Properties

Label 1520.2.d.h.609.4
Level $1520$
Weight $2$
Character 1520.609
Analytic conductor $12.137$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.16516096.1
Defining polynomial: \( x^{6} + 9x^{4} + 13x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 609.4
Root \(1.30397i\) of defining polynomial
Character \(\chi\) \(=\) 1520.609
Dual form 1520.2.d.h.609.3

$q$-expansion

\(f(q)\) \(=\) \(q+0.537080i q^{3} +(-2.07772 + 0.826491i) q^{5} +3.18676i q^{7} +2.71155 q^{9} +O(q^{10})\) \(q+0.537080i q^{3} +(-2.07772 + 0.826491i) q^{5} +3.18676i q^{7} +2.71155 q^{9} -4.15544 q^{11} -2.07086i q^{13} +(-0.443892 - 1.11590i) q^{15} +5.79470i q^{17} -1.00000 q^{19} -1.71155 q^{21} -2.60794i q^{23} +(3.63383 - 3.43443i) q^{25} +3.06756i q^{27} -6.00000 q^{29} -2.59933 q^{31} -2.23180i q^{33} +(-2.63383 - 6.62119i) q^{35} +4.30266i q^{37} +1.11222 q^{39} -0.599328 q^{41} +3.18676i q^{43} +(-5.63383 + 2.24107i) q^{45} -11.7086i q^{47} -3.15544 q^{49} -3.11222 q^{51} -11.7503i q^{53} +(8.63383 - 3.43443i) q^{55} -0.537080i q^{57} -1.71155 q^{59} -8.75476 q^{61} +8.64104i q^{63} +(1.71155 + 4.30266i) q^{65} -4.76228i q^{67} +1.40067 q^{69} -13.7115 q^{71} +2.72714i q^{73} +(1.84456 + 1.95166i) q^{75} -13.2424i q^{77} -1.40067 q^{79} +6.48711 q^{81} -7.07154i q^{83} +(-4.78926 - 12.0398i) q^{85} -3.22248i q^{87} -16.5353 q^{89} +6.59933 q^{91} -1.39605i q^{93} +(2.07772 - 0.826491i) q^{95} +2.07086i q^{97} -11.2677 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{5} - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{5} - 14 q^{9} - 2 q^{11} - 10 q^{15} - 6 q^{19} + 20 q^{21} + 3 q^{25} - 36 q^{29} + 3 q^{35} - 8 q^{39} + 12 q^{41} - 15 q^{45} + 4 q^{49} - 4 q^{51} + 33 q^{55} + 20 q^{59} - 14 q^{61} - 20 q^{65} + 24 q^{69} - 52 q^{71} + 34 q^{75} - 24 q^{79} + 38 q^{81} + 13 q^{85} - 24 q^{89} + 24 q^{91} + q^{95} - 30 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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 0
\(3\) 0.537080i 0.310083i 0.987908 + 0.155042i \(0.0495512\pi\)
−0.987908 + 0.155042i \(0.950449\pi\)
\(4\) 0 0
\(5\) −2.07772 + 0.826491i −0.929184 + 0.369618i
\(6\) 0 0
\(7\) 3.18676i 1.20448i 0.798314 + 0.602241i \(0.205725\pi\)
−0.798314 + 0.602241i \(0.794275\pi\)
\(8\) 0 0
\(9\) 2.71155 0.903848
\(10\) 0 0
\(11\) −4.15544 −1.25291 −0.626456 0.779457i \(-0.715495\pi\)
−0.626456 + 0.779457i \(0.715495\pi\)
\(12\) 0 0
\(13\) 2.07086i 0.574353i −0.957878 0.287176i \(-0.907283\pi\)
0.957878 0.287176i \(-0.0927166\pi\)
\(14\) 0 0
\(15\) −0.443892 1.11590i −0.114612 0.288124i
\(16\) 0 0
\(17\) 5.79470i 1.40542i 0.711476 + 0.702710i \(0.248027\pi\)
−0.711476 + 0.702710i \(0.751973\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −1.71155 −0.373490
\(22\) 0 0
\(23\) 2.60794i 0.543793i −0.962327 0.271896i \(-0.912349\pi\)
0.962327 0.271896i \(-0.0876508\pi\)
\(24\) 0 0
\(25\) 3.63383 3.43443i 0.726765 0.686886i
\(26\) 0 0
\(27\) 3.06756i 0.590352i
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −2.59933 −0.466853 −0.233427 0.972374i \(-0.574994\pi\)
−0.233427 + 0.972374i \(0.574994\pi\)
\(32\) 0 0
\(33\) 2.23180i 0.388507i
\(34\) 0 0
\(35\) −2.63383 6.62119i −0.445198 1.11919i
\(36\) 0 0
\(37\) 4.30266i 0.707353i 0.935368 + 0.353677i \(0.115069\pi\)
−0.935368 + 0.353677i \(0.884931\pi\)
\(38\) 0 0
\(39\) 1.11222 0.178097
\(40\) 0 0
\(41\) −0.599328 −0.0935993 −0.0467997 0.998904i \(-0.514902\pi\)
−0.0467997 + 0.998904i \(0.514902\pi\)
\(42\) 0 0
\(43\) 3.18676i 0.485976i 0.970029 + 0.242988i \(0.0781276\pi\)
−0.970029 + 0.242988i \(0.921872\pi\)
\(44\) 0 0
\(45\) −5.63383 + 2.24107i −0.839841 + 0.334078i
\(46\) 0 0
