Properties

Label 3456.2.i.l.2305.6
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: \(x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729\)
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 2305.6
Root \(-1.15879 + 1.28733i\) of defining polynomial
Character \(\chi\) \(=\) 3456.2305
Dual form 3456.2.i.l.1153.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.74260 - 3.01828i) q^{5} +(1.34988 + 2.33807i) q^{7} +O(q^{10})\) \(q+(1.74260 - 3.01828i) q^{5} +(1.34988 + 2.33807i) q^{7} +(-2.84274 - 4.92377i) q^{11} +(1.76055 - 3.04937i) q^{13} -7.65970 q^{17} +2.02060 q^{19} +(-0.0370909 + 0.0642434i) q^{23} +(-3.57334 - 6.18921i) q^{25} +(-2.46032 - 4.26140i) q^{29} +(-3.72257 + 6.44769i) q^{31} +9.40925 q^{35} -5.00631 q^{37} +(-0.482053 + 0.834941i) q^{41} +(0.255495 + 0.442530i) q^{43} +(-2.83509 - 4.91053i) q^{47} +(-0.144369 + 0.250055i) q^{49} -10.4058 q^{53} -19.8151 q^{55} +(-4.47636 + 7.75329i) q^{59} +(-1.46032 - 2.52935i) q^{61} +(-6.13589 - 10.6277i) q^{65} +(-1.56829 + 2.71635i) q^{67} +8.19647 q^{71} +5.21796 q^{73} +(7.67474 - 13.2930i) q^{77} +(0.716260 + 1.24060i) q^{79} +(1.74052 + 3.01467i) q^{83} +(-13.3478 + 23.1191i) q^{85} +12.4058 q^{89} +9.50616 q^{91} +(3.52110 - 6.09873i) q^{95} +(-3.50265 - 6.06677i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{5} + 6 q^{7} + O(q^{10}) \) \( 12 q + 2 q^{5} + 6 q^{7} - 4 q^{11} + 10 q^{13} - 4 q^{17} + 4 q^{19} - 8 q^{23} - 14 q^{25} + 2 q^{29} + 8 q^{31} - 8 q^{35} + 2 q^{41} - 2 q^{43} + 14 q^{47} - 18 q^{49} - 24 q^{53} - 16 q^{55} - 6 q^{59} + 14 q^{61} + 8 q^{65} + 4 q^{67} + 28 q^{71} + 60 q^{73} - 2 q^{77} + 16 q^{79} - 24 q^{83} + 16 q^{85} + 48 q^{89} - 52 q^{91} + 20 q^{95} - 14 q^{97} + O(q^{100}) \)

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
\(5\) 1.74260 3.01828i 0.779317 1.34982i −0.153019 0.988223i \(-0.548900\pi\)
0.932336 0.361593i \(-0.117767\pi\)
\(6\) 0 0
\(7\) 1.34988 + 2.33807i 0.510208 + 0.883706i 0.999930 + 0.0118274i \(0.00376488\pi\)
−0.489722 + 0.871879i \(0.662902\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.84274 4.92377i −0.857119 1.48457i −0.874665 0.484727i \(-0.838919\pi\)
0.0175468 0.999846i \(-0.494414\pi\)
\(12\) 0 0
\(13\) 1.76055 3.04937i 0.488289 0.845742i −0.511620 0.859212i \(-0.670954\pi\)
0.999909 + 0.0134701i \(0.00428779\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −7.65970 −1.85775 −0.928875 0.370392i \(-0.879223\pi\)
−0.928875 + 0.370392i \(0.879223\pi\)
\(18\) 0 0
\(19\) 2.02060 0.463557 0.231778 0.972769i \(-0.425546\pi\)
0.231778 + 0.972769i \(0.425546\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −0.0370909 + 0.0642434i −0.00773399 + 0.0133957i −0.869866 0.493287i \(-0.835795\pi\)
0.862133 + 0.506683i \(0.169128\pi\)
\(24\) 0 0
\(25\) −3.57334 6.18921i −0.714669 1.23784i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.46032 4.26140i −0.456870 0.791321i 0.541924 0.840428i \(-0.317696\pi\)
−0.998794 + 0.0491062i \(0.984363\pi\)
\(30\) 0 0
\(31\) −3.72257 + 6.44769i −0.668594 + 1.15804i 0.309704 + 0.950833i \(0.399770\pi\)
−0.978297 + 0.207205i \(0.933563\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 9.40925 1.59045
\(36\) 0 0
\(37\) −5.00631 −0.823033 −0.411516 0.911402i \(-0.635001\pi\)
−0.411516 + 0.911402i \(0.635001\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.482053 + 0.834941i −0.0752841 + 0.130396i −0.901210 0.433383i \(-0.857320\pi\)
0.825926 + 0.563779i \(0.190653\pi\)
\(42\) 0 0
\(43\) 0.255495 + 0.442530i 0.0389626 + 0.0674852i 0.884849 0.465878i \(-0.154261\pi\)
−0.845887 + 0.533363i \(0.820928\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.83509 4.91053i −0.413541 0.716274i 0.581733 0.813380i \(-0.302375\pi\)
−0.995274 + 0.0971059i \(0.969041\pi\)
