Properties

Label 585.2.i.c.391.1
Level $585$
Weight $2$
Character 585.391
Analytic conductor $4.671$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 391.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 585.391
Dual form 585.2.i.c.196.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(0.500000 + 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +1.73205i q^{6} +(0.500000 + 0.866025i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +1.00000 q^{10} +(-1.00000 - 1.73205i) q^{11} +(1.50000 - 0.866025i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(1.50000 - 0.866025i) q^{15} +(0.500000 + 0.866025i) q^{16} -4.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{20} +1.73205i q^{21} +(1.00000 - 1.73205i) q^{22} +(1.50000 - 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(1.50000 + 0.866025i) q^{30} +(-4.00000 + 6.92820i) q^{31} +(2.50000 - 4.33013i) q^{32} -3.46410i q^{33} +(-2.00000 - 3.46410i) q^{34} +1.00000 q^{35} +3.00000 q^{36} +4.00000 q^{37} +(1.50000 - 0.866025i) q^{39} +(1.50000 - 2.59808i) q^{40} +(-4.50000 + 7.79423i) q^{41} +(-1.50000 + 0.866025i) q^{42} +(4.00000 + 6.92820i) q^{43} -2.00000 q^{44} +3.00000 q^{45} +3.00000 q^{46} +(-6.50000 - 11.2583i) q^{47} +1.73205i q^{48} +(3.00000 - 5.19615i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-6.00000 - 3.46410i) q^{51} +(-0.500000 - 0.866025i) q^{52} -10.0000 q^{53} +(-4.50000 + 2.59808i) q^{54} -2.00000 q^{55} +(1.50000 + 2.59808i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(-3.00000 + 5.19615i) q^{59} -1.73205i q^{60} +(0.500000 + 0.866025i) q^{61} -8.00000 q^{62} +(-1.50000 + 2.59808i) q^{63} +7.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(3.00000 - 1.73205i) q^{66} +(0.500000 - 0.866025i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(4.50000 - 2.59808i) q^{69} +(0.500000 + 0.866025i) q^{70} -6.00000 q^{71} +(4.50000 + 7.79423i) q^{72} -12.0000 q^{73} +(2.00000 + 3.46410i) q^{74} -1.73205i q^{75} +(1.00000 - 1.73205i) q^{77} +(1.50000 + 0.866025i) q^{78} +(3.00000 + 5.19615i) q^{79} +1.00000 q^{80} +(-4.50000 + 7.79423i) q^{81} -9.00000 q^{82} +(-5.50000 - 9.52628i) q^{83} +(1.50000 + 0.866025i) q^{84} +(-2.00000 + 3.46410i) q^{85} +(-4.00000 + 6.92820i) q^{86} +1.73205i q^{87} +(-3.00000 - 5.19615i) q^{88} +5.00000 q^{89} +(1.50000 + 2.59808i) q^{90} +1.00000 q^{91} +(-1.50000 - 2.59808i) q^{92} +(-12.0000 + 6.92820i) q^{93} +(6.50000 - 11.2583i) q^{94} +(7.50000 - 4.33013i) q^{96} +(1.00000 + 1.73205i) q^{97} +6.00000 q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + 3 q^{3} + q^{4} + q^{5} + q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + 3 q^{3} + q^{4} + q^{5} + q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{10} - 2 q^{11} + 3 q^{12} + q^{13} - q^{14} + 3 q^{15} + q^{16} - 8 q^{17} - 3 q^{18} - q^{20} + 2 q^{22} + 3 q^{23} + 9 q^{24} - q^{25} + 2 q^{26} + 2 q^{28} + q^{29} + 3 q^{30} - 8 q^{31} + 5 q^{32} - 4 q^{34} + 2 q^{35} + 6 q^{36} + 8 q^{37} + 3 q^{39} + 3 q^{40} - 9 q^{41} - 3 q^{42} + 8 q^{43} - 4 q^{44} + 6 q^{45} + 6 q^{46} - 13 q^{47} + 6 q^{49} + q^{50} - 12 q^{51} - q^{52} - 20 q^{53} - 9 q^{54} - 4 q^{55} + 3 q^{56} - q^{58} - 6 q^{59} + q^{61} - 16 q^{62} - 3 q^{63} + 14 q^{64} - q^{65} + 6 q^{66} + q^{67} - 4 q^{68} + 9 q^{69} + q^{70} - 12 q^{71} + 9 q^{72} - 24 q^{73} + 4 q^{74} + 2 q^{77} + 3 q^{78} + 6 q^{79} + 2 q^{80} - 9 q^{81} - 18 q^{82} - 11 q^{83} + 3 q^{84} - 4 q^{85} - 8 q^{86} - 6 q^{88} + 10 q^{89} + 3 q^{90} + 2 q^{91} - 3 q^{92} - 24 q^{93} + 13 q^{94} + 15 q^{96} + 2 q^{97} + 12 q^{98} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i 0.986869 0.161521i \(-0.0516399\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 1.73205i 0.707107i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i \(-0.106148\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 1.00000 0.316228
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) 1.50000 0.866025i 0.433013 0.250000i
\(13\) 0.500000 0.866025i 0.138675 0.240192i
\(14\) −0.500000 + 0.866025i −0.133631 + 0.231455i
\(15\) 1.50000 0.866025i 0.387298 0.223607i
\(16\) 0.500000 + 0.866025i 0.125000 + 0.216506i
\(17\) −4.00000 −0.970143 −0.485071 0.874475i \(-0.661206\pi\)
−0.485071 + 0.874475i \(0.661206\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 1.73205i 0.377964i
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 4.50000 + 2.59808i 0.918559 + 0.530330i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.00000 0.196116
\(27\) 5.19615i 1.00000i
\(28\) 1.00000 0.188982
\(29\) 0.500000 + 0.866025i 0.0928477 + 0.160817i 0.908708 0.417432i \(-0.137070\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(30\) 1.50000 + 0.866025i 0.273861 + 0.158114i
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) 2.50000 4.33013i 0.441942 0.765466i
\(33\) 3.46410i 0.603023i
\(34\) −2.00000 3.46410i −0.342997 0.594089i
\(35\) 1.00000 0.169031
\(36\) 3.00000 0.500000
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) 0 0
\(39\) 1.50000 0.866025i 0.240192 0.138675i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) −4.50000 + 7.79423i −0.702782 + 1.21725i 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) −1.50000 + 0.866025i −0.231455 + 0.133631i
