Properties

Label 4020.2.g.c.1609.35
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.g (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0998616126\)
Analytic rank: \(0\)
Dimension: \(38\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1609.35
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.16

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000i q^{3}\) \(+(1.96624 - 1.06486i) q^{5}\) \(-4.32230i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000i q^{3}\) \(+(1.96624 - 1.06486i) q^{5}\) \(-4.32230i q^{7}\) \(-1.00000 q^{9}\) \(+3.68751 q^{11}\) \(+4.58547i q^{13}\) \(+(1.06486 + 1.96624i) q^{15}\) \(+7.89141i q^{17}\) \(+4.22571 q^{19}\) \(+4.32230 q^{21}\) \(+1.04462i q^{23}\) \(+(2.73216 - 4.18752i) q^{25}\) \(-1.00000i q^{27}\) \(-5.93796 q^{29}\) \(+5.66037 q^{31}\) \(+3.68751i q^{33}\) \(+(-4.60263 - 8.49866i) q^{35}\) \(+11.2388i q^{37}\) \(-4.58547 q^{39}\) \(+1.36096 q^{41}\) \(+6.90749i q^{43}\) \(+(-1.96624 + 1.06486i) q^{45}\) \(+0.227862i q^{47}\) \(-11.6823 q^{49}\) \(-7.89141 q^{51}\) \(-4.37470i q^{53}\) \(+(7.25051 - 3.92667i) q^{55}\) \(+4.22571i q^{57}\) \(+6.83840 q^{59}\) \(+4.41474 q^{61}\) \(+4.32230i q^{63}\) \(+(4.88286 + 9.01611i) q^{65}\) \(+1.00000i q^{67}\) \(-1.04462 q^{69}\) \(-6.97099 q^{71}\) \(-1.49940i q^{73}\) \(+(4.18752 + 2.73216i) q^{75}\) \(-15.9385i q^{77}\) \(-5.16488 q^{79}\) \(+1.00000 q^{81}\) \(+10.3758i q^{83}\) \(+(8.40322 + 15.5164i) q^{85}\) \(-5.93796i q^{87}\) \(+2.71428 q^{89}\) \(+19.8198 q^{91}\) \(+5.66037i q^{93}\) \(+(8.30873 - 4.49977i) q^{95}\) \(-8.15818i q^{97}\) \(-3.68751 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).

\(n\) \(1141\) \(2011\) \(2681\) \(3217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) 1.96624 1.06486i 0.879327 0.476218i
\(6\) 0 0
\(7\) 4.32230i 1.63368i −0.576867 0.816838i \(-0.695725\pi\)
0.576867 0.816838i \(-0.304275\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.68751 1.11183 0.555913 0.831240i \(-0.312369\pi\)
0.555913 + 0.831240i \(0.312369\pi\)
\(12\) 0 0
\(13\) 4.58547i 1.27178i 0.771780 + 0.635890i \(0.219367\pi\)
−0.771780 + 0.635890i \(0.780633\pi\)
\(14\) 0 0
\(15\) 1.06486 + 1.96624i 0.274945 + 0.507680i
\(16\) 0 0
\(17\) 7.89141i 1.91395i 0.290172 + 0.956974i \(0.406287\pi\)
−0.290172 + 0.956974i \(0.593713\pi\)
\(18\) 0 0
\(19\) 4.22571 0.969444 0.484722 0.874668i \(-0.338921\pi\)
0.484722 + 0.874668i \(0.338921\pi\)
\(20\) 0 0
\(21\) 4.32230 0.943203
\(22\) 0 0
\(23\) 1.04462i 0.217818i 0.994052 + 0.108909i \(0.0347357\pi\)
−0.994052 + 0.108909i \(0.965264\pi\)
\(24\) 0 0
\(25\) 2.73216 4.18752i 0.546433 0.837503i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −5.93796 −1.10265 −0.551325 0.834290i \(-0.685878\pi\)
−0.551325 + 0.834290i \(0.685878\pi\)
\(30\) 0 0
\(31\) 5.66037 1.01663 0.508316 0.861170i \(-0.330268\pi\)
0.508316 + 0.861170i \(0.330268\pi\)
\(32\) 0 0
\(33\) 3.68751i 0.641913i
\(34\) 0 0
\(35\) −4.60263 8.49866i −0.777986 1.43654i
\(36\) 0 0
\(37\) 11.2388i 1.84765i 0.382810 + 0.923827i \(0.374956\pi\)
−0.382810 + 0.923827i \(0.625044\pi\)
\(38\) 0 0
\(39\) −4.58547 −0.734262
\(40\) 0 0
\(41\) 1.36096 0.212545 0.106273 0.994337i \(-0.466108\pi\)
0.106273 + 0.994337i \(0.466108\pi\)
\(42\) 0 0
\(43\) 6.90749i 1.05338i 0.850057 + 0.526691i \(0.176567\pi\)
−0.850057 + 0.526691i \(0.823433\pi\)
\(44\) 0 0
\(45\) −1.96624 + 1.06486i −0.293109 + 0.158739i
\(46\) 0 0
\(47\) 0.227862i 0.0332371i 0.999862 + 0.0166185i \(0.00529009\pi\)
−0.999862 + 0.0166185i \(0.994710\pi\)
\(48\) 0 0
\(49\) −11.6823 −1.66890
