Properties

Label 325.2.c.e.51.2
Level $325$
Weight $2$
Character 325.51
Analytic conductor $2.595$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 51.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 325.51
Dual form 325.2.c.e.51.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000i q^{6} +3.00000i q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +2.00000 q^{3} +1.00000 q^{4} +2.00000i q^{6} +3.00000i q^{8} +1.00000 q^{9} -2.00000i q^{11} +2.00000 q^{12} +(-2.00000 + 3.00000i) q^{13} -1.00000 q^{16} +1.00000i q^{18} -6.00000i q^{19} +2.00000 q^{22} +6.00000 q^{23} +6.00000i q^{24} +(-3.00000 - 2.00000i) q^{26} -4.00000 q^{27} -6.00000 q^{29} -6.00000i q^{31} +5.00000i q^{32} -4.00000i q^{33} +1.00000 q^{36} -6.00000i q^{37} +6.00000 q^{38} +(-4.00000 + 6.00000i) q^{39} +8.00000i q^{41} -6.00000 q^{43} -2.00000i q^{44} +6.00000i q^{46} +8.00000i q^{47} -2.00000 q^{48} +7.00000 q^{49} +(-2.00000 + 3.00000i) q^{52} -12.0000 q^{53} -4.00000i q^{54} -12.0000i q^{57} -6.00000i q^{58} +2.00000i q^{59} +6.00000 q^{61} +6.00000 q^{62} -7.00000 q^{64} +4.00000 q^{66} -12.0000i q^{67} +12.0000 q^{69} +2.00000i q^{71} +3.00000i q^{72} -6.00000i q^{73} +6.00000 q^{74} -6.00000i q^{76} +(-6.00000 - 4.00000i) q^{78} -11.0000 q^{81} -8.00000 q^{82} -4.00000i q^{83} -6.00000i q^{86} -12.0000 q^{87} +6.00000 q^{88} -8.00000i q^{89} +6.00000 q^{92} -12.0000i q^{93} -8.00000 q^{94} +10.0000i q^{96} +6.00000i q^{97} +7.00000i q^{98} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{3} + 2 q^{4} + 2 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{3} + 2 q^{4} + 2 q^{9} + 4 q^{12} - 4 q^{13} - 2 q^{16} + 4 q^{22} + 12 q^{23} - 6 q^{26} - 8 q^{27} - 12 q^{29} + 2 q^{36} + 12 q^{38} - 8 q^{39} - 12 q^{43} - 4 q^{48} + 14 q^{49} - 4 q^{52} - 24 q^{53} + 12 q^{61} + 12 q^{62} - 14 q^{64} + 8 q^{66} + 24 q^{69} + 12 q^{74} - 12 q^{78} - 22 q^{81} - 16 q^{82} - 24 q^{87} + 12 q^{88} + 12 q^{92} - 16 q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i 0.935414 + 0.353553i \(0.115027\pi\)
−0.935414 + 0.353553i \(0.884973\pi\)
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 2.00000i 0.816497i
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 3.00000i 1.06066i
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) 2.00000 0.577350
\(13\) −2.00000 + 3.00000i −0.554700 + 0.832050i
\(14\) 0 0
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.00000i 1.37649i −0.725476 0.688247i \(-0.758380\pi\)
0.725476 0.688247i \(-0.241620\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.00000 0.426401
\(23\) 6.00000 1.25109 0.625543 0.780189i \(-0.284877\pi\)
0.625543 + 0.780189i \(0.284877\pi\)
\(24\) 6.00000i 1.22474i
\(25\) 0 0
\(26\) −3.00000 2.00000i −0.588348 0.392232i
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 6.00000i 1.07763i −0.842424 0.538816i \(-0.818872\pi\)
0.842424 0.538816i \(-0.181128\pi\)
\(32\) 5.00000i 0.883883i
\(33\) 4.00000i 0.696311i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 6.00000i 0.986394i −0.869918 0.493197i \(-0.835828\pi\)
0.869918 0.493197i \(-0.164172\pi\)
\(38\) 6.00000 0.973329
\(39\) −4.00000 + 6.00000i −0.640513 + 0.960769i
\(40\) 0 0
\(41\) 8.00000i 1.24939i 0.780869 + 0.624695i \(0.214777\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 2.00000i 0.301511i
