Properties

Label 546.2.c.e.337.1
Level $546$
Weight $2$
Character 546.337
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{17})\)
Defining polynomial: \(x^{4} + 9 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 337.1
Root \(-2.56155i\) of defining polynomial
Character \(\chi\) \(=\) 546.337
Dual form 546.2.c.e.337.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.56155i q^{5} +1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -3.56155i q^{5} +1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} -3.56155 q^{10} -5.56155i q^{11} +1.00000 q^{12} +(3.56155 + 0.561553i) q^{13} +1.00000 q^{14} +3.56155i q^{15} +1.00000 q^{16} -6.68466 q^{17} -1.00000i q^{18} +1.56155i q^{19} +3.56155i q^{20} -1.00000i q^{21} -5.56155 q^{22} -6.68466 q^{23} -1.00000i q^{24} -7.68466 q^{25} +(0.561553 - 3.56155i) q^{26} -1.00000 q^{27} -1.00000i q^{28} +1.56155 q^{29} +3.56155 q^{30} +6.24621i q^{31} -1.00000i q^{32} +5.56155i q^{33} +6.68466i q^{34} +3.56155 q^{35} -1.00000 q^{36} -10.6847i q^{37} +1.56155 q^{38} +(-3.56155 - 0.561553i) q^{39} +3.56155 q^{40} -4.00000i q^{41} -1.00000 q^{42} -6.43845 q^{43} +5.56155i q^{44} -3.56155i q^{45} +6.68466i q^{46} +10.2462i q^{47} -1.00000 q^{48} -1.00000 q^{49} +7.68466i q^{50} +6.68466 q^{51} +(-3.56155 - 0.561553i) q^{52} +4.87689 q^{53} +1.00000i q^{54} -19.8078 q^{55} -1.00000 q^{56} -1.56155i q^{57} -1.56155i q^{58} -4.24621i q^{59} -3.56155i q^{60} -1.56155 q^{61} +6.24621 q^{62} +1.00000i q^{63} -1.00000 q^{64} +(2.00000 - 12.6847i) q^{65} +5.56155 q^{66} +1.12311i q^{67} +6.68466 q^{68} +6.68466 q^{69} -3.56155i q^{70} -9.36932i q^{71} +1.00000i q^{72} -11.5616i q^{73} -10.6847 q^{74} +7.68466 q^{75} -1.56155i q^{76} +5.56155 q^{77} +(-0.561553 + 3.56155i) q^{78} +16.0000 q^{79} -3.56155i q^{80} +1.00000 q^{81} -4.00000 q^{82} +2.00000i q^{83} +1.00000i q^{84} +23.8078i q^{85} +6.43845i q^{86} -1.56155 q^{87} +5.56155 q^{88} +8.00000i q^{89} -3.56155 q^{90} +(-0.561553 + 3.56155i) q^{91} +6.68466 q^{92} -6.24621i q^{93} +10.2462 q^{94} +5.56155 q^{95} +1.00000i q^{96} -10.0000i q^{97} +1.00000i q^{98} -5.56155i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{3} - 4q^{4} + 4q^{9} + O(q^{10}) \) \( 4q - 4q^{3} - 4q^{4} + 4q^{9} - 6q^{10} + 4q^{12} + 6q^{13} + 4q^{14} + 4q^{16} - 2q^{17} - 14q^{22} - 2q^{23} - 6q^{25} - 6q^{26} - 4q^{27} - 2q^{29} + 6q^{30} + 6q^{35} - 4q^{36} - 2q^{38} - 6q^{39} + 6q^{40} - 4q^{42} - 34q^{43} - 4q^{48} - 4q^{49} + 2q^{51} - 6q^{52} + 36q^{53} - 38q^{55} - 4q^{56} + 2q^{61} - 8q^{62} - 4q^{64} + 8q^{65} + 14q^{66} + 2q^{68} + 2q^{69} - 18q^{74} + 6q^{75} + 14q^{77} + 6q^{78} + 64q^{79} + 4q^{81} - 16q^{82} + 2q^{87} + 14q^{88} - 6q^{90} + 6q^{91} + 2q^{92} + 8q^{94} + 14q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.00000 −0.577350
\(4\) −1.00000 −0.500000
\(5\) 3.56155i 1.59277i −0.604787 0.796387i \(-0.706742\pi\)
0.604787 0.796387i \(-0.293258\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 1.00000i 0.377964i
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 0.333333
\(10\) −3.56155 −1.12626
\(11\) 5.56155i 1.67687i −0.545001 0.838436i \(-0.683471\pi\)
0.545001 0.838436i \(-0.316529\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.56155 + 0.561553i 0.987797 + 0.155747i
\(14\) 1.00000 0.267261
\(15\) 3.56155i 0.919589i
\(16\) 1.00000 0.250000
\(17\) −6.68466 −1.62127 −0.810634 0.585553i \(-0.800877\pi\)
−0.810634 + 0.585553i \(0.800877\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.56155i 0.358245i 0.983827 + 0.179122i \(0.0573258\pi\)
−0.983827 + 0.179122i \(0.942674\pi\)
\(20\) 3.56155i 0.796387i
\(21\) 1.00000i 0.218218i
\(22\) −5.56155 −1.18573
\(23\) −6.68466 −1.39385 −0.696924 0.717145i \(-0.745448\pi\)
−0.696924 + 0.717145i \(0.745448\pi\)
\(24\) 1.00000i 0.204124i
\(25\) −7.68466 −1.53693
\(26\) 0.561553 3.56155i 0.110130 0.698478i
\(27\) −1.00000 −0.192450
\(28\) 1.00000i 0.188982i
\(29\) 1.56155 0.289973 0.144987 0.989434i \(-0.453686\pi\)
0.144987 + 0.989434i \(0.453686\pi\)
\(30\) 3.56155 0.650248
\(31\) 6.24621i 1.12185i 0.827866 + 0.560926i \(0.189555\pi\)
−0.827866 + 0.560926i \(0.810445\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 5.56155i 0.968142i
\(34\) 6.68466i 1.14641i
\(35\) 3.56155 0.602012
\(36\) −1.00000 −0.166667
\(37\) 10.6847i 1.75655i −0.478159 0.878274i \(-0.658696\pi\)
0.478159 0.878274i \(-0.341304\pi\)
