Properties

Label 546.2.l.c.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.c.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} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.50000 - 6.06218i) q^{17} -1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} +(1.00000 - 1.73205i) q^{20} -1.00000 q^{21} +(1.50000 - 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-2.50000 - 4.33013i) q^{29} +(-1.00000 + 1.73205i) q^{30} -2.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +7.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} +5.00000 q^{38} +(-1.00000 - 3.46410i) q^{39} +2.00000 q^{40} +(2.50000 + 4.33013i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-1.00000 + 1.73205i) q^{43} +3.00000 q^{44} +(1.00000 - 1.73205i) q^{45} +(3.00000 - 5.19615i) q^{46} -1.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} -7.00000 q^{51} +(-2.50000 + 2.59808i) q^{52} +3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(3.00000 + 5.19615i) q^{55} +(-0.500000 + 0.866025i) q^{56} -5.00000 q^{57} +(2.50000 - 4.33013i) q^{58} +(3.00000 - 5.19615i) q^{59} -2.00000 q^{60} +(-3.50000 + 6.06218i) q^{61} +(-1.00000 - 1.73205i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(-7.00000 - 1.73205i) q^{65} -3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(3.50000 + 6.06218i) q^{68} +(-3.00000 + 5.19615i) q^{69} -2.00000 q^{70} +(-4.00000 + 6.92820i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +(2.50000 + 4.33013i) q^{76} -3.00000 q^{77} +(2.50000 - 2.59808i) q^{78} +3.00000 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.50000 + 4.33013i) q^{82} -8.00000 q^{83} +(0.500000 - 0.866025i) q^{84} +(-7.00000 + 12.1244i) q^{85} -2.00000 q^{86} +(-2.50000 + 4.33013i) q^{87} +(1.50000 + 2.59808i) q^{88} +(5.50000 + 9.52628i) q^{89} +2.00000 q^{90} +(2.50000 - 2.59808i) q^{91} +6.00000 q^{92} +(1.00000 + 1.73205i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(-5.00000 + 8.66025i) q^{95} -1.00000 q^{96} +(1.00000 - 1.73205i) q^{97} +(0.500000 - 0.866025i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} - 4q^{5} + q^{6} + q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} - 4q^{5} + q^{6} + q^{7} - 2q^{8} - q^{9} - 2q^{10} - 3q^{11} + 2q^{12} + 7q^{13} + 2q^{14} + 2q^{15} - q^{16} + 7q^{17} - 2q^{18} + 5q^{19} + 2q^{20} - 2q^{21} + 3q^{22} - 6q^{23} + q^{24} - 2q^{25} + 2q^{26} + 2q^{27} + q^{28} - 5q^{29} - 2q^{30} - 4q^{31} + q^{32} - 3q^{33} + 14q^{34} - 2q^{35} - q^{36} + 2q^{37} + 10q^{38} - 2q^{39} + 4q^{40} + 5q^{41} - q^{42} - 2q^{43} + 6q^{44} + 2q^{45} + 6q^{46} - 2q^{47} - q^{48} - q^{49} - q^{50} - 14q^{51} - 5q^{52} + 6q^{53} + q^{54} + 6q^{55} - q^{56} - 10q^{57} + 5q^{58} + 6q^{59} - 4q^{60} - 7q^{61} - 2q^{62} + q^{63} + 2q^{64} - 14q^{65} - 6q^{66} - 2q^{67} + 7q^{68} - 6q^{69} - 4q^{70} - 8q^{71} + q^{72} + 24q^{73} - 2q^{74} + q^{75} + 5q^{76} - 6q^{77} + 5q^{78} + 6q^{79} + 2q^{80} - q^{81} - 5q^{82} - 16q^{83} + q^{84} - 14q^{85} - 4q^{86} - 5q^{87} + 3q^{88} + 11q^{89} + 4q^{90} + 5q^{91} + 12q^{92} + 2q^{93} - q^{94} - 10q^{95} - 2q^{96} + 2q^{97} + q^{98} + 6q^{99} + O(q^{100}) \)

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
\(5\) −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
\(11\) −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
\(15\) 1.00000 + 1.73205i 0.258199 + 0.447214i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.50000 6.06218i 0.848875 1.47029i −0.0333386 0.999444i \(-0.510614\pi\)
0.882213 0.470850i \(-0.156053\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.50000 4.33013i 0.573539 0.993399i −0.422659 0.906289i \(-0.638903\pi\)
0.996199 0.0871106i \(-0.0277634\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) −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
\(25\) −1.00000 −0.200000
\(26\) 1.00000 + 3.46410i 0.196116 + 0.679366i
\(27\) 1.00000 0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) −2.50000 4.33013i −0.464238 0.804084i 0.534928 0.844897i \(-0.320339\pi\)
−0.999167 + 0.0408130i \(0.987005\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 7.00000 1.20049
\(35\) −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 \(0.780765\pi\)
\(38\) 5.00000 0.811107
\(39\) −1.00000 3.46410i −0.160128 0.554700i
\(40\) 2.00000 0.316228
\(41\) 2.50000 + 4.33013i 0.390434 + 0.676252i 0.992507 0.122189i \(-0.0389915\pi\)
−0.602072 + 0.798441i \(0.705658\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −1.00000 + 1.73205i −0.152499 + 0.264135i −0.932145 0.362084i \(-0.882065\pi\)
0.779647 + 0.626219i \(0.215399\pi\)
\(44\) 3.00000 0.452267
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) −1.00000 −0.145865 −0.0729325 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) −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
\(51\) −7.00000 −0.980196
\(52\) −2.50000 + 2.59808i −0.346688 + 0.360288i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 3.00000 + 5.19615i 0.404520 + 0.700649i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) −5.00000 −0.662266
\(58\) 2.50000 4.33013i 0.328266 0.568574i
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) −2.00000 −0.258199
