Properties

Label 70.2.e.b.51.1
Level $70$
Weight $2$
Character 70.51
Analytic conductor $0.559$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 70 = 2 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 70.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.558952814149\)
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 51.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 70.51
Dual form 70.2.e.b.11.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -2.00000 q^{6} +(-2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(1.00000 - 1.73205i) q^{12} +5.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{20} +(-5.00000 - 1.73205i) q^{21} +3.00000 q^{22} +(-1.50000 + 2.59808i) q^{23} +(1.00000 + 1.73205i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.50000 + 4.33013i) q^{26} +4.00000 q^{27} +(2.50000 + 0.866025i) q^{28} -6.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(2.00000 + 3.46410i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 - 5.19615i) q^{33} +6.00000 q^{34} +(0.500000 + 2.59808i) q^{35} +1.00000 q^{36} +(-5.50000 + 9.52628i) q^{37} +(0.500000 + 0.866025i) q^{38} +(5.00000 + 8.66025i) q^{39} +(0.500000 - 0.866025i) q^{40} +3.00000 q^{41} +(4.00000 - 3.46410i) q^{42} -10.0000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-1.50000 - 2.59808i) q^{46} +(-1.50000 + 2.59808i) q^{47} -2.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(6.00000 - 10.3923i) q^{51} +(-2.50000 - 4.33013i) q^{52} +(-1.50000 - 2.59808i) q^{53} +(-2.00000 + 3.46410i) q^{54} -3.00000 q^{55} +(-2.00000 + 1.73205i) q^{56} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(-1.00000 - 1.73205i) q^{60} +(2.00000 - 3.46410i) q^{61} -4.00000 q^{62} +(-0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(2.50000 - 4.33013i) q^{65} +(3.00000 + 5.19615i) q^{66} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} -6.00000 q^{69} +(-2.50000 - 0.866025i) q^{70} +12.0000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(2.00000 + 3.46410i) q^{73} +(-5.50000 - 9.52628i) q^{74} +(1.00000 - 1.73205i) q^{75} -1.00000 q^{76} +(7.50000 + 2.59808i) q^{77} -10.0000 q^{78} +(5.00000 - 8.66025i) q^{79} +(0.500000 + 0.866025i) q^{80} +(5.50000 + 9.52628i) q^{81} +(-1.50000 + 2.59808i) q^{82} -12.0000 q^{83} +(1.00000 + 5.19615i) q^{84} -6.00000 q^{85} +(5.00000 - 8.66025i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(-3.00000 + 5.19615i) q^{89} -1.00000 q^{90} +(-10.0000 + 8.66025i) q^{91} +3.00000 q^{92} +(-4.00000 + 6.92820i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-0.500000 - 0.866025i) q^{95} +(1.00000 - 1.73205i) q^{96} +14.0000 q^{97} +(5.50000 + 4.33013i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + O(q^{10}) \) \( 2 q - q^{2} + 2 q^{3} - q^{4} + q^{5} - 4 q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{10} - 3 q^{11} + 2 q^{12} + 10 q^{13} - q^{14} + 4 q^{15} - q^{16} - 6 q^{17} - q^{18} + q^{19} - 2 q^{20} - 10 q^{21} + 6 q^{22} - 3 q^{23} + 2 q^{24} - q^{25} - 5 q^{26} + 8 q^{27} + 5 q^{28} - 12 q^{29} - 2 q^{30} + 4 q^{31} - q^{32} + 6 q^{33} + 12 q^{34} + q^{35} + 2 q^{36} - 11 q^{37} + q^{38} + 10 q^{39} + q^{40} + 6 q^{41} + 8 q^{42} - 20 q^{43} - 3 q^{44} + q^{45} - 3 q^{46} - 3 q^{47} - 4 q^{48} + 2 q^{49} + 2 q^{50} + 12 q^{51} - 5 q^{52} - 3 q^{53} - 4 q^{54} - 6 q^{55} - 4 q^{56} + 4 q^{57} + 6 q^{58} - 2 q^{60} + 4 q^{61} - 8 q^{62} - q^{63} + 2 q^{64} + 5 q^{65} + 6 q^{66} + 4 q^{67} - 6 q^{68} - 12 q^{69} - 5 q^{70} + 24 q^{71} - q^{72} + 4 q^{73} - 11 q^{74} + 2 q^{75} - 2 q^{76} + 15 q^{77} - 20 q^{78} + 10 q^{79} + q^{80} + 11 q^{81} - 3 q^{82} - 24 q^{83} + 2 q^{84} - 12 q^{85} + 10 q^{86} - 12 q^{87} - 3 q^{88} - 6 q^{89} - 2 q^{90} - 20 q^{91} + 6 q^{92} - 8 q^{93} - 3 q^{94} - q^{95} + 2 q^{96} + 28 q^{97} + 11 q^{98} + 6 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(57\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 1.00000 + 1.73205i 0.577350 + 1.00000i 0.995782 + 0.0917517i \(0.0292466\pi\)
−0.418432 + 0.908248i \(0.637420\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −2.00000 −0.816497
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 1.00000 1.73205i 0.288675 0.500000i
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −0.500000 2.59808i −0.133631 0.694365i
\(15\) 2.00000 0.516398
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) −0.500000 0.866025i −0.117851 0.204124i
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) −1.00000 −0.223607
\(21\) −5.00000 1.73205i −1.09109 0.377964i
\(22\) 3.00000 0.639602
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 1.00000 + 1.73205i 0.204124 + 0.353553i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −2.50000 + 4.33013i −0.490290 + 0.849208i
\(27\) 4.00000 0.769800
\(28\) 2.50000 + 0.866025i 0.472456 + 0.163663i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.00000 5.19615i 0.522233 0.904534i
\(34\) 6.00000 1.02899
\(35\) 0.500000 + 2.59808i 0.0845154 + 0.439155i
\(36\) 1.00000 0.166667
