Properties

Label 38.2.c.a.7.1
Level $38$
Weight $2$
Character 38.7
Analytic conductor $0.303$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.303431527681\)
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 7.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 38.7
Dual form 38.2.c.a.11.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -4.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} -4.00000 q^{7} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +3.00000 q^{11} +1.00000 q^{12} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +2.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} +(2.00000 + 3.46410i) q^{21} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} -2.00000 q^{26} -5.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} +(-3.00000 + 5.19615i) q^{34} +(1.00000 + 1.73205i) q^{36} -10.0000 q^{37} +(-4.00000 - 1.73205i) q^{38} +2.00000 q^{39} +(-4.50000 - 7.79423i) q^{41} +(-2.00000 + 3.46410i) q^{42} +(2.00000 + 3.46410i) q^{43} +(-1.50000 + 2.59808i) q^{44} +6.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} +9.00000 q^{49} +5.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(-2.50000 - 4.33013i) q^{54} +4.00000 q^{56} +(4.00000 + 1.73205i) q^{57} +(4.50000 + 7.79423i) q^{59} +(2.00000 - 3.46410i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-4.00000 + 6.92820i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(3.50000 - 6.06218i) q^{67} -6.00000 q^{68} -6.00000 q^{69} +(3.00000 + 5.19615i) q^{71} +(-1.00000 + 1.73205i) q^{72} +(0.500000 + 0.866025i) q^{73} +(-5.00000 - 8.66025i) q^{74} -5.00000 q^{75} +(-0.500000 - 4.33013i) q^{76} -12.0000 q^{77} +(1.00000 + 1.73205i) q^{78} +(2.00000 + 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +3.00000 q^{83} -4.00000 q^{84} +(-2.00000 + 3.46410i) q^{86} -3.00000 q^{88} +(-3.00000 + 5.19615i) q^{89} +(4.00000 - 6.92820i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-1.00000 - 1.73205i) q^{93} -1.00000 q^{96} +(-8.50000 - 14.7224i) q^{97} +(4.50000 + 7.79423i) q^{98} +(3.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} + q^{6} - 8q^{7} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} + q^{6} - 8q^{7} - 2q^{8} + 2q^{9} + 6q^{11} + 2q^{12} - 2q^{13} - 4q^{14} - q^{16} + 6q^{17} + 4q^{18} - 7q^{19} + 4q^{21} + 3q^{22} + 6q^{23} + q^{24} + 5q^{25} - 4q^{26} - 10q^{27} + 4q^{28} + 4q^{31} + q^{32} - 3q^{33} - 6q^{34} + 2q^{36} - 20q^{37} - 8q^{38} + 4q^{39} - 9q^{41} - 4q^{42} + 4q^{43} - 3q^{44} + 12q^{46} - q^{48} + 18q^{49} + 10q^{50} + 6q^{51} - 2q^{52} - 6q^{53} - 5q^{54} + 8q^{56} + 8q^{57} + 9q^{59} + 4q^{61} + 2q^{62} - 8q^{63} + 2q^{64} + 3q^{66} + 7q^{67} - 12q^{68} - 12q^{69} + 6q^{71} - 2q^{72} + q^{73} - 10q^{74} - 10q^{75} - q^{76} - 24q^{77} + 2q^{78} + 4q^{79} - q^{81} + 9q^{82} + 6q^{83} - 8q^{84} - 4q^{86} - 6q^{88} - 6q^{89} + 8q^{91} + 6q^{92} - 2q^{93} - 2q^{96} - 17q^{97} + 9q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 1.00000 0.288675
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −2.00000 3.46410i −0.534522 0.925820i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 2.00000 0.471405
\(19\) −3.50000 + 2.59808i −0.802955 + 0.596040i
\(20\) 0 0
\(21\) 2.00000 + 3.46410i 0.436436 + 0.755929i
\(22\) 1.50000 + 2.59808i 0.319801 + 0.553912i
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 2.50000 4.33013i 0.500000 0.866025i
\(26\) −2.00000 −0.392232
\(27\) −5.00000 −0.962250
\(28\) 2.00000 3.46410i 0.377964 0.654654i
\(29\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) −3.00000 + 5.19615i −0.514496 + 0.891133i
\(35\) 0 0
\(36\) 1.00000 + 1.73205i 0.166667 + 0.288675i
\(37\) −10.0000 −1.64399 −0.821995 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) −4.00000 1.73205i −0.648886 0.280976i
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) −4.50000 7.79423i −0.702782 1.21725i −0.967486 0.252924i \(-0.918608\pi\)
0.264704 0.964330i \(-0.414726\pi\)
\(42\) −2.00000 + 3.46410i −0.308607 + 0.534522i
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 9.00000 1.28571
\(50\) 5.00000 0.707107
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) −2.50000 4.33013i −0.340207 0.589256i
\(55\) 0 0