\(38\) 1.56155 0.253317
\(39\) −3.56155 0.561553i −0.570305 0.0899204i
\(40\) 3.56155 0.563131
\(41\) 4.00000i 0.624695i −0.949968 0.312348i \(-0.898885\pi\)
0.949968 0.312348i \(-0.101115\pi\)
\(42\) −1.00000 −0.154303
\(43\) −6.43845 −0.981854 −0.490927 0.871201i \(-0.663342\pi\)
−0.490927 + 0.871201i \(0.663342\pi\)
\(44\) 5.56155i 0.838436i
\(45\) 3.56155i 0.530925i
\(46\) 6.68466i 0.985599i
\(47\) 10.2462i 1.49456i 0.664507 + 0.747282i \(0.268641\pi\)
−0.664507 + 0.747282i \(0.731359\pi\)
\(48\) −1.00000 −0.144338
\(49\) −1.00000 −0.142857
\(50\) 7.68466i 1.08677i
\(51\) 6.68466 0.936039
\(52\) −3.56155 0.561553i −0.493899 0.0778734i
\(53\) 4.87689 0.669893 0.334946 0.942237i \(-0.391282\pi\)
0.334946 + 0.942237i \(0.391282\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −19.8078 −2.67088
\(56\) −1.00000 −0.133631
\(57\) 1.56155i 0.206833i
\(58\) 1.56155i 0.205042i
\(59\) 4.24621i 0.552810i −0.961041 0.276405i \(-0.910857\pi\)
0.961041 0.276405i \(-0.0891431\pi\)
\(60\) 3.56155i 0.459794i
\(61\) −1.56155 −0.199936 −0.0999682 0.994991i \(-0.531874\pi\)
−0.0999682 + 0.994991i \(0.531874\pi\)
\(62\) 6.24621 0.793270
\(63\) 1.00000i 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 2.00000 12.6847i 0.248069 1.57334i
\(66\) 5.56155 0.684580
\(67\) 1.12311i 0.137209i 0.997644 + 0.0686046i \(0.0218547\pi\)
−0.997644 + 0.0686046i \(0.978145\pi\)
\(68\) 6.68466 0.810634
\(69\) 6.68466 0.804738
\(70\) 3.56155i 0.425687i
\(71\) 9.36932i 1.11193i −0.831205 0.555967i \(-0.812348\pi\)
0.831205 0.555967i \(-0.187652\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 11.5616i 1.35318i −0.736361 0.676589i \(-0.763458\pi\)
0.736361 0.676589i \(-0.236542\pi\)
\(74\) −10.6847 −1.24207
\(75\) 7.68466 0.887348
\(76\) 1.56155i 0.179122i
\(77\) 5.56155 0.633798
\(78\) −0.561553 + 3.56155i −0.0635833 + 0.403266i
\(79\) 16.0000 1.80014 0.900070 0.435745i \(-0.143515\pi\)
0.900070 + 0.435745i \(0.143515\pi\)
\(80\) 3.56155i 0.398194i
\(81\) 1.00000 0.111111
\(82\) −4.00000 −0.441726
\(83\) 2.00000i 0.219529i 0.993958 + 0.109764i \(0.0350096\pi\)
−0.993958 + 0.109764i \(0.964990\pi\)
\(84\) 1.00000i 0.109109i
\(85\) 23.8078i 2.58231i
\(86\) 6.43845i 0.694276i
\(87\) −1.56155 −0.167416
\(88\) 5.56155 0.592864
\(89\) 8.00000i 0.847998i 0.905663 + 0.423999i \(0.139374\pi\)
−0.905663 + 0.423999i \(0.860626\pi\)
\(90\) −3.56155 −0.375421
\(91\) −0.561553 + 3.56155i −0.0588667 + 0.373352i
\(92\) 6.68466 0.696924
\(93\) 6.24621i 0.647702i
\(94\) 10.2462 1.05682
\(95\) 5.56155 0.570603
\(96\) 1.00000i 0.102062i
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 5.56155i 0.558957i
\(100\) 7.68466 0.768466
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 6.68466i 0.661880i
\(103\) 1.80776 0.178124 0.0890621 0.996026i \(-0.471613\pi\)
0.0890621 + 0.996026i \(0.471613\pi\)
\(104\) −0.561553 + 3.56155i −0.0550648 + 0.349239i
\(105\) −3.56155 −0.347572
\(106\) 4.87689i 0.473686i
\(107\) −4.87689 −0.471467 −0.235734 0.971818i \(-0.575749\pi\)
−0.235734 + 0.971818i \(0.575749\pi\)
\(108\) 1.00000 0.0962250
\(109\) 12.9309i 1.23855i −0.785173 0.619276i \(-0.787426\pi\)
0.785173 0.619276i \(-0.212574\pi\)
\(110\) 19.8078i 1.88860i
\(111\) 10.6847i 1.01414i
\(112\) 1.00000i 0.0944911i
\(113\) 20.2462 1.90460 0.952302 0.305158i \(-0.0987093\pi\)
0.952302 + 0.305158i \(0.0987093\pi\)
\(114\) −1.56155 −0.146253
\(115\) 23.8078i 2.22009i
\(116\) −1.56155 −0.144987
\(117\) 3.56155 + 0.561553i 0.329266 + 0.0519156i
\(118\) −4.24621 −0.390895
\(119\) 6.68466i 0.612782i
\(120\) −3.56155 −0.325124
\(121\) −19.9309 −1.81190
\(122\) 1.56155i 0.141376i
\(123\) 4.00000i 0.360668i
\(124\) 6.24621i 0.560926i
\(125\) 9.56155i 0.855211i
\(126\) 1.00000 0.0890871
\(127\) 10.2462 0.909204 0.454602 0.890695i \(-0.349781\pi\)
0.454602 + 0.890695i \(0.349781\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 6.43845 0.566874
\(130\) −12.6847 2.00000i −1.11252 0.175412i
\(131\) −1.56155 −0.136434 −0.0682168 0.997671i \(-0.521731\pi\)
−0.0682168 + 0.997671i \(0.521731\pi\)
\(132\) 5.56155i 0.484071i
\(133\) −1.56155 −0.135404
\(134\) 1.12311 0.0970215
\(135\) 3.56155i 0.306530i
\(136\) 6.68466i 0.573205i
\(137\) 6.68466i 0.571109i −0.958362 0.285554i \(-0.907822\pi\)
0.958362 0.285554i \(-0.0921777\pi\)
\(138\) 6.68466i 0.569036i
\(139\) 10.2462 0.869072 0.434536 0.900654i \(-0.356912\pi\)
