Properties

Label 390.2.i.c.211.1
Level $390$
Weight $2$
Character 390.211
Analytic conductor $3.114$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
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 \(\chi\) \(=\) 390.211
Dual form 390.2.i.c.61.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +1.00000 q^{12} +(1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(0.500000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} -1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 - 0.866025i) q^{20} +2.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +1.00000 q^{25} +(-2.50000 + 2.59808i) q^{26} +1.00000 q^{27} +(-1.00000 - 1.73205i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(-0.500000 + 0.866025i) q^{30} +5.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(1.50000 - 2.59808i) q^{33} -6.00000 q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.50000 + 6.06218i) q^{37} -2.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +1.00000 q^{40} +(-3.00000 - 5.19615i) q^{41} +(1.00000 + 1.73205i) q^{42} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +(0.500000 - 0.866025i) q^{45} +(1.50000 - 2.59808i) q^{46} -3.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.500000 + 0.866025i) q^{50} +6.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} -6.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(1.00000 - 1.73205i) q^{56} +2.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(4.50000 - 7.79423i) q^{59} -1.00000 q^{60} +(-1.00000 + 1.73205i) q^{61} +(2.50000 + 4.33013i) q^{62} +(-1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 - 3.46410i) q^{65} +3.00000 q^{66} +(-4.00000 - 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{69} +2.00000 q^{70} +(6.00000 - 10.3923i) q^{71} +(0.500000 - 0.866025i) q^{72} +14.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} -6.00000 q^{77} +(3.50000 + 0.866025i) q^{78} +5.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(-1.00000 + 1.73205i) q^{84} +(3.00000 - 5.19615i) q^{85} +1.00000 q^{86} +(-1.50000 + 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(9.00000 + 15.5885i) q^{89} +1.00000 q^{90} +(-7.00000 - 1.73205i) q^{91} +3.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(1.00000 - 1.73205i) q^{95} -1.00000 q^{96} +(-7.00000 + 12.1244i) q^{97} +(-1.50000 + 2.59808i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} - 2q^{5} + q^{6} - 2q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} - 2q^{5} + q^{6} - 2q^{7} - 2q^{8} - q^{9} - q^{10} + 3q^{11} + 2q^{12} + 2q^{13} - 4q^{14} + q^{15} - q^{16} - 6q^{17} - 2q^{18} - 2q^{19} + q^{20} + 4q^{21} - 3q^{22} - 3q^{23} + q^{24} + 2q^{25} - 5q^{26} + 2q^{27} - 2q^{28} - 3q^{29} - q^{30} + 10q^{31} + q^{32} + 3q^{33} - 12q^{34} + 2q^{35} - q^{36} + 7q^{37} - 4q^{38} + 5q^{39} + 2q^{40} - 6q^{41} + 2q^{42} + q^{43} - 6q^{44} + q^{45} + 3q^{46} - 6q^{47} - q^{48} + 3q^{49} + q^{50} + 12q^{51} - 7q^{52} - 12q^{53} + q^{54} - 3q^{55} + 2q^{56} + 4q^{57} + 3q^{58} + 9q^{59} - 2q^{60} - 2q^{61} + 5q^{62} - 2q^{63} + 2q^{64} - 2q^{65} + 6q^{66} - 8q^{67} - 6q^{68} - 3q^{69} + 4q^{70} + 12q^{71} + q^{72} + 28q^{73} - 7q^{74} - q^{75} - 2q^{76} - 12q^{77} + 7q^{78} + 10q^{79} + q^{80} - q^{81} + 6q^{82} - 12q^{83} - 2q^{84} + 6q^{85} + 2q^{86} - 3q^{87} - 3q^{88} + 18q^{89} + 2q^{90} - 14q^{91} + 6q^{92} - 5q^{93} - 3q^{94} + 2q^{95} - 2q^{96} - 14q^{97} - 3q^{98} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) −1.00000 −0.447214
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) −1.00000 + 1.73205i −0.377964 + 0.654654i −0.990766 0.135583i \(-0.956709\pi\)
0.612801 + 0.790237i \(0.290043\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) 1.50000 + 2.59808i 0.452267 + 0.783349i 0.998526 0.0542666i \(-0.0172821\pi\)
−0.546259 + 0.837616i \(0.683949\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 + 3.46410i 0.277350 + 0.960769i
\(14\) −2.00000 −0.534522
\(15\) 0.500000 + 0.866025i 0.129099 + 0.223607i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0.500000 0.866025i 0.111803 0.193649i
\(21\) 2.00000 0.436436
\(22\) −1.50000 + 2.59808i −0.319801 + 0.553912i
\(23\) −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
\(26\) −2.50000 + 2.59808i −0.490290 + 0.509525i
\(27\) 1.00000 0.192450
\(28\) −1.00000 1.73205i −0.188982 0.327327i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 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
\(33\) 1.50000 2.59808i 0.261116 0.452267i
\(34\) −6.00000 −1.02899
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) −2.00000 −0.324443
\(39\) 2.50000 2.59808i 0.400320 0.416025i
\(40\) 1.00000 0.158114
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) 1.00000 + 1.73205i 0.154303 + 0.267261i
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 0.500000 + 0.866025i 0.0707107 + 0.122474i
\(51\) 6.00000 0.840168
\(52\) −3.50000 0.866025i −0.485363 0.120096i