\(43\) 4.00000 + 6.92820i 0.609994 + 1.05654i 0.991241 + 0.132068i \(0.0421616\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −2.00000 −0.301511
\(45\) 3.00000 0.447214
\(46\) 3.00000 0.442326
\(47\) −6.50000 11.2583i −0.948122 1.64220i −0.749375 0.662145i \(-0.769646\pi\)
−0.198747 0.980051i \(-0.563687\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 3.00000 5.19615i 0.428571 0.742307i
\(50\) 0.500000 0.866025i 0.0707107 0.122474i
\(51\) −6.00000 3.46410i −0.840168 0.485071i
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) −10.0000 −1.37361 −0.686803 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) −4.50000 + 2.59808i −0.612372 + 0.353553i
\(55\) −2.00000 −0.269680
\(56\) 1.50000 + 2.59808i 0.200446 + 0.347183i
\(57\) 0 0
\(58\) −0.500000 + 0.866025i −0.0656532 + 0.113715i
\(59\) −3.00000 + 5.19615i −0.390567 + 0.676481i −0.992524 0.122047i \(-0.961054\pi\)
0.601958 + 0.798528i \(0.294388\pi\)
\(60\) 1.73205i 0.223607i
\(61\) 0.500000 + 0.866025i 0.0640184 + 0.110883i 0.896258 0.443533i \(-0.146275\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −8.00000 −1.01600
\(63\) −1.50000 + 2.59808i −0.188982 + 0.327327i
\(64\) 7.00000 0.875000
\(65\) −0.500000 0.866025i −0.0620174 0.107417i
\(66\) 3.00000 1.73205i 0.369274 0.213201i
\(67\) 0.500000 0.866025i 0.0610847 0.105802i −0.833866 0.551967i \(-0.813877\pi\)
0.894951 + 0.446165i \(0.147211\pi\)
\(68\) −2.00000 + 3.46410i −0.242536 + 0.420084i
\(69\) 4.50000 2.59808i 0.541736 0.312772i
\(70\) 0.500000 + 0.866025i 0.0597614 + 0.103510i
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 4.50000 + 7.79423i 0.530330 + 0.918559i
\(73\) −12.0000 −1.40449 −0.702247 0.711934i \(-0.747820\pi\)
−0.702247 + 0.711934i \(0.747820\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 1.73205i 0.200000i
\(76\) 0 0
\(77\) 1.00000 1.73205i 0.113961 0.197386i
\(78\) 1.50000 + 0.866025i 0.169842 + 0.0980581i
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 1.00000 0.111803
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −9.00000 −0.993884
\(83\) −5.50000 9.52628i −0.603703 1.04565i −0.992255 0.124218i \(-0.960358\pi\)
0.388552 0.921427i \(-0.372976\pi\)
\(84\) 1.50000 + 0.866025i 0.163663 + 0.0944911i
\(85\) −2.00000 + 3.46410i −0.216930 + 0.375735i
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) 1.73205i 0.185695i
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) 5.00000 0.529999 0.264999 0.964249i \(-0.414628\pi\)
0.264999 + 0.964249i \(0.414628\pi\)
\(90\) 1.50000 + 2.59808i 0.158114 + 0.273861i
\(91\) 1.00000 0.104828
\(92\) −1.50000 2.59808i −0.156386 0.270868i
\(93\) −12.0000 + 6.92820i −1.24434 + 0.718421i
\(94\) 6.50000 11.2583i 0.670424 1.16121i
\(95\) 0 0
\(96\) 7.50000 4.33013i 0.765466 0.441942i
\(97\) 1.00000 + 1.73205i 0.101535 + 0.175863i 0.912317 0.409484i \(-0.134291\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) 6.00000 0.606092
\(99\) 3.00000 5.19615i 0.301511 0.522233i
\(100\) −1.00000 −0.100000
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 6.92820i 0.685994i
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) 1.50000 2.59808i 0.147087 0.254762i
\(105\) 1.50000 + 0.866025i 0.146385 + 0.0845154i
\(106\) −5.00000 8.66025i −0.485643 0.841158i
\(107\) 13.0000 1.25676 0.628379 0.777908i \(-0.283719\pi\)
0.628379 + 0.777908i \(0.283719\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) 1.00000 0.0957826 0.0478913 0.998853i \(-0.484750\pi\)
0.0478913 + 0.998853i \(0.484750\pi\)
\(110\) −1.00000 1.73205i −0.0953463 0.165145i
\(111\) 6.00000 + 3.46410i 0.569495 + 0.328798i
\(112\) −0.500000 + 0.866025i −0.0472456 + 0.0818317i
\(113\) −2.00000 + 3.46410i −0.188144 + 0.325875i −0.944632 0.328133i \(-0.893581\pi\)
0.756487 + 0.654008i \(0.226914\pi\)
\(114\) 0 0
\(115\) −1.50000 2.59808i −0.139876 0.242272i
\(116\) 1.00000 0.0928477
\(117\) 3.00000 0.277350
\(118\) −6.00000 −0.552345
\(119\) −2.00000 3.46410i −0.183340 0.317554i
\(120\) 4.50000 2.59808i 0.410792 0.237171i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) −0.500000 + 0.866025i −0.0452679 + 0.0784063i
\(123\) −13.5000 + 7.79423i −1.21725 + 0.702782i
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) −1.00000 −0.0894427
\(126\) −3.00000 −0.267261
\(127\) 13.0000 1.15356 0.576782 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) −1.50000 2.59808i −0.132583 0.229640i
\(129\) 13.8564i 1.21999i
\(130\) 0.500000 0.866025i 0.0438529 0.0759555i
\(131\) −7.00000 + 12.1244i −0.611593 + 1.05931i 0.379379 + 0.925241i \(0.376138\pi\)
−0.990972 + 0.134069i \(0.957196\pi\)
\(132\) −3.00000 1.73205i −0.261116 0.150756i
\(133\) 0 0
\(134\) 1.00000 0.0863868
\(135\) 4.50000 + 2.59808i 0.387298 + 0.223607i
\(136\) −12.0000 −1.02899
\(137\) −8.00000 13.8564i −0.683486 1.18383i −0.973910 0.226935i \(-0.927130\pi\)
0.290424 0.956898i \(-0.406204\pi\)
\(138\) 4.50000 + 2.59808i 0.383065 + 0.221163i
\(139\) 6.00000 10.3923i 0.508913 0.881464i −0.491033 0.871141i \(-0.663381\pi\)
0.999947 0.0103230i \(-0.00328598\pi\)
\(140\) 0.500000 0.866025i 0.0422577 0.0731925i