\(37\) −5.50000 + 9.52628i −0.904194 + 1.56611i −0.0821995 + 0.996616i \(0.526194\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0.500000 + 0.866025i 0.0811107 + 0.140488i
\(39\) 5.00000 + 8.66025i 0.800641 + 1.38675i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 4.00000 3.46410i 0.617213 0.534522i
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0.500000 + 0.866025i 0.0745356 + 0.129099i
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) −2.00000 −0.288675
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 1.00000 0.141421
\(51\) 6.00000 10.3923i 0.840168 1.45521i
\(52\) −2.50000 4.33013i −0.346688 0.600481i
\(53\) −1.50000 2.59808i −0.206041 0.356873i 0.744423 0.667708i \(-0.232725\pi\)
−0.950464 + 0.310835i \(0.899391\pi\)
\(54\) −2.00000 + 3.46410i −0.272166 + 0.471405i
\(55\) −3.00000 −0.404520
\(56\) −2.00000 + 1.73205i −0.267261 + 0.231455i
\(57\) 2.00000 0.264906
\(58\) 3.00000 5.19615i 0.393919 0.682288i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) −1.00000 1.73205i −0.129099 0.223607i
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) −4.00000 −0.508001
\(63\) −0.500000 2.59808i −0.0629941 0.327327i
\(64\) 1.00000 0.125000
\(65\) 2.50000 4.33013i 0.310087 0.537086i
\(66\) 3.00000 + 5.19615i 0.369274 + 0.639602i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) −6.00000 −0.722315
\(70\) −2.50000 0.866025i −0.298807 0.103510i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 2.00000 + 3.46410i 0.234082 + 0.405442i 0.959006 0.283387i \(-0.0914581\pi\)
−0.724923 + 0.688830i \(0.758125\pi\)
\(74\) −5.50000 9.52628i −0.639362 1.10741i
\(75\) 1.00000 1.73205i 0.115470 0.200000i
\(76\) −1.00000 −0.114708
\(77\) 7.50000 + 2.59808i 0.854704 + 0.296078i
\(78\) −10.0000 −1.13228
\(79\) 5.00000 8.66025i 0.562544 0.974355i −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 1.00000 + 5.19615i 0.109109 + 0.566947i
\(85\) −6.00000 −0.650791
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) −6.00000 10.3923i −0.643268 1.11417i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) −1.00000 −0.105409
\(91\) −10.0000 + 8.66025i −1.04828 + 0.907841i
\(92\) 3.00000 0.312772
\(93\) −4.00000 + 6.92820i −0.414781 + 0.718421i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) −0.500000 0.866025i −0.0512989 0.0888523i
\(96\) 1.00000 1.73205i 0.102062 0.176777i
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) 3.00000 0.301511
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 6.00000 + 10.3923i 0.597022 + 1.03407i 0.993258 + 0.115924i \(0.0369830\pi\)
−0.396236 + 0.918149i \(0.629684\pi\)
\(102\) 6.00000 + 10.3923i 0.594089 + 1.02899i
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 5.00000 0.490290
\(105\) −4.00000 + 3.46410i −0.390360 + 0.338062i
\(106\) 3.00000 0.291386
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) −2.00000 3.46410i −0.192450 0.333333i
\(109\) 2.00000 + 3.46410i 0.191565 + 0.331801i 0.945769 0.324840i \(-0.105310\pi\)
−0.754204 + 0.656640i \(0.771977\pi\)
\(110\) 1.50000 2.59808i 0.143019 0.247717i
\(111\) −22.0000 −2.08815
\(112\) −0.500000 2.59808i −0.0472456 0.245495i
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) −1.00000 + 1.73205i −0.0936586 + 0.162221i
\(115\) 1.50000 + 2.59808i 0.139876 + 0.242272i
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) −2.50000 + 4.33013i −0.231125 + 0.400320i
\(118\) 0 0
\(119\) 15.0000 + 5.19615i 1.37505 + 0.476331i
\(120\) 2.00000 0.182574
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 2.00000 + 3.46410i 0.181071 + 0.313625i
\(123\) 3.00000 + 5.19615i 0.270501 + 0.468521i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) −1.00000 −0.0894427
\(126\) 2.50000 + 0.866025i 0.222718 + 0.0771517i
\(127\) −19.0000 −1.68598 −0.842989 0.537931i \(-0.819206\pi\)
−0.842989 + 0.537931i \(0.819206\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −10.0000 17.3205i −0.880451 1.52499i
\(130\) 2.50000 + 4.33013i 0.219265 + 0.379777i
\(131\) −1.50000 + 2.59808i −0.131056 + 0.226995i −0.924084 0.382190i \(-0.875170\pi\)
0.793028 + 0.609185i \(0.208503\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0.500000 + 2.59808i 0.0433555 + 0.225282i
\(134\) −4.00000 −0.345547
\(135\) 2.00000 3.46410i 0.172133 0.298142i
\(136\) −3.00000 5.19615i −0.257248 0.445566i
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 3.00000 5.19615i 0.255377 0.442326i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 1.73205i 0.169031 0.146385i
\(141\) −6.00000 −0.505291
\(142\) −6.00000 + 10.3923i −0.503509 + 0.872103i
\(143\) −7.50000 12.9904i −0.627182 1.08631i
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) −3.00000 + 5.19615i −0.249136 + 0.431517i
\(146\) −4.00000 −0.331042
\(147\) 13.0000 5.19615i 1.07222 0.428571i
\(148\) 11.0000 0.904194
\(149\) −9.00000 + 15.5885i −0.737309 + 1.27706i 0.216394 + 0.976306i \(0.430570\pi\)
−0.953703 + 0.300750i \(0.902763\pi\)
\(150\) 1.00000 + 1.73205i 0.0816497 + 0.141421i
\(151\) −7.00000 12.1244i −0.569652 0.986666i −0.996600 0.0823900i \(-0.973745\pi\)
