Properties

Label 28.2.f.a.19.1
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 19.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 28.19
Dual form 28.2.f.a.3.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 + 0.366025i) q^{2} +(0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-1.73205 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.36603 + 0.366025i) 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} +(2.36603 + 0.633975i) q^{10} +(0.866025 - 0.500000i) q^{11} +(3.00000 + 1.73205i) q^{12} +3.46410i q^{13} +(3.09808 + 2.09808i) 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} +(-4.73205 - 1.26795i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-1.26795 - 4.73205i) q^{26} +5.19615 q^{27} +(-5.00000 - 1.73205i) q^{28} +4.00000 q^{29} +(1.09808 + 4.09808i) q^{30} +(-0.866025 - 1.50000i) q^{31} +(-1.46410 + 5.46410i) 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} +(1.90192 - 7.09808i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(4.73205 - 1.26795i) q^{40} -3.46410i q^{41} +(-0.464102 + 6.46410i) q^{42} -2.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(-1.36603 - 0.366025i) 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} +(-7.09808 + 1.90192i) q^{54} -1.73205 q^{55} +(7.46410 + 0.535898i) q^{56} -9.00000 q^{57} +(-5.46410 + 1.46410i) 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} +(-2.36603 - 0.633975i) q^{66} +(2.59808 - 1.50000i) q^{67} +(-1.73205 + 3.00000i) q^{68} +1.73205i q^{69} +(-2.83013 - 5.83013i) q^{70} +14.0000i q^{71} +(7.50000 - 4.33013i) q^{73} +(1.09808 - 4.09808i) 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} +(1.26795 + 4.73205i) q^{82} -13.8564 q^{83} +(-1.73205 - 9.00000i) q^{84} +3.00000 q^{85} +(0.732051 + 2.73205i) q^{86} +(3.46410 + 6.00000i) q^{87} +(-0.732051 + 2.73205i) q^{88} +(13.5000 + 7.79423i) q^{89} +(6.92820 - 6.00000i) q^{91} +2.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(-3.16987 + 11.8301i) q^{94} +(7.79423 - 4.50000i) q^{95} +(-9.46410 + 2.53590i) q^{96} -17.3205i q^{97} +(-1.16987 - 9.83013i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 0.366025i −0.965926 + 0.258819i
\(3\) 0.866025 + 1.50000i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 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
\(10\) 2.36603 + 0.633975i 0.748203 + 0.200480i
\(11\) 0.866025 0.500000i 0.261116 0.150756i −0.363727 0.931505i \(-0.618496\pi\)
0.624844 + 0.780750i \(0.285163\pi\)
\(12\) 3.00000 + 1.73205i 0.866025 + 0.500000i
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) 3.09808 + 2.09808i 0.827996 + 0.560734i
\(15\) 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 \(0.369927\pi\)
−0.993399 + 0.114708i \(0.963407\pi\)
\(20\) −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 \(-0.300087\pi\)
−0.406986 + 0.913434i \(0.633420\pi\)
\(24\) −4.73205 1.26795i −0.965926 0.258819i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) −1.26795 4.73205i −0.248665 0.928032i
\(27\) 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 \(0.378881\pi\)
\(30\) 1.09808 + 4.09808i 0.200480 + 0.748203i
\(31\) −0.866025 1.50000i −0.155543 0.269408i 0.777714 0.628619i \(-0.216379\pi\)
−0.933257 + 0.359211i \(0.883046\pi\)
\(32\) −1.46410 + 5.46410i −0.258819 + 0.965926i
\(33\) 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 \(0.245980\pi\)
\(38\) 1.90192 7.09808i 0.308533 1.15146i
