Properties

Label 78.2.e.b.55.1
Level $78$
Weight $2$
Character 78.55
Analytic conductor $0.623$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 78 = 2 \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 78.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.622833135766\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 78.55
Dual form 78.2.e.b.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.00000 - 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.00000 - 1.73205i) q^{11} -1.00000 q^{12} +(2.50000 - 2.59808i) q^{13} +2.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.50000 + 4.33013i) q^{17} -1.00000 q^{18} +(1.00000 - 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.00000 q^{25} +(3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 1.73205i) q^{28} +(4.50000 + 7.79423i) q^{29} +(0.500000 - 0.866025i) q^{30} -4.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{33} -5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.50000 + 9.52628i) q^{37} +2.00000 q^{38} +(3.50000 + 0.866025i) q^{39} +1.00000 q^{40} +(-2.50000 - 4.33013i) q^{41} +(1.00000 + 1.73205i) q^{42} +(-5.00000 + 8.66025i) q^{43} +2.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(3.00000 - 5.19615i) q^{46} +2.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(-2.00000 - 3.46410i) q^{50} -5.00000 q^{51} +(1.00000 + 3.46410i) q^{52} -1.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} +(-1.00000 + 1.73205i) q^{56} +2.00000 q^{57} +(-4.50000 + 7.79423i) q^{58} +(4.00000 - 6.92820i) q^{59} +1.00000 q^{60} +(5.50000 - 9.52628i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(1.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-2.50000 + 2.59808i) q^{65} +2.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(3.00000 - 5.19615i) q^{69} -2.00000 q^{70} +(7.00000 - 12.1244i) q^{71} +(0.500000 - 0.866025i) q^{72} -13.0000 q^{73} +(-5.50000 + 9.52628i) q^{74} +(-2.00000 - 3.46410i) q^{75} +(1.00000 + 1.73205i) q^{76} -4.00000 q^{77} +(1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.50000 - 4.33013i) q^{82} +6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(2.50000 - 4.33013i) q^{85} -10.0000 q^{86} +(-4.50000 + 7.79423i) q^{87} +(1.00000 + 1.73205i) q^{88} +(-1.00000 - 1.73205i) q^{89} +1.00000 q^{90} +(-2.00000 - 6.92820i) q^{91} +6.00000 q^{92} +(-2.00000 - 3.46410i) q^{93} +(1.00000 + 1.73205i) q^{94} +(-1.00000 + 1.73205i) q^{95} +1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +(-1.50000 + 2.59808i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} - q^{4} - 2 q^{5} - q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - q^{10} - 2 q^{11} - 2 q^{12} + 5 q^{13} + 4 q^{14} - q^{15} - q^{16} - 5 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 4 q^{21} + 2 q^{22} - 6 q^{23} - q^{24} - 8 q^{25} + 7 q^{26} - 2 q^{27} + 2 q^{28} + 9 q^{29} + q^{30} - 8 q^{31} + q^{32} + 2 q^{33} - 10 q^{34} - 2 q^{35} - q^{36} + 11 q^{37} + 4 q^{38} + 7 q^{39} + 2 q^{40} - 5 q^{41} + 2 q^{42} - 10 q^{43} + 4 q^{44} + q^{45} + 6 q^{46} + 4 q^{47} + q^{48} + 3 q^{49} - 4 q^{50} - 10 q^{51} + 2 q^{52} - 2 q^{53} - q^{54} + 2 q^{55} - 2 q^{56} + 4 q^{57} - 9 q^{58} + 8 q^{59} + 2 q^{60} + 11 q^{61} - 4 q^{62} + 2 q^{63} + 2 q^{64} - 5 q^{65} + 4 q^{66} - 2 q^{67} - 5 q^{68} + 6 q^{69} - 4 q^{70} + 14 q^{71} + q^{72} - 26 q^{73} - 11 q^{74} - 4 q^{75} + 2 q^{76} - 8 q^{77} + 2 q^{78} - 8 q^{79} + q^{80} - q^{81} + 5 q^{82} + 12 q^{83} - 2 q^{84} + 5 q^{85} - 20 q^{86} - 9 q^{87} + 2 q^{88} - 2 q^{89} + 2 q^{90} - 4 q^{91} + 12 q^{92} - 4 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} + 2 q^{97} - 3 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/78\mathbb{Z}\right)^\times\).

\(n\) \(53\) \(67\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.00000 −0.447214 −0.223607 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i \(-0.709957\pi\)
0.990766 + 0.135583i \(0.0432908\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.50000 2.59808i 0.693375 0.720577i
\(14\) 2.00000 0.534522
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.50000 + 4.33013i −0.606339 + 1.05021i 0.385499 + 0.922708i \(0.374029\pi\)
−0.991838 + 0.127502i \(0.959304\pi\)
\(18\) −1.00000 −0.235702
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 2.00000 0.436436
\(22\) 1.00000 1.73205i 0.213201 0.369274i
\(23\) −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
\(25\) −4.00000 −0.800000
\(26\) 3.50000 + 0.866025i 0.686406 + 0.169842i
\(27\) −1.00000 −0.192450
\(28\) 1.00000 + 1.73205i 0.188982 + 0.327327i
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 0.500000 0.866025i 0.0912871 0.158114i
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) −5.00000 −0.857493
\(35\) −1.00000 + 1.73205i −0.169031 + 0.292770i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 5.50000 + 9.52628i 0.904194 + 1.56611i 0.821995 + 0.569495i \(0.192861\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 2.00000 0.324443
\(39\) 3.50000 + 0.866025i 0.560449 + 0.138675i
\(40\) 1.00000 0.158114
\(41\) −2.50000 4.33013i −0.390434 0.676252i 0.602072 0.798441i \(-0.294342\pi\)
