Properties

Label 525.2.i.f.226.1
Level $525$
Weight $2$
Character 525.226
Analytic conductor $4.192$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 525.226
Dual form 525.2.i.f.151.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 + 2.36603i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.73205 - 4.73205i) q^{4} +2.73205 q^{6} +(-0.866025 - 2.50000i) q^{7} +9.46410 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.36603 + 2.36603i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-2.73205 - 4.73205i) q^{4} +2.73205 q^{6} +(-0.866025 - 2.50000i) q^{7} +9.46410 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.366025 - 0.633975i) q^{11} +(-2.73205 + 4.73205i) q^{12} -2.26795 q^{13} +(7.09808 + 1.36603i) q^{14} +(-7.46410 + 12.9282i) q^{16} +(1.63397 + 2.83013i) q^{17} +(-1.36603 - 2.36603i) q^{18} +(-2.23205 + 3.86603i) q^{19} +(-1.73205 + 2.00000i) q^{21} +2.00000 q^{22} +(-2.36603 + 4.09808i) q^{23} +(-4.73205 - 8.19615i) q^{24} +(3.09808 - 5.36603i) q^{26} +1.00000 q^{27} +(-9.46410 + 10.9282i) q^{28} -4.19615 q^{29} +(0.232051 + 0.401924i) q^{31} +(-10.9282 - 18.9282i) q^{32} +(-0.366025 + 0.633975i) q^{33} -8.92820 q^{34} +5.46410 q^{36} +(-1.59808 + 2.76795i) q^{37} +(-6.09808 - 10.5622i) q^{38} +(1.13397 + 1.96410i) q^{39} -0.732051 q^{41} +(-2.36603 - 6.83013i) q^{42} -3.19615 q^{43} +(-2.00000 + 3.46410i) q^{44} +(-6.46410 - 11.1962i) q^{46} +(1.00000 - 1.73205i) q^{47} +14.9282 q^{48} +(-5.50000 + 4.33013i) q^{49} +(1.63397 - 2.83013i) q^{51} +(6.19615 + 10.7321i) q^{52} +(6.19615 + 10.7321i) q^{53} +(-1.36603 + 2.36603i) q^{54} +(-8.19615 - 23.6603i) q^{56} +4.46410 q^{57} +(5.73205 - 9.92820i) q^{58} +(0.0980762 + 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} -1.26795 q^{62} +(2.59808 + 0.500000i) q^{63} +29.8564 q^{64} +(-1.00000 - 1.73205i) q^{66} +(-7.33013 - 12.6962i) q^{67} +(8.92820 - 15.4641i) q^{68} +4.73205 q^{69} +6.19615 q^{71} +(-4.73205 + 8.19615i) q^{72} +(6.33013 + 10.9641i) q^{73} +(-4.36603 - 7.56218i) q^{74} +24.3923 q^{76} +(-1.26795 + 1.46410i) q^{77} -6.19615 q^{78} +(3.69615 - 6.40192i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -15.1244 q^{83} +(14.1962 + 2.73205i) q^{84} +(4.36603 - 7.56218i) q^{86} +(2.09808 + 3.63397i) q^{87} +(-3.46410 - 6.00000i) q^{88} +(-7.56218 + 13.0981i) q^{89} +(1.96410 + 5.66987i) q^{91} +25.8564 q^{92} +(0.232051 - 0.401924i) q^{93} +(2.73205 + 4.73205i) q^{94} +(-10.9282 + 18.9282i) q^{96} -14.9282 q^{97} +(-2.73205 - 18.9282i) q^{98} +0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 4q^{4} + 4q^{6} + 24q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 4q^{4} + 4q^{6} + 24q^{8} - 2q^{9} + 2q^{11} - 4q^{12} - 16q^{13} + 18q^{14} - 16q^{16} + 10q^{17} - 2q^{18} - 2q^{19} + 8q^{22} - 6q^{23} - 12q^{24} + 2q^{26} + 4q^{27} - 24q^{28} + 4q^{29} - 6q^{31} - 16q^{32} + 2q^{33} - 8q^{34} + 8q^{36} + 4q^{37} - 14q^{38} + 8q^{39} + 4q^{41} - 6q^{42} + 8q^{43} - 8q^{44} - 12q^{46} + 4q^{47} + 32q^{48} - 22q^{49} + 10q^{51} + 4q^{52} + 4q^{53} - 2q^{54} - 12q^{56} + 4q^{57} + 16q^{58} - 10q^{59} - 8q^{61} - 12q^{62} + 64q^{64} - 4q^{66} - 12q^{67} + 8q^{68} + 12q^{69} + 4q^{71} - 12q^{72} + 8q^{73} - 14q^{74} + 56q^{76} - 12q^{77} - 4q^{78} - 6q^{79} - 2q^{81} + 4q^{82} - 12q^{83} + 36q^{84} + 14q^{86} - 2q^{87} - 6q^{89} - 6q^{91} + 48q^{92} - 6q^{93} + 4q^{94} - 16q^{96} - 32q^{97} - 4q^{98} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 2.36603i −0.965926 + 1.67303i −0.258819 + 0.965926i \(0.583333\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −2.73205 4.73205i −1.36603 2.36603i
\(5\) 0 0
\(6\) 2.73205 1.11536
\(7\) −0.866025 2.50000i −0.327327 0.944911i
\(8\) 9.46410 3.34607
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.366025 0.633975i −0.110361 0.191151i 0.805555 0.592521i \(-0.201867\pi\)
−0.915916 + 0.401371i \(0.868534\pi\)
\(12\) −2.73205 + 4.73205i −0.788675 + 1.36603i
\(13\) −2.26795 −0.629016 −0.314508 0.949255i \(-0.601840\pi\)
−0.314508 + 0.949255i \(0.601840\pi\)
\(14\) 7.09808 + 1.36603i 1.89704 + 0.365086i
\(15\) 0 0
\(16\) −7.46410 + 12.9282i −1.86603 + 3.23205i
\(17\) 1.63397 + 2.83013i 0.396297 + 0.686407i 0.993266 0.115858i \(-0.0369617\pi\)
−0.596969 + 0.802264i \(0.703628\pi\)
\(18\) −1.36603 2.36603i −0.321975 0.557678i
\(19\) −2.23205 + 3.86603i −0.512068 + 0.886927i 0.487835 + 0.872936i \(0.337787\pi\)
−0.999902 + 0.0139909i \(0.995546\pi\)
\(20\) 0 0
\(21\) −1.73205 + 2.00000i −0.377964 + 0.436436i
\(22\) 2.00000 0.426401
\(23\) −2.36603 + 4.09808i −0.493350 + 0.854508i −0.999971 0.00766135i \(-0.997561\pi\)
0.506620 + 0.862169i \(0.330895\pi\)
\(24\) −4.73205 8.19615i −0.965926 1.67303i
\(25\) 0 0
\(26\) 3.09808 5.36603i 0.607583 1.05236i
\(27\) 1.00000 0.192450
\(28\) −9.46410 + 10.9282i −1.78855 + 2.06524i
\(29\) −4.19615 −0.779206 −0.389603 0.920983i \(-0.627388\pi\)
−0.389603 + 0.920983i \(0.627388\pi\)
\(30\) 0 0
\(31\) 0.232051 + 0.401924i 0.0416776 + 0.0721876i 0.886112 0.463472i \(-0.153396\pi\)
−0.844434 + 0.535659i \(0.820063\pi\)
\(32\) −10.9282 18.9282i −1.93185 3.34607i
