Properties

Label 546.2.i.d.79.1
Level $546$
Weight $2$
Character 546.79
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
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 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.79
Dual form 546.2.i.d.235.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.50000 + 4.33013i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-3.50000 + 6.06218i) q^{19} +(-2.00000 - 1.73205i) q^{21} -5.00000 q^{22} +(-1.00000 + 1.73205i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} -1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} -9.00000 q^{29} +(-0.500000 - 0.866025i) q^{32} +(-2.50000 + 4.33013i) q^{33} +7.00000 q^{34} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(-3.50000 - 6.06218i) q^{38} +(-0.500000 - 0.866025i) q^{39} +4.00000 q^{41} +(2.50000 - 0.866025i) q^{42} +2.00000 q^{43} +(2.50000 - 4.33013i) q^{44} +(-1.00000 - 1.73205i) q^{46} +(1.50000 - 2.59808i) q^{47} -1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} -5.00000 q^{50} +(3.50000 - 6.06218i) q^{51} +(0.500000 + 0.866025i) q^{52} +(-0.500000 - 0.866025i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-2.50000 + 0.866025i) q^{56} -7.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-3.50000 - 6.06218i) q^{59} +(-6.50000 + 11.2583i) q^{61} +(0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-2.50000 - 4.33013i) q^{66} +(-1.50000 - 2.59808i) q^{67} +(-3.50000 + 6.06218i) q^{68} -2.00000 q^{69} +9.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-2.50000 + 4.33013i) q^{75} +7.00000 q^{76} +(-10.0000 - 8.66025i) q^{77} +1.00000 q^{78} +(-7.00000 + 12.1244i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.00000 + 3.46410i) q^{82} +16.0000 q^{83} +(-0.500000 + 2.59808i) q^{84} +(-1.00000 + 1.73205i) q^{86} +(-4.50000 - 7.79423i) q^{87} +(2.50000 + 4.33013i) q^{88} +(6.00000 - 10.3923i) q^{89} +(2.50000 - 0.866025i) q^{91} +2.00000 q^{92} +(1.50000 + 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} +6.00000 q^{97} +(1.00000 + 6.92820i) q^{98} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} + q^{3} - q^{4} - 2q^{6} - 5q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} + q^{3} - q^{4} - 2q^{6} - 5q^{7} + 2q^{8} - q^{9} + 5q^{11} + q^{12} - 2q^{13} + q^{14} - q^{16} - 7q^{17} - q^{18} - 7q^{19} - 4q^{21} - 10q^{22} - 2q^{23} + q^{24} + 5q^{25} + q^{26} - 2q^{27} + 4q^{28} - 18q^{29} - q^{32} - 5q^{33} + 14q^{34} + 2q^{36} - 4q^{37} - 7q^{38} - q^{39} + 8q^{41} + 5q^{42} + 4q^{43} + 5q^{44} - 2q^{46} + 3q^{47} - 2q^{48} + 11q^{49} - 10q^{50} + 7q^{51} + q^{52} - q^{53} + q^{54} - 5q^{56} - 14q^{57} + 9q^{58} - 7q^{59} - 13q^{61} + q^{63} + 2q^{64} - 5q^{66} - 3q^{67} - 7q^{68} - 4q^{69} + 18q^{71} - q^{72} + 10q^{73} - 4q^{74} - 5q^{75} + 14q^{76} - 20q^{77} + 2q^{78} - 14q^{79} - q^{81} - 4q^{82} + 32q^{83} - q^{84} - 2q^{86} - 9q^{87} + 5q^{88} + 12q^{89} + 5q^{91} + 4q^{92} + 3q^{94} + q^{96} + 12q^{97} + 2q^{98} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\)

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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) −1.00000 −0.408248
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.50000 + 4.33013i 0.753778 + 1.30558i 0.945979 + 0.324227i \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) −1.00000 −0.277350
\(14\) 0.500000 2.59808i 0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.50000 6.06218i −0.848875 1.47029i −0.882213 0.470850i \(-0.843947\pi\)
0.0333386 0.999444i \(-0.489386\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) −5.00000 −1.06600
\(23\) −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i \(-0.900196\pi\)
0.742732 + 0.669588i \(0.233529\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −1.00000 −0.192450
\(28\) 2.00000 + 1.73205i 0.377964 + 0.327327i
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −2.50000 + 4.33013i −0.435194 + 0.753778i
\(34\) 7.00000 1.20049
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) −3.50000 6.06218i −0.567775 0.983415i
\(39\) −0.500000 0.866025i −0.0800641 0.138675i
\(40\) 0 0
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) 2.50000 0.866025i 0.385758 0.133631i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) 2.50000 4.33013i 0.376889 0.652791i
\(45\) 0 0
\(46\) −1.00000 1.73205i −0.147442 0.255377i
\(47\) 1.50000 2.59808i 0.218797 0.378968i −0.735643 0.677369i \(-0.763120\pi\)
0.954441 + 0.298401i \(0.0964533\pi\)
\(48\) −1.00000 −0.144338
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) −5.00000 −0.707107
\(51\) 3.50000 6.06218i 0.490098 0.848875i
