Properties

Label 1512.2.s.l.1297.3
Level $1512$
Weight $2$
Character 1512.1297
Analytic conductor $12.073$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.s (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1297.3
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1512.1297
Dual form 1512.2.s.l.865.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.23025 - 2.13086i) q^{5} +(-0.0665372 - 2.64491i) q^{7} +O(q^{10})\) \(q+(1.23025 - 2.13086i) q^{5} +(-0.0665372 - 2.64491i) q^{7} +(0.433463 + 0.750780i) q^{11} -1.46050 q^{13} +(-0.933463 - 1.61680i) q^{17} +(1.29679 - 2.24611i) q^{19} +(0.796790 - 1.38008i) q^{23} +(-0.527042 - 0.912864i) q^{25} +5.78794 q^{29} +(-4.78434 - 8.28671i) q^{31} +(-5.71780 - 3.11213i) q^{35} +(1.66012 - 2.87541i) q^{37} +2.78074 q^{41} -10.7089 q^{43} +(-6.74484 + 11.6824i) q^{47} +(-6.99115 + 0.351971i) q^{49} +(3.32383 + 5.75705i) q^{53} +2.13307 q^{55} +(-3.21780 - 5.57339i) q^{59} +(3.09358 - 5.35824i) q^{61} +(-1.79679 + 3.11213i) q^{65} +(-0.850874 - 1.47376i) q^{67} +1.14027 q^{71} +(-5.08113 - 8.80077i) q^{73} +(1.95691 - 1.19643i) q^{77} +(3.39037 - 5.87229i) q^{79} -9.75583 q^{83} -4.59358 q^{85} +(-4.96050 + 8.59185i) q^{89} +(0.0971780 + 3.86291i) q^{91} +(-3.19076 - 5.52655i) q^{95} +2.81284 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{5} - 4q^{7} + O(q^{10}) \) \( 6q + q^{5} - 4q^{7} - q^{11} + 4q^{13} - 2q^{17} + 5q^{19} + 2q^{23} + 6q^{25} + 2q^{29} - 4q^{31} - 6q^{35} + 8q^{37} - 6q^{43} - 3q^{47} - 12q^{49} + 8q^{53} + 20q^{55} + 9q^{59} + 13q^{61} - 8q^{65} + 16q^{67} - 2q^{71} - 3q^{73} + 7q^{77} + 12q^{79} + 2q^{83} - 22q^{85} - 17q^{89} - 13q^{91} + 28q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(5\) 1.23025 2.13086i 0.550186 0.952949i −0.448075 0.893996i \(-0.647890\pi\)
0.998261 0.0589535i \(-0.0187764\pi\)
\(6\) 0 0
\(7\) −0.0665372 2.64491i −0.0251487 0.999684i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.433463 + 0.750780i 0.130694 + 0.226369i 0.923944 0.382527i \(-0.124946\pi\)
−0.793250 + 0.608896i \(0.791613\pi\)
\(12\) 0 0
\(13\) −1.46050 −0.405071 −0.202536 0.979275i \(-0.564918\pi\)
−0.202536 + 0.979275i \(0.564918\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.933463 1.61680i −0.226398 0.392133i 0.730340 0.683084i \(-0.239362\pi\)
−0.956738 + 0.290951i \(0.906028\pi\)
\(18\) 0 0
\(19\) 1.29679 2.24611i 0.297504 0.515292i −0.678060 0.735006i \(-0.737179\pi\)
0.975564 + 0.219714i \(0.0705125\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.796790 1.38008i 0.166142 0.287767i −0.770918 0.636934i \(-0.780202\pi\)
0.937060 + 0.349168i \(0.113536\pi\)
\(24\) 0 0
\(25\) −0.527042 0.912864i −0.105408 0.182573i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.78794 1.07479 0.537396 0.843330i \(-0.319408\pi\)
0.537396 + 0.843330i \(0.319408\pi\)
\(30\) 0 0
\(31\) −4.78434 8.28671i −0.859292 1.48834i −0.872605 0.488426i \(-0.837571\pi\)
0.0133129 0.999911i \(-0.495762\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −5.71780 3.11213i −0.966485 0.526046i
\(36\) 0 0
\(37\) 1.66012 2.87541i 0.272921 0.472714i −0.696687 0.717375i \(-0.745343\pi\)
0.969609 + 0.244661i \(0.0786767\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.78074 0.434278 0.217139 0.976141i \(-0.430327\pi\)
0.217139 + 0.976141i \(0.430327\pi\)
\(42\) 0 0
\(43\) −10.7089 −1.63310 −0.816549 0.577276i \(-0.804116\pi\)
−0.816549 + 0.577276i \(0.804116\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.74484 + 11.6824i −0.983836 + 1.70405i −0.336839 + 0.941562i \(0.609358\pi\)
−0.646998 + 0.762492i \(0.723976\pi\)
\(48\) 0 0
\(49\) −6.99115 + 0.351971i −0.998735 + 0.0502815i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.32383 + 5.75705i 0.456563 + 0.790791i 0.998777 0.0494499i \(-0.0157468\pi\)
