Properties

Label 1950.2.i.n.451.1
Level $1950$
Weight $2$
Character 1950.451
Analytic conductor $15.571$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
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: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 451.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1950.451
Dual form 1950.2.i.n.601.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 + 3.46410i −0.277350 + 0.960769i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.00000 1.73205i −0.229416 0.397360i 0.728219 0.685344i \(-0.240348\pi\)
−0.957635 + 0.287984i \(0.907015\pi\)
\(20\) 0 0
\(21\) 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 \(-0.732076\pi\)
0.978961 + 0.204046i \(0.0654092\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) −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 −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) 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
\(35\) 0 0
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −3.50000 + 6.06218i −0.575396 + 0.996616i 0.420602 + 0.907245i \(0.361819\pi\)
−0.995998 + 0.0893706i \(0.971514\pi\)
\(38\) 2.00000 0.324443
\(39\) 2.50000 + 2.59808i 0.400320 + 0.416025i
\(40\) 0 0
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) −1.00000 + 1.73205i −0.154303 + 0.267261i
\(43\) −0.500000 0.866025i −0.0762493 0.132068i 0.825380 0.564578i \(-0.190961\pi\)
−0.901629 + 0.432511i \(0.857628\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) 1.50000 + 2.59808i 0.221163 + 0.383065i
\(47\) 3.00000 0.437595 0.218797 0.975770i \(-0.429787\pi\)
0.218797 + 0.975770i \(0.429787\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0 0
\(51\) 6.00000 0.840168
\(52\) 3.50000 0.866025i 0.485363 0.120096i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 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 0.994769 + 0.102151i \(0.0325726\pi\)
−0.408919 + 0.912571i \(0.634094\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) −2.50000 + 4.33013i −0.317500 + 0.549927i
\(63\) 1.00000 1.73205i 0.125988 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.00000 0.369274
\(67\) 4.00000 6.92820i 0.488678 0.846415i −0.511237 0.859440i \(-0.670813\pi\)
0.999915 + 0.0130248i \(0.00414604\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) −1.50000 2.59808i −0.180579 0.312772i
\(70\) 0 0
\(71\) 6.00000 + 10.3923i 0.712069 + 1.23334i 0.964079 + 0.265615i \(0.0855750\pi\)
−0.252010 + 0.967725i \(0.581092\pi\)
\(72\) −0.500000 0.866025i −0.0589256 0.102062i
\(73\) −14.0000 −1.63858 −0.819288 0.573382i \(-0.805631\pi\)
−0.819288 + 0.573382i \(0.805631\pi\)
\(74\) −3.50000 6.06218i −0.406867 0.704714i
\(75\) 0 0
\(76\) −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 0
\(81\) −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 \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −1.00000 1.73205i −0.109109 0.188982i
\(85\) 0 0
\(86\) 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 0.217354 0.976093i \(-0.430258\pi\)
0.736644 0.676280i \(-0.236409\pi\)
\(90\) 0 0
\(91\) −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
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 7.00000 + 12.1244i 0.710742 + 1.23104i 0.964579 + 0.263795i \(0.0849741\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) −3.00000 + 5.19615i −0.297044 + 0.514496i
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) −1.00000 + 3.46410i −0.0980581 + 0.339683i
\(105\) 0 0
\(106\) −3.00000 + 5.19615i −0.291386 + 0.504695i
