Properties

Label 3456.2.i.l.2305.5
Level $3456$
Weight $2$
Character 3456.2305
Analytic conductor $27.596$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3456 = 2^{7} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3456.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.5962989386\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 1152)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.5
Root \(0.952418 - 1.44669i\) of defining polynomial
Character \(\chi\) \(=\) 3456.2305
Dual form 3456.2.i.l.1153.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.24278 - 2.15256i) q^{5} +(0.909142 + 1.57468i) q^{7} +O(q^{10})\) \(q+(1.24278 - 2.15256i) q^{5} +(0.909142 + 1.57468i) q^{7} +(-0.598407 - 1.03647i) q^{11} +(-2.83342 + 4.90762i) q^{13} +5.30021 q^{17} -4.55980 q^{19} +(2.01328 - 3.48711i) q^{23} +(-0.589008 - 1.02019i) q^{25} +(3.01513 + 5.22236i) q^{29} +(2.81647 - 4.87827i) q^{31} +4.51946 q^{35} +5.18127 q^{37} +(-4.57620 + 7.92621i) q^{41} +(3.99129 + 6.91313i) q^{43} +(-1.39470 - 2.41570i) q^{47} +(1.84692 - 3.19896i) q^{49} +1.54470 q^{53} -2.97475 q^{55} +(1.85725 - 3.21686i) q^{59} +(4.01513 + 6.95441i) q^{61} +(7.04263 + 12.1982i) q^{65} +(-6.91372 + 11.9749i) q^{67} +11.1794 q^{71} +12.3969 q^{73} +(1.08807 - 1.88460i) q^{77} +(4.36480 + 7.56006i) q^{79} +(-8.89267 - 15.4025i) q^{83} +(6.58700 - 11.4090i) q^{85} +0.455297 q^{89} -10.3039 q^{91} +(-5.66683 + 9.81524i) q^{95} +(-1.01640 - 1.76045i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{5} + 6 q^{7} - 4 q^{11} + 10 q^{13} - 4 q^{17} + 4 q^{19} - 8 q^{23} - 14 q^{25} + 2 q^{29} + 8 q^{31} - 8 q^{35} + 2 q^{41} - 2 q^{43} + 14 q^{47} - 18 q^{49} - 24 q^{53} - 16 q^{55} - 6 q^{59} + 14 q^{61} + 8 q^{65} + 4 q^{67} + 28 q^{71} + 60 q^{73} - 2 q^{77} + 16 q^{79} - 24 q^{83} + 16 q^{85} + 48 q^{89} - 52 q^{91} + 20 q^{95} - 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).

\(n\) \(2053\) \(2431\) \(2945\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(4\) 0 0
\(5\) 1.24278 2.15256i 0.555788 0.962654i −0.442053 0.896989i \(-0.645750\pi\)
0.997842 0.0656650i \(-0.0209169\pi\)
\(6\) 0 0
\(7\) 0.909142 + 1.57468i 0.343623 + 0.595173i 0.985103 0.171967i \(-0.0550123\pi\)
−0.641479 + 0.767140i \(0.721679\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.598407 1.03647i −0.180426 0.312508i 0.761599 0.648048i \(-0.224414\pi\)
−0.942026 + 0.335540i \(0.891081\pi\)
\(12\) 0 0
\(13\) −2.83342 + 4.90762i −0.785848 + 1.36113i 0.142643 + 0.989774i \(0.454440\pi\)
−0.928491 + 0.371355i \(0.878893\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.30021 1.28549 0.642745 0.766080i \(-0.277795\pi\)
0.642745 + 0.766080i \(0.277795\pi\)
\(18\) 0 0
\(19\) −4.55980 −1.04609 −0.523045 0.852305i \(-0.675204\pi\)
−0.523045 + 0.852305i \(0.675204\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.01328 3.48711i 0.419798 0.727112i −0.576120 0.817365i \(-0.695434\pi\)
0.995919 + 0.0902526i \(0.0287674\pi\)
\(24\) 0 0
\(25\) −0.589008 1.02019i −0.117802 0.204038i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.01513 + 5.22236i 0.559896 + 0.969768i 0.997505 + 0.0706027i \(0.0224923\pi\)
−0.437609 + 0.899166i \(0.644174\pi\)
\(30\) 0 0
\(31\) 2.81647 4.87827i 0.505853 0.876163i −0.494124 0.869391i \(-0.664511\pi\)
0.999977 0.00677135i \(-0.00215540\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.51946 0.763928
\(36\) 0 0
\(37\) 5.18127 0.851796 0.425898 0.904771i \(-0.359958\pi\)
0.425898 + 0.904771i \(0.359958\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −4.57620 + 7.92621i −0.714682 + 1.23787i 0.248400 + 0.968658i \(0.420095\pi\)
−0.963082 + 0.269208i \(0.913238\pi\)
\(42\) 0 0
\(43\) 3.99129 + 6.91313i 0.608667 + 1.05424i 0.991460 + 0.130408i \(0.0416287\pi\)
