Properties

Label 108.5.g.a.89.3
Level 108
Weight 5
Character 108.89
Analytic conductor 11.164
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.g (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{10} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.3
Root \(3.72537 + 4.42407i\) of \(x^{8} - 3 x^{7} + 6 x^{6} + 121 x^{5} + 1104 x^{4} - 1647 x^{3} + 6529 x^{2} + 85254 x + 440076\)
Character \(\chi\) \(=\) 108.89
Dual form 108.5.g.a.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(7.67992 - 4.43400i) q^{5} +(-30.9381 + 53.5864i) q^{7} +O(q^{10})\) \(q+(7.67992 - 4.43400i) q^{5} +(-30.9381 + 53.5864i) q^{7} +(-94.7648 - 54.7125i) q^{11} +(77.8628 + 134.862i) q^{13} +395.955i q^{17} +140.350 q^{19} +(-802.818 + 463.507i) q^{23} +(-273.179 + 473.160i) q^{25} +(-323.853 - 186.976i) q^{29} +(521.830 + 903.837i) q^{31} +548.719i q^{35} -194.990 q^{37} +(2344.14 - 1353.39i) q^{41} +(-167.963 + 290.920i) q^{43} +(-2468.76 - 1425.34i) q^{47} +(-713.836 - 1236.40i) q^{49} +2765.43i q^{53} -970.381 q^{55} +(4354.55 - 2514.10i) q^{59} +(3523.59 - 6103.03i) q^{61} +(1195.96 + 690.488i) q^{65} +(-3439.96 - 5958.19i) q^{67} -821.812i q^{71} +4091.53 q^{73} +(5863.69 - 3385.40i) q^{77} +(-3783.56 + 6553.32i) q^{79} +(-6777.78 - 3913.15i) q^{83} +(1755.67 + 3040.90i) q^{85} +1283.28i q^{89} -9635.72 q^{91} +(1077.88 - 622.313i) q^{95} +(1890.33 - 3274.14i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 9q^{5} + 13q^{7} + O(q^{10}) \) \( 8q + 9q^{5} + 13q^{7} + 18q^{11} - 5q^{13} + 562q^{19} + 1719q^{23} + 353q^{25} - 2115q^{29} + 187q^{31} + 16q^{37} + 7920q^{41} - 68q^{43} - 13689q^{47} - 327q^{49} - 1818q^{55} + 20052q^{59} - 1937q^{61} - 25965q^{65} + 154q^{67} - 7802q^{73} + 25641q^{77} - 2195q^{79} - 37017q^{83} - 3042q^{85} + 15830q^{91} + 37116q^{95} + 7282q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 7.67992 4.43400i 0.307197 0.177360i −0.338475 0.940976i \(-0.609911\pi\)
0.645671 + 0.763615i \(0.276578\pi\)
\(6\) 0 0
\(7\) −30.9381 + 53.5864i −0.631390 + 1.09360i 0.355877 + 0.934533i \(0.384182\pi\)
−0.987268 + 0.159068i \(0.949151\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −94.7648 54.7125i −0.783180 0.452169i 0.0543761 0.998521i \(-0.482683\pi\)
−0.837556 + 0.546351i \(0.816016\pi\)
\(12\) 0 0
\(13\) 77.8628 + 134.862i 0.460727 + 0.798002i 0.998997 0.0447702i \(-0.0142556\pi\)
−0.538271 + 0.842772i \(0.680922\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 395.955i 1.37009i 0.728502 + 0.685044i \(0.240217\pi\)
−0.728502 + 0.685044i \(0.759783\pi\)
\(18\) 0 0
\(19\) 140.350 0.388782 0.194391 0.980924i \(-0.437727\pi\)
0.194391 + 0.980924i \(0.437727\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −802.818 + 463.507i −1.51761 + 0.876195i −0.517829 + 0.855484i \(0.673260\pi\)
−0.999785 + 0.0207115i \(0.993407\pi\)
\(24\) 0 0
\(25\) −273.179 + 473.160i −0.437087 + 0.757056i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −323.853 186.976i −0.385080 0.222326i 0.294946 0.955514i \(-0.404698\pi\)
−0.680026 + 0.733188i \(0.738032\pi\)
\(30\) 0 0
\(31\) 521.830 + 903.837i 0.543008 + 0.940517i 0.998729 + 0.0503946i \(0.0160479\pi\)
−0.455722 + 0.890122i \(0.650619\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 548.719i 0.447934i
\(36\) 0 0
\(37\) −194.990 −0.142432 −0.0712162 0.997461i \(-0.522688\pi\)
−0.0712162 + 0.997461i \(0.522688\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2344.14 1353.39i 1.39449 0.805110i 0.400682 0.916217i \(-0.368773\pi\)
0.993808 + 0.111108i \(0.0354398\pi\)
\(42\) 0 0
\(43\) −167.963 + 290.920i −0.0908397 + 0.157339i −0.907865 0.419263i \(-0.862288\pi\)
0.817025 + 0.576602i \(0.195622\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2468.76 1425.34i −1.11759 0.645241i −0.176805 0.984246i \(-0.556576\pi\)