\(45\) 0 0
\(46\) 6.00000i 0.884652i
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) −2.00000 −0.288675
\(49\) 7.00000 1.00000
\(50\) 0 0
\(51\) 0 0
\(52\) −2.00000 + 3.00000i −0.277350 + 0.416025i
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 4.00000i 0.544331i
\(55\) 0 0
\(56\) 0 0
\(57\) 12.0000i 1.58944i
\(58\) 6.00000i 0.787839i
\(59\) 2.00000i 0.260378i 0.991489 + 0.130189i \(0.0415584\pi\)
−0.991489 + 0.130189i \(0.958442\pi\)
\(60\) 0 0
\(61\) 6.00000 0.768221 0.384111 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) 6.00000 0.762001
\(63\) 0 0
\(64\) −7.00000 −0.875000
\(65\) 0 0
\(66\) 4.00000 0.492366
\(67\) 12.0000i 1.46603i −0.680211 0.733017i \(-0.738112\pi\)
0.680211 0.733017i \(-0.261888\pi\)
\(68\) 0 0
\(69\) 12.0000 1.44463
\(70\) 0 0
\(71\) 2.00000i 0.237356i 0.992933 + 0.118678i \(0.0378657\pi\)
−0.992933 + 0.118678i \(0.962134\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 6.00000i 0.702247i −0.936329 0.351123i \(-0.885800\pi\)
0.936329 0.351123i \(-0.114200\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) −6.00000 4.00000i −0.679366 0.452911i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) −8.00000 −0.883452
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.00000i 0.646997i
\(87\) −12.0000 −1.28654
\(88\) 6.00000 0.639602
\(89\) 8.00000i 0.847998i −0.905663 0.423999i \(-0.860626\pi\)
0.905663 0.423999i \(-0.139374\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 12.0000i 1.24434i
\(94\) −8.00000 −0.825137
\(95\) 0 0
\(96\) 10.0000i 1.02062i
\(97\) 6.00000i 0.609208i 0.952479 + 0.304604i \(0.0985241\pi\)
−0.952479 + 0.304604i \(0.901476\pi\)
\(98\) 7.00000i 0.707107i
\(99\) 2.00000i 0.201008i
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) −9.00000 6.00000i −0.882523 0.588348i
\(105\) 0 0
\(106\) 12.0000i 1.16554i
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) −4.00000 −0.384900
\(109\) 12.0000i 1.14939i 0.818367 + 0.574696i \(0.194880\pi\)
−0.818367 + 0.574696i \(0.805120\pi\)
\(110\) 0 0
\(111\) 12.0000i 1.13899i
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 12.0000 1.12390
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) −2.00000 + 3.00000i −0.184900 + 0.277350i
\(118\) −2.00000 −0.184115
\(119\) 0 0
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 6.00000i 0.543214i
\(123\) 16.0000i 1.44267i
\(124\) 6.00000i 0.538816i
\(125\) 0 0
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 3.00000i 0.265165i
\(129\) −12.0000 −1.05654
\(130\) 0 0
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 4.00000i 0.348155i
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000i 0.170872i −0.996344 0.0854358i \(-0.972772\pi\)
0.996344 0.0854358i \(-0.0272282\pi\)
\(138\) 12.0000i 1.02151i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 16.0000i 1.34744i
\(142\) −2.00000 −0.167836
\(143\) 6.00000 + 4.00000i 0.501745 + 0.334497i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 6.00000 0.496564
\(147\) 14.0000 1.15470
\(148\) 6.00000i 0.493197i
\(149\) 20.0000i 1.63846i 0.573462 + 0.819232i \(0.305600\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(150\) 0 0
\(151\) 18.0000i 1.46482i 0.680864 + 0.732410i \(0.261604\pi\)
−0.680864 + 0.732410i \(0.738396\pi\)
\(152\) 18.0000 1.45999
