Properties

Label 108.5.g.a.17.3
Level 108
Weight 5
Character 108.17
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 17.3
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 \(\chi\) \(=\) 108.17
Dual form 108.5.g.a.89.3

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.645671 0.763615i \(-0.276578\pi\)
−0.338475 + 0.940976i \(0.609911\pi\)
\(6\) 0 0
\(7\) −30.9381 53.5864i −0.631390 1.09360i −0.987268 0.159068i \(-0.949151\pi\)
0.355877 0.934533i \(-0.384182\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −94.7648 + 54.7125i −0.783180 + 0.452169i −0.837556 0.546351i \(-0.816016\pi\)
0.0543761 + 0.998521i \(0.482683\pi\)
\(12\) 0 0
\(13\) 77.8628 134.862i 0.460727 0.798002i −0.538271 0.842772i \(-0.680922\pi\)
0.998997 + 0.0447702i \(0.0142556\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 395.955i 1.37009i −0.728502 0.685044i \(-0.759783\pi\)
0.728502 0.685044i \(-0.240217\pi\)
\(18\) 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 −0.999785 0.0207115i \(-0.993407\pi\)
−0.517829 0.855484i \(-0.673260\pi\)
\(24\) 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 −0.680026 0.733188i \(-0.738032\pi\)
0.294946 + 0.955514i \(0.404698\pi\)
\(30\) 0 0
\(31\) 521.830 903.837i 0.543008 0.940517i −0.455722 0.890122i \(-0.650619\pi\)
0.998729 0.0503946i \(-0.0160479\pi\)
\(32\) 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 0.993808 0.111108i \(-0.0354398\pi\)
0.400682 + 0.916217i \(0.368773\pi\)
\(42\) 0 0
\(43\) −167.963 290.920i −0.0908397 0.157339i 0.817025 0.576602i \(-0.195622\pi\)
−0.907865 + 0.419263i \(0.862288\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2468.76 + 1425.34i −1.11759 + 0.645241i −0.940785 0.339005i \(-0.889910\pi\)
−0.176805 + 0.984246i \(0.556576\pi\)
\(48\) 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 \(-0.836176\pi\)
0.870457 0.492245i \(-0.163824\pi\)
\(54\) 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 0.971298 0.237866i \(-0.0764479\pi\)
0.279651 + 0.960102i \(0.409781\pi\)
\(60\) 0 0
\(61\) 3523.59 + 6103.03i 0.946947 + 1.64016i 0.751806 + 0.659384i \(0.229183\pi\)
0.195140 + 0.980775i \(0.437484\pi\)
\(62\) 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 0.173242 + 0.984879i \(0.444576\pi\)
−0.939551 + 0.342408i \(0.888758\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 821.812i 0.163026i 0.996672 + 0.0815128i \(0.0259752\pi\)
−0.996672 + 0.0815128i \(0.974025\pi\)
\(72\) 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 −0.991854 0.127382i \(-0.959343\pi\)
0.385611 0.922661i \(-0.373991\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6777.78 + 3913.15i −0.983855 + 0.568029i −0.903432 0.428732i \(-0.858961\pi\)
−0.0804236 + 0.996761i \(0.525627\pi\)
\(84\) 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 \(-0.974187\pi\)
0.996714 0.0810051i \(-0.0258130\pi\)
\(90\) 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 0.948821 0.315816i \(-0.102278\pi\)
−0.747915 + 0.663795i \(0.768945\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1034.99 597.553i 0.101460 0.0585779i −0.448411 0.893827i \(-0.648010\pi\)
0.549871 + 0.835249i \(0.314677\pi\)
\(102\) 0 0
\(103\) 6767.50 11721.6i 0.637901 1.10488i −0.347991 0.937498i \(-0.613136\pi\)
0.985892 0.167380i \(-0.0535306\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18095.0i 1.58049i −0.612792 0.790244i \(-0.709954\pi\)
0.612792 0.790244i \(-0.290046\pi\)
\(108\) 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 −0.00133098 0.999999i \(-0.500424\pi\)
−0.866690 + 0.498847i \(0.833757\pi\)
\(114\) 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 0.176842 0.984239i \(-0.443412\pi\)
−0.763955 + 0.645270i \(0.776745\pi\)
\(132\) 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 0.319637 0.947540i \(-0.396439\pi\)
0.980412 + 0.196956i \(0.0631055\pi\)
\(138\) 0 0
\(139\) 4747.58 8223.05i 0.245721 0.425602i −0.716613 0.697471i \(-0.754309\pi\)
0.962334 + 0.271869i \(0.0876419\pi\)
\(140\) 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 0.460522 0.887648i \(-0.347662\pi\)
−0.538465 + 0.842648i \(0.680995\pi\)
\(150\) 0 0
