Properties

Label 966.2.i.c.277.1
Level $966$
Weight $2$
Character 966.277
Analytic conductor $7.714$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 966.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.71354883526\)
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 277.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 966.277
Dual form 966.2.i.c.415.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(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} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.50000 - 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +2.00000 q^{13} +(-2.00000 + 1.73205i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.00000 + 1.73205i) q^{19} +1.00000 q^{20} +(-2.50000 - 0.866025i) q^{21} -3.00000 q^{22} +(-0.500000 - 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(2.50000 + 0.866025i) q^{28} -7.00000 q^{29} +(0.500000 + 0.866025i) q^{30} +(-3.50000 + 6.06218i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} -2.00000 q^{34} +(-2.00000 + 1.73205i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(1.00000 - 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -2.00000 q^{41} +(0.500000 + 2.59808i) q^{42} -6.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-3.00000 - 5.19615i) q^{47} -1.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} -4.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(4.50000 - 7.79423i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +2.00000 q^{57} +(3.50000 + 6.06218i) q^{58} +(4.50000 - 7.79423i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-3.00000 - 5.19615i) q^{61} +7.00000 q^{62} +(-2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(-1.50000 + 2.59808i) q^{66} +(-5.00000 + 8.66025i) q^{67} +(1.00000 + 1.73205i) q^{68} -1.00000 q^{69} +(2.50000 + 0.866025i) q^{70} -8.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(5.00000 - 8.66025i) q^{73} +(1.00000 - 1.73205i) q^{74} +(-2.00000 - 3.46410i) q^{75} -2.00000 q^{76} +(-7.50000 - 2.59808i) q^{77} -2.00000 q^{78} +(7.50000 + 12.9904i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} +1.00000 q^{83} +(2.00000 - 1.73205i) q^{84} -2.00000 q^{85} +(3.00000 + 5.19615i) q^{86} +(-3.50000 + 6.06218i) q^{87} +(1.50000 - 2.59808i) q^{88} +1.00000 q^{90} +(-1.00000 - 5.19615i) q^{91} +1.00000 q^{92} +(3.50000 + 6.06218i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(1.00000 - 1.73205i) q^{95} +(0.500000 + 0.866025i) q^{96} +5.00000 q^{97} +(5.50000 + 4.33013i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q - q^{2} + q^{3} - q^{4} - q^{5} - 2 q^{6} - q^{7} + 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + q^{12} + 4 q^{13} - 4 q^{14} - 2 q^{15} - q^{16} + 2 q^{17} - q^{18} + 2 q^{19} + 2 q^{20} - 5 q^{21} - 6 q^{22} - q^{23} + q^{24} + 4 q^{25} - 2 q^{26} - 2 q^{27} + 5 q^{28} - 14 q^{29} + q^{30} - 7 q^{31} - q^{32} - 3 q^{33} - 4 q^{34} - 4 q^{35} + 2 q^{36} + 2 q^{37} + 2 q^{38} + 2 q^{39} - q^{40} - 4 q^{41} + q^{42} - 12 q^{43} + 3 q^{44} - q^{45} - q^{46} - 6 q^{47} - 2 q^{48} - 13 q^{49} - 8 q^{50} - 2 q^{51} - 2 q^{52} + 9 q^{53} + q^{54} - 6 q^{55} - q^{56} + 4 q^{57} + 7 q^{58} + 9 q^{59} + q^{60} - 6 q^{61} + 14 q^{62} - 4 q^{63} + 2 q^{64} - 2 q^{65} - 3 q^{66} - 10 q^{67} + 2 q^{68} - 2 q^{69} + 5 q^{70} - 16 q^{71} - q^{72} + 10 q^{73} + 2 q^{74} - 4 q^{75} - 4 q^{76} - 15 q^{77} - 4 q^{78} + 15 q^{79} - q^{80} - q^{81} + 2 q^{82} + 2 q^{83} + 4 q^{84} - 4 q^{85} + 6 q^{86} - 7 q^{87} + 3 q^{88} + 2 q^{90} - 2 q^{91} + 2 q^{92} + 7 q^{93} - 6 q^{94} + 2 q^{95} + q^{96} + 10 q^{97} + 11 q^{98} - 6 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(829\) \(925\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −2.00000 + 1.73205i −0.534522 + 0.462910i
\(15\) −1.00000 −0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) −0.500000 + 0.866025i −0.117851 + 0.204124i
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 1.00000 0.223607
\(21\) −2.50000 0.866025i −0.545545 0.188982i
\(22\) −3.00000 −0.639602
\(23\) −0.500000 0.866025i −0.104257 0.180579i
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) −1.00000 −0.192450
\(28\) 2.50000 + 0.866025i 0.472456 + 0.163663i
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) 0.500000 + 0.866025i 0.0912871 + 0.158114i
\(31\) −3.50000 + 6.06218i −0.628619 + 1.08880i 0.359211 + 0.933257i \(0.383046\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) −2.00000 −0.342997
\(35\) −2.00000 + 1.73205i −0.338062 + 0.292770i
\(36\) 1.00000 0.166667
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) 1.00000 1.73205i 0.160128 0.277350i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0.500000 + 2.59808i 0.0771517 + 0.400892i
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) −3.00000 5.19615i −0.437595 0.757937i 0.559908 0.828554i \(-0.310836\pi\)
−0.997503 + 0.0706177i \(0.977503\pi\)
\(48\) −1.00000 −0.144338
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) −4.00000 −0.565685
\(51\) −1.00000 1.73205i −0.140028 0.242536i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i \(-0.621227\pi\)