−0.542213 + 0.840241i \(0.682413\pi\)
\(54\) 0 0
\(55\) 2.13307 0.287624
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.21780 5.57339i −0.418922 0.725594i 0.576909 0.816808i \(-0.304259\pi\)
−0.995831 + 0.0912142i \(0.970925\pi\)
\(60\) 0 0
\(61\) 3.09358 5.35824i 0.396092 0.686052i −0.597148 0.802131i \(-0.703699\pi\)
0.993240 + 0.116079i \(0.0370327\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.79679 + 3.11213i −0.222864 + 0.386012i
\(66\) 0 0
\(67\) −0.850874 1.47376i −0.103951 0.180048i 0.809358 0.587315i \(-0.199815\pi\)
−0.913309 + 0.407267i \(0.866482\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.14027 0.135325 0.0676627 0.997708i \(-0.478446\pi\)
0.0676627 + 0.997708i \(0.478446\pi\)
\(72\) 0 0
\(73\) −5.08113 8.80077i −0.594701 1.03005i −0.993589 0.113053i \(-0.963937\pi\)
0.398888 0.917000i \(-0.369396\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.95691 1.19643i 0.223010 0.136345i
\(78\) 0 0
\(79\) 3.39037 5.87229i 0.381446 0.660684i −0.609823 0.792538i \(-0.708759\pi\)
0.991269 + 0.131853i \(0.0420928\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −9.75583 −1.07084 −0.535421 0.844585i \(-0.679847\pi\)
−0.535421 + 0.844585i \(0.679847\pi\)
\(84\) 0 0
\(85\) −4.59358 −0.498244
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.96050 + 8.59185i −0.525812 + 0.910734i 0.473735 + 0.880667i \(0.342905\pi\)
−0.999548 + 0.0300667i \(0.990428\pi\)
\(90\) 0 0
\(91\) 0.0971780 + 3.86291i 0.0101870 + 0.404943i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.19076 5.52655i −0.327365 0.567012i
\(96\) 0 0
\(97\) 2.81284 0.285601 0.142800 0.989752i \(-0.454389\pi\)
0.142800 + 0.989752i \(0.454389\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −0.176168 0.305132i −0.0175294 0.0303618i 0.857128 0.515104i \(-0.172247\pi\)
−0.874657 + 0.484742i \(0.838913\pi\)
\(102\) 0 0
\(103\) 5.09358 8.82234i 0.501885 0.869291i −0.498112 0.867113i \(-0.665973\pi\)
0.999998 0.00217831i \(-0.000693378\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.83628 3.18054i 0.177520 0.307474i −0.763510 0.645796i \(-0.776526\pi\)
0.941031 + 0.338321i \(0.109859\pi\)
\(108\) 0 0
\(109\) −3.97509 6.88506i −0.380745 0.659470i 0.610424 0.792075i \(-0.290999\pi\)
−0.991169 + 0.132605i \(0.957666\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 18.4035 1.73126 0.865628 0.500688i \(-0.166920\pi\)
0.865628 + 0.500688i \(0.166920\pi\)
\(114\) 0 0
\(115\) −1.96050 3.39569i −0.182818 0.316650i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −4.21420 + 2.57651i −0.386315 + 0.236188i
\(120\) 0 0
\(121\) 5.12422 8.87541i 0.465838 0.806855i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.70895 0.868394
\(126\) 0 0
\(127\) 1.24844 0.110781 0.0553906 0.998465i \(-0.482360\pi\)
0.0553906 + 0.998465i \(0.482360\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.84728 8.39573i 0.423508 0.733538i −0.572771 0.819715i \(-0.694132\pi\)
0.996280 + 0.0861770i \(0.0274651\pi\)
\(132\) 0 0
\(133\) −6.02704 3.28045i −0.522611 0.284451i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.51459 + 4.35540i 0.214836 + 0.372107i 0.953222 0.302272i \(-0.0977450\pi\)
−0.738386 + 0.674378i \(0.764412\pi\)
\(138\) 0 0
\(139\) 2.80564 0.237972 0.118986 0.992896i \(-0.462036\pi\)
0.118986 + 0.992896i \(0.462036\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.633074 1.09652i −0.0529403 0.0916954i
\(144\) 0 0
\(145\) 7.12062 12.3333i 0.591335 1.02422i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.19289 15.9226i 0.753111 1.30443i −0.193197 0.981160i \(-0.561886\pi\)
0.946308 0.323267i \(-0.104781\pi\)
\(150\) 0 0
\(151\) 7.39397 + 12.8067i 0.601713 + 1.04220i 0.992562 + 0.121742i \(0.0388480\pi\)
−0.390849 + 0.920455i \(0.627819\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −23.5438 −1.89108
