Properties

Label 722.2.c.g.429.1
Level $722$
Weight $2$
Character 722.429
Analytic conductor $5.765$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.76519902594\)
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 429.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 722.429
Dual form 722.2.c.g.653.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-1.50000 - 2.59808i) q^{6} -3.00000 q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(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} +(-1.50000 - 2.59808i) q^{6} -3.00000 q^{7} -1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{10} -2.00000 q^{11} -3.00000 q^{12} +(-1.50000 - 2.59808i) q^{13} +(-1.50000 + 2.59808i) q^{14} +(3.00000 + 5.19615i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.500000 - 0.866025i) q^{17} -6.00000 q^{18} +2.00000 q^{20} +(-4.50000 + 7.79423i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(-2.50000 - 4.33013i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(0.500000 + 0.866025i) q^{25} -3.00000 q^{26} -9.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +(-1.50000 - 2.59808i) q^{29} +6.00000 q^{30} +6.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{33} +(-0.500000 - 0.866025i) q^{34} +(3.00000 - 5.19615i) q^{35} +(-3.00000 + 5.19615i) q^{36} -6.00000 q^{37} -9.00000 q^{39} +(1.00000 - 1.73205i) q^{40} +(6.00000 - 10.3923i) q^{41} +(4.50000 + 7.79423i) q^{42} +(5.00000 - 8.66025i) q^{43} +(1.00000 + 1.73205i) q^{44} +12.0000 q^{45} -5.00000 q^{46} +(4.00000 + 6.92820i) q^{47} +(1.50000 + 2.59808i) q^{48} +2.00000 q^{49} +1.00000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(-1.50000 + 2.59808i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(-4.50000 + 7.79423i) q^{54} +(2.00000 - 3.46410i) q^{55} +3.00000 q^{56} -3.00000 q^{58} +(1.50000 - 2.59808i) q^{59} +(3.00000 - 5.19615i) q^{60} +(3.00000 - 5.19615i) q^{62} +(9.00000 + 15.5885i) q^{63} +1.00000 q^{64} +6.00000 q^{65} +(3.00000 + 5.19615i) q^{66} +(7.50000 + 12.9904i) q^{67} -1.00000 q^{68} -15.0000 q^{69} +(-3.00000 - 5.19615i) q^{70} +(3.00000 + 5.19615i) q^{72} +(5.50000 - 9.52628i) q^{73} +(-3.00000 + 5.19615i) q^{74} +3.00000 q^{75} +6.00000 q^{77} +(-4.50000 + 7.79423i) q^{78} +(-6.00000 + 10.3923i) q^{79} +(-1.00000 - 1.73205i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-6.00000 - 10.3923i) q^{82} +2.00000 q^{83} +9.00000 q^{84} +(1.00000 + 1.73205i) q^{85} +(-5.00000 - 8.66025i) q^{86} -9.00000 q^{87} +2.00000 q^{88} +(3.00000 + 5.19615i) q^{89} +(6.00000 - 10.3923i) q^{90} +(4.50000 + 7.79423i) q^{91} +(-2.50000 + 4.33013i) q^{92} +(9.00000 - 15.5885i) q^{93} +8.00000 q^{94} +3.00000 q^{96} +(6.00000 - 10.3923i) q^{97} +(1.00000 - 1.73205i) q^{98} +(6.00000 + 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 3q^{3} - q^{4} - 2q^{5} - 3q^{6} - 6q^{7} - 2q^{8} - 6q^{9} + O(q^{10}) \) \( 2q + q^{2} + 3q^{3} - q^{4} - 2q^{5} - 3q^{6} - 6q^{7} - 2q^{8} - 6q^{9} + 2q^{10} - 4q^{11} - 6q^{12} - 3q^{13} - 3q^{14} + 6q^{15} - q^{16} + q^{17} - 12q^{18} + 4q^{20} - 9q^{21} - 2q^{22} - 5q^{23} - 3q^{24} + q^{25} - 6q^{26} - 18q^{27} + 3q^{28} - 3q^{29} + 12q^{30} + 12q^{31} + q^{32} - 6q^{33} - q^{34} + 6q^{35} - 6q^{36} - 12q^{37} - 18q^{39} + 2q^{40} + 12q^{41} + 9q^{42} + 10q^{43} + 2q^{44} + 24q^{45} - 10q^{46} + 8q^{47} + 3q^{48} + 4q^{49} + 2q^{50} - 3q^{51} - 3q^{52} - 3q^{53} - 9q^{54} + 4q^{55} + 6q^{56} - 6q^{58} + 3q^{59} + 6q^{60} + 6q^{62} + 18q^{63} + 2q^{64} + 12q^{65} + 6q^{66} + 15q^{67} - 2q^{68} - 30q^{69} - 6q^{70} + 6q^{72} + 11q^{73} - 6q^{74} + 6q^{75} + 12q^{77} - 9q^{78} - 12q^{79} - 2q^{80} - 9q^{81} - 12q^{82} + 4q^{83} + 18q^{84} + 2q^{85} - 10q^{86} - 18q^{87} + 4q^{88} + 6q^{89} + 12q^{90} + 9q^{91} - 5q^{92} + 18q^{93} + 16q^{94} + 6q^{96} + 12q^{97} + 2q^{98} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 \(-0.166667\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) −1.50000 2.59808i −0.612372 1.06066i
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 5.19615i −1.00000 1.73205i
\(10\) 1.00000 + 1.73205i 0.316228 + 0.547723i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) −3.00000 −0.866025
\(13\) −1.50000 2.59808i −0.416025 0.720577i 0.579510 0.814965i \(-0.303244\pi\)
−0.995535 + 0.0943882i \(0.969911\pi\)
\(14\) −1.50000 + 2.59808i −0.400892 + 0.694365i
\(15\) 3.00000 + 5.19615i 0.774597 + 1.34164i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.500000 0.866025i 0.121268 0.210042i −0.799000 0.601331i \(-0.794637\pi\)
0.920268 + 0.391289i \(0.127971\pi\)
\(18\) −6.00000 −1.41421
\(19\) 0 0
\(20\) 2.00000 0.447214
\(21\) −4.50000 + 7.79423i −0.981981 + 1.70084i
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) −2.50000 4.33013i −0.521286 0.902894i −0.999694 0.0247559i \(-0.992119\pi\)
0.478407 0.878138i \(-0.341214\pi\)
\(24\) −1.50000 + 2.59808i −0.306186 + 0.530330i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −3.00000 −0.588348
\(27\) −9.00000 −1.73205
\(28\) 1.50000 + 2.59808i 0.283473 + 0.490990i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 6.00000 1.09545