0.989828 0.142269i \(-0.0454398\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −3.00000 −0.404520
\(56\) −0.500000 2.59808i −0.0668153 0.347183i
\(57\) 2.00000 0.264906
\(58\) 3.50000 + 6.06218i 0.459573 + 0.796003i
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 7.00000 0.889001
\(63\) −2.00000 + 1.73205i −0.251976 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) −1.00000 1.73205i −0.124035 0.214834i
\(66\) −1.50000 + 2.59808i −0.184637 + 0.319801i
\(67\) −5.00000 + 8.66025i −0.610847 + 1.05802i 0.380251 + 0.924883i \(0.375838\pi\)
−0.991098 + 0.133135i \(0.957496\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) −1.00000 −0.120386
\(70\) 2.50000 + 0.866025i 0.298807 + 0.103510i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i \(-0.634347\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) −2.00000 −0.229416
\(77\) −7.50000 2.59808i −0.854704 0.296078i
\(78\) −2.00000 −0.226455
\(79\) 7.50000 + 12.9904i 0.843816 + 1.46153i 0.886646 + 0.462450i \(0.153029\pi\)
−0.0428296 + 0.999082i \(0.513637\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.00000 + 1.73205i 0.110432 + 0.191273i
\(83\) 1.00000 0.109764 0.0548821 0.998493i \(-0.482522\pi\)
0.0548821 + 0.998493i \(0.482522\pi\)
\(84\) 2.00000 1.73205i 0.218218 0.188982i
\(85\) −2.00000 −0.216930
\(86\) 3.00000 + 5.19615i 0.323498 + 0.560316i
\(87\) −3.50000 + 6.06218i −0.375239 + 0.649934i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 1.00000 0.105409
\(91\) −1.00000 5.19615i −0.104828 0.544705i
\(92\) 1.00000 0.104257
\(93\) 3.50000 + 6.06218i 0.362933 + 0.628619i
\(94\) −3.00000 + 5.19615i −0.309426 + 0.535942i
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) −3.00000 −0.301511
\(100\) 2.00000 + 3.46410i 0.200000 + 0.346410i
\(101\) 5.00000 8.66025i 0.497519 0.861727i −0.502477 0.864590i \(-0.667578\pi\)
0.999996 + 0.00286291i \(0.000911295\pi\)
\(102\) −1.00000 + 1.73205i −0.0990148 + 0.171499i
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) 2.00000 0.196116
\(105\) 0.500000 + 2.59808i 0.0487950 + 0.253546i
\(106\) −9.00000 −0.874157
\(107\) −1.50000 2.59808i −0.145010 0.251166i 0.784366 0.620298i \(-0.212988\pi\)
−0.929377 + 0.369132i \(0.879655\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i \(-0.992302\pi\)
0.520794 + 0.853682i \(0.325636\pi\)
\(110\) 1.50000 + 2.59808i 0.143019 + 0.247717i
\(111\) 2.00000 0.189832
\(112\) −2.00000 + 1.73205i −0.188982 + 0.163663i
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) −0.500000 + 0.866025i −0.0466252 + 0.0807573i
\(116\) 3.50000 6.06218i 0.324967 0.562859i
\(117\) −1.00000 1.73205i −0.0924500 0.160128i
\(118\) −9.00000 −0.828517
\(119\) −5.00000 1.73205i −0.458349 0.158777i
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −3.00000 + 5.19615i −0.271607 + 0.470438i
\(123\) −1.00000 + 1.73205i −0.0901670 + 0.156174i
\(124\) −3.50000 6.06218i −0.314309 0.544400i
\(125\) −9.00000 −0.804984
\(126\) 2.50000 + 0.866025i 0.222718 + 0.0771517i
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −3.00000 + 5.19615i −0.264135 + 0.457496i
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) −3.50000 6.06218i −0.305796 0.529655i 0.671642 0.740876i \(-0.265589\pi\)
−0.977438 + 0.211221i \(0.932256\pi\)
\(132\) 3.00000 0.261116
\(133\) 4.00000 3.46410i 0.346844 0.300376i
\(134\) 10.0000 0.863868
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 0.500000 + 0.866025i 0.0425628 + 0.0737210i
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) −0.500000 2.59808i −0.0422577 0.219578i
\(141\) −6.00000 −0.505291
\(142\) 4.00000 + 6.92820i 0.335673 + 0.581402i
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 3.50000 + 6.06218i 0.290659 + 0.503436i
\(146\) −10.0000 −0.827606
\(147\) −1.00000 + 6.92820i −0.0824786 + 0.571429i
\(148\) −2.00000 −0.164399
\(149\) 11.0000 + 19.0526i 0.901155 + 1.56085i 0.825997 + 0.563675i \(0.190613\pi\)
0.0751583 + 0.997172i \(0.476054\pi\)
\(150\) −2.00000 + 3.46410i −0.163299 + 0.282843i
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) −2.00000 −0.161690
\(154\) 1.50000 + 7.79423i 0.120873 + 0.628077i
\(155\) 7.00000 0.562254
\(156\) 1.00000 + 1.73205i 0.0800641 + 0.138675i
\(157\) −3.00000 + 5.19615i −0.239426 + 0.414698i −0.960550 0.278108i \(-0.910293\pi\)
0.721124 + 0.692806i \(0.243626\pi\)
\(158\) 7.50000 12.9904i 0.596668 1.03346i
\(159\) −4.50000 7.79423i −0.356873 0.618123i
\(160\) 1.00000 0.0790569
\(161\) −2.00000 + 1.73205i −0.157622 + 0.136505i
\(162\) 1.00000 0.0785674
\(163\) −1.00000 1.73205i −0.0783260 0.135665i 0.824202 0.566296i \(-0.191624\pi\)
−0.902528 + 0.430632i \(0.858291\pi\)
\(164\) 1.00000 1.73205i 0.0780869 0.135250i
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) −0.500000 0.866025i −0.0388075 0.0672166i
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) −2.50000 0.866025i −0.192879 0.0668153i
\(169\) −9.00000 −0.692308
\(170\) 1.00000 + 1.73205i 0.0766965 + 0.132842i
\(171\) 1.00000 1.73205i 0.0764719 0.132453i
\(172\) 3.00000 5.19615i 0.228748 0.396203i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 7.00000 0.530669