0.434536 + 0.900654i \(0.356912\pi\)
\(140\) −3.56155 −0.301006
\(141\) 10.2462i 0.862887i
\(142\) −9.36932 −0.786256
\(143\) 3.12311 19.8078i 0.261167 1.65641i
\(144\) 1.00000 0.0833333
\(145\) 5.56155i 0.461862i
\(146\) −11.5616 −0.956841
\(147\) 1.00000 0.0824786
\(148\) 10.6847i 0.878274i
\(149\) 10.0000i 0.819232i −0.912258 0.409616i \(-0.865663\pi\)
0.912258 0.409616i \(-0.134337\pi\)
\(150\) 7.68466i 0.627450i
\(151\) 16.6847i 1.35778i −0.734241 0.678889i \(-0.762462\pi\)
0.734241 0.678889i \(-0.237538\pi\)
\(152\) −1.56155 −0.126659
\(153\) −6.68466 −0.540423
\(154\) 5.56155i 0.448163i
\(155\) 22.2462 1.78686
\(156\) 3.56155 + 0.561553i 0.285152 + 0.0449602i
\(157\) −11.8078 −0.942362 −0.471181 0.882037i \(-0.656172\pi\)
−0.471181 + 0.882037i \(0.656172\pi\)
\(158\) 16.0000i 1.27289i
\(159\) −4.87689 −0.386763
\(160\) −3.56155 −0.281565
\(161\) 6.68466i 0.526825i
\(162\) 1.00000i 0.0785674i
\(163\) 9.12311i 0.714577i −0.933994 0.357288i \(-0.883701\pi\)
0.933994 0.357288i \(-0.116299\pi\)
\(164\) 4.00000i 0.312348i
\(165\) 19.8078 1.54203
\(166\) 2.00000 0.155230
\(167\) 11.8078i 0.913712i 0.889541 + 0.456856i \(0.151025\pi\)
−0.889541 + 0.456856i \(0.848975\pi\)
\(168\) 1.00000 0.0771517
\(169\) 12.3693 + 4.00000i 0.951486 + 0.307692i
\(170\) 23.8078 1.82597
\(171\) 1.56155i 0.119415i
\(172\) 6.43845 0.490927
\(173\) −3.75379 −0.285395 −0.142698 0.989766i \(-0.545578\pi\)
−0.142698 + 0.989766i \(0.545578\pi\)
\(174\) 1.56155i 0.118381i
\(175\) 7.68466i 0.580906i
\(176\) 5.56155i 0.419218i
\(177\) 4.24621i 0.319165i
\(178\) 8.00000 0.599625
\(179\) 11.1231 0.831380 0.415690 0.909506i \(-0.363540\pi\)
0.415690 + 0.909506i \(0.363540\pi\)
\(180\) 3.56155i 0.265462i
\(181\) −13.3693 −0.993733 −0.496867 0.867827i \(-0.665516\pi\)
−0.496867 + 0.867827i \(0.665516\pi\)
\(182\) 3.56155 + 0.561553i 0.264000 + 0.0416251i
\(183\) 1.56155 0.115433
\(184\) 6.68466i 0.492800i
\(185\) −38.0540 −2.79778
\(186\) −6.24621 −0.457994
\(187\) 37.1771i 2.71866i
\(188\) 10.2462i 0.747282i
\(189\) 1.00000i 0.0727393i
\(190\) 5.56155i 0.403477i
\(191\) −24.0540 −1.74048 −0.870242 0.492624i \(-0.836038\pi\)
−0.870242 + 0.492624i \(0.836038\pi\)
\(192\) 1.00000 0.0721688
\(193\) 12.0000i 0.863779i 0.901927 + 0.431889i \(0.142153\pi\)
−0.901927 + 0.431889i \(0.857847\pi\)
\(194\) −10.0000 −0.717958
\(195\) −2.00000 + 12.6847i −0.143223 + 0.908367i
\(196\) 1.00000 0.0714286
\(197\) 6.00000i 0.427482i 0.976890 + 0.213741i \(0.0685649\pi\)
−0.976890 + 0.213741i \(0.931435\pi\)
\(198\) −5.56155 −0.395242
\(199\) 4.93087 0.349540 0.174770 0.984609i \(-0.444082\pi\)
0.174770 + 0.984609i \(0.444082\pi\)
\(200\) 7.68466i 0.543387i
\(201\) 1.12311i 0.0792178i
\(202\) 6.00000i 0.422159i
\(203\) 1.56155i 0.109600i
\(204\) −6.68466 −0.468020
\(205\) −14.2462 −0.994999
\(206\) 1.80776i 0.125953i
\(207\) −6.68466 −0.464616
\(208\) 3.56155 + 0.561553i 0.246949 + 0.0389367i
\(209\) 8.68466 0.600730
\(210\) 3.56155i 0.245770i
\(211\) 7.80776 0.537509 0.268754 0.963209i \(-0.413388\pi\)
0.268754 + 0.963209i \(0.413388\pi\)
\(212\) −4.87689 −0.334946
\(213\) 9.36932i 0.641975i
\(214\) 4.87689i 0.333378i
\(215\) 22.9309i 1.56387i
\(216\) 1.00000i 0.0680414i
\(217\) −6.24621 −0.424020
\(218\) −12.9309 −0.875789
\(219\) 11.5616i 0.781257i
\(220\) 19.8078 1.33544
\(221\) −23.8078 3.75379i −1.60148 0.252507i
\(222\) 10.6847 0.717107
\(223\) 1.75379i 0.117442i 0.998274 + 0.0587212i \(0.0187023\pi\)
−0.998274 + 0.0587212i \(0.981298\pi\)
\(224\) 1.00000 0.0668153
\(225\) −7.68466 −0.512311
\(226\) 20.2462i 1.34676i
\(227\) 17.6155i 1.16918i 0.811328 + 0.584592i \(0.198745\pi\)
−0.811328 + 0.584592i \(0.801255\pi\)
\(228\) 1.56155i 0.103416i
\(229\) 2.00000i 0.132164i −0.997814 0.0660819i \(-0.978950\pi\)
0.997814 0.0660819i \(-0.0210498\pi\)
\(230\) 23.8078 1.56984
\(231\) −5.56155 −0.365923
\(232\) 1.56155i 0.102521i
\(233\) 2.00000 0.131024 0.0655122 0.997852i \(-0.479132\pi\)
0.0655122 + 0.997852i \(0.479132\pi\)
\(234\) 0.561553 3.56155i 0.0367099 0.232826i
\(235\) 36.4924 2.38050
\(236\) 4.24621i 0.276405i
\(237\) −16.0000 −1.03931
\(238\) −6.68466 −0.433302
\(239\) 14.2462i 0.921511i −0.887527 0.460755i \(-0.847579\pi\)
0.887527 0.460755i \(-0.152421\pi\)
\(240\) 3.56155i 0.229897i
\(241\) 6.00000i 0.386494i −0.981150 0.193247i \(-0.938098\pi\)
0.981150 0.193247i \(-0.0619019\pi\)