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 + 6.00000i −0.320256 + 0.480384i
\(157\) −12.0000 −0.957704 −0.478852 0.877896i \(-0.658947\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) 0 0
\(159\) −24.0000 −1.90332
\(160\) 0 0
\(161\) 0 0
\(162\) 11.0000i 0.864242i
\(163\) 12.0000i 0.939913i 0.882690 + 0.469956i \(0.155730\pi\)
−0.882690 + 0.469956i \(0.844270\pi\)
\(164\) 8.00000i 0.624695i
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) 16.0000i 1.23812i 0.785345 + 0.619059i \(0.212486\pi\)
−0.785345 + 0.619059i \(0.787514\pi\)
\(168\) 0 0
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) 0 0
\(171\) 6.00000i 0.458831i
\(172\) −6.00000 −0.457496
\(173\) 12.0000 0.912343 0.456172 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(174\) 12.0000i 0.909718i
\(175\) 0 0
\(176\) 2.00000i 0.150756i
\(177\) 4.00000i 0.300658i
\(178\) 8.00000 0.599625
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 12.0000 0.887066
\(184\) 18.0000i 1.32698i
\(185\) 0 0
\(186\) 12.0000 0.879883
\(187\) 0 0
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −14.0000 −1.01036
\(193\) 6.00000i 0.431889i −0.976406 0.215945i \(-0.930717\pi\)
0.976406 0.215945i \(-0.0692831\pi\)
\(194\) −6.00000 −0.430775
\(195\) 0 0
\(196\) 7.00000 0.500000
\(197\) 2.00000i 0.142494i 0.997459 + 0.0712470i \(0.0226979\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 2.00000 0.142134
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 0 0
\(201\) 24.0000i 1.69283i
\(202\) 6.00000i 0.422159i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 6.00000i 0.418040i
\(207\) 6.00000 0.417029
\(208\) 2.00000 3.00000i 0.138675 0.208013i
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −12.0000 −0.824163
\(213\) 4.00000i 0.274075i
\(214\) 6.00000i 0.410152i
\(215\) 0 0
\(216\) 12.0000i 0.816497i
\(217\) 0 0
\(218\) −12.0000 −0.812743
\(219\) 12.0000i 0.810885i
\(220\) 0 0
\(221\) 0 0
\(222\) 12.0000 0.805387
\(223\) 24.0000i 1.60716i 0.595198 + 0.803579i \(0.297074\pi\)
−0.595198 + 0.803579i \(0.702926\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.00000i 0.265489i 0.991150 + 0.132745i \(0.0423790\pi\)
−0.991150 + 0.132745i \(0.957621\pi\)
\(228\) 12.0000i 0.794719i
\(229\) 12.0000i 0.792982i −0.918039 0.396491i \(-0.870228\pi\)
0.918039 0.396491i \(-0.129772\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 18.0000i 1.18176i
\(233\) −24.0000 −1.57229 −0.786146 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) −3.00000 2.00000i −0.196116 0.130744i
\(235\) 0 0
\(236\) 2.00000i 0.130189i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.0000i 0.646846i −0.946254 0.323423i \(-0.895166\pi\)
0.946254 0.323423i \(-0.104834\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 7.00000i 0.449977i
\(243\) −10.0000 −0.641500
\(244\) 6.00000 0.384111
\(245\) 0 0
\(246\) −16.0000 −1.02012
\(247\) 18.0000 + 12.0000i 1.14531 + 0.763542i
\(248\) 18.0000 1.14300
\(249\) 8.00000i 0.506979i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 12.0000i 0.754434i
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 12.0000i 0.747087i
\(259\) 0 0
\(260\) 0 0
\(261\) −6.00000 −0.371391
\(262\) 12.0000i 0.741362i
\(263\) 6.00000 0.369976 0.184988 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 12.0000 0.738549