\(107\) −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) 0.500000 + 0.866025i 0.0481125 + 0.0833333i
\(109\) 14.0000 1.34096 0.670478 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) 0 0
\(111\) 3.50000 + 6.06218i 0.332205 + 0.575396i
\(112\) −2.00000 −0.188982
\(113\) 7.50000 + 12.9904i 0.705541 + 1.22203i 0.966496 + 0.256681i \(0.0826291\pi\)
−0.260955 + 0.965351i \(0.584038\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) 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 0
\(121\) 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
\(125\) 0 0
\(126\) 1.00000 + 1.73205i 0.0890871 + 0.154303i
\(127\) 7.00000 12.1244i 0.621150 1.07586i −0.368122 0.929777i \(-0.619999\pi\)
0.989272 0.146085i \(-0.0466674\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −1.00000 −0.0880451
\(130\) 0 0
\(131\) 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
\(135\) 0 0
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 3.00000 0.255377
\(139\) −7.00000 12.1244i −0.593732 1.02837i −0.993724 0.111856i \(-0.964321\pi\)
0.399992 0.916519i \(-0.369013\pi\)
\(140\) 0 0
\(141\) 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
\(145\) 0 0
\(146\) 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 0.989355 0.145519i \(-0.0464853\pi\)
−0.620701 + 0.784047i \(0.713152\pi\)
\(150\) 0 0
\(151\) 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
\(155\) 0 0
\(156\) 1.00000 3.46410i 0.0800641 0.277350i
\(157\) 13.0000 1.03751 0.518756 0.854922i \(-0.326395\pi\)
0.518756 + 0.854922i \(0.326395\pi\)
\(158\) −2.50000 + 4.33013i −0.198889 + 0.344486i
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) 6.00000 0.472866
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −6.50000 11.2583i −0.509119 0.881820i −0.999944 0.0105623i \(-0.996638\pi\)
0.490825 0.871258i \(-0.336695\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) −4.50000 + 7.79423i −0.348220 + 0.603136i −0.985933 0.167139i \(-0.946547\pi\)
0.637713 + 0.770274i \(0.279881\pi\)
\(168\) 2.00000 0.154303
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) 0 0
\(171\) −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 \(-0.0158870\pi\)
−0.542583 + 0.840002i \(0.682554\pi\)
\(174\) −3.00000 −0.227429
\(175\) 0 0
\(176\) 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 −0.804508 0.593942i \(-0.797571\pi\)
0.916623 + 0.399753i \(0.130904\pi\)
\(180\) 0 0
\(181\) −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
\(185\) 0 0
\(186\) 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
\(190\) 0 0
\(191\) 6.00000 + 10.3923i 0.434145 + 0.751961i 0.997225 0.0744412i \(-0.0237173\pi\)
−0.563081 + 0.826402i \(0.690384\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −2.00000 + 3.46410i −0.143963 + 0.249351i −0.928986 0.370116i \(-0.879318\pi\)
0.785022 + 0.619467i \(0.212651\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 12.0000 20.7846i 0.854965 1.48084i −0.0217133 0.999764i \(-0.506912\pi\)
0.876678 0.481078i \(-0.159755\pi\)
\(198\) 1.50000 2.59808i 0.106600 0.184637i
\(199\) −4.00000 6.92820i −0.283552 0.491127i 0.688705 0.725042i \(-0.258180\pi\)
−0.972257 + 0.233915i \(0.924846\pi\)
\(200\) 0 0
\(201\) −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
\(205\) 0 0
\(206\) 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
\(210\) 0 0
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 12.0000 0.822226
\(214\) −3.00000 5.19615i −0.205076 0.355202i
\(215\) 0 0
\(216\) −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
\(220\) 0 0
\(221\) −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 \(-0.942010\pi\)