\(141\) 22.5167i 1.89624i
\(142\) −3.00000 5.19615i −0.251754 0.436051i
\(143\) −2.00000 −0.167248
\(144\) −1.50000 + 2.59808i −0.125000 + 0.216506i
\(145\) 1.00000 0.0830455
\(146\) −6.00000 10.3923i −0.496564 0.860073i
\(147\) 9.00000 5.19615i 0.742307 0.428571i
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i \(-0.794119\pi\)
0.920904 + 0.389789i \(0.127452\pi\)
\(150\) 1.50000 0.866025i 0.122474 0.0707107i
\(151\) −5.00000 8.66025i −0.406894 0.704761i 0.587646 0.809118i \(-0.300055\pi\)
−0.994540 + 0.104357i \(0.966722\pi\)
\(152\) 0 0
\(153\) −6.00000 10.3923i −0.485071 0.840168i
\(154\) 2.00000 0.161165
\(155\) 4.00000 + 6.92820i 0.321288 + 0.556487i
\(156\) 1.73205i 0.138675i
\(157\) −9.00000 + 15.5885i −0.718278 + 1.24409i 0.243403 + 0.969925i \(0.421736\pi\)
−0.961681 + 0.274169i \(0.911597\pi\)
\(158\) −3.00000 + 5.19615i −0.238667 + 0.413384i
\(159\) −15.0000 8.66025i −1.18958 0.686803i
\(160\) −2.50000 4.33013i −0.197642 0.342327i
\(161\) 3.00000 0.236433
\(162\) −9.00000 −0.707107
\(163\) −12.0000 −0.939913 −0.469956 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 4.50000 + 7.79423i 0.351391 + 0.608627i
\(165\) −3.00000 1.73205i −0.233550 0.134840i
\(166\) 5.50000 9.52628i 0.426883 0.739383i
\(167\) 1.50000 2.59808i 0.116073 0.201045i −0.802135 0.597143i \(-0.796303\pi\)
0.918208 + 0.396098i \(0.129636\pi\)
\(168\) 5.19615i 0.400892i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 6.00000 + 10.3923i 0.456172 + 0.790112i 0.998755 0.0498898i \(-0.0158870\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(174\) −1.50000 + 0.866025i −0.113715 + 0.0656532i
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) 1.00000 1.73205i 0.0753778 0.130558i
\(177\) −9.00000 + 5.19615i −0.676481 + 0.390567i
\(178\) 2.50000 + 4.33013i 0.187383 + 0.324557i
\(179\) 6.00000 0.448461 0.224231 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 1.50000 2.59808i 0.111803 0.193649i
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0.500000 + 0.866025i 0.0370625 + 0.0641941i
\(183\) 1.73205i 0.128037i
\(184\) 4.50000 7.79423i 0.331744 0.574598i
\(185\) 2.00000 3.46410i 0.147043 0.254686i
\(186\) −12.0000 6.92820i −0.879883 0.508001i
\(187\) 4.00000 + 6.92820i 0.292509 + 0.506640i
\(188\) −13.0000 −0.948122
\(189\) −4.50000 + 2.59808i −0.327327 + 0.188982i
\(190\) 0 0
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 10.5000 + 6.06218i 0.757772 + 0.437500i
\(193\) 1.00000 1.73205i 0.0719816 0.124676i −0.827788 0.561041i \(-0.810401\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) 1.73205i 0.124035i
\(196\) −3.00000 5.19615i −0.214286 0.371154i
\(197\) −24.0000 −1.70993 −0.854965 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) 6.00000 0.426401
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) 1.50000 0.866025i 0.105802 0.0610847i
\(202\) 3.00000 5.19615i 0.211079 0.365600i
\(203\) −0.500000 + 0.866025i −0.0350931 + 0.0607831i
\(204\) −6.00000 + 3.46410i −0.420084 + 0.242536i
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) 16.0000 1.11477
\(207\) 9.00000 0.625543
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 1.73205i 0.119523i
\(211\) −3.00000 + 5.19615i −0.206529 + 0.357718i −0.950619 0.310361i \(-0.899550\pi\)
0.744090 + 0.668079i \(0.232883\pi\)
\(212\) −5.00000 + 8.66025i −0.343401 + 0.594789i
\(213\) −9.00000 5.19615i −0.616670 0.356034i
\(214\) 6.50000 + 11.2583i 0.444331 + 0.769604i
\(215\) 8.00000 0.545595
\(216\) 15.5885i 1.06066i
\(217\) −8.00000 −0.543075
\(218\) 0.500000 + 0.866025i 0.0338643 + 0.0586546i
\(219\) −18.0000 10.3923i −1.21633 0.702247i
\(220\) −1.00000 + 1.73205i −0.0674200 + 0.116775i
\(221\) −2.00000 + 3.46410i −0.134535 + 0.233021i
\(222\) 6.92820i 0.464991i
\(223\) 8.50000 + 14.7224i 0.569202 + 0.985887i 0.996645 + 0.0818447i \(0.0260811\pi\)
−0.427443 + 0.904042i \(0.640586\pi\)
\(224\) 5.00000 0.334077
\(225\) 1.50000 2.59808i 0.100000 0.173205i
\(226\) −4.00000 −0.266076
\(227\) −2.00000 3.46410i −0.132745 0.229920i 0.791989 0.610535i \(-0.209046\pi\)
−0.924734 + 0.380615i \(0.875712\pi\)
\(228\) 0 0
\(229\) 6.50000 11.2583i 0.429532 0.743971i −0.567300 0.823511i \(-0.692012\pi\)
0.996832 + 0.0795401i \(0.0253452\pi\)
\(230\) 1.50000 2.59808i 0.0989071 0.171312i
\(231\) 3.00000 1.73205i 0.197386 0.113961i
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) 1.50000 + 2.59808i 0.0980581 + 0.169842i
\(235\) −13.0000 −0.848026
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) 10.3923i 0.675053i
\(238\) 2.00000 3.46410i 0.129641 0.224544i
\(239\) 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 1.50000 + 0.866025i 0.0968246 + 0.0559017i
\(241\) 11.5000 + 19.9186i 0.740780 + 1.28307i 0.952141 + 0.305661i \(0.0988773\pi\)
−0.211360 + 0.977408i \(0.567789\pi\)
\(242\) 7.00000 0.449977
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 1.00000 0.0640184
\(245\) −3.00000 5.19615i −0.191663 0.331970i
\(246\) −13.5000 7.79423i −0.860729 0.496942i
\(247\) 0 0
\(248\) −12.0000 + 20.7846i −0.762001 + 1.31982i
\(249\) 19.0526i 1.20741i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 1.50000 + 2.59808i 0.0944911 + 0.163663i
