Properties

Label 950.2.e.d.201.1
Level $950$
Weight $2$
Character 950.201
Analytic conductor $7.586$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
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: no (minimal twist has level 38)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 950.201
Dual form 950.2.e.d.501.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 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 \(-0.0772105\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −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 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) −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 −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 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 \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 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 0.264704 + 0.964330i \(0.414726\pi\)
−0.967486 + 0.252924i \(0.918608\pi\)
\(42\) 2.00000 + 3.46410i 0.308607 + 0.534522i
\(43\) −2.00000 + 3.46410i −0.304997 + 0.528271i −0.977261 0.212041i \(-0.931989\pi\)
0.672264 + 0.740312i \(0.265322\pi\)
\(44\) −1.50000 2.59808i −0.226134 0.391675i
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 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 \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) −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 −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 0 0
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) −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 \(-0.307305\pi\)
−0.996659 + 0.0816792i \(0.973972\pi\)
\(68\) 6.00000 0.727607
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) 1.00000 + 1.73205i 0.117851 + 0.204124i
\(73\) −0.500000 + 0.866025i −0.0585206 + 0.101361i −0.893801 0.448463i \(-0.851972\pi\)
0.835281 + 0.549823i \(0.185305\pi\)
\(74\) −5.00000 + 8.66025i −0.581238 + 1.00673i
\(75\) 0 0
\(76\) −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 −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 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 \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) −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 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 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 −0.00593185 0.999982i \(-0.501888\pi\)
0.868976 0.494854i \(-0.164778\pi\)
\(98\) −4.50000 + 7.79423i −0.454569 + 0.787336i
\(99\) 3.00000 + 5.19615i 0.301511 + 0.522233i
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) −6.00000 −0.594089
\(103\) −2.00000 −0.197066 −0.0985329 0.995134i \(-0.531415\pi\)
−0.0985329 + 0.995134i \(0.531415\pi\)
\(104\) 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 −0.173316 0.984866i \(-0.555448\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(110\) 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 \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 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 \(-0.138384\pi\)
−0.818241 + 0.574875i \(0.805051\pi\)
\(128\) −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 −0.992865 0.119241i \(-0.961954\pi\)
0.599699 + 0.800226i \(0.295287\pi\)
\(132\) −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 \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 3.00000 5.19615i 0.255377 0.442326i
\(139\) −5.50000 9.52628i −0.466504 0.808008i 0.532764 0.846264i \(-0.321153\pi\)
−0.999268 + 0.0382553i \(0.987820\pi\)
\(140\) 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 0.216394 + 0.976306i \(0.430570\pi\)
−0.953703 + 0.300750i \(0.902763\pi\)
\(150\) 0 0
\(151\) −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 0.347299 + 0.937754i \(0.387099\pi\)
−0.985769 + 0.168107i \(0.946235\pi\)
\(158\) 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 \(-0.232880\pi\)
0.744097 + 0.668071i \(0.232880\pi\)
\(164\) 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 −0.785687 0.618624i \(-0.787690\pi\)
−0.142901 0.989737i \(-0.545643\pi\)
\(168\) 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 \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −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 0.826465 0.562988i \(-0.190348\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(182\) −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 \(-0.810401\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) 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 \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −6.00000 −0.426401
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) 0 0
\(201\) −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 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 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 \(-0.678036\pi\)
0.999362 + 0.0357107i \(0.0113695\pi\)
\(224\) −2.00000 3.46410i −0.133631 0.231455i
\(225\) 0 0
\(226\) 7.50000 12.9904i 0.498893 0.864107i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 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 \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) −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 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) 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 0.909475 0.415759i \(-0.136484\pi\)