\(156\) 0 0
\(157\) 8.07227 + 13.9816i 0.644237 + 1.11585i 0.984477 + 0.175513i \(0.0561585\pi\)
−0.340240 + 0.940339i \(0.610508\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −3.70321 2.01561i −0.291854 0.158853i
\(162\) 0 0
\(163\) −9.40496 + 16.2899i −0.736653 + 1.27592i 0.217341 + 0.976096i \(0.430262\pi\)
−0.953994 + 0.299825i \(0.903072\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.3025 1.02938 0.514690 0.857376i \(-0.327907\pi\)
0.514690 + 0.857376i \(0.327907\pi\)
\(168\) 0 0
\(169\) −10.8669 −0.835917
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.379379 0.657103i 0.0288436 0.0499586i −0.851243 0.524771i \(-0.824151\pi\)
0.880087 + 0.474813i \(0.157484\pi\)
\(174\) 0 0
\(175\) −2.37938 + 1.45472i −0.179864 + 0.109967i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −0.550486 0.953469i −0.0411452 0.0712656i 0.844719 0.535209i \(-0.179767\pi\)
−0.885865 + 0.463944i \(0.846434\pi\)
\(180\) 0 0
\(181\) −14.2235 −1.05723 −0.528613 0.848863i \(-0.677288\pi\)
−0.528613 + 0.848863i \(0.677288\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.08472 7.07495i −0.300315 0.520161i
\(186\) 0 0
\(187\) 0.809243 1.40165i 0.0591777 0.102499i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.80778 + 3.13117i −0.130806 + 0.226563i −0.923988 0.382422i \(-0.875090\pi\)
0.793181 + 0.608986i \(0.208423\pi\)
\(192\) 0 0
\(193\) 11.9050 + 20.6200i 0.856938 + 1.48426i 0.874836 + 0.484420i \(0.160969\pi\)
−0.0178981 + 0.999840i \(0.505697\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 18.8348 1.34193 0.670963 0.741491i \(-0.265881\pi\)
0.670963 + 0.741491i \(0.265881\pi\)
\(198\) 0 0
\(199\) −6.64027 11.5013i −0.470716 0.815305i 0.528723 0.848795i \(-0.322671\pi\)
−0.999439 + 0.0334899i \(0.989338\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.385113 15.3086i −0.0270296 1.07445i
\(204\) 0 0
\(205\) 3.42101 5.92536i 0.238934 0.413845i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2.24844 0.155528
\(210\) 0 0
\(211\) −7.86693 −0.541581 −0.270791 0.962638i \(-0.587285\pi\)
−0.270791 + 0.962638i \(0.587285\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −13.1747 + 22.8193i −0.898507 + 1.55626i
\(216\) 0 0
\(217\) −21.5993 + 13.2055i −1.46626 + 0.896450i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.36333 + 2.36135i 0.0917073 + 0.158842i
\(222\) 0 0
\(223\) 15.0364 1.00691 0.503455 0.864021i \(-0.332062\pi\)
0.503455 + 0.864021i \(0.332062\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.38298 + 2.39539i 0.0917914 + 0.158987i 0.908265 0.418395i \(-0.137407\pi\)
−0.816474 + 0.577383i \(0.804074\pi\)
\(228\) 0 0
\(229\) 7.30399 12.6509i 0.482661 0.835993i −0.517141 0.855900i \(-0.673004\pi\)
0.999802 + 0.0199069i \(0.00633698\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −3.68716 + 6.38635i −0.241554 + 0.418383i −0.961157 0.276002i \(-0.910990\pi\)
0.719603 + 0.694385i \(0.244324\pi\)
\(234\) 0 0
\(235\) 16.5957 + 28.7446i 1.08259 + 1.87509i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −12.9531 −0.837867 −0.418934 0.908017i \(-0.637596\pi\)
−0.418934 + 0.908017i \(0.637596\pi\)
\(240\) 0 0
\(241\) 7.98968 + 13.8385i 0.514661 + 0.891419i 0.999855 + 0.0170123i \(0.00541545\pi\)
−0.485195 + 0.874406i \(0.661251\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −7.85087 + 15.3302i −0.501574 + 0.979408i
\(246\) 0 0
\(247\) −1.89397 + 3.28045i −0.120510 + 0.208730i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −11.5510 −0.729090 −0.364545 0.931186i \(-0.618776\pi\)
−0.364545 + 0.931186i \(0.618776\pi\)
\(252\) 0 0
\(253\) 1.38151 0.0868551
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 13.0687 22.6356i 0.815201 1.41197i −0.0939817 0.995574i \(-0.529960\pi\)
0.909183 0.416396i \(-0.136707\pi\)
