Properties

Label 920.2.e.c.369.4
Level $920$
Weight $2$
Character 920.369
Analytic conductor $7.346$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} - 1594 x^{7} + 2464 x^{6} + 9568 x^{5} + 15457 x^{4} + 4336 x^{3} + 128 x^{2} - 512 x + 1024\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.4
Root \(-1.13508 - 1.13508i\) of defining polynomial
Character \(\chi\) \(=\) 920.369
Dual form 920.2.e.c.369.13

$q$-expansion

\(f(q)\) \(=\) \(q-2.51561i q^{3} +(-1.92655 - 1.13508i) q^{5} -4.64022i q^{7} -3.32827 q^{9} +O(q^{10})\) \(q-2.51561i q^{3} +(-1.92655 - 1.13508i) q^{5} -4.64022i q^{7} -3.32827 q^{9} -1.64944 q^{11} -1.91631i q^{13} +(-2.85542 + 4.84643i) q^{15} +0.969195i q^{17} +4.91039 q^{19} -11.6730 q^{21} -1.00000i q^{23} +(2.42317 + 4.37359i) q^{25} +0.825798i q^{27} -7.48480 q^{29} +7.77655 q^{31} +4.14935i q^{33} +(-5.26704 + 8.93961i) q^{35} +7.63254i q^{37} -4.82068 q^{39} +5.79719 q^{41} +3.77230i q^{43} +(6.41207 + 3.77787i) q^{45} -2.22605i q^{47} -14.5317 q^{49} +2.43811 q^{51} -11.2963i q^{53} +(3.17773 + 1.87226i) q^{55} -12.3526i q^{57} -10.1233 q^{59} +6.06140 q^{61} +15.4439i q^{63} +(-2.17517 + 3.69186i) q^{65} +12.0618i q^{67} -2.51561 q^{69} +3.01159 q^{71} -16.6439i q^{73} +(11.0022 - 6.09574i) q^{75} +7.65379i q^{77} +0.163787 q^{79} -7.90743 q^{81} +5.66822i q^{83} +(1.10012 - 1.86720i) q^{85} +18.8288i q^{87} +3.90271 q^{89} -8.89211 q^{91} -19.5627i q^{93} +(-9.46010 - 5.57371i) q^{95} +1.79123i q^{97} +5.48979 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 2 q^{5} - 22 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{5} - 22 q^{9} + 14 q^{11} + 6 q^{15} - 22 q^{19} + 12 q^{25} - 44 q^{29} + 18 q^{31} + 20 q^{35} + 14 q^{41} + 14 q^{45} - 78 q^{49} - 38 q^{51} + 30 q^{55} - 64 q^{59} + 34 q^{61} + 6 q^{65} + 6 q^{69} + 30 q^{71} + 56 q^{75} + 4 q^{79} + 48 q^{81} + 52 q^{85} - 92 q^{89} - 70 q^{91} + 38 q^{95} - 122 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 2.51561i 1.45239i −0.687491 0.726193i \(-0.741288\pi\)
0.687491 0.726193i \(-0.258712\pi\)
\(4\) 0 0
\(5\) −1.92655 1.13508i −0.861578 0.507625i
\(6\) 0 0
\(7\) 4.64022i 1.75384i −0.480636 0.876920i \(-0.659594\pi\)
0.480636 0.876920i \(-0.340406\pi\)
\(8\) 0 0
\(9\) −3.32827 −1.10942
\(10\) 0 0
\(11\) −1.64944 −0.497326 −0.248663 0.968590i \(-0.579991\pi\)
−0.248663 + 0.968590i \(0.579991\pi\)
\(12\) 0 0
\(13\) 1.91631i 0.531489i −0.964043 0.265745i \(-0.914382\pi\)
0.964043 0.265745i \(-0.0856178\pi\)
\(14\) 0 0
\(15\) −2.85542 + 4.84643i −0.737267 + 1.25134i
\(16\) 0 0
\(17\) 0.969195i 0.235064i 0.993069 + 0.117532i \(0.0374983\pi\)
−0.993069 + 0.117532i \(0.962502\pi\)
\(18\) 0 0
\(19\) 4.91039 1.12652 0.563261 0.826279i \(-0.309547\pi\)
0.563261 + 0.826279i \(0.309547\pi\)
\(20\) 0 0
\(21\) −11.6730 −2.54725
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 2.42317 + 4.37359i 0.484634 + 0.874717i
\(26\) 0 0
\(27\) 0.825798i 0.158925i
\(28\) 0 0
\(29\) −7.48480 −1.38989 −0.694946 0.719062i \(-0.744572\pi\)
−0.694946 + 0.719062i \(0.744572\pi\)
\(30\) 0 0
\(31\) 7.77655 1.39671 0.698355 0.715751i \(-0.253916\pi\)
0.698355 + 0.715751i \(0.253916\pi\)
\(32\) 0 0
\(33\) 4.14935i 0.722309i
\(34\) 0 0
\(35\) −5.26704 + 8.93961i −0.890293 + 1.51107i
\(36\) 0 0
\(37\) 7.63254i 1.25478i 0.778704 + 0.627391i \(0.215877\pi\)
−0.778704 + 0.627391i \(0.784123\pi\)
\(38\) 0 0
\(39\) −4.82068 −0.771927
\(40\) 0 0
\(41\) 5.79719 0.905368 0.452684 0.891671i \(-0.350466\pi\)
0.452684 + 0.891671i \(0.350466\pi\)
\(42\) 0 0
\(43\) 3.77230i 0.575270i 0.957740 + 0.287635i \(0.0928691\pi\)
−0.957740 + 0.287635i \(0.907131\pi\)
\(44\) 0 0