\(265\) 0 0
\(266\) 0 0
\(267\) 16.0000i 0.979184i
\(268\) 12.0000i 0.733017i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) 0 0
\(271\) 6.00000i 0.364474i −0.983255 0.182237i \(-0.941666\pi\)
0.983255 0.182237i \(-0.0583338\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 0 0
\(276\) 12.0000 0.722315
\(277\) 12.0000 0.721010 0.360505 0.932757i \(-0.382604\pi\)
0.360505 + 0.932757i \(0.382604\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 6.00000i 0.359211i
\(280\) 0 0
\(281\) 8.00000i 0.477240i −0.971113 0.238620i \(-0.923305\pi\)
0.971113 0.238620i \(-0.0766950\pi\)
\(282\) −16.0000 −0.952786
\(283\) −22.0000 −1.30776 −0.653882 0.756596i \(-0.726861\pi\)
−0.653882 + 0.756596i \(0.726861\pi\)
\(284\) 2.00000i 0.118678i
\(285\) 0 0
\(286\) −4.00000 + 6.00000i −0.236525 + 0.354787i
\(287\) 0 0
\(288\) 5.00000i 0.294628i
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 12.0000i 0.703452i
\(292\) 6.00000i 0.351123i
\(293\) 26.0000i 1.51894i −0.650545 0.759468i \(-0.725459\pi\)
0.650545 0.759468i \(-0.274541\pi\)
\(294\) 14.0000i 0.816497i
\(295\) 0 0
\(296\) 18.0000 1.04623
\(297\) 8.00000i 0.464207i
\(298\) −20.0000 −1.15857
\(299\) −12.0000 + 18.0000i −0.693978 + 1.04097i
\(300\) 0 0
\(301\) 0 0
\(302\) −18.0000 −1.03578
\(303\) 12.0000 0.689382
\(304\) 6.00000i 0.344124i
\(305\) 0 0
\(306\) 0 0
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 0 0
\(309\) 12.0000 0.682656
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) −18.0000 12.0000i −1.01905 0.679366i
\(313\) 8.00000 0.452187 0.226093 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) 12.0000i 0.677199i
\(315\) 0 0
\(316\) 0 0
\(317\) 2.00000i 0.112331i 0.998421 + 0.0561656i \(0.0178875\pi\)
−0.998421 + 0.0561656i \(0.982113\pi\)
\(318\) 24.0000i 1.34585i
\(319\) 12.0000i 0.671871i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) −11.0000 −0.611111
\(325\) 0 0
\(326\) −12.0000 −0.664619
\(327\) 24.0000i 1.32720i
\(328\) −24.0000 −1.32518
\(329\) 0 0
\(330\) 0 0
\(331\) 30.0000i 1.64895i 0.565899 + 0.824475i \(0.308529\pi\)
−0.565899 + 0.824475i \(0.691471\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 6.00000i 0.328798i
\(334\) −16.0000 −0.875481
\(335\) 0 0
\(336\) 0 0
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) 12.0000 5.00000i 0.652714 0.271964i
\(339\) 0 0
\(340\) 0 0
\(341\) −12.0000 −0.649836
\(342\) 6.00000 0.324443
\(343\) 0 0
\(344\) 18.0000i 0.970495i
\(345\) 0 0
\(346\) 12.0000i 0.645124i
\(347\) 6.00000 0.322097 0.161048 0.986947i \(-0.448512\pi\)
0.161048 + 0.986947i \(0.448512\pi\)
\(348\) −12.0000 −0.643268
\(349\) 12.0000i 0.642345i 0.947021 + 0.321173i \(0.104077\pi\)
−0.947021 + 0.321173i \(0.895923\pi\)
\(350\) 0 0
\(351\) 8.00000 12.0000i 0.427008 0.640513i
\(352\) 10.0000 0.533002
\(353\) 14.0000i 0.745145i −0.928003 0.372572i \(-0.878476\pi\)
0.928003 0.372572i \(-0.121524\pi\)
\(354\) −4.00000 −0.212598
\(355\) 0 0
\(356\) 8.00000i 0.423999i
\(357\) 0 0
\(358\) 12.0000i 0.634220i
\(359\) 2.00000i 0.105556i −0.998606 0.0527780i \(-0.983192\pi\)
0.998606 0.0527780i \(-0.0168076\pi\)
\(360\) 0 0
\(361\) −17.0000 −0.894737
\(362\) 2.00000i 0.105118i
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) 0 0
\(366\) 12.0000i 0.627250i
