Properties

Label 1152.2.w.a.1007.2
Level $1152$
Weight $2$
Character 1152.1007
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 1007.2
Character \(\chi\) \(=\) 1152.1007
Dual form 1152.2.w.a.143.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.11994 - 2.70378i) q^{5} +(-1.57144 - 1.57144i) q^{7} +O(q^{10})\) \(q+(-1.11994 - 2.70378i) q^{5} +(-1.57144 - 1.57144i) q^{7} +(1.00153 + 2.41791i) q^{11} +(-6.48559 - 2.68642i) q^{13} +0.520719 q^{17} +(-2.95774 + 7.14062i) q^{19} +(1.35340 + 1.35340i) q^{23} +(-2.52064 + 2.52064i) q^{25} +(5.31381 + 2.20105i) q^{29} +1.54505i q^{31} +(-2.48892 + 6.00877i) q^{35} +(-3.79897 + 1.57359i) q^{37} +(1.08917 - 1.08917i) q^{41} +(2.71012 - 1.12257i) q^{43} +11.1855i q^{47} -2.06113i q^{49} +(-3.70104 + 1.53302i) q^{53} +(5.41584 - 5.41584i) q^{55} +(-3.19376 + 1.32290i) q^{59} +(-3.78169 + 9.12981i) q^{61} +20.5443i q^{65} +(-10.9492 - 4.53532i) q^{67} +(6.83579 - 6.83579i) q^{71} +(2.94667 + 2.94667i) q^{73} +(2.22576 - 5.37346i) q^{77} -8.79533 q^{79} +(-13.9866 - 5.79342i) q^{83} +(-0.583176 - 1.40791i) q^{85} +(7.09089 + 7.09089i) q^{89} +(5.97019 + 14.4133i) q^{91} +22.6192 q^{95} -5.91713 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + O(q^{10}) \) \( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{7}{8}\right)\)

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
\(5\) −1.11994 2.70378i −0.500854 1.20917i −0.949019 0.315218i \(-0.897922\pi\)
0.448165 0.893951i \(-0.352078\pi\)
\(6\) 0 0
\(7\) −1.57144 1.57144i −0.593950 0.593950i 0.344746 0.938696i \(-0.387965\pi\)
−0.938696 + 0.344746i \(0.887965\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.00153 + 2.41791i 0.301973 + 0.729027i 0.999917 + 0.0128746i \(0.00409824\pi\)
−0.697944 + 0.716152i \(0.745902\pi\)
\(12\) 0 0
\(13\) −6.48559 2.68642i −1.79878 0.745079i −0.986917 0.161230i \(-0.948454\pi\)
−0.811863 0.583848i \(-0.801546\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.520719 0.126293 0.0631465 0.998004i \(-0.479886\pi\)
0.0631465 + 0.998004i \(0.479886\pi\)
\(18\) 0 0
\(19\) −2.95774 + 7.14062i −0.678552 + 1.63817i 0.0881038 + 0.996111i \(0.471919\pi\)
−0.766656 + 0.642058i \(0.778081\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.35340 + 1.35340i 0.282204 + 0.282204i 0.833987 0.551784i \(-0.186053\pi\)
−0.551784 + 0.833987i \(0.686053\pi\)
\(24\) 0 0
\(25\) −2.52064 + 2.52064i −0.504128 + 0.504128i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.31381 + 2.20105i 0.986750 + 0.408725i 0.816922 0.576748i \(-0.195679\pi\)
0.169828 + 0.985474i \(0.445679\pi\)
\(30\) 0 0
\(31\) 1.54505i 0.277498i 0.990328 + 0.138749i \(0.0443082\pi\)
−0.990328 + 0.138749i \(0.955692\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.48892 + 6.00877i −0.420704 + 1.01567i
\(36\) 0 0
\(37\) −3.79897 + 1.57359i −0.624548 + 0.258696i −0.672434 0.740157i \(-0.734751\pi\)
0.0478869 + 0.998853i \(0.484751\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.08917 1.08917i 0.170100 0.170100i −0.616923 0.787023i \(-0.711621\pi\)
0.787023 + 0.616923i \(0.211621\pi\)
\(42\) 0 0
\(43\) 2.71012 1.12257i 0.413290 0.171190i −0.166343 0.986068i \(-0.553196\pi\)
0.579633 + 0.814878i \(0.303196\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.1855i 1.63157i 0.578358 + 0.815783i \(0.303694\pi\)
−0.578358 + 0.815783i \(0.696306\pi\)
\(48\) 0 0
\(49\) 2.06113i 0.294447i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.70104 + 1.53302i −0.508377 + 0.210577i −0.622103 0.782936i \(-0.713721\pi\)
0.113726 + 0.993512i \(0.463721\pi\)
\(54\) 0 0
\(55\) 5.41584 5.41584i 0.730272 0.730272i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.19376 + 1.32290i −0.415792 + 0.172227i −0.580765 0.814071i \(-0.697246\pi\)
0.164973 + 0.986298i \(0.447246\pi\)