0.426948 0.904276i \(-0.359589\pi\)
\(152\) 0.500000 0.866025i 0.0405554 0.0702439i
\(153\) 6.00000 0.485071
\(154\) −6.00000 + 5.19615i −0.483494 + 0.418718i
\(155\) 4.00000 0.321288
\(156\) 5.00000 8.66025i 0.400320 0.693375i
\(157\) −2.50000 4.33013i −0.199522 0.345582i 0.748852 0.662738i \(-0.230606\pi\)
−0.948373 + 0.317156i \(0.897272\pi\)
\(158\) 5.00000 + 8.66025i 0.397779 + 0.688973i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) −1.00000 −0.0790569
\(161\) −1.50000 7.79423i −0.118217 0.614271i
\(162\) −11.0000 −0.864242
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) −1.50000 2.59808i −0.117130 0.202876i
\(165\) −3.00000 5.19615i −0.233550 0.404520i
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) 9.00000 0.696441 0.348220 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(168\) −5.00000 1.73205i −0.385758 0.133631i
\(169\) 12.0000 0.923077
\(170\) 3.00000 5.19615i 0.230089 0.398527i
\(171\) 0.500000 + 0.866025i 0.0382360 + 0.0662266i
\(172\) 5.00000 + 8.66025i 0.381246 + 0.660338i
\(173\) −1.50000 + 2.59808i −0.114043 + 0.197528i −0.917397 0.397974i \(-0.869713\pi\)
0.803354 + 0.595502i \(0.203047\pi\)
\(174\) 12.0000 0.909718
\(175\) 2.50000 + 0.866025i 0.188982 + 0.0654654i
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) 1.50000 + 2.59808i 0.112115 + 0.194189i 0.916623 0.399753i \(-0.130904\pi\)
−0.804508 + 0.593942i \(0.797571\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −2.50000 12.9904i −0.185312 0.962911i
\(183\) 8.00000 0.591377
\(184\) −1.50000 + 2.59808i −0.110581 + 0.191533i
\(185\) 5.50000 + 9.52628i 0.404368 + 0.700386i
\(186\) −4.00000 6.92820i −0.293294 0.508001i
\(187\) −9.00000 + 15.5885i −0.658145 + 1.13994i
\(188\) 3.00000 0.218797
\(189\) −8.00000 + 6.92820i −0.581914 + 0.503953i
\(190\) 1.00000 0.0725476
\(191\) −6.00000 + 10.3923i −0.434145 + 0.751961i −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) 1.00000 + 1.73205i 0.0721688 + 0.125000i
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) −7.00000 + 12.1244i −0.502571 + 0.870478i
\(195\) 10.0000 0.716115
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) 2.00000 + 3.46410i 0.141776 + 0.245564i 0.928166 0.372168i \(-0.121385\pi\)
−0.786389 + 0.617731i \(0.788052\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) −12.0000 −0.844317
\(203\) 12.0000 10.3923i 0.842235 0.729397i
\(204\) −12.0000 −0.840168
\(205\) 1.50000 2.59808i 0.104765 0.181458i
\(206\) 2.00000 + 3.46410i 0.139347 + 0.241355i
\(207\) −1.50000 2.59808i −0.104257 0.180579i
\(208\) −2.50000 + 4.33013i −0.173344 + 0.300240i
\(209\) −3.00000 −0.207514
\(210\) −1.00000 5.19615i −0.0690066 0.358569i
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 12.0000 + 20.7846i 0.822226 + 1.42414i
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) −5.00000 + 8.66025i −0.340997 + 0.590624i
\(216\) 4.00000 0.272166
\(217\) −10.0000 3.46410i −0.678844 0.235159i
\(218\) −4.00000 −0.270914
\(219\) −4.00000 + 6.92820i −0.270295 + 0.468165i
\(220\) 1.50000 + 2.59808i 0.101130 + 0.175162i
\(221\) −15.0000 25.9808i −1.00901 1.74766i
\(222\) 11.0000 19.0526i 0.738272 1.27872i
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 2.50000 + 0.866025i 0.167038 + 0.0578638i
\(225\) 1.00000 0.0666667
\(226\) −6.00000 + 10.3923i −0.399114 + 0.691286i
\(227\) 12.0000 + 20.7846i 0.796468 + 1.37952i 0.921903 + 0.387421i \(0.126634\pi\)
−0.125435 + 0.992102i \(0.540033\pi\)
\(228\) −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 \(-0.209391\pi\)
\(230\) −3.00000 −0.197814
\(231\) 3.00000 + 15.5885i 0.197386 + 1.02565i
\(232\) −6.00000 −0.393919
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −2.50000 4.33013i −0.163430 0.283069i
\(235\) 1.50000 + 2.59808i 0.0978492 + 0.169480i
\(236\) 0 0
\(237\) 20.0000 1.29914
\(238\) −12.0000 + 10.3923i −0.777844 + 0.673633i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −1.00000 + 1.73205i −0.0645497 + 0.111803i
\(241\) 12.5000 + 21.6506i 0.805196 + 1.39464i 0.916159 + 0.400815i \(0.131273\pi\)
−0.110963 + 0.993825i \(0.535394\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) −5.00000 + 8.66025i −0.320750 + 0.555556i
\(244\) −4.00000 −0.256074
\(245\) −5.50000 4.33013i −0.351382 0.276642i
\(246\) −6.00000 −0.382546
\(247\) 2.50000 4.33013i 0.159071 0.275519i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) −12.0000 20.7846i −0.760469 1.31717i
\(250\) 0.500000 0.866025i 0.0316228 0.0547723i
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) −2.00000 + 1.73205i −0.125988 + 0.109109i
\(253\) 9.00000 0.565825
\(254\) 9.50000 16.4545i 0.596083 1.03245i
\(255\) −6.00000 10.3923i −0.375735 0.650791i
\(256\) −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 \(0.0445601\pi\)
\(258\) 20.0000 1.24515
\(259\) −5.50000 28.5788i −0.341753 1.77580i
\(260\) −5.00000 −0.310087
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) −1.50000 2.59808i −0.0926703 0.160510i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 3.00000 5.19615i 0.184637 0.319801i