\(242\) 19.9309i 1.28120i
\(243\) −1.00000 −0.0641500
\(244\) 1.56155 0.0999682
\(245\) 3.56155i 0.227539i
\(246\) 4.00000 0.255031
\(247\) −0.876894 + 5.56155i −0.0557955 + 0.353873i
\(248\) −6.24621 −0.396635
\(249\) 2.00000i 0.126745i
\(250\) 9.56155 0.604726
\(251\) 22.0540 1.39203 0.696017 0.718025i \(-0.254954\pi\)
0.696017 + 0.718025i \(0.254954\pi\)
\(252\) 1.00000i 0.0629941i
\(253\) 37.1771i 2.33730i
\(254\) 10.2462i 0.642904i
\(255\) 23.8078i 1.49090i
\(256\) 1.00000 0.0625000
\(257\) −26.0000 −1.62184 −0.810918 0.585160i \(-0.801032\pi\)
−0.810918 + 0.585160i \(0.801032\pi\)
\(258\) 6.43845i 0.400840i
\(259\) 10.6847 0.663912
\(260\) −2.00000 + 12.6847i −0.124035 + 0.786669i
\(261\) 1.56155 0.0966577
\(262\) 1.56155i 0.0964731i
\(263\) −23.3693 −1.44101 −0.720507 0.693448i \(-0.756091\pi\)
−0.720507 + 0.693448i \(0.756091\pi\)
\(264\) −5.56155 −0.342290
\(265\) 17.3693i 1.06699i
\(266\) 1.56155i 0.0957449i
\(267\) 8.00000i 0.489592i
\(268\) 1.12311i 0.0686046i
\(269\) 31.3693 1.91262 0.956311 0.292353i \(-0.0944382\pi\)
0.956311 + 0.292353i \(0.0944382\pi\)
\(270\) 3.56155 0.216749
\(271\) 8.00000i 0.485965i 0.970031 + 0.242983i \(0.0781258\pi\)
−0.970031 + 0.242983i \(0.921874\pi\)
\(272\) −6.68466 −0.405317
\(273\) 0.561553 3.56155i 0.0339867 0.215555i
\(274\) −6.68466 −0.403835
\(275\) 42.7386i 2.57724i
\(276\) −6.68466 −0.402369
\(277\) −10.8769 −0.653529 −0.326765 0.945106i \(-0.605958\pi\)
−0.326765 + 0.945106i \(0.605958\pi\)
\(278\) 10.2462i 0.614527i
\(279\) 6.24621i 0.373951i
\(280\) 3.56155i 0.212843i
\(281\) 6.00000i 0.357930i −0.983855 0.178965i \(-0.942725\pi\)
0.983855 0.178965i \(-0.0572749\pi\)
\(282\) −10.2462 −0.610153
\(283\) −4.87689 −0.289901 −0.144951 0.989439i \(-0.546302\pi\)
−0.144951 + 0.989439i \(0.546302\pi\)
\(284\) 9.36932i 0.555967i
\(285\) −5.56155 −0.329438
\(286\) −19.8078 3.12311i −1.17126 0.184673i
\(287\) 4.00000 0.236113
\(288\) 1.00000i 0.0589256i
\(289\) 27.6847 1.62851
\(290\) −5.56155 −0.326586
\(291\) 10.0000i 0.586210i
\(292\) 11.5616i 0.676589i
\(293\) 7.75379i 0.452981i 0.974013 + 0.226491i \(0.0727253\pi\)
−0.974013 + 0.226491i \(0.927275\pi\)
\(294\) 1.00000i 0.0583212i
\(295\) −15.1231 −0.880501
\(296\) 10.6847 0.621033
\(297\) 5.56155i 0.322714i
\(298\) −10.0000 −0.579284
\(299\) −23.8078 3.75379i −1.37684 0.217087i
\(300\) −7.68466 −0.443674
\(301\) 6.43845i 0.371106i
\(302\) −16.6847 −0.960094
\(303\) −6.00000 −0.344691
\(304\) 1.56155i 0.0895612i
\(305\) 5.56155i 0.318454i
\(306\) 6.68466i 0.382136i
\(307\) 26.2462i 1.49795i −0.662598 0.748975i \(-0.730546\pi\)
0.662598 0.748975i \(-0.269454\pi\)
\(308\) −5.56155 −0.316899
\(309\) −1.80776 −0.102840
\(310\) 22.2462i 1.26350i
\(311\) −0.492423 −0.0279227 −0.0139614 0.999903i \(-0.504444\pi\)
−0.0139614 + 0.999903i \(0.504444\pi\)
\(312\) 0.561553 3.56155i 0.0317917 0.201633i
\(313\) 32.2462 1.82266 0.911332 0.411673i \(-0.135055\pi\)
0.911332 + 0.411673i \(0.135055\pi\)
\(314\) 11.8078i 0.666351i
\(315\) 3.56155 0.200671
\(316\) −16.0000 −0.900070
\(317\) 3.36932i 0.189240i 0.995513 + 0.0946198i \(0.0301636\pi\)
−0.995513 + 0.0946198i \(0.969836\pi\)
\(318\) 4.87689i 0.273483i
\(319\) 8.68466i 0.486248i
\(320\) 3.56155i 0.199097i
\(321\) 4.87689 0.272202
\(322\) −6.68466 −0.372521
\(323\) 10.4384i 0.580811i
\(324\) −1.00000 −0.0555556
\(325\) −27.3693 4.31534i −1.51818 0.239372i
\(326\) −9.12311 −0.505282
\(327\) 12.9309i 0.715079i
\(328\) 4.00000 0.220863
\(329\) −10.2462 −0.564892
\(330\) 19.8078i 1.09038i
\(331\) 1.12311i 0.0617315i 0.999524 + 0.0308657i \(0.00982643\pi\)
−0.999524 + 0.0308657i \(0.990174\pi\)
\(332\) 2.00000i 0.109764i
\(333\) 10.6847i 0.585516i
\(334\) 11.8078 0.646092
\(335\) 4.00000 0.218543
\(336\) 1.00000i 0.0545545i
\(337\) 20.0540 1.09241 0.546205 0.837652i \(-0.316072\pi\)
0.546205 + 0.837652i \(0.316072\pi\)
\(338\) 4.00000 12.3693i 0.217571 0.672802i
\(339\) −20.2462 −1.09962
\(340\) 23.8078i 1.29116i
\(341\) 34.7386 1.88120
\(342\) 1.56155 0.0844391
\(343\) 1.00000i 0.0539949i
\(344\) 6.43845i 0.347138i
\(345\) 23.8078i 1.28177i
\(346\) 3.75379i 0.201805i
\(347\) −24.4924 −1.31482 −0.657411 0.753532i \(-0.728348\pi\)
−0.657411 + 0.753532i \(0.728348\pi\)
\(348\) 1.56155 0.0837080
\(349\) 3.36932i 0.180355i −0.995926 0.0901777i \(-0.971256\pi\)
0.995926 0.0901777i \(-0.0287435\pi\)
\(350\) −7.68466 −0.410762
