Properties

Label 1014.2.e.g.991.1
Level $1014$
Weight $2$
Character 1014.991
Analytic conductor $8.097$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1014.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 991.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.991
Dual form 1014.2.e.g.529.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.267949 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +0.267949 q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.366025 + 0.633975i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.133975 - 0.232051i) q^{10} +(-2.36603 - 4.09808i) q^{11} +1.00000 q^{12} +0.732051 q^{14} +(-0.133975 - 0.232051i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.13397 - 1.96410i) q^{17} +1.00000 q^{18} +(-0.633975 + 1.09808i) q^{19} +(-0.133975 + 0.232051i) q^{20} +0.732051 q^{21} +(-2.36603 + 4.09808i) q^{22} +(3.09808 + 5.36603i) q^{23} +(-0.500000 - 0.866025i) q^{24} -4.92820 q^{25} +1.00000 q^{27} +(-0.366025 - 0.633975i) q^{28} +(-1.23205 - 2.13397i) q^{29} +(-0.133975 + 0.232051i) q^{30} -5.46410 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.36603 + 4.09808i) q^{33} -2.26795 q^{34} +(-0.0980762 + 0.169873i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.23205 - 9.06218i) q^{37} +1.26795 q^{38} +0.267949 q^{40} +(-5.69615 - 9.86603i) q^{41} +(-0.366025 - 0.633975i) q^{42} +(-3.83013 + 6.63397i) q^{43} +4.73205 q^{44} +(-0.133975 + 0.232051i) q^{45} +(3.09808 - 5.36603i) q^{46} -8.19615 q^{47} +(-0.500000 + 0.866025i) q^{48} +(3.23205 + 5.59808i) q^{49} +(2.46410 + 4.26795i) q^{50} -2.26795 q^{51} +0.464102 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.633975 - 1.09808i) q^{55} +(-0.366025 + 0.633975i) q^{56} +1.26795 q^{57} +(-1.23205 + 2.13397i) q^{58} +(-4.00000 + 6.92820i) q^{59} +0.267949 q^{60} +(-0.598076 + 1.03590i) q^{61} +(2.73205 + 4.73205i) q^{62} +(-0.366025 - 0.633975i) q^{63} +1.00000 q^{64} +4.73205 q^{66} +(5.56218 + 9.63397i) q^{67} +(1.13397 + 1.96410i) q^{68} +(3.09808 - 5.36603i) q^{69} +0.196152 q^{70} +(-0.633975 + 1.09808i) q^{71} +(-0.500000 + 0.866025i) q^{72} -9.73205 q^{73} +(-5.23205 + 9.06218i) q^{74} +(2.46410 + 4.26795i) q^{75} +(-0.633975 - 1.09808i) q^{76} +3.46410 q^{77} -9.46410 q^{79} +(-0.133975 - 0.232051i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.69615 + 9.86603i) q^{82} +10.1962 q^{83} +(-0.366025 + 0.633975i) q^{84} +(0.303848 - 0.526279i) q^{85} +7.66025 q^{86} +(-1.23205 + 2.13397i) q^{87} +(-2.36603 - 4.09808i) q^{88} +(1.26795 + 2.19615i) q^{89} +0.267949 q^{90} -6.19615 q^{92} +(2.73205 + 4.73205i) q^{93} +(4.09808 + 7.09808i) q^{94} +(-0.169873 + 0.294229i) q^{95} +1.00000 q^{96} +(3.00000 - 5.19615i) q^{97} +(3.23205 - 5.59808i) q^{98} +4.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 8 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} - 4 q^{10} - 6 q^{11} + 4 q^{12} - 4 q^{14} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} - 6 q^{19} - 4 q^{20} - 4 q^{21} - 6 q^{22} + 2 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{27} + 2 q^{28} + 2 q^{29} - 4 q^{30} - 8 q^{31} - 2 q^{32} - 6 q^{33} - 16 q^{34} + 10 q^{35} - 2 q^{36} - 14 q^{37} + 12 q^{38} + 8 q^{40} - 2 q^{41} + 2 q^{42} + 2 q^{43} + 12 q^{44} - 4 q^{45} + 2 q^{46} - 12 q^{47} - 2 q^{48} + 6 q^{49} - 4 q^{50} - 16 q^{51} - 12 q^{53} - 2 q^{54} - 6 q^{55} + 2 q^{56} + 12 q^{57} + 2 q^{58} - 16 q^{59} + 8 q^{60} + 8 q^{61} + 4 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{66} - 2 q^{67} + 8 q^{68} + 2 q^{69} - 20 q^{70} - 6 q^{71} - 2 q^{72} - 32 q^{73} - 14 q^{74} - 4 q^{75} - 6 q^{76} - 24 q^{79} - 4 q^{80} - 2 q^{81} - 2 q^{82} + 20 q^{83} + 2 q^{84} + 22 q^{85} - 4 q^{86} + 2 q^{87} - 6 q^{88} + 12 q^{89} + 8 q^{90} - 4 q^{92} + 4 q^{93} + 6 q^{94} - 18 q^{95} + 4 q^{96} + 12 q^{97} + 6 q^{98} + 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.267949 0.119831 0.0599153 0.998203i \(-0.480917\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −0.366025 + 0.633975i −0.138345 + 0.239620i −0.926870 0.375382i \(-0.877511\pi\)
0.788526 + 0.615002i \(0.210845\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.133975 0.232051i −0.0423665 0.0733809i
\(11\) −2.36603 4.09808i −0.713384 1.23562i −0.963580 0.267421i \(-0.913828\pi\)
0.250196 0.968195i \(-0.419505\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 0.732051 0.195649
\(15\) −0.133975 0.232051i −0.0345921 0.0599153i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.13397 1.96410i 0.275029 0.476365i −0.695113 0.718900i \(-0.744646\pi\)
0.970143 + 0.242536i \(0.0779791\pi\)
\(18\) 1.00000 0.235702
\(19\) −0.633975 + 1.09808i −0.145444 + 0.251916i −0.929538 0.368725i \(-0.879794\pi\)
0.784095 + 0.620641i \(0.213128\pi\)
\(20\) −0.133975 + 0.232051i −0.0299576 + 0.0518881i
\(21\) 0.732051 0.159747
\(22\) −2.36603 + 4.09808i −0.504438 + 0.873713i
\(23\) 3.09808 + 5.36603i 0.645994 + 1.11889i 0.984071 + 0.177775i \(0.0568901\pi\)
−0.338078 + 0.941118i \(0.609777\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −4.92820 −0.985641
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −0.366025 0.633975i −0.0691723 0.119810i
\(29\) −1.23205 2.13397i −0.228786 0.396269i 0.728663 0.684873i \(-0.240142\pi\)
−0.957449 + 0.288604i \(0.906809\pi\)
\(30\) −0.133975 + 0.232051i −0.0244603 + 0.0423665i
\(31\) −5.46410 −0.981382 −0.490691 0.871334i \(-0.663256\pi\)
−0.490691 + 0.871334i \(0.663256\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.36603 + 4.09808i −0.411872 + 0.713384i
