Properties

Label 4020.2.g.c.1609.3
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 1609.3
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.22

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(-2.06455 + 0.858848i) q^{5}\) \(+3.58783i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(-2.06455 + 0.858848i) q^{5}\) \(+3.58783i q^{7}\) \(-1.00000 q^{9}\) \(+0.928323 q^{11}\) \(+5.62224i q^{13}\) \(+(0.858848 + 2.06455i) q^{15}\) \(+6.87254i q^{17}\) \(-7.74568 q^{19}\) \(+3.58783 q^{21}\) \(+6.77684i q^{23}\) \(+(3.52476 - 3.54628i) q^{25}\) \(+1.00000i q^{27}\) \(-2.69720 q^{29}\) \(-2.29620 q^{31}\) \(-0.928323i q^{33}\) \(+(-3.08140 - 7.40727i) q^{35}\) \(-10.1915i q^{37}\) \(+5.62224 q^{39}\) \(-2.54924 q^{41}\) \(-0.670329i q^{43}\) \(+(2.06455 - 0.858848i) q^{45}\) \(-10.2725i q^{47}\) \(-5.87254 q^{49}\) \(+6.87254 q^{51}\) \(-3.41538i q^{53}\) \(+(-1.91657 + 0.797289i) q^{55}\) \(+7.74568i q^{57}\) \(+1.49167 q^{59}\) \(+11.8427 q^{61}\) \(-3.58783i q^{63}\) \(+(-4.82865 - 11.6074i) q^{65}\) \(-1.00000i q^{67}\) \(+6.77684 q^{69}\) \(+3.25041 q^{71}\) \(-15.6623i q^{73}\) \(+(-3.54628 - 3.52476i) q^{75}\) \(+3.33067i q^{77}\) \(-4.76733 q^{79}\) \(+1.00000 q^{81}\) \(+6.48826i q^{83}\) \(+(-5.90247 - 14.1887i) q^{85}\) \(+2.69720i q^{87}\) \(-12.1791 q^{89}\) \(-20.1716 q^{91}\) \(+2.29620i q^{93}\) \(+(15.9914 - 6.65236i) q^{95}\) \(+11.1180i q^{97}\) \(-0.928323 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −2.06455 + 0.858848i −0.923296 + 0.384089i
\(6\) 0 0
\(7\) 3.58783i 1.35607i 0.735028 + 0.678036i \(0.237169\pi\)
−0.735028 + 0.678036i \(0.762831\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 0.928323 0.279900 0.139950 0.990159i \(-0.455306\pi\)
0.139950 + 0.990159i \(0.455306\pi\)
\(12\) 0 0
\(13\) 5.62224i 1.55933i 0.626198 + 0.779664i \(0.284610\pi\)
−0.626198 + 0.779664i \(0.715390\pi\)
\(14\) 0 0
\(15\) 0.858848 + 2.06455i 0.221754 + 0.533065i
\(16\) 0 0
\(17\) 6.87254i 1.66684i 0.552643 + 0.833418i \(0.313619\pi\)
−0.552643 + 0.833418i \(0.686381\pi\)
\(18\) 0 0
\(19\) −7.74568 −1.77698 −0.888490 0.458896i \(-0.848245\pi\)
−0.888490 + 0.458896i \(0.848245\pi\)
\(20\) 0 0
\(21\) 3.58783 0.782929
\(22\) 0 0
\(23\) 6.77684i 1.41307i 0.707678 + 0.706535i \(0.249743\pi\)
−0.707678 + 0.706535i \(0.750257\pi\)
\(24\) 0 0
\(25\) 3.52476 3.54628i 0.704952 0.709255i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −2.69720 −0.500858 −0.250429 0.968135i \(-0.580572\pi\)
−0.250429 + 0.968135i \(0.580572\pi\)
\(30\) 0 0
\(31\) −2.29620 −0.412409 −0.206204 0.978509i \(-0.566111\pi\)
−0.206204 + 0.978509i \(0.566111\pi\)
\(32\) 0 0
\(33\) 0.928323i 0.161600i
\(34\) 0 0
\(35\) −3.08140 7.40727i −0.520852 1.25206i
\(36\) 0 0
\(37\) 10.1915i 1.67548i −0.546071 0.837739i \(-0.683877\pi\)
0.546071 0.837739i \(-0.316123\pi\)
\(38\) 0 0
\(39\) 5.62224 0.900278
\(40\) 0 0
\(41\) −2.54924 −0.398125 −0.199062 0.979987i \(-0.563790\pi\)
−0.199062 + 0.979987i \(0.563790\pi\)
\(42\) 0 0
\(43\) 0.670329i 0.102224i −0.998693 0.0511121i \(-0.983723\pi\)
0.998693 0.0511121i \(-0.0162766\pi\)
\(44\) 0 0
\(45\) 2.06455 0.858848i 0.307765 0.128030i
\(46\) 0 0
\(47\) 10.2725i 1.49840i −0.662343 0.749201i \(-0.730438\pi\)
0.662343 0.749201i \(-0.269562\pi\)
\(48\) 0 0
\(49\) −5.87254 −0.838934
\(50\) 0 0
\(51\) 6.87254 0.962348
\(52\) 0 0
\(53\) 3.41538i 0.469139i −0.972099 0.234570i \(-0.924632\pi\)
0.972099 0.234570i \(-0.0753681\pi\)
\(54\) 0 0
\(55\) −1.91657 + 0.797289i −0.258431 + 0.107506i
\(56\) 0 0
\(57\) 7.74568i 1.02594i