\(56\) 4.00000 0.534522
\(57\) 4.00000 + 1.73205i 0.529813 + 0.229416i
\(58\) 0 0
\(59\) 4.50000 + 7.79423i 0.585850 + 1.01472i 0.994769 + 0.102151i \(0.0325726\pi\)
−0.408919 + 0.912571i \(0.634094\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 1.00000 + 1.73205i 0.127000 + 0.219971i
\(63\) −4.00000 + 6.92820i −0.503953 + 0.872872i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.50000 2.59808i 0.184637 0.319801i
\(67\) 3.50000 6.06218i 0.427593 0.740613i −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) −6.00000 −0.727607
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 3.00000 + 5.19615i 0.356034 + 0.616670i 0.987294 0.158901i \(-0.0507952\pi\)
−0.631260 + 0.775571i \(0.717462\pi\)
\(72\) −1.00000 + 1.73205i −0.117851 + 0.204124i
\(73\) 0.500000 + 0.866025i 0.0585206 + 0.101361i 0.893801 0.448463i \(-0.148028\pi\)
−0.835281 + 0.549823i \(0.814695\pi\)
\(74\) −5.00000 8.66025i −0.581238 1.00673i
\(75\) −5.00000 −0.577350
\(76\) −0.500000 4.33013i −0.0573539 0.496700i
\(77\) −12.0000 −1.36753
\(78\) 1.00000 + 1.73205i 0.113228 + 0.196116i
\(79\) 2.00000 + 3.46410i 0.225018 + 0.389742i 0.956325 0.292306i \(-0.0944227\pi\)
−0.731307 + 0.682048i \(0.761089\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) 3.00000 0.329293 0.164646 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) −4.00000 −0.436436
\(85\) 0 0
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 0 0
\(91\) 4.00000 6.92820i 0.419314 0.726273i
\(92\) 3.00000 + 5.19615i 0.312772 + 0.541736i
\(93\) −1.00000 1.73205i −0.103695 0.179605i
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −8.50000 14.7224i −0.863044 1.49484i −0.868976 0.494854i \(-0.835222\pi\)
0.00593185 0.999982i \(-0.498112\pi\)
\(98\) 4.50000 + 7.79423i 0.454569 + 0.787336i
\(99\) 3.00000 5.19615i 0.301511 0.522233i
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 6.00000 0.594089
\(103\) 2.00000 0.197066 0.0985329 0.995134i \(-0.468585\pi\)
0.0985329 + 0.995134i \(0.468585\pi\)
\(104\) 1.00000 1.73205i 0.0980581 0.169842i
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 2.50000 4.33013i 0.240563 0.416667i
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0 0
\(111\) 5.00000 + 8.66025i 0.474579 + 0.821995i
\(112\) 2.00000 + 3.46410i 0.188982 + 0.327327i
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) 0.500000 + 4.33013i 0.0468293 + 0.405554i
\(115\) 0 0
\(116\) 0 0
\(117\) 2.00000 + 3.46410i 0.184900 + 0.320256i
\(118\) −4.50000 + 7.79423i −0.414259 + 0.717517i
\(119\) −12.0000 20.7846i −1.10004 1.90532i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 4.00000 0.362143
\(123\) −4.50000 + 7.79423i −0.405751 + 0.702782i
\(124\) −1.00000 + 1.73205i −0.0898027 + 0.155543i
\(125\) 0 0
\(126\) −8.00000 −0.712697
\(127\) −1.00000 + 1.73205i −0.0887357 + 0.153695i −0.906977 0.421180i \(-0.861616\pi\)
0.818241 + 0.574875i \(0.194949\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 0 0
\(131\) −4.50000 7.79423i −0.393167 0.680985i 0.599699 0.800226i \(-0.295287\pi\)
−0.992865 + 0.119241i \(0.961954\pi\)
\(132\) 3.00000 0.261116
\(133\) 14.0000 10.3923i 1.21395 0.901127i
\(134\) 7.00000 0.604708
\(135\) 0 0
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) −3.00000 5.19615i −0.255377 0.442326i
\(139\) −5.50000 + 9.52628i −0.466504 + 0.808008i −0.999268 0.0382553i \(-0.987820\pi\)
0.532764 + 0.846264i \(0.321153\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) −0.500000 + 0.866025i −0.0413803 + 0.0716728i
\(147\) −4.50000 7.79423i −0.371154 0.642857i
\(148\) 5.00000 8.66025i 0.410997 0.711868i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) −2.50000 4.33013i −0.204124 0.353553i
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 3.50000 2.59808i 0.283887 0.210732i
\(153\) 12.0000 0.970143
\(154\) −6.00000 10.3923i −0.483494 0.837436i
\(155\) 0 0
\(156\) −1.00000 + 1.73205i −0.0800641 + 0.138675i
\(157\) 8.00000 + 13.8564i 0.638470 + 1.10586i 0.985769 + 0.168107i \(0.0537655\pi\)
−0.347299 + 0.937754i \(0.612901\pi\)
\(158\) −2.00000 + 3.46410i −0.159111 + 0.275589i
\(159\) 6.00000 0.475831
\(160\) 0 0
\(161\) −12.0000 + 20.7846i −0.945732 + 1.63806i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) 9.00000 0.702782
