Properties

Label 4020.2.g.c.1609.17
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 1609.17
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.36

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(2.08125 - 0.817560i) q^{5}\) \(+3.41849i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(2.08125 - 0.817560i) q^{5}\) \(+3.41849i q^{7}\) \(-1.00000 q^{9}\) \(+5.18352 q^{11}\) \(-5.24487i q^{13}\) \(+(-0.817560 - 2.08125i) q^{15}\) \(+7.93273i q^{17}\) \(+1.59836 q^{19}\) \(+3.41849 q^{21}\) \(+7.16283i q^{23}\) \(+(3.66319 - 3.40309i) q^{25}\) \(+1.00000i q^{27}\) \(+6.58679 q^{29}\) \(-5.96221 q^{31}\) \(-5.18352i q^{33}\) \(+(2.79482 + 7.11473i) q^{35}\) \(+10.2629i q^{37}\) \(-5.24487 q^{39}\) \(-8.07835 q^{41}\) \(+0.663360i q^{43}\) \(+(-2.08125 + 0.817560i) q^{45}\) \(+7.08264i q^{47}\) \(-4.68609 q^{49}\) \(+7.93273 q^{51}\) \(-11.5654i q^{53}\) \(+(10.7882 - 4.23784i) q^{55}\) \(-1.59836i q^{57}\) \(+1.90150 q^{59}\) \(+1.14296 q^{61}\) \(-3.41849i q^{63}\) \(+(-4.28800 - 10.9159i) q^{65}\) \(-1.00000i q^{67}\) \(+7.16283 q^{69}\) \(+1.39500 q^{71}\) \(-6.22878i q^{73}\) \(+(-3.40309 - 3.66319i) q^{75}\) \(+17.7198i q^{77}\) \(-1.75892 q^{79}\) \(+1.00000 q^{81}\) \(+12.9936i q^{83}\) \(+(6.48548 + 16.5100i) q^{85}\) \(-6.58679i q^{87}\) \(-6.29938 q^{89}\) \(+17.9296 q^{91}\) \(+5.96221i q^{93}\) \(+(3.32658 - 1.30675i) q^{95}\) \(+4.62505i q^{97}\) \(-5.18352 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 2.08125 0.817560i 0.930763 0.365624i
\(6\) 0 0
\(7\) 3.41849i 1.29207i 0.763308 + 0.646034i \(0.223574\pi\)
−0.763308 + 0.646034i \(0.776426\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 5.18352 1.56289 0.781446 0.623973i \(-0.214483\pi\)
0.781446 + 0.623973i \(0.214483\pi\)
\(12\) 0 0
\(13\) 5.24487i 1.45467i −0.686285 0.727333i \(-0.740760\pi\)
0.686285 0.727333i \(-0.259240\pi\)
\(14\) 0 0
\(15\) −0.817560 2.08125i −0.211093 0.537376i
\(16\) 0 0
\(17\) 7.93273i 1.92397i 0.273105 + 0.961984i \(0.411949\pi\)
−0.273105 + 0.961984i \(0.588051\pi\)
\(18\) 0 0
\(19\) 1.59836 0.366688 0.183344 0.983049i \(-0.441308\pi\)
0.183344 + 0.983049i \(0.441308\pi\)
\(20\) 0 0
\(21\) 3.41849 0.745976
\(22\) 0 0
\(23\) 7.16283i 1.49355i 0.665075 + 0.746777i \(0.268400\pi\)
−0.665075 + 0.746777i \(0.731600\pi\)
\(24\) 0 0
\(25\) 3.66319 3.40309i 0.732638 0.680619i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 6.58679 1.22314 0.611568 0.791192i \(-0.290539\pi\)
0.611568 + 0.791192i \(0.290539\pi\)
\(30\) 0 0
\(31\) −5.96221 −1.07085 −0.535423 0.844584i \(-0.679848\pi\)
−0.535423 + 0.844584i \(0.679848\pi\)
\(32\) 0 0
\(33\) 5.18352i 0.902336i
\(34\) 0 0
\(35\) 2.79482 + 7.11473i 0.472412 + 1.20261i
\(36\) 0 0
\(37\) 10.2629i 1.68720i 0.536969 + 0.843602i \(0.319569\pi\)
−0.536969 + 0.843602i \(0.680431\pi\)
\(38\) 0 0
\(39\) −5.24487 −0.839852
\(40\) 0 0
\(41\) −8.07835 −1.26163 −0.630813 0.775935i \(-0.717279\pi\)
−0.630813 + 0.775935i \(0.717279\pi\)
\(42\) 0 0
\(43\) 0.663360i 0.101161i 0.998720 + 0.0505807i \(0.0161072\pi\)
−0.998720 + 0.0505807i \(0.983893\pi\)
\(44\) 0 0
\(45\) −2.08125 + 0.817560i −0.310254 + 0.121875i
\(46\) 0 0
\(47\) 7.08264i 1.03311i 0.856254 + 0.516555i \(0.172786\pi\)
−0.856254 + 0.516555i \(0.827214\pi\)
\(48\) 0 0
\(49\) −4.68609 −0.669442
\(50\) 0 0
\(51\) 7.93273 1.11080
\(52\) 0 0
\(53\) 11.5654i 1.58863i −0.607504 0.794316i \(-0.707829\pi\)
0.607504 0.794316i \(-0.292171\pi\)
\(54\) 0 0
\(55\) 10.7882 4.23784i 1.45468 0.571431i
\(56\) 0 0
\(57\) 1.59836i 0.211707i