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −1.50000 2.59808i −0.202260 0.350325i
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 2.00000 0.264906
\(58\) 1.50000 2.59808i 0.196960 0.341144i
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) −1.00000 −0.129099
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) 2.50000 + 4.33013i 0.317500 + 0.549927i
\(63\) −1.00000 1.73205i −0.125988 0.218218i
\(64\) 1.00000 0.125000
\(65\) −1.00000 3.46410i −0.124035 0.429669i
\(66\) 3.00000 0.369274
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) −1.50000 + 2.59808i −0.180579 + 0.312772i
\(70\) 2.00000 0.239046
\(71\) 6.00000 10.3923i 0.712069 1.23334i −0.252010 0.967725i \(-0.581092\pi\)
0.964079 0.265615i \(-0.0855750\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) −6.00000 −0.683763
\(78\) 3.50000 + 0.866025i 0.396297 + 0.0980581i
\(79\) 5.00000 0.562544 0.281272 0.959628i \(-0.409244\pi\)
0.281272 + 0.959628i \(0.409244\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −1.00000 + 1.73205i −0.109109 + 0.188982i
\(85\) 3.00000 5.19615i 0.325396 0.563602i
\(86\) 1.00000 0.107833
\(87\) −1.50000 + 2.59808i −0.160817 + 0.278543i
\(88\) −1.50000 2.59808i −0.159901 0.276956i
\(89\) 9.00000 + 15.5885i 0.953998 + 1.65237i 0.736644 + 0.676280i \(0.236409\pi\)
0.217354 + 0.976093i \(0.430258\pi\)
\(90\) 1.00000 0.105409
\(91\) −7.00000 1.73205i −0.733799 0.181568i
\(92\) 3.00000 0.312772
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) −1.50000 2.59808i −0.154713 0.267971i
\(95\) 1.00000 1.73205i 0.102598 0.177705i
\(96\) −1.00000 −0.102062
\(97\) −7.00000 + 12.1244i −0.710742 + 1.23104i 0.253837 + 0.967247i \(0.418307\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) −1.50000 + 2.59808i −0.151523 + 0.262445i
\(99\) −3.00000 −0.301511
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 3.00000 + 5.19615i 0.297044 + 0.514496i
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) −1.00000 3.46410i −0.0980581 0.339683i
\(105\) −2.00000 −0.195180
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 1.50000 2.59808i 0.143019 0.247717i
\(111\) 3.50000 6.06218i 0.332205 0.575396i
\(112\) 2.00000 0.188982
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 1.50000 + 2.59808i 0.139876 + 0.242272i
\(116\) 3.00000 0.278543
\(117\) −3.50000 0.866025i −0.323575 0.0800641i
\(118\) 9.00000 0.828517
\(119\) −6.00000 10.3923i −0.550019 0.952661i
\(120\) −0.500000 0.866025i −0.0456435 0.0790569i
\(121\) 1.00000 1.73205i 0.0909091 0.157459i
\(122\) −2.00000 −0.181071
\(123\) −3.00000 + 5.19615i −0.270501 + 0.468521i
\(124\) −2.50000 + 4.33013i −0.224507 + 0.388857i
\(125\) −1.00000 −0.0894427
\(126\) 1.00000 1.73205i 0.0890871 0.154303i
\(127\) −7.00000 12.1244i −0.621150 1.07586i −0.989272 0.146085i \(-0.953333\pi\)
0.368122 0.929777i \(-0.380001\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −1.00000 −0.0880451
\(130\) 2.50000 2.59808i 0.219265 0.227866i
\(131\) 9.00000 0.786334 0.393167 0.919467i \(-0.371379\pi\)
0.393167 + 0.919467i \(0.371379\pi\)
\(132\) 1.50000 + 2.59808i 0.130558 + 0.226134i
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) 4.00000 6.92820i 0.345547 0.598506i
\(135\) −1.00000 −0.0860663
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) −3.00000 −0.255377
\(139\) −7.00000 + 12.1244i −0.593732 + 1.02837i 0.399992 + 0.916519i \(0.369013\pi\)
−0.993724 + 0.111856i \(0.964321\pi\)
\(140\) 1.00000 + 1.73205i 0.0845154 + 0.146385i
\(141\) 1.50000 + 2.59808i 0.126323 + 0.218797i
\(142\) 12.0000 1.00702
\(143\) −7.50000 + 7.79423i −0.627182 + 0.651786i
\(144\) 1.00000 0.0833333
\(145\) 1.50000 + 2.59808i 0.124568 + 0.215758i
\(146\) 7.00000 + 12.1244i 0.579324 + 1.00342i
\(147\) 1.50000 2.59808i 0.123718 0.214286i
\(148\) −7.00000 −0.575396
\(149\) 4.50000 7.79423i 0.368654 0.638528i −0.620701 0.784047i \(-0.713152\pi\)
0.989355 + 0.145519i \(0.0464853\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) −3.00000 5.19615i −0.242536 0.420084i
\(154\) −3.00000 5.19615i −0.241747 0.418718i
\(155\) −5.00000 −0.401610
\(156\) 1.00000 + 3.46410i 0.0800641 + 0.277350i
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) 2.50000 + 4.33013i 0.198889 + 0.344486i
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) −0.500000 + 0.866025i −0.0395285 + 0.0684653i
\(161\) 6.00000 0.472866
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) 6.50000 11.2583i 0.509119 0.881820i −0.490825 0.871258i \(-0.663305\pi\)
0.999944 0.0105623i \(-0.00336213\pi\)
\(164\) 6.00000 0.468521
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 4.50000 + 7.79423i 0.348220 + 0.603136i 0.985933 0.167139i \(-0.0534527\pi\)
−0.637713 + 0.770274i \(0.720119\pi\)
\(168\) −2.00000 −0.154303
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 6.00000 0.460179
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) −6.00000 + 10.3923i −0.456172 + 0.790112i −0.998755 0.0498898i \(-0.984113\pi\)
