Properties

Label 1840.2.e.g.369.6
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} - 20 x^{3} + 64 x^{2} - 32 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 920)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.6
Root \(1.55369 + 1.55369i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.g.369.9

$q$-expansion

\(f(q)\) \(=\) \(q-0.356372i q^{3} +(0.376266 + 2.20418i) q^{5} -2.46376i q^{7} +2.87300 q^{9} +O(q^{10})\) \(q-0.356372i q^{3} +(0.376266 + 2.20418i) q^{5} -2.46376i q^{7} +2.87300 q^{9} -1.61574 q^{11} +2.62553i q^{13} +(0.785509 - 0.134090i) q^{15} -2.58924i q^{17} +4.02550 q^{19} -0.878013 q^{21} +1.00000i q^{23} +(-4.71685 + 1.65872i) q^{25} -2.09297i q^{27} +7.08580 q^{29} +4.58371 q^{31} +0.575803i q^{33} +(5.43057 - 0.927026i) q^{35} +2.96054i q^{37} +0.935665 q^{39} -5.71155 q^{41} -2.30448i q^{43} +(1.08101 + 6.33262i) q^{45} -6.88317i q^{47} +0.929907 q^{49} -0.922731 q^{51} +6.76467i q^{53} +(-0.607946 - 3.56138i) q^{55} -1.43457i q^{57} +2.53432 q^{59} +9.25564 q^{61} -7.07837i q^{63} +(-5.78715 + 0.987896i) q^{65} +15.7285i q^{67} +0.356372 q^{69} +5.25113 q^{71} -6.03858i q^{73} +(0.591120 + 1.68095i) q^{75} +3.98078i q^{77} -1.35712 q^{79} +7.87312 q^{81} -8.59500i q^{83} +(5.70716 - 0.974241i) q^{85} -2.52518i q^{87} +8.84084 q^{89} +6.46867 q^{91} -1.63350i q^{93} +(1.51466 + 8.87293i) q^{95} +8.01314i q^{97} -4.64201 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 14q + 2q^{5} - 4q^{9} + 14q^{11} + 6q^{15} - 14q^{19} - 12q^{21} - 14q^{25} + 22q^{29} + 20q^{31} + 2q^{35} - 48q^{39} - 32q^{41} - 26q^{45} + 34q^{49} + 14q^{51} + 38q^{55} - 22q^{59} + 10q^{61} - 38q^{65} + 6q^{69} + 28q^{71} + 24q^{75} - 64q^{79} - 10q^{81} - 50q^{85} + 48q^{89} + 14q^{91} + 30q^{95} - 122q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 0.356372i 0.205751i −0.994694 0.102876i \(-0.967196\pi\)
0.994694 0.102876i \(-0.0328044\pi\)
\(4\) 0 0
\(5\) 0.376266 + 2.20418i 0.168271 + 0.985741i
\(6\) 0 0
\(7\) 2.46376i 0.931212i −0.884992 0.465606i \(-0.845836\pi\)
0.884992 0.465606i \(-0.154164\pi\)
\(8\) 0 0
\(9\) 2.87300 0.957666
\(10\) 0 0
\(11\) −1.61574 −0.487163 −0.243581 0.969880i \(-0.578322\pi\)
−0.243581 + 0.969880i \(0.578322\pi\)
\(12\) 0 0
\(13\) 2.62553i 0.728191i 0.931362 + 0.364096i \(0.118622\pi\)
−0.931362 + 0.364096i \(0.881378\pi\)
\(14\) 0 0
\(15\) 0.785509 0.134090i 0.202817 0.0346220i
\(16\) 0 0
\(17\) 2.58924i 0.627982i −0.949426 0.313991i \(-0.898334\pi\)
0.949426 0.313991i \(-0.101666\pi\)
\(18\) 0 0
\(19\) 4.02550 0.923512 0.461756 0.887007i \(-0.347220\pi\)
0.461756 + 0.887007i \(0.347220\pi\)
\(20\) 0 0
\(21\) −0.878013 −0.191598
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −4.71685 + 1.65872i −0.943370 + 0.331743i
\(26\) 0 0
\(27\) 2.09297i 0.402793i
\(28\) 0 0
\(29\) 7.08580 1.31580 0.657900 0.753106i \(-0.271445\pi\)
0.657900 + 0.753106i \(0.271445\pi\)
\(30\) 0 0
\(31\) 4.58371 0.823258 0.411629 0.911352i \(-0.364960\pi\)
0.411629 + 0.911352i \(0.364960\pi\)
\(32\) 0 0
\(33\) 0.575803i 0.100234i
\(34\) 0 0
\(35\) 5.43057 0.927026i 0.917934 0.156696i
\(36\) 0 0
\(37\) 2.96054i 0.486710i 0.969937 + 0.243355i \(0.0782480\pi\)
−0.969937 + 0.243355i \(0.921752\pi\)
\(38\) 0 0
\(39\) 0.935665 0.149826
\(40\) 0 0
\(41\) −5.71155 −0.891995 −0.445997 0.895034i \(-0.647151\pi\)
−0.445997 + 0.895034i \(0.647151\pi\)
\(42\) 0 0
\(43\) 2.30448i 0.351430i −0.984441 0.175715i \(-0.943776\pi\)
0.984441 0.175715i \(-0.0562237\pi\)
\(44\) 0 0
\(45\) 1.08101 + 6.33262i 0.161148 + 0.944011i
\(46\) 0 0
\(47\) 6.88317i 1.00401i −0.864864 0.502007i \(-0.832595\pi\)
0.864864 0.502007i \(-0.167405\pi\)