\(265\) −3.00000 −0.184289
\(266\) −2.50000 0.866025i −0.153285 0.0530994i
\(267\) −12.0000 −0.734388
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) 2.00000 + 3.46410i 0.121716 + 0.210819i
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 6.00000 0.363803
\(273\) −25.0000 8.66025i −1.51307 0.524142i
\(274\) 12.0000 0.724947
\(275\) −1.50000 + 2.59808i −0.0904534 + 0.156670i
\(276\) 3.00000 + 5.19615i 0.180579 + 0.312772i
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) 2.00000 3.46410i 0.119952 0.207763i
\(279\) −4.00000 −0.239474
\(280\) 0.500000 + 2.59808i 0.0298807 + 0.155265i
\(281\) −3.00000 −0.178965 −0.0894825 0.995988i \(-0.528521\pi\)
−0.0894825 + 0.995988i \(0.528521\pi\)
\(282\) 3.00000 5.19615i 0.178647 0.309426i
\(283\) −13.0000 22.5167i −0.772770 1.33848i −0.936039 0.351895i \(-0.885537\pi\)
0.163270 0.986581i \(-0.447796\pi\)
\(284\) −6.00000 10.3923i −0.356034 0.616670i
\(285\) 1.00000 1.73205i 0.0592349 0.102598i
\(286\) 15.0000 0.886969
\(287\) −6.00000 + 5.19615i −0.354169 + 0.306719i
\(288\) 1.00000 0.0589256
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) 14.0000 + 24.2487i 0.820695 + 1.42148i
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) −27.0000 −1.57736 −0.788678 0.614806i \(-0.789234\pi\)
−0.788678 + 0.614806i \(0.789234\pi\)
\(294\) −2.00000 + 13.8564i −0.116642 + 0.808122i
\(295\) 0 0
\(296\) −5.50000 + 9.52628i −0.319681 + 0.553704i
\(297\) −6.00000 10.3923i −0.348155 0.603023i
\(298\) −9.00000 15.5885i −0.521356 0.903015i
\(299\) −7.50000 + 12.9904i −0.433736 + 0.751253i
\(300\) −2.00000 −0.115470
\(301\) 20.0000 17.3205i 1.15278 0.998337i
\(302\) 14.0000 0.805609
\(303\) −12.0000 + 20.7846i −0.689382 + 1.19404i
\(304\) 0.500000 + 0.866025i 0.0286770 + 0.0496700i
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) −1.50000 7.79423i −0.0854704 0.444117i
\(309\) 8.00000 0.455104
\(310\) −2.00000 + 3.46410i −0.113592 + 0.196748i
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) 5.00000 + 8.66025i 0.283069 + 0.490290i
\(313\) −4.00000 + 6.92820i −0.226093 + 0.391605i −0.956647 0.291250i \(-0.905929\pi\)
0.730554 + 0.682855i \(0.239262\pi\)
\(314\) 5.00000 0.282166
\(315\) −2.50000 0.866025i −0.140859 0.0487950i
\(316\) −10.0000 −0.562544
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 3.00000 + 5.19615i 0.168232 + 0.291386i
\(319\) 9.00000 + 15.5885i 0.503903 + 0.872786i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 24.0000 1.33955
\(322\) 7.50000 + 2.59808i 0.417959 + 0.144785i
\(323\) −6.00000 −0.333849
\(324\) 5.50000 9.52628i 0.305556 0.529238i
\(325\) −2.50000 4.33013i −0.138675 0.240192i
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) −4.00000 + 6.92820i −0.221201 + 0.383131i
\(328\) 3.00000 0.165647
\(329\) −1.50000 7.79423i −0.0826977 0.429710i
\(330\) 6.00000 0.330289
\(331\) 3.50000 6.06218i 0.192377 0.333207i −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) 6.00000 + 10.3923i 0.329293 + 0.570352i
\(333\) −5.50000 9.52628i −0.301398 0.522037i
\(334\) −4.50000 + 7.79423i −0.246229 + 0.426481i
\(335\) 4.00000 0.218543
\(336\) 4.00000 3.46410i 0.218218 0.188982i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 12.0000 + 20.7846i 0.651751 + 1.12887i
\(340\) 3.00000 + 5.19615i 0.162698 + 0.281801i
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) −1.00000 −0.0540738
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) −10.0000 −0.539164
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) −1.50000 2.59808i −0.0806405 0.139673i
\(347\) −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i \(-0.943860\pi\)
0.340293 0.940319i \(-0.389474\pi\)
\(348\) −6.00000 + 10.3923i −0.321634 + 0.557086i
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −2.00000 + 1.73205i −0.106904 + 0.0925820i
\(351\) 20.0000 1.06752
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) −6.00000 10.3923i −0.319348 0.553127i 0.661004 0.750382i \(-0.270130\pi\)
−0.980352 + 0.197256i \(0.936797\pi\)
\(354\) 0 0
\(355\) 6.00000 10.3923i 0.318447 0.551566i
\(356\) 6.00000 0.317999
\(357\) 6.00000 + 31.1769i 0.317554 + 1.65006i
\(358\) −3.00000 −0.158555
\(359\) −3.00000 + 5.19615i −0.158334 + 0.274242i −0.934268 0.356572i \(-0.883946\pi\)
0.775934 + 0.630814i \(0.217279\pi\)
\(360\) 0.500000 + 0.866025i 0.0263523 + 0.0456435i
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) −1.00000 + 1.73205i −0.0525588 + 0.0910346i
\(363\) 4.00000 0.209946
\(364\) 12.5000 + 4.33013i 0.655178 + 0.226960i
\(365\) 4.00000 0.209370
\(366\) −4.00000 + 6.92820i −0.209083 + 0.362143i
\(367\) 0.500000 + 0.866025i 0.0260998 + 0.0452062i 0.878780 0.477227i \(-0.158358\pi\)
−0.852680 + 0.522433i \(0.825025\pi\)
\(368\) −1.50000 2.59808i −0.0781929 0.135434i
\(369\) −1.50000 + 2.59808i −0.0780869 + 0.135250i
\(370\) −11.0000 −0.571863
\(371\) 7.50000 + 2.59808i 0.389381 + 0.134885i
\(372\) 8.00000 0.414781
\(373\) 17.0000 29.4449i 0.880227 1.52460i 0.0291379 0.999575i \(-0.490724\pi\)
