Properties

Label 966.2.i.d.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.d.415.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.500000 + 0.866025i) q^{12} -6.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +3.00000 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} -3.00000 q^{20} +(-0.500000 + 2.59808i) q^{21} +1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} +(3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} -7.00000 q^{29} +(-1.50000 - 2.59808i) q^{30} +(-3.50000 + 6.06218i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} -2.00000 q^{34} +(-6.00000 - 5.19615i) q^{35} +1.00000 q^{36} +(1.00000 + 1.73205i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-3.00000 + 5.19615i) q^{39} +(1.50000 + 2.59808i) q^{40} -10.0000 q^{41} +(2.50000 - 0.866025i) q^{42} +2.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(1.50000 - 2.59808i) q^{45} +(0.500000 - 0.866025i) q^{46} +(-3.00000 - 5.19615i) q^{47} -1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(-1.00000 - 1.73205i) q^{51} +(3.00000 - 5.19615i) q^{52} +(-5.50000 + 9.52628i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{55} +(-2.50000 + 0.866025i) q^{56} +2.00000 q^{57} +(3.50000 + 6.06218i) q^{58} +(-7.50000 + 12.9904i) q^{59} +(-1.50000 + 2.59808i) q^{60} +(1.00000 + 1.73205i) q^{61} +7.00000 q^{62} +(2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-9.00000 - 15.5885i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-1.00000 + 1.73205i) q^{67} +(1.00000 + 1.73205i) q^{68} +1.00000 q^{69} +(-1.50000 + 7.79423i) q^{70} +(-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} +(0.500000 - 2.59808i) q^{77} +6.00000 q^{78} +(5.50000 + 9.52628i) q^{79} +(1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(5.00000 + 8.66025i) q^{82} +13.0000 q^{83} +(-2.00000 - 1.73205i) q^{84} +6.00000 q^{85} +(-1.00000 - 1.73205i) q^{86} +(-3.50000 + 6.06218i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-4.00000 - 6.92820i) q^{89} -3.00000 q^{90} +(15.0000 - 5.19615i) q^{91} -1.00000 q^{92} +(3.50000 + 6.06218i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(0.500000 + 0.866025i) q^{96} +1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q - q^{2} + q^{3} - q^{4} + 3 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} + 3 q^{10} - q^{11} + q^{12} - 12 q^{13} + 4 q^{14} + 6 q^{15} - q^{16} + 2 q^{17} - q^{18} + 2 q^{19} - 6 q^{20} - q^{21} + 2 q^{22} + q^{23} + q^{24} - 4 q^{25} + 6 q^{26} - 2 q^{27} + q^{28} - 14 q^{29} - 3 q^{30} - 7 q^{31} - q^{32} + q^{33} - 4 q^{34} - 12 q^{35} + 2 q^{36} + 2 q^{37} + 2 q^{38} - 6 q^{39} + 3 q^{40} - 20 q^{41} + 5 q^{42} + 4 q^{43} - q^{44} + 3 q^{45} + q^{46} - 6 q^{47} - 2 q^{48} + 11 q^{49} + 8 q^{50} - 2 q^{51} + 6 q^{52} - 11 q^{53} + q^{54} - 6 q^{55} - 5 q^{56} + 4 q^{57} + 7 q^{58} - 15 q^{59} - 3 q^{60} + 2 q^{61} + 14 q^{62} + 4 q^{63} + 2 q^{64} - 18 q^{65} + q^{66} - 2 q^{67} + 2 q^{68} + 2 q^{69} - 3 q^{70} - q^{72} + 10 q^{73} + 2 q^{74} + 4 q^{75} - 4 q^{76} + q^{77} + 12 q^{78} + 11 q^{79} + 3 q^{80} - q^{81} + 10 q^{82} + 26 q^{83} - 4 q^{84} + 12 q^{85} - 2 q^{86} - 7 q^{87} - q^{88} - 8 q^{89} - 6 q^{90} + 30 q^{91} - 2 q^{92} + 7 q^{93} - 6 q^{94} - 6 q^{95} + q^{96} + 2 q^{97} - 13 q^{98} + 2 q^{99} + O(q^{100}) \)

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
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) −1.00000 −0.408248
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i −0.931505 0.363727i \(-0.881504\pi\)
0.780750 + 0.624844i \(0.214837\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −6.00000 −1.66410 −0.832050 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.00000 + 1.73205i 0.534522 + 0.462910i
\(15\) 3.00000 0.774597
\(16\) −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 \(0.759652\pi\)
\(20\) −3.00000 −0.670820
\(21\) −0.500000 + 2.59808i −0.109109 + 0.566947i
\(22\) 1.00000 0.213201
\(23\) 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
\(26\) 3.00000 + 5.19615i 0.588348 + 1.01905i
\(27\) −1.00000 −0.192450
\(28\) 0.500000 2.59808i 0.0944911 0.490990i
\(29\) −7.00000 −1.29987 −0.649934 0.759991i \(-0.725203\pi\)
−0.649934 + 0.759991i \(0.725203\pi\)
\(30\) −1.50000 2.59808i −0.273861 0.474342i
\(31\) −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
\(33\) 0.500000 + 0.866025i 0.0870388 + 0.150756i
\(34\) −2.00000 −0.342997
\(35\) −6.00000 5.19615i −1.01419 0.878310i
\(36\) 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
\(39\) −3.00000 + 5.19615i −0.480384 + 0.832050i
\(40\) 1.50000 + 2.59808i 0.237171 + 0.410792i
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 2.50000 0.866025i 0.385758 0.133631i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 1.50000 2.59808i 0.223607 0.387298i
\(46\) 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
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 4.00000 0.565685
\(51\) −1.00000 1.73205i −0.140028 0.242536i
\(52\) 3.00000 5.19615i 0.416025 0.720577i
\(53\) −5.50000 + 9.52628i −0.755483 + 1.30854i 0.189651 + 0.981852i \(0.439264\pi\)