\(58\) 0 0
\(59\) 1.90150 0.247554 0.123777 0.992310i \(-0.460499\pi\)
0.123777 + 0.992310i \(0.460499\pi\)
\(60\) 0 0
\(61\) 1.14296 0.146341 0.0731705 0.997319i \(-0.476688\pi\)
0.0731705 + 0.997319i \(0.476688\pi\)
\(62\) 0 0
\(63\) 3.41849i 0.430690i
\(64\) 0 0
\(65\) −4.28800 10.9159i −0.531861 1.35395i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) 7.16283 0.862303
\(70\) 0 0
\(71\) 1.39500 0.165556 0.0827780 0.996568i \(-0.473621\pi\)
0.0827780 + 0.996568i \(0.473621\pi\)
\(72\) 0 0
\(73\) 6.22878i 0.729023i −0.931199 0.364512i \(-0.881236\pi\)
0.931199 0.364512i \(-0.118764\pi\)
\(74\) 0 0
\(75\) −3.40309 3.66319i −0.392955 0.422989i
\(76\) 0 0
\(77\) 17.7198i 2.01936i
\(78\) 0 0
\(79\) −1.75892 −0.197894 −0.0989469 0.995093i \(-0.531547\pi\)
−0.0989469 + 0.995093i \(0.531547\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.9936i 1.42624i 0.701044 + 0.713118i \(0.252718\pi\)
−0.701044 + 0.713118i \(0.747282\pi\)
\(84\) 0 0
\(85\) 6.48548 + 16.5100i 0.703449 + 1.79076i
\(86\) 0 0
\(87\) 6.58679i 0.706178i
\(88\) 0 0
\(89\) −6.29938 −0.667733 −0.333867 0.942620i \(-0.608354\pi\)
−0.333867 + 0.942620i \(0.608354\pi\)
\(90\) 0 0
\(91\) 17.9296 1.87953
\(92\) 0 0
\(93\) 5.96221i 0.618253i
\(94\) 0 0
\(95\) 3.32658 1.30675i 0.341300 0.134070i
\(96\) 0 0
\(97\) 4.62505i 0.469603i 0.972043 + 0.234801i \(0.0754440\pi\)
−0.972043 + 0.234801i \(0.924556\pi\)
\(98\) 0 0
\(99\) −5.18352 −0.520964
\(100\) 0 0
\(101\) 9.37470 0.932818 0.466409 0.884569i \(-0.345548\pi\)
0.466409 + 0.884569i \(0.345548\pi\)
\(102\) 0 0
\(103\) 7.81662i 0.770194i 0.922876 + 0.385097i \(0.125832\pi\)
−0.922876 + 0.385097i \(0.874168\pi\)
\(104\) 0 0
\(105\) 7.11473 2.79482i 0.694327 0.272747i
\(106\) 0 0
\(107\) 9.25657i 0.894867i −0.894317 0.447433i \(-0.852338\pi\)
0.894317 0.447433i \(-0.147662\pi\)
\(108\) 0 0
\(109\) −16.7849 −1.60770 −0.803849 0.594834i \(-0.797218\pi\)
−0.803849 + 0.594834i \(0.797218\pi\)
\(110\) 0 0
\(111\) 10.2629 0.974108
\(112\) 0 0
\(113\) 0.985409i 0.0926995i 0.998925 + 0.0463497i \(0.0147589\pi\)
−0.998925 + 0.0463497i \(0.985241\pi\)
\(114\) 0 0
\(115\) 5.85605 + 14.9076i 0.546079 + 1.39014i
\(116\) 0 0
\(117\) 5.24487i 0.484889i
\(118\) 0 0
\(119\) −27.1180 −2.48590
\(120\) 0 0
\(121\) 15.8689 1.44263
\(122\) 0 0
\(123\) 8.07835i 0.728400i
\(124\) 0 0
\(125\) 4.84177 10.0776i 0.433061 0.901364i
\(126\) 0 0
\(127\) 3.93033i 0.348760i −0.984678 0.174380i \(-0.944208\pi\)
0.984678 0.174380i \(-0.0557921\pi\)
\(128\) 0 0
\(129\) 0.663360 0.0584056
\(130\) 0 0
\(131\) −17.9128 −1.56504 −0.782522 0.622622i \(-0.786067\pi\)
−0.782522 + 0.622622i \(0.786067\pi\)
\(132\) 0 0
\(133\) 5.46397i 0.473786i
\(134\) 0 0
\(135\) 0.817560 + 2.08125i 0.0703644 + 0.179125i
\(136\) 0 0
\(137\) 5.44440i 0.465146i 0.972579 + 0.232573i \(0.0747145\pi\)
−0.972579 + 0.232573i \(0.925286\pi\)
\(138\) 0 0
\(139\) 12.3886 1.05079 0.525395 0.850858i \(-0.323917\pi\)
0.525395 + 0.850858i \(0.323917\pi\)
\(140\) 0 0
\(141\) 7.08264 0.596466
\(142\) 0 0
\(143\) 27.1869i 2.27349i
\(144\) 0 0
\(145\) 13.7088 5.38510i 1.13845 0.447208i
\(146\) 0 0
\(147\) 4.68609i 0.386502i
\(148\) 0 0
\(149\) 10.4378 0.855094 0.427547 0.903993i \(-0.359378\pi\)
0.427547 + 0.903993i \(0.359378\pi\)
\(150\) 0 0
\(151\) 2.58130 0.210064 0.105032 0.994469i \(-0.466506\pi\)
0.105032 + 0.994469i \(0.466506\pi\)
\(152\) 0 0
\(153\) 7.93273i 0.641323i
\(154\) 0 0
\(155\) −12.4088 + 4.87447i −0.996703 + 0.391527i
\(156\) 0 0
\(157\) 2.37987i 0.189934i 0.995480 + 0.0949672i \(0.0302746\pi\)
