Properties

Label 3024.2.q.l.2305.10
Level $3024$
Weight $2$
Character 3024.2305
Analytic conductor $24.147$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2305.10
Character \(\chi\) \(=\) 3024.2305
Dual form 3024.2.q.l.2881.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.59750 + 2.76695i) q^{5} +(1.66645 - 2.05498i) q^{7} +O(q^{10})\) \(q+(1.59750 + 2.76695i) q^{5} +(1.66645 - 2.05498i) q^{7} +(1.14139 - 1.97695i) q^{11} +(-0.675051 + 1.16922i) q^{13} +(-2.21425 - 3.83519i) q^{17} +(3.69214 - 6.39497i) q^{19} +(3.23479 + 5.60283i) q^{23} +(-2.60400 + 4.51026i) q^{25} +(1.06167 + 1.83887i) q^{29} +0.632308 q^{31} +(8.34818 + 1.32814i) q^{35} +(1.92885 - 3.34087i) q^{37} +(5.05124 - 8.74900i) q^{41} +(-4.24701 - 7.35603i) q^{43} +6.53173 q^{47} +(-1.44591 - 6.84904i) q^{49} +(-2.39950 - 4.15606i) q^{53} +7.29349 q^{55} +6.20383 q^{59} -8.91093 q^{61} -4.31357 q^{65} +3.01570 q^{67} -15.3791 q^{71} +(4.36577 + 7.56173i) q^{73} +(-2.16053 - 5.64002i) q^{77} +1.87610 q^{79} +(-3.00140 - 5.19857i) q^{83} +(7.07451 - 12.2534i) q^{85} +(-2.65390 + 4.59668i) q^{89} +(1.27780 + 3.33566i) q^{91} +23.5927 q^{95} +(7.44539 + 12.8958i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{5} - 5q^{7} + O(q^{10}) \) \( 22q - q^{5} - 5q^{7} + 3q^{11} + 7q^{13} + q^{17} - 13q^{19} - 22q^{25} + 7q^{29} + 12q^{31} + 2q^{35} + 6q^{37} - 4q^{41} - 2q^{43} - 34q^{47} - 25q^{49} - q^{53} - 2q^{55} + 42q^{59} - 62q^{61} - 6q^{65} - 52q^{67} - 32q^{71} + 17q^{73} + q^{77} - 32q^{79} - 36q^{83} + 28q^{85} + 2q^{89} - 15q^{91} + 48q^{95} + 19q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(5\) 1.59750 + 2.76695i 0.714423 + 1.23742i 0.963182 + 0.268851i \(0.0866441\pi\)
−0.248759 + 0.968566i \(0.580023\pi\)
\(6\) 0 0
\(7\) 1.66645 2.05498i 0.629857 0.776711i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.14139 1.97695i 0.344143 0.596073i −0.641055 0.767495i \(-0.721503\pi\)
0.985198 + 0.171422i \(0.0548362\pi\)
\(12\) 0 0
\(13\) −0.675051 + 1.16922i −0.187225 + 0.324284i −0.944324 0.329017i \(-0.893283\pi\)
0.757099 + 0.653300i \(0.226616\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.21425 3.83519i −0.537033 0.930169i −0.999062 0.0433042i \(-0.986212\pi\)
0.462028 0.886865i \(-0.347122\pi\)
\(18\) 0 0
\(19\) 3.69214 6.39497i 0.847034 1.46711i −0.0368084 0.999322i \(-0.511719\pi\)
0.883843 0.467784i \(-0.154948\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.23479 + 5.60283i 0.674501 + 1.16827i 0.976614 + 0.214999i \(0.0689747\pi\)
−0.302113 + 0.953272i \(0.597692\pi\)
\(24\) 0 0
\(25\) −2.60400 + 4.51026i −0.520800 + 0.902053i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.06167 + 1.83887i 0.197148 + 0.341470i 0.947602 0.319452i \(-0.103499\pi\)
−0.750455 + 0.660922i \(0.770166\pi\)
\(30\) 0 0
\(31\) 0.632308 0.113566 0.0567830 0.998387i \(-0.481916\pi\)
0.0567830 + 0.998387i \(0.481916\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 8.34818 + 1.32814i 1.41110 + 0.224496i
\(36\) 0 0
\(37\) 1.92885 3.34087i 0.317102 0.549236i −0.662780 0.748814i \(-0.730624\pi\)
0.979882 + 0.199578i \(0.0639570\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.05124 8.74900i 0.788871 1.36636i −0.137788 0.990462i \(-0.543999\pi\)
0.926659 0.375903i \(-0.122667\pi\)
\(42\) 0 0
\(43\) −4.24701 7.35603i −0.647663 1.12178i −0.983680 0.179929i \(-0.942413\pi\)
0.336017 0.941856i \(-0.390920\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.53173 0.952751 0.476375 0.879242i \(-0.341950\pi\)
0.476375 + 0.879242i \(0.341950\pi\)
\(48\) 0 0
\(49\) −1.44591 6.84904i −0.206559 0.978434i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.39950 4.15606i −0.329597 0.570879i 0.652835 0.757500i \(-0.273580\pi\)
−0.982432 + 0.186621i \(0.940246\pi\)
\(54\) 0 0
\(55\) 7.29349 0.983454
