Properties

Label 4020.2.g.c.1609.14
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 1609.14
Character \(\chi\) = 4020.1609
Dual form 4020.2.g.c.1609.33

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000i q^{3}\) \(+(1.34274 + 1.78803i) q^{5}\) \(+0.521655i q^{7}\) \(-1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000i q^{3}\) \(+(1.34274 + 1.78803i) q^{5}\) \(+0.521655i q^{7}\) \(-1.00000 q^{9}\) \(-3.11151 q^{11}\) \(-5.31690i q^{13}\) \(+(1.78803 - 1.34274i) q^{15}\) \(+5.37821i q^{17}\) \(+0.478140 q^{19}\) \(+0.521655 q^{21}\) \(-9.04648i q^{23}\) \(+(-1.39410 + 4.80172i) q^{25}\) \(+1.00000i q^{27}\) \(+3.80917 q^{29}\) \(+3.77664 q^{31}\) \(+3.11151i q^{33}\) \(+(-0.932734 + 0.700447i) q^{35}\) \(+5.87811i q^{37}\) \(-5.31690 q^{39}\) \(+5.50011 q^{41}\) \(+2.92028i q^{43}\) \(+(-1.34274 - 1.78803i) q^{45}\) \(-11.7573i q^{47}\) \(+6.72788 q^{49}\) \(+5.37821 q^{51}\) \(-13.8500i q^{53}\) \(+(-4.17794 - 5.56346i) q^{55}\) \(-0.478140i q^{57}\) \(-2.17583 q^{59}\) \(-7.47318 q^{61}\) \(-0.521655i q^{63}\) \(+(9.50677 - 7.13921i) q^{65}\) \(-1.00000i q^{67}\) \(-9.04648 q^{69}\) \(-4.15816 q^{71}\) \(-8.31980i q^{73}\) \(+(4.80172 + 1.39410i) q^{75}\) \(-1.62313i q^{77}\) \(+6.27946 q^{79}\) \(+1.00000 q^{81}\) \(-5.47106i q^{83}\) \(+(-9.61639 + 7.22153i) q^{85}\) \(-3.80917i q^{87}\) \(+14.7914 q^{89}\) \(+2.77358 q^{91}\) \(-3.77664i q^{93}\) \(+(0.642017 + 0.854928i) q^{95}\) \(+18.8652i q^{97}\) \(+3.11151 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(38q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 56q^{29} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut -\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 60q^{41} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 70q^{49} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut -\mathstrut 52q^{59} \) \(\mathstrut +\mathstrut 48q^{61} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut -\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 38q^{81} \) \(\mathstrut +\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 36q^{95} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.34274 + 1.78803i 0.600492 + 0.799631i
\(6\) 0 0
\(7\) 0.521655i 0.197167i 0.995129 + 0.0985835i \(0.0314311\pi\)
−0.995129 + 0.0985835i \(0.968569\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −3.11151 −0.938154 −0.469077 0.883157i \(-0.655413\pi\)
−0.469077 + 0.883157i \(0.655413\pi\)
\(12\) 0 0
\(13\) 5.31690i 1.47464i −0.675543 0.737321i \(-0.736091\pi\)
0.675543 0.737321i \(-0.263909\pi\)
\(14\) 0 0
\(15\) 1.78803 1.34274i 0.461667 0.346694i
\(16\) 0 0
\(17\) 5.37821i 1.30441i 0.758044 + 0.652203i \(0.226155\pi\)
−0.758044 + 0.652203i \(0.773845\pi\)
\(18\) 0 0
\(19\) 0.478140 0.109693 0.0548464 0.998495i \(-0.482533\pi\)
0.0548464 + 0.998495i \(0.482533\pi\)
\(20\) 0 0
\(21\) 0.521655 0.113834
\(22\) 0 0
\(23\) 9.04648i 1.88632i −0.332336 0.943161i \(-0.607837\pi\)
0.332336 0.943161i \(-0.392163\pi\)
\(24\) 0 0
\(25\) −1.39410 + 4.80172i −0.278820 + 0.960343i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 3.80917 0.707345 0.353672 0.935369i \(-0.384933\pi\)
0.353672 + 0.935369i \(0.384933\pi\)
\(30\) 0 0
\(31\) 3.77664 0.678305 0.339153 0.940731i \(-0.389860\pi\)
0.339153 + 0.940731i \(0.389860\pi\)
\(32\) 0 0
\(33\) 3.11151i 0.541644i
\(34\) 0 0
\(35\) −0.932734 + 0.700447i −0.157661 + 0.118397i
\(36\) 0 0
\(37\) 5.87811i 0.966356i 0.875522 + 0.483178i \(0.160518\pi\)
−0.875522 + 0.483178i \(0.839482\pi\)
\(38\) 0 0
\(39\) −5.31690 −0.851385
\(40\) 0 0
\(41\) 5.50011 0.858973 0.429486 0.903073i \(-0.358695\pi\)
