Properties

Label 570.2.i.d.121.1
Level $570$
Weight $2$
Character 570.121
Analytic conductor $4.551$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
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 121.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.2.i.d.391.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +6.00000 q^{11} +1.00000 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(3.00000 + 5.19615i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +1.00000 q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} +11.0000 q^{37} +(0.500000 + 4.33013i) q^{38} +5.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{44} -1.00000 q^{45} -6.00000 q^{46} +(-6.00000 + 10.3923i) q^{47} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} -1.00000 q^{50} +(-2.50000 - 4.33013i) q^{52} +(6.00000 - 10.3923i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.00000 + 5.19615i) q^{55} +1.00000 q^{56} +(-0.500000 - 4.33013i) q^{57} -6.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 + 0.866025i) q^{60} +(3.50000 - 6.06218i) q^{61} +(2.50000 + 4.33013i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} -5.00000 q^{65} +(3.00000 - 5.19615i) q^{66} +(0.500000 - 0.866025i) q^{67} +6.00000 q^{69} +(0.500000 - 0.866025i) q^{70} +(0.500000 - 0.866025i) q^{72} +(0.500000 + 0.866025i) q^{73} +(5.50000 + 9.52628i) q^{74} +1.00000 q^{75} +(-3.50000 + 2.59808i) q^{76} -6.00000 q^{77} +(2.50000 + 4.33013i) q^{78} +(3.50000 + 6.06218i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} -1.00000 q^{84} +(-0.500000 + 0.866025i) q^{86} +6.00000 q^{87} -6.00000 q^{88} +(6.00000 - 10.3923i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(2.50000 - 4.33013i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-2.50000 - 4.33013i) q^{93} -12.0000 q^{94} +(0.500000 + 4.33013i) q^{95} -1.00000 q^{96} +(-7.00000 - 12.1244i) q^{97} +(-3.00000 - 5.19615i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} + q^{5} + q^{6} - 2q^{7} - 2q^{8} - q^{9} - q^{10} + 12q^{11} + 2q^{12} - 5q^{13} - q^{14} + q^{15} - q^{16} - 2q^{18} + 8q^{19} - 2q^{20} + q^{21} + 6q^{22} - 6q^{23} + q^{24} - q^{25} - 10q^{26} + 2q^{27} + q^{28} - 6q^{29} + 2q^{30} + 10q^{31} + q^{32} - 6q^{33} - q^{35} - q^{36} + 22q^{37} + q^{38} + 10q^{39} - q^{40} - 6q^{41} - q^{42} + q^{43} - 6q^{44} - 2q^{45} - 12q^{46} - 12q^{47} - q^{48} - 12q^{49} - 2q^{50} - 5q^{52} + 12q^{53} + q^{54} + 6q^{55} + 2q^{56} - q^{57} - 12q^{58} - 6q^{59} + q^{60} + 7q^{61} + 5q^{62} + q^{63} + 2q^{64} - 10q^{65} + 6q^{66} + q^{67} + 12q^{69} + q^{70} + q^{72} + q^{73} + 11q^{74} + 2q^{75} - 7q^{76} - 12q^{77} + 5q^{78} + 7q^{79} + q^{80} - q^{81} + 6q^{82} - 12q^{83} - 2q^{84} - q^{86} + 12q^{87} - 12q^{88} + 12q^{89} - q^{90} + 5q^{91} - 6q^{92} - 5q^{93} - 24q^{94} + q^{95} - 2q^{96} - 14q^{97} - 6q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 1.00000 0.288675
\(13\) −2.50000 + 4.33013i −0.693375 + 1.20096i 0.277350 + 0.960769i \(0.410544\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0.500000 0.866025i 0.129099 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) −1.00000 −0.235702
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) −1.00000 −0.223607
\(21\) 0.500000 + 0.866025i 0.109109 + 0.188982i
\(22\) 3.00000 + 5.19615i 0.639602 + 1.10782i
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −5.00000 −0.980581
\(27\) 1.00000 0.192450
\(28\) 0.500000 0.866025i 0.0944911 0.163663i
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 1.00000 0.182574
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −3.00000 5.19615i −0.522233 0.904534i
\(34\) 0 0
\(35\) −0.500000 0.866025i −0.0845154 0.146385i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 11.0000 1.80839 0.904194 0.427121i \(-0.140472\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0.500000 + 4.33013i 0.0811107 + 0.702439i
\(39\) 5.00000 0.800641
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) −0.500000 + 0.866025i −0.0771517 + 0.133631i
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) −3.00000 + 5.19615i −0.452267 + 0.783349i
\(45\) −1.00000 −0.149071
\(46\) −6.00000 −0.884652
\(47\) −6.00000 + 10.3923i −0.875190 + 1.51587i −0.0186297 + 0.999826i \(0.505930\pi\)
−0.856560 + 0.516047i \(0.827403\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −6.00000 −0.857143
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) −2.50000 4.33013i −0.346688 0.600481i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 3.00000 + 5.19615i 0.404520 + 0.700649i
\(56\) 1.00000 0.133631
\(57\) −0.500000 4.33013i −0.0662266 0.573539i
