Properties

Label 3456.2.i.l.2305.1
Level $3456$
Weight $2$
Character 3456.2305
Analytic conductor $27.596$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 2305.1
Root \(-0.433633 - 1.67689i\) of defining polynomial
Character \(\chi\) \(=\) 3456.2305
Dual form 3456.2.i.l.1153.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.22043 + 3.84590i) q^{5} +(1.45488 + 2.51992i) q^{7} +O(q^{10})\) \(q+(-2.22043 + 3.84590i) q^{5} +(1.45488 + 2.51992i) q^{7} +(-1.08263 - 1.87517i) q^{11} +(1.96377 - 3.40135i) q^{13} -1.79720 q^{17} -1.76882 q^{19} +(3.44197 - 5.96166i) q^{23} +(-7.36062 - 12.7490i) q^{25} +(-2.87353 - 4.97710i) q^{29} +(3.27671 - 5.67542i) q^{31} -12.9218 q^{35} +2.51332 q^{37} +(3.68420 - 6.38122i) q^{41} +(-2.53640 - 4.39317i) q^{43} +(4.98598 + 8.63597i) q^{47} +(-0.733339 + 1.27018i) q^{49} -3.30620 q^{53} +9.61562 q^{55} +(-2.30090 + 3.98528i) q^{59} +(-1.87353 - 3.24505i) q^{61} +(8.72084 + 15.1049i) q^{65} +(-2.36045 + 4.08841i) q^{67} -0.907539 q^{71} -1.87740 q^{73} +(3.15019 - 5.45629i) q^{77} +(1.23661 + 2.14187i) q^{79} +(-1.09251 - 1.89227i) q^{83} +(3.99056 - 6.91185i) q^{85} +5.30620 q^{89} +11.4282 q^{91} +(3.92754 - 6.80271i) q^{95} +(4.45302 + 7.71286i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{5} + 6 q^{7} - 4 q^{11} + 10 q^{13} - 4 q^{17} + 4 q^{19} - 8 q^{23} - 14 q^{25} + 2 q^{29} + 8 q^{31} - 8 q^{35} + 2 q^{41} - 2 q^{43} + 14 q^{47} - 18 q^{49} - 24 q^{53} - 16 q^{55} - 6 q^{59} + 14 q^{61} + 8 q^{65} + 4 q^{67} + 28 q^{71} + 60 q^{73} - 2 q^{77} + 16 q^{79} - 24 q^{83} + 16 q^{85} + 48 q^{89} - 52 q^{91} + 20 q^{95} - 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −2.22043 + 3.84590i −0.993006 + 1.71994i −0.394260 + 0.918999i \(0.628999\pi\)
−0.598746 + 0.800939i \(0.704334\pi\)
\(6\) 0 0
\(7\) 1.45488 + 2.51992i 0.549892 + 0.952441i 0.998281 + 0.0586028i \(0.0186645\pi\)
−0.448389 + 0.893838i \(0.648002\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.08263 1.87517i −0.326425 0.565385i 0.655374 0.755304i \(-0.272511\pi\)
−0.981800 + 0.189919i \(0.939178\pi\)
\(12\) 0 0
\(13\) 1.96377 3.40135i 0.544652 0.943366i −0.453976 0.891014i \(-0.649995\pi\)
0.998629 0.0523518i \(-0.0166717\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.79720 −0.435885 −0.217943 0.975962i \(-0.569935\pi\)
−0.217943 + 0.975962i \(0.569935\pi\)
\(18\) 0 0
\(19\) −1.76882 −0.405795 −0.202898 0.979200i \(-0.565036\pi\)
−0.202898 + 0.979200i \(0.565036\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.44197 5.96166i 0.717700 1.24309i −0.244209 0.969723i \(-0.578528\pi\)
0.961909 0.273370i \(-0.0881384\pi\)
\(24\) 0 0
\(25\) −7.36062 12.7490i −1.47212 2.54979i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.87353 4.97710i −0.533601 0.924224i −0.999230 0.0392435i \(-0.987505\pi\)
0.465629 0.884980i \(-0.345828\pi\)
\(30\) 0 0
\(31\) 3.27671 5.67542i 0.588514 1.01934i −0.405913 0.913912i \(-0.633047\pi\)
0.994427 0.105425i \(-0.0336201\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −12.9218 −2.18419
\(36\) 0 0
\(37\) 2.51332 0.413187 0.206593 0.978427i \(-0.433762\pi\)
0.206593 + 0.978427i \(0.433762\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.68420 6.38122i 0.575376 0.996580i −0.420625 0.907235i \(-0.638189\pi\)
0.996001 0.0893453i \(-0.0284775\pi\)
\(42\) 0 0
\(43\) −2.53640 4.39317i −0.386797 0.669953i 0.605219 0.796059i \(-0.293085\pi\)
−0.992017 + 0.126106i \(0.959752\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 4.98598 + 8.63597i 0.727280 + 1.25969i 0.958029 + 0.286673i \(0.0925493\pi\)
−0.230748 + 0.973013i \(0.574117\pi\)
\(48\) 0 0
\(49\) −0.733339 + 1.27018i −0.104763 + 0.181454i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.30620 −0.454141 −0.227070 0.973878i \(-0.572915\pi\)