\(50\) 0 0
\(51\) −7.89141 −1.10502
\(52\) 0 0
\(53\) 4.37470i 0.600911i −0.953796 0.300456i \(-0.902861\pi\)
0.953796 0.300456i \(-0.0971387\pi\)
\(54\) 0 0
\(55\) 7.25051 3.92667i 0.977659 0.529472i
\(56\) 0 0
\(57\) 4.22571i 0.559709i
\(58\) 0 0
\(59\) 6.83840 0.890284 0.445142 0.895460i \(-0.353153\pi\)
0.445142 + 0.895460i \(0.353153\pi\)
\(60\) 0 0
\(61\) 4.41474 0.565249 0.282625 0.959231i \(-0.408795\pi\)
0.282625 + 0.959231i \(0.408795\pi\)
\(62\) 0 0
\(63\) 4.32230i 0.544559i
\(64\) 0 0
\(65\) 4.88286 + 9.01611i 0.605644 + 1.11831i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −1.04462 −0.125757
\(70\) 0 0
\(71\) −6.97099 −0.827304 −0.413652 0.910435i \(-0.635747\pi\)
−0.413652 + 0.910435i \(0.635747\pi\)
\(72\) 0 0
\(73\) 1.49940i 0.175491i −0.996143 0.0877455i \(-0.972034\pi\)
0.996143 0.0877455i \(-0.0279662\pi\)
\(74\) 0 0
\(75\) 4.18752 + 2.73216i 0.483533 + 0.315483i
\(76\) 0 0
\(77\) 15.9385i 1.81636i
\(78\) 0 0
\(79\) −5.16488 −0.581094 −0.290547 0.956861i \(-0.593837\pi\)
−0.290547 + 0.956861i \(0.593837\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 10.3758i 1.13889i 0.822030 + 0.569444i \(0.192842\pi\)
−0.822030 + 0.569444i \(0.807158\pi\)
\(84\) 0 0
\(85\) 8.40322 + 15.5164i 0.911457 + 1.68299i
\(86\) 0 0
\(87\) 5.93796i 0.636616i
\(88\) 0 0
\(89\) 2.71428 0.287713 0.143856 0.989599i \(-0.454050\pi\)
0.143856 + 0.989599i \(0.454050\pi\)
\(90\) 0 0
\(91\) 19.8198 2.07768
\(92\) 0 0
\(93\) 5.66037i 0.586953i
\(94\) 0 0
\(95\) 8.30873 4.49977i 0.852458 0.461667i
\(96\) 0 0
\(97\) 8.15818i 0.828338i −0.910200 0.414169i \(-0.864072\pi\)
0.910200 0.414169i \(-0.135928\pi\)
\(98\) 0 0
\(99\) −3.68751 −0.370609
\(100\) 0 0
\(101\) 2.75538 0.274171 0.137085 0.990559i \(-0.456227\pi\)
0.137085 + 0.990559i \(0.456227\pi\)
\(102\) 0 0
\(103\) 11.5307i 1.13615i 0.822975 + 0.568077i \(0.192312\pi\)
−0.822975 + 0.568077i \(0.807688\pi\)
\(104\) 0 0
\(105\) 8.49866 4.60263i 0.829384 0.449170i
\(106\) 0 0
\(107\) 12.8485i 1.24211i −0.783767 0.621055i \(-0.786704\pi\)
0.783767 0.621055i \(-0.213296\pi\)
\(108\) 0 0
\(109\) 3.68327 0.352793 0.176397 0.984319i \(-0.443556\pi\)
0.176397 + 0.984319i \(0.443556\pi\)
\(110\) 0 0
\(111\) −11.2388 −1.06674
\(112\) 0 0
\(113\) 7.93123i 0.746108i −0.927810 0.373054i \(-0.878311\pi\)
0.927810 0.373054i \(-0.121689\pi\)
\(114\) 0 0
\(115\) 1.11237 + 2.05396i 0.103729 + 0.191533i
\(116\) 0 0
\(117\) 4.58547i 0.423926i
\(118\) 0 0
\(119\) 34.1091 3.12677
\(120\) 0 0
\(121\) 2.59773 0.236157
\(122\) 0 0
\(123\) 1.36096i 0.122713i
\(124\) 0 0
\(125\) 0.912975 11.1430i 0.0816590 0.996660i
\(126\) 0 0
\(127\) 6.32450i 0.561208i −0.959824 0.280604i \(-0.909465\pi\)
0.959824 0.280604i \(-0.0905348\pi\)
\(128\) 0 0
\(129\) −6.90749 −0.608170
\(130\) 0 0
\(131\) 8.81351 0.770040 0.385020 0.922908i \(-0.374195\pi\)
0.385020 + 0.922908i \(0.374195\pi\)
\(132\) 0 0
\(133\) 18.2648i 1.58376i
\(134\) 0 0
\(135\) −1.06486 1.96624i −0.0916482 0.169227i
\(136\) 0 0
\(137\) 8.13167i 0.694735i −0.937729 0.347368i \(-0.887076\pi\)
0.937729 0.347368i \(-0.112924\pi\)
\(138\) 0 0
\(139\) 4.35176 0.369111 0.184556 0.982822i \(-0.440915\pi\)
0.184556 + 0.982822i \(0.440915\pi\)
\(140\) 0 0
\(141\) −0.227862 −0.0191894
\(142\) 0 0
\(143\) 16.9089i 1.41400i
\(144\) 0 0
\(145\) −11.6754 + 6.32307i −0.969591 + 0.525102i
\(146\) 0 0
\(147\) 11.6823i 0.963538i
\(148\) 0 0
\(149\) 5.32537 0.436271 0.218136 0.975918i \(-0.430002\pi\)
0.218136 + 0.975918i \(0.430002\pi\)
\(150\) 0 0
\(151\) 14.9734 1.21852 0.609260 0.792970i \(-0.291466\pi\)