\(367\) 18.0000 0.939592 0.469796 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) −6.00000 −0.312772
\(369\) 8.00000i 0.416463i
\(370\) 0 0
\(371\) 0 0
\(372\) 12.0000i 0.622171i
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −24.0000 −1.23771
\(377\) 12.0000 18.0000i 0.618031 0.927047i
\(378\) 0 0
\(379\) 18.0000i 0.924598i 0.886724 + 0.462299i \(0.152975\pi\)
−0.886724 + 0.462299i \(0.847025\pi\)
\(380\) 0 0
\(381\) 4.00000 0.204926
\(382\) 0 0
\(383\) 8.00000i 0.408781i 0.978889 + 0.204390i \(0.0655212\pi\)
−0.978889 + 0.204390i \(0.934479\pi\)
\(384\) 6.00000i 0.306186i
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) −6.00000 −0.304997
\(388\) 6.00000i 0.304604i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 21.0000i 1.06066i
\(393\) −24.0000 −1.21064
\(394\) −2.00000 −0.100759
\(395\) 0 0
\(396\) 2.00000i 0.100504i
\(397\) 18.0000i 0.903394i 0.892171 + 0.451697i \(0.149181\pi\)
−0.892171 + 0.451697i \(0.850819\pi\)
\(398\) 24.0000i 1.20301i
\(399\) 0 0
\(400\) 0 0
\(401\) 16.0000i 0.799002i −0.916733 0.399501i \(-0.869183\pi\)
0.916733 0.399501i \(-0.130817\pi\)
\(402\) 24.0000 1.19701
\(403\) 18.0000 + 12.0000i 0.896644 + 0.597763i
\(404\) 6.00000 0.298511
\(405\) 0 0
\(406\) 0 0
\(407\) −12.0000 −0.594818
\(408\) 0 0
\(409\) 24.0000i 1.18672i −0.804936 0.593362i \(-0.797800\pi\)
0.804936 0.593362i \(-0.202200\pi\)
\(410\) 0 0
\(411\) 4.00000i 0.197305i
\(412\) 6.00000 0.295599
\(413\) 0 0
\(414\) 6.00000i 0.294884i
\(415\) 0 0
\(416\) −15.0000 10.0000i −0.735436 0.490290i
\(417\) 8.00000 0.391762
\(418\) 12.0000i 0.586939i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 36.0000i 1.75453i −0.480004 0.877266i \(-0.659365\pi\)
0.480004 0.877266i \(-0.340635\pi\)
\(422\) 12.0000i 0.584151i
\(423\) 8.00000i 0.388973i
\(424\) 36.0000i 1.74831i
\(425\) 0 0
\(426\) −4.00000 −0.193801
\(427\) 0 0
\(428\) 6.00000 0.290021
\(429\) 12.0000 + 8.00000i 0.579365 + 0.386244i
\(430\) 0 0
\(431\) 10.0000i 0.481683i 0.970564 + 0.240842i \(0.0774234\pi\)
−0.970564 + 0.240842i \(0.922577\pi\)
\(432\) 4.00000 0.192450
\(433\) 16.0000 0.768911 0.384455 0.923144i \(-0.374389\pi\)
0.384455 + 0.923144i \(0.374389\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 12.0000i 0.574696i
\(437\) 36.0000i 1.72211i
\(438\) 12.0000 0.573382
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 7.00000 0.333333
\(442\) 0 0
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 12.0000i 0.569495i
\(445\) 0 0
\(446\) −24.0000 −1.13643
\(447\) 40.0000i 1.89194i
\(448\) 0 0
\(449\) 16.0000i 0.755087i −0.925992 0.377543i \(-0.876769\pi\)
0.925992 0.377543i \(-0.123231\pi\)
\(450\) 0 0
\(451\) 16.0000 0.753411
\(452\) 0 0
\(453\) 36.0000i 1.69143i
\(454\) −4.00000 −0.187729
\(455\) 0 0
\(456\) 36.0000 1.68585
\(457\) 30.0000i 1.40334i 0.712502 + 0.701670i \(0.247562\pi\)
−0.712502 + 0.701670i \(0.752438\pi\)
\(458\) 12.0000 0.560723
\(459\) 0 0
\(460\) 0 0
\(461\) 4.00000i 0.186299i 0.995652 + 0.0931493i \(0.0296934\pi\)
−0.995652 + 0.0931493i \(0.970307\pi\)
\(462\) 0 0
\(463\) 24.0000i 1.11537i −0.830051 0.557687i \(-0.811689\pi\)
0.830051 0.557687i \(-0.188311\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) 24.0000i 1.11178i
\(467\) −18.0000 −0.832941 −0.416470 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) −2.00000 + 3.00000i −0.0924500 + 0.138675i