\(253\) −6.00000 −0.377217
\(254\) 6.50000 + 11.2583i 0.407846 + 0.706410i
\(255\) −6.00000 + 3.46410i −0.375735 + 0.216930i
\(256\) 8.50000 14.7224i 0.531250 0.920152i
\(257\) 11.0000 19.0526i 0.686161 1.18847i −0.286909 0.957958i \(-0.592628\pi\)
0.973070 0.230508i \(-0.0740389\pi\)
\(258\) −12.0000 + 6.92820i −0.747087 + 0.431331i
\(259\) 2.00000 + 3.46410i 0.124274 + 0.215249i
\(260\) −1.00000 −0.0620174
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) −14.0000 −0.864923
\(263\) 8.00000 + 13.8564i 0.493301 + 0.854423i 0.999970 0.00771799i \(-0.00245674\pi\)
−0.506669 + 0.862141i \(0.669123\pi\)
\(264\) 10.3923i 0.639602i
\(265\) −5.00000 + 8.66025i −0.307148 + 0.531995i
\(266\) 0 0
\(267\) 7.50000 + 4.33013i 0.458993 + 0.264999i
\(268\) −0.500000 0.866025i −0.0305424 0.0529009i
\(269\) 9.00000 0.548740 0.274370 0.961624i \(-0.411531\pi\)
0.274370 + 0.961624i \(0.411531\pi\)
\(270\) 5.19615i 0.316228i
\(271\) −4.00000 −0.242983 −0.121491 0.992592i \(-0.538768\pi\)
−0.121491 + 0.992592i \(0.538768\pi\)
\(272\) −2.00000 3.46410i −0.121268 0.210042i
\(273\) 1.50000 + 0.866025i 0.0907841 + 0.0524142i
\(274\) 8.00000 13.8564i 0.483298 0.837096i
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 5.19615i 0.312772i
\(277\) 10.0000 + 17.3205i 0.600842 + 1.04069i 0.992694 + 0.120660i \(0.0385012\pi\)
−0.391852 + 0.920028i \(0.628166\pi\)
\(278\) 12.0000 0.719712
\(279\) −24.0000 −1.43684
\(280\) 3.00000 0.179284
\(281\) 13.5000 + 23.3827i 0.805342 + 1.39489i 0.916060 + 0.401042i \(0.131352\pi\)
−0.110717 + 0.993852i \(0.535315\pi\)
\(282\) 19.5000 11.2583i 1.16121 0.670424i
\(283\) 6.50000 11.2583i 0.386385 0.669238i −0.605575 0.795788i \(-0.707057\pi\)
0.991960 + 0.126550i \(0.0403903\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) −1.00000 1.73205i −0.0591312 0.102418i
\(287\) −9.00000 −0.531253
\(288\) 15.0000 0.883883
\(289\) −1.00000 −0.0588235
\(290\) 0.500000 + 0.866025i 0.0293610 + 0.0508548i
\(291\) 3.46410i 0.203069i
\(292\) −6.00000 + 10.3923i −0.351123 + 0.608164i
\(293\) −2.00000 + 3.46410i −0.116841 + 0.202375i −0.918514 0.395388i \(-0.870610\pi\)
0.801673 + 0.597763i \(0.203944\pi\)
\(294\) 9.00000 + 5.19615i 0.524891 + 0.303046i
\(295\) 3.00000 + 5.19615i 0.174667 + 0.302532i
\(296\) 12.0000 0.697486
\(297\) 9.00000 5.19615i 0.522233 0.301511i
\(298\) 3.00000 0.173785
\(299\) −1.50000 2.59808i −0.0867472 0.150251i
\(300\) −1.50000 0.866025i −0.0866025 0.0500000i
\(301\) −4.00000 + 6.92820i −0.230556 + 0.399335i
\(302\) 5.00000 8.66025i 0.287718 0.498342i
\(303\) 10.3923i 0.597022i
\(304\) 0 0
\(305\) 1.00000 0.0572598
\(306\) 6.00000 10.3923i 0.342997 0.594089i
\(307\) −19.0000 −1.08439 −0.542194 0.840254i \(-0.682406\pi\)
−0.542194 + 0.840254i \(0.682406\pi\)
\(308\) −1.00000 1.73205i −0.0569803 0.0986928i
\(309\) 24.0000 13.8564i 1.36531 0.788263i
\(310\) −4.00000 + 6.92820i −0.227185 + 0.393496i
\(311\) 2.00000 3.46410i 0.113410 0.196431i −0.803733 0.594990i \(-0.797156\pi\)
0.917143 + 0.398559i \(0.130489\pi\)
\(312\) 4.50000 2.59808i 0.254762 0.147087i
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) −18.0000 −1.01580
\(315\) 1.50000 + 2.59808i 0.0845154 + 0.146385i
\(316\) 6.00000 0.337526
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 17.3205i 0.971286i
\(319\) 1.00000 1.73205i 0.0559893 0.0969762i
\(320\) 3.50000 6.06218i 0.195656 0.338886i
\(321\) 19.5000 + 11.2583i 1.08838 + 0.628379i
\(322\) 1.50000 + 2.59808i 0.0835917 + 0.144785i
\(323\) 0 0
\(324\) 4.50000 + 7.79423i 0.250000 + 0.433013i
\(325\) −1.00000 −0.0554700
\(326\) −6.00000 10.3923i −0.332309 0.575577i
\(327\) 1.50000 + 0.866025i 0.0829502 + 0.0478913i
\(328\) −13.5000 + 23.3827i −0.745413 + 1.29109i
\(329\) 6.50000 11.2583i 0.358357 0.620692i
\(330\) 3.46410i 0.190693i
\(331\) 9.00000 + 15.5885i 0.494685 + 0.856819i 0.999981 0.00612670i \(-0.00195020\pi\)
−0.505296 + 0.862946i \(0.668617\pi\)
\(332\) −11.0000 −0.603703
\(333\) 6.00000 + 10.3923i 0.328798 + 0.569495i
\(334\) 3.00000 0.164153
\(335\) −0.500000 0.866025i −0.0273179 0.0473160i
\(336\) −1.50000 + 0.866025i −0.0818317 + 0.0472456i
\(337\) −10.0000 + 17.3205i −0.544735 + 0.943508i 0.453889 + 0.891058i \(0.350036\pi\)
−0.998624 + 0.0524499i \(0.983297\pi\)
\(338\) 0.500000 0.866025i 0.0271964 0.0471056i
\(339\) −6.00000 + 3.46410i −0.325875 + 0.188144i
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) 16.0000 0.866449
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 12.0000 + 20.7846i 0.646997 + 1.12063i
\(345\) 5.19615i 0.279751i
\(346\) −6.00000 + 10.3923i −0.322562 + 0.558694i
\(347\) 14.0000 24.2487i 0.751559 1.30174i −0.195507 0.980702i \(-0.562635\pi\)
0.947067 0.321037i \(-0.104031\pi\)
\(348\) 1.50000 + 0.866025i 0.0804084 + 0.0464238i
\(349\) 4.50000 + 7.79423i 0.240879 + 0.417215i 0.960965 0.276670i \(-0.0892308\pi\)
−0.720086 + 0.693885i \(0.755897\pi\)
\(350\) 1.00000 0.0534522
\(351\) 4.50000 + 2.59808i 0.240192 + 0.138675i
\(352\) −10.0000 −0.533002
\(353\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) −9.00000 5.19615i −0.478345 0.276172i
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 2.50000 4.33013i 0.132500 0.229496i