\(175\) −10.0000 3.46410i −0.755929 0.261861i
\(176\) −3.00000 −0.226134
\(177\) −4.50000 7.79423i −0.338241 0.585850i
\(178\) 0 0
\(179\) 6.00000 10.3923i 0.448461 0.776757i −0.549825 0.835280i \(-0.685306\pi\)
0.998286 + 0.0585225i \(0.0186389\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) 16.0000 1.18927 0.594635 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(182\) −4.00000 + 3.46410i −0.296500 + 0.256776i
\(183\) −6.00000 −0.443533
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) 1.00000 1.73205i 0.0735215 0.127343i
\(186\) 3.50000 6.06218i 0.256632 0.444500i
\(187\) −3.00000 5.19615i −0.219382 0.379980i
\(188\) 6.00000 0.437595
\(189\) 0.500000 + 2.59808i 0.0363696 + 0.188982i
\(190\) −2.00000 −0.145095
\(191\) −5.00000 8.66025i −0.361787 0.626634i 0.626468 0.779447i \(-0.284500\pi\)
−0.988255 + 0.152813i \(0.951167\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 11.5000 19.9186i 0.827788 1.43377i −0.0719816 0.997406i \(-0.522932\pi\)
0.899770 0.436365i \(-0.143734\pi\)
\(194\) −2.50000 4.33013i −0.179490 0.310885i
\(195\) −2.00000 −0.143223
\(196\) 1.00000 6.92820i 0.0714286 0.494872i
\(197\) 14.0000 0.997459 0.498729 0.866758i \(-0.333800\pi\)
0.498729 + 0.866758i \(0.333800\pi\)
\(198\) 1.50000 + 2.59808i 0.106600 + 0.184637i
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) 5.00000 + 8.66025i 0.352673 + 0.610847i
\(202\) −10.0000 −0.703598
\(203\) 3.50000 + 18.1865i 0.245652 + 1.27644i
\(204\) 2.00000 0.140028
\(205\) 1.00000 + 1.73205i 0.0698430 + 0.120972i
\(206\) 4.00000 6.92820i 0.278693 0.482711i
\(207\) −0.500000 + 0.866025i −0.0347524 + 0.0601929i
\(208\) −1.00000 1.73205i −0.0693375 0.120096i
\(209\) 6.00000 0.415029
\(210\) 2.00000 1.73205i 0.138013 0.119523i
\(211\) 6.00000 0.413057 0.206529 0.978441i \(-0.433783\pi\)
0.206529 + 0.978441i \(0.433783\pi\)
\(212\) 4.50000 + 7.79423i 0.309061 + 0.535310i
\(213\) −4.00000 + 6.92820i −0.274075 + 0.474713i
\(214\) −1.50000 + 2.59808i −0.102538 + 0.177601i
\(215\) 3.00000 + 5.19615i 0.204598 + 0.354375i
\(216\) −1.00000 −0.0680414
\(217\) 17.5000 + 6.06218i 1.18798 + 0.411527i
\(218\) 10.0000 0.677285
\(219\) −5.00000 8.66025i −0.337869 0.585206i
\(220\) 1.50000 2.59808i 0.101130 0.175162i
\(221\) 2.00000 3.46410i 0.134535 0.233021i
\(222\) −1.00000 1.73205i −0.0671156 0.116248i
\(223\) 13.0000 0.870544 0.435272 0.900299i \(-0.356652\pi\)
0.435272 + 0.900299i \(0.356652\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) −4.00000 −0.266667
\(226\) −5.00000 8.66025i −0.332595 0.576072i
\(227\) 4.50000 7.79423i 0.298675 0.517321i −0.677158 0.735838i \(-0.736789\pi\)
0.975833 + 0.218517i \(0.0701218\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) −11.0000 19.0526i −0.726900 1.25903i −0.958187 0.286143i \(-0.907627\pi\)
0.231287 0.972886i \(-0.425707\pi\)
\(230\) 1.00000 0.0659380
\(231\) −6.00000 + 5.19615i −0.394771 + 0.341882i
\(232\) −7.00000 −0.459573
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) −1.00000 + 1.73205i −0.0653720 + 0.113228i
\(235\) −3.00000 + 5.19615i −0.195698 + 0.338960i
\(236\) 4.50000 + 7.79423i 0.292925 + 0.507361i
\(237\) 15.0000 0.974355
\(238\) 1.00000 + 5.19615i 0.0648204 + 0.336817i
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) 13.5000 23.3827i 0.869611 1.50621i 0.00721719 0.999974i \(-0.497703\pi\)
0.862394 0.506237i \(-0.168964\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 6.00000 0.384111
\(245\) 5.50000 + 4.33013i 0.351382 + 0.276642i
\(246\) 2.00000 0.127515
\(247\) 2.00000 + 3.46410i 0.127257 + 0.220416i
\(248\) −3.50000 + 6.06218i −0.222250 + 0.384949i
\(249\) 0.500000 0.866025i 0.0316862 0.0548821i
\(250\) 4.50000 + 7.79423i 0.284605 + 0.492950i
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) −0.500000 2.59808i −0.0314970 0.163663i
\(253\) −3.00000 −0.188608
\(254\) 3.50000 + 6.06218i 0.219610 + 0.380375i
\(255\) −1.00000 + 1.73205i −0.0626224 + 0.108465i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 2.00000 + 3.46410i 0.124757 + 0.216085i 0.921638 0.388051i \(-0.126852\pi\)
−0.796881 + 0.604136i \(0.793518\pi\)
\(258\) 6.00000 0.373544
\(259\) 4.00000 3.46410i 0.248548 0.215249i
\(260\) 2.00000 0.124035
\(261\) 3.50000 + 6.06218i 0.216645 + 0.375239i
\(262\) −3.50000 + 6.06218i −0.216231 + 0.374523i
\(263\) 1.00000 1.73205i 0.0616626 0.106803i −0.833546 0.552450i \(-0.813693\pi\)
0.895209 + 0.445647i \(0.147026\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) −9.00000 −0.552866
\(266\) −5.00000 1.73205i −0.306570 0.106199i
\(267\) 0 0
\(268\) −5.00000 8.66025i −0.305424 0.529009i
\(269\) 13.5000 23.3827i 0.823110 1.42567i −0.0802460 0.996775i \(-0.525571\pi\)
0.903356 0.428892i \(-0.141096\pi\)
\(270\) 0.500000 0.866025i 0.0304290 0.0527046i
\(271\) 4.50000 + 7.79423i 0.273356 + 0.473466i 0.969719 0.244224i \(-0.0785331\pi\)
−0.696363 + 0.717689i \(0.745200\pi\)
\(272\) −2.00000 −0.121268
\(273\) −5.00000 1.73205i −0.302614 0.104828i
\(274\) −6.00000 −0.362473
\(275\) −6.00000 10.3923i −0.361814 0.626680i
\(276\) 0.500000 0.866025i 0.0300965 0.0521286i
