Properties

Label 1400.2.x.a.993.4
Level $1400$
Weight $2$
Character 1400.993
Analytic conductor $11.179$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1400.x (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1790562830\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: 16.0.29960650073923649536.7
Defining polynomial: \(x^{16} - 7 x^{12} + 40 x^{8} - 112 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{22} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 993.4
Root \(-1.32968 + 0.481610i\) of defining polynomial
Character \(\chi\) \(=\) 1400.993
Dual form 1400.2.x.a.657.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.848071 + 0.848071i) q^{3} +(2.61441 + 0.406039i) q^{7} +1.56155i q^{9} +O(q^{10})\) \(q+(-0.848071 + 0.848071i) q^{3} +(2.61441 + 0.406039i) q^{7} +1.56155i q^{9} -2.56155 q^{11} +(2.17238 - 2.17238i) q^{13} +(2.17238 + 2.17238i) q^{17} +8.54312 q^{19} +(-2.56155 + 1.87285i) q^{21} +(-5.03680 - 5.03680i) q^{23} +(-3.86852 - 3.86852i) q^{27} +5.68466i q^{29} +4.79741i q^{31} +(2.17238 - 2.17238i) q^{33} +(2.82843 - 2.82843i) q^{37} +3.68466i q^{39} +8.54312i q^{41} +(0.620058 + 0.620058i) q^{43} +(-0.848071 - 0.848071i) q^{47} +(6.67026 + 2.12311i) q^{49} -3.68466 q^{51} +(4.41674 + 4.41674i) q^{53} +(-7.24517 + 7.24517i) q^{57} +3.74571 q^{59} -4.79741i q^{61} +(-0.634052 + 4.08254i) q^{63} +(2.20837 - 2.20837i) q^{67} +8.54312 q^{69} -10.2462 q^{71} +(3.39228 - 3.39228i) q^{73} +(-6.69695 - 1.04009i) q^{77} +8.80776i q^{79} +1.87689 q^{81} +(-5.66906 + 5.66906i) q^{83} +(-4.82099 - 4.82099i) q^{87} +4.79741 q^{89} +(6.56155 - 4.79741i) q^{91} +(-4.06854 - 4.06854i) q^{93} +(13.3017 + 13.3017i) q^{97} -4.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 8q^{11} - 8q^{21} + 40q^{51} - 32q^{71} + 96q^{81} + 72q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) −0.848071 + 0.848071i −0.489634 + 0.489634i −0.908191 0.418557i \(-0.862536\pi\)
0.418557 + 0.908191i \(0.362536\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.61441 + 0.406039i 0.988154 + 0.153468i
\(8\) 0 0
\(9\) 1.56155i 0.520518i
\(10\) 0 0
\(11\) −2.56155 −0.772337 −0.386169 0.922428i \(-0.626202\pi\)
−0.386169 + 0.922428i \(0.626202\pi\)
\(12\) 0 0
\(13\) 2.17238 2.17238i 0.602509 0.602509i −0.338469 0.940978i \(-0.609909\pi\)
0.940978 + 0.338469i \(0.109909\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.17238 + 2.17238i 0.526879 + 0.526879i 0.919640 0.392761i \(-0.128480\pi\)
−0.392761 + 0.919640i \(0.628480\pi\)
\(18\) 0 0
\(19\) 8.54312 1.95993 0.979963 0.199181i \(-0.0638282\pi\)
0.979963 + 0.199181i \(0.0638282\pi\)
\(20\) 0 0
\(21\) −2.56155 + 1.87285i −0.558977 + 0.408690i
\(22\) 0 0
\(23\) −5.03680 5.03680i −1.05024 1.05024i −0.998669 0.0515755i \(-0.983576\pi\)
−0.0515755 0.998669i \(-0.516424\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.86852 3.86852i −0.744497 0.744497i
\(28\) 0 0
\(29\) 5.68466i 1.05561i 0.849364 + 0.527807i \(0.176986\pi\)
−0.849364 + 0.527807i \(0.823014\pi\)
\(30\) 0 0
\(31\) 4.79741i 0.861641i 0.902438 + 0.430820i \(0.141776\pi\)
−0.902438 + 0.430820i \(0.858224\pi\)
\(32\) 0 0
\(33\) 2.17238 2.17238i 0.378162 0.378162i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.82843 2.82843i 0.464991 0.464991i −0.435297 0.900287i \(-0.643356\pi\)
0.900287 + 0.435297i \(0.143356\pi\)
\(38\) 0 0
\(39\) 3.68466i 0.590018i
\(40\) 0 0
\(41\) 8.54312i 1.33421i 0.744963 + 0.667105i \(0.232467\pi\)
−0.744963 + 0.667105i \(0.767533\pi\)
\(42\) 0 0
\(43\) 0.620058 + 0.620058i 0.0945580 + 0.0945580i 0.752803 0.658245i \(-0.228701\pi\)
−0.658245 + 0.752803i \(0.728701\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.848071 0.848071i −0.123704 0.123704i 0.642545 0.766248i \(-0.277879\pi\)
−0.766248 + 0.642545i \(0.777879\pi\)
\(48\) 0 0
\(49\) 6.67026 + 2.12311i 0.952895 + 0.303301i