−0.940785 + 0.339005i \(0.889910\pi\)
\(48\) 0 0
\(49\) −713.836 1236.40i −0.297308 0.514952i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2765.43i 0.984490i 0.870457 + 0.492245i \(0.163824\pi\)
−0.870457 + 0.492245i \(0.836176\pi\)
\(54\) 0 0
\(55\) −970.381 −0.320787
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4354.55 2514.10i 1.25095 0.722236i 0.279651 0.960102i \(-0.409781\pi\)
0.971298 + 0.237866i \(0.0764479\pi\)
\(60\) 0 0
\(61\) 3523.59 6103.03i 0.946947 1.64016i 0.195140 0.980775i \(-0.437484\pi\)
0.751806 0.659384i \(-0.229183\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1195.96 + 690.488i 0.283067 + 0.163429i
\(66\) 0 0
\(67\) −3439.96 5958.19i −0.766309 1.32729i −0.939551 0.342408i \(-0.888758\pi\)
0.173242 0.984879i \(-0.444576\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 821.812i 0.163026i −0.996672 0.0815128i \(-0.974025\pi\)
0.996672 0.0815128i \(-0.0259752\pi\)
\(72\) 0 0
\(73\) 4091.53 0.767786 0.383893 0.923378i \(-0.374583\pi\)
0.383893 + 0.923378i \(0.374583\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5863.69 3385.40i 0.988985 0.570991i
\(78\) 0 0
\(79\) −3783.56 + 6553.32i −0.606243 + 1.05004i 0.385611 + 0.922661i \(0.373991\pi\)
−0.991854 + 0.127382i \(0.959343\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6777.78 3913.15i −0.983855 0.568029i −0.0804236 0.996761i \(-0.525627\pi\)
−0.903432 + 0.428732i \(0.858961\pi\)
\(84\) 0 0
\(85\) 1755.67 + 3040.90i 0.242999 + 0.420886i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1283.28i 0.162010i 0.996714 + 0.0810051i \(0.0258130\pi\)
−0.996714 + 0.0810051i \(0.974187\pi\)
\(90\) 0 0
\(91\) −9635.72 −1.16359
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1077.88 622.313i 0.119432 0.0689544i
\(96\) 0 0
\(97\) 1890.33 3274.14i 0.200906 0.347979i −0.747915 0.663795i \(-0.768945\pi\)
0.948821 + 0.315816i \(0.102278\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1034.99 + 597.553i 0.101460 + 0.0585779i 0.549871 0.835249i \(-0.314677\pi\)
−0.448411 + 0.893827i \(0.648010\pi\)
\(102\) 0 0
\(103\) 6767.50 + 11721.6i 0.637901 + 1.10488i 0.985892 + 0.167380i \(0.0535306\pi\)
−0.347991 + 0.937498i \(0.613136\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18095.0i 1.58049i 0.612792 + 0.790244i \(0.290046\pi\)
−0.612792 + 0.790244i \(0.709954\pi\)
\(108\) 0 0
\(109\) 10676.5 0.898621 0.449311 0.893376i \(-0.351670\pi\)
0.449311 + 0.893376i \(0.351670\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11083.8 + 6399.21i −0.868021 + 0.501152i −0.866690 0.498847i \(-0.833757\pi\)
−0.00133098 + 0.999999i \(0.500424\pi\)
\(114\) 0 0
\(115\) −4110.39 + 7119.40i −0.310804 + 0.538329i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −21217.8 12250.1i −1.49833 0.865060i
\(120\) 0 0
\(121\) −1333.59 2309.85i −0.0910861 0.157766i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10387.6i 0.664807i
\(126\) 0 0
\(127\) 449.363 0.0278606 0.0139303 0.999903i \(-0.495566\pi\)
0.0139303 + 0.999903i \(0.495566\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −10075.4 + 5817.06i −0.587113 + 0.338970i −0.763955 0.645270i \(-0.776745\pi\)
0.176842 + 0.984239i \(0.443412\pi\)
\(132\) 0 0
\(133\) −4342.17 + 7520.86i −0.245473 + 0.425172i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 24400.6 + 14087.7i 1.30005 + 0.750584i 0.980412 0.196956i \(-0.0631055\pi\)
0.319637 + 0.947540i \(0.396439\pi\)
\(138\) 0 0
\(139\) 4747.58 + 8223.05i 0.245721 + 0.425602i 0.962334 0.271869i \(-0.0876419\pi\)
−0.716613 + 0.697471i \(0.754309\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 17040.3i 0.833305i
\(144\) 0 0
\(145\) −3316.22 −0.157727
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1730.39 + 999.043i −0.0779422 + 0.0449999i −0.538465 0.842648i \(-0.680995\pi\)
