Properties

Label 1840.2.e.d.369.5
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.527896576.2
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} + 7 x^{4} - 10 x^{3} + 8 x^{2} + 4 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 115)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.5
Root \(0.790245 - 0.790245i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.d.369.4

$q$-expansion

\(f(q)\) \(=\) \(q+0.580491i q^{3} +(-0.209755 - 2.22621i) q^{5} +0.315061i q^{7} +2.66303 q^{9} +O(q^{10})\) \(q+0.580491i q^{3} +(-0.209755 - 2.22621i) q^{5} +0.315061i q^{7} +2.66303 q^{9} +4.34797 q^{11} +4.58049i q^{13} +(1.29229 - 0.121761i) q^{15} -0.917461i q^{17} +2.76748 q^{19} -0.182890 q^{21} +1.00000i q^{23} +(-4.91201 + 0.933914i) q^{25} +3.28734i q^{27} -7.03291 q^{29} +0.867829 q^{31} +2.52396i q^{33} +(0.701392 - 0.0660856i) q^{35} -4.68904i q^{37} -2.65893 q^{39} +4.69184 q^{41} -9.08944i q^{43} +(-0.558583 - 5.92846i) q^{45} +8.24762i q^{47} +6.90074 q^{49} +0.532578 q^{51} +10.9048i q^{53} +(-0.912006 - 9.67948i) q^{55} +1.60650i q^{57} +1.50205 q^{59} +11.4634 q^{61} +0.839018i q^{63} +(10.1971 - 0.960779i) q^{65} -1.68494i q^{67} -0.580491 q^{69} +5.36578 q^{71} -10.1484i q^{73} +(-0.542129 - 2.85138i) q^{75} +1.36988i q^{77} +7.39760 q^{79} +6.08082 q^{81} +15.3052i q^{83} +(-2.04246 + 0.192442i) q^{85} -4.08254i q^{87} +10.9326 q^{89} -1.44314 q^{91} +0.503767i q^{93} +(-0.580491 - 6.16098i) q^{95} -14.2158i q^{97} +11.5788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 6q^{5} - 8q^{9} + O(q^{10}) \) \( 8q - 6q^{5} - 8q^{9} - 4q^{11} - 6q^{15} - 8q^{19} - 4q^{21} - 16q^{25} - 8q^{29} - 28q^{35} - 16q^{39} - 16q^{41} + 24q^{45} - 20q^{51} + 16q^{55} - 16q^{61} - 14q^{65} + 4q^{69} + 48q^{71} + 48q^{79} + 16q^{81} + 12q^{85} + 16q^{89} - 52q^{91} + 4q^{95} + 72q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 0.580491i 0.335147i 0.985860 + 0.167573i \(0.0535931\pi\)
−0.985860 + 0.167573i \(0.946407\pi\)
\(4\) 0 0
\(5\) −0.209755 2.22621i −0.0938051 0.995591i
\(6\) 0 0
\(7\) 0.315061i 0.119082i 0.998226 + 0.0595410i \(0.0189637\pi\)
−0.998226 + 0.0595410i \(0.981036\pi\)
\(8\) 0 0
\(9\) 2.66303 0.887677
\(10\) 0 0
\(11\) 4.34797 1.31096 0.655481 0.755212i \(-0.272466\pi\)
0.655481 + 0.755212i \(0.272466\pi\)
\(12\) 0 0
\(13\) 4.58049i 1.27040i 0.772348 + 0.635200i \(0.219082\pi\)
−0.772348 + 0.635200i \(0.780918\pi\)
\(14\) 0 0
\(15\) 1.29229 0.121761i 0.333669 0.0314385i
\(16\) 0 0
\(17\) 0.917461i 0.222517i −0.993792 0.111258i \(-0.964512\pi\)
0.993792 0.111258i \(-0.0354881\pi\)
\(18\) 0 0
\(19\) 2.76748 0.634903 0.317451 0.948275i \(-0.397173\pi\)
0.317451 + 0.948275i \(0.397173\pi\)
\(20\) 0 0
\(21\) −0.182890 −0.0399099
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −4.91201 + 0.933914i −0.982401 + 0.186783i
\(26\) 0 0
\(27\) 3.28734i 0.632648i
\(28\) 0 0
\(29\) −7.03291 −1.30598 −0.652989 0.757367i \(-0.726485\pi\)
−0.652989 + 0.757367i \(0.726485\pi\)
\(30\) 0 0
\(31\) 0.867829 0.155867 0.0779333 0.996959i \(-0.475168\pi\)
0.0779333 + 0.996959i \(0.475168\pi\)
\(32\) 0 0
\(33\) 2.52396i 0.439364i
\(34\) 0 0
\(35\) 0.701392 0.0660856i 0.118557 0.0111705i
\(36\) 0 0
\(37\) 4.68904i 0.770873i −0.922734 0.385436i \(-0.874051\pi\)
0.922734 0.385436i \(-0.125949\pi\)
\(38\) 0 0
\(39\) −2.65893 −0.425770
\(40\) 0 0
\(41\) 4.69184 0.732742 0.366371 0.930469i \(-0.380600\pi\)
0.366371 + 0.930469i \(0.380600\pi\)
\(42\) 0 0
\(43\) 9.08944i 1.38613i −0.720877 0.693063i \(-0.756261\pi\)
0.720877 0.693063i \(-0.243739\pi\)
\(44\) 0 0
\(45\) −0.558583 5.92846i −0.0832686 0.883763i
\(46\) 0 0
\(47\) 8.24762i 1.20304i 0.798858 + 0.601519i \(0.205438\pi\)