\(50\) 0 0
\(51\) −3.68466 −0.515955
\(52\) 0 0
\(53\) 4.41674 + 4.41674i 0.606686 + 0.606686i 0.942078 0.335393i \(-0.108869\pi\)
−0.335393 + 0.942078i \(0.608869\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −7.24517 + 7.24517i −0.959646 + 0.959646i
\(58\) 0 0
\(59\) 3.74571 0.487649 0.243825 0.969819i \(-0.421598\pi\)
0.243825 + 0.969819i \(0.421598\pi\)
\(60\) 0 0
\(61\) 4.79741i 0.614246i −0.951670 0.307123i \(-0.900634\pi\)
0.951670 0.307123i \(-0.0993662\pi\)
\(62\) 0 0
\(63\) −0.634052 + 4.08254i −0.0798830 + 0.514351i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 2.20837 2.20837i 0.269795 0.269795i −0.559222 0.829018i \(-0.688900\pi\)
0.829018 + 0.559222i \(0.188900\pi\)
\(68\) 0 0
\(69\) 8.54312 1.02847
\(70\) 0 0
\(71\) −10.2462 −1.21600 −0.608001 0.793936i \(-0.708028\pi\)
−0.608001 + 0.793936i \(0.708028\pi\)
\(72\) 0 0
\(73\) 3.39228 3.39228i 0.397037 0.397037i −0.480150 0.877186i \(-0.659418\pi\)
0.877186 + 0.480150i \(0.159418\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.69695 1.04009i −0.763188 0.118529i
\(78\) 0 0
\(79\) 8.80776i 0.990951i 0.868622 + 0.495475i \(0.165006\pi\)
−0.868622 + 0.495475i \(0.834994\pi\)
\(80\) 0 0
\(81\) 1.87689 0.208544
\(82\) 0 0
\(83\) −5.66906 + 5.66906i −0.622260 + 0.622260i −0.946109 0.323849i \(-0.895023\pi\)
0.323849 + 0.946109i \(0.395023\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.82099 4.82099i −0.516865 0.516865i
\(88\) 0 0
\(89\) 4.79741 0.508525 0.254262 0.967135i \(-0.418167\pi\)
0.254262 + 0.967135i \(0.418167\pi\)
\(90\) 0 0
\(91\) 6.56155 4.79741i 0.687838 0.502905i
\(92\) 0 0
\(93\) −4.06854 4.06854i −0.421888 0.421888i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.3017 + 13.3017i 1.35058 + 1.35058i 0.885009 + 0.465573i \(0.154152\pi\)
0.465573 + 0.885009i \(0.345848\pi\)
\(98\) 0 0
\(99\) 4.00000i 0.402015i
\(100\) 0 0
\(101\) 18.1379i 1.80479i 0.430907 + 0.902396i \(0.358194\pi\)
−0.430907 + 0.902396i \(0.641806\pi\)
\(102\) 0 0
\(103\) −9.53758 + 9.53758i −0.939766 + 0.939766i −0.998286 0.0585205i \(-0.981362\pi\)
0.0585205 + 0.998286i \(0.481362\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.86522 7.86522i 0.760360 0.760360i −0.216027 0.976387i \(-0.569310\pi\)
0.976387 + 0.216027i \(0.0693101\pi\)
\(108\) 0 0
\(109\) 9.68466i 0.927622i 0.885934 + 0.463811i \(0.153518\pi\)
−0.885934 + 0.463811i \(0.846482\pi\)
\(110\) 0 0
\(111\) 4.79741i 0.455350i
\(112\) 0 0
\(113\) 12.9020 + 12.9020i 1.21372 + 1.21372i 0.969794 + 0.243926i \(0.0784354\pi\)
0.243926 + 0.969794i \(0.421565\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.39228 + 3.39228i 0.313617 + 0.313617i
\(118\) 0 0
\(119\) 4.79741 + 6.56155i 0.439778 + 0.601497i
\(120\) 0 0
\(121\) −4.43845 −0.403495
\(122\) 0 0
\(123\) −7.24517 7.24517i −0.653275 0.653275i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −3.44849 + 3.44849i −0.306004 + 0.306004i −0.843357 0.537354i \(-0.819424\pi\)
0.537354 + 0.843357i \(0.319424\pi\)
\(128\) 0 0
\(129\) −1.05171 −0.0925975
\(130\) 0 0
\(131\) 1.05171i 0.0918880i −0.998944 0.0459440i \(-0.985370\pi\)
0.998944 0.0459440i \(-0.0146296\pi\)
\(132\) 0 0
\(133\) 22.3352 + 3.46884i 1.93671 + 0.300787i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.58831 + 1.58831i −0.135699 + 0.135699i −0.771693 0.635995i \(-0.780590\pi\)
0.635995 + 0.771693i \(0.280590\pi\)
\(138\) 0 0
\(139\) 3.74571 0.317707 0.158853 0.987302i \(-0.449220\pi\)
0.158853 + 0.987302i \(0.449220\pi\)
\(140\) 0 0
\(141\) 1.43845 0.121139
\(142\) 0 0
\(143\) −5.56466 + 5.56466i −0.465340 + 0.465340i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −7.45740 + 3.85631i −0.615076 + 0.318063i
\(148\) 0 0
\(149\) 12.2462i 1.00325i −0.865086 0.501624i \(-0.832736\pi\)
0.865086 0.501624i \(-0.167264\pi\)
\(150\) 0 0
