Properties

Label 1440.2.x.q.127.1
Level $1440$
Weight $2$
Character 1440.127
Analytic conductor $11.498$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.4984578911\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1698758656.6
Defining polynomial: \(x^{8} + 18 x^{6} + 97 x^{4} + 176 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: no (minimal twist has level 480)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 127.1
Root \(3.16053i\) of defining polynomial
Character \(\chi\) \(=\) 1440.127
Dual form 1440.2.x.q.703.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.23483 + 0.0743018i) q^{5} +(-3.16053 + 3.16053i) q^{7} +O(q^{10})\) \(q+(-2.23483 + 0.0743018i) q^{5} +(-3.16053 + 3.16053i) q^{7} -4.46967i q^{11} +(-2.51929 + 2.51929i) q^{13} +(2.30913 + 2.30913i) q^{17} +2.61827 q^{19} +(-1.64124 - 1.64124i) q^{23} +(4.98896 - 0.332104i) q^{25} -8.17246i q^{29} -4.00000i q^{31} +(6.82843 - 7.29809i) q^{35} +(5.80177 + 5.80177i) q^{37} +2.61827 q^{41} +(-5.14949 - 5.14949i) q^{43} +(-0.679824 + 0.679824i) q^{47} -12.9779i q^{49} +(7.81739 - 7.81739i) q^{53} +(0.332104 + 9.98896i) q^{55} -4.88998 q^{59} +12.2751 q^{61} +(5.44301 - 5.81739i) q^{65} +(9.44670 - 9.44670i) q^{67} -5.65685i q^{71} +(-5.61827 + 5.61827i) q^{73} +(14.1265 + 14.1265i) q^{77} -3.57969 q^{79} +(-1.34403 - 1.34403i) q^{83} +(-5.33210 - 4.98896i) q^{85} +17.6348i q^{89} -15.9246i q^{91} +(-5.85140 + 0.194542i) q^{95} +(-1.32106 - 1.32106i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{7} + O(q^{10}) \) \( 8 q - 4 q^{7} - 12 q^{13} + 4 q^{17} - 8 q^{19} - 4 q^{25} + 32 q^{35} + 12 q^{37} - 8 q^{41} + 24 q^{43} + 24 q^{47} - 4 q^{53} + 4 q^{55} - 16 q^{59} + 24 q^{61} - 4 q^{65} + 24 q^{67} - 16 q^{73} + 32 q^{77} - 16 q^{79} + 16 q^{83} - 44 q^{85} - 40 q^{95} + 32 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(991\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\) \(-1\)

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 0
\(4\) 0 0
\(5\) −2.23483 + 0.0743018i −0.999448 + 0.0332288i
\(6\) 0 0
\(7\) −3.16053 + 3.16053i −1.19457 + 1.19457i −0.218799 + 0.975770i \(0.570214\pi\)
−0.975770 + 0.218799i \(0.929786\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.46967i 1.34766i −0.738889 0.673828i \(-0.764649\pi\)
0.738889 0.673828i \(-0.235351\pi\)
\(12\) 0 0
\(13\) −2.51929 + 2.51929i −0.698726 + 0.698726i −0.964136 0.265410i \(-0.914493\pi\)
0.265410 + 0.964136i \(0.414493\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.30913 + 2.30913i 0.560047 + 0.560047i 0.929321 0.369273i \(-0.120393\pi\)
−0.369273 + 0.929321i \(0.620393\pi\)
\(18\) 0 0
\(19\) 2.61827 0.600672 0.300336 0.953833i \(-0.402901\pi\)
0.300336 + 0.953833i \(0.402901\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.64124 1.64124i −0.342222 0.342222i 0.514980 0.857202i \(-0.327799\pi\)
−0.857202 + 0.514980i \(0.827799\pi\)
\(24\) 0 0
\(25\) 4.98896 0.332104i 0.997792 0.0664208i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 8.17246i 1.51759i −0.651331 0.758794i \(-0.725789\pi\)
0.651331 0.758794i \(-0.274211\pi\)
\(30\) 0 0
\(31\) 4.00000i 0.718421i −0.933257 0.359211i \(-0.883046\pi\)
0.933257 0.359211i \(-0.116954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6.82843 7.29809i 1.15421 1.23360i
\(36\) 0 0
\(37\) 5.80177 + 5.80177i 0.953805 + 0.953805i 0.998979 0.0451739i \(-0.0143842\pi\)
−0.0451739 + 0.998979i \(0.514384\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.61827 0.408905 0.204453 0.978876i \(-0.434459\pi\)
0.204453 + 0.978876i \(0.434459\pi\)
\(42\) 0 0
\(43\) −5.14949 5.14949i −0.785290 0.785290i 0.195428 0.980718i \(-0.437390\pi\)
