Properties

Label 105.2.i.d.46.2
Level $105$
Weight $2$
Character 105.46
Analytic conductor $0.838$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.838429221223\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 46.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 105.46
Dual form 105.2.i.d.16.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 + 2.36603i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.73205 + 4.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.73205 q^{6} +(0.866025 - 2.50000i) q^{7} -9.46410 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(1.36603 + 2.36603i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.73205 + 4.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +2.73205 q^{6} +(0.866025 - 2.50000i) q^{7} -9.46410 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.36603 - 2.36603i) q^{10} +(-0.366025 + 0.633975i) q^{11} +(2.73205 + 4.73205i) q^{12} +2.26795 q^{13} +(7.09808 - 1.36603i) q^{14} -1.00000 q^{15} +(-7.46410 - 12.9282i) q^{16} +(-1.63397 + 2.83013i) q^{17} +(1.36603 - 2.36603i) q^{18} +(-2.23205 - 3.86603i) q^{19} +5.46410 q^{20} +(-1.73205 - 2.00000i) q^{21} -2.00000 q^{22} +(2.36603 + 4.09808i) q^{23} +(-4.73205 + 8.19615i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.09808 + 5.36603i) q^{26} -1.00000 q^{27} +(9.46410 + 10.9282i) q^{28} -4.19615 q^{29} +(-1.36603 - 2.36603i) q^{30} +(0.232051 - 0.401924i) q^{31} +(10.9282 - 18.9282i) q^{32} +(0.366025 + 0.633975i) q^{33} -8.92820 q^{34} +(-2.59808 + 0.500000i) q^{35} +5.46410 q^{36} +(1.59808 + 2.76795i) q^{37} +(6.09808 - 10.5622i) q^{38} +(1.13397 - 1.96410i) q^{39} +(4.73205 + 8.19615i) q^{40} -0.732051 q^{41} +(2.36603 - 6.83013i) q^{42} +3.19615 q^{43} +(-2.00000 - 3.46410i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-6.46410 + 11.1962i) q^{46} +(-1.00000 - 1.73205i) q^{47} -14.9282 q^{48} +(-5.50000 - 4.33013i) q^{49} -2.73205 q^{50} +(1.63397 + 2.83013i) q^{51} +(-6.19615 + 10.7321i) q^{52} +(-6.19615 + 10.7321i) q^{53} +(-1.36603 - 2.36603i) q^{54} +0.732051 q^{55} +(-8.19615 + 23.6603i) q^{56} -4.46410 q^{57} +(-5.73205 - 9.92820i) q^{58} +(0.0980762 - 0.169873i) q^{59} +(2.73205 - 4.73205i) q^{60} +(-2.00000 - 3.46410i) q^{61} +1.26795 q^{62} +(-2.59808 + 0.500000i) q^{63} +29.8564 q^{64} +(-1.13397 - 1.96410i) q^{65} +(-1.00000 + 1.73205i) q^{66} +(7.33013 - 12.6962i) q^{67} +(-8.92820 - 15.4641i) q^{68} +4.73205 q^{69} +(-4.73205 - 5.46410i) q^{70} +6.19615 q^{71} +(4.73205 + 8.19615i) q^{72} +(-6.33013 + 10.9641i) q^{73} +(-4.36603 + 7.56218i) q^{74} +(0.500000 + 0.866025i) q^{75} +24.3923 q^{76} +(1.26795 + 1.46410i) q^{77} +6.19615 q^{78} +(3.69615 + 6.40192i) q^{79} +(-7.46410 + 12.9282i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +15.1244 q^{83} +(14.1962 - 2.73205i) q^{84} +3.26795 q^{85} +(4.36603 + 7.56218i) q^{86} +(-2.09808 + 3.63397i) q^{87} +(3.46410 - 6.00000i) q^{88} +(-7.56218 - 13.0981i) q^{89} -2.73205 q^{90} +(1.96410 - 5.66987i) q^{91} -25.8564 q^{92} +(-0.232051 - 0.401924i) q^{93} +(2.73205 - 4.73205i) q^{94} +(-2.23205 + 3.86603i) q^{95} +(-10.9282 - 18.9282i) q^{96} +14.9282 q^{97} +(2.73205 - 18.9282i) q^{98} +0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 2q^{3} - 4q^{4} - 2q^{5} + 4q^{6} - 24q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + 2q^{2} + 2q^{3} - 4q^{4} - 2q^{5} + 4q^{6} - 24q^{8} - 2q^{9} + 2q^{10} + 2q^{11} + 4q^{12} + 16q^{13} + 18q^{14} - 4q^{15} - 16q^{16} - 10q^{17} + 2q^{18} - 2q^{19} + 8q^{20} - 8q^{22} + 6q^{23} - 12q^{24} - 2q^{25} + 2q^{26} - 4q^{27} + 24q^{28} + 4q^{29} - 2q^{30} - 6q^{31} + 16q^{32} - 2q^{33} - 8q^{34} + 8q^{36} - 4q^{37} + 14q^{38} + 8q^{39} + 12q^{40} + 4q^{41} + 6q^{42} - 8q^{43} - 8q^{44} - 2q^{45} - 12q^{46} - 4q^{47} - 32q^{48} - 22q^{49} - 4q^{50} + 10q^{51} - 4q^{52} - 4q^{53} - 2q^{54} - 4q^{55} - 12q^{56} - 4q^{57} - 16q^{58} - 10q^{59} + 4q^{60} - 8q^{61} + 12q^{62} + 64q^{64} - 8q^{65} - 4q^{66} + 12q^{67} - 8q^{68} + 12q^{69} - 12q^{70} + 4q^{71} + 12q^{72} - 8q^{73} - 14q^{74} + 2q^{75} + 56q^{76} + 12q^{77} + 4q^{78} - 6q^{79} - 16q^{80} - 2q^{81} - 4q^{82} + 12q^{83} + 36q^{84} + 20q^{85} + 14q^{86} + 2q^{87} - 6q^{89} - 4q^{90} - 6q^{91} - 48q^{92} + 6q^{93} + 4q^{94} - 2q^{95} - 16q^{96} + 32q^{97} + 4q^{98} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 + 2.36603i 0.965926 + 1.67303i 0.707107 + 0.707107i \(0.250000\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −2.73205 + 4.73205i −1.36603 + 2.36603i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 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
