Properties

Label 1950.2.bc.d.901.1
Level $1950$
Weight $2$
Character 1950.901
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
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 901.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.901
Dual form 1950.2.bc.d.751.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.633975 + 0.366025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-0.633975 + 0.366025i) q^{7} -1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.09808 - 2.36603i) q^{11} +1.00000 q^{12} +(-2.59808 + 2.50000i) q^{13} +0.732051 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.13397 + 1.96410i) q^{17} +1.00000i q^{18} +(-1.09808 + 0.633975i) q^{19} +0.732051i q^{21} +(2.36603 + 4.09808i) q^{22} +(3.09808 - 5.36603i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(3.50000 - 0.866025i) q^{26} -1.00000 q^{27} +(-0.633975 - 0.366025i) q^{28} +(-1.23205 + 2.13397i) q^{29} +5.46410i q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.09808 + 2.36603i) q^{33} -2.26795i q^{34} +(0.500000 - 0.866025i) q^{36} +(9.06218 + 5.23205i) q^{37} +1.26795 q^{38} +(0.866025 + 3.50000i) q^{39} +(9.86603 + 5.69615i) q^{41} +(0.366025 - 0.633975i) q^{42} +(-3.83013 - 6.63397i) q^{43} -4.73205i q^{44} +(-5.36603 + 3.09808i) q^{46} +8.19615i q^{47} +(0.500000 + 0.866025i) q^{48} +(-3.23205 + 5.59808i) q^{49} +2.26795 q^{51} +(-3.46410 - 1.00000i) q^{52} -0.464102 q^{53} +(0.866025 + 0.500000i) q^{54} +(0.366025 + 0.633975i) q^{56} +1.26795i q^{57} +(2.13397 - 1.23205i) q^{58} +(6.92820 - 4.00000i) q^{59} +(-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} +(-1.09808 + 0.633975i) q^{71} +(-0.866025 + 0.500000i) q^{72} +9.73205i q^{73} +(-5.23205 - 9.06218i) q^{74} +(-1.09808 - 0.633975i) q^{76} +3.46410 q^{77} +(1.00000 - 3.46410i) q^{78} -9.46410 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.69615 - 9.86603i) q^{82} +10.1962i q^{83} +(-0.633975 + 0.366025i) q^{84} +7.66025i q^{86} +(1.23205 + 2.13397i) q^{87} +(-2.36603 + 4.09808i) q^{88} +(2.19615 + 1.26795i) q^{89} +(0.732051 - 2.53590i) q^{91} +6.19615 q^{92} +(4.73205 + 2.73205i) q^{93} +(4.09808 - 7.09808i) q^{94} -1.00000i q^{96} +(-5.19615 + 3.00000i) q^{97} +(5.59808 - 3.23205i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{3} + 2q^{4} - 6q^{7} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{3} + 2q^{4} - 6q^{7} - 2q^{9} - 6q^{11} + 4q^{12} - 4q^{14} - 2q^{16} + 8q^{17} + 6q^{19} + 6q^{22} + 2q^{23} + 14q^{26} - 4q^{27} - 6q^{28} + 2q^{29} - 6q^{33} + 2q^{36} + 12q^{37} + 12q^{38} + 36q^{41} - 2q^{42} + 2q^{43} - 18q^{46} + 2q^{48} - 6q^{49} + 16q^{51} + 12q^{53} - 2q^{56} + 12q^{58} + 8q^{61} + 4q^{62} + 6q^{63} - 4q^{64} + 12q^{66} + 42q^{67} - 8q^{68} - 2q^{69} + 6q^{71} - 14q^{74} + 6q^{76} + 4q^{78} - 24q^{79} - 2q^{81} - 2q^{82} - 6q^{84} - 2q^{87} - 6q^{88} - 12q^{89} - 4q^{91} + 4q^{92} + 12q^{93} + 6q^{94} + 12q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 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 0
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) −0.633975 + 0.366025i −0.239620 + 0.138345i −0.615002 0.788526i \(-0.710845\pi\)
0.375382 + 0.926870i \(0.377511\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −4.09808 2.36603i −1.23562 0.713384i −0.267421 0.963580i \(-0.586172\pi\)
−0.968195 + 0.250196i \(0.919505\pi\)
\(12\) 1.00000 0.288675
\(13\) −2.59808 + 2.50000i −0.720577 + 0.693375i
\(14\) 0.732051 0.195649
\(15\) 0 0
\(16\) −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 \(0.744646\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −1.09808 + 0.633975i −0.251916 + 0.145444i −0.620641 0.784095i \(-0.713128\pi\)
0.368725 + 0.929538i \(0.379794\pi\)
\(20\) 0 0
\(21\) 0.732051i 0.159747i
\(22\) 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 \(-0.0568901\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 0 0
\(26\) 3.50000 0.866025i 0.686406 0.169842i
