Properties

Label 3456.2.i.l.1153.6
Level $3456$
Weight $2$
Character 3456.1153
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 1153.6
Root \(-1.15879 - 1.28733i\) of defining polynomial
Character \(\chi\) \(=\) 3456.1153
Dual form 3456.2.i.l.2305.6

$q$-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 \(\left(\mathbb{Z}/3456\mathbb{Z}\right)^\times\).

\(n\) \(2053\) \(2431\) \(2945\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 1.74260 + 3.01828i 0.779317 + 1.34982i 0.932336 + 0.361593i \(0.117767\pi\)
−0.153019 + 0.988223i \(0.548900\pi\)
\(6\) 0 0
\(7\) 1.34988 2.33807i 0.510208 0.883706i −0.489722 0.871879i \(-0.662902\pi\)
0.999930 0.0118274i \(-0.00376488\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −2.84274 + 4.92377i −0.857119 + 1.48457i 0.0175468 + 0.999846i \(0.494414\pi\)
−0.874665 + 0.484727i \(0.838919\pi\)
\(12\) 0 0
\(13\) 1.76055 + 3.04937i 0.488289 + 0.845742i 0.999909 0.0134701i \(-0.00428779\pi\)
−0.511620 + 0.859212i \(0.670954\pi\)
\(14\) 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 0.862133 0.506683i \(-0.169128\pi\)
−0.869866 + 0.493287i \(0.835795\pi\)
\(24\) 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 −0.998794 0.0491062i \(-0.984363\pi\)
0.541924 + 0.840428i \(0.317696\pi\)
\(30\) 0 0
\(31\) −3.72257 6.44769i −0.668594 1.15804i −0.978297 0.207205i \(-0.933563\pi\)
0.309704 0.950833i \(-0.399770\pi\)
\(32\) 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 0.825926 0.563779i \(-0.190653\pi\)
−0.901210 + 0.433383i \(0.857320\pi\)
\(42\) 0 0
\(43\) 0.255495 0.442530i 0.0389626 0.0674852i −0.845887 0.533363i \(-0.820928\pi\)
0.884849 + 0.465878i \(0.154261\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.83509 + 4.91053i −0.413541 + 0.716274i −0.995274 0.0971059i \(-0.969041\pi\)
0.581733 + 0.813380i \(0.302375\pi\)
\(48\) 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 −0.995149 0.0983788i \(-0.968634\pi\)
0.412376 0.911014i \(-0.364699\pi\)
\(60\) 0 0
\(61\) −1.46032 + 2.52935i −0.186975 + 0.323849i −0.944240 0.329258i \(-0.893202\pi\)
0.757266 + 0.653107i \(0.226535\pi\)
\(62\) 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 0.754183 0.656665i \(-0.228033\pi\)
−0.945780 + 0.324809i \(0.894700\pi\)
\(68\) 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 −0.822916 0.568163i \(-0.807654\pi\)
0.903502 + 0.428585i \(0.140988\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.74052 3.01467i 0.191047 0.330903i −0.754551 0.656242i \(-0.772145\pi\)
0.945597 + 0.325339i \(0.105478\pi\)
\(84\) 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 −0.987227 0.159318i \(-0.949071\pi\)
0.631587 + 0.775305i \(0.282404\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 4.44237 7.69441i 0.442032 0.765623i −0.555808 0.831311i \(-0.687591\pi\)
0.997840 + 0.0656882i \(0.0209243\pi\)
\(102\) 0 0
\(103\) 2.65012 + 4.59014i 0.261124 + 0.452280i 0.966541 0.256513i \(-0.0825736\pi\)
−0.705417 + 0.708792i \(0.749240\pi\)
\(104\) 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 0.794624 0.607102i \(-0.207668\pi\)
−0.923078 + 0.384613i \(0.874335\pi\)
\(114\) 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 0.840239 0.542217i \(-0.182415\pi\)
−0.889693 + 0.456560i \(0.849081\pi\)
\(132\) 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 −0.969333 0.245750i \(-0.920966\pi\)
0.697492 + 0.716592i \(0.254299\pi\)