\(33\) −0.366025 + 0.633975i −0.0637168 + 0.110361i
\(34\) −8.92820 −1.53117
\(35\) 0 0
\(36\) 5.46410 0.910684
\(37\) −1.59808 + 2.76795i −0.262722 + 0.455048i −0.966964 0.254912i \(-0.917954\pi\)
0.704242 + 0.709960i \(0.251287\pi\)
\(38\) −6.09808 10.5622i −0.989239 1.71341i
\(39\) 1.13397 + 1.96410i 0.181581 + 0.314508i
\(40\) 0 0
\(41\) −0.732051 −0.114327 −0.0571636 0.998365i \(-0.518206\pi\)
−0.0571636 + 0.998365i \(0.518206\pi\)
\(42\) −2.36603 6.83013i −0.365086 1.05391i
\(43\) −3.19615 −0.487409 −0.243704 0.969850i \(-0.578363\pi\)
−0.243704 + 0.969850i \(0.578363\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 0 0
\(46\) −6.46410 11.1962i −0.953080 1.65078i
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 14.9282 2.15470
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 0 0
\(51\) 1.63397 2.83013i 0.228802 0.396297i
\(52\) 6.19615 + 10.7321i 0.859252 + 1.48827i
\(53\) 6.19615 + 10.7321i 0.851107 + 1.47416i 0.880210 + 0.474584i \(0.157402\pi\)
−0.0291032 + 0.999576i \(0.509265\pi\)
\(54\) −1.36603 + 2.36603i −0.185893 + 0.321975i
\(55\) 0 0
\(56\) −8.19615 23.6603i −1.09526 3.16173i
\(57\) 4.46410 0.591285
\(58\) 5.73205 9.92820i 0.752655 1.30364i
\(59\) 0.0980762 + 0.169873i 0.0127684 + 0.0221156i 0.872339 0.488901i \(-0.162602\pi\)
−0.859571 + 0.511017i \(0.829269\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) −1.26795 −0.161030
\(63\) 2.59808 + 0.500000i 0.327327 + 0.0629941i
\(64\) 29.8564 3.73205
\(65\) 0 0
\(66\) −1.00000 1.73205i −0.123091 0.213201i
\(67\) −7.33013 12.6962i −0.895518 1.55108i −0.833163 0.553028i \(-0.813472\pi\)
−0.0623548 0.998054i \(-0.519861\pi\)
\(68\) 8.92820 15.4641i 1.08270 1.87530i
\(69\) 4.73205 0.569672
\(70\) 0 0
\(71\) 6.19615 0.735348 0.367674 0.929955i \(-0.380154\pi\)
0.367674 + 0.929955i \(0.380154\pi\)
\(72\) −4.73205 + 8.19615i −0.557678 + 0.965926i
\(73\) 6.33013 + 10.9641i 0.740885 + 1.28325i 0.952093 + 0.305810i \(0.0989271\pi\)
−0.211207 + 0.977441i \(0.567740\pi\)
\(74\) −4.36603 7.56218i −0.507540 0.879085i
\(75\) 0 0
\(76\) 24.3923 2.79799
\(77\) −1.26795 + 1.46410i −0.144496 + 0.166850i
\(78\) −6.19615 −0.701576
\(79\) 3.69615 6.40192i 0.415850 0.720273i −0.579668 0.814853i \(-0.696818\pi\)
0.995517 + 0.0945803i \(0.0301509\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) −15.1244 −1.66011 −0.830057 0.557679i \(-0.811692\pi\)
−0.830057 + 0.557679i \(0.811692\pi\)
\(84\) 14.1962 + 2.73205i 1.54893 + 0.298091i
\(85\) 0 0
\(86\) 4.36603 7.56218i 0.470801 0.815451i
\(87\) 2.09808 + 3.63397i 0.224937 + 0.389603i
\(88\) −3.46410 6.00000i −0.369274 0.639602i
\(89\) −7.56218 + 13.0981i −0.801589 + 1.38839i 0.116980 + 0.993134i \(0.462679\pi\)
−0.918570 + 0.395259i \(0.870655\pi\)
\(90\) 0 0
\(91\) 1.96410 + 5.66987i 0.205894 + 0.594364i
\(92\) 25.8564 2.69572
\(93\) 0.232051 0.401924i 0.0240625 0.0416776i
\(94\) 2.73205 + 4.73205i 0.281790 + 0.488074i
\(95\) 0 0
\(96\) −10.9282 + 18.9282i −1.11536 + 1.93185i
\(97\) −14.9282 −1.51573 −0.757865 0.652412i \(-0.773757\pi\)
−0.757865 + 0.652412i \(0.773757\pi\)
\(98\) −2.73205 18.9282i −0.275979 1.91204i
\(99\) 0.732051 0.0735739
\(100\) 0 0
\(101\) 3.63397 + 6.29423i 0.361594 + 0.626299i 0.988223 0.153018i \(-0.0488993\pi\)
−0.626629 + 0.779317i \(0.715566\pi\)
\(102\) 4.46410 + 7.73205i 0.442012 + 0.765587i
\(103\) −4.59808 + 7.96410i −0.453062 + 0.784726i −0.998574 0.0533764i \(-0.983002\pi\)
0.545513 + 0.838103i \(0.316335\pi\)
\(104\) −21.4641 −2.10473
\(105\) 0 0
\(106\) −33.8564 −3.28842
\(107\) 1.09808 1.90192i 0.106155 0.183866i −0.808054 0.589108i \(-0.799479\pi\)
0.914210 + 0.405242i \(0.132813\pi\)
\(108\) −2.73205 4.73205i −0.262892 0.455342i
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) 3.19615 0.303365
\(112\) 38.7846 + 7.46410i 3.66480 + 0.705291i
\(113\) −8.92820 −0.839895 −0.419947 0.907548i \(-0.637951\pi\)
−0.419947 + 0.907548i \(0.637951\pi\)
\(114\) −6.09808 + 10.5622i −0.571137 + 0.989239i
\(115\) 0 0
\(116\) 11.4641 + 19.8564i 1.06442 + 1.84362i
\(117\) 1.13397 1.96410i 0.104836 0.181581i
\(118\) −0.535898 −0.0493334
\(119\) 5.66025 6.53590i 0.518875 0.599145i
\(120\) 0 0
\(121\) 5.23205 9.06218i 0.475641 0.823834i
\(122\) −5.46410 9.46410i −0.494697 0.856840i
\(123\) 0.366025 + 0.633975i 0.0330034 + 0.0571636i
\(124\) 1.26795 2.19615i 0.113865 0.197220i
\(125\) 0 0
\(126\) −4.73205 + 5.46410i −0.421565 + 0.486781i
\(127\) −4.80385 −0.426273 −0.213136 0.977022i \(-0.568368\pi\)
−0.213136 + 0.977022i \(0.568368\pi\)
\(128\) −18.9282 + 32.7846i −1.67303 + 2.89778i
\(129\) 1.59808 + 2.76795i 0.140703 + 0.243704i
\(130\) 0 0
\(131\) −7.73205 + 13.3923i −0.675552 + 1.17009i 0.300755 + 0.953702i \(0.402761\pi\)
−0.976307 + 0.216390i \(0.930572\pi\)
\(132\) 4.00000 0.348155
\(133\) 11.5981 + 2.23205i 1.00568 + 0.193543i
\(134\) 40.0526 3.46001
\(135\) 0 0
\(136\) 15.4641 + 26.7846i 1.32604 + 2.29676i
\(137\) 1.09808 + 1.90192i 0.0938150 + 0.162492i 0.909113 0.416549i \(-0.136760\pi\)
−0.815298 + 0.579041i \(0.803427\pi\)
\(138\) −6.46410 + 11.1962i −0.550261 + 0.953080i
\(139\) 5.92820 0.502824 0.251412 0.967880i \(-0.419105\pi\)