−0.992507 + 0.122189i \(0.961009\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) −5.00000 + 8.66025i −0.762493 + 1.32068i 0.179069 + 0.983836i \(0.442691\pi\)
−0.941562 + 0.336840i \(0.890642\pi\)
\(44\) 2.00000 0.301511
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) −5.00000 −0.700140
\(52\) 1.00000 + 3.46410i 0.138675 + 0.480384i
\(53\) −1.00000 −0.137361 −0.0686803 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 1.00000 + 1.73205i 0.134840 + 0.233550i
\(56\) −1.00000 + 1.73205i −0.133631 + 0.231455i
\(57\) 2.00000 0.264906
\(58\) −4.50000 + 7.79423i −0.590879 + 1.02343i
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) 1.00000 0.129099
\(61\) 5.50000 9.52628i 0.704203 1.21972i −0.262776 0.964857i \(-0.584638\pi\)
0.966978 0.254858i \(-0.0820288\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) 1.00000 + 1.73205i 0.125988 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) −2.50000 + 2.59808i −0.310087 + 0.322252i
\(66\) 2.00000 0.246183
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) −2.50000 4.33013i −0.303170 0.525105i
\(69\) 3.00000 5.19615i 0.361158 0.625543i
\(70\) −2.00000 −0.239046
\(71\) 7.00000 12.1244i 0.830747 1.43890i −0.0666994 0.997773i \(-0.521247\pi\)
0.897447 0.441123i \(-0.145420\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −13.0000 −1.52153 −0.760767 0.649025i \(-0.775177\pi\)
−0.760767 + 0.649025i \(0.775177\pi\)
\(74\) −5.50000 + 9.52628i −0.639362 + 1.10741i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 1.00000 + 1.73205i 0.114708 + 0.198680i
\(77\) −4.00000 −0.455842
\(78\) 1.00000 + 3.46410i 0.113228 + 0.392232i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 2.50000 4.33013i 0.276079 0.478183i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −1.00000 + 1.73205i −0.109109 + 0.188982i
\(85\) 2.50000 4.33013i 0.271163 0.469668i
\(86\) −10.0000 −1.07833
\(87\) −4.50000 + 7.79423i −0.482451 + 0.835629i
\(88\) 1.00000 + 1.73205i 0.106600 + 0.184637i
\(89\) −1.00000 1.73205i −0.106000 0.183597i 0.808146 0.588982i \(-0.200471\pi\)
−0.914146 + 0.405385i \(0.867138\pi\)
\(90\) 1.00000 0.105409
\(91\) −2.00000 6.92820i −0.209657 0.726273i
\(92\) 6.00000 0.625543
\(93\) −2.00000 3.46410i −0.207390 0.359211i
\(94\) 1.00000 + 1.73205i 0.103142 + 0.178647i
\(95\) −1.00000 + 1.73205i −0.102598 + 0.177705i
\(96\) 1.00000 0.102062
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) −1.50000 + 2.59808i −0.151523 + 0.262445i
\(99\) 2.00000 0.201008
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) 2.50000 + 4.33013i 0.248759 + 0.430864i 0.963182 0.268851i \(-0.0866439\pi\)
−0.714423 + 0.699715i \(0.753311\pi\)
\(102\) −2.50000 4.33013i −0.247537 0.428746i
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) −2.50000 + 2.59808i −0.245145 + 0.254762i
\(105\) −2.00000 −0.195180
\(106\) −0.500000 0.866025i −0.0485643 0.0841158i
\(107\) 9.00000 + 15.5885i 0.870063 + 1.50699i 0.861931 + 0.507026i \(0.169255\pi\)
0.00813215 + 0.999967i \(0.497411\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −2.00000 −0.191565 −0.0957826 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) −1.00000 + 1.73205i −0.0953463 + 0.165145i
\(111\) −5.50000 + 9.52628i −0.522037 + 0.904194i
\(112\) −2.00000 −0.188982
\(113\) 1.50000 2.59808i 0.141108 0.244406i −0.786806 0.617200i \(-0.788267\pi\)
0.927914 + 0.372794i \(0.121600\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 3.00000 + 5.19615i 0.279751 + 0.484544i
\(116\) −9.00000 −0.835629
\(117\) 1.00000 + 3.46410i 0.0924500 + 0.320256i
\(118\) 8.00000 0.736460
\(119\) 5.00000 + 8.66025i 0.458349 + 0.793884i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 11.0000 0.995893
\(123\) 2.50000 4.33013i 0.225417 0.390434i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 9.00000 0.804984
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) 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
\(129\) −10.0000 −0.880451
\(130\) −3.50000 0.866025i −0.306970 0.0759555i
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 1.00000 + 1.73205i 0.0870388 + 0.150756i
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 1.00000 1.73205i 0.0863868 0.149626i
\(135\) 1.00000 0.0860663
\(136\) 2.50000 4.33013i 0.214373 0.371305i
\(137\) −8.50000 + 14.7224i −0.726204 + 1.25782i 0.232273 + 0.972651i \(0.425384\pi\)
−0.958477 + 0.285171i \(0.907949\pi\)
\(138\) 6.00000 0.510754
\(139\) 6.00000 10.3923i 0.508913 0.881464i −0.491033 0.871141i \(-0.663381\pi\)
0.999947 0.0103230i \(-0.00328598\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) 1.00000 + 1.73205i 0.0842152 + 0.145865i
\(142\) 14.0000 1.17485
\(143\) −7.00000 1.73205i −0.585369 0.144841i
\(144\) 1.00000 0.0833333
\(145\) −4.50000 7.79423i −0.373705 0.647275i
\(146\) −6.50000 11.2583i −0.537944 0.931746i
\(147\) −1.50000 + 2.59808i −0.123718 + 0.214286i
\(148\) −11.0000 −0.904194
\(149\) −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i \(-0.872548\pi\)
0.798019 + 0.602632i \(0.205881\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) −6.00000 −0.488273 −0.244137 0.969741i \(-0.578505\pi\)
−0.244137 + 0.969741i \(0.578505\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) −2.50000 4.33013i −0.202113 0.350070i