\(58\) 0 0
\(59\) 1.49167 0.194199 0.0970995 0.995275i \(-0.469044\pi\)
0.0970995 + 0.995275i \(0.469044\pi\)
\(60\) 0 0
\(61\) 11.8427 1.51630 0.758150 0.652080i \(-0.226104\pi\)
0.758150 + 0.652080i \(0.226104\pi\)
\(62\) 0 0
\(63\) 3.58783i 0.452024i
\(64\) 0 0
\(65\) −4.82865 11.6074i −0.598920 1.43972i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) 6.77684 0.815836
\(70\) 0 0
\(71\) 3.25041 0.385753 0.192876 0.981223i \(-0.438218\pi\)
0.192876 + 0.981223i \(0.438218\pi\)
\(72\) 0 0
\(73\) 15.6623i 1.83313i −0.399885 0.916565i \(-0.630950\pi\)
0.399885 0.916565i \(-0.369050\pi\)
\(74\) 0 0
\(75\) −3.54628 3.52476i −0.409489 0.407004i
\(76\) 0 0
\(77\) 3.33067i 0.379565i
\(78\) 0 0
\(79\) −4.76733 −0.536366 −0.268183 0.963368i \(-0.586423\pi\)
−0.268183 + 0.963368i \(0.586423\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 6.48826i 0.712179i 0.934452 + 0.356090i \(0.115890\pi\)
−0.934452 + 0.356090i \(0.884110\pi\)
\(84\) 0 0
\(85\) −5.90247 14.1887i −0.640213 1.53898i
\(86\) 0 0
\(87\) 2.69720i 0.289170i
\(88\) 0 0
\(89\) −12.1791 −1.29099 −0.645493 0.763766i \(-0.723348\pi\)
−0.645493 + 0.763766i \(0.723348\pi\)
\(90\) 0 0
\(91\) −20.1716 −2.11456
\(92\) 0 0
\(93\) 2.29620i 0.238104i
\(94\) 0 0
\(95\) 15.9914 6.65236i 1.64068 0.682518i
\(96\) 0 0
\(97\) 11.1180i 1.12887i 0.825479 + 0.564433i \(0.190905\pi\)
−0.825479 + 0.564433i \(0.809095\pi\)
\(98\) 0 0
\(99\) −0.928323 −0.0933000
\(100\) 0 0
\(101\) 14.0099 1.39403 0.697017 0.717054i \(-0.254510\pi\)
0.697017 + 0.717054i \(0.254510\pi\)
\(102\) 0 0
\(103\) 11.6012i 1.14310i −0.820567 0.571550i \(-0.806342\pi\)
0.820567 0.571550i \(-0.193658\pi\)
\(104\) 0 0
\(105\) −7.40727 + 3.08140i −0.722875 + 0.300714i
\(106\) 0 0
\(107\) 20.4097i 1.97308i 0.163509 + 0.986542i \(0.447719\pi\)
−0.163509 + 0.986542i \(0.552281\pi\)
\(108\) 0 0
\(109\) −3.36850 −0.322644 −0.161322 0.986902i \(-0.551576\pi\)
−0.161322 + 0.986902i \(0.551576\pi\)
\(110\) 0 0
\(111\) −10.1915 −0.967338
\(112\) 0 0
\(113\) 15.8775i 1.49363i 0.665033 + 0.746814i \(0.268417\pi\)
−0.665033 + 0.746814i \(0.731583\pi\)
\(114\) 0 0
\(115\) −5.82028 13.9912i −0.542744 1.30468i
\(116\) 0 0
\(117\) 5.62224i 0.519776i
\(118\) 0 0
\(119\) −24.6575 −2.26035
\(120\) 0 0
\(121\) −10.1382 −0.921656
\(122\) 0 0
\(123\) 2.54924i 0.229857i
\(124\) 0 0
\(125\) −4.23134 + 10.3487i −0.378463 + 0.925617i
\(126\) 0 0
\(127\) 7.35252i 0.652431i 0.945295 + 0.326215i \(0.105773\pi\)
−0.945295 + 0.326215i \(0.894227\pi\)
\(128\) 0 0
\(129\) −0.670329 −0.0590192
\(130\) 0 0
\(131\) 17.2871 1.51038 0.755192 0.655504i \(-0.227544\pi\)
0.755192 + 0.655504i \(0.227544\pi\)
\(132\) 0 0
\(133\) 27.7902i 2.40972i
\(134\) 0 0
\(135\) −0.858848 2.06455i −0.0739179 0.177688i
\(136\) 0 0
\(137\) 6.25580i 0.534469i −0.963632 0.267235i \(-0.913890\pi\)
0.963632 0.267235i \(-0.0861098\pi\)
\(138\) 0 0
\(139\) 18.7158 1.58745 0.793727 0.608274i \(-0.208138\pi\)
0.793727 + 0.608274i \(0.208138\pi\)
\(140\) 0 0
\(141\) −10.2725 −0.865102
\(142\) 0 0
\(143\) 5.21925i 0.436456i
\(144\) 0 0
\(145\) 5.56851 2.31649i 0.462440 0.192374i
\(146\) 0 0
\(147\) 5.87254i 0.484359i
\(148\) 0 0
\(149\) −10.5604 −0.865145 −0.432572 0.901599i \(-0.642394\pi\)
−0.432572 + 0.901599i \(0.642394\pi\)
\(150\) 0 0
\(151\) −0.707027 −0.0575371 −0.0287685 0.999586i \(-0.509159\pi\)
−0.0287685 + 0.999586i \(0.509159\pi\)
\(152\) 0 0
\(153\) 6.87254i 0.555612i
\(154\) 0 0
\(155\) 4.74062 1.97208i 0.380776 0.158402i
\(156\) 0 0
\(157\) 6.97439i 0.556617i −0.960492 0.278308i \(-0.910226\pi\)