0.851089 0.525022i \(-0.175943\pi\)
\(374\) −9.00000 15.5885i −0.465379 0.806060i
\(375\) −1.00000 1.73205i −0.0516398 0.0894427i
\(376\) −1.50000 + 2.59808i −0.0773566 + 0.133986i
\(377\) −30.0000 −1.54508
\(378\) −2.00000 10.3923i −0.102869 0.534522i
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) −0.500000 + 0.866025i −0.0256495 + 0.0444262i
\(381\) −19.0000 32.9090i −0.973399 1.68598i
\(382\) −6.00000 10.3923i −0.306987 0.531717i
\(383\) −7.50000 + 12.9904i −0.383232 + 0.663777i −0.991522 0.129937i \(-0.958522\pi\)
0.608290 + 0.793715i \(0.291856\pi\)
\(384\) −2.00000 −0.102062
\(385\) 6.00000 5.19615i 0.305788 0.264820i
\(386\) −4.00000 −0.203595
\(387\) 5.00000 8.66025i 0.254164 0.440225i
\(388\) −7.00000 12.1244i −0.355371 0.615521i
\(389\) 12.0000 + 20.7846i 0.608424 + 1.05382i 0.991500 + 0.130105i \(0.0415314\pi\)
−0.383076 + 0.923717i \(0.625135\pi\)
\(390\) −5.00000 + 8.66025i −0.253185 + 0.438529i
\(391\) 18.0000 0.910299
\(392\) 1.00000 6.92820i 0.0505076 0.349927i
\(393\) −6.00000 −0.302660
\(394\) 1.50000 2.59808i 0.0755689 0.130889i
\(395\) −5.00000 8.66025i −0.251577 0.435745i
\(396\) −1.50000 2.59808i −0.0753778 0.130558i
\(397\) −1.00000 + 1.73205i −0.0501886 + 0.0869291i −0.890028 0.455905i \(-0.849316\pi\)
0.839840 + 0.542834i \(0.182649\pi\)
\(398\) −4.00000 −0.200502
\(399\) −4.00000 + 3.46410i −0.200250 + 0.173422i
\(400\) 1.00000 0.0500000
\(401\) −10.5000 + 18.1865i −0.524345 + 0.908192i 0.475253 + 0.879849i \(0.342356\pi\)
−0.999598 + 0.0283431i \(0.990977\pi\)
\(402\) −4.00000 6.92820i −0.199502 0.345547i
\(403\) 10.0000 + 17.3205i 0.498135 + 0.862796i
\(404\) 6.00000 10.3923i 0.298511 0.517036i
\(405\) 11.0000 0.546594
\(406\) 3.00000 + 15.5885i 0.148888 + 0.773642i
\(407\) 33.0000 1.63575
\(408\) 6.00000 10.3923i 0.297044 0.514496i
\(409\) 11.0000 + 19.0526i 0.543915 + 0.942088i 0.998674 + 0.0514740i \(0.0163919\pi\)
−0.454759 + 0.890614i \(0.650275\pi\)
\(410\) 1.50000 + 2.59808i 0.0740797 + 0.128310i
\(411\) 12.0000 20.7846i 0.591916 1.02523i
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 3.00000 0.147442
\(415\) −6.00000 + 10.3923i −0.294528 + 0.510138i
\(416\) −2.50000 4.33013i −0.122573 0.212302i
\(417\) −4.00000 6.92820i −0.195881 0.339276i
\(418\) 1.50000 2.59808i 0.0733674 0.127076i
\(419\) 15.0000 0.732798 0.366399 0.930458i \(-0.380591\pi\)
0.366399 + 0.930458i \(0.380591\pi\)
\(420\) 5.00000 + 1.73205i 0.243975 + 0.0845154i
\(421\) −34.0000 −1.65706 −0.828529 0.559946i \(-0.810822\pi\)
−0.828529 + 0.559946i \(0.810822\pi\)
\(422\) 0.500000 0.866025i 0.0243396 0.0421575i
\(423\) −1.50000 2.59808i −0.0729325 0.126323i
\(424\) −1.50000 2.59808i −0.0728464 0.126174i
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) −24.0000 −1.16280
\(427\) 2.00000 + 10.3923i 0.0967868 + 0.502919i
\(428\) −12.0000 −0.580042
\(429\) 15.0000 25.9808i 0.724207 1.25436i
\(430\) −5.00000 8.66025i −0.241121 0.417635i
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) −2.00000 + 3.46410i −0.0962250 + 0.166667i
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 8.00000 6.92820i 0.384012 0.332564i
\(435\) −12.0000 −0.575356
\(436\) 2.00000 3.46410i 0.0957826 0.165900i
\(437\) 1.50000 + 2.59808i 0.0717547 + 0.124283i
\(438\) −4.00000 6.92820i −0.191127 0.331042i
\(439\) 5.00000 8.66025i 0.238637 0.413331i −0.721686 0.692220i \(-0.756633\pi\)
0.960323 + 0.278889i \(0.0899661\pi\)
\(440\) −3.00000 −0.143019
\(441\) 5.50000 + 4.33013i 0.261905 + 0.206197i
\(442\) 30.0000 1.42695
\(443\) 12.0000 20.7846i 0.570137 0.987507i −0.426414 0.904528i \(-0.640223\pi\)
0.996551 0.0829786i \(-0.0264433\pi\)
\(444\) 11.0000 + 19.0526i 0.522037 + 0.904194i
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) −4.00000 + 6.92820i −0.189405 + 0.328060i
\(447\) −36.0000 −1.70274
\(448\) −2.00000 + 1.73205i −0.0944911 + 0.0818317i
\(449\) −3.00000 −0.141579 −0.0707894 0.997491i \(-0.522552\pi\)
−0.0707894 + 0.997491i \(0.522552\pi\)
\(450\) −0.500000 + 0.866025i −0.0235702 + 0.0408248i
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) 14.0000 24.2487i 0.657777 1.13930i
\(454\) −24.0000 −1.12638
\(455\) 2.50000 + 12.9904i 0.117202 + 0.608998i
\(456\) 2.00000 0.0936586
\(457\) 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) 14.0000 + 24.2487i 0.654177 + 1.13307i
\(459\) −12.0000 20.7846i −0.560112 0.970143i
\(460\) 1.50000 2.59808i 0.0699379 0.121136i
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) −15.0000 5.19615i −0.697863 0.241747i
\(463\) −19.0000 −0.883005 −0.441502 0.897260i \(-0.645554\pi\)
−0.441502 + 0.897260i \(0.645554\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 4.00000 + 6.92820i 0.185496 + 0.321288i
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) 9.00000 15.5885i 0.416470 0.721348i −0.579111 0.815249i \(-0.696600\pi\)
0.995582 + 0.0939008i \(0.0299336\pi\)
\(468\) 5.00000 0.231125
\(469\) −10.0000 3.46410i −0.461757 0.159957i
\(470\) −3.00000 −0.138380
\(471\) 5.00000 8.66025i 0.230388 0.399043i