\(48\) 0 0
\(49\) 0.929907 0.132844
\(50\) 0 0
\(51\) −0.922731 −0.129208
\(52\) 0 0
\(53\) 6.76467i 0.929199i 0.885521 + 0.464600i \(0.153802\pi\)
−0.885521 + 0.464600i \(0.846198\pi\)
\(54\) 0 0
\(55\) −0.607946 3.56138i −0.0819754 0.480216i
\(56\) 0 0
\(57\) 1.43457i 0.190014i
\(58\) 0 0
\(59\) 2.53432 0.329941 0.164970 0.986299i \(-0.447247\pi\)
0.164970 + 0.986299i \(0.447247\pi\)
\(60\) 0 0
\(61\) 9.25564 1.18506 0.592532 0.805547i \(-0.298129\pi\)
0.592532 + 0.805547i \(0.298129\pi\)
\(62\) 0 0
\(63\) 7.07837i 0.891791i
\(64\) 0 0
\(65\) −5.78715 + 0.987896i −0.717808 + 0.122533i
\(66\) 0 0
\(67\) 15.7285i 1.92154i 0.277347 + 0.960770i \(0.410545\pi\)
−0.277347 + 0.960770i \(0.589455\pi\)
\(68\) 0 0
\(69\) 0.356372 0.0429021
\(70\) 0 0
\(71\) 5.25113 0.623194 0.311597 0.950214i \(-0.399136\pi\)
0.311597 + 0.950214i \(0.399136\pi\)
\(72\) 0 0
\(73\) 6.03858i 0.706762i −0.935479 0.353381i \(-0.885032\pi\)
0.935479 0.353381i \(-0.114968\pi\)
\(74\) 0 0
\(75\) 0.591120 + 1.68095i 0.0682566 + 0.194100i
\(76\) 0 0
\(77\) 3.98078i 0.453652i
\(78\) 0 0
\(79\) −1.35712 −0.152688 −0.0763439 0.997082i \(-0.524325\pi\)
−0.0763439 + 0.997082i \(0.524325\pi\)
\(80\) 0 0
\(81\) 7.87312 0.874791
\(82\) 0 0
\(83\) 8.59500i 0.943423i −0.881753 0.471712i \(-0.843636\pi\)
0.881753 0.471712i \(-0.156364\pi\)
\(84\) 0 0
\(85\) 5.70716 0.974241i 0.619028 0.105671i
\(86\) 0 0
\(87\) 2.52518i 0.270727i
\(88\) 0 0
\(89\) 8.84084 0.937127 0.468564 0.883430i \(-0.344772\pi\)
0.468564 + 0.883430i \(0.344772\pi\)
\(90\) 0 0
\(91\) 6.46867 0.678100
\(92\) 0 0
\(93\) 1.63350i 0.169386i
\(94\) 0 0
\(95\) 1.51466 + 8.87293i 0.155400 + 0.910344i
\(96\) 0 0
\(97\) 8.01314i 0.813611i 0.913515 + 0.406806i \(0.133357\pi\)
−0.913515 + 0.406806i \(0.866643\pi\)
\(98\) 0 0
\(99\) −4.64201 −0.466539
\(100\) 0 0
\(101\) −6.33185 −0.630043 −0.315021 0.949085i \(-0.602012\pi\)
−0.315021 + 0.949085i \(0.602012\pi\)
\(102\) 0 0
\(103\) 13.1901i 1.29966i 0.760078 + 0.649831i \(0.225161\pi\)
−0.760078 + 0.649831i \(0.774839\pi\)
\(104\) 0 0
\(105\) −0.330366 1.93530i −0.0322404 0.188866i
\(106\) 0 0
\(107\) 9.54923i 0.923159i −0.887099 0.461580i \(-0.847283\pi\)
0.887099 0.461580i \(-0.152717\pi\)
\(108\) 0 0
\(109\) 17.5622 1.68215 0.841077 0.540915i \(-0.181922\pi\)
0.841077 + 0.540915i \(0.181922\pi\)
\(110\) 0 0
\(111\) 1.05505 0.100141
\(112\) 0 0
\(113\) 1.54267i 0.145122i 0.997364 + 0.0725611i \(0.0231172\pi\)
−0.997364 + 0.0725611i \(0.976883\pi\)
\(114\) 0 0
\(115\) −2.20418 + 0.376266i −0.205541 + 0.0350869i
\(116\) 0 0
\(117\) 7.54315i 0.697364i
\(118\) 0 0
\(119\) −6.37925 −0.584785
\(120\) 0 0
\(121\) −8.38940 −0.762673
\(122\) 0 0
\(123\) 2.03544i 0.183529i
\(124\) 0 0
\(125\) −5.43090 9.77268i −0.485755 0.874095i
\(126\) 0 0
\(127\) 12.4256i 1.10260i 0.834308 + 0.551299i \(0.185868\pi\)
−0.834308 + 0.551299i \(0.814132\pi\)
\(128\) 0 0
\(129\) −0.821251 −0.0723071
\(130\) 0 0
\(131\) 11.3191 0.988957 0.494479 0.869190i \(-0.335359\pi\)
0.494479 + 0.869190i \(0.335359\pi\)
\(132\) 0 0
\(133\) 9.91784i 0.859986i
\(134\) 0 0
\(135\) 4.61329 0.787513i 0.397049 0.0677783i
\(136\) 0 0
\(137\) 4.94093i 0.422132i −0.977472 0.211066i \(-0.932306\pi\)
0.977472 0.211066i \(-0.0676936\pi\)
\(138\) 0 0
\(139\) −2.93101 −0.248605 −0.124303 0.992244i \(-0.539669\pi\)
−0.124303 + 0.992244i \(0.539669\pi\)
\(140\) 0 0
\(141\) −2.45297 −0.206577
\(142\) 0 0
\(143\) 4.24216i 0.354748i
\(144\) 0 0
\(145\) 2.66614 + 15.6184i 0.221411 + 1.29704i
\(146\) 0 0
\(147\) 0.331393i 0.0273328i
\(148\) 0 0
\(149\) 5.09023 0.417008 0.208504 0.978022i \(-0.433141\pi\)
0.208504 + 0.978022i \(0.433141\pi\)
\(150\) 0 0
