Properties

Label 2268.2.l.j.109.2
Level $2268$
Weight $2$
Character 2268.109
Analytic conductor $18.110$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2268.l (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.1100711784\)
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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 756)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.2
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 2268.109
Dual form 2268.2.l.j.541.2

$q$-expansion

\(f(q)\) \(=\) \(q+0.866926 q^{5} +(-0.0665372 + 2.64491i) q^{7} +O(q^{10})\) \(q+0.866926 q^{5} +(-0.0665372 + 2.64491i) q^{7} +3.51459 q^{11} +(0.933463 - 1.61680i) q^{13} +(-3.25729 + 5.64180i) q^{17} +(2.69076 + 4.66053i) q^{19} -8.64766 q^{23} -4.24844 q^{25} +(1.75729 + 3.04372i) q^{29} +(0.933463 + 1.61680i) q^{31} +(-0.0576828 + 2.29294i) q^{35} +(1.39037 + 2.40819i) q^{37} +(5.19076 - 8.99066i) q^{41} +(2.89037 + 5.00627i) q^{43} +(3.08113 - 5.33667i) q^{47} +(-6.99115 - 0.351971i) q^{49} +(2.80039 - 4.85041i) q^{53} +3.04689 q^{55} +(-2.82383 - 4.89102i) q^{59} +(-5.14766 + 8.91601i) q^{61} +(0.809243 - 1.40165i) q^{65} +(0.676168 + 1.17116i) q^{67} -2.08619 q^{71} +(-3.62422 + 6.27733i) q^{73} +(-0.233851 + 9.29579i) q^{77} +(-5.83842 + 10.1124i) q^{79} +(3.43346 + 5.94693i) q^{83} +(-2.82383 + 4.89102i) q^{85} +(-3.28074 - 5.68240i) q^{89} +(4.21420 + 2.57651i) q^{91} +(2.33269 + 4.04033i) q^{95} +(1.64766 + 2.85384i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 2q^{5} - 4q^{7} + O(q^{10}) \) \( 6q - 2q^{5} - 4q^{7} - 10q^{11} + 2q^{13} - 4q^{17} - 3q^{19} - 28q^{23} + 20q^{25} - 5q^{29} + 2q^{31} + 26q^{35} + 12q^{41} + 9q^{43} - 9q^{47} - 12q^{49} + 6q^{53} + 16q^{55} - 5q^{59} - 7q^{61} + 24q^{65} + 16q^{67} - 22q^{71} + q^{73} + 13q^{77} + 8q^{79} + 17q^{83} - 5q^{85} - 3q^{89} + 5q^{91} + 32q^{95} - 14q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1541\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 0.866926 0.387701 0.193850 0.981031i \(-0.437902\pi\)
0.193850 + 0.981031i \(0.437902\pi\)
\(6\) 0 0
\(7\) −0.0665372 + 2.64491i −0.0251487 + 0.999684i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.51459 1.05969 0.529844 0.848095i \(-0.322250\pi\)
0.529844 + 0.848095i \(0.322250\pi\)
\(12\) 0 0
\(13\) 0.933463 1.61680i 0.258896 0.448421i −0.707050 0.707163i \(-0.749975\pi\)
0.965946 + 0.258742i \(0.0833080\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.25729 + 5.64180i −0.790010 + 1.36834i 0.135950 + 0.990716i \(0.456591\pi\)
−0.925960 + 0.377622i \(0.876742\pi\)
\(18\) 0 0
\(19\) 2.69076 + 4.66053i 0.617302 + 1.06920i 0.989976 + 0.141236i \(0.0451077\pi\)
−0.372674 + 0.927962i \(0.621559\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −8.64766 −1.80316 −0.901581 0.432610i \(-0.857593\pi\)
−0.901581 + 0.432610i \(0.857593\pi\)
\(24\) 0 0
\(25\) −4.24844 −0.849688
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.75729 + 3.04372i 0.326321 + 0.565205i 0.981779 0.190027i \(-0.0608575\pi\)
−0.655457 + 0.755232i \(0.727524\pi\)
\(30\) 0 0
\(31\) 0.933463 + 1.61680i 0.167655 + 0.290387i 0.937595 0.347730i \(-0.113047\pi\)
−0.769940 + 0.638116i \(0.779714\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.0576828 + 2.29294i −0.00975018 + 0.387578i
\(36\) 0 0
\(37\) 1.39037 + 2.40819i 0.228575 + 0.395904i 0.957386 0.288811i \(-0.0932600\pi\)
−0.728811 + 0.684715i \(0.759927\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.19076 8.99066i 0.810660 1.40410i −0.101743 0.994811i \(-0.532442\pi\)
0.912403 0.409294i \(-0.134225\pi\)
\(42\) 0 0
\(43\) 2.89037 + 5.00627i 0.440777 + 0.763448i 0.997747 0.0670841i \(-0.0213696\pi\)
−0.556970 + 0.830532i \(0.688036\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.08113 5.33667i 0.449428 0.778433i −0.548920 0.835875i \(-0.684961\pi\)