\(48\) 0 0
\(49\) −0.144369 + 0.250055i −0.0206242 + 0.0357221i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10.4058 −1.42935 −0.714676 0.699455i \(-0.753426\pi\)
−0.714676 + 0.699455i \(0.753426\pi\)
\(54\) 0 0
\(55\) −19.8151 −2.67187
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.47636 + 7.75329i −0.582773 + 1.00939i 0.412376 + 0.911014i \(0.364699\pi\)
−0.995149 + 0.0983788i \(0.968634\pi\)
\(60\) 0 0
\(61\) −1.46032 2.52935i −0.186975 0.323849i 0.757266 0.653107i \(-0.226535\pi\)
−0.944240 + 0.329258i \(0.893202\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −6.13589 10.6277i −0.761064 1.31820i
\(66\) 0 0
\(67\) −1.56829 + 2.71635i −0.191597 + 0.331855i −0.945780 0.324809i \(-0.894700\pi\)
0.754183 + 0.656665i \(0.228033\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 8.19647 0.972742 0.486371 0.873752i \(-0.338320\pi\)
0.486371 + 0.873752i \(0.338320\pi\)
\(72\) 0 0
\(73\) 5.21796 0.610716 0.305358 0.952238i \(-0.401224\pi\)
0.305358 + 0.952238i \(0.401224\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 7.67474 13.2930i 0.874617 1.51488i
\(78\) 0 0
\(79\) 0.716260 + 1.24060i 0.0805855 + 0.139578i 0.903502 0.428585i \(-0.140988\pi\)
−0.822916 + 0.568163i \(0.807654\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.74052 + 3.01467i 0.191047 + 0.330903i 0.945597 0.325339i \(-0.105478\pi\)
−0.754551 + 0.656242i \(0.772145\pi\)
\(84\) 0 0
\(85\) −13.3478 + 23.1191i −1.44778 + 2.50762i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.4058 1.31502 0.657509 0.753447i \(-0.271610\pi\)
0.657509 + 0.753447i \(0.271610\pi\)
\(90\) 0 0
\(91\) 9.50616 0.996516
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.52110 6.09873i 0.361258 0.625717i
\(96\) 0 0
\(97\) −3.50265 6.06677i −0.355640 0.615987i 0.631587 0.775305i \(-0.282404\pi\)
−0.987227 + 0.159318i \(0.949071\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.44237 + 7.69441i 0.442032 + 0.765623i 0.997840 0.0656882i \(-0.0209243\pi\)
−0.555808 + 0.831311i \(0.687591\pi\)
\(102\) 0 0
\(103\) 2.65012 4.59014i 0.261124 0.452280i −0.705417 0.708792i \(-0.749240\pi\)
0.966541 + 0.256513i \(0.0825736\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.53993 0.728912 0.364456 0.931221i \(-0.381255\pi\)
0.364456 + 0.931221i \(0.381255\pi\)
\(108\) 0 0
\(109\) −13.8840 −1.32984 −0.664922 0.746913i \(-0.731535\pi\)
−0.664922 + 0.746913i \(0.731535\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.36549 + 2.36510i −0.128454 + 0.222489i −0.923078 0.384613i \(-0.874335\pi\)
0.794624 + 0.607102i \(0.207668\pi\)
\(114\) 0 0
\(115\) 0.129270 + 0.223902i 0.0120545 + 0.0208789i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.3397 17.9089i −0.947839 1.64171i
\(120\) 0 0
\(121\) −10.6624 + 18.4677i −0.969305 + 1.67889i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −7.48166 −0.669180
\(126\) 0 0
\(127\) 5.89964 0.523509 0.261754 0.965135i \(-0.415699\pi\)
0.261754 + 0.965135i \(0.415699\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.566027 + 0.980388i −0.0494540 + 0.0856569i −0.889693 0.456560i \(-0.849081\pi\)
0.840239 + 0.542217i \(0.182415\pi\)
\(132\) 0 0
\(133\) 2.72757 + 4.72429i 0.236510 + 0.409648i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.18182 5.51107i −0.271841 0.470843i 0.697492 0.716592i \(-0.254299\pi\)
−0.969333 + 0.245750i \(0.920966\pi\)
\(138\) 0 0
\(139\) 11.2001 19.3992i 0.949983 1.64542i 0.204531 0.978860i \(-0.434433\pi\)
0.745453 0.666559i \(-0.232233\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −20.0192 −1.67409
\(144\) 0 0
\(145\) −17.1495 −1.42418
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.939215 1.62677i 0.0769435 0.133270i −0.824986 0.565153i \(-0.808817\pi\)
0.901930 + 0.431883i \(0.142151\pi\)
\(150\) 0 0