−0.814795 + 0.579748i \(0.803151\pi\)
\(252\) 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 \(-0.136840\pi\)
−0.815442 + 0.578838i \(0.803506\pi\)
\(258\) −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 \(-0.953967\pi\)
0.619586 + 0.784929i \(0.287301\pi\)
\(264\) 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 −0.988908 0.148527i \(-0.952547\pi\)
0.623082 + 0.782157i \(0.285880\pi\)
\(270\) 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 5.19615i −0.181902 0.315063i
\(273\) 8.00000 0.484182
\(274\) −9.00000 −0.543710
\(275\) 0 0
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) 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 −0.916060 0.401042i \(-0.868648\pi\)
0.110717 0.993852i \(-0.464685\pi\)
\(282\) 0 0
\(283\) 2.50000 4.33013i 0.148610 0.257399i −0.782104 0.623148i \(-0.785854\pi\)
0.930714 + 0.365748i \(0.119187\pi\)
\(284\) −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 \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 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
\(300\) 0 0
\(301\) −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 \(-0.897348\pi\)
0.748694 + 0.662916i \(0.230681\pi\)
\(308\) −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 −0.999065 0.0432311i \(-0.986235\pi\)
0.462093 0.886831i \(-0.347098\pi\)
\(314\) −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 −0.999980 0.00635137i \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) −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
\(325\) 0 0
\(326\) −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 \(-0.736479\pi\)
0.976045 + 0.217567i \(0.0698121\pi\)
\(338\) 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 \(-0.910997\pi\)
0.719590 + 0.694399i \(0.244330\pi\)
\(348\) 0 0
\(349\) −4.00000 −0.214115 −0.107058 0.994253i \(-0.534143\pi\)
−0.107058 + 0.994253i \(0.534143\pi\)
\(350\) 0 0
\(351\) 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 \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) 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 −0.775934 0.630814i \(-0.782721\pi\)
0.934268 + 0.356572i \(0.116054\pi\)
\(360\) 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 −0.996129 0.0879086i \(-0.971982\pi\)
0.421933 0.906627i \(-0.361352\pi\)
\(368\) 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 \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) −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 −0.119974 + 0.992777i \(0.538281\pi\)
−0.799783 + 0.600289i \(0.795052\pi\)
\(384\) 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 0.810326 + 0.585980i \(0.199290\pi\)
0.102311 + 0.994753i \(0.467376\pi\)
\(390\) 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 \(-0.914074\pi\)
0.712843 + 0.701324i \(0.247407\pi\)
\(398\) −10.0000 −0.501255
\(399\) −16.0000 + 6.92820i −0.801002 + 0.346844i
\(400\) 0 0
\(401\) 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i \(-0.597840\pi\)
0.976714 0.214544i \(-0.0688266\pi\)
\(402\) 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 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 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 −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) −10.0000 17.3205i −0.486792 0.843149i
\(423\) 0 0
\(424\) 3.00000 + 5.19615i 0.145693 + 0.252347i
\(425\) 0 0
\(426\) 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 0.959985 + 0.280052i \(0.0903517\pi\)
−0.237460 + 0.971397i \(0.576315\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) 13.0000 + 22.5167i 0.624740 + 1.08208i 0.988591 + 0.150624i \(0.0481284\pi\)
−0.363851 + 0.931457i \(0.618538\pi\)
\(434\) −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 −0.983310 0.181938i \(-0.941763\pi\)
0.649218 + 0.760602i \(0.275096\pi\)
\(440\) 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 \(-0.0980821\pi\)
−0.739100 + 0.673596i \(0.764749\pi\)
\(444\) −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 \(0.431882\pi\)
\(450\) 0 0
\(451\) −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 \(-0.537310\pi\)
−0.116945 + 0.993138i \(0.537310\pi\)
\(458\) 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 −0.927392 0.374091i \(-0.877955\pi\)
0.787668 + 0.616100i \(0.211288\pi\)
\(462\) 6.00000 + 10.3923i 0.279145 + 0.483494i
\(463\) 34.0000 1.58011 0.790057 0.613033i \(-0.210051\pi\)
0.790057 + 0.613033i \(0.210051\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 1.50000 + 2.59808i 0.0694862 + 0.120354i
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 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
\(475\) 0 0
\(476\) 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 −0.903859 0.427830i \(-0.859278\pi\)
0.0814184 0.996680i \(-0.474055\pi\)
\(480\) 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 \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 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 −0.437955 0.898997i \(-0.644297\pi\)
