Properties

Label 3024.2.q.l.2881.8
Level $3024$
Weight $2$
Character 3024.2881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2881.8
Character \(\chi\) \(=\) 3024.2881
Dual form 3024.2.q.l.2305.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.05220 - 1.82246i) q^{5} +(-2.58382 - 0.569079i) q^{7} +O(q^{10})\) \(q+(1.05220 - 1.82246i) q^{5} +(-2.58382 - 0.569079i) q^{7} +(-0.199532 - 0.345600i) q^{11} +(1.44292 + 2.49921i) q^{13} +(0.176596 - 0.305873i) q^{17} +(-2.84888 - 4.93440i) q^{19} +(0.438682 - 0.759820i) q^{23} +(0.285756 + 0.494945i) q^{25} +(-0.874997 + 1.51554i) q^{29} -9.13490 q^{31} +(-3.75582 + 4.11014i) q^{35} +(-3.39555 - 5.88127i) q^{37} +(-1.20377 - 2.08499i) q^{41} +(-0.276745 + 0.479336i) q^{43} +11.7372 q^{47} +(6.35230 + 2.94080i) q^{49} +(2.07821 - 3.59956i) q^{53} -0.839790 q^{55} -9.32421 q^{59} -10.0720 q^{61} +6.07296 q^{65} -1.20241 q^{67} -14.6826 q^{71} +(0.315636 - 0.546697i) q^{73} +(0.318883 + 1.00652i) q^{77} +2.48729 q^{79} +(-4.59366 + 7.95645i) q^{83} +(-0.371628 - 0.643678i) q^{85} +(-7.29358 - 12.6328i) q^{89} +(-2.30601 - 7.27866i) q^{91} -11.9903 q^{95} +(-7.84245 + 13.5835i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 1.05220 1.82246i 0.470558 0.815030i −0.528876 0.848699i \(-0.677386\pi\)
0.999433 + 0.0336699i \(0.0107195\pi\)
\(6\) 0 0
\(7\) −2.58382 0.569079i −0.976594 0.215092i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.199532 0.345600i −0.0601612 0.104202i 0.834376 0.551195i \(-0.185828\pi\)
−0.894537 + 0.446993i \(0.852495\pi\)
\(12\) 0 0
\(13\) 1.44292 + 2.49921i 0.400194 + 0.693157i 0.993749 0.111637i \(-0.0356093\pi\)
−0.593555 + 0.804794i \(0.702276\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.176596 0.305873i 0.0428308 0.0741851i −0.843815 0.536634i \(-0.819696\pi\)
0.886646 + 0.462449i \(0.153029\pi\)
\(18\) 0 0
\(19\) −2.84888 4.93440i −0.653578 1.13203i −0.982248 0.187585i \(-0.939934\pi\)
0.328670 0.944445i \(-0.393399\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.438682 0.759820i 0.0914716 0.158433i −0.816659 0.577121i \(-0.804176\pi\)
0.908131 + 0.418687i \(0.137510\pi\)
\(24\) 0 0
\(25\) 0.285756 + 0.494945i 0.0571513 + 0.0989889i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −0.874997 + 1.51554i −0.162483 + 0.281429i −0.935759 0.352641i \(-0.885284\pi\)
0.773276 + 0.634070i \(0.218617\pi\)
\(30\) 0 0
\(31\) −9.13490 −1.64068 −0.820339 0.571878i \(-0.806215\pi\)
−0.820339 + 0.571878i \(0.806215\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.75582 + 4.11014i −0.634850 + 0.694740i
\(36\) 0 0
\(37\) −3.39555 5.88127i −0.558225 0.966874i −0.997645 0.0685922i \(-0.978149\pi\)
0.439420 0.898282i \(-0.355184\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.20377 2.08499i −0.187997 0.325621i 0.756585 0.653895i \(-0.226866\pi\)
−0.944582 + 0.328274i \(0.893533\pi\)
\(42\) 0 0
\(43\) −0.276745 + 0.479336i −0.0422032 + 0.0730981i −0.886355 0.463005i \(-0.846771\pi\)
0.844152 + 0.536104i \(0.180104\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.7372 1.71205 0.856023 0.516939i \(-0.172928\pi\)
0.856023 + 0.516939i \(0.172928\pi\)
\(48\) 0 0
\(49\) 6.35230 + 2.94080i 0.907471 + 0.420114i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.07821 3.59956i 0.285464 0.494437i −0.687258 0.726413i \(-0.741186\pi\)
0.972721 + 0.231976i \(0.0745191\pi\)
\(54\) 0 0
\(55\) −0.839790 −0.113237
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −9.32421 −1.21391 −0.606954 0.794737i \(-0.707609\pi\)
−0.606954 + 0.794737i \(0.707609\pi\)
\(60\) 0 0
\(61\) −10.0720 −1.28959 −0.644795 0.764356i \(-0.723057\pi\)
−0.644795 + 0.764356i \(0.723057\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.07296 0.753258
