Properties

Label 1840.2.e.g.369.3
Level $1840$
Weight $2$
Character 1840.369
Analytic conductor $14.692$
Analytic rank $0$
Dimension $14$
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 2 x^{11} + 39 x^{10} - 10 x^{9} + 2 x^{8} - 26 x^{7} + 297 x^{6} - 116 x^{5} + 24 x^{4} - 20 x^{3} + 64 x^{2} - 32 x + 8\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 920)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.3
Root \(-1.27121 - 1.27121i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.g.369.12

$q$-expansion

\(f(q)\) \(=\) \(q-1.78665i q^{3} +(1.46089 + 1.69287i) q^{5} +1.75578i q^{7} -0.192116 q^{9} +O(q^{10})\) \(q-1.78665i q^{3} +(1.46089 + 1.69287i) q^{5} +1.75578i q^{7} -0.192116 q^{9} +4.77574 q^{11} +1.72967i q^{13} +(3.02456 - 2.61010i) q^{15} +7.81453i q^{17} -2.43970 q^{19} +3.13696 q^{21} +1.00000i q^{23} +(-0.731587 + 4.94619i) q^{25} -5.01670i q^{27} -7.86235 q^{29} -6.14217 q^{31} -8.53258i q^{33} +(-2.97230 + 2.56501i) q^{35} +6.83324i q^{37} +3.09031 q^{39} -2.50416 q^{41} +3.26755i q^{43} +(-0.280660 - 0.325226i) q^{45} +8.46487i q^{47} +3.91724 q^{49} +13.9618 q^{51} -2.76559i q^{53} +(6.97685 + 8.08469i) q^{55} +4.35889i q^{57} +1.91706 q^{59} -3.50364 q^{61} -0.337313i q^{63} +(-2.92810 + 2.52686i) q^{65} -12.7649i q^{67} +1.78665 q^{69} +13.3973 q^{71} +0.0111737i q^{73} +(8.83710 + 1.30709i) q^{75} +8.38515i q^{77} -16.6960 q^{79} -9.53944 q^{81} +2.64145i q^{83} +(-13.2289 + 11.4162i) q^{85} +14.0473i q^{87} +13.1729 q^{89} -3.03692 q^{91} +10.9739i q^{93} +(-3.56414 - 4.13009i) q^{95} -15.8568i q^{97} -0.917494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{5} - 4q^{9} + O(q^{10}) \) \( 14q + 2q^{5} - 4q^{9} + 14q^{11} + 6q^{15} - 14q^{19} - 12q^{21} - 14q^{25} + 22q^{29} + 20q^{31} + 2q^{35} - 48q^{39} - 32q^{41} - 26q^{45} + 34q^{49} + 14q^{51} + 38q^{55} - 22q^{59} + 10q^{61} - 38q^{65} + 6q^{69} + 28q^{71} + 24q^{75} - 64q^{79} - 10q^{81} - 50q^{85} + 48q^{89} + 14q^{91} + 30q^{95} - 122q^{99} + O(q^{100}) \)

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
\(3\) 1.78665i 1.03152i −0.856732 0.515761i \(-0.827509\pi\)
0.856732 0.515761i \(-0.172491\pi\)
\(4\) 0 0
\(5\) 1.46089 + 1.69287i 0.653331 + 0.757072i
\(6\) 0 0
\(7\) 1.75578i 0.663622i 0.943346 + 0.331811i \(0.107660\pi\)
−0.943346 + 0.331811i \(0.892340\pi\)
\(8\) 0 0