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) −1.00000 1.73205i −0.127000 0.219971i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) −7.00000 1.73205i −0.868243 0.214834i
\(66\) −3.00000 −0.369274
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 3.50000 + 6.06218i 0.424437 + 0.735147i
\(69\) −3.00000 + 5.19615i −0.361158 + 0.625543i
\(70\) −2.00000 −0.239046
\(71\) −4.00000 + 6.92820i −0.474713 + 0.822226i −0.999581 0.0289572i \(-0.990781\pi\)
0.524868 + 0.851184i \(0.324115\pi\)
\(72\) 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
\(76\) 2.50000 + 4.33013i 0.286770 + 0.496700i
\(77\) −3.00000 −0.341882
\(78\) 2.50000 2.59808i 0.283069 0.294174i
\(79\) 3.00000 0.337526 0.168763 0.985657i \(-0.446023\pi\)
0.168763 + 0.985657i \(0.446023\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.50000 + 4.33013i −0.276079 + 0.478183i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0.500000 0.866025i 0.0545545 0.0944911i
\(85\) −7.00000 + 12.1244i −0.759257 + 1.31507i
\(86\) −2.00000 −0.215666
\(87\) −2.50000 + 4.33013i −0.268028 + 0.464238i
\(88\) 1.50000 + 2.59808i 0.159901 + 0.276956i
\(89\) 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
\(91\) 2.50000 2.59808i 0.262071 0.272352i
\(92\) 6.00000 0.625543
\(93\) 1.00000 + 1.73205i 0.103695 + 0.179605i
\(94\) −0.500000 0.866025i −0.0515711 0.0893237i
\(95\) −5.00000 + 8.66025i −0.512989 + 0.888523i
\(96\) −1.00000 −0.102062
\(97\) 1.00000 1.73205i 0.101535 0.175863i −0.810782 0.585348i \(-0.800958\pi\)
0.912317 + 0.409484i \(0.134291\pi\)
\(98\) 0.500000 0.866025i 0.0505076 0.0874818i
\(99\) 3.00000 0.301511
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −7.00000 12.1244i −0.696526 1.20642i −0.969664 0.244443i \(-0.921395\pi\)
0.273138 0.961975i \(-0.411939\pi\)
\(102\) −3.50000 6.06218i −0.346552 0.600245i
\(103\) 10.0000 0.985329 0.492665 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) −3.50000 0.866025i −0.343203 0.0849208i
\(105\) 2.00000 0.195180
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) −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
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) −3.00000 + 5.19615i −0.286039 + 0.495434i
\(111\) 1.00000 1.73205i 0.0949158 0.164399i
\(112\) −1.00000 −0.0944911
\(113\) −3.00000 + 5.19615i −0.282216 + 0.488813i −0.971930 0.235269i \(-0.924403\pi\)
0.689714 + 0.724082i \(0.257736\pi\)
\(114\) −2.50000 4.33013i −0.234146 0.405554i
\(115\) 6.00000 + 10.3923i 0.559503 + 0.969087i
\(116\) 5.00000 0.464238
\(117\) −2.50000 + 2.59808i −0.231125 + 0.240192i
\(118\) 6.00000 0.552345
\(119\) −3.50000 6.06218i −0.320844 0.555719i
\(120\) −1.00000 1.73205i −0.0912871 0.158114i
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −7.00000 −0.633750
\(123\) 2.50000 4.33013i 0.225417 0.390434i
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) 12.0000 1.07331
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) 6.00000 + 10.3923i 0.532414 + 0.922168i 0.999284 + 0.0378419i \(0.0120483\pi\)
−0.466870 + 0.884326i \(0.654618\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 2.00000 0.176090
\(130\) −2.00000 6.92820i −0.175412 0.607644i
\(131\) 8.00000 0.698963 0.349482 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) −1.50000 2.59808i −0.130558 0.226134i
\(133\) −2.50000 4.33013i −0.216777 0.375470i
\(134\) 1.00000 1.73205i 0.0863868 0.149626i
\(135\) −2.00000 −0.172133
\(136\) −3.50000 + 6.06218i −0.300123 + 0.519827i
\(137\) −9.00000 + 15.5885i −0.768922 + 1.33181i 0.169226 + 0.985577i \(0.445873\pi\)
−0.938148 + 0.346235i \(0.887460\pi\)
\(138\) −6.00000 −0.510754
\(139\) 9.50000 16.4545i 0.805779 1.39565i −0.109984 0.993933i \(-0.535080\pi\)
0.915764 0.401718i \(-0.131587\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) 0.500000 + 0.866025i 0.0421076 + 0.0729325i
\(142\) −8.00000 −0.671345
\(143\) −3.00000 10.3923i −0.250873 0.869048i
\(144\) 1.00000 0.0833333
\(145\) 5.00000 + 8.66025i 0.415227 + 0.719195i
\(146\) 6.00000 + 10.3923i 0.496564 + 0.860073i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) −2.00000 −0.164399
\(149\) −7.00000 + 12.1244i −0.573462 + 0.993266i 0.422744 + 0.906249i \(0.361067\pi\)
−0.996207 + 0.0870170i \(0.972267\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 13.0000 1.05792 0.528962 0.848645i \(-0.322581\pi\)
0.528962 + 0.848645i \(0.322581\pi\)
\(152\) −2.50000 + 4.33013i −0.202777 + 0.351220i
\(153\) 3.50000 + 6.06218i 0.282958 + 0.490098i
\(154\) −1.50000 2.59808i −0.120873 0.209359i
\(155\) 4.00000 0.321288
\(156\) 3.50000 + 0.866025i 0.280224 + 0.0693375i
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 1.50000 + 2.59808i 0.119334 + 0.206692i
\(159\) −1.50000 2.59808i −0.118958 0.206041i
\(160\) −1.00000 + 1.73205i −0.0790569 + 0.136931i
\(161\) −6.00000 −0.472866
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 7.00000 12.1244i 0.548282 0.949653i −0.450110 0.892973i \(-0.648615\pi\)
0.998392 0.0566798i \(-0.0180514\pi\)
\(164\) −5.00000 −0.390434
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) −4.00000 6.92820i −0.310460 0.537733i
