Properties

Label 4020.2.g.c.1609.4
Level 4020
Weight 2
Character 4020.1609
Analytic conductor 32.100
Analytic rank 0
Dimension 38
CM No

Related objects

Downloads

Learn more about

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 1609.4
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.23

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(-2.02556 - 0.947153i) q^{5}\) \(+2.95752i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(-2.02556 - 0.947153i) q^{5}\) \(+2.95752i q^{7}\) \(-1.00000 q^{9}\) \(+2.74672 q^{11}\) \(-5.48947i q^{13}\) \(+(-0.947153 + 2.02556i) q^{15}\) \(-0.836518i q^{17}\) \(-7.78037 q^{19}\) \(+2.95752 q^{21}\) \(-1.14420i q^{23}\) \(+(3.20580 + 3.83703i) q^{25}\) \(+1.00000i q^{27}\) \(+3.28812 q^{29}\) \(+5.40904 q^{31}\) \(-2.74672i q^{33}\) \(+(2.80122 - 5.99064i) q^{35}\) \(+4.63135i q^{37}\) \(-5.48947 q^{39}\) \(+1.97291 q^{41}\) \(-5.74443i q^{43}\) \(+(2.02556 + 0.947153i) q^{45}\) \(-2.67357i q^{47}\) \(-1.74693 q^{49}\) \(-0.836518 q^{51}\) \(+3.93268i q^{53}\) \(+(-5.56366 - 2.60157i) q^{55}\) \(+7.78037i q^{57}\) \(-12.2982 q^{59}\) \(-8.93068 q^{61}\) \(-2.95752i q^{63}\) \(+(-5.19937 + 11.1193i) q^{65}\) \(-1.00000i q^{67}\) \(-1.14420 q^{69}\) \(-5.94317 q^{71}\) \(+0.964685i q^{73}\) \(+(3.83703 - 3.20580i) q^{75}\) \(+8.12349i q^{77}\) \(-12.7034 q^{79}\) \(+1.00000 q^{81}\) \(-9.18552i q^{83}\) \(+(-0.792310 + 1.69442i) q^{85}\) \(-3.28812i q^{87}\) \(+8.47078 q^{89}\) \(+16.2352 q^{91}\) \(-5.40904i q^{93}\) \(+(15.7596 + 7.36920i) q^{95}\) \(-2.98952i q^{97}\) \(-2.74672 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −2.02556 0.947153i −0.905859 0.423580i
\(6\) 0 0
\(7\) 2.95752i 1.11784i 0.829222 + 0.558919i \(0.188784\pi\)
−0.829222 + 0.558919i \(0.811216\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 2.74672 0.828169 0.414084 0.910239i \(-0.364102\pi\)
0.414084 + 0.910239i \(0.364102\pi\)
\(12\) 0 0
\(13\) 5.48947i 1.52251i −0.648455 0.761253i \(-0.724584\pi\)
0.648455 0.761253i \(-0.275416\pi\)
\(14\) 0 0
\(15\) −0.947153 + 2.02556i −0.244554 + 0.522998i
\(16\) 0 0
\(17\) 0.836518i 0.202885i −0.994841 0.101443i \(-0.967654\pi\)
0.994841 0.101443i \(-0.0323458\pi\)
\(18\) 0 0
\(19\) −7.78037 −1.78494 −0.892469 0.451108i \(-0.851029\pi\)
−0.892469 + 0.451108i \(0.851029\pi\)
\(20\) 0 0
\(21\) 2.95752 0.645384
\(22\) 0 0
\(23\) 1.14420i 0.238583i −0.992859 0.119291i \(-0.961938\pi\)
0.992859 0.119291i \(-0.0380623\pi\)
\(24\) 0 0
\(25\) 3.20580 + 3.83703i 0.641160 + 0.767407i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 3.28812 0.610589 0.305295 0.952258i \(-0.401245\pi\)
0.305295 + 0.952258i \(0.401245\pi\)
\(30\) 0 0
\(31\) 5.40904 0.971493 0.485746 0.874100i \(-0.338548\pi\)
0.485746 + 0.874100i \(0.338548\pi\)
\(32\) 0 0
\(33\) 2.74672i 0.478143i
\(34\) 0 0
\(35\) 2.80122 5.99064i 0.473493 1.01260i
\(36\) 0 0
\(37\) 4.63135i 0.761389i 0.924701 + 0.380695i \(0.124315\pi\)
−0.924701 + 0.380695i \(0.875685\pi\)
\(38\) 0 0
\(39\) −5.48947 −0.879019
\(40\) 0 0
\(41\) 1.97291 0.308117 0.154059 0.988062i \(-0.450766\pi\)
0.154059 + 0.988062i \(0.450766\pi\)
\(42\) 0 0
\(43\) 5.74443i 0.876017i −0.898971 0.438009i \(-0.855684\pi\)
0.898971 0.438009i \(-0.144316\pi\)
\(44\) 0 0
\(45\) 2.02556 + 0.947153i 0.301953 + 0.141193i
\(46\) 0 0
\(47\) 2.67357i 0.389980i −0.980805 0.194990i \(-0.937533\pi\)
0.980805 0.194990i \(-0.0624675\pi\)
\(48\) 0 0
\(49\) −1.74693 −0.249561
\(50\) 0 0
\(51\) −0.836518 −0.117136
\(52\) 0 0
\(53\) 3.93268i 0.540196i 0.962833 + 0.270098i \(0.0870561\pi\)
