Properties

Label 920.2.e.b.369.13
Level $920$
Weight $2$
Character 920.369
Analytic conductor $7.346$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} - 20 x^{3} + 64 x^{2} - 32 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.13
Root \(0.285770 + 0.285770i\) of defining polynomial
Character \(\chi\) \(=\) 920.369
Dual form 920.2.e.b.369.2

$q$-expansion

\(f(q)\) \(=\) \(q+2.49931i q^{3} +(2.11714 + 0.719533i) q^{5} +2.92777i q^{7} -3.24657 q^{9} +O(q^{10})\) \(q+2.49931i q^{3} +(2.11714 + 0.719533i) q^{5} +2.92777i q^{7} -3.24657 q^{9} -4.10909 q^{11} +0.0122971i q^{13} +(-1.79834 + 5.29139i) q^{15} +0.155378i q^{17} -4.32471 q^{19} -7.31743 q^{21} +1.00000i q^{23} +(3.96454 + 3.04670i) q^{25} -0.616262i q^{27} +6.79978 q^{29} +2.20713 q^{31} -10.2699i q^{33} +(-2.10663 + 6.19850i) q^{35} -4.60741i q^{37} -0.0307342 q^{39} -7.67826 q^{41} -8.38997i q^{43} +(-6.87344 - 2.33602i) q^{45} +6.38116i q^{47} -1.57186 q^{49} -0.388339 q^{51} +7.80358i q^{53} +(-8.69951 - 2.95662i) q^{55} -10.8088i q^{57} +14.1275 q^{59} +7.05297 q^{61} -9.50523i q^{63} +(-0.00884814 + 0.0260346i) q^{65} +7.31363i q^{67} -2.49931 q^{69} -5.84061 q^{71} -0.727674i q^{73} +(-7.61466 + 9.90864i) q^{75} -12.0305i q^{77} -4.81003 q^{79} -8.19948 q^{81} -7.75797i q^{83} +(-0.111800 + 0.328957i) q^{85} +16.9948i q^{87} -6.77560 q^{89} -0.0360030 q^{91} +5.51631i q^{93} +(-9.15602 - 3.11177i) q^{95} +14.8705i q^{97} +13.3405 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 14q + 2q^{5} - 4q^{9} - 14q^{11} - 6q^{15} + 14q^{19} - 12q^{21} - 14q^{25} + 22q^{29} - 20q^{31} - 2q^{35} + 48q^{39} - 32q^{41} - 26q^{45} + 34q^{49} - 14q^{51} - 38q^{55} + 22q^{59} + 10q^{61} - 38q^{65} + 6q^{69} - 28q^{71} - 24q^{75} + 64q^{79} - 10q^{81} - 50q^{85} + 48q^{89} - 14q^{91} - 30q^{95} + 122q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.49931i 1.44298i 0.692425 + 0.721490i \(0.256542\pi\)
−0.692425 + 0.721490i \(0.743458\pi\)
\(4\) 0 0
\(5\) 2.11714 + 0.719533i 0.946813 + 0.321785i
\(6\) 0 0
\(7\) 2.92777i 1.10659i 0.832984 + 0.553297i \(0.186631\pi\)
−0.832984 + 0.553297i \(0.813369\pi\)
\(8\) 0 0
\(9\) −3.24657 −1.08219
\(10\) 0 0
\(11\) −4.10909 −1.23894 −0.619468 0.785022i \(-0.712652\pi\)
−0.619468 + 0.785022i \(0.712652\pi\)
\(12\) 0 0
\(13\) 0.0122971i 0.00341059i 0.999999 + 0.00170530i \(0.000542813\pi\)
−0.999999 + 0.00170530i \(0.999457\pi\)
\(14\) 0 0
\(15\) −1.79834 + 5.29139i −0.464329 + 1.36623i
\(16\) 0 0
\(17\) 0.155378i 0.0376847i 0.999822 + 0.0188424i \(0.00599807\pi\)
−0.999822 + 0.0188424i \(0.994002\pi\)
\(18\) 0 0
\(19\) −4.32471 −0.992158 −0.496079 0.868277i \(-0.665227\pi\)
−0.496079 + 0.868277i \(0.665227\pi\)
\(20\) 0 0
\(21\) −7.31743 −1.59679
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 3.96454 + 3.04670i 0.792909 + 0.609340i
\(26\) 0 0
\(27\) 0.616262i 0.118600i
\(28\) 0 0
\(29\) 6.79978 1.26269 0.631344 0.775503i \(-0.282504\pi\)
0.631344 + 0.775503i \(0.282504\pi\)
\(30\) 0 0
\(31\) 2.20713 0.396412 0.198206 0.980160i \(-0.436489\pi\)
0.198206 + 0.980160i \(0.436489\pi\)
\(32\) 0 0
\(33\) 10.2699i 1.78776i
\(34\) 0 0
\(35\) −2.10663 + 6.19850i −0.356085 + 1.04774i
\(36\) 0 0
\(37\) 4.60741i 0.757453i −0.925509 0.378726i \(-0.876362\pi\)
0.925509 0.378726i \(-0.123638\pi\)
\(38\) 0 0
\(39\) −0.0307342 −0.00492142
\(40\) 0 0
\(41\) −7.67826 −1.19914 −0.599571 0.800321i \(-0.704662\pi\)
−0.599571 + 0.800321i \(0.704662\pi\)
\(42\) 0 0
\(43\) 8.38997i 1.27946i −0.768600 0.639729i \(-0.779046\pi\)
0.768600 0.639729i \(-0.220954\pi\)
\(44\) 0 0
\(45\) −6.87344 2.33602i −1.02463 0.348233i
\(46\) 0 0
\(47\) 6.38116i 0.930787i 0.885104 + 0.465394i \(0.154087\pi\)
