Properties

Label 1840.2.e.f.369.11
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1840.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6924739719\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 24 x^{10} + 188 x^{8} + 530 x^{6} + 508 x^{4} + 80 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 460)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.11
Root \(1.65047i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.f.369.2

$q$-expansion

\(f(q)\) \(=\) \(q+2.80150i q^{3} +(-2.17393 + 0.523461i) q^{5} -4.50896i q^{7} -4.84843 q^{9} +O(q^{10})\) \(q+2.80150i q^{3} +(-2.17393 + 0.523461i) q^{5} -4.50896i q^{7} -4.84843 q^{9} +4.10479 q^{11} +4.10245i q^{13} +(-1.46648 - 6.09029i) q^{15} -2.26588i q^{17} +6.77484 q^{19} +12.6319 q^{21} +1.00000i q^{23} +(4.45198 - 2.27594i) q^{25} -5.17837i q^{27} -4.13863 q^{29} -1.84124 q^{31} +11.4996i q^{33} +(2.36026 + 9.80218i) q^{35} +11.1155i q^{37} -11.4930 q^{39} +8.36833 q^{41} +5.43473i q^{43} +(10.5402 - 2.53796i) q^{45} +0.593285i q^{47} -13.3307 q^{49} +6.34787 q^{51} -1.70512i q^{53} +(-8.92353 + 2.14870i) q^{55} +18.9797i q^{57} +6.19772 q^{59} -11.3814 q^{61} +21.8614i q^{63} +(-2.14747 - 8.91846i) q^{65} +5.78978i q^{67} -2.80150 q^{69} +11.9915 q^{71} +0.363592i q^{73} +(6.37605 + 12.4722i) q^{75} -18.5083i q^{77} +1.75692 q^{79} -0.0380417 q^{81} -9.72171i q^{83} +(1.18610 + 4.92587i) q^{85} -11.5944i q^{87} +17.2208 q^{89} +18.4978 q^{91} -5.15825i q^{93} +(-14.7281 + 3.54636i) q^{95} +4.38314i q^{97} -19.9018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 20 q^{9} + O(q^{10}) \) \( 12 q - 20 q^{9} - 4 q^{11} - 2 q^{15} + 8 q^{19} + 8 q^{25} - 10 q^{29} - 18 q^{31} + 10 q^{35} - 16 q^{39} - 2 q^{41} + 2 q^{45} - 38 q^{49} + 24 q^{51} - 16 q^{55} - 22 q^{59} - 8 q^{61} + 38 q^{65} - 8 q^{69} + 34 q^{71} - 16 q^{75} + 20 q^{79} + 28 q^{81} + 6 q^{85} + 48 q^{89} + 8 q^{91} - 12 q^{95} - 32 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(3\) 2.80150i 1.61745i 0.588187 + 0.808725i \(0.299842\pi\)
−0.588187 + 0.808725i \(0.700158\pi\)
\(4\) 0 0
\(5\) −2.17393 + 0.523461i −0.972213 + 0.234099i
\(6\) 0 0
\(7\) 4.50896i 1.70423i −0.523357 0.852113i \(-0.675321\pi\)
0.523357 0.852113i \(-0.324679\pi\)
\(8\) 0 0
\(9\) −4.84843 −1.61614
\(10\) 0 0
\(11\) 4.10479 1.23764 0.618820 0.785533i \(-0.287611\pi\)
0.618820 + 0.785533i \(0.287611\pi\)
\(12\) 0 0
\(13\) 4.10245i 1.13781i 0.822402 + 0.568907i \(0.192634\pi\)
−0.822402 + 0.568907i \(0.807366\pi\)
\(14\) 0 0
\(15\) −1.46648 6.09029i −0.378643 1.57250i
\(16\) 0 0
\(17\) 2.26588i 0.549556i −0.961508 0.274778i \(-0.911396\pi\)
0.961508 0.274778i \(-0.0886044\pi\)
\(18\) 0 0
\(19\) 6.77484 1.55425 0.777127 0.629343i \(-0.216676\pi\)
0.777127 + 0.629343i \(0.216676\pi\)
\(20\) 0 0
\(21\) 12.6319 2.75650
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 4.45198 2.27594i 0.890395 0.455188i
\(26\) 0 0
\(27\) 5.17837i 0.996579i
\(28\) 0 0
\(29\) −4.13863 −0.768525 −0.384263 0.923224i \(-0.625544\pi\)
−0.384263 + 0.923224i \(0.625544\pi\)
\(30\) 0 0
\(31\) −1.84124 −0.330697 −0.165349 0.986235i \(-0.552875\pi\)
−0.165349 + 0.986235i \(0.552875\pi\)
\(32\) 0 0
\(33\) 11.4996i 2.00182i
\(34\) 0 0
\(35\) 2.36026 + 9.80218i 0.398958 + 1.65687i
\(36\) 0 0
\(37\) 11.1155i 1.82738i 0.406411 + 0.913690i \(0.366780\pi\)
−0.406411 + 0.913690i \(0.633220\pi\)
\(38\) 0 0
\(39\) −11.4930 −1.84036
\(40\) 0 0
\(41\) 8.36833 1.30691 0.653457 0.756964i \(-0.273318\pi\)
0.653457 + 0.756964i \(0.273318\pi\)
\(42\) 0 0
\(43\) 5.43473i 0.828789i 0.910097 + 0.414395i \(0.136007\pi\)
−0.910097 + 0.414395i \(0.863993\pi\)
\(44\) 0 0