−0.962833 + 0.270098i \(0.912944\pi\)
\(54\) 0 0
\(55\) −5.56366 2.60157i −0.750204 0.350796i
\(56\) 0 0
\(57\) 7.78037i 1.03053i
\(58\) 0 0
\(59\) −12.2982 −1.60109 −0.800543 0.599276i \(-0.795455\pi\)
−0.800543 + 0.599276i \(0.795455\pi\)
\(60\) 0 0
\(61\) −8.93068 −1.14346 −0.571728 0.820443i \(-0.693727\pi\)
−0.571728 + 0.820443i \(0.693727\pi\)
\(62\) 0 0
\(63\) 2.95752i 0.372613i
\(64\) 0 0
\(65\) −5.19937 + 11.1193i −0.644903 + 1.37918i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −1.14420 −0.137746
\(70\) 0 0
\(71\) −5.94317 −0.705325 −0.352662 0.935751i \(-0.614724\pi\)
−0.352662 + 0.935751i \(0.614724\pi\)
\(72\) 0 0
\(73\) 0.964685i 0.112908i 0.998405 + 0.0564539i \(0.0179794\pi\)
−0.998405 + 0.0564539i \(0.982021\pi\)
\(74\) 0 0
\(75\) 3.83703 3.20580i 0.443063 0.370174i
\(76\) 0 0
\(77\) 8.12349i 0.925758i
\(78\) 0 0
\(79\) −12.7034 −1.42924 −0.714621 0.699512i \(-0.753401\pi\)
−0.714621 + 0.699512i \(0.753401\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 9.18552i 1.00824i −0.863633 0.504121i \(-0.831817\pi\)
0.863633 0.504121i \(-0.168183\pi\)
\(84\) 0 0
\(85\) −0.792310 + 1.69442i −0.0859381 + 0.183785i
\(86\) 0 0
\(87\) 3.28812i 0.352524i
\(88\) 0 0
\(89\) 8.47078 0.897901 0.448950 0.893557i \(-0.351798\pi\)
0.448950 + 0.893557i \(0.351798\pi\)
\(90\) 0 0
\(91\) 16.2352 1.70191
\(92\) 0 0
\(93\) 5.40904i 0.560892i
\(94\) 0 0
\(95\) 15.7596 + 7.36920i 1.61690 + 0.756064i
\(96\) 0 0
\(97\) 2.98952i 0.303539i −0.988416 0.151770i \(-0.951503\pi\)
0.988416 0.151770i \(-0.0484972\pi\)
\(98\) 0 0
\(99\) −2.74672 −0.276056
\(100\) 0 0
\(101\) −8.23279 −0.819194 −0.409597 0.912267i \(-0.634331\pi\)
−0.409597 + 0.912267i \(0.634331\pi\)
\(102\) 0 0
\(103\) 4.19798i 0.413639i −0.978379 0.206819i \(-0.933689\pi\)
0.978379 0.206819i \(-0.0663113\pi\)
\(104\) 0 0
\(105\) −5.99064 2.80122i −0.584627 0.273372i
\(106\) 0 0
\(107\) 1.91266i 0.184904i 0.995717 + 0.0924519i \(0.0294704\pi\)
−0.995717 + 0.0924519i \(0.970530\pi\)
\(108\) 0 0
\(109\) −7.87248 −0.754047 −0.377024 0.926204i \(-0.623052\pi\)
−0.377024 + 0.926204i \(0.623052\pi\)
\(110\) 0 0
\(111\) 4.63135 0.439588
\(112\) 0 0
\(113\) 18.9099i 1.77890i 0.457036 + 0.889448i \(0.348911\pi\)
−0.457036 + 0.889448i \(0.651089\pi\)
\(114\) 0 0
\(115\) −1.08374 + 2.31765i −0.101059 + 0.216122i
\(116\) 0 0
\(117\) 5.48947i 0.507502i
\(118\) 0 0
\(119\) 2.47402 0.226793
\(120\) 0 0
\(121\) −3.45550 −0.314137
\(122\) 0 0
\(123\) 1.97291i 0.177892i
\(124\) 0 0
\(125\) −2.85929 10.8085i −0.255743 0.966745i
\(126\) 0 0
\(127\) 0.152806i 0.0135593i −0.999977 0.00677966i \(-0.997842\pi\)
0.999977 0.00677966i \(-0.00215805\pi\)
\(128\) 0 0
\(129\) −5.74443 −0.505769
\(130\) 0 0
\(131\) −12.4130 −1.08453 −0.542265 0.840208i \(-0.682433\pi\)
−0.542265 + 0.840208i \(0.682433\pi\)
\(132\) 0 0
\(133\) 23.0106i 1.99527i
\(134\) 0 0
\(135\) 0.947153 2.02556i 0.0815180 0.174333i
\(136\) 0 0
\(137\) 8.99009i 0.768075i 0.923317 + 0.384038i \(0.125467\pi\)
−0.923317 + 0.384038i \(0.874533\pi\)
\(138\) 0 0
\(139\) −22.8040 −1.93421 −0.967104 0.254380i \(-0.918128\pi\)
−0.967104 + 0.254380i \(0.918128\pi\)
\(140\) 0 0
\(141\) −2.67357 −0.225155
\(142\) 0 0
\(143\) 15.0781i 1.26089i
\(144\) 0 0
\(145\) −6.66030 3.11436i −0.553108 0.258633i
\(146\) 0 0
\(147\) 1.74693i 0.144084i
\(148\) 0 0
\(149\) 5.72732 0.469200 0.234600 0.972092i \(-0.424622\pi\)
0.234600 + 0.972092i \(0.424622\pi\)
\(150\) 0 0
\(151\) −13.3074 −1.08294 −0.541471 0.840720i \(-0.682132\pi\)
−0.541471 + 0.840720i \(0.682132\pi\)
\(152\) 0 0
\(153\) 0.836518i 0.0676284i
