Properties

Label 930.2.i.f.811.1
Level $930$
Weight $2$
Character 930.811
Analytic conductor $7.426$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 811.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 930.811
Dual form 930.2.i.f.211.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.50000 - 4.33013i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.00000 - 3.46410i) q^{13} +(0.500000 - 0.866025i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(1.00000 - 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(1.00000 - 1.73205i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(0.500000 + 0.866025i) q^{21} +(-2.50000 - 4.33013i) q^{22} -4.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +3.00000 q^{29} +1.00000 q^{30} +(3.50000 + 4.33013i) q^{31} +1.00000 q^{32} +5.00000 q^{33} +(1.00000 - 1.73205i) q^{34} -1.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(2.00000 - 3.46410i) q^{37} +(1.00000 - 1.73205i) q^{38} +4.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-2.00000 - 3.46410i) q^{41} +(0.500000 + 0.866025i) q^{42} +(2.00000 - 3.46410i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(-0.500000 + 0.866025i) q^{45} -4.00000 q^{46} +2.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.00000 + 5.19615i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(1.00000 + 1.73205i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-1.50000 - 2.59808i) q^{53} +1.00000 q^{54} +(-2.50000 + 4.33013i) q^{55} +(0.500000 - 0.866025i) q^{56} +(1.00000 + 1.73205i) q^{57} +3.00000 q^{58} +(-1.50000 + 2.59808i) q^{59} +1.00000 q^{60} +(3.50000 + 4.33013i) q^{62} -1.00000 q^{63} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +5.00000 q^{66} +(2.00000 + 3.46410i) q^{67} +(1.00000 - 1.73205i) q^{68} +(2.00000 - 3.46410i) q^{69} -1.00000 q^{70} +(-4.00000 - 6.92820i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(1.00000 - 1.73205i) q^{76} -5.00000 q^{77} +4.00000 q^{78} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.00000 - 3.46410i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(0.500000 + 0.866025i) q^{84} -2.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-1.50000 + 2.59808i) q^{87} +(-2.50000 - 4.33013i) q^{88} +18.0000 q^{89} +(-0.500000 + 0.866025i) q^{90} -4.00000 q^{91} -4.00000 q^{92} +(-5.50000 + 0.866025i) q^{93} +2.00000 q^{94} -2.00000 q^{95} +(-0.500000 + 0.866025i) q^{96} -1.00000 q^{97} +(3.00000 + 5.19615i) q^{98} +(-2.50000 + 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{9} - q^{10} - 5 q^{11} - q^{12} - 4 q^{13} + q^{14} + 2 q^{15} + 2 q^{16} + 2 q^{17} - q^{18} + 2 q^{19} - q^{20} + q^{21} - 5 q^{22} - 8 q^{23} - q^{24} - q^{25} - 4 q^{26} + 2 q^{27} + q^{28} + 6 q^{29} + 2 q^{30} + 7 q^{31} + 2 q^{32} + 10 q^{33} + 2 q^{34} - 2 q^{35} - q^{36} + 4 q^{37} + 2 q^{38} + 8 q^{39} - q^{40} - 4 q^{41} + q^{42} + 4 q^{43} - 5 q^{44} - q^{45} - 8 q^{46} + 4 q^{47} - q^{48} + 6 q^{49} - q^{50} + 2 q^{51} - 4 q^{52} - 3 q^{53} + 2 q^{54} - 5 q^{55} + q^{56} + 2 q^{57} + 6 q^{58} - 3 q^{59} + 2 q^{60} + 7 q^{62} - 2 q^{63} + 2 q^{64} - 4 q^{65} + 10 q^{66} + 4 q^{67} + 2 q^{68} + 4 q^{69} - 2 q^{70} - 8 q^{71} - q^{72} - 2 q^{73} + 4 q^{74} - q^{75} + 2 q^{76} - 10 q^{77} + 8 q^{78} - q^{80} - q^{81} - 4 q^{82} - 9 q^{83} + q^{84} - 4 q^{85} + 4 q^{86} - 3 q^{87} - 5 q^{88} + 36 q^{89} - q^{90} - 8 q^{91} - 8 q^{92} - 11 q^{93} + 4 q^{94} - 4 q^{95} - q^{96} - 2 q^{97} + 6 q^{98} - 5 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 1.00000 0.500000
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 0.500000 0.866025i 0.188982 0.327327i −0.755929 0.654654i \(-0.772814\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) −0.500000 + 0.866025i −0.144338 + 0.250000i
\(13\) −2.00000 3.46410i −0.554700 0.960769i −0.997927 0.0643593i \(-0.979500\pi\)
0.443227 0.896410i \(-0.353834\pi\)
\(14\) 0.500000 0.866025i 0.133631 0.231455i
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 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 −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 0.500000 + 0.866025i 0.109109 + 0.188982i
\(22\) −2.50000 4.33013i −0.533002 0.923186i
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −2.00000 3.46410i −0.392232 0.679366i
\(27\) 1.00000 0.192450
\(28\) 0.500000 0.866025i 0.0944911 0.163663i
\(29\) 3.00000 0.557086 0.278543 0.960424i \(-0.410149\pi\)
0.278543 + 0.960424i \(0.410149\pi\)
\(30\) 1.00000 0.182574
\(31\) 3.50000 + 4.33013i 0.628619 + 0.777714i
\(32\) 1.00000 0.176777
\(33\) 5.00000 0.870388
\(34\) 1.00000 1.73205i 0.171499 0.297044i
\(35\) −1.00000 −0.169031
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 2.00000 3.46410i 0.328798 0.569495i −0.653476 0.756948i \(-0.726690\pi\)
0.982274 + 0.187453i \(0.0600231\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) 4.00000 0.640513
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −2.00000 3.46410i −0.312348 0.541002i 0.666523 0.745485i \(-0.267782\pi\)
−0.978870 + 0.204483i \(0.934449\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) −2.50000 4.33013i −0.376889 0.652791i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) −4.00000 −0.589768