0.960492 0.278308i \(-0.0897737\pi\)
\(158\) 0 0
\(159\) −3.41538 −0.270858
\(160\) 0 0
\(161\) −24.3142 −1.91623
\(162\) 0 0
\(163\) 18.3193i 1.43488i −0.696622 0.717438i \(-0.745315\pi\)
0.696622 0.717438i \(-0.254685\pi\)
\(164\) 0 0
\(165\) 0.797289 + 1.91657i 0.0620689 + 0.149205i
\(166\) 0 0
\(167\) 5.82349i 0.450635i −0.974285 0.225318i \(-0.927658\pi\)
0.974285 0.225318i \(-0.0723419\pi\)
\(168\) 0 0
\(169\) −18.6095 −1.43150
\(170\) 0 0
\(171\) 7.74568 0.592327
\(172\) 0 0
\(173\) 18.5918i 1.41351i −0.707459 0.706754i \(-0.750159\pi\)
0.707459 0.706754i \(-0.249841\pi\)
\(174\) 0 0
\(175\) 12.7234 + 12.6462i 0.961802 + 0.955966i
\(176\) 0 0
\(177\) 1.49167i 0.112121i
\(178\) 0 0
\(179\) −0.0429121 −0.00320740 −0.00160370 0.999999i \(-0.500510\pi\)
−0.00160370 + 0.999999i \(0.500510\pi\)
\(180\) 0 0
\(181\) 0.122684 0.00911900 0.00455950 0.999990i \(-0.498549\pi\)
0.00455950 + 0.999990i \(0.498549\pi\)
\(182\) 0 0
\(183\) 11.8427i 0.875436i
\(184\) 0 0
\(185\) 8.75298 + 21.0410i 0.643532 + 1.54696i
\(186\) 0 0
\(187\) 6.37994i 0.466547i
\(188\) 0 0
\(189\) −3.58783 −0.260976
\(190\) 0 0
\(191\) −14.4113 −1.04276 −0.521382 0.853323i \(-0.674583\pi\)
−0.521382 + 0.853323i \(0.674583\pi\)
\(192\) 0 0
\(193\) 2.81325i 0.202502i −0.994861 0.101251i \(-0.967715\pi\)
0.994861 0.101251i \(-0.0322846\pi\)
\(194\) 0 0
\(195\) −11.6074 + 4.82865i −0.831224 + 0.345787i
\(196\) 0 0
\(197\) 11.4350i 0.814707i −0.913271 0.407353i \(-0.866452\pi\)
0.913271 0.407353i \(-0.133548\pi\)
\(198\) 0 0
\(199\) −24.3724 −1.72772 −0.863858 0.503736i \(-0.831958\pi\)
−0.863858 + 0.503736i \(0.831958\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 9.67710i 0.679199i
\(204\) 0 0
\(205\) 5.26305 2.18941i 0.367587 0.152915i
\(206\) 0 0
\(207\) 6.77684i 0.471023i
\(208\) 0 0
\(209\) −7.19049 −0.497377
\(210\) 0 0
\(211\) 2.29939 0.158296 0.0791482 0.996863i \(-0.474780\pi\)
0.0791482 + 0.996863i \(0.474780\pi\)
\(212\) 0 0
\(213\) 3.25041i 0.222715i
\(214\) 0 0
\(215\) 0.575711 + 1.38393i 0.0392631 + 0.0943832i
\(216\) 0 0
\(217\) 8.23836i 0.559257i
\(218\) 0 0
\(219\) −15.6623 −1.05836
\(220\) 0 0
\(221\) −38.6390 −2.59914
\(222\) 0 0
\(223\) 8.59585i 0.575620i 0.957687 + 0.287810i \(0.0929272\pi\)
−0.957687 + 0.287810i \(0.907073\pi\)
\(224\) 0 0
\(225\) −3.52476 + 3.54628i −0.234984 + 0.236418i
\(226\) 0 0
\(227\) 11.8063i 0.783611i 0.920048 + 0.391806i \(0.128149\pi\)
−0.920048 + 0.391806i \(0.871851\pi\)
\(228\) 0 0
\(229\) 23.4280 1.54817 0.774083 0.633084i \(-0.218211\pi\)
0.774083 + 0.633084i \(0.218211\pi\)
\(230\) 0 0
\(231\) 3.33067 0.219142
\(232\) 0 0
\(233\) 8.43414i 0.552539i 0.961080 + 0.276270i \(0.0890982\pi\)
−0.961080 + 0.276270i \(0.910902\pi\)
\(234\) 0 0
\(235\) 8.82254 + 21.2082i 0.575519 + 1.38347i
\(236\) 0 0
\(237\) 4.76733i 0.309671i
\(238\) 0 0
\(239\) −16.3248 −1.05596 −0.527982 0.849256i \(-0.677051\pi\)
−0.527982 + 0.849256i \(0.677051\pi\)
\(240\) 0 0
\(241\) 11.9934 0.772565 0.386283 0.922380i \(-0.373759\pi\)
0.386283 + 0.922380i \(0.373759\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 12.1242 5.04362i 0.774584 0.322225i
\(246\) 0 0
\(247\) 43.5480i 2.77090i
\(248\) 0 0
\(249\) 6.48826 0.411177
\(250\) 0 0
\(251\) −26.3699 −1.66445 −0.832226 0.554436i \(-0.812934\pi\)
−0.832226 + 0.554436i \(0.812934\pi\)
\(252\) 0 0
\(253\) 6.29110i 0.395518i
\(254\) 0 0
\(255\) −14.1887 + 5.90247i −0.888532 + 0.369627i
\(256\) 0 0
\(257\) 20.5740i 1.28337i 0.766968 + 0.641685i \(0.221764\pi\)
