Properties

Label 504.2.c.f.253.4
Level 504
Weight 2
Character 504.253
Analytic conductor 4.024
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.386672896.3
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 253.4
Root \(-0.835949 - 1.14070i\) of \(x^{8} - x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} - 4 x^{2} + 16\)
Character \(\chi\) \(=\) 504.253
Dual form 504.2.c.f.253.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.835949 + 1.14070i) q^{2} +(-0.602380 - 1.90713i) q^{4} +0.467138i q^{5} +1.00000 q^{7} +(2.67901 + 0.907128i) q^{8} +O(q^{10})\) \(q+(-0.835949 + 1.14070i) q^{2} +(-0.602380 - 1.90713i) q^{4} +0.467138i q^{5} +1.00000 q^{7} +(2.67901 + 0.907128i) q^{8} +(-0.532862 - 0.390503i) q^{10} -4.87666i q^{11} -4.56279i q^{13} +(-0.835949 + 1.14070i) q^{14} +(-3.27428 + 2.29763i) q^{16} -6.09565 q^{17} +1.34379i q^{19} +(0.890891 - 0.281394i) q^{20} +(5.56279 + 4.07663i) q^{22} +4.09565 q^{23} +4.78178 q^{25} +(5.20476 + 3.81426i) q^{26} +(-0.602380 - 1.90713i) q^{28} -7.78178i q^{29} +4.40952 q^{31} +(0.116226 - 5.65566i) q^{32} +(5.09565 - 6.95329i) q^{34} +0.467138i q^{35} -4.40952i q^{37} +(-1.53286 - 1.12334i) q^{38} +(-0.423754 + 1.25147i) q^{40} +6.09565 q^{41} +4.15327i q^{43} +(-9.30041 + 2.93760i) q^{44} +(-3.42375 + 4.67190i) q^{46} +6.68759 q^{47} +1.00000 q^{49} +(-3.99732 + 5.45457i) q^{50} +(-8.70182 + 2.74853i) q^{52} +1.34379i q^{53} +2.27807 q^{55} +(2.67901 + 0.907128i) q^{56} +(8.87666 + 6.50517i) q^{58} -4.00000i q^{59} -5.49706i q^{61} +(-3.68613 + 5.02993i) q^{62} +(6.35424 + 4.86042i) q^{64} +2.13145 q^{65} +5.90658i q^{67} +(3.67190 + 11.6252i) q^{68} +(-0.532862 - 0.390503i) q^{70} +4.72339 q^{71} -12.0599 q^{73} +(5.02993 + 3.68613i) q^{74} +(2.56279 - 0.809475i) q^{76} -4.87666i q^{77} -16.1913 q^{79} +(-1.07331 - 1.52954i) q^{80} +(-5.09565 + 6.95329i) q^{82} +13.7533i q^{83} -2.84751i q^{85} +(-4.73762 - 3.47192i) q^{86} +(4.42375 - 13.0646i) q^{88} -7.96420 q^{89} -4.56279i q^{91} +(-2.46714 - 7.81093i) q^{92} +(-5.59048 + 7.62851i) q^{94} -0.627737 q^{95} -12.8789 q^{97} +(-0.835949 + 1.14070i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} + 8q^{7} + 6q^{8} + O(q^{10}) \) \( 8q + 2q^{4} + 8q^{7} + 6q^{8} - 4q^{10} - 6q^{16} - 4q^{17} - 24q^{20} - 12q^{23} - 24q^{25} + 28q^{26} + 2q^{28} + 8q^{31} + 30q^{32} - 4q^{34} - 12q^{38} + 28q^{40} + 4q^{41} - 16q^{44} + 4q^{46} + 8q^{49} + 20q^{50} - 12q^{52} - 8q^{55} + 6q^{56} + 44q^{58} - 12q^{62} + 26q^{64} + 16q^{65} + 16q^{68} - 4q^{70} + 28q^{71} - 8q^{73} - 4q^{74} - 24q^{76} - 40q^{79} + 4q^{80} + 4q^{82} - 24q^{86} + 4q^{88} - 20q^{89} - 20q^{92} - 72q^{94} - 40q^{95} + 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.835949 + 1.14070i −0.591105 + 0.806595i
\(3\) 0 0
\(4\) −0.602380 1.90713i −0.301190 0.953564i
\(5\) 0.467138i 0.208910i 0.994530 + 0.104455i \(0.0333099\pi\)
−0.994530 + 0.104455i \(0.966690\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.67901 + 0.907128i 0.947175 + 0.320718i
\(9\) 0 0
\(10\) −0.532862 0.390503i −0.168506 0.123488i
\(11\) 4.87666i 1.47037i −0.677868 0.735184i \(-0.737096\pi\)
0.677868 0.735184i \(-0.262904\pi\)
\(12\) 0 0
\(13\) 4.56279i 1.26549i −0.774360 0.632745i \(-0.781928\pi\)
0.774360 0.632745i \(-0.218072\pi\)
\(14\) −0.835949 + 1.14070i −0.223417 + 0.304864i
\(15\) 0 0
\(16\) −3.27428 + 2.29763i −0.818569 + 0.574408i
\(17\) −6.09565 −1.47841 −0.739206 0.673479i \(-0.764799\pi\)
−0.739206 + 0.673479i \(0.764799\pi\)
\(18\) 0 0
\(19\) 1.34379i 0.308288i 0.988048 + 0.154144i \(0.0492619\pi\)
−0.988048 + 0.154144i \(0.950738\pi\)
\(20\) 0.890891 0.281394i 0.199209 0.0629217i
\(21\) 0 0
\(22\) 5.56279 + 4.07663i 1.18599 + 0.869141i
\(23\) 4.09565 0.854002 0.427001 0.904251i \(-0.359570\pi\)
0.427001 + 0.904251i \(0.359570\pi\)
\(24\) 0 0
\(25\) 4.78178 0.956357
\(26\) 5.20476 + 3.81426i 1.02074 + 0.748037i
\(27\) 0 0
\(28\) −0.602380 1.90713i −0.113839 0.360413i
\(29\) 7.78178i 1.44504i −0.691350 0.722520i \(-0.742984\pi\)
0.691350 0.722520i \(-0.257016\pi\)
\(30\) 0 0
\(31\) 4.40952 0.791973 0.395987 0.918256i \(-0.370403\pi\)
0.395987 + 0.918256i \(0.370403\pi\)
\(32\) 0.116226 5.65566i 0.0205460 0.999789i
\(33\) 0 0
\(34\) 5.09565 6.95329i 0.873897 1.19248i
\(35\) 0.467138i 0.0789607i
\(36\) 0 0
\(37\) 4.40952i 0.724921i −0.931999 0.362460i \(-0.881937\pi\)
0.931999 0.362460i \(-0.118063\pi\)
\(38\) −1.53286 1.12334i −0.248663 0.182230i
\(39\) 0 0