−0.227070 + 0.973878i \(0.572915\pi\)
\(54\) 0 0
\(55\) 9.61562 1.29657
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.30090 + 3.98528i −0.299552 + 0.518839i −0.976033 0.217621i \(-0.930170\pi\)
0.676482 + 0.736459i \(0.263504\pi\)
\(60\) 0 0
\(61\) −1.87353 3.24505i −0.239881 0.415485i 0.720799 0.693144i \(-0.243775\pi\)
−0.960680 + 0.277658i \(0.910442\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 8.72084 + 15.1049i 1.08169 + 1.87354i
\(66\) 0 0
\(67\) −2.36045 + 4.08841i −0.288374 + 0.499479i −0.973422 0.229019i \(-0.926448\pi\)
0.685047 + 0.728498i \(0.259781\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −0.907539 −0.107705 −0.0538525 0.998549i \(-0.517150\pi\)
−0.0538525 + 0.998549i \(0.517150\pi\)
\(72\) 0 0
\(73\) −1.87740 −0.219733 −0.109866 0.993946i \(-0.535042\pi\)
−0.109866 + 0.993946i \(0.535042\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.15019 5.45629i 0.358998 0.621802i
\(78\) 0 0
\(79\) 1.23661 + 2.14187i 0.139129 + 0.240979i 0.927167 0.374648i \(-0.122236\pi\)
−0.788038 + 0.615627i \(0.788903\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.09251 1.89227i −0.119918 0.207704i 0.799817 0.600244i \(-0.204930\pi\)
−0.919735 + 0.392540i \(0.871597\pi\)
\(84\) 0 0
\(85\) 3.99056 6.91185i 0.432837 0.749696i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.30620 0.562456 0.281228 0.959641i \(-0.409258\pi\)
0.281228 + 0.959641i \(0.409258\pi\)
\(90\) 0 0
\(91\) 11.4282 1.19800
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 3.92754 6.80271i 0.402958 0.697943i
\(96\) 0 0
\(97\) 4.45302 + 7.71286i 0.452136 + 0.783123i 0.998519 0.0544132i \(-0.0173288\pi\)
−0.546382 + 0.837536i \(0.683995\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.689326 + 1.19395i 0.0685905 + 0.118802i 0.898281 0.439421i \(-0.144816\pi\)
−0.829691 + 0.558224i \(0.811483\pi\)
\(102\) 0 0
\(103\) 2.54512 4.40828i 0.250778 0.434361i −0.712962 0.701203i \(-0.752647\pi\)
0.963740 + 0.266842i \(0.0859801\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −17.2062 −1.66338 −0.831692 0.555238i \(-0.812627\pi\)
−0.831692 + 0.555238i \(0.812627\pi\)
\(108\) 0 0
\(109\) 6.59351 0.631544 0.315772 0.948835i \(-0.397737\pi\)
0.315772 + 0.948835i \(0.397737\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.90072 15.4165i 0.837309 1.45026i −0.0548276 0.998496i \(-0.517461\pi\)
0.892137 0.451766i \(-0.149206\pi\)
\(114\) 0 0
\(115\) 15.2853 + 26.4749i 1.42536 + 2.46880i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.61471 4.52881i −0.239690 0.415155i
\(120\) 0 0
\(121\) 3.15582 5.46604i 0.286893 0.496913i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 43.1706 3.86130
\(126\) 0 0
\(127\) −18.2258 −1.61728 −0.808639 0.588305i \(-0.799795\pi\)
−0.808639 + 0.588305i \(0.799795\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.33057 7.50076i 0.378363 0.655345i −0.612461 0.790501i \(-0.709820\pi\)
0.990824 + 0.135156i \(0.0431537\pi\)
\(132\) 0 0
\(133\) −2.57342 4.45729i −0.223144 0.386496i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.774446 + 1.34138i 0.0661654 + 0.114602i 0.897210 0.441603i \(-0.145590\pi\)
−0.831045 + 0.556205i \(0.812257\pi\)
\(138\) 0 0
\(139\) −9.78618 + 16.9502i −0.830053 + 1.43769i 0.0679426 + 0.997689i \(0.478357\pi\)
−0.897996 + 0.440005i \(0.854977\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −8.50416 −0.711154
\(144\) 0 0
\(145\) 25.5219 2.11948
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.945984 1.63849i 0.0774980 0.134230i −0.824672 0.565612i \(-0.808640\pi\)
0.902170 + 0.431381i \(0.141974\pi\)
\(150\) 0 0
\(151\) −4.27927 7.41191i −0.348242 0.603173i 0.637695 0.770289i \(-0.279888\pi\)