0.648626 + 0.761107i \(0.275344\pi\)
\(224\) 1.00000 1.73205i 0.0668153 0.115728i
\(225\) 0 0
\(226\) −15.0000 −0.997785
\(227\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(228\) 1.00000 + 1.73205i 0.0662266 + 0.114708i
\(229\) 14.0000 0.925146 0.462573 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 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 \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) −1.00000 + 3.46410i −0.0653720 + 0.226455i
\(235\) 0 0
\(236\) 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 0
\(241\) −8.50000 14.7224i −0.547533 0.948355i −0.998443 0.0557856i \(-0.982234\pi\)
0.450910 0.892570i \(-0.351100\pi\)
\(242\) −2.00000 −0.128565
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −1.00000 + 1.73205i −0.0640184 + 0.110883i
\(245\) 0 0
\(246\) −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 0
\(251\) −7.50000 12.9904i −0.473396 0.819946i 0.526140 0.850398i \(-0.323639\pi\)
−0.999536 + 0.0304521i \(0.990305\pi\)
\(252\) −2.00000 −0.125988
\(253\) −4.50000 7.79423i −0.282913 0.490019i
\(254\) 7.00000 + 12.1244i 0.439219 + 0.760750i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.5000 + 18.1865i −0.654972 + 1.13444i 0.326929 + 0.945049i \(0.393986\pi\)
−0.981901 + 0.189396i \(0.939347\pi\)
\(258\) 0.500000 0.866025i 0.0311286 0.0539164i
\(259\) −14.0000 −0.869918
\(260\) 0 0
\(261\) 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 \(-0.986370\pi\)
0.536614 + 0.843828i \(0.319703\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) 0 0
\(266\) 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 −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) −6.00000 −0.363803
\(273\) −2.00000 + 6.92820i −0.121046 + 0.419314i
\(274\) −9.00000 −0.543710
\(275\) 0 0
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) −0.500000 0.866025i −0.0300421 0.0520344i 0.850613 0.525792i \(-0.176231\pi\)
−0.880656 + 0.473757i \(0.842897\pi\)
\(278\) 14.0000 0.839664
\(279\) −2.50000 4.33013i −0.149671 0.259238i
\(280\) 0 0
\(281\) 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 −0.124096 + 0.992270i \(0.539603\pi\)
−0.797283 + 0.603606i \(0.793730\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) −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
\(290\) 0 0
\(291\) 14.0000 0.820695
\(292\) 7.00000 + 12.1244i 0.409644 + 0.709524i
\(293\) −15.0000 25.9808i −0.876309 1.51781i −0.855361 0.518032i \(-0.826665\pi\)
−0.0209480 0.999781i \(-0.506668\pi\)
\(294\) 3.00000 0.174964
\(295\) 0 0
\(296\) −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
\(300\) 0 0
\(301\) 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
\(305\) 0 0
\(306\) 3.00000 + 5.19615i 0.171499 + 0.297044i
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) −3.00000 5.19615i −0.170941 0.296078i
\(309\) −7.00000 + 12.1244i −0.398216 + 0.689730i
\(310\) 0 0
\(311\) −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 \(-0.572595\pi\)
−0.226093 + 0.974106i \(0.572595\pi\)
\(314\) −6.50000 + 11.2583i −0.366816 + 0.635344i
\(315\) 0 0
\(316\) −2.50000 4.33013i −0.140636 0.243589i
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 3.00000 + 5.19615i 0.168232 + 0.291386i
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) 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
\(325\) 0 0
\(326\) 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
\(330\) 0 0
\(331\) −16.0000 27.7128i −0.879440 1.52323i −0.851957 0.523612i \(-0.824584\pi\)
−0.0274825 0.999622i \(-0.508749\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 7.00000 0.383598
