Properties

Label 714.2.i.i.205.1
Level $714$
Weight $2$
Character 714.205
Analytic conductor $5.701$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 714.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.70131870432\)
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 205.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 714.205
Dual form 714.2.i.i.613.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(1.00000 + 1.73205i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(0.500000 + 2.59808i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +1.00000 q^{20} +(-2.50000 - 0.866025i) q^{21} +2.00000 q^{22} +(-4.00000 + 6.92820i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} -1.00000 q^{27} +(2.50000 + 0.866025i) q^{28} +3.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(1.50000 + 2.59808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} -1.00000 q^{34} +(-0.500000 - 2.59808i) q^{35} +1.00000 q^{36} +(-2.00000 + 3.46410i) q^{37} +(2.00000 + 3.46410i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +1.00000 q^{41} +(-2.00000 + 1.73205i) q^{42} -4.00000 q^{43} +(1.00000 - 1.73205i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(4.00000 + 6.92820i) q^{46} +(4.50000 - 7.79423i) q^{47} -1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +4.00000 q^{50} +(0.500000 - 0.866025i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{54} -2.00000 q^{55} +(2.00000 - 1.73205i) q^{56} -4.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(-5.50000 - 9.52628i) q^{59} +(0.500000 + 0.866025i) q^{60} +3.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(1.00000 + 1.73205i) q^{66} +(6.00000 + 10.3923i) q^{67} +(-0.500000 + 0.866025i) q^{68} -8.00000 q^{69} +(-2.50000 - 0.866025i) q^{70} +4.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-3.00000 - 5.19615i) q^{73} +(2.00000 + 3.46410i) q^{74} +(-2.00000 + 3.46410i) q^{75} +4.00000 q^{76} +(-5.00000 - 1.73205i) q^{77} +1.00000 q^{78} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.500000 - 0.866025i) q^{82} +9.00000 q^{83} +(0.500000 + 2.59808i) q^{84} +1.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(1.50000 + 2.59808i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(3.00000 - 5.19615i) q^{89} -1.00000 q^{90} +(-2.00000 + 1.73205i) q^{91} +8.00000 q^{92} +(-1.50000 + 2.59808i) q^{93} +(-4.50000 - 7.79423i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(-0.500000 + 0.866025i) q^{96} +8.00000 q^{97} +(-5.50000 - 4.33013i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q + q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{8} - q^{9} + q^{10} + 2 q^{11} + q^{12} + 2 q^{13} + q^{14} - 2 q^{15} - q^{16} - q^{17} + q^{18} - 4 q^{19} + 2 q^{20} - 5 q^{21} + 4 q^{22} - 8 q^{23} - q^{24} + 4 q^{25} + q^{26} - 2 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 3 q^{31} + q^{32} - 2 q^{33} - 2 q^{34} - q^{35} + 2 q^{36} - 4 q^{37} + 4 q^{38} + q^{39} + q^{40} + 2 q^{41} - 4 q^{42} - 8 q^{43} + 2 q^{44} - q^{45} + 8 q^{46} + 9 q^{47} - 2 q^{48} + 2 q^{49} + 8 q^{50} + q^{51} - q^{52} - q^{54} - 4 q^{55} + 4 q^{56} - 8 q^{57} + 3 q^{58} - 11 q^{59} + q^{60} + 6 q^{62} - q^{63} + 2 q^{64} - q^{65} + 2 q^{66} + 12 q^{67} - q^{68} - 16 q^{69} - 5 q^{70} + 8 q^{71} + q^{72} - 6 q^{73} + 4 q^{74} - 4 q^{75} + 8 q^{76} - 10 q^{77} + 2 q^{78} - q^{80} - q^{81} + q^{82} + 18 q^{83} + q^{84} + 2 q^{85} - 4 q^{86} + 3 q^{87} - 2 q^{88} + 6 q^{89} - 2 q^{90} - 4 q^{91} + 16 q^{92} - 3 q^{93} - 9 q^{94} - 4 q^{95} - q^{96} + 16 q^{97} - 11 q^{98} - 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/714\mathbb{Z}\right)^\times\).

\(n\) \(239\) \(409\) \(547\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i −0.955901 0.293691i \(-0.905116\pi\)
0.732294 + 0.680989i \(0.238450\pi\)
\(6\) 1.00000 0.408248
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.500000 0.866025i −0.121268 0.210042i
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −2.00000 + 3.46410i −0.458831 + 0.794719i −0.998899 0.0469020i \(-0.985065\pi\)
0.540068 + 0.841621i \(0.318398\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.50000 0.866025i −0.545545 0.188982i
\(22\) 2.00000 0.426401
\(23\) −4.00000 + 6.92820i −0.834058 + 1.44463i 0.0607377 + 0.998154i \(0.480655\pi\)
−0.894795 + 0.446476i \(0.852679\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 2.00000 + 3.46410i 0.400000 + 0.692820i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) −1.00000 −0.192450
\(28\) 2.50000 + 0.866025i 0.472456 + 0.163663i
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i \(-0.0798387\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −1.00000 + 1.73205i −0.174078 + 0.301511i
\(34\) −1.00000 −0.171499
\(35\) −0.500000 2.59808i −0.0845154 0.439155i
\(36\) 1.00000 0.166667
\(37\) −2.00000 + 3.46410i −0.328798 + 0.569495i −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) 0.500000 + 0.866025i 0.0800641 + 0.138675i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 1.00000 0.156174 0.0780869 0.996947i \(-0.475119\pi\)