\(9\) −0.192116 −0.0640385
\(10\) 0 0
\(11\) 4.77574 1.43994 0.719970 0.694005i \(-0.244155\pi\)
0.719970 + 0.694005i \(0.244155\pi\)
\(12\) 0 0
\(13\) 1.72967i 0.479724i 0.970807 + 0.239862i \(0.0771022\pi\)
−0.970807 + 0.239862i \(0.922898\pi\)
\(14\) 0 0
\(15\) 3.02456 2.61010i 0.780937 0.673926i
\(16\) 0 0
\(17\) 7.81453i 1.89530i 0.319309 + 0.947651i \(0.396549\pi\)
−0.319309 + 0.947651i \(0.603451\pi\)
\(18\) 0 0
\(19\) −2.43970 −0.559706 −0.279853 0.960043i \(-0.590286\pi\)
−0.279853 + 0.960043i \(0.590286\pi\)
\(20\) 0 0
\(21\) 3.13696 0.684541
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −0.731587 + 4.94619i −0.146317 + 0.989238i
\(26\) 0 0
\(27\) 5.01670i 0.965465i
\(28\) 0 0
\(29\) −7.86235 −1.46000 −0.730001 0.683446i \(-0.760480\pi\)
−0.730001 + 0.683446i \(0.760480\pi\)
\(30\) 0 0
\(31\) −6.14217 −1.10317 −0.551583 0.834120i \(-0.685976\pi\)
−0.551583 + 0.834120i \(0.685976\pi\)
\(32\) 0 0
\(33\) 8.53258i 1.48533i
\(34\) 0 0
\(35\) −2.97230 + 2.56501i −0.502410 + 0.433565i
\(36\) 0 0
\(37\) 6.83324i 1.12338i 0.827349 + 0.561689i \(0.189848\pi\)
−0.827349 + 0.561689i \(0.810152\pi\)
\(38\) 0 0
\(39\) 3.09031 0.494846
\(40\) 0 0
\(41\) −2.50416 −0.391084 −0.195542 0.980695i \(-0.562647\pi\)
−0.195542 + 0.980695i \(0.562647\pi\)
\(42\) 0 0
\(43\) 3.26755i 0.498297i 0.968465 + 0.249148i \(0.0801507\pi\)
−0.968465 + 0.249148i \(0.919849\pi\)
\(44\) 0 0
\(45\) −0.280660 0.325226i −0.0418383 0.0484818i
\(46\) 0 0
\(47\) 8.46487i 1.23473i 0.786678 + 0.617364i \(0.211799\pi\)
−0.786678 + 0.617364i \(0.788201\pi\)
\(48\) 0 0
\(49\) 3.91724 0.559605
\(50\) 0 0
\(51\) 13.9618 1.95505
\(52\) 0 0
\(53\) 2.76559i 0.379883i −0.981795 0.189942i \(-0.939170\pi\)
0.981795 0.189942i \(-0.0608299\pi\)
\(54\) 0 0
\(55\) 6.97685 + 8.08469i 0.940758 + 1.09014i
\(56\) 0 0
\(57\) 4.35889i 0.577349i
\(58\) 0 0
\(59\) 1.91706 0.249580 0.124790 0.992183i \(-0.460174\pi\)
0.124790 + 0.992183i \(0.460174\pi\)
\(60\) 0 0
\(61\) −3.50364 −0.448595 −0.224297 0.974521i \(-0.572009\pi\)
−0.224297 + 0.974521i \(0.572009\pi\)
\(62\) 0 0
\(63\) 0.337313i 0.0424974i
\(64\) 0 0
\(65\) −2.92810 + 2.52686i −0.363186 + 0.313418i
\(66\) 0 0
\(67\) 12.7649i 1.55948i −0.626102 0.779741i \(-0.715351\pi\)
0.626102 0.779741i \(-0.284649\pi\)
\(68\) 0 0
\(69\) 1.78665 0.215087
\(70\) 0 0