0.998349 + 0.0574417i \(0.0182943\pi\)
\(48\) 0 0
\(49\) −6.99115 0.351971i −0.998735 0.0502815i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.80039 4.85041i 0.384663 0.666256i −0.607059 0.794656i \(-0.707651\pi\)
0.991722 + 0.128401i \(0.0409844\pi\)
\(54\) 0 0
\(55\) 3.04689 0.410842
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2.82383 4.89102i −0.367632 0.636757i 0.621563 0.783364i \(-0.286498\pi\)
−0.989195 + 0.146607i \(0.953165\pi\)
\(60\) 0 0
\(61\) −5.14766 + 8.91601i −0.659091 + 1.14158i 0.321761 + 0.946821i \(0.395725\pi\)
−0.980851 + 0.194758i \(0.937608\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.809243 1.40165i 0.100374 0.173853i
\(66\) 0 0
\(67\) 0.676168 + 1.17116i 0.0826071 + 0.143080i 0.904369 0.426751i \(-0.140342\pi\)
−0.821762 + 0.569831i \(0.807009\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.08619 −0.247585 −0.123792 0.992308i \(-0.539506\pi\)
−0.123792 + 0.992308i \(0.539506\pi\)
\(72\) 0 0
\(73\) −3.62422 + 6.27733i −0.424183 + 0.734706i −0.996344 0.0854351i \(-0.972772\pi\)
0.572161 + 0.820141i \(0.306105\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.233851 + 9.29579i −0.0266498 + 1.05935i
\(78\) 0 0
\(79\) −5.83842 + 10.1124i −0.656874 + 1.13774i 0.324547 + 0.945870i \(0.394788\pi\)
−0.981421 + 0.191869i \(0.938545\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.43346 + 5.94693i 0.376871 + 0.652761i 0.990605 0.136752i \(-0.0436665\pi\)
−0.613734 + 0.789513i \(0.710333\pi\)
\(84\) 0 0
\(85\) −2.82383 + 4.89102i −0.306288 + 0.530506i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −3.28074 5.68240i −0.347758 0.602334i 0.638093 0.769959i \(-0.279723\pi\)
−0.985851 + 0.167625i \(0.946390\pi\)
\(90\) 0 0
\(91\) 4.21420 + 2.57651i 0.441768 + 0.270091i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.33269 + 4.04033i 0.239329 + 0.414529i
\(96\) 0 0
\(97\) 1.64766 + 2.85384i 0.167295 + 0.289763i 0.937468 0.348072i \(-0.113163\pi\)
−0.770173 + 0.637835i \(0.779830\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.89610 −0.188669 −0.0943347 0.995541i \(-0.530072\pi\)
−0.0943347 + 0.995541i \(0.530072\pi\)
\(102\) 0 0
\(103\) −7.00000 −0.689730 −0.344865 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.69076 + 16.7849i 0.936841 + 1.62266i 0.771318 + 0.636450i \(0.219598\pi\)
0.165523 + 0.986206i \(0.447069\pi\)
\(108\) 0 0
\(109\) −4.51459 + 7.81950i −0.432419 + 0.748972i −0.997081 0.0763503i \(-0.975673\pi\)
0.564662 + 0.825322i \(0.309007\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.233851 + 0.405042i −0.0219989 + 0.0381031i −0.876815 0.480827i \(-0.840336\pi\)
0.854816 + 0.518931i \(0.173670\pi\)
\(114\) 0 0
\(115\) −7.49688 −0.699088
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −14.7053 8.99066i −1.34804 0.824172i
\(120\) 0 0
\(121\) 1.35234 0.122940
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −8.01771 −0.717126
\(126\) 0 0
\(127\) 14.6768 1.30236 0.651180 0.758924i \(-0.274274\pi\)
0.651180 + 0.758924i \(0.274274\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 14.2484 1.24489 0.622446 0.782663i \(-0.286139\pi\)
0.622446 + 0.782663i \(0.286139\pi\)
\(132\) 0 0
\(133\) −12.5057 + 6.80672i −1.08438 + 0.590218i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −17.2953 −1.47764 −0.738820 0.673903i \(-0.764617\pi\)
−0.738820 + 0.673903i \(0.764617\pi\)
\(138\) 0 0
\(139\) 6.06654 10.5076i 0.514557 0.891239i −0.485300 0.874348i \(-0.661290\pi\)
0.999857 0.0168913i \(-0.00537693\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.28074 5.68240i 0.274349 0.475187i
\(144\) 0 0
\(145\) 1.52344 + 2.63868i 0.126515 + 0.219131i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 4.94299 0.404946 0.202473 0.979288i \(-0.435102\pi\)