\(45\) 6.41207 + 3.77787i 0.955855 + 0.563171i
\(46\) 0 0
\(47\) 2.22605i 0.324702i −0.986733 0.162351i \(-0.948092\pi\)
0.986733 0.162351i \(-0.0519077\pi\)
\(48\) 0 0
\(49\) −14.5317 −2.07595
\(50\) 0 0
\(51\) 2.43811 0.341404
\(52\) 0 0
\(53\) 11.2963i 1.55166i −0.630941 0.775831i \(-0.717331\pi\)
0.630941 0.775831i \(-0.282669\pi\)
\(54\) 0 0
\(55\) 3.17773 + 1.87226i 0.428485 + 0.252455i
\(56\) 0 0
\(57\) 12.3526i 1.63614i
\(58\) 0 0
\(59\) −10.1233 −1.31794 −0.658968 0.752171i \(-0.729007\pi\)
−0.658968 + 0.752171i \(0.729007\pi\)
\(60\) 0 0
\(61\) 6.06140 0.776083 0.388042 0.921642i \(-0.373152\pi\)
0.388042 + 0.921642i \(0.373152\pi\)
\(62\) 0 0
\(63\) 15.4439i 1.94575i
\(64\) 0 0
\(65\) −2.17517 + 3.69186i −0.269797 + 0.457919i
\(66\) 0 0
\(67\) 12.0618i 1.47358i 0.676119 + 0.736792i \(0.263660\pi\)
−0.676119 + 0.736792i \(0.736340\pi\)
\(68\) 0 0
\(69\) −2.51561 −0.302843
\(70\) 0 0
\(71\) 3.01159 0.357411 0.178705 0.983903i \(-0.442809\pi\)
0.178705 + 0.983903i \(0.442809\pi\)
\(72\) 0 0
\(73\) 16.6439i 1.94802i −0.226495 0.974012i \(-0.572727\pi\)
0.226495 0.974012i \(-0.427273\pi\)
\(74\) 0 0
\(75\) 11.0022 6.09574i 1.27043 0.703875i
\(76\) 0 0
\(77\) 7.65379i 0.872230i
\(78\) 0 0
\(79\) 0.163787 0.0184275 0.00921377 0.999958i \(-0.497067\pi\)
0.00921377 + 0.999958i \(0.497067\pi\)
\(80\) 0 0
\(81\) −7.90743 −0.878603
\(82\) 0 0
\(83\) 5.66822i 0.622168i 0.950382 + 0.311084i \(0.100692\pi\)
−0.950382 + 0.311084i \(0.899308\pi\)
\(84\) 0 0
\(85\) 1.10012 1.86720i 0.119325 0.202526i
\(86\) 0 0
\(87\) 18.8288i 2.01866i
\(88\) 0 0
\(89\) 3.90271 0.413687 0.206843 0.978374i \(-0.433681\pi\)
0.206843 + 0.978374i \(0.433681\pi\)
\(90\) 0 0
\(91\) −8.89211 −0.932147
\(92\) 0 0
\(93\) 19.5627i 2.02856i
\(94\) 0 0
\(95\) −9.46010 5.57371i −0.970586 0.571850i
\(96\) 0 0
\(97\) 1.79123i 0.181872i 0.995857 + 0.0909362i \(0.0289859\pi\)
−0.995857 + 0.0909362i \(0.971014\pi\)
\(98\) 0 0
\(99\) 5.48979 0.551745
\(100\) 0 0
\(101\) −7.68775 −0.764960 −0.382480 0.923964i \(-0.624930\pi\)
−0.382480 + 0.923964i \(0.624930\pi\)
\(102\) 0 0
\(103\) 2.30773i 0.227387i 0.993516 + 0.113694i \(0.0362682\pi\)
−0.993516 + 0.113694i \(0.963732\pi\)
\(104\) 0 0
\(105\) 22.4885 + 13.2498i 2.19466 + 1.29305i
\(106\) 0 0
\(107\) 10.7032i 1.03472i −0.855768 0.517359i \(-0.826915\pi\)
0.855768 0.517359i \(-0.173085\pi\)
\(108\) 0 0
\(109\) −7.94739 −0.761222 −0.380611 0.924735i \(-0.624286\pi\)
−0.380611 + 0.924735i \(0.624286\pi\)
\(110\) 0 0
\(111\) 19.2005 1.82243
\(112\) 0 0
\(113\) 14.5761i 1.37120i 0.727977 + 0.685602i \(0.240461\pi\)
−0.727977 + 0.685602i \(0.759539\pi\)
\(114\) 0 0
\(115\) −1.13508 + 1.92655i −0.105847 + 0.179651i
\(116\) 0 0
\(117\) 6.37800i 0.589646i
\(118\) 0 0
\(119\) 4.49728 0.412265
\(120\) 0 0
\(121\) −8.27934 −0.752667
\(122\) 0 0
\(123\) 14.5834i 1.31494i
\(124\) 0 0
\(125\) 0.296037 11.1764i 0.0264784 0.999649i
\(126\) 0 0
\(127\) 21.8047i 1.93485i −0.253158 0.967425i \(-0.581469\pi\)
0.253158 0.967425i \(-0.418531\pi\)
\(128\) 0 0
\(129\) 9.48962 0.835514
\(130\) 0 0
\(131\) −3.66922 −0.320581 −0.160290 0.987070i \(-0.551243\pi\)
−0.160290 + 0.987070i \(0.551243\pi\)
\(132\) 0 0
\(133\) 22.7853i 1.97574i
\(134\) 0 0
\(135\) 0.937350 1.59094i 0.0806742 0.136926i
\(136\) 0 0
\(137\) 3.42421i 0.292550i 0.989244 + 0.146275i \(0.0467284\pi\)
−0.989244 + 0.146275i \(0.953272\pi\)
\(138\) 0 0
\(139\) 12.2838 1.04190 0.520950 0.853587i \(-0.325578\pi\)
0.520950 + 0.853587i \(0.325578\pi\)
\(140\) 0 0
\(141\) −5.59985 −0.471593
\(142\) 0 0
\(143\) 3.16085i 0.264323i
\(144\) 0 0
\(145\) 14.4198 + 8.49588i 1.19750 + 0.705544i
\(146\) 0 0