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 3.00000 + 5.19615i 0.428571 + 0.742307i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 1.00000 + 1.73205i 0.140028 + 0.242536i
\(52\) −2.00000 3.46410i −0.277350 0.480384i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) 1.00000 0.136083
\(55\) −2.50000 + 4.33013i −0.337100 + 0.583874i
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 1.00000 + 1.73205i 0.132453 + 0.229416i
\(58\) 3.00000 0.393919
\(59\) −1.50000 + 2.59808i −0.195283 + 0.338241i −0.946993 0.321253i \(-0.895896\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(60\) 1.00000 0.129099
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 3.50000 + 4.33013i 0.444500 + 0.549927i
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) −2.00000 + 3.46410i −0.248069 + 0.429669i
\(66\) 5.00000 0.615457
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 2.00000 3.46410i 0.240772 0.417029i
\(70\) −1.00000 −0.119523
\(71\) −4.00000 6.92820i −0.474713 0.822226i 0.524868 0.851184i \(-0.324115\pi\)
−0.999581 + 0.0289572i \(0.990781\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 1.00000 1.73205i 0.114708 0.198680i
\(77\) −5.00000 −0.569803
\(78\) 4.00000 0.452911
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −2.00000 3.46410i −0.220863 0.382546i
\(83\) −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i \(-0.331110\pi\)
−0.999976 + 0.00698436i \(0.997777\pi\)
\(84\) 0.500000 + 0.866025i 0.0545545 + 0.0944911i
\(85\) −2.00000 −0.216930
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) −1.50000 + 2.59808i −0.160817 + 0.278543i
\(88\) −2.50000 4.33013i −0.266501 0.461593i
\(89\) 18.0000 1.90800 0.953998 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) −0.500000 + 0.866025i −0.0527046 + 0.0912871i
\(91\) −4.00000 −0.419314
\(92\) −4.00000 −0.417029
\(93\) −5.50000 + 0.866025i −0.570323 + 0.0898027i
\(94\) 2.00000 0.206284
\(95\) −2.00000 −0.205196
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) 3.00000 + 5.19615i 0.303046 + 0.524891i
\(99\) −2.50000 + 4.33013i −0.251259 + 0.435194i
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −5.00000 −0.497519 −0.248759 0.968565i \(-0.580023\pi\)
−0.248759 + 0.968565i \(0.580023\pi\)
\(102\) 1.00000 + 1.73205i 0.0990148 + 0.171499i
\(103\) 2.50000 + 4.33013i 0.246332 + 0.426660i 0.962505 0.271263i \(-0.0874412\pi\)
−0.716173 + 0.697923i \(0.754108\pi\)
\(104\) −2.00000 3.46410i −0.196116 0.339683i
\(105\) 0.500000 0.866025i 0.0487950 0.0845154i
\(106\) −1.50000 2.59808i −0.145693 0.252347i
\(107\) −8.50000 + 14.7224i −0.821726 + 1.42327i 0.0826699 + 0.996577i \(0.473655\pi\)
−0.904396 + 0.426694i \(0.859678\pi\)
\(108\) 1.00000 0.0962250
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −2.50000 + 4.33013i −0.238366 + 0.412861i
\(111\) 2.00000 + 3.46410i 0.189832 + 0.328798i
\(112\) 0.500000 0.866025i 0.0472456 0.0818317i
\(113\) 2.00000 + 3.46410i 0.188144 + 0.325875i 0.944632 0.328133i \(-0.106419\pi\)
−0.756487 + 0.654008i \(0.773086\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 2.00000 + 3.46410i 0.186501 + 0.323029i
\(116\) 3.00000 0.278543
\(117\) −2.00000 + 3.46410i −0.184900 + 0.320256i
\(118\) −1.50000 + 2.59808i −0.138086 + 0.239172i
\(119\) −1.00000 1.73205i −0.0916698 0.158777i
\(120\) 1.00000 0.0912871
\(121\) −7.00000 + 12.1244i −0.636364 + 1.10221i
\(122\) 0 0
\(123\) 4.00000 0.360668
\(124\) 3.50000 + 4.33013i 0.314309 + 0.388857i
\(125\) 1.00000 0.0894427
\(126\) −1.00000 −0.0890871
\(127\) −8.50000 + 14.7224i −0.754253 + 1.30640i 0.191492 + 0.981494i \(0.438667\pi\)
−0.945745 + 0.324910i \(0.894666\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) −2.00000 + 3.46410i −0.175412 + 0.303822i
\(131\) −2.00000 + 3.46410i −0.174741 + 0.302660i −0.940072 0.340977i \(-0.889242\pi\)
0.765331 + 0.643637i \(0.222575\pi\)
\(132\) 5.00000 0.435194
\(133\) −1.00000 1.73205i −0.0867110 0.150188i
\(134\) 2.00000 + 3.46410i 0.172774 + 0.299253i
\(135\) −0.500000 0.866025i −0.0430331 0.0745356i
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) −7.00000 12.1244i −0.598050 1.03585i −0.993109 0.117198i \(-0.962609\pi\)
0.395058 0.918656i \(-0.370724\pi\)
\(138\) 2.00000 3.46410i 0.170251 0.294884i
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) −1.00000 −0.0845154
\(141\) −1.00000 + 1.73205i −0.0842152 + 0.145865i
\(142\) −4.00000 6.92820i −0.335673 0.581402i
\(143\) −10.0000 + 17.3205i −0.836242 + 1.44841i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −1.50000 2.59808i −0.124568 0.215758i
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) −6.00000 −0.494872
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) 5.50000 9.52628i 0.450578 0.780423i −0.547844 0.836580i \(-0.684551\pi\)
0.998422 + 0.0561570i \(0.0178847\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) −5.00000 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) −2.00000 −0.161690
\(154\) −5.00000 −0.402911
\(155\) 2.00000 5.19615i 0.160644 0.417365i
\(156\) 4.00000 0.320256
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 0 0