\(27\) −1.00000 −0.192450
\(28\) −0.633975 0.366025i −0.119810 0.0691723i
\(29\) −1.23205 + 2.13397i −0.228786 + 0.396269i −0.957449 0.288604i \(-0.906809\pi\)
0.728663 + 0.684873i \(0.240142\pi\)
\(30\) 0 0
\(31\) 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 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 9.06218 + 5.23205i 1.48981 + 0.860144i 0.999932 0.0116456i \(-0.00370701\pi\)
0.489881 + 0.871789i \(0.337040\pi\)
\(38\) 1.26795 0.205689
\(39\) 0.866025 + 3.50000i 0.138675 + 0.560449i
\(40\) 0 0
\(41\) 9.86603 + 5.69615i 1.54081 + 0.889590i 0.998788 + 0.0492283i \(0.0156762\pi\)
0.542027 + 0.840361i \(0.317657\pi\)
\(42\) 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 \(-0.365215\pi\)
\(44\) 4.73205i 0.713384i
\(45\) 0 0
\(46\) −5.36603 + 3.09808i −0.791177 + 0.456786i
\(47\) 8.19615i 1.19553i 0.801671 + 0.597766i \(0.203945\pi\)
−0.801671 + 0.597766i \(0.796055\pi\)
\(48\) 0.500000 + 0.866025i 0.0721688 + 0.125000i
\(49\) −3.23205 + 5.59808i −0.461722 + 0.799725i
\(50\) 0 0
\(51\) 2.26795 0.317576
\(52\) −3.46410 1.00000i −0.480384 0.138675i
\(53\) −0.464102 −0.0637493 −0.0318746 0.999492i \(-0.510148\pi\)
−0.0318746 + 0.999492i \(0.510148\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 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 \(-0.492317\pi\)
0.877841 + 0.478953i \(0.158984\pi\)
\(60\) 0 0
\(61\) −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
\(63\) 0.633975 + 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 0.955313 0.295595i \(-0.0955179\pi\)
0.221664 + 0.975123i \(0.428851\pi\)
\(68\) −1.13397 + 1.96410i −0.137515 + 0.238182i
\(69\) −3.09808 5.36603i −0.372965 0.645994i
\(70\) 0 0
\(71\) −1.09808 + 0.633975i −0.130318 + 0.0752389i −0.563742 0.825951i \(-0.690639\pi\)
0.433424 + 0.901190i \(0.357305\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 9.73205i 1.13905i 0.821974 + 0.569525i \(0.192873\pi\)
−0.821974 + 0.569525i \(0.807127\pi\)
\(74\) −5.23205 9.06218i −0.608214 1.05346i
\(75\) 0 0
\(76\) −1.09808 0.633975i −0.125958 0.0727219i
\(77\) 3.46410 0.394771
\(78\) 1.00000 3.46410i 0.113228 0.392232i
\(79\) −9.46410 −1.06479 −0.532397 0.846495i \(-0.678709\pi\)
−0.532397 + 0.846495i \(0.678709\pi\)
\(80\) 0 0
\(81\) −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 \(0.189040\pi\)
−0.828772 + 0.559587i \(0.810960\pi\)
\(84\) −0.633975 + 0.366025i −0.0691723 + 0.0399366i
\(85\) 0 0
\(86\) 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 \(-0.290422\pi\)
−0.379068 + 0.925369i \(0.623755\pi\)
\(90\) 0 0
\(91\) 0.732051 2.53590i 0.0767398 0.265834i
\(92\) 6.19615 0.645994
\(93\) 4.73205 + 2.73205i 0.490691 + 0.283300i
\(94\) 4.09808 7.09808i 0.422684 0.732111i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −5.19615 + 3.00000i −0.527589 + 0.304604i −0.740034 0.672569i \(-0.765191\pi\)
0.212445 + 0.977173i \(0.431857\pi\)
\(98\) 5.59808 3.23205i 0.565491 0.326486i
\(99\) 4.73205i 0.475589i
\(100\) 0 0
\(101\) −5.96410 + 10.3301i −0.593450 + 1.02789i 0.400313 + 0.916378i \(0.368901\pi\)
−0.993764 + 0.111508i \(0.964432\pi\)
\(102\) −1.96410 1.13397i −0.194475 0.112280i
\(103\) −18.7321 −1.84572 −0.922862 0.385131i \(-0.874156\pi\)
−0.922862 + 0.385131i \(0.874156\pi\)
\(104\) 2.50000 + 2.59808i 0.245145 + 0.254762i
\(105\) 0 0
\(106\) 0.401924 + 0.232051i 0.0390383 + 0.0225388i
\(107\) −0.0980762 + 0.169873i −0.00948139 + 0.0164222i −0.870727 0.491766i \(-0.836351\pi\)
0.861246 + 0.508189i \(0.169685\pi\)
\(108\) −0.500000 0.866025i −0.0481125 0.0833333i
\(109\) 5.46410i 0.523366i 0.965154 + 0.261683i \(0.0842775\pi\)
−0.965154 + 0.261683i \(0.915723\pi\)
\(110\) 0 0
\(111\) 9.06218 5.23205i 0.860144 0.496604i
\(112\) 0.732051i 0.0691723i
\(113\) −9.33013 16.1603i −0.877705 1.52023i −0.853854 0.520513i \(-0.825741\pi\)
−0.0238510 0.999716i \(-0.507593\pi\)
\(114\) 0.633975 1.09808i 0.0593772 0.102844i
\(115\) 0 0
\(116\) −2.46410 −0.228786