\(151\) 1855.61 + 3214.02i 0.0813830 + 0.140959i 0.903844 0.427862i \(-0.140733\pi\)
−0.822461 + 0.568821i \(0.807400\pi\)
\(152\) 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 −0.894092 0.447883i \(-0.852178\pi\)
0.834924 + 0.550365i \(0.185511\pi\)
\(158\) 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 0.563339 0.826226i \(-0.309517\pi\)
−0.433863 + 0.900979i \(0.642850\pi\)
\(168\) 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 0.0177101 0.999843i \(-0.494362\pi\)
0.874745 + 0.484584i \(0.161029\pi\)
\(174\) 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 \(0.0297368\pi\)
−0.995639 + 0.0932852i \(0.970263\pi\)
\(180\) 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 −0.189631 0.981855i \(-0.560729\pi\)
0.755496 + 0.655153i \(0.227396\pi\)
\(192\) 0 0
\(193\) −20081.7 + 34782.5i −0.539121 + 0.933784i 0.459831 + 0.888006i \(0.347910\pi\)
−0.998952 + 0.0457779i \(0.985423\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3622.11i 0.0933318i −0.998911 0.0466659i \(-0.985140\pi\)
0.998911 0.0466659i \(-0.0148596\pi\)
\(198\) 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 −0.857317 0.514790i \(-0.827870\pi\)
0.874479 + 0.485063i \(0.161203\pi\)
\(212\) 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 0.694143 0.719837i \(-0.255784\pi\)
−0.970469 + 0.241227i \(0.922450\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 39178.5 22619.7i 0.760319 0.438970i −0.0690916 0.997610i \(-0.522010\pi\)
0.829410 + 0.558640i \(0.188677\pi\)
\(228\) 0 0
\(229\) 40074.3 69410.7i 0.764178 1.32360i −0.176502 0.984300i \(-0.556478\pi\)
0.940680 0.339295i \(-0.110189\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 90756.0i 1.67172i 0.548942 + 0.835860i \(0.315031\pi\)
−0.548942 + 0.835860i \(0.684969\pi\)
\(234\) 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 0.493787 0.869583i \(-0.335612\pi\)
−0.506187 + 0.862424i \(0.668946\pi\)
\(240\) 0 0
\(241\) −37158.1 64359.7i −0.639764 1.10810i −0.985484 0.169766i \(-0.945699\pi\)
0.345721 0.938337i \(-0.387634\pi\)
\(242\) 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 \(-0.958695\pi\)
0.991593 0.129398i \(-0.0413045\pi\)
\(252\) 0 0
\(253\) 101439. 1.58475
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −108732. 62776.2i −1.64623 0.950449i −0.978553 0.205995i \(-0.933957\pi\)
−0.667673 0.744454i \(-0.732710\pi\)
\(258\) 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 −0.395590 0.918427i \(-0.629460\pi\)
0.597586 + 0.801805i \(0.296127\pi\)
\(264\) 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 \(-0.825144\pi\)
0.852877 0.522112i \(-0.174856\pi\)
\(270\) 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 −0.999531 0.0306193i \(-0.990252\pi\)
0.473248 0.880929i \(-0.343081\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −57384.8 + 33131.1i −0.726749 + 0.419589i −0.817232 0.576309i \(-0.804492\pi\)
0.0904828 + 0.995898i \(0.471159\pi\)
\(282\) 0 0
\(283\) −7288.93 + 12624.8i −0.0910104 + 0.157635i −0.907937 0.419108i \(-0.862343\pi\)
0.816926 + 0.576742i \(0.195676\pi\)
\(284\) 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 0.0709185 0.997482i \(-0.477407\pi\)
−0.828386 + 0.560158i \(0.810740\pi\)
\(294\) 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 0.981285 0.192563i \(-0.0616800\pi\)
0.323878 + 0.946099i \(0.395013\pi\)
\(312\) 0 0
\(313\) 37866.9 + 65587.3i 0.386519 + 0.669470i 0.991979 0.126406i \(-0.0403441\pi\)
−0.605460 + 0.795876i \(0.707011\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 80308.7 46366.3i 0.799179 0.461406i −0.0440049 0.999031i \(-0.514012\pi\)
0.843184 + 0.537625i \(0.180678\pi\)
\(318\) 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 0.840305 0.542114i \(-0.182376\pi\)
−0.889637 + 0.456668i \(0.849043\pi\)
\(332\) 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 0.420831 + 0.907139i \(0.361738\pi\)
−0.996021 + 0.0891187i \(0.971595\pi\)
\(338\) 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 0.955177 0.296034i \(-0.0956641\pi\)
0.221216 + 0.975225i \(0.428997\pi\)
\(348\) 0 0
\(349\) −7232.92 12527.8i −0.0593831 0.102855i 0.834806 0.550545i \(-0.185580\pi\)