\(167\) 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
\(170\) −14.0000 −1.07375
\(171\) 2.50000 + 4.33013i 0.191180 + 0.331133i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) −6.00000 + 10.3923i −0.456172 + 0.790112i −0.998755 0.0498898i \(-0.984113\pi\)
0.542583 + 0.840002i \(0.317446\pi\)
\(174\) −5.00000 −0.379049
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) −1.50000 + 2.59808i −0.113067 + 0.195837i
\(177\) −6.00000 −0.450988
\(178\) −5.50000 + 9.52628i −0.412242 + 0.714025i
\(179\) −10.0000 17.3205i −0.747435 1.29460i −0.949048 0.315130i \(-0.897952\pi\)
0.201613 0.979465i \(-0.435382\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) −9.00000 −0.668965 −0.334482 0.942402i \(-0.608561\pi\)
−0.334482 + 0.942402i \(0.608561\pi\)
\(182\) 3.50000 + 0.866025i 0.259437 + 0.0641941i
\(183\) 7.00000 0.517455
\(184\) 3.00000 + 5.19615i 0.221163 + 0.383065i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) −1.00000 + 1.73205i −0.0733236 + 0.127000i
\(187\) −21.0000 −1.53567
\(188\) 0.500000 0.866025i 0.0364662 0.0631614i
\(189\) 0.500000 0.866025i 0.0363696 0.0629941i
\(190\) −10.0000 −0.725476
\(191\) 2.00000 3.46410i 0.144715 0.250654i −0.784552 0.620063i \(-0.787107\pi\)
0.929267 + 0.369410i \(0.120440\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) −6.50000 11.2583i −0.467880 0.810392i 0.531446 0.847092i \(-0.321649\pi\)
−0.999326 + 0.0366998i \(0.988315\pi\)
\(194\) 2.00000 0.143592
\(195\) 2.00000 + 6.92820i 0.143223 + 0.496139i
\(196\) 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
\(199\) 13.0000 22.5167i 0.921546 1.59616i 0.124521 0.992217i \(-0.460261\pi\)
0.797025 0.603947i \(-0.206406\pi\)
\(200\) 1.00000 0.0707107
\(201\) −1.00000 + 1.73205i −0.0705346 + 0.122169i
\(202\) 7.00000 12.1244i 0.492518 0.853067i
\(203\) −5.00000 −0.350931
\(204\) 3.50000 6.06218i 0.245049 0.424437i
\(205\) −5.00000 8.66025i −0.349215 0.604858i
\(206\) 5.00000 + 8.66025i 0.348367 + 0.603388i
\(207\) 6.00000 0.417029
\(208\) −1.00000 3.46410i −0.0693375 0.240192i
\(209\) −15.0000 −1.03757
\(210\) 1.00000 + 1.73205i 0.0690066 + 0.119523i
\(211\) 5.00000 + 8.66025i 0.344214 + 0.596196i 0.985211 0.171347i \(-0.0548120\pi\)
−0.640996 + 0.767544i \(0.721479\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 8.00000 0.548151
\(214\) 7.50000 12.9904i 0.512689 0.888004i
\(215\) 2.00000 3.46410i 0.136399 0.236250i
\(216\) −1.00000 −0.0680414
\(217\) −1.00000 + 1.73205i −0.0678844 + 0.117579i
\(218\) −8.00000 13.8564i −0.541828 0.938474i
\(219\) −6.00000 10.3923i −0.405442 0.702247i
\(220\) −6.00000 −0.404520
\(221\) 17.5000 18.1865i 1.17718 1.22336i
\(222\) 2.00000 0.134231
\(223\) 2.00000 + 3.46410i 0.133930 + 0.231973i 0.925188 0.379509i \(-0.123907\pi\)
−0.791258 + 0.611482i \(0.790574\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) −6.00000 −0.399114
\(227\) −7.00000 + 12.1244i −0.464606 + 0.804722i −0.999184 0.0403978i \(-0.987137\pi\)
0.534577 + 0.845120i \(0.320471\pi\)
\(228\) 2.50000 4.33013i 0.165567 0.286770i
\(229\) 27.0000 1.78421 0.892105 0.451828i \(-0.149228\pi\)
0.892105 + 0.451828i \(0.149228\pi\)
\(230\) −6.00000 + 10.3923i −0.395628 + 0.685248i
\(231\) 1.50000 + 2.59808i 0.0986928 + 0.170941i
\(232\) 2.50000 + 4.33013i 0.164133 + 0.284287i
\(233\) 26.0000 1.70332 0.851658 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) −3.50000 0.866025i −0.228802 0.0566139i
\(235\) 2.00000 0.130466
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) −1.50000 2.59808i −0.0974355 0.168763i
\(238\) 3.50000 6.06218i 0.226871 0.392953i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 1.00000 1.73205i 0.0645497 0.111803i
\(241\) −14.0000 + 24.2487i −0.901819 + 1.56200i −0.0766885 + 0.997055i \(0.524435\pi\)
−0.825131 + 0.564942i \(0.808899\pi\)
\(242\) 2.00000 0.128565
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −3.50000 6.06218i −0.224065 0.388091i
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) 5.00000 0.318788
\(247\) 12.5000 12.9904i 0.795356 0.826558i
\(248\) 2.00000 0.127000
\(249\) 4.00000 + 6.92820i 0.253490 + 0.439057i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 6.00000 10.3923i 0.378717 0.655956i −0.612159 0.790735i \(-0.709699\pi\)
0.990876 + 0.134778i \(0.0430322\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −9.00000 + 15.5885i −0.565825 + 0.980038i
\(254\) −6.00000 + 10.3923i −0.376473 + 0.652071i
\(255\) 14.0000 0.876714
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.50000 + 12.9904i 0.467837 + 0.810318i 0.999325 0.0367485i \(-0.0117000\pi\)
−0.531487 + 0.847066i \(0.678367\pi\)
\(258\) 1.00000 + 1.73205i 0.0622573 + 0.107833i
\(259\) 2.00000 0.124274
\(260\) 5.00000 5.19615i 0.310087 0.322252i
\(261\) 5.00000 0.309492
\(262\) 4.00000 + 6.92820i 0.247121 + 0.428026i
\(263\) 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) 1.50000 2.59808i 0.0923186 0.159901i
\(265\) −6.00000 −0.368577
\(266\) 2.50000 4.33013i 0.153285 0.265497i
\(267\) 5.50000 9.52628i 0.336595 0.582999i
\(268\) 2.00000 0.122169
\(269\) 12.0000 20.7846i 0.731653 1.26726i −0.224523 0.974469i \(-0.572083\pi\)