−0.980718 + 0.195428i \(0.937390\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.679824 + 0.679824i −0.0991625 + 0.0991625i −0.754948 0.655785i \(-0.772338\pi\)
0.655785 + 0.754948i \(0.272338\pi\)
\(48\) 0 0
\(49\) 12.9779i 1.85399i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.81739 7.81739i 1.07380 1.07380i 0.0767501 0.997050i \(-0.475546\pi\)
0.997050 0.0767501i \(-0.0244544\pi\)
\(54\) 0 0
\(55\) 0.332104 + 9.98896i 0.0447809 + 1.34691i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.88998 −0.636621 −0.318311 0.947986i \(-0.603115\pi\)
−0.318311 + 0.947986i \(0.603115\pi\)
\(60\) 0 0
\(61\) 12.2751 1.57167 0.785834 0.618437i \(-0.212234\pi\)
0.785834 + 0.618437i \(0.212234\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 5.44301 5.81739i 0.675122 0.721558i
\(66\) 0 0
\(67\) 9.44670 9.44670i 1.15410 1.15410i 0.168375 0.985723i \(-0.446148\pi\)
0.985723 0.168375i \(-0.0538518\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.65685i 0.671345i −0.941979 0.335673i \(-0.891036\pi\)
0.941979 0.335673i \(-0.108964\pi\)
\(72\) 0 0
\(73\) −5.61827 + 5.61827i −0.657569 + 0.657569i −0.954804 0.297235i \(-0.903935\pi\)
0.297235 + 0.954804i \(0.403935\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 14.1265 + 14.1265i 1.60987 + 1.60987i
\(78\) 0 0
\(79\) −3.57969 −0.402746 −0.201373 0.979515i \(-0.564540\pi\)
−0.201373 + 0.979515i \(0.564540\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.34403 1.34403i −0.147527 0.147527i 0.629486 0.777012i \(-0.283266\pi\)
−0.777012 + 0.629486i \(0.783266\pi\)
\(84\) 0 0
\(85\) −5.33210 4.98896i −0.578348 0.541129i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 17.6348i 1.86928i 0.355593 + 0.934641i \(0.384279\pi\)
−0.355593 + 0.934641i \(0.615721\pi\)
\(90\) 0 0
\(91\) 15.9246i 1.66935i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.85140 + 0.194542i −0.600341 + 0.0199596i
\(96\) 0 0
\(97\) −1.32106 1.32106i −0.134134 0.134134i 0.636852 0.770986i \(-0.280236\pi\)
−0.770986 + 0.636852i \(0.780236\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.47702 0.146969 0.0734845 0.997296i \(-0.476588\pi\)
0.0734845 + 0.997296i \(0.476588\pi\)
\(102\) 0 0
\(103\) −9.11459 9.11459i −0.898088 0.898088i 0.0971794 0.995267i \(-0.469018\pi\)
−0.995267 + 0.0971794i \(0.969018\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.06155 + 2.06155i −0.199298 + 0.199298i −0.799699 0.600401i \(-0.795008\pi\)
0.600401 + 0.799699i \(0.295008\pi\)
\(108\) 0 0
\(109\) 9.70279i 0.929359i −0.885479 0.464679i \(-0.846170\pi\)
0.885479 0.464679i \(-0.153830\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 4.63020 4.63020i 0.435572 0.435572i −0.454946 0.890519i \(-0.650342\pi\)
0.890519 + 0.454946i \(0.150342\pi\)
\(114\) 0 0
\(115\) 3.78984 + 3.54595i 0.353405 + 0.330661i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −14.5962 −1.33803
\(120\) 0 0
\(121\) −8.97792 −0.816174
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −11.1248 + 1.11289i −0.995034 + 0.0995396i
\(126\) 0 0
\(127\) 10.1991 10.1991i 0.905025 0.905025i −0.0908403 0.995865i \(-0.528955\pi\)
0.995865 + 0.0908403i \(0.0289553\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 12.4697i 1.08948i −0.838605 0.544740i \(-0.816628\pi\)
0.838605 0.544740i \(-0.183372\pi\)
\(132\) 0 0
\(133\) −8.27512 + 8.27512i −0.717544 + 0.717544i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −4.63020 4.63020i −0.395584 0.395584i 0.481088 0.876672i \(-0.340242\pi\)
−0.876672 + 0.481088i \(0.840242\pi\)
\(138\) 0 0
\(139\) −3.00735 −0.255080 −0.127540 0.991833i \(-0.540708\pi\)
−0.127540 + 0.991833i \(0.540708\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 11.2604 + 11.2604i 0.941642 + 0.941642i
\(144\) 0 0
\(145\) 0.607228 + 18.2641i 0.0504276 + 1.51675i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.148604i 0.0121741i −0.999981 0.00608704i \(-0.998062\pi\)