\(357\) 6.92820i 0.366679i
\(358\) 3.00000 + 5.19615i 0.158555 + 0.274625i
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 9.00000 0.474342
\(361\) −19.0000 −1.00000
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 10.5000 6.06218i 0.551107 0.318182i
\(364\) 0.500000 0.866025i 0.0262071 0.0453921i
\(365\) −6.00000 + 10.3923i −0.314054 + 0.543958i
\(366\) −1.50000 + 0.866025i −0.0784063 + 0.0452679i
\(367\) 16.0000 + 27.7128i 0.835193 + 1.44660i 0.893873 + 0.448320i \(0.147978\pi\)
−0.0586798 + 0.998277i \(0.518689\pi\)
\(368\) 3.00000 0.156386
\(369\) −27.0000 −1.40556
\(370\) 4.00000 0.207950
\(371\) −5.00000 8.66025i −0.259587 0.449618i
\(372\) 13.8564i 0.718421i
\(373\) 7.00000 12.1244i 0.362446 0.627775i −0.625917 0.779890i \(-0.715275\pi\)
0.988363 + 0.152115i \(0.0486083\pi\)
\(374\) −4.00000 + 6.92820i −0.206835 + 0.358249i
\(375\) −1.50000 0.866025i −0.0774597 0.0447214i
\(376\) −19.5000 33.7750i −1.00564 1.74181i
\(377\) 1.00000 0.0515026
\(378\) −4.50000 2.59808i −0.231455 0.133631i
\(379\) −26.0000 −1.33553 −0.667765 0.744372i \(-0.732749\pi\)
−0.667765 + 0.744372i \(0.732749\pi\)
\(380\) 0 0
\(381\) 19.5000 + 11.2583i 0.999015 + 0.576782i
\(382\) −6.00000 + 10.3923i −0.306987 + 0.531717i
\(383\) 6.00000 10.3923i 0.306586 0.531022i −0.671027 0.741433i \(-0.734147\pi\)
0.977613 + 0.210411i \(0.0674801\pi\)
\(384\) 5.19615i 0.265165i
\(385\) −1.00000 1.73205i −0.0509647 0.0882735i
\(386\) 2.00000 0.101797
\(387\) −12.0000 + 20.7846i −0.609994 + 1.05654i
\(388\) 2.00000 0.101535
\(389\) 15.5000 + 26.8468i 0.785881 + 1.36119i 0.928471 + 0.371404i \(0.121124\pi\)
−0.142590 + 0.989782i \(0.545543\pi\)
\(390\) 1.50000 0.866025i 0.0759555 0.0438529i
\(391\) −6.00000 + 10.3923i −0.303433 + 0.525561i
\(392\) 9.00000 15.5885i 0.454569 0.787336i
\(393\) −21.0000 + 12.1244i −1.05931 + 0.611593i
\(394\) −12.0000 20.7846i −0.604551 1.04711i
\(395\) 6.00000 0.301893
\(396\) −3.00000 5.19615i −0.150756 0.261116i
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 10.0000 + 17.3205i 0.501255 + 0.868199i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) −11.0000 + 19.0526i −0.549314 + 0.951439i 0.449008 + 0.893528i \(0.351777\pi\)
−0.998322 + 0.0579116i \(0.981556\pi\)
\(402\) 1.50000 + 0.866025i 0.0748132 + 0.0431934i
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) −6.00000 −0.298511
\(405\) 4.50000 + 7.79423i 0.223607 + 0.387298i
\(406\) −1.00000 −0.0496292
\(407\) −4.00000 6.92820i −0.198273 0.343418i
\(408\) −18.0000 10.3923i −0.891133 0.514496i
\(409\) −15.0000 + 25.9808i −0.741702 + 1.28467i 0.210017 + 0.977698i \(0.432648\pi\)
−0.951720 + 0.306968i \(0.900685\pi\)
\(410\) −4.50000 + 7.79423i −0.222239 + 0.384930i
\(411\) 27.7128i 1.36697i
\(412\) −8.00000 13.8564i −0.394132 0.682656i
\(413\) −6.00000 −0.295241
\(414\) 4.50000 + 7.79423i 0.221163 + 0.383065i
\(415\) −11.0000 −0.539969
\(416\) −2.50000 4.33013i −0.122573 0.212302i
\(417\) 18.0000 10.3923i 0.881464 0.508913i
\(418\) 0 0
\(419\) 5.00000 8.66025i 0.244266 0.423081i −0.717659 0.696395i \(-0.754786\pi\)
0.961925 + 0.273314i \(0.0881197\pi\)
\(420\) 1.50000 0.866025i 0.0731925 0.0422577i
\(421\) 7.00000 + 12.1244i 0.341159 + 0.590905i 0.984648 0.174550i \(-0.0558472\pi\)
−0.643489 + 0.765455i \(0.722514\pi\)
\(422\) −6.00000 −0.292075
\(423\) 19.5000 33.7750i 0.948122 1.64220i
\(424\) −30.0000 −1.45693
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 10.3923i 0.503509i
\(427\) −0.500000 + 0.866025i −0.0241967 + 0.0419099i
\(428\) 6.50000 11.2583i 0.314189 0.544192i
\(429\) −3.00000 1.73205i −0.144841 0.0836242i
\(430\) 4.00000 + 6.92820i 0.192897 + 0.334108i
\(431\) 26.0000 1.25238 0.626188 0.779672i \(-0.284614\pi\)
0.626188 + 0.779672i \(0.284614\pi\)
\(432\) −4.50000 + 2.59808i −0.216506 + 0.125000i
\(433\) −32.0000 −1.53782 −0.768911 0.639356i \(-0.779201\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(434\) −4.00000 6.92820i −0.192006 0.332564i
\(435\) 1.50000 + 0.866025i 0.0719195 + 0.0415227i
\(436\) 0.500000 0.866025i 0.0239457 0.0414751i
\(437\) 0 0
\(438\) 20.7846i 0.993127i
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) −6.00000 −0.286039
\(441\) 18.0000 0.857143
\(442\) −4.00000 −0.190261
\(443\) −8.50000 14.7224i −0.403847 0.699484i 0.590339 0.807155i \(-0.298994\pi\)
−0.994187 + 0.107671i \(0.965661\pi\)
\(444\) 6.00000 3.46410i 0.284747 0.164399i
\(445\) 2.50000 4.33013i 0.118511 0.205268i
\(446\) −8.50000 + 14.7224i −0.402487 + 0.697127i
\(447\) 4.50000 2.59808i 0.212843 0.122885i
\(448\) 3.50000 + 6.06218i 0.165359 + 0.286411i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 3.00000 0.141421
\(451\) 18.0000 0.847587
\(452\) 2.00000 + 3.46410i 0.0940721 + 0.162938i
\(453\) 17.3205i 0.813788i
\(454\) 2.00000 3.46410i 0.0938647 0.162578i
\(455\) 0.500000 0.866025i 0.0234404 0.0405999i
\(456\) 0 0
\(457\) 8.00000 + 13.8564i 0.374224 + 0.648175i 0.990211 0.139581i \(-0.0445757\pi\)
−0.615986 + 0.787757i \(0.711242\pi\)
\(458\) 13.0000 0.607450
\(459\) 20.7846i 0.970143i
\(460\) −3.00000 −0.139876
\(461\) −6.50000 11.2583i −0.302735 0.524353i 0.674019 0.738714i \(-0.264566\pi\)