0.956176 0.292791i \(-0.0945841\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) −1.00000 1.73205i −0.0607457 0.105215i 0.834053 0.551684i \(-0.186015\pi\)
−0.894799 + 0.446469i \(0.852681\pi\)
\(272\) −7.00000 −0.424437
\(273\) −3.50000 0.866025i −0.211830 0.0524142i
\(274\) −18.0000 −1.08742
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) −3.00000 5.19615i −0.180579 0.312772i
\(277\) −3.00000 + 5.19615i −0.180253 + 0.312207i −0.941966 0.335707i \(-0.891025\pi\)
0.761714 + 0.647913i \(0.224358\pi\)
\(278\) 19.0000 1.13954
\(279\) 1.00000 1.73205i 0.0598684 0.103695i
\(280\) 1.00000 1.73205i 0.0597614 0.103510i
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) −0.500000 + 0.866025i −0.0297746 + 0.0515711i
\(283\) −14.0000 24.2487i −0.832214 1.44144i −0.896279 0.443491i \(-0.853740\pi\)
0.0640654 0.997946i \(-0.479593\pi\)
\(284\) −4.00000 6.92820i −0.237356 0.411113i
\(285\) 10.0000 0.592349
\(286\) 7.50000 7.79423i 0.443484 0.460882i
\(287\) 5.00000 0.295141
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) −5.00000 + 8.66025i −0.293610 + 0.508548i
\(291\) −2.00000 −0.117242
\(292\) −6.00000 + 10.3923i −0.351123 + 0.608164i
\(293\) −6.00000 + 10.3923i −0.350524 + 0.607125i −0.986341 0.164714i \(-0.947330\pi\)
0.635818 + 0.771839i \(0.280663\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −6.00000 + 10.3923i −0.349334 + 0.605063i
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) −1.50000 2.59808i −0.0870388 0.150756i
\(298\) −14.0000 −0.810998
\(299\) −6.00000 20.7846i −0.346989 1.20201i
\(300\) −1.00000 −0.0577350
\(301\) 1.00000 + 1.73205i 0.0576390 + 0.0998337i
\(302\) 6.50000 + 11.2583i 0.374033 + 0.647844i
\(303\) −7.00000 + 12.1244i −0.402139 + 0.696526i
\(304\) −5.00000 −0.286770
\(305\) 7.00000 12.1244i 0.400819 0.694239i
\(306\) −3.50000 + 6.06218i −0.200082 + 0.346552i
\(307\) 9.00000 0.513657 0.256829 0.966457i \(-0.417322\pi\)
0.256829 + 0.966457i \(0.417322\pi\)
\(308\) 1.50000 2.59808i 0.0854704 0.148039i
\(309\) −5.00000 8.66025i −0.284440 0.492665i
\(310\) 2.00000 + 3.46410i 0.113592 + 0.196748i
\(311\) 23.0000 1.30421 0.652105 0.758129i \(-0.273886\pi\)
0.652105 + 0.758129i \(0.273886\pi\)
\(312\) 1.00000 + 3.46410i 0.0566139 + 0.196116i
\(313\) 28.0000 1.58265 0.791327 0.611393i \(-0.209391\pi\)
0.791327 + 0.611393i \(0.209391\pi\)
\(314\) −9.00000 15.5885i −0.507899 0.879708i
\(315\) −1.00000 1.73205i −0.0563436 0.0975900i
\(316\) −1.50000 + 2.59808i −0.0843816 + 0.146153i
\(317\) 30.0000 1.68497 0.842484 0.538721i \(-0.181092\pi\)
0.842484 + 0.538721i \(0.181092\pi\)
\(318\) 1.50000 2.59808i 0.0841158 0.145693i
\(319\) −7.50000 + 12.9904i −0.419919 + 0.727322i
\(320\) −2.00000 −0.111803
\(321\) −7.50000 + 12.9904i −0.418609 + 0.725052i
\(322\) −3.00000 5.19615i −0.167183 0.289570i
\(323\) −17.5000 30.3109i −0.973726 1.68654i
\(324\) 1.00000 0.0555556
\(325\) −3.50000 0.866025i −0.194145 0.0480384i
\(326\) 14.0000 0.775388
\(327\) 8.00000 + 13.8564i 0.442401 + 0.766261i
\(328\) −2.50000 4.33013i −0.138039 0.239091i
\(329\) −0.500000 + 0.866025i −0.0275659 + 0.0477455i
\(330\) 6.00000 0.330289
\(331\) −11.0000 + 19.0526i −0.604615 + 1.04722i 0.387498 + 0.921871i \(0.373340\pi\)
−0.992112 + 0.125353i \(0.959994\pi\)
\(332\) 4.00000 6.92820i 0.219529 0.380235i
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) 2.00000 + 3.46410i 0.109272 + 0.189264i
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) −17.0000 −0.926049 −0.463025 0.886345i \(-0.653236\pi\)
−0.463025 + 0.886345i \(0.653236\pi\)
\(338\) 0.500000 + 12.9904i 0.0271964 + 0.706584i
\(339\) 6.00000 0.325875
\(340\) −7.00000 12.1244i −0.379628 0.657536i
\(341\) 3.00000 + 5.19615i 0.162459 + 0.281387i
\(342\) −2.50000 + 4.33013i −0.135185 + 0.234146i
\(343\) −1.00000 −0.0539949
\(344\) 1.00000 1.73205i 0.0539164 0.0933859i
\(345\) 6.00000 10.3923i 0.323029 0.559503i
\(346\) −12.0000 −0.645124
\(347\) −8.50000 + 14.7224i −0.456304 + 0.790342i −0.998762 0.0497412i \(-0.984160\pi\)
0.542458 + 0.840083i \(0.317494\pi\)
\(348\) −2.50000 4.33013i −0.134014 0.232119i
\(349\) 9.00000 + 15.5885i 0.481759 + 0.834431i 0.999781 0.0209364i \(-0.00666475\pi\)
−0.518022 + 0.855367i \(0.673331\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 3.50000 + 0.866025i 0.186816 + 0.0462250i
\(352\) −3.00000 −0.159901
\(353\) −7.00000 12.1244i −0.372572 0.645314i 0.617388 0.786659i \(-0.288191\pi\)
−0.989960 + 0.141344i \(0.954858\pi\)
\(354\) −3.00000 5.19615i −0.159448 0.276172i
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) −11.0000 −0.582999
\(357\) −3.50000 + 6.06218i −0.185240 + 0.320844i
\(358\) 10.0000 17.3205i 0.528516 0.915417i
\(359\) 18.0000 0.950004 0.475002 0.879985i \(-0.342447\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(360\) −1.00000 + 1.73205i −0.0527046 + 0.0912871i
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) −4.50000 7.79423i −0.236515 0.409656i
\(363\) −2.00000 −0.104973
\(364\) 1.00000 + 3.46410i 0.0524142 + 0.181568i
\(365\) −24.0000 −1.25622
\(366\) 3.50000 + 6.06218i 0.182948 + 0.316875i
\(367\) 5.00000 + 8.66025i 0.260998 + 0.452062i 0.966507 0.256639i \(-0.0826151\pi\)