\(277\) 4.00000 6.92820i 0.240337 0.416275i −0.720473 0.693482i \(-0.756075\pi\)
0.960810 + 0.277207i \(0.0894088\pi\)
\(278\) −7.00000 12.1244i −0.419832 0.727171i
\(279\) 7.00000 0.419079
\(280\) −2.00000 + 1.73205i −0.119523 + 0.103510i
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 3.00000 + 5.19615i 0.178647 + 0.309426i
\(283\) −3.00000 + 5.19615i −0.178331 + 0.308879i −0.941309 0.337546i \(-0.890403\pi\)
0.762978 + 0.646425i \(0.223737\pi\)
\(284\) 4.00000 6.92820i 0.237356 0.411113i
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) −6.00000 −0.354787
\(287\) 1.00000 + 5.19615i 0.0590281 + 0.306719i
\(288\) 1.00000 0.0589256
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 3.50000 6.06218i 0.205527 0.355983i
\(291\) 2.50000 4.33013i 0.146553 0.253837i
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) 19.0000 1.10999 0.554996 0.831853i \(-0.312720\pi\)
0.554996 + 0.831853i \(0.312720\pi\)
\(294\) 6.50000 2.59808i 0.379088 0.151523i
\(295\) −9.00000 −0.524000
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) −1.50000 + 2.59808i −0.0870388 + 0.150756i
\(298\) 11.0000 19.0526i 0.637213 1.10369i
\(299\) −1.00000 1.73205i −0.0578315 0.100167i
\(300\) 4.00000 0.230940
\(301\) 3.00000 + 15.5885i 0.172917 + 0.898504i
\(302\) −5.00000 −0.287718
\(303\) −5.00000 8.66025i −0.287242 0.497519i
\(304\) 1.00000 1.73205i 0.0573539 0.0993399i
\(305\) −3.00000 + 5.19615i −0.171780 + 0.297531i
\(306\) 1.00000 + 1.73205i 0.0571662 + 0.0990148i
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) 6.00000 5.19615i 0.341882 0.296078i
\(309\) 8.00000 0.455104
\(310\) −3.50000 6.06218i −0.198787 0.344309i
\(311\) 1.00000 1.73205i 0.0567048 0.0982156i −0.836280 0.548303i \(-0.815274\pi\)
0.892984 + 0.450088i \(0.148607\pi\)
\(312\) 1.00000 1.73205i 0.0566139 0.0980581i
\(313\) 12.5000 + 21.6506i 0.706542 + 1.22377i 0.966132 + 0.258047i \(0.0830791\pi\)
−0.259590 + 0.965719i \(0.583588\pi\)
\(314\) 6.00000 0.338600
\(315\) 2.50000 + 0.866025i 0.140859 + 0.0487950i
\(316\) −15.0000 −0.843816
\(317\) 15.5000 + 26.8468i 0.870567 + 1.50787i 0.861411 + 0.507908i \(0.169581\pi\)
0.00915525 + 0.999958i \(0.497086\pi\)
\(318\) −4.50000 + 7.79423i −0.252347 + 0.437079i
\(319\) −10.5000 + 18.1865i −0.587887 + 1.01825i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −3.00000 −0.167444
\(322\) 2.50000 + 0.866025i 0.139320 + 0.0482617i
\(323\) 4.00000 0.222566
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 4.00000 6.92820i 0.221880 0.384308i
\(326\) −1.00000 + 1.73205i −0.0553849 + 0.0959294i
\(327\) 5.00000 + 8.66025i 0.276501 + 0.478913i
\(328\) −2.00000 −0.110432
\(329\) −12.0000 + 10.3923i −0.661581 + 0.572946i
\(330\) 3.00000 0.165145
\(331\) −5.00000 8.66025i −0.274825 0.476011i 0.695266 0.718752i \(-0.255287\pi\)
−0.970091 + 0.242742i \(0.921953\pi\)
\(332\) −0.500000 + 0.866025i −0.0274411 + 0.0475293i
\(333\) 1.00000 1.73205i 0.0547997 0.0949158i
\(334\) −3.00000 5.19615i −0.164153 0.284321i
\(335\) 10.0000 0.546358
\(336\) 0.500000 + 2.59808i 0.0272772 + 0.141737i
\(337\) −9.00000 −0.490261 −0.245131 0.969490i \(-0.578831\pi\)
−0.245131 + 0.969490i \(0.578831\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 5.00000 8.66025i 0.271563 0.470360i
\(340\) 1.00000 1.73205i 0.0542326 0.0939336i
\(341\) 10.5000 + 18.1865i 0.568607 + 0.984856i
\(342\) −2.00000 −0.108148
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −6.00000 −0.323498
\(345\) 0.500000 + 0.866025i 0.0269191 + 0.0466252i
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) −18.0000 + 31.1769i −0.966291 + 1.67366i −0.260184 + 0.965559i \(0.583783\pi\)
−0.706107 + 0.708105i \(0.749550\pi\)
\(348\) −3.50000 6.06218i −0.187620 0.324967i
\(349\) 16.0000 0.856460 0.428230 0.903670i \(-0.359137\pi\)
0.428230 + 0.903670i \(0.359137\pi\)
\(350\) 2.00000 + 10.3923i 0.106904 + 0.555492i
\(351\) −2.00000 −0.106752
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) 13.0000 22.5167i 0.691920 1.19844i −0.279288 0.960207i \(-0.590098\pi\)
0.971208 0.238233i \(-0.0765683\pi\)
\(354\) −4.50000 + 7.79423i −0.239172 + 0.414259i
\(355\) 4.00000 + 6.92820i 0.212298 + 0.367711i
\(356\) 0 0
\(357\) −4.00000 + 3.46410i −0.211702 + 0.183340i
\(358\) −12.0000 −0.634220
\(359\) −15.0000 25.9808i −0.791670 1.37121i −0.924932 0.380131i \(-0.875879\pi\)
0.133263 0.991081i \(-0.457455\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −8.00000 13.8564i −0.420471 0.728277i
\(363\) 2.00000 0.104973
\(364\) 5.00000 + 1.73205i 0.262071 + 0.0907841i
\(365\) −10.0000 −0.523424
\(366\) 3.00000 + 5.19615i 0.156813 + 0.271607i
\(367\) −3.50000 + 6.06218i −0.182699 + 0.316443i −0.942799 0.333363i \(-0.891817\pi\)
0.760100 + 0.649806i \(0.225150\pi\)
\(368\) −0.500000 + 0.866025i −0.0260643 + 0.0451447i
\(369\) 1.00000 + 1.73205i 0.0520579 + 0.0901670i
\(370\) −2.00000 −0.103975
\(371\) −22.5000 7.79423i −1.16814 0.404656i
\(372\) −7.00000 −0.362933
\(373\) −16.0000 27.7128i −0.828449 1.43492i −0.899255 0.437425i \(-0.855891\pi\)
0.0708063 0.997490i \(-0.477443\pi\)
\(374\) −3.00000 + 5.19615i −0.155126 + 0.268687i