0.202473 + 0.979288i \(0.435102\pi\)
\(150\) 0 0
\(151\) 16.2484 1.32228 0.661140 0.750263i \(-0.270073\pi\)
0.661140 + 0.750263i \(0.270073\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.809243 + 1.40165i 0.0649999 + 0.112583i
\(156\) 0 0
\(157\) 0.699612 + 1.21176i 0.0558351 + 0.0967092i 0.892592 0.450865i \(-0.148885\pi\)
−0.836757 + 0.547575i \(0.815551\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0.575392 22.8723i 0.0453472 1.80259i
\(162\) 0 0
\(163\) 10.0723 + 17.4457i 0.788921 + 1.36645i 0.926628 + 0.375979i \(0.122693\pi\)
−0.137707 + 0.990473i \(0.543973\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.09572 + 8.82604i −0.394318 + 0.682979i −0.993014 0.117997i \(-0.962353\pi\)
0.598696 + 0.800977i \(0.295686\pi\)
\(168\) 0 0
\(169\) 4.75729 + 8.23988i 0.365946 + 0.633837i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −10.4050 + 18.0219i −0.791074 + 1.37018i 0.134228 + 0.990950i \(0.457145\pi\)
−0.925302 + 0.379230i \(0.876189\pi\)
\(174\) 0 0
\(175\) 0.282679 11.2368i 0.0213686 0.849419i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 11.6819 20.2336i 0.873146 1.51233i 0.0144222 0.999896i \(-0.495409\pi\)
0.858724 0.512438i \(-0.171258\pi\)
\(180\) 0 0
\(181\) 9.33463 0.693837 0.346919 0.937895i \(-0.387228\pi\)
0.346919 + 0.937895i \(0.387228\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.20535 + 2.08772i 0.0886188 + 0.153492i
\(186\) 0 0
\(187\) −11.4481 + 19.8286i −0.837164 + 1.45001i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.4911 21.6353i 0.903828 1.56548i 0.0813442 0.996686i \(-0.474079\pi\)
0.822483 0.568789i \(-0.192588\pi\)
\(192\) 0 0
\(193\) 11.9715 + 20.7352i 0.861727 + 1.49256i 0.870261 + 0.492592i \(0.163950\pi\)
−0.00853356 + 0.999964i \(0.502716\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 5.13307 0.365716 0.182858 0.983139i \(-0.441465\pi\)
0.182858 + 0.983139i \(0.441465\pi\)
\(198\) 0 0
\(199\) 3.50000 6.06218i 0.248108 0.429736i −0.714893 0.699234i \(-0.753524\pi\)
0.963001 + 0.269498i \(0.0868577\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −8.16731 + 4.44537i −0.573233 + 0.312004i
\(204\) 0 0
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 9.45691 + 16.3798i 0.654148 + 1.13302i
\(210\) 0 0
\(211\) 2.77188 4.80104i 0.190824 0.330517i −0.754699 0.656071i \(-0.772217\pi\)
0.945524 + 0.325553i \(0.105551\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.50573 + 4.34006i 0.170890 + 0.295990i
\(216\) 0 0
\(217\) −4.33842 + 2.36135i −0.294511 + 0.160299i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.08113 + 10.5328i 0.409061 + 0.708514i
\(222\) 0 0
\(223\) −9.80039 16.9748i −0.656283 1.13671i −0.981571 0.191100i \(-0.938795\pi\)
0.325288 0.945615i \(-0.394539\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 16.1445 1.07155 0.535776 0.844360i \(-0.320019\pi\)
0.535776 + 0.844360i \(0.320019\pi\)
\(228\) 0 0
\(229\) −22.6768 −1.49853 −0.749264 0.662272i \(-0.769593\pi\)
−0.749264 + 0.662272i \(0.769593\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.85234 + 3.20834i 0.121351 + 0.210185i 0.920301 0.391212i \(-0.127944\pi\)
−0.798950 + 0.601398i \(0.794611\pi\)
\(234\) 0 0
\(235\) 2.67111 4.62649i 0.174244 0.301799i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.809243 1.40165i 0.0523456 0.0906652i −0.838665 0.544647i \(-0.816664\pi\)
0.891011 + 0.453982i \(0.149997\pi\)
\(240\) 0 0
\(241\) 4.20155 0.270646 0.135323 0.990802i \(-0.456793\pi\)
0.135323 + 0.990802i \(0.456793\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.06080 0.305132i −0.387210 0.0194942i
\(246\) 0 0
\(247\) 10.0469 0.639268
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −19.5438 −1.23359 −0.616796 0.787123i \(-0.711570\pi\)
−0.616796 + 0.787123i \(0.711570\pi\)
\(252\) 0 0
\(253\) −30.3930 −1.91079