\(47\) 11.7086i 1.70787i −0.520376 0.853937i \(-0.674208\pi\)
0.520376 0.853937i \(-0.325792\pi\)
\(48\) 0 0
\(49\) −3.15544 −0.450777
\(50\) 0 0
\(51\) −3.11222 −0.435798
\(52\) 0 0
\(53\) 11.7503i 1.61403i −0.590529 0.807017i \(-0.701081\pi\)
0.590529 0.807017i \(-0.298919\pi\)
\(54\) 0 0
\(55\) 8.63383 3.43443i 1.16418 0.463098i
\(56\) 0 0
\(57\) 0.537080i 0.0711380i
\(58\) 0 0
\(59\) −1.71155 −0.222824 −0.111412 0.993774i \(-0.535537\pi\)
−0.111412 + 0.993774i \(0.535537\pi\)
\(60\) 0 0
\(61\) −8.75476 −1.12093 −0.560466 0.828177i \(-0.689378\pi\)
−0.560466 + 0.828177i \(0.689378\pi\)
\(62\) 0 0
\(63\) 8.64104i 1.08867i
\(64\) 0 0
\(65\) 1.71155 + 4.30266i 0.212291 + 0.533679i
\(66\) 0 0
\(67\) 4.76228i 0.581805i −0.956753 0.290902i \(-0.906044\pi\)
0.956753 0.290902i \(-0.0939555\pi\)
\(68\) 0 0
\(69\) 1.40067 0.168621
\(70\) 0 0
\(71\) −13.7115 −1.62726 −0.813631 0.581382i \(-0.802512\pi\)
−0.813631 + 0.581382i \(0.802512\pi\)
\(72\) 0 0
\(73\) 2.72714i 0.319188i 0.987183 + 0.159594i \(0.0510185\pi\)
−0.987183 + 0.159594i \(0.948982\pi\)
\(74\) 0 0
\(75\) 1.84456 + 1.95166i 0.212992 + 0.225358i
\(76\) 0 0
\(77\) 13.2424i 1.50911i
\(78\) 0 0
\(79\) −1.40067 −0.157588 −0.0787939 0.996891i \(-0.525107\pi\)
−0.0787939 + 0.996891i \(0.525107\pi\)
\(80\) 0 0
\(81\) 6.48711 0.720790
\(82\) 0 0
\(83\) 7.07154i 0.776203i −0.921617 0.388101i \(-0.873131\pi\)
0.921617 0.388101i \(-0.126869\pi\)
\(84\) 0 0
\(85\) −4.78926 12.0398i −0.519469 1.30589i
\(86\) 0 0
\(87\) 3.22248i 0.345486i
\(88\) 0 0
\(89\) −16.5353 −1.75274 −0.876370 0.481639i \(-0.840042\pi\)
−0.876370 + 0.481639i \(0.840042\pi\)
\(90\) 0 0
\(91\) 6.59933 0.691798
\(92\) 0 0
\(93\) 1.39605i 0.144763i
\(94\) 0 0
\(95\) 2.07772 0.826491i 0.213169 0.0847961i
\(96\) 0 0
\(97\) 2.07086i 0.210264i 0.994458 + 0.105132i \(0.0335265\pi\)
−0.994458 + 0.105132i \(0.966474\pi\)
\(98\) 0 0
\(99\) −11.2677 −1.13244
\(100\) 0 0
\(101\) −1.71155 −0.170305 −0.0851525 0.996368i \(-0.527138\pi\)
−0.0851525 + 0.996368i \(0.527138\pi\)
\(102\) 0 0
\(103\) 5.75296i 0.566856i 0.958994 + 0.283428i \(0.0914716\pi\)
−0.958994 + 0.283428i \(0.908528\pi\)
\(104\) 0 0
\(105\) 3.55611 1.41458i 0.347041 0.138048i
\(106\) 0 0
\(107\) 15.4324i 1.49191i 0.665996 + 0.745955i \(0.268007\pi\)
−0.665996 + 0.745955i \(0.731993\pi\)
\(108\) 0 0
\(109\) −11.7115 −1.12176 −0.560881 0.827896i \(-0.689538\pi\)
−0.560881 + 0.827896i \(0.689538\pi\)
\(110\) 0 0
\(111\) −2.31087 −0.219338
\(112\) 0 0
\(113\) 10.5927i 0.996477i 0.867040 + 0.498239i \(0.166020\pi\)
−0.867040 + 0.498239i \(0.833980\pi\)
\(114\) 0 0
\(115\) 2.15544 + 5.41856i 0.200996 + 0.505283i
\(116\) 0 0
\(117\) 5.61523i 0.519128i
\(118\) 0 0
\(119\) −18.4663 −1.69280
\(120\) 0 0
\(121\) 6.26765 0.569787
\(122\) 0 0
\(123\) 0.321887i 0.0290236i
\(124\) 0 0
\(125\) −4.71155 + 10.1391i −0.421413 + 0.906869i
\(126\) 0 0
\(127\) 6.07484i 0.539055i 0.962993 + 0.269528i \(0.0868676\pi\)
−0.962993 + 0.269528i \(0.913132\pi\)
\(128\) 0 0
\(129\) −1.71155 −0.150693
\(130\) 0 0
\(131\) 13.5785 1.18636 0.593181 0.805069i \(-0.297872\pi\)
0.593181 + 0.805069i \(0.297872\pi\)
\(132\) 0 0
\(133\) 3.18676i 0.276327i
\(134\) 0 0
\(135\) −2.53531 6.37352i −0.218204 0.548545i
\(136\) 0 0
\(137\) 7.94302i 0.678618i −0.940675 0.339309i \(-0.889807\pi\)
0.940675 0.339309i \(-0.110193\pi\)
\(138\) 0 0
\(139\) 3.26765 0.277159 0.138579 0.990351i \(-0.455746\pi\)
0.138579 + 0.990351i \(0.455746\pi\)
\(140\) 0 0
\(141\) 6.28845 0.529583
\(142\) 0 0
\(143\) 8.60532i 0.719613i
\(144\) 0 0
\(145\) 12.4663 4.95894i 1.03527 0.411818i
\(146\) 0 0
\(147\) 1.69472i 0.139778i
\(148\) 0 0
