Properties

Label 4020.2.g.c.1609.15
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 1609.15
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.34

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(1.96436 + 1.06831i) q^{5}\) \(-3.03191i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(1.96436 + 1.06831i) q^{5}\) \(-3.03191i q^{7}\) \(-1.00000 q^{9}\) \(+2.01519 q^{11}\) \(+1.13975i q^{13}\) \(+(1.06831 - 1.96436i) q^{15}\) \(+0.286135i q^{17}\) \(-1.78093 q^{19}\) \(-3.03191 q^{21}\) \(+7.18704i q^{23}\) \(+(2.71741 + 4.19710i) q^{25}\) \(+1.00000i q^{27}\) \(+8.82296 q^{29}\) \(+2.29610 q^{31}\) \(-2.01519i q^{33}\) \(+(3.23903 - 5.95576i) q^{35}\) \(+2.36755i q^{37}\) \(+1.13975 q^{39}\) \(+5.15374 q^{41}\) \(-2.11893i q^{43}\) \(+(-1.96436 - 1.06831i) q^{45}\) \(-6.00381i q^{47}\) \(-2.19247 q^{49}\) \(+0.286135 q^{51}\) \(+9.22119i q^{53}\) \(+(3.95856 + 2.15285i) q^{55}\) \(+1.78093i q^{57}\) \(+5.81688 q^{59}\) \(+7.84468 q^{61}\) \(+3.03191i q^{63}\) \(+(-1.21761 + 2.23888i) q^{65}\) \(-1.00000i q^{67}\) \(+7.18704 q^{69}\) \(+5.24595 q^{71}\) \(-8.12823i q^{73}\) \(+(4.19710 - 2.71741i) q^{75}\) \(-6.10987i q^{77}\) \(-13.3077 q^{79}\) \(+1.00000 q^{81}\) \(-9.42607i q^{83}\) \(+(-0.305682 + 0.562071i) q^{85}\) \(-8.82296i q^{87}\) \(+1.93173 q^{89}\) \(+3.45562 q^{91}\) \(-2.29610i q^{93}\) \(+(-3.49839 - 1.90259i) q^{95}\) \(+5.99160i q^{97}\) \(-2.01519 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.96436 + 1.06831i 0.878488 + 0.477764i
\(6\) 0 0
\(7\) 3.03191i 1.14595i −0.819572 0.572977i \(-0.805788\pi\)
0.819572 0.572977i \(-0.194212\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 2.01519 0.607603 0.303801 0.952735i \(-0.401744\pi\)
0.303801 + 0.952735i \(0.401744\pi\)
\(12\) 0 0
\(13\) 1.13975i 0.316110i 0.987430 + 0.158055i \(0.0505224\pi\)
−0.987430 + 0.158055i \(0.949478\pi\)
\(14\) 0 0
\(15\) 1.06831 1.96436i 0.275837 0.507195i
\(16\) 0 0
\(17\) 0.286135i 0.0693979i 0.999398 + 0.0346989i \(0.0110472\pi\)
−0.999398 + 0.0346989i \(0.988953\pi\)
\(18\) 0 0
\(19\) −1.78093 −0.408574 −0.204287 0.978911i \(-0.565488\pi\)
−0.204287 + 0.978911i \(0.565488\pi\)
\(20\) 0 0
\(21\) −3.03191 −0.661617
\(22\) 0 0
\(23\) 7.18704i 1.49860i 0.662230 + 0.749301i \(0.269610\pi\)
−0.662230 + 0.749301i \(0.730390\pi\)
\(24\) 0 0
\(25\) 2.71741 + 4.19710i 0.543483 + 0.839420i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 8.82296 1.63838 0.819192 0.573520i \(-0.194422\pi\)
0.819192 + 0.573520i \(0.194422\pi\)
\(30\) 0 0
\(31\) 2.29610 0.412392 0.206196 0.978511i \(-0.433892\pi\)
0.206196 + 0.978511i \(0.433892\pi\)
\(32\) 0 0
\(33\) 2.01519i 0.350800i
\(34\) 0 0
\(35\) 3.23903 5.95576i 0.547496 1.00671i
\(36\) 0 0
\(37\) 2.36755i 0.389223i 0.980880 + 0.194612i \(0.0623446\pi\)
−0.980880 + 0.194612i \(0.937655\pi\)
\(38\) 0 0
\(39\) 1.13975 0.182506
\(40\) 0 0
\(41\) 5.15374 0.804879 0.402440 0.915446i \(-0.368162\pi\)
0.402440 + 0.915446i \(0.368162\pi\)
\(42\) 0 0
\(43\) 2.11893i 0.323134i −0.986862 0.161567i \(-0.948345\pi\)
0.986862 0.161567i \(-0.0516548\pi\)
\(44\) 0 0
\(45\) −1.96436 1.06831i −0.292829 0.159255i
\(46\) 0 0
\(47\) 6.00381i 0.875746i −0.899037 0.437873i \(-0.855732\pi\)
0.899037 0.437873i \(-0.144268\pi\)
\(48\) 0 0
\(49\) −2.19247 −0.313210
\(50\) 0 0
\(51\) 0.286135 0.0400669
\(52\) 0 0
\(53\) 9.22119i 1.26663i 0.773895 + 0.633314i \(0.218306\pi\)
−0.773895 + 0.633314i \(0.781694\pi\)
\(54\) 0 0
\(55\) 3.95856 + 2.15285i 0.533772 + 0.290291i
\(56\) 0 0
\(57\) 1.78093i 0.235890i
\(58\) 0 0