\(151\) −4.31534 −0.351178 −0.175589 0.984464i \(-0.556183\pi\)
−0.175589 + 0.984464i \(0.556183\pi\)
\(152\) 0 0
\(153\) −3.39228 + 3.39228i −0.274250 + 0.274250i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −6.78456 6.78456i −0.541467 0.541467i 0.382492 0.923959i \(-0.375066\pi\)
−0.923959 + 0.382492i \(0.875066\pi\)
\(158\) 0 0
\(159\) −7.49141 −0.594108
\(160\) 0 0
\(161\) −11.1231 15.2134i −0.876624 1.19898i
\(162\) 0 0
\(163\) −13.5221 13.5221i −1.05913 1.05913i −0.998138 0.0609926i \(-0.980573\pi\)
−0.0609926 0.998138i \(-0.519427\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.63263 7.63263i −0.590631 0.590631i 0.347171 0.937802i \(-0.387142\pi\)
−0.937802 + 0.347171i \(0.887142\pi\)
\(168\) 0 0
\(169\) 3.56155i 0.273966i
\(170\) 0 0
\(171\) 13.3405i 1.02018i
\(172\) 0 0
\(173\) 9.90941 9.90941i 0.753399 0.753399i −0.221713 0.975112i \(-0.571165\pi\)
0.975112 + 0.221713i \(0.0711648\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.17662 + 3.17662i −0.238770 + 0.238770i
\(178\) 0 0
\(179\) 14.2462i 1.06481i −0.846489 0.532406i \(-0.821288\pi\)
0.846489 0.532406i \(-0.178712\pi\)
\(180\) 0 0
\(181\) 20.8319i 1.54843i −0.632925 0.774213i \(-0.718146\pi\)
0.632925 0.774213i \(-0.281854\pi\)
\(182\) 0 0
\(183\) 4.06854 + 4.06854i 0.300755 + 0.300755i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −5.56466 5.56466i −0.406928 0.406928i
\(188\) 0 0
\(189\) −8.54312 11.6847i −0.621420 0.849934i
\(190\) 0 0
\(191\) 14.5616 1.05364 0.526818 0.849978i \(-0.323385\pi\)
0.526818 + 0.849978i \(0.323385\pi\)
\(192\) 0 0
\(193\) −12.9020 12.9020i −0.928708 0.928708i 0.0689148 0.997623i \(-0.478046\pi\)
−0.997623 + 0.0689148i \(0.978046\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00505 6.00505i 0.427842 0.427842i −0.460051 0.887893i \(-0.652169\pi\)
0.887893 + 0.460051i \(0.152169\pi\)
\(198\) 0 0
\(199\) −17.0862 −1.21121 −0.605605 0.795765i \(-0.707069\pi\)
−0.605605 + 0.795765i \(0.707069\pi\)
\(200\) 0 0
\(201\) 3.74571i 0.264202i
\(202\) 0 0
\(203\) −2.30820 + 14.8620i −0.162004 + 1.04311i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 7.86522 7.86522i 0.546671 0.546671i
\(208\) 0 0
\(209\) −21.8836 −1.51372
\(210\) 0 0
\(211\) 20.1771 1.38905 0.694524 0.719470i \(-0.255615\pi\)
0.694524 + 0.719470i \(0.255615\pi\)
\(212\) 0 0
\(213\) 8.68951 8.68951i 0.595395 0.595395i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.94794 + 12.5424i −0.132235 + 0.851433i
\(218\) 0 0
\(219\) 5.75379i 0.388805i
\(220\) 0 0
\(221\) 9.43845 0.634899
\(222\) 0 0
\(223\) 12.9299 12.9299i 0.865848 0.865848i −0.126162 0.992010i \(-0.540266\pi\)
0.992010 + 0.126162i \(0.0402659\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 14.6260 + 14.6260i 0.970762 + 0.970762i 0.999585 0.0288226i \(-0.00917579\pi\)
−0.0288226 + 0.999585i \(0.509176\pi\)
\(228\) 0 0
\(229\) 8.54312 0.564545 0.282273 0.959334i \(-0.408912\pi\)
0.282273 + 0.959334i \(0.408912\pi\)
\(230\) 0 0
\(231\) 6.56155 4.79741i 0.431718 0.315646i
\(232\) 0 0
\(233\) −16.9706 16.9706i −1.11178 1.11178i −0.992910 0.118869i \(-0.962073\pi\)
−0.118869 0.992910i \(-0.537927\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −7.46960 7.46960i −0.485203 0.485203i
\(238\) 0 0
\(239\) 0.807764i 0.0522499i −0.999659 0.0261250i \(-0.991683\pi\)
0.999659 0.0261250i \(-0.00831678\pi\)
\(240\) 0 0
\(241\) 16.0345i 1.03287i −0.856325 0.516437i \(-0.827258\pi\)
0.856325 0.516437i \(-0.172742\pi\)
\(242\) 0 0
\(243\) 10.0138 10.0138i 0.642387 0.642387i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 18.5589 18.5589i 1.18087 1.18087i
\(248\) 0 0
\(249\) 9.61553i 0.609359i
\(250\) 0 0
\(251\) 3.74571i 0.236427i 0.992988 + 0.118213i \(0.0377167\pi\)
−0.992988 + 0.118213i \(0.962283\pi\)
\(252\) 0 0
