Properties

Label 3024.2.q.l.2305.8
Level $3024$
Weight $2$
Character 3024.2305
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 2305.8
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.8

$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

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

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
\(5\) 1.05220 + 1.82246i 0.470558 + 0.815030i 0.999433 0.0336699i \(-0.0107195\pi\)
−0.528876 + 0.848699i \(0.677386\pi\)
\(6\) 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 −0.894537 0.446993i \(-0.852495\pi\)
0.834376 + 0.551195i \(0.185828\pi\)
\(12\) 0 0
\(13\) 1.44292 2.49921i 0.400194 0.693157i −0.593555 0.804794i \(-0.702276\pi\)
0.993749 + 0.111637i \(0.0356093\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.176596 + 0.305873i 0.0428308 + 0.0741851i 0.886646 0.462449i \(-0.153029\pi\)
−0.843815 + 0.536634i \(0.819696\pi\)
\(18\) 0 0
\(19\) −2.84888 + 4.93440i −0.653578 + 1.13203i 0.328670 + 0.944445i \(0.393399\pi\)
−0.982248 + 0.187585i \(0.939934\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.438682 + 0.759820i 0.0914716 + 0.158433i 0.908131 0.418687i \(-0.137510\pi\)
−0.816659 + 0.577121i \(0.804176\pi\)
\(24\) 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 0.773276 0.634070i \(-0.218617\pi\)
−0.935759 + 0.352641i \(0.885284\pi\)
\(30\) 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 0.439420 + 0.898282i \(0.355184\pi\)
−0.997645 + 0.0685922i \(0.978149\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −1.20377 + 2.08499i −0.187997 + 0.325621i −0.944582 0.328274i \(-0.893533\pi\)
0.756585 + 0.653895i \(0.226866\pi\)
\(42\) 0 0
\(43\) −0.276745 0.479336i −0.0422032 0.0730981i 0.844152 0.536104i \(-0.180104\pi\)
−0.886355 + 0.463005i \(0.846771\pi\)
\(44\) 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 0.972721 0.231976i \(-0.0745191\pi\)
−0.687258 + 0.726413i \(0.741186\pi\)
\(54\) 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 0.883905 0.467666i \(-0.154905\pi\)
−0.846963 + 0.531652i \(0.821572\pi\)
\(74\) 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 −0.999988 0.00487885i \(-0.998447\pi\)
0.495769 0.868455i \(-0.334886\pi\)
\(84\) 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 0.162729 + 0.986671i \(0.447971\pi\)
−0.935846 + 0.352408i \(0.885363\pi\)
\(90\) 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 −0.922023 0.387134i \(-0.873465\pi\)
0.125744 0.992063i \(-0.459868\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −0.0464285 + 0.0804166i −0.00461981 + 0.00800175i −0.868326 0.495994i \(-0.834804\pi\)
0.863706 + 0.503996i \(0.168137\pi\)
\(102\) 0 0
\(103\) −9.95769 17.2472i −0.981161 1.69942i −0.657891 0.753113i \(-0.728551\pi\)
−0.323270 0.946307i \(-0.604782\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.89225 + 5.00953i −0.279605 + 0.484290i −0.971287 0.237913i \(-0.923537\pi\)
0.691682 + 0.722202i \(0.256870\pi\)
\(108\) 0 0
\(109\) −6.25516 10.8343i −0.599136 1.03773i −0.992949 0.118543i \(-0.962178\pi\)
0.393813 0.919191i \(-0.371156\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.69411 + 2.93428i −0.159368 + 0.276034i −0.934641 0.355593i \(-0.884279\pi\)
0.775273 + 0.631627i \(0.217612\pi\)
\(114\) 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 0.991640 + 0.129034i \(0.0411877\pi\)
−0.384073 + 0.923303i \(0.625479\pi\)
\(132\) 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 −0.367273 0.930113i \(-0.619709\pi\)
0.989138 0.146989i \(-0.0469581\pi\)
\(138\) 0 0
\(139\) 3.63996 6.30460i 0.308737 0.534749i −0.669349 0.742948i \(-0.733427\pi\)
0.978086 + 0.208199i \(0.0667603\pi\)
\(140\) 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 0.850867 0.525382i \(-0.176077\pi\)
−0.880427 + 0.474181i \(0.842744\pi\)
\(150\) 0 0
\(151\) 10.9022 18.8831i 0.887207 1.53669i 0.0440432 0.999030i \(-0.485976\pi\)
0.843163 0.537657i \(-0.180691\pi\)
\(152\) 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 −0.950675 0.310188i \(-0.899608\pi\)
0.743968 + 0.668215i \(0.232941\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.83710 + 11.8422i −0.529071 + 0.916378i 0.470354 + 0.882478i \(0.344126\pi\)
−0.999425 + 0.0339001i \(0.989207\pi\)
\(168\) 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 0.762557 + 0.646921i \(0.223944\pi\)
0.178971 + 0.983854i \(0.442723\pi\)
\(180\) 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 0.595098 0.803653i \(-0.297113\pi\)
−0.993533 + 0.113543i \(0.963780\pi\)
\(200\) 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 −0.878845 0.477108i \(-0.841685\pi\)