0.429486 + 0.903073i \(0.358695\pi\)
\(42\) 0 0
\(43\) 2.92028i 0.445339i 0.974894 + 0.222670i \(0.0714771\pi\)
−0.974894 + 0.222670i \(0.928523\pi\)
\(44\) 0 0
\(45\) −1.34274 1.78803i −0.200164 0.266544i
\(46\) 0 0
\(47\) 11.7573i 1.71497i −0.514505 0.857487i \(-0.672024\pi\)
0.514505 0.857487i \(-0.327976\pi\)
\(48\) 0 0
\(49\) 6.72788 0.961125
\(50\) 0 0
\(51\) 5.37821 0.753099
\(52\) 0 0
\(53\) 13.8500i 1.90244i −0.308508 0.951222i \(-0.599830\pi\)
0.308508 0.951222i \(-0.400170\pi\)
\(54\) 0 0
\(55\) −4.17794 5.56346i −0.563354 0.750177i
\(56\) 0 0
\(57\) 0.478140i 0.0633312i
\(58\) 0 0
\(59\) −2.17583 −0.283269 −0.141635 0.989919i \(-0.545236\pi\)
−0.141635 + 0.989919i \(0.545236\pi\)
\(60\) 0 0
\(61\) −7.47318 −0.956842 −0.478421 0.878131i \(-0.658791\pi\)
−0.478421 + 0.878131i \(0.658791\pi\)
\(62\) 0 0
\(63\) 0.521655i 0.0657223i
\(64\) 0 0
\(65\) 9.50677 7.13921i 1.17917 0.885510i
\(66\) 0 0
\(67\) 1.00000i 0.122169i
\(68\) 0 0
\(69\) −9.04648 −1.08907
\(70\) 0 0
\(71\) −4.15816 −0.493482 −0.246741 0.969081i \(-0.579360\pi\)
−0.246741 + 0.969081i \(0.579360\pi\)
\(72\) 0 0
\(73\) 8.31980i 0.973759i −0.873469 0.486879i \(-0.838135\pi\)
0.873469 0.486879i \(-0.161865\pi\)
\(74\) 0 0
\(75\) 4.80172 + 1.39410i 0.554455 + 0.160977i
\(76\) 0 0
\(77\) 1.62313i 0.184973i
\(78\) 0 0
\(79\) 6.27946 0.706494 0.353247 0.935530i \(-0.385077\pi\)
0.353247 + 0.935530i \(0.385077\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 5.47106i 0.600527i −0.953856 0.300264i \(-0.902925\pi\)
0.953856 0.300264i \(-0.0970746\pi\)
\(84\) 0 0
\(85\) −9.61639 + 7.22153i −1.04304 + 0.783285i
\(86\) 0 0
\(87\) 3.80917i 0.408386i
\(88\) 0 0
\(89\) 14.7914 1.56789 0.783944 0.620832i \(-0.213205\pi\)
0.783944 + 0.620832i \(0.213205\pi\)
\(90\) 0 0
\(91\) 2.77358 0.290751
\(92\) 0 0
\(93\) 3.77664i 0.391620i
\(94\) 0 0
\(95\) 0.642017 + 0.854928i 0.0658696 + 0.0877138i
\(96\) 0 0
\(97\) 18.8652i 1.91547i 0.287653 + 0.957735i \(0.407125\pi\)
−0.287653 + 0.957735i \(0.592875\pi\)
\(98\) 0 0
\(99\) 3.11151 0.312718
\(100\) 0 0
\(101\) 10.9616 1.09072 0.545361 0.838201i \(-0.316393\pi\)
0.545361 + 0.838201i \(0.316393\pi\)
\(102\) 0 0
\(103\) 13.1101i 1.29178i −0.763431 0.645890i \(-0.776487\pi\)
0.763431 0.645890i \(-0.223513\pi\)
\(104\) 0 0
\(105\) 0.700447 + 0.932734i 0.0683566 + 0.0910255i
\(106\) 0 0
\(107\) 13.9550i 1.34908i 0.738239 + 0.674539i \(0.235658\pi\)
−0.738239 + 0.674539i \(0.764342\pi\)
\(108\) 0 0
\(109\) 9.26791 0.887705 0.443853 0.896100i \(-0.353611\pi\)
0.443853 + 0.896100i \(0.353611\pi\)
\(110\) 0 0
\(111\) 5.87811 0.557926
\(112\) 0 0
\(113\) 9.92649i 0.933805i −0.884309 0.466903i \(-0.845370\pi\)
0.884309 0.466903i \(-0.154630\pi\)
\(114\) 0 0
\(115\) 16.1754 12.1471i 1.50836 1.13272i
\(116\) 0 0
\(117\) 5.31690i 0.491547i
\(118\) 0 0
\(119\) −2.80557 −0.257186
\(120\) 0 0
\(121\) −1.31853 −0.119867
\(122\) 0 0
\(123\) 5.50011i 0.495928i
\(124\) 0 0
\(125\) −10.4575 + 3.95477i −0.935349 + 0.353725i
\(126\) 0 0
\(127\) 6.53959i 0.580295i 0.956982 + 0.290147i \(0.0937044\pi\)
−0.956982 + 0.290147i \(0.906296\pi\)
\(128\) 0 0
\(129\) 2.92028 0.257117
\(130\) 0 0
\(131\) 9.36980 0.818643 0.409322 0.912390i \(-0.365765\pi\)
0.409322 + 0.912390i \(0.365765\pi\)
\(132\) 0 0
\(133\) 0.249424i 0.0216278i
\(134\) 0 0
\(135\) −1.78803 + 1.34274i −0.153889 + 0.115565i
\(136\) 0 0
\(137\) 19.3515i 1.65331i −0.562711 0.826654i \(-0.690241\pi\)
0.562711 0.826654i \(-0.309759\pi\)
\(138\) 0 0
\(139\) 20.0859 1.70367 0.851834 0.523812i \(-0.175491\pi\)
0.851834 + 0.523812i \(0.175491\pi\)
\(140\) 0 0
\(141\) −11.7573 −0.990141
\(142\) 0 0