−0.995480 + 0.0949672i \(0.969725\pi\)
\(158\) 0 0
\(159\) −11.5654 −0.917197
\(160\) 0 0
\(161\) −24.4861 −1.92977
\(162\) 0 0
\(163\) 8.42295i 0.659737i −0.944027 0.329868i \(-0.892996\pi\)
0.944027 0.329868i \(-0.107004\pi\)
\(164\) 0 0
\(165\) −4.23784 10.7882i −0.329916 0.839860i
\(166\) 0 0
\(167\) 5.31683i 0.411428i 0.978612 + 0.205714i \(0.0659517\pi\)
−0.978612 + 0.205714i \(0.934048\pi\)
\(168\) 0 0
\(169\) −14.5087 −1.11605
\(170\) 0 0
\(171\) −1.59836 −0.122229
\(172\) 0 0
\(173\) 15.2214i 1.15726i −0.815591 0.578629i \(-0.803588\pi\)
0.815591 0.578629i \(-0.196412\pi\)
\(174\) 0 0
\(175\) 11.6334 + 12.5226i 0.879406 + 0.946619i
\(176\) 0 0
\(177\) 1.90150i 0.142925i
\(178\) 0 0
\(179\) 13.6194 1.01796 0.508980 0.860779i \(-0.330023\pi\)
0.508980 + 0.860779i \(0.330023\pi\)
\(180\) 0 0
\(181\) −5.42287 −0.403079 −0.201539 0.979480i \(-0.564594\pi\)
−0.201539 + 0.979480i \(0.564594\pi\)
\(182\) 0 0
\(183\) 1.14296i 0.0844900i
\(184\) 0 0
\(185\) 8.39051 + 21.3596i 0.616883 + 1.57039i
\(186\) 0 0
\(187\) 41.1195i 3.00695i
\(188\) 0 0
\(189\) −3.41849 −0.248659
\(190\) 0 0
\(191\) 3.71059 0.268489 0.134244 0.990948i \(-0.457139\pi\)
0.134244 + 0.990948i \(0.457139\pi\)
\(192\) 0 0
\(193\) 4.66970i 0.336133i 0.985776 + 0.168066i \(0.0537523\pi\)
−0.985776 + 0.168066i \(0.946248\pi\)
\(194\) 0 0
\(195\) −10.9159 + 4.28800i −0.781703 + 0.307070i
\(196\) 0 0
\(197\) 21.7808i 1.55182i 0.630844 + 0.775909i \(0.282709\pi\)
−0.630844 + 0.775909i \(0.717291\pi\)
\(198\) 0 0
\(199\) 26.0873 1.84928 0.924641 0.380840i \(-0.124365\pi\)
0.924641 + 0.380840i \(0.124365\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 22.5169i 1.58038i
\(204\) 0 0
\(205\) −16.8131 + 6.60454i −1.17427 + 0.461281i
\(206\) 0 0
\(207\) 7.16283i 0.497851i
\(208\) 0 0
\(209\) 8.28512 0.573094
\(210\) 0 0
\(211\) 25.5255 1.75725 0.878626 0.477511i \(-0.158461\pi\)
0.878626 + 0.477511i \(0.158461\pi\)
\(212\) 0 0
\(213\) 1.39500i 0.0955838i
\(214\) 0 0
\(215\) 0.542337 + 1.38062i 0.0369871 + 0.0941573i
\(216\) 0 0
\(217\) 20.3818i 1.38361i
\(218\) 0 0
\(219\) −6.22878 −0.420902
\(220\) 0 0
\(221\) 41.6061 2.79873
\(222\) 0 0
\(223\) 17.1864i 1.15089i −0.817842 0.575443i \(-0.804830\pi\)
0.817842 0.575443i \(-0.195170\pi\)
\(224\) 0 0
\(225\) −3.66319 + 3.40309i −0.244213 + 0.226873i
\(226\) 0 0
\(227\) 10.5003i 0.696926i −0.937322 0.348463i \(-0.886704\pi\)
0.937322 0.348463i \(-0.113296\pi\)
\(228\) 0 0
\(229\) 6.29601 0.416052 0.208026 0.978123i \(-0.433296\pi\)
0.208026 + 0.978123i \(0.433296\pi\)
\(230\) 0 0
\(231\) 17.7198 1.16588
\(232\) 0 0
\(233\) 27.9039i 1.82804i −0.405664 0.914022i \(-0.632960\pi\)
0.405664 0.914022i \(-0.367040\pi\)
\(234\) 0 0
\(235\) 5.79049 + 14.7407i 0.377730 + 0.961580i
\(236\) 0 0
\(237\) 1.75892i 0.114254i
\(238\) 0 0
\(239\) 23.3664 1.51145 0.755725 0.654889i \(-0.227285\pi\)
0.755725 + 0.654889i \(0.227285\pi\)
\(240\) 0 0
\(241\) −20.9579 −1.35002 −0.675009 0.737810i \(-0.735860\pi\)
−0.675009 + 0.737810i \(0.735860\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −9.75292 + 3.83116i −0.623091 + 0.244764i
\(246\) 0 0
\(247\) 8.38318i 0.533409i
\(248\) 0 0
\(249\) 12.9936 0.823438
\(250\) 0 0
\(251\) −11.0003 −0.694336 −0.347168 0.937803i \(-0.612857\pi\)
−0.347168 + 0.937803i \(0.612857\pi\)
\(252\) 0 0
\(253\) 37.1287i 2.33426i
\(254\) 0 0
\(255\) 16.5100 6.48548i 1.03389 0.406137i
\(256\) 0 0
\(257\) 22.4819i 1.40238i −0.712974 0.701190i \(-0.752652\pi\)
0.712974 0.701190i \(-0.247348\pi\)
\(258\) 0 0