\(147\) 36.5560i 3.01509i
\(148\) 0 0
\(149\) −1.42737 −0.116935 −0.0584675 0.998289i \(-0.518621\pi\)
−0.0584675 + 0.998289i \(0.518621\pi\)
\(150\) 0 0
\(151\) 16.9521 1.37954 0.689772 0.724027i \(-0.257711\pi\)
0.689772 + 0.724027i \(0.257711\pi\)
\(152\) 0 0
\(153\) 3.22574i 0.260786i
\(154\) 0 0
\(155\) −14.9819 8.82704i −1.20338 0.709005i
\(156\) 0 0
\(157\) 19.6335i 1.56693i −0.621438 0.783464i \(-0.713451\pi\)
0.621438 0.783464i \(-0.286549\pi\)
\(158\) 0 0
\(159\) −28.4169 −2.25361
\(160\) 0 0
\(161\) −4.64022 −0.365701
\(162\) 0 0
\(163\) 13.4311i 1.05200i −0.850483 0.526002i \(-0.823690\pi\)
0.850483 0.526002i \(-0.176310\pi\)
\(164\) 0 0
\(165\) 4.70986 7.99392i 0.366662 0.622326i
\(166\) 0 0
\(167\) 2.14523i 0.166003i −0.996549 0.0830013i \(-0.973549\pi\)
0.996549 0.0830013i \(-0.0264506\pi\)
\(168\) 0 0
\(169\) 9.32775 0.717519
\(170\) 0 0
\(171\) −16.3431 −1.24979
\(172\) 0 0
\(173\) 2.04953i 0.155823i −0.996960 0.0779115i \(-0.975175\pi\)
0.996960 0.0779115i \(-0.0248252\pi\)
\(174\) 0 0
\(175\) 20.2944 11.2440i 1.53411 0.849970i
\(176\) 0 0
\(177\) 25.4661i 1.91415i
\(178\) 0 0
\(179\) −18.8683 −1.41028 −0.705140 0.709068i \(-0.749116\pi\)
−0.705140 + 0.709068i \(0.749116\pi\)
\(180\) 0 0
\(181\) −4.49843 −0.334366 −0.167183 0.985926i \(-0.553467\pi\)
−0.167183 + 0.985926i \(0.553467\pi\)
\(182\) 0 0
\(183\) 15.2481i 1.12717i
\(184\) 0 0
\(185\) 8.66358 14.7045i 0.636959 1.08109i
\(186\) 0 0
\(187\) 1.59863i 0.116904i
\(188\) 0 0
\(189\) 3.83189 0.278729
\(190\) 0 0
\(191\) 20.0622 1.45165 0.725823 0.687881i \(-0.241459\pi\)
0.725823 + 0.687881i \(0.241459\pi\)
\(192\) 0 0
\(193\) 4.77197i 0.343494i 0.985141 + 0.171747i \(0.0549412\pi\)
−0.985141 + 0.171747i \(0.945059\pi\)
\(194\) 0 0
\(195\) 9.28727 + 5.47188i 0.665075 + 0.391849i
\(196\) 0 0
\(197\) 15.7807i 1.12433i −0.827026 0.562164i \(-0.809969\pi\)
0.827026 0.562164i \(-0.190031\pi\)
\(198\) 0 0
\(199\) −12.0195 −0.852039 −0.426020 0.904714i \(-0.640085\pi\)
−0.426020 + 0.904714i \(0.640085\pi\)
\(200\) 0 0
\(201\) 30.3427 2.14021
\(202\) 0 0
\(203\) 34.7312i 2.43765i
\(204\) 0 0
\(205\) −11.1686 6.58029i −0.780046 0.459588i
\(206\) 0 0
\(207\) 3.32827i 0.231331i
\(208\) 0 0
\(209\) −8.09942 −0.560248
\(210\) 0 0
\(211\) 16.0791 1.10693 0.553467 0.832871i \(-0.313304\pi\)
0.553467 + 0.832871i \(0.313304\pi\)
\(212\) 0 0
\(213\) 7.57598i 0.519098i
\(214\) 0 0
\(215\) 4.28188 7.26752i 0.292022 0.495640i
\(216\) 0 0
\(217\) 36.0850i 2.44961i
\(218\) 0 0
\(219\) −41.8696 −2.82928
\(220\) 0 0
\(221\) 1.85728 0.124934
\(222\) 0 0
\(223\) 18.2248i 1.22042i −0.792239 0.610211i \(-0.791085\pi\)
0.792239 0.610211i \(-0.208915\pi\)
\(224\) 0 0
\(225\) −8.06496 14.5565i −0.537664 0.970432i
\(226\) 0 0
\(227\) 10.5475i 0.700065i −0.936737 0.350033i \(-0.886170\pi\)
0.936737 0.350033i \(-0.113830\pi\)
\(228\) 0 0
\(229\) −22.0719 −1.45855 −0.729276 0.684219i \(-0.760143\pi\)
−0.729276 + 0.684219i \(0.760143\pi\)
\(230\) 0 0
\(231\) 19.2539 1.26681
\(232\) 0 0
\(233\) 11.9562i 0.783277i 0.920119 + 0.391638i \(0.128092\pi\)
−0.920119 + 0.391638i \(0.871908\pi\)
\(234\) 0 0
\(235\) −2.52675 + 4.28858i −0.164827 + 0.279756i
\(236\) 0 0
\(237\) 0.412025i 0.0267639i
\(238\) 0 0
\(239\) 0.163761 0.0105928 0.00529640 0.999986i \(-0.498314\pi\)
0.00529640 + 0.999986i \(0.498314\pi\)
\(240\) 0 0
\(241\) −6.69099 −0.431004 −0.215502 0.976503i \(-0.569139\pi\)
−0.215502 + 0.976503i \(0.569139\pi\)
\(242\) 0 0
\(243\) 22.3694i 1.43500i
\(244\) 0 0
\(245\) 27.9960 + 16.4947i 1.78860 + 1.05381i
\(246\) 0 0
\(247\) 9.40984i 0.598734i
\(248\) 0 0
\(249\) 14.2590 0.903628
\(250\) 0 0