\(159\) 3.00000 0.237915
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −2.00000 + 3.46410i −0.157622 + 0.273009i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −8.00000 −0.626608 −0.313304 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) −2.00000 3.46410i −0.156174 0.270501i
\(165\) −2.50000 4.33013i −0.194625 0.337100i
\(166\) −4.50000 7.79423i −0.349268 0.604949i
\(167\) −8.00000 + 13.8564i −0.619059 + 1.07224i 0.370599 + 0.928793i \(0.379152\pi\)
−0.989658 + 0.143448i \(0.954181\pi\)
\(168\) 0.500000 + 0.866025i 0.0385758 + 0.0668153i
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) −2.00000 −0.153393
\(171\) −2.00000 −0.152944
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 1.50000 + 2.59808i 0.114043 + 0.197528i 0.917397 0.397974i \(-0.130287\pi\)
−0.803354 + 0.595502i \(0.796953\pi\)
\(174\) −1.50000 + 2.59808i −0.113715 + 0.196960i
\(175\) 0.500000 + 0.866025i 0.0377964 + 0.0654654i
\(176\) −2.50000 4.33013i −0.188445 0.326396i
\(177\) −1.50000 2.59808i −0.112747 0.195283i
\(178\) 18.0000 1.34916
\(179\) 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 11.0000 + 19.0526i 0.817624 + 1.41617i 0.907429 + 0.420206i \(0.138042\pi\)
−0.0898051 + 0.995959i \(0.528624\pi\)
\(182\) −4.00000 −0.296500
\(183\) 0 0
\(184\) −4.00000 −0.294884
\(185\) −4.00000 −0.294086
\(186\) −5.50000 + 0.866025i −0.403280 + 0.0635001i
\(187\) −10.0000 −0.731272
\(188\) 2.00000 0.145865
\(189\) 0.500000 0.866025i 0.0363696 0.0629941i
\(190\) −2.00000 −0.145095
\(191\) 4.00000 + 6.92820i 0.289430 + 0.501307i 0.973674 0.227946i \(-0.0732010\pi\)
−0.684244 + 0.729253i \(0.739868\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −0.500000 + 0.866025i −0.0359908 + 0.0623379i −0.883460 0.468507i \(-0.844792\pi\)
0.847469 + 0.530845i \(0.178125\pi\)
\(194\) −1.00000 −0.0717958
\(195\) −2.00000 3.46410i −0.143223 0.248069i
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) −13.0000 22.5167i −0.926212 1.60425i −0.789601 0.613621i \(-0.789712\pi\)
−0.136611 0.990625i \(-0.543621\pi\)
\(198\) −2.50000 + 4.33013i −0.177667 + 0.307729i
\(199\) 2.50000 + 4.33013i 0.177220 + 0.306955i 0.940927 0.338608i \(-0.109956\pi\)
−0.763707 + 0.645563i \(0.776623\pi\)
\(200\) −0.500000 + 0.866025i −0.0353553 + 0.0612372i
\(201\) −4.00000 −0.282138
\(202\) −5.00000 −0.351799
\(203\) 1.50000 2.59808i 0.105279 0.182349i
\(204\) 1.00000 + 1.73205i 0.0700140 + 0.121268i
\(205\) −2.00000 + 3.46410i −0.139686 + 0.241943i
\(206\) 2.50000 + 4.33013i 0.174183 + 0.301694i
\(207\) 2.00000 + 3.46410i 0.139010 + 0.240772i
\(208\) −2.00000 3.46410i −0.138675 0.240192i
\(209\) −10.0000 −0.691714
\(210\) 0.500000 0.866025i 0.0345033 0.0597614i
\(211\) −11.0000 + 19.0526i −0.757271 + 1.31163i 0.186966 + 0.982366i \(0.440135\pi\)
−0.944237 + 0.329266i \(0.893199\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) 8.00000 0.548151
\(214\) −8.50000 + 14.7224i −0.581048 + 1.00640i
\(215\) −4.00000 −0.272798
\(216\) 1.00000 0.0680414
\(217\) 5.50000 0.866025i 0.373364 0.0587896i
\(218\) 14.0000 0.948200
\(219\) 2.00000 0.135147
\(220\) −2.50000 + 4.33013i −0.168550 + 0.291937i
\(221\) −8.00000 −0.538138
\(222\) 2.00000 + 3.46410i 0.134231 + 0.232495i
\(223\) −1.50000 + 2.59808i −0.100447 + 0.173980i −0.911869 0.410481i \(-0.865361\pi\)
0.811422 + 0.584461i \(0.198694\pi\)
\(224\) 0.500000 0.866025i 0.0334077 0.0578638i
\(225\) 1.00000 0.0666667
\(226\) 2.00000 + 3.46410i 0.133038 + 0.230429i
\(227\) −2.50000 4.33013i −0.165931 0.287401i 0.771055 0.636769i \(-0.219730\pi\)
−0.936985 + 0.349368i \(0.886396\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) 14.0000 24.2487i 0.925146 1.60240i 0.133820 0.991006i \(-0.457276\pi\)
0.791326 0.611394i \(-0.209391\pi\)
\(230\) 2.00000 + 3.46410i 0.131876 + 0.228416i
\(231\) 2.50000 4.33013i 0.164488 0.284901i
\(232\) 3.00000 0.196960
\(233\) 4.00000 0.262049 0.131024 0.991379i \(-0.458173\pi\)
0.131024 + 0.991379i \(0.458173\pi\)
\(234\) −2.00000 + 3.46410i −0.130744 + 0.226455i
\(235\) −1.00000 1.73205i −0.0652328 0.112987i
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) 0 0
\(238\) −1.00000 1.73205i −0.0648204 0.112272i
\(239\) 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i \(0.116196\pi\)
−0.157893 + 0.987456i \(0.550470\pi\)
\(240\) 1.00000 0.0645497
\(241\) −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i \(-0.905720\pi\)
0.731001 + 0.682376i \(0.239053\pi\)
\(242\) −7.00000 + 12.1244i −0.449977 + 0.779383i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 3.00000 5.19615i 0.191663 0.331970i
\(246\) 4.00000 0.255031
\(247\) −8.00000 −0.509028
\(248\) 3.50000 + 4.33013i 0.222250 + 0.274963i
\(249\) 9.00000 0.570352
\(250\) 1.00000 0.0632456
\(251\) 14.0000 24.2487i 0.883672 1.53057i 0.0364441 0.999336i \(-0.488397\pi\)
0.847228 0.531229i \(-0.178270\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 10.0000 + 17.3205i 0.628695 + 1.08893i
\(254\) −8.50000 + 14.7224i −0.533337 + 0.923768i
\(255\) 1.00000 1.73205i 0.0626224 0.108465i
\(256\) 1.00000 0.0625000
\(257\) −6.00000 10.3923i −0.374270 0.648254i 0.615948 0.787787i \(-0.288773\pi\)