\(117\) 3.46410 + 1.00000i 0.320256 + 0.0924500i
\(118\) −8.00000 −0.736460
\(119\) −1.43782 0.830127i −0.131805 0.0760976i
\(120\) 0 0
\(121\) 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
\(125\) 0 0
\(126\) −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 \(0.875576\pi\)
\(128\) 0.866025 + 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 0
\(136\) 1.96410 1.13397i 0.168420 0.0972375i
\(137\) 1.66987 0.964102i 0.142667 0.0823688i −0.426968 0.904267i \(-0.640418\pi\)
0.569634 + 0.821898i \(0.307085\pi\)
\(138\) 6.19615i 0.527452i
\(139\) 4.92820 + 8.53590i 0.418005 + 0.724005i 0.995739 0.0922197i \(-0.0293962\pi\)
−0.577734 + 0.816225i \(0.696063\pi\)
\(140\) 0 0
\(141\) 7.09808 + 4.09808i 0.597766 + 0.345120i
\(142\) 1.26795 0.106404
\(143\) 16.5622 4.09808i 1.38500 0.342698i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 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 \(-0.703305\pi\)
0.397228 + 0.917720i \(0.369972\pi\)
\(150\) 0 0
\(151\) 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
\(155\) 0 0
\(156\) −2.59808 + 2.50000i −0.208013 + 0.200160i
\(157\) 23.5885 1.88256 0.941282 0.337622i \(-0.109622\pi\)
0.941282 + 0.337622i \(0.109622\pi\)
\(158\) 8.19615 + 4.73205i 0.652051 + 0.376462i
\(159\) −0.232051 + 0.401924i −0.0184028 + 0.0318746i
\(160\) 0 0
\(161\) 4.53590i 0.357479i
\(162\) 0.866025 0.500000i 0.0680414 0.0392837i
\(163\) 5.66025 3.26795i 0.443345 0.255966i −0.261670 0.965157i \(-0.584273\pi\)
0.705016 + 0.709192i \(0.250940\pi\)
\(164\) 11.3923i 0.889590i
\(165\) 0 0
\(166\) 5.09808 8.83013i 0.395687 0.685351i
\(167\) −2.19615 1.26795i −0.169943 0.0981169i 0.412616 0.910905i \(-0.364615\pi\)
−0.582559 + 0.812788i \(0.697949\pi\)
\(168\) 0.732051 0.0564789
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) 0 0
\(171\) 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 0.988897 + 0.148602i \(0.0474774\pi\)
−0.365755 + 0.930711i \(0.619189\pi\)
\(174\) 2.46410i 0.186803i
\(175\) 0 0
\(176\) 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 −0.0784298 0.996920i \(-0.524991\pi\)
0.902573 0.430538i \(-0.141676\pi\)
\(180\) 0 0
\(181\) −8.80385 −0.654385 −0.327192 0.944958i \(-0.606103\pi\)
−0.327192 + 0.944958i \(0.606103\pi\)
\(182\) −1.90192 + 1.83013i −0.140980 + 0.135658i
\(183\) −1.19615 −0.0884221
\(184\) −5.36603 3.09808i −0.395589 0.228393i
\(185\) 0 0
\(186\) −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 0
\(191\) −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
\(193\) −7.16025 4.13397i −0.515406 0.297570i 0.219647 0.975579i \(-0.429510\pi\)
−0.735053 + 0.678009i \(0.762843\pi\)
\(194\) 6.00000 0.430775
\(195\) 0 0
\(196\) −6.46410 −0.461722
\(197\) −8.53590 4.92820i −0.608158 0.351120i 0.164086 0.986446i \(-0.447532\pi\)
−0.772244 + 0.635326i \(0.780866\pi\)
\(198\) 2.36603 4.09808i 0.168146 0.291238i
\(199\) −1.90192 3.29423i −0.134824 0.233522i 0.790706 0.612196i \(-0.209714\pi\)
−0.925530 + 0.378674i \(0.876380\pi\)
\(200\) 0 0
\(201\) 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
\(205\) 0 0
\(206\) 16.2224 + 9.36603i 1.13027 + 0.652562i
\(207\) −6.19615 −0.430662
\(208\) −0.866025 3.50000i −0.0600481 0.242681i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) 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
\(213\) 1.26795i 0.0868784i
\(214\) 0.169873 0.0980762i 0.0116123 0.00670435i
\(215\) 0 0
\(216\) 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
\(220\) 0 0
\(221\) −7.85641 2.26795i −0.528479 0.152559i
\(222\) −10.4641 −0.702305
\(223\) 11.3205 + 6.53590i 0.758077 + 0.437676i 0.828605 0.559834i \(-0.189135\pi\)
−0.0705277 + 0.997510i \(0.522468\pi\)
\(224\) −0.366025 + 0.633975i −0.0244561 + 0.0423592i
\(225\) 0 0
\(226\) 18.6603i 1.24126i
\(227\) −1.56218 + 0.901924i −0.103685 + 0.0598628i −0.550946 0.834541i \(-0.685733\pi\)
0.447261 + 0.894404i \(0.352400\pi\)