−0.976755 + 0.214361i \(0.931233\pi\)
\(462\) 3.00000 + 1.73205i 0.139573 + 0.0805823i
\(463\) 18.0000 31.1769i 0.836531 1.44891i −0.0562469 0.998417i \(-0.517913\pi\)
0.892778 0.450497i \(-0.148753\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) 13.8564i 0.642575i
\(466\) 2.00000 + 3.46410i 0.0926482 + 0.160471i
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 1.50000 2.59808i 0.0693375 0.120096i
\(469\) 1.00000 0.0461757
\(470\) −6.50000 11.2583i −0.299823 0.519308i
\(471\) −27.0000 + 15.5885i −1.24409 + 0.718278i
\(472\) −9.00000 + 15.5885i −0.414259 + 0.717517i
\(473\) 8.00000 13.8564i 0.367840 0.637118i
\(474\) −9.00000 + 5.19615i −0.413384 + 0.238667i
\(475\) 0 0
\(476\) −4.00000 −0.183340
\(477\) −15.0000 25.9808i −0.686803 1.18958i
\(478\) 24.0000 1.09773
\(479\) −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i \(-0.210436\pi\)
−0.926388 + 0.376571i \(0.877103\pi\)
\(480\) 8.66025i 0.395285i
\(481\) 2.00000 3.46410i 0.0911922 0.157949i
\(482\) −11.5000 + 19.9186i −0.523811 + 0.907267i
\(483\) 4.50000 + 2.59808i 0.204757 + 0.118217i
\(484\) −3.50000 6.06218i −0.159091 0.275554i
\(485\) 2.00000 0.0908153
\(486\) −13.5000 7.79423i −0.612372 0.353553i
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 1.50000 + 2.59808i 0.0679018 + 0.117609i
\(489\) −18.0000 10.3923i −0.813988 0.469956i
\(490\) 3.00000 5.19615i 0.135526 0.234738i
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 15.5885i 0.702782i
\(493\) −2.00000 3.46410i −0.0900755 0.156015i
\(494\) 0 0
\(495\) −3.00000 5.19615i −0.134840 0.233550i
\(496\) −8.00000 −0.359211
\(497\) −3.00000 5.19615i −0.134568 0.233079i
\(498\) 16.5000 9.52628i 0.739383 0.426883i
\(499\) 10.0000 17.3205i 0.447661 0.775372i −0.550572 0.834788i \(-0.685590\pi\)
0.998233 + 0.0594153i \(0.0189236\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 4.50000 2.59808i 0.201045 0.116073i
\(502\) 0 0
\(503\) 39.0000 1.73892 0.869462 0.494000i \(-0.164466\pi\)
0.869462 + 0.494000i \(0.164466\pi\)
\(504\) −4.50000 + 7.79423i −0.200446 + 0.347183i
\(505\) −6.00000 −0.266996
\(506\) −3.00000 5.19615i −0.133366 0.230997i
\(507\) 1.73205i 0.0769231i
\(508\) 6.50000 11.2583i 0.288391 0.499508i
\(509\) −7.50000 + 12.9904i −0.332432 + 0.575789i −0.982988 0.183669i \(-0.941202\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(510\) −6.00000 3.46410i −0.265684 0.153393i
\(511\) −6.00000 10.3923i −0.265424 0.459728i
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) 22.0000 0.970378
\(515\) −8.00000 13.8564i −0.352522 0.610586i
\(516\) 12.0000 + 6.92820i 0.528271 + 0.304997i
\(517\) −13.0000 + 22.5167i −0.571739 + 0.990282i
\(518\) −2.00000 + 3.46410i −0.0878750 + 0.152204i
\(519\) 20.7846i 0.912343i
\(520\) −1.50000 2.59808i −0.0657794 0.113933i
\(521\) 3.00000 0.131432 0.0657162 0.997838i \(-0.479067\pi\)
0.0657162 + 0.997838i \(0.479067\pi\)
\(522\) −3.00000 −0.131306
\(523\) 21.0000 0.918266 0.459133 0.888368i \(-0.348160\pi\)
0.459133 + 0.888368i \(0.348160\pi\)
\(524\) 7.00000 + 12.1244i 0.305796 + 0.529655i
\(525\) 1.50000 0.866025i 0.0654654 0.0377964i
\(526\) −8.00000 + 13.8564i −0.348817 + 0.604168i
\(527\) 16.0000 27.7128i 0.696971 1.20719i
\(528\) 3.00000 1.73205i 0.130558 0.0753778i
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) −10.0000 −0.434372
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) 4.50000 + 7.79423i 0.194917 + 0.337606i
\(534\) 8.66025i 0.374766i
\(535\) 6.50000 11.2583i 0.281020 0.486740i
\(536\) 1.50000 2.59808i 0.0647901 0.112220i
\(537\) 9.00000 + 5.19615i 0.388379 + 0.224231i
\(538\) 4.50000 + 7.79423i 0.194009 + 0.336033i
\(539\) −12.0000 −0.516877
\(540\) 4.50000 2.59808i 0.193649 0.111803i
\(541\) 5.00000 0.214967 0.107483 0.994207i \(-0.465721\pi\)
0.107483 + 0.994207i \(0.465721\pi\)
\(542\) −2.00000 3.46410i −0.0859074 0.148796i
\(543\) −10.5000 6.06218i −0.450598 0.260153i
\(544\) −10.0000 + 17.3205i −0.428746 + 0.742611i
\(545\) 0.500000 0.866025i 0.0214176 0.0370965i
\(546\) 1.73205i 0.0741249i
\(547\) −22.5000 38.9711i −0.962031 1.66629i −0.717390 0.696672i \(-0.754663\pi\)
−0.244641 0.969614i \(-0.578670\pi\)
\(548\) −16.0000 −0.683486
\(549\) −1.50000 + 2.59808i −0.0640184 + 0.110883i
\(550\) −2.00000 −0.0852803
\(551\) 0 0
\(552\) 13.5000 7.79423i 0.574598 0.331744i
\(553\) −3.00000 + 5.19615i −0.127573 + 0.220963i
\(554\) −10.0000 + 17.3205i −0.424859 + 0.735878i
\(555\) 6.00000 3.46410i 0.254686 0.147043i
\(556\) −6.00000 10.3923i −0.254457 0.440732i
\(557\) 22.0000 0.932170 0.466085 0.884740i \(-0.345664\pi\)
0.466085 + 0.884740i \(0.345664\pi\)
\(558\) −12.0000 20.7846i −0.508001 0.879883i
\(559\) 8.00000 0.338364
\(560\) 0.500000 + 0.866025i 0.0211289 + 0.0365963i
\(561\) 13.8564i 0.585018i
\(562\) −13.5000 + 23.3827i −0.569463 + 0.986339i
\(563\) 9.50000 16.4545i 0.400377 0.693474i −0.593394 0.804912i \(-0.702212\pi\)
0.993771 + 0.111438i \(0.0355457\pi\)
\(564\) −19.5000 11.2583i −0.821098 0.474061i
\(565\) 2.00000 + 3.46410i 0.0841406 + 0.145736i
\(566\) 13.0000 0.546431
\(567\) −9.00000 −0.377964
\(568\) −18.0000 −0.755263