0.460522 + 0.887648i \(0.347662\pi\)
\(150\) 0 0
\(151\) 1855.61 3214.02i 0.0813830 0.140959i −0.822461 0.568821i \(-0.807400\pi\)
0.903844 + 0.427862i \(0.140733\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 8015.23 + 4627.59i 0.333620 + 0.192616i
\(156\) 0 0
\(157\) −1458.43 2526.07i −0.0591679 0.102482i 0.834924 0.550365i \(-0.185511\pi\)
−0.894092 + 0.447883i \(0.852178\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 57360.2i 2.21289i
\(162\) 0 0
\(163\) −5975.21 −0.224894 −0.112447 0.993658i \(-0.535869\pi\)
−0.112447 + 0.993658i \(0.535869\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 3610.95 2084.78i 0.129476 0.0747529i −0.433863 0.900979i \(-0.642850\pi\)
0.563339 + 0.826226i \(0.309517\pi\)
\(168\) 0 0
\(169\) 2155.27 3733.05i 0.0754622 0.130704i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 26710.3 + 15421.2i 0.892455 + 0.515259i 0.874745 0.484584i \(-0.161029\pi\)
0.0177101 + 0.999843i \(0.494362\pi\)
\(174\) 0 0
\(175\) −16903.3 29277.4i −0.551945 0.955996i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5977.90i 0.186570i −0.995639 0.0932852i \(-0.970263\pi\)
0.995639 0.0932852i \(-0.0297368\pi\)
\(180\) 0 0
\(181\) −6456.49 −0.197079 −0.0985393 0.995133i \(-0.531417\pi\)
−0.0985393 + 0.995133i \(0.531417\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1497.51 + 864.586i −0.0437548 + 0.0252618i
\(186\) 0 0
\(187\) 21663.7 37522.6i 0.619511 1.07302i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 20643.3 + 11918.4i 0.565865 + 0.326703i 0.755496 0.655153i \(-0.227396\pi\)
−0.189631 + 0.981855i \(0.560729\pi\)
\(192\) 0 0
\(193\) −20081.7 34782.5i −0.539121 0.933784i −0.998952 0.0457779i \(-0.985423\pi\)
0.459831 0.888006i \(-0.347910\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3622.11i 0.0933318i 0.998911 + 0.0466659i \(0.0148596\pi\)
−0.998911 + 0.0466659i \(0.985140\pi\)
\(198\) 0 0
\(199\) 46416.3 1.17210 0.586049 0.810276i \(-0.300683\pi\)
0.586049 + 0.810276i \(0.300683\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 20038.8 11569.4i 0.486272 0.280749i
\(204\) 0 0
\(205\) 12001.9 20787.8i 0.285589 0.494654i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −13300.3 7678.91i −0.304486 0.175795i
\(210\) 0 0
\(211\) 764.093 + 1323.45i 0.0171625 + 0.0297264i 0.874479 0.485063i \(-0.161203\pi\)
−0.857317 + 0.514790i \(0.827870\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2978.99i 0.0644453i
\(216\) 0 0
\(217\) −64577.8 −1.37140
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −53399.4 + 30830.2i −1.09333 + 0.631235i
\(222\) 0 0
\(223\) −13741.4 + 23800.8i −0.276326 + 0.478610i −0.970469 0.241227i \(-0.922450\pi\)
0.694143 + 0.719837i \(0.255784\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 39178.5 + 22619.7i 0.760319 + 0.438970i 0.829410 0.558640i \(-0.188677\pi\)
−0.0690916 + 0.997610i \(0.522010\pi\)
\(228\) 0 0
\(229\) 40074.3 + 69410.7i 0.764178 + 1.32360i 0.940680 + 0.339295i \(0.110189\pi\)
−0.176502 + 0.984300i \(0.556478\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 90756.0i 1.67172i −0.548942 0.835860i \(-0.684969\pi\)
0.548942 0.835860i \(-0.315031\pi\)
\(234\) 0 0
\(235\) −25279.8 −0.457760
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −708.324 + 408.951i −0.0124004 + 0.00715938i −0.506187 0.862424i \(-0.668946\pi\)
0.493787 + 0.869583i \(0.335612\pi\)
\(240\) 0 0
\(241\) −37158.1 + 64359.7i −0.639764 + 1.10810i 0.345721 + 0.938337i \(0.387634\pi\)
−0.985484 + 0.169766i \(0.945699\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −10964.4 6330.30i −0.182664 0.105461i
\(246\) 0 0
\(247\) 10928.1 + 18928.0i 0.179122 + 0.310249i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16304.4i 0.258796i 0.991593 + 0.129398i \(0.0413045\pi\)
−0.991593 + 0.129398i \(0.958695\pi\)
