Properties

Label 1014.2.i.a.361.1
Level $1014$
Weight $2$
Character 1014.361
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.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.09683076496\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1014.361
Dual form 1014.2.i.a.823.1

$q$-expansion

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

Character values

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

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.267949i 0.119831i −0.998203 0.0599153i \(-0.980917\pi\)
0.998203 0.0599153i \(-0.0190830\pi\)
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) −0.633975 0.366025i −0.239620 0.138345i 0.375382 0.926870i \(-0.377511\pi\)
−0.615002 + 0.788526i \(0.710845\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0.133975 + 0.232051i 0.0423665 + 0.0733809i
\(11\) 4.09808 2.36603i 1.23562 0.713384i 0.267421 0.963580i \(-0.413828\pi\)
0.968195 + 0.250196i \(0.0804951\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 0.732051 0.195649
\(15\) −0.232051 + 0.133975i −0.0599153 + 0.0345921i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.13397 + 1.96410i −0.275029 + 0.476365i −0.970143 0.242536i \(-0.922021\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.09808 + 0.633975i 0.251916 + 0.145444i 0.620641 0.784095i \(-0.286872\pi\)
−0.368725 + 0.929538i \(0.620206\pi\)
\(20\) −0.232051 0.133975i −0.0518881 0.0299576i
\(21\) 0.732051i 0.159747i
\(22\) −2.36603 + 4.09808i −0.504438 + 0.873713i
\(23\) −3.09808 5.36603i −0.645994 1.11889i −0.984071 0.177775i \(-0.943110\pi\)
0.338078 0.941118i \(-0.390223\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 4.92820 0.985641
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −0.633975 + 0.366025i −0.119810 + 0.0691723i
\(29\) −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
\(31\) 5.46410i 0.981382i 0.871334 + 0.490691i \(0.163256\pi\)
−0.871334 + 0.490691i \(0.836744\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) −4.09808 2.36603i −0.713384 0.411872i
\(34\) 2.26795i 0.388950i
\(35\) −0.0980762 + 0.169873i −0.0165779 + 0.0287138i
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 9.06218 5.23205i 1.48981 0.860144i 0.489881 0.871789i \(-0.337040\pi\)
0.999932 + 0.0116456i \(0.00370701\pi\)
\(38\) −1.26795 −0.205689
\(39\) 0 0
\(40\) 0.267949 0.0423665
\(41\) −9.86603 + 5.69615i −1.54081 + 0.889590i −0.542027 + 0.840361i \(0.682343\pi\)
−0.998788 + 0.0492283i \(0.984324\pi\)
\(42\) −0.366025 0.633975i −0.0564789 0.0978244i
\(43\) 3.83013 6.63397i 0.584089 1.01167i −0.410899 0.911681i \(-0.634785\pi\)
0.994988 0.0999910i \(-0.0318814\pi\)
\(44\) 4.73205i 0.713384i
\(45\) 0.232051 + 0.133975i 0.0345921 + 0.0199718i
\(46\) 5.36603 + 3.09808i 0.791177 + 0.456786i
\(47\) 8.19615i 1.19553i −0.801671 0.597766i \(-0.796055\pi\)
0.801671 0.597766i \(-0.203945\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −3.23205 5.59808i −0.461722 0.799725i
\(50\) −4.26795 + 2.46410i −0.603579 + 0.348477i
\(51\) 2.26795 0.317576
\(52\) 0 0
\(53\) 0.464102 0.0637493 0.0318746 0.999492i \(-0.489852\pi\)
0.0318746 + 0.999492i \(0.489852\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) −0.633975 1.09808i −0.0854851 0.148065i
\(56\) 0.366025 0.633975i 0.0489122 0.0847184i
\(57\) 1.26795i 0.167944i
\(58\) 2.13397 + 1.23205i 0.280205 + 0.161776i
\(59\) −6.92820 4.00000i −0.901975 0.520756i −0.0241347 0.999709i \(-0.507683\pi\)
−0.877841 + 0.478953i \(0.841016\pi\)
\(60\) 0.267949i 0.0345921i
\(61\) −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
\(63\) 0.633975 0.366025i 0.0798733 0.0461149i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 4.73205 0.582475
\(67\) 9.63397 5.56218i 1.17698 0.679528i 0.221664 0.975123i \(-0.428851\pi\)
0.955313 + 0.295595i \(0.0955179\pi\)
\(68\) 1.13397 + 1.96410i 0.137515 + 0.238182i
\(69\) −3.09808 + 5.36603i −0.372965 + 0.645994i
\(70\) 0.196152i 0.0234447i
\(71\) 1.09808 + 0.633975i 0.130318 + 0.0752389i 0.563742 0.825951i \(-0.309361\pi\)
−0.433424 + 0.901190i \(0.642695\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 9.73205i 1.13905i −0.821974 0.569525i \(-0.807127\pi\)
0.821974 0.569525i \(-0.192873\pi\)
\(74\) −5.23205 + 9.06218i −0.608214 + 1.05346i
\(75\) −2.46410 4.26795i −0.284530 0.492820i
\(76\) 1.09808 0.633975i 0.125958 0.0727219i
\(77\) −3.46410 −0.394771
\(78\) 0 0
\(79\) −9.46410 −1.06479 −0.532397 0.846495i \(-0.678709\pi\)
−0.532397 + 0.846495i \(0.678709\pi\)
\(80\) −0.232051 + 0.133975i −0.0259441 + 0.0149788i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 5.69615 9.86603i 0.629035 1.08952i
\(83\) 10.1962i 1.11917i −0.828772 0.559587i \(-0.810960\pi\)
0.828772 0.559587i \(-0.189040\pi\)
\(84\) 0.633975 + 0.366025i 0.0691723 + 0.0399366i
\(85\) 0.526279 + 0.303848i 0.0570830 + 0.0329569i
