Properties

Label 966.2.i.d.415.1
Level $966$
Weight $2$
Character 966.415
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 415.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 966.415
Dual form 966.2.i.d.277.1

$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) −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 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 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 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) −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 −0.987829 0.155543i \(-0.950287\pi\)
0.359211 0.933257i \(-0.383046\pi\)
\(32\) −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 −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 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 −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) −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 −0.945134 0.326683i \(-0.894069\pi\)
0.189651 0.981852i \(-0.439264\pi\)
\(54\) 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 −0.675178 0.737655i \(-0.735933\pi\)
−0.301239 0.953549i \(-0.597400\pi\)
\(60\) −1.50000 2.59808i −0.193649 0.335410i
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 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 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 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 0.994850 + 0.101361i \(0.0323196\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 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 −0.370907 0.928670i \(-0.620953\pi\)
0.989705 0.143120i \(-0.0457135\pi\)
\(80\) 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 −0.996326 0.0856373i \(-0.972707\pi\)
0.572327 + 0.820025i \(0.306041\pi\)
\(90\) −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 0.999996 0.00286291i \(-0.000911295\pi\)
−0.502477 + 0.864590i \(0.667578\pi\)
\(102\) −1.00000 1.73205i −0.0990148 0.171499i
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) −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 −0.0826699 0.996577i \(-0.526345\pi\)
0.904396 0.426694i \(-0.140322\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i \(0.0672444\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(110\) 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 −0.977438 0.211221i \(-0.932256\pi\)
0.671642 + 0.740876i \(0.265589\pi\)
\(132\) −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 0.820141 0.572161i \(-0.193895\pi\)
−0.905577 + 0.424182i \(0.860562\pi\)
\(138\) −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 −0.994847 0.101391i \(-0.967671\pi\)
0.585231 + 0.810867i \(0.301004\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) −9.50000 16.4545i −0.773099 1.33905i −0.935857 0.352381i \(-0.885372\pi\)
0.162758 0.986666i \(-0.447961\pi\)
\(152\) 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 −0.853646 0.520854i \(-0.825614\pi\)
−0.0242497 0.999706i \(-0.507720\pi\)
\(158\) 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 −0.992665 0.120900i \(-0.961422\pi\)
0.601035 + 0.799223i \(0.294755\pi\)
\(164\) 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 −0.991082 0.133250i \(-0.957459\pi\)
0.610939 + 0.791677i \(0.290792\pi\)
\(174\) 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 0.781551 0.623841i \(-0.214429\pi\)
−0.931038 + 0.364922i \(0.881096\pi\)
\(180\) 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 −0.176406 + 0.984317i \(0.556447\pi\)
−0.764241 + 0.644931i \(0.776886\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 11.5000 + 19.9186i 0.827788 + 1.43377i 0.899770 + 0.436365i \(0.143734\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) −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 −0.965272 0.261245i \(-0.915867\pi\)
0.256391 0.966573i \(-0.417466\pi\)
\(200\) −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 0.996996 0.0774548i \(-0.0246793\pi\)
−0.565576 + 0.824696i \(0.691346\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 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 0.404674 + 0.914461i \(0.367385\pi\)
−0.994283 + 0.106773i \(0.965948\pi\)
\(234\) 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 0.956456 0.291877i \(-0.0942799\pi\)
−0.731001 + 0.682376i \(0.760947\pi\)
\(242\) 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 −0.615948 0.787787i \(-0.711227\pi\)
0.990217 + 0.139533i \(0.0445601\pi\)
\(258\) −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 0.758585 0.651575i \(-0.225891\pi\)
−0.943572 + 0.331166i \(0.892558\pi\)
\(264\) 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 −0.846764 0.531969i \(-0.821452\pi\)
−0.0373168 0.999303i \(-0.511881\pi\)
\(270\) −1.50000 2.59808i −0.0912871 0.158114i
\(271\) 0.500000 0.866025i 0.0303728 0.0526073i −0.850439 0.526073i \(-0.823664\pi\)
0.880812 + 0.473466i \(0.156997\pi\)
\(272\) −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 0.720473 0.693482i \(-0.243925\pi\)
−0.960810 + 0.277207i \(0.910591\pi\)
\(278\) 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 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 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 0.768345 0.640036i \(-0.221080\pi\)
−0.938460 + 0.345389i \(0.887747\pi\)
\(312\) −3.00000 5.19615i −0.169842 0.294174i
\(313\) −13.5000 + 23.3827i −0.763065 + 1.32167i 0.178198 + 0.983995i \(0.442973\pi\)
−0.941263 + 0.337673i \(0.890360\pi\)
\(314\) 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 −0.574819 0.818280i \(-0.694928\pi\)
0.996061 + 0.0886679i \(0.0282610\pi\)
\(318\) 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 −0.606980 0.794717i \(-0.707619\pi\)
0.991735 + 0.128302i \(0.0409527\pi\)
\(332\) −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 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) −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 0.617388 0.786659i \(-0.288191\pi\)
−0.989960 + 0.141344i \(0.954858\pi\)
\(354\) 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 −0.934268 0.356572i \(-0.883946\pi\)
