i \(0.630073\pi\)
\(20\) 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 −0.587565 0.809177i \(-0.699913\pi\)
0.406986 + 0.913434i \(0.366580\pi\)
\(24\) −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 −0.777714 0.628619i \(-0.783621\pi\)
0.933257 + 0.359211i \(0.116954\pi\)
\(32\) 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 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) 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 \(0.0871893\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(42\) 6.46410 0.464102i 0.997433 0.0716124i
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 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 −0.987222 0.159352i \(-0.949059\pi\)
0.355608 0.934635i \(-0.384274\pi\)
\(48\) −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 −0.829640 0.558298i \(-0.811454\pi\)
0.898321 + 0.439340i \(0.144788\pi\)
\(54\) −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 −0.645861 0.763455i \(-0.723502\pi\)
0.984102 + 0.177605i \(0.0568349\pi\)
\(60\) −3.00000 + 5.19615i −0.387298 + 0.670820i
\(61\) −4.50000 + 2.59808i −0.576166 + 0.332650i −0.759608 0.650381i \(-0.774609\pi\)
0.183442 + 0.983030i \(0.441276\pi\)
\(62\) −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 0.332830 0.942987i \(-0.391996\pi\)
−0.650236 + 0.759733i \(0.725330\pi\)
\(68\) 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 \(0.312086\pi\)
−0.556650 + 0.830747i \(0.687914\pi\)
\(72\) 0 0
\(73\) 7.50000 + 4.33013i 0.877809 + 0.506803i 0.869935 0.493166i \(-0.164160\pi\)
0.00787336 + 0.999969i \(0.497494\pi\)
\(74\) −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 −0.869641 0.493684i \(-0.835650\pi\)
−0.00727784 + 0.999974i \(0.502317\pi\)
\(80\) −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 0.433800 0.901009i \(-0.357172\pi\)
0.997197 + 0.0748225i \(0.0238390\pi\)
\(90\) 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 \(0.342000\pi\)
−0.476240 + 0.879316i \(0.658000\pi\)
\(98\) −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 0.0780696 0.996948i \(-0.475124\pi\)
−0.824347 + 0.566084i \(0.808458\pi\)
\(102\) −1.09808 4.09808i −0.108726 0.405770i
\(103\) 4.33013 + 7.50000i 0.426660 + 0.738997i 0.996574 0.0827075i \(-0.0263567\pi\)
−0.569914 + 0.821705i \(0.693023\pi\)
\(104\) 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 0.155238 0.987877i \(-0.450386\pi\)
0.933146 + 0.359498i \(0.117052\pi\)
\(108\) 9.00000 + 5.19615i 0.866025 + 0.500000i
\(109\) −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i \(-0.975180\pi\)
0.565940 + 0.824447i \(0.308513\pi\)
\(110\) 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 \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) −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 0.729921 0.683531i \(-0.239557\pi\)
−0.956916 + 0.290365i \(0.906223\pi\)
\(132\) −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 −0.886594 0.462549i \(-0.846935\pi\)
0.843876 + 0.536538i \(0.180268\pi\)
\(138\) −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 0.844818 0.535054i \(-0.179709\pi\)
−0.885779 + 0.464107i \(0.846375\pi\)
\(150\) −4.73205 + 1.26795i −0.386370 + 0.103528i
\(151\) 6.06218 + 3.50000i 0.493333 + 0.284826i 0.725956 0.687741i \(-0.241398\pi\)
−0.232623 + 0.972567i \(0.574731\pi\)
\(152\) −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 0.558661 0.829396i \(-0.311315\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) 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 −0.996678 0.0814491i \(-0.974045\pi\)
−0.427802 + 0.903873i \(0.640712\pi\)
\(164\) 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 −0.842876 0.538107i \(-0.819140\pi\)
