Properties

Label 3120.2.l.q.1249.5
Level $3120$
Weight $2$
Character 3120.1249
Analytic conductor $24.913$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3120.l (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.9133254306\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \( x^{10} + 13x^{8} + 56x^{6} + 97x^{4} + 61x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 1560)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1249.5
Root \(1.28447i\) of defining polynomial
Character \(\chi\) \(=\) 3120.1249
Dual form 3120.2.l.q.1249.10

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{3} +(2.23081 + 0.153266i) q^{5} -3.71215i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{3} +(2.23081 + 0.153266i) q^{5} -3.71215i q^{7} -1.00000 q^{9} -3.31842 q^{11} +1.00000i q^{13} +(0.153266 - 2.23081i) q^{15} -1.55706i q^{17} -5.33709 q^{19} -3.71215 q^{21} -0.442940i q^{23} +(4.95302 + 0.683813i) q^{25} +1.00000i q^{27} -2.56894 q^{29} -0.613062 q^{31} +3.31842i q^{33} +(0.568944 - 8.28109i) q^{35} +0.257322i q^{37} +1.00000 q^{39} -10.6114 q^{41} -12.6935i q^{43} +(-2.23081 - 0.153266i) q^{45} +7.44442i q^{47} -6.78003 q^{49} -1.55706 q^{51} -5.39521i q^{53} +(-7.40275 - 0.508599i) q^{55} +5.33709i q^{57} -13.1358 q^{59} -5.27452 q^{61} +3.71215i q^{63} +(-0.153266 + 2.23081i) q^{65} +10.5384i q^{67} -0.442940 q^{69} -0.311845 q^{71} +9.46841i q^{73} +(0.683813 - 4.95302i) q^{75} +12.3184i q^{77} +16.1871 q^{79} +1.00000 q^{81} -11.7546i q^{83} +(0.238644 - 3.47350i) q^{85} +2.56894i q^{87} +4.58762 q^{89} +3.71215 q^{91} +0.613062i q^{93} +(-11.9060 - 0.817993i) q^{95} -10.8500i q^{97} +3.31842 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 2 q^{5} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 2 q^{5} - 10 q^{9} - 10 q^{11} + 12 q^{19} + 2 q^{21} + 6 q^{25} - 4 q^{29} - 16 q^{35} + 10 q^{39} - 2 q^{41} - 2 q^{45} - 4 q^{49} - 14 q^{51} - 10 q^{55} + 40 q^{59} - 38 q^{61} - 6 q^{69} - 26 q^{71} + 4 q^{75} + 14 q^{79} + 10 q^{81} + 24 q^{85} - 18 q^{89} - 2 q^{91} - 32 q^{95} + 10 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3120\mathbb{Z}\right)^\times\).

\(n\) \(1951\) \(2081\) \(2341\) \(2497\) \(2641\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\) \(1\)

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
\(3\) 1.00000i 0.577350i
\(4\) 0 0
\(5\) 2.23081 + 0.153266i 0.997648 + 0.0685425i
\(6\) 0 0
\(7\) 3.71215i 1.40306i −0.712640 0.701530i \(-0.752501\pi\)
0.712640 0.701530i \(-0.247499\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) −3.31842 −1.00054 −0.500270 0.865869i \(-0.666766\pi\)
−0.500270 + 0.865869i \(0.666766\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.277350i
\(14\) 0 0
\(15\) 0.153266 2.23081i 0.0395730 0.575992i
\(16\) 0 0
\(17\) 1.55706i 0.377642i −0.982011 0.188821i \(-0.939533\pi\)
0.982011 0.188821i \(-0.0604667\pi\)
\(18\) 0 0
\(19\) −5.33709 −1.22441 −0.612207 0.790698i \(-0.709718\pi\)
−0.612207 + 0.790698i \(0.709718\pi\)
\(20\) 0 0
\(21\) −3.71215 −0.810057
\(22\) 0 0
\(23\) 0.442940i 0.0923594i −0.998933 0.0461797i \(-0.985295\pi\)
0.998933 0.0461797i \(-0.0147047\pi\)
\(24\) 0 0
\(25\) 4.95302 + 0.683813i 0.990604 + 0.136763i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −2.56894 −0.477041 −0.238521 0.971137i \(-0.576662\pi\)
−0.238521 + 0.971137i \(0.576662\pi\)
\(30\) 0 0
\(31\) −0.613062 −0.110109 −0.0550546 0.998483i \(-0.517533\pi\)
−0.0550546 + 0.998483i \(0.517533\pi\)
\(32\) 0 0
\(33\) 3.31842i 0.577662i
\(34\) 0 0
\(35\) 0.568944 8.28109i 0.0961692 1.39976i
\(36\) 0 0
\(37\) 0.257322i 0.0423034i 0.999776 + 0.0211517i \(0.00673331\pi\)
