Properties

Label 1014.2.e.i.529.2
Level $1014$
Weight $2$
Character 1014.529
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: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
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 529.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.529
Dual form 1014.2.e.i.991.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} - 2 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{14} + 4 q^{15} - 2 q^{16} + 8 q^{17} - 4 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} - 6 q^{22} + 2 q^{23} + 2 q^{24} + 8 q^{25} + 4 q^{27} - 2 q^{28} + 2 q^{29} - 4 q^{30} + 8 q^{31} + 2 q^{32} + 6 q^{33} + 16 q^{34} + 10 q^{35} - 2 q^{36} + 14 q^{37} + 12 q^{38} + 8 q^{40} + 2 q^{41} + 2 q^{42} + 2 q^{43} - 12 q^{44} + 4 q^{45} - 2 q^{46} + 12 q^{47} - 2 q^{48} + 6 q^{49} + 4 q^{50} - 16 q^{51} - 12 q^{53} + 2 q^{54} - 6 q^{55} + 2 q^{56} - 12 q^{57} - 2 q^{58} + 16 q^{59} - 8 q^{60} + 8 q^{61} + 4 q^{62} - 2 q^{63} + 4 q^{64} + 12 q^{66} + 2 q^{67} + 8 q^{68} + 2 q^{69} + 20 q^{70} + 6 q^{71} + 2 q^{72} + 32 q^{73} - 14 q^{74} - 4 q^{75} + 6 q^{76} - 24 q^{79} + 4 q^{80} - 2 q^{81} - 2 q^{82} - 20 q^{83} - 2 q^{84} - 22 q^{85} + 4 q^{86} + 2 q^{87} - 6 q^{88} - 12 q^{89} + 8 q^{90} - 4 q^{92} - 4 q^{93} + 6 q^{94} - 18 q^{95} - 4 q^{96} - 12 q^{97} - 6 q^{98} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 \(-0.519083\pi\)
−0.0599153 + 0.998203i \(0.519083\pi\)
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 0.366025 + 0.633975i 0.138345 + 0.239620i 0.926870 0.375382i \(-0.122489\pi\)
−0.788526 + 0.615002i \(0.789155\pi\)
\(8\) −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 −0.250196 0.968195i \(-0.580495\pi\)
0.963580 0.267421i \(-0.0861715\pi\)
\(12\) 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 0.970143 0.242536i \(-0.0779791\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0.633975 + 1.09808i 0.145444 + 0.251916i 0.929538 0.368725i \(-0.120206\pi\)
−0.784095 + 0.620641i \(0.786872\pi\)
\(20\) 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 −0.338078 0.941118i \(-0.609777\pi\)
0.984071 0.177775i \(-0.0568901\pi\)
\(24\) 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 −0.957449 0.288604i \(-0.906809\pi\)
0.728663 + 0.684873i \(0.240142\pi\)
\(30\) −0.133975 0.232051i −0.0244603 0.0423665i
\(31\) 5.46410 0.981382 0.490691 0.871334i \(-0.336744\pi\)
0.490691 + 0.871334i \(0.336744\pi\)
\(32\) 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 −0.0116456 0.999932i \(-0.503707\pi\)
0.871789 0.489881i \(-0.162960\pi\)
\(38\) 1.26795 0.205689
\(39\) 0 0
\(40\) 0.267949 0.0423665
\(41\) 5.69615 9.86603i 0.889590 1.54081i 0.0492283 0.998788i \(-0.484324\pi\)
0.840361 0.542027i \(-0.182343\pi\)
\(42\) −0.366025 + 0.633975i −0.0564789 + 0.0978244i
\(43\) −3.83013 6.63397i −0.584089 1.01167i −0.994988 0.0999910i \(-0.968119\pi\)
0.410899 0.911681i \(-0.365215\pi\)
\(44\) −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 \(-0.296055\pi\)
0.597766 + 0.801671i \(0.296055\pi\)
\(48\) −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 0.999709 + 0.0241347i \(0.00768307\pi\)
−0.478953 + 0.877841i \(0.658984\pi\)
\(60\) −0.267949 −0.0345921
\(61\) −0.598076 1.03590i −0.0765758 0.132633i 0.825195 0.564848i \(-0.191065\pi\)
−0.901770 + 0.432215i \(0.857732\pi\)
\(62\) 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 0.295595 + 0.955313i \(0.404482\pi\)