\(151\) 14.3645 1.16897 0.584485 0.811405i \(-0.301297\pi\)
0.584485 + 0.811405i \(0.301297\pi\)
\(152\) 0 0
\(153\) 7.43888i 0.601398i
\(154\) 0 0
\(155\) 1.72469 + 10.1033i 0.138530 + 0.811519i
\(156\) 0 0
\(157\) 7.34146i 0.585912i 0.956126 + 0.292956i \(0.0946390\pi\)
−0.956126 + 0.292956i \(0.905361\pi\)
\(158\) 0 0
\(159\) 2.41074 0.191184
\(160\) 0 0
\(161\) 2.46376 0.194171
\(162\) 0 0
\(163\) 2.12762i 0.166648i 0.996523 + 0.0833240i \(0.0265536\pi\)
−0.996523 + 0.0833240i \(0.973446\pi\)
\(164\) 0 0
\(165\) −1.26917 + 0.216655i −0.0988051 + 0.0168665i
\(166\) 0 0
\(167\) 2.16080i 0.167208i 0.996499 + 0.0836039i \(0.0266431\pi\)
−0.996499 + 0.0836039i \(0.973357\pi\)
\(168\) 0 0
\(169\) 6.10659 0.469738
\(170\) 0 0
\(171\) 11.5652 0.884417
\(172\) 0 0
\(173\) 18.6210i 1.41573i −0.706350 0.707863i \(-0.749659\pi\)
0.706350 0.707863i \(-0.250341\pi\)
\(174\) 0 0
\(175\) 4.08667 + 11.6212i 0.308923 + 0.878477i
\(176\) 0 0
\(177\) 0.903162i 0.0678858i
\(178\) 0 0
\(179\) −13.4670 −1.00657 −0.503287 0.864119i \(-0.667876\pi\)
−0.503287 + 0.864119i \(0.667876\pi\)
\(180\) 0 0
\(181\) 12.2927 0.913706 0.456853 0.889542i \(-0.348977\pi\)
0.456853 + 0.889542i \(0.348977\pi\)
\(182\) 0 0
\(183\) 3.29845i 0.243828i
\(184\) 0 0
\(185\) −6.52558 + 1.11395i −0.479770 + 0.0818992i
\(186\) 0 0
\(187\) 4.18352i 0.305930i
\(188\) 0 0
\(189\) −5.15657 −0.375085
\(190\) 0 0
\(191\) 2.07099 0.149852 0.0749258 0.997189i \(-0.476128\pi\)
0.0749258 + 0.997189i \(0.476128\pi\)
\(192\) 0 0
\(193\) 25.7996i 1.85710i −0.371209 0.928549i \(-0.621057\pi\)
0.371209 0.928549i \(-0.378943\pi\)
\(194\) 0 0
\(195\) 0.352058 + 2.06238i 0.0252114 + 0.147690i
\(196\) 0 0
\(197\) 4.21443i 0.300266i −0.988666 0.150133i \(-0.952030\pi\)
0.988666 0.150133i \(-0.0479702\pi\)
\(198\) 0 0
\(199\) −22.0428 −1.56257 −0.781285 0.624175i \(-0.785435\pi\)
−0.781285 + 0.624175i \(0.785435\pi\)
\(200\) 0 0
\(201\) 5.60519 0.395359
\(202\) 0 0
\(203\) 17.4577i 1.22529i
\(204\) 0 0
\(205\) −2.14906 12.5893i −0.150097 0.879276i
\(206\) 0 0
\(207\) 2.87300i 0.199687i
\(208\) 0 0
\(209\) −6.50414 −0.449901
\(210\) 0 0
\(211\) −28.9217 −1.99105 −0.995524 0.0945049i \(-0.969873\pi\)
−0.995524 + 0.0945049i \(0.969873\pi\)
\(212\) 0 0
\(213\) 1.87135i 0.128223i
\(214\) 0 0
\(215\) 5.07949 0.867096i 0.346418 0.0591354i
\(216\) 0 0
\(217\) 11.2931i 0.766628i
\(218\) 0 0
\(219\) −2.15198 −0.145417
\(220\) 0 0
\(221\) 6.79812 0.457291
\(222\) 0 0
\(223\) 6.63731i 0.444467i 0.974993 + 0.222234i \(0.0713348\pi\)
−0.974993 + 0.222234i \(0.928665\pi\)
\(224\) 0 0
\(225\) −13.5515 + 4.76549i −0.903433 + 0.317699i
\(226\) 0 0
\(227\) 0.370367i 0.0245821i −0.999924 0.0122911i \(-0.996088\pi\)
0.999924 0.0122911i \(-0.00391246\pi\)
\(228\) 0 0
\(229\) 11.5625 0.764073 0.382036 0.924147i \(-0.375223\pi\)
0.382036 + 0.924147i \(0.375223\pi\)
\(230\) 0 0
\(231\) 1.41864 0.0933395
\(232\) 0 0
\(233\) 16.8534i 1.10410i −0.833810 0.552051i \(-0.813845\pi\)
0.833810 0.552051i \(-0.186155\pi\)
\(234\) 0 0
\(235\) 15.1718 2.58990i 0.989697 0.168946i
\(236\) 0 0
\(237\) 0.483639i 0.0314157i
\(238\) 0 0
\(239\) −17.7742 −1.14972 −0.574859 0.818252i \(-0.694943\pi\)
−0.574859 + 0.818252i \(0.694943\pi\)
\(240\) 0 0
\(241\) −26.6318 −1.71551 −0.857754 0.514061i \(-0.828141\pi\)
−0.857754 + 0.514061i \(0.828141\pi\)
\(242\) 0 0
\(243\) 9.08467i 0.582782i
\(244\) 0 0
\(245\) 0.349892 + 2.04969i 0.0223538 + 0.130950i
\(246\) 0 0
\(247\) 10.5691i 0.672493i
\(248\) 0 0
\(249\) −3.06301 −0.194111
\(250\) 0 0
\(251\) −16.8599 −1.06419 −0.532094 0.846685i \(-0.678595\pi\)
−0.532094 + 0.846685i \(0.678595\pi\)
\(252\) 0 0
\(253\) 1.61574i 0.101580i