\(258\) 0 0
\(259\) −7.71566 4.19954i −0.479428 0.260947i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 10.5993 + 18.3586i 0.653582 + 1.13204i 0.982247 + 0.187590i \(0.0600677\pi\)
−0.328666 + 0.944446i \(0.606599\pi\)
\(264\) 0 0
\(265\) 16.3566 1.00478
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.05195 3.55408i −0.125109 0.216696i 0.796666 0.604419i \(-0.206595\pi\)
−0.921776 + 0.387723i \(0.873262\pi\)
\(270\) 0 0
\(271\) −0.710602 + 1.23080i −0.0431660 + 0.0747657i −0.886801 0.462151i \(-0.847078\pi\)
0.843635 + 0.536917i \(0.180411\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.456906 0.791385i 0.0275525 0.0477223i
\(276\) 0 0
\(277\) 13.0811 + 22.6572i 0.785969 + 1.36134i 0.928419 + 0.371536i \(0.121169\pi\)
−0.142450 + 0.989802i \(0.545498\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.111094 0.00662728 0.00331364 0.999995i \(-0.498945\pi\)
0.00331364 + 0.999995i \(0.498945\pi\)
\(282\) 0 0
\(283\) −5.66012 9.80361i −0.336459 0.582764i 0.647305 0.762231i \(-0.275896\pi\)
−0.983764 + 0.179467i \(0.942563\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.185023 7.35481i −0.0109215 0.434141i
\(288\) 0 0
\(289\) 6.75729 11.7040i 0.397488 0.688469i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −13.5290 −0.790372 −0.395186 0.918601i \(-0.629320\pi\)
−0.395186 + 0.918601i \(0.629320\pi\)
\(294\) 0 0
\(295\) −15.8348 −0.921939
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.16372 + 2.01561i −0.0672994 + 0.116566i
\(300\) 0 0
\(301\) 0.712544 + 28.3242i 0.0410703 + 1.63258i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −7.61177 13.1840i −0.435849 0.754912i
\(306\) 0 0
\(307\) 26.0187 1.48496 0.742482 0.669866i \(-0.233649\pi\)
0.742482 + 0.669866i \(0.233649\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 17.5687 + 30.4298i 0.996228 + 1.72552i 0.573262 + 0.819372i \(0.305678\pi\)
0.422966 + 0.906146i \(0.360989\pi\)
\(312\) 0 0
\(313\) −12.1768 + 21.0909i −0.688276 + 1.19213i 0.284119 + 0.958789i \(0.408299\pi\)
−0.972395 + 0.233340i \(0.925035\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −17.6264 + 30.5297i −0.989995 + 1.71472i −0.372798 + 0.927913i \(0.621602\pi\)
−0.617197 + 0.786809i \(0.711732\pi\)
\(318\) 0 0
\(319\) 2.50885 + 4.34546i 0.140469 + 0.243299i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.84202 −0.269417
\(324\) 0 0
\(325\) 0.769748 + 1.33324i 0.0426979 + 0.0739550i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 31.3478 + 17.0622i 1.72826 + 0.940670i
\(330\) 0 0
\(331\) 8.96410 15.5263i 0.492712 0.853402i −0.507253 0.861797i \(-0.669339\pi\)
0.999965 + 0.00839547i \(0.00267239\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −4.18716 −0.228769
\(336\) 0 0
\(337\) 18.5801 1.01212 0.506062 0.862497i \(-0.331101\pi\)
0.506062 + 0.862497i \(0.331101\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 4.14766 7.18396i 0.224609 0.389033i
\(342\) 0 0
\(343\) 1.39610 + 18.4676i 0.0753825 + 0.997155i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.8171 29.1281i −0.902790 1.56368i −0.823857 0.566798i \(-0.808182\pi\)
−0.0789333 0.996880i \(-0.525151\pi\)
\(348\) 0 0
\(349\) 26.1301 1.39871 0.699357 0.714772i \(-0.253470\pi\)
0.699357 + 0.714772i \(0.253470\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6.61177 + 11.4519i 0.351909 + 0.609524i 0.986584 0.163255i \(-0.0521994\pi\)
−0.634675 + 0.772779i \(0.718866\pi\)
\(354\) 0 0
\(355\) 1.40282 2.42976i 0.0744541 0.128958i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.97296 3.41726i 0.104129 0.180356i −0.809253 0.587460i \(-0.800128\pi\)
0.913382 + 0.407104i \(0.133461\pi\)
\(360\) 0 0
\(361\) 6.13667 + 10.6290i 0.322983 + 0.559423i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −25.0043 −1.30878
\(366\) 0 0