−0.975123 + 0.221664i \(0.928851\pi\)
\(68\) 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 \(-0.142695\pi\)
−0.825951 + 0.563742i \(0.809361\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 9.73205 1.13905 0.569525 0.821974i \(-0.307127\pi\)
0.569525 + 0.821974i \(0.307127\pi\)
\(74\) −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 \(-0.689040\pi\)
−0.559587 + 0.828772i \(0.689040\pi\)
\(84\) 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 \(-0.876245\pi\)
0.790967 + 0.611859i \(0.209578\pi\)
\(90\) 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 \(-0.265191\pi\)
−0.977173 + 0.212445i \(0.931857\pi\)
\(98\) −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 −0.400313 0.916378i \(-0.631099\pi\)
0.993764 0.111508i \(-0.0355680\pi\)
\(102\) −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 −0.861246 0.508189i \(-0.830315\pi\)
0.870727 + 0.491766i \(0.163649\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 5.46410 0.523366 0.261683 0.965154i \(-0.415723\pi\)
0.261683 + 0.965154i \(0.415723\pi\)
\(110\) 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 0.853854 + 0.520513i \(0.174259\pi\)
0.0238510 + 0.999716i \(0.492407\pi\)
\(114\) −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 0.132321 + 0.991207i \(0.457757\pi\)
−0.924571 + 0.381010i \(0.875576\pi\)
\(128\) 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 \(-0.192915\pi\)
−0.904267 + 0.426968i \(0.859582\pi\)
\(138\) 6.19615 0.527452
\(139\) 4.92820 + 8.53590i 0.418005 + 0.724005i 0.995739 0.0922197i \(-0.0293962\pi\)
−0.577734 + 0.816225i \(0.696063\pi\)
\(140\) −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 \(-0.130028\pi\)
−0.802870 + 0.596154i \(0.796695\pi\)
\(150\) −2.46410 4.26795i −0.201193 0.348477i
\(151\) −3.26795 −0.265942 −0.132971 0.991120i \(-0.542452\pi\)
−0.132971 + 0.991120i \(0.542452\pi\)
\(152\) −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 \(-0.249060\pi\)
−0.965157 + 0.261670i \(0.915727\pi\)
\(164\) −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 \(-0.864615\pi\)
0.812788 + 0.582559i \(0.197949\pi\)
\(168\) 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 0.988897 + 0.148602i \(0.0474774\pi\)
−0.365755 + 0.930711i \(0.619189\pi\)
\(174\) −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 0.0784298 + 0.996920i \(0.475009\pi\)
−0.902573 + 0.430538i \(0.858324\pi\)
\(180\) 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 0.713052 0.701111i \(-0.247312\pi\)
−0.963706 + 0.266966i \(0.913979\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −4.13397 + 7.16025i −0.297570 + 0.515406i −0.975579 0.219647i \(-0.929510\pi\)
0.678009 + 0.735053i \(0.262843\pi\)
\(194\) −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 \(-0.719134\pi\)
0.986446 + 0.164086i \(0.0524676\pi\)
\(198\) −2.36603 + 4.09808i −0.168146 + 0.291238i
\(199\) 1.90192 + 3.29423i 0.134824 + 0.233522i 0.925530 0.378674i \(-0.123620\pi\)
−0.790706 + 0.612196i \(0.790286\pi\)
\(200\) 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 −0.780476 0.625186i \(-0.785023\pi\)
0.931665 + 0.363319i \(0.118356\pi\)
\(212\) −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 \(-0.977532\pi\)
0.559834 + 0.828605i \(0.310865\pi\)
\(224\) −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 \(-0.185733\pi\)
−0.894404 + 0.447261i \(0.852400\pi\)