\(40\) −0.423754 + 1.25147i −0.0670013 + 0.197874i
\(41\) 6.09565 0.951981 0.475990 0.879450i \(-0.342090\pi\)
0.475990 + 0.879450i \(0.342090\pi\)
\(42\) 0 0
\(43\) 4.15327i 0.633368i 0.948531 + 0.316684i \(0.102569\pi\)
−0.948531 + 0.316684i \(0.897431\pi\)
\(44\) −9.30041 + 2.93760i −1.40209 + 0.442860i
\(45\) 0 0
\(46\) −3.42375 + 4.67190i −0.504805 + 0.688834i
\(47\) 6.68759 0.975485 0.487743 0.872988i \(-0.337820\pi\)
0.487743 + 0.872988i \(0.337820\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −3.99732 + 5.45457i −0.565307 + 0.771392i
\(51\) 0 0
\(52\) −8.70182 + 2.74853i −1.20673 + 0.381153i
\(53\) 1.34379i 0.184584i 0.995732 + 0.0922922i \(0.0294194\pi\)
−0.995732 + 0.0922922i \(0.970581\pi\)
\(54\) 0 0
\(55\) 2.27807 0.307175
\(56\) 2.67901 + 0.907128i 0.357998 + 0.121220i
\(57\) 0 0
\(58\) 8.87666 + 6.50517i 1.16556 + 0.854171i
\(59\) 4.00000i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838471\pi\)
\(60\) 0 0
\(61\) 5.49706i 0.703827i −0.936033 0.351913i \(-0.885531\pi\)
0.936033 0.351913i \(-0.114469\pi\)
\(62\) −3.68613 + 5.02993i −0.468139 + 0.638801i
\(63\) 0 0
\(64\) 6.35424 + 4.86042i 0.794280 + 0.607552i
\(65\) 2.13145 0.264374
\(66\) 0 0
\(67\) 5.90658i 0.721604i 0.932642 + 0.360802i \(0.117497\pi\)
−0.932642 + 0.360802i \(0.882503\pi\)
\(68\) 3.67190 + 11.6252i 0.445283 + 1.40976i
\(69\) 0 0
\(70\) −0.532862 0.390503i −0.0636892 0.0466740i
\(71\) 4.72339 0.560563 0.280281 0.959918i \(-0.409572\pi\)
0.280281 + 0.959918i \(0.409572\pi\)
\(72\) 0 0
\(73\) −12.0599 −1.41150 −0.705749 0.708462i \(-0.749390\pi\)
−0.705749 + 0.708462i \(0.749390\pi\)
\(74\) 5.02993 + 3.68613i 0.584717 + 0.428504i
\(75\) 0 0
\(76\) 2.56279 0.809475i 0.293972 0.0928531i
\(77\) 4.87666i 0.555747i
\(78\) 0 0
\(79\) −16.1913 −1.82166 −0.910832 0.412778i \(-0.864559\pi\)
−0.910832 + 0.412778i \(0.864559\pi\)
\(80\) −1.07331 1.52954i −0.120000 0.171008i
\(81\) 0 0
\(82\) −5.09565 + 6.95329i −0.562721 + 0.767863i
\(83\) 13.7533i 1.50962i 0.655942 + 0.754811i \(0.272272\pi\)
−0.655942 + 0.754811i \(0.727728\pi\)
\(84\) 0 0
\(85\) 2.84751i 0.308856i
\(86\) −4.73762 3.47192i −0.510871 0.374387i
\(87\) 0 0
\(88\) 4.42375 13.0646i 0.471574 1.39269i
\(89\) −7.96420 −0.844204 −0.422102 0.906548i \(-0.638708\pi\)
−0.422102 + 0.906548i \(0.638708\pi\)
\(90\) 0 0
\(91\) 4.56279i 0.478310i
\(92\) −2.46714 7.81093i −0.257217 0.814346i
\(93\) 0 0
\(94\) −5.59048 + 7.62851i −0.576614 + 0.786821i
\(95\) −0.627737 −0.0644044
\(96\) 0 0
\(97\) −12.8789 −1.30765 −0.653827 0.756644i \(-0.726837\pi\)
−0.653827 + 0.756644i \(0.726837\pi\)
\(98\) −0.835949 + 1.14070i −0.0844436 + 0.115228i
\(99\) 0 0
\(100\) −2.88045 9.11947i −0.288045 0.911947i
\(101\) 2.22045i 0.220943i −0.993879 0.110472i \(-0.964764\pi\)
0.993879 0.110472i \(-0.0352361\pi\)
\(102\) 0 0
\(103\) 11.0971 1.09343 0.546715 0.837319i \(-0.315878\pi\)
0.546715 + 0.837319i \(0.315878\pi\)
\(104\) 4.13903 12.2238i 0.405866 1.19864i
\(105\) 0 0
\(106\) −1.53286 1.12334i −0.148885 0.109109i
\(107\) 3.12334i 0.301945i −0.988538 0.150972i \(-0.951760\pi\)
0.988538 0.150972i \(-0.0482405\pi\)
\(108\) 0 0
\(109\) 10.6876i 1.02369i −0.859079 0.511843i \(-0.828963\pi\)
0.859079 0.511843i \(-0.171037\pi\)
\(110\) −1.90435 + 2.59859i −0.181573 + 0.247766i
\(111\) 0 0
\(112\) −3.27428 + 2.29763i −0.309390 + 0.217106i
\(113\) 12.0599 1.13450 0.567248 0.823547i \(-0.308008\pi\)
0.567248 + 0.823547i \(0.308008\pi\)
\(114\) 0 0
\(115\) 1.91323i 0.178410i
\(116\) −14.8409 + 4.68759i −1.37794 + 0.435232i
\(117\) 0 0
\(118\) 4.56279 + 3.34379i 0.420039 + 0.307821i
\(119\) −6.09565 −0.558787
\(120\) 0 0
\(121\) −12.7818 −1.16198
\(122\) 6.27048 + 4.59526i 0.567703 + 0.416036i
\(123\) 0 0
\(124\) −2.65621 8.40952i −0.238534 0.755197i
\(125\) 4.56944i 0.408703i
\(126\) 0 0
\(127\) 18.8789 1.67523 0.837615 0.546261i \(-0.183949\pi\)
0.837615 + 0.546261i \(0.183949\pi\)
\(128\) −10.8561 + 3.18520i −0.959551 + 0.281534i
\(129\) 0 0
\(130\) −1.78178 + 2.43134i −0.156273 + 0.213243i
\(131\) 4.93428i 0.431110i 0.976492 + 0.215555i \(0.0691560\pi\)
−0.976492 + 0.215555i \(0.930844\pi\)
\(132\) 0 0
\(133\) 1.34379i 0.116522i
\(134\) −6.73762 4.93760i −0.582042 0.426544i
\(135\) 0 0
\(136\) −16.3303 5.52954i −1.40031 0.474154i
\(137\) −19.0103 −1.62416 −0.812082 0.583544i \(-0.801666\pi\)
−0.812082 + 0.583544i \(0.801666\pi\)
\(138\) 0 0
\(139\) 10.4380i 0.885339i 0.896685 + 0.442669i \(0.145968\pi\)