0.999981 0.00608704i \(-0.00193758\pi\)
\(150\) 0 0
\(151\) 20.6200i 1.67804i 0.544104 + 0.839018i \(0.316870\pi\)
−0.544104 + 0.839018i \(0.683130\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.297207 + 8.93933i 0.0238723 + 0.718024i
\(156\) 0 0
\(157\) −9.77969 9.77969i −0.780504 0.780504i 0.199412 0.979916i \(-0.436097\pi\)
−0.979916 + 0.199412i \(0.936097\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 10.3744 0.817615
\(162\) 0 0
\(163\) 10.4081 + 10.4081i 0.815226 + 0.815226i 0.985412 0.170186i \(-0.0544368\pi\)
−0.170186 + 0.985412i \(0.554437\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.06155 6.06155i 0.469057 0.469057i −0.432552 0.901609i \(-0.642387\pi\)
0.901609 + 0.432552i \(0.142387\pi\)
\(168\) 0 0
\(169\) 0.306334i 0.0235641i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −0.355074 + 0.355074i −0.0269957 + 0.0269957i −0.720476 0.693480i \(-0.756077\pi\)
0.693480 + 0.720476i \(0.256077\pi\)
\(174\) 0 0
\(175\) −14.7181 + 16.8174i −1.11259 + 1.27127i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −15.7521 −1.17737 −0.588685 0.808362i \(-0.700354\pi\)
−0.588685 + 0.808362i \(0.700354\pi\)
\(180\) 0 0
\(181\) 7.77996 0.578280 0.289140 0.957287i \(-0.406631\pi\)
0.289140 + 0.957287i \(0.406631\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −13.3971 12.5349i −0.984972 0.921585i
\(186\) 0 0
\(187\) 10.3211 10.3211i 0.754751 0.754751i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.35965i 0.677240i 0.940923 + 0.338620i \(0.109960\pi\)
−0.940923 + 0.338620i \(0.890040\pi\)
\(192\) 0 0
\(193\) 17.1759 17.1759i 1.23635 1.23635i 0.274863 0.961483i \(-0.411368\pi\)
0.961483 0.274863i \(-0.0886325\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.83947 1.83947i −0.131057 0.131057i 0.638536 0.769592i \(-0.279541\pi\)
−0.769592 + 0.638536i \(0.779541\pi\)
\(198\) 0 0
\(199\) −0.442397 −0.0313607 −0.0156804 0.999877i \(-0.504991\pi\)
−0.0156804 + 0.999877i \(0.504991\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 25.8293 + 25.8293i 1.81286 + 1.81286i
\(204\) 0 0
\(205\) −5.85140 + 0.194542i −0.408679 + 0.0135874i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 11.7028i 0.809499i
\(210\) 0 0
\(211\) 5.30633i 0.365303i 0.983178 + 0.182652i \(0.0584680\pi\)
−0.983178 + 0.182652i \(0.941532\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 11.8909 + 11.1256i 0.810950 + 0.758762i
\(216\) 0 0
\(217\) 12.6421 + 12.6421i 0.858203 + 0.858203i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −11.6348 −0.782639
\(222\) 0 0
\(223\) 5.48159 + 5.48159i 0.367075 + 0.367075i 0.866409 0.499335i \(-0.166422\pi\)
−0.499335 + 0.866409i \(0.666422\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.51649 9.51649i 0.631632 0.631632i −0.316845 0.948477i \(-0.602624\pi\)
0.948477 + 0.316845i \(0.102624\pi\)
\(228\) 0 0
\(229\) 5.25862i 0.347500i −0.984790 0.173750i \(-0.944412\pi\)
0.984790 0.173750i \(-0.0555884\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.92740 + 2.92740i −0.191781 + 0.191781i −0.796465 0.604684i \(-0.793299\pi\)
0.604684 + 0.796465i \(0.293299\pi\)
\(234\) 0 0
\(235\) 1.46878 1.56980i 0.0958126 0.102403i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 12.6421 0.817751 0.408876 0.912590i \(-0.365921\pi\)
0.408876 + 0.912590i \(0.365921\pi\)
\(240\) 0 0
\(241\) 14.5650 0.938211 0.469106 0.883142i \(-0.344576\pi\)
0.469106 + 0.883142i \(0.344576\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.964283 + 29.0035i 0.0616058 + 1.85296i
\(246\) 0 0
\(247\) −6.59619 + 6.59619i −0.419705 + 0.419705i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 18.5468i 1.17067i −0.810793 0.585333i \(-0.800964\pi\)