\(52\) 0.500000 + 0.866025i 0.0693375 + 0.120096i
\(53\) −0.500000 0.866025i −0.0686803 0.118958i 0.829640 0.558298i \(-0.188546\pi\)
−0.898321 + 0.439340i \(0.855212\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) −7.00000 −0.927173
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −3.50000 6.06218i −0.455661 0.789228i 0.543065 0.839691i \(-0.317264\pi\)
−0.998726 + 0.0504625i \(0.983930\pi\)
\(60\) 0 0
\(61\) −6.50000 + 11.2583i −0.832240 + 1.44148i 0.0640184 + 0.997949i \(0.479608\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) 0.500000 2.59808i 0.0629941 0.327327i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.50000 4.33013i −0.307729 0.533002i
\(67\) −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) −3.50000 + 6.06218i −0.424437 + 0.735147i
\(69\) −2.00000 −0.240772
\(70\) 0 0
\(71\) 9.00000 1.06810 0.534052 0.845452i \(-0.320669\pi\)
0.534052 + 0.845452i \(0.320669\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 5.00000 + 8.66025i 0.585206 + 1.01361i 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) −2.00000 3.46410i −0.232495 0.402694i
\(75\) −2.50000 + 4.33013i −0.288675 + 0.500000i
\(76\) 7.00000 0.802955
\(77\) −10.0000 8.66025i −1.13961 0.986928i
\(78\) 1.00000 0.113228
\(79\) −7.00000 + 12.1244i −0.787562 + 1.36410i 0.139895 + 0.990166i \(0.455323\pi\)
−0.927457 + 0.373930i \(0.878010\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.00000 + 3.46410i −0.220863 + 0.382546i
\(83\) 16.0000 1.75623 0.878114 0.478451i \(-0.158802\pi\)
0.878114 + 0.478451i \(0.158802\pi\)
\(84\) −0.500000 + 2.59808i −0.0545545 + 0.283473i
\(85\) 0 0
\(86\) −1.00000 + 1.73205i −0.107833 + 0.186772i
\(87\) −4.50000 7.79423i −0.482451 0.835629i
\(88\) 2.50000 + 4.33013i 0.266501 + 0.461593i
\(89\) 6.00000 10.3923i 0.635999 1.10158i −0.350304 0.936636i \(-0.613922\pi\)
0.986303 0.164946i \(-0.0527450\pi\)
\(90\) 0 0
\(91\) 2.50000 0.866025i 0.262071 0.0907841i
\(92\) 2.00000 0.208514
\(93\) 0 0
\(94\) 1.50000 + 2.59808i 0.154713 + 0.267971i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 6.00000 0.609208 0.304604 0.952479i \(-0.401476\pi\)
0.304604 + 0.952479i \(0.401476\pi\)
\(98\) 1.00000 + 6.92820i 0.101015 + 0.699854i
\(99\) −5.00000 −0.502519
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 3.50000 + 6.06218i 0.346552 + 0.600245i
\(103\) 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i \(-0.669356\pi\)
0.999964 + 0.00844953i \(0.00268960\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) −4.00000 6.92820i −0.383131 0.663602i 0.608377 0.793648i \(-0.291821\pi\)
−0.991508 + 0.130046i \(0.958487\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 0.500000 2.59808i 0.0472456 0.245495i
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 3.50000 6.06218i 0.327805 0.567775i
\(115\) 0 0
\(116\) 4.50000 + 7.79423i 0.417815 + 0.723676i
\(117\) 0.500000 0.866025i 0.0462250 0.0800641i
\(118\) 7.00000 0.644402
\(119\) 14.0000 + 12.1244i 1.28338 + 1.11144i
\(120\) 0 0
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) −6.50000 11.2583i −0.588482 1.01928i
\(123\) 2.00000 + 3.46410i 0.180334 + 0.312348i
\(124\) 0 0
\(125\) 0 0
\(126\) 2.00000 + 1.73205i 0.178174 + 0.154303i
\(127\) 22.0000 1.95218 0.976092 0.217357i \(-0.0697436\pi\)
0.976092 + 0.217357i \(0.0697436\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 1.00000 + 1.73205i 0.0880451 + 0.152499i
\(130\) 0 0
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 5.00000 0.435194
\(133\) 3.50000 18.1865i 0.303488 1.57697i
\(134\) 3.00000 0.259161
\(135\) 0 0
\(136\) −3.50000 6.06218i −0.300123 0.519827i
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 1.00000 1.73205i 0.0851257 0.147442i
\(139\) 16.0000 1.35710 0.678551 0.734553i \(-0.262608\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) −4.50000 + 7.79423i −0.377632 + 0.654077i
\(143\) −2.50000 4.33013i −0.209061 0.362103i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) −10.0000 −0.827606
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) 4.00000 0.328798
\(149\) −5.00000 + 8.66025i −0.409616 + 0.709476i −0.994847 0.101391i \(-0.967671\pi\)
0.585231 + 0.810867i \(0.301004\pi\)
\(150\) −2.50000 4.33013i −0.204124 0.353553i
\(151\) 8.50000 + 14.7224i 0.691720 + 1.19809i 0.971274 + 0.237964i \(0.0764802\pi\)
−0.279554 + 0.960130i \(0.590186\pi\)
\(152\) −3.50000 + 6.06218i −0.283887 + 0.491708i
\(153\) 7.00000 0.565916
\(154\) 12.5000 4.33013i 1.00728 0.348932i
\(155\) 0 0
\(156\) −0.500000 + 0.866025i −0.0400320 + 0.0693375i
\(157\) −5.50000 9.52628i −0.438948 0.760280i 0.558661 0.829396i \(-0.311315\pi\)
−0.997609 + 0.0691164i \(0.977982\pi\)