−0.999776 + 0.0211517i \(0.993267\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) −10.6114 −1.65722 −0.828611 0.559826i \(-0.810868\pi\)
−0.828611 + 0.559826i \(0.810868\pi\)
\(42\) 0 0
\(43\) 12.6935i 1.93574i −0.251450 0.967870i \(-0.580907\pi\)
0.251450 0.967870i \(-0.419093\pi\)
\(44\) 0 0
\(45\) −2.23081 0.153266i −0.332549 0.0228475i
\(46\) 0 0
\(47\) 7.44442i 1.08588i 0.839771 + 0.542940i \(0.182689\pi\)
−0.839771 + 0.542940i \(0.817311\pi\)
\(48\) 0 0
\(49\) −6.78003 −0.968576
\(50\) 0 0
\(51\) −1.55706 −0.218032
\(52\) 0 0
\(53\) 5.39521i 0.741089i −0.928815 0.370545i \(-0.879171\pi\)
0.928815 0.370545i \(-0.120829\pi\)
\(54\) 0 0
\(55\) −7.40275 0.508599i −0.998187 0.0685795i
\(56\) 0 0
\(57\) 5.33709i 0.706915i
\(58\) 0 0
\(59\) −13.1358 −1.71014 −0.855068 0.518516i \(-0.826485\pi\)
−0.855068 + 0.518516i \(0.826485\pi\)
\(60\) 0 0
\(61\) −5.27452 −0.675333 −0.337667 0.941266i \(-0.609638\pi\)
−0.337667 + 0.941266i \(0.609638\pi\)
\(62\) 0 0
\(63\) 3.71215i 0.467687i
\(64\) 0 0
\(65\) −0.153266 + 2.23081i −0.0190103 + 0.276698i
\(66\) 0 0
\(67\) 10.5384i 1.28747i 0.765248 + 0.643736i \(0.222617\pi\)
−0.765248 + 0.643736i \(0.777383\pi\)
\(68\) 0 0
\(69\) −0.442940 −0.0533237
\(70\) 0 0
\(71\) −0.311845 −0.0370092 −0.0185046 0.999829i \(-0.505891\pi\)
−0.0185046 + 0.999829i \(0.505891\pi\)
\(72\) 0 0
\(73\) 9.46841i 1.10819i 0.832452 + 0.554097i \(0.186936\pi\)
−0.832452 + 0.554097i \(0.813064\pi\)
\(74\) 0 0
\(75\) 0.683813 4.95302i 0.0789599 0.571925i
\(76\) 0 0
\(77\) 12.3184i 1.40382i
\(78\) 0 0
\(79\) 16.1871 1.82119 0.910597 0.413295i \(-0.135622\pi\)
0.910597 + 0.413295i \(0.135622\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 11.7546i 1.29023i −0.764084 0.645117i \(-0.776809\pi\)
0.764084 0.645117i \(-0.223191\pi\)
\(84\) 0 0
\(85\) 0.238644 3.47350i 0.0258845 0.376754i
\(86\) 0 0
\(87\) 2.56894i 0.275420i
\(88\) 0 0
\(89\) 4.58762 0.486287 0.243144 0.969990i \(-0.421821\pi\)
0.243144 + 0.969990i \(0.421821\pi\)
\(90\) 0 0
\(91\) 3.71215 0.389139
\(92\) 0 0
\(93\) 0.613062i 0.0635716i
\(94\) 0 0
\(95\) −11.9060 0.817993i −1.22153 0.0839243i
\(96\) 0 0
\(97\) 10.8500i 1.10165i −0.834619 0.550827i \(-0.814312\pi\)
0.834619 0.550827i \(-0.185688\pi\)
\(98\) 0 0
\(99\) 3.31842 0.333513
\(100\) 0 0
\(101\) 1.68306 0.167471 0.0837356 0.996488i \(-0.473315\pi\)
0.0837356 + 0.996488i \(0.473315\pi\)
\(102\) 0 0
\(103\) 1.78535i 0.175916i −0.996124 0.0879578i \(-0.971966\pi\)
0.996124 0.0879578i \(-0.0280341\pi\)
\(104\) 0 0
\(105\) −8.28109 0.568944i −0.808152 0.0555233i
\(106\) 0 0
\(107\) 1.11943i 0.108220i 0.998535 + 0.0541098i \(0.0172321\pi\)
−0.998535 + 0.0541098i \(0.982768\pi\)
\(108\) 0 0
\(109\) 0.914914 0.0876329 0.0438164 0.999040i \(-0.486048\pi\)
0.0438164 + 0.999040i \(0.486048\pi\)
\(110\) 0 0
\(111\) 0.257322 0.0244239
\(112\) 0 0
\(113\) 2.41386i 0.227077i 0.993534 + 0.113538i \(0.0362185\pi\)
−0.993534 + 0.113538i \(0.963782\pi\)
\(114\) 0 0
\(115\) 0.0678875 0.988115i 0.00633054 0.0921422i
\(116\) 0 0
\(117\) 1.00000i 0.0924500i
\(118\) 0 0
\(119\) −5.78003 −0.529855
\(120\) 0 0
\(121\) 0.0118848 0.00108043
\(122\) 0 0
\(123\) 10.6114i 0.956797i
\(124\) 0 0
\(125\) 10.9444 + 2.28458i 0.978900 + 0.204339i
\(126\) 0 0
\(127\) 14.0418i 1.24601i −0.782218 0.623005i \(-0.785912\pi\)
0.782218 0.623005i \(-0.214088\pi\)
\(128\) 0 0
\(129\) −12.6935 −1.11760
\(130\) 0 0
\(131\) −13.7650 −1.20265 −0.601327 0.799003i \(-0.705361\pi\)
−0.601327 + 0.799003i \(0.705361\pi\)
\(132\) 0 0
\(133\) 19.8121i 1.71792i
\(134\) 0 0
\(135\) −0.153266 + 2.23081i −0.0131910 + 0.191997i
\(136\) 0 0
\(137\) 6.50470i 0.555734i 0.960620 + 0.277867i \(0.0896275\pi\)
−0.960620 + 0.277867i \(0.910373\pi\)
\(138\) 0 0
\(139\) 9.78003 0.829532 0.414766 0.909928i \(-0.363863\pi\)