−0.990217 + 0.139533i \(0.955440\pi\)
\(258\) 2.00000 + 3.46410i 0.124515 + 0.215666i
\(259\) −2.00000 3.46410i −0.124274 0.215249i
\(260\) −2.00000 + 3.46410i −0.124035 + 0.214834i
\(261\) −1.50000 2.59808i −0.0928477 0.160817i
\(262\) −2.00000 + 3.46410i −0.123560 + 0.214013i
\(263\) −14.0000 −0.863277 −0.431638 0.902047i \(-0.642064\pi\)
−0.431638 + 0.902047i \(0.642064\pi\)
\(264\) 5.00000 0.307729
\(265\) −1.50000 + 2.59808i −0.0921443 + 0.159599i
\(266\) −1.00000 1.73205i −0.0613139 0.106199i
\(267\) −9.00000 + 15.5885i −0.550791 + 0.953998i
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −5.00000 8.66025i −0.304855 0.528025i 0.672374 0.740212i \(-0.265275\pi\)
−0.977229 + 0.212187i \(0.931941\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) 15.0000 0.911185 0.455593 0.890188i \(-0.349427\pi\)
0.455593 + 0.890188i \(0.349427\pi\)
\(272\) 1.00000 1.73205i 0.0606339 0.105021i
\(273\) 2.00000 3.46410i 0.121046 0.209657i
\(274\) −7.00000 12.1244i −0.422885 0.732459i
\(275\) 5.00000 0.301511
\(276\) 2.00000 3.46410i 0.120386 0.208514i
\(277\) 18.0000 1.08152 0.540758 0.841178i \(-0.318138\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) 10.0000 0.599760
\(279\) 2.00000 5.19615i 0.119737 0.311086i
\(280\) −1.00000 −0.0597614
\(281\) −10.0000 −0.596550 −0.298275 0.954480i \(-0.596411\pi\)
−0.298275 + 0.954480i \(0.596411\pi\)
\(282\) −1.00000 + 1.73205i −0.0595491 + 0.103142i
\(283\) 12.0000 0.713326 0.356663 0.934233i \(-0.383914\pi\)
0.356663 + 0.934233i \(0.383914\pi\)
\(284\) −4.00000 6.92820i −0.237356 0.411113i
\(285\) 1.00000 1.73205i 0.0592349 0.102598i
\(286\) −10.0000 + 17.3205i −0.591312 + 1.02418i
\(287\) −4.00000 −0.236113
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −1.50000 2.59808i −0.0880830 0.152564i
\(291\) 0.500000 0.866025i 0.0293105 0.0507673i
\(292\) −1.00000 1.73205i −0.0585206 0.101361i
\(293\) −9.50000 + 16.4545i −0.554996 + 0.961281i 0.442908 + 0.896567i \(0.353947\pi\)
−0.997904 + 0.0647140i \(0.979386\pi\)
\(294\) −6.00000 −0.349927
\(295\) 3.00000 0.174667
\(296\) 2.00000 3.46410i 0.116248 0.201347i
\(297\) −2.50000 4.33013i −0.145065 0.251259i
\(298\) 5.50000 9.52628i 0.318606 0.551843i
\(299\) 8.00000 + 13.8564i 0.462652 + 0.801337i
\(300\) −0.500000 0.866025i −0.0288675 0.0500000i
\(301\) −2.00000 3.46410i −0.115278 0.199667i
\(302\) −5.00000 −0.287718
\(303\) 2.50000 4.33013i 0.143621 0.248759i
\(304\) 1.00000 1.73205i 0.0573539 0.0993399i
\(305\) 0 0
\(306\) −2.00000 −0.114332
\(307\) −1.00000 + 1.73205i −0.0570730 + 0.0988534i −0.893150 0.449758i \(-0.851510\pi\)
0.836077 + 0.548612i \(0.184843\pi\)
\(308\) −5.00000 −0.284901
\(309\) −5.00000 −0.284440
\(310\) 2.00000 5.19615i 0.113592 0.295122i
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) 4.00000 0.226455
\(313\) 17.5000 30.3109i 0.989158 1.71327i 0.367402 0.930062i \(-0.380247\pi\)
0.621757 0.783210i \(-0.286419\pi\)
\(314\) 8.00000 0.451466
\(315\) 0.500000 + 0.866025i 0.0281718 + 0.0487950i
\(316\) 0 0
\(317\) 0.500000 0.866025i 0.0280828 0.0486408i −0.851642 0.524123i \(-0.824393\pi\)
0.879725 + 0.475482i \(0.157726\pi\)
\(318\) 3.00000 0.168232
\(319\) −7.50000 12.9904i −0.419919 0.727322i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) −8.50000 14.7224i −0.474424 0.821726i
\(322\) −2.00000 + 3.46410i −0.111456 + 0.193047i
\(323\) −2.00000 3.46410i −0.111283 0.192748i
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 4.00000 0.221880
\(326\) −8.00000 −0.443079
\(327\) −7.00000 + 12.1244i −0.387101 + 0.670478i
\(328\) −2.00000 3.46410i −0.110432 0.191273i
\(329\) 1.00000 1.73205i 0.0551318 0.0954911i
\(330\) −2.50000 4.33013i −0.137620 0.238366i
\(331\) −2.00000 3.46410i −0.109930 0.190404i 0.805812 0.592172i \(-0.201729\pi\)
−0.915742 + 0.401768i \(0.868396\pi\)
\(332\) −4.50000 7.79423i −0.246970 0.427764i
\(333\) −4.00000 −0.219199
\(334\) −8.00000 + 13.8564i −0.437741 + 0.758189i
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) −3.00000 −0.163420 −0.0817102 0.996656i \(-0.526038\pi\)
−0.0817102 + 0.996656i \(0.526038\pi\)
\(338\) −1.50000 + 2.59808i −0.0815892 + 0.141317i
\(339\) −4.00000 −0.217250
\(340\) −2.00000 −0.108465
\(341\) 10.0000 25.9808i 0.541530 1.40694i
\(342\) −2.00000 −0.108148
\(343\) 13.0000 0.701934
\(344\) 2.00000 3.46410i 0.107833 0.186772i
\(345\) −4.00000 −0.215353
\(346\) 1.50000 + 2.59808i 0.0806405 + 0.139673i
\(347\) 0.500000 0.866025i 0.0268414 0.0464907i −0.852293 0.523065i \(-0.824788\pi\)
0.879134 + 0.476575i \(0.158122\pi\)
\(348\) −1.50000 + 2.59808i −0.0804084 + 0.139272i
\(349\) 34.0000 1.81998 0.909989 0.414632i \(-0.136090\pi\)
0.909989 + 0.414632i \(0.136090\pi\)
\(350\) 0.500000 + 0.866025i 0.0267261 + 0.0462910i
\(351\) −2.00000 3.46410i −0.106752 0.184900i
\(352\) −2.50000 4.33013i −0.133250 0.230797i
\(353\) 7.00000 12.1244i 0.372572 0.645314i −0.617388 0.786659i \(-0.711809\pi\)
0.989960 + 0.141344i \(0.0451425\pi\)
\(354\) −1.50000 2.59808i −0.0797241 0.138086i
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) 18.0000 0.953998
\(357\) 2.00000 0.105851