−0.798858 + 0.601519i \(0.794562\pi\)
\(48\) 0 0
\(49\) 6.90074 0.985819
\(50\) 0 0
\(51\) 0.532578 0.0745758
\(52\) 0 0
\(53\) 10.9048i 1.49789i 0.662630 + 0.748947i \(0.269440\pi\)
−0.662630 + 0.748947i \(0.730560\pi\)
\(54\) 0 0
\(55\) −0.912006 9.67948i −0.122975 1.30518i
\(56\) 0 0
\(57\) 1.60650i 0.212786i
\(58\) 0 0
\(59\) 1.50205 0.195550 0.0977750 0.995209i \(-0.468827\pi\)
0.0977750 + 0.995209i \(0.468827\pi\)
\(60\) 0 0
\(61\) 11.4634 1.46774 0.733870 0.679290i \(-0.237712\pi\)
0.733870 + 0.679290i \(0.237712\pi\)
\(62\) 0 0
\(63\) 0.839018i 0.105706i
\(64\) 0 0
\(65\) 10.1971 0.960779i 1.26480 0.119170i
\(66\) 0 0
\(67\) 1.68494i 0.205848i −0.994689 0.102924i \(-0.967180\pi\)
0.994689 0.102924i \(-0.0328198\pi\)
\(68\) 0 0
\(69\) −0.580491 −0.0698829
\(70\) 0 0
\(71\) 5.36578 0.636801 0.318401 0.947956i \(-0.396854\pi\)
0.318401 + 0.947956i \(0.396854\pi\)
\(72\) 0 0
\(73\) 10.1484i 1.18778i −0.804548 0.593888i \(-0.797592\pi\)
0.804548 0.593888i \(-0.202408\pi\)
\(74\) 0 0
\(75\) −0.542129 2.85138i −0.0625997 0.329248i
\(76\) 0 0
\(77\) 1.36988i 0.156112i
\(78\) 0 0
\(79\) 7.39760 0.832295 0.416148 0.909297i \(-0.363380\pi\)
0.416148 + 0.909297i \(0.363380\pi\)
\(80\) 0 0
\(81\) 6.08082 0.675647
\(82\) 0 0
\(83\) 15.3052i 1.67997i 0.542611 + 0.839984i \(0.317436\pi\)
−0.542611 + 0.839984i \(0.682564\pi\)
\(84\) 0 0
\(85\) −2.04246 + 0.192442i −0.221536 + 0.0208732i
\(86\) 0 0
\(87\) 4.08254i 0.437694i
\(88\) 0 0
\(89\) 10.9326 1.15885 0.579424 0.815026i \(-0.303277\pi\)
0.579424 + 0.815026i \(0.303277\pi\)
\(90\) 0 0
\(91\) −1.44314 −0.151282
\(92\) 0 0
\(93\) 0.503767i 0.0522382i
\(94\) 0 0
\(95\) −0.580491 6.16098i −0.0595571 0.632103i
\(96\) 0 0
\(97\) 14.2158i 1.44340i −0.692208 0.721698i \(-0.743362\pi\)
0.692208 0.721698i \(-0.256638\pi\)
\(98\) 0 0
\(99\) 11.5788 1.16371
\(100\) 0 0
\(101\) −8.16508 −0.812456 −0.406228 0.913772i \(-0.633156\pi\)
−0.406228 + 0.913772i \(0.633156\pi\)
\(102\) 0 0
\(103\) 0.287338i 0.0283122i −0.999900 0.0141561i \(-0.995494\pi\)
0.999900 0.0141561i \(-0.00450618\pi\)
\(104\) 0 0
\(105\) 0.0383621 + 0.407152i 0.00374375 + 0.0397340i
\(106\) 0 0
\(107\) 14.0935i 1.36247i −0.732063 0.681237i \(-0.761442\pi\)
0.732063 0.681237i \(-0.238558\pi\)
\(108\) 0 0
\(109\) −1.76338 −0.168901 −0.0844506 0.996428i \(-0.526914\pi\)
−0.0844506 + 0.996428i \(0.526914\pi\)
\(110\) 0 0
\(111\) 2.72194 0.258355
\(112\) 0 0
\(113\) 0.315061i 0.0296385i −0.999890 0.0148192i \(-0.995283\pi\)
0.999890 0.0148192i \(-0.00471728\pi\)
\(114\) 0 0
\(115\) 2.22621 0.209755i 0.207595 0.0195597i
\(116\) 0 0
\(117\) 12.1980i 1.12770i
\(118\) 0 0
\(119\) 0.289056 0.0264978
\(120\) 0 0
\(121\) 7.90483 0.718621
\(122\) 0 0
\(123\) 2.72357i 0.245576i
\(124\) 0 0
\(125\) 3.10940 + 10.7393i 0.278114 + 0.960548i
\(126\) 0 0
\(127\) 21.3284i 1.89259i 0.323300 + 0.946296i \(0.395208\pi\)
−0.323300 + 0.946296i \(0.604792\pi\)
\(128\) 0 0
\(129\) 5.27634 0.464556
\(130\) 0 0
\(131\) −8.11373 −0.708900 −0.354450 0.935075i \(-0.615332\pi\)
−0.354450 + 0.935075i \(0.615332\pi\)
\(132\) 0 0
\(133\) 0.871925i 0.0756055i
\(134\) 0 0
\(135\) 7.31830 0.689534i 0.629859 0.0593456i
\(136\) 0 0
\(137\) 7.22680i 0.617427i −0.951155 0.308713i \(-0.900102\pi\)
0.951155 0.308713i \(-0.0998984\pi\)
\(138\) 0 0
\(139\) −10.8431 −0.919701 −0.459850 0.887996i \(-0.652097\pi\)
−0.459850 + 0.887996i \(0.652097\pi\)
\(140\) 0 0
\(141\) −4.78767 −0.403194
\(142\) 0 0
\(143\) 19.9158i 1.66545i
\(144\) 0 0
\(145\) 1.47518 + 15.6567i 0.122507 + 1.30022i
\(146\) 0 0
\(147\) 4.00582i 0.330394i
\(148\) 0 0
\(149\) 7.90074 0.647254 0.323627 0.946185i \(-0.395098\pi\)
