Properties

Label 462.2.i.b.331.1
Level $462$
Weight $2$
Character 462.331
Analytic conductor $3.689$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.68908857338\)
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 331.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 462.331
Dual form 462.2.i.b.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} -4.00000 q^{13} +(-2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(0.500000 + 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{19} +(-0.500000 + 2.59808i) q^{21} -1.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-2.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 + 2.59808i) q^{28} -9.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -3.00000 q^{34} +1.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(2.00000 + 3.46410i) q^{39} -6.00000 q^{41} +(2.00000 + 1.73205i) q^{42} +11.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} +5.00000 q^{50} +(-1.50000 + 2.59808i) q^{51} +(2.00000 + 3.46410i) q^{52} +(0.500000 - 0.866025i) q^{54} +(2.00000 + 1.73205i) q^{56} -1.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(-4.50000 - 7.79423i) q^{59} +(5.00000 - 8.66025i) q^{61} -2.00000 q^{62} +(2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-1.50000 + 2.59808i) q^{68} -3.00000 q^{69} +3.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(2.00000 + 3.46410i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(2.50000 - 4.33013i) q^{75} -1.00000 q^{76} +(-0.500000 + 2.59808i) q^{77} +4.00000 q^{78} +(8.00000 - 13.8564i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} +(2.50000 - 0.866025i) q^{84} +(5.50000 - 9.52628i) q^{86} +(4.50000 + 7.79423i) q^{87} +(0.500000 + 0.866025i) q^{88} +(8.00000 + 6.92820i) q^{91} -3.00000 q^{92} +(-1.00000 + 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} -1.00000 q^{97} +(6.50000 + 2.59808i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q + q^{2} - q^{3} - q^{4} - 2 q^{6} - 4 q^{7} - 2 q^{8} - q^{9} - q^{11} - q^{12} - 8 q^{13} - 5 q^{14} - q^{16} - 3 q^{17} + q^{18} + q^{19} - q^{21} - 2 q^{22} + 3 q^{23} + q^{24} + 5 q^{25} - 4 q^{26} + 2 q^{27} - q^{28} - 18 q^{29} - 2 q^{31} + q^{32} - q^{33} - 6 q^{34} + 2 q^{36} + 7 q^{37} - q^{38} + 4 q^{39} - 12 q^{41} + 4 q^{42} + 22 q^{43} - q^{44} - 3 q^{46} + 3 q^{47} + 2 q^{48} + 2 q^{49} + 10 q^{50} - 3 q^{51} + 4 q^{52} + q^{54} + 4 q^{56} - 2 q^{57} - 9 q^{58} - 9 q^{59} + 10 q^{61} - 4 q^{62} + 5 q^{63} + 2 q^{64} + q^{66} + 4 q^{67} - 3 q^{68} - 6 q^{69} + 6 q^{71} + q^{72} + 4 q^{73} - 7 q^{74} + 5 q^{75} - 2 q^{76} - q^{77} + 8 q^{78} + 16 q^{79} - q^{81} - 6 q^{82} + 5 q^{84} + 11 q^{86} + 9 q^{87} + q^{88} + 16 q^{91} - 6 q^{92} - 2 q^{93} - 3 q^{94} + q^{96} - 2 q^{97} + 13 q^{98} + 2 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −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
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) −2.50000 + 0.866025i −0.668153 + 0.231455i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) −0.500000 + 2.59808i −0.109109 + 0.566947i
\(22\) −1.00000 −0.213201
\(23\) 1.50000 2.59808i 0.312772 0.541736i −0.666190 0.745782i \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) −2.00000 + 3.46410i −0.392232 + 0.679366i
\(27\) 1.00000 0.192450
\(28\) −0.500000 + 2.59808i −0.0944911 + 0.490990i
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) −3.00000 −0.514496
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) −0.500000 0.866025i −0.0811107 0.140488i
\(39\) 2.00000 + 3.46410i 0.320256 + 0.554700i
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 2.00000 + 1.73205i 0.308607 + 0.267261i
\(43\) 11.0000 1.67748 0.838742 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) 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
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 5.00000 0.707107
\(51\) −1.50000 + 2.59808i −0.210042 + 0.363803i
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 2.00000 + 1.73205i 0.267261 + 0.231455i
\(57\) −1.00000 −0.132453
\(58\) −4.50000 + 7.79423i −0.590879 + 1.02343i
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) −2.00000 −0.254000