−0.705509 + 0.708700i \(0.749282\pi\)
\(368\) −3.00000 + 5.19615i −0.156386 + 0.270868i
\(369\) −5.00000 −0.260290
\(370\) 2.00000 3.46410i 0.103975 0.180090i
\(371\) 1.50000 2.59808i 0.0778761 0.134885i
\(372\) −2.00000 −0.103695
\(373\) −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i \(-0.866355\pi\)
0.809591 + 0.586994i \(0.199689\pi\)
\(374\) −10.5000 18.1865i −0.542942 0.940403i
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 1.00000 0.0515711
\(377\) −5.00000 17.3205i −0.257513 0.892052i
\(378\) 1.00000 0.0514344
\(379\) 10.0000 + 17.3205i 0.513665 + 0.889695i 0.999874 + 0.0158521i \(0.00504609\pi\)
−0.486209 + 0.873843i \(0.661621\pi\)
\(380\) −5.00000 8.66025i −0.256495 0.444262i
\(381\) 6.00000 10.3923i 0.307389 0.532414i
\(382\) 4.00000 0.204658
\(383\) −15.5000 + 26.8468i −0.792013 + 1.37181i 0.132706 + 0.991155i \(0.457633\pi\)
−0.924719 + 0.380651i \(0.875700\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 6.00000 0.305788
\(386\) 6.50000 11.2583i 0.330841 0.573034i
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) 1.00000 + 1.73205i 0.0507673 + 0.0879316i
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) −5.00000 + 5.19615i −0.253185 + 0.263117i
\(391\) −42.0000 −2.12403
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) −4.00000 6.92820i −0.201773 0.349482i
\(394\) −4.50000 + 7.79423i −0.226707 + 0.392668i
\(395\) −6.00000 −0.301893
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) 7.50000 12.9904i 0.376414 0.651969i −0.614123 0.789210i \(-0.710490\pi\)
0.990538 + 0.137241i \(0.0438236\pi\)
\(398\) 26.0000 1.30326
\(399\) −2.50000 + 4.33013i −0.125157 + 0.216777i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) −2.00000 −0.0997509
\(403\) −7.00000 1.73205i −0.348695 0.0862796i
\(404\) 14.0000 0.696526
\(405\) 1.00000 + 1.73205i 0.0496904 + 0.0860663i
\(406\) −2.50000 4.33013i −0.124073 0.214901i
\(407\) 3.00000 5.19615i 0.148704 0.257564i
\(408\) 7.00000 0.346552
\(409\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(410\) 5.00000 8.66025i 0.246932 0.427699i
\(411\) 18.0000 0.887875
\(412\) −5.00000 + 8.66025i −0.246332 + 0.426660i
\(413\) −3.00000 5.19615i −0.147620 0.255686i
\(414\) 3.00000 + 5.19615i 0.147442 + 0.255377i
\(415\) 16.0000 0.785409
\(416\) 2.50000 2.59808i 0.122573 0.127381i
\(417\) −19.0000 −0.930434
\(418\) −7.50000 12.9904i −0.366837 0.635380i
\(419\) −2.00000 3.46410i −0.0977064 0.169232i 0.813029 0.582224i \(-0.197817\pi\)
−0.910735 + 0.412991i \(0.864484\pi\)
\(420\) −1.00000 + 1.73205i −0.0487950 + 0.0845154i
\(421\) −22.0000 −1.07221 −0.536107 0.844150i \(-0.680106\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) −5.00000 + 8.66025i −0.243396 + 0.421575i
\(423\) 0.500000 0.866025i 0.0243108 0.0421076i
\(424\) −3.00000 −0.145693
\(425\) −3.50000 + 6.06218i −0.169775 + 0.294059i
\(426\) 4.00000 + 6.92820i 0.193801 + 0.335673i
\(427\) 3.50000 + 6.06218i 0.169377 + 0.293369i
\(428\) 15.0000 0.725052
\(429\) −7.50000 + 7.79423i −0.362103 + 0.376309i
\(430\) 4.00000 0.192897
\(431\) 4.00000 + 6.92820i 0.192673 + 0.333720i 0.946135 0.323772i \(-0.104951\pi\)
−0.753462 + 0.657491i \(0.771618\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −13.0000 + 22.5167i −0.624740 + 1.08208i 0.363851 + 0.931457i \(0.381462\pi\)
−0.988591 + 0.150624i \(0.951872\pi\)
\(434\) −2.00000 −0.0960031
\(435\) 5.00000 8.66025i 0.239732 0.415227i
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) −30.0000 −1.43509
\(438\) 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 \(0.863764\pi\)
\(440\) −3.00000 5.19615i −0.143019 0.247717i
\(441\) 1.00000 0.0476190
\(442\) 24.5000 + 6.06218i 1.16535 + 0.288348i
\(443\) 15.0000 0.712672 0.356336 0.934358i \(-0.384026\pi\)
0.356336 + 0.934358i \(0.384026\pi\)
\(444\) 1.00000 + 1.73205i 0.0474579 + 0.0821995i
\(445\) −11.0000 19.0526i −0.521450 0.903178i
\(446\) −2.00000 + 3.46410i −0.0947027 + 0.164030i
\(447\) 14.0000 0.662177
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) 19.0000 32.9090i 0.896665 1.55307i 0.0649356 0.997889i \(-0.479316\pi\)
0.831730 0.555181i \(-0.187351\pi\)
\(450\) 1.00000 0.0471405
\(451\) 7.50000 12.9904i 0.353161 0.611693i
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) −6.50000 11.2583i −0.305397 0.528962i
\(454\) −14.0000 −0.657053
\(455\) −5.00000 + 5.19615i −0.234404 + 0.243599i
\(456\) 5.00000 0.234146
\(457\) −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i \(-0.958593\pi\)
0.383437 0.923567i \(-0.374740\pi\)
\(458\) 13.5000 + 23.3827i 0.630814 + 1.09260i
\(459\) 3.50000 6.06218i 0.163366 0.282958i
\(460\) −12.0000 −0.559503
\(461\) −4.00000 + 6.92820i −0.186299 + 0.322679i −0.944013 0.329907i \(-0.892983\pi\)
0.757715 + 0.652586i \(0.226316\pi\)
\(462\) −1.50000 + 2.59808i −0.0697863 + 0.120873i
\(463\) −31.0000 −1.44069 −0.720346 0.693615i \(-0.756017\pi\)
−0.720346 + 0.693615i \(0.756017\pi\)
\(464\) −2.50000 + 4.33013i −0.116060 + 0.201021i
\(465\) −2.00000 3.46410i −0.0927478 0.160644i
\(466\) 13.0000 + 22.5167i 0.602213 + 1.04306i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −1.00000 3.46410i −0.0462250 0.160128i