0.323627 + 0.946185i \(0.395098\pi\)
\(150\) 0 0
\(151\) 8.03700 0.654042 0.327021 0.945017i \(-0.393955\pi\)
0.327021 + 0.945017i \(0.393955\pi\)
\(152\) 0 0
\(153\) 2.44323i 0.197523i
\(154\) 0 0
\(155\) −0.182031 1.93197i −0.0146211 0.155179i
\(156\) 0 0
\(157\) 4.75928i 0.379832i −0.981800 0.189916i \(-0.939178\pi\)
0.981800 0.189916i \(-0.0608216\pi\)
\(158\) 0 0
\(159\) −6.33016 −0.502014
\(160\) 0 0
\(161\) −0.315061 −0.0248303
\(162\) 0 0
\(163\) 2.11545i 0.165695i −0.996562 0.0828473i \(-0.973599\pi\)
0.996562 0.0828473i \(-0.0264014\pi\)
\(164\) 0 0
\(165\) 5.61885 0.529411i 0.437427 0.0412146i
\(166\) 0 0
\(167\) 15.8760i 1.22852i −0.789102 0.614262i \(-0.789454\pi\)
0.789102 0.614262i \(-0.210546\pi\)
\(168\) 0 0
\(169\) −7.98090 −0.613915
\(170\) 0 0
\(171\) 7.36988 0.563589
\(172\) 0 0
\(173\) 0.0767241i 0.00583323i −0.999996 0.00291661i \(-0.999072\pi\)
0.999996 0.00291661i \(-0.000928388\pi\)
\(174\) 0 0
\(175\) −0.294240 1.54758i −0.0222425 0.116986i
\(176\) 0 0
\(177\) 0.871925i 0.0655379i
\(178\) 0 0
\(179\) −20.7247 −1.54904 −0.774520 0.632549i \(-0.782009\pi\)
−0.774520 + 0.632549i \(0.782009\pi\)
\(180\) 0 0
\(181\) −11.5610 −0.859319 −0.429660 0.902991i \(-0.641366\pi\)
−0.429660 + 0.902991i \(0.641366\pi\)
\(182\) 0 0
\(183\) 6.65441i 0.491908i
\(184\) 0 0
\(185\) −10.4388 + 0.983546i −0.767474 + 0.0723118i
\(186\) 0 0
\(187\) 3.98909i 0.291711i
\(188\) 0 0
\(189\) −1.03571 −0.0753371
\(190\) 0 0
\(191\) −21.9683 −1.58957 −0.794784 0.606892i \(-0.792416\pi\)
−0.794784 + 0.606892i \(0.792416\pi\)
\(192\) 0 0
\(193\) 20.2914i 1.46061i 0.683122 + 0.730305i \(0.260622\pi\)
−0.683122 + 0.730305i \(0.739378\pi\)
\(194\) 0 0
\(195\) 0.557723 + 5.91934i 0.0399394 + 0.423893i
\(196\) 0 0
\(197\) 8.62159i 0.614263i −0.951667 0.307131i \(-0.900631\pi\)
0.951667 0.307131i \(-0.0993691\pi\)
\(198\) 0 0
\(199\) 20.7796 1.47302 0.736512 0.676424i \(-0.236471\pi\)
0.736512 + 0.676424i \(0.236471\pi\)
\(200\) 0 0
\(201\) 0.978092 0.0689893
\(202\) 0 0
\(203\) 2.21580i 0.155519i
\(204\) 0 0
\(205\) −0.984135 10.4450i −0.0687350 0.729512i
\(206\) 0 0
\(207\) 2.66303i 0.185093i
\(208\) 0 0
\(209\) 12.0329 0.832334
\(210\) 0 0
\(211\) 4.16508 0.286736 0.143368 0.989669i \(-0.454207\pi\)
0.143368 + 0.989669i \(0.454207\pi\)
\(212\) 0 0
\(213\) 3.11479i 0.213422i
\(214\) 0 0
\(215\) −20.2350 + 1.90655i −1.38001 + 0.130026i
\(216\) 0 0
\(217\) 0.273419i 0.0185609i
\(218\) 0 0
\(219\) 5.89103 0.398079
\(220\) 0 0
\(221\) 4.20242 0.282685
\(222\) 0 0
\(223\) 18.7618i 1.25638i −0.778060 0.628190i \(-0.783796\pi\)
0.778060 0.628190i \(-0.216204\pi\)
\(224\) 0 0
\(225\) −13.0808 + 2.48704i −0.872055 + 0.165803i
\(226\) 0 0
\(227\) 10.9637i 0.727689i −0.931460 0.363845i \(-0.881464\pi\)
0.931460 0.363845i \(-0.118536\pi\)
\(228\) 0 0
\(229\) −25.9367 −1.71394 −0.856971 0.515364i \(-0.827657\pi\)
−0.856971 + 0.515364i \(0.827657\pi\)
\(230\) 0 0
\(231\) −0.795201 −0.0523204
\(232\) 0 0
\(233\) 8.23942i 0.539783i 0.962891 + 0.269891i \(0.0869878\pi\)
−0.962891 + 0.269891i \(0.913012\pi\)
\(234\) 0 0
\(235\) 18.3609 1.72998i 1.19773 0.112851i
\(236\) 0 0
\(237\) 4.29424i 0.278941i
\(238\) 0 0
\(239\) 16.0508 1.03824 0.519120 0.854701i \(-0.326260\pi\)
0.519120 + 0.854701i \(0.326260\pi\)
\(240\) 0 0
\(241\) −2.09755 −0.135115 −0.0675574 0.997715i \(-0.521521\pi\)
−0.0675574 + 0.997715i \(0.521521\pi\)
\(242\) 0 0
\(243\) 13.3919i 0.859089i
\(244\) 0 0
\(245\) −1.44746 15.3625i −0.0924749 0.981473i
\(246\) 0 0
\(247\) 12.6764i 0.806580i
\(248\) 0 0
\(249\) −8.88455 −0.563036
\(250\) 0 0
\(251\) 13.7018 0.864847 0.432423 0.901671i \(-0.357659\pi\)