\(86\) 7.66025i 0.826026i
\(87\) −1.23205 + 2.13397i −0.132090 + 0.228786i
\(88\) 2.36603 + 4.09808i 0.252219 + 0.436856i
\(89\) −2.19615 + 1.26795i −0.232792 + 0.134402i −0.611859 0.790967i \(-0.709578\pi\)
0.379068 + 0.925369i \(0.376245\pi\)
\(90\) −0.267949 −0.0282443
\(91\) 0 0
\(92\) −6.19615 −0.645994
\(93\) 4.73205 2.73205i 0.490691 0.283300i
\(94\) 4.09808 + 7.09808i 0.422684 + 0.732111i
\(95\) 0.169873 0.294229i 0.0174286 0.0301872i
\(96\) 1.00000i 0.102062i
\(97\) −5.19615 3.00000i −0.527589 0.304604i 0.212445 0.977173i \(-0.431857\pi\)
−0.740034 + 0.672569i \(0.765191\pi\)
\(98\) 5.59808 + 3.23205i 0.565491 + 0.326486i
\(99\) 4.73205i 0.475589i
\(100\) 2.46410 4.26795i 0.246410 0.426795i
\(101\) −5.96410 10.3301i −0.593450 1.02789i −0.993764 0.111508i \(-0.964432\pi\)
0.400313 0.916378i \(-0.368901\pi\)
\(102\) −1.96410 + 1.13397i −0.194475 + 0.112280i
\(103\) 18.7321 1.84572 0.922862 0.385131i \(-0.125844\pi\)
0.922862 + 0.385131i \(0.125844\pi\)
\(104\) 0 0
\(105\) 0.196152 0.0191425
\(106\) −0.401924 + 0.232051i −0.0390383 + 0.0225388i
\(107\) 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
\(109\) 5.46410i 0.523366i 0.965154 + 0.261683i \(0.0842775\pi\)
−0.965154 + 0.261683i \(0.915723\pi\)
\(110\) 1.09808 + 0.633975i 0.104697 + 0.0604471i
\(111\) −9.06218 5.23205i −0.860144 0.496604i
\(112\) 0.732051i 0.0691723i
\(113\) 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
\(115\) −1.43782 + 0.830127i −0.134078 + 0.0774097i
\(116\) −2.46410 −0.228786
\(117\) 0 0
\(118\) 8.00000 0.736460
\(119\) 1.43782 0.830127i 0.131805 0.0760976i
\(120\) −0.133975 0.232051i −0.0122302 0.0211832i
\(121\) 5.69615 9.86603i 0.517832 0.896911i
\(122\) 1.19615i 0.108295i
\(123\) 9.86603 + 5.69615i 0.889590 + 0.513605i
\(124\) 4.73205 + 2.73205i 0.424951 + 0.245345i
\(125\) 2.66025i 0.237940i
\(126\) −0.366025 + 0.633975i −0.0326081 + 0.0564789i
\(127\) 8.92820 + 15.4641i 0.792250 + 1.37222i 0.924571 + 0.381010i \(0.124424\pi\)
−0.132321 + 0.991207i \(0.542243\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −7.66025 −0.674448
\(130\) 0 0
\(131\) 13.4641 1.17636 0.588182 0.808729i \(-0.299844\pi\)
0.588182 + 0.808729i \(0.299844\pi\)
\(132\) −4.09808 + 2.36603i −0.356692 + 0.205936i
\(133\) −0.464102 0.803848i −0.0402427 0.0697024i
\(134\) −5.56218 + 9.63397i −0.480499 + 0.832249i
\(135\) 0.267949i 0.0230614i
\(136\) −1.96410 1.13397i −0.168420 0.0972375i
\(137\) 1.66987 + 0.964102i 0.142667 + 0.0823688i 0.569634 0.821898i \(-0.307085\pi\)
−0.426968 + 0.904267i \(0.640418\pi\)
\(138\) 6.19615i 0.527452i
\(139\) 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
\(141\) −7.09808 + 4.09808i −0.597766 + 0.345120i
\(142\) −1.26795 −0.106404
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −0.571797 + 0.330127i −0.0474851 + 0.0274156i
\(146\) 4.86603 + 8.42820i 0.402715 + 0.697523i
\(147\) −3.23205 + 5.59808i −0.266575 + 0.461722i
\(148\) 10.4641i 0.860144i
\(149\) 2.42820 + 1.40192i 0.198926 + 0.114850i 0.596154 0.802870i \(-0.296695\pi\)
−0.397228 + 0.917720i \(0.630028\pi\)
\(150\) 4.26795 + 2.46410i 0.348477 + 0.201193i
\(151\) 3.26795i 0.265942i 0.991120 + 0.132971i \(0.0424517\pi\)
−0.991120 + 0.132971i \(0.957548\pi\)
\(152\) −0.633975 + 1.09808i −0.0514221 + 0.0890657i
\(153\) −1.13397 1.96410i −0.0916764 0.158788i
\(154\) 3.00000 1.73205i 0.241747 0.139573i
\(155\) 1.46410 0.117599
\(156\) 0 0
\(157\) −23.5885 −1.88256 −0.941282 0.337622i \(-0.890378\pi\)
−0.941282 + 0.337622i \(0.890378\pi\)
\(158\) 8.19615 4.73205i 0.652051 0.376462i
\(159\) −0.232051 0.401924i −0.0184028 0.0318746i
\(160\) 0.133975 0.232051i 0.0105916 0.0183452i
\(161\) 4.53590i 0.357479i
\(162\) 0.866025 + 0.500000i 0.0680414 + 0.0392837i
\(163\) 5.66025 + 3.26795i 0.443345 + 0.255966i 0.705016 0.709192i \(-0.250940\pi\)
−0.261670 + 0.965157i \(0.584273\pi\)
\(164\) 11.3923i 0.889590i
\(165\) −0.633975 + 1.09808i −0.0493549 + 0.0854851i
\(166\) 5.09808 + 8.83013i 0.395687 + 0.685351i
\(167\) −2.19615 + 1.26795i −0.169943 + 0.0981169i −0.582559 0.812788i \(-0.697949\pi\)
0.412616 + 0.910905i \(0.364615\pi\)
\(168\) −0.732051 −0.0564789
\(169\) 0 0
\(170\) −0.607695 −0.0466081
\(171\) −1.09808 + 0.633975i −0.0839720 + 0.0484812i
\(172\) −3.83013 6.63397i −0.292044 0.505836i
\(173\) −8.19615 + 14.1962i −0.623142 + 1.07931i 0.365755 + 0.930711i \(0.380811\pi\)
−0.988897 + 0.148602i \(0.952523\pi\)
\(174\) 2.46410i 0.186803i
\(175\) −3.12436 1.80385i −0.236179 0.136358i
\(176\) −4.09808 2.36603i −0.308904 0.178346i
\(177\) 8.00000i 0.601317i
\(178\) 1.26795 2.19615i 0.0950368 0.164609i
\(179\) 11.0263 + 19.0981i 0.824143 + 1.42746i 0.902573 + 0.430538i \(0.141676\pi\)
−0.0784298 + 0.996920i \(0.524991\pi\)
\(180\) 0.232051 0.133975i 0.0172960 0.00998588i
\(181\) −8.80385 −0.654385 −0.327192 0.944958i \(-0.606103\pi\)