0.251412 + 0.967880i \(0.419105\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) −8.46410 + 14.6603i −0.710292 + 1.23026i
\(143\) 0.830127 + 1.43782i 0.0694187 + 0.120237i
\(144\) −7.46410 12.9282i −0.622008 1.07735i
\(145\) 0 0
\(146\) −34.5885 −2.86256
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) 17.4641 1.43554
\(149\) −2.92820 + 5.07180i −0.239888 + 0.415498i −0.960682 0.277651i \(-0.910444\pi\)
0.720794 + 0.693149i \(0.243777\pi\)
\(150\) 0 0
\(151\) 4.46410 + 7.73205i 0.363283 + 0.629225i 0.988499 0.151227i \(-0.0483223\pi\)
−0.625216 + 0.780452i \(0.714989\pi\)
\(152\) −21.1244 + 36.5885i −1.71341 + 2.96772i
\(153\) −3.26795 −0.264198
\(154\) −1.73205 5.00000i −0.139573 0.402911i
\(155\) 0 0
\(156\) 6.19615 10.7321i 0.496089 0.859252i
\(157\) 3.19615 + 5.53590i 0.255081 + 0.441813i 0.964917 0.262553i \(-0.0845646\pi\)
−0.709837 + 0.704366i \(0.751231\pi\)
\(158\) 10.0981 + 17.4904i 0.803360 + 1.39146i
\(159\) 6.19615 10.7321i 0.491387 0.851107i
\(160\) 0 0
\(161\) 12.2942 + 2.36603i 0.968921 + 0.186469i
\(162\) 2.73205 0.214650
\(163\) 10.9282 18.9282i 0.855963 1.48257i −0.0197859 0.999804i \(-0.506298\pi\)
0.875749 0.482767i \(-0.160368\pi\)
\(164\) 2.00000 + 3.46410i 0.156174 + 0.270501i
\(165\) 0 0
\(166\) 20.6603 35.7846i 1.60355 2.77742i
\(167\) 17.6603 1.36659 0.683296 0.730142i \(-0.260546\pi\)
0.683296 + 0.730142i \(0.260546\pi\)
\(168\) −16.3923 + 18.9282i −1.26469 + 1.46034i
\(169\) −7.85641 −0.604339
\(170\) 0 0
\(171\) −2.23205 3.86603i −0.170689 0.295642i
\(172\) 8.73205 + 15.1244i 0.665813 + 1.15322i
\(173\) 7.26795 12.5885i 0.552572 0.957083i −0.445516 0.895274i \(-0.646980\pi\)
0.998088 0.0618087i \(-0.0196869\pi\)
\(174\) −11.4641 −0.869091
\(175\) 0 0
\(176\) 10.9282 0.823744
\(177\) 0.0980762 0.169873i 0.00737186 0.0127684i
\(178\) −20.6603 35.7846i −1.54855 2.68217i
\(179\) 5.00000 + 8.66025i 0.373718 + 0.647298i 0.990134 0.140122i \(-0.0447496\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(180\) 0 0
\(181\) −24.3205 −1.80773 −0.903865 0.427819i \(-0.859282\pi\)
−0.903865 + 0.427819i \(0.859282\pi\)
\(182\) −16.0981 3.09808i −1.19327 0.229645i
\(183\) 4.00000 0.295689
\(184\) −22.3923 + 38.7846i −1.65078 + 2.85924i
\(185\) 0 0
\(186\) 0.633975 + 1.09808i 0.0464853 + 0.0805149i
\(187\) 1.19615 2.07180i 0.0874713 0.151505i
\(188\) −10.9282 −0.797021
\(189\) −0.866025 2.50000i −0.0629941 0.181848i
\(190\) 0 0
\(191\) 4.46410 7.73205i 0.323011 0.559472i −0.658097 0.752933i \(-0.728638\pi\)
0.981108 + 0.193462i \(0.0619716\pi\)
\(192\) −14.9282 25.8564i −1.07735 1.86603i
\(193\) 0.598076 + 1.03590i 0.0430505 + 0.0745656i 0.886748 0.462254i \(-0.152959\pi\)
−0.843697 + 0.536819i \(0.819626\pi\)
\(194\) 20.3923 35.3205i 1.46408 2.53586i
\(195\) 0 0
\(196\) 35.5167 + 14.1962i 2.53690 + 1.01401i
\(197\) 0.339746 0.0242059 0.0121029 0.999927i \(-0.496147\pi\)
0.0121029 + 0.999927i \(0.496147\pi\)
\(198\) −1.00000 + 1.73205i −0.0710669 + 0.123091i
\(199\) −11.0000 19.0526i −0.779769 1.35060i −0.932075 0.362267i \(-0.882003\pi\)
0.152305 0.988334i \(-0.451330\pi\)
\(200\) 0 0
\(201\) −7.33013 + 12.6962i −0.517027 + 0.895518i
\(202\) −19.8564 −1.39709
\(203\) 3.63397 + 10.4904i 0.255055 + 0.736280i
\(204\) −17.8564 −1.25020
\(205\) 0 0
\(206\) −12.5622 21.7583i −0.875248 1.51597i
\(207\) −2.36603 4.09808i −0.164450 0.284836i
\(208\) 16.9282 29.3205i 1.17376 2.03301i
\(209\) 3.26795 0.226049
\(210\) 0 0
\(211\) 7.07180 0.486843 0.243421 0.969921i \(-0.421730\pi\)
0.243421 + 0.969921i \(0.421730\pi\)
\(212\) 33.8564 58.6410i 2.32527 4.02748i
\(213\) −3.09808 5.36603i −0.212277 0.367674i
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 0 0
\(216\) 9.46410 0.643951
\(217\) 0.803848 0.928203i 0.0545687 0.0630105i
\(218\) 30.0526 2.03542
\(219\) 6.33013 10.9641i 0.427750 0.740885i
\(220\) 0 0
\(221\) −3.70577 6.41858i −0.249277 0.431761i
\(222\) −4.36603 + 7.56218i −0.293028 + 0.507540i
\(223\) 20.3923 1.36557 0.682785 0.730619i \(-0.260769\pi\)
0.682785 + 0.730619i \(0.260769\pi\)
\(224\) −37.8564 + 43.7128i −2.52939 + 2.92069i
\(225\) 0 0
\(226\) 12.1962 21.1244i 0.811276 1.40517i
\(227\) −0.830127 1.43782i −0.0550975 0.0954316i 0.837161 0.546956i \(-0.184214\pi\)
−0.892259 + 0.451525i \(0.850880\pi\)
\(228\) −12.1962 21.1244i −0.807710 1.39899i
\(229\) 1.50000 2.59808i 0.0991228 0.171686i −0.812199 0.583380i \(-0.801730\pi\)
0.911322 + 0.411695i \(0.135063\pi\)
\(230\) 0 0
\(231\) 1.90192 + 0.366025i 0.125137 + 0.0240827i
\(232\) −39.7128 −2.60727
\(233\) 8.66025 15.0000i 0.567352 0.982683i −0.429474 0.903079i \(-0.641301\pi\)
0.996827 0.0796037i \(-0.0253655\pi\)
\(234\) 3.09808 + 5.36603i 0.202528 + 0.350788i
\(235\) 0 0
\(236\) 0.535898 0.928203i 0.0348840 0.0604209i
\(237\) −7.39230 −0.480182
\(238\) 7.73205 + 22.3205i 0.501194 + 1.44682i
\(239\) 7.07180 0.457437 0.228718 0.973493i \(-0.426547\pi\)
0.228718 + 0.973493i \(0.426547\pi\)
\(240\) 0 0
\(241\) −6.73205 11.6603i −0.433650 0.751103i 0.563535 0.826092i \(-0.309441\pi\)
−0.997184 + 0.0749893i \(0.976108\pi\)