0.0780869 + 0.996947i \(0.475119\pi\)
\(42\) −2.00000 + 1.73205i −0.308607 + 0.267261i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) 4.00000 + 6.92820i 0.589768 + 1.02151i
\(47\) 4.50000 7.79423i 0.656392 1.13691i −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 4.00000 0.565685
\(51\) 0.500000 0.866025i 0.0700140 0.121268i
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −2.00000 −0.269680
\(56\) 2.00000 1.73205i 0.267261 0.231455i
\(57\) −4.00000 −0.529813
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) −5.50000 9.52628i −0.716039 1.24022i −0.962557 0.271078i \(-0.912620\pi\)
0.246518 0.969138i \(-0.420713\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 3.00000 0.381000
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) 1.00000 0.125000
\(65\) −0.500000 + 0.866025i −0.0620174 + 0.107417i
\(66\) 1.00000 + 1.73205i 0.123091 + 0.213201i
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) −0.500000 + 0.866025i −0.0606339 + 0.105021i
\(69\) −8.00000 −0.963087
\(70\) −2.50000 0.866025i −0.298807 0.103510i
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −3.00000 5.19615i −0.351123 0.608164i 0.635323 0.772246i \(-0.280867\pi\)
−0.986447 + 0.164083i \(0.947534\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) 4.00000 0.458831
\(77\) −5.00000 1.73205i −0.569803 0.197386i
\(78\) 1.00000 0.113228
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0.500000 0.866025i 0.0552158 0.0956365i
\(83\) 9.00000 0.987878 0.493939 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) 0.500000 + 2.59808i 0.0545545 + 0.283473i
\(85\) 1.00000 0.108465
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 1.50000 + 2.59808i 0.160817 + 0.278543i
\(88\) −1.00000 1.73205i −0.106600 0.184637i
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) −1.00000 −0.105409
\(91\) −2.00000 + 1.73205i −0.209657 + 0.181568i
\(92\) 8.00000 0.834058
\(93\) −1.50000 + 2.59808i −0.155543 + 0.269408i
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) −2.00000 3.46410i −0.205196 0.355409i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) −5.50000 4.33013i −0.555584 0.437409i
\(99\) −2.00000 −0.201008
\(100\) 2.00000 3.46410i 0.200000 0.346410i
\(101\) −7.00000 12.1244i −0.696526 1.20642i −0.969664 0.244443i \(-0.921395\pi\)
0.273138 0.961975i \(-0.411939\pi\)
\(102\) −0.500000 0.866025i −0.0495074 0.0857493i
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 2.00000 1.73205i 0.195180 0.169031i
\(106\) 0 0
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) −1.00000 + 1.73205i −0.0953463 + 0.165145i
\(111\) −4.00000 −0.379663
\(112\) −0.500000 2.59808i −0.0472456 0.245495i
\(113\) 15.0000 1.41108 0.705541 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) −2.00000 + 3.46410i −0.187317 + 0.324443i
\(115\) −4.00000 6.92820i −0.373002 0.646058i
\(116\) −1.50000 2.59808i −0.139272 0.241225i
\(117\) −0.500000 + 0.866025i −0.0462250 + 0.0800641i
\(118\) −11.0000 −1.01263
\(119\) 2.50000 + 0.866025i 0.229175 + 0.0793884i
\(120\) 1.00000 0.0912871
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) 0.500000 + 0.866025i 0.0450835 + 0.0780869i
\(124\) 1.50000 2.59808i 0.134704 0.233314i
\(125\) −9.00000 −0.804984
\(126\) −2.50000 0.866025i −0.222718 0.0771517i
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) 0.500000 + 0.866025i 0.0438529 + 0.0759555i
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 2.00000 0.174078
\(133\) −2.00000 10.3923i −0.173422 0.901127i
\(134\) 12.0000 1.03664
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 0.500000 + 0.866025i 0.0428746 + 0.0742611i
\(137\) −10.0000 17.3205i −0.854358 1.47979i −0.877240 0.480053i \(-0.840618\pi\)
0.0228820 0.999738i \(-0.492716\pi\)
\(138\) −4.00000 + 6.92820i −0.340503 + 0.589768i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) −2.00000 + 1.73205i −0.169031 + 0.146385i
\(141\) 9.00000 0.757937
\(142\) 2.00000 3.46410i 0.167836 0.290701i
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −1.50000 + 2.59808i −0.124568 + 0.215758i
\(146\) −6.00000 −0.496564
\(147\) 6.50000 2.59808i 0.536111 0.214286i
\(148\) 4.00000 0.328798
\(149\) 1.00000 1.73205i 0.0819232 0.141895i −0.822153 0.569267i \(-0.807227\pi\)
0.904076 + 0.427372i \(0.140560\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) 2.00000 + 3.46410i 0.162758 + 0.281905i 0.935857 0.352381i \(-0.114628\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 2.00000 3.46410i 0.162221 0.280976i
\(153\) 1.00000 0.0808452
\(154\) −4.00000 + 3.46410i −0.322329 + 0.279145i
\(155\) −3.00000 −0.240966
\(156\) 0.500000 0.866025i 0.0400320 0.0693375i
\(157\) −0.500000 0.866025i −0.0399043 0.0691164i 0.845383 0.534160i \(-0.179372\pi\)
−0.885288 + 0.465044i \(0.846039\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) −4.00000 20.7846i −0.315244 1.63806i
\(162\) −1.00000 −0.0785674
\(163\) −8.00000 + 13.8564i −0.626608 + 1.08532i 0.361619 + 0.932326i \(0.382224\pi\)
−0.988227 + 0.152992i \(0.951109\pi\)