−0.327192 + 0.944958i \(0.606103\pi\)
\(182\) 0 0
\(183\) 1.19615 0.0884221
\(184\) 5.36603 3.09808i 0.395589 0.228393i
\(185\) −1.40192 2.42820i −0.103071 0.178525i
\(186\) −2.73205 + 4.73205i −0.200324 + 0.346971i
\(187\) 10.7321i 0.784805i
\(188\) −7.09808 4.09808i −0.517680 0.298883i
\(189\) −0.633975 0.366025i −0.0461149 0.0266244i
\(190\) 0.339746i 0.0246478i
\(191\) −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
\(193\) −7.16025 + 4.13397i −0.515406 + 0.297570i −0.735053 0.678009i \(-0.762843\pi\)
0.219647 + 0.975579i \(0.429510\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) −6.46410 −0.461722
\(197\) −8.53590 + 4.92820i −0.608158 + 0.351120i −0.772244 0.635326i \(-0.780866\pi\)
0.164086 + 0.986446i \(0.447532\pi\)
\(198\) −2.36603 4.09808i −0.168146 0.291238i
\(199\) −1.90192 + 3.29423i −0.134824 + 0.233522i −0.925530 0.378674i \(-0.876380\pi\)
0.790706 + 0.612196i \(0.209714\pi\)
\(200\) 4.92820i 0.348477i
\(201\) −9.63397 5.56218i −0.679528 0.392326i
\(202\) 10.3301 + 5.96410i 0.726825 + 0.419633i
\(203\) 1.80385i 0.126605i
\(204\) 1.13397 1.96410i 0.0793941 0.137515i
\(205\) 1.52628 + 2.64359i 0.106600 + 0.184637i
\(206\) −16.2224 + 9.36603i −1.13027 + 0.652562i
\(207\) 6.19615 0.430662
\(208\) 0 0
\(209\) 6.00000 0.415029
\(210\) −0.169873 + 0.0980762i −0.0117223 + 0.00676790i
\(211\) 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
\(213\) 1.26795i 0.0868784i
\(214\) −0.169873 0.0980762i −0.0116123 0.00670435i
\(215\) −1.77757 1.02628i −0.121229 0.0699917i
\(216\) 1.00000i 0.0680414i
\(217\) 2.00000 3.46410i 0.135769 0.235159i
\(218\) −2.73205 4.73205i −0.185038 0.320495i
\(219\) −8.42820 + 4.86603i −0.569525 + 0.328816i
\(220\) −1.26795 −0.0854851
\(221\) 0 0
\(222\) 10.4641 0.702305
\(223\) 11.3205 6.53590i 0.758077 0.437676i −0.0705277 0.997510i \(-0.522468\pi\)
0.828605 + 0.559834i \(0.189135\pi\)
\(224\) −0.366025 0.633975i −0.0244561 0.0423592i
\(225\) −2.46410 + 4.26795i −0.164273 + 0.284530i
\(226\) 18.6603i 1.24126i
\(227\) −1.56218 0.901924i −0.103685 0.0598628i 0.447261 0.894404i \(-0.352400\pi\)
−0.550946 + 0.834541i \(0.685733\pi\)
\(228\) −1.09808 0.633975i −0.0727219 0.0419860i
\(229\) 15.8564i 1.04782i 0.851773 + 0.523910i \(0.175527\pi\)
−0.851773 + 0.523910i \(0.824473\pi\)
\(230\) 0.830127 1.43782i 0.0547370 0.0948072i
\(231\) 1.73205 + 3.00000i 0.113961 + 0.197386i
\(232\) 2.13397 1.23205i 0.140102 0.0808881i
\(233\) −19.8564 −1.30084 −0.650418 0.759576i \(-0.725406\pi\)
−0.650418 + 0.759576i \(0.725406\pi\)
\(234\) 0 0
\(235\) −2.19615 −0.143261
\(236\) −6.92820 + 4.00000i −0.450988 + 0.260378i
\(237\) 4.73205 + 8.19615i 0.307380 + 0.532397i
\(238\) −0.830127 + 1.43782i −0.0538091 + 0.0932002i
\(239\) 9.66025i 0.624870i 0.949939 + 0.312435i \(0.101145\pi\)
−0.949939 + 0.312435i \(0.898855\pi\)
\(240\) 0.232051 + 0.133975i 0.0149788 + 0.00864802i
\(241\) 15.2321 + 8.79423i 0.981183 + 0.566486i 0.902627 0.430424i \(-0.141636\pi\)
0.0785557 + 0.996910i \(0.474969\pi\)
\(242\) 11.3923i 0.732325i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0.598076 + 1.03590i 0.0382879 + 0.0663166i
\(245\) −1.50000 + 0.866025i −0.0958315 + 0.0553283i
\(246\) −11.3923 −0.726347
\(247\) 0 0
\(248\) −5.46410 −0.346971
\(249\) −8.83013 + 5.09808i −0.559587 + 0.323077i
\(250\) 1.33013 + 2.30385i 0.0841246 + 0.145708i
\(251\) 3.26795 5.66025i 0.206271 0.357272i −0.744266 0.667883i \(-0.767200\pi\)
0.950537 + 0.310611i \(0.100534\pi\)
\(252\) 0.732051i 0.0461149i
\(253\) −25.3923 14.6603i −1.59640 0.921682i
\(254\) −15.4641 8.92820i −0.970304 0.560205i
\(255\) 0.607695i 0.0380553i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 13.3301 + 23.0885i 0.831510 + 1.44022i 0.896840 + 0.442355i \(0.145857\pi\)
−0.0653297 + 0.997864i \(0.520810\pi\)
\(258\) 6.63397 3.83013i 0.413013 0.238453i
\(259\) −7.66025 −0.475985
\(260\) 0 0
\(261\) 2.46410 0.152524
\(262\) −11.6603 + 6.73205i −0.720373 + 0.415907i
\(263\) −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
\(265\) 0.124356i 0.00763911i
\(266\) 0.803848 + 0.464102i 0.0492871 + 0.0284559i
\(267\) 2.19615 + 1.26795i 0.134402 + 0.0775972i
\(268\) 11.1244i 0.679528i
\(269\) 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
\(271\) 5.07180 2.92820i 0.308090 0.177876i −0.337982 0.941153i \(-0.609744\pi\)
0.646071 + 0.763277i \(0.276411\pi\)
\(272\) 2.26795 0.137515
\(273\) 0 0
\(274\) −1.92820 −0.116487
\(275\) 20.1962 11.6603i 1.21787 0.703140i
\(276\) 3.09808 + 5.36603i 0.186482 + 0.322997i
\(277\) −1.13397 + 1.96410i −0.0681339 + 0.118011i −0.898080 0.439832i \(-0.855038\pi\)
0.829946 + 0.557844i \(0.188371\pi\)
\(278\) 9.85641i 0.591148i
\(279\) −4.73205 2.73205i −0.283300 0.163564i
\(280\) −0.169873 0.0980762i −0.0101519 0.00586117i
\(281\) 22.3205i 1.33153i −0.746162 0.665765i \(-0.768105\pi\)