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −3.00000 + 5.19615i −0.522233 + 0.904534i
\(34\) −0.500000 0.866025i −0.0857493 0.148522i
\(35\) 3.00000 5.19615i 0.507093 0.878310i
\(36\) −3.00000 + 5.19615i −0.500000 + 0.866025i
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 0 0
\(39\) −9.00000 −1.44115
\(40\) 1.00000 1.73205i 0.158114 0.273861i
\(41\) 6.00000 10.3923i 0.937043 1.62301i 0.166092 0.986110i \(-0.446885\pi\)
0.770950 0.636895i \(-0.219782\pi\)
\(42\) 4.50000 + 7.79423i 0.694365 + 1.20268i
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 12.0000 1.78885
\(46\) −5.00000 −0.737210
\(47\) 4.00000 + 6.92820i 0.583460 + 1.01058i 0.995066 + 0.0992202i \(0.0316348\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(48\) 1.50000 + 2.59808i 0.216506 + 0.375000i
\(49\) 2.00000 0.285714
\(50\) 1.00000 0.141421
\(51\) −1.50000 2.59808i −0.210042 0.363803i
\(52\) −1.50000 + 2.59808i −0.208013 + 0.360288i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) −4.50000 + 7.79423i −0.612372 + 1.06066i
\(55\) 2.00000 3.46410i 0.269680 0.467099i
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) −3.00000 −0.393919
\(59\) 1.50000 2.59808i 0.195283 0.338241i −0.751710 0.659494i \(-0.770771\pi\)
0.946993 + 0.321253i \(0.104104\pi\)
\(60\) 3.00000 5.19615i 0.387298 0.670820i
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 3.00000 5.19615i 0.381000 0.659912i
\(63\) 9.00000 + 15.5885i 1.13389 + 1.96396i
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 3.00000 + 5.19615i 0.369274 + 0.639602i
\(67\) 7.50000 + 12.9904i 0.916271 + 1.58703i 0.805030 + 0.593234i \(0.202149\pi\)
0.111241 + 0.993793i \(0.464517\pi\)
\(68\) −1.00000 −0.121268
\(69\) −15.0000 −1.80579
\(70\) −3.00000 5.19615i −0.358569 0.621059i
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 3.00000 + 5.19615i 0.353553 + 0.612372i
\(73\) 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i \(-0.610721\pi\)
0.984594 0.174855i \(-0.0559458\pi\)
\(74\) −3.00000 + 5.19615i −0.348743 + 0.604040i
\(75\) 3.00000 0.346410
\(76\) 0 0
\(77\) 6.00000 0.683763
\(78\) −4.50000 + 7.79423i −0.509525 + 0.882523i
\(79\) −6.00000 + 10.3923i −0.675053 + 1.16923i 0.301401 + 0.953498i \(0.402546\pi\)
−0.976453 + 0.215728i \(0.930788\pi\)
\(80\) −1.00000 1.73205i −0.111803 0.193649i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −6.00000 10.3923i −0.662589 1.14764i
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 9.00000 0.981981
\(85\) 1.00000 + 1.73205i 0.108465 + 0.187867i
\(86\) −5.00000 8.66025i −0.539164 0.933859i
\(87\) −9.00000 −0.964901
\(88\) 2.00000 0.213201
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 6.00000 10.3923i 0.632456 1.09545i
\(91\) 4.50000 + 7.79423i 0.471728 + 0.817057i
\(92\) −2.50000 + 4.33013i −0.260643 + 0.451447i
\(93\) 9.00000 15.5885i 0.933257 1.61645i
\(94\) 8.00000 0.825137
\(95\) 0 0
\(96\) 3.00000 0.306186
\(97\) 6.00000 10.3923i 0.609208 1.05518i −0.382164 0.924095i \(-0.624821\pi\)
0.991371 0.131084i \(-0.0418458\pi\)
\(98\) 1.00000 1.73205i 0.101015 0.174964i
\(99\) 6.00000 + 10.3923i 0.603023 + 1.04447i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) −3.00000 −0.297044
\(103\) −6.00000 −0.591198 −0.295599 0.955312i \(-0.595519\pi\)
−0.295599 + 0.955312i \(0.595519\pi\)
\(104\) 1.50000 + 2.59808i 0.147087 + 0.254762i
\(105\) −9.00000 15.5885i −0.878310 1.52128i
\(106\) −3.00000 −0.291386
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 4.50000 + 7.79423i 0.433013 + 0.750000i
\(109\) 1.50000 2.59808i 0.143674 0.248851i −0.785203 0.619238i \(-0.787442\pi\)
0.928877 + 0.370387i \(0.120775\pi\)
\(110\) −2.00000 3.46410i −0.190693 0.330289i
\(111\) −9.00000 + 15.5885i −0.854242 + 1.47959i
\(112\) 1.50000 2.59808i 0.141737 0.245495i
\(113\) −12.0000 −1.12887 −0.564433 0.825479i \(-0.690905\pi\)
−0.564433 + 0.825479i \(0.690905\pi\)
\(114\) 0 0
\(115\) 10.0000 0.932505
\(116\) −1.50000 + 2.59808i −0.139272 + 0.241225i
\(117\) −9.00000 + 15.5885i −0.832050 + 1.44115i
\(118\) −1.50000 2.59808i −0.138086 0.239172i
\(119\) −1.50000 + 2.59808i −0.137505 + 0.238165i
\(120\) −3.00000 5.19615i −0.273861 0.474342i
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) −18.0000 31.1769i −1.62301 2.81113i
\(124\) −3.00000 5.19615i −0.269408 0.466628i
\(125\) −12.0000 −1.07331
\(126\) 18.0000 1.60357
\(127\) 6.00000 + 10.3923i 0.532414 + 0.922168i 0.999284 + 0.0378419i \(0.0120483\pi\)
−0.466870 + 0.884326i \(0.654618\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −15.0000 25.9808i −1.32068 2.28748i
\(130\) 3.00000 5.19615i 0.263117 0.455733i
\(131\) −7.00000 + 12.1244i −0.611593 + 1.05931i 0.379379 + 0.925241i \(0.376138\pi\)
−0.990972 + 0.134069i \(0.957196\pi\)
\(132\) 6.00000 0.522233
\(133\) 0 0
\(134\) 15.0000 1.29580
\(135\) 9.00000 15.5885i 0.774597 1.34164i
\(136\) −0.500000 + 0.866025i −0.0428746 + 0.0742611i
\(137\) −9.50000 16.4545i −0.811640 1.40580i −0.911716 0.410822i \(-0.865242\pi\)
0.100076 0.994980i \(-0.468091\pi\)
\(138\) −7.50000 + 12.9904i −0.638442 + 1.10581i