\(59\) 5.81688 0.757294 0.378647 0.925541i \(-0.376390\pi\)
0.378647 + 0.925541i \(0.376390\pi\)
\(60\) 0 0
\(61\) 7.84468 1.00441 0.502204 0.864749i \(-0.332523\pi\)
0.502204 + 0.864749i \(0.332523\pi\)
\(62\) 0 0
\(63\) 3.03191i 0.381985i
\(64\) 0 0
\(65\) −1.21761 + 2.23888i −0.151026 + 0.277699i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) 7.18704 0.865218
\(70\) 0 0
\(71\) 5.24595 0.622579 0.311290 0.950315i \(-0.399239\pi\)
0.311290 + 0.950315i \(0.399239\pi\)
\(72\) 0 0
\(73\) 8.12823i 0.951337i −0.879625 0.475669i \(-0.842206\pi\)
0.879625 0.475669i \(-0.157794\pi\)
\(74\) 0 0
\(75\) 4.19710 2.71741i 0.484640 0.313780i
\(76\) 0 0
\(77\) 6.10987i 0.696285i
\(78\) 0 0
\(79\) −13.3077 −1.49723 −0.748615 0.663004i \(-0.769281\pi\)
−0.748615 + 0.663004i \(0.769281\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 9.42607i 1.03465i −0.855791 0.517323i \(-0.826929\pi\)
0.855791 0.517323i \(-0.173071\pi\)
\(84\) 0 0
\(85\) −0.305682 + 0.562071i −0.0331558 + 0.0609652i
\(86\) 0 0
\(87\) 8.82296i 0.945921i
\(88\) 0 0
\(89\) 1.93173 0.204763 0.102382 0.994745i \(-0.467354\pi\)
0.102382 + 0.994745i \(0.467354\pi\)
\(90\) 0 0
\(91\) 3.45562 0.362248
\(92\) 0 0
\(93\) 2.29610i 0.238094i
\(94\) 0 0
\(95\) −3.49839 1.90259i −0.358927 0.195202i
\(96\) 0 0
\(97\) 5.99160i 0.608355i 0.952615 + 0.304178i \(0.0983816\pi\)
−0.952615 + 0.304178i \(0.901618\pi\)
\(98\) 0 0
\(99\) −2.01519 −0.202534
\(100\) 0 0
\(101\) −0.706768 −0.0703261 −0.0351630 0.999382i \(-0.511195\pi\)
−0.0351630 + 0.999382i \(0.511195\pi\)
\(102\) 0 0
\(103\) 0.437107i 0.0430694i −0.999768 0.0215347i \(-0.993145\pi\)
0.999768 0.0215347i \(-0.00685524\pi\)
\(104\) 0 0
\(105\) −5.95576 3.23903i −0.581222 0.316097i
\(106\) 0 0
\(107\) 16.8841i 1.63225i −0.577878 0.816123i \(-0.696119\pi\)
0.577878 0.816123i \(-0.303881\pi\)
\(108\) 0 0
\(109\) 1.00505 0.0962667 0.0481334 0.998841i \(-0.484673\pi\)
0.0481334 + 0.998841i \(0.484673\pi\)
\(110\) 0 0
\(111\) 2.36755 0.224718
\(112\) 0 0
\(113\) 7.58363i 0.713407i −0.934218 0.356704i \(-0.883901\pi\)
0.934218 0.356704i \(-0.116099\pi\)
\(114\) 0 0
\(115\) −7.67801 + 14.1179i −0.715978 + 1.31650i
\(116\) 0 0
\(117\) 1.13975i 0.105370i
\(118\) 0 0
\(119\) 0.867535 0.0795268
\(120\) 0 0
\(121\) −6.93901 −0.630819
\(122\) 0 0
\(123\) 5.15374i 0.464697i
\(124\) 0 0
\(125\) 0.854158 + 11.1477i 0.0763983 + 0.997077i
\(126\) 0 0
\(127\) 9.38467i 0.832755i −0.909192 0.416377i \(-0.863300\pi\)
0.909192 0.416377i \(-0.136700\pi\)
\(128\) 0 0
\(129\) −2.11893 −0.186561
\(130\) 0 0
\(131\) 16.3056 1.42462 0.712312 0.701863i \(-0.247648\pi\)
0.712312 + 0.701863i \(0.247648\pi\)
\(132\) 0 0
\(133\) 5.39963i 0.468207i
\(134\) 0 0
\(135\) −1.06831 + 1.96436i −0.0919458 + 0.169065i
\(136\) 0 0
\(137\) 16.0046i 1.36736i 0.729781 + 0.683681i \(0.239622\pi\)
−0.729781 + 0.683681i \(0.760378\pi\)
\(138\) 0 0
\(139\) −6.81926 −0.578402 −0.289201 0.957268i \(-0.593390\pi\)
−0.289201 + 0.957268i \(0.593390\pi\)
\(140\) 0 0
\(141\) −6.00381 −0.505612
\(142\) 0 0
\(143\) 2.29682i 0.192069i
\(144\) 0 0
\(145\) 17.3315 + 9.42569i 1.43930 + 0.782761i
\(146\) 0 0
\(147\) 2.19247i 0.180832i
\(148\) 0 0
\(149\) −18.6381 −1.52689 −0.763447 0.645870i \(-0.776495\pi\)
−0.763447 + 0.645870i \(0.776495\pi\)
\(150\) 0 0
\(151\) 1.11827 0.0910037 0.0455018 0.998964i \(-0.485511\pi\)
0.0455018 + 0.998964i \(0.485511\pi\)
\(152\) 0 0
\(153\) 0.286135i 0.0231326i
\(154\) 0 0
\(155\) 4.51036 + 2.45295i 0.362281 + 0.197026i
\(156\) 0 0
\(157\) 0.581889i 0.0464398i 0.999730 + 0.0232199i \(0.00739179\pi\)