\(242\) 14.2942 + 24.7583i 0.918868 + 1.59153i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 21.8564 1.39921
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) 5.06218 8.76795i 0.322099 0.557891i
\(248\) 2.19615 + 3.80385i 0.139456 + 0.241545i
\(249\) 7.56218 + 13.0981i 0.479234 + 0.830057i
\(250\) 0 0
\(251\) −24.5885 −1.55201 −0.776005 0.630727i \(-0.782757\pi\)
−0.776005 + 0.630727i \(0.782757\pi\)
\(252\) −4.73205 13.6603i −0.298091 0.860515i
\(253\) 3.46410 0.217786
\(254\) 6.56218 11.3660i 0.411748 0.713168i
\(255\) 0 0
\(256\) −21.8564 37.8564i −1.36603 2.36603i
\(257\) −2.83013 + 4.90192i −0.176538 + 0.305774i −0.940693 0.339260i \(-0.889823\pi\)
0.764154 + 0.645034i \(0.223157\pi\)
\(258\) −8.73205 −0.543634
\(259\) 8.30385 + 1.59808i 0.515976 + 0.0992996i
\(260\) 0 0
\(261\) 2.09808 3.63397i 0.129868 0.224937i
\(262\) −21.1244 36.5885i −1.30507 2.26044i
\(263\) 4.19615 + 7.26795i 0.258746 + 0.448161i 0.965906 0.258892i \(-0.0833575\pi\)
−0.707160 + 0.707053i \(0.750024\pi\)
\(264\) −3.46410 + 6.00000i −0.213201 + 0.369274i
\(265\) 0 0
\(266\) −21.1244 + 24.3923i −1.29522 + 1.49559i
\(267\) 15.1244 0.925596
\(268\) −40.0526 + 69.3731i −2.44660 + 4.23763i
\(269\) 6.26795 + 10.8564i 0.382164 + 0.661927i 0.991371 0.131084i \(-0.0418457\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(270\) 0 0
\(271\) −1.53590 + 2.66025i −0.0932992 + 0.161599i −0.908897 0.417020i \(-0.863075\pi\)
0.815598 + 0.578619i \(0.196408\pi\)
\(272\) −48.7846 −2.95800
\(273\) 3.92820 4.53590i 0.237746 0.274525i
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) −12.9282 22.3923i −0.778186 1.34786i
\(277\) −7.33013 12.6962i −0.440425 0.762838i 0.557296 0.830314i \(-0.311839\pi\)
−0.997721 + 0.0674759i \(0.978505\pi\)
\(278\) −8.09808 + 14.0263i −0.485690 + 0.841240i
\(279\) −0.464102 −0.0277850
\(280\) 0 0
\(281\) 13.8564 0.826604 0.413302 0.910594i \(-0.364375\pi\)
0.413302 + 0.910594i \(0.364375\pi\)
\(282\) 2.73205 4.73205i 0.162691 0.281790i
\(283\) −12.0622 20.8923i −0.717022 1.24192i −0.962174 0.272434i \(-0.912171\pi\)
0.245152 0.969485i \(-0.421162\pi\)
\(284\) −16.9282 29.3205i −1.00450 1.73985i
\(285\) 0 0
\(286\) −4.53590 −0.268213
\(287\) 0.633975 + 1.83013i 0.0374223 + 0.108029i
\(288\) 21.8564 1.28790
\(289\) 3.16025 5.47372i 0.185897 0.321984i
\(290\) 0 0
\(291\) 7.46410 + 12.9282i 0.437553 + 0.757865i
\(292\) 34.5885 59.9090i 2.02414 3.50591i
\(293\) −18.9282 −1.10580 −0.552899 0.833248i \(-0.686478\pi\)
−0.552899 + 0.833248i \(0.686478\pi\)
\(294\) −15.0263 + 11.8301i −0.876350 + 0.689947i
\(295\) 0 0
\(296\) −15.1244 + 26.1962i −0.879085 + 1.52262i
\(297\) −0.366025 0.633975i −0.0212389 0.0367869i
\(298\) −8.00000 13.8564i −0.463428 0.802680i
\(299\) 5.36603 9.29423i 0.310325 0.537499i
\(300\) 0 0
\(301\) 2.76795 + 7.99038i 0.159542 + 0.460558i
\(302\) −24.3923 −1.40362
\(303\) 3.63397 6.29423i 0.208766 0.361594i
\(304\) −33.3205 57.7128i −1.91106 3.31006i
\(305\) 0 0
\(306\) 4.46410 7.73205i 0.255196 0.442012i
\(307\) 32.1244 1.83343 0.916717 0.399537i \(-0.130829\pi\)
0.916717 + 0.399537i \(0.130829\pi\)
\(308\) 10.3923 + 2.00000i 0.592157 + 0.113961i
\(309\) 9.19615 0.523151
\(310\) 0 0
\(311\) −4.56218 7.90192i −0.258697 0.448077i 0.707196 0.707018i \(-0.249960\pi\)
−0.965893 + 0.258941i \(0.916627\pi\)
\(312\) 10.7321 + 18.5885i 0.607583 + 1.05236i
\(313\) −6.33013 + 10.9641i −0.357800 + 0.619728i −0.987593 0.157035i \(-0.949806\pi\)
0.629793 + 0.776763i \(0.283140\pi\)
\(314\) −17.4641 −0.985556
\(315\) 0 0
\(316\) −40.3923 −2.27224
\(317\) −14.2224 + 24.6340i −0.798811 + 1.38358i 0.121579 + 0.992582i \(0.461204\pi\)
−0.920391 + 0.391000i \(0.872129\pi\)
\(318\) 16.9282 + 29.3205i 0.949286 + 1.64421i
\(319\) 1.53590 + 2.66025i 0.0859938 + 0.148946i
\(320\) 0 0
\(321\) −2.19615 −0.122577
\(322\) −22.3923 + 25.8564i −1.24787 + 1.44092i
\(323\) −14.5885 −0.811723
\(324\) −2.73205 + 4.73205i −0.151781 + 0.262892i
\(325\) 0 0
\(326\) 29.8564 + 51.7128i 1.65359 + 2.86411i
\(327\) −5.50000 + 9.52628i −0.304151 + 0.526804i
\(328\) −6.92820 −0.382546
\(329\) −5.19615 1.00000i −0.286473 0.0551318i
\(330\) 0 0
\(331\) −4.03590 + 6.99038i −0.221833 + 0.384226i −0.955365 0.295429i \(-0.904537\pi\)
0.733532 + 0.679655i \(0.237871\pi\)
\(332\) 41.3205 + 71.5692i 2.26776 + 3.92787i
\(333\) −1.59808 2.76795i −0.0875740 0.151683i
\(334\) −24.1244 + 41.7846i −1.32003 + 2.28635i
\(335\) 0 0
\(336\) −12.9282 37.3205i −0.705291 2.03600i
\(337\) −17.9808 −0.979475 −0.489737 0.871870i \(-0.662907\pi\)
−0.489737 + 0.871870i \(0.662907\pi\)
\(338\) 10.7321 18.5885i 0.583747 1.01108i
\(339\) 4.46410 + 7.73205i 0.242457 + 0.419947i
\(340\) 0 0
\(341\) 0.169873 0.294229i 0.00919914 0.0159334i
\(342\) 12.1962 0.659492
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) −30.2487 −1.63090
\(345\) 0 0
\(346\) 19.8564 + 34.3923i 1.06749 + 1.84894i
\(347\) −10.5359 18.2487i −0.565597 0.979642i −0.996994 0.0774801i \(-0.975313\pi\)
0.431397 0.902162i \(-0.358021\pi\)
\(348\) 11.4641 19.8564i 0.614540 1.06442i
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 0 0
\(351\) −2.26795 −0.121054