\(34\) −2.26795 −0.388950
\(35\) −0.0980762 + 0.169873i −0.0165779 + 0.0287138i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −5.23205 9.06218i −0.860144 1.48981i −0.871789 0.489881i \(-0.837040\pi\)
0.0116456 0.999932i \(-0.496293\pi\)
\(38\) 1.26795 0.205689
\(39\) 0 0
\(40\) 0.267949 0.0423665
\(41\) −5.69615 9.86603i −0.889590 1.54081i −0.840361 0.542027i \(-0.817657\pi\)
−0.0492283 0.998788i \(-0.515676\pi\)
\(42\) −0.366025 0.633975i −0.0564789 0.0978244i
\(43\) −3.83013 + 6.63397i −0.584089 + 1.01167i 0.410899 + 0.911681i \(0.365215\pi\)
−0.994988 + 0.0999910i \(0.968119\pi\)
\(44\) 4.73205 0.713384
\(45\) −0.133975 + 0.232051i −0.0199718 + 0.0345921i
\(46\) 3.09808 5.36603i 0.456786 0.791177i
\(47\) −8.19615 −1.19553 −0.597766 0.801671i \(-0.703945\pi\)
−0.597766 + 0.801671i \(0.703945\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) 3.23205 + 5.59808i 0.461722 + 0.799725i
\(50\) 2.46410 + 4.26795i 0.348477 + 0.603579i
\(51\) −2.26795 −0.317576
\(52\) 0 0
\(53\) 0.464102 0.0637493 0.0318746 0.999492i \(-0.489852\pi\)
0.0318746 + 0.999492i \(0.489852\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) −0.633975 1.09808i −0.0854851 0.148065i
\(56\) −0.366025 + 0.633975i −0.0489122 + 0.0847184i
\(57\) 1.26795 0.167944
\(58\) −1.23205 + 2.13397i −0.161776 + 0.280205i
\(59\) −4.00000 + 6.92820i −0.520756 + 0.901975i 0.478953 + 0.877841i \(0.341016\pi\)
−0.999709 + 0.0241347i \(0.992317\pi\)
\(60\) 0.267949 0.0345921
\(61\) −0.598076 + 1.03590i −0.0765758 + 0.132633i −0.901770 0.432215i \(-0.857732\pi\)
0.825195 + 0.564848i \(0.191065\pi\)
\(62\) 2.73205 + 4.73205i 0.346971 + 0.600971i
\(63\) −0.366025 0.633975i −0.0461149 0.0798733i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.73205 0.582475
\(67\) 5.56218 + 9.63397i 0.679528 + 1.17698i 0.975123 + 0.221664i \(0.0711488\pi\)
−0.295595 + 0.955313i \(0.595518\pi\)
\(68\) 1.13397 + 1.96410i 0.137515 + 0.238182i
\(69\) 3.09808 5.36603i 0.372965 0.645994i
\(70\) 0.196152 0.0234447
\(71\) −0.633975 + 1.09808i −0.0752389 + 0.130318i −0.901190 0.433424i \(-0.857305\pi\)
0.825951 + 0.563742i \(0.190639\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −9.73205 −1.13905 −0.569525 0.821974i \(-0.692873\pi\)
−0.569525 + 0.821974i \(0.692873\pi\)
\(74\) −5.23205 + 9.06218i −0.608214 + 1.05346i
\(75\) 2.46410 + 4.26795i 0.284530 + 0.492820i
\(76\) −0.633975 1.09808i −0.0727219 0.125958i
\(77\) 3.46410 0.394771
\(78\) 0 0
\(79\) −9.46410 −1.06479 −0.532397 0.846495i \(-0.678709\pi\)
−0.532397 + 0.846495i \(0.678709\pi\)
\(80\) −0.133975 0.232051i −0.0149788 0.0259441i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −5.69615 + 9.86603i −0.629035 + 1.08952i
\(83\) 10.1962 1.11917 0.559587 0.828772i \(-0.310960\pi\)
0.559587 + 0.828772i \(0.310960\pi\)
\(84\) −0.366025 + 0.633975i −0.0399366 + 0.0691723i
\(85\) 0.303848 0.526279i 0.0329569 0.0570830i
\(86\) 7.66025 0.826026
\(87\) −1.23205 + 2.13397i −0.132090 + 0.228786i
\(88\) −2.36603 4.09808i −0.252219 0.436856i
\(89\) 1.26795 + 2.19615i 0.134402 + 0.232792i 0.925369 0.379068i \(-0.123755\pi\)
−0.790967 + 0.611859i \(0.790422\pi\)
\(90\) 0.267949 0.0282443
\(91\) 0 0
\(92\) −6.19615 −0.645994
\(93\) 2.73205 + 4.73205i 0.283300 + 0.490691i
\(94\) 4.09808 + 7.09808i 0.422684 + 0.732111i
\(95\) −0.169873 + 0.294229i −0.0174286 + 0.0301872i
\(96\) 1.00000 0.102062
\(97\) 3.00000 5.19615i 0.304604 0.527589i −0.672569 0.740034i \(-0.734809\pi\)
0.977173 + 0.212445i \(0.0681426\pi\)
\(98\) 3.23205 5.59808i 0.326486 0.565491i
\(99\) 4.73205 0.475589
\(100\) 2.46410 4.26795i 0.246410 0.426795i
\(101\) 5.96410 + 10.3301i 0.593450 + 1.02789i 0.993764 + 0.111508i \(0.0355680\pi\)
−0.400313 + 0.916378i \(0.631099\pi\)
\(102\) 1.13397 + 1.96410i 0.112280 + 0.194475i
\(103\) −18.7321 −1.84572 −0.922862 0.385131i \(-0.874156\pi\)
−0.922862 + 0.385131i \(0.874156\pi\)
\(104\) 0 0
\(105\) 0.196152 0.0191425
\(106\) −0.232051 0.401924i −0.0225388 0.0390383i
\(107\) 0.0980762 + 0.169873i 0.00948139 + 0.0164222i 0.870727 0.491766i \(-0.163649\pi\)
−0.861246 + 0.508189i \(0.830315\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −5.46410 −0.523366 −0.261683 0.965154i \(-0.584277\pi\)
−0.261683 + 0.965154i \(0.584277\pi\)
\(110\) −0.633975 + 1.09808i −0.0604471 + 0.104697i
\(111\) −5.23205 + 9.06218i −0.496604 + 0.860144i
\(112\) 0.732051 0.0691723
\(113\) 9.33013 16.1603i 0.877705 1.52023i 0.0238510 0.999716i \(-0.492407\pi\)
0.853854 0.520513i \(-0.174259\pi\)
\(114\) −0.633975 1.09808i −0.0593772 0.102844i
\(115\) 0.830127 + 1.43782i 0.0774097 + 0.134078i
\(116\) 2.46410 0.228786
\(117\) 0 0
\(118\) 8.00000 0.736460
\(119\) 0.830127 + 1.43782i 0.0760976 + 0.131805i
\(120\) −0.133975 0.232051i −0.0122302 0.0211832i
\(121\) −5.69615 + 9.86603i −0.517832 + 0.896911i
\(122\) 1.19615 0.108295
\(123\) −5.69615 + 9.86603i −0.513605 + 0.889590i
\(124\) 2.73205 4.73205i 0.245345 0.424951i
\(125\) −2.66025 −0.237940
\(126\) −0.366025 + 0.633975i −0.0326081 + 0.0564789i
\(127\) −8.92820 15.4641i −0.792250 1.37222i −0.924571 0.381010i \(-0.875576\pi\)
0.132321 0.991207i \(-0.457757\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 7.66025 0.674448
\(130\) 0 0
\(131\) 13.4641 1.17636 0.588182 0.808729i \(-0.299844\pi\)
0.588182 + 0.808729i \(0.299844\pi\)
\(132\) −2.36603 4.09808i −0.205936 0.356692i
\(133\) −0.464102 0.803848i −0.0402427 0.0697024i
\(134\) 5.56218 9.63397i 0.480499 0.832249i
\(135\) 0.267949 0.0230614