\(60\) 0 0
\(61\) −3.78169 + 9.12981i −0.484196 + 1.16895i 0.473403 + 0.880846i \(0.343026\pi\)
−0.957598 + 0.288106i \(0.906974\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 20.5443i 2.54820i
\(66\) 0 0
\(67\) −10.9492 4.53532i −1.33766 0.554077i −0.404830 0.914392i \(-0.632669\pi\)
−0.932831 + 0.360314i \(0.882669\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.83579 6.83579i 0.811259 0.811259i −0.173564 0.984823i \(-0.555528\pi\)
0.984823 + 0.173564i \(0.0555282\pi\)
\(72\) 0 0
\(73\) 2.94667 + 2.94667i 0.344882 + 0.344882i 0.858199 0.513317i \(-0.171584\pi\)
−0.513317 + 0.858199i \(0.671584\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.22576 5.37346i 0.253649 0.612362i
\(78\) 0 0
\(79\) −8.79533 −0.989552 −0.494776 0.869021i \(-0.664750\pi\)
−0.494776 + 0.869021i \(0.664750\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −13.9866 5.79342i −1.53522 0.635911i −0.554655 0.832081i \(-0.687150\pi\)
−0.980570 + 0.196170i \(0.937150\pi\)
\(84\) 0 0
\(85\) −0.583176 1.40791i −0.0632544 0.152710i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.09089 + 7.09089i 0.751633 + 0.751633i 0.974784 0.223151i \(-0.0716343\pi\)
−0.223151 + 0.974784i \(0.571634\pi\)
\(90\) 0 0
\(91\) 5.97019 + 14.4133i 0.625846 + 1.51092i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 22.6192 2.32068
\(96\) 0 0
\(97\) −5.91713 −0.600793 −0.300397 0.953814i \(-0.597119\pi\)
−0.300397 + 0.953814i \(0.597119\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.62448 11.1645i −0.460153 1.11091i −0.968334 0.249657i \(-0.919682\pi\)
0.508182 0.861250i \(-0.330318\pi\)
\(102\) 0 0
\(103\) −12.0132 12.0132i −1.18369 1.18369i −0.978780 0.204913i \(-0.934309\pi\)
−0.204913 0.978780i \(-0.565691\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −5.56773 13.4417i −0.538253 1.29946i −0.925941 0.377667i \(-0.876726\pi\)
0.387688 0.921791i \(-0.373274\pi\)
\(108\) 0 0
\(109\) −5.97381 2.47443i −0.572187 0.237008i 0.0777792 0.996971i \(-0.475217\pi\)
−0.649966 + 0.759963i \(0.725217\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −10.0445 −0.944908 −0.472454 0.881355i \(-0.656632\pi\)
−0.472454 + 0.881355i \(0.656632\pi\)
\(114\) 0 0
\(115\) 2.14357 5.17504i 0.199889 0.482575i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.818281 0.818281i −0.0750117 0.0750117i
\(120\) 0 0
\(121\) 2.93496 2.93496i 0.266815 0.266815i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −3.88069 1.60743i −0.347099 0.143773i
\(126\) 0 0
\(127\) 12.2276i 1.08503i 0.840047 + 0.542513i \(0.182527\pi\)
−0.840047 + 0.542513i \(0.817473\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −2.18881 + 5.28425i −0.191237 + 0.461687i −0.990194 0.139702i \(-0.955386\pi\)
0.798957 + 0.601389i \(0.205386\pi\)
\(132\) 0 0
\(133\) 15.8690 6.57316i 1.37602 0.569965i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.53314 + 3.53314i −0.301856 + 0.301856i −0.841740 0.539883i \(-0.818468\pi\)
0.539883 + 0.841740i \(0.318468\pi\)
\(138\) 0 0
\(139\) −4.17495 + 1.72932i −0.354115 + 0.146679i −0.552648 0.833415i \(-0.686382\pi\)
0.198533 + 0.980094i \(0.436382\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 18.3721i 1.53635i
\(144\) 0 0
\(145\) 16.8325i 1.39786i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 15.4396 6.39531i 1.26486 0.523924i 0.353465 0.935448i \(-0.385003\pi\)
0.911399 + 0.411524i \(0.135003\pi\)
\(150\) 0 0
\(151\) −0.199339 + 0.199339i −0.0162220 + 0.0162220i −0.715171 0.698949i \(-0.753651\pi\)
0.698949 + 0.715171i \(0.253651\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.17747 1.73036i 0.335542 0.138986i
\(156\) 0 0
\(157\) −2.24745 + 5.42583i −0.179366 + 0.433028i −0.987834 0.155512i \(-0.950297\pi\)
0.808468 + 0.588540i \(0.200297\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.25359i 0.335230i