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.20383 0.807670 0.403835 0.914832i \(-0.367677\pi\)
0.403835 + 0.914832i \(0.367677\pi\)
\(60\) 0 0
\(61\) −8.91093 −1.14093 −0.570464 0.821323i \(-0.693236\pi\)
−0.570464 + 0.821323i \(0.693236\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.31357 −0.535033
\(66\) 0 0
\(67\) 3.01570 0.368426 0.184213 0.982886i \(-0.441026\pi\)
0.184213 + 0.982886i \(0.441026\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −15.3791 −1.82516 −0.912580 0.408899i \(-0.865913\pi\)
−0.912580 + 0.408899i \(0.865913\pi\)
\(72\) 0 0
\(73\) 4.36577 + 7.56173i 0.510974 + 0.885033i 0.999919 + 0.0127186i \(0.00404857\pi\)
−0.488945 + 0.872315i \(0.662618\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.16053 5.64002i −0.246215 0.642740i
\(78\) 0 0
\(79\) 1.87610 0.211078 0.105539 0.994415i \(-0.466343\pi\)
0.105539 + 0.994415i \(0.466343\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −3.00140 5.19857i −0.329446 0.570617i 0.652956 0.757396i \(-0.273529\pi\)
−0.982402 + 0.186779i \(0.940195\pi\)
\(84\) 0 0
\(85\) 7.07451 12.2534i 0.767338 1.32907i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.65390 + 4.59668i −0.281313 + 0.487248i −0.971708 0.236184i \(-0.924103\pi\)
0.690396 + 0.723432i \(0.257436\pi\)
\(90\) 0 0
\(91\) 1.27780 + 3.33566i 0.133949 + 0.349673i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 23.5927 2.42056
\(96\) 0 0
\(97\) 7.44539 + 12.8958i 0.755965 + 1.30937i 0.944893 + 0.327378i \(0.106165\pi\)
−0.188929 + 0.981991i \(0.560502\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −7.00299 + 12.1295i −0.696824 + 1.20693i 0.272738 + 0.962088i \(0.412071\pi\)
−0.969562 + 0.244846i \(0.921263\pi\)
\(102\) 0 0
\(103\) 8.03055 + 13.9093i 0.791274 + 1.37053i 0.925179 + 0.379532i \(0.123915\pi\)
−0.133905 + 0.990994i \(0.542752\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.26820 2.19658i 0.122601 0.212352i −0.798191 0.602404i \(-0.794210\pi\)
0.920793 + 0.390052i \(0.127543\pi\)
\(108\) 0 0
\(109\) 8.10946 + 14.0460i 0.776746 + 1.34536i 0.933808 + 0.357775i \(0.116464\pi\)
−0.157062 + 0.987589i \(0.550202\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.61499 + 2.79725i −0.151926 + 0.263143i −0.931935 0.362625i \(-0.881881\pi\)
0.780010 + 0.625767i \(0.215214\pi\)
\(114\) 0 0
\(115\) −10.3352 + 17.9010i −0.963759 + 1.66928i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −11.5712 1.84089i −1.06073 0.168754i
\(120\) 0 0
\(121\) 2.89445 + 5.01333i 0.263131 + 0.455757i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.664575 −0.0594414
\(126\) 0 0
\(127\) 12.6429 1.12187 0.560936 0.827859i \(-0.310441\pi\)
0.560936 + 0.827859i \(0.310441\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −9.53430 16.5139i −0.833015 1.44282i −0.895636 0.444787i \(-0.853279\pi\)
0.0626210 0.998037i \(-0.480054\pi\)
\(132\) 0 0
\(133\) −6.98881 18.2442i −0.606007 1.58197i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.38236 5.85842i 0.288975 0.500519i −0.684591 0.728928i \(-0.740019\pi\)
0.973565 + 0.228409i \(0.0733523\pi\)
\(138\) 0 0
\(139\) 6.57218 11.3834i 0.557445 0.965524i −0.440263 0.897869i \(-0.645115\pi\)
0.997709 0.0676550i \(-0.0215517\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1.54100 + 2.66908i 0.128865 + 0.223200i
\(144\) 0 0
\(145\) −3.39204 + 5.87518i −0.281693 + 0.487907i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.140257 + 0.242932i 0.0114903 + 0.0199018i 0.871713 0.490016i \(-0.163009\pi\)
−0.860223 + 0.509918i \(0.829676\pi\)
\(150\) 0 0
\(151\) 4.42899 7.67123i 0.360426 0.624276i −0.627605 0.778532i \(-0.715965\pi\)
0.988031 + 0.154256i \(0.0492980\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.01011 + 1.74956i 0.0811341 + 0.140528i
\(156\) 0 0