0.810793 0.585333i \(-0.199036\pi\)
\(252\) 0 0
\(253\) −7.33579 + 7.33579i −0.461197 + 0.461197i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −13.2485 13.2485i −0.826417 0.826417i 0.160602 0.987019i \(-0.448656\pi\)
−0.987019 + 0.160602i \(0.948656\pi\)
\(258\) 0 0
\(259\) −36.6734 −2.27877
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −22.5806 22.5806i −1.39238 1.39238i −0.819967 0.572411i \(-0.806008\pi\)
−0.572411 0.819967i \(-0.693992\pi\)
\(264\) 0 0
\(265\) −16.8897 + 18.0514i −1.03753 + 1.10889i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.82019i 0.415834i −0.978146 0.207917i \(-0.933332\pi\)
0.978146 0.207917i \(-0.0666684\pi\)
\(270\) 0 0
\(271\) 2.74138i 0.166527i −0.996528 0.0832634i \(-0.973466\pi\)
0.996528 0.0832634i \(-0.0265343\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.48440 22.2990i −0.0895124 1.34468i
\(276\) 0 0
\(277\) −7.75583 7.75583i −0.466003 0.466003i 0.434614 0.900617i \(-0.356885\pi\)
−0.900617 + 0.434614i \(0.856885\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.54110 −0.270899 −0.135450 0.990784i \(-0.543248\pi\)
−0.135450 + 0.990784i \(0.543248\pi\)
\(282\) 0 0
\(283\) 7.91295 + 7.91295i 0.470376 + 0.470376i 0.902036 0.431660i \(-0.142072\pi\)
−0.431660 + 0.902036i \(0.642072\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.27512 + 8.27512i −0.488465 + 0.488465i
\(288\) 0 0
\(289\) 6.33579i 0.372694i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −15.0999 + 15.0999i −0.882143 + 0.882143i −0.993752 0.111609i \(-0.964400\pi\)
0.111609 + 0.993752i \(0.464400\pi\)
\(294\) 0 0
\(295\) 10.9283 0.363334i 0.636270 0.0211541i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 8.26952 0.478239
\(300\) 0 0
\(301\) 32.5502 1.87617
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −27.4329 + 0.912064i −1.57080 + 0.0522246i
\(306\) 0 0
\(307\) 4.43197 4.43197i 0.252946 0.252946i −0.569232 0.822177i \(-0.692759\pi\)
0.822177 + 0.569232i \(0.192759\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 23.5355i 1.33458i 0.744799 + 0.667288i \(0.232545\pi\)
−0.744799 + 0.667288i \(0.767455\pi\)
\(312\) 0 0
\(313\) −18.6035 + 18.6035i −1.05153 + 1.05153i −0.0529364 + 0.998598i \(0.516858\pi\)
−0.998598 + 0.0529364i \(0.983142\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7.56953 7.56953i −0.425147 0.425147i 0.461824 0.886971i \(-0.347195\pi\)
−0.886971 + 0.461824i \(0.847195\pi\)
\(318\) 0 0
\(319\) −36.5282 −2.04518
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 6.04594 + 6.04594i 0.336405 + 0.336405i
\(324\) 0 0
\(325\) −11.7320 + 13.4053i −0.650773 + 0.743593i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4.29721i 0.236913i
\(330\) 0 0
\(331\) 13.8020i 0.758629i −0.925268 0.379314i \(-0.876160\pi\)
0.925268 0.379314i \(-0.123840\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −20.4099 + 21.8137i −1.11511 + 1.19181i
\(336\) 0 0
\(337\) 10.9541 + 10.9541i 0.596706 + 0.596706i 0.939434 0.342729i \(-0.111351\pi\)
−0.342729 + 0.939434i \(0.611351\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −17.8787 −0.968184
\(342\) 0 0
\(343\) 18.8934 + 18.8934i 1.02015 + 1.02015i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −13.3934 + 13.3934i −0.718995 + 0.718995i −0.968399 0.249405i \(-0.919765\pi\)
0.249405 + 0.968399i \(0.419765\pi\)
\(348\) 0 0
\(349\) 21.6035i 1.15641i −0.815891 0.578206i \(-0.803753\pi\)
0.815891 0.578206i \(-0.196247\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −25.9678 + 25.9678i −1.38212 + 1.38212i −0.541286 + 0.840839i \(0.682062\pi\)
−0.840839 + 0.541286i \(0.817938\pi\)
\(354\) 0 0
\(355\) 0.420314 + 12.6421i 0.0223080 + 0.670974i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.93933 0.471800 0.235900 0.971777i \(-0.424196\pi\)