\(10\) 1.36603 2.36603i 0.431975 0.748203i
\(11\) −0.366025 + 0.633975i −0.110361 + 0.191151i −0.915916 0.401371i \(-0.868534\pi\)
0.805555 + 0.592521i \(0.201867\pi\)
\(12\) 2.73205 + 4.73205i 0.788675 + 1.36603i
\(13\) 2.26795 0.629016 0.314508 0.949255i \(-0.398160\pi\)
0.314508 + 0.949255i \(0.398160\pi\)
\(14\) 7.09808 1.36603i 1.89704 0.365086i
\(15\) −1.00000 −0.258199
\(16\) −7.46410 12.9282i −1.86603 3.23205i
\(17\) −1.63397 + 2.83013i −0.396297 + 0.686407i −0.993266 0.115858i \(-0.963038\pi\)
0.596969 + 0.802264i \(0.296372\pi\)
\(18\) 1.36603 2.36603i 0.321975 0.557678i
\(19\) −2.23205 3.86603i −0.512068 0.886927i −0.999902 0.0139909i \(-0.995546\pi\)
0.487835 0.872936i \(-0.337787\pi\)
\(20\) 5.46410 1.22181
\(21\) −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 \(-0.00243871\pi\)
−0.506620 + 0.862169i \(0.669105\pi\)
\(24\) −4.73205 + 8.19615i −0.965926 + 1.67303i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 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 \(0.627388\pi\)
\(30\) −1.36603 2.36603i −0.249401 0.431975i
\(31\) 0.232051 0.401924i 0.0416776 0.0721876i −0.844434 0.535659i \(-0.820063\pi\)
0.886112 + 0.463472i \(0.153396\pi\)
\(32\) 10.9282 18.9282i 1.93185 3.34607i
\(33\) 0.366025 + 0.633975i 0.0637168 + 0.110361i
\(34\) −8.92820 −1.53117
\(35\) −2.59808 + 0.500000i −0.439155 + 0.0845154i
\(36\) 5.46410 0.910684
\(37\) 1.59808 + 2.76795i 0.262722 + 0.455048i 0.966964 0.254912i \(-0.0820464\pi\)
−0.704242 + 0.709960i \(0.748713\pi\)
\(38\) 6.09808 10.5622i 0.989239 1.71341i
\(39\) 1.13397 1.96410i 0.181581 0.314508i
\(40\) 4.73205 + 8.19615i 0.748203 + 1.29593i
\(41\) −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 \(-0.421637\pi\)
0.243704 + 0.969850i \(0.421637\pi\)
\(44\) −2.00000 3.46410i −0.301511 0.522233i
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) −6.46410 + 11.1962i −0.953080 + 1.65078i
\(47\) −1.00000 1.73205i −0.145865 0.252646i 0.783830 0.620975i \(-0.213263\pi\)
−0.929695 + 0.368329i \(0.879930\pi\)
\(48\) −14.9282 −2.15470
\(49\) −5.50000 4.33013i −0.785714 0.618590i
\(50\) −2.73205 −0.386370
\(51\) 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 0.0291032 + 0.999576i \(0.490735\pi\)
−0.880210 + 0.474584i \(0.842598\pi\)
\(54\) −1.36603 2.36603i −0.185893 0.321975i
\(55\) 0.732051 0.0987097
\(56\) −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 −0.859571 0.511017i \(-0.829269\pi\)
0.872339 + 0.488901i \(0.162602\pi\)
\(60\) 2.73205 4.73205i 0.352706 0.610905i
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 1.26795 0.161030
\(63\) −2.59808 + 0.500000i −0.327327 + 0.0629941i
\(64\) 29.8564 3.73205
\(65\) −1.13397 1.96410i −0.140652 0.243617i
\(66\) −1.00000 + 1.73205i −0.123091 + 0.213201i
\(67\) 7.33013 12.6962i 0.895518 1.55108i 0.0623548 0.998054i \(-0.480139\pi\)
0.833163 0.553028i \(-0.186528\pi\)
\(68\) −8.92820 15.4641i −1.08270 1.87530i
\(69\) 4.73205 0.569672
\(70\) −4.73205 5.46410i −0.565588 0.653085i
\(71\) 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 0.211207 + 0.977441i \(0.432260\pi\)
−0.952093 + 0.305810i \(0.901073\pi\)
\(74\) −4.36603 + 7.56218i −0.507540 + 0.879085i
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 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 0.995517 0.0945803i \(-0.0301509\pi\)
−0.579668 + 0.814853i \(0.696818\pi\)
\(80\) −7.46410 + 12.9282i −0.834512 + 1.44542i
\(81\) −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 \(-0.188308\pi\)
0.830057 + 0.557679i \(0.188308\pi\)
\(84\) 14.1962 2.73205i 1.54893 0.298091i
\(85\) 3.26795 0.354459
\(86\) 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 −0.918570 0.395259i \(-0.870655\pi\)
0.116980 0.993134i \(-0.462679\pi\)
\(90\) −2.73205 −0.287983
\(91\) 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
\(95\) −2.23205 + 3.86603i −0.229004 + 0.396646i
\(96\) −10.9282 18.9282i −1.11536 1.93185i
\(97\) 14.9282 1.51573 0.757865 0.652412i \(-0.226243\pi\)
0.757865 + 0.652412i \(0.226243\pi\)
\(98\) 2.73205 18.9282i 0.275979 1.91204i
\(99\) 0.732051 0.0735739
\(100\) −2.73205 4.73205i −0.273205 0.473205i
\(101\) 3.63397 6.29423i 0.361594 0.626299i −0.626629 0.779317i \(-0.715566\pi\)
0.988223 + 0.153018i \(0.0488993\pi\)
\(102\) −4.46410 + 7.73205i −0.442012 + 0.765587i
\(103\) 4.59808 + 7.96410i 0.453062 + 0.784726i 0.998574 0.0533764i \(-0.0169983\pi\)