\(39\) −5.19615 + 3.00000i −0.832050 + 0.480384i
\(40\) 4.73205 1.26795i 0.748203 0.200480i
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) −0.464102 + 6.46410i −0.0716124 + 0.997433i
\(43\) 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
\(46\) −1.36603 0.366025i −0.201409 0.0539675i
\(47\) 4.33013 7.50000i 0.631614 1.09399i −0.355608 0.934635i \(-0.615726\pi\)
0.987222 0.159352i \(-0.0509405\pi\)
\(48\) 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 \(0.811454\pi\)
\(54\) −7.09808 + 1.90192i −0.965926 + 0.258819i
\(55\) −1.73205 −0.233550
\(56\) 7.46410 + 0.535898i 0.997433 + 0.0716124i
\(57\) −9.00000 −1.19208
\(58\) −5.46410 + 1.46410i −0.717472 + 0.192246i
\(59\) −2.59808 4.50000i −0.338241 0.585850i 0.645861 0.763455i \(-0.276498\pi\)
−0.984102 + 0.177605i \(0.943165\pi\)
\(60\) −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
\(66\) −2.36603 0.633975i −0.291238 0.0780369i
\(67\) 2.59808 1.50000i 0.317406 0.183254i −0.332830 0.942987i \(-0.608004\pi\)
0.650236 + 0.759733i \(0.274670\pi\)
\(68\) −1.73205 + 3.00000i −0.210042 + 0.363803i
\(69\) 1.73205i 0.208514i
\(70\) −2.83013 5.83013i −0.338265 0.696833i
\(71\) 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 0.00787336 0.999969i \(-0.497494\pi\)
0.869935 + 0.493166i \(0.164160\pi\)
\(74\) 1.09808 4.09808i 0.127649 0.476392i
\(75\) 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 \(-0.164350\pi\)
0.00727784 + 0.999974i \(0.497683\pi\)
\(80\) −6.00000 + 3.46410i −0.670820 + 0.387298i
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) 1.26795 + 4.73205i 0.140022 + 0.522568i
\(83\) −13.8564 −1.52094 −0.760469 0.649374i \(-0.775031\pi\)
−0.760469 + 0.649374i \(0.775031\pi\)
\(84\) −1.73205 9.00000i −0.188982 0.981981i
\(85\) 3.00000 0.325396
\(86\) 0.732051 + 2.73205i 0.0789391 + 0.294605i
\(87\) 3.46410 + 6.00000i 0.371391 + 0.643268i
\(88\) −0.732051 + 2.73205i −0.0780369 + 0.291238i
\(89\) 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
\(94\) −3.16987 + 11.8301i −0.326947 + 1.22018i
\(95\) 7.79423 4.50000i 0.799671 0.461690i
\(96\) −9.46410 + 2.53590i −0.965926 + 0.258819i
\(97\) 17.3205i 1.75863i −0.476240 0.879316i \(-0.658000\pi\)
0.476240 0.879316i \(-0.342000\pi\)
\(98\) −1.16987 9.83013i −0.118175 0.992993i
\(99\) 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 \(0.475124\pi\)
\(102\) 4.09808 + 1.09808i 0.405770 + 0.108726i
\(103\) −4.33013 + 7.50000i −0.426660 + 0.738997i −0.996574 0.0827075i \(-0.973643\pi\)
0.569914 + 0.821705i \(0.306977\pi\)
\(104\) −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 \(-0.549614\pi\)
−0.933146 + 0.359498i \(0.882948\pi\)
\(108\) 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 \(0.975180\pi\)
\(110\) 2.36603 0.633975i 0.225592 0.0604471i
\(111\) −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 \(0.771189\pi\)
\(114\) 12.2942 3.29423i 1.15146 0.308533i
\(115\) −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
\(122\) 7.09808 + 1.90192i 0.642630 + 0.172192i
\(123\) 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 \(-0.0857705\pi\)
\(128\) 2.92820 + 10.9282i 0.258819 + 0.965926i
\(129\) 3.00000 1.73205i 0.264135 0.152499i
\(130\) −2.19615 + 8.19615i −0.192615 + 0.718850i
\(131\) 2.59808 4.50000i 0.226995 0.393167i −0.729921 0.683531i \(-0.760443\pi\)
0.956916 + 0.290365i \(0.0937766\pi\)
\(132\) 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