−0.945134 + 0.326683i \(0.894069\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −3.00000 −0.404520
\(56\) −2.50000 + 0.866025i −0.334077 + 0.115728i
\(57\) 2.00000 0.264906
\(58\) 3.50000 + 6.06218i 0.459573 + 0.796003i
\(59\) −7.50000 + 12.9904i −0.976417 + 1.69120i −0.301239 + 0.953549i \(0.597400\pi\)
−0.675178 + 0.737655i \(0.735933\pi\)
\(60\) −1.50000 + 2.59808i −0.193649 + 0.335410i
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) 7.00000 0.889001
\(63\) 2.00000 + 1.73205i 0.251976 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) −9.00000 15.5885i −1.11631 1.93351i
\(66\) 0.500000 0.866025i 0.0615457 0.106600i
\(67\) −1.00000 + 1.73205i −0.122169 + 0.211604i −0.920623 0.390453i \(-0.872318\pi\)
0.798454 + 0.602056i \(0.205652\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 1.00000 0.120386
\(70\) −1.50000 + 7.79423i −0.179284 + 0.931589i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −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
\(77\) 0.500000 2.59808i 0.0569803 0.296078i
\(78\) 6.00000 0.679366
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) 1.50000 2.59808i 0.167705 0.290474i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 5.00000 + 8.66025i 0.552158 + 0.956365i
\(83\) 13.0000 1.42694 0.713468 0.700688i \(-0.247124\pi\)
0.713468 + 0.700688i \(0.247124\pi\)
\(84\) −2.00000 1.73205i −0.218218 0.188982i
\(85\) 6.00000 0.650791
\(86\) −1.00000 1.73205i −0.107833 0.186772i
\(87\) −3.50000 + 6.06218i −0.375239 + 0.649934i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) −4.00000 6.92820i −0.423999 0.734388i 0.572327 0.820025i \(-0.306041\pi\)
−0.996326 + 0.0856373i \(0.972707\pi\)
\(90\) −3.00000 −0.316228
\(91\) 15.0000 5.19615i 1.57243 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
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 1.00000 0.101535 0.0507673 0.998711i \(-0.483833\pi\)
0.0507673 + 0.998711i \(0.483833\pi\)
\(98\) −6.50000 2.59808i −0.656599 0.262445i
\(99\) 1.00000 0.100504
\(100\) −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
\(103\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(104\) −6.00000 −0.588348
\(105\) −7.50000 + 2.59808i −0.731925 + 0.253546i
\(106\) 11.0000 1.06841
\(107\) 8.50000 + 14.7224i 0.821726 + 1.42327i 0.904396 + 0.426694i \(0.140322\pi\)
−0.0826699 + 0.996577i \(0.526345\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 7.00000 12.1244i 0.670478 1.16130i −0.307290 0.951616i \(-0.599422\pi\)
0.977769 0.209687i \(-0.0672444\pi\)
\(110\) 1.50000 + 2.59808i 0.143019 + 0.247717i
\(111\) 2.00000 0.189832
\(112\) 2.00000 + 1.73205i 0.188982 + 0.163663i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −1.00000 1.73205i −0.0936586 0.162221i
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) 3.50000 6.06218i 0.324967 0.562859i
\(117\) 3.00000 + 5.19615i 0.277350 + 0.480384i
\(118\) 15.0000 1.38086
\(119\) −1.00000 + 5.19615i −0.0916698 + 0.476331i
\(120\) 3.00000 0.273861
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 1.00000 1.73205i 0.0905357 0.156813i
\(123\) −5.00000 + 8.66025i −0.450835 + 0.780869i
\(124\) −3.50000 6.06218i −0.314309 0.544400i
\(125\) 3.00000 0.268328
\(126\) 0.500000 2.59808i 0.0445435 0.231455i
\(127\) 17.0000 1.50851 0.754253 0.656584i \(-0.227999\pi\)
0.754253 + 0.656584i \(0.227999\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 1.00000 1.73205i 0.0880451 0.152499i
\(130\) −9.00000 + 15.5885i −0.789352 + 1.36720i
\(131\) −3.50000 6.06218i −0.305796 0.529655i 0.671642 0.740876i \(-0.265589\pi\)
−0.977438 + 0.211221i \(0.932256\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −4.00000 3.46410i −0.346844 0.300376i
\(134\) 2.00000 0.172774
\(135\) −1.50000 2.59808i −0.129099 0.223607i
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) −1.00000 + 1.73205i −0.0854358 + 0.147979i −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) −0.500000 0.866025i −0.0425628 0.0737210i
\(139\) −2.00000 −0.169638 −0.0848189 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 7.50000 2.59808i 0.633866 0.219578i
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −10.5000 18.1865i −0.871978 1.51031i
\(146\) −10.0000 −0.827606
\(147\) −1.00000 6.92820i −0.0824786 0.571429i
\(148\) −2.00000 −0.164399
\(149\) −5.00000 8.66025i −0.409616 0.709476i 0.585231 0.810867i \(-0.301004\pi\)
−0.994847 + 0.101391i \(0.967671\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) −9.50000 + 16.4545i −0.773099 + 1.33905i 0.162758 + 0.986666i \(0.447961\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) −2.00000 −0.161690
\(154\) −2.50000 + 0.866025i −0.201456 + 0.0697863i
\(155\) −21.0000 −1.68676
\(156\) −3.00000 5.19615i −0.240192 0.416025i
\(157\) −11.0000 + 19.0526i −0.877896 + 1.52056i −0.0242497 + 0.999706i \(0.507720\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(158\) 5.50000 9.52628i 0.437557 0.757870i
\(159\) 5.50000 + 9.52628i 0.436178 + 0.755483i
\(160\) −3.00000 −0.237171
\(161\) −2.00000 1.73205i −0.157622 0.136505i
\(162\) 1.00000 0.0785674
\(163\) −5.00000 8.66025i −0.391630 0.678323i 0.601035 0.799223i \(-0.294755\pi\)