\(58\) −6.00000 −0.787839
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0.500000 + 0.866025i 0.0645497 + 0.111803i
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 2.50000 + 4.33013i 0.317500 + 0.549927i
\(63\) 0.500000 0.866025i 0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) −5.00000 −0.620174
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) 0.500000 0.866025i 0.0610847 0.105802i −0.833866 0.551967i \(-0.813877\pi\)
0.894951 + 0.446165i \(0.147211\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0.500000 0.866025i 0.0597614 0.103510i
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 0.500000 + 0.866025i 0.0585206 + 0.101361i 0.893801 0.448463i \(-0.148028\pi\)
−0.835281 + 0.549823i \(0.814695\pi\)
\(74\) 5.50000 + 9.52628i 0.639362 + 1.10741i
\(75\) 1.00000 0.115470
\(76\) −3.50000 + 2.59808i −0.401478 + 0.298020i
\(77\) −6.00000 −0.683763
\(78\) 2.50000 + 4.33013i 0.283069 + 0.490290i
\(79\) 3.50000 + 6.06218i 0.393781 + 0.682048i 0.992945 0.118578i \(-0.0378336\pi\)
−0.599164 + 0.800626i \(0.704500\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −1.00000 −0.109109
\(85\) 0 0
\(86\) −0.500000 + 0.866025i −0.0539164 + 0.0933859i
\(87\) 6.00000 0.643268
\(88\) −6.00000 −0.639602
\(89\) 6.00000 10.3923i 0.635999 1.10158i −0.350304 0.936636i \(-0.613922\pi\)
0.986303 0.164946i \(-0.0527450\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) 2.50000 4.33013i 0.262071 0.453921i
\(92\) −3.00000 5.19615i −0.312772 0.541736i
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) −12.0000 −1.23771
\(95\) 0.500000 + 4.33013i 0.0512989 + 0.444262i
\(96\) −1.00000 −0.102062
\(97\) −7.00000 12.1244i −0.710742 1.23104i −0.964579 0.263795i \(-0.915026\pi\)
0.253837 0.967247i \(-0.418307\pi\)
\(98\) −3.00000 5.19615i −0.303046 0.524891i
\(99\) −3.00000 + 5.19615i −0.301511 + 0.522233i
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 11.0000 1.08386 0.541931 0.840423i \(-0.317693\pi\)
0.541931 + 0.840423i \(0.317693\pi\)
\(104\) 2.50000 4.33013i 0.245145 0.424604i
\(105\) −0.500000 + 0.866025i −0.0487950 + 0.0845154i
\(106\) 12.0000 1.16554
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) −3.00000 + 5.19615i −0.286039 + 0.495434i
\(111\) −5.50000 9.52628i −0.522037 0.904194i
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 3.50000 2.59808i 0.327805 0.243332i
\(115\) −6.00000 −0.559503
\(116\) −3.00000 5.19615i −0.278543 0.482451i
\(117\) −2.50000 4.33013i −0.231125 0.400320i
\(118\) 3.00000 5.19615i 0.276172 0.478345i
\(119\) 0 0
\(120\) −0.500000 + 0.866025i −0.0456435 + 0.0790569i
\(121\) 25.0000 2.27273
\(122\) 7.00000 0.633750
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) −1.00000 −0.0894427
\(126\) 1.00000 0.0890871
\(127\) 8.00000 13.8564i 0.709885 1.22956i −0.255014 0.966937i \(-0.582080\pi\)
0.964899 0.262620i \(-0.0845865\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0.500000 0.866025i 0.0440225 0.0762493i
\(130\) −2.50000 4.33013i −0.219265 0.379777i
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 6.00000 0.522233
\(133\) −4.00000 1.73205i −0.346844 0.150188i
\(134\) 1.00000 0.0863868
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) 3.00000 + 5.19615i 0.255377 + 0.442326i
\(139\) 0.500000 0.866025i 0.0424094 0.0734553i −0.844042 0.536278i \(-0.819830\pi\)
0.886451 + 0.462822i \(0.153163\pi\)
\(140\) 1.00000 0.0845154
\(141\) 12.0000 1.01058
\(142\) 0 0
\(143\) −15.0000 + 25.9808i −1.25436 + 2.17262i
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) −0.500000 + 0.866025i −0.0413803 + 0.0716728i
\(147\) 3.00000 + 5.19615i 0.247436 + 0.428571i
\(148\) −5.50000 + 9.52628i −0.452097 + 0.783055i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −4.00000 1.73205i −0.324443 0.140488i
\(153\) 0 0
\(154\) −3.00000 5.19615i −0.241747 0.418718i
\(155\) 2.50000 + 4.33013i 0.200805 + 0.347804i
\(156\) −2.50000 + 4.33013i −0.200160 + 0.346688i
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) −3.50000 + 6.06218i −0.278445 + 0.482281i
\(159\) −12.0000 −0.951662
\(160\) 1.00000 0.0790569
\(161\) 3.00000 5.19615i 0.236433 0.409514i
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 6.00000 0.468521
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 9.00000 15.5885i 0.696441 1.20627i −0.273252 0.961943i \(-0.588099\pi\)
0.969693 0.244328i \(-0.0785675\pi\)
\(168\) −0.500000 0.866025i −0.0385758 0.0668153i
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) 0 0
\(171\) −3.50000 + 2.59808i −0.267652 + 0.198680i
\(172\) −1.00000 −0.0762493