\(251\) 6.90434 0.435798 0.217899 0.975971i \(-0.430080\pi\)
0.217899 + 0.975971i \(0.430080\pi\)
\(252\) 0 0
\(253\) 1.64944i 0.103700i
\(254\) 0 0
\(255\) −4.69714 2.76746i −0.294146 0.173305i
\(256\) 0 0
\(257\) 25.3210i 1.57948i 0.613440 + 0.789742i \(0.289785\pi\)
−0.613440 + 0.789742i \(0.710215\pi\)
\(258\) 0 0
\(259\) 35.4167 2.20069
\(260\) 0 0
\(261\) 24.9114 1.54198
\(262\) 0 0
\(263\) 9.56021i 0.589508i −0.955573 0.294754i \(-0.904762\pi\)
0.955573 0.294754i \(-0.0952377\pi\)
\(264\) 0 0
\(265\) −12.8222 + 21.7628i −0.787662 + 1.33688i
\(266\) 0 0
\(267\) 9.81768i 0.600832i
\(268\) 0 0
\(269\) 28.7061 1.75024 0.875120 0.483905i \(-0.160782\pi\)
0.875120 + 0.483905i \(0.160782\pi\)
\(270\) 0 0
\(271\) 3.19440 0.194046 0.0970229 0.995282i \(-0.469068\pi\)
0.0970229 + 0.995282i \(0.469068\pi\)
\(272\) 0 0
\(273\) 22.3691i 1.35384i
\(274\) 0 0
\(275\) −3.99688 7.21398i −0.241021 0.435020i
\(276\) 0 0
\(277\) 17.2490i 1.03639i 0.855261 + 0.518197i \(0.173397\pi\)
−0.855261 + 0.518197i \(0.826603\pi\)
\(278\) 0 0
\(279\) −25.8825 −1.54954
\(280\) 0 0
\(281\) 12.1604 0.725430 0.362715 0.931900i \(-0.381850\pi\)
0.362715 + 0.931900i \(0.381850\pi\)
\(282\) 0 0
\(283\) 11.0741i 0.658287i 0.944280 + 0.329144i \(0.106760\pi\)
−0.944280 + 0.329144i \(0.893240\pi\)
\(284\) 0 0
\(285\) −14.0212 + 23.7979i −0.830547 + 1.40967i
\(286\) 0 0
\(287\) 26.9002i 1.58787i
\(288\) 0 0
\(289\) 16.0607 0.944745
\(290\) 0 0
\(291\) 4.50604 0.264149
\(292\) 0 0
\(293\) 21.1811i 1.23741i 0.785623 + 0.618706i \(0.212343\pi\)
−0.785623 + 0.618706i \(0.787657\pi\)
\(294\) 0 0
\(295\) 19.5029 + 11.4908i 1.13551 + 0.669017i
\(296\) 0 0
\(297\) 1.36211i 0.0790374i
\(298\) 0 0
\(299\) −1.91631 −0.110823
\(300\) 0 0
\(301\) 17.5043 1.00893
\(302\) 0 0
\(303\) 19.3393i 1.11102i
\(304\) 0 0
\(305\) −11.6776 6.88020i −0.668656 0.393959i
\(306\) 0 0
\(307\) 20.2792i 1.15739i −0.815543 0.578697i \(-0.803562\pi\)
0.815543 0.578697i \(-0.196438\pi\)
\(308\) 0 0
\(309\) 5.80534 0.330254
\(310\) 0 0
\(311\) 34.4696 1.95459 0.977295 0.211882i \(-0.0679592\pi\)
0.977295 + 0.211882i \(0.0679592\pi\)
\(312\) 0 0
\(313\) 16.4447i 0.929510i 0.885439 + 0.464755i \(0.153858\pi\)
−0.885439 + 0.464755i \(0.846142\pi\)
\(314\) 0 0
\(315\) 17.5301 29.7534i 0.987712 1.67642i
\(316\) 0 0
\(317\) 1.18172i 0.0663720i −0.999449 0.0331860i \(-0.989435\pi\)
0.999449 0.0331860i \(-0.0105654\pi\)
\(318\) 0 0
\(319\) 12.3458 0.691230
\(320\) 0 0
\(321\) −26.9251 −1.50281
\(322\) 0 0
\(323\) 4.75913i 0.264805i
\(324\) 0 0
\(325\) 8.38115 4.64355i 0.464903 0.257578i
\(326\) 0 0
\(327\) 19.9925i 1.10559i
\(328\) 0 0
\(329\) −10.3294 −0.569476
\(330\) 0 0
\(331\) −33.6576 −1.84999 −0.924996 0.379977i \(-0.875932\pi\)
−0.924996 + 0.379977i \(0.875932\pi\)
\(332\) 0 0
\(333\) 25.4032i 1.39208i
\(334\) 0 0
\(335\) 13.6912 23.2376i 0.748028 1.26961i
\(336\) 0 0
\(337\) 5.29846i 0.288625i −0.989532 0.144313i \(-0.953903\pi\)
0.989532 0.144313i \(-0.0460971\pi\)
\(338\) 0 0
\(339\) 36.6677 1.99152
\(340\) 0 0
\(341\) −12.8270 −0.694620
\(342\) 0 0
\(343\) 34.9487i 1.88705i
\(344\) 0 0
\(345\) 4.84643 + 2.85542i 0.260923 + 0.153731i
\(346\) 0 0
\(347\) 33.6842i 1.80826i −0.427256 0.904131i \(-0.640520\pi\)
0.427256 0.904131i \(-0.359480\pi\)
\(348\) 0 0
\(349\) −19.2892 −1.03253 −0.516264 0.856430i \(-0.672678\pi\)
−0.516264 + 0.856430i \(0.672678\pi\)
\(350\) 0 0
\(351\) 1.58249 0.0844668
\(352\) 0 0
\(353\) 6.05334i 0.322187i 0.986939 + 0.161093i \(0.0515020\pi\)
−0.986939 + 0.161093i \(0.948498\pi\)
\(354\) 0 0
\(355\) −5.80198 3.41841i −0.307937 0.181431i
\(356\) 0 0
\(357\) 11.3134i 0.598768i
\(358\) 0 0
