Properties

Label 108.5.g.a.89.4
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 89.4
Root \(-3.41053 - 2.74723i\) 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.17.4

$q$-expansion

\(f(q)\) \(=\) \(q+(34.8718 - 20.1332i) q^{5} +(-7.38688 + 12.7945i) q^{7} +O(q^{10})\) \(q+(34.8718 - 20.1332i) q^{5} +(-7.38688 + 12.7945i) q^{7} +(70.7125 + 40.8259i) q^{11} +(-139.053 - 240.848i) q^{13} -10.8854i q^{17} +532.815 q^{19} +(702.045 - 405.326i) q^{23} +(498.193 - 862.895i) q^{25} +(257.640 + 148.749i) q^{29} +(-97.5447 - 168.952i) q^{31} +594.887i q^{35} -2097.18 q^{37} +(1359.41 - 784.854i) q^{41} +(46.0863 - 79.8239i) q^{43} +(-1849.15 - 1067.61i) q^{47} +(1091.37 + 1890.30i) q^{49} +2579.42i q^{53} +3287.82 q^{55} +(-1349.04 + 778.868i) q^{59} +(-2685.97 + 4652.24i) q^{61} +(-9698.07 - 5599.19i) q^{65} +(-457.641 - 792.658i) q^{67} +8215.93i q^{71} -3438.63 q^{73} +(-1044.69 + 603.152i) q^{77} +(-2316.17 + 4011.73i) q^{79} +(5195.52 + 2999.63i) q^{83} +(-219.158 - 379.593i) q^{85} -8434.43i q^{89} +4108.69 q^{91} +(18580.2 - 10727.3i) q^{95} +(3015.58 - 5223.13i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 9q^{5} + 13q^{7} + O(q^{10}) \) \( 8q + 9q^{5} + 13q^{7} + 18q^{11} - 5q^{13} + 562q^{19} + 1719q^{23} + 353q^{25} - 2115q^{29} + 187q^{31} + 16q^{37} + 7920q^{41} - 68q^{43} - 13689q^{47} - 327q^{49} - 1818q^{55} + 20052q^{59} - 1937q^{61} - 25965q^{65} + 154q^{67} - 7802q^{73} + 25641q^{77} - 2195q^{79} - 37017q^{83} - 3042q^{85} + 15830q^{91} + 37116q^{95} + 7282q^{97} + O(q^{100}) \)

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
\(5\) 34.8718 20.1332i 1.39487 0.805329i 0.401021 0.916069i \(-0.368655\pi\)
0.993849 + 0.110740i \(0.0353221\pi\)
\(6\) 0 0
\(7\) −7.38688 + 12.7945i −0.150753 + 0.261111i −0.931504 0.363730i \(-0.881503\pi\)
0.780752 + 0.624841i \(0.214836\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 70.7125 + 40.8259i 0.584400 + 0.337404i 0.762880 0.646540i \(-0.223785\pi\)
−0.178480 + 0.983944i \(0.557118\pi\)
\(12\) 0 0
\(13\) −139.053 240.848i −0.822801 1.42513i −0.903588 0.428402i \(-0.859077\pi\)
0.0807868 0.996731i \(-0.474257\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 10.8854i 0.0376658i −0.999823 0.0188329i \(-0.994005\pi\)
0.999823 0.0188329i \(-0.00599505\pi\)
\(18\) 0 0
\(19\) 532.815 1.47594 0.737971 0.674833i \(-0.235784\pi\)
0.737971 + 0.674833i \(0.235784\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 702.045 405.326i 1.32712 0.766211i 0.342264 0.939604i \(-0.388806\pi\)
0.984853 + 0.173393i \(0.0554730\pi\)
\(24\) 0 0
\(25\) 498.193 862.895i 0.797109 1.38063i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 257.640 + 148.749i 0.306350 + 0.176871i 0.645292 0.763936i \(-0.276736\pi\)
−0.338942 + 0.940807i \(0.610069\pi\)
\(30\) 0 0
\(31\) −97.5447 168.952i −0.101503 0.175809i 0.810801 0.585322i \(-0.199032\pi\)
−0.912304 + 0.409513i \(0.865699\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 594.887i 0.485622i
\(36\) 0 0
\(37\) −2097.18 −1.53191 −0.765954 0.642896i \(-0.777733\pi\)
−0.765954 + 0.642896i \(0.777733\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1359.41 784.854i 0.808689 0.466897i −0.0378113 0.999285i \(-0.512039\pi\)
0.846500 + 0.532388i \(0.178705\pi\)
\(42\) 0 0
\(43\) 46.0863 79.8239i 0.0249250 0.0431714i −0.853294 0.521430i \(-0.825399\pi\)
0.878219 + 0.478259i \(0.158732\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1849.15 1067.61i −0.837098 0.483299i 0.0191789 0.999816i \(-0.493895\pi\)
−0.856277 + 0.516517i \(0.827228\pi\)
\(48\) 0 0
\(49\) 1091.37 + 1890.30i 0.454547 + 0.787299i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2579.42i 0.918271i 0.888366 + 0.459135i \(0.151841\pi\)
−0.888366 + 0.459135i \(0.848159\pi\)