\(154\) 0 0
\(155\) −10.9564 5.12319i −0.880035 0.411505i
\(156\) 0 0
\(157\) 17.9141i 1.42970i −0.699276 0.714852i \(-0.746494\pi\)
0.699276 0.714852i \(-0.253506\pi\)
\(158\) 0 0
\(159\) 3.93268 0.311882
\(160\) 0 0
\(161\) 3.38400 0.266697
\(162\) 0 0
\(163\) 13.5544i 1.06167i 0.847476 + 0.530833i \(0.178121\pi\)
−0.847476 + 0.530833i \(0.821879\pi\)
\(164\) 0 0
\(165\) −2.60157 + 5.56366i −0.202532 + 0.433130i
\(166\) 0 0
\(167\) 14.9256i 1.15498i 0.816398 + 0.577490i \(0.195968\pi\)
−0.816398 + 0.577490i \(0.804032\pi\)
\(168\) 0 0
\(169\) −17.1343 −1.31802
\(170\) 0 0
\(171\) 7.78037 0.594980
\(172\) 0 0
\(173\) 15.4705i 1.17620i 0.808787 + 0.588102i \(0.200125\pi\)
−0.808787 + 0.588102i \(0.799875\pi\)
\(174\) 0 0
\(175\) −11.3481 + 9.48122i −0.857836 + 0.716713i
\(176\) 0 0
\(177\) 12.2982i 0.924387i
\(178\) 0 0
\(179\) 16.5415 1.23637 0.618185 0.786032i \(-0.287868\pi\)
0.618185 + 0.786032i \(0.287868\pi\)
\(180\) 0 0
\(181\) −15.9855 −1.18819 −0.594096 0.804394i \(-0.702490\pi\)
−0.594096 + 0.804394i \(0.702490\pi\)
\(182\) 0 0
\(183\) 8.93068i 0.660175i
\(184\) 0 0
\(185\) 4.38660 9.38108i 0.322509 0.689711i
\(186\) 0 0
\(187\) 2.29768i 0.168023i
\(188\) 0 0
\(189\) −2.95752 −0.215128
\(190\) 0 0
\(191\) −9.89989 −0.716331 −0.358166 0.933658i \(-0.616598\pi\)
−0.358166 + 0.933658i \(0.616598\pi\)
\(192\) 0 0
\(193\) 13.9755i 1.00598i −0.864292 0.502990i \(-0.832233\pi\)
0.864292 0.502990i \(-0.167767\pi\)
\(194\) 0 0
\(195\) 11.1193 + 5.19937i 0.796267 + 0.372335i
\(196\) 0 0
\(197\) 5.47194i 0.389859i 0.980817 + 0.194930i \(0.0624479\pi\)
−0.980817 + 0.194930i \(0.937552\pi\)
\(198\) 0 0
\(199\) 2.21401 0.156947 0.0784736 0.996916i \(-0.474995\pi\)
0.0784736 + 0.996916i \(0.474995\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 9.72469i 0.682540i
\(204\) 0 0
\(205\) −3.99626 1.86865i −0.279111 0.130512i
\(206\) 0 0
\(207\) 1.14420i 0.0795276i
\(208\) 0 0
\(209\) −21.3705 −1.47823
\(210\) 0 0
\(211\) −28.0506 −1.93108 −0.965542 0.260249i \(-0.916195\pi\)
−0.965542 + 0.260249i \(0.916195\pi\)
\(212\) 0 0
\(213\) 5.94317i 0.407219i
\(214\) 0 0
\(215\) −5.44086 + 11.6357i −0.371063 + 0.793548i
\(216\) 0 0
\(217\) 15.9974i 1.08597i
\(218\) 0 0
\(219\) 0.964685 0.0651873
\(220\) 0 0
\(221\) −4.59204 −0.308894
\(222\) 0 0
\(223\) 1.83158i 0.122652i −0.998118 0.0613258i \(-0.980467\pi\)
0.998118 0.0613258i \(-0.0195329\pi\)
\(224\) 0 0
\(225\) −3.20580 3.83703i −0.213720 0.255802i
\(226\) 0 0
\(227\) 13.2018i 0.876232i −0.898919 0.438116i \(-0.855646\pi\)
0.898919 0.438116i \(-0.144354\pi\)
\(228\) 0 0
\(229\) −12.7004 −0.839269 −0.419634 0.907693i \(-0.637842\pi\)
−0.419634 + 0.907693i \(0.637842\pi\)
\(230\) 0 0
\(231\) 8.12349 0.534487
\(232\) 0 0
\(233\) 13.7551i 0.901129i 0.892744 + 0.450564i \(0.148777\pi\)
−0.892744 + 0.450564i \(0.851223\pi\)
\(234\) 0 0
\(235\) −2.53228 + 5.41548i −0.165188 + 0.353267i
\(236\) 0 0
\(237\) 12.7034i 0.825173i
\(238\) 0 0
\(239\) 3.29614 0.213210 0.106605 0.994301i \(-0.466002\pi\)
0.106605 + 0.994301i \(0.466002\pi\)
\(240\) 0 0
\(241\) 0.789127 0.0508321 0.0254161 0.999677i \(-0.491909\pi\)
0.0254161 + 0.999677i \(0.491909\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 3.53851 + 1.65461i 0.226067 + 0.105709i
\(246\) 0 0
\(247\) 42.7101i 2.71758i
\(248\) 0 0
\(249\) −9.18552 −0.582108
\(250\) 0 0
\(251\) 18.4247 1.16295 0.581477 0.813563i \(-0.302475\pi\)
0.581477 + 0.813563i \(0.302475\pi\)
\(252\) 0 0
\(253\) 3.14281i 0.197587i
\(254\) 0 0
\(255\) 1.69442 + 0.792310i 0.106109 + 0.0496164i