\(63\) 2.50000 0.866025i 0.314970 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.500000 + 0.866025i 0.0615457 + 0.106600i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −1.50000 + 2.59808i −0.181902 + 0.315063i
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) −3.50000 6.06218i −0.406867 0.704714i
\(75\) 2.50000 4.33013i 0.288675 0.500000i
\(76\) −1.00000 −0.114708
\(77\) −0.500000 + 2.59808i −0.0569803 + 0.296078i
\(78\) 4.00000 0.452911
\(79\) 8.00000 13.8564i 0.900070 1.55897i 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.00000 + 5.19615i −0.331295 + 0.573819i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 2.50000 0.866025i 0.272772 0.0944911i
\(85\) 0 0
\(86\) 5.50000 9.52628i 0.593080 1.02725i
\(87\) 4.50000 + 7.79423i 0.482451 + 0.835629i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) 8.00000 + 6.92820i 0.838628 + 0.726273i
\(92\) −3.00000 −0.312772
\(93\) −1.00000 + 1.73205i −0.103695 + 0.179605i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 0 0
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 6.50000 + 2.59808i 0.656599 + 0.262445i
\(99\) 1.00000 0.100504
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 1.50000 + 2.59808i 0.148522 + 0.257248i
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) 0 0
\(107\) 9.00000 15.5885i 0.870063 1.50699i 0.00813215 0.999967i \(-0.497411\pi\)
0.861931 0.507026i \(-0.169255\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 2.50000 0.866025i 0.236228 0.0818317i
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) −0.500000 + 0.866025i −0.0468293 + 0.0811107i
\(115\) 0 0
\(116\) 4.50000 + 7.79423i 0.417815 + 0.723676i
\(117\) 2.00000 3.46410i 0.184900 0.320256i
\(118\) −9.00000 −0.828517
\(119\) −1.50000 + 7.79423i −0.137505 + 0.714496i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −5.00000 8.66025i −0.452679 0.784063i
\(123\) 3.00000 + 5.19615i 0.270501 + 0.468521i
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 0 0
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −5.50000 9.52628i −0.484248 0.838742i
\(130\) 0 0
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 1.00000 0.0870388
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 1.50000 + 2.59808i 0.128624 + 0.222783i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) −1.50000 + 2.59808i −0.127688 + 0.221163i
\(139\) −19.0000 −1.61156 −0.805779 0.592216i \(-0.798253\pi\)
−0.805779 + 0.592216i \(0.798253\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 1.50000 2.59808i 0.125877 0.218026i
\(143\) 2.00000 + 3.46410i 0.167248 + 0.289683i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 5.50000 4.33013i 0.453632 0.357143i
\(148\) −7.00000 −0.575396
\(149\) −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i \(-0.953515\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(150\) −2.50000 4.33013i −0.204124 0.353553i
\(151\) 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) −0.500000 + 0.866025i −0.0405554 + 0.0702439i
\(153\) 3.00000 0.242536
\(154\) 2.00000 + 1.73205i 0.161165 + 0.139573i
\(155\) 0 0
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) −8.00000 13.8564i −0.636446 1.10236i
\(159\) 0 0
\(160\) 0 0
\(161\) −7.50000 + 2.59808i −0.591083 + 0.204757i
\(162\) −1.00000 −0.0785674
\(163\) −1.00000 + 1.73205i −0.0783260 + 0.135665i −0.902528 0.430632i \(-0.858291\pi\)
0.824202 + 0.566296i \(0.191624\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0.500000 2.59808i 0.0385758 0.200446i
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0.500000 + 0.866025i 0.0382360 + 0.0662266i
\(172\) −5.50000 9.52628i −0.419371 0.726372i
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 9.00000 0.682288
\(175\) 2.50000 12.9904i 0.188982 0.981981i
\(176\) 1.00000 0.0753778
\(177\) −4.50000 + 7.79423i −0.338241 + 0.585850i
\(178\) 0 0
\(179\) 7.50000 + 12.9904i 0.560576 + 0.970947i 0.997446 + 0.0714220i \(0.0227537\pi\)
−0.436870 + 0.899525i \(0.643913\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 10.0000 3.46410i 0.741249 0.256776i
\(183\) −10.0000 −0.739221
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) 0 0
\(186\) 1.00000 + 1.73205i 0.0733236 + 0.127000i
\(187\) −1.50000 + 2.59808i −0.109691 + 0.189990i
\(188\) −3.00000 −0.218797
\(189\) −2.00000 1.73205i −0.145479 0.125988i