\(136\) 1.26795 4.73205i 0.108726 0.405770i
\(137\) −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i \(-0.180268\pi\)
−0.886594 + 0.462549i \(0.846935\pi\)
\(138\) −0.633975 2.36603i −0.0539675 0.201409i
\(139\) 6.92820 0.587643 0.293821 0.955860i \(-0.405073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(140\) 6.00000 + 6.92820i 0.507093 + 0.585540i
\(141\) 15.0000 1.26323
\(142\) −5.12436 19.1244i −0.430026 1.60488i
\(143\) 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 \(0.179709\pi\)
\(150\) −1.26795 + 4.73205i −0.103528 + 0.386370i
\(151\) −6.06218 + 3.50000i −0.493333 + 0.284826i −0.725956 0.687741i \(-0.758602\pi\)
0.232623 + 0.972567i \(0.425269\pi\)
\(152\) −3.80385 14.1962i −0.308533 1.15146i
\(153\) 0 0
\(154\) 3.73205 + 0.267949i 0.300737 + 0.0215920i
\(155\) 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 \(0.311315\pi\)
\(158\) −12.2942 3.29423i −0.978076 0.262075i
\(159\) −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 \(-0.0259548\pi\)
0.427802 + 0.903873i \(0.359288\pi\)
\(164\) −3.46410 6.00000i −0.270501 0.468521i
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) 18.9282 5.07180i 1.46911 0.393648i
\(167\) 17.3205 1.34030 0.670151 0.742225i \(-0.266230\pi\)
0.670151 + 0.742225i \(0.266230\pi\)
\(168\) 5.66025 + 11.6603i 0.436698 + 0.899608i
\(169\) 1.00000 0.0769231
\(170\) −4.09808 + 1.09808i −0.314308 + 0.0842186i
\(171\) 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
\(178\) −21.2942 5.70577i −1.59607 0.427666i
\(179\) −16.4545 + 9.50000i −1.22987 + 0.710063i −0.967002 0.254770i \(-0.918000\pi\)
−0.262864 + 0.964833i \(0.584667\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) −7.26795 + 10.7321i −0.538736 + 0.795513i
\(183\) 9.00000i 0.665299i
\(184\) −2.73205 + 0.732051i −0.201409 + 0.0539675i
\(185\) 4.50000 2.59808i 0.330847 0.191014i
\(186\) −1.09808 + 4.09808i −0.0805149 + 0.300486i
\(187\) −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 \(-0.344852\pi\)
−0.531004 + 0.847369i \(0.678185\pi\)
\(192\) 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 \(0.651810\pi\)
\(194\) 6.33975 + 23.6603i 0.455167 + 1.69871i
\(195\) 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 \(-0.872515\pi\)
0.122782 0.992434i \(-0.460818\pi\)
\(200\) 5.46410 + 1.46410i 0.386370 + 0.103528i
\(201\) 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
\(206\) 3.16987 11.8301i 0.220856 0.824244i
\(207\) 0 0
\(208\) 12.0000 + 6.92820i 0.832050 + 0.480384i
\(209\) 5.19615i 0.359425i
\(210\) 6.29423 9.29423i 0.434343 0.641363i
\(211\) 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
\(214\) 17.7583 + 4.75833i 1.21393 + 0.325273i
\(215\) −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
\(222\) 7.09808 1.90192i 0.476392 0.127649i
\(223\) −6.92820 −0.463947 −0.231973 0.972722i \(-0.574518\pi\)
−0.231973 + 0.972722i \(0.574518\pi\)
\(224\) 13.4641 6.53590i 0.899608 0.436698i
\(225\) 0 0
\(226\) 21.8564 5.85641i 1.45387 0.389562i
\(227\) 9.52628 + 16.5000i 0.632281 + 1.09514i 0.987084 + 0.160202i \(0.0512147\pi\)
−0.354803 + 0.934941i \(0.615452\pi\)
\(228\) −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
\(238\) −6.46410 0.464102i −0.419005 0.0300832i
\(239\) 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 −0.637883 0.770133i \(-0.720190\pi\)
0.348013 + 0.937490i \(0.386857\pi\)
\(242\) 3.66025 13.6603i 0.235290 0.878114i