\(151\) −0.183779 0.318315i −0.0149557 0.0259041i 0.858451 0.512896i \(-0.171427\pi\)
−0.873406 + 0.486992i \(0.838094\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 12.9739 + 22.4715i 1.04209 + 1.80496i
\(156\) 0 0
\(157\) 7.15363 12.3905i 0.570922 0.988866i −0.425550 0.904935i \(-0.639919\pi\)
0.996472 0.0839309i \(-0.0267475\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.200274 −0.0157838
\(162\) 0 0
\(163\) −3.02958 −0.237295 −0.118648 0.992936i \(-0.537856\pi\)
−0.118648 + 0.992936i \(0.537856\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.629519 + 1.09036i −0.0487137 + 0.0843745i −0.889354 0.457219i \(-0.848846\pi\)
0.840640 + 0.541594i \(0.182179\pi\)
\(168\) 0 0
\(169\) 0.300915 + 0.521200i 0.0231473 + 0.0400923i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −7.14845 12.3815i −0.543487 0.941347i −0.998700 0.0509644i \(-0.983771\pi\)
0.455214 0.890382i \(-0.349563\pi\)
\(174\) 0 0
\(175\) 9.64719 16.7094i 0.729259 1.26311i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.7991 0.956647 0.478324 0.878184i \(-0.341245\pi\)
0.478324 + 0.878184i \(0.341245\pi\)
\(180\) 0 0
\(181\) −10.4986 −0.780355 −0.390177 0.920740i \(-0.627586\pi\)
−0.390177 + 0.920740i \(0.627586\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −8.72403 + 15.1105i −0.641403 + 1.11094i
\(186\) 0 0
\(187\) 21.7746 + 37.7146i 1.59231 + 2.75797i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.09526 7.09320i −0.296323 0.513246i 0.678969 0.734167i \(-0.262427\pi\)
−0.975292 + 0.220921i \(0.929094\pi\)
\(192\) 0 0
\(193\) −1.46146 + 2.53132i −0.105198 + 0.182208i −0.913819 0.406122i \(-0.866881\pi\)
0.808621 + 0.588330i \(0.200214\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.44174 0.316461 0.158230 0.987402i \(-0.449421\pi\)
0.158230 + 0.987402i \(0.449421\pi\)
\(198\) 0 0
\(199\) −14.6898 −1.04133 −0.520665 0.853761i \(-0.674316\pi\)
−0.520665 + 0.853761i \(0.674316\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.64228 11.5048i 0.466197 0.807477i
\(204\) 0 0
\(205\) 1.68006 + 2.90994i 0.117340 + 0.203239i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.74404 9.94896i −0.397323 0.688184i
\(210\) 0 0
\(211\) 2.04700 3.54551i 0.140921 0.244083i −0.786923 0.617052i \(-0.788327\pi\)
0.927844 + 0.372969i \(0.121660\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.78091 0.121457
\(216\) 0 0
\(217\) −20.1002 −1.36449
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −13.4853 + 23.3572i −0.907120 + 1.57118i
\(222\) 0 0
\(223\) −6.24612 10.8186i −0.418271 0.724467i 0.577494 0.816395i \(-0.304030\pi\)
−0.995766 + 0.0919276i \(0.970697\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.52721 + 7.84136i 0.300482 + 0.520449i 0.976245 0.216669i \(-0.0695193\pi\)
−0.675764 + 0.737118i \(0.736186\pi\)
\(228\) 0 0
\(229\) 13.1073 22.7024i 0.866152 1.50022i 0.000252919 1.00000i \(-0.499919\pi\)
0.865899 0.500219i \(-0.166747\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.41840 −0.0929224 −0.0464612 0.998920i \(-0.514794\pi\)
−0.0464612 + 0.998920i \(0.514794\pi\)
\(234\) 0 0
\(235\) −19.7618 −1.28912
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −8.18200 + 14.1716i −0.529250 + 0.916688i 0.470168 + 0.882577i \(0.344193\pi\)
−0.999418 + 0.0341107i \(0.989140\pi\)
\(240\) 0 0
\(241\) −5.17500 8.96336i −0.333351 0.577381i 0.649816 0.760092i \(-0.274846\pi\)
−0.983167 + 0.182711i \(0.941513\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.503157 + 0.871493i 0.0321455 + 0.0556776i
\(246\) 0 0
\(247\) 3.55737 6.16154i 0.226350 0.392049i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −26.9624 −1.70185 −0.850927 0.525283i \(-0.823959\pi\)
−0.850927 + 0.525283i \(0.823959\pi\)
\(252\) 0 0
\(253\) 0.421759 0.0265158