\(351\) −3.56155 0.561553i −0.190102 0.0299735i
\(352\) −5.56155 −0.296432
\(353\) 18.2462i 0.971148i 0.874196 + 0.485574i \(0.161389\pi\)
−0.874196 + 0.485574i \(0.838611\pi\)
\(354\) 4.24621 0.225684
\(355\) −33.3693 −1.77106
\(356\) 8.00000i 0.423999i
\(357\) 6.68466i 0.353790i
\(358\) 11.1231i 0.587874i
\(359\) 23.6155i 1.24638i −0.782071 0.623190i \(-0.785836\pi\)
0.782071 0.623190i \(-0.214164\pi\)
\(360\) 3.56155 0.187710
\(361\) 16.5616 0.871661
\(362\) 13.3693i 0.702676i
\(363\) 19.9309 1.04610
\(364\) 0.561553 3.56155i 0.0294334 0.186676i
\(365\) −41.1771 −2.15531
\(366\) 1.56155i 0.0816237i
\(367\) 0.630683 0.0329214 0.0164607 0.999865i \(-0.494760\pi\)
0.0164607 + 0.999865i \(0.494760\pi\)
\(368\) −6.68466 −0.348462
\(369\) 4.00000i 0.208232i
\(370\) 38.0540i 1.97833i
\(371\) 4.87689i 0.253196i
\(372\) 6.24621i 0.323851i
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 37.1771 1.92238
\(375\) 9.56155i 0.493756i
\(376\) −10.2462 −0.528408
\(377\) 5.56155 + 0.876894i 0.286435 + 0.0451624i
\(378\) −1.00000 −0.0514344
\(379\) 18.8769i 0.969641i 0.874614 + 0.484820i \(0.161115\pi\)
−0.874614 + 0.484820i \(0.838885\pi\)
\(380\) −5.56155 −0.285302
\(381\) −10.2462 −0.524929
\(382\) 24.0540i 1.23071i
\(383\) 17.5616i 0.897353i −0.893694 0.448677i \(-0.851895\pi\)
0.893694 0.448677i \(-0.148105\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 19.8078i 1.00950i
\(386\) 12.0000 0.610784
\(387\) −6.43845 −0.327285
\(388\) 10.0000i 0.507673i
\(389\) 27.1231 1.37520 0.687598 0.726092i \(-0.258665\pi\)
0.687598 + 0.726092i \(0.258665\pi\)
\(390\) 12.6847 + 2.00000i 0.642313 + 0.101274i
\(391\) 44.6847 2.25980
\(392\) 1.00000i 0.0505076i
\(393\) 1.56155 0.0787699
\(394\) 6.00000 0.302276
\(395\) 56.9848i 2.86722i
\(396\) 5.56155i 0.279479i
\(397\) 15.3693i 0.771364i −0.922632 0.385682i \(-0.873966\pi\)
0.922632 0.385682i \(-0.126034\pi\)
\(398\) 4.93087i 0.247162i
\(399\) 1.56155 0.0781754
\(400\) −7.68466 −0.384233
\(401\) 30.9848i 1.54731i 0.633608 + 0.773655i \(0.281573\pi\)
−0.633608 + 0.773655i \(0.718427\pi\)
\(402\) −1.12311 −0.0560154
\(403\) −3.50758 + 22.2462i −0.174725 + 1.10816i
\(404\) −6.00000 −0.298511
\(405\) 3.56155i 0.176975i
\(406\) 1.56155 0.0774986
\(407\) −59.4233 −2.94550
\(408\) 6.68466i 0.330940i
\(409\) 13.8078i 0.682750i −0.939927 0.341375i \(-0.889107\pi\)
0.939927 0.341375i \(-0.110893\pi\)
\(410\) 14.2462i 0.703570i
\(411\) 6.68466i 0.329730i
\(412\) −1.80776 −0.0890621
\(413\) 4.24621 0.208942
\(414\) 6.68466i 0.328533i
\(415\) 7.12311 0.349660
\(416\) 0.561553 3.56155i 0.0275324 0.174619i
\(417\) −10.2462 −0.501759
\(418\) 8.68466i 0.424781i
\(419\) −20.6847 −1.01051 −0.505256 0.862970i \(-0.668602\pi\)
−0.505256 + 0.862970i \(0.668602\pi\)
\(420\) 3.56155 0.173786
\(421\) 10.0000i 0.487370i 0.969854 + 0.243685i \(0.0783563\pi\)
−0.969854 + 0.243685i \(0.921644\pi\)
\(422\) 7.80776i 0.380076i
\(423\) 10.2462i 0.498188i
\(424\) 4.87689i 0.236843i
\(425\) 51.3693 2.49178
\(426\) 9.36932 0.453945
\(427\) 1.56155i 0.0755688i
\(428\) 4.87689 0.235734
\(429\) −3.12311 + 19.8078i −0.150785 + 0.956328i
\(430\) 22.9309 1.10582
\(431\) 29.8617i 1.43839i −0.694809 0.719195i \(-0.744511\pi\)
0.694809 0.719195i \(-0.255489\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 23.3693 1.12306 0.561529 0.827457i \(-0.310213\pi\)
0.561529 + 0.827457i \(0.310213\pi\)
\(434\) 6.24621i 0.299828i
\(435\) 5.56155i 0.266656i
\(436\) 12.9309i 0.619276i
\(437\) 10.4384i 0.499339i
\(438\) 11.5616 0.552432
\(439\) −8.93087 −0.426247 −0.213124 0.977025i \(-0.568364\pi\)
−0.213124 + 0.977025i \(0.568364\pi\)
\(440\) 19.8078i 0.944298i
\(441\) −1.00000 −0.0476190
\(442\) −3.75379 + 23.8078i −0.178550 + 1.13242i
\(443\) 6.63068 0.315033 0.157517 0.987516i \(-0.449651\pi\)
0.157517 + 0.987516i \(0.449651\pi\)
\(444\) 10.6847i 0.507071i
\(445\) 28.4924 1.35067
\(446\) 1.75379 0.0830443
\(447\) 10.0000i 0.472984i
\(448\) 1.00000i 0.0472456i
\(449\) 9.31534i 0.439618i 0.975543 + 0.219809i \(0.0705434\pi\)
−0.975543 + 0.219809i \(0.929457\pi\)
\(450\) 7.68466i 0.362258i
\(451\) −22.2462 −1.04753
\(452\) −20.2462 −0.952302
\(453\) 16.6847i 0.783914i
\(454\) 17.6155 0.826738
\(455\) 12.6847 + 2.00000i 0.594666 + 0.0937614i
\(456\) 1.56155 0.0731264
\(457\) 16.0000i 0.748448i 0.927338 + 0.374224i \(0.122091\pi\)
−0.927338 + 0.374224i \(0.877909\pi\)