\(569\) 19.0000 + 32.9090i 0.796521 + 1.37962i 0.921869 + 0.387503i \(0.126662\pi\)
−0.125347 + 0.992113i \(0.540004\pi\)
\(570\) 0 0
\(571\) −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) −1.00000 + 1.73205i −0.0418121 + 0.0724207i
\(573\) 20.7846i 0.868290i
\(574\) −4.50000 7.79423i −0.187826 0.325325i
\(575\) −3.00000 −0.125109
\(576\) 10.5000 + 18.1865i 0.437500 + 0.757772i
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) 3.00000 1.73205i 0.124676 0.0719816i
\(580\) 0.500000 0.866025i 0.0207614 0.0359597i
\(581\) 5.50000 9.52628i 0.228178 0.395217i
\(582\) −3.00000 + 1.73205i −0.124354 + 0.0717958i
\(583\) 10.0000 + 17.3205i 0.414158 + 0.717342i
\(584\) −36.0000 −1.48969
\(585\) 1.50000 2.59808i 0.0620174 0.107417i
\(586\) −4.00000 −0.165238
\(587\) −18.5000 32.0429i −0.763577 1.32255i −0.940996 0.338418i \(-0.890108\pi\)
0.177419 0.984135i \(-0.443225\pi\)
\(588\) 10.3923i 0.428571i
\(589\) 0 0
\(590\) −3.00000 + 5.19615i −0.123508 + 0.213922i
\(591\) −36.0000 20.7846i −1.48084 0.854965i
\(592\) 2.00000 + 3.46410i 0.0821995 + 0.142374i
\(593\) −4.00000 −0.164260 −0.0821302 0.996622i \(-0.526172\pi\)
−0.0821302 + 0.996622i \(0.526172\pi\)
\(594\) 9.00000 + 5.19615i 0.369274 + 0.213201i
\(595\) −4.00000 −0.163984
\(596\) −1.50000 2.59808i −0.0614424 0.106421i
\(597\) 30.0000 + 17.3205i 1.22782 + 0.708881i
\(598\) 1.50000 2.59808i 0.0613396 0.106243i
\(599\) −13.0000 + 22.5167i −0.531166 + 0.920006i 0.468173 + 0.883637i \(0.344912\pi\)
−0.999338 + 0.0363689i \(0.988421\pi\)
\(600\) 5.19615i 0.212132i
\(601\) −5.00000 8.66025i −0.203954 0.353259i 0.745845 0.666120i \(-0.232046\pi\)
−0.949799 + 0.312861i \(0.898713\pi\)
\(602\) −8.00000 −0.326056
\(603\) 3.00000 0.122169
\(604\) −10.0000 −0.406894
\(605\) −3.50000 6.06218i −0.142295 0.246463i
\(606\) 9.00000 5.19615i 0.365600 0.211079i
\(607\) 11.5000 19.9186i 0.466771 0.808470i −0.532509 0.846424i \(-0.678751\pi\)
0.999279 + 0.0379540i \(0.0120840\pi\)
\(608\) 0 0
\(609\) −1.50000 + 0.866025i −0.0607831 + 0.0350931i
\(610\) 0.500000 + 0.866025i 0.0202444 + 0.0350643i
\(611\) −13.0000 −0.525924
\(612\) −12.0000 −0.485071
\(613\) 24.0000 0.969351 0.484675 0.874694i \(-0.338938\pi\)
0.484675 + 0.874694i \(0.338938\pi\)
\(614\) −9.50000 16.4545i −0.383389 0.664049i
\(615\) 15.5885i 0.628587i
\(616\) 3.00000 5.19615i 0.120873 0.209359i
\(617\) 24.0000 41.5692i 0.966204 1.67351i 0.259858 0.965647i \(-0.416324\pi\)
0.706346 0.707867i \(-0.250342\pi\)
\(618\) 24.0000 + 13.8564i 0.965422 + 0.557386i
\(619\) −20.0000 34.6410i −0.803868 1.39234i −0.917053 0.398766i \(-0.869439\pi\)
0.113185 0.993574i \(-0.463895\pi\)
\(620\) 8.00000 0.321288
\(621\) 13.5000 + 7.79423i 0.541736 + 0.312772i
\(622\) 4.00000 0.160385
\(623\) 2.50000 + 4.33013i 0.100160 + 0.173483i
\(624\) 1.50000 + 0.866025i 0.0600481 + 0.0346688i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 7.00000 12.1244i 0.279776 0.484587i
\(627\) 0 0
\(628\) 9.00000 + 15.5885i 0.359139 + 0.622047i
\(629\) −16.0000 −0.637962
\(630\) −1.50000 + 2.59808i −0.0597614 + 0.103510i
\(631\) 4.00000 0.159237 0.0796187 0.996825i \(-0.474630\pi\)
0.0796187 + 0.996825i \(0.474630\pi\)
\(632\) 9.00000 + 15.5885i 0.358001 + 0.620076i
\(633\) −9.00000 + 5.19615i −0.357718 + 0.206529i
\(634\) −9.00000 + 15.5885i −0.357436 + 0.619097i
\(635\) 6.50000 11.2583i 0.257945 0.446773i
\(636\) −15.0000 + 8.66025i −0.594789 + 0.343401i
\(637\) −3.00000 5.19615i −0.118864 0.205879i
\(638\) 2.00000 0.0791808
\(639\) −9.00000 15.5885i −0.356034 0.616670i
\(640\) −3.00000 −0.118585
\(641\) −20.5000 35.5070i −0.809701 1.40244i −0.913071 0.407801i \(-0.866296\pi\)
0.103370 0.994643i \(-0.467038\pi\)
\(642\) 22.5167i 0.888662i
\(643\) 9.50000 16.4545i 0.374643 0.648901i −0.615630 0.788035i \(-0.711098\pi\)
0.990274 + 0.139134i \(0.0444318\pi\)
\(644\) 1.50000 2.59808i 0.0591083 0.102379i
\(645\) 12.0000 + 6.92820i 0.472500 + 0.272798i
\(646\) 0 0
\(647\) −7.00000 −0.275198 −0.137599 0.990488i \(-0.543939\pi\)
−0.137599 + 0.990488i \(0.543939\pi\)
\(648\) −13.5000 + 23.3827i −0.530330 + 0.918559i
\(649\) 12.0000 0.471041
\(650\) −0.500000 0.866025i −0.0196116 0.0339683i
\(651\) −12.0000 6.92820i −0.470317 0.271538i
\(652\) −6.00000 + 10.3923i −0.234978 + 0.406994i
\(653\) 18.0000 31.1769i 0.704394 1.22005i −0.262515 0.964928i \(-0.584552\pi\)
0.966910 0.255119i \(-0.0821147\pi\)
\(654\) 1.73205i 0.0677285i
\(655\) 7.00000 + 12.1244i 0.273513 + 0.473738i
\(656\) −9.00000 −0.351391
\(657\) −18.0000 31.1769i −0.702247 1.21633i
\(658\) 13.0000 0.506793
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) −3.00000 + 1.73205i −0.116775 + 0.0674200i
\(661\) −13.0000 + 22.5167i −0.505641 + 0.875797i 0.494337 + 0.869270i \(0.335411\pi\)
−0.999979 + 0.00652642i \(0.997923\pi\)
\(662\) −9.00000 + 15.5885i −0.349795 + 0.605863i
\(663\) −6.00000 + 3.46410i −0.233021 + 0.134535i
\(664\) −16.5000 28.5788i −0.640324 1.10907i
\(665\) 0 0
\(666\) −6.00000 + 10.3923i −0.232495 + 0.402694i
\(667\) 3.00000 0.116160
\(668\) −1.50000 2.59808i −0.0580367 0.100523i
\(669\) 29.4449i 1.13840i
\(670\) 0.500000 0.866025i 0.0193167 0.0334575i
\(671\) 1.00000 1.73205i 0.0386046 0.0668651i
