Properties

Label 154.2.e.a.67.1
Level $154$
Weight $2$
Character 154.67
Analytic conductor $1.230$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.22969619113\)
Analytic rank: \(1\)
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 67.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 154.67
Dual form 154.2.e.a.23.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +3.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +3.00000 q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(-1.00000 + 1.73205i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.50000 - 2.59808i) q^{12} -7.00000 q^{13} +(0.500000 + 2.59808i) q^{14} +6.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-3.00000 + 5.19615i) q^{18} +2.00000 q^{20} +(6.00000 - 5.19615i) q^{21} -1.00000 q^{22} +(4.00000 + 6.92820i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(0.500000 - 0.866025i) q^{25} +(3.50000 + 6.06218i) q^{26} +9.00000 q^{27} +(2.00000 - 1.73205i) q^{28} -5.00000 q^{29} +(-3.00000 - 5.19615i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +2.00000 q^{34} +(1.00000 + 5.19615i) q^{35} +6.00000 q^{36} +(-2.00000 - 3.46410i) q^{37} +(10.5000 - 18.1865i) q^{39} +(-1.00000 - 1.73205i) q^{40} +4.00000 q^{41} +(-7.50000 - 2.59808i) q^{42} -8.00000 q^{43} +(0.500000 + 0.866025i) q^{44} +(-6.00000 + 10.3923i) q^{45} +(4.00000 - 6.92820i) q^{46} +(-1.00000 - 1.73205i) q^{47} +3.00000 q^{48} +(5.50000 + 4.33013i) q^{49} -1.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(3.50000 - 6.06218i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-4.50000 - 7.79423i) q^{54} -2.00000 q^{55} +(-2.50000 - 0.866025i) q^{56} +(2.50000 + 4.33013i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(-0.500000 - 0.866025i) q^{61} +4.00000 q^{62} +(3.00000 + 15.5885i) q^{63} +1.00000 q^{64} +(7.00000 + 12.1244i) q^{65} +(1.50000 - 2.59808i) q^{66} +(-4.50000 + 7.79423i) q^{67} +(-1.00000 - 1.73205i) q^{68} -24.0000 q^{69} +(4.00000 - 3.46410i) q^{70} -2.00000 q^{71} +(-3.00000 - 5.19615i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(1.50000 + 2.59808i) q^{75} +(-2.00000 + 1.73205i) q^{77} -21.0000 q^{78} +(-4.50000 - 7.79423i) q^{79} +(-1.00000 + 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-2.00000 - 3.46410i) q^{82} +6.00000 q^{83} +(1.50000 + 7.79423i) q^{84} +4.00000 q^{85} +(4.00000 + 6.92820i) q^{86} +(7.50000 - 12.9904i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-3.00000 - 5.19615i) q^{89} +12.0000 q^{90} +(17.5000 + 6.06218i) q^{91} -8.00000 q^{92} +(-6.00000 - 10.3923i) q^{93} +(-1.00000 + 1.73205i) q^{94} +(-1.50000 - 2.59808i) q^{96} +7.00000 q^{97} +(1.00000 - 6.92820i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 6 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 6 q^{6} - 5 q^{7} + 2 q^{8} - 6 q^{9} - 2 q^{10} + q^{11} - 3 q^{12} - 14 q^{13} + q^{14} + 12 q^{15} - q^{16} - 2 q^{17} - 6 q^{18} + 4 q^{20} + 12 q^{21} - 2 q^{22} + 8 q^{23} - 3 q^{24} + q^{25} + 7 q^{26} + 18 q^{27} + 4 q^{28} - 10 q^{29} - 6 q^{30} - 4 q^{31} - q^{32} + 3 q^{33} + 4 q^{34} + 2 q^{35} + 12 q^{36} - 4 q^{37} + 21 q^{39} - 2 q^{40} + 8 q^{41} - 15 q^{42} - 16 q^{43} + q^{44} - 12 q^{45} + 8 q^{46} - 2 q^{47} + 6 q^{48} + 11 q^{49} - 2 q^{50} - 6 q^{51} + 7 q^{52} + 6 q^{53} - 9 q^{54} - 4 q^{55} - 5 q^{56} + 5 q^{58} - 3 q^{59} - 6 q^{60} - q^{61} + 8 q^{62} + 6 q^{63} + 2 q^{64} + 14 q^{65} + 3 q^{66} - 9 q^{67} - 2 q^{68} - 48 q^{69} + 8 q^{70} - 4 q^{71} - 6 q^{72} - 4 q^{73} - 4 q^{74} + 3 q^{75} - 4 q^{77} - 42 q^{78} - 9 q^{79} - 2 q^{80} - 9 q^{81} - 4 q^{82} + 12 q^{83} + 3 q^{84} + 8 q^{85} + 8 q^{86} + 15 q^{87} + q^{88} - 6 q^{89} + 24 q^{90} + 35 q^{91} - 16 q^{92} - 12 q^{93} - 2 q^{94} - 3 q^{96} + 14 q^{97} + 2 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −1.50000 + 2.59808i −0.866025 + 1.50000i 1.00000i \(0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 3.00000 1.22474
\(7\) −2.50000 0.866025i −0.944911 0.327327i
\(8\) 1.00000 0.353553
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) −1.00000 + 1.73205i −0.316228 + 0.547723i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) −1.50000 2.59808i −0.433013 0.750000i
\(13\) −7.00000 −1.94145 −0.970725 0.240192i \(-0.922790\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) 6.00000 1.54919
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) −3.00000 + 5.19615i −0.707107 + 1.22474i
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 2.00000 0.447214
\(21\) 6.00000 5.19615i 1.30931 1.13389i
\(22\) −1.00000 −0.213201
\(23\) 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i \(0.147321\pi\)
−0.0607377 + 0.998154i \(0.519345\pi\)
\(24\) −1.50000 + 2.59808i −0.306186 + 0.530330i
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 3.50000 + 6.06218i 0.686406 + 1.18889i
\(27\) 9.00000 1.73205
\(28\) 2.00000 1.73205i 0.377964 0.327327i
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) −3.00000 5.19615i −0.547723 0.948683i
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 2.00000 0.342997