\(45\) 10.5402 2.53796i 1.57123 0.378337i
\(46\) 0 0
\(47\) 0.593285i 0.0865396i 0.999063 + 0.0432698i \(0.0137775\pi\)
−0.999063 + 0.0432698i \(0.986222\pi\)
\(48\) 0 0
\(49\) −13.3307 −1.90439
\(50\) 0 0
\(51\) 6.34787 0.888879
\(52\) 0 0
\(53\) 1.70512i 0.234216i −0.993119 0.117108i \(-0.962638\pi\)
0.993119 0.117108i \(-0.0373624\pi\)
\(54\) 0 0
\(55\) −8.92353 + 2.14870i −1.20325 + 0.289730i
\(56\) 0 0
\(57\) 18.9797i 2.51393i
\(58\) 0 0
\(59\) 6.19772 0.806874 0.403437 0.915007i \(-0.367815\pi\)
0.403437 + 0.915007i \(0.367815\pi\)
\(60\) 0 0
\(61\) −11.3814 −1.45724 −0.728620 0.684919i \(-0.759838\pi\)
−0.728620 + 0.684919i \(0.759838\pi\)
\(62\) 0 0
\(63\) 21.8614i 2.75427i
\(64\) 0 0
\(65\) −2.14747 8.91846i −0.266361 1.10620i
\(66\) 0 0
\(67\) 5.78978i 0.707335i 0.935371 + 0.353667i \(0.115066\pi\)
−0.935371 + 0.353667i \(0.884934\pi\)
\(68\) 0 0
\(69\) −2.80150 −0.337261
\(70\) 0 0
\(71\) 11.9915 1.42312 0.711562 0.702623i \(-0.247988\pi\)
0.711562 + 0.702623i \(0.247988\pi\)
\(72\) 0 0
\(73\) 0.363592i 0.0425552i 0.999774 + 0.0212776i \(0.00677338\pi\)
−0.999774 + 0.0212776i \(0.993227\pi\)
\(74\) 0 0
\(75\) 6.37605 + 12.4722i 0.736243 + 1.44017i
\(76\) 0 0
\(77\) 18.5083i 2.10922i
\(78\) 0 0
\(79\) 1.75692 0.197669 0.0988344 0.995104i \(-0.468489\pi\)
0.0988344 + 0.995104i \(0.468489\pi\)
\(80\) 0 0
\(81\) −0.0380417 −0.00422685
\(82\) 0 0
\(83\) 9.72171i 1.06710i −0.845770 0.533548i \(-0.820858\pi\)
0.845770 0.533548i \(-0.179142\pi\)
\(84\) 0 0
\(85\) 1.18610 + 4.92587i 0.128650 + 0.534286i
\(86\) 0 0
\(87\) 11.5944i 1.24305i
\(88\) 0 0
\(89\) 17.2208 1.82540 0.912698 0.408634i \(-0.133995\pi\)
0.912698 + 0.408634i \(0.133995\pi\)
\(90\) 0 0
\(91\) 18.4978 1.93909
\(92\) 0 0
\(93\) 5.15825i 0.534886i
\(94\) 0 0
\(95\) −14.7281 + 3.54636i −1.51107 + 0.363849i
\(96\) 0 0
\(97\) 4.38314i 0.445040i 0.974928 + 0.222520i \(0.0714283\pi\)
−0.974928 + 0.222520i \(0.928572\pi\)
\(98\) 0 0
\(99\) −19.9018 −2.00020
\(100\) 0 0
\(101\) −3.21428 −0.319833 −0.159917 0.987131i \(-0.551123\pi\)
−0.159917 + 0.987131i \(0.551123\pi\)
\(102\) 0 0
\(103\) 2.09140i 0.206072i −0.994678 0.103036i \(-0.967144\pi\)
0.994678 0.103036i \(-0.0328556\pi\)
\(104\) 0 0
\(105\) −27.4609 + 6.61229i −2.67990 + 0.645294i
\(106\) 0 0
\(107\) 1.81411i 0.175377i 0.996148 + 0.0876885i \(0.0279480\pi\)
−0.996148 + 0.0876885i \(0.972052\pi\)
\(108\) 0 0
\(109\) −3.16716 −0.303359 −0.151679 0.988430i \(-0.548468\pi\)
−0.151679 + 0.988430i \(0.548468\pi\)
\(110\) 0 0
\(111\) −31.1402 −2.95570
\(112\) 0 0
\(113\) 13.0407i 1.22677i 0.789785 + 0.613384i \(0.210192\pi\)
−0.789785 + 0.613384i \(0.789808\pi\)
\(114\) 0 0
\(115\) −0.523461 2.17393i −0.0488130 0.202720i
\(116\) 0 0
\(117\) 19.8904i 1.83887i
\(118\) 0 0
\(119\) −10.2168 −0.936568
\(120\) 0 0
\(121\) 5.84927 0.531752
\(122\) 0 0
\(123\) 23.4439i 2.11387i
\(124\) 0 0
\(125\) −8.48694 + 7.27818i −0.759095 + 0.650980i
\(126\) 0 0
\(127\) 12.0290i 1.06740i 0.845674 + 0.533700i \(0.179199\pi\)
−0.845674 + 0.533700i \(0.820801\pi\)
\(128\) 0 0
\(129\) −15.2254 −1.34052
\(130\) 0 0
\(131\) −1.33814 −0.116914 −0.0584571 0.998290i \(-0.518618\pi\)
−0.0584571 + 0.998290i \(0.518618\pi\)
\(132\) 0 0
\(133\) 30.5475i 2.64880i
\(134\) 0 0
\(135\) 2.71068 + 11.2574i 0.233298 + 0.968886i
\(136\) 0 0
\(137\) 8.53176i 0.728917i 0.931220 + 0.364459i \(0.118746\pi\)
−0.931220 + 0.364459i \(0.881254\pi\)
\(138\) 0 0
\(139\) −19.2021 −1.62870 −0.814352 0.580371i \(-0.802908\pi\)
−0.814352 + 0.580371i \(0.802908\pi\)
\(140\) 0 0
\(141\) −1.66209 −0.139973
\(142\) 0 0
\(143\) 16.8397i 1.40820i
\(144\) 0 0
\(145\) 8.99712 2.16641i 0.747170 0.179911i