\(164\) −0.500000 0.866025i −0.0390434 0.0676252i
\(165\) −1.00000 1.73205i −0.0778499 0.134840i
\(166\) 4.50000 7.79423i 0.349268 0.604949i
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 2.50000 + 0.866025i 0.192879 + 0.0668153i
\(169\) −12.0000 −0.923077
\(170\) 0.500000 0.866025i 0.0383482 0.0664211i
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) 3.00000 0.227429
\(175\) −10.0000 3.46410i −0.755929 0.261861i
\(176\) −2.00000 −0.150756
\(177\) 5.50000 9.52628i 0.413405 0.716039i
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) 10.5000 + 18.1865i 0.784807 + 1.35933i 0.929114 + 0.369792i \(0.120571\pi\)
−0.144308 + 0.989533i \(0.546095\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 16.0000 1.18927 0.594635 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(182\) 0.500000 + 2.59808i 0.0370625 + 0.192582i
\(183\) 0 0
\(184\) 4.00000 6.92820i 0.294884 0.510754i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) 1.50000 + 2.59808i 0.109985 + 0.190500i
\(187\) 1.00000 1.73205i 0.0731272 0.126660i
\(188\) −9.00000 −0.656392
\(189\) 2.00000 1.73205i 0.145479 0.125988i
\(190\) −4.00000 −0.290191
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i \(0.00142465\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) 4.00000 6.92820i 0.287183 0.497416i
\(195\) −1.00000 −0.0716115
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 1.00000 0.0712470 0.0356235 0.999365i \(-0.488658\pi\)
0.0356235 + 0.999365i \(0.488658\pi\)
\(198\) −1.00000 + 1.73205i −0.0710669 + 0.123091i
\(199\) 2.50000 + 4.33013i 0.177220 + 0.306955i 0.940927 0.338608i \(-0.109956\pi\)
−0.763707 + 0.645563i \(0.776623\pi\)
\(200\) −2.00000 3.46410i −0.141421 0.244949i
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) −14.0000 −0.985037
\(203\) −6.00000 + 5.19615i −0.421117 + 0.364698i
\(204\) −1.00000 −0.0700140
\(205\) −0.500000 + 0.866025i −0.0349215 + 0.0604858i
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) −4.00000 6.92820i −0.278019 0.481543i
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) −8.00000 −0.553372
\(210\) −0.500000 2.59808i −0.0345033 0.179284i
\(211\) 3.00000 0.206529 0.103264 0.994654i \(-0.467071\pi\)
0.103264 + 0.994654i \(0.467071\pi\)
\(212\) 0 0
\(213\) 2.00000 + 3.46410i 0.137038 + 0.237356i
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) 2.00000 3.46410i 0.136399 0.236250i
\(216\) 1.00000 0.0680414
\(217\) −7.50000 2.59808i −0.509133 0.176369i
\(218\) 16.0000 1.08366
\(219\) 3.00000 5.19615i 0.202721 0.351123i
\(220\) 1.00000 + 1.73205i 0.0674200 + 0.116775i
\(221\) −0.500000 0.866025i −0.0336336 0.0582552i
\(222\) −2.00000 + 3.46410i −0.134231 + 0.232495i
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) −2.50000 0.866025i −0.167038 0.0578638i
\(225\) −4.00000 −0.266667
\(226\) 7.50000 12.9904i 0.498893 0.864107i
\(227\) −5.00000 8.66025i −0.331862 0.574801i 0.651015 0.759065i \(-0.274343\pi\)
−0.982877 + 0.184263i \(0.941010\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) 4.50000 7.79423i 0.297368 0.515057i −0.678165 0.734910i \(-0.737224\pi\)
0.975533 + 0.219853i \(0.0705577\pi\)
\(230\) −8.00000 −0.527504
\(231\) −1.00000 5.19615i −0.0657952 0.341882i
\(232\) −3.00000 −0.196960
\(233\) 5.50000 9.52628i 0.360317 0.624087i −0.627696 0.778459i \(-0.716002\pi\)
0.988013 + 0.154371i \(0.0493352\pi\)
\(234\) 0.500000 + 0.866025i 0.0326860 + 0.0566139i
\(235\) 4.50000 + 7.79423i 0.293548 + 0.508439i
\(236\) −5.50000 + 9.52628i −0.358020 + 0.620108i
\(237\) 0 0
\(238\) 2.00000 1.73205i 0.129641 0.112272i
\(239\) 13.0000 0.840900 0.420450 0.907316i \(-0.361872\pi\)
0.420450 + 0.907316i \(0.361872\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) −9.00000 15.5885i −0.579741 1.00414i −0.995509 0.0946700i \(-0.969820\pi\)
0.415768 0.909471i \(-0.363513\pi\)
\(242\) −3.50000 6.06218i −0.224989 0.389692i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 5.50000 + 4.33013i 0.351382 + 0.276642i
\(246\) 1.00000 0.0637577
\(247\) −2.00000 + 3.46410i −0.127257 + 0.220416i
\(248\) −1.50000 2.59808i −0.0952501 0.164978i
\(249\) 4.50000 + 7.79423i 0.285176 + 0.493939i
\(250\) −4.50000 + 7.79423i −0.284605 + 0.492950i
\(251\) 23.0000 1.45175 0.725874 0.687828i \(-0.241436\pi\)
0.725874 + 0.687828i \(0.241436\pi\)
\(252\) −2.00000 + 1.73205i −0.125988 + 0.109109i
\(253\) −16.0000 −1.00591
\(254\) −4.00000 + 6.92820i −0.250982 + 0.434714i
\(255\) 0.500000 + 0.866025i 0.0313112 + 0.0542326i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.00000 + 12.1244i −0.436648 + 0.756297i −0.997429 0.0716680i \(-0.977168\pi\)
0.560781 + 0.827964i \(0.310501\pi\)
\(258\) −4.00000 −0.249029
\(259\) −2.00000 10.3923i −0.124274 0.645746i
\(260\) 1.00000 0.0620174
\(261\) −1.50000 + 2.59808i −0.0928477 + 0.160817i
\(262\) −3.00000 5.19615i −0.185341 0.321019i
\(263\) 4.00000 + 6.92820i 0.246651 + 0.427211i 0.962594 0.270947i \(-0.0873367\pi\)
−0.715944 + 0.698158i \(0.754003\pi\)
\(264\) 1.00000 1.73205i 0.0615457 0.106600i
\(265\) 0 0