\(358\) 4.50000 7.79423i 0.237832 0.411938i
\(359\) −10.0000 17.3205i −0.527780 0.914141i −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 11.0000 + 19.0526i 0.578147 + 1.00138i
\(363\) −7.00000 12.1244i −0.367405 0.636364i
\(364\) −4.00000 −0.209657
\(365\) −1.00000 + 1.73205i −0.0523424 + 0.0906597i
\(366\) 0 0
\(367\) 12.0000 + 20.7846i 0.626395 + 1.08495i 0.988269 + 0.152721i \(0.0488036\pi\)
−0.361874 + 0.932227i \(0.617863\pi\)
\(368\) −4.00000 −0.208514
\(369\) −2.00000 + 3.46410i −0.104116 + 0.180334i
\(370\) −4.00000 −0.207950
\(371\) −3.00000 −0.155752
\(372\) −5.50000 + 0.866025i −0.285162 + 0.0449013i
\(373\) 2.00000 0.103556 0.0517780 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) −10.0000 −0.517088
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 2.00000 0.103142
\(377\) −6.00000 10.3923i −0.309016 0.535231i
\(378\) 0.500000 0.866025i 0.0257172 0.0445435i
\(379\) −1.00000 + 1.73205i −0.0513665 + 0.0889695i −0.890565 0.454855i \(-0.849691\pi\)
0.839199 + 0.543825i \(0.183024\pi\)
\(380\) −2.00000 −0.102598
\(381\) −8.50000 14.7224i −0.435468 0.754253i
\(382\) 4.00000 + 6.92820i 0.204658 + 0.354478i
\(383\) 14.0000 + 24.2487i 0.715367 + 1.23905i 0.962818 + 0.270151i \(0.0870736\pi\)
−0.247451 + 0.968900i \(0.579593\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 2.50000 + 4.33013i 0.127412 + 0.220684i
\(386\) −0.500000 + 0.866025i −0.0254493 + 0.0440795i
\(387\) −4.00000 −0.203331
\(388\) −1.00000 −0.0507673
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) −2.00000 3.46410i −0.101274 0.175412i
\(391\) −4.00000 + 6.92820i −0.202289 + 0.350374i
\(392\) 3.00000 + 5.19615i 0.151523 + 0.262445i
\(393\) −2.00000 3.46410i −0.100887 0.174741i
\(394\) −13.0000 22.5167i −0.654931 1.13437i
\(395\) 0 0
\(396\) −2.50000 + 4.33013i −0.125630 + 0.217597i
\(397\) −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) 2.50000 + 4.33013i 0.125314 + 0.217050i
\(399\) 2.00000 0.100125
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) −4.00000 −0.199502
\(403\) 8.00000 20.7846i 0.398508 1.03536i
\(404\) −5.00000 −0.248759
\(405\) 1.00000 0.0496904
\(406\) 1.50000 2.59808i 0.0744438 0.128940i
\(407\) −20.0000 −0.991363
\(408\) 1.00000 + 1.73205i 0.0495074 + 0.0857493i
\(409\) 8.50000 14.7224i 0.420298 0.727977i −0.575670 0.817682i \(-0.695259\pi\)
0.995968 + 0.0897044i \(0.0285922\pi\)
\(410\) −2.00000 + 3.46410i −0.0987730 + 0.171080i
\(411\) 14.0000 0.690569
\(412\) 2.50000 + 4.33013i 0.123166 + 0.213330i
\(413\) 1.50000 + 2.59808i 0.0738102 + 0.127843i
\(414\) 2.00000 + 3.46410i 0.0982946 + 0.170251i
\(415\) −4.50000 + 7.79423i −0.220896 + 0.382604i
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) −5.00000 + 8.66025i −0.244851 + 0.424094i
\(418\) −10.0000 −0.489116
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0.500000 0.866025i 0.0243975 0.0422577i
\(421\) −10.0000 17.3205i −0.487370 0.844150i 0.512524 0.858673i \(-0.328710\pi\)
−0.999895 + 0.0145228i \(0.995377\pi\)
\(422\) −11.0000 + 19.0526i −0.535472 + 0.927464i
\(423\) −1.00000 1.73205i −0.0486217 0.0842152i
\(424\) −1.50000 2.59808i −0.0728464 0.126174i
\(425\) 1.00000 + 1.73205i 0.0485071 + 0.0840168i
\(426\) 8.00000 0.387601
\(427\) 0 0
\(428\) −8.50000 + 14.7224i −0.410863 + 0.711636i
\(429\) −10.0000 17.3205i −0.482805 0.836242i
\(430\) −4.00000 −0.192897
\(431\) 11.0000 19.0526i 0.529851 0.917729i −0.469542 0.882910i \(-0.655581\pi\)
0.999394 0.0348195i \(-0.0110856\pi\)
\(432\) 1.00000 0.0481125
\(433\) −22.0000 −1.05725 −0.528626 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) 5.50000 0.866025i 0.264008 0.0415705i
\(435\) 3.00000 0.143839
\(436\) 14.0000 0.670478
\(437\) −4.00000 + 6.92820i −0.191346 + 0.331421i
\(438\) 2.00000 0.0955637
\(439\) 4.50000 + 7.79423i 0.214773 + 0.371998i 0.953202 0.302333i \(-0.0977654\pi\)
−0.738429 + 0.674331i \(0.764432\pi\)
\(440\) −2.50000 + 4.33013i −0.119183 + 0.206431i
\(441\) 3.00000 5.19615i 0.142857 0.247436i
\(442\) −8.00000 −0.380521
\(443\) −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) −1.50000 + 2.59808i −0.0710271 + 0.123022i
\(447\) 5.50000 + 9.52628i 0.260141 + 0.450578i
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 1.00000 0.0471405
\(451\) −10.0000 + 17.3205i −0.470882 + 0.815591i
\(452\) 2.00000 + 3.46410i 0.0940721 + 0.162938i
\(453\) 2.50000 4.33013i 0.117460 0.203447i
\(454\) −2.50000 4.33013i −0.117331 0.203223i
\(455\) 2.00000 + 3.46410i 0.0937614 + 0.162400i
\(456\) 1.00000 + 1.73205i 0.0468293 + 0.0811107i
\(457\) −18.0000 −0.842004 −0.421002 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) 14.0000 24.2487i 0.654177 1.13307i
\(459\) 1.00000 1.73205i 0.0466760 0.0808452i
\(460\) 2.00000 + 3.46410i 0.0932505 + 0.161515i
\(461\) 21.0000 0.978068 0.489034 0.872265i \(-0.337349\pi\)
0.489034 + 0.872265i \(0.337349\pi\)
\(462\) 2.50000 4.33013i 0.116311 0.201456i
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) 3.00000 0.139272
\(465\) 3.50000 + 4.33013i 0.162309 + 0.200805i
\(466\) 4.00000 0.185296
\(467\) 33.0000 1.52706 0.763529 0.645774i \(-0.223465\pi\)
0.763529 + 0.645774i \(0.223465\pi\)