−0.896685 + 0.442669i \(0.854032\pi\)
\(140\) 0.890891 0.281394i 0.0752941 0.0237822i
\(141\) 0 0
\(142\) −3.94851 + 5.38795i −0.331352 + 0.452147i
\(143\) −22.2512 −1.86073
\(144\) 0 0
\(145\) 3.63516 0.301884
\(146\) 10.0814 13.7566i 0.834344 1.13851i
\(147\) 0 0
\(148\) −8.40952 + 2.65621i −0.691258 + 0.218339i
\(149\) 6.65621i 0.545298i −0.962114 0.272649i \(-0.912100\pi\)
0.962114 0.272649i \(-0.0878997\pi\)
\(150\) 0 0
\(151\) −2.68759 −0.218713 −0.109356 0.994003i \(-0.534879\pi\)
−0.109356 + 0.994003i \(0.534879\pi\)
\(152\) −1.21899 + 3.60004i −0.0988735 + 0.292002i
\(153\) 0 0
\(154\) 5.56279 + 4.07663i 0.448262 + 0.328505i
\(155\) 2.05985i 0.165451i
\(156\) 0 0
\(157\) 23.1351i 1.84639i 0.384338 + 0.923193i \(0.374430\pi\)
−0.384338 + 0.923193i \(0.625570\pi\)
\(158\) 13.5351 18.4694i 1.07679 1.46934i
\(159\) 0 0
\(160\) 2.64197 + 0.0542935i 0.208866 + 0.00429228i
\(161\) 4.09565 0.322783
\(162\) 0 0
\(163\) 12.0380i 0.942891i −0.881895 0.471446i \(-0.843732\pi\)
0.881895 0.471446i \(-0.156268\pi\)
\(164\) −3.67190 11.6252i −0.286727 0.907775i
\(165\) 0 0
\(166\) −15.6884 11.4971i −1.21765 0.892345i
\(167\) −9.01034 −0.697241 −0.348621 0.937264i \(-0.613350\pi\)
−0.348621 + 0.937264i \(0.613350\pi\)
\(168\) 0 0
\(169\) −7.81904 −0.601465
\(170\) 3.24814 + 2.38037i 0.249121 + 0.182566i
\(171\) 0 0
\(172\) 7.92082 2.50185i 0.603957 0.190764i
\(173\) 9.59271i 0.729321i −0.931141 0.364660i \(-0.881185\pi\)
0.931141 0.364660i \(-0.118815\pi\)
\(174\) 0 0
\(175\) 4.78178 0.361469
\(176\) 11.2048 + 15.9675i 0.844591 + 1.20360i
\(177\) 0 0
\(178\) 6.65766 9.08474i 0.499013 0.680930i
\(179\) 7.69278i 0.574985i 0.957783 + 0.287493i \(0.0928217\pi\)
−0.957783 + 0.287493i \(0.907178\pi\)
\(180\) 0 0
\(181\) 15.2504i 1.13355i 0.823872 + 0.566776i \(0.191809\pi\)
−0.823872 + 0.566776i \(0.808191\pi\)
\(182\) 5.20476 + 3.81426i 0.385802 + 0.282732i
\(183\) 0 0
\(184\) 10.9723 + 3.71528i 0.808889 + 0.273894i
\(185\) 2.05985 0.151443
\(186\) 0 0
\(187\) 29.7264i 2.17381i
\(188\) −4.02847 12.7541i −0.293806 0.930188i
\(189\) 0 0
\(190\) 0.524756 0.716058i 0.0380698 0.0519483i
\(191\) 4.72339 0.341772 0.170886 0.985291i \(-0.445337\pi\)
0.170886 + 0.985291i \(0.445337\pi\)
\(192\) 0 0
\(193\) 22.3379 1.60792 0.803959 0.594684i \(-0.202723\pi\)
0.803959 + 0.594684i \(0.202723\pi\)
\(194\) 10.7661 14.6909i 0.772960 1.05475i
\(195\) 0 0
\(196\) −0.602380 1.90713i −0.0430271 0.136223i
\(197\) 1.53510i 0.109371i −0.998504 0.0546855i \(-0.982584\pi\)
0.998504 0.0546855i \(-0.0174156\pi\)
\(198\) 0 0
\(199\) −14.6876 −1.04118 −0.520588 0.853808i \(-0.674287\pi\)
−0.520588 + 0.853808i \(0.674287\pi\)
\(200\) 12.8105 + 4.33769i 0.905837 + 0.306721i
\(201\) 0 0
\(202\) 2.53286 + 1.85618i 0.178212 + 0.130601i
\(203\) 7.78178i 0.546174i
\(204\) 0 0
\(205\) 2.84751i 0.198879i
\(206\) −9.27661 + 12.6584i −0.646332 + 0.881955i
\(207\) 0 0
\(208\) 10.4836 + 14.9398i 0.726907 + 1.03589i
\(209\) 6.55322 0.453296
\(210\) 0 0
\(211\) 22.8409i 1.57243i −0.617953 0.786215i \(-0.712038\pi\)
0.617953 0.786215i \(-0.287962\pi\)
\(212\) 2.56279 0.809475i 0.176013 0.0555949i
\(213\) 0 0
\(214\) 3.56279 + 2.61095i 0.243547 + 0.178481i
\(215\) −1.94015 −0.132317
\(216\) 0 0
\(217\) 4.40952 0.299338
\(218\) 12.1913 + 8.93428i 0.825699 + 0.605105i
\(219\) 0 0
\(220\) −1.37226 4.34457i −0.0925180 0.292911i
\(221\) 27.8132i 1.87092i
\(222\) 0 0
\(223\) 21.4321 1.43520 0.717600 0.696455i \(-0.245240\pi\)
0.717600 + 0.696455i \(0.245240\pi\)
\(224\) 0.116226 5.65566i 0.00776567 0.377885i
\(225\) 0 0
\(226\) −10.0814 + 13.7566i −0.670606 + 0.915078i
\(227\) 29.3169i 1.94583i 0.231164 + 0.972915i \(0.425747\pi\)
−0.231164 + 0.972915i \(0.574253\pi\)
\(228\) 0 0
\(229\) 22.5074i 1.48733i −0.668552 0.743666i \(-0.733086\pi\)
0.668552 0.743666i \(-0.266914\pi\)
\(230\) −2.18242 1.59936i −0.143904 0.105459i
\(231\) 0 0
\(232\) 7.05908 20.8475i 0.463451 1.36871i
\(233\) 0.687589 0.0450454 0.0225227 0.999746i \(-0.492830\pi\)
0.0225227 + 0.999746i \(0.492830\pi\)
\(234\) 0 0
\(235\) 3.12402i 0.203789i
\(236\) −7.62851 + 2.40952i −0.496574 + 0.156846i
\(237\) 0 0
\(238\) 5.09565 6.95329i 0.330302 0.450715i
\(239\) 9.59936 0.620931 0.310466 0.950585i \(-0.399515\pi\)
0.310466 + 0.950585i \(0.399515\pi\)
\(240\) 0 0
\(241\) 0.496287 0.0319687 0.0159843 0.999872i \(-0.494912\pi\)
0.0159843 + 0.999872i \(0.494912\pi\)
\(242\) 10.6849 14.5801i 0.686852 0.937247i
\(243\) 0 0