−0.766968 + 0.641685i \(0.778236\pi\)
\(258\) 0 0
\(259\) 36.5655 2.27207
\(260\) 0 0
\(261\) 2.69720 0.166953
\(262\) 0 0
\(263\) 4.88398i 0.301159i −0.988598 0.150580i \(-0.951886\pi\)
0.988598 0.150580i \(-0.0481140\pi\)
\(264\) 0 0
\(265\) 2.93330 + 7.05124i 0.180191 + 0.433154i
\(266\) 0 0
\(267\) 12.1791i 0.745351i
\(268\) 0 0
\(269\) 6.13025 0.373768 0.186884 0.982382i \(-0.440161\pi\)
0.186884 + 0.982382i \(0.440161\pi\)
\(270\) 0 0
\(271\) −4.75729 −0.288985 −0.144492 0.989506i \(-0.546155\pi\)
−0.144492 + 0.989506i \(0.546155\pi\)
\(272\) 0 0
\(273\) 20.1716i 1.22084i
\(274\) 0 0
\(275\) 3.27212 3.29209i 0.197316 0.198521i
\(276\) 0 0
\(277\) 24.2685i 1.45816i −0.684431 0.729078i \(-0.739949\pi\)
0.684431 0.729078i \(-0.260051\pi\)
\(278\) 0 0
\(279\) 2.29620 0.137470
\(280\) 0 0
\(281\) −9.71136 −0.579331 −0.289666 0.957128i \(-0.593544\pi\)
−0.289666 + 0.957128i \(0.593544\pi\)
\(282\) 0 0
\(283\) 10.4400i 0.620593i −0.950640 0.310296i \(-0.899572\pi\)
0.950640 0.310296i \(-0.100428\pi\)
\(284\) 0 0
\(285\) −6.65236 15.9914i −0.394052 0.947247i
\(286\) 0 0
\(287\) 9.14625i 0.539886i
\(288\) 0 0
\(289\) −30.2318 −1.77834
\(290\) 0 0
\(291\) 11.1180 0.651751
\(292\) 0 0
\(293\) 4.75711i 0.277913i 0.990298 + 0.138957i \(0.0443749\pi\)
−0.990298 + 0.138957i \(0.955625\pi\)
\(294\) 0 0
\(295\) −3.07963 + 1.28112i −0.179303 + 0.0745896i
\(296\) 0 0
\(297\) 0.928323i 0.0538668i
\(298\) 0 0
\(299\) −38.1010 −2.20344
\(300\) 0 0
\(301\) 2.40503 0.138623
\(302\) 0 0
\(303\) 14.0099i 0.804846i
\(304\) 0 0
\(305\) −24.4498 + 10.1711i −1.39999 + 0.582393i
\(306\) 0 0
\(307\) 20.6235i 1.17704i 0.808481 + 0.588522i \(0.200290\pi\)
−0.808481 + 0.588522i \(0.799710\pi\)
\(308\) 0 0
\(309\) −11.6012 −0.659969
\(310\) 0 0
\(311\) 12.4806 0.707709 0.353854 0.935301i \(-0.384871\pi\)
0.353854 + 0.935301i \(0.384871\pi\)
\(312\) 0 0
\(313\) 22.4911i 1.27127i 0.771989 + 0.635635i \(0.219262\pi\)
−0.771989 + 0.635635i \(0.780738\pi\)
\(314\) 0 0
\(315\) 3.08140 + 7.40727i 0.173617 + 0.417352i
\(316\) 0 0
\(317\) 7.97888i 0.448138i 0.974573 + 0.224069i \(0.0719341\pi\)
−0.974573 + 0.224069i \(0.928066\pi\)
\(318\) 0 0
\(319\) −2.50387 −0.140190
\(320\) 0 0
\(321\) 20.4097 1.13916
\(322\) 0 0
\(323\) 53.2325i 2.96193i
\(324\) 0 0
\(325\) 19.9380 + 19.8170i 1.10596 + 1.09925i
\(326\) 0 0
\(327\) 3.36850i 0.186278i
\(328\) 0 0
\(329\) 36.8561 2.03194
\(330\) 0 0
\(331\) −23.4582 −1.28938 −0.644689 0.764445i \(-0.723013\pi\)
−0.644689 + 0.764445i \(0.723013\pi\)
\(332\) 0 0
\(333\) 10.1915i 0.558493i
\(334\) 0 0
\(335\) 0.858848 + 2.06455i 0.0469239 + 0.112799i
\(336\) 0 0
\(337\) 9.71327i 0.529116i −0.964370 0.264558i \(-0.914774\pi\)
0.964370 0.264558i \(-0.0852260\pi\)
\(338\) 0 0
\(339\) 15.8775 0.862347
\(340\) 0 0
\(341\) −2.13161 −0.115433
\(342\) 0 0
\(343\) 4.04515i 0.218418i
\(344\) 0 0
\(345\) −13.9912 + 5.82028i −0.753258 + 0.313353i
\(346\) 0 0
\(347\) 7.90213i 0.424208i 0.977247 + 0.212104i \(0.0680316\pi\)
−0.977247 + 0.212104i \(0.931968\pi\)
\(348\) 0 0
\(349\) 25.4309 1.36129 0.680644 0.732615i \(-0.261700\pi\)
0.680644 + 0.732615i \(0.261700\pi\)
\(350\) 0 0
\(351\) −5.62224 −0.300093
\(352\) 0 0
\(353\) 19.3652i 1.03071i 0.856978 + 0.515353i \(0.172339\pi\)
−0.856978 + 0.515353i \(0.827661\pi\)
\(354\) 0 0
\(355\) −6.71065 + 2.79161i −0.356164 + 0.148163i
\(356\) 0 0
\(357\) 24.6575i 1.30501i
\(358\) 0 0
\(359\) 2.49695 0.131784 0.0658921 0.997827i \(-0.479011\pi\)
0.0658921 + 0.997827i \(0.479011\pi\)
\(360\) 0 0
\(361\) 40.9955 2.15766
\(362\) 0 0