\(334\) −4.50000 7.79423i −0.246229 0.426481i
\(335\) 0 0
\(336\) −1.00000 + 1.73205i −0.0545545 + 0.0944911i
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) 11.5000 6.06218i 0.625518 0.329739i
\(339\) 15.0000 0.814688
\(340\) 0 0
\(341\) 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
\(345\) 0 0
\(346\) −12.0000 −0.645124
\(347\) −15.0000 25.9808i −0.805242 1.39472i −0.916127 0.400887i \(-0.868702\pi\)
0.110885 0.993833i \(-0.464631\pi\)
\(348\) 1.50000 2.59808i 0.0804084 0.139272i
\(349\) −4.00000 + 6.92820i −0.214115 + 0.370858i −0.952998 0.302975i \(-0.902020\pi\)
0.738883 + 0.673833i \(0.235353\pi\)
\(350\) 0 0
\(351\) 1.00000 3.46410i 0.0533761 0.184900i
\(352\) −3.00000 −0.159901
\(353\) 15.0000 25.9808i 0.798369 1.38282i −0.122308 0.992492i \(-0.539030\pi\)
0.920677 0.390324i \(-0.127637\pi\)
\(354\) −4.50000 + 7.79423i −0.239172 + 0.414259i
\(355\) 0 0
\(356\) −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 0
\(361\) 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
\(365\) 0 0
\(366\) 1.00000 1.73205i 0.0522708 0.0905357i
\(367\) 10.0000 17.3205i 0.521996 0.904123i −0.477677 0.878536i \(-0.658521\pi\)
0.999673 0.0255875i \(-0.00814566\pi\)
\(368\) 1.50000 + 2.59808i 0.0781929 + 0.135434i
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) 6.00000 + 10.3923i 0.311504 + 0.539542i
\(372\) −5.00000 −0.259238
\(373\) −12.5000 21.6506i −0.647225 1.12103i −0.983783 0.179364i \(-0.942596\pi\)
0.336557 0.941663i \(-0.390737\pi\)
\(374\) −9.00000 + 15.5885i −0.465379 + 0.806060i
\(375\) 0 0
\(376\) 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 −0.299249 + 0.954175i \(0.596736\pi\)
−0.676715 + 0.736245i \(0.736597\pi\)
\(380\) 0 0
\(381\) −7.00000 12.1244i −0.358621 0.621150i
\(382\) −12.0000 −0.613973
\(383\) −10.5000 18.1865i −0.536525 0.929288i −0.999088 0.0427020i \(-0.986403\pi\)
0.462563 0.886586i \(-0.346930\pi\)
\(384\) 0.500000 + 0.866025i 0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −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 \(0.475768\pi\)
\(390\) 0 0
\(391\) 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
\(395\) 0 0
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) −15.5000 26.8468i −0.777923 1.34740i −0.933137 0.359521i \(-0.882940\pi\)
0.155214 0.987881i \(-0.450393\pi\)
\(398\) 8.00000 0.401004
\(399\) −2.00000 3.46410i −0.100125 0.173422i
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 8.00000 0.399004
\(403\) −5.00000 + 17.3205i −0.249068 + 0.862796i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 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 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) 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 −0.681426 0.731887i \(-0.738640\pi\)
0.974546 + 0.224189i \(0.0719734\pi\)
\(420\) 0 0
\(421\) −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
\(425\) 0 0
\(426\) −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
\(430\) 0 0
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 0.500000 0.866025i 0.0240563 0.0416667i
\(433\) −20.0000 34.6410i −0.961139 1.66474i −0.719650 0.694337i \(-0.755698\pi\)
−0.241489 0.970404i \(-0.577636\pi\)
\(434\) −10.0000 −0.480015
\(435\) 0 0
\(436\) −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 −0.814344 0.580383i \(-0.802903\pi\)
0.909798 + 0.415051i \(0.136236\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 6.00000 20.7846i 0.285391 0.988623i
\(443\) 36.0000 1.71041 0.855206 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 3.50000 6.06218i 0.166103 0.287698i