0.414766 + 0.909928i \(0.363863\pi\)
\(140\) 0 0
\(141\) 7.44442 0.626933
\(142\) 0 0
\(143\) 3.31842i 0.277500i
\(144\) 0 0
\(145\) −5.73082 0.393731i −0.475919 0.0326976i
\(146\) 0 0
\(147\) 6.78003i 0.559208i
\(148\) 0 0
\(149\) 5.93148 0.485926 0.242963 0.970036i \(-0.421881\pi\)
0.242963 + 0.970036i \(0.421881\pi\)
\(150\) 0 0
\(151\) 0.272818 0.0222016 0.0111008 0.999938i \(-0.496466\pi\)
0.0111008 + 0.999938i \(0.496466\pi\)
\(152\) 0 0
\(153\) 1.55706i 0.125881i
\(154\) 0 0
\(155\) −1.36763 0.0939614i −0.109850 0.00754716i
\(156\) 0 0
\(157\) 14.6561i 1.16969i −0.811146 0.584844i \(-0.801156\pi\)
0.811146 0.584844i \(-0.198844\pi\)
\(158\) 0 0
\(159\) −5.39521 −0.427868
\(160\) 0 0
\(161\) −1.64426 −0.129586
\(162\) 0 0
\(163\) 3.48345i 0.272845i 0.990651 + 0.136422i \(0.0435604\pi\)
−0.990651 + 0.136422i \(0.956440\pi\)
\(164\) 0 0
\(165\) −0.508599 + 7.40275i −0.0395944 + 0.576304i
\(166\) 0 0
\(167\) 4.69135i 0.363028i 0.983388 + 0.181514i \(0.0580998\pi\)
−0.983388 + 0.181514i \(0.941900\pi\)
\(168\) 0 0
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 5.33709 0.408138
\(172\) 0 0
\(173\) 3.26475i 0.248214i 0.992269 + 0.124107i \(0.0396067\pi\)
−0.992269 + 0.124107i \(0.960393\pi\)
\(174\) 0 0
\(175\) 2.53841 18.3863i 0.191886 1.38988i
\(176\) 0 0
\(177\) 13.1358i 0.987348i
\(178\) 0 0
\(179\) 19.7204 1.47397 0.736987 0.675907i \(-0.236248\pi\)
0.736987 + 0.675907i \(0.236248\pi\)
\(180\) 0 0
\(181\) −22.0558 −1.63940 −0.819698 0.572796i \(-0.805859\pi\)
−0.819698 + 0.572796i \(0.805859\pi\)
\(182\) 0 0
\(183\) 5.27452i 0.389904i
\(184\) 0 0
\(185\) −0.0394386 + 0.574036i −0.00289958 + 0.0422040i
\(186\) 0 0
\(187\) 5.16697i 0.377846i
\(188\) 0 0
\(189\) 3.71215 0.270019
\(190\) 0 0
\(191\) −22.2729 −1.61161 −0.805805 0.592182i \(-0.798267\pi\)
−0.805805 + 0.592182i \(0.798267\pi\)
\(192\) 0 0
\(193\) 15.7733i 1.13539i −0.823241 0.567693i \(-0.807836\pi\)
0.823241 0.567693i \(-0.192164\pi\)
\(194\) 0 0
\(195\) 2.23081 + 0.153266i 0.159752 + 0.0109756i
\(196\) 0 0
\(197\) 2.72871i 0.194413i 0.995264 + 0.0972063i \(0.0309907\pi\)
−0.995264 + 0.0972063i \(0.969009\pi\)
\(198\) 0 0
\(199\) −22.1029 −1.56684 −0.783418 0.621495i \(-0.786526\pi\)
−0.783418 + 0.621495i \(0.786526\pi\)
\(200\) 0 0
\(201\) 10.5384 0.743322
\(202\) 0 0
\(203\) 9.53630i 0.669317i
\(204\) 0 0
\(205\) −23.6720 1.62636i −1.65332 0.113590i
\(206\) 0 0
\(207\) 0.442940i 0.0307865i
\(208\) 0 0
\(209\) 17.7107 1.22507
\(210\) 0 0
\(211\) −1.01720 −0.0700268 −0.0350134 0.999387i \(-0.511147\pi\)
−0.0350134 + 0.999387i \(0.511147\pi\)
\(212\) 0 0
\(213\) 0.311845i 0.0213672i
\(214\) 0 0
\(215\) 1.94548 28.3168i 0.132680 1.93119i
\(216\) 0 0
\(217\) 2.27578i 0.154490i
\(218\) 0 0
\(219\) 9.46841 0.639816
\(220\) 0 0
\(221\) 1.55706 0.104739
\(222\) 0 0
\(223\) 6.85535i 0.459068i 0.973301 + 0.229534i \(0.0737202\pi\)
−0.973301 + 0.229534i \(0.926280\pi\)
\(224\) 0 0
\(225\) −4.95302 0.683813i −0.330201 0.0455875i
\(226\) 0 0
\(227\) 2.88224i 0.191301i 0.995415 + 0.0956504i \(0.0304931\pi\)
−0.995415 + 0.0956504i \(0.969507\pi\)
\(228\) 0 0
\(229\) −14.1857 −0.937416 −0.468708 0.883353i \(-0.655280\pi\)
−0.468708 + 0.883353i \(0.655280\pi\)
\(230\) 0 0
\(231\) 12.3184 0.810494
\(232\) 0 0
\(233\) 0.429354i 0.0281279i 0.999901 + 0.0140639i \(0.00447684\pi\)
−0.999901 + 0.0140639i \(0.995523\pi\)
\(234\) 0 0
\(235\) −1.14097 + 16.6071i −0.0744289 + 1.08333i
\(236\) 0 0
\(237\) 16.1871i 1.05147i
\(238\) 0 0
\(239\) 19.7255 1.27594 0.637969 0.770062i \(-0.279775\pi\)
0.637969 + 0.770062i \(0.279775\pi\)
\(240\) 0 0
\(241\) 19.6598 1.26640 0.633200 0.773988i \(-0.281741\pi\)
0.633200 + 0.773988i \(0.281741\pi\)