\(253\) 12.9020 + 12.9020i 0.811143 + 0.811143i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.68951 + 8.68951i 0.542037 + 0.542037i 0.924126 0.382089i \(-0.124795\pi\)
−0.382089 + 0.924126i \(0.624795\pi\)
\(258\) 0 0
\(259\) 8.54312 6.24621i 0.530843 0.388121i
\(260\) 0 0
\(261\) −8.87689 −0.549466
\(262\) 0 0
\(263\) −12.2820 12.2820i −0.757338 0.757338i 0.218499 0.975837i \(-0.429884\pi\)
−0.975837 + 0.218499i \(0.929884\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −4.06854 + 4.06854i −0.248991 + 0.248991i
\(268\) 0 0
\(269\) −17.0862 −1.04177 −0.520883 0.853628i \(-0.674397\pi\)
−0.520883 + 0.853628i \(0.674397\pi\)
\(270\) 0 0
\(271\) 21.8836i 1.32934i −0.747139 0.664668i \(-0.768573\pi\)
0.747139 0.664668i \(-0.231427\pi\)
\(272\) 0 0
\(273\) −1.49612 + 9.63320i −0.0905491 + 0.583028i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 4.41674 4.41674i 0.265376 0.265376i −0.561858 0.827234i \(-0.689913\pi\)
0.827234 + 0.561858i \(0.189913\pi\)
\(278\) 0 0
\(279\) −7.49141 −0.448499
\(280\) 0 0
\(281\) 4.56155 0.272119 0.136060 0.990701i \(-0.456556\pi\)
0.136060 + 0.990701i \(0.456556\pi\)
\(282\) 0 0
\(283\) −12.9299 + 12.9299i −0.768601 + 0.768601i −0.977860 0.209260i \(-0.932895\pi\)
0.209260 + 0.977860i \(0.432895\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.46884 + 22.3352i −0.204759 + 1.31841i
\(288\) 0 0
\(289\) 7.56155i 0.444797i
\(290\) 0 0
\(291\) −22.5616 −1.32258
\(292\) 0 0
\(293\) 3.12485 3.12485i 0.182556 0.182556i −0.609913 0.792469i \(-0.708796\pi\)
0.792469 + 0.609913i \(0.208796\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 9.90941 + 9.90941i 0.575003 + 0.575003i
\(298\) 0 0
\(299\) −21.8836 −1.26556
\(300\) 0 0
\(301\) 1.36932 + 1.87285i 0.0789261 + 0.107949i
\(302\) 0 0
\(303\) −15.3823 15.3823i −0.883687 0.883687i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −9.32878 9.32878i −0.532421 0.532421i 0.388871 0.921292i \(-0.372865\pi\)
−0.921292 + 0.388871i \(0.872865\pi\)
\(308\) 0 0
\(309\) 16.1771i 0.920282i
\(310\) 0 0
\(311\) 12.2888i 0.696835i −0.937339 0.348418i \(-0.886719\pi\)
0.937339 0.348418i \(-0.113281\pi\)
\(312\) 0 0
\(313\) −21.0387 + 21.0387i −1.18918 + 1.18918i −0.211885 + 0.977295i \(0.567960\pi\)
−0.977295 + 0.211885i \(0.932040\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 24.5639 24.5639i 1.37965 1.37965i 0.534443 0.845205i \(-0.320522\pi\)
0.845205 0.534443i \(-0.179478\pi\)
\(318\) 0 0
\(319\) 14.5616i 0.815290i
\(320\) 0 0
\(321\) 13.3405i 0.744596i
\(322\) 0 0
\(323\) 18.5589 + 18.5589i 1.03264 + 1.03264i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −8.21327 8.21327i −0.454195 0.454195i
\(328\) 0 0
\(329\) −1.87285 2.56155i −0.103254 0.141223i
\(330\) 0 0
\(331\) 26.7386 1.46969 0.734844 0.678236i \(-0.237255\pi\)
0.734844 + 0.678236i \(0.237255\pi\)
\(332\) 0 0
\(333\) 4.41674 + 4.41674i 0.242036 + 0.242036i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −20.1472 + 20.1472i −1.09749 + 1.09749i −0.102783 + 0.994704i \(0.532775\pi\)
−0.994704 + 0.102783i \(0.967225\pi\)
\(338\) 0 0
\(339\) −21.8836 −1.18856
\(340\) 0 0
\(341\) 12.2888i 0.665477i
\(342\) 0 0
\(343\) 16.5767 + 8.25906i 0.895059 + 0.445947i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.79668 + 3.79668i −0.203816 + 0.203816i −0.801633 0.597816i \(-0.796035\pi\)
0.597816 + 0.801633i \(0.296035\pi\)
\(348\) 0 0
\(349\) −8.54312 −0.457303 −0.228651 0.973508i \(-0.573432\pi\)
−0.228651 + 0.973508i \(0.573432\pi\)
\(350\) 0 0
\(351\) −16.8078 −0.897132
\(352\) 0 0
\(353\) 8.00447 8.00447i 0.426035 0.426035i −0.461240 0.887275i \(-0.652595\pi\)
0.887275 + 0.461240i \(0.152595\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −9.63320 1.49612i −0.509843 0.0791829i
\(358\) 0 0
\(359\) 22.7386i 1.20010i −0.799963 0.600050i \(-0.795148\pi\)
0.799963 0.600050i \(-0.204852\pi\)
\(360\) 0 0
\(361\) 53.9848 2.84131