−0.894189 + 0.447690i \(0.852247\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 8348.17 4819.82i 0.0669949 0.0386795i −0.466128 0.884717i \(-0.654352\pi\)
0.533123 + 0.846038i \(0.321018\pi\)
\(354\) 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 \(-0.929602\pi\)
0.975643 0.219364i \(-0.0703982\pi\)
\(360\) 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 0.993712 + 0.111969i \(0.0357157\pi\)
−0.399888 + 0.916564i \(0.630951\pi\)
\(368\) 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 −0.613410 0.789764i \(-0.710203\pi\)
0.990661 + 0.136347i \(0.0435361\pi\)
\(374\) 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 0.336812 0.941572i \(-0.390651\pi\)
−0.647019 + 0.762474i \(0.723985\pi\)
\(384\) 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 0.206435 0.978460i \(-0.433814\pi\)
0.950589 + 0.310452i \(0.100480\pi\)
\(390\) 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 0.783461 0.621441i \(-0.213453\pi\)
−0.146453 + 0.989218i \(0.546786\pi\)
\(402\) 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 −0.920850 0.389917i \(-0.872504\pi\)
0.798103 + 0.602521i \(0.205837\pi\)
\(410\) 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 0.232470 0.972603i \(-0.425319\pi\)
−0.726064 + 0.687627i \(0.758652\pi\)
\(420\) 0 0
\(421\) 110257. + 190971.i 0.622074 + 1.07746i 0.989099 + 0.147253i \(0.0470432\pi\)
−0.367024 + 0.930211i \(0.619623\pi\)
\(422\) 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 \(0.192733\pi\)
−0.822224 + 0.569163i \(0.807267\pi\)
\(432\) 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 −0.997808 0.0661804i \(-0.978919\pi\)
0.441590 0.897217i \(-0.354415\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −174614. + 100814.i −0.889759 + 0.513703i −0.873864 0.486171i \(-0.838393\pi\)
−0.0158954 + 0.999874i \(0.505060\pi\)
\(444\) 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 \(-0.889736\pi\)
0.940599 0.339519i \(-0.110264\pi\)
\(450\) 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 −0.853696 0.520772i \(-0.825644\pi\)
−0.0241542 0.999708i \(-0.507689\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 42379.8 24468.0i 0.199415 0.115132i −0.396968 0.917833i \(-0.629938\pi\)
0.596382 + 0.802700i \(0.296604\pi\)
\(462\) 0 0
\(463\) 143514. 248574.i 0.669472 1.15956i −0.308580 0.951198i \(-0.599854\pi\)
0.978052 0.208361i \(-0.0668128\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 43613.3i 0.199979i −0.994988 0.0999896i \(-0.968119\pi\)
0.994988 0.0999896i \(-0.0318809\pi\)
\(468\) 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 0.00107799 0.999999i \(-0.499657\pi\)
0.866564 + 0.499066i \(0.166324\pi\)
\(480\) 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 0.166796 0.985991i \(-0.446658\pi\)
−0.770496 + 0.637445i \(0.779991\pi\)
\(492\) 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 0.247999 + 0.968760i \(0.420227\pi\)
−0.962971 + 0.269607i \(0.913106\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 180472.i 0.713301i 0.934238 + 0.356651i \(0.116081\pi\)
−0.934238 + 0.356651i \(0.883919\pi\)
\(504\) 0 0
\(505\) 10598.2 0.0415575
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −345324. 199373.i −1.33288 0.769540i −0.347142 0.937813i \(-0.612848\pi\)
−0.985740 + 0.168273i \(0.946181\pi\)
\(510\) 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 \(0.352179\pi\)
−0.447880 + 0.894094i \(0.647821\pi\)
\(522\) 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 0.996356 0.0852925i \(-0.0271825\pi\)
−0.572043 + 0.820223i \(0.693849\pi\)
\(548\) 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 \(-0.974701\pi\)
0.996843 0.0793962i \(-0.0252992\pi\)
\(558\) 0 0
\(559\) −52312.1 −0.167409
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 342365. + 197665.i 1.08012 + 0.623608i 0.930929 0.365200i \(-0.118999\pi\)
0.149192 + 0.988808i \(0.452333\pi\)
\(564\) 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 −0.111527 0.993761i \(-0.535574\pi\)
0.804859 + 0.593466i \(0.202241\pi\)
\(570\) 0 0
\(571\) −226228. + 391839.i −0.693864 + 1.20181i 0.276697 + 0.960957i \(0.410760\pi\)
−0.970562 + 0.240851i \(0.922573\pi\)