0.432423 + 0.901671i \(0.357659\pi\)
\(252\) 0 0
\(253\) 4.34797i 0.273354i
\(254\) 0 0
\(255\) −0.111711 1.18563i −0.00699559 0.0742470i
\(256\) 0 0
\(257\) 0.998281i 0.0622711i 0.999515 + 0.0311355i \(0.00991235\pi\)
−0.999515 + 0.0311355i \(0.990088\pi\)
\(258\) 0 0
\(259\) 1.47733 0.0917971
\(260\) 0 0
\(261\) −18.7288 −1.15929
\(262\) 0 0
\(263\) 9.18527i 0.566388i −0.959063 0.283194i \(-0.908606\pi\)
0.959063 0.283194i \(-0.0913940\pi\)
\(264\) 0 0
\(265\) 24.2764 2.28734i 1.49129 0.140510i
\(266\) 0 0
\(267\) 6.34625i 0.388384i
\(268\) 0 0
\(269\) −21.4398 −1.30721 −0.653603 0.756837i \(-0.726744\pi\)
−0.653603 + 0.756837i \(0.726744\pi\)
\(270\) 0 0
\(271\) 25.2488 1.53376 0.766878 0.641793i \(-0.221809\pi\)
0.766878 + 0.641793i \(0.221809\pi\)
\(272\) 0 0
\(273\) 0.837727i 0.0507016i
\(274\) 0 0
\(275\) −21.3572 + 4.06063i −1.28789 + 0.244865i
\(276\) 0 0
\(277\) 30.8114i 1.85128i −0.378409 0.925638i \(-0.623529\pi\)
0.378409 0.925638i \(-0.376471\pi\)
\(278\) 0 0
\(279\) 2.31105 0.138359
\(280\) 0 0
\(281\) 3.60821 0.215248 0.107624 0.994192i \(-0.465676\pi\)
0.107624 + 0.994192i \(0.465676\pi\)
\(282\) 0 0
\(283\) 5.23942i 0.311451i 0.987800 + 0.155726i \(0.0497716\pi\)
−0.987800 + 0.155726i \(0.950228\pi\)
\(284\) 0 0
\(285\) 3.57639 0.336970i 0.211847 0.0199604i
\(286\) 0 0
\(287\) 1.47822i 0.0872565i
\(288\) 0 0
\(289\) 16.1583 0.950486
\(290\) 0 0
\(291\) 8.25214 0.483749
\(292\) 0 0
\(293\) 1.90074i 0.111042i 0.998458 + 0.0555211i \(0.0176820\pi\)
−0.998458 + 0.0555211i \(0.982318\pi\)
\(294\) 0 0
\(295\) −0.315061 3.34387i −0.0183436 0.194688i
\(296\) 0 0
\(297\) 14.2932i 0.829378i
\(298\) 0 0
\(299\) −4.58049 −0.264897
\(300\) 0 0
\(301\) 2.86373 0.165063
\(302\) 0 0
\(303\) 4.73975i 0.272292i
\(304\) 0 0
\(305\) −2.40450 25.5199i −0.137681 1.46127i
\(306\) 0 0
\(307\) 2.82467i 0.161213i 0.996746 + 0.0806063i \(0.0256856\pi\)
−0.996746 + 0.0806063i \(0.974314\pi\)
\(308\) 0 0
\(309\) 0.166797 0.00948875
\(310\) 0 0
\(311\) −16.1028 −0.913107 −0.456554 0.889696i \(-0.650916\pi\)
−0.456554 + 0.889696i \(0.650916\pi\)
\(312\) 0 0
\(313\) 26.3740i 1.49075i 0.666648 + 0.745373i \(0.267728\pi\)
−0.666648 + 0.745373i \(0.732272\pi\)
\(314\) 0 0
\(315\) 1.86783 0.175988i 0.105240 0.00991579i
\(316\) 0 0
\(317\) 15.5020i 0.870682i 0.900266 + 0.435341i \(0.143372\pi\)
−0.900266 + 0.435341i \(0.856628\pi\)
\(318\) 0 0
\(319\) −30.5789 −1.71209
\(320\) 0 0
\(321\) 8.18117 0.456628
\(322\) 0 0
\(323\) 2.53905i 0.141277i
\(324\) 0 0
\(325\) −4.27779 22.4994i −0.237289 1.24804i
\(326\) 0 0
\(327\) 1.02363i 0.0566067i
\(328\) 0 0
\(329\) −2.59851 −0.143260
\(330\) 0 0
\(331\) −19.0302 −1.04599 −0.522997 0.852335i \(-0.675186\pi\)
−0.522997 + 0.852335i \(0.675186\pi\)
\(332\) 0 0
\(333\) 12.4870i 0.684286i
\(334\) 0 0
\(335\) −3.75102 + 0.353423i −0.204940 + 0.0193096i
\(336\) 0 0
\(337\) 4.09354i 0.222989i 0.993765 + 0.111495i \(0.0355638\pi\)
−0.993765 + 0.111495i \(0.964436\pi\)
\(338\) 0 0
\(339\) 0.182890 0.00993324
\(340\) 0 0
\(341\) 3.77329 0.204335
\(342\) 0 0
\(343\) 4.37959i 0.236475i
\(344\) 0 0
\(345\) 0.121761 + 1.29229i 0.00655537 + 0.0695748i
\(346\) 0 0
\(347\) 17.4357i 0.935997i −0.883729 0.467998i \(-0.844975\pi\)
0.883729 0.467998i \(-0.155025\pi\)
\(348\) 0 0
\(349\) −8.48770 −0.454336 −0.227168 0.973856i \(-0.572947\pi\)
−0.227168 + 0.973856i \(0.572947\pi\)
\(350\) 0 0
\(351\) −15.0576 −0.803716
\(352\) 0 0
\(353\) 20.5696i 1.09481i 0.836868 + 0.547404i \(0.184384\pi\)
−0.836868 + 0.547404i \(0.815616\pi\)
\(354\) 0 0
\(355\) −1.12550 11.9453i −0.0597352 0.633993i
\(356\) 0 0
\(357\) 0.167795i 0.00888064i
\(358\) 0 0
\(359\) −22.4121 −1.18286 −0.591432 0.806355i \(-0.701437\pi\)