\(266\) −10.0000 3.46410i −0.613139 0.212398i
\(267\) 6.00000 0.367194
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) 2.50000 + 4.33013i 0.152428 + 0.264013i 0.932119 0.362151i \(-0.117958\pi\)
−0.779692 + 0.626164i \(0.784624\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −9.00000 + 15.5885i −0.546711 + 0.946931i 0.451786 + 0.892126i \(0.350787\pi\)
−0.998497 + 0.0548050i \(0.982546\pi\)
\(272\) 1.00000 0.0606339
\(273\) −2.50000 0.866025i −0.151307 0.0524142i
\(274\) −20.0000 −1.20824
\(275\) −4.00000 + 6.92820i −0.241209 + 0.417786i
\(276\) 4.00000 + 6.92820i 0.240772 + 0.417029i
\(277\) −14.0000 24.2487i −0.841178 1.45696i −0.888899 0.458103i \(-0.848529\pi\)
0.0477206 0.998861i \(-0.484804\pi\)
\(278\) 0 0
\(279\) −3.00000 −0.179605
\(280\) 0.500000 + 2.59808i 0.0298807 + 0.155265i
\(281\) 20.0000 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) 4.50000 7.79423i 0.267971 0.464140i
\(283\) 6.50000 + 11.2583i 0.386385 + 0.669238i 0.991960 0.126550i \(-0.0403903\pi\)
−0.605575 + 0.795788i \(0.707057\pi\)
\(284\) −2.00000 3.46410i −0.118678 0.205557i
\(285\) 2.00000 3.46410i 0.118470 0.205196i
\(286\) 2.00000 0.118262
\(287\) −2.00000 + 1.73205i −0.118056 + 0.102240i
\(288\) −1.00000 −0.0589256
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 1.50000 + 2.59808i 0.0880830 + 0.152564i
\(291\) 4.00000 + 6.92820i 0.234484 + 0.406138i
\(292\) −3.00000 + 5.19615i −0.175562 + 0.304082i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 1.00000 6.92820i 0.0583212 0.404061i
\(295\) 11.0000 0.640445
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) −1.00000 1.73205i −0.0580259 0.100504i
\(298\) −1.00000 1.73205i −0.0579284 0.100335i
\(299\) −4.00000 + 6.92820i −0.231326 + 0.400668i
\(300\) 4.00000 0.230940
\(301\) 8.00000 6.92820i 0.461112 0.399335i
\(302\) 4.00000 0.230174
\(303\) 7.00000 12.1244i 0.402139 0.696526i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) 0 0
\(306\) 0.500000 0.866025i 0.0285831 0.0495074i
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 1.00000 + 5.19615i 0.0569803 + 0.296078i
\(309\) −14.0000 −0.796432
\(310\) −1.50000 + 2.59808i −0.0851943 + 0.147561i
\(311\) 9.00000 + 15.5885i 0.510343 + 0.883940i 0.999928 + 0.0119847i \(0.00381495\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(312\) −0.500000 0.866025i −0.0283069 0.0490290i
\(313\) −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i \(-0.905929\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 2.50000 + 0.866025i 0.140859 + 0.0487950i
\(316\) 0 0
\(317\) 5.50000 9.52628i 0.308911 0.535049i −0.669214 0.743070i \(-0.733369\pi\)
0.978124 + 0.208021i \(0.0667022\pi\)
\(318\) 0 0
\(319\) 3.00000 + 5.19615i 0.167968 + 0.290929i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 12.0000 0.669775
\(322\) −20.0000 6.92820i −1.11456 0.386094i
\(323\) 4.00000 0.222566
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 2.00000 + 3.46410i 0.110940 + 0.192154i
\(326\) 8.00000 + 13.8564i 0.443079 + 0.767435i
\(327\) −8.00000 + 13.8564i −0.442401 + 0.766261i
\(328\) −1.00000 −0.0552158
\(329\) 4.50000 + 23.3827i 0.248093 + 1.28913i
\(330\) −2.00000 −0.110096
\(331\) 11.0000 19.0526i 0.604615 1.04722i −0.387498 0.921871i \(-0.626660\pi\)
0.992112 0.125353i \(-0.0400062\pi\)
\(332\) −4.50000 7.79423i −0.246970 0.427764i
\(333\) −2.00000 3.46410i −0.109599 0.189832i
\(334\) 1.00000 1.73205i 0.0547176 0.0947736i
\(335\) −12.0000 −0.655630
\(336\) 2.00000 1.73205i 0.109109 0.0944911i
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 7.50000 + 12.9904i 0.407344 + 0.705541i
\(340\) −0.500000 0.866025i −0.0271163 0.0469668i
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) −4.00000 −0.216295
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 4.00000 0.215666
\(345\) 4.00000 6.92820i 0.215353 0.373002i
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) 2.00000 + 3.46410i 0.107366 + 0.185963i 0.914702 0.404128i \(-0.132425\pi\)
−0.807337 + 0.590091i \(0.799092\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) 27.0000 1.44528 0.722638 0.691226i \(-0.242929\pi\)
0.722638 + 0.691226i \(0.242929\pi\)
\(350\) −8.00000 + 6.92820i −0.427618 + 0.370328i
\(351\) −1.00000 −0.0533761
\(352\) −1.00000 + 1.73205i −0.0533002 + 0.0923186i
\(353\) −14.0000 24.2487i −0.745145 1.29063i −0.950127 0.311863i \(-0.899047\pi\)
0.204982 0.978766i \(-0.434286\pi\)
\(354\) −5.50000 9.52628i −0.292322 0.506316i
\(355\) −2.00000 + 3.46410i −0.106149 + 0.183855i
\(356\) −6.00000 −0.317999
\(357\) 0.500000 + 2.59808i 0.0264628 + 0.137505i
\(358\) 21.0000 1.10988
\(359\) −7.50000 + 12.9904i −0.395835 + 0.685606i −0.993207 0.116358i \(-0.962878\pi\)
0.597372 + 0.801964i \(0.296211\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 1.50000 + 2.59808i 0.0789474 + 0.136741i
\(362\) 8.00000 13.8564i 0.420471 0.728277i
\(363\) 7.00000 0.367405
\(364\) 2.50000 + 0.866025i 0.131036 + 0.0453921i
\(365\) 6.00000 0.314054
\(366\) 0 0
\(367\) 16.0000 + 27.7128i 0.835193 + 1.44660i 0.893873 + 0.448320i \(0.147978\pi\)