\(54\) 0 0
\(55\) 3287.82 1.08688
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1349.04 + 778.868i −0.387544 + 0.223748i −0.681095 0.732195i \(-0.738496\pi\)
0.293552 + 0.955943i \(0.405163\pi\)
\(60\) 0 0
\(61\) −2685.97 + 4652.24i −0.721842 + 1.25027i 0.238419 + 0.971162i \(0.423371\pi\)
−0.960261 + 0.279105i \(0.909962\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −9698.07 5599.19i −2.29540 1.32525i
\(66\) 0 0
\(67\) −457.641 792.658i −0.101947 0.176578i 0.810540 0.585684i \(-0.199174\pi\)
−0.912487 + 0.409106i \(0.865841\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8215.93i 1.62982i 0.579587 + 0.814910i \(0.303214\pi\)
−0.579587 + 0.814910i \(0.696786\pi\)
\(72\) 0 0
\(73\) −3438.63 −0.645267 −0.322634 0.946524i \(-0.604568\pi\)
−0.322634 + 0.946524i \(0.604568\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1044.69 + 603.152i −0.176200 + 0.101729i
\(78\) 0 0
\(79\) −2316.17 + 4011.73i −0.371122 + 0.642802i −0.989738 0.142891i \(-0.954360\pi\)
0.618617 + 0.785693i \(0.287693\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5195.52 + 2999.63i 0.754176 + 0.435424i 0.827201 0.561907i \(-0.189932\pi\)
−0.0730250 + 0.997330i \(0.523265\pi\)
\(84\) 0 0
\(85\) −219.158 379.593i −0.0303333 0.0525389i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8434.43i 1.06482i −0.846487 0.532409i \(-0.821287\pi\)
0.846487 0.532409i \(-0.178713\pi\)
\(90\) 0 0
\(91\) 4108.69 0.496158
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 18580.2 10727.3i 2.05875 1.18862i
\(96\) 0 0
\(97\) 3015.58 5223.13i 0.320499 0.555121i −0.660092 0.751185i \(-0.729483\pi\)
0.980591 + 0.196064i \(0.0628160\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −5181.24 2991.39i −0.507915 0.293245i 0.224061 0.974575i \(-0.428069\pi\)
−0.731976 + 0.681330i \(0.761402\pi\)
\(102\) 0 0
\(103\) 765.718 + 1326.26i 0.0721763 + 0.125013i 0.899855 0.436189i \(-0.143672\pi\)
−0.827679 + 0.561202i \(0.810339\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 20499.8i 1.79053i 0.445536 + 0.895264i \(0.353013\pi\)
−0.445536 + 0.895264i \(0.646987\pi\)
\(108\) 0 0
\(109\) −9404.21 −0.791534 −0.395767 0.918351i \(-0.629521\pi\)
−0.395767 + 0.918351i \(0.629521\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2598.59 + 1500.29i −0.203507 + 0.117495i −0.598290 0.801279i \(-0.704153\pi\)
0.394783 + 0.918774i \(0.370820\pi\)
\(114\) 0 0
\(115\) 16321.0 28268.8i 1.23410 2.13753i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 139.273 + 80.4092i 0.00983496 + 0.00567822i
\(120\) 0 0
\(121\) −3987.00 6905.69i −0.272317 0.471668i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 14954.4i 0.957081i
\(126\) 0 0
\(127\) 9817.40 0.608680 0.304340 0.952563i \(-0.401564\pi\)
0.304340 + 0.952563i \(0.401564\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 553.194 319.387i 0.0322356 0.0186112i −0.483796 0.875181i \(-0.660742\pi\)
0.516031 + 0.856570i \(0.327409\pi\)
\(132\) 0 0
\(133\) −3935.84 + 6817.07i −0.222502 + 0.385385i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 27716.3 + 16002.0i 1.47670 + 0.852575i 0.999654 0.0263010i \(-0.00837284\pi\)
0.477050 + 0.878876i \(0.341706\pi\)
\(138\) 0 0
\(139\) 2792.13 + 4836.11i 0.144513 + 0.250303i 0.929191 0.369600i \(-0.120505\pi\)
−0.784678 + 0.619903i \(0.787172\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 22707.9i 1.11047i
\(144\) 0 0
\(145\) 11979.2 0.569758
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7118.75 4110.01i 0.320650 0.185127i −0.331032 0.943619i \(-0.607397\pi\)
0.651682 + 0.758492i \(0.274064\pi\)
\(150\) 0 0
\(151\) −10236.0 + 17729.2i −0.448927 + 0.777564i −0.998316 0.0580020i \(-0.981527\pi\)
0.549389 + 0.835566i \(0.314860\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −6803.11 3927.78i −0.283168 0.163487i