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 14.8380 25.7001i 0.925568 1.60313i 0.134922 0.990856i \(-0.456922\pi\)
0.790646 0.612274i \(-0.209745\pi\)
\(258\) 0 0
\(259\) −6.75794 11.7051i −0.419918 0.727319i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.46961 2.54544i −0.0906200 0.156959i 0.817152 0.576422i \(-0.195552\pi\)
−0.907772 + 0.419464i \(0.862218\pi\)
\(264\) 0 0
\(265\) −18.1333 + 31.4078i −1.11392 + 1.92936i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −13.4251 −0.818541 −0.409270 0.912413i \(-0.634217\pi\)
−0.409270 + 0.912413i \(0.634217\pi\)
\(270\) 0 0
\(271\) −31.3320 −1.90329 −0.951643 0.307207i \(-0.900606\pi\)
−0.951643 + 0.307207i \(0.900606\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −20.3162 + 35.1887i −1.22511 + 2.12196i
\(276\) 0 0
\(277\) 4.78089 + 8.28075i 0.287256 + 0.497542i 0.973154 0.230156i \(-0.0739236\pi\)
−0.685898 + 0.727698i \(0.740590\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.39152 5.87429i −0.202321 0.350431i 0.746955 0.664875i \(-0.231515\pi\)
−0.949276 + 0.314444i \(0.898182\pi\)
\(282\) 0 0
\(283\) 9.61895 16.6605i 0.571787 0.990364i −0.424595 0.905383i \(-0.639584\pi\)
0.996383 0.0849812i \(-0.0270830\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.60286 −0.153642
\(288\) 0 0
\(289\) 41.6710 2.45124
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.63884 + 9.76676i −0.329425 + 0.570580i −0.982398 0.186801i \(-0.940188\pi\)
0.652973 + 0.757381i \(0.273521\pi\)
\(294\) 0 0
\(295\) 15.6011 + 27.0218i 0.908329 + 1.57327i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.130601 + 0.226207i 0.00755285 + 0.0130819i
\(300\) 0 0
\(301\) −0.689776 + 1.19473i −0.0397580 + 0.0688629i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10.1790 −0.582850
\(306\) 0 0
\(307\) 22.2819 1.27169 0.635846 0.771816i \(-0.280651\pi\)
0.635846 + 0.771816i \(0.280651\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −12.0604 + 20.8893i −0.683884 + 1.18452i 0.289902 + 0.957056i \(0.406377\pi\)
−0.973786 + 0.227466i \(0.926956\pi\)
\(312\) 0 0
\(313\) 14.5297 + 25.1661i 0.821265 + 1.42247i 0.904741 + 0.425962i \(0.140064\pi\)
−0.0834762 + 0.996510i \(0.526602\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.2862 28.2085i −0.914724 1.58435i −0.807305 0.590134i \(-0.799075\pi\)
−0.107418 0.994214i \(-0.534258\pi\)
\(318\) 0 0
\(319\) −13.9881 + 24.2281i −0.783183 + 1.35651i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −15.4772 −0.861173
\(324\) 0 0
\(325\) −25.1642 −1.39586
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 7.65409 13.2573i 0.421984 0.730897i
\(330\) 0 0
\(331\) −8.05963 13.9597i −0.442997 0.767293i 0.554913 0.831908i \(-0.312751\pi\)
−0.997910 + 0.0646148i \(0.979418\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5.46581 + 9.46706i 0.298629 + 0.517241i
\(336\) 0 0
\(337\) 12.6119 21.8445i 0.687015 1.18995i −0.285783 0.958294i \(-0.592254\pi\)
0.972799 0.231651i \(-0.0744128\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 42.3292 2.29226
\(342\) 0 0
\(343\) 18.1188 0.978325
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.16774 3.75464i 0.116371 0.201560i −0.801956 0.597383i \(-0.796207\pi\)
0.918327 + 0.395823i \(0.129541\pi\)
\(348\) 0 0
\(349\) −9.77744 16.9350i −0.523374 0.906511i −0.999630 0.0272042i \(-0.991340\pi\)
0.476255 0.879307i \(-0.341994\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.13835 15.8281i −0.486385 0.842444i 0.513492 0.858094i \(-0.328352\pi\)
−0.999878 + 0.0156502i \(0.995018\pi\)
\(354\) 0 0
\(355\) 14.2832 24.7392i 0.758074 1.31302i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.41976 0.180488 0.0902440 0.995920i \(-0.471235\pi\)
0.0902440 + 0.995920i \(0.471235\pi\)
\(360\) 0 0
\(361\) −14.9172 −0.785115