−0.992665 + 0.120900i \(0.961422\pi\)
\(164\) 5.00000 8.66025i 0.390434 0.676252i
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) −6.50000 11.2583i −0.504498 0.873816i
\(167\) 6.00000 0.464294 0.232147 0.972681i \(-0.425425\pi\)
0.232147 + 0.972681i \(0.425425\pi\)
\(168\) −0.500000 + 2.59808i −0.0385758 + 0.200446i
\(169\) 23.0000 1.76923
\(170\) −3.00000 5.19615i −0.230089 0.398527i
\(171\) 1.00000 1.73205i 0.0764719 0.132453i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −5.00000 8.66025i −0.380143 0.658427i 0.610939 0.791677i \(-0.290792\pi\)
−0.991082 + 0.133250i \(0.957459\pi\)
\(174\) 7.00000 0.530669
\(175\) 2.00000 10.3923i 0.151186 0.785584i
\(176\) 1.00000 0.0753778
\(177\) 7.50000 + 12.9904i 0.563735 + 0.976417i
\(178\) −4.00000 + 6.92820i −0.299813 + 0.519291i
\(179\) −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) 1.50000 + 2.59808i 0.111803 + 0.193649i
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −12.0000 10.3923i −0.889499 0.770329i
\(183\) 2.00000 0.147844
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 3.50000 6.06218i 0.256632 0.444500i
\(187\) 1.00000 + 1.73205i 0.0731272 + 0.126660i
\(188\) 6.00000 0.437595
\(189\) 2.50000 0.866025i 0.181848 0.0629941i
\(190\) 6.00000 0.435286
\(191\) −13.0000 22.5167i −0.940647 1.62925i −0.764241 0.644931i \(-0.776886\pi\)
−0.176406 0.984317i \(-0.556447\pi\)
\(192\) 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 \(-0.143734\pi\)
\(194\) −0.500000 0.866025i −0.0358979 0.0621770i
\(195\) −18.0000 −1.28901
\(196\) 1.00000 + 6.92820i 0.0714286 + 0.494872i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) −0.500000 0.866025i −0.0355335 0.0615457i
\(199\) −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) −2.00000 + 3.46410i −0.141421 + 0.244949i
\(201\) 1.00000 + 1.73205i 0.0705346 + 0.122169i
\(202\) −10.0000 −0.703598
\(203\) 17.5000 6.06218i 1.22826 0.425481i
\(204\) 2.00000 0.140028
\(205\) −15.0000 25.9808i −1.04765 1.81458i
\(206\) 0 0
\(207\) 0.500000 0.866025i 0.0347524 0.0601929i
\(208\) 3.00000 + 5.19615i 0.208013 + 0.360288i
\(209\) −2.00000 −0.138343
\(210\) 6.00000 + 5.19615i 0.414039 + 0.358569i
\(211\) 6.00000 0.413057 0.206529 0.978441i \(-0.433783\pi\)
0.206529 + 0.978441i \(0.433783\pi\)
\(212\) −5.50000 9.52628i −0.377742 0.654268i
\(213\) 0 0
\(214\) 8.50000 14.7224i 0.581048 1.00640i
\(215\) 3.00000 + 5.19615i 0.204598 + 0.354375i
\(216\) −1.00000 −0.0680414
\(217\) 3.50000 18.1865i 0.237595 1.23458i
\(218\) −14.0000 −0.948200
\(219\) −5.00000 8.66025i −0.337869 0.585206i
\(220\) 1.50000 2.59808i 0.101130 0.175162i
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) −1.00000 1.73205i −0.0671156 0.116248i
\(223\) 21.0000 1.40626 0.703132 0.711059i \(-0.251784\pi\)
0.703132 + 0.711059i \(0.251784\pi\)
\(224\) 0.500000 2.59808i 0.0334077 0.173591i
\(225\) 4.00000 0.266667
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) 6.50000 11.2583i 0.431420 0.747242i −0.565576 0.824696i \(-0.691346\pi\)
0.996996 + 0.0774548i \(0.0246793\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 3.00000 0.197814
\(231\) −2.00000 1.73205i −0.131590 0.113961i
\(232\) −7.00000 −0.459573
\(233\) −9.00000 15.5885i −0.589610 1.02123i −0.994283 0.106773i \(-0.965948\pi\)
0.404674 0.914461i \(-0.367385\pi\)
\(234\) 3.00000 5.19615i 0.196116 0.339683i
\(235\) 9.00000 15.5885i 0.587095 1.01688i
\(236\) −7.50000 12.9904i −0.488208 0.845602i
\(237\) 11.0000 0.714527
\(238\) 5.00000 1.73205i 0.324102 0.112272i
\(239\) 20.0000 1.29369 0.646846 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) −1.50000 2.59808i −0.0968246 0.167705i
\(241\) 3.50000 6.06218i 0.225455 0.390499i −0.731001 0.682376i \(-0.760947\pi\)
0.956456 + 0.291877i \(0.0942799\pi\)
\(242\) 5.00000 8.66025i 0.321412 0.556702i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −2.00000 −0.128037
\(245\) 19.5000 + 7.79423i 1.24581 + 0.497955i
\(246\) 10.0000 0.637577
\(247\) −6.00000 10.3923i −0.381771 0.661247i
\(248\) −3.50000 + 6.06218i −0.222250 + 0.384949i
\(249\) 6.50000 11.2583i 0.411921 0.713468i
\(250\) −1.50000 2.59808i −0.0948683 0.164317i
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) −2.50000 + 0.866025i −0.157485 + 0.0545545i
\(253\) −1.00000 −0.0628695
\(254\) −8.50000 14.7224i −0.533337 0.923768i
\(255\) 3.00000 5.19615i 0.187867 0.325396i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.00000 + 10.3923i 0.374270 + 0.648254i 0.990217 0.139533i \(-0.0445601\pi\)
−0.615948 + 0.787787i \(0.711227\pi\)
\(258\) −2.00000 −0.124515
\(259\) −4.00000 3.46410i −0.248548 0.215249i
\(260\) 18.0000 1.11631
\(261\) 3.50000 + 6.06218i 0.216645 + 0.375239i
\(262\) −3.50000 + 6.06218i −0.216231 + 0.374523i
\(263\) −3.00000 + 5.19615i −0.184988 + 0.320408i −0.943572 0.331166i \(-0.892558\pi\)
0.758585 + 0.651575i \(0.225891\pi\)
\(264\) 0.500000 + 0.866025i 0.0307729 + 0.0533002i
\(265\) −33.0000 −2.02717
\(266\) −1.00000 + 5.19615i −0.0613139 + 0.318597i
\(267\) −8.00000 −0.489592
\(268\) −1.00000 1.73205i −0.0610847 0.105802i
\(269\) −14.5000 + 25.1147i −0.884081 + 1.53127i −0.0373168 + 0.999303i \(0.511881\pi\)