0.746162 0.665765i \(-0.231895\pi\)
\(282\) 4.09808 7.09808i 0.244037 0.422684i
\(283\) 4.16987 + 7.22243i 0.247873 + 0.429329i 0.962936 0.269732i \(-0.0869350\pi\)
−0.715062 + 0.699061i \(0.753602\pi\)
\(284\) 1.09808 0.633975i 0.0651588 0.0376195i
\(285\) −0.339746 −0.0201248
\(286\) 0 0
\(287\) 8.33975 0.492280
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) 5.92820 + 10.2679i 0.348718 + 0.603997i
\(290\) 0.330127 0.571797i 0.0193857 0.0335771i
\(291\) 6.00000i 0.351726i
\(292\) −8.42820 4.86603i −0.493223 0.284763i
\(293\) 12.5718 + 7.25833i 0.734452 + 0.424036i 0.820049 0.572294i \(-0.193946\pi\)
−0.0855965 + 0.996330i \(0.527280\pi\)
\(294\) 6.46410i 0.376994i
\(295\) −1.07180 + 1.85641i −0.0624024 + 0.108084i
\(296\) 5.23205 + 9.06218i 0.304107 + 0.526728i
\(297\) 4.09808 2.36603i 0.237795 0.137291i
\(298\) −2.80385 −0.162423
\(299\) 0 0
\(300\) −4.92820 −0.284530
\(301\) −4.85641 + 2.80385i −0.279919 + 0.161611i
\(302\) −1.63397 2.83013i −0.0940247 0.162856i
\(303\) −5.96410 + 10.3301i −0.342629 + 0.593450i
\(304\) 1.26795i 0.0727219i
\(305\) 0.277568 + 0.160254i 0.0158935 + 0.00917612i
\(306\) 1.96410 + 1.13397i 0.112280 + 0.0648250i
\(307\) 8.58846i 0.490169i 0.969502 + 0.245085i \(0.0788157\pi\)
−0.969502 + 0.245085i \(0.921184\pi\)
\(308\) −1.73205 + 3.00000i −0.0986928 + 0.170941i
\(309\) −9.36603 16.2224i −0.532815 0.922862i
\(310\) −1.26795 + 0.732051i −0.0720147 + 0.0415777i
\(311\) −15.6603 −0.888012 −0.444006 0.896024i \(-0.646443\pi\)
−0.444006 + 0.896024i \(0.646443\pi\)
\(312\) 0 0
\(313\) 13.4641 0.761036 0.380518 0.924774i \(-0.375746\pi\)
0.380518 + 0.924774i \(0.375746\pi\)
\(314\) 20.4282 11.7942i 1.15283 0.665587i
\(315\) −0.0980762 0.169873i −0.00552597 0.00957126i
\(316\) −4.73205 + 8.19615i −0.266199 + 0.461070i
\(317\) 3.33975i 0.187579i −0.995592 0.0937894i \(-0.970102\pi\)
0.995592 0.0937894i \(-0.0298980\pi\)
\(318\) 0.401924 + 0.232051i 0.0225388 + 0.0130128i
\(319\) −10.0981 5.83013i −0.565384 0.326424i
\(320\) 0.267949i 0.0149788i
\(321\) 0.0980762 0.169873i 0.00547408 0.00948139i
\(322\) −2.26795 3.92820i −0.126388 0.218910i
\(323\) −2.49038 + 1.43782i −0.138569 + 0.0800026i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −6.53590 −0.361990
\(327\) 4.73205 2.73205i 0.261683 0.151083i
\(328\) −5.69615 9.86603i −0.314517 0.544760i
\(329\) −3.00000 + 5.19615i −0.165395 + 0.286473i
\(330\) 1.26795i 0.0697983i
\(331\) 17.3205 + 10.0000i 0.952021 + 0.549650i 0.893708 0.448649i \(-0.148095\pi\)
0.0583130 + 0.998298i \(0.481428\pi\)
\(332\) −8.83013 5.09808i −0.484616 0.279793i
\(333\) 10.4641i 0.573429i
\(334\) 1.26795 2.19615i 0.0693791 0.120168i
\(335\) −1.49038 2.58142i −0.0814282 0.141038i
\(336\) 0.633975 0.366025i 0.0345861 0.0199683i
\(337\) −6.85641 −0.373492 −0.186746 0.982408i \(-0.559794\pi\)
−0.186746 + 0.982408i \(0.559794\pi\)
\(338\) 0 0
\(339\) −18.6603 −1.01349
\(340\) 0.526279 0.303848i 0.0285415 0.0164784i
\(341\) 12.9282 + 22.3923i 0.700101 + 1.21261i
\(342\) 0.633975 1.09808i 0.0342814 0.0593772i
\(343\) 9.85641i 0.532196i
\(344\) 6.63397 + 3.83013i 0.357680 + 0.206507i
\(345\) 1.43782 + 0.830127i 0.0774097 + 0.0446925i
\(346\) 16.3923i 0.881256i
\(347\) −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
\(349\) −16.7321 + 9.66025i −0.895646 + 0.517102i −0.875785 0.482701i \(-0.839656\pi\)
−0.0198610 + 0.999803i \(0.506322\pi\)
\(350\) 3.60770 0.192839
\(351\) 0 0
\(352\) 4.73205 0.252219
\(353\) −17.1340 + 9.89230i −0.911949 + 0.526514i −0.881058 0.473008i \(-0.843168\pi\)
−0.0308916 + 0.999523i \(0.509835\pi\)
\(354\) −4.00000 6.92820i −0.212598 0.368230i
\(355\) 0.169873 0.294229i 0.00901592 0.0156160i
\(356\) 2.53590i 0.134402i
\(357\) −1.43782 0.830127i −0.0760976 0.0439350i
\(358\) −19.0981 11.0263i −1.00936 0.582757i
\(359\) 23.1244i 1.22046i 0.792226 + 0.610228i \(0.208922\pi\)
−0.792226 + 0.610228i \(0.791078\pi\)
\(360\) −0.133975 + 0.232051i −0.00706108 + 0.0122302i
\(361\) −8.69615 15.0622i −0.457692 0.792746i
\(362\) 7.62436 4.40192i 0.400727 0.231360i
\(363\) −11.3923 −0.597941
\(364\) 0 0
\(365\) −2.60770 −0.136493
\(366\) −1.03590 + 0.598076i −0.0541473 + 0.0312619i
\(367\) 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
\(369\) 11.3923i 0.593060i
\(370\) 2.42820 + 1.40192i 0.126236 + 0.0728825i
\(371\) −0.294229 0.169873i −0.0152756 0.00881937i
\(372\) 5.46410i 0.283300i
\(373\) 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
\(375\) −2.30385 + 1.33013i −0.118970 + 0.0686875i
\(376\) 8.19615 0.422684
\(377\) 0 0
\(378\) 0.732051 0.0376526
\(379\) −1.26795 + 0.732051i −0.0651302 + 0.0376029i −0.532211 0.846611i \(-0.678639\pi\)
0.467081 + 0.884214i \(0.345306\pi\)
\(380\) −0.169873 0.294229i −0.00871430 0.0150936i
\(381\) 8.92820 15.4641i 0.457406 0.792250i