\(146\) 0 0
\(147\) 37.3461i 3.08025i
\(148\) 0 0
\(149\) 13.9657 1.14412 0.572058 0.820213i \(-0.306145\pi\)
0.572058 + 0.820213i \(0.306145\pi\)
\(150\) 0 0
\(151\) 9.38572 0.763799 0.381900 0.924204i \(-0.375270\pi\)
0.381900 + 0.924204i \(0.375270\pi\)
\(152\) 0 0
\(153\) 10.9859i 0.888161i
\(154\) 0 0
\(155\) 4.00274 0.963819i 0.321508 0.0774158i
\(156\) 0 0
\(157\) 22.3649i 1.78491i 0.451133 + 0.892457i \(0.351020\pi\)
−0.451133 + 0.892457i \(0.648980\pi\)
\(158\) 0 0
\(159\) 4.77690 0.378833
\(160\) 0 0
\(161\) 4.50896 0.355356
\(162\) 0 0
\(163\) 5.91327i 0.463163i −0.972816 0.231581i \(-0.925610\pi\)
0.972816 0.231581i \(-0.0743900\pi\)
\(164\) 0 0
\(165\) −6.01958 24.9993i −0.468624 1.94619i
\(166\) 0 0
\(167\) 8.73957i 0.676288i 0.941094 + 0.338144i \(0.109799\pi\)
−0.941094 + 0.338144i \(0.890201\pi\)
\(168\) 0 0
\(169\) −3.83010 −0.294623
\(170\) 0 0
\(171\) −32.8473 −2.51190
\(172\) 0 0
\(173\) 10.5284i 0.800462i −0.916414 0.400231i \(-0.868930\pi\)
0.916414 0.400231i \(-0.131070\pi\)
\(174\) 0 0
\(175\) −10.2621 20.0738i −0.775743 1.51744i
\(176\) 0 0
\(177\) 17.3629i 1.30508i
\(178\) 0 0
\(179\) −3.29655 −0.246396 −0.123198 0.992382i \(-0.539315\pi\)
−0.123198 + 0.992382i \(0.539315\pi\)
\(180\) 0 0
\(181\) 15.7994 1.17436 0.587180 0.809456i \(-0.300238\pi\)
0.587180 + 0.809456i \(0.300238\pi\)
\(182\) 0 0
\(183\) 31.8850i 2.35701i
\(184\) 0 0
\(185\) −5.81854 24.1644i −0.427788 1.77660i
\(186\) 0 0
\(187\) 9.30095i 0.680153i
\(188\) 0 0
\(189\) −23.3491 −1.69840
\(190\) 0 0
\(191\) 19.9965 1.44689 0.723447 0.690380i \(-0.242557\pi\)
0.723447 + 0.690380i \(0.242557\pi\)
\(192\) 0 0
\(193\) 0.613407i 0.0441540i 0.999756 + 0.0220770i \(0.00702790\pi\)
−0.999756 + 0.0220770i \(0.992972\pi\)
\(194\) 0 0
\(195\) 24.9851 6.01615i 1.78922 0.430826i
\(196\) 0 0
\(197\) 4.63996i 0.330584i 0.986245 + 0.165292i \(0.0528566\pi\)
−0.986245 + 0.165292i \(0.947143\pi\)
\(198\) 0 0
\(199\) −13.1446 −0.931795 −0.465898 0.884839i \(-0.654269\pi\)
−0.465898 + 0.884839i \(0.654269\pi\)
\(200\) 0 0
\(201\) −16.2201 −1.14408
\(202\) 0 0
\(203\) 18.6609i 1.30974i
\(204\) 0 0
\(205\) −18.1922 + 4.38049i −1.27060 + 0.305947i
\(206\) 0 0
\(207\) 4.84843i 0.336989i
\(208\) 0 0
\(209\) 27.8093 1.92361
\(210\) 0 0
\(211\) 6.76863 0.465972 0.232986 0.972480i \(-0.425150\pi\)
0.232986 + 0.972480i \(0.425150\pi\)
\(212\) 0 0
\(213\) 33.5941i 2.30183i
\(214\) 0 0
\(215\) −2.84487 11.8148i −0.194019 0.805759i
\(216\) 0 0
\(217\) 8.30209i 0.563583i
\(218\) 0 0
\(219\) −1.01860 −0.0688308
\(220\) 0 0
\(221\) 9.29565 0.625293
\(222\) 0 0
\(223\) 5.46851i 0.366199i −0.983094 0.183099i \(-0.941387\pi\)
0.983094 0.183099i \(-0.0586130\pi\)
\(224\) 0 0
\(225\) −21.5851 + 11.0347i −1.43901 + 0.735648i
\(226\) 0 0
\(227\) 5.55927i 0.368981i 0.982834 + 0.184491i \(0.0590636\pi\)
−0.982834 + 0.184491i \(0.940936\pi\)
\(228\) 0 0
\(229\) 6.33693 0.418756 0.209378 0.977835i \(-0.432856\pi\)
0.209378 + 0.977835i \(0.432856\pi\)
\(230\) 0 0
\(231\) 51.8511 3.41155
\(232\) 0 0
\(233\) 9.84557i 0.645005i −0.946569 0.322502i \(-0.895476\pi\)
0.946569 0.322502i \(-0.104524\pi\)
\(234\) 0 0
\(235\) −0.310562 1.28976i −0.0202588 0.0841349i
\(236\) 0 0
\(237\) 4.92201i 0.319719i
\(238\) 0 0
\(239\) 25.9526 1.67873 0.839366 0.543567i \(-0.182926\pi\)
0.839366 + 0.543567i \(0.182926\pi\)
\(240\) 0 0
\(241\) −12.3220 −0.793729 −0.396865 0.917877i \(-0.629902\pi\)
−0.396865 + 0.917877i \(0.629902\pi\)
\(242\) 0 0
\(243\) 15.6417i 1.00342i
\(244\) 0 0
\(245\) 28.9801 6.97811i 1.85147 0.445815i
\(246\) 0 0
\(247\) 27.7934i 1.76845i
\(248\) 0 0
\(249\) 27.2354 1.72597
\(250\) 0 0