\(445\) 0 0
\(446\) −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 −0.881680 0.471848i \(-0.843587\pi\)
0.0322072 0.999481i \(-0.489746\pi\)
\(450\) 0 0
\(451\) 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
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 1.00000 1.73205i 0.0467780 0.0810219i −0.841688 0.539964i \(-0.818438\pi\)
0.888466 + 0.458942i \(0.151771\pi\)
\(458\) −7.00000 + 12.1244i −0.327089 + 0.566534i
\(459\) −3.00000 5.19615i −0.140028 0.242536i
\(460\) 0 0
\(461\) −7.50000 12.9904i −0.349310 0.605022i 0.636817 0.771015i \(-0.280251\pi\)
−0.986127 + 0.165992i \(0.946917\pi\)
\(462\) 3.00000 + 5.19615i 0.139573 + 0.241747i
\(463\) 34.0000 1.58011 0.790057 0.613033i \(-0.210051\pi\)
0.790057 + 0.613033i \(0.210051\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 0 0
\(466\) 10.5000 18.1865i 0.486403 0.842475i
\(467\) −18.0000 −0.832941 −0.416470 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) −2.50000 2.59808i −0.115563 0.120096i
\(469\) 16.0000 0.738811
\(470\) 0 0
\(471\) 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
\(475\) 0 0
\(476\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 0 0
\(481\) −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
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 1.00000 + 1.73205i 0.0453143 + 0.0784867i 0.887793 0.460243i \(-0.152238\pi\)
−0.842479 + 0.538730i \(0.818904\pi\)
\(488\) −1.00000 1.73205i −0.0452679 0.0784063i
\(489\) −13.0000 −0.587880
\(490\) 0 0
\(491\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(492\) 3.00000 5.19615i 0.135250 0.234261i
\(493\) −18.0000 −0.810679
\(494\) −2.00000 + 6.92820i −0.0899843 + 0.311715i
\(495\) 0 0
\(496\) −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 0
\(501\) 4.50000 + 7.79423i 0.201045 + 0.348220i
\(502\) 15.0000 0.669483
\(503\) 12.0000 + 20.7846i 0.535054 + 0.926740i 0.999161 + 0.0409609i \(0.0130419\pi\)
−0.464107 + 0.885779i \(0.653625\pi\)
\(504\) 1.00000 1.73205i 0.0445435 0.0771517i
\(505\) 0 0
\(506\) 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 −0.897352 0.441315i \(-0.854512\pi\)
0.830866 + 0.556473i \(0.187846\pi\)
\(510\) 0 0
\(511\) −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
\(515\) 0 0
\(516\) 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
\(520\) 0 0
\(521\) −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 \(-0.756023\pi\)
0.960856 + 0.277047i \(0.0893559\pi\)
\(524\) −4.50000 7.79423i −0.196583 0.340492i
\(525\) 0 0
\(526\) −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
\(530\) 0 0
\(531\) 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
\(535\) 0 0
\(536\) 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 0
\(541\) 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
\(545\) 0 0
\(546\) −5.00000 5.19615i −0.213980 0.222375i
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) −1.00000 + 1.73205i −0.0426790 + 0.0739221i
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) −7.00000 + 12.1244i −0.296866 + 0.514187i
\(557\) −3.00000 + 5.19615i −0.127114 + 0.220168i −0.922557 0.385860i \(-0.873905\pi\)
0.795443 + 0.606028i \(0.207238\pi\)
\(558\) 5.00000 0.211667
\(559\) 3.50000 0.866025i 0.148034 0.0366290i
\(560\) 0 0
\(561\) 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 0.943560 + 0.331202i \(0.107454\pi\)
−0.184950 + 0.982748i \(0.559212\pi\)
\(564\) −3.00000 −0.126323
\(565\) 0 0
\(566\) −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 −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −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