\(256\) 0 0
\(257\) 24.3790i 1.52072i 0.649502 + 0.760360i \(0.274977\pi\)
−0.649502 + 0.760360i \(0.725023\pi\)
\(258\) 0 0
\(259\) −13.6973 −0.851109
\(260\) 0 0
\(261\) −3.28812 −0.203530
\(262\) 0 0
\(263\) 16.1653i 0.996796i 0.866948 + 0.498398i \(0.166078\pi\)
−0.866948 + 0.498398i \(0.833922\pi\)
\(264\) 0 0
\(265\) 3.72485 7.96589i 0.228816 0.489341i
\(266\) 0 0
\(267\) 8.47078i 0.518403i
\(268\) 0 0
\(269\) 16.3842 0.998961 0.499481 0.866325i \(-0.333524\pi\)
0.499481 + 0.866325i \(0.333524\pi\)
\(270\) 0 0
\(271\) 12.4620 0.757015 0.378508 0.925598i \(-0.376437\pi\)
0.378508 + 0.925598i \(0.376437\pi\)
\(272\) 0 0
\(273\) 16.2352i 0.982601i
\(274\) 0 0
\(275\) 8.80545 + 10.5393i 0.530989 + 0.635542i
\(276\) 0 0
\(277\) 16.7278i 1.00507i −0.864556 0.502537i \(-0.832400\pi\)
0.864556 0.502537i \(-0.167600\pi\)
\(278\) 0 0
\(279\) −5.40904 −0.323831
\(280\) 0 0
\(281\) −5.16809 −0.308302 −0.154151 0.988047i \(-0.549264\pi\)
−0.154151 + 0.988047i \(0.549264\pi\)
\(282\) 0 0
\(283\) 12.1242i 0.720707i −0.932816 0.360354i \(-0.882656\pi\)
0.932816 0.360354i \(-0.117344\pi\)
\(284\) 0 0
\(285\) 7.36920 15.7596i 0.436514 0.933519i
\(286\) 0 0
\(287\) 5.83493i 0.344425i
\(288\) 0 0
\(289\) 16.3002 0.958838
\(290\) 0 0
\(291\) −2.98952 −0.175248
\(292\) 0 0
\(293\) 30.9443i 1.80779i 0.427759 + 0.903893i \(0.359303\pi\)
−0.427759 + 0.903893i \(0.640697\pi\)
\(294\) 0 0
\(295\) 24.9107 + 11.6483i 1.45036 + 0.678188i
\(296\) 0 0
\(297\) 2.74672i 0.159381i
\(298\) 0 0
\(299\) −6.28107 −0.363244
\(300\) 0 0
\(301\) 16.9893 0.979245
\(302\) 0 0
\(303\) 8.23279i 0.472962i
\(304\) 0 0
\(305\) 18.0896 + 8.45872i 1.03581 + 0.484345i
\(306\) 0 0
\(307\) 9.72403i 0.554980i −0.960729 0.277490i \(-0.910497\pi\)
0.960729 0.277490i \(-0.0895025\pi\)
\(308\) 0 0
\(309\) −4.19798 −0.238815
\(310\) 0 0
\(311\) −33.3633 −1.89186 −0.945929 0.324373i \(-0.894847\pi\)
−0.945929 + 0.324373i \(0.894847\pi\)
\(312\) 0 0
\(313\) 7.42253i 0.419546i 0.977750 + 0.209773i \(0.0672726\pi\)
−0.977750 + 0.209773i \(0.932727\pi\)
\(314\) 0 0
\(315\) −2.80122 + 5.99064i −0.157831 + 0.337534i
\(316\) 0 0
\(317\) 33.8359i 1.90041i −0.311623 0.950206i \(-0.600873\pi\)
0.311623 0.950206i \(-0.399127\pi\)
\(318\) 0 0
\(319\) 9.03157 0.505671
\(320\) 0 0
\(321\) 1.91266 0.106754
\(322\) 0 0
\(323\) 6.50842i 0.362138i
\(324\) 0 0
\(325\) 21.0633 17.5982i 1.16838 0.976171i
\(326\) 0 0
\(327\) 7.87248i 0.435349i
\(328\) 0 0
\(329\) 7.90713 0.435934
\(330\) 0 0
\(331\) −10.2746 −0.564746 −0.282373 0.959305i \(-0.591122\pi\)
−0.282373 + 0.959305i \(0.591122\pi\)
\(332\) 0 0
\(333\) 4.63135i 0.253796i
\(334\) 0 0
\(335\) −0.947153 + 2.02556i −0.0517485 + 0.110668i
\(336\) 0 0
\(337\) 21.3148i 1.16109i −0.814228 0.580546i \(-0.802839\pi\)
0.814228 0.580546i \(-0.197161\pi\)
\(338\) 0 0
\(339\) 18.9099 1.02705
\(340\) 0 0
\(341\) 14.8572 0.804560
\(342\) 0 0
\(343\) 15.5361i 0.838869i
\(344\) 0 0
\(345\) 2.31765 + 1.08374i 0.124778 + 0.0583464i
\(346\) 0 0
\(347\) 13.7129i 0.736149i 0.929796 + 0.368075i \(0.119983\pi\)
−0.929796 + 0.368075i \(0.880017\pi\)
\(348\) 0 0
\(349\) −6.67969 −0.357556 −0.178778 0.983889i \(-0.557214\pi\)
−0.178778 + 0.983889i \(0.557214\pi\)
\(350\) 0 0
\(351\) 5.48947 0.293006
\(352\) 0 0
\(353\) 5.46529i 0.290888i −0.989367 0.145444i \(-0.953539\pi\)
0.989367 0.145444i \(-0.0464610\pi\)
\(354\) 0 0
\(355\) 12.0383 + 5.62909i 0.638925 + 0.298761i
\(356\) 0 0
\(357\) 2.47402i 0.130939i
\(358\) 0 0
\(359\) −24.4078 −1.28819 −0.644097 0.764944i \(-0.722767\pi\)
−0.644097 + 0.764944i \(0.722767\pi\)