\(382\) 6.92820i 0.354478i
\(383\) 4.73205 + 2.73205i 0.241797 + 0.139601i 0.616002 0.787744i \(-0.288751\pi\)
−0.374206 + 0.927346i \(0.622085\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0.928203i 0.0473056i
\(386\) 4.13397 7.16025i 0.210414 0.364447i
\(387\) 3.83013 + 6.63397i 0.194696 + 0.337224i
\(388\) −5.19615 + 3.00000i −0.263795 + 0.152302i
\(389\) 29.7846 1.51014 0.755070 0.655644i \(-0.227603\pi\)
0.755070 + 0.655644i \(0.227603\pi\)
\(390\) 0 0
\(391\) 14.0526 0.710668
\(392\) 5.59808 3.23205i 0.282746 0.163243i
\(393\) −6.73205 11.6603i −0.339587 0.588182i
\(394\) 4.92820 8.53590i 0.248279 0.430032i
\(395\) 2.53590i 0.127595i
\(396\) 4.09808 + 2.36603i 0.205936 + 0.118897i
\(397\) 0.339746 + 0.196152i 0.0170514 + 0.00984461i 0.508501 0.861061i \(-0.330200\pi\)
−0.491450 + 0.870906i \(0.663533\pi\)
\(398\) 3.80385i 0.190670i
\(399\) −0.464102 + 0.803848i −0.0232341 + 0.0402427i
\(400\) −2.46410 4.26795i −0.123205 0.213397i
\(401\) 18.9904 10.9641i 0.948334 0.547521i 0.0557713 0.998444i \(-0.482238\pi\)
0.892563 + 0.450922i \(0.148905\pi\)
\(402\) 11.1244 0.554832
\(403\) 0 0
\(404\) −11.9282 −0.593450
\(405\) −0.232051 + 0.133975i −0.0115307 + 0.00665725i
\(406\) −0.901924 1.56218i −0.0447617 0.0775296i
\(407\) 24.7583 42.8827i 1.22722 2.12562i
\(408\) 2.26795i 0.112280i
\(409\) 12.3564 + 7.13397i 0.610985 + 0.352752i 0.773351 0.633978i \(-0.218579\pi\)
−0.162366 + 0.986731i \(0.551912\pi\)
\(410\) −2.64359 1.52628i −0.130558 0.0753776i
\(411\) 1.92820i 0.0951113i
\(412\) 9.36603 16.2224i 0.461431 0.799222i
\(413\) 2.92820 + 5.07180i 0.144087 + 0.249567i
\(414\) −5.36603 + 3.09808i −0.263726 + 0.152262i
\(415\) −2.73205 −0.134111
\(416\) 0 0
\(417\) −9.85641 −0.482670
\(418\) −5.19615 + 3.00000i −0.254152 + 0.146735i
\(419\) 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
\(421\) 32.7128i 1.59432i −0.603765 0.797162i \(-0.706333\pi\)
0.603765 0.797162i \(-0.293667\pi\)
\(422\) −3.80385 2.19615i −0.185168 0.106907i
\(423\) 7.09808 + 4.09808i 0.345120 + 0.199255i
\(424\) 0.464102i 0.0225388i
\(425\) −5.58846 + 9.67949i −0.271080 + 0.469524i
\(426\) 0.633975 + 1.09808i 0.0307162 + 0.0532020i
\(427\) 0.758330 0.437822i 0.0366982 0.0211877i
\(428\) 0.196152 0.00948139
\(429\) 0 0
\(430\) 2.05256 0.0989832
\(431\) 9.63397 5.56218i 0.464052 0.267921i −0.249694 0.968325i \(-0.580330\pi\)
0.713747 + 0.700404i \(0.246997\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −7.42820 + 12.8660i −0.356977 + 0.618302i −0.987454 0.157906i \(-0.949526\pi\)
0.630478 + 0.776208i \(0.282859\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 0.571797 + 0.330127i 0.0274156 + 0.0158284i
\(436\) 4.73205 + 2.73205i 0.226624 + 0.130842i
\(437\) 7.85641i 0.375823i
\(438\) 4.86603 8.42820i 0.232508 0.402715i
\(439\) −8.83013 15.2942i −0.421439 0.729954i 0.574642 0.818405i \(-0.305141\pi\)
−0.996080 + 0.0884515i \(0.971808\pi\)
\(440\) 1.09808 0.633975i 0.0523487 0.0302236i
\(441\) 6.46410 0.307814
\(442\) 0 0
\(443\) 36.3923 1.72905 0.864525 0.502589i \(-0.167619\pi\)
0.864525 + 0.502589i \(0.167619\pi\)
\(444\) −9.06218 + 5.23205i −0.430072 + 0.248302i
\(445\) 0.339746 + 0.588457i 0.0161055 + 0.0278955i
\(446\) −6.53590 + 11.3205i −0.309484 + 0.536042i
\(447\) 2.80385i 0.132617i
\(448\) 0.633975 + 0.366025i 0.0299525 + 0.0172931i
\(449\) 20.1962 + 11.6603i 0.953115 + 0.550281i 0.894047 0.447973i \(-0.147854\pi\)
0.0590680 + 0.998254i \(0.481187\pi\)
\(450\) 4.92820i 0.232318i
\(451\) −26.9545 + 46.6865i −1.26924 + 2.19838i
\(452\) −9.33013 16.1603i −0.438852 0.760114i
\(453\) 2.83013 1.63397i 0.132971 0.0767708i
\(454\) 1.80385 0.0846588
\(455\) 0 0
\(456\) 1.26795 0.0593772
\(457\) −16.1603 + 9.33013i −0.755945 + 0.436445i −0.827838 0.560967i \(-0.810429\pi\)
0.0718931 + 0.997412i \(0.477096\pi\)
\(458\) −7.92820 13.7321i −0.370461 0.641657i
\(459\) −1.13397 + 1.96410i −0.0529294 + 0.0916764i
\(460\) 1.66025i 0.0774097i
\(461\) 22.2846 + 12.8660i 1.03790 + 0.599231i 0.919237 0.393704i \(-0.128807\pi\)
0.118661 + 0.992935i \(0.462140\pi\)
\(462\) −3.00000 1.73205i −0.139573 0.0805823i
\(463\) 28.0526i 1.30371i −0.758342 0.651856i \(-0.773990\pi\)
0.758342 0.651856i \(-0.226010\pi\)
\(464\) −1.23205 + 2.13397i −0.0571965 + 0.0990673i
\(465\) −0.732051 1.26795i −0.0339480 0.0587997i
\(466\) 17.1962 9.92820i 0.796596 0.459915i
\(467\) 12.5885 0.582524 0.291262 0.956643i \(-0.405925\pi\)
0.291262 + 0.956643i \(0.405925\pi\)
\(468\) 0 0
\(469\) −8.14359 −0.376036
\(470\) 1.90192 1.09808i 0.0877292 0.0506505i
\(471\) 11.7942 + 20.4282i 0.543449 + 0.941282i
\(472\) 4.00000 6.92820i 0.184115 0.318896i
\(473\) 36.2487i 1.66672i
\(474\) −8.19615 4.73205i −0.376462 0.217350i
\(475\) 5.41154 + 3.12436i 0.248299 + 0.143355i
\(476\) 1.66025i 0.0760976i
\(477\) −0.232051 + 0.401924i −0.0106249 + 0.0184028i