\(154\) −2.00000 3.46410i −0.161165 0.279145i
\(155\) 4.00000 0.321288
\(156\) −2.50000 + 2.59808i −0.200160 + 0.208013i
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) −2.00000 3.46410i −0.159111 0.275589i
\(159\) −0.500000 0.866025i −0.0396526 0.0686803i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) −12.0000 −0.945732
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −10.0000 + 17.3205i −0.783260 + 1.35665i 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 5.00000 0.390434
\(165\) −1.00000 + 1.73205i −0.0778499 + 0.134840i
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) −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 −0.154303
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 5.00000 0.383482
\(171\) 1.00000 + 1.73205i 0.0764719 + 0.132453i
\(172\) −5.00000 8.66025i −0.381246 0.660338i
\(173\) 11.0000 19.0526i 0.836315 1.44854i −0.0566411 0.998395i \(-0.518039\pi\)
0.892956 0.450145i \(-0.148628\pi\)
\(174\) −9.00000 −0.682288
\(175\) −4.00000 + 6.92820i −0.302372 + 0.523723i
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 8.00000 0.601317
\(178\) 1.00000 1.73205i 0.0749532 0.129823i
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 5.00000 5.19615i 0.370625 0.385164i
\(183\) 11.0000 0.813143
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) −5.50000 9.52628i −0.404368 0.700386i
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) 10.0000 0.731272
\(188\) −1.00000 + 1.73205i −0.0729325 + 0.126323i
\(189\) −1.00000 + 1.73205i −0.0727393 + 0.125988i
\(190\) −2.00000 −0.145095
\(191\) −2.00000 + 3.46410i −0.144715 + 0.250654i −0.929267 0.369410i \(-0.879560\pi\)
0.784552 + 0.620063i \(0.212893\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 8.50000 + 14.7224i 0.611843 + 1.05974i 0.990930 + 0.134382i \(0.0429051\pi\)
−0.379086 + 0.925361i \(0.623762\pi\)
\(194\) 2.00000 0.143592
\(195\) −3.50000 0.866025i −0.250640 0.0620174i
\(196\) −3.00000 −0.214286
\(197\) −3.00000 5.19615i −0.213741 0.370211i 0.739141 0.673550i \(-0.235232\pi\)
−0.952882 + 0.303340i \(0.901898\pi\)
\(198\) 1.00000 + 1.73205i 0.0710669 + 0.123091i
\(199\) −5.00000 + 8.66025i −0.354441 + 0.613909i −0.987022 0.160585i \(-0.948662\pi\)
0.632581 + 0.774494i \(0.281995\pi\)
\(200\) 4.00000 0.282843
\(201\) 1.00000 1.73205i 0.0705346 0.122169i
\(202\) −2.50000 + 4.33013i −0.175899 + 0.304667i
\(203\) 18.0000 1.26335
\(204\) 2.50000 4.33013i 0.175035 0.303170i
\(205\) 2.50000 + 4.33013i 0.174608 + 0.302429i
\(206\) 5.00000 + 8.66025i 0.348367 + 0.603388i
\(207\) 6.00000 0.417029
\(208\) −3.50000 0.866025i −0.242681 0.0600481i
\(209\) −4.00000 −0.276686
\(210\) −1.00000 1.73205i −0.0690066 0.119523i
\(211\) −12.0000 20.7846i −0.826114 1.43087i −0.901065 0.433684i \(-0.857213\pi\)
0.0749508 0.997187i \(-0.476120\pi\)
\(212\) 0.500000 0.866025i 0.0343401 0.0594789i
\(213\) 14.0000 0.959264
\(214\) −9.00000 + 15.5885i −0.615227 + 1.06561i
\(215\) 5.00000 8.66025i 0.340997 0.590624i
\(216\) 1.00000 0.0680414
\(217\) −4.00000 + 6.92820i −0.271538 + 0.470317i
\(218\) −1.00000 1.73205i −0.0677285 0.117309i
\(219\) −6.50000 11.2583i −0.439229 0.760767i
\(220\) −2.00000 −0.134840
\(221\) 5.00000 + 17.3205i 0.336336 + 1.16510i
\(222\) −11.0000 −0.738272
\(223\) 8.00000 + 13.8564i 0.535720 + 0.927894i 0.999128 + 0.0417488i \(0.0132929\pi\)
−0.463409 + 0.886145i \(0.653374\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) 2.00000 3.46410i 0.133333 0.230940i
\(226\) 3.00000 0.199557
\(227\) −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −3.00000 + 5.19615i −0.197814 + 0.342624i
\(231\) −2.00000 3.46410i −0.131590 0.227921i
\(232\) −4.50000 7.79423i −0.295439 0.511716i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −2.50000 + 2.59808i −0.163430 + 0.169842i
\(235\) −2.00000 −0.130466
\(236\) 4.00000 + 6.92820i 0.260378 + 0.450988i
\(237\) −2.00000 3.46410i −0.129914 0.225018i
\(238\) −5.00000 + 8.66025i −0.324102 + 0.561361i
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) −0.500000 + 0.866025i −0.0322749 + 0.0559017i
\(241\) −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i \(-0.905720\pi\)
0.731001 + 0.682376i \(0.239053\pi\)
\(242\) 7.00000 0.449977
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 5.50000 + 9.52628i 0.352101 + 0.609858i
\(245\) −1.50000 2.59808i −0.0958315 0.165985i
\(246\) 5.00000 0.318788
\(247\) −2.00000 6.92820i −0.127257 0.440831i
\(248\) 4.00000 0.254000
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 4.50000 + 7.79423i 0.284605 + 0.492950i
\(251\) −2.00000 + 3.46410i −0.126239 + 0.218652i −0.922217 0.386674i \(-0.873624\pi\)
0.795978 + 0.605326i \(0.206957\pi\)
\(252\) −2.00000 −0.125988
\(253\) −6.00000 + 10.3923i −0.377217 + 0.653359i
\(254\) −6.00000 + 10.3923i −0.376473 + 0.652071i
\(255\) 5.00000 0.313112
\(256\) −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 \(0.803506\pi\)
\(258\) −5.00000 8.66025i −0.311286 0.539164i
\(259\) 22.0000 1.36701
\(260\) −1.00000 3.46410i −0.0620174 0.214834i
\(261\) −9.00000 −0.557086
\(262\) −4.00000 6.92820i −0.247121 0.428026i
\(263\) −7.00000 12.1244i −0.431638 0.747620i 0.565376 0.824833i \(-0.308731\pi\)