\(149\) −8.44389 −0.691751 −0.345875 0.938280i \(-0.612418\pi\)
−0.345875 + 0.938280i \(0.612418\pi\)
\(150\) 0 0
\(151\) −0.887783 −0.0722468 −0.0361234 0.999347i \(-0.511501\pi\)
−0.0361234 + 0.999347i \(0.511501\pi\)
\(152\) 0 0
\(153\) 15.7126i 1.27029i
\(154\) 0 0
\(155\) 5.40067 2.14832i 0.433792 0.172557i
\(156\) 0 0
\(157\) 4.14172i 0.330545i 0.986248 + 0.165273i \(0.0528504\pi\)
−0.986248 + 0.165273i \(0.947150\pi\)
\(158\) 0 0
\(159\) 6.31087 0.500485
\(160\) 0 0
\(161\) 8.31087 0.654989
\(162\) 0 0
\(163\) 24.7126i 1.93564i −0.251647 0.967819i \(-0.580972\pi\)
0.251647 0.967819i \(-0.419028\pi\)
\(164\) 0 0
\(165\) 1.84456 + 4.63706i 0.143599 + 0.360994i
\(166\) 0 0
\(167\) 3.60464i 0.278935i 0.990227 + 0.139468i \(0.0445391\pi\)
−0.990227 + 0.139468i \(0.955461\pi\)
\(168\) 0 0
\(169\) 8.71155 0.670119
\(170\) 0 0
\(171\) −2.71155 −0.207357
\(172\) 0 0
\(173\) 22.4205i 1.70460i 0.523054 + 0.852300i \(0.324793\pi\)
−0.523054 + 0.852300i \(0.675207\pi\)
\(174\) 0 0
\(175\) 10.9447 + 11.5801i 0.827342 + 0.875376i
\(176\) 0 0
\(177\) 0.919237i 0.0690941i
\(178\) 0 0
\(179\) −5.13464 −0.383781 −0.191890 0.981416i \(-0.561462\pi\)
−0.191890 + 0.981416i \(0.561462\pi\)
\(180\) 0 0
\(181\) 20.8462 1.54948 0.774742 0.632277i \(-0.217880\pi\)
0.774742 + 0.632277i \(0.217880\pi\)
\(182\) 0 0
\(183\) 4.70201i 0.347583i
\(184\) 0 0
\(185\) −3.55611 8.93972i −0.261450 0.657261i
\(186\) 0 0
\(187\) 24.0795i 1.76087i
\(188\) 0 0
\(189\) −9.77557 −0.711068
\(190\) 0 0
\(191\) 5.26765 0.381154 0.190577 0.981672i \(-0.438964\pi\)
0.190577 + 0.981672i \(0.438964\pi\)
\(192\) 0 0
\(193\) 2.07086i 0.149064i −0.997219 0.0745318i \(-0.976254\pi\)
0.997219 0.0745318i \(-0.0237462\pi\)
\(194\) 0 0
\(195\) −2.31087 + 0.919237i −0.165485 + 0.0658279i
\(196\) 0 0
\(197\) 10.4318i 0.743232i 0.928387 + 0.371616i \(0.121196\pi\)
−0.928387 + 0.371616i \(0.878804\pi\)
\(198\) 0 0
\(199\) −2.73235 −0.193691 −0.0968455 0.995299i \(-0.530875\pi\)
−0.0968455 + 0.995299i \(0.530875\pi\)
\(200\) 0 0
\(201\) 2.55773 0.180408
\(202\) 0 0
\(203\) 19.1206i 1.34200i
\(204\) 0 0
\(205\) 1.24524 0.495339i 0.0869710 0.0345960i
\(206\) 0 0
\(207\) 7.07154i 0.491506i
\(208\) 0 0
\(209\) 4.15544 0.287438
\(210\) 0 0
\(211\) 15.7340 1.08317 0.541585 0.840646i \(-0.317824\pi\)
0.541585 + 0.840646i \(0.317824\pi\)
\(212\) 0 0
\(213\) 7.36420i 0.504586i
\(214\) 0 0
\(215\) −2.63383 6.62119i −0.179625 0.451561i
\(216\) 0 0
\(217\) 8.28343i 0.562316i
\(218\) 0 0
\(219\) −1.46469 −0.0989748
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 18.8219i 1.26041i 0.776430 + 0.630203i \(0.217028\pi\)
−0.776430 + 0.630203i \(0.782972\pi\)
\(224\) 0 0
\(225\) 9.85328 9.31261i 0.656886 0.620841i
\(226\) 0 0
\(227\) 14.4418i 0.958533i 0.877669 + 0.479267i \(0.159097\pi\)
−0.877669 + 0.479267i \(0.840903\pi\)
\(228\) 0 0
\(229\) 4.17785 0.276080 0.138040 0.990427i \(-0.455920\pi\)
0.138040 + 0.990427i \(0.455920\pi\)
\(230\) 0 0
\(231\) 7.11222 0.467950
\(232\) 0 0
\(233\) 12.0847i 0.791697i −0.918316 0.395849i \(-0.870450\pi\)
0.918316 0.395849i \(-0.129550\pi\)
\(234\) 0 0
\(235\) 9.67705 + 24.3272i 0.631261 + 1.58693i
\(236\) 0 0
\(237\) 0.752273i 0.0488654i
\(238\) 0 0
\(239\) −11.3541 −0.734435 −0.367218 0.930135i \(-0.619690\pi\)
−0.367218 + 0.930135i \(0.619690\pi\)
\(240\) 0 0
\(241\) −3.40067 −0.219057 −0.109528 0.993984i \(-0.534934\pi\)
−0.109528 + 0.993984i \(0.534934\pi\)
\(242\) 0 0
\(243\) 12.6868i 0.813857i
\(244\) 0 0
\(245\) 6.55611 2.60794i 0.418854 0.166615i
\(246\) 0 0
\(247\) 2.07086i 0.131766i
\(248\) 0 0
\(249\) 3.79798 0.240687
\(250\) 0 0
\(251\) −3.04322 −0.192086 −0.0960432 0.995377i \(-0.530619\pi\)
