Properties

Label 546.2.l.a.211.1
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(1\)
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 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.a.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(-3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(-2.50000 + 4.33013i) q^{19} +1.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} -5.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +3.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.00000 + 3.46410i) q^{37} +5.00000 q^{38} +(1.00000 + 3.46410i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +3.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} +9.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.50000 + 4.33013i) q^{50} +3.00000 q^{51} +(2.50000 - 2.59808i) q^{52} -9.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 + 0.866025i) q^{56} +5.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(-7.00000 - 12.1244i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} -4.00000 q^{73} +(2.00000 - 3.46410i) q^{74} +(2.50000 + 4.33013i) q^{75} +(-2.50000 - 4.33013i) q^{76} +3.00000 q^{77} +(2.50000 - 2.59808i) q^{78} -1.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} -6.00000 q^{83} +(-0.500000 + 0.866025i) q^{84} +8.00000 q^{86} +(1.50000 - 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(4.50000 + 7.79423i) q^{89} +(2.50000 - 2.59808i) q^{91} +6.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(-4.50000 - 7.79423i) q^{94} +1.00000 q^{96} +(-4.00000 + 6.92820i) q^{97} +(-0.500000 + 0.866025i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{3} - q^{4} - q^{6} - q^{7} + 2q^{8} - q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{3} - q^{4} - q^{6} - q^{7} + 2q^{8} - q^{9} - 3q^{11} + 2q^{12} - 7q^{13} + 2q^{14} - q^{16} - 3q^{17} + 2q^{18} - 5q^{19} + 2q^{21} - 3q^{22} - 6q^{23} - q^{24} - 10q^{25} + 2q^{26} + 2q^{27} - q^{28} + 3q^{29} - 8q^{31} - q^{32} - 3q^{33} + 6q^{34} - q^{36} + 4q^{37} + 10q^{38} + 2q^{39} + 3q^{41} - q^{42} - 8q^{43} + 6q^{44} - 6q^{46} + 18q^{47} - q^{48} - q^{49} + 5q^{50} + 6q^{51} + 5q^{52} - 18q^{53} - q^{54} - q^{56} + 10q^{57} + 3q^{58} + 6q^{59} - 5q^{61} + 4q^{62} - q^{63} + 2q^{64} + 6q^{66} - 14q^{67} - 3q^{68} - 6q^{69} + 6q^{71} - q^{72} - 8q^{73} + 4q^{74} + 5q^{75} - 5q^{76} + 6q^{77} + 5q^{78} - 2q^{79} - q^{81} + 3q^{82} - 12q^{83} - q^{84} + 16q^{86} + 3q^{87} - 3q^{88} + 9q^{89} + 5q^{91} + 12q^{92} + 4q^{93} - 9q^{94} + 2q^{96} - 8q^{97} - q^{98} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −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 0.288675
\(13\) −3.50000 0.866025i −0.970725 0.240192i
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 1.00000 0.235702
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) −3.00000 5.19615i −0.625543 1.08347i −0.988436 0.151642i \(-0.951544\pi\)
0.362892 0.931831i \(-0.381789\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −5.00000 −1.00000
\(26\) 1.00000 + 3.46410i 0.196116 + 0.679366i
\(27\) 1.00000 0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 3.00000 0.514496
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 2.00000 + 3.46410i 0.328798 + 0.569495i 0.982274 0.187453i \(-0.0600231\pi\)
−0.653476 + 0.756948i \(0.726690\pi\)
\(38\) 5.00000 0.811107
\(39\) 1.00000 + 3.46410i 0.160128 + 0.554700i
\(40\) 0 0
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −4.00000 + 6.92820i −0.609994 + 1.05654i 0.381246 + 0.924473i \(0.375495\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 3.00000 0.452267
\(45\) 0 0
\(46\) −3.00000 + 5.19615i −0.442326 + 0.766131i
\(47\) 9.00000 1.31278 0.656392 0.754420i \(-0.272082\pi\)
0.656392 + 0.754420i \(0.272082\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 2.50000 + 4.33013i 0.353553 + 0.612372i
\(51\) 3.00000 0.420084
\(52\) 2.50000 2.59808i 0.346688 0.360288i
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 5.00000 0.662266
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) 2.00000 + 3.46410i 0.254000 + 0.439941i
\(63\) −0.500000 0.866025i −0.0629941 0.109109i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) −7.00000 12.1244i −0.855186 1.48123i −0.876472 0.481452i \(-0.840109\pi\)
0.0212861 0.999773i \(-0.493224\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) −3.00000 + 5.19615i −0.361158 + 0.625543i
\(70\) 0 0