\(367\) 9.97509 + 17.2774i 0.520696 + 0.901871i 0.999710 + 0.0240645i \(0.00766071\pi\)
−0.479015 + 0.877807i \(0.659006\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 15.0057 9.17431i 0.779059 0.476306i
\(372\) 0 0
\(373\) −16.4035 + 28.4117i −0.849341 + 1.47110i 0.0324567 + 0.999473i \(0.489667\pi\)
−0.881797 + 0.471628i \(0.843666\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −8.45331 −0.435367
\(378\) 0 0
\(379\) 6.51886 0.334851 0.167426 0.985885i \(-0.446455\pi\)
0.167426 + 0.985885i \(0.446455\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 14.1460 24.5016i 0.722827 1.25197i −0.237035 0.971501i \(-0.576176\pi\)
0.959862 0.280472i \(-0.0904911\pi\)
\(384\) 0 0
\(385\) −0.141929 5.64180i −0.00723337 0.287533i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7.86546 13.6234i −0.398795 0.690733i 0.594783 0.803887i \(-0.297238\pi\)
−0.993578 + 0.113154i \(0.963905\pi\)
\(390\) 0 0
\(391\) −2.97509 −0.150457
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.34202 14.4488i −0.419733 0.726998i
\(396\) 0 0
\(397\) 15.7448 27.2709i 0.790211 1.36869i −0.135625 0.990760i \(-0.543304\pi\)
0.925836 0.377925i \(-0.123362\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.17111 2.02842i 0.0584823 0.101294i −0.835302 0.549791i \(-0.814707\pi\)
0.893784 + 0.448497i \(0.148041\pi\)
\(402\) 0 0
\(403\) 6.98755 + 12.1028i 0.348075 + 0.602883i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.87839 0.142677
\(408\) 0 0
\(409\) −6.13142 10.6199i −0.303179 0.525122i 0.673675 0.739028i \(-0.264715\pi\)
−0.976854 + 0.213906i \(0.931381\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14.5270 + 8.88164i −0.714829 + 0.437037i
\(414\) 0 0
\(415\) −12.0021 + 20.7883i −0.589162 + 1.02046i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13.3743 0.653378 0.326689 0.945132i \(-0.394067\pi\)
0.326689 + 0.945132i \(0.394067\pi\)
\(420\) 0 0
\(421\) −34.0905 −1.66147 −0.830734 0.556670i \(-0.812079\pi\)
−0.830734 + 0.556670i \(0.812079\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −0.983948 + 1.70425i −0.0477285 + 0.0826682i
\(426\) 0 0
\(427\) −14.3779 7.82573i −0.695796 0.378714i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 20.3370 + 35.2246i 0.979597 + 1.69671i 0.663846 + 0.747869i \(0.268923\pi\)
0.315751 + 0.948842i \(0.397744\pi\)
\(432\) 0 0
\(433\) −2.43560 −0.117047 −0.0585237 0.998286i \(-0.518639\pi\)
−0.0585237 + 0.998286i \(0.518639\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.06654 3.57935i −0.0988559 0.171223i
\(438\) 0 0
\(439\) 9.55408 16.5482i 0.455992 0.789801i −0.542753 0.839892i \(-0.682618\pi\)
0.998745 + 0.0500918i \(0.0159514\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.3224 30.0032i 0.823011 1.42550i −0.0804197 0.996761i \(-0.525626\pi\)
0.903430 0.428735i \(-0.141041\pi\)
\(444\) 0 0
\(445\) 12.2053 + 21.1403i 0.578589 + 1.00215i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 18.9167 0.892736 0.446368 0.894849i \(-0.352717\pi\)
0.446368 + 0.894849i \(0.352717\pi\)
\(450\) 0 0
\(451\) 1.20535 + 2.08772i 0.0567575 + 0.0983070i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 8.35087 + 4.54528i 0.391495 + 0.213086i
\(456\) 0 0
\(457\) −4.11702 + 7.13089i −0.192586 + 0.333569i −0.946107 0.323855i \(-0.895021\pi\)
0.753520 + 0.657425i \(0.228354\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.78074 −0.222661 −0.111331 0.993783i \(-0.535511\pi\)
−0.111331 + 0.993783i \(0.535511\pi\)
\(462\) 0 0
\(463\) −24.2163 −1.12543 −0.562714 0.826651i \(-0.690243\pi\)
−0.562714 + 0.826651i \(0.690243\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.05622 3.56148i 0.0951505 0.164806i −0.814521 0.580134i \(-0.803000\pi\)
0.909671 + 0.415329i \(0.136333\pi\)
\(468\) 0 0