\(359\) −15.9564 −0.842149 −0.421074 0.907026i \(-0.638347\pi\)
−0.421074 + 0.907026i \(0.638347\pi\)
\(360\) 0 0
\(361\) 5.11195 0.269050
\(362\) 0 0
\(363\) 20.8275i 1.09316i
\(364\) 0 0
\(365\) −18.8923 + 32.0653i −0.988866 + 1.67838i
\(366\) 0 0
\(367\) 13.7786i 0.719237i 0.933099 + 0.359619i \(0.117093\pi\)
−0.933099 + 0.359619i \(0.882907\pi\)
\(368\) 0 0
\(369\) −19.2946 −1.00444
\(370\) 0 0
\(371\) −52.4172 −2.72137
\(372\) 0 0
\(373\) 13.0667i 0.676566i −0.941044 0.338283i \(-0.890154\pi\)
0.941044 0.338283i \(-0.109846\pi\)
\(374\) 0 0
\(375\) −28.1155 0.744713i −1.45188 0.0384568i
\(376\) 0 0
\(377\) 14.3432i 0.738713i
\(378\) 0 0
\(379\) 36.1458 1.85668 0.928342 0.371727i \(-0.121234\pi\)
0.928342 + 0.371727i \(0.121234\pi\)
\(380\) 0 0
\(381\) −54.8519 −2.81015
\(382\) 0 0
\(383\) 20.4289i 1.04387i 0.852987 + 0.521933i \(0.174789\pi\)
−0.852987 + 0.521933i \(0.825211\pi\)
\(384\) 0 0
\(385\) 8.68769 14.7454i 0.442766 0.751495i
\(386\) 0 0
\(387\) 12.5552i 0.638218i
\(388\) 0 0
\(389\) −37.3561 −1.89403 −0.947015 0.321189i \(-0.895917\pi\)
−0.947015 + 0.321189i \(0.895917\pi\)
\(390\) 0 0
\(391\) 0.969195 0.0490143
\(392\) 0 0
\(393\) 9.23030i 0.465607i
\(394\) 0 0
\(395\) −0.315544 0.185913i −0.0158768 0.00935428i
\(396\) 0 0
\(397\) 9.73956i 0.488814i 0.969673 + 0.244407i \(0.0785934\pi\)
−0.969673 + 0.244407i \(0.921407\pi\)
\(398\) 0 0
\(399\) −57.3189 −2.86953
\(400\) 0 0
\(401\) −26.8802 −1.34233 −0.671166 0.741307i \(-0.734206\pi\)
−0.671166 + 0.741307i \(0.734206\pi\)
\(402\) 0 0
\(403\) 14.9023i 0.742336i
\(404\) 0 0
\(405\) 15.2340 + 8.97560i 0.756985 + 0.446001i
\(406\) 0 0
\(407\) 12.5895i 0.624036i
\(408\) 0 0
\(409\) −23.8307 −1.17835 −0.589175 0.808005i \(-0.700547\pi\)
−0.589175 + 0.808005i \(0.700547\pi\)
\(410\) 0 0
\(411\) 8.61395 0.424895
\(412\) 0 0
\(413\) 46.9742i 2.31145i
\(414\) 0 0
\(415\) 6.43391 10.9201i 0.315828 0.536047i
\(416\) 0 0
\(417\) 30.9012i 1.51324i
\(418\) 0 0
\(419\) −16.8463 −0.822995 −0.411497 0.911411i \(-0.634994\pi\)
−0.411497 + 0.911411i \(0.634994\pi\)
\(420\) 0 0
\(421\) 10.4397 0.508798 0.254399 0.967099i \(-0.418122\pi\)
0.254399 + 0.967099i \(0.418122\pi\)
\(422\) 0 0
\(423\) 7.40888i 0.360232i
\(424\) 0 0
\(425\) −4.23886 + 2.34852i −0.205615 + 0.113920i
\(426\) 0 0
\(427\) 28.1263i 1.36113i
\(428\) 0 0
\(429\) 7.95145 0.383899
\(430\) 0 0
\(431\) 15.3189 0.737886 0.368943 0.929452i \(-0.379720\pi\)
0.368943 + 0.929452i \(0.379720\pi\)
\(432\) 0 0
\(433\) 17.5759i 0.844642i −0.906446 0.422321i \(-0.861216\pi\)
0.906446 0.422321i \(-0.138784\pi\)
\(434\) 0 0
\(435\) 21.3723 36.2746i 1.02472 1.73923i
\(436\) 0 0
\(437\) 4.91039i 0.234896i
\(438\) 0 0
\(439\) −26.7104 −1.27482 −0.637408 0.770527i \(-0.719993\pi\)
−0.637408 + 0.770527i \(0.719993\pi\)
\(440\) 0 0
\(441\) 48.3654 2.30311
\(442\) 0 0
\(443\) 14.9540i 0.710487i −0.934774 0.355243i \(-0.884398\pi\)
0.934774 0.355243i \(-0.115602\pi\)
\(444\) 0 0
\(445\) −7.51876 4.42990i −0.356423 0.209998i
\(446\) 0 0
\(447\) 3.59071i 0.169835i
\(448\) 0 0
\(449\) 6.46847 0.305266 0.152633 0.988283i \(-0.451225\pi\)
0.152633 + 0.988283i \(0.451225\pi\)
\(450\) 0 0
\(451\) −9.56213 −0.450263
\(452\) 0 0
\(453\) 42.6448i 2.00363i
\(454\) 0 0
\(455\) 17.1311 + 10.0933i 0.803117 + 0.473181i
\(456\) 0 0
\(457\) 41.1286i 1.92391i 0.273202 + 0.961957i \(0.411917\pi\)
−0.273202 + 0.961957i \(0.588083\pi\)
\(458\) 0 0
\(459\) −0.800359 −0.0373576
\(460\) 0 0
\(461\) 12.9053 0.601060 0.300530 0.953772i \(-0.402836\pi\)
0.300530 + 0.953772i \(0.402836\pi\)
\(462\) 0 0
\(463\) 6.74237i 0.313344i 0.987651 + 0.156672i \(0.0500766\pi\)
−0.987651 + 0.156672i \(0.949923\pi\)