\(66\) 0 0
\(67\) −1.20241 −0.146898 −0.0734488 0.997299i \(-0.523401\pi\)
−0.0734488 + 0.997299i \(0.523401\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −14.6826 −1.74250 −0.871250 0.490840i \(-0.836690\pi\)
−0.871250 + 0.490840i \(0.836690\pi\)
\(72\) 0 0
\(73\) 0.315636 0.546697i 0.0369423 0.0639860i −0.846963 0.531652i \(-0.821572\pi\)
0.883905 + 0.467666i \(0.154905\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.318883 + 1.00652i 0.0363400 + 0.114703i
\(78\) 0 0
\(79\) 2.48729 0.279842 0.139921 0.990163i \(-0.455315\pi\)
0.139921 + 0.990163i \(0.455315\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.59366 + 7.95645i −0.504219 + 0.873333i 0.495769 + 0.868455i \(0.334886\pi\)
−0.999988 + 0.00487885i \(0.998447\pi\)
\(84\) 0 0
\(85\) −0.371628 0.643678i −0.0403087 0.0698167i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.29358 12.6328i −0.773118 1.33908i −0.935846 0.352408i \(-0.885363\pi\)
0.162729 0.986671i \(-0.447971\pi\)
\(90\) 0 0
\(91\) −2.30601 7.27866i −0.241735 0.763011i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −11.9903 −1.23018
\(96\) 0 0
\(97\) −7.84245 + 13.5835i −0.796280 + 1.37920i 0.125744 + 0.992063i \(0.459868\pi\)
−0.922023 + 0.387134i \(0.873465\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −0.0464285 0.0804166i −0.00461981 0.00800175i 0.863706 0.503996i \(-0.168137\pi\)
−0.868326 + 0.495994i \(0.834804\pi\)
\(102\) 0 0
\(103\) −9.95769 + 17.2472i −0.981161 + 1.69942i −0.323270 + 0.946307i \(0.604782\pi\)
−0.657891 + 0.753113i \(0.728551\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.89225 5.00953i −0.279605 0.484290i 0.691682 0.722202i \(-0.256870\pi\)
−0.971287 + 0.237913i \(0.923537\pi\)
\(108\) 0 0
\(109\) −6.25516 + 10.8343i −0.599136 + 1.03773i 0.393813 + 0.919191i \(0.371156\pi\)
−0.992949 + 0.118543i \(0.962178\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.69411 2.93428i −0.159368 0.276034i 0.775273 0.631627i \(-0.217612\pi\)
−0.934641 + 0.355593i \(0.884279\pi\)
\(114\) 0 0
\(115\) −0.923161 1.59896i −0.0860853 0.149104i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.630359 + 0.689825i −0.0577849 + 0.0632362i
\(120\) 0 0
\(121\) 5.42037 9.38836i 0.492761 0.853488i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.7247 1.04869
\(126\) 0 0
\(127\) −14.7348 −1.30750 −0.653752 0.756709i \(-0.726806\pi\)
−0.653752 + 0.756709i \(0.726806\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.95392 12.0445i 0.607567 1.05234i −0.384073 0.923303i \(-0.625479\pi\)
0.991640 0.129034i \(-0.0411877\pi\)
\(132\) 0 0
\(133\) 4.55294 + 14.3709i 0.394790 + 1.24611i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 7.27874 + 12.6072i 0.621865 + 1.07710i 0.989138 + 0.146989i \(0.0469581\pi\)
−0.367273 + 0.930113i \(0.619709\pi\)
\(138\) 0 0
\(139\) 3.63996 + 6.30460i 0.308737 + 0.534749i 0.978086 0.208199i \(-0.0667603\pi\)
−0.669349 + 0.742948i \(0.733427\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.575818 0.997347i 0.0481523 0.0834023i
\(144\) 0 0
\(145\) 1.84134 + 3.18930i 0.152915 + 0.264857i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −0.360832 + 0.624979i −0.0295605 + 0.0512003i −0.880427 0.474181i \(-0.842744\pi\)
0.850867 + 0.525382i \(0.176077\pi\)
\(150\) 0 0
\(151\) 10.9022 + 18.8831i 0.887207 + 1.53669i 0.843163 + 0.537657i \(0.180691\pi\)
0.0440432 + 0.999030i \(0.485976\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −9.61173 + 16.6480i −0.772033 + 1.33720i
\(156\) 0 0
\(157\) 5.17973 0.413387 0.206694 0.978406i \(-0.433730\pi\)
0.206694 + 0.978406i \(0.433730\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.56588 + 1.71360i −0.123408 + 0.135050i
\(162\) 0 0