\(156\) 0 0
\(157\) −12896.9 22338.2i −0.523224 0.906250i −0.999635 0.0270273i \(-0.991396\pi\)
0.476411 0.879223i \(-0.341937\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 11976.4i 0.462034i
\(162\) 0 0
\(163\) −16488.3 −0.620584 −0.310292 0.950641i \(-0.600427\pi\)
−0.310292 + 0.950641i \(0.600427\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −34263.0 + 19781.8i −1.22855 + 0.709304i −0.966727 0.255812i \(-0.917657\pi\)
−0.261824 + 0.965116i \(0.584324\pi\)
\(168\) 0 0
\(169\) −24391.2 + 42246.8i −0.854004 + 1.47918i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −4204.22 2427.31i −0.140473 0.0811022i 0.428116 0.903724i \(-0.359177\pi\)
−0.568589 + 0.822621i \(0.692511\pi\)
\(174\) 0 0
\(175\) 7360.19 + 12748.2i 0.240333 + 0.416268i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4764.02i 0.148685i −0.997233 0.0743425i \(-0.976314\pi\)
0.997233 0.0743425i \(-0.0236858\pi\)
\(180\) 0 0
\(181\) 3741.40 0.114203 0.0571014 0.998368i \(-0.481814\pi\)
0.0571014 + 0.998368i \(0.481814\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −73132.4 + 42223.0i −2.13681 + 1.23369i
\(186\) 0 0
\(187\) 444.406 769.734i 0.0127086 0.0220119i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9003.63 5198.25i −0.246803 0.142492i 0.371496 0.928434i \(-0.378845\pi\)
−0.618300 + 0.785943i \(0.712178\pi\)
\(192\) 0 0
\(193\) 21606.1 + 37422.9i 0.580045 + 1.00467i 0.995473 + 0.0950419i \(0.0302985\pi\)
−0.415428 + 0.909626i \(0.636368\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 49899.7i 1.28578i −0.765960 0.642889i \(-0.777736\pi\)
0.765960 0.642889i \(-0.222264\pi\)
\(198\) 0 0
\(199\) −7613.76 −0.192262 −0.0961310 0.995369i \(-0.530647\pi\)
−0.0961310 + 0.995369i \(0.530647\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3806.32 + 2197.58i −0.0923662 + 0.0533276i
\(204\) 0 0
\(205\) 31603.3 54738.5i 0.752011 1.30252i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 37676.6 + 21752.6i 0.862541 + 0.497988i
\(210\) 0 0
\(211\) 28097.7 + 48666.7i 0.631112 + 1.09312i 0.987325 + 0.158713i \(0.0507344\pi\)
−0.356213 + 0.934405i \(0.615932\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 3711.47i 0.0802913i
\(216\) 0 0
\(217\) 2882.21 0.0612076
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2621.72 + 1513.65i −0.0536788 + 0.0309915i
\(222\) 0 0
\(223\) −18961.1 + 32841.6i −0.381289 + 0.660412i −0.991247 0.132022i \(-0.957853\pi\)
0.609958 + 0.792434i \(0.291186\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8461.24 4885.10i −0.164203 0.0948029i 0.415646 0.909526i \(-0.363555\pi\)
−0.579850 + 0.814723i \(0.696889\pi\)
\(228\) 0 0
\(229\) −18965.0 32848.4i −0.361645 0.626387i 0.626587 0.779352i \(-0.284451\pi\)
−0.988232 + 0.152964i \(0.951118\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3372.35i 0.0621185i −0.999518 0.0310592i \(-0.990112\pi\)
0.999518 0.0310592i \(-0.00988805\pi\)
\(234\) 0 0
\(235\) −85977.4 −1.55686
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 64618.9 37307.7i 1.13126 0.653135i 0.187011 0.982358i \(-0.440120\pi\)
0.944252 + 0.329223i \(0.106787\pi\)
\(240\) 0 0
\(241\) 12127.1 21004.7i 0.208796 0.361645i −0.742540 0.669802i \(-0.766379\pi\)
0.951336 + 0.308157i \(0.0997122\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 76115.8 + 43945.5i 1.26807 + 0.732120i
\(246\) 0 0
\(247\) −74089.7 128327.i −1.21441 2.10341i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 25543.7i 0.405449i 0.979236 + 0.202724i \(0.0649795\pi\)
−0.979236 + 0.202724i \(0.935020\pi\)
\(252\) 0 0
\(253\) 66191.1 1.03409
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −18961.7 + 10947.6i −0.287086 + 0.165749i −0.636627 0.771172i \(-0.719671\pi\)