\(251\) 7.68797 0.485261 0.242630 0.970119i \(-0.421990\pi\)
0.242630 + 0.970119i \(0.421990\pi\)
\(252\) 0 0
\(253\) 4.10479i 0.258066i
\(254\) 0 0
\(255\) −13.7998 + 3.32286i −0.864180 + 0.208086i
\(256\) 0 0
\(257\) 19.7126i 1.22964i −0.788669 0.614818i \(-0.789229\pi\)
0.788669 0.614818i \(-0.210771\pi\)
\(258\) 0 0
\(259\) 50.1195 3.11427
\(260\) 0 0
\(261\) 20.0659 1.24205
\(262\) 0 0
\(263\) 2.96836i 0.183037i −0.995803 0.0915183i \(-0.970828\pi\)
0.995803 0.0915183i \(-0.0291720\pi\)
\(264\) 0 0
\(265\) 0.892564 + 3.70682i 0.0548297 + 0.227708i
\(266\) 0 0
\(267\) 48.2440i 2.95249i
\(268\) 0 0
\(269\) −0.417916 −0.0254808 −0.0127404 0.999919i \(-0.504056\pi\)
−0.0127404 + 0.999919i \(0.504056\pi\)
\(270\) 0 0
\(271\) −10.1776 −0.618245 −0.309122 0.951022i \(-0.600035\pi\)
−0.309122 + 0.951022i \(0.600035\pi\)
\(272\) 0 0
\(273\) 51.8216i 3.13639i
\(274\) 0 0
\(275\) 18.2744 9.34224i 1.10199 0.563358i
\(276\) 0 0
\(277\) 18.8176i 1.13064i 0.824871 + 0.565321i \(0.191248\pi\)
−0.824871 + 0.565321i \(0.808752\pi\)
\(278\) 0 0
\(279\) 8.92713 0.534454
\(280\) 0 0
\(281\) −25.9609 −1.54870 −0.774350 0.632757i \(-0.781923\pi\)
−0.774350 + 0.632757i \(0.781923\pi\)
\(282\) 0 0
\(283\) 22.2612i 1.32329i 0.749817 + 0.661646i \(0.230142\pi\)
−0.749817 + 0.661646i \(0.769858\pi\)
\(284\) 0 0
\(285\) −9.93515 41.2607i −0.588508 2.44407i
\(286\) 0 0
\(287\) 37.7325i 2.22728i
\(288\) 0 0
\(289\) 11.8658 0.697988
\(290\) 0 0
\(291\) −12.2794 −0.719830
\(292\) 0 0
\(293\) 2.21032i 0.129128i −0.997914 0.0645641i \(-0.979434\pi\)
0.997914 0.0645641i \(-0.0205657\pi\)
\(294\) 0 0
\(295\) −13.4734 + 3.24426i −0.784453 + 0.188888i
\(296\) 0 0
\(297\) 21.2561i 1.23341i
\(298\) 0 0
\(299\) −4.10245 −0.237251
\(300\) 0 0
\(301\) 24.5050 1.41244
\(302\) 0 0
\(303\) 9.00483i 0.517314i
\(304\) 0 0
\(305\) 24.7424 5.95772i 1.41675 0.341138i
\(306\) 0 0
\(307\) 19.7730i 1.12851i −0.825602 0.564253i \(-0.809164\pi\)
0.825602 0.564253i \(-0.190836\pi\)
\(308\) 0 0
\(309\) 5.85906 0.333310
\(310\) 0 0
\(311\) −12.1593 −0.689490 −0.344745 0.938696i \(-0.612035\pi\)
−0.344745 + 0.938696i \(0.612035\pi\)
\(312\) 0 0
\(313\) 34.0793i 1.92628i 0.269003 + 0.963139i \(0.413306\pi\)
−0.269003 + 0.963139i \(0.586694\pi\)
\(314\) 0 0
\(315\) −11.4436 47.5252i −0.644772 2.67774i
\(316\) 0 0
\(317\) 3.66161i 0.205657i 0.994699 + 0.102828i \(0.0327892\pi\)
−0.994699 + 0.102828i \(0.967211\pi\)
\(318\) 0 0
\(319\) −16.9882 −0.951157
\(320\) 0 0
\(321\) −5.08225 −0.283663
\(322\) 0 0
\(323\) 15.3510i 0.854150i
\(324\) 0 0
\(325\) 9.33693 + 18.2640i 0.517920 + 1.01311i
\(326\) 0 0
\(327\) 8.87281i 0.490667i
\(328\) 0 0
\(329\) 2.67510 0.147483
\(330\) 0 0
\(331\) −3.50062 −0.192412 −0.0962058 0.995361i \(-0.530671\pi\)
−0.0962058 + 0.995361i \(0.530671\pi\)
\(332\) 0 0
\(333\) 53.8928i 2.95331i
\(334\) 0 0
\(335\) −3.03073 12.5866i −0.165586 0.687680i
\(336\) 0 0
\(337\) 33.3643i 1.81747i −0.417373 0.908735i \(-0.637049\pi\)
0.417373 0.908735i \(-0.362951\pi\)
\(338\) 0 0
\(339\) −36.5336 −1.98423
\(340\) 0 0
\(341\) −7.55791 −0.409284
\(342\) 0 0
\(343\) 28.5450i 1.54128i
\(344\) 0 0
\(345\) 6.09029 1.46648i 0.327890 0.0789525i
\(346\) 0 0
\(347\) 5.80416i 0.311584i −0.987790 0.155792i \(-0.950207\pi\)
0.987790 0.155792i \(-0.0497929\pi\)
\(348\) 0 0
\(349\) 0.496058 0.0265534 0.0132767 0.999912i \(-0.495774\pi\)
0.0132767 + 0.999912i \(0.495774\pi\)
\(350\) 0 0
\(351\) 21.2440 1.13392
\(352\) 0 0
\(353\) 5.80547i 0.308994i 0.987993 + 0.154497i \(0.0493757\pi\)
−0.987993 + 0.154497i \(0.950624\pi\)
\(354\) 0 0
\(355\) −26.0686 + 6.27706i −1.38358 + 0.333152i
\(356\) 0 0
\(357\) 28.6223i 1.51485i