\(464\) 0 0
\(465\) −22.2054 + 37.6885i −1.02975 + 1.74776i
\(466\) 0 0
\(467\) 9.30704i 0.430678i 0.976539 + 0.215339i \(0.0690857\pi\)
−0.976539 + 0.215339i \(0.930914\pi\)
\(468\) 0 0
\(469\) 55.9695 2.58443
\(470\) 0 0
\(471\) −49.3902 −2.27578
\(472\) 0 0
\(473\) 6.22220i 0.286097i
\(474\) 0 0
\(475\) 11.8987 + 21.4760i 0.545950 + 0.985387i
\(476\) 0 0
\(477\) 37.5970i 1.72145i
\(478\) 0 0
\(479\) −31.6673 −1.44691 −0.723457 0.690370i \(-0.757448\pi\)
−0.723457 + 0.690370i \(0.757448\pi\)
\(480\) 0 0
\(481\) 14.6263 0.666903
\(482\) 0 0
\(483\) 11.6730i 0.531139i
\(484\) 0 0
\(485\) 2.03320 3.45090i 0.0923229 0.156697i
\(486\) 0 0
\(487\) 16.7582i 0.759385i −0.925113 0.379693i \(-0.876030\pi\)
0.925113 0.379693i \(-0.123970\pi\)
\(488\) 0 0
\(489\) −33.7873 −1.52792
\(490\) 0 0
\(491\) 24.5811 1.10933 0.554666 0.832073i \(-0.312846\pi\)
0.554666 + 0.832073i \(0.312846\pi\)
\(492\) 0 0
\(493\) 7.25423i 0.326714i
\(494\) 0 0
\(495\) −10.5763 6.23138i −0.475372 0.280080i
\(496\) 0 0
\(497\) 13.9745i 0.626841i
\(498\) 0 0
\(499\) −2.25368 −0.100888 −0.0504442 0.998727i \(-0.516064\pi\)
−0.0504442 + 0.998727i \(0.516064\pi\)
\(500\) 0 0
\(501\) −5.39654 −0.241100
\(502\) 0 0
\(503\) 10.8452i 0.483566i −0.970330 0.241783i \(-0.922268\pi\)
0.970330 0.241783i \(-0.0777322\pi\)
\(504\) 0 0
\(505\) 14.8108 + 8.72624i 0.659073 + 0.388313i
\(506\) 0 0
\(507\) 23.4649i 1.04211i
\(508\) 0 0
\(509\) −19.6490 −0.870926 −0.435463 0.900207i \(-0.643415\pi\)
−0.435463 + 0.900207i \(0.643415\pi\)
\(510\) 0 0
\(511\) −77.2316 −3.41652
\(512\) 0 0
\(513\) 4.05499i 0.179032i
\(514\) 0 0
\(515\) 2.61947 4.44595i 0.115427 0.195912i
\(516\) 0 0
\(517\) 3.67174i 0.161483i
\(518\) 0 0
\(519\) −5.15581 −0.226315
\(520\) 0 0
\(521\) 19.9000 0.871836 0.435918 0.899986i \(-0.356424\pi\)
0.435918 + 0.899986i \(0.356424\pi\)
\(522\) 0 0
\(523\) 20.4617i 0.894726i 0.894352 + 0.447363i \(0.147637\pi\)
−0.894352 + 0.447363i \(0.852363\pi\)
\(524\) 0 0
\(525\) −28.2856 51.0527i −1.23448 2.22812i
\(526\) 0 0
\(527\) 7.53700i 0.328317i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 33.6930 1.46215
\(532\) 0 0
\(533\) 11.1092i 0.481194i
\(534\) 0 0
\(535\) −12.1490 + 20.6202i −0.525249 + 0.891491i
\(536\) 0 0
\(537\) 47.4651i 2.04827i
\(538\) 0 0
\(539\) 23.9692 1.03243
\(540\) 0 0
\(541\) −4.86543 −0.209181 −0.104591 0.994515i \(-0.533353\pi\)
−0.104591 + 0.994515i \(0.533353\pi\)
\(542\) 0 0
\(543\) 11.3163i 0.485628i
\(544\) 0 0
\(545\) 15.3110 + 9.02096i 0.655852 + 0.386415i
\(546\) 0 0
\(547\) 33.3411i 1.42556i 0.701386 + 0.712781i \(0.252565\pi\)
−0.701386 + 0.712781i \(0.747435\pi\)
\(548\) 0 0
\(549\) −20.1740 −0.861005
\(550\) 0 0
\(551\) −36.7533 −1.56574
\(552\) 0 0
\(553\) 0.760011i 0.0323189i
\(554\) 0 0
\(555\) −36.9906 21.7941i −1.57016 0.925110i
\(556\) 0 0
\(557\) 19.3928i 0.821697i −0.911704 0.410849i \(-0.865232\pi\)
0.911704 0.410849i \(-0.134768\pi\)
\(558\) 0 0
\(559\) 7.22890 0.305750
\(560\) 0 0
\(561\) −4.02153 −0.169789
\(562\) 0 0
\(563\) 7.49245i 0.315769i 0.987458 + 0.157884i \(0.0504674\pi\)
−0.987458 + 0.157884i \(0.949533\pi\)
\(564\) 0 0
\(565\) 16.5451 28.0815i 0.696057 1.18140i
\(566\) 0 0
\(567\) 36.6922i 1.54093i
\(568\) 0 0
\(569\) 3.26375 0.136823 0.0684117 0.997657i \(-0.478207\pi\)
0.0684117 + 0.997657i \(0.478207\pi\)
\(570\) 0 0
\(571\) 14.9738 0.626636 0.313318 0.949648i \(-0.398559\pi\)
0.313318 + 0.949648i \(0.398559\pi\)
\(572\) 0 0
\(573\) 50.4685i 2.10835i
\(574\) 0 0
\(575\) 4.37359 2.42317i 0.182391 0.101053i
\(576\) 0 0
\(577\) 21.5111i 0.895520i −0.894154 0.447760i \(-0.852222\pi\)
0.894154 0.447760i \(-0.147778\pi\)