\(363\) 10.1382i 0.532118i
\(364\) 0 0
\(365\) 13.4515 + 32.3356i 0.704085 + 1.69252i
\(366\) 0 0
\(367\) 13.3963i 0.699283i 0.936884 + 0.349641i \(0.113697\pi\)
−0.936884 + 0.349641i \(0.886303\pi\)
\(368\) 0 0
\(369\) 2.54924 0.132708
\(370\) 0 0
\(371\) 12.2538 0.636187
\(372\) 0 0
\(373\) 23.7845i 1.23152i 0.787935 + 0.615758i \(0.211150\pi\)
−0.787935 + 0.615758i \(0.788850\pi\)
\(374\) 0 0
\(375\) 10.3487 + 4.23134i 0.534405 + 0.218505i
\(376\) 0 0
\(377\) 15.1643i 0.781001i
\(378\) 0 0
\(379\) −7.45536 −0.382956 −0.191478 0.981497i \(-0.561328\pi\)
−0.191478 + 0.981497i \(0.561328\pi\)
\(380\) 0 0
\(381\) 7.35252 0.376681
\(382\) 0 0
\(383\) 12.0554i 0.616002i 0.951386 + 0.308001i \(0.0996600\pi\)
−0.951386 + 0.308001i \(0.900340\pi\)
\(384\) 0 0
\(385\) −2.86054 6.87634i −0.145787 0.350451i
\(386\) 0 0
\(387\) 0.670329i 0.0340747i
\(388\) 0 0
\(389\) 5.27674 0.267542 0.133771 0.991012i \(-0.457291\pi\)
0.133771 + 0.991012i \(0.457291\pi\)
\(390\) 0 0
\(391\) −46.5741 −2.35535
\(392\) 0 0
\(393\) 17.2871i 0.872021i
\(394\) 0 0
\(395\) 9.84240 4.09441i 0.495225 0.206012i
\(396\) 0 0
\(397\) 22.4153i 1.12499i 0.826800 + 0.562496i \(0.190159\pi\)
−0.826800 + 0.562496i \(0.809841\pi\)
\(398\) 0 0
\(399\) −27.7902 −1.39125
\(400\) 0 0
\(401\) −4.73635 −0.236522 −0.118261 0.992983i \(-0.537732\pi\)
−0.118261 + 0.992983i \(0.537732\pi\)
\(402\) 0 0
\(403\) 12.9098i 0.643081i
\(404\) 0 0
\(405\) −2.06455 + 0.858848i −0.102588 + 0.0426765i
\(406\) 0 0
\(407\) 9.46104i 0.468966i
\(408\) 0 0
\(409\) −23.3376 −1.15397 −0.576986 0.816754i \(-0.695771\pi\)
−0.576986 + 0.816754i \(0.695771\pi\)
\(410\) 0 0
\(411\) −6.25580 −0.308576
\(412\) 0 0
\(413\) 5.35186i 0.263348i
\(414\) 0 0
\(415\) −5.57243 13.3954i −0.273540 0.657553i
\(416\) 0 0
\(417\) 18.7158i 0.916517i
\(418\) 0 0
\(419\) −36.9545 −1.80534 −0.902672 0.430329i \(-0.858397\pi\)
−0.902672 + 0.430329i \(0.858397\pi\)
\(420\) 0 0
\(421\) 22.3448 1.08902 0.544508 0.838755i \(-0.316716\pi\)
0.544508 + 0.838755i \(0.316716\pi\)
\(422\) 0 0
\(423\) 10.2725i 0.499467i
\(424\) 0 0
\(425\) 24.3719 + 24.2240i 1.18221 + 1.17504i
\(426\) 0 0
\(427\) 42.4895i 2.05621i
\(428\) 0 0
\(429\) 5.21925 0.251988
\(430\) 0 0
\(431\) −24.8712 −1.19800 −0.599002 0.800747i \(-0.704436\pi\)
−0.599002 + 0.800747i \(0.704436\pi\)
\(432\) 0 0
\(433\) 32.4150i 1.55777i −0.627168 0.778884i \(-0.715786\pi\)
0.627168 0.778884i \(-0.284214\pi\)
\(434\) 0 0
\(435\) −2.31649 5.56851i −0.111067 0.266990i
\(436\) 0 0
\(437\) 52.4913i 2.51100i
\(438\) 0 0
\(439\) 3.50099 0.167093 0.0835467 0.996504i \(-0.473375\pi\)
0.0835467 + 0.996504i \(0.473375\pi\)
\(440\) 0 0
\(441\) 5.87254 0.279645
\(442\) 0 0
\(443\) 10.4807i 0.497952i 0.968510 + 0.248976i \(0.0800940\pi\)
−0.968510 + 0.248976i \(0.919906\pi\)
\(444\) 0 0
\(445\) 25.1445 10.4600i 1.19196 0.495853i
\(446\) 0 0
\(447\) 10.5604i 0.499492i
\(448\) 0 0
\(449\) 20.7324 0.978422 0.489211 0.872165i \(-0.337285\pi\)
0.489211 + 0.872165i \(0.337285\pi\)
\(450\) 0 0
\(451\) −2.36652 −0.111435
\(452\) 0 0
\(453\) 0.707027i 0.0332190i
\(454\) 0 0
\(455\) 41.6454 17.3244i 1.95237 0.812179i
\(456\) 0 0
\(457\) 4.98131i 0.233016i 0.993190 + 0.116508i \(0.0371700\pi\)
−0.993190 + 0.116508i \(0.962830\pi\)
\(458\) 0 0
\(459\) −6.87254 −0.320783
\(460\) 0 0
\(461\) 1.26383 0.0588623 0.0294312 0.999567i \(-0.490630\pi\)
0.0294312 + 0.999567i \(0.490630\pi\)
\(462\) 0 0
\(463\) 13.0429i 0.606155i −0.952966 0.303077i \(-0.901986\pi\)
0.952966 0.303077i \(-0.0980141\pi\)
\(464\) 0 0