\(162\) 0 0
\(163\) −4.85740 2.01200i −0.380461 0.157592i 0.184253 0.982879i \(-0.441013\pi\)
−0.564714 + 0.825287i \(0.691013\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −14.1373 + 14.1373i −1.09397 + 1.09397i −0.0988739 + 0.995100i \(0.531524\pi\)
−0.995100 + 0.0988739i \(0.968476\pi\)
\(168\) 0 0
\(169\) 25.6537 + 25.6537i 1.97336 + 1.97336i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3.98598 + 9.62302i −0.303049 + 0.731625i 0.696847 + 0.717219i \(0.254585\pi\)
−0.999896 + 0.0144051i \(0.995415\pi\)
\(174\) 0 0
\(175\) 7.92208 0.598853
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 17.3296 + 7.17815i 1.29527 + 0.536520i 0.920553 0.390618i \(-0.127739\pi\)
0.374721 + 0.927138i \(0.377739\pi\)
\(180\) 0 0
\(181\) −1.80823 4.36545i −0.134404 0.324481i 0.842320 0.538977i \(-0.181189\pi\)
−0.976725 + 0.214496i \(0.931189\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.50928 + 8.50928i 0.625614 + 0.625614i
\(186\) 0 0
\(187\) 0.521516 + 1.25905i 0.0381370 + 0.0920709i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.95000 0.502885 0.251442 0.967872i \(-0.419095\pi\)
0.251442 + 0.967872i \(0.419095\pi\)
\(192\) 0 0
\(193\) 10.4125 0.749511 0.374756 0.927124i \(-0.377727\pi\)
0.374756 + 0.927124i \(0.377727\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.52349 8.50645i −0.251038 0.606059i 0.747250 0.664543i \(-0.231374\pi\)
−0.998288 + 0.0584832i \(0.981374\pi\)
\(198\) 0 0
\(199\) 5.74862 + 5.74862i 0.407509 + 0.407509i 0.880869 0.473360i \(-0.156959\pi\)
−0.473360 + 0.880869i \(0.656959\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.89153 11.8092i −0.343318 0.828843i
\(204\) 0 0
\(205\) −4.16470 1.72507i −0.290875 0.120484i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −20.2276 −1.39917
\(210\) 0 0
\(211\) −3.53929 + 8.54461i −0.243655 + 0.588235i −0.997640 0.0686560i \(-0.978129\pi\)
0.753985 + 0.656891i \(0.228129\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6.07037 6.07037i −0.413996 0.413996i
\(216\) 0 0
\(217\) 2.42795 2.42795i 0.164820 0.164820i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.37717 1.39887i −0.227173 0.0940982i
\(222\) 0 0
\(223\) 11.5406i 0.772814i −0.922328 0.386407i \(-0.873716\pi\)
0.922328 0.386407i \(-0.126284\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −5.48691 + 13.2466i −0.364179 + 0.879205i 0.630501 + 0.776188i \(0.282849\pi\)
−0.994680 + 0.103017i \(0.967151\pi\)
\(228\) 0 0
\(229\) 4.29256 1.77804i 0.283661 0.117496i −0.236317 0.971676i \(-0.575940\pi\)
0.519977 + 0.854180i \(0.325940\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.05679 9.05679i 0.593330 0.593330i −0.345199 0.938529i \(-0.612189\pi\)
0.938529 + 0.345199i \(0.112189\pi\)
\(234\) 0 0
\(235\) 30.2430 12.5271i 1.97284 0.817177i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 8.04485i 0.520378i −0.965558 0.260189i \(-0.916215\pi\)
0.965558 0.260189i \(-0.0837849\pi\)
\(240\) 0 0
\(241\) 19.0228i 1.22536i −0.790329 0.612682i \(-0.790091\pi\)
0.790329 0.612682i \(-0.209909\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −5.57284 + 2.30835i −0.356036 + 0.147475i
\(246\) 0 0
\(247\) 38.3654 38.3654i 2.44113 2.44113i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7.25290 + 3.00425i −0.457799 + 0.189626i −0.599651 0.800261i \(-0.704694\pi\)
0.141853 + 0.989888i \(0.454694\pi\)
\(252\) 0 0
\(253\) −1.91693 + 4.62787i −0.120516 + 0.290952i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 23.0041i 1.43496i −0.696581 0.717478i \(-0.745297\pi\)
0.696581 0.717478i \(-0.254703\pi\)
\(258\) 0 0
\(259\) 8.44268 + 3.49707i 0.524603 + 0.217298i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.44247 1.44247i 0.0889468 0.0889468i −0.661233 0.750180i \(-0.729967\pi\)