−0.985937 + 0.167116i \(0.946555\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 14.5514 + 25.2038i 1.16880 + 2.02441i
\(156\) 0 0
\(157\) 2.22265 3.84974i 0.177387 0.307242i −0.763598 0.645692i \(-0.776569\pi\)
0.940985 + 0.338449i \(0.109902\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 20.0306 1.57863
\(162\) 0 0
\(163\) −18.8817 −1.47893 −0.739465 0.673195i \(-0.764922\pi\)
−0.739465 + 0.673195i \(0.764922\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.31394 + 7.47197i −0.333823 + 0.578198i −0.983258 0.182219i \(-0.941672\pi\)
0.649435 + 0.760417i \(0.275005\pi\)
\(168\) 0 0
\(169\) −1.21280 2.10063i −0.0932924 0.161587i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.91423 + 6.77965i 0.297594 + 0.515447i 0.975585 0.219623i \(-0.0704826\pi\)
−0.677991 + 0.735070i \(0.737149\pi\)
\(174\) 0 0
\(175\) 21.4176 37.0964i 1.61902 2.80422i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 13.6390 1.01943 0.509714 0.860344i \(-0.329751\pi\)
0.509714 + 0.860344i \(0.329751\pi\)
\(180\) 0 0
\(181\) −0.504672 −0.0375120 −0.0187560 0.999824i \(-0.505971\pi\)
−0.0187560 + 0.999824i \(0.505971\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −5.58064 + 9.66596i −0.410297 + 0.710655i
\(186\) 0 0
\(187\) 1.94571 + 3.37006i 0.142284 + 0.246443i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.0083 + 17.3349i 0.724175 + 1.25431i 0.959313 + 0.282345i \(0.0911124\pi\)
−0.235138 + 0.971962i \(0.575554\pi\)
\(192\) 0 0
\(193\) −1.08462 + 1.87862i −0.0780726 + 0.135226i −0.902418 0.430861i \(-0.858210\pi\)
0.824346 + 0.566087i \(0.191543\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.67460 0.404298 0.202149 0.979355i \(-0.435207\pi\)
0.202149 + 0.979355i \(0.435207\pi\)
\(198\) 0 0
\(199\) −11.5032 −0.815439 −0.407719 0.913107i \(-0.633676\pi\)
−0.407719 + 0.913107i \(0.633676\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8.36126 14.4821i 0.586846 1.01645i
\(204\) 0 0
\(205\) 16.3610 + 28.3381i 1.14270 + 1.97922i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.91498 + 3.31684i 0.132462 + 0.229431i
\(210\) 0 0
\(211\) 10.3177 17.8707i 0.710297 1.23027i −0.254449 0.967086i \(-0.581894\pi\)
0.964746 0.263184i \(-0.0847726\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 22.5276 1.53637
\(216\) 0 0
\(217\) 19.0688 1.29448
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.52929 + 6.11292i −0.237406 + 0.411199i
\(222\) 0 0
\(223\) 2.54291 + 4.40444i 0.170286 + 0.294943i 0.938520 0.345226i \(-0.112198\pi\)
−0.768234 + 0.640169i \(0.778864\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.14484 15.8393i −0.606964 1.05129i −0.991738 0.128282i \(-0.959054\pi\)
0.384773 0.923011i \(-0.374280\pi\)
\(228\) 0 0
\(229\) 9.62341 16.6682i 0.635933 1.10147i −0.350384 0.936606i \(-0.613949\pi\)
0.986317 0.164862i \(-0.0527178\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −16.4263 −1.07612 −0.538061 0.842906i \(-0.680843\pi\)
−0.538061 + 0.842906i \(0.680843\pi\)
\(234\) 0 0
\(235\) −44.2841 −2.88878
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 9.08563 15.7368i 0.587700 1.01793i −0.406833 0.913503i \(-0.633367\pi\)
0.994533 0.104424i \(-0.0332999\pi\)
\(240\) 0 0
\(241\) −11.4344 19.8050i −0.736556 1.27575i −0.954037 0.299688i \(-0.903117\pi\)
0.217481 0.976065i \(-0.430216\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.25666 5.64070i −0.208060 0.360371i
\(246\) 0 0
\(247\) −3.47356 + 6.01639i −0.221017 + 0.382813i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0.139530 0.00880707 0.00440353 0.999990i \(-0.498598\pi\)
0.00440353 + 0.999990i \(0.498598\pi\)
\(252\) 0 0
\(253\) −14.9055 −0.937102
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.17682 12.4306i 0.447678 0.775400i −0.550557 0.834798i \(-0.685585\pi\)