\(243\) 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
\(248\) 4.73205 + 1.26795i 0.300486 + 0.0805149i
\(249\) −12.0000 20.7846i −0.760469 1.31717i
\(250\) −4.43782 16.5622i −0.280673 1.04748i
\(251\) 3.46410 0.218652 0.109326 0.994006i \(-0.465131\pi\)
0.109326 + 0.994006i \(0.465131\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) 2.19615 + 8.19615i 0.137799 + 0.514272i
\(255\) 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
\(262\) −1.90192 + 7.09808i −0.117501 + 0.438521i
\(263\) 19.9186 11.5000i 1.22823 0.709120i 0.261573 0.965184i \(-0.415759\pi\)
0.966660 + 0.256063i \(0.0824256\pi\)
\(264\) −4.73205 + 1.26795i −0.291238 + 0.0780369i
\(265\) 1.73205i 0.106399i
\(266\) −17.4904 + 8.49038i −1.07240 + 0.520579i
\(267\) 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 \(0.0925091\pi\)
\(270\) 12.2942 + 3.29423i 0.748203 + 0.200480i
\(271\) −7.79423 + 13.5000i −0.473466 + 0.820067i −0.999539 0.0303728i \(-0.990331\pi\)
0.526073 + 0.850439i \(0.323664\pi\)
\(272\) 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 \(0.705619\pi\)
\(278\) −9.46410 + 2.53590i −0.567619 + 0.152093i
\(279\) 0 0
\(280\) −10.7321 7.26795i −0.641363 0.434343i
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) −20.4904 + 5.49038i −1.22018 + 0.326947i
\(283\) 6.06218 + 10.5000i 0.360359 + 0.624160i 0.988020 0.154327i \(-0.0493208\pi\)
−0.627661 + 0.778487i \(0.715988\pi\)
\(284\) 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
\(290\) 9.46410 + 2.53590i 0.555751 + 0.148913i
\(291\) 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 \(-0.207677\pi\)
\(294\) 13.7321 10.2679i 0.800869 0.598839i
\(295\) 9.00000i 0.524000i
\(296\) −2.19615 8.19615i −0.127649 0.476392i
\(297\) 4.50000 2.59808i 0.261116 0.150756i
\(298\) 0.366025 1.36603i 0.0212033 0.0791317i
\(299\) −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 \(-0.702104\pi\)
−0.593120 + 0.805114i \(0.702104\pi\)
\(308\) −5.19615 + 1.00000i −0.296078 + 0.0569803i
\(309\) −15.0000 −0.853320
\(310\) −1.09808 4.09808i −0.0623665 0.232755i
\(311\) 4.33013 + 7.50000i 0.245539 + 0.425286i 0.962283 0.272050i \(-0.0877017\pi\)
−0.716744 + 0.697336i \(0.754368\pi\)
\(312\) 4.39230 16.3923i 0.248665 0.928032i
\(313\) 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 \(0.266631\pi\)
\(318\) 0.633975 2.36603i 0.0355515 0.132680i
\(319\) 3.46410 2.00000i 0.193952 0.111979i
\(320\) −6.92820 + 12.0000i −0.387298 + 0.670820i
\(321\) 22.5167i 1.25676i
\(322\) 1.63397 + 3.36603i 0.0910578 + 0.187581i
\(323\) 9.00000i 0.500773i
\(324\) 15.5885 + 9.00000i 0.866025 + 0.500000i
\(325\) 6.00000 3.46410i 0.332820 0.192154i
\(326\) −28.6865 7.68653i −1.58880 0.425718i
\(327\) 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 \(-0.394953\pi\)
−0.657264 + 0.753660i \(0.728286\pi\)
\(332\) −24.0000 + 13.8564i −1.31717 + 0.760469i
\(333\) 0 0
\(334\) −23.6603 + 6.33975i −1.29463 + 0.346895i
\(335\) −5.19615 −0.283896
\(336\) −12.0000 13.8564i −0.654654 0.755929i
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −1.36603 + 0.366025i −0.0743020 + 0.0199092i
\(339\) −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
\(346\) 16.5622 + 4.43782i 0.890388 + 0.238579i
\(347\) −11.2583 + 6.50000i −0.604379 + 0.348938i −0.770762 0.637123i \(-0.780124\pi\)
0.166383 + 0.986061i \(0.446791\pi\)
\(348\) 12.0000 + 6.92820i 0.643268 + 0.371391i