\(136\) 1.13397 1.96410i 0.0972375 0.168420i
\(137\) 0.964102 1.66987i 0.0823688 0.142667i −0.821898 0.569634i \(-0.807085\pi\)
0.904267 + 0.426968i \(0.140418\pi\)
\(138\) −6.19615 −0.527452
\(139\) 4.92820 8.53590i 0.418005 0.724005i −0.577734 0.816225i \(-0.696063\pi\)
0.995739 + 0.0922197i \(0.0293962\pi\)
\(140\) −0.0980762 0.169873i −0.00828895 0.0143569i
\(141\) 4.09808 + 7.09808i 0.345120 + 0.597766i
\(142\) 1.26795 0.106404
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −0.330127 0.571797i −0.0274156 0.0474851i
\(146\) 4.86603 + 8.42820i 0.402715 + 0.697523i
\(147\) 3.23205 5.59808i 0.266575 0.461722i
\(148\) 10.4641 0.860144
\(149\) −1.40192 + 2.42820i −0.114850 + 0.198926i −0.917720 0.397228i \(-0.869972\pi\)
0.802870 + 0.596154i \(0.203305\pi\)
\(150\) 2.46410 4.26795i 0.201193 0.348477i
\(151\) 3.26795 0.265942 0.132971 0.991120i \(-0.457548\pi\)
0.132971 + 0.991120i \(0.457548\pi\)
\(152\) −0.633975 + 1.09808i −0.0514221 + 0.0890657i
\(153\) 1.13397 + 1.96410i 0.0916764 + 0.158788i
\(154\) −1.73205 3.00000i −0.139573 0.241747i
\(155\) −1.46410 −0.117599
\(156\) 0 0
\(157\) −23.5885 −1.88256 −0.941282 0.337622i \(-0.890378\pi\)
−0.941282 + 0.337622i \(0.890378\pi\)
\(158\) 4.73205 + 8.19615i 0.376462 + 0.652051i
\(159\) −0.232051 0.401924i −0.0184028 0.0318746i
\(160\) −0.133975 + 0.232051i −0.0105916 + 0.0183452i
\(161\) −4.53590 −0.357479
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 3.26795 5.66025i 0.255966 0.443345i −0.709192 0.705016i \(-0.750940\pi\)
0.965157 + 0.261670i \(0.0842733\pi\)
\(164\) 11.3923 0.889590
\(165\) −0.633975 + 1.09808i −0.0493549 + 0.0854851i
\(166\) −5.09808 8.83013i −0.395687 0.685351i
\(167\) 1.26795 + 2.19615i 0.0981169 + 0.169943i 0.910905 0.412616i \(-0.135385\pi\)
−0.812788 + 0.582559i \(0.802051\pi\)
\(168\) 0.732051 0.0564789
\(169\) 0 0
\(170\) −0.607695 −0.0466081
\(171\) −0.633975 1.09808i −0.0484812 0.0839720i
\(172\) −3.83013 6.63397i −0.292044 0.505836i
\(173\) 8.19615 14.1962i 0.623142 1.07931i −0.365755 0.930711i \(-0.619189\pi\)
0.988897 0.148602i \(-0.0474774\pi\)
\(174\) 2.46410 0.186803
\(175\) 1.80385 3.12436i 0.136358 0.236179i
\(176\) −2.36603 + 4.09808i −0.178346 + 0.308904i
\(177\) 8.00000 0.601317
\(178\) 1.26795 2.19615i 0.0950368 0.164609i
\(179\) −11.0263 19.0981i −0.824143 1.42746i −0.902573 0.430538i \(-0.858324\pi\)
0.0784298 0.996920i \(-0.475009\pi\)
\(180\) −0.133975 0.232051i −0.00998588 0.0172960i
\(181\) 8.80385 0.654385 0.327192 0.944958i \(-0.393897\pi\)
0.327192 + 0.944958i \(0.393897\pi\)
\(182\) 0 0
\(183\) 1.19615 0.0884221
\(184\) 3.09808 + 5.36603i 0.228393 + 0.395589i
\(185\) −1.40192 2.42820i −0.103071 0.178525i
\(186\) 2.73205 4.73205i 0.200324 0.346971i
\(187\) −10.7321 −0.784805
\(188\) 4.09808 7.09808i 0.298883 0.517680i
\(189\) −0.366025 + 0.633975i −0.0266244 + 0.0461149i
\(190\) 0.339746 0.0246478
\(191\) −3.46410 + 6.00000i −0.250654 + 0.434145i −0.963706 0.266966i \(-0.913979\pi\)
0.713052 + 0.701111i \(0.247312\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 4.13397 + 7.16025i 0.297570 + 0.515406i 0.975579 0.219647i \(-0.0704905\pi\)
−0.678009 + 0.735053i \(0.737157\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) −6.46410 −0.461722
\(197\) −4.92820 8.53590i −0.351120 0.608158i 0.635326 0.772244i \(-0.280866\pi\)
−0.986446 + 0.164086i \(0.947532\pi\)
\(198\) −2.36603 4.09808i −0.168146 0.291238i
\(199\) 1.90192 3.29423i 0.134824 0.233522i −0.790706 0.612196i \(-0.790286\pi\)
0.925530 + 0.378674i \(0.123620\pi\)
\(200\) −4.92820 −0.348477
\(201\) 5.56218 9.63397i 0.392326 0.679528i
\(202\) 5.96410 10.3301i 0.419633 0.726825i
\(203\) 1.80385 0.126605
\(204\) 1.13397 1.96410i 0.0793941 0.137515i
\(205\) −1.52628 2.64359i −0.106600 0.184637i
\(206\) 9.36603 + 16.2224i 0.652562 + 1.13027i
\(207\) −6.19615 −0.430662
\(208\) 0 0
\(209\) 6.00000 0.415029
\(210\) −0.0980762 0.169873i −0.00676790 0.0117223i
\(211\) 2.19615 + 3.80385i 0.151189 + 0.261868i 0.931665 0.363319i \(-0.118356\pi\)
−0.780476 + 0.625186i \(0.785023\pi\)
\(212\) −0.232051 + 0.401924i −0.0159373 + 0.0276042i
\(213\) 1.26795 0.0868784
\(214\) 0.0980762 0.169873i 0.00670435 0.0116123i
\(215\) −1.02628 + 1.77757i −0.0699917 + 0.121229i
\(216\) 1.00000 0.0680414
\(217\) 2.00000 3.46410i 0.135769 0.235159i
\(218\) 2.73205 + 4.73205i 0.185038 + 0.320495i
\(219\) 4.86603 + 8.42820i 0.328816 + 0.569525i
\(220\) 1.26795 0.0854851
\(221\) 0 0
\(222\) 10.4641 0.702305
\(223\) 6.53590 + 11.3205i 0.437676 + 0.758077i 0.997510 0.0705277i \(-0.0224683\pi\)
−0.559834 + 0.828605i \(0.689135\pi\)
\(224\) −0.366025 0.633975i −0.0244561 0.0423592i
\(225\) 2.46410 4.26795i 0.164273 0.284530i
\(226\) −18.6603 −1.24126
\(227\) 0.901924 1.56218i 0.0598628 0.103685i −0.834541 0.550946i \(-0.814267\pi\)
0.894404 + 0.447261i \(0.147600\pi\)
\(228\) −0.633975 + 1.09808i −0.0419860 + 0.0727219i
\(229\) 15.8564 1.04782 0.523910 0.851773i \(-0.324473\pi\)
0.523910 + 0.851773i \(0.324473\pi\)
\(230\) 0.830127 1.43782i 0.0547370 0.0948072i
\(231\) −1.73205 3.00000i −0.113961 0.197386i
\(232\) −1.23205 2.13397i −0.0808881 0.140102i
\(233\) 19.8564 1.30084 0.650418 0.759576i \(-0.274594\pi\)
0.650418 + 0.759576i \(0.274594\pi\)
\(234\) 0 0
\(235\) −2.19615 −0.143261
\(236\) −4.00000 6.92820i −0.260378 0.450988i
\(237\) 4.73205 + 8.19615i 0.307380 + 0.532397i
\(238\) 0.830127 1.43782i 0.0538091 0.0932002i
\(239\) −9.66025 −0.624870 −0.312435 0.949939i \(-0.601145\pi\)