−0.591432 + 0.806355i \(0.701437\pi\)
\(360\) 0 0
\(361\) −11.3411 −0.596898
\(362\) 0 0
\(363\) 4.58868i 0.240843i
\(364\) 0 0
\(365\) −22.5923 + 2.12866i −1.18254 + 0.111419i
\(366\) 0 0
\(367\) 21.9401i 1.14526i −0.819812 0.572632i \(-0.805922\pi\)
0.819812 0.572632i \(-0.194078\pi\)
\(368\) 0 0
\(369\) 12.4945 0.650438
\(370\) 0 0
\(371\) −3.43569 −0.178372
\(372\) 0 0
\(373\) 0.853821i 0.0442092i 0.999756 + 0.0221046i \(0.00703668\pi\)
−0.999756 + 0.0221046i \(0.992963\pi\)
\(374\) 0 0
\(375\) −6.23404 + 1.80498i −0.321924 + 0.0932088i
\(376\) 0 0
\(377\) 32.2142i 1.65911i
\(378\) 0 0
\(379\) −2.52049 −0.129469 −0.0647345 0.997903i \(-0.520620\pi\)
−0.0647345 + 0.997903i \(0.520620\pi\)
\(380\) 0 0
\(381\) −12.3810 −0.634296
\(382\) 0 0
\(383\) 13.5983i 0.694841i 0.937709 + 0.347420i \(0.112942\pi\)
−0.937709 + 0.347420i \(0.887058\pi\)
\(384\) 0 0
\(385\) 3.04963 0.287338i 0.155424 0.0146441i
\(386\) 0 0
\(387\) 24.2055i 1.23043i
\(388\) 0 0
\(389\) −10.7398 −0.544527 −0.272264 0.962223i \(-0.587772\pi\)
−0.272264 + 0.962223i \(0.587772\pi\)
\(390\) 0 0
\(391\) 0.917461 0.0463980
\(392\) 0 0
\(393\) 4.70995i 0.237585i
\(394\) 0 0
\(395\) −1.55168 16.4686i −0.0780735 0.828625i
\(396\) 0 0
\(397\) 19.5868i 0.983031i −0.870869 0.491516i \(-0.836443\pi\)
0.870869 0.491516i \(-0.163557\pi\)
\(398\) 0 0
\(399\) −0.506145 −0.0253389
\(400\) 0 0
\(401\) −8.01209 −0.400105 −0.200052 0.979785i \(-0.564111\pi\)
−0.200052 + 0.979785i \(0.564111\pi\)
\(402\) 0 0
\(403\) 3.97508i 0.198013i
\(404\) 0 0
\(405\) −1.27548 13.5372i −0.0633791 0.672668i
\(406\) 0 0
\(407\) 20.3878i 1.01058i
\(408\) 0 0
\(409\) 28.2350 1.39613 0.698065 0.716034i \(-0.254045\pi\)
0.698065 + 0.716034i \(0.254045\pi\)
\(410\) 0 0
\(411\) 4.19509 0.206929
\(412\) 0 0
\(413\) 0.473237i 0.0232865i
\(414\) 0 0
\(415\) 34.0726 3.21034i 1.67256 0.157590i
\(416\) 0 0
\(417\) 6.29433i 0.308235i
\(418\) 0 0
\(419\) −21.9470 −1.07218 −0.536091 0.844160i \(-0.680100\pi\)
−0.536091 + 0.844160i \(0.680100\pi\)
\(420\) 0 0
\(421\) 0.747198 0.0364162 0.0182081 0.999834i \(-0.494204\pi\)
0.0182081 + 0.999834i \(0.494204\pi\)
\(422\) 0 0
\(423\) 21.9637i 1.06791i
\(424\) 0 0
\(425\) 0.856830 + 4.50657i 0.0415624 + 0.218601i
\(426\) 0 0
\(427\) 3.61168i 0.174781i
\(428\) 0 0
\(429\) −11.5610 −0.558168
\(430\) 0 0
\(431\) −27.3642 −1.31808 −0.659042 0.752106i \(-0.729038\pi\)
−0.659042 + 0.752106i \(0.729038\pi\)
\(432\) 0 0
\(433\) 25.4265i 1.22192i 0.791662 + 0.610960i \(0.209216\pi\)
−0.791662 + 0.610960i \(0.790784\pi\)
\(434\) 0 0
\(435\) −9.08858 + 0.856331i −0.435764 + 0.0410579i
\(436\) 0 0
\(437\) 2.76748i 0.132386i
\(438\) 0 0
\(439\) −30.8097 −1.47047 −0.735233 0.677815i \(-0.762927\pi\)
−0.735233 + 0.677815i \(0.762927\pi\)
\(440\) 0 0
\(441\) 18.3769 0.875089
\(442\) 0 0
\(443\) 24.5778i 1.16773i 0.811852 + 0.583863i \(0.198459\pi\)
−0.811852 + 0.583863i \(0.801541\pi\)
\(444\) 0 0
\(445\) −2.29315 24.3381i −0.108706 1.15374i
\(446\) 0 0
\(447\) 4.58631i 0.216925i
\(448\) 0 0
\(449\) −38.6816 −1.82550 −0.912749 0.408522i \(-0.866044\pi\)
−0.912749 + 0.408522i \(0.866044\pi\)
\(450\) 0 0
\(451\) 20.4000 0.960597
\(452\) 0 0
\(453\) 4.66541i 0.219200i
\(454\) 0 0
\(455\) 0.302704 + 3.21272i 0.0141910 + 0.150615i
\(456\) 0 0
\(457\) 6.40041i 0.299398i 0.988732 + 0.149699i \(0.0478305\pi\)
−0.988732 + 0.149699i \(0.952169\pi\)
\(458\) 0 0
\(459\) 3.01600 0.140775
\(460\) 0 0
\(461\) −23.8337 −1.11005 −0.555024 0.831835i \(-0.687291\pi\)
−0.555024 + 0.831835i \(0.687291\pi\)
\(462\) 0 0
\(463\) 26.5529i 1.23402i 0.786957 + 0.617008i \(0.211655\pi\)
−0.786957 + 0.617008i \(0.788345\pi\)