\(157\) −1.92894 −0.153946 −0.0769731 0.997033i \(-0.524526\pi\)
−0.0769731 + 0.997033i \(0.524526\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 16.9043 + 2.68936i 1.33225 + 0.211952i
\(162\) 0 0
\(163\) 12.1983 21.1281i 0.955446 1.65488i 0.222100 0.975024i \(-0.428709\pi\)
0.733345 0.679856i \(-0.237958\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.75658 4.77453i 0.213310 0.369464i −0.739438 0.673224i \(-0.764909\pi\)
0.952749 + 0.303760i \(0.0982421\pi\)
\(168\) 0 0
\(169\) 5.58861 + 9.67976i 0.429893 + 0.744597i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −12.6052 −0.958355 −0.479178 0.877718i \(-0.659065\pi\)
−0.479178 + 0.877718i \(0.659065\pi\)
\(174\) 0 0
\(175\) 4.92909 + 12.8673i 0.372604 + 0.972676i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.10472 + 8.84164i 0.381545 + 0.660855i 0.991283 0.131747i \(-0.0420588\pi\)
−0.609738 + 0.792603i \(0.708725\pi\)
\(180\) 0 0
\(181\) −16.2398 −1.20710 −0.603548 0.797327i \(-0.706247\pi\)
−0.603548 + 0.797327i \(0.706247\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 12.3254 0.906179
\(186\) 0 0
\(187\) −10.1093 −0.739265
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.94120 −0.285175 −0.142587 0.989782i \(-0.545542\pi\)
−0.142587 + 0.989782i \(0.545542\pi\)
\(192\) 0 0
\(193\) −5.74112 −0.413255 −0.206627 0.978420i \(-0.566249\pi\)
−0.206627 + 0.978420i \(0.566249\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.67480 0.546807 0.273403 0.961899i \(-0.411851\pi\)
0.273403 + 0.961899i \(0.411851\pi\)
\(198\) 0 0
\(199\) 2.26928 + 3.93050i 0.160865 + 0.278626i 0.935179 0.354175i \(-0.115238\pi\)
−0.774314 + 0.632801i \(0.781905\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 5.54807 + 0.882659i 0.389398 + 0.0619505i
\(204\) 0 0
\(205\) 32.2774 2.25435
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.42836 14.5983i −0.583002 1.00979i
\(210\) 0 0
\(211\) −9.84097 + 17.0451i −0.677480 + 1.17343i 0.298257 + 0.954486i \(0.403595\pi\)
−0.975737 + 0.218944i \(0.929739\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 13.5692 23.5025i 0.925410 1.60286i
\(216\) 0 0
\(217\) 1.05371 1.29938i 0.0715304 0.0882079i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 5.97891 0.402185
\(222\) 0 0
\(223\) −6.63518 11.4925i −0.444324 0.769592i 0.553681 0.832729i \(-0.313223\pi\)
−0.998005 + 0.0631368i \(0.979890\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.0305 + 19.1053i −0.732118 + 1.26807i 0.223858 + 0.974622i \(0.428135\pi\)
−0.955976 + 0.293445i \(0.905198\pi\)
\(228\) 0 0
\(229\) 8.92359 + 15.4561i 0.589688 + 1.02137i 0.994273 + 0.106869i \(0.0340825\pi\)
−0.404585 + 0.914500i \(0.632584\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 7.84409 13.5864i 0.513883 0.890072i −0.485987 0.873966i \(-0.661540\pi\)
0.999870 0.0161061i \(-0.00512696\pi\)
\(234\) 0 0
\(235\) 10.4344 + 18.0730i 0.680667 + 1.17895i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.0639656 + 0.110792i −0.00413759 + 0.00716652i −0.868087 0.496412i \(-0.834650\pi\)
0.863949 + 0.503579i \(0.167984\pi\)
\(240\) 0 0
\(241\) −7.54343 + 13.0656i −0.485915 + 0.841630i −0.999869 0.0161883i \(-0.994847\pi\)
0.513954 + 0.857818i \(0.328180\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 16.6411 14.9421i 1.06316 0.954616i
\(246\) 0 0
\(247\) 4.98476 + 8.63386i 0.317173 + 0.549359i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.3738 0.781030 0.390515 0.920596i \(-0.372297\pi\)
0.390515 + 0.920596i \(0.372297\pi\)
\(252\) 0 0
\(253\) 14.7687 0.928499
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.0433 + 19.1276i 0.688865 + 1.19315i 0.972205 + 0.234130i \(0.0752240\pi\)
−0.283340 + 0.959019i \(0.591443\pi\)
\(258\) 0 0