\(139\) −3.00000 5.19615i −0.254457 0.440732i 0.710291 0.703908i \(-0.248563\pi\)
−0.964748 + 0.263176i \(0.915230\pi\)
\(140\) −6.00000 −0.507093
\(141\) 24.0000 2.02116
\(142\) 0 0
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 6.00000 0.500000
\(145\) 6.00000 0.498273
\(146\) −5.50000 9.52628i −0.455183 0.788400i
\(147\) 3.00000 5.19615i 0.247436 0.428571i
\(148\) 3.00000 + 5.19615i 0.246598 + 0.427121i
\(149\) 4.00000 6.92820i 0.327693 0.567581i −0.654361 0.756182i \(-0.727062\pi\)
0.982054 + 0.188602i \(0.0603956\pi\)
\(150\) 1.50000 2.59808i 0.122474 0.212132i
\(151\) 18.0000 1.46482 0.732410 0.680864i \(-0.238396\pi\)
0.732410 + 0.680864i \(0.238396\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 3.00000 5.19615i 0.241747 0.418718i
\(155\) −6.00000 + 10.3923i −0.481932 + 0.834730i
\(156\) 4.50000 + 7.79423i 0.360288 + 0.624038i
\(157\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(158\) 6.00000 + 10.3923i 0.477334 + 0.826767i
\(159\) −9.00000 −0.713746
\(160\) −2.00000 −0.158114
\(161\) 7.50000 + 12.9904i 0.591083 + 1.02379i
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) −6.00000 −0.469956 −0.234978 0.972001i \(-0.575502\pi\)
−0.234978 + 0.972001i \(0.575502\pi\)
\(164\) −12.0000 −0.937043
\(165\) −6.00000 10.3923i −0.467099 0.809040i
\(166\) 1.00000 1.73205i 0.0776151 0.134433i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 4.50000 7.79423i 0.347183 0.601338i
\(169\) 2.00000 3.46410i 0.153846 0.266469i
\(170\) 2.00000 0.153393
\(171\) 0 0
\(172\) −10.0000 −0.762493
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) −4.50000 + 7.79423i −0.341144 + 0.590879i
\(175\) −1.50000 2.59808i −0.113389 0.196396i
\(176\) 1.00000 1.73205i 0.0753778 0.130558i
\(177\) −4.50000 7.79423i −0.338241 0.585850i
\(178\) 6.00000 0.449719
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −6.00000 10.3923i −0.447214 0.774597i
\(181\) 9.00000 + 15.5885i 0.668965 + 1.15868i 0.978194 + 0.207693i \(0.0665956\pi\)
−0.309229 + 0.950988i \(0.600071\pi\)
\(182\) 9.00000 0.667124
\(183\) 0 0
\(184\) 2.50000 + 4.33013i 0.184302 + 0.319221i
\(185\) 6.00000 10.3923i 0.441129 0.764057i
\(186\) −9.00000 15.5885i −0.659912 1.14300i
\(187\) −1.00000 + 1.73205i −0.0731272 + 0.126660i
\(188\) 4.00000 6.92820i 0.291730 0.505291i
\(189\) 27.0000 1.96396
\(190\) 0 0
\(191\) −11.0000 −0.795932 −0.397966 0.917400i \(-0.630284\pi\)
−0.397966 + 0.917400i \(0.630284\pi\)
\(192\) 1.50000 2.59808i 0.108253 0.187500i
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) −6.00000 10.3923i −0.430775 0.746124i
\(195\) 9.00000 15.5885i 0.644503 1.11631i
\(196\) −1.00000 1.73205i −0.0714286 0.123718i
\(197\) 4.00000 0.284988 0.142494 0.989796i \(-0.454488\pi\)
0.142494 + 0.989796i \(0.454488\pi\)
\(198\) 12.0000 0.852803
\(199\) 3.50000 + 6.06218i 0.248108 + 0.429736i 0.963001 0.269498i \(-0.0868577\pi\)
−0.714893 + 0.699234i \(0.753524\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 45.0000 3.17406
\(202\) −10.0000 −0.703598
\(203\) 4.50000 + 7.79423i 0.315838 + 0.547048i
\(204\) −1.50000 + 2.59808i −0.105021 + 0.181902i
\(205\) 12.0000 + 20.7846i 0.838116 + 1.45166i
\(206\) −3.00000 + 5.19615i −0.209020 + 0.362033i
\(207\) −15.0000 + 25.9808i −1.04257 + 1.80579i
\(208\) 3.00000 0.208013
\(209\) 0 0
\(210\) −18.0000 −1.24212
\(211\) 1.50000 2.59808i 0.103264 0.178859i −0.809763 0.586756i \(-0.800405\pi\)
0.913028 + 0.407898i \(0.133738\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 0 0
\(214\) 1.50000 2.59808i 0.102538 0.177601i
\(215\) 10.0000 + 17.3205i 0.681994 + 1.18125i
\(216\) 9.00000 0.612372
\(217\) −18.0000 −1.22192
\(218\) −1.50000 2.59808i −0.101593 0.175964i
\(219\) −16.5000 28.5788i −1.11497 1.93118i
\(220\) −4.00000 −0.269680
\(221\) −3.00000 −0.201802
\(222\) 9.00000 + 15.5885i 0.604040 + 1.04623i
\(223\) 9.00000 15.5885i 0.602685 1.04388i −0.389728 0.920930i \(-0.627431\pi\)
0.992413 0.122950i \(-0.0392356\pi\)
\(224\) −1.50000 2.59808i −0.100223 0.173591i
\(225\) 3.00000 5.19615i 0.200000 0.346410i
\(226\) −6.00000 + 10.3923i −0.399114 + 0.691286i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) −12.0000 −0.792982 −0.396491 0.918039i \(-0.629772\pi\)
−0.396491 + 0.918039i \(0.629772\pi\)
\(230\) 5.00000 8.66025i 0.329690 0.571040i
\(231\) 9.00000 15.5885i 0.592157 1.02565i
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) −7.00000 + 12.1244i −0.458585 + 0.794293i −0.998886 0.0471787i \(-0.984977\pi\)
0.540301 + 0.841472i \(0.318310\pi\)
\(234\) 9.00000 + 15.5885i 0.588348 + 1.01905i
\(235\) −16.0000 −1.04372
\(236\) −3.00000 −0.195283
\(237\) 18.0000 + 31.1769i 1.16923 + 2.02516i
\(238\) 1.50000 + 2.59808i 0.0972306 + 0.168408i
\(239\) 1.00000 0.0646846 0.0323423 0.999477i \(-0.489703\pi\)
0.0323423 + 0.999477i \(0.489703\pi\)
\(240\) −6.00000 −0.387298
\(241\) 12.0000 + 20.7846i 0.772988 + 1.33885i 0.935918 + 0.352217i \(0.114572\pi\)
−0.162930 + 0.986638i \(0.552095\pi\)
\(242\) −3.50000 + 6.06218i −0.224989 + 0.389692i
\(243\) 0 0
\(244\) 0 0
\(245\) −2.00000 + 3.46410i −0.127775 + 0.221313i