\(254\) 0 0
\(255\) −0.347192 2.03387i −0.0217420 0.127366i
\(256\) 0 0
\(257\) 8.33024i 0.519626i −0.965659 0.259813i \(-0.916339\pi\)
0.965659 0.259813i \(-0.0836610\pi\)
\(258\) 0 0
\(259\) 7.29405 0.453230
\(260\) 0 0
\(261\) 20.3575 1.26010
\(262\) 0 0
\(263\) 15.0389i 0.927337i −0.886009 0.463669i \(-0.846533\pi\)
0.886009 0.463669i \(-0.153467\pi\)
\(264\) 0 0
\(265\) −14.9106 + 2.54531i −0.915950 + 0.156357i
\(266\) 0 0
\(267\) 3.15063i 0.192815i
\(268\) 0 0
\(269\) 7.01922 0.427969 0.213985 0.976837i \(-0.431356\pi\)
0.213985 + 0.976837i \(0.431356\pi\)
\(270\) 0 0
\(271\) −4.40129 −0.267359 −0.133680 0.991025i \(-0.542679\pi\)
−0.133680 + 0.991025i \(0.542679\pi\)
\(272\) 0 0
\(273\) 2.30525i 0.139520i
\(274\) 0 0
\(275\) 7.62118 2.68005i 0.459575 0.161613i
\(276\) 0 0
\(277\) 8.41544i 0.505634i −0.967514 0.252817i \(-0.918643\pi\)
0.967514 0.252817i \(-0.0813571\pi\)
\(278\) 0 0
\(279\) 13.1690 0.788406
\(280\) 0 0
\(281\) −15.0068 −0.895233 −0.447617 0.894226i \(-0.647727\pi\)
−0.447617 + 0.894226i \(0.647727\pi\)
\(282\) 0 0
\(283\) 7.09122i 0.421529i 0.977537 + 0.210765i \(0.0675953\pi\)
−0.977537 + 0.210765i \(0.932405\pi\)
\(284\) 0 0
\(285\) 3.16206 0.539781i 0.187304 0.0319738i
\(286\) 0 0
\(287\) 14.0719i 0.830637i
\(288\) 0 0
\(289\) 10.2958 0.605638
\(290\) 0 0
\(291\) 2.85566 0.167402
\(292\) 0 0
\(293\) 28.0567i 1.63909i 0.573015 + 0.819545i \(0.305774\pi\)
−0.573015 + 0.819545i \(0.694226\pi\)
\(294\) 0 0
\(295\) 0.953579 + 5.58612i 0.0555195 + 0.325236i
\(296\) 0 0
\(297\) 3.38169i 0.196225i
\(298\) 0 0
\(299\) −2.62553 −0.151838
\(300\) 0 0
\(301\) −5.67767 −0.327256
\(302\) 0 0
\(303\) 2.25649i 0.129632i
\(304\) 0 0
\(305\) 3.48258 + 20.4011i 0.199412 + 1.16817i
\(306\) 0 0
\(307\) 29.2707i 1.67057i 0.549820 + 0.835283i \(0.314696\pi\)
−0.549820 + 0.835283i \(0.685304\pi\)
\(308\) 0 0
\(309\) 4.70059 0.267407
\(310\) 0 0
\(311\) 15.8111 0.896563 0.448281 0.893893i \(-0.352036\pi\)
0.448281 + 0.893893i \(0.352036\pi\)
\(312\) 0 0
\(313\) 9.98602i 0.564443i 0.959349 + 0.282222i \(0.0910713\pi\)
−0.959349 + 0.282222i \(0.908929\pi\)
\(314\) 0 0
\(315\) 15.6020 2.66335i 0.879074 0.150063i
\(316\) 0 0
\(317\) 13.7683i 0.773302i 0.922226 + 0.386651i \(0.126368\pi\)
−0.922226 + 0.386651i \(0.873632\pi\)
\(318\) 0 0
\(319\) −11.4488 −0.641008
\(320\) 0 0
\(321\) −3.40308 −0.189941
\(322\) 0 0
\(323\) 10.4230i 0.579950i
\(324\) 0 0
\(325\) −4.35501 12.3842i −0.241572 0.686953i
\(326\) 0 0
\(327\) 6.25868i 0.346106i
\(328\) 0 0
\(329\) −16.9584 −0.934950
\(330\) 0 0
\(331\) −18.6765 −1.02656 −0.513278 0.858223i \(-0.671569\pi\)
−0.513278 + 0.858223i \(0.671569\pi\)
\(332\) 0 0
\(333\) 8.50564i 0.466106i
\(334\) 0 0
\(335\) −34.6685 + 5.91809i −1.89414 + 0.323340i
\(336\) 0 0
\(337\) 13.8915i 0.756716i 0.925659 + 0.378358i \(0.123511\pi\)
−0.925659 + 0.378358i \(0.876489\pi\)
\(338\) 0 0
\(339\) 0.549764 0.0298591
\(340\) 0 0
\(341\) −7.40606 −0.401060
\(342\) 0 0
\(343\) 19.5374i 1.05492i
\(344\) 0 0
\(345\) 0.134090 + 0.785509i 0.00721919 + 0.0422904i
\(346\) 0 0
\(347\) 0.706854i 0.0379459i 0.999820 + 0.0189730i \(0.00603964\pi\)
−0.999820 + 0.0189730i \(0.993960\pi\)
\(348\) 0 0
\(349\) −6.93817 −0.371392 −0.185696 0.982607i \(-0.559454\pi\)
−0.185696 + 0.982607i \(0.559454\pi\)
\(350\) 0 0
\(351\) 5.49516 0.293310
\(352\) 0 0
\(353\) 0.413170i 0.0219908i 0.999940 + 0.0109954i \(0.00350002\pi\)
−0.999940 + 0.0109954i \(0.996500\pi\)
\(354\) 0 0
\(355\) 1.97582 + 11.5744i 0.104866 + 0.614308i
\(356\) 0 0
\(357\) 2.27338i 0.120320i
\(358\) 0 0
\(359\) −32.6209 −1.72167 −0.860834 0.508886i \(-0.830057\pi\)