−0.545513 + 0.838103i \(0.683665\pi\)
\(104\) −21.4641 −2.10473
\(105\) −0.866025 + 2.50000i −0.0845154 + 0.243975i
\(106\) −33.8564 −3.28842
\(107\) −1.09808 1.90192i −0.106155 0.183866i 0.808054 0.589108i \(-0.200521\pi\)
−0.914210 + 0.405242i \(0.867187\pi\)
\(108\) 2.73205 4.73205i 0.262892 0.455342i
\(109\) −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i \(0.343277\pi\)
−0.999512 + 0.0312328i \(0.990057\pi\)
\(110\) 1.00000 + 1.73205i 0.0953463 + 0.165145i
\(111\) 3.19615 0.303365
\(112\) −38.7846 + 7.46410i −3.66480 + 0.705291i
\(113\) 8.92820 0.839895 0.419947 0.907548i \(-0.362049\pi\)
0.419947 + 0.907548i \(0.362049\pi\)
\(114\) −6.09808 10.5622i −0.571137 0.989239i
\(115\) 2.36603 4.09808i 0.220633 0.382148i
\(116\) 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
\(120\) 9.46410 0.863950
\(121\) 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
\(125\) 1.00000 0.0894427
\(126\) −4.73205 5.46410i −0.421565 0.486781i
\(127\) 4.80385 0.426273 0.213136 0.977022i \(-0.431632\pi\)
0.213136 + 0.977022i \(0.431632\pi\)
\(128\) 18.9282 + 32.7846i 1.67303 + 2.89778i
\(129\) 1.59808 2.76795i 0.140703 0.243704i
\(130\) 3.09808 5.36603i 0.271719 0.470632i
\(131\) −7.73205 13.3923i −0.675552 1.17009i −0.976307 0.216390i \(-0.930572\pi\)
0.300755 0.953702i \(-0.402761\pi\)
\(132\) −4.00000 −0.348155
\(133\) −11.5981 + 2.23205i −1.00568 + 0.193543i
\(134\) 40.0526 3.46001
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 15.4641 26.7846i 1.32604 2.29676i
\(137\) −1.09808 + 1.90192i −0.0938150 + 0.162492i −0.909113 0.416549i \(-0.863240\pi\)
0.815298 + 0.579041i \(0.196573\pi\)
\(138\) 6.46410 + 11.1962i 0.550261 + 0.953080i
\(139\) 5.92820 0.502824 0.251412 0.967880i \(-0.419105\pi\)
0.251412 + 0.967880i \(0.419105\pi\)
\(140\) 4.73205 13.6603i 0.399931 1.15450i
\(141\) −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
\(145\) 2.09808 + 3.63397i 0.174236 + 0.301785i
\(146\) −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 0.720794 0.693149i \(-0.243777\pi\)
−0.960682 + 0.277651i \(0.910444\pi\)
\(150\) −1.36603 + 2.36603i −0.111536 + 0.193185i
\(151\) 4.46410 7.73205i 0.363283 0.629225i −0.625216 0.780452i \(-0.714989\pi\)
0.988499 + 0.151227i \(0.0483223\pi\)
\(152\) 21.1244 + 36.5885i 1.71341 + 2.96772i
\(153\) 3.26795 0.264198
\(154\) −1.73205 + 5.00000i −0.139573 + 0.402911i
\(155\) −0.464102 −0.0372775
\(156\) 6.19615 + 10.7321i 0.496089 + 0.859252i
\(157\) −3.19615 + 5.53590i −0.255081 + 0.441813i −0.964917 0.262553i \(-0.915435\pi\)
0.709837 + 0.704366i \(0.248769\pi\)
\(158\) −10.0981 + 17.4904i −0.803360 + 1.39146i
\(159\) 6.19615 + 10.7321i 0.491387 + 0.851107i
\(160\) −21.8564 −1.72790
\(161\) 12.2942 2.36603i 0.968921 0.186469i
\(162\) −2.73205 −0.214650
\(163\) −10.9282 18.9282i −0.855963 1.48257i −0.875749 0.482767i \(-0.839632\pi\)
0.0197859 0.999804i \(-0.493702\pi\)
\(164\) 2.00000 3.46410i 0.156174 0.270501i
\(165\) 0.366025 0.633975i 0.0284950 0.0493549i
\(166\) 20.6603 + 35.7846i 1.60355 + 2.77742i
\(167\) −17.6603 −1.36659 −0.683296 0.730142i \(-0.739454\pi\)
−0.683296 + 0.730142i \(0.739454\pi\)
\(168\) 16.3923 + 18.9282i 1.26469 + 1.46034i
\(169\) −7.85641 −0.604339
\(170\) 4.46410 + 7.73205i 0.342381 + 0.593021i
\(171\) −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 −0.998088 0.0618087i \(-0.980313\pi\)
0.445516 0.895274i \(-0.353020\pi\)
\(174\) −11.4641 −0.869091
\(175\) 1.73205 + 2.00000i 0.130931 + 0.151186i
\(176\) 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 −0.616417 0.787420i \(-0.711416\pi\)
0.990134 + 0.140122i \(0.0447496\pi\)
\(180\) −2.73205 4.73205i −0.203635 0.352706i
\(181\) −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
\(185\) 1.59808 2.76795i 0.117493 0.203504i
\(186\) 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
\(190\) −12.1962 −0.884802
\(191\) 4.46410 + 7.73205i 0.323011 + 0.559472i 0.981108 0.193462i \(-0.0619716\pi\)
−0.658097 + 0.752933i \(0.728638\pi\)
\(192\) 14.9282 25.8564i 1.07735 1.86603i
\(193\) −0.598076 + 1.03590i −0.0430505 + 0.0745656i −0.886748 0.462254i \(-0.847041\pi\)
0.843697 + 0.536819i \(0.180374\pi\)
\(194\) 20.3923 + 35.3205i 1.46408 + 2.53586i
\(195\) −2.26795 −0.162411
\(196\) 35.5167 14.1962i 2.53690 1.01401i
\(197\) −0.339746 −0.0242059 −0.0121029 0.999927i \(-0.503853\pi\)
−0.0121029 + 0.999927i \(0.503853\pi\)
\(198\) 1.00000 + 1.73205i 0.0710669 + 0.123091i
\(199\) −11.0000 + 19.0526i −0.779769 + 1.35060i 0.152305 + 0.988334i \(0.451330\pi\)