\(465\) −1.97208 4.74062i −0.0914532 0.219841i
\(466\) 0 0
\(467\) 38.0737i 1.76184i 0.473265 + 0.880920i \(0.343075\pi\)
−0.473265 + 0.880920i \(0.656925\pi\)
\(468\) 0 0
\(469\) 3.58783 0.165671
\(470\) 0 0
\(471\) −6.97439 −0.321363
\(472\) 0 0
\(473\) 0.622282i 0.0286126i
\(474\) 0 0
\(475\) −27.3017 + 27.4683i −1.25269 + 1.26033i
\(476\) 0 0
\(477\) 3.41538i 0.156380i
\(478\) 0 0
\(479\) −31.0184 −1.41727 −0.708634 0.705577i \(-0.750688\pi\)
−0.708634 + 0.705577i \(0.750688\pi\)
\(480\) 0 0
\(481\) 57.2992 2.61262
\(482\) 0 0
\(483\) 24.3142i 1.10633i
\(484\) 0 0
\(485\) −9.54871 22.9538i −0.433584 1.04228i
\(486\) 0 0
\(487\) 17.0052i 0.770577i −0.922796 0.385288i \(-0.874102\pi\)
0.922796 0.385288i \(-0.125898\pi\)
\(488\) 0 0
\(489\) −18.3193 −0.828426
\(490\) 0 0
\(491\) −4.53723 −0.204762 −0.102381 0.994745i \(-0.532646\pi\)
−0.102381 + 0.994745i \(0.532646\pi\)
\(492\) 0 0
\(493\) 18.5366i 0.834847i
\(494\) 0 0
\(495\) 1.91657 0.797289i 0.0861435 0.0358355i
\(496\) 0 0
\(497\) 11.6619i 0.523109i
\(498\) 0 0
\(499\) −25.7313 −1.15189 −0.575945 0.817489i \(-0.695366\pi\)
−0.575945 + 0.817489i \(0.695366\pi\)
\(500\) 0 0
\(501\) −5.82349 −0.260174
\(502\) 0 0
\(503\) 19.8694i 0.885932i 0.896538 + 0.442966i \(0.146074\pi\)
−0.896538 + 0.442966i \(0.853926\pi\)
\(504\) 0 0
\(505\) −28.9241 + 12.0324i −1.28711 + 0.535433i
\(506\) 0 0
\(507\) 18.6095i 0.826479i
\(508\) 0 0
\(509\) −24.0462 −1.06583 −0.532916 0.846168i \(-0.678904\pi\)
−0.532916 + 0.846168i \(0.678904\pi\)
\(510\) 0 0
\(511\) 56.1936 2.48586
\(512\) 0 0
\(513\) 7.74568i 0.341980i
\(514\) 0 0
\(515\) 9.96367 + 23.9513i 0.439052 + 1.05542i
\(516\) 0 0
\(517\) 9.53622i 0.419403i
\(518\) 0 0
\(519\) −18.5918 −0.816090
\(520\) 0 0
\(521\) 35.2617 1.54484 0.772422 0.635109i \(-0.219045\pi\)
0.772422 + 0.635109i \(0.219045\pi\)
\(522\) 0 0
\(523\) 41.9031i 1.83230i −0.400839 0.916148i \(-0.631281\pi\)
0.400839 0.916148i \(-0.368719\pi\)
\(524\) 0 0
\(525\) 12.6462 12.7234i 0.551927 0.555296i
\(526\) 0 0
\(527\) 15.7807i 0.687418i
\(528\) 0 0
\(529\) −22.9256 −0.996766
\(530\) 0 0
\(531\) −1.49167 −0.0647330
\(532\) 0 0
\(533\) 14.3324i 0.620807i
\(534\) 0 0
\(535\) −17.5289 42.1370i −0.757839 1.82174i
\(536\) 0 0
\(537\) 0.0429121i 0.00185179i
\(538\) 0 0
\(539\) −5.45161 −0.234818
\(540\) 0 0
\(541\) 28.7752 1.23714 0.618571 0.785729i \(-0.287712\pi\)
0.618571 + 0.785729i \(0.287712\pi\)
\(542\) 0 0
\(543\) 0.122684i 0.00526485i
\(544\) 0 0
\(545\) 6.95444 2.89303i 0.297896 0.123924i
\(546\) 0 0
\(547\) 32.5449i 1.39152i −0.718274 0.695761i \(-0.755067\pi\)
0.718274 0.695761i \(-0.244933\pi\)
\(548\) 0 0
\(549\) −11.8427 −0.505433
\(550\) 0 0
\(551\) 20.8916 0.890014
\(552\) 0 0
\(553\) 17.1044i 0.727352i
\(554\) 0 0
\(555\) 21.0410 8.75298i 0.893139 0.371543i
\(556\) 0 0
\(557\) 39.9011i 1.69066i −0.534242 0.845332i \(-0.679403\pi\)
0.534242 0.845332i \(-0.320597\pi\)
\(558\) 0 0
\(559\) 3.76875 0.159401
\(560\) 0 0
\(561\) 6.37994 0.269361
\(562\) 0 0
\(563\) 31.7320i 1.33735i 0.743557 + 0.668673i \(0.233137\pi\)
−0.743557 + 0.668673i \(0.766863\pi\)
\(564\) 0 0
\(565\) −13.6363 32.7799i −0.573686 1.37906i
\(566\) 0 0
\(567\) 3.58783i 0.150675i
\(568\) 0 0
\(569\) 5.70307 0.239085 0.119542 0.992829i \(-0.461857\pi\)
0.119542 + 0.992829i \(0.461857\pi\)
\(570\) 0 0
\(571\) −32.3786 −1.35500 −0.677500 0.735523i \(-0.736937\pi\)
−0.677500 + 0.735523i \(0.736937\pi\)
\(572\) 0 0
\(573\) 14.4113i 0.602040i
\(574\) 0 0
\(575\) 24.0326 + 23.8867i 1.00223 + 0.996146i
\(576\) 0 0