−0.0586798 + 0.998277i \(0.518689\pi\)
\(368\) −4.00000 6.92820i −0.208514 0.361158i
\(369\) −0.500000 + 0.866025i −0.0260290 + 0.0450835i
\(370\) −4.00000 −0.207950
\(371\) 0 0
\(372\) 3.00000 0.155543
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) −1.00000 1.73205i −0.0517088 0.0895622i
\(375\) −4.50000 7.79423i −0.232379 0.402492i
\(376\) −4.50000 + 7.79423i −0.232070 + 0.401957i
\(377\) 3.00000 0.154508
\(378\) −0.500000 2.59808i −0.0257172 0.133631i
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) −2.00000 + 3.46410i −0.102598 + 0.177705i
\(381\) −4.00000 6.92820i −0.204926 0.354943i
\(382\) 1.50000 + 2.59808i 0.0767467 + 0.132929i
\(383\) −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) 1.00000 0.0510310
\(385\) 4.00000 3.46410i 0.203859 0.176547i
\(386\) 14.0000 0.712581
\(387\) 2.00000 3.46410i 0.101666 0.176090i
\(388\) −4.00000 6.92820i −0.203069 0.351726i
\(389\) 1.00000 + 1.73205i 0.0507020 + 0.0878185i 0.890263 0.455448i \(-0.150521\pi\)
−0.839561 + 0.543266i \(0.817187\pi\)
\(390\) −0.500000 + 0.866025i −0.0253185 + 0.0438529i
\(391\) 8.00000 0.404577
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) 6.00000 0.302660
\(394\) 0.500000 0.866025i 0.0251896 0.0436297i
\(395\) 0 0
\(396\) 1.00000 + 1.73205i 0.0502519 + 0.0870388i
\(397\) 4.00000 6.92820i 0.200754 0.347717i −0.748017 0.663679i \(-0.768994\pi\)
0.948772 + 0.315963i \(0.102327\pi\)
\(398\) 5.00000 0.250627
\(399\) 8.00000 6.92820i 0.400501 0.346844i
\(400\) −4.00000 −0.200000
\(401\) −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 6.00000 + 10.3923i 0.299253 + 0.518321i
\(403\) 1.50000 + 2.59808i 0.0747203 + 0.129419i
\(404\) −7.00000 + 12.1244i −0.348263 + 0.603209i
\(405\) 1.00000 0.0496904
\(406\) 1.50000 + 7.79423i 0.0744438 + 0.386821i
\(407\) −8.00000 −0.396545
\(408\) −0.500000 + 0.866025i −0.0247537 + 0.0428746i
\(409\) −13.0000 22.5167i −0.642809 1.11338i −0.984803 0.173675i \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) 0.500000 + 0.866025i 0.0246932 + 0.0427699i
\(411\) 10.0000 17.3205i 0.493264 0.854358i
\(412\) 14.0000 0.689730
\(413\) 27.5000 + 9.52628i 1.35319 + 0.468758i
\(414\) −8.00000 −0.393179
\(415\) −4.50000 + 7.79423i −0.220896 + 0.382604i
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) 0 0
\(418\) −4.00000 + 6.92820i −0.195646 + 0.338869i
\(419\) 4.00000 0.195413 0.0977064 0.995215i \(-0.468849\pi\)
0.0977064 + 0.995215i \(0.468849\pi\)
\(420\) −2.50000 0.866025i −0.121988 0.0422577i
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 1.50000 2.59808i 0.0730189 0.126472i
\(423\) 4.50000 + 7.79423i 0.218797 + 0.378968i
\(424\) 0 0
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 4.00000 0.193801
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) −1.00000 + 1.73205i −0.0482805 + 0.0836242i
\(430\) −2.00000 3.46410i −0.0964486 0.167054i
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) 19.0000 0.913082 0.456541 0.889702i \(-0.349088\pi\)
0.456541 + 0.889702i \(0.349088\pi\)
\(434\) −6.00000 + 5.19615i −0.288009 + 0.249423i
\(435\) −3.00000 −0.143839
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) −16.0000 27.7128i −0.765384 1.32568i
\(438\) −3.00000 5.19615i −0.143346 0.248282i
\(439\) 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i \(-0.825737\pi\)
0.877711 + 0.479191i \(0.159070\pi\)
\(440\) 2.00000 0.0953463
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) −1.00000 −0.0475651
\(443\) −16.5000 + 28.5788i −0.783939 + 1.35782i 0.145692 + 0.989330i \(0.453459\pi\)
−0.929631 + 0.368492i \(0.879874\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) −8.00000 + 13.8564i −0.378811 + 0.656120i
\(447\) 2.00000 0.0945968
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) −2.00000 + 3.46410i −0.0942809 + 0.163299i
\(451\) 1.00000 + 1.73205i 0.0470882 + 0.0815591i
\(452\) −7.50000 12.9904i −0.352770 0.611016i
\(453\) −2.00000 + 3.46410i −0.0939682 + 0.162758i
\(454\) −10.0000 −0.469323
\(455\) −0.500000 2.59808i −0.0234404 0.121800i
\(456\) 4.00000 0.187317
\(457\) −0.500000 + 0.866025i −0.0233890 + 0.0405110i −0.877483 0.479608i \(-0.840779\pi\)
0.854094 + 0.520119i \(0.174112\pi\)
\(458\) −4.50000 7.79423i −0.210271 0.364200i
\(459\) 0.500000 + 0.866025i 0.0233380 + 0.0404226i
\(460\) −4.00000 + 6.92820i −0.186501 + 0.323029i
\(461\) −20.0000 −0.931493 −0.465746 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) −5.00000 1.73205i −0.232621 0.0805823i
\(463\) −18.0000 −0.836531 −0.418265 0.908325i \(-0.637362\pi\)
−0.418265 + 0.908325i \(0.637362\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) −1.50000 2.59808i −0.0695608 0.120483i
\(466\) −5.50000 9.52628i −0.254783 0.441296i
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) 1.00000 0.0462250
\(469\) −30.0000 10.3923i −1.38527 0.479872i
\(470\) 9.00000 0.415139
\(471\) 0.500000 0.866025i 0.0230388 0.0399043i
\(472\) 5.50000 + 9.52628i 0.253158 + 0.438483i
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 0 0
