Properties

Label 546.2.l.f.211.1
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
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: \(0\)
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 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.f.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} -1.00000 q^{12} +(-2.50000 + 2.59808i) q^{13} -1.00000 q^{14} +(-1.00000 - 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} -1.00000 q^{18} +(-3.00000 + 5.19615i) q^{19} +(1.00000 - 1.73205i) q^{20} -1.00000 q^{21} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} -1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(-3.00000 - 5.19615i) q^{29} +(1.00000 - 1.73205i) q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} -1.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} -6.00000 q^{38} +(-3.50000 - 0.866025i) q^{39} +2.00000 q^{40} +(5.00000 + 8.66025i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-1.50000 + 2.59808i) q^{43} +(1.00000 - 1.73205i) q^{45} +(1.50000 - 2.59808i) q^{46} +6.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} -1.00000 q^{51} +(-1.00000 - 3.46410i) q^{52} +7.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.500000 - 0.866025i) q^{56} -6.00000 q^{57} +(3.00000 - 5.19615i) q^{58} +(3.50000 - 6.06218i) q^{59} +2.00000 q^{60} +(-5.50000 + 9.52628i) q^{61} +(2.50000 + 4.33013i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(5.00000 - 5.19615i) q^{65} +(6.50000 + 11.2583i) q^{67} +(-0.500000 - 0.866025i) q^{68} +(1.50000 - 2.59808i) q^{69} +2.00000 q^{70} +(1.50000 - 2.59808i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-3.00000 - 5.19615i) q^{76} +(-1.00000 - 3.46410i) q^{78} -4.00000 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} -15.0000 q^{83} +(0.500000 - 0.866025i) q^{84} +(1.00000 - 1.73205i) q^{85} -3.00000 q^{86} +(3.00000 - 5.19615i) q^{87} +(5.50000 + 9.52628i) q^{89} +2.00000 q^{90} +(-1.00000 - 3.46410i) q^{91} +3.00000 q^{92} +(2.50000 + 4.33013i) q^{93} +(3.00000 + 5.19615i) q^{94} +(6.00000 - 10.3923i) q^{95} +1.00000 q^{96} +(-6.00000 + 10.3923i) q^{97} +(0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} - 4q^{5} - q^{6} - q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} - 4q^{5} - q^{6} - q^{7} - 2q^{8} - q^{9} - 2q^{10} - 2q^{12} - 5q^{13} - 2q^{14} - 2q^{15} - q^{16} - q^{17} - 2q^{18} - 6q^{19} + 2q^{20} - 2q^{21} - 3q^{23} - q^{24} - 2q^{25} - 7q^{26} - 2q^{27} - q^{28} - 6q^{29} + 2q^{30} + 10q^{31} + q^{32} - 2q^{34} + 2q^{35} - q^{36} + 2q^{37} - 12q^{38} - 7q^{39} + 4q^{40} + 10q^{41} - q^{42} - 3q^{43} + 2q^{45} + 3q^{46} + 12q^{47} + q^{48} - q^{49} - q^{50} - 2q^{51} - 2q^{52} + 14q^{53} - q^{54} + q^{56} - 12q^{57} + 6q^{58} + 7q^{59} + 4q^{60} - 11q^{61} + 5q^{62} - q^{63} + 2q^{64} + 10q^{65} + 13q^{67} - q^{68} + 3q^{69} + 4q^{70} + 3q^{71} + q^{72} + 24q^{73} - 2q^{74} - q^{75} - 6q^{76} - 2q^{78} - 8q^{79} + 2q^{80} - q^{81} - 10q^{82} - 30q^{83} + q^{84} + 2q^{85} - 6q^{86} + 6q^{87} + 11q^{89} + 4q^{90} - 2q^{91} + 6q^{92} + 5q^{93} + 6q^{94} + 12q^{95} + 2q^{96} - 12q^{97} + q^{98} + O(q^{100}) \)

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
\(5\) −2.00000 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) −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
\(10\) −1.00000 1.73205i −0.316228 0.547723i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.50000 + 2.59808i −0.693375 + 0.720577i
\(14\) −1.00000 −0.267261
\(15\) −1.00000 1.73205i −0.258199 0.447214i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.500000 + 0.866025i −0.121268 + 0.210042i −0.920268 0.391289i \(-0.872029\pi\)
0.799000 + 0.601331i \(0.205363\pi\)
\(18\) −1.00000 −0.235702
\(19\) −3.00000 + 5.19615i −0.688247 + 1.19208i 0.284157 + 0.958778i \(0.408286\pi\)
−0.972404 + 0.233301i \(0.925047\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −1.00000 −0.200000
\(26\) −3.50000 0.866025i −0.686406 0.169842i
\(27\) −1.00000 −0.192450
\(28\) −0.500000 0.866025i −0.0944911 0.163663i
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 1.00000 1.73205i 0.182574 0.316228i
\(31\) 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
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) −6.00000 −0.973329
\(39\) −3.50000 0.866025i −0.560449 0.138675i
\(40\) 2.00000 0.316228
\(41\) 5.00000 + 8.66025i 0.780869 + 1.35250i 0.931436 + 0.363905i \(0.118557\pi\)
−0.150567 + 0.988600i \(0.548110\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −1.50000 + 2.59808i −0.228748 + 0.396203i −0.957437 0.288641i \(-0.906796\pi\)
0.728689 + 0.684844i \(0.240130\pi\)
\(44\) 0 0
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −0.500000 0.866025i −0.0707107 0.122474i
\(51\) −1.00000 −0.140028
\(52\) −1.00000 3.46410i −0.138675 0.480384i
\(53\) 7.00000 0.961524 0.480762 0.876851i \(-0.340360\pi\)
0.480762 + 0.876851i \(0.340360\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) −6.00000 −0.794719
\(58\) 3.00000 5.19615i 0.393919 0.682288i