−0.932075 + 0.362267i \(0.882003\pi\)
\(200\) 4.73205 8.19615i 0.334607 0.579555i
\(201\) −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
\(205\) 0.366025 + 0.633975i 0.0255643 + 0.0442787i
\(206\) −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
\(210\) −7.09808 + 1.36603i −0.489814 + 0.0942647i
\(211\) 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
\(215\) −1.59808 2.76795i −0.108988 0.188773i
\(216\) 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
\(220\) −2.00000 + 3.46410i −0.134840 + 0.233550i
\(221\) −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 \(-0.739231\pi\)
−0.682785 + 0.730619i \(0.739231\pi\)
\(224\) −37.8564 43.7128i −2.52939 2.92069i
\(225\) 1.00000 0.0666667
\(226\) 12.1962 + 21.1244i 0.811276 + 1.40517i
\(227\) 0.830127 1.43782i 0.0550975 0.0954316i −0.837161 0.546956i \(-0.815786\pi\)
0.892259 + 0.451525i \(0.149120\pi\)
\(228\) 12.1962 21.1244i 0.807710 1.39899i
\(229\) 1.50000 + 2.59808i 0.0991228 + 0.171686i 0.911322 0.411695i \(-0.135063\pi\)
−0.812199 + 0.583380i \(0.801730\pi\)
\(230\) 12.9282 0.852460
\(231\) 1.90192 0.366025i 0.125137 0.0240827i
\(232\) 39.7128 2.60727
\(233\) −8.66025 15.0000i −0.567352 0.982683i −0.996827 0.0796037i \(-0.974635\pi\)
0.429474 0.903079i \(-0.358699\pi\)
\(234\) 3.09808 5.36603i 0.202528 0.350788i
\(235\) −1.00000 + 1.73205i −0.0652328 + 0.112987i
\(236\) 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 \(0.426547\pi\)
\(240\) 7.46410 + 12.9282i 0.481806 + 0.834512i
\(241\) −6.73205 + 11.6603i −0.433650 + 0.751103i −0.997184 0.0749893i \(-0.976108\pi\)
0.563535 + 0.826092i \(0.309441\pi\)
\(242\) −14.2942 + 24.7583i −0.918868 + 1.59153i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 21.8564 1.39921
\(245\) −1.00000 + 6.92820i −0.0638877 + 0.442627i
\(246\) −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
\(250\) 1.36603 + 2.36603i 0.0863950 + 0.149641i
\(251\) −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
\(255\) 1.63397 2.83013i 0.102323 0.177229i
\(256\) −21.8564 + 37.8564i −1.36603 + 2.36603i
\(257\) 2.83013 + 4.90192i 0.176538 + 0.305774i 0.940693 0.339260i \(-0.110177\pi\)
−0.764154 + 0.645034i \(0.776843\pi\)
\(258\) 8.73205 0.543634
\(259\) 8.30385 1.59808i 0.515976 0.0992996i
\(260\) 12.3923 0.768538
\(261\) 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 \(-0.916643\pi\)
0.707160 + 0.707053i \(0.249976\pi\)
\(264\) −3.46410 6.00000i −0.213201 0.369274i
\(265\) 12.3923 0.761253
\(266\) −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 −0.609208 0.793011i \(-0.708512\pi\)
0.991371 + 0.131084i \(0.0418457\pi\)
\(270\) −1.36603 + 2.36603i −0.0831337 + 0.143992i
\(271\) −1.53590 2.66025i −0.0932992 0.161599i 0.815598 0.578619i \(-0.196408\pi\)
−0.908897 + 0.417020i \(0.863075\pi\)
\(272\) 48.7846 2.95800
\(273\) −3.92820 4.53590i −0.237746 0.274525i
\(274\) −6.00000 −0.362473
\(275\) −0.366025 0.633975i −0.0220722 0.0382301i
\(276\) −12.9282 + 22.3923i −0.778186 + 1.34786i
\(277\) 7.33013 12.6962i 0.440425 0.762838i −0.557296 0.830314i \(-0.688161\pi\)
0.997721 + 0.0674759i \(0.0214946\pi\)
\(278\) 8.09808 + 14.0263i 0.485690 + 0.841240i
\(279\) −0.464102 −0.0277850
\(280\) 24.5885 4.73205i 1.46944 0.282794i
\(281\) 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 −0.245152 0.969485i \(-0.578838\pi\)
0.962174 0.272434i \(-0.0878287\pi\)
\(284\) −16.9282 + 29.3205i −1.00450 + 1.73985i
\(285\) 2.23205 + 3.86603i 0.132215 + 0.229004i
\(286\) −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
\(290\) −5.73205 + 9.92820i −0.336598 + 0.583004i
\(291\) 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 \(-0.313522\pi\)
0.552899 + 0.833248i \(0.313522\pi\)
\(294\) −15.0263 11.8301i −0.876350 0.689947i
\(295\) −0.196152 −0.0114204
\(296\) −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
\(300\) −5.46410 −0.315470
\(301\) 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
\(305\) −2.00000 + 3.46410i −0.114520 + 0.198354i
\(306\) 4.46410 + 7.73205i 0.255196 + 0.442012i
\(307\) −32.1244 −1.83343 −0.916717 0.399537i \(-0.869171\pi\)
−0.916717 + 0.399537i \(0.869171\pi\)
\(308\) −10.3923 + 2.00000i −0.592157 + 0.113961i
\(309\) 9.19615 0.523151
\(310\) −0.633975 1.09808i −0.0360073 0.0623665i
\(311\) −4.56218 + 7.90192i −0.258697 + 0.448077i −0.965893 0.258941i \(-0.916627\pi\)
0.707196 + 0.707018i \(0.249960\pi\)
\(312\) −10.7321 + 18.5885i −0.607583 + 1.05236i
\(313\) 6.33013 + 10.9641i 0.357800 + 0.619728i 0.987593 0.157035i \(-0.0501936\pi\)