\(259\) −3.65111 9.53115i −0.226869 0.592237i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3.89678 6.74943i 0.240286 0.416187i −0.720510 0.693445i \(-0.756092\pi\)
0.960796 + 0.277257i \(0.0894255\pi\)
\(264\) 0 0
\(265\) 7.66641 13.2786i 0.470944 0.815698i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.85738 + 6.68119i 0.235189 + 0.407359i 0.959328 0.282295i \(-0.0910958\pi\)
−0.724139 + 0.689654i \(0.757762\pi\)
\(270\) 0 0
\(271\) −12.5744 + 21.7795i −0.763839 + 1.32301i 0.177019 + 0.984207i \(0.443355\pi\)
−0.940858 + 0.338801i \(0.889979\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.94438 + 10.2960i 0.358460 + 0.620870i
\(276\) 0 0
\(277\) 3.98137 6.89593i 0.239217 0.414336i −0.721273 0.692651i \(-0.756443\pi\)
0.960490 + 0.278315i \(0.0897759\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −13.3385 23.1030i −0.795710 1.37821i −0.922388 0.386266i \(-0.873765\pi\)
0.126678 0.991944i \(-0.459569\pi\)
\(282\) 0 0
\(283\) −14.4399 −0.858364 −0.429182 0.903218i \(-0.641198\pi\)
−0.429182 + 0.903218i \(0.641198\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −9.56144 24.9600i −0.564394 1.47334i
\(288\) 0 0
\(289\) −1.30577 + 2.26166i −0.0768099 + 0.133039i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.27703 14.3362i 0.483549 0.837532i −0.516272 0.856424i \(-0.672681\pi\)
0.999822 + 0.0188927i \(0.00601408\pi\)
\(294\) 0 0
\(295\) 9.91061 + 17.1657i 0.577018 + 0.999424i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.73460 −0.505135
\(300\) 0 0
\(301\) −22.1939 3.53090i −1.27924 0.203518i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −14.2352 24.6561i −0.815105 1.41180i
\(306\) 0 0
\(307\) −10.9233 −0.623425 −0.311713 0.950176i \(-0.600903\pi\)
−0.311713 + 0.950176i \(0.600903\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.25360 −0.297904 −0.148952 0.988844i \(-0.547590\pi\)
−0.148952 + 0.988844i \(0.547590\pi\)
\(312\) 0 0
\(313\) 21.5184 1.21629 0.608145 0.793826i \(-0.291914\pi\)
0.608145 + 0.793826i \(0.291914\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.5323 0.984710 0.492355 0.870394i \(-0.336136\pi\)
0.492355 + 0.870394i \(0.336136\pi\)
\(318\) 0 0
\(319\) 4.84714 0.271388
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −32.7012 −1.81954
\(324\) 0 0
\(325\) −3.51567 6.08932i −0.195014 0.337774i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 10.8848 13.4226i 0.600097 0.740012i
\(330\) 0 0
\(331\) −6.27589 −0.344954 −0.172477 0.985014i \(-0.555177\pi\)
−0.172477 + 0.985014i \(0.555177\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.81757 + 8.34428i 0.263212 + 0.455897i
\(336\) 0 0
\(337\) 13.5924 23.5427i 0.740426 1.28246i −0.211876 0.977297i \(-0.567957\pi\)
0.952302 0.305159i \(-0.0987095\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.721712 1.25004i 0.0390829 0.0676936i
\(342\) 0 0
\(343\) −16.4842 8.44222i −0.890063 0.455837i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −19.1808 −1.02968 −0.514840 0.857286i \(-0.672149\pi\)
−0.514840 + 0.857286i \(0.672149\pi\)
\(348\) 0 0
\(349\) 10.1028 + 17.4985i 0.540789 + 0.936675i 0.998859 + 0.0477584i \(0.0152078\pi\)
−0.458069 + 0.888916i \(0.651459\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −14.2499 + 24.6816i −0.758448 + 1.31367i 0.185193 + 0.982702i \(0.440709\pi\)
−0.943642 + 0.330969i \(0.892624\pi\)
\(354\) 0 0
\(355\) −24.5680 42.5531i −1.30394 2.25848i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.4572 26.7727i 0.815802 1.41301i −0.0929489 0.995671i \(-0.529629\pi\)
0.908751 0.417339i \(-0.137037\pi\)
\(360\) 0 0
\(361\) −17.7638 30.7677i −0.934934 1.61935i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −13.9486 + 24.1597i −0.730103 + 1.26458i
\(366\) 0 0
\(367\) −3.41547 + 5.91577i −0.178286 + 0.308801i −0.941294 0.337589i \(-0.890389\pi\)