0.998234 + 0.0593974i \(0.0189179\pi\)
\(258\) 0 0
\(259\) 3.65657 + 6.33336i 0.227208 + 0.393536i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.968751 + 1.67793i 0.0597357 + 0.103465i 0.894347 0.447374i \(-0.147641\pi\)
−0.834611 + 0.550840i \(0.814308\pi\)
\(264\) 0 0
\(265\) 7.34118 12.7153i 0.450965 0.781094i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.91415 −0.604477 −0.302238 0.953232i \(-0.597734\pi\)
−0.302238 + 0.953232i \(0.597734\pi\)
\(270\) 0 0
\(271\) −4.56777 −0.277472 −0.138736 0.990329i \(-0.544304\pi\)
−0.138736 + 0.990329i \(0.544304\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −15.9377 + 27.6048i −0.961077 + 1.66463i
\(276\) 0 0
\(277\) −14.4728 25.0676i −0.869585 1.50616i −0.862422 0.506190i \(-0.831053\pi\)
−0.00716263 0.999974i \(-0.502280\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −11.1351 19.2865i −0.664262 1.15054i −0.979485 0.201518i \(-0.935412\pi\)
0.315223 0.949018i \(-0.397921\pi\)
\(282\) 0 0
\(283\) 6.79946 11.7770i 0.404186 0.700071i −0.590040 0.807374i \(-0.700888\pi\)
0.994226 + 0.107303i \(0.0342215\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 21.4403 1.26558
\(288\) 0 0
\(289\) −13.7701 −0.810004
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.21821 12.5023i 0.421693 0.730393i −0.574413 0.818566i \(-0.694770\pi\)
0.996105 + 0.0881730i \(0.0281028\pi\)
\(294\) 0 0
\(295\) −10.2180 17.6980i −0.594913 1.03042i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −13.5185 23.4147i −0.781794 1.35411i
\(300\) 0 0
\(301\) 7.38030 12.7831i 0.425394 0.736804i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 16.6401 0.952812
\(306\) 0 0
\(307\) −16.5451 −0.944280 −0.472140 0.881524i \(-0.656518\pi\)
−0.472140 + 0.881524i \(0.656518\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.19366 8.99568i 0.294505 0.510098i −0.680364 0.732874i \(-0.738178\pi\)
0.974870 + 0.222776i \(0.0715118\pi\)
\(312\) 0 0
\(313\) −6.76501 11.7173i −0.382381 0.662303i 0.609021 0.793154i \(-0.291562\pi\)
−0.991402 + 0.130851i \(0.958229\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 11.9869 + 20.7619i 0.673251 + 1.16611i 0.976977 + 0.213346i \(0.0684360\pi\)
−0.303726 + 0.952760i \(0.598231\pi\)
\(318\) 0 0
\(319\) −6.22194 + 10.7767i −0.348362 + 0.603380i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.17893 0.176880
\(324\) 0 0
\(325\) −57.8183 −3.20718
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −14.5080 + 25.1286i −0.799851 + 1.38538i
\(330\) 0 0
\(331\) −1.29103 2.23612i −0.0709612 0.122908i 0.828362 0.560194i \(-0.189273\pi\)
−0.899323 + 0.437285i \(0.855940\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −10.4824 18.1561i −0.572715 0.991972i
\(336\) 0 0
\(337\) −1.79736 + 3.11313i −0.0979087 + 0.169583i −0.910819 0.412806i \(-0.864549\pi\)
0.812910 + 0.582389i \(0.197882\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −14.1899 −0.768424
\(342\) 0 0
\(343\) 16.1006 0.869351
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.85180 + 10.1356i −0.314141 + 0.544108i −0.979255 0.202634i \(-0.935050\pi\)
0.665114 + 0.746742i \(0.268383\pi\)
\(348\) 0 0
\(349\) 9.34856 + 16.1922i 0.500417 + 0.866747i 1.00000 0.000481224i \(0.000153178\pi\)
−0.499583 + 0.866266i \(0.666513\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −14.3410 24.8394i −0.763295 1.32207i −0.941143 0.338008i \(-0.890247\pi\)
0.177848 0.984058i \(-0.443086\pi\)
\(354\) 0 0
\(355\) 2.01513 3.49030i 0.106952 0.185246i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.8202 0.834958 0.417479 0.908687i \(-0.362914\pi\)
0.417479 + 0.908687i \(0.362914\pi\)
\(360\) 0 0
\(361\) −15.8713 −0.835330