\(190\) 0 0
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 5.00000 + 8.66025i 0.359908 + 0.623379i 0.987945 0.154805i \(-0.0494748\pi\)
−0.628037 + 0.778183i \(0.716141\pi\)
\(194\) −0.500000 + 0.866025i −0.0358979 + 0.0621770i
\(195\) 0 0
\(196\) 5.50000 4.33013i 0.392857 0.309295i
\(197\) −21.0000 −1.49619 −0.748094 0.663593i \(-0.769031\pi\)
−0.748094 + 0.663593i \(0.769031\pi\)
\(198\) 0.500000 0.866025i 0.0355335 0.0615457i
\(199\) −10.0000 17.3205i −0.708881 1.22782i −0.965272 0.261245i \(-0.915867\pi\)
0.256391 0.966573i \(-0.417466\pi\)
\(200\) −2.50000 4.33013i −0.176777 0.306186i
\(201\) 2.00000 3.46410i 0.141069 0.244339i
\(202\) −15.0000 −1.05540
\(203\) 18.0000 + 15.5885i 1.26335 + 1.09410i
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) −2.00000 3.46410i −0.139347 0.241355i
\(207\) 1.50000 + 2.59808i 0.104257 + 0.180579i
\(208\) 2.00000 3.46410i 0.138675 0.240192i
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 0 0
\(213\) −1.50000 2.59808i −0.102778 0.178017i
\(214\) −9.00000 15.5885i −0.615227 1.06561i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) −1.00000 + 5.19615i −0.0678844 + 0.352738i
\(218\) 10.0000 0.677285
\(219\) 2.00000 3.46410i 0.135147 0.234082i
\(220\) 0 0
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) −3.50000 + 6.06218i −0.234905 + 0.406867i
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0.500000 2.59808i 0.0334077 0.173591i
\(225\) −5.00000 −0.333333
\(226\) 6.00000 10.3923i 0.399114 0.691286i
\(227\) −9.00000 15.5885i −0.597351 1.03464i −0.993210 0.116331i \(-0.962887\pi\)
0.395860 0.918311i \(-0.370447\pi\)
\(228\) 0.500000 + 0.866025i 0.0331133 + 0.0573539i
\(229\) −13.0000 + 22.5167i −0.859064 + 1.48794i 0.0137585 + 0.999905i \(0.495620\pi\)
−0.872823 + 0.488037i \(0.837713\pi\)
\(230\) 0 0
\(231\) 2.50000 0.866025i 0.164488 0.0569803i
\(232\) 9.00000 0.590879
\(233\) −4.50000 + 7.79423i −0.294805 + 0.510617i −0.974939 0.222470i \(-0.928588\pi\)
0.680135 + 0.733087i \(0.261921\pi\)
\(234\) −2.00000 3.46410i −0.130744 0.226455i
\(235\) 0 0
\(236\) −4.50000 + 7.79423i −0.292925 + 0.507361i
\(237\) −16.0000 −1.03931
\(238\) 6.00000 + 5.19615i 0.388922 + 0.336817i
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 14.0000 + 24.2487i 0.901819 + 1.56200i 0.825131 + 0.564942i \(0.191101\pi\)
0.0766885 + 0.997055i \(0.475565\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −10.0000 −0.640184
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) −2.00000 + 3.46410i −0.127257 + 0.220416i
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 0 0
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) −2.00000 1.73205i −0.125988 0.109109i
\(253\) −3.00000 −0.188608
\(254\) −0.500000 + 0.866025i −0.0313728 + 0.0543393i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −6.00000 + 10.3923i −0.374270 + 0.648254i −0.990217 0.139533i \(-0.955440\pi\)
0.615948 + 0.787787i \(0.288773\pi\)
\(258\) −11.0000 −0.684830
\(259\) −17.5000 + 6.06218i −1.08740 + 0.376685i
\(260\) 0 0
\(261\) 4.50000 7.79423i 0.278543 0.482451i
\(262\) 9.00000 + 15.5885i 0.556022 + 0.963058i
\(263\) 9.00000 + 15.5885i 0.554964 + 0.961225i 0.997906 + 0.0646755i \(0.0206012\pi\)
−0.442943 + 0.896550i \(0.646065\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) 0 0
\(266\) −0.500000 + 2.59808i −0.0306570 + 0.159298i
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 3.00000 0.181902
\(273\) 2.00000 10.3923i 0.121046 0.628971i
\(274\) −12.0000 −0.724947
\(275\) 2.50000 4.33013i 0.150756 0.261116i
\(276\) 1.50000 + 2.59808i 0.0902894 + 0.156386i
\(277\) −16.0000 27.7128i −0.961347 1.66510i −0.719125 0.694881i \(-0.755457\pi\)
−0.242222 0.970221i \(-0.577876\pi\)
\(278\) −9.50000 + 16.4545i −0.569772 + 0.986874i
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −15.0000 −0.894825 −0.447412 0.894328i \(-0.647654\pi\)
−0.447412 + 0.894328i \(0.647654\pi\)
\(282\) −1.50000 + 2.59808i −0.0893237 + 0.154713i
\(283\) −10.0000 17.3205i −0.594438 1.02960i −0.993626 0.112728i \(-0.964041\pi\)
0.399188 0.916869i \(-0.369292\pi\)
\(284\) −1.50000 2.59808i −0.0890086 0.154167i
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 12.0000 + 10.3923i 0.708338 + 0.613438i