0.763007 + 0.646390i \(0.223722\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −12.5393 1.99491i −0.651007 0.103571i
\(372\) 0 0
\(373\) −3.38245 5.85858i −0.175137 0.303346i 0.765072 0.643945i \(-0.222703\pi\)
−0.940209 + 0.340599i \(0.889370\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.86673 −0.147644
\(378\) 0 0
\(379\) 7.62967 0.391910 0.195955 0.980613i \(-0.437219\pi\)
0.195955 + 0.980613i \(0.437219\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.21132 + 5.56217i 0.164091 + 0.284214i 0.936332 0.351116i \(-0.114198\pi\)
−0.772241 + 0.635329i \(0.780864\pi\)
\(384\) 0 0
\(385\) 12.1542 14.9880i 0.619436 0.763860i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −7.92675 + 13.7295i −0.401902 + 0.696115i −0.993955 0.109784i \(-0.964984\pi\)
0.592053 + 0.805899i \(0.298317\pi\)
\(390\) 0 0
\(391\) 14.3253 24.8121i 0.724460 1.25480i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.99707 + 5.19107i 0.150799 + 0.261191i
\(396\) 0 0
\(397\) −8.56287 + 14.8313i −0.429758 + 0.744363i −0.996852 0.0792903i \(-0.974735\pi\)
0.567093 + 0.823654i \(0.308068\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 11.8845 + 20.5846i 0.593486 + 1.02795i 0.993759 + 0.111552i \(0.0355821\pi\)
−0.400273 + 0.916396i \(0.631085\pi\)
\(402\) 0 0
\(403\) −0.426840 + 0.739309i −0.0212624 + 0.0368276i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.40316 7.62649i −0.218256 0.378031i
\(408\) 0 0
\(409\) 15.1189 0.747582 0.373791 0.927513i \(-0.378058\pi\)
0.373791 + 0.927513i \(0.378058\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 10.3383 12.7488i 0.508717 0.627326i
\(414\) 0 0
\(415\) 9.58945 16.6094i 0.470728 0.815324i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.82673 4.89604i 0.138095 0.239187i −0.788681 0.614803i \(-0.789236\pi\)
0.926775 + 0.375616i \(0.122569\pi\)
\(420\) 0 0
\(421\) −12.5088 21.6658i −0.609640 1.05593i −0.991300 0.131625i \(-0.957981\pi\)
0.381660 0.924303i \(-0.375353\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 23.0636 1.11875
\(426\) 0 0
\(427\) −14.8496 + 18.3118i −0.718622 + 0.886171i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 10.4514 + 18.1024i 0.503428 + 0.871962i 0.999992 + 0.00396247i \(0.00126130\pi\)
−0.496564 + 0.868000i \(0.665405\pi\)
\(432\) 0 0
\(433\) −21.2708 −1.02221 −0.511104 0.859519i \(-0.670763\pi\)
−0.511104 + 0.859519i \(0.670763\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 47.7732 2.28530
\(438\) 0 0
\(439\) −17.1817 −0.820040 −0.410020 0.912077i \(-0.634478\pi\)
−0.410020 + 0.912077i \(0.634478\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.7436 −0.605467 −0.302734 0.953075i \(-0.597899\pi\)
−0.302734 + 0.953075i \(0.597899\pi\)
\(444\) 0 0
\(445\) −16.9584 −0.803905
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −31.5913 −1.49088 −0.745442 0.666570i \(-0.767762\pi\)
−0.745442 + 0.666570i \(0.767762\pi\)
\(450\) 0 0
\(451\) −11.5309 19.9721i −0.542969 0.940449i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −7.18833 + 8.86432i −0.336994 + 0.415566i
\(456\) 0 0
\(457\) −7.30486 −0.341707 −0.170853 0.985296i \(-0.554652\pi\)
−0.170853 + 0.985296i \(0.554652\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 13.3651 + 23.1491i 0.622477 + 1.07816i 0.989023 + 0.147761i \(0.0472068\pi\)
−0.366546 + 0.930400i \(0.619460\pi\)
\(462\) 0 0
\(463\) 1.75608 3.04161i 0.0816117 0.141356i −0.822331 0.569010i \(-0.807327\pi\)
0.903942 + 0.427654i \(0.140660\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.80239 + 13.5141i −0.361052 + 0.625360i −0.988134 0.153593i \(-0.950915\pi\)
0.627083 + 0.778953i \(0.284249\pi\)
\(468\) 0 0
\(469\) 5.02550 6.19721i 0.232056 0.286161i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −19.3900 −0.891554
\(474\) 0 0