0.235900 + 0.971777i \(0.424196\pi\)
\(360\) 0 0
\(361\) −12.1447 −0.639193
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 12.1384 12.9733i 0.635355 0.679056i
\(366\) 0 0
\(367\) 13.7788 13.7788i 0.719248 0.719248i −0.249204 0.968451i \(-0.580169\pi\)
0.968451 + 0.249204i \(0.0801688\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 49.4142i 2.56546i
\(372\) 0 0
\(373\) −12.4439 + 12.4439i −0.644321 + 0.644321i −0.951615 0.307294i \(-0.900576\pi\)
0.307294 + 0.951615i \(0.400576\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 20.5888 + 20.5888i 1.06038 + 1.06038i
\(378\) 0 0
\(379\) 34.9190 1.79367 0.896835 0.442366i \(-0.145861\pi\)
0.896835 + 0.442366i \(0.145861\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.69455 5.69455i −0.290978 0.290978i 0.546489 0.837467i \(-0.315964\pi\)
−0.837467 + 0.546489i \(0.815964\pi\)
\(384\) 0 0
\(385\) −32.6200 30.5208i −1.66247 1.55548i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8.44581i 0.428220i −0.976810 0.214110i \(-0.931315\pi\)
0.976810 0.214110i \(-0.0686850\pi\)
\(390\) 0 0
\(391\) 7.57969i 0.383321i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.00000 0.265977i 0.402524 0.0133828i
\(396\) 0 0
\(397\) 18.0769 + 18.0769i 0.907253 + 0.907253i 0.996050 0.0887965i \(-0.0283021\pi\)
−0.0887965 + 0.996050i \(0.528302\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 31.8787 1.59194 0.795972 0.605333i \(-0.206960\pi\)
0.795972 + 0.605333i \(0.206960\pi\)
\(402\) 0 0
\(403\) 10.0772 + 10.0772i 0.501980 + 0.501980i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 25.9320 25.9320i 1.28540 1.28540i
\(408\) 0 0
\(409\) 27.3063i 1.35021i −0.737721 0.675106i \(-0.764098\pi\)
0.737721 0.675106i \(-0.235902\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 15.4549 15.4549i 0.760488 0.760488i
\(414\) 0 0
\(415\) 3.10355 + 2.90382i 0.152347 + 0.142543i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −16.1412 −0.788551 −0.394275 0.918992i \(-0.629004\pi\)
−0.394275 + 0.918992i \(0.629004\pi\)
\(420\) 0 0
\(421\) −20.6200 −1.00496 −0.502480 0.864589i \(-0.667579\pi\)
−0.502480 + 0.864589i \(0.667579\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 12.2871 + 10.7533i 0.596010 + 0.521612i
\(426\) 0 0
\(427\) −38.7959 + 38.7959i −1.87747 + 1.87747i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.54848i 0.122756i 0.998115 + 0.0613779i \(0.0195495\pi\)
−0.998115 + 0.0613779i \(0.980451\pi\)
\(432\) 0 0
\(433\) 6.77996 6.77996i 0.325824 0.325824i −0.525172 0.850996i \(-0.675999\pi\)
0.850996 + 0.525172i \(0.175999\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.29721 4.29721i −0.205563 0.205563i
\(438\) 0 0
\(439\) 15.0698 0.719243 0.359622 0.933098i \(-0.382906\pi\)
0.359622 + 0.933098i \(0.382906\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.69059 + 9.69059i 0.460414 + 0.460414i 0.898791 0.438377i \(-0.144447\pi\)
−0.438377 + 0.898791i \(0.644447\pi\)
\(444\) 0 0
\(445\) −1.31030 39.4108i −0.0621139 1.86825i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 20.1759i 0.952158i −0.879402 0.476079i \(-0.842058\pi\)
0.879402 0.476079i \(-0.157942\pi\)
\(450\) 0 0
\(451\) 11.7028i 0.551063i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.18323 + 35.5888i 0.0554705 + 1.66843i
\(456\) 0 0
\(457\) −0.579686 0.579686i −0.0271165 0.0271165i 0.693419 0.720535i \(-0.256104\pi\)
−0.720535 + 0.693419i \(0.756104\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.40164 0.205005 0.102503 0.994733i \(-0.467315\pi\)
0.102503 + 0.994733i \(0.467315\pi\)
\(462\) 0 0
\(463\) −0.786155 0.786155i −0.0365357 0.0365357i 0.688603 0.725139i \(-0.258224\pi\)