0.852610 + 0.522548i \(0.175018\pi\)
\(212\) 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 0.992284 0.123984i \(-0.0395670\pi\)
−0.603515 + 0.797352i \(0.706234\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.16624 8.94818i 0.342895 0.593912i −0.642074 0.766643i \(-0.721926\pi\)
0.984969 + 0.172731i \(0.0552591\pi\)
\(228\) 0 0
\(229\) 1.86191 + 3.22493i 0.123039 + 0.213109i 0.920965 0.389646i \(-0.127403\pi\)
−0.797926 + 0.602756i \(0.794069\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −13.3649 + 23.1488i −0.875566 + 1.51653i −0.0194083 + 0.999812i \(0.506178\pi\)
−0.856158 + 0.516714i \(0.827155\pi\)
\(234\) 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 −0.549305 0.835622i \(-0.685107\pi\)
0.998322 + 0.0579007i \(0.0184407\pi\)
\(240\) 0 0
\(241\) −7.45280 + 12.9086i −0.480077 + 0.831518i −0.999739 0.0228542i \(-0.992725\pi\)
0.519662 + 0.854372i \(0.326058\pi\)
\(242\) 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 0.989720 0.143017i \(-0.0456803\pi\)
−0.618716 + 0.785615i \(0.712347\pi\)
\(258\) 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 0.184915 + 0.982755i \(0.440799\pi\)
−0.943548 + 0.331236i \(0.892534\pi\)
\(264\) 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 0.583113 0.812391i \(-0.301835\pi\)
−0.995108 + 0.0987947i \(0.968501\pi\)
\(270\) 0 0
\(271\) 1.34195 2.32433i 0.0815177 0.141193i −0.822384 0.568932i \(-0.807357\pi\)
0.903902 + 0.427740i \(0.140690\pi\)
\(272\) 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 0.423949 + 0.905686i \(0.360644\pi\)
−0.996322 + 0.0856928i \(0.972690\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −14.2006 24.5962i −0.847139 1.46729i −0.883751 0.467958i \(-0.844990\pi\)
0.0366118 0.999330i \(-0.488343\pi\)
\(282\) 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 0.472399 + 0.881385i \(0.343388\pi\)
−0.999501 + 0.0315825i \(0.989945\pi\)
\(294\) 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 −0.523442 0.852061i \(-0.675353\pi\)
0.999628 + 0.0272840i \(0.00868584\pi\)
\(338\) 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 0.996158 + 0.0875692i \(0.0279099\pi\)
−0.422242 + 0.906483i \(0.638757\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −15.6880 + 27.1724i −0.834987 + 1.44624i 0.0590538 + 0.998255i \(0.481192\pi\)
−0.894041 + 0.447985i \(0.852142\pi\)
\(354\) 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 −0.857643 0.514245i \(-0.828072\pi\)
0.874171 + 0.485618i \(0.161405\pi\)
\(360\) 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 −0.905249 0.424881i \(-0.860316\pi\)
0.820582 + 0.571528i \(0.193649\pi\)
\(368\) 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 0.963111 + 0.269103i \(0.0867272\pi\)
−0.248506 + 0.968630i \(0.579939\pi\)
\(374\) 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 0.924437 0.381334i \(-0.124535\pi\)
−0.792463 + 0.609919i \(0.791202\pi\)
\(384\) 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 −0.0588576 0.998266i \(-0.518746\pi\)
0.893953 0.448161i \(-0.147921\pi\)
\(390\) 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 −0.876172 0.481999i \(-0.839911\pi\)
0.855509 + 0.517788i \(0.173244\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.86923 17.0940i −0.492846 0.853634i 0.507120 0.861875i \(-0.330710\pi\)
−0.999966 + 0.00824153i \(0.997377\pi\)
\(402\) 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 −0.855920 0.517109i \(-0.827008\pi\)
0.875789 + 0.482694i \(0.160342\pi\)
\(420\) 0 0
\(421\) 5.12114 + 8.87008i 0.249589 + 0.432301i 0.963412 0.268025i \(-0.0863711\pi\)
−0.713823 + 0.700326i \(0.753038\pi\)
\(422\) 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 0.927905 + 0.372817i \(0.121608\pi\)
−0.141083 + 0.989998i \(0.545059\pi\)
\(432\) 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 0.527560 0.849518i \(-0.323107\pi\)
−0.999484 + 0.0321215i \(0.989774\pi\)
\(462\) 0 0
\(463\) −12.7106 + 22.0154i −0.590712 + 1.02314i 0.403424 + 0.915013i \(0.367820\pi\)
−0.994137 + 0.108131i \(0.965513\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.40661 + 7.63248i −0.203914 + 0.353189i −0.949786 0.312900i \(-0.898700\pi\)
0.745872 + 0.666089i \(0.232033\pi\)
\(468\) 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 0.443515 + 0.896267i \(0.353731\pi\)
−0.997947 + 0.0640383i \(0.979602\pi\)
\(480\) 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 0.961691 0.274135i \(-0.0883916\pi\)
−0.718254 + 0.695781i \(0.755058\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 11.3934 19.7340i 0.514179 0.890584i −0.485686 0.874134i \(-0.661430\pi\)