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 9.09285 15.7493i 0.475941 0.824355i
\(366\) 0 0
\(367\) 5.46341 + 9.46291i 0.285188 + 0.493960i 0.972655 0.232256i \(-0.0746107\pi\)
−0.687467 + 0.726216i \(0.741277\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −14.0467 24.3296i −0.729267 1.26313i
\(372\) 0 0
\(373\) 10.4603 18.1178i 0.541615 0.938104i −0.457197 0.889366i \(-0.651147\pi\)
0.998812 0.0487387i \(-0.0155202\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −17.3261 −0.892338
\(378\) 0 0
\(379\) −18.0219 −0.925725 −0.462862 0.886430i \(-0.653178\pi\)
−0.462862 + 0.886430i \(0.653178\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.4732 21.6042i 0.637350 1.10392i −0.348662 0.937249i \(-0.613364\pi\)
0.986012 0.166674i \(-0.0533028\pi\)
\(384\) 0 0
\(385\) −26.7481 46.3290i −1.36321 2.36115i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.96347 + 12.0611i 0.353062 + 0.611522i 0.986784 0.162039i \(-0.0518071\pi\)
−0.633722 + 0.773561i \(0.718474\pi\)
\(390\) 0 0
\(391\) 0.284105 0.492085i 0.0143678 0.0248858i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 4.99263 0.251206
\(396\) 0 0
\(397\) −6.54840 −0.328655 −0.164327 0.986406i \(-0.552545\pi\)
−0.164327 + 0.986406i \(0.552545\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 12.1738 21.0857i 0.607933 1.05297i −0.383648 0.923480i \(-0.625332\pi\)
0.991581 0.129491i \(-0.0413344\pi\)
\(402\) 0 0
\(403\) 13.1076 + 22.7030i 0.652934 + 1.13092i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 14.2317 + 24.6499i 0.705437 + 1.22185i
\(408\) 0 0
\(409\) 8.08792 14.0087i 0.399922 0.692685i −0.593794 0.804617i \(-0.702371\pi\)
0.993716 + 0.111932i \(0.0357040\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −24.1703 −1.18934
\(414\) 0 0
\(415\) 12.1322 0.595544
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 17.2436 29.8668i 0.842405 1.45909i −0.0454518 0.998967i \(-0.514473\pi\)
0.887856 0.460121i \(-0.152194\pi\)
\(420\) 0 0
\(421\) 15.6909 + 27.1774i 0.764728 + 1.32455i 0.940390 + 0.340097i \(0.110460\pi\)
−0.175662 + 0.984451i \(0.556207\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 27.3708 + 47.4075i 1.32768 + 2.29960i
\(426\) 0 0
\(427\) 3.94252 6.82864i 0.190792 0.330461i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 12.1491 0.585200 0.292600 0.956235i \(-0.405480\pi\)
0.292600 + 0.956235i \(0.405480\pi\)
\(432\) 0 0
\(433\) 2.40374 0.115517 0.0577583 0.998331i \(-0.481605\pi\)
0.0577583 + 0.998331i \(0.481605\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.0749458 + 0.129810i −0.00358514 + 0.00620965i
\(438\) 0 0
\(439\) −18.6941 32.3792i −0.892222 1.54537i −0.837206 0.546888i \(-0.815812\pi\)
−0.0550162 0.998485i \(-0.517521\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.22340 + 7.31515i 0.200660 + 0.347553i 0.948741 0.316054i \(-0.102358\pi\)
−0.748081 + 0.663607i \(0.769025\pi\)
\(444\) 0 0
\(445\) 21.6185 37.4443i 1.02481 1.77503i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −18.6531 −0.880295 −0.440147 0.897926i \(-0.645074\pi\)
−0.440147 + 0.897926i \(0.645074\pi\)
\(450\) 0 0
\(451\) 5.48141 0.258109
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 16.5655 28.6922i 0.776601 1.34511i
\(456\) 0 0
\(457\) −8.91748 15.4455i −0.417142 0.722511i 0.578509 0.815676i \(-0.303635\pi\)
−0.995651 + 0.0931650i \(0.970302\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.0563 17.4181i −0.468370 0.811240i 0.530977 0.847386i \(-0.321825\pi\)
−0.999347 + 0.0361463i \(0.988492\pi\)
\(462\) 0 0
\(463\) 4.10747 7.11435i 0.190890 0.330632i −0.754655 0.656122i \(-0.772196\pi\)
0.945546 + 0.325490i \(0.105529\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19.3274 0.894364 0.447182 0.894443i \(-0.352428\pi\)