0.997532 0.0702185i \(-0.0223697\pi\)
\(500\) 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 \(-0.123960\pi\)
−0.791361 + 0.611349i \(0.790627\pi\)
\(504\) 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 0.999307 + 0.0372243i \(0.0118516\pi\)
−0.467416 + 0.884037i \(0.654815\pi\)
\(510\) 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 −0.990873 0.134801i \(-0.956961\pi\)
0.378695 0.925521i \(-0.376373\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) −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 −0.754032 0.656837i \(-0.771894\pi\)
−0.191821 0.981430i \(-0.561439\pi\)
\(542\) 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 \(-0.193920\pi\)
−0.905610 + 0.424111i \(0.860587\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) −4.00000 + 6.92820i −0.170716 + 0.295689i
\(550\) 0 0
\(551\) 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 0.999952 + 0.00979220i \(0.00311700\pi\)
−0.491496 + 0.870880i \(0.663550\pi\)
\(558\) −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 \(-0.354084\pi\)
0.442522 + 0.896758i \(0.354084\pi\)
\(564\) 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
\(575\) 0 0
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) −11.0000 −0.457936 −0.228968 0.973434i \(-0.573535\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) 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 \(-0.912990\pi\)
0.715226 + 0.698893i \(0.246324\pi\)
\(588\) −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 \(-0.308570\pi\)
−0.996976 + 0.0777165i \(0.975237\pi\)
\(594\) −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 0.920783 0.390075i \(-0.127551\pi\)
−0.798206 + 0.602384i \(0.794218\pi\)
\(600\) 0 0
\(601\) −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 \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) −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 \(-0.820473\pi\)
0.885514 + 0.464614i \(0.153807\pi\)
\(614\) −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 \(-0.147433\pi\)
−0.834251 + 0.551385i \(0.814100\pi\)
\(618\) −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
\(625\) 0 0
\(626\) 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 0.997718 + 0.0675178i \(0.0215080\pi\)
−0.440387 + 0.897808i \(0.645159\pi\)
\(632\) 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 −0.167247 0.985915i \(-0.553488\pi\)
0.937451 0.348117i \(-0.113179\pi\)
\(642\) 0 0
\(643\) −21.5000 + 37.2391i −0.847877 + 1.46857i 0.0352216 + 0.999380i \(0.488786\pi\)
−0.883099 + 0.469187i \(0.844547\pi\)
\(644\) −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 \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 13.5000 23.3827i 0.529921 0.917851i
\(650\) 0 0
\(651\) 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 \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) 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 −0.968052 0.250748i \(-0.919323\pi\)
0.266872 0.963732i \(-0.414010\pi\)
\(660\) 0 0
\(661\) 20.0000 + 34.6410i 0.777910 + 1.34738i 0.933144 + 0.359502i \(0.117053\pi\)
−0.155235 + 0.987878i \(0.549613\pi\)
\(662\) −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 \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) 5.50000 + 9.52628i 0.211852 + 0.366939i
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) −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 \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) −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
\(700\) 0 0
\(701\) 12.0000 20.7846i 0.453234 0.785024i −0.545351 0.838208i \(-0.683604\pi\)
0.998585 + 0.0531839i \(0.0169370\pi\)
\(702\) −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 0.704118 0.710083i \(-0.251342\pi\)
−0.967009 + 0.254743i \(0.918009\pi\)
\(710\) 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 0.438141 + 0.898906i \(0.355637\pi\)
−0.997546 + 0.0700124i \(0.977696\pi\)
\(720\) 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 −0.400362 0.916357i \(-0.631116\pi\)
0.993770 0.111454i \(-0.0355509\pi\)
\(728\) 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 \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 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 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) 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 \(-0.940442\pi\)
0.652369 + 0.757902i \(0.273775\pi\)
\(744\) 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 −0.970744 0.240118i \(-0.922814\pi\)
0.277424 0.960748i \(-0.410519\pi\)
\(752\) 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 \(-0.891502\pi\)
0.760741 + 0.649056i \(0.224836\pi\)
\(758\) 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 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) −2.00000 −0.0719816
\(773\) −24.0000 41.5692i −0.863220 1.49514i −0.868804 0.495156i \(-0.835111\pi\)
0.00558380 0.999984i \(-0.498223\pi\)
\(774\) 4.00000 6.92820i 0.143777 0.249029i
\(775\) 0 0
\(776\) 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
\(786\) −9.00000 −0.321019
\(787\) 7.00000 0.249523 0.124762 0.992187i