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 3.00000 + 5.19615i 0.227429 + 0.393919i
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) −3.00000 5.19615i −0.226134 0.391675i
\(177\) −3.00000 + 5.19615i −0.225494 + 0.390567i
\(178\) 12.0000 0.899438
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) −13.0000 + 22.5167i −0.966282 + 1.67365i −0.260153 + 0.965567i \(0.583773\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 5.00000 0.370625
\(183\) −7.00000 −0.517455
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) 5.50000 + 9.52628i 0.404368 + 0.700386i
\(186\) 2.50000 4.33013i 0.183309 0.317500i
\(187\) 0 0
\(188\) −6.00000 10.3923i −0.437595 0.757937i
\(189\) −1.00000 −0.0727393
\(190\) −3.50000 + 2.59808i −0.253917 + 0.188484i
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −2.50000 4.33013i −0.179954 0.311689i 0.761911 0.647682i \(-0.224262\pi\)
−0.941865 + 0.335993i \(0.890928\pi\)
\(194\) 7.00000 12.1244i 0.502571 0.870478i
\(195\) 2.50000 + 4.33013i 0.179029 + 0.310087i
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −6.00000 −0.426401
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −1.00000 −0.0705346
\(202\) 6.00000 0.422159
\(203\) 3.00000 5.19615i 0.210559 0.364698i
\(204\) 0 0
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) 5.50000 + 9.52628i 0.383203 + 0.663727i
\(207\) −3.00000 5.19615i −0.208514 0.361158i
\(208\) 5.00000 0.346688
\(209\) 24.0000 + 10.3923i 1.66011 + 0.718851i
\(210\) −1.00000 −0.0690066
\(211\) 6.50000 + 11.2583i 0.447478 + 0.775055i 0.998221 0.0596196i \(-0.0189888\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −0.500000 + 0.866025i −0.0340997 + 0.0590624i
\(216\) −1.00000 −0.0680414
\(217\) −5.00000 −0.339422
\(218\) 7.00000 12.1244i 0.474100 0.821165i
\(219\) 0.500000 0.866025i 0.0337869 0.0585206i
\(220\) −6.00000 −0.404520
\(221\) 0 0
\(222\) 5.50000 9.52628i 0.369136 0.639362i
\(223\) 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) −0.500000 0.866025i −0.0333333 0.0577350i
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) −18.0000 −1.19470 −0.597351 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 4.00000 + 1.73205i 0.264906 + 0.114708i
\(229\) −25.0000 −1.65205 −0.826023 0.563636i \(-0.809402\pi\)
−0.826023 + 0.563636i \(0.809402\pi\)
\(230\) −3.00000 5.19615i −0.197814 0.342624i
\(231\) 3.00000 + 5.19615i 0.197386 + 0.341882i
\(232\) 3.00000 5.19615i 0.196960 0.341144i
\(233\) 6.00000 + 10.3923i 0.393073 + 0.680823i 0.992853 0.119342i \(-0.0380786\pi\)
−0.599780 + 0.800165i \(0.704745\pi\)
\(234\) 2.50000 4.33013i 0.163430 0.283069i
\(235\) −12.0000 −0.782794
\(236\) 6.00000 0.390567
\(237\) 3.50000 6.06218i 0.227349 0.393781i
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 12.5000 + 21.6506i 0.803530 + 1.39176i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 3.50000 + 6.06218i 0.224065 + 0.388091i
\(245\) −3.00000 5.19615i −0.191663 0.331970i
\(246\) −6.00000 −0.382546
\(247\) −17.5000 + 12.9904i −1.11350 + 0.826558i
\(248\) −5.00000 −0.317500
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −3.00000 + 5.19615i −0.189358 + 0.327978i −0.945036 0.326965i \(-0.893974\pi\)
0.755678 + 0.654943i \(0.227307\pi\)
\(252\) 0.500000 + 0.866025i 0.0314970 + 0.0545545i
\(253\) −18.0000 + 31.1769i −1.13165 + 1.96008i
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 1.00000 0.0622573
\(259\) −11.0000 −0.683507
\(260\) 2.50000 4.33013i 0.155043 0.268543i
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) 3.00000 5.19615i 0.185341 0.321019i
\(263\) 3.00000 + 5.19615i 0.184988 + 0.320408i 0.943572 0.331166i \(-0.107442\pi\)
−0.758585 + 0.651575i \(0.774109\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) 12.0000 0.737154
\(266\) −0.500000 4.33013i −0.0306570 0.265497i
\(267\) −12.0000 −0.734388
\(268\) 0.500000 + 0.866025i 0.0305424 + 0.0529009i
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 0 0
\(273\) −5.00000 −0.302614
\(274\) 6.00000 0.362473
\(275\) −3.00000 + 5.19615i −0.180907 + 0.313340i
\(276\) −3.00000 + 5.19615i −0.180579 + 0.312772i
\(277\) 14.0000 0.841178 0.420589 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 1.00000 0.0599760
\(279\) −2.50000 + 4.33013i −0.149671 + 0.259238i
\(280\) 0.500000 + 0.866025i 0.0298807 + 0.0517549i
\(281\) −9.00000 + 15.5885i −0.536895 + 0.929929i 0.462174 + 0.886789i \(0.347070\pi\)
−0.999069 + 0.0431402i \(0.986264\pi\)
\(282\) 6.00000 + 10.3923i 0.357295 + 0.618853i
\(283\) 8.00000 + 13.8564i 0.475551 + 0.823678i 0.999608 0.0280052i \(-0.00891551\pi\)
−0.524057 + 0.851683i \(0.675582\pi\)
\(284\) 0 0
\(285\) 3.50000 2.59808i 0.207322 0.153897i