0.609260 + 0.792970i \(0.291466\pi\)
\(152\) 0 0
\(153\) 7.89141i 0.637983i
\(154\) 0 0
\(155\) 11.1296 6.02748i 0.893953 0.484139i
\(156\) 0 0
\(157\) 23.0196i 1.83717i −0.395227 0.918583i \(-0.629334\pi\)
0.395227 0.918583i \(-0.370666\pi\)
\(158\) 0 0
\(159\) 4.37470 0.346936
\(160\) 0 0
\(161\) 4.51515 0.355844
\(162\) 0 0
\(163\) 19.1669i 1.50127i −0.660719 0.750633i \(-0.729749\pi\)
0.660719 0.750633i \(-0.270251\pi\)
\(164\) 0 0
\(165\) 3.92667 + 7.25051i 0.305691 + 0.564452i
\(166\) 0 0
\(167\) 14.7151i 1.13869i −0.822099 0.569345i \(-0.807197\pi\)
0.822099 0.569345i \(-0.192803\pi\)
\(168\) 0 0
\(169\) −8.02650 −0.617423
\(170\) 0 0
\(171\) −4.22571 −0.323148
\(172\) 0 0
\(173\) 14.7906i 1.12451i 0.826965 + 0.562253i \(0.190065\pi\)
−0.826965 + 0.562253i \(0.809935\pi\)
\(174\) 0 0
\(175\) −18.0997 11.8092i −1.36821 0.892694i
\(176\) 0 0
\(177\) 6.83840i 0.514006i
\(178\) 0 0
\(179\) −16.7747 −1.25380 −0.626898 0.779101i \(-0.715676\pi\)
−0.626898 + 0.779101i \(0.715676\pi\)
\(180\) 0 0
\(181\) 18.8727 1.40279 0.701397 0.712771i \(-0.252560\pi\)
0.701397 + 0.712771i \(0.252560\pi\)
\(182\) 0 0
\(183\) 4.41474i 0.326347i
\(184\) 0 0
\(185\) 11.9677 + 22.0982i 0.879886 + 1.62469i
\(186\) 0 0
\(187\) 29.0997i 2.12798i
\(188\) 0 0
\(189\) −4.32230 −0.314401
\(190\) 0 0
\(191\) 4.24583 0.307217 0.153609 0.988132i \(-0.450910\pi\)
0.153609 + 0.988132i \(0.450910\pi\)
\(192\) 0 0
\(193\) 17.8178i 1.28255i −0.767311 0.641275i \(-0.778406\pi\)
0.767311 0.641275i \(-0.221594\pi\)
\(194\) 0 0
\(195\) −9.01611 + 4.88286i −0.645657 + 0.349669i
\(196\) 0 0
\(197\) 7.79528i 0.555391i 0.960669 + 0.277696i \(0.0895706\pi\)
−0.960669 + 0.277696i \(0.910429\pi\)
\(198\) 0 0
\(199\) 1.01866 0.0722111 0.0361055 0.999348i \(-0.488505\pi\)
0.0361055 + 0.999348i \(0.488505\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 25.6656i 1.80137i
\(204\) 0 0
\(205\) 2.67596 1.44922i 0.186897 0.101218i
\(206\) 0 0
\(207\) 1.04462i 0.0726059i
\(208\) 0 0
\(209\) 15.5823 1.07785
\(210\) 0 0
\(211\) 16.9281 1.16538 0.582689 0.812695i \(-0.302001\pi\)
0.582689 + 0.812695i \(0.302001\pi\)
\(212\) 0 0
\(213\) 6.97099i 0.477644i
\(214\) 0 0
\(215\) 7.35548 + 13.5817i 0.501640 + 0.926267i
\(216\) 0 0
\(217\) 24.4658i 1.66085i
\(218\) 0 0
\(219\) 1.49940 0.101320
\(220\) 0 0
\(221\) −36.1858 −2.43412
\(222\) 0 0
\(223\) 19.6720i 1.31733i 0.752435 + 0.658666i \(0.228879\pi\)
−0.752435 + 0.658666i \(0.771121\pi\)
\(224\) 0 0
\(225\) −2.73216 + 4.18752i −0.182144 + 0.279168i
\(226\) 0 0
\(227\) 21.8906i 1.45293i 0.687203 + 0.726466i \(0.258838\pi\)
−0.687203 + 0.726466i \(0.741162\pi\)
\(228\) 0 0
\(229\) −3.28727 −0.217229 −0.108614 0.994084i \(-0.534641\pi\)
−0.108614 + 0.994084i \(0.534641\pi\)
\(230\) 0 0
\(231\) 15.9385 1.04868
\(232\) 0 0
\(233\) 10.4772i 0.686382i 0.939266 + 0.343191i \(0.111508\pi\)
−0.939266 + 0.343191i \(0.888492\pi\)
\(234\) 0 0
\(235\) 0.242640 + 0.448030i 0.0158281 + 0.0292263i
\(236\) 0 0
\(237\) 5.16488i 0.335495i
\(238\) 0 0
\(239\) −19.8748 −1.28559 −0.642796 0.766038i \(-0.722226\pi\)
−0.642796 + 0.766038i \(0.722226\pi\)
\(240\) 0 0
\(241\) −11.2871 −0.727065 −0.363533 0.931581i \(-0.618429\pi\)
−0.363533 + 0.931581i \(0.618429\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −22.9701 + 12.4399i −1.46751 + 0.794759i
\(246\) 0 0
\(247\) 19.3768i 1.23292i
\(248\) 0 0
\(249\) −10.3758 −0.657537
\(250\) 0 0
\(251\) −30.1154 −1.90087 −0.950434 0.310928i \(-0.899360\pi\)
−0.950434 + 0.310928i \(0.899360\pi\)
\(252\) 0 0
\(253\) 3.85204i 0.242175i