0.775934 + 0.630814i \(0.217279\pi\)
\(360\) 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 0.686018 0.727585i \(-0.259357\pi\)
−0.973116 + 0.230317i \(0.926024\pi\)
\(368\) 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 −0.995347 0.0963587i \(-0.969280\pi\)
0.581122 + 0.813816i \(0.302614\pi\)
\(374\) 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 −0.994753 0.102302i \(-0.967379\pi\)
0.585973 + 0.810331i \(0.300713\pi\)
\(384\) −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 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 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 −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) 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 −0.911633 0.411005i \(-0.865178\pi\)
0.811758 + 0.583994i \(0.198511\pi\)
\(402\) 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 0.529657 0.848212i \(-0.322321\pi\)
−0.999402 + 0.0345902i \(0.988987\pi\)
\(410\) −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 0.606471 0.795106i \(-0.292585\pi\)
−0.991817 + 0.127666i \(0.959251\pi\)
\(432\) 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 −0.279119 0.960257i \(-0.590042\pi\)
0.971166 0.238404i \(-0.0766244\pi\)
\(440\) −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 −0.966591 0.256323i \(-0.917489\pi\)
0.705278 + 0.708931i \(0.250822\pi\)
\(444\) −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 −0.708233 0.705979i \(-0.750507\pi\)
0.965512 + 0.260358i \(0.0838407\pi\)
\(458\) 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 −0.536352 0.843995i \(-0.680198\pi\)
0.999097 + 0.0424970i \(0.0135313\pi\)
\(468\) −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 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) −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 0.854475 0.519493i \(-0.173879\pi\)
−0.877132 + 0.480250i \(0.840546\pi\)
\(488\) 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 −0.732137 0.681157i \(-0.761477\pi\)
0.955968 + 0.293471i \(0.0948104\pi\)
\(500\) −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 −0.650556 0.759458i \(-0.725464\pi\)
0.982988 + 0.183669i \(0.0587976\pi\)
\(510\) −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 −0.896126 0.443800i \(-0.853630\pi\)
0.0637207 0.997968i \(-0.479703\pi\)
\(522\) 3.50000 + 6.06218i 0.153191 + 0.265334i
\(523\) −2.00000 + 3.46410i −0.0874539 + 0.151475i −0.906434 0.422347i \(-0.861206\pi\)
0.818980 + 0.573822i \(0.194540\pi\)
\(524\) 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 −0.284624 0.958639i \(-0.591869\pi\)
0.972518 0.232828i \(-0.0747978\pi\)
\(542\) 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 0.996359 + 0.0852559i \(0.0271708\pi\)
−0.424346 + 0.905500i \(0.639496\pi\)
\(558\) −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 −0.868064 0.496452i \(-0.834636\pi\)
0.00409232 0.999992i \(-0.498697\pi\)
\(564\) 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 −0.963948 0.266090i \(-0.914268\pi\)
0.712415 + 0.701758i \(0.247601\pi\)
\(570\) 3.00000 + 5.19615i 0.125656 + 0.217643i
\(571\) −6.00000 10.3923i −0.251092 0.434904i 0.712735 0.701434i \(-0.247456\pi\)
−0.963827 + 0.266529i \(0.914123\pi\)
\(572\) 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 0.999719 + 0.0236970i \(0.00754370\pi\)
−0.479337 + 0.877631i \(0.659123\pi\)
\(578\) 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 −0.994961 0.100262i \(-0.968032\pi\)
0.584310 + 0.811530i \(0.301365\pi\)
\(594\) −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 0.655018 0.755613i \(-0.272661\pi\)
−0.981889 + 0.189456i \(0.939328\pi\)
\(600\) 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 −0.606258 0.795268i \(-0.707330\pi\)
0.991851 + 0.127401i \(0.0406635\pi\)
\(608\) −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 0.997007 + 0.0773084i \(0.0246326\pi\)
−0.431553 + 0.902088i \(0.642034\pi\)
\(614\) −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 0.917053 + 0.398766i \(0.130561\pi\)
−0.113185 + 0.993574i \(0.536105\pi\)
\(620\) 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 0.993098 0.117286i \(-0.0374195\pi\)
−0.598122 + 0.801405i \(0.704086\pi\)
\(642\) −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 0.564629 0.825345i \(-0.309019\pi\)
−0.997084 + 0.0763112i \(0.975686\pi\)
\(648\) −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 −0.235439 0.971889i \(-0.575653\pi\)
0.959400 0.282048i \(-0.0910138\pi\)
\(654\) −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 0.688301 + 0.725426i \(0.258357\pi\)
0.284087 + 0.958799i \(0.408310\pi\)
\(662\) 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 −0.555856 0.831279i \(-0.687609\pi\)
0.997836 + 0.0657455i \(0.0209426\pi\)
\(678\) 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 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) 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 0.0181572 0.999835i \(-0.494220\pi\)
0.856804 0.515642i \(-0.172447\pi\)
\(692\) 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 −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) 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 −0.153037 + 0.988220i \(0.548906\pi\)
−0.779305 + 0.626644i \(0.784428\pi\)
\(720\) −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 −0.620107 0.784517i \(-0.712911\pi\)
0.989465 + 0.144770i \(0.0462441\pi\)
\(734\) 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 0.965571 0.260138i \(-0.0837682\pi\)
−0.708072 + 0.706140i \(0.750435\pi\)
\(740\) −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 0.0167534 + 0.999860i \(0.494667\pi\)
−0.874281 + 0.485421i \(0.838666\pi\)
\(752\) −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 0.180957 + 0.983491i \(0.442080\pi\)
−0.942207 + 0.335032i \(0.891253\pi\)
\(762\) −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 0.964014 0.265852i \(-0.0856532\pi\)
−0.712241 + 0.701935i \(0.752320\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) −14.0000 + 24.2487i −0.502895 + 0.871039i
\(776\) 1.00000 0.0358979