\(358\) 0 0
\(359\) 28.3473 1.49611 0.748057 0.663635i \(-0.230987\pi\)
0.748057 + 0.663635i \(0.230987\pi\)
\(360\) 0 0
\(361\) 26.8984 1.41571
\(362\) 0 0
\(363\) 16.3868i 0.860081i
\(364\) 0 0
\(365\) −0.190326 0.790424i −0.00996212 0.0413727i
\(366\) 0 0
\(367\) 24.2615i 1.26644i −0.773972 0.633219i \(-0.781733\pi\)
0.773972 0.633219i \(-0.218267\pi\)
\(368\) 0 0
\(369\) −40.5732 −2.11216
\(370\) 0 0
\(371\) −7.68832 −0.399158
\(372\) 0 0
\(373\) 22.6261i 1.17153i −0.810479 0.585767i \(-0.800793\pi\)
0.810479 0.585767i \(-0.199207\pi\)
\(374\) 0 0
\(375\) −20.3898 23.7762i −1.05293 1.22780i
\(376\) 0 0
\(377\) 16.9785i 0.874439i
\(378\) 0 0
\(379\) 6.43791 0.330693 0.165347 0.986236i \(-0.447126\pi\)
0.165347 + 0.986236i \(0.447126\pi\)
\(380\) 0 0
\(381\) −33.6993 −1.72647
\(382\) 0 0
\(383\) 14.5145i 0.741657i 0.928701 + 0.370829i \(0.120926\pi\)
−0.928701 + 0.370829i \(0.879074\pi\)
\(384\) 0 0
\(385\) 9.68838 + 40.2359i 0.493766 + 2.05061i
\(386\) 0 0
\(387\) 26.3499i 1.33944i
\(388\) 0 0
\(389\) 26.1850 1.32763 0.663815 0.747897i \(-0.268936\pi\)
0.663815 + 0.747897i \(0.268936\pi\)
\(390\) 0 0
\(391\) 2.26588 0.114590
\(392\) 0 0
\(393\) 3.74882i 0.189103i
\(394\) 0 0
\(395\) −3.81942 + 0.919678i −0.192176 + 0.0462740i
\(396\) 0 0
\(397\) 20.6074i 1.03426i 0.855908 + 0.517129i \(0.172999\pi\)
−0.855908 + 0.517129i \(0.827001\pi\)
\(398\) 0 0
\(399\) 85.5789 4.28430
\(400\) 0 0
\(401\) 12.4900 0.623719 0.311859 0.950128i \(-0.399048\pi\)
0.311859 + 0.950128i \(0.399048\pi\)
\(402\) 0 0
\(403\) 7.55361i 0.376272i
\(404\) 0 0
\(405\) 0.0827001 0.0199133i 0.00410940 0.000989501i
\(406\) 0 0
\(407\) 45.6268i 2.26164i
\(408\) 0 0
\(409\) −9.11740 −0.450826 −0.225413 0.974263i \(-0.572373\pi\)
−0.225413 + 0.974263i \(0.572373\pi\)
\(410\) 0 0
\(411\) −23.9018 −1.17899
\(412\) 0 0
\(413\) 27.9453i 1.37510i
\(414\) 0 0
\(415\) 5.08894 + 21.1344i 0.249806 + 1.03744i
\(416\) 0 0
\(417\) 53.7949i 2.63435i
\(418\) 0 0
\(419\) −7.12358 −0.348010 −0.174005 0.984745i \(-0.555671\pi\)
−0.174005 + 0.984745i \(0.555671\pi\)
\(420\) 0 0
\(421\) 7.13707 0.347840 0.173920 0.984760i \(-0.444357\pi\)
0.173920 + 0.984760i \(0.444357\pi\)
\(422\) 0 0
\(423\) 2.87650i 0.139860i
\(424\) 0 0
\(425\) −5.15700 10.0876i −0.250151 0.489322i
\(426\) 0 0
\(427\) 51.3183i 2.48347i
\(428\) 0 0
\(429\) −47.1764 −2.27770
\(430\) 0 0
\(431\) 14.2840 0.688036 0.344018 0.938963i \(-0.388212\pi\)
0.344018 + 0.938963i \(0.388212\pi\)
\(432\) 0 0
\(433\) 17.5102i 0.841485i 0.907180 + 0.420743i \(0.138230\pi\)
−0.907180 + 0.420743i \(0.861770\pi\)
\(434\) 0 0
\(435\) 6.06922 + 25.2055i 0.290997 + 1.20851i
\(436\) 0 0
\(437\) 6.77484i 0.324084i
\(438\) 0 0
\(439\) 0.991828 0.0473374 0.0236687 0.999720i \(-0.492465\pi\)
0.0236687 + 0.999720i \(0.492465\pi\)
\(440\) 0 0
\(441\) 64.6330 3.07776
\(442\) 0 0
\(443\) 2.99095i 0.142105i 0.997473 + 0.0710523i \(0.0226357\pi\)
−0.997473 + 0.0710523i \(0.977364\pi\)
\(444\) 0 0
\(445\) −37.4368 + 9.01440i −1.77467 + 0.427323i
\(446\) 0 0
\(447\) 39.1250i 1.85055i
\(448\) 0 0
\(449\) −20.8981 −0.986244 −0.493122 0.869960i \(-0.664144\pi\)
−0.493122 + 0.869960i \(0.664144\pi\)
\(450\) 0 0
\(451\) 34.3502 1.61749
\(452\) 0 0
\(453\) 26.2941i 1.23541i
\(454\) 0 0
\(455\) −40.2130 + 9.68287i −1.88521 + 0.453940i
\(456\) 0 0
\(457\) 33.4482i 1.56464i −0.622877 0.782320i \(-0.714036\pi\)
0.622877 0.782320i \(-0.285964\pi\)
\(458\) 0 0
\(459\) −11.7336 −0.547676
\(460\) 0 0
\(461\) 8.53331 0.397436 0.198718 0.980057i \(-0.436322\pi\)
0.198718 + 0.980057i \(0.436322\pi\)
\(462\) 0 0
\(463\) 13.5937i 0.631751i 0.948801 + 0.315876i \(0.102298\pi\)