\(71\) 3.00000 5.19615i 0.356034 0.616670i −0.631260 0.775571i \(-0.717462\pi\)
0.987294 + 0.158901i \(0.0507952\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) 2.50000 + 4.33013i 0.288675 + 0.500000i
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) 3.00000 0.341882
\(78\) 2.50000 2.59808i 0.283069 0.294174i
\(79\) −1.00000 −0.112509 −0.0562544 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −0.500000 + 0.866025i −0.0545545 + 0.0944911i
\(85\) 0 0
\(86\) 8.00000 0.862662
\(87\) 1.50000 2.59808i 0.160817 0.278543i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 4.50000 + 7.79423i 0.476999 + 0.826187i 0.999653 0.0263586i \(-0.00839118\pi\)
−0.522654 + 0.852545i \(0.675058\pi\)
\(90\) 0 0
\(91\) 2.50000 2.59808i 0.262071 0.272352i
\(92\) 6.00000 0.625543
\(93\) 2.00000 + 3.46410i 0.207390 + 0.359211i
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) −4.00000 + 6.92820i −0.406138 + 0.703452i −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) 3.00000 0.301511
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) −1.50000 2.59808i −0.148522 0.257248i
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −3.50000 0.866025i −0.343203 0.0849208i
\(105\) 0 0
\(106\) 4.50000 + 7.79423i 0.437079 + 0.757042i
\(107\) −7.50000 12.9904i −0.725052 1.25583i −0.958952 0.283567i \(-0.908482\pi\)
0.233900 0.972261i \(-0.424851\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 2.00000 3.46410i 0.189832 0.328798i
\(112\) 1.00000 0.0944911
\(113\) 6.00000 10.3923i 0.564433 0.977626i −0.432670 0.901553i \(-0.642428\pi\)
0.997102 0.0760733i \(-0.0242383\pi\)
\(114\) −2.50000 4.33013i −0.234146 0.405554i
\(115\) 0 0
\(116\) −3.00000 −0.278543
\(117\) 2.50000 2.59808i 0.231125 0.240192i
\(118\) −6.00000 −0.552345
\(119\) −1.50000 2.59808i −0.137505 0.238165i
\(120\) 0 0
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) 5.00000 0.452679
\(123\) 1.50000 2.59808i 0.135250 0.234261i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 0 0
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) −4.00000 6.92820i −0.354943 0.614779i 0.632166 0.774833i \(-0.282166\pi\)
−0.987108 + 0.160055i \(0.948833\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −1.50000 2.59808i −0.130558 0.226134i
\(133\) −2.50000 4.33013i −0.216777 0.375470i
\(134\) −7.00000 + 12.1244i −0.604708 + 1.04738i
\(135\) 0 0
\(136\) −1.50000 + 2.59808i −0.128624 + 0.222783i
\(137\) 9.00000 15.5885i 0.768922 1.33181i −0.169226 0.985577i \(-0.554127\pi\)
0.938148 0.346235i \(-0.112540\pi\)
\(138\) 6.00000 0.510754
\(139\) 6.50000 11.2583i 0.551323 0.954919i −0.446857 0.894606i \(-0.647457\pi\)
0.998179 0.0603135i \(-0.0192101\pi\)
\(140\) 0 0
\(141\) −4.50000 7.79423i −0.378968 0.656392i
\(142\) −6.00000 −0.503509
\(143\) 3.00000 + 10.3923i 0.250873 + 0.869048i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 2.00000 + 3.46410i 0.165521 + 0.286691i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) −4.00000 −0.328798
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 2.50000 4.33013i 0.204124 0.353553i
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) −2.50000 + 4.33013i −0.202777 + 0.351220i
\(153\) −1.50000 2.59808i −0.121268 0.210042i
\(154\) −1.50000 2.59808i −0.120873 0.209359i
\(155\) 0 0
\(156\) −3.50000 0.866025i −0.280224 0.0693375i
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 0.500000 + 0.866025i 0.0397779 + 0.0688973i
\(159\) 4.50000 + 7.79423i 0.356873 + 0.618123i
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) 3.00000 + 5.19615i 0.232845 + 0.403300i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 1.00000 0.0771517
\(169\) 11.5000 + 6.06218i 0.884615 + 0.466321i
\(170\) 0 0
\(171\) −2.50000 4.33013i −0.191180 0.331133i
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) −3.00000 −0.227429
\(175\) 2.50000 4.33013i 0.188982 0.327327i
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) −6.00000 −0.450988
\(178\) 4.50000 7.79423i 0.337289 0.584202i
\(179\) −12.0000 20.7846i −0.896922 1.55351i −0.831408 0.555663i \(-0.812464\pi\)
−0.0655145 0.997852i \(-0.520869\pi\)
\(180\) 0 0
\(181\) 17.0000 1.26360 0.631800 0.775131i \(-0.282316\pi\)
0.631800 + 0.775131i \(0.282316\pi\)
\(182\) −3.50000 0.866025i −0.259437 0.0641941i
\(183\) 5.00000 0.369611
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) 0 0
