Properties

Label 1170.2.e.d.469.2
Level $1170$
Weight $2$
Character 1170.469
Analytic conductor $9.342$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
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 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 469.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.469
Dual form 1170.2.e.d.469.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} -1.00000i q^{8} +(1.00000 + 2.00000i) q^{10} +6.00000 q^{11} +1.00000i q^{13} +1.00000 q^{16} -6.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} +6.00000i q^{22} -6.00000i q^{23} +(3.00000 - 4.00000i) q^{25} -1.00000 q^{26} +2.00000 q^{29} +4.00000 q^{31} +1.00000i q^{32} -10.0000i q^{37} -6.00000i q^{38} +(-1.00000 - 2.00000i) q^{40} +6.00000 q^{41} +8.00000i q^{43} -6.00000 q^{44} +6.00000 q^{46} +8.00000i q^{47} +7.00000 q^{49} +(4.00000 + 3.00000i) q^{50} -1.00000i q^{52} +6.00000i q^{53} +(12.0000 - 6.00000i) q^{55} +2.00000i q^{58} +10.0000 q^{59} -6.00000 q^{61} +4.00000i q^{62} -1.00000 q^{64} +(1.00000 + 2.00000i) q^{65} -4.00000i q^{67} +8.00000 q^{71} +6.00000i q^{73} +10.0000 q^{74} +6.00000 q^{76} -16.0000 q^{79} +(2.00000 - 1.00000i) q^{80} +6.00000i q^{82} -4.00000i q^{83} -8.00000 q^{86} -6.00000i q^{88} -10.0000 q^{89} +6.00000i q^{92} -8.00000 q^{94} +(-12.0000 + 6.00000i) q^{95} -2.00000i q^{97} +7.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 4q^{5} + O(q^{10}) \) \( 2q - 2q^{4} + 4q^{5} + 2q^{10} + 12q^{11} + 2q^{16} - 12q^{19} - 4q^{20} + 6q^{25} - 2q^{26} + 4q^{29} + 8q^{31} - 2q^{40} + 12q^{41} - 12q^{44} + 12q^{46} + 14q^{49} + 8q^{50} + 24q^{55} + 20q^{59} - 12q^{61} - 2q^{64} + 2q^{65} + 16q^{71} + 20q^{74} + 12q^{76} - 32q^{79} + 4q^{80} - 16q^{86} - 20q^{89} - 16q^{94} - 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 0 0
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.00000 + 2.00000i 0.316228 + 0.632456i
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) −2.00000 + 1.00000i −0.447214 + 0.223607i
\(21\) 0 0
\(22\) 6.00000i 1.27920i
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) −1.00000 −0.196116
\(27\) 0 0
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000i 1.64399i −0.569495 0.821995i \(-0.692861\pi\)
0.569495 0.821995i \(-0.307139\pi\)
\(38\) 6.00000i 0.973329i
\(39\) 0 0
\(40\) −1.00000 2.00000i −0.158114 0.316228i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) −6.00000 −0.904534
\(45\) 0 0
\(46\) 6.00000 0.884652
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 0 0
\(49\) 7.00000 1.00000
\(50\) 4.00000 + 3.00000i 0.565685 + 0.424264i
\(51\) 0 0
\(52\) 1.00000i 0.138675i
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 0 0
\(55\) 12.0000 6.00000i 1.61808 0.809040i
\(56\) 0 0
\(57\) 0 0
\(58\) 2.00000i 0.262613i
\(59\) 10.0000 1.30189 0.650945 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.00000 + 2.00000i 0.124035 + 0.248069i
\(66\) 0 0
\(67\) 4.00000i 0.488678i −0.969690 0.244339i \(-0.921429\pi\)