−0.312435 + 0.949939i \(0.601145\pi\)
\(240\) −0.133975 + 0.232051i −0.00864802 + 0.0149788i
\(241\) 8.79423 15.2321i 0.566486 0.981183i −0.430424 0.902627i \(-0.641636\pi\)
0.996910 0.0785557i \(-0.0250308\pi\)
\(242\) 11.3923 0.732325
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −0.598076 1.03590i −0.0382879 0.0663166i
\(245\) 0.866025 + 1.50000i 0.0553283 + 0.0958315i
\(246\) 11.3923 0.726347
\(247\) 0 0
\(248\) −5.46410 −0.346971
\(249\) −5.09808 8.83013i −0.323077 0.559587i
\(250\) 1.33013 + 2.30385i 0.0841246 + 0.145708i
\(251\) −3.26795 + 5.66025i −0.206271 + 0.357272i −0.950537 0.310611i \(-0.899466\pi\)
0.744266 + 0.667883i \(0.232800\pi\)
\(252\) 0.732051 0.0461149
\(253\) 14.6603 25.3923i 0.921682 1.59640i
\(254\) −8.92820 + 15.4641i −0.560205 + 0.970304i
\(255\) −0.607695 −0.0380553
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −13.3301 23.0885i −0.831510 1.44022i −0.896840 0.442355i \(-0.854143\pi\)
0.0653297 0.997864i \(-0.479190\pi\)
\(258\) −3.83013 6.63397i −0.238453 0.413013i
\(259\) 7.66025 0.475985
\(260\) 0 0
\(261\) 2.46410 0.152524
\(262\) −6.73205 11.6603i −0.415907 0.720373i
\(263\) −14.0263 24.2942i −0.864897 1.49805i −0.867149 0.498049i \(-0.834050\pi\)
0.00225153 0.999997i \(-0.499283\pi\)
\(264\) −2.36603 + 4.09808i −0.145619 + 0.252219i
\(265\) 0.124356 0.00763911
\(266\) −0.464102 + 0.803848i −0.0284559 + 0.0492871i
\(267\) 1.26795 2.19615i 0.0775972 0.134402i
\(268\) −11.1244 −0.679528
\(269\) 0.732051 1.26795i 0.0446339 0.0773082i −0.842845 0.538156i \(-0.819121\pi\)
0.887479 + 0.460848i \(0.152455\pi\)
\(270\) −0.133975 0.232051i −0.00815343 0.0141222i
\(271\) −2.92820 5.07180i −0.177876 0.308090i 0.763277 0.646071i \(-0.223589\pi\)
−0.941153 + 0.337982i \(0.890256\pi\)
\(272\) −2.26795 −0.137515
\(273\) 0 0
\(274\) −1.92820 −0.116487
\(275\) 11.6603 + 20.1962i 0.703140 + 1.21787i
\(276\) 3.09808 + 5.36603i 0.186482 + 0.322997i
\(277\) 1.13397 1.96410i 0.0681339 0.118011i −0.829946 0.557844i \(-0.811629\pi\)
0.898080 + 0.439832i \(0.144962\pi\)
\(278\) −9.85641 −0.591148
\(279\) 2.73205 4.73205i 0.163564 0.283300i
\(280\) −0.0980762 + 0.169873i −0.00586117 + 0.0101519i
\(281\) −22.3205 −1.33153 −0.665765 0.746162i \(-0.731895\pi\)
−0.665765 + 0.746162i \(0.731895\pi\)
\(282\) 4.09808 7.09808i 0.244037 0.422684i
\(283\) −4.16987 7.22243i −0.247873 0.429329i 0.715062 0.699061i \(-0.246398\pi\)
−0.962936 + 0.269732i \(0.913065\pi\)
\(284\) −0.633975 1.09808i −0.0376195 0.0651588i
\(285\) 0.339746 0.0201248
\(286\) 0 0
\(287\) 8.33975 0.492280
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) 5.92820 + 10.2679i 0.348718 + 0.603997i
\(290\) −0.330127 + 0.571797i −0.0193857 + 0.0335771i
\(291\) −6.00000 −0.351726
\(292\) 4.86603 8.42820i 0.284763 0.493223i
\(293\) 7.25833 12.5718i 0.424036 0.734452i −0.572294 0.820049i \(-0.693946\pi\)
0.996330 + 0.0855965i \(0.0272796\pi\)
\(294\) −6.46410 −0.376994
\(295\) −1.07180 + 1.85641i −0.0624024 + 0.108084i
\(296\) −5.23205 9.06218i −0.304107 0.526728i
\(297\) −2.36603 4.09808i −0.137291 0.237795i
\(298\) 2.80385 0.162423
\(299\) 0 0
\(300\) −4.92820 −0.284530
\(301\) −2.80385 4.85641i −0.161611 0.279919i
\(302\) −1.63397 2.83013i −0.0940247 0.162856i
\(303\) 5.96410 10.3301i 0.342629 0.593450i
\(304\) 1.26795 0.0727219
\(305\) −0.160254 + 0.277568i −0.00917612 + 0.0158935i
\(306\) 1.13397 1.96410i 0.0648250 0.112280i
\(307\) 8.58846 0.490169 0.245085 0.969502i \(-0.421184\pi\)
0.245085 + 0.969502i \(0.421184\pi\)
\(308\) −1.73205 + 3.00000i −0.0986928 + 0.170941i
\(309\) 9.36603 + 16.2224i 0.532815 + 0.922862i
\(310\) 0.732051 + 1.26795i 0.0415777 + 0.0720147i
\(311\) 15.6603 0.888012 0.444006 0.896024i \(-0.353557\pi\)
0.444006 + 0.896024i \(0.353557\pi\)
\(312\) 0 0
\(313\) 13.4641 0.761036 0.380518 0.924774i \(-0.375746\pi\)
0.380518 + 0.924774i \(0.375746\pi\)
\(314\) 11.7942 + 20.4282i 0.665587 + 1.15283i
\(315\) −0.0980762 0.169873i −0.00552597 0.00957126i
\(316\) 4.73205 8.19615i 0.266199 0.461070i
\(317\) 3.33975 0.187579 0.0937894 0.995592i \(-0.470102\pi\)
0.0937894 + 0.995592i \(0.470102\pi\)
\(318\) −0.232051 + 0.401924i −0.0130128 + 0.0225388i
\(319\) −5.83013 + 10.0981i −0.326424 + 0.565384i
\(320\) 0.267949 0.0149788
\(321\) 0.0980762 0.169873i 0.00547408 0.00948139i
\(322\) 2.26795 + 3.92820i 0.126388 + 0.218910i
\(323\) 1.43782 + 2.49038i 0.0800026 + 0.138569i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.53590 −0.361990
\(327\) 2.73205 + 4.73205i 0.151083 + 0.261683i
\(328\) −5.69615 9.86603i −0.314517 0.544760i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) 1.26795 0.0697983
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) −5.09808 + 8.83013i −0.279793 + 0.484616i
\(333\) 10.4641 0.573429
\(334\) 1.26795 2.19615i 0.0693791 0.120168i
\(335\) 1.49038 + 2.58142i 0.0814282 + 0.141038i
\(336\) −0.366025 0.633975i −0.0199683 0.0345861i
\(337\) 6.85641 0.373492 0.186746 0.982408i \(-0.440206\pi\)
0.186746 + 0.982408i \(0.440206\pi\)
\(338\) 0 0
\(339\) −18.6603 −1.01349
\(340\) 0.303848 + 0.526279i 0.0164784 + 0.0285415i
\(341\) 12.9282 + 22.3923i 0.700101 + 1.21261i
\(342\) −0.633975 + 1.09808i −0.0342814 + 0.0593772i
\(343\) −9.85641 −0.532196
\(344\) −3.83013 + 6.63397i −0.206507 + 0.357680i
\(345\) 0.830127 1.43782i 0.0446925 0.0774097i
\(346\) −16.3923 −0.881256
\(347\) −4.43782 + 7.68653i −0.238235 + 0.412635i −0.960208 0.279286i \(-0.909902\pi\)
0.721973 + 0.691921i \(0.243235\pi\)