\(259\) −35.0835 −2.17998
\(260\) 0 0
\(261\) −6.58679 −0.407712
\(262\) 0 0
\(263\) 19.3224i 1.19147i −0.803181 0.595735i \(-0.796861\pi\)
0.803181 0.595735i \(-0.203139\pi\)
\(264\) 0 0
\(265\) −9.45543 24.0705i −0.580842 1.47864i
\(266\) 0 0
\(267\) 6.29938i 0.385516i
\(268\) 0 0
\(269\) −3.71965 −0.226791 −0.113396 0.993550i \(-0.536173\pi\)
−0.113396 + 0.993550i \(0.536173\pi\)
\(270\) 0 0
\(271\) 15.3434 0.932043 0.466022 0.884773i \(-0.345687\pi\)
0.466022 + 0.884773i \(0.345687\pi\)
\(272\) 0 0
\(273\) 17.9296i 1.08515i
\(274\) 0 0
\(275\) 18.9882 17.6400i 1.14503 1.06373i
\(276\) 0 0
\(277\) 25.6005i 1.53818i −0.639138 0.769092i \(-0.720709\pi\)
0.639138 0.769092i \(-0.279291\pi\)
\(278\) 0 0
\(279\) 5.96221 0.356948
\(280\) 0 0
\(281\) 24.1995 1.44362 0.721811 0.692090i \(-0.243310\pi\)
0.721811 + 0.692090i \(0.243310\pi\)
\(282\) 0 0
\(283\) 10.3634i 0.616037i 0.951380 + 0.308019i \(0.0996659\pi\)
−0.951380 + 0.308019i \(0.900334\pi\)
\(284\) 0 0
\(285\) −1.30675 3.32658i −0.0774054 0.197049i
\(286\) 0 0
\(287\) 27.6158i 1.63011i
\(288\) 0 0
\(289\) −45.9281 −2.70166
\(290\) 0 0
\(291\) 4.62505 0.271125
\(292\) 0 0
\(293\) 4.91431i 0.287097i 0.989643 + 0.143549i \(0.0458513\pi\)
−0.989643 + 0.143549i \(0.954149\pi\)
\(294\) 0 0
\(295\) 3.95749 1.55459i 0.230414 0.0905116i
\(296\) 0 0
\(297\) 5.18352i 0.300779i
\(298\) 0 0
\(299\) 37.5681 2.17262
\(300\) 0 0
\(301\) −2.26769 −0.130708
\(302\) 0 0
\(303\) 9.37470i 0.538563i
\(304\) 0 0
\(305\) 2.37878 0.934439i 0.136209 0.0535058i
\(306\) 0 0
\(307\) 2.87657i 0.164175i −0.996625 0.0820873i \(-0.973841\pi\)
0.996625 0.0820873i \(-0.0261586\pi\)
\(308\) 0 0
\(309\) 7.81662 0.444672
\(310\) 0 0
\(311\) 6.15003 0.348736 0.174368 0.984681i \(-0.444212\pi\)
0.174368 + 0.984681i \(0.444212\pi\)
\(312\) 0 0
\(313\) 4.46096i 0.252149i 0.992021 + 0.126074i \(0.0402378\pi\)
−0.992021 + 0.126074i \(0.959762\pi\)
\(314\) 0 0
\(315\) −2.79482 7.11473i −0.157471 0.400870i
\(316\) 0 0
\(317\) 14.7678i 0.829444i −0.909948 0.414722i \(-0.863879\pi\)
0.909948 0.414722i \(-0.136121\pi\)
\(318\) 0 0
\(319\) 34.1428 1.91163
\(320\) 0 0
\(321\) −9.25657 −0.516652
\(322\) 0 0
\(323\) 12.6793i 0.705496i
\(324\) 0 0
\(325\) −17.8488 19.2130i −0.990073 1.06574i
\(326\) 0 0
\(327\) 16.7849i 0.928205i
\(328\) 0 0
\(329\) −24.2120 −1.33485
\(330\) 0 0
\(331\) 13.0188 0.715578 0.357789 0.933802i \(-0.383531\pi\)
0.357789 + 0.933802i \(0.383531\pi\)
\(332\) 0 0
\(333\) 10.2629i 0.562401i
\(334\) 0 0
\(335\) −0.817560 2.08125i −0.0446681 0.113711i
\(336\) 0 0
\(337\) 5.35694i 0.291811i 0.989299 + 0.145906i \(0.0466096\pi\)
−0.989299 + 0.145906i \(0.953390\pi\)
\(338\) 0 0
\(339\) 0.985409 0.0535201
\(340\) 0 0
\(341\) −30.9053 −1.67362
\(342\) 0 0
\(343\) 7.91008i 0.427104i
\(344\) 0 0
\(345\) 14.9076 5.85605i 0.802600 0.315279i
\(346\) 0 0
\(347\) 28.3748i 1.52324i −0.648025 0.761619i \(-0.724405\pi\)
0.648025 0.761619i \(-0.275595\pi\)
\(348\) 0 0
\(349\) −18.6940 −1.00067 −0.500335 0.865832i \(-0.666790\pi\)
−0.500335 + 0.865832i \(0.666790\pi\)
\(350\) 0 0
\(351\) 5.24487 0.279951
\(352\) 0 0
\(353\) 15.5467i 0.827465i −0.910399 0.413732i \(-0.864225\pi\)
0.910399 0.413732i \(-0.135775\pi\)
\(354\) 0 0
\(355\) 2.90334 1.14050i 0.154093 0.0605313i
\(356\) 0 0
\(357\) 27.1180i 1.43523i
\(358\) 0 0
\(359\) 34.8793 1.84086 0.920430 0.390908i \(-0.127839\pi\)
0.920430 + 0.390908i \(0.127839\pi\)
\(360\) 0 0
\(361\) −16.4453 −0.865540
\(362\) 0 0
\(363\) 15.8689i 0.832903i
\(364\) 0 0
\(365\) −5.09240 12.9636i −0.266549 0.678548i