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) 0.535898 7.46410i 0.0286450 0.398973i
\(351\) 18.0000i 0.960769i
\(352\) 1.46410 + 5.46410i 0.0780369 + 0.291238i
\(353\) −25.5000 + 14.7224i −1.35723 + 0.783596i −0.989249 0.146238i \(-0.953283\pi\)
−0.367979 + 0.929834i \(0.619950\pi\)
\(354\) −3.29423 + 12.2942i −0.175086 + 0.653431i
\(355\) 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 \(-0.125727\pi\)
0.128260 + 0.991741i \(0.459061\pi\)
\(360\) 0 0
\(361\) −4.00000 6.92820i −0.210526 0.364642i
\(362\) −2.53590 9.46410i −0.133284 0.497422i
\(363\) −17.3205 −0.909091
\(364\) 6.00000 17.3205i 0.314485 0.907841i
\(365\) −15.0000 −0.785136
\(366\) 3.29423 + 12.2942i 0.172192 + 0.642630i
\(367\) 0.866025 + 1.50000i 0.0452062 + 0.0782994i 0.887743 0.460339i \(-0.152272\pi\)
−0.842537 + 0.538639i \(0.818939\pi\)
\(368\) 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 \(-0.103656\pi\)
\(374\) 0.633975 2.36603i 0.0327820 0.122344i
\(375\) −18.1865 + 10.5000i −0.939149 + 0.542218i
\(376\) 6.33975 + 23.6603i 0.326947 + 1.22018i
\(377\) 13.8564i 0.713641i
\(378\) 16.0981 + 10.9019i 0.827996 + 0.560734i
\(379\) 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
\(382\) 1.36603 + 0.366025i 0.0698919 + 0.0187275i
\(383\) −2.59808 + 4.50000i −0.132755 + 0.229939i −0.924738 0.380605i \(-0.875716\pi\)
0.791982 + 0.610544i \(0.209049\pi\)
\(384\) −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 \(0.673364\pi\)
\(390\) −14.1962 + 3.80385i −0.718850 + 0.192615i
\(391\) −1.73205 −0.0875936
\(392\) −11.8564 15.8564i −0.598839 0.800869i
\(393\) 9.00000 0.453990
\(394\) −21.8564 + 5.85641i −1.10111 + 0.295041i
\(395\) −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 \(-0.0280523\pi\)
\(402\) −7.09808 1.90192i −0.354020 0.0948593i
\(403\) 5.19615 3.00000i 0.258839 0.149441i
\(404\) −8.66025 + 15.0000i −0.430864 + 0.746278i
\(405\) 15.5885i 0.774597i
\(406\) 12.3923 + 8.39230i 0.615020 + 0.416503i
\(407\) 3.00000i 0.148704i
\(408\) 8.19615 2.19615i 0.405770 0.108726i
\(409\) 22.5000 12.9904i 1.11255 0.642333i 0.173064 0.984911i \(-0.444633\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) 2.19615 8.19615i 0.108460 0.404779i
\(411\) 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
\(416\) −18.9282 5.07180i −0.928032 0.248665i
\(417\) 6.00000 + 10.3923i 0.293821 + 0.508913i
\(418\) −1.90192 7.09808i −0.0930261 0.347178i
\(419\) 20.7846 1.01539 0.507697 0.861536i \(-0.330497\pi\)
0.507697 + 0.861536i \(0.330497\pi\)
\(420\) −5.19615 + 15.0000i −0.253546 + 0.731925i
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 3.66025 + 13.6603i 0.178178 + 0.664971i
\(423\) 0 0
\(424\) −2.73205 0.732051i −0.132680 0.0355515i
\(425\) 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
\(430\) 1.26795 4.73205i 0.0611459 0.228200i
\(431\) −19.9186 + 11.5000i −0.959444 + 0.553936i −0.896002 0.444050i \(-0.853541\pi\)
−0.0634424 + 0.997985i \(0.520208\pi\)
\(432\) 10.3923 18.0000i 0.500000 0.866025i
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) 0.464102 6.46410i 0.0222776 0.310287i
\(435\) 12.0000i 0.575356i
\(436\) −15.5885 9.00000i −0.746552 0.431022i
\(437\) −4.50000 + 2.59808i −0.215264 + 0.124283i
\(438\) −20.4904 5.49038i −0.979068 0.262341i
\(439\) 11.2583 19.5000i 0.537331 0.930684i −0.461716 0.887028i \(-0.652766\pi\)
0.999047 0.0436563i \(-0.0139007\pi\)
\(440\) 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 \(-0.465661\pi\)