−0.629793 + 0.776763i \(0.716860\pi\)
\(314\) −17.4641 −0.985556
\(315\) 1.73205 + 2.00000i 0.0975900 + 0.112687i
\(316\) −40.3923 −2.27224
\(317\) 14.2224 + 24.6340i 0.798811 + 1.38358i 0.920391 + 0.391000i \(0.127871\pi\)
−0.121579 + 0.992582i \(0.538796\pi\)
\(318\) −16.9282 + 29.3205i −0.949286 + 1.64421i
\(319\) 1.53590 2.66025i 0.0859938 0.148946i
\(320\) −14.9282 25.8564i −0.834512 1.44542i
\(321\) −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
\(325\) −1.13397 + 1.96410i −0.0629016 + 0.108949i
\(326\) 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
\(330\) 2.00000 0.110096
\(331\) −4.03590 6.99038i −0.221833 0.384226i 0.733532 0.679655i \(-0.237871\pi\)
−0.955365 + 0.295429i \(0.904537\pi\)
\(332\) −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
\(335\) −14.6603 −0.800975
\(336\) −12.9282 + 37.3205i −0.705291 + 2.03600i
\(337\) 17.9808 0.979475 0.489737 0.871870i \(-0.337093\pi\)
0.489737 + 0.871870i \(0.337093\pi\)
\(338\) −10.7321 18.5885i −0.583747 1.01108i
\(339\) 4.46410 7.73205i 0.242457 0.419947i
\(340\) −8.92820 + 15.4641i −0.484200 + 0.838659i
\(341\) 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
\(345\) −2.36603 4.09808i −0.127383 0.220633i
\(346\) 19.8564 34.3923i 1.06749 1.84894i
\(347\) 10.5359 18.2487i 0.565597 0.979642i −0.431397 0.902162i \(-0.641979\pi\)
0.996994 0.0774801i \(-0.0246874\pi\)
\(348\) −11.4641 19.8564i −0.614540 1.06442i
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) −2.36603 + 6.83013i −0.126469 + 0.365086i
\(351\) −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 \(-0.806836\pi\)
0.904600 + 0.426262i \(0.140170\pi\)
\(354\) 0.267949 0.464102i 0.0142413 0.0246667i
\(355\) −3.09808 5.36603i −0.164429 0.284799i
\(356\) 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 0.882270 0.470743i \(-0.156014\pi\)
−0.848811 + 0.528697i \(0.822681\pi\)
\(360\) 4.73205 8.19615i 0.249401 0.431975i
\(361\) −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
\(365\) 12.6603 0.662668
\(366\) −5.46410 9.46410i −0.285613 0.494697i
\(367\) −5.59808 + 9.69615i −0.292217 + 0.506135i −0.974334 0.225108i \(-0.927726\pi\)
0.682117 + 0.731244i \(0.261060\pi\)
\(368\) 35.3205 61.1769i 1.84121 3.18907i
\(369\) 0.366025 + 0.633975i 0.0190545 + 0.0330034i
\(370\) 8.73205 0.453958
\(371\) 21.4641 + 24.7846i 1.11436 + 1.28675i
\(372\) 2.53590 0.131480
\(373\) −13.2583 22.9641i −0.686490 1.18904i −0.972966 0.230949i \(-0.925817\pi\)
0.286476 0.958088i \(-0.407516\pi\)
\(374\) 3.26795 5.66025i 0.168982 0.292685i
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 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 \(0.448099\pi\)
\(380\) −12.1962 21.1244i −0.625649 1.08366i
\(381\) 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 0.993432 + 0.114425i \(0.0365027\pi\)
−0.397621 + 0.917550i \(0.630164\pi\)
\(384\) 37.8564 1.93185
\(385\) 0.633975 1.83013i 0.0323103 0.0932719i
\(386\) −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 −0.926431 0.376464i \(-0.877140\pi\)
0.789243 + 0.614081i \(0.210473\pi\)
\(390\) −3.09808 5.36603i −0.156877 0.271719i
\(391\) −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
\(395\) 3.69615 6.40192i 0.185974 0.322116i
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) 15.5981 + 27.0167i 0.782845 + 1.35593i 0.930278 + 0.366855i \(0.119566\pi\)
−0.147433 + 0.989072i \(0.547101\pi\)
\(398\) −60.1051 −3.01280
\(399\) −3.86603 + 11.1603i −0.193543 + 0.558712i
\(400\) 14.9282 0.746410
\(401\) 8.19615 + 14.1962i 0.409296 + 0.708922i 0.994811 0.101740i \(-0.0324409\pi\)
−0.585515 + 0.810662i \(0.699108\pi\)
\(402\) 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
\(405\) 1.00000 0.0496904
\(406\) −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 −0.902266 0.431180i \(-0.858097\pi\)
0.824546 + 0.565795i \(0.191431\pi\)
\(410\) −1.00000 + 1.73205i −0.0493865 + 0.0855399i
\(411\) 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
\(415\) −7.56218 13.0981i −0.371213 0.642959i
\(416\) 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 \(0.833487\pi\)
\(420\) −9.46410 10.9282i −0.461801 0.533242i
\(421\) 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
\(425\) −1.63397 2.83013i −0.0792594 0.137281i
\(426\) 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
\(430\) 4.36603 7.56218i 0.210548 0.364681i
\(431\) −8.66025 + 15.0000i −0.417150 + 0.722525i −0.995651 0.0931566i \(-0.970304\pi\)
0.578502 + 0.815681i \(0.303638\pi\)