−0.860834 + 0.508886i \(0.830057\pi\)
\(360\) 0 0
\(361\) −2.79537 −0.147125
\(362\) 0 0
\(363\) 2.98974i 0.156921i
\(364\) 0 0
\(365\) 13.3101 2.27211i 0.696685 0.118928i
\(366\) 0 0
\(367\) 13.5293i 0.706223i 0.935581 + 0.353112i \(0.114876\pi\)
−0.935581 + 0.353112i \(0.885124\pi\)
\(368\) 0 0
\(369\) −16.4093 −0.854234
\(370\) 0 0
\(371\) 16.6665 0.865282
\(372\) 0 0
\(373\) 20.7690i 1.07538i −0.843143 0.537689i \(-0.819297\pi\)
0.843143 0.537689i \(-0.180703\pi\)
\(374\) 0 0
\(375\) −3.48271 + 1.93542i −0.179846 + 0.0999447i
\(376\) 0 0
\(377\) 18.6040i 0.958153i
\(378\) 0 0
\(379\) −25.0528 −1.28688 −0.643438 0.765498i \(-0.722493\pi\)
−0.643438 + 0.765498i \(0.722493\pi\)
\(380\) 0 0
\(381\) 4.42815 0.226861
\(382\) 0 0
\(383\) 4.51677i 0.230796i −0.993319 0.115398i \(-0.963186\pi\)
0.993319 0.115398i \(-0.0368144\pi\)
\(384\) 0 0
\(385\) −8.77437 + 1.49783i −0.447183 + 0.0763365i
\(386\) 0 0
\(387\) 6.62076i 0.336552i
\(388\) 0 0
\(389\) −0.455188 −0.0230789 −0.0115395 0.999933i \(-0.503673\pi\)
−0.0115395 + 0.999933i \(0.503673\pi\)
\(390\) 0 0
\(391\) 2.58924 0.130943
\(392\) 0 0
\(393\) 4.03382i 0.203479i
\(394\) 0 0
\(395\) −0.510637 2.99134i −0.0256929 0.150511i
\(396\) 0 0
\(397\) 15.0798i 0.756832i −0.925636 0.378416i \(-0.876469\pi\)
0.925636 0.378416i \(-0.123531\pi\)
\(398\) 0 0
\(399\) −3.53444 −0.176943
\(400\) 0 0
\(401\) −38.0845 −1.90185 −0.950924 0.309424i \(-0.899864\pi\)
−0.950924 + 0.309424i \(0.899864\pi\)
\(402\) 0 0
\(403\) 12.0347i 0.599489i
\(404\) 0 0
\(405\) 2.96238 + 17.3538i 0.147202 + 0.862317i
\(406\) 0 0
\(407\) 4.78345i 0.237107i
\(408\) 0 0
\(409\) −16.3672 −0.809305 −0.404653 0.914470i \(-0.632608\pi\)
−0.404653 + 0.914470i \(0.632608\pi\)
\(410\) 0 0
\(411\) −1.76081 −0.0868543
\(412\) 0 0
\(413\) 6.24396i 0.307245i
\(414\) 0 0
\(415\) 18.9449 3.23400i 0.929971 0.158751i
\(416\) 0 0
\(417\) 1.04453i 0.0511509i
\(418\) 0 0
\(419\) −5.32621 −0.260202 −0.130101 0.991501i \(-0.541530\pi\)
−0.130101 + 0.991501i \(0.541530\pi\)
\(420\) 0 0
\(421\) −11.3000 −0.550730 −0.275365 0.961340i \(-0.588799\pi\)
−0.275365 + 0.961340i \(0.588799\pi\)
\(422\) 0 0
\(423\) 19.7753i 0.961510i
\(424\) 0 0
\(425\) 4.29481 + 12.2130i 0.208329 + 0.592420i
\(426\) 0 0
\(427\) 22.8036i 1.10355i
\(428\) 0 0
\(429\) −1.51179 −0.0729898
\(430\) 0 0
\(431\) −33.6364 −1.62021 −0.810105 0.586285i \(-0.800590\pi\)
−0.810105 + 0.586285i \(0.800590\pi\)
\(432\) 0 0
\(433\) 18.3932i 0.883920i 0.897035 + 0.441960i \(0.145717\pi\)
−0.897035 + 0.441960i \(0.854283\pi\)
\(434\) 0 0
\(435\) 5.56595 0.950137i 0.266867 0.0455556i
\(436\) 0 0
\(437\) 4.02550i 0.192566i
\(438\) 0 0
\(439\) 28.7628 1.37277 0.686387 0.727236i \(-0.259196\pi\)
0.686387 + 0.727236i \(0.259196\pi\)
\(440\) 0 0
\(441\) 2.67162 0.127220
\(442\) 0 0
\(443\) 22.2359i 1.05646i −0.849102 0.528229i \(-0.822856\pi\)
0.849102 0.528229i \(-0.177144\pi\)
\(444\) 0 0
\(445\) 3.32650 + 19.4868i 0.157691 + 0.923764i
\(446\) 0 0
\(447\) 1.81401i 0.0857999i
\(448\) 0 0
\(449\) −28.4538 −1.34282 −0.671409 0.741087i \(-0.734311\pi\)
−0.671409 + 0.741087i \(0.734311\pi\)
\(450\) 0 0
\(451\) 9.22836 0.434547
\(452\) 0 0
\(453\) 5.11912i 0.240517i
\(454\) 0 0
\(455\) 2.43394 + 14.2581i 0.114105 + 0.668431i
\(456\) 0 0
\(457\) 7.58512i 0.354817i −0.984137 0.177408i \(-0.943229\pi\)
0.984137 0.177408i \(-0.0567714\pi\)
\(458\) 0 0
\(459\) −5.41920 −0.252947
\(460\) 0 0
\(461\) 6.02951 0.280822 0.140411 0.990093i \(-0.455158\pi\)
0.140411 + 0.990093i \(0.455158\pi\)
\(462\) 0 0
\(463\) 24.2763i 1.12821i −0.825701 0.564107i \(-0.809220\pi\)
0.825701 0.564107i \(-0.190780\pi\)
\(464\) 0 0
\(465\) 3.60054 0.614631i 0.166971 0.0285028i