\(35\) 1.00000 + 5.19615i 0.169031 + 0.878310i
\(36\) 6.00000 1.00000
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 0 0
\(39\) 10.5000 18.1865i 1.68135 2.91218i
\(40\) −1.00000 1.73205i −0.158114 0.273861i
\(41\) 4.00000 0.624695 0.312348 0.949968i \(-0.398885\pi\)
0.312348 + 0.949968i \(0.398885\pi\)
\(42\) −7.50000 2.59808i −1.15728 0.400892i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 0.500000 + 0.866025i 0.0753778 + 0.130558i
\(45\) −6.00000 + 10.3923i −0.894427 + 1.54919i
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) 3.00000 0.433013
\(49\) 5.50000 + 4.33013i 0.785714 + 0.618590i
\(50\) −1.00000 −0.141421
\(51\) −3.00000 5.19615i −0.420084 0.727607i
\(52\) 3.50000 6.06218i 0.485363 0.840673i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) −4.50000 7.79423i −0.612372 1.06066i
\(55\) −2.00000 −0.269680
\(56\) −2.50000 0.866025i −0.334077 0.115728i
\(57\) 0 0
\(58\) 2.50000 + 4.33013i 0.328266 + 0.568574i
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) −3.00000 + 5.19615i −0.387298 + 0.670820i
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 4.00000 0.508001
\(63\) 3.00000 + 15.5885i 0.377964 + 1.96396i
\(64\) 1.00000 0.125000
\(65\) 7.00000 + 12.1244i 0.868243 + 1.50384i
\(66\) 1.50000 2.59808i 0.184637 0.319801i
\(67\) −4.50000 + 7.79423i −0.549762 + 0.952217i 0.448528 + 0.893769i \(0.351948\pi\)
−0.998290 + 0.0584478i \(0.981385\pi\)
\(68\) −1.00000 1.73205i −0.121268 0.210042i
\(69\) −24.0000 −2.88926
\(70\) 4.00000 3.46410i 0.478091 0.414039i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) −3.00000 5.19615i −0.353553 0.612372i
\(73\) −2.00000 + 3.46410i −0.234082 + 0.405442i −0.959006 0.283387i \(-0.908542\pi\)
0.724923 + 0.688830i \(0.241875\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 1.50000 + 2.59808i 0.173205 + 0.300000i
\(76\) 0 0
\(77\) −2.00000 + 1.73205i −0.227921 + 0.197386i
\(78\) −21.0000 −2.37778
\(79\) −4.50000 7.79423i −0.506290 0.876919i −0.999974 0.00727784i \(-0.997683\pi\)
0.493684 0.869641i \(-0.335650\pi\)
\(80\) −1.00000 + 1.73205i −0.111803 + 0.193649i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −2.00000 3.46410i −0.220863 0.382546i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 1.50000 + 7.79423i 0.163663 + 0.850420i
\(85\) 4.00000 0.433861
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) 7.50000 12.9904i 0.804084 1.39272i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) −3.00000 5.19615i −0.317999 0.550791i 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 12.0000 1.26491
\(91\) 17.5000 + 6.06218i 1.83450 + 0.635489i
\(92\) −8.00000 −0.834058
\(93\) −6.00000 10.3923i −0.622171 1.07763i
\(94\) −1.00000 + 1.73205i −0.103142 + 0.178647i
\(95\) 0 0
\(96\) −1.50000 2.59808i −0.153093 0.265165i
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 1.00000 6.92820i 0.101015 0.699854i
\(99\) −6.00000 −0.603023
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) −3.00000 + 5.19615i −0.297044 + 0.514496i
\(103\) −9.00000 15.5885i −0.886796 1.53598i −0.843641 0.536908i \(-0.819592\pi\)
−0.0431555 0.999068i \(-0.513741\pi\)
\(104\) −7.00000 −0.686406
\(105\) −15.0000 5.19615i −1.46385 0.507093i
\(106\) −6.00000 −0.582772
\(107\) −1.00000 1.73205i −0.0966736 0.167444i 0.813632 0.581380i \(-0.197487\pi\)
−0.910306 + 0.413936i \(0.864154\pi\)
\(108\) −4.50000 + 7.79423i −0.433013 + 0.750000i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 1.00000 + 1.73205i 0.0953463 + 0.165145i
\(111\) 12.0000 1.13899
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) 5.00000 0.470360 0.235180 0.971952i \(-0.424432\pi\)
0.235180 + 0.971952i \(0.424432\pi\)
\(114\) 0 0
\(115\) 8.00000 13.8564i 0.746004 1.29212i
\(116\) 2.50000 4.33013i 0.232119 0.402042i
\(117\) 21.0000 + 36.3731i 1.94145 + 3.36269i
\(118\) 3.00000 0.276172
\(119\) 4.00000 3.46410i 0.366679 0.317554i
\(120\) 6.00000 0.547723
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) −0.500000 + 0.866025i −0.0452679 + 0.0784063i
\(123\) −6.00000 + 10.3923i −0.541002 + 0.937043i
\(124\) −2.00000 3.46410i −0.179605 0.311086i
\(125\) −12.0000 −1.07331
\(126\) 12.0000 10.3923i 1.06904 0.925820i
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 12.0000 20.7846i 1.05654 1.82998i
\(130\) 7.00000 12.1244i 0.613941 1.06338i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) −3.00000 −0.261116
\(133\) 0 0
\(134\) 9.00000 0.777482
\(135\) −9.00000 15.5885i −0.774597 1.34164i
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i \(-0.874238\pi\)
0.794808 + 0.606861i \(0.207572\pi\)
\(138\) 12.0000 + 20.7846i 1.02151 + 1.76930i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −5.00000 1.73205i −0.422577 0.146385i
\(141\) 6.00000 0.505291
\(142\) 1.00000 + 1.73205i 0.0839181 + 0.145350i
\(143\) −3.50000 + 6.06218i −0.292685 + 0.506945i
\(144\) −3.00000 + 5.19615i −0.250000 + 0.433013i
\(145\) 5.00000 + 8.66025i 0.415227 + 0.719195i
\(146\) 4.00000 0.331042
\(147\) −19.5000 + 7.79423i −1.60833 + 0.642857i
\(148\) 4.00000 0.328798