0.969690 0.244339i \(-0.0785709\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 6.00000i 0.702247i 0.936329 + 0.351123i \(0.114200\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 10.0000 1.16248
\(75\) 0 0
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) 0 0
\(79\) −16.0000 −1.80014 −0.900070 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) 2.00000 1.00000i 0.223607 0.111803i
\(81\) 0 0
\(82\) 6.00000i 0.662589i
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) 6.00000i 0.639602i
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) −12.0000 + 6.00000i −1.23117 + 0.615587i
\(96\) 0 0
\(97\) 2.00000i 0.203069i −0.994832 0.101535i \(-0.967625\pi\)
0.994832 0.101535i \(-0.0323753\pi\)
\(98\) 7.00000i 0.707107i
\(99\) 0 0
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 10.0000i 0.985329i −0.870219 0.492665i \(-0.836023\pi\)
0.870219 0.492665i \(-0.163977\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 16.0000i 1.54678i 0.633932 + 0.773389i \(0.281440\pi\)
−0.633932 + 0.773389i \(0.718560\pi\)
\(108\) 0 0
\(109\) 16.0000 1.53252 0.766261 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 6.00000 + 12.0000i 0.572078 + 1.14416i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.00000i 0.752577i −0.926503 0.376288i \(-0.877200\pi\)
0.926503 0.376288i \(-0.122800\pi\)
\(114\) 0 0
\(115\) −6.00000 12.0000i −0.559503 1.11901i
\(116\) −2.00000 −0.185695
\(117\) 0 0
\(118\) 10.0000i 0.920575i
\(119\) 0 0
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 6.00000i 0.543214i
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 0 0
\(127\) 18.0000i 1.59724i 0.601834 + 0.798621i \(0.294437\pi\)
−0.601834 + 0.798621i \(0.705563\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −2.00000 + 1.00000i −0.175412 + 0.0877058i
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000i 0.170872i 0.996344 + 0.0854358i \(0.0272282\pi\)
−0.996344 + 0.0854358i \(0.972772\pi\)
\(138\) 0 0
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.00000i 0.671345i
\(143\) 6.00000i 0.501745i
\(144\) 0 0
\(145\) 4.00000 2.00000i 0.332182 0.166091i
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 10.0000i 0.821995i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 0 0
\(154\) 0 0
\(155\) 8.00000 4.00000i 0.642575 0.321288i
\(156\) 0 0
\(157\) 2.00000i 0.159617i 0.996810 + 0.0798087i \(0.0254309\pi\)
−0.996810 + 0.0798087i \(0.974569\pi\)
\(158\) 16.0000i 1.27289i
\(159\) 0 0
\(160\) 1.00000 + 2.00000i 0.0790569 + 0.158114i
\(161\) 0 0
\(162\) 0 0
\(163\) 12.0000i 0.939913i 0.882690 + 0.469956i \(0.155730\pi\)
−0.882690 + 0.469956i \(0.844270\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) 4.00000 0.310460
\(167\) 8.00000i 0.619059i 0.950890 + 0.309529i \(0.100171\pi\)
−0.950890 + 0.309529i \(0.899829\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000i 0.609994i
\(173\) 18.0000i 1.36851i −0.729241 0.684257i \(-0.760127\pi\)
0.729241 0.684257i \(-0.239873\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.00000 0.452267
\(177\) 0 0
\(178\) 10.0000i 0.749532i
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.00000 −0.442326