\(366\) 0 0
\(367\) 12.4800i 0.651452i −0.945464 0.325726i \(-0.894391\pi\)
0.945464 0.325726i \(-0.105609\pi\)
\(368\) 0 0
\(369\) 8.07835 0.420542
\(370\) 0 0
\(371\) 39.5363 2.05262
\(372\) 0 0
\(373\) 5.61837i 0.290908i 0.989365 + 0.145454i \(0.0464643\pi\)
−0.989365 + 0.145454i \(0.953536\pi\)
\(374\) 0 0
\(375\) −10.0776 4.84177i −0.520403 0.250028i
\(376\) 0 0
\(377\) 34.5469i 1.77926i
\(378\) 0 0
\(379\) 12.6866 0.651669 0.325834 0.945427i \(-0.394355\pi\)
0.325834 + 0.945427i \(0.394355\pi\)
\(380\) 0 0
\(381\) −3.93033 −0.201357
\(382\) 0 0
\(383\) 22.8508i 1.16762i 0.811889 + 0.583811i \(0.198439\pi\)
−0.811889 + 0.583811i \(0.801561\pi\)
\(384\) 0 0
\(385\) 14.4870 + 36.8794i 0.738328 + 1.87955i
\(386\) 0 0
\(387\) 0.663360i 0.0337205i
\(388\) 0 0
\(389\) 37.2207 1.88716 0.943581 0.331142i \(-0.107434\pi\)
0.943581 + 0.331142i \(0.107434\pi\)
\(390\) 0 0
\(391\) −56.8208 −2.87355
\(392\) 0 0
\(393\) 17.9128i 0.903579i
\(394\) 0 0
\(395\) −3.66075 + 1.43802i −0.184192 + 0.0723548i
\(396\) 0 0
\(397\) 0.301013i 0.0151074i −0.999971 0.00755370i \(-0.997596\pi\)
0.999971 0.00755370i \(-0.00240444\pi\)
\(398\) 0 0
\(399\) 5.46397 0.273541
\(400\) 0 0
\(401\) 0.0301904 0.00150764 0.000753818 1.00000i \(-0.499760\pi\)
0.000753818 1.00000i \(0.499760\pi\)
\(402\) 0 0
\(403\) 31.2711i 1.55772i
\(404\) 0 0
\(405\) 2.08125 0.817560i 0.103418 0.0406249i
\(406\) 0 0
\(407\) 53.1978i 2.63692i
\(408\) 0 0
\(409\) −9.13879 −0.451884 −0.225942 0.974141i \(-0.572546\pi\)
−0.225942 + 0.974141i \(0.572546\pi\)
\(410\) 0 0
\(411\) 5.44440 0.268552
\(412\) 0 0
\(413\) 6.50025i 0.319856i
\(414\) 0 0
\(415\) 10.6231 + 27.0430i 0.521466 + 1.32749i
\(416\) 0 0
\(417\) 12.3886i 0.606674i
\(418\) 0 0
\(419\) 0.473003 0.0231077 0.0115539 0.999933i \(-0.496322\pi\)
0.0115539 + 0.999933i \(0.496322\pi\)
\(420\) 0 0
\(421\) −31.6592 −1.54297 −0.771487 0.636245i \(-0.780487\pi\)
−0.771487 + 0.636245i \(0.780487\pi\)
\(422\) 0 0
\(423\) 7.08264i 0.344370i
\(424\) 0 0
\(425\) 26.9958 + 29.0591i 1.30949 + 1.40957i
\(426\) 0 0
\(427\) 3.90720i 0.189083i
\(428\) 0 0
\(429\) −27.1869 −1.31260
\(430\) 0 0
\(431\) −15.9666 −0.769084 −0.384542 0.923108i \(-0.625641\pi\)
−0.384542 + 0.923108i \(0.625641\pi\)
\(432\) 0 0
\(433\) 11.5387i 0.554516i 0.960795 + 0.277258i \(0.0894257\pi\)
−0.960795 + 0.277258i \(0.910574\pi\)
\(434\) 0 0
\(435\) −5.38510 13.7088i −0.258196 0.657284i
\(436\) 0 0
\(437\) 11.4488i 0.547668i
\(438\) 0 0
\(439\) −18.1762 −0.867501 −0.433750 0.901033i \(-0.642810\pi\)
−0.433750 + 0.901033i \(0.642810\pi\)
\(440\) 0 0
\(441\) 4.68609 0.223147
\(442\) 0 0
\(443\) 15.0286i 0.714032i −0.934098 0.357016i \(-0.883794\pi\)
0.934098 0.357016i \(-0.116206\pi\)
\(444\) 0 0
\(445\) −13.1106 + 5.15013i −0.621501 + 0.244139i
\(446\) 0 0
\(447\) 10.4378i 0.493689i
\(448\) 0 0
\(449\) −6.19596 −0.292405 −0.146203 0.989255i \(-0.546705\pi\)
−0.146203 + 0.989255i \(0.546705\pi\)
\(450\) 0 0
\(451\) −41.8743 −1.97178
\(452\) 0 0
\(453\) 2.58130i 0.121280i
\(454\) 0 0
\(455\) 37.3159 14.6585i 1.74939 0.687201i
\(456\) 0 0
\(457\) 2.21675i 0.103695i 0.998655 + 0.0518476i \(0.0165110\pi\)
−0.998655 + 0.0518476i \(0.983489\pi\)
\(458\) 0 0
\(459\) −7.93273 −0.370268
\(460\) 0 0
\(461\) −7.01529 −0.326735 −0.163367 0.986565i \(-0.552236\pi\)
−0.163367 + 0.986565i \(0.552236\pi\)
\(462\) 0 0
\(463\) 6.89526i 0.320450i 0.987081 + 0.160225i \(0.0512219\pi\)
−0.987081 + 0.160225i \(0.948778\pi\)
\(464\) 0 0
\(465\) 4.87447 + 12.4088i 0.226048 + 0.575447i