\(242\) 0 0
\(243\) 1.00000i 0.0641500i
\(244\) 0 0
\(245\) −15.1250 1.03915i −0.966298 0.0663886i
\(246\) 0 0
\(247\) 5.33709i 0.339591i
\(248\) 0 0
\(249\) −11.7546 −0.744917
\(250\) 0 0
\(251\) −23.4175 −1.47810 −0.739051 0.673650i \(-0.764726\pi\)
−0.739051 + 0.673650i \(0.764726\pi\)
\(252\) 0 0
\(253\) 1.46986i 0.0924093i
\(254\) 0 0
\(255\) −3.47350 0.238644i −0.217519 0.0149444i
\(256\) 0 0
\(257\) 30.7987i 1.92117i −0.277981 0.960586i \(-0.589665\pi\)
0.277981 0.960586i \(-0.410335\pi\)
\(258\) 0 0
\(259\) 0.955216 0.0593543
\(260\) 0 0
\(261\) 2.56894 0.159014
\(262\) 0 0
\(263\) 24.1471i 1.48897i 0.667638 + 0.744486i \(0.267305\pi\)
−0.667638 + 0.744486i \(0.732695\pi\)
\(264\) 0 0
\(265\) 0.826900 12.0357i 0.0507961 0.739346i
\(266\) 0 0
\(267\) 4.58762i 0.280758i
\(268\) 0 0
\(269\) −12.7557 −0.777726 −0.388863 0.921295i \(-0.627132\pi\)
−0.388863 + 0.921295i \(0.627132\pi\)
\(270\) 0 0
\(271\) 10.4222 0.633102 0.316551 0.948575i \(-0.397475\pi\)
0.316551 + 0.948575i \(0.397475\pi\)
\(272\) 0 0
\(273\) 3.71215i 0.224669i
\(274\) 0 0
\(275\) −16.4362 2.26918i −0.991139 0.136836i
\(276\) 0 0
\(277\) 19.9404i 1.19810i −0.800710 0.599052i \(-0.795544\pi\)
0.800710 0.599052i \(-0.204456\pi\)
\(278\) 0 0
\(279\) 0.613062 0.0367031
\(280\) 0 0
\(281\) 28.5272 1.70179 0.850895 0.525336i \(-0.176060\pi\)
0.850895 + 0.525336i \(0.176060\pi\)
\(282\) 0 0
\(283\) 19.1888i 1.14066i −0.821416 0.570329i \(-0.806816\pi\)
0.821416 0.570329i \(-0.193184\pi\)
\(284\) 0 0
\(285\) −0.817993 + 11.9060i −0.0484537 + 0.705253i
\(286\) 0 0
\(287\) 39.3910i 2.32518i
\(288\) 0 0
\(289\) 14.5756 0.857386
\(290\) 0 0
\(291\) −10.8500 −0.636040
\(292\) 0 0
\(293\) 11.9828i 0.700045i −0.936741 0.350022i \(-0.886174\pi\)
0.936741 0.350022i \(-0.113826\pi\)
\(294\) 0 0
\(295\) −29.3035 2.01327i −1.70611 0.117217i
\(296\) 0 0
\(297\) 3.31842i 0.192554i
\(298\) 0 0
\(299\) 0.442940 0.0256159
\(300\) 0 0
\(301\) −47.1201 −2.71596
\(302\) 0 0
\(303\) 1.68306i 0.0966895i
\(304\) 0 0
\(305\) −11.7664 0.808403i −0.673745 0.0462890i
\(306\) 0 0
\(307\) 25.0299i 1.42853i 0.699874 + 0.714267i \(0.253240\pi\)
−0.699874 + 0.714267i \(0.746760\pi\)
\(308\) 0 0
\(309\) −1.78535 −0.101565
\(310\) 0 0
\(311\) −27.6360 −1.56710 −0.783548 0.621331i \(-0.786592\pi\)
−0.783548 + 0.621331i \(0.786592\pi\)
\(312\) 0 0
\(313\) 14.5441i 0.822083i 0.911617 + 0.411042i \(0.134835\pi\)
−0.911617 + 0.411042i \(0.865165\pi\)
\(314\) 0 0
\(315\) −0.568944 + 8.28109i −0.0320564 + 0.466587i
\(316\) 0 0
\(317\) 8.00364i 0.449529i −0.974413 0.224765i \(-0.927839\pi\)
0.974413 0.224765i \(-0.0721613\pi\)
\(318\) 0 0
\(319\) 8.52483 0.477299
\(320\) 0 0
\(321\) 1.11943 0.0624806
\(322\) 0 0
\(323\) 8.31017i 0.462390i
\(324\) 0 0
\(325\) −0.683813 + 4.95302i −0.0379311 + 0.274744i
\(326\) 0 0
\(327\) 0.914914i 0.0505949i
\(328\) 0 0
\(329\) 27.6348 1.52355
\(330\) 0 0
\(331\) −5.59929 −0.307765 −0.153882 0.988089i \(-0.549178\pi\)
−0.153882 + 0.988089i \(0.549178\pi\)
\(332\) 0 0
\(333\) 0.257322i 0.0141011i
\(334\) 0 0
\(335\) −1.61518 + 23.5092i −0.0882465 + 1.28444i
\(336\) 0 0
\(337\) 34.5802i 1.88370i −0.336027 0.941852i \(-0.609083\pi\)
0.336027 0.941852i \(-0.390917\pi\)
\(338\) 0 0
\(339\) 2.41386 0.131103
\(340\) 0 0
\(341\) 2.03440 0.110169
\(342\) 0 0
\(343\) 0.816545i 0.0440893i
\(344\) 0 0
\(345\) −0.988115 0.0678875i −0.0531983 0.00365494i
\(346\) 0 0
\(347\) 31.0537i 1.66705i 0.552482 + 0.833525i \(0.313681\pi\)
−0.552482 + 0.833525i \(0.686319\pi\)
\(348\) 0 0
\(349\) −2.94804 −0.157805 −0.0789026 0.996882i \(-0.525142\pi\)
−0.0789026 + 0.996882i \(0.525142\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 1.80547i 0.0960957i 0.998845 + 0.0480478i \(0.0153000\pi\)