\(478\) −4.83013 8.36603i −0.220925 0.382653i
\(479\) 22.9808 13.2679i 1.05002 0.606228i 0.127363 0.991856i \(-0.459349\pi\)
0.922654 + 0.385628i \(0.126015\pi\)
\(480\) −0.267949 −0.0122302
\(481\) 0 0
\(482\) −17.5885 −0.801132
\(483\) 3.92820 2.26795i 0.178739 0.103195i
\(484\) −5.69615 9.86603i −0.258916 0.448456i
\(485\) −0.803848 + 1.39230i −0.0365008 + 0.0632213i
\(486\) 1.00000i 0.0453609i
\(487\) 18.2942 + 10.5622i 0.828991 + 0.478618i 0.853507 0.521081i \(-0.174471\pi\)
−0.0245163 + 0.999699i \(0.507805\pi\)
\(488\) −1.03590 0.598076i −0.0468929 0.0270736i
\(489\) 6.53590i 0.295564i
\(490\) 0.866025 1.50000i 0.0391230 0.0677631i
\(491\) 2.63397 + 4.56218i 0.118870 + 0.205888i 0.919320 0.393511i \(-0.128740\pi\)
−0.800450 + 0.599399i \(0.795406\pi\)
\(492\) 9.86603 5.69615i 0.444795 0.256802i
\(493\) 5.58846 0.251691
\(494\) 0 0
\(495\) 1.26795 0.0569901
\(496\) 4.73205 2.73205i 0.212475 0.122673i
\(497\) −0.464102 0.803848i −0.0208178 0.0360575i
\(498\) 5.09808 8.83013i 0.228450 0.395687i
\(499\) 32.0000i 1.43252i −0.697835 0.716258i \(-0.745853\pi\)
0.697835 0.716258i \(-0.254147\pi\)
\(500\) −2.30385 1.33013i −0.103031 0.0594851i
\(501\) 2.19615 + 1.26795i 0.0981169 + 0.0566478i
\(502\) 6.53590i 0.291711i
\(503\) 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
\(505\) −2.76795 + 1.59808i −0.123172 + 0.0711135i
\(506\) 29.3205 1.30346
\(507\) 0 0
\(508\) 17.8564 0.792250
\(509\) −8.89230 + 5.13397i −0.394144 + 0.227559i −0.683954 0.729525i \(-0.739741\pi\)
0.289810 + 0.957084i \(0.406408\pi\)
\(510\) 0.303848 + 0.526279i 0.0134546 + 0.0233040i
\(511\) −3.56218 + 6.16987i −0.157581 + 0.272939i
\(512\) 1.00000i 0.0441942i
\(513\) 1.09808 + 0.633975i 0.0484812 + 0.0279907i
\(514\) −23.0885 13.3301i −1.01839 0.587967i
\(515\) 5.01924i 0.221174i
\(516\) −3.83013 + 6.63397i −0.168612 + 0.292044i
\(517\) −19.3923 33.5885i −0.852873 1.47722i
\(518\) 6.63397 3.83013i 0.291480 0.168286i
\(519\) 16.3923 0.719542
\(520\) 0 0
\(521\) −17.4449 −0.764273 −0.382137 0.924106i \(-0.624812\pi\)
−0.382137 + 0.924106i \(0.624812\pi\)
\(522\) −2.13397 + 1.23205i −0.0934015 + 0.0539254i
\(523\) −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
\(525\) 3.60770i 0.157453i
\(526\) 24.2942 + 14.0263i 1.05928 + 0.611575i
\(527\) −10.7321 6.19615i −0.467495 0.269909i
\(528\) 4.73205i 0.205936i
\(529\) −7.69615 + 13.3301i −0.334615 + 0.579571i
\(530\) 0.0621778 + 0.107695i 0.00270083 + 0.00467798i
\(531\) 6.92820 4.00000i 0.300658 0.173585i
\(532\) −0.928203 −0.0402427
\(533\) 0 0
\(534\) −2.53590 −0.109739
\(535\) 0.0455173 0.0262794i 0.00196789 0.00113616i
\(536\) 5.56218 + 9.63397i 0.240249 + 0.416124i
\(537\) 11.0263 19.0981i 0.475819 0.824143i
\(538\) 1.46410i 0.0631219i
\(539\) −26.4904 15.2942i −1.14102 0.658769i
\(540\) −0.232051 0.133975i −0.00998588 0.00576535i
\(541\) 40.3205i 1.73351i 0.498731 + 0.866757i \(0.333800\pi\)
−0.498731 + 0.866757i \(0.666200\pi\)
\(542\) −2.92820 + 5.07180i −0.125777 + 0.217852i
\(543\) 4.40192 + 7.62436i 0.188905 + 0.327192i
\(544\) −1.96410 + 1.13397i −0.0842102 + 0.0486188i
\(545\) 1.46410 0.0627152
\(546\) 0 0
\(547\) 6.19615 0.264928 0.132464 0.991188i \(-0.457711\pi\)
0.132464 + 0.991188i \(0.457711\pi\)
\(548\) 1.66987 0.964102i 0.0713334 0.0411844i
\(549\) −0.598076 1.03590i −0.0255253 0.0442111i
\(550\) −11.6603 + 20.1962i −0.497195 + 0.861167i
\(551\) 3.12436i 0.133102i
\(552\) −5.36603 3.09808i −0.228393 0.131863i
\(553\) 6.00000 + 3.46410i 0.255146 + 0.147309i
\(554\) 2.26795i 0.0963559i
\(555\) −1.40192 + 2.42820i −0.0595084 + 0.103071i
\(556\) −4.92820 8.53590i −0.209002 0.362003i
\(557\) −26.3038 + 15.1865i −1.11453 + 0.643474i −0.939999 0.341178i \(-0.889174\pi\)
−0.174531 + 0.984652i \(0.555841\pi\)
\(558\) 5.46410 0.231314
\(559\) 0 0
\(560\) 0.196152 0.00828895
\(561\) 9.29423 5.36603i 0.392403 0.226554i
\(562\) 11.1603 + 19.3301i 0.470767 + 0.815392i
\(563\) 10.5359 18.2487i 0.444035 0.769091i −0.553949 0.832550i \(-0.686880\pi\)
0.997984 + 0.0634589i \(0.0202132\pi\)
\(564\) 8.19615i 0.345120i
\(565\) −4.33013 2.50000i −0.182170 0.105176i
\(566\) −7.22243 4.16987i −0.303581 0.175273i
\(567\) 0.732051i 0.0307432i
\(568\) −0.633975 + 1.09808i −0.0266010 + 0.0460743i
\(569\) −19.3205 33.4641i −0.809958 1.40289i −0.912893 0.408200i \(-0.866157\pi\)
0.102935 0.994688i \(-0.467177\pi\)
\(570\) 0.294229 0.169873i 0.0123239 0.00711520i
\(571\) 24.0526 1.00657 0.503284 0.864121i \(-0.332125\pi\)
0.503284 + 0.864121i \(0.332125\pi\)
\(572\) 0 0
\(573\) 6.92820 0.289430
\(574\) −7.22243 + 4.16987i −0.301458 + 0.174047i
\(575\) −15.2679 26.4449i −0.636717 1.10283i
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 0.267949i 0.0111549i −0.999984 0.00557744i \(-0.998225\pi\)
0.999984 0.00557744i \(-0.00177536\pi\)