\(149\) 5.00000 + 8.66025i 0.409616 + 0.709476i 0.994847 0.101391i \(-0.0323294\pi\)
−0.585231 + 0.810867i \(0.698996\pi\)
\(150\) 1.50000 2.59808i 0.122474 0.212132i
\(151\) 1.50000 2.59808i 0.122068 0.211428i −0.798515 0.601975i \(-0.794381\pi\)
0.920583 + 0.390547i \(0.127714\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) 2.50000 + 0.866025i 0.201456 + 0.0697863i
\(155\) 8.00000 0.642575
\(156\) 10.5000 + 18.1865i 0.840673 + 1.45609i
\(157\) −8.00000 + 13.8564i −0.638470 + 1.10586i 0.347299 + 0.937754i \(0.387099\pi\)
−0.985769 + 0.168107i \(0.946235\pi\)
\(158\) −4.50000 + 7.79423i −0.358001 + 0.620076i
\(159\) 9.00000 + 15.5885i 0.713746 + 1.23625i
\(160\) 2.00000 0.158114
\(161\) −4.00000 20.7846i −0.315244 1.63806i
\(162\) 9.00000 0.707107
\(163\) 8.50000 + 14.7224i 0.665771 + 1.15315i 0.979076 + 0.203497i \(0.0652307\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) −2.00000 + 3.46410i −0.156174 + 0.270501i
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 19.0000 1.47026 0.735132 0.677924i \(-0.237120\pi\)
0.735132 + 0.677924i \(0.237120\pi\)
\(168\) 6.00000 5.19615i 0.462910 0.400892i
\(169\) 36.0000 2.76923
\(170\) −2.00000 3.46410i −0.153393 0.265684i
\(171\) 0 0
\(172\) 4.00000 6.92820i 0.304997 0.528271i
\(173\) −12.5000 21.6506i −0.950357 1.64607i −0.744652 0.667453i \(-0.767384\pi\)
−0.205706 0.978614i \(-0.565949\pi\)
\(174\) −15.0000 −1.13715
\(175\) −2.00000 + 1.73205i −0.151186 + 0.130931i
\(176\) −1.00000 −0.0753778
\(177\) −4.50000 7.79423i −0.338241 0.585850i
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) −9.50000 + 16.4545i −0.710063 + 1.22987i 0.254770 + 0.967002i \(0.418000\pi\)
−0.964833 + 0.262864i \(0.915333\pi\)
\(180\) −6.00000 10.3923i −0.447214 0.774597i
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) −3.50000 18.1865i −0.259437 1.34808i
\(183\) 3.00000 0.221766
\(184\) 4.00000 + 6.92820i 0.294884 + 0.510754i
\(185\) −4.00000 + 6.92820i −0.294086 + 0.509372i
\(186\) −6.00000 + 10.3923i −0.439941 + 0.762001i
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) 2.00000 0.145865
\(189\) −22.5000 7.79423i −1.63663 0.566947i
\(190\) 0 0
\(191\) −1.00000 1.73205i −0.0723575 0.125327i 0.827577 0.561353i \(-0.189719\pi\)
−0.899934 + 0.436026i \(0.856386\pi\)
\(192\) −1.50000 + 2.59808i −0.108253 + 0.187500i
\(193\) −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i \(-0.926299\pi\)
0.685388 + 0.728178i \(0.259632\pi\)
\(194\) −3.50000 6.06218i −0.251285 0.435239i
\(195\) −42.0000 −3.00768
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 3.00000 + 5.19615i 0.213201 + 0.369274i
\(199\) −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −13.5000 23.3827i −0.952217 1.64929i
\(202\) −9.00000 −0.633238
\(203\) 12.5000 + 4.33013i 0.877328 + 0.303915i
\(204\) 6.00000 0.420084
\(205\) −4.00000 6.92820i −0.279372 0.483887i
\(206\) −9.00000 + 15.5885i −0.627060 + 1.08610i
\(207\) 24.0000 41.5692i 1.66812 2.88926i
\(208\) 3.50000 + 6.06218i 0.242681 + 0.420336i
\(209\) 0 0
\(210\) 3.00000 + 15.5885i 0.207020 + 1.07571i
\(211\) −20.0000 −1.37686 −0.688428 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) −1.00000 + 1.73205i −0.0683586 + 0.118401i
\(215\) 8.00000 + 13.8564i 0.545595 + 0.944999i
\(216\) 9.00000 0.612372
\(217\) 8.00000 6.92820i 0.543075 0.470317i
\(218\) −2.00000 −0.135457
\(219\) −6.00000 10.3923i −0.405442 0.702247i
\(220\) 1.00000 1.73205i 0.0674200 0.116775i
\(221\) 7.00000 12.1244i 0.470871 0.815572i
\(222\) −6.00000 10.3923i −0.402694 0.697486i
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 2.00000 1.73205i 0.133631 0.115728i
\(225\) −6.00000 −0.400000
\(226\) −2.50000 4.33013i −0.166298 0.288036i
\(227\) 1.00000 1.73205i 0.0663723 0.114960i −0.830930 0.556378i \(-0.812191\pi\)
0.897302 + 0.441417i \(0.145524\pi\)
\(228\) 0 0
\(229\) 14.0000 + 24.2487i 0.925146 + 1.60240i 0.791326 + 0.611394i \(0.209391\pi\)
0.133820 + 0.991006i \(0.457276\pi\)
\(230\) −16.0000 −1.05501
\(231\) −1.50000 7.79423i −0.0986928 0.512823i
\(232\) −5.00000 −0.328266
\(233\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(234\) 21.0000 36.3731i 1.37281 2.37778i
\(235\) −2.00000 + 3.46410i −0.130466 + 0.225973i
\(236\) −1.50000 2.59808i −0.0976417 0.169120i
\(237\) 27.0000 1.75384
\(238\) −5.00000 1.73205i −0.324102 0.112272i
\(239\) −5.00000 −0.323423 −0.161712 0.986838i \(-0.551701\pi\)
−0.161712 + 0.986838i \(0.551701\pi\)
\(240\) −3.00000 5.19615i −0.193649 0.335410i
\(241\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(242\) −0.500000 + 0.866025i −0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 1.00000 0.0640184
\(245\) 2.00000 13.8564i 0.127775 0.885253i
\(246\) 12.0000 0.765092
\(247\) 0 0
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) −9.00000 + 15.5885i −0.570352 + 0.987878i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) −15.0000 5.19615i −0.944911 0.327327i
\(253\) 8.00000 0.502956
\(254\) 9.50000 + 16.4545i 0.596083 + 1.03245i
\(255\) −6.00000 + 10.3923i −0.375735 + 0.650791i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) −24.0000 −1.49417