−0.997015 + 0.0772134i \(0.975398\pi\)
\(264\) −1.00000 + 1.73205i −0.0615457 + 0.106600i
\(265\) 1.00000 0.0614295
\(266\) 2.00000 3.46410i 0.122628 0.212398i
\(267\) 1.00000 1.73205i 0.0611990 0.106000i
\(268\) 2.00000 0.122169
\(269\) 7.00000 12.1244i 0.426798 0.739235i −0.569789 0.821791i \(-0.692975\pi\)
0.996586 + 0.0825561i \(0.0263084\pi\)
\(270\) 0.500000 + 0.866025i 0.0304290 + 0.0527046i
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) 5.00000 0.303170
\(273\) 5.00000 5.19615i 0.302614 0.314485i
\(274\) −17.0000 −1.02701
\(275\) 4.00000 + 6.92820i 0.241209 + 0.417786i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) 5.50000 9.52628i 0.330463 0.572379i −0.652140 0.758099i \(-0.726128\pi\)
0.982603 + 0.185720i \(0.0594618\pi\)
\(278\) 12.0000 0.719712
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) 1.00000 1.73205i 0.0597614 0.103510i
\(281\) 25.0000 1.49137 0.745687 0.666296i \(-0.232121\pi\)
0.745687 + 0.666296i \(0.232121\pi\)
\(282\) −1.00000 + 1.73205i −0.0595491 + 0.103142i
\(283\) −13.0000 22.5167i −0.772770 1.33848i −0.936039 0.351895i \(-0.885537\pi\)
0.163270 0.986581i \(-0.447796\pi\)
\(284\) 7.00000 + 12.1244i 0.415374 + 0.719448i
\(285\) −2.00000 −0.118470
\(286\) −2.00000 6.92820i −0.118262 0.409673i
\(287\) −10.0000 −0.590281
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) 2.00000 0.117242
\(292\) 6.50000 11.2583i 0.380384 0.658844i
\(293\) 0.500000 0.866025i 0.0292103 0.0505937i −0.851051 0.525084i \(-0.824034\pi\)
0.880261 + 0.474490i \(0.157367\pi\)
\(294\) −3.00000 −0.174964
\(295\) −4.00000 + 6.92820i −0.232889 + 0.403376i
\(296\) −5.50000 9.52628i −0.319681 0.553704i
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) −3.00000 −0.173785
\(299\) −21.0000 5.19615i −1.21446 0.300501i
\(300\) 4.00000 0.230940
\(301\) 10.0000 + 17.3205i 0.576390 + 0.998337i
\(302\) −3.00000 5.19615i −0.172631 0.299005i
\(303\) −2.50000 + 4.33013i −0.143621 + 0.248759i
\(304\) −2.00000 −0.114708
\(305\) −5.50000 + 9.52628i −0.314929 + 0.545473i
\(306\) 2.50000 4.33013i 0.142915 0.247537i
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) 2.00000 3.46410i 0.113961 0.197386i
\(309\) 5.00000 + 8.66025i 0.284440 + 0.492665i
\(310\) 2.00000 + 3.46410i 0.113592 + 0.196748i
\(311\) 6.00000 0.340229 0.170114 0.985424i \(-0.445586\pi\)
0.170114 + 0.985424i \(0.445586\pi\)
\(312\) −3.50000 0.866025i −0.198148 0.0490290i
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) −3.50000 6.06218i −0.197516 0.342108i
\(315\) −1.00000 1.73205i −0.0563436 0.0975900i
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) −33.0000 −1.85346 −0.926732 0.375722i \(-0.877395\pi\)
−0.926732 + 0.375722i \(0.877395\pi\)
\(318\) 0.500000 0.866025i 0.0280386 0.0485643i
\(319\) 9.00000 15.5885i 0.503903 0.872786i
\(320\) −1.00000 −0.0559017
\(321\) −9.00000 + 15.5885i −0.502331 + 0.870063i
\(322\) −6.00000 10.3923i −0.334367 0.579141i
\(323\) 5.00000 + 8.66025i 0.278207 + 0.481869i
\(324\) 1.00000 0.0555556
\(325\) −10.0000 + 10.3923i −0.554700 + 0.576461i
\(326\) −20.0000 −1.10770
\(327\) −1.00000 1.73205i −0.0553001 0.0957826i
\(328\) 2.50000 + 4.33013i 0.138039 + 0.239091i
\(329\) 2.00000 3.46410i 0.110264 0.190982i
\(330\) −2.00000 −0.110096
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) −3.00000 + 5.19615i −0.164646 + 0.285176i
\(333\) −11.0000 −0.602796
\(334\) 12.0000 20.7846i 0.656611 1.13728i
\(335\) 1.00000 + 1.73205i 0.0546358 + 0.0946320i
\(336\) −1.00000 1.73205i −0.0545545 0.0944911i
\(337\) −9.00000 −0.490261 −0.245131 0.969490i \(-0.578831\pi\)
−0.245131 + 0.969490i \(0.578831\pi\)
\(338\) 11.0000 6.92820i 0.598321 0.376845i
\(339\) 3.00000 0.162938
\(340\) 2.50000 + 4.33013i 0.135582 + 0.234834i
\(341\) 4.00000 + 6.92820i 0.216612 + 0.375183i
\(342\) −1.00000 + 1.73205i −0.0540738 + 0.0936586i
\(343\) 20.0000 1.07990
\(344\) 5.00000 8.66025i 0.269582 0.466930i
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) 22.0000 1.18273
\(347\) −3.00000 + 5.19615i −0.161048 + 0.278944i −0.935245 0.354001i \(-0.884821\pi\)
0.774197 + 0.632945i \(0.218154\pi\)
\(348\) −4.50000 7.79423i −0.241225 0.417815i
\(349\) −3.00000 5.19615i −0.160586 0.278144i 0.774493 0.632583i \(-0.218005\pi\)
−0.935079 + 0.354439i \(0.884672\pi\)
\(350\) −8.00000 −0.427618
\(351\) −2.50000 + 2.59808i −0.133440 + 0.138675i
\(352\) −2.00000 −0.106600
\(353\) −8.50000 14.7224i −0.452409 0.783596i 0.546126 0.837703i \(-0.316102\pi\)
−0.998535 + 0.0541072i \(0.982769\pi\)
\(354\) 4.00000 + 6.92820i 0.212598 + 0.368230i
\(355\) −7.00000 + 12.1244i −0.371521 + 0.643494i
\(356\) 2.00000 0.106000
\(357\) −5.00000 + 8.66025i −0.264628 + 0.458349i
\(358\) −3.00000 + 5.19615i −0.158555 + 0.274625i
\(359\) −30.0000 −1.58334 −0.791670 0.610949i \(-0.790788\pi\)
−0.791670 + 0.610949i \(0.790788\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 2.50000 + 4.33013i 0.131397 + 0.227586i
\(363\) 7.00000 0.367405
\(364\) 7.00000 + 1.73205i 0.366900 + 0.0907841i
\(365\) 13.0000 0.680451
\(366\) 5.50000 + 9.52628i 0.287490 + 0.497947i
\(367\) 1.00000 + 1.73205i 0.0521996 + 0.0904123i 0.890945 0.454112i \(-0.150043\pi\)