\(252\) 0 0
\(253\) 101439. 1.58475
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −108732. + 62776.2i −1.64623 + 0.950449i −0.667673 + 0.744454i \(0.732710\pi\)
−0.978553 + 0.205995i \(0.933957\pi\)
\(258\) 0 0
\(259\) 6032.63 10448.8i 0.0899305 0.155764i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 13971.9 + 8066.67i 0.201996 + 0.116623i 0.597586 0.801805i \(-0.296127\pi\)
−0.395590 + 0.918427i \(0.629460\pi\)
\(264\) 0 0
\(265\) 12261.9 + 21238.3i 0.174609 + 0.302432i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 75561.0i 1.04422i 0.852877 + 0.522112i \(0.174856\pi\)
−0.852877 + 0.522112i \(0.825144\pi\)
\(270\) 0 0
\(271\) −14842.2 −0.202097 −0.101049 0.994881i \(-0.532220\pi\)
−0.101049 + 0.994881i \(0.532220\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 51775.5 29892.6i 0.684635 0.395274i
\(276\) 0 0
\(277\) −40381.1 + 69942.2i −0.526283 + 0.911548i 0.473248 + 0.880929i \(0.343081\pi\)
−0.999531 + 0.0306193i \(0.990252\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −57384.8 33131.1i −0.726749 0.419589i 0.0904828 0.995898i \(-0.471159\pi\)
−0.817232 + 0.576309i \(0.804492\pi\)
\(282\) 0 0
\(283\) −7288.93 12624.8i −0.0910104 0.157635i 0.816926 0.576742i \(-0.195676\pi\)
−0.907937 + 0.419108i \(0.862343\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 167485.i 2.03335i
\(288\) 0 0
\(289\) −73259.5 −0.877139
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −65027.8 + 37543.8i −0.757467 + 0.437324i −0.828386 0.560158i \(-0.810740\pi\)
0.0709185 + 0.997482i \(0.477407\pi\)
\(294\) 0 0
\(295\) 22295.1 38616.2i 0.256192 0.443737i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −125019. 72179.9i −1.39841 0.807373i
\(300\) 0 0
\(301\) −10392.9 18001.0i −0.114711 0.198685i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 62494.4i 0.671802i
\(306\) 0 0
\(307\) 146994. 1.55963 0.779817 0.626007i \(-0.215312\pi\)
0.779817 + 0.626007i \(0.215312\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 126237. 72882.7i 1.30516 0.753536i 0.323878 0.946099i \(-0.395013\pi\)
0.981285 + 0.192563i \(0.0616800\pi\)
\(312\) 0 0
\(313\) 37866.9 65587.3i 0.386519 0.669470i −0.605460 0.795876i \(-0.707011\pi\)
0.991979 + 0.126406i \(0.0403441\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 80308.7 + 46366.3i 0.799179 + 0.461406i 0.843184 0.537625i \(-0.180678\pi\)
−0.0440049 + 0.999031i \(0.514012\pi\)
\(318\) 0 0
\(319\) 20459.9 + 35437.6i 0.201058 + 0.348243i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 55572.4i 0.532665i
\(324\) 0 0
\(325\) −85082.0 −0.805510
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 152757. 88194.5i 1.41127 0.814798i
\(330\) 0 0
\(331\) −5404.90 + 9361.56i −0.0493323 + 0.0854461i −0.889637 0.456668i \(-0.849043\pi\)
0.840305 + 0.542114i \(0.182376\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −52837.3 30505.6i −0.470816 0.271825i
\(336\) 0 0
\(337\) −65323.7 113144.i −0.575190 0.996258i −0.996021 0.0891187i \(-0.971595\pi\)
0.420831 0.907139i \(-0.361738\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 114203.i 0.982125i
\(342\) 0 0
\(343\) −60225.9 −0.511912
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 141648. 81780.7i 1.17639 0.679191i 0.221216 0.975225i \(-0.428997\pi\)
0.955177 + 0.296034i \(0.0956641\pi\)
\(348\) 0 0
\(349\) −7232.92 + 12527.8i −0.0593831 + 0.102855i −0.894189 0.447690i \(-0.852247\pi\)
0.834806 + 0.550545i \(0.185580\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8348.17 + 4819.82i 0.0669949 + 0.0386795i 0.533123 0.846038i \(-0.321018\pi\)
−0.466128 + 0.884717i \(0.654352\pi\)
\(354\) 0 0
\(355\) −3643.92 6311.45i −0.0289143 0.0500810i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 56543.7i 0.438728i 0.975643 + 0.219364i \(0.0703982\pi\)
−0.975643 + 0.219364i \(0.929602\pi\)