\(288\) −1.00000 −0.0589256
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0 0
\(291\) 0.500000 + 0.866025i 0.0293105 + 0.0507673i
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) −1.00000 6.92820i −0.0583212 0.404061i
\(295\) 0 0
\(296\) −3.50000 + 6.06218i −0.203433 + 0.352357i
\(297\) −0.500000 0.866025i −0.0290129 0.0502519i
\(298\) 4.50000 + 7.79423i 0.260678 + 0.451508i
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) −5.00000 −0.288675
\(301\) −22.0000 19.0526i −1.26806 1.09817i
\(302\) 19.0000 1.09333
\(303\) −7.50000 + 12.9904i −0.430864 + 0.746278i
\(304\) 0.500000 + 0.866025i 0.0286770 + 0.0496700i
\(305\) 0 0
\(306\) 1.50000 2.59808i 0.0857493 0.148522i
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 2.50000 0.866025i 0.142451 0.0493464i
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 10.5000 + 18.1865i 0.595400 + 1.03126i 0.993490 + 0.113917i \(0.0363399\pi\)
−0.398090 + 0.917346i \(0.630327\pi\)
\(312\) −2.00000 3.46410i −0.113228 0.196116i
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 13.0000 0.733632
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 6.00000 10.3923i 0.336994 0.583690i −0.646872 0.762598i \(-0.723923\pi\)
0.983866 + 0.178908i \(0.0572566\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) −1.50000 + 7.79423i −0.0835917 + 0.434355i
\(323\) −3.00000 −0.166924
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) −10.0000 17.3205i −0.554700 0.960769i
\(326\) 1.00000 + 1.73205i 0.0553849 + 0.0959294i
\(327\) 5.00000 8.66025i 0.276501 0.478913i
\(328\) 6.00000 0.331295
\(329\) −7.50000 + 2.59808i −0.413488 + 0.143237i
\(330\) 0 0
\(331\) 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) 0 0
\(333\) 3.50000 + 6.06218i 0.191799 + 0.332205i
\(334\) 6.00000 10.3923i 0.328305 0.568642i
\(335\) 0 0
\(336\) −2.00000 1.73205i −0.109109 0.0944911i
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 1.50000 2.59808i 0.0815892 0.141317i
\(339\) −6.00000 10.3923i −0.325875 0.564433i
\(340\) 0 0
\(341\) −1.00000 + 1.73205i −0.0541530 + 0.0937958i
\(342\) 1.00000 0.0540738
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −11.0000 −0.593080
\(345\) 0 0
\(346\) −3.00000 5.19615i −0.161281 0.279347i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 4.50000 7.79423i 0.241225 0.417815i
\(349\) 8.00000 0.428230 0.214115 0.976808i \(-0.431313\pi\)
0.214115 + 0.976808i \(0.431313\pi\)
\(350\) −10.0000 8.66025i −0.534522 0.462910i
\(351\) −4.00000 −0.213504
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 4.50000 + 7.79423i 0.239172 + 0.414259i
\(355\) 0 0
\(356\) 0 0
\(357\) 7.50000 2.59808i 0.396942 0.137505i
\(358\) 15.0000 0.792775
\(359\) 9.00000 15.5885i 0.475002 0.822727i −0.524588 0.851356i \(-0.675781\pi\)
0.999590 + 0.0286287i \(0.00911406\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −5.00000 + 8.66025i −0.262794 + 0.455173i
\(363\) 1.00000 0.0524864
\(364\) 2.00000 10.3923i 0.104828 0.544705i
\(365\) 0 0
\(366\) −5.00000 + 8.66025i −0.261354 + 0.452679i
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 3.00000 5.19615i 0.156174 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 2.00000 0.103695
\(373\) 11.0000 19.0526i 0.569558 0.986504i −0.427051 0.904227i \(-0.640448\pi\)
0.996610 0.0822766i \(-0.0262191\pi\)
\(374\) 1.50000 + 2.59808i 0.0775632 + 0.134343i
\(375\) 0 0
\(376\) −1.50000 + 2.59808i −0.0773566 + 0.133986i
\(377\) 36.0000 1.85409
\(378\) −2.50000 + 0.866025i −0.128586 + 0.0445435i
\(379\) 14.0000 0.719132 0.359566 0.933120i \(-0.382925\pi\)
0.359566 + 0.933120i \(0.382925\pi\)
\(380\) 0 0
\(381\) 0.500000 + 0.866025i 0.0256158 + 0.0443678i
\(382\) 0 0
\(383\) −7.50000 + 12.9904i −0.383232 + 0.663777i −0.991522 0.129937i \(-0.958522\pi\)
0.608290 + 0.793715i \(0.291856\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) −5.50000 + 9.52628i −0.279581 + 0.484248i
\(388\) 0.500000 + 0.866025i 0.0253837 + 0.0439658i
\(389\) −6.00000 10.3923i −0.304212 0.526911i 0.672874 0.739758i \(-0.265060\pi\)
−0.977086 + 0.212847i \(0.931726\pi\)
\(390\) 0 0
\(391\) −9.00000 −0.455150
\(392\) −1.00000 6.92820i −0.0505076 0.349927i
\(393\) 18.0000 0.907980
\(394\) −10.5000 + 18.1865i −0.528982 + 0.916224i