0.542583 + 0.840002i \(0.317446\pi\)
\(174\) −3.00000 −0.227429
\(175\) −1.00000 + 1.73205i −0.0755929 + 0.130931i
\(176\) 1.50000 2.59808i 0.113067 0.195837i
\(177\) −9.00000 −0.676481
\(178\) −9.00000 + 15.5885i −0.674579 + 1.16840i
\(179\) 1.50000 + 2.59808i 0.112115 + 0.194189i 0.916623 0.399753i \(-0.130904\pi\)
−0.804508 + 0.593942i \(0.797571\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −16.0000 −1.18927 −0.594635 0.803996i \(-0.702704\pi\)
−0.594635 + 0.803996i \(0.702704\pi\)
\(182\) −2.00000 6.92820i −0.148250 0.513553i
\(183\) 2.00000 0.147844
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) −3.50000 6.06218i −0.257325 0.445700i
\(186\) 2.50000 4.33013i 0.183309 0.317500i
\(187\) −18.0000 −1.31629
\(188\) 1.50000 2.59808i 0.109399 0.189484i
\(189\) −1.00000 + 1.73205i −0.0727393 + 0.125988i
\(190\) 2.00000 0.145095
\(191\) 6.00000 10.3923i 0.434145 0.751961i −0.563081 0.826402i \(-0.690384\pi\)
0.997225 + 0.0744412i \(0.0237173\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) −14.0000 −1.00514
\(195\) −2.50000 + 2.59808i −0.179029 + 0.186052i
\(196\) −3.00000 −0.214286
\(197\) −12.0000 20.7846i −0.854965 1.48084i −0.876678 0.481078i \(-0.840245\pi\)
0.0217133 0.999764i \(-0.493088\pi\)
\(198\) −1.50000 2.59808i −0.106600 0.184637i
\(199\) −4.00000 + 6.92820i −0.283552 + 0.491127i −0.972257 0.233915i \(-0.924846\pi\)
0.688705 + 0.725042i \(0.258180\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) 3.00000 5.19615i 0.211079 0.365600i
\(203\) 6.00000 0.421117
\(204\) −3.00000 + 5.19615i −0.210042 + 0.363803i
\(205\) 3.00000 + 5.19615i 0.209529 + 0.362915i
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 3.00000 0.208514
\(208\) 2.50000 2.59808i 0.173344 0.180144i
\(209\) −6.00000 −0.415029
\(210\) −1.00000 1.73205i −0.0690066 0.119523i
\(211\) −10.0000 17.3205i −0.688428 1.19239i −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) 3.00000 5.19615i 0.206041 0.356873i
\(213\) −12.0000 −0.822226
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) −0.500000 + 0.866025i −0.0340997 + 0.0590624i
\(216\) −1.00000 −0.0680414
\(217\) −5.00000 + 8.66025i −0.339422 + 0.587896i
\(218\) 7.00000 + 12.1244i 0.474100 + 0.821165i
\(219\) −7.00000 12.1244i −0.473016 0.819288i
\(220\) 3.00000 0.202260
\(221\) −21.0000 5.19615i −1.41261 0.349531i
\(222\) 7.00000 0.469809
\(223\) 5.00000 + 8.66025i 0.334825 + 0.579934i 0.983451 0.181173i \(-0.0579895\pi\)
−0.648626 + 0.761107i \(0.724656\pi\)
\(224\) 1.00000 + 1.73205i 0.0668153 + 0.115728i
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) −15.0000 −0.997785
\(227\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) −1.50000 + 2.59808i −0.0989071 + 0.171312i
\(231\) 3.00000 + 5.19615i 0.197386 + 0.341882i
\(232\) 1.50000 + 2.59808i 0.0984798 + 0.170572i
\(233\) 21.0000 1.37576 0.687878 0.725826i \(-0.258542\pi\)
0.687878 + 0.725826i \(0.258542\pi\)
\(234\) −1.00000 3.46410i −0.0653720 0.226455i
\(235\) 3.00000 0.195698
\(236\) 4.50000 + 7.79423i 0.292925 + 0.507361i
\(237\) −2.50000 4.33013i −0.162392 0.281272i
\(238\) 6.00000 10.3923i 0.388922 0.673633i
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0.500000 0.866025i 0.0322749 0.0559017i
\(241\) −8.50000 + 14.7224i −0.547533 + 0.948355i 0.450910 + 0.892570i \(0.351100\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 2.00000 0.128565
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −1.00000 1.73205i −0.0640184 0.110883i
\(245\) −1.50000 2.59808i −0.0958315 0.165985i
\(246\) −6.00000 −0.382546
\(247\) −7.00000 1.73205i −0.445399 0.110208i
\(248\) −5.00000 −0.317500
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) −7.50000 + 12.9904i −0.473396 + 0.819946i −0.999536 0.0304521i \(-0.990305\pi\)
0.526140 + 0.850398i \(0.323639\pi\)
\(252\) 2.00000 0.125988
\(253\) 4.50000 7.79423i 0.282913 0.490019i
\(254\) 7.00000 12.1244i 0.439219 0.760750i
\(255\) −6.00000 −0.375735
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 10.5000 + 18.1865i 0.654972 + 1.13444i 0.981901 + 0.189396i \(0.0606529\pi\)
−0.326929 + 0.945049i \(0.606014\pi\)
\(258\) −0.500000 0.866025i −0.0311286 0.0539164i
\(259\) −14.0000 −0.869918
\(260\) 3.50000 + 0.866025i 0.217061 + 0.0537086i
\(261\) 3.00000 0.185695
\(262\) 4.50000 + 7.79423i 0.278011 + 0.481529i
\(263\) 7.50000 + 12.9904i 0.462470 + 0.801021i 0.999083 0.0428069i \(-0.0136300\pi\)
−0.536614 + 0.843828i \(0.680297\pi\)
\(264\) −1.50000 + 2.59808i −0.0923186 + 0.159901i
\(265\) 6.00000 0.368577
\(266\) 2.00000 3.46410i 0.122628 0.212398i
\(267\) 9.00000 15.5885i 0.550791 0.953998i
\(268\) 8.00000 0.488678
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) −0.500000 0.866025i −0.0304290 0.0527046i
\(271\) −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i \(-0.275099\pi\)
−0.983312 + 0.181928i \(0.941766\pi\)