\(71\) 13.3973 1.58997 0.794984 0.606630i \(-0.207479\pi\)
0.794984 + 0.606630i \(0.207479\pi\)
\(72\) 0 0
\(73\) 0.0111737i 0.00130778i 1.00000 0.000653890i \(0.000208140\pi\)
−1.00000 0.000653890i \(0.999792\pi\)
\(74\) 0 0
\(75\) 8.83710 + 1.30709i 1.02042 + 0.150930i
\(76\) 0 0
\(77\) 8.38515i 0.955577i
\(78\) 0 0
\(79\) −16.6960 −1.87844 −0.939222 0.343310i \(-0.888452\pi\)
−0.939222 + 0.343310i \(0.888452\pi\)
\(80\) 0 0
\(81\) −9.53944 −1.05994
\(82\) 0 0
\(83\) 2.64145i 0.289937i 0.989436 + 0.144969i \(0.0463081\pi\)
−0.989436 + 0.144969i \(0.953692\pi\)
\(84\) 0 0
\(85\) −13.2289 + 11.4162i −1.43488 + 1.23826i
\(86\) 0 0
\(87\) 14.0473i 1.50602i
\(88\) 0 0
\(89\) 13.1729 1.39632 0.698160 0.715942i \(-0.254002\pi\)
0.698160 + 0.715942i \(0.254002\pi\)
\(90\) 0 0
\(91\) −3.03692 −0.318356
\(92\) 0 0
\(93\) 10.9739i 1.13794i
\(94\) 0 0
\(95\) −3.56414 4.13009i −0.365673 0.423738i
\(96\) 0 0
\(97\) 15.8568i 1.61001i −0.593268 0.805005i \(-0.702162\pi\)
0.593268 0.805005i \(-0.297838\pi\)
\(98\) 0 0
\(99\) −0.917494 −0.0922117
\(100\) 0 0
\(101\) 15.6987 1.56208 0.781040 0.624481i \(-0.214689\pi\)
0.781040 + 0.624481i \(0.214689\pi\)
\(102\) 0 0
\(103\) 8.37467i 0.825180i −0.910917 0.412590i \(-0.864624\pi\)
0.910917 0.412590i \(-0.135376\pi\)
\(104\) 0 0
\(105\) 4.58277 + 5.31046i 0.447232 + 0.518247i
\(106\) 0 0
\(107\) 6.52262i 0.630565i −0.948998 0.315283i \(-0.897901\pi\)
0.948998 0.315283i \(-0.102099\pi\)
\(108\) 0 0
\(109\) 8.11474 0.777251 0.388626 0.921396i \(-0.372950\pi\)
0.388626 + 0.921396i \(0.372950\pi\)
\(110\) 0 0
\(111\) 12.2086 1.15879
\(112\) 0 0
\(113\) 12.9224i 1.21563i −0.794077 0.607817i \(-0.792045\pi\)
0.794077 0.607817i \(-0.207955\pi\)
\(114\) 0 0
\(115\) −1.69287 + 1.46089i −0.157861 + 0.136229i
\(116\) 0 0
\(117\) 0.332296i 0.0307208i
\(118\) 0 0
\(119\) −13.7206 −1.25776
\(120\) 0 0
\(121\) 11.8077 1.07343
\(122\) 0 0
\(123\) 4.47406i 0.403412i
\(124\) 0 0
\(125\) −9.44200 + 5.98737i −0.844518 + 0.535527i
\(126\) 0 0
\(127\) 7.05406i 0.625947i 0.949762 + 0.312973i \(0.101325\pi\)
−0.949762 + 0.312973i \(0.898675\pi\)
\(128\) 0 0
\(129\) 5.83797 0.514004
\(130\) 0 0
\(131\) 11.1585 0.974923 0.487461 0.873145i \(-0.337923\pi\)
0.487461 + 0.873145i \(0.337923\pi\)
\(132\) 0 0
\(133\) 4.28358i 0.371434i
\(134\) 0 0
\(135\) 8.49261 7.32887i 0.730927 0.630768i
\(136\) 0 0
