Properties

Label 714.2.i.i.613.1
Level $714$
Weight $2$
Character 714.613
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 613.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 714.613
Dual form 714.2.i.i.205.1

$q$-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 \(\left(\mathbb{Z}/714\mathbb{Z}\right)^\times\).

\(n\) \(239\) \(409\) \(547\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 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 −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 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 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 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 −0.894795 0.446476i \(-0.852679\pi\)
0.0607377 0.998154i \(-0.480655\pi\)
\(24\) −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 −0.699301 0.714827i \(-0.746505\pi\)
0.968709 + 0.248199i \(0.0798387\pi\)
\(32\) 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 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) 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 0.981543 + 0.191243i \(0.0612518\pi\)
−0.325150 + 0.945662i \(0.605415\pi\)
\(48\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(54\) −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 0.246518 + 0.969138i \(0.420713\pi\)
−0.962557 + 0.271078i \(0.912620\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 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 −0.222571 0.974916i \(-0.571445\pi\)
0.955588 0.294706i \(-0.0952216\pi\)
\(68\) −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 −0.986447 0.164083i \(-0.947534\pi\)
0.635323 + 0.772246i \(0.280867\pi\)
\(74\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) −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 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) −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 0.273138 + 0.961975i \(0.411939\pi\)
−0.969664 + 0.244443i \(0.921395\pi\)
\(102\) −0.500000 + 0.866025i −0.0495074 + 0.0857493i
\(103\) −7.00000 12.1244i −0.689730 1.19465i −0.971925 0.235291i \(-0.924396\pi\)
0.282194 0.959357i \(-0.408938\pi\)
\(104\) −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 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 8.00000 13.8564i 0.766261 1.32720i −0.173316 0.984866i \(-0.555448\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(110\) −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 0.966803 0.255524i \(-0.0822479\pi\)
−0.704692 + 0.709514i \(0.748915\pi\)
\(132\) 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 0.0228820 + 0.999738i \(0.492716\pi\)
−0.877240 + 0.480053i \(0.840618\pi\)
\(138\) −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 0.904076 0.427372i \(-0.140560\pi\)
−0.822153 + 0.569267i \(0.807227\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) 2.00000 3.46410i 0.162758 0.281905i −0.773099 0.634285i \(-0.781294\pi\)
0.935857 + 0.352381i \(0.114628\pi\)
\(152\) 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 −0.885288 0.465044i \(-0.846039\pi\)
0.845383 + 0.534160i \(0.179372\pi\)
\(158\) 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 −0.988227 0.152992i \(-0.951109\pi\)
0.361619 0.932326i \(-0.382224\pi\)
\(164\) −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 −0.920722 0.390218i \(-0.872399\pi\)
0.122422 0.992478i \(-0.460934\pi\)
\(174\) 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 −0.144308 0.989533i \(-0.546095\pi\)
0.929114 0.369792i \(-0.120571\pi\)
\(180\) −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 0.806641 0.591041i \(-0.201283\pi\)
−0.915177 + 0.403051i \(0.867950\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i \(-0.665242\pi\)
0.999990 0.00447566i \(-0.00142465\pi\)
\(194\) 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 −0.763707 0.645563i \(-0.776623\pi\)
0.940927 + 0.338608i \(0.109956\pi\)
\(200\) −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 −0.982877 0.184263i \(-0.941010\pi\)
0.651015 + 0.759065i \(0.274343\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) 4.50000 + 7.79423i 0.297368 + 0.515057i 0.975533 0.219853i \(-0.0705577\pi\)
−0.678165 + 0.734910i \(0.737224\pi\)
\(230\) −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 0.988013 0.154371i \(-0.0493352\pi\)
−0.627696 + 0.778459i \(0.716002\pi\)
\(234\) 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 0.415768 + 0.909471i \(0.363513\pi\)
−0.995509 + 0.0946700i \(0.969820\pi\)
\(242\) −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 0.560781 0.827964i \(-0.310501\pi\)
−0.997429 + 0.0716680i \(0.977168\pi\)
\(258\) −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 −0.715944 0.698158i \(-0.754003\pi\)
0.962594 + 0.270947i \(0.0873367\pi\)
\(264\) 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 −0.779692 0.626164i \(-0.784624\pi\)
0.932119 + 0.362151i \(0.117958\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −9.00000 15.5885i −0.546711 0.946931i −0.998497 0.0548050i \(-0.982546\pi\)
0.451786 0.892126i \(-0.350787\pi\)
\(272\) 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 0.0477206 + 0.998861i \(0.484804\pi\)
−0.888899 + 0.458103i \(0.848529\pi\)
\(278\) 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 −0.605575 0.795788i \(-0.707057\pi\)
0.991960 + 0.126550i \(0.0403903\pi\)
\(284\) −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 −0.489585 0.871956i \(-0.662852\pi\)
0.999928 0.0119847i \(-0.00381495\pi\)
\(312\) −0.500000 + 0.866025i −0.0283069 + 0.0490290i
\(313\) −4.00000 6.92820i −0.226093 0.391605i 0.730554 0.682855i \(-0.239262\pi\)
−0.956647 + 0.291250i \(0.905929\pi\)
\(314\) −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 0.978124 0.208021i \(-0.0667022\pi\)
−0.669214 + 0.743070i \(0.733369\pi\)
\(318\) 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 0.992112 + 0.125353i \(0.0400062\pi\)
−0.387498 + 0.921871i \(0.626660\pi\)
\(332\) −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 −0.807337 0.590091i \(-0.799092\pi\)
0.914702 + 0.404128i \(0.132425\pi\)