−0.382794 + 0.923834i \(0.625038\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.39470 2.41570i −0.203438 0.352366i 0.746196 0.665727i \(-0.231878\pi\)
−0.949634 + 0.313361i \(0.898545\pi\)
\(48\) 0 0
\(49\) 1.84692 3.19896i 0.263846 0.456994i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.54470 0.212181 0.106091 0.994356i \(-0.466167\pi\)
0.106091 + 0.994356i \(0.466167\pi\)
\(54\) 0 0
\(55\) −2.97475 −0.401116
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.85725 3.21686i 0.241794 0.418799i −0.719431 0.694563i \(-0.755598\pi\)
0.961225 + 0.275764i \(0.0889309\pi\)
\(60\) 0 0
\(61\) 4.01513 + 6.95441i 0.514085 + 0.890421i 0.999866 + 0.0163411i \(0.00520175\pi\)
−0.485781 + 0.874080i \(0.661465\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.04263 + 12.1982i 0.873531 + 1.51300i
\(66\) 0 0
\(67\) −6.91372 + 11.9749i −0.844645 + 1.46297i 0.0412836 + 0.999147i \(0.486855\pi\)
−0.885929 + 0.463821i \(0.846478\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.1794 1.32675 0.663376 0.748287i \(-0.269123\pi\)
0.663376 + 0.748287i \(0.269123\pi\)
\(72\) 0 0
\(73\) 12.3969 1.45095 0.725473 0.688251i \(-0.241621\pi\)
0.725473 + 0.688251i \(0.241621\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.08807 1.88460i 0.123998 0.214770i
\(78\) 0 0
\(79\) 4.36480 + 7.56006i 0.491079 + 0.850573i 0.999947 0.0102710i \(-0.00326940\pi\)
−0.508869 + 0.860844i \(0.669936\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −8.89267 15.4025i −0.976097 1.69065i −0.676267 0.736657i \(-0.736403\pi\)
−0.299830 0.953993i \(-0.596930\pi\)
\(84\) 0 0
\(85\) 6.58700 11.4090i 0.714461 1.23748i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.455297 0.0482614 0.0241307 0.999709i \(-0.492318\pi\)
0.0241307 + 0.999709i \(0.492318\pi\)
\(90\) 0 0
\(91\) −10.3039 −1.08014
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.66683 + 9.81524i −0.581405 + 1.00702i
\(96\) 0 0
\(97\) −1.01640 1.76045i −0.103199 0.178747i 0.809802 0.586704i \(-0.199575\pi\)
−0.913001 + 0.407957i \(0.866241\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.06107 + 5.30192i 0.304587 + 0.527561i 0.977169 0.212462i \(-0.0681481\pi\)
−0.672582 + 0.740023i \(0.734815\pi\)
\(102\) 0 0
\(103\) 3.09086 5.35352i 0.304551 0.527498i −0.672610 0.739997i \(-0.734827\pi\)
0.977161 + 0.212499i \(0.0681602\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.2193 −1.56798 −0.783990 0.620774i \(-0.786818\pi\)
−0.783990 + 0.620774i \(0.786818\pi\)
\(108\) 0 0
\(109\) 2.08460 0.199669 0.0998344 0.995004i \(-0.468169\pi\)
0.0998344 + 0.995004i \(0.468169\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.45933 + 2.52763i −0.137282 + 0.237779i −0.926467 0.376376i \(-0.877170\pi\)
0.789185 + 0.614156i \(0.210503\pi\)
\(114\) 0 0
\(115\) −5.00414 8.66742i −0.466638 0.808241i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 4.81865 + 8.34614i 0.441725 + 0.765090i
\(120\) 0 0
\(121\) 4.78382 8.28582i 0.434893 0.753256i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.49978 0.849686
\(126\) 0 0
\(127\) 15.0618 1.33652 0.668261 0.743926i \(-0.267039\pi\)
0.668261 + 0.743926i \(0.267039\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.89311 + 3.27896i −0.165402 + 0.286484i −0.936798 0.349871i \(-0.886225\pi\)
0.771396 + 0.636355i \(0.219559\pi\)
\(132\) 0 0
\(133\) −4.14551 7.18023i −0.359461 0.622605i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.39448 11.0756i −0.546317 0.946250i −0.998523 0.0543357i \(-0.982696\pi\)
0.452205 0.891914i \(-0.350637\pi\)
\(138\) 0 0
\(139\) 4.46539 7.73428i 0.378749 0.656013i −0.612131 0.790756i \(-0.709688\pi\)
0.990881 + 0.134743i \(0.0430209\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.78214 0.567151
\(144\) 0 0
\(145\) 14.9886 1.24473