\(458\) −2.00000 −0.0934539
\(459\) 6.68466 0.312013
\(460\) 23.8078i 1.11004i
\(461\) 36.9309i 1.72004i −0.510259 0.860021i \(-0.670450\pi\)
0.510259 0.860021i \(-0.329550\pi\)
\(462\) 5.56155i 0.258747i
\(463\) 30.5464i 1.41961i 0.704397 + 0.709806i \(0.251217\pi\)
−0.704397 + 0.709806i \(0.748783\pi\)
\(464\) 1.56155 0.0724933
\(465\) −22.2462 −1.03164
\(466\) 2.00000i 0.0926482i
\(467\) 1.56155 0.0722600 0.0361300 0.999347i \(-0.488497\pi\)
0.0361300 + 0.999347i \(0.488497\pi\)
\(468\) −3.56155 0.561553i −0.164633 0.0259578i
\(469\) −1.12311 −0.0518602
\(470\) 36.4924i 1.68327i
\(471\) 11.8078 0.544073
\(472\) 4.24621 0.195448
\(473\) 35.8078i 1.64644i
\(474\) 16.0000i 0.734904i
\(475\) 12.0000i 0.550598i
\(476\) 6.68466i 0.306391i
\(477\) 4.87689 0.223298
\(478\) −14.2462 −0.651607
\(479\) 12.3002i 0.562010i −0.959706 0.281005i \(-0.909332\pi\)
0.959706 0.281005i \(-0.0906677\pi\)
\(480\) 3.56155 0.162562
\(481\) 6.00000 38.0540i 0.273576 1.73511i
\(482\) −6.00000 −0.273293
\(483\) 6.68466i 0.304162i
\(484\) 19.9309 0.905949
\(485\) −35.6155 −1.61722
\(486\) 1.00000i 0.0453609i
\(487\) 13.7538i 0.623244i 0.950206 + 0.311622i \(0.100872\pi\)
−0.950206 + 0.311622i \(0.899128\pi\)
\(488\) 1.56155i 0.0706882i
\(489\) 9.12311i 0.412561i
\(490\) 3.56155 0.160895
\(491\) −10.2462 −0.462405 −0.231203 0.972906i \(-0.574266\pi\)
−0.231203 + 0.972906i \(0.574266\pi\)
\(492\) 4.00000i 0.180334i
\(493\) −10.4384 −0.470124
\(494\) 5.56155 + 0.876894i 0.250226 + 0.0394533i
\(495\) −19.8078 −0.890293
\(496\) 6.24621i 0.280463i
\(497\) 9.36932 0.420271
\(498\) −2.00000 −0.0896221
\(499\) 1.50758i 0.0674884i 0.999431 + 0.0337442i \(0.0107432\pi\)
−0.999431 + 0.0337442i \(0.989257\pi\)
\(500\) 9.56155i 0.427606i
\(501\) 11.8078i 0.527532i
\(502\) 22.0540i 0.984317i
\(503\) 35.6155 1.58802 0.794009 0.607906i \(-0.207990\pi\)
0.794009 + 0.607906i \(0.207990\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 21.3693i 0.950922i
\(506\) 37.1771 1.65272
\(507\) −12.3693 4.00000i −0.549341 0.177646i
\(508\) −10.2462 −0.454602
\(509\) 2.68466i 0.118995i −0.998228 0.0594977i \(-0.981050\pi\)
0.998228 0.0594977i \(-0.0189499\pi\)
\(510\) −23.8078 −1.05423
\(511\) 11.5616 0.511453
\(512\) 1.00000i 0.0441942i
\(513\) 1.56155i 0.0689442i
\(514\) 26.0000i 1.14681i
\(515\) 6.43845i 0.283712i
\(516\) −6.43845 −0.283437
\(517\) 56.9848 2.50619
\(518\) 10.6847i 0.469457i
\(519\) 3.75379 0.164773
\(520\) 12.6847 + 2.00000i 0.556259 + 0.0877058i
\(521\) 8.05398 0.352851 0.176426 0.984314i \(-0.443547\pi\)
0.176426 + 0.984314i \(0.443547\pi\)
\(522\) 1.56155i 0.0683473i
\(523\) −8.49242 −0.371348 −0.185674 0.982611i \(-0.559447\pi\)
−0.185674 + 0.982611i \(0.559447\pi\)
\(524\) 1.56155 0.0682168
\(525\) 7.68466i 0.335386i
\(526\) 23.3693i 1.01895i
\(527\) 41.7538i 1.81882i
\(528\) 5.56155i 0.242036i
\(529\) 21.6847 0.942811
\(530\) −17.3693 −0.754475
\(531\) 4.24621i 0.184270i
\(532\) 1.56155 0.0677019
\(533\) 2.24621 14.2462i 0.0972942 0.617072i
\(534\) −8.00000 −0.346194
\(535\) 17.3693i 0.750941i
\(536\) −1.12311 −0.0485108
\(537\) −11.1231 −0.479997
\(538\) 31.3693i 1.35243i
\(539\) 5.56155i 0.239553i
\(540\) 3.56155i 0.153265i
\(541\) 6.19224i 0.266225i 0.991101 + 0.133113i \(0.0424972\pi\)
−0.991101 + 0.133113i \(0.957503\pi\)
\(542\) 8.00000 0.343629
\(543\) 13.3693 0.573732
\(544\) 6.68466i 0.286602i
\(545\) −46.0540 −1.97274
\(546\) −3.56155 0.561553i −0.152420 0.0240322i
\(547\) 28.9848 1.23930 0.619651 0.784877i \(-0.287274\pi\)
0.619651 + 0.784877i \(0.287274\pi\)
\(548\) 6.68466i 0.285554i
\(549\) −1.56155 −0.0666455
\(550\) 42.7386 1.82238
\(551\) 2.43845i 0.103881i
\(552\) 6.68466i 0.284518i
\(553\) 16.0000i 0.680389i
\(554\) 10.8769i 0.462115i
\(555\) 38.0540 1.61530
\(556\) −10.2462 −0.434536
\(557\) 16.2462i 0.688374i −0.938901 0.344187i \(-0.888155\pi\)
0.938901 0.344187i \(-0.111845\pi\)
\(558\) 6.24621 0.264423
\(559\) −22.9309 3.61553i −0.969872 0.152921i
\(560\) 3.56155 0.150503
\(561\) 37.1771i 1.56962i
\(562\) −6.00000 −0.253095
\(563\) 38.0540 1.60378 0.801892 0.597469i \(-0.203827\pi\)
0.801892 + 0.597469i \(0.203827\pi\)
\(564\) 10.2462i 0.431443i
\(565\) 72.1080i 3.03360i
\(566\) 4.87689i 0.204991i
\(567\) 1.00000i 0.0419961i
\(568\) 9.36932 0.393128
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 5.56155i 0.232948i
\(571\) −18.2462 −0.763580 −0.381790 0.924249i \(-0.624692\pi\)