−0.885104 + 0.465394i \(0.845913\pi\)
\(48\) 0 0
\(49\) −1.57186 −0.224551
\(50\) 0 0
\(51\) −0.388339 −0.0543783
\(52\) 0 0
\(53\) 7.80358i 1.07190i 0.844248 + 0.535952i \(0.180047\pi\)
−0.844248 + 0.535952i \(0.819953\pi\)
\(54\) 0 0
\(55\) −8.69951 2.95662i −1.17304 0.398671i
\(56\) 0 0
\(57\) 10.8088i 1.43166i
\(58\) 0 0
\(59\) 14.1275 1.83924 0.919622 0.392805i \(-0.128495\pi\)
0.919622 + 0.392805i \(0.128495\pi\)
\(60\) 0 0
\(61\) 7.05297 0.903040 0.451520 0.892261i \(-0.350882\pi\)
0.451520 + 0.892261i \(0.350882\pi\)
\(62\) 0 0
\(63\) 9.50523i 1.19755i
\(64\) 0 0
\(65\) −0.00884814 + 0.0260346i −0.00109748 + 0.00322919i
\(66\) 0 0
\(67\) 7.31363i 0.893502i 0.894658 + 0.446751i \(0.147419\pi\)
−0.894658 + 0.446751i \(0.852581\pi\)
\(68\) 0 0
\(69\) −2.49931 −0.300882
\(70\) 0 0
\(71\) −5.84061 −0.693153 −0.346576 0.938022i \(-0.612656\pi\)
−0.346576 + 0.938022i \(0.612656\pi\)
\(72\) 0 0
\(73\) 0.727674i 0.0851678i −0.999093 0.0425839i \(-0.986441\pi\)
0.999093 0.0425839i \(-0.0135590\pi\)
\(74\) 0 0
\(75\) −7.61466 + 9.90864i −0.879266 + 1.14415i
\(76\) 0 0
\(77\) 12.0305i 1.37100i
\(78\) 0 0
\(79\) −4.81003 −0.541171 −0.270586 0.962696i \(-0.587217\pi\)
−0.270586 + 0.962696i \(0.587217\pi\)
\(80\) 0 0
\(81\) −8.19948 −0.911054
\(82\) 0 0
\(83\) 7.75797i 0.851548i −0.904830 0.425774i \(-0.860002\pi\)
0.904830 0.425774i \(-0.139998\pi\)
\(84\) 0 0
\(85\) −0.111800 + 0.328957i −0.0121264 + 0.0356804i
\(86\) 0 0
\(87\) 16.9948i 1.82203i
\(88\) 0 0
\(89\) −6.77560 −0.718212 −0.359106 0.933297i \(-0.616918\pi\)
−0.359106 + 0.933297i \(0.616918\pi\)
\(90\) 0 0
\(91\) −0.0360030 −0.00377414
\(92\) 0 0
\(93\) 5.51631i 0.572014i
\(94\) 0 0
\(95\) −9.15602 3.11177i −0.939388 0.319261i
\(96\) 0 0
\(97\) 14.8705i 1.50987i 0.655799 + 0.754935i \(0.272332\pi\)
−0.655799 + 0.754935i \(0.727668\pi\)
\(98\) 0 0
\(99\) 13.3405 1.34077
\(100\) 0 0
\(101\) −13.0023 −1.29378 −0.646889 0.762584i \(-0.723930\pi\)
−0.646889 + 0.762584i \(0.723930\pi\)
\(102\) 0 0
\(103\) 1.85814i 0.183088i 0.995801 + 0.0915442i \(0.0291803\pi\)
−0.995801 + 0.0915442i \(0.970820\pi\)
\(104\) 0 0
\(105\) −15.4920 5.26513i −1.51186 0.513824i
\(106\) 0 0
\(107\) 0.471267i 0.0455591i 0.999741 + 0.0227795i \(0.00725158\pi\)
−0.999741 + 0.0227795i \(0.992748\pi\)
\(108\) 0 0
\(109\) 1.83022 0.175303 0.0876515 0.996151i \(-0.472064\pi\)
0.0876515 + 0.996151i \(0.472064\pi\)
\(110\) 0 0
\(111\) 11.5154 1.09299
\(112\) 0 0
\(113\) 7.81151i 0.734845i −0.930054 0.367422i \(-0.880240\pi\)
0.930054 0.367422i \(-0.119760\pi\)
\(114\) 0 0
\(115\) −0.719533 + 2.11714i −0.0670968 + 0.197424i
\(116\) 0 0
\(117\) 0.0399233i 0.00369091i
\(118\) 0 0
\(119\) −0.454912 −0.0417017
\(120\) 0 0
\(121\) 5.88461 0.534964
\(122\) 0 0
\(123\) 19.1904i 1.73034i
\(124\) 0 0
\(125\) 6.20129 + 9.30291i 0.554660 + 0.832077i
\(126\) 0 0
\(127\) 7.62237i 0.676376i −0.941079 0.338188i \(-0.890186\pi\)
0.941079 0.338188i \(-0.109814\pi\)
\(128\) 0 0
\(129\) 20.9692 1.84623
\(130\) 0 0
\(131\) 19.4575 1.70001 0.850007 0.526772i \(-0.176598\pi\)
0.850007 + 0.526772i \(0.176598\pi\)
\(132\) 0 0
\(133\) 12.6618i 1.09792i
\(134\) 0 0
\(135\) 0.443421 1.30471i 0.0381636 0.112292i
\(136\) 0 0
\(137\) 16.3163i 1.39399i 0.717074 + 0.696997i \(0.245481\pi\)
−0.717074 + 0.696997i \(0.754519\pi\)
\(138\) 0 0
\(139\) 19.9289 1.69035 0.845175 0.534490i \(-0.179496\pi\)
0.845175 + 0.534490i \(0.179496\pi\)
\(140\) 0 0
\(141\) −15.9485 −1.34311
\(142\) 0 0
\(143\) 0.0505297i 0.00422551i
\(144\) 0 0
\(145\) 14.3961 + 4.89267i 1.19553 + 0.406314i
\(146\) 0 0
\(147\) 3.92857i 0.324023i
\(148\) 0 0