\(186\) 2.00000 3.46410i 0.146647 0.254000i
\(187\) 9.00000 0.658145
\(188\) −4.50000 + 7.79423i −0.328196 + 0.568453i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) 0 0
\(191\) −9.00000 + 15.5885i −0.651217 + 1.12794i 0.331611 + 0.943416i \(0.392408\pi\)
−0.982828 + 0.184525i \(0.940925\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 9.50000 + 16.4545i 0.683825 + 1.18442i 0.973805 + 0.227387i \(0.0730182\pi\)
−0.289980 + 0.957033i \(0.593649\pi\)
\(194\) 8.00000 0.574367
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 4.50000 + 7.79423i 0.320612 + 0.555316i 0.980614 0.195947i \(-0.0627782\pi\)
−0.660003 + 0.751263i \(0.729445\pi\)
\(198\) −1.50000 2.59808i −0.106600 0.184637i
\(199\) −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) −5.00000 −0.353553
\(201\) −7.00000 + 12.1244i −0.493742 + 0.855186i
\(202\) −3.00000 + 5.19615i −0.211079 + 0.365600i
\(203\) −3.00000 −0.210559
\(204\) −1.50000 + 2.59808i −0.105021 + 0.181902i
\(205\) 0 0
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) 6.00000 0.417029
\(208\) 1.00000 + 3.46410i 0.0693375 + 0.240192i
\(209\) 15.0000 1.03757
\(210\) 0 0
\(211\) 5.00000 + 8.66025i 0.344214 + 0.596196i 0.985211 0.171347i \(-0.0548120\pi\)
−0.640996 + 0.767544i \(0.721479\pi\)
\(212\) 4.50000 7.79423i 0.309061 0.535310i
\(213\) −6.00000 −0.411113
\(214\) −7.50000 + 12.9904i −0.512689 + 0.888004i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) 2.00000 3.46410i 0.135769 0.235159i
\(218\) 5.00000 + 8.66025i 0.338643 + 0.586546i
\(219\) 2.00000 + 3.46410i 0.135147 + 0.234082i
\(220\) 0 0
\(221\) 7.50000 7.79423i 0.504505 0.524297i
\(222\) −4.00000 −0.268462
\(223\) −4.00000 6.92820i −0.267860 0.463947i 0.700449 0.713702i \(-0.252983\pi\)
−0.968309 + 0.249756i \(0.919650\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) 2.50000 4.33013i 0.166667 0.288675i
\(226\) −12.0000 −0.798228
\(227\) 9.00000 15.5885i 0.597351 1.03464i −0.395860 0.918311i \(-0.629553\pi\)
0.993210 0.116331i \(-0.0371134\pi\)
\(228\) −2.50000 + 4.33013i −0.165567 + 0.286770i
\(229\) 17.0000 1.12339 0.561696 0.827344i \(-0.310149\pi\)
0.561696 + 0.827344i \(0.310149\pi\)
\(230\) 0 0
\(231\) −1.50000 2.59808i −0.0986928 0.170941i
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) −12.0000 −0.786146 −0.393073 0.919507i \(-0.628588\pi\)
−0.393073 + 0.919507i \(0.628588\pi\)
\(234\) −3.50000 0.866025i −0.228802 0.0566139i
\(235\) 0 0
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) 0.500000 + 0.866025i 0.0324785 + 0.0562544i
\(238\) −1.50000 + 2.59808i −0.0972306 + 0.168408i
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −4.00000 + 6.92820i −0.257663 + 0.446285i −0.965615 0.259975i \(-0.916286\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) −2.00000 −0.128565
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −2.50000 4.33013i −0.160046 0.277208i
\(245\) 0 0
\(246\) −3.00000 −0.191273
\(247\) 12.5000 12.9904i 0.795356 0.826558i
\(248\) −4.00000 −0.254000
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 0 0
\(251\) −15.0000 + 25.9808i −0.946792 + 1.63989i −0.194668 + 0.980869i \(0.562363\pi\)
−0.752124 + 0.659022i \(0.770970\pi\)
\(252\) 1.00000 0.0629941
\(253\) −9.00000 + 15.5885i −0.565825 + 0.980038i
\(254\) −4.00000 + 6.92820i −0.250982 + 0.434714i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.50000 12.9904i −0.467837 0.810318i 0.531487 0.847066i \(-0.321633\pi\)
−0.999325 + 0.0367485i \(0.988300\pi\)
\(258\) −4.00000 6.92820i −0.249029 0.431331i
\(259\) −4.00000 −0.248548
\(260\) 0 0
\(261\) −3.00000 −0.185695
\(262\) 0 0
\(263\) −9.00000 15.5885i −0.554964 0.961225i −0.997906 0.0646755i \(-0.979399\pi\)
0.442943 0.896550i \(-0.353935\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 0 0
\(266\) −2.50000 + 4.33013i −0.153285 + 0.265497i
\(267\) 4.50000 7.79423i 0.275396 0.476999i
\(268\) 14.0000 0.855186
\(269\) −12.0000 + 20.7846i −0.731653 + 1.26726i 0.224523 + 0.974469i \(0.427917\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) 0 0
\(271\) 14.0000 + 24.2487i 0.850439 + 1.47300i 0.880812 + 0.473466i \(0.156997\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) 3.00000 0.181902
\(273\) −3.50000 0.866025i −0.211830 0.0524142i
\(274\) −18.0000 −1.08742
\(275\) 7.50000 + 12.9904i 0.452267 + 0.783349i
\(276\) −3.00000 5.19615i −0.180579 0.312772i