0.750180 + 0.661233i \(0.229967\pi\)
\(264\) 0 0
\(265\) 8.28991 + 8.28991i 0.509245 + 0.509245i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.77582 + 4.28722i −0.108274 + 0.261396i −0.968725 0.248137i \(-0.920182\pi\)
0.860451 + 0.509533i \(0.170182\pi\)
\(270\) 0 0
\(271\) −2.52337 −0.153284 −0.0766419 0.997059i \(-0.524420\pi\)
−0.0766419 + 0.997059i \(0.524420\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.61916 3.57017i −0.519755 0.215290i
\(276\) 0 0
\(277\) −3.50691 8.46643i −0.210710 0.508699i 0.782823 0.622245i \(-0.213779\pi\)
−0.993533 + 0.113546i \(0.963779\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.34778 5.34778i −0.319022 0.319022i 0.529369 0.848391i \(-0.322429\pi\)
−0.848391 + 0.529369i \(0.822429\pi\)
\(282\) 0 0
\(283\) 10.0243 + 24.2009i 0.595885 + 1.43859i 0.877741 + 0.479136i \(0.159050\pi\)
−0.281856 + 0.959457i \(0.590950\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.42315 −0.202062
\(288\) 0 0
\(289\) −16.7289 −0.984050
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.12975 14.7985i −0.358104 0.864539i −0.995567 0.0940580i \(-0.970016\pi\)
0.637463 0.770481i \(-0.279984\pi\)
\(294\) 0 0
\(295\) 7.15366 + 7.15366i 0.416502 + 0.416502i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −5.14180 12.4134i −0.297358 0.717886i
\(300\) 0 0
\(301\) −6.02286 2.49475i −0.347152 0.143795i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 28.9203 1.65597
\(306\) 0 0
\(307\) 6.63881 16.0275i 0.378897 0.914738i −0.613276 0.789869i \(-0.710149\pi\)
0.992173 0.124870i \(-0.0398513\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −15.0561 15.0561i −0.853754 0.853754i 0.136839 0.990593i \(-0.456306\pi\)
−0.990593 + 0.136839i \(0.956306\pi\)
\(312\) 0 0
\(313\) 4.19455 4.19455i 0.237090 0.237090i −0.578554 0.815644i \(-0.696383\pi\)
0.815644 + 0.578554i \(0.196383\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.3097 + 5.51307i 0.747549 + 0.309645i 0.723741 0.690072i \(-0.242421\pi\)
0.0238078 + 0.999717i \(0.492421\pi\)
\(318\) 0 0
\(319\) 15.0527i 0.842791i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.54015 + 3.71826i −0.0856964 + 0.206889i
\(324\) 0 0
\(325\) 23.1193 9.57633i 1.28243 0.531199i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 17.5773 17.5773i 0.969069 0.969069i
\(330\) 0 0
\(331\) −5.98959 + 2.48097i −0.329218 + 0.136366i −0.541169 0.840914i \(-0.682018\pi\)
0.211951 + 0.977280i \(0.432018\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 34.6836i 1.89497i
\(336\) 0 0
\(337\) 29.6988i 1.61779i 0.587950 + 0.808897i \(0.299935\pi\)
−0.587950 + 0.808897i \(0.700065\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.73578 + 1.54741i −0.202304 + 0.0837969i
\(342\) 0 0
\(343\) −14.2391 + 14.2391i −0.768837 + 0.768837i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 29.8947 12.3828i 1.60483 0.664744i 0.612745 0.790281i \(-0.290065\pi\)
0.992089 + 0.125537i \(0.0400654\pi\)
\(348\) 0 0
\(349\) −8.37790 + 20.2260i −0.448459 + 1.08268i 0.524441 + 0.851447i \(0.324274\pi\)
−0.972899 + 0.231228i \(0.925726\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.58104i 0.137375i −0.997638 0.0686874i \(-0.978119\pi\)
0.997638 0.0686874i \(-0.0218811\pi\)
\(354\) 0 0
\(355\) −26.1382 10.8268i −1.38727 0.574627i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11.3463 + 11.3463i −0.598834 + 0.598834i −0.940002 0.341168i \(-0.889177\pi\)
0.341168 + 0.940002i \(0.389177\pi\)
\(360\) 0 0
\(361\) −28.8051 28.8051i −1.51606 1.51606i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.66705 11.2673i 0.244285 0.589755i
\(366\) 0 0
\(367\) −8.71339 −0.454835 −0.227418 0.973797i \(-0.573028\pi\)
−0.227418 + 0.973797i \(0.573028\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.22503 + 3.40692i 0.427022 + 0.176878i