−0.381790 + 0.924249i \(0.624692\pi\)
\(572\) −3.12311 + 19.8078i −0.130584 + 0.828204i
\(573\) 24.0540 1.00487
\(574\) 4.00000i 0.166957i
\(575\) 51.3693 2.14225
\(576\) −1.00000 −0.0416667
\(577\) 7.75379i 0.322794i −0.986890 0.161397i \(-0.948400\pi\)
0.986890 0.161397i \(-0.0516000\pi\)
\(578\) 27.6847i 1.15153i
\(579\) 12.0000i 0.498703i
\(580\) 5.56155i 0.230931i
\(581\) −2.00000 −0.0829740
\(582\) 10.0000 0.414513
\(583\) 27.1231i 1.12332i
\(584\) 11.5616 0.478420
\(585\) 2.00000 12.6847i 0.0826898 0.524446i
\(586\) 7.75379 0.320306
\(587\) 37.1231i 1.53223i 0.642701 + 0.766117i \(0.277814\pi\)
−0.642701 + 0.766117i \(0.722186\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −9.75379 −0.401898
\(590\) 15.1231i 0.622608i
\(591\) 6.00000i 0.246807i
\(592\) 10.6847i 0.439137i
\(593\) 28.0000i 1.14982i 0.818216 + 0.574911i \(0.194963\pi\)
−0.818216 + 0.574911i \(0.805037\pi\)
\(594\) 5.56155 0.228193
\(595\) −23.8078 −0.976023
\(596\) 10.0000i 0.409616i
\(597\) −4.93087 −0.201807
\(598\) −3.75379 + 23.8078i −0.153504 + 0.973572i
\(599\) 30.3002 1.23803 0.619016 0.785378i \(-0.287532\pi\)
0.619016 + 0.785378i \(0.287532\pi\)
\(600\) 7.68466i 0.313725i
\(601\) −31.8617 −1.29967 −0.649834 0.760076i \(-0.725161\pi\)
−0.649834 + 0.760076i \(0.725161\pi\)
\(602\) −6.43845 −0.262412
\(603\) 1.12311i 0.0457364i
\(604\) 16.6847i 0.678889i
\(605\) 70.9848i 2.88594i
\(606\) 6.00000i 0.243733i
\(607\) −28.5464 −1.15866 −0.579331 0.815092i \(-0.696686\pi\)
−0.579331 + 0.815092i \(0.696686\pi\)
\(608\) 1.56155 0.0633293
\(609\) 1.56155i 0.0632773i
\(610\) 5.56155 0.225181
\(611\) −5.75379 + 36.4924i −0.232773 + 1.47633i
\(612\) 6.68466 0.270211
\(613\) 1.80776i 0.0730149i 0.999333 + 0.0365075i \(0.0116233\pi\)
−0.999333 + 0.0365075i \(0.988377\pi\)
\(614\) −26.2462 −1.05921
\(615\) 14.2462 0.574463
\(616\) 5.56155i 0.224081i
\(617\) 6.19224i 0.249290i −0.992201 0.124645i \(-0.960221\pi\)
0.992201 0.124645i \(-0.0397792\pi\)
\(618\) 1.80776i 0.0727189i
\(619\) 30.9309i 1.24322i 0.783328 + 0.621608i \(0.213520\pi\)
−0.783328 + 0.621608i \(0.786480\pi\)
\(620\) −22.2462 −0.893429
\(621\) 6.68466 0.268246
\(622\) 0.492423i 0.0197443i
\(623\) −8.00000 −0.320513
\(624\) −3.56155 0.561553i −0.142576 0.0224801i
\(625\) −4.36932 −0.174773
\(626\) 32.2462i 1.28882i
\(627\) −8.68466 −0.346832
\(628\) 11.8078 0.471181
\(629\) 71.4233i 2.84783i
\(630\) 3.56155i 0.141896i
\(631\) 12.6847i 0.504968i −0.967601 0.252484i \(-0.918752\pi\)
0.967601 0.252484i \(-0.0812476\pi\)
\(632\) 16.0000i 0.636446i
\(633\) −7.80776 −0.310331
\(634\) 3.36932 0.133813
\(635\) 36.4924i 1.44816i
\(636\) 4.87689 0.193381
\(637\) −3.56155 0.561553i −0.141114 0.0222495i
\(638\) −8.68466 −0.343829
\(639\) 9.36932i 0.370644i
\(640\) 3.56155 0.140783
\(641\) 30.1080 1.18919 0.594596 0.804024i \(-0.297312\pi\)
0.594596 + 0.804024i \(0.297312\pi\)
\(642\) 4.87689i 0.192476i
\(643\) 0.192236i 0.00758105i 0.999993 + 0.00379052i \(0.00120656\pi\)
−0.999993 + 0.00379052i \(0.998793\pi\)
\(644\) 6.68466i 0.263412i
\(645\) 22.9309i 0.902902i
\(646\) −10.4384 −0.410695
\(647\) 10.6307 0.417935 0.208968 0.977923i \(-0.432990\pi\)
0.208968 + 0.977923i \(0.432990\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −23.6155 −0.926991
\(650\) −4.31534 + 27.3693i −0.169262 + 1.07351i
\(651\) 6.24621 0.244808
\(652\) 9.12311i 0.357288i
\(653\) −29.5616 −1.15683 −0.578416 0.815742i \(-0.696329\pi\)
−0.578416 + 0.815742i \(0.696329\pi\)
\(654\) 12.9309 0.505637
\(655\) 5.56155i 0.217308i
\(656\) 4.00000i 0.156174i
\(657\) 11.5616i 0.451059i
\(658\) 10.2462i 0.399439i
\(659\) 12.8769 0.501613 0.250806 0.968037i \(-0.419304\pi\)
0.250806 + 0.968037i \(0.419304\pi\)
\(660\) −19.8078 −0.771016
\(661\) 44.7386i 1.74013i 0.492936 + 0.870066i \(0.335924\pi\)
−0.492936 + 0.870066i \(0.664076\pi\)
\(662\) 1.12311 0.0436507
\(663\) 23.8078 + 3.75379i 0.924617 + 0.145785i
\(664\) −2.00000 −0.0776151
\(665\) 5.56155i 0.215668i
\(666\) −10.6847 −0.414022
\(667\) −10.4384 −0.404178
\(668\) 11.8078i 0.456856i
\(669\) 1.75379i 0.0678054i
\(670\) 4.00000i 0.154533i
\(671\) 8.68466i 0.335268i
\(672\) −1.00000 −0.0385758
\(673\) 37.8078 1.45738 0.728691 0.684843i \(-0.240129\pi\)
0.728691 + 0.684843i \(0.240129\pi\)
\(674\) 20.0540i 0.772450i
\(675\) 7.68466 0.295783
\(676\) −12.3693 4.00000i −0.475743 0.153846i