\(59\) 3.50000 6.06218i 0.455661 0.789228i −0.543065 0.839691i \(-0.682736\pi\)
0.998726 + 0.0504625i \(0.0160695\pi\)
\(60\) 2.00000 0.258199
\(61\) −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) 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 5.19615i 0.620174 0.644503i
\(66\) 0 0
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) −0.500000 0.866025i −0.0606339 0.105021i
\(69\) 1.50000 2.59808i 0.180579 0.312772i
\(70\) 2.00000 0.239046
\(71\) 1.50000 2.59808i 0.178017 0.308335i −0.763184 0.646181i \(-0.776365\pi\)
0.941201 + 0.337846i \(0.109698\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 12.0000 1.40449 0.702247 0.711934i \(-0.252180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) −3.00000 5.19615i −0.344124 0.596040i
\(77\) 0 0
\(78\) −1.00000 3.46410i −0.113228 0.392232i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −5.00000 + 8.66025i −0.552158 + 0.956365i
\(83\) −15.0000 −1.64646 −0.823232 0.567705i \(-0.807831\pi\)
−0.823232 + 0.567705i \(0.807831\pi\)
\(84\) 0.500000 0.866025i 0.0545545 0.0944911i
\(85\) 1.00000 1.73205i 0.108465 0.187867i
\(86\) −3.00000 −0.323498
\(87\) 3.00000 5.19615i 0.321634 0.557086i
\(88\) 0 0
\(89\) 5.50000 + 9.52628i 0.582999 + 1.00978i 0.995122 + 0.0986553i \(0.0314541\pi\)
−0.412123 + 0.911128i \(0.635213\pi\)
\(90\) 2.00000 0.210819
\(91\) −1.00000 3.46410i −0.104828 0.363137i
\(92\) 3.00000 0.312772
\(93\) 2.50000 + 4.33013i 0.259238 + 0.449013i
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 6.00000 10.3923i 0.615587 1.06623i
\(96\) 1.00000 0.102062
\(97\) −6.00000 + 10.3923i −0.609208 + 1.05518i 0.382164 + 0.924095i \(0.375179\pi\)
−0.991371 + 0.131084i \(0.958154\pi\)
\(98\) 0.500000 0.866025i 0.0505076 0.0874818i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −2.00000 3.46410i −0.199007 0.344691i 0.749199 0.662344i \(-0.230438\pi\)
−0.948207 + 0.317653i \(0.897105\pi\)
\(102\) −0.500000 0.866025i −0.0495074 0.0857493i
\(103\) −1.00000 −0.0985329 −0.0492665 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) 2.50000 2.59808i 0.245145 0.254762i
\(105\) 2.00000 0.195180
\(106\) 3.50000 + 6.06218i 0.339950 + 0.588811i
\(107\) −1.00000 1.73205i −0.0966736 0.167444i 0.813632 0.581380i \(-0.197487\pi\)
−0.910306 + 0.413936i \(0.864154\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) −1.00000 + 1.73205i −0.0949158 + 0.164399i
\(112\) 1.00000 0.0944911
\(113\) −6.00000 + 10.3923i −0.564433 + 0.977626i 0.432670 + 0.901553i \(0.357572\pi\)
−0.997102 + 0.0760733i \(0.975762\pi\)
\(114\) −3.00000 5.19615i −0.280976 0.486664i
\(115\) 3.00000 + 5.19615i 0.279751 + 0.484544i
\(116\) 6.00000 0.557086
\(117\) −1.00000 3.46410i −0.0924500 0.320256i
\(118\) 7.00000 0.644402
\(119\) −0.500000 0.866025i −0.0458349 0.0793884i
\(120\) 1.00000 + 1.73205i 0.0912871 + 0.158114i
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) −11.0000 −0.995893
\(123\) −5.00000 + 8.66025i −0.450835 + 0.780869i
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) 12.0000 1.07331
\(126\) 0.500000 0.866025i 0.0445435 0.0771517i
\(127\) 2.00000 + 3.46410i 0.177471 + 0.307389i 0.941014 0.338368i \(-0.109875\pi\)
−0.763542 + 0.645758i \(0.776542\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −3.00000 −0.264135
\(130\) 7.00000 + 1.73205i 0.613941 + 0.151911i
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) 0 0
\(133\) −3.00000 5.19615i −0.260133 0.450564i
\(134\) −6.50000 + 11.2583i −0.561514 + 0.972572i
\(135\) 2.00000 0.172133
\(136\) 0.500000 0.866025i 0.0428746 0.0742611i
\(137\) 6.00000 10.3923i 0.512615 0.887875i −0.487278 0.873247i \(-0.662010\pi\)
0.999893 0.0146279i \(-0.00465636\pi\)
\(138\) 3.00000 0.255377
\(139\) −2.00000 + 3.46410i −0.169638 + 0.293821i −0.938293 0.345843i \(-0.887593\pi\)
0.768655 + 0.639664i \(0.220926\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) 3.00000 + 5.19615i 0.252646 + 0.437595i
\(142\) 3.00000 0.251754
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 6.00000 + 10.3923i 0.498273 + 0.863034i
\(146\) 6.00000 + 10.3923i 0.496564 + 0.860073i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) −2.00000 −0.164399
\(149\) 7.50000 12.9904i 0.614424 1.06421i −0.376061 0.926595i \(-0.622722\pi\)
0.990485 0.137619i \(-0.0439449\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 3.00000 5.19615i 0.243332 0.421464i
\(153\) −0.500000 0.866025i −0.0404226 0.0700140i
\(154\) 0 0
\(155\) −10.0000 −0.803219
\(156\) 2.50000 2.59808i 0.200160 0.208013i
\(157\) 22.0000 1.75579 0.877896 0.478852i \(-0.158947\pi\)
0.877896 + 0.478852i \(0.158947\pi\)
\(158\) −2.00000 3.46410i −0.159111 0.275589i
\(159\) 3.50000 + 6.06218i 0.277568 + 0.480762i
\(160\) −1.00000 + 1.73205i −0.0790569 + 0.136931i
\(161\) 3.00000 0.236433
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −2.50000 + 4.33013i −0.195815 + 0.339162i −0.947167 0.320740i \(-0.896069\pi\)
0.751352 + 0.659901i \(0.229402\pi\)
\(164\) −10.0000 −0.780869
\(165\) 0 0