−0.999730 + 0.0232199i \(0.992608\pi\)
\(158\) 0 0
\(159\) 9.22119 0.731288
\(160\) 0 0
\(161\) 21.7904 1.71733
\(162\) 0 0
\(163\) 6.09462i 0.477367i −0.971097 0.238684i \(-0.923284\pi\)
0.971097 0.238684i \(-0.0767159\pi\)
\(164\) 0 0
\(165\) 2.15285 3.95856i 0.167599 0.308173i
\(166\) 0 0
\(167\) 1.44027i 0.111451i −0.998446 0.0557257i \(-0.982253\pi\)
0.998446 0.0557257i \(-0.0177472\pi\)
\(168\) 0 0
\(169\) 11.7010 0.900074
\(170\) 0 0
\(171\) 1.78093 0.136191
\(172\) 0 0
\(173\) 15.1024i 1.14821i 0.818781 + 0.574106i \(0.194650\pi\)
−0.818781 + 0.574106i \(0.805350\pi\)
\(174\) 0 0
\(175\) 12.7252 8.23895i 0.961937 0.622806i
\(176\) 0 0
\(177\) 5.81688i 0.437224i
\(178\) 0 0
\(179\) −12.0255 −0.898825 −0.449412 0.893324i \(-0.648367\pi\)
−0.449412 + 0.893324i \(0.648367\pi\)
\(180\) 0 0
\(181\) 19.1277 1.42175 0.710876 0.703317i \(-0.248299\pi\)
0.710876 + 0.703317i \(0.248299\pi\)
\(182\) 0 0
\(183\) 7.84468i 0.579895i
\(184\) 0 0
\(185\) −2.52929 + 4.65072i −0.185957 + 0.341928i
\(186\) 0 0
\(187\) 0.576616i 0.0421663i
\(188\) 0 0
\(189\) 3.03191 0.220539
\(190\) 0 0
\(191\) 0.785469 0.0568345 0.0284173 0.999596i \(-0.490953\pi\)
0.0284173 + 0.999596i \(0.490953\pi\)
\(192\) 0 0
\(193\) 3.88940i 0.279965i 0.990154 + 0.139983i \(0.0447046\pi\)
−0.990154 + 0.139983i \(0.955295\pi\)
\(194\) 0 0
\(195\) 2.23888 + 1.21761i 0.160330 + 0.0871950i
\(196\) 0 0
\(197\) 17.5055i 1.24721i −0.781738 0.623607i \(-0.785667\pi\)
0.781738 0.623607i \(-0.214333\pi\)
\(198\) 0 0
\(199\) 7.28359 0.516320 0.258160 0.966102i \(-0.416884\pi\)
0.258160 + 0.966102i \(0.416884\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 26.7504i 1.87751i
\(204\) 0 0
\(205\) 10.1238 + 5.50581i 0.707077 + 0.384543i
\(206\) 0 0
\(207\) 7.18704i 0.499534i
\(208\) 0 0
\(209\) −3.58892 −0.248251
\(210\) 0 0
\(211\) −3.44237 −0.236982 −0.118491 0.992955i \(-0.537806\pi\)
−0.118491 + 0.992955i \(0.537806\pi\)
\(212\) 0 0
\(213\) 5.24595i 0.359446i
\(214\) 0 0
\(215\) 2.26368 4.16234i 0.154382 0.283869i
\(216\) 0 0
\(217\) 6.96156i 0.472582i
\(218\) 0 0
\(219\) −8.12823 −0.549255
\(220\) 0 0
\(221\) −0.326123 −0.0219374
\(222\) 0 0
\(223\) 2.03546i 0.136304i 0.997675 + 0.0681521i \(0.0217103\pi\)
−0.997675 + 0.0681521i \(0.978290\pi\)
\(224\) 0 0
\(225\) −2.71741 4.19710i −0.181161 0.279807i
\(226\) 0 0
\(227\) 2.69664i 0.178982i 0.995988 + 0.0894910i \(0.0285240\pi\)
−0.995988 + 0.0894910i \(0.971476\pi\)
\(228\) 0 0
\(229\) −20.5001 −1.35468 −0.677342 0.735668i \(-0.736868\pi\)
−0.677342 + 0.735668i \(0.736868\pi\)
\(230\) 0 0
\(231\) −6.10987 −0.402000
\(232\) 0 0
\(233\) 14.0115i 0.917927i −0.888455 0.458964i \(-0.848221\pi\)
0.888455 0.458964i \(-0.151779\pi\)
\(234\) 0 0
\(235\) 6.41395 11.7936i 0.418400 0.769332i
\(236\) 0 0
\(237\) 13.3077i 0.864427i
\(238\) 0 0
\(239\) 18.8898 1.22188 0.610940 0.791677i \(-0.290792\pi\)
0.610940 + 0.791677i \(0.290792\pi\)
\(240\) 0 0
\(241\) −5.81348 −0.374479 −0.187240 0.982314i \(-0.559954\pi\)
−0.187240 + 0.982314i \(0.559954\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −4.30680 2.34224i −0.275151 0.149641i
\(246\) 0 0
\(247\) 2.02982i 0.129154i
\(248\) 0 0
\(249\) −9.42607 −0.597353
\(250\) 0 0
\(251\) 21.5194 1.35829 0.679147 0.734002i \(-0.262350\pi\)
0.679147 + 0.734002i \(0.262350\pi\)
\(252\) 0 0
\(253\) 14.4832i 0.910554i
\(254\) 0 0
\(255\) 0.562071 + 0.305682i 0.0351983 + 0.0191425i
\(256\) 0 0
\(257\) 21.8474i 1.36281i 0.731909 + 0.681403i \(0.238630\pi\)
−0.731909 + 0.681403i \(0.761370\pi\)
\(258\) 0 0