0.447182 + 0.894443i \(0.352428\pi\)
\(468\) 0 0
\(469\) −8.46802 −0.391017
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.45261 2.51600i 0.0667911 0.115686i
\(474\) 0 0
\(475\) −7.22029 12.5059i −0.331290 0.573811i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 21.1597 + 36.6498i 0.966814 + 1.67457i 0.704661 + 0.709544i \(0.251099\pi\)
0.262152 + 0.965027i \(0.415568\pi\)
\(480\) 0 0
\(481\) −8.81387 + 15.2661i −0.401878 + 0.696073i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −24.4149 −1.10863
\(486\) 0 0
\(487\) 1.36060 0.0616547 0.0308273 0.999525i \(-0.490186\pi\)
0.0308273 + 0.999525i \(0.490186\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 15.6328 27.0768i 0.705497 1.22196i −0.261015 0.965335i \(-0.584057\pi\)
0.966512 0.256622i \(-0.0826096\pi\)
\(492\) 0 0
\(493\) 18.8453 + 32.6410i 0.848750 + 1.47008i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 11.0643 + 19.1639i 0.496301 + 0.859618i
\(498\) 0 0
\(499\) −7.37981 + 12.7822i −0.330366 + 0.572210i −0.982584 0.185821i \(-0.940505\pi\)
0.652218 + 0.758032i \(0.273839\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −44.6336 −1.99011 −0.995056 0.0993124i \(-0.968336\pi\)
−0.995056 + 0.0993124i \(0.968336\pi\)
\(504\) 0 0
\(505\) 30.9652 1.37793
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.854549 1.48012i 0.0378772 0.0656053i −0.846465 0.532444i \(-0.821274\pi\)
0.884343 + 0.466839i \(0.154607\pi\)
\(510\) 0 0
\(511\) 7.04364 + 12.1999i 0.311592 + 0.539694i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.23621 15.9976i −0.406996 0.704938i
\(516\) 0 0
\(517\) −16.1189 + 27.9187i −0.708907 + 1.22786i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 10.6018 0.464475 0.232237 0.972659i \(-0.425395\pi\)
0.232237 + 0.972659i \(0.425395\pi\)
\(522\) 0 0
\(523\) −27.1565 −1.18747 −0.593736 0.804660i \(-0.702348\pi\)
−0.593736 + 0.804660i \(0.702348\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 28.5138 49.3874i 1.24208 2.15135i
\(528\) 0 0
\(529\) 11.4972 + 19.9138i 0.499880 + 0.865818i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.69736 + 2.93991i 0.0735208 + 0.127342i
\(534\) 0 0
\(535\) 13.1391 22.7576i 0.568053 0.983897i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.64162 0.0707094
\(540\) 0 0
\(541\) 35.1225 1.51003 0.755017 0.655705i \(-0.227629\pi\)
0.755017 + 0.655705i \(0.227629\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −24.1943 + 41.9057i −1.03637 + 1.79504i
\(546\) 0 0
\(547\) 13.0029 + 22.5218i 0.555966 + 0.962961i 0.997828 + 0.0658781i \(0.0209849\pi\)
−0.441862 + 0.897083i \(0.645682\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −4.97131 8.61057i −0.211785 0.366822i
\(552\) 0 0
\(553\) −1.93373 + 3.34932i −0.0822307 + 0.142428i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 28.8670 1.22314 0.611568 0.791192i \(-0.290539\pi\)
0.611568 + 0.791192i \(0.290539\pi\)
\(558\) 0 0
\(559\) 1.79925 0.0761000
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −0.876491 + 1.51813i −0.0369397 + 0.0639815i −0.883904 0.467668i \(-0.845094\pi\)
0.846964 + 0.531649i \(0.178428\pi\)
\(564\) 0 0
\(565\) 4.75901 + 8.24285i 0.200213 + 0.346779i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13.3974 + 23.2049i 0.561647 + 0.972801i 0.997353 + 0.0727120i \(0.0231654\pi\)
−0.435706 + 0.900089i \(0.643501\pi\)
\(570\) 0 0
\(571\) −12.6759 + 21.9553i −0.530471 + 0.918803i 0.468897 + 0.883253i \(0.344652\pi\)
−0.999368 + 0.0355497i \(0.988682\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.530154 0.0221090
\(576\) 0 0
\(577\) 33.8507 1.40922 0.704612 0.709593i \(-0.251121\pi\)
0.704612 + 0.709593i \(0.251121\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −4.69900 + 8.13890i −0.194947 + 0.337659i
\(582\) 0 0