\(472\) 0 0
\(473\) 15.0000 + 25.9808i 0.689701 + 1.19460i
\(474\) −10.0000 + 17.3205i −0.459315 + 0.795557i
\(475\) −1.00000 −0.0458831
\(476\) −3.00000 15.5885i −0.137505 0.714496i
\(477\) 3.00000 0.137361
\(478\) −3.00000 + 5.19615i −0.137217 + 0.237666i
\(479\) −12.0000 20.7846i −0.548294 0.949673i −0.998392 0.0566937i \(-0.981944\pi\)
0.450098 0.892979i \(-0.351389\pi\)
\(480\) −1.00000 1.73205i −0.0456435 0.0790569i
\(481\) −27.5000 + 47.6314i −1.25389 + 2.17180i
\(482\) −25.0000 −1.13872
\(483\) 12.0000 10.3923i 0.546019 0.472866i
\(484\) −2.00000 −0.0909091
\(485\) 7.00000 12.1244i 0.317854 0.550539i
\(486\) −5.00000 8.66025i −0.226805 0.392837i
\(487\) 8.00000 + 13.8564i 0.362515 + 0.627894i 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) 2.00000 3.46410i 0.0905357 0.156813i
\(489\) 8.00000 0.361773
\(490\) 6.50000 2.59808i 0.293640 0.117369i
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 3.00000 5.19615i 0.135250 0.234261i
\(493\) 18.0000 + 31.1769i 0.810679 + 1.40414i
\(494\) 2.50000 + 4.33013i 0.112480 + 0.194822i
\(495\) 1.50000 2.59808i 0.0674200 0.116775i
\(496\) −4.00000 −0.179605
\(497\) −24.0000 + 20.7846i −1.07655 + 0.932317i
\(498\) 24.0000 1.07547
\(499\) 14.0000 24.2487i 0.626726 1.08552i −0.361478 0.932381i \(-0.617728\pi\)
0.988204 0.153141i \(-0.0489388\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 9.00000 + 15.5885i 0.402090 + 0.696441i
\(502\) 7.50000 12.9904i 0.334741 0.579789i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) −0.500000 2.59808i −0.0222718 0.115728i
\(505\) 12.0000 0.533993
\(506\) −4.50000 + 7.79423i −0.200049 + 0.346496i
\(507\) 12.0000 + 20.7846i 0.532939 + 0.923077i
\(508\) 9.50000 + 16.4545i 0.421494 + 0.730050i
\(509\) −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i \(-0.875786\pi\)
0.791849 + 0.610718i \(0.209119\pi\)
\(510\) 12.0000 0.531369
\(511\) −10.0000 3.46410i −0.442374 0.153243i
\(512\) 1.00000 0.0441942
\(513\) 2.00000 3.46410i 0.0883022 0.152944i
\(514\) 6.00000 + 10.3923i 0.264649 + 0.458385i
\(515\) −2.00000 3.46410i −0.0881305 0.152647i
\(516\) −10.0000 + 17.3205i −0.440225 + 0.762493i
\(517\) 9.00000 0.395820
\(518\) 27.5000 + 9.52628i 1.20828 + 0.418561i
\(519\) −6.00000 −0.263371
\(520\) 2.50000 4.33013i 0.109632 0.189889i
\(521\) −16.5000 28.5788i −0.722878 1.25206i −0.959841 0.280543i \(-0.909485\pi\)
0.236963 0.971519i \(-0.423848\pi\)
\(522\) 3.00000 + 5.19615i 0.131306 + 0.227429i
\(523\) −10.0000 + 17.3205i −0.437269 + 0.757373i −0.997478 0.0709788i \(-0.977388\pi\)
0.560208 + 0.828352i \(0.310721\pi\)
\(524\) 3.00000 0.131056
\(525\) 1.00000 + 5.19615i 0.0436436 + 0.226779i
\(526\) 0 0
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) 3.00000 + 5.19615i 0.130558 + 0.226134i
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 1.50000 2.59808i 0.0651558 0.112853i
\(531\) 0 0
\(532\) 2.00000 1.73205i 0.0867110 0.0750939i
\(533\) 15.0000 0.649722
\(534\) 6.00000 10.3923i 0.259645 0.449719i
\(535\) −6.00000 10.3923i −0.259403 0.449299i
\(536\) 2.00000 + 3.46410i 0.0863868 + 0.149626i
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) −12.0000 −0.517357
\(539\) −19.5000 + 7.79423i −0.839924 + 0.335721i
\(540\) −4.00000 −0.172133
\(541\) −4.00000 + 6.92820i −0.171973 + 0.297867i −0.939110 0.343617i \(-0.888348\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) 2.00000 + 3.46410i 0.0858282 + 0.148659i
\(544\) −3.00000 + 5.19615i −0.128624 + 0.222783i
\(545\) 4.00000 0.171341
\(546\) 20.0000 17.3205i 0.855921 0.741249i
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) 2.00000 + 3.46410i 0.0853579 + 0.147844i
\(550\) −1.50000 2.59808i −0.0639602 0.110782i
\(551\) −3.00000 + 5.19615i −0.127804 + 0.221364i
\(552\) −6.00000 −0.255377
\(553\) 5.00000 + 25.9808i 0.212622 + 1.10481i
\(554\) 2.00000 0.0849719
\(555\) −11.0000 + 19.0526i −0.466924 + 0.808736i
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) 13.5000 + 23.3827i 0.572013 + 0.990756i 0.996359 + 0.0852559i \(0.0271708\pi\)
−0.424346 + 0.905500i \(0.639496\pi\)
\(558\) 2.00000 3.46410i 0.0846668 0.146647i
\(559\) −50.0000 −2.11477
\(560\) −2.50000 0.866025i −0.105644 0.0365963i
\(561\) −36.0000 −1.51992
\(562\) 1.50000 2.59808i 0.0632737 0.109593i
\(563\) 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i \(-0.0428299\pi\)
−0.611656 + 0.791123i \(0.709497\pi\)
\(564\) 3.00000 + 5.19615i 0.126323 + 0.218797i
\(565\) 6.00000 10.3923i 0.252422 0.437208i
\(566\) 26.0000 1.09286
\(567\) −27.5000 9.52628i −1.15489 0.400066i
\(568\) 12.0000 0.503509
\(569\) 1.50000 2.59808i 0.0628833 0.108917i −0.832870 0.553469i \(-0.813304\pi\)
0.895753 + 0.444552i \(0.146637\pi\)
\(570\) 1.00000 + 1.73205i 0.0418854 + 0.0725476i
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) −7.50000 + 12.9904i −0.313591 + 0.543155i
\(573\) −24.0000 −1.00261
\(574\) −1.50000 7.79423i −0.0626088 0.325325i
\(575\) 3.00000 0.125109
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −10.0000 17.3205i −0.416305 0.721062i 0.579259 0.815144i \(-0.303342\pi\)