\(272\) 6.00000 0.363803
\(273\) 2.00000 + 6.92820i 0.121046 + 0.419314i
\(274\) −9.00000 −0.543710
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) −1.50000 2.59808i −0.0902894 0.156386i
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) −14.0000 −0.839664
\(279\) −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 \(0.319597\pi\)
\(282\) −1.50000 + 2.59808i −0.0893237 + 0.154713i
\(283\) 15.5000 + 26.8468i 0.921379 + 1.59588i 0.797283 + 0.603606i \(0.206270\pi\)
0.124096 + 0.992270i \(0.460397\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) −2.00000 −0.118470
\(286\) −10.5000 2.59808i −0.620878 0.153627i
\(287\) 12.0000 0.708338
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) −1.50000 + 2.59808i −0.0880830 + 0.152564i
\(291\) 14.0000 0.820695
\(292\) −7.00000 + 12.1244i −0.409644 + 0.709524i
\(293\) 15.0000 25.9808i 0.876309 1.51781i 0.0209480 0.999781i \(-0.493332\pi\)
0.855361 0.518032i \(-0.173335\pi\)
\(294\) 3.00000 0.174964
\(295\) −4.50000 + 7.79423i −0.262000 + 0.453798i
\(296\) −3.50000 6.06218i −0.203433 0.352357i
\(297\) 1.50000 + 2.59808i 0.0870388 + 0.150756i
\(298\) 9.00000 0.521356
\(299\) 7.50000 7.79423i 0.433736 0.450752i
\(300\) 1.00000 0.0577350
\(301\) 1.00000 + 1.73205i 0.0576390 + 0.0998337i
\(302\) 4.00000 + 6.92820i 0.230174 + 0.398673i
\(303\) −3.00000 + 5.19615i −0.172345 + 0.298511i
\(304\) 2.00000 0.114708
\(305\) 1.00000 1.73205i 0.0572598 0.0991769i
\(306\) 3.00000 5.19615i 0.171499 0.297044i
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 3.00000 5.19615i 0.170941 0.296078i
\(309\) −7.00000 12.1244i −0.398216 0.689730i
\(310\) −2.50000 4.33013i −0.141990 0.245935i
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) −2.50000 + 2.59808i −0.141535 + 0.147087i
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) −6.50000 11.2583i −0.366816 0.635344i
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) −2.50000 + 4.33013i −0.140636 + 0.243589i
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) −3.00000 + 5.19615i −0.168232 + 0.291386i
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) −1.00000 −0.0559017
\(321\) 3.00000 5.19615i 0.167444 0.290021i
\(322\) 3.00000 + 5.19615i 0.167183 + 0.289570i
\(323\) −6.00000 10.3923i −0.333849 0.578243i
\(324\) 1.00000 0.0555556
\(325\) 1.00000 + 3.46410i 0.0554700 + 0.192154i
\(326\) 13.0000 0.720003
\(327\) −7.00000 12.1244i −0.387101 0.670478i
\(328\) 3.00000 + 5.19615i 0.165647 + 0.286910i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) −3.00000 −0.165145
\(331\) −16.0000 + 27.7128i −0.879440 + 1.52323i −0.0274825 + 0.999622i \(0.508749\pi\)
−0.851957 + 0.523612i \(0.824584\pi\)
\(332\) 3.00000 5.19615i 0.164646 0.285176i
\(333\) −7.00000 −0.383598
\(334\) −4.50000 + 7.79423i −0.246229 + 0.426481i
\(335\) 4.00000 + 6.92820i 0.218543 + 0.378528i
\(336\) −1.00000 1.73205i −0.0545545 0.0944911i
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −11.5000 6.06218i −0.625518 0.329739i
\(339\) 15.0000 0.814688
\(340\) 3.00000 + 5.19615i 0.162698 + 0.281801i
\(341\) 7.50000 + 12.9904i 0.406148 + 0.703469i
\(342\) 1.00000 1.73205i 0.0540738 0.0936586i
\(343\) −20.0000 −1.07990
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) 1.50000 2.59808i 0.0807573 0.139876i
\(346\) −12.0000 −0.645124
\(347\) 15.0000 25.9808i 0.805242 1.39472i −0.110885 0.993833i \(-0.535369\pi\)
0.916127 0.400887i \(-0.131298\pi\)
\(348\) −1.50000 2.59808i −0.0804084 0.139272i
\(349\) −4.00000 6.92820i −0.214115 0.370858i 0.738883 0.673833i \(-0.235353\pi\)
−0.952998 + 0.302975i \(0.902020\pi\)
\(350\) −2.00000 −0.106904
\(351\) 1.00000 + 3.46410i 0.0533761 + 0.184900i
\(352\) 3.00000 0.159901
\(353\) −15.0000 25.9808i −0.798369 1.38282i −0.920677 0.390324i \(-0.872363\pi\)
0.122308 0.992492i \(-0.460970\pi\)
\(354\) −4.50000 7.79423i −0.239172 0.414259i
\(355\) −6.00000 + 10.3923i −0.318447 + 0.551566i
\(356\) −18.0000 −0.953998
\(357\) −6.00000 + 10.3923i −0.317554 + 0.550019i
\(358\) −1.50000 + 2.59808i −0.0792775 + 0.137313i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −8.00000 13.8564i −0.420471 0.728277i
\(363\) −2.00000 −0.104973
\(364\) 5.00000 5.19615i 0.262071 0.272352i
\(365\) −14.0000 −0.732793
\(366\) 1.00000 + 1.73205i 0.0522708 + 0.0905357i
\(367\) −10.0000 17.3205i −0.521996 0.904123i −0.999673 0.0255875i \(-0.991854\pi\)
0.477677 0.878536i \(-0.341479\pi\)
\(368\) −1.50000 + 2.59808i −0.0781929 + 0.135434i
\(369\) 6.00000 0.312348
\(370\) 3.50000 6.06218i 0.181956 0.315158i
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 5.00000 0.259238
\(373\) 12.5000 21.6506i 0.647225 1.12103i −0.336557 0.941663i \(-0.609263\pi\)
0.983783 0.179364i \(-0.0574041\pi\)
\(374\) −9.00000 15.5885i −0.465379 0.806060i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 3.00000 0.154713
\(377\) 7.50000 7.79423i 0.386270 0.401423i
\(378\) −2.00000 −0.102869