−0.0960432 + 0.995377i \(0.530619\pi\)
\(252\) 0 0
\(253\) 10.8371i 0.681324i
\(254\) 0 0
\(255\) 6.46631 2.57222i 0.404936 0.161079i
\(256\) 0 0
\(257\) 17.2881i 1.07840i 0.842177 + 0.539201i \(0.181274\pi\)
−0.842177 + 0.539201i \(0.818726\pi\)
\(258\) 0 0
\(259\) −13.7115 −0.851994
\(260\) 0 0
\(261\) −16.2693 −1.00704
\(262\) 0 0
\(263\) 1.19336i 0.0735859i −0.999323 0.0367930i \(-0.988286\pi\)
0.999323 0.0367930i \(-0.0117142\pi\)
\(264\) 0 0
\(265\) 9.71155 + 24.4139i 0.596575 + 1.49973i
\(266\) 0 0
\(267\) 8.88078i 0.543495i
\(268\) 0 0
\(269\) −22.1089 −1.34800 −0.674000 0.738731i \(-0.735425\pi\)
−0.674000 + 0.738731i \(0.735425\pi\)
\(270\) 0 0
\(271\) 4.08644 0.248234 0.124117 0.992268i \(-0.460390\pi\)
0.124117 + 0.992268i \(0.460390\pi\)
\(272\) 0 0
\(273\) 3.54437i 0.214515i
\(274\) 0 0
\(275\) −15.1001 + 14.2716i −0.910572 + 0.860607i
\(276\) 0 0
\(277\) 10.0199i 0.602037i −0.953618 0.301019i \(-0.902673\pi\)
0.953618 0.301019i \(-0.0973266\pi\)
\(278\) 0 0
\(279\) −7.04820 −0.421964
\(280\) 0 0
\(281\) 0.599328 0.0357529 0.0178765 0.999840i \(-0.494309\pi\)
0.0178765 + 0.999840i \(0.494309\pi\)
\(282\) 0 0
\(283\) 5.41856i 0.322100i 0.986946 + 0.161050i \(0.0514880\pi\)
−0.986946 + 0.161050i \(0.948512\pi\)
\(284\) 0 0
\(285\) 0.443892 + 1.11590i 0.0262939 + 0.0661003i
\(286\) 0 0
\(287\) 1.90991i 0.112739i
\(288\) 0 0
\(289\) −16.5785 −0.975207
\(290\) 0 0
\(291\) −1.11222 −0.0651993
\(292\) 0 0
\(293\) 3.46691i 0.202539i −0.994859 0.101269i \(-0.967710\pi\)
0.994859 0.101269i \(-0.0322904\pi\)
\(294\) 0 0
\(295\) 3.55611 1.41458i 0.207045 0.0823598i
\(296\) 0 0
\(297\) 12.7470i 0.739658i
\(298\) 0 0
\(299\) −5.40067 −0.312329
\(300\) 0 0
\(301\) −10.1554 −0.585350
\(302\) 0 0
\(303\) 0.919237i 0.0528088i
\(304\) 0 0
\(305\) 18.1899 7.23573i 1.04155 0.414317i
\(306\) 0 0
\(307\) 16.5901i 0.946846i 0.880835 + 0.473423i \(0.156982\pi\)
−0.880835 + 0.473423i \(0.843018\pi\)
\(308\) 0 0
\(309\) −3.08980 −0.175772
\(310\) 0 0
\(311\) 4.15544 0.235633 0.117817 0.993035i \(-0.462411\pi\)
0.117817 + 0.993035i \(0.462411\pi\)
\(312\) 0 0
\(313\) 0.919237i 0.0519583i 0.999662 + 0.0259792i \(0.00827036\pi\)
−0.999662 + 0.0259792i \(0.991730\pi\)
\(314\) 0 0
\(315\) −7.14174 17.9537i −0.402391 1.01157i
\(316\) 0 0
\(317\) 26.7292i 1.50126i −0.660723 0.750630i \(-0.729750\pi\)
0.660723 0.750630i \(-0.270250\pi\)
\(318\) 0 0
\(319\) 24.9326 1.39596
\(320\) 0 0
\(321\) −8.28845 −0.462616
\(322\) 0 0
\(323\) 5.79470i 0.322426i
\(324\) 0 0
\(325\) −7.11222 7.52514i −0.394515 0.417420i
\(326\) 0 0
\(327\) 6.29004i 0.347840i
\(328\) 0 0
\(329\) 37.3125 2.05710
\(330\) 0 0
\(331\) −8.00000 −0.439720 −0.219860 0.975531i \(-0.570560\pi\)
−0.219860 + 0.975531i \(0.570560\pi\)
\(332\) 0 0
\(333\) 11.6669i 0.639340i
\(334\) 0 0
\(335\) 3.93598 + 9.89467i 0.215045 + 0.540604i
\(336\) 0 0
\(337\) 22.5040i 1.22587i 0.790133 + 0.612935i \(0.210011\pi\)
−0.790133 + 0.612935i \(0.789989\pi\)
\(338\) 0 0
\(339\) −5.68913 −0.308991
\(340\) 0 0
\(341\) 10.8013 0.584926
\(342\) 0 0
\(343\) 12.2517i 0.661530i
\(344\) 0 0
\(345\) −2.91020 + 1.15764i −0.156680 + 0.0623254i
\(346\) 0 0
\(347\) 14.4543i 0.775946i 0.921671 + 0.387973i \(0.126825\pi\)
−0.921671 + 0.387973i \(0.873175\pi\)
\(348\) 0 0
\(349\) 13.3541 0.714828 0.357414 0.933946i \(-0.383658\pi\)
0.357414 + 0.933946i \(0.383658\pi\)
\(350\) 0 0
\(351\) 6.35248 0.339070
\(352\) 0 0
\(353\) 17.6410i 0.938937i −0.882949 0.469469i \(-0.844446\pi\)
0.882949 0.469469i \(-0.155554\pi\)
\(354\) 0 0
\(355\) 28.4887 11.3325i 1.51202 0.601465i
\(356\) 0 0
\(357\) 9.91789i 0.524910i
\(358\) 0 0