\(158\) −7.00000 12.1244i −0.556890 0.964562i
\(159\) 0.500000 0.866025i 0.0396526 0.0686803i
\(160\) 0 0
\(161\) 1.00000 5.19615i 0.0788110 0.409514i
\(162\) 1.00000 0.0785674
\(163\) −6.50000 + 11.2583i −0.509119 + 0.881820i 0.490825 + 0.871258i \(0.336695\pi\)
−0.999944 + 0.0105623i \(0.996638\pi\)
\(164\) −2.00000 3.46410i −0.156174 0.270501i
\(165\) 0 0
\(166\) −8.00000 + 13.8564i −0.620920 + 1.07547i
\(167\) −5.00000 −0.386912 −0.193456 0.981109i \(-0.561970\pi\)
−0.193456 + 0.981109i \(0.561970\pi\)
\(168\) −2.00000 1.73205i −0.154303 0.133631i
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −3.50000 6.06218i −0.267652 0.463586i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 6.50000 11.2583i 0.494186 0.855955i −0.505792 0.862656i \(-0.668800\pi\)
0.999978 + 0.00670064i \(0.00213290\pi\)
\(174\) 9.00000 0.682288
\(175\) −10.0000 8.66025i −0.755929 0.654654i
\(176\) −5.00000 −0.376889
\(177\) 3.50000 6.06218i 0.263076 0.455661i
\(178\) 6.00000 + 10.3923i 0.449719 + 0.778936i
\(179\) 5.00000 + 8.66025i 0.373718 + 0.647298i 0.990134 0.140122i \(-0.0447496\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(180\) 0 0
\(181\) −11.0000 −0.817624 −0.408812 0.912619i \(-0.634057\pi\)
−0.408812 + 0.912619i \(0.634057\pi\)
\(182\) −0.500000 + 2.59808i −0.0370625 + 0.192582i
\(183\) −13.0000 −0.960988
\(184\) −1.00000 + 1.73205i −0.0737210 + 0.127688i
\(185\) 0 0
\(186\) 0 0
\(187\) 17.5000 30.3109i 1.27973 2.21655i
\(188\) −3.00000 −0.218797
\(189\) 2.50000 0.866025i 0.181848 0.0629941i
\(190\) 0 0
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 4.00000 + 6.92820i 0.287926 + 0.498703i 0.973315 0.229475i \(-0.0737008\pi\)
−0.685388 + 0.728178i \(0.740368\pi\)
\(194\) −3.00000 + 5.19615i −0.215387 + 0.373062i
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 22.0000 1.56744 0.783718 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 2.50000 4.33013i 0.177667 0.307729i
\(199\) −9.00000 15.5885i −0.637993 1.10504i −0.985873 0.167497i \(-0.946431\pi\)
0.347879 0.937539i \(-0.386902\pi\)
\(200\) 2.50000 + 4.33013i 0.176777 + 0.306186i
\(201\) 1.50000 2.59808i 0.105802 0.183254i
\(202\) −6.00000 −0.422159
\(203\) 22.5000 7.79423i 1.57919 0.547048i
\(204\) −7.00000 −0.490098
\(205\) 0 0
\(206\) 5.00000 + 8.66025i 0.348367 + 0.603388i
\(207\) −1.00000 1.73205i −0.0695048 0.120386i
\(208\) 0.500000 0.866025i 0.0346688 0.0600481i
\(209\) −35.0000 −2.42100
\(210\) 0 0
\(211\) −26.0000 −1.78991 −0.894957 0.446153i \(-0.852794\pi\)
−0.894957 + 0.446153i \(0.852794\pi\)
\(212\) −0.500000 + 0.866025i −0.0343401 + 0.0594789i
\(213\) 4.50000 + 7.79423i 0.308335 + 0.534052i
\(214\) 0 0
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 8.00000 0.541828
\(219\) −5.00000 + 8.66025i −0.337869 + 0.585206i
\(220\) 0 0
\(221\) 3.50000 + 6.06218i 0.235435 + 0.407786i
\(222\) 2.00000 3.46410i 0.134231 0.232495i
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 2.00000 + 1.73205i 0.133631 + 0.115728i
\(225\) −5.00000 −0.333333
\(226\) −0.500000 + 0.866025i −0.0332595 + 0.0576072i
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 3.50000 + 6.06218i 0.231793 + 0.401478i
\(229\) −9.00000 + 15.5885i −0.594737 + 1.03011i 0.398847 + 0.917017i \(0.369410\pi\)
−0.993584 + 0.113097i \(0.963923\pi\)
\(230\) 0 0
\(231\) 2.50000 12.9904i 0.164488 0.854704i
\(232\) −9.00000 −0.590879
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 0.500000 + 0.866025i 0.0326860 + 0.0566139i
\(235\) 0 0
\(236\) −3.50000 + 6.06218i −0.227831 + 0.394614i
\(237\) −14.0000 −0.909398
\(238\) −17.5000 + 6.06218i −1.13436 + 0.392953i
\(239\) −1.00000 −0.0646846 −0.0323423 0.999477i \(-0.510297\pi\)
−0.0323423 + 0.999477i \(0.510297\pi\)
\(240\) 0 0
\(241\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(242\) −7.00000 12.1244i −0.449977 0.779383i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 13.0000 0.832240
\(245\) 0 0
\(246\) −4.00000 −0.255031
\(247\) 3.50000 6.06218i 0.222700 0.385727i
\(248\) 0 0
\(249\) 8.00000 + 13.8564i 0.506979 + 0.878114i
\(250\) 0 0
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) −2.50000 + 0.866025i −0.157485 + 0.0545545i
\(253\) −10.0000 −0.628695
\(254\) −11.0000 + 19.0526i −0.690201 + 1.19546i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.00000 12.1244i 0.436648 0.756297i −0.560781 0.827964i \(-0.689499\pi\)
0.997429 + 0.0716680i \(0.0228322\pi\)
\(258\) −2.00000 −0.124515
\(259\) 2.00000 10.3923i 0.124274 0.645746i
\(260\) 0 0
\(261\) 4.50000 7.79423i 0.278543 0.482451i
\(262\) −9.00000 15.5885i −0.556022 0.963058i