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.56148 −0.409294 −0.204647 0.978836i \(-0.565605\pi\)
−0.204647 + 0.978836i \(0.565605\pi\)
\(258\) 0 0
\(259\) −6.46197 + 3.51717i −0.401527 + 0.218546i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −19.3815 −1.19512 −0.597558 0.801826i \(-0.703862\pi\)
−0.597558 + 0.801826i \(0.703862\pi\)
\(264\) 0 0
\(265\) 2.42773 4.20495i 0.149134 0.258308i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7.24271 + 12.5447i −0.441596 + 0.764866i −0.997808 0.0661742i \(-0.978921\pi\)
0.556213 + 0.831040i \(0.312254\pi\)
\(270\) 0 0
\(271\) −2.67617 4.63526i −0.162566 0.281572i 0.773222 0.634135i \(-0.218644\pi\)
−0.935788 + 0.352563i \(0.885310\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −14.9315 −0.900405
\(276\) 0 0
\(277\) 12.2193 0.734184 0.367092 0.930185i \(-0.380353\pi\)
0.367092 + 0.930185i \(0.380353\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −4.55768 7.89414i −0.271889 0.470925i 0.697457 0.716627i \(-0.254315\pi\)
−0.969345 + 0.245702i \(0.920982\pi\)
\(282\) 0 0
\(283\) −6.90496 11.9597i −0.410457 0.710933i 0.584483 0.811406i \(-0.301298\pi\)
−0.994940 + 0.100474i \(0.967964\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 23.4341 + 14.3273i 1.38327 + 0.845715i
\(288\) 0 0
\(289\) −12.7199 22.0316i −0.748231 1.29597i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 14.0723 24.3739i 0.822111 1.42394i −0.0819965 0.996633i \(-0.526130\pi\)
0.904107 0.427305i \(-0.140537\pi\)
\(294\) 0 0
\(295\) −2.44805 4.24015i −0.142531 0.246871i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.07227 + 13.9816i −0.466832 + 0.808576i
\(300\) 0 0
\(301\) −13.4335 + 7.31168i −0.774292 + 0.421438i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −4.46264 + 7.72952i −0.255530 + 0.442591i
\(306\) 0 0
\(307\) 7.24844 0.413690 0.206845 0.978374i \(-0.433680\pi\)
0.206845 + 0.978374i \(0.433680\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.86693 + 6.69771i 0.219273 + 0.379792i 0.954586 0.297936i \(-0.0962981\pi\)
−0.735313 + 0.677728i \(0.762965\pi\)
\(312\) 0 0
\(313\) 4.92840 8.53624i 0.278570 0.482497i −0.692460 0.721456i \(-0.743473\pi\)
0.971030 + 0.238960i \(0.0768063\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.36186 16.2152i 0.525815 0.910738i −0.473733 0.880668i \(-0.657094\pi\)
0.999548 0.0300693i \(-0.00957280\pi\)
\(318\) 0 0
\(319\) 6.17617 + 10.6974i 0.345799 + 0.598941i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −35.0584 −1.95070
\(324\) 0 0
\(325\) −3.96576 + 6.86890i −0.219981 + 0.381018i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 13.9100 + 8.50440i 0.766884 + 0.468863i
\(330\) 0 0
\(331\) 9.46264 16.3898i 0.520114 0.900864i −0.479613 0.877480i \(-0.659223\pi\)
0.999727 0.0233833i \(-0.00744380\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0.586187 + 1.01531i 0.0320268 + 0.0554721i
\(336\) 0 0
\(337\) −14.6388 + 25.3552i −0.797427 + 1.38118i 0.123860 + 0.992300i \(0.460473\pi\)
−0.921287 + 0.388884i \(0.872861\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.28074 + 5.68240i 0.177662 + 0.307719i
\(342\) 0 0
\(343\) 1.39610 18.4676i 0.0753825 0.997155i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.5438 18.2623i −0.566019 0.980374i −0.996954 0.0779908i \(-0.975150\pi\)
0.430935 0.902383i \(-0.358184\pi\)
\(348\) 0 0
\(349\) −16.5957 28.7446i −0.888348 1.53866i −0.841827 0.539747i \(-0.818520\pi\)
−0.0465210 0.998917i \(-0.514813\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 21.7237 1.15624 0.578119 0.815953i \(-0.303787\pi\)
0.578119 + 0.815953i \(0.303787\pi\)
\(354\) 0 0
\(355\) −1.80857 −0.0959889
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.37578 + 5.84702i 0.178167 + 0.308594i 0.941253 0.337703i \(-0.109650\pi\)
−0.763086 + 0.646297i \(0.776317\pi\)