\(286\) −30.0000 −1.77394
\(287\) 3.00000 + 5.19615i 0.177084 + 0.306719i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) −7.00000 + 12.1244i −0.410347 + 0.710742i
\(292\) −1.00000 −0.0585206
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) −3.00000 + 5.19615i −0.174964 + 0.303046i
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) −11.0000 −0.639362
\(297\) 6.00000 0.348155
\(298\) −9.00000 + 15.5885i −0.521356 + 0.903015i
\(299\) −15.0000 25.9808i −0.867472 1.50251i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) −0.500000 0.866025i −0.0288195 0.0499169i
\(302\) 4.00000 + 6.92820i 0.230174 + 0.398673i
\(303\) −6.00000 −0.344691
\(304\) −0.500000 4.33013i −0.0286770 0.248350i
\(305\) 7.00000 0.400819
\(306\) 0 0
\(307\) −10.0000 17.3205i −0.570730 0.988534i −0.996491 0.0836980i \(-0.973327\pi\)
0.425761 0.904836i \(-0.360006\pi\)
\(308\) 3.00000 5.19615i 0.170941 0.296078i
\(309\) −5.50000 9.52628i −0.312884 0.541931i
\(310\) −2.50000 + 4.33013i −0.141990 + 0.245935i
\(311\) 6.00000 0.340229 0.170114 0.985424i \(-0.445586\pi\)
0.170114 + 0.985424i \(0.445586\pi\)
\(312\) −5.00000 −0.283069
\(313\) 11.0000 19.0526i 0.621757 1.07691i −0.367402 0.930062i \(-0.619753\pi\)
0.989158 0.146852i \(-0.0469141\pi\)
\(314\) −6.50000 + 11.2583i −0.366816 + 0.635344i
\(315\) 1.00000 0.0563436
\(316\) −7.00000 −0.393781
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) −6.00000 10.3923i −0.336463 0.582772i
\(319\) −18.0000 + 31.1769i −1.00781 + 1.74557i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) 6.00000 + 10.3923i 0.334887 + 0.580042i
\(322\) 6.00000 0.334367
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −2.50000 4.33013i −0.138675 0.240192i
\(326\) 5.50000 + 9.52628i 0.304617 + 0.527612i
\(327\) −7.00000 + 12.1244i −0.387101 + 0.670478i
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) 6.00000 10.3923i 0.330791 0.572946i
\(330\) 6.00000 0.330289
\(331\) 29.0000 1.59398 0.796992 0.603990i \(-0.206423\pi\)
0.796992 + 0.603990i \(0.206423\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) −5.50000 + 9.52628i −0.301398 + 0.522037i
\(334\) 18.0000 0.984916
\(335\) 1.00000 0.0546358
\(336\) 0.500000 0.866025i 0.0272772 0.0472456i
\(337\) −5.50000 9.52628i −0.299604 0.518930i 0.676441 0.736497i \(-0.263521\pi\)
−0.976045 + 0.217567i \(0.930188\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 9.00000 + 15.5885i 0.488813 + 0.846649i
\(340\) 0 0
\(341\) 30.0000 1.62459
\(342\) −4.00000 1.73205i −0.216295 0.0936586i
\(343\) 13.0000 0.701934
\(344\) −0.500000 0.866025i −0.0269582 0.0466930i
\(345\) 3.00000 + 5.19615i 0.161515 + 0.279751i
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) −3.00000 + 5.19615i −0.160817 + 0.278543i
\(349\) −19.0000 −1.01705 −0.508523 0.861048i \(-0.669808\pi\)
−0.508523 + 0.861048i \(0.669808\pi\)
\(350\) 1.00000 0.0534522
\(351\) −2.50000 + 4.33013i −0.133440 + 0.231125i
\(352\) 3.00000 5.19615i 0.159901 0.276956i
\(353\) 18.0000 0.958043 0.479022 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) −6.00000 −0.318896
\(355\) 0 0
\(356\) 6.00000 + 10.3923i 0.317999 + 0.550791i
\(357\) 0 0
\(358\) 9.00000 + 15.5885i 0.475665 + 0.823876i
\(359\) 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i \(-0.116054\pi\)
−0.775934 + 0.630814i \(0.782721\pi\)
\(360\) 1.00000 0.0527046
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) −26.0000 −1.36653
\(363\) −12.5000 21.6506i −0.656080 1.13636i
\(364\) 2.50000 + 4.33013i 0.131036 + 0.226960i
\(365\) −0.500000 + 0.866025i −0.0261712 + 0.0453298i
\(366\) −3.50000 6.06218i −0.182948 0.316875i
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 6.00000 0.312772
\(369\) 6.00000 0.312348
\(370\) −5.50000 + 9.52628i −0.285931 + 0.495248i
\(371\) −6.00000 + 10.3923i −0.311504 + 0.539542i
\(372\) 5.00000 0.259238
\(373\) 2.00000 0.103556 0.0517780 0.998659i \(-0.483511\pi\)
0.0517780 + 0.998659i \(0.483511\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 6.00000 10.3923i 0.309426 0.535942i
\(377\) −15.0000 25.9808i −0.772539 1.33808i
\(378\) −0.500000 0.866025i −0.0257172 0.0445435i
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) −4.00000 1.73205i −0.205196 0.0888523i
\(381\) −16.0000 −0.819705
\(382\) 6.00000 + 10.3923i 0.306987 + 0.531717i
\(383\) 6.00000 + 10.3923i 0.306586 + 0.531022i 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) −3.00000 5.19615i −0.152894 0.264820i
\(386\) 2.50000 4.33013i 0.127247 0.220398i
\(387\) −1.00000 −0.0508329
\(388\) 14.0000 0.710742