\(166\) −7.50000 12.9904i −0.582113 1.00825i
\(167\) −4.00000 6.92820i −0.309529 0.536120i 0.668730 0.743505i \(-0.266838\pi\)
−0.978259 + 0.207385i \(0.933505\pi\)
\(168\) 1.00000 0.0771517
\(169\) −0.500000 12.9904i −0.0384615 0.999260i
\(170\) 2.00000 0.153393
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) −1.50000 2.59808i −0.114374 0.198101i
\(173\) −2.00000 + 3.46410i −0.152057 + 0.263371i −0.931984 0.362500i \(-0.881923\pi\)
0.779926 + 0.625871i \(0.215256\pi\)
\(174\) 6.00000 0.454859
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) 0 0
\(177\) 7.00000 0.526152
\(178\) −5.50000 + 9.52628i −0.412242 + 0.714025i
\(179\) −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i \(-0.238654\pi\)
−0.956088 + 0.293079i \(0.905320\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 2.50000 2.59808i 0.185312 0.192582i
\(183\) −11.0000 −0.813143
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) −2.50000 + 4.33013i −0.183309 + 0.317500i
\(187\) 0 0
\(188\) −3.00000 + 5.19615i −0.218797 + 0.378968i
\(189\) 0.500000 0.866025i 0.0363696 0.0629941i
\(190\) 12.0000 0.870572
\(191\) 4.50000 7.79423i 0.325609 0.563971i −0.656027 0.754738i \(-0.727764\pi\)
0.981635 + 0.190767i \(0.0610975\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −5.00000 8.66025i −0.359908 0.623379i 0.628037 0.778183i \(-0.283859\pi\)
−0.987945 + 0.154805i \(0.950525\pi\)
\(194\) −12.0000 −0.861550
\(195\) 7.00000 + 1.73205i 0.501280 + 0.124035i
\(196\) 1.00000 0.0714286
\(197\) 6.50000 + 11.2583i 0.463106 + 0.802123i 0.999114 0.0420901i \(-0.0134016\pi\)
−0.536008 + 0.844213i \(0.680068\pi\)
\(198\) 0 0
\(199\) −4.50000 + 7.79423i −0.318997 + 0.552518i −0.980279 0.197619i \(-0.936679\pi\)
0.661282 + 0.750137i \(0.270013\pi\)
\(200\) 1.00000 0.0707107
\(201\) −6.50000 + 11.2583i −0.458475 + 0.794101i
\(202\) 2.00000 3.46410i 0.140720 0.243733i
\(203\) 6.00000 0.421117
\(204\) 0.500000 0.866025i 0.0350070 0.0606339i
\(205\) −10.0000 17.3205i −0.698430 1.20972i
\(206\) −0.500000 0.866025i −0.0348367 0.0603388i
\(207\) 3.00000 0.208514
\(208\) 3.50000 + 0.866025i 0.242681 + 0.0600481i
\(209\) 0 0
\(210\) 1.00000 + 1.73205i 0.0690066 + 0.119523i
\(211\) 2.00000 + 3.46410i 0.137686 + 0.238479i 0.926620 0.375999i \(-0.122700\pi\)
−0.788935 + 0.614477i \(0.789367\pi\)
\(212\) −3.50000 + 6.06218i −0.240381 + 0.416352i
\(213\) 3.00000 0.205557
\(214\) 1.00000 1.73205i 0.0683586 0.118401i
\(215\) 3.00000 5.19615i 0.204598 0.354375i
\(216\) 1.00000 0.0680414
\(217\) −2.50000 + 4.33013i −0.169711 + 0.293948i
\(218\) 2.00000 + 3.46410i 0.135457 + 0.234619i
\(219\) 6.00000 + 10.3923i 0.405442 + 0.702247i
\(220\) 0 0
\(221\) −1.00000 3.46410i −0.0672673 0.233021i
\(222\) −2.00000 −0.134231
\(223\) 3.50000 + 6.06218i 0.234377 + 0.405953i 0.959092 0.283096i \(-0.0913615\pi\)
−0.724714 + 0.689050i \(0.758028\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) −12.0000 −0.798228
\(227\) −10.0000 + 17.3205i −0.663723 + 1.14960i 0.315906 + 0.948790i \(0.397691\pi\)
−0.979630 + 0.200812i \(0.935642\pi\)
\(228\) 3.00000 5.19615i 0.198680 0.344124i
\(229\) −17.0000 −1.12339 −0.561696 0.827344i \(-0.689851\pi\)
−0.561696 + 0.827344i \(0.689851\pi\)
\(230\) −3.00000 + 5.19615i −0.197814 + 0.342624i
\(231\) 0 0
\(232\) 3.00000 + 5.19615i 0.196960 + 0.341144i
\(233\) −8.00000 −0.524097 −0.262049 0.965055i \(-0.584398\pi\)
−0.262049 + 0.965055i \(0.584398\pi\)
\(234\) 2.50000 2.59808i 0.163430 0.169842i
\(235\) −12.0000 −0.782794
\(236\) 3.50000 + 6.06218i 0.227831 + 0.394614i
\(237\) −2.00000 3.46410i −0.129914 0.225018i
\(238\) 0.500000 0.866025i 0.0324102 0.0561361i
\(239\) −29.0000 −1.87585 −0.937927 0.346833i \(-0.887257\pi\)
−0.937927 + 0.346833i \(0.887257\pi\)
\(240\) −1.00000 + 1.73205i −0.0645497 + 0.111803i
\(241\) 9.00000 15.5885i 0.579741 1.00414i −0.415768 0.909471i \(-0.636487\pi\)
0.995509 0.0946700i \(-0.0301796\pi\)
\(242\) 11.0000 0.707107
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.50000 9.52628i −0.352101 0.609858i
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) −10.0000 −0.637577
\(247\) −6.00000 20.7846i −0.381771 1.32249i
\(248\) −5.00000 −0.317500
\(249\) −7.50000 12.9904i −0.475293 0.823232i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 3.50000 6.06218i 0.220918 0.382641i −0.734169 0.678967i \(-0.762428\pi\)
0.955087 + 0.296326i \(0.0957613\pi\)
\(252\) 1.00000 0.0629941
\(253\) 0 0
\(254\) −2.00000 + 3.46410i −0.125491 + 0.217357i
\(255\) 2.00000 0.125245
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 5.50000 + 9.52628i 0.343081 + 0.594233i 0.985003 0.172536i \(-0.0551963\pi\)
−0.641923 + 0.766769i \(0.721863\pi\)
\(258\) −1.50000 2.59808i −0.0933859 0.161749i
\(259\) −2.00000 −0.124274
\(260\) 2.00000 + 6.92820i 0.124035 + 0.429669i
\(261\) 6.00000 0.371391
\(262\) −7.50000 12.9904i −0.463352 0.802548i
\(263\) −14.0000 24.2487i −0.863277 1.49524i −0.868748 0.495255i \(-0.835075\pi\)
0.00547092 0.999985i \(-0.498259\pi\)
\(264\) 0 0