\(469\) 0 0
\(470\) 0 0
\(471\) −24.0000 −1.10586
\(472\) −6.00000 −0.276172
\(473\) 12.0000i 0.551761i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 10.0000 0.457389
\(479\) 22.0000i 1.00521i 0.864517 + 0.502603i \(0.167624\pi\)
−0.864517 + 0.502603i \(0.832376\pi\)
\(480\) 0 0
\(481\) 18.0000 + 12.0000i 0.820729 + 0.547153i
\(482\) 0 0
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) 0 0
\(486\) 10.0000i 0.453609i
\(487\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(488\) 18.0000i 0.814822i
\(489\) 24.0000i 1.08532i
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 16.0000i 0.721336i
\(493\) 0 0
\(494\) −12.0000 + 18.0000i −0.539906 + 0.809858i
\(495\) 0 0
\(496\) 6.00000i 0.269408i
\(497\) 0 0
\(498\) 8.00000 0.358489
\(499\) 6.00000i 0.268597i −0.990941 0.134298i \(-0.957122\pi\)
0.990941 0.134298i \(-0.0428781\pi\)
\(500\) 0 0
\(501\) 32.0000i 1.42965i
\(502\) 12.0000i 0.535586i
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 12.0000 0.533465
\(507\) −10.0000 24.0000i −0.444116 1.06588i
\(508\) 2.00000 0.0887357
\(509\) 20.0000i 0.886484i −0.896402 0.443242i \(-0.853828\pi\)
0.896402 0.443242i \(-0.146172\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 11.0000i 0.486136i
\(513\) 24.0000i 1.05963i
\(514\) 0 0
\(515\) 0 0
\(516\) −12.0000 −0.528271
\(517\) 16.0000 0.703679
\(518\) 0 0
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 6.00000i 0.262613i
\(523\) 42.0000 1.83653 0.918266 0.395964i \(-0.129590\pi\)
0.918266 + 0.395964i \(0.129590\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 6.00000i 0.261612i
\(527\) 0 0
\(528\) 4.00000i 0.174078i
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 2.00000i 0.0867926i
\(532\) 0 0
\(533\) −24.0000 16.0000i −1.03956 0.693037i
\(534\) 16.0000 0.692388
\(535\) 0 0
\(536\) 36.0000 1.55496
\(537\) 24.0000 1.03568
\(538\) 18.0000i 0.776035i
\(539\) 14.0000i 0.603023i
\(540\) 0 0
\(541\) 12.0000i 0.515920i −0.966156 0.257960i \(-0.916950\pi\)
0.966156 0.257960i \(-0.0830503\pi\)
\(542\) 6.00000 0.257722
\(543\) −4.00000 −0.171656
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −18.0000 −0.769624 −0.384812 0.922995i \(-0.625734\pi\)
−0.384812 + 0.922995i \(0.625734\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 6.00000 0.256074
\(550\) 0 0
\(551\) 36.0000i 1.53365i
\(552\) 36.0000i 1.53226i
\(553\) 0 0
\(554\) 12.0000i 0.509831i
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) 14.0000i 0.593199i −0.955002 0.296600i \(-0.904147\pi\)
0.955002 0.296600i \(-0.0958526\pi\)
\(558\) 6.00000 0.254000
\(559\) 12.0000 18.0000i 0.507546 0.761319i
\(560\) 0 0
\(561\) 0 0
\(562\) 8.00000 0.337460
\(563\) −30.0000 −1.26435 −0.632175 0.774826i \(-0.717837\pi\)
−0.632175 + 0.774826i \(0.717837\pi\)
\(564\) 16.0000i 0.673722i
\(565\) 0 0
\(566\) 22.0000i 0.924729i
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) 6.00000 + 4.00000i 0.250873 + 0.167248i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −7.00000 −0.291667
\(577\) 18.0000i 0.749350i −0.927156 0.374675i \(-0.877754\pi\)
0.927156 0.374675i \(-0.122246\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 12.0000i 0.498703i
\(580\) 0 0
\(581\) 0 0
\(582\) −12.0000 −0.497416
\(583\) 24.0000i 0.993978i