\(185\) −10.0000 20.0000i −0.735215 1.47043i
\(186\) 0 0
\(187\) 0 0
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) −6.00000 12.0000i −0.435286 0.870572i
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 10.0000i 0.719816i 0.932988 + 0.359908i \(0.117192\pi\)
−0.932988 + 0.359908i \(0.882808\pi\)
\(194\) 2.00000 0.143592
\(195\) 0 0
\(196\) −7.00000 −0.500000
\(197\) 22.0000i 1.56744i −0.621117 0.783718i \(-0.713321\pi\)
0.621117 0.783718i \(-0.286679\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −4.00000 3.00000i −0.282843 0.212132i
\(201\) 0 0
\(202\) 2.00000i 0.140720i
\(203\) 0 0
\(204\) 0 0
\(205\) 12.0000 6.00000i 0.838116 0.419058i
\(206\) 10.0000 0.696733
\(207\) 0 0
\(208\) 1.00000i 0.0693375i
\(209\) −36.0000 −2.49017
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 6.00000i 0.412082i
\(213\) 0 0
\(214\) −16.0000 −1.09374
\(215\) 8.00000 + 16.0000i 0.545595 + 1.09119i
\(216\) 0 0
\(217\) 0 0
\(218\) 16.0000i 1.08366i
\(219\) 0 0
\(220\) −12.0000 + 6.00000i −0.809040 + 0.404520i
\(221\) 0 0
\(222\) 0 0
\(223\) 4.00000i 0.267860i 0.990991 + 0.133930i \(0.0427597\pi\)
−0.990991 + 0.133930i \(0.957240\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 8.00000 0.532152
\(227\) 20.0000i 1.32745i −0.747978 0.663723i \(-0.768975\pi\)
0.747978 0.663723i \(-0.231025\pi\)
\(228\) 0 0
\(229\) −20.0000 −1.32164 −0.660819 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) 12.0000 6.00000i 0.791257 0.395628i
\(231\) 0 0
\(232\) 2.00000i 0.131306i
\(233\) 8.00000i 0.524097i 0.965055 + 0.262049i \(0.0843981\pi\)
−0.965055 + 0.262049i \(0.915602\pi\)
\(234\) 0 0
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) −10.0000 −0.650945
\(237\) 0 0
\(238\) 0 0
\(239\) −28.0000 −1.81117 −0.905585 0.424165i \(-0.860568\pi\)
−0.905585 + 0.424165i \(0.860568\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 25.0000i 1.60706i
\(243\) 0 0
\(244\) 6.00000 0.384111
\(245\) 14.0000 7.00000i 0.894427 0.447214i
\(246\) 0 0
\(247\) 6.00000i 0.381771i
\(248\) 4.00000i 0.254000i
\(249\) 0 0
\(250\) 11.0000 + 2.00000i 0.695701 + 0.126491i
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) 36.0000i 2.26330i
\(254\) −18.0000 −1.12942
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 24.0000i 1.49708i −0.663090 0.748539i \(-0.730755\pi\)
0.663090 0.748539i \(-0.269245\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.00000 2.00000i −0.0620174 0.124035i
\(261\) 0 0
\(262\) 12.0000i 0.741362i
\(263\) 6.00000i 0.369976i 0.982741 + 0.184988i \(0.0592246\pi\)
−0.982741 + 0.184988i \(0.940775\pi\)
\(264\) 0 0
\(265\) 6.00000 + 12.0000i 0.368577 + 0.737154i
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000i 0.244339i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 18.0000 24.0000i 1.08544 1.44725i
\(276\) 0 0
\(277\) 26.0000i 1.56219i −0.624413 0.781094i \(-0.714662\pi\)
0.624413 0.781094i \(-0.285338\pi\)
\(278\) 8.00000i 0.479808i
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) 4.00000i 0.237775i −0.992908 0.118888i \(-0.962067\pi\)