\(475\) 19.2287 + 33.3050i 0.882272 + 1.52814i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 8.54444 14.7994i 0.390405 0.676202i −0.602098 0.798422i \(-0.705668\pi\)
0.992503 + 0.122221i \(0.0390015\pi\)
\(480\) 0 0
\(481\) 2.60415 + 4.51052i 0.118739 + 0.205662i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −23.7880 + 41.2020i −1.08016 + 1.87089i
\(486\) 0 0
\(487\) 12.9335 + 22.4014i 0.586072 + 1.01511i 0.994741 + 0.102423i \(0.0326597\pi\)
−0.408669 + 0.912683i \(0.634007\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.51452 + 13.0155i −0.339126 + 0.587383i −0.984269 0.176679i \(-0.943465\pi\)
0.645143 + 0.764062i \(0.276798\pi\)
\(492\) 0 0
\(493\) 4.70160 8.14342i 0.211750 0.366761i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −25.6284 + 31.6037i −1.14959 + 1.41762i
\(498\) 0 0
\(499\) 7.62094 + 13.1999i 0.341160 + 0.590907i 0.984648 0.174549i \(-0.0558468\pi\)
−0.643488 + 0.765456i \(0.722513\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 18.6284 0.830599 0.415299 0.909685i \(-0.363677\pi\)
0.415299 + 0.909685i \(0.363677\pi\)
\(504\) 0 0
\(505\) −44.7491 −1.99131
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.72333 6.44899i −0.165034 0.285847i 0.771634 0.636067i \(-0.219440\pi\)
−0.936667 + 0.350221i \(0.886107\pi\)
\(510\) 0 0
\(511\) 22.8145 + 3.62964i 1.00926 + 0.160566i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −25.6576 + 44.4402i −1.13061 + 1.95827i
\(516\) 0 0
\(517\) 7.45527 12.9129i 0.327882 0.567909i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 11.3853 + 19.7200i 0.498800 + 0.863947i 0.999999 0.00138491i \(-0.000440830\pi\)
−0.501199 + 0.865332i \(0.667107\pi\)
\(522\) 0 0
\(523\) −16.5092 + 28.5949i −0.721899 + 1.25037i 0.238339 + 0.971182i \(0.423397\pi\)
−0.960238 + 0.279184i \(0.909936\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.40009 2.42502i −0.0609887 0.105636i
\(528\) 0 0
\(529\) −9.42780 + 16.3294i −0.409904 + 0.709975i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.81969 + 11.8120i 0.295393 + 0.511636i
\(534\) 0 0
\(535\) 8.10378 0.350357
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −15.1906 4.95894i −0.654304 0.213597i
\(540\) 0 0
\(541\) 8.53464 14.7824i 0.366933 0.635546i −0.622151 0.782897i \(-0.713741\pi\)
0.989084 + 0.147351i \(0.0470745\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −25.9097 + 44.8769i −1.10985 + 1.92232i
\(546\) 0 0
\(547\) −16.3574 28.3318i −0.699390 1.21138i −0.968678 0.248319i \(-0.920122\pi\)
0.269288 0.963060i \(-0.413212\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 15.6794 0.667963
\(552\) 0 0
\(553\) 3.12642 3.85536i 0.132949 0.163946i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −17.0783 29.5806i −0.723633 1.25337i −0.959534 0.281592i \(-0.909138\pi\)
0.235902 0.971777i \(-0.424196\pi\)
\(558\) 0 0
\(559\) 11.4678 0.485036
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.67074 −0.407573 −0.203786 0.979015i \(-0.565325\pi\)
−0.203786 + 0.979015i \(0.565325\pi\)
\(564\) 0 0
\(565\) −10.3198 −0.434157
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −11.1274 −0.466484 −0.233242 0.972419i \(-0.574933\pi\)
−0.233242 + 0.972419i \(0.574933\pi\)
\(570\) 0 0
\(571\) −0.729305 −0.0305205 −0.0152602 0.999884i \(-0.504858\pi\)
−0.0152602 + 0.999884i \(0.504858\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −33.6937 −1.40512
\(576\) 0 0
\(577\) 9.49359 + 16.4434i 0.395223 + 0.684547i 0.993130 0.117019i \(-0.0373338\pi\)
−0.597906 + 0.801566i \(0.704001\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −15.6846 2.49532i −0.650709 0.103523i
\(582\) 0 0
\(583\) −10.9551 −0.453714
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.30535 2.26093i −0.0538775 0.0933185i 0.837829 0.545933i \(-0.183825\pi\)