−0.846764 + 0.531969i \(0.821452\pi\)
\(270\) −1.50000 + 2.59808i −0.0912871 + 0.158114i
\(271\) 0.500000 + 0.866025i 0.0303728 + 0.0526073i 0.880812 0.473466i \(-0.156997\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −2.00000 −0.121268
\(273\) 3.00000 15.5885i 0.181568 0.943456i
\(274\) 2.00000 0.120824
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) −0.500000 + 0.866025i −0.0300965 + 0.0521286i
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) 1.00000 + 1.73205i 0.0599760 + 0.103882i
\(279\) 7.00000 0.419079
\(280\) −6.00000 5.19615i −0.358569 0.310530i
\(281\) 20.0000 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) 3.00000 + 5.19615i 0.178647 + 0.309426i
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) 0 0
\(285\) 3.00000 + 5.19615i 0.177705 + 0.307794i
\(286\) −6.00000 −0.354787
\(287\) 25.0000 8.66025i 1.47570 0.511199i
\(288\) 1.00000 0.0589256
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −10.5000 + 18.1865i −0.616581 + 1.06795i
\(291\) 0.500000 0.866025i 0.0293105 0.0507673i
\(292\) 5.00000 + 8.66025i 0.292603 + 0.506803i
\(293\) −1.00000 −0.0584206 −0.0292103 0.999573i \(-0.509299\pi\)
−0.0292103 + 0.999573i \(0.509299\pi\)
\(294\) −5.50000 + 4.33013i −0.320767 + 0.252538i
\(295\) −45.0000 −2.62000
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) 0.500000 0.866025i 0.0290129 0.0502519i
\(298\) −5.00000 + 8.66025i −0.289642 + 0.501675i
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) −4.00000 −0.230940
\(301\) −5.00000 + 1.73205i −0.288195 + 0.0998337i
\(302\) 19.0000 1.09333
\(303\) −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
\(307\) 6.00000 0.342438 0.171219 0.985233i \(-0.445229\pi\)
0.171219 + 0.985233i \(0.445229\pi\)
\(308\) 2.00000 + 1.73205i 0.113961 + 0.0986928i
\(309\) 0 0
\(310\) 10.5000 + 18.1865i 0.596360 + 1.03293i
\(311\) −3.00000 + 5.19615i −0.170114 + 0.294647i −0.938460 0.345389i \(-0.887747\pi\)
0.768345 + 0.640036i \(0.221080\pi\)
\(312\) −3.00000 + 5.19615i −0.169842 + 0.294174i
\(313\) −13.5000 23.3827i −0.763065 1.32167i −0.941263 0.337673i \(-0.890360\pi\)
0.178198 0.983995i \(-0.442973\pi\)
\(314\) 22.0000 1.24153
\(315\) −1.50000 + 7.79423i −0.0845154 + 0.439155i
\(316\) −11.0000 −0.618798
\(317\) 7.50000 + 12.9904i 0.421242 + 0.729612i 0.996061 0.0886679i \(-0.0282610\pi\)
−0.574819 + 0.818280i \(0.694928\pi\)
\(318\) 5.50000 9.52628i 0.308425 0.534207i
\(319\) 3.50000 6.06218i 0.195962 0.339417i
\(320\) 1.50000 + 2.59808i 0.0838525 + 0.145237i
\(321\) 17.0000 0.948847
\(322\) −0.500000 + 2.59808i −0.0278639 + 0.144785i
\(323\) 4.00000 0.222566
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 12.0000 20.7846i 0.665640 1.15292i
\(326\) −5.00000 + 8.66025i −0.276924 + 0.479647i
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) −10.0000 −0.552158
\(329\) 12.0000 + 10.3923i 0.661581 + 0.572946i
\(330\) 3.00000 0.165145
\(331\) 7.00000 + 12.1244i 0.384755 + 0.666415i 0.991735 0.128302i \(-0.0409527\pi\)
−0.606980 + 0.794717i \(0.707619\pi\)
\(332\) −6.50000 + 11.2583i −0.356734 + 0.617881i
\(333\) 1.00000 1.73205i 0.0547997 0.0949158i
\(334\) −3.00000 5.19615i −0.164153 0.284321i
\(335\) −6.00000 −0.327815
\(336\) 2.50000 0.866025i 0.136386 0.0472456i
\(337\) 35.0000 1.90657 0.953286 0.302070i \(-0.0976776\pi\)
0.953286 + 0.302070i \(0.0976776\pi\)
\(338\) −11.5000 19.9186i −0.625518 1.08343i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) −3.50000 6.06218i −0.189536 0.328285i
\(342\) −2.00000 −0.108148
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 2.00000 0.107833
\(345\) 1.50000 + 2.59808i 0.0807573 + 0.139876i
\(346\) −5.00000 + 8.66025i −0.268802 + 0.465578i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) −3.50000 6.06218i −0.187620 0.324967i
\(349\) −24.0000 −1.28469 −0.642345 0.766415i \(-0.722038\pi\)
−0.642345 + 0.766415i \(0.722038\pi\)
\(350\) −10.0000 + 3.46410i −0.534522 + 0.185164i
\(351\) 6.00000 0.320256
\(352\) −0.500000 0.866025i −0.0266501 0.0461593i
\(353\) −7.00000 + 12.1244i −0.372572 + 0.645314i −0.989960 0.141344i \(-0.954858\pi\)
0.617388 + 0.786659i \(0.288191\pi\)
\(354\) 7.50000 12.9904i 0.398621 0.690431i
\(355\) 0 0
\(356\) 8.00000 0.423999
\(357\) 4.00000 + 3.46410i 0.211702 + 0.183340i
\(358\) 4.00000 0.211407
\(359\) −3.00000 5.19615i −0.158334 0.274242i 0.775934 0.630814i \(-0.217279\pi\)
−0.934268 + 0.356572i \(0.883946\pi\)
\(360\) 1.50000 2.59808i 0.0790569 0.136931i
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) 8.00000 + 13.8564i 0.420471 + 0.728277i
\(363\) 10.0000 0.524864
\(364\) −3.00000 + 15.5885i −0.157243 + 0.817057i
\(365\) 30.0000 1.57027
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) −5.50000 + 9.52628i −0.287098 + 0.497268i −0.973116 0.230317i \(-0.926024\pi\)
0.686018 + 0.727585i \(0.259357\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) 5.00000 + 8.66025i 0.260290 + 0.450835i
\(370\) 6.00000 0.311925
\(371\) 5.50000 28.5788i 0.285546 1.48374i
\(372\) −7.00000 −0.362933
\(373\) −8.00000 13.8564i −0.414224 0.717458i 0.581122 0.813816i \(-0.302614\pi\)