\(352\) −8.00000 + 13.8564i −0.426401 + 0.738549i
\(353\) −1.56218 2.70577i −0.0831463 0.144014i 0.821453 0.570276i \(-0.193164\pi\)
−0.904600 + 0.426262i \(0.859830\pi\)
\(354\) 0.267949 + 0.464102i 0.0142413 + 0.0246667i
\(355\) 0 0
\(356\) 82.6410 4.37997
\(357\) −8.49038 1.63397i −0.449359 0.0864791i
\(358\) −27.3205 −1.44393
\(359\) 0.633975 1.09808i 0.0334599 0.0579542i −0.848811 0.528697i \(-0.822681\pi\)
0.882270 + 0.470743i \(0.156014\pi\)
\(360\) 0 0
\(361\) −0.464102 0.803848i −0.0244264 0.0423078i
\(362\) 33.2224 57.5429i 1.74613 3.02439i
\(363\) −10.4641 −0.549223
\(364\) 21.4641 24.7846i 1.12502 1.29907i
\(365\) 0 0
\(366\) −5.46410 + 9.46410i −0.285613 + 0.494697i
\(367\) 5.59808 + 9.69615i 0.292217 + 0.506135i 0.974334 0.225108i \(-0.0722736\pi\)
−0.682117 + 0.731244i \(0.738940\pi\)
\(368\) −35.3205 61.1769i −1.84121 3.18907i
\(369\) 0.366025 0.633975i 0.0190545 0.0330034i
\(370\) 0 0
\(371\) 21.4641 24.7846i 1.11436 1.28675i
\(372\) −2.53590 −0.131480
\(373\) 13.2583 22.9641i 0.686490 1.18904i −0.286476 0.958088i \(-0.592484\pi\)
0.972966 0.230949i \(-0.0741829\pi\)
\(374\) 3.26795 + 5.66025i 0.168982 + 0.292685i
\(375\) 0 0
\(376\) 9.46410 16.3923i 0.488074 0.845369i
\(377\) 9.51666 0.490133
\(378\) 7.09808 + 1.36603i 0.365086 + 0.0702608i
\(379\) 6.32051 0.324663 0.162331 0.986736i \(-0.448099\pi\)
0.162331 + 0.986736i \(0.448099\pi\)
\(380\) 0 0
\(381\) 2.40192 + 4.16025i 0.123054 + 0.213136i
\(382\) 12.1962 + 21.1244i 0.624009 + 1.08082i
\(383\) −11.6603 + 20.1962i −0.595811 + 1.03198i 0.397621 + 0.917550i \(0.369836\pi\)
−0.993432 + 0.114425i \(0.963497\pi\)
\(384\) 37.8564 1.93185
\(385\) 0 0
\(386\) −3.26795 −0.166334
\(387\) 1.59808 2.76795i 0.0812348 0.140703i
\(388\) 40.7846 + 70.6410i 2.07052 + 3.58625i
\(389\) −2.70577 4.68653i −0.137188 0.237617i 0.789243 0.614081i \(-0.210473\pi\)
−0.926431 + 0.376464i \(0.877140\pi\)
\(390\) 0 0
\(391\) −15.4641 −0.782053
\(392\) −52.0526 + 40.9808i −2.62905 + 2.06984i
\(393\) 15.4641 0.780061
\(394\) −0.464102 + 0.803848i −0.0233811 + 0.0404973i
\(395\) 0 0
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) −15.5981 + 27.0167i −0.782845 + 1.35593i 0.147433 + 0.989072i \(0.452899\pi\)
−0.930278 + 0.366855i \(0.880434\pi\)
\(398\) 60.1051 3.01280
\(399\) −3.86603 11.1603i −0.193543 0.558712i
\(400\) 0 0
\(401\) 8.19615 14.1962i 0.409296 0.708922i −0.585515 0.810662i \(-0.699108\pi\)
0.994811 + 0.101740i \(0.0324409\pi\)
\(402\) −20.0263 34.6865i −0.998820 1.73001i
\(403\) −0.526279 0.911543i −0.0262158 0.0454072i
\(404\) 19.8564 34.3923i 0.987893 1.71108i
\(405\) 0 0
\(406\) −29.7846 5.73205i −1.47819 0.284477i
\(407\) 2.33975 0.115977
\(408\) 15.4641 26.7846i 0.765587 1.32604i
\(409\) −1.57180 2.72243i −0.0777203 0.134616i 0.824546 0.565795i \(-0.191431\pi\)
−0.902266 + 0.431180i \(0.858097\pi\)
\(410\) 0 0
\(411\) 1.09808 1.90192i 0.0541641 0.0938150i
\(412\) 50.2487 2.47558
\(413\) 0.339746 0.392305i 0.0167178 0.0193041i
\(414\) 12.9282 0.635387
\(415\) 0 0
\(416\) 24.7846 + 42.9282i 1.21517 + 2.10473i
\(417\) −2.96410 5.13397i −0.145153 0.251412i
\(418\) −4.46410 + 7.73205i −0.218346 + 0.378187i
\(419\) −35.4641 −1.73253 −0.866267 0.499581i \(-0.833487\pi\)
−0.866267 + 0.499581i \(0.833487\pi\)
\(420\) 0 0
\(421\) 0.0717968 0.00349916 0.00174958 0.999998i \(-0.499443\pi\)
0.00174958 + 0.999998i \(0.499443\pi\)
\(422\) −9.66025 + 16.7321i −0.470254 + 0.814503i
\(423\) 1.00000 + 1.73205i 0.0486217 + 0.0842152i
\(424\) 58.6410 + 101.569i 2.84786 + 4.93264i
\(425\) 0 0
\(426\) 16.9282 0.820174
\(427\) 10.3923 + 2.00000i 0.502919 + 0.0967868i
\(428\) −12.0000 −0.580042
\(429\) 0.830127 1.43782i 0.0400789 0.0694187i
\(430\) 0 0
\(431\) −8.66025 15.0000i −0.417150 0.722525i 0.578502 0.815681i \(-0.303638\pi\)
−0.995651 + 0.0931566i \(0.970304\pi\)
\(432\) −7.46410 + 12.9282i −0.359117 + 0.622008i
\(433\) −15.1962 −0.730280 −0.365140 0.930953i \(-0.618979\pi\)
−0.365140 + 0.930953i \(0.618979\pi\)
\(434\) 1.09808 + 3.16987i 0.0527093 + 0.152159i
\(435\) 0 0
\(436\) −30.0526 + 52.0526i −1.43926 + 2.49287i
\(437\) −10.5622 18.2942i −0.505257 0.875132i
\(438\) 17.2942 + 29.9545i 0.826350 + 1.43128i
\(439\) −0.267949 + 0.464102i −0.0127885 + 0.0221504i −0.872349 0.488884i \(-0.837404\pi\)
0.859560 + 0.511034i \(0.170737\pi\)
\(440\) 0 0
\(441\) −1.00000 6.92820i −0.0476190 0.329914i
\(442\) 20.2487 0.963133
\(443\) 4.73205 8.19615i 0.224827 0.389411i −0.731441 0.681905i \(-0.761152\pi\)
0.956267 + 0.292494i \(0.0944851\pi\)
\(444\) −8.73205 15.1244i −0.414405 0.717770i
\(445\) 0 0
\(446\) −27.8564 + 48.2487i −1.31904 + 2.28464i
\(447\) 5.85641 0.276999
\(448\) −25.8564 74.6410i −1.22160 3.52646i
\(449\) −35.8564 −1.69217 −0.846084 0.533049i \(-0.821046\pi\)
−0.846084 + 0.533049i \(0.821046\pi\)
\(450\) 0 0
\(451\) 0.267949 + 0.464102i 0.0126172 + 0.0218537i
\(452\) 24.3923 + 42.2487i 1.14732 + 1.98721i
\(453\) 4.46410 7.73205i 0.209742 0.363283i
\(454\) 4.53590 0.212880
\(455\) 0 0
\(456\) 42.2487 1.97848
\(457\) −8.33013 + 14.4282i −0.389667 + 0.674923i −0.992405 0.123016i \(-0.960743\pi\)