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.65170 8.05698i 0.381082 0.660054i −0.610135 0.792297i \(-0.708885\pi\)
0.991217 + 0.132244i \(0.0422182\pi\)
\(150\) 0 0
\(151\) 7.83527 + 13.5711i 0.637625 + 1.10440i 0.985953 + 0.167026i \(0.0534164\pi\)
−0.348328 + 0.937373i \(0.613250\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −7.00051 12.1252i −0.562294 0.973922i
\(156\) 0 0
\(157\) 9.75491 16.8960i 0.778526 1.34845i −0.154265 0.988030i \(-0.549301\pi\)
0.932791 0.360418i \(-0.117366\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.32144 0.577010
\(162\) 0 0
\(163\) −5.02888 −0.393892 −0.196946 0.980414i \(-0.563102\pi\)
−0.196946 + 0.980414i \(0.563102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.65066 + 13.2513i −0.592026 + 1.02542i 0.401933 + 0.915669i \(0.368338\pi\)
−0.993959 + 0.109750i \(0.964995\pi\)
\(168\) 0 0
\(169\) −9.55650 16.5523i −0.735115 1.27326i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 5.30192 + 9.18320i 0.403098 + 0.698186i 0.994098 0.108486i \(-0.0346001\pi\)
−0.591000 + 0.806671i \(0.701267\pi\)
\(174\) 0 0
\(175\) 1.07098 1.85500i 0.0809588 0.140225i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.27314 0.693107 0.346553 0.938030i \(-0.387352\pi\)
0.346553 + 0.938030i \(0.387352\pi\)
\(180\) 0 0
\(181\) −2.32975 −0.173169 −0.0865845 0.996245i \(-0.527595\pi\)
−0.0865845 + 0.996245i \(0.527595\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.43918 11.1530i 0.473418 0.819985i
\(186\) 0 0
\(187\) −3.17169 5.49352i −0.231937 0.401726i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.54208 + 14.7953i 0.618083 + 1.07055i 0.989835 + 0.142219i \(0.0454238\pi\)
−0.371752 + 0.928332i \(0.621243\pi\)
\(192\) 0 0
\(193\) −12.1360 + 21.0202i −0.873568 + 1.51306i −0.0152882 + 0.999883i \(0.504867\pi\)
−0.858280 + 0.513182i \(0.828467\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −15.6971 −1.11837 −0.559186 0.829042i \(-0.688886\pi\)
−0.559186 + 0.829042i \(0.688886\pi\)
\(198\) 0 0
\(199\) −14.4764 −1.02620 −0.513101 0.858328i \(-0.671503\pi\)
−0.513101 + 0.858328i \(0.671503\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5.48237 + 9.49574i −0.384787 + 0.666470i
\(204\) 0 0
\(205\) 11.3744 + 19.7011i 0.794424 + 1.37598i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.72862 + 4.72610i 0.188742 + 0.326911i
\(210\) 0 0
\(211\) 3.21103 5.56167i 0.221056 0.382881i −0.734073 0.679071i \(-0.762383\pi\)
0.955129 + 0.296190i \(0.0957162\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 19.8412 1.35316
\(216\) 0 0
\(217\) 10.2423 0.695291
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −15.0177 + 26.0114i −1.01020 + 1.74972i
\(222\) 0 0
\(223\) −7.90683 13.6950i −0.529481 0.917087i −0.999409 0.0343825i \(-0.989054\pi\)
0.469928 0.882705i \(-0.344280\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.00928 + 5.21223i 0.199733 + 0.345948i 0.948442 0.316951i \(-0.102659\pi\)
−0.748709 + 0.662899i \(0.769326\pi\)
\(228\) 0 0
\(229\) 13.8177 23.9329i 0.913098 1.58153i 0.103436 0.994636i \(-0.467016\pi\)
0.809662 0.586896i \(-0.199650\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 12.1858 0.798321 0.399161 0.916881i \(-0.369302\pi\)
0.399161 + 0.916881i \(0.369302\pi\)
\(234\) 0 0
\(235\) −6.93324 −0.452275
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.82794 13.5584i 0.506347 0.877019i −0.493626 0.869674i \(-0.664329\pi\)
0.999973 0.00734451i \(-0.00233785\pi\)
\(240\) 0 0
\(241\) 9.39281 + 16.2688i 0.605044 + 1.04797i 0.992045 + 0.125887i \(0.0401778\pi\)
−0.387001 + 0.922079i \(0.626489\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.59064 7.95121i −0.293285 0.507984i
\(246\) 0 0
\(247\) 12.9198 22.3778i 0.822068 1.42386i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −11.1684 −0.704942 −0.352471 0.935823i \(-0.614658\pi\)