−0.995347 + 0.0963587i \(0.969280\pi\)
\(374\) 1.00000 1.73205i 0.0517088 0.0895622i
\(375\) 1.50000 2.59808i 0.0774597 0.134164i
\(376\) −3.00000 5.19615i −0.154713 0.267971i
\(377\) 42.0000 2.16311
\(378\) −2.00000 1.73205i −0.102869 0.0890871i
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) −3.00000 5.19615i −0.153897 0.266557i
\(381\) 8.50000 14.7224i 0.435468 0.754253i
\(382\) −13.0000 + 22.5167i −0.665138 + 1.15205i
\(383\) −8.00000 13.8564i −0.408781 0.708029i 0.585973 0.810331i \(-0.300713\pi\)
−0.994753 + 0.102302i \(0.967379\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 7.50000 2.59808i 0.382235 0.132410i
\(386\) −23.0000 −1.17067
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) −0.500000 + 0.866025i −0.0253837 + 0.0439658i
\(389\) −3.00000 + 5.19615i −0.152106 + 0.263455i −0.932002 0.362454i \(-0.881939\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(390\) 9.00000 + 15.5885i 0.455733 + 0.789352i
\(391\) 2.00000 0.101144
\(392\) 5.50000 4.33013i 0.277792 0.218704i
\(393\) −7.00000 −0.353103
\(394\) 1.00000 + 1.73205i 0.0503793 + 0.0872595i
\(395\) −16.5000 + 28.5788i −0.830205 + 1.43796i
\(396\) −0.500000 + 0.866025i −0.0251259 + 0.0435194i
\(397\) −1.00000 1.73205i −0.0501886 0.0869291i 0.839840 0.542834i \(-0.182649\pi\)
−0.890028 + 0.455905i \(0.849316\pi\)
\(398\) 20.0000 1.00251
\(399\) −5.00000 + 1.73205i −0.250313 + 0.0867110i
\(400\) 4.00000 0.200000
\(401\) −2.00000 3.46410i −0.0998752 0.172989i 0.811758 0.583994i \(-0.198511\pi\)
−0.911633 + 0.411005i \(0.865178\pi\)
\(402\) 1.00000 1.73205i 0.0498755 0.0863868i
\(403\) 21.0000 36.3731i 1.04608 1.81187i
\(404\) 5.00000 + 8.66025i 0.248759 + 0.430864i
\(405\) −3.00000 −0.149071
\(406\) −14.0000 12.1244i −0.694808 0.601722i
\(407\) −2.00000 −0.0991363
\(408\) −1.00000 1.73205i −0.0495074 0.0857493i
\(409\) −9.50000 + 16.4545i −0.469745 + 0.813622i −0.999402 0.0345902i \(-0.988987\pi\)
0.529657 + 0.848212i \(0.322321\pi\)
\(410\) −15.0000 + 25.9808i −0.740797 + 1.28310i
\(411\) 1.00000 + 1.73205i 0.0493264 + 0.0854358i
\(412\) 0 0
\(413\) 7.50000 38.9711i 0.369051 1.91764i
\(414\) −1.00000 −0.0491473
\(415\) 19.5000 + 33.7750i 0.957217 + 1.65795i
\(416\) 3.00000 5.19615i 0.147087 0.254762i
\(417\) −1.00000 + 1.73205i −0.0489702 + 0.0848189i
\(418\) 1.00000 + 1.73205i 0.0489116 + 0.0847174i
\(419\) 4.00000 0.195413 0.0977064 0.995215i \(-0.468849\pi\)
0.0977064 + 0.995215i \(0.468849\pi\)
\(420\) 1.50000 7.79423i 0.0731925 0.380319i
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −3.00000 5.19615i −0.146038 0.252945i
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) −5.50000 + 9.52628i −0.267104 + 0.462637i
\(425\) 4.00000 + 6.92820i 0.194029 + 0.336067i
\(426\) 0 0
\(427\) −4.00000 3.46410i −0.193574 0.167640i
\(428\) −17.0000 −0.821726
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) 3.00000 5.19615i 0.144673 0.250581i
\(431\) −8.00000 + 13.8564i −0.385346 + 0.667440i −0.991817 0.127666i \(-0.959251\pi\)
0.606471 + 0.795106i \(0.292585\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) −17.5000 + 6.06218i −0.840027 + 0.290994i
\(435\) −21.0000 −1.00687
\(436\) 7.00000 + 12.1244i 0.335239 + 0.580651i
\(437\) −1.00000 + 1.73205i −0.0478365 + 0.0828552i
\(438\) −5.00000 + 8.66025i −0.238909 + 0.413803i
\(439\) 14.5000 + 25.1147i 0.692047 + 1.19866i 0.971166 + 0.238404i \(0.0766244\pi\)
−0.279119 + 0.960257i \(0.590042\pi\)
\(440\) −3.00000 −0.143019
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 12.0000 0.570782
\(443\) −5.50000 9.52628i −0.261313 0.452607i 0.705278 0.708931i \(-0.250822\pi\)
−0.966591 + 0.256323i \(0.917489\pi\)
\(444\) −1.00000 + 1.73205i −0.0474579 + 0.0821995i
\(445\) 12.0000 20.7846i 0.568855 0.985285i
\(446\) −10.5000 18.1865i −0.497189 0.861157i
\(447\) −10.0000 −0.472984
\(448\) −2.50000 + 0.866025i −0.118114 + 0.0409159i
\(449\) −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
\(451\) 5.00000 8.66025i 0.235441 0.407795i
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 9.50000 + 16.4545i 0.446349 + 0.773099i
\(454\) −13.0000 −0.610120
\(455\) 36.0000 + 31.1769i 1.68771 + 1.46160i
\(456\) 2.00000 0.0936586
\(457\) 5.50000 + 9.52628i 0.257279 + 0.445621i 0.965512 0.260358i \(-0.0838407\pi\)
−0.708233 + 0.705979i \(0.750507\pi\)
\(458\) 5.00000 8.66025i 0.233635 0.404667i
\(459\) −1.00000 + 1.73205i −0.0466760 + 0.0808452i
\(460\) −1.50000 2.59808i −0.0699379 0.121136i
\(461\) −30.0000 −1.39724 −0.698620 0.715493i \(-0.746202\pi\)
−0.698620 + 0.715493i \(0.746202\pi\)
\(462\) −0.500000 + 2.59808i −0.0232621 + 0.120873i
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 3.50000 + 6.06218i 0.162483 + 0.281430i
\(465\) −10.5000 + 18.1865i −0.486926 + 0.843380i
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) 10.0000 + 17.3205i 0.462745 + 0.801498i 0.999097 0.0424970i \(-0.0135313\pi\)
−0.536352 + 0.843995i \(0.680198\pi\)
\(468\) −6.00000 −0.277350
\(469\) 1.00000 5.19615i 0.0461757 0.239936i
\(470\) −18.0000 −0.830278
\(471\) 11.0000 + 19.0526i 0.506853 + 0.877896i
\(472\) −7.50000 + 12.9904i −0.345215 + 0.597931i