\(360\) 0 0
\(361\) 41.5341 2.18601
\(362\) 0 0
\(363\) 3.45550i 0.181367i
\(364\) 0 0
\(365\) 0.913704 1.95403i 0.0478255 0.102279i
\(366\) 0 0
\(367\) 33.8706i 1.76803i 0.467456 + 0.884016i \(0.345171\pi\)
−0.467456 + 0.884016i \(0.654829\pi\)
\(368\) 0 0
\(369\) −1.97291 −0.102706
\(370\) 0 0
\(371\) −11.6310 −0.603851
\(372\) 0 0
\(373\) 3.71356i 0.192281i −0.995368 0.0961403i \(-0.969350\pi\)
0.995368 0.0961403i \(-0.0306498\pi\)
\(374\) 0 0
\(375\) −10.8085 + 2.85929i −0.558150 + 0.147653i
\(376\) 0 0
\(377\) 18.0501i 0.929626i
\(378\) 0 0
\(379\) −12.9135 −0.663322 −0.331661 0.943399i \(-0.607609\pi\)
−0.331661 + 0.943399i \(0.607609\pi\)
\(380\) 0 0
\(381\) −0.152806 −0.00782848
\(382\) 0 0
\(383\) 35.5864i 1.81838i −0.416380 0.909191i \(-0.636701\pi\)
0.416380 0.909191i \(-0.363299\pi\)
\(384\) 0 0
\(385\) 7.69419 16.4546i 0.392132 0.838606i
\(386\) 0 0
\(387\) 5.74443i 0.292006i
\(388\) 0 0
\(389\) −0.159135 −0.00806848 −0.00403424 0.999992i \(-0.501284\pi\)
−0.00403424 + 0.999992i \(0.501284\pi\)
\(390\) 0 0
\(391\) −0.957146 −0.0484050
\(392\) 0 0
\(393\) 12.4130i 0.626153i
\(394\) 0 0
\(395\) 25.7315 + 12.0320i 1.29469 + 0.605398i
\(396\) 0 0
\(397\) 19.4448i 0.975904i −0.872870 0.487952i \(-0.837744\pi\)
0.872870 0.487952i \(-0.162256\pi\)
\(398\) 0 0
\(399\) −23.0106 −1.15197
\(400\) 0 0
\(401\) −9.15915 −0.457386 −0.228693 0.973499i \(-0.573445\pi\)
−0.228693 + 0.973499i \(0.573445\pi\)
\(402\) 0 0
\(403\) 29.6928i 1.47910i
\(404\) 0 0
\(405\) −2.02556 0.947153i −0.100651 0.0470644i
\(406\) 0 0
\(407\) 12.7210i 0.630559i
\(408\) 0 0
\(409\) 26.3811 1.30446 0.652232 0.758020i \(-0.273833\pi\)
0.652232 + 0.758020i \(0.273833\pi\)
\(410\) 0 0
\(411\) 8.99009 0.443448
\(412\) 0 0
\(413\) 36.3721i 1.78975i
\(414\) 0 0
\(415\) −8.70009 + 18.6058i −0.427071 + 0.913324i
\(416\) 0 0
\(417\) 22.8040i 1.11672i
\(418\) 0 0
\(419\) −16.0978 −0.786430 −0.393215 0.919447i \(-0.628637\pi\)
−0.393215 + 0.919447i \(0.628637\pi\)
\(420\) 0 0
\(421\) 0.554657 0.0270323 0.0135162 0.999909i \(-0.495698\pi\)
0.0135162 + 0.999909i \(0.495698\pi\)
\(422\) 0 0
\(423\) 2.67357i 0.129993i
\(424\) 0 0
\(425\) 3.20975 2.68171i 0.155696 0.130082i
\(426\) 0 0
\(427\) 26.4127i 1.27820i
\(428\) 0 0
\(429\) −15.0781 −0.727976
\(430\) 0 0
\(431\) 6.64879 0.320261 0.160130 0.987096i \(-0.448809\pi\)
0.160130 + 0.987096i \(0.448809\pi\)
\(432\) 0 0
\(433\) 10.5054i 0.504856i 0.967616 + 0.252428i \(0.0812290\pi\)
−0.967616 + 0.252428i \(0.918771\pi\)
\(434\) 0 0
\(435\) −3.11436 + 6.66030i −0.149322 + 0.319337i
\(436\) 0 0
\(437\) 8.90232i 0.425856i
\(438\) 0 0
\(439\) −7.56850 −0.361225 −0.180612 0.983554i \(-0.557808\pi\)
−0.180612 + 0.983554i \(0.557808\pi\)
\(440\) 0 0
\(441\) 1.74693 0.0831870
\(442\) 0 0
\(443\) 33.0123i 1.56846i 0.620469 + 0.784231i \(0.286942\pi\)
−0.620469 + 0.784231i \(0.713058\pi\)
\(444\) 0 0
\(445\) −17.1581 8.02313i −0.813371 0.380333i
\(446\) 0 0
\(447\) 5.72732i 0.270893i
\(448\) 0 0
\(449\) 2.62923 0.124081 0.0620405 0.998074i \(-0.480239\pi\)
0.0620405 + 0.998074i \(0.480239\pi\)
\(450\) 0 0
\(451\) 5.41905 0.255173
\(452\) 0 0
\(453\) 13.3074i 0.625237i
\(454\) 0 0
\(455\) −32.8855 15.3773i −1.54169 0.720897i
\(456\) 0 0
\(457\) 21.9731i 1.02786i −0.857833 0.513929i \(-0.828190\pi\)
0.857833 0.513929i \(-0.171810\pi\)
\(458\) 0 0
\(459\) 0.836518 0.0390453
\(460\) 0 0
\(461\) −37.4409 −1.74380 −0.871899 0.489686i \(-0.837111\pi\)
−0.871899 + 0.489686i \(0.837111\pi\)
\(462\) 0 0
\(463\) 16.7261i 0.777326i 0.921380 + 0.388663i \(0.127063\pi\)