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) −13.0000 −0.779688
\(279\) 2.00000 3.46410i 0.119737 0.207390i
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) −4.50000 + 7.79423i −0.267971 + 0.464140i
\(283\) 2.00000 + 3.46410i 0.118888 + 0.205919i 0.919327 0.393494i \(-0.128734\pi\)
−0.800439 + 0.599414i \(0.795400\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) 0 0
\(286\) 7.50000 7.79423i 0.443484 0.460882i
\(287\) −3.00000 −0.177084
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 8.00000 0.468968
\(292\) 2.00000 3.46410i 0.117041 0.202721i
\(293\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(294\) 1.00000 0.0583212
\(295\) 0 0
\(296\) 2.00000 + 3.46410i 0.116248 + 0.201347i
\(297\) −1.50000 2.59808i −0.0870388 0.150756i
\(298\) 6.00000 0.347571
\(299\) 6.00000 + 20.7846i 0.346989 + 1.20201i
\(300\) −5.00000 −0.288675
\(301\) −4.00000 6.92820i −0.230556 0.399335i
\(302\) −8.50000 14.7224i −0.489120 0.847181i
\(303\) −3.00000 + 5.19615i −0.172345 + 0.298511i
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) −1.50000 + 2.59808i −0.0857493 + 0.148522i
\(307\) 11.0000 0.627803 0.313902 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) −1.50000 + 2.59808i −0.0854704 + 0.148039i
\(309\) −4.00000 6.92820i −0.227552 0.394132i
\(310\) 0 0
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 1.00000 + 3.46410i 0.0566139 + 0.196116i
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 11.0000 + 19.0526i 0.620766 + 1.07520i
\(315\) 0 0
\(316\) 0.500000 0.866025i 0.0281272 0.0487177i
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 4.50000 7.79423i 0.252347 0.437079i
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) 0 0
\(321\) −7.50000 + 12.9904i −0.418609 + 0.725052i
\(322\) −3.00000 5.19615i −0.167183 0.289570i
\(323\) −7.50000 12.9904i −0.417311 0.722804i
\(324\) 1.00000 0.0555556
\(325\) 17.5000 + 4.33013i 0.970725 + 0.240192i
\(326\) −16.0000 −0.886158
\(327\) 5.00000 + 8.66025i 0.276501 + 0.478913i
\(328\) 1.50000 + 2.59808i 0.0828236 + 0.143455i
\(329\) −4.50000 + 7.79423i −0.248093 + 0.429710i
\(330\) 0 0
\(331\) 5.00000 8.66025i 0.274825 0.476011i −0.695266 0.718752i \(-0.744713\pi\)
0.970091 + 0.242742i \(0.0780468\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) −4.00000 −0.219199
\(334\) 0 0
\(335\) 0 0
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) −25.0000 −1.36184 −0.680918 0.732359i \(-0.738419\pi\)
−0.680918 + 0.732359i \(0.738419\pi\)
\(338\) −0.500000 12.9904i −0.0271964 0.706584i
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) −2.50000 + 4.33013i −0.135185 + 0.234146i
\(343\) 1.00000 0.0539949
\(344\) −4.00000 + 6.92820i −0.215666 + 0.373544i
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) 13.5000 23.3827i 0.724718 1.25525i −0.234372 0.972147i \(-0.575303\pi\)
0.959090 0.283101i \(-0.0913633\pi\)
\(348\) 1.50000 + 2.59808i 0.0804084 + 0.139272i
\(349\) −1.00000 1.73205i −0.0535288 0.0927146i 0.838019 0.545640i \(-0.183714\pi\)
−0.891548 + 0.452926i \(0.850380\pi\)
\(350\) −5.00000 −0.267261
\(351\) −3.50000 0.866025i −0.186816 0.0462250i
\(352\) 3.00000 0.159901
\(353\) 9.00000 + 15.5885i 0.479022 + 0.829690i 0.999711 0.0240566i \(-0.00765819\pi\)
−0.520689 + 0.853746i \(0.674325\pi\)
\(354\) 3.00000 + 5.19615i 0.159448 + 0.276172i
\(355\) 0 0
\(356\) −9.00000 −0.476999
\(357\) −1.50000 + 2.59808i −0.0793884 + 0.137505i
\(358\) −12.0000 + 20.7846i −0.634220 + 1.09850i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) −8.50000 14.7224i −0.446750 0.773794i
\(363\) −2.00000 −0.104973
\(364\) 1.00000 + 3.46410i 0.0524142 + 0.181568i
\(365\) 0 0
\(366\) −2.50000 4.33013i −0.130677 0.226339i
\(367\) −1.00000 1.73205i −0.0521996 0.0904123i 0.838745 0.544524i \(-0.183290\pi\)
−0.890945 + 0.454112i \(0.849957\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) −3.00000 −0.156174
\(370\) 0 0
\(371\) 4.50000 7.79423i 0.233628 0.404656i
\(372\) −4.00000 −0.207390
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) −4.50000 7.79423i −0.232689 0.403030i
\(375\) 0 0
\(376\) 9.00000 0.464140
\(377\) −3.00000 10.3923i −0.154508 0.535231i
\(378\) 1.00000 0.0514344
\(379\) 17.0000 + 29.4449i 0.873231 + 1.51248i 0.858635 + 0.512588i \(0.171313\pi\)
0.0145964 + 0.999893i \(0.495354\pi\)
\(380\) 0 0
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 18.0000 0.920960