\(165\) 0 0
\(166\) 1.50000 + 2.59808i 0.116423 + 0.201650i
\(167\) 12.0000 20.7846i 0.928588 1.60836i 0.142901 0.989737i \(-0.454357\pi\)
0.785687 0.618624i \(-0.212310\pi\)
\(168\) −2.00000 3.46410i −0.154303 0.267261i
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) 1.00000 + 8.66025i 0.0764719 + 0.662266i
\(172\) −4.00000 −0.304997
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) −10.0000 + 17.3205i −0.755929 + 1.30931i
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 4.50000 7.79423i 0.338241 0.585850i
\(178\) −6.00000 −0.449719
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 0 0
\(181\) −1.00000 + 1.73205i −0.0743294 + 0.128742i −0.900794 0.434246i \(-0.857015\pi\)
0.826465 + 0.562988i \(0.190348\pi\)
\(182\) 8.00000 0.592999
\(183\) −4.00000 −0.295689
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) 1.00000 1.73205i 0.0733236 0.127000i
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) 0 0
\(189\) 20.0000 1.45479
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 8.50000 14.7224i 0.610264 1.05701i
\(195\) 0 0
\(196\) −4.50000 + 7.79423i −0.321429 + 0.556731i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 6.00000 0.426401
\(199\) 5.00000 8.66025i 0.354441 0.613909i −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) −2.50000 + 4.33013i −0.176777 + 0.306186i
\(201\) −7.00000 −0.493742
\(202\) 0 0
\(203\) 0 0
\(204\) 3.00000 + 5.19615i 0.210042 + 0.363803i
\(205\) 0 0
\(206\) 1.00000 + 1.73205i 0.0696733 + 0.120678i
\(207\) −6.00000 10.3923i −0.417029 0.722315i
\(208\) 2.00000 0.138675
\(209\) −10.5000 + 7.79423i −0.726300 + 0.539138i
\(210\) 0 0
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) 0 0
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) −8.00000 −0.543075
\(218\) −8.00000 + 13.8564i −0.541828 + 0.938474i
\(219\) 0.500000 0.866025i 0.0337869 0.0585206i
\(220\) 0 0
\(221\) −12.0000 −0.807207
\(222\) −5.00000 + 8.66025i −0.335578 + 0.581238i
\(223\) −7.00000 12.1244i −0.468755 0.811907i 0.530607 0.847618i \(-0.321964\pi\)
−0.999362 + 0.0357107i \(0.988630\pi\)
\(224\) −2.00000 + 3.46410i −0.133631 + 0.231455i
\(225\) −5.00000 8.66025i −0.333333 0.577350i
\(226\) 7.50000 + 12.9904i 0.498893 + 0.864107i
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) −3.50000 + 2.59808i −0.231793 + 0.172062i
\(229\) −16.0000 −1.05731 −0.528655 0.848837i \(-0.677303\pi\)
−0.528655 + 0.848837i \(0.677303\pi\)
\(230\) 0 0
\(231\) 6.00000 + 10.3923i 0.394771 + 0.683763i
\(232\) 0 0
\(233\) −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i \(-0.197997\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(234\) −2.00000 + 3.46410i −0.130744 + 0.226455i
\(235\) 0 0
\(236\) −9.00000 −0.585850
\(237\) 2.00000 3.46410i 0.129914 0.225018i
\(238\) 12.0000 20.7846i 0.777844 1.34727i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) −1.00000 1.73205i −0.0642824 0.111340i
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) 2.00000 + 3.46410i 0.128037 + 0.221766i
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) −1.00000 8.66025i −0.0636285 0.551039i
\(248\) −2.00000 −0.127000
\(249\) −1.50000 2.59808i −0.0950586 0.164646i
\(250\) 0 0
\(251\) 1.50000 2.59808i 0.0946792 0.163989i −0.814795 0.579748i \(-0.803151\pi\)
0.909475 + 0.415759i \(0.136484\pi\)
\(252\) −4.00000 6.92820i −0.251976 0.436436i
\(253\) 9.00000 15.5885i 0.565825 0.980038i
\(254\) −2.00000 −0.125491
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.50000 + 2.59808i −0.0935674 + 0.162064i −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 4.00000 0.249029
\(259\) 40.0000 2.48548
\(260\) 0 0
\(261\) 0 0
\(262\) 4.50000 7.79423i 0.278011 0.481529i
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 1.50000 + 2.59808i 0.0923186 + 0.159901i
\(265\) 0 0
\(266\) 16.0000 + 6.92820i 0.981023 + 0.424795i
\(267\) 6.00000 0.367194
\(268\) 3.50000 + 6.06218i 0.213797 + 0.370306i
\(269\) −6.00000 10.3923i −0.365826 0.633630i 0.623082 0.782157i \(-0.285880\pi\)
−0.988908 + 0.148527i \(0.952547\pi\)
\(270\) 0 0
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 3.00000 5.19615i 0.181902 0.315063i
\(273\) −8.00000 −0.484182