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) −2.50000 + 4.33013i −0.126592 + 0.219265i
\(391\) 0 0
\(392\) 6.00000 0.303046
\(393\) −3.00000 + 5.19615i −0.151330 + 0.262111i
\(394\) −9.00000 15.5885i −0.453413 0.785335i
\(395\) −3.50000 + 6.06218i −0.176104 + 0.305021i
\(396\) −3.00000 5.19615i −0.150756 0.261116i
\(397\) 12.5000 + 21.6506i 0.627357 + 1.08661i 0.988080 + 0.153941i \(0.0491966\pi\)
−0.360723 + 0.932673i \(0.617470\pi\)
\(398\) 7.00000 0.350878
\(399\) 0.500000 + 4.33013i 0.0250313 + 0.216777i
\(400\) 1.00000 0.0500000
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) −0.500000 0.866025i −0.0249377 0.0431934i
\(403\) −12.5000 + 21.6506i −0.622669 + 1.07849i
\(404\) 3.00000 + 5.19615i 0.149256 + 0.258518i
\(405\) 0.500000 0.866025i 0.0248452 0.0430331i
\(406\) 6.00000 0.297775
\(407\) 66.0000 3.27150
\(408\) 0 0
\(409\) −1.00000 + 1.73205i −0.0494468 + 0.0856444i −0.889689 0.456566i \(-0.849079\pi\)
0.840243 + 0.542211i \(0.182412\pi\)
\(410\) 6.00000 0.296319
\(411\) −6.00000 −0.295958
\(412\) −5.50000 + 9.52628i −0.270966 + 0.469326i
\(413\) 3.00000 + 5.19615i 0.147620 + 0.255686i
\(414\) 3.00000 5.19615i 0.147442 0.255377i
\(415\) −3.00000 5.19615i −0.147264 0.255069i
\(416\) 2.50000 + 4.33013i 0.122573 + 0.212302i
\(417\) −1.00000 −0.0489702
\(418\) 3.00000 + 25.9808i 0.146735 + 1.27076i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) −0.500000 0.866025i −0.0243975 0.0422577i
\(421\) −13.0000 22.5167i −0.633581 1.09739i −0.986814 0.161859i \(-0.948251\pi\)
0.353233 0.935536i \(-0.385082\pi\)
\(422\) −6.50000 + 11.2583i −0.316415 + 0.548047i
\(423\) −6.00000 10.3923i −0.291730 0.505291i
\(424\) −6.00000 + 10.3923i −0.291386 + 0.504695i
\(425\) 0 0
\(426\) 0 0
\(427\) −3.50000 + 6.06218i −0.169377 + 0.293369i
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 30.0000 1.44841
\(430\) −1.00000 −0.0482243
\(431\) 12.0000 20.7846i 0.578020 1.00116i −0.417687 0.908591i \(-0.637159\pi\)
0.995706 0.0925683i \(-0.0295076\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 3.50000 6.06218i 0.168199 0.291330i −0.769588 0.638541i \(-0.779538\pi\)
0.937787 + 0.347212i \(0.112871\pi\)
\(434\) −2.50000 4.33013i −0.120004 0.207853i
\(435\) 3.00000 + 5.19615i 0.143839 + 0.249136i
\(436\) 14.0000 0.670478
\(437\) −21.0000 + 15.5885i −1.00457 + 0.745697i
\(438\) 1.00000 0.0477818
\(439\) −5.50000 9.52628i −0.262501 0.454665i 0.704405 0.709798i \(-0.251214\pi\)
−0.966906 + 0.255134i \(0.917881\pi\)
\(440\) −3.00000 5.19615i −0.143019 0.247717i
\(441\) 3.00000 5.19615i 0.142857 0.247436i
\(442\) 0 0
\(443\) 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 0.522037
\(445\) 12.0000 0.568855
\(446\) −0.500000 + 0.866025i −0.0236757 + 0.0410075i
\(447\) 9.00000 15.5885i 0.425685 0.737309i
\(448\) −1.00000 −0.0472456
\(449\) 24.0000 1.13263 0.566315 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) 0.500000 0.866025i 0.0235702 0.0408248i
\(451\) −18.0000 31.1769i −0.847587 1.46806i
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) −4.00000 6.92820i −0.187936 0.325515i
\(454\) −9.00000 15.5885i −0.422391 0.731603i
\(455\) 5.00000 0.234404
\(456\) 0.500000 + 4.33013i 0.0234146 + 0.202777i
\(457\) 11.0000 0.514558 0.257279 0.966337i \(-0.417174\pi\)
0.257279 + 0.966337i \(0.417174\pi\)
\(458\) −12.5000 21.6506i −0.584087 1.01167i
\(459\) 0 0
\(460\) 3.00000 5.19615i 0.139876 0.242272i
\(461\) −18.0000 31.1769i −0.838344 1.45205i −0.891279 0.453456i \(-0.850191\pi\)
0.0529352 0.998598i \(-0.483142\pi\)
\(462\) −3.00000 + 5.19615i −0.139573 + 0.241747i
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 6.00000 0.278543
\(465\) 2.50000 4.33013i 0.115935 0.200805i
\(466\) −6.00000 + 10.3923i −0.277945 + 0.481414i
\(467\) −6.00000 −0.277647 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(468\) 5.00000 0.231125
\(469\) −0.500000 + 0.866025i −0.0230879 + 0.0399893i
\(470\) −6.00000 10.3923i −0.276759 0.479361i
\(471\) 6.50000 11.2583i 0.299504 0.518756i
\(472\) 3.00000 + 5.19615i 0.138086 + 0.239172i
\(473\) 3.00000 + 5.19615i 0.137940 + 0.238919i
\(474\) 7.00000 0.321521
\(475\) −3.50000 + 2.59808i −0.160591 + 0.119208i
\(476\) 0 0
\(477\) 6.00000 + 10.3923i 0.274721 + 0.475831i
\(478\) −9.00000 15.5885i −0.411650 0.712999i
\(479\) −3.00000 + 5.19615i −0.137073 + 0.237418i −0.926388 0.376571i \(-0.877103\pi\)
0.789314 + 0.613990i \(0.210436\pi\)
\(480\) −0.500000 0.866025i −0.0228218 0.0395285i
\(481\) −27.5000 + 47.6314i −1.25389 + 2.17180i
\(482\) −5.00000 −0.227744
\(483\) −6.00000 −0.273009
\(484\) −12.5000 + 21.6506i −0.568182 + 0.984120i
\(485\) 7.00000 12.1244i 0.317854 0.550539i