0.992908 0.118888i \(-0.0379328\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 2.00000 + 4.00000i 0.117444 + 0.234888i
\(291\) 0 0
\(292\) 6.00000i 0.351123i
\(293\) 14.0000i 0.817889i 0.912559 + 0.408944i \(0.134103\pi\)
−0.912559 + 0.408944i \(0.865897\pi\)
\(294\) 0 0
\(295\) 20.0000 10.0000i 1.16445 0.582223i
\(296\) −10.0000 −0.581238
\(297\) 0 0
\(298\) 0 0
\(299\) 6.00000 0.346989
\(300\) 0 0
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) −6.00000 −0.344124
\(305\) −12.0000 + 6.00000i −0.687118 + 0.343559i
\(306\) 0 0
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.00000 + 8.00000i 0.227185 + 0.454369i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 16.0000i 0.904373i −0.891923 0.452187i \(-0.850644\pi\)
0.891923 0.452187i \(-0.149356\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 16.0000 0.900070
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) −2.00000 + 1.00000i −0.111803 + 0.0559017i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 4.00000 + 3.00000i 0.221880 + 0.166410i
\(326\) −12.0000 −0.664619
\(327\) 0 0
\(328\) 6.00000i 0.331295i
\(329\) 0 0
\(330\) 0 0
\(331\) −26.0000 −1.42909 −0.714545 0.699590i \(-0.753366\pi\)
−0.714545 + 0.699590i \(0.753366\pi\)
\(332\) 4.00000i 0.219529i
\(333\) 0 0
\(334\) −8.00000 −0.437741
\(335\) −4.00000 8.00000i −0.218543 0.437087i
\(336\) 0 0
\(337\) 8.00000i 0.435788i −0.975972 0.217894i \(-0.930081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) 0 0
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) 0 0
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) 18.0000 0.967686
\(347\) 32.0000i 1.71785i 0.512101 + 0.858925i \(0.328867\pi\)
−0.512101 + 0.858925i \(0.671133\pi\)
\(348\) 0 0
\(349\) −8.00000 −0.428230 −0.214115 0.976808i \(-0.568687\pi\)
−0.214115 + 0.976808i \(0.568687\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.00000i 0.319801i
\(353\) 10.0000i 0.532246i 0.963939 + 0.266123i \(0.0857428\pi\)
−0.963939 + 0.266123i \(0.914257\pi\)
\(354\) 0 0
\(355\) 16.0000 8.00000i 0.849192 0.424596i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 12.0000i 0.634220i
\(359\) −12.0000 −0.633336 −0.316668 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 2.00000i 0.105118i
\(363\) 0 0
\(364\) 0 0
\(365\) 6.00000 + 12.0000i 0.314054 + 0.628109i
\(366\) 0 0
\(367\) 6.00000i 0.313197i −0.987662 0.156599i \(-0.949947\pi\)
0.987662 0.156599i \(-0.0500529\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 0 0
\(370\) 20.0000 10.0000i 1.03975 0.519875i
\(371\) 0 0
\(372\) 0 0
\(373\) 10.0000i 0.517780i −0.965907 0.258890i \(-0.916643\pi\)
0.965907 0.258890i \(-0.0833568\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 8.00000 0.412568
\(377\) 2.00000i 0.103005i
\(378\) 0 0
\(379\) −22.0000 −1.13006 −0.565032 0.825069i \(-0.691136\pi\)
−0.565032 + 0.825069i \(0.691136\pi\)
\(380\) 12.0000 6.00000i 0.615587 0.307794i
\(381\) 0 0
\(382\) 8.00000i 0.409316i
\(383\) 20.0000i 1.02195i 0.859595 + 0.510976i \(0.170716\pi\)
−0.859595 + 0.510976i \(0.829284\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −10.0000 −0.508987