−0.352471 + 0.935823i \(0.614658\pi\)
\(252\) 0 0
\(253\) −4.81905 −0.302971
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.19941 + 5.54154i −0.199574 + 0.345672i −0.948390 0.317106i \(-0.897289\pi\)
0.748817 + 0.662777i \(0.230622\pi\)
\(258\) 0 0
\(259\) 4.71051 + 8.15885i 0.292697 + 0.506966i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −6.71632 11.6330i −0.414146 0.717322i 0.581192 0.813766i \(-0.302586\pi\)
−0.995338 + 0.0964440i \(0.969253\pi\)
\(264\) 0 0
\(265\) 1.91973 3.32507i 0.117928 0.204257i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 26.6295 1.62363 0.811814 0.583916i \(-0.198480\pi\)
0.811814 + 0.583916i \(0.198480\pi\)
\(270\) 0 0
\(271\) 14.9630 0.908936 0.454468 0.890763i \(-0.349829\pi\)
0.454468 + 0.890763i \(0.349829\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.704933 + 1.22098i −0.0425091 + 0.0736278i
\(276\) 0 0
\(277\) 8.36861 + 14.4949i 0.502821 + 0.870912i 0.999995 + 0.00326057i \(0.00103787\pi\)
−0.497174 + 0.867651i \(0.665629\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.80547 + 4.85922i 0.167361 + 0.289877i 0.937491 0.348009i \(-0.113142\pi\)
−0.770131 + 0.637886i \(0.779809\pi\)
\(282\) 0 0
\(283\) 6.41074 11.1037i 0.381079 0.660048i −0.610138 0.792295i \(-0.708886\pi\)
0.991217 + 0.132247i \(0.0422194\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −16.6417 −0.982326
\(288\) 0 0
\(289\) 11.0923 0.652487
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.24047 + 12.5409i −0.422993 + 0.732645i −0.996231 0.0867441i \(-0.972354\pi\)
0.573238 + 0.819389i \(0.305687\pi\)
\(294\) 0 0
\(295\) −4.61632 7.99570i −0.268772 0.465528i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 11.4089 + 19.7609i 0.659796 + 1.14280i
\(300\) 0 0
\(301\) −7.25731 + 12.5700i −0.418304 + 0.724524i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 19.9597 1.14289
\(306\) 0 0
\(307\) −19.4320 −1.10905 −0.554523 0.832169i \(-0.687099\pi\)
−0.554523 + 0.832169i \(0.687099\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.47547 + 6.01968i −0.197076 + 0.341345i −0.947579 0.319522i \(-0.896478\pi\)
0.750503 + 0.660867i \(0.229811\pi\)
\(312\) 0 0
\(313\) −2.19252 3.79756i −0.123929 0.214651i 0.797385 0.603471i \(-0.206216\pi\)
−0.921314 + 0.388820i \(0.872883\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 15.6742 + 27.1485i 0.880350 + 1.52481i 0.850952 + 0.525244i \(0.176026\pi\)
0.0293983 + 0.999568i \(0.490641\pi\)
\(318\) 0 0
\(319\) 3.60855 6.25020i 0.202040 0.349944i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −24.1679 −1.34474
\(324\) 0 0
\(325\) 6.67562 0.370297
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.53597 4.39243i 0.139812 0.242162i
\(330\) 0 0
\(331\) 11.1515 + 19.3150i 0.612943 + 1.06165i 0.990742 + 0.135760i \(0.0433477\pi\)
−0.377799 + 0.925888i \(0.623319\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 17.1845 + 29.7644i 0.938888 + 1.62620i
\(336\) 0 0
\(337\) −10.4077 + 18.0266i −0.566943 + 0.981974i 0.429923 + 0.902866i \(0.358541\pi\)
−0.996866 + 0.0791086i \(0.974793\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −6.74158 −0.365077
\(342\) 0 0
\(343\) 19.4444 1.04990
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 14.4912 25.0995i 0.777929 1.34741i −0.155204 0.987882i \(-0.549604\pi\)
0.933133 0.359530i \(-0.117063\pi\)
\(348\) 0 0
\(349\) −7.60709 13.1759i −0.407198 0.705288i 0.587377 0.809314i \(-0.300161\pi\)
−0.994575 + 0.104026i \(0.966827\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6.78818 + 11.7575i 0.361298 + 0.625787i 0.988175 0.153332i \(-0.0490003\pi\)
−0.626877 + 0.779119i \(0.715667\pi\)
\(354\) 0 0
\(355\) 13.8935 24.0643i 0.737393 1.27720i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −31.6623 −1.67107 −0.835536 0.549436i \(-0.814842\pi\)