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.16863 7.22028i 0.218196 0.377927i
\(366\) 0 0
\(367\) 13.1383 + 22.7563i 0.685815 + 1.18787i 0.973180 + 0.230046i \(0.0738876\pi\)
−0.287364 + 0.957821i \(0.592779\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.81011 8.33136i −0.249729 0.432543i
\(372\) 0 0
\(373\) 10.8735 18.8335i 0.563010 0.975162i −0.434222 0.900806i \(-0.642977\pi\)
0.997232 0.0743558i \(-0.0236901\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −22.5718 −1.16251
\(378\) 0 0
\(379\) 32.8861 1.68925 0.844623 0.535362i \(-0.179825\pi\)
0.844623 + 0.535362i \(0.179825\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.81269 + 10.0679i −0.297015 + 0.514444i −0.975452 0.220214i \(-0.929324\pi\)
0.678437 + 0.734659i \(0.262658\pi\)
\(384\) 0 0
\(385\) 13.9896 + 24.2306i 0.712974 + 1.23491i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.61687 + 6.26460i 0.183383 + 0.317628i 0.943030 0.332707i \(-0.107962\pi\)
−0.759648 + 0.650335i \(0.774629\pi\)
\(390\) 0 0
\(391\) −6.18591 + 10.7143i −0.312835 + 0.541846i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −10.9832 −0.552625
\(396\) 0 0
\(397\) 29.8911 1.50019 0.750095 0.661330i \(-0.230008\pi\)
0.750095 + 0.661330i \(0.230008\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −3.03226 + 5.25202i −0.151424 + 0.262273i −0.931751 0.363098i \(-0.881719\pi\)
0.780327 + 0.625371i \(0.215052\pi\)
\(402\) 0 0
\(403\) −12.8694 22.2905i −0.641071 1.11037i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.72099 4.71290i −0.134875 0.233610i
\(408\) 0 0
\(409\) −14.4396 + 25.0101i −0.713993 + 1.23667i 0.249354 + 0.968412i \(0.419782\pi\)
−0.963347 + 0.268259i \(0.913552\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −13.3901 −0.658884
\(414\) 0 0
\(415\) 9.70332 0.476317
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.63281 + 9.75631i −0.275181 + 0.476627i −0.970181 0.242383i \(-0.922071\pi\)
0.695000 + 0.719010i \(0.255404\pi\)
\(420\) 0 0
\(421\) −6.03050 10.4451i −0.293909 0.509065i 0.680822 0.732449i \(-0.261623\pi\)
−0.974730 + 0.223384i \(0.928289\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 13.2285 + 22.9125i 0.641677 + 1.11142i
\(426\) 0 0
\(427\) 5.45151 9.44229i 0.263817 0.456944i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 25.5079 1.22867 0.614336 0.789045i \(-0.289424\pi\)
0.614336 + 0.789045i \(0.289424\pi\)
\(432\) 0 0
\(433\) 29.4513 1.41534 0.707670 0.706543i \(-0.249746\pi\)
0.707670 + 0.706543i \(0.249746\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.08823 + 10.5451i −0.291239 + 0.504441i
\(438\) 0 0
\(439\) 17.8086 + 30.8454i 0.849959 + 1.47217i 0.881244 + 0.472662i \(0.156707\pi\)
−0.0312845 + 0.999511i \(0.509960\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6.60886 + 11.4469i 0.313996 + 0.543857i 0.979224 0.202783i \(-0.0649987\pi\)
−0.665227 + 0.746641i \(0.731665\pi\)
\(444\) 0 0
\(445\) −11.7820 + 20.4071i −0.558522 + 0.967389i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.83739 0.275483 0.137742 0.990468i \(-0.456016\pi\)
0.137742 + 0.990468i \(0.456016\pi\)
\(450\) 0 0
\(451\) −15.9545 −0.751269
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −25.3755 + 43.9517i −1.18962 + 2.06049i
\(456\) 0 0
\(457\) −13.5037 23.3891i −0.631677 1.09410i −0.987209 0.159433i \(-0.949034\pi\)
0.355532 0.934664i \(-0.384300\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.78550 3.09258i −0.0831591 0.144036i 0.821446 0.570286i \(-0.193168\pi\)
−0.904605 + 0.426250i \(0.859834\pi\)
\(462\) 0 0
\(463\) −19.8396 + 34.3631i −0.922023 + 1.59699i −0.125742 + 0.992063i \(0.540131\pi\)
−0.796281 + 0.604927i \(0.793202\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.8522 0.872376 0.436188 0.899855i \(-0.356328\pi\)