−0.807155 + 0.590339i \(0.798994\pi\)
\(444\) −9.00000 + 5.19615i −0.427121 + 0.246598i
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) 9.46410 2.53590i 0.448138 0.120078i
\(447\) −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 \(0.280769\pi\)
\(458\) 21.2942 + 5.70577i 0.995014 + 0.266613i
\(459\) −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 \(-0.132154\pi\)
\(462\) 2.83013 + 5.83013i 0.131669 + 0.271242i
\(463\) 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
\(466\) −2.56218 + 9.56218i −0.118691 + 0.442959i
\(467\) −4.33013 + 7.50000i −0.200374 + 0.347059i −0.948649 0.316330i \(-0.897549\pi\)
0.748275 + 0.663389i \(0.230883\pi\)
\(468\) 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
\(472\) 14.1962 + 3.80385i 0.653431 + 0.175086i
\(473\) −1.00000 1.73205i −0.0459800 0.0796398i
\(474\) −5.70577 21.2942i −0.262075 0.978076i
\(475\) 10.3923 0.476832
\(476\) 9.00000 1.73205i 0.412514 0.0793884i
\(477\) 0 0
\(478\) 7.32051 + 27.3205i 0.334832 + 1.24961i
\(479\) −6.06218 10.5000i −0.276988 0.479757i 0.693647 0.720315i \(-0.256003\pi\)
−0.970635 + 0.240558i \(0.922670\pi\)
\(480\) 16.3923 + 4.39230i 0.748203 + 0.200480i
\(481\) −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 \(-0.418791\pi\)
0.964177 + 0.265260i \(0.0854576\pi\)
\(488\) 14.1962 3.80385i 0.642630 0.172192i
\(489\) 36.3731i 1.64485i
\(490\) −6.75833 + 15.7583i −0.305310 + 0.711889i
\(491\) 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
\(494\) 24.5885 + 6.58846i 1.10629 + 0.296429i
\(495\) 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 \(-0.619854\pi\)
−0.989205 + 0.146538i \(0.953187\pi\)
\(500\) 12.1244 + 21.0000i 0.542218 + 0.939149i
\(501\) 15.0000 + 25.9808i 0.670151 + 1.16073i
\(502\) −4.73205 + 1.26795i −0.211202 + 0.0565913i
\(503\) 6.92820 0.308913 0.154457 0.988000i \(-0.450637\pi\)
0.154457 + 0.988000i \(0.450637\pi\)
\(504\) 0 0
\(505\) 15.0000 0.667491
\(506\) −1.36603 + 0.366025i −0.0607272 + 0.0162718i
\(507\) 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
\(514\) −7.09808 1.90192i −0.313083 0.0838903i
\(515\) 12.9904 7.50000i 0.572425 0.330489i
\(516\) 3.46410 6.00000i 0.152499 0.264135i
\(517\) 8.66025i 0.380878i
\(518\) −10.0981 + 4.90192i −0.443684 + 0.215378i
\(519\) 21.0000i 0.921798i
\(520\) 4.39230 + 16.3923i 0.192615 + 0.718850i
\(521\) 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 \(0.358961\pi\)
−0.996761 + 0.0804241i \(0.974373\pi\)
\(524\) 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
\(530\) 0.633975 + 2.36603i 0.0275381 + 0.102774i
\(531\) 0 0
\(532\) 20.7846 18.0000i 0.901127 0.780399i
\(533\) 12.0000 0.519778
\(534\) −9.88269 36.8827i −0.427666 1.59607i
\(535\) 11.2583 + 19.5000i 0.486740 + 0.843059i
\(536\) −2.19615 + 8.19615i −0.0948593 + 0.354020i
\(537\) −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 \(0.0327407\pi\)
\(542\) 5.70577 21.2942i 0.245084 0.914665i
\(543\) −10.3923 + 6.00000i −0.445976 + 0.257485i
\(544\) −2.53590 9.46410i −0.108726 0.405770i
\(545\) 15.5885i 0.667736i
\(546\) −22.3923 1.60770i −0.958302 0.0688030i
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −1.73205 1.00000i −0.0739895 0.0427179i
\(549\) 0 0
\(550\) 2.73205 + 0.732051i 0.116495 + 0.0312148i
\(551\) −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
\(562\) 5.46410 1.46410i 0.230489 0.0617594i