\(395\) 0 0
\(396\) −0.500000 0.866025i −0.0251259 0.0435194i
\(397\) 6.50000 11.2583i 0.326226 0.565039i −0.655534 0.755166i \(-0.727556\pi\)
0.981760 + 0.190126i \(0.0608897\pi\)
\(398\) −20.0000 −1.00251
\(399\) 2.00000 + 1.73205i 0.100125 + 0.0867110i
\(400\) −5.00000 −0.250000
\(401\) 3.00000 5.19615i 0.149813 0.259483i −0.781345 0.624099i \(-0.785466\pi\)
0.931158 + 0.364615i \(0.118800\pi\)
\(402\) −2.00000 3.46410i −0.0997509 0.172774i
\(403\) 4.00000 + 6.92820i 0.199254 + 0.345118i
\(404\) −7.50000 + 12.9904i −0.373139 + 0.646296i
\(405\) 0 0
\(406\) 22.5000 7.79423i 1.11666 0.386821i
\(407\) −7.00000 −0.346977
\(408\) 1.50000 2.59808i 0.0742611 0.128624i
\(409\) −7.00000 12.1244i −0.346128 0.599511i 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(410\) 0 0
\(411\) −6.00000 + 10.3923i −0.295958 + 0.512615i
\(412\) −4.00000 −0.197066
\(413\) −4.50000 + 23.3827i −0.221431 + 1.15059i
\(414\) 3.00000 0.147442
\(415\) 0 0
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) 9.50000 + 16.4545i 0.465217 + 0.805779i
\(418\) −0.500000 + 0.866025i −0.0244558 + 0.0423587i
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) −2.00000 + 3.46410i −0.0973585 + 0.168630i
\(423\) 1.50000 + 2.59808i 0.0729325 + 0.126323i
\(424\) 0 0
\(425\) 7.50000 12.9904i 0.363803 0.630126i
\(426\) −3.00000 −0.145350
\(427\) −25.0000 + 8.66025i −1.20983 + 0.419099i
\(428\) −18.0000 −0.870063
\(429\) 2.00000 3.46410i 0.0965609 0.167248i
\(430\) 0 0
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 29.0000 1.39365 0.696826 0.717241i \(-0.254595\pi\)
0.696826 + 0.717241i \(0.254595\pi\)
\(434\) 4.00000 + 3.46410i 0.192006 + 0.166282i
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) −1.50000 2.59808i −0.0717547 0.124283i
\(438\) −2.00000 3.46410i −0.0955637 0.165521i
\(439\) 18.5000 32.0429i 0.882957 1.52933i 0.0349192 0.999390i \(-0.488883\pi\)
0.848038 0.529936i \(-0.177784\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 12.0000 0.570782
\(443\) −1.50000 + 2.59808i −0.0712672 + 0.123438i −0.899457 0.437009i \(-0.856038\pi\)
0.828190 + 0.560448i \(0.189371\pi\)
\(444\) 3.50000 + 6.06218i 0.166103 + 0.287698i
\(445\) 0 0
\(446\) 4.00000 6.92820i 0.189405 0.328060i
\(447\) 9.00000 0.425685
\(448\) −2.00000 1.73205i −0.0944911 0.0818317i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) −2.50000 + 4.33013i −0.117851 + 0.204124i
\(451\) 3.00000 + 5.19615i 0.141264 + 0.244677i
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) 9.50000 16.4545i 0.446349 0.773099i
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) −1.00000 + 1.73205i −0.0467780 + 0.0810219i −0.888466 0.458942i \(-0.848229\pi\)
0.841688 + 0.539964i \(0.181562\pi\)
\(458\) 13.0000 + 22.5167i 0.607450 + 1.05213i
\(459\) −1.50000 2.59808i −0.0700140 0.121268i
\(460\) 0 0
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) 0.500000 2.59808i 0.0232621 0.120873i
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 0 0
\(466\) 4.50000 + 7.79423i 0.208458 + 0.361061i
\(467\) 16.5000 28.5788i 0.763529 1.32247i −0.177492 0.984122i \(-0.556798\pi\)
0.941021 0.338349i \(-0.109868\pi\)
\(468\) −4.00000 −0.184900
\(469\) 2.00000 10.3923i 0.0923514 0.479872i
\(470\) 0 0
\(471\) 6.50000 11.2583i 0.299504 0.518756i
\(472\) 4.50000 + 7.79423i 0.207129 + 0.358758i
\(473\) −5.50000 9.52628i −0.252890 0.438019i
\(474\) −8.00000 + 13.8564i −0.367452 + 0.636446i
\(475\) 5.00000 0.229416
\(476\) 7.50000 2.59808i 0.343762 0.119083i
\(477\) 0 0
\(478\) −12.0000 + 20.7846i −0.548867 + 0.950666i
\(479\) −3.00000 5.19615i −0.137073 0.237418i 0.789314 0.613990i \(-0.210436\pi\)
−0.926388 + 0.376571i \(0.877103\pi\)
\(480\) 0 0
\(481\) −14.0000 + 24.2487i −0.638345 + 1.10565i
\(482\) 28.0000 1.27537
\(483\) 6.00000 + 5.19615i 0.273009 + 0.236433i
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 2.00000 + 3.46410i 0.0906287 + 0.156973i 0.907776 0.419456i \(-0.137779\pi\)
−0.817147 + 0.576429i \(0.804446\pi\)
\(488\) −5.00000 + 8.66025i −0.226339 + 0.392031i
\(489\) 2.00000 0.0904431
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 3.00000 5.19615i 0.135250 0.234261i
\(493\) 13.5000 + 23.3827i 0.608009 + 1.05310i