\(583\) 29.5811 + 51.2360i 1.22513 + 2.12198i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.2279 + 19.4474i 0.463427 + 0.802679i 0.999129 0.0417284i \(-0.0132864\pi\)
−0.535702 + 0.844407i \(0.679953\pi\)
\(588\) 0 0
\(589\) −7.52182 + 13.0282i −0.309931 + 0.536817i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9.35530 0.384176 0.192088 0.981378i \(-0.438474\pi\)
0.192088 + 0.981378i \(0.438474\pi\)
\(594\) 0 0
\(595\) −72.0721 −2.95467
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −12.2259 + 21.1759i −0.499538 + 0.865226i −1.00000 0.000533153i \(-0.999830\pi\)
0.500462 + 0.865759i \(0.333164\pi\)
\(600\) 0 0
\(601\) −6.64643 11.5120i −0.271114 0.469583i 0.698034 0.716065i \(-0.254059\pi\)
−0.969147 + 0.246482i \(0.920725\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 37.1605 + 64.3639i 1.51079 + 2.61677i
\(606\) 0 0
\(607\) 18.1403 31.4198i 0.736290 1.27529i −0.217864 0.975979i \(-0.569909\pi\)
0.954155 0.299313i \(-0.0967576\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −19.9653 −0.807710
\(612\) 0 0
\(613\) −6.73390 −0.271980 −0.135990 0.990710i \(-0.543421\pi\)
−0.135990 + 0.990710i \(0.543421\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.553446 + 0.958597i −0.0222809 + 0.0385917i −0.876951 0.480580i \(-0.840426\pi\)
0.854670 + 0.519172i \(0.173759\pi\)
\(618\) 0 0
\(619\) 7.60418 + 13.1708i 0.305638 + 0.529380i 0.977403 0.211384i \(-0.0677970\pi\)
−0.671765 + 0.740764i \(0.734464\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 16.7464 + 29.0057i 0.670932 + 1.16209i
\(624\) 0 0
\(625\) 4.82915 8.36432i 0.193166 0.334573i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 38.3469 1.52899
\(630\) 0 0
\(631\) −29.2163 −1.16308 −0.581541 0.813517i \(-0.697550\pi\)
−0.581541 + 0.813517i \(0.697550\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 10.2807 17.8068i 0.407979 0.706641i
\(636\) 0 0
\(637\) 0.508339 + 0.880468i 0.0201411 + 0.0348854i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 13.4412 + 23.2809i 0.530897 + 0.919540i 0.999350 + 0.0360519i \(0.0114782\pi\)
−0.468453 + 0.883488i \(0.655189\pi\)
\(642\) 0 0
\(643\) −6.36207 + 11.0194i −0.250896 + 0.434564i −0.963773 0.266725i \(-0.914058\pi\)
0.712877 + 0.701289i \(0.247392\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 47.3838 1.86285 0.931425 0.363933i \(-0.118566\pi\)
0.931425 + 0.363933i \(0.118566\pi\)
\(648\) 0 0
\(649\) 50.9006 1.99802
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4.13506 7.16213i 0.161817 0.280276i −0.773703 0.633548i \(-0.781598\pi\)
0.935521 + 0.353272i \(0.114931\pi\)
\(654\) 0 0
\(655\) 1.97272 + 3.41686i 0.0770807 + 0.133508i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.00770 1.74539i −0.0392544 0.0679906i 0.845731 0.533610i \(-0.179165\pi\)
−0.884985 + 0.465619i \(0.845832\pi\)
\(660\) 0 0
\(661\) −1.70432 + 2.95196i −0.0662902 + 0.114818i −0.897266 0.441491i \(-0.854450\pi\)
0.830975 + 0.556309i \(0.187783\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 19.0123 0.737266
\(666\) 0 0
\(667\) 0.365022 0.0141337
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.30261 + 14.3805i −0.320519 + 0.555155i
\(672\) 0 0
\(673\) 7.56791 + 13.1080i 0.291722 + 0.505277i 0.974217 0.225613i \(-0.0724386\pi\)
−0.682495 + 0.730890i \(0.739105\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9.31110 + 16.1273i 0.357855 + 0.619822i 0.987602 0.156978i \(-0.0501750\pi\)
−0.629748 + 0.776800i \(0.716842\pi\)
\(678\) 0 0
\(679\) 9.45634 16.3789i 0.362901 0.628563i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −38.4656 −1.47185 −0.735923 0.677066i \(-0.763251\pi\)
−0.735923 + 0.677066i \(0.763251\pi\)
\(684\) 0 0
\(685\) −22.1786 −0.847401
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −18.3200 + 31.7312i −0.697938 + 1.20886i