\(228\) −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 0
\(231\) 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 \(-0.274594\pi\)
0.650418 + 0.759576i \(0.274594\pi\)
\(234\) −2.50000 2.59808i −0.163430 0.169842i
\(235\) 0 0
\(236\) 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 0
\(241\) −15.2321 + 8.79423i −0.981183 + 0.566486i −0.902627 0.430424i \(-0.858364\pi\)
−0.0785557 + 0.996910i \(0.525031\pi\)
\(242\) 11.3923i 0.732325i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0.598076 1.03590i 0.0382879 0.0663166i
\(245\) 0 0
\(246\) −11.3923 −0.726347
\(247\) 1.26795 4.39230i 0.0806777 0.279476i
\(248\) 5.46410 0.346971
\(249\) 8.83013 + 5.09808i 0.559587 + 0.323077i
\(250\) 0 0
\(251\) 3.26795 + 5.66025i 0.206271 + 0.357272i 0.950537 0.310611i \(-0.100534\pi\)
−0.744266 + 0.667883i \(0.767200\pi\)
\(252\) 0.732051i 0.0461149i
\(253\) −25.3923 + 14.6603i −1.59640 + 0.921682i
\(254\) 15.4641 8.92820i 0.970304 0.560205i
\(255\) 0 0
\(256\) −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 \(0.854143\pi\)
\(258\) 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 −0.00225153 0.999997i \(-0.500717\pi\)
0.867149 0.498049i \(-0.165950\pi\)
\(264\) 2.36603 + 4.09808i 0.145619 + 0.252219i
\(265\) 0 0
\(266\) −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 0.887479 0.460848i \(-0.152455\pi\)
−0.842845 + 0.538156i \(0.819121\pi\)
\(270\) 0 0
\(271\) −5.07180 2.92820i −0.308090 0.177876i 0.337982 0.941153i \(-0.390256\pi\)
−0.646071 + 0.763277i \(0.723589\pi\)
\(272\) −2.26795 −0.137515
\(273\) −1.83013 1.90192i −0.110764 0.115110i
\(274\) −1.92820 −0.116487
\(275\) 0 0
\(276\) 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 \(0.811629\pi\)
\(278\) 9.85641i 0.591148i
\(279\) 4.73205 2.73205i 0.283300 0.163564i
\(280\) 0 0
\(281\) 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 \(-0.913065\pi\)
0.715062 + 0.699061i \(0.246398\pi\)
\(284\) −1.09808 0.633975i −0.0651588 0.0376195i
\(285\) 0 0
\(286\) −16.3923 4.73205i −0.969297 0.279812i
\(287\) −8.33975 −0.492280
\(288\) −0.866025 0.500000i −0.0510310 0.0294628i
\(289\) 5.92820 10.2679i 0.348718 0.603997i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) −8.42820 + 4.86603i −0.493223 + 0.284763i
\(293\) 12.5718 7.25833i 0.734452 0.424036i −0.0855965 0.996330i \(-0.527280\pi\)
0.820049 + 0.572294i \(0.193946\pi\)
\(294\) 6.46410i 0.376994i
\(295\) 0 0
\(296\) 5.23205 9.06218i 0.304107 0.526728i
\(297\) 4.09808 + 2.36603i 0.237795 + 0.137291i
\(298\) 2.80385 0.162423
\(299\) 5.36603 + 21.6865i 0.310325 + 1.25416i
\(300\) 0 0
\(301\) 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 0
\(306\) −1.96410 + 1.13397i −0.112280 + 0.0648250i
\(307\) 8.58846i 0.490169i −0.969502 0.245085i \(-0.921184\pi\)
0.969502 0.245085i \(-0.0788157\pi\)
\(308\) 1.73205 + 3.00000i 0.0986928 + 0.170941i
\(309\) −9.36603 + 16.2224i −0.532815 + 0.922862i
\(310\) 0 0
\(311\) −15.6603 −0.888012 −0.444006 0.896024i \(-0.646443\pi\)
−0.444006 + 0.896024i \(0.646443\pi\)
\(312\) 3.50000 0.866025i 0.198148 0.0490290i
\(313\) −13.4641 −0.761036 −0.380518 0.924774i \(-0.624254\pi\)
−0.380518 + 0.924774i \(0.624254\pi\)
\(314\) −20.4282 11.7942i −1.15283 0.665587i
\(315\) 0 0
\(316\) −4.73205 8.19615i −0.266199 0.461070i
\(317\) 3.33975i 0.187579i 0.995592 + 0.0937894i \(0.0298980\pi\)
−0.995592 + 0.0937894i \(0.970102\pi\)
\(318\) 0.401924 0.232051i 0.0225388 0.0130128i
\(319\) 10.0981 5.83013i 0.565384 0.326424i
\(320\) 0 0
\(321\) 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
\(330\) 0 0
\(331\) −17.3205 + 10.0000i −0.952021 + 0.549650i −0.893708 0.448649i \(-0.851905\pi\)
−0.0583130 + 0.998298i \(0.518572\pi\)
\(332\) −8.83013 + 5.09808i −0.484616 + 0.279793i
\(333\) 10.4641i 0.573429i
\(334\) 1.26795 + 2.19615i 0.0693791 + 0.120168i
\(335\) 0 0
\(336\) −0.633975 0.366025i −0.0345861 0.0199683i
\(337\) 6.85641 0.373492 0.186746 0.982408i \(-0.440206\pi\)