\(259\) 7.17820 0.446032
\(260\) 0 0
\(261\) −8.82296 −0.546128
\(262\) 0 0
\(263\) 4.11910i 0.253994i −0.991903 0.126997i \(-0.959466\pi\)
0.991903 0.126997i \(-0.0405339\pi\)
\(264\) 0 0
\(265\) −9.85112 + 18.1137i −0.605149 + 1.11272i
\(266\) 0 0
\(267\) 1.93173i 0.118220i
\(268\) 0 0
\(269\) −19.3683 −1.18090 −0.590452 0.807073i \(-0.701050\pi\)
−0.590452 + 0.807073i \(0.701050\pi\)
\(270\) 0 0
\(271\) −4.63445 −0.281523 −0.140761 0.990044i \(-0.544955\pi\)
−0.140761 + 0.990044i \(0.544955\pi\)
\(272\) 0 0
\(273\) 3.45562i 0.209144i
\(274\) 0 0
\(275\) 5.47611 + 8.45796i 0.330222 + 0.510034i
\(276\) 0 0
\(277\) 0.126860i 0.00762231i −0.999993 0.00381115i \(-0.998787\pi\)
0.999993 0.00381115i \(-0.00121313\pi\)
\(278\) 0 0
\(279\) −2.29610 −0.137464
\(280\) 0 0
\(281\) −19.0912 −1.13888 −0.569442 0.822032i \(-0.692841\pi\)
−0.569442 + 0.822032i \(0.692841\pi\)
\(282\) 0 0
\(283\) 1.07191i 0.0637185i 0.999492 + 0.0318592i \(0.0101428\pi\)
−0.999492 + 0.0318592i \(0.989857\pi\)
\(284\) 0 0
\(285\) −1.90259 + 3.49839i −0.112700 + 0.207227i
\(286\) 0 0
\(287\) 15.6257i 0.922355i
\(288\) 0 0
\(289\) 16.9181 0.995184
\(290\) 0 0
\(291\) 5.99160 0.351234
\(292\) 0 0
\(293\) 27.5814i 1.61132i −0.592378 0.805660i \(-0.701811\pi\)
0.592378 0.805660i \(-0.298189\pi\)
\(294\) 0 0
\(295\) 11.4264 + 6.21425i 0.665273 + 0.361808i
\(296\) 0 0
\(297\) 2.01519i 0.116933i
\(298\) 0 0
\(299\) −8.19144 −0.473723
\(300\) 0 0
\(301\) −6.42440 −0.370296
\(302\) 0 0
\(303\) 0.706768i 0.0406028i
\(304\) 0 0
\(305\) 15.4098 + 8.38057i 0.882360 + 0.479870i
\(306\) 0 0
\(307\) 9.66181i 0.551429i 0.961240 + 0.275714i \(0.0889144\pi\)
−0.961240 + 0.275714i \(0.911086\pi\)
\(308\) 0 0
\(309\) −0.437107 −0.0248661
\(310\) 0 0
\(311\) 0.912234 0.0517280 0.0258640 0.999665i \(-0.491766\pi\)
0.0258640 + 0.999665i \(0.491766\pi\)
\(312\) 0 0
\(313\) 1.74134i 0.0984263i 0.998788 + 0.0492131i \(0.0156714\pi\)
−0.998788 + 0.0492131i \(0.984329\pi\)
\(314\) 0 0
\(315\) −3.23903 + 5.95576i −0.182499 + 0.335569i
\(316\) 0 0
\(317\) 24.5696i 1.37997i −0.723825 0.689984i \(-0.757618\pi\)
0.723825 0.689984i \(-0.242382\pi\)
\(318\) 0 0
\(319\) 17.7799 0.995486
\(320\) 0 0
\(321\) −16.8841 −0.942378
\(322\) 0 0
\(323\) 0.509587i 0.0283542i
\(324\) 0 0
\(325\) −4.78365 + 3.09718i −0.265349 + 0.171800i
\(326\) 0 0
\(327\) 1.00505i 0.0555796i
\(328\) 0 0
\(329\) −18.2030 −1.00356
\(330\) 0 0
\(331\) 28.1837 1.54911 0.774557 0.632504i \(-0.217973\pi\)
0.774557 + 0.632504i \(0.217973\pi\)
\(332\) 0 0
\(333\) 2.36755i 0.129741i
\(334\) 0 0
\(335\) 1.06831 1.96436i 0.0583682 0.107324i
\(336\) 0 0
\(337\) 19.0449i 1.03744i 0.854944 + 0.518721i \(0.173592\pi\)
−0.854944 + 0.518721i \(0.826408\pi\)
\(338\) 0 0
\(339\) −7.58363 −0.411886
\(340\) 0 0
\(341\) 4.62708 0.250570
\(342\) 0 0
\(343\) 14.5760i 0.787030i
\(344\) 0 0
\(345\) 14.1179 + 7.67801i 0.760084 + 0.413370i
\(346\) 0 0
\(347\) 10.2409i 0.549762i −0.961478 0.274881i \(-0.911362\pi\)
0.961478 0.274881i \(-0.0886385\pi\)
\(348\) 0 0
\(349\) 22.2558 1.19132 0.595662 0.803235i \(-0.296890\pi\)
0.595662 + 0.803235i \(0.296890\pi\)
\(350\) 0 0
\(351\) −1.13975 −0.0608354
\(352\) 0 0
\(353\) 4.04721i 0.215411i −0.994183 0.107706i \(-0.965650\pi\)
0.994183 0.107706i \(-0.0343504\pi\)
\(354\) 0 0
\(355\) 10.3049 + 5.60432i 0.546929 + 0.297446i
\(356\) 0 0
\(357\) 0.867535i 0.0459148i
\(358\) 0 0
\(359\) −9.41735 −0.497029 −0.248514 0.968628i \(-0.579942\pi\)
−0.248514 + 0.968628i \(0.579942\pi\)
\(360\) 0 0
\(361\) −15.8283 −0.833067
\(362\) 0 0
\(363\) 6.93901i 0.364204i