\(149\) 8.04540 0.659105 0.329552 0.944137i \(-0.393102\pi\)
0.329552 + 0.944137i \(0.393102\pi\)
\(150\) 0 0
\(151\) 3.40963 0.277472 0.138736 0.990329i \(-0.455696\pi\)
0.138736 + 0.990329i \(0.455696\pi\)
\(152\) 0 0
\(153\) 0.504446i 0.0407821i
\(154\) 0 0
\(155\) 4.67279 + 1.58810i 0.375328 + 0.127559i
\(156\) 0 0
\(157\) 21.1868i 1.69089i −0.534061 0.845446i \(-0.679335\pi\)
0.534061 0.845446i \(-0.320665\pi\)
\(158\) 0 0
\(159\) −19.5036 −1.54674
\(160\) 0 0
\(161\) −2.92777 −0.230741
\(162\) 0 0
\(163\) 20.9487i 1.64083i 0.571769 + 0.820415i \(0.306257\pi\)
−0.571769 + 0.820415i \(0.693743\pi\)
\(164\) 0 0
\(165\) 7.38953 21.7428i 0.575274 1.69267i
\(166\) 0 0
\(167\) 10.9861i 0.850131i 0.905163 + 0.425065i \(0.139749\pi\)
−0.905163 + 0.425065i \(0.860251\pi\)
\(168\) 0 0
\(169\) 12.9998 0.999988
\(170\) 0 0
\(171\) 14.0405 1.07370
\(172\) 0 0
\(173\) 4.31110i 0.327767i 0.986480 + 0.163884i \(0.0524021\pi\)
−0.986480 + 0.163884i \(0.947598\pi\)
\(174\) 0 0
\(175\) −8.92005 + 11.6073i −0.674292 + 0.877429i
\(176\) 0 0
\(177\) 35.3091i 2.65399i
\(178\) 0 0
\(179\) 19.0791 1.42604 0.713018 0.701146i \(-0.247328\pi\)
0.713018 + 0.701146i \(0.247328\pi\)
\(180\) 0 0
\(181\) 4.09312 0.304239 0.152120 0.988362i \(-0.451390\pi\)
0.152120 + 0.988362i \(0.451390\pi\)
\(182\) 0 0
\(183\) 17.6276i 1.30307i
\(184\) 0 0
\(185\) 3.31518 9.75451i 0.243737 0.717166i
\(186\) 0 0
\(187\) 0.638462i 0.0466890i
\(188\) 0 0
\(189\) 1.80428 0.131242
\(190\) 0 0
\(191\) 6.21032 0.449363 0.224682 0.974432i \(-0.427866\pi\)
0.224682 + 0.974432i \(0.427866\pi\)
\(192\) 0 0
\(193\) 13.2674i 0.955005i 0.878630 + 0.477503i \(0.158458\pi\)
−0.878630 + 0.477503i \(0.841542\pi\)
\(194\) 0 0
\(195\) −0.0650686 0.0221143i −0.00465966 0.00158364i
\(196\) 0 0
\(197\) 13.8836i 0.989163i −0.869131 0.494582i \(-0.835321\pi\)
0.869131 0.494582i \(-0.164679\pi\)
\(198\) 0 0
\(199\) 22.8004 1.61628 0.808139 0.588992i \(-0.200475\pi\)
0.808139 + 0.588992i \(0.200475\pi\)
\(200\) 0 0
\(201\) −18.2791 −1.28931
\(202\) 0 0
\(203\) 19.9082i 1.39728i
\(204\) 0 0
\(205\) −16.2559 5.52476i −1.13536 0.385866i
\(206\) 0 0
\(207\) 3.24657i 0.225652i
\(208\) 0 0
\(209\) 17.7706 1.22922
\(210\) 0 0
\(211\) −0.698944 −0.0481173 −0.0240587 0.999711i \(-0.507659\pi\)
−0.0240587 + 0.999711i \(0.507659\pi\)
\(212\) 0 0
\(213\) 14.5975i 1.00021i
\(214\) 0 0
\(215\) 6.03686 17.7627i 0.411711 1.21141i
\(216\) 0 0
\(217\) 6.46197i 0.438667i
\(218\) 0 0
\(219\) 1.81869 0.122895
\(220\) 0 0
\(221\) −0.00191069 −0.000128527
\(222\) 0 0
\(223\) 27.3719i 1.83296i −0.400082 0.916480i \(-0.631018\pi\)
0.400082 0.916480i \(-0.368982\pi\)
\(224\) 0 0
\(225\) −12.8712 9.89134i −0.858079 0.659422i
\(226\) 0 0
\(227\) 10.6070i 0.704011i −0.935998 0.352005i \(-0.885500\pi\)
0.935998 0.352005i \(-0.114500\pi\)
\(228\) 0 0
\(229\) −3.11433 −0.205801 −0.102900 0.994692i \(-0.532812\pi\)
−0.102900 + 0.994692i \(0.532812\pi\)
\(230\) 0 0
\(231\) 30.0680 1.97833
\(232\) 0 0
\(233\) 23.5295i 1.54147i 0.637156 + 0.770735i \(0.280111\pi\)
−0.637156 + 0.770735i \(0.719889\pi\)
\(234\) 0 0
\(235\) −4.59145 + 13.5098i −0.299513 + 0.881281i
\(236\) 0 0
\(237\) 12.0218i 0.780899i
\(238\) 0 0
\(239\) −24.4214 −1.57969 −0.789844 0.613308i \(-0.789838\pi\)
−0.789844 + 0.613308i \(0.789838\pi\)
\(240\) 0 0
\(241\) 27.5525 1.77481 0.887407 0.460986i \(-0.152504\pi\)
0.887407 + 0.460986i \(0.152504\pi\)
\(242\) 0 0
\(243\) 22.3419i 1.43323i
\(244\) 0 0
\(245\) −3.32784 1.13101i −0.212608 0.0722573i
\(246\) 0 0
\(247\) 0.0531813i 0.00338385i
\(248\) 0 0
\(249\) 19.3896 1.22877
\(250\) 0 0
\(251\) −25.3692 −1.60129 −0.800645 0.599139i \(-0.795510\pi\)
−0.800645 + 0.599139i \(0.795510\pi\)