\(274\) −9.00000 −0.543710
\(275\) 7.50000 12.9904i 0.452267 0.783349i
\(276\) 3.00000 5.19615i 0.180579 0.312772i
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) −11.0000 −0.659736
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) 0 0
\(281\) −13.5000 + 23.3827i −0.805342 + 1.39489i 0.110717 + 0.993852i \(0.464685\pi\)
−0.916060 + 0.401042i \(0.868648\pi\)
\(282\) 0 0
\(283\) −2.50000 4.33013i −0.148610 0.257399i 0.782104 0.623148i \(-0.214146\pi\)
−0.930714 + 0.365748i \(0.880813\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 18.0000 + 31.1769i 1.06251 + 1.84032i
\(288\) −1.00000 1.73205i −0.0589256 0.102062i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) −8.50000 + 14.7224i −0.498279 + 0.863044i
\(292\) −1.00000 −0.0585206
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 4.50000 7.79423i 0.262445 0.454569i
\(295\) 0 0
\(296\) 10.0000 0.581238
\(297\) −15.0000 −0.870388
\(298\) 9.00000 15.5885i 0.521356 0.903015i
\(299\) 6.00000 + 10.3923i 0.346989 + 0.601003i
\(300\) 2.50000 4.33013i 0.144338 0.250000i
\(301\) −8.00000 13.8564i −0.461112 0.798670i
\(302\) −5.00000 8.66025i −0.287718 0.498342i
\(303\) 0 0
\(304\) 4.00000 + 1.73205i 0.229416 + 0.0993399i
\(305\) 0 0
\(306\) 6.00000 + 10.3923i 0.342997 + 0.594089i
\(307\) 3.50000 + 6.06218i 0.199756 + 0.345987i 0.948449 0.316929i \(-0.102652\pi\)
−0.748694 + 0.662916i \(0.769319\pi\)
\(308\) 6.00000 10.3923i 0.341882 0.592157i
\(309\) −1.00000 1.73205i −0.0568880 0.0985329i
\(310\) 0 0
\(311\) −30.0000 −1.70114 −0.850572 0.525859i \(-0.823744\pi\)
−0.850572 + 0.525859i \(0.823744\pi\)
\(312\) −2.00000 −0.113228
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) −8.00000 + 13.8564i −0.451466 + 0.781962i
\(315\) 0 0
\(316\) −4.00000 −0.225018
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 3.00000 + 5.19615i 0.168232 + 0.291386i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −24.0000 −1.33747
\(323\) −24.0000 10.3923i −1.33540 0.578243i
\(324\) 1.00000 0.0555556
\(325\) 5.00000 + 8.66025i 0.277350 + 0.480384i
\(326\) −9.50000 16.4545i −0.526156 0.911330i
\(327\) 8.00000 13.8564i 0.442401 0.766261i
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) −1.50000 + 2.59808i −0.0823232 + 0.142588i
\(333\) −10.0000 + 17.3205i −0.547997 + 0.949158i
\(334\) 24.0000 1.31322
\(335\) 0 0
\(336\) 2.00000 3.46410i 0.109109 0.188982i
\(337\) −5.50000 9.52628i −0.299604 0.518930i 0.676441 0.736497i \(-0.263521\pi\)
−0.976045 + 0.217567i \(0.930188\pi\)
\(338\) −4.50000 + 7.79423i −0.244768 + 0.423950i
\(339\) −7.50000 12.9904i −0.407344 0.705541i
\(340\) 0 0
\(341\) 6.00000 0.324918
\(342\) −7.00000 + 5.19615i −0.378517 + 0.280976i
\(343\) −8.00000 −0.431959
\(344\) −2.00000 3.46410i −0.107833 0.186772i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) 4.50000 + 7.79423i 0.241573 + 0.418416i 0.961162 0.275983i \(-0.0890035\pi\)
−0.719590 + 0.694399i \(0.755670\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) −20.0000 −1.06904
\(351\) 5.00000 8.66025i 0.266880 0.462250i
\(352\) 1.50000 2.59808i 0.0799503 0.138478i
\(353\) 3.00000 0.159674 0.0798369 0.996808i \(-0.474560\pi\)
0.0798369 + 0.996808i \(0.474560\pi\)
\(354\) 9.00000 0.478345
\(355\) 0 0
\(356\) −3.00000 5.19615i −0.159000 0.275396i
\(357\) −12.0000 + 20.7846i −0.635107 + 1.10004i
\(358\) 4.50000 + 7.79423i 0.237832 + 0.411938i
\(359\) 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i \(-0.116054\pi\)
−0.775934 + 0.630814i \(0.782721\pi\)
\(360\) 0 0
\(361\) 5.50000 18.1865i 0.289474 0.957186i
\(362\) −2.00000 −0.105118
\(363\) 1.00000 + 1.73205i 0.0524864 + 0.0909091i
\(364\) 4.00000 + 6.92820i 0.209657 + 0.363137i
\(365\) 0 0
\(366\) −2.00000 3.46410i −0.104542 0.181071i
\(367\) 11.0000 19.0526i 0.574195 0.994535i −0.421933 0.906627i \(-0.638648\pi\)
0.996129 0.0879086i \(-0.0280183\pi\)
\(368\) −6.00000 −0.312772
\(369\) −18.0000 −0.937043
\(370\) 0 0
\(371\) 12.0000 20.7846i 0.623009 1.07908i
\(372\) 2.00000 0.103695
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) −9.00000 + 15.5885i −0.465379 + 0.806060i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 10.0000 + 17.3205i 0.514344 + 0.890871i