\(577\) 12.8739i 0.535947i 0.963426 + 0.267974i \(0.0863540\pi\)
−0.963426 + 0.267974i \(0.913646\pi\)
\(578\) 0 0
\(579\) −2.81325 −0.116915
\(580\) 0 0
\(581\) −23.2788 −0.965767
\(582\) 0 0
\(583\) 3.17058i 0.131312i
\(584\) 0 0
\(585\) 4.82865 + 11.6074i 0.199640 + 0.479907i
\(586\) 0 0
\(587\) 0.341249i 0.0140849i 0.999975 + 0.00704243i \(0.00224170\pi\)
−0.999975 + 0.00704243i \(0.997758\pi\)
\(588\) 0 0
\(589\) 17.7856 0.732843
\(590\) 0 0
\(591\) −11.4350 −0.470371
\(592\) 0 0
\(593\) 10.9708i 0.450518i 0.974299 + 0.225259i \(0.0723228\pi\)
−0.974299 + 0.225259i \(0.927677\pi\)
\(594\) 0 0
\(595\) 50.9067 21.1771i 2.08697 0.868175i
\(596\) 0 0
\(597\) 24.3724i 0.997497i
\(598\) 0 0
\(599\) 25.0535 1.02366 0.511829 0.859088i \(-0.328968\pi\)
0.511829 + 0.859088i \(0.328968\pi\)
\(600\) 0 0
\(601\) 31.3181 1.27749 0.638745 0.769418i \(-0.279454\pi\)
0.638745 + 0.769418i \(0.279454\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 20.9309 8.70719i 0.850961 0.353998i
\(606\) 0 0
\(607\) 5.72286i 0.232284i 0.993233 + 0.116142i \(0.0370527\pi\)
−0.993233 + 0.116142i \(0.962947\pi\)
\(608\) 0 0
\(609\) −9.67710 −0.392136
\(610\) 0 0
\(611\) 57.7546 2.33650
\(612\) 0 0
\(613\) 1.31428i 0.0530831i 0.999648 + 0.0265415i \(0.00844943\pi\)
−0.999648 + 0.0265415i \(0.991551\pi\)
\(614\) 0 0
\(615\) −2.18941 5.26305i −0.0882856 0.212226i
\(616\) 0 0
\(617\) 6.05542i 0.243782i −0.992543 0.121891i \(-0.961104\pi\)
0.992543 0.121891i \(-0.0388959\pi\)
\(618\) 0 0
\(619\) 30.9572 1.24427 0.622137 0.782908i \(-0.286265\pi\)
0.622137 + 0.782908i \(0.286265\pi\)
\(620\) 0 0
\(621\) −6.77684 −0.271945
\(622\) 0 0
\(623\) 43.6967i 1.75067i
\(624\) 0 0
\(625\) −0.152143 24.9995i −0.00608573 0.999981i
\(626\) 0 0
\(627\) 7.19049i 0.287161i
\(628\) 0 0
\(629\) 70.0417 2.79275
\(630\) 0 0
\(631\) −13.6183 −0.542138 −0.271069 0.962560i \(-0.587377\pi\)
−0.271069 + 0.962560i \(0.587377\pi\)
\(632\) 0 0
\(633\) 2.29939i 0.0913924i
\(634\) 0 0
\(635\) −6.31470 15.1797i −0.250591 0.602387i
\(636\) 0 0
\(637\) 33.0168i 1.30817i
\(638\) 0 0
\(639\) −3.25041 −0.128584
\(640\) 0 0
\(641\) 35.2258 1.39134 0.695668 0.718363i \(-0.255108\pi\)
0.695668 + 0.718363i \(0.255108\pi\)
\(642\) 0 0
\(643\) 18.6823i 0.736759i −0.929675 0.368380i \(-0.879913\pi\)
0.929675 0.368380i \(-0.120087\pi\)
\(644\) 0 0
\(645\) 1.38393 0.575711i 0.0544922 0.0226686i
\(646\) 0 0
\(647\) 25.4400i 1.00015i −0.865982 0.500075i \(-0.833306\pi\)
0.865982 0.500075i \(-0.166694\pi\)
\(648\) 0 0
\(649\) 1.38475 0.0543563
\(650\) 0 0
\(651\) −8.23836 −0.322887
\(652\) 0 0
\(653\) 19.7060i 0.771155i 0.922676 + 0.385577i \(0.125998\pi\)
−0.922676 + 0.385577i \(0.874002\pi\)
\(654\) 0 0
\(655\) −35.6902 + 14.8470i −1.39453 + 0.580121i
\(656\) 0 0
\(657\) 15.6623i 0.611044i
\(658\) 0 0
\(659\) −22.8827 −0.891384 −0.445692 0.895186i \(-0.647042\pi\)
−0.445692 + 0.895186i \(0.647042\pi\)
\(660\) 0 0
\(661\) 30.1151 1.17134 0.585671 0.810549i \(-0.300831\pi\)
0.585671 + 0.810549i \(0.300831\pi\)
\(662\) 0 0
\(663\) 38.6390i 1.50062i
\(664\) 0 0
\(665\) 23.8676 + 57.3743i 0.925544 + 2.22488i
\(666\) 0 0
\(667\) 18.2785i 0.707747i
\(668\) 0 0
\(669\) 8.59585 0.332335
\(670\) 0 0
\(671\) 10.9938 0.424412
\(672\) 0 0
\(673\) 3.96661i 0.152902i −0.997073 0.0764508i \(-0.975641\pi\)
0.997073 0.0764508i \(-0.0243588\pi\)
\(674\) 0 0
\(675\) 3.54628 + 3.52476i 0.136496 + 0.135668i
\(676\) 0 0
\(677\) 35.4909i 1.36403i −0.731339 0.682014i \(-0.761104\pi\)
0.731339 0.682014i \(-0.238896\pi\)
\(678\) 0 0
\(679\) −39.8896 −1.53082