\(263\) 2.00000 + 3.46410i 0.123325 + 0.213606i 0.921077 0.389380i \(-0.127311\pi\)
−0.797752 + 0.602986i \(0.793977\pi\)
\(264\) −2.50000 + 4.33013i −0.153864 + 0.266501i
\(265\) 0 0
\(266\) 14.0000 + 12.1244i 0.858395 + 0.743392i
\(267\) 12.0000 0.734388
\(268\) −1.50000 + 2.59808i −0.0916271 + 0.158703i
\(269\) −11.5000 19.9186i −0.701167 1.21446i −0.968057 0.250730i \(-0.919329\pi\)
0.266890 0.963727i \(-0.414004\pi\)
\(270\) 0 0
\(271\) −1.50000 + 2.59808i −0.0911185 + 0.157822i −0.907982 0.419009i \(-0.862378\pi\)
0.816864 + 0.576831i \(0.195711\pi\)
\(272\) 7.00000 0.424437
\(273\) 2.00000 + 1.73205i 0.121046 + 0.104828i
\(274\) −12.0000 −0.724947
\(275\) −12.5000 + 21.6506i −0.753778 + 1.30558i
\(276\) 1.00000 + 1.73205i 0.0601929 + 0.104257i
\(277\) −9.50000 16.4545i −0.570800 0.988654i −0.996484 0.0837823i \(-0.973300\pi\)
0.425684 0.904872i \(-0.360033\pi\)
\(278\) −8.00000 + 13.8564i −0.479808 + 0.831052i
\(279\) 0 0
\(280\) 0 0
\(281\) −24.0000 −1.43172 −0.715860 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) −1.50000 + 2.59808i −0.0893237 + 0.154713i
\(283\) 5.00000 + 8.66025i 0.297219 + 0.514799i 0.975499 0.220005i \(-0.0706075\pi\)
−0.678280 + 0.734804i \(0.737274\pi\)
\(284\) −4.50000 7.79423i −0.267026 0.462502i
\(285\) 0 0
\(286\) 5.00000 0.295656
\(287\) −10.0000 + 3.46410i −0.590281 + 0.204479i
\(288\) 1.00000 0.0589256
\(289\) −16.0000 + 27.7128i −0.941176 + 1.63017i
\(290\) 0 0
\(291\) 3.00000 + 5.19615i 0.175863 + 0.304604i
\(292\) 5.00000 8.66025i 0.292603 0.506803i
\(293\) −30.0000 −1.75262 −0.876309 0.481749i \(-0.840002\pi\)
−0.876309 + 0.481749i \(0.840002\pi\)
\(294\) −5.50000 + 4.33013i −0.320767 + 0.252538i
\(295\) 0 0
\(296\) −2.00000 + 3.46410i −0.116248 + 0.201347i
\(297\) −2.50000 4.33013i −0.145065 0.251259i
\(298\) −5.00000 8.66025i −0.289642 0.501675i
\(299\) 1.00000 1.73205i 0.0578315 0.100167i
\(300\) 5.00000 0.288675
\(301\) −5.00000 + 1.73205i −0.288195 + 0.0998337i
\(302\) −17.0000 −0.978240
\(303\) −3.00000 + 5.19615i −0.172345 + 0.298511i
\(304\) −3.50000 6.06218i −0.200739 0.347690i
\(305\) 0 0
\(306\) −3.50000 + 6.06218i −0.200082 + 0.346552i
\(307\) 19.0000 1.08439 0.542194 0.840254i \(-0.317594\pi\)
0.542194 + 0.840254i \(0.317594\pi\)
\(308\) −2.50000 + 12.9904i −0.142451 + 0.740196i
\(309\) 10.0000 0.568880
\(310\) 0 0
\(311\) −10.0000 17.3205i −0.567048 0.982156i −0.996856 0.0792356i \(-0.974752\pi\)
0.429808 0.902920i \(-0.358581\pi\)
\(312\) −0.500000 0.866025i −0.0283069 0.0490290i
\(313\) 3.00000 5.19615i 0.169570 0.293704i −0.768699 0.639611i \(-0.779095\pi\)
0.938269 + 0.345907i \(0.112429\pi\)
\(314\) 11.0000 0.620766
\(315\) 0 0
\(316\) 14.0000 0.787562
\(317\) −13.0000 + 22.5167i −0.730153 + 1.26466i 0.226665 + 0.973973i \(0.427218\pi\)
−0.956818 + 0.290689i \(0.906116\pi\)
\(318\) 0.500000 + 0.866025i 0.0280386 + 0.0485643i
\(319\) −22.5000 38.9711i −1.25976 2.18197i
\(320\) 0 0
\(321\) 0 0
\(322\) 4.00000 + 3.46410i 0.222911 + 0.193047i
\(323\) 49.0000 2.72643
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −2.50000 4.33013i −0.138675 0.240192i
\(326\) −6.50000 11.2583i −0.360002 0.623541i
\(327\) 4.00000 6.92820i 0.221201 0.383131i
\(328\) 4.00000 0.220863
\(329\) −1.50000 + 7.79423i −0.0826977 + 0.429710i
\(330\) 0 0
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) −8.00000 13.8564i −0.439057 0.760469i
\(333\) −2.00000 3.46410i −0.109599 0.189832i
\(334\) 2.50000 4.33013i 0.136794 0.236934i
\(335\) 0 0
\(336\) 2.50000 0.866025i 0.136386 0.0472456i
\(337\) −33.0000 −1.79762 −0.898812 0.438334i \(-0.855569\pi\)
−0.898812 + 0.438334i \(0.855569\pi\)
\(338\) −0.500000 + 0.866025i −0.0271964 + 0.0471056i
\(339\) 0.500000 + 0.866025i 0.0271563 + 0.0470360i
\(340\) 0 0
\(341\) 0 0
\(342\) 7.00000 0.378517
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 2.00000 0.107833
\(345\) 0 0
\(346\) 6.50000 + 11.2583i 0.349442 + 0.605252i
\(347\) 8.00000 + 13.8564i 0.429463 + 0.743851i 0.996826 0.0796169i \(-0.0253697\pi\)
−0.567363 + 0.823468i \(0.692036\pi\)
\(348\) −4.50000 + 7.79423i −0.241225 + 0.417815i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 12.5000 4.33013i 0.668153 0.231455i
\(351\) 1.00000 0.0533761
\(352\) 2.50000 4.33013i 0.133250 0.230797i
\(353\) −1.00000 1.73205i −0.0532246 0.0921878i 0.838186 0.545385i \(-0.183617\pi\)
−0.891410 + 0.453197i \(0.850283\pi\)
\(354\) 3.50000 + 6.06218i 0.186023 + 0.322201i
\(355\) 0 0
\(356\) −12.0000 −0.635999
\(357\) −3.50000 + 18.1865i −0.185240 + 0.962533i
\(358\) −10.0000 −0.528516
\(359\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 5.50000 9.52628i 0.289074 0.500690i