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) 18.0000 + 31.1769i 0.919757 + 1.59307i 0.799783 + 0.600289i \(0.204948\pi\)
0.119974 + 0.992777i \(0.461719\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 0 0
\(386\) 1.00000 1.73205i 0.0508987 0.0881591i
\(387\) 8.00000 0.406663
\(388\) 17.0000 0.863044
\(389\) 18.0000 31.1769i 0.912636 1.58073i 0.102311 0.994753i \(-0.467376\pi\)
0.810326 0.585980i \(-0.199290\pi\)
\(390\) 0 0
\(391\) 36.0000 1.82060
\(392\) −9.00000 −0.454569
\(393\) −4.50000 + 7.79423i −0.226995 + 0.393167i
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 0 0
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) 5.00000 + 8.66025i 0.250943 + 0.434646i 0.963786 0.266678i \(-0.0859261\pi\)
−0.712843 + 0.701324i \(0.752593\pi\)
\(398\) 10.0000 0.501255
\(399\) −16.0000 6.92820i −0.801002 0.346844i
\(400\) −5.00000 −0.250000
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) −3.50000 6.06218i −0.174564 0.302354i
\(403\) −2.00000 + 3.46410i −0.0996271 + 0.172559i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −30.0000 −1.48704
\(408\) −3.00000 + 5.19615i −0.148522 + 0.257248i
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 0 0
\(411\) 9.00000 0.443937
\(412\) −1.00000 + 1.73205i −0.0492665 + 0.0853320i
\(413\) −18.0000 31.1769i −0.885722 1.53412i
\(414\) 6.00000 10.3923i 0.294884 0.510754i
\(415\) 0 0
\(416\) 1.00000 + 1.73205i 0.0490290 + 0.0849208i
\(417\) 11.0000 0.538672
\(418\) −12.0000 5.19615i −0.586939 0.254152i
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i \(-0.0883103\pi\)
−0.718076 + 0.695965i \(0.754977\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 0 0
\(424\) 3.00000 5.19615i 0.145693 0.252347i
\(425\) 30.0000 1.45521
\(426\) 6.00000 0.290701
\(427\) −8.00000 + 13.8564i −0.387147 + 0.670559i
\(428\) 0 0
\(429\) 6.00000 0.289683
\(430\) 0 0
\(431\) 15.0000 25.9808i 0.722525 1.25145i −0.237460 0.971397i \(-0.576315\pi\)
0.959985 0.280052i \(-0.0903517\pi\)
\(432\) 2.50000 + 4.33013i 0.120281 + 0.208333i
\(433\) −13.0000 + 22.5167i −0.624740 + 1.08208i 0.363851 + 0.931457i \(0.381462\pi\)
−0.988591 + 0.150624i \(0.951872\pi\)
\(434\) −4.00000 6.92820i −0.192006 0.332564i
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) 3.00000 + 25.9808i 0.143509 + 1.24283i
\(438\) 1.00000 0.0477818
\(439\) −7.00000 12.1244i −0.334092 0.578664i 0.649218 0.760602i \(-0.275096\pi\)
−0.983310 + 0.181938i \(0.941763\pi\)
\(440\) 0 0
\(441\) 9.00000 15.5885i 0.428571 0.742307i
\(442\) −6.00000 10.3923i −0.285391 0.494312i
\(443\) −4.50000 + 7.79423i −0.213801 + 0.370315i −0.952901 0.303281i \(-0.901918\pi\)
0.739100 + 0.673596i \(0.235251\pi\)
\(444\) −10.0000 −0.474579
\(445\) 0 0
\(446\) 7.00000 12.1244i 0.331460 0.574105i
\(447\) −9.00000 + 15.5885i −0.425685 + 0.737309i
\(448\) −4.00000 −0.188982
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 5.00000 8.66025i 0.235702 0.408248i
\(451\) −13.5000 23.3827i −0.635690 1.10105i
\(452\) −7.50000 + 12.9904i −0.352770 + 0.611016i
\(453\) 5.00000 + 8.66025i 0.234920 + 0.406894i
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) 0 0
\(456\) −4.00000 1.73205i −0.187317 0.0811107i
\(457\) 5.00000 0.233890 0.116945 0.993138i \(-0.462690\pi\)
0.116945 + 0.993138i \(0.462690\pi\)
\(458\) −8.00000 13.8564i −0.373815 0.647467i
\(459\) −15.0000 25.9808i −0.700140 1.21268i
\(460\) 0 0
\(461\) −3.00000 5.19615i −0.139724 0.242009i 0.787668 0.616100i \(-0.211288\pi\)
−0.927392 + 0.374091i \(0.877955\pi\)
\(462\) −6.00000 + 10.3923i −0.279145 + 0.483494i
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.50000 2.59808i 0.0694862 0.120354i
\(467\) −27.0000 −1.24941 −0.624705 0.780860i \(-0.714781\pi\)
−0.624705 + 0.780860i \(0.714781\pi\)
\(468\) −4.00000 −0.184900
\(469\) −14.0000 + 24.2487i −0.646460 + 1.11970i
\(470\) 0 0
\(471\) 8.00000 13.8564i 0.368621 0.638470i
\(472\) −4.50000 7.79423i −0.207129 0.358758i
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) 4.00000 0.183726
\(475\) 2.50000 + 21.6506i 0.114708 + 0.993399i
\(476\) 24.0000 1.10004
\(477\) 6.00000 + 10.3923i 0.274721 + 0.475831i
\(478\) −6.00000 10.3923i −0.274434 0.475333i