\(137\) 2.71462i 0.231926i −0.993254 0.115963i \(-0.963005\pi\)
0.993254 0.115963i \(-0.0369953\pi\)
\(138\) 0 0
\(139\) 13.0913 1.11039 0.555197 0.831719i \(-0.312643\pi\)
0.555197 + 0.831719i \(0.312643\pi\)
\(140\) 0 0
\(141\) 15.1238 1.27365
\(142\) 0 0
\(143\) 8.26046i 0.690774i
\(144\) 0 0
\(145\) −11.4861 13.3099i −0.953865 1.10533i
\(146\) 0 0
\(147\) 6.99873i 0.577245i
\(148\) 0 0
\(149\) 12.0898 0.990435 0.495217 0.868769i \(-0.335088\pi\)
0.495217 + 0.868769i \(0.335088\pi\)
\(150\) 0 0
\(151\) −14.9430 −1.21604 −0.608021 0.793921i \(-0.708036\pi\)
−0.608021 + 0.793921i \(0.708036\pi\)
\(152\) 0 0
\(153\) 1.50129i 0.121372i
\(154\) 0 0
\(155\) −8.97305 10.3979i −0.720732 0.835177i
\(156\) 0 0
\(157\) 4.78395i 0.381800i −0.981609 0.190900i \(-0.938859\pi\)
0.981609 0.190900i \(-0.0611407\pi\)
\(158\) 0 0
\(159\) −4.94114 −0.391858
\(160\) 0 0
\(161\) −1.75578 −0.138375
\(162\) 0 0
\(163\) 5.49063i 0.430059i −0.976608 0.215030i \(-0.931015\pi\)
0.976608 0.215030i \(-0.0689848\pi\)
\(164\) 0 0
\(165\) 14.4445 12.4652i 1.12450 0.970413i
\(166\) 0 0
\(167\) 7.26932i 0.562517i −0.959632 0.281258i \(-0.909248\pi\)
0.959632 0.281258i \(-0.0907518\pi\)
\(168\) 0 0
\(169\) 10.0082 0.769865
\(170\) 0 0
\(171\) 0.468705 0.0358427
\(172\) 0 0
\(173\) 7.50892i 0.570893i −0.958395 0.285446i \(-0.907858\pi\)
0.958395 0.285446i \(-0.0921418\pi\)
\(174\) 0 0
\(175\) −8.68442 1.28451i −0.656480 0.0970995i
\(176\) 0 0
\(177\) 3.42511i 0.257447i
\(178\) 0 0
\(179\) −5.73414 −0.428590 −0.214295 0.976769i \(-0.568745\pi\)
−0.214295 + 0.976769i \(0.568745\pi\)
\(180\) 0 0
\(181\) 25.2262 1.87505 0.937523 0.347923i \(-0.113113\pi\)
0.937523 + 0.347923i \(0.113113\pi\)
\(182\) 0 0
\(183\) 6.25977i 0.462736i
\(184\) 0 0
\(185\) −11.5678 + 9.98263i −0.850478 + 0.733937i
\(186\) 0 0
\(187\) 37.3202i 2.72912i
\(188\) 0 0
\(189\) 8.80823 0.640704
\(190\) 0 0
\(191\) −3.63151 −0.262767 −0.131383 0.991332i \(-0.541942\pi\)
−0.131383 + 0.991332i \(0.541942\pi\)
\(192\) 0 0
\(193\) 21.7050i 1.56236i 0.624307 + 0.781179i \(0.285381\pi\)
−0.624307 + 0.781179i \(0.714619\pi\)
\(194\) 0 0
\(195\) 4.51461 + 5.23148i 0.323298 + 0.374634i
\(196\) 0 0
\(197\) 7.26526i 0.517628i −0.965927 0.258814i \(-0.916668\pi\)
0.965927 0.258814i \(-0.0833317\pi\)
\(198\) 0 0
\(199\) 6.52705 0.462690 0.231345 0.972872i \(-0.425687\pi\)