\(359\) 12.4663 0.657947 0.328973 0.944339i \(-0.393297\pi\)
0.328973 + 0.944339i \(0.393297\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 3.36623i 0.176681i
\(364\) 0 0
\(365\) −2.25396 5.66623i −0.117977 0.296584i
\(366\) 0 0
\(367\) 16.4291i 0.857594i 0.903401 + 0.428797i \(0.141062\pi\)
−0.903401 + 0.428797i \(0.858938\pi\)
\(368\) 0 0
\(369\) −1.62511 −0.0845996
\(370\) 0 0
\(371\) 37.4455 1.94407
\(372\) 0 0
\(373\) 5.29334i 0.274079i 0.990566 + 0.137039i \(0.0437587\pi\)
−0.990566 + 0.137039i \(0.956241\pi\)
\(374\) 0 0
\(375\) −5.44551 2.53048i −0.281205 0.130673i
\(376\) 0 0
\(377\) 12.4252i 0.639928i
\(378\) 0 0
\(379\) 14.5353 0.746629 0.373314 0.927705i \(-0.378221\pi\)
0.373314 + 0.927705i \(0.378221\pi\)
\(380\) 0 0
\(381\) −3.26268 −0.167152
\(382\) 0 0
\(383\) 0.453598i 0.0231778i 0.999933 + 0.0115889i \(0.00368894\pi\)
−0.999933 + 0.0115889i \(0.996311\pi\)
\(384\) 0 0
\(385\) 10.9447 + 27.5139i 0.557794 + 1.40224i
\(386\) 0 0
\(387\) 8.64104i 0.439249i
\(388\) 0 0
\(389\) −16.1554 −0.819113 −0.409557 0.912285i \(-0.634317\pi\)
−0.409557 + 0.912285i \(0.634317\pi\)
\(390\) 0 0
\(391\) 15.1122 0.764258
\(392\) 0 0
\(393\) 7.29276i 0.367871i
\(394\) 0 0
\(395\) 2.91020 1.15764i 0.146428 0.0582473i
\(396\) 0 0
\(397\) 32.7563i 1.64399i 0.569495 + 0.821995i \(0.307139\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(398\) 0 0
\(399\) 1.71155 0.0856844
\(400\) 0 0
\(401\) 12.0864 0.603568 0.301784 0.953376i \(-0.402418\pi\)
0.301784 + 0.953376i \(0.402418\pi\)
\(402\) 0 0
\(403\) 5.38284i 0.268138i
\(404\) 0 0
\(405\) −13.4784 + 5.36154i −0.669747 + 0.266417i
\(406\) 0 0
\(407\) 17.8794i 0.886251i
\(408\) 0 0
\(409\) 19.1346 0.946147 0.473073 0.881023i \(-0.343145\pi\)
0.473073 + 0.881023i \(0.343145\pi\)
\(410\) 0 0
\(411\) 4.26604 0.210428
\(412\) 0 0
\(413\) 5.45428i 0.268388i
\(414\) 0 0
\(415\) 5.84456 + 14.6927i 0.286898 + 0.721235i
\(416\) 0 0
\(417\) 1.75499i 0.0859423i
\(418\) 0 0
\(419\) 8.04484 0.393016 0.196508 0.980502i \(-0.437040\pi\)
0.196508 + 0.980502i \(0.437040\pi\)
\(420\) 0 0
\(421\) −29.3591 −1.43087 −0.715437 0.698678i \(-0.753772\pi\)
−0.715437 + 0.698678i \(0.753772\pi\)
\(422\) 0 0
\(423\) 31.7484i 1.54366i
\(424\) 0 0
\(425\) 19.9015 + 21.0569i 0.965364 + 1.02141i
\(426\) 0 0
\(427\) 27.8993i 1.35014i
\(428\) 0 0
\(429\) −4.62175 −0.223140
\(430\) 0 0
\(431\) 32.0448 1.54355 0.771773 0.635898i \(-0.219370\pi\)
0.771773 + 0.635898i \(0.219370\pi\)
\(432\) 0 0
\(433\) 0.482831i 0.0232034i −0.999933 0.0116017i \(-0.996307\pi\)
0.999933 0.0116017i \(-0.00369301\pi\)
\(434\) 0 0
\(435\) 2.66335 + 6.69541i 0.127698 + 0.321020i
\(436\) 0 0
\(437\) 2.60794i 0.124755i
\(438\) 0 0
\(439\) −27.3591 −1.30578 −0.652889 0.757454i \(-0.726443\pi\)
−0.652889 + 0.757454i \(0.726443\pi\)
\(440\) 0 0
\(441\) −8.55611 −0.407434
\(442\) 0 0
\(443\) 23.3815i 1.11089i 0.831554 + 0.555444i \(0.187452\pi\)
−0.831554 + 0.555444i \(0.812548\pi\)
\(444\) 0 0
\(445\) 34.3557 13.6663i 1.62862 0.647844i
\(446\) 0 0
\(447\) 4.53505i 0.214500i
\(448\) 0 0
\(449\) −23.1346 −1.09179 −0.545895 0.837853i \(-0.683810\pi\)
−0.545895 + 0.837853i \(0.683810\pi\)
\(450\) 0 0
\(451\) 2.49047 0.117272
\(452\) 0 0
\(453\) 0.476811i 0.0224025i
\(454\) 0 0
\(455\) −13.7115 + 5.45428i −0.642807 + 0.255701i
\(456\) 0 0
\(457\) 21.2503i 0.994049i 0.867736 + 0.497025i \(0.165574\pi\)
−0.867736 + 0.497025i \(0.834426\pi\)
\(458\) 0 0
\(459\) −17.7756 −0.829692
\(460\) 0 0
\(461\) 31.5785 1.47076 0.735379 0.677656i \(-0.237004\pi\)
0.735379 + 0.677656i \(0.237004\pi\)
\(462\) 0 0
\(463\) 15.6119i 0.725547i −0.931877 0.362774i \(-0.881830\pi\)