\(383\) −4.50000 + 7.79423i −0.229939 + 0.398266i −0.957790 0.287469i \(-0.907186\pi\)
0.727851 + 0.685736i \(0.240519\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) 9.50000 16.4545i 0.483537 0.837511i
\(387\) −4.00000 6.92820i −0.203331 0.352180i
\(388\) −4.00000 6.92820i −0.203069 0.351726i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 0 0
\(394\) 4.50000 7.79423i 0.226707 0.392668i
\(395\) 0 0
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) 18.5000 32.0429i 0.928488 1.60819i 0.142636 0.989775i \(-0.454442\pi\)
0.785853 0.618414i \(-0.212224\pi\)
\(398\) 20.0000 1.00251
\(399\) −2.50000 + 4.33013i −0.125157 + 0.216777i
\(400\) 2.50000 + 4.33013i 0.125000 + 0.216506i
\(401\) −15.0000 25.9808i −0.749064 1.29742i −0.948272 0.317460i \(-0.897170\pi\)
0.199207 0.979957i \(-0.436163\pi\)
\(402\) 14.0000 0.698257
\(403\) 14.0000 + 3.46410i 0.697390 + 0.172559i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 1.50000 + 2.59808i 0.0744438 + 0.128940i
\(407\) 6.00000 10.3923i 0.297409 0.515127i
\(408\) 3.00000 0.148522
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) 0 0
\(411\) −18.0000 −0.887875
\(412\) −4.00000 + 6.92820i −0.197066 + 0.341328i
\(413\) 3.00000 + 5.19615i 0.147620 + 0.255686i
\(414\) −3.00000 5.19615i −0.147442 0.255377i
\(415\) 0 0
\(416\) 2.50000 2.59808i 0.122573 0.127381i
\(417\) −13.0000 −0.636613
\(418\) −7.50000 12.9904i −0.366837 0.635380i
\(419\) −3.00000 5.19615i −0.146560 0.253849i 0.783394 0.621525i \(-0.213487\pi\)
−0.929954 + 0.367677i \(0.880153\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 5.00000 8.66025i 0.243396 0.421575i
\(423\) −4.50000 + 7.79423i −0.218797 + 0.378968i
\(424\) −9.00000 −0.437079
\(425\) 7.50000 12.9904i 0.363803 0.630126i
\(426\) 3.00000 + 5.19615i 0.145350 + 0.251754i
\(427\) −2.50000 4.33013i −0.120983 0.209550i
\(428\) 15.0000 0.725052
\(429\) 7.50000 7.79423i 0.362103 0.376309i
\(430\) 0 0
\(431\) 15.0000 + 25.9808i 0.722525 + 1.25145i 0.959985 + 0.280052i \(0.0903517\pi\)
−0.237460 + 0.971397i \(0.576315\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 17.0000 29.4449i 0.816968 1.41503i −0.0909384 0.995857i \(-0.528987\pi\)
0.907906 0.419173i \(-0.137680\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) 30.0000 1.43509
\(438\) 2.00000 3.46410i 0.0955637 0.165521i
\(439\) 2.00000 + 3.46410i 0.0954548 + 0.165333i 0.909798 0.415051i \(-0.136236\pi\)
−0.814344 + 0.580383i \(0.802903\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) −10.5000 2.59808i −0.499434 0.123578i
\(443\) −9.00000 −0.427603 −0.213801 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) 0 0
\(446\) −4.00000 + 6.92820i −0.189405 + 0.328060i
\(447\) 6.00000 0.283790
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −6.00000 + 10.3923i −0.283158 + 0.490443i −0.972161 0.234315i \(-0.924715\pi\)
0.689003 + 0.724758i \(0.258049\pi\)
\(450\) −5.00000 −0.235702
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) 6.00000 + 10.3923i 0.282216 + 0.488813i
\(453\) −8.50000 14.7224i −0.399365 0.691720i
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) 5.00000 0.234146
\(457\) 5.00000 + 8.66025i 0.233890 + 0.405110i 0.958950 0.283577i \(-0.0915211\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) −8.50000 14.7224i −0.397179 0.687934i
\(459\) −1.50000 + 2.59808i −0.0700140 + 0.121268i
\(460\) 0 0
\(461\) 6.00000 10.3923i 0.279448 0.484018i −0.691800 0.722089i \(-0.743182\pi\)
0.971248 + 0.238071i \(0.0765153\pi\)
\(462\) −1.50000 + 2.59808i −0.0697863 + 0.120873i
\(463\) 5.00000 0.232370 0.116185 0.993228i \(-0.462933\pi\)
0.116185 + 0.993228i \(0.462933\pi\)
\(464\) 1.50000 2.59808i 0.0696358 0.120613i
\(465\) 0 0
\(466\) 6.00000 + 10.3923i 0.277945 + 0.481414i
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 1.00000 + 3.46410i 0.0462250 + 0.160128i
\(469\) 14.0000 0.646460
\(470\) 0 0
\(471\) 11.0000 + 19.0526i 0.506853 + 0.877896i
\(472\) 3.00000 5.19615i 0.138086 0.239172i
\(473\) 24.0000 1.10352
\(474\) 0.500000 0.866025i 0.0229658 0.0397779i
\(475\) 12.5000 21.6506i 0.573539 0.993399i
\(476\) 3.00000 0.137505
\(477\) 4.50000 7.79423i 0.206041 0.356873i
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) −13.5000 23.3827i −0.616831 1.06838i −0.990060 0.140643i \(-0.955083\pi\)
0.373230 0.927739i \(-0.378250\pi\)
\(480\) 0 0
\(481\) −4.00000 13.8564i −0.182384 0.631798i
\(482\) 8.00000 0.364390