\(469\) −3.84135 + 2.34855i −0.177377 + 0.108446i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.64193 8.04006i −0.213436 0.369682i
\(474\) 0 0
\(475\) −2.73385 −0.125438
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 11.2917 + 19.5578i 0.515932 + 0.893621i 0.999829 + 0.0184957i \(0.00588771\pi\)
−0.483897 + 0.875125i \(0.660779\pi\)
\(480\) 0 0
\(481\) −2.42461 + 4.19954i −0.110553 + 0.191483i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.46050 5.99377i 0.157133 0.272163i
\(486\) 0 0
\(487\) 21.0957 + 36.5389i 0.955938 + 1.65573i 0.732207 + 0.681083i \(0.238491\pi\)
0.223731 + 0.974651i \(0.428176\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −17.2911 −0.780334 −0.390167 0.920744i \(-0.627583\pi\)
−0.390167 + 0.920744i \(0.627583\pi\)
\(492\) 0 0
\(493\) −5.40282 9.35796i −0.243331 0.421461i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.0758705 3.01592i −0.00340326 0.135283i
\(498\) 0 0
\(499\) 9.49494 16.4457i 0.425052 0.736211i −0.571373 0.820690i \(-0.693589\pi\)
0.996425 + 0.0844788i \(0.0269225\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 17.8961 0.797948 0.398974 0.916962i \(-0.369366\pi\)
0.398974 + 0.916962i \(0.369366\pi\)
\(504\) 0 0
\(505\) −0.866926 −0.0385777
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12.5125 21.6722i 0.554605 0.960604i −0.443329 0.896359i \(-0.646203\pi\)
0.997934 0.0642448i \(-0.0204639\pi\)
\(510\) 0 0
\(511\) −22.9392 + 14.0247i −1.01477 + 0.620417i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −12.5328 21.7074i −0.552260 0.956543i
\(516\) 0 0
\(517\) −11.6946 −0.514326
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −17.8078 30.8440i −0.780173 1.35130i −0.931841 0.362868i \(-0.881798\pi\)
0.151668 0.988432i \(-0.451536\pi\)
\(522\) 0 0
\(523\) 9.47656 16.4139i 0.414381 0.717729i −0.580982 0.813916i \(-0.697331\pi\)
0.995363 + 0.0961874i \(0.0306648\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −8.93200 + 15.4707i −0.389084 + 0.673913i
\(528\) 0 0
\(529\) 10.2303 + 17.7193i 0.444794 + 0.770405i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.06128 −0.175914
\(534\) 0 0
\(535\) −4.51819 7.82573i −0.195338 0.338336i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.29465 5.09624i −0.141911 0.219511i
\(540\) 0 0
\(541\) 8.66012 14.9998i 0.372327 0.644890i −0.617596 0.786496i \(-0.711893\pi\)
0.989923 + 0.141606i \(0.0452265\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −19.5615 −0.837922
\(546\) 0 0
\(547\) −6.06128 −0.259162 −0.129581 0.991569i \(-0.541363\pi\)
−0.129581 + 0.991569i \(0.541363\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.50573 13.0003i 0.319755 0.553832i
\(552\) 0 0
\(553\) −15.7573 8.57651i −0.670068 0.364710i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.16372 + 14.1400i 0.345908 + 0.599130i 0.985518 0.169569i \(-0.0542377\pi\)
−0.639611 + 0.768699i \(0.720904\pi\)
\(558\) 0 0
\(559\) 15.6405 0.661521
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 12.5826 + 21.7937i 0.530293 + 0.918494i 0.999375 + 0.0353399i \(0.0112514\pi\)
−0.469082 + 0.883154i \(0.655415\pi\)
\(564\) 0 0
\(565\) 22.6409 39.2153i 0.952512 1.64980i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.1929 + 29.7790i −0.720764 + 1.24840i 0.239931 + 0.970790i \(0.422875\pi\)
−0.960694 + 0.277609i \(0.910458\pi\)
\(570\) 0 0
\(571\) 4.28580 + 7.42322i 0.179355 + 0.310652i 0.941660 0.336566i \(-0.109266\pi\)
−0.762305 + 0.647218i \(0.775932\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.67977 −0.0700511
\(576\) 0 0
\(577\) −13.7199 23.7636i −0.571168 0.989293i −0.996446 0.0842299i \(-0.973157\pi\)
0.425278 0.905063i \(-0.360176\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.649126 + 25.8033i 0.0269303 + 1.07050i
\(582\) 0 0