\(348\) 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 0.204982 + 0.978766i \(0.434286\pi\)
−0.950127 + 0.311863i \(0.899047\pi\)
\(354\) −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 0.597372 0.801964i \(-0.296211\pi\)
−0.993207 + 0.116358i \(0.962878\pi\)
\(360\) 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 −0.0586798 0.998277i \(-0.518689\pi\)
0.893873 0.448320i \(-0.147978\pi\)
\(368\) −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 0.508065 0.861319i \(-0.330361\pi\)
−0.999956 + 0.00933789i \(0.997028\pi\)
\(374\) −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 −0.990702 0.136047i \(-0.956560\pi\)
0.377531 0.925997i \(-0.376773\pi\)
\(384\) 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 −0.839561 0.543266i \(-0.817187\pi\)
0.890263 + 0.455448i \(0.150521\pi\)
\(390\) −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 0.948772 0.315963i \(-0.102327\pi\)
−0.748017 + 0.663679i \(0.768994\pi\)
\(398\) 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 −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 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 0.341994 + 0.939702i \(0.388898\pi\)
−0.984803 + 0.173675i \(0.944436\pi\)
\(410\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 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 0.877711 0.479191i \(-0.159070\pi\)
−0.853847 + 0.520524i \(0.825737\pi\)
\(440\) 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 −0.929631 0.368492i \(-0.879874\pi\)
0.145692 0.989330i \(-0.453459\pi\)
\(444\) 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 0.854094 0.520119i \(-0.174112\pi\)
−0.877483 + 0.479608i \(0.840779\pi\)
\(458\) −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 0.898642 0.438682i \(-0.144554\pi\)
−0.829231 + 0.558906i \(0.811221\pi\)
\(468\) 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 0.399704 + 0.916644i \(0.369113\pi\)
−0.993689 + 0.112168i \(0.964220\pi\)
\(480\) −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 −0.379203 0.925313i \(-0.623802\pi\)
0.990947 0.134257i \(-0.0428648\pi\)
\(488\) 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 0.683062 0.730361i \(-0.260648\pi\)
−0.974042 + 0.226369i \(0.927315\pi\)
\(500\) 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 −0.989385 0.145315i \(-0.953580\pi\)
0.368846 0.929490i \(-0.379753\pi\)
\(510\) 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 −0.954519 0.298150i \(-0.903630\pi\)
0.735465 + 0.677563i \(0.236964\pi\)
\(522\) 1.50000 2.59808i 0.0656532 0.113715i
\(523\) 20.0000 + 34.6410i 0.874539 + 1.51475i 0.857253 + 0.514895i \(0.172169\pi\)
0.0172859 + 0.999851i \(0.494497\pi\)
\(524\) −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 0.972518 + 0.232828i \(0.0747978\pi\)
−0.284624 + 0.958639i \(0.591869\pi\)
\(542\) 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 −0.984239 0.176841i \(-0.943412\pi\)
0.645269 + 0.763956i \(0.276745\pi\)
\(558\) −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 −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) −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 0.886225 0.463255i \(-0.153319\pi\)
−0.844303 + 0.535866i \(0.819985\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) 6.00000 10.3923i 0.251092 0.434904i −0.712735 0.701434i \(-0.752544\pi\)
0.963827 + 0.266529i \(0.0858769\pi\)
\(572\) 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 −0.666616 0.745402i \(-0.732258\pi\)
0.978845 + 0.204605i \(0.0655910\pi\)
\(578\) 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 0.546777 0.837278i \(-0.315855\pi\)
−0.998493 + 0.0548835i \(0.982521\pi\)
\(594\) −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 −0.956237 0.292595i \(-0.905481\pi\)
0.731513 + 0.681828i \(0.238815\pi\)
\(600\) 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 0.855700 0.517472i \(-0.173127\pi\)
−0.875994 + 0.482322i \(0.839794\pi\)
\(608\) −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 −0.474509 0.880251i \(-0.657374\pi\)
0.999574 0.0291886i \(-0.00929235\pi\)
\(614\) 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 0.434551 + 0.900647i \(0.356907\pi\)
−0.997259 + 0.0739910i \(0.976426\pi\)
\(620\) 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 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) 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 0.334756 + 0.942305i \(0.391346\pi\)
−0.983438 + 0.181245i \(0.941987\pi\)
\(648\) 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 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 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 −0.105749 + 0.994393i \(0.533724\pi\)
−0.808295 + 0.588778i \(0.799609\pi\)
\(662\) −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 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 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 −0.825222 0.564809i \(-0.808950\pi\)
0.901750 + 0.432259i \(0.142283\pi\)
\(684\) −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 0.835059 + 0.550160i \(0.185433\pi\)
0.0589228 + 0.998263i \(0.481233\pi\)
\(692\) 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 0.926781 + 0.375602i \(0.122564\pi\)
−0.138109 + 0.990417i \(0.544103\pi\)
\(710\) 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 0.779305 + 0.626644i \(0.215572\pi\)
0.153037 + 0.988220i \(0.451094\pi\)
\(720\) 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 0.588177 0.808732i \(-0.299846\pi\)
−0.994471 + 0.105010i \(0.966513\pi\)
\(734\) 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 0.163693 + 0.986511i \(0.447659\pi\)
−0.936190 + 0.351494i \(0.885674\pi\)
\(740\) −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 0.999964 0.00849853i \(-0.00270520\pi\)
−0.507342 + 0.861745i \(0.669372\pi\)
\(752\) 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 0.982514 + 0.186187i \(0.0596129\pi\)
−0.330015 + 0.943976i \(0.607054\pi\)
\(762\) −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 0.0729331 + 0.997337i \(0.476764\pi\)
−0.900186 + 0.435507i \(0.856569\pi\)
\(774\) −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