\(375\) −4.50000 + 7.79423i −0.232379 + 0.402492i
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) −14.0000 −0.721037
\(378\) 2.00000 1.73205i 0.102869 0.0890871i
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 1.00000 + 1.73205i 0.0512989 + 0.0888523i
\(381\) −3.50000 + 6.06218i −0.179310 + 0.310575i
\(382\) −5.00000 + 8.66025i −0.255822 + 0.443097i
\(383\) −4.00000 6.92820i −0.204390 0.354015i 0.745548 0.666452i \(-0.232188\pi\)
−0.949938 + 0.312437i \(0.898855\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 1.50000 + 7.79423i 0.0764471 + 0.397231i
\(386\) −23.0000 −1.17067
\(387\) 3.00000 + 5.19615i 0.152499 + 0.264135i
\(388\) −2.50000 + 4.33013i −0.126918 + 0.219829i
\(389\) −19.0000 + 32.9090i −0.963338 + 1.66855i −0.249323 + 0.968420i \(0.580208\pi\)
−0.714015 + 0.700130i \(0.753125\pi\)
\(390\) 1.00000 + 1.73205i 0.0506370 + 0.0877058i
\(391\) −2.00000 −0.101144
\(392\) −6.50000 + 2.59808i −0.328300 + 0.131223i
\(393\) −7.00000 −0.353103
\(394\) −7.00000 12.1244i −0.352655 0.610816i
\(395\) 7.50000 12.9904i 0.377366 0.653617i
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) 19.0000 + 32.9090i 0.953583 + 1.65165i 0.737579 + 0.675261i \(0.235969\pi\)
0.216004 + 0.976392i \(0.430698\pi\)
\(398\) −4.00000 −0.200502
\(399\) −1.00000 5.19615i −0.0500626 0.260133i
\(400\) −4.00000 −0.200000
\(401\) −2.00000 3.46410i −0.0998752 0.172989i 0.811758 0.583994i \(-0.198511\pi\)
−0.911633 + 0.411005i \(0.865178\pi\)
\(402\) 5.00000 8.66025i 0.249377 0.431934i
\(403\) −7.00000 + 12.1244i −0.348695 + 0.603957i
\(404\) 5.00000 + 8.66025i 0.248759 + 0.430864i
\(405\) 1.00000 0.0496904
\(406\) 14.0000 12.1244i 0.694808 0.601722i
\(407\) 6.00000 0.297409
\(408\) −1.00000 1.73205i −0.0495074 0.0857493i
\(409\) 14.5000 25.1147i 0.716979 1.24184i −0.245212 0.969469i \(-0.578858\pi\)
0.962191 0.272374i \(-0.0878089\pi\)
\(410\) 1.00000 1.73205i 0.0493865 0.0855399i
\(411\) −3.00000 5.19615i −0.147979 0.256307i
\(412\) −8.00000 −0.394132
\(413\) −22.5000 7.79423i −1.10715 0.383529i
\(414\) 1.00000 0.0491473
\(415\) −0.500000 0.866025i −0.0245440 0.0425115i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 7.00000 12.1244i 0.342791 0.593732i
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) −36.0000 −1.75872 −0.879358 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) −2.50000 0.866025i −0.121988 0.0422577i
\(421\) −18.0000 −0.877266 −0.438633 0.898666i \(-0.644537\pi\)
−0.438633 + 0.898666i \(0.644537\pi\)
\(422\) −3.00000 5.19615i −0.146038 0.252945i
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 4.50000 7.79423i 0.218539 0.378521i
\(425\) −4.00000 6.92820i −0.194029 0.336067i
\(426\) 8.00000 0.387601
\(427\) −12.0000 + 10.3923i −0.580721 + 0.502919i
\(428\) 3.00000 0.145010
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) 3.00000 5.19615i 0.144673 0.250581i
\(431\) 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
\(433\) 38.0000 1.82616 0.913082 0.407777i \(-0.133696\pi\)
0.913082 + 0.407777i \(0.133696\pi\)
\(434\) −3.50000 18.1865i −0.168005 0.872982i
\(435\) 7.00000 0.335624
\(436\) −5.00000 8.66025i −0.239457 0.414751i
\(437\) 1.00000 1.73205i 0.0478365 0.0828552i
\(438\) −5.00000 + 8.66025i −0.238909 + 0.413803i
\(439\) −17.5000 30.3109i −0.835229 1.44666i −0.893843 0.448379i \(-0.852001\pi\)
0.0586141 0.998281i \(-0.481332\pi\)
\(440\) −3.00000 −0.143019
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) −4.00000 −0.190261
\(443\) 14.5000 + 25.1147i 0.688916 + 1.19324i 0.972189 + 0.234198i \(0.0752464\pi\)
−0.283273 + 0.959039i \(0.591420\pi\)
\(444\) −1.00000 + 1.73205i −0.0474579 + 0.0821995i
\(445\) 0 0
\(446\) −6.50000 11.2583i −0.307784 0.533097i
\(447\) 22.0000 1.04056
\(448\) −0.500000 2.59808i −0.0236228 0.122748i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 2.00000 + 3.46410i 0.0942809 + 0.163299i
\(451\) −3.00000 + 5.19615i −0.141264 + 0.244677i
\(452\) −5.00000 + 8.66025i −0.235180 + 0.407344i
\(453\) −2.50000 4.33013i −0.117460 0.203447i
\(454\) −9.00000 −0.422391
\(455\) −4.00000 + 3.46410i −0.187523 + 0.162400i
\(456\) 2.00000 0.0936586
\(457\) −0.500000 0.866025i −0.0233890 0.0405110i 0.854094 0.520119i \(-0.174112\pi\)
−0.877483 + 0.479608i \(0.840779\pi\)
\(458\) −11.0000 + 19.0526i −0.513996 + 0.890268i
\(459\) −1.00000 + 1.73205i −0.0466760 + 0.0808452i
\(460\) −0.500000 0.866025i −0.0233126 0.0403786i
\(461\) 2.00000 0.0931493 0.0465746 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 7.50000 + 2.59808i 0.348932 + 0.120873i
\(463\) −8.00000 −0.371792 −0.185896 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 3.50000 + 6.06218i 0.162483 + 0.281430i
\(465\) 3.50000 6.06218i 0.162309 0.281127i
\(466\) 3.00000 5.19615i 0.138972 0.240707i
\(467\) −2.00000 3.46410i −0.0925490 0.160300i 0.816034 0.578004i \(-0.196168\pi\)
−0.908583 + 0.417704i \(0.862835\pi\)
\(468\) 2.00000 0.0924500
\(469\) 25.0000 + 8.66025i 1.15439 + 0.399893i
\(470\) 6.00000 0.276759
\(471\) 3.00000 + 5.19615i 0.138233 + 0.239426i
\(472\) 4.50000 7.79423i 0.207129 0.358758i