\(479\) −18.0000 + 31.1769i −0.822441 + 1.42451i 0.0814184 + 0.996680i \(0.474055\pi\)
−0.903859 + 0.427830i \(0.859278\pi\)
\(480\) 0 0
\(481\) 10.0000 17.3205i 0.455961 0.789747i
\(482\) −5.00000 −0.227744
\(483\) 24.0000 1.09204
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) 0 0
\(486\) −16.0000 −0.725775
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −2.00000 + 3.46410i −0.0905357 + 0.156813i
\(489\) 9.50000 + 16.4545i 0.429605 + 0.744097i
\(490\) 0 0
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) −4.50000 7.79423i −0.202876 0.351391i
\(493\) 0 0
\(494\) 7.00000 5.19615i 0.314945 0.233786i
\(495\) 0 0
\(496\) −1.00000 1.73205i −0.0449013 0.0777714i
\(497\) −12.0000 20.7846i −0.538274 0.932317i
\(498\) 1.50000 2.59808i 0.0672166 0.116423i
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0 0
\(501\) −24.0000 −1.07224
\(502\) 3.00000 0.133897
\(503\) −3.00000 + 5.19615i −0.133763 + 0.231685i −0.925124 0.379664i \(-0.876040\pi\)
0.791361 + 0.611349i \(0.209373\pi\)
\(504\) 4.00000 6.92820i 0.178174 0.308607i
\(505\) 0 0
\(506\) 18.0000 0.800198
\(507\) 4.50000 7.79423i 0.199852 0.346154i
\(508\) −1.00000 1.73205i −0.0443678 0.0768473i
\(509\) 12.0000 20.7846i 0.531891 0.921262i −0.467416 0.884037i \(-0.654815\pi\)
0.999307 0.0372243i \(-0.0118516\pi\)
\(510\) 0 0
\(511\) −2.00000 3.46410i −0.0884748 0.153243i
\(512\) −1.00000 −0.0441942
\(513\) 17.5000 12.9904i 0.772644 0.573539i
\(514\) −3.00000 −0.132324
\(515\) 0 0
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) 0 0
\(518\) 20.0000 + 34.6410i 0.878750 + 1.52204i
\(519\) −3.00000 + 5.19615i −0.131685 + 0.228086i
\(520\) 0 0
\(521\) 9.00000 0.394297 0.197149 0.980374i \(-0.436832\pi\)
0.197149 + 0.980374i \(0.436832\pi\)
\(522\) 0 0
\(523\) 14.0000 24.2487i 0.612177 1.06032i −0.378695 0.925521i \(-0.623627\pi\)
0.990873 0.134801i \(-0.0430394\pi\)
\(524\) 9.00000 0.393167
\(525\) 20.0000 0.872872
\(526\) −6.00000 + 10.3923i −0.261612 + 0.453126i
\(527\) 6.00000 + 10.3923i 0.261364 + 0.452696i
\(528\) −1.50000 + 2.59808i −0.0652791 + 0.113067i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 18.0000 0.781133
\(532\) 2.00000 + 17.3205i 0.0867110 + 0.750939i
\(533\) 18.0000 0.779667
\(534\) 3.00000 + 5.19615i 0.129823 + 0.224860i
\(535\) 0 0
\(536\) −3.50000 + 6.06218i −0.151177 + 0.261846i
\(537\) −4.50000 7.79423i −0.194189 0.336346i
\(538\) 6.00000 10.3923i 0.258678 0.448044i
\(539\) 27.0000 1.16297
\(540\) 0 0
\(541\) −22.0000 + 38.1051i −0.945854 + 1.63827i −0.191821 + 0.981430i \(0.561439\pi\)
−0.754032 + 0.656837i \(0.771894\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 2.00000 0.0858282
\(544\) 6.00000 0.257248
\(545\) 0 0
\(546\) −4.00000 6.92820i −0.171184 0.296500i
\(547\) 2.00000 3.46410i 0.0855138 0.148114i −0.820096 0.572226i \(-0.806080\pi\)
0.905610 + 0.424111i \(0.139413\pi\)
\(548\) −4.50000 7.79423i −0.192230 0.332953i
\(549\) −4.00000 6.92820i −0.170716 0.295689i
\(550\) 15.0000 0.639602
\(551\) 0 0
\(552\) 6.00000 0.255377
\(553\) −8.00000 13.8564i −0.340195 0.589234i
\(554\) 4.00000 + 6.92820i 0.169944 + 0.294351i
\(555\) 0 0
\(556\) −5.50000 9.52628i −0.233252 0.404004i
\(557\) −12.0000 + 20.7846i −0.508456 + 0.880672i 0.491496 + 0.870880i \(0.336450\pi\)
−0.999952 + 0.00979220i \(0.996883\pi\)
\(558\) 4.00000 0.169334
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 9.00000 15.5885i 0.379980 0.658145i
\(562\) −27.0000 −1.13893
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2.50000 4.33013i 0.105083 0.182009i
\(567\) 2.00000 + 3.46410i 0.0839921 + 0.145479i
\(568\) −3.00000 5.19615i −0.125877 0.218026i
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) −3.00000 5.19615i −0.125436 0.217262i
\(573\) −6.00000 10.3923i −0.250654 0.434145i
\(574\) −18.0000 + 31.1769i −0.751305 + 1.30130i
\(575\) −15.0000 25.9808i −0.625543 1.08347i
\(576\) 1.00000 1.73205i 0.0416667 0.0721688i
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) −19.0000 −0.790296
\(579\) −1.00000 + 1.73205i −0.0415586 + 0.0719816i
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) −17.0000 −0.704673
\(583\) −9.00000 + 15.5885i −0.372742 + 0.645608i
\(584\) −0.500000 0.866025i −0.0206901 0.0358364i
\(585\) 0 0