\(466\) 0 0
\(467\) 2.92697i 0.135444i 0.997704 + 0.0677220i \(0.0215731\pi\)
−0.997704 + 0.0677220i \(0.978427\pi\)
\(468\) 0 0
\(469\) 3.41849 0.157851
\(470\) 0 0
\(471\) 2.37987 0.109659
\(472\) 0 0
\(473\) 3.43854i 0.158104i
\(474\) 0 0
\(475\) 5.85508 5.43936i 0.268650 0.249575i
\(476\) 0 0
\(477\) 11.5654i 0.529544i
\(478\) 0 0
\(479\) −28.3826 −1.29684 −0.648418 0.761285i \(-0.724569\pi\)
−0.648418 + 0.761285i \(0.724569\pi\)
\(480\) 0 0
\(481\) 53.8274 2.45432
\(482\) 0 0
\(483\) 24.4861i 1.11416i
\(484\) 0 0
\(485\) 3.78126 + 9.62588i 0.171698 + 0.437089i
\(486\) 0 0
\(487\) 20.0285i 0.907579i −0.891109 0.453789i \(-0.850072\pi\)
0.891109 0.453789i \(-0.149928\pi\)
\(488\) 0 0
\(489\) −8.42295 −0.380899
\(490\) 0 0
\(491\) 5.61015 0.253183 0.126591 0.991955i \(-0.459596\pi\)
0.126591 + 0.991955i \(0.459596\pi\)
\(492\) 0 0
\(493\) 52.2512i 2.35328i
\(494\) 0 0
\(495\) −10.7882 + 4.23784i −0.484894 + 0.190477i
\(496\) 0 0
\(497\) 4.76880i 0.213910i
\(498\) 0 0
\(499\) −14.1619 −0.633974 −0.316987 0.948430i \(-0.602671\pi\)
−0.316987 + 0.948430i \(0.602671\pi\)
\(500\) 0 0
\(501\) 5.31683 0.237538
\(502\) 0 0
\(503\) 0.705378i 0.0314513i −0.999876 0.0157256i \(-0.994994\pi\)
0.999876 0.0157256i \(-0.00500583\pi\)
\(504\) 0 0
\(505\) 19.5111 7.66439i 0.868232 0.341061i
\(506\) 0 0
\(507\) 14.5087i 0.644354i
\(508\) 0 0
\(509\) 40.4309 1.79207 0.896035 0.443984i \(-0.146435\pi\)
0.896035 + 0.443984i \(0.146435\pi\)
\(510\) 0 0
\(511\) 21.2930 0.941948
\(512\) 0 0
\(513\) 1.59836i 0.0705692i
\(514\) 0 0
\(515\) 6.39056 + 16.2683i 0.281602 + 0.716868i
\(516\) 0 0
\(517\) 36.7131i 1.61464i
\(518\) 0 0
\(519\) −15.2214 −0.668143
\(520\) 0 0
\(521\) −21.4333 −0.939011 −0.469506 0.882929i \(-0.655568\pi\)
−0.469506 + 0.882929i \(0.655568\pi\)
\(522\) 0 0
\(523\) 34.4820i 1.50779i −0.656994 0.753895i \(-0.728172\pi\)
0.656994 0.753895i \(-0.271828\pi\)
\(524\) 0 0
\(525\) 12.5226 11.6334i 0.546530 0.507725i
\(526\) 0 0
\(527\) 47.2966i 2.06027i
\(528\) 0 0
\(529\) −28.3061 −1.23070
\(530\) 0 0
\(531\) −1.90150 −0.0825179
\(532\) 0 0
\(533\) 42.3699i 1.83524i
\(534\) 0 0
\(535\) −7.56781 19.2652i −0.327185 0.832908i
\(536\) 0 0
\(537\) 13.6194i 0.587719i
\(538\) 0 0
\(539\) −24.2905 −1.04626
\(540\) 0 0
\(541\) −7.74511 −0.332988 −0.166494 0.986042i \(-0.553245\pi\)
−0.166494 + 0.986042i \(0.553245\pi\)
\(542\) 0 0
\(543\) 5.42287i 0.232718i
\(544\) 0 0
\(545\) −34.9335 + 13.7226i −1.49638 + 0.587813i
\(546\) 0 0
\(547\) 5.58452i 0.238777i 0.992848 + 0.119388i \(0.0380934\pi\)
−0.992848 + 0.119388i \(0.961907\pi\)
\(548\) 0 0
\(549\) −1.14296 −0.0487803
\(550\) 0 0
\(551\) 10.5280 0.448510
\(552\) 0 0
\(553\) 6.01285i 0.255692i
\(554\) 0 0
\(555\) 21.3596 8.39051i 0.906663 0.356157i
\(556\) 0 0
\(557\) 4.65576i 0.197271i 0.995124 + 0.0986355i \(0.0314478\pi\)
−0.995124 + 0.0986355i \(0.968552\pi\)
\(558\) 0 0
\(559\) 3.47924 0.147156
\(560\) 0 0
\(561\) 41.1195 1.73607
\(562\) 0 0
\(563\) 7.52137i 0.316988i 0.987360 + 0.158494i \(0.0506639\pi\)
−0.987360 + 0.158494i \(0.949336\pi\)
\(564\) 0 0
\(565\) 0.805631 + 2.05088i 0.0338932 + 0.0862812i
\(566\) 0 0
\(567\) 3.41849i 0.143563i
\(568\) 0 0
\(569\) −47.1101 −1.97496 −0.987479 0.157752i \(-0.949575\pi\)
−0.987479 + 0.157752i \(0.949575\pi\)
\(570\) 0 0
\(571\) 47.2241 1.97627 0.988133 0.153600i \(-0.0490868\pi\)
0.988133 + 0.153600i \(0.0490868\pi\)
\(572\) 0 0
\(573\) 3.71059i 0.155012i
\(574\) 0 0
\(575\) 24.3758 + 26.2388i 1.01654 + 1.09423i
\(576\) 0 0