\(387\) 0 0
\(388\) 2.00000i 0.101535i
\(389\) −14.0000 −0.709828 −0.354914 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 7.00000i 0.353553i
\(393\) 0 0
\(394\) 22.0000 1.10834
\(395\) −32.0000 + 16.0000i −1.61009 + 0.805047i
\(396\) 0 0
\(397\) 18.0000i 0.903394i 0.892171 + 0.451697i \(0.149181\pi\)
−0.892171 + 0.451697i \(0.850819\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) −14.0000 −0.699127 −0.349563 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 0 0
\(403\) 4.00000i 0.199254i
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) 0 0
\(407\) 60.0000i 2.97409i
\(408\) 0 0
\(409\) −30.0000 −1.48340 −0.741702 0.670729i \(-0.765981\pi\)
−0.741702 + 0.670729i \(0.765981\pi\)
\(410\) 6.00000 + 12.0000i 0.296319 + 0.592638i
\(411\) 0 0
\(412\) 10.0000i 0.492665i
\(413\) 0 0
\(414\) 0 0
\(415\) −4.00000 8.00000i −0.196352 0.392705i
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) 36.0000i 1.76082i
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) −8.00000 −0.389896 −0.194948 0.980814i \(-0.562454\pi\)
−0.194948 + 0.980814i \(0.562454\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 16.0000i 0.773389i
\(429\) 0 0
\(430\) −16.0000 + 8.00000i −0.771589 + 0.385794i
\(431\) 8.00000 0.385346 0.192673 0.981263i \(-0.438284\pi\)
0.192673 + 0.981263i \(0.438284\pi\)
\(432\) 0 0
\(433\) 24.0000i 1.15337i 0.816968 + 0.576683i \(0.195653\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −16.0000 −0.766261
\(437\) 36.0000i 1.72211i
\(438\) 0 0
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) −6.00000 12.0000i −0.286039 0.572078i
\(441\) 0 0
\(442\) 0 0
\(443\) 32.0000i 1.52037i 0.649709 + 0.760183i \(0.274891\pi\)
−0.649709 + 0.760183i \(0.725109\pi\)
\(444\) 0 0
\(445\) −20.0000 + 10.0000i −0.948091 + 0.474045i
\(446\) −4.00000 −0.189405
\(447\) 0 0
\(448\) 0 0
\(449\) −34.0000 −1.60456 −0.802280 0.596948i \(-0.796380\pi\)
−0.802280 + 0.596948i \(0.796380\pi\)
\(450\) 0 0
\(451\) 36.0000 1.69517
\(452\) 8.00000i 0.376288i
\(453\) 0 0
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 0 0
\(457\) 18.0000i 0.842004i −0.907060 0.421002i \(-0.861678\pi\)
0.907060 0.421002i \(-0.138322\pi\)
\(458\) 20.0000i 0.934539i
\(459\) 0 0
\(460\) 6.00000 + 12.0000i 0.279751 + 0.559503i
\(461\) −36.0000 −1.67669 −0.838344 0.545142i \(-0.816476\pi\)
−0.838344 + 0.545142i \(0.816476\pi\)
\(462\) 0 0
\(463\) 16.0000i 0.743583i −0.928316 0.371792i \(-0.878744\pi\)
0.928316 0.371792i \(-0.121256\pi\)
\(464\) 2.00000 0.0928477
\(465\) 0 0
\(466\) −8.00000 −0.370593
\(467\) 40.0000i 1.85098i −0.378773 0.925490i \(-0.623654\pi\)
0.378773 0.925490i \(-0.376346\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −16.0000 + 8.00000i −0.738025 + 0.369012i
\(471\) 0 0
\(472\) 10.0000i 0.460287i
\(473\) 48.0000i 2.20704i
\(474\) 0 0
\(475\) −18.0000 + 24.0000i −0.825897 + 1.10120i
\(476\) 0 0
\(477\) 0 0
\(478\) 28.0000i 1.28069i
\(479\) 20.0000 0.913823 0.456912 0.889512i \(-0.348956\pi\)
0.456912 + 0.889512i \(0.348956\pi\)
\(480\) 0 0
\(481\) 10.0000 0.455961