\(563\) 11.2583 + 19.5000i 0.474482 + 0.821827i 0.999573 0.0292191i \(-0.00930205\pi\)
−0.525091 + 0.851046i \(0.675969\pi\)
\(564\) 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 \(0.0788181\pi\)
\(570\) −21.2942 5.70577i −0.891917 0.238988i
\(571\) 18.1865 10.5000i 0.761083 0.439411i −0.0686016 0.997644i \(-0.521854\pi\)
0.829684 + 0.558233i \(0.188520\pi\)
\(572\) 6.00000 + 3.46410i 0.250873 + 0.144841i
\(573\) 1.73205i 0.0723575i
\(574\) 7.26795 10.7321i 0.303358 0.447947i
\(575\) 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 \(0.573535\pi\)
\(578\) 5.12436 19.1244i 0.213145 0.795468i
\(579\) −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
\(584\) −6.33975 + 23.6603i −0.262341 + 0.979068i
\(585\) 0 0
\(586\) 7.60770 + 28.3923i 0.314271 + 1.17288i
\(587\) −6.92820 −0.285958 −0.142979 0.989726i \(-0.545668\pi\)
−0.142979 + 0.989726i \(0.545668\pi\)
\(588\) −15.0000 + 19.0526i −0.618590 + 0.785714i
\(589\) 9.00000 0.370839
\(590\) −3.29423 12.2942i −0.135621 0.506145i
\(591\) 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
\(598\) 1.26795 4.73205i 0.0518503 0.193508i
\(599\) −14.7224 + 8.50000i −0.601542 + 0.347301i −0.769648 0.638468i \(-0.779568\pi\)
0.168106 + 0.985769i \(0.446235\pi\)
\(600\) 2.53590 + 9.46410i 0.103528 + 0.386370i
\(601\) 38.1051i 1.55434i 0.629291 + 0.777170i \(0.283346\pi\)
−0.629291 + 0.777170i \(0.716654\pi\)
\(602\) 4.19615 6.19615i 0.171022 0.252536i
\(603\) 0 0
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) 15.0000 8.66025i 0.609837 0.352089i
\(606\) 20.4904 + 5.49038i 0.832365 + 0.223031i
\(607\) 7.79423 13.5000i 0.316358 0.547948i −0.663367 0.748294i \(-0.730873\pi\)
0.979725 + 0.200346i \(0.0642066\pi\)
\(608\) −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 \(0.618008\pi\)
\(614\) 28.3923 7.60770i 1.14582 0.307022i
\(615\) −10.3923 −0.419058
\(616\) 6.73205 3.26795i 0.271242 0.131669i
\(617\) 20.0000 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(618\) 20.4904 5.49038i 0.824244 0.220856i
\(619\) 7.79423 + 13.5000i 0.313276 + 0.542611i 0.979070 0.203526i \(-0.0652400\pi\)
−0.665793 + 0.746136i \(0.731907\pi\)
\(620\) 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
\(626\) −2.36603 0.633975i −0.0945654 0.0253387i
\(627\) −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 \(-0.203697\pi\)
\(632\) −24.5885 + 6.58846i −0.978076 + 0.262075i
\(633\) 15.0000 8.66025i 0.596196 0.344214i
\(634\) 4.02628 15.0263i 0.159904 0.596770i
\(635\) −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
\(640\) 5.07180 18.9282i 0.200480 0.748203i
\(641\) 6.50000 + 11.2583i 0.256735 + 0.444677i 0.965365 0.260902i \(-0.0840201\pi\)
−0.708631 + 0.705580i \(0.750687\pi\)
\(642\) 8.24167 + 30.7583i 0.325273 + 1.21393i
\(643\) 13.8564 0.546443 0.273222 0.961951i \(-0.411911\pi\)
0.273222 + 0.961951i \(0.411911\pi\)
\(644\) −3.46410 4.00000i −0.136505 0.157622i
\(645\) −6.00000 −0.236250
\(646\) 3.29423 + 12.2942i 0.129610 + 0.483710i
\(647\) −16.4545 28.5000i −0.646892 1.12045i −0.983861 0.178935i \(-0.942735\pi\)
0.336968 0.941516i \(-0.390598\pi\)
\(648\) −24.5885 6.58846i −0.965926 0.258819i
\(649\) −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 \(0.959215\pi\)
\(654\) −5.70577 + 21.2942i −0.223113 + 0.832670i
\(655\) −7.79423 + 4.50000i −0.304546 + 0.175830i
\(656\) −12.0000 6.92820i −0.468521 0.270501i
\(657\) 0 0
\(658\) 29.1506 14.1506i 1.13641 0.551649i