\(469\) −2.00000 −0.0923514
\(470\) 1.00000 + 1.73205i 0.0461266 + 0.0798935i
\(471\) 9.00000 + 15.5885i 0.414698 + 0.718278i
\(472\) −3.00000 + 5.19615i −0.138086 + 0.239172i
\(473\) 6.00000 0.275880
\(474\) 1.50000 2.59808i 0.0688973 0.119334i
\(475\) −2.50000 + 4.33013i −0.114708 + 0.198680i
\(476\) 7.00000 0.320844
\(477\) −1.50000 + 2.59808i −0.0686803 + 0.118958i
\(478\) 6.00000 + 10.3923i 0.274434 + 0.475333i
\(479\) −10.5000 18.1865i −0.479757 0.830964i 0.519973 0.854183i \(-0.325942\pi\)
−0.999730 + 0.0232187i \(0.992609\pi\)
\(480\) 2.00000 0.0912871
\(481\) 2.00000 + 6.92820i 0.0911922 + 0.315899i
\(482\) −28.0000 −1.27537
\(483\) 3.00000 + 5.19615i 0.136505 + 0.236433i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) −2.00000 + 3.46410i −0.0908153 + 0.157297i
\(486\) −1.00000 −0.0453609
\(487\) −17.5000 + 30.3109i −0.793001 + 1.37352i 0.131100 + 0.991369i \(0.458149\pi\)
−0.924101 + 0.382148i \(0.875184\pi\)
\(488\) 3.50000 6.06218i 0.158438 0.274422i
\(489\) −14.0000 −0.633102
\(490\) −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 \(0.775556\pi\)
\(492\) 2.50000 + 4.33013i 0.112709 + 0.195217i
\(493\) −35.0000 −1.57632
\(494\) 17.5000 + 4.33013i 0.787362 + 0.194822i
\(495\) −6.00000 −0.269680
\(496\) 1.00000 + 1.73205i 0.0449013 + 0.0777714i
\(497\) 4.00000 + 6.92820i 0.179425 + 0.310772i
\(498\) −4.00000 + 6.92820i −0.179244 + 0.310460i
\(499\) 14.0000 0.626726 0.313363 0.949633i \(-0.398544\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) 12.0000 0.535586
\(503\) −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
\(505\) 14.0000 + 24.2487i 0.622992 + 1.07905i
\(506\) −18.0000 −0.800198
\(507\) −0.500000 12.9904i −0.0222058 0.576923i
\(508\) −12.0000 −0.532414
\(509\) 20.0000 + 34.6410i 0.886484 + 1.53544i 0.844003 + 0.536339i \(0.180193\pi\)
0.0424816 + 0.999097i \(0.486474\pi\)
\(510\) 7.00000 + 12.1244i 0.309965 + 0.536875i
\(511\) 6.00000 10.3923i 0.265424 0.459728i
\(512\) −1.00000 −0.0441942
\(513\) 2.50000 4.33013i 0.110378 0.191180i
\(514\) −7.50000 + 12.9904i −0.330811 + 0.572981i
\(515\) −20.0000 −0.881305
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 1.50000 + 2.59808i 0.0659699 + 0.114263i
\(518\) 1.00000 + 1.73205i 0.0439375 + 0.0761019i
\(519\) 12.0000 0.526742
\(520\) 7.00000 + 1.73205i 0.306970 + 0.0759555i
\(521\) 21.0000 0.920027 0.460013 0.887912i \(-0.347845\pi\)
0.460013 + 0.887912i \(0.347845\pi\)
\(522\) 2.50000 + 4.33013i 0.109422 + 0.189525i
\(523\) −19.5000 33.7750i −0.852675 1.47688i −0.878785 0.477218i \(-0.841645\pi\)
0.0261094 0.999659i \(-0.491688\pi\)
\(524\) −4.00000 + 6.92820i −0.174741 + 0.302660i
\(525\) 1.00000 0.0436436
\(526\) −12.0000 + 20.7846i −0.523225 + 0.906252i
\(527\) −7.00000 + 12.1244i −0.304925 + 0.528145i
\(528\) 3.00000 0.130558
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −3.00000 5.19615i −0.130312 0.225706i
\(531\) 3.00000 + 5.19615i 0.130189 + 0.225494i
\(532\) 5.00000 0.216777
\(533\) 5.00000 + 17.3205i 0.216574 + 0.750234i
\(534\) 11.0000 0.476017
\(535\) 15.0000 + 25.9808i 0.648507 + 1.12325i
\(536\) 1.00000 + 1.73205i 0.0431934 + 0.0748132i
\(537\) −10.0000 + 17.3205i −0.431532 + 0.747435i
\(538\) 24.0000 1.03471
\(539\) −1.50000 + 2.59808i −0.0646096 + 0.111907i
\(540\) 1.00000 1.73205i 0.0430331 0.0745356i
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 1.00000 1.73205i 0.0429537 0.0743980i
\(543\) 4.50000 + 7.79423i 0.193113 + 0.334482i
\(544\) −3.50000 6.06218i −0.150061 0.259914i
\(545\) 32.0000 1.37073
\(546\) −1.00000 3.46410i −0.0427960 0.148250i
\(547\) −32.0000 −1.36822 −0.684111 0.729378i \(-0.739809\pi\)
−0.684111 + 0.729378i \(0.739809\pi\)
\(548\) −9.00000 15.5885i −0.384461 0.665906i
\(549\) −3.50000 6.06218i −0.149376 0.258727i
\(550\) −1.50000 + 2.59808i −0.0639602 + 0.110782i
\(551\) −25.0000 −1.06504
\(552\) 3.00000 5.19615i 0.127688 0.221163i
\(553\) 1.50000 2.59808i 0.0637865 0.110481i
\(554\) −6.00000 −0.254916
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) 9.50000 + 16.4545i 0.402890 + 0.697826i
\(557\) 7.50000 + 12.9904i 0.317785 + 0.550420i 0.980026 0.198871i \(-0.0637276\pi\)
−0.662240 + 0.749291i \(0.730394\pi\)
\(558\) 2.00000 0.0846668
\(559\) −5.00000 + 5.19615i −0.211477 + 0.219774i
\(560\) 2.00000 0.0845154
\(561\) 10.5000 + 18.1865i 0.443310 + 0.767836i
\(562\) 8.00000 + 13.8564i 0.337460 + 0.584497i
\(563\) −15.0000 + 25.9808i −0.632175 + 1.09496i 0.354932 + 0.934892i \(0.384504\pi\)
−0.987106 + 0.160066i \(0.948829\pi\)
\(564\) −1.00000 −0.0421076
\(565\) 6.00000 10.3923i 0.252422 0.437208i
\(566\) 14.0000 24.2487i 0.588464 1.01925i
\(567\) −1.00000 −0.0419961
\(568\) 4.00000 6.92820i 0.167836 0.290701i
\(569\) 22.0000 + 38.1051i 0.922288 + 1.59745i 0.795866 + 0.605473i \(0.207016\pi\)
0.126422 + 0.991977i \(0.459651\pi\)
\(570\) 5.00000 + 8.66025i 0.209427 + 0.362738i
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 10.5000 + 2.59808i 0.439027 + 0.108631i
\(573\) −4.00000 −0.167102
\(574\) 2.50000 + 4.33013i 0.104348 + 0.180736i