\(246\) −36.0000 −2.29528
\(247\) 0 0
\(248\) −6.00000 −0.381000
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) −6.00000 + 10.3923i −0.379473 + 0.657267i
\(251\) 10.0000 + 17.3205i 0.631194 + 1.09326i 0.987308 + 0.158818i \(0.0507683\pi\)
−0.356113 + 0.934443i \(0.615898\pi\)
\(252\) 9.00000 15.5885i 0.566947 0.981981i
\(253\) 5.00000 + 8.66025i 0.314347 + 0.544466i
\(254\) 12.0000 0.752947
\(255\) 6.00000 0.375735
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) −30.0000 −1.86772
\(259\) 18.0000 1.11847
\(260\) −3.00000 5.19615i −0.186052 0.322252i
\(261\) −9.00000 + 15.5885i −0.557086 + 0.964901i
\(262\) 7.00000 + 12.1244i 0.432461 + 0.749045i
\(263\) 4.00000 6.92820i 0.246651 0.427211i −0.715944 0.698158i \(-0.754003\pi\)
0.962594 + 0.270947i \(0.0873367\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 18.0000 1.10158
\(268\) 7.50000 12.9904i 0.458135 0.793514i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) −9.00000 15.5885i −0.547723 0.948683i
\(271\) 5.50000 9.52628i 0.334101 0.578680i −0.649211 0.760609i \(-0.724901\pi\)
0.983312 + 0.181928i \(0.0582339\pi\)
\(272\) 0.500000 + 0.866025i 0.0303170 + 0.0525105i
\(273\) 27.0000 1.63411
\(274\) −19.0000 −1.14783
\(275\) −1.00000 1.73205i −0.0603023 0.104447i
\(276\) 7.50000 + 12.9904i 0.451447 + 0.781929i
\(277\) 30.0000 1.80253 0.901263 0.433273i \(-0.142641\pi\)
0.901263 + 0.433273i \(0.142641\pi\)
\(278\) −6.00000 −0.359856
\(279\) −18.0000 31.1769i −1.07763 1.86651i
\(280\) −3.00000 + 5.19615i −0.179284 + 0.310530i
\(281\) 6.00000 + 10.3923i 0.357930 + 0.619953i 0.987615 0.156898i \(-0.0501493\pi\)
−0.629685 + 0.776851i \(0.716816\pi\)
\(282\) 12.0000 20.7846i 0.714590 1.23771i
\(283\) 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i \(-0.696728\pi\)
0.995544 + 0.0942988i \(0.0300609\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 6.00000 0.354787
\(287\) −18.0000 + 31.1769i −1.06251 + 1.84032i
\(288\) 3.00000 5.19615i 0.176777 0.306186i
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) 3.00000 5.19615i 0.176166 0.305129i
\(291\) −18.0000 31.1769i −1.05518 1.82762i
\(292\) −11.0000 −0.643726
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) −3.00000 5.19615i −0.174964 0.303046i
\(295\) 3.00000 + 5.19615i 0.174667 + 0.302532i
\(296\) 6.00000 0.348743
\(297\) 18.0000 1.04447
\(298\) −4.00000 6.92820i −0.231714 0.401340i
\(299\) −7.50000 + 12.9904i −0.433736 + 0.751253i
\(300\) −1.50000 2.59808i −0.0866025 0.150000i
\(301\) −15.0000 + 25.9808i −0.864586 + 1.49751i
\(302\) 9.00000 15.5885i 0.517892 0.897015i
\(303\) −30.0000 −1.72345
\(304\) 0 0
\(305\) 0 0
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) 6.00000 10.3923i 0.342438 0.593120i −0.642447 0.766330i \(-0.722081\pi\)
0.984885 + 0.173210i \(0.0554140\pi\)
\(308\) −3.00000 5.19615i −0.170941 0.296078i
\(309\) −9.00000 + 15.5885i −0.511992 + 0.886796i
\(310\) 6.00000 + 10.3923i 0.340777 + 0.590243i
\(311\) −11.0000 −0.623753 −0.311876 0.950123i \(-0.600957\pi\)
−0.311876 + 0.950123i \(0.600957\pi\)
\(312\) 9.00000 0.509525
\(313\) −10.5000 18.1865i −0.593495 1.02796i −0.993757 0.111563i \(-0.964414\pi\)
0.400262 0.916401i \(-0.368919\pi\)
\(314\) 0 0
\(315\) −36.0000 −2.02837
\(316\) 12.0000 0.675053
\(317\) −16.5000 28.5788i −0.926732 1.60515i −0.788751 0.614713i \(-0.789272\pi\)
−0.137981 0.990435i \(-0.544061\pi\)
\(318\) −4.50000 + 7.79423i −0.252347 + 0.437079i
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) −1.00000 + 1.73205i −0.0559017 + 0.0968246i
\(321\) 4.50000 7.79423i 0.251166 0.435031i
\(322\) 15.0000 0.835917
\(323\) 0 0
\(324\) 9.00000 0.500000
\(325\) 1.50000 2.59808i 0.0832050 0.144115i
\(326\) −3.00000 + 5.19615i −0.166155 + 0.287788i
\(327\) −4.50000 7.79423i −0.248851 0.431022i
\(328\) −6.00000 + 10.3923i −0.331295 + 0.573819i
\(329\) −12.0000 20.7846i −0.661581 1.14589i
\(330\) −12.0000 −0.660578
\(331\) −9.00000 −0.494685 −0.247342 0.968928i \(-0.579557\pi\)
−0.247342 + 0.968928i \(0.579557\pi\)
\(332\) −1.00000 1.73205i −0.0548821 0.0950586i
\(333\) 18.0000 + 31.1769i 0.986394 + 1.70848i
\(334\) −12.0000 −0.656611
\(335\) −30.0000 −1.63908
\(336\) −4.50000 7.79423i −0.245495 0.425210i
\(337\) 9.00000 15.5885i 0.490261 0.849157i −0.509676 0.860366i \(-0.670235\pi\)
0.999937 + 0.0112091i \(0.00356804\pi\)
\(338\) −2.00000 3.46410i −0.108786 0.188422i
\(339\) −18.0000 + 31.1769i −0.977626 + 1.69330i
\(340\) 1.00000 1.73205i 0.0542326 0.0939336i
\(341\) −12.0000 −0.649836
\(342\) 0 0
\(343\) 15.0000 0.809924
\(344\) −5.00000 + 8.66025i −0.269582 + 0.466930i
\(345\) 15.0000 25.9808i 0.807573 1.39876i
\(346\) 9.00000 + 15.5885i 0.483843 + 0.838041i
\(347\) −8.00000 + 13.8564i −0.429463 + 0.743851i −0.996826 0.0796169i \(-0.974630\pi\)
0.567363 + 0.823468i \(0.307964\pi\)
\(348\) 4.50000 + 7.79423i 0.241225 + 0.417815i
\(349\) 28.0000 1.49881 0.749403 0.662114i \(-0.230341\pi\)
0.749403 + 0.662114i \(0.230341\pi\)
\(350\) −3.00000 −0.160357
\(351\) 13.5000 + 23.3827i 0.720577 + 1.24808i
\(352\) −1.00000 1.73205i −0.0533002 0.0923186i