\(364\) 0 0
\(365\) 8.68350 15.9668i 0.454515 0.835739i
\(366\) 0 0
\(367\) 29.5169i 1.54077i 0.637581 + 0.770384i \(0.279935\pi\)
−0.637581 + 0.770384i \(0.720065\pi\)
\(368\) 0 0
\(369\) −5.15374 −0.268293
\(370\) 0 0
\(371\) 27.9578 1.45150
\(372\) 0 0
\(373\) 5.77992i 0.299273i −0.988741 0.149636i \(-0.952190\pi\)
0.988741 0.149636i \(-0.0478103\pi\)
\(374\) 0 0
\(375\) 11.1477 0.854158i 0.575663 0.0441086i
\(376\) 0 0
\(377\) 10.0560i 0.517910i
\(378\) 0 0
\(379\) 17.4720 0.897478 0.448739 0.893663i \(-0.351873\pi\)
0.448739 + 0.893663i \(0.351873\pi\)
\(380\) 0 0
\(381\) −9.38467 −0.480791
\(382\) 0 0
\(383\) 26.6307i 1.36076i 0.732858 + 0.680382i \(0.238186\pi\)
−0.732858 + 0.680382i \(0.761814\pi\)
\(384\) 0 0
\(385\) 6.52726 12.0020i 0.332660 0.611678i
\(386\) 0 0
\(387\) 2.11893i 0.107711i
\(388\) 0 0
\(389\) −17.5671 −0.890687 −0.445343 0.895360i \(-0.646918\pi\)
−0.445343 + 0.895360i \(0.646918\pi\)
\(390\) 0 0
\(391\) −2.05646 −0.104000
\(392\) 0 0
\(393\) 16.3056i 0.822507i
\(394\) 0 0
\(395\) −26.1411 14.2168i −1.31530 0.715323i
\(396\) 0 0
\(397\) 21.6927i 1.08872i 0.838851 + 0.544362i \(0.183228\pi\)
−0.838851 + 0.544362i \(0.816772\pi\)
\(398\) 0 0
\(399\) 5.39963 0.270319
\(400\) 0 0
\(401\) −12.1350 −0.605992 −0.302996 0.952992i \(-0.597987\pi\)
−0.302996 + 0.952992i \(0.597987\pi\)
\(402\) 0 0
\(403\) 2.61698i 0.130361i
\(404\) 0 0
\(405\) 1.96436 + 1.06831i 0.0976098 + 0.0530849i
\(406\) 0 0
\(407\) 4.77107i 0.236493i
\(408\) 0 0
\(409\) −1.20024 −0.0593481 −0.0296740 0.999560i \(-0.509447\pi\)
−0.0296740 + 0.999560i \(0.509447\pi\)
\(410\) 0 0
\(411\) 16.0046 0.789447
\(412\) 0 0
\(413\) 17.6363i 0.867824i
\(414\) 0 0
\(415\) 10.0700 18.5162i 0.494316 0.908923i
\(416\) 0 0
\(417\) 6.81926i 0.333941i
\(418\) 0 0
\(419\) 1.86288 0.0910077 0.0455038 0.998964i \(-0.485511\pi\)
0.0455038 + 0.998964i \(0.485511\pi\)
\(420\) 0 0
\(421\) 26.6384 1.29828 0.649139 0.760670i \(-0.275130\pi\)
0.649139 + 0.760670i \(0.275130\pi\)
\(422\) 0 0
\(423\) 6.00381i 0.291915i
\(424\) 0 0
\(425\) −1.20094 + 0.777547i −0.0582540 + 0.0377166i
\(426\) 0 0
\(427\) 23.7843i 1.15101i
\(428\) 0 0
\(429\) 2.29682 0.110891
\(430\) 0 0
\(431\) −1.88140 −0.0906237 −0.0453118 0.998973i \(-0.514428\pi\)
−0.0453118 + 0.998973i \(0.514428\pi\)
\(432\) 0 0
\(433\) 15.6245i 0.750866i −0.926849 0.375433i \(-0.877494\pi\)
0.926849 0.375433i \(-0.122506\pi\)
\(434\) 0 0
\(435\) 9.42569 17.3315i 0.451927 0.830980i
\(436\) 0 0
\(437\) 12.7996i 0.612289i
\(438\) 0 0
\(439\) 8.78323 0.419201 0.209600 0.977787i \(-0.432784\pi\)
0.209600 + 0.977787i \(0.432784\pi\)
\(440\) 0 0
\(441\) 2.19247 0.104403
\(442\) 0 0
\(443\) 10.2846i 0.488636i −0.969695 0.244318i \(-0.921436\pi\)
0.969695 0.244318i \(-0.0785640\pi\)
\(444\) 0 0
\(445\) 3.79461 + 2.06369i 0.179882 + 0.0978285i
\(446\) 0 0
\(447\) 18.6381i 0.881553i
\(448\) 0 0
\(449\) 16.0066 0.755396 0.377698 0.925929i \(-0.376716\pi\)
0.377698 + 0.925929i \(0.376716\pi\)
\(450\) 0 0
\(451\) 10.3858 0.489047
\(452\) 0 0
\(453\) 1.11827i 0.0525410i
\(454\) 0 0
\(455\) 6.78808 + 3.69169i 0.318230 + 0.173069i
\(456\) 0 0
\(457\) 15.8643i 0.742101i −0.928613 0.371050i \(-0.878998\pi\)
0.928613 0.371050i \(-0.121002\pi\)
\(458\) 0 0
\(459\) −0.286135 −0.0133556
\(460\) 0 0
\(461\) −12.6941 −0.591225 −0.295613 0.955308i \(-0.595524\pi\)
−0.295613 + 0.955308i \(0.595524\pi\)
\(462\) 0 0
\(463\) 1.01404i 0.0471264i 0.999722 + 0.0235632i \(0.00750109\pi\)
−0.999722 + 0.0235632i \(0.992499\pi\)
\(464\) 0 0
\(465\) 2.45295 4.51036i 0.113753 0.209163i