\(254\) 0 0
\(255\) −15.5164 + 8.40322i −0.971673 + 0.526230i
\(256\) 0 0
\(257\) 26.5811i 1.65808i 0.559186 + 0.829042i \(0.311114\pi\)
−0.559186 + 0.829042i \(0.688886\pi\)
\(258\) 0 0
\(259\) 48.5776 3.01847
\(260\) 0 0
\(261\) 5.93796 0.367550
\(262\) 0 0
\(263\) 10.5190i 0.648629i 0.945949 + 0.324315i \(0.105134\pi\)
−0.945949 + 0.324315i \(0.894866\pi\)
\(264\) 0 0
\(265\) −4.65843 8.60169i −0.286165 0.528398i
\(266\) 0 0
\(267\) 2.71428i 0.166111i
\(268\) 0 0
\(269\) 0.906058 0.0552433 0.0276217 0.999618i \(-0.491207\pi\)
0.0276217 + 0.999618i \(0.491207\pi\)
\(270\) 0 0
\(271\) 11.0749 0.672750 0.336375 0.941728i \(-0.390799\pi\)
0.336375 + 0.941728i \(0.390799\pi\)
\(272\) 0 0
\(273\) 19.8198i 1.19955i
\(274\) 0 0
\(275\) 10.0749 15.4415i 0.607538 0.931158i
\(276\) 0 0
\(277\) 3.74825i 0.225211i 0.993640 + 0.112605i \(0.0359196\pi\)
−0.993640 + 0.112605i \(0.964080\pi\)
\(278\) 0 0
\(279\) −5.66037 −0.338878
\(280\) 0 0
\(281\) −17.7546 −1.05915 −0.529576 0.848263i \(-0.677649\pi\)
−0.529576 + 0.848263i \(0.677649\pi\)
\(282\) 0 0
\(283\) 19.6755i 1.16959i 0.811183 + 0.584793i \(0.198824\pi\)
−0.811183 + 0.584793i \(0.801176\pi\)
\(284\) 0 0
\(285\) 4.49977 + 8.30873i 0.266543 + 0.492167i
\(286\) 0 0
\(287\) 5.88246i 0.347230i
\(288\) 0 0
\(289\) −45.2744 −2.66320
\(290\) 0 0
\(291\) 8.15818 0.478241
\(292\) 0 0
\(293\) 16.3514i 0.955259i −0.878561 0.477629i \(-0.841496\pi\)
0.878561 0.477629i \(-0.158504\pi\)
\(294\) 0 0
\(295\) 13.4459 7.28191i 0.782851 0.423969i
\(296\) 0 0
\(297\) 3.68751i 0.213971i
\(298\) 0 0
\(299\) −4.79006 −0.277016
\(300\) 0 0
\(301\) 29.8562 1.72088
\(302\) 0 0
\(303\) 2.75538i 0.158293i
\(304\) 0 0
\(305\) 8.68042 4.70106i 0.497039 0.269182i
\(306\) 0 0
\(307\) 0.589802i 0.0336618i −0.999858 0.0168309i \(-0.994642\pi\)
0.999858 0.0168309i \(-0.00535770\pi\)
\(308\) 0 0
\(309\) −11.5307 −0.655959
\(310\) 0 0
\(311\) 13.3850 0.758994 0.379497 0.925193i \(-0.376097\pi\)
0.379497 + 0.925193i \(0.376097\pi\)
\(312\) 0 0
\(313\) 15.9356i 0.900735i −0.892843 0.450368i \(-0.851293\pi\)
0.892843 0.450368i \(-0.148707\pi\)
\(314\) 0 0
\(315\) 4.60263 + 8.49866i 0.259329 + 0.478845i
\(316\) 0 0
\(317\) 16.4627i 0.924640i −0.886713 0.462320i \(-0.847017\pi\)
0.886713 0.462320i \(-0.152983\pi\)
\(318\) 0 0
\(319\) −21.8963 −1.22596
\(320\) 0 0
\(321\) 12.8485 0.717133
\(322\) 0 0
\(323\) 33.3468i 1.85547i
\(324\) 0 0
\(325\) 19.2017 + 12.5282i 1.06512 + 0.694942i
\(326\) 0 0
\(327\) 3.68327i 0.203685i
\(328\) 0 0
\(329\) 0.984887 0.0542986
\(330\) 0 0
\(331\) 32.0995 1.76435 0.882175 0.470923i \(-0.156079\pi\)
0.882175 + 0.470923i \(0.156079\pi\)
\(332\) 0 0
\(333\) 11.2388i 0.615885i
\(334\) 0 0
\(335\) 1.06486 + 1.96624i 0.0581793 + 0.107427i
\(336\) 0 0
\(337\) 2.03842i 0.111040i −0.998458 0.0555198i \(-0.982318\pi\)
0.998458 0.0555198i \(-0.0176816\pi\)
\(338\) 0 0
\(339\) 7.93123 0.430766
\(340\) 0 0
\(341\) 20.8727 1.13032
\(342\) 0 0
\(343\) 20.2382i 1.09276i
\(344\) 0 0
\(345\) −2.05396 + 1.11237i −0.110582 + 0.0598878i
\(346\) 0 0
\(347\) 16.6466i 0.893639i 0.894624 + 0.446819i \(0.147443\pi\)
−0.894624 + 0.446819i \(0.852557\pi\)
\(348\) 0 0
\(349\) 21.7609 1.16484 0.582418 0.812889i \(-0.302107\pi\)
0.582418 + 0.812889i \(0.302107\pi\)
\(350\) 0 0
\(351\) 4.58547 0.244754
\(352\) 0 0
\(353\) 12.5331i 0.667069i 0.942738 + 0.333535i \(0.108241\pi\)
−0.942738 + 0.333535i \(0.891759\pi\)
\(354\) 0 0
\(355\) −13.7066 + 7.42310i −0.727471 + 0.393977i
\(356\) 0 0
\(357\) 34.1091i 1.80524i
\(358\) 0 0
\(359\) −21.5144 −1.13549 −0.567743 0.823206i \(-0.692183\pi\)