\(163\) −2.63906 4.57098i −0.206707 0.358027i 0.743968 0.668215i \(-0.232941\pi\)
−0.950675 + 0.310188i \(0.899608\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.83710 11.8422i −0.529071 0.916378i −0.999425 0.0339001i \(-0.989207\pi\)
0.470354 0.882478i \(-0.344126\pi\)
\(168\) 0 0
\(169\) 2.33596 4.04599i 0.179689 0.311230i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −20.1824 −1.53444 −0.767218 0.641386i \(-0.778360\pi\)
−0.767218 + 0.641386i \(0.778360\pi\)
\(174\) 0 0
\(175\) −0.456682 1.44147i −0.0345219 0.108965i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.5968 21.8183i 0.941528 1.63077i 0.178971 0.983854i \(-0.442723\pi\)
0.762557 0.646921i \(-0.223944\pi\)
\(180\) 0 0
\(181\) −17.2815 −1.28453 −0.642263 0.766485i \(-0.722004\pi\)
−0.642263 + 0.766485i \(0.722004\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −14.2912 −1.05071
\(186\) 0 0
\(187\) −0.140946 −0.0103070
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.01898 −0.363161 −0.181580 0.983376i \(-0.558121\pi\)
−0.181580 + 0.983376i \(0.558121\pi\)
\(192\) 0 0
\(193\) −5.43765 −0.391411 −0.195705 0.980663i \(-0.562700\pi\)
−0.195705 + 0.980663i \(0.562700\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −5.95839 −0.424517 −0.212259 0.977214i \(-0.568082\pi\)
−0.212259 + 0.977214i \(0.568082\pi\)
\(198\) 0 0
\(199\) −5.62062 + 9.73520i −0.398435 + 0.690110i −0.993533 0.113543i \(-0.963780\pi\)
0.595098 + 0.803653i \(0.297113\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.12330 3.41795i 0.219213 0.239893i
\(204\) 0 0
\(205\) −5.06643 −0.353855
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.13689 + 1.96914i −0.0786401 + 0.136209i
\(210\) 0 0
\(211\) −0.381084 0.660057i −0.0262349 0.0454402i 0.852610 0.522548i \(-0.175018\pi\)
−0.878845 + 0.477108i \(0.841685\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.582381 + 1.00871i 0.0397181 + 0.0687937i
\(216\) 0 0
\(217\) 23.6030 + 5.19848i 1.60228 + 0.352896i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.01926 0.0685626
\(222\) 0 0
\(223\) 5.80556 10.0555i 0.388769 0.673368i −0.603515 0.797352i \(-0.706234\pi\)
0.992284 + 0.123984i \(0.0395670\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.16624 + 8.94818i 0.342895 + 0.593912i 0.984969 0.172731i \(-0.0552591\pi\)
−0.642074 + 0.766643i \(0.721926\pi\)
\(228\) 0 0
\(229\) 1.86191 3.22493i 0.123039 0.213109i −0.797926 0.602756i \(-0.794069\pi\)
0.920965 + 0.389646i \(0.127403\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.3649 23.1488i −0.875566 1.51653i −0.856158 0.516714i \(-0.827155\pi\)
−0.0194083 0.999812i \(-0.506178\pi\)
\(234\) 0 0
\(235\) 12.3499 21.3906i 0.805616 1.39537i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 6.94164 + 12.0233i 0.449018 + 0.777721i 0.998322 0.0579007i \(-0.0184407\pi\)
−0.549305 + 0.835622i \(0.685107\pi\)
\(240\) 0 0
\(241\) −7.45280 12.9086i −0.480077 0.831518i 0.519662 0.854372i \(-0.326058\pi\)
−0.999739 + 0.0228542i \(0.992725\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 12.0434 8.48251i 0.769423 0.541928i
\(246\) 0 0
\(247\) 8.22142 14.2399i 0.523116 0.906064i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 22.5515 1.42344 0.711720 0.702464i \(-0.247917\pi\)
0.711720 + 0.702464i \(0.247917\pi\)
\(252\) 0 0
\(253\) −0.350125 −0.0220122
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.94765 10.3016i 0.371004 0.642598i −0.618716 0.785615i \(-0.712347\pi\)
0.989720 + 0.143017i \(0.0456803\pi\)
\(258\) 0 0
\(259\) 5.42660 + 17.1285i 0.337193 + 1.06431i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.3030 21.3094i −0.758633 1.31399i −0.943548 0.331236i \(-0.892534\pi\)
0.184915 0.982755i \(-0.440799\pi\)
\(264\) 0 0