\(143\) 16.5436i 1.38344i
\(144\) 0 0
\(145\) 5.11472 + 6.81090i 0.424754 + 0.565615i
\(146\) 0 0
\(147\) 6.72788i 0.554906i
\(148\) 0 0
\(149\) −8.78079 −0.719350 −0.359675 0.933078i \(-0.617113\pi\)
−0.359675 + 0.933078i \(0.617113\pi\)
\(150\) 0 0
\(151\) 4.86906 0.396238 0.198119 0.980178i \(-0.436517\pi\)
0.198119 + 0.980178i \(0.436517\pi\)
\(152\) 0 0
\(153\) 5.37821i 0.434802i
\(154\) 0 0
\(155\) 5.07105 + 6.75275i 0.407316 + 0.542394i
\(156\) 0 0
\(157\) 8.22949i 0.656785i −0.944541 0.328393i \(-0.893493\pi\)
0.944541 0.328393i \(-0.106507\pi\)
\(158\) 0 0
\(159\) −13.8500 −1.09838
\(160\) 0 0
\(161\) 4.71914 0.371920
\(162\) 0 0
\(163\) 2.02693i 0.158761i 0.996844 + 0.0793806i \(0.0252942\pi\)
−0.996844 + 0.0793806i \(0.974706\pi\)
\(164\) 0 0
\(165\) −5.56346 + 4.17794i −0.433115 + 0.325252i
\(166\) 0 0
\(167\) 15.5470i 1.20307i −0.798848 0.601533i \(-0.794557\pi\)
0.798848 0.601533i \(-0.205443\pi\)
\(168\) 0 0
\(169\) −15.2694 −1.17457
\(170\) 0 0
\(171\) −0.478140 −0.0365643
\(172\) 0 0
\(173\) 18.3736i 1.39692i 0.715650 + 0.698459i \(0.246131\pi\)
−0.715650 + 0.698459i \(0.753869\pi\)
\(174\) 0 0
\(175\) −2.50484 0.727238i −0.189348 0.0549741i
\(176\) 0 0
\(177\) 2.17583i 0.163546i
\(178\) 0 0
\(179\) 17.2319 1.28797 0.643986 0.765037i \(-0.277279\pi\)
0.643986 + 0.765037i \(0.277279\pi\)
\(180\) 0 0
\(181\) 19.1646 1.42449 0.712246 0.701930i \(-0.247678\pi\)
0.712246 + 0.701930i \(0.247678\pi\)
\(182\) 0 0
\(183\) 7.47318i 0.552433i
\(184\) 0 0
\(185\) −10.5102 + 7.89278i −0.772728 + 0.580289i
\(186\) 0 0
\(187\) 16.7343i 1.22373i
\(188\) 0 0
\(189\) −0.521655 −0.0379448
\(190\) 0 0
\(191\) −10.8740 −0.786814 −0.393407 0.919365i \(-0.628704\pi\)
−0.393407 + 0.919365i \(0.628704\pi\)
\(192\) 0 0
\(193\) 0.422686i 0.0304256i −0.999884 0.0152128i \(-0.995157\pi\)
0.999884 0.0152128i \(-0.00484257\pi\)
\(194\) 0 0
\(195\) −7.13921 9.50677i −0.511249 0.680794i
\(196\) 0 0
\(197\) 9.02213i 0.642800i −0.946944 0.321400i \(-0.895847\pi\)
0.946944 0.321400i \(-0.104153\pi\)
\(198\) 0 0
\(199\) 2.32112 0.164540 0.0822698 0.996610i \(-0.473783\pi\)
0.0822698 + 0.996610i \(0.473783\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 1.98707i 0.139465i
\(204\) 0 0
\(205\) 7.38521 + 9.83436i 0.515806 + 0.686861i
\(206\) 0 0
\(207\) 9.04648i 0.628774i
\(208\) 0 0
\(209\) −1.48773 −0.102909
\(210\) 0 0
\(211\) 9.63198 0.663093 0.331546 0.943439i \(-0.392430\pi\)
0.331546 + 0.943439i \(0.392430\pi\)
\(212\) 0 0
\(213\) 4.15816i 0.284912i
\(214\) 0 0
\(215\) −5.22155 + 3.92118i −0.356107 + 0.267422i
\(216\) 0 0
\(217\) 1.97010i 0.133739i
\(218\) 0 0
\(219\) −8.31980 −0.562200
\(220\) 0 0
\(221\) 28.5954 1.92353
\(222\) 0 0
\(223\) 14.1438i 0.947141i −0.880756 0.473570i \(-0.842965\pi\)
0.880756 0.473570i \(-0.157035\pi\)
\(224\) 0 0
\(225\) 1.39410 4.80172i 0.0929400 0.320114i
\(226\) 0 0
\(227\) 9.52142i 0.631959i −0.948766 0.315979i \(-0.897667\pi\)
0.948766 0.315979i \(-0.102333\pi\)
\(228\) 0 0
\(229\) −14.5476 −0.961334 −0.480667 0.876903i \(-0.659605\pi\)
−0.480667 + 0.876903i \(0.659605\pi\)
\(230\) 0 0
\(231\) −1.62313 −0.106794
\(232\) 0 0
\(233\) 23.7819i 1.55800i 0.627021 + 0.779002i \(0.284274\pi\)
−0.627021 + 0.779002i \(0.715726\pi\)
\(234\) 0 0
\(235\) 21.0224 15.7870i 1.37135 1.02983i
\(236\) 0 0
\(237\) 6.27946i 0.407895i
\(238\) 0 0
\(239\) 5.68266 0.367581 0.183790 0.982965i \(-0.441163\pi\)
0.183790 + 0.982965i \(0.441163\pi\)
\(240\) 0 0
\(241\) 5.38321 0.346763 0.173382 0.984855i \(-0.444531\pi\)
0.173382 + 0.984855i \(0.444531\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) 9.03379 + 12.0296i 0.577148 + 0.768546i