0.186746 + 0.982408i \(0.440206\pi\)
\(338\) −6.92820 + 11.0000i −0.376845 + 0.598321i
\(339\) −18.6603 −1.01349
\(340\) 0 0
\(341\) 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
\(345\) 0 0
\(346\) 16.3923i 0.881256i
\(347\) 4.43782 + 7.68653i 0.238235 + 0.412635i 0.960208 0.279286i \(-0.0900979\pi\)
−0.721973 + 0.691921i \(0.756765\pi\)
\(348\) −1.23205 + 2.13397i −0.0660449 + 0.114393i
\(349\) 16.7321 + 9.66025i 0.895646 + 0.517102i 0.875785 0.482701i \(-0.160344\pi\)
0.0198610 + 0.999803i \(0.493678\pi\)
\(350\) 0 0
\(351\) 2.59808 2.50000i 0.138675 0.133440i
\(352\) −4.73205 −0.252219
\(353\) −17.1340 9.89230i −0.911949 0.526514i −0.0308916 0.999523i \(-0.509835\pi\)
−0.881058 + 0.473008i \(0.843168\pi\)
\(354\) −4.00000 + 6.92820i −0.212598 + 0.368230i
\(355\) 0 0
\(356\) 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 0
\(361\) −8.69615 + 15.0622i −0.457692 + 0.792746i
\(362\) 7.62436 + 4.40192i 0.400727 + 0.231360i
\(363\) 11.3923 0.597941
\(364\) 2.56218 0.633975i 0.134295 0.0332293i
\(365\) 0 0
\(366\) 1.03590 + 0.598076i 0.0541473 + 0.0312619i
\(367\) −7.36603 + 12.7583i −0.384503 + 0.665979i −0.991700 0.128572i \(-0.958961\pi\)
0.607197 + 0.794551i \(0.292294\pi\)
\(368\) 3.09808 + 5.36603i 0.161498 + 0.279723i
\(369\) 11.3923i 0.593060i
\(370\) 0 0
\(371\) 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 \(-0.252312\pi\)
−0.967780 + 0.251797i \(0.918978\pi\)
\(374\) −5.36603 + 9.29423i −0.277471 + 0.480593i
\(375\) 0 0
\(376\) 8.19615 0.422684
\(377\) −2.13397 8.62436i −0.109905 0.444177i
\(378\) −0.732051 −0.0376526
\(379\) 1.26795 + 0.732051i 0.0651302 + 0.0376029i 0.532211 0.846611i \(-0.321361\pi\)
−0.467081 + 0.884214i \(0.654694\pi\)
\(380\) 0 0
\(381\) 8.92820 + 15.4641i 0.457406 + 0.792250i
\(382\) 6.92820i 0.354478i
\(383\) 4.73205 2.73205i 0.241797 0.139601i −0.374206 0.927346i \(-0.622085\pi\)
0.616002 + 0.787744i \(0.288751\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 0 0
\(386\) 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
\(395\) 0 0
\(396\) −4.09808 + 2.36603i −0.205936 + 0.118897i
\(397\) 0.339746 0.196152i 0.0170514 0.00984461i −0.491450 0.870906i \(-0.663533\pi\)
0.508501 + 0.861061i \(0.330200\pi\)
\(398\) 3.80385i 0.190670i
\(399\) −0.464102 0.803848i −0.0232341 0.0402427i
\(400\) 0 0
\(401\) −18.9904 10.9641i −0.948334 0.547521i −0.0557713 0.998444i \(-0.517762\pi\)
−0.892563 + 0.450922i \(0.851095\pi\)
\(402\) −11.1244 −0.554832
\(403\) −13.6603 14.1962i −0.680466 0.707161i
\(404\) −11.9282 −0.593450
\(405\) 0 0
\(406\) −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 \(-0.781421\pi\)
0.162366 + 0.986731i \(0.448088\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) 9.85641 0.482670
\(418\) −5.19615 3.00000i −0.254152 0.146735i
\(419\) 5.26795 9.12436i 0.257356 0.445754i −0.708177 0.706035i \(-0.750482\pi\)
0.965533 + 0.260281i \(0.0838153\pi\)
\(420\) 0 0
\(421\) 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
\(425\) 0 0
\(426\) 0.633975 1.09808i 0.0307162 0.0532020i
\(427\) 0.758330 + 0.437822i 0.0366982 + 0.0211877i
\(428\) −0.196152 −0.00948139
\(429\) 4.73205 16.3923i 0.228466 0.791428i
\(430\) 0 0
\(431\) −9.63397 5.56218i −0.464052 0.267921i 0.249694 0.968325i \(-0.419670\pi\)
−0.713747 + 0.700404i \(0.753003\pi\)
\(432\) 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 \(0.717141\pi\)
\(434\) 4.00000i 0.192006i
\(435\) 0 0
\(436\) −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 −0.996080 0.0884515i \(-0.971808\pi\)
0.574642 + 0.818405i \(0.305141\pi\)
\(440\) 0 0
\(441\) 6.46410 0.307814
\(442\) 5.66987 + 5.89230i 0.269688 + 0.280268i
\(443\) −36.3923 −1.72905 −0.864525 0.502589i \(-0.832381\pi\)
−0.864525 + 0.502589i \(0.832381\pi\)
\(444\) 9.06218 + 5.23205i 0.430072 + 0.248302i
\(445\) 0 0
\(446\) −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 \(-0.852146\pi\)
−0.0590680 + 0.998254i \(0.518813\pi\)