\(265\) −14.0000 −0.860013
\(266\) 3.00000 5.19615i 0.183942 0.318597i
\(267\) −5.50000 + 9.52628i −0.336595 + 0.582999i
\(268\) −13.0000 −0.794101
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 1.00000 + 1.73205i 0.0608581 + 0.105409i
\(271\) −13.5000 23.3827i −0.820067 1.42040i −0.905632 0.424064i \(-0.860603\pi\)
0.0855654 0.996333i \(-0.472730\pi\)
\(272\) 1.00000 0.0606339
\(273\) 2.50000 2.59808i 0.151307 0.157243i
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 1.50000 + 2.59808i 0.0902894 + 0.156386i
\(277\) 2.00000 3.46410i 0.120168 0.208138i −0.799666 0.600446i \(-0.794990\pi\)
0.919834 + 0.392308i \(0.128323\pi\)
\(278\) −4.00000 −0.239904
\(279\) −2.50000 + 4.33013i −0.149671 + 0.259238i
\(280\) −1.00000 + 1.73205i −0.0597614 + 0.103510i
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) 1.50000 + 2.59808i 0.0890086 + 0.154167i
\(285\) 12.0000 0.710819
\(286\) 0 0
\(287\) −10.0000 −0.590281
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) −6.00000 + 10.3923i −0.352332 + 0.610257i
\(291\) −12.0000 −0.703452
\(292\) −6.00000 + 10.3923i −0.351123 + 0.608164i
\(293\) −12.0000 + 20.7846i −0.701047 + 1.21425i 0.267052 + 0.963682i \(0.413951\pi\)
−0.968099 + 0.250568i \(0.919383\pi\)
\(294\) 1.00000 0.0583212
\(295\) −7.00000 + 12.1244i −0.407556 + 0.705907i
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 0 0
\(298\) 15.0000 0.868927
\(299\) 10.5000 + 2.59808i 0.607231 + 0.150251i
\(300\) 1.00000 0.0577350
\(301\) −1.50000 2.59808i −0.0864586 0.149751i
\(302\) 2.00000 + 3.46410i 0.115087 + 0.199337i
\(303\) 2.00000 3.46410i 0.114897 0.199007i
\(304\) 6.00000 0.344124
\(305\) 11.0000 19.0526i 0.629858 1.09095i
\(306\) 0.500000 0.866025i 0.0285831 0.0495074i
\(307\) −18.0000 −1.02731 −0.513657 0.857996i \(-0.671710\pi\)
−0.513657 + 0.857996i \(0.671710\pi\)
\(308\) 0 0
\(309\) −0.500000 0.866025i −0.0284440 0.0492665i
\(310\) −5.00000 8.66025i −0.283981 0.491869i
\(311\) 14.0000 0.793867 0.396934 0.917847i \(-0.370074\pi\)
0.396934 + 0.917847i \(0.370074\pi\)
\(312\) 3.50000 + 0.866025i 0.198148 + 0.0490290i
\(313\) −32.0000 −1.80875 −0.904373 0.426742i \(-0.859661\pi\)
−0.904373 + 0.426742i \(0.859661\pi\)
\(314\) 11.0000 + 19.0526i 0.620766 + 1.07520i
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) −3.50000 + 6.06218i −0.196270 + 0.339950i
\(319\) 0 0
\(320\) −2.00000 −0.111803
\(321\) 1.00000 1.73205i 0.0558146 0.0966736i
\(322\) 1.50000 + 2.59808i 0.0835917 + 0.144785i
\(323\) −3.00000 5.19615i −0.166924 0.289122i
\(324\) 1.00000 0.0555556
\(325\) 2.50000 2.59808i 0.138675 0.144115i
\(326\) −5.00000 −0.276924
\(327\) 2.00000 + 3.46410i 0.110600 + 0.191565i
\(328\) −5.00000 8.66025i −0.276079 0.478183i
\(329\) −3.00000 + 5.19615i −0.165395 + 0.286473i
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) 7.50000 12.9904i 0.411616 0.712940i
\(333\) −2.00000 −0.109599
\(334\) 4.00000 6.92820i 0.218870 0.379094i
\(335\) −13.0000 22.5167i −0.710266 1.23022i
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 11.0000 6.92820i 0.598321 0.376845i
\(339\) −12.0000 −0.651751
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) 0 0
\(342\) 3.00000 5.19615i 0.162221 0.280976i
\(343\) 1.00000 0.0539949
\(344\) 1.50000 2.59808i 0.0808746 0.140079i
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) −4.00000 −0.215041
\(347\) −13.0000 + 22.5167i −0.697877 + 1.20876i 0.271325 + 0.962488i \(0.412538\pi\)
−0.969201 + 0.246270i \(0.920795\pi\)
\(348\) 3.00000 + 5.19615i 0.160817 + 0.278543i
\(349\) −14.5000 25.1147i −0.776167 1.34436i −0.934136 0.356917i \(-0.883828\pi\)
0.157969 0.987444i \(-0.449505\pi\)
\(350\) 1.00000 0.0534522
\(351\) 2.50000 2.59808i 0.133440 0.138675i
\(352\) 0 0
\(353\) 10.5000 + 18.1865i 0.558859 + 0.967972i 0.997592 + 0.0693543i \(0.0220939\pi\)
−0.438733 + 0.898617i \(0.644573\pi\)
\(354\) 3.50000 + 6.06218i 0.186023 + 0.322201i
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) −11.0000 −0.582999
\(357\) 0.500000 0.866025i 0.0264628 0.0458349i
\(358\) 3.00000 5.19615i 0.158555 0.274625i
\(359\) 16.0000 0.844448 0.422224 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) −1.00000 + 1.73205i −0.0527046 + 0.0912871i
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) 5.00000 + 8.66025i 0.262794 + 0.455173i
\(363\) 11.0000 0.577350
\(364\) 3.50000 + 0.866025i 0.183450 + 0.0453921i
\(365\) −24.0000 −1.25622
\(366\) −5.50000 9.52628i −0.287490 0.497947i
\(367\) −7.50000 12.9904i −0.391497 0.678092i 0.601150 0.799136i \(-0.294709\pi\)
−0.992647 + 0.121044i \(0.961376\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) −10.0000 −0.520579
\(370\) 2.00000 3.46410i 0.103975 0.180090i
\(371\) −3.50000 + 6.06218i −0.181711 + 0.314733i
\(372\) −5.00000 −0.259238
\(373\) 4.00000 6.92820i 0.207112 0.358729i −0.743691 0.668523i \(-0.766927\pi\)
0.950804 + 0.309794i \(0.100260\pi\)
\(374\) 0 0
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) −6.00000 −0.309426