\(432\) 7.46410 + 12.9282i 0.359117 + 0.622008i
\(433\) 15.1962 0.730280 0.365140 0.930953i \(-0.381021\pi\)
0.365140 + 0.930953i \(0.381021\pi\)
\(434\) 1.09808 3.16987i 0.0527093 0.152159i
\(435\) 4.19615 0.201190
\(436\) −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 0.859560 0.511034i \(-0.170737\pi\)
−0.872349 + 0.488884i \(0.837404\pi\)
\(440\) −6.92820 −0.330289
\(441\) −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 \(-0.238848\pi\)
−0.956267 + 0.292494i \(0.905515\pi\)
\(444\) −8.73205 + 15.1244i −0.414405 + 0.717770i
\(445\) −7.56218 + 13.0981i −0.358482 + 0.620908i
\(446\) −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 \(0.821046\pi\)
\(450\) 1.36603 + 2.36603i 0.0643951 + 0.111536i
\(451\) 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
\(455\) −5.89230 + 1.13397i −0.276236 + 0.0531615i
\(456\) 42.2487 1.97848
\(457\) 8.33013 + 14.4282i 0.389667 + 0.674923i 0.992405 0.123016i \(-0.0392568\pi\)
−0.602738 + 0.797939i \(0.705923\pi\)
\(458\) −4.09808 + 7.09808i −0.191491 + 0.331671i
\(459\) 1.63397 2.83013i 0.0762674 0.132099i
\(460\) 12.9282 + 22.3923i 0.602781 + 1.04405i
\(461\) 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 \(-0.295988\pi\)
0.597935 + 0.801545i \(0.295988\pi\)
\(464\) 31.3205 + 54.2487i 1.45402 + 2.51843i
\(465\) −0.232051 + 0.401924i −0.0107611 + 0.0186388i
\(466\) 23.6603 40.9808i 1.09604 1.89840i
\(467\) 0.0717968 + 0.124356i 0.00332236 + 0.00575449i 0.867682 0.497120i \(-0.165609\pi\)
−0.864359 + 0.502874i \(0.832276\pi\)
\(468\) 12.3923 0.572834
\(469\) −25.3923 29.3205i −1.17251 1.35390i
\(470\) −5.46410 −0.252040
\(471\) 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
\(475\) 4.46410 0.204827
\(476\) −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 −0.948751 0.316025i \(-0.897652\pi\)
0.748061 + 0.663630i \(0.230985\pi\)
\(480\) −10.9282 + 18.9282i −0.498802 + 0.863950i
\(481\) 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
\(485\) −7.46410 12.9282i −0.338927 0.587039i
\(486\) −1.36603 + 2.36603i −0.0619642 + 0.107325i
\(487\) 0.205771 0.356406i 0.00932439 0.0161503i −0.861326 0.508053i \(-0.830365\pi\)
0.870650 + 0.491903i \(0.163699\pi\)
\(488\) 18.9282 + 32.7846i 0.856840 + 1.48409i
\(489\) −21.8564 −0.988381
\(490\) −17.7583 + 7.09808i −0.802240 + 0.320658i
\(491\) −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
\(495\) −0.366025 0.633975i −0.0164516 0.0284950i
\(496\) −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 0.976808 0.214115i \(-0.0686868\pi\)
−0.673833 + 0.738883i \(0.735353\pi\)
\(500\) −2.73205 + 4.73205i −0.122181 + 0.211624i
\(501\) −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 \(-0.396028\pi\)
0.320861 + 0.947126i \(0.396028\pi\)
\(504\) 24.5885 4.73205i 1.09526 0.210782i
\(505\) −7.26795 −0.323419
\(506\) −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 0.811376 0.584525i \(-0.198719\pi\)
−0.911901 + 0.410410i \(0.865386\pi\)
\(510\) 8.92820 0.395347
\(511\) 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
\(515\) 4.59808 7.96410i 0.202615 0.350940i
\(516\) 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
\(520\) 10.7321 + 18.5885i 0.470632 + 0.815158i
\(521\) 2.73205 4.73205i 0.119693 0.207315i −0.799953 0.600063i \(-0.795142\pi\)
0.919646 + 0.392748i \(0.128476\pi\)
\(522\) −5.73205 + 9.92820i −0.250885 + 0.434546i
\(523\) 13.8660 + 24.0167i 0.606319 + 1.05018i 0.991842 + 0.127477i \(0.0406878\pi\)
−0.385523 + 0.922698i \(0.625979\pi\)
\(524\) 84.4974 3.69129
\(525\) 2.59808 0.500000i 0.113389 0.0218218i
\(526\) −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
\(530\) 16.9282 + 29.3205i 0.735314 + 1.27360i
\(531\) −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
\(535\) −1.09808 + 1.90192i −0.0474740 + 0.0822273i
\(536\) −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
\(540\) −5.46410 −0.235137
\(541\) −2.89230 5.00962i −0.124350 0.215380i 0.797129 0.603809i \(-0.206351\pi\)
−0.921479 + 0.388429i \(0.873018\pi\)
\(542\) 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
\(545\) 11.0000 0.471188
\(546\) 5.36603 15.4904i 0.229645 0.662927i
\(547\) −26.2487 −1.12231 −0.561157 0.827709i \(-0.689644\pi\)
−0.561157 + 0.827709i \(0.689644\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) −2.00000 + 3.46410i −0.0853579 + 0.147844i
\(550\) 1.00000 1.73205i 0.0426401 0.0738549i
\(551\) 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
\(555\) −1.59808 2.76795i −0.0678346 0.117493i
\(556\) −16.1962 + 28.0526i −0.686870 + 1.18969i