\(586\) 12.0000 + 20.7846i 0.495715 + 0.858604i
\(587\) 6.00000 + 10.3923i 0.247647 + 0.428936i 0.962872 0.269957i \(-0.0870095\pi\)
−0.715226 + 0.698893i \(0.753676\pi\)
\(588\) 9.00000 0.371154
\(589\) −7.00000 + 5.19615i −0.288430 + 0.214104i
\(590\) 0 0
\(591\) −9.00000 15.5885i −0.370211 0.641223i
\(592\) 5.00000 + 8.66025i 0.205499 + 0.355934i
\(593\) 10.5000 18.1865i 0.431183 0.746831i −0.565792 0.824548i \(-0.691430\pi\)
0.996976 + 0.0777165i \(0.0247629\pi\)
\(594\) −7.50000 12.9904i −0.307729 0.533002i
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) −10.0000 −0.409273
\(598\) −6.00000 + 10.3923i −0.245358 + 0.424973i
\(599\) 3.00000 5.19615i 0.122577 0.212309i −0.798206 0.602384i \(-0.794218\pi\)
0.920783 + 0.390075i \(0.127551\pi\)
\(600\) 5.00000 0.204124
\(601\) −13.0000 −0.530281 −0.265141 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) 8.00000 13.8564i 0.326056 0.564745i
\(603\) −7.00000 12.1244i −0.285062 0.493742i
\(604\) 5.00000 8.66025i 0.203447 0.352381i
\(605\) 0 0
\(606\) 0 0
\(607\) 20.0000 0.811775 0.405887 0.913923i \(-0.366962\pi\)
0.405887 + 0.913923i \(0.366962\pi\)
\(608\) 0.500000 + 4.33013i 0.0202777 + 0.175610i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) −3.50000 + 6.06218i −0.141249 + 0.244650i
\(615\) 0 0
\(616\) 12.0000 0.483494
\(617\) −1.50000 + 2.59808i −0.0603877 + 0.104595i −0.894639 0.446790i \(-0.852567\pi\)
0.834251 + 0.551385i \(0.185900\pi\)
\(618\) 1.00000 1.73205i 0.0402259 0.0696733i
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) −15.0000 + 25.9808i −0.601929 + 1.04257i
\(622\) −15.0000 25.9808i −0.601445 1.04173i
\(623\) 12.0000 20.7846i 0.480770 0.832718i
\(624\) −1.00000 1.73205i −0.0400320 0.0693375i
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 19.0000 0.759393
\(627\) 12.0000 + 5.19615i 0.479234 + 0.207514i
\(628\) −16.0000 −0.638470
\(629\) −30.0000 51.9615i −1.19618 2.07184i
\(630\) 0 0
\(631\) 14.0000 24.2487i 0.557331 0.965326i −0.440387 0.897808i \(-0.645159\pi\)
0.997718 0.0675178i \(-0.0215080\pi\)
\(632\) −2.00000 3.46410i −0.0795557 0.137795i
\(633\) −10.0000 + 17.3205i −0.397464 + 0.688428i
\(634\) 18.0000 0.714871
\(635\) 0 0
\(636\) −3.00000 + 5.19615i −0.118958 + 0.206041i
\(637\) −9.00000 + 15.5885i −0.356593 + 0.617637i
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) 19.5000 + 33.7750i 0.770204 + 1.33403i 0.937451 + 0.348117i \(0.113179\pi\)
−0.167247 + 0.985915i \(0.553488\pi\)
\(642\) 0 0
\(643\) 21.5000 + 37.2391i 0.847877 + 1.46857i 0.883099 + 0.469187i \(0.155453\pi\)
−0.0352216 + 0.999380i \(0.511214\pi\)
\(644\) −12.0000 20.7846i −0.472866 0.819028i
\(645\) 0 0
\(646\) −3.00000 25.9808i −0.118033 1.02220i
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 13.5000 + 23.3827i 0.529921 + 0.917851i
\(650\) −5.00000 + 8.66025i −0.196116 + 0.339683i
\(651\) 4.00000 + 6.92820i 0.156772 + 0.271538i
\(652\) 9.50000 16.4545i 0.372049 0.644407i
\(653\) −12.0000 −0.469596 −0.234798 0.972044i \(-0.575443\pi\)
−0.234798 + 0.972044i \(0.575443\pi\)
\(654\) 16.0000 0.625650
\(655\) 0 0
\(656\) −4.50000 + 7.79423i −0.175695 + 0.304314i
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) −18.0000 + 31.1769i −0.701180 + 1.21448i 0.266872 + 0.963732i \(0.414010\pi\)
−0.968052 + 0.250748i \(0.919323\pi\)
\(660\) 0 0
\(661\) 20.0000 34.6410i 0.777910 1.34738i −0.155235 0.987878i \(-0.549613\pi\)
0.933144 0.359502i \(-0.117053\pi\)
\(662\) 2.50000 + 4.33013i 0.0971653 + 0.168295i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) −3.00000 −0.116423
\(665\) 0 0
\(666\) −20.0000 −0.774984
\(667\) 0 0
\(668\) 12.0000 + 20.7846i 0.464294 + 0.804181i
\(669\) −7.00000 + 12.1244i −0.270636 + 0.468755i
\(670\) 0 0
\(671\) 6.00000 10.3923i 0.231627 0.401190i
\(672\) 4.00000 0.154303
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 5.50000 9.52628i 0.211852 0.366939i
\(675\) −12.5000 + 21.6506i −0.481125 + 0.833333i
\(676\) −9.00000 −0.346154
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 7.50000 12.9904i 0.288036 0.498893i
\(679\) 34.0000 + 58.8897i 1.30480 + 2.25998i
\(680\) 0 0
\(681\) −1.50000 2.59808i −0.0574801 0.0995585i