−0.995565 + 0.0940813i \(0.970009\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) −4.00000 + 6.92820i −0.166234 + 0.287926i
\(580\) 6.00000 0.249136
\(581\) 24.0000 20.7846i 0.995688 0.862291i
\(582\) −28.0000 −1.16064
\(583\) −4.50000 + 7.79423i −0.186371 + 0.322804i
\(584\) 2.00000 + 3.46410i 0.0827606 + 0.143346i
\(585\) 2.50000 + 4.33013i 0.103362 + 0.179029i
\(586\) 13.5000 23.3827i 0.557680 0.965930i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −11.0000 8.66025i −0.453632 0.357143i
\(589\) 4.00000 0.164817
\(590\) 0 0
\(591\) −3.00000 5.19615i −0.123404 0.213741i
\(592\) −5.50000 9.52628i −0.226049 0.391528i
\(593\) 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i \(-0.568551\pi\)
0.952869 0.303383i \(-0.0981160\pi\)
\(594\) 12.0000 0.492366
\(595\) 12.0000 10.3923i 0.491952 0.426043i
\(596\) 18.0000 0.737309
\(597\) −4.00000 + 6.92820i −0.163709 + 0.283552i
\(598\) −7.50000 12.9904i −0.306698 0.531216i
\(599\) −21.0000 36.3731i −0.858037 1.48616i −0.873799 0.486287i \(-0.838351\pi\)
0.0157622 0.999876i \(-0.494983\pi\)
\(600\) 1.00000 1.73205i 0.0408248 0.0707107i
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 5.00000 + 25.9808i 0.203785 + 1.05890i
\(603\) −4.00000 −0.162893
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) −1.00000 1.73205i −0.0406558 0.0704179i
\(606\) −12.0000 20.7846i −0.487467 0.844317i
\(607\) 9.50000 16.4545i 0.385593 0.667867i −0.606258 0.795268i \(-0.707330\pi\)
0.991851 + 0.127401i \(0.0406635\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 30.0000 + 10.3923i 1.21566 + 0.421117i
\(610\) 4.00000 0.161955
\(611\) −7.50000 + 12.9904i −0.303418 + 0.525535i
\(612\) −3.00000 5.19615i −0.121268 0.210042i
\(613\) −23.5000 40.7032i −0.949156 1.64399i −0.747208 0.664590i \(-0.768606\pi\)
−0.201948 0.979396i \(-0.564727\pi\)
\(614\) −1.00000 + 1.73205i −0.0403567 + 0.0698999i
\(615\) 6.00000 0.241943
\(616\) 7.50000 + 2.59808i 0.302184 + 0.104679i
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −4.00000 + 6.92820i −0.160904 + 0.278693i
\(619\) 0.500000 + 0.866025i 0.0200967 + 0.0348085i 0.875899 0.482495i \(-0.160269\pi\)
−0.855802 + 0.517303i \(0.826936\pi\)
\(620\) −2.00000 3.46410i −0.0803219 0.139122i
\(621\) −6.00000 + 10.3923i −0.240772 + 0.417029i
\(622\) 12.0000 0.481156
\(623\) −3.00000 15.5885i −0.120192 0.624538i
\(624\) −10.0000 −0.400320
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −4.00000 6.92820i −0.159872 0.276907i
\(627\) −3.00000 5.19615i −0.119808 0.207514i
\(628\) −2.50000 + 4.33013i −0.0997609 + 0.172791i
\(629\) 66.0000 2.63159
\(630\) 2.00000 1.73205i 0.0796819 0.0690066i
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 5.00000 8.66025i 0.198889 0.344486i
\(633\) −1.00000 1.73205i −0.0397464 0.0688428i
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) −9.50000 + 16.4545i −0.376996 + 0.652976i
\(636\) −6.00000 −0.237915
\(637\) 5.00000 34.6410i 0.198107 1.37253i
\(638\) −18.0000 −0.712627
\(639\) −6.00000 + 10.3923i −0.237356 + 0.411113i
\(640\) 0.500000 + 0.866025i 0.0197642 + 0.0342327i
\(641\) 22.5000 + 38.9711i 0.888697 + 1.53927i 0.841417 + 0.540386i \(0.181722\pi\)
0.0472793 + 0.998882i \(0.484945\pi\)
\(642\) −12.0000 + 20.7846i −0.473602 + 0.820303i
\(643\) 38.0000 1.49857 0.749287 0.662246i \(-0.230396\pi\)
0.749287 + 0.662246i \(0.230396\pi\)
\(644\) −6.00000 + 5.19615i −0.236433 + 0.204757i
\(645\) −20.0000 −0.787499
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) 10.5000 + 18.1865i 0.412798 + 0.714986i 0.995194 0.0979182i \(-0.0312184\pi\)
−0.582397 + 0.812905i \(0.697885\pi\)
\(648\) 5.50000 + 9.52628i 0.216060 + 0.374228i
\(649\) 0 0
\(650\) 5.00000 0.196116
\(651\) −4.00000 20.7846i −0.156772 0.814613i
\(652\) −4.00000 −0.156652
\(653\) −10.5000 + 18.1865i −0.410897 + 0.711694i −0.994988 0.0999939i \(-0.968118\pi\)
0.584091 + 0.811688i \(0.301451\pi\)
\(654\) −4.00000 6.92820i −0.156412 0.270914i
\(655\) 1.50000 + 2.59808i 0.0586098 + 0.101515i
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) −4.00000 −0.156055
\(658\) 7.50000 + 2.59808i 0.292380 + 0.101284i
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) −3.00000 + 5.19615i −0.116775 + 0.202260i
\(661\) −22.0000 38.1051i −0.855701 1.48212i −0.875993 0.482323i \(-0.839793\pi\)
0.0202925 0.999794i \(-0.493540\pi\)
\(662\) 3.50000 + 6.06218i 0.136031 + 0.235613i
\(663\) 30.0000 51.9615i 1.16510 2.01802i
\(664\) −12.0000 −0.465690
\(665\) 2.50000 + 0.866025i 0.0969458 + 0.0335830i
\(666\) 11.0000 0.426241
\(667\) 9.00000 15.5885i 0.348481 0.603587i
\(668\) −4.50000 7.79423i −0.174110 0.301568i
\(669\) 8.00000 + 13.8564i 0.309298 + 0.535720i
\(670\) −2.00000 + 3.46410i −0.0772667 + 0.133830i
\(671\) −12.0000 −0.463255
\(672\) 1.00000 + 5.19615i 0.0385758 + 0.200446i
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −7.00000 + 12.1244i −0.269630 + 0.467013i
\(675\) −2.00000 3.46410i −0.0769800 0.133333i