\(246\) 0 0
\(247\) 2.54222i 0.161758i
\(248\) 0 0
\(249\) −5.47106 −0.346715
\(250\) 0 0
\(251\) −15.4504 −0.975220 −0.487610 0.873061i \(-0.662131\pi\)
−0.487610 + 0.873061i \(0.662131\pi\)
\(252\) 0 0
\(253\) 28.1482i 1.76966i
\(254\) 0 0
\(255\) 7.22153 + 9.61639i 0.452230 + 0.602202i
\(256\) 0 0
\(257\) 11.4600i 0.714853i 0.933941 + 0.357426i \(0.116346\pi\)
−0.933941 + 0.357426i \(0.883654\pi\)
\(258\) 0 0
\(259\) −3.06635 −0.190533
\(260\) 0 0
\(261\) −3.80917 −0.235782
\(262\) 0 0
\(263\) 30.5405i 1.88321i −0.336719 0.941605i \(-0.609317\pi\)
0.336719 0.941605i \(-0.390683\pi\)
\(264\) 0 0
\(265\) 24.7642 18.5969i 1.52125 1.14240i
\(266\) 0 0
\(267\) 14.7914i 0.905220i
\(268\) 0 0
\(269\) −7.29684 −0.444896 −0.222448 0.974945i \(-0.571405\pi\)
−0.222448 + 0.974945i \(0.571405\pi\)
\(270\) 0 0
\(271\) −12.6066 −0.765798 −0.382899 0.923790i \(-0.625074\pi\)
−0.382899 + 0.923790i \(0.625074\pi\)
\(272\) 0 0
\(273\) 2.77358i 0.167865i
\(274\) 0 0
\(275\) 4.33775 14.9406i 0.261576 0.900950i
\(276\) 0 0
\(277\) 17.6688i 1.06162i 0.847492 + 0.530809i \(0.178112\pi\)
−0.847492 + 0.530809i \(0.821888\pi\)
\(278\) 0 0
\(279\) −3.77664 −0.226102
\(280\) 0 0
\(281\) 2.79446 0.166704 0.0833518 0.996520i \(-0.473437\pi\)
0.0833518 + 0.996520i \(0.473437\pi\)
\(282\) 0 0
\(283\) 0.406056i 0.0241375i −0.999927 0.0120687i \(-0.996158\pi\)
0.999927 0.0120687i \(-0.00384170\pi\)
\(284\) 0 0
\(285\) 0.854928 0.642017i 0.0506416 0.0380298i
\(286\) 0 0
\(287\) 2.86916i 0.169361i
\(288\) 0 0
\(289\) −11.9251 −0.701476
\(290\) 0 0
\(291\) 18.8652 1.10590
\(292\) 0 0
\(293\) 10.9198i 0.637944i −0.947764 0.318972i \(-0.896662\pi\)
0.947764 0.318972i \(-0.103338\pi\)
\(294\) 0 0
\(295\) −2.92158 3.89045i −0.170101 0.226511i
\(296\) 0 0
\(297\) 3.11151i 0.180548i
\(298\) 0 0
\(299\) −48.0992 −2.78165
\(300\) 0 0
\(301\) −1.52338 −0.0878062
\(302\) 0 0
\(303\) 10.9616i 0.629728i
\(304\) 0 0
\(305\) −10.0345 13.3623i −0.574576 0.765121i
\(306\) 0 0
\(307\) 2.14641i 0.122502i 0.998122 + 0.0612512i \(0.0195091\pi\)
−0.998122 + 0.0612512i \(0.980491\pi\)
\(308\) 0 0
\(309\) −13.1101 −0.745809
\(310\) 0 0
\(311\) −24.7310 −1.40237 −0.701184 0.712981i \(-0.747345\pi\)
−0.701184 + 0.712981i \(0.747345\pi\)
\(312\) 0 0
\(313\) 20.4415i 1.15542i −0.816242 0.577711i \(-0.803946\pi\)
0.816242 0.577711i \(-0.196054\pi\)
\(314\) 0 0
\(315\) 0.932734 0.700447i 0.0525536 0.0394657i
\(316\) 0 0
\(317\) 17.1454i 0.962984i −0.876451 0.481492i \(-0.840095\pi\)
0.876451 0.481492i \(-0.159905\pi\)
\(318\) 0 0
\(319\) −11.8522 −0.663598
\(320\) 0 0
\(321\) 13.9550 0.778891
\(322\) 0 0
\(323\) 2.57153i 0.143084i
\(324\) 0 0
\(325\) 25.5302 + 7.41228i 1.41616 + 0.411159i
\(326\) 0 0
\(327\) 9.26791i 0.512517i
\(328\) 0 0
\(329\) 6.13324 0.338136
\(330\) 0 0
\(331\) −16.2384 −0.892544 −0.446272 0.894897i \(-0.647249\pi\)
−0.446272 + 0.894897i \(0.647249\pi\)
\(332\) 0 0
\(333\) 5.87811i 0.322119i
\(334\) 0 0
\(335\) 1.78803 1.34274i 0.0976905 0.0733617i
\(336\) 0 0
\(337\) 12.1370i 0.661142i −0.943781 0.330571i \(-0.892759\pi\)
0.943781 0.330571i \(-0.107241\pi\)
\(338\) 0 0
\(339\) −9.92649 −0.539133
\(340\) 0 0
\(341\) −11.7510 −0.636355
\(342\) 0 0
\(343\) 7.16121i 0.386669i
\(344\) 0 0
\(345\) −12.1471 16.1754i −0.653976 0.870853i
\(346\) 0 0
\(347\) 9.65658i 0.518392i −0.965825 0.259196i \(-0.916542\pi\)
0.965825 0.259196i \(-0.0834576\pi\)
\(348\) 0 0
\(349\) −8.00457 −0.428475 −0.214237 0.976782i \(-0.568727\pi\)
−0.214237 + 0.976782i \(0.568727\pi\)
\(350\) 0 0
\(351\) 5.31690 0.283795
\(352\) 0 0
\(353\) 15.5108i 0.825556i 0.910832 + 0.412778i \(0.135442\pi\)