−0.838745 + 0.544524i \(0.816710\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) 5.00000 0.260290
\(370\) 5.50000 9.52628i 0.285931 0.495248i
\(371\) −1.00000 + 1.73205i −0.0519174 + 0.0899236i
\(372\) 4.00000 0.207390
\(373\) −4.50000 + 7.79423i −0.233001 + 0.403570i −0.958690 0.284453i \(-0.908188\pi\)
0.725689 + 0.688023i \(0.241521\pi\)
\(374\) 5.00000 + 8.66025i 0.258544 + 0.447811i
\(375\) 4.50000 + 7.79423i 0.232379 + 0.402492i
\(376\) −2.00000 −0.103142
\(377\) 31.5000 + 7.79423i 1.62233 + 0.401423i
\(378\) −2.00000 −0.102869
\(379\) −6.00000 10.3923i −0.308199 0.533817i 0.669769 0.742569i \(-0.266393\pi\)
−0.977969 + 0.208752i \(0.933060\pi\)
\(380\) −1.00000 1.73205i −0.0512989 0.0888523i
\(381\) −6.00000 + 10.3923i −0.307389 + 0.532414i
\(382\) −4.00000 −0.204658
\(383\) −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 4.00000 0.203859
\(386\) −8.50000 + 14.7224i −0.432639 + 0.749352i
\(387\) −5.00000 8.66025i −0.254164 0.440225i
\(388\) 1.00000 + 1.73205i 0.0507673 + 0.0879316i
\(389\) 19.0000 0.963338 0.481669 0.876353i \(-0.340031\pi\)
0.481669 + 0.876353i \(0.340031\pi\)
\(390\) −1.00000 3.46410i −0.0506370 0.175412i
\(391\) 30.0000 1.51717
\(392\) −1.50000 2.59808i −0.0757614 0.131223i
\(393\) −4.00000 6.92820i −0.201773 0.349482i
\(394\) 3.00000 5.19615i 0.151138 0.261778i
\(395\) 4.00000 0.201262
\(396\) −1.00000 + 1.73205i −0.0502519 + 0.0870388i
\(397\) 9.00000 15.5885i 0.451697 0.782362i −0.546795 0.837267i \(-0.684152\pi\)
0.998492 + 0.0549046i \(0.0174855\pi\)
\(398\) −10.0000 −0.501255
\(399\) 2.00000 3.46410i 0.100125 0.173422i
\(400\) 2.00000 + 3.46410i 0.100000 + 0.173205i
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) 2.00000 0.0997509
\(403\) −10.0000 + 10.3923i −0.498135 + 0.517678i
\(404\) −5.00000 −0.248759
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) 9.00000 + 15.5885i 0.446663 + 0.773642i
\(407\) 11.0000 19.0526i 0.545250 0.944400i
\(408\) 5.00000 0.247537
\(409\) −11.5000 + 19.9186i −0.568638 + 0.984911i 0.428063 + 0.903749i \(0.359196\pi\)
−0.996701 + 0.0811615i \(0.974137\pi\)
\(410\) −2.50000 + 4.33013i −0.123466 + 0.213850i
\(411\) −17.0000 −0.838548
\(412\) −5.00000 + 8.66025i −0.246332 + 0.426660i
\(413\) −8.00000 13.8564i −0.393654 0.681829i
\(414\) 3.00000 + 5.19615i 0.147442 + 0.255377i
\(415\) −6.00000 −0.294528
\(416\) −1.00000 3.46410i −0.0490290 0.169842i
\(417\) 12.0000 0.587643
\(418\) −2.00000 3.46410i −0.0978232 0.169435i
\(419\) 16.0000 + 27.7128i 0.781651 + 1.35386i 0.930979 + 0.365072i \(0.118956\pi\)
−0.149328 + 0.988788i \(0.547711\pi\)
\(420\) 1.00000 1.73205i 0.0487950 0.0845154i
\(421\) −23.0000 −1.12095 −0.560476 0.828171i \(-0.689382\pi\)
−0.560476 + 0.828171i \(0.689382\pi\)
\(422\) 12.0000 20.7846i 0.584151 1.01178i
\(423\) −1.00000 + 1.73205i −0.0486217 + 0.0842152i
\(424\) 1.00000 0.0485643
\(425\) 10.0000 17.3205i 0.485071 0.840168i
\(426\) 7.00000 + 12.1244i 0.339151 + 0.587427i
\(427\) −11.0000 19.0526i −0.532327 0.922018i
\(428\) −18.0000 −0.870063
\(429\) −2.00000 6.92820i −0.0965609 0.334497i
\(430\) 10.0000 0.482243
\(431\) 1.00000 + 1.73205i 0.0481683 + 0.0834300i 0.889104 0.457705i \(-0.151328\pi\)
−0.840936 + 0.541135i \(0.817995\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 10.5000 18.1865i 0.504598 0.873989i −0.495388 0.868672i \(-0.664974\pi\)
0.999986 0.00531724i \(-0.00169254\pi\)
\(434\) −8.00000 −0.384012
\(435\) 4.50000 7.79423i 0.215758 0.373705i
\(436\) 1.00000 1.73205i 0.0478913 0.0829502i
\(437\) −12.0000 −0.574038
\(438\) 6.50000 11.2583i 0.310582 0.537944i
\(439\) −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) −1.00000 1.73205i −0.0476731 0.0825723i
\(441\) −3.00000 −0.142857
\(442\) −12.5000 + 12.9904i −0.594564 + 0.617889i
\(443\) 20.0000 0.950229 0.475114 0.879924i \(-0.342407\pi\)
0.475114 + 0.879924i \(0.342407\pi\)
\(444\) −5.50000 9.52628i −0.261018 0.452097i
\(445\) 1.00000 + 1.73205i 0.0474045 + 0.0821071i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) −3.00000 −0.141895
\(448\) 1.00000 1.73205i 0.0472456 0.0818317i
\(449\) 15.0000 25.9808i 0.707894 1.22611i −0.257743 0.966213i \(-0.582979\pi\)
0.965637 0.259895i \(-0.0836878\pi\)
\(450\) 4.00000 0.188562
\(451\) −5.00000 + 8.66025i −0.235441 + 0.407795i
\(452\) 1.50000 + 2.59808i 0.0705541 + 0.122203i
\(453\) −3.00000 5.19615i −0.140952 0.244137i
\(454\) −14.0000 −0.657053
\(455\) 2.00000 + 6.92820i 0.0937614 + 0.324799i
\(456\) −2.00000 −0.0936586
\(457\) −1.50000 2.59808i −0.0701670 0.121533i 0.828807 0.559534i \(-0.189020\pi\)
−0.898974 + 0.438001i \(0.855687\pi\)
\(458\) 5.00000 + 8.66025i 0.233635 + 0.404667i
\(459\) 2.50000 4.33013i 0.116690 0.202113i
\(460\) −6.00000 −0.279751
\(461\) −1.50000 + 2.59808i −0.0698620 + 0.121004i −0.898840 0.438276i \(-0.855589\pi\)
0.828978 + 0.559281i \(0.188923\pi\)
\(462\) 2.00000 3.46410i 0.0930484 0.161165i
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 4.50000 7.79423i 0.208907 0.361838i
\(465\) 2.00000 + 3.46410i 0.0927478 + 0.160644i
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) −22.0000 −1.01804 −0.509019 0.860755i \(-0.669992\pi\)
−0.509019 + 0.860755i \(0.669992\pi\)