\(466\) 0 0
\(467\) 5.99614i 0.277468i 0.990330 + 0.138734i \(0.0443034\pi\)
−0.990330 + 0.138734i \(0.955697\pi\)
\(468\) 0 0
\(469\) 38.7511 1.78936
\(470\) 0 0
\(471\) 2.61629 0.120552
\(472\) 0 0
\(473\) 3.72343i 0.171203i
\(474\) 0 0
\(475\) −18.9877 + 6.67716i −0.871214 + 0.306369i
\(476\) 0 0
\(477\) 19.4349i 0.889863i
\(478\) 0 0
\(479\) −17.5065 −0.799892 −0.399946 0.916539i \(-0.630971\pi\)
−0.399946 + 0.916539i \(0.630971\pi\)
\(480\) 0 0
\(481\) −7.77299 −0.354418
\(482\) 0 0
\(483\) 0.878013i 0.0399510i
\(484\) 0 0
\(485\) −17.6624 + 3.01507i −0.802010 + 0.136907i
\(486\) 0 0
\(487\) 31.6269i 1.43315i −0.697509 0.716576i \(-0.745708\pi\)
0.697509 0.716576i \(-0.254292\pi\)
\(488\) 0 0
\(489\) 0.758224 0.0342881
\(490\) 0 0
\(491\) −24.7642 −1.11759 −0.558797 0.829305i \(-0.688737\pi\)
−0.558797 + 0.829305i \(0.688737\pi\)
\(492\) 0 0
\(493\) 18.3468i 0.826299i
\(494\) 0 0
\(495\) −1.74663 10.2318i −0.0785051 0.459887i
\(496\) 0 0
\(497\) 12.9375i 0.580326i
\(498\) 0 0
\(499\) 37.7906 1.69174 0.845871 0.533388i \(-0.179081\pi\)
0.845871 + 0.533388i \(0.179081\pi\)
\(500\) 0 0
\(501\) 0.770049 0.0344032
\(502\) 0 0
\(503\) 1.40481i 0.0626376i −0.999509 0.0313188i \(-0.990029\pi\)
0.999509 0.0313188i \(-0.00997071\pi\)
\(504\) 0 0
\(505\) −2.38246 13.9566i −0.106018 0.621059i
\(506\) 0 0
\(507\) 2.17622i 0.0966492i
\(508\) 0 0
\(509\) −30.4044 −1.34765 −0.673825 0.738891i \(-0.735350\pi\)
−0.673825 + 0.738891i \(0.735350\pi\)
\(510\) 0 0
\(511\) −14.8776 −0.658146
\(512\) 0 0
\(513\) 8.42525i 0.371984i
\(514\) 0 0
\(515\) −29.0735 + 4.96299i −1.28113 + 0.218696i
\(516\) 0 0
\(517\) 11.1214i 0.489118i
\(518\) 0 0
\(519\) −6.63599 −0.291288
\(520\) 0 0
\(521\) −13.3500 −0.584873 −0.292437 0.956285i \(-0.594466\pi\)
−0.292437 + 0.956285i \(0.594466\pi\)
\(522\) 0 0
\(523\) 8.71026i 0.380873i −0.981699 0.190437i \(-0.939010\pi\)
0.981699 0.190437i \(-0.0609904\pi\)
\(524\) 0 0
\(525\) 4.14145 1.45637i 0.180748 0.0635614i
\(526\) 0 0
\(527\) 11.8683i 0.516991i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 7.28111 0.315973
\(532\) 0 0
\(533\) 14.9959i 0.649543i
\(534\) 0 0
\(535\) 21.0483 3.59305i 0.909996 0.155341i
\(536\) 0 0
\(537\) 4.79927i 0.207104i
\(538\) 0 0
\(539\) −1.50248 −0.0647166
\(540\) 0 0
\(541\) 21.2922 0.915423 0.457711 0.889101i \(-0.348669\pi\)
0.457711 + 0.889101i \(0.348669\pi\)
\(542\) 0 0
\(543\) 4.38075i 0.187996i
\(544\) 0 0
\(545\) 6.60806 + 38.7103i 0.283058 + 1.65817i
\(546\) 0 0
\(547\) 7.27222i 0.310937i 0.987841 + 0.155469i \(0.0496888\pi\)
−0.987841 + 0.155469i \(0.950311\pi\)
\(548\) 0 0
\(549\) 26.5914 1.13490
\(550\) 0 0
\(551\) 28.5238 1.21516
\(552\) 0 0
\(553\) 3.34361i 0.142185i
\(554\) 0 0
\(555\) 0.396980 + 2.32553i 0.0168509 + 0.0987133i
\(556\) 0 0
\(557\) 27.0665i 1.14684i 0.819260 + 0.573422i \(0.194384\pi\)
−0.819260 + 0.573422i \(0.805616\pi\)
\(558\) 0 0
\(559\) 6.05048 0.255908
\(560\) 0 0
\(561\) 1.49089 0.0629454
\(562\) 0 0
\(563\) 12.7921i 0.539124i −0.962983 0.269562i \(-0.913121\pi\)
0.962983 0.269562i \(-0.0868790\pi\)
\(564\) 0 0
\(565\) −3.40033 + 0.580454i −0.143053 + 0.0244199i
\(566\) 0 0
\(567\) 19.3974i 0.814616i
\(568\) 0 0
\(569\) 13.3013 0.557621 0.278810 0.960346i \(-0.410060\pi\)
0.278810 + 0.960346i \(0.410060\pi\)
\(570\) 0 0
\(571\) −31.8239 −1.33179 −0.665894 0.746046i \(-0.731950\pi\)
−0.665894 + 0.746046i \(0.731950\pi\)
\(572\) 0 0
\(573\) 0.738043i 0.0308322i
\(574\) 0 0
\(575\) −1.65872 4.71685i −0.0691733 0.196706i
\(576\) 0 0
\(577\) 26.0091i 1.08277i −0.840774 0.541386i \(-0.817900\pi\)
0.840774 0.541386i \(-0.182100\pi\)
\(578\) 0 0