\(468\) −2.00000 + 3.46410i −0.0924500 + 0.160128i
\(469\) 4.00000 0.184703
\(470\) −1.00000 1.73205i −0.0461266 0.0798935i
\(471\) −4.00000 + 6.92820i −0.184310 + 0.319235i
\(472\) −1.50000 + 2.59808i −0.0690431 + 0.119586i
\(473\) −20.0000 −0.919601
\(474\) 0 0
\(475\) 1.00000 + 1.73205i 0.0458831 + 0.0794719i
\(476\) −1.00000 1.73205i −0.0458349 0.0793884i
\(477\) −1.50000 + 2.59808i −0.0686803 + 0.118958i
\(478\) 12.0000 + 20.7846i 0.548867 + 0.950666i
\(479\) −7.00000 + 12.1244i −0.319838 + 0.553976i −0.980454 0.196748i \(-0.936962\pi\)
0.660616 + 0.750724i \(0.270295\pi\)
\(480\) 1.00000 0.0456435
\(481\) −16.0000 −0.729537
\(482\) −3.50000 + 6.06218i −0.159421 + 0.276125i
\(483\) −2.00000 3.46410i −0.0910032 0.157622i
\(484\) −7.00000 + 12.1244i −0.318182 + 0.551107i
\(485\) 0.500000 + 0.866025i 0.0227038 + 0.0393242i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −21.5000 37.2391i −0.974258 1.68746i −0.682362 0.731014i \(-0.739047\pi\)
−0.291896 0.956450i \(-0.594286\pi\)
\(488\) 0 0
\(489\) 4.00000 6.92820i 0.180886 0.313304i
\(490\) 3.00000 5.19615i 0.135526 0.234738i
\(491\) 7.50000 + 12.9904i 0.338470 + 0.586248i 0.984145 0.177365i \(-0.0567572\pi\)
−0.645675 + 0.763612i \(0.723424\pi\)
\(492\) 4.00000 0.180334
\(493\) 3.00000 5.19615i 0.135113 0.234023i
\(494\) −8.00000 −0.359937
\(495\) 5.00000 0.224733
\(496\) 3.50000 + 4.33013i 0.157155 + 0.194428i
\(497\) −8.00000 −0.358849
\(498\) 9.00000 0.403300
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.00000 13.8564i −0.357414 0.619059i
\(502\) 14.0000 24.2487i 0.624851 1.08227i
\(503\) −18.0000 + 31.1769i −0.802580 + 1.39011i 0.115332 + 0.993327i \(0.463207\pi\)
−0.917912 + 0.396783i \(0.870127\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 2.50000 + 4.33013i 0.111249 + 0.192688i
\(506\) 10.0000 + 17.3205i 0.444554 + 0.769991i
\(507\) −1.50000 2.59808i −0.0666173 0.115385i
\(508\) −8.50000 + 14.7224i −0.377127 + 0.653202i
\(509\) 4.50000 + 7.79423i 0.199459 + 0.345473i 0.948353 0.317217i \(-0.102748\pi\)
−0.748894 + 0.662690i \(0.769415\pi\)
\(510\) 1.00000 1.73205i 0.0442807 0.0766965i
\(511\) −2.00000 −0.0884748
\(512\) 1.00000 0.0441942
\(513\) 1.00000 1.73205i 0.0441511 0.0764719i
\(514\) −6.00000 10.3923i −0.264649 0.458385i
\(515\) 2.50000 4.33013i 0.110163 0.190808i
\(516\) 2.00000 + 3.46410i 0.0880451 + 0.152499i
\(517\) −5.00000 8.66025i −0.219900 0.380878i
\(518\) −2.00000 3.46410i −0.0878750 0.152204i
\(519\) −3.00000 −0.131685
\(520\) −2.00000 + 3.46410i −0.0877058 + 0.151911i
\(521\) 14.0000 24.2487i 0.613351 1.06236i −0.377320 0.926083i \(-0.623154\pi\)
0.990671 0.136272i \(-0.0435123\pi\)
\(522\) −1.50000 2.59808i −0.0656532 0.113715i
\(523\) −24.0000 −1.04945 −0.524723 0.851273i \(-0.675831\pi\)
−0.524723 + 0.851273i \(0.675831\pi\)
\(524\) −2.00000 + 3.46410i −0.0873704 + 0.151330i
\(525\) −1.00000 −0.0436436
\(526\) −14.0000 −0.610429
\(527\) 11.0000 1.73205i 0.479168 0.0754493i
\(528\) 5.00000 0.217597
\(529\) −7.00000 −0.304348
\(530\) −1.50000 + 2.59808i −0.0651558 + 0.112853i
\(531\) 3.00000 0.130189
\(532\) −1.00000 1.73205i −0.0433555 0.0750939i
\(533\) −8.00000 + 13.8564i −0.346518 + 0.600188i
\(534\) −9.00000 + 15.5885i −0.389468 + 0.674579i
\(535\) 17.0000 0.734974
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) 4.50000 + 7.79423i 0.194189 + 0.336346i
\(538\) −5.00000 8.66025i −0.215565 0.373370i
\(539\) 15.0000 25.9808i 0.646096 1.11907i
\(540\) −0.500000 0.866025i −0.0215166 0.0372678i
\(541\) −16.0000 + 27.7128i −0.687894 + 1.19147i 0.284624 + 0.958639i \(0.408131\pi\)
−0.972518 + 0.232828i \(0.925202\pi\)
\(542\) 15.0000 0.644305
\(543\) −22.0000 −0.944110
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) −7.00000 12.1244i −0.299847 0.519350i
\(546\) 2.00000 3.46410i 0.0855921 0.148250i
\(547\) −21.0000 36.3731i −0.897895 1.55520i −0.830180 0.557495i \(-0.811762\pi\)
−0.0677151 0.997705i \(-0.521571\pi\)
\(548\) −7.00000 12.1244i −0.299025 0.517927i
\(549\) 0 0
\(550\) 5.00000 0.213201
\(551\) 3.00000 5.19615i 0.127804 0.221364i
\(552\) 2.00000 3.46410i 0.0851257 0.147442i
\(553\) 0 0
\(554\) 18.0000 0.764747
\(555\) 2.00000 3.46410i 0.0848953 0.147043i
\(556\) 10.0000 0.424094
\(557\) 13.0000 0.550828 0.275414 0.961326i \(-0.411185\pi\)
0.275414 + 0.961326i \(0.411185\pi\)
\(558\) 2.00000 5.19615i 0.0846668 0.219971i
\(559\) −16.0000 −0.676728
\(560\) −1.00000 −0.0422577
\(561\) 5.00000 8.66025i 0.211100 0.365636i
\(562\) −10.0000 −0.421825
\(563\) 8.50000 + 14.7224i 0.358232 + 0.620477i 0.987666 0.156578i \(-0.0500463\pi\)
−0.629433 + 0.777055i \(0.716713\pi\)
\(564\) −1.00000 + 1.73205i −0.0421076 + 0.0729325i
\(565\) 2.00000 3.46410i 0.0841406 0.145736i
\(566\) 12.0000 0.504398
\(567\) 0.500000 + 0.866025i 0.0209980 + 0.0363696i
\(568\) −4.00000 6.92820i −0.167836 0.290701i
\(569\) 12.0000 + 20.7846i 0.503066 + 0.871336i 0.999994 + 0.00354413i \(0.00112814\pi\)
−0.496928 + 0.867792i \(0.665539\pi\)
\(570\) 1.00000 1.73205i 0.0418854 0.0725476i
\(571\) 15.0000 + 25.9808i 0.627730 + 1.08726i 0.988006 + 0.154415i \(0.0493493\pi\)