\(348\) −1.23205 2.13397i −0.0660449 0.114393i
\(349\) 9.66025 + 16.7321i 0.517102 + 0.895646i 0.999803 + 0.0198610i \(0.00632238\pi\)
−0.482701 + 0.875785i \(0.660344\pi\)
\(350\) −3.60770 −0.192839
\(351\) 0 0
\(352\) 4.73205 0.252219
\(353\) −9.89230 17.1340i −0.526514 0.911949i −0.999523 0.0308916i \(-0.990165\pi\)
0.473008 0.881058i \(-0.343168\pi\)
\(354\) −4.00000 6.92820i −0.212598 0.368230i
\(355\) −0.169873 + 0.294229i −0.00901592 + 0.0156160i
\(356\) −2.53590 −0.134402
\(357\) 0.830127 1.43782i 0.0439350 0.0760976i
\(358\) −11.0263 + 19.0981i −0.582757 + 1.00936i
\(359\) 23.1244 1.22046 0.610228 0.792226i \(-0.291078\pi\)
0.610228 + 0.792226i \(0.291078\pi\)
\(360\) −0.133975 + 0.232051i −0.00706108 + 0.0122302i
\(361\) 8.69615 + 15.0622i 0.457692 + 0.792746i
\(362\) −4.40192 7.62436i −0.231360 0.400727i
\(363\) 11.3923 0.597941
\(364\) 0 0
\(365\) −2.60770 −0.136493
\(366\) −0.598076 1.03590i −0.0312619 0.0541473i
\(367\) 7.36603 + 12.7583i 0.384503 + 0.665979i 0.991700 0.128572i \(-0.0410394\pi\)
−0.607197 + 0.794551i \(0.707706\pi\)
\(368\) 3.09808 5.36603i 0.161498 0.279723i
\(369\) 11.3923 0.593060
\(370\) −1.40192 + 2.42820i −0.0728825 + 0.126236i
\(371\) −0.169873 + 0.294229i −0.00881937 + 0.0152756i
\(372\) −5.46410 −0.283300
\(373\) 5.13397 8.89230i 0.265827 0.460426i −0.701953 0.712223i \(-0.747688\pi\)
0.967780 + 0.251797i \(0.0810216\pi\)
\(374\) 5.36603 + 9.29423i 0.277471 + 0.480593i
\(375\) 1.33013 + 2.30385i 0.0686875 + 0.118970i
\(376\) −8.19615 −0.422684
\(377\) 0 0
\(378\) 0.732051 0.0376526
\(379\) −0.732051 1.26795i −0.0376029 0.0651302i 0.846611 0.532211i \(-0.178639\pi\)
−0.884214 + 0.467081i \(0.845306\pi\)
\(380\) −0.169873 0.294229i −0.00871430 0.0150936i
\(381\) −8.92820 + 15.4641i −0.457406 + 0.792250i
\(382\) 6.92820 0.354478
\(383\) −2.73205 + 4.73205i −0.139601 + 0.241797i −0.927346 0.374206i \(-0.877915\pi\)
0.787744 + 0.616002i \(0.211249\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0.928203 0.0473056
\(386\) 4.13397 7.16025i 0.210414 0.364447i
\(387\) −3.83013 6.63397i −0.194696 0.337224i
\(388\) 3.00000 + 5.19615i 0.152302 + 0.263795i
\(389\) −29.7846 −1.51014 −0.755070 0.655644i \(-0.772397\pi\)
−0.755070 + 0.655644i \(0.772397\pi\)
\(390\) 0 0
\(391\) 14.0526 0.710668
\(392\) 3.23205 + 5.59808i 0.163243 + 0.282746i
\(393\) −6.73205 11.6603i −0.339587 0.588182i
\(394\) −4.92820 + 8.53590i −0.248279 + 0.430032i
\(395\) −2.53590 −0.127595
\(396\) −2.36603 + 4.09808i −0.118897 + 0.205936i
\(397\) 0.196152 0.339746i 0.00984461 0.0170514i −0.861061 0.508501i \(-0.830200\pi\)
0.870906 + 0.491450i \(0.163533\pi\)
\(398\) −3.80385 −0.190670
\(399\) −0.464102 + 0.803848i −0.0232341 + 0.0402427i
\(400\) 2.46410 + 4.26795i 0.123205 + 0.213397i
\(401\) −10.9641 18.9904i −0.547521 0.948334i −0.998444 0.0557713i \(-0.982238\pi\)
0.450922 0.892563i \(-0.351095\pi\)
\(402\) −11.1244 −0.554832
\(403\) 0 0
\(404\) −11.9282 −0.593450
\(405\) −0.133975 0.232051i −0.00665725 0.0115307i
\(406\) −0.901924 1.56218i −0.0447617 0.0775296i
\(407\) −24.7583 + 42.8827i −1.22722 + 2.12562i
\(408\) −2.26795 −0.112280
\(409\) −7.13397 + 12.3564i −0.352752 + 0.610985i −0.986731 0.162366i \(-0.948088\pi\)
0.633978 + 0.773351i \(0.281421\pi\)
\(410\) −1.52628 + 2.64359i −0.0753776 + 0.130558i
\(411\) −1.92820 −0.0951113
\(412\) 9.36603 16.2224i 0.461431 0.799222i
\(413\) −2.92820 5.07180i −0.144087 0.249567i
\(414\) 3.09808 + 5.36603i 0.152262 + 0.263726i
\(415\) 2.73205 0.134111
\(416\) 0 0
\(417\) −9.85641 −0.482670
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) 5.26795 + 9.12436i 0.257356 + 0.445754i 0.965533 0.260281i \(-0.0838153\pi\)
−0.708177 + 0.706035i \(0.750482\pi\)
\(420\) −0.0980762 + 0.169873i −0.00478563 + 0.00828895i
\(421\) 32.7128 1.59432 0.797162 0.603765i \(-0.206333\pi\)
0.797162 + 0.603765i \(0.206333\pi\)
\(422\) 2.19615 3.80385i 0.106907 0.185168i
\(423\) 4.09808 7.09808i 0.199255 0.345120i
\(424\) 0.464102 0.0225388
\(425\) −5.58846 + 9.67949i −0.271080 + 0.469524i
\(426\) −0.633975 1.09808i −0.0307162 0.0532020i
\(427\) −0.437822 0.758330i −0.0211877 0.0366982i
\(428\) −0.196152 −0.00948139
\(429\) 0 0
\(430\) 2.05256 0.0989832
\(431\) 5.56218 + 9.63397i 0.267921 + 0.464052i 0.968325 0.249694i \(-0.0803302\pi\)
−0.700404 + 0.713747i \(0.746997\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 7.42820 12.8660i 0.356977 0.618302i −0.630478 0.776208i \(-0.717141\pi\)
0.987454 + 0.157906i \(0.0504742\pi\)
\(434\) −4.00000 −0.192006
\(435\) −0.330127 + 0.571797i −0.0158284 + 0.0274156i
\(436\) 2.73205 4.73205i 0.130842 0.226624i
\(437\) −7.85641 −0.375823
\(438\) 4.86603 8.42820i 0.232508 0.402715i
\(439\) 8.83013 + 15.2942i 0.421439 + 0.729954i 0.996080 0.0884515i \(-0.0281918\pi\)
−0.574642 + 0.818405i \(0.694859\pi\)
\(440\) −0.633975 1.09808i −0.0302236 0.0523487i
\(441\) −6.46410 −0.307814
\(442\) 0 0
\(443\) 36.3923 1.72905 0.864525 0.502589i \(-0.167619\pi\)
0.864525 + 0.502589i \(0.167619\pi\)
\(444\) −5.23205 9.06218i −0.248302 0.430072i
\(445\) 0.339746 + 0.588457i 0.0161055 + 0.0278955i
\(446\) 6.53590 11.3205i 0.309484 0.536042i
\(447\) 2.80385 0.132617
\(448\) −0.366025 + 0.633975i −0.0172931 + 0.0299525i
\(449\) 11.6603 20.1962i 0.550281 0.953115i −0.447973 0.894047i \(-0.647854\pi\)
0.998254 0.0590680i \(-0.0188129\pi\)
\(450\) −4.92820 −0.232318
\(451\) −26.9545 + 46.6865i −1.26924 + 2.19838i
\(452\) 9.33013 + 16.1603i 0.438852 + 0.760114i
\(453\) −1.63397 2.83013i −0.0767708 0.132971i