0.931877 0.362774i \(-0.118170\pi\)
\(464\) 0 0
\(465\) 1.15382 + 2.90059i 0.0535071 + 0.134512i
\(466\) 0 0
\(467\) 29.8264i 1.38020i 0.723713 + 0.690101i \(0.242434\pi\)
−0.723713 + 0.690101i \(0.757566\pi\)
\(468\) 0 0
\(469\) 15.1762 0.700774
\(470\) 0 0
\(471\) −2.22443 −0.102496
\(472\) 0 0
\(473\) 13.2424i 0.608885i
\(474\) 0 0
\(475\) −3.63383 + 3.43443i −0.166731 + 0.157582i
\(476\) 0 0
\(477\) 31.8616i 1.45884i
\(478\) 0 0
\(479\) 4.53531 0.207223 0.103612 0.994618i \(-0.466960\pi\)
0.103612 + 0.994618i \(0.466960\pi\)
\(480\) 0 0
\(481\) 8.91020 0.406270
\(482\) 0 0
\(483\) 4.46360i 0.203101i
\(484\) 0 0
\(485\) −1.71155 4.30266i −0.0777173 0.195374i
\(486\) 0 0
\(487\) 39.2550i 1.77881i −0.457116 0.889407i \(-0.651118\pi\)
0.457116 0.889407i \(-0.348882\pi\)
\(488\) 0 0
\(489\) 13.2726 0.600209
\(490\) 0 0
\(491\) −38.8910 −1.75513 −0.877564 0.479460i \(-0.840832\pi\)
−0.877564 + 0.479460i \(0.840832\pi\)
\(492\) 0 0
\(493\) 34.7682i 1.56588i
\(494\) 0 0
\(495\) 23.4110 9.31261i 1.05225 0.418571i
\(496\) 0 0
\(497\) 43.6954i 1.96001i
\(498\) 0 0
\(499\) 4.73235 0.211849 0.105924 0.994374i \(-0.466220\pi\)
0.105924 + 0.994374i \(0.466220\pi\)
\(500\) 0 0
\(501\) −1.93598 −0.0864931
\(502\) 0 0
\(503\) 1.85567i 0.0827400i 0.999144 + 0.0413700i \(0.0131722\pi\)
−0.999144 + 0.0413700i \(0.986828\pi\)
\(504\) 0 0
\(505\) 3.55611 1.41458i 0.158245 0.0629478i
\(506\) 0 0
\(507\) 4.67880i 0.207793i
\(508\) 0 0
\(509\) −22.8878 −1.01448 −0.507242 0.861804i \(-0.669335\pi\)
−0.507242 + 0.861804i \(0.669335\pi\)
\(510\) 0 0
\(511\) −8.69074 −0.384456
\(512\) 0 0
\(513\) 3.06756i 0.135436i
\(514\) 0 0
\(515\) −4.75476 11.9530i −0.209520 0.526713i
\(516\) 0 0
\(517\) 48.6543i 2.13982i
\(518\) 0 0
\(519\) −12.0416 −0.528568
\(520\) 0 0
\(521\) −29.7340 −1.30267 −0.651334 0.758791i \(-0.725790\pi\)
−0.651334 + 0.758791i \(0.725790\pi\)
\(522\) 0 0
\(523\) 30.6497i 1.34022i 0.742263 + 0.670109i \(0.233752\pi\)
−0.742263 + 0.670109i \(0.766248\pi\)
\(524\) 0 0
\(525\) −6.21946 + 5.87818i −0.271439 + 0.256545i
\(526\) 0 0
\(527\) 15.0623i 0.656125i
\(528\) 0 0
\(529\) 16.1987 0.704289
\(530\) 0 0
\(531\) −4.64093 −0.201399
\(532\) 0 0
\(533\) 1.24112i 0.0537590i
\(534\) 0 0
\(535\) −12.7548 32.0643i −0.551437 1.38626i
\(536\) 0 0
\(537\) 2.75771i 0.119004i
\(538\) 0 0
\(539\) 13.1122 0.564783
\(540\) 0 0
\(541\) 2.21946 0.0954220 0.0477110 0.998861i \(-0.484807\pi\)
0.0477110 + 0.998861i \(0.484807\pi\)
\(542\) 0 0
\(543\) 11.1961i 0.480469i
\(544\) 0 0
\(545\) 24.3333 9.67948i 1.04232 0.414623i
\(546\) 0 0
\(547\) 14.4297i 0.616970i 0.951229 + 0.308485i \(0.0998220\pi\)
−0.951229 + 0.308485i \(0.900178\pi\)
\(548\) 0 0
\(549\) −23.7389 −1.01315
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 4.46360i 0.189812i
\(554\) 0 0
\(555\) 4.80134 1.90991i 0.203806 0.0810714i
\(556\) 0 0
\(557\) 19.4610i 0.824588i 0.911051 + 0.412294i \(0.135272\pi\)
−0.911051 + 0.412294i \(0.864728\pi\)
\(558\) 0 0
\(559\) 6.59933 0.279122
\(560\) 0 0
\(561\) 12.9326 0.546016
\(562\) 0 0
\(563\) 12.3649i 0.521118i −0.965458 0.260559i \(-0.916093\pi\)
0.965458 0.260559i \(-0.0839068\pi\)
\(564\) 0 0
\(565\) −8.75476 22.0086i −0.368316 0.925911i
\(566\) 0 0
\(567\) 20.6729i 0.868179i
\(568\) 0 0
\(569\) −15.0898 −0.632597 −0.316299 0.948660i \(-0.602440\pi\)
−0.316299 + 0.948660i \(0.602440\pi\)
\(570\) 0 0
\(571\) −17.1571 −0.718000 −0.359000 0.933337i \(-0.616882\pi\)
−0.359000 + 0.933337i \(0.616882\pi\)
\(572\) 0 0
\(573\) 2.82915i 0.118190i
\(574\) 0 0
\(575\) −8.95678 9.47680i −0.373524 0.395210i
\(576\) 0 0
\(577\) 22.5165i 0.937374i −0.883364 0.468687i \(-0.844727\pi\)