\(363\) −14.0000 −0.734809
\(364\) −2.00000 1.73205i −0.104828 0.0907841i
\(365\) 0 0
\(366\) 6.50000 11.2583i 0.339760 0.588482i
\(367\) −1.00000 1.73205i −0.0521996 0.0904123i 0.838745 0.544524i \(-0.183290\pi\)
−0.890945 + 0.454112i \(0.849957\pi\)
\(368\) −1.00000 1.73205i −0.0521286 0.0902894i
\(369\) −2.00000 + 3.46410i −0.104116 + 0.180334i
\(370\) 0 0
\(371\) 2.00000 + 1.73205i 0.103835 + 0.0899236i
\(372\) 0 0
\(373\) 10.5000 18.1865i 0.543669 0.941663i −0.455020 0.890481i \(-0.650368\pi\)
0.998689 0.0511818i \(-0.0162988\pi\)
\(374\) 17.5000 + 30.3109i 0.904903 + 1.56734i
\(375\) 0 0
\(376\) 1.50000 2.59808i 0.0773566 0.133986i
\(377\) 9.00000 0.463524
\(378\) −0.500000 + 2.59808i −0.0257172 + 0.133631i
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 11.0000 + 19.0526i 0.563547 + 0.976092i
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) −4.00000 + 6.92820i −0.204390 + 0.354015i −0.949938 0.312437i \(-0.898855\pi\)
0.745548 + 0.666452i \(0.232188\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −8.00000 −0.407189
\(387\) −1.00000 + 1.73205i −0.0508329 + 0.0880451i
\(388\) −3.00000 5.19615i −0.152302 0.263795i
\(389\) 11.5000 + 19.9186i 0.583073 + 1.00991i 0.995113 + 0.0987463i \(0.0314832\pi\)
−0.412039 + 0.911166i \(0.635183\pi\)
\(390\) 0 0
\(391\) 14.0000 0.708010
\(392\) 5.50000 4.33013i 0.277792 0.218704i
\(393\) −18.0000 −0.907980
\(394\) −11.0000 + 19.0526i −0.554172 + 0.959854i
\(395\) 0 0
\(396\) 2.50000 + 4.33013i 0.125630 + 0.217597i
\(397\) 1.00000 1.73205i 0.0501886 0.0869291i −0.839840 0.542834i \(-0.817351\pi\)
0.890028 + 0.455905i \(0.150684\pi\)
\(398\) 18.0000 0.902258
\(399\) 17.5000 6.06218i 0.876096 0.303488i
\(400\) −5.00000 −0.250000
\(401\) 19.0000 32.9090i 0.948815 1.64340i 0.200888 0.979614i \(-0.435617\pi\)
0.747927 0.663781i \(-0.231049\pi\)
\(402\) 1.50000 + 2.59808i 0.0748132 + 0.129580i
\(403\) 0 0
\(404\) 3.00000 5.19615i 0.149256 0.258518i
\(405\) 0 0
\(406\) −4.50000 + 23.3827i −0.223331 + 1.16046i
\(407\) −20.0000 −0.991363
\(408\) 3.50000 6.06218i 0.173276 0.300123i
\(409\) 2.00000 + 3.46410i 0.0988936 + 0.171289i 0.911227 0.411905i \(-0.135136\pi\)
−0.812333 + 0.583193i \(0.801803\pi\)
\(410\) 0 0
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) −10.0000 −0.492665
\(413\) 14.0000 + 12.1244i 0.688895 + 0.596601i
\(414\) 2.00000 0.0982946
\(415\) 0 0
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 8.00000 + 13.8564i 0.391762 + 0.678551i
\(418\) 17.5000 30.3109i 0.855953 1.48255i
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) 0 0
\(421\) 38.0000 1.85201 0.926003 0.377515i \(-0.123221\pi\)
0.926003 + 0.377515i \(0.123221\pi\)
\(422\) 13.0000 22.5167i 0.632830 1.09609i
\(423\) 1.50000 + 2.59808i 0.0729325 + 0.126323i
\(424\) −0.500000 0.866025i −0.0242821 0.0420579i
\(425\) 17.5000 30.3109i 0.848875 1.47029i
\(426\) −9.00000 −0.436051
\(427\) 6.50000 33.7750i 0.314557 1.63449i
\(428\) 0 0
\(429\) 2.50000 4.33013i 0.120701 0.209061i
\(430\) 0 0
\(431\) 8.00000 + 13.8564i 0.385346 + 0.667440i 0.991817 0.127666i \(-0.0407486\pi\)
−0.606471 + 0.795106i \(0.707415\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −11.0000 −0.528626 −0.264313 0.964437i \(-0.585145\pi\)
−0.264313 + 0.964437i \(0.585145\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.00000 + 6.92820i −0.191565 + 0.331801i
\(437\) −7.00000 12.1244i −0.334855 0.579987i
\(438\) −5.00000 8.66025i −0.238909 0.413803i
\(439\) 11.0000 19.0526i 0.525001 0.909329i −0.474575 0.880215i \(-0.657398\pi\)
0.999576 0.0291138i \(-0.00926853\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) −7.00000 −0.332956
\(443\) 2.00000 3.46410i 0.0950229 0.164584i −0.814595 0.580030i \(-0.803041\pi\)
0.909618 + 0.415445i \(0.136374\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) 0 0
\(446\) 0.500000 0.866025i 0.0236757 0.0410075i
\(447\) −10.0000 −0.472984
\(448\) −2.50000 + 0.866025i −0.118114 + 0.0409159i
\(449\) 4.00000 0.188772 0.0943858 0.995536i \(-0.469911\pi\)
0.0943858 + 0.995536i \(0.469911\pi\)
\(450\) 2.50000 4.33013i 0.117851 0.204124i
\(451\) 10.0000 + 17.3205i 0.470882 + 0.815591i
\(452\) −0.500000 0.866025i −0.0235180 0.0407344i
\(453\) −8.50000 + 14.7224i −0.399365 + 0.691720i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) −7.00000 −0.327805
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −9.00000 15.5885i −0.420542 0.728401i
\(459\) 3.50000 + 6.06218i 0.163366 + 0.282958i
\(460\) 0 0
\(461\) −8.00000 −0.372597 −0.186299 0.982493i \(-0.559649\pi\)
−0.186299 + 0.982493i \(0.559649\pi\)
\(462\) 10.0000 + 8.66025i 0.465242 + 0.402911i