−0.921380 + 0.388663i \(0.872937\pi\)
\(464\) 0 0
\(465\) −5.12319 + 10.9564i −0.237582 + 0.508089i
\(466\) 0 0
\(467\) 15.5719i 0.720583i −0.932840 0.360291i \(-0.882677\pi\)
0.932840 0.360291i \(-0.117323\pi\)
\(468\) 0 0
\(469\) 2.95752 0.136566
\(470\) 0 0
\(471\) −17.9141 −0.825440
\(472\) 0 0
\(473\) 15.7784i 0.725490i
\(474\) 0 0
\(475\) −24.9423 29.8535i −1.14443 1.36977i
\(476\) 0 0
\(477\) 3.93268i 0.180065i
\(478\) 0 0
\(479\) −13.6312 −0.622824 −0.311412 0.950275i \(-0.600802\pi\)
−0.311412 + 0.950275i \(0.600802\pi\)
\(480\) 0 0
\(481\) 25.4237 1.15922
\(482\) 0 0
\(483\) 3.38400i 0.153978i
\(484\) 0 0
\(485\) −2.83153 + 6.05545i −0.128573 + 0.274964i
\(486\) 0 0
\(487\) 22.3372i 1.01219i −0.862477 0.506097i \(-0.831088\pi\)
0.862477 0.506097i \(-0.168912\pi\)
\(488\) 0 0
\(489\) 13.5544 0.612953
\(490\) 0 0
\(491\) 19.4758 0.878928 0.439464 0.898260i \(-0.355168\pi\)
0.439464 + 0.898260i \(0.355168\pi\)
\(492\) 0 0
\(493\) 2.75057i 0.123880i
\(494\) 0 0
\(495\) 5.56366 + 2.60157i 0.250068 + 0.116932i
\(496\) 0 0
\(497\) 17.5771i 0.788438i
\(498\) 0 0
\(499\) 13.1507 0.588708 0.294354 0.955696i \(-0.404895\pi\)
0.294354 + 0.955696i \(0.404895\pi\)
\(500\) 0 0
\(501\) 14.9256 0.666828
\(502\) 0 0
\(503\) 9.16789i 0.408776i −0.978890 0.204388i \(-0.934480\pi\)
0.978890 0.204388i \(-0.0655204\pi\)
\(504\) 0 0
\(505\) 16.6760 + 7.79772i 0.742074 + 0.346994i
\(506\) 0 0
\(507\) 17.1343i 0.760962i
\(508\) 0 0
\(509\) 0.688601 0.0305217 0.0152609 0.999884i \(-0.495142\pi\)
0.0152609 + 0.999884i \(0.495142\pi\)
\(510\) 0 0
\(511\) −2.85307 −0.126213
\(512\) 0 0
\(513\) 7.78037i 0.343512i
\(514\) 0 0
\(515\) −3.97613 + 8.50326i −0.175209 + 0.374698i
\(516\) 0 0
\(517\) 7.34356i 0.322969i
\(518\) 0 0
\(519\) 15.4705 0.679082
\(520\) 0 0
\(521\) 38.5420 1.68856 0.844278 0.535905i \(-0.180029\pi\)
0.844278 + 0.535905i \(0.180029\pi\)
\(522\) 0 0
\(523\) 14.7842i 0.646468i 0.946319 + 0.323234i \(0.104770\pi\)
−0.946319 + 0.323234i \(0.895230\pi\)
\(524\) 0 0
\(525\) 9.48122 + 11.3481i 0.413795 + 0.495272i
\(526\) 0 0
\(527\) 4.52476i 0.197102i
\(528\) 0 0
\(529\) 21.6908 0.943078
\(530\) 0 0
\(531\) 12.2982 0.533695
\(532\) 0 0
\(533\) 10.8303i 0.469110i
\(534\) 0 0
\(535\) 1.81158 3.87421i 0.0783215 0.167497i
\(536\) 0 0
\(537\) 16.5415i 0.713819i
\(538\) 0 0
\(539\) −4.79833 −0.206679
\(540\) 0 0
\(541\) −23.1951 −0.997235 −0.498617 0.866822i \(-0.666159\pi\)
−0.498617 + 0.866822i \(0.666159\pi\)
\(542\) 0 0
\(543\) 15.9855i 0.686003i
\(544\) 0 0
\(545\) 15.9462 + 7.45645i 0.683060 + 0.319399i
\(546\) 0 0
\(547\) 27.5999i 1.18009i −0.807371 0.590044i \(-0.799110\pi\)
0.807371 0.590044i \(-0.200890\pi\)
\(548\) 0 0
\(549\) 8.93068 0.381152
\(550\) 0 0
\(551\) −25.5828 −1.08986
\(552\) 0 0
\(553\) 37.5705i 1.59766i
\(554\) 0 0
\(555\) −9.38108 4.38660i −0.398205 0.186201i
\(556\) 0 0
\(557\) 2.27768i 0.0965086i 0.998835 + 0.0482543i \(0.0153658\pi\)
−0.998835 + 0.0482543i \(0.984634\pi\)
\(558\) 0 0
\(559\) −31.5339 −1.33374
\(560\) 0 0
\(561\) −2.29768 −0.0970083
\(562\) 0 0
\(563\) 29.1148i 1.22704i −0.789679 0.613521i \(-0.789753\pi\)
0.789679 0.613521i \(-0.210247\pi\)
\(564\) 0 0
\(565\) 17.9106 38.3032i 0.753504 1.61143i
\(566\) 0 0
\(567\) 2.95752i 0.124204i
\(568\) 0 0
\(569\) −37.2631 −1.56215 −0.781075 0.624437i \(-0.785329\pi\)
−0.781075 + 0.624437i \(0.785329\pi\)
\(570\) 0 0
\(571\) −7.77045 −0.325183 −0.162592 0.986693i \(-0.551985\pi\)
−0.162592 + 0.986693i \(0.551985\pi\)
\(572\) 0 0
\(573\) 9.89989i 0.413574i
\(574\) 0 0
\(575\) 4.39035 3.66809i 0.183090 0.152970i