\(482\) 22.0000i 1.00207i
\(483\) 0 0
\(484\) −25.0000 −1.13636
\(485\) −2.00000 4.00000i −0.0908153 0.181631i
\(486\) 0 0
\(487\) 12.0000i 0.543772i 0.962329 + 0.271886i \(0.0876473\pi\)
−0.962329 + 0.271886i \(0.912353\pi\)
\(488\) 6.00000i 0.271607i
\(489\) 0 0
\(490\) 7.00000 + 14.0000i 0.316228 + 0.632456i
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 6.00000 0.269953
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 0 0
\(499\) 6.00000 0.268597 0.134298 0.990941i \(-0.457122\pi\)
0.134298 + 0.990941i \(0.457122\pi\)
\(500\) −2.00000 + 11.0000i −0.0894427 + 0.491935i
\(501\) 0 0
\(502\) 8.00000i 0.357057i
\(503\) 26.0000i 1.15928i 0.814872 + 0.579641i \(0.196807\pi\)
−0.814872 + 0.579641i \(0.803193\pi\)
\(504\) 0 0
\(505\) 4.00000 2.00000i 0.177998 0.0889988i
\(506\) 36.0000 1.60040
\(507\) 0 0
\(508\) 18.0000i 0.798621i
\(509\) 24.0000 1.06378 0.531891 0.846813i \(-0.321482\pi\)
0.531891 + 0.846813i \(0.321482\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 24.0000 1.05859
\(515\) −10.0000 20.0000i −0.440653 0.881305i
\(516\) 0 0
\(517\) 48.0000i 2.11104i
\(518\) 0 0
\(519\) 0 0
\(520\) 2.00000 1.00000i 0.0877058 0.0438529i
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 0 0
\(523\) 40.0000i 1.74908i 0.484955 + 0.874539i \(0.338836\pi\)
−0.484955 + 0.874539i \(0.661164\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) 0 0
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) −12.0000 + 6.00000i −0.521247 + 0.260623i
\(531\) 0 0
\(532\) 0 0
\(533\) 6.00000i 0.259889i
\(534\) 0 0
\(535\) 16.0000 + 32.0000i 0.691740 + 1.38348i
\(536\) −4.00000 −0.172774
\(537\) 0 0
\(538\) 14.0000i 0.603583i
\(539\) 42.0000 1.80907
\(540\) 0 0
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 0 0
\(544\) 0 0
\(545\) 32.0000 16.0000i 1.37073 0.685365i
\(546\) 0 0
\(547\) 12.0000i 0.513083i −0.966533 0.256541i \(-0.917417\pi\)
0.966533 0.256541i \(-0.0825830\pi\)
\(548\) 2.00000i 0.0854358i
\(549\) 0 0
\(550\) 24.0000 + 18.0000i 1.02336 + 0.767523i
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) 0 0
\(554\) 26.0000 1.10463
\(555\) 0 0
\(556\) 8.00000 0.339276
\(557\) 2.00000i 0.0847427i −0.999102 0.0423714i \(-0.986509\pi\)
0.999102 0.0423714i \(-0.0134913\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0000i 0.421825i
\(563\) 24.0000i 1.01148i 0.862686 + 0.505740i \(0.168780\pi\)
−0.862686 + 0.505740i \(0.831220\pi\)
\(564\) 0 0
\(565\) −8.00000 16.0000i −0.336563 0.673125i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 8.00000i 0.335673i
\(569\) 22.0000 0.922288 0.461144 0.887325i \(-0.347439\pi\)
0.461144 + 0.887325i \(0.347439\pi\)
\(570\) 0 0
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 6.00000i 0.250873i
\(573\) 0 0
\(574\) 0 0
\(575\) −24.0000 18.0000i −1.00087 0.750652i
\(576\) 0 0
\(577\) 2.00000i 0.0832611i 0.999133 + 0.0416305i \(0.0132552\pi\)
−0.999133 + 0.0416305i \(0.986745\pi\)
\(578\) 17.0000i 0.707107i
\(579\) 0 0
\(580\) −4.00000 + 2.00000i −0.166091 + 0.0830455i
\(581\) 0 0
\(582\) 0 0
\(583\) 36.0000i 1.49097i
\(584\) 6.00000 0.248282