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) −8.00000 3.46410i −0.305888 0.132453i
\(685\) 0 0
\(686\) −4.00000 6.92820i −0.152721 0.264520i
\(687\) 8.00000 + 13.8564i 0.305219 + 0.528655i
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) 0 0
\(691\) 44.0000 1.67384 0.836919 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) 6.00000 0.228086
\(693\) −12.0000 + 20.7846i −0.455842 + 0.789542i
\(694\) −4.50000 + 7.79423i −0.170818 + 0.295865i
\(695\) 0 0
\(696\) 0 0
\(697\) 27.0000 46.7654i 1.02270 1.77136i
\(698\) −2.00000 3.46410i −0.0757011 0.131118i
\(699\) −1.50000 + 2.59808i −0.0567352 + 0.0982683i
\(700\) −10.0000 17.3205i −0.377964 0.654654i
\(701\) 12.0000 + 20.7846i 0.453234 + 0.785024i 0.998585 0.0531839i \(-0.0169370\pi\)
−0.545351 + 0.838208i \(0.683604\pi\)
\(702\) 10.0000 0.377426
\(703\) 35.0000 25.9808i 1.32005 0.979883i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) 1.50000 + 2.59808i 0.0564532 + 0.0977799i
\(707\) 0 0
\(708\) 4.50000 + 7.79423i 0.169120 + 0.292925i
\(709\) −7.00000 + 12.1244i −0.262891 + 0.455340i −0.967009 0.254743i \(-0.918009\pi\)
0.704118 + 0.710083i \(0.251342\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 3.00000 5.19615i 0.112430 0.194734i
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) −24.0000 −0.898177
\(715\) 0 0
\(716\) −4.50000 + 7.79423i −0.168173 + 0.291284i
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) −15.0000 25.9808i −0.559406 0.968919i −0.997546 0.0700124i \(-0.977696\pi\)
0.438141 0.898906i \(-0.355637\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 18.5000 4.33013i 0.688499 0.161151i
\(723\) 5.00000 0.185952
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 0 0
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) −16.0000 27.7128i −0.593407 1.02781i −0.993770 0.111454i \(-0.964449\pi\)
0.400362 0.916357i \(-0.368884\pi\)
\(728\) −4.00000 + 6.92820i −0.148250 + 0.256776i
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 2.00000 3.46410i 0.0739221 0.128037i
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 22.0000 0.812035
\(735\) 0 0
\(736\) −3.00000 5.19615i −0.110581 0.191533i
\(737\) 10.5000 18.1865i 0.386772 0.669910i
\(738\) −9.00000 15.5885i −0.331295 0.573819i
\(739\) −17.5000 30.3109i −0.643748 1.11500i −0.984589 0.174883i \(-0.944045\pi\)
0.340841 0.940121i \(-0.389288\pi\)
\(740\) 0 0
\(741\) −7.00000 + 5.19615i −0.257151 + 0.190885i
\(742\) 24.0000 0.881068
\(743\) 9.00000 + 15.5885i 0.330178 + 0.571885i 0.982547 0.186017i \(-0.0595579\pi\)
−0.652369 + 0.757902i \(0.726225\pi\)
\(744\) 1.00000 + 1.73205i 0.0366618 + 0.0635001i
\(745\) 0 0
\(746\) −2.00000 3.46410i −0.0732252 0.126830i
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) −18.0000 −0.658145
\(749\) 0 0
\(750\) 0 0
\(751\) −19.0000 + 32.9090i −0.693320 + 1.20087i 0.277424 + 0.960748i \(0.410519\pi\)
−0.970744 + 0.240118i \(0.922814\pi\)
\(752\) 0 0
\(753\) −3.00000 −0.109326
\(754\) 0 0
\(755\) 0 0
\(756\) −10.0000 + 17.3205i −0.363696 + 0.629941i
\(757\) 5.00000 + 8.66025i 0.181728 + 0.314762i 0.942469 0.334293i \(-0.108498\pi\)
−0.760741 + 0.649056i \(0.775164\pi\)
\(758\) −14.0000 24.2487i −0.508503 0.880753i
\(759\) −18.0000 −0.653359
\(760\) 0 0
\(761\) −39.0000 −1.41375 −0.706874 0.707339i \(-0.749895\pi\)
−0.706874 + 0.707339i \(0.749895\pi\)
\(762\) 1.00000 + 1.73205i 0.0362262 + 0.0627456i
\(763\) −32.0000 55.4256i −1.15848 2.00654i
\(764\) −6.00000 + 10.3923i −0.217072 + 0.375980i
\(765\) 0 0
\(766\) −18.0000 + 31.1769i −0.650366 + 1.12647i
\(767\) −18.0000 −0.649942
\(768\) 1.00000 0.0360844
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) 2.00000 0.0719816
\(773\) 24.0000 41.5692i 0.863220 1.49514i −0.00558380 0.999984i \(-0.501777\pi\)
0.868804 0.495156i \(-0.164889\pi\)
\(774\) 4.00000 + 6.92820i 0.143777 + 0.249029i
\(775\) 5.00000 8.66025i 0.179605 0.311086i
\(776\) 8.50000 + 14.7224i 0.305132 + 0.528505i
\(777\) −20.0000 34.6410i −0.717496 1.24274i
\(778\) 36.0000 1.29066
\(779\) 36.0000 + 15.5885i 1.28983 + 0.558514i
\(780\) 0 0
\(781\) 9.00000 + 15.5885i 0.322045 + 0.557799i
\(782\) 18.0000 + 31.1769i 0.643679 + 1.11488i
\(783\) 0 0
\(784\) −4.50000 7.79423i −0.160714 0.278365i
\(785\) 0 0