\(454\) −1.80385 −0.0846588
\(455\) 0 0
\(456\) 1.26795 0.0593772
\(457\) −9.33013 16.1603i −0.436445 0.755945i 0.560967 0.827838i \(-0.310429\pi\)
−0.997412 + 0.0718931i \(0.977096\pi\)
\(458\) −7.92820 13.7321i −0.370461 0.641657i
\(459\) 1.13397 1.96410i 0.0529294 0.0916764i
\(460\) −1.66025 −0.0774097
\(461\) −12.8660 + 22.2846i −0.599231 + 1.03790i 0.393704 + 0.919237i \(0.371193\pi\)
−0.992935 + 0.118661i \(0.962140\pi\)
\(462\) −1.73205 + 3.00000i −0.0805823 + 0.139573i
\(463\) −28.0526 −1.30371 −0.651856 0.758342i \(-0.726010\pi\)
−0.651856 + 0.758342i \(0.726010\pi\)
\(464\) −1.23205 + 2.13397i −0.0571965 + 0.0990673i
\(465\) 0.732051 + 1.26795i 0.0339480 + 0.0587997i
\(466\) −9.92820 17.1962i −0.459915 0.796596i
\(467\) −12.5885 −0.582524 −0.291262 0.956643i \(-0.594075\pi\)
−0.291262 + 0.956643i \(0.594075\pi\)
\(468\) 0 0
\(469\) −8.14359 −0.376036
\(470\) 1.09808 + 1.90192i 0.0506505 + 0.0877292i
\(471\) 11.7942 + 20.4282i 0.543449 + 0.941282i
\(472\) −4.00000 + 6.92820i −0.184115 + 0.318896i
\(473\) 36.2487 1.66672
\(474\) 4.73205 8.19615i 0.217350 0.376462i
\(475\) 3.12436 5.41154i 0.143355 0.248299i
\(476\) −1.66025 −0.0760976
\(477\) −0.232051 + 0.401924i −0.0106249 + 0.0184028i
\(478\) 4.83013 + 8.36603i 0.220925 + 0.382653i
\(479\) −13.2679 22.9808i −0.606228 1.05002i −0.991856 0.127363i \(-0.959349\pi\)
0.385628 0.922654i \(-0.373985\pi\)
\(480\) 0.267949 0.0122302
\(481\) 0 0
\(482\) −17.5885 −0.801132
\(483\) 2.26795 + 3.92820i 0.103195 + 0.178739i
\(484\) −5.69615 9.86603i −0.258916 0.448456i
\(485\) 0.803848 1.39230i 0.0365008 0.0632213i
\(486\) 1.00000 0.0453609
\(487\) −10.5622 + 18.2942i −0.478618 + 0.828991i −0.999699 0.0245163i \(-0.992195\pi\)
0.521081 + 0.853507i \(0.325529\pi\)
\(488\) −0.598076 + 1.03590i −0.0270736 + 0.0468929i
\(489\) −6.53590 −0.295564
\(490\) 0.866025 1.50000i 0.0391230 0.0677631i
\(491\) −2.63397 4.56218i −0.118870 0.205888i 0.800450 0.599399i \(-0.204594\pi\)
−0.919320 + 0.393511i \(0.871260\pi\)
\(492\) −5.69615 9.86603i −0.256802 0.444795i
\(493\) −5.58846 −0.251691
\(494\) 0 0
\(495\) 1.26795 0.0569901
\(496\) 2.73205 + 4.73205i 0.122673 + 0.212475i
\(497\) −0.464102 0.803848i −0.0208178 0.0360575i
\(498\) −5.09808 + 8.83013i −0.228450 + 0.395687i
\(499\) 32.0000 1.43252 0.716258 0.697835i \(-0.245853\pi\)
0.716258 + 0.697835i \(0.245853\pi\)
\(500\) 1.33013 2.30385i 0.0594851 0.103031i
\(501\) 1.26795 2.19615i 0.0566478 0.0981169i
\(502\) 6.53590 0.291711
\(503\) 5.49038 9.50962i 0.244804 0.424013i −0.717272 0.696793i \(-0.754610\pi\)
0.962076 + 0.272780i \(0.0879431\pi\)
\(504\) −0.366025 0.633975i −0.0163041 0.0282395i
\(505\) 1.59808 + 2.76795i 0.0711135 + 0.123172i
\(506\) −29.3205 −1.30346
\(507\) 0 0
\(508\) 17.8564 0.792250
\(509\) −5.13397 8.89230i −0.227559 0.394144i 0.729525 0.683954i \(-0.239741\pi\)
−0.957084 + 0.289810i \(0.906408\pi\)
\(510\) 0.303848 + 0.526279i 0.0134546 + 0.0233040i
\(511\) 3.56218 6.16987i 0.157581 0.272939i
\(512\) 1.00000 0.0441942
\(513\) −0.633975 + 1.09808i −0.0279907 + 0.0484812i
\(514\) −13.3301 + 23.0885i −0.587967 + 1.01839i
\(515\) −5.01924 −0.221174
\(516\) −3.83013 + 6.63397i −0.168612 + 0.292044i
\(517\) 19.3923 + 33.5885i 0.852873 + 1.47722i
\(518\) −3.83013 6.63397i −0.168286 0.291480i
\(519\) −16.3923 −0.719542
\(520\) 0 0
\(521\) −17.4449 −0.764273 −0.382137 0.924106i \(-0.624812\pi\)
−0.382137 + 0.924106i \(0.624812\pi\)
\(522\) −1.23205 2.13397i −0.0539254 0.0934015i
\(523\) −18.2224 31.5622i −0.796811 1.38012i −0.921683 0.387945i \(-0.873185\pi\)
0.124871 0.992173i \(-0.460148\pi\)
\(524\) −6.73205 + 11.6603i −0.294091 + 0.509381i
\(525\) −3.60770 −0.157453
\(526\) −14.0263 + 24.2942i −0.611575 + 1.05928i
\(527\) −6.19615 + 10.7321i −0.269909 + 0.467495i
\(528\) 4.73205 0.205936
\(529\) −7.69615 + 13.3301i −0.334615 + 0.579571i
\(530\) −0.0621778 0.107695i −0.00270083 0.00467798i
\(531\) −4.00000 6.92820i −0.173585 0.300658i
\(532\) 0.928203 0.0402427
\(533\) 0 0
\(534\) −2.53590 −0.109739
\(535\) 0.0262794 + 0.0455173i 0.00113616 + 0.00196789i
\(536\) 5.56218 + 9.63397i 0.240249 + 0.416124i
\(537\) −11.0263 + 19.0981i −0.475819 + 0.824143i
\(538\) −1.46410 −0.0631219
\(539\) 15.2942 26.4904i 0.658769 1.14102i
\(540\) −0.133975 + 0.232051i −0.00576535 + 0.00998588i
\(541\) 40.3205 1.73351 0.866757 0.498731i \(-0.166200\pi\)
0.866757 + 0.498731i \(0.166200\pi\)
\(542\) −2.92820 + 5.07180i −0.125777 + 0.217852i
\(543\) −4.40192 7.62436i −0.188905 0.327192i
\(544\) 1.13397 + 1.96410i 0.0486188 + 0.0842102i
\(545\) −1.46410 −0.0627152
\(546\) 0 0
\(547\) 6.19615 0.264928 0.132464 0.991188i \(-0.457711\pi\)
0.132464 + 0.991188i \(0.457711\pi\)
\(548\) 0.964102 + 1.66987i 0.0411844 + 0.0713334i
\(549\) −0.598076 1.03590i −0.0255253 0.0442111i
\(550\) 11.6603 20.1962i 0.497195 0.861167i
\(551\) 3.12436 0.133102
\(552\) 3.09808 5.36603i 0.131863 0.228393i
\(553\) 3.46410 6.00000i 0.147309 0.255146i
\(554\) −2.26795 −0.0963559
\(555\) −1.40192 + 2.42820i −0.0595084 + 0.103071i
\(556\) 4.92820 + 8.53590i 0.209002 + 0.362003i
\(557\) 15.1865 + 26.3038i 0.643474 + 1.11453i 0.984652 + 0.174531i \(0.0558409\pi\)
−0.341178 + 0.939999i \(0.610826\pi\)
\(558\) −5.46410 −0.231314
\(559\) 0 0
\(560\) 0.196152 0.00828895
\(561\) 5.36603 + 9.29423i 0.226554 + 0.392403i
\(562\) 11.1603 + 19.3301i 0.470767 + 0.815392i
\(563\) −10.5359 + 18.2487i −0.444035 + 0.769091i −0.997984 0.0634589i \(-0.979787\pi\)
0.553949 + 0.832550i \(0.313120\pi\)