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) 2.00000 + 3.46410i 0.0831172 + 0.143963i
\(580\) 0 0
\(581\) 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
\(585\) 0 0
\(586\) 30.0000 1.23929
\(587\) 9.00000 15.5885i 0.371470 0.643404i −0.618322 0.785925i \(-0.712187\pi\)
0.989792 + 0.142520i \(0.0455206\pi\)
\(588\) −1.50000 + 2.59808i −0.0618590 + 0.107143i
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) 0 0
\(591\) −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 \(-0.687044\pi\)
−0.554379 + 0.832265i \(0.687044\pi\)
\(594\) −1.50000 2.59808i −0.0615457 0.106600i
\(595\) 0 0
\(596\) 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 0
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) 1.00000 + 1.73205i 0.0407570 + 0.0705931i
\(603\) −8.00000 −0.325785
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 0 0
\(606\) −6.00000 −0.243733
\(607\) −11.0000 19.0526i −0.446476 0.773320i 0.551678 0.834058i \(-0.313988\pi\)
−0.998154 + 0.0607380i \(0.980655\pi\)
\(608\) −1.00000 + 1.73205i −0.0405554 + 0.0702439i
\(609\) −3.00000 + 5.19615i −0.121566 + 0.210559i
\(610\) 0 0
\(611\) −3.00000 + 10.3923i −0.121367 + 0.420428i
\(612\) −6.00000 −0.242536
\(613\) −15.5000 + 26.8468i −0.626039 + 1.08433i 0.362300 + 0.932062i \(0.381992\pi\)
−0.988339 + 0.152270i \(0.951342\pi\)
\(614\) 4.00000 6.92820i 0.161427 0.279600i
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) 10.5000 + 18.1865i 0.422714 + 0.732162i 0.996204 0.0870504i \(-0.0277441\pi\)
−0.573490 + 0.819213i \(0.694411\pi\)
\(618\) −7.00000 12.1244i −0.281581 0.487713i
\(619\) −46.0000 −1.84890 −0.924448 0.381308i \(-0.875474\pi\)
−0.924448 + 0.381308i \(0.875474\pi\)
\(620\) 0 0
\(621\) −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
\(625\) 0 0
\(626\) 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
\(630\) 0 0
\(631\) 8.00000 + 13.8564i 0.318475 + 0.551615i 0.980170 0.198158i \(-0.0634960\pi\)
−0.661695 + 0.749773i \(0.730163\pi\)
\(632\) 5.00000 0.198889
\(633\) 10.0000 + 17.3205i 0.397464 + 0.688428i
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) 0 0
\(636\) −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 0
\(641\) −3.00000 5.19615i −0.118493 0.205236i 0.800678 0.599095i \(-0.204473\pi\)
−0.919171 + 0.393860i \(0.871140\pi\)
\(642\) −6.00000 −0.236801
\(643\) −8.00000 13.8564i −0.315489 0.546443i 0.664052 0.747686i \(-0.268835\pi\)
−0.979541 + 0.201243i \(0.935502\pi\)
\(644\) −3.00000 5.19615i −0.118217 0.204757i
\(645\) 0 0
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) 12.0000 20.7846i 0.471769 0.817127i −0.527710 0.849425i \(-0.676949\pi\)
0.999478 + 0.0322975i \(0.0102824\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 27.0000 1.05984
\(650\) 0 0
\(651\) 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 \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 7.00000 + 12.1244i 0.273722 + 0.474100i
\(655\) 0 0
\(656\) −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 0.682161 0.731202i \(-0.261040\pi\)
−0.974320 + 0.225168i \(0.927707\pi\)
\(660\) 0 0
\(661\) −16.0000 + 27.7128i −0.622328 + 1.07790i 0.366723 + 0.930330i \(0.380480\pi\)
−0.989051 + 0.147573i \(0.952854\pi\)
\(662\) 32.0000 1.24372
\(663\) −6.00000 + 20.7846i −0.233021 + 0.807207i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) −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 \(-0.857898\pi\)
0.824901 + 0.565278i \(0.191231\pi\)
\(674\) 7.00000 12.1244i 0.269630 0.467013i
\(675\) 0 0