−0.835536 + 0.549436i \(0.814842\pi\)
\(360\) 0 0
\(361\) 1.79179 0.0943046
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 15.4066 26.6850i 0.806419 1.39676i
\(366\) 0 0
\(367\) 4.90625 + 8.49788i 0.256104 + 0.443585i 0.965195 0.261532i \(-0.0842276\pi\)
−0.709091 + 0.705117i \(0.750894\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.40435 + 2.43241i 0.0729105 + 0.126285i
\(372\) 0 0
\(373\) 4.98487 8.63404i 0.258107 0.447054i −0.707628 0.706585i \(-0.750235\pi\)
0.965735 + 0.259531i \(0.0835681\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −34.1725 −1.75997
\(378\) 0 0
\(379\) −30.2351 −1.55307 −0.776537 0.630072i \(-0.783026\pi\)
−0.776537 + 0.630072i \(0.783026\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.86835 17.0925i 0.504249 0.873386i −0.495739 0.868472i \(-0.665103\pi\)
0.999988 0.00491371i \(-0.00156409\pi\)
\(384\) 0 0
\(385\) −2.70447 4.68429i −0.137833 0.238733i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.60577 6.24537i −0.182820 0.316653i 0.760020 0.649900i \(-0.225189\pi\)
−0.942840 + 0.333247i \(0.891856\pi\)
\(390\) 0 0
\(391\) 10.6708 18.4824i 0.539647 0.934696i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 21.6980 1.09174
\(396\) 0 0
\(397\) −20.8930 −1.04859 −0.524296 0.851536i \(-0.675671\pi\)
−0.524296 + 0.851536i \(0.675671\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.59174 2.75697i 0.0794877 0.137677i −0.823541 0.567256i \(-0.808005\pi\)
0.903029 + 0.429580i \(0.141338\pi\)
\(402\) 0 0
\(403\) 15.9605 + 27.6443i 0.795047 + 1.37706i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.10051 5.37024i −0.153687 0.266193i
\(408\) 0 0
\(409\) 11.5046 19.9265i 0.568865 0.985302i −0.427814 0.903867i \(-0.640716\pi\)
0.996679 0.0814356i \(-0.0259505\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6.75403 0.332344
\(414\) 0 0
\(415\) −44.2065 −2.17001
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.36640 2.36667i 0.0667528 0.115619i −0.830717 0.556694i \(-0.812069\pi\)
0.897470 + 0.441075i \(0.145403\pi\)
\(420\) 0 0
\(421\) −2.98079 5.16288i −0.145275 0.251624i 0.784201 0.620507i \(-0.213073\pi\)
−0.929475 + 0.368884i \(0.879740\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.12187 5.40724i −0.151433 0.262289i
\(426\) 0 0
\(427\) −7.30065 + 12.6451i −0.353303 + 0.611939i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −20.5125 −0.988051 −0.494026 0.869447i \(-0.664475\pi\)
−0.494026 + 0.869447i \(0.664475\pi\)
\(432\) 0 0
\(433\) −41.5464 −1.99659 −0.998295 0.0583639i \(-0.981412\pi\)
−0.998295 + 0.0583639i \(0.981412\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −9.18017 + 15.9005i −0.439147 + 0.760625i
\(438\) 0 0
\(439\) 15.0834 + 26.1253i 0.719894 + 1.24689i 0.961042 + 0.276404i \(0.0891428\pi\)
−0.241148 + 0.970488i \(0.577524\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 9.67554 + 16.7585i 0.459699 + 0.796222i 0.998945 0.0459267i \(-0.0146241\pi\)
−0.539246 + 0.842148i \(0.681291\pi\)
\(444\) 0 0
\(445\) 0.565834 0.980054i 0.0268231 0.0464590i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −13.4220 −0.633424 −0.316712 0.948522i \(-0.602579\pi\)
−0.316712 + 0.948522i \(0.602579\pi\)
\(450\) 0 0
\(451\) 10.9537 0.515790
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −12.8055 + 22.1798i −0.600331 + 1.03980i
\(456\) 0 0
\(457\) −3.06037 5.30072i −0.143158 0.247957i 0.785526 0.618828i \(-0.212392\pi\)
−0.928684 + 0.370871i \(0.879059\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5.80084 10.0473i −0.270172 0.467952i 0.698734 0.715382i \(-0.253747\pi\)
−0.968906 + 0.247430i \(0.920414\pi\)
\(462\) 0 0
\(463\) 4.42830 7.67005i 0.205801 0.356457i −0.744587 0.667526i \(-0.767353\pi\)