\(265\) −4.37337 7.57490i −0.268654 0.465322i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6.75722 + 11.7039i −0.411995 + 0.713597i −0.995108 0.0987947i \(-0.968501\pi\)
0.583113 + 0.812391i \(0.301835\pi\)
\(270\) 0 0
\(271\) 1.34195 + 2.32433i 0.0815177 + 0.141193i 0.903902 0.427740i \(-0.140690\pi\)
−0.822384 + 0.568932i \(0.807357\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.114035 0.197515i 0.00687658 0.0119106i
\(276\) 0 0
\(277\) −9.52618 16.4998i −0.572373 0.991379i −0.996322 0.0856928i \(-0.972690\pi\)
0.423949 0.905686i \(-0.360644\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −14.2006 + 24.5962i −0.847139 + 1.46729i 0.0366118 + 0.999330i \(0.488343\pi\)
−0.883751 + 0.467958i \(0.844990\pi\)
\(282\) 0 0
\(283\) 15.4221 0.916749 0.458374 0.888759i \(-0.348432\pi\)
0.458374 + 0.888759i \(0.348432\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.92381 + 6.07230i 0.113559 + 0.358436i
\(288\) 0 0
\(289\) 8.43763 + 14.6144i 0.496331 + 0.859671i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −9.02253 15.6275i −0.527102 0.912967i −0.999501 0.0315825i \(-0.989945\pi\)
0.472399 0.881385i \(-0.343388\pi\)
\(294\) 0 0
\(295\) −9.81092 + 16.9930i −0.571214 + 0.989371i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.53194 0.146426
\(300\) 0 0
\(301\) 0.987841 1.08103i 0.0569382 0.0623096i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10.5978 + 18.3559i −0.606826 + 1.05105i
\(306\) 0 0
\(307\) 7.30860 0.417124 0.208562 0.978009i \(-0.433122\pi\)
0.208562 + 0.978009i \(0.433122\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −23.7792 −1.34839 −0.674197 0.738551i \(-0.735510\pi\)
−0.674197 + 0.738551i \(0.735510\pi\)
\(312\) 0 0
\(313\) −18.2907 −1.03385 −0.516925 0.856031i \(-0.672923\pi\)
−0.516925 + 0.856031i \(0.672923\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.68988 0.263410 0.131705 0.991289i \(-0.457955\pi\)
0.131705 + 0.991289i \(0.457955\pi\)
\(318\) 0 0
\(319\) 0.698360 0.0391007
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.01240 −0.111973
\(324\) 0 0
\(325\) −0.824648 + 1.42833i −0.0457432 + 0.0792296i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −30.3268 6.67938i −1.67197 0.368246i
\(330\) 0 0
\(331\) 11.4287 0.628176 0.314088 0.949394i \(-0.398301\pi\)
0.314088 + 0.949394i \(0.398301\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.26517 + 2.19134i −0.0691238 + 0.119726i
\(336\) 0 0
\(337\) 8.74160 + 15.1409i 0.476185 + 0.824777i 0.999628 0.0272840i \(-0.00868584\pi\)
−0.523442 + 0.852061i \(0.675353\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.82271 + 3.15702i 0.0987051 + 0.170962i
\(342\) 0 0
\(343\) −14.7397 11.2135i −0.795868 0.605470i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 14.1186 0.757925 0.378962 0.925412i \(-0.376281\pi\)
0.378962 + 0.925412i \(0.376281\pi\)
\(348\) 0 0
\(349\) 10.7216 18.5704i 0.573916 0.994052i −0.422242 0.906483i \(-0.638757\pi\)
0.996158 0.0875692i \(-0.0279099\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −15.6880 27.1724i −0.834987 1.44624i −0.894041 0.447985i \(-0.852142\pi\)
0.0590538 0.998255i \(-0.481192\pi\)
\(354\) 0 0
\(355\) −15.4490 + 26.7584i −0.819946 + 1.42019i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.313156 + 0.542402i 0.0165277 + 0.0286269i 0.874171 0.485618i \(-0.161405\pi\)
−0.857643 + 0.514245i \(0.828072\pi\)
\(360\) 0 0
\(361\) −6.73223 + 11.6606i −0.354328 + 0.613714i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.664223 1.15047i −0.0347670 0.0602182i
\(366\) 0 0
\(367\) −1.62199 2.80936i −0.0846670 0.146648i 0.820582 0.571528i \(-0.193649\pi\)
−0.905249 + 0.424881i \(0.860316\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7.41815 + 8.11796i −0.385131 + 0.421464i