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) 36.0000 1.38359 0.691796 0.722093i \(-0.256820\pi\)
0.691796 + 0.722093i \(0.256820\pi\)
\(678\) −7.50000 + 12.9904i −0.288036 + 0.498893i
\(679\) −14.0000 + 24.2487i −0.537271 + 0.930580i
\(680\) 0 0
\(681\) 0 0
\(682\) 7.50000 + 12.9904i 0.287190 + 0.497427i
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) −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
\(690\) 0 0
\(691\) 23.0000 39.8372i 0.874961 1.51548i 0.0181572 0.999835i \(-0.494220\pi\)
0.856804 0.515642i \(-0.172447\pi\)
\(692\) 6.00000 10.3923i 0.228086 0.395056i
\(693\) −3.00000 5.19615i −0.113961 0.197386i
\(694\) 30.0000 1.13878
\(695\) 0 0
\(696\) 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
\(700\) 0 0
\(701\) −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
\(705\) 0 0
\(706\) 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 −0.992686 0.120723i \(-0.961479\pi\)
0.391794 0.920053i \(-0.371855\pi\)
\(710\) 0 0
\(711\) −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
\(715\) 0 0
\(716\) −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 −0.977539 0.210752i \(-0.932409\pi\)
0.306253 0.951950i \(-0.400925\pi\)
\(720\) 0 0
\(721\) −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
\(725\) 0 0
\(726\) −1.00000 + 1.73205i −0.0371135 + 0.0642824i
\(727\) 4.00000 0.148352 0.0741759 0.997245i \(-0.476367\pi\)
0.0741759 + 0.997245i \(0.476367\pi\)
\(728\) −7.00000 + 1.73205i −0.259437 + 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 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 \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 10.0000 + 17.3205i 0.369107 + 0.639312i
\(735\) 0 0
\(736\) −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 −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) 0 0
\(741\) 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 \(-0.886124\pi\)
0.771598 + 0.636111i \(0.219458\pi\)
\(744\) 2.50000 4.33013i 0.0916544 0.158750i
\(745\) 0 0
\(746\) 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 0
\(751\) −20.5000 + 35.5070i −0.748056 + 1.29567i 0.200698 + 0.979653i \(0.435679\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) −15.0000 −0.546630
\(754\) 10.5000 2.59808i 0.382387 0.0946164i
\(755\) 0 0
\(756\) −1.00000 + 1.73205i −0.0363696 + 0.0629941i
\(757\) 19.0000 32.9090i 0.690567 1.19610i −0.281086 0.959683i \(-0.590695\pi\)
0.971652 0.236414i \(-0.0759722\pi\)
\(758\) −19.0000 32.9090i −0.690111 1.19531i
\(759\) −9.00000 −0.326679
\(760\) 0 0
\(761\) 6.00000 + 10.3923i 0.217500 + 0.376721i 0.954043 0.299670i \(-0.0968765\pi\)
−0.736543 + 0.676391i \(0.763543\pi\)
\(762\) 14.0000 0.507166
\(763\) 14.0000 + 24.2487i 0.506834 + 0.877862i
\(764\) 6.00000 10.3923i 0.217072 0.375980i
\(765\) 0 0
\(766\) 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 −0.724701 0.689063i \(-0.758022\pi\)
0.959097 + 0.283078i \(0.0913554\pi\)
\(770\) 0 0
\(771\) 10.5000 + 18.1865i 0.378148 + 0.654972i
\(772\) 4.00000 0.143963
\(773\) −24.0000 41.5692i −0.863220 1.49514i −0.868804 0.495156i \(-0.835111\pi\)
0.00558380 0.999984i \(-0.498223\pi\)
\(774\) −0.500000 0.866025i −0.0179721 0.0311286i
\(775\) 0 0
\(776\) 7.00000 + 12.1244i 0.251285 + 0.435239i
\(777\) −7.00000 + 12.1244i −0.251124 + 0.434959i
\(778\) −1.50000 + 2.59808i −0.0537776 + 0.0931455i
\(779\) 12.0000 0.429945
\(780\) 0 0
\(781\) 36.0000 1.28818
\(782\) −9.00000 + 15.5885i −0.321839 + 0.557442i
\(783\) 1.50000 2.59808i 0.0536056 0.0928477i
\(784\) 1.50000 + 2.59808i 0.0535714 + 0.0927884i
\(785\) 0 0
\(786\) 4.50000