\(362\) 0 0
\(363\) 3.76412 3.76412i 0.197565 0.197565i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.24035 + 4.24035i 0.221345 + 0.221345i 0.809064 0.587720i \(-0.199974\pi\)
−0.587720 + 0.809064i \(0.699974\pi\)
\(368\) 0 0
\(369\) −13.3405 −0.694480
\(370\) 0 0
\(371\) 9.75379 + 13.3405i 0.506391 + 0.692606i
\(372\) 0 0
\(373\) −14.1421 14.1421i −0.732252 0.732252i 0.238813 0.971065i \(-0.423242\pi\)
−0.971065 + 0.238813i \(0.923242\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 12.3492 + 12.3492i 0.636017 + 0.636017i
\(378\) 0 0
\(379\) 9.75379i 0.501018i −0.968114 0.250509i \(-0.919402\pi\)
0.968114 0.250509i \(-0.0805980\pi\)
\(380\) 0 0
\(381\) 5.84912i 0.299659i
\(382\) 0 0
\(383\) 3.76412 3.76412i 0.192337 0.192337i −0.604368 0.796705i \(-0.706574\pi\)
0.796705 + 0.604368i \(0.206574\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −0.968253 + 0.968253i −0.0492191 + 0.0492191i
\(388\) 0 0
\(389\) 24.5616i 1.24532i 0.782492 + 0.622660i \(0.213948\pi\)
−0.782492 + 0.622660i \(0.786052\pi\)
\(390\) 0 0
\(391\) 21.8836i 1.10670i
\(392\) 0 0
\(393\) 0.891921 + 0.891921i 0.0449914 + 0.0449914i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −10.8619 10.8619i −0.545142 0.545142i 0.379889 0.925032i \(-0.375962\pi\)
−0.925032 + 0.379889i \(0.875962\pi\)
\(398\) 0 0
\(399\) −21.8836 + 16.0000i −1.09555 + 0.801002i
\(400\) 0 0
\(401\) −27.9309 −1.39480 −0.697401 0.716682i \(-0.745660\pi\)
−0.697401 + 0.716682i \(0.745660\pi\)
\(402\) 0 0
\(403\) 10.4218 + 10.4218i 0.519146 + 0.519146i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.24517 + 7.24517i −0.359130 + 0.359130i
\(408\) 0 0
\(409\) 5.84912 0.289220 0.144610 0.989489i \(-0.453807\pi\)
0.144610 + 0.989489i \(0.453807\pi\)
\(410\) 0 0
\(411\) 2.69400i 0.132885i
\(412\) 0 0
\(413\) 9.79280 + 1.52090i 0.481872 + 0.0748388i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −3.17662 + 3.17662i −0.155560 + 0.155560i
\(418\) 0 0
\(419\) −13.3405 −0.651727 −0.325864 0.945417i \(-0.605655\pi\)
−0.325864 + 0.945417i \(0.605655\pi\)
\(420\) 0 0
\(421\) 1.68466 0.0821052 0.0410526 0.999157i \(-0.486929\pi\)
0.0410526 + 0.999157i \(0.486929\pi\)
\(422\) 0 0
\(423\) 1.32431 1.32431i 0.0643900 0.0643900i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.94794 12.5424i 0.0942673 0.606969i
\(428\) 0 0
\(429\) 9.43845i 0.455693i
\(430\) 0 0
\(431\) −22.5616 −1.08675 −0.543376 0.839490i \(-0.682854\pi\)
−0.543376 + 0.839490i \(0.682854\pi\)
\(432\) 0 0
\(433\) −20.7713 + 20.7713i −0.998205 + 0.998205i −0.999998 0.00179335i \(-0.999429\pi\)
0.00179335 + 0.999998i \(0.499429\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −43.0299 43.0299i −2.05840 2.05840i
\(438\) 0 0
\(439\) 24.5776 1.17303 0.586513 0.809939i \(-0.300500\pi\)
0.586513 + 0.809939i \(0.300500\pi\)
\(440\) 0 0
\(441\) −3.31534 + 10.4160i −0.157873 + 0.495999i
\(442\) 0 0
\(443\) −22.0074 22.0074i −1.04560 1.04560i −0.998909 0.0466918i \(-0.985132\pi\)
−0.0466918 0.998909i \(-0.514868\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 10.3857 + 10.3857i 0.491224 + 0.491224i
\(448\) 0 0
\(449\) 17.0540i 0.804827i −0.915458 0.402413i \(-0.868171\pi\)
0.915458 0.402413i \(-0.131829\pi\)
\(450\) 0 0
\(451\) 21.8836i 1.03046i
\(452\) 0 0
\(453\) 3.65971 3.65971i 0.171948 0.171948i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 15.3823 15.3823i 0.719551 0.719551i −0.248962 0.968513i \(-0.580089\pi\)
0.968513 + 0.248962i \(0.0800894\pi\)
\(458\) 0 0
\(459\) 16.8078i 0.784519i
\(460\) 0 0
\(461\) 11.2371i 0.523365i 0.965154 + 0.261682i \(0.0842773\pi\)
−0.965154 + 0.261682i \(0.915723\pi\)
\(462\) 0 0
\(463\) 25.1840 + 25.1840i 1.17040 + 1.17040i 0.982115 + 0.188284i \(0.0602926\pi\)
0.188284 + 0.982115i \(0.439707\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 14.6260 + 14.6260i 0.676811 + 0.676811i 0.959277 0.282466i \(-0.0911526\pi\)