\(572\) 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 −0.500347 0.865825i \(-0.666794\pi\)
0.499653 + 0.866225i \(0.333461\pi\)
\(588\) 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 \(-0.995049\pi\)
0.999879 0.0155548i \(-0.00495145\pi\)
\(594\) 0 0
\(595\) −217268. −0.613708
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13902.7 + 8026.70i 0.0387475 + 0.0223709i 0.519249 0.854623i \(-0.326212\pi\)
−0.480501 + 0.876994i \(0.659545\pi\)
\(600\) 0 0
\(601\) −267567. 463439.i −0.740769 1.28305i −0.952145 0.305645i \(-0.901128\pi\)
0.211376 0.977405i \(-0.432205\pi\)
\(602\) 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 −0.810003 0.586425i \(-0.800535\pi\)
0.912861 + 0.408271i \(0.133868\pi\)
\(608\) 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 0.497527 0.867448i \(-0.334241\pi\)
−0.502469 + 0.864595i \(0.667575\pi\)
\(618\) 0 0
\(619\) −3964.87 6867.36i −0.0103478 0.0179229i 0.860805 0.508935i \(-0.169961\pi\)
−0.871153 + 0.491012i \(0.836627\pi\)
\(620\) 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 −0.704733 0.709473i \(-0.748933\pi\)
0.262055 + 0.965053i \(0.415600\pi\)
\(642\) 0 0
\(643\) 39984.7 69255.6i 0.0967101 0.167507i −0.813611 0.581410i \(-0.802501\pi\)
0.910321 + 0.413903i \(0.135835\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 247483.i 0.591203i −0.955311 0.295601i \(-0.904480\pi\)
0.955311 0.295601i \(-0.0955200\pi\)
\(648\) 0 0
\(649\) −550211. −1.30629
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −35706.7 20615.3i −0.0837382 0.0483463i 0.457546 0.889186i \(-0.348728\pi\)
−0.541284 + 0.840840i \(0.682062\pi\)
\(654\) 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 0.651772 0.758415i \(-0.274026\pi\)
0.982693 0.185244i \(-0.0593074\pi\)
\(660\) 0 0
\(661\) −120074. + 207974.i −0.274818 + 0.475999i −0.970089 0.242749i \(-0.921951\pi\)
0.695271 + 0.718747i \(0.255284\pi\)
\(662\) 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 0.956140 0.292909i \(-0.0946233\pi\)
−0.731737 + 0.681587i \(0.761290\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −295368. + 170531.i −0.644446 + 0.372071i −0.786325 0.617813i \(-0.788019\pi\)
0.141879 + 0.989884i \(0.454686\pi\)
\(678\) 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 \(-0.701001\pi\)
0.590326 0.807165i \(-0.298999\pi\)
\(684\) 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 0.996325 0.0856546i \(-0.0272981\pi\)
−0.572341 + 0.820015i \(0.693965\pi\)
\(692\) 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 \(-0.979667\pi\)
0.997961 0.0638344i \(-0.0203329\pi\)
\(702\) 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 −0.741240 0.671241i \(-0.765762\pi\)
−0.210692 0.977553i \(-0.567572\pi\)
\(710\) 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 \(0.0338841\pi\)
−0.994340 + 0.106249i \(0.966116\pi\)
\(720\) 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 0.740107 0.672489i \(-0.234775\pi\)
−0.952446 + 0.304707i \(0.901441\pi\)
\(728\) 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 −0.889544 0.456849i \(-0.848978\pi\)
0.840415 + 0.541944i \(0.182311\pi\)
\(734\) 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 0.954505 0.298194i \(-0.0963842\pi\)
0.219009 + 0.975723i \(0.429718\pi\)
\(744\) 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 −0.664262 0.747500i \(-0.731254\pi\)
0.979485 + 0.201518i \(0.0645873\pi\)
\(752\) 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 0.642275 0.766475i \(-0.277991\pi\)
−0.342649 + 0.939463i \(0.611324\pi\)
\(762\) 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 −0.644629 0.764495i \(-0.722988\pi\)
0.984387 + 0.176018i \(0.0563216\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 817430.i 1.36802i −0.729474 0.684009i \(-0.760235\pi\)
0.729474 0.684009i \(-0.239765\pi\)
\(774\) 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 −0.903009 0.429623i \(-0.858647\pi\)
0.823568 + 0.567217i \(0.191980\pi\)
\(788\) 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 0.708801 0.705408i \(-0.249236\pi\)
−0.256501 + 0.966544i \(0.582570\pi\)
\(798\) 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