\(450\) 0 0
\(451\) −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 0.0718931 0.997412i \(-0.477096\pi\)
−0.827838 + 0.560967i \(0.810429\pi\)
\(458\) 7.92820 13.7321i 0.370461 0.641657i
\(459\) −1.13397 1.96410i −0.0529294 0.0916764i
\(460\) 0 0
\(461\) −22.2846 + 12.8660i −1.03790 + 0.599231i −0.919237 0.393704i \(-0.871193\pi\)
−0.118661 + 0.992935i \(0.537860\pi\)
\(462\) −3.00000 + 1.73205i −0.139573 + 0.0805823i
\(463\) 28.0526i 1.30371i 0.758342 + 0.651856i \(0.226010\pi\)
−0.758342 + 0.651856i \(0.773990\pi\)
\(464\) −1.23205 2.13397i −0.0571965 0.0990673i
\(465\) 0 0
\(466\) −17.1962 9.92820i −0.796596 0.459915i
\(467\) −12.5885 −0.582524 −0.291262 0.956643i \(-0.594075\pi\)
−0.291262 + 0.956643i \(0.594075\pi\)
\(468\) 0.866025 + 3.50000i 0.0400320 + 0.161788i
\(469\) −8.14359 −0.376036
\(470\) 0 0
\(471\) 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
\(475\) 0 0
\(476\) 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 \(-0.540651\pi\)
−0.922654 + 0.385628i \(0.873985\pi\)
\(480\) 0 0
\(481\) −36.6244 + 9.06218i −1.66993 + 0.413200i
\(482\) 17.5885 0.801132
\(483\) 3.92820 + 2.26795i 0.178739 + 0.103195i
\(484\) −5.69615 + 9.86603i −0.258916 + 0.448456i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 18.2942 10.5622i 0.828991 0.478618i −0.0245163 0.999699i \(-0.507805\pi\)
0.853507 + 0.521081i \(0.174471\pi\)
\(488\) −1.03590 + 0.598076i −0.0468929 + 0.0270736i
\(489\) 6.53590i 0.295564i
\(490\) 0 0
\(491\) 2.63397 4.56218i 0.118870 0.205888i −0.800450 0.599399i \(-0.795406\pi\)
0.919320 + 0.393511i \(0.128740\pi\)
\(492\) 9.86603 + 5.69615i 0.444795 + 0.256802i
\(493\) −5.58846 −0.251691
\(494\) −3.29423 + 3.16987i −0.148214 + 0.142619i
\(495\) 0 0
\(496\) −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 \(-0.254147\pi\)
\(500\) 0 0
\(501\) −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 \(-0.245390\pi\)
−0.962076 + 0.272780i \(0.912057\pi\)
\(504\) 0.366025 0.633975i 0.0163041 0.0282395i
\(505\) 0 0
\(506\) 29.3205 1.30346
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) −17.8564 −0.792250
\(509\) 8.89230 + 5.13397i 0.394144 + 0.227559i 0.683954 0.729525i \(-0.260259\pi\)
−0.289810 + 0.957084i \(0.593592\pi\)
\(510\) 0 0
\(511\) −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
\(515\) 0 0
\(516\) −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 −0.124871 0.992173i \(-0.539852\pi\)
0.921683 0.387945i \(-0.126815\pi\)
\(524\) 6.73205 + 11.6603i 0.294091 + 0.509381i
\(525\) 0 0
\(526\) −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 0
\(531\) −6.92820 4.00000i −0.300658 0.173585i
\(532\) 0.928203 0.0402427
\(533\) −39.8731 + 9.86603i −1.72709 + 0.427345i
\(534\) −2.53590 −0.109739
\(535\) 0 0
\(536\) 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 0
\(541\) 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
\(545\) 0 0
\(546\) 0.633975 + 2.56218i 0.0271316 + 0.109651i
\(547\) −6.19615 −0.264928 −0.132464 0.991188i \(-0.542289\pi\)
−0.132464 + 0.991188i \(0.542289\pi\)
\(548\) 1.66987 + 0.964102i 0.0713334 + 0.0411844i
\(549\) −0.598076 + 1.03590i −0.0255253 + 0.0442111i
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) −4.92820 + 8.53590i −0.209002 + 0.362003i
\(557\) −26.3038 15.1865i −1.11453 0.643474i −0.174531 0.984652i \(-0.555841\pi\)
−0.939999 + 0.341178i \(0.889174\pi\)
\(558\) −5.46410 −0.231314
\(559\) 26.5359 + 7.66025i 1.12235 + 0.323994i
\(560\) 0 0
\(561\) −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 \(-0.313120\pi\)
−0.997984 + 0.0634589i \(0.979787\pi\)
\(564\) 8.19615i 0.345120i
\(565\) 0 0
\(566\) 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 0.102935 + 0.994688i \(0.467177\pi\)
−0.912893 + 0.408200i \(0.866157\pi\)
\(570\) 0 0
\(571\) 24.0526 1.00657 0.503284 0.864121i \(-0.332125\pi\)
0.503284 + 0.864121i \(0.332125\pi\)
\(572\) 11.8301 + 12.2942i 0.494642 + 0.514048i