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) −6.00000 5.19615i −0.269137 0.233079i
\(498\) 0 0
\(499\) 5.00000 8.66025i 0.223831 0.387686i −0.732137 0.681157i \(-0.761477\pi\)
0.955968 + 0.293471i \(0.0948104\pi\)
\(500\) 0 0
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 7.50000 12.9904i 0.334741 0.579789i
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) −2.50000 + 0.866025i −0.111359 + 0.0385758i
\(505\) 0 0
\(506\) −1.50000 + 2.59808i −0.0666831 + 0.115499i
\(507\) −1.50000 2.59808i −0.0666173 0.115385i
\(508\) 0.500000 + 0.866025i 0.0221839 + 0.0384237i
\(509\) 18.0000 31.1769i 0.797836 1.38189i −0.123187 0.992384i \(-0.539311\pi\)
0.921023 0.389509i \(-0.127355\pi\)
\(510\) 0 0
\(511\) 2.00000 10.3923i 0.0884748 0.459728i
\(512\) −1.00000 −0.0441942
\(513\) 0.500000 0.866025i 0.0220755 0.0382360i
\(514\) 6.00000 + 10.3923i 0.264649 + 0.458385i
\(515\) 0 0
\(516\) −5.50000 + 9.52628i −0.242124 + 0.419371i
\(517\) −3.00000 −0.131940
\(518\) −3.50000 + 18.1865i −0.153781 + 0.799070i
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 15.0000 + 25.9808i 0.657162 + 1.13824i 0.981347 + 0.192244i \(0.0615766\pi\)
−0.324185 + 0.945994i \(0.605090\pi\)
\(522\) −4.50000 7.79423i −0.196960 0.341144i
\(523\) 2.00000 3.46410i 0.0874539 0.151475i −0.818980 0.573822i \(-0.805460\pi\)
0.906434 + 0.422347i \(0.138794\pi\)
\(524\) 18.0000 0.786334
\(525\) −12.5000 + 4.33013i −0.545545 + 0.188982i
\(526\) 18.0000 0.784837
\(527\) −3.00000 + 5.19615i −0.130682 + 0.226348i
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 0 0
\(531\) 9.00000 0.390567
\(532\) 2.00000 + 1.73205i 0.0867110 + 0.0750939i
\(533\) 24.0000 1.03956
\(534\) 0 0
\(535\) 0 0
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 7.50000 12.9904i 0.323649 0.560576i
\(538\) −6.00000 −0.258678
\(539\) 5.50000 4.33013i 0.236902 0.186512i
\(540\) 0 0
\(541\) −10.0000 + 17.3205i −0.429934 + 0.744667i −0.996867 0.0790969i \(-0.974796\pi\)
0.566933 + 0.823764i \(0.308130\pi\)
\(542\) −8.00000 13.8564i −0.343629 0.595184i
\(543\) 5.00000 + 8.66025i 0.214571 + 0.371647i
\(544\) 1.50000 2.59808i 0.0643120 0.111392i
\(545\) 0 0
\(546\) −8.00000 6.92820i −0.342368 0.296500i
\(547\) −19.0000 −0.812381 −0.406191 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) 5.00000 + 8.66025i 0.213395 + 0.369611i
\(550\) −2.50000 4.33013i −0.106600 0.184637i
\(551\) −4.50000 + 7.79423i −0.191706 + 0.332045i
\(552\) 3.00000 0.127688
\(553\) −40.0000 + 13.8564i −1.70097 + 0.589234i
\(554\) −32.0000 −1.35955
\(555\) 0 0
\(556\) 9.50000 + 16.4545i 0.402890 + 0.697826i
\(557\) −22.5000 38.9711i −0.953356 1.65126i −0.738087 0.674705i \(-0.764271\pi\)
−0.215268 0.976555i \(-0.569063\pi\)
\(558\) 1.00000 1.73205i 0.0423334 0.0733236i
\(559\) −44.0000 −1.86100
\(560\) 0 0
\(561\) 3.00000 0.126660
\(562\) −7.50000 + 12.9904i −0.316368 + 0.547966i
\(563\) 18.0000 + 31.1769i 0.758610 + 1.31395i 0.943560 + 0.331202i \(0.107454\pi\)
−0.184950 + 0.982748i \(0.559212\pi\)
\(564\) 1.50000 + 2.59808i 0.0631614 + 0.109399i
\(565\) 0 0
\(566\) −20.0000 −0.840663
\(567\) −0.500000 + 2.59808i −0.0209980 + 0.109109i
\(568\) −3.00000 −0.125877
\(569\) 10.5000 18.1865i 0.440183 0.762419i −0.557520 0.830164i \(-0.688247\pi\)
0.997703 + 0.0677445i \(0.0215803\pi\)
\(570\) 0 0
\(571\) −14.5000 25.1147i −0.606806 1.05102i −0.991763 0.128085i \(-0.959117\pi\)
0.384957 0.922934i \(-0.374216\pi\)
\(572\) 2.00000 3.46410i 0.0836242 0.144841i
\(573\) 0 0
\(574\) 15.0000 5.19615i 0.626088 0.216883i
\(575\) 15.0000 0.625543
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 11.0000 + 19.0526i 0.457936 + 0.793168i 0.998852 0.0479084i \(-0.0152556\pi\)
−0.540916 + 0.841077i \(0.681922\pi\)
\(578\) −4.00000 6.92820i −0.166378 0.288175i
\(579\) 5.00000 8.66025i 0.207793 0.359908i
\(580\) 0 0
\(581\) 0 0
\(582\) 1.00000 0.0414513
\(583\) 0 0
\(584\) −2.00000 3.46410i −0.0827606 0.143346i
\(585\) 0 0
\(586\) 4.50000 7.79423i 0.185893 0.321977i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −6.50000 2.59808i −0.268055 0.107143i
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 10.5000 + 18.1865i 0.431912 + 0.748094i
\(592\) 3.50000 + 6.06218i 0.143849 + 0.249154i
\(593\) −4.50000 + 7.79423i −0.184793 + 0.320071i −0.943507 0.331353i \(-0.892495\pi\)