\(372\) 0 0
\(373\) 1.56395 + 3.77570i 0.0809781 + 0.195498i 0.959183 0.282786i \(-0.0912587\pi\)
−0.878205 + 0.478285i \(0.841259\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −28.5503 28.5503i −1.47041 1.47041i
\(378\) 0 0
\(379\) −8.85643 21.3813i −0.454925 1.09828i −0.970427 0.241397i \(-0.922395\pi\)
0.515502 0.856888i \(-0.327605\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −3.90996 −0.199790 −0.0998949 0.994998i \(-0.531851\pi\)
−0.0998949 + 0.994998i \(0.531851\pi\)
\(384\) 0 0
\(385\) −17.0214 −0.867490
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.92740 + 9.48159i 0.199127 + 0.480736i 0.991627 0.129137i \(-0.0412206\pi\)
−0.792500 + 0.609872i \(0.791221\pi\)
\(390\) 0 0
\(391\) 0.704742 + 0.704742i 0.0356403 + 0.0356403i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9.85028 + 23.7807i 0.495621 + 1.19654i
\(396\) 0 0
\(397\) 15.8590 + 6.56903i 0.795942 + 0.329690i 0.743330 0.668925i \(-0.233245\pi\)
0.0526124 + 0.998615i \(0.483245\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −18.8741 −0.942529 −0.471265 0.881992i \(-0.656202\pi\)
−0.471265 + 0.881992i \(0.656202\pi\)
\(402\) 0 0
\(403\) 4.15064 10.0205i 0.206758 0.499158i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.60957 7.60957i −0.377193 0.377193i
\(408\) 0 0
\(409\) −9.68899 + 9.68899i −0.479089 + 0.479089i −0.904840 0.425751i \(-0.860010\pi\)
0.425751 + 0.904840i \(0.360010\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.09768 + 2.93995i 0.349254 + 0.144666i
\(414\) 0 0
\(415\) 44.3049i 2.17484i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13.8806 33.5108i 0.678114 1.63711i −0.0893350 0.996002i \(-0.528474\pi\)
0.767449 0.641110i \(-0.221526\pi\)
\(420\) 0 0
\(421\) 23.7882 9.85339i 1.15937 0.480225i 0.281702 0.959502i \(-0.409101\pi\)
0.877664 + 0.479277i \(0.159101\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.31254 + 1.31254i −0.0636678 + 0.0636678i
\(426\) 0 0
\(427\) 20.2897 8.40427i 0.981887 0.406711i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.02776i 0.0495056i −0.999694 0.0247528i \(-0.992120\pi\)
0.999694 0.0247528i \(-0.00787987\pi\)
\(432\) 0 0
\(433\) 21.3662i 1.02680i −0.858151 0.513398i \(-0.828386\pi\)
0.858151 0.513398i \(-0.171614\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −13.6671 + 5.66111i −0.653787 + 0.270807i
\(438\) 0 0
\(439\) −13.4689 + 13.4689i −0.642835 + 0.642835i −0.951251 0.308417i \(-0.900201\pi\)
0.308417 + 0.951251i \(0.400201\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.92612 + 2.04047i −0.234047 + 0.0969454i −0.496625 0.867965i \(-0.665427\pi\)
0.262578 + 0.964911i \(0.415427\pi\)
\(444\) 0 0
\(445\) 11.2308 27.1136i 0.532393 1.28531i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 22.2980i 1.05231i 0.850390 + 0.526153i \(0.176366\pi\)
−0.850390 + 0.526153i \(0.823634\pi\)
\(450\) 0 0
\(451\) 3.72436 + 1.54268i 0.175373 + 0.0726419i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 32.2842 32.2842i 1.51351 1.51351i
\(456\) 0 0
\(457\) −6.58505 6.58505i −0.308035 0.308035i 0.536112 0.844147i \(-0.319893\pi\)
−0.844147 + 0.536112i \(0.819893\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14.3380 + 34.6150i −0.667788 + 1.61218i 0.117515 + 0.993071i \(0.462507\pi\)
−0.785303 + 0.619112i \(0.787493\pi\)
\(462\) 0 0
\(463\) 14.4728 0.672607 0.336304 0.941754i \(-0.390823\pi\)
0.336304 + 0.941754i \(0.390823\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9.73511 + 4.03241i 0.450487 + 0.186598i 0.596380 0.802703i \(-0.296605\pi\)
−0.145892 + 0.989300i \(0.546605\pi\)
\(468\) 0 0
\(469\) 10.0791 + 24.3331i 0.465410 + 1.12360i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.42854 + 5.42854i 0.249605 + 0.249605i
\(474\) 0 0