−0.282466 + 0.959277i \(0.591153\pi\)
\(468\) 0 0
\(469\) 6.67026 4.87689i 0.308004 0.225194i
\(470\) 0 0
\(471\) 11.5076 0.530241
\(472\) 0 0
\(473\) −1.58831 1.58831i −0.0730306 0.0730306i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −6.89697 + 6.89697i −0.315791 + 0.315791i
\(478\) 0 0
\(479\) 38.9699 1.78058 0.890290 0.455395i \(-0.150502\pi\)
0.890290 + 0.455395i \(0.150502\pi\)
\(480\) 0 0
\(481\) 12.2888i 0.560322i
\(482\) 0 0
\(483\) 22.3352 + 3.46884i 1.01629 + 0.157838i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −13.5221 + 13.5221i −0.612744 + 0.612744i −0.943660 0.330916i \(-0.892642\pi\)
0.330916 + 0.943660i \(0.392642\pi\)
\(488\) 0 0
\(489\) 22.9354 1.03717
\(490\) 0 0
\(491\) −7.68466 −0.346804 −0.173402 0.984851i \(-0.555476\pi\)
−0.173402 + 0.984851i \(0.555476\pi\)
\(492\) 0 0
\(493\) −12.3492 + 12.3492i −0.556181 + 0.556181i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −26.7878 4.16037i −1.20160 0.186618i
\(498\) 0 0
\(499\) 36.8078i 1.64774i 0.566777 + 0.823871i \(0.308190\pi\)
−0.566777 + 0.823871i \(0.691810\pi\)
\(500\) 0 0
\(501\) 12.9460 0.578386
\(502\) 0 0
\(503\) −7.84144 + 7.84144i −0.349632 + 0.349632i −0.859973 0.510340i \(-0.829520\pi\)
0.510340 + 0.859973i \(0.329520\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −3.02045 3.02045i −0.134143 0.134143i
\(508\) 0 0
\(509\) −20.8319 −0.923359 −0.461680 0.887047i \(-0.652753\pi\)
−0.461680 + 0.887047i \(0.652753\pi\)
\(510\) 0 0
\(511\) 10.2462 7.49141i 0.453266 0.331401i
\(512\) 0 0
\(513\) −33.0492 33.0492i −1.45916 1.45916i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 2.17238 + 2.17238i 0.0955410 + 0.0955410i
\(518\) 0 0
\(519\) 16.8078i 0.737779i
\(520\) 0 0
\(521\) 19.7802i 0.866588i 0.901253 + 0.433294i \(0.142649\pi\)
−0.901253 + 0.433294i \(0.857351\pi\)
\(522\) 0 0
\(523\) 12.4536 12.4536i 0.544559 0.544559i −0.380303 0.924862i \(-0.624180\pi\)
0.924862 + 0.380303i \(0.124180\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.4218 + 10.4218i −0.453980 + 0.453980i
\(528\) 0 0
\(529\) 27.7386i 1.20603i
\(530\) 0 0
\(531\) 5.84912i 0.253830i
\(532\) 0 0
\(533\) 18.5589 + 18.5589i 0.803874 + 0.803874i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 12.0818 + 12.0818i 0.521368 + 0.521368i
\(538\) 0 0
\(539\) −17.0862 5.43845i −0.735956 0.234251i
\(540\) 0 0
\(541\) −0.0691303 −0.00297214 −0.00148607 0.999999i \(-0.500473\pi\)
−0.00148607 + 0.999999i \(0.500473\pi\)
\(542\) 0 0
\(543\) 17.6670 + 17.6670i 0.758162 + 0.758162i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −19.5271 + 19.5271i −0.834920 + 0.834920i −0.988185 0.153265i \(-0.951021\pi\)
0.153265 + 0.988185i \(0.451021\pi\)
\(548\) 0 0
\(549\) 7.49141 0.319726
\(550\) 0 0
\(551\) 48.5647i 2.06893i
\(552\) 0 0
\(553\) −3.57630 + 23.0271i −0.152080 + 0.979212i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 27.7405 27.7405i 1.17540 1.17540i 0.194503 0.980902i \(-0.437691\pi\)
0.980902 0.194503i \(-0.0623093\pi\)
\(558\) 0 0
\(559\) 2.69400 0.113944
\(560\) 0 0
\(561\) 9.43845 0.398492
\(562\) 0 0
\(563\) 23.7917 23.7917i 1.00270 1.00270i 0.00270634 0.999996i \(-0.499139\pi\)
0.999996 0.00270634i \(-0.000861457\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.90697 + 0.762093i 0.206073 + 0.0320049i
\(568\) 0 0
\(569\) 12.7386i 0.534031i 0.963692 + 0.267016i \(0.0860375\pi\)
−0.963692 + 0.267016i \(0.913962\pi\)
\(570\) 0 0
\(571\) −38.2462 −1.60055 −0.800277 0.599630i \(-0.795314\pi\)
−0.800277 + 0.599630i \(0.795314\pi\)
\(572\) 0 0
\(573\) −12.3492 + 12.3492i −0.515896 + 0.515896i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 16.6940 + 16.6940i 0.694979 + 0.694979i 0.963323 0.268344i \(-0.0864763\pi\)
−0.268344 + 0.963323i \(0.586476\pi\)