\(466\) 0 0
\(467\) 12.0950i 0.559690i −0.960045 0.279845i \(-0.909717\pi\)
0.960045 0.279845i \(-0.0902831\pi\)
\(468\) 0 0
\(469\) −3.03191 −0.140001
\(470\) 0 0
\(471\) 0.581889 0.0268120
\(472\) 0 0
\(473\) 4.27005i 0.196337i
\(474\) 0 0
\(475\) −4.83953 7.47475i −0.222053 0.342965i
\(476\) 0 0
\(477\) 9.22119i 0.422209i
\(478\) 0 0
\(479\) −28.1334 −1.28545 −0.642724 0.766097i \(-0.722196\pi\)
−0.642724 + 0.766097i \(0.722196\pi\)
\(480\) 0 0
\(481\) −2.69842 −0.123037
\(482\) 0 0
\(483\) 21.7904i 0.991500i
\(484\) 0 0
\(485\) −6.40091 + 11.7697i −0.290650 + 0.534433i
\(486\) 0 0
\(487\) 4.12111i 0.186745i −0.995631 0.0933726i \(-0.970235\pi\)
0.995631 0.0933726i \(-0.0297648\pi\)
\(488\) 0 0
\(489\) −6.09462 −0.275608
\(490\) 0 0
\(491\) −35.7563 −1.61366 −0.806830 0.590784i \(-0.798818\pi\)
−0.806830 + 0.590784i \(0.798818\pi\)
\(492\) 0 0
\(493\) 2.52456i 0.113700i
\(494\) 0 0
\(495\) −3.95856 2.15285i −0.177924 0.0967636i
\(496\) 0 0
\(497\) 15.9052i 0.713447i
\(498\) 0 0
\(499\) 3.35528 0.150203 0.0751014 0.997176i \(-0.476072\pi\)
0.0751014 + 0.997176i \(0.476072\pi\)
\(500\) 0 0
\(501\) −1.44027 −0.0643465
\(502\) 0 0
\(503\) 5.41068i 0.241250i 0.992698 + 0.120625i \(0.0384899\pi\)
−0.992698 + 0.120625i \(0.961510\pi\)
\(504\) 0 0
\(505\) −1.38835 0.755050i −0.0617806 0.0335993i
\(506\) 0 0
\(507\) 11.7010i 0.519658i
\(508\) 0 0
\(509\) −3.12069 −0.138322 −0.0691611 0.997606i \(-0.522032\pi\)
−0.0691611 + 0.997606i \(0.522032\pi\)
\(510\) 0 0
\(511\) −24.6441 −1.09019
\(512\) 0 0
\(513\) 1.78093i 0.0786301i
\(514\) 0 0
\(515\) 0.466967 0.858634i 0.0205770 0.0378359i
\(516\) 0 0
\(517\) 12.0988i 0.532105i
\(518\) 0 0
\(519\) 15.1024 0.662920
\(520\) 0 0
\(521\) 17.5687 0.769698 0.384849 0.922980i \(-0.374254\pi\)
0.384849 + 0.922980i \(0.374254\pi\)
\(522\) 0 0
\(523\) 12.2164i 0.534185i 0.963671 + 0.267093i \(0.0860630\pi\)
−0.963671 + 0.267093i \(0.913937\pi\)
\(524\) 0 0
\(525\) −8.23895 12.7252i −0.359577 0.555375i
\(526\) 0 0
\(527\) 0.656994i 0.0286191i
\(528\) 0 0
\(529\) −28.6535 −1.24581
\(530\) 0 0
\(531\) −5.81688 −0.252431
\(532\) 0 0
\(533\) 5.87399i 0.254431i
\(534\) 0 0
\(535\) 18.0375 33.1664i 0.779829 1.43391i
\(536\) 0 0
\(537\) 12.0255i 0.518937i
\(538\) 0 0
\(539\) −4.41824 −0.190307
\(540\) 0 0
\(541\) 15.0129 0.645457 0.322728 0.946492i \(-0.395400\pi\)
0.322728 + 0.946492i \(0.395400\pi\)
\(542\) 0 0
\(543\) 19.1277i 0.820849i
\(544\) 0 0
\(545\) 1.97429 + 1.07371i 0.0845692 + 0.0459928i
\(546\) 0 0
\(547\) 28.6577i 1.22531i 0.790349 + 0.612657i \(0.209899\pi\)
−0.790349 + 0.612657i \(0.790101\pi\)
\(548\) 0 0
\(549\) −7.84468 −0.334803
\(550\) 0 0
\(551\) −15.7131 −0.669401
\(552\) 0 0
\(553\) 40.3477i 1.71576i
\(554\) 0 0
\(555\) 4.65072 + 2.52929i 0.197412 + 0.107362i
\(556\) 0 0
\(557\) 11.1937i 0.474294i −0.971474 0.237147i \(-0.923788\pi\)
0.971474 0.237147i \(-0.0762123\pi\)
\(558\) 0 0
\(559\) 2.41505 0.102146
\(560\) 0 0
\(561\) 0.576616 0.0243447
\(562\) 0 0
\(563\) 10.1174i 0.426397i 0.977009 + 0.213198i \(0.0683881\pi\)
−0.977009 + 0.213198i \(0.931612\pi\)
\(564\) 0 0
\(565\) 8.10169 14.8970i 0.340841 0.626720i
\(566\) 0 0
\(567\) 3.03191i 0.127328i
\(568\) 0 0
\(569\) −31.0516 −1.30175 −0.650875 0.759185i \(-0.725598\pi\)
−0.650875 + 0.759185i \(0.725598\pi\)
\(570\) 0 0
\(571\) −1.08661 −0.0454731 −0.0227366 0.999741i \(-0.507238\pi\)
−0.0227366 + 0.999741i \(0.507238\pi\)
\(572\) 0 0
\(573\) 0.785469i 0.0328134i
\(574\) 0 0
\(575\) −30.1647 + 19.5302i −1.25796 + 0.814464i
\(576\) 0 0