\(578\) 0 0
\(579\) 12.0044 0.498886
\(580\) 0 0
\(581\) 26.3018 1.09118
\(582\) 0 0
\(583\) 18.6326i 0.771681i
\(584\) 0 0
\(585\) 7.23957 12.2875i 0.299319 0.508026i
\(586\) 0 0
\(587\) 1.76395i 0.0728059i 0.999337 + 0.0364030i \(0.0115900\pi\)
−0.999337 + 0.0364030i \(0.988410\pi\)
\(588\) 0 0
\(589\) 38.1859 1.57342
\(590\) 0 0
\(591\) −39.6980 −1.63296
\(592\) 0 0
\(593\) 8.68465i 0.356636i 0.983973 + 0.178318i \(0.0570656\pi\)
−0.983973 + 0.178318i \(0.942934\pi\)
\(594\) 0 0
\(595\) −8.66423 5.10479i −0.355199 0.209276i
\(596\) 0 0
\(597\) 30.2363i 1.23749i
\(598\) 0 0
\(599\) 23.3988 0.956049 0.478024 0.878347i \(-0.341353\pi\)
0.478024 + 0.878347i \(0.341353\pi\)
\(600\) 0 0
\(601\) 21.0536 0.858794 0.429397 0.903116i \(-0.358726\pi\)
0.429397 + 0.903116i \(0.358726\pi\)
\(602\) 0 0
\(603\) 40.1450i 1.63483i
\(604\) 0 0
\(605\) 15.9505 + 9.39774i 0.648481 + 0.382072i
\(606\) 0 0
\(607\) 35.0489i 1.42259i −0.702892 0.711296i \(-0.748108\pi\)
0.702892 0.711296i \(-0.251892\pi\)
\(608\) 0 0
\(609\) 87.3699 3.54041
\(610\) 0 0
\(611\) −4.26580 −0.172576
\(612\) 0 0
\(613\) 27.5922i 1.11444i 0.830365 + 0.557219i \(0.188132\pi\)
−0.830365 + 0.557219i \(0.811868\pi\)
\(614\) 0 0
\(615\) −16.5534 + 28.0957i −0.667498 + 1.13293i
\(616\) 0 0
\(617\) 8.22209i 0.331009i −0.986209 0.165504i \(-0.947075\pi\)
0.986209 0.165504i \(-0.0529252\pi\)
\(618\) 0 0
\(619\) 19.5042 0.783940 0.391970 0.919978i \(-0.371794\pi\)
0.391970 + 0.919978i \(0.371794\pi\)
\(620\) 0 0
\(621\) 0.825798 0.0331381
\(622\) 0 0
\(623\) 18.1095i 0.725540i
\(624\) 0 0
\(625\) −13.2565 + 21.1959i −0.530260 + 0.847835i
\(626\) 0 0
\(627\) 20.3749i 0.813696i
\(628\) 0 0
\(629\) −7.39742 −0.294955
\(630\) 0 0
\(631\) −7.59833 −0.302485 −0.151242 0.988497i \(-0.548327\pi\)
−0.151242 + 0.988497i \(0.548327\pi\)
\(632\) 0 0
\(633\) 40.4488i 1.60770i
\(634\) 0 0
\(635\) −24.7501 + 42.0077i −0.982178 + 1.66702i
\(636\) 0 0
\(637\) 27.8472i 1.10335i
\(638\) 0 0
\(639\) −10.0234 −0.396520
\(640\) 0 0
\(641\) −2.02749 −0.0800809 −0.0400405 0.999198i \(-0.512749\pi\)
−0.0400405 + 0.999198i \(0.512749\pi\)
\(642\) 0 0
\(643\) 21.7200i 0.856554i −0.903647 0.428277i \(-0.859121\pi\)
0.903647 0.428277i \(-0.140879\pi\)
\(644\) 0 0
\(645\) −18.2822 10.7715i −0.719861 0.424128i
\(646\) 0 0
\(647\) 12.3675i 0.486216i −0.969999 0.243108i \(-0.921833\pi\)
0.969999 0.243108i \(-0.0781670\pi\)
\(648\) 0 0
\(649\) 16.6978 0.655444
\(650\) 0 0
\(651\) −90.7755 −3.55777
\(652\) 0 0
\(653\) 24.8363i 0.971921i 0.873981 + 0.485960i \(0.161530\pi\)
−0.873981 + 0.485960i \(0.838470\pi\)
\(654\) 0 0
\(655\) 7.06892 + 4.16487i 0.276205 + 0.162735i
\(656\) 0 0
\(657\) 55.3955i 2.16118i
\(658\) 0 0
\(659\) 29.4867 1.14864 0.574319 0.818631i \(-0.305267\pi\)
0.574319 + 0.818631i \(0.305267\pi\)
\(660\) 0 0
\(661\) 42.3911 1.64882 0.824411 0.565992i \(-0.191507\pi\)
0.824411 + 0.565992i \(0.191507\pi\)
\(662\) 0 0
\(663\) 4.67218i 0.181452i
\(664\) 0 0
\(665\) −25.8633 + 43.8970i −1.00293 + 1.70225i
\(666\) 0 0
\(667\) 7.48480i 0.289813i
\(668\) 0 0
\(669\) −45.8464 −1.77252
\(670\) 0 0
\(671\) −9.99794 −0.385966
\(672\) 0 0
\(673\) 20.5867i 0.793559i −0.917914 0.396779i \(-0.870128\pi\)
0.917914 0.396779i \(-0.129872\pi\)
\(674\) 0 0
\(675\) −3.61170 + 2.00105i −0.139014 + 0.0770203i
\(676\) 0 0
\(677\) 12.8416i 0.493545i 0.969073 + 0.246772i \(0.0793700\pi\)
−0.969073 + 0.246772i \(0.920630\pi\)
\(678\) 0 0
\(679\) 8.31173 0.318975
\(680\) 0 0
\(681\) −26.5335 −1.01676
\(682\) 0 0
\(683\) 47.1531i 1.80426i −0.431460 0.902132i \(-0.642001\pi\)
0.431460 0.902132i \(-0.357999\pi\)
\(684\) 0 0