0.349541 + 0.936921i \(0.386338\pi\)
\(258\) 0 0
\(259\) 15491.6 26832.3i 0.230939 0.399998i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6539.22 3775.42i −0.0945397 0.0545825i 0.451985 0.892026i \(-0.350716\pi\)
−0.546524 + 0.837443i \(0.684049\pi\)
\(264\) 0 0
\(265\) 51932.1 + 89949.0i 0.739510 + 1.28087i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 106275.i 1.46868i −0.678780 0.734342i \(-0.737491\pi\)
0.678780 0.734342i \(-0.262509\pi\)
\(270\) 0 0
\(271\) 82971.5 1.12977 0.564885 0.825170i \(-0.308920\pi\)
0.564885 + 0.825170i \(0.308920\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 70456.9 40678.3i 0.931661 0.537895i
\(276\) 0 0
\(277\) 32616.8 56494.0i 0.425091 0.736280i −0.571338 0.820715i \(-0.693575\pi\)
0.996429 + 0.0844353i \(0.0269086\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 82142.7 + 47425.1i 1.04029 + 0.600614i 0.919917 0.392114i \(-0.128256\pi\)
0.120378 + 0.992728i \(0.461590\pi\)
\(282\) 0 0
\(283\) −52834.0 91511.3i −0.659692 1.14262i −0.980695 0.195542i \(-0.937354\pi\)
0.321004 0.947078i \(-0.395980\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 23190.5i 0.281544i
\(288\) 0 0
\(289\) 83402.5 0.998581
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 61404.7 35452.0i 0.715264 0.412958i −0.0977432 0.995212i \(-0.531162\pi\)
0.813007 + 0.582254i \(0.197829\pi\)
\(294\) 0 0
\(295\) −31362.3 + 54321.0i −0.360382 + 0.624200i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −195243. 112724.i −2.18391 1.26088i
\(300\) 0 0
\(301\) 680.869 + 1179.30i 0.00751503 + 0.0130164i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 216309.i 2.32528i
\(306\) 0 0
\(307\) 27339.7 0.290079 0.145040 0.989426i \(-0.453669\pi\)
0.145040 + 0.989426i \(0.453669\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −88117.5 + 50874.6i −0.911048 + 0.525994i −0.880768 0.473548i \(-0.842973\pi\)
−0.0302797 + 0.999541i \(0.509640\pi\)
\(312\) 0 0
\(313\) 22810.8 39509.5i 0.232837 0.403286i −0.725805 0.687901i \(-0.758532\pi\)
0.958642 + 0.284615i \(0.0918658\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −20556.7 11868.4i −0.204567 0.118107i 0.394217 0.919017i \(-0.371016\pi\)
−0.598784 + 0.800911i \(0.704349\pi\)
\(318\) 0 0
\(319\) 12145.6 + 21036.8i 0.119354 + 0.206727i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 5799.91i 0.0555925i
\(324\) 0 0
\(325\) −277102. −2.62345
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 27318.9 15772.6i 0.252389 0.145717i
\(330\) 0 0
\(331\) −63701.2 + 110334.i −0.581422 + 1.00705i 0.413889 + 0.910327i \(0.364170\pi\)
−0.995311 + 0.0967256i \(0.969163\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −31917.5 18427.6i −0.284406 0.164202i
\(336\) 0 0
\(337\) 8353.80 + 14469.2i 0.0735571 + 0.127405i 0.900458 0.434943i \(-0.143232\pi\)
−0.826901 + 0.562348i \(0.809898\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15929.4i 0.136990i
\(342\) 0 0
\(343\) −67719.0 −0.575602
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 153069. 88374.3i 1.27124 0.733951i 0.296019 0.955182i \(-0.404341\pi\)
0.975221 + 0.221231i \(0.0710074\pi\)
\(348\) 0 0
\(349\) −49219.9 + 85251.3i −0.404101 + 0.699923i −0.994216 0.107396i \(-0.965749\pi\)
0.590116 + 0.807319i \(0.299082\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −108285. 62518.3i −0.868997 0.501716i −0.00198242 0.999998i \(-0.500631\pi\)
−0.867015 + 0.498282i \(0.833964\pi\)
\(354\) 0 0
\(355\) 165413. + 286504.i 1.31254 + 2.27339i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 130777.i 1.01471i 0.861737 + 0.507356i \(0.169377\pi\)
−0.861737 + 0.507356i \(0.830623\pi\)
\(360\) 0 0
\(361\) 153571. 1.17840
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −119911. + 69230.7i −0.900064 + 0.519652i