\(244\) −10.4836 + 3.31132i −0.671144 + 0.211986i
\(245\) 0.467138i 0.0298443i
\(246\) 0 0
\(247\) 6.13145 0.390135
\(248\) 11.8132 + 4.00000i 0.750137 + 0.254000i
\(249\) 0 0
\(250\) −5.21234 3.81982i −0.329658 0.241586i
\(251\) 22.1359i 1.39721i 0.715509 + 0.698603i \(0.246195\pi\)
−0.715509 + 0.698603i \(0.753805\pi\)
\(252\) 0 0
\(253\) 19.9731i 1.25570i
\(254\) −15.7818 + 21.5351i −0.990237 + 1.35123i
\(255\) 0 0
\(256\) 5.44178 15.0462i 0.340111 0.940385i
\(257\) −2.28695 −0.142656 −0.0713281 0.997453i \(-0.522724\pi\)
−0.0713281 + 0.997453i \(0.522724\pi\)
\(258\) 0 0
\(259\) 4.40952i 0.273994i
\(260\) −1.28394 4.06495i −0.0796267 0.252097i
\(261\) 0 0
\(262\) −5.62851 4.12480i −0.347731 0.254831i
\(263\) 30.1555 1.85947 0.929734 0.368232i \(-0.120037\pi\)
0.929734 + 0.368232i \(0.120037\pi\)
\(264\) 0 0
\(265\) −0.627737 −0.0385616
\(266\) −1.53286 1.12334i −0.0939858 0.0688766i
\(267\) 0 0
\(268\) 11.2646 3.55801i 0.688096 0.217340i
\(269\) 9.47748i 0.577852i 0.957351 + 0.288926i \(0.0932982\pi\)
−0.957351 + 0.288926i \(0.906702\pi\)
\(270\) 0 0
\(271\) −13.2855 −0.807036 −0.403518 0.914972i \(-0.632213\pi\)
−0.403518 + 0.914972i \(0.632213\pi\)
\(272\) 19.9589 14.0056i 1.21018 0.849212i
\(273\) 0 0
\(274\) 15.8917 21.6850i 0.960051 1.31004i
\(275\) 23.3191i 1.40620i
\(276\) 0 0
\(277\) 26.8475i 1.61311i 0.591159 + 0.806555i \(0.298671\pi\)
−0.591159 + 0.806555i \(0.701329\pi\)
\(278\) −11.9066 8.72562i −0.714109 0.523328i
\(279\) 0 0
\(280\) −0.423754 + 1.25147i −0.0253241 + 0.0747895i
\(281\) −11.8686 −0.708018 −0.354009 0.935242i \(-0.615182\pi\)
−0.354009 + 0.935242i \(0.615182\pi\)
\(282\) 0 0
\(283\) 2.46937i 0.146789i −0.997303 0.0733944i \(-0.976617\pi\)
0.997303 0.0733944i \(-0.0233832\pi\)
\(284\) −2.84527 9.00811i −0.168836 0.534533i
\(285\) 0 0
\(286\) 18.6008 25.3818i 1.09989 1.50086i
\(287\) 6.09565 0.359815
\(288\) 0 0
\(289\) 20.1570 1.18570
\(290\) −3.03881 + 4.14662i −0.178445 + 0.243498i
\(291\) 0 0
\(292\) 7.26461 + 22.9997i 0.425129 + 1.34595i
\(293\) 22.7899i 1.33140i 0.746220 + 0.665700i \(0.231867\pi\)
−0.746220 + 0.665700i \(0.768133\pi\)
\(294\) 0 0
\(295\) 1.86855 0.108791
\(296\) 4.00000 11.8132i 0.232495 0.686626i
\(297\) 0 0
\(298\) 7.59271 + 5.56425i 0.439834 + 0.322328i
\(299\) 18.6876i 1.08073i
\(300\) 0 0
\(301\) 4.15327i 0.239390i
\(302\) 2.24669 3.06572i 0.129282 0.176413i
\(303\) 0 0
\(304\) −3.08754 4.39996i −0.177083 0.252355i
\(305\) 2.56788 0.147037
\(306\) 0 0
\(307\) 9.34379i 0.533279i −0.963796 0.266639i \(-0.914087\pi\)
0.963796 0.266639i \(-0.0859132\pi\)
\(308\) −9.30041 + 2.93760i −0.529940 + 0.167385i
\(309\) 0 0
\(310\) −2.34967 1.72193i −0.133452 0.0977991i
\(311\) −6.68759 −0.379218 −0.189609 0.981860i \(-0.560722\pi\)
−0.189609 + 0.981860i \(0.560722\pi\)
\(312\) 0 0
\(313\) −15.6381 −0.883916 −0.441958 0.897036i \(-0.645716\pi\)
−0.441958 + 0.897036i \(0.645716\pi\)
\(314\) −26.3902 19.3398i −1.48928 1.09141i
\(315\) 0 0
\(316\) 9.75331 + 30.8789i 0.548667 + 1.73707i
\(317\) 9.34379i 0.524800i 0.964959 + 0.262400i \(0.0845139\pi\)
−0.964959 + 0.262400i \(0.915486\pi\)
\(318\) 0 0
\(319\) −37.9491 −2.12474
\(320\) −2.27048 + 2.96830i −0.126924 + 0.165933i
\(321\) 0 0
\(322\) −3.42375 + 4.67190i −0.190798 + 0.260355i
\(323\) 8.19130i 0.455776i
\(324\) 0 0
\(325\) 21.8183i 1.21026i
\(326\) 13.7317 + 10.0632i 0.760531 + 0.557348i
\(327\) 0 0
\(328\) 16.3303 + 5.52954i 0.901692 + 0.305318i
\(329\) 6.68759 0.368699
\(330\) 0 0
\(331\) 5.40874i 0.297291i 0.988891 + 0.148646i \(0.0474914\pi\)
−0.988891 + 0.148646i \(0.952509\pi\)
\(332\) 26.2293 8.28472i 1.43952 0.454683i
\(333\) 0 0
\(334\) 7.53218 10.2781i 0.412143 0.562391i
\(335\) −2.75919 −0.150750
\(336\) 0 0
\(337\) −6.55614 −0.357136 −0.178568 0.983928i \(-0.557146\pi\)
−0.178568 + 0.983928i \(0.557146\pi\)
\(338\) 6.53631 8.91915i 0.355529 0.485138i
\(339\) 0 0
\(340\) −5.43056 + 1.71528i −0.294514 + 0.0930242i
\(341\) 21.5037i 1.16449i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −3.76755 + 11.1267i −0.203133 + 0.599910i
\(345\) 0 0
\(346\) 10.9424 + 8.01902i 0.588266 + 0.431105i
\(347\) 24.9964i 1.34187i −0.741514 0.670937i \(-0.765892\pi\)
0.741514 0.670937i \(-0.234108\pi\)
\(348\) 0 0
\(349\) 27.1921i 1.45556i 0.685811 + 0.727779i \(0.259447\pi\)
−0.685811 + 0.727779i \(0.740553\pi\)
\(350\) −3.99732 + 5.45457i −0.213666 + 0.291559i
\(351\) 0 0
\(352\) −27.5807 0.566794i −1.47006 0.0302102i