\(353\) −31.0000 −1.64996 −0.824982 0.565159i \(-0.808815\pi\)
−0.824982 + 0.565159i \(0.808815\pi\)
\(354\) −9.00000 −0.478345
\(355\) 0 0
\(356\) 3.00000 5.19615i 0.159000 0.275396i
\(357\) 4.50000 + 7.79423i 0.238165 + 0.412514i
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) −9.50000 + 16.4545i −0.501391 + 0.868434i 0.498608 + 0.866828i \(0.333845\pi\)
−0.999999 + 0.00160673i \(0.999489\pi\)
\(360\) −12.0000 −0.632456
\(361\) 0 0
\(362\) 18.0000 0.946059
\(363\) −10.5000 + 18.1865i −0.551107 + 0.954545i
\(364\) 4.50000 7.79423i 0.235864 0.408529i
\(365\) 11.0000 + 19.0526i 0.575766 + 0.997257i
\(366\) 0 0
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 5.00000 0.260643
\(369\) −72.0000 −3.74817
\(370\) −6.00000 10.3923i −0.311925 0.540270i
\(371\) 4.50000 + 7.79423i 0.233628 + 0.404656i
\(372\) −18.0000 −0.933257
\(373\) 21.0000 1.08734 0.543669 0.839299i \(-0.317035\pi\)
0.543669 + 0.839299i \(0.317035\pi\)
\(374\) 1.00000 + 1.73205i 0.0517088 + 0.0895622i
\(375\) −18.0000 + 31.1769i −0.929516 + 1.60997i
\(376\) −4.00000 6.92820i −0.206284 0.357295i
\(377\) −4.50000 + 7.79423i −0.231762 + 0.401423i
\(378\) 13.5000 23.3827i 0.694365 1.20268i
\(379\) −3.00000 −0.154100 −0.0770498 0.997027i \(-0.524550\pi\)
−0.0770498 + 0.997027i \(0.524550\pi\)
\(380\) 0 0
\(381\) 36.0000 1.84434
\(382\) −5.50000 + 9.52628i −0.281404 + 0.487407i
\(383\) 9.00000 15.5885i 0.459879 0.796533i −0.539076 0.842257i \(-0.681226\pi\)
0.998954 + 0.0457244i \(0.0145596\pi\)
\(384\) −1.50000 2.59808i −0.0765466 0.132583i
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) −3.00000 5.19615i −0.152696 0.264477i
\(387\) −60.0000 −3.04997
\(388\) −12.0000 −0.609208
\(389\) −13.0000 22.5167i −0.659126 1.14164i −0.980842 0.194804i \(-0.937593\pi\)
0.321716 0.946836i \(-0.395740\pi\)
\(390\) −9.00000 15.5885i −0.455733 0.789352i
\(391\) −5.00000 −0.252861
\(392\) −2.00000 −0.101015
\(393\) 21.0000 + 36.3731i 1.05931 + 1.83478i
\(394\) 2.00000 3.46410i 0.100759 0.174519i
\(395\) −12.0000 20.7846i −0.603786 1.04579i
\(396\) 6.00000 10.3923i 0.301511 0.522233i
\(397\) −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) 7.00000 0.350878
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 18.0000 31.1769i 0.898877 1.55690i 0.0699455 0.997551i \(-0.477717\pi\)
0.828932 0.559350i \(-0.188949\pi\)
\(402\) 22.5000 38.9711i 1.12220 1.94370i
\(403\) −9.00000 15.5885i −0.448322 0.776516i
\(404\) −5.00000 + 8.66025i −0.248759 + 0.430864i
\(405\) −9.00000 15.5885i −0.447214 0.774597i
\(406\) 9.00000 0.446663
\(407\) 12.0000 0.594818
\(408\) 1.50000 + 2.59808i 0.0742611 + 0.128624i
\(409\) 3.00000 + 5.19615i 0.148340 + 0.256933i 0.930614 0.366002i \(-0.119274\pi\)
−0.782274 + 0.622935i \(0.785940\pi\)
\(410\) 24.0000 1.18528
\(411\) −57.0000 −2.81160
\(412\) 3.00000 + 5.19615i 0.147799 + 0.255996i
\(413\) −4.50000 + 7.79423i −0.221431 + 0.383529i
\(414\) 15.0000 + 25.9808i 0.737210 + 1.27688i
\(415\) −2.00000 + 3.46410i −0.0981761 + 0.170046i
\(416\) 1.50000 2.59808i 0.0735436 0.127381i
\(417\) −18.0000 −0.881464
\(418\) 0 0
\(419\) −14.0000 −0.683945 −0.341972 0.939710i \(-0.611095\pi\)
−0.341972 + 0.939710i \(0.611095\pi\)
\(420\) −9.00000 + 15.5885i −0.439155 + 0.760639i
\(421\) −13.5000 + 23.3827i −0.657950 + 1.13960i 0.323196 + 0.946332i \(0.395243\pi\)
−0.981146 + 0.193270i \(0.938091\pi\)
\(422\) −1.50000 2.59808i −0.0730189 0.126472i
\(423\) 24.0000 41.5692i 1.16692 2.02116i
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) 1.00000 0.0485071
\(426\) 0 0
\(427\) 0 0
\(428\) −1.50000 2.59808i −0.0725052 0.125583i
\(429\) 18.0000 0.869048
\(430\) 20.0000 0.964486
\(431\) 12.0000 + 20.7846i 0.578020 + 1.00116i 0.995706 + 0.0925683i \(0.0295076\pi\)
−0.417687 + 0.908591i \(0.637159\pi\)
\(432\) 4.50000 7.79423i 0.216506 0.375000i
\(433\) 15.0000 + 25.9808i 0.720854 + 1.24856i 0.960658 + 0.277734i \(0.0895835\pi\)
−0.239804 + 0.970821i \(0.577083\pi\)
\(434\) −9.00000 + 15.5885i −0.432014 + 0.748270i
\(435\) 9.00000 15.5885i 0.431517 0.747409i
\(436\) −3.00000 −0.143674
\(437\) 0 0
\(438\) −33.0000 −1.57680
\(439\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) −2.00000 + 3.46410i −0.0953463 + 0.165145i
\(441\) −6.00000 10.3923i −0.285714 0.494872i
\(442\) −1.50000 + 2.59808i −0.0713477 + 0.123578i
\(443\) 11.0000 + 19.0526i 0.522626 + 0.905214i 0.999653 + 0.0263261i \(0.00838082\pi\)
−0.477028 + 0.878888i \(0.658286\pi\)
\(444\) 18.0000 0.854242
\(445\) −12.0000 −0.568855
\(446\) −9.00000 15.5885i −0.426162 0.738135i
\(447\) −12.0000 20.7846i −0.567581 0.983078i
\(448\) −3.00000 −0.141737
\(449\) −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
\(451\) −12.0000 + 20.7846i −0.565058 + 0.978709i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) 27.0000 46.7654i 1.26857 2.19723i
\(454\) −1.50000 + 2.59808i −0.0703985 + 0.121934i
\(455\) −18.0000 −0.843853
\(456\) 0 0
\(457\) 1.00000 0.0467780 0.0233890 0.999726i \(-0.492554\pi\)
0.0233890 + 0.999726i \(0.492554\pi\)
\(458\) −6.00000 + 10.3923i −0.280362 + 0.485601i