\(259\) 2.00000 + 10.3923i 0.124274 + 0.645746i
\(260\) −14.0000 −0.868243
\(261\) 15.0000 + 25.9808i 0.928477 + 1.60817i
\(262\) 0 0
\(263\) −13.5000 + 23.3827i −0.832446 + 1.44184i 0.0636476 + 0.997972i \(0.479727\pi\)
−0.896093 + 0.443866i \(0.853607\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 18.0000 1.10158
\(268\) −4.50000 7.79423i −0.274881 0.476108i
\(269\) 12.0000 20.7846i 0.731653 1.26726i −0.224523 0.974469i \(-0.572083\pi\)
0.956176 0.292791i \(-0.0945841\pi\)
\(270\) −9.00000 + 15.5885i −0.547723 + 0.948683i
\(271\) 5.50000 + 9.52628i 0.334101 + 0.578680i 0.983312 0.181928i \(-0.0582339\pi\)
−0.649211 + 0.760609i \(0.724901\pi\)
\(272\) 2.00000 0.121268
\(273\) −42.0000 + 36.3731i −2.54196 + 2.20140i
\(274\) 3.00000 0.181237
\(275\) −0.500000 0.866025i −0.0301511 0.0522233i
\(276\) 12.0000 20.7846i 0.722315 1.25109i
\(277\) 4.50000 7.79423i 0.270379 0.468310i −0.698580 0.715532i \(-0.746184\pi\)
0.968959 + 0.247222i \(0.0795177\pi\)
\(278\) 2.00000 + 3.46410i 0.119952 + 0.207763i
\(279\) 24.0000 1.43684
\(280\) 1.00000 + 5.19615i 0.0597614 + 0.310530i
\(281\) −28.0000 −1.67034 −0.835170 0.549992i \(-0.814631\pi\)
−0.835170 + 0.549992i \(0.814631\pi\)
\(282\) −3.00000 5.19615i −0.178647 0.309426i
\(283\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(284\) 1.00000 1.73205i 0.0593391 0.102778i
\(285\) 0 0
\(286\) 7.00000 0.413919
\(287\) −10.0000 3.46410i −0.590281 0.204479i
\(288\) 6.00000 0.353553
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 5.00000 8.66025i 0.293610 0.508548i
\(291\) −10.5000 + 18.1865i −0.615521 + 1.06611i
\(292\) −2.00000 3.46410i −0.117041 0.202721i
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 16.5000 + 12.9904i 0.962300 + 0.757614i
\(295\) 6.00000 0.349334
\(296\) −2.00000 3.46410i −0.116248 0.201347i
\(297\) 4.50000 7.79423i 0.261116 0.452267i
\(298\) 5.00000 8.66025i 0.289642 0.501675i
\(299\) −28.0000 48.4974i −1.61928 2.80468i
\(300\) −3.00000 −0.173205
\(301\) 20.0000 + 6.92820i 1.15278 + 0.399335i
\(302\) −3.00000 −0.172631
\(303\) 13.5000 + 23.3827i 0.775555 + 1.34330i
\(304\) 0 0
\(305\) −1.00000 + 1.73205i −0.0572598 + 0.0991769i
\(306\) −6.00000 10.3923i −0.342997 0.594089i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −0.500000 2.59808i −0.0284901 0.148039i
\(309\) 54.0000 3.07195
\(310\) −4.00000 6.92820i −0.227185 0.393496i
\(311\) 5.00000 8.66025i 0.283524 0.491078i −0.688726 0.725022i \(-0.741830\pi\)
0.972250 + 0.233944i \(0.0751631\pi\)
\(312\) 10.5000 18.1865i 0.594445 1.02961i
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) 16.0000 0.902932
\(315\) 24.0000 20.7846i 1.35225 1.17108i
\(316\) 9.00000 0.506290
\(317\) 6.00000 + 10.3923i 0.336994 + 0.583690i 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) 9.00000 15.5885i 0.504695 0.874157i
\(319\) −2.50000 + 4.33013i −0.139973 + 0.242441i
\(320\) −1.00000 1.73205i −0.0559017 0.0968246i
\(321\) 6.00000 0.334887
\(322\) −16.0000 + 13.8564i −0.891645 + 0.772187i
\(323\) 0 0
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) −3.50000 + 6.06218i −0.194145 + 0.336269i
\(326\) 8.50000 14.7224i 0.470771 0.815400i
\(327\) 3.00000 + 5.19615i 0.165900 + 0.287348i
\(328\) 4.00000 0.220863
\(329\) 1.00000 + 5.19615i 0.0551318 + 0.286473i
\(330\) −6.00000 −0.330289
\(331\) −6.50000 11.2583i −0.357272 0.618814i 0.630232 0.776407i \(-0.282960\pi\)
−0.987504 + 0.157593i \(0.949627\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) −12.0000 + 20.7846i −0.657596 + 1.13899i
\(334\) −9.50000 16.4545i −0.519817 0.900349i
\(335\) 18.0000 0.983445
\(336\) −7.50000 2.59808i −0.409159 0.141737i
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) −18.0000 31.1769i −0.979071 1.69580i
\(339\) −7.50000 + 12.9904i −0.407344 + 0.705541i
\(340\) −2.00000 + 3.46410i −0.108465 + 0.187867i
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) −8.00000 −0.431331
\(345\) 24.0000 + 41.5692i 1.29212 + 2.23801i
\(346\) −12.5000 + 21.6506i −0.672004 + 1.16395i
\(347\) 11.0000 19.0526i 0.590511 1.02279i −0.403653 0.914912i \(-0.632260\pi\)
0.994164 0.107883i \(-0.0344071\pi\)
\(348\) 7.50000 + 12.9904i 0.402042 + 0.696358i
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 2.50000 + 0.866025i 0.133631 + 0.0462910i
\(351\) −63.0000 −3.36269
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 9.00000 15.5885i 0.479022 0.829690i −0.520689 0.853746i \(-0.674325\pi\)
0.999711 + 0.0240566i \(0.00765819\pi\)
\(354\) −4.50000 + 7.79423i −0.239172 + 0.414259i
\(355\) 2.00000 + 3.46410i 0.106149 + 0.183855i
\(356\) 6.00000 0.317999
\(357\) 3.00000 + 15.5885i 0.158777 + 0.825029i
\(358\) 19.0000 1.00418
\(359\) 9.50000 + 16.4545i 0.501391 + 0.868434i 0.999999 + 0.00160673i \(0.000511438\pi\)
−0.498608 + 0.866828i \(0.666155\pi\)
\(360\) −6.00000 + 10.3923i −0.316228 + 0.547723i
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 11.0000 + 19.0526i 0.578147 + 1.00138i
\(363\) 3.00000 0.157459
\(364\) −14.0000 + 12.1244i −0.733799 + 0.635489i