0.602738 + 0.797939i \(0.294077\pi\)
\(458\) 4.09808 + 7.09808i 0.191491 + 0.331671i
\(459\) 1.63397 + 2.83013i 0.0762674 + 0.132099i
\(460\) 0 0
\(461\) 16.9808 0.790873 0.395436 0.918493i \(-0.370593\pi\)
0.395436 + 0.918493i \(0.370593\pi\)
\(462\) −3.46410 + 4.00000i −0.161165 + 0.186097i
\(463\) −25.7321 −1.19587 −0.597935 0.801545i \(-0.704012\pi\)
−0.597935 + 0.801545i \(0.704012\pi\)
\(464\) 31.3205 54.2487i 1.45402 2.51843i
\(465\) 0 0
\(466\) 23.6603 + 40.9808i 1.09604 + 1.89840i
\(467\) −0.0717968 + 0.124356i −0.00332236 + 0.00575449i −0.867682 0.497120i \(-0.834391\pi\)
0.864359 + 0.502874i \(0.167724\pi\)
\(468\) −12.3923 −0.572834
\(469\) −25.3923 + 29.3205i −1.17251 + 1.35390i
\(470\) 0 0
\(471\) 3.19615 5.53590i 0.147271 0.255081i
\(472\) 0.928203 + 1.60770i 0.0427240 + 0.0740002i
\(473\) 1.16987 + 2.02628i 0.0537908 + 0.0931684i
\(474\) 10.0981 17.4904i 0.463820 0.803360i
\(475\) 0 0
\(476\) −46.3923 8.92820i −2.12639 0.409224i
\(477\) −12.3923 −0.567405
\(478\) −9.66025 + 16.7321i −0.441850 + 0.765306i
\(479\) −4.39230 7.60770i −0.200690 0.347604i 0.748061 0.663630i \(-0.230985\pi\)
−0.948751 + 0.316025i \(0.897652\pi\)
\(480\) 0 0
\(481\) 3.62436 6.27757i 0.165256 0.286232i
\(482\) 36.7846 1.67549
\(483\) −4.09808 11.8301i −0.186469 0.538289i
\(484\) −57.1769 −2.59895
\(485\) 0 0
\(486\) −1.36603 2.36603i −0.0619642 0.107325i
\(487\) −0.205771 0.356406i −0.00932439 0.0161503i 0.861326 0.508053i \(-0.169635\pi\)
−0.870650 + 0.491903i \(0.836301\pi\)
\(488\) −18.9282 + 32.7846i −0.856840 + 1.48409i
\(489\) −21.8564 −0.988381
\(490\) 0 0
\(491\) −38.2487 −1.72614 −0.863070 0.505084i \(-0.831461\pi\)
−0.863070 + 0.505084i \(0.831461\pi\)
\(492\) 2.00000 3.46410i 0.0901670 0.156174i
\(493\) −6.85641 11.8756i −0.308797 0.534852i
\(494\) 13.8301 + 23.9545i 0.622247 + 1.07776i
\(495\) 0 0
\(496\) −6.92820 −0.311086
\(497\) −5.36603 15.4904i −0.240699 0.694839i
\(498\) −41.3205 −1.85162
\(499\) 6.76795 11.7224i 0.302975 0.524768i −0.673833 0.738883i \(-0.735353\pi\)
0.976808 + 0.214115i \(0.0686868\pi\)
\(500\) 0 0
\(501\) −8.83013 15.2942i −0.394501 0.683296i
\(502\) 33.5885 58.1769i 1.49913 2.59656i
\(503\) −14.3923 −0.641721 −0.320861 0.947126i \(-0.603972\pi\)
−0.320861 + 0.947126i \(0.603972\pi\)
\(504\) 24.5885 + 4.73205i 1.09526 + 0.210782i
\(505\) 0 0
\(506\) −4.73205 + 8.19615i −0.210365 + 0.364363i
\(507\) 3.92820 + 6.80385i 0.174458 + 0.302169i
\(508\) 13.1244 + 22.7321i 0.582299 + 1.00857i
\(509\) −2.26795 + 3.92820i −0.100525 + 0.174115i −0.911901 0.410410i \(-0.865386\pi\)
0.811376 + 0.584525i \(0.198719\pi\)
\(510\) 0 0
\(511\) 21.9282 25.3205i 0.970047 1.12011i
\(512\) 43.7128 1.93185
\(513\) −2.23205 + 3.86603i −0.0985475 + 0.170689i
\(514\) −7.73205 13.3923i −0.341046 0.590709i
\(515\) 0 0
\(516\) 8.73205 15.1244i 0.384407 0.665813i
\(517\) −1.46410 −0.0643911
\(518\) −15.1244 + 17.4641i −0.664526 + 0.767329i
\(519\) −14.5359 −0.638055
\(520\) 0 0
\(521\) 2.73205 + 4.73205i 0.119693 + 0.207315i 0.919646 0.392748i \(-0.128476\pi\)
−0.799953 + 0.600063i \(0.795142\pi\)
\(522\) 5.73205 + 9.92820i 0.250885 + 0.434546i
\(523\) −13.8660 + 24.0167i −0.606319 + 1.05018i 0.385523 + 0.922698i \(0.374021\pi\)
−0.991842 + 0.127477i \(0.959312\pi\)
\(524\) 84.4974 3.69129
\(525\) 0 0
\(526\) −22.9282 −0.999717
\(527\) −0.758330 + 1.31347i −0.0330334 + 0.0572155i
\(528\) −5.46410 9.46410i −0.237795 0.411872i
\(529\) 0.303848 + 0.526279i 0.0132108 + 0.0228817i
\(530\) 0 0
\(531\) −0.196152 −0.00851229
\(532\) −21.1244 60.9808i −0.915857 2.64385i
\(533\) 1.66025 0.0719136
\(534\) −20.6603 + 35.7846i −0.894057 + 1.54855i
\(535\) 0 0
\(536\) −69.3731 120.158i −2.99646 5.19002i
\(537\) 5.00000 8.66025i 0.215766 0.373718i
\(538\) −34.2487 −1.47657
\(539\) 4.75833 + 1.90192i 0.204956 + 0.0819217i
\(540\) 0 0
\(541\) −2.89230 + 5.00962i −0.124350 + 0.215380i −0.921479 0.388429i \(-0.873018\pi\)
0.797129 + 0.603809i \(0.206351\pi\)
\(542\) −4.19615 7.26795i −0.180240 0.312185i
\(543\) 12.1603 + 21.0622i 0.521846 + 0.903865i
\(544\) 35.7128 61.8564i 1.53117 2.65207i
\(545\) 0 0
\(546\) 5.36603 + 15.4904i 0.229645 + 0.662927i
\(547\) 26.2487 1.12231 0.561157 0.827709i \(-0.310356\pi\)
0.561157 + 0.827709i \(0.310356\pi\)
\(548\) 6.00000 10.3923i 0.256307 0.443937i
\(549\) −2.00000 3.46410i −0.0853579 0.147844i
\(550\) 0 0
\(551\) 9.36603 16.2224i 0.399006 0.691099i
\(552\) 44.7846 1.90616
\(553\) −19.2058 3.69615i −0.816712 0.157176i
\(554\) 40.0526 1.70167
\(555\) 0 0
\(556\) −16.1962 28.0526i −0.686870 1.18969i
\(557\) 7.39230 + 12.8038i 0.313222 + 0.542516i 0.979058 0.203582i \(-0.0652583\pi\)
−0.665836 + 0.746098i \(0.731925\pi\)
\(558\) 0.633975 1.09808i 0.0268383 0.0464853i
\(559\) 7.24871 0.306588
\(560\) 0 0
\(561\) −2.39230 −0.101003
\(562\) −18.9282 + 32.7846i −0.798438 + 1.38294i
\(563\) −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i \(-0.290503\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(564\) 5.46410 + 9.46410i 0.230080 + 0.398511i
\(565\) 0 0
\(566\) 65.9090 2.77036
\(567\) −1.73205 + 2.00000i −0.0727393 + 0.0839921i