−0.567743 + 0.823206i \(0.692183\pi\)
\(360\) 0 0
\(361\) −1.14340 −0.0601789
\(362\) 0 0
\(363\) 2.59773i 0.136345i
\(364\) 0 0
\(365\) −1.59664 2.94816i −0.0835720 0.154314i
\(366\) 0 0
\(367\) 13.6410i 0.712052i −0.934476 0.356026i \(-0.884131\pi\)
0.934476 0.356026i \(-0.115869\pi\)
\(368\) 0 0
\(369\) −1.36096 −0.0708485
\(370\) 0 0
\(371\) −18.9088 −0.981694
\(372\) 0 0
\(373\) 29.8002i 1.54300i −0.636231 0.771498i \(-0.719508\pi\)
0.636231 0.771498i \(-0.280492\pi\)
\(374\) 0 0
\(375\) 11.1430 + 0.912975i 0.575422 + 0.0471458i
\(376\) 0 0
\(377\) 27.2283i 1.40233i
\(378\) 0 0
\(379\) −30.1563 −1.54902 −0.774512 0.632559i \(-0.782005\pi\)
−0.774512 + 0.632559i \(0.782005\pi\)
\(380\) 0 0
\(381\) 6.32450 0.324014
\(382\) 0 0
\(383\) 5.16543i 0.263941i −0.991254 0.131971i \(-0.957870\pi\)
0.991254 0.131971i \(-0.0421305\pi\)
\(384\) 0 0
\(385\) −16.9722 31.3389i −0.864985 1.59718i
\(386\) 0 0
\(387\) 6.90749i 0.351127i
\(388\) 0 0
\(389\) 24.9691 1.26598 0.632992 0.774159i \(-0.281827\pi\)
0.632992 + 0.774159i \(0.281827\pi\)
\(390\) 0 0
\(391\) −8.24351 −0.416892
\(392\) 0 0
\(393\) 8.81351i 0.444583i
\(394\) 0 0
\(395\) −10.1554 + 5.49985i −0.510972 + 0.276727i
\(396\) 0 0
\(397\) 33.8747i 1.70012i −0.526685 0.850060i \(-0.676565\pi\)
0.526685 0.850060i \(-0.323435\pi\)
\(398\) 0 0
\(399\) 18.2648 0.914382
\(400\) 0 0
\(401\) −37.5275 −1.87403 −0.937016 0.349286i \(-0.886424\pi\)
−0.937016 + 0.349286i \(0.886424\pi\)
\(402\) 0 0
\(403\) 25.9554i 1.29293i
\(404\) 0 0
\(405\) 1.96624 1.06486i 0.0977030 0.0529131i
\(406\) 0 0
\(407\) 41.4433i 2.05427i
\(408\) 0 0
\(409\) −38.5255 −1.90496 −0.952481 0.304597i \(-0.901478\pi\)
−0.952481 + 0.304597i \(0.901478\pi\)
\(410\) 0 0
\(411\) 8.13167 0.401106
\(412\) 0 0
\(413\) 29.5576i 1.45444i
\(414\) 0 0
\(415\) 11.0487 + 20.4012i 0.542359 + 1.00146i
\(416\) 0 0
\(417\) 4.35176i 0.213107i
\(418\) 0 0
\(419\) −3.95992 −0.193455 −0.0967274 0.995311i \(-0.530837\pi\)
−0.0967274 + 0.995311i \(0.530837\pi\)
\(420\) 0 0
\(421\) −24.5101 −1.19455 −0.597274 0.802038i \(-0.703749\pi\)
−0.597274 + 0.802038i \(0.703749\pi\)
\(422\) 0 0
\(423\) 0.227862i 0.0110790i
\(424\) 0 0
\(425\) 33.0454 + 21.5606i 1.60294 + 1.04584i
\(426\) 0 0
\(427\) 19.0818i 0.923434i
\(428\) 0 0
\(429\) −16.9089 −0.816372
\(430\) 0 0
\(431\) −37.0414 −1.78422 −0.892110 0.451819i \(-0.850775\pi\)
−0.892110 + 0.451819i \(0.850775\pi\)
\(432\) 0 0
\(433\) 12.3638i 0.594164i −0.954852 0.297082i \(-0.903986\pi\)
0.954852 0.297082i \(-0.0960136\pi\)
\(434\) 0 0
\(435\) −6.32307 11.6754i −0.303168 0.559794i
\(436\) 0 0
\(437\) 4.41425i 0.211162i
\(438\) 0 0
\(439\) 15.0541 0.718492 0.359246 0.933243i \(-0.383034\pi\)
0.359246 + 0.933243i \(0.383034\pi\)
\(440\) 0 0
\(441\) 11.6823 0.556299
\(442\) 0 0
\(443\) 24.4444i 1.16139i −0.814122 0.580694i \(-0.802781\pi\)
0.814122 0.580694i \(-0.197219\pi\)
\(444\) 0 0
\(445\) 5.33691 2.89032i 0.252994 0.137014i
\(446\) 0 0
\(447\) 5.32537i 0.251881i
\(448\) 0 0
\(449\) −1.53808 −0.0725864 −0.0362932 0.999341i \(-0.511555\pi\)
−0.0362932 + 0.999341i \(0.511555\pi\)
\(450\) 0 0
\(451\) 5.01854 0.236314
\(452\) 0 0
\(453\) 14.9734i 0.703513i
\(454\) 0 0
\(455\) 38.9703 21.1052i 1.82696 0.989427i
\(456\) 0 0
\(457\) 17.2881i 0.808705i 0.914603 + 0.404353i \(0.132503\pi\)
−0.914603 + 0.404353i \(0.867497\pi\)
\(458\) 0 0
\(459\) 7.89141 0.368340
\(460\) 0 0
\(461\) 39.7237 1.85012 0.925058 0.379826i \(-0.124016\pi\)
0.925058 + 0.379826i \(0.124016\pi\)
\(462\) 0 0