−0.360276 + 0.932846i \(0.617317\pi\)
\(572\) −10.0000 + 17.3205i −0.418121 + 0.724207i
\(573\) −8.00000 −0.334205
\(574\) −4.00000 −0.166957
\(575\) 2.00000 3.46410i 0.0834058 0.144463i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 9.00000 15.5885i 0.374675 0.648956i −0.615603 0.788056i \(-0.711088\pi\)
0.990278 + 0.139100i \(0.0444210\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) −0.500000 0.866025i −0.0207793 0.0359908i
\(580\) −1.50000 2.59808i −0.0622841 0.107879i
\(581\) −9.00000 −0.373383
\(582\) 0.500000 0.866025i 0.0207257 0.0358979i
\(583\) −7.50000 + 12.9904i −0.310618 + 0.538007i
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) 4.00000 0.165380
\(586\) −9.50000 + 16.4545i −0.392441 + 0.679728i
\(587\) 27.0000 1.11441 0.557205 0.830375i \(-0.311874\pi\)
0.557205 + 0.830375i \(0.311874\pi\)
\(588\) −6.00000 −0.247436
\(589\) 11.0000 1.73205i 0.453247 0.0713679i
\(590\) 3.00000 0.123508
\(591\) 26.0000 1.06950
\(592\) 2.00000 3.46410i 0.0821995 0.142374i
\(593\) 22.0000 0.903432 0.451716 0.892162i \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) −2.50000 4.33013i −0.102576 0.177667i
\(595\) −1.00000 + 1.73205i −0.0409960 + 0.0710072i
\(596\) 5.50000 9.52628i 0.225289 0.390212i
\(597\) −5.00000 −0.204636
\(598\) 8.00000 + 13.8564i 0.327144 + 0.566631i
\(599\) 18.0000 + 31.1769i 0.735460 + 1.27385i 0.954521 + 0.298143i \(0.0963673\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) 21.0000 36.3731i 0.856608 1.48369i −0.0185374 0.999828i \(-0.505901\pi\)
0.875145 0.483860i \(-0.160766\pi\)
\(602\) −2.00000 3.46410i −0.0815139 0.141186i
\(603\) 2.00000 3.46410i 0.0814463 0.141069i
\(604\) −5.00000 −0.203447
\(605\) 14.0000 0.569181
\(606\) 2.50000 4.33013i 0.101556 0.175899i
\(607\) −24.0000 41.5692i −0.974130 1.68724i −0.682777 0.730627i \(-0.739228\pi\)
−0.291353 0.956616i \(-0.594105\pi\)
\(608\) 1.00000 1.73205i 0.0405554 0.0702439i
\(609\) 1.50000 + 2.59808i 0.0607831 + 0.105279i
\(610\) 0 0
\(611\) −4.00000 6.92820i −0.161823 0.280285i
\(612\) −2.00000 −0.0808452
\(613\) −12.0000 + 20.7846i −0.484675 + 0.839482i −0.999845 0.0176058i \(-0.994396\pi\)
0.515170 + 0.857088i \(0.327729\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) −2.00000 3.46410i −0.0806478 0.139686i
\(616\) −5.00000 −0.201456
\(617\) −6.00000 + 10.3923i −0.241551 + 0.418378i −0.961156 0.276005i \(-0.910989\pi\)
0.719605 + 0.694383i \(0.244323\pi\)
\(618\) −5.00000 −0.201129
\(619\) −34.0000 −1.36658 −0.683288 0.730149i \(-0.739451\pi\)
−0.683288 + 0.730149i \(0.739451\pi\)
\(620\) 2.00000 5.19615i 0.0803219 0.208683i
\(621\) −4.00000 −0.160514
\(622\) 20.0000 0.801927
\(623\) 9.00000 15.5885i 0.360577 0.624538i
\(624\) 4.00000 0.160128
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 17.5000 30.3109i 0.699441 1.21147i
\(627\) 5.00000 8.66025i 0.199681 0.345857i
\(628\) 8.00000 0.319235
\(629\) −4.00000 6.92820i −0.159490 0.276246i
\(630\) 0.500000 + 0.866025i 0.0199205 + 0.0345033i
\(631\) −5.50000 9.52628i −0.218952 0.379235i 0.735536 0.677485i \(-0.236930\pi\)
−0.954488 + 0.298250i \(0.903597\pi\)
\(632\) 0 0
\(633\) −11.0000 19.0526i −0.437211 0.757271i
\(634\) 0.500000 0.866025i 0.0198575 0.0343943i
\(635\) 17.0000 0.674624
\(636\) 3.00000 0.118958
\(637\) 12.0000 20.7846i 0.475457 0.823516i
\(638\) −7.50000 12.9904i −0.296928 0.514294i
\(639\) −4.00000 + 6.92820i −0.158238 + 0.274075i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −6.00000 10.3923i −0.236986 0.410471i 0.722862 0.690992i \(-0.242826\pi\)
−0.959848 + 0.280521i \(0.909493\pi\)
\(642\) −8.50000 14.7224i −0.335468 0.581048i
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) −2.00000 + 3.46410i −0.0788110 + 0.136505i
\(645\) 2.00000 3.46410i 0.0787499 0.136399i
\(646\) −2.00000 3.46410i −0.0786889 0.136293i
\(647\) 18.0000 0.707653 0.353827 0.935311i \(-0.384880\pi\)
0.353827 + 0.935311i \(0.384880\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 15.0000 0.588802
\(650\) 4.00000 0.156893
\(651\) −2.00000 + 5.19615i −0.0783862 + 0.203653i
\(652\) −8.00000 −0.313304
\(653\) 21.0000 0.821794 0.410897 0.911682i \(-0.365216\pi\)
0.410897 + 0.911682i \(0.365216\pi\)
\(654\) −7.00000 + 12.1244i −0.273722 + 0.474100i
\(655\) 4.00000 0.156293
\(656\) −2.00000 3.46410i −0.0780869 0.135250i
\(657\) −1.00000 + 1.73205i −0.0390137 + 0.0675737i
\(658\) 1.00000 1.73205i 0.0389841 0.0675224i
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) −2.50000 4.33013i −0.0973124 0.168550i
\(661\) 18.0000 + 31.1769i 0.700119 + 1.21264i 0.968424 + 0.249308i \(0.0802030\pi\)
−0.268306 + 0.963334i \(0.586464\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) 4.00000 6.92820i 0.155347 0.269069i
\(664\) −4.50000 7.79423i −0.174634 0.302475i
\(665\) −1.00000 + 1.73205i −0.0387783 + 0.0671660i
\(666\) −4.00000 −0.154997
\(667\) −12.0000 −0.464642
\(668\) −8.00000 + 13.8564i −0.309529 + 0.536120i
\(669\) −1.50000 2.59808i −0.0579934 0.100447i
\(670\) 2.00000 3.46410i 0.0772667 0.133830i
\(671\) 0 0
\(672\) 0.500000 + 0.866025i 0.0192879 + 0.0334077i
\(673\) −16.5000 28.5788i −0.636028 1.10163i −0.986296 0.164984i \(-0.947243\pi\)