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) −5.50000 9.52628i −0.252623 0.437557i
\(475\) −8.00000 −0.367065
\(476\) −4.00000 3.46410i −0.183340 0.158777i
\(477\) 11.0000 0.503655
\(478\) −10.0000 17.3205i −0.457389 0.792222i
\(479\) −10.0000 + 17.3205i −0.456912 + 0.791394i −0.998796 0.0490589i \(-0.984378\pi\)
0.541884 + 0.840453i \(0.317711\pi\)
\(480\) −1.50000 + 2.59808i −0.0684653 + 0.118585i
\(481\) −6.00000 10.3923i −0.273576 0.473848i
\(482\) −7.00000 −0.318841
\(483\) −2.50000 + 0.866025i −0.113754 + 0.0394055i
\(484\) −10.0000 −0.454545
\(485\) 1.50000 + 2.59808i 0.0681115 + 0.117973i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) −0.500000 + 0.866025i −0.0226572 + 0.0392434i −0.877132 0.480250i \(-0.840546\pi\)
0.854475 + 0.519493i \(0.173879\pi\)
\(488\) 1.00000 + 1.73205i 0.0452679 + 0.0784063i
\(489\) −10.0000 −0.452216
\(490\) −3.00000 20.7846i −0.135526 0.938953i
\(491\) −29.0000 −1.30875 −0.654376 0.756169i \(-0.727069\pi\)
−0.654376 + 0.756169i \(0.727069\pi\)
\(492\) −5.00000 8.66025i −0.225417 0.390434i
\(493\) −7.00000 + 12.1244i −0.315264 + 0.546054i
\(494\) −6.00000 + 10.3923i −0.269953 + 0.467572i
\(495\) 1.50000 + 2.59808i 0.0674200 + 0.116775i
\(496\) 7.00000 0.314309
\(497\) 0 0
\(498\) −13.0000 −0.582544
\(499\) 5.00000 + 8.66025i 0.223831 + 0.387686i 0.955968 0.293471i \(-0.0948104\pi\)
−0.732137 + 0.681157i \(0.761477\pi\)
\(500\) −1.50000 + 2.59808i −0.0670820 + 0.116190i
\(501\) 3.00000 5.19615i 0.134030 0.232147i
\(502\) 7.50000 + 12.9904i 0.334741 + 0.579789i
\(503\) −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
\(505\) 30.0000 1.33498
\(506\) 0.500000 + 0.866025i 0.0222277 + 0.0384995i
\(507\) 11.5000 19.9186i 0.510733 0.884615i
\(508\) −8.50000 + 14.7224i −0.377127 + 0.653202i
\(509\) 7.50000 + 12.9904i 0.332432 + 0.575789i 0.982988 0.183669i \(-0.0587976\pi\)
−0.650556 + 0.759458i \(0.725464\pi\)
\(510\) −6.00000 −0.265684
\(511\) −5.00000 + 25.9808i −0.221187 + 1.14932i
\(512\) 1.00000 0.0441942
\(513\) −1.00000 1.73205i −0.0441511 0.0764719i
\(514\) 6.00000 10.3923i 0.264649 0.458385i
\(515\) 0 0
\(516\) 1.00000 + 1.73205i 0.0440225 + 0.0762493i
\(517\) 6.00000 0.263880
\(518\) −1.00000 + 5.19615i −0.0439375 + 0.228306i
\(519\) −10.0000 −0.438951
\(520\) −9.00000 15.5885i −0.394676 0.683599i
\(521\) −19.0000 + 32.9090i −0.832405 + 1.44177i 0.0637207 + 0.997968i \(0.479703\pi\)
−0.896126 + 0.443800i \(0.853630\pi\)
\(522\) 3.50000 6.06218i 0.153191 0.265334i
\(523\) −2.00000 3.46410i −0.0874539 0.151475i 0.818980 0.573822i \(-0.194540\pi\)
−0.906434 + 0.422347i \(0.861206\pi\)
\(524\) 7.00000 0.305796
\(525\) −8.00000 6.92820i −0.349149 0.302372i
\(526\) 6.00000 0.261612
\(527\) 7.00000 + 12.1244i 0.304925 + 0.528145i
\(528\) 0.500000 0.866025i 0.0217597 0.0376889i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) 16.5000 + 28.5788i 0.716714 + 1.24139i
\(531\) 15.0000 0.650945
\(532\) 5.00000 1.73205i 0.216777 0.0750939i
\(533\) 60.0000 2.59889
\(534\) 4.00000 + 6.92820i 0.173097 + 0.299813i
\(535\) −25.5000 + 44.1673i −1.10246 + 1.90952i
\(536\) −1.00000 + 1.73205i −0.0431934 + 0.0748132i
\(537\) 2.00000 + 3.46410i 0.0863064 + 0.149487i
\(538\) 29.0000 1.25028
\(539\) 1.00000 + 6.92820i 0.0430730 + 0.298419i
\(540\) 3.00000 0.129099
\(541\) 16.0000 + 27.7128i 0.687894 + 1.19147i 0.972518 + 0.232828i \(0.0747978\pi\)
−0.284624 + 0.958639i \(0.591869\pi\)
\(542\) 0.500000 0.866025i 0.0214768 0.0371990i
\(543\) −8.00000 + 13.8564i −0.343313 + 0.594635i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) 42.0000 1.79908
\(546\) −15.0000 + 5.19615i −0.641941 + 0.222375i
\(547\) 18.0000 0.769624 0.384812 0.922995i \(-0.374266\pi\)
0.384812 + 0.922995i \(0.374266\pi\)
\(548\) −1.00000 1.73205i −0.0427179 0.0739895i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) −7.00000 12.1244i −0.298210 0.516515i
\(552\) 1.00000 0.0425628
\(553\) −22.0000 19.0526i −0.935535 0.810197i
\(554\) 8.00000 0.339887
\(555\) 3.00000 + 5.19615i 0.127343 + 0.220564i
\(556\) 1.00000 1.73205i 0.0424094 0.0734553i
\(557\) 13.5000 23.3827i 0.572013 0.990756i −0.424346 0.905500i \(-0.639496\pi\)
0.996359 0.0852559i \(-0.0271708\pi\)
\(558\) −3.50000 6.06218i −0.148167 0.256632i
\(559\) −12.0000 −0.507546
\(560\) −1.50000 + 7.79423i −0.0633866 + 0.329366i
\(561\) 2.00000 0.0844401
\(562\) −10.0000 17.3205i −0.421825 0.730622i
\(563\) −20.5000 + 35.5070i −0.863972 + 1.49644i 0.00409232 + 0.999992i \(0.498697\pi\)
−0.868064 + 0.496452i \(0.834636\pi\)
\(564\) 3.00000 5.19615i 0.126323 0.218797i
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 14.0000 0.588464
\(567\) 0.500000 2.59808i 0.0209980 0.109109i
\(568\) 0 0
\(569\) −6.00000 10.3923i −0.251533 0.435668i 0.712415 0.701758i \(-0.247601\pi\)
−0.963948 + 0.266090i \(0.914268\pi\)
\(570\) 3.00000 5.19615i 0.125656 0.217643i
\(571\) −6.00000 + 10.3923i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) 3.00000 + 5.19615i 0.125436 + 0.217262i
\(573\) −26.0000 −1.08617
\(574\) −20.0000 17.3205i −0.834784 0.722944i
\(575\) −4.00000 −0.166812