\(252\) 0 0
\(253\) 4.10909i 0.258336i
\(254\) 0 0
\(255\) −0.822167 0.279423i −0.0514861 0.0174981i
\(256\) 0 0
\(257\) 19.8501i 1.23822i −0.785306 0.619108i \(-0.787494\pi\)
0.785306 0.619108i \(-0.212506\pi\)
\(258\) 0 0
\(259\) 13.4894 0.838193
\(260\) 0 0
\(261\) −22.0760 −1.36647
\(262\) 0 0
\(263\) 22.9087i 1.41261i 0.707906 + 0.706306i \(0.249640\pi\)
−0.707906 + 0.706306i \(0.750360\pi\)
\(264\) 0 0
\(265\) −5.61493 + 16.5213i −0.344923 + 1.01489i
\(266\) 0 0
\(267\) 16.9344i 1.03637i
\(268\) 0 0
\(269\) −1.03048 −0.0628295 −0.0314148 0.999506i \(-0.510001\pi\)
−0.0314148 + 0.999506i \(0.510001\pi\)
\(270\) 0 0
\(271\) −3.79576 −0.230576 −0.115288 0.993332i \(-0.536779\pi\)
−0.115288 + 0.993332i \(0.536779\pi\)
\(272\) 0 0
\(273\) 0.0899829i 0.00544601i
\(274\) 0 0
\(275\) −16.2907 12.5192i −0.982364 0.754934i
\(276\) 0 0
\(277\) 1.48782i 0.0893946i 0.999001 + 0.0446973i \(0.0142323\pi\)
−0.999001 + 0.0446973i \(0.985768\pi\)
\(278\) 0 0
\(279\) −7.16560 −0.428993
\(280\) 0 0
\(281\) −10.2796 −0.613228 −0.306614 0.951834i \(-0.599196\pi\)
−0.306614 + 0.951834i \(0.599196\pi\)
\(282\) 0 0
\(283\) 4.62427i 0.274884i −0.990510 0.137442i \(-0.956112\pi\)
0.990510 0.137442i \(-0.0438881\pi\)
\(284\) 0 0
\(285\) 7.77730 22.8838i 0.460688 1.35552i
\(286\) 0 0
\(287\) 22.4802i 1.32697i
\(288\) 0 0
\(289\) 16.9759 0.998580
\(290\) 0 0
\(291\) −37.1661 −2.17871
\(292\) 0 0
\(293\) 16.3067i 0.952650i 0.879269 + 0.476325i \(0.158031\pi\)
−0.879269 + 0.476325i \(0.841969\pi\)
\(294\) 0 0
\(295\) 29.9099 + 10.1652i 1.74142 + 0.591841i
\(296\) 0 0
\(297\) 2.53228i 0.146938i
\(298\) 0 0
\(299\) −0.0122971 −0.000711158
\(300\) 0 0
\(301\) 24.5639 1.41584
\(302\) 0 0
\(303\) 32.4969i 1.86690i
\(304\) 0 0
\(305\) 14.9321 + 5.07484i 0.855010 + 0.290585i
\(306\) 0 0
\(307\) 9.28659i 0.530014i −0.964246 0.265007i \(-0.914626\pi\)
0.964246 0.265007i \(-0.0853743\pi\)
\(308\) 0 0
\(309\) −4.64409 −0.264193
\(310\) 0 0
\(311\) −24.3713 −1.38197 −0.690984 0.722870i \(-0.742822\pi\)
−0.690984 + 0.722870i \(0.742822\pi\)
\(312\) 0 0
\(313\) 15.0048i 0.848119i 0.905634 + 0.424060i \(0.139395\pi\)
−0.905634 + 0.424060i \(0.860605\pi\)
\(314\) 0 0
\(315\) 6.83933 20.1239i 0.385352 1.13385i
\(316\) 0 0
\(317\) 7.84747i 0.440758i 0.975414 + 0.220379i \(0.0707294\pi\)
−0.975414 + 0.220379i \(0.929271\pi\)
\(318\) 0 0
\(319\) −27.9409 −1.56439
\(320\) 0 0
\(321\) −1.17784 −0.0657408
\(322\) 0 0
\(323\) 0.671966i 0.0373892i
\(324\) 0 0
\(325\) −0.0374655 + 0.0487523i −0.00207821 + 0.00270429i
\(326\) 0 0
\(327\) 4.57429i 0.252959i
\(328\) 0 0
\(329\) −18.6826 −1.03000
\(330\) 0 0
\(331\) 9.28156 0.510160 0.255080 0.966920i \(-0.417898\pi\)
0.255080 + 0.966920i \(0.417898\pi\)
\(332\) 0 0
\(333\) 14.9583i 0.819709i
\(334\) 0 0
\(335\) −5.26240 + 15.4840i −0.287515 + 0.845979i
\(336\) 0 0
\(337\) 26.3760i 1.43679i −0.695634 0.718397i \(-0.744876\pi\)
0.695634 0.718397i \(-0.255124\pi\)
\(338\) 0 0
\(339\) 19.5234 1.06037
\(340\) 0 0
\(341\) −9.06928 −0.491129
\(342\) 0 0
\(343\) 15.8924i 0.858107i
\(344\) 0 0
\(345\) −5.29139 1.79834i −0.284879 0.0968193i
\(346\) 0 0
\(347\) 18.3316i 0.984093i −0.870569 0.492047i \(-0.836249\pi\)
0.870569 0.492047i \(-0.163751\pi\)
\(348\) 0 0
\(349\) 32.2759 1.72769 0.863845 0.503758i \(-0.168050\pi\)
0.863845 + 0.503758i \(0.168050\pi\)
\(350\) 0 0
\(351\) 0.00757822 0.000404495
\(352\) 0 0
\(353\) 29.5653i 1.57360i 0.617208 + 0.786800i \(0.288264\pi\)
−0.617208 + 0.786800i \(0.711736\pi\)
\(354\) 0 0
\(355\) −12.3654 4.20251i −0.656286 0.223046i
\(356\) 0 0
\(357\) 1.13697i 0.0601747i
\(358\) 0 0
\(359\) −33.4169 −1.76368 −0.881838 0.471552i \(-0.843694\pi\)