\(360\) 0 0
\(361\) −110623. −0.848849
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 31422.6 18141.9i 0.235861 0.136175i
\(366\) 0 0
\(367\) 79981.5 138532.i 0.593824 1.02853i −0.399888 0.916564i \(-0.630951\pi\)
0.993712 0.111969i \(-0.0357157\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −148190. 85557.3i −1.07664 0.621598i
\(372\) 0 0
\(373\) 52486.5 + 90909.4i 0.377251 + 0.653418i 0.990661 0.136347i \(-0.0435361\pi\)
−0.613410 + 0.789764i \(0.710203\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 58234.0i 0.409727i
\(378\) 0 0
\(379\) 25050.7 0.174398 0.0871989 0.996191i \(-0.472208\pi\)
0.0871989 + 0.996191i \(0.472208\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −45503.9 + 26271.7i −0.310207 + 0.179098i −0.647019 0.762474i \(-0.723985\pi\)
0.336812 + 0.941572i \(0.390651\pi\)
\(384\) 0 0
\(385\) 30021.8 51999.2i 0.202542 0.350813i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 175082. + 101084.i 1.15702 + 0.668008i 0.950589 0.310452i \(-0.100480\pi\)
0.206435 + 0.978460i \(0.433814\pi\)
\(390\) 0 0
\(391\) −183528. 317880.i −1.20046 2.07926i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 67105.3i 0.430093i
\(396\) 0 0
\(397\) 303603. 1.92631 0.963154 0.268951i \(-0.0866770\pi\)
0.963154 + 0.268951i \(0.0866770\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 102431. 59138.8i 0.637007 0.367776i −0.146453 0.989218i \(-0.546786\pi\)
0.783461 + 0.621441i \(0.213453\pi\)
\(402\) 0 0
\(403\) −81262.3 + 140750.i −0.500356 + 0.866642i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 18478.2 + 10668.4i 0.111550 + 0.0644036i
\(408\) 0 0
\(409\) −20533.2 35564.6i −0.122747 0.212604i 0.798103 0.602521i \(-0.205837\pi\)
−0.920850 + 0.389917i \(0.872504\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 311127.i 1.82405i
\(414\) 0 0
\(415\) −69403.7 −0.402983
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −86655.8 + 50030.8i −0.493594 + 0.284976i −0.726064 0.687627i \(-0.758652\pi\)
0.232470 + 0.972603i \(0.425319\pi\)
\(420\) 0 0
\(421\) 110257. 190971.i 0.622074 1.07746i −0.367024 0.930211i \(-0.619623\pi\)
0.989099 0.147253i \(-0.0470432\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −187350. 108167.i −1.03723 0.598847i
\(426\) 0 0
\(427\) 218026. + 377633.i 1.19579 + 2.07116i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 211457.i 1.13833i −0.822224 0.569163i \(-0.807267\pi\)
0.822224 0.569163i \(-0.192733\pi\)
\(432\) 0 0
\(433\) −106655. −0.568859 −0.284430 0.958697i \(-0.591804\pi\)
−0.284430 + 0.958697i \(0.591804\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −112676. + 65053.4i −0.590021 + 0.340649i
\(438\) 0 0
\(439\) −107195. + 185667.i −0.556218 + 0.963397i 0.441590 + 0.897217i \(0.354415\pi\)
−0.997808 + 0.0661804i \(0.978919\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −174614. 100814.i −0.889759 0.513703i −0.0158954 0.999874i \(-0.505060\pi\)
−0.873864 + 0.486171i \(0.838393\pi\)
\(444\) 0 0
\(445\) 5690.08 + 9855.50i 0.0287341 + 0.0497690i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 136895.i 0.679039i 0.940599 + 0.339519i \(0.110264\pi\)
−0.940599 + 0.339519i \(0.889736\pi\)
\(450\) 0 0
\(451\) −296189. −1.45618
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −74001.5 + 42724.8i −0.357452 + 0.206375i
\(456\) 0 0
\(457\) −183338. + 317551.i −0.877850 + 1.52048i −0.0241542 + 0.999708i \(0.507689\pi\)
−0.853696 + 0.520772i \(0.825644\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 42379.8 + 24468.0i 0.199415 + 0.115132i 0.596382 0.802700i \(-0.296604\pi\)
−0.396968 + 0.917833i \(0.629938\pi\)
\(462\) 0 0
\(463\) 143514. + 248574.i 0.669472 + 1.15956i 0.978052 + 0.208361i \(0.0668128\pi\)
−0.308580 + 0.951198i \(0.599854\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 43613.3i 0.199979i 0.994988 + 0.0999896i \(0.0318809\pi\)