\(475\) −16.0000 −0.734130
\(476\) −0.500000 2.59808i −0.0229175 0.119083i
\(477\) 0 0
\(478\) 6.50000 11.2583i 0.297303 0.514944i
\(479\) −13.0000 22.5167i −0.593985 1.02881i −0.993689 0.112168i \(-0.964220\pi\)
0.399704 0.916644i \(-0.369113\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) −18.0000 −0.819878
\(483\) 16.0000 13.8564i 0.728025 0.630488i
\(484\) −7.00000 −0.318182
\(485\) −4.00000 + 6.92820i −0.181631 + 0.314594i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 13.5000 + 23.3827i 0.611743 + 1.05957i 0.990947 + 0.134257i \(0.0428648\pi\)
−0.379203 + 0.925313i \(0.623802\pi\)
\(488\) 0 0
\(489\) −16.0000 −0.723545
\(490\) 6.50000 2.59808i 0.293640 0.117369i
\(491\) 28.0000 1.26362 0.631811 0.775122i \(-0.282312\pi\)
0.631811 + 0.775122i \(0.282312\pi\)
\(492\) 0.500000 0.866025i 0.0225417 0.0390434i
\(493\) −1.50000 2.59808i −0.0675566 0.117011i
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) 1.00000 1.73205i 0.0449467 0.0778499i
\(496\) −3.00000 −0.134704
\(497\) −8.00000 + 6.92820i −0.358849 + 0.310772i
\(498\) 9.00000 0.403300
\(499\) −6.50000 + 11.2583i −0.290980 + 0.503992i −0.974042 0.226369i \(-0.927315\pi\)
0.683062 + 0.730361i \(0.260648\pi\)
\(500\) 4.50000 + 7.79423i 0.201246 + 0.348569i
\(501\) 1.00000 + 1.73205i 0.0446767 + 0.0773823i
\(502\) 11.5000 19.9186i 0.513270 0.889010i
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0.500000 + 2.59808i 0.0222718 + 0.115728i
\(505\) 14.0000 0.622992
\(506\) −8.00000 + 13.8564i −0.355643 + 0.615992i
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) 4.00000 + 6.92820i 0.177471 + 0.307389i
\(509\) −14.0000 + 24.2487i −0.620539 + 1.07481i 0.368846 + 0.929490i \(0.379753\pi\)
−0.989385 + 0.145315i \(0.953580\pi\)
\(510\) 1.00000 0.0442807
\(511\) 15.0000 + 5.19615i 0.663561 + 0.229864i
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 3.46410i 0.0883022 0.152944i
\(514\) 7.00000 + 12.1244i 0.308757 + 0.534782i
\(515\) −7.00000 12.1244i −0.308457 0.534263i
\(516\) −2.00000 + 3.46410i −0.0880451 + 0.152499i
\(517\) 18.0000 0.791639
\(518\) −10.0000 3.46410i −0.439375 0.152204i
\(519\) −21.0000 −0.921798
\(520\) 0.500000 0.866025i 0.0219265 0.0379777i
\(521\) −5.00000 8.66025i −0.219054 0.379413i 0.735465 0.677563i \(-0.236964\pi\)
−0.954519 + 0.298150i \(0.903630\pi\)
\(522\) 1.50000 + 2.59808i 0.0656532 + 0.113715i
\(523\) 20.0000 34.6410i 0.874539 1.51475i 0.0172859 0.999851i \(-0.494497\pi\)
0.857253 0.514895i \(-0.172169\pi\)
\(524\) −6.00000 −0.262111
\(525\) −2.00000 10.3923i −0.0872872 0.453557i
\(526\) 8.00000 0.348817
\(527\) 1.50000 2.59808i 0.0653410 0.113174i
\(528\) −1.00000 1.73205i −0.0435194 0.0753778i
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) 0 0
\(531\) 11.0000 0.477359
\(532\) −8.00000 + 6.92820i −0.346844 + 0.300376i
\(533\) 1.00000 0.0433148
\(534\) 3.00000 5.19615i 0.129823 0.224860i
\(535\) 6.00000 + 10.3923i 0.259403 + 0.449299i
\(536\) −6.00000 10.3923i −0.259161 0.448879i
\(537\) −10.5000 + 18.1865i −0.453108 + 0.784807i
\(538\) 5.00000 0.215565
\(539\) 13.0000 5.19615i 0.559950 0.223814i
\(540\) −1.00000 −0.0430331
\(541\) 16.0000 27.7128i 0.687894 1.19147i −0.284624 0.958639i \(-0.591869\pi\)
0.972518 0.232828i \(-0.0747978\pi\)
\(542\) 9.00000 + 15.5885i 0.386583 + 0.669582i
\(543\) 8.00000 + 13.8564i 0.343313 + 0.594635i
\(544\) 0.500000 0.866025i 0.0214373 0.0371305i
\(545\) −16.0000 −0.685365
\(546\) −2.00000 + 1.73205i −0.0855921 + 0.0741249i
\(547\) −41.0000 −1.75303 −0.876517 0.481371i \(-0.840139\pi\)
−0.876517 + 0.481371i \(0.840139\pi\)
\(548\) −10.0000 + 17.3205i −0.427179 + 0.739895i
\(549\) 0 0
\(550\) 4.00000 + 6.92820i 0.170561 + 0.295420i
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 8.00000 0.340503
\(553\) 0 0
\(554\) −28.0000 −1.18961
\(555\) 2.00000 3.46410i 0.0848953 0.147043i
\(556\) 0 0
\(557\) −8.00000 13.8564i −0.338971 0.587115i 0.645269 0.763956i \(-0.276745\pi\)
−0.984239 + 0.176841i \(0.943412\pi\)
\(558\) −1.50000 + 2.59808i −0.0635001 + 0.109985i
\(559\) −4.00000 −0.169182
\(560\) 2.50000 + 0.866025i 0.105644 + 0.0365963i
\(561\) 2.00000 0.0844401
\(562\) 10.0000 17.3205i 0.421825 0.730622i
\(563\) −6.00000 10.3923i −0.252870 0.437983i 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) −4.50000 7.79423i −0.189484 0.328196i
\(565\) −7.50000 + 12.9904i −0.315527 + 0.546509i
\(566\) 13.0000 0.546431
\(567\) 2.50000 + 0.866025i 0.104990 + 0.0363696i
\(568\) −4.00000 −0.167836
\(569\) 1.00000 1.73205i 0.0419222 0.0726113i −0.844303 0.535866i \(-0.819985\pi\)
0.886225 + 0.463255i \(0.153319\pi\)
\(570\) −2.00000 3.46410i −0.0837708 0.145095i
\(571\) 6.00000 + 10.3923i 0.251092 + 0.434904i 0.963827 0.266529i \(-0.0858769\pi\)
−0.712735 + 0.701434i \(0.752544\pi\)
\(572\) 1.00000 1.73205i 0.0418121 0.0724207i
\(573\) −3.00000 −0.125327
\(574\) 0.500000 + 2.59808i 0.0208696 + 0.108442i
\(575\) −32.0000 −1.33449
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 7.50000 + 12.9904i 0.312229 + 0.540797i 0.978845 0.204605i \(-0.0655910\pi\)