\(379\) −19.0000 32.9090i −0.975964 1.69042i −0.676715 0.736245i \(-0.736597\pi\)
−0.299249 0.954175i \(-0.596736\pi\)
\(380\) 1.00000 + 1.73205i 0.0512989 + 0.0888523i
\(381\) −7.00000 + 12.1244i −0.358621 + 0.621150i
\(382\) 12.0000 0.613973
\(383\) 10.5000 18.1865i 0.536525 0.929288i −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 6.00000 0.305788
\(386\) −2.00000 + 3.46410i −0.101797 + 0.176318i
\(387\) 0.500000 + 0.866025i 0.0254164 + 0.0440225i
\(388\) −7.00000 12.1244i −0.355371 0.615521i
\(389\) 3.00000 0.152106 0.0760530 0.997104i \(-0.475768\pi\)
0.0760530 + 0.997104i \(0.475768\pi\)
\(390\) −3.50000 0.866025i −0.177229 0.0438529i
\(391\) 18.0000 0.910299
\(392\) −1.50000 2.59808i −0.0757614 0.131223i
\(393\) −4.50000 7.79423i −0.226995 0.393167i
\(394\) 12.0000 20.7846i 0.604551 1.04711i
\(395\) −5.00000 −0.251577
\(396\) 1.50000 2.59808i 0.0753778 0.130558i
\(397\) 15.5000 26.8468i 0.777923 1.34740i −0.155214 0.987881i \(-0.549607\pi\)
0.933137 0.359521i \(-0.117060\pi\)
\(398\) −8.00000 −0.401004
\(399\) −2.00000 + 3.46410i −0.100125 + 0.173422i
\(400\) −0.500000 0.866025i −0.0250000 0.0433013i
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) −8.00000 −0.399004
\(403\) 5.00000 + 17.3205i 0.249068 + 0.862796i
\(404\) 6.00000 0.298511
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) 3.00000 + 5.19615i 0.148888 + 0.257881i
\(407\) −10.5000 + 18.1865i −0.520466 + 0.901473i
\(408\) −6.00000 −0.297044
\(409\) 5.00000 8.66025i 0.247234 0.428222i −0.715523 0.698589i \(-0.753812\pi\)
0.962757 + 0.270367i \(0.0871450\pi\)
\(410\) −3.00000 + 5.19615i −0.148159 + 0.256620i
\(411\) 9.00000 0.443937
\(412\) −7.00000 + 12.1244i −0.344865 + 0.597324i
\(413\) 9.00000 + 15.5885i 0.442861 + 0.767058i
\(414\) 1.50000 + 2.59808i 0.0737210 + 0.127688i
\(415\) 6.00000 0.294528
\(416\) 3.50000 + 0.866025i 0.171602 + 0.0424604i
\(417\) 14.0000 0.685583
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) 6.00000 + 10.3923i 0.293119 + 0.507697i 0.974546 0.224189i \(-0.0719734\pi\)
−0.681426 + 0.731887i \(0.738640\pi\)
\(420\) 1.00000 1.73205i 0.0487950 0.0845154i
\(421\) −16.0000 −0.779792 −0.389896 0.920859i \(-0.627489\pi\)
−0.389896 + 0.920859i \(0.627489\pi\)
\(422\) 10.0000 17.3205i 0.486792 0.843149i
\(423\) 1.50000 2.59808i 0.0729325 0.126323i
\(424\) 6.00000 0.291386
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) −6.00000 10.3923i −0.290701 0.503509i
\(427\) −2.00000 3.46410i −0.0967868 0.167640i
\(428\) −6.00000 −0.290021
\(429\) 10.5000 + 2.59808i 0.506945 + 0.125436i
\(430\) −1.00000 −0.0482243
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 20.0000 34.6410i 0.961139 1.66474i 0.241489 0.970404i \(-0.422364\pi\)
0.719650 0.694337i \(-0.244302\pi\)
\(434\) −10.0000 −0.480015
\(435\) 1.50000 2.59808i 0.0719195 0.124568i
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 6.00000 0.287019
\(438\) 7.00000 12.1244i 0.334473 0.579324i
\(439\) 2.00000 + 3.46410i 0.0954548 + 0.165333i 0.909798 0.415051i \(-0.136236\pi\)
−0.814344 + 0.580383i \(0.802903\pi\)
\(440\) 1.50000 + 2.59808i 0.0715097 + 0.123858i
\(441\) −3.00000 −0.142857
\(442\) −6.00000 20.7846i −0.285391 0.988623i
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 3.50000 + 6.06218i 0.166103 + 0.287698i
\(445\) −9.00000 15.5885i −0.426641 0.738964i
\(446\) −5.00000 + 8.66025i −0.236757 + 0.410075i
\(447\) −9.00000 −0.425685
\(448\) −1.00000 + 1.73205i −0.0472456 + 0.0818317i
\(449\) −18.0000 + 31.1769i −0.849473 + 1.47133i 0.0322072 + 0.999481i \(0.489746\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) −7.50000 12.9904i −0.352770 0.611016i
\(453\) −4.00000 6.92820i −0.187936 0.325515i
\(454\) 0 0
\(455\) 7.00000 + 1.73205i 0.328165 + 0.0811998i
\(456\) −2.00000 −0.0936586
\(457\) −1.00000 1.73205i −0.0467780 0.0810219i 0.841688 0.539964i \(-0.181562\pi\)
−0.888466 + 0.458942i \(0.848229\pi\)
\(458\) 7.00000 + 12.1244i 0.327089 + 0.566534i
\(459\) −3.00000 + 5.19615i −0.140028 + 0.242536i
\(460\) −3.00000 −0.139876
\(461\) −7.50000 + 12.9904i −0.349310 + 0.605022i −0.986127 0.165992i \(-0.946917\pi\)
0.636817 + 0.771015i \(0.280251\pi\)
\(462\) −3.00000 + 5.19615i −0.139573 + 0.241747i
\(463\) −34.0000 −1.58011 −0.790057 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) −1.50000 + 2.59808i −0.0696358 + 0.120613i
\(465\) 2.50000 + 4.33013i 0.115935 + 0.200805i
\(466\) 10.5000 + 18.1865i 0.486403 + 0.842475i
\(467\) 18.0000 0.832941 0.416470 0.909149i \(-0.363267\pi\)
0.416470 + 0.909149i \(0.363267\pi\)
\(468\) 2.50000 2.59808i 0.115563 0.120096i
\(469\) 16.0000 0.738811
\(470\) 1.50000 + 2.59808i 0.0691898 + 0.119840i
\(471\) 6.50000 + 11.2583i 0.299504 + 0.518756i
\(472\) −4.50000 + 7.79423i −0.207129 + 0.358758i
\(473\) 3.00000 0.137940
\(474\) 2.50000 4.33013i 0.114829 0.198889i
\(475\) −1.00000 + 1.73205i −0.0458831 + 0.0794719i
\(476\) 12.0000 0.550019