−0.998845 + 0.0480478i \(0.984700\pi\)
\(354\) 0 0
\(355\) −0.695666 0.0477951i −0.0369221 0.00253670i
\(356\) 0 0
\(357\) 5.78003i 0.305912i
\(358\) 0 0
\(359\) −9.29216 −0.490422 −0.245211 0.969470i \(-0.578857\pi\)
−0.245211 + 0.969470i \(0.578857\pi\)
\(360\) 0 0
\(361\) 9.48457 0.499188
\(362\) 0 0
\(363\) 0.0118848i 0.000623788i
\(364\) 0 0
\(365\) −1.45118 + 21.1222i −0.0759583 + 1.10559i
\(366\) 0 0
\(367\) 18.0955i 0.944579i −0.881444 0.472289i \(-0.843428\pi\)
0.881444 0.472289i \(-0.156572\pi\)
\(368\) 0 0
\(369\) 10.6114 0.552407
\(370\) 0 0
\(371\) −20.0278 −1.03979
\(372\) 0 0
\(373\) 29.4689i 1.52584i −0.646491 0.762922i \(-0.723764\pi\)
0.646491 0.762922i \(-0.276236\pi\)
\(374\) 0 0
\(375\) 2.28458 10.9444i 0.117975 0.565168i
\(376\) 0 0
\(377\) 2.56894i 0.132307i
\(378\) 0 0
\(379\) −21.2489 −1.09148 −0.545740 0.837954i \(-0.683751\pi\)
−0.545740 + 0.837954i \(0.683751\pi\)
\(380\) 0 0
\(381\) −14.0418 −0.719384
\(382\) 0 0
\(383\) 8.19163i 0.418573i 0.977854 + 0.209286i \(0.0671141\pi\)
−0.977854 + 0.209286i \(0.932886\pi\)
\(384\) 0 0
\(385\) −1.88799 + 27.4801i −0.0962211 + 1.40052i
\(386\) 0 0
\(387\) 12.6935i 0.645247i
\(388\) 0 0
\(389\) 24.4557 1.23995 0.619976 0.784621i \(-0.287142\pi\)
0.619976 + 0.784621i \(0.287142\pi\)
\(390\) 0 0
\(391\) −0.689684 −0.0348788
\(392\) 0 0
\(393\) 13.7650i 0.694352i
\(394\) 0 0
\(395\) 36.1104 + 2.48093i 1.81691 + 0.124829i
\(396\) 0 0
\(397\) 34.4916i 1.73108i −0.500837 0.865541i \(-0.666975\pi\)
0.500837 0.865541i \(-0.333025\pi\)
\(398\) 0 0
\(399\) 19.8121 0.991844
\(400\) 0 0
\(401\) −16.9434 −0.846114 −0.423057 0.906103i \(-0.639043\pi\)
−0.423057 + 0.906103i \(0.639043\pi\)
\(402\) 0 0
\(403\) 0.613062i 0.0305388i
\(404\) 0 0
\(405\) 2.23081 + 0.153266i 0.110850 + 0.00761583i
\(406\) 0 0
\(407\) 0.853901i 0.0423263i
\(408\) 0 0
\(409\) 3.05299 0.150961 0.0754804 0.997147i \(-0.475951\pi\)
0.0754804 + 0.997147i \(0.475951\pi\)
\(410\) 0 0
\(411\) 6.50470 0.320853
\(412\) 0 0
\(413\) 48.7620i 2.39942i
\(414\) 0 0
\(415\) 1.80158 26.2223i 0.0884358 1.28720i
\(416\) 0 0
\(417\) 9.78003i 0.478930i
\(418\) 0 0
\(419\) 20.9567 1.02380 0.511902 0.859044i \(-0.328941\pi\)
0.511902 + 0.859044i \(0.328941\pi\)
\(420\) 0 0
\(421\) −37.4462 −1.82502 −0.912508 0.409059i \(-0.865857\pi\)
−0.912508 + 0.409059i \(0.865857\pi\)
\(422\) 0 0
\(423\) 7.44442i 0.361960i
\(424\) 0 0
\(425\) 1.06474 7.71215i 0.0516473 0.374094i
\(426\) 0 0
\(427\) 19.5798i 0.947533i
\(428\) 0 0
\(429\) −3.31842 −0.160215
\(430\) 0 0
\(431\) 27.2671 1.31341 0.656706 0.754147i \(-0.271949\pi\)
0.656706 + 0.754147i \(0.271949\pi\)
\(432\) 0 0
\(433\) 12.5679i 0.603975i 0.953312 + 0.301988i \(0.0976501\pi\)
−0.953312 + 0.301988i \(0.902350\pi\)
\(434\) 0 0
\(435\) −0.393731 + 5.73082i −0.0188780 + 0.274772i
\(436\) 0 0
\(437\) 2.36401i 0.113086i
\(438\) 0 0
\(439\) 14.7241 0.702742 0.351371 0.936236i \(-0.385716\pi\)
0.351371 + 0.936236i \(0.385716\pi\)
\(440\) 0 0
\(441\) 6.78003 0.322859
\(442\) 0 0
\(443\) 8.65996i 0.411447i −0.978610 0.205724i \(-0.934045\pi\)
0.978610 0.205724i \(-0.0659548\pi\)
\(444\) 0 0
\(445\) 10.2341 + 0.703125i 0.485143 + 0.0333313i
\(446\) 0 0
\(447\) 5.93148i 0.280549i
\(448\) 0 0
\(449\) 21.5690 1.01791 0.508953 0.860795i \(-0.330033\pi\)
0.508953 + 0.860795i \(0.330033\pi\)
\(450\) 0 0
\(451\) 35.2130 1.65812
\(452\) 0 0
\(453\) 0.272818i 0.0128181i
\(454\) 0 0
\(455\) 8.28109 + 0.568944i 0.388224 + 0.0266725i
\(456\) 0 0
\(457\) 0.192394i 0.00899982i 0.999990 + 0.00449991i \(0.00143237\pi\)
−0.999990 + 0.00449991i \(0.998568\pi\)
\(458\) 0 0
\(459\) 1.55706 0.0726773
\(460\) 0 0
\(461\) −12.0821 −0.562720 −0.281360 0.959602i \(-0.590785\pi\)