\(578\) 0 0
\(579\) 21.8836 0.909453
\(580\) 0 0
\(581\) −17.1231 + 12.5194i −0.710386 + 0.519391i
\(582\) 0 0
\(583\) −11.3137 11.3137i −0.468566 0.468566i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.41273 + 6.41273i 0.264682 + 0.264682i 0.826953 0.562271i \(-0.190072\pi\)
−0.562271 + 0.826953i \(0.690072\pi\)
\(588\) 0 0
\(589\) 40.9848i 1.68875i
\(590\) 0 0
\(591\) 10.1854i 0.418972i
\(592\) 0 0
\(593\) −19.1338 + 19.1338i −0.785730 + 0.785730i −0.980791 0.195061i \(-0.937510\pi\)
0.195061 + 0.980791i \(0.437510\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 14.4903 14.4903i 0.593050 0.593050i
\(598\) 0 0
\(599\) 35.6847i 1.45804i −0.684495 0.729018i \(-0.739977\pi\)
0.684495 0.729018i \(-0.260023\pi\)
\(600\) 0 0
\(601\) 22.9354i 0.935552i −0.883847 0.467776i \(-0.845055\pi\)
0.883847 0.467776i \(-0.154945\pi\)
\(602\) 0 0
\(603\) 3.44849 + 3.44849i 0.140433 + 0.140433i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 7.84144 + 7.84144i 0.318274 + 0.318274i 0.848104 0.529830i \(-0.177744\pi\)
−0.529830 + 0.848104i \(0.677744\pi\)
\(608\) 0 0
\(609\) −10.6465 14.5616i −0.431419 0.590064i
\(610\) 0 0
\(611\) −3.68466 −0.149065
\(612\) 0 0
\(613\) −21.3873 21.3873i −0.863825 0.863825i 0.127955 0.991780i \(-0.459159\pi\)
−0.991780 + 0.127955i \(0.959159\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(618\) 0 0
\(619\) 44.8190 1.80143 0.900714 0.434413i \(-0.143044\pi\)
0.900714 + 0.434413i \(0.143044\pi\)
\(620\) 0 0
\(621\) 38.9699i 1.56381i
\(622\) 0 0
\(623\) 12.5424 + 1.94794i 0.502500 + 0.0780425i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 18.5589 18.5589i 0.741170 0.741170i
\(628\) 0 0
\(629\) 12.2888 0.489987
\(630\) 0 0
\(631\) 0.807764 0.0321566 0.0160783 0.999871i \(-0.494882\pi\)
0.0160783 + 0.999871i \(0.494882\pi\)
\(632\) 0 0
\(633\) −17.1116 + 17.1116i −0.680125 + 0.680125i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 19.1025 9.87814i 0.756869 0.391386i
\(638\) 0 0
\(639\) 16.0000i 0.632950i
\(640\) 0 0
\(641\) −4.73863 −0.187165 −0.0935824 0.995612i \(-0.529832\pi\)
−0.0935824 + 0.995612i \(0.529832\pi\)
\(642\) 0 0
\(643\) 19.9232 19.9232i 0.785696 0.785696i −0.195090 0.980785i \(-0.562500\pi\)
0.980785 + 0.195090i \(0.0624998\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 21.1431 + 21.1431i 0.831222 + 0.831222i 0.987684 0.156462i \(-0.0500087\pi\)
−0.156462 + 0.987684i \(0.550009\pi\)
\(648\) 0 0
\(649\) −9.59482 −0.376630
\(650\) 0 0
\(651\) −8.98485 12.2888i −0.352144 0.481637i
\(652\) 0 0
\(653\) −14.1421 14.1421i −0.553425 0.553425i 0.374003 0.927428i \(-0.377985\pi\)
−0.927428 + 0.374003i \(0.877985\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 5.29723 + 5.29723i 0.206665 + 0.206665i
\(658\) 0 0
\(659\) 1.93087i 0.0752160i 0.999293 + 0.0376080i \(0.0119738\pi\)
−0.999293 + 0.0376080i \(0.988026\pi\)
\(660\) 0 0
\(661\) 43.7673i 1.70235i −0.524882 0.851175i \(-0.675890\pi\)
0.524882 0.851175i \(-0.324110\pi\)
\(662\) 0 0
\(663\) −8.00447 + 8.00447i −0.310868 + 0.310868i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 28.6325 28.6325i 1.10865 1.10865i
\(668\) 0 0
\(669\) 21.9309i 0.847896i
\(670\) 0 0
\(671\) 12.2888i 0.474405i
\(672\) 0 0
\(673\) −24.9121 24.9121i −0.960292 0.960292i 0.0389496 0.999241i \(-0.487599\pi\)
−0.999241 + 0.0389496i \(0.987599\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −30.6807 30.6807i −1.17916 1.17916i −0.979960 0.199196i \(-0.936167\pi\)
−0.199196 0.979960i \(-0.563833\pi\)
\(678\) 0 0
\(679\) 29.3751 + 40.1771i 1.12731 + 1.54185i
\(680\) 0 0
\(681\) −24.8078 −0.950636
\(682\) 0 0
\(683\) −13.8703 13.8703i −0.530731 0.530731i 0.390059 0.920790i \(-0.372455\pi\)
−0.920790 + 0.390059i \(0.872455\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −7.24517 + 7.24517i −0.276420 + 0.276420i