\(659\) 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 −0.987085 0.160196i \(-0.948788\pi\)
−0.354809 + 0.934939i \(0.615454\pi\)
\(662\) 9.56218 + 2.56218i 0.371645 + 0.0995819i
\(663\) 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
\(670\) 7.09808 1.90192i 0.274223 0.0734777i
\(671\) −5.19615 −0.200595
\(672\) 21.4641 + 14.5359i 0.827996 + 0.560734i
\(673\) 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
\(682\) 2.36603 + 0.633975i 0.0905998 + 0.0242761i
\(683\) 21.6506 12.5000i 0.828439 0.478299i −0.0248792 0.999690i \(-0.507920\pi\)
0.853318 + 0.521391i \(0.174587\pi\)
\(684\) 0 0
\(685\) 1.73205i 0.0661783i
\(686\) −17.6340 + 19.3660i −0.673268 + 0.739398i
\(687\) 27.0000i 1.03011i
\(688\) −6.92820 4.00000i −0.264135 0.152499i
\(689\) −3.00000 + 1.73205i −0.114291 + 0.0659859i
\(690\) −1.09808 + 4.09808i −0.0418030 + 0.156011i
\(691\) 6.06218 10.5000i 0.230616 0.399439i −0.727373 0.686242i \(-0.759259\pi\)
0.957990 + 0.286803i \(0.0925925\pi\)
\(692\) −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
\(696\) −18.9282 5.07180i −0.717472 0.192246i
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) −3.80385 14.1962i −0.143978 0.537332i
\(699\) 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 \(0.663370\pi\)
\(702\) −6.58846 24.5885i −0.248665 0.928032i
\(703\) −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 \(0.112613\pi\)
\(710\) −8.87564 + 33.1244i −0.333097 + 1.24313i
\(711\) 0 0
\(712\) −42.5885 + 11.4115i −1.59607 + 0.427666i
\(713\) 1.73205i 0.0648658i
\(714\) −4.90192 10.0981i −0.183450 0.377911i
\(715\) 6.00000i 0.224387i
\(716\) −19.0000 + 32.9090i −0.710063 + 1.22987i
\(717\) 30.0000 17.3205i 1.12037 0.646846i
\(718\) −31.4186 8.41858i −1.17253 0.314179i
\(719\) 12.9904 22.5000i 0.484459 0.839108i −0.515381 0.856961i \(-0.672350\pi\)
0.999841 + 0.0178527i \(0.00568298\pi\)
\(720\) 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
\(726\) 23.6603 6.33975i 0.878114 0.235290i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) −1.85641 + 25.8564i −0.0688030 + 0.958302i
\(729\) 27.0000 1.00000
\(730\) 20.4904 5.49038i 0.758383 0.203208i
\(731\) 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 \(0.720687\pi\)
−0.985634 + 0.168898i \(0.945979\pi\)
\(740\) 5.19615 9.00000i 0.191014 0.330847i
\(741\) 31.1769i 1.14531i
\(742\) −0.267949 + 3.73205i −0.00983672 + 0.137008i
\(743\) 34.0000i 1.24734i 0.781688 + 0.623670i \(0.214359\pi\)
−0.781688 + 0.623670i \(0.785641\pi\)
\(744\) 2.19615 + 8.19615i 0.0805149 + 0.300486i
\(745\) 1.50000 0.866025i 0.0549557 0.0317287i
\(746\) −10.6147 + 39.6147i −0.388633 + 1.45040i
\(747\) 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 \(-0.484099\pi\)
−0.839978 + 0.542621i \(0.817432\pi\)
\(752\) −17.3205 30.0000i −0.631614 1.09399i
\(753\) 3.00000 + 5.19615i 0.109326 + 0.189358i
\(754\) −5.07180 18.9282i −0.184704 0.689325i
\(755\) 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 \(0.837369\pi\)
\(758\) −2.92820 10.9282i −0.106357 0.396930i
\(759\) 0.866025 + 1.50000i 0.0314347 + 0.0544466i
\(760\) −6.58846 + 24.5885i −0.238988 + 0.891917i
\(761\) 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
\(766\) 1.90192 7.09808i 0.0687193 0.256464i
\(767\) 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 \(-0.0198944\pi\)
\(770\) −5.36603 3.63397i −0.193378 0.130959i
\(771\) 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