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 12.5000 21.6506i 0.520382 0.901328i −0.479337 0.877631i \(-0.659123\pi\)
0.999719 0.0236970i \(-0.00754370\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) −11.5000 19.9186i −0.477924 0.827788i
\(580\) 21.0000 0.871978
\(581\) −32.5000 + 11.2583i −1.34833 + 0.467074i
\(582\) −1.00000 −0.0414513
\(583\) −5.50000 9.52628i −0.227787 0.394538i
\(584\) 5.00000 8.66025i 0.206901 0.358364i
\(585\) −9.00000 + 15.5885i −0.372104 + 0.644503i
\(586\) 0.500000 + 0.866025i 0.0206548 + 0.0357752i
\(587\) −3.00000 −0.123823 −0.0619116 0.998082i \(-0.519720\pi\)
−0.0619116 + 0.998082i \(0.519720\pi\)
\(588\) 6.50000 + 2.59808i 0.268055 + 0.107143i
\(589\) −14.0000 −0.576860
\(590\) 22.5000 + 38.9711i 0.926310 + 1.60442i
\(591\) −1.00000 + 1.73205i −0.0411345 + 0.0712470i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −10.0000 17.3205i −0.410651 0.711268i 0.584310 0.811530i \(-0.301365\pi\)
−0.994961 + 0.100262i \(0.968032\pi\)
\(594\) −1.00000 −0.0410305
\(595\) −15.0000 + 5.19615i −0.614940 + 0.213021i
\(596\) 10.0000 0.409616
\(597\) 10.0000 + 17.3205i 0.409273 + 0.708881i
\(598\) −3.00000 + 5.19615i −0.122679 + 0.212486i
\(599\) −8.00000 + 13.8564i −0.326871 + 0.566157i −0.981889 0.189456i \(-0.939328\pi\)
0.655018 + 0.755613i \(0.272661\pi\)
\(600\) 2.00000 + 3.46410i 0.0816497 + 0.141421i
\(601\) −17.0000 −0.693444 −0.346722 0.937968i \(-0.612705\pi\)
−0.346722 + 0.937968i \(0.612705\pi\)
\(602\) 4.00000 + 3.46410i 0.163028 + 0.141186i
\(603\) 2.00000 0.0814463
\(604\) −9.50000 16.4545i −0.386550 0.669523i
\(605\) −15.0000 + 25.9808i −0.609837 + 1.05627i
\(606\) −5.00000 + 8.66025i −0.203111 + 0.351799i
\(607\) 9.50000 + 16.4545i 0.385593 + 0.667867i 0.991851 0.127401i \(-0.0406635\pi\)
−0.606258 + 0.795268i \(0.707330\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 3.50000 18.1865i 0.141827 0.736956i
\(610\) 6.00000 0.242933
\(611\) 18.0000 + 31.1769i 0.728202 + 1.26128i
\(612\) 1.00000 1.73205i 0.0404226 0.0700140i
\(613\) 14.0000 24.2487i 0.565455 0.979396i −0.431553 0.902088i \(-0.642034\pi\)
0.997007 0.0773084i \(-0.0246326\pi\)
\(614\) −3.00000 5.19615i −0.121070 0.209700i
\(615\) −30.0000 −1.20972
\(616\) 0.500000 2.59808i 0.0201456 0.104679i
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) 20.0000 34.6410i 0.803868 1.39234i −0.113185 0.993574i \(-0.536105\pi\)
0.917053 0.398766i \(-0.130561\pi\)
\(620\) 10.5000 18.1865i 0.421690 0.730389i
\(621\) −0.500000 0.866025i −0.0200643 0.0347524i
\(622\) 6.00000 0.240578
\(623\) 16.0000 + 13.8564i 0.641026 + 0.555145i
\(624\) 6.00000 0.240192
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −13.5000 + 23.3827i −0.539569 + 0.934560i
\(627\) −1.00000 + 1.73205i −0.0399362 + 0.0691714i
\(628\) −11.0000 19.0526i −0.438948 0.760280i
\(629\) 4.00000 0.159490
\(630\) 7.50000 2.59808i 0.298807 0.103510i
\(631\) −21.0000 −0.835997 −0.417998 0.908448i \(-0.637268\pi\)
−0.417998 + 0.908448i \(0.637268\pi\)
\(632\) 5.50000 + 9.52628i 0.218778 + 0.378935i
\(633\) 3.00000 5.19615i 0.119239 0.206529i
\(634\) 7.50000 12.9904i 0.297863 0.515914i
\(635\) 25.5000 + 44.1673i 1.01194 + 1.75273i
\(636\) −11.0000 −0.436178
\(637\) −33.0000 + 25.9808i −1.30751 + 1.02940i
\(638\) −7.00000 −0.277133
\(639\) 0 0
\(640\) 1.50000 2.59808i 0.0592927 0.102698i
\(641\) 10.0000 17.3205i 0.394976 0.684119i −0.598122 0.801405i \(-0.704086\pi\)
0.993098 + 0.117286i \(0.0374195\pi\)
\(642\) −8.50000 14.7224i −0.335468 0.581048i
\(643\) 44.0000 1.73519 0.867595 0.497271i \(-0.165665\pi\)
0.867595 + 0.497271i \(0.165665\pi\)
\(644\) 2.50000 0.866025i 0.0985138 0.0341262i
\(645\) 6.00000 0.236250
\(646\) −2.00000 3.46410i −0.0786889 0.136293i
\(647\) −11.0000 + 19.0526i −0.432455 + 0.749033i −0.997084 0.0763112i \(-0.975686\pi\)
0.564629 + 0.825345i \(0.309019\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −7.50000 12.9904i −0.294401 0.509917i
\(650\) −24.0000 −0.941357
\(651\) −14.0000 12.1244i −0.548703 0.475191i
\(652\) 10.0000 0.391630
\(653\) 18.5000 + 32.0429i 0.723961 + 1.25394i 0.959400 + 0.282048i \(0.0910138\pi\)
−0.235439 + 0.971889i \(0.575653\pi\)
\(654\) −7.00000 + 12.1244i −0.273722 + 0.474100i
\(655\) 10.5000 18.1865i 0.410269 0.710607i
\(656\) 5.00000 + 8.66025i 0.195217 + 0.338126i
\(657\) −10.0000 −0.390137
\(658\) 3.00000 15.5885i 0.116952 0.607701i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) 25.0000 43.3013i 0.972387 1.68422i 0.284087 0.958799i \(-0.408310\pi\)
0.688301 0.725426i \(-0.258357\pi\)
\(662\) 7.00000 12.1244i 0.272063 0.471226i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) 13.0000 0.504498
\(665\) 3.00000 15.5885i 0.116335 0.604494i
\(666\) −2.00000 −0.0774984
\(667\) −3.50000 6.06218i −0.135521 0.234728i
\(668\) −3.00000 + 5.19615i −0.116073 + 0.201045i
\(669\) 10.5000 18.1865i 0.405953 0.703132i
\(670\) 3.00000 + 5.19615i 0.115900 + 0.200745i
\(671\) −2.00000 −0.0772091
\(672\) −2.00000 1.73205i −0.0771517 0.0668153i
\(673\) −7.00000 −0.269830 −0.134915 0.990857i \(-0.543076\pi\)
−0.134915 + 0.990857i \(0.543076\pi\)
\(674\) −17.5000 30.3109i −0.674075 1.16753i