\(366\) 0 0
\(367\) 64119.3 111058.i 0.476054 0.824550i −0.523569 0.851983i \(-0.675400\pi\)
0.999624 + 0.0274329i \(0.00873325\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −33002.3 19053.9i −0.239771 0.138432i
\(372\) 0 0
\(373\) −31604.2 54740.0i −0.227157 0.393448i 0.729807 0.683653i \(-0.239610\pi\)
−0.956964 + 0.290205i \(0.906276\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 82736.1i 0.582120i
\(378\) 0 0
\(379\) −101202. −0.704547 −0.352273 0.935897i \(-0.614591\pi\)
−0.352273 + 0.935897i \(0.614591\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 16878.5 9744.83i 0.115063 0.0664319i −0.441364 0.897328i \(-0.645505\pi\)
0.556427 + 0.830896i \(0.312172\pi\)
\(384\) 0 0
\(385\) −24286.8 + 42065.9i −0.163851 + 0.283798i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −49519.1 28589.9i −0.327245 0.188935i 0.327372 0.944895i \(-0.393837\pi\)
−0.654617 + 0.755960i \(0.727170\pi\)
\(390\) 0 0
\(391\) −4412.14 7642.04i −0.0288599 0.0499869i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 186528.i 1.19550i
\(396\) 0 0
\(397\) −75878.7 −0.481436 −0.240718 0.970595i \(-0.577383\pi\)
−0.240718 + 0.970595i \(0.577383\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −210130. + 121319.i −1.30677 + 0.754464i −0.981556 0.191176i \(-0.938770\pi\)
−0.325215 + 0.945640i \(0.605437\pi\)
\(402\) 0 0
\(403\) −27127.9 + 46986.8i −0.167034 + 0.289312i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −148297. 85619.2i −0.895248 0.516871i
\(408\) 0 0
\(409\) −60915.8 105509.i −0.364153 0.630731i 0.624487 0.781035i \(-0.285308\pi\)
−0.988640 + 0.150304i \(0.951975\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 23013.6i 0.134923i
\(414\) 0 0
\(415\) 241569. 1.40264
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 107882. 62285.6i 0.614498 0.354780i −0.160226 0.987080i \(-0.551222\pi\)
0.774724 + 0.632300i \(0.217889\pi\)
\(420\) 0 0
\(421\) −12647.9 + 21906.8i −0.0713600 + 0.123599i −0.899498 0.436926i \(-0.856067\pi\)
0.828138 + 0.560525i \(0.189401\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −9392.97 5423.03i −0.0520026 0.0300237i
\(426\) 0 0
\(427\) −39682.0 68731.2i −0.217639 0.376962i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 153800.i 0.827944i 0.910290 + 0.413972i \(0.135859\pi\)
−0.910290 + 0.413972i \(0.864141\pi\)
\(432\) 0 0
\(433\) 112975. 0.602569 0.301285 0.953534i \(-0.402585\pi\)
0.301285 + 0.953534i \(0.402585\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 374060. 215963.i 1.95875 1.13088i
\(438\) 0 0
\(439\) 89083.3 154297.i 0.462239 0.800622i −0.536833 0.843689i \(-0.680379\pi\)
0.999072 + 0.0430665i \(0.0137127\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 258569. + 149285.i 1.31756 + 0.760691i 0.983335 0.181804i \(-0.0581935\pi\)
0.334221 + 0.942495i \(0.391527\pi\)
\(444\) 0 0
\(445\) −169812. 294123.i −0.857529 1.48528i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 201956.i 1.00176i −0.865516 0.500881i \(-0.833009\pi\)
0.865516 0.500881i \(-0.166991\pi\)
\(450\) 0 0
\(451\) 128169. 0.630131
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 143277. 82721.1i 0.692076 0.399570i
\(456\) 0 0
\(457\) −147659. + 255752.i −0.707011 + 1.22458i 0.258949 + 0.965891i \(0.416624\pi\)
−0.965961 + 0.258689i \(0.916710\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 171120. + 98796.4i 0.805193 + 0.464878i 0.845284 0.534318i \(-0.179431\pi\)
−0.0400909 + 0.999196i \(0.512765\pi\)
\(462\) 0 0
\(463\) −43231.3 74878.8i −0.201668 0.349299i 0.747398 0.664376i \(-0.231303\pi\)
−0.949066 + 0.315078i \(0.897969\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 249159.i 1.14247i −0.820788 0.571233i \(-0.806465\pi\)
0.820788 0.571233i \(-0.193535\pi\)
\(468\) 0 0