−0.725139 + 0.688603i \(0.758224\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −19.6430 + 19.6430i −0.908970 + 0.908970i −0.996189 0.0872190i \(-0.972202\pi\)
0.0872190 + 0.996189i \(0.472202\pi\)
\(468\) 0 0
\(469\) 59.7132i 2.75730i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −23.0165 + 23.0165i −1.05830 + 1.05830i
\(474\) 0 0
\(475\) 13.0624 0.869539i 0.599346 0.0398972i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 30.6274 1.39940 0.699701 0.714436i \(-0.253316\pi\)
0.699701 + 0.714436i \(0.253316\pi\)
\(480\) 0 0
\(481\) −29.2327 −1.33290
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.05051 + 2.85420i 0.138517 + 0.129602i
\(486\) 0 0
\(487\) 24.7641 24.7641i 1.12217 1.12217i 0.130752 0.991415i \(-0.458261\pi\)
0.991415 0.130752i \(-0.0417392\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 23.3318i 1.05295i −0.850190 0.526475i \(-0.823513\pi\)
0.850190 0.526475i \(-0.176487\pi\)
\(492\) 0 0
\(493\) 18.8713 18.8713i 0.849921 0.849921i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.8787 + 17.8787i 0.801968 + 0.801968i
\(498\) 0 0
\(499\) −40.4051 −1.80878 −0.904389 0.426708i \(-0.859673\pi\)
−0.904389 + 0.426708i \(0.859673\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −0.160805 0.160805i −0.00716996 0.00716996i 0.703513 0.710683i \(-0.251614\pi\)
−0.710683 + 0.703513i \(0.751614\pi\)
\(504\) 0 0
\(505\) −3.30089 + 0.109745i −0.146888 + 0.00488360i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.4862i 0.509115i −0.967058 0.254558i \(-0.918070\pi\)
0.967058 0.254558i \(-0.0819299\pi\)
\(510\) 0 0
\(511\) 35.5134i 1.57102i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 21.0468 + 19.6924i 0.927434 + 0.867749i
\(516\) 0 0
\(517\) 3.03858 + 3.03858i 0.133637 + 0.133637i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −16.3744 −0.717374 −0.358687 0.933458i \(-0.616776\pi\)
−0.358687 + 0.933458i \(0.616776\pi\)
\(522\) 0 0
\(523\) 5.02638 + 5.02638i 0.219788 + 0.219788i 0.808409 0.588621i \(-0.200329\pi\)
−0.588621 + 0.808409i \(0.700329\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 9.23654 9.23654i 0.402350 0.402350i
\(528\) 0 0
\(529\) 17.6127i 0.765768i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.59619 + 6.59619i −0.285713 + 0.285713i
\(534\) 0 0
\(535\) 4.45405 4.76041i 0.192565 0.205810i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −58.0070 −2.49854
\(540\) 0 0
\(541\) −32.3302 −1.38998 −0.694992 0.719017i \(-0.744592\pi\)
−0.694992 + 0.719017i \(0.744592\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.720935 + 21.6841i 0.0308815 + 0.928846i
\(546\) 0 0
\(547\) −8.01165 + 8.01165i −0.342554 + 0.342554i −0.857327 0.514773i \(-0.827876\pi\)
0.514773 + 0.857327i \(0.327876\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 21.3977i 0.911573i
\(552\) 0 0
\(553\) 11.3137 11.3137i 0.481108 0.481108i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −0.138448 0.138448i −0.00586624 0.00586624i 0.704168 0.710034i \(-0.251320\pi\)
−0.710034 + 0.704168i \(0.751320\pi\)
\(558\) 0 0
\(559\) 25.9461 1.09740
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −14.7843 14.7843i −0.623082 0.623082i 0.323236 0.946318i \(-0.395229\pi\)
−0.946318 + 0.323236i \(0.895229\pi\)
\(564\) 0 0
\(565\) −10.0037 + 10.6918i −0.420858 + 0.449805i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 29.9558i 1.25581i −0.778288 0.627907i \(-0.783912\pi\)
0.778288 0.627907i \(-0.216088\pi\)
\(570\) 0 0
\(571\) 8.52134i 0.356607i 0.983976 + 0.178303i \(0.0570609\pi\)
−0.983976 + 0.178303i \(0.942939\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8.73314 7.64301i −0.364197 0.318736i
\(576\) 0 0
\(577\) 10.9779 + 10.9779i 0.457017 + 0.457017i 0.897675 0.440658i \(-0.145255\pi\)