\(577\) 10.2750i 0.427754i 0.976861 + 0.213877i \(0.0686092\pi\)
−0.976861 + 0.213877i \(0.931391\pi\)
\(578\) 0 0
\(579\) 3.88940 0.161638
\(580\) 0 0
\(581\) −28.5790 −1.18566
\(582\) 0 0
\(583\) 18.5825i 0.769607i
\(584\) 0 0
\(585\) 1.21761 2.23888i 0.0503420 0.0925663i
\(586\) 0 0
\(587\) 1.27942i 0.0528072i −0.999651 0.0264036i \(-0.991594\pi\)
0.999651 0.0264036i \(-0.00840550\pi\)
\(588\) 0 0
\(589\) −4.08920 −0.168493
\(590\) 0 0
\(591\) −17.5055 −0.720079
\(592\) 0 0
\(593\) 17.8438i 0.732757i −0.930466 0.366378i \(-0.880598\pi\)
0.930466 0.366378i \(-0.119402\pi\)
\(594\) 0 0
\(595\) 1.70415 + 0.926799i 0.0698633 + 0.0379950i
\(596\) 0 0
\(597\) 7.28359i 0.298098i
\(598\) 0 0
\(599\) −11.5071 −0.470167 −0.235084 0.971975i \(-0.575536\pi\)
−0.235084 + 0.971975i \(0.575536\pi\)
\(600\) 0 0
\(601\) 28.9325 1.18018 0.590090 0.807337i \(-0.299092\pi\)
0.590090 + 0.807337i \(0.299092\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −13.6307 7.41303i −0.554167 0.301383i
\(606\) 0 0
\(607\) 12.9942i 0.527418i 0.964602 + 0.263709i \(0.0849458\pi\)
−0.964602 + 0.263709i \(0.915054\pi\)
\(608\) 0 0
\(609\) −26.7504 −1.08398
\(610\) 0 0
\(611\) 6.84285 0.276832
\(612\) 0 0
\(613\) 43.0239i 1.73772i 0.495059 + 0.868859i \(0.335146\pi\)
−0.495059 + 0.868859i \(0.664854\pi\)
\(614\) 0 0
\(615\) 5.50581 10.1238i 0.222016 0.408231i
\(616\) 0 0
\(617\) 38.0193i 1.53060i 0.643675 + 0.765299i \(0.277409\pi\)
−0.643675 + 0.765299i \(0.722591\pi\)
\(618\) 0 0
\(619\) −32.5438 −1.30804 −0.654022 0.756475i \(-0.726920\pi\)
−0.654022 + 0.756475i \(0.726920\pi\)
\(620\) 0 0
\(621\) −7.18704 −0.288406
\(622\) 0 0
\(623\) 5.85683i 0.234649i
\(624\) 0 0
\(625\) −10.2313 + 22.8105i −0.409253 + 0.912421i
\(626\) 0 0
\(627\) 3.58892i 0.143328i
\(628\) 0 0
\(629\) −0.677439 −0.0270113
\(630\) 0 0
\(631\) 19.9220 0.793082 0.396541 0.918017i \(-0.370210\pi\)
0.396541 + 0.918017i \(0.370210\pi\)
\(632\) 0 0
\(633\) 3.44237i 0.136822i
\(634\) 0 0
\(635\) 10.0258 18.4349i 0.397860 0.731565i
\(636\) 0 0
\(637\) 2.49887i 0.0990089i
\(638\) 0 0
\(639\) −5.24595 −0.207526
\(640\) 0 0
\(641\) 46.5081 1.83696 0.918479 0.395470i \(-0.129418\pi\)
0.918479 + 0.395470i \(0.129418\pi\)
\(642\) 0 0
\(643\) 19.6172i 0.773627i 0.922158 + 0.386813i \(0.126424\pi\)
−0.922158 + 0.386813i \(0.873576\pi\)
\(644\) 0 0
\(645\) −4.16234 2.26368i −0.163892 0.0891324i
\(646\) 0 0
\(647\) 22.8812i 0.899551i 0.893142 + 0.449776i \(0.148496\pi\)
−0.893142 + 0.449776i \(0.851504\pi\)
\(648\) 0 0
\(649\) 11.7221 0.460134
\(650\) 0 0
\(651\) −6.96156 −0.272845
\(652\) 0 0
\(653\) 17.4979i 0.684747i 0.939564 + 0.342373i \(0.111231\pi\)
−0.939564 + 0.342373i \(0.888769\pi\)
\(654\) 0 0
\(655\) 32.0300 + 17.4194i 1.25151 + 0.680634i
\(656\) 0 0
\(657\) 8.12823i 0.317112i
\(658\) 0 0
\(659\) −33.7414 −1.31438 −0.657190 0.753725i \(-0.728255\pi\)
−0.657190 + 0.753725i \(0.728255\pi\)
\(660\) 0 0
\(661\) −16.3764 −0.636967 −0.318484 0.947928i \(-0.603174\pi\)
−0.318484 + 0.947928i \(0.603174\pi\)
\(662\) 0 0
\(663\) 0.326123i 0.0126656i
\(664\) 0 0
\(665\) −5.76849 + 10.6068i −0.223692 + 0.411314i
\(666\) 0 0
\(667\) 63.4110i 2.45528i
\(668\) 0 0
\(669\) 2.03546 0.0786953
\(670\) 0 0
\(671\) 15.8085 0.610281
\(672\) 0 0
\(673\) 6.66168i 0.256789i −0.991723 0.128395i \(-0.959018\pi\)
0.991723 0.128395i \(-0.0409824\pi\)
\(674\) 0 0
\(675\) −4.19710 + 2.71741i −0.161547 + 0.104593i
\(676\) 0 0
\(677\) 17.0720i 0.656129i −0.944655 0.328064i \(-0.893604\pi\)
0.944655 0.328064i \(-0.106396\pi\)
\(678\) 0 0
\(679\) 18.1660 0.697147