0.0445762 + 0.999006i \(0.485806\pi\)
\(174\) 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 0.967002 0.254770i \(-0.0819996\pi\)
0.262864 + 0.964833i \(0.415333\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i −0.966282 0.257485i \(-0.917106\pi\)
0.966282 0.257485i \(-0.0828937\pi\)
\(182\) −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 −0.468341 0.883548i \(-0.655148\pi\)
0.531004 + 0.847369i \(0.321815\pi\)
\(192\) 12.0000 + 6.92820i 0.866025 + 0.500000i
\(193\) 7.50000 12.9904i 0.539862 0.935068i −0.459049 0.888411i \(-0.651810\pi\)
0.998911 0.0466572i \(-0.0148568\pi\)
\(194\) 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 −0.122782 0.992434i \(-0.539182\pi\)
0.920864 0.389885i \(-0.127485\pi\)
\(200\) −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 \(-0.888145\pi\)
0.938891 0.344214i \(-0.111855\pi\)
\(212\) −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 0.354803 + 0.934941i \(0.384548\pi\)
−0.987084 + 0.160202i \(0.948785\pi\)
\(228\) 15.5885 + 9.00000i 1.03237 + 0.596040i
\(229\) −13.5000 + 7.79423i −0.892105 + 0.515057i −0.874630 0.484790i \(-0.838896\pi\)
−0.0174746 + 0.999847i \(0.505563\pi\)
\(230\) −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 0.957599 0.288106i \(-0.0930254\pi\)
−0.728306 + 0.685252i \(0.759692\pi\)
\(234\) 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 \(-0.776088\pi\)
0.762620 0.646846i \(-0.223912\pi\)
\(240\) 10.3923 6.00000i 0.670820 0.387298i
\(241\) −4.50000 2.59808i −0.289870 0.167357i 0.348013 0.937490i \(-0.386857\pi\)
−0.637883 + 0.770133i \(0.720190\pi\)
\(242\) −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 −0.353039 0.935609i \(-0.614852\pi\)
0.633741 + 0.773545i \(0.281518\pi\)
\(258\) 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 −0.261573 0.965184i \(-0.584241\pi\)
−0.966660 + 0.256063i \(0.917574\pi\)
\(264\) −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 0.958065 0.286552i \(-0.0925091\pi\)
0.230871 + 0.972984i \(0.425842\pi\)
\(270\) −3.29423 12.2942i −0.200480 0.748203i
\(271\) 7.79423 + 13.5000i 0.473466 + 0.820067i 0.999539 0.0303728i \(-0.00966946\pi\)
−0.526073 + 0.850439i \(0.676336\pi\)
\(272\) 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 −0.601975 0.798515i \(-0.705619\pi\)
0.992522 + 0.122068i \(0.0389525\pi\)
\(278\) −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 −0.988020 0.154327i \(-0.950679\pi\)
0.627661 + 0.778487i \(0.284012\pi\)
\(284\) 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 \(0.207677\pi\)
−0.794606 + 0.607125i \(0.792323\pi\)
\(294\) 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 −0.962283 0.272050i \(-0.912298\pi\)
0.716744 + 0.697336i \(0.245632\pi\)
\(312\) −16.3923 + 4.39230i −0.928032 + 0.248665i
\(313\) 1.50000 0.866025i 0.0847850 0.0489506i −0.457008 0.889463i \(-0.651079\pi\)
0.541793 + 0.840512i \(0.317746\pi\)
\(314\) 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 0.669214 0.743070i \(-0.266631\pi\)
−0.978124 + 0.208021i \(0.933298\pi\)
\(318\) 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 −0.324057 0.946038i \(-0.605047\pi\)
0.657264 + 0.753660i \(0.271714\pi\)
\(332\) −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 0.770762 0.637123i \(-0.219876\pi\)
−0.166383 + 0.986061i \(0.553209\pi\)
\(348\) 12.0000 6.92820i 0.643268 0.371391i
\(349\) 10.3923i 0.556287i −0.960539 0.278144i \(-0.910281\pi\)
0.960539 0.278144i \(-0.0897191\pi\)
\(350\) 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 −0.367979 0.929834i \(-0.619950\pi\)
−0.989249 + 0.146238i \(0.953283\pi\)
\(354\) 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 −0.923003 0.384794i \(-0.874273\pi\)