−0.994988 + 0.0999896i \(0.968119\pi\)
\(468\) 0 0
\(469\) 425704. 1.93536
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 31833.9 18379.3i 0.142288 0.0821498i
\(474\) 0 0
\(475\) −38340.8 + 66408.2i −0.169931 + 0.294330i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 199073. + 114935.i 0.867642 + 0.500933i 0.866564 0.499066i \(-0.166324\pi\)
0.00107799 + 0.999999i \(0.499657\pi\)
\(480\) 0 0
\(481\) −15182.5 26296.8i −0.0656224 0.113661i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 33526.8i 0.142531i
\(486\) 0 0
\(487\) −15921.9 −0.0671330 −0.0335665 0.999436i \(-0.510687\pi\)
−0.0335665 + 0.999436i \(0.510687\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −145540. + 84027.8i −0.603699 + 0.348546i −0.770496 0.637445i \(-0.779991\pi\)
0.166796 + 0.985991i \(0.446658\pi\)
\(492\) 0 0
\(493\) 74034.3 128231.i 0.304606 0.527594i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 44038.0 + 25425.3i 0.178285 + 0.102933i
\(498\) 0 0
\(499\) −178029. 308355.i −0.714971 1.23837i −0.962971 0.269607i \(-0.913106\pi\)
0.247999 0.968760i \(-0.420227\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 180472.i 0.713301i −0.934238 0.356651i \(-0.883919\pi\)
0.934238 0.356651i \(-0.116081\pi\)
\(504\) 0 0
\(505\) 10598.2 0.0415575
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −345324. + 199373.i −1.33288 + 0.769540i −0.985740 0.168273i \(-0.946181\pi\)
−0.347142 + 0.937813i \(0.612848\pi\)
\(510\) 0 0
\(511\) −126584. + 219250.i −0.484772 + 0.839651i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 103948. + 60014.2i 0.391922 + 0.226277i
\(516\) 0 0
\(517\) 155967. + 270143.i 0.583516 + 1.01068i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 485387.i 1.78819i −0.447880 0.894094i \(-0.647821\pi\)
0.447880 0.894094i \(-0.352179\pi\)
\(522\) 0 0
\(523\) 80589.4 0.294628 0.147314 0.989090i \(-0.452937\pi\)
0.147314 + 0.989090i \(0.452937\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −357879. + 206621.i −1.28859 + 0.743968i
\(528\) 0 0
\(529\) 289758. 501875.i 1.03544 1.79343i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 365042. + 210757.i 1.28496 + 0.741871i
\(534\) 0 0
\(535\) 80233.3 + 138968.i 0.280316 + 0.485521i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 156223.i 0.537734i
\(540\) 0 0
\(541\) −446700. −1.52623 −0.763117 0.646260i \(-0.776332\pi\)
−0.763117 + 0.646260i \(0.776332\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 81994.8 47339.7i 0.276053 0.159380i
\(546\) 0 0
\(547\) 126958. 219898.i 0.424312 0.734931i −0.572043 0.820223i \(-0.693849\pi\)
0.996356 + 0.0852925i \(0.0271825\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −45452.8 26242.2i −0.149712 0.0864364i
\(552\) 0 0
\(553\) −234113. 405495.i −0.765552 1.32597i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 49265.2i 0.158792i 0.996843 + 0.0793962i \(0.0252992\pi\)
−0.996843 + 0.0793962i \(0.974701\pi\)
\(558\) 0 0
\(559\) −52312.1 −0.167409
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 342365. 197665.i 1.08012 0.623608i 0.149192 0.988808i \(-0.452333\pi\)
0.930929 + 0.365200i \(0.118999\pi\)
\(564\) 0 0
\(565\) −56748.3 + 98290.9i −0.177769 + 0.307905i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 224474. + 129600.i 0.693332 + 0.400296i 0.804859 0.593466i \(-0.202241\pi\)
−0.111527 + 0.993761i \(0.535574\pi\)
\(570\) 0 0
\(571\) −226228. 391839.i −0.693864 1.20181i −0.970562 0.240851i \(-0.922573\pi\)
0.276697 0.960957i \(-0.410760\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 506482.i 1.53189i
\(576\) 0 0
\(577\) 499076. 1.49905 0.749523 0.661978i \(-0.230283\pi\)
0.749523 + 0.661978i \(0.230283\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 419384. 242131.i 1.24239 0.717296i