\(573\) −6.92820 −0.289430
\(574\) 7.22243 + 4.16987i 0.301458 + 0.174047i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) 0.267949i 0.0111549i 0.999984 + 0.00557744i \(0.00177536\pi\)
−0.999984 + 0.00557744i \(0.998225\pi\)
\(578\) −10.2679 + 5.92820i −0.427090 + 0.246581i
\(579\) −7.16025 + 4.13397i −0.297570 + 0.171802i
\(580\) 0 0
\(581\) −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 0.185999 0.982550i \(-0.440448\pi\)
−0.757914 + 0.652355i \(0.773781\pi\)
\(588\) −3.23205 + 5.59808i −0.133288 + 0.230861i
\(589\) −3.46410 6.00000i −0.142736 0.247226i
\(590\) 0 0
\(591\) −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 \(0.273217\pi\)
−0.653698 + 0.756756i \(0.726783\pi\)
\(594\) −2.36603 4.09808i −0.0970792 0.168146i
\(595\) 0 0
\(596\) −2.42820 1.40192i −0.0994631 0.0574250i
\(597\) −3.80385 −0.155681
\(598\) 6.19615 21.4641i 0.253380 0.877732i
\(599\) −9.46410 −0.386693 −0.193346 0.981131i \(-0.561934\pi\)
−0.193346 + 0.981131i \(0.561934\pi\)
\(600\) 0 0
\(601\) 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
\(603\) 11.1244i 0.453019i
\(604\) −2.83013 + 1.63397i −0.115156 + 0.0664855i
\(605\) 0 0
\(606\) 11.9282i 0.484550i
\(607\) 0.392305 + 0.679492i 0.0159232 + 0.0275797i 0.873877 0.486147i \(-0.161598\pi\)
−0.857954 + 0.513726i \(0.828265\pi\)
\(608\) −0.633975 + 1.09808i −0.0257111 + 0.0445329i
\(609\) −1.56218 0.901924i −0.0633026 0.0365478i
\(610\) 0 0
\(611\) −20.4904 21.2942i −0.828952 0.861472i
\(612\) 2.26795 0.0916764
\(613\) −9.86603 5.69615i −0.398485 0.230065i 0.287345 0.957827i \(-0.407227\pi\)
−0.685830 + 0.727762i \(0.740561\pi\)
\(614\) −4.29423 + 7.43782i −0.173301 + 0.300166i
\(615\) 0 0
\(616\) 3.46410i 0.139573i
\(617\) 30.5263 17.6244i 1.22894 0.709530i 0.262133 0.965032i \(-0.415574\pi\)
0.966809 + 0.255502i \(0.0822407\pi\)
\(618\) 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 0
\(621\) −3.09808 + 5.36603i −0.124322 + 0.215331i
\(622\) 13.5622 + 7.83013i 0.543794 + 0.313959i
\(623\) −1.85641 −0.0743754
\(624\) −3.46410 1.00000i −0.138675 0.0400320i
\(625\) 0 0
\(626\) 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 0
\(631\) 41.3205 23.8564i 1.64494 0.949709i 0.665904 0.746037i \(-0.268046\pi\)
0.979039 0.203671i \(-0.0652874\pi\)
\(632\) 9.46410i 0.376462i
\(633\) −2.19615 3.80385i −0.0872892 0.151189i
\(634\) 1.66987 2.89230i 0.0663191 0.114868i
\(635\) 0 0
\(636\) −0.464102 −0.0184028
\(637\) −5.59808 22.6244i −0.221804 0.896410i
\(638\) −11.6603 −0.461634
\(639\) 1.09808 + 0.633975i 0.0434392 + 0.0250796i
\(640\) 0 0
\(641\) 12.9904 + 22.5000i 0.513089 + 0.888697i 0.999885 + 0.0151806i \(0.00483233\pi\)
−0.486796 + 0.873516i \(0.661834\pi\)
\(642\) 0.196152i 0.00774152i
\(643\) 12.0000 6.92820i 0.473234 0.273222i −0.244359 0.969685i \(-0.578577\pi\)
0.717592 + 0.696463i \(0.245244\pi\)
\(644\) −3.92820 + 2.26795i −0.154793 + 0.0893697i
\(645\) 0 0
\(646\) 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 \(0.994098\pi\)
\(648\) 0.866025 + 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 \(-0.899427\pi\)
0.744348 + 0.667792i \(0.232760\pi\)
\(654\) −2.73205 4.73205i −0.106832 0.185038i
\(655\) 0 0
\(656\) −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 −0.950205 0.311627i \(-0.899126\pi\)
0.205225 0.978715i \(-0.434207\pi\)
\(660\) 0 0
\(661\) 8.13397 + 4.69615i 0.316375 + 0.182659i 0.649776 0.760126i \(-0.274863\pi\)
−0.333401 + 0.942785i \(0.608196\pi\)
\(662\) 20.0000 0.777322
\(663\) −5.89230 + 5.66987i −0.228838 + 0.220200i
\(664\) 10.1962 0.395687
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) 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 \(-0.920758\pi\)
0.697959 + 0.716138i \(0.254092\pi\)
\(674\) −5.93782 3.42820i −0.228716 0.132049i
\(675\) 0 0
\(676\) 11.5000 6.06218i 0.442308 0.233161i
\(677\) 38.5359 1.48105 0.740527 0.672026i \(-0.234576\pi\)
0.740527 + 0.672026i \(0.234576\pi\)