\(377\) 21.0000 + 5.19615i 1.08156 + 0.267615i
\(378\) 1.00000 0.0514344
\(379\) −6.00000 10.3923i −0.308199 0.533817i 0.669769 0.742569i \(-0.266393\pi\)
−0.977969 + 0.208752i \(0.933060\pi\)
\(380\) 6.00000 + 10.3923i 0.307794 + 0.533114i
\(381\) −2.00000 + 3.46410i −0.102463 + 0.177471i
\(382\) 9.00000 0.460480
\(383\) −2.00000 + 3.46410i −0.102195 + 0.177007i −0.912589 0.408879i \(-0.865920\pi\)
0.810394 + 0.585886i \(0.199253\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) 5.00000 8.66025i 0.254493 0.440795i
\(387\) −1.50000 2.59808i −0.0762493 0.132068i
\(388\) −6.00000 10.3923i −0.304604 0.527589i
\(389\) −5.00000 −0.253510 −0.126755 0.991934i \(-0.540456\pi\)
−0.126755 + 0.991934i \(0.540456\pi\)
\(390\) 2.00000 + 6.92820i 0.101274 + 0.350823i
\(391\) 3.00000 0.151717
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) −7.50000 12.9904i −0.378325 0.655278i
\(394\) −6.50000 + 11.2583i −0.327465 + 0.567186i
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) −6.50000 + 11.2583i −0.326226 + 0.565039i −0.981760 0.190126i \(-0.939110\pi\)
0.655534 + 0.755166i \(0.272444\pi\)
\(398\) −9.00000 −0.451129
\(399\) 3.00000 5.19615i 0.150188 0.260133i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) 12.0000 + 20.7846i 0.599251 + 1.03793i 0.992932 + 0.118686i \(0.0378683\pi\)
−0.393680 + 0.919247i \(0.628798\pi\)
\(402\) −13.0000 −0.648381
\(403\) −12.5000 + 12.9904i −0.622669 + 0.647097i
\(404\) 4.00000 0.199007
\(405\) 1.00000 + 1.73205i 0.0496904 + 0.0860663i
\(406\) 3.00000 + 5.19615i 0.148888 + 0.257881i
\(407\) 0 0
\(408\) 1.00000 0.0495074
\(409\) 1.00000 1.73205i 0.0494468 0.0856444i −0.840243 0.542211i \(-0.817588\pi\)
0.889689 + 0.456566i \(0.150921\pi\)
\(410\) 10.0000 17.3205i 0.493865 0.855399i
\(411\) 12.0000 0.591916
\(412\) 0.500000 0.866025i 0.0246332 0.0426660i
\(413\) 3.50000 + 6.06218i 0.172224 + 0.298300i
\(414\) 1.50000 + 2.59808i 0.0737210 + 0.127688i
\(415\) 30.0000 1.47264
\(416\) 1.00000 + 3.46410i 0.0490290 + 0.169842i
\(417\) −4.00000 −0.195881
\(418\) 0 0
\(419\) −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i \(-0.286076\pi\)
−0.989000 + 0.147918i \(0.952743\pi\)
\(420\) −1.00000 + 1.73205i −0.0487950 + 0.0845154i
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) −2.00000 + 3.46410i −0.0973585 + 0.168630i
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) −7.00000 −0.339950
\(425\) 0.500000 0.866025i 0.0242536 0.0420084i
\(426\) 1.50000 + 2.59808i 0.0726752 + 0.125877i
\(427\) −5.50000 9.52628i −0.266164 0.461009i
\(428\) 2.00000 0.0966736
\(429\) 0 0
\(430\) 6.00000 0.289346
\(431\) 6.50000 + 11.2583i 0.313094 + 0.542295i 0.979030 0.203714i \(-0.0653012\pi\)
−0.665937 + 0.746008i \(0.731968\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −8.00000 + 13.8564i −0.384455 + 0.665896i −0.991693 0.128624i \(-0.958944\pi\)
0.607238 + 0.794520i \(0.292277\pi\)
\(434\) −5.00000 −0.240008
\(435\) −6.00000 + 10.3923i −0.287678 + 0.498273i
\(436\) −2.00000 + 3.46410i −0.0957826 + 0.165900i
\(437\) 18.0000 0.861057
\(438\) −6.00000 + 10.3923i −0.286691 + 0.496564i
\(439\) −2.00000 3.46410i −0.0954548 0.165333i 0.814344 0.580383i \(-0.197097\pi\)
−0.909798 + 0.415051i \(0.863764\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 2.50000 2.59808i 0.118913 0.123578i
\(443\) 18.0000 0.855206 0.427603 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(444\) −1.00000 1.73205i −0.0474579 0.0821995i
\(445\) −11.0000 19.0526i −0.521450 0.903178i
\(446\) −3.50000 + 6.06218i −0.165730 + 0.287052i
\(447\) 15.0000 0.709476
\(448\) −0.500000 + 0.866025i −0.0236228 + 0.0409159i
\(449\) −7.00000 + 12.1244i −0.330350 + 0.572184i −0.982581 0.185837i \(-0.940500\pi\)
0.652230 + 0.758021i \(0.273834\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) 2.00000 + 3.46410i 0.0939682 + 0.162758i
\(454\) −20.0000 −0.938647
\(455\) 2.00000 + 6.92820i 0.0937614 + 0.324799i
\(456\) 6.00000 0.280976
\(457\) 20.5000 + 35.5070i 0.958950 + 1.66095i 0.725059 + 0.688686i \(0.241812\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) −8.50000 14.7224i −0.397179 0.687934i
\(459\) 0.500000 0.866025i 0.0233380 0.0404226i
\(460\) −6.00000 −0.279751
\(461\) −8.00000 + 13.8564i −0.372597 + 0.645357i −0.989964 0.141318i \(-0.954866\pi\)
0.617367 + 0.786675i \(0.288199\pi\)
\(462\) 0 0
\(463\) 34.0000 1.58011 0.790057 0.613033i \(-0.210051\pi\)
0.790057 + 0.613033i \(0.210051\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) −5.00000 8.66025i −0.231869 0.401610i
\(466\) −4.00000 6.92820i −0.185296 0.320943i
\(467\) 27.0000 1.24941 0.624705 0.780860i \(-0.285219\pi\)
0.624705 + 0.780860i \(0.285219\pi\)
\(468\) 3.50000 + 0.866025i 0.161788 + 0.0400320i
\(469\) −13.0000 −0.600284
\(470\) −6.00000 10.3923i −0.276759 0.479361i
\(471\) 11.0000 + 19.0526i 0.506853 + 0.877896i
\(472\) −3.50000 + 6.06218i −0.161101 + 0.279034i
\(473\) 0 0
\(474\) 2.00000 3.46410i 0.0918630 0.159111i
\(475\) 3.00000 5.19615i 0.137649 0.238416i
\(476\) 1.00000 0.0458349