\(365\) 8.00000 0.418739
\(366\) −1.50000 2.59808i −0.0784063 0.135804i
\(367\) −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i \(-0.866625\pi\)
0.809093 + 0.587680i \(0.199959\pi\)
\(368\) 4.00000 6.92820i 0.208514 0.361158i
\(369\) −12.0000 20.7846i −0.624695 1.08200i
\(370\) 8.00000 0.415900
\(371\) −12.0000 + 10.3923i −0.623009 + 0.539542i
\(372\) 12.0000 0.622171
\(373\) −5.50000 9.52628i −0.284779 0.493252i 0.687776 0.725923i \(-0.258587\pi\)
−0.972556 + 0.232671i \(0.925254\pi\)
\(374\) 1.00000 1.73205i 0.0517088 0.0895622i
\(375\) 18.0000 31.1769i 0.929516 1.60997i
\(376\) −1.00000 1.73205i −0.0515711 0.0893237i
\(377\) 35.0000 1.80259
\(378\) 4.50000 + 23.3827i 0.231455 + 1.20268i
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 0 0
\(381\) 28.5000 49.3634i 1.46010 2.52897i
\(382\) −1.00000 + 1.73205i −0.0511645 + 0.0886194i
\(383\) −13.0000 22.5167i −0.664269 1.15055i −0.979483 0.201527i \(-0.935410\pi\)
0.315214 0.949021i \(-0.397924\pi\)
\(384\) 3.00000 0.153093
\(385\) 5.00000 + 1.73205i 0.254824 + 0.0882735i
\(386\) 8.00000 0.407189
\(387\) 24.0000 + 41.5692i 1.21999 + 2.11308i
\(388\) −3.50000 + 6.06218i −0.177686 + 0.307760i
\(389\) −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i \(-0.984165\pi\)
0.542445 + 0.840091i \(0.317499\pi\)
\(390\) 21.0000 + 36.3731i 1.06338 + 1.84182i
\(391\) −16.0000 −0.809155
\(392\) 5.50000 + 4.33013i 0.277792 + 0.218704i
\(393\) 0 0
\(394\) −7.50000 12.9904i −0.377845 0.654446i
\(395\) −9.00000 + 15.5885i −0.452839 + 0.784340i
\(396\) 3.00000 5.19615i 0.150756 0.261116i
\(397\) −3.00000 5.19615i −0.150566 0.260787i 0.780870 0.624694i \(-0.214776\pi\)
−0.931436 + 0.363906i \(0.881443\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 4.50000 + 7.79423i 0.224719 + 0.389225i 0.956235 0.292599i \(-0.0945202\pi\)
−0.731516 + 0.681824i \(0.761187\pi\)
\(402\) −13.5000 + 23.3827i −0.673319 + 1.16622i
\(403\) 14.0000 24.2487i 0.697390 1.20791i
\(404\) 4.50000 + 7.79423i 0.223883 + 0.387777i
\(405\) 18.0000 0.894427
\(406\) −2.50000 12.9904i −0.124073 0.644702i
\(407\) −4.00000 −0.198273
\(408\) −3.00000 5.19615i −0.148522 0.257248i
\(409\) −11.0000 + 19.0526i −0.543915 + 0.942088i 0.454759 + 0.890614i \(0.349725\pi\)
−0.998674 + 0.0514740i \(0.983608\pi\)
\(410\) −4.00000 + 6.92820i −0.197546 + 0.342160i
\(411\) −4.50000 7.79423i −0.221969 0.384461i
\(412\) 18.0000 0.886796
\(413\) 6.00000 5.19615i 0.295241 0.255686i
\(414\) −48.0000 −2.35907
\(415\) −6.00000 10.3923i −0.294528 0.510138i
\(416\) 3.50000 6.06218i 0.171602 0.297223i
\(417\) 6.00000 10.3923i 0.293821 0.508913i
\(418\) 0 0
\(419\) 16.0000 0.781651 0.390826 0.920465i \(-0.372190\pi\)
0.390826 + 0.920465i \(0.372190\pi\)
\(420\) 12.0000 10.3923i 0.585540 0.507093i
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 10.0000 + 17.3205i 0.486792 + 0.843149i
\(423\) −6.00000 + 10.3923i −0.291730 + 0.505291i
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) −6.00000 −0.290701
\(427\) 0.500000 + 2.59808i 0.0241967 + 0.125730i
\(428\) 2.00000 0.0966736
\(429\) −10.5000 18.1865i −0.506945 0.878054i
\(430\) 8.00000 13.8564i 0.385794 0.668215i
\(431\) −12.5000 + 21.6506i −0.602104 + 1.04287i 0.390398 + 0.920646i \(0.372337\pi\)
−0.992502 + 0.122228i \(0.960996\pi\)
\(432\) −4.50000 7.79423i −0.216506 0.375000i
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) −10.0000 3.46410i −0.480015 0.166282i
\(435\) −30.0000 −1.43839
\(436\) 1.00000 + 1.73205i 0.0478913 + 0.0829502i
\(437\) 0 0
\(438\) −6.00000 + 10.3923i −0.286691 + 0.496564i
\(439\) 2.50000 + 4.33013i 0.119318 + 0.206666i 0.919498 0.393095i \(-0.128596\pi\)
−0.800179 + 0.599761i \(0.795262\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 6.00000 41.5692i 0.285714 1.97949i
\(442\) −14.0000 −0.665912
\(443\) −18.0000 31.1769i −0.855206 1.48126i −0.876454 0.481486i \(-0.840097\pi\)
0.0212481 0.999774i \(-0.493236\pi\)
\(444\) −6.00000 + 10.3923i −0.284747 + 0.493197i
\(445\) −6.00000 + 10.3923i −0.284427 + 0.492642i
\(446\) −2.00000 3.46410i −0.0947027 0.164030i
\(447\) −30.0000 −1.41895
\(448\) −2.50000 0.866025i −0.118114 0.0409159i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 3.00000 + 5.19615i 0.141421 + 0.244949i
\(451\) 2.00000 3.46410i 0.0941763 0.163118i
\(452\) −2.50000 + 4.33013i −0.117590 + 0.203672i
\(453\) 4.50000 + 7.79423i 0.211428 + 0.366205i
\(454\) −2.00000 −0.0938647
\(455\) −7.00000 36.3731i −0.328165 1.70520i
\(456\) 0 0
\(457\) −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i \(-0.272855\pi\)
−0.982004 + 0.188858i \(0.939521\pi\)
\(458\) 14.0000 24.2487i 0.654177 1.13307i
\(459\) −9.00000 + 15.5885i −0.420084 + 0.727607i
\(460\) 8.00000 + 13.8564i 0.373002 + 0.646058i
\(461\) 27.0000 1.25752 0.628758 0.777601i \(-0.283564\pi\)
0.628758 + 0.777601i \(0.283564\pi\)
\(462\) −6.00000 + 5.19615i −0.279145 + 0.241747i
\(463\) −2.00000 −0.0929479 −0.0464739 0.998920i \(-0.514798\pi\)
−0.0464739 + 0.998920i \(0.514798\pi\)
\(464\) 2.50000 + 4.33013i 0.116060 + 0.201021i