\(576\) 0 0
\(577\) 39.9697i 1.66396i −0.554806 0.831980i \(-0.687207\pi\)
0.554806 0.831980i \(-0.312793\pi\)
\(578\) 0 0
\(579\) −13.9755 −0.580802
\(580\) 0 0
\(581\) 27.1664 1.12705
\(582\) 0 0
\(583\) 10.8020i 0.447373i
\(584\) 0 0
\(585\) 5.19937 11.1193i 0.214968 0.459725i
\(586\) 0 0
\(587\) 32.4241i 1.33829i 0.743134 + 0.669143i \(0.233339\pi\)
−0.743134 + 0.669143i \(0.766661\pi\)
\(588\) 0 0
\(589\) −42.0844 −1.73406
\(590\) 0 0
\(591\) 5.47194 0.225085
\(592\) 0 0
\(593\) 27.3374i 1.12261i 0.827608 + 0.561306i \(0.189701\pi\)
−0.827608 + 0.561306i \(0.810299\pi\)
\(594\) 0 0
\(595\) −5.01128 2.34327i −0.205442 0.0960649i
\(596\) 0 0
\(597\) 2.21401i 0.0906135i
\(598\) 0 0
\(599\) −44.1243 −1.80287 −0.901435 0.432915i \(-0.857485\pi\)
−0.901435 + 0.432915i \(0.857485\pi\)
\(600\) 0 0
\(601\) 28.9423 1.18058 0.590290 0.807191i \(-0.299014\pi\)
0.590290 + 0.807191i \(0.299014\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 6.99934 + 3.27289i 0.284563 + 0.133062i
\(606\) 0 0
\(607\) 28.5954i 1.16065i −0.814384 0.580326i \(-0.802925\pi\)
0.814384 0.580326i \(-0.197075\pi\)
\(608\) 0 0
\(609\) 9.72469 0.394064
\(610\) 0 0
\(611\) −14.6765 −0.593747
\(612\) 0 0
\(613\) 21.3445i 0.862096i 0.902329 + 0.431048i \(0.141856\pi\)
−0.902329 + 0.431048i \(0.858144\pi\)
\(614\) 0 0
\(615\) −1.86865 + 3.99626i −0.0753513 + 0.161145i
\(616\) 0 0
\(617\) 13.0558i 0.525608i −0.964849 0.262804i \(-0.915353\pi\)
0.964849 0.262804i \(-0.0846473\pi\)
\(618\) 0 0
\(619\) −0.0190092 −0.000764043 −0.000382021 1.00000i \(-0.500122\pi\)
−0.000382021 1.00000i \(0.500122\pi\)
\(620\) 0 0
\(621\) 1.14420 0.0459153
\(622\) 0 0
\(623\) 25.0525i 1.00371i
\(624\) 0 0
\(625\) −4.44567 + 24.6015i −0.177827 + 0.984062i
\(626\) 0 0
\(627\) 21.3705i 0.853457i
\(628\) 0 0
\(629\) 3.87421 0.154475
\(630\) 0 0
\(631\) 12.3875 0.493138 0.246569 0.969125i \(-0.420697\pi\)
0.246569 + 0.969125i \(0.420697\pi\)
\(632\) 0 0
\(633\) 28.0506i 1.11491i
\(634\) 0 0
\(635\) −0.144730 + 0.309517i −0.00574345 + 0.0122828i
\(636\) 0 0
\(637\) 9.58971i 0.379958i
\(638\) 0 0
\(639\) 5.94317 0.235108
\(640\) 0 0
\(641\) 26.3167 1.03945 0.519723 0.854335i \(-0.326035\pi\)
0.519723 + 0.854335i \(0.326035\pi\)
\(642\) 0 0
\(643\) 42.6412i 1.68161i −0.541342 0.840803i \(-0.682084\pi\)
0.541342 0.840803i \(-0.317916\pi\)
\(644\) 0 0
\(645\) 11.6357 + 5.44086i 0.458155 + 0.214233i
\(646\) 0 0
\(647\) 46.1030i 1.81250i −0.422747 0.906248i \(-0.638934\pi\)
0.422747 0.906248i \(-0.361066\pi\)
\(648\) 0 0
\(649\) −33.7797 −1.32597
\(650\) 0 0
\(651\) 15.9974 0.626986
\(652\) 0 0
\(653\) 47.8854i 1.87390i −0.349460 0.936951i \(-0.613635\pi\)
0.349460 0.936951i \(-0.386365\pi\)
\(654\) 0 0
\(655\) 25.1433 + 11.7570i 0.982430 + 0.459385i
\(656\) 0 0
\(657\) 0.964685i 0.0376359i
\(658\) 0 0
\(659\) 41.9626 1.63463 0.817315 0.576192i \(-0.195462\pi\)
0.817315 + 0.576192i \(0.195462\pi\)
\(660\) 0 0
\(661\) 3.99221 0.155279 0.0776394 0.996982i \(-0.475262\pi\)
0.0776394 + 0.996982i \(0.475262\pi\)
\(662\) 0 0
\(663\) 4.59204i 0.178340i
\(664\) 0 0
\(665\) −21.7946 + 46.6094i −0.845157 + 1.80743i
\(666\) 0 0
\(667\) 3.76228i 0.145676i
\(668\) 0 0
\(669\) −1.83158 −0.0708129
\(670\) 0 0
\(671\) −24.5301 −0.946974
\(672\) 0 0
\(673\) 18.6406i 0.718543i −0.933233 0.359271i \(-0.883025\pi\)
0.933233 0.359271i \(-0.116975\pi\)
\(674\) 0 0
\(675\) −3.83703 + 3.20580i −0.147688 + 0.123391i
\(676\) 0 0
\(677\) 14.6577i 0.563342i −0.959511 0.281671i \(-0.909111\pi\)
0.959511 0.281671i \(-0.0908887\pi\)
\(678\) 0 0