−0.891706 + 0.452615i \(0.850491\pi\)
\(588\) 0 0
\(589\) 2.33457 4.04359i 0.0961942 0.166613i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 7.92622 13.7286i 0.325491 0.563767i −0.656121 0.754656i \(-0.727804\pi\)
0.981612 + 0.190889i \(0.0611371\pi\)
\(594\) 0 0
\(595\) −13.3913 34.9576i −0.548988 1.43312i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 15.8610 0.648063 0.324032 0.946046i \(-0.394962\pi\)
0.324032 + 0.946046i \(0.394962\pi\)
\(600\) 0 0
\(601\) 0.834141 + 1.44477i 0.0340253 + 0.0589336i 0.882537 0.470244i \(-0.155834\pi\)
−0.848511 + 0.529177i \(0.822501\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9.24774 + 16.0176i −0.375974 + 0.651207i
\(606\) 0 0
\(607\) −18.2555 31.6194i −0.740968 1.28339i −0.952055 0.305926i \(-0.901034\pi\)
0.211088 0.977467i \(-0.432299\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.40925 + 7.63705i −0.178379 + 0.308962i
\(612\) 0 0
\(613\) 18.2957 + 31.6891i 0.738958 + 1.27991i 0.952965 + 0.303080i \(0.0980150\pi\)
−0.214007 + 0.976832i \(0.568652\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.10936 8.84967i 0.205695 0.356274i −0.744659 0.667445i \(-0.767388\pi\)
0.950354 + 0.311171i \(0.100721\pi\)
\(618\) 0 0
\(619\) −12.3664 + 21.4193i −0.497049 + 0.860914i −0.999994 0.00340432i \(-0.998916\pi\)
0.502945 + 0.864318i \(0.332250\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 5.02353 + 13.1138i 0.201264 + 0.525395i
\(624\) 0 0
\(625\) 11.9584 + 20.7125i 0.478334 + 0.828499i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −17.0838 −0.681177
\(630\) 0 0
\(631\) −42.1420 −1.67765 −0.838823 0.544404i \(-0.816756\pi\)
−0.838823 + 0.544404i \(0.816756\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 20.1969 + 34.9821i 0.801491 + 1.38822i
\(636\) 0 0
\(637\) 8.98411 + 2.93285i 0.355964 + 0.116204i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.16519 + 2.01817i −0.0460222 + 0.0797128i −0.888119 0.459614i \(-0.847988\pi\)
0.842097 + 0.539327i \(0.181321\pi\)
\(642\) 0 0
\(643\) −16.5035 + 28.5850i −0.650836 + 1.12728i 0.332085 + 0.943250i \(0.392248\pi\)
−0.982920 + 0.184031i \(0.941085\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.4187 18.0458i −0.409603 0.709452i 0.585243 0.810858i \(-0.300999\pi\)
−0.994845 + 0.101406i \(0.967666\pi\)
\(648\) 0 0
\(649\) 7.08101 12.2647i 0.277954 0.481430i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24.4176 42.2925i −0.955534 1.65503i −0.733142 0.680075i \(-0.761947\pi\)
−0.222391 0.974958i \(-0.571386\pi\)
\(654\) 0 0
\(655\) 30.4620 52.7618i 1.19025 2.06157i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.272662 + 0.472265i 0.0106214 + 0.0183968i 0.871287 0.490773i \(-0.163286\pi\)
−0.860666 + 0.509170i \(0.829952\pi\)
\(660\) 0 0
\(661\) −46.4250 −1.80572 −0.902861 0.429933i \(-0.858537\pi\)
−0.902861 + 0.429933i \(0.858537\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 39.3160 48.4827i 1.52461 1.88008i
\(666\) 0 0
\(667\) −6.86858 + 11.8967i −0.265953 + 0.460643i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −10.1709 + 17.6165i −0.392642 + 0.680076i
\(672\) 0 0
\(673\) −16.9838 29.4168i −0.654677 1.13393i −0.981975 0.189013i \(-0.939471\pi\)
0.327298 0.944921i \(-0.393862\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −31.2851 −1.20238 −0.601191 0.799105i \(-0.705307\pi\)
−0.601191 + 0.799105i \(0.705307\pi\)
\(678\) 0 0
\(679\) 38.9080 + 6.18999i 1.49315 + 0.237550i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.289712 + 0.501795i 0.0110855 + 0.0192007i 0.871515 0.490369i \(-0.163138\pi\)
−0.860429 + 0.509570i \(0.829805\pi\)
\(684\) 0 0
\(685\) 21.6133 0.825801
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 6.47915 0.246836
\(690\) 0 0
\(691\) −2.21565 −0.0842872 −0.0421436 0.999112i \(-0.513419\pi\)