0.758714 + 0.651424i \(0.225828\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 9.00000 0.368654
\(597\) −10.0000 + 17.3205i −0.409273 + 0.708881i
\(598\) 6.00000 + 10.3923i 0.245358 + 0.424973i
\(599\) −24.0000 41.5692i −0.980613 1.69847i −0.660006 0.751260i \(-0.729446\pi\)
−0.320607 0.947212i \(-0.603887\pi\)
\(600\) −2.50000 + 4.33013i −0.102062 + 0.176777i
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) −27.5000 + 9.52628i −1.12082 + 0.388262i
\(603\) −4.00000 −0.162893
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) 0 0
\(606\) 7.50000 + 12.9904i 0.304667 + 0.527698i
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 1.00000 0.0405554
\(609\) 4.50000 23.3827i 0.182349 0.947514i
\(610\) 0 0
\(611\) −6.00000 + 10.3923i −0.242734 + 0.420428i
\(612\) −1.50000 2.59808i −0.0606339 0.105021i
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) −2.00000 + 3.46410i −0.0807134 + 0.139800i
\(615\) 0 0
\(616\) 0.500000 2.59808i 0.0201456 0.104679i
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) −2.00000 + 3.46410i −0.0804518 + 0.139347i
\(619\) −7.00000 12.1244i −0.281354 0.487319i 0.690365 0.723462i \(-0.257450\pi\)
−0.971718 + 0.236143i \(0.924117\pi\)
\(620\) 0 0
\(621\) 1.50000 2.59808i 0.0601929 0.104257i
\(622\) 21.0000 0.842023
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −0.500000 0.866025i −0.0199840 0.0346133i
\(627\) 0.500000 + 0.866025i 0.0199681 + 0.0345857i
\(628\) 6.50000 11.2583i 0.259378 0.449256i
\(629\) −21.0000 −0.837325
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) −8.00000 + 13.8564i −0.318223 + 0.551178i
\(633\) 2.00000 + 3.46410i 0.0794929 + 0.137686i
\(634\) −6.00000 10.3923i −0.238290 0.412731i
\(635\) 0 0
\(636\) 0 0
\(637\) −4.00000 27.7128i −0.158486 1.09802i
\(638\) 9.00000 0.356313
\(639\) −1.50000 + 2.59808i −0.0593391 + 0.102778i
\(640\) 0 0
\(641\) −9.00000 15.5885i −0.355479 0.615707i 0.631721 0.775196i \(-0.282349\pi\)
−0.987200 + 0.159489i \(0.949015\pi\)
\(642\) −9.00000 + 15.5885i −0.355202 + 0.615227i
\(643\) −46.0000 −1.81406 −0.907031 0.421063i \(-0.861657\pi\)
−0.907031 + 0.421063i \(0.861657\pi\)
\(644\) 6.00000 + 5.19615i 0.236433 + 0.204757i
\(645\) 0 0
\(646\) −1.50000 + 2.59808i −0.0590167 + 0.102220i
\(647\) −24.0000 41.5692i −0.943537 1.63425i −0.758654 0.651494i \(-0.774142\pi\)
−0.184884 0.982760i \(-0.559191\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −4.50000 + 7.79423i −0.176640 + 0.305950i
\(650\) −20.0000 −0.784465
\(651\) 5.00000 1.73205i 0.195965 0.0678844i
\(652\) 2.00000 0.0783260
\(653\) −12.0000 + 20.7846i −0.469596 + 0.813365i −0.999396 0.0347583i \(-0.988934\pi\)
0.529799 + 0.848123i \(0.322267\pi\)
\(654\) −5.00000 8.66025i −0.195515 0.338643i
\(655\) 0 0
\(656\) 3.00000 5.19615i 0.117130 0.202876i
\(657\) −4.00000 −0.156055
\(658\) −1.50000 + 7.79423i −0.0584761 + 0.303851i
\(659\) −18.0000 −0.701180 −0.350590 0.936529i \(-0.614019\pi\)
−0.350590 + 0.936529i \(0.614019\pi\)
\(660\) 0 0
\(661\) −17.5000 30.3109i −0.680671 1.17896i −0.974776 0.223184i \(-0.928355\pi\)
0.294105 0.955773i \(-0.404978\pi\)
\(662\) −5.00000 8.66025i −0.194331 0.336590i
\(663\) 6.00000 10.3923i 0.233021 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 7.00000 0.271244
\(667\) −13.5000 + 23.3827i −0.522722 + 0.905381i
\(668\) −6.00000 10.3923i −0.232147 0.402090i
\(669\) −4.00000 6.92820i −0.154649 0.267860i
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) −2.50000 + 0.866025i −0.0964396 + 0.0334077i
\(673\) 44.0000 1.69608 0.848038 0.529936i \(-0.177784\pi\)
0.848038 + 0.529936i \(0.177784\pi\)
\(674\) −5.00000 + 8.66025i −0.192593 + 0.333581i
\(675\) 2.50000 + 4.33013i 0.0962250 + 0.166667i
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) 16.5000 28.5788i 0.634147 1.09837i −0.352549 0.935793i \(-0.614685\pi\)
0.986695 0.162581i \(-0.0519817\pi\)
\(678\) −12.0000 −0.460857
\(679\) 2.00000 + 1.73205i 0.0767530 + 0.0664700i
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) 1.00000 + 1.73205i 0.0382920 + 0.0663237i
\(683\) −16.5000 28.5788i −0.631355 1.09354i −0.987275 0.159022i \(-0.949166\pi\)
0.355920 0.934516i \(-0.384168\pi\)
\(684\) 0.500000 0.866025i 0.0191180 0.0331133i