\(228\) 0.633975 + 1.09808i 0.0419860 + 0.0727219i
\(229\) −15.8564 −1.04782 −0.523910 0.851773i \(-0.675527\pi\)
−0.523910 + 0.851773i \(0.675527\pi\)
\(230\) 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 \(-0.398855\pi\)
0.312435 + 0.949939i \(0.398855\pi\)
\(240\) 0.133975 + 0.232051i 0.00864802 + 0.0149788i
\(241\) −8.79423 15.2321i −0.566486 0.981183i −0.996910 0.0785557i \(-0.974969\pi\)
0.430424 0.902627i \(-0.358364\pi\)
\(242\) −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 0.744266 0.667883i \(-0.232800\pi\)
−0.950537 + 0.310611i \(0.899466\pi\)
\(252\) −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 0.0653297 + 0.997864i \(0.479190\pi\)
−0.896840 + 0.442355i \(0.854143\pi\)
\(258\) 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 0.00225153 + 0.999997i \(0.499283\pi\)
−0.867149 + 0.498049i \(0.834050\pi\)
\(264\) −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 0.887479 0.460848i \(-0.152455\pi\)
−0.842845 + 0.538156i \(0.819121\pi\)
\(270\) −0.133975 + 0.232051i −0.00815343 + 0.0141222i
\(271\) 2.92820 5.07180i 0.177876 0.308090i −0.763277 0.646071i \(-0.776411\pi\)
0.941153 + 0.337982i \(0.109744\pi\)
\(272\) −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 0.898080 0.439832i \(-0.144962\pi\)
−0.829946 + 0.557844i \(0.811629\pi\)
\(278\) 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 \(-0.268105\pi\)
0.665765 + 0.746162i \(0.268105\pi\)
\(282\) 4.09808 + 7.09808i 0.244037 + 0.422684i
\(283\) −4.16987 + 7.22243i −0.247873 + 0.429329i −0.962936 0.269732i \(-0.913065\pi\)
0.715062 + 0.699061i \(0.246398\pi\)
\(284\) 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 \(-0.306054\pi\)
−0.996330 + 0.0855965i \(0.972720\pi\)
\(294\) 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 \(-0.578816\pi\)
−0.245085 + 0.969502i \(0.578816\pi\)
\(308\) −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 \(-0.529898\pi\)
−0.0937894 + 0.995592i \(0.529898\pi\)
\(318\) 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 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 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 0.721973 0.691921i \(-0.243235\pi\)
−0.960208 + 0.279286i \(0.909902\pi\)
\(348\) −1.23205 + 2.13397i −0.0660449 + 0.114393i
\(349\) −9.66025 + 16.7321i −0.517102 + 0.895646i 0.482701 + 0.875785i \(0.339656\pi\)
−0.999803 + 0.0198610i \(0.993678\pi\)
\(350\) −3.60770 −0.192839
\(351\) 0 0
\(352\) 4.73205 0.252219
\(353\) 9.89230 17.1340i 0.526514 0.911949i −0.473008 0.881058i \(-0.656832\pi\)
0.999523 0.0308916i \(-0.00983466\pi\)
\(354\) −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 \(-0.708922\pi\)
−0.610228 + 0.792226i \(0.708922\pi\)
\(360\) −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 −0.607197 0.794551i \(-0.707706\pi\)
0.991700 + 0.128572i \(0.0410394\pi\)
\(368\) 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 0.967780 0.251797i \(-0.0810216\pi\)
−0.701953 + 0.712223i \(0.747688\pi\)
\(374\) 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 \(-0.821361\pi\)
0.884214 + 0.467081i \(0.154694\pi\)
\(380\) −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 \(-0.122085\pi\)
−0.787744 + 0.616002i \(0.788751\pi\)
\(384\) 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 \(-0.169800\pi\)
−0.870906 + 0.491450i \(0.836467\pi\)
\(398\) 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 −0.450922 0.892563i \(-0.648905\pi\)