\(583\) −2.88151 + 4.99093i −0.119340 + 0.206703i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.8276 0.488178 0.244089 0.969753i \(-0.421511\pi\)
0.244089 + 0.969753i \(0.421511\pi\)
\(588\) 0 0
\(589\) −24.8171 −1.02257
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −10.9964 + 19.0463i −0.451568 + 0.782139i −0.998484 0.0550489i \(-0.982469\pi\)
0.546916 + 0.837188i \(0.315802\pi\)
\(594\) 0 0
\(595\) 0.305644 + 12.1496i 0.0125302 + 0.498086i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 13.3640 + 23.1471i 0.546038 + 0.945766i 0.998541 + 0.0540029i \(0.0171980\pi\)
−0.452503 + 0.891763i \(0.649469\pi\)
\(600\) 0 0
\(601\) −2.20914 −0.0901127 −0.0450563 0.998984i \(-0.514347\pi\)
−0.0450563 + 0.998984i \(0.514347\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −12.6082 21.8380i −0.512595 0.887840i
\(606\) 0 0
\(607\) 8.66012 14.9998i 0.351503 0.608822i −0.635010 0.772504i \(-0.719004\pi\)
0.986513 + 0.163683i \(0.0523373\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 9.85087 17.0622i 0.398524 0.690263i
\(612\) 0 0
\(613\) −8.18570 14.1780i −0.330617 0.572646i 0.652016 0.758205i \(-0.273924\pi\)
−0.982633 + 0.185560i \(0.940590\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17.6198 −0.709348 −0.354674 0.934990i \(-0.615408\pi\)
−0.354674 + 0.934990i \(0.615408\pi\)
\(618\) 0 0
\(619\) 2.26236 + 3.91852i 0.0909318 + 0.157498i 0.907903 0.419179i \(-0.137682\pi\)
−0.816972 + 0.576678i \(0.804349\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 23.0548 + 12.5484i 0.923669 + 0.502742i
\(624\) 0 0
\(625\) 14.5797 25.2527i 0.583187 1.01011i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.19863 −0.247155
\(630\) 0 0
\(631\) −4.99280 −0.198760 −0.0993802 0.995050i \(-0.531686\pi\)
−0.0993802 + 0.995050i \(0.531686\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.53590 2.66025i 0.0609502 0.105569i
\(636\) 0 0
\(637\) 10.2106 0.514055i 0.404559 0.0203676i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −21.3602 36.9970i −0.843677 1.46129i −0.886765 0.462221i \(-0.847053\pi\)
0.0430873 0.999071i \(-0.486281\pi\)
\(642\) 0 0
\(643\) 16.8200 0.663318 0.331659 0.943399i \(-0.392392\pi\)
0.331659 + 0.943399i \(0.392392\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 23.5548 + 40.7980i 0.926033 + 1.60394i 0.789891 + 0.613247i \(0.210137\pi\)
0.136142 + 0.990689i \(0.456530\pi\)
\(648\) 0 0
\(649\) 2.78959 4.83172i 0.109501 0.189661i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −21.6967 + 37.5798i −0.849057 + 1.47061i 0.0329939 + 0.999456i \(0.489496\pi\)
−0.882051 + 0.471154i \(0.843838\pi\)
\(654\) 0 0
\(655\) −11.9267 20.6577i −0.466016 0.807164i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −31.1049 −1.21167 −0.605837 0.795589i \(-0.707161\pi\)
−0.605837 + 0.795589i \(0.707161\pi\)
\(660\) 0 0
\(661\) 1.74484 + 3.02215i 0.0678665 + 0.117548i 0.897962 0.440073i \(-0.145047\pi\)
−0.830095 + 0.557621i \(0.811714\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −14.4050 + 8.80700i −0.558600 + 0.341521i
\(666\) 0 0
\(667\) 4.61177 7.98781i 0.178568 0.309289i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.36381 0.207067
\(672\) 0 0
\(673\) −2.25175 −0.0867988 −0.0433994 0.999058i \(-0.513819\pi\)
−0.0433994 + 0.999058i \(0.513819\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.6623 34.0560i 0.755682 1.30888i −0.189353 0.981909i \(-0.560639\pi\)
0.945035 0.326970i \(-0.106028\pi\)
\(678\) 0 0
\(679\) −0.187159 7.43972i −0.00718249 0.285510i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −3.24338 5.61770i −0.124104 0.214955i 0.797278 0.603612i \(-0.206272\pi\)
−0.921383 + 0.388657i \(0.872939\pi\)
\(684\) 0 0
\(685\) 12.3743 0.472798
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −4.85447 8.40819i −0.184941 0.320327i
\(690\) 0 0
\(691\) 10.7843 18.6790i 0.410256 0.710583i −0.584662 0.811277i \(-0.698773\pi\)