\(477\) −3.50000 + 6.06218i −0.160254 + 0.277568i
\(478\) −14.5000 25.1147i −0.663215 1.14872i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) −2.00000 −0.0912871
\(481\) −7.00000 1.73205i −0.319173 0.0789747i
\(482\) 18.0000 0.819878
\(483\) 1.50000 + 2.59808i 0.0682524 + 0.118217i
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 12.0000 20.7846i 0.544892 0.943781i
\(486\) 1.00000 0.0453609
\(487\) −6.00000 + 10.3923i −0.271886 + 0.470920i −0.969345 0.245705i \(-0.920981\pi\)
0.697459 + 0.716625i \(0.254314\pi\)
\(488\) 5.50000 9.52628i 0.248973 0.431234i
\(489\) −5.00000 −0.226108
\(490\) −1.00000 + 1.73205i −0.0451754 + 0.0782461i
\(491\) 4.00000 + 6.92820i 0.180517 + 0.312665i 0.942057 0.335453i \(-0.108889\pi\)
−0.761539 + 0.648119i \(0.775556\pi\)
\(492\) −5.00000 8.66025i −0.225417 0.390434i
\(493\) 6.00000 0.270226
\(494\) 15.0000 15.5885i 0.674882 0.701358i
\(495\) 0 0
\(496\) −2.50000 4.33013i −0.112253 0.194428i
\(497\) 1.50000 + 2.59808i 0.0672842 + 0.116540i
\(498\) 7.50000 12.9904i 0.336083 0.582113i
\(499\) −17.0000 −0.761025 −0.380512 0.924776i \(-0.624252\pi\)
−0.380512 + 0.924776i \(0.624252\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 4.00000 6.92820i 0.178707 0.309529i
\(502\) 7.00000 0.312425
\(503\) 4.00000 6.92820i 0.178351 0.308913i −0.762965 0.646440i \(-0.776257\pi\)
0.941316 + 0.337527i \(0.109590\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) 4.00000 + 6.92820i 0.177998 + 0.308301i
\(506\) 0 0
\(507\) 11.0000 6.92820i 0.488527 0.307692i
\(508\) −4.00000 −0.177471
\(509\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(510\) 1.00000 + 1.73205i 0.0442807 + 0.0766965i
\(511\) −6.00000 + 10.3923i −0.265424 + 0.459728i
\(512\) −1.00000 −0.0441942
\(513\) 3.00000 5.19615i 0.132453 0.229416i
\(514\) −5.50000 + 9.52628i −0.242595 + 0.420186i
\(515\) 2.00000 0.0881305
\(516\) 1.50000 2.59808i 0.0660338 0.114374i
\(517\) 0 0
\(518\) −1.00000 1.73205i −0.0439375 0.0761019i
\(519\) −4.00000 −0.175581
\(520\) −5.00000 + 5.19615i −0.219265 + 0.227866i
\(521\) 34.0000 1.48957 0.744784 0.667306i \(-0.232553\pi\)
0.744784 + 0.667306i \(0.232553\pi\)
\(522\) 3.00000 + 5.19615i 0.131306 + 0.227429i
\(523\) 18.0000 + 31.1769i 0.787085 + 1.36327i 0.927746 + 0.373213i \(0.121744\pi\)
−0.140660 + 0.990058i \(0.544923\pi\)
\(524\) 7.50000 12.9904i 0.327639 0.567487i
\(525\) 1.00000 0.0436436
\(526\) 14.0000 24.2487i 0.610429 1.05729i
\(527\) −2.50000 + 4.33013i −0.108902 + 0.188623i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) −7.00000 12.1244i −0.304061 0.526648i
\(531\) 3.50000 + 6.06218i 0.151887 + 0.263076i
\(532\) 6.00000 0.260133
\(533\) −35.0000 8.66025i −1.51602 0.375117i
\(534\) −11.0000 −0.476017
\(535\) 2.00000 + 3.46410i 0.0864675 + 0.149766i
\(536\) −6.50000 11.2583i −0.280757 0.486286i
\(537\) 3.00000 5.19615i 0.129460 0.224231i
\(538\) 6.00000 0.258678
\(539\) 0 0
\(540\) −1.00000 + 1.73205i −0.0430331 + 0.0745356i
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 13.5000 23.3827i 0.579875 1.00437i
\(543\) 5.00000 + 8.66025i 0.214571 + 0.371647i
\(544\) 0.500000 + 0.866025i 0.0214373 + 0.0371305i
\(545\) −8.00000 −0.342682
\(546\) 3.50000 + 0.866025i 0.149786 + 0.0370625i
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 6.00000 + 10.3923i 0.256307 + 0.443937i
\(549\) −5.50000 9.52628i −0.234734 0.406572i
\(550\) 0 0
\(551\) 36.0000 1.53365
\(552\) −1.50000 + 2.59808i −0.0638442 + 0.110581i
\(553\) 2.00000 3.46410i 0.0850487 0.147309i
\(554\) 4.00000 0.169944
\(555\) 2.00000 3.46410i 0.0848953 0.147043i
\(556\) −2.00000 3.46410i −0.0848189 0.146911i
\(557\) 15.5000 + 26.8468i 0.656756 + 1.13753i 0.981450 + 0.191716i \(0.0614052\pi\)
−0.324694 + 0.945819i \(0.605261\pi\)
\(558\) −5.00000 −0.211667
\(559\) −3.00000 10.3923i −0.126886 0.439548i
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) −12.0000 + 20.7846i −0.505740 + 0.875967i 0.494238 + 0.869326i \(0.335447\pi\)
−0.999978 + 0.00664037i \(0.997886\pi\)
\(564\) −6.00000 −0.252646
\(565\) 12.0000 20.7846i 0.504844 0.874415i
\(566\) 7.00000 12.1244i 0.294232 0.509625i
\(567\) 1.00000 0.0419961
\(568\) −1.50000 + 2.59808i −0.0629386 + 0.109013i
\(569\) −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i \(-0.950200\pi\)
0.358954 0.933355i \(-0.383134\pi\)
\(570\) 6.00000 + 10.3923i 0.251312 + 0.435286i
\(571\) 23.0000 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) 0 0
\(573\) 9.00000 0.375980
\(574\) −5.00000 8.66025i −0.208696 0.361472i
\(575\) 1.50000 + 2.59808i 0.0625543 + 0.108347i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 42.0000 1.74848 0.874241 0.485491i \(-0.161359\pi\)
0.874241 + 0.485491i \(0.161359\pi\)
\(578\) −8.00000 + 13.8564i −0.332756 + 0.576351i
\(579\) 5.00000 8.66025i 0.207793 0.359908i
\(580\) −12.0000 −0.498273
\(581\) 7.50000 12.9904i 0.311152 0.538932i
\(582\) −6.00000 10.3923i −0.248708 0.430775i
\(583\) 0 0
\(584\) −12.0000 −0.496564
\(585\) 2.00000 + 6.92820i 0.0826898 + 0.286446i