−0.910832 + 0.412778i \(0.864558\pi\)
\(354\) 0 0
\(355\) −5.58332 7.43491i −0.296332 0.394604i
\(356\) 0 0
\(357\) 2.80557i 0.148486i
\(358\) 0 0
\(359\) 12.7425 0.672523 0.336261 0.941769i \(-0.390837\pi\)
0.336261 + 0.941769i \(0.390837\pi\)
\(360\) 0 0
\(361\) −18.7714 −0.987967
\(362\) 0 0
\(363\) 1.31853i 0.0692051i
\(364\) 0 0
\(365\) 14.8760 11.1713i 0.778648 0.584734i
\(366\) 0 0
\(367\) 2.40243i 0.125406i −0.998032 0.0627029i \(-0.980028\pi\)
0.998032 0.0627029i \(-0.0199720\pi\)
\(368\) 0 0
\(369\) −5.50011 −0.286324
\(370\) 0 0
\(371\) 7.22492 0.375099
\(372\) 0 0
\(373\) 4.44244i 0.230021i −0.993364 0.115010i \(-0.963310\pi\)
0.993364 0.115010i \(-0.0366901\pi\)
\(374\) 0 0
\(375\) 3.95477 + 10.4575i 0.204223 + 0.540024i
\(376\) 0 0
\(377\) 20.2530i 1.04308i
\(378\) 0 0
\(379\) 11.3897 0.585047 0.292524 0.956258i \(-0.405505\pi\)
0.292524 + 0.956258i \(0.405505\pi\)
\(380\) 0 0
\(381\) 6.53959 0.335033
\(382\) 0 0
\(383\) 37.1019i 1.89582i −0.318537 0.947910i \(-0.603192\pi\)
0.318537 0.947910i \(-0.396808\pi\)
\(384\) 0 0
\(385\) 2.90221 2.17944i 0.147910 0.111075i
\(386\) 0 0
\(387\) 2.92028i 0.148446i
\(388\) 0 0
\(389\) −12.3456 −0.625946 −0.312973 0.949762i \(-0.601325\pi\)
−0.312973 + 0.949762i \(0.601325\pi\)
\(390\) 0 0
\(391\) 48.6538 2.46053
\(392\) 0 0
\(393\) 9.36980i 0.472644i
\(394\) 0 0
\(395\) 8.43168 + 11.2279i 0.424244 + 0.564935i
\(396\) 0 0
\(397\) 12.5577i 0.630255i 0.949049 + 0.315128i \(0.102047\pi\)
−0.949049 + 0.315128i \(0.897953\pi\)
\(398\) 0 0
\(399\) 0.249424 0.0124868
\(400\) 0 0
\(401\) 22.3287 1.11504 0.557521 0.830163i \(-0.311753\pi\)
0.557521 + 0.830163i \(0.311753\pi\)
\(402\) 0 0
\(403\) 20.0800i 1.00026i
\(404\) 0 0
\(405\) 1.34274 + 1.78803i 0.0667213 + 0.0888479i
\(406\) 0 0
\(407\) 18.2898i 0.906591i
\(408\) 0 0
\(409\) 4.45818 0.220443 0.110221 0.993907i \(-0.464844\pi\)
0.110221 + 0.993907i \(0.464844\pi\)
\(410\) 0 0
\(411\) −19.3515 −0.954538
\(412\) 0 0
\(413\) 1.13503i 0.0558513i
\(414\) 0 0
\(415\) 9.78242 7.34621i 0.480200 0.360611i
\(416\) 0 0
\(417\) 20.0859i 0.983613i
\(418\) 0 0
\(419\) −0.0503944 −0.00246193 −0.00123096 0.999999i \(-0.500392\pi\)
−0.00123096 + 0.999999i \(0.500392\pi\)
\(420\) 0 0
\(421\) 21.0091 1.02392 0.511960 0.859009i \(-0.328920\pi\)
0.511960 + 0.859009i \(0.328920\pi\)
\(422\) 0 0
\(423\) 11.7573i 0.571658i
\(424\) 0 0
\(425\) −25.8246 7.49775i −1.25268 0.363694i
\(426\) 0 0
\(427\) 3.89842i 0.188658i
\(428\) 0 0
\(429\) 16.5436 0.798730
\(430\) 0 0
\(431\) −32.8705 −1.58332 −0.791659 0.610963i \(-0.790782\pi\)
−0.791659 + 0.610963i \(0.790782\pi\)
\(432\) 0 0
\(433\) 27.1919i 1.30676i 0.757030 + 0.653380i \(0.226649\pi\)
−0.757030 + 0.653380i \(0.773351\pi\)
\(434\) 0 0
\(435\) 6.81090 5.11472i 0.326558 0.245232i
\(436\) 0 0
\(437\) 4.32548i 0.206916i
\(438\) 0 0
\(439\) −7.84487 −0.374415 −0.187208 0.982320i \(-0.559944\pi\)
−0.187208 + 0.982320i \(0.559944\pi\)
\(440\) 0 0
\(441\) −6.72788 −0.320375
\(442\) 0 0
\(443\) 19.0129i 0.903331i 0.892187 + 0.451666i \(0.149170\pi\)
−0.892187 + 0.451666i \(0.850830\pi\)
\(444\) 0 0
\(445\) 19.8610 + 26.4475i 0.941503 + 1.25373i
\(446\) 0 0
\(447\) 8.78079i 0.415317i
\(448\) 0 0
\(449\) −5.40771 −0.255206 −0.127603 0.991825i \(-0.540728\pi\)
−0.127603 + 0.991825i \(0.540728\pi\)
\(450\) 0 0
\(451\) −17.1136 −0.805849
\(452\) 0 0
\(453\) 4.86906i 0.228768i
\(454\) 0 0
\(455\) 3.72420 + 4.95925i 0.174593 + 0.232493i
\(456\) 0 0
\(457\) 35.9620i 1.68223i 0.540854 + 0.841117i \(0.318101\pi\)
−0.540854 + 0.841117i \(0.681899\pi\)
\(458\) 0 0
\(459\) −5.37821 −0.251033
\(460\) 0 0