\(579\) −9.19426 −0.382101
\(580\) 0 0
\(581\) −21.1760 −0.878527
\(582\) 0 0
\(583\) 10.9299i 0.452671i
\(584\) 0 0
\(585\) −16.6265 + 2.83823i −0.687420 + 0.117346i
\(586\) 0 0
\(587\) 39.4259i 1.62728i −0.581367 0.813641i \(-0.697482\pi\)
0.581367 0.813641i \(-0.302518\pi\)
\(588\) 0 0
\(589\) 18.4517 0.760289
\(590\) 0 0
\(591\) −1.50191 −0.0617801
\(592\) 0 0
\(593\) 20.8918i 0.857922i 0.903323 + 0.428961i \(0.141120\pi\)
−0.903323 + 0.428961i \(0.858880\pi\)
\(594\) 0 0
\(595\) −2.40029 14.0610i −0.0984024 0.576446i
\(596\) 0 0
\(597\) 7.85542i 0.321501i
\(598\) 0 0
\(599\) 12.7986 0.522938 0.261469 0.965212i \(-0.415793\pi\)
0.261469 + 0.965212i \(0.415793\pi\)
\(600\) 0 0
\(601\) −18.7566 −0.765099 −0.382550 0.923935i \(-0.624954\pi\)
−0.382550 + 0.923935i \(0.624954\pi\)
\(602\) 0 0
\(603\) 45.1879i 1.84019i
\(604\) 0 0
\(605\) −3.15664 18.4918i −0.128336 0.751797i
\(606\) 0 0
\(607\) 1.51153i 0.0613512i −0.999529 0.0306756i \(-0.990234\pi\)
0.999529 0.0306756i \(-0.00976588\pi\)
\(608\) 0 0
\(609\) −6.22142 −0.252105
\(610\) 0 0
\(611\) 18.0720 0.731114
\(612\) 0 0
\(613\) 39.5673i 1.59811i −0.601259 0.799054i \(-0.705334\pi\)
0.601259 0.799054i \(-0.294666\pi\)
\(614\) 0 0
\(615\) −4.48648 + 0.765865i −0.180912 + 0.0308826i
\(616\) 0 0
\(617\) 41.0023i 1.65069i −0.564629 0.825345i \(-0.690981\pi\)
0.564629 0.825345i \(-0.309019\pi\)
\(618\) 0 0
\(619\) 10.9089 0.438464 0.219232 0.975673i \(-0.429645\pi\)
0.219232 + 0.975673i \(0.429645\pi\)
\(620\) 0 0
\(621\) 2.09297 0.0839880
\(622\) 0 0
\(623\) 21.7817i 0.872664i
\(624\) 0 0
\(625\) 19.4973 15.6478i 0.779893 0.625913i
\(626\) 0 0
\(627\) 2.31789i 0.0925677i
\(628\) 0 0
\(629\) 7.66555 0.305645
\(630\) 0 0
\(631\) 24.7516 0.985347 0.492674 0.870214i \(-0.336020\pi\)
0.492674 + 0.870214i \(0.336020\pi\)
\(632\) 0 0
\(633\) 10.3069i 0.409661i
\(634\) 0 0
\(635\) −27.3884 + 4.67534i −1.08688 + 0.185535i
\(636\) 0 0
\(637\) 2.44150i 0.0967357i
\(638\) 0 0
\(639\) 15.0865 0.596812
\(640\) 0 0
\(641\) 33.5110 1.32360 0.661802 0.749679i \(-0.269792\pi\)
0.661802 + 0.749679i \(0.269792\pi\)
\(642\) 0 0
\(643\) 9.15767i 0.361143i −0.983562 0.180572i \(-0.942205\pi\)
0.983562 0.180572i \(-0.0577947\pi\)
\(644\) 0 0
\(645\) −0.309008 1.81019i −0.0121672 0.0712761i
\(646\) 0 0
\(647\) 30.8011i 1.21092i 0.795877 + 0.605458i \(0.207010\pi\)
−0.795877 + 0.605458i \(0.792990\pi\)
\(648\) 0 0
\(649\) −4.09480 −0.160735
\(650\) 0 0
\(651\) −4.02455 −0.157735
\(652\) 0 0
\(653\) 25.4779i 0.997026i 0.866882 + 0.498513i \(0.166120\pi\)
−0.866882 + 0.498513i \(0.833880\pi\)
\(654\) 0 0
\(655\) 4.25900 + 24.9494i 0.166413 + 0.974855i
\(656\) 0 0
\(657\) 17.3488i 0.676843i
\(658\) 0 0
\(659\) 2.34417 0.0913159 0.0456580 0.998957i \(-0.485462\pi\)
0.0456580 + 0.998957i \(0.485462\pi\)
\(660\) 0 0
\(661\) 43.4164 1.68870 0.844351 0.535791i \(-0.179987\pi\)
0.844351 + 0.535791i \(0.179987\pi\)
\(662\) 0 0
\(663\) 2.42266i 0.0940883i
\(664\) 0 0
\(665\) 21.8607 3.73174i 0.847723 0.144711i
\(666\) 0 0
\(667\) 7.08580i 0.274363i
\(668\) 0 0
\(669\) 2.36535 0.0914498
\(670\) 0 0
\(671\) −14.9547 −0.577319
\(672\) 0 0
\(673\) 48.4902i 1.86916i −0.355754 0.934580i \(-0.615776\pi\)
0.355754 0.934580i \(-0.384224\pi\)
\(674\) 0 0
\(675\) 3.47165 + 9.87223i 0.133624 + 0.379982i
\(676\) 0 0
\(677\) 46.9213i 1.80333i 0.432435 + 0.901665i \(0.357655\pi\)
−0.432435 + 0.901665i \(0.642345\pi\)
\(678\) 0 0
\(679\) 19.7424 0.757645
\(680\) 0 0
\(681\) −0.131988 −0.00505780
\(682\) 0 0
\(683\) 15.3660i 0.587965i 0.955811 + 0.293983i \(0.0949808\pi\)
−0.955811 + 0.293983i \(0.905019\pi\)
\(684\) 0 0
\(685\) 10.8907 1.85910i 0.416113 0.0710327i