\(477\) 3.00000 5.19615i 0.137361 0.237915i
\(478\) 12.0000 + 20.7846i 0.548867 + 0.950666i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 1.00000 0.0456435
\(481\) −17.5000 + 18.1865i −0.797931 + 0.829235i
\(482\) −17.0000 −0.774329
\(483\) −3.00000 5.19615i −0.136505 0.236433i
\(484\) 1.00000 + 1.73205i 0.0454545 + 0.0787296i
\(485\) 7.00000 12.1244i 0.317854 0.550539i
\(486\) −1.00000 −0.0453609
\(487\) −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) 1.00000 1.73205i 0.0452679 0.0784063i
\(489\) −13.0000 −0.587880
\(490\) 1.50000 2.59808i 0.0677631 0.117369i
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) −3.00000 5.19615i −0.135250 0.234261i
\(493\) 18.0000 0.810679
\(494\) −2.00000 6.92820i −0.0899843 0.311715i
\(495\) 3.00000 0.134840
\(496\) −2.50000 4.33013i −0.112253 0.194428i
\(497\) 12.0000 + 20.7846i 0.538274 + 0.932317i
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 4.50000 7.79423i 0.201045 0.348220i
\(502\) −15.0000 −0.669483
\(503\) −12.0000 + 20.7846i −0.535054 + 0.926740i 0.464107 + 0.885779i \(0.346375\pi\)
−0.999161 + 0.0409609i \(0.986958\pi\)
\(504\) 1.00000 + 1.73205i 0.0445435 + 0.0771517i
\(505\) 3.00000 + 5.19615i 0.133498 + 0.231226i
\(506\) 9.00000 0.400099
\(507\) 11.5000 + 6.06218i 0.510733 + 0.269231i
\(508\) 14.0000 0.621150
\(509\) −1.50000 2.59808i −0.0664863 0.115158i 0.830866 0.556473i \(-0.187846\pi\)
−0.897352 + 0.441315i \(0.854512\pi\)
\(510\) −3.00000 5.19615i −0.132842 0.230089i
\(511\) −14.0000 + 24.2487i −0.619324 + 1.07270i
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 + 1.73205i −0.0441511 + 0.0764719i
\(514\) −10.5000 + 18.1865i −0.463135 + 0.802174i
\(515\) −14.0000 −0.616914
\(516\) 0.500000 0.866025i 0.0220113 0.0381246i
\(517\) −4.50000 7.79423i −0.197910 0.342790i
\(518\) −7.00000 12.1244i −0.307562 0.532714i
\(519\) 12.0000 0.526742
\(520\) 1.00000 + 3.46410i 0.0438529 + 0.151911i
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 1.50000 + 2.59808i 0.0656532 + 0.113715i
\(523\) −5.50000 9.52628i −0.240498 0.416555i 0.720358 0.693602i \(-0.243977\pi\)
−0.960856 + 0.277047i \(0.910644\pi\)
\(524\) −4.50000 + 7.79423i −0.196583 + 0.340492i
\(525\) 2.00000 0.0872872
\(526\) −7.50000 + 12.9904i −0.327016 + 0.566408i
\(527\) −15.0000 + 25.9808i −0.653410 + 1.13174i
\(528\) −3.00000 −0.130558
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 3.00000 + 5.19615i 0.130312 + 0.225706i
\(531\) 4.50000 + 7.79423i 0.195283 + 0.338241i
\(532\) 4.00000 0.173422
\(533\) 15.0000 15.5885i 0.649722 0.675211i
\(534\) 18.0000 0.778936
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) 4.00000 + 6.92820i 0.172774 + 0.299253i
\(537\) 1.50000 2.59808i 0.0647298 0.112115i
\(538\) −18.0000 −0.776035
\(539\) −4.50000 + 7.79423i −0.193829 + 0.335721i
\(540\) 0.500000 0.866025i 0.0215166 0.0372678i
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 5.50000 9.52628i 0.236245 0.409189i
\(543\) 8.00000 + 13.8564i 0.343313 + 0.594635i
\(544\) 3.00000 + 5.19615i 0.128624 + 0.222783i
\(545\) −14.0000 −0.599694
\(546\) −5.00000 + 5.19615i −0.213980 + 0.222375i
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) −4.50000 7.79423i −0.192230 0.332953i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) −1.50000 + 2.59808i −0.0639602 + 0.110782i
\(551\) 6.00000 0.255609
\(552\) 1.50000 2.59808i 0.0638442 0.110581i
\(553\) −5.00000 + 8.66025i −0.212622 + 0.368271i
\(554\) 1.00000 0.0424859
\(555\) −3.50000 + 6.06218i −0.148567 + 0.257325i
\(556\) −7.00000 12.1244i −0.296866 0.514187i
\(557\) 3.00000 + 5.19615i 0.127114 + 0.220168i 0.922557 0.385860i \(-0.126095\pi\)
−0.795443 + 0.606028i \(0.792762\pi\)
\(558\) −5.00000 −0.211667
\(559\) 3.50000 + 0.866025i 0.148034 + 0.0366290i
\(560\) −2.00000 −0.0845154
\(561\) 9.00000 + 15.5885i 0.379980 + 0.658145i
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) −18.0000 + 31.1769i −0.758610 + 1.31395i 0.184950 + 0.982748i \(0.440788\pi\)
−0.943560 + 0.331202i \(0.892546\pi\)
\(564\) −3.00000 −0.126323
\(565\) 7.50000 12.9904i 0.315527 0.546509i
\(566\) −15.5000 + 26.8468i −0.651514 + 1.12845i
\(567\) 2.00000 0.0839921
\(568\) −6.00000 + 10.3923i −0.251754 + 0.436051i
\(569\) −3.00000 5.19615i −0.125767 0.217834i 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) −1.00000 1.73205i −0.0418854 0.0725476i
\(571\) −40.0000 −1.67395 −0.836974 0.547243i \(-0.815677\pi\)
−0.836974 + 0.547243i \(0.815677\pi\)
\(572\) −3.00000 10.3923i −0.125436 0.434524i
\(573\) −12.0000 −0.501307
\(574\) 6.00000 + 10.3923i 0.250435 + 0.433766i
\(575\) −1.50000 2.59808i −0.0625543 0.108347i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) 2.00000 3.46410i 0.0831172 0.143963i
\(580\) −3.00000 −0.124568
\(581\) 6.00000 10.3923i 0.248922 0.431145i
\(582\) 7.00000 + 12.1244i 0.290159 + 0.502571i
\(583\) −9.00000 15.5885i −0.372742 0.645608i
\(584\) −14.0000 −0.579324