0.950388 + 0.311068i \(0.100687\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.20231 0.333283 0.166642 0.986018i \(-0.446708\pi\)
0.166642 + 0.986018i \(0.446708\pi\)
\(468\) 0 0
\(469\) −25.1422 −1.16096
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.77684 8.27372i 0.219639 0.380426i
\(474\) 0 0
\(475\) 2.68576 + 4.65187i 0.123231 + 0.213443i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.2521 21.2213i −0.559815 0.969628i −0.997511 0.0705051i \(-0.977539\pi\)
0.437696 0.899123i \(-0.355794\pi\)
\(480\) 0 0
\(481\) −14.6807 + 25.4277i −0.669382 + 1.15940i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5.05263 −0.229428
\(486\) 0 0
\(487\) −37.7200 −1.70926 −0.854629 0.519239i \(-0.826215\pi\)
−0.854629 + 0.519239i \(0.826215\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0.203651 0.352734i 0.00919063 0.0159186i −0.861394 0.507938i \(-0.830408\pi\)
0.870584 + 0.492020i \(0.163741\pi\)
\(492\) 0 0
\(493\) 15.9808 + 27.6796i 0.719741 + 1.24663i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.1637 + 17.6040i 0.455903 + 0.789647i
\(498\) 0 0
\(499\) −3.73644 + 6.47171i −0.167266 + 0.289714i −0.937458 0.348099i \(-0.886827\pi\)
0.770192 + 0.637813i \(0.220161\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 34.5169 1.53903 0.769517 0.638626i \(-0.220497\pi\)
0.769517 + 0.638626i \(0.220497\pi\)
\(504\) 0 0
\(505\) 15.2169 0.677145
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.41136 + 2.44454i −0.0625572 + 0.108352i −0.895608 0.444845i \(-0.853259\pi\)
0.833051 + 0.553197i \(0.186592\pi\)
\(510\) 0 0
\(511\) 11.2705 + 19.5211i 0.498579 + 0.863564i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.68252 13.3065i −0.338532 0.586355i
\(516\) 0 0
\(517\) −1.66920 + 2.89114i −0.0734114 + 0.127152i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.11300 −0.399248 −0.199624 0.979873i \(-0.563972\pi\)
−0.199624 + 0.979873i \(0.563972\pi\)
\(522\) 0 0
\(523\) 1.96313 0.0858418 0.0429209 0.999078i \(-0.486334\pi\)
0.0429209 + 0.999078i \(0.486334\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 14.9279 25.8559i 0.650269 1.12630i
\(528\) 0 0
\(529\) 3.39339 + 5.87752i 0.147539 + 0.255544i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −25.9325 44.9165i −1.12326 1.94555i
\(534\) 0 0
\(535\) −20.1570 + 34.9130i −0.871465 + 1.50942i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.42084 −0.190419
\(540\) 0 0
\(541\) 3.46053 0.148780 0.0743899 0.997229i \(-0.476299\pi\)
0.0743899 + 0.997229i \(0.476299\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.59070 4.48723i 0.110974 0.192212i
\(546\) 0 0
\(547\) −4.80884 8.32915i −0.205611 0.356129i 0.744716 0.667381i \(-0.232585\pi\)
−0.950327 + 0.311252i \(0.899252\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −13.7484 23.8129i −0.585702 1.01447i
\(552\) 0 0
\(553\) −7.93645 + 13.7463i −0.337492 + 0.584554i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9.47602 −0.401512 −0.200756 0.979641i \(-0.564340\pi\)
−0.200756 + 0.979641i \(0.564340\pi\)
\(558\) 0 0
\(559\) −45.2360 −1.91328
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −20.8982 + 36.1967i −0.880753 + 1.52551i −0.0302481 + 0.999542i \(0.509630\pi\)
−0.850505 + 0.525967i \(0.823704\pi\)
\(564\) 0 0
\(565\) 3.62725 + 6.28257i 0.152599 + 0.264310i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.74041 16.8709i −0.408339 0.707265i 0.586364 0.810047i \(-0.300559\pi\)
−0.994704 + 0.102783i \(0.967225\pi\)
\(570\) 0 0
\(571\) 9.27352 16.0622i 0.388085 0.672182i −0.604107 0.796903i \(-0.706470\pi\)
0.992192 + 0.124721i \(0.0398035\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.74336 −0.197812
\(576\) 0 0
\(577\) 28.5458 1.18838 0.594188 0.804326i \(-0.297473\pi\)