\(678\) 16.1603 + 9.33013i 0.620631 + 0.358321i
\(679\) 2.19615 3.80385i 0.0842806 0.145978i
\(680\) 0 0
\(681\) 1.80385i 0.0691236i
\(682\) −22.3923 + 12.9282i −0.857446 + 0.495046i
\(683\) 32.7846 18.9282i 1.25447 0.724268i 0.282475 0.959275i \(-0.408845\pi\)
0.971994 + 0.235007i \(0.0755114\pi\)
\(684\) 1.26795i 0.0484812i
\(685\) 0 0
\(686\) −4.92820 + 8.53590i −0.188160 + 0.325902i
\(687\) 13.7321 + 7.92820i 0.523910 + 0.302480i
\(688\) 7.66025 0.292044
\(689\) 1.20577 1.16025i 0.0459362 0.0442022i
\(690\) 0 0
\(691\) 22.8109 + 13.1699i 0.867767 + 0.501006i 0.866606 0.498994i \(-0.166297\pi\)
0.00116153 + 0.999999i \(0.499630\pi\)
\(692\) −8.19615 + 14.1962i −0.311571 + 0.539657i
\(693\) −1.73205 3.00000i −0.0657952 0.113961i
\(694\) 8.87564i 0.336915i
\(695\) 0 0
\(696\) 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
\(700\) 0 0
\(701\) −31.3205 −1.18296 −0.591480 0.806320i \(-0.701456\pi\)
−0.591480 + 0.806320i \(0.701456\pi\)
\(702\) −3.50000 + 0.866025i −0.132099 + 0.0326860i
\(703\) −13.2679 −0.500410
\(704\) 4.09808 + 2.36603i 0.154452 + 0.0891729i
\(705\) 0 0
\(706\) 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 \(-0.388317\pi\)
0.985118 + 0.171880i \(0.0549841\pi\)
\(710\) 0 0
\(711\) 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 0.575737 0.817635i \(-0.304715\pi\)
−0.995961 + 0.0897860i \(0.971382\pi\)
\(720\) 0 0
\(721\) 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
\(725\) 0 0
\(726\) −9.86603 5.69615i −0.366163 0.211404i
\(727\) 20.9808 0.778133 0.389067 0.921210i \(-0.372798\pi\)
0.389067 + 0.921210i \(0.372798\pi\)
\(728\) −2.53590 0.732051i −0.0939866 0.0271316i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 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 \(0.114121\pi\)
−0.936416 + 0.350891i \(0.885879\pi\)
\(734\) 12.7583 7.36603i 0.470919 0.271885i
\(735\) 0 0
\(736\) 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 \(-0.268914\pi\)
−0.315724 + 0.948851i \(0.602247\pi\)
\(740\) 0 0
\(741\) −3.16987 3.29423i −0.116448 0.121017i
\(742\) −0.339746 −0.0124725
\(743\) 23.9090 + 13.8038i 0.877135 + 0.506414i 0.869713 0.493558i \(-0.164304\pi\)
0.00742221 + 0.999972i \(0.497637\pi\)
\(744\) 2.73205 4.73205i 0.100162 0.173485i
\(745\) 0 0
\(746\) 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
\(750\) 0 0
\(751\) 7.95448 13.7776i 0.290263 0.502751i −0.683609 0.729849i \(-0.739590\pi\)
0.973872 + 0.227098i \(0.0729238\pi\)
\(752\) −7.09808 4.09808i −0.258840 0.149441i
\(753\) 6.53590 0.238181
\(754\) −2.46410 + 8.53590i −0.0897373 + 0.310859i
\(755\) 0 0
\(756\) 0.633975 + 0.366025i 0.0230574 + 0.0133122i
\(757\) 3.53590 6.12436i 0.128514 0.222593i −0.794587 0.607151i \(-0.792312\pi\)
0.923101 + 0.384557i \(0.125646\pi\)
\(758\) −0.732051 1.26795i −0.0265893 0.0460540i
\(759\) 29.3205i 1.06427i
\(760\) 0 0
\(761\) −20.1962 + 11.6603i −0.732110 + 0.422684i −0.819194 0.573517i \(-0.805579\pi\)
0.0870836 + 0.996201i \(0.472245\pi\)
\(762\) 17.8564i 0.646869i
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) 3.46410 6.00000i 0.125327 0.217072i
\(765\) 0 0
\(766\) −5.46410 −0.197426
\(767\) −8.00000 + 27.7128i −0.288863 + 1.00065i
\(768\) −1.00000 −0.0360844
\(769\) −13.9808 8.07180i −0.504159 0.291076i 0.226270 0.974065i \(-0.427347\pi\)
−0.730429 + 0.682988i \(0.760680\pi\)
\(770\) 0 0
\(771\) 13.3301 + 23.0885i 0.480073 + 0.831510i
\(772\) 8.26795i 0.297570i
\(773\) −30.3731 + 17.5359i −1.09244 + 0.630722i −0.934226 0.356682i \(-0.883908\pi\)
−0.158217 + 0.987404i \(0.550575\pi\)
\(774\) 6.63397 3.83013i 0.238453 0.137671i
\(775\) 0 0
\(776\) 3.00000 + 5.19615i 0.107694 + 0.186531i
\(777\) −3.83013 + 6.63397i −0.137405 + 0.237993i
\(778\) −25.7942 14.8923i −0.924768 0.533915i
\(779\) −14.4449 −0.517541
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) −12.1699 7.02628i −0.435194 0.251259i
\(783\) 1.23205 2.13397i 0.0440299 0.0762620i
\(784\)