\(138\) 0 0
\(139\) 11.2001 + 19.3992i 0.949983 + 1.64542i 0.745453 + 0.666559i \(0.232233\pi\)
0.204531 + 0.978860i \(0.434433\pi\)
\(140\) 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 0.901930 0.431883i \(-0.142151\pi\)
−0.824986 + 0.565153i \(0.808817\pi\)
\(150\) 0 0
\(151\) −0.183779 + 0.318315i −0.0149557 + 0.0259041i −0.873406 0.486992i \(-0.838094\pi\)
0.858451 + 0.512896i \(0.171427\pi\)
\(152\) 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 0.996472 + 0.0839309i \(0.0267475\pi\)
−0.425550 + 0.904935i \(0.639919\pi\)
\(158\) 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 0.840640 0.541594i \(-0.182179\pi\)
−0.889354 + 0.457219i \(0.848846\pi\)
\(168\) 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 0.455214 + 0.890382i \(0.349563\pi\)
−0.998700 + 0.0509644i \(0.983771\pi\)
\(174\) 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 −0.975292 0.220921i \(-0.929094\pi\)
0.678969 + 0.734167i \(0.262427\pi\)
\(192\) 0 0
\(193\) −1.46146 2.53132i −0.105198 0.182208i 0.808621 0.588330i \(-0.200214\pi\)
−0.913819 + 0.406122i \(0.866881\pi\)
\(194\) 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 0.927844 0.372969i \(-0.121660\pi\)
−0.786923 + 0.617052i \(0.788327\pi\)
\(212\) 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 −0.995766 0.0919276i \(-0.970697\pi\)
0.577494 + 0.816395i \(0.304030\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.52721 7.84136i 0.300482 0.520449i −0.675764 0.737118i \(-0.736186\pi\)
0.976245 + 0.216669i \(0.0695193\pi\)
\(228\) 0 0
\(229\) 13.1073 + 22.7024i 0.866152 + 1.50022i 0.865899 + 0.500219i \(0.166747\pi\)
0.000252919 1.00000i \(0.499919\pi\)
\(230\) 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 −0.999418 0.0341107i \(-0.989140\pi\)
0.470168 0.882577i \(-0.344193\pi\)
\(240\) 0 0
\(241\) −5.17500 + 8.96336i −0.333351 + 0.577381i −0.983167 0.182711i \(-0.941513\pi\)
0.649816 + 0.760092i \(0.274846\pi\)
\(242\) 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 0.790646 + 0.612274i \(0.209745\pi\)
0.134922 + 0.990856i \(0.456922\pi\)
\(258\) 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 −0.907772 0.419464i \(-0.862218\pi\)
0.817152 + 0.576422i \(0.195552\pi\)
\(264\) 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 −0.685898 0.727698i \(-0.740590\pi\)
0.973154 + 0.230156i \(0.0739236\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −3.39152 + 5.87429i −0.202321 + 0.350431i −0.949276 0.314444i \(-0.898182\pi\)
0.746955 + 0.664875i \(0.231515\pi\)
\(282\) 0 0
\(283\) 9.61895 + 16.6605i 0.571787 + 0.990364i 0.996383 + 0.0849812i \(0.0270830\pi\)
−0.424595 + 0.905383i \(0.639584\pi\)
\(284\) 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 0.652973 0.757381i \(-0.273521\pi\)
−0.982398 + 0.186801i \(0.940188\pi\)
\(294\) 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 −0.973786 0.227466i \(-0.926956\pi\)
0.289902 0.957056i \(-0.406377\pi\)
\(312\) 0 0
\(313\) 14.5297 25.1661i 0.821265 1.42247i −0.0834762 0.996510i \(-0.526602\pi\)
0.904741 0.425962i \(-0.140064\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −16.2862 + 28.2085i −0.914724 + 1.58435i −0.107418 + 0.994214i \(0.534258\pi\)
−0.807305 + 0.590134i \(0.799075\pi\)
\(318\) 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 −0.997910 0.0646148i \(-0.979418\pi\)
0.554913 + 0.831908i \(0.312751\pi\)