\(575\) 3.00000 + 5.19615i 0.125109 + 0.216695i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 20.0000 0.832611 0.416305 0.909225i \(-0.363325\pi\)
0.416305 + 0.909225i \(0.363325\pi\)
\(578\) 16.0000 27.7128i 0.665512 1.15270i
\(579\) −6.50000 + 11.2583i −0.270131 + 0.467880i
\(580\) −10.0000 −0.415227
\(581\) −4.00000 + 6.92820i −0.165948 + 0.287430i
\(582\) −1.00000 1.73205i −0.0414513 0.0717958i
\(583\) −4.50000 7.79423i −0.186371 0.322804i
\(584\) −12.0000 −0.496564
\(585\) 5.00000 5.19615i 0.206725 0.214834i
\(586\) −12.0000 −0.495715
\(587\) −5.00000 8.66025i −0.206372 0.357447i 0.744197 0.667960i \(-0.232832\pi\)
−0.950569 + 0.310513i \(0.899499\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) −12.0000 −0.494032
\(591\) 4.50000 7.79423i 0.185105 0.320612i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −13.0000 −0.533846 −0.266923 0.963718i \(-0.586007\pi\)
−0.266923 + 0.963718i \(0.586007\pi\)
\(594\) 1.50000 2.59808i 0.0615457 0.106600i
\(595\) 7.00000 + 12.1244i 0.286972 + 0.497050i
\(596\) −7.00000 12.1244i −0.286731 0.496633i
\(597\) −26.0000 −1.06411
\(598\) 15.0000 15.5885i 0.613396 0.637459i
\(599\) −26.0000 −1.06233 −0.531166 0.847268i \(-0.678246\pi\)
−0.531166 + 0.847268i \(0.678246\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) −19.0000 32.9090i −0.775026 1.34238i −0.934780 0.355228i \(-0.884403\pi\)
0.159754 0.987157i \(-0.448930\pi\)
\(602\) −1.00000 + 1.73205i −0.0407570 + 0.0705931i
\(603\) 2.00000 0.0814463
\(604\) −6.50000 + 11.2583i −0.264481 + 0.458095i
\(605\) −2.00000 + 3.46410i −0.0813116 + 0.140836i
\(606\) −14.0000 −0.568711
\(607\) 15.0000 25.9808i 0.608831 1.05453i −0.382602 0.923913i \(-0.624972\pi\)
0.991433 0.130613i \(-0.0416947\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 2.50000 + 4.33013i 0.101305 + 0.175466i
\(610\) 14.0000 0.566843
\(611\) −3.50000 0.866025i −0.141595 0.0350356i
\(612\) −7.00000 −0.282958
\(613\) 14.0000 + 24.2487i 0.565455 + 0.979396i 0.997007 + 0.0773084i \(0.0246326\pi\)
−0.431553 + 0.902088i \(0.642034\pi\)
\(614\) 4.50000 + 7.79423i 0.181605 + 0.314549i
\(615\) −5.00000 + 8.66025i −0.201619 + 0.349215i
\(616\) 3.00000 0.120873
\(617\) 10.0000 17.3205i 0.402585 0.697297i −0.591452 0.806340i \(-0.701445\pi\)
0.994037 + 0.109043i \(0.0347785\pi\)
\(618\) 5.00000 8.66025i 0.201129 0.348367i
\(619\) 41.0000 1.64793 0.823965 0.566641i \(-0.191757\pi\)
0.823965 + 0.566641i \(0.191757\pi\)
\(620\) −2.00000 + 3.46410i −0.0803219 + 0.139122i
\(621\) −3.00000 5.19615i −0.120386 0.208514i
\(622\) 11.5000 + 19.9186i 0.461108 + 0.798662i
\(623\) 11.0000 0.440706
\(624\) −2.50000 + 2.59808i −0.100080 + 0.104006i
\(625\) −19.0000 −0.760000
\(626\) 14.0000 + 24.2487i 0.559553 + 0.969173i
\(627\) 7.50000 + 12.9904i 0.299521 + 0.518786i
\(628\) 9.00000 15.5885i 0.359139 0.622047i
\(629\) 14.0000 0.558217
\(630\) 1.00000 1.73205i 0.0398410 0.0690066i
\(631\) −7.50000 + 12.9904i −0.298570 + 0.517139i −0.975809 0.218624i \(-0.929843\pi\)
0.677239 + 0.735763i \(0.263176\pi\)
\(632\) −3.00000 −0.119334
\(633\) 5.00000 8.66025i 0.198732 0.344214i
\(634\) 15.0000 + 25.9808i 0.595726 + 1.03183i
\(635\) −12.0000 20.7846i −0.476205 0.824812i
\(636\) 3.00000 0.118958
\(637\) −1.00000 3.46410i −0.0396214 0.137253i
\(638\) −15.0000 −0.593856
\(639\) −4.00000 6.92820i −0.158238 0.274075i
\(640\) −1.00000 1.73205i −0.0395285 0.0684653i
\(641\) −9.00000 + 15.5885i −0.355479 + 0.615707i −0.987200 0.159489i \(-0.949015\pi\)
0.631721 + 0.775196i \(0.282349\pi\)
\(642\) −15.0000 −0.592003
\(643\) 24.5000 42.4352i 0.966186 1.67348i 0.259791 0.965665i \(-0.416346\pi\)
0.706395 0.707818i \(-0.250320\pi\)
\(644\) 3.00000 5.19615i 0.118217 0.204757i
\(645\) −4.00000 −0.157500
\(646\) 17.5000 30.3109i 0.688528 1.19257i
\(647\) −0.500000 0.866025i −0.0196570 0.0340470i 0.856030 0.516927i \(-0.172924\pi\)
−0.875687 + 0.482880i \(0.839591\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −18.0000 −0.706562
\(650\) −1.00000 3.46410i −0.0392232 0.135873i
\(651\) 2.00000 0.0783862
\(652\) 7.00000 + 12.1244i 0.274141 + 0.474826i
\(653\) −13.5000 23.3827i −0.528296 0.915035i −0.999456 0.0329874i \(-0.989498\pi\)
0.471160 0.882048i \(-0.343835\pi\)
\(654\) −8.00000 + 13.8564i −0.312825 + 0.541828i
\(655\) −16.0000 −0.625172
\(656\) 2.50000 4.33013i 0.0976086 0.169063i
\(657\) −6.00000 + 10.3923i −0.234082 + 0.405442i
\(658\) −1.00000 −0.0389841
\(659\) 13.5000 23.3827i 0.525885 0.910860i −0.473660 0.880708i \(-0.657067\pi\)
0.999545 0.0301523i \(-0.00959924\pi\)
\(660\) 3.00000 + 5.19615i 0.116775 + 0.202260i
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) −22.0000 −0.855054
\(663\) −24.5000 6.06218i −0.951501 0.235435i
\(664\) 8.00000 0.310460
\(665\) 5.00000 + 8.66025i 0.193892 + 0.335830i
\(666\) −1.00000 1.73205i −0.0387492 0.0671156i
\(667\) −15.0000 + 25.9808i −0.580802 + 1.00598i
\(668\) 0 0
\(669\) 2.00000 3.46410i 0.0773245 0.133930i
\(670\) −2.00000 + 3.46410i −0.0772667 + 0.133830i
\(671\) 21.0000 0.810696
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) −11.5000 19.9186i −0.443292 0.767805i 0.554639 0.832091i \(-0.312856\pi\)
−0.997932 + 0.0642860i \(0.979523\pi\)