0.594188 + 0.804326i \(0.297473\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16.1694 28.0062i 0.670820 1.16189i
\(582\) 0 0
\(583\) −0.924361 1.60104i −0.0382831 0.0663083i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.49840 2.59531i −0.0618457 0.107120i 0.833445 0.552603i \(-0.186365\pi\)
−0.895290 + 0.445483i \(0.853032\pi\)
\(588\) 0 0
\(589\) −12.8425 + 22.2439i −0.529168 + 0.916545i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −24.7528 −1.01648 −0.508238 0.861216i \(-0.669703\pi\)
−0.508238 + 0.861216i \(0.669703\pi\)
\(594\) 0 0
\(595\) 23.9541 0.982022
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19.2808 33.3954i 0.787794 1.36450i −0.139522 0.990219i \(-0.544557\pi\)
0.927316 0.374280i \(-0.122110\pi\)
\(600\) 0 0
\(601\) −15.4398 26.7426i −0.629804 1.09085i −0.987591 0.157050i \(-0.949802\pi\)
0.357786 0.933803i \(-0.383532\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11.8905 20.5949i −0.483417 0.837302i
\(606\) 0 0
\(607\) −14.1298 + 24.4736i −0.573512 + 0.993352i 0.422689 + 0.906275i \(0.361086\pi\)
−0.996202 + 0.0870777i \(0.972247\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15.8071 0.639487
\(612\) 0 0
\(613\) −28.6419 −1.15684 −0.578419 0.815740i \(-0.696330\pi\)
−0.578419 + 0.815740i \(0.696330\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.80372 + 3.12413i −0.0726150 + 0.125773i −0.900047 0.435794i \(-0.856468\pi\)
0.827432 + 0.561566i \(0.189801\pi\)
\(618\) 0 0
\(619\) 4.76132 + 8.24686i 0.191374 + 0.331469i 0.945706 0.325024i \(-0.105372\pi\)
−0.754332 + 0.656493i \(0.772039\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.413930 + 0.716947i 0.0165837 + 0.0287239i
\(624\) 0 0
\(625\) 14.7512 25.5498i 0.590047 1.02199i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 27.4619 1.09498
\(630\) 0 0
\(631\) 30.5885 1.21771 0.608855 0.793281i \(-0.291629\pi\)
0.608855 + 0.793281i \(0.291629\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 18.7186 32.4215i 0.742824 1.28661i
\(636\) 0 0
\(637\) 10.4662 + 18.1280i 0.414686 + 0.718257i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.09007 7.08420i −0.161548 0.279809i 0.773876 0.633337i \(-0.218315\pi\)
−0.935424 + 0.353528i \(0.884982\pi\)
\(642\) 0 0
\(643\) 13.0611 22.6225i 0.515079 0.892144i −0.484768 0.874643i \(-0.661096\pi\)
0.999847 0.0175005i \(-0.00557087\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −22.0170 −0.865577 −0.432789 0.901495i \(-0.642470\pi\)
−0.432789 + 0.901495i \(0.642470\pi\)
\(648\) 0 0
\(649\) −4.44557 −0.174504
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.14611 + 1.98512i −0.0448508 + 0.0776839i −0.887579 0.460655i \(-0.847615\pi\)
0.842729 + 0.538339i \(0.180948\pi\)
\(654\) 0 0
\(655\) 4.70544 + 8.15006i 0.183857 + 0.318449i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −3.29926 5.71449i −0.128521 0.222605i 0.794583 0.607156i \(-0.207690\pi\)
−0.923104 + 0.384551i \(0.874356\pi\)
\(660\) 0 0
\(661\) 2.88305 4.99359i 0.112138 0.194228i −0.804494 0.593960i \(-0.797564\pi\)
0.916632 + 0.399732i \(0.130897\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −20.6078 −0.799137
\(666\) 0 0
\(667\) 24.2813 0.940174
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.80537 8.32314i 0.185509 0.321311i
\(672\) 0 0
\(673\) −22.6226 39.1835i −0.872038 1.51041i −0.859885 0.510488i \(-0.829465\pi\)
−0.0121528 0.999926i \(-0.503868\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.70089 6.41013i −0.142237 0.246361i 0.786102 0.618097i \(-0.212096\pi\)
−0.928339 + 0.371736i \(0.878763\pi\)
\(678\) 0 0
\(679\) 1.84810 3.20100i 0.0709235 0.122843i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.88608 −0.378281 −0.189140 0.981950i \(-0.560570\pi\)
−0.189140 + 0.981950i \(0.560570\pi\)
\(684\) 0 0
\(685\) −31.7878 −1.21455