\(332\) 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 0.972799 + 0.231651i \(0.0744128\pi\)
−0.285783 + 0.958294i \(0.592254\pi\)
\(338\) 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 0.918327 0.395823i \(-0.129541\pi\)
−0.801956 + 0.597383i \(0.796207\pi\)
\(348\) 0 0
\(349\) −9.77744 + 16.9350i −0.523374 + 0.906511i 0.476255 + 0.879307i \(0.341994\pi\)
−0.999630 + 0.0272042i \(0.991340\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.13835 + 15.8281i −0.486385 + 0.842444i −0.999878 0.0156502i \(-0.995018\pi\)
0.513492 + 0.858094i \(0.328352\pi\)
\(354\) 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 −0.687467 0.726216i \(-0.741277\pi\)
0.972655 + 0.232256i \(0.0746107\pi\)
\(368\) 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 0.998812 + 0.0487387i \(0.0155202\pi\)
−0.457197 + 0.889366i \(0.651147\pi\)
\(374\) 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 0.986012 + 0.166674i \(0.0533028\pi\)
−0.348662 + 0.937249i \(0.613364\pi\)
\(384\) 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 −0.633722 0.773561i \(-0.718474\pi\)
0.986784 + 0.162039i \(0.0518071\pi\)
\(390\) 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 0.991581 + 0.129491i \(0.0413344\pi\)
−0.383648 + 0.923480i \(0.625332\pi\)
\(402\) 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 0.993716 0.111932i \(-0.0357040\pi\)
−0.593794 + 0.804617i \(0.702371\pi\)
\(410\) 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 0.887856 + 0.460121i \(0.152194\pi\)
−0.0454518 + 0.998967i \(0.514473\pi\)
\(420\) 0 0
\(421\) 15.6909 27.1774i 0.764728 1.32455i −0.175662 0.984451i \(-0.556207\pi\)
0.940390 0.340097i \(-0.110460\pi\)
\(422\) 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 −0.0550162 + 0.998485i \(0.517521\pi\)
−0.837206 + 0.546888i \(0.815812\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.22340 7.31515i 0.200660 0.347553i −0.748081 0.663607i \(-0.769025\pi\)
0.948741 + 0.316054i \(0.102358\pi\)
\(444\) 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 −0.995651 0.0931650i \(-0.970302\pi\)
0.578509 + 0.815676i \(0.303635\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10.0563 + 17.4181i −0.468370 + 0.811240i −0.999347 0.0361463i \(-0.988492\pi\)
0.530977 + 0.847386i \(0.321825\pi\)
\(462\) 0 0
\(463\) 4.10747 + 7.11435i 0.190890 + 0.330632i 0.945546 0.325490i \(-0.105529\pi\)
−0.754655 + 0.656122i \(0.772196\pi\)
\(464\) 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 0.262152 0.965027i \(-0.415568\pi\)
0.704661 0.709544i \(-0.251099\pi\)
\(480\) 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 0.966512 + 0.256622i \(0.0826096\pi\)
−0.261015 + 0.965335i \(0.584057\pi\)
\(492\) 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 0.652218 0.758032i \(-0.273839\pi\)
−0.982584 + 0.185821i \(0.940505\pi\)
\(500\) 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 0.884343 0.466839i \(-0.154607\pi\)
−0.846465 + 0.532444i \(0.821274\pi\)
\(510\) 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 −0.441862 0.897083i \(-0.645682\pi\)
0.997828 0.0658781i \(-0.0209849\pi\)
\(548\) 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 0.846964 0.531649i \(-0.178428\pi\)
−0.883904 + 0.467668i \(0.845094\pi\)
\(564\) 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 −0.435706 0.900089i \(-0.643501\pi\)
0.997353 0.0727120i \(-0.0231654\pi\)