\(568\) 58.6410 2.46052
\(569\) −16.2224 + 28.0981i −0.680080 + 1.17793i 0.294876 + 0.955535i \(0.404722\pi\)
−0.974956 + 0.222397i \(0.928612\pi\)
\(570\) 0 0
\(571\) −9.30385 16.1147i −0.389354 0.674381i 0.603009 0.797734i \(-0.293968\pi\)
−0.992363 + 0.123354i \(0.960635\pi\)
\(572\) 4.53590 7.85641i 0.189655 0.328493i
\(573\) −8.92820 −0.372981
\(574\) −5.19615 1.00000i −0.216883 0.0417392i
\(575\) 0 0
\(576\) −14.9282 + 25.8564i −0.622008 + 1.07735i
\(577\) 14.3301 + 24.8205i 0.596571 + 1.03329i 0.993323 + 0.115365i \(0.0368039\pi\)
−0.396752 + 0.917926i \(0.629863\pi\)
\(578\) 8.63397 + 14.9545i 0.359126 + 0.622024i
\(579\) 0.598076 1.03590i 0.0248552 0.0430505i
\(580\) 0 0
\(581\) 13.0981 + 37.8109i 0.543400 + 1.56866i
\(582\) −40.7846 −1.69058
\(583\) 4.53590 7.85641i 0.187858 0.325379i
\(584\) 59.9090 + 103.765i 2.47905 + 4.29384i
\(585\) 0 0
\(586\) 25.8564 44.7846i 1.06812 1.85004i
\(587\) −40.7321 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(588\) −5.46410 37.8564i −0.225336 1.56117i
\(589\) −2.07180 −0.0853669
\(590\) 0 0
\(591\) −0.169873 0.294229i −0.00698764 0.0121029i
\(592\) −23.8564 41.3205i −0.980492 1.69826i
\(593\) 13.9545 24.1699i 0.573042 0.992538i −0.423209 0.906032i \(-0.639097\pi\)
0.996251 0.0865058i \(-0.0275701\pi\)
\(594\) 2.00000 0.0820610
\(595\) 0 0
\(596\) 32.0000 1.31077
\(597\) −11.0000 + 19.0526i −0.450200 + 0.779769i
\(598\) 14.6603 + 25.3923i 0.599502 + 1.03837i
\(599\) 19.1244 + 33.1244i 0.781400 + 1.35342i 0.931126 + 0.364697i \(0.118827\pi\)
−0.149726 + 0.988727i \(0.547839\pi\)
\(600\) 0 0
\(601\) −0.0717968 −0.00292865 −0.00146433 0.999999i \(-0.500466\pi\)
−0.00146433 + 0.999999i \(0.500466\pi\)
\(602\) −22.6865 4.36603i −0.924634 0.177946i
\(603\) 14.6603 0.597012
\(604\) 24.3923 42.2487i 0.992509 1.71908i
\(605\) 0 0
\(606\) 9.92820 + 17.1962i 0.403306 + 0.698546i
\(607\) 1.59808 2.76795i 0.0648639 0.112348i −0.831770 0.555121i \(-0.812672\pi\)
0.896634 + 0.442773i \(0.146005\pi\)
\(608\) 97.5692 3.95695
\(609\) 7.26795 8.39230i 0.294512 0.340073i
\(610\) 0 0
\(611\) −2.26795 + 3.92820i −0.0917514 + 0.158918i
\(612\) 8.92820 + 15.4641i 0.360901 + 0.625099i
\(613\) −13.4641 23.3205i −0.543810 0.941906i −0.998681 0.0513490i \(-0.983648\pi\)
0.454871 0.890557i \(-0.349685\pi\)
\(614\) −43.8827 + 76.0070i −1.77096 + 3.06739i
\(615\) 0 0
\(616\) −12.0000 + 13.8564i −0.483494 + 0.558291i
\(617\) 36.2487 1.45932 0.729659 0.683811i \(-0.239679\pi\)
0.729659 + 0.683811i \(0.239679\pi\)
\(618\) −12.5622 + 21.7583i −0.505325 + 0.875248i
\(619\) 15.0359 + 26.0429i 0.604344 + 1.04675i 0.992155 + 0.125015i \(0.0398980\pi\)
−0.387811 + 0.921739i \(0.626769\pi\)
\(620\) 0 0
\(621\) −2.36603 + 4.09808i −0.0949453 + 0.164450i
\(622\) 24.9282 0.999530
\(623\) 39.2942 + 7.56218i 1.57429 + 0.302972i
\(624\) −33.8564 −1.35534
\(625\) 0 0
\(626\) −17.2942 29.9545i −0.691216 1.19722i
\(627\) −1.63397 2.83013i −0.0652547 0.113024i
\(628\) 17.4641 30.2487i 0.696894 1.20705i
\(629\) −10.4449 −0.416464
\(630\) 0 0
\(631\) 48.7846 1.94208 0.971042 0.238908i \(-0.0767893\pi\)
0.971042 + 0.238908i \(0.0767893\pi\)
\(632\) 34.9808 60.5885i 1.39146 2.41008i
\(633\) −3.53590 6.12436i −0.140539 0.243421i
\(634\) −38.8564 67.3013i −1.54319 2.67287i
\(635\) 0 0
\(636\) −67.7128 −2.68499
\(637\) 12.4737 9.82051i 0.494227 0.389103i
\(638\) −8.39230 −0.332255
\(639\) −3.09808 + 5.36603i −0.122558 + 0.212277i
\(640\) 0 0
\(641\) −1.90192 3.29423i −0.0751215 0.130114i 0.826018 0.563644i \(-0.190601\pi\)
−0.901139 + 0.433530i \(0.857268\pi\)
\(642\) 3.00000 5.19615i 0.118401 0.205076i
\(643\) −4.51666 −0.178120 −0.0890599 0.996026i \(-0.528386\pi\)
−0.0890599 + 0.996026i \(0.528386\pi\)
\(644\) −22.3923 64.6410i −0.882380 2.54721i
\(645\) 0 0
\(646\) 19.9282 34.5167i 0.784065 1.35804i
\(647\) −13.9545 24.1699i −0.548607 0.950216i −0.998370 0.0570678i \(-0.981825\pi\)
0.449763 0.893148i \(-0.351508\pi\)
\(648\) −4.73205 8.19615i −0.185893 0.321975i
\(649\) 0.0717968 0.124356i 0.00281827 0.00488139i
\(650\) 0 0
\(651\) −1.20577 0.232051i −0.0472579 0.00909479i
\(652\) −119.426 −4.67707
\(653\) −22.2942 + 38.6147i −0.872441 + 1.51111i −0.0129762 + 0.999916i \(0.504131\pi\)
−0.859464 + 0.511196i \(0.829203\pi\)
\(654\) −15.0263 26.0263i −0.587574 1.01771i
\(655\) 0 0
\(656\) 5.46410 9.46410i 0.213337 0.369511i
\(657\) −12.6603 −0.493924
\(658\) 9.46410 10.9282i 0.368949 0.426026i
\(659\) 2.92820 0.114067 0.0570333 0.998372i \(-0.481836\pi\)
0.0570333 + 0.998372i \(0.481836\pi\)
\(660\) 0 0
\(661\) −5.23205 9.06218i −0.203503 0.352478i 0.746152 0.665776i \(-0.231899\pi\)
−0.949655 + 0.313298i \(0.898566\pi\)
\(662\) −11.0263 19.0981i −0.428549 0.742268i
\(663\) −3.70577 + 6.41858i −0.143920 + 0.249277i
\(664\) −143.138 −5.55485
\(665\) 0 0
\(666\) 8.73205 0.338360
\(667\) 9.92820 17.1962i 0.384422 0.665838i
\(668\) −48.2487 83.5692i −1.86680 3.23339i
\(669\) −10.1962 17.6603i −0.394206 0.682785i
\(670\) 0 0
\(671\) 2.92820 0.113042
\(672\) 56.7846 + 10.9282i 2.19051 + 0.421565i
\(673\) 27.3397 1.05387 0.526935 0.849906i \(-0.323341\pi\)