\(486\) −1.00000 −0.0453609
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) −3.50000 + 6.06218i −0.158438 + 0.274422i
\(489\) −5.50000 9.52628i −0.248719 0.430793i
\(490\) 3.00000 5.19615i 0.135526 0.234738i
\(491\) 6.00000 + 10.3923i 0.270776 + 0.468998i 0.969061 0.246822i \(-0.0793863\pi\)
−0.698285 + 0.715820i \(0.746053\pi\)
\(492\) −3.00000 5.19615i −0.135250 0.234261i
\(493\) 0 0
\(494\) −20.0000 8.66025i −0.899843 0.389643i
\(495\) −6.00000 −0.269680
\(496\) −2.50000 4.33013i −0.112253 0.194428i
\(497\) 0 0
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 0.500000 + 0.866025i 0.0223831 + 0.0387686i 0.877000 0.480490i \(-0.159541\pi\)
−0.854617 + 0.519259i \(0.826208\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) −18.0000 −0.804181
\(502\) −6.00000 −0.267793
\(503\) 12.0000 20.7846i 0.535054 0.926740i −0.464107 0.885779i \(-0.653625\pi\)
0.999161 0.0409609i \(-0.0130419\pi\)
\(504\) −0.500000 + 0.866025i −0.0222718 + 0.0385758i
\(505\) 6.00000 0.266996
\(506\) −36.0000 −1.60040
\(507\) −6.00000 + 10.3923i −0.266469 + 0.461538i
\(508\) 8.00000 + 13.8564i 0.354943 + 0.614779i
\(509\) 18.0000 31.1769i 0.797836 1.38189i −0.123187 0.992384i \(-0.539311\pi\)
0.921023 0.389509i \(-0.127355\pi\)
\(510\) 0 0
\(511\) −0.500000 0.866025i −0.0221187 0.0383107i
\(512\) −1.00000 −0.0441942
\(513\) 4.00000 + 1.73205i 0.176604 + 0.0764719i
\(514\) −6.00000 −0.264649
\(515\) 5.50000 + 9.52628i 0.242359 + 0.419778i
\(516\) 0.500000 + 0.866025i 0.0220113 + 0.0381246i
\(517\) −36.0000 + 62.3538i −1.58328 + 2.74232i
\(518\) −5.50000 9.52628i −0.241656 0.418561i
\(519\) −3.00000 + 5.19615i −0.131685 + 0.228086i
\(520\) 5.00000 0.219265
\(521\) −24.0000 −1.05146 −0.525730 0.850652i \(-0.676208\pi\)
−0.525730 + 0.850652i \(0.676208\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) 15.5000 26.8468i 0.677768 1.17393i −0.297884 0.954602i \(-0.596281\pi\)
0.975652 0.219326i \(-0.0703858\pi\)
\(524\) 6.00000 0.262111
\(525\) −1.00000 −0.0436436
\(526\) −3.00000 + 5.19615i −0.130806 + 0.226563i
\(527\) 0 0
\(528\) −3.00000 + 5.19615i −0.130558 + 0.226134i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 6.00000 + 10.3923i 0.260623 + 0.451413i
\(531\) 6.00000 0.260378
\(532\) 3.50000 2.59808i 0.151744 0.112641i
\(533\) 30.0000 1.29944
\(534\) −6.00000 10.3923i −0.259645 0.449719i
\(535\) −6.00000 10.3923i −0.259403 0.449299i
\(536\) −0.500000 + 0.866025i −0.0215967 + 0.0374066i
\(537\) −9.00000 15.5885i −0.388379 0.672692i
\(538\) 9.00000 15.5885i 0.388018 0.672066i
\(539\) −36.0000 −1.55063
\(540\) −1.00000 −0.0430331
\(541\) −5.50000 + 9.52628i −0.236463 + 0.409567i −0.959697 0.281037i \(-0.909322\pi\)
0.723234 + 0.690604i \(0.242655\pi\)
\(542\) −8.00000 + 13.8564i −0.343629 + 0.595184i
\(543\) 26.0000 1.11577
\(544\) 0 0
\(545\) 7.00000 12.1244i 0.299847 0.519350i
\(546\) −2.50000 4.33013i −0.106990 0.185312i
\(547\) 6.50000 11.2583i 0.277920 0.481371i −0.692948 0.720988i \(-0.743688\pi\)
0.970868 + 0.239616i \(0.0770217\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 3.50000 + 6.06218i 0.149376 + 0.258727i
\(550\) −6.00000 −0.255841
\(551\) −21.0000 + 15.5885i −0.894630 + 0.664091i
\(552\) −6.00000 −0.255377
\(553\) −3.50000 6.06218i −0.148835 0.257790i
\(554\) 7.00000 + 12.1244i 0.297402 + 0.515115i
\(555\) 5.50000 9.52628i 0.233462 0.404368i
\(556\) 0.500000 + 0.866025i 0.0212047 + 0.0367277i
\(557\) 6.00000 10.3923i 0.254228 0.440336i −0.710457 0.703740i \(-0.751512\pi\)
0.964686 + 0.263404i \(0.0848453\pi\)
\(558\) −5.00000 −0.211667
\(559\) −5.00000 −0.211477
\(560\) −0.500000 + 0.866025i −0.0211289 + 0.0365963i
\(561\) 0 0
\(562\) −18.0000 −0.759284
\(563\) −6.00000 −0.252870 −0.126435 0.991975i \(-0.540353\pi\)
−0.126435 + 0.991975i \(0.540353\pi\)
\(564\) −6.00000 + 10.3923i −0.252646 + 0.437595i
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) −8.00000 + 13.8564i −0.336265 + 0.582428i
\(567\) 0.500000 + 0.866025i 0.0209980 + 0.0363696i
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 4.00000 + 1.73205i 0.167542 + 0.0725476i
\(571\) 23.0000 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) −15.0000 25.9808i −0.627182 1.08631i
\(573\) −6.00000 10.3923i −0.250654 0.434145i
\(574\) −3.00000 + 5.19615i −0.125218 + 0.216883i
\(575\) −3.00000 5.19615i −0.125109 0.216695i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 17.0000 0.707107
\(579\) −2.50000 + 4.33013i −0.103896 + 0.179954i
\(580\) 3.00000 5.19615i 0.124568 0.215758i
\(581\) 6.00000 0.248922
\(582\) −14.0000 −0.580319
\(583\) 36.0000 62.3538i 1.49097 2.58243i