\(570\) 0 0
\(571\) −12.6759 21.9553i −0.530471 0.918803i −0.999368 0.0355497i \(-0.988682\pi\)
0.468897 0.883253i \(-0.344652\pi\)
\(572\) 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 −0.535702 0.844407i \(-0.679953\pi\)
0.999129 + 0.0417284i \(0.0132864\pi\)
\(588\) 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 0.500462 0.865759i \(-0.333164\pi\)
−1.00000 0.000533153i \(0.999830\pi\)
\(600\) 0 0
\(601\) −6.64643 + 11.5120i −0.271114 + 0.469583i −0.969147 0.246482i \(-0.920725\pi\)
0.698034 + 0.716065i \(0.254059\pi\)
\(602\) 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 0.954155 + 0.299313i \(0.0967576\pi\)
−0.217864 + 0.975979i \(0.569909\pi\)
\(608\) 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 0.854670 0.519172i \(-0.173759\pi\)
−0.876951 + 0.480580i \(0.840426\pi\)
\(618\) 0 0
\(619\) 7.60418 13.1708i 0.305638 0.529380i −0.671765 0.740764i \(-0.734464\pi\)
0.977403 + 0.211384i \(0.0677970\pi\)
\(620\) 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 −0.468453 0.883488i \(-0.655189\pi\)
0.999350 0.0360519i \(-0.0114782\pi\)
\(642\) 0 0
\(643\) −6.36207 11.0194i −0.250896 0.434564i 0.712877 0.701289i \(-0.247392\pi\)
−0.963773 + 0.266725i \(0.914058\pi\)
\(644\) 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 0.935521 0.353272i \(-0.114931\pi\)
−0.773703 + 0.633548i \(0.781598\pi\)
\(654\) 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 −0.884985 0.465619i \(-0.845832\pi\)
0.845731 + 0.533610i \(0.179165\pi\)
\(660\) 0 0
\(661\) −1.70432 2.95196i −0.0662902 0.114818i 0.830975 0.556309i \(-0.187783\pi\)
−0.897266 + 0.441491i \(0.854450\pi\)
\(662\) 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 −0.682495 0.730890i \(-0.739105\pi\)
0.974217 + 0.225613i \(0.0724386\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 9.31110 16.1273i 0.357855 0.619822i −0.629748 0.776800i \(-0.716842\pi\)
0.987602 + 0.156978i \(0.0501750\pi\)
\(678\) 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 −0.566992 0.823723i \(-0.691893\pi\)
0.996861 + 0.0791683i \(0.0252264\pi\)
\(692\) 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 −0.682802 0.730604i \(-0.739239\pi\)
0.974122 + 0.226022i \(0.0725720\pi\)
\(710\) 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 −0.913381 0.407105i \(-0.866538\pi\)
0.809254 + 0.587459i \(0.199872\pi\)
\(728\) 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 0.955612 0.294628i \(-0.0951958\pi\)
−0.732962 + 0.680270i \(0.761863\pi\)
\(734\) 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 −0.998252 0.0591018i \(-0.981176\pi\)
0.447942 0.894062i \(-0.352157\pi\)
\(744\) 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 0.938893 0.344208i \(-0.111853\pi\)
−0.767540 + 0.641001i \(0.778519\pi\)
\(752\) 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 0.962390 0.271673i \(-0.0875769\pi\)
−0.716471 + 0.697617i \(0.754244\pi\)
\(762\) 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 −0.936730 0.350054i \(-0.886163\pi\)
0.165209 0.986259i \(-0.447170\pi\)
\(770\) 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 0.939357 + 0.342940i \(0.111423\pi\)
−0.172684 + 0.984977i \(0.555244\pi\)
\(788\) 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 0.999835 0.0181431i \(-0.00577543\pi\)
−0.515630 + 0.856811i \(0.672442\pi\)
\(798\) 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