\(584\) 18.0000 0.744845
\(585\) 0 0
\(586\) 26.0000 1.07405
\(587\) 20.0000i 0.825488i −0.910847 0.412744i \(-0.864570\pi\)
0.910847 0.412744i \(-0.135430\pi\)
\(588\) 14.0000 0.577350
\(589\) −36.0000 −1.48335
\(590\) 0 0
\(591\) 4.00000i 0.164538i
\(592\) 6.00000i 0.246598i
\(593\) 22.0000i 0.903432i −0.892162 0.451716i \(-0.850812\pi\)
0.892162 0.451716i \(-0.149188\pi\)
\(594\) −8.00000 −0.328244
\(595\) 0 0
\(596\) 20.0000i 0.819232i
\(597\) 48.0000 1.96451
\(598\) −18.0000 12.0000i −0.736075 0.490716i
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 0 0
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) 12.0000i 0.488678i
\(604\) 18.0000i 0.732410i
\(605\) 0 0
\(606\) 12.0000i 0.487467i
\(607\) 18.0000 0.730597 0.365299 0.930890i \(-0.380967\pi\)
0.365299 + 0.930890i \(0.380967\pi\)
\(608\) 30.0000 1.21666
\(609\) 0 0
\(610\) 0 0
\(611\) −24.0000 16.0000i −0.970936 0.647291i
\(612\) 0 0
\(613\) 30.0000i 1.21169i 0.795583 + 0.605844i \(0.207165\pi\)
−0.795583 + 0.605844i \(0.792835\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) 34.0000i 1.36879i −0.729112 0.684394i \(-0.760067\pi\)
0.729112 0.684394i \(-0.239933\pi\)
\(618\) 12.0000i 0.482711i
\(619\) 18.0000i 0.723481i 0.932279 + 0.361741i \(0.117817\pi\)
−0.932279 + 0.361741i \(0.882183\pi\)
\(620\) 0 0
\(621\) −24.0000 −0.963087
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) 4.00000 6.00000i 0.160128 0.240192i
\(625\) 0 0
\(626\) 8.00000i 0.319744i
\(627\) −24.0000 −0.958468
\(628\) −12.0000 −0.478852
\(629\) 0 0
\(630\) 0 0
\(631\) 30.0000i 1.19428i −0.802137 0.597141i \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) 0 0
\(633\) −24.0000 −0.953914
\(634\) −2.00000 −0.0794301
\(635\) 0 0
\(636\) −24.0000 −0.951662
\(637\) −14.0000 + 21.0000i −0.554700 + 0.832050i
\(638\) −12.0000 −0.475085
\(639\) 2.00000i 0.0791188i
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 36.0000i 1.41970i −0.704352 0.709851i \(-0.748762\pi\)
0.704352 0.709851i \(-0.251238\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −6.00000 −0.235884 −0.117942 0.993020i \(-0.537630\pi\)
−0.117942 + 0.993020i \(0.537630\pi\)
\(648\) 33.0000i 1.29636i
\(649\) 4.00000 0.157014
\(650\) 0 0
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) −36.0000 −1.40879 −0.704394 0.709809i \(-0.748781\pi\)
−0.704394 + 0.709809i \(0.748781\pi\)
\(654\) −24.0000 −0.938474
\(655\) 0 0
\(656\) 8.00000i 0.312348i
\(657\) 6.00000i 0.234082i
\(658\) 0 0
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 12.0000i 0.466746i 0.972387 + 0.233373i \(0.0749763\pi\)
−0.972387 + 0.233373i \(0.925024\pi\)
\(662\) −30.0000 −1.16598
\(663\) 0 0
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) −36.0000 −1.39393
\(668\) 16.0000i 0.619059i
\(669\) 48.0000i 1.85579i
\(670\) 0 0
\(671\) 12.0000i 0.463255i
\(672\) 0 0
\(673\) 48.0000 1.85026 0.925132 0.379646i \(-0.123954\pi\)
0.925132 + 0.379646i \(0.123954\pi\)
\(674\) 32.0000i 1.23259i
\(675\) 0 0
\(676\) −5.00000 12.0000i −0.192308 0.461538i
\(677\) −36.0000 −1.38359 −0.691796 0.722093i \(-0.743180\pi\)
−0.691796 + 0.722093i \(0.743180\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 8.00000i 0.306561i
\(682\) 12.0000i 0.459504i
\(683\) 44.0000i 1.68361i −0.539779 0.841807i \(-0.681492\pi\)