\(464\) 0 0
\(465\) 1.12149 0.105667i 0.0520078 0.00490021i
\(466\) 0 0
\(467\) 18.6049i 0.860931i 0.902607 + 0.430465i \(0.141651\pi\)
−0.902607 + 0.430465i \(0.858349\pi\)
\(468\) 0 0
\(469\) 0.530859 0.0245128
\(470\) 0 0
\(471\) 2.76272 0.127300
\(472\) 0 0
\(473\) 39.5206i 1.81716i
\(474\) 0 0
\(475\) −13.5939 + 2.58459i −0.623729 + 0.118589i
\(476\) 0 0
\(477\) 29.0399i 1.32965i
\(478\) 0 0
\(479\) 29.9627 1.36903 0.684514 0.728999i \(-0.260014\pi\)
0.684514 + 0.728999i \(0.260014\pi\)
\(480\) 0 0
\(481\) 21.4781 0.979316
\(482\) 0 0
\(483\) 0.182890i 0.00832180i
\(484\) 0 0
\(485\) −31.6473 + 2.98183i −1.43703 + 0.135398i
\(486\) 0 0
\(487\) 37.2265i 1.68689i −0.537214 0.843446i \(-0.680523\pi\)
0.537214 0.843446i \(-0.319477\pi\)
\(488\) 0 0
\(489\) 1.22800 0.0555320
\(490\) 0 0
\(491\) 0.691841 0.0312224 0.0156112 0.999878i \(-0.495031\pi\)
0.0156112 + 0.999878i \(0.495031\pi\)
\(492\) 0 0
\(493\) 6.45242i 0.290602i
\(494\) 0 0
\(495\) −2.42870 25.7768i −0.109162 1.15858i
\(496\) 0 0
\(497\) 1.69055i 0.0758315i
\(498\) 0 0
\(499\) −24.7988 −1.11014 −0.555072 0.831802i \(-0.687309\pi\)
−0.555072 + 0.831802i \(0.687309\pi\)
\(500\) 0 0
\(501\) 9.21589 0.411735
\(502\) 0 0
\(503\) 22.6049i 1.00790i −0.863732 0.503951i \(-0.831879\pi\)
0.863732 0.503951i \(-0.168121\pi\)
\(504\) 0 0
\(505\) 1.71266 + 18.1772i 0.0762125 + 0.808873i
\(506\) 0 0
\(507\) 4.63284i 0.205752i
\(508\) 0 0
\(509\) 19.1240 0.847655 0.423828 0.905743i \(-0.360686\pi\)
0.423828 + 0.905743i \(0.360686\pi\)
\(510\) 0 0
\(511\) 3.19735 0.141443
\(512\) 0 0
\(513\) 9.09763i 0.401670i
\(514\) 0 0
\(515\) −0.639674 + 0.0602704i −0.0281874 + 0.00265583i
\(516\) 0 0
\(517\) 35.8604i 1.57714i
\(518\) 0 0
\(519\) 0.0445377 0.00195499
\(520\) 0 0
\(521\) 12.8425 0.562638 0.281319 0.959614i \(-0.409228\pi\)
0.281319 + 0.959614i \(0.409228\pi\)
\(522\) 0 0
\(523\) 32.8289i 1.43551i 0.696298 + 0.717753i \(0.254829\pi\)
−0.696298 + 0.717753i \(0.745171\pi\)
\(524\) 0 0
\(525\) 0.898358 0.170804i 0.0392076 0.00745449i
\(526\) 0 0
\(527\) 0.796199i 0.0346830i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) 21.4909i 0.930876i
\(534\) 0 0
\(535\) −31.3752 + 2.95618i −1.35647 + 0.127807i
\(536\) 0 0
\(537\) 12.0305i 0.519156i
\(538\) 0 0
\(539\) 30.0042 1.29237
\(540\) 0 0
\(541\) −25.7261 −1.10605 −0.553026 0.833164i \(-0.686527\pi\)
−0.553026 + 0.833164i \(0.686527\pi\)
\(542\) 0 0
\(543\) 6.71103i 0.287998i
\(544\) 0 0
\(545\) 0.369877 + 3.92565i 0.0158438 + 0.168157i
\(546\) 0 0
\(547\) 36.0191i 1.54006i 0.638005 + 0.770032i \(0.279760\pi\)
−0.638005 + 0.770032i \(0.720240\pi\)
\(548\) 0 0
\(549\) 30.5274 1.30288
\(550\) 0 0
\(551\) −19.4634 −0.829169
\(552\) 0 0
\(553\) 2.33070i 0.0991114i
\(554\) 0 0
\(555\) −0.570940 6.05961i −0.0242350 0.257216i
\(556\) 0 0
\(557\) 36.2148i 1.53447i 0.641366 + 0.767235i \(0.278368\pi\)
−0.641366 + 0.767235i \(0.721632\pi\)
\(558\) 0 0
\(559\) 41.6341 1.76094
\(560\) 0 0
\(561\) 2.31563 0.0977660
\(562\) 0 0
\(563\) 23.3308i 0.983277i 0.870799 + 0.491638i \(0.163602\pi\)
−0.870799 + 0.491638i \(0.836398\pi\)
\(564\) 0 0
\(565\) −0.701392 + 0.0660856i −0.0295078 + 0.00278024i
\(566\) 0 0
\(567\) 1.91583i 0.0804574i
\(568\) 0 0
\(569\) −15.6845 −0.657529 −0.328764 0.944412i \(-0.606632\pi\)
−0.328764 + 0.944412i \(0.606632\pi\)
\(570\) 0 0
\(571\) −38.7600 −1.62206 −0.811028 0.585007i \(-0.801092\pi\)
−0.811028 + 0.585007i \(0.801092\pi\)
\(572\) 0 0
\(573\) 12.7524i 0.532738i
\(574\) 0 0
\(575\) −0.933914 4.91201i −0.0389469 0.204845i
\(576\) 0 0
\(577\) 21.5902i 0.898812i −0.893328 0.449406i \(-0.851636\pi\)
0.893328 0.449406i \(-0.148364\pi\)