−0.281360 + 0.959602i \(0.590785\pi\)
\(462\) 0 0
\(463\) 25.7245i 1.19552i −0.801676 0.597759i \(-0.796058\pi\)
0.801676 0.597759i \(-0.203942\pi\)
\(464\) 0 0
\(465\) −0.0939614 + 1.36763i −0.00435736 + 0.0634221i
\(466\) 0 0
\(467\) 18.4317i 0.852918i 0.904507 + 0.426459i \(0.140239\pi\)
−0.904507 + 0.426459i \(0.859761\pi\)
\(468\) 0 0
\(469\) 39.1201 1.80640
\(470\) 0 0
\(471\) −14.6561 −0.675319
\(472\) 0 0
\(473\) 42.1223i 1.93679i
\(474\) 0 0
\(475\) −26.4347 3.64957i −1.21291 0.167454i
\(476\) 0 0
\(477\) 5.39521i 0.247030i
\(478\) 0 0
\(479\) 25.5826 1.16890 0.584450 0.811430i \(-0.301310\pi\)
0.584450 + 0.811430i \(0.301310\pi\)
\(480\) 0 0
\(481\) −0.257322 −0.0117329
\(482\) 0 0
\(483\) 1.64426i 0.0748164i
\(484\) 0 0
\(485\) 1.66294 24.2044i 0.0755101 1.09906i
\(486\) 0 0
\(487\) 30.1997i 1.36848i −0.729258 0.684239i \(-0.760134\pi\)
0.729258 0.684239i \(-0.239866\pi\)
\(488\) 0 0
\(489\) 3.48345 0.157527
\(490\) 0 0
\(491\) 10.7256 0.484039 0.242020 0.970271i \(-0.422190\pi\)
0.242020 + 0.970271i \(0.422190\pi\)
\(492\) 0 0
\(493\) 4.00000i 0.180151i
\(494\) 0 0
\(495\) 7.40275 + 0.508599i 0.332729 + 0.0228598i
\(496\) 0 0
\(497\) 1.15761i 0.0519260i
\(498\) 0 0
\(499\) 7.01044 0.313830 0.156915 0.987612i \(-0.449845\pi\)
0.156915 + 0.987612i \(0.449845\pi\)
\(500\) 0 0
\(501\) 4.69135 0.209594
\(502\) 0 0
\(503\) 32.2604i 1.43842i 0.694793 + 0.719210i \(0.255496\pi\)
−0.694793 + 0.719210i \(0.744504\pi\)
\(504\) 0 0
\(505\) 3.75459 + 0.257956i 0.167077 + 0.0114789i
\(506\) 0 0
\(507\) 1.00000i 0.0444116i
\(508\) 0 0
\(509\) −17.3631 −0.769604 −0.384802 0.922999i \(-0.625730\pi\)
−0.384802 + 0.922999i \(0.625730\pi\)
\(510\) 0 0
\(511\) 35.1481 1.55486
\(512\) 0 0
\(513\) 5.33709i 0.235638i
\(514\) 0 0
\(515\) 0.273632 3.98277i 0.0120577 0.175502i
\(516\) 0 0
\(517\) 24.7037i 1.08647i
\(518\) 0 0
\(519\) 3.26475 0.143307
\(520\) 0 0
\(521\) 27.6513 1.21142 0.605712 0.795684i \(-0.292888\pi\)
0.605712 + 0.795684i \(0.292888\pi\)
\(522\) 0 0
\(523\) 7.49745i 0.327840i 0.986474 + 0.163920i \(0.0524140\pi\)
−0.986474 + 0.163920i \(0.947586\pi\)
\(524\) 0 0
\(525\) −18.3863 2.53841i −0.802445 0.110785i
\(526\) 0 0
\(527\) 0.954575i 0.0415819i
\(528\) 0 0
\(529\) 22.8038 0.991470
\(530\) 0 0
\(531\) 13.1358 0.570045
\(532\) 0 0
\(533\) 10.6114i 0.459630i
\(534\) 0 0
\(535\) −0.171571 + 2.49724i −0.00741764 + 0.107965i
\(536\) 0 0
\(537\) 19.7204i 0.850999i
\(538\) 0 0
\(539\) 22.4990 0.969099
\(540\) 0 0
\(541\) 18.8836 0.811871 0.405936 0.913902i \(-0.366946\pi\)
0.405936 + 0.913902i \(0.366946\pi\)
\(542\) 0 0
\(543\) 22.0558i 0.946506i
\(544\) 0 0
\(545\) 2.04100 + 0.140225i 0.0874268 + 0.00600658i
\(546\) 0 0
\(547\) 21.3808i 0.914178i −0.889421 0.457089i \(-0.848892\pi\)
0.889421 0.457089i \(-0.151108\pi\)
\(548\) 0 0
\(549\) 5.27452 0.225111
\(550\) 0 0
\(551\) 13.7107 0.584095
\(552\) 0 0
\(553\) 60.0890i 2.55524i
\(554\) 0 0
\(555\) 0.574036 + 0.0394386i 0.0243665 + 0.00167407i
\(556\) 0 0
\(557\) 3.80681i 0.161300i −0.996743 0.0806498i \(-0.974300\pi\)
0.996743 0.0806498i \(-0.0256995\pi\)
\(558\) 0 0
\(559\) 12.6935 0.536878
\(560\) 0 0
\(561\) 5.16697 0.218150
\(562\) 0 0
\(563\) 29.3983i 1.23899i −0.785001 0.619495i \(-0.787338\pi\)
0.785001 0.619495i \(-0.212662\pi\)
\(564\) 0 0
\(565\) −0.369961 + 5.38486i −0.0155644 + 0.226543i
\(566\) 0 0
\(567\) 3.71215i 0.155896i
\(568\) 0 0
\(569\) −12.4014 −0.519892 −0.259946 0.965623i \(-0.583705\pi\)
−0.259946 + 0.965623i \(0.583705\pi\)
\(570\) 0 0
\(571\) 4.56899 0.191206 0.0956032 0.995420i \(-0.469522\pi\)
0.0956032 + 0.995420i \(0.469522\pi\)
\(572\) 0 0
\(573\) 22.2729i 0.930463i
\(574\) 0 0
\(575\) 0.302888 2.19389i 0.0126313 0.0914916i