\(360\) 0 0
\(361\) −4.98035 + 8.62622i −0.262124 + 0.454012i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.14193 + 5.44198i −0.164456 + 0.284846i
\(366\) 0 0
\(367\) 35.0875 1.83155 0.915777 0.401687i \(-0.131576\pi\)
0.915777 + 0.401687i \(0.131576\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.6426 + 7.72952i 0.656371 + 0.401297i
\(372\) 0 0
\(373\) 17.4677 0.904443 0.452222 0.891906i \(-0.350632\pi\)
0.452222 + 0.891906i \(0.350632\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 6.56148 0.337933
\(378\) 0 0
\(379\) 2.86693 0.147264 0.0736320 0.997285i \(-0.476541\pi\)
0.0736320 + 0.997285i \(0.476541\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.84922 −0.247783 −0.123892 0.992296i \(-0.539538\pi\)
−0.123892 + 0.992296i \(0.539538\pi\)
\(384\) 0 0
\(385\) −0.202731 + 8.05876i −0.0103322 + 0.410712i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 26.4107 1.33908 0.669538 0.742778i \(-0.266492\pi\)
0.669538 + 0.742778i \(0.266492\pi\)
\(390\) 0 0
\(391\) 28.1680 48.7884i 1.42452 2.46733i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.06148 + 8.76673i −0.254670 + 0.441102i
\(396\) 0 0
\(397\) −14.5095 25.1312i −0.728212 1.26130i −0.957638 0.287975i \(-0.907018\pi\)
0.229426 0.973326i \(-0.426315\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −33.9076 −1.69326 −0.846632 0.532179i \(-0.821373\pi\)
−0.846632 + 0.532179i \(0.821373\pi\)
\(402\) 0 0
\(403\) 3.48541 0.173621
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.88658 + 8.46380i 0.242219 + 0.419535i
\(408\) 0 0
\(409\) 18.1337 + 31.4086i 0.896656 + 1.55305i 0.831741 + 0.555163i \(0.187344\pi\)
0.0649147 + 0.997891i \(0.479322\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 13.1242 7.14336i 0.645801 0.351502i
\(414\) 0 0
\(415\) 2.97656 + 5.15555i 0.146113 + 0.253076i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 11.0615 19.1590i 0.540388 0.935980i −0.458493 0.888698i \(-0.651611\pi\)
0.998882 0.0472823i \(-0.0150560\pi\)
\(420\) 0 0
\(421\) −3.23764 5.60776i −0.157793 0.273306i 0.776279 0.630389i \(-0.217105\pi\)
−0.934073 + 0.357083i \(0.883771\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 13.8384 23.9688i 0.671262 1.16266i
\(426\) 0 0
\(427\) −23.2396 14.2084i −1.12464 0.687592i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.99115 + 3.44877i −0.0959101 + 0.166121i −0.909988 0.414634i \(-0.863909\pi\)
0.814078 + 0.580756i \(0.197243\pi\)
\(432\) 0 0
\(433\) −26.4690 −1.27202 −0.636011 0.771680i \(-0.719417\pi\)
−0.636011 + 0.771680i \(0.719417\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −23.2688 40.3027i −1.11310 1.92794i
\(438\) 0 0
\(439\) 5.39610 9.34633i 0.257542 0.446076i −0.708041 0.706171i \(-0.750421\pi\)
0.965583 + 0.260096i \(0.0837541\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.138809 + 0.240425i −0.00659502 + 0.0114229i −0.869304 0.494278i \(-0.835433\pi\)
0.862709 + 0.505701i \(0.168766\pi\)
\(444\) 0 0
\(445\) −2.84416 4.92622i −0.134826 0.233525i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.277618 −0.0131016 −0.00655081 0.999979i \(-0.502085\pi\)
−0.00655081 + 0.999979i \(0.502085\pi\)
\(450\) 0 0
\(451\) 18.2434 31.5985i 0.859047 1.48791i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.65340 + 2.23364i 0.171274 + 0.104715i
\(456\) 0 0
\(457\) 18.8384 32.6291i 0.881224 1.52633i 0.0312431 0.999512i \(-0.490053\pi\)
0.849981 0.526813i \(-0.176613\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −3.92461 6.79762i −0.182787 0.316597i 0.760041 0.649875i \(-0.225179\pi\)
−0.942829 + 0.333278i \(0.891845\pi\)
\(462\) 0 0
\(463\) 0.266149 0.460984i 0.0123690 0.0214237i −0.859775 0.510674i \(-0.829396\pi\)
0.872144 + 0.489250i \(0.162729\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.84348 6.65711i −0.177855 0.308054i 0.763291 0.646055i \(-0.223583\pi\)