\(578\) −10.2679 5.92820i −0.427090 0.246581i
\(579\) 7.16025 + 4.13397i 0.297570 + 0.171802i
\(580\) 0.660254i 0.0274156i
\(581\) −3.73205 + 6.46410i −0.154832 + 0.268176i
\(582\) −3.00000 5.19615i −0.124354 0.215387i
\(583\) 1.90192 1.09808i 0.0787696 0.0454777i
\(584\) 9.73205 0.402715
\(585\) 0 0
\(586\) −14.5167 −0.599678
\(587\) −13.8564 + 8.00000i −0.571915 + 0.330195i −0.757914 0.652355i \(-0.773781\pi\)
0.185999 + 0.982550i \(0.440448\pi\)
\(588\) 3.23205 + 5.59808i 0.133288 + 0.230861i
\(589\) −3.46410 + 6.00000i −0.142736 + 0.247226i
\(590\) 2.14359i 0.0882503i
\(591\) 8.53590 + 4.92820i 0.351120 + 0.202719i
\(592\) −9.06218 5.23205i −0.372453 0.215036i
\(593\) 36.8564i 1.51351i −0.653698 0.756756i \(-0.726783\pi\)
0.653698 0.756756i \(-0.273217\pi\)
\(594\) −2.36603 + 4.09808i −0.0970792 + 0.168146i
\(595\) −0.222432 0.385263i −0.00911882 0.0157943i
\(596\) 2.42820 1.40192i 0.0994631 0.0574250i
\(597\) 3.80385 0.155681
\(598\) 0 0
\(599\) −9.46410 −0.386693 −0.193346 0.981131i \(-0.561934\pi\)
−0.193346 + 0.981131i \(0.561934\pi\)
\(600\) 4.26795 2.46410i 0.174238 0.100597i
\(601\) 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
\(603\) 11.1244i 0.453019i
\(604\) 2.83013 + 1.63397i 0.115156 + 0.0664855i
\(605\) −2.64359 1.52628i −0.107477 0.0620521i
\(606\) 11.9282i 0.484550i
\(607\) −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
\(609\) 1.56218 0.901924i 0.0633026 0.0365478i
\(610\) −0.320508 −0.0129770
\(611\) 0 0
\(612\) −2.26795 −0.0916764
\(613\) −9.86603 + 5.69615i −0.398485 + 0.230065i −0.685830 0.727762i \(-0.740561\pi\)
0.287345 + 0.957827i \(0.407227\pi\)
\(614\) −4.29423 7.43782i −0.173301 0.300166i
\(615\) 1.52628 2.64359i 0.0615455 0.106600i
\(616\) 3.46410i 0.139573i
\(617\) 30.5263 + 17.6244i 1.22894 + 0.709530i 0.966809 0.255502i \(-0.0822407\pi\)
0.262133 + 0.965032i \(0.415574\pi\)
\(618\) 16.2224 + 9.36603i 0.652562 + 0.376757i
\(619\) 10.5359i 0.423474i 0.977327 + 0.211737i \(0.0679119\pi\)
−0.977327 + 0.211737i \(0.932088\pi\)
\(620\) 0.732051 1.26795i 0.0293999 0.0509221i
\(621\) −3.09808 5.36603i −0.124322 0.215331i
\(622\) 13.5622 7.83013i 0.543794 0.313959i
\(623\) 1.85641 0.0743754
\(624\) 0 0
\(625\) 23.9282 0.957128
\(626\) −11.6603 + 6.73205i −0.466037 + 0.269067i
\(627\) −3.00000 5.19615i −0.119808 0.207514i
\(628\) −11.7942 + 20.4282i −0.470641 + 0.815174i
\(629\) 23.7321i 0.946259i
\(630\) 0.169873 + 0.0980762i 0.00676790 + 0.00390745i
\(631\) −41.3205 23.8564i −1.64494 0.949709i −0.979039 0.203671i \(-0.934713\pi\)
−0.665904 0.746037i \(-0.731954\pi\)
\(632\) 9.46410i 0.376462i
\(633\) 2.19615 3.80385i 0.0872892 0.151189i
\(634\) 1.66987 + 2.89230i 0.0663191 + 0.114868i
\(635\) 4.14359 2.39230i 0.164433 0.0949357i
\(636\) −0.464102 −0.0184028
\(637\) 0 0
\(638\) 11.6603 0.461634
\(639\) −1.09808 + 0.633975i −0.0434392 + 0.0250796i
\(640\) −0.133975 0.232051i −0.00529581 0.00917261i
\(641\) 12.9904 22.5000i 0.513089 0.888697i −0.486796 0.873516i \(-0.661834\pi\)
0.999885 0.0151806i \(-0.00483233\pi\)
\(642\) 0.196152i 0.00774152i
\(643\) 12.0000 + 6.92820i 0.473234 + 0.273222i 0.717592 0.696463i \(-0.245244\pi\)
−0.244359 + 0.969685i \(0.578577\pi\)
\(644\) 3.92820 + 2.26795i 0.154793 + 0.0893697i
\(645\) 2.05256i 0.0808194i
\(646\) 1.43782 2.49038i 0.0565704 0.0979827i
\(647\) 13.1244 + 22.7321i 0.515972 + 0.893689i 0.999828 + 0.0185417i \(0.00590236\pi\)
−0.483856 + 0.875147i \(0.660764\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) −37.8564 −1.48599
\(650\) 0 0
\(651\) −4.00000 −0.156772
\(652\) 5.66025 3.26795i 0.221673 0.127983i
\(653\) 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
\(655\) 3.60770i 0.140964i
\(656\) 9.86603 + 5.69615i 0.385204 + 0.222397i
\(657\) 8.42820 + 4.86603i 0.328816 + 0.189842i
\(658\) 6.00000i 0.233904i
\(659\) −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
\(661\) −8.13397 + 4.69615i −0.316375 + 0.182659i −0.649776 0.760126i \(-0.725137\pi\)
0.333401 + 0.942785i \(0.391804\pi\)
\(662\) −20.0000 −0.777322
\(663\) 0 0
\(664\) 10.1962 0.395687
\(665\) −0.215390 + 0.124356i −0.00835248 + 0.00482231i
\(666\) −5.23205 9.06218i −0.202738 0.351152i
\(667\) −7.63397 + 13.2224i −0.295589 + 0.511975i
\(668\) 2.53590i 0.0981169i
\(669\) −11.3205 6.53590i −0.437676 0.252692i
\(670\) 2.58142 + 1.49038i 0.0997288 + 0.0575784i
\(671\) 5.66025i 0.218512i
\(672\) −0.366025 + 0.633975i −0.0141197 + 0.0244561i
\(673\) 7.03590 + 12.1865i 0.271214 + 0.469756i 0.969173 0.246381i \(-0.0792416\pi\)
−0.697959 + 0.716138i \(0.745908\pi\)
\(674\) 5.93782 3.42820i 0.228716 0.132049i
\(675\) 4.92820 0.189687
\(676\) 0 0
\(677\) −38.5359 −1.48105 −0.740527 0.672026i \(-0.765424\pi\)
−0.740527 + 0.672026i \(0.765424\pi\)
\(678\) 16.1603 9.33013i 0.620631 0.358321i
\(679\) 2.19615 + 3.80385i 0.0842806 + 0.145978i