0.539779 0.841807i \(-0.318508\pi\)
\(684\) 6.00000i 0.229416i
\(685\) 0 0
\(686\) 0 0
\(687\) 24.0000i 0.915657i
\(688\) 6.00000 0.228748
\(689\) 24.0000 36.0000i 0.914327 1.37149i
\(690\) 0 0
\(691\) 42.0000i 1.59776i −0.601494 0.798878i \(-0.705427\pi\)
0.601494 0.798878i \(-0.294573\pi\)
\(692\) 12.0000 0.456172
\(693\) 0 0
\(694\) 6.00000i 0.227757i
\(695\) 0 0
\(696\) 36.0000i 1.36458i
\(697\) 0 0
\(698\) −12.0000 −0.454207
\(699\) −48.0000 −1.81553
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 12.0000 + 8.00000i 0.452911 + 0.301941i
\(703\) −36.0000 −1.35777
\(704\) 14.0000i 0.527645i
\(705\) 0 0
\(706\) 14.0000 0.526897
\(707\) 0 0
\(708\) 4.00000i 0.150329i
\(709\) 12.0000i 0.450669i −0.974281 0.225335i \(-0.927652\pi\)
0.974281 0.225335i \(-0.0723476\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 24.0000 0.899438
\(713\) 36.0000i 1.34821i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 20.0000i 0.746914i
\(718\) 2.00000 0.0746393
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) 0 0
\(724\) −2.00000 −0.0743294
\(725\) 0 0
\(726\) 14.0000i 0.519589i
\(727\) 26.0000 0.964287 0.482143 0.876092i \(-0.339858\pi\)
0.482143 + 0.876092i \(0.339858\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 12.0000 0.443533
\(733\) 42.0000i 1.55131i −0.631160 0.775653i \(-0.717421\pi\)
0.631160 0.775653i \(-0.282579\pi\)
\(734\) 18.0000i 0.664392i
\(735\) 0 0
\(736\) 30.0000i 1.10581i
\(737\) −24.0000 −0.884051
\(738\) −8.00000 −0.294484
\(739\) 6.00000i 0.220714i −0.993892 0.110357i \(-0.964801\pi\)
0.993892 0.110357i \(-0.0351994\pi\)
\(740\) 0 0
\(741\) 36.0000 + 24.0000i 1.32249 + 0.881662i
\(742\) 0 0
\(743\) 16.0000i 0.586983i −0.955962 0.293492i \(-0.905183\pi\)
0.955962 0.293492i \(-0.0948173\pi\)
\(744\) 36.0000 1.31982
\(745\) 0 0
\(746\) 4.00000i 0.146450i
\(747\) 4.00000i 0.146352i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 24.0000 0.874609
\(754\) 18.0000 + 12.0000i 0.655521 + 0.437014i
\(755\) 0 0
\(756\) 0 0
\(757\) −20.0000 −0.726912 −0.363456 0.931611i \(-0.618403\pi\)
−0.363456 + 0.931611i \(0.618403\pi\)
\(758\) −18.0000 −0.653789
\(759\) 24.0000i 0.871145i
\(760\) 0 0
\(761\) 40.0000i 1.45000i 0.688749 + 0.724999i \(0.258160\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 4.00000i 0.144905i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −8.00000 −0.289052
\(767\) −6.00000 4.00000i −0.216647 0.144432i
\(768\) −34.0000 −1.22687
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.00000i 0.215945i
\(773\) 38.0000i 1.36677i 0.730061 + 0.683383i \(0.239492\pi\)
−0.730061 + 0.683383i \(0.760508\pi\)
\(774\) 6.00000i 0.215666i
\(775\) 0 0
\(776\) −18.0000 −0.646162
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) 48.0000 1.71978
\(780\) 0 0
\(781\) 4.00000 0.143131
\(782\) 0 0
\(783\) 24.0000 0.857690
\(784\) −7.00000 −0.250000
\(785\) 0 0
\(786\) 24.0000i 0.856052i
\(787\) 12.0000i 0.427754i −0.976861 0.213877i \(-0.931391\pi\)
0.976861 0.213877i \(-0.0686091\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 12.0000 0.427211
\(790\) 0 0
\(791\) 0 0
\(792\) 6.00000 0.213201
\(793\) −12.0000 + 18.0000i −0.426132 + 0.639199i
\(794\) −18.0000 −0.638796
\(795\) 0 0
\(796\) 24.0000 0.850657
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\)