\(461\) 10.3829 0.483578 0.241789 0.970329i \(-0.422266\pi\)
0.241789 + 0.970329i \(0.422266\pi\)
\(462\) 0 0
\(463\) 22.5835i 1.04955i −0.851242 0.524773i \(-0.824150\pi\)
0.851242 0.524773i \(-0.175850\pi\)
\(464\) 0 0
\(465\) 6.75275 5.07105i 0.313151 0.235164i
\(466\) 0 0
\(467\) 21.7035i 1.00432i −0.864775 0.502159i \(-0.832539\pi\)
0.864775 0.502159i \(-0.167461\pi\)
\(468\) 0 0
\(469\) 0.521655 0.0240878
\(470\) 0 0
\(471\) −8.22949 −0.379195
\(472\) 0 0
\(473\) 9.08648i 0.417797i
\(474\) 0 0
\(475\) −0.666574 + 2.29589i −0.0305845 + 0.105343i
\(476\) 0 0
\(477\) 13.8500i 0.634148i
\(478\) 0 0
\(479\) 22.9860 1.05026 0.525129 0.851023i \(-0.324017\pi\)
0.525129 + 0.851023i \(0.324017\pi\)
\(480\) 0 0
\(481\) 31.2533 1.42503
\(482\) 0 0
\(483\) 4.71914i 0.214728i
\(484\) 0 0
\(485\) −33.7315 + 25.3310i −1.53167 + 1.15022i
\(486\) 0 0
\(487\) 36.0187i 1.63216i 0.577937 + 0.816082i \(0.303858\pi\)
−0.577937 + 0.816082i \(0.696142\pi\)
\(488\) 0 0
\(489\) 2.02693 0.0916608
\(490\) 0 0
\(491\) 17.6698 0.797425 0.398713 0.917076i \(-0.369457\pi\)
0.398713 + 0.917076i \(0.369457\pi\)
\(492\) 0 0
\(493\) 20.4865i 0.922665i
\(494\) 0 0
\(495\) 4.17794 + 5.56346i 0.187785 + 0.250059i
\(496\) 0 0
\(497\) 2.16912i 0.0972984i
\(498\) 0 0
\(499\) −11.6980 −0.523676 −0.261838 0.965112i \(-0.584329\pi\)
−0.261838 + 0.965112i \(0.584329\pi\)
\(500\) 0 0
\(501\) −15.5470 −0.694590
\(502\) 0 0
\(503\) 37.6247i 1.67760i −0.544439 0.838800i \(-0.683257\pi\)
0.544439 0.838800i \(-0.316743\pi\)
\(504\) 0 0
\(505\) 14.7186 + 19.5997i 0.654969 + 0.872175i
\(506\) 0 0
\(507\) 15.2694i 0.678138i
\(508\) 0 0
\(509\) −25.8119 −1.14409 −0.572046 0.820222i \(-0.693850\pi\)
−0.572046 + 0.820222i \(0.693850\pi\)
\(510\) 0 0
\(511\) 4.34006 0.191993
\(512\) 0 0
\(513\) 0.478140i 0.0211104i
\(514\) 0 0
\(515\) 23.4413 17.6035i 1.03295 0.775703i
\(516\) 0 0
\(517\) 36.5828i 1.60891i
\(518\) 0 0
\(519\) 18.3736 0.806511
\(520\) 0 0
\(521\) −11.9851 −0.525077 −0.262539 0.964921i \(-0.584560\pi\)
−0.262539 + 0.964921i \(0.584560\pi\)
\(522\) 0 0
\(523\) 15.9557i 0.697692i 0.937180 + 0.348846i \(0.113426\pi\)
−0.937180 + 0.348846i \(0.886574\pi\)
\(524\) 0 0
\(525\) −0.727238 + 2.50484i −0.0317393 + 0.109320i
\(526\) 0 0
\(527\) 20.3116i 0.884785i
\(528\) 0 0
\(529\) −58.8388 −2.55821
\(530\) 0 0
\(531\) 2.17583 0.0944231
\(532\) 0 0
\(533\) 29.2435i 1.26668i
\(534\) 0 0
\(535\) −24.9519 + 18.7379i −1.07876 + 0.810110i
\(536\) 0 0
\(537\) 17.2319i 0.743611i
\(538\) 0 0
\(539\) −20.9338 −0.901684
\(540\) 0 0
\(541\) 19.6119 0.843180 0.421590 0.906787i \(-0.361472\pi\)
0.421590 + 0.906787i \(0.361472\pi\)
\(542\) 0 0
\(543\) 19.1646i 0.822431i
\(544\) 0 0
\(545\) 12.4444 + 16.5713i 0.533059 + 0.709837i
\(546\) 0 0
\(547\) 29.4397i 1.25875i 0.777101 + 0.629376i \(0.216689\pi\)
−0.777101 + 0.629376i \(0.783311\pi\)
\(548\) 0 0
\(549\) 7.47318 0.318947
\(550\) 0 0
\(551\) 1.82131 0.0775906
\(552\) 0 0
\(553\) 3.27571i 0.139297i
\(554\) 0 0
\(555\) 7.89278 + 10.5102i 0.335030 + 0.446135i
\(556\) 0 0
\(557\) 26.4467i 1.12058i 0.828296 + 0.560291i \(0.189311\pi\)
−0.828296 + 0.560291i \(0.810689\pi\)
\(558\) 0 0
\(559\) 15.5268 0.656716
\(560\) 0 0
\(561\) −16.7343 −0.706523
\(562\) 0 0
\(563\) 7.06240i 0.297645i 0.988864 + 0.148822i \(0.0475483\pi\)
−0.988864 + 0.148822i \(0.952452\pi\)
\(564\) 0 0
\(565\) 17.7489 13.3287i 0.746700 0.560742i
\(566\) 0 0
\(567\) 0.521655i 0.0219074i
\(568\) 0 0
\(569\) −30.9071 −1.29569 −0.647846 0.761772i \(-0.724330\pi\)
−0.647846 + 0.761772i \(0.724330\pi\)
\(570\) 0 0
\(571\) 4.05811 0.169827 0.0849133 0.996388i \(-0.472939\pi\)