−0.440658 + 0.897675i \(0.645255\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.49571 0.352461
\(582\) 0 0
\(583\) −34.9411 34.9411i −1.44711 1.44711i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.0174 18.0174i 0.743657 0.743657i −0.229623 0.973280i \(-0.573749\pi\)
0.973280 + 0.229623i \(0.0737492\pi\)
\(588\) 0 0
\(589\) 10.4731i 0.431536i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 25.8906 25.8906i 1.06320 1.06320i 0.0653359 0.997863i \(-0.479188\pi\)
0.997863 0.0653359i \(-0.0208119\pi\)
\(594\) 0 0
\(595\) 32.6200 1.08452i 1.33729 0.0444611i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.89517 −0.363447 −0.181723 0.983350i \(-0.558168\pi\)
−0.181723 + 0.983350i \(0.558168\pi\)
\(600\) 0 0
\(601\) 35.3393 1.44152 0.720761 0.693184i \(-0.243793\pi\)
0.720761 + 0.693184i \(0.243793\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 20.0641 0.667075i 0.815724 0.0271205i
\(606\) 0 0
\(607\) −4.90926 + 4.90926i −0.199261 + 0.199261i −0.799683 0.600422i \(-0.794999\pi\)
0.600422 + 0.799683i \(0.294999\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 3.42535i 0.138575i
\(612\) 0 0
\(613\) 1.87894 1.87894i 0.0758896 0.0758896i −0.668143 0.744033i \(-0.732911\pi\)
0.744033 + 0.668143i \(0.232911\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.07260 + 5.07260i 0.204215 + 0.204215i 0.801803 0.597588i \(-0.203874\pi\)
−0.597588 + 0.801803i \(0.703874\pi\)
\(618\) 0 0
\(619\) −46.2769 −1.86003 −0.930013 0.367527i \(-0.880204\pi\)
−0.930013 + 0.367527i \(0.880204\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −55.7352 55.7352i −2.23299 2.23299i
\(624\) 0 0
\(625\) 24.7794 3.31371i 0.991177 0.132548i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 26.7941i 1.06835i
\(630\) 0 0
\(631\) 36.6457i 1.45884i −0.684066 0.729421i \(-0.739790\pi\)
0.684066 0.729421i \(-0.260210\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −22.0355 + 23.5511i −0.874453 + 0.934598i
\(636\) 0 0
\(637\) 32.6952 + 32.6952i 1.29543 + 1.29543i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 12.1520 0.479976 0.239988 0.970776i \(-0.422857\pi\)
0.239988 + 0.970776i \(0.422857\pi\)
\(642\) 0 0
\(643\) 6.53122 + 6.53122i 0.257566 + 0.257566i 0.824064 0.566497i \(-0.191702\pi\)
−0.566497 + 0.824064i \(0.691702\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 17.6192 17.6192i 0.692681 0.692681i −0.270140 0.962821i \(-0.587070\pi\)
0.962821 + 0.270140i \(0.0870701\pi\)
\(648\) 0 0
\(649\) 21.8566i 0.857946i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.727677 + 0.727677i −0.0284762 + 0.0284762i −0.721202 0.692725i \(-0.756410\pi\)
0.692725 + 0.721202i \(0.256410\pi\)
\(654\) 0 0
\(655\) 0.926519 + 27.8676i 0.0362021 + 1.08888i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 44.9004 1.74907 0.874535 0.484963i \(-0.161167\pi\)
0.874535 + 0.484963i \(0.161167\pi\)
\(660\) 0 0
\(661\) 14.9320 0.580786 0.290393 0.956907i \(-0.406214\pi\)
0.290393 + 0.956907i \(0.406214\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 17.8787 19.1084i 0.693305 0.740991i
\(666\) 0 0
\(667\) −13.4130 + 13.4130i −0.519352 + 0.519352i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 54.8657i 2.11807i
\(672\) 0 0
\(673\) 2.55583 2.55583i 0.0985200 0.0985200i −0.656129 0.754649i \(-0.727807\pi\)
0.754649 + 0.656129i \(0.227807\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −17.7147 17.7147i −0.680832 0.680832i 0.279356 0.960188i \(-0.409879\pi\)
−0.960188 + 0.279356i \(0.909879\pi\)
\(678\) 0 0
\(679\) 8.35052 0.320464
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −11.3968 11.3968i −0.436086 0.436086i 0.454606 0.890693i \(-0.349780\pi\)
−0.890693 + 0.454606i \(0.849780\pi\)
\(684\) 0 0