0.998444 0.0557713i \(-0.0177618\pi\)
\(402\) −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 \(-0.0519125\pi\)
−0.633978 + 0.773351i \(0.718579\pi\)
\(410\) 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 −0.708177 0.706035i \(-0.750482\pi\)
0.965533 + 0.260281i \(0.0838153\pi\)
\(420\) −0.0980762 0.169873i −0.00478563 0.00828895i
\(421\) −32.7128 −1.59432 −0.797162 0.603765i \(-0.793667\pi\)
−0.797162 + 0.603765i \(0.793667\pi\)
\(422\) −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 \(-0.919670\pi\)
0.700404 + 0.713747i \(0.253003\pi\)
\(432\) −0.500000 + 0.866025i −0.0240563 + 0.0416667i
\(433\) 7.42820 + 12.8660i 0.356977 + 0.618302i 0.987454 0.157906i \(-0.0504742\pi\)
−0.630478 + 0.776208i \(0.717141\pi\)
\(434\) 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 −0.574642 0.818405i \(-0.694859\pi\)
0.996080 + 0.0884515i \(0.0281918\pi\)
\(440\) 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 −0.998254 0.0590680i \(-0.981187\pi\)
0.447973 0.894047i \(-0.352146\pi\)
\(450\) 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 \(-0.689571\pi\)
0.997412 + 0.0718931i \(0.0229040\pi\)
\(458\) −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 0.992935 + 0.118661i \(0.0378601\pi\)
−0.393704 + 0.919237i \(0.628807\pi\)
\(462\) 1.73205 + 3.00000i 0.0805823 + 0.139573i
\(463\) 28.0526 1.30371 0.651856 0.758342i \(-0.273990\pi\)
0.651856 + 0.758342i \(0.273990\pi\)
\(464\) −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 −0.385628 0.922654i \(-0.626015\pi\)
0.991856 0.127363i \(-0.0406515\pi\)
\(480\) 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 \(-0.00780457\pi\)
−0.521081 + 0.853507i \(0.674471\pi\)
\(488\) 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 −0.919320 0.393511i \(-0.871260\pi\)
0.800450 + 0.599399i \(0.204594\pi\)
\(492\) 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 \(-0.754147\pi\)
−0.716258 + 0.697835i \(0.754147\pi\)
\(500\) −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 0.962076 0.272780i \(-0.0879431\pi\)
−0.717272 + 0.696793i \(0.754610\pi\)
\(504\) −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 \(-0.760259\pi\)
0.957084 + 0.289810i \(0.0935921\pi\)
\(510\) 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 0.124871 + 0.992173i \(0.460148\pi\)
−0.921683 + 0.387945i \(0.873185\pi\)
\(524\) −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 \(-0.833800\pi\)
−0.866757 + 0.498731i \(0.833800\pi\)
\(542\) −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 0.341178 + 0.939999i \(0.389174\pi\)
−0.984652 + 0.174531i \(0.944159\pi\)
\(558\) −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 0.553949 0.832550i \(-0.313120\pi\)
−0.997984 + 0.0634589i \(0.979787\pi\)
\(564\) 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 −0.102935 0.994688i \(-0.532823\pi\)
0.912893 0.408200i \(-0.133843\pi\)
\(570\) 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 \(-0.501775\pi\)
−0.00557744 + 0.999984i \(0.501775\pi\)
\(578\) −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 \(-0.726219\pi\)
0.982550 + 0.185999i \(0.0595520\pi\)
\(588\) 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 \(-0.226783\pi\)
0.756756 + 0.653698i \(0.226783\pi\)
\(594\) −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 −0.799218 0.601041i \(-0.794753\pi\)
0.920126 + 0.391622i \(0.128086\pi\)