\(585\) 3.50000 + 0.866025i 0.144707 + 0.0358057i
\(586\) 30.0000 1.23929
\(587\) −9.00000 15.5885i −0.371470 0.643404i 0.618322 0.785925i \(-0.287813\pi\)
−0.989792 + 0.142520i \(0.954479\pi\)
\(588\) 1.50000 + 2.59808i 0.0618590 + 0.107143i
\(589\) −5.00000 + 8.66025i −0.206021 + 0.356840i
\(590\) −9.00000 −0.370524
\(591\) −12.0000 + 20.7846i −0.493614 + 0.854965i
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) 27.0000 1.10876 0.554379 0.832265i \(-0.312956\pi\)
0.554379 + 0.832265i \(0.312956\pi\)
\(594\) −1.50000 + 2.59808i −0.0615457 + 0.106600i
\(595\) 6.00000 + 10.3923i 0.245976 + 0.426043i
\(596\) 4.50000 + 7.79423i 0.184327 + 0.319264i
\(597\) 8.00000 0.327418
\(598\) 10.5000 + 2.59808i 0.429377 + 0.106243i
\(599\) 6.00000 0.245153 0.122577 0.992459i \(-0.460884\pi\)
0.122577 + 0.992459i \(0.460884\pi\)
\(600\) 0.500000 + 0.866025i 0.0204124 + 0.0353553i
\(601\) 9.50000 + 16.4545i 0.387513 + 0.671192i 0.992114 0.125336i \(-0.0400009\pi\)
−0.604601 + 0.796528i \(0.706668\pi\)
\(602\) −1.00000 + 1.73205i −0.0407570 + 0.0705931i
\(603\) 8.00000 0.325785
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) −6.00000 −0.243733
\(607\) 11.0000 19.0526i 0.446476 0.773320i −0.551678 0.834058i \(-0.686012\pi\)
0.998154 + 0.0607380i \(0.0193454\pi\)
\(608\) 1.00000 + 1.73205i 0.0405554 + 0.0702439i
\(609\) −3.00000 5.19615i −0.121566 0.210559i
\(610\) 2.00000 0.0809776
\(611\) −3.00000 10.3923i −0.121367 0.420428i
\(612\) 6.00000 0.242536
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) 4.00000 + 6.92820i 0.161427 + 0.279600i
\(615\) 3.00000 5.19615i 0.120972 0.209529i
\(616\) 6.00000 0.241747
\(617\) −10.5000 + 18.1865i −0.422714 + 0.732162i −0.996204 0.0870504i \(-0.972256\pi\)
0.573490 + 0.819213i \(0.305589\pi\)
\(618\) 7.00000 12.1244i 0.281581 0.487713i
\(619\) −46.0000 −1.84890 −0.924448 0.381308i \(-0.875474\pi\)
−0.924448 + 0.381308i \(0.875474\pi\)
\(620\) 2.50000 4.33013i 0.100402 0.173902i
\(621\) −1.50000 2.59808i −0.0601929 0.104257i
\(622\) −6.00000 10.3923i −0.240578 0.416693i
\(623\) −36.0000 −1.44231
\(624\) −3.50000 0.866025i −0.140112 0.0346688i
\(625\) 1.00000 0.0400000
\(626\) 4.00000 + 6.92820i 0.159872 + 0.276907i
\(627\) 3.00000 + 5.19615i 0.119808 + 0.207514i
\(628\) 6.50000 11.2583i 0.259378 0.449256i
\(629\) −42.0000 −1.67465
\(630\) −1.00000 + 1.73205i −0.0398410 + 0.0690066i
\(631\) 8.00000 13.8564i 0.318475 0.551615i −0.661695 0.749773i \(-0.730163\pi\)
0.980170 + 0.198158i \(0.0634960\pi\)
\(632\) −5.00000 −0.198889
\(633\) −10.0000 + 17.3205i −0.397464 + 0.688428i
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 7.00000 + 12.1244i 0.277787 + 0.481140i
\(636\) −6.00000 −0.237915
\(637\) −7.50000 + 7.79423i −0.297161 + 0.308819i
\(638\) 9.00000 0.356313
\(639\) 6.00000 + 10.3923i 0.237356 + 0.411113i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −3.00000 + 5.19615i −0.118493 + 0.205236i −0.919171 0.393860i \(-0.871140\pi\)
0.800678 + 0.599095i \(0.204473\pi\)
\(642\) 6.00000 0.236801
\(643\) 8.00000 13.8564i 0.315489 0.546443i −0.664052 0.747686i \(-0.731165\pi\)
0.979541 + 0.201243i \(0.0644981\pi\)
\(644\) −3.00000 + 5.19615i −0.118217 + 0.204757i
\(645\) 1.00000 0.0393750
\(646\) 6.00000 10.3923i 0.236067 0.408880i
\(647\) −12.0000 20.7846i −0.471769 0.817127i 0.527710 0.849425i \(-0.323051\pi\)
−0.999478 + 0.0322975i \(0.989718\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 27.0000 1.05984
\(650\) −2.50000 + 2.59808i −0.0980581 + 0.101905i
\(651\) 10.0000 0.391931
\(652\) 6.50000 + 11.2583i 0.254560 + 0.440910i
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 7.00000 12.1244i 0.273722 0.474100i
\(655\) −9.00000 −0.351659
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) −7.00000 + 12.1244i −0.273096 + 0.473016i
\(658\) 6.00000 0.233904
\(659\) −7.50000 + 12.9904i −0.292159 + 0.506033i −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) −1.50000 2.59808i −0.0583874 0.101130i
\(661\) −16.0000 27.7128i −0.622328 1.07790i −0.989051 0.147573i \(-0.952854\pi\)
0.366723 0.930330i \(-0.380480\pi\)
\(662\) −32.0000 −1.24372
\(663\) 6.00000 + 20.7846i 0.233021 + 0.807207i
\(664\) 6.00000 0.232845
\(665\) 2.00000 + 3.46410i 0.0775567 + 0.134332i
\(666\) −3.50000 6.06218i −0.135622 0.234905i
\(667\) −4.50000 + 7.79423i −0.174241 + 0.301794i
\(668\) −9.00000 −0.348220
\(669\) 5.00000 8.66025i 0.193311 0.334825i
\(670\) −4.00000 + 6.92820i −0.154533 + 0.267660i
\(671\) −6.00000 −0.231627
\(672\) 1.00000 1.73205i 0.0385758 0.0668153i
\(673\) 2.00000 + 3.46410i 0.0770943 + 0.133531i 0.901995 0.431746i \(-0.142102\pi\)
−0.824901 + 0.565278i \(0.808769\pi\)
\(674\) 7.00000 + 12.1244i 0.269630 + 0.467013i
\(675\) 1.00000 0.0384900
\(676\) −0.500000 12.9904i −0.0192308 0.499630i
\(677\) −36.0000 −1.38359 −0.691796 0.722093i \(-0.743180\pi\)
−0.691796 + 0.722093i \(0.743180\pi\)