\(468\) −3.50000 0.866025i −0.161788 0.0400320i
\(469\) −4.00000 −0.184703
\(470\) −1.00000 1.73205i −0.0461266 0.0798935i
\(471\) −3.50000 6.06218i −0.161271 0.279330i
\(472\) −4.00000 + 6.92820i −0.184115 + 0.318896i
\(473\) 20.0000 0.919601
\(474\) 2.00000 3.46410i 0.0918630 0.159111i
\(475\) −4.00000 + 6.92820i −0.183533 + 0.317888i
\(476\) −10.0000 −0.458349
\(477\) 0.500000 0.866025i 0.0228934 0.0396526i
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) −16.0000 27.7128i −0.731059 1.26623i −0.956431 0.291958i \(-0.905693\pi\)
0.225372 0.974273i \(-0.427640\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 38.5000 + 9.52628i 1.75545 + 0.434361i
\(482\) −7.00000 −0.318841
\(483\) −6.00000 10.3923i −0.273009 0.472866i
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) −1.00000 + 1.73205i −0.0454077 + 0.0786484i
\(486\) 1.00000 0.0453609
\(487\) 13.0000 22.5167i 0.589086 1.02033i −0.405266 0.914199i \(-0.632821\pi\)
0.994352 0.106129i \(-0.0338455\pi\)
\(488\) −5.50000 + 9.52628i −0.248973 + 0.431234i
\(489\) −20.0000 −0.904431
\(490\) 1.50000 2.59808i 0.0677631 0.117369i
\(491\) 15.0000 + 25.9808i 0.676941 + 1.17250i 0.975898 + 0.218229i \(0.0700279\pi\)
−0.298957 + 0.954267i \(0.596639\pi\)
\(492\) 2.50000 + 4.33013i 0.112709 + 0.195217i
\(493\) −45.0000 −2.02670
\(494\) 5.00000 5.19615i 0.224961 0.233786i
\(495\) −2.00000 −0.0898933
\(496\) 2.00000 + 3.46410i 0.0898027 + 0.155543i
\(497\) −14.0000 24.2487i −0.627986 1.08770i
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) −4.50000 + 7.79423i −0.201246 + 0.348569i
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) −4.00000 −0.178529
\(503\) 7.00000 12.1244i 0.312115 0.540598i −0.666705 0.745321i \(-0.732296\pi\)
0.978820 + 0.204723i \(0.0656294\pi\)
\(504\) −1.00000 1.73205i −0.0445435 0.0771517i
\(505\) −2.50000 4.33013i −0.111249 0.192688i
\(506\) −12.0000 −0.533465
\(507\) 11.0000 6.92820i 0.488527 0.307692i
\(508\) −12.0000 −0.532414
\(509\) −7.50000 12.9904i −0.332432 0.575789i 0.650556 0.759458i \(-0.274536\pi\)
−0.982988 + 0.183669i \(0.941202\pi\)
\(510\) 2.50000 + 4.33013i 0.110702 + 0.191741i
\(511\) −13.0000 + 22.5167i −0.575086 + 0.996078i
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 + 1.73205i −0.0441511 + 0.0764719i
\(514\) −1.50000 + 2.59808i −0.0661622 + 0.114596i
\(515\) −10.0000 −0.440653
\(516\) 5.00000 8.66025i 0.220113 0.381246i
\(517\) −2.00000 3.46410i −0.0879599 0.152351i
\(518\) 11.0000 + 19.0526i 0.483312 + 0.837121i
\(519\) 22.0000 0.965693
\(520\) 2.50000 2.59808i 0.109632 0.113933i
\(521\) 25.0000 1.09527 0.547635 0.836717i \(-0.315528\pi\)
0.547635 + 0.836717i \(0.315528\pi\)
\(522\) −4.50000 7.79423i −0.196960 0.341144i
\(523\) 19.0000 + 32.9090i 0.830812 + 1.43901i 0.897395 + 0.441228i \(0.145457\pi\)
−0.0665832 + 0.997781i \(0.521210\pi\)
\(524\) 4.00000 6.92820i 0.174741 0.302660i
\(525\) −8.00000 −0.349149
\(526\) 7.00000 12.1244i 0.305215 0.528647i
\(527\) 10.0000 17.3205i 0.435607 0.754493i
\(528\) −2.00000 −0.0870388
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0.500000 + 0.866025i 0.0217186 + 0.0376177i
\(531\) 4.00000 + 6.92820i 0.173585 + 0.300658i
\(532\) 4.00000 0.173422
\(533\) −17.5000 4.33013i −0.758009 0.187559i
\(534\) 2.00000 0.0865485
\(535\) −9.00000 15.5885i −0.389104 0.673948i
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) 14.0000 0.603583
\(539\) 3.00000 5.19615i 0.129219 0.223814i
\(540\) −0.500000 + 0.866025i −0.0215166 + 0.0372678i
\(541\) −7.00000 −0.300954 −0.150477 0.988614i \(-0.548081\pi\)
−0.150477 + 0.988614i \(0.548081\pi\)
\(542\) 4.00000 6.92820i 0.171815 0.297592i
\(543\) 2.50000 + 4.33013i 0.107285 + 0.185824i
\(544\) 2.50000 + 4.33013i 0.107187 + 0.185653i
\(545\) 2.00000 0.0856706
\(546\) 7.00000 + 1.73205i 0.299572 + 0.0741249i
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) −8.50000 14.7224i −0.363102 0.628911i
\(549\) 5.50000 + 9.52628i 0.234734 + 0.406572i
\(550\) −4.00000 + 6.92820i −0.170561 + 0.295420i
\(551\) 18.0000 0.766826
\(552\) −3.00000 + 5.19615i −0.127688 + 0.221163i
\(553\) −4.00000 + 6.92820i −0.170097 + 0.294617i
\(554\) 11.0000 0.467345
\(555\) 5.50000 9.52628i 0.233462 0.404368i
\(556\) 6.00000 + 10.3923i 0.254457 + 0.440732i
\(557\) 4.50000 + 7.79423i 0.190671 + 0.330252i 0.945473 0.325701i \(-0.105600\pi\)
−0.754802 + 0.655953i \(0.772267\pi\)
\(558\) 4.00000 0.169334
\(559\) 10.0000 + 34.6410i 0.422955 + 1.46516i
\(560\) 2.00000 0.0845154
\(561\) 5.00000 + 8.66025i 0.211100 + 0.365636i
\(562\) 12.5000 + 21.6506i 0.527281 + 0.913277i
\(563\) −20.0000 + 34.6410i −0.842900 + 1.45994i 0.0445334 + 0.999008i \(0.485820\pi\)
−0.887433 + 0.460937i \(0.847513\pi\)
\(564\) −2.00000 −0.0842152
\(565\) −1.50000 + 2.59808i −0.0631055 + 0.109302i
\(566\) 13.0000 22.5167i 0.546431 0.946446i
\(567\) −2.00000 −0.0839921
\(568\) −7.00000 + 12.1244i −0.293713 + 0.508727i
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) −1.00000 1.73205i −0.0418854 0.0725476i
\(571\) −2.00000 −0.0836974 −0.0418487 0.999124i \(-0.513325\pi\)
−0.0418487 + 0.999124i \(0.513325\pi\)
\(572\) 5.00000 5.19615i 0.209061 0.217262i
\(573\) −4.00000 −0.167102