\(372\) 0 0
\(373\) 13.8013 23.9046i 0.714606 1.23773i −0.248506 0.968630i \(-0.579939\pi\)
0.963111 0.269103i \(-0.0867272\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.05021 −0.260099
\(378\) 0 0
\(379\) 12.7800 0.656463 0.328231 0.944597i \(-0.393547\pi\)
0.328231 + 0.944597i \(0.393547\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.58278 4.47351i 0.131974 0.228586i −0.792463 0.609919i \(-0.791202\pi\)
0.924437 + 0.381334i \(0.124535\pi\)
\(384\) 0 0
\(385\) 2.16987 + 0.477906i 0.110587 + 0.0243564i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 16.4707 + 28.5280i 0.835095 + 1.44643i 0.893953 + 0.448161i \(0.147921\pi\)
−0.0588576 + 0.998266i \(0.518746\pi\)
\(390\) 0 0
\(391\) −0.154939 0.268362i −0.00783560 0.0135717i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.61712 4.53299i 0.131682 0.228079i
\(396\) 0 0
\(397\) −0.411705 0.713095i −0.0206629 0.0357892i 0.855509 0.517788i \(-0.173244\pi\)
−0.876172 + 0.481999i \(0.839911\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.86923 + 17.0940i −0.492846 + 0.853634i −0.999966 0.00824153i \(-0.997377\pi\)
0.507120 + 0.861875i \(0.330710\pi\)
\(402\) 0 0
\(403\) −13.1809 22.8301i −0.656590 1.13725i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.35504 + 2.34700i −0.0671670 + 0.116337i
\(408\) 0 0
\(409\) −25.2551 −1.24879 −0.624393 0.781110i \(-0.714654\pi\)
−0.624393 + 0.781110i \(0.714654\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 24.0921 + 5.30621i 1.18550 + 0.261101i
\(414\) 0 0
\(415\) 9.66688 + 16.7435i 0.474528 + 0.821907i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0.406717 + 0.704455i 0.0198694 + 0.0344149i 0.875789 0.482694i \(-0.160342\pi\)
−0.855920 + 0.517109i \(0.827008\pi\)
\(420\) 0 0
\(421\) 5.12114 8.87008i 0.249589 0.432301i −0.713823 0.700326i \(-0.753038\pi\)
0.963412 + 0.268025i \(0.0863711\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.201854 0.00979134
\(426\) 0 0
\(427\) 26.0243 + 5.73177i 1.25941 + 0.277380i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 16.3348 28.2928i 0.786822 1.36281i −0.141083 0.989998i \(-0.545059\pi\)
0.927905 0.372817i \(-0.121608\pi\)
\(432\) 0 0
\(433\) −14.3151 −0.687941 −0.343970 0.938980i \(-0.611772\pi\)
−0.343970 + 0.938980i \(0.611772\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.99901 −0.239135
\(438\) 0 0
\(439\) 9.86660 0.470907 0.235453 0.971886i \(-0.424342\pi\)
0.235453 + 0.971886i \(0.424342\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 37.2801 1.77123 0.885615 0.464419i \(-0.153737\pi\)
0.885615 + 0.464419i \(0.153737\pi\)
\(444\) 0 0
\(445\) −30.6972 −1.45519
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 36.2926 1.71276 0.856378 0.516350i \(-0.172710\pi\)
0.856378 + 0.516350i \(0.172710\pi\)
\(450\) 0 0
\(451\) −0.480382 + 0.832046i −0.0226203 + 0.0391795i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −15.6915 3.45599i −0.735627 0.162019i
\(456\) 0 0
\(457\) −13.1943 −0.617205 −0.308602 0.951191i \(-0.599861\pi\)
−0.308602 + 0.951191i \(0.599861\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.1326 + 17.5502i −0.471924 + 0.817396i −0.999484 0.0321215i \(-0.989774\pi\)
0.527560 + 0.849518i \(0.323107\pi\)
\(462\) 0 0
\(463\) −12.7106 22.0154i −0.590712 1.02314i −0.994137 0.108131i \(-0.965513\pi\)
0.403424 0.915013i \(-0.367820\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.40661 7.63248i −0.203914 0.353189i 0.745872 0.666089i \(-0.232033\pi\)
−0.949786 + 0.312900i \(0.898700\pi\)
\(468\) 0 0
\(469\) 3.10681 + 0.684265i 0.143459 + 0.0315964i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.220878 0.0101560
\(474\) 0 0