0.0849133 + 0.996388i \(0.472939\pi\)
\(572\) 0 0
\(573\) 10.8740i 0.454267i
\(574\) 0 0
\(575\) 43.4386 + 12.6117i 1.81152 + 0.525944i
\(576\) 0 0
\(577\) 15.4193i 0.641912i 0.947094 + 0.320956i \(0.104004\pi\)
−0.947094 + 0.320956i \(0.895996\pi\)
\(578\) 0 0
\(579\) −0.422686 −0.0175662
\(580\) 0 0
\(581\) 2.85401 0.118404
\(582\) 0 0
\(583\) 43.0943i 1.78479i
\(584\) 0 0
\(585\) −9.50677 + 7.13921i −0.393057 + 0.295170i
\(586\) 0 0
\(587\) 13.6593i 0.563778i 0.959447 + 0.281889i \(0.0909610\pi\)
−0.959447 + 0.281889i \(0.909039\pi\)
\(588\) 0 0
\(589\) 1.80576 0.0744052
\(590\) 0 0
\(591\) −9.02213 −0.371121
\(592\) 0 0
\(593\) 3.36005i 0.137981i 0.997617 + 0.0689903i \(0.0219778\pi\)
−0.997617 + 0.0689903i \(0.978022\pi\)
\(594\) 0 0
\(595\) −3.76715 5.01643i −0.154438 0.205654i
\(596\) 0 0
\(597\) 2.32112i 0.0949969i
\(598\) 0 0
\(599\) 27.0750 1.10625 0.553126 0.833097i \(-0.313435\pi\)
0.553126 + 0.833097i \(0.313435\pi\)
\(600\) 0 0
\(601\) −5.20937 −0.212495 −0.106247 0.994340i \(-0.533884\pi\)
−0.106247 + 0.994340i \(0.533884\pi\)
\(602\) 0 0
\(603\) 1.00000i 0.0407231i
\(604\) 0 0
\(605\) −1.77045 2.35758i −0.0719789 0.0958491i
\(606\) 0 0
\(607\) 10.1446i 0.411755i −0.978578 0.205877i \(-0.933995\pi\)
0.978578 0.205877i \(-0.0660048\pi\)
\(608\) 0 0
\(609\) 1.98707 0.0805201
\(610\) 0 0
\(611\) −62.5122 −2.52897
\(612\) 0 0
\(613\) 44.0310i 1.77840i −0.457523 0.889198i \(-0.651263\pi\)
0.457523 0.889198i \(-0.348737\pi\)
\(614\) 0 0
\(615\) 9.83436 7.38521i 0.396559 0.297801i
\(616\) 0 0
\(617\) 9.02385i 0.363286i 0.983364 + 0.181643i \(0.0581416\pi\)
−0.983364 + 0.181643i \(0.941858\pi\)
\(618\) 0 0
\(619\) 7.17585 0.288422 0.144211 0.989547i \(-0.453936\pi\)
0.144211 + 0.989547i \(0.453936\pi\)
\(620\) 0 0
\(621\) 9.04648 0.363023
\(622\) 0 0
\(623\) 7.71602i 0.309136i
\(624\) 0 0
\(625\) −21.1130 13.3881i −0.844519 0.535526i
\(626\) 0 0
\(627\) 1.48773i 0.0594144i
\(628\) 0 0
\(629\) −31.6137 −1.26052
\(630\) 0 0
\(631\) 43.2028 1.71988 0.859939 0.510397i \(-0.170502\pi\)
0.859939 + 0.510397i \(0.170502\pi\)
\(632\) 0 0
\(633\) 9.63198i 0.382837i
\(634\) 0 0
\(635\) −11.6930 + 8.78097i −0.464022 + 0.348462i
\(636\) 0 0
\(637\) 35.7714i 1.41732i
\(638\) 0 0
\(639\) 4.15816 0.164494
\(640\) 0 0
\(641\) −0.226417 −0.00894293 −0.00447146 0.999990i \(-0.501423\pi\)
−0.00447146 + 0.999990i \(0.501423\pi\)
\(642\) 0 0
\(643\) 21.9852i 0.867013i 0.901150 + 0.433507i \(0.142724\pi\)
−0.901150 + 0.433507i \(0.857276\pi\)
\(644\) 0 0
\(645\) 3.92118 + 5.22155i 0.154396 + 0.205598i
\(646\) 0 0
\(647\) 26.8931i 1.05728i −0.848847 0.528639i \(-0.822702\pi\)
0.848847 0.528639i \(-0.177298\pi\)
\(648\) 0 0
\(649\) 6.77012 0.265750
\(650\) 0 0
\(651\) 1.97010 0.0772144
\(652\) 0 0
\(653\) 27.0902i 1.06012i 0.847960 + 0.530060i \(0.177831\pi\)
−0.847960 + 0.530060i \(0.822169\pi\)
\(654\) 0 0
\(655\) 12.5812 + 16.7535i 0.491588 + 0.654613i
\(656\) 0 0
\(657\) 8.31980i 0.324586i
\(658\) 0 0
\(659\) −40.7849 −1.58875 −0.794376 0.607426i \(-0.792202\pi\)
−0.794376 + 0.607426i \(0.792202\pi\)
\(660\) 0 0
\(661\) 18.4312 0.716889 0.358445 0.933551i \(-0.383307\pi\)
0.358445 + 0.933551i \(0.383307\pi\)
\(662\) 0 0
\(663\) 28.5954i 1.11055i
\(664\) 0 0
\(665\) −0.445977 + 0.334911i −0.0172943 + 0.0129873i
\(666\) 0 0
\(667\) 34.4596i 1.33428i
\(668\) 0 0
\(669\) −14.1438 −0.546832
\(670\) 0 0
\(671\) 23.2528 0.897665
\(672\) 0 0
\(673\) 39.6813i 1.52960i 0.644266 + 0.764802i \(0.277163\pi\)
−0.644266 + 0.764802i \(0.722837\pi\)
\(674\) 0 0
\(675\) −4.80172 1.39410i −0.184818 0.0536589i
\(676\) 0 0
\(677\) 32.8173i 1.26127i 0.776079 + 0.630635i \(0.217206\pi\)