\(586\) −24.0000 −0.991431
\(587\) −1.50000 2.59808i −0.0619116 0.107234i 0.833408 0.552658i \(-0.186386\pi\)
−0.895320 + 0.445424i \(0.853053\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) −15.0000 + 25.9808i −0.618064 + 1.07052i
\(590\) −14.0000 −0.576371
\(591\) −6.50000 + 11.2583i −0.267374 + 0.463106i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) 35.0000 1.43728 0.718639 0.695383i \(-0.244765\pi\)
0.718639 + 0.695383i \(0.244765\pi\)
\(594\) 0 0
\(595\) 1.00000 + 1.73205i 0.0409960 + 0.0710072i
\(596\) 7.50000 + 12.9904i 0.307212 + 0.532107i
\(597\) −9.00000 −0.368345
\(598\) 3.00000 + 10.3923i 0.122679 + 0.424973i
\(599\) −27.0000 −1.10319 −0.551595 0.834112i \(-0.685981\pi\)
−0.551595 + 0.834112i \(0.685981\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) −23.0000 39.8372i −0.938190 1.62499i −0.768845 0.639435i \(-0.779168\pi\)
−0.169344 0.985557i \(-0.554165\pi\)
\(602\) 1.50000 2.59808i 0.0611354 0.105890i
\(603\) −13.0000 −0.529401
\(604\) −2.00000 + 3.46410i −0.0813788 + 0.140952i
\(605\) −11.0000 + 19.0526i −0.447214 + 0.774597i
\(606\) 4.00000 0.162489
\(607\) 17.5000 30.3109i 0.710303 1.23028i −0.254440 0.967088i \(-0.581891\pi\)
0.964743 0.263193i \(-0.0847754\pi\)
\(608\) 3.00000 + 5.19615i 0.121666 + 0.210732i
\(609\) 3.00000 + 5.19615i 0.121566 + 0.210559i
\(610\) 22.0000 0.890754
\(611\) −15.0000 + 15.5885i −0.606835 + 0.630641i
\(612\) 1.00000 0.0404226
\(613\) 11.0000 + 19.0526i 0.444286 + 0.769526i 0.998002 0.0631797i \(-0.0201241\pi\)
−0.553716 + 0.832705i \(0.686791\pi\)
\(614\) −9.00000 15.5885i −0.363210 0.629099i
\(615\) 10.0000 17.3205i 0.403239 0.698430i
\(616\) 0 0
\(617\) 4.00000 6.92820i 0.161034 0.278919i −0.774206 0.632934i \(-0.781850\pi\)
0.935240 + 0.354015i \(0.115184\pi\)
\(618\) 0.500000 0.866025i 0.0201129 0.0348367i
\(619\) 38.0000 1.52735 0.763674 0.645601i \(-0.223393\pi\)
0.763674 + 0.645601i \(0.223393\pi\)
\(620\) 5.00000 8.66025i 0.200805 0.347804i
\(621\) 1.50000 + 2.59808i 0.0601929 + 0.104257i
\(622\) 7.00000 + 12.1244i 0.280674 + 0.486142i
\(623\) −11.0000 −0.440706
\(624\) 1.00000 + 3.46410i 0.0400320 + 0.138675i
\(625\) −19.0000 −0.760000
\(626\) −16.0000 27.7128i −0.639489 1.10763i
\(627\) 0 0
\(628\) −11.0000 + 19.0526i −0.438948 + 0.760280i
\(629\) −2.00000 −0.0797452
\(630\) −1.00000 + 1.73205i −0.0398410 + 0.0690066i
\(631\) 20.0000 34.6410i 0.796187 1.37904i −0.125895 0.992044i \(-0.540180\pi\)
0.922082 0.386994i \(-0.126486\pi\)
\(632\) 4.00000 0.159111
\(633\) −2.00000 + 3.46410i −0.0794929 + 0.137686i
\(634\) 1.50000 + 2.59808i 0.0595726 + 0.103183i
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) −7.00000 −0.277568
\(637\) 3.50000 + 0.866025i 0.138675 + 0.0343132i
\(638\) 0 0
\(639\) 1.50000 + 2.59808i 0.0593391 + 0.102778i
\(640\) −1.00000 1.73205i −0.0395285 0.0684653i
\(641\) −18.0000 + 31.1769i −0.710957 + 1.23141i 0.253541 + 0.967325i \(0.418405\pi\)
−0.964498 + 0.264089i \(0.914929\pi\)
\(642\) 2.00000 0.0789337
\(643\) 7.00000 12.1244i 0.276053 0.478138i −0.694347 0.719640i \(-0.744307\pi\)
0.970400 + 0.241502i \(0.0776401\pi\)
\(644\) −1.50000 + 2.59808i −0.0591083 + 0.102379i
\(645\) 6.00000 0.236250
\(646\) 3.00000 5.19615i 0.118033 0.204440i
\(647\) 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i \(-0.129037\pi\)
−0.801010 + 0.598651i \(0.795704\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 0 0
\(650\) 3.50000 + 0.866025i 0.137281 + 0.0339683i
\(651\) −5.00000 −0.195965
\(652\) −2.50000 4.33013i −0.0979076 0.169581i
\(653\) −7.50000 12.9904i −0.293498 0.508353i 0.681137 0.732156i \(-0.261486\pi\)
−0.974634 + 0.223803i \(0.928153\pi\)
\(654\) −2.00000 + 3.46410i −0.0782062 + 0.135457i
\(655\) 30.0000 1.17220
\(656\) 5.00000 8.66025i 0.195217 0.338126i
\(657\) −6.00000 + 10.3923i −0.234082 + 0.405442i
\(658\) −6.00000 −0.233904
\(659\) −3.00000 + 5.19615i −0.116863 + 0.202413i −0.918523 0.395367i \(-0.870617\pi\)
0.801660 + 0.597781i \(0.203951\pi\)
\(660\) 0 0
\(661\) −11.5000 19.9186i −0.447298 0.774743i 0.550911 0.834564i \(-0.314280\pi\)
−0.998209 + 0.0598209i \(0.980947\pi\)
\(662\) −20.0000 −0.777322
\(663\) 2.50000 2.59808i 0.0970920 0.100901i
\(664\) 15.0000 0.582113
\(665\) 6.00000 + 10.3923i 0.232670 + 0.402996i
\(666\) −1.00000 1.73205i −0.0387492 0.0671156i
\(667\) −9.00000 + 15.5885i −0.348481 + 0.603587i
\(668\) 8.00000 0.309529
\(669\) −3.50000 + 6.06218i −0.135318 + 0.234377i
\(670\) 13.0000 22.5167i 0.502234 0.869894i
\(671\) 0 0
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) 12.5000 + 21.6506i 0.481840 + 0.834571i 0.999783 0.0208444i \(-0.00663546\pi\)
−0.517943 + 0.855415i \(0.673302\pi\)
\(674\) 17.0000 + 29.4449i 0.654816 + 1.13417i
\(675\) 1.00000 0.0384900
\(676\) 11.5000 + 6.06218i 0.442308 + 0.233161i
\(677\) 4.00000 0.153732 0.0768662 0.997041i \(-0.475509\pi\)
0.0768662 + 0.997041i \(0.475509\pi\)
\(678\) −6.00000 10.3923i −0.230429 0.399114i
\(679\) −6.00000 10.3923i −0.230259 0.398820i