\(475\) 1.62817 2.82008i 0.0747056 0.129394i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −12.1343 21.0173i −0.554433 0.960305i −0.997947 0.0640383i \(-0.979602\pi\)
0.443515 0.896267i \(-0.353731\pi\)
\(480\) 0 0
\(481\) 9.79902 16.9724i 0.446797 0.773875i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16.5036 + 28.5851i 0.749391 + 1.29798i
\(486\) 0 0
\(487\) 5.37220 9.30492i 0.243438 0.421646i −0.718254 0.695781i \(-0.755058\pi\)
0.961691 + 0.274135i \(0.0883916\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11.3934 + 19.7340i 0.514179 + 0.890584i 0.999865 + 0.0164507i \(0.00523665\pi\)
−0.485686 + 0.874134i \(0.661430\pi\)
\(492\) 0 0
\(493\) 0.309042 + 0.535276i 0.0139185 + 0.0241076i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 37.9372 + 8.35553i 1.70171 + 0.374797i
\(498\) 0 0
\(499\) 11.5755 20.0493i 0.518189 0.897530i −0.481588 0.876398i \(-0.659940\pi\)
0.999777 0.0211317i \(-0.00672693\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 9.43360 0.420623 0.210312 0.977634i \(-0.432552\pi\)
0.210312 + 0.977634i \(0.432552\pi\)
\(504\) 0 0
\(505\) −0.195408 −0.00869555
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −4.72981 + 8.19228i −0.209645 + 0.363116i −0.951603 0.307331i \(-0.900564\pi\)
0.741957 + 0.670447i \(0.233898\pi\)
\(510\) 0 0
\(511\) −1.12666 + 1.23295i −0.0498405 + 0.0545424i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 20.9549 + 36.2950i 0.923385 + 1.59935i
\(516\) 0 0
\(517\) −2.34195 4.05637i −0.102999 0.178399i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 14.3368 24.8320i 0.628105 1.08791i −0.359826 0.933019i \(-0.617164\pi\)
0.987932 0.154891i \(-0.0495026\pi\)
\(522\) 0 0
\(523\) 13.5104 + 23.4006i 0.590767 + 1.02324i 0.994129 + 0.108198i \(0.0345081\pi\)
−0.403362 + 0.915040i \(0.632159\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.61319 + 2.79412i −0.0702715 + 0.121714i
\(528\) 0 0
\(529\) 11.1151 + 19.2519i 0.483266 + 0.837041i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.47389 6.01696i 0.150471 0.260624i
\(534\) 0 0
\(535\) −12.1729 −0.526280
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.251148 2.78214i −0.0108177 0.119835i
\(540\) 0 0
\(541\) −1.52907 2.64842i −0.0657397 0.113864i 0.831282 0.555851i \(-0.187607\pi\)
−0.897022 + 0.441986i \(0.854274\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 13.1633 + 22.7996i 0.563856 + 0.976627i
\(546\) 0 0
\(547\) −3.58144 + 6.20323i −0.153131 + 0.265231i −0.932377 0.361487i \(-0.882269\pi\)
0.779246 + 0.626719i \(0.215602\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9.97105 0.424781
\(552\) 0 0
\(553\) −6.42672 1.41546i −0.273292 0.0601916i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.3518 24.8580i 0.608104 1.05327i −0.383449 0.923562i \(-0.625264\pi\)
0.991553 0.129704i \(-0.0414028\pi\)
\(558\) 0 0
\(559\) −1.59729 −0.0675580
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 35.7719 1.50761 0.753803 0.657101i \(-0.228218\pi\)
0.753803 + 0.657101i \(0.228218\pi\)
\(564\) 0 0
\(565\) −7.13016 −0.299968
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 25.2002 1.05645 0.528223 0.849106i \(-0.322858\pi\)
0.528223 + 0.849106i \(0.322858\pi\)
\(570\) 0 0
\(571\) 6.04938 0.253159 0.126579 0.991956i \(-0.459600\pi\)
0.126579 + 0.991956i \(0.459600\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.501425 0.0209109
\(576\) 0 0
\(577\) 9.57977 16.5926i 0.398811 0.690761i −0.594768 0.803897i \(-0.702756\pi\)
0.993580 + 0.113136i \(0.0360896\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 16.3970 17.9439i 0.680264 0.744439i
\(582\) 0 0
\(583\) −1.65868 −0.0686953