−0.881838 + 0.471552i \(0.843694\pi\)
\(360\) 0 0
\(361\) −0.296842 −0.0156232
\(362\) 0 0
\(363\) 14.7075i 0.771943i
\(364\) 0 0
\(365\) 0.523585 1.54059i 0.0274057 0.0806379i
\(366\) 0 0
\(367\) 25.4764i 1.32986i −0.746908 0.664928i \(-0.768462\pi\)
0.746908 0.664928i \(-0.231538\pi\)
\(368\) 0 0
\(369\) 24.9280 1.29770
\(370\) 0 0
\(371\) −22.8471 −1.18616
\(372\) 0 0
\(373\) 3.28172i 0.169921i 0.996384 + 0.0849605i \(0.0270764\pi\)
−0.996384 + 0.0849605i \(0.972924\pi\)
\(374\) 0 0
\(375\) −23.2509 + 15.4990i −1.20067 + 0.800363i
\(376\) 0 0
\(377\) 0.0836174i 0.00430651i
\(378\) 0 0
\(379\) −5.66762 −0.291126 −0.145563 0.989349i \(-0.546499\pi\)
−0.145563 + 0.989349i \(0.546499\pi\)
\(380\) 0 0
\(381\) 19.0507 0.975997
\(382\) 0 0
\(383\) 34.4343i 1.75951i −0.475428 0.879755i \(-0.657707\pi\)
0.475428 0.879755i \(-0.342293\pi\)
\(384\) 0 0
\(385\) 8.65633 25.4702i 0.441167 1.29808i
\(386\) 0 0
\(387\) 27.2387i 1.38462i
\(388\) 0 0
\(389\) 14.3737 0.728773 0.364387 0.931248i \(-0.381279\pi\)
0.364387 + 0.931248i \(0.381279\pi\)
\(390\) 0 0
\(391\) −0.155378 −0.00785781
\(392\) 0 0
\(393\) 48.6305i 2.45309i
\(394\) 0 0
\(395\) −10.1835 3.46098i −0.512388 0.174141i
\(396\) 0 0
\(397\) 14.6149i 0.733500i −0.930319 0.366750i \(-0.880470\pi\)
0.930319 0.366750i \(-0.119530\pi\)
\(398\) 0 0
\(399\) 31.6458 1.58427
\(400\) 0 0
\(401\) −3.65553 −0.182548 −0.0912742 0.995826i \(-0.529094\pi\)
−0.0912742 + 0.995826i \(0.529094\pi\)
\(402\) 0 0
\(403\) 0.0271412i 0.00135200i
\(404\) 0 0
\(405\) −17.3594 5.89980i −0.862597 0.293163i
\(406\) 0 0
\(407\) 18.9322i 0.938436i
\(408\) 0 0
\(409\) −4.40926 −0.218024 −0.109012 0.994040i \(-0.534769\pi\)
−0.109012 + 0.994040i \(0.534769\pi\)
\(410\) 0 0
\(411\) −40.7795 −2.01150
\(412\) 0 0
\(413\) 41.3621i 2.03530i
\(414\) 0 0
\(415\) 5.58212 16.4247i 0.274015 0.806257i
\(416\) 0 0
\(417\) 49.8087i 2.43914i
\(418\) 0 0
\(419\) −32.5906 −1.59216 −0.796078 0.605195i \(-0.793095\pi\)
−0.796078 + 0.605195i \(0.793095\pi\)
\(420\) 0 0
\(421\) 4.23954 0.206622 0.103311 0.994649i \(-0.467056\pi\)
0.103311 + 0.994649i \(0.467056\pi\)
\(422\) 0 0
\(423\) 20.7169i 1.00729i
\(424\) 0 0
\(425\) −0.473391 + 0.616003i −0.0229628 + 0.0298806i
\(426\) 0 0
\(427\) 20.6495i 0.999299i
\(428\) 0 0
\(429\) 0.126290 0.00609732
\(430\) 0 0
\(431\) 1.81123 0.0872436 0.0436218 0.999048i \(-0.486110\pi\)
0.0436218 + 0.999048i \(0.486110\pi\)
\(432\) 0 0
\(433\) 1.76263i 0.0847068i 0.999103 + 0.0423534i \(0.0134855\pi\)
−0.999103 + 0.0423534i \(0.986514\pi\)
\(434\) 0 0
\(435\) −12.2283 + 35.9803i −0.586303 + 1.72512i
\(436\) 0 0
\(437\) 4.32471i 0.206879i
\(438\) 0 0
\(439\) 26.7848 1.27837 0.639184 0.769054i \(-0.279272\pi\)
0.639184 + 0.769054i \(0.279272\pi\)
\(440\) 0 0
\(441\) 5.10316 0.243008
\(442\) 0 0
\(443\) 16.6631i 0.791686i −0.918318 0.395843i \(-0.870452\pi\)
0.918318 0.395843i \(-0.129548\pi\)
\(444\) 0 0
\(445\) −14.3449 4.87527i −0.680012 0.231110i
\(446\) 0 0
\(447\) 20.1080i 0.951075i
\(448\) 0 0
\(449\) 34.1236 1.61039 0.805196 0.593008i \(-0.202060\pi\)
0.805196 + 0.593008i \(0.202060\pi\)
\(450\) 0 0
\(451\) 31.5507 1.48566
\(452\) 0 0
\(453\) 8.52174i 0.400386i
\(454\) 0 0
\(455\) −0.0762234 0.0259054i −0.00357341 0.00121446i
\(456\) 0 0
\(457\) 24.5980i 1.15065i −0.817926 0.575324i \(-0.804876\pi\)
0.817926 0.575324i \(-0.195124\pi\)
\(458\) 0 0
\(459\) 0.0957537 0.00446940
\(460\) 0 0
\(461\) −10.7297 −0.499733 −0.249866 0.968280i \(-0.580387\pi\)
−0.249866 + 0.968280i \(0.580387\pi\)
\(462\) 0 0
\(463\) 22.3124i 1.03695i 0.855094 + 0.518473i \(0.173499\pi\)
−0.855094 + 0.518473i \(0.826501\pi\)