\(582\) 0 0
\(583\) 151304. 262066.i 0.445156 0.771033i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −238.906 137.932i −0.000693347 0.000400304i 0.499653 0.866225i \(-0.333461\pi\)
−0.500347 + 0.865825i \(0.666794\pi\)
\(588\) 0 0
\(589\) 73239.0 + 126854.i 0.211111 + 0.365656i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 10939.7i 0.0311096i 0.999879 + 0.0155548i \(0.00495145\pi\)
−0.999879 + 0.0155548i \(0.995049\pi\)
\(594\) 0 0
\(595\) −217268. −0.613708
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13902.7 8026.70i 0.0387475 0.0223709i −0.480501 0.876994i \(-0.659545\pi\)
0.519249 + 0.854623i \(0.326212\pi\)
\(600\) 0 0
\(601\) −267567. + 463439.i −0.740769 + 1.28305i 0.211376 + 0.977405i \(0.432205\pi\)
−0.952145 + 0.305645i \(0.901128\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −20483.7 11826.3i −0.0559627 0.0323101i
\(606\) 0 0
\(607\) 37897.7 + 65640.8i 0.102858 + 0.178154i 0.912861 0.408271i \(-0.133868\pi\)
−0.810003 + 0.586425i \(0.800535\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 443923.i 1.18912i
\(612\) 0 0
\(613\) −279865. −0.744778 −0.372389 0.928077i \(-0.621461\pi\)
−0.372389 + 0.928077i \(0.621461\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1881.09 + 1086.05i −0.00494128 + 0.00285285i −0.502469 0.864595i \(-0.667575\pi\)
0.497527 + 0.867448i \(0.334241\pi\)
\(618\) 0 0
\(619\) −3964.87 + 6867.36i −0.0103478 + 0.0179229i −0.871153 0.491012i \(-0.836627\pi\)
0.860805 + 0.508935i \(0.169961\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −68766.5 39702.4i −0.177174 0.102292i
\(624\) 0 0
\(625\) −124678. 215949.i −0.319176 0.552830i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 77207.3i 0.195145i
\(630\) 0 0
\(631\) 546257. 1.37195 0.685975 0.727625i \(-0.259376\pi\)
0.685975 + 0.727625i \(0.259376\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3451.07 1992.48i 0.00855868 0.00494135i
\(636\) 0 0
\(637\) 111162. 192539.i 0.273955 0.474504i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −181888. 105013.i −0.442677 0.255580i 0.262055 0.965053i \(-0.415600\pi\)
−0.704733 + 0.709473i \(0.748933\pi\)
\(642\) 0 0
\(643\) 39984.7 + 69255.6i 0.0967101 + 0.167507i 0.910321 0.413903i \(-0.135835\pi\)
−0.813611 + 0.581410i \(0.802501\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 247483.i 0.591203i 0.955311 + 0.295601i \(0.0955200\pi\)
−0.955311 + 0.295601i \(0.904480\pi\)
\(648\) 0 0
\(649\) −550211. −1.30629
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −35706.7 + 20615.3i −0.0837382 + 0.0483463i −0.541284 0.840840i \(-0.682062\pi\)
0.457546 + 0.889186i \(0.348728\pi\)
\(654\) 0 0
\(655\) −51585.7 + 89349.1i −0.120239 + 0.208261i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 709817. + 409813.i 1.63446 + 0.943659i 0.982693 + 0.185244i \(0.0593074\pi\)
0.651772 + 0.758415i \(0.274026\pi\)
\(660\) 0 0
\(661\) −120074. 207974.i −0.274818 0.475999i 0.695271 0.718747i \(-0.255284\pi\)
−0.970089 + 0.242749i \(0.921951\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 77012.8i 0.174149i
\(666\) 0 0
\(667\) 346660. 0.779205
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −667824. + 385568.i −1.48326 + 0.856360i
\(672\) 0 0
\(673\) 101639. 176044.i 0.224404 0.388679i −0.731737 0.681587i \(-0.761290\pi\)
0.956140 + 0.292909i \(0.0946233\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −295368. 170531.i −0.644446 0.372071i 0.141879 0.989884i \(-0.454686\pi\)
−0.786325 + 0.617813i \(0.788019\pi\)
\(678\) 0 0
\(679\) 116966. + 202591.i 0.253700 + 0.439422i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 753067.i 1.61433i 0.590326 + 0.807165i \(0.298999\pi\)
−0.590326 + 0.807165i \(0.701001\pi\)
\(684\) 0 0
\(685\) 249860. 0.532495