\(680\) −1.00000 + 1.73205i −0.0383482 + 0.0664211i
\(681\) −20.0000 −0.766402
\(682\) 0 0
\(683\) −23.0000 + 39.8372i −0.880071 + 1.52433i −0.0288092 + 0.999585i \(0.509172\pi\)
−0.851261 + 0.524742i \(0.824162\pi\)
\(684\) 6.00000 0.229416
\(685\) −12.0000 + 20.7846i −0.458496 + 0.794139i
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) −8.50000 14.7224i −0.324295 0.561696i
\(688\) 3.00000 0.114374
\(689\) −17.5000 + 18.1865i −0.666697 + 0.692852i
\(690\) −6.00000 −0.228416
\(691\) −22.0000 38.1051i −0.836919 1.44959i −0.892458 0.451130i \(-0.851021\pi\)
0.0555386 0.998457i \(-0.482312\pi\)
\(692\) −2.00000 3.46410i −0.0760286 0.131685i
\(693\) 0 0
\(694\) −26.0000 −0.986947
\(695\) 4.00000 6.92820i 0.151729 0.262802i
\(696\) −3.00000 + 5.19615i −0.113715 + 0.196960i
\(697\) −10.0000 −0.378777
\(698\) 14.5000 25.1147i 0.548833 0.950607i
\(699\) −4.00000 6.92820i −0.151294 0.262049i
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) −27.0000 −1.01978 −0.509888 0.860241i \(-0.670313\pi\)
−0.509888 + 0.860241i \(0.670313\pi\)
\(702\) 3.50000 + 0.866025i 0.132099 + 0.0326860i
\(703\) −12.0000 −0.452589
\(704\) 0 0
\(705\) −6.00000 10.3923i −0.225973 0.391397i
\(706\) −10.5000 + 18.1865i −0.395173 + 0.684459i
\(707\) 4.00000 0.150435
\(708\) −3.50000 + 6.06218i −0.131538 + 0.227831i
\(709\) −20.0000 + 34.6410i −0.751116 + 1.30097i 0.196167 + 0.980571i \(0.437151\pi\)
−0.947282 + 0.320400i \(0.896183\pi\)
\(710\) −6.00000 −0.225176
\(711\) 2.00000 3.46410i 0.0750059 0.129914i
\(712\) −5.50000 9.52628i −0.206121 0.357012i
\(713\) −7.50000 12.9904i −0.280877 0.486494i
\(714\) 1.00000 0.0374241
\(715\) 0 0
\(716\) 6.00000 0.224231
\(717\) −14.5000 25.1147i −0.541512 0.937927i
\(718\) 8.00000 + 13.8564i 0.298557 + 0.517116i
\(719\) 14.0000 24.2487i 0.522112 0.904324i −0.477557 0.878601i \(-0.658478\pi\)
0.999669 0.0257237i \(-0.00818900\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 0.500000 0.866025i 0.0186210 0.0322525i
\(722\) 8.50000 14.7224i 0.316337 0.547912i
\(723\) 18.0000 0.669427
\(724\) −5.00000 + 8.66025i −0.185824 + 0.321856i
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 5.50000 + 9.52628i 0.204124 + 0.353553i
\(727\) 33.0000 1.22390 0.611951 0.790896i \(-0.290385\pi\)
0.611951 + 0.790896i \(0.290385\pi\)
\(728\) 1.00000 + 3.46410i 0.0370625 + 0.128388i
\(729\) 1.00000 0.0370370
\(730\) −12.0000 20.7846i −0.444140 0.769273i
\(731\) −1.50000 2.59808i −0.0554795 0.0960933i
\(732\) 5.50000 9.52628i 0.203286 0.352101i
\(733\) 25.0000 0.923396 0.461698 0.887037i \(-0.347240\pi\)
0.461698 + 0.887037i \(0.347240\pi\)
\(734\) 7.50000 12.9904i 0.276830 0.479484i
\(735\) −1.00000 + 1.73205i −0.0368856 + 0.0638877i
\(736\) −3.00000 −0.110581
\(737\) 0 0
\(738\) −5.00000 8.66025i −0.184053 0.318788i
\(739\) −4.50000 7.79423i −0.165535 0.286715i 0.771310 0.636460i \(-0.219602\pi\)
−0.936845 + 0.349744i \(0.886268\pi\)
\(740\) 4.00000 0.147043
\(741\) 15.0000 15.5885i 0.551039 0.572656i
\(742\) −7.00000 −0.256978
\(743\) −21.5000 37.2391i −0.788759 1.36617i −0.926728 0.375733i \(-0.877391\pi\)
0.137969 0.990437i \(-0.455942\pi\)
\(744\) −2.50000 4.33013i −0.0916544 0.158750i
\(745\) −15.0000 + 25.9808i −0.549557 + 0.951861i
\(746\) 8.00000 0.292901
\(747\) 7.50000 12.9904i 0.274411 0.475293i
\(748\) 0 0
\(749\) 2.00000 0.0730784
\(750\) −6.00000 + 10.3923i −0.219089 + 0.379473i
\(751\) 19.0000 + 32.9090i 0.693320 + 1.20087i 0.970744 + 0.240118i \(0.0771860\pi\)
−0.277424 + 0.960748i \(0.589481\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 7.00000 0.255094
\(754\) 6.00000 + 20.7846i 0.218507 + 0.756931i
\(755\) −8.00000 −0.291150
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) 1.00000 + 1.73205i 0.0363456 + 0.0629525i 0.883626 0.468193i \(-0.155095\pi\)
−0.847280 + 0.531146i \(0.821762\pi\)
\(758\) 6.00000 10.3923i 0.217930 0.377466i
\(759\) 0 0
\(760\) −6.00000 + 10.3923i −0.217643 + 0.376969i
\(761\) −11.0000 + 19.0526i −0.398750 + 0.690655i −0.993572 0.113203i \(-0.963889\pi\)
0.594822 + 0.803857i \(0.297222\pi\)
\(762\) −4.00000 −0.144905
\(763\) −2.00000 + 3.46410i −0.0724049 + 0.125409i
\(764\) 4.50000 + 7.79423i 0.162804 + 0.281985i
\(765\) 1.00000 + 1.73205i 0.0361551 + 0.0626224i
\(766\) −4.00000 −0.144526
\(767\) 7.00000 + 24.2487i 0.252755 + 0.875570i
\(768\) −1.00000 −0.0360844
\(769\) 20.0000 + 34.6410i 0.721218 + 1.24919i 0.960512 + 0.278240i \(0.0897509\pi\)
−0.239293 + 0.970947i \(0.576916\pi\)
\(770\) 0 0
\(771\) −5.50000 + 9.52628i −0.198078 + 0.343081i
\(772\) 10.0000 0.359908
\(773\) −15.0000 + 25.9808i −0.539513 + 0.934463i 0.459418 + 0.888220i \(0.348058\pi\)
−0.998930 + 0.0462427i \(0.985275\pi\)
\(774\) 1.50000 2.59808i 0.0539164 0.0933859i
\(775\) −5.00000 −0.179605
\(776\) 6.00000 10.3923i 0.215387 0.373062i
\(777\) −1.00000 1.73205i −0.0358748 0.0621370i
\(778\) −2.50000 4.33013i −0.0896293 0.155243i
\(779\) −60.0000 −2.14972
\(780\) −5.00000 + 5.19615i −0.179029 + 0.186052i