0.350268 0.936650i \(-0.386091\pi\)
\(674\) −3.00000 −0.115556
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) −1.50000 + 2.59808i −0.0576923 + 0.0999260i
\(677\) 23.5000 + 40.7032i 0.903178 + 1.56435i 0.823344 + 0.567543i \(0.192106\pi\)
0.0798344 + 0.996808i \(0.474561\pi\)
\(678\) −4.00000 −0.153619
\(679\) −0.500000 + 0.866025i −0.0191882 + 0.0332350i
\(680\) −2.00000 −0.0766965
\(681\) 5.00000 0.191600
\(682\) 10.0000 25.9808i 0.382920 0.994855i
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) −2.00000 −0.0764719
\(685\) −7.00000 + 12.1244i −0.267456 + 0.463248i
\(686\) 13.0000 0.496342
\(687\) 14.0000 + 24.2487i 0.534133 + 0.925146i
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) −4.00000 −0.152277
\(691\) −5.00000 8.66025i −0.190209 0.329452i 0.755110 0.655598i \(-0.227583\pi\)
−0.945319 + 0.326146i \(0.894250\pi\)
\(692\) 1.50000 + 2.59808i 0.0570214 + 0.0987640i
\(693\) 2.50000 + 4.33013i 0.0949671 + 0.164488i
\(694\) 0.500000 0.866025i 0.0189797 0.0328739i
\(695\) −5.00000 8.66025i −0.189661 0.328502i
\(696\) −1.50000 + 2.59808i −0.0568574 + 0.0984798i
\(697\) −8.00000 −0.303022
\(698\) 34.0000 1.28692
\(699\) −2.00000 + 3.46410i −0.0756469 + 0.131024i
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) 4.50000 7.79423i 0.169963 0.294384i −0.768444 0.639917i \(-0.778969\pi\)
0.938406 + 0.345533i \(0.112302\pi\)
\(702\) −2.00000 3.46410i −0.0754851 0.130744i
\(703\) −4.00000 6.92820i −0.150863 0.261302i
\(704\) −2.50000 4.33013i −0.0942223 0.163198i
\(705\) 2.00000 0.0753244
\(706\) 7.00000 12.1244i 0.263448 0.456306i
\(707\) −2.50000 + 4.33013i −0.0940222 + 0.162851i
\(708\) −1.50000 2.59808i −0.0563735 0.0976417i
\(709\) 12.0000 0.450669 0.225335 0.974281i \(-0.427652\pi\)
0.225335 + 0.974281i \(0.427652\pi\)
\(710\) −4.00000 + 6.92820i −0.150117 + 0.260011i
\(711\) 0 0
\(712\) 18.0000 0.674579
\(713\) −14.0000 17.3205i −0.524304 0.648658i
\(714\) 2.00000 0.0748481
\(715\) 20.0000 0.747958
\(716\) 4.50000 7.79423i 0.168173 0.291284i
\(717\) −24.0000 −0.896296
\(718\) −10.0000 17.3205i −0.373197 0.646396i
\(719\) −21.0000 + 36.3731i −0.783168 + 1.35649i 0.146920 + 0.989148i \(0.453064\pi\)
−0.930087 + 0.367338i \(0.880269\pi\)
\(720\) −0.500000 + 0.866025i −0.0186339 + 0.0322749i
\(721\) 5.00000 0.186210
\(722\) 7.50000 + 12.9904i 0.279121 + 0.483452i
\(723\) −3.50000 6.06218i −0.130166 0.225455i
\(724\) 11.0000 + 19.0526i 0.408812 + 0.708083i
\(725\) −1.50000 + 2.59808i −0.0557086 + 0.0964901i
\(726\) −7.00000 12.1244i −0.259794 0.449977i
\(727\) 13.5000 23.3827i 0.500687 0.867216i −0.499312 0.866422i \(-0.666414\pi\)
1.00000 0.000793791i \(-0.000252672\pi\)
\(728\) −4.00000 −0.148250
\(729\) 1.00000 0.0370370
\(730\) −1.00000 + 1.73205i −0.0370117 + 0.0641061i
\(731\) −4.00000 6.92820i −0.147945 0.256249i
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) 12.0000 + 20.7846i 0.442928 + 0.767174i
\(735\) 3.00000 + 5.19615i 0.110657 + 0.191663i
\(736\) −4.00000 −0.147442
\(737\) 10.0000 17.3205i 0.368355 0.638009i
\(738\) −2.00000 + 3.46410i −0.0736210 + 0.127515i
\(739\) −21.0000 36.3731i −0.772497 1.33800i −0.936190 0.351494i \(-0.885674\pi\)
0.163693 0.986511i \(-0.447659\pi\)
\(740\) −4.00000 −0.147043
\(741\) 4.00000 6.92820i 0.146944 0.254514i
\(742\) −3.00000 −0.110133
\(743\) −46.0000 −1.68758 −0.843788 0.536676i \(-0.819680\pi\)
−0.843788 + 0.536676i \(0.819680\pi\)
\(744\) −5.50000 + 0.866025i −0.201640 + 0.0317500i
\(745\) −11.0000 −0.403009
\(746\) 2.00000 0.0732252
\(747\) −4.50000 + 7.79423i −0.164646 + 0.285176i
\(748\) −10.0000 −0.365636
\(749\) 8.50000 + 14.7224i 0.310583 + 0.537946i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) −7.50000 + 12.9904i −0.273679 + 0.474026i −0.969801 0.243898i \(-0.921574\pi\)
0.696122 + 0.717923i \(0.254907\pi\)
\(752\) 2.00000 0.0729325
\(753\) 14.0000 + 24.2487i 0.510188 + 0.883672i
\(754\) −6.00000 10.3923i −0.218507 0.378465i
\(755\) 2.50000 + 4.33013i 0.0909843 + 0.157589i
\(756\) 0.500000 0.866025i 0.0181848 0.0314970i
\(757\) 10.0000 + 17.3205i 0.363456 + 0.629525i 0.988527 0.151043i \(-0.0482633\pi\)
−0.625071 + 0.780568i \(0.714930\pi\)
\(758\) −1.00000 + 1.73205i −0.0363216 + 0.0629109i
\(759\) −20.0000 −0.725954
\(760\) −2.00000 −0.0725476
\(761\) −25.0000 + 43.3013i −0.906249 + 1.56967i −0.0870179 + 0.996207i \(0.527734\pi\)
−0.819231 + 0.573463i \(0.805600\pi\)
\(762\) −8.50000 14.7224i −0.307923 0.533337i
\(763\) 7.00000 12.1244i 0.253417 0.438931i
\(764\) 4.00000 + 6.92820i 0.144715 + 0.250654i
\(765\) 1.00000 + 1.73205i 0.0361551 + 0.0626224i
\(766\) 14.0000 + 24.2487i 0.505841 + 0.876142i
\(767\) 12.0000 0.433295
\(768\) −0.500000 + 0.866025i −0.0180422 + 0.0312500i
\(769\) 11.5000 19.9186i 0.414701 0.718283i −0.580696 0.814120i \(-0.697220\pi\)
0.995397 + 0.0958377i \(0.0305530\pi\)
\(770\) 2.50000 + 4.33013i 0.0900937 + 0.156047i
\(771\) 12.0000 0.432169
\(772\) −0.500000 + 0.866025i −0.0179954 + 0.0311689i
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) −4.00000 −0.143777
\(775\) −5.50000 + 0.866025i −0.197566 + 0.0311086i
\(776\)