−0.666616 + 0.745402i \(0.732258\pi\)
\(578\) 0.500000 + 0.866025i 0.0207973 + 0.0360219i
\(579\) −7.00000 + 12.1244i −0.290910 + 0.503871i
\(580\) 3.00000 0.124568
\(581\) −18.0000 + 15.5885i −0.746766 + 0.646718i
\(582\) 8.00000 0.331611
\(583\) 0 0
\(584\) 3.00000 + 5.19615i 0.124141 + 0.215018i
\(585\) −0.500000 0.866025i −0.0206725 0.0358057i
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) −5.50000 4.33013i −0.226816 0.178571i
\(589\) −12.0000 −0.494451
\(590\) 5.50000 9.52628i 0.226431 0.392191i
\(591\) 0.500000 + 0.866025i 0.0205673 + 0.0356235i
\(592\) −2.00000 3.46410i −0.0821995 0.142374i
\(593\) −11.0000 + 19.0526i −0.451716 + 0.782395i −0.998493 0.0548835i \(-0.982521\pi\)
0.546777 + 0.837278i \(0.315855\pi\)
\(594\) −2.00000 −0.0820610
\(595\) −2.00000 + 1.73205i −0.0819920 + 0.0710072i
\(596\) −2.00000 −0.0819232
\(597\) −2.50000 + 4.33013i −0.102318 + 0.177220i
\(598\) 4.00000 + 6.92820i 0.163572 + 0.283315i
\(599\) −5.50000 9.52628i −0.224724 0.389233i 0.731513 0.681828i \(-0.238815\pi\)
−0.956237 + 0.292595i \(0.905481\pi\)
\(600\) 2.00000 3.46410i 0.0816497 0.141421i
\(601\) −14.0000 −0.571072 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(602\) −2.00000 10.3923i −0.0815139 0.423559i
\(603\) −12.0000 −0.488678
\(604\) 2.00000 3.46410i 0.0813788 0.140952i
\(605\) 3.50000 + 6.06218i 0.142295 + 0.246463i
\(606\) −7.00000 12.1244i −0.284356 0.492518i
\(607\) −0.500000 + 0.866025i −0.0202944 + 0.0351509i −0.875994 0.482322i \(-0.839794\pi\)
0.855700 + 0.517472i \(0.173127\pi\)
\(608\) −4.00000 −0.162221
\(609\) −7.50000 2.59808i −0.303915 0.105279i
\(610\) 0 0
\(611\) 4.50000 7.79423i 0.182051 0.315321i
\(612\) −0.500000 0.866025i −0.0202113 0.0350070i
\(613\) 13.0000 + 22.5167i 0.525065 + 0.909439i 0.999574 + 0.0291886i \(0.00929235\pi\)
−0.474509 + 0.880251i \(0.657374\pi\)
\(614\) 10.0000 17.3205i 0.403567 0.698999i
\(615\) −1.00000 −0.0403239
\(616\) 5.00000 + 1.73205i 0.201456 + 0.0697863i
\(617\) 17.0000 0.684394 0.342197 0.939628i \(-0.388829\pi\)
0.342197 + 0.939628i \(0.388829\pi\)
\(618\) −7.00000 + 12.1244i −0.281581 + 0.487713i
\(619\) −14.0000 24.2487i −0.562708 0.974638i −0.997259 0.0739910i \(-0.976426\pi\)
0.434551 0.900647i \(-0.356907\pi\)
\(620\) 1.50000 + 2.59808i 0.0602414 + 0.104341i
\(621\) 4.00000 6.92820i 0.160514 0.278019i
\(622\) 18.0000 0.721734
\(623\) 3.00000 + 15.5885i 0.120192 + 0.624538i
\(624\) −1.00000 −0.0400320
\(625\) −5.50000 + 9.52628i −0.220000 + 0.381051i
\(626\) 4.00000 + 6.92820i 0.159872 + 0.276907i
\(627\) −4.00000 6.92820i −0.159745 0.276686i
\(628\) −0.500000 + 0.866025i −0.0199522 + 0.0345582i
\(629\) 4.00000 0.159490
\(630\) 2.00000 1.73205i 0.0796819 0.0690066i
\(631\) −38.0000 −1.51276 −0.756378 0.654135i \(-0.773033\pi\)
−0.756378 + 0.654135i \(0.773033\pi\)
\(632\) 0 0
\(633\) 1.50000 + 2.59808i 0.0596196 + 0.103264i
\(634\) −5.50000 9.52628i −0.218433 0.378337i
\(635\) 4.00000 6.92820i 0.158735 0.274937i
\(636\) 0 0
\(637\) 1.00000 6.92820i 0.0396214 0.274505i
\(638\) 6.00000 0.237542
\(639\) −2.00000 + 3.46410i −0.0791188 + 0.137038i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 6.00000 10.3923i 0.236801 0.410152i
\(643\) 45.0000 1.77463 0.887313 0.461167i \(-0.152569\pi\)
0.887313 + 0.461167i \(0.152569\pi\)
\(644\) −16.0000 + 13.8564i −0.630488 + 0.546019i
\(645\) 4.00000 0.157500
\(646\) 2.00000 3.46410i 0.0786889 0.136293i
\(647\) −16.5000 28.5788i −0.648682 1.12355i −0.983438 0.181245i \(-0.941987\pi\)
0.334756 0.942305i \(-0.391346\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 11.0000 19.0526i 0.431788 0.747878i
\(650\) 4.00000 0.156893
\(651\) −1.50000 7.79423i −0.0587896 0.305480i
\(652\) 16.0000 0.626608
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 8.00000 + 13.8564i 0.312825 + 0.541828i
\(655\) 3.00000 + 5.19615i 0.117220 + 0.203030i
\(656\) −0.500000 + 0.866025i −0.0195217 + 0.0338126i
\(657\) 6.00000 0.234082
\(658\) 22.5000 + 7.79423i 0.877141 + 0.303851i
\(659\) 39.0000 1.51922 0.759612 0.650376i \(-0.225389\pi\)
0.759612 + 0.650376i \(0.225389\pi\)
\(660\) −1.00000 + 1.73205i −0.0389249 + 0.0674200i
\(661\) −23.5000 40.7032i −0.914044 1.58317i −0.808295 0.588778i \(-0.799609\pi\)
−0.105749 0.994393i \(-0.533724\pi\)
\(662\) −11.0000 19.0526i −0.427527 0.740499i
\(663\) 0.500000 0.866025i 0.0194184 0.0336336i
\(664\) −9.00000 −0.349268
\(665\) 10.0000 + 3.46410i 0.387783 + 0.134332i
\(666\) −4.00000 −0.154997
\(667\) −12.0000 + 20.7846i −0.464642 + 0.804783i
\(668\) −1.00000 1.73205i −0.0386912 0.0670151i
\(669\) −8.00000 13.8564i −0.309298 0.535720i
\(670\) −6.00000 + 10.3923i −0.231800 + 0.401490i
\(671\) 0 0
\(672\) −0.500000 2.59808i −0.0192879 0.100223i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 17.0000 29.4449i 0.654816 1.13417i
\(675\) −2.00000 3.46410i −0.0769800 0.133333i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −3.00000 + 5.19615i −0.115299 + 0.199704i −0.917899 0.396813i \(-0.870116\pi\)