0.999865 0.0164507i \(-0.00523665\pi\)
\(492\) 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 0.999777 + 0.0211317i \(0.00672693\pi\)
−0.481588 + 0.876398i \(0.659940\pi\)
\(500\) 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 0.741957 0.670447i \(-0.233898\pi\)
−0.951603 + 0.307331i \(0.900564\pi\)
\(510\) 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 0.987932 + 0.154891i \(0.0495026\pi\)
−0.359826 + 0.933019i \(0.617164\pi\)
\(522\) 0 0
\(523\) 13.5104 23.4006i 0.590767 1.02324i −0.403362 0.915040i \(-0.632159\pi\)
0.994129 0.108198i \(-0.0345081\pi\)
\(524\) 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 −0.897022 0.441986i \(-0.854274\pi\)
0.831282 + 0.555851i \(0.187607\pi\)
\(542\) 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 0.779246 0.626719i \(-0.215602\pi\)
−0.932377 + 0.361487i \(0.882269\pi\)
\(548\) 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 0.991553 + 0.129704i \(0.0414028\pi\)
−0.383449 + 0.923562i \(0.625264\pi\)
\(558\) 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 0.993580 0.113136i \(-0.0360896\pi\)
−0.594768 + 0.803897i \(0.702756\pi\)
\(578\) 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 0.942820 + 0.333301i \(0.108163\pi\)
−0.182763 + 0.983157i \(0.558504\pi\)
\(588\) 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 −0.989327 0.145715i \(-0.953452\pi\)
0.620856 + 0.783925i \(0.286785\pi\)
\(594\) 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 0.998856 + 0.0478200i \(0.0152274\pi\)
−0.458015 + 0.888945i \(0.651439\pi\)
\(602\) 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 −0.875895 0.482501i \(-0.839729\pi\)
0.0200897 0.999798i \(-0.493605\pi\)
\(608\) 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 0.851525 0.524313i \(-0.175678\pi\)
−0.879831 + 0.475286i \(0.842345\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.76787 11.7223i 0.272464 0.471922i −0.697028 0.717044i \(-0.745495\pi\)
0.969492 + 0.245122i \(0.0788280\pi\)
\(618\) 0 0
\(619\) −14.9122 + 25.8288i −0.599374 + 1.03815i 0.393540 + 0.919308i \(0.371250\pi\)
−0.992914 + 0.118838i \(0.962083\pi\)
\(620\) 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 −0.349409 0.936970i \(-0.613618\pi\)
0.986145 0.165888i \(-0.0530489\pi\)
\(642\) 0 0
\(643\) −1.16002 + 2.00921i −0.0457465 + 0.0792353i −0.887992 0.459859i \(-0.847900\pi\)
0.842245 + 0.539094i \(0.181233\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.06813 + 1.85005i 0.0419924 + 0.0727329i 0.886258 0.463193i \(-0.153296\pi\)
−0.844265 + 0.535925i \(0.819963\pi\)
\(648\) 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 0.894221 0.447625i \(-0.147730\pi\)
−0.834765 + 0.550606i \(0.814397\pi\)
\(654\) 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 −0.936852 0.349726i \(-0.886275\pi\)
0.165554 0.986201i \(-0.447059\pi\)
\(660\) 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 0.769612 0.638512i \(-0.220450\pi\)
−0.937773 + 0.347248i \(0.887116\pi\)
\(674\) 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 0.644123 0.764922i \(-0.277222\pi\)
−0.984503 + 0.175366i \(0.943889\pi\)
\(684\) 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 −0.833948 0.551843i \(-0.813925\pi\)
0.894884 + 0.446299i \(0.147258\pi\)
\(720\) 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 0.959640 0.281230i \(-0.0907424\pi\)
−0.723373 + 0.690458i \(0.757409\pi\)
\(728\) 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 0.768755 0.639543i \(-0.220876\pi\)
−0.938238 + 0.345990i \(0.887543\pi\)
\(734\) 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 0.873053 + 0.487626i \(0.162137\pi\)
−0.0142303 + 0.999899i \(0.504530\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.62654 + 13.2095i −0.279790 + 0.484611i −0.971333 0.237725i \(-0.923598\pi\)
0.691542 + 0.722336i \(0.256932\pi\)
\(744\) 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 0.918114 0.396317i \(-0.129712\pi\)
−0.802277 + 0.596952i \(0.796378\pi\)
\(752\) 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 0.654519 0.756046i \(-0.272871\pi\)
−0.982014 + 0.188807i \(0.939538\pi\)
\(762\) 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 −0.895446 0.445170i \(-0.853143\pi\)
0.833252 + 0.552894i \(0.186477\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 20.1837 + 34.9592i 0.725957 + 1.25740i 0.958579 + 0.284828i \(0.0919364\pi\)
−0.232621 + 0.972567i \(0.574730\pi\)
\(774\) 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 −0.766817 0.641865i \(-0.778161\pi\)
0.939280 + 0.343151i \(0.111494\pi\)