\(557\) −7.39230 + 12.8038i −0.313222 + 0.542516i −0.979058 0.203582i \(-0.934742\pi\)
0.665836 + 0.746098i \(0.268075\pi\)
\(558\) −0.633975 1.09808i −0.0268383 0.0464853i
\(559\) 7.24871 0.306588
\(560\) 25.8564 + 29.8564i 1.09263 + 1.26166i
\(561\) −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 \(-0.709497\pi\)
0.990961 + 0.134148i \(0.0428299\pi\)
\(564\) 5.46410 9.46410i 0.230080 0.398511i
\(565\) −4.46410 7.73205i −0.187806 0.325290i
\(566\) 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 −0.974956 0.222397i \(-0.928612\pi\)
0.294876 0.955535i \(-0.404722\pi\)
\(570\) −6.09808 + 10.5622i −0.255420 + 0.442401i
\(571\) −9.30385 + 16.1147i −0.389354 + 0.674381i −0.992363 0.123354i \(-0.960635\pi\)
0.603009 + 0.797734i \(0.293968\pi\)
\(572\) −4.53590 7.85641i −0.189655 0.328493i
\(573\) 8.92820 0.372981
\(574\) −5.19615 + 1.00000i −0.216883 + 0.0417392i
\(575\) −4.73205 −0.197340
\(576\) −14.9282 25.8564i −0.622008 1.07735i
\(577\) −14.3301 + 24.8205i −0.596571 + 1.03329i 0.396752 + 0.917926i \(0.370137\pi\)
−0.993323 + 0.115365i \(0.963196\pi\)
\(578\) −8.63397 + 14.9545i −0.359126 + 0.622024i
\(579\) 0.598076 + 1.03590i 0.0248552 + 0.0430505i
\(580\) −22.9282 −0.952042
\(581\) 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
\(585\) −1.13397 + 1.96410i −0.0468841 + 0.0812056i
\(586\) 25.8564 + 44.7846i 1.06812 + 1.85004i
\(587\) 40.7321 1.68119 0.840596 0.541663i \(-0.182205\pi\)
0.840596 + 0.541663i \(0.182205\pi\)
\(588\) 5.46410 37.8564i 0.225336 1.56117i
\(589\) −2.07180 −0.0853669
\(590\) −0.267949 0.464102i −0.0110313 0.0191068i
\(591\) −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 −0.996251 0.0865058i \(-0.972430\pi\)
0.423209 0.906032i \(-0.360903\pi\)
\(594\) 2.00000 0.0820610
\(595\) 2.83013 8.16987i 0.116024 0.334932i
\(596\) 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 −0.149726 0.988727i \(-0.547839\pi\)
0.931126 0.364697i \(-0.118827\pi\)
\(600\) −4.73205 8.19615i −0.193185 0.334607i
\(601\) −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
\(605\) 5.23205 9.06218i 0.212713 0.368430i
\(606\) 9.92820 17.1962i 0.403306 0.698546i
\(607\) −1.59808 2.76795i −0.0648639 0.112348i 0.831770 0.555121i \(-0.187328\pi\)
−0.896634 + 0.442773i \(0.853995\pi\)
\(608\) −97.5692 −3.95695
\(609\) 7.26795 + 8.39230i 0.294512 + 0.340073i
\(610\) −10.9282 −0.442470
\(611\) −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 −0.454871 0.890557i \(-0.650315\pi\)
0.998681 0.0513490i \(-0.0163521\pi\)
\(614\) −43.8827 76.0070i −1.77096 3.06739i
\(615\) 0.732051 0.0295191
\(616\) −12.0000 13.8564i −0.483494 0.558291i
\(617\) −36.2487 −1.45932 −0.729659 0.683811i \(-0.760321\pi\)
−0.729659 + 0.683811i \(0.760321\pi\)
\(618\) 12.5622 + 21.7583i 0.505325 + 0.875248i
\(619\) 15.0359 26.0429i 0.604344 1.04675i −0.387811 0.921739i \(-0.626769\pi\)
0.992155 0.125015i \(-0.0398980\pi\)
\(620\) 1.26795 2.19615i 0.0509221 0.0881996i
\(621\) −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
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −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
\(630\) −2.36603 + 6.83013i −0.0942647 + 0.272119i
\(631\) 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
\(635\) −2.40192 4.16025i −0.0953174 0.165095i
\(636\) −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
\(640\) 18.9282 32.7846i 0.748203 1.29593i
\(641\) −1.90192 + 3.29423i −0.0751215 + 0.130114i −0.901139 0.433530i \(-0.857268\pi\)
0.826018 + 0.563644i \(0.190601\pi\)
\(642\) −3.00000 5.19615i −0.118401 0.205076i
\(643\) 4.51666 0.178120 0.0890599 0.996026i \(-0.471614\pi\)
0.0890599 + 0.996026i \(0.471614\pi\)
\(644\) −22.3923 + 64.6410i −0.882380 + 2.54721i
\(645\) −3.19615 −0.125848
\(646\) 19.9282 + 34.5167i 0.784065 + 1.35804i
\(647\) 13.9545 24.1699i 0.548607 0.950216i −0.449763 0.893148i \(-0.648492\pi\)
0.998370 0.0570678i \(-0.0181751\pi\)
\(648\) 4.73205 8.19615i 0.185893 0.321975i
\(649\) 0.0717968 + 0.124356i 0.00281827 + 0.00488139i
\(650\) −6.19615 −0.243033
\(651\) −1.20577 + 0.232051i −0.0472579 + 0.00909479i
\(652\) 119.426 4.67707
\(653\) 22.2942 + 38.6147i 0.872441 + 1.51111i 0.859464 + 0.511196i \(0.170797\pi\)
0.0129762 + 0.999916i \(0.495869\pi\)
\(654\) −15.0263 + 26.0263i −0.587574 + 1.01771i
\(655\) −7.73205 + 13.3923i −0.302116 + 0.523281i
\(656\) 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 \(0.481836\pi\)
\(660\) 2.00000 + 3.46410i 0.0778499 + 0.134840i