\(473\) −9.00000 + 15.5885i −0.413820 + 0.716758i
\(474\) −7.50000 12.9904i −0.344486 0.596668i
\(475\) 8.00000 0.367065
\(476\) 4.00000 3.46410i 0.183340 0.158777i
\(477\) −9.00000 −0.412082
\(478\) 6.00000 + 10.3923i 0.274434 + 0.475333i
\(479\) −14.0000 + 24.2487i −0.639676 + 1.10795i 0.345827 + 0.938298i \(0.387598\pi\)
−0.985504 + 0.169654i \(0.945735\pi\)
\(480\) 0.500000 0.866025i 0.0228218 0.0395285i
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) −27.0000 −1.22982
\(483\) 0.500000 + 2.59808i 0.0227508 + 0.118217i
\(484\) −2.00000 −0.0909091
\(485\) −2.50000 4.33013i −0.113519 0.196621i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 7.50000 12.9904i 0.339857 0.588650i −0.644548 0.764564i \(-0.722955\pi\)
0.984406 + 0.175913i \(0.0562878\pi\)
\(488\) −3.00000 5.19615i −0.135804 0.235219i
\(489\) −2.00000 −0.0904431
\(490\) 1.00000 6.92820i 0.0451754 0.312984i
\(491\) 19.0000 0.857458 0.428729 0.903433i \(-0.358962\pi\)
0.428729 + 0.903433i \(0.358962\pi\)
\(492\) −1.00000 1.73205i −0.0450835 0.0780869i
\(493\) −7.00000 + 12.1244i −0.315264 + 0.546054i
\(494\) 2.00000 3.46410i 0.0899843 0.155857i
\(495\) 1.50000 + 2.59808i 0.0674200 + 0.116775i
\(496\) 7.00000 0.314309
\(497\) 4.00000 + 20.7846i 0.179425 + 0.932317i
\(498\) −1.00000 −0.0448111
\(499\) −3.00000 5.19615i −0.134298 0.232612i 0.791031 0.611776i \(-0.209545\pi\)
−0.925329 + 0.379165i \(0.876211\pi\)
\(500\) 4.50000 7.79423i 0.201246 0.348569i
\(501\) 3.00000 5.19615i 0.134030 0.232147i
\(502\) 1.50000 + 2.59808i 0.0669483 + 0.115958i
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) −2.00000 + 1.73205i −0.0890871 + 0.0771517i
\(505\) −10.0000 −0.444994
\(506\) 1.50000 + 2.59808i 0.0666831 + 0.115499i
\(507\) −4.50000 + 7.79423i −0.199852 + 0.346154i
\(508\) 3.50000 6.06218i 0.155287 0.268966i
\(509\) −8.50000 14.7224i −0.376756 0.652560i 0.613832 0.789436i \(-0.289627\pi\)
−0.990588 + 0.136876i \(0.956294\pi\)
\(510\) 2.00000 0.0885615
\(511\) −25.0000 8.66025i −1.10593 0.383107i
\(512\) 1.00000 0.0441942
\(513\) −1.00000 1.73205i −0.0441511 0.0764719i
\(514\) 2.00000 3.46410i 0.0882162 0.152795i
\(515\) 4.00000 6.92820i 0.176261 0.305293i
\(516\) −3.00000 5.19615i −0.132068 0.228748i
\(517\) −18.0000 −0.791639
\(518\) −5.00000 1.73205i −0.219687 0.0761019i
\(519\) 6.00000 0.263371
\(520\) −1.00000 1.73205i −0.0438529 0.0759555i
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) 3.50000 6.06218i 0.153191 0.265334i
\(523\) 6.00000 + 10.3923i 0.262362 + 0.454424i 0.966869 0.255273i \(-0.0821653\pi\)
−0.704507 + 0.709697i \(0.748832\pi\)
\(524\) 7.00000 0.305796
\(525\) −8.00000 + 6.92820i −0.349149 + 0.302372i
\(526\) −2.00000 −0.0872041
\(527\) 7.00000 + 12.1244i 0.304925 + 0.528145i
\(528\) −1.50000 + 2.59808i −0.0652791 + 0.113067i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) 4.50000 + 7.79423i 0.195468 + 0.338560i
\(531\) −9.00000 −0.390567
\(532\) 1.00000 + 5.19615i 0.0433555 + 0.225282i
\(533\) −4.00000 −0.173259
\(534\) 0 0
\(535\) −1.50000 + 2.59808i −0.0648507 + 0.112325i
\(536\) −5.00000 + 8.66025i −0.215967 + 0.374066i
\(537\) −6.00000 10.3923i −0.258919 0.448461i
\(538\) −27.0000 −1.16405
\(539\) −3.00000 + 20.7846i −0.129219 + 0.895257i
\(540\) −1.00000 −0.0430331
\(541\) 4.00000 + 6.92820i 0.171973 + 0.297867i 0.939110 0.343617i \(-0.111652\pi\)
−0.767136 + 0.641484i \(0.778319\pi\)
\(542\) 4.50000 7.79423i 0.193292 0.334791i
\(543\) 8.00000 13.8564i 0.343313 0.594635i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) 10.0000 0.428353
\(546\) 1.00000 + 5.19615i 0.0427960 + 0.222375i
\(547\) −38.0000 −1.62476 −0.812381 0.583127i \(-0.801829\pi\)
−0.812381 + 0.583127i \(0.801829\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) −6.00000 + 10.3923i −0.255841 + 0.443129i
\(551\) −7.00000 12.1244i −0.298210 0.516515i
\(552\) −1.00000 −0.0425628
\(553\) 30.0000 25.9808i 1.27573 1.10481i
\(554\) −8.00000 −0.339887
\(555\) −1.00000 1.73205i −0.0424476 0.0735215i
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) −16.5000 + 28.5788i −0.699127 + 1.21092i 0.269642 + 0.962961i \(0.413095\pi\)
−0.968769 + 0.247964i \(0.920239\pi\)
\(558\) −3.50000 6.06218i −0.148167 0.256632i
\(559\) −12.0000 −0.507546
\(560\) 2.50000 + 0.866025i 0.105644 + 0.0365963i
\(561\) −6.00000 −0.253320
\(562\) 2.00000 + 3.46410i 0.0843649 + 0.146124i
\(563\) 1.50000 2.59808i 0.0632175 0.109496i −0.832684 0.553748i \(-0.813197\pi\)
0.895902 + 0.444252i \(0.146530\pi\)
\(564\) 3.00000 5.19615i 0.126323 0.218797i
\(565\) −5.00000 8.66025i −0.210352 0.364340i
\(566\) 6.00000 0.252199
\(567\) 2.50000 + 0.866025i 0.104990 + 0.0363696i
\(568\) −8.00000 −0.335673
\(569\) 18.0000 + 31.1769i 0.754599 + 1.30700i 0.945573 + 0.325409i \(0.105502\pi\)
−0.190974 + 0.981595i \(0.561165\pi\)
\(570\) −1.00000 + 1.73205i −0.0418854 + 0.0725476i
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) −10.0000 −0.417756
\(574\) 4.00000 3.46410i 0.166957 0.144589i
\(575\) −4.00000 −0.166812
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 16.5000 28.5788i 0.686904 1.18975i −0.285930 0.958250i \(-0.592303\pi\)