\(574\) −5.00000 8.66025i −0.208696 0.361472i
\(575\) 12.0000 + 20.7846i 0.500435 + 0.866778i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 27.0000 1.12402 0.562012 0.827129i \(-0.310027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) −8.50000 + 14.7224i −0.353248 + 0.611843i
\(580\) 9.00000 0.373705
\(581\) 6.00000 10.3923i 0.248922 0.431145i
\(582\) 1.00000 + 1.73205i 0.0414513 + 0.0717958i
\(583\) 1.00000 + 1.73205i 0.0414158 + 0.0717342i
\(584\) 13.0000 0.537944
\(585\) −1.00000 3.46410i −0.0413449 0.143223i
\(586\) 1.00000 0.0413096
\(587\) 16.0000 + 27.7128i 0.660391 + 1.14383i 0.980513 + 0.196454i \(0.0629426\pi\)
−0.320122 + 0.947376i \(0.603724\pi\)
\(588\) −1.50000 2.59808i −0.0618590 0.107143i
\(589\) −4.00000 + 6.92820i −0.164817 + 0.285472i
\(590\) −8.00000 −0.329355
\(591\) 3.00000 5.19615i 0.123404 0.213741i
\(592\) 5.50000 9.52628i 0.226049 0.391528i
\(593\) −39.0000 −1.60154 −0.800769 0.598973i \(-0.795576\pi\)
−0.800769 + 0.598973i \(0.795576\pi\)
\(594\) −1.00000 + 1.73205i −0.0410305 + 0.0710669i
\(595\) −5.00000 8.66025i −0.204980 0.355036i
\(596\) −1.50000 2.59808i −0.0614424 0.106421i
\(597\) −10.0000 −0.409273
\(598\) −6.00000 20.7846i −0.245358 0.849946i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) −5.50000 9.52628i −0.224350 0.388585i 0.731774 0.681547i \(-0.238692\pi\)
−0.956124 + 0.292962i \(0.905359\pi\)
\(602\) −10.0000 + 17.3205i −0.407570 + 0.705931i
\(603\) 2.00000 0.0814463
\(604\) 3.00000 5.19615i 0.122068 0.211428i
\(605\) −3.50000 + 6.06218i −0.142295 + 0.246463i
\(606\) −5.00000 −0.203111
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) −1.00000 1.73205i −0.0405554 0.0702439i
\(609\) 9.00000 + 15.5885i 0.364698 + 0.631676i
\(610\) −11.0000 −0.445377
\(611\) 5.00000 5.19615i 0.202278 0.210214i
\(612\) 5.00000 0.202113
\(613\) −6.50000 11.2583i −0.262533 0.454720i 0.704382 0.709821i \(-0.251224\pi\)
−0.966914 + 0.255102i \(0.917891\pi\)
\(614\) −7.00000 12.1244i −0.282497 0.489299i
\(615\) −2.50000 + 4.33013i −0.100810 + 0.174608i
\(616\) 4.00000 0.161165
\(617\) 7.50000 12.9904i 0.301939 0.522973i −0.674636 0.738150i \(-0.735700\pi\)
0.976575 + 0.215177i \(0.0690329\pi\)
\(618\) −5.00000 + 8.66025i −0.201129 + 0.348367i
\(619\) 32.0000 1.28619 0.643094 0.765787i \(-0.277650\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) −2.00000 + 3.46410i −0.0803219 + 0.139122i
\(621\) 3.00000 + 5.19615i 0.120386 + 0.208514i
\(622\) 3.00000 + 5.19615i 0.120289 + 0.208347i
\(623\) −4.00000 −0.160257
\(624\) −1.00000 3.46410i −0.0400320 0.138675i
\(625\) 11.0000 0.440000
\(626\) 3.00000 + 5.19615i 0.119904 + 0.207680i
\(627\) −2.00000 3.46410i −0.0798723 0.138343i
\(628\) 3.50000 6.06218i 0.139665 0.241907i
\(629\) −55.0000 −2.19299
\(630\) 1.00000 1.73205i 0.0398410 0.0690066i
\(631\) −6.00000 + 10.3923i −0.238856 + 0.413711i −0.960386 0.278672i \(-0.910106\pi\)
0.721530 + 0.692383i \(0.243439\pi\)
\(632\) 4.00000 0.159111
\(633\) 12.0000 20.7846i 0.476957 0.826114i
\(634\) −16.5000 28.5788i −0.655299 1.13501i
\(635\) −6.00000 10.3923i −0.238103 0.412406i
\(636\) 1.00000 0.0396526
\(637\) 10.5000 + 2.59808i 0.416025 + 0.102940i
\(638\) 18.0000 0.712627
\(639\) 7.00000 + 12.1244i 0.276916 + 0.479632i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −2.50000 + 4.33013i −0.0987441 + 0.171030i −0.911165 0.412042i \(-0.864816\pi\)
0.812421 + 0.583071i \(0.198149\pi\)
\(642\) −18.0000 −0.710403
\(643\) −4.00000 + 6.92820i −0.157745 + 0.273222i −0.934055 0.357129i \(-0.883756\pi\)
0.776310 + 0.630351i \(0.217089\pi\)
\(644\) 6.00000 10.3923i 0.236433 0.409514i
\(645\) 10.0000 0.393750
\(646\) −5.00000 + 8.66025i −0.196722 + 0.340733i
\(647\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −16.0000 −0.628055
\(650\) −14.0000 3.46410i −0.549125 0.135873i
\(651\) −8.00000 −0.313545
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) 11.0000 + 19.0526i 0.430463 + 0.745584i 0.996913 0.0785119i \(-0.0250169\pi\)
−0.566450 + 0.824096i \(0.691684\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) 8.00000 0.312586
\(656\) −2.50000 + 4.33013i −0.0976086 + 0.169063i
\(657\) 6.50000 11.2583i 0.253589 0.439229i
\(658\) 4.00000 0.155936
\(659\) −12.0000 + 20.7846i −0.467454 + 0.809653i −0.999309 0.0371821i \(-0.988162\pi\)
0.531855 + 0.846836i \(0.321495\pi\)
\(660\) −1.00000 1.73205i −0.0389249 0.0674200i
\(661\) −12.5000 21.6506i −0.486194 0.842112i 0.513680 0.857982i \(-0.328282\pi\)
−0.999874 + 0.0158695i \(0.994948\pi\)
\(662\) 28.0000 1.08825
\(663\) −12.5000 + 12.9904i −0.485460 + 0.504505i
\(664\) −6.00000 −0.232845
\(665\) 2.00000 + 3.46410i 0.0775567 + 0.134332i
\(666\) −5.50000 9.52628i −0.213121 0.369136i
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) 24.0000 0.928588
\(669\) −8.00000 + 13.8564i −0.309298 + 0.535720i
\(670\) −1.00000 + 1.73205i −0.0386334 + 0.0669150i
\(671\) −22.0000 −0.849301
\(672\) 1.00000 1.73205i 0.0385758 0.0668153i
\(673\) −21.5000 37.2391i −0.828764 1.43546i −0.899008 0.437932i \(-0.855711\pi\)
0.0702442 0.997530i \(-0.477622\pi\)
\(674\) −4.50000 7.79423i −0.173334 0.300222i
\(675\) 4.00000 0.153960
\(676\) 11.5000 + 6.06218i 0.442308 + 0.233161i