\(475\) −10.5435 25.4543i −0.483770 1.16792i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −30.2779 −1.38343 −0.691717 0.722169i \(-0.743145\pi\)
−0.691717 + 0.722169i \(0.743145\pi\)
\(480\) 0 0
\(481\) 28.8659 1.31617
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 6.62685 + 15.9986i 0.300910 + 0.726461i
\(486\) 0 0
\(487\) −11.6078 11.6078i −0.526000 0.526000i 0.393377 0.919377i \(-0.371307\pi\)
−0.919377 + 0.393377i \(0.871307\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 4.08448 + 9.86082i 0.184330 + 0.445012i 0.988850 0.148913i \(-0.0475774\pi\)
−0.804520 + 0.593925i \(0.797577\pi\)
\(492\) 0 0
\(493\) 2.76700 + 1.14613i 0.124620 + 0.0516191i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −21.4841 −0.963695
\(498\) 0 0
\(499\) −10.5238 + 25.4066i −0.471109 + 1.13736i 0.492565 + 0.870276i \(0.336059\pi\)
−0.963674 + 0.267082i \(0.913941\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 16.9786 + 16.9786i 0.757040 + 0.757040i 0.975783 0.218742i \(-0.0701954\pi\)
−0.218742 + 0.975783i \(0.570195\pi\)
\(504\) 0 0
\(505\) −25.0072 + 25.0072i −1.11280 + 1.11280i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 25.0892 + 10.3923i 1.11206 + 0.460630i 0.861646 0.507509i \(-0.169434\pi\)
0.250413 + 0.968139i \(0.419434\pi\)
\(510\) 0 0
\(511\) 9.26105i 0.409685i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −19.0269 + 45.9351i −0.838427 + 2.02414i
\(516\) 0 0
\(517\) −27.0454 + 11.2026i −1.18946 + 0.492688i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.51029 + 3.51029i −0.153789 + 0.153789i −0.779808 0.626019i \(-0.784683\pi\)
0.626019 + 0.779808i \(0.284683\pi\)
\(522\) 0 0
\(523\) 2.65762 1.10082i 0.116209 0.0481355i −0.323821 0.946118i \(-0.604968\pi\)
0.440031 + 0.897983i \(0.354968\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.804535i 0.0350461i
\(528\) 0 0
\(529\) 19.3366i 0.840722i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9.98990 + 4.13795i −0.432711 + 0.179235i
\(534\) 0 0
\(535\) −30.1079 + 30.1079i −1.30168 + 1.30168i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.98361 2.06428i 0.214659 0.0889148i
\(540\) 0 0
\(541\) 8.33435 20.1209i 0.358322 0.865066i −0.637214 0.770687i \(-0.719913\pi\)
0.995536 0.0943790i \(-0.0300866\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 18.9231i 0.810577i
\(546\) 0 0
\(547\) −15.3897 6.37463i −0.658017 0.272560i 0.0285868 0.999591i \(-0.490899\pi\)
−0.686604 + 0.727032i \(0.740899\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −31.4337 + 31.4337i −1.33912 + 1.33912i
\(552\) 0 0
\(553\) 13.8214 + 13.8214i 0.587744 + 0.587744i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.13010 7.55673i 0.132627 0.320189i −0.843590 0.536989i \(-0.819562\pi\)
0.976216 + 0.216800i \(0.0695618\pi\)
\(558\) 0 0
\(559\) −20.5924 −0.870968
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0.345832 + 0.143248i 0.0145751 + 0.00603719i 0.389959 0.920832i \(-0.372489\pi\)
−0.375384 + 0.926869i \(0.622489\pi\)
\(564\) 0 0
\(565\) 11.2493 + 27.1582i 0.473261 + 1.14255i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 31.8289 + 31.8289i 1.33434 + 1.33434i 0.901447 + 0.432890i \(0.142506\pi\)
0.432890 + 0.901447i \(0.357494\pi\)
\(570\) 0 0
\(571\) −7.49818 18.1022i −0.313789 0.757554i −0.999558 0.0297343i \(-0.990534\pi\)
0.685769 0.727819i \(-0.259466\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6.82287 −0.284533
\(576\) 0 0
\(577\) −19.6358 −0.817447 −0.408724 0.912658i \(-0.634026\pi\)
−0.408724 + 0.912658i \(0.634026\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12.8751 + 31.0831i 0.534147 + 1.28955i
\(582\) 0 0
\(583\) −7.41340 7.41340i −0.307032 0.307032i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.01640 + 19.3533i 0.330872 + 0.798796i 0.998523 + 0.0543221i \(0.0172998\pi\)