\(459\) −4.50000 + 7.79423i −0.210042 + 0.363803i
\(460\) −5.00000 8.66025i −0.233126 0.403786i
\(461\) −2.00000 + 3.46410i −0.0931493 + 0.161339i −0.908835 0.417156i \(-0.863027\pi\)
0.815685 + 0.578496i \(0.196360\pi\)
\(462\) −9.00000 15.5885i −0.418718 0.725241i
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 3.00000 0.139272
\(465\) 18.0000 + 31.1769i 0.834730 + 1.44579i
\(466\) 7.00000 + 12.1244i 0.324269 + 0.561650i
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) 18.0000 0.832050
\(469\) −22.5000 38.9711i −1.03895 1.79952i
\(470\) −8.00000 + 13.8564i −0.369012 + 0.639148i
\(471\) 0 0
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) −10.0000 + 17.3205i −0.459800 + 0.796398i
\(474\) 36.0000 1.65353
\(475\) 0 0
\(476\) 3.00000 0.137505
\(477\) −9.00000 + 15.5885i −0.412082 + 0.713746i
\(478\) 0.500000 0.866025i 0.0228695 0.0396111i
\(479\) 20.0000 + 34.6410i 0.913823 + 1.58279i 0.808615 + 0.588338i \(0.200218\pi\)
0.105208 + 0.994450i \(0.466449\pi\)
\(480\) −3.00000 + 5.19615i −0.136931 + 0.237171i
\(481\) 9.00000 + 15.5885i 0.410365 + 0.710772i
\(482\) 24.0000 1.09317
\(483\) 45.0000 2.04757
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 12.0000 + 20.7846i 0.544892 + 0.943781i
\(486\) 0 0
\(487\) 18.0000 0.815658 0.407829 0.913058i \(-0.366286\pi\)
0.407829 + 0.913058i \(0.366286\pi\)
\(488\) 0 0
\(489\) −9.00000 + 15.5885i −0.406994 + 0.704934i
\(490\) 2.00000 + 3.46410i 0.0903508 + 0.156492i
\(491\) −4.00000 + 6.92820i −0.180517 + 0.312665i −0.942057 0.335453i \(-0.891111\pi\)
0.761539 + 0.648119i \(0.224444\pi\)
\(492\) −18.0000 + 31.1769i −0.811503 + 1.40556i
\(493\) −3.00000 −0.135113
\(494\) 0 0
\(495\) −24.0000 −1.07872
\(496\) −3.00000 + 5.19615i −0.134704 + 0.233314i
\(497\) 0 0
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) −9.00000 + 15.5885i −0.402895 + 0.697835i −0.994074 0.108705i \(-0.965329\pi\)
0.591179 + 0.806541i \(0.298663\pi\)
\(500\) 6.00000 + 10.3923i 0.268328 + 0.464758i
\(501\) −36.0000 −1.60836
\(502\) 20.0000 0.892644
\(503\) −0.500000 0.866025i −0.0222939 0.0386142i 0.854663 0.519183i \(-0.173764\pi\)
−0.876957 + 0.480569i \(0.840430\pi\)
\(504\) −9.00000 15.5885i −0.400892 0.694365i
\(505\) 20.0000 0.889988
\(506\) 10.0000 0.444554
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) 6.00000 10.3923i 0.266207 0.461084i
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 3.00000 5.19615i 0.132842 0.230089i
\(511\) −16.5000 + 28.5788i −0.729917 + 1.26425i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −18.0000 −0.793946
\(515\) 6.00000 10.3923i 0.264392 0.457940i
\(516\) −15.0000 + 25.9808i −0.660338 + 1.14374i
\(517\) −8.00000 13.8564i −0.351840 0.609404i
\(518\) 9.00000 15.5885i 0.395437 0.684917i
\(519\) 27.0000 + 46.7654i 1.18517 + 2.05277i
\(520\) −6.00000 −0.263117
\(521\) 12.0000 0.525730 0.262865 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 9.00000 + 15.5885i 0.393919 + 0.682288i
\(523\) 4.50000 + 7.79423i 0.196771 + 0.340818i 0.947480 0.319816i \(-0.103621\pi\)
−0.750708 + 0.660634i \(0.770288\pi\)
\(524\) 14.0000 0.611593
\(525\) −9.00000 −0.392792
\(526\) −4.00000 6.92820i −0.174408 0.302084i
\(527\) 3.00000 5.19615i 0.130682 0.226348i
\(528\) −3.00000 5.19615i −0.130558 0.226134i
\(529\) −1.00000 + 1.73205i −0.0434783 + 0.0753066i
\(530\) 3.00000 5.19615i 0.130312 0.225706i
\(531\) −18.0000 −0.781133
\(532\) 0 0
\(533\) −36.0000 −1.55933
\(534\) 9.00000 15.5885i 0.389468 0.674579i
\(535\) −3.00000 + 5.19615i −0.129701 + 0.224649i
\(536\) −7.50000 12.9904i −0.323951 0.561099i
\(537\) 18.0000 31.1769i 0.776757 1.34538i
\(538\) 3.00000 + 5.19615i 0.129339 + 0.224022i
\(539\) −4.00000 −0.172292
\(540\) −18.0000 −0.774597
\(541\) −1.00000 1.73205i −0.0429934 0.0744667i 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) −5.50000 9.52628i −0.236245 0.409189i
\(543\) 54.0000 2.31736
\(544\) 1.00000 0.0428746
\(545\) 3.00000 + 5.19615i 0.128506 + 0.222579i
\(546\) 13.5000 23.3827i 0.577747 1.00069i
\(547\) −18.0000 31.1769i −0.769624 1.33303i −0.937767 0.347266i \(-0.887110\pi\)
0.168142 0.985763i \(-0.446223\pi\)
\(548\) −9.50000 + 16.4545i −0.405820 + 0.702901i
\(549\) 0 0
\(550\) −2.00000 −0.0852803
\(551\) 0 0
\(552\) 15.0000 0.638442
\(553\) 18.0000 31.1769i 0.765438 1.32578i
\(554\) 15.0000 25.9808i 0.637289 1.10382i
\(555\) −18.0000 31.1769i −0.764057 1.32339i
\(556\) −3.00000 + 5.19615i −0.127228 + 0.220366i
\(557\) −11.0000 19.0526i −0.466085 0.807283i 0.533165 0.846011i \(-0.321003\pi\)
−0.999250 + 0.0387286i \(0.987669\pi\)
\(558\) −36.0000 −1.52400
\(559\) −30.0000 −1.26886
\(560\) 3.00000 + 5.19615i 0.126773 + 0.219578i
\(561\) 3.00000 + 5.19615i 0.126660 + 0.219382i
\(562\) 12.0000 0.506189
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) −12.0000 20.7846i −0.505291 0.875190i
\(565\) 12.0000 20.7846i 0.504844 0.874415i
\(566\) −7.00000 12.1244i −0.294232 0.509625i
\(567\) 13.5000 23.3827i 0.566947 0.981981i
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −32.0000 −1.33916 −0.669579 0.742741i \(-0.733526\pi\)