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) 1.50000 + 2.59808i 0.0694862 + 0.120354i
\(467\) 3.00000 5.19615i 0.138823 0.240449i −0.788228 0.615383i \(-0.789001\pi\)
0.927052 + 0.374934i \(0.122335\pi\)
\(468\) −1.00000 −0.0462250
\(469\) 6.00000 + 5.19615i 0.277054 + 0.239936i
\(470\) 0 0
\(471\) 5.50000 9.52628i 0.253427 0.438948i
\(472\) −3.50000 6.06218i −0.161101 0.279034i
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) 7.00000 12.1244i 0.321521 0.556890i
\(475\) −35.0000 −1.60591
\(476\) 3.50000 18.1865i 0.160422 0.833578i
\(477\) 1.00000 0.0457869
\(478\) 0.500000 0.866025i 0.0228695 0.0396111i
\(479\) 5.50000 + 9.52628i 0.251301 + 0.435267i 0.963884 0.266321i \(-0.0858081\pi\)
−0.712583 + 0.701588i \(0.752475\pi\)
\(480\) 0 0
\(481\) 2.00000 3.46410i 0.0911922 0.157949i
\(482\) 0 0
\(483\) 5.00000 1.73205i 0.227508 0.0788110i
\(484\) 14.0000 0.636364
\(485\) 0 0
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 2.50000 + 4.33013i 0.113286 + 0.196217i 0.917093 0.398673i \(-0.130529\pi\)
−0.803807 + 0.594890i \(0.797196\pi\)
\(488\) −6.50000 + 11.2583i −0.294241 + 0.509641i
\(489\) −13.0000 −0.587880
\(490\) 0 0
\(491\) −22.0000 −0.992846 −0.496423 0.868081i \(-0.665354\pi\)
−0.496423 + 0.868081i \(0.665354\pi\)
\(492\) 2.00000 3.46410i 0.0901670 0.156174i
\(493\) 31.5000 + 54.5596i 1.41869 + 2.45724i
\(494\) 3.50000 + 6.06218i 0.157472 + 0.272750i
\(495\) 0 0
\(496\) 0 0
\(497\) −22.5000 + 7.79423i −1.00926 + 0.349619i
\(498\) −16.0000 −0.716977
\(499\) −20.0000 + 34.6410i −0.895323 + 1.55074i −0.0619186 + 0.998081i \(0.519722\pi\)
−0.833404 + 0.552664i \(0.813611\pi\)
\(500\) 0 0
\(501\) −2.50000 4.33013i −0.111692 0.193456i
\(502\) −9.00000 + 15.5885i −0.401690 + 0.695747i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0.500000 2.59808i 0.0222718 0.115728i
\(505\) 0 0
\(506\) 5.00000 8.66025i 0.222277 0.384995i
\(507\) 0.500000 + 0.866025i 0.0222058 + 0.0384615i
\(508\) −11.0000 19.0526i −0.488046 0.845321i
\(509\) −12.0000 + 20.7846i −0.531891 + 0.921262i 0.467416 + 0.884037i \(0.345185\pi\)
−0.999307 + 0.0372243i \(0.988148\pi\)
\(510\) 0 0
\(511\) −20.0000 17.3205i −0.884748 0.766214i
\(512\) 1.00000 0.0441942
\(513\) 3.50000 6.06218i 0.154529 0.267652i
\(514\) 7.00000 + 12.1244i 0.308757 + 0.534782i
\(515\) 0 0
\(516\) 1.00000 1.73205i 0.0440225 0.0762493i
\(517\) 15.0000 0.659699
\(518\) 8.00000 + 6.92820i 0.351500 + 0.304408i
\(519\) 13.0000 0.570637
\(520\) 0 0
\(521\) 19.0000 + 32.9090i 0.832405 + 1.44177i 0.896126 + 0.443800i \(0.146370\pi\)
−0.0637207 + 0.997968i \(0.520297\pi\)
\(522\) 4.50000 + 7.79423i 0.196960 + 0.341144i
\(523\) −13.0000 + 22.5167i −0.568450 + 0.984585i 0.428269 + 0.903651i \(0.359124\pi\)
−0.996719 + 0.0809336i \(0.974210\pi\)
\(524\) 18.0000 0.786334
\(525\) 2.50000 12.9904i 0.109109 0.566947i
\(526\) −4.00000 −0.174408
\(527\) 0 0
\(528\) −2.50000 4.33013i −0.108799 0.188445i
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) 0 0
\(531\) 7.00000 0.303774
\(532\) −17.5000 + 6.06218i −0.758721 + 0.262829i
\(533\) −4.00000 −0.173259
\(534\) −6.00000 + 10.3923i −0.259645 + 0.449719i
\(535\) 0 0
\(536\) −1.50000 2.59808i −0.0647901 0.112220i
\(537\) −5.00000 + 8.66025i −0.215766 + 0.373718i
\(538\) 23.0000 0.991600
\(539\) 32.5000 + 12.9904i 1.39987 + 0.559535i
\(540\) 0 0
\(541\) −8.00000 + 13.8564i −0.343947 + 0.595733i −0.985162 0.171628i \(-0.945097\pi\)
0.641215 + 0.767361i \(0.278431\pi\)
\(542\) −1.50000 2.59808i −0.0644305 0.111597i
\(543\) −5.50000 9.52628i −0.236028 0.408812i
\(544\) −3.50000 + 6.06218i −0.150061 + 0.259914i
\(545\) 0 0
\(546\) −2.50000 + 0.866025i −0.106990 + 0.0370625i
\(547\) −38.0000 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) −6.50000 11.2583i −0.277413 0.480494i
\(550\) −12.5000 21.6506i −0.533002 0.923186i
\(551\) 31.5000 54.5596i 1.34195 2.32432i
\(552\) −2.00000 −0.0851257
\(553\) 7.00000 36.3731i 0.297670 1.54674i
\(554\) 19.0000 0.807233
\(555\) 0 0
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) −9.00000 15.5885i −0.381342 0.660504i 0.609912 0.792469i \(-0.291205\pi\)
−0.991254 + 0.131965i \(0.957871\pi\)
\(558\) 0 0
\(559\) −2.00000 −0.0845910
\(560\) 0 0
\(561\) 35.0000 1.47770
\(562\) 12.0000 20.7846i 0.506189 0.876746i
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) −1.50000 2.59808i −0.0631614 0.109399i
\(565\) 0 0
\(566\) −10.0000 −0.420331
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) 9.00000 0.377632
\(569\) 15.5000 26.8468i 0.649794 1.12548i −0.333378 0.942793i \(-0.608189\pi\)
0.983172 0.182683i \(-0.0584781\pi\)
\(570\) 0 0