−0.941146 + 0.338001i \(0.890249\pi\)
\(468\) 0 0
\(469\) −3.14260 + 1.71048i −0.145112 + 0.0789827i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 10.1585 + 17.5950i 0.467086 + 0.809017i
\(474\) 0 0
\(475\) −11.4315 19.8000i −0.524514 0.908485i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −22.1914 −1.01395 −0.506976 0.861960i \(-0.669237\pi\)
−0.506976 + 0.861960i \(0.669237\pi\)
\(480\) 0 0
\(481\) 5.19143 0.236709
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.42840 + 2.47406i 0.0648604 + 0.112341i
\(486\) 0 0
\(487\) 3.99115 6.91287i 0.180856 0.313252i −0.761316 0.648381i \(-0.775447\pi\)
0.942172 + 0.335129i \(0.108780\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 19.0526 33.0001i 0.859833 1.48927i −0.0122552 0.999925i \(-0.503901\pi\)
0.872088 0.489349i \(-0.162766\pi\)
\(492\) 0 0
\(493\) −22.8961 −1.03119
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.138809 5.51779i 0.00622644 0.247507i
\(498\) 0 0
\(499\) 15.4500 0.691637 0.345818 0.938301i \(-0.387601\pi\)
0.345818 + 0.938301i \(0.387601\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.78074 0.0793992 0.0396996 0.999212i \(-0.487360\pi\)
0.0396996 + 0.999212i \(0.487360\pi\)
\(504\) 0 0
\(505\) −1.64378 −0.0731473
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.78074 0.344875 0.172438 0.985020i \(-0.444836\pi\)
0.172438 + 0.985020i \(0.444836\pi\)
\(510\) 0 0
\(511\) −16.3619 10.0034i −0.723806 0.442526i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −6.06848 −0.267409
\(516\) 0 0
\(517\) 10.8289 18.7562i 0.476254 0.824896i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.10963 + 3.65399i −0.0924246 + 0.160084i −0.908531 0.417818i \(-0.862795\pi\)
0.816106 + 0.577902i \(0.196128\pi\)
\(522\) 0 0
\(523\) 1.02850 + 1.78142i 0.0449734 + 0.0778962i 0.887636 0.460546i \(-0.152346\pi\)
−0.842662 + 0.538442i \(0.819013\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −12.1623 −0.529796
\(528\) 0 0
\(529\) 51.7821 2.25140
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −9.69076 16.7849i −0.419753 0.727034i
\(534\) 0 0
\(535\) 8.40116 + 14.5512i 0.363214 + 0.629105i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −24.5710 1.23703i −1.05835 0.0532827i
\(540\) 0 0
\(541\) −8.63881 14.9629i −0.371411 0.643303i 0.618372 0.785886i \(-0.287793\pi\)
−0.989783 + 0.142582i \(0.954459\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.91381 + 6.77892i −0.167649 + 0.290377i
\(546\) 0 0
\(547\) 10.4246 + 18.0560i 0.445724 + 0.772017i 0.998102 0.0615768i \(-0.0196129\pi\)
−0.552378 + 0.833594i \(0.686280\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9.45691 + 16.3798i −0.402878 + 0.697805i
\(552\) 0 0
\(553\) −26.3581 16.1150i −1.12086 0.685279i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.64387 + 11.5075i −0.281510 + 0.487589i −0.971757 0.235985i \(-0.924169\pi\)
0.690247 + 0.723574i \(0.257502\pi\)
\(558\) 0 0
\(559\) 10.7922 0.456462
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 15.1965 + 26.3211i 0.640456 + 1.10930i 0.985331 + 0.170653i \(0.0545879\pi\)
−0.344875 + 0.938648i \(0.612079\pi\)
\(564\) 0 0
\(565\) −0.202731 + 0.351141i −0.00852898 + 0.0147726i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −21.8530 + 37.8505i −0.916126 + 1.58678i −0.110881 + 0.993834i \(0.535367\pi\)
−0.805245 + 0.592943i \(0.797966\pi\)
\(570\) 0 0
\(571\) 19.1065 + 33.0934i 0.799583 + 1.38492i 0.919888 + 0.392181i \(0.128279\pi\)
−0.120306 + 0.992737i \(0.538387\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 36.7391 1.53213
\(576\) 0 0
\(577\) −16.5957 + 28.7446i −0.690889 + 1.19665i 0.280658 + 0.959808i \(0.409447\pi\)
−0.971547 + 0.236847i \(0.923886\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −15.9576 + 8.68552i −0.662032 + 0.360336i