−0.669579 + 0.742741i \(0.733526\pi\)
\(572\) 3.00000 5.19615i 0.125436 0.217262i
\(573\) −16.5000 + 28.5788i −0.689297 + 1.19390i
\(574\) 18.0000 + 31.1769i 0.751305 + 1.30130i
\(575\) 2.50000 4.33013i 0.104257 0.180579i
\(576\) −3.00000 5.19615i −0.125000 0.216506i
\(577\) 15.0000 0.624458 0.312229 0.950007i \(-0.398924\pi\)
0.312229 + 0.950007i \(0.398924\pi\)
\(578\) 16.0000 0.665512
\(579\) −9.00000 15.5885i −0.374027 0.647834i
\(580\) −3.00000 5.19615i −0.124568 0.215758i
\(581\) −6.00000 −0.248922
\(582\) −36.0000 −1.49225
\(583\) 3.00000 + 5.19615i 0.124247 + 0.215203i
\(584\) −5.50000 + 9.52628i −0.227592 + 0.394200i
\(585\) −18.0000 31.1769i −0.744208 1.28901i
\(586\) 4.50000 7.79423i 0.185893 0.321977i
\(587\) 14.0000 24.2487i 0.577842 1.00085i −0.417885 0.908500i \(-0.637228\pi\)
0.995726 0.0923513i \(-0.0294383\pi\)
\(588\) −6.00000 −0.247436
\(589\) 0 0
\(590\) 6.00000 0.247016
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) 3.00000 5.19615i 0.123299 0.213561i
\(593\) 1.00000 + 1.73205i 0.0410651 + 0.0711268i 0.885827 0.464015i \(-0.153592\pi\)
−0.844762 + 0.535142i \(0.820258\pi\)
\(594\) 9.00000 15.5885i 0.369274 0.639602i
\(595\) −3.00000 5.19615i −0.122988 0.213021i
\(596\) −8.00000 −0.327693
\(597\) 21.0000 0.859473
\(598\) 7.50000 + 12.9904i 0.306698 + 0.531216i
\(599\) −18.0000 31.1769i −0.735460 1.27385i −0.954521 0.298143i \(-0.903633\pi\)
0.219061 0.975711i \(-0.429701\pi\)
\(600\) −3.00000 −0.122474
\(601\) 6.00000 0.244745 0.122373 0.992484i \(-0.460950\pi\)
0.122373 + 0.992484i \(0.460950\pi\)
\(602\) 15.0000 + 25.9808i 0.611354 + 1.05890i
\(603\) 45.0000 77.9423i 1.83254 3.17406i
\(604\) −9.00000 15.5885i −0.366205 0.634285i
\(605\) 7.00000 12.1244i 0.284590 0.492925i
\(606\) −15.0000 + 25.9808i −0.609333 + 1.05540i
\(607\) 12.0000 0.487065 0.243532 0.969893i \(-0.421694\pi\)
0.243532 + 0.969893i \(0.421694\pi\)
\(608\) 0 0
\(609\) 27.0000 1.09410
\(610\) 0 0
\(611\) 12.0000 20.7846i 0.485468 0.840855i
\(612\) 3.00000 + 5.19615i 0.121268 + 0.210042i
\(613\) −9.00000 + 15.5885i −0.363507 + 0.629612i −0.988535 0.150990i \(-0.951754\pi\)
0.625029 + 0.780602i \(0.285087\pi\)
\(614\) −6.00000 10.3923i −0.242140 0.419399i
\(615\) 72.0000 2.90332
\(616\) −6.00000 −0.241747
\(617\) −5.00000 8.66025i −0.201292 0.348649i 0.747653 0.664090i \(-0.231181\pi\)
−0.948945 + 0.315441i \(0.897847\pi\)
\(618\) 9.00000 + 15.5885i 0.362033 + 0.627060i
\(619\) −24.0000 −0.964641 −0.482321 0.875995i \(-0.660206\pi\)
−0.482321 + 0.875995i \(0.660206\pi\)
\(620\) 12.0000 0.481932
\(621\) 22.5000 + 38.9711i 0.902894 + 1.56386i
\(622\) −5.50000 + 9.52628i −0.220530 + 0.381969i
\(623\) −9.00000 15.5885i −0.360577 0.624538i
\(624\) 4.50000 7.79423i 0.180144 0.312019i
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) −21.0000 −0.839329
\(627\) 0 0
\(628\) 0 0
\(629\) −3.00000 + 5.19615i −0.119618 + 0.207184i
\(630\) −18.0000 + 31.1769i −0.717137 + 1.24212i
\(631\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(632\) 6.00000 10.3923i 0.238667 0.413384i
\(633\) −4.50000 7.79423i −0.178859 0.309793i
\(634\) −33.0000 −1.31060
\(635\) −24.0000 −0.952411
\(636\) 4.50000 + 7.79423i 0.178437 + 0.309061i
\(637\) −3.00000 5.19615i −0.118864 0.205879i
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) 1.00000 + 1.73205i 0.0395285 + 0.0684653i
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) −4.50000 7.79423i −0.177601 0.307614i
\(643\) −16.0000 + 27.7128i −0.630978 + 1.09289i 0.356374 + 0.934344i \(0.384013\pi\)
−0.987352 + 0.158543i \(0.949320\pi\)
\(644\) 7.50000 12.9904i 0.295541 0.511893i
\(645\) 60.0000 2.36250
\(646\) 0 0
\(647\) −23.0000 −0.904223 −0.452112 0.891961i \(-0.649329\pi\)
−0.452112 + 0.891961i \(0.649329\pi\)
\(648\) 4.50000 7.79423i 0.176777 0.306186i
\(649\) −3.00000 + 5.19615i −0.117760 + 0.203967i
\(650\) −1.50000 2.59808i −0.0588348 0.101905i
\(651\) −27.0000 + 46.7654i −1.05821 + 1.83288i
\(652\) 3.00000 + 5.19615i 0.117489 + 0.203497i
\(653\) −10.0000 −0.391330 −0.195665 0.980671i \(-0.562687\pi\)
−0.195665 + 0.980671i \(0.562687\pi\)
\(654\) −9.00000 −0.351928
\(655\) −14.0000 24.2487i −0.547025 0.947476i
\(656\) 6.00000 + 10.3923i 0.234261 + 0.405751i
\(657\) −66.0000 −2.57491
\(658\) −24.0000 −0.935617
\(659\) −7.50000 12.9904i −0.292159 0.506033i 0.682161 0.731202i \(-0.261040\pi\)
−0.974320 + 0.225168i \(0.927707\pi\)
\(660\) −6.00000 + 10.3923i −0.233550 + 0.404520i
\(661\) 7.50000 + 12.9904i 0.291716 + 0.505267i 0.974216 0.225619i \(-0.0724404\pi\)
−0.682499 + 0.730886i \(0.739107\pi\)
\(662\) −4.50000 + 7.79423i −0.174897 + 0.302931i
\(663\) −4.50000 + 7.79423i −0.174766 + 0.302703i
\(664\) −2.00000 −0.0776151
\(665\) 0 0
\(666\) 36.0000 1.39497
\(667\) −7.50000 + 12.9904i −0.290401 + 0.502990i
\(668\) −6.00000 + 10.3923i −0.232147 + 0.402090i
\(669\) −27.0000 46.7654i −1.04388 1.80805i
\(670\) −15.0000 + 25.9808i −0.579501 + 1.00372i
\(671\) 0 0
\(672\) −9.00000 −0.347183
\(673\) 48.0000 1.85026 0.925132 0.379646i \(-0.123954\pi\)
0.925132 + 0.379646i \(0.123954\pi\)
\(674\) −9.00000 15.5885i −0.346667 0.600445i