\(353\) 30.2870 1.61201 0.806006 0.591907i \(-0.201625\pi\)
0.806006 + 0.591907i \(0.201625\pi\)
\(354\) 0 0
\(355\) 2.20647i 0.117107i
\(356\) 4.79747 + 15.1888i 0.254266 + 0.805002i
\(357\) 0 0
\(358\) −8.77513 6.43077i −0.463780 0.339877i
\(359\) −6.59194 −0.347909 −0.173955 0.984754i \(-0.555655\pi\)
−0.173955 + 0.984754i \(0.555655\pi\)
\(360\) 0 0
\(361\) 17.1942 0.904959
\(362\) −17.3961 12.7485i −0.914317 0.670048i
\(363\) 0 0
\(364\) −8.70182 + 2.74853i −0.456099 + 0.144062i
\(365\) 5.63361i 0.294877i
\(366\) 0 0
\(367\) −6.68759 −0.349089 −0.174545 0.984649i \(-0.555845\pi\)
−0.174545 + 0.984649i \(0.555845\pi\)
\(368\) −13.4103 + 9.41030i −0.699060 + 0.490546i
\(369\) 0 0
\(370\) −1.72193 + 2.34967i −0.0895189 + 0.122153i
\(371\) 1.34379i 0.0697663i
\(372\) 0 0
\(373\) 17.1256i 0.886729i 0.896341 + 0.443364i \(0.146215\pi\)
−0.896341 + 0.443364i \(0.853785\pi\)
\(374\) −33.9088 24.8497i −1.75338 1.28495i
\(375\) 0 0
\(376\) 17.9161 + 6.06650i 0.923955 + 0.312856i
\(377\) −35.5066 −1.82868
\(378\) 0 0
\(379\) 16.7094i 0.858305i 0.903232 + 0.429152i \(0.141188\pi\)
−0.903232 + 0.429152i \(0.858812\pi\)
\(380\) 0.378136 + 1.19717i 0.0193980 + 0.0614138i
\(381\) 0 0
\(382\) −3.94851 + 5.38795i −0.202023 + 0.275672i
\(383\) 9.94015 0.507918 0.253959 0.967215i \(-0.418267\pi\)
0.253959 + 0.967215i \(0.418267\pi\)
\(384\) 0 0
\(385\) 2.27807 0.116101
\(386\) −18.6734 + 25.4808i −0.950449 + 1.29694i
\(387\) 0 0
\(388\) 7.75798 + 24.5617i 0.393852 + 1.24693i
\(389\) 19.2884i 0.977961i 0.872295 + 0.488981i \(0.162631\pi\)
−0.872295 + 0.488981i \(0.837369\pi\)
\(390\) 0 0
\(391\) −24.9657 −1.26257
\(392\) 2.67901 + 0.907128i 0.135311 + 0.0458169i
\(393\) 0 0
\(394\) 1.75108 + 1.28326i 0.0882181 + 0.0646498i
\(395\) 7.56357i 0.380564i
\(396\) 0 0
\(397\) 23.4417i 1.17650i −0.808678 0.588252i \(-0.799816\pi\)
0.808678 0.588252i \(-0.200184\pi\)
\(398\) 12.2781 16.7541i 0.615444 0.839807i
\(399\) 0 0
\(400\) −15.6569 + 10.9868i −0.782844 + 0.549339i
\(401\) 16.0029 0.799147 0.399574 0.916701i \(-0.369158\pi\)
0.399574 + 0.916701i \(0.369158\pi\)
\(402\) 0 0
\(403\) 20.1197i 1.00223i
\(404\) −4.23469 + 1.33756i −0.210683 + 0.0665459i
\(405\) 0 0
\(406\) 8.87666 + 6.50517i 0.440541 + 0.322846i
\(407\) −21.5037 −1.06590
\(408\) 0 0
\(409\) 15.5665 0.769713 0.384856 0.922976i \(-0.374251\pi\)
0.384856 + 0.922976i \(0.374251\pi\)
\(410\) −3.24814 2.38037i −0.160414 0.117558i
\(411\) 0 0
\(412\) −6.68467 21.1636i −0.329330 1.04266i
\(413\) 4.00000i 0.196827i
\(414\) 0 0
\(415\) −6.42469 −0.315376
\(416\) −25.8056 0.530314i −1.26522 0.0260008i
\(417\) 0 0
\(418\) −5.47816 + 7.47524i −0.267946 + 0.365626i
\(419\) 1.31241i 0.0641155i 0.999486 + 0.0320577i \(0.0102060\pi\)
−0.999486 + 0.0320577i \(0.989794\pi\)
\(420\) 0 0
\(421\) 3.66655i 0.178697i 0.996000 + 0.0893483i \(0.0284784\pi\)
−0.996000 + 0.0893483i \(0.971522\pi\)
\(422\) 26.0545 + 19.0938i 1.26831 + 0.929471i
\(423\) 0 0
\(424\) −1.21899 + 3.60004i −0.0591996 + 0.174834i
\(425\) −29.1481 −1.41389
\(426\) 0 0
\(427\) 5.49706i 0.266022i
\(428\) −5.95662 + 1.88144i −0.287924 + 0.0909428i
\(429\) 0 0
\(430\) 1.62186 2.21312i 0.0782132 0.106726i
\(431\) −20.0957 −0.967973 −0.483987 0.875075i \(-0.660812\pi\)
−0.483987 + 0.875075i \(0.660812\pi\)
\(432\) 0 0
\(433\) 8.68759 0.417499 0.208749 0.977969i \(-0.433061\pi\)
0.208749 + 0.977969i \(0.433061\pi\)
\(434\) −3.68613 + 5.02993i −0.176940 + 0.241444i
\(435\) 0 0
\(436\) −20.3826 + 6.43799i −0.976150 + 0.308324i
\(437\) 5.50371i 0.263278i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 6.10298 + 2.06650i 0.290948 + 0.0985166i
\(441\) 0 0
\(442\) −31.7264 23.2504i −1.50907 1.10591i
\(443\) 4.57012i 0.217133i −0.994089 0.108566i \(-0.965374\pi\)
0.994089 0.108566i \(-0.0346260\pi\)
\(444\) 0 0
\(445\) 3.72038i 0.176363i
\(446\) −17.9161 + 24.4476i −0.848354 + 1.15763i
\(447\) 0 0
\(448\) 6.35424 + 4.86042i 0.300209 + 0.229633i
\(449\) 3.94015 0.185947 0.0929735 0.995669i \(-0.470363\pi\)
0.0929735 + 0.995669i \(0.470363\pi\)
\(450\) 0 0
\(451\) 29.7264i 1.39976i
\(452\) −7.26461 22.9997i −0.341699 1.08181i
\(453\) 0 0
\(454\) −33.4417 24.5074i −1.56950 1.15019i
\(455\) 2.13145 0.0999239
\(456\) 0 0
\(457\) 40.0207 1.87209 0.936044 0.351882i \(-0.114458\pi\)
0.936044 + 0.351882i \(0.114458\pi\)
\(458\) 25.6741 + 18.8150i 1.19967 + 0.879169i
\(459\) 0 0
\(460\) 3.64878 1.15249i 0.170125 0.0537352i