\(686\) 0 0
\(687\) 4.12056i 0.157209i
\(688\) 0 0
\(689\) −17.7609 −0.676635
\(690\) 0 0
\(691\) 40.0235 1.52257 0.761283 0.648419i \(-0.224570\pi\)
0.761283 + 0.648419i \(0.224570\pi\)
\(692\) 0 0
\(693\) 11.4368i 0.434447i
\(694\) 0 0
\(695\) −1.10284 6.46049i −0.0418331 0.245060i
\(696\) 0 0
\(697\) 14.7886i 0.560157i
\(698\) 0 0
\(699\) −6.00607 −0.227171
\(700\) 0 0
\(701\) −28.2943 −1.06866 −0.534331 0.845276i \(-0.679436\pi\)
−0.534331 + 0.845276i \(0.679436\pi\)
\(702\) 0 0
\(703\) 11.9177i 0.449483i
\(704\) 0 0
\(705\) −0.922967 5.40679i −0.0347610 0.203631i
\(706\) 0 0
\(707\) 15.6001i 0.586703i
\(708\) 0 0
\(709\) −26.8823 −1.00959 −0.504793 0.863240i \(-0.668431\pi\)
−0.504793 + 0.863240i \(0.668431\pi\)
\(710\) 0 0
\(711\) −3.89900 −0.146224
\(712\) 0 0
\(713\) 4.58371i 0.171661i
\(714\) 0 0
\(715\) 9.35051 1.59618i 0.349689 0.0596937i
\(716\) 0 0
\(717\) 6.33423i 0.236556i
\(718\) 0 0
\(719\) 11.2624 0.420015 0.210008 0.977700i \(-0.432651\pi\)
0.210008 + 0.977700i \(0.432651\pi\)
\(720\) 0 0
\(721\) 32.4973 1.21026
\(722\) 0 0
\(723\) 9.49084i 0.352968i
\(724\) 0 0
\(725\) −33.4226 + 11.7533i −1.24129 + 0.436508i
\(726\) 0 0
\(727\) 2.07629i 0.0770054i −0.999258 0.0385027i \(-0.987741\pi\)
0.999258 0.0385027i \(-0.0122588\pi\)
\(728\) 0 0
\(729\) 20.3818 0.754883
\(730\) 0 0
\(731\) −5.96684 −0.220692
\(732\) 0 0
\(733\) 16.6294i 0.614221i −0.951674 0.307111i \(-0.900638\pi\)
0.951674 0.307111i \(-0.0993621\pi\)
\(734\) 0 0
\(735\) 0.730450 0.124692i 0.0269431 0.00459932i
\(736\) 0 0
\(737\) 25.4131i 0.936103i
\(738\) 0 0
\(739\) 50.8052 1.86890 0.934450 0.356095i \(-0.115892\pi\)
0.934450 + 0.356095i \(0.115892\pi\)
\(740\) 0 0
\(741\) 3.76652 0.138366
\(742\) 0 0
\(743\) 31.3667i 1.15073i 0.817896 + 0.575366i \(0.195141\pi\)
−0.817896 + 0.575366i \(0.804859\pi\)
\(744\) 0 0
\(745\) 1.91528 + 11.2198i 0.0701703 + 0.411062i
\(746\) 0 0
\(747\) 24.6934i 0.903485i
\(748\) 0 0
\(749\) −23.5270 −0.859657
\(750\) 0 0
\(751\) −41.2551 −1.50542 −0.752711 0.658351i \(-0.771254\pi\)
−0.752711 + 0.658351i \(0.771254\pi\)
\(752\) 0 0
\(753\) 6.00839i 0.218958i
\(754\) 0 0
\(755\) 5.40488 + 31.6621i 0.196704 + 1.15230i
\(756\) 0 0
\(757\) 11.3081i 0.411000i 0.978657 + 0.205500i \(0.0658820\pi\)
−0.978657 + 0.205500i \(0.934118\pi\)
\(758\) 0 0
\(759\) −0.575803 −0.0209003
\(760\) 0 0
\(761\) −4.32880 −0.156919 −0.0784594 0.996917i \(-0.525000\pi\)
−0.0784594 + 0.996917i \(0.525000\pi\)
\(762\) 0 0
\(763\) 43.2690i 1.56644i
\(764\) 0 0
\(765\) 16.3967 2.79899i 0.592822 0.101198i
\(766\) 0 0
\(767\) 6.65395i 0.240260i
\(768\) 0 0
\(769\) −40.6517 −1.46594 −0.732968 0.680263i \(-0.761866\pi\)
−0.732968 + 0.680263i \(0.761866\pi\)
\(770\) 0 0
\(771\) −2.96866 −0.106914
\(772\) 0 0
\(773\) 37.9716i 1.36574i −0.730538 0.682872i \(-0.760731\pi\)
0.730538 0.682872i \(-0.239269\pi\)
\(774\) 0 0
\(775\) −21.6206 + 7.60307i −0.776636 + 0.273110i
\(776\) 0 0
\(777\) 2.59940i 0.0932528i
\(778\) 0 0
\(779\) −22.9918 −0.823768
\(780\) 0 0
\(781\) −8.48443 −0.303597
\(782\) 0 0
\(783\) 14.8304i 0.529994i
\(784\) 0 0
\(785\) −16.1819 + 2.76234i −0.577557 + 0.0985920i
\(786\) 0 0
\(787\) 55.1654i 1.96643i 0.182443 + 0.983216i \(0.441599\pi\)
−0.182443 + 0.983216i \(0.558401\pi\)
\(788\) 0 0
\(789\) −5.35944 −0.190801
\(790\) 0 0
\(791\) 3.80076 0.135140
\(792\) 0 0
\(793\) 24.3010i 0.862952i
\(794\) 0 0
\(795\) 0.907078 + 5.31371i 0.0321707 + 0.188458i
\(796\) 0 0
\(797\) 33.0601i 1.17105i 0.810655 + 0.585524i \(0.199111\pi\)
−0.810655 + 0.585524i \(0.800889\pi\)
\(798\) 0 0
\(799\) −17.8222 −0.630503
\(800\) 0 0
\(801\) 25.3997 0.897455
\(802\) 0 0
\(803\) 9.75675i