\(678\) 7.50000 + 12.9904i 0.288036 + 0.498893i
\(679\) −14.0000 24.2487i −0.537271 0.930580i
\(680\) −3.00000 + 5.19615i −0.115045 + 0.199263i
\(681\) 0 0
\(682\) −7.50000 + 12.9904i −0.287190 + 0.497427i
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) 2.00000 0.0764719
\(685\) 4.50000 7.79423i 0.171936 0.297802i
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) −7.00000 12.1244i −0.267067 0.462573i
\(688\) −1.00000 −0.0381246
\(689\) −6.00000 20.7846i −0.228582 0.791831i
\(690\) 3.00000 0.114208
\(691\) 23.0000 + 39.8372i 0.874961 + 1.51548i 0.856804 + 0.515642i \(0.172447\pi\)
0.0181572 + 0.999835i \(0.494220\pi\)
\(692\) −6.00000 10.3923i −0.228086 0.395056i
\(693\) 3.00000 5.19615i 0.113961 0.197386i
\(694\) 30.0000 1.13878
\(695\) 7.00000 12.1244i 0.265525 0.459903i
\(696\) 1.50000 2.59808i 0.0568574 0.0984798i
\(697\) 36.0000 1.36360
\(698\) 4.00000 6.92820i 0.151402 0.262236i
\(699\) −10.5000 18.1865i −0.397146 0.687878i
\(700\) −1.00000 1.73205i −0.0377964 0.0654654i
\(701\) −21.0000 −0.793159 −0.396580 0.918000i \(-0.629803\pi\)
−0.396580 + 0.918000i \(0.629803\pi\)
\(702\) −2.50000 + 2.59808i −0.0943564 + 0.0980581i
\(703\) −14.0000 −0.528020
\(704\) 1.50000 + 2.59808i 0.0565334 + 0.0979187i
\(705\) −1.50000 2.59808i −0.0564933 0.0978492i
\(706\) 15.0000 25.9808i 0.564532 0.977799i
\(707\) 12.0000 0.451306
\(708\) 4.50000 7.79423i 0.169120 0.292925i
\(709\) −16.0000 + 27.7128i −0.600893 + 1.04078i 0.391794 + 0.920053i \(0.371855\pi\)
−0.992686 + 0.120723i \(0.961479\pi\)
\(710\) −12.0000 −0.450352
\(711\) −2.50000 + 4.33013i −0.0937573 + 0.162392i
\(712\) −9.00000 15.5885i −0.337289 0.584202i
\(713\) −7.50000 12.9904i −0.280877 0.486494i
\(714\) −12.0000 −0.449089
\(715\) 7.50000 7.79423i 0.280484 0.291488i
\(716\) −3.00000 −0.112115
\(717\) −12.0000 20.7846i −0.448148 0.776215i
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) −18.0000 + 31.1769i −0.671287 + 1.16270i 0.306253 + 0.951950i \(0.400925\pi\)
−0.977539 + 0.210752i \(0.932409\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −14.0000 + 24.2487i −0.521387 + 0.903069i
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) 17.0000 0.632237
\(724\) 8.00000 13.8564i 0.297318 0.514969i
\(725\) −1.50000 2.59808i −0.0557086 0.0964901i
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −4.00000 −0.148352 −0.0741759 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) 7.00000 + 1.73205i 0.259437 + 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) −7.00000 12.1244i −0.259082 0.448743i
\(731\) 3.00000 + 5.19615i 0.110959 + 0.192187i
\(732\) −1.00000 + 1.73205i −0.0369611 + 0.0640184i
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 10.0000 17.3205i 0.369107 0.639312i
\(735\) −1.50000 + 2.59808i −0.0553283 + 0.0958315i
\(736\) −3.00000 −0.110581
\(737\) 12.0000 20.7846i 0.442026 0.765611i
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) 7.00000 0.257325
\(741\) 2.00000 + 6.92820i 0.0734718 + 0.254514i
\(742\) 12.0000 0.440534
\(743\) 4.50000 + 7.79423i 0.165089 + 0.285943i 0.936687 0.350168i \(-0.113876\pi\)
−0.771598 + 0.636111i \(0.780542\pi\)
\(744\) 2.50000 + 4.33013i 0.0916544 + 0.158750i
\(745\) −4.50000 + 7.79423i −0.164867 + 0.285558i
\(746\) 25.0000 0.915315
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 9.00000 15.5885i 0.329073 0.569970i
\(749\) −12.0000 −0.438470
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) −20.5000 35.5070i −0.748056 1.29567i −0.948753 0.316017i \(-0.897654\pi\)
0.200698 0.979653i \(-0.435679\pi\)
\(752\) 1.50000 + 2.59808i 0.0546994 + 0.0947421i
\(753\) 15.0000 0.546630
\(754\) 10.5000 + 2.59808i 0.382387 + 0.0946164i
\(755\) −8.00000 −0.291150
\(756\) −1.00000 1.73205i −0.0363696 0.0629941i
\(757\) −19.0000 32.9090i −0.690567 1.19610i −0.971652 0.236414i \(-0.924028\pi\)
0.281086 0.959683i \(-0.409305\pi\)
\(758\) 19.0000 32.9090i 0.690111 1.19531i
\(759\) −9.00000 −0.326679
\(760\) −1.00000 + 1.73205i −0.0362738 + 0.0628281i
\(761\) 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i \(-0.763543\pi\)
0.954043 + 0.299670i \(0.0968765\pi\)
\(762\) −14.0000 −0.507166
\(763\) −14.0000 + 24.2487i −0.506834 + 0.877862i
\(764\) 6.00000 + 10.3923i 0.217072 + 0.375980i
\(765\) 3.00000 + 5.19615i 0.108465 + 0.187867i
\(766\) 21.0000 0.758761
\(767\) 31.5000 + 7.79423i 1.13740 + 0.281433i
\(768\) 1.00000 0.0360844
\(769\) 6.50000 + 11.2583i 0.234396 + 0.405986i 0.959097 0.283078i \(-0.0913554\pi\)
−0.724701 + 0.689063i \(0.758022\pi\)
\(770\) 3.00000 + 5.19615i 0.108112 + 0.187256i
\(771\) 10.5000 18.1865i 0.378148 0.654972i
\(772\) −4.00000 −0.143963
\(773\) 24.0000 41.5692i 0.863220 1.49514i −0.00558380 0.999984i \(-0.501777\pi\)
0.868804 0.495156i \(-0.164889\pi\)
\(774\) −0.500000 + 0.866025i −0.0179721 + 0.0311286i
\(775\) 5.00000 0.179605
\(776\) 7.00000 12.1244i 0.251285 0.435239i
\(777\) 7.00000 + 12.1244i 0.251124 +