\(578\) 0 0
\(579\) −11.7790 −0.489518
\(580\) 0 0
\(581\) −4.82209 −0.200054
\(582\) 0 0
\(583\) 47.4139i 1.96368i
\(584\) 0 0
\(585\) 27.1553 2.55858i 1.12273 0.105784i
\(586\) 0 0
\(587\) 24.3902i 1.00669i −0.864086 0.503345i \(-0.832103\pi\)
0.864086 0.503345i \(-0.167897\pi\)
\(588\) 0 0
\(589\) 2.40170 0.0989602
\(590\) 0 0
\(591\) 5.00476 0.205868
\(592\) 0 0
\(593\) 13.9747i 0.573874i 0.957949 + 0.286937i \(0.0926370\pi\)
−0.957949 + 0.286937i \(0.907363\pi\)
\(594\) 0 0
\(595\) −0.0606309 0.643500i −0.00248562 0.0263809i
\(596\) 0 0
\(597\) 12.0623i 0.493679i
\(598\) 0 0
\(599\) −20.9932 −0.857758 −0.428879 0.903362i \(-0.641091\pi\)
−0.428879 + 0.903362i \(0.641091\pi\)
\(600\) 0 0
\(601\) −13.3007 −0.542546 −0.271273 0.962502i \(-0.587445\pi\)
−0.271273 + 0.962502i \(0.587445\pi\)
\(602\) 0 0
\(603\) 4.48704i 0.182726i
\(604\) 0 0
\(605\) −1.65807 17.5978i −0.0674103 0.715452i
\(606\) 0 0
\(607\) 12.3549i 0.501469i 0.968056 + 0.250734i \(0.0806721\pi\)
−0.968056 + 0.250734i \(0.919328\pi\)
\(608\) 0 0
\(609\) 1.28625 0.0521215
\(610\) 0 0
\(611\) −37.7781 −1.52834
\(612\) 0 0
\(613\) 14.6291i 0.590865i 0.955364 + 0.295432i \(0.0954637\pi\)
−0.955364 + 0.295432i \(0.904536\pi\)
\(614\) 0 0
\(615\) 6.06324 0.571281i 0.244493 0.0230363i
\(616\) 0 0
\(617\) 17.3723i 0.699384i 0.936865 + 0.349692i \(0.113714\pi\)
−0.936865 + 0.349692i \(0.886286\pi\)
\(618\) 0 0
\(619\) 40.0049 1.60793 0.803967 0.594674i \(-0.202719\pi\)
0.803967 + 0.594674i \(0.202719\pi\)
\(620\) 0 0
\(621\) −3.28734 −0.131916
\(622\) 0 0
\(623\) 3.44443i 0.137998i
\(624\) 0 0
\(625\) 23.2556 9.17479i 0.930224 0.366991i
\(626\) 0 0
\(627\) 6.98499i 0.278954i
\(628\) 0 0
\(629\) −4.30201 −0.171532
\(630\) 0 0
\(631\) −15.7992 −0.628956 −0.314478 0.949265i \(-0.601829\pi\)
−0.314478 + 0.949265i \(0.601829\pi\)
\(632\) 0 0
\(633\) 2.41779i 0.0960985i
\(634\) 0 0
\(635\) 47.4815 4.47374i 1.88425 0.177535i
\(636\) 0 0
\(637\) 31.6088i 1.25238i
\(638\) 0 0
\(639\) 14.2892 0.565273
\(640\) 0 0
\(641\) −37.3861 −1.47666 −0.738332 0.674437i \(-0.764386\pi\)
−0.738332 + 0.674437i \(0.764386\pi\)
\(642\) 0 0
\(643\) 44.1766i 1.74216i −0.491145 0.871078i \(-0.663421\pi\)
0.491145 0.871078i \(-0.336579\pi\)
\(644\) 0 0
\(645\) −1.10674 11.7462i −0.0435777 0.462507i
\(646\) 0 0
\(647\) 4.88521i 0.192058i 0.995379 + 0.0960288i \(0.0306141\pi\)
−0.995379 + 0.0960288i \(0.969386\pi\)
\(648\) 0 0
\(649\) 6.53086 0.256359
\(650\) 0 0
\(651\) −0.158717 −0.00622063
\(652\) 0 0
\(653\) 36.6211i 1.43309i −0.697540 0.716546i \(-0.745722\pi\)
0.697540 0.716546i \(-0.254278\pi\)
\(654\) 0 0
\(655\) 1.70189 + 18.0628i 0.0664984 + 0.705774i
\(656\) 0 0
\(657\) 27.0254i 1.05436i
\(658\) 0 0
\(659\) −10.3388 −0.402743 −0.201371 0.979515i \(-0.564540\pi\)
−0.201371 + 0.979515i \(0.564540\pi\)
\(660\) 0 0
\(661\) 6.46980 0.251646 0.125823 0.992053i \(-0.459843\pi\)
0.125823 + 0.992053i \(0.459843\pi\)
\(662\) 0 0
\(663\) 2.43947i 0.0947411i
\(664\) 0 0
\(665\) 1.94109 0.182890i 0.0752722 0.00709218i
\(666\) 0 0
\(667\) 7.03291i 0.272315i
\(668\) 0 0
\(669\) 10.8910 0.421071
\(670\) 0 0
\(671\) 49.8426 1.92415
\(672\) 0 0
\(673\) 30.1889i 1.16370i −0.813297 0.581849i \(-0.802330\pi\)
0.813297 0.581849i \(-0.197670\pi\)
\(674\) 0 0
\(675\) −3.07009 16.1474i −0.118168 0.621515i
\(676\) 0 0
\(677\) 0.443226i 0.0170345i 0.999964 + 0.00851727i \(0.00271117\pi\)
−0.999964 + 0.00851727i \(0.997289\pi\)
\(678\) 0 0
\(679\) 4.47885 0.171882
\(680\) 0 0
\(681\) 6.36436 0.243883
\(682\) 0 0
\(683\) 25.7553i 0.985498i 0.870171 + 0.492749i \(0.164008\pi\)
−0.870171 + 0.492749i \(0.835992\pi\)
\(684\) 0 0
\(685\) −16.0884 + 1.51585i −0.614704 + 0.0579178i