0.972834 0.231502i \(-0.0743641\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) −11.5000 19.9186i −0.477924 0.827788i
\(580\) −7.00000 −0.290659
\(581\) −0.500000 2.59808i −0.0207435 0.107786i
\(582\) −5.00000 −0.207257
\(583\) −13.5000 23.3827i −0.559113 0.968412i
\(584\) 5.00000 8.66025i 0.206901 0.358364i
\(585\) −1.00000 + 1.73205i −0.0413449 + 0.0716115i
\(586\) −9.50000 16.4545i −0.392441 0.679728i
\(587\) −3.00000 −0.123823 −0.0619116 0.998082i \(-0.519720\pi\)
−0.0619116 + 0.998082i \(0.519720\pi\)
\(588\) −5.50000 4.33013i −0.226816 0.178571i
\(589\) −14.0000 −0.576860
\(590\) 4.50000 + 7.79423i 0.185262 + 0.320883i
\(591\) 7.00000 12.1244i 0.287942 0.498729i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) 6.00000 + 10.3923i 0.246390 + 0.426761i 0.962522 0.271205i \(-0.0874221\pi\)
−0.716131 + 0.697966i \(0.754089\pi\)
\(594\) 3.00000 0.123091
\(595\) 1.00000 + 5.19615i 0.0409960 + 0.213021i
\(596\) −22.0000 −0.901155
\(597\) −2.00000 3.46410i −0.0818546 0.141776i
\(598\) −1.00000 + 1.73205i −0.0408930 + 0.0708288i
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) −2.00000 3.46410i −0.0816497 0.141421i
\(601\) 23.0000 0.938190 0.469095 0.883148i \(-0.344580\pi\)
0.469095 + 0.883148i \(0.344580\pi\)
\(602\) 12.0000 10.3923i 0.489083 0.423559i
\(603\) 10.0000 0.407231
\(604\) 2.50000 + 4.33013i 0.101724 + 0.176190i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) −5.00000 + 8.66025i −0.203111 + 0.351799i
\(607\) −10.5000 18.1865i −0.426182 0.738169i 0.570348 0.821403i \(-0.306808\pi\)
−0.996530 + 0.0832344i \(0.973475\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 17.5000 + 6.06218i 0.709136 + 0.245652i
\(610\) 6.00000 0.242933
\(611\) −6.00000 10.3923i −0.242734 0.420428i
\(612\) 1.00000 1.73205i 0.0404226 0.0700140i
\(613\) −18.0000 + 31.1769i −0.727013 + 1.25922i 0.231127 + 0.972924i \(0.425759\pi\)
−0.958140 + 0.286300i \(0.907575\pi\)
\(614\) 1.00000 + 1.73205i 0.0403567 + 0.0698999i
\(615\) 2.00000 0.0806478
\(616\) −7.50000 2.59808i −0.302184 0.104679i
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −4.00000 6.92820i −0.160904 0.278693i
\(619\) 8.00000 13.8564i 0.321547 0.556936i −0.659260 0.751915i \(-0.729130\pi\)
0.980807 + 0.194979i \(0.0624638\pi\)
\(620\) −3.50000 + 6.06218i −0.140563 + 0.243463i
\(621\) 0.500000 + 0.866025i 0.0200643 + 0.0347524i
\(622\) −2.00000 −0.0801927
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 12.5000 21.6506i 0.499600 0.865333i
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) −3.00000 5.19615i −0.119713 0.207349i
\(629\) 4.00000 0.159490
\(630\) −0.500000 2.59808i −0.0199205 0.103510i
\(631\) 31.0000 1.23409 0.617045 0.786928i \(-0.288330\pi\)
0.617045 + 0.786928i \(0.288330\pi\)
\(632\) 7.50000 + 12.9904i 0.298334 + 0.516730i
\(633\) 3.00000 5.19615i 0.119239 0.206529i
\(634\) 15.5000 26.8468i 0.615584 1.06622i
\(635\) 3.50000 + 6.06218i 0.138893 + 0.240570i
\(636\) 9.00000 0.356873
\(637\) −13.0000 + 5.19615i −0.515079 + 0.205879i
\(638\) 21.0000 0.831398
\(639\) 4.00000 + 6.92820i 0.158238 + 0.274075i
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 6.00000 10.3923i 0.236986 0.410471i −0.722862 0.690992i \(-0.757174\pi\)
0.959848 + 0.280521i \(0.0905072\pi\)
\(642\) 1.50000 + 2.59808i 0.0592003 + 0.102538i
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) −0.500000 2.59808i −0.0197028 0.102379i
\(645\) 6.00000 0.236250
\(646\) −2.00000 3.46410i −0.0786889 0.136293i
\(647\) −19.0000 + 32.9090i −0.746967 + 1.29378i 0.202303 + 0.979323i \(0.435157\pi\)
−0.949270 + 0.314462i \(0.898176\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −13.5000 23.3827i −0.529921 0.917851i
\(650\) −8.00000 −0.313786
\(651\) 14.0000 12.1244i 0.548703 0.475191i
\(652\) 2.00000 0.0783260
\(653\) −5.50000 9.52628i −0.215232 0.372792i 0.738113 0.674678i \(-0.235717\pi\)
−0.953344 + 0.301885i \(0.902384\pi\)
\(654\) 5.00000 8.66025i 0.195515 0.338643i
\(655\) −3.50000 + 6.06218i −0.136756 + 0.236869i
\(656\) 1.00000 + 1.73205i 0.0390434 + 0.0676252i
\(657\) −10.0000 −0.390137
\(658\) 15.0000 + 5.19615i 0.584761 + 0.202567i
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) −19.0000 + 32.9090i −0.739014 + 1.28001i 0.213925 + 0.976850i \(0.431375\pi\)
−0.952940 + 0.303160i \(0.901958\pi\)
\(662\) −5.00000 + 8.66025i −0.194331 + 0.336590i
\(663\) −2.00000 3.46410i −0.0776736 0.134535i
\(664\) 1.00000 0.0388075
\(665\) −5.00000 1.73205i −0.193892 0.0671660i
\(666\) −2.00000 −0.0774984
\(667\) 3.50000 + 6.06218i 0.135521 + 0.234728i
\(668\) −3.00000 + 5.19615i −0.116073 + 0.201045i
\(669\) 6.50000 11.2583i 0.251305 0.435272i
\(670\) −5.00000 8.66025i −0.193167 0.334575i
\(671\) −18.0000 −0.694882
\(672\) 2.00000 1.73205i 0.0771517 0.0668153i
\(673\) 25.0000 0.963679 0.481840 0.876259i \(-0.339969\pi\)
0.481840 + 0.876259i \(0.339969\pi\)
\(674\) 4.50000 + 7.79423i 0.173334 + 0.300222i
\(675\) −2.00000 + 3.46410i −0.0769800 + 0.133333i
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) 17.5000 + 30.3109i 0.672580 + 1.16494i 0.977170 + 0.212459i \(0.0681471\pi\)