−0.948801 + 0.315876i \(0.897702\pi\)
\(464\) 0 0
\(465\) 2.70014 + 11.2137i 0.125216 + 0.520023i
\(466\) 0 0
\(467\) 31.3442i 1.45044i −0.688518 0.725219i \(-0.741738\pi\)
0.688518 0.725219i \(-0.258262\pi\)
\(468\) 0 0
\(469\) 26.1059 1.20546
\(470\) 0 0
\(471\) −62.6554 −2.88701
\(472\) 0 0
\(473\) 22.3084i 1.02574i
\(474\) 0 0
\(475\) 30.1614 15.4191i 1.38390 0.707478i
\(476\) 0 0
\(477\) 8.26715i 0.378527i
\(478\) 0 0
\(479\) 20.0701 0.917027 0.458513 0.888687i \(-0.348382\pi\)
0.458513 + 0.888687i \(0.348382\pi\)
\(480\) 0 0
\(481\) −45.6009 −2.07922
\(482\) 0 0
\(483\) 12.6319i 0.574770i
\(484\) 0 0
\(485\) −2.29440 9.52866i −0.104183 0.432674i
\(486\) 0 0
\(487\) 26.8679i 1.21750i −0.793362 0.608750i \(-0.791671\pi\)
0.793362 0.608750i \(-0.208329\pi\)
\(488\) 0 0
\(489\) 16.5660 0.749143
\(490\) 0 0
\(491\) −33.2592 −1.50097 −0.750483 0.660890i \(-0.770179\pi\)
−0.750483 + 0.660890i \(0.770179\pi\)
\(492\) 0 0
\(493\) 9.37764i 0.422348i
\(494\) 0 0
\(495\) 43.2651 10.4178i 1.94462 0.468245i
\(496\) 0 0
\(497\) 54.0690i 2.42533i
\(498\) 0 0
\(499\) −24.4726 −1.09554 −0.547772 0.836627i \(-0.684524\pi\)
−0.547772 + 0.836627i \(0.684524\pi\)
\(500\) 0 0
\(501\) −24.4839 −1.09386
\(502\) 0 0
\(503\) 39.8607i 1.77730i −0.458585 0.888650i \(-0.651644\pi\)
0.458585 0.888650i \(-0.348356\pi\)
\(504\) 0 0
\(505\) 6.98764 1.68255i 0.310946 0.0748726i
\(506\) 0 0
\(507\) 10.7300i 0.476537i
\(508\) 0 0
\(509\) −20.4456 −0.906237 −0.453119 0.891450i \(-0.649689\pi\)
−0.453119 + 0.891450i \(0.649689\pi\)
\(510\) 0 0
\(511\) 1.63942 0.0725237
\(512\) 0 0
\(513\) 35.0826i 1.54894i
\(514\) 0 0
\(515\) 1.09477 + 4.54656i 0.0482411 + 0.200345i
\(516\) 0 0
\(517\) 2.43531i 0.107105i
\(518\) 0 0
\(519\) 29.4955 1.29471
\(520\) 0 0
\(521\) −30.3985 −1.33178 −0.665892 0.746048i \(-0.731949\pi\)
−0.665892 + 0.746048i \(0.731949\pi\)
\(522\) 0 0
\(523\) 4.27912i 0.187113i −0.995614 0.0935564i \(-0.970176\pi\)
0.995614 0.0935564i \(-0.0298235\pi\)
\(524\) 0 0
\(525\) 56.2368 28.7494i 2.45438 1.25473i
\(526\) 0 0
\(527\) 4.17203i 0.181737i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) −30.0492 −1.30402
\(532\) 0 0
\(533\) 34.3306i 1.48703i
\(534\) 0 0
\(535\) −0.949618 3.94376i −0.0410556 0.170504i
\(536\) 0 0
\(537\) 9.23529i 0.398532i
\(538\) 0 0
\(539\) −54.7198 −2.35695
\(540\) 0 0
\(541\) −3.60876 −0.155153 −0.0775764 0.996986i \(-0.524718\pi\)
−0.0775764 + 0.996986i \(0.524718\pi\)
\(542\) 0 0
\(543\) 44.2621i 1.89947i
\(544\) 0 0
\(545\) 6.88519 1.65788i 0.294929 0.0710159i
\(546\) 0 0
\(547\) 30.6519i 1.31058i −0.755377 0.655290i \(-0.772546\pi\)
0.755377 0.655290i \(-0.227454\pi\)
\(548\) 0 0
\(549\) 55.1819 2.35511
\(550\) 0 0
\(551\) −28.0386 −1.19448
\(552\) 0 0
\(553\) 7.92187i 0.336872i
\(554\) 0 0
\(555\) 67.6967 16.3007i 2.87357 0.691925i
\(556\) 0 0
\(557\) 45.9504i 1.94698i −0.228725 0.973491i \(-0.573456\pi\)
0.228725 0.973491i \(-0.426544\pi\)
\(558\) 0 0
\(559\) −22.2957 −0.943009
\(560\) 0 0
\(561\) 26.0566 1.10011
\(562\) 0 0
\(563\) 4.30591i 0.181472i 0.995875 + 0.0907362i \(0.0289220\pi\)
−0.995875 + 0.0907362i \(0.971078\pi\)
\(564\) 0 0
\(565\) −6.82631 28.3497i −0.287185 1.19268i
\(566\) 0 0
\(567\) 0.171528i 0.00720351i
\(568\) 0 0
\(569\) −29.4627 −1.23514 −0.617571 0.786515i \(-0.711883\pi\)
−0.617571 + 0.786515i \(0.711883\pi\)
\(570\) 0 0
\(571\) 31.7317 1.32793 0.663966 0.747763i \(-0.268872\pi\)
0.663966 + 0.747763i \(0.268872\pi\)
\(572\) 0 0
\(573\) 56.0202i 2.34028i
\(574\) 0 0
\(575\) 2.27594 + 4.45198i 0.0949132 + 0.185660i
\(576\) 0 0
\(577\) 24.1386i 1.00490i 0.864606 + 0.502451i \(0.167568\pi\)