\(571\) 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i \(0.0668588\pi\)
−0.308443 + 0.951243i \(0.599808\pi\)
\(572\) −2.50000 + 4.33013i −0.104530 + 0.181052i
\(573\) 12.0000 0.501307
\(574\) 2.00000 10.3923i 0.0834784 0.433766i
\(575\) −10.0000 −0.417029
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i \(-0.0725410\pi\)
−0.682730 + 0.730670i \(0.739208\pi\)
\(578\) −16.0000 27.7128i −0.665512 1.15270i
\(579\) −4.00000 + 6.92820i −0.166234 + 0.287926i
\(580\) 0 0
\(581\) −40.0000 + 13.8564i −1.65948 + 0.574861i
\(582\) −6.00000 −0.248708
\(583\) 2.50000 4.33013i 0.103539 0.179336i
\(584\) 5.00000 + 8.66025i 0.206901 + 0.358364i
\(585\) 0 0
\(586\) 15.0000 25.9808i 0.619644 1.07326i
\(587\) −45.0000 −1.85735 −0.928674 0.370896i \(-0.879051\pi\)
−0.928674 + 0.370896i \(0.879051\pi\)
\(588\) −1.00000 6.92820i −0.0412393 0.285714i
\(589\) 0 0
\(590\) 0 0
\(591\) 11.0000 + 19.0526i 0.452480 + 0.783718i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 9.00000 15.5885i 0.368345 0.637993i
\(598\) 1.00000 + 1.73205i 0.0408930 + 0.0708288i
\(599\) 8.00000 + 13.8564i 0.326871 + 0.566157i 0.981889 0.189456i \(-0.0606724\pi\)
−0.655018 + 0.755613i \(0.727339\pi\)
\(600\) −2.50000 + 4.33013i −0.102062 + 0.176777i
\(601\) 25.0000 1.01977 0.509886 0.860242i \(-0.329688\pi\)
0.509886 + 0.860242i \(0.329688\pi\)
\(602\) 1.00000 5.19615i 0.0407570 0.211779i
\(603\) 3.00000 0.122169
\(604\) 8.50000 14.7224i 0.345860 0.599047i
\(605\) 0 0
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) 7.00000 12.1244i 0.284121 0.492112i −0.688274 0.725450i \(-0.741632\pi\)
0.972396 + 0.233338i \(0.0749648\pi\)
\(608\) 7.00000 0.283887
\(609\) 18.0000 + 15.5885i 0.729397 + 0.631676i
\(610\) 0 0
\(611\) −1.50000 + 2.59808i −0.0606835 + 0.105107i
\(612\) −3.50000 6.06218i −0.141479 0.245049i
\(613\) −4.00000 6.92820i −0.161558 0.279827i 0.773869 0.633345i \(-0.218319\pi\)
−0.935428 + 0.353518i \(0.884985\pi\)
\(614\) −9.50000 + 16.4545i −0.383389 + 0.664049i
\(615\) 0 0
\(616\) −10.0000 8.66025i −0.402911 0.348932i
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −5.00000 + 8.66025i −0.201129 + 0.348367i
\(619\) 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i \(-0.0350048\pi\)
−0.592025 + 0.805919i \(0.701671\pi\)
\(620\) 0 0
\(621\) 1.00000 1.73205i 0.0401286 0.0695048i
\(622\) 20.0000 0.801927
\(623\) −6.00000 + 31.1769i −0.240385 + 1.24908i
\(624\) 1.00000 0.0400320
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) −17.5000 30.3109i −0.698883 1.21050i
\(628\) −5.50000 + 9.52628i −0.219474 + 0.380140i
\(629\) 28.0000 1.11643
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −7.00000 + 12.1244i −0.278445 + 0.482281i
\(633\) −13.0000 22.5167i −0.516704 0.894957i
\(634\) −13.0000 22.5167i −0.516296 0.894251i
\(635\) 0 0
\(636\) −1.00000 −0.0396526
\(637\) −5.50000 + 4.33013i −0.217918 + 0.171566i
\(638\) 45.0000 1.78157
\(639\) −4.50000 + 7.79423i −0.178017 + 0.308335i
\(640\) 0 0
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) 0 0
\(643\) −9.00000 −0.354925 −0.177463 0.984128i \(-0.556789\pi\)
−0.177463 + 0.984128i \(0.556789\pi\)
\(644\) −5.00000 + 1.73205i −0.197028 + 0.0682524i
\(645\) 0 0
\(646\) −24.5000 + 42.4352i −0.963940 + 1.66959i
\(647\) 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i \(-0.129037\pi\)
−0.801010 + 0.598651i \(0.795704\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 17.5000 30.3109i 0.686935 1.18981i
\(650\) 5.00000 0.196116
\(651\) 0 0
\(652\) 13.0000 0.509119
\(653\) 11.0000 19.0526i 0.430463 0.745584i −0.566450 0.824096i \(-0.691684\pi\)
0.996913 + 0.0785119i \(0.0250169\pi\)
\(654\) 4.00000 + 6.92820i 0.156412 + 0.270914i
\(655\) 0 0
\(656\) −2.00000 + 3.46410i −0.0780869 + 0.135250i
\(657\) −10.0000 −0.390137
\(658\) −6.00000 5.19615i −0.233904 0.202567i
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 2.00000 + 3.46410i 0.0777910 + 0.134738i 0.902297 0.431116i \(-0.141880\pi\)
−0.824506 + 0.565854i \(0.808547\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) −3.50000 + 6.06218i −0.135929 + 0.235435i
\(664\) 16.0000 0.620920
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 9.00000 15.5885i 0.348481 0.603587i
\(668\) 2.50000 + 4.33013i 0.0967279 + 0.167538i
\(669\) −0.500000 0.866025i −0.0193311 0.0334825i
\(670\) 0 0
\(671\) −65.0000 −2.50930
\(672\) −0.500000 + 2.59808i −0.0192879 + 0.100223i
\(673\) 22.0000 0.848038 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(674\) 16.5000 28.5788i 0.635556 1.10082i
\(675\) −2.50000 4.33013i −0.0962250 0.166667i
\(676\) −0.500000 0.866025i −0.0192308 0.0333087i