\(464\) 0 0
\(465\) −3.96917 + 11.6788i −0.184066 + 0.541591i
\(466\) 0 0
\(467\) 20.0218i 0.926497i −0.886229 0.463248i \(-0.846684\pi\)
0.886229 0.463248i \(-0.153316\pi\)
\(468\) 0 0
\(469\) −21.4127 −0.988744
\(470\) 0 0
\(471\) 52.9525 2.43992
\(472\) 0 0
\(473\) 34.4751i 1.58517i
\(474\) 0 0
\(475\) −17.1455 13.1761i −0.786691 0.604561i
\(476\) 0 0
\(477\) 25.3349i 1.16001i
\(478\) 0 0
\(479\) 7.61905 0.348123 0.174062 0.984735i \(-0.444311\pi\)
0.174062 + 0.984735i \(0.444311\pi\)
\(480\) 0 0
\(481\) 0.0566576 0.00258336
\(482\) 0 0
\(483\) 7.31743i 0.332954i
\(484\) 0 0
\(485\) −10.6998 + 31.4829i −0.485854 + 1.42956i
\(486\) 0 0
\(487\) 21.5163i 0.974997i 0.873124 + 0.487499i \(0.162091\pi\)
−0.873124 + 0.487499i \(0.837909\pi\)
\(488\) 0 0
\(489\) −52.3574 −2.36768
\(490\) 0 0
\(491\) −10.3705 −0.468015 −0.234007 0.972235i \(-0.575184\pi\)
−0.234007 + 0.972235i \(0.575184\pi\)
\(492\) 0 0
\(493\) 1.05654i 0.0475841i
\(494\) 0 0
\(495\) 28.2436 + 9.59890i 1.26945 + 0.431438i
\(496\) 0 0
\(497\) 17.1000i 0.767039i
\(498\) 0 0
\(499\) 16.2850 0.729018 0.364509 0.931200i \(-0.381237\pi\)
0.364509 + 0.931200i \(0.381237\pi\)
\(500\) 0 0
\(501\) −27.4577 −1.22672
\(502\) 0 0
\(503\) 16.9326i 0.754986i −0.926012 0.377493i \(-0.876786\pi\)
0.926012 0.377493i \(-0.123214\pi\)
\(504\) 0 0
\(505\) −27.5277 9.35559i −1.22497 0.416318i
\(506\) 0 0
\(507\) 32.4907i 1.44296i
\(508\) 0 0
\(509\) −39.0075 −1.72898 −0.864488 0.502654i \(-0.832357\pi\)
−0.864488 + 0.502654i \(0.832357\pi\)
\(510\) 0 0
\(511\) 2.13046 0.0942462
\(512\) 0 0
\(513\) 2.66516i 0.117670i
\(514\) 0 0
\(515\) −1.33700 + 3.93395i −0.0589151 + 0.173350i
\(516\) 0 0
\(517\) 26.2207i 1.15319i
\(518\) 0 0
\(519\) −10.7748 −0.472961
\(520\) 0 0
\(521\) 33.1380 1.45180 0.725902 0.687798i \(-0.241423\pi\)
0.725902 + 0.687798i \(0.241423\pi\)
\(522\) 0 0
\(523\) 12.4056i 0.542460i −0.962515 0.271230i \(-0.912570\pi\)
0.962515 0.271230i \(-0.0874304\pi\)
\(524\) 0 0
\(525\) −29.0103 22.2940i −1.26611 0.972990i
\(526\) 0 0
\(527\) 0.342939i 0.0149387i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) −45.8660 −1.99041
\(532\) 0 0
\(533\) 0.0944201i 0.00408979i
\(534\) 0 0
\(535\) −0.339092 + 0.997737i −0.0146602 + 0.0431359i
\(536\) 0 0
\(537\) 47.6846i 2.05774i
\(538\) 0 0
\(539\) 6.45891 0.278205
\(540\) 0 0
\(541\) −8.53472 −0.366936 −0.183468 0.983026i \(-0.558732\pi\)
−0.183468 + 0.983026i \(0.558732\pi\)
\(542\) 0 0
\(543\) 10.2300i 0.439011i
\(544\) 0 0
\(545\) 3.87482 + 1.31690i 0.165979 + 0.0564099i
\(546\) 0 0
\(547\) 6.45828i 0.276136i 0.990423 + 0.138068i \(0.0440893\pi\)
−0.990423 + 0.138068i \(0.955911\pi\)
\(548\) 0 0
\(549\) −22.8980 −0.977262
\(550\) 0 0
\(551\) −29.4071 −1.25279
\(552\) 0 0
\(553\) 14.0827i 0.598857i
\(554\) 0 0
\(555\) 24.3796 + 8.28568i 1.03486 + 0.351708i
\(556\) 0 0
\(557\) 4.08413i 0.173050i −0.996250 0.0865251i \(-0.972424\pi\)
0.996250 0.0865251i \(-0.0275763\pi\)
\(558\) 0 0
\(559\) 0.103172 0.00436371
\(560\) 0 0
\(561\) 1.59572 0.0673713
\(562\) 0 0
\(563\) 15.4494i 0.651114i 0.945522 + 0.325557i \(0.105552\pi\)
−0.945522 + 0.325557i \(0.894448\pi\)
\(564\) 0 0
\(565\) 5.62064 16.5380i 0.236462 0.695761i
\(566\) 0 0
\(567\) 24.0062i 1.00817i
\(568\) 0 0
\(569\) −42.2633 −1.77177 −0.885886 0.463903i \(-0.846448\pi\)
−0.885886 + 0.463903i \(0.846448\pi\)
\(570\) 0 0
\(571\) −2.74497 −0.114873 −0.0574367 0.998349i \(-0.518293\pi\)
−0.0574367 + 0.998349i \(0.518293\pi\)
\(572\) 0 0
\(573\) 15.5215i 0.648422i
\(574\) 0 0
\(575\) −3.04670 + 3.96454i −0.127056 + 0.165333i
\(576\) 0 0
\(577\) 8.93871i 0.372123i 0.982538 + 0.186062i \(0.0595724\pi\)