0.231345 + 0.972872i \(0.425687\pi\)
\(200\) 0 0
\(201\) −22.8064 −1.60864
\(202\) 0 0
\(203\) 13.8046i 0.968890i
\(204\) 0 0
\(205\) −3.65831 4.23921i −0.255508 0.296079i
\(206\) 0 0
\(207\) 0.192116i 0.0133530i
\(208\) 0 0
\(209\) −11.6514 −0.805944
\(210\) 0 0
\(211\) 22.7856 1.56863 0.784313 0.620365i \(-0.213016\pi\)
0.784313 + 0.620365i \(0.213016\pi\)
\(212\) 0 0
\(213\) 23.9363i 1.64009i
\(214\) 0 0
\(215\) −5.53152 + 4.77354i −0.377247 + 0.325553i
\(216\) 0 0
\(217\) 10.7843i 0.732086i
\(218\) 0 0
\(219\) 0.0199634 0.00134900
\(220\) 0 0
\(221\) −13.5165 −0.909221
\(222\) 0 0
\(223\) 6.86315i 0.459591i −0.973239 0.229795i \(-0.926194\pi\)
0.973239 0.229795i \(-0.0738057\pi\)
\(224\) 0 0
\(225\) 0.140549 0.950240i 0.00936995 0.0633493i
\(226\) 0 0
\(227\) 17.5001i 1.16152i 0.814074 + 0.580761i \(0.197245\pi\)
−0.814074 + 0.580761i \(0.802755\pi\)
\(228\) 0 0
\(229\) 23.8643 1.57700 0.788498 0.615038i \(-0.210859\pi\)
0.788498 + 0.615038i \(0.210859\pi\)
\(230\) 0 0
\(231\) 14.9813 0.985699
\(232\) 0 0
\(233\) 21.8957i 1.43444i −0.696849 0.717218i \(-0.745415\pi\)
0.696849 0.717218i \(-0.254585\pi\)
\(234\) 0 0
\(235\) −14.3299 + 12.3663i −0.934779 + 0.806686i
\(236\) 0 0
\(237\) 29.8299i 1.93766i
\(238\) 0 0
\(239\) −19.3443 −1.25128 −0.625639 0.780113i \(-0.715162\pi\)
−0.625639 + 0.780113i \(0.715162\pi\)
\(240\) 0 0
\(241\) 11.4761 0.739240 0.369620 0.929183i \(-0.379488\pi\)
0.369620 + 0.929183i \(0.379488\pi\)
\(242\) 0 0
\(243\) 1.99352i 0.127884i
\(244\) 0 0
\(245\) 5.72266 + 6.63135i 0.365607 + 0.423662i
\(246\) 0 0
\(247\) 4.21988i 0.268504i
\(248\) 0 0
\(249\) 4.71935 0.299077
\(250\) 0 0
\(251\) −17.0040 −1.07328 −0.536641 0.843811i \(-0.680307\pi\)
−0.536641 + 0.843811i \(0.680307\pi\)
\(252\) 0 0
\(253\) 4.77574i 0.300248i
\(254\) 0 0
\(255\) 20.3967 + 23.6355i 1.27729 + 1.48011i
\(256\) 0 0
\(257\) 14.6462i 0.913607i 0.889568 + 0.456803i \(0.151006\pi\)
−0.889568 + 0.456803i \(0.848994\pi\)
\(258\) 0 0
\(259\) −11.9977 −0.745499
\(260\) 0 0
\(261\) 1.51048 0.0934964
\(262\) 0 0
\(263\) 10.2641i 0.632912i −0.948607 0.316456i \(-0.897507\pi\)
0.948607 0.316456i \(-0.102493\pi\)
\(264\) 0 0
\(265\) 4.68178 4.04023i 0.287599 0.248190i
\(266\) 0 0
\(267\) 23.5353i 1.44034i
\(268\) 0 0
\(269\) 2.61485 0.159430 0.0797150 0.996818i \(-0.474599\pi\)
0.0797150 + 0.996818i \(0.474599\pi\)