−0.667651 + 0.744474i \(0.732700\pi\)
\(588\) 0 0
\(589\) −11.0326 4.56984i −0.454589 0.188297i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 26.2206 1.07675 0.538376 0.842704i \(-0.319038\pi\)
0.538376 + 0.842704i \(0.319038\pi\)
\(594\) 0 0
\(595\) −1.29603 + 3.12888i −0.0531319 + 0.128272i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −13.4497 13.4497i −0.549542 0.549542i 0.376767 0.926308i \(-0.377036\pi\)
−0.926308 + 0.376767i \(0.877036\pi\)
\(600\) 0 0
\(601\) −10.7760 + 10.7760i −0.439562 + 0.439562i −0.891864 0.452303i \(-0.850603\pi\)
0.452303 + 0.891864i \(0.350603\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −11.2225 4.64851i −0.456259 0.188989i
\(606\) 0 0
\(607\) 5.71428i 0.231936i −0.993253 0.115968i \(-0.963003\pi\)
0.993253 0.115968i \(-0.0369969\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 30.0488 72.5443i 1.21565 2.93483i
\(612\) 0 0
\(613\) −25.0980 + 10.3959i −1.01370 + 0.419887i −0.826802 0.562493i \(-0.809842\pi\)
−0.186895 + 0.982380i \(0.559842\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 7.07388 7.07388i 0.284784 0.284784i −0.550230 0.835013i \(-0.685460\pi\)
0.835013 + 0.550230i \(0.185460\pi\)
\(618\) 0 0
\(619\) −32.9781 + 13.6600i −1.32550 + 0.549041i −0.929369 0.369151i \(-0.879648\pi\)
−0.396134 + 0.918193i \(0.629648\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 22.2859i 0.892865i
\(624\) 0 0
\(625\) 30.1164i 1.20465i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.97820 + 0.819397i −0.0788760 + 0.0326715i
\(630\) 0 0
\(631\) 2.15849 2.15849i 0.0859280 0.0859280i −0.662836 0.748764i \(-0.730647\pi\)
0.748764 + 0.662836i \(0.230647\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 33.0608 13.6943i 1.31198 0.543440i
\(636\) 0 0
\(637\) −5.53705 + 13.3676i −0.219386 + 0.529645i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 38.0487i 1.50283i −0.659827 0.751417i \(-0.729371\pi\)
0.659827 0.751417i \(-0.270629\pi\)
\(642\) 0 0
\(643\) 16.7464 + 6.93660i 0.660414 + 0.273553i 0.687613 0.726077i \(-0.258659\pi\)
−0.0271985 + 0.999630i \(0.508659\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.77745 + 1.77745i −0.0698786 + 0.0698786i −0.741182 0.671304i \(-0.765735\pi\)
0.671304 + 0.741182i \(0.265735\pi\)
\(648\) 0 0
\(649\) −6.39729 6.39729i −0.251116 0.251116i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.13694 + 19.6443i −0.318423 + 0.768742i 0.680915 + 0.732363i \(0.261582\pi\)
−0.999338 + 0.0363791i \(0.988418\pi\)
\(654\) 0 0
\(655\) 16.7388 0.654039
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5.72478 + 2.37128i 0.223006 + 0.0923720i 0.491389 0.870940i \(-0.336489\pi\)
−0.268383 + 0.963312i \(0.586489\pi\)
\(660\) 0 0
\(661\) −14.6754 35.4296i −0.570808 1.37805i −0.900868 0.434092i \(-0.857069\pi\)
0.330061 0.943960i \(-0.392931\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −35.5448 35.5448i −1.37837 1.37837i
\(666\) 0 0
\(667\) 4.21281 + 10.1706i 0.163121 + 0.393808i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −25.8625 −0.998411
\(672\) 0 0
\(673\) −32.6272 −1.25768 −0.628842 0.777533i \(-0.716471\pi\)
−0.628842 + 0.777533i \(0.716471\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.1224 + 26.8518i 0.427468 + 1.03200i 0.980088 + 0.198565i \(0.0636281\pi\)
−0.552620 + 0.833433i \(0.686372\pi\)
\(678\) 0 0
\(679\) 9.29844 + 9.29844i 0.356841 + 0.356841i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.38525 + 3.34428i 0.0530050 + 0.127965i 0.948164 0.317782i \(-0.102938\pi\)
−0.895159 + 0.445747i \(0.852938\pi\)
\(684\) 0 0
\(685\) 13.5098 + 5.59593i 0.516181 + 0.213809i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 28.1218 1.07135
\(690\) 0 0
\(691\) 13.4910 32.5702i 0.513223 1.23903i −0.428775 0.903411i \(-0.641055\pi\)