\(584\) −0.500000 0.866025i −0.0206901 0.0358364i
\(585\) 2.50000 4.33013i 0.103362 0.179029i
\(586\) −9.00000 15.5885i −0.371787 0.643953i
\(587\) −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i \(-0.287813\pi\)
−0.989792 + 0.142520i \(0.954479\pi\)
\(588\) −6.00000 −0.247436
\(589\) 20.0000 + 8.66025i 0.824086 + 0.356840i
\(590\) 6.00000 0.247016
\(591\) 9.00000 + 15.5885i 0.370211 + 0.641223i
\(592\) −5.50000 9.52628i −0.226049 0.391528i
\(593\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(594\) 3.00000 + 5.19615i 0.123091 + 0.213201i
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) −7.00000 −0.286491
\(598\) 15.0000 25.9808i 0.613396 1.06243i
\(599\) −24.0000 + 41.5692i −0.980613 + 1.69847i −0.320607 + 0.947212i \(0.603887\pi\)
−0.660006 + 0.751260i \(0.729446\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −1.00000 −0.0407909 −0.0203954 0.999792i \(-0.506493\pi\)
−0.0203954 + 0.999792i \(0.506493\pi\)
\(602\) 0.500000 0.866025i 0.0203785 0.0352966i
\(603\) 0.500000 + 0.866025i 0.0203616 + 0.0352673i
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) 12.5000 + 21.6506i 0.508197 + 0.880223i
\(606\) −3.00000 5.19615i −0.121867 0.211079i
\(607\) −1.00000 −0.0405887 −0.0202944 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) 3.50000 2.59808i 0.141944 0.105366i
\(609\) −6.00000 −0.243132
\(610\) 3.50000 + 6.06218i 0.141711 + 0.245450i
\(611\) −30.0000 51.9615i −1.21367 2.10214i
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 10.0000 17.3205i 0.403567 0.698999i
\(615\) −6.00000 −0.241943
\(616\) 6.00000 0.241747
\(617\) 12.0000 20.7846i 0.483102 0.836757i −0.516710 0.856161i \(-0.672843\pi\)
0.999812 + 0.0194037i \(0.00617676\pi\)
\(618\) 5.50000 9.52628i 0.221242 0.383203i
\(619\) 11.0000 0.442127 0.221064 0.975259i \(-0.429047\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(620\) −5.00000 −0.200805
\(621\) −3.00000 + 5.19615i −0.120386 + 0.208514i
\(622\) 3.00000 + 5.19615i 0.120289 + 0.208347i
\(623\) −6.00000 + 10.3923i −0.240385 + 0.416359i
\(624\) −2.50000 4.33013i −0.100080 0.173344i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 22.0000 0.879297
\(627\) −3.00000 25.9808i −0.119808 1.03757i
\(628\) −13.0000 −0.518756
\(629\) 0 0
\(630\) 0.500000 + 0.866025i 0.0199205 + 0.0345033i
\(631\) 3.50000 6.06218i 0.139333 0.241331i −0.787911 0.615789i \(-0.788838\pi\)
0.927244 + 0.374457i \(0.122171\pi\)
\(632\) −3.50000 6.06218i −0.139223 0.241140i
\(633\) 6.50000 11.2583i 0.258352 0.447478i
\(634\) 18.0000 0.714871
\(635\) 16.0000 0.634941
\(636\) 6.00000 10.3923i 0.237915 0.412082i
\(637\) 15.0000 25.9808i 0.594322 1.02940i
\(638\) −36.0000 −1.42525
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 18.0000 + 31.1769i 0.710957 + 1.23141i 0.964498 + 0.264089i \(0.0850714\pi\)
−0.253541 + 0.967325i \(0.581595\pi\)
\(642\) −6.00000 + 10.3923i −0.236801 + 0.410152i
\(643\) −14.5000 25.1147i −0.571824 0.990429i −0.996379 0.0850262i \(-0.972903\pi\)
0.424555 0.905402i \(-0.360431\pi\)
\(644\) 3.00000 + 5.19615i 0.118217 + 0.204757i
\(645\) 1.00000 0.0393750
\(646\) 0 0
\(647\) −42.0000 −1.65119 −0.825595 0.564263i \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −18.0000 31.1769i −0.706562 1.22380i
\(650\) 2.50000 4.33013i 0.0980581 0.169842i
\(651\) 2.50000 + 4.33013i 0.0979827 + 0.169711i
\(652\) −5.50000 + 9.52628i −0.215397 + 0.373078i
\(653\) −24.0000 −0.939193 −0.469596 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) −14.0000 −0.547443
\(655\) 3.00000 5.19615i 0.117220 0.203030i
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) −1.00000 −0.0390137
\(658\) 12.0000 0.467809
\(659\) −15.0000 + 25.9808i −0.584317 + 1.01207i 0.410643 + 0.911796i \(0.365304\pi\)
−0.994960 + 0.100271i \(0.968029\pi\)
\(660\) 3.00000 + 5.19615i 0.116775 + 0.202260i
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) 14.5000 + 25.1147i 0.563559 + 0.976112i
\(663\) 0 0
\(664\) 6.00000 0.232845
\(665\) −0.500000 4.33013i −0.0193892 0.167915i
\(666\) −11.0000 −0.426241
\(667\) −18.0000 31.1769i −0.696963 1.20717i
\(668\) 9.00000 + 15.5885i 0.348220 + 0.603136i
\(669\) 0.500000 0.866025i 0.0193311 0.0334825i
\(670\) 0.500000 + 0.866025i 0.0193167 + 0.0334575i
\(671\) 21.0000 36.3731i 0.810696 1.40417i
\(672\) 1.00000 0.0385758
\(673\) −19.0000 −0.732396 −0.366198 0.930537i \(-0.619341\pi\)
−0.366198 + 0.930537i \(0.619341\pi\)
\(674\) 5.50000 9.52628i 0.211852 0.366939i
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 12.0000 0.461538
\(677\) −12.0000 −0.461197 −0.230599 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) −9.00000 + 15.5885i −0.345643 + 0.598671i