\(463\) 21.7437i 1.01051i −0.862969 0.505257i \(-0.831398\pi\)
0.862969 0.505257i \(-0.168602\pi\)
\(464\) 0 0
\(465\) 6.02748 + 11.1296i 0.279518 + 0.516124i
\(466\) 0 0
\(467\) 17.1176i 0.792108i 0.918227 + 0.396054i \(0.129621\pi\)
−0.918227 + 0.396054i \(0.870379\pi\)
\(468\) 0 0
\(469\) 4.32230 0.199585
\(470\) 0 0
\(471\) 23.0196 1.06069
\(472\) 0 0
\(473\) 25.4714i 1.17118i
\(474\) 0 0
\(475\) 11.5453 17.6952i 0.529736 0.811912i
\(476\) 0 0
\(477\) 4.37470i 0.200304i
\(478\) 0 0
\(479\) 33.0239 1.50890 0.754449 0.656358i \(-0.227904\pi\)
0.754449 + 0.656358i \(0.227904\pi\)
\(480\) 0 0
\(481\) −51.5353 −2.34981
\(482\) 0 0
\(483\) 4.51515i 0.205446i
\(484\) 0 0
\(485\) −8.68729 16.0409i −0.394470 0.728380i
\(486\) 0 0
\(487\) 26.9318i 1.22040i −0.792249 0.610198i \(-0.791090\pi\)
0.792249 0.610198i \(-0.208910\pi\)
\(488\) 0 0
\(489\) 19.1669 0.866756
\(490\) 0 0
\(491\) 26.7624 1.20777 0.603886 0.797071i \(-0.293618\pi\)
0.603886 + 0.797071i \(0.293618\pi\)
\(492\) 0 0
\(493\) 46.8589i 2.11042i
\(494\) 0 0
\(495\) −7.25051 + 3.92667i −0.325886 + 0.176491i
\(496\) 0 0
\(497\) 30.1307i 1.35155i
\(498\) 0 0
\(499\) 18.7069 0.837435 0.418717 0.908117i \(-0.362480\pi\)
0.418717 + 0.908117i \(0.362480\pi\)
\(500\) 0 0
\(501\) 14.7151 0.657423
\(502\) 0 0
\(503\) 37.1869i 1.65808i −0.559189 0.829040i \(-0.688887\pi\)
0.559189 0.829040i \(-0.311113\pi\)
\(504\) 0 0
\(505\) 5.41773 2.93409i 0.241086 0.130565i
\(506\) 0 0
\(507\) 8.02650i 0.356469i
\(508\) 0 0
\(509\) −5.39023 −0.238918 −0.119459 0.992839i \(-0.538116\pi\)
−0.119459 + 0.992839i \(0.538116\pi\)
\(510\) 0 0
\(511\) −6.48084 −0.286695
\(512\) 0 0
\(513\) 4.22571i 0.186570i
\(514\) 0 0
\(515\) 12.2785 + 22.6721i 0.541057 + 0.999051i
\(516\) 0 0
\(517\) 0.840243i 0.0369538i
\(518\) 0 0
\(519\) −14.7906 −0.649234
\(520\) 0 0
\(521\) −18.7511 −0.821500 −0.410750 0.911748i \(-0.634733\pi\)
−0.410750 + 0.911748i \(0.634733\pi\)
\(522\) 0 0
\(523\) 1.43214i 0.0626230i −0.999510 0.0313115i \(-0.990032\pi\)
0.999510 0.0313115i \(-0.00996839\pi\)
\(524\) 0 0
\(525\) 11.8092 18.0997i 0.515397 0.789936i
\(526\) 0 0
\(527\) 44.6683i 1.94578i
\(528\) 0 0
\(529\) 21.9088 0.952555
\(530\) 0 0
\(531\) −6.83840 −0.296761
\(532\) 0 0
\(533\) 6.24061i 0.270311i
\(534\) 0 0
\(535\) −13.6818 25.2631i −0.591515 1.09222i
\(536\) 0 0
\(537\) 16.7747i 0.723880i
\(538\) 0 0
\(539\) −43.0785 −1.85552
\(540\) 0 0
\(541\) 2.35121 0.101087 0.0505433 0.998722i \(-0.483905\pi\)
0.0505433 + 0.998722i \(0.483905\pi\)
\(542\) 0 0
\(543\) 18.8727i 0.809904i
\(544\) 0 0
\(545\) 7.24218 3.92215i 0.310221 0.168007i
\(546\) 0 0
\(547\) 41.0405i 1.75476i 0.479793 + 0.877382i \(0.340712\pi\)
−0.479793 + 0.877382i \(0.659288\pi\)
\(548\) 0 0
\(549\) −4.41474 −0.188416
\(550\) 0 0
\(551\) −25.0921 −1.06896
\(552\) 0 0
\(553\) 22.3241i 0.949319i
\(554\) 0 0
\(555\) −22.0982 + 11.9677i −0.938017 + 0.508003i
\(556\) 0 0
\(557\) 3.09843i 0.131285i 0.997843 + 0.0656424i \(0.0209097\pi\)
−0.997843 + 0.0656424i \(0.979090\pi\)
\(558\) 0 0
\(559\) −31.6740 −1.33967
\(560\) 0 0
\(561\) −29.0997 −1.22859
\(562\) 0 0
\(563\) 15.9187i 0.670891i −0.942060 0.335446i \(-0.891113\pi\)
0.942060 0.335446i \(-0.108887\pi\)
\(564\) 0 0
\(565\) −8.44562 15.5947i −0.355310 0.656073i
\(566\) 0 0
\(567\) 4.32230i 0.181520i
\(568\) 0 0
\(569\) 28.1166 1.17871 0.589355 0.807874i \(-0.299382\pi\)
0.589355 + 0.807874i \(0.299382\pi\)
\(570\) 0 0
\(571\) −21.2535 −0.889431 −0.444716 0.895672i \(-0.646695\pi\)
−0.444716 + 0.895672i \(0.646695\pi\)
\(572\) 0 0
\(573\) 4.24583i 0.177372i
\(574\) 0 0