\(577\) 31.2367i 1.30040i 0.759762 + 0.650201i \(0.225315\pi\)
−0.759762 + 0.650201i \(0.774685\pi\)
\(578\) 0 0
\(579\) 4.66970 0.194066
\(580\) 0 0
\(581\) −44.4186 −1.84279
\(582\) 0 0
\(583\) 59.9496i 2.48286i
\(584\) 0 0
\(585\) 4.28800 + 10.9159i 0.177287 + 0.451316i
\(586\) 0 0
\(587\) 14.6525i 0.604772i −0.953186 0.302386i \(-0.902217\pi\)
0.953186 0.302386i \(-0.0977832\pi\)
\(588\) 0 0
\(589\) −9.52975 −0.392666
\(590\) 0 0
\(591\) 21.7808 0.895943
\(592\) 0 0
\(593\) 43.6008i 1.79047i 0.445593 + 0.895236i \(0.352993\pi\)
−0.445593 + 0.895236i \(0.647007\pi\)
\(594\) 0 0
\(595\) −56.4392 + 22.1706i −2.31378 + 0.908905i
\(596\) 0 0
\(597\) 26.0873i 1.06768i
\(598\) 0 0
\(599\) −22.8903 −0.935271 −0.467636 0.883921i \(-0.654894\pi\)
−0.467636 + 0.883921i \(0.654894\pi\)
\(600\) 0 0
\(601\) 16.4901 0.672645 0.336322 0.941747i \(-0.390817\pi\)
0.336322 + 0.941747i \(0.390817\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) 33.0272 12.9738i 1.34275 0.527460i
\(606\) 0 0
\(607\) 10.0851i 0.409344i 0.978831 + 0.204672i \(0.0656127\pi\)
−0.978831 + 0.204672i \(0.934387\pi\)
\(608\) 0 0
\(609\) 22.5169 0.912431
\(610\) 0 0
\(611\) 37.1476 1.50283
\(612\) 0 0
\(613\) 23.8535i 0.963434i 0.876327 + 0.481717i \(0.159987\pi\)
−0.876327 + 0.481717i \(0.840013\pi\)
\(614\) 0 0
\(615\) 6.60454 + 16.8131i 0.266321 + 0.677968i
\(616\) 0 0
\(617\) 0.706932i 0.0284600i −0.999899 0.0142300i \(-0.995470\pi\)
0.999899 0.0142300i \(-0.00452971\pi\)
\(618\) 0 0
\(619\) 36.6278 1.47220 0.736099 0.676874i \(-0.236666\pi\)
0.736099 + 0.676874i \(0.236666\pi\)
\(620\) 0 0
\(621\) −7.16283 −0.287434
\(622\) 0 0
\(623\) 21.5344i 0.862757i
\(624\) 0 0
\(625\) 1.83792 24.9323i 0.0735167 0.997294i
\(626\) 0 0
\(627\) 8.28512i 0.330876i
\(628\) 0 0
\(629\) −81.4125 −3.24613
\(630\) 0 0
\(631\) −36.4962 −1.45289 −0.726445 0.687225i \(-0.758829\pi\)
−0.726445 + 0.687225i \(0.758829\pi\)
\(632\) 0 0
\(633\) 25.5255i 1.01455i
\(634\) 0 0
\(635\) −3.21328 8.17999i −0.127515 0.324613i
\(636\) 0 0
\(637\) 24.5780i 0.973814i
\(638\) 0 0
\(639\) −1.39500 −0.0551853
\(640\) 0 0
\(641\) 5.86090 0.231492 0.115746 0.993279i \(-0.463074\pi\)
0.115746 + 0.993279i \(0.463074\pi\)
\(642\) 0 0
\(643\) 14.6775i 0.578825i −0.957205 0.289412i \(-0.906540\pi\)
0.957205 0.289412i \(-0.0934599\pi\)
\(644\) 0 0
\(645\) 1.38062 0.542337i 0.0543617 0.0213545i
\(646\) 0 0
\(647\) 17.5924i 0.691630i −0.938303 0.345815i \(-0.887603\pi\)
0.938303 0.345815i \(-0.112397\pi\)
\(648\) 0 0
\(649\) 9.85645 0.386900
\(650\) 0 0
\(651\) −20.3818 −0.798825
\(652\) 0 0
\(653\) 9.97398i 0.390312i −0.980772 0.195156i \(-0.937479\pi\)
0.980772 0.195156i \(-0.0625213\pi\)
\(654\) 0 0
\(655\) −37.2809 + 14.6448i −1.45669 + 0.572218i
\(656\) 0 0
\(657\) 6.22878i 0.243008i
\(658\) 0 0
\(659\) −12.5427 −0.488595 −0.244298 0.969700i \(-0.578557\pi\)
−0.244298 + 0.969700i \(0.578557\pi\)
\(660\) 0 0
\(661\) 8.99415 0.349832 0.174916 0.984583i \(-0.444035\pi\)
0.174916 + 0.984583i \(0.444035\pi\)
\(662\) 0 0
\(663\) 41.6061i 1.61585i
\(664\) 0 0
\(665\) 4.46713 + 11.3719i 0.173228 + 0.440983i
\(666\) 0 0
\(667\) 47.1801i 1.82682i
\(668\) 0 0
\(669\) −17.1864 −0.664464
\(670\) 0 0
\(671\) 5.92456 0.228715
\(672\) 0 0
\(673\) 0.182820i 0.00704719i −0.999994 0.00352360i \(-0.998878\pi\)
0.999994 0.00352360i \(-0.00112160\pi\)
\(674\) 0 0
\(675\) 3.40309 + 3.66319i 0.130985 + 0.140996i
\(676\) 0 0
\(677\) 48.2910i 1.85598i −0.372610 0.927988i \(-0.621537\pi\)
0.372610 0.927988i \(-0.378463\pi\)
\(678\) 0 0
\(679\) −15.8107 −0.606759