0.526935 + 0.849906i \(0.323341\pi\)
\(674\) 24.5622 42.5429i 0.946100 1.63869i
\(675\) 0 0
\(676\) 21.4641 + 37.1769i 0.825542 + 1.42988i
\(677\) −16.5622 + 28.6865i −0.636536 + 1.10251i 0.349651 + 0.936880i \(0.386300\pi\)
−0.986187 + 0.165633i \(0.947033\pi\)
\(678\) −24.3923 −0.936781
\(679\) 12.9282 + 37.3205i 0.496139 + 1.43223i
\(680\) 0 0
\(681\) −0.830127 + 1.43782i −0.0318105 + 0.0550975i
\(682\) 0.464102 + 0.803848i 0.0177714 + 0.0307809i
\(683\) −14.0263 24.2942i −0.536701 0.929593i −0.999079 0.0429101i \(-0.986337\pi\)
0.462378 0.886683i \(-0.346996\pi\)
\(684\) −12.1962 + 21.1244i −0.466332 + 0.807710i
\(685\) 0 0
\(686\) −44.9545 + 23.2224i −1.71637 + 0.886637i
\(687\) −3.00000 −0.114457
\(688\) 23.8564 41.3205i 0.909517 1.57533i
\(689\) −14.0526 24.3397i −0.535360 0.927270i
\(690\) 0 0
\(691\) −4.42820 + 7.66987i −0.168457 + 0.291776i −0.937877 0.346967i \(-0.887212\pi\)
0.769421 + 0.638742i \(0.220545\pi\)
\(692\) −79.4256 −3.01931
\(693\) −0.633975 1.83013i −0.0240827 0.0695208i
\(694\) 57.5692 2.18530
\(695\) 0 0
\(696\) 19.8564 + 34.3923i 0.752655 + 1.30364i
\(697\) −1.19615 2.07180i −0.0453075 0.0784749i
\(698\) −30.0526 + 52.0526i −1.13751 + 1.97022i
\(699\) −17.3205 −0.655122
\(700\) 0 0
\(701\) −8.58846 −0.324382 −0.162191 0.986759i \(-0.551856\pi\)
−0.162191 + 0.986759i \(0.551856\pi\)
\(702\) 3.09808 5.36603i 0.116929 0.202528i
\(703\) −7.13397 12.3564i −0.269063 0.466031i
\(704\) −10.9282 18.9282i −0.411872 0.713384i
\(705\) 0 0
\(706\) 8.53590 0.321253
\(707\) 12.5885 14.5359i 0.473438 0.546679i
\(708\) −1.07180 −0.0402806
\(709\) 0.535898 0.928203i 0.0201261 0.0348594i −0.855787 0.517328i \(-0.826927\pi\)
0.875913 + 0.482469i \(0.160260\pi\)
\(710\) 0 0
\(711\) 3.69615 + 6.40192i 0.138617 + 0.240091i
\(712\) −71.5692 + 123.962i −2.68217 + 4.64565i
\(713\) −2.19615 −0.0822466
\(714\) 15.4641 17.8564i 0.578729 0.668259i
\(715\) 0 0
\(716\) 27.3205 47.3205i 1.02102 1.76845i
\(717\) −3.53590 6.12436i −0.132051 0.228718i
\(718\) 1.73205 + 3.00000i 0.0646396 + 0.111959i
\(719\) 10.2679 17.7846i 0.382930 0.663254i −0.608550 0.793516i \(-0.708248\pi\)
0.991480 + 0.130262i \(0.0415817\pi\)
\(720\) 0 0
\(721\) 23.8923 + 4.59808i 0.889796 + 0.171241i
\(722\) 2.53590 0.0943764
\(723\) −6.73205 + 11.6603i −0.250368 + 0.433650i
\(724\) 66.4449 + 115.086i 2.46940 + 4.27713i
\(725\) 0 0
\(726\) 14.2942 24.7583i 0.530509 0.918868i
\(727\) 13.3397 0.494744 0.247372 0.968921i \(-0.420433\pi\)
0.247372 + 0.968921i \(0.420433\pi\)
\(728\) 18.5885 + 53.6603i 0.688934 + 1.98878i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −5.22243 9.04552i −0.193159 0.334561i
\(732\) −10.9282 18.9282i −0.403918 0.699607i
\(733\) −0.669873 + 1.16025i −0.0247423 + 0.0428550i −0.878131 0.478419i \(-0.841210\pi\)
0.853389 + 0.521274i \(0.174543\pi\)
\(734\) −30.5885 −1.12904
\(735\) 0 0
\(736\) 103.426 3.81232
\(737\) −5.36603 + 9.29423i −0.197660 + 0.342357i
\(738\) 1.00000 + 1.73205i 0.0368105 + 0.0637577i
\(739\) −13.8923 24.0622i −0.511037 0.885142i −0.999918 0.0127913i \(-0.995928\pi\)
0.488881 0.872350i \(-0.337405\pi\)
\(740\) 0 0
\(741\) −10.1244 −0.371927
\(742\) 29.3205 + 84.6410i 1.07639 + 3.10727i
\(743\) 15.9090 0.583643 0.291822 0.956473i \(-0.405739\pi\)
0.291822 + 0.956473i \(0.405739\pi\)
\(744\) 2.19615 3.80385i 0.0805149 0.139456i
\(745\) 0 0
\(746\) 36.2224 + 62.7391i 1.32620 + 2.29704i
\(747\) 7.56218 13.0981i 0.276686 0.479234i
\(748\) −13.0718 −0.477952
\(749\) −5.70577 1.09808i −0.208484 0.0401228i
\(750\) 0 0
\(751\) −9.03590 + 15.6506i −0.329725 + 0.571100i −0.982457 0.186489i \(-0.940289\pi\)
0.652732 + 0.757588i \(0.273623\pi\)
\(752\) 14.9282 + 25.8564i 0.544376 + 0.942886i
\(753\) 12.2942 + 21.2942i 0.448027 + 0.776005i
\(754\) −13.0000 + 22.5167i −0.473432 + 0.820008i
\(755\) 0 0
\(756\) −9.46410 + 10.9282i −0.344206 + 0.397455i
\(757\) 27.8564 1.01246 0.506229 0.862399i \(-0.331039\pi\)
0.506229 + 0.862399i \(0.331039\pi\)
\(758\) −8.63397 + 14.9545i −0.313600 + 0.543171i
\(759\) −1.73205 3.00000i −0.0628695 0.108893i
\(760\) 0 0
\(761\) −23.3660 + 40.4711i −0.847018 + 1.46708i 0.0368396 + 0.999321i \(0.488271\pi\)
−0.883857 + 0.467757i \(0.845062\pi\)
\(762\) −13.1244 −0.475445
\(763\) −19.0526 + 22.0000i −0.689749 + 0.796453i
\(764\) −48.7846 −1.76497
\(765\) 0 0
\(766\) −31.8564 55.1769i −1.15102 1.99362i
\(767\) −0.222432 0.385263i −0.00803155 0.0139111i
\(768\) −21.8564 + 37.8564i −0.788675 + 1.36603i
\(769\) 52.3205 1.88673 0.943363 0.331763i \(-0.107643\pi\)
0.943363 + 0.331763i \(0.107643\pi\)
\(770\) 0 0
\(771\) 5.66025 0.203849
\(772\) 3.26795 5.66025i 0.117616 0.203717i
\(773\) 21.7583 + 37.6865i 0.782593 + 1.35549i 0.930427 + 0.366478i \(0.119437\pi\)
−0.147834 + 0.989012i \(0.547230\pi\)
\(774\) 4.36603 + 7.56218i 0.156934 + 0.271817i
\(775\) 0 0
\(776\) −141.282 −5.07173
\(777\) −2.76795 7.99038i −0.0992996 0.286653i
\(778\) 14.7846 0.530054
\(779\) 1.63397 2.83013i 0.0585432 0.101400i
\(780\) 0 0
\(781\) −2.26795 3.92820i −0.0811536 0.140562i
\(782\) 21.1244 36.5885i 0.755405 1.30840i
\(783\) −4.19615 −0.149958