0.436188 + 0.899855i \(0.356328\pi\)
\(468\) 0 0
\(469\) −13.7366 −0.634299
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −5.49197 + 9.51237i −0.252521 + 0.437379i
\(474\) 0 0
\(475\) 13.0196 + 22.5506i 0.597381 + 1.03469i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −11.0879 19.2049i −0.506621 0.877492i −0.999971 0.00766167i \(-0.997561\pi\)
0.493350 0.869831i \(-0.335772\pi\)
\(480\) 0 0
\(481\) 4.93558 8.54867i 0.225043 0.389786i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −39.5505 −1.79590
\(486\) 0 0
\(487\) −17.9432 −0.813086 −0.406543 0.913632i \(-0.633266\pi\)
−0.406543 + 0.913632i \(0.633266\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.71919 + 2.97773i −0.0775861 + 0.134383i −0.902208 0.431301i \(-0.858055\pi\)
0.824622 + 0.565684i \(0.191388\pi\)
\(492\) 0 0
\(493\) 5.16431 + 8.94485i 0.232589 + 0.402856i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.32036 2.28693i −0.0592262 0.102583i
\(498\) 0 0
\(499\) 5.41124 9.37254i 0.242240 0.419572i −0.719112 0.694894i \(-0.755451\pi\)
0.961352 + 0.275322i \(0.0887845\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −9.71510 −0.433175 −0.216587 0.976263i \(-0.569493\pi\)
−0.216587 + 0.976263i \(0.569493\pi\)
\(504\) 0 0
\(505\) −6.12240 −0.272443
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 17.5991 30.4825i 0.780066 1.35111i −0.151837 0.988406i \(-0.548519\pi\)
0.931903 0.362708i \(-0.118148\pi\)
\(510\) 0 0
\(511\) −2.73138 4.73090i −0.120829 0.209283i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 11.3025 + 19.5766i 0.498049 + 0.862646i
\(516\) 0 0
\(517\) 10.7960 18.6991i 0.474806 0.822387i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7.57440 0.331840 0.165920 0.986139i \(-0.446941\pi\)
0.165920 + 0.986139i \(0.446941\pi\)
\(522\) 0 0
\(523\) 10.0630 0.440025 0.220013 0.975497i \(-0.429390\pi\)
0.220013 + 0.975497i \(0.429390\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.88890 + 10.1999i −0.256525 + 0.444314i
\(528\) 0 0
\(529\) −12.1943 21.1211i −0.530187 0.918310i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −14.4699 25.0625i −0.626759 1.08558i
\(534\) 0 0
\(535\) 38.2051 66.1732i 1.65175 2.86092i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.17574 0.136789
\(540\) 0 0
\(541\) −26.2133 −1.12700 −0.563498 0.826117i \(-0.690545\pi\)
−0.563498 + 0.826117i \(0.690545\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −14.6404 + 25.3580i −0.627127 + 1.08622i
\(546\) 0 0
\(547\) 9.57620 + 16.5865i 0.409449 + 0.709186i 0.994828 0.101574i \(-0.0323878\pi\)
−0.585379 + 0.810760i \(0.699054\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 5.08276 + 8.80359i 0.216533 + 0.375046i
\(552\) 0 0
\(553\) −3.59823 + 6.23232i −0.153012 + 0.265025i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −22.5019 −0.953435 −0.476717 0.879057i \(-0.658173\pi\)
−0.476717 + 0.879057i \(0.658173\pi\)
\(558\) 0 0
\(559\) −19.9236 −0.842680
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −12.7085 + 22.0118i −0.535599 + 0.927685i 0.463535 + 0.886079i \(0.346581\pi\)
−0.999134 + 0.0416066i \(0.986752\pi\)
\(564\) 0 0
\(565\) 39.5268 + 68.4625i 1.66291 + 2.88024i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.14798 15.8448i −0.383503 0.664247i 0.608057 0.793893i \(-0.291949\pi\)
−0.991560 + 0.129646i \(0.958616\pi\)
\(570\) 0 0
\(571\) 1.27484 2.20808i 0.0533503 0.0924054i −0.838117 0.545491i \(-0.816343\pi\)
0.891467 + 0.453085i \(0.149677\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −101.340 −4.22617
\(576\) 0 0
\(577\) 2.22842 0.0927702 0.0463851 0.998924i \(-0.485230\pi\)
0.0463851 + 0.998924i \(0.485230\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.17892 5.50606i 0.131884 0.228430i