\(685\) 3.88676 6.59690i 0.148506 0.252054i
\(686\) 0 0
\(687\) 55.5242i 2.11838i
\(688\) 0 0
\(689\) −21.6472 −0.824691
\(690\) 0 0
\(691\) 29.9278 1.13851 0.569253 0.822163i \(-0.307233\pi\)
0.569253 + 0.822163i \(0.307233\pi\)
\(692\) 0 0
\(693\) 25.4739i 0.967673i
\(694\) 0 0
\(695\) −23.6653 13.9432i −0.897678 0.528894i
\(696\) 0 0
\(697\) 5.61860i 0.212820i
\(698\) 0 0
\(699\) 30.0771 1.13762
\(700\) 0 0
\(701\) 15.7689 0.595585 0.297793 0.954631i \(-0.403750\pi\)
0.297793 + 0.954631i \(0.403750\pi\)
\(702\) 0 0
\(703\) 37.4788i 1.41354i
\(704\) 0 0
\(705\) 10.7884 + 6.35630i 0.406314 + 0.239392i
\(706\) 0 0
\(707\) 35.6729i 1.34162i
\(708\) 0 0
\(709\) 0.221825 0.00833080 0.00416540 0.999991i \(-0.498674\pi\)
0.00416540 + 0.999991i \(0.498674\pi\)
\(710\) 0 0
\(711\) −0.545129 −0.0204439
\(712\) 0 0
\(713\) 7.77655i 0.291234i
\(714\) 0 0
\(715\) 3.58783 6.08952i 0.134177 0.227735i
\(716\) 0 0
\(717\) 0.411958i 0.0153848i
\(718\) 0 0
\(719\) 43.2546 1.61312 0.806562 0.591149i \(-0.201325\pi\)
0.806562 + 0.591149i \(0.201325\pi\)
\(720\) 0 0
\(721\) 10.7084 0.398801
\(722\) 0 0
\(723\) 16.8319i 0.625984i
\(724\) 0 0
\(725\) −18.1369 32.7354i −0.673589 1.21576i
\(726\) 0 0
\(727\) 8.90379i 0.330223i 0.986275 + 0.165112i \(0.0527985\pi\)
−0.986275 + 0.165112i \(0.947202\pi\)
\(728\) 0 0
\(729\) 32.5502 1.20556
\(730\) 0 0
\(731\) −3.65609 −0.135226
\(732\) 0 0
\(733\) 14.0655i 0.519521i 0.965673 + 0.259761i \(0.0836436\pi\)
−0.965673 + 0.259761i \(0.916356\pi\)
\(734\) 0 0
\(735\) 41.4941 70.4268i 1.53053 2.59773i
\(736\) 0 0
\(737\) 19.8953i 0.732852i
\(738\) 0 0
\(739\) 37.4096 1.37614 0.688068 0.725646i \(-0.258459\pi\)
0.688068 + 0.725646i \(0.258459\pi\)
\(740\) 0 0
\(741\) −23.6714 −0.869592
\(742\) 0 0
\(743\) 7.48682i 0.274665i 0.990525 + 0.137332i \(0.0438528\pi\)
−0.990525 + 0.137332i \(0.956147\pi\)
\(744\) 0 0
\(745\) 2.74990 + 1.62019i 0.100749 + 0.0593591i
\(746\) 0 0
\(747\) 18.8654i 0.690248i
\(748\) 0 0
\(749\) −49.6653 −1.81473
\(750\) 0 0
\(751\) 29.0524 1.06014 0.530069 0.847955i \(-0.322166\pi\)
0.530069 + 0.847955i \(0.322166\pi\)
\(752\) 0 0
\(753\) 17.3686i 0.632947i
\(754\) 0 0
\(755\) −32.6591 19.2421i −1.18858 0.700291i
\(756\) 0 0
\(757\) 52.0910i 1.89328i −0.322295 0.946639i \(-0.604454\pi\)
0.322295 0.946639i \(-0.395546\pi\)
\(758\) 0 0
\(759\) 4.14935 0.150612
\(760\) 0 0
\(761\) 21.8693 0.792762 0.396381 0.918086i \(-0.370266\pi\)
0.396381 + 0.918086i \(0.370266\pi\)
\(762\) 0 0
\(763\) 36.8777i 1.33506i
\(764\) 0 0
\(765\) −3.66149 + 6.21455i −0.132381 + 0.224687i
\(766\) 0 0
\(767\) 19.3993i 0.700469i
\(768\) 0 0
\(769\) −40.9646 −1.47722 −0.738611 0.674132i \(-0.764518\pi\)
−0.738611 + 0.674132i \(0.764518\pi\)
\(770\) 0 0
\(771\) 63.6977 2.29402
\(772\) 0 0
\(773\) 31.3674i 1.12821i 0.825704 + 0.564103i \(0.190778\pi\)
−0.825704 + 0.564103i \(0.809222\pi\)
\(774\) 0 0
\(775\) 18.8439 + 34.0114i 0.676893 + 1.22173i
\(776\) 0 0
\(777\) 89.0945i 3.19625i
\(778\) 0 0
\(779\) 28.4665 1.01992
\(780\) 0 0
\(781\) −4.96746 −0.177750
\(782\) 0 0
\(783\) 6.18093i 0.220888i
\(784\) 0 0
\(785\) −22.2857 + 37.8249i −0.795411 + 1.35003i
\(786\) 0 0
\(787\) 17.8694i 0.636977i 0.947927 + 0.318489i \(0.103175\pi\)
−0.947927 + 0.318489i \(0.896825\pi\)
\(788\) 0 0
\(789\) −24.0497 −0.856192
\(790\) 0 0
\(791\) 67.6364 2.40487
\(792\) 0 0
\(793\) 11.6155i 0.412480i
\(794\) 0 0
\(795\) 54.7466 + 32.2556i 1.94166 + 1.14399i
\(796\) 0 0
\(797\) 22.0293i 0.780319i 0.920747 + 0.390159i \(0.127580\pi\)
−0.920747 + 0.390159i \(0.872420\pi\)
\(798\) 0 0
\(799\) 2.15747 0.0763259
\(800\) 0 0
\(801\) −12.9893 −0.458953
\(802\) 0 0