−0.0421436 + 0.999112i \(0.513419\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 41.9962 1.59301
\(696\) 0 0
\(697\) −44.7387 −1.69460
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.74299 −0.179140 −0.0895702 0.995981i \(-0.528549\pi\)
−0.0895702 + 0.995981i \(0.528549\pi\)
\(702\) 0 0
\(703\) −14.2432 24.6699i −0.537192 0.930444i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 13.2559 + 34.6043i 0.498539 + 1.30143i
\(708\) 0 0
\(709\) −23.3765 −0.877923 −0.438962 0.898506i \(-0.644654\pi\)
−0.438962 + 0.898506i \(0.644654\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.04539 + 3.54272i 0.0766004 + 0.132676i
\(714\) 0 0
\(715\) −4.92348 + 8.52771i −0.184128 + 0.318918i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.0256 22.5610i 0.485772 0.841382i −0.514094 0.857734i \(-0.671872\pi\)
0.999866 + 0.0163516i \(0.00520511\pi\)
\(720\) 0 0
\(721\) 41.9659 + 6.67649i 1.56289 + 0.248645i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −11.0584 −0.410698
\(726\) 0 0
\(727\) −5.79712 10.0409i −0.215003 0.372396i 0.738270 0.674505i \(-0.235643\pi\)
−0.953274 + 0.302108i \(0.902310\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −18.8078 + 32.5761i −0.695633 + 1.20487i
\(732\) 0 0
\(733\) 17.6743 + 30.6128i 0.652816 + 1.13071i 0.982436 + 0.186597i \(0.0597459\pi\)
−0.329620 + 0.944114i \(0.606921\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.44210 5.96189i 0.126791 0.219609i
\(738\) 0 0
\(739\) −4.66968 8.08812i −0.171777 0.297526i 0.767264 0.641331i \(-0.221617\pi\)
−0.939041 + 0.343805i \(0.888284\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −14.6308 + 25.3412i −0.536750 + 0.929679i 0.462326 + 0.886710i \(0.347015\pi\)
−0.999076 + 0.0429687i \(0.986318\pi\)
\(744\) 0 0
\(745\) −0.448120 + 0.776167i −0.0164179 + 0.0284366i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −2.40056 6.26662i −0.0877146 0.228977i
\(750\) 0 0
\(751\) 13.3106 + 23.0547i 0.485712 + 0.841278i 0.999865 0.0164202i \(-0.00522696\pi\)
−0.514153 + 0.857699i \(0.671894\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 28.3012 1.02999
\(756\) 0 0
\(757\) −35.3183 −1.28367 −0.641833 0.766845i \(-0.721826\pi\)
−0.641833 + 0.766845i \(0.721826\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 15.7824 + 27.3359i 0.572112 + 0.990927i 0.996349 + 0.0853760i \(0.0272091\pi\)
−0.424237 + 0.905551i \(0.639458\pi\)
\(762\) 0 0
\(763\) 42.3783 + 6.74210i 1.53420 + 0.244080i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −4.18790 + 7.25366i −0.151216 + 0.261914i
\(768\) 0 0
\(769\) −23.8477 + 41.3055i −0.859972 + 1.48951i 0.0119829 + 0.999928i \(0.496186\pi\)
−0.871955 + 0.489587i \(0.837148\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −20.7219 35.8914i −0.745314 1.29092i −0.950048 0.312105i \(-0.898966\pi\)
0.204733 0.978818i \(-0.434367\pi\)
\(774\) 0 0
\(775\) −1.64653 + 2.85188i −0.0591452 + 0.102442i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −37.2997 64.6050i −1.33640 2.31472i
\(780\) 0 0
\(781\) −17.5536 + 30.4036i −0.628116 + 1.08793i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.08148 5.33728i −0.109983 0.190496i
\(786\) 0 0
\(787\) 26.3177 0.938125 0.469063 0.883165i \(-0.344592\pi\)
0.469063 + 0.883165i \(0.344592\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.05700 + 7.98024i 0.108694 + 0.283745i
\(792\) 0 0
\(793\) 6.01533 10.4189i 0.213611 0.369984i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.42109 + 14.5858i −0.298290 + 0.516654i −0.975745 0.218911i \(-0.929750\pi\)
0.677455 + 0.735565i \(0.263083\pi\)
\(798\) 0 0
\(799\) −14.4629 25.0504i −0.511659 0.886220i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 19.9322 0.703392
\(804\) 0 0
\(805\) 19.5633 + 51.0697i 0.689516 + 1.79997i
\(806\) 0