\(680\) 0 0
\(681\) −10.5003 −0.402371
\(682\) 0 0
\(683\) 45.2104i 1.72993i −0.501833 0.864965i \(-0.667341\pi\)
0.501833 0.864965i \(-0.332659\pi\)
\(684\) 0 0
\(685\) 4.45112 + 11.3311i 0.170069 + 0.432941i
\(686\) 0 0
\(687\) 6.29601i 0.240208i
\(688\) 0 0
\(689\) −60.6592 −2.31093
\(690\) 0 0
\(691\) −26.6390 −1.01339 −0.506697 0.862124i \(-0.669134\pi\)
−0.506697 + 0.862124i \(0.669134\pi\)
\(692\) 0 0
\(693\) 17.7198i 0.673121i
\(694\) 0 0
\(695\) 25.7838 10.1285i 0.978037 0.384194i
\(696\) 0 0
\(697\) 64.0833i 2.42733i
\(698\) 0 0
\(699\) −27.9039 −1.05542
\(700\) 0 0
\(701\) −36.7808 −1.38919 −0.694596 0.719400i \(-0.744417\pi\)
−0.694596 + 0.719400i \(0.744417\pi\)
\(702\) 0 0
\(703\) 16.4037i 0.618678i
\(704\) 0 0
\(705\) 14.7407 5.79049i 0.555168 0.218082i
\(706\) 0 0
\(707\) 32.0474i 1.20526i
\(708\) 0 0
\(709\) −8.39744 −0.315372 −0.157686 0.987489i \(-0.550403\pi\)
−0.157686 + 0.987489i \(0.550403\pi\)
\(710\) 0 0
\(711\) 1.75892 0.0659646
\(712\) 0 0
\(713\) 42.7063i 1.59936i
\(714\) 0 0
\(715\) −22.2270 56.5828i −0.831241 2.11608i
\(716\) 0 0
\(717\) 23.3664i 0.872636i
\(718\) 0 0
\(719\) −44.8620 −1.67307 −0.836536 0.547913i \(-0.815423\pi\)
−0.836536 + 0.547913i \(0.815423\pi\)
\(720\) 0 0
\(721\) −26.7210 −0.995144
\(722\) 0 0
\(723\) 20.9579i 0.779433i
\(724\) 0 0
\(725\) 24.1287 22.4155i 0.896116 0.832490i
\(726\) 0 0
\(727\) 39.2720i 1.45652i 0.685301 + 0.728260i \(0.259671\pi\)
−0.685301 + 0.728260i \(0.740329\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −5.26225 −0.194631
\(732\) 0 0
\(733\) 20.9749i 0.774726i 0.921927 + 0.387363i \(0.126614\pi\)
−0.921927 + 0.387363i \(0.873386\pi\)
\(734\) 0 0
\(735\) 3.83116 + 9.75292i 0.141315 + 0.359742i
\(736\) 0 0
\(737\) 5.18352i 0.190938i
\(738\) 0 0
\(739\) −1.13014 −0.0415728 −0.0207864 0.999784i \(-0.506617\pi\)
−0.0207864 + 0.999784i \(0.506617\pi\)
\(740\) 0 0
\(741\) −8.38318 −0.307964
\(742\) 0 0
\(743\) 48.0720i 1.76359i 0.471633 + 0.881795i \(0.343665\pi\)
−0.471633 + 0.881795i \(0.656335\pi\)
\(744\) 0 0
\(745\) 21.7236 8.53349i 0.795889 0.312643i
\(746\) 0 0
\(747\) 12.9936i 0.475412i
\(748\) 0 0
\(749\) 31.6435 1.15623
\(750\) 0 0
\(751\) 34.0475 1.24241 0.621206 0.783647i \(-0.286643\pi\)
0.621206 + 0.783647i \(0.286643\pi\)
\(752\) 0 0
\(753\) 11.0003i 0.400875i
\(754\) 0 0
\(755\) 5.37233 2.11037i 0.195519 0.0768043i
\(756\) 0 0
\(757\) 1.62146i 0.0589329i 0.999566 + 0.0294665i \(0.00938082\pi\)
−0.999566 + 0.0294665i \(0.990619\pi\)
\(758\) 0 0
\(759\) 37.1287 1.34769
\(760\) 0 0
\(761\) −9.62522 −0.348914 −0.174457 0.984665i \(-0.555817\pi\)
−0.174457 + 0.984665i \(0.555817\pi\)
\(762\) 0 0
\(763\) 57.3789i 2.07726i
\(764\) 0 0
\(765\) −6.48548 16.5100i −0.234483 0.596919i
\(766\) 0 0
\(767\) 9.97311i 0.360108i
\(768\) 0 0
\(769\) −43.3671 −1.56386 −0.781929 0.623367i \(-0.785764\pi\)
−0.781929 + 0.623367i \(0.785764\pi\)
\(770\) 0 0
\(771\) −22.4819 −0.809665
\(772\) 0 0
\(773\) 23.1785i 0.833672i −0.908982 0.416836i \(-0.863139\pi\)
0.908982 0.416836i \(-0.136861\pi\)
\(774\) 0 0
\(775\) −21.8407 + 20.2900i −0.784542 + 0.728837i
\(776\) 0 0
\(777\) 35.0835i 1.25861i
\(778\) 0 0
\(779\) −12.9121 −0.462623
\(780\) 0 0
\(781\) 7.23102 0.258746
\(782\) 0 0
\(783\) 6.58679i 0.235393i
\(784\) 0 0
\(785\) 1.94569 + 4.95310i 0.0694446 + 0.176784i
\(786\) 0 0
\(787\) 23.5640i 0.839967i 0.907532 + 0.419984i \(0.137964\pi\)
−0.907532 + 0.419984i \(0.862036\pi\)
\(788\) 0 0
\(789\) −19.3224 −0.687895
\(790\) 0 0
\(791\) −3.36861 −0.119774
\(792\) 0 0