0.802600 + 0.596518i \(0.203449\pi\)
\(678\) 15.0000 0.576072
\(679\) −16.0000 + 13.8564i −0.614024 + 0.531760i
\(680\) −1.00000 −0.0383482
\(681\) 5.00000 8.66025i 0.191600 0.331862i
\(682\) 3.00000 + 5.19615i 0.114876 + 0.198971i
\(683\) 2.00000 + 3.46410i 0.0765279 + 0.132550i 0.901750 0.432259i \(-0.142283\pi\)
−0.825222 + 0.564809i \(0.808950\pi\)
\(684\) −2.00000 + 3.46410i −0.0764719 + 0.132453i
\(685\) 20.0000 0.764161
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 9.00000 0.343371
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 0 0
\(690\) −4.00000 6.92820i −0.152277 0.263752i
\(691\) 23.5000 40.7032i 0.893982 1.54842i 0.0589228 0.998263i \(-0.481233\pi\)
0.835059 0.550160i \(-0.185433\pi\)
\(692\) 21.0000 0.798300
\(693\) 4.00000 3.46410i 0.151947 0.131590i
\(694\) 4.00000 0.151838
\(695\) 0 0
\(696\) −1.50000 2.59808i −0.0568574 0.0984798i
\(697\) −0.500000 0.866025i −0.0189389 0.0328031i
\(698\) 13.5000 23.3827i 0.510983 0.885048i
\(699\) 11.0000 0.416058
\(700\) 2.00000 + 10.3923i 0.0755929 + 0.392792i
\(701\) 20.0000 0.755390 0.377695 0.925930i \(-0.376717\pi\)
0.377695 + 0.925930i \(0.376717\pi\)
\(702\) −0.500000 + 0.866025i −0.0188713 + 0.0326860i
\(703\) −8.00000 13.8564i −0.301726 0.522604i
\(704\) 1.00000 + 1.73205i 0.0376889 + 0.0652791i
\(705\) −4.50000 + 7.79423i −0.169480 + 0.293548i
\(706\) −28.0000 −1.05379
\(707\) 35.0000 + 12.1244i 1.31631 + 0.455983i
\(708\) −11.0000 −0.413405
\(709\) 21.0000 36.3731i 0.788672 1.36602i −0.138109 0.990417i \(-0.544103\pi\)
0.926781 0.375602i \(-0.122564\pi\)
\(710\) 2.00000 + 3.46410i 0.0750587 + 0.130005i
\(711\) 0 0
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) −24.0000 −0.898807
\(714\) 2.50000 + 0.866025i 0.0935601 + 0.0324102i
\(715\) −2.00000 −0.0747958
\(716\) 10.5000 18.1865i 0.392403 0.679663i
\(717\) 6.50000 + 11.2583i 0.242747 + 0.420450i
\(718\) 7.50000 + 12.9904i 0.279898 + 0.484797i
\(719\) 25.0000 43.3013i 0.932343 1.61486i 0.153037 0.988220i \(-0.451094\pi\)
0.779305 0.626644i \(-0.215572\pi\)
\(720\) 1.00000 0.0372678
\(721\) −7.00000 36.3731i −0.260694 1.35460i
\(722\) 3.00000 0.111648
\(723\) 9.00000 15.5885i 0.334714 0.579741i
\(724\) −8.00000 13.8564i −0.297318 0.514969i
\(725\) 6.00000 + 10.3923i 0.222834 + 0.385961i
\(726\) 3.50000 6.06218i 0.129897 0.224989i
\(727\) 26.0000 0.964287 0.482143 0.876092i \(-0.339858\pi\)
0.482143 + 0.876092i \(0.339858\pi\)
\(728\) 2.00000 1.73205i 0.0741249 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 2.00000 + 3.46410i 0.0739727 + 0.128124i
\(732\) 0 0
\(733\) −11.0000 + 19.0526i −0.406294 + 0.703722i −0.994471 0.105010i \(-0.966513\pi\)
0.588177 + 0.808732i \(0.299846\pi\)
\(734\) 32.0000 1.18114
\(735\) −1.00000 + 6.92820i −0.0368856 + 0.255551i
\(736\) −8.00000 −0.294884
\(737\) −12.0000 + 20.7846i −0.442026 + 0.765611i
\(738\) 0.500000 + 0.866025i 0.0184053 + 0.0318788i
\(739\) −21.0000 36.3731i −0.772497 1.33800i −0.936190 0.351494i \(-0.885674\pi\)
0.163693 0.986511i \(-0.447659\pi\)
\(740\) −2.00000 + 3.46410i −0.0735215 + 0.127343i
\(741\) −4.00000 −0.146944
\(742\) 0 0
\(743\) −16.0000 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(744\) 1.50000 2.59808i 0.0549927 0.0952501i
\(745\) 1.00000 + 1.73205i 0.0366372 + 0.0634574i
\(746\) 9.50000 + 16.4545i 0.347820 + 0.602441i
\(747\) −4.50000 + 7.79423i −0.164646 + 0.285176i
\(748\) −2.00000 −0.0731272
\(749\) 6.00000 + 31.1769i 0.219235 + 1.13918i
\(750\) −9.00000 −0.328634
\(751\) 13.5000 23.3827i 0.492622 0.853246i −0.507342 0.861745i \(-0.669372\pi\)
0.999964 + 0.00849853i \(0.00270520\pi\)
\(752\) 4.50000 + 7.79423i 0.164098 + 0.284226i
\(753\) 11.5000 + 19.9186i 0.419083 + 0.725874i
\(754\) 1.50000 2.59808i 0.0546268 0.0946164i
\(755\) −4.00000 −0.145575
\(756\) −2.50000 0.866025i −0.0909241 0.0314970i
\(757\) 27.0000 0.981332 0.490666 0.871348i \(-0.336754\pi\)
0.490666 + 0.871348i \(0.336754\pi\)
\(758\) 4.00000 6.92820i 0.145287 0.251644i
\(759\) −8.00000 13.8564i −0.290382 0.502956i
\(760\) 2.00000 + 3.46410i 0.0725476 + 0.125656i
\(761\) 18.0000 31.1769i 0.652499 1.13016i −0.330015 0.943976i \(-0.607054\pi\)
0.982514 0.186187i \(-0.0596129\pi\)
\(762\) −8.00000 −0.289809
\(763\) −40.0000 13.8564i −1.44810 0.501636i
\(764\) 3.00000 0.108536
\(765\) −0.500000 + 0.866025i −0.0180775 + 0.0313112i
\(766\) 12.0000 + 20.7846i 0.433578 + 0.750978i
\(767\) −5.50000 9.52628i −0.198593 0.343974i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) −46.0000 −1.65880 −0.829401 0.558653i \(-0.811318\pi\)
−0.829401 + 0.558653i \(0.811318\pi\)
\(770\) −1.00000 5.19615i −0.0360375 0.187256i
\(771\) −14.0000 −0.504198
\(772\) 7.00000 12.1244i 0.251936 0.436365i
\(773\) −23.0000 39.8372i −0.827253 1.43284i −0.900186 0.435507i \(-0.856569\pi\)
0.0729331 0.997337i \(-0.476764\pi\)
\(774\) −2.00000 3.46410i −0.0718885 0.124515i
\(775\) −6.00000 + 10.3923i −0.215526 + 0.373303i
\(776\) −8.00000 −0.287183
\(777\) 8.00000 6.92820i 0.286998 0.248548i
\(778\) 2.00000 0.0717035