\(602\) −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 0.857954 0.513726i \(-0.171735\pi\)
−0.873877 + 0.486147i \(0.838402\pi\)
\(608\) −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 \(-0.759439\pi\)
0.957827 + 0.287345i \(0.0927726\pi\)
\(614\) −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 0.965032 + 0.262133i \(0.0844260\pi\)
−0.255502 + 0.966809i \(0.582241\pi\)
\(618\) −9.36603 16.2224i −0.376757 0.652562i
\(619\) −10.5359 −0.423474 −0.211737 0.977327i \(-0.567912\pi\)
−0.211737 + 0.977327i \(0.567912\pi\)
\(620\) 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 0.746037 + 0.665904i \(0.231954\pi\)
0.203671 + 0.979039i \(0.434713\pi\)
\(632\) 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 −0.999885 0.0151806i \(-0.995168\pi\)
0.486796 0.873516i \(-0.338166\pi\)
\(642\) 0.196152 0.00774152
\(643\) 6.92820 + 12.0000i 0.273222 + 0.473234i 0.969685 0.244359i \(-0.0785774\pi\)
−0.696463 + 0.717592i \(0.745244\pi\)
\(644\) −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 0.483856 + 0.875147i \(0.339236\pi\)
−0.999828 + 0.0185417i \(0.994098\pi\)
\(648\) 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 −0.744348 0.667792i \(-0.767240\pi\)
0.950499 + 0.310728i \(0.100573\pi\)
\(654\) 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 −0.950205 0.311627i \(-0.899126\pi\)
0.205225 0.978715i \(-0.434207\pi\)
\(660\) −0.633975 + 1.09808i −0.0246774 + 0.0427426i
\(661\) −4.69615 + 8.13397i −0.182659 + 0.316375i −0.942785 0.333401i \(-0.891804\pi\)
0.760126 + 0.649776i \(0.225137\pi\)
\(662\) 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 −0.969173 0.246381i \(-0.920758\pi\)
0.697959 + 0.716138i \(0.254092\pi\)
\(674\) 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 −0.959275 0.282475i \(-0.908845\pi\)
0.235007 0.971994i \(-0.424489\pi\)
\(684\) −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 −0.498994 0.866606i \(-0.666297\pi\)
0.999999 0.00116153i \(-0.000369728\pi\)
\(692\) 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 0.939077 + 0.343707i \(0.111683\pi\)
−0.171880 + 0.985118i \(0.554984\pi\)
\(710\) −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 0.995961 0.0897860i \(-0.0286183\pi\)
−0.575737 + 0.817635i \(0.695285\pi\)
\(720\) −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 \(-0.614121\pi\)
−0.350891 + 0.936416i \(0.614121\pi\)
\(734\) −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 \(-0.897753\pi\)
0.747851 + 0.663867i \(0.231086\pi\)
\(740\) 2.80385 0.103071
\(741\) 0 0
\(742\) 0.339746 0.0124725
\(743\) −13.8038 + 23.9090i −0.506414 + 0.877135i 0.493558 + 0.869713i \(0.335696\pi\)
−0.999972 + 0.00742221i \(0.997637\pi\)
\(744\) 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 −0.973872 0.227098i \(-0.927076\pi\)
0.683609 + 0.729849i \(0.260410\pi\)
\(752\) −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 −0.923101 0.384557i \(-0.874354\pi\)
0.794587 + 0.607151i \(0.207688\pi\)
\(758\) −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 \(-0.305579\pi\)
−0.996201 + 0.0870836i \(0.972245\pi\)
\(762\) −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 \(-0.927347\pi\)
0.682988 + 0.730429i \(0.260680\pi\)
\(770\) −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 −0.987404 0.158217i \(-0.949425\pi\)
0.356682 0.934226i \(-0.383908\pi\)
\(774\) 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