\(677\) −12.5000 + 21.6506i −0.480414 + 0.832102i −0.999748 0.0224702i \(-0.992847\pi\)
0.519333 + 0.854572i \(0.326180\pi\)
\(678\) −1.00000 −0.0384048
\(679\) −15.0000 + 5.19615i −0.575647 + 0.199410i
\(680\) 0 0
\(681\) 6.00000 10.3923i 0.229920 0.398234i
\(682\) 0 0
\(683\) 20.0000 + 34.6410i 0.765279 + 1.32550i 0.940099 + 0.340901i \(0.110732\pi\)
−0.174820 + 0.984600i \(0.555934\pi\)
\(684\) −3.50000 + 6.06218i −0.133826 + 0.231793i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) −18.0000 −0.686743
\(688\) −1.00000 + 1.73205i −0.0381246 + 0.0660338i
\(689\) 0.500000 + 0.866025i 0.0190485 + 0.0329929i
\(690\) 0 0
\(691\) −2.50000 + 4.33013i −0.0951045 + 0.164726i −0.909652 0.415371i \(-0.863652\pi\)
0.814548 + 0.580097i \(0.196985\pi\)
\(692\) −13.0000 −0.494186
\(693\) 12.5000 4.33013i 0.474836 0.164488i
\(694\) −16.0000 −0.607352
\(695\) 0 0
\(696\) −4.50000 7.79423i −0.170572 0.295439i
\(697\) −14.0000 24.2487i −0.530288 0.918485i
\(698\) −1.00000 + 1.73205i −0.0378506 + 0.0655591i
\(699\) 3.00000 0.113470
\(700\) −2.50000 + 12.9904i −0.0944911 + 0.490990i
\(701\) −42.0000 −1.58632 −0.793159 0.609015i \(-0.791565\pi\)
−0.793159 + 0.609015i \(0.791565\pi\)
\(702\) −0.500000 + 0.866025i −0.0188713 + 0.0326860i
\(703\) −14.0000 24.2487i −0.528020 0.914557i
\(704\) 2.50000 + 4.33013i 0.0942223 + 0.163198i
\(705\) 0 0
\(706\) 2.00000 0.0752710
\(707\) −12.0000 10.3923i −0.451306 0.390843i
\(708\) −7.00000 −0.263076
\(709\) 23.0000 39.8372i 0.863783 1.49612i −0.00446726 0.999990i \(-0.501422\pi\)
0.868250 0.496126i \(-0.165245\pi\)
\(710\) 0 0
\(711\) −7.00000 12.1244i −0.262521 0.454699i
\(712\) 6.00000 10.3923i 0.224860 0.389468i
\(713\) 0 0
\(714\) −14.0000 12.1244i −0.523937 0.453743i
\(715\) 0 0
\(716\) 5.00000 8.66025i 0.186859 0.323649i
\(717\) −0.500000 0.866025i −0.0186728 0.0323423i
\(718\) 0 0
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 0 0
\(721\) −5.00000 + 25.9808i −0.186210 + 0.967574i
\(722\) 30.0000 1.11648
\(723\) 0 0
\(724\) 5.50000 + 9.52628i 0.204406 + 0.354041i
\(725\) −22.5000 38.9711i −0.835629 1.44735i
\(726\) 7.00000 12.1244i 0.259794 0.449977i
\(727\) −8.00000 −0.296704 −0.148352 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) 2.50000 0.866025i 0.0926562 0.0320970i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.00000 12.1244i −0.258904 0.448435i
\(732\) 6.50000 + 11.2583i 0.240247 + 0.416120i
\(733\) −7.00000 + 12.1244i −0.258551 + 0.447823i −0.965854 0.259087i \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) 2.00000 0.0738213
\(735\) 0 0
\(736\) 2.00000 0.0737210
\(737\) 7.50000 12.9904i 0.276266 0.478507i
\(738\) −2.00000 3.46410i −0.0736210 0.127515i
\(739\) 14.0000 + 24.2487i 0.514998 + 0.892003i 0.999849 + 0.0174060i \(0.00554079\pi\)
−0.484850 + 0.874597i \(0.661126\pi\)
\(740\) 0 0
\(741\) 7.00000 0.257151
\(742\) −2.50000 + 0.866025i −0.0917779 + 0.0317928i
\(743\) −5.00000 −0.183432 −0.0917161 0.995785i \(-0.529235\pi\)
−0.0917161 + 0.995785i \(0.529235\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 10.5000 + 18.1865i 0.384432 + 0.665856i
\(747\) −8.00000 + 13.8564i −0.292705 + 0.506979i
\(748\) −35.0000 −1.27973
\(749\) 0 0
\(750\) 0 0
\(751\) −16.0000 + 27.7128i −0.583848 + 1.01125i 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) 9.00000 + 15.5885i 0.327978 + 0.568075i
\(754\) −4.50000 + 7.79423i −0.163880 + 0.283849i
\(755\) 0 0
\(756\) −2.00000 1.73205i −0.0727393 0.0629941i
\(757\) 29.0000 1.05402 0.527011 0.849858i \(-0.323312\pi\)
0.527011 + 0.849858i \(0.323312\pi\)
\(758\) 2.00000 3.46410i 0.0726433 0.125822i
\(759\) −5.00000 8.66025i −0.181489 0.314347i
\(760\) 0 0
\(761\) 4.00000 6.92820i 0.145000 0.251147i −0.784373 0.620289i \(-0.787015\pi\)
0.929373 + 0.369142i \(0.120348\pi\)
\(762\) −22.0000 −0.796976
\(763\) 16.0000 + 13.8564i 0.579239 + 0.501636i
\(764\) −12.0000 −0.434145
\(765\) 0 0
\(766\) −4.00000 6.92820i −0.144526 0.250326i
\(767\) 3.50000 + 6.06218i 0.126378 + 0.218893i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) 14.0000 0.504198
\(772\) 4.00000 6.92820i 0.143963 0.249351i
\(773\) 17.0000 + 29.4449i 0.611448 + 1.05906i 0.990997 + 0.133887i \(0.0427458\pi\)
−0.379549 + 0.925172i \(0.623921\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) 0 0
\(776\) 6.00000 0.215387
\(777\) 10.0000 3.46410i 0.358748 0.124274i
\(778\) −23.0000 −0.824590
\(779\) −14.0000 + 24.2487i −0.501602 + 0.868800i
\(780\) 0 0
\(781\) 22.5000 + 38.9711i 0.805113 + 1.39450i
\(782\) −7.00000 + 12.1244i −0.250319 + 0.433566i
\(783\) 9.00000 0.321634
\(784\) 1.00000 + 6.92820i 0.0357143 + 0.247436i
\(785\) 0