\(582\) 0 0
\(583\) 9.84221 17.0472i 0.407623 0.706024i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.89610 + 3.28415i 0.0782606 + 0.135551i 0.902500 0.430691i \(-0.141730\pi\)
−0.824239 + 0.566242i \(0.808397\pi\)
\(588\) 0 0
\(589\) −5.02344 + 8.70086i −0.206987 + 0.358513i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.81810 + 3.14904i 0.0746603 + 0.129315i 0.900938 0.433947i \(-0.142879\pi\)
−0.826278 + 0.563262i \(0.809546\pi\)
\(594\) 0 0
\(595\) −12.7484 7.79423i −0.522635 0.319532i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19.4253 + 33.6456i 0.793696 + 1.37472i 0.923664 + 0.383203i \(0.125179\pi\)
−0.129969 + 0.991518i \(0.541488\pi\)
\(600\) 0 0
\(601\) −16.3619 28.3396i −0.667414 1.15600i −0.978625 0.205655i \(-0.934068\pi\)
0.311210 0.950341i \(-0.399266\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.17237 0.0476638
\(606\) 0 0
\(607\) −27.8099 −1.12877 −0.564385 0.825512i \(-0.690887\pi\)
−0.564385 + 0.825512i \(0.690887\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −5.75223 9.96316i −0.232710 0.403066i
\(612\) 0 0
\(613\) 14.9684 25.9260i 0.604567 1.04714i −0.387553 0.921848i \(-0.626680\pi\)
0.992120 0.125293i \(-0.0399872\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −15.2091 + 26.3430i −0.612297 + 1.06053i 0.378555 + 0.925579i \(0.376421\pi\)
−0.990852 + 0.134951i \(0.956912\pi\)
\(618\) 0 0
\(619\) 23.3054 0.936725 0.468363 0.883536i \(-0.344844\pi\)
0.468363 + 0.883536i \(0.344844\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 15.2478 8.29918i 0.610889 0.332500i
\(624\) 0 0
\(625\) 14.2914 0.571658
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −18.1154 −0.722307
\(630\) 0 0
\(631\) 4.60078 0.183154 0.0915770 0.995798i \(-0.470809\pi\)
0.0915770 + 0.995798i \(0.470809\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 12.7237 0.504926
\(636\) 0 0
\(637\) −7.09504 + 10.9748i −0.281116 + 0.434836i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −4.66537 −0.184271 −0.0921356 0.995746i \(-0.529369\pi\)
−0.0921356 + 0.995746i \(0.529369\pi\)
\(642\) 0 0
\(643\) 11.1996 19.3983i 0.441670 0.764994i −0.556144 0.831086i \(-0.687720\pi\)
0.997814 + 0.0660918i \(0.0210530\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 19.8619 34.4018i 0.780850 1.35247i −0.150596 0.988595i \(-0.548119\pi\)
0.931447 0.363877i \(-0.118547\pi\)
\(648\) 0 0
\(649\) −9.92461 17.1899i −0.389575 0.674764i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 38.1052 1.49117 0.745587 0.666409i \(-0.232169\pi\)
0.745587 + 0.666409i \(0.232169\pi\)
\(654\) 0 0
\(655\) 12.3523 0.482646
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 14.1660 + 24.5363i 0.551831 + 0.955799i 0.998143 + 0.0609214i \(0.0194039\pi\)
−0.446312 + 0.894878i \(0.647263\pi\)
\(660\) 0 0
\(661\) −21.5387 37.3061i −0.837759 1.45104i −0.891765 0.452500i \(-0.850532\pi\)
0.0540059 0.998541i \(-0.482801\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −10.8415 + 5.90092i −0.420417 + 0.228828i
\(666\) 0 0
\(667\) −15.1965 26.3211i −0.588411 1.01916i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −18.0919 + 31.3361i −0.698431 + 1.20972i
\(672\) 0 0
\(673\) −11.3815 19.7134i −0.438725 0.759894i 0.558866 0.829258i \(-0.311236\pi\)
−0.997591 + 0.0693635i \(0.977903\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 19.4253 33.6456i 0.746574 1.29310i −0.202881 0.979203i \(-0.565031\pi\)
0.949456 0.313901i \(-0.101636\pi\)
\(678\) 0 0
\(679\) −7.65779 + 4.16804i −0.293879 + 0.159955i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.328893 + 0.569659i −0.0125847 + 0.0217974i −0.872249 0.489062i \(-0.837339\pi\)
0.859664 + 0.510859i \(0.170673\pi\)
\(684\) 0 0
\(685\) −14.9938 −0.572882