0.883364 0.468687i \(-0.155273\pi\)
\(578\) 0 0
\(579\) 1.11222 0.0462222
\(580\) 0 0
\(581\) 22.5353 0.934922
\(582\) 0 0
\(583\) 48.8278i 2.02224i
\(584\) 0 0
\(585\) 4.64093 + 11.6669i 0.191879 + 0.482365i
\(586\) 0 0
\(587\) 7.49544i 0.309370i −0.987964 0.154685i \(-0.950564\pi\)
0.987964 0.154685i \(-0.0494363\pi\)
\(588\) 0 0
\(589\) 2.59933 0.107103
\(590\) 0 0
\(591\) −5.60269 −0.230464
\(592\) 0 0
\(593\) 27.8094i 1.14199i −0.820952 0.570997i \(-0.806557\pi\)
0.820952 0.570997i \(-0.193443\pi\)
\(594\) 0 0
\(595\) 38.3678 15.2622i 1.57293 0.625690i
\(596\) 0 0
\(597\) 1.46749i 0.0600603i
\(598\) 0 0
\(599\) −45.4903 −1.85869 −0.929343 0.369219i \(-0.879625\pi\)
−0.929343 + 0.369219i \(0.879625\pi\)
\(600\) 0 0
\(601\) −16.5993 −0.677101 −0.338550 0.940948i \(-0.609937\pi\)
−0.338550 + 0.940948i \(0.609937\pi\)
\(602\) 0 0
\(603\) 12.9131i 0.525863i
\(604\) 0 0
\(605\) −13.0224 + 5.18016i −0.529437 + 0.210603i
\(606\) 0 0
\(607\) 5.08417i 0.206360i 0.994663 + 0.103180i \(0.0329018\pi\)
−0.994663 + 0.103180i \(0.967098\pi\)
\(608\) 0 0
\(609\) 10.2693 0.416132
\(610\) 0 0
\(611\) −24.2469 −0.980923
\(612\) 0 0
\(613\) 4.63706i 0.187289i −0.995606 0.0936445i \(-0.970148\pi\)
0.995606 0.0936445i \(-0.0298517\pi\)
\(614\) 0 0
\(615\) 0.266037 + 0.668791i 0.0107276 + 0.0269683i
\(616\) 0 0
\(617\) 40.2874i 1.62191i 0.585108 + 0.810955i \(0.301052\pi\)
−0.585108 + 0.810955i \(0.698948\pi\)
\(618\) 0 0
\(619\) −43.3815 −1.74365 −0.871825 0.489818i \(-0.837063\pi\)
−0.871825 + 0.489818i \(0.837063\pi\)
\(620\) 0 0
\(621\) 8.00000 0.321029
\(622\) 0 0
\(623\) 52.6940i 2.11114i
\(624\) 0 0
\(625\) 1.40939 24.9602i 0.0563757 0.998410i
\(626\) 0 0
\(627\) 2.23180i 0.0891296i
\(628\) 0 0
\(629\) −24.9326 −0.994129
\(630\) 0 0
\(631\) −7.53369 −0.299911 −0.149956 0.988693i \(-0.547913\pi\)
−0.149956 + 0.988693i \(0.547913\pi\)
\(632\) 0 0
\(633\) 8.45040i 0.335873i
\(634\) 0 0
\(635\) −5.02080 12.6218i −0.199244 0.500881i
\(636\) 0 0
\(637\) 6.53446i 0.258905i
\(638\) 0 0
\(639\) −37.1795 −1.47080
\(640\) 0 0
\(641\) −23.3075 −0.920591 −0.460296 0.887766i \(-0.652257\pi\)
−0.460296 + 0.887766i \(0.652257\pi\)
\(642\) 0 0
\(643\) 1.87419i 0.0739110i 0.999317 + 0.0369555i \(0.0117660\pi\)
−0.999317 + 0.0369555i \(0.988234\pi\)
\(644\) 0 0
\(645\) 3.55611 1.41458i 0.140022 0.0556989i
\(646\) 0 0
\(647\) 47.0371i 1.84922i 0.380917 + 0.924609i \(0.375608\pi\)
−0.380917 + 0.924609i \(0.624392\pi\)
\(648\) 0 0
\(649\) 7.11222 0.279179
\(650\) 0 0
\(651\) 4.44887 0.174365
\(652\) 0 0
\(653\) 24.1630i 0.945571i −0.881178 0.472785i \(-0.843249\pi\)
0.881178 0.472785i \(-0.156751\pi\)
\(654\) 0 0
\(655\) −28.2124 + 11.2225i −1.10235 + 0.438500i
\(656\) 0 0
\(657\) 7.39477i 0.288497i
\(658\) 0 0
\(659\) 10.2885 0.400781 0.200391 0.979716i \(-0.435779\pi\)
0.200391 + 0.979716i \(0.435779\pi\)
\(660\) 0 0
\(661\) 5.93598 0.230883 0.115441 0.993314i \(-0.463172\pi\)
0.115441 + 0.993314i \(0.463172\pi\)
\(662\) 0 0
\(663\) 6.44496i 0.250302i
\(664\) 0 0
\(665\) 2.63383 + 6.62119i 0.102135 + 0.256759i
\(666\) 0 0
\(667\) 15.6476i 0.605879i
\(668\) 0 0
\(669\) −10.1089 −0.390831
\(670\) 0 0
\(671\) 36.3799 1.40443
\(672\) 0 0
\(673\) 40.7053i 1.56907i 0.620082 + 0.784537i \(0.287099\pi\)
−0.620082 + 0.784537i \(0.712901\pi\)
\(674\) 0 0
\(675\) 10.5353 + 11.1470i 0.405504 + 0.429047i
\(676\) 0 0
\(677\) 18.8761i 0.725469i 0.931893 + 0.362734i \(0.118157\pi\)
−0.931893 + 0.362734i \(0.881843\pi\)
\(678\) 0 0
\(679\) −6.59933 −0.253259
\(680\) 0 0
\(681\) −7.75638 −0.297225
\(682\) 0 0
\(683\) 19.6576i 0.752179i −0.926583 0.376089i \(-0.877269\pi\)
0.926583 0.376089i \(-0.122731\pi\)