\(582\) 0 0
\(583\) 3.57939 + 6.19968i 0.148243 + 0.256765i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15.2694 26.4473i −0.630234 1.09160i −0.987504 0.157596i \(-0.949626\pi\)
0.357270 0.934001i \(-0.383708\pi\)
\(588\) 0 0
\(589\) −5.79591 + 10.0388i −0.238816 + 0.413642i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 5.96281 0.244863 0.122432 0.992477i \(-0.460931\pi\)
0.122432 + 0.992477i \(0.460931\pi\)
\(594\) 0 0
\(595\) 23.2231 0.952055
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.29265 7.43508i 0.175393 0.303789i −0.764904 0.644144i \(-0.777214\pi\)
0.940297 + 0.340355i \(0.110547\pi\)
\(600\) 0 0
\(601\) 1.44648 + 2.50538i 0.0590033 + 0.102197i 0.894018 0.448031i \(-0.147874\pi\)
−0.835015 + 0.550227i \(0.814541\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 14.0146 + 24.2739i 0.569773 + 0.986876i
\(606\) 0 0
\(607\) 9.96773 17.2646i 0.404577 0.700749i −0.589695 0.807626i \(-0.700752\pi\)
0.994272 + 0.106877i \(0.0340853\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 39.1653 1.58446
\(612\) 0 0
\(613\) 35.4941 1.43359 0.716797 0.697282i \(-0.245607\pi\)
0.716797 + 0.697282i \(0.245607\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.6891 27.1743i 0.631618 1.09399i −0.355603 0.934637i \(-0.615724\pi\)
0.987221 0.159357i \(-0.0509422\pi\)
\(618\) 0 0
\(619\) 16.7289 + 28.9752i 0.672389 + 1.16461i 0.977225 + 0.212207i \(0.0680652\pi\)
−0.304835 + 0.952405i \(0.598601\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 7.71987 + 13.3712i 0.309290 + 0.535706i
\(624\) 0 0
\(625\) −59.0543 + 102.285i −2.36217 + 4.09140i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −4.51694 −0.180102
\(630\) 0 0
\(631\) −8.12216 −0.323338 −0.161669 0.986845i \(-0.551688\pi\)
−0.161669 + 0.986845i \(0.551688\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 40.4691 70.0945i 1.60597 2.78162i
\(636\) 0 0
\(637\) 2.88022 + 4.98869i 0.114119 + 0.197659i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10.4782 + 18.1488i 0.413865 + 0.716836i 0.995309 0.0967511i \(-0.0308451\pi\)
−0.581443 + 0.813587i \(0.697512\pi\)
\(642\) 0 0
\(643\) 16.3547 28.3272i 0.644967 1.11712i −0.339342 0.940663i \(-0.610204\pi\)
0.984309 0.176453i \(-0.0564623\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.7820 −0.738395 −0.369198 0.929351i \(-0.620367\pi\)
−0.369198 + 0.929351i \(0.620367\pi\)
\(648\) 0 0
\(649\) 9.96410 0.391125
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.85977 + 8.41736i −0.190177 + 0.329397i −0.945309 0.326176i \(-0.894240\pi\)
0.755132 + 0.655573i \(0.227573\pi\)
\(654\) 0 0
\(655\) 19.2314 + 33.3098i 0.751435 + 1.30152i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −16.1773 28.0198i −0.630177 1.09150i −0.987515 0.157523i \(-0.949649\pi\)
0.357338 0.933975i \(-0.383684\pi\)
\(660\) 0 0
\(661\) −13.0319 + 22.5719i −0.506883 + 0.877946i 0.493086 + 0.869981i \(0.335869\pi\)
−0.999968 + 0.00796563i \(0.997464\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 22.8564 0.886333
\(666\) 0 0
\(667\) −39.5624 −1.53186
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −4.05668 + 7.02637i −0.156606 + 0.271250i
\(672\) 0 0
\(673\) 16.6951 + 28.9167i 0.643549 + 1.11466i 0.984635 + 0.174627i \(0.0558719\pi\)
−0.341086 + 0.940032i \(0.610795\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.6991 + 21.9955i 0.488065 + 0.845354i 0.999906 0.0137265i \(-0.00436941\pi\)
−0.511840 + 0.859081i \(0.671036\pi\)
\(678\) 0 0
\(679\) −12.9572 + 22.4425i −0.497252 + 0.861266i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 37.2800 1.42648 0.713241 0.700919i \(-0.247227\pi\)
0.713241 + 0.700919i \(0.247227\pi\)
\(684\) 0 0
\(685\) −6.87841 −0.262811