\(685\) 0 0
\(686\) −8.50000 16.4545i −0.324532 0.628235i
\(687\) 26.0000 0.991962
\(688\) −5.50000 + 9.52628i −0.209686 + 0.363186i
\(689\) 0 0
\(690\) 0 0
\(691\) −25.0000 + 43.3013i −0.951045 + 1.64726i −0.207875 + 0.978155i \(0.566655\pi\)
−0.743170 + 0.669102i \(0.766679\pi\)
\(692\) −6.00000 −0.228086
\(693\) −2.00000 1.73205i −0.0759737 0.0657952i
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) −4.50000 7.79423i −0.170572 0.295439i
\(697\) 9.00000 + 15.5885i 0.340899 + 0.590455i
\(698\) 4.00000 6.92820i 0.151402 0.262236i
\(699\) 9.00000 0.340411
\(700\) −12.5000 + 4.33013i −0.472456 + 0.163663i
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) −2.00000 + 3.46410i −0.0754851 + 0.130744i
\(703\) −3.50000 6.06218i −0.132005 0.228639i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) −7.50000 + 38.9711i −0.282067 + 1.46566i
\(708\) 9.00000 0.338241
\(709\) −17.5000 + 30.3109i −0.657226 + 1.13835i 0.324104 + 0.946021i \(0.394937\pi\)
−0.981331 + 0.192328i \(0.938396\pi\)
\(710\) 0 0
\(711\) 8.00000 + 13.8564i 0.300023 + 0.519656i
\(712\) 0 0
\(713\) −6.00000 −0.224702
\(714\) 1.50000 7.79423i 0.0561361 0.291692i
\(715\) 0 0
\(716\) 7.50000 12.9904i 0.280288 0.485473i
\(717\) 12.0000 + 20.7846i 0.448148 + 0.776215i
\(718\) −9.00000 15.5885i −0.335877 0.581756i
\(719\) −4.50000 + 7.79423i −0.167822 + 0.290676i −0.937654 0.347571i \(-0.887007\pi\)
0.769832 + 0.638247i \(0.220340\pi\)
\(720\) 0 0
\(721\) −10.0000 + 3.46410i −0.372419 + 0.129010i
\(722\) 18.0000 0.669891
\(723\) 14.0000 24.2487i 0.520666 0.901819i
\(724\) 5.00000 + 8.66025i 0.185824 + 0.321856i
\(725\) −22.5000 38.9711i −0.835629 1.44735i
\(726\) 0.500000 0.866025i 0.0185567 0.0321412i
\(727\) −22.0000 −0.815935 −0.407967 0.912996i \(-0.633762\pi\)
−0.407967 + 0.912996i \(0.633762\pi\)
\(728\) −8.00000 6.92820i −0.296500 0.256776i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −16.5000 28.5788i −0.610275 1.05703i
\(732\) 5.00000 + 8.66025i 0.184805 + 0.320092i
\(733\) −7.00000 + 12.1244i −0.258551 + 0.447823i −0.965854 0.259087i \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) 4.00000 0.147643
\(735\) 0 0
\(736\) 3.00000 0.110581
\(737\) 2.00000 3.46410i 0.0736709 0.127602i
\(738\) −3.00000 5.19615i −0.110432 0.191273i
\(739\) 2.00000 + 3.46410i 0.0735712 + 0.127429i 0.900464 0.434930i \(-0.143227\pi\)
−0.826893 + 0.562360i \(0.809894\pi\)
\(740\) 0 0
\(741\) 4.00000 0.146944
\(742\) 0 0
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 1.00000 1.73205i 0.0366618 0.0635001i
\(745\) 0 0
\(746\) −11.0000 19.0526i −0.402739 0.697564i
\(747\) 0 0
\(748\) 3.00000 0.109691
\(749\) −45.0000 + 15.5885i −1.64426 + 0.569590i
\(750\) 0 0
\(751\) −1.00000 + 1.73205i −0.0364905 + 0.0632034i −0.883694 0.468065i \(-0.844951\pi\)
0.847203 + 0.531269i \(0.178285\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) −7.50000 12.9904i −0.273315 0.473396i
\(754\) 18.0000 31.1769i 0.655521 1.13540i
\(755\) 0 0
\(756\) −0.500000 + 2.59808i −0.0181848 + 0.0944911i
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) 7.00000 12.1244i 0.254251 0.440376i
\(759\) 1.50000 + 2.59808i 0.0544466 + 0.0943042i
\(760\) 0 0
\(761\) −15.0000 + 25.9808i −0.543750 + 0.941802i 0.454935 + 0.890525i \(0.349663\pi\)
−0.998684 + 0.0512772i \(0.983671\pi\)
\(762\) 1.00000 0.0362262
\(763\) 5.00000 25.9808i 0.181012 0.940567i
\(764\) 0 0
\(765\) 0 0
\(766\) 7.50000 + 12.9904i 0.270986 + 0.469362i
\(767\) 18.0000 + 31.1769i 0.649942 + 1.12573i
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 50.0000 1.80305 0.901523 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) 5.00000 8.66025i 0.179954 0.311689i
\(773\) −27.0000 46.7654i −0.971123 1.68203i −0.692179 0.721726i \(-0.743349\pi\)
−0.278944 0.960307i \(-0.589984\pi\)
\(774\) 5.50000 + 9.52628i 0.197693 + 0.342415i
\(775\) 5.00000 8.66025i 0.179605 0.311086i
\(776\) 1.00000 0.0358979
\(777\) 14.0000 + 12.1244i 0.502247 + 0.434959i
\(778\) −12.0000 −0.430221
\(779\) −3.00000 + 5.19615i −0.107486 + 0.186171i
\(780\) 0 0
\(781\) −1.50000 2.59808i −0.0536742 0.0929665i
\(782\) −4.50000 + 7.79423i −0.160920 + 0.278721i
\(783\) −9.00000 −0.321634
\(784\) −6.50000 2.59808i −0.232143