\(674\) −8.50000 14.7224i −0.327408 0.567087i
\(675\) −1.00000 −0.0384900
\(676\) −11.0000 + 6.92820i −0.423077 + 0.266469i
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 3.00000 + 5.19615i 0.115214 + 0.199557i
\(679\) −1.00000 1.73205i −0.0383765 0.0664700i
\(680\) 7.00000 12.1244i 0.268438 0.464948i
\(681\) 14.0000 0.536481
\(682\) −3.00000 + 5.19615i −0.114876 + 0.198971i
\(683\) −18.0000 + 31.1769i −0.688751 + 1.19295i 0.283491 + 0.958975i \(0.408507\pi\)
−0.972242 + 0.233977i \(0.924826\pi\)
\(684\) −5.00000 −0.191180
\(685\) 18.0000 31.1769i 0.687745 1.19121i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) −13.5000 23.3827i −0.515057 0.892105i
\(688\) 2.00000 0.0762493
\(689\) 10.5000 + 2.59808i 0.400018 + 0.0989788i
\(690\) 12.0000 0.456832
\(691\) −20.0000 34.6410i −0.760836 1.31781i −0.942420 0.334431i \(-0.891456\pi\)
0.181584 0.983375i \(-0.441877\pi\)
\(692\) −6.00000 10.3923i −0.228086 0.395056i
\(693\) 1.50000 2.59808i 0.0569803 0.0986928i
\(694\) −17.0000 −0.645311
\(695\) −19.0000 + 32.9090i −0.720711 + 1.24831i
\(696\) 2.50000 4.33013i 0.0947623 0.164133i
\(697\) 35.0000 1.32572
\(698\) −9.00000 + 15.5885i −0.340655 + 0.590032i
\(699\) −13.0000 22.5167i −0.491705 0.851658i
\(700\) −0.500000 0.866025i −0.0188982 0.0327327i
\(701\) 13.0000 0.491003 0.245502 0.969396i \(-0.421047\pi\)
0.245502 + 0.969396i \(0.421047\pi\)
\(702\) 1.00000 + 3.46410i 0.0377426 + 0.130744i
\(703\) 10.0000 0.377157
\(704\) −1.50000 2.59808i −0.0565334 0.0979187i
\(705\) −1.00000 1.73205i −0.0376622 0.0652328i
\(706\) 7.00000 12.1244i 0.263448 0.456306i
\(707\) −14.0000 −0.526524
\(708\) 3.00000 5.19615i 0.112747 0.195283i
\(709\) 14.0000 24.2487i 0.525781 0.910679i −0.473768 0.880650i \(-0.657106\pi\)
0.999549 0.0300298i \(-0.00956021\pi\)
\(710\) 16.0000 0.600469
\(711\) −1.50000 + 2.59808i −0.0562544 + 0.0974355i
\(712\) −5.50000 9.52628i −0.206121 0.357012i
\(713\) 6.00000 + 10.3923i 0.224702 + 0.389195i
\(714\) −7.00000 −0.261968
\(715\) 6.00000 + 20.7846i 0.224387 + 0.777300i
\(716\) 20.0000 0.747435
\(717\) −6.00000 10.3923i −0.224074 0.388108i
\(718\) 9.00000 + 15.5885i 0.335877 + 0.581756i
\(719\) 7.50000 12.9904i 0.279703 0.484459i −0.691608 0.722273i \(-0.743097\pi\)
0.971311 + 0.237814i \(0.0764307\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 5.00000 8.66025i 0.186210 0.322525i
\(722\) 3.00000 5.19615i 0.111648 0.193381i
\(723\) 28.0000 1.04133
\(724\) 4.50000 7.79423i 0.167241 0.289670i
\(725\) 2.50000 + 4.33013i 0.0928477 + 0.160817i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) −2.50000 + 2.59808i −0.0926562 + 0.0962911i
\(729\) 1.00000 0.0370370
\(730\) −12.0000 20.7846i −0.444140 0.769273i
\(731\) 7.00000 + 12.1244i 0.258904 + 0.448435i
\(732\) −3.50000 + 6.06218i −0.129364 + 0.224065i
\(733\) −7.00000 −0.258551 −0.129275 0.991609i \(-0.541265\pi\)
−0.129275 + 0.991609i \(0.541265\pi\)
\(734\) −5.00000 + 8.66025i −0.184553 + 0.319656i
\(735\) 1.00000 1.73205i 0.0368856 0.0638877i
\(736\) −6.00000 −0.221163
\(737\) −3.00000 + 5.19615i −0.110506 + 0.191403i
\(738\) −2.50000 4.33013i −0.0920263 0.159394i
\(739\) 7.00000 + 12.1244i 0.257499 + 0.446002i 0.965571 0.260138i \(-0.0837682\pi\)
−0.708072 + 0.706140i \(0.750435\pi\)
\(740\) 4.00000 0.147043
\(741\) −17.5000 4.33013i −0.642879 0.159071i
\(742\) 3.00000 0.110133
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) −1.00000 1.73205i −0.0366618 0.0635001i
\(745\) 14.0000 24.2487i 0.512920 0.888404i
\(746\) −4.00000 −0.146450
\(747\) 4.00000 6.92820i 0.146352 0.253490i
\(748\) 10.5000 18.1865i 0.383918 0.664966i
\(749\) −15.0000 −0.548088
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) 16.5000 + 28.5788i 0.602094 + 1.04286i 0.992504 + 0.122216i \(0.0389999\pi\)
−0.390410 + 0.920641i \(0.627667\pi\)
\(752\) 0.500000 + 0.866025i 0.0182331 + 0.0315807i
\(753\) −12.0000 −0.437304
\(754\) 12.5000 12.9904i 0.455223 0.473082i
\(755\) −26.0000 −0.946237
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) −16.0000 27.7128i −0.581530 1.00724i −0.995298 0.0968571i \(-0.969121\pi\)
0.413768 0.910382i \(-0.364212\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 18.0000 0.653359
\(760\) 5.00000 8.66025i 0.181369 0.314140i
\(761\) 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i \(-0.727548\pi\)
0.981764 + 0.190101i \(0.0608816\pi\)
\(762\) 12.0000 0.434714
\(763\) −8.00000 + 13.8564i −0.289619 + 0.501636i
\(764\) 2.00000 + 3.46410i 0.0723575 + 0.125327i
\(765\) −7.00000 12.1244i −0.253086 0.438357i
\(766\) −31.0000 −1.12008
\(767\) 15.0000 15.5885i 0.541619 0.562867i
\(768\) 1.00000 0.0360844
\(769\) −23.0000 39.8372i −0.829401 1.43657i −0.898509 0.438956i \(-0.855348\pi\)
0.0691074 0.997609i \(-0.477985\pi\)
\(770\) 3.00000 + 5.19615i 0.108112 + 0.187256i
\(771\) 7.50000 12.9904i 0.270106 0.467837i
\(772\) 13.0000 0.467880
\(773\) 5.00000 8.66025i 0.179838 0.311488i −0.761987 0.647592i \(-0.775776\pi\)
0.941825 + 0.336104i \(0.109109\pi\)
\(774\) 1.00000 1.73205i 0.0359443 0.0622573i
\(775\) 2.00000 0.0718421
\(776\) −1.00000 + 1.73205i −0.0358979 + 0.0621770i
\(777\)