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6.49261 + 11.2455i −0.247349 + 0.428421i
\(690\) 0 0
\(691\) −6.41730 11.1151i −0.244126 0.422838i 0.717760 0.696291i \(-0.245168\pi\)
−0.961885 + 0.273453i \(0.911834\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −43.4591 75.2733i −1.64850 2.85528i
\(696\) 0 0
\(697\) −6.62125 + 11.4683i −0.250798 + 0.434395i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.89156 0.260290 0.130145 0.991495i \(-0.458456\pi\)
0.130145 + 0.991495i \(0.458456\pi\)
\(702\) 0 0
\(703\) −4.44561 −0.167669
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.00577 + 3.47410i −0.0754347 + 0.130657i
\(708\) 0 0
\(709\) 10.1178 + 17.5246i 0.379983 + 0.658150i 0.991059 0.133422i \(-0.0425964\pi\)
−0.611076 + 0.791572i \(0.709263\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −22.5566 39.0693i −0.844753 1.46316i
\(714\) 0 0
\(715\) 18.8829 32.7061i 0.706180 1.22314i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −44.1706 −1.64729 −0.823643 0.567108i \(-0.808062\pi\)
−0.823643 + 0.567108i \(0.808062\pi\)
\(720\) 0 0
\(721\) 14.8114 0.551604
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −42.3019 + 73.2690i −1.57105 + 2.72114i
\(726\) 0 0
\(727\) 7.29193 + 12.6300i 0.270443 + 0.468421i 0.968975 0.247158i \(-0.0794965\pi\)
−0.698532 + 0.715578i \(0.746163\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.55842 + 7.89542i 0.168599 + 0.292023i
\(732\) 0 0
\(733\) 16.4444 28.4826i 0.607388 1.05203i −0.384281 0.923216i \(-0.625551\pi\)
0.991669 0.128811i \(-0.0411161\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.2220 0.376531
\(738\) 0 0
\(739\) 35.3966 1.30208 0.651042 0.759041i \(-0.274332\pi\)
0.651042 + 0.759041i \(0.274332\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18.8177 + 32.5932i −0.690353 + 1.19573i 0.281369 + 0.959600i \(0.409212\pi\)
−0.971722 + 0.236127i \(0.924122\pi\)
\(744\) 0 0
\(745\) 4.20098 + 7.27631i 0.153912 + 0.266584i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −25.0329 43.3582i −0.914682 1.58427i
\(750\) 0 0
\(751\) 8.38950 14.5310i 0.306137 0.530245i −0.671377 0.741116i \(-0.734297\pi\)
0.977514 + 0.210871i \(0.0676300\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 38.0073 1.38323
\(756\) 0 0
\(757\) 19.4825 0.708103 0.354051 0.935226i \(-0.384804\pi\)
0.354051 + 0.935226i \(0.384804\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9.49573 16.4471i 0.344220 0.596206i −0.640992 0.767548i \(-0.721477\pi\)
0.985212 + 0.171341i \(0.0548101\pi\)
\(762\) 0 0
\(763\) 9.59276 + 16.6151i 0.347281 + 0.601508i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.03688 + 15.6523i 0.326303 + 0.565173i
\(768\) 0 0
\(769\) 21.2098 36.7365i 0.764846 1.32475i −0.175482 0.984483i \(-0.556148\pi\)
0.940328 0.340270i \(-0.110518\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.55333 −0.0918368 −0.0459184 0.998945i \(-0.514621\pi\)
−0.0459184 + 0.998945i \(0.514621\pi\)
\(774\) 0 0
\(775\) −96.4744 −3.46546
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.51670 + 11.2872i −0.233485 + 0.404408i
\(780\) 0 0
\(781\) 0.982529 + 1.70179i 0.0351577 + 0.0608949i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 9.87046 + 17.0961i 0.352292 + 0.610188i
\(786\) 0 0
\(787\) −6.70128 + 11.6069i −0.238875 + 0.413743i −0.960392 0.278654i \(-0.910112\pi\)
0.721517 + 0.692397i \(0.243445\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 51.7978 1.84172
\(792\) 0 0
\(793\) −14.7167 −0.522606
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 16.0873 27.8640i 0.569840 0.986992i −0.426741 0.904374i \(-0.640338\pi\)
0.996581 0.0826182i \(-0.0263282\pi\)
\(798\) 0 0
\(799\) −8.96082 15.5206i −0.317011 0.549079i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0