\(483\) −3.00000 5.19615i −0.136505 0.236433i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 0 0
\(486\) 1.00000 0.0453609
\(487\) −11.5000 + 19.9186i −0.521115 + 0.902597i 0.478584 + 0.878042i \(0.341150\pi\)
−0.999698 + 0.0245553i \(0.992183\pi\)
\(488\) −2.50000 + 4.33013i −0.113170 + 0.196016i
\(489\) −16.0000 −0.723545
\(490\) 0 0
\(491\) −18.0000 31.1769i −0.812329 1.40699i −0.911230 0.411897i \(-0.864866\pi\)
0.0989017 0.995097i \(-0.468467\pi\)
\(492\) 1.50000 + 2.59808i 0.0676252 + 0.117130i
\(493\) −9.00000 −0.405340
\(494\) −17.5000 4.33013i −0.787362 0.194822i
\(495\) 0 0
\(496\) 2.00000 + 3.46410i 0.0898027 + 0.155543i
\(497\) 3.00000 + 5.19615i 0.134568 + 0.233079i
\(498\) 3.00000 5.19615i 0.134433 0.232845i
\(499\) −40.0000 −1.79065 −0.895323 0.445418i \(-0.853055\pi\)
−0.895323 + 0.445418i \(0.853055\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 30.0000 1.33897
\(503\) −12.0000 + 20.7846i −0.535054 + 0.926740i 0.464107 + 0.885779i \(0.346375\pi\)
−0.999161 + 0.0409609i \(0.986958\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) 0 0
\(506\) 18.0000 0.800198
\(507\) −0.500000 12.9904i −0.0222058 0.576923i
\(508\) 8.00000 0.354943
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) 2.00000 3.46410i 0.0884748 0.153243i
\(512\) 1.00000 0.0441942
\(513\) −2.50000 + 4.33013i −0.110378 + 0.191180i
\(514\) −7.50000 + 12.9904i −0.330811 + 0.572981i
\(515\) 0 0
\(516\) −4.00000 + 6.92820i −0.176090 + 0.304997i
\(517\) −13.5000 23.3827i −0.593729 1.02837i
\(518\) 2.00000 + 3.46410i 0.0878750 + 0.152204i
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) 27.0000 1.18289 0.591446 0.806345i \(-0.298557\pi\)
0.591446 + 0.806345i \(0.298557\pi\)
\(522\) 1.50000 + 2.59808i 0.0656532 + 0.113715i
\(523\) −14.5000 25.1147i −0.634041 1.09819i −0.986718 0.162446i \(-0.948062\pi\)
0.352677 0.935745i \(-0.385272\pi\)
\(524\) 0 0
\(525\) −5.00000 −0.218218
\(526\) −9.00000 + 15.5885i −0.392419 + 0.679689i
\(527\) 6.00000 10.3923i 0.261364 0.452696i
\(528\) 3.00000 0.130558
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 3.00000 + 5.19615i 0.130189 + 0.225494i
\(532\) 5.00000 0.216777
\(533\) −3.00000 10.3923i −0.129944 0.450141i
\(534\) −9.00000 −0.389468
\(535\) 0 0
\(536\) −7.00000 12.1244i −0.302354 0.523692i
\(537\) −12.0000 + 20.7846i −0.517838 + 0.896922i
\(538\) 24.0000 1.03471
\(539\) −1.50000 + 2.59808i −0.0646096 + 0.111907i
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 14.0000 24.2487i 0.601351 1.04157i
\(543\) −8.50000 14.7224i −0.364770 0.631800i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) 0 0
\(546\) 1.00000 + 3.46410i 0.0427960 + 0.148250i
\(547\) −22.0000 −0.940652 −0.470326 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) 9.00000 + 15.5885i 0.384461 + 0.665906i
\(549\) −2.50000 4.33013i −0.106697 0.184805i
\(550\) 7.50000 12.9904i 0.319801 0.553912i
\(551\) −15.0000 −0.639021
\(552\) −3.00000 + 5.19615i −0.127688 + 0.221163i
\(553\) 0.500000 0.866025i 0.0212622 0.0368271i
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 6.50000 + 11.2583i 0.275661 + 0.477460i
\(557\) 7.50000 + 12.9904i 0.317785 + 0.550420i 0.980026 0.198871i \(-0.0637276\pi\)
−0.662240 + 0.749291i \(0.730394\pi\)
\(558\) −4.00000 −0.169334
\(559\) 20.0000 20.7846i 0.845910 0.879095i
\(560\) 0 0
\(561\) −4.50000 7.79423i −0.189990 0.329073i
\(562\) −3.00000 5.19615i −0.126547 0.219186i
\(563\) −12.0000 + 20.7846i −0.505740 + 0.875967i 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) 9.00000 0.378968
\(565\) 0 0
\(566\) 2.00000 3.46410i 0.0840663 0.145607i
\(567\) 1.00000 0.0419961
\(568\) 3.00000 5.19615i 0.125877 0.218026i
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 0 0
\(571\) 2.00000 0.0836974 0.0418487 0.999124i \(-0.486675\pi\)
0.0418487 + 0.999124i \(0.486675\pi\)
\(572\) −10.5000 2.59808i −0.439027 0.108631i
\(573\) 18.0000 0.751961
\(574\) 1.50000 + 2.59808i 0.0626088 + 0.108442i
\(575\) 15.0000 + 25.9808i 0.625543 + 1.08347i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 4.00000 6.92820i 0.166378 0.288175i
\(579\) 9.50000 16.4545i 0.394807 0.683825i
\(580\) 0 0
\(581\) 3.00000 5.19615i 0.124461 0.215573i
\(582\) −4.00000 6.92820i −0.165805 0.287183i
\(583\) 13.5000 + 23.3827i 0.559113 + 0.968412i
\(584\) −4.00000 −0.165521
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) 10.0000 17.3205i 0.412043 0.713679i