\(465\) −12.0000 + 20.7846i −0.556487 + 0.963863i
\(466\) 0 0
\(467\) −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i \(-0.256221\pi\)
−0.970799 + 0.239892i \(0.922888\pi\)
\(468\) −42.0000 −1.94145
\(469\) 18.0000 15.5885i 0.831163 0.719808i
\(470\) 4.00000 0.184506
\(471\) −24.0000 41.5692i −1.10586 1.91541i
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) −4.00000 + 6.92820i −0.183920 + 0.318559i
\(474\) −13.5000 23.3827i −0.620076 1.07400i
\(475\) 0 0
\(476\) 1.00000 + 5.19615i 0.0458349 + 0.238165i
\(477\) −36.0000 −1.64833
\(478\) 2.50000 + 4.33013i 0.114347 + 0.198055i
\(479\) 0.500000 0.866025i 0.0228456 0.0395697i −0.854377 0.519654i \(-0.826061\pi\)
0.877222 + 0.480085i \(0.159394\pi\)
\(480\) −3.00000 + 5.19615i −0.136931 + 0.237171i
\(481\) 14.0000 + 24.2487i 0.638345 + 1.10565i
\(482\) 0 0
\(483\) 60.0000 + 20.7846i 2.73009 + 0.945732i
\(484\) 1.00000 0.0454545
\(485\) −7.00000 12.1244i −0.317854 0.550539i
\(486\) 0 0
\(487\) 20.0000 34.6410i 0.906287 1.56973i 0.0871056 0.996199i \(-0.472238\pi\)
0.819181 0.573535i \(-0.194428\pi\)
\(488\) −0.500000 0.866025i −0.0226339 0.0392031i
\(489\) −51.0000 −2.30630
\(490\) −13.0000 + 5.19615i −0.587280 + 0.234738i
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) −6.00000 10.3923i −0.270501 0.468521i
\(493\) 5.00000 8.66025i 0.225189 0.390038i
\(494\) 0 0
\(495\) 6.00000 + 10.3923i 0.269680 + 0.467099i
\(496\) 4.00000 0.179605
\(497\) 5.00000 + 1.73205i 0.224281 + 0.0776931i
\(498\) 18.0000 0.806599
\(499\) −10.0000 17.3205i −0.447661 0.775372i 0.550572 0.834788i \(-0.314410\pi\)
−0.998233 + 0.0594153i \(0.981076\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) −28.5000 + 49.3634i −1.27329 + 2.20540i
\(502\) 12.0000 + 20.7846i 0.535586 + 0.927663i
\(503\) 3.00000 0.133763 0.0668817 0.997761i \(-0.478695\pi\)
0.0668817 + 0.997761i \(0.478695\pi\)
\(504\) 3.00000 + 15.5885i 0.133631 + 0.694365i
\(505\) −18.0000 −0.800989
\(506\) −4.00000 6.92820i −0.177822 0.307996i
\(507\) −54.0000 + 93.5307i −2.39822 + 4.15385i
\(508\) 9.50000 16.4545i 0.421494 0.730050i
\(509\) 11.0000 + 19.0526i 0.487566 + 0.844490i 0.999898 0.0142980i \(-0.00455136\pi\)
−0.512331 + 0.858788i \(0.671218\pi\)
\(510\) 12.0000 0.531369
\(511\) 8.00000 6.92820i 0.353899 0.306486i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −1.50000 + 2.59808i −0.0661622 + 0.114596i
\(515\) −18.0000 + 31.1769i −0.793175 + 1.37382i
\(516\) 12.0000 + 20.7846i 0.528271 + 0.914991i
\(517\) −2.00000 −0.0879599
\(518\) 8.00000 6.92820i 0.351500 0.304408i
\(519\) 75.0000 3.29213
\(520\) 7.00000 + 12.1244i 0.306970 + 0.531688i
\(521\) −5.00000 + 8.66025i −0.219054 + 0.379413i −0.954519 0.298150i \(-0.903630\pi\)
0.735465 + 0.677563i \(0.236964\pi\)
\(522\) 15.0000 25.9808i 0.656532 1.13715i
\(523\) 5.00000 + 8.66025i 0.218635 + 0.378686i 0.954391 0.298560i \(-0.0965063\pi\)
−0.735756 + 0.677247i \(0.763173\pi\)
\(524\) 0 0
\(525\) −1.50000 7.79423i −0.0654654 0.340168i
\(526\) 27.0000 1.17726
\(527\) −4.00000 6.92820i −0.174243 0.301797i
\(528\) 1.50000 2.59808i 0.0652791 0.113067i
\(529\) −20.5000 + 35.5070i −0.891304 + 1.54378i
\(530\) 6.00000 + 10.3923i 0.260623 + 0.451413i
\(531\) 18.0000 0.781133
\(532\) 0 0
\(533\) −28.0000 −1.21281
\(534\) −9.00000 15.5885i −0.389468 0.674579i
\(535\) −2.00000 + 3.46410i −0.0864675 + 0.149766i
\(536\) −4.50000 + 7.79423i −0.194370 + 0.336659i
\(537\) −28.5000 49.3634i −1.22987 2.13019i
\(538\) −24.0000 −1.03471
\(539\) 6.50000 2.59808i 0.279975 0.111907i
\(540\) 18.0000 0.774597
\(541\) −2.50000 4.33013i −0.107483 0.186167i 0.807267 0.590187i \(-0.200946\pi\)
−0.914750 + 0.404020i \(0.867613\pi\)
\(542\) 5.50000 9.52628i 0.236245 0.409189i
\(543\) 33.0000 57.1577i 1.41617 2.45287i
\(544\) −1.00000 1.73205i −0.0428746 0.0742611i
\(545\) −4.00000 −0.171341
\(546\) 52.5000 + 18.1865i 2.24679 + 0.778312i
\(547\) 30.0000 1.28271 0.641354 0.767245i \(-0.278373\pi\)
0.641354 + 0.767245i \(0.278373\pi\)
\(548\) −1.50000 2.59808i −0.0640768 0.110984i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) 0 0
\(552\) −24.0000 −1.02151
\(553\) 4.50000 + 23.3827i 0.191359 + 0.994333i
\(554\) −9.00000 −0.382373
\(555\) −12.0000 20.7846i −0.509372 0.882258i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −13.0000 + 22.5167i −0.550828 + 0.954062i 0.447387 + 0.894340i \(0.352355\pi\)
−0.998215 + 0.0597213i \(0.980979\pi\)
\(558\) −12.0000 20.7846i −0.508001 0.879883i
\(559\) 56.0000 2.36855
\(560\) 4.00000 3.46410i 0.169031 0.146385i
\(561\) −6.00000 −0.253320
\(562\) 14.0000 + 24.2487i 0.590554 + 1.02287i
\(563\) −10.0000 + 17.3205i −0.421450 + 0.729972i −0.996082 0.0884397i \(-0.971812\pi\)
0.574632 + 0.818412i \(0.305145\pi\)
\(564\) −3.00000 + 5.19615i −0.126323 + 0.218797i
\(565\) −5.00000 8.66025i −0.210352 0.364340i
\(566\) 0 0
\(567\) 18.0000 15.5885i 0.755929 0.654654i
\(568\) −2.00000 −0.0839181
\(569\) 6.00000 + 10.3923i 0.251533 + 0.435668i 0.963948 0.266090i \(-0.0857319\pi\)
−0.712415 + 0.701758i \(0.752399\pi\)
\(570\) 0 0