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.37679 + 7.58082i −0.166742 + 0.288806i
\(690\) 0 0
\(691\) −4.43367 7.67934i −0.168665 0.292136i 0.769286 0.638905i \(-0.220612\pi\)
−0.937951 + 0.346769i \(0.887279\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −11.0990 19.2240i −0.421009 0.729209i
\(696\) 0 0
\(697\) −24.2548 + 42.0106i −0.918717 + 1.59126i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −38.9889 −1.47259 −0.736296 0.676660i \(-0.763427\pi\)
−0.736296 + 0.676660i \(0.763427\pi\)
\(702\) 0 0
\(703\) −23.6256 −0.891055
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.56589 + 9.64040i −0.209327 + 0.362564i
\(708\) 0 0
\(709\) −5.12709 8.88039i −0.192552 0.333510i 0.753543 0.657398i \(-0.228343\pi\)
−0.946095 + 0.323888i \(0.895010\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −11.3407 19.6427i −0.424712 0.735623i
\(714\) 0 0
\(715\) 8.42872 14.5990i 0.315216 0.545970i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 16.8003 0.626545 0.313272 0.949663i \(-0.398575\pi\)
0.313272 + 0.949663i \(0.398575\pi\)
\(720\) 0 0
\(721\) 11.2401 0.418604
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.55187 6.15203i 0.131913 0.228481i
\(726\) 0 0
\(727\) 9.98309 + 17.2912i 0.370252 + 0.641296i 0.989604 0.143818i \(-0.0459379\pi\)
−0.619352 + 0.785113i \(0.712605\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 21.1547 + 36.6410i 0.782436 + 1.35522i
\(732\) 0 0
\(733\) −2.98307 + 5.16683i −0.110182 + 0.190841i −0.915844 0.401535i \(-0.868477\pi\)
0.805661 + 0.592376i \(0.201810\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 16.5489 0.609585
\(738\) 0 0
\(739\) 0.673830 0.0247872 0.0123936 0.999923i \(-0.496055\pi\)
0.0123936 + 0.999923i \(0.496055\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15.4737 + 26.8013i −0.567676 + 0.983244i 0.429119 + 0.903248i \(0.358824\pi\)
−0.996795 + 0.0799963i \(0.974509\pi\)
\(744\) 0 0
\(745\) −11.5621 20.0261i −0.423602 0.733700i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −14.7457 25.5402i −0.538794 0.933219i
\(750\) 0 0
\(751\) 0.0124745 0.0216064i 0.000455200 0.000788429i −0.865798 0.500394i \(-0.833188\pi\)
0.866253 + 0.499606i \(0.166522\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 38.9501 1.41754
\(756\) 0 0
\(757\) −2.61883 −0.0951829 −0.0475914 0.998867i \(-0.515155\pi\)
−0.0475914 + 0.998867i \(0.515155\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −4.19437 + 7.26486i −0.152046 + 0.263351i −0.931979 0.362511i \(-0.881919\pi\)
0.779934 + 0.625862i \(0.215253\pi\)
\(762\) 0 0
\(763\) 1.89520 + 3.28258i 0.0686109 + 0.118837i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 10.5247 + 18.2294i 0.380027 + 0.658225i
\(768\) 0 0
\(769\) −1.00513 + 1.74094i −0.0362460 + 0.0627800i −0.883579 0.468281i \(-0.844873\pi\)
0.847333 + 0.531061i \(0.178207\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −10.2064 −0.367099 −0.183550 0.983010i \(-0.558759\pi\)
−0.183550 + 0.983010i \(0.558759\pi\)
\(774\) 0 0
\(775\) −6.63569 −0.238361
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 20.8666 36.1419i 0.747622 1.29492i
\(780\) 0 0
\(781\) −6.68983 11.5871i −0.239381 0.414620i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −24.2464 41.9960i −0.865392 1.49890i
\(786\) 0 0
\(787\) 13.6213 23.5928i 0.485547 0.840991i −0.514315 0.857601i \(-0.671954\pi\)
0.999862 + 0.0166097i \(0.00528727\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.30694 −0.188693
\(792\) 0 0
\(793\) −45.5062 −1.61597
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.73924 + 11.6727i −0.238716 + 0.413468i −0.960346 0.278810i \(-0.910060\pi\)
0.721630 + 0.692279i \(0.243393\pi\)
\(798\) 0 0
\(799\) −7.39223 12.8037i −0.261518 0.452963i
\(800\) 0 0
\(801\) 0 0
\(802\) 0