−0.864606 + 0.502451i \(0.832432\pi\)
\(578\) 0 0
\(579\) −1.71846 −0.0714169
\(580\) 0 0
\(581\) −43.8348 −1.81857
\(582\) 0 0
\(583\) 6.99915i 0.289875i
\(584\) 0 0
\(585\) 10.4119 + 43.2405i 0.430478 + 1.78777i
\(586\) 0 0
\(587\) 33.9551i 1.40148i −0.713419 0.700738i \(-0.752854\pi\)
0.713419 0.700738i \(-0.247146\pi\)
\(588\) 0 0
\(589\) −12.4741 −0.513988
\(590\) 0 0
\(591\) −12.9989 −0.534702
\(592\) 0 0
\(593\) 6.84201i 0.280968i 0.990083 + 0.140484i \(0.0448658\pi\)
−0.990083 + 0.140484i \(0.955134\pi\)
\(594\) 0 0
\(595\) 22.2105 5.34807i 0.910544 0.219250i
\(596\) 0 0
\(597\) 36.8246i 1.50713i
\(598\) 0 0
\(599\) 26.6172 1.08755 0.543775 0.839231i \(-0.316995\pi\)
0.543775 + 0.839231i \(0.316995\pi\)
\(600\) 0 0
\(601\) 15.0702 0.614728 0.307364 0.951592i \(-0.400553\pi\)
0.307364 + 0.951592i \(0.400553\pi\)
\(602\) 0 0
\(603\) 28.0713i 1.14315i
\(604\) 0 0
\(605\) −12.7159 + 3.06186i −0.516976 + 0.124482i
\(606\) 0 0
\(607\) 43.4205i 1.76238i −0.472761 0.881191i \(-0.656742\pi\)
0.472761 0.881191i \(-0.343258\pi\)
\(608\) 0 0
\(609\) −52.2787 −2.11844
\(610\) 0 0
\(611\) −2.43392 −0.0984660
\(612\) 0 0
\(613\) 4.59633i 0.185644i −0.995683 0.0928220i \(-0.970411\pi\)
0.995683 0.0928220i \(-0.0295888\pi\)
\(614\) 0 0
\(615\) −12.2720 50.9655i −0.494854 2.05513i
\(616\) 0 0
\(617\) 30.4809i 1.22712i 0.789650 + 0.613558i \(0.210262\pi\)
−0.789650 + 0.613558i \(0.789738\pi\)
\(618\) 0 0
\(619\) −37.0511 −1.48921 −0.744605 0.667506i \(-0.767362\pi\)
−0.744605 + 0.667506i \(0.767362\pi\)
\(620\) 0 0
\(621\) 5.17837 0.207801
\(622\) 0 0
\(623\) 77.6477i 3.11089i
\(624\) 0 0
\(625\) 14.6402 20.2649i 0.585608 0.810594i
\(626\) 0 0
\(627\) 77.9078i 3.11134i
\(628\) 0 0
\(629\) 25.1864 1.00425
\(630\) 0 0
\(631\) 29.3035 1.16655 0.583276 0.812274i \(-0.301770\pi\)
0.583276 + 0.812274i \(0.301770\pi\)
\(632\) 0 0
\(633\) 18.9624i 0.753686i
\(634\) 0 0
\(635\) −6.29671 26.1502i −0.249877 1.03774i
\(636\) 0 0
\(637\) 54.6886i 2.16684i
\(638\) 0 0
\(639\) −58.1397 −2.29997
\(640\) 0 0
\(641\) −11.3307 −0.447536 −0.223768 0.974642i \(-0.571836\pi\)
−0.223768 + 0.974642i \(0.571836\pi\)
\(642\) 0 0
\(643\) 28.2340i 1.11344i 0.830700 + 0.556721i \(0.187941\pi\)
−0.830700 + 0.556721i \(0.812059\pi\)
\(644\) 0 0
\(645\) 33.0991 7.96992i 1.30327 0.313815i
\(646\) 0 0
\(647\) 30.0192i 1.18018i −0.807338 0.590089i \(-0.799093\pi\)
0.807338 0.590089i \(-0.200907\pi\)
\(648\) 0 0
\(649\) 25.4403 0.998619
\(650\) 0 0
\(651\) −23.2584 −0.911567
\(652\) 0 0
\(653\) 23.7192i 0.928204i −0.885782 0.464102i \(-0.846377\pi\)
0.885782 0.464102i \(-0.153623\pi\)
\(654\) 0 0
\(655\) 2.90904 0.700467i 0.113666 0.0273695i
\(656\) 0 0
\(657\) 1.76285i 0.0687752i
\(658\) 0 0
\(659\) −16.8488 −0.656336 −0.328168 0.944619i \(-0.606431\pi\)
−0.328168 + 0.944619i \(0.606431\pi\)
\(660\) 0 0
\(661\) −23.4941 −0.913816 −0.456908 0.889514i \(-0.651043\pi\)
−0.456908 + 0.889514i \(0.651043\pi\)
\(662\) 0 0
\(663\) 26.0418i 1.01138i
\(664\) 0 0
\(665\) 15.9904 + 66.4082i 0.620082 + 2.57520i
\(666\) 0 0
\(667\) 4.13863i 0.160249i
\(668\) 0 0
\(669\) 15.3201 0.592308
\(670\) 0 0
\(671\) −46.7182 −1.80354
\(672\) 0 0
\(673\) 19.9329i 0.768358i 0.923259 + 0.384179i \(0.125515\pi\)
−0.923259 + 0.384179i \(0.874485\pi\)
\(674\) 0 0
\(675\) −11.7857 23.0540i −0.453630 0.887349i
\(676\) 0 0
\(677\) 33.9965i 1.30659i −0.757102 0.653296i \(-0.773386\pi\)
0.757102 0.653296i \(-0.226614\pi\)
\(678\) 0 0
\(679\) 19.7634 0.758450
\(680\) 0 0
\(681\) −15.5743 −0.596809
\(682\) 0 0
\(683\) 11.8223i 0.452367i 0.974085 + 0.226183i \(0.0726248\pi\)
−0.974085 + 0.226183i \(0.927375\pi\)
\(684\) 0 0