\(679\) 8.84155 0.339308
\(680\) 0 0
\(681\) −13.2018 −0.505893
\(682\) 0 0
\(683\) 36.0897i 1.38094i −0.723363 0.690468i \(-0.757405\pi\)
0.723363 0.690468i \(-0.242595\pi\)
\(684\) 0 0
\(685\) 8.51499 18.2100i 0.325341 0.695768i
\(686\) 0 0
\(687\) 12.7004i 0.484552i
\(688\) 0 0
\(689\) 21.5884 0.822451
\(690\) 0 0
\(691\) 15.5459 0.591396 0.295698 0.955282i \(-0.404448\pi\)
0.295698 + 0.955282i \(0.404448\pi\)
\(692\) 0 0
\(693\) 8.12349i 0.308586i
\(694\) 0 0
\(695\) 46.1909 + 21.5989i 1.75212 + 0.819292i
\(696\) 0 0
\(697\) 1.65038i 0.0625125i
\(698\) 0 0
\(699\) 13.7551 0.520267
\(700\) 0 0
\(701\) 36.1326 1.36471 0.682355 0.731021i \(-0.260956\pi\)
0.682355 + 0.731021i \(0.260956\pi\)
\(702\) 0 0
\(703\) 36.0336i 1.35903i
\(704\) 0 0
\(705\) 5.41548 + 2.53228i 0.203959 + 0.0953712i
\(706\) 0 0
\(707\) 24.3487i 0.915725i
\(708\) 0 0
\(709\) −42.2485 −1.58668 −0.793338 0.608781i \(-0.791659\pi\)
−0.793338 + 0.608781i \(0.791659\pi\)
\(710\) 0 0
\(711\) 12.7034 0.476414
\(712\) 0 0
\(713\) 6.18904i 0.231782i
\(714\) 0 0
\(715\) −14.2812 + 30.5416i −0.534088 + 1.14219i
\(716\) 0 0
\(717\) 3.29614i 0.123097i
\(718\) 0 0
\(719\) 13.7436 0.512551 0.256275 0.966604i \(-0.417505\pi\)
0.256275 + 0.966604i \(0.417505\pi\)
\(720\) 0 0
\(721\) 12.4156 0.462381
\(722\) 0 0
\(723\) 0.789127i 0.0293479i
\(724\) 0 0
\(725\) 10.5411 + 12.6166i 0.391486 + 0.468570i
\(726\) 0 0
\(727\) 23.6271i 0.876281i 0.898907 + 0.438140i \(0.144363\pi\)
−0.898907 + 0.438140i \(0.855637\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −4.80532 −0.177731
\(732\) 0 0
\(733\) 41.9518i 1.54953i 0.632252 + 0.774763i \(0.282131\pi\)
−0.632252 + 0.774763i \(0.717869\pi\)
\(734\) 0 0
\(735\) 1.65461 3.53851i 0.0610311 0.130520i
\(736\) 0 0
\(737\) 2.74672i 0.101177i
\(738\) 0 0
\(739\) 19.3488 0.711758 0.355879 0.934532i \(-0.384181\pi\)
0.355879 + 0.934532i \(0.384181\pi\)
\(740\) 0 0
\(741\) 42.7101 1.56900
\(742\) 0 0
\(743\) 8.54217i 0.313382i 0.987648 + 0.156691i \(0.0500827\pi\)
−0.987648 + 0.156691i \(0.949917\pi\)
\(744\) 0 0
\(745\) −11.6010 5.42465i −0.425029 0.198744i
\(746\) 0 0
\(747\) 9.18552i 0.336080i
\(748\) 0 0
\(749\) −5.65673 −0.206692
\(750\) 0 0
\(751\) 9.22485 0.336620 0.168310 0.985734i \(-0.446169\pi\)
0.168310 + 0.985734i \(0.446169\pi\)
\(752\) 0 0
\(753\) 18.4247i 0.671432i
\(754\) 0 0
\(755\) 26.9550 + 12.6042i 0.980992 + 0.458712i
\(756\) 0 0
\(757\) 16.6768i 0.606129i 0.952970 + 0.303064i \(0.0980097\pi\)
−0.952970 + 0.303064i \(0.901990\pi\)
\(758\) 0 0
\(759\) −3.14281 −0.114077
\(760\) 0 0
\(761\) 37.6354 1.36428 0.682142 0.731220i \(-0.261049\pi\)
0.682142 + 0.731220i \(0.261049\pi\)
\(762\) 0 0
\(763\) 23.2830i 0.842902i
\(764\) 0 0
\(765\) 0.792310 1.69442i 0.0286460 0.0612618i
\(766\) 0 0
\(767\) 67.5105i 2.43766i
\(768\) 0 0
\(769\) −42.7260 −1.54074 −0.770369 0.637598i \(-0.779928\pi\)
−0.770369 + 0.637598i \(0.779928\pi\)
\(770\) 0 0
\(771\) 24.3790 0.877988
\(772\) 0 0
\(773\) 1.98882i 0.0715330i −0.999360 0.0357665i \(-0.988613\pi\)
0.999360 0.0357665i \(-0.0113873\pi\)
\(774\) 0 0
\(775\) 17.3403 + 20.7547i 0.622883 + 0.745530i
\(776\) 0 0
\(777\) 13.6973i 0.491388i
\(778\) 0 0
\(779\) −15.3500 −0.549970
\(780\) 0 0
\(781\) −16.3243 −0.584128
\(782\) 0 0
\(783\) 3.28812i 0.117508i
\(784\) 0 0
\(785\) −16.9674 + 36.2862i −0.605594 + 1.29511i
\(786\) 0 0
\(787\) 0.0279170i 0.000995132i −1.00000 0.000497566i \(-0.999842\pi\)
1.00000 0.000497566i \(-0.000158380\pi\)
\(788\) 0 0
\(789\) 16.1653 0.575500
\(790\) 0 0
\(791\) −55.9265 −1.98852
\(792\) 0