\(679\) 7.00000 + 12.1244i 0.268635 + 0.465290i
\(680\) 0 0
\(681\) 9.00000 + 15.5885i 0.344881 + 0.597351i
\(682\) 15.0000 + 25.9808i 0.574380 + 0.994855i
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −0.500000 4.33013i −0.0191180 0.165567i
\(685\) 6.00000 0.229248
\(686\) 6.50000 + 11.2583i 0.248171 + 0.429845i
\(687\) 12.5000 + 21.6506i 0.476905 + 0.826023i
\(688\) 0.500000 0.866025i 0.0190623 0.0330169i
\(689\) 30.0000 + 51.9615i 1.14291 + 1.97958i
\(690\) −3.00000 + 5.19615i −0.114208 + 0.197814i
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 6.00000 0.228086
\(693\) 3.00000 5.19615i 0.113961 0.197386i
\(694\) −6.00000 + 10.3923i −0.227757 + 0.394486i
\(695\) 1.00000 0.0379322
\(696\) −6.00000 −0.227429
\(697\) 0 0
\(698\) −9.50000 16.4545i −0.359580 0.622811i
\(699\) 6.00000 10.3923i 0.226941 0.393073i
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(702\) −5.00000 −0.188713
\(703\) 44.0000 + 19.0526i 1.65949 + 0.718581i
\(704\) 6.00000 0.226134
\(705\) 6.00000 + 10.3923i 0.225973 + 0.391397i
\(706\) 9.00000 + 15.5885i 0.338719 + 0.586679i
\(707\) −3.00000 + 5.19615i −0.112827 + 0.195421i
\(708\) −3.00000 5.19615i −0.112747 0.195283i
\(709\) 0.500000 0.866025i 0.0187779 0.0325243i −0.856484 0.516174i \(-0.827356\pi\)
0.875262 + 0.483650i \(0.160689\pi\)
\(710\) 0 0
\(711\) −7.00000 −0.262521
\(712\) −6.00000 + 10.3923i −0.224860 + 0.389468i
\(713\) −15.0000 + 25.9808i −0.561754 + 0.972987i
\(714\) 0 0
\(715\) −30.0000 −1.12194
\(716\) −9.00000 + 15.5885i −0.336346 + 0.582568i
\(717\) 9.00000 + 15.5885i 0.336111 + 0.582162i
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) 21.0000 + 36.3731i 0.783168 + 1.35649i 0.930087 + 0.367338i \(0.119731\pi\)
−0.146920 + 0.989148i \(0.546936\pi\)
\(720\) 0.500000 + 0.866025i 0.0186339 + 0.0322749i
\(721\) −11.0000 −0.409661
\(722\) −5.50000 + 18.1865i −0.204689 + 0.676833i
\(723\) 5.00000 0.185952
\(724\) −13.0000 22.5167i −0.483141 0.836825i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 12.5000 21.6506i 0.463919 0.803530i
\(727\) −17.5000 30.3109i −0.649039 1.12417i −0.983353 0.181707i \(-0.941838\pi\)
0.334314 0.942462i \(-0.391496\pi\)
\(728\) −2.50000 + 4.33013i −0.0926562 + 0.160485i
\(729\) 1.00000 0.0370370
\(730\) −1.00000 −0.0370117
\(731\) 0 0
\(732\) 3.50000 6.06218i 0.129364 0.224065i
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) −17.0000 −0.627481
\(735\) −3.00000 + 5.19615i −0.110657 + 0.191663i
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) 3.00000 5.19615i 0.110506 0.191403i
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) −20.5000 35.5070i −0.754105 1.30615i −0.945818 0.324697i \(-0.894738\pi\)
0.191714 0.981451i \(-0.438596\pi\)
\(740\) −11.0000 −0.404368
\(741\) 20.0000 + 8.66025i 0.734718 + 0.318142i
\(742\) −12.0000 −0.440534
\(743\) −9.00000 15.5885i −0.330178 0.571885i 0.652369 0.757902i \(-0.273775\pi\)
−0.982547 + 0.186017i \(0.940442\pi\)
\(744\) 2.50000 + 4.33013i 0.0916544 + 0.158750i
\(745\) −9.00000 + 15.5885i −0.329734 + 0.571117i
\(746\) 1.00000 + 1.73205i 0.0366126 + 0.0634149i
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) −2.50000 + 4.33013i −0.0912263 + 0.158009i −0.908027 0.418911i \(-0.862412\pi\)
0.816801 + 0.576919i \(0.195745\pi\)
\(752\) 12.0000 0.437595
\(753\) 6.00000 0.218652
\(754\) 15.0000 25.9808i 0.546268 0.946164i
\(755\) 4.00000 + 6.92820i 0.145575 + 0.252143i
\(756\) 0.500000 0.866025i 0.0181848 0.0314970i
\(757\) 15.5000 + 26.8468i 0.563357 + 0.975763i 0.997200 + 0.0747748i \(0.0238238\pi\)
−0.433843 + 0.900988i \(0.642843\pi\)
\(758\) −9.50000 16.4545i −0.345056 0.597654i
\(759\) 36.0000 1.30672
\(760\) −0.500000 4.33013i −0.0181369 0.157070i
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) −8.00000 13.8564i −0.289809 0.501965i
\(763\) 7.00000 + 12.1244i 0.253417 + 0.438931i
\(764\) −6.00000 + 10.3923i −0.217072 + 0.375980i
\(765\) 0 0
\(766\) −6.00000 + 10.3923i −0.216789 + 0.375489i
\(767\) 30.0000 1.08324
\(768\) 1.00000 0.0360844
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 3.00000 5.19615i 0.108112 0.187256i
\(771\) 6.00000 0.216085
\(772\) 5.00000 0.179954
\(773\) 15.0000 25.9808i 0.539513 0.934463i −0.459418 0.888220i \(-0.651942\pi\)
0.998930 0.0462427i \(-0.0147248\pi\)
\(774\) −0.500000 0.866025i −0.0179721 0.0311286i
\(775\) −2.50000 + 4.33013i −0.0898027 + 0.155543i
\(776\) 7.00000 + 12.1244i 0.251285 + 0.435239i
\(777\) 5.50000 + 9.52628i 0.197311 + 0.341753i
\(778\) 6.00000 0.215110
\(779\) −3.00000 25.9808i −0.107486 0.930857i