\(575\) 4.37435 + 2.85406i 0.182423 + 0.119023i
\(576\) 0 0
\(577\) 44.9336i 1.87061i 0.353842 + 0.935305i \(0.384875\pi\)
−0.353842 + 0.935305i \(0.615125\pi\)
\(578\) 0 0
\(579\) 17.8178 0.740480
\(580\) 0 0
\(581\) 44.8472 1.86057
\(582\) 0 0
\(583\) 16.1317i 0.668109i
\(584\) 0 0
\(585\) −4.88286 9.01611i −0.201881 0.372770i
\(586\) 0 0
\(587\) 14.3953i 0.594157i 0.954853 + 0.297078i \(0.0960123\pi\)
−0.954853 + 0.297078i \(0.903988\pi\)
\(588\) 0 0
\(589\) 23.9191 0.985568
\(590\) 0 0
\(591\) −7.79528 −0.320655
\(592\) 0 0
\(593\) 15.5990i 0.640576i −0.947320 0.320288i \(-0.896220\pi\)
0.947320 0.320288i \(-0.103780\pi\)
\(594\) 0 0
\(595\) 67.0664 36.3212i 2.74946 1.48903i
\(596\) 0 0
\(597\) 1.01866i 0.0416911i
\(598\) 0 0
\(599\) −8.80305 −0.359683 −0.179841 0.983696i \(-0.557558\pi\)
−0.179841 + 0.983696i \(0.557558\pi\)
\(600\) 0 0
\(601\) −5.90124 −0.240717 −0.120358 0.992731i \(-0.538404\pi\)
−0.120358 + 0.992731i \(0.538404\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 5.10774 2.76621i 0.207659 0.112462i
\(606\) 0 0
\(607\) 42.2861i 1.71634i −0.513367 0.858169i \(-0.671602\pi\)
0.513367 0.858169i \(-0.328398\pi\)
\(608\) 0 0
\(609\) −25.6656 −1.04002
\(610\) 0 0
\(611\) −1.04485 −0.0422702
\(612\) 0 0
\(613\) 18.3331i 0.740469i −0.928938 0.370234i \(-0.879277\pi\)
0.928938 0.370234i \(-0.120723\pi\)
\(614\) 0 0
\(615\) 1.44922 + 2.67596i 0.0584382 + 0.107905i
\(616\) 0 0
\(617\) 21.0364i 0.846892i 0.905921 + 0.423446i \(0.139180\pi\)
−0.905921 + 0.423446i \(0.860820\pi\)
\(618\) 0 0
\(619\) −8.00519 −0.321756 −0.160878 0.986974i \(-0.551433\pi\)
−0.160878 + 0.986974i \(0.551433\pi\)
\(620\) 0 0
\(621\) 1.04462 0.0419190
\(622\) 0 0
\(623\) 11.7319i 0.470030i
\(624\) 0 0
\(625\) −10.0706 22.8820i −0.402823 0.915278i
\(626\) 0 0
\(627\) 15.5823i 0.622299i
\(628\) 0 0
\(629\) −88.6903 −3.53632
\(630\) 0 0
\(631\) 38.5012 1.53271 0.766354 0.642418i \(-0.222069\pi\)
0.766354 + 0.642418i \(0.222069\pi\)
\(632\) 0 0
\(633\) 16.9281i 0.672831i
\(634\) 0 0
\(635\) −6.73468 12.4355i −0.267258 0.493486i
\(636\) 0 0
\(637\) 53.5687i 2.12247i
\(638\) 0 0
\(639\) 6.97099 0.275768
\(640\) 0 0
\(641\) −36.6360 −1.44703 −0.723517 0.690307i \(-0.757476\pi\)
−0.723517 + 0.690307i \(0.757476\pi\)
\(642\) 0 0
\(643\) 0.482014i 0.0190088i −0.999955 0.00950439i \(-0.996975\pi\)
0.999955 0.00950439i \(-0.00302539\pi\)
\(644\) 0 0
\(645\) −13.5817 + 7.35548i −0.534781 + 0.289622i
\(646\) 0 0
\(647\) 42.4176i 1.66761i −0.552060 0.833804i \(-0.686158\pi\)
0.552060 0.833804i \(-0.313842\pi\)
\(648\) 0 0
\(649\) 25.2167 0.989841
\(650\) 0 0
\(651\) 24.4658 0.958891
\(652\) 0 0
\(653\) 1.57080i 0.0614703i −0.999528 0.0307352i \(-0.990215\pi\)
0.999528 0.0307352i \(-0.00978485\pi\)
\(654\) 0 0
\(655\) 17.3294 9.38512i 0.677117 0.366707i
\(656\) 0 0
\(657\) 1.49940i 0.0584970i
\(658\) 0 0
\(659\) 1.85440 0.0722370 0.0361185 0.999348i \(-0.488501\pi\)
0.0361185 + 0.999348i \(0.488501\pi\)
\(660\) 0 0
\(661\) 17.8088 0.692683 0.346342 0.938108i \(-0.387424\pi\)
0.346342 + 0.938108i \(0.387424\pi\)
\(662\) 0 0
\(663\) 36.1858i 1.40534i
\(664\) 0 0
\(665\) −19.4494 35.9128i −0.754214 1.39264i
\(666\) 0 0
\(667\) 6.20289i 0.240177i
\(668\) 0 0
\(669\) −19.6720 −0.760562
\(670\) 0 0
\(671\) 16.2794 0.628459
\(672\) 0 0
\(673\) 8.76791i 0.337978i 0.985618 + 0.168989i \(0.0540502\pi\)
−0.985618 + 0.168989i \(0.945950\pi\)
\(674\) 0 0
\(675\) −4.18752 2.73216i −0.161178 0.105161i
\(676\) 0 0
\(677\) 14.2467i 0.547547i 0.961794 + 0.273773i \(0.0882718\pi\)
−0.961794 + 0.273773i \(0.911728\pi\)