\(571\) −11.0000 + 19.0526i −0.460336 + 0.797325i −0.998978 0.0452101i \(-0.985604\pi\)
0.538642 + 0.842535i \(0.318938\pi\)
\(572\) −3.50000 6.06218i −0.146342 0.253472i
\(573\) 6.00000 0.250654
\(574\) 2.00000 + 10.3923i 0.0834784 + 0.433766i
\(575\) 8.00000 0.333623
\(576\) −3.00000 5.19615i −0.125000 0.216506i
\(577\) 21.5000 37.2391i 0.895057 1.55028i 0.0613223 0.998118i \(-0.480468\pi\)
0.833734 0.552166i \(-0.186198\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) −12.0000 20.7846i −0.498703 0.863779i
\(580\) −10.0000 −0.415227
\(581\) −15.0000 5.19615i −0.622305 0.215573i
\(582\) 21.0000 0.870478
\(583\) −3.00000 5.19615i −0.124247 0.215203i
\(584\) −2.00000 + 3.46410i −0.0827606 + 0.143346i
\(585\) 42.0000 72.7461i 1.73649 3.00768i
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) 27.0000 1.11441 0.557205 0.830375i \(-0.311874\pi\)
0.557205 + 0.830375i \(0.311874\pi\)
\(588\) 3.00000 20.7846i 0.123718 0.857143i
\(589\) 0 0
\(590\) −3.00000 5.19615i −0.123508 0.213922i
\(591\) −22.5000 + 38.9711i −0.925526 + 1.60306i
\(592\) −2.00000 + 3.46410i −0.0821995 + 0.142374i
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) −9.00000 −0.369274
\(595\) −10.0000 3.46410i −0.409960 0.142014i
\(596\) −10.0000 −0.409616
\(597\) −6.00000 10.3923i −0.245564 0.425329i
\(598\) −28.0000 + 48.4974i −1.14501 + 1.98321i
\(599\) −18.0000 + 31.1769i −0.735460 + 1.27385i 0.219061 + 0.975711i \(0.429701\pi\)
−0.954521 + 0.298143i \(0.903633\pi\)
\(600\) 1.50000 + 2.59808i 0.0612372 + 0.106066i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −4.00000 20.7846i −0.163028 0.847117i
\(603\) 54.0000 2.19905
\(604\) 1.50000 + 2.59808i 0.0610341 + 0.105714i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 13.5000 23.3827i 0.548400 0.949857i
\(607\) −4.00000 6.92820i −0.162355 0.281207i 0.773358 0.633970i \(-0.218576\pi\)
−0.935713 + 0.352763i \(0.885242\pi\)
\(608\) 0 0
\(609\) −30.0000 + 25.9808i −1.21566 + 1.05279i
\(610\) 2.00000 0.0809776
\(611\) 7.00000 + 12.1244i 0.283190 + 0.490499i
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) 19.0000 32.9090i 0.767403 1.32918i −0.171564 0.985173i \(-0.554882\pi\)
0.938967 0.344008i \(-0.111785\pi\)
\(614\) −1.00000 1.73205i −0.0403567 0.0698999i
\(615\) 24.0000 0.967773
\(616\) −2.00000 + 1.73205i −0.0805823 + 0.0697863i
\(617\) −15.0000 −0.603877 −0.301939 0.953327i \(-0.597634\pi\)
−0.301939 + 0.953327i \(0.597634\pi\)
\(618\) −27.0000 46.7654i −1.08610 1.88118i
\(619\) 14.0000 24.2487i 0.562708 0.974638i −0.434551 0.900647i \(-0.643093\pi\)
0.997259 0.0739910i \(-0.0235736\pi\)
\(620\) −4.00000 + 6.92820i −0.160644 + 0.278243i
\(621\) 36.0000 + 62.3538i 1.44463 + 2.50217i
\(622\) −10.0000 −0.400963
\(623\) 3.00000 + 15.5885i 0.120192 + 0.624538i
\(624\) −21.0000 −0.840673
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) −0.500000 + 0.866025i −0.0199840 + 0.0346133i
\(627\) 0 0
\(628\) −8.00000 13.8564i −0.319235 0.552931i
\(629\) 8.00000 0.318981
\(630\) −30.0000 10.3923i −1.19523 0.414039i
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) −4.50000 7.79423i −0.179000 0.310038i
\(633\) 30.0000 51.9615i 1.19239 2.06529i
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) 19.0000 + 32.9090i 0.753992 + 1.30595i
\(636\) −18.0000 −0.713746
\(637\) −38.5000 30.3109i −1.52543 1.20096i
\(638\) 5.00000 0.197952
\(639\) 6.00000 + 10.3923i 0.237356 + 0.411113i
\(640\) −1.00000 + 1.73205i −0.0395285 + 0.0684653i
\(641\) 13.5000 23.3827i 0.533218 0.923561i −0.466029 0.884769i \(-0.654316\pi\)
0.999247 0.0387913i \(-0.0123508\pi\)
\(642\) −3.00000 5.19615i −0.118401 0.205076i
\(643\) 31.0000 1.22252 0.611260 0.791430i \(-0.290663\pi\)
0.611260 + 0.791430i \(0.290663\pi\)
\(644\) 20.0000 + 6.92820i 0.788110 + 0.273009i
\(645\) −48.0000 −1.89000
\(646\) 0 0
\(647\) −15.0000 + 25.9808i −0.589711 + 1.02141i 0.404559 + 0.914512i \(0.367425\pi\)
−0.994270 + 0.106897i \(0.965908\pi\)
\(648\) −4.50000 + 7.79423i −0.176777 + 0.306186i
\(649\) 1.50000 + 2.59808i 0.0588802 + 0.101983i
\(650\) 7.00000 0.274563
\(651\) 6.00000 + 31.1769i 0.235159 + 1.22192i
\(652\) −17.0000 −0.665771
\(653\) −20.0000 34.6410i −0.782660 1.35561i −0.930387 0.366579i \(-0.880529\pi\)
0.147726 0.989028i \(-0.452805\pi\)
\(654\) 3.00000 5.19615i 0.117309 0.203186i
\(655\) 0 0
\(656\) −2.00000 3.46410i −0.0780869 0.135250i
\(657\) 24.0000 0.936329
\(658\) 4.00000 3.46410i 0.155936 0.135045i
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 3.00000 + 5.19615i 0.116775 + 0.202260i
\(661\) 11.0000 19.0526i 0.427850 0.741059i −0.568831 0.822454i \(-0.692604\pi\)
0.996682 + 0.0813955i \(0.0259377\pi\)
\(662\) −6.50000 + 11.2583i −0.252630 + 0.437567i
\(663\) 21.0000 + 36.3731i 0.815572 + 1.41261i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 24.0000 0.929981
\(667\) −20.0000 34.6410i −0.774403 1.34131i
\(668\) −9.50000 + 16.4545i −0.367566 + 0.636643i
\(669\) −6.00000 + 10.3923i −0.231973 + 0.401790i
\(670\) −9.00000 15.5885i −0.347700 0.602235i
\(671\) −1.00000 −0.0386046