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) −24.0000 −0.988903
\(590\) 10.0000 + 20.0000i 0.411693 + 0.823387i
\(591\) 0 0
\(592\) 10.0000i 0.410997i
\(593\) 6.00000i 0.246390i −0.992382 0.123195i \(-0.960686\pi\)
0.992382 0.123195i \(-0.0393141\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 6.00000i 0.245358i
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 50.0000 25.0000i 2.03279 1.01639i
\(606\) 0 0
\(607\) 2.00000i 0.0811775i −0.999176 0.0405887i \(-0.987077\pi\)
0.999176 0.0405887i \(-0.0129233\pi\)
\(608\) 6.00000i 0.243332i
\(609\) 0 0
\(610\) −6.00000 12.0000i −0.242933 0.485866i
\(611\) −8.00000 −0.323645
\(612\) 0 0
\(613\) 38.0000i 1.53481i −0.641165 0.767403i \(-0.721549\pi\)
0.641165 0.767403i \(-0.278451\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) 0 0
\(619\) −38.0000 −1.52735 −0.763674 0.645601i \(-0.776607\pi\)
−0.763674 + 0.645601i \(0.776607\pi\)
\(620\) −8.00000 + 4.00000i −0.321288 + 0.160644i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 16.0000 0.639489
\(627\) 0 0
\(628\) 2.00000i 0.0798087i
\(629\) 0 0
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 16.0000i 0.636446i
\(633\) 0 0
\(634\) −18.0000 −0.714871
\(635\) 18.0000 + 36.0000i 0.714308 + 1.42862i
\(636\) 0 0
\(637\) 7.00000i 0.277350i
\(638\) 12.0000i 0.475085i
\(639\) 0 0
\(640\) −1.00000 2.00000i −0.0395285 0.0790569i
\(641\) 42.0000 1.65890 0.829450 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 0 0
\(643\) 44.0000i 1.73519i 0.497271 + 0.867595i \(0.334335\pi\)
−0.497271 + 0.867595i \(0.665665\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 14.0000i 0.550397i 0.961387 + 0.275198i \(0.0887435\pi\)
−0.961387 + 0.275198i \(0.911256\pi\)
\(648\) 0 0
\(649\) 60.0000 2.35521
\(650\) −3.00000 + 4.00000i −0.117670 + 0.156893i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) 6.00000i 0.234798i −0.993085 0.117399i \(-0.962544\pi\)
0.993085 0.117399i \(-0.0374557\pi\)
\(654\) 0 0
\(655\) −24.0000 + 12.0000i −0.937758 + 0.468879i
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) −28.0000 −1.08907 −0.544537 0.838737i \(-0.683295\pi\)
−0.544537 + 0.838737i \(0.683295\pi\)
\(662\) 26.0000i 1.01052i
\(663\) 0 0
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) 0 0
\(667\) 12.0000i 0.464642i
\(668\) 8.00000i 0.309529i
\(669\) 0 0
\(670\) 8.00000 4.00000i 0.309067 0.154533i
\(671\) −36.0000 −1.38976
\(672\) 0 0
\(673\) 44.0000i 1.69608i 0.529936 + 0.848038i \(0.322216\pi\)
−0.529936 + 0.848038i \(0.677784\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 38.0000i 1.46046i 0.683202 + 0.730229i \(0.260587\pi\)
−0.683202 + 0.730229i \(0.739413\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 24.0000i 0.919007i
\(683\) 12.0000i 0.459167i 0.973289 + 0.229584i \(0.0737364\pi\)
−0.973289 + 0.229584i \(0.926264\pi\)
\(684\) 0 0
\(685\) 2.00000 + 4.00000i 0.0764161 + 0.152832i
\(686\) 0 0
\(687\) 0 0
\(688\) 8.00000i 0.304997i
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) 22.0000 0.836919 0.418460 0.908235i \(-0.362570\pi\)