0.941998 0.335618i \(-0.108945\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.35143 + 9.35143i 0.354720 + 0.354720i
\(696\) 0 0
\(697\) 0.567153 0.567153i 0.0214825 0.0214825i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3.25729 1.34921i −0.123026 0.0509590i 0.320321 0.947309i \(-0.396209\pi\)
−0.443347 + 0.896350i \(0.646209\pi\)
\(702\) 0 0
\(703\) 31.7813i 1.19865i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.2772 + 24.8115i −0.386515 + 0.933131i
\(708\) 0 0
\(709\) −27.0551 + 11.2066i −1.01607 + 0.420872i −0.827667 0.561219i \(-0.810332\pi\)
−0.188407 + 0.982091i \(0.560332\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.09107 + 2.09107i −0.0783110 + 0.0783110i
\(714\) 0 0
\(715\) −49.6742 + 20.5757i −1.85771 + 0.769488i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.87831i 0.256518i −0.991741 0.128259i \(-0.959061\pi\)
0.991741 0.128259i \(-0.0409389\pi\)
\(720\) 0 0
\(721\) 37.7561i 1.40611i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −18.9422 + 7.84614i −0.703497 + 0.291398i
\(726\) 0 0
\(727\) −8.61474 + 8.61474i −0.319503 + 0.319503i −0.848576 0.529073i \(-0.822540\pi\)
0.529073 + 0.848576i \(0.322540\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.41121 0.584544i 0.0521956 0.0216201i
\(732\) 0 0
\(733\) 6.86842 16.5818i 0.253691 0.612464i −0.744806 0.667282i \(-0.767458\pi\)
0.998496 + 0.0548178i \(0.0174578\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 31.0165i 1.14251i
\(738\) 0 0
\(739\) −8.65828 3.58638i −0.318500 0.131927i 0.217706 0.976014i \(-0.430143\pi\)
−0.536205 + 0.844088i \(0.680143\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.87413 + 5.87413i −0.215501 + 0.215501i −0.806599 0.591098i \(-0.798694\pi\)
0.591098 + 0.806599i \(0.298694\pi\)
\(744\) 0 0
\(745\) −34.5830 34.5830i −1.26702 1.26702i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12.3735 + 29.8723i −0.452118 + 1.09151i
\(750\) 0 0
\(751\) −3.89687 −0.142199 −0.0710993 0.997469i \(-0.522651\pi\)
−0.0710993 + 0.997469i \(0.522651\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.762219 + 0.315721i 0.0277400 + 0.0114903i
\(756\) 0 0
\(757\) −4.04702 9.77036i −0.147091 0.355110i 0.833112 0.553105i \(-0.186557\pi\)
−0.980203 + 0.197995i \(0.936557\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −13.3848 13.3848i −0.485198 0.485198i 0.421589 0.906787i \(-0.361472\pi\)
−0.906787 + 0.421589i \(0.861472\pi\)
\(762\) 0 0
\(763\) 5.49908 + 13.2759i 0.199080 + 0.480621i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 24.2673 0.876241
\(768\) 0 0
\(769\) 5.94152 0.214257 0.107128 0.994245i \(-0.465834\pi\)
0.107128 + 0.994245i \(0.465834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3.97648 + 9.60006i 0.143024 + 0.345290i 0.979117 0.203297i \(-0.0651658\pi\)
−0.836093 + 0.548588i \(0.815166\pi\)
\(774\) 0 0
\(775\) −3.89450 3.89450i −0.139895 0.139895i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.55587 + 10.9988i 0.163231 + 0.394075i
\(780\) 0 0
\(781\) 23.3746 + 9.68206i 0.836408 + 0.346451i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 17.1873 0.613440
\(786\) 0 0
\(787\) −6.79001 + 16.3925i −0.242038 + 0.584331i −0.997485 0.0708787i \(-0.977420\pi\)
0.755447 + 0.655210i \(0.227420\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 15.7844 + 15.7844i 0.561228 + 0.561228i
\(792\) 0 0
\(793\) 49.0530 49.0530i 1.74192 1.74192i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.96338 3.71275i −0.317499 0.131512i 0.218242 0.975895i \(-0.429968\pi\)
−0.535741 + 0.844382i \(0.679968\pi\)
\(798\) 0 0
\(799\) 5.82448i 0.206055i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.17360 + 10.0760i −0.147283 + 0.355573i
\(804\) 0 0
\(805\) −11.5008 + 4.76378i −0.405349 +