\(675\) 2.00000 3.46410i 0.0769800 0.133333i
\(676\) −11.5000 + 19.9186i −0.442308 + 0.766099i
\(677\) 11.5000 + 19.9186i 0.441981 + 0.765533i 0.997836 0.0657455i \(-0.0209426\pi\)
−0.555856 + 0.831279i \(0.687609\pi\)
\(678\) 6.00000 0.230429
\(679\) −2.50000 + 0.866025i −0.0959412 + 0.0332350i
\(680\) 6.00000 0.230089
\(681\) −6.50000 11.2583i −0.249081 0.431420i
\(682\) −3.50000 + 6.06218i −0.134022 + 0.232133i
\(683\) −4.50000 + 7.79423i −0.172188 + 0.298238i −0.939184 0.343413i \(-0.888417\pi\)
0.766997 + 0.641651i \(0.221750\pi\)
\(684\) 1.00000 + 1.73205i 0.0382360 + 0.0662266i
\(685\) −6.00000 −0.229248
\(686\) 18.5000 + 0.866025i 0.706333 + 0.0330650i
\(687\) 10.0000 0.381524
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) 33.0000 57.1577i 1.25720 2.17753i
\(690\) 1.50000 2.59808i 0.0571040 0.0989071i
\(691\) 23.0000 + 39.8372i 0.874961 + 1.51548i 0.856804 + 0.515642i \(0.172447\pi\)
0.0181572 + 0.999835i \(0.494220\pi\)
\(692\) 10.0000 0.380143
\(693\) −2.50000 + 0.866025i −0.0949671 + 0.0328976i
\(694\) −12.0000 −0.455514
\(695\) −3.00000 5.19615i −0.113796 0.197101i
\(696\) −3.50000 + 6.06218i −0.132667 + 0.229786i
\(697\) −10.0000 + 17.3205i −0.378777 + 0.656061i
\(698\) 12.0000 + 20.7846i 0.454207 + 0.786709i
\(699\) −18.0000 −0.680823
\(700\) 8.00000 + 6.92820i 0.302372 + 0.261861i
\(701\) −5.00000 −0.188847 −0.0944237 0.995532i \(-0.530101\pi\)
−0.0944237 + 0.995532i \(0.530101\pi\)
\(702\) −3.00000 5.19615i −0.113228 0.196116i
\(703\) −2.00000 + 3.46410i −0.0754314 + 0.130651i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) −9.00000 15.5885i −0.338960 0.587095i
\(706\) 14.0000 0.526897
\(707\) −5.00000 + 25.9808i −0.188044 + 0.977107i
\(708\) −15.0000 −0.563735
\(709\) 2.00000 + 3.46410i 0.0751116 + 0.130097i 0.901135 0.433539i \(-0.142735\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(710\) 0 0
\(711\) 5.50000 9.52628i 0.206266 0.357263i
\(712\) −4.00000 6.92820i −0.149906 0.259645i
\(713\) −7.00000 −0.262152
\(714\) 1.00000 5.19615i 0.0374241 0.194461i
\(715\) 18.0000 0.673162
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) 10.0000 17.3205i 0.373457 0.646846i
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) −25.0000 43.3013i −0.932343 1.61486i −0.779305 0.626644i \(-0.784428\pi\)
−0.153037 0.988220i \(-0.548906\pi\)
\(720\) −3.00000 −0.111803
\(721\) 0 0
\(722\) −15.0000 −0.558242
\(723\) −3.50000 6.06218i −0.130166 0.225455i
\(724\) 8.00000 13.8564i 0.297318 0.514969i
\(725\) 14.0000 24.2487i 0.519947 0.900575i
\(726\) −5.00000 8.66025i −0.185567 0.321412i
\(727\) 1.00000 0.0370879 0.0185440 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(728\) 15.0000 5.19615i 0.555937 0.192582i
\(729\) 1.00000 0.0370370
\(730\) −15.0000 25.9808i −0.555175 0.961591i
\(731\) 2.00000 3.46410i 0.0739727 0.128124i
\(732\) −1.00000 + 1.73205i −0.0369611 + 0.0640184i
\(733\) 10.0000 + 17.3205i 0.369358 + 0.639748i 0.989465 0.144770i \(-0.0462441\pi\)
−0.620107 + 0.784517i \(0.712911\pi\)
\(734\) 11.0000 0.406017
\(735\) 16.5000 12.9904i 0.608612 0.479157i
\(736\) −1.00000 −0.0368605
\(737\) −1.00000 1.73205i −0.0368355 0.0638009i
\(738\) 5.00000 8.66025i 0.184053 0.318788i
\(739\) 7.00000 12.1244i 0.257499 0.446002i −0.708072 0.706140i \(-0.750435\pi\)
0.965571 + 0.260138i \(0.0837682\pi\)
\(740\) −3.00000 5.19615i −0.110282 0.191014i
\(741\) −12.0000 −0.440831
\(742\) −27.5000 + 9.52628i −1.00956 + 0.349721i
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 3.50000 + 6.06218i 0.128316 + 0.222250i
\(745\) 15.0000 25.9808i 0.549557 0.951861i
\(746\) −8.00000 + 13.8564i −0.292901 + 0.507319i
\(747\) −6.50000 11.2583i −0.237823 0.411921i
\(748\) −2.00000 −0.0731272
\(749\) −34.0000 29.4449i −1.24233 1.07589i
\(750\) −3.00000 −0.109545
\(751\) −23.5000 40.7032i −0.857527 1.48528i −0.874281 0.485421i \(-0.838666\pi\)
0.0167534 0.999860i \(-0.494667\pi\)
\(752\) −3.00000 + 5.19615i −0.109399 + 0.189484i
\(753\) −7.50000 + 12.9904i −0.273315 + 0.473396i
\(754\) −21.0000 36.3731i −0.764775 1.32463i
\(755\) −57.0000 −2.07444
\(756\) −0.500000 + 2.59808i −0.0181848 + 0.0944911i
\(757\) 16.0000 0.581530 0.290765 0.956795i \(-0.406090\pi\)
0.290765 + 0.956795i \(0.406090\pi\)
\(758\) 2.00000 + 3.46410i 0.0726433 + 0.125822i
\(759\) −0.500000 + 0.866025i −0.0181489 + 0.0314347i
\(760\) −3.00000 + 5.19615i −0.108821 + 0.188484i
\(761\) −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) −17.0000 −0.615845
\(763\) −7.00000 + 36.3731i −0.253417 + 1.31679i
\(764\) 26.0000 0.940647
\(765\) −3.00000 5.19615i −0.108465 0.187867i
\(766\) −8.00000 + 13.8564i −0.289052 + 0.500652i
\(767\) 45.0000 77.9423i 1.62486 2.81433i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −29.0000 −1.04577 −0.522883 0.852404i \(-0.675144\pi\)
−0.522883 + 0.852404i \(0.675144\pi\)
\(770\) −6.00000 5.19615i −0.216225 0.187256i
\(771\) 12.0000 0.432169
\(772\) 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 \(0.0856532\pi\)
\(774\) −1.00000 + 1.73205i −0.0359443 + 0.0622573i
\(775\) −14.0000 24.2487i −0.502895 0.871039i
\(776\) 1.00000 0.0358979
\(777\) −5.000