\(270\) 0 0
\(271\) −9.87492 −0.599859 −0.299929 0.953961i \(-0.596963\pi\)
−0.299929 + 0.953961i \(0.596963\pi\)
\(272\) 0 0
\(273\) 5.42591i 0.328391i
\(274\) 0 0
\(275\) −3.49387 + 23.6217i −0.210688 + 1.42444i
\(276\) 0 0
\(277\) 4.21949i 0.253525i 0.991933 + 0.126762i \(0.0404585\pi\)
−0.991933 + 0.126762i \(0.959541\pi\)
\(278\) 0 0
\(279\) 1.18001 0.0706451
\(280\) 0 0
\(281\) −13.4058 −0.799724 −0.399862 0.916575i \(-0.630942\pi\)
−0.399862 + 0.916575i \(0.630942\pi\)
\(282\) 0 0
\(283\) 5.66084i 0.336502i 0.985744 + 0.168251i \(0.0538119\pi\)
−0.985744 + 0.168251i \(0.946188\pi\)
\(284\) 0 0
\(285\) −7.37902 + 6.36787i −0.437095 + 0.377200i
\(286\) 0 0
\(287\) 4.39676i 0.259532i
\(288\) 0 0
\(289\) −44.0668 −2.59217
\(290\) 0 0
\(291\) −28.3305 −1.66076
\(292\) 0 0
\(293\) 5.70404i 0.333233i 0.986022 + 0.166617i \(0.0532842\pi\)
−0.986022 + 0.166617i \(0.946716\pi\)
\(294\) 0 0
\(295\) 2.80062 + 3.24532i 0.163058 + 0.188950i
\(296\) 0 0
\(297\) 23.9585i 1.39021i
\(298\) 0 0
\(299\) −1.72967 −0.100029
\(300\) 0 0
\(301\) −5.73710 −0.330681
\(302\) 0 0
\(303\) 28.0481i 1.61132i
\(304\) 0 0
\(305\) −5.11844 5.93119i −0.293081 0.339619i
\(306\) 0 0
\(307\) 14.8943i 0.850065i 0.905178 + 0.425033i \(0.139737\pi\)
−0.905178 + 0.425033i \(0.860263\pi\)
\(308\) 0 0
\(309\) −14.9626 −0.851192
\(310\) 0 0
\(311\) 10.0355 0.569059 0.284530 0.958667i \(-0.408163\pi\)
0.284530 + 0.958667i \(0.408163\pi\)
\(312\) 0 0
\(313\) 23.5043i 1.32854i −0.747491 0.664272i \(-0.768742\pi\)
0.747491 0.664272i \(-0.231258\pi\)
\(314\) 0 0
\(315\) 0.571025 0.492777i 0.0321736 0.0277649i
\(316\) 0 0
\(317\) 7.94093i 0.446007i 0.974818 + 0.223004i \(0.0715862\pi\)
−0.974818 + 0.223004i \(0.928414\pi\)
\(318\) 0 0
\(319\) −37.5486 −2.10232
\(320\) 0 0
\(321\) −11.6536 −0.650442
\(322\) 0 0
\(323\) 19.0651i 1.06081i
\(324\) 0 0
\(325\) −8.55527 1.26540i −0.474561 0.0701919i
\(326\) 0 0
\(327\) 14.4982i 0.801752i
\(328\) 0 0
\(329\) −14.8625 −0.819393
\(330\) 0 0
\(331\) −6.31442 −0.347072 −0.173536 0.984828i \(-0.555519\pi\)
−0.173536 + 0.984828i \(0.555519\pi\)
\(332\) 0 0
\(333\) 1.31277i 0.0719394i
\(334\) 0 0
\(335\) 21.6093 18.6482i 1.18064 1.01886i
\(336\) 0 0
\(337\) 23.4516i 1.27749i −0.769418 0.638746i \(-0.779453\pi\)
0.769418 0.638746i \(-0.220547\pi\)
\(338\) 0 0
\(339\) −23.0877 −1.25395