−0.128260 + 0.991741i \(0.540939\pi\)
\(360\) 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 −0.887743 0.460339i \(-0.847728\pi\)
0.842537 + 0.538639i \(0.181061\pi\)
\(368\) −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 0.947444 + 0.319921i \(0.103656\pi\)
−0.196663 + 0.980471i \(0.563010\pi\)
\(374\) 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 \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) 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 0.924738 0.380605i \(-0.124284\pi\)
−0.791982 + 0.610544i \(0.790951\pi\)
\(384\) 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 −0.518110 0.855314i \(-0.673364\pi\)
0.999779 + 0.0210389i \(0.00669738\pi\)
\(390\) −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 −0.0250943 0.999685i \(-0.507989\pi\)
0.853206 + 0.521575i \(0.174655\pi\)
\(398\) −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 0.996119 + 0.0880147i \(0.0280523\pi\)
−0.421837 + 0.906672i \(0.638614\pi\)
\(402\) −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 0.939490 0.342578i \(-0.111300\pi\)
0.173064 + 0.984911i \(0.444633\pi\)
\(410\) −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 0.896002 0.444050i \(-0.146459\pi\)
0.0634424 + 0.997985i \(0.479792\pi\)
\(432\) −10.3923 18.0000i −0.500000 0.866025i
\(433\) 10.3923i 0.499422i 0.968320 + 0.249711i \(0.0803357\pi\)
−0.968320 + 0.249711i \(0.919664\pi\)
\(434\) −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 −0.999047 0.0436563i \(-0.986099\pi\)
0.461716 0.887028i \(-0.347234\pi\)
\(440\) −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 −0.107671 0.994187i \(-0.534339\pi\)
0.807155 + 0.590339i \(0.201006\pi\)
\(444\) −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 0.635561 0.772051i \(-0.280769\pi\)
−0.986396 + 0.164386i \(0.947436\pi\)
\(458\) 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 \(0.132154\pi\)
−0.915047 + 0.403348i \(0.867846\pi\)
\(462\) −5.83013 2.83013i −0.271242 0.131669i
\(463\) 30.0000i 1.39422i 0.716965 + 0.697109i \(0.245531\pi\)
−0.716965 + 0.697109i \(0.754469\pi\)
\(464\) 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 0.948649 0.316330i \(-0.102451\pi\)
−0.748275 + 0.663389i \(0.769117\pi\)
\(468\) 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 −0.693647 0.720315i \(-0.743997\pi\)
0.970635 + 0.240558i \(0.0773304\pi\)
\(480\) −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 −0.252367 0.967632i \(-0.581209\pi\)
−0.964177 + 0.265260i \(0.914542\pi\)
\(488\) 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 \(-0.743191\pi\)
0.691820 0.722070i \(-0.256809\pi\)
\(492\) 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 0.367697 0.929946i \(-0.380146\pi\)
0.989205 + 0.146538i \(0.0468131\pi\)
\(500\) −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 −0.248910 0.968527i \(-0.580072\pi\)
0.714314 + 0.699825i \(0.246739\pi\)
\(510\) 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 0.532498 0.846431i \(-0.321253\pi\)
−0.466782 + 0.884372i \(0.654587\pi\)
\(522\) 0 0
\(523\) 12.9904 + 22.5000i 0.568030 + 0.983856i 0.996761 + 0.0804241i \(0.0256275\pi\)
−0.428731 + 0.903432i \(0.641039\pi\)
\(524\) 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 0.994715 0.102677i \(-0.0327407\pi\)
−0.586278 + 0.810110i \(0.699407\pi\)
\(542\) 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 0.145802 + 0.989314i \(0.453424\pi\)
−0.929672 + 0.368389i \(0.879909\pi\)
\(558\) 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 −0.999573 0.0292191i \(-0.990698\pi\)
0.525091 + 0.851046i \(0.324031\pi\)