\(576\) 0 0
\(577\) 27.4496i 1.14274i −0.820692 0.571370i \(-0.806412\pi\)
0.820692 0.571370i \(-0.193588\pi\)
\(578\) 0 0
\(579\) −15.7733 −0.655515
\(580\) 0 0
\(581\) −43.6348 −1.81028
\(582\) 0 0
\(583\) 17.9036i 0.741489i
\(584\) 0 0
\(585\) 0.153266 2.23081i 0.00633675 0.0922326i
\(586\) 0 0
\(587\) 19.5191i 0.805641i −0.915279 0.402820i \(-0.868030\pi\)
0.915279 0.402820i \(-0.131970\pi\)
\(588\) 0 0
\(589\) 3.27197 0.134819
\(590\) 0 0
\(591\) 2.72871 0.112244
\(592\) 0 0
\(593\) 14.8539i 0.609975i −0.952356 0.304987i \(-0.901348\pi\)
0.952356 0.304987i \(-0.0986523\pi\)
\(594\) 0 0
\(595\) −12.8942 0.885881i −0.528609 0.0363176i
\(596\) 0 0
\(597\) 22.1029i 0.904613i
\(598\) 0 0
\(599\) −42.6098 −1.74099 −0.870494 0.492178i \(-0.836201\pi\)
−0.870494 + 0.492178i \(0.836201\pi\)
\(600\) 0 0
\(601\) 34.4960 1.40712 0.703561 0.710635i \(-0.251592\pi\)
0.703561 + 0.710635i \(0.251592\pi\)
\(602\) 0 0
\(603\) 10.5384i 0.429157i
\(604\) 0 0
\(605\) 0.0265126 + 0.00182153i 0.00107789 + 7.40555e-5i
\(606\) 0 0
\(607\) 44.0061i 1.78615i −0.449906 0.893076i \(-0.648543\pi\)
0.449906 0.893076i \(-0.351457\pi\)
\(608\) 0 0
\(609\) 9.53630 0.386430
\(610\) 0 0
\(611\) −7.44442 −0.301169
\(612\) 0 0
\(613\) 11.4907i 0.464104i 0.972703 + 0.232052i \(0.0745439\pi\)
−0.972703 + 0.232052i \(0.925456\pi\)
\(614\) 0 0
\(615\) −1.62636 + 23.6720i −0.0655812 + 0.954547i
\(616\) 0 0
\(617\) 47.2506i 1.90224i 0.308823 + 0.951120i \(0.400065\pi\)
−0.308823 + 0.951120i \(0.599935\pi\)
\(618\) 0 0
\(619\) 25.5964 1.02881 0.514403 0.857549i \(-0.328014\pi\)
0.514403 + 0.857549i \(0.328014\pi\)
\(620\) 0 0
\(621\) 0.442940 0.0177746
\(622\) 0 0
\(623\) 17.0299i 0.682290i
\(624\) 0 0
\(625\) 24.0648 + 6.77388i 0.962592 + 0.270955i
\(626\) 0 0
\(627\) 17.7107i 0.707297i
\(628\) 0 0
\(629\) 0.400665 0.0159756
\(630\) 0 0
\(631\) −6.54777 −0.260663 −0.130331 0.991470i \(-0.541604\pi\)
−0.130331 + 0.991470i \(0.541604\pi\)
\(632\) 0 0
\(633\) 1.01720i 0.0404300i
\(634\) 0 0
\(635\) 2.15213 31.3246i 0.0854046 1.24308i
\(636\) 0 0
\(637\) 6.78003i 0.268635i
\(638\) 0 0
\(639\) 0.311845 0.0123364
\(640\) 0 0
\(641\) −0.899023 −0.0355093 −0.0177546 0.999842i \(-0.505652\pi\)
−0.0177546 + 0.999842i \(0.505652\pi\)
\(642\) 0 0
\(643\) 2.48862i 0.0981416i 0.998795 + 0.0490708i \(0.0156260\pi\)
−0.998795 + 0.0490708i \(0.984374\pi\)
\(644\) 0 0
\(645\) −28.3168 1.94548i −1.11497 0.0766031i
\(646\) 0 0
\(647\) 0.773002i 0.0303898i −0.999885 0.0151949i \(-0.995163\pi\)
0.999885 0.0151949i \(-0.00483688\pi\)
\(648\) 0 0
\(649\) 43.5901 1.71106
\(650\) 0 0
\(651\) 2.27578 0.0891948
\(652\) 0 0
\(653\) 43.1740i 1.68953i −0.535139 0.844764i \(-0.679741\pi\)
0.535139 0.844764i \(-0.320259\pi\)
\(654\) 0 0
\(655\) −30.7071 2.10970i −1.19983 0.0824328i
\(656\) 0 0
\(657\) 9.46841i 0.369398i
\(658\) 0 0
\(659\) −39.3552 −1.53306 −0.766530 0.642208i \(-0.778019\pi\)
−0.766530 + 0.642208i \(0.778019\pi\)
\(660\) 0 0
\(661\) −20.7673 −0.807756 −0.403878 0.914813i \(-0.632338\pi\)
−0.403878 + 0.914813i \(0.632338\pi\)
\(662\) 0 0
\(663\) 1.55706i 0.0604712i
\(664\) 0 0
\(665\) −3.03651 + 44.1970i −0.117751 + 1.71388i
\(666\) 0 0
\(667\) 1.13789i 0.0440592i
\(668\) 0 0
\(669\) 6.85535 0.265043
\(670\) 0 0
\(671\) 17.5031 0.675698
\(672\) 0 0
\(673\) 49.6479i 1.91379i −0.290439 0.956893i \(-0.593801\pi\)
0.290439 0.956893i \(-0.406199\pi\)
\(674\) 0 0
\(675\) −0.683813 + 4.95302i −0.0263200 + 0.190642i
\(676\) 0 0
\(677\) 30.5884i 1.17561i 0.809004 + 0.587803i \(0.200007\pi\)
−0.809004 + 0.587803i \(0.799993\pi\)
\(678\) 0 0
\(679\) −40.2769 −1.54569
\(680\) 0 0
\(681\) 2.88224 0.110448
\(682\) 0 0
\(683\) 28.9405i 1.10738i −0.832724 0.553688i \(-0.813220\pi\)