\(680\) 0 0
\(681\) 2.69664 0.103335
\(682\) 0 0
\(683\) 20.3173i 0.777420i −0.921360 0.388710i \(-0.872921\pi\)
0.921360 0.388710i \(-0.127079\pi\)
\(684\) 0 0
\(685\) −17.0979 + 31.4387i −0.653276 + 1.20121i
\(686\) 0 0
\(687\) 20.5001i 0.782127i
\(688\) 0 0
\(689\) −10.5099 −0.400394
\(690\) 0 0
\(691\) −21.0742 −0.801700 −0.400850 0.916144i \(-0.631285\pi\)
−0.400850 + 0.916144i \(0.631285\pi\)
\(692\) 0 0
\(693\) 6.10987i 0.232095i
\(694\) 0 0
\(695\) −13.3955 7.28511i −0.508120 0.276340i
\(696\) 0 0
\(697\) 1.47467i 0.0558569i
\(698\) 0 0
\(699\) −14.0115 −0.529965
\(700\) 0 0
\(701\) 51.1935 1.93355 0.966775 0.255628i \(-0.0822824\pi\)
0.966775 + 0.255628i \(0.0822824\pi\)
\(702\) 0 0
\(703\) 4.21645i 0.159026i
\(704\) 0 0
\(705\) −11.7936 6.41395i −0.444174 0.241563i
\(706\) 0 0
\(707\) 2.14286i 0.0805905i
\(708\) 0 0
\(709\) −36.5172 −1.37143 −0.685717 0.727869i \(-0.740511\pi\)
−0.685717 + 0.727869i \(0.740511\pi\)
\(710\) 0 0
\(711\) 13.3077 0.499077
\(712\) 0 0
\(713\) 16.5022i 0.618011i
\(714\) 0 0
\(715\) −2.45372 + 4.51177i −0.0917639 + 0.168731i
\(716\) 0 0
\(717\) 18.8898i 0.705453i
\(718\) 0 0
\(719\) 26.7800 0.998724 0.499362 0.866393i \(-0.333568\pi\)
0.499362 + 0.866393i \(0.333568\pi\)
\(720\) 0 0
\(721\) −1.32527 −0.0493555
\(722\) 0 0
\(723\) 5.81348i 0.216206i
\(724\) 0 0
\(725\) 23.9756 + 37.0309i 0.890433 + 1.37529i
\(726\) 0 0
\(727\) 31.7238i 1.17657i 0.808653 + 0.588286i \(0.200197\pi\)
−0.808653 + 0.588286i \(0.799803\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0.606300 0.0224248
\(732\) 0 0
\(733\) 27.7555i 1.02517i −0.858636 0.512586i \(-0.828688\pi\)
0.858636 0.512586i \(-0.171312\pi\)
\(734\) 0 0
\(735\) −2.34224 + 4.30680i −0.0863950 + 0.158859i
\(736\) 0 0
\(737\) 2.01519i 0.0742305i
\(738\) 0 0
\(739\) 7.32633 0.269503 0.134752 0.990879i \(-0.456976\pi\)
0.134752 + 0.990879i \(0.456976\pi\)
\(740\) 0 0
\(741\) −2.02982 −0.0745673
\(742\) 0 0
\(743\) 7.64123i 0.280329i 0.990128 + 0.140165i \(0.0447632\pi\)
−0.990128 + 0.140165i \(0.955237\pi\)
\(744\) 0 0
\(745\) −36.6120 19.9114i −1.34136 0.729496i
\(746\) 0 0
\(747\) 9.42607i 0.344882i
\(748\) 0 0
\(749\) −51.1910 −1.87048
\(750\) 0 0
\(751\) −13.7049 −0.500098 −0.250049 0.968233i \(-0.580447\pi\)
−0.250049 + 0.968233i \(0.580447\pi\)
\(752\) 0 0
\(753\) 21.5194i 0.784211i
\(754\) 0 0
\(755\) 2.19669 + 1.19466i 0.0799456 + 0.0434783i
\(756\) 0 0
\(757\) 6.05817i 0.220188i 0.993921 + 0.110094i \(0.0351152\pi\)
−0.993921 + 0.110094i \(0.964885\pi\)
\(758\) 0 0
\(759\) 14.4832 0.525709
\(760\) 0 0
\(761\) 13.7656 0.499004 0.249502 0.968374i \(-0.419733\pi\)
0.249502 + 0.968374i \(0.419733\pi\)
\(762\) 0 0
\(763\) 3.04723i 0.110317i
\(764\) 0 0
\(765\) 0.305682 0.562071i 0.0110519 0.0203217i
\(766\) 0 0
\(767\) 6.62980i 0.239388i
\(768\) 0 0
\(769\) −52.3289 −1.88703 −0.943515 0.331330i \(-0.892503\pi\)
−0.943515 + 0.331330i \(0.892503\pi\)
\(770\) 0 0
\(771\) 21.8474 0.786816
\(772\) 0 0
\(773\) 13.6707i 0.491700i −0.969308 0.245850i \(-0.920933\pi\)
0.969308 0.245850i \(-0.0790670\pi\)
\(774\) 0 0
\(775\) 6.23945 + 9.63696i 0.224128 + 0.346170i
\(776\) 0 0
\(777\) 7.17820i 0.257516i
\(778\) 0 0
\(779\) −9.17847 −0.328853
\(780\) 0 0
\(781\) 10.5716 0.378281
\(782\) 0 0
\(783\) 8.82296i 0.315307i
\(784\) 0 0
\(785\) −0.621640 + 1.14304i −0.0221873 + 0.0407968i
\(786\) 0 0
\(787\) 9.49527i 0.338470i 0.985576 + 0.169235i \(0.0541297\pi\)
−0.985576 + 0.169235i \(0.945870\pi\)
\(788\) 0 0
\(789\) −4.11910 −0.146644
\(790\) 0 0
\(791\) −22.9929 −0.817532
\(792\) 0