\(469\) 13522.2 0.0614753
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6517.76 3763.03i 0.0291324 0.0168196i
\(474\) 0 0
\(475\) 265445. 459763.i 1.17649 2.03773i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 363916. + 210107.i 1.58610 + 0.915734i 0.993941 + 0.109911i \(0.0350566\pi\)
0.592157 + 0.805823i \(0.298277\pi\)
\(480\) 0 0
\(481\) 291620. + 505101.i 1.26046 + 2.18317i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 242853.i 1.03243i
\(486\) 0 0
\(487\) −394498. −1.66336 −0.831680 0.555255i \(-0.812621\pi\)
−0.831680 + 0.555255i \(0.812621\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −291929. + 168545.i −1.21092 + 0.699123i −0.962959 0.269647i \(-0.913093\pi\)
−0.247958 + 0.968771i \(0.579760\pi\)
\(492\) 0 0
\(493\) 1619.19 2804.52i 0.00666199 0.0115389i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −105118. 60690.1i −0.425565 0.245700i
\(498\) 0 0
\(499\) −227950. 394821.i −0.915458 1.58562i −0.806230 0.591602i \(-0.798496\pi\)
−0.109227 0.994017i \(-0.534838\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 33893.3i 0.133961i 0.997754 + 0.0669804i \(0.0213365\pi\)
−0.997754 + 0.0669804i \(0.978663\pi\)
\(504\) 0 0
\(505\) −240905. −0.944635
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −186058. + 107421.i −0.718147 + 0.414622i −0.814070 0.580766i \(-0.802753\pi\)
0.0959233 + 0.995389i \(0.469420\pi\)
\(510\) 0 0
\(511\) 25400.7 43995.4i 0.0972758 0.168487i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 53403.9 + 30832.7i 0.201353 + 0.116251i
\(516\) 0 0
\(517\) −87171.9 150986.i −0.326134 0.564880i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 256109.i 0.943516i 0.881728 + 0.471758i \(0.156380\pi\)
−0.881728 + 0.471758i \(0.843620\pi\)
\(522\) 0 0
\(523\) 372105. 1.36038 0.680192 0.733034i \(-0.261896\pi\)
0.680192 + 0.733034i \(0.261896\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1839.12 + 1061.81i −0.00662198 + 0.00382320i
\(528\) 0 0
\(529\) 188657. 326764.i 0.674159 1.16768i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −378060. 218273.i −1.33078 0.768327i
\(534\) 0 0
\(535\) 412726. + 714863.i 1.44196 + 2.49755i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 178224.i 0.613464i
\(540\) 0 0
\(541\) 38292.3 0.130833 0.0654164 0.997858i \(-0.479162\pi\)
0.0654164 + 0.997858i \(0.479162\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −327941. + 189337.i −1.10409 + 0.637445i
\(546\) 0 0
\(547\) −251103. + 434923.i −0.839223 + 1.45358i 0.0513228 + 0.998682i \(0.483656\pi\)
−0.890545 + 0.454894i \(0.849677\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 137275. + 79255.5i 0.452155 + 0.261052i
\(552\) 0 0
\(553\) −34218.6 59268.3i −0.111895 0.193808i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 601940.i 1.94018i −0.242737 0.970092i \(-0.578045\pi\)
0.242737 0.970092i \(-0.421955\pi\)
\(558\) 0 0
\(559\) −25633.9 −0.0820333
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −135970. + 78502.5i −0.428970 + 0.247666i −0.698908 0.715212i \(-0.746330\pi\)
0.269938 + 0.962878i \(0.412997\pi\)
\(564\) 0 0
\(565\) −60411.5 + 104636.i −0.189244 + 0.327781i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 422713. + 244054.i 1.30563 + 0.753808i 0.981364 0.192156i \(-0.0615481\pi\)
0.324270 + 0.945965i \(0.394881\pi\)
\(570\) 0 0
\(571\) 85604.0 + 148270.i 0.262556 + 0.454760i 0.966920 0.255078i \(-0.0821013\pi\)
−0.704365 + 0.709838i \(0.748768\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 807721.i 2.44301i
\(576\) 0 0
\(577\) −120517. −0.361990 −0.180995 0.983484i \(-0.557932\pi\)
−0.180995 + 0.983484i \(0.557932\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −76757.3 + 44315.9i −0.227388 + 0.131283i
\(582\) 0 0