0.832724 0.553688i \(-0.186780\pi\)
\(684\) 0 0
\(685\) −0.996947 + 14.5107i −0.0380914 + 0.554427i
\(686\) 0 0
\(687\) 14.1857i 0.541218i
\(688\) 0 0
\(689\) 5.39521 0.205541
\(690\) 0 0
\(691\) 31.9739 1.21635 0.608173 0.793805i \(-0.291903\pi\)
0.608173 + 0.793805i \(0.291903\pi\)
\(692\) 0 0
\(693\) 12.3184i 0.467939i
\(694\) 0 0
\(695\) 21.8174 + 1.49894i 0.827581 + 0.0568581i
\(696\) 0 0
\(697\) 16.5226i 0.625837i
\(698\) 0 0
\(699\) 0.429354 0.0162396
\(700\) 0 0
\(701\) 4.51673 0.170595 0.0852973 0.996356i \(-0.472816\pi\)
0.0852973 + 0.996356i \(0.472816\pi\)
\(702\) 0 0
\(703\) 1.37335i 0.0517969i
\(704\) 0 0
\(705\) 16.6071 + 1.14097i 0.625459 + 0.0429716i
\(706\) 0 0
\(707\) 6.24778i 0.234972i
\(708\) 0 0
\(709\) 29.7979 1.11908 0.559542 0.828802i \(-0.310977\pi\)
0.559542 + 0.828802i \(0.310977\pi\)
\(710\) 0 0
\(711\) −16.1871 −0.607065
\(712\) 0 0
\(713\) 0.271550i 0.0101696i
\(714\) 0 0
\(715\) 0.508599 7.40275i 0.0190205 0.276847i
\(716\) 0 0
\(717\) 19.7255i 0.736663i
\(718\) 0 0
\(719\) 41.8431 1.56049 0.780243 0.625477i \(-0.215096\pi\)
0.780243 + 0.625477i \(0.215096\pi\)
\(720\) 0 0
\(721\) −6.62747 −0.246820
\(722\) 0 0
\(723\) 19.6598i 0.731157i
\(724\) 0 0
\(725\) −12.7240 1.75668i −0.472559 0.0652413i
\(726\) 0 0
\(727\) 15.4317i 0.572330i 0.958180 + 0.286165i \(0.0923806\pi\)
−0.958180 + 0.286165i \(0.907619\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −19.7645 −0.731018
\(732\) 0 0
\(733\) 39.1794i 1.44712i 0.690260 + 0.723561i \(0.257496\pi\)
−0.690260 + 0.723561i \(0.742504\pi\)
\(734\) 0 0
\(735\) −1.03915 + 15.1250i −0.0383295 + 0.557893i
\(736\) 0 0
\(737\) 34.9708i 1.28817i
\(738\) 0 0
\(739\) 32.5361 1.19686 0.598430 0.801175i \(-0.295791\pi\)
0.598430 + 0.801175i \(0.295791\pi\)
\(740\) 0 0
\(741\) −5.33709 −0.196063
\(742\) 0 0
\(743\) 8.13346i 0.298388i −0.988808 0.149194i \(-0.952332\pi\)
0.988808 0.149194i \(-0.0476679\pi\)
\(744\) 0 0
\(745\) 13.2320 + 0.909092i 0.484783 + 0.0333065i
\(746\) 0 0
\(747\) 11.7546i 0.430078i
\(748\) 0 0
\(749\) 4.15550 0.151839
\(750\) 0 0
\(751\) 48.9359 1.78570 0.892848 0.450358i \(-0.148704\pi\)
0.892848 + 0.450358i \(0.148704\pi\)
\(752\) 0 0
\(753\) 23.4175i 0.853382i
\(754\) 0 0
\(755\) 0.608605 + 0.0418136i 0.0221494 + 0.00152175i
\(756\) 0 0
\(757\) 3.54775i 0.128945i 0.997919 + 0.0644726i \(0.0205365\pi\)
−0.997919 + 0.0644726i \(0.979463\pi\)
\(758\) 0 0
\(759\) 1.46986 0.0533525
\(760\) 0 0
\(761\) 40.8645 1.48134 0.740669 0.671870i \(-0.234509\pi\)
0.740669 + 0.671870i \(0.234509\pi\)
\(762\) 0 0
\(763\) 3.39630i 0.122954i
\(764\) 0 0
\(765\) −0.238644 + 3.47350i −0.00862818 + 0.125585i
\(766\) 0 0
\(767\) 13.1358i 0.474306i
\(768\) 0 0
\(769\) 42.6263 1.53714 0.768571 0.639764i \(-0.220968\pi\)
0.768571 + 0.639764i \(0.220968\pi\)
\(770\) 0 0
\(771\) −30.7987 −1.10919
\(772\) 0 0
\(773\) 36.3873i 1.30876i 0.756166 + 0.654379i \(0.227070\pi\)
−0.756166 + 0.654379i \(0.772930\pi\)
\(774\) 0 0
\(775\) −3.03651 0.419220i −0.109075 0.0150588i
\(776\) 0 0
\(777\) 0.955216i 0.0342682i
\(778\) 0 0
\(779\) 56.6340 2.02912
\(780\) 0 0
\(781\) 1.03483 0.0370291
\(782\) 0 0
\(783\) 2.56894i 0.0918066i
\(784\) 0 0
\(785\) 2.24628 32.6951i 0.0801733 1.16694i
\(786\) 0 0
\(787\) 12.7280i 0.453705i 0.973929 + 0.226853i \(0.0728436\pi\)
−0.973929 + 0.226853i \(0.927156\pi\)
\(788\) 0 0
\(789\) 24.1471 0.859658
\(790\) 0 0
\(791\) 8.96059 0.318602
\(792\) 0 0
\(793\) 5.27452i 0.187304i
\(794\) 0 0
\(795\) −12.0357 0.826900i −0.426862 0.0293271i
\(796\) 0 0
\(797\) 20.3707i 0.721566i −0.932650 0.360783i \(-0.882510\pi\)
0.932650 0.360783i \(-0.117490\pi\)
\(798\) 0 0
\(799\) 11.5914 0.410074
\(800\) 0 0