−0.982538 + 0.186062i \(0.940428\pi\)
\(578\) 0 0
\(579\) −33.1593 −1.37805
\(580\) 0 0
\(581\) 22.7136 0.942318
\(582\) 0 0
\(583\) 32.0656i 1.32802i
\(584\) 0 0
\(585\) 0.0287261 0.0845232i 0.00118768 0.00349460i
\(586\) 0 0
\(587\) 5.90821i 0.243858i 0.992539 + 0.121929i \(0.0389080\pi\)
−0.992539 + 0.121929i \(0.961092\pi\)
\(588\) 0 0
\(589\) −9.54520 −0.393303
\(590\) 0 0
\(591\) 34.6994 1.42734
\(592\) 0 0
\(593\) 27.8823i 1.14499i −0.819909 0.572494i \(-0.805976\pi\)
0.819909 0.572494i \(-0.194024\pi\)
\(594\) 0 0
\(595\) −0.963111 0.327324i −0.0394837 0.0134190i
\(596\) 0 0
\(597\) 56.9854i 2.33226i
\(598\) 0 0
\(599\) −10.5644 −0.431648 −0.215824 0.976432i \(-0.569244\pi\)
−0.215824 + 0.976432i \(0.569244\pi\)
\(600\) 0 0
\(601\) 35.8910 1.46403 0.732013 0.681291i \(-0.238581\pi\)
0.732013 + 0.681291i \(0.238581\pi\)
\(602\) 0 0
\(603\) 23.7442i 0.966940i
\(604\) 0 0
\(605\) 12.4585 + 4.23417i 0.506511 + 0.172143i
\(606\) 0 0
\(607\) 29.0640i 1.17967i −0.807524 0.589835i \(-0.799193\pi\)
0.807524 0.589835i \(-0.200807\pi\)
\(608\) 0 0
\(609\) −49.7569 −2.01625
\(610\) 0 0
\(611\) −0.0784695 −0.00317454
\(612\) 0 0
\(613\) 24.4282i 0.986644i −0.869847 0.493322i \(-0.835782\pi\)
0.869847 0.493322i \(-0.164218\pi\)
\(614\) 0 0
\(615\) 13.8081 40.6287i 0.556797 1.63831i
\(616\) 0 0
\(617\) 29.5614i 1.19010i 0.803689 + 0.595049i \(0.202867\pi\)
−0.803689 + 0.595049i \(0.797133\pi\)
\(618\) 0 0
\(619\) 30.5880 1.22944 0.614718 0.788747i \(-0.289270\pi\)
0.614718 + 0.788747i \(0.289270\pi\)
\(620\) 0 0
\(621\) 0.616262 0.0247298
\(622\) 0 0
\(623\) 19.8374i 0.794769i
\(624\) 0 0
\(625\) 6.43523 + 24.1576i 0.257409 + 0.966303i
\(626\) 0 0
\(627\) 44.4144i 1.77374i
\(628\) 0 0
\(629\) 0.715890 0.0285444
\(630\) 0 0
\(631\) 10.5713 0.420835 0.210418 0.977612i \(-0.432518\pi\)
0.210418 + 0.977612i \(0.432518\pi\)
\(632\) 0 0
\(633\) 1.74688i 0.0694323i
\(634\) 0 0
\(635\) 5.48455 16.1376i 0.217648 0.640402i
\(636\) 0 0
\(637\) 0.0193293i 0.000765853i
\(638\) 0 0
\(639\) 18.9620 0.750123
\(640\) 0 0
\(641\) −20.4738 −0.808666 −0.404333 0.914612i \(-0.632496\pi\)
−0.404333 + 0.914612i \(0.632496\pi\)
\(642\) 0 0
\(643\) 18.4989i 0.729525i −0.931101 0.364763i \(-0.881150\pi\)
0.931101 0.364763i \(-0.118850\pi\)
\(644\) 0 0
\(645\) 44.3946 + 15.0880i 1.74804 + 0.594090i
\(646\) 0 0
\(647\) 18.6328i 0.732531i 0.930510 + 0.366266i \(0.119364\pi\)
−0.930510 + 0.366266i \(0.880636\pi\)
\(648\) 0 0
\(649\) −58.0511 −2.27871
\(650\) 0 0
\(651\) −16.1505 −0.632988
\(652\) 0 0
\(653\) 30.5290i 1.19469i −0.801983 0.597347i \(-0.796222\pi\)
0.801983 0.597347i \(-0.203778\pi\)
\(654\) 0 0
\(655\) 41.1943 + 14.0003i 1.60959 + 0.547039i
\(656\) 0 0
\(657\) 2.36245i 0.0921678i
\(658\) 0 0
\(659\) 26.6231 1.03709 0.518545 0.855051i \(-0.326474\pi\)
0.518545 + 0.855051i \(0.326474\pi\)
\(660\) 0 0
\(661\) −13.0529 −0.507700 −0.253850 0.967244i \(-0.581697\pi\)
−0.253850 + 0.967244i \(0.581697\pi\)
\(662\) 0 0
\(663\) 0.00477543i 0.000185462i
\(664\) 0 0
\(665\) 9.11057 26.8067i 0.353293 1.03952i
\(666\) 0 0
\(667\) 6.79978i 0.263289i
\(668\) 0 0
\(669\) 68.4110 2.64492
\(670\) 0 0
\(671\) −28.9813 −1.11881
\(672\) 0 0
\(673\) 28.9120i 1.11448i −0.830353 0.557238i \(-0.811861\pi\)
0.830353 0.557238i \(-0.188139\pi\)
\(674\) 0 0
\(675\) 1.87757 2.44320i 0.0722676 0.0940388i
\(676\) 0 0
\(677\) 12.4824i 0.479738i −0.970805 0.239869i \(-0.922896\pi\)
0.970805 0.239869i \(-0.0771045\pi\)
\(678\) 0 0
\(679\) −43.5375 −1.67081
\(680\) 0 0
\(681\) 26.5102 1.01587
\(682\) 0 0
\(683\) 40.0241i 1.53148i −0.643150 0.765740i \(-0.722373\pi\)
0.643150 0.765740i \(-0.277627\pi\)
\(684\) 0 0