\(661\) −5.23205 + 9.06218i −0.203503 + 0.352478i −0.949655 0.313298i \(-0.898566\pi\)
0.746152 + 0.665776i \(0.231899\pi\)
\(662\) 11.0263 19.0981i 0.428549 0.742268i
\(663\) 3.70577 + 6.41858i 0.143920 + 0.249277i
\(664\) −143.138 −5.55485
\(665\) 7.73205 + 8.92820i 0.299836 + 0.346221i
\(666\) 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
\(670\) −20.0263 34.6865i −0.773683 1.34006i
\(671\) 2.92820 0.113042
\(672\) −56.7846 + 10.9282i −2.19051 + 0.421565i
\(673\) −27.3397 −1.05387 −0.526935 0.849906i \(-0.676659\pi\)
−0.526935 + 0.849906i \(0.676659\pi\)
\(674\) 24.5622 + 42.5429i 0.946100 + 1.63869i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 21.4641 37.1769i 0.825542 1.42988i
\(677\) 16.5622 + 28.6865i 0.636536 + 1.10251i 0.986187 + 0.165633i \(0.0529668\pi\)
−0.349651 + 0.936880i \(0.613700\pi\)
\(678\) 24.3923 0.936781
\(679\) 12.9282 37.3205i 0.496139 1.43223i
\(680\) −30.9282 −1.18604
\(681\) −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 −0.462378 0.886683i \(-0.653004\pi\)
0.999079 0.0429101i \(-0.0136629\pi\)
\(684\) −12.1962 21.1244i −0.466332 0.807710i
\(685\) 2.19615 0.0839107
\(686\) −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
\(690\) 6.46410 11.1962i 0.246084 0.426230i
\(691\) −4.42820 7.66987i −0.168457 0.291776i 0.769421 0.638742i \(-0.220545\pi\)
−0.937877 + 0.346967i \(0.887212\pi\)
\(692\) 79.4256 3.01931
\(693\) 0.633975 1.83013i 0.0240827 0.0695208i
\(694\) 57.5692 2.18530
\(695\) −2.96410 5.13397i −0.112435 0.194743i
\(696\) 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
\(700\) −14.1962 + 2.73205i −0.536564 + 0.103262i
\(701\) −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
\(705\) 1.00000 + 1.73205i 0.0376622 + 0.0652328i
\(706\) 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 0.875913 0.482469i \(-0.160260\pi\)
−0.855787 + 0.517328i \(0.826927\pi\)
\(710\) 8.46410 14.6603i 0.317652 0.550190i
\(711\) 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
\(715\) 1.66025 0.0620900
\(716\) 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 0.991480 0.130262i \(-0.0415817\pi\)
−0.608550 + 0.793516i \(0.708248\pi\)
\(720\) 14.9282 0.556341
\(721\) 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
\(725\) 2.09808 3.63397i 0.0779206 0.134962i
\(726\) 14.2942 + 24.7583i 0.530509 + 0.918868i
\(727\) −13.3397 −0.494744 −0.247372 0.968921i \(-0.579567\pi\)
−0.247372 + 0.968921i \(0.579567\pi\)
\(728\) −18.5885 + 53.6603i −0.688934 + 1.98878i
\(729\) 1.00000 0.0370370
\(730\) 17.2942 + 29.9545i 0.640088 + 1.10867i
\(731\) −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 \(-0.158790\pi\)
−0.853389 + 0.521274i \(0.825457\pi\)
\(734\) −30.5885 −1.12904
\(735\) 5.50000 + 4.33013i 0.202871 + 0.159719i
\(736\) 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 0.488881 + 0.872350i \(0.337405\pi\)
−0.999918 + 0.0127913i \(0.995928\pi\)
\(740\) 8.73205 + 15.1244i 0.320997 + 0.555982i
\(741\) −10.1244 −0.371927
\(742\) −29.3205 + 84.6410i −1.07639 + 3.10727i
\(743\) −15.9090 −0.583643 −0.291822 0.956473i \(-0.594261\pi\)
−0.291822 + 0.956473i \(0.594261\pi\)
\(744\) 2.19615 + 3.80385i 0.0805149 + 0.139456i
\(745\) −2.92820 + 5.07180i −0.107281 + 0.185816i
\(746\) 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
\(750\) 2.73205 0.0997604
\(751\) −9.03590 15.6506i −0.329725 0.571100i 0.652732 0.757588i \(-0.273623\pi\)
−0.982457 + 0.186489i \(0.940289\pi\)
\(752\) −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
\(755\) −8.92820 −0.324931
\(756\) −9.46410 10.9282i −0.344206 0.397455i
\(757\) −27.8564 −1.01246 −0.506229 0.862399i \(-0.668961\pi\)
−0.506229 + 0.862399i \(0.668961\pi\)
\(758\) 8.63397 + 14.9545i 0.313600 + 0.543171i
\(759\) −1.73205 + 3.00000i −0.0628695 + 0.108893i
\(760\) 21.1244 36.5885i 0.766261 1.32720i
\(761\) −23.3660 40.4711i −0.847018 1.46708i −0.883857 0.467757i \(-0.845062\pi\)
0.0368396 0.999321i \(-0.488271\pi\)
\(762\) 13.1244 0.475445
\(763\) 19.0526 + 22.0000i 0.689749 + 0.796453i
\(764\) −48.7846 −1.76497
\(765\) −1.63397 2.83013i −0.0590765 0.102323i
\(766\) −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 \(0.107643\pi\)
\(770\) 5.19615 1.00000i 0.187256 0.0360375i
\(771\) 5.66025 0.203849
\(772\) −3.26795 5.66025i −0.117616 0.203717i
\(773\) −21.7583 + 37.6865i −0.782593 + 1.35549i 0.147834 + 0.989012i \(0.452770\pi\)
−0.930427 + 0.366478i \(0.880563\pi\)
\(774\) 4.36603 7.56218i 0.156934 0.271817i
\(775\) 0.232051 + 0.401924i 0.00833551 + 0.0144375i
\(776\) −141.282