\(564\) −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 0.969500 0.245092i \(-0.0788181\pi\)
−0.697006 + 0.717066i \(0.745485\pi\)
\(570\) −5.70577 21.2942i −0.238988 0.891917i
\(571\) −18.1865 10.5000i −0.761083 0.439411i 0.0686016 0.997644i \(-0.478146\pi\)
−0.829684 + 0.558233i \(0.811480\pi\)
\(572\) 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 −0.228968 0.973434i \(-0.573535\pi\)
−0.957503 + 0.288425i \(0.906868\pi\)
\(578\) −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 −0.750886 0.660432i \(-0.770373\pi\)
0.196508 + 0.980502i \(0.437040\pi\)
\(594\) 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 0.769648 0.638468i \(-0.220432\pi\)
−0.168106 + 0.985769i \(0.553765\pi\)
\(600\) 9.46410 + 2.53590i 0.386370 + 0.103528i
\(601\) 38.1051i 1.55434i −0.629291 0.777170i \(-0.716654\pi\)
0.629291 0.777170i \(-0.283346\pi\)
\(602\) −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 0.663367 0.748294i \(-0.269127\pi\)
−0.979725 + 0.200346i \(0.935793\pi\)
\(608\) 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 −0.362300 0.932062i \(-0.618008\pi\)
0.988339 0.152270i \(-0.0486583\pi\)
\(614\) 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 −0.979070 0.203526i \(-0.934760\pi\)
0.665793 + 0.746136i \(0.268093\pi\)
\(620\) 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 \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) 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 −0.708631 0.705580i \(-0.750687\pi\)
0.965365 + 0.260902i \(0.0840201\pi\)
\(642\) 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 −0.336968 0.941516i \(-0.609402\pi\)
0.983861 0.178935i \(-0.0572651\pi\)
\(648\) 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 −0.991803 0.127780i \(-0.959215\pi\)
0.385241 0.922816i \(-0.374118\pi\)
\(654\) −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 \(0.265238\pi\)
−0.672458 + 0.740135i \(0.734762\pi\)
\(660\) 5.19615 3.00000i 0.202260 0.116775i
\(661\) −34.5000 19.9186i −1.34189 0.774743i −0.354809 0.934939i \(-0.615454\pi\)
−0.987085 + 0.160196i \(0.948788\pi\)
\(662\) −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 −0.997933 0.0642672i \(-0.979529\pi\)
−0.443309 + 0.896369i \(0.646196\pi\)
\(678\) −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 0.0248792 0.999690i \(-0.492080\pi\)
−0.853318 + 0.521391i \(0.825413\pi\)
\(684\) 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 0.727373 0.686242i \(-0.240741\pi\)
−0.957990 + 0.286803i \(0.907407\pi\)
\(692\) 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 0.938069 0.346449i \(-0.112613\pi\)
−0.769068 + 0.639167i \(0.779279\pi\)
\(710\) −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 0.515381 0.856961i \(-0.327650\pi\)
−0.999841 + 0.0178527i \(0.994317\pi\)
\(720\) 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 0.392337 0.919822i \(-0.371667\pi\)
0.992757 + 0.120137i \(0.0383334\pi\)
\(734\) 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 0.985634 + 0.168898i \(0.0540208\pi\)
0.639087 + 0.769135i \(0.279313\pi\)
\(740\) −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 \(0.214359\pi\)
−0.781688 + 0.623670i \(0.785641\pi\)
\(744\) −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 −0.0499348 0.998752i \(-0.515901\pi\)
0.839978 + 0.542621i \(0.182568\pi\)
\(752\) 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 −0.170179 0.985413i \(-0.554435\pi\)
0.768303 + 0.640086i \(0.221101\pi\)
\(762\) 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 \(0.0198944\pi\)
−0.998048 + 0.0624593i \(0.980106\pi\)
\(770\) −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 0.846702 0.532068i \(-0.178585\pi\)
−0.0374331 + 0.999299i \(0.511918\pi\)
\(774\)