\(590\) 0 0
\(591\) 4.50000 7.79423i 0.185105 0.320612i
\(592\) 2.00000 3.46410i 0.0821995 0.142374i
\(593\) −15.0000 −0.615976 −0.307988 0.951390i \(-0.599656\pi\)
−0.307988 + 0.951390i \(0.599656\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) 0 0
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 20.0000 0.818546
\(598\) 15.0000 15.5885i 0.613396 0.637459i
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 2.50000 + 4.33013i 0.102062 + 0.176777i
\(601\) 20.0000 + 34.6410i 0.815817 + 1.41304i 0.908740 + 0.417363i \(0.137046\pi\)
−0.0929227 + 0.995673i \(0.529621\pi\)
\(602\) −4.00000 + 6.92820i −0.163028 + 0.282372i
\(603\) 14.0000 0.570124
\(604\) −8.50000 + 14.7224i −0.345860 + 0.599047i
\(605\) 0 0
\(606\) 6.00000 0.243733
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 1.50000 + 2.59808i 0.0607831 + 0.105279i
\(610\) 0 0
\(611\) −31.5000 7.79423i −1.27435 0.315321i
\(612\) 3.00000 0.121268
\(613\) −4.00000 6.92820i −0.161558 0.279827i 0.773869 0.633345i \(-0.218319\pi\)
−0.935428 + 0.353518i \(0.884985\pi\)
\(614\) −5.50000 9.52628i −0.221962 0.384449i
\(615\) 0 0
\(616\) 3.00000 0.120873
\(617\) 9.00000 15.5885i 0.362326 0.627568i −0.626017 0.779809i \(-0.715316\pi\)
0.988343 + 0.152242i \(0.0486493\pi\)
\(618\) −4.00000 + 6.92820i −0.160904 + 0.278693i
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 0 0
\(621\) −3.00000 5.19615i −0.120386 0.208514i
\(622\) 7.50000 + 12.9904i 0.300723 + 0.520867i
\(623\) −9.00000 −0.360577
\(624\) 2.50000 2.59808i 0.100080 0.104006i
\(625\) 25.0000 1.00000
\(626\) 11.0000 + 19.0526i 0.439648 + 0.761493i
\(627\) −7.50000 12.9904i −0.299521 0.518786i
\(628\) 11.0000 19.0526i 0.438948 0.760280i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −11.5000 + 19.9186i −0.457808 + 0.792946i −0.998845 0.0480524i \(-0.984699\pi\)
0.541037 + 0.840999i \(0.318032\pi\)
\(632\) −1.00000 −0.0397779
\(633\) 5.00000 8.66025i 0.198732 0.344214i
\(634\) 3.00000 + 5.19615i 0.119145 + 0.206366i
\(635\) 0 0
\(636\) −9.00000 −0.356873
\(637\) 1.00000 + 3.46410i 0.0396214 + 0.137253i
\(638\) −9.00000 −0.356313
\(639\) 3.00000 + 5.19615i 0.118678 + 0.205557i
\(640\) 0 0
\(641\) −3.00000 + 5.19615i −0.118493 + 0.205236i −0.919171 0.393860i \(-0.871140\pi\)
0.800678 + 0.599095i \(0.204473\pi\)
\(642\) 15.0000 0.592003
\(643\) −8.50000 + 14.7224i −0.335207 + 0.580596i −0.983525 0.180774i \(-0.942140\pi\)
0.648317 + 0.761370i \(0.275473\pi\)
\(644\) −3.00000 + 5.19615i −0.118217 + 0.204757i
\(645\) 0 0
\(646\) −7.50000 + 12.9904i −0.295084 + 0.511100i
\(647\) 22.5000 + 38.9711i 0.884566 + 1.53211i 0.846210 + 0.532850i \(0.178879\pi\)
0.0383563 + 0.999264i \(0.487788\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −18.0000 −0.706562
\(650\) −5.00000 17.3205i −0.196116 0.679366i
\(651\) −4.00000 −0.156772
\(652\) 8.00000 + 13.8564i 0.313304 + 0.542659i
\(653\) 16.5000 + 28.5788i 0.645695 + 1.11838i 0.984141 + 0.177390i \(0.0567655\pi\)
−0.338446 + 0.940986i \(0.609901\pi\)
\(654\) 5.00000 8.66025i 0.195515 0.338643i
\(655\) 0 0
\(656\) 1.50000 2.59808i 0.0585652 0.101438i
\(657\) 2.00000 3.46410i 0.0780274 0.135147i
\(658\) 9.00000 0.350857
\(659\) 7.50000 12.9904i 0.292159 0.506033i −0.682161 0.731202i \(-0.738960\pi\)
0.974320 + 0.225168i \(0.0722932\pi\)
\(660\) 0 0
\(661\) 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) −10.0000 −0.388661
\(663\) −10.5000 2.59808i −0.407786 0.100901i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 2.00000 + 3.46410i 0.0774984 + 0.134231i
\(667\) 9.00000 15.5885i 0.348481 0.603587i
\(668\) 0 0
\(669\) −4.00000 + 6.92820i −0.154649 + 0.267860i
\(670\) 0 0
\(671\) 15.0000 0.579069
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) 0.500000 + 0.866025i 0.0192736 + 0.0333828i 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) 12.5000 + 21.6506i 0.481482 + 0.833951i
\(675\) −5.00000 −0.192450
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 6.00000 + 10.3923i 0.230429 + 0.399114i
\(679\) −4.00000 6.92820i −0.153506 0.265880i
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 6.00000 10.3923i 0.229752 0.397942i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) 5.00000 0.191180
\(685\) 0 0
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) −8.50000 14.7224i −0.324295 0.561696i
\(688\) 8.00000 0.304997