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −372953. + 215324.i −0.785625 + 0.453581i
\(690\) 0 0
\(691\) 202444. 350643.i 0.423983 0.734361i −0.572341 0.820015i \(-0.693965\pi\)
0.996325 + 0.0856546i \(0.0272981\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 72922.0 + 42101.6i 0.150970 + 0.0871623i
\(696\) 0 0
\(697\) 535881. + 928174.i 1.10307 + 1.91057i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 62736.6i 0.127669i 0.997961 + 0.0638344i \(0.0203329\pi\)
−0.997961 + 0.0638344i \(0.979667\pi\)
\(702\) 0 0
\(703\) −27366.9 −0.0553751
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −64041.4 + 36974.3i −0.128122 + 0.0739710i
\(708\) 0 0
\(709\) −478518. + 828817.i −0.951931 + 1.64879i −0.210692 + 0.977553i \(0.567572\pi\)
−0.741240 + 0.671241i \(0.765762\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −837870. 483744.i −1.64815 0.951562i
\(714\) 0 0
\(715\) −75556.6 130868.i −0.147795 0.255989i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 109853.i 0.212498i −0.994340 0.106249i \(-0.966116\pi\)
0.994340 0.106249i \(-0.0338841\pi\)
\(720\) 0 0
\(721\) −837495. −1.61106
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 176940. 102156.i 0.336627 0.194352i
\(726\) 0 0
\(727\) −112227. + 194383.i −0.212339 + 0.367781i −0.952446 0.304707i \(-0.901441\pi\)
0.740107 + 0.672489i \(0.234775\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −115191. 66505.6i −0.215568 0.124458i
\(732\) 0 0
\(733\) −26396.8 45720.6i −0.0491296 0.0850950i 0.840415 0.541944i \(-0.182311\pi\)
−0.889544 + 0.456849i \(0.848978\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 752836.i 1.38601i
\(738\) 0 0
\(739\) 639035. 1.17013 0.585067 0.810985i \(-0.301068\pi\)
0.585067 + 0.810985i \(0.301068\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 647838. 374029.i 1.17351 0.677529i 0.219009 0.975723i \(-0.429718\pi\)
0.954505 + 0.298194i \(0.0963842\pi\)
\(744\) 0 0
\(745\) −8859.52 + 15345.1i −0.0159624 + 0.0276477i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −969646. 559826.i −1.72842 0.997905i
\(750\) 0 0
\(751\) 177786. + 307935.i 0.315223 + 0.545983i 0.979485 0.201518i \(-0.0645873\pi\)
−0.664262 + 0.747500i \(0.731254\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 32911.2i 0.0577364i
\(756\) 0 0
\(757\) 173106. 0.302079 0.151040 0.988528i \(-0.451738\pi\)
0.151040 + 0.988528i \(0.451738\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 173520. 100182.i 0.299626 0.172989i −0.342649 0.939463i \(-0.611324\pi\)
0.642275 + 0.766475i \(0.277991\pi\)
\(762\) 0 0
\(763\) −330311. + 572116.i −0.567381 + 0.982732i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 678115. + 391510.i 1.15269 + 0.665506i
\(768\) 0 0
\(769\) 200920. + 348003.i 0.339758 + 0.588478i 0.984387 0.176018i \(-0.0563216\pi\)
−0.644629 + 0.764495i \(0.722988\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 817430.i 1.36802i 0.729474 + 0.684009i \(0.239765\pi\)
−0.729474 + 0.684009i \(0.760235\pi\)
\(774\) 0 0
\(775\) −570213. −0.949366
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 329000. 189948.i 0.542153 0.313012i
\(780\) 0 0
\(781\) −44963.4 + 77878.9i −0.0737152 + 0.127678i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −22401.2 12933.4i −0.0363524 0.0209881i
\(786\) 0 0
\(787\) −49202.8 85221.7i −0.0794402 0.137594i 0.823568 0.567217i \(-0.191980\pi\)
−0.903009 + 0.429623i \(0.858647\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 791919.i 1.26569i
\(792\) 0 0
\(793\) 1.09743e6 1.74513
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 287305. 165876.i 0.452300 0.261136i −0.256501 0.966544i \(-0.582570\pi\)
0.708801 + 0.705408i \(0.249236\pi\)
\(798\) 0 0
\(799\) 564370. 977517.i 0.884036 1.53120i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −387733. 223858.i −0.601314 0.347169i