\(461\) 34.6031i 1.61162i −0.592171 0.805812i \(-0.701729\pi\)
0.592171 0.805812i \(-0.298271\pi\)
\(462\) 0 0
\(463\) 0.191302 0.00889055 0.00444528 0.999990i \(-0.498585\pi\)
0.00444528 + 0.999990i \(0.498585\pi\)
\(464\) 17.8797 + 25.4797i 0.830043 + 1.18287i
\(465\) 0 0
\(466\) −0.574789 + 0.784331i −0.0266266 + 0.0363334i
\(467\) 4.49784i 0.208135i 0.994570 + 0.104068i \(0.0331858\pi\)
−0.994570 + 0.104068i \(0.966814\pi\)
\(468\) 0 0
\(469\) 5.90658i 0.272741i
\(470\) −3.56357 2.61152i −0.164375 0.120461i
\(471\) 0 0
\(472\) 3.62851 10.7161i 0.167016 0.493247i
\(473\) 20.2541 0.931283
\(474\) 0 0
\(475\) 6.42573i 0.294833i
\(476\) 3.67190 + 11.6252i 0.168301 + 0.532840i
\(477\) 0 0
\(478\) −8.02457 + 10.9500i −0.367036 + 0.500840i
\(479\) 22.2512 1.01668 0.508341 0.861156i \(-0.330259\pi\)
0.508341 + 0.861156i \(0.330259\pi\)
\(480\) 0 0
\(481\) −20.1197 −0.917380
\(482\) −0.414870 + 0.566113i −0.0188968 + 0.0257857i
\(483\) 0 0
\(484\) 7.69949 + 24.3765i 0.349977 + 1.10802i
\(485\) 6.01621i 0.273182i
\(486\) 0 0
\(487\) −1.86855 −0.0846721 −0.0423360 0.999103i \(-0.513480\pi\)
−0.0423360 + 0.999103i \(0.513480\pi\)
\(488\) 4.98654 14.7267i 0.225730 0.666647i
\(489\) 0 0
\(490\) −0.532862 0.390503i −0.0240723 0.0176411i
\(491\) 17.6374i 0.795965i −0.917393 0.397982i \(-0.869711\pi\)
0.917393 0.397982i \(-0.130289\pi\)
\(492\) 0 0
\(493\) 47.4350i 2.13637i
\(494\) −5.12558 + 6.99413i −0.230611 + 0.314681i
\(495\) 0 0
\(496\) −14.4380 + 10.1314i −0.648285 + 0.454916i
\(497\) 4.72339 0.211873
\(498\) 0 0
\(499\) 21.5854i 0.966295i −0.875539 0.483147i \(-0.839494\pi\)
0.875539 0.483147i \(-0.160506\pi\)
\(500\) 8.71450 2.75254i 0.389724 0.123097i
\(501\) 0 0
\(502\) −25.2504 18.5045i −1.12698 0.825896i
\(503\) −5.24081 −0.233676 −0.116838 0.993151i \(-0.537276\pi\)
−0.116838 + 0.993151i \(0.537276\pi\)
\(504\) 0 0
\(505\) 1.03726 0.0461573
\(506\) 22.7832 + 16.6965i 1.01284 + 0.742249i
\(507\) 0 0
\(508\) −11.3723 36.0045i −0.504563 1.59744i
\(509\) 18.3357i 0.812715i 0.913714 + 0.406358i \(0.133201\pi\)
−0.913714 + 0.406358i \(0.866799\pi\)
\(510\) 0 0
\(511\) −12.0599 −0.533496
\(512\) 12.6141 + 18.7852i 0.557468 + 0.830198i
\(513\) 0 0
\(514\) 1.91178 2.60872i 0.0843248 0.115066i
\(515\) 5.18388i 0.228429i
\(516\) 0 0
\(517\) 32.6131i 1.43432i
\(518\) 5.02993 + 3.68613i 0.221002 + 0.161959i
\(519\) 0 0
\(520\) 5.71018 + 1.93350i 0.250408 + 0.0847895i
\(521\) −6.78033 −0.297051 −0.148526 0.988909i \(-0.547453\pi\)
−0.148526 + 0.988909i \(0.547453\pi\)
\(522\) 0 0
\(523\) 23.5066i 1.02787i −0.857828 0.513937i \(-0.828187\pi\)
0.857828 0.513937i \(-0.171813\pi\)
\(524\) 9.41030 2.97231i 0.411091 0.129846i
\(525\) 0 0
\(526\) −25.2085 + 34.3983i −1.09914 + 1.49984i
\(527\) −26.8789 −1.17086
\(528\) 0 0
\(529\) −6.22564 −0.270680
\(530\) 0.524756 0.716058i 0.0227939 0.0311036i
\(531\) 0 0
\(532\) 2.56279 0.809475i 0.111111 0.0350952i
\(533\) 27.8132i 1.20472i
\(534\) 0 0
\(535\) 1.45903 0.0630794
\(536\) −5.35803 + 15.8238i −0.231432 + 0.683485i
\(537\) 0 0
\(538\) −10.8109 7.92268i −0.466092 0.341571i
\(539\) 4.87666i 0.210052i
\(540\) 0 0
\(541\) 5.21526i 0.224222i 0.993696 + 0.112111i \(0.0357611\pi\)
−0.993696 + 0.112111i \(0.964239\pi\)
\(542\) 11.1060 15.1547i 0.477043 0.650951i
\(543\) 0 0
\(544\) −0.708473 + 34.4749i −0.0303755 + 1.47810i
\(545\) 4.99257 0.213858
\(546\) 0 0
\(547\) 27.2951i 1.16705i 0.812094 + 0.583526i \(0.198327\pi\)
−0.812094 + 0.583526i \(0.801673\pi\)
\(548\) 11.4514 + 36.2552i 0.489182 + 1.54874i
\(549\) 0 0
\(550\) 26.6000 + 19.4936i 1.13423 + 0.831209i
\(551\) 10.4571 0.445488
\(552\) 0 0
\(553\) −16.1913 −0.688524
\(554\) −30.6249 22.4431i −1.30113 0.953518i
\(555\) 0 0
\(556\) 19.9066 6.28763i 0.844227 0.266655i
\(557\) 4.78766i 0.202859i 0.994843 + 0.101430i \(0.0323417\pi\)
−0.994843 + 0.101430i \(0.967658\pi\)
\(558\) 0 0
\(559\) 18.9505 0.801520
\(560\) −1.07331 1.52954i −0.0453556 0.0646348i
\(561\) 0 0
\(562\) 9.92150 13.5384i 0.418513 0.571084i
\(563\) 18.7445i 0.789988i −0.918684 0.394994i \(-0.870747\pi\)
0.918684 0.394994i \(-0.129253\pi\)
\(564\) 0 0
\(565\) 5.63361i 0.237008i
\(566\) 2.81680 + 2.06427i 0.118399 + 0.0867676i
\(567\) 0 0
\(568\) 12.6540 + 4.28472i 0.530951 + 0.179783i
\(569\) −27.6950 −1.16104 −0.580518 0.814248i \(-0.697150\pi\)
−0.580518 + 0.814248i \(0.697150\pi\)
\(570\) 0 0
\(571\) 17.4132i 0.728720i −0.931258 0.364360i \(-0.881288\pi\)
0.931258 0.364360i \(-0.118712\pi\)