\(564\) −8.19615 −0.345120
\(565\) 2.50000 4.33013i 0.105176 0.182170i
\(566\) −4.16987 + 7.22243i −0.175273 + 0.303581i
\(567\) 0.732051 0.0307432
\(568\) −0.633975 + 1.09808i −0.0266010 + 0.0460743i
\(569\) 19.3205 + 33.4641i 0.809958 + 1.40289i 0.912893 + 0.408200i \(0.133843\pi\)
−0.102935 + 0.994688i \(0.532823\pi\)
\(570\) −0.169873 0.294229i −0.00711520 0.0123239i
\(571\) −24.0526 −1.00657 −0.503284 0.864121i \(-0.667875\pi\)
−0.503284 + 0.864121i \(0.667875\pi\)
\(572\) 0 0
\(573\) 6.92820 0.289430
\(574\) −4.16987 7.22243i −0.174047 0.301458i
\(575\) −15.2679 26.4449i −0.636717 1.10283i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 0.267949 0.0111549 0.00557744 0.999984i \(-0.498225\pi\)
0.00557744 + 0.999984i \(0.498225\pi\)
\(578\) 5.92820 10.2679i 0.246581 0.427090i
\(579\) 4.13397 7.16025i 0.171802 0.297570i
\(580\) 0.660254 0.0274156
\(581\) −3.73205 + 6.46410i −0.154832 + 0.268176i
\(582\) 3.00000 + 5.19615i 0.124354 + 0.215387i
\(583\) −1.09808 1.90192i −0.0454777 0.0787696i
\(584\) −9.73205 −0.402715
\(585\) 0 0
\(586\) −14.5167 −0.599678
\(587\) −8.00000 13.8564i −0.330195 0.571915i 0.652355 0.757914i \(-0.273781\pi\)
−0.982550 + 0.185999i \(0.940448\pi\)
\(588\) 3.23205 + 5.59808i 0.133288 + 0.230861i
\(589\) 3.46410 6.00000i 0.142736 0.247226i
\(590\) 2.14359 0.0882503
\(591\) −4.92820 + 8.53590i −0.202719 + 0.351120i
\(592\) −5.23205 + 9.06218i −0.215036 + 0.372453i
\(593\) −36.8564 −1.51351 −0.756756 0.653698i \(-0.773217\pi\)
−0.756756 + 0.653698i \(0.773217\pi\)
\(594\) −2.36603 + 4.09808i −0.0970792 + 0.168146i
\(595\) 0.222432 + 0.385263i 0.00911882 + 0.0157943i
\(596\) −1.40192 2.42820i −0.0574250 0.0994631i
\(597\) −3.80385 −0.155681
\(598\) 0 0
\(599\) −9.46410 −0.386693 −0.193346 0.981131i \(-0.561934\pi\)
−0.193346 + 0.981131i \(0.561934\pi\)
\(600\) 2.46410 + 4.26795i 0.100597 + 0.174238i
\(601\) 2.96410 + 5.13397i 0.120908 + 0.209419i 0.920126 0.391622i \(-0.128086\pi\)
−0.799218 + 0.601041i \(0.794753\pi\)
\(602\) −2.80385 + 4.85641i −0.114276 + 0.197932i
\(603\) −11.1244 −0.453019
\(604\) −1.63397 + 2.83013i −0.0664855 + 0.115156i
\(605\) −1.52628 + 2.64359i −0.0620521 + 0.107477i
\(606\) −11.9282 −0.484550
\(607\) −0.392305 + 0.679492i −0.0159232 + 0.0275797i −0.873877 0.486147i \(-0.838402\pi\)
0.857954 + 0.513726i \(0.171735\pi\)
\(608\) −0.633975 1.09808i −0.0257111 0.0445329i
\(609\) −0.901924 1.56218i −0.0365478 0.0633026i
\(610\) 0.320508 0.0129770
\(611\) 0 0
\(612\) −2.26795 −0.0916764
\(613\) −5.69615 9.86603i −0.230065 0.398485i 0.727762 0.685830i \(-0.240561\pi\)
−0.957827 + 0.287345i \(0.907227\pi\)
\(614\) −4.29423 7.43782i −0.173301 0.300166i
\(615\) −1.52628 + 2.64359i −0.0615455 + 0.106600i
\(616\) 3.46410 0.139573
\(617\) −17.6244 + 30.5263i −0.709530 + 1.22894i 0.255502 + 0.966809i \(0.417759\pi\)
−0.965032 + 0.262133i \(0.915574\pi\)
\(618\) 9.36603 16.2224i 0.376757 0.652562i
\(619\) 10.5359 0.423474 0.211737 0.977327i \(-0.432088\pi\)
0.211737 + 0.977327i \(0.432088\pi\)
\(620\) 0.732051 1.26795i 0.0293999 0.0509221i
\(621\) 3.09808 + 5.36603i 0.124322 + 0.215331i
\(622\) −7.83013 13.5622i −0.313959 0.543794i
\(623\) −1.85641 −0.0743754
\(624\) 0 0
\(625\) 23.9282 0.957128
\(626\) −6.73205 11.6603i −0.269067 0.466037i
\(627\) −3.00000 5.19615i −0.119808 0.207514i
\(628\) 11.7942 20.4282i 0.470641 0.815174i
\(629\) −23.7321 −0.946259
\(630\) −0.0980762 + 0.169873i −0.00390745 + 0.00676790i
\(631\) −23.8564 + 41.3205i −0.949709 + 1.64494i −0.203671 + 0.979039i \(0.565287\pi\)
−0.746037 + 0.665904i \(0.768046\pi\)
\(632\) −9.46410 −0.376462
\(633\) 2.19615 3.80385i 0.0872892 0.151189i
\(634\) −1.66987 2.89230i −0.0663191 0.114868i
\(635\) −2.39230 4.14359i −0.0949357 0.164433i
\(636\) 0.464102 0.0184028
\(637\) 0 0
\(638\) 11.6603 0.461634
\(639\) −0.633975 1.09808i −0.0250796 0.0434392i
\(640\) −0.133975 0.232051i −0.00529581 0.00917261i
\(641\) −12.9904 + 22.5000i −0.513089 + 0.888697i 0.486796 + 0.873516i \(0.338166\pi\)
−0.999885 + 0.0151806i \(0.995168\pi\)
\(642\) −0.196152 −0.00774152
\(643\) −6.92820 + 12.0000i −0.273222 + 0.473234i −0.969685 0.244359i \(-0.921423\pi\)
0.696463 + 0.717592i \(0.254756\pi\)
\(644\) 2.26795 3.92820i 0.0893697 0.154793i
\(645\) 2.05256 0.0808194
\(646\) 1.43782 2.49038i 0.0565704 0.0979827i
\(647\) −13.1244 22.7321i −0.515972 0.893689i −0.999828 0.0185417i \(-0.994098\pi\)
0.483856 0.875147i \(-0.339236\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 37.8564 1.48599
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) 3.26795 + 5.66025i 0.127983 + 0.221673i
\(653\) 5.26795 + 9.12436i 0.206151 + 0.357064i 0.950499 0.310728i \(-0.100573\pi\)
−0.744348 + 0.667792i \(0.767240\pi\)
\(654\) 2.73205 4.73205i 0.106832 0.185038i
\(655\) 3.60770 0.140964
\(656\) −5.69615 + 9.86603i −0.222397 + 0.385204i
\(657\) 4.86603 8.42820i 0.189842 0.328816i
\(658\) −6.00000 −0.233904
\(659\) −19.1244 + 33.1244i −0.744979 + 1.29034i 0.205225 + 0.978715i \(0.434207\pi\)
−0.950205 + 0.311627i \(0.899126\pi\)
\(660\) −0.633975 1.09808i −0.0246774 0.0427426i
\(661\) 4.69615 + 8.13397i 0.182659 + 0.316375i 0.942785 0.333401i \(-0.108196\pi\)
−0.760126 + 0.649776i \(0.774863\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) 10.1962 0.395687
\(665\) −0.124356 0.215390i −0.00482231 0.00835248i
\(666\) −5.23205 9.06218i −0.202738 0.351152i
\(667\) 7.63397 13.2224i 0.295589 0.511975i
\(668\) −2.53590 −0.0981169
\(669\) 6.53590 11.3205i 0.252692 0.437676i