−0.776079 + 0.630635i \(0.782794\pi\)
\(678\) 0 0
\(679\) −9.84111 −0.377667
\(680\) 0 0
\(681\) −9.52142 −0.364862
\(682\) 0 0
\(683\) 9.83828i 0.376451i 0.982126 + 0.188226i \(0.0602736\pi\)
−0.982126 + 0.188226i \(0.939726\pi\)
\(684\) 0 0
\(685\) 34.6010 25.9840i 1.32204 0.992797i
\(686\) 0 0
\(687\) 14.5476i 0.555027i
\(688\) 0 0
\(689\) −73.6390 −2.80542
\(690\) 0 0
\(691\) 8.86946 0.337410 0.168705 0.985667i \(-0.446041\pi\)
0.168705 + 0.985667i \(0.446041\pi\)
\(692\) 0 0
\(693\) 1.62313i 0.0616577i
\(694\) 0 0
\(695\) 26.9702 + 35.9143i 1.02304 + 1.36231i
\(696\) 0 0
\(697\) 29.5807i 1.12045i
\(698\) 0 0
\(699\) 23.7819 0.899514
\(700\) 0 0
\(701\) −48.8271 −1.84418 −0.922088 0.386981i \(-0.873518\pi\)
−0.922088 + 0.386981i \(0.873518\pi\)
\(702\) 0 0
\(703\) 2.81056i 0.106002i
\(704\) 0 0
\(705\) −15.7870 21.0224i −0.594571 0.791748i
\(706\) 0 0
\(707\) 5.71818i 0.215054i
\(708\) 0 0
\(709\) −22.5117 −0.845445 −0.422723 0.906259i \(-0.638926\pi\)
−0.422723 + 0.906259i \(0.638926\pi\)
\(710\) 0 0
\(711\) −6.27946 −0.235498
\(712\) 0 0
\(713\) 34.1653i 1.27950i
\(714\) 0 0
\(715\) −29.5804 + 22.2137i −1.10624 + 0.830745i
\(716\) 0 0
\(717\) 5.68266i 0.212223i
\(718\) 0 0
\(719\) −14.9316 −0.556855 −0.278427 0.960457i \(-0.589813\pi\)
−0.278427 + 0.960457i \(0.589813\pi\)
\(720\) 0 0
\(721\) 6.83896 0.254696
\(722\) 0 0
\(723\) 5.38321i 0.200204i
\(724\) 0 0
\(725\) −5.31036 + 18.2905i −0.197222 + 0.679294i
\(726\) 0 0
\(727\) 37.4214i 1.38788i −0.720031 0.693942i \(-0.755873\pi\)
0.720031 0.693942i \(-0.244127\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −15.7059 −0.580903
\(732\) 0 0
\(733\) 29.4317i 1.08709i −0.839381 0.543543i \(-0.817083\pi\)
0.839381 0.543543i \(-0.182917\pi\)
\(734\) 0 0
\(735\) 12.0296 9.03379i 0.443720 0.333216i
\(736\) 0 0
\(737\) 3.11151i 0.114614i
\(738\) 0 0
\(739\) −18.3247 −0.674084 −0.337042 0.941490i \(-0.609426\pi\)
−0.337042 + 0.941490i \(0.609426\pi\)
\(740\) 0 0
\(741\) −2.54222 −0.0933908
\(742\) 0 0
\(743\) 16.6195i 0.609710i 0.952399 + 0.304855i \(0.0986079\pi\)
−0.952399 + 0.304855i \(0.901392\pi\)
\(744\) 0 0
\(745\) −11.7903 15.7003i −0.431964 0.575215i
\(746\) 0 0
\(747\) 5.47106i 0.200176i
\(748\) 0 0
\(749\) −7.27968 −0.265994
\(750\) 0 0
\(751\) 0.409716 0.0149507 0.00747537 0.999972i \(-0.497620\pi\)
0.00747537 + 0.999972i \(0.497620\pi\)
\(752\) 0 0
\(753\) 15.4504i 0.563044i
\(754\) 0 0
\(755\) 6.53788 + 8.70602i 0.237938 + 0.316845i
\(756\) 0 0
\(757\) 14.2090i 0.516434i −0.966087 0.258217i \(-0.916865\pi\)
0.966087 0.258217i \(-0.0831350\pi\)
\(758\) 0 0
\(759\) 28.1482 1.02171
\(760\) 0 0
\(761\) −48.4596 −1.75666 −0.878330 0.478055i \(-0.841342\pi\)
−0.878330 + 0.478055i \(0.841342\pi\)
\(762\) 0 0
\(763\) 4.83465i 0.175026i
\(764\) 0 0
\(765\) 9.61639 7.22153i 0.347681 0.261095i
\(766\) 0 0
\(767\) 11.5687i 0.417721i
\(768\) 0 0
\(769\) 3.46238 0.124857 0.0624283 0.998049i \(-0.480116\pi\)
0.0624283 + 0.998049i \(0.480116\pi\)
\(770\) 0 0
\(771\) 11.4600 0.412721
\(772\) 0 0
\(773\) 29.2434i 1.05181i 0.850542 + 0.525907i \(0.176274\pi\)
−0.850542 + 0.525907i \(0.823726\pi\)
\(774\) 0 0
\(775\) −5.26502 + 18.1344i −0.189125 + 0.651406i
\(776\) 0 0
\(777\) 3.06635i 0.110005i
\(778\) 0 0
\(779\) 2.62982 0.0942231
\(780\) 0 0
\(781\) 12.9381 0.462963
\(782\) 0 0
\(783\) 3.80917i 0.136129i
\(784\) 0 0
\(785\) 14.7146 11.0501i 0.525186 0.394394i
\(786\) 0 0
\(787\) 29.1776i 1.04007i 0.854145 + 0.520035i \(0.174081\pi\)
−0.854145 + 0.520035i \(0.825919\pi\)
\(788\) 0 0
\(789\) −30.5405 −1.08727
\(790\) 0 0
\(791\) 5.17820 0.184116
\(792\) 0 0