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 18.4147 31.8953i 0.760058 1.31646i −0.182763 0.983157i \(-0.558504\pi\)
0.942820 0.333301i \(-0.108163\pi\)
\(588\) 0 0
\(589\) 26.0242 + 45.0753i 1.07231 + 1.85730i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.97285 15.5414i −0.368471 0.638210i 0.620856 0.783925i \(-0.286785\pi\)
−0.989327 + 0.145715i \(0.953452\pi\)
\(594\) 0 0
\(595\) 0.593918 + 1.87464i 0.0243482 + 0.0768526i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −40.4913 −1.65443 −0.827215 0.561885i \(-0.810076\pi\)
−0.827215 + 0.561885i \(0.810076\pi\)
\(600\) 0 0
\(601\) 13.2589 22.9651i 0.540841 0.936765i −0.458015 0.888945i \(-0.651439\pi\)
0.998856 0.0478200i \(-0.0152274\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11.4066 19.7568i −0.463745 0.803230i
\(606\) 0 0
\(607\) −21.0848 + 36.5200i −0.855806 + 1.48230i 0.0200897 + 0.999798i \(0.493605\pi\)
−0.875895 + 0.482501i \(0.839729\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16.9358 + 29.3337i 0.685151 + 1.18672i
\(612\) 0 0
\(613\) −0.700827 + 1.21387i −0.0283061 + 0.0490277i −0.879831 0.475286i \(-0.842345\pi\)
0.851525 + 0.524313i \(0.175678\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.76787 + 11.7223i 0.272464 + 0.471922i 0.969492 0.245122i \(-0.0788280\pi\)
−0.697028 + 0.717044i \(0.745495\pi\)
\(618\) 0 0
\(619\) −14.9122 25.8288i −0.599374 1.03815i −0.992914 0.118838i \(-0.962083\pi\)
0.393540 0.919308i \(-0.371250\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.6562 + 36.7917i 0.466997 + 1.47403i
\(624\) 0 0
\(625\) 10.9079 18.8930i 0.436316 0.755722i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.39856 −0.0956369
\(630\) 0 0
\(631\) −6.84708 −0.272578 −0.136289 0.990669i \(-0.543518\pi\)
−0.136289 + 0.990669i \(0.543518\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −15.5040 + 26.8536i −0.615256 + 1.06565i
\(636\) 0 0
\(637\) 1.81618 + 20.1191i 0.0719598 + 0.797147i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 16.1209 + 27.9221i 0.636735 + 1.10286i 0.986145 + 0.165888i \(0.0530489\pi\)
−0.349409 + 0.936970i \(0.613618\pi\)
\(642\) 0 0
\(643\) −1.16002 2.00921i −0.0457465 0.0792353i 0.842245 0.539094i \(-0.181233\pi\)
−0.887992 + 0.459859i \(0.847900\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.06813 1.85005i 0.0419924 0.0727329i −0.844265 0.535925i \(-0.819963\pi\)
0.886258 + 0.463193i \(0.153296\pi\)
\(648\) 0 0
\(649\) 1.86048 + 3.22244i 0.0730302 + 0.126492i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.51932 2.63155i 0.0594558 0.102980i −0.834765 0.550606i \(-0.814397\pi\)
0.894221 + 0.447625i \(0.147730\pi\)
\(654\) 0 0
\(655\) −14.6338 25.3465i −0.571790 0.990370i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −19.8000 + 34.2946i −0.771298 + 1.33593i 0.165554 + 0.986201i \(0.447059\pi\)
−0.936852 + 0.349726i \(0.886275\pi\)
\(660\) 0 0
\(661\) 6.12398 0.238195 0.119098 0.992883i \(-0.462000\pi\)
0.119098 + 0.992883i \(0.462000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 30.9810 + 6.82345i 1.20139 + 0.264602i
\(666\) 0 0
\(667\) 0.767691 + 1.32968i 0.0297251 + 0.0514854i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.00969 + 3.48089i 0.0775832 + 0.134378i
\(672\) 0 0
\(673\) −4.36248 + 7.55603i −0.168161 + 0.291264i −0.937773 0.347248i \(-0.887116\pi\)
0.769612 + 0.638512i \(0.220450\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −14.9601 −0.574965 −0.287482 0.957786i \(-0.592818\pi\)
−0.287482 + 0.957786i \(0.592818\pi\)
\(678\) 0 0
\(679\) 27.9936 30.6345i 1.07430 1.17564i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8.89558 + 15.4076i −0.340380 + 0.589555i −0.984503 0.175366i \(-0.943889\pi\)
0.644123 + 0.764922i \(0.277222\pi\)
\(684\) 0 0
\(685\) 30.6347 1.17049