\(670\) 1.49038 2.58142i 0.0575784 0.0997288i
\(671\) 5.66025 0.218512
\(672\) −0.366025 + 0.633975i −0.0141197 + 0.0244561i
\(673\) −7.03590 12.1865i −0.271214 0.469756i 0.697959 0.716138i \(-0.254092\pi\)
−0.969173 + 0.246381i \(0.920758\pi\)
\(674\) −3.42820 5.93782i −0.132049 0.228716i
\(675\) −4.92820 −0.189687
\(676\) 0 0
\(677\) −38.5359 −1.48105 −0.740527 0.672026i \(-0.765424\pi\)
−0.740527 + 0.672026i \(0.765424\pi\)
\(678\) 9.33013 + 16.1603i 0.358321 + 0.620631i
\(679\) 2.19615 + 3.80385i 0.0842806 + 0.145978i
\(680\) 0.303848 0.526279i 0.0116520 0.0201819i
\(681\) −1.80385 −0.0691236
\(682\) 12.9282 22.3923i 0.495046 0.857446i
\(683\) 18.9282 32.7846i 0.724268 1.25447i −0.235007 0.971994i \(-0.575511\pi\)
0.959275 0.282475i \(-0.0911553\pi\)
\(684\) 1.26795 0.0484812
\(685\) 0.258330 0.447441i 0.00987029 0.0170958i
\(686\) 4.92820 + 8.53590i 0.188160 + 0.325902i
\(687\) −7.92820 13.7321i −0.302480 0.523910i
\(688\) 7.66025 0.292044
\(689\) 0 0
\(690\) −1.66025 −0.0632048
\(691\) −13.1699 22.8109i −0.501006 0.867767i −0.999999 0.00116153i \(-0.999630\pi\)
0.498994 0.866606i \(-0.333703\pi\)
\(692\) 8.19615 + 14.1962i 0.311571 + 0.539657i
\(693\) −1.73205 + 3.00000i −0.0657952 + 0.113961i
\(694\) 8.87564 0.336915
\(695\) 1.32051 2.28719i 0.0500897 0.0867580i
\(696\) −1.23205 + 2.13397i −0.0467008 + 0.0808881i
\(697\) −25.8372 −0.978653
\(698\) 9.66025 16.7321i 0.365646 0.633317i
\(699\) −9.92820 17.1962i −0.375519 0.650418i
\(700\) 1.80385 + 3.12436i 0.0681790 + 0.118090i
\(701\) 31.3205 1.18296 0.591480 0.806320i \(-0.298544\pi\)
0.591480 + 0.806320i \(0.298544\pi\)
\(702\) 0 0
\(703\) 13.2679 0.500410
\(704\) −2.36603 4.09808i −0.0891729 0.154452i
\(705\) 1.09808 + 1.90192i 0.0413559 + 0.0716306i
\(706\) −9.89230 + 17.1340i −0.372302 + 0.644846i
\(707\) −8.73205 −0.328403
\(708\) −4.00000 + 6.92820i −0.150329 + 0.260378i
\(709\) −20.4282 + 35.3827i −0.767197 + 1.32882i 0.171880 + 0.985118i \(0.445016\pi\)
−0.939077 + 0.343707i \(0.888317\pi\)
\(710\) 0.339746 0.0127504
\(711\) 4.73205 8.19615i 0.177466 0.307380i
\(712\) 1.26795 + 2.19615i 0.0475184 + 0.0823043i
\(713\) −16.9282 29.3205i −0.633966 1.09806i
\(714\) −1.66025 −0.0621334
\(715\) 0 0
\(716\) 22.0526 0.824143
\(717\) 4.83013 + 8.36603i 0.180384 + 0.312435i
\(718\) −11.5622 20.0263i −0.431497 0.747374i
\(719\) 11.2679 19.5167i 0.420224 0.727849i −0.575737 0.817635i \(-0.695285\pi\)
0.995961 + 0.0897860i \(0.0286183\pi\)
\(720\) 0.267949 0.00998588
\(721\) 6.85641 11.8756i 0.255346 0.442272i
\(722\) 8.69615 15.0622i 0.323637 0.560556i
\(723\) −17.5885 −0.654122
\(724\) −4.40192 + 7.62436i −0.163596 + 0.283357i
\(725\) 6.07180 + 10.5167i 0.225501 + 0.390579i
\(726\) −5.69615 9.86603i −0.211404 0.366163i
\(727\) 20.9808 0.778133 0.389067 0.921210i \(-0.372798\pi\)
0.389067 + 0.921210i \(0.372798\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 1.30385 + 2.25833i 0.0482576 + 0.0835846i
\(731\) 8.68653 + 15.0455i 0.321283 + 0.556479i
\(732\) −0.598076 + 1.03590i −0.0221055 + 0.0382879i
\(733\) 19.0000 0.701781 0.350891 0.936416i \(-0.385879\pi\)
0.350891 + 0.936416i \(0.385879\pi\)
\(734\) 7.36603 12.7583i 0.271885 0.470919i
\(735\) 0.866025 1.50000i 0.0319438 0.0553283i
\(736\) −6.19615 −0.228393
\(737\) 26.3205 45.5885i 0.969528 1.67927i
\(738\) −5.69615 9.86603i −0.209678 0.363173i
\(739\) 5.46410 + 9.46410i 0.201000 + 0.348143i 0.948851 0.315724i \(-0.102247\pi\)
−0.747851 + 0.663867i \(0.768914\pi\)
\(740\) 2.80385 0.103071
\(741\) 0 0
\(742\) 0.339746 0.0124725
\(743\) 13.8038 + 23.9090i 0.506414 + 0.877135i 0.999972 + 0.00742221i \(0.00236259\pi\)
−0.493558 + 0.869713i \(0.664304\pi\)
\(744\) 2.73205 + 4.73205i 0.100162 + 0.173485i
\(745\) −0.375644 + 0.650635i −0.0137625 + 0.0238374i
\(746\) −10.2679 −0.375936
\(747\) −5.09808 + 8.83013i −0.186529 + 0.323077i
\(748\) 5.36603 9.29423i 0.196201 0.339831i
\(749\) −0.143594 −0.00524679
\(750\) 1.33013 2.30385i 0.0485694 0.0841246i
\(751\) −7.95448 13.7776i −0.290263 0.502751i 0.683609 0.729849i \(-0.260410\pi\)
−0.973872 + 0.227098i \(0.927076\pi\)
\(752\) 4.09808 + 7.09808i 0.149441 + 0.258840i
\(753\) 6.53590 0.238181
\(754\) 0 0
\(755\) 0.875644 0.0318680
\(756\) −0.366025 0.633975i −0.0133122 0.0230574i
\(757\) −3.53590 6.12436i −0.128514 0.222593i 0.794587 0.607151i \(-0.207688\pi\)
−0.923101 + 0.384557i \(0.874354\pi\)
\(758\) −0.732051 + 1.26795i −0.0265893 + 0.0460540i
\(759\) −29.3205 −1.06427
\(760\) −0.169873 + 0.294229i −0.00616194 + 0.0106728i
\(761\) 11.6603 20.1962i 0.422684 0.732110i −0.573517 0.819194i \(-0.694421\pi\)
0.996201 + 0.0870836i \(0.0277547\pi\)
\(762\) 17.8564 0.646869
\(763\) 2.00000 3.46410i 0.0724049 0.125409i
\(764\) −3.46410 6.00000i −0.125327 0.217072i
\(765\) 0.303848 + 0.526279i 0.0109856 + 0.0190277i
\(766\) 5.46410 0.197426
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 8.07180 + 13.9808i 0.291076 + 0.504159i 0.974065 0.226270i \(-0.0726533\pi\)
−0.682988 + 0.730429i \(0.739320\pi\)
\(770\) −0.464102 0.803848i −0.0167251 0.0289687i
\(771\) −13.3301 + 23.0885i −0.480073 + 0.831510i
\(772\) −8.26795 −0.297570
\(773\) 17.5359 30.3731i 0.630722 1.09244i −0.356682 0.934226i \(-0.616092\pi\)
0.987404 0.158217i \(-0.0505747\pi\)
\(774\) −3.83013 + 6.63397i −0.137671 + 0.238453i
\(775\) 26.9282 0.967290
\(776\) 3.00000 5.19615i 0.107694 0.186531i
\(777\) −3.83013 6.63397i −0.137405 0.237993i
\(778\) 14.8923 + 25.7942i 0.533915 + 0.924768i
\(779\) 14.4449 0.517541