\(685\) −11.7401 + 34.5438i −0.448566 + 1.31985i
\(686\) 0 0
\(687\) 7.78369i 0.296966i
\(688\) 0 0
\(689\) −0.0959612 −0.00365583
\(690\) 0 0
\(691\) −38.9938 −1.48340 −0.741698 0.670734i \(-0.765979\pi\)
−0.741698 + 0.670734i \(0.765979\pi\)
\(692\) 0 0
\(693\) 39.0578i 1.48368i
\(694\) 0 0
\(695\) 42.1923 + 14.3395i 1.60044 + 0.543929i
\(696\) 0 0
\(697\) 1.19303i 0.0451894i
\(698\) 0 0
\(699\) −58.8077 −2.22431
\(700\) 0 0
\(701\) 21.9042 0.827309 0.413655 0.910434i \(-0.364252\pi\)
0.413655 + 0.910434i \(0.364252\pi\)
\(702\) 0 0
\(703\) 19.9257i 0.751513i
\(704\) 0 0
\(705\) −33.7652 11.4755i −1.27167 0.432192i
\(706\) 0 0
\(707\) 38.0678i 1.43169i
\(708\) 0 0
\(709\) −32.1360 −1.20689 −0.603447 0.797403i \(-0.706207\pi\)
−0.603447 + 0.797403i \(0.706207\pi\)
\(710\) 0 0
\(711\) 15.6161 0.585650
\(712\) 0 0
\(713\) 2.20713i 0.0826576i
\(714\) 0 0
\(715\) 0.0363578 0.106978i 0.00135970 0.00400077i
\(716\) 0 0
\(717\) 61.0367i 2.27946i
\(718\) 0 0
\(719\) 24.4018 0.910033 0.455017 0.890483i \(-0.349633\pi\)
0.455017 + 0.890483i \(0.349633\pi\)
\(720\) 0 0
\(721\) −5.44023 −0.202605
\(722\) 0 0
\(723\) 68.8625i 2.56102i
\(724\) 0 0
\(725\) 26.9580 + 20.7169i 1.00120 + 0.769407i
\(726\) 0 0
\(727\) 34.8573i 1.29279i −0.763005 0.646393i \(-0.776277\pi\)
0.763005 0.646393i \(-0.223723\pi\)
\(728\) 0 0
\(729\) 31.2409 1.15707
\(730\) 0 0
\(731\) 1.30362 0.0482161
\(732\) 0 0
\(733\) 30.7343i 1.13520i −0.823306 0.567598i \(-0.807873\pi\)
0.823306 0.567598i \(-0.192127\pi\)
\(734\) 0 0
\(735\) 2.82674 8.31733i 0.104266 0.306789i
\(736\) 0 0
\(737\) 30.0523i 1.10699i
\(738\) 0 0
\(739\) 38.7573 1.42571 0.712855 0.701312i \(-0.247402\pi\)
0.712855 + 0.701312i \(0.247402\pi\)
\(740\) 0 0
\(741\) 0.132917 0.00488282
\(742\) 0 0
\(743\) 43.0371i 1.57888i −0.613830 0.789438i \(-0.710372\pi\)
0.613830 0.789438i \(-0.289628\pi\)
\(744\) 0 0
\(745\) 17.0332 + 5.78893i 0.624049 + 0.212090i
\(746\) 0 0
\(747\) 25.1868i 0.921538i
\(748\) 0 0
\(749\) −1.37976 −0.0504154
\(750\) 0 0
\(751\) −35.3761 −1.29089 −0.645447 0.763805i \(-0.723329\pi\)
−0.645447 + 0.763805i \(0.723329\pi\)
\(752\) 0 0
\(753\) 63.4056i 2.31063i
\(754\) 0 0
\(755\) 7.21866 + 2.45334i 0.262714 + 0.0892862i
\(756\) 0 0
\(757\) 51.2605i 1.86309i −0.363621 0.931547i \(-0.618460\pi\)
0.363621 0.931547i \(-0.381540\pi\)
\(758\) 0 0
\(759\) 10.2699 0.372774
\(760\) 0 0
\(761\) −13.4331 −0.486950 −0.243475 0.969907i \(-0.578287\pi\)
−0.243475 + 0.969907i \(0.578287\pi\)
\(762\) 0 0
\(763\) 5.35846i 0.193989i
\(764\) 0 0
\(765\) 0.362966 1.06798i 0.0131231 0.0386130i
\(766\) 0 0
\(767\) 0.173727i 0.00627291i
\(768\) 0 0
\(769\) 24.7779 0.893512 0.446756 0.894656i \(-0.352579\pi\)
0.446756 + 0.894656i \(0.352579\pi\)
\(770\) 0 0
\(771\) 49.6117 1.78672
\(772\) 0 0
\(773\) 11.9946i 0.431417i −0.976458 0.215708i \(-0.930794\pi\)
0.976458 0.215708i \(-0.0692061\pi\)
\(774\) 0 0
\(775\) 8.75026 + 6.72446i 0.314319 + 0.241550i
\(776\) 0 0
\(777\) 33.7144i 1.20950i
\(778\) 0 0
\(779\) 33.2063 1.18974
\(780\) 0 0
\(781\) 23.9996 0.858772
\(782\) 0 0
\(783\) 4.19045i 0.149755i
\(784\) 0 0
\(785\) 15.2446 44.8554i 0.544103 1.60096i
\(786\) 0 0
\(787\) 10.4110i 0.371114i 0.982634 + 0.185557i \(0.0594089\pi\)
−0.982634 + 0.185557i \(0.940591\pi\)
\(788\) 0 0
\(789\) −57.2561 −2.03837
\(790\) 0 0
\(791\) 22.8703 0.813175
\(792\) 0 0
\(793\) 0.0867308i 0.00307990i
\(794\) 0 0
\(795\) −41.2918 14.0335i −1.46447 0.497717i
\(796\) 0 0
\(797\) 28.0848i 0.994814i 0.867517 + 0.497407i \(0.165714\pi\)
−0.867517 + 0.497407i \(0.834286\pi\)
\(798\) 0 0
\(799\) −0.991492 −0.0350765
\(800\) 0 0
\(801\) 21.9975 0.777243
\(802\) 0 0
\(803\)