\(677\) −46.0000 −1.76792 −0.883962 0.467559i \(-0.845134\pi\)
−0.883962 + 0.467559i \(0.845134\pi\)
\(678\) 1.50000 + 2.59808i 0.0576072 + 0.0997785i
\(679\) −2.00000 3.46410i −0.0767530 0.132940i
\(680\) −2.50000 + 4.33013i −0.0958706 + 0.166053i
\(681\) −14.0000 −0.536481
\(682\) −4.00000 + 6.92820i −0.153168 + 0.265295i
\(683\) 20.0000 34.6410i 0.765279 1.32550i −0.174820 0.984600i \(-0.555934\pi\)
0.940099 0.340901i \(-0.110732\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 8.50000 14.7224i 0.324768 0.562515i
\(686\) 10.0000 + 17.3205i 0.381802 + 0.661300i
\(687\) 5.00000 + 8.66025i 0.190762 + 0.330409i
\(688\) 10.0000 0.381246
\(689\) −2.50000 + 2.59808i −0.0952424 + 0.0989788i
\(690\) −6.00000 −0.228416
\(691\) 1.00000 + 1.73205i 0.0380418 + 0.0658903i 0.884419 0.466693i \(-0.154555\pi\)
−0.846378 + 0.532583i \(0.821221\pi\)
\(692\) 11.0000 + 19.0526i 0.418157 + 0.724270i
\(693\) 2.00000 3.46410i 0.0759737 0.131590i
\(694\) −6.00000 −0.227757
\(695\) −6.00000 + 10.3923i −0.227593 + 0.394203i
\(696\) 4.50000 7.79423i 0.170572 0.295439i
\(697\) 25.0000 0.946943
\(698\) 3.00000 5.19615i 0.113552 0.196677i
\(699\) −3.00000 5.19615i −0.113470 0.196537i
\(700\) −4.00000 6.92820i −0.151186 0.261861i
\(701\) 34.0000 1.28416 0.642081 0.766637i \(-0.278071\pi\)
0.642081 + 0.766637i \(0.278071\pi\)
\(702\) −3.50000 0.866025i −0.132099 0.0326860i
\(703\) 22.0000 0.829746
\(704\) −1.00000 1.73205i −0.0376889 0.0652791i
\(705\) −1.00000 1.73205i −0.0376622 0.0652328i
\(706\) 8.50000 14.7224i 0.319902 0.554086i
\(707\) 10.0000 0.376089
\(708\) −4.00000 + 6.92820i −0.150329 + 0.260378i
\(709\) 7.50000 12.9904i 0.281668 0.487864i −0.690127 0.723688i \(-0.742446\pi\)
0.971796 + 0.235824i \(0.0757789\pi\)
\(710\) −14.0000 −0.525411
\(711\) 2.00000 3.46410i 0.0750059 0.129914i
\(712\) 1.00000 + 1.73205i 0.0374766 + 0.0649113i
\(713\) 12.0000 + 20.7846i 0.449404 + 0.778390i
\(714\) −10.0000 −0.374241
\(715\) 7.00000 + 1.73205i 0.261785 + 0.0647750i
\(716\) −6.00000 −0.224231
\(717\) −3.00000 5.19615i −0.112037 0.194054i
\(718\) −15.0000 25.9808i −0.559795 0.969593i
\(719\) −12.0000 + 20.7846i −0.447524 + 0.775135i −0.998224 0.0595683i \(-0.981028\pi\)
0.550700 + 0.834703i \(0.314361\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 10.0000 17.3205i 0.372419 0.645049i
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) −7.00000 −0.260333
\(724\) −2.50000 + 4.33013i −0.0929118 + 0.160928i
\(725\) −18.0000 31.1769i −0.668503 1.15788i
\(726\) 3.50000 + 6.06218i 0.129897 + 0.224989i
\(727\) 2.00000 0.0741759 0.0370879 0.999312i \(-0.488192\pi\)
0.0370879 + 0.999312i \(0.488192\pi\)
\(728\) 2.00000 + 6.92820i 0.0741249 + 0.256776i
\(729\) 1.00000 0.0370370
\(730\) 6.50000 + 11.2583i 0.240576 + 0.416689i
\(731\) −25.0000 43.3013i −0.924658 1.60156i
\(732\) −5.50000 + 9.52628i −0.203286 + 0.352101i
\(733\) 13.0000 0.480166 0.240083 0.970752i \(-0.422825\pi\)
0.240083 + 0.970752i \(0.422825\pi\)
\(734\) −1.00000 + 1.73205i −0.0369107 + 0.0639312i
\(735\) 1.50000 2.59808i 0.0553283 0.0958315i
\(736\) −6.00000 −0.221163
\(737\) −2.00000 + 3.46410i −0.0736709 + 0.127602i
\(738\) 2.50000 + 4.33013i 0.0920263 + 0.159394i
\(739\) −8.00000 13.8564i −0.294285 0.509716i 0.680534 0.732717i \(-0.261748\pi\)
−0.974818 + 0.223001i \(0.928415\pi\)
\(740\) 11.0000 0.404368
\(741\) 5.00000 5.19615i 0.183680 0.190885i
\(742\) −2.00000 −0.0734223
\(743\) 6.00000 + 10.3923i 0.220119 + 0.381257i 0.954844 0.297108i \(-0.0960222\pi\)
−0.734725 + 0.678365i \(0.762689\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) 1.50000 2.59808i 0.0549557 0.0951861i
\(746\) −9.00000 −0.329513
\(747\) −3.00000 + 5.19615i −0.109764 + 0.190117i
\(748\) −5.00000 + 8.66025i −0.182818 + 0.316650i
\(749\) 36.0000 1.31541
\(750\) −4.50000 + 7.79423i −0.164317 + 0.284605i
\(751\) −13.0000 22.5167i −0.474377 0.821645i 0.525193 0.850983i \(-0.323993\pi\)
−0.999570 + 0.0293387i \(0.990660\pi\)
\(752\) −1.00000 1.73205i −0.0364662 0.0631614i
\(753\) −4.00000 −0.145768
\(754\) 9.00000 + 31.1769i 0.327761 + 1.13540i
\(755\) 6.00000 0.218362
\(756\) −1.00000 1.73205i −0.0363696 0.0629941i
\(757\) 9.00000 + 15.5885i 0.327111 + 0.566572i 0.981937 0.189207i \(-0.0605917\pi\)
−0.654827 + 0.755779i \(0.727258\pi\)
\(758\) 6.00000 10.3923i 0.217930 0.377466i
\(759\) −12.0000 −0.435572
\(760\) 1.00000 1.73205i 0.0362738 0.0628281i
\(761\) −17.0000 + 29.4449i −0.616250 + 1.06738i 0.373914 + 0.927463i \(0.378015\pi\)
−0.990164 + 0.139912i \(0.955318\pi\)
\(762\) −12.0000 −0.434714
\(763\) −2.00000 + 3.46410i −0.0724049 + 0.125409i
\(764\) −2.00000 3.46410i −0.0723575 0.125327i
\(765\) 2.50000 + 4.33013i 0.0903877 + 0.156556i
\(766\) −24.0000 −0.867155
\(767\) −8.00000 27.7128i −0.288863 1.00065i
\(768\) −1.00000 −0.0360844
\(769\) 17.0000 + 29.4449i 0.613036 + 1.06181i 0.990726 + 0.135877i \(0.0433852\pi\)
−0.377690 + 0.925932i \(0.623282\pi\)
\(770\) 2.00000 + 3.46410i 0.0720750 + 0.124838i
\(771\) −1.50000 + 2.59808i −0.0540212 + 0.0935674i
\(772\) −17.0000 −0.611843
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) 5.00000 8.66025i 0.179721 0.311286i
\(775\) 16.0000 0.574737