\(690\) 0 0
\(691\) 11.2999 + 19.5720i 0.429869 + 0.744555i 0.996861 0.0791683i \(-0.0252264\pi\)
−0.566992 + 0.823723i \(0.691893\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −39.0348 67.6103i −1.48068 2.56460i
\(696\) 0 0
\(697\) 3.69238 6.39540i 0.139859 0.242243i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 37.8883 1.43102 0.715510 0.698602i \(-0.246194\pi\)
0.715510 + 0.698602i \(0.246194\pi\)
\(702\) 0 0
\(703\) −10.1157 −0.381523
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −11.9934 + 20.7731i −0.451057 + 0.781253i
\(708\) 0 0
\(709\) 7.75701 + 13.4355i 0.291321 + 0.504582i 0.974122 0.226022i \(-0.0725720\pi\)
−0.682802 + 0.730604i \(0.739239\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.276147 0.478301i −0.0103418 0.0179125i
\(714\) 0 0
\(715\) −34.8855 + 60.4235i −1.30464 + 2.25971i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −29.8701 −1.11397 −0.556983 0.830524i \(-0.688041\pi\)
−0.556983 + 0.830524i \(0.688041\pi\)
\(720\) 0 0
\(721\) 14.3094 0.532910
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −17.5831 + 30.4549i −0.653021 + 1.13107i
\(726\) 0 0
\(727\) −2.80759 4.86288i −0.104128 0.180354i 0.809254 0.587459i \(-0.199872\pi\)
−0.913381 + 0.407105i \(0.866538\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.95701 3.38965i −0.0723828 0.125371i
\(732\) 0 0
\(733\) 6.02803 10.4409i 0.222650 0.385642i −0.732962 0.680270i \(-0.761863\pi\)
0.955612 + 0.294628i \(0.0951958\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 17.8329 0.656885
\(738\) 0 0
\(739\) −43.8187 −1.61190 −0.805948 0.591986i \(-0.798344\pi\)
−0.805948 + 0.591986i \(0.798344\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −15.0004 + 25.9814i −0.550310 + 0.953164i 0.447942 + 0.894062i \(0.352157\pi\)
−0.998252 + 0.0591018i \(0.981176\pi\)
\(744\) 0 0
\(745\) −3.27336 5.66963i −0.119927 0.207719i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10.1780 + 17.6288i 0.371897 + 0.644144i
\(750\) 0 0
\(751\) 4.69583 8.13342i 0.171353 0.296793i −0.767540 0.641001i \(-0.778519\pi\)
0.938893 + 0.344208i \(0.111853\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.28102 −0.0466210
\(756\) 0 0
\(757\) 21.7285 0.789737 0.394868 0.918738i \(-0.370790\pi\)
0.394868 + 0.918738i \(0.370790\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.78398 11.7502i 0.245919 0.425944i −0.716471 0.697617i \(-0.754244\pi\)
0.962390 + 0.271673i \(0.0875769\pi\)
\(762\) 0 0
\(763\) −18.7417 32.4617i −0.678497 1.17519i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 15.7617 + 27.3001i 0.569124 + 0.985751i
\(768\) 0 0
\(769\) −21.3949 + 37.0571i −0.771520 + 1.33631i 0.165209 + 0.986259i \(0.447170\pi\)
−0.936730 + 0.350054i \(0.886163\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −12.4288 −0.447034 −0.223517 0.974700i \(-0.571754\pi\)
−0.223517 + 0.974700i \(0.571754\pi\)
\(774\) 0 0
\(775\) 53.2081 1.91129
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.974036 + 1.68708i −0.0348984 + 0.0604459i
\(780\) 0 0
\(781\) −23.3004 40.3576i −0.833756 1.44411i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −24.9319 43.1833i −0.889858 1.54128i
\(786\) 0 0
\(787\) 21.5079 37.2527i 0.766673 1.32792i −0.172684 0.984977i \(-0.555244\pi\)
0.939357 0.342940i \(-0.111423\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.37300 −0.262154
\(792\) 0 0
\(793\) −10.2839 −0.365191
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 13.6697 23.6766i 0.484205 0.838668i −0.515630 0.856811i \(-0.672442\pi\)
0.999835 + 0.0181431i \(0.00577543\pi\)
\(798\) 0 0
\(799\) 21.7160 + 37.6132i 0.768256 + 1.33066i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −14.8333 25.6921i −0.523456 0.906653i
\(804\) 0 0