\(680\) −0.303848 + 0.526279i −0.0116520 + 0.0201819i
\(681\) 1.80385i 0.0691236i
\(682\) −22.3923 12.9282i −0.857446 0.495046i
\(683\) 32.7846 + 18.9282i 1.25447 + 0.724268i 0.971994 0.235007i \(-0.0755114\pi\)
0.282475 + 0.959275i \(0.408845\pi\)
\(684\) 1.26795i 0.0484812i
\(685\) 0.258330 0.447441i 0.00987029 0.0170958i
\(686\) −4.92820 8.53590i −0.188160 0.325902i
\(687\) 13.7321 7.92820i 0.523910 0.302480i
\(688\) −7.66025 −0.292044
\(689\) 0 0
\(690\) −1.66025 −0.0632048
\(691\) −22.8109 + 13.1699i −0.867767 + 0.501006i −0.866606 0.498994i \(-0.833703\pi\)
−0.00116153 + 0.999999i \(0.500370\pi\)
\(692\) 8.19615 + 14.1962i 0.311571 + 0.539657i
\(693\) 1.73205 3.00000i 0.0657952 0.113961i
\(694\) 8.87564i 0.336915i
\(695\) −2.28719 1.32051i −0.0867580 0.0500897i
\(696\) −2.13397 1.23205i −0.0808881 0.0467008i
\(697\) 25.8372i 0.978653i
\(698\) 9.66025 16.7321i 0.365646 0.633317i
\(699\) 9.92820 + 17.1962i 0.375519 + 0.650418i
\(700\) −3.12436 + 1.80385i −0.118090 + 0.0681790i
\(701\) −31.3205 −1.18296 −0.591480 0.806320i \(-0.701456\pi\)
−0.591480 + 0.806320i \(0.701456\pi\)
\(702\) 0 0
\(703\) 13.2679 0.500410
\(704\) −4.09808 + 2.36603i −0.154452 + 0.0891729i
\(705\) 1.09808 + 1.90192i 0.0413559 + 0.0716306i
\(706\) 9.89230 17.1340i 0.372302 0.644846i
\(707\) 8.73205i 0.328403i
\(708\) 6.92820 + 4.00000i 0.260378 + 0.150329i
\(709\) −35.3827 20.4282i −1.32882 0.767197i −0.343707 0.939077i \(-0.611683\pi\)
−0.985118 + 0.171880i \(0.945016\pi\)
\(710\) 0.339746i 0.0127504i
\(711\) 4.73205 8.19615i 0.177466 0.307380i
\(712\) −1.26795 2.19615i −0.0475184 0.0823043i
\(713\) 29.3205 16.9282i 1.09806 0.633966i
\(714\) 1.66025 0.0621334
\(715\) 0 0
\(716\) 22.0526 0.824143
\(717\) 8.36603 4.83013i 0.312435 0.180384i
\(718\) −11.5622 20.0263i −0.431497 0.747374i
\(719\) −11.2679 + 19.5167i −0.420224 + 0.727849i −0.995961 0.0897860i \(-0.971382\pi\)
0.575737 + 0.817635i \(0.304715\pi\)
\(720\) 0.267949i 0.00998588i
\(721\) −11.8756 6.85641i −0.442272 0.255346i
\(722\) 15.0622 + 8.69615i 0.560556 + 0.323637i
\(723\) 17.5885i 0.654122i
\(724\) −4.40192 + 7.62436i −0.163596 + 0.283357i
\(725\) −6.07180 10.5167i −0.225501 0.390579i
\(726\) 9.86603 5.69615i 0.366163 0.211404i
\(727\) −20.9808 −0.778133 −0.389067 0.921210i \(-0.627202\pi\)
−0.389067 + 0.921210i \(0.627202\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 2.25833 1.30385i 0.0835846 0.0482576i
\(731\) 8.68653 + 15.0455i 0.321283 + 0.556479i
\(732\) 0.598076 1.03590i 0.0221055 0.0382879i
\(733\) 19.0000i 0.701781i −0.936416 0.350891i \(-0.885879\pi\)
0.936416 0.350891i \(-0.114121\pi\)
\(734\) −12.7583 7.36603i −0.470919 0.271885i
\(735\) 1.50000 + 0.866025i 0.0553283 + 0.0319438i
\(736\) 6.19615i 0.228393i
\(737\) 26.3205 45.5885i 0.969528 1.67927i
\(738\) 5.69615 + 9.86603i 0.209678 + 0.363173i
\(739\) −9.46410 + 5.46410i −0.348143 + 0.201000i −0.663867 0.747851i \(-0.731086\pi\)
0.315724 + 0.948851i \(0.397753\pi\)
\(740\) −2.80385 −0.103071
\(741\) 0 0
\(742\) 0.339746 0.0124725
\(743\) 23.9090 13.8038i 0.877135 0.506414i 0.00742221 0.999972i \(-0.497637\pi\)
0.869713 + 0.493558i \(0.164304\pi\)
\(744\) 2.73205 + 4.73205i 0.100162 + 0.173485i
\(745\) 0.375644 0.650635i 0.0137625 0.0238374i
\(746\) 10.2679i 0.375936i
\(747\) 8.83013 + 5.09808i 0.323077 + 0.186529i
\(748\) 9.29423 + 5.36603i 0.339831 + 0.196201i
\(749\) 0.143594i 0.00524679i
\(750\) 1.33013 2.30385i 0.0485694 0.0841246i
\(751\) 7.95448 + 13.7776i 0.290263 + 0.502751i 0.973872 0.227098i \(-0.0729238\pi\)
−0.683609 + 0.729849i \(0.739590\pi\)
\(752\) −7.09808 + 4.09808i −0.258840 + 0.149441i
\(753\) −6.53590 −0.238181
\(754\) 0 0
\(755\) 0.875644 0.0318680
\(756\) −0.633975 + 0.366025i −0.0230574 + 0.0133122i
\(757\) −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
\(759\) 29.3205i 1.06427i
\(760\) 0.294229 + 0.169873i 0.0106728 + 0.00616194i
\(761\) 20.1962 + 11.6603i 0.732110 + 0.422684i 0.819194 0.573517i \(-0.194421\pi\)
−0.0870836 + 0.996201i \(0.527755\pi\)
\(762\) 17.8564i 0.646869i
\(763\) 2.00000 3.46410i 0.0724049 0.125409i
\(764\) 3.46410 + 6.00000i 0.125327 + 0.217072i
\(765\) −0.526279 + 0.303848i −0.0190277 + 0.0109856i
\(766\) −5.46410 −0.197426
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 13.9808 8.07180i 0.504159 0.291076i −0.226270 0.974065i \(-0.572653\pi\)
0.730429 + 0.682988i \(0.239320\pi\)
\(770\) −0.464102 0.803848i −0.0167251 0.0289687i
\(771\) 13.3301 23.0885i 0.480073 0.831510i
\(772\) 8.26795i 0.297570i
\(773\) −30.3731 17.5359i −1.09244 0.630722i −0.158217 0.987404i \(-0.550575\pi\)
−0.934226 + 0.356682i \(0.883908\pi\)
\(774\) −6.63397 3.83013i −0.238453 0.137671i
\(775\) 26.9282i 0.967290i
\(776\) 3.00000 5.19615i 0.107694 0.186531i
\(777\) 3.83013 + 6.63397i 0.137405 + 0.237993i
\(778\) −25.7942 + 14.8923i