\(672\) 1.50000 + 7.79423i 0.0578638 + 0.300669i
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 6.00000 + 10.3923i 0.231111 + 0.400297i
\(675\) 4.50000 7.79423i 0.173205 0.300000i
\(676\) −18.0000 + 31.1769i −0.692308 + 1.19911i
\(677\) −7.00000 12.1244i −0.269032 0.465977i 0.699580 0.714554i \(-0.253370\pi\)
−0.968612 + 0.248577i \(0.920037\pi\)
\(678\) 15.0000 0.576072
\(679\) −17.5000 6.06218i −0.671588 0.232645i
\(680\) 4.00000 0.153393
\(681\) 3.00000 + 5.19615i 0.114960 + 0.199117i
\(682\) 2.00000 3.46410i 0.0765840 0.132647i
\(683\) −10.5000 + 18.1865i −0.401771 + 0.695888i −0.993940 0.109926i \(-0.964939\pi\)
0.592168 + 0.805814i \(0.298272\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) −8.50000 + 16.4545i −0.324532 + 0.628235i
\(687\) −84.0000 −3.20480
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) −21.0000 + 36.3731i −0.800036 + 1.38570i
\(690\) 24.0000 41.5692i 0.913664 1.58251i
\(691\) −16.5000 28.5788i −0.627690 1.08719i −0.988014 0.154363i \(-0.950667\pi\)
0.360325 0.932827i \(-0.382666\pi\)
\(692\) 25.0000 0.950357
\(693\) 15.0000 + 5.19615i 0.569803 + 0.197386i
\(694\) −22.0000 −0.835109
\(695\) 4.00000 + 6.92820i 0.151729 + 0.262802i
\(696\) 7.50000 12.9904i 0.284287 0.492399i
\(697\) −4.00000 + 6.92820i −0.151511 + 0.262424i
\(698\) −1.00000 1.73205i −0.0378506 0.0655591i
\(699\) 0 0
\(700\) −0.500000 2.59808i −0.0188982 0.0981981i
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 31.5000 + 54.5596i 1.18889 + 2.05922i
\(703\) 0 0
\(704\) 0.500000 0.866025i 0.0188445 0.0326396i
\(705\) −6.00000 10.3923i −0.225973 0.391397i
\(706\) −18.0000 −0.677439
\(707\) −18.0000 + 15.5885i −0.676960 + 0.586264i
\(708\) 9.00000 0.338241
\(709\) 24.0000 + 41.5692i 0.901339 + 1.56116i 0.825758 + 0.564025i \(0.190748\pi\)
0.0755813 + 0.997140i \(0.475919\pi\)
\(710\) 2.00000 3.46410i 0.0750587 0.130005i
\(711\) −27.0000 + 46.7654i −1.01258 + 1.75384i
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) −32.0000 −1.19841
\(714\) 12.0000 10.3923i 0.449089 0.388922i
\(715\) 14.0000 0.523570
\(716\) −9.50000 16.4545i −0.355032 0.614933i
\(717\) 7.50000 12.9904i 0.280093 0.485135i
\(718\) 9.50000 16.4545i 0.354537 0.614076i
\(719\) 19.0000 + 32.9090i 0.708580 + 1.22730i 0.965384 + 0.260834i \(0.0839974\pi\)
−0.256803 + 0.966464i \(0.582669\pi\)
\(720\) 12.0000 0.447214
\(721\) 9.00000 + 46.7654i 0.335178 + 1.74163i
\(722\) −19.0000 −0.707107
\(723\) 0 0
\(724\) 11.0000 19.0526i 0.408812 0.708083i
\(725\) −2.50000 + 4.33013i −0.0928477 + 0.160817i
\(726\) −1.50000 2.59808i −0.0556702 0.0964237i
\(727\) −22.0000 −0.815935 −0.407967 0.912996i \(-0.633762\pi\)
−0.407967 + 0.912996i \(0.633762\pi\)
\(728\) 17.5000 + 6.06218i 0.648593 + 0.224679i
\(729\) −27.0000 −1.00000
\(730\) −4.00000 6.92820i −0.148047 0.256424i
\(731\) 8.00000 13.8564i 0.295891 0.512498i
\(732\) −1.50000 + 2.59808i −0.0554416 + 0.0960277i
\(733\) 9.50000 + 16.4545i 0.350891 + 0.607760i 0.986406 0.164328i \(-0.0525456\pi\)
−0.635515 + 0.772088i \(0.719212\pi\)
\(734\) 4.00000 0.147643
\(735\) 33.0000 + 25.9808i 1.21722 + 0.958315i
\(736\) −8.00000 −0.294884
\(737\) 4.50000 + 7.79423i 0.165760 + 0.287104i
\(738\) −12.0000 + 20.7846i −0.441726 + 0.765092i
\(739\) −21.0000 + 36.3731i −0.772497 + 1.33800i 0.163693 + 0.986511i \(0.447659\pi\)
−0.936190 + 0.351494i \(0.885674\pi\)
\(740\) −4.00000 6.92820i −0.147043 0.254686i
\(741\) 0 0
\(742\) 15.0000 + 5.19615i 0.550667 + 0.190757i
\(743\) 12.0000 0.440237 0.220119 0.975473i \(-0.429356\pi\)
0.220119 + 0.975473i \(0.429356\pi\)
\(744\) −6.00000 10.3923i −0.219971 0.381000i
\(745\) 10.0000 17.3205i 0.366372 0.634574i
\(746\) −5.50000 + 9.52628i −0.201369 + 0.348782i
\(747\) −18.0000 31.1769i −0.658586 1.14070i
\(748\) −2.00000 −0.0731272
\(749\) 1.00000 + 5.19615i 0.0365392 + 0.189863i
\(750\) −36.0000 −1.31453
\(751\) −14.0000 24.2487i −0.510867 0.884848i −0.999921 0.0125942i \(-0.995991\pi\)
0.489053 0.872254i \(-0.337342\pi\)
\(752\) −1.00000 + 1.73205i −0.0364662 + 0.0631614i
\(753\) 36.0000 62.3538i 1.31191 2.27230i
\(754\) −17.5000 30.3109i −0.637312 1.10386i
\(755\) −6.00000 −0.218362
\(756\) 18.0000 15.5885i 0.654654 0.566947i
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −0.500000 0.866025i −0.0181608 0.0314555i
\(759\) −12.0000 + 20.7846i −0.435572 + 0.754434i
\(760\) 0 0
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) −57.0000 −2.06489
\(763\) −4.00000 + 3.46410i −0.144810 + 0.125409i
\(764\) 2.00000 0.0723575
\(765\) −12.0000 20.7846i −0.433861 0.751469i
\(766\) −13.0000 + 22.5167i −0.469709 + 0.813560i
\(767\) 10.5000 18.1865i 0.379133 0.656678i
\(768\) −1.50000 2.59808i −0.0541266 0.0937500i
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) −1.00000 5.19615i −0.0360375 0.187256i
\(771\) 9.00000 0.324127
\(772\) −4.00000 6.92820i −0.143963 0.249351i
\(773\) −12.0000 + 20.7846i −0.431610 + 0.747570i −0.997012 0.0772449i \(-0.975388\pi\)
0.565402 + 0.824815i \(0.308721\pi\)
\(774\) 24.0000 41.5692i 0.862662 1.49417i
\(775\) 2.00000 + 3.46410i