\(583\) −105307. + 182397.i −0.309828 + 0.536638i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −40161.9 23187.5i −0.116557 0.0672942i 0.440588 0.897709i \(-0.354770\pi\)
−0.557145 + 0.830415i \(0.688103\pi\)
\(588\) 0 0
\(589\) −51973.3 90020.3i −0.149813 0.259484i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 511267.i 1.45391i 0.686683 + 0.726957i \(0.259066\pi\)
−0.686683 + 0.726957i \(0.740934\pi\)
\(594\) 0 0
\(595\) 6475.59 0.0182913
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −558562. + 322486.i −1.55675 + 0.898787i −0.559180 + 0.829046i \(0.688884\pi\)
−0.997565 + 0.0697410i \(0.977783\pi\)
\(600\) 0 0
\(601\) −296605. + 513735.i −0.821163 + 1.42230i 0.0836541 + 0.996495i \(0.473341\pi\)
−0.904817 + 0.425801i \(0.859992\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −278067. 160542.i −0.759695 0.438610i
\(606\) 0 0
\(607\) −220510. 381935.i −0.598482 1.03660i −0.993045 0.117733i \(-0.962437\pi\)
0.394563 0.918869i \(-0.370896\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 593817.i 1.59063i
\(612\) 0 0
\(613\) −397447. −1.05769 −0.528845 0.848718i \(-0.677375\pi\)
−0.528845 + 0.848718i \(0.677375\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1401.15 808.953i 0.00368056 0.00212497i −0.498159 0.867086i \(-0.665990\pi\)
0.501839 + 0.864961i \(0.332657\pi\)
\(618\) 0 0
\(619\) −274485. + 475422.i −0.716370 + 1.24079i 0.246059 + 0.969255i \(0.420864\pi\)
−0.962429 + 0.271535i \(0.912469\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 107914. + 62304.1i 0.278036 + 0.160524i
\(624\) 0 0
\(625\) 10290.7 + 17824.0i 0.0263442 + 0.0456294i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 22828.7i 0.0577005i
\(630\) 0 0
\(631\) 378413. 0.950403 0.475202 0.879877i \(-0.342375\pi\)
0.475202 + 0.879877i \(0.342375\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 342350. 197656.i 0.849030 0.490188i
\(636\) 0 0
\(637\) 303517. 525707.i 0.748004 1.29558i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 62090.7 + 35848.1i 0.151116 + 0.0872469i 0.573651 0.819100i \(-0.305526\pi\)
−0.422535 + 0.906346i \(0.638860\pi\)
\(642\) 0 0
\(643\) −83582.4 144769.i −0.202159 0.350149i 0.747065 0.664751i \(-0.231462\pi\)
−0.949224 + 0.314602i \(0.898129\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 678022.i 1.61970i −0.586635 0.809852i \(-0.699548\pi\)
0.586635 0.809852i \(-0.300452\pi\)
\(648\) 0 0
\(649\) −127192. −0.301974
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 256473. 148075.i 0.601472 0.347260i −0.168149 0.985762i \(-0.553779\pi\)
0.769620 + 0.638502i \(0.220446\pi\)
\(654\) 0 0
\(655\) 12860.6 22275.2i 0.0299763 0.0519204i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −684065. 394945.i −1.57517 0.909423i −0.995520 0.0945561i \(-0.969857\pi\)
−0.579648 0.814867i \(-0.696810\pi\)
\(660\) 0 0
\(661\) 212744. + 368484.i 0.486917 + 0.843365i 0.999887 0.0150418i \(-0.00478812\pi\)
−0.512970 + 0.858407i \(0.671455\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 316964.i 0.716749i
\(666\) 0 0
\(667\) 241167. 0.542083
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −379864. + 219314.i −0.843690 + 0.487104i
\(672\) 0 0
\(673\) 181403. 314199.i 0.400511 0.693705i −0.593277 0.804998i \(-0.702166\pi\)
0.993788 + 0.111294i \(0.0354994\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 747854. + 431774.i 1.63170 + 0.942061i 0.983570 + 0.180528i \(0.0577808\pi\)
0.648127 + 0.761532i \(0.275553\pi\)
\(678\) 0 0
\(679\) 44551.4 + 77165.3i 0.0966322 + 0.167372i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 323967.i 0.694479i −0.937776 0.347239i \(-0.887119\pi\)
0.937776 0.347239i \(-0.112881\pi\)
\(684\) 0 0
\(685\) 1.28869e6 2.74641
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 621248. 358678.i 1.30866 0.755554i