\(677\) 31.3693 1.20562 0.602810 0.797884i \(-0.294048\pi\)
0.602810 + 0.797884i \(0.294048\pi\)
\(678\) 20.2462i 0.777551i
\(679\) 10.0000 0.383765
\(680\) −23.8078 −0.912986
\(681\) 17.6155i 0.675029i
\(682\) 34.7386i 1.33021i
\(683\) 0.684658i 0.0261977i −0.999914 0.0130989i \(-0.995830\pi\)
0.999914 0.0130989i \(-0.00416962\pi\)
\(684\) 1.56155i 0.0597075i
\(685\) −23.8078 −0.909648
\(686\) −1.00000 −0.0381802
\(687\) 2.00000i 0.0763048i
\(688\) −6.43845 −0.245463
\(689\) 17.3693 + 2.73863i 0.661718 + 0.104334i
\(690\) −23.8078 −0.906346
\(691\) 36.4924i 1.38824i −0.719861 0.694119i \(-0.755794\pi\)
0.719861 0.694119i \(-0.244206\pi\)
\(692\) 3.75379 0.142698
\(693\) 5.56155 0.211266
\(694\) 24.4924i 0.929720i
\(695\) 36.4924i 1.38424i
\(696\) 1.56155i 0.0591905i
\(697\) 26.7386i 1.01280i
\(698\) −3.36932 −0.127531
\(699\) −2.00000 −0.0756469
\(700\) 7.68466i 0.290453i
\(701\) −3.61553 −0.136557 −0.0682783 0.997666i \(-0.521751\pi\)
−0.0682783 + 0.997666i \(0.521751\pi\)
\(702\) −0.561553 + 3.56155i −0.0211944 + 0.134422i
\(703\) 16.6847 0.629274
\(704\) 5.56155i 0.209609i
\(705\) −36.4924 −1.37438
\(706\) 18.2462 0.686705
\(707\) 6.00000i 0.225653i
\(708\) 4.24621i 0.159582i
\(709\) 31.7538i 1.19254i −0.802784 0.596269i \(-0.796649\pi\)
0.802784 0.596269i \(-0.203351\pi\)
\(710\) 33.3693i 1.25233i
\(711\) 16.0000 0.600047
\(712\) −8.00000 −0.299813
\(713\) 41.7538i 1.56369i
\(714\) 6.68466 0.250167
\(715\) −70.5464 11.1231i −2.63829 0.415981i
\(716\) −11.1231 −0.415690
\(717\) 14.2462i 0.532035i
\(718\) −23.6155 −0.881324
\(719\) 13.7538 0.512930 0.256465 0.966554i \(-0.417442\pi\)
0.256465 + 0.966554i \(0.417442\pi\)
\(720\) 3.56155i 0.132731i
\(721\) 1.80776i 0.0673247i
\(722\) 16.5616i 0.616357i
\(723\) 6.00000i 0.223142i
\(724\) 13.3693 0.496867
\(725\) −12.0000 −0.445669
\(726\) 19.9309i 0.739704i
\(727\) −48.9309 −1.81475 −0.907373 0.420327i \(-0.861915\pi\)
−0.907373 + 0.420327i \(0.861915\pi\)
\(728\) −3.56155 0.561553i −0.132000 0.0208125i
\(729\) 1.00000 0.0370370
\(730\) 41.1771i 1.52403i
\(731\) 43.0388 1.59185
\(732\) −1.56155 −0.0577167
\(733\) 22.8769i 0.844977i 0.906368 + 0.422489i \(0.138843\pi\)
−0.906368 + 0.422489i \(0.861157\pi\)
\(734\) 0.630683i 0.0232789i
\(735\) 3.56155i 0.131370i
\(736\) 6.68466i 0.246400i
\(737\) 6.24621 0.230082
\(738\) −4.00000 −0.147242
\(739\) 17.6155i 0.647998i 0.946057 + 0.323999i \(0.105027\pi\)
−0.946057 + 0.323999i \(0.894973\pi\)
\(740\) 38.0540 1.39889
\(741\) 0.876894 5.56155i 0.0322135 0.204309i
\(742\) 4.87689 0.179036
\(743\) 16.0000i 0.586983i 0.955962 + 0.293492i \(0.0948173\pi\)
−0.955962 + 0.293492i \(0.905183\pi\)
\(744\) 6.24621 0.228997
\(745\) −35.6155 −1.30485
\(746\) 6.00000i 0.219676i
\(747\) 2.00000i 0.0731762i
\(748\) 37.1771i 1.35933i
\(749\) 4.87689i 0.178198i
\(750\) −9.56155 −0.349139
\(751\) 2.24621 0.0819654 0.0409827 0.999160i \(-0.486951\pi\)
0.0409827 + 0.999160i \(0.486951\pi\)
\(752\) 10.2462i 0.373641i
\(753\) −22.0540 −0.803692
\(754\) 0.876894 5.56155i 0.0319346 0.202540i
\(755\) −59.4233 −2.16264
\(756\) 1.00000i 0.0363696i
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 18.8769 0.685640
\(759\) 37.1771i 1.34944i
\(760\) 5.56155i 0.201739i
\(761\) 39.1231i 1.41821i 0.705102 + 0.709106i \(0.250901\pi\)
−0.705102 + 0.709106i \(0.749099\pi\)
\(762\) 10.2462i 0.371181i
\(763\) 12.9309 0.468129
\(764\) 24.0540 0.870242
\(765\) 23.8078i 0.860772i
\(766\) −17.5616 −0.634525
\(767\) 2.38447 15.1231i 0.0860983 0.546064i
\(768\) −1.00000 −0.0360844
\(769\) 8.43845i 0.304298i 0.988358 + 0.152149i \(0.0486194\pi\)
−0.988358 + 0.152149i \(0.951381\pi\)
\(770\) −19.8078 −0.713822
\(771\) 26.0000 0.936367
\(772\) 12.0000i 0.431889i
\(773\) 12.9309i 0.465091i −0.972586 0.232546i \(-0.925295\pi\)
0.972586 0.232546i \(-0.0747055\pi\)
\(774\) 6.43845i 0.231425i
\(775\) 48.0000i 1.72421i
\(776\) 10.0000 0.358979
\(777\) −10.6847 −0.383310
\(778\) 27.1231i 0.972410i
\(779\) 6.24621 0.223794
\(780\) 2.00000 12.6847i 0.0716115 0.454184i
\(781\) −52.1080 −1.86457
\(782\) 44.6847i 1.59792i
\(783\) −1.56155 −0.0558053
\(784\) −1.00000 −0.0357143
\(785\) 42.0540i 1.50097i
\(786\) 1.56155i 0.0556987i
\(787\) 17.0691i 0.608449i −0.952600 0.304224i \(-0.901603\pi\)
0.952600 0.304224i \(-0.0983973\pi\)
\(788\) 6.00000i 0.213741i
\(789\) 23.3693 0.831970
\(790\) −56.9848 −2.02743
\(791\)