\(676\) −6.00000 10.3923i −0.230769 0.399704i
\(677\) 1.50000 2.59808i 0.0576497 0.0998522i −0.835760 0.549095i \(-0.814973\pi\)
0.893410 + 0.449242i \(0.148306\pi\)
\(678\) −24.0000 −0.921714
\(679\) −28.0000 + 24.2487i −1.07454 + 0.930580i
\(680\) −6.00000 −0.230089
\(681\) −24.0000 + 41.5692i −0.919682 + 1.59294i
\(682\) 6.00000 + 10.3923i 0.229752 + 0.397942i
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 0.500000 0.866025i 0.0191180 0.0331133i
\(685\) −12.0000 −0.458496
\(686\) −18.5000 + 0.866025i −0.706333 + 0.0330650i
\(687\) 56.0000 2.13653
\(688\) 5.00000 8.66025i 0.190623 0.330169i
\(689\) −7.50000 12.9904i −0.285727 0.494894i
\(690\) −3.00000 5.19615i −0.114208 0.197814i
\(691\) −16.0000 + 27.7128i −0.608669 + 1.05425i 0.382791 + 0.923835i \(0.374963\pi\)
−0.991460 + 0.130410i \(0.958371\pi\)
\(692\) 3.00000 0.114043
\(693\) −6.00000 + 5.19615i −0.227921 + 0.197386i
\(694\) 24.0000 0.911028
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) −6.00000 10.3923i −0.227429 0.393919i
\(697\) −9.00000 15.5885i −0.340899 0.590455i
\(698\) 5.00000 8.66025i 0.189253 0.327795i
\(699\) 12.0000 0.453882
\(700\) −0.500000 2.59808i −0.0188982 0.0981981i
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) −10.0000 + 17.3205i −0.377426 + 0.653720i
\(703\) 5.50000 + 9.52628i 0.207436 + 0.359290i
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) −3.00000 + 5.19615i −0.112987 + 0.195698i
\(706\) 12.0000 0.451626
\(707\) −30.0000 10.3923i −1.12827 0.390843i
\(708\) 0 0
\(709\) −7.00000 + 12.1244i −0.262891 + 0.455340i −0.967009 0.254743i \(-0.918009\pi\)
0.704118 + 0.710083i \(0.251342\pi\)
\(710\) 6.00000 + 10.3923i 0.225176 + 0.390016i
\(711\) 5.00000 + 8.66025i 0.187515 + 0.324785i
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) −12.0000 −0.449404
\(714\) −30.0000 10.3923i −1.12272 0.388922i
\(715\) −15.0000 −0.560968
\(716\) 1.50000 2.59808i 0.0560576 0.0970947i
\(717\) 6.00000 + 10.3923i 0.224074 + 0.388108i
\(718\) −3.00000 5.19615i −0.111959 0.193919i
\(719\) 18.0000 31.1769i 0.671287 1.16270i −0.306253 0.951950i \(-0.599075\pi\)
0.977539 0.210752i \(-0.0675914\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 2.00000 + 10.3923i 0.0744839 + 0.387030i
\(722\) −18.0000 −0.669891
\(723\) −25.0000 + 43.3013i −0.929760 + 1.61039i
\(724\) −1.00000 1.73205i −0.0371647 0.0643712i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) −2.00000 + 3.46410i −0.0742270 + 0.128565i
\(727\) 29.0000 1.07555 0.537775 0.843088i \(-0.319265\pi\)
0.537775 + 0.843088i \(0.319265\pi\)
\(728\) −10.0000 + 8.66025i −0.370625 + 0.320970i
\(729\) 13.0000 0.481481
\(730\) −2.00000 + 3.46410i −0.0740233 + 0.128212i
\(731\) 30.0000 + 51.9615i 1.10959 + 1.92187i
\(732\) −4.00000 6.92820i −0.147844 0.256074i
\(733\) −23.5000 + 40.7032i −0.867992 + 1.50341i −0.00394730 + 0.999992i \(0.501256\pi\)
−0.864045 + 0.503415i \(0.832077\pi\)
\(734\) −1.00000 −0.0369107
\(735\) 2.00000 13.8564i 0.0737711 0.511101i
\(736\) 3.00000 0.110581
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) −1.50000 2.59808i −0.0552158 0.0956365i
\(739\) 18.5000 + 32.0429i 0.680534 + 1.17872i 0.974818 + 0.223001i \(0.0715853\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 5.50000 9.52628i 0.202184 0.350193i
\(741\) 10.0000 0.367359
\(742\) −6.00000 + 5.19615i −0.220267 + 0.190757i
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) −4.00000 + 6.92820i −0.146647 + 0.254000i
\(745\) 9.00000 + 15.5885i 0.329734 + 0.571117i
\(746\) 17.0000 + 29.4449i 0.622414 + 1.07805i
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 18.0000 0.658145
\(749\) 6.00000 + 31.1769i 0.219235 + 1.13918i
\(750\) 2.00000 0.0730297
\(751\) −13.0000 + 22.5167i −0.474377 + 0.821645i −0.999570 0.0293387i \(-0.990660\pi\)
0.525193 + 0.850983i \(0.323993\pi\)
\(752\) −1.50000 2.59808i −0.0546994 0.0947421i
\(753\) −15.0000 25.9808i −0.546630 0.946792i
\(754\) 15.0000 25.9808i 0.546268 0.946164i
\(755\) −14.0000 −0.509512
\(756\) 10.0000 + 3.46410i 0.363696 + 0.125988i
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) 12.5000 21.6506i 0.454020 0.786386i
\(759\) 9.00000 + 15.5885i 0.326679 + 0.565825i
\(760\) −0.500000 0.866025i −0.0181369 0.0314140i
\(761\) 25.5000 44.1673i 0.924374 1.60106i 0.131810 0.991275i \(-0.457921\pi\)
0.792564 0.609788i \(-0.208745\pi\)
\(762\) 38.0000 1.37659
\(763\) −10.0000 3.46410i −0.362024 0.125409i
\(764\) 12.0000 0.434145
\(765\) 3.00000 5.19615i 0.108465 0.187867i
\(766\) −7.50000 12.9904i −0.270986 0.469362i
\(767\) 0 0
\(768\) 1.00000 1.73205i 0.0360844 0.0625000i
\(769\) −49.0000 −1.76699 −0.883493 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 1.50000 + 7.79423i 0.0540562 + 0.280885i
\(771\) 24.0000 0.864339
\(772\) 2.00000 3.46410i 0.0719816 0.124676i
\(773\) −19.5000 33.7750i −0.701366 1.21480i −0.967987 0.251000i \(-0.919240\pi\)
0.266621 0.963802i \(-0.414093\pi\)
\(774\) 5.00000 + 8.66025i 0.179721 + 0.311286i
\(775\) 2.00000 3.46410i 0.0718421 0.124434i
\(776\) 14.0000 0.502571