\(690\) 0 0
\(691\) 328629. 569202.i 0.688255 1.19209i −0.284147 0.958781i \(-0.591710\pi\)
0.972402 0.233312i \(-0.0749563\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 194733. + 112429.i 0.403153 + 0.232760i
\(696\) 0 0
\(697\) −8543.45 14797.7i −0.0175860 0.0304599i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 695995.i 1.41635i 0.706038 + 0.708174i \(0.250481\pi\)
−0.706038 + 0.708174i \(0.749519\pi\)
\(702\) 0 0
\(703\) −1.11741e6 −2.26101
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 76546.5 44194.1i 0.153139 0.0884150i
\(708\) 0 0
\(709\) 215242. 372810.i 0.428188 0.741643i −0.568525 0.822666i \(-0.692486\pi\)
0.996712 + 0.0810236i \(0.0258189\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −136961. 79074.7i −0.269413 0.155546i
\(714\) 0 0
\(715\) −457183. 791864.i −0.894289 1.54895i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 435311.i 0.842059i −0.907047 0.421029i \(-0.861669\pi\)
0.907047 0.421029i \(-0.138331\pi\)
\(720\) 0 0
\(721\) −22625.1 −0.0435231
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 256709. 148211.i 0.488388 0.281971i
\(726\) 0 0
\(727\) 3053.98 5289.64i 0.00577826 0.0100082i −0.863122 0.504996i \(-0.831494\pi\)
0.868900 + 0.494988i \(0.164827\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −868.916 501.669i −0.00162608 0.000938820i
\(732\) 0 0
\(733\) 184878. + 320218.i 0.344094 + 0.595989i 0.985189 0.171473i \(-0.0548526\pi\)
−0.641094 + 0.767462i \(0.721519\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 74734.4i 0.137590i
\(738\) 0 0
\(739\) −381087. −0.697807 −0.348904 0.937159i \(-0.613446\pi\)
−0.348904 + 0.937159i \(0.613446\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 370613. 213974.i 0.671341 0.387599i −0.125243 0.992126i \(-0.539971\pi\)
0.796585 + 0.604527i \(0.206638\pi\)
\(744\) 0 0
\(745\) 165496. 286647.i 0.298177 0.516457i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −262283. 151429.i −0.467527 0.269927i
\(750\) 0 0
\(751\) 211790. + 366831.i 0.375514 + 0.650408i 0.990404 0.138204i \(-0.0441330\pi\)
−0.614890 + 0.788613i \(0.710800\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 824333.i 1.44614i
\(756\) 0 0
\(757\) −910525. −1.58891 −0.794457 0.607321i \(-0.792244\pi\)
−0.794457 + 0.607321i \(0.792244\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 612058. 353372.i 1.05687 0.610187i 0.132309 0.991209i \(-0.457761\pi\)
0.924566 + 0.381022i \(0.124428\pi\)
\(762\) 0 0
\(763\) 69467.8 120322.i 0.119326 0.206678i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 375177. + 216609.i 0.637743 + 0.368201i
\(768\) 0 0
\(769\) −247932. 429430.i −0.419256 0.726173i 0.576609 0.817021i \(-0.304376\pi\)
−0.995865 + 0.0908474i \(0.971042\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 834415.i 1.39644i 0.715882 + 0.698221i \(0.246025\pi\)
−0.715882 + 0.698221i \(0.753975\pi\)
\(774\) 0 0
\(775\) −194384. −0.323637
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 724312. 418182.i 1.19358 0.689112i
\(780\) 0 0
\(781\) −335422. + 580968.i −0.549908 + 0.952468i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −899478. 519314.i −1.45966 0.842734i
\(786\) 0 0
\(787\) −64818.1 112268.i −0.104652 0.181262i 0.808944 0.587886i \(-0.200039\pi\)
−0.913596 + 0.406623i \(0.866706\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 44330.0i 0.0708508i
\(792\) 0 0
\(793\) 1.49398e6 2.37573
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 146748. 84725.1i 0.231024 0.133382i −0.380021 0.924978i \(-0.624083\pi\)
0.611044 + 0.791597i \(0.290750\pi\)
\(798\) 0 0
\(799\) −11621.3 + 20128.7i −0.0182038 + 0.0315299i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −243154. 140385.i −0.377094 0.217716i