\(572\) 13.4036 + 42.4358i 0.560435 + 1.77433i
\(573\) 0 0
\(574\) −5.09565 + 6.95329i −0.212688 + 0.290225i
\(575\) 19.5845 0.816731
\(576\) 0 0
\(577\) −6.81904 −0.283880 −0.141940 0.989875i \(-0.545334\pi\)
−0.141940 + 0.989875i \(0.545334\pi\)
\(578\) −16.8502 + 22.9930i −0.700875 + 0.956382i
\(579\) 0 0
\(580\) −2.18975 6.93272i −0.0909244 0.287866i
\(581\) 13.7533i 0.570584i
\(582\) 0 0
\(583\) 6.55322 0.271407
\(584\) −32.3085 10.9398i −1.33694 0.452694i
\(585\) 0 0
\(586\) −25.9964 19.0512i −1.07390 0.786997i
\(587\) 9.81025i 0.404912i 0.979291 + 0.202456i \(0.0648924\pi\)
−0.979291 + 0.202456i \(0.935108\pi\)
\(588\) 0 0
\(589\) 5.92549i 0.244155i
\(590\) −1.56201 + 2.13145i −0.0643070 + 0.0877504i
\(591\) 0 0
\(592\) 10.1314 + 14.4380i 0.416400 + 0.593398i
\(593\) 39.0913 1.60529 0.802644 0.596458i \(-0.203426\pi\)
0.802644 + 0.596458i \(0.203426\pi\)
\(594\) 0 0
\(595\) 2.84751i 0.116736i
\(596\) −12.6942 + 4.00956i −0.519976 + 0.164238i
\(597\) 0 0
\(598\) 21.3169 + 15.6219i 0.871712 + 0.638826i
\(599\) −22.0270 −0.899998 −0.449999 0.893029i \(-0.648576\pi\)
−0.449999 + 0.893029i \(0.648576\pi\)
\(600\) 0 0
\(601\) −20.2512 −0.826062 −0.413031 0.910717i \(-0.635530\pi\)
−0.413031 + 0.910717i \(0.635530\pi\)
\(602\) −4.73762 3.47192i −0.193091 0.141505i
\(603\) 0 0
\(604\) 1.61895 + 5.12558i 0.0658741 + 0.208557i
\(605\) 5.97085i 0.242750i
\(606\) 0 0
\(607\) 44.4454 1.80398 0.901991 0.431755i \(-0.142105\pi\)
0.901991 + 0.431755i \(0.142105\pi\)
\(608\) 7.60004 + 0.156184i 0.308223 + 0.00633409i
\(609\) 0 0
\(610\) −2.14662 + 2.92918i −0.0869141 + 0.118599i
\(611\) 30.5141i 1.23447i
\(612\) 0 0
\(613\) 47.6263i 1.92361i 0.273737 + 0.961805i \(0.411740\pi\)
−0.273737 + 0.961805i \(0.588260\pi\)
\(614\) 10.6584 + 7.81093i 0.430140 + 0.315224i
\(615\) 0 0
\(616\) 4.42375 13.0646i 0.178238 0.526389i
\(617\) 3.01034 0.121192 0.0605959 0.998162i \(-0.480700\pi\)
0.0605959 + 0.998162i \(0.480700\pi\)
\(618\) 0 0
\(619\) 18.5141i 0.744143i −0.928204 0.372071i \(-0.878648\pi\)
0.928204 0.372071i \(-0.121352\pi\)
\(620\) 3.92840 1.24081i 0.157768 0.0498323i
\(621\) 0 0
\(622\) 5.59048 7.62851i 0.224158 0.305876i
\(623\) −7.96420 −0.319079
\(624\) 0 0
\(625\) 21.7744 0.870974
\(626\) 13.0726 17.8383i 0.522487 0.712962i
\(627\) 0 0
\(628\) 44.1217 13.9361i 1.76065 0.556113i
\(629\) 26.8789i 1.07173i
\(630\) 0 0
\(631\) 10.2658 0.408676 0.204338 0.978900i \(-0.434496\pi\)
0.204338 + 0.978900i \(0.434496\pi\)
\(632\) −43.3767 14.6876i −1.72543 0.584241i
\(633\) 0 0
\(634\) −10.6584 7.81093i −0.423301 0.310212i
\(635\) 8.81904i 0.349973i
\(636\) 0 0
\(637\) 4.56279i 0.180784i
\(638\) 31.7235 43.2884i 1.25594 1.71380i
\(639\) 0 0
\(640\) −1.48793 5.07128i −0.0588154 0.200460i
\(641\) 16.9358 0.668925 0.334462 0.942409i \(-0.391445\pi\)
0.334462 + 0.942409i \(0.391445\pi\)
\(642\) 0 0
\(643\) 19.5189i 0.769750i 0.922969 + 0.384875i \(0.125755\pi\)
−0.922969 + 0.384875i \(0.874245\pi\)
\(644\) −2.46714 7.81093i −0.0972188 0.307794i
\(645\) 0 0
\(646\) 9.34379 + 6.84751i 0.367627 + 0.269412i
\(647\) 23.3723 0.918858 0.459429 0.888214i \(-0.348054\pi\)
0.459429 + 0.888214i \(0.348054\pi\)
\(648\) 0 0
\(649\) −19.5066 −0.765702
\(650\) 24.8880 + 18.2389i 0.976189 + 0.715390i
\(651\) 0 0
\(652\) −22.9581 + 7.25147i −0.899108 + 0.283989i
\(653\) 1.45903i 0.0570963i 0.999592 + 0.0285481i \(0.00908839\pi\)
−0.999592 + 0.0285481i \(0.990912\pi\)
\(654\) 0 0
\(655\) −2.30499 −0.0900632
\(656\) −19.9589 + 14.0056i −0.779262 + 0.546825i
\(657\) 0 0
\(658\) −5.59048 + 7.62851i −0.217940 + 0.297390i
\(659\) 10.8929i 0.424326i 0.977234 + 0.212163i \(0.0680508\pi\)
−0.977234 + 0.212163i \(0.931949\pi\)
\(660\) 0 0
\(661\) 8.69715i 0.338280i −0.985592 0.169140i \(-0.945901\pi\)
0.985592 0.169140i \(-0.0540990\pi\)
\(662\) −6.16974 4.52143i −0.239794 0.175730i
\(663\) 0 0
\(664\) −12.4760 + 36.8453i −0.484164 + 1.42988i
\(665\) −0.627737 −0.0243426
\(666\) 0 0
\(667\) 31.8715i 1.23407i
\(668\) 5.42765 + 17.1839i 0.210002 + 0.664864i
\(669\) 0 0
\(670\) 2.30654 3.14740i 0.0891093 0.121595i
\(671\) −26.8073 −1.03488
\(672\) 0 0
\(673\) 18.0447 0.695571 0.347786 0.937574i \(-0.386934\pi\)
0.347786 + 0.937574i \(0.386934\pi\)
\(674\) 5.48060 7.47857i 0.211105 0.288064i
\(675\) 0 0
\(676\) 4.71003 + 14.9119i 0.181155 + 0.573535i
\(677\) 28.7781i 1.10603i −0.833170 0.553017i \(-0.813476\pi\)
0.833170 0.553017i \(-0.186524\pi\)