\(688\) 0 0
\(689\) 19.1896 0.731067
\(690\) 0 0
\(691\) 13.3405i 0.507498i 0.967270 + 0.253749i \(0.0816637\pi\)
−0.967270 + 0.253749i \(0.918336\pi\)
\(692\) 0 0
\(693\) 1.62416 10.4576i 0.0616966 0.397253i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −18.5589 + 18.5589i −0.702967 + 0.702967i
\(698\) 0 0
\(699\) 28.7845 1.08873
\(700\) 0 0
\(701\) 12.0691 0.455845 0.227922 0.973679i \(-0.426807\pi\)
0.227922 + 0.973679i \(0.426807\pi\)
\(702\) 0 0
\(703\) 24.1636 24.1636i 0.911347 0.911347i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.36472 + 47.4200i −0.276979 + 1.78341i
\(708\) 0 0
\(709\) 9.19224i 0.345222i −0.984990 0.172611i \(-0.944780\pi\)
0.984990 0.172611i \(-0.0552203\pi\)
\(710\) 0 0
\(711\) −13.7538 −0.515807
\(712\) 0 0
\(713\) 24.1636 24.1636i 0.904933 0.904933i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.685041 + 0.685041i 0.0255833 + 0.0255833i
\(718\) 0 0
\(719\) −14.3922 −0.536740 −0.268370 0.963316i \(-0.586485\pi\)
−0.268370 + 0.963316i \(0.586485\pi\)
\(720\) 0 0
\(721\) −28.8078 + 21.0625i −1.07286 + 0.784408i
\(722\) 0 0
\(723\) 13.5984 + 13.5984i 0.505730 + 0.505730i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −21.1431 21.1431i −0.784155 0.784155i 0.196374 0.980529i \(-0.437083\pi\)
−0.980529 + 0.196374i \(0.937083\pi\)
\(728\) 0 0
\(729\) 22.6155i 0.837612i
\(730\) 0 0
\(731\) 2.69400i 0.0996412i
\(732\) 0 0
\(733\) 29.7282 29.7282i 1.09804 1.09804i 0.103398 0.994640i \(-0.467029\pi\)
0.994640 0.103398i \(-0.0329714\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.65685 + 5.65685i −0.208373 + 0.208373i
\(738\) 0 0
\(739\) 22.4233i 0.824854i 0.910991 + 0.412427i \(0.135319\pi\)
−0.910991 + 0.412427i \(0.864681\pi\)
\(740\) 0 0
\(741\) 31.4785i 1.15639i
\(742\) 0 0
\(743\) −0.968253 0.968253i −0.0355218 0.0355218i 0.689123 0.724645i \(-0.257996\pi\)
−0.724645 + 0.689123i \(0.757996\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −8.85254 8.85254i −0.323897 0.323897i
\(748\) 0 0
\(749\) 23.7565 17.3693i 0.868044 0.634661i
\(750\) 0 0
\(751\) 38.5616 1.40713 0.703566 0.710630i \(-0.251590\pi\)
0.703566 + 0.710630i \(0.251590\pi\)
\(752\) 0 0
\(753\) −3.17662 3.17662i −0.115763 0.115763i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.24012 + 1.24012i −0.0450728 + 0.0450728i −0.729284 0.684211i \(-0.760147\pi\)
0.684211 + 0.729284i \(0.260147\pi\)
\(758\) 0 0
\(759\) −21.8836 −0.794326
\(760\) 0 0
\(761\) 21.8836i 0.793282i 0.917974 + 0.396641i \(0.129824\pi\)
−0.917974 + 0.396641i \(0.870176\pi\)
\(762\) 0 0
\(763\) −3.93235 + 25.3197i −0.142361 + 0.916633i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.13709 8.13709i 0.293813 0.293813i
\(768\) 0 0
\(769\) 41.6639 1.50244 0.751219 0.660053i \(-0.229466\pi\)
0.751219 + 0.660053i \(0.229466\pi\)
\(770\) 0 0
\(771\) −14.7386 −0.530799
\(772\) 0 0
\(773\) −26.8708 + 26.8708i −0.966476 + 0.966476i −0.999456 0.0329796i \(-0.989500\pi\)
0.0329796 + 0.999456i \(0.489500\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −1.94794 + 12.5424i −0.0698819 + 0.449956i
\(778\) 0 0
\(779\) 72.9848i 2.61495i
\(780\) 0 0
\(781\) 26.2462 0.939163
\(782\) 0 0
\(783\) 21.9912 21.9912i 0.785902 0.785902i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −6.14530 6.14530i −0.219056 0.219056i 0.589044 0.808101i \(-0.299504\pi\)
−0.808101 + 0.589044i \(0.799504\pi\)
\(788\) 0 0
\(789\) 20.8319 0.741637
\(790\) 0 0
\(791\) 28.4924 + 38.9699i 1.01307 + 1.38561i
\(792\) 0 0
\(793\) −10.4218 10.4218i −0.370089 0.370089i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −37.4653 37.4653i −1.32709 1.32709i −0.907899 0.419190i \(-0.862314\pi\)
−0.419190 0.907899i \(-0.637686\pi\)
\(798\) 0 0
\(799\) 3.68466i 0.130354i
\(800\) 0 0
\(801\) 7.49141i 0.264696i
\(802\) 0 0
\(803\) −8.68951 + 8.68951i −0.306646 + 0.306646