\(678\) 0 0
\(679\) −35.2621 −1.35324
\(680\) 0 0
\(681\) −21.8906 −0.838850
\(682\) 0 0
\(683\) 7.19495i 0.275307i −0.990480 0.137654i \(-0.956044\pi\)
0.990480 0.137654i \(-0.0439561\pi\)
\(684\) 0 0
\(685\) −8.65905 15.9888i −0.330845 0.610899i
\(686\) 0 0
\(687\) 3.28727i 0.125417i
\(688\) 0 0
\(689\) 20.0600 0.764227
\(690\) 0 0
\(691\) 10.2758 0.390911 0.195455 0.980713i \(-0.437382\pi\)
0.195455 + 0.980713i \(0.437382\pi\)
\(692\) 0 0
\(693\) 15.9385i 0.605454i
\(694\) 0 0
\(695\) 8.55658 4.63400i 0.324570 0.175778i
\(696\) 0 0
\(697\) 10.7399i 0.406801i
\(698\) 0 0
\(699\) −10.4772 −0.396283
\(700\) 0 0
\(701\) 4.73210 0.178729 0.0893644 0.995999i \(-0.471516\pi\)
0.0893644 + 0.995999i \(0.471516\pi\)
\(702\) 0 0
\(703\) 47.4920i 1.79120i
\(704\) 0 0
\(705\) −0.448030 + 0.242640i −0.0168738 + 0.00913835i
\(706\) 0 0
\(707\) 11.9096i 0.447906i
\(708\) 0 0
\(709\) −23.8274 −0.894858 −0.447429 0.894319i \(-0.647660\pi\)
−0.447429 + 0.894319i \(0.647660\pi\)
\(710\) 0 0
\(711\) 5.16488 0.193698
\(712\) 0 0
\(713\) 5.91292i 0.221441i
\(714\) 0 0
\(715\) 18.0056 + 33.2470i 0.673371 + 1.24337i
\(716\) 0 0
\(717\) 19.8748i 0.742236i
\(718\) 0 0
\(719\) 5.11082 0.190601 0.0953007 0.995449i \(-0.469619\pi\)
0.0953007 + 0.995449i \(0.469619\pi\)
\(720\) 0 0
\(721\) 49.8391 1.85611
\(722\) 0 0
\(723\) 11.2871i 0.419771i
\(724\) 0 0
\(725\) −16.2235 + 24.8653i −0.602524 + 0.923474i
\(726\) 0 0
\(727\) 30.2795i 1.12300i −0.827475 0.561502i \(-0.810224\pi\)
0.827475 0.561502i \(-0.189776\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −54.5098 −2.01612
\(732\) 0 0
\(733\) 21.5837i 0.797213i −0.917122 0.398607i \(-0.869494\pi\)
0.917122 0.398607i \(-0.130506\pi\)
\(734\) 0 0
\(735\) −12.4399 22.9701i −0.458854 0.847265i
\(736\) 0 0
\(737\) 3.68751i 0.135831i
\(738\) 0 0
\(739\) −51.2289 −1.88449 −0.942243 0.334929i \(-0.891288\pi\)
−0.942243 + 0.334929i \(0.891288\pi\)
\(740\) 0 0
\(741\) −19.3768 −0.711826
\(742\) 0 0
\(743\) 42.0409i 1.54233i −0.636634 0.771166i \(-0.719674\pi\)
0.636634 0.771166i \(-0.280326\pi\)
\(744\) 0 0
\(745\) 10.4709 5.67075i 0.383625 0.207760i
\(746\) 0 0
\(747\) 10.3758i 0.379629i
\(748\) 0 0
\(749\) −55.5350 −2.02921
\(750\) 0 0
\(751\) −15.1306 −0.552125 −0.276062 0.961140i \(-0.589030\pi\)
−0.276062 + 0.961140i \(0.589030\pi\)
\(752\) 0 0
\(753\) 30.1154i 1.09747i
\(754\) 0 0
\(755\) 29.4413 15.9446i 1.07148 0.580282i
\(756\) 0 0
\(757\) 46.7505i 1.69918i 0.527447 + 0.849588i \(0.323149\pi\)
−0.527447 + 0.849588i \(0.676851\pi\)
\(758\) 0 0
\(759\) −3.85204 −0.139820
\(760\) 0 0
\(761\) 27.2113 0.986410 0.493205 0.869913i \(-0.335825\pi\)
0.493205 + 0.869913i \(0.335825\pi\)
\(762\) 0 0
\(763\) 15.9202i 0.576350i
\(764\) 0 0
\(765\) −8.40322 15.5164i −0.303819 0.560996i
\(766\) 0 0
\(767\) 31.3573i 1.13224i
\(768\) 0 0
\(769\) −8.97578 −0.323675 −0.161838 0.986817i \(-0.551742\pi\)
−0.161838 + 0.986817i \(0.551742\pi\)
\(770\) 0 0
\(771\) −26.5811 −0.957295
\(772\) 0 0
\(773\) 29.6344i 1.06587i 0.846155 + 0.532937i \(0.178912\pi\)
−0.846155 + 0.532937i \(0.821088\pi\)
\(774\) 0 0
\(775\) 15.4651 23.7029i 0.555521 0.851433i
\(776\) 0 0
\(777\) 48.5776i 1.74271i
\(778\) 0 0
\(779\) 5.75100 0.206051
\(780\) 0 0
\(781\) −25.7056 −0.919819
\(782\) 0 0
\(783\) 5.93796i 0.212205i
\(784\) 0 0
\(785\) −24.5126 45.2620i −0.874892 1.61547i
\(786\) 0 0
\(787\) 16.6729i 0.594325i −0.954827 0.297162i \(-0.903960\pi\)
0.954827 0.297162i \(-0.0960403\pi\)
\(788\) 0 0
\(789\) −10.5190 −0.374486
\(790\) 0 0
\(791\) −34.2812 −1.21890
\(792\) 0 0