\(340\) 0 0
\(341\) −29.3334 −1.58849
\(342\) 0 0
\(343\) 19.1683i 1.03499i
\(344\) 0 0
\(345\) 2.61010 + 3.02456i 0.140523 + 0.162837i
\(346\) 0 0
\(347\) 15.4757i 0.830780i −0.909643 0.415390i \(-0.863645\pi\)
0.909643 0.415390i \(-0.136355\pi\)
\(348\) 0 0
\(349\) 25.5514 1.36773 0.683867 0.729607i \(-0.260297\pi\)
0.683867 + 0.729607i \(0.260297\pi\)
\(350\) 0 0
\(351\) 8.67724 0.463157
\(352\) 0 0
\(353\) 23.5917i 1.25566i 0.778352 + 0.627829i \(0.216056\pi\)
−0.778352 + 0.627829i \(0.783944\pi\)
\(354\) 0 0
\(355\) 19.5720 + 22.6798i 1.03878 + 1.20372i
\(356\) 0 0
\(357\) 24.5139i 1.29741i
\(358\) 0 0
\(359\) 3.14840 0.166166 0.0830832 0.996543i \(-0.473523\pi\)
0.0830832 + 0.996543i \(0.473523\pi\)
\(360\) 0 0
\(361\) −13.0479 −0.686729
\(362\) 0 0
\(363\) 21.0963i 1.10727i
\(364\) 0 0
\(365\) −0.0189155 + 0.0163235i −0.000990084 + 0.000854413i
\(366\) 0 0
\(367\) 32.4297i 1.69282i 0.532534 + 0.846408i \(0.321240\pi\)
−0.532534 + 0.846408i \(0.678760\pi\)
\(368\) 0 0
\(369\) 0.481088 0.0250445
\(370\) 0 0
\(371\) 4.85577 0.252099
\(372\) 0 0
\(373\) 7.99302i 0.413863i −0.978355 0.206931i \(-0.933652\pi\)
0.978355 0.206931i \(-0.0663477\pi\)
\(374\) 0 0
\(375\) 10.6973 + 16.8695i 0.552408 + 0.871140i
\(376\) 0 0
\(377\) 13.5993i 0.700398i
\(378\) 0 0
\(379\) 8.96061 0.460275 0.230138 0.973158i \(-0.426082\pi\)
0.230138 + 0.973158i \(0.426082\pi\)
\(380\) 0 0
\(381\) 12.6031 0.645678
\(382\) 0 0
\(383\) 36.7195i 1.87628i −0.346255 0.938141i \(-0.612547\pi\)
0.346255 0.938141i \(-0.387453\pi\)
\(384\) 0 0
\(385\) −14.1949 + 12.2498i −0.723441 + 0.624308i
\(386\) 0 0
\(387\) 0.627747i 0.0319102i
\(388\) 0 0
\(389\) −0.0627294 −0.00318051 −0.00159025 0.999999i \(-0.500506\pi\)
−0.00159025 + 0.999999i \(0.500506\pi\)
\(390\) 0 0
\(391\) −7.81453 −0.395198
\(392\) 0 0
\(393\) 19.9363i 1.00565i
\(394\) 0 0
\(395\) −24.3910 28.2640i −1.22725 1.42212i
\(396\) 0 0
\(397\) 20.9714i 1.05252i 0.850323 + 0.526262i \(0.176407\pi\)
−0.850323 + 0.526262i \(0.823593\pi\)
\(398\) 0 0
\(399\) −7.65326 −0.383142
\(400\) 0 0
\(401\) −13.8567 −0.691972 −0.345986 0.938240i \(-0.612456\pi\)
−0.345986 + 0.938240i \(0.612456\pi\)
\(402\) 0 0
\(403\) 10.6239i 0.529215i
\(404\) 0 0
\(405\) −13.9361 16.1490i −0.692490 0.802450i
\(406\) 0 0
\(407\) 32.6338i 1.61760i
\(408\) 0 0