\(672\) 7.50000 + 4.33013i 0.289319 + 0.167038i
\(673\) −9.00000 15.5885i −0.346925 0.600891i 0.638777 0.769392i \(-0.279441\pi\)
−0.985701 + 0.168501i \(0.946107\pi\)
\(674\) −20.0000 −0.770371
\(675\) 4.50000 2.59808i 0.173205 0.100000i
\(676\) −1.00000 −0.0384615
\(677\) 21.0000 + 36.3731i 0.807096 + 1.39793i 0.914867 + 0.403755i \(0.132295\pi\)
−0.107772 + 0.994176i \(0.534372\pi\)
\(678\) −6.00000 3.46410i −0.230429 0.133038i
\(679\) −1.00000 + 1.73205i −0.0383765 + 0.0664700i
\(680\) −6.00000 + 10.3923i −0.230089 + 0.398527i
\(681\) 6.92820i 0.265489i
\(682\) 8.00000 + 13.8564i 0.306336 + 0.530589i
\(683\) 4.00000 0.153056 0.0765279 0.997067i \(-0.475617\pi\)
0.0765279 + 0.997067i \(0.475617\pi\)
\(684\) 0 0
\(685\) −16.0000 −0.611329
\(686\) 6.50000 + 11.2583i 0.248171 + 0.429845i
\(687\) 19.5000 11.2583i 0.743971 0.429532i
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) −5.00000 + 8.66025i −0.190485 + 0.329929i
\(690\) 4.50000 2.59808i 0.171312 0.0989071i
\(691\) 25.0000 + 43.3013i 0.951045 + 1.64726i 0.743170 + 0.669102i \(0.233321\pi\)
0.207875 + 0.978155i \(0.433345\pi\)
\(692\) 12.0000 0.456172
\(693\) 6.00000 0.227921
\(694\) 28.0000 1.06287
\(695\) −6.00000 10.3923i −0.227593 0.394203i
\(696\) 5.19615i 0.196960i
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) −4.50000 + 7.79423i −0.170328 + 0.295016i
\(699\) 6.00000 + 3.46410i 0.226941 + 0.131024i
\(700\) −0.500000 0.866025i −0.0188982 0.0327327i
\(701\) 7.00000 0.264386 0.132193 0.991224i \(-0.457798\pi\)
0.132193 + 0.991224i \(0.457798\pi\)
\(702\) 5.19615i 0.196116i
\(703\) 0 0
\(704\) −7.00000 12.1244i −0.263822 0.456954i
\(705\) −19.5000 11.2583i −0.734412 0.424013i
\(706\) 0 0
\(707\) 3.00000 5.19615i 0.112827 0.195421i
\(708\) 10.3923i 0.390567i
\(709\) −21.5000 37.2391i −0.807449 1.39854i −0.914625 0.404303i \(-0.867514\pi\)
0.107176 0.994240i \(-0.465819\pi\)
\(710\) −6.00000 −0.225176
\(711\) −9.00000 + 15.5885i −0.337526 + 0.584613i
\(712\) 15.0000 0.562149
\(713\) 12.0000 + 20.7846i 0.449404 + 0.778390i
\(714\) 6.00000 3.46410i 0.224544 0.129641i
\(715\) −1.00000 + 1.73205i −0.0373979 + 0.0647750i
\(716\) 3.00000 5.19615i 0.112115 0.194189i
\(717\) 36.0000 20.7846i 1.34444 0.776215i
\(718\) 4.00000 + 6.92820i 0.149279 + 0.258558i
\(719\) −26.0000 −0.969636 −0.484818 0.874615i \(-0.661114\pi\)
−0.484818 + 0.874615i \(0.661114\pi\)
\(720\) 1.50000 + 2.59808i 0.0559017 + 0.0968246i
\(721\) 16.0000 0.595871
\(722\) −9.50000 16.4545i −0.353553 0.612372i
\(723\) 39.8372i 1.48156i
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) 0.500000 0.866025i 0.0185695 0.0321634i
\(726\) 10.5000 + 6.06218i 0.389692 + 0.224989i
\(727\) −16.5000 28.5788i −0.611951 1.05993i −0.990911 0.134517i \(-0.957052\pi\)
0.378960 0.925413i \(-0.376282\pi\)
\(728\) 3.00000 0.111187
\(729\) −27.0000 −1.00000
\(730\) −12.0000 −0.444140
\(731\) −16.0000 27.7128i −0.591781 1.02500i
\(732\) 1.50000 + 0.866025i 0.0554416 + 0.0320092i
\(733\) 7.00000 12.1244i 0.258551 0.447823i −0.707303 0.706910i \(-0.750088\pi\)
0.965854 + 0.259087i \(0.0834217\pi\)
\(734\) −16.0000 + 27.7128i −0.590571 + 1.02290i
\(735\) 10.3923i 0.383326i
\(736\) −7.50000 12.9904i −0.276454 0.478832i
\(737\) −2.00000 −0.0736709
\(738\) −13.5000 23.3827i −0.496942 0.860729i
\(739\) 6.00000 0.220714 0.110357 0.993892i \(-0.464801\pi\)
0.110357 + 0.993892i \(0.464801\pi\)
\(740\) −2.00000 3.46410i −0.0735215 0.127343i
\(741\) 0 0
\(742\) 5.00000 8.66025i 0.183556 0.317928i
\(743\) −16.5000 + 28.5788i −0.605326 + 1.04846i 0.386674 + 0.922217i \(0.373624\pi\)
−0.992000 + 0.126239i \(0.959709\pi\)
\(744\) −36.0000 + 20.7846i −1.31982 + 0.762001i
\(745\) −1.50000 2.59808i −0.0549557 0.0951861i
\(746\) 14.0000 0.512576
\(747\) 16.5000 28.5788i 0.603703 1.04565i
\(748\) 8.00000 0.292509
\(749\) 6.50000 + 11.2583i 0.237505 + 0.411370i
\(750\) 1.73205i 0.0632456i
\(751\) 11.0000 19.0526i 0.401396 0.695238i −0.592499 0.805571i \(-0.701859\pi\)
0.993895 + 0.110333i \(0.0351919\pi\)
\(752\) 6.50000 11.2583i 0.237031 0.410549i
\(753\) 0 0
\(754\) 0.500000 + 0.866025i 0.0182089 + 0.0315388i
\(755\) −10.0000 −0.363937
\(756\) 5.19615i 0.188982i
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −13.0000 22.5167i −0.472181 0.817842i
\(759\) −9.00000 5.19615i −0.326679 0.188608i
\(760\) 0 0
\(761\) −13.5000 + 23.3827i −0.489375 + 0.847622i −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 22.5167i 0.815693i
\(763\) 0.500000 + 0.866025i 0.0181012 + 0.0313522i
\(764\) 12.0000 0.434145
\(765\) −12.0000 −0.433861
\(766\) 12.0000 0.433578
\(767\) 3.00000 + 5.19615i 0.108324 + 0.187622i
\(768\) 25.5000 14.7224i 0.920152 0.531250i
\(769\) −8.50000 + 14.7224i −0.306518 + 0.530904i −0.977598 0.210480i \(-0.932497\pi\)
0.671080 + 0.741385i \(0.265831\pi\)
\(770\) 1.00000 1.73205i 0.0360375 0.0624188i
\(771\) 33.0000 19.0526i 1.18847 0.686161i
\(772\) −1.00000 1.73205i −0.0359908 0.0623379i
\(773\) −8.00000 −0.287740 −0.143870 0.989597i \(-0.545955\pi\)
−0.143870 + 0.989597i \(0.545955\pi\)
\(774\) −24.0000 −0.862662
\(775\) 8.00000 0.287368
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) 6.92820i