\(675\) −4.50000 7.79423i −0.173205 0.300000i
\(676\) −4.00000 −0.153846
\(677\) −3.00000 −0.115299 −0.0576497 0.998337i \(-0.518361\pi\)
−0.0576497 + 0.998337i \(0.518361\pi\)
\(678\) 18.0000 + 31.1769i 0.691286 + 1.19734i
\(679\) −18.0000 + 31.1769i −0.690777 + 1.19646i
\(680\) −1.00000 1.73205i −0.0383482 0.0664211i
\(681\) −4.50000 + 7.79423i −0.172440 + 0.298675i
\(682\) −6.00000 + 10.3923i −0.229752 + 0.397942i
\(683\) 36.0000 1.37750 0.688751 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 38.0000 1.45191
\(686\) 7.50000 12.9904i 0.286351 0.495975i
\(687\) −18.0000 + 31.1769i −0.686743 + 1.18947i
\(688\) 5.00000 + 8.66025i 0.190623 + 0.330169i
\(689\) −4.50000 + 7.79423i −0.171436 + 0.296936i
\(690\) −15.0000 25.9808i −0.571040 0.989071i
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 18.0000 0.684257
\(693\) −18.0000 31.1769i −0.683763 1.18431i
\(694\) 8.00000 + 13.8564i 0.303676 + 0.525982i
\(695\) 12.0000 0.455186
\(696\) 9.00000 0.341144
\(697\) −6.00000 10.3923i −0.227266 0.393637i
\(698\) 14.0000 24.2487i 0.529908 0.917827i
\(699\) 21.0000 + 36.3731i 0.794293 + 1.37576i
\(700\) −1.50000 + 2.59808i −0.0566947 + 0.0981981i
\(701\) 20.0000 34.6410i 0.755390 1.30837i −0.189791 0.981825i \(-0.560781\pi\)
0.945180 0.326549i \(-0.105886\pi\)
\(702\) 27.0000 1.01905
\(703\) 0 0
\(704\) −2.00000 −0.0753778
\(705\) −24.0000 + 41.5692i −0.903892 + 1.56559i
\(706\) −15.5000 + 26.8468i −0.583350 + 1.01039i
\(707\) 15.0000 + 25.9808i 0.564133 + 0.977107i
\(708\) −4.50000 + 7.79423i −0.169120 + 0.292925i
\(709\) 4.00000 + 6.92820i 0.150223 + 0.260194i 0.931309 0.364229i \(-0.118667\pi\)
−0.781086 + 0.624423i \(0.785334\pi\)
\(710\) 0 0
\(711\) 72.0000 2.70021
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) −15.0000 25.9808i −0.561754 0.972987i
\(714\) 9.00000 0.336817
\(715\) −12.0000 −0.448775
\(716\) −6.00000 10.3923i −0.224231 0.388379i
\(717\) 1.50000 2.59808i 0.0560185 0.0970269i
\(718\) 9.50000 + 16.4545i 0.354537 + 0.614076i
\(719\) 21.5000 37.2391i 0.801815 1.38878i −0.116606 0.993178i \(-0.537201\pi\)
0.918421 0.395606i \(-0.129465\pi\)
\(720\) −6.00000 + 10.3923i −0.223607 + 0.387298i
\(721\) 18.0000 0.670355
\(722\) 0 0
\(723\) 72.0000 2.67771
\(724\) 9.00000 15.5885i 0.334482 0.579340i
\(725\) 1.50000 2.59808i 0.0557086 0.0964901i
\(726\) 10.5000 + 18.1865i 0.389692 + 0.674966i
\(727\) 17.5000 30.3109i 0.649039 1.12417i −0.334314 0.942462i \(-0.608504\pi\)
0.983353 0.181707i \(-0.0581622\pi\)
\(728\) −4.50000 7.79423i −0.166781 0.288873i
\(729\) −27.0000 −1.00000
\(730\) 22.0000 0.814257
\(731\) −5.00000 8.66025i −0.184932 0.320311i
\(732\) 0 0
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) −8.00000 −0.295285
\(735\) 6.00000 + 10.3923i 0.221313 + 0.383326i
\(736\) 2.50000 4.33013i 0.0921512 0.159611i
\(737\) −15.0000 25.9808i −0.552532 0.957014i
\(738\) −36.0000 + 62.3538i −1.32518 + 2.29528i
\(739\) 6.00000 10.3923i 0.220714 0.382287i −0.734311 0.678813i \(-0.762495\pi\)
0.955025 + 0.296526i \(0.0958281\pi\)
\(740\) −12.0000 −0.441129
\(741\) 0 0
\(742\) 9.00000 0.330400
\(743\) 3.00000 5.19615i 0.110059 0.190628i −0.805735 0.592277i \(-0.798229\pi\)
0.915794 + 0.401648i \(0.131563\pi\)
\(744\) −9.00000 + 15.5885i −0.329956 + 0.571501i
\(745\) 8.00000 + 13.8564i 0.293097 + 0.507659i
\(746\) 10.5000 18.1865i 0.384432 0.665856i
\(747\) −6.00000 10.3923i −0.219529 0.380235i
\(748\) 2.00000 0.0731272
\(749\) −9.00000 −0.328853
\(750\) 18.0000 + 31.1769i 0.657267 + 1.13842i
\(751\) 6.00000 + 10.3923i 0.218943 + 0.379221i 0.954485 0.298259i \(-0.0964058\pi\)
−0.735542 + 0.677479i \(0.763072\pi\)
\(752\) −8.00000 −0.291730
\(753\) 60.0000 2.18652
\(754\) 4.50000 + 7.79423i 0.163880 + 0.283849i
\(755\) −18.0000 + 31.1769i −0.655087 + 1.13464i
\(756\) −13.5000 23.3827i −0.490990 0.850420i
\(757\) −6.00000 + 10.3923i −0.218074 + 0.377715i −0.954219 0.299109i \(-0.903311\pi\)
0.736145 + 0.676824i \(0.236644\pi\)
\(758\) −1.50000 + 2.59808i −0.0544825 + 0.0943664i
\(759\) 30.0000 1.08893
\(760\) 0 0
\(761\) −13.0000 −0.471250 −0.235625 0.971844i \(-0.575714\pi\)
−0.235625 + 0.971844i \(0.575714\pi\)
\(762\) 18.0000 31.1769i 0.652071 1.12942i
\(763\) −4.50000 + 7.79423i −0.162911 + 0.282170i
\(764\) 5.50000 + 9.52628i 0.198983 + 0.344649i
\(765\) 6.00000 10.3923i 0.216930 0.375735i
\(766\) −9.00000 15.5885i −0.325183 0.563234i
\(767\) −9.00000 −0.324971
\(768\) −3.00000 −0.108253
\(769\) 7.50000 + 12.9904i 0.270457 + 0.468445i 0.968979 0.247143i \(-0.0794919\pi\)
−0.698522 + 0.715589i \(0.746159\pi\)
\(770\) 6.00000 + 10.3923i 0.216225 + 0.374513i
\(771\) −54.0000 −1.94476
\(772\) −6.00000 −0.215945
\(773\) 7.50000 + 12.9904i 0.269756 + 0.467232i 0.968799 0.247849i \(-0.0797235\pi\)
−0.699043 + 0.715080i \(0.746390\pi\)
\(774\) −30.0000 + 51.9615i −1.07833 + 1.86772i
\(775\) 3.00000 + 5.19615i 0.107763 + 0.186651i
\(776\) −6.00000 + 10.3923i −0.215387 + 0.373062i
\(777\) 27.0000 46.7654i 0.968620 1.67770i
\(778\) −26.0000 −0.932145
\(779\) 0 0
\(780\) −18.0000 −0.644503
\(781\)