\(686\) 0 0
\(687\) 15.0560i 0.574422i
\(688\) 0 0
\(689\) −49.9495 −1.90292
\(690\) 0 0
\(691\) −16.1707 −0.615162 −0.307581 0.951522i \(-0.599520\pi\)
−0.307581 + 0.951522i \(0.599520\pi\)
\(692\) 0 0
\(693\) 3.64802i 0.138577i
\(694\) 0 0
\(695\) 2.27439 + 24.1390i 0.0862726 + 0.915646i
\(696\) 0 0
\(697\) 4.30458i 0.163048i
\(698\) 0 0
\(699\) −4.78291 −0.180906
\(700\) 0 0
\(701\) −26.5049 −1.00107 −0.500537 0.865715i \(-0.666864\pi\)
−0.500537 + 0.865715i \(0.666864\pi\)
\(702\) 0 0
\(703\) 12.9768i 0.489429i
\(704\) 0 0
\(705\) 1.00423 + 10.6583i 0.0378217 + 0.401416i
\(706\) 0 0
\(707\) 2.57250i 0.0967489i
\(708\) 0 0
\(709\) −38.6885 −1.45298 −0.726488 0.687179i \(-0.758849\pi\)
−0.726488 + 0.687179i \(0.758849\pi\)
\(710\) 0 0
\(711\) 19.7000 0.738809
\(712\) 0 0
\(713\) 0.867829i 0.0325004i
\(714\) 0 0
\(715\) 44.3368 4.17744i 1.65810 0.156227i
\(716\) 0 0
\(717\) 9.31735i 0.347963i
\(718\) 0 0
\(719\) 43.7242 1.63064 0.815319 0.579012i \(-0.196562\pi\)
0.815319 + 0.579012i \(0.196562\pi\)
\(720\) 0 0
\(721\) 0.0905291 0.00337148
\(722\) 0 0
\(723\) 1.21761i 0.0452833i
\(724\) 0 0
\(725\) 34.5457 6.56813i 1.28299 0.243934i
\(726\) 0 0
\(727\) 37.2280i 1.38071i −0.723471 0.690355i \(-0.757455\pi\)
0.723471 0.690355i \(-0.242545\pi\)
\(728\) 0 0
\(729\) 10.4686 0.387726
\(730\) 0 0
\(731\) −8.33921 −0.308437
\(732\) 0 0
\(733\) 27.9656i 1.03293i −0.856308 0.516466i \(-0.827247\pi\)
0.856308 0.516466i \(-0.172753\pi\)
\(734\) 0 0
\(735\) 8.91778 0.840238i 0.328937 0.0309926i
\(736\) 0 0
\(737\) 7.32606i 0.269859i
\(738\) 0 0
\(739\) −30.4555 −1.12032 −0.560162 0.828383i \(-0.689261\pi\)
−0.560162 + 0.828383i \(0.689261\pi\)
\(740\) 0 0
\(741\) −7.35854 −0.270323
\(742\) 0 0
\(743\) 1.97918i 0.0726090i 0.999341 + 0.0363045i \(0.0115586\pi\)
−0.999341 + 0.0363045i \(0.988441\pi\)
\(744\) 0 0
\(745\) −1.65722 17.5887i −0.0607157 0.644400i
\(746\) 0 0
\(747\) 40.7583i 1.49127i
\(748\) 0 0
\(749\) 4.44033 0.162246
\(750\) 0 0
\(751\) −5.77719 −0.210813 −0.105406 0.994429i \(-0.533614\pi\)
−0.105406 + 0.994429i \(0.533614\pi\)
\(752\) 0 0
\(753\) 7.95374i 0.289851i
\(754\) 0 0
\(755\) −1.68580 17.8920i −0.0613525 0.651158i
\(756\) 0 0
\(757\) 26.9857i 0.980814i −0.871494 0.490407i \(-0.836848\pi\)
0.871494 0.490407i \(-0.163152\pi\)
\(758\) 0 0
\(759\) −2.52396 −0.0916138
\(760\) 0 0
\(761\) 5.95209 0.215763 0.107881 0.994164i \(-0.465593\pi\)
0.107881 + 0.994164i \(0.465593\pi\)
\(762\) 0 0
\(763\) 0.555573i 0.0201131i
\(764\) 0 0
\(765\) −5.43913 + 0.512478i −0.196652 + 0.0185287i
\(766\) 0 0
\(767\) 6.88012i 0.248427i
\(768\) 0 0
\(769\) 29.5669 1.06621 0.533104 0.846050i \(-0.321025\pi\)
0.533104 + 0.846050i \(0.321025\pi\)
\(770\) 0 0
\(771\) −0.579493 −0.0208699
\(772\) 0 0
\(773\) 2.24223i 0.0806474i −0.999187 0.0403237i \(-0.987161\pi\)
0.999187 0.0403237i \(-0.0128389\pi\)
\(774\) 0 0
\(775\) −4.26278 + 0.810478i −0.153124 + 0.0291132i
\(776\) 0 0
\(777\) 0.857579i 0.0307655i
\(778\) 0 0
\(779\) 12.9846 0.465220
\(780\) 0 0
\(781\) 23.3302 0.834822
\(782\) 0 0
\(783\) 23.1195i 0.826225i
\(784\) 0 0
\(785\) −10.5952 + 0.998281i −0.378157 + 0.0356302i
\(786\) 0 0
\(787\) 6.28634i 0.224084i 0.993703 + 0.112042i \(0.0357391\pi\)
−0.993703 + 0.112042i \(0.964261\pi\)
\(788\) 0 0
\(789\) 5.33197 0.189823
\(790\) 0 0
\(791\) 0.0992637 0.00352941
\(792\) 0 0
\(793\) 52.5081i 1.86462i
\(794\) 0 0
\(795\) 1.32778 + 14.0922i 0.0470915 + 0.499801i
\(796\) 0 0
\(797\) 15.5627i 0.551258i −0.961264 0.275629i \(-0.911114\pi\)
0.961264 0.275629i \(-0.0888862\pi\)
\(798\) 0 0
\(799\) 7.56687 0.267696
\(800\) 0 0
\(801\) 29.1137 1.02868
\(802\) 0 0