0.994917 + 0.100694i \(0.0321062\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.45165 5.97843i 0.130929 0.226775i
\(696\) 0 0
\(697\) −2.59572 4.49591i −0.0983197 0.170295i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 21.6329 0.817063 0.408531 0.912744i \(-0.366041\pi\)
0.408531 + 0.912744i \(0.366041\pi\)
\(702\) 0 0
\(703\) −4.30564 7.45759i −0.162390 0.281268i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.795327 + 0.486253i −0.0299114 + 0.0182874i
\(708\) 0 0
\(709\) 10.8370 18.7702i 0.406991 0.704928i −0.587560 0.809180i \(-0.699912\pi\)
0.994551 + 0.104252i \(0.0332449\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −15.2484 −0.571059
\(714\) 0 0
\(715\) −3.11537 −0.116508
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −18.8669 + 32.6785i −0.703618 + 1.21870i 0.263571 + 0.964640i \(0.415100\pi\)
−0.967188 + 0.254061i \(0.918234\pi\)
\(720\) 0 0
\(721\) −23.6732 12.8851i −0.881638 0.479865i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3.05049 5.28360i −0.113292 0.196228i
\(726\) 0 0
\(727\) −36.6414 −1.35896 −0.679478 0.733696i \(-0.737794\pi\)
−0.679478 + 0.733696i \(0.737794\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9.99640 + 17.3143i 0.369730 + 0.640392i
\(732\) 0 0
\(733\) −5.69289 + 9.86038i −0.210272 + 0.364201i −0.951800 0.306721i \(-0.900768\pi\)
0.741528 + 0.670922i \(0.234102\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0.737644 1.27764i 0.0271715 0.0470624i
\(738\) 0 0
\(739\) −16.0349 27.7733i −0.589854 1.02166i −0.994251 0.107073i \(-0.965852\pi\)
0.404397 0.914583i \(-0.367481\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −25.7516 −0.944733 −0.472367 0.881402i \(-0.656600\pi\)
−0.472367 + 0.881402i \(0.656600\pi\)
\(744\) 0 0
\(745\) −22.6192 39.1775i −0.828702 1.43535i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8.53443 4.64519i −0.311841 0.169732i
\(750\) 0 0
\(751\) 7.64766 13.2461i 0.279067 0.483359i −0.692086 0.721815i \(-0.743308\pi\)
0.971153 + 0.238456i \(0.0766414\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 36.3858 1.32421
\(756\) 0 0
\(757\) −37.2891 −1.35529 −0.677647 0.735387i \(-0.737000\pi\)
−0.677647 + 0.735387i \(0.737000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −18.1431 + 31.4247i −0.657686 + 1.13915i 0.323527 + 0.946219i \(0.395131\pi\)
−0.981213 + 0.192927i \(0.938202\pi\)
\(762\) 0 0
\(763\) −17.9459 + 10.9719i −0.649686 + 0.397209i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.69961 + 8.13997i 0.169693 + 0.293917i
\(768\) 0 0
\(769\) 32.0908 1.15723 0.578613 0.815602i \(-0.303594\pi\)
0.578613 + 0.815602i \(0.303594\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −18.7178 32.4202i −0.673232 1.16607i −0.976982 0.213321i \(-0.931572\pi\)
0.303750 0.952752i \(-0.401761\pi\)
\(774\) 0 0
\(775\) −5.04309 + 8.73489i −0.181153 + 0.313767i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.60603 6.24583i 0.129200 0.223780i
\(780\) 0 0
\(781\) 0.494265 + 0.856093i 0.0176862 + 0.0306334i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 39.7237 1.41780
\(786\) 0 0
\(787\) −14.4751 25.0716i −0.515981 0.893706i −0.999828 0.0185531i \(-0.994094\pi\)
0.483847 0.875153i \(-0.339239\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.22452 48.6757i −0.0435388 1.73071i
\(792\) 0 0
\(793\) −4.51819 + 7.82573i −0.160446 + 0.277900i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −37.9941 −1.34582 −0.672911 0.739724i \(-0.734956\pi\)
−0.672911 + 0.739724i \(0.734956\pi\)
\(798\) 0 0
\(799\) 25.1842 0.890954
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.40496 7.62961i 0.155448 0.269243i
\(804\) 0 0
\(805\) −8.85087 + 5.41131i −0.311952 + 0.190724i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0