0.418460 + 0.908235i \(0.362570\pi\)
\(692\) 18.0000i 0.684257i
\(693\) 0 0
\(694\) −32.0000 −1.21470
\(695\) −16.0000 + 8.00000i −0.606915 + 0.303457i
\(696\) 0 0
\(697\) 0 0
\(698\) 8.00000i 0.302804i
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 60.0000i 2.26294i
\(704\) −6.00000 −0.226134
\(705\) 0 0
\(706\) −10.0000 −0.376355
\(707\) 0 0
\(708\) 0 0
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) 8.00000 + 16.0000i 0.300235 + 0.600469i
\(711\) 0 0
\(712\) 10.0000i 0.374766i
\(713\) 24.0000i 0.898807i
\(714\) 0 0
\(715\) 6.00000 + 12.0000i 0.224387 + 0.448775i
\(716\) 12.0000 0.448461
\(717\) 0 0
\(718\) 12.0000i 0.447836i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) 0 0
\(724\) 2.00000 0.0743294
\(725\) 6.00000 8.00000i 0.222834 0.297113i
\(726\) 0 0
\(727\) 38.0000i 1.40934i −0.709534 0.704671i \(-0.751095\pi\)
0.709534 0.704671i \(-0.248905\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −12.0000 + 6.00000i −0.444140 + 0.222070i
\(731\) 0 0
\(732\) 0 0
\(733\) 26.0000i 0.960332i −0.877178 0.480166i \(-0.840576\pi\)
0.877178 0.480166i \(-0.159424\pi\)
\(734\) 6.00000 0.221464
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 24.0000i 0.884051i
\(738\) 0 0
\(739\) 22.0000 0.809283 0.404642 0.914475i \(-0.367396\pi\)
0.404642 + 0.914475i \(0.367396\pi\)
\(740\) 10.0000 + 20.0000i 0.367607 + 0.735215i
\(741\) 0 0
\(742\) 0 0
\(743\) 52.0000i 1.90769i −0.300291 0.953847i \(-0.597084\pi\)
0.300291 0.953847i \(-0.402916\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 0 0
\(754\) −2.00000 −0.0728357
\(755\) −16.0000 + 8.00000i −0.582300 + 0.291150i
\(756\) 0 0
\(757\) 10.0000i 0.363456i −0.983349 0.181728i \(-0.941831\pi\)
0.983349 0.181728i \(-0.0581691\pi\)
\(758\) 22.0000i 0.799076i
\(759\) 0 0
\(760\) 6.00000 + 12.0000i 0.217643 + 0.435286i
\(761\) −30.0000 −1.08750 −0.543750 0.839248i \(-0.682996\pi\)
−0.543750 + 0.839248i \(0.682996\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) −20.0000 −0.722629
\(767\) 10.0000i 0.361079i
\(768\) 0 0
\(769\) 54.0000 1.94729 0.973645 0.228069i \(-0.0732413\pi\)
0.973645 + 0.228069i \(0.0732413\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.0000i 0.359908i
\(773\) 18.0000i 0.647415i 0.946157 + 0.323708i \(0.104929\pi\)
−0.946157 + 0.323708i \(0.895071\pi\)
\(774\) 0 0
\(775\) 12.0000 16.0000i 0.431053 0.574737i
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) 14.0000i 0.501924i
\(779\) −36.0000 −1.28983
\(780\) 0 0
\(781\) 48.0000 1.71758
\(782\) 0 0
\(783\) 0 0
\(784\) 7.00000 0.250000
\(785\) 2.00000 + 4.00000i 0.0713831 + 0.142766i
\(786\) 0 0
\(787\) 12.0000i 0.427754i 0.976861 + 0.213877i \(0.0686091\pi\)
−0.976861 + 0.213877i \(0.931391\pi\)
\(788\) 22.0000i 0.783718i
\(789\) 0 0
\(790\) −16.0000 32.0000i −0.569254 1.13851i
\(791\) 0 0
\(792\) 0 0
\(793\) 6.00000i 0.213066i
\(794\) −18.0000 −0.638796
\(795\) 0 0
\(796\) 16.0000 0.567105
\(797\) 42.0000i 1.48772i 0.668338 + 0.743858i \(0.267006\pi\)
−0.668338 + 0.743858i \(0.732994\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 4.00000 + 3.00000i