\(680\) 0 0
\(681\) 11.8063 0.452418
\(682\) 0 0
\(683\) 10.2681i 0.392899i 0.980514 + 0.196450i \(0.0629412\pi\)
−0.980514 + 0.196450i \(0.937059\pi\)
\(684\) 0 0
\(685\) 5.37278 + 12.9154i 0.205283 + 0.493473i
\(686\) 0 0
\(687\) 23.4280i 0.893834i
\(688\) 0 0
\(689\) 19.2021 0.731542
\(690\) 0 0
\(691\) 10.9612 0.416983 0.208492 0.978024i \(-0.433145\pi\)
0.208492 + 0.978024i \(0.433145\pi\)
\(692\) 0 0
\(693\) 3.33067i 0.126522i
\(694\) 0 0
\(695\) −38.6398 + 16.0740i −1.46569 + 0.609723i
\(696\) 0 0
\(697\) 17.5198i 0.663608i
\(698\) 0 0
\(699\) 8.43414 0.319009
\(700\) 0 0
\(701\) −34.9366 −1.31954 −0.659769 0.751469i \(-0.729346\pi\)
−0.659769 + 0.751469i \(0.729346\pi\)
\(702\) 0 0
\(703\) 78.9404i 2.97729i
\(704\) 0 0
\(705\) 21.2082 8.82254i 0.798746 0.332276i
\(706\) 0 0
\(707\) 50.2651i 1.89041i
\(708\) 0 0
\(709\) −46.3013 −1.73888 −0.869442 0.494036i \(-0.835521\pi\)
−0.869442 + 0.494036i \(0.835521\pi\)
\(710\) 0 0
\(711\) 4.76733 0.178789
\(712\) 0 0
\(713\) 15.5610i 0.582763i
\(714\) 0 0
\(715\) −4.48255 10.7754i −0.167638 0.402978i
\(716\) 0 0
\(717\) 16.3248i 0.609661i
\(718\) 0 0
\(719\) 30.9488 1.15419 0.577097 0.816675i \(-0.304185\pi\)
0.577097 + 0.816675i \(0.304185\pi\)
\(720\) 0 0
\(721\) 41.6232 1.55013
\(722\) 0 0
\(723\) 11.9934i 0.446041i
\(724\) 0 0
\(725\) −9.50698 + 9.56502i −0.353080 + 0.355236i
\(726\) 0 0
\(727\) 3.19242i 0.118400i 0.998246 + 0.0592001i \(0.0188550\pi\)
−0.998246 + 0.0592001i \(0.981145\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 4.60686 0.170391
\(732\) 0 0
\(733\) 1.42238i 0.0525369i −0.999655 0.0262684i \(-0.991638\pi\)
0.999655 0.0262684i \(-0.00836247\pi\)
\(734\) 0 0
\(735\) −5.04362 12.1242i −0.186037 0.447206i
\(736\) 0 0
\(737\) 0.928323i 0.0341952i
\(738\) 0 0
\(739\) −21.9270 −0.806599 −0.403299 0.915068i \(-0.632137\pi\)
−0.403299 + 0.915068i \(0.632137\pi\)
\(740\) 0 0
\(741\) −43.5480 −1.59978
\(742\) 0 0
\(743\) 37.8836i 1.38981i −0.719099 0.694907i \(-0.755445\pi\)
0.719099 0.694907i \(-0.244555\pi\)
\(744\) 0 0
\(745\) 21.8026 9.06982i 0.798785 0.332292i
\(746\) 0 0
\(747\) 6.48826i 0.237393i
\(748\) 0 0
\(749\) −73.2267 −2.67565
\(750\) 0 0
\(751\) −2.81778 −0.102822 −0.0514111 0.998678i \(-0.516372\pi\)
−0.0514111 + 0.998678i \(0.516372\pi\)
\(752\) 0 0
\(753\) 26.3699i 0.960972i
\(754\) 0 0
\(755\) 1.45970 0.607229i 0.0531237 0.0220993i
\(756\) 0 0
\(757\) 3.57996i 0.130116i −0.997881 0.0650579i \(-0.979277\pi\)
0.997881 0.0650579i \(-0.0207232\pi\)
\(758\) 0 0
\(759\) 6.29110 0.228353
\(760\) 0 0
\(761\) −21.5794 −0.782252 −0.391126 0.920337i \(-0.627914\pi\)
−0.391126 + 0.920337i \(0.627914\pi\)
\(762\) 0 0
\(763\) 12.0856i 0.437528i
\(764\) 0 0
\(765\) 5.90247 + 14.1887i 0.213404 + 0.512994i
\(766\) 0 0
\(767\) 8.38653i 0.302820i
\(768\) 0 0
\(769\) 25.8781 0.933187 0.466593 0.884472i \(-0.345481\pi\)
0.466593 + 0.884472i \(0.345481\pi\)
\(770\) 0 0
\(771\) 20.5740 0.740954
\(772\) 0 0
\(773\) 44.4485i 1.59870i 0.600866 + 0.799350i \(0.294823\pi\)
−0.600866 + 0.799350i \(0.705177\pi\)
\(774\) 0 0
\(775\) −8.09354 + 8.14294i −0.290728 + 0.292503i
\(776\) 0 0
\(777\) 36.5655i 1.31178i
\(778\) 0 0
\(779\) 19.7456 0.707460
\(780\) 0 0
\(781\) 3.01743 0.107972
\(782\) 0 0
\(783\) 2.69720i 0.0963901i
\(784\) 0 0
\(785\) 5.98994 + 14.3990i 0.213790 + 0.513922i
\(786\) 0 0
\(787\) 21.6381i 0.771316i −0.922642 0.385658i \(-0.873974\pi\)
0.922642 0.385658i \(-0.126026\pi\)
\(788\) 0 0
\(789\) −4.88398 −0.173874
\(790\) 0 0
\(791\) −56.9657 −2.02547
\(792\) 0 0