\(685\) 10.6918 + 10.0037i 0.408511 + 0.382221i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 39.3886i 1.50058i
\(690\) 0 0
\(691\) 6.94671i 0.264265i −0.991232 0.132133i \(-0.957818\pi\)
0.991232 0.132133i \(-0.0421825\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.72093 0.223452i 0.254940 0.00847601i
\(696\) 0 0
\(697\) 6.04594 + 6.04594i 0.229006 + 0.229006i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 9.70621 0.366598 0.183299 0.983057i \(-0.441322\pi\)
0.183299 + 0.983057i \(0.441322\pi\)
\(702\) 0 0
\(703\) 15.1906 + 15.1906i 0.572924 + 0.572924i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.66817 + 4.66817i −0.175565 + 0.175565i
\(708\) 0 0
\(709\) 10.7414i 0.403401i −0.979447 0.201700i \(-0.935353\pi\)
0.979447 0.201700i \(-0.0646467\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −6.56496 + 6.56496i −0.245860 + 0.245860i
\(714\) 0 0
\(715\) −26.0018 24.3284i −0.972411 0.909832i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 43.8640 1.63585 0.817925 0.575325i \(-0.195124\pi\)
0.817925 + 0.575325i \(0.195124\pi\)
\(720\) 0 0
\(721\) 57.6139 2.14565
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.71411 40.7721i −0.100799 1.51424i
\(726\) 0 0
\(727\) −9.95522 + 9.95522i −0.369219 + 0.369219i −0.867192 0.497974i \(-0.834078\pi\)
0.497974 + 0.867192i \(0.334078\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 23.7817i 0.879599i
\(732\) 0 0
\(733\) 16.9924 16.9924i 0.627628 0.627628i −0.319843 0.947471i \(-0.603630\pi\)
0.947471 + 0.319843i \(0.103630\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −42.2236 42.2236i −1.55533 1.55533i
\(738\) 0 0
\(739\) −27.9025 −1.02641 −0.513205 0.858266i \(-0.671542\pi\)
−0.513205 + 0.858266i \(0.671542\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 20.2907 + 20.2907i 0.744395 + 0.744395i 0.973420 0.229025i \(-0.0735539\pi\)
−0.229025 + 0.973420i \(0.573554\pi\)
\(744\) 0 0
\(745\) 0.0110415 + 0.332104i 0.000404530 + 0.0121674i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 13.0312i 0.476150i
\(750\) 0 0
\(751\) 1.97054i 0.0719061i 0.999353 + 0.0359531i \(0.0114467\pi\)
−0.999353 + 0.0359531i \(0.988553\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.53211 46.0824i −0.0557591 1.67711i
\(756\) 0 0
\(757\) 9.13933 + 9.13933i 0.332175 + 0.332175i 0.853412 0.521237i \(-0.174529\pi\)
−0.521237 + 0.853412i \(0.674529\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 23.7800 0.862023 0.431011 0.902346i \(-0.358157\pi\)
0.431011 + 0.902346i \(0.358157\pi\)
\(762\) 0 0
\(763\) 30.6660 + 30.6660i 1.11018 + 1.11018i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.3193 12.3193i 0.444824 0.444824i
\(768\) 0 0
\(769\) 17.7022i 0.638359i −0.947694 0.319180i \(-0.896593\pi\)
0.947694 0.319180i \(-0.103407\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.30178 + 9.30178i −0.334562 + 0.334562i −0.854316 0.519754i \(-0.826024\pi\)
0.519754 + 0.854316i \(0.326024\pi\)
\(774\) 0 0
\(775\) −1.32842 19.9558i −0.0477181 0.716835i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.85534 0.245618
\(780\) 0 0
\(781\) −25.2843 −0.904742
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 22.5826 + 21.1293i 0.806008 + 0.754138i
\(786\) 0 0
\(787\) 18.1642 18.1642i 0.647484 0.647484i −0.304900 0.952384i \(-0.598623\pi\)
0.952384 + 0.304900i \(0.0986230\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 29.2678i 1.04064i
\(792\) 0 0
\(793\) −30.9246 + 30.9246i −1.09817 + 1.09817i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 4.75098 + 4.75098i 0.168289 + 0.168289i 0.786227 0.617938i \(-0.212032\pi\)
−0.617938 + 0.786227i \(0.712032\pi\)
\(798\) 0 0
\(799\) −3.13961 −0.111071
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 25.1118 + 25.1118i 0.886176 + 0.886176i