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 11.9948 0.456964
\(690\) 0 0
\(691\) 29.5389 1.12371 0.561856 0.827235i \(-0.310087\pi\)
0.561856 + 0.827235i \(0.310087\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 15.3198 0.581115
\(696\) 0 0
\(697\) −0.850324 −0.0322083
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −27.7740 −1.04901 −0.524504 0.851408i \(-0.675749\pi\)
−0.524504 + 0.851408i \(0.675749\pi\)
\(702\) 0 0
\(703\) −19.3470 + 33.5100i −0.729687 + 1.26385i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.0741998 + 0.234204i 0.00279057 + 0.00880814i
\(708\) 0 0
\(709\) 47.0984 1.76882 0.884409 0.466712i \(-0.154562\pi\)
0.884409 + 0.466712i \(0.154562\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −4.00732 + 6.94088i −0.150075 + 0.259938i
\(714\) 0 0
\(715\) −1.21175 2.09881i −0.0453169 0.0784912i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.63394 + 2.83007i 0.0609357 + 0.105544i 0.894884 0.446299i \(-0.147258\pi\)
−0.833948 + 0.551843i \(0.813925\pi\)
\(720\) 0 0
\(721\) 35.5440 38.8971i 1.32373 1.44860i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −1.00014 −0.0371444
\(726\) 0 0
\(727\) 6.37047 11.0340i 0.236268 0.409228i −0.723373 0.690458i \(-0.757409\pi\)
0.959640 + 0.281230i \(0.0907424\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.0977441 + 0.169298i 0.00361520 + 0.00626170i
\(732\) 0 0
\(733\) −4.58858 + 7.94765i −0.169483 + 0.293553i −0.938238 0.345990i \(-0.887543\pi\)
0.768755 + 0.639543i \(0.220876\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.239919 + 0.415552i 0.00883754 + 0.0153071i
\(738\) 0 0
\(739\) 23.3467 40.4377i 0.858823 1.48752i −0.0142303 0.999899i \(-0.504530\pi\)
0.873053 0.487626i \(-0.162137\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.62654 13.2095i −0.279790 0.484611i 0.691542 0.722336i \(-0.256932\pi\)
−0.971333 + 0.237725i \(0.923598\pi\)
\(744\) 0 0
\(745\) 0.759333 + 1.31520i 0.0278198 + 0.0481853i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.62226 + 14.5897i 0.168894 + 0.533095i
\(750\) 0 0
\(751\) 3.17443 5.49828i 0.115837 0.200635i −0.802277 0.596952i \(-0.796378\pi\)
0.918114 + 0.396317i \(0.129712\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 45.8850 1.66993
\(756\) 0 0
\(757\) 28.4278 1.03323 0.516614 0.856219i \(-0.327192\pi\)
0.516614 + 0.856219i \(0.327192\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.03437 + 15.6480i −0.327496 + 0.567239i −0.982014 0.188807i \(-0.939538\pi\)
0.654519 + 0.756046i \(0.272871\pi\)
\(762\) 0 0
\(763\) 22.3278 24.4341i 0.808320 0.884575i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −13.4541 23.3032i −0.485799 0.841429i
\(768\) 0 0
\(769\) −1.72471 2.98728i −0.0621946 0.107724i 0.833252 0.552894i \(-0.186477\pi\)
−0.895446 + 0.445170i \(0.853143\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.1837 34.9592i 0.725957 1.25740i −0.232621 0.972567i \(-0.574730\pi\)
0.958579 0.284828i \(-0.0919364\pi\)
\(774\) 0 0
\(775\) −2.61036 4.52127i −0.0937668 0.162409i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.85880 + 11.8798i −0.245742 + 0.425638i
\(780\) 0 0
\(781\) 2.92964 + 5.07429i 0.104831 + 0.181572i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 5.45010 9.43985i 0.194522 0.336923i
\(786\) 0 0
\(787\) −18.3206 −0.653060 −0.326530 0.945187i \(-0.605879\pi\)
−0.326530 + 0.945187i \(0.605879\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.70744 + 8.54575i 0.0962656 + 0.303852i
\(792\) 0 0
\(793\) −14.5331 25.1721i −0.516086 0.893888i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 4.86884 + 8.43307i 0.172463 + 0.298715i 0.939280 0.343151i \(-0.111494\pi\)
−0.766817 + 0.641865i \(0.778161\pi\)