\(684\) 0 0
\(685\) 6.56483 + 16.5034i 0.250829 + 0.630561i
\(686\) 0 0
\(687\) 2.24384i 0.0856079i
\(688\) 0 0
\(689\) −24.3333 −0.927025
\(690\) 0 0
\(691\) 48.2451 1.83533 0.917665 0.397354i \(-0.130072\pi\)
0.917665 + 0.397354i \(0.130072\pi\)
\(692\) 0 0
\(693\) 35.9073i 1.36401i
\(694\) 0 0
\(695\) −6.78926 + 2.70068i −0.257531 + 0.102443i
\(696\) 0 0
\(697\) 3.47293i 0.131546i
\(698\) 0 0
\(699\) 6.49047 0.245492
\(700\) 0 0
\(701\) 0.512889 0.0193715 0.00968577 0.999953i \(-0.496917\pi\)
0.00968577 + 0.999953i \(0.496917\pi\)
\(702\) 0 0
\(703\) 4.30266i 0.162278i
\(704\) 0 0
\(705\) −13.0656 + 5.19735i −0.492080 + 0.195743i
\(706\) 0 0
\(707\) 5.45428i 0.205129i
\(708\) 0 0
\(709\) 8.84618 0.332225 0.166113 0.986107i \(-0.446878\pi\)
0.166113 + 0.986107i \(0.446878\pi\)
\(710\) 0 0
\(711\) −3.79798 −0.142436
\(712\) 0 0
\(713\) 6.77889i 0.253871i
\(714\) 0 0
\(715\) −7.11222 17.8794i −0.265982 0.668653i
\(716\) 0 0
\(717\) 6.09806i 0.227736i
\(718\) 0 0
\(719\) 7.84456 0.292553 0.146276 0.989244i \(-0.453271\pi\)
0.146276 + 0.989244i \(0.453271\pi\)
\(720\) 0 0
\(721\) −18.3333 −0.682767
\(722\) 0 0
\(723\) 1.82643i 0.0679258i
\(724\) 0 0
\(725\) −21.8030 + 20.6066i −0.809742 + 0.765309i
\(726\) 0 0
\(727\) 2.91130i 0.107974i 0.998542 + 0.0539870i \(0.0171930\pi\)
−0.998542 + 0.0539870i \(0.982807\pi\)
\(728\) 0 0
\(729\) 12.6475 0.468427
\(730\) 0 0
\(731\) −18.4663 −0.683001
\(732\) 0 0
\(733\) 33.7775i 1.24760i 0.781584 + 0.623800i \(0.214412\pi\)
−0.781584 + 0.623800i \(0.785588\pi\)
\(734\) 0 0
\(735\) 1.40067 + 3.52116i 0.0516646 + 0.129880i
\(736\) 0 0
\(737\) 19.7893i 0.728950i
\(738\) 0 0
\(739\) −35.8030 −1.31703 −0.658517 0.752566i \(-0.728816\pi\)
−0.658517 + 0.752566i \(0.728816\pi\)
\(740\) 0 0
\(741\) −1.11222 −0.0408583
\(742\) 0 0
\(743\) 5.66948i 0.207993i −0.994578 0.103996i \(-0.966837\pi\)
0.994578 0.103996i \(-0.0331631\pi\)
\(744\) 0 0
\(745\) 17.5440 6.97880i 0.642763 0.255683i
\(746\) 0 0
\(747\) 19.1748i 0.701569i
\(748\) 0 0
\(749\) −49.1795 −1.79698
\(750\) 0 0
\(751\) 27.4679 1.00232 0.501159 0.865355i \(-0.332907\pi\)
0.501159 + 0.865355i \(0.332907\pi\)
\(752\) 0 0
\(753\) 1.63445i 0.0595628i
\(754\) 0 0
\(755\) 1.84456 0.733744i 0.0671305 0.0267037i
\(756\) 0 0
\(757\) 41.6370i 1.51332i −0.653806 0.756662i \(-0.726829\pi\)
0.653806 0.756662i \(-0.273171\pi\)
\(758\) 0 0
\(759\) −5.82040 −0.211267
\(760\) 0 0
\(761\) −9.46967 −0.343275 −0.171638 0.985160i \(-0.554906\pi\)
−0.171638 + 0.985160i \(0.554906\pi\)
\(762\) 0 0
\(763\) 37.3219i 1.35114i
\(764\) 0 0
\(765\) −12.9863 32.6463i −0.469521 1.18033i
\(766\) 0 0
\(767\) 3.54437i 0.127980i
\(768\) 0 0
\(769\) −1.90858 −0.0688253 −0.0344127 0.999408i \(-0.510956\pi\)
−0.0344127 + 0.999408i \(0.510956\pi\)
\(770\) 0 0
\(771\) −9.28510 −0.334395
\(772\) 0 0
\(773\) 28.4007i 1.02150i 0.859729 + 0.510751i \(0.170633\pi\)
−0.859729 + 0.510751i \(0.829367\pi\)
\(774\) 0 0
\(775\) −9.44551 + 8.92721i −0.339293 + 0.320675i
\(776\) 0 0
\(777\) 7.36420i 0.264189i
\(778\) 0 0
\(779\) 0.599328 0.0214732
\(780\) 0 0
\(781\) 56.9775 2.03881
\(782\) 0 0
\(783\) 18.4053i 0.657753i
\(784\) 0 0
\(785\) −3.42309 8.60532i −0.122175 0.307137i
\(786\) 0 0
\(787\) 15.6708i 0.558605i −0.960203 0.279303i \(-0.909897\pi\)
0.960203 0.279303i \(-0.0901033\pi\)
\(788\) 0 0
\(789\) 0.640931 0.0228178
\(790\) 0 0
\(791\) −33.7564 −1.20024
\(792\) 0 0
\(793\) 18.1299i 0.643811i
\(794\) 0 0
\(795\) −13.1122 + 5.21588i −0.465042 + 0.184988i
\(796\) 0 0
\(797\) 36.9225i 1.30786i −0.756554 0.653932i \(-0.773118\pi\)
0.756554 0.653932i \(-0.226882\pi\)
\(798\) 0 0
\(799\) 67.8478 2.40028
\(800\) 0