\(685\) −4.46604 18.5475i −0.170639 0.708663i
\(686\) 0 0
\(687\) 17.7529i 0.677316i
\(688\) 0 0
\(689\) 6.99517 0.266495
\(690\) 0 0
\(691\) 39.0765 1.48654 0.743271 0.668991i \(-0.233273\pi\)
0.743271 + 0.668991i \(0.233273\pi\)
\(692\) 0 0
\(693\) 89.7362i 3.40880i
\(694\) 0 0
\(695\) 41.7442 10.0516i 1.58345 0.381278i
\(696\) 0 0
\(697\) 18.9616i 0.718222i
\(698\) 0 0
\(699\) 27.5824 1.04326
\(700\) 0 0
\(701\) −36.3454 −1.37275 −0.686373 0.727250i \(-0.740798\pi\)
−0.686373 + 0.727250i \(0.740798\pi\)
\(702\) 0 0
\(703\) 75.3059i 2.84021i
\(704\) 0 0
\(705\) 3.61328 0.870040i 0.136084 0.0327676i
\(706\) 0 0
\(707\) 14.4931i 0.545068i
\(708\) 0 0
\(709\) 16.6781 0.626359 0.313179 0.949694i \(-0.398606\pi\)
0.313179 + 0.949694i \(0.398606\pi\)
\(710\) 0 0
\(711\) −8.51829 −0.319461
\(712\) 0 0
\(713\) 1.84124i 0.0689551i
\(714\) 0 0
\(715\) −8.81492 36.6084i −0.329659 1.36907i
\(716\) 0 0
\(717\) 72.7062i 2.71526i
\(718\) 0 0
\(719\) −24.1134 −0.899278 −0.449639 0.893210i \(-0.648447\pi\)
−0.449639 + 0.893210i \(0.648447\pi\)
\(720\) 0 0
\(721\) −9.43003 −0.351193
\(722\) 0 0
\(723\) 34.5201i 1.28382i
\(724\) 0 0
\(725\) −18.4251 + 9.41928i −0.684291 + 0.349823i
\(726\) 0 0
\(727\) 3.05594i 0.113339i −0.998393 0.0566693i \(-0.981952\pi\)
0.998393 0.0566693i \(-0.0180481\pi\)
\(728\) 0 0
\(729\) 43.7062 1.61875
\(730\) 0 0
\(731\) 12.3144 0.455466
\(732\) 0 0
\(733\) 49.2230i 1.81809i −0.416696 0.909046i \(-0.636812\pi\)
0.416696 0.909046i \(-0.363188\pi\)
\(734\) 0 0
\(735\) 19.5492 + 81.1879i 0.721083 + 2.99466i
\(736\) 0 0
\(737\) 23.7658i 0.875425i
\(738\) 0 0
\(739\) 13.1179 0.482548 0.241274 0.970457i \(-0.422435\pi\)
0.241274 + 0.970457i \(0.422435\pi\)
\(740\) 0 0
\(741\) −77.8634 −2.86038
\(742\) 0 0
\(743\) 14.9149i 0.547173i −0.961847 0.273587i \(-0.911790\pi\)
0.961847 0.273587i \(-0.0882100\pi\)
\(744\) 0 0
\(745\) −30.3605 + 7.31050i −1.11232 + 0.267836i
\(746\) 0 0
\(747\) 47.1350i 1.72458i
\(748\) 0 0
\(749\) 8.17977 0.298882
\(750\) 0 0
\(751\) −7.40642 −0.270264 −0.135132 0.990828i \(-0.543146\pi\)
−0.135132 + 0.990828i \(0.543146\pi\)
\(752\) 0 0
\(753\) 21.5379i 0.784884i
\(754\) 0 0
\(755\) −20.4039 + 4.91306i −0.742575 + 0.178804i
\(756\) 0 0
\(757\) 1.37246i 0.0498831i −0.999689 0.0249415i \(-0.992060\pi\)
0.999689 0.0249415i \(-0.00793996\pi\)
\(758\) 0 0
\(759\) −11.4996 −0.417408
\(760\) 0 0
\(761\) −33.9083 −1.22918 −0.614588 0.788849i \(-0.710678\pi\)
−0.614588 + 0.788849i \(0.710678\pi\)
\(762\) 0 0
\(763\) 14.2806i 0.516992i
\(764\) 0 0
\(765\) −5.75071 23.8827i −0.207917 0.863481i
\(766\) 0 0
\(767\) 25.4258i 0.918073i
\(768\) 0 0
\(769\) −7.17267 −0.258653 −0.129327 0.991602i \(-0.541282\pi\)
−0.129327 + 0.991602i \(0.541282\pi\)
\(770\) 0 0
\(771\) 55.2248 1.98887
\(772\) 0 0
\(773\) 3.13634i 0.112806i 0.998408 + 0.0564031i \(0.0179632\pi\)
−0.998408 + 0.0564031i \(0.982037\pi\)
\(774\) 0 0
\(775\) −8.19718 + 4.19056i −0.294451 + 0.150529i
\(776\) 0 0
\(777\) 140.410i 5.03718i
\(778\) 0 0
\(779\) 56.6941 2.03128
\(780\) 0 0
\(781\) 49.2224 1.76131
\(782\) 0 0
\(783\) 21.4314i 0.765896i
\(784\) 0 0
\(785\) −11.7072 48.6198i −0.417846 1.73532i
\(786\) 0 0
\(787\) 0.546252i 0.0194718i −0.999953 0.00973589i \(-0.996901\pi\)
0.999953 0.00973589i \(-0.00309908\pi\)
\(788\) 0 0
\(789\) 8.31586 0.296052
\(790\) 0 0
\(791\) 58.8001 2.09069
\(792\) 0 0
\(793\) 46.6916i 1.65807i
\(794\) 0 0
\(795\) −10.3847 + 2.50052i −0.368306 + 0.0886843i
\(796\) 0 0
\(797\) 45.0453i 1.59559i 0.602931 + 0.797794i \(0.294000\pi\)
−0.602931 + 0.797794i \(0.706000\pi\)
\(798\) 0 0
\(799\) 1.34431 0.0475584
\(800\) 0 0
\(801\) −83.4936 −2.95010
\(802\) 0 0