\(689\) 31.5000 + 7.79423i 1.20005 + 0.296936i
\(690\) 0 0
\(691\) −4.00000 6.92820i −0.152167 0.263561i 0.779857 0.625958i \(-0.215292\pi\)
−0.932024 + 0.362397i \(0.881959\pi\)
\(692\) −9.00000 15.5885i −0.342129 0.592584i
\(693\) −1.50000 + 2.59808i −0.0569803 + 0.0986928i
\(694\) −27.0000 −1.02491
\(695\) 0 0
\(696\) 1.50000 2.59808i 0.0568574 0.0984798i
\(697\) −9.00000 −0.340899
\(698\) −1.00000 + 1.73205i −0.0378506 + 0.0655591i
\(699\) 6.00000 + 10.3923i 0.226941 + 0.393073i
\(700\) 2.50000 + 4.33013i 0.0944911 + 0.163663i
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) 1.00000 + 3.46410i 0.0377426 + 0.130744i
\(703\) −20.0000 −0.754314
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) 0 0
\(706\) 9.00000 15.5885i 0.338719 0.586679i
\(707\) 6.00000 0.225653
\(708\) 3.00000 5.19615i 0.112747 0.195283i
\(709\) −1.00000 + 1.73205i −0.0375558 + 0.0650485i −0.884192 0.467123i \(-0.845291\pi\)
0.846637 + 0.532172i \(0.178624\pi\)
\(710\) 0 0
\(711\) 0.500000 0.866025i 0.0187515 0.0324785i
\(712\) 4.50000 + 7.79423i 0.168645 + 0.292101i
\(713\) 12.0000 + 20.7846i 0.449404 + 0.778390i
\(714\) 3.00000 0.112272
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) −3.00000 5.19615i −0.112037 0.194054i
\(718\) 6.00000 + 10.3923i 0.223918 + 0.387837i
\(719\) −13.5000 + 23.3827i −0.503465 + 0.872027i 0.496527 + 0.868021i \(0.334608\pi\)
−0.999992 + 0.00400572i \(0.998725\pi\)
\(720\) 0 0
\(721\) −4.00000 + 6.92820i −0.148968 + 0.258020i
\(722\) −3.00000 + 5.19615i −0.111648 + 0.193381i
\(723\) 8.00000 0.297523
\(724\) −8.50000 + 14.7224i −0.315900 + 0.547155i
\(725\) −7.50000 12.9904i −0.278543 0.482451i
\(726\) 1.00000 + 1.73205i 0.0371135 + 0.0642824i
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 2.50000 2.59808i 0.0926562 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) −2.50000 + 4.33013i −0.0924027 + 0.160046i
\(733\) −49.0000 −1.80986 −0.904928 0.425564i \(-0.860076\pi\)
−0.904928 + 0.425564i \(0.860076\pi\)
\(734\) −1.00000 + 1.73205i −0.0369107 + 0.0639312i
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) −21.0000 + 36.3731i −0.773545 + 1.33982i
\(738\) 1.50000 + 2.59808i 0.0552158 + 0.0956365i
\(739\) 5.00000 + 8.66025i 0.183928 + 0.318573i 0.943215 0.332184i \(-0.107785\pi\)
−0.759287 + 0.650756i \(0.774452\pi\)
\(740\) 0 0
\(741\) −17.5000 4.33013i −0.642879 0.159071i
\(742\) −9.00000 −0.330400
\(743\) 12.0000 + 20.7846i 0.440237 + 0.762513i 0.997707 0.0676840i \(-0.0215610\pi\)
−0.557470 + 0.830197i \(0.688228\pi\)
\(744\) 2.00000 + 3.46410i 0.0733236 + 0.127000i
\(745\) 0 0
\(746\) 14.0000 0.512576
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) −4.50000 + 7.79423i −0.164536 + 0.284985i
\(749\) 15.0000 0.548088
\(750\) 0 0
\(751\) −5.50000 9.52628i −0.200698 0.347619i 0.748056 0.663636i \(-0.230988\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) −4.50000 7.79423i −0.164098 0.284226i
\(753\) 30.0000 1.09326
\(754\) −7.50000 + 7.79423i −0.273134 + 0.283849i
\(755\) 0 0
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) −1.00000 1.73205i −0.0363456 0.0629525i 0.847280 0.531146i \(-0.178238\pi\)
−0.883626 + 0.468193i \(0.844905\pi\)
\(758\) 17.0000 29.4449i 0.617468 1.06949i
\(759\) 18.0000 0.653359
\(760\) 0 0
\(761\) 21.0000 36.3731i 0.761249 1.31852i −0.180957 0.983491i \(-0.557920\pi\)
0.942207 0.335032i \(-0.108747\pi\)
\(762\) 8.00000 0.289809
\(763\) 5.00000 8.66025i 0.181012 0.313522i
\(764\) −9.00000 15.5885i −0.325609 0.563971i
\(765\) 0 0
\(766\) 9.00000 0.325183
\(767\) −15.0000 + 15.5885i −0.541619 + 0.562867i
\(768\) 1.00000 0.0360844
\(769\) −22.0000 38.1051i −0.793340 1.37411i −0.923888 0.382664i \(-0.875007\pi\)
0.130547 0.991442i \(-0.458327\pi\)
\(770\) 0 0
\(771\) −7.50000 + 12.9904i −0.270106 + 0.467837i
\(772\) −19.0000 −0.683825
\(773\) −9.00000 + 15.5885i −0.323708 + 0.560678i −0.981250 0.192740i \(-0.938263\pi\)
0.657542 + 0.753418i \(0.271596\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) 20.0000 0.718421
\(776\) −4.00000 + 6.92820i −0.143592 + 0.248708i
\(777\) 2.00000 + 3.46410i 0.0717496 + 0.124274i
\(778\) 3.00000 + 5.19615i 0.107555 + 0.186291i
\(779\) −15.0000 −0.537431
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) −9.00000 15.5885i −0.321839 0.557442i
\(783\) 1.50000 + 2.59808i 0.0536056 + 0.0928477i
\(784\) −0.500000 + 0.866025i −0.0178571 + 0.0309295i