\(678\) 0 0
\(679\) −12.8789 −0.494246
\(680\) 2.58305 7.62851i 0.0990556 0.292540i
\(681\) 0 0
\(682\) 24.5292 + 17.9760i 0.939273 + 0.688337i
\(683\) 34.4431i 1.31793i 0.752174 + 0.658965i \(0.229005\pi\)
−0.752174 + 0.658965i \(0.770995\pi\)
\(684\) 0 0
\(685\) 8.88044i 0.339304i
\(686\) −0.835949 + 1.14070i −0.0319167 + 0.0435520i
\(687\) 0 0
\(688\) −9.54268 13.5990i −0.363811 0.518455i
\(689\) 6.13145 0.233590
\(690\) 0 0
\(691\) 41.5651i 1.58121i 0.612325 + 0.790606i \(0.290234\pi\)
−0.612325 + 0.790606i \(0.709766\pi\)
\(692\) −18.2945 + 5.77846i −0.695454 + 0.219664i
\(693\) 0 0
\(694\) 28.5133 + 20.8957i 1.08235 + 0.793189i
\(695\) −4.87598 −0.184956
\(696\) 0 0
\(697\) −37.1570 −1.40742
\(698\) −31.0179 22.7312i −1.17405 0.860388i
\(699\) 0 0
\(700\) −2.88045 9.11947i −0.108871 0.344684i
\(701\) 46.7804i 1.76687i −0.468553 0.883435i \(-0.655225\pi\)
0.468553 0.883435i \(-0.344775\pi\)
\(702\) 0 0
\(703\) 5.92549 0.223484
\(704\) 23.7026 30.9874i 0.893325 1.16788i
\(705\) 0 0
\(706\) −25.3183 + 34.5482i −0.952868 + 1.30024i
\(707\) 2.22045i 0.0835087i
\(708\) 0 0
\(709\) 8.43643i 0.316837i −0.987372 0.158418i \(-0.949360\pi\)
0.987372 0.158418i \(-0.0506395\pi\)
\(710\) −2.51692 1.84450i −0.0944582 0.0692227i
\(711\) 0 0
\(712\) −21.3362 7.22455i −0.799608 0.270752i
\(713\) 18.0599 0.676347
\(714\) 0 0
\(715\) 10.3943i 0.388727i
\(716\) 14.6711 4.63398i 0.548286 0.173180i
\(717\) 0 0
\(718\) 5.51052 7.51940i 0.205651 0.280622i
\(719\) 38.4425 1.43366 0.716831 0.697247i \(-0.245592\pi\)
0.716831 + 0.697247i \(0.245592\pi\)
\(720\) 0 0
\(721\) 11.0971 0.413278
\(722\) −14.3735 + 19.6134i −0.534926 + 0.729935i
\(723\) 0 0
\(724\) 29.0844 9.18652i 1.08091 0.341414i
\(725\) 37.2108i 1.38197i
\(726\) 0 0
\(727\) −17.5484 −0.650834 −0.325417 0.945571i \(-0.605505\pi\)
−0.325417 + 0.945571i \(0.605505\pi\)
\(728\) 4.13903 12.2238i 0.153403 0.453043i
\(729\) 0 0
\(730\) 6.42624 + 4.70941i 0.237846 + 0.174303i
\(731\) 25.3169i 0.936379i
\(732\) 0 0
\(733\) 38.8272i 1.43412i −0.697013 0.717058i \(-0.745488\pi\)
0.697013 0.717058i \(-0.254512\pi\)
\(734\) 5.59048 7.62851i 0.206348 0.281574i
\(735\) 0 0
\(736\) 0.476021 23.1636i 0.0175464 0.853822i
\(737\) 28.8044 1.06102
\(738\) 0 0
\(739\) 13.9066i 0.511562i −0.966735 0.255781i \(-0.917667\pi\)
0.966735 0.255781i \(-0.0823326\pi\)
\(740\) −1.24081 3.92840i −0.0456132 0.144411i
\(741\) 0 0
\(742\) −1.53286 1.12334i −0.0562732 0.0412392i
\(743\) −40.2300 −1.47590 −0.737948 0.674858i \(-0.764205\pi\)
−0.737948 + 0.674858i \(0.764205\pi\)
\(744\) 0 0
\(745\) 3.10936 0.113918
\(746\) −19.5351 14.3161i −0.715231 0.524150i
\(747\) 0 0
\(748\) 56.6921 17.9066i 2.07287 0.654730i
\(749\) 3.12334i 0.114124i
\(750\) 0 0
\(751\) 16.9957 0.620181 0.310091 0.950707i \(-0.399641\pi\)
0.310091 + 0.950707i \(0.399641\pi\)
\(752\) −21.8970 + 15.3656i −0.798502 + 0.560326i
\(753\) 0 0
\(754\) 29.6817 40.5023i 1.08094 1.47501i
\(755\) 1.25547i 0.0456914i
\(756\) 0 0
\(757\) 9.43212i 0.342816i −0.985200 0.171408i \(-0.945168\pi\)
0.985200 0.171408i \(-0.0548316\pi\)
\(758\) −19.0604 13.9682i −0.692304 0.507348i
\(759\) 0 0
\(760\) −1.68172 0.569438i −0.0610023 0.0206557i
\(761\) 9.41098 0.341148 0.170574 0.985345i \(-0.445438\pi\)
0.170574 + 0.985345i \(0.445438\pi\)
\(762\) 0 0
\(763\) 10.6876i 0.386917i
\(764\) −2.84527 9.00811i −0.102938 0.325902i
\(765\) 0 0
\(766\) −8.30945 + 11.3387i −0.300233 + 0.409684i
\(767\) −18.2512 −0.659011
\(768\) 0 0
\(769\) 27.6950 0.998708 0.499354 0.866398i \(-0.333571\pi\)
0.499354 + 0.866398i \(0.333571\pi\)
\(770\) −1.90435 + 2.59859i −0.0686280 + 0.0936466i
\(771\) 0 0
\(772\) −13.4559 42.6013i −0.484289 1.53325i
\(773\) 33.8993i 1.21927i 0.792682 + 0.609636i \(0.208684\pi\)
−0.792682 + 0.609636i \(0.791316\pi\)
\(774\) 0 0
\(775\) 21.0854 0.757409
\(776\) −34.5027 11.6828i −1.23858 0.419388i
\(777\) 0 0
\(778\) −22.0022 16.1241i −0.788818 0.578078i
\(779\) 8.19130i 0.293484i
\(780\) 0 0
\(781\) 23.0343i 0.824234i
\(782\) 20.8700 28.4783i 0.746310 1.01838i
\(783\) 0 0
\(784\) −3.27428 + 2.29763i −0.116938 + 0.0820583i
\(785\) −10.8073 −0.385729
\(786\) 0 0
\(787\) 31.2001i 1.11216i 0.831128 + 0.556082i \(0.187696\pi\)
−0.831128 + 0.556082i \(0.812304\pi\)
\(788\) −2.92763 + 0.924711i −0.104292 + 0.0329415i
\(789\) 0 0
\(790\) 8.62774 + 6.32275i 0.306961 + 0.224953i
\(791\) 12.0599 0.428799
\(792\) 0 0
\(793\) −25.0819 −0.890686
\(794\) 26.7399 + 19.5960i