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.22812 9.05536i −0.199175 0.344982i
\(690\) 0 0
\(691\) 2.36186 4.09087i 0.0898496 0.155624i −0.817598 0.575790i \(-0.804695\pi\)
0.907447 + 0.420166i \(0.138028\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 5.25924 9.10926i 0.199494 0.345534i
\(696\) 0 0
\(697\) 33.8157 + 58.5704i 1.28086 + 2.21851i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 48.1560 1.81883 0.909414 0.415893i \(-0.136531\pi\)
0.909414 + 0.415893i \(0.136531\pi\)
\(702\) 0 0
\(703\) −7.48229 + 12.9597i −0.282200 + 0.488785i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.126162 5.01503i 0.00474479 0.188610i
\(708\) 0 0
\(709\) −0.271884 + 0.470916i −0.0102108 + 0.0176856i −0.871086 0.491131i \(-0.836584\pi\)
0.860875 + 0.508817i \(0.169917\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.07227 13.9816i −0.302309 0.523614i
\(714\) 0 0
\(715\) 2.84416 4.92622i 0.106365 0.184230i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −25.3068 43.8327i −0.943784 1.63468i −0.758167 0.652060i \(-0.773905\pi\)
−0.185617 0.982622i \(-0.559428\pi\)
\(720\) 0 0
\(721\) 0.465761 18.5144i 0.0173458 0.689512i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.46576 12.9311i −0.277271 0.480248i
\(726\) 0 0
\(727\) −11.6527 20.1831i −0.432176 0.748550i 0.564885 0.825170i \(-0.308921\pi\)
−0.997060 + 0.0766196i \(0.975587\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −37.6591 −1.39287
\(732\) 0 0
\(733\) −44.6122 −1.64779 −0.823895 0.566742i \(-0.808204\pi\)
−0.823895 + 0.566742i \(0.808204\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.37645 + 4.11614i 0.0875378 + 0.151620i
\(738\) 0 0
\(739\) −18.9392 + 32.8037i −0.696690 + 1.20670i 0.272918 + 0.962037i \(0.412011\pi\)
−0.969608 + 0.244665i \(0.921322\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 8.02850 13.9058i 0.294537 0.510154i −0.680340 0.732897i \(-0.738168\pi\)
0.974877 + 0.222743i \(0.0715012\pi\)
\(744\) 0 0
\(745\) 4.28520 0.156998
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −45.0394 + 24.5144i −1.64570 + 0.895737i
\(750\) 0 0
\(751\) 9.73385 0.355193 0.177597 0.984103i \(-0.443168\pi\)
0.177597 + 0.984103i \(0.443168\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 14.0862 0.512649
\(756\) 0 0
\(757\) −16.7922 −0.610323 −0.305162 0.952301i \(-0.598710\pi\)
−0.305162 + 0.952301i \(0.598710\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −19.2877 −0.699180 −0.349590 0.936903i \(-0.613679\pi\)
−0.349590 + 0.936903i \(0.613679\pi\)
\(762\) 0 0
\(763\) −20.3815 12.4610i −0.737860 0.451118i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10.5438 −0.380713
\(768\) 0 0
\(769\) 0.794654 1.37638i 0.0286559 0.0496335i −0.851342 0.524611i \(-0.824211\pi\)
0.879998 + 0.474978i \(0.157544\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 10.2769 17.8002i 0.369636 0.640228i −0.619873 0.784702i \(-0.712816\pi\)
0.989509 + 0.144474i \(0.0461491\pi\)
\(774\) 0 0
\(775\) −3.96576 6.86890i −0.142454 0.246738i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 55.8683 2.00169
\(780\) 0 0
\(781\) −7.33209 −0.262363
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.606511 + 1.05051i 0.0216473 + 0.0374942i
\(786\) 0 0
\(787\) 15.1946 + 26.3177i 0.541627 + 0.938126i 0.998811 + 0.0487536i \(0.0155249\pi\)
−0.457184 + 0.889372i \(0.651142\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.05574 0.645466i −0.0375378 0.0229501i
\(792\) 0 0
\(793\) 9.61030 + 16.6455i 0.341272 + 0.591100i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −22.7060 + 39.3280i −0.804288 + 1.39307i 0.112482 + 0.993654i \(0.464120\pi\)
−0.916770 + 0.399415i \(0.869213\pi\)
\(798\) 0 0
\(799\) 20.0723 + 34.7662i 0.710106 + 1.22994i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −12.7376 + 22.0622i −0.449502 +