−0.304590 + 0.952483i \(0.598520\pi\)
\(678\) −10.0000 −0.384048
\(679\) −2.50000 12.9904i −0.0959412 0.498525i
\(680\) −2.00000 −0.0766965
\(681\) −4.50000 7.79423i −0.172440 0.298675i
\(682\) 10.5000 18.1865i 0.402066 0.696398i
\(683\) 11.5000 19.9186i 0.440035 0.762163i −0.557656 0.830072i \(-0.688299\pi\)
0.997692 + 0.0679085i \(0.0216326\pi\)
\(684\) 1.00000 + 1.73205i 0.0382360 + 0.0662266i
\(685\) −6.00000 −0.229248
\(686\) 8.50000 16.4545i 0.324532 0.628235i
\(687\) −22.0000 −0.839352
\(688\) 3.00000 + 5.19615i 0.114374 + 0.198101i
\(689\) 9.00000 15.5885i 0.342873 0.593873i
\(690\) 0.500000 0.866025i 0.0190347 0.0329690i
\(691\) 11.0000 + 19.0526i 0.418460 + 0.724793i 0.995785 0.0917209i \(-0.0292368\pi\)
−0.577325 + 0.816514i \(0.695903\pi\)
\(692\) −6.00000 −0.228086
\(693\) 1.50000 + 7.79423i 0.0569803 + 0.296078i
\(694\) 36.0000 1.36654
\(695\) −7.00000 12.1244i −0.265525 0.459903i
\(696\) −3.50000 + 6.06218i −0.132667 + 0.229786i
\(697\) −2.00000 + 3.46410i −0.0757554 + 0.131212i
\(698\) −8.00000 13.8564i −0.302804 0.524473i
\(699\) 6.00000 0.226941
\(700\) 8.00000 6.92820i 0.302372 0.261861i
\(701\) −1.00000 −0.0377695 −0.0188847 0.999822i \(-0.506012\pi\)
−0.0188847 + 0.999822i \(0.506012\pi\)
\(702\) 1.00000 + 1.73205i 0.0377426 + 0.0653720i
\(703\) −2.00000 + 3.46410i −0.0754314 + 0.130651i
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 3.00000 + 5.19615i 0.112987 + 0.195698i
\(706\) −26.0000 −0.978523
\(707\) −25.0000 8.66025i −0.940222 0.325702i
\(708\) 9.00000 0.338241
\(709\) 14.0000 + 24.2487i 0.525781 + 0.910679i 0.999549 + 0.0300298i \(0.00956021\pi\)
−0.473768 + 0.880650i \(0.657106\pi\)
\(710\) 4.00000 6.92820i 0.150117 0.260011i
\(711\) 7.50000 12.9904i 0.281272 0.487177i
\(712\) 0 0
\(713\) 7.00000 0.262152
\(714\) 5.00000 + 1.73205i 0.187120 + 0.0648204i
\(715\) −6.00000 −0.224387
\(716\) 6.00000 + 10.3923i 0.224231 + 0.388379i
\(717\) −6.00000 + 10.3923i −0.224074 + 0.388108i
\(718\) −15.0000 + 25.9808i −0.559795 + 0.969593i
\(719\) 15.0000 + 25.9808i 0.559406 + 0.968919i 0.997546 + 0.0700124i \(0.0223039\pi\)
−0.438141 + 0.898906i \(0.644363\pi\)
\(720\) 1.00000 0.0372678
\(721\) 16.0000 13.8564i 0.595871 0.516040i
\(722\) −15.0000 −0.558242
\(723\) −13.5000 23.3827i −0.502070 0.869611i
\(724\) −8.00000 + 13.8564i −0.297318 + 0.514969i
\(725\) −14.0000 + 24.2487i −0.519947 + 0.900575i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) 5.00000 0.185440 0.0927199 0.995692i \(-0.470444\pi\)
0.0927199 + 0.995692i \(0.470444\pi\)
\(728\) −1.00000 5.19615i −0.0370625 0.192582i
\(729\) 1.00000 0.0370370
\(730\) 5.00000 + 8.66025i 0.185058 + 0.320530i
\(731\) −6.00000 + 10.3923i −0.221918 + 0.384373i
\(732\) 3.00000 5.19615i 0.110883 0.192055i
\(733\) 14.0000 + 24.2487i 0.517102 + 0.895647i 0.999803 + 0.0198613i \(0.00632248\pi\)
−0.482701 + 0.875785i \(0.660344\pi\)
\(734\) 7.00000 0.258375
\(735\) 6.50000 2.59808i 0.239756 0.0958315i
\(736\) 1.00000 0.0368605
\(737\) 15.0000 + 25.9808i 0.552532 + 0.957014i
\(738\) 1.00000 1.73205i 0.0368105 0.0637577i
\(739\) 7.00000 12.1244i 0.257499 0.446002i −0.708072 0.706140i \(-0.750435\pi\)
0.965571 + 0.260138i \(0.0837682\pi\)
\(740\) 1.00000 + 1.73205i 0.0367607 + 0.0636715i
\(741\) 4.00000 0.146944
\(742\) 4.50000 + 23.3827i 0.165200 + 0.858405i
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 3.50000 + 6.06218i 0.128316 + 0.222250i
\(745\) 11.0000 19.0526i 0.403009 0.698032i
\(746\) −16.0000 + 27.7128i −0.585802 + 1.01464i
\(747\) −0.500000 0.866025i −0.0182940 0.0316862i
\(748\) 6.00000 0.219382
\(749\) −6.00000 + 5.19615i −0.219235 + 0.189863i
\(750\) 9.00000 0.328634
\(751\) −5.50000 9.52628i −0.200698 0.347619i 0.748056 0.663636i \(-0.230988\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) −1.50000 + 2.59808i −0.0546630 + 0.0946792i
\(754\) 7.00000 + 12.1244i 0.254925 + 0.441543i
\(755\) −5.00000 −0.181969
\(756\) −2.50000 0.866025i −0.0909241 0.0314970i
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 2.00000 + 3.46410i 0.0726433 + 0.125822i
\(759\) −1.50000 + 2.59808i −0.0544466 + 0.0943042i
\(760\) 1.00000 1.73205i 0.0362738 0.0628281i
\(761\) −9.00000 15.5885i −0.326250 0.565081i 0.655515 0.755182i \(-0.272452\pi\)
−0.981764 + 0.190101i \(0.939118\pi\)
\(762\) 7.00000 0.253583
\(763\) 25.0000 + 8.66025i 0.905061 + 0.313522i
\(764\) 10.0000 0.361787
\(765\) 1.00000 + 1.73205i 0.0361551 + 0.0626224i
\(766\) −4.00000 + 6.92820i −0.144526 + 0.250326i
\(767\) 9.00000 15.5885i 0.324971 0.562867i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 15.0000 0.540914 0.270457 0.962732i \(-0.412825\pi\)
0.270457 + 0.962732i \(0.412825\pi\)
\(770\) 6.00000 5.19615i 0.216225 0.187256i
\(771\) 4.00000 0.144056
\(772\) 11.5000 + 19.9186i 0.413894 + 0.716886i
\(773\) 7.00000 12.1244i 0.251773 0.436083i −0.712241 0.701935i \(-0.752320\pi\)
0.964014 + 0.265852i \(0.0856532\pi\)
\(774\) 3.00000 5.19615i 0.107833 0.186772i
\(775\) 14.0000 + 24.2487i 0.502895 + 0.871039i
\(776\) 5.00000 0.179490
\(777\) −1.00000 5.19615i −0.0358748 0.186411i<