\(409\) −12.5868 −0.622378 −0.311189 0.950348i \(-0.600727\pi\)
−0.311189 + 0.950348i \(0.600727\pi\)
\(410\) 0 0
\(411\) −4.85007 −0.239236
\(412\) 0 0
\(413\) 3.36593i 0.165627i
\(414\) 0 0
\(415\) −4.47162 + 3.85888i −0.219503 + 0.189425i
\(416\) 0 0
\(417\) 23.3896i 1.14540i
\(418\) 0 0
\(419\) −32.4927 −1.58737 −0.793685 0.608328i \(-0.791840\pi\)
−0.793685 + 0.608328i \(0.791840\pi\)
\(420\) 0 0
\(421\) 18.8356 0.917992 0.458996 0.888438i \(-0.348209\pi\)
0.458996 + 0.888438i \(0.348209\pi\)
\(422\) 0 0
\(423\) 1.62623i 0.0790702i
\(424\) 0 0
\(425\) −38.6521 5.71701i −1.87490 0.277316i
\(426\) 0 0
\(427\) 6.15162i 0.297698i
\(428\) 0 0
\(429\) 14.7585 0.712549
\(430\) 0 0
\(431\) −1.66739 −0.0803155 −0.0401577 0.999193i \(-0.512786\pi\)
−0.0401577 + 0.999193i \(0.512786\pi\)
\(432\) 0 0
\(433\) 5.83595i 0.280458i −0.990119 0.140229i \(-0.955216\pi\)
0.990119 0.140229i \(-0.0447839\pi\)
\(434\) 0 0
\(435\) −23.7801 + 20.5215i −1.14017 + 0.983933i
\(436\) 0 0
\(437\) 2.43970i 0.116707i
\(438\) 0 0
\(439\) 30.5742 1.45923 0.729614 0.683860i \(-0.239700\pi\)
0.729614 + 0.683860i \(0.239700\pi\)
\(440\) 0 0
\(441\) −0.752562 −0.0358363
\(442\) 0 0
\(443\) 34.9173i 1.65897i −0.558530 0.829485i \(-0.688634\pi\)
0.558530 0.829485i \(-0.311366\pi\)
\(444\) 0 0
\(445\) 19.2441 + 22.2999i 0.912259 + 1.05712i
\(446\) 0 0
\(447\) 21.6002i 1.02166i
\(448\) 0 0
\(449\) 33.1265 1.56334 0.781668 0.623694i \(-0.214369\pi\)
0.781668 + 0.623694i \(0.214369\pi\)
\(450\) 0 0
\(451\) −11.9592 −0.563138
\(452\) 0 0
\(453\) 26.6978i 1.25437i
\(454\) 0 0
\(455\) −4.43661 5.14109i −0.207992 0.241018i
\(456\) 0 0
\(457\) 4.27252i 0.199860i −0.994994 0.0999299i \(-0.968138\pi\)
0.994994 0.0999299i \(-0.0318619\pi\)
\(458\) 0 0
\(459\) 39.2032 1.82985
\(460\) 0 0
\(461\) −38.4702 −1.79173 −0.895867 0.444322i \(-0.853444\pi\)
−0.895867 + 0.444322i \(0.853444\pi\)
\(462\) 0 0
\(463\) 8.94727i 0.415815i 0.978148 + 0.207908i \(0.0666653\pi\)
−0.978148 + 0.207908i \(0.933335\pi\)
\(464\) 0 0
\(465\) −18.5773 + 16.0317i −0.861503 + 0.743452i
\(466\) 0 0
\(467\) 16.3171i 0.755064i −0.925996 0.377532i \(-0.876773\pi\)
0.925996 0.377532i \(-0.123227\pi\)
\(468\) 0 0
\(469\) 22.4124 1.03491
\(470\) 0 0
\(471\) −8.54723 −0.393836
\(472\) 0 0
\(473\) 15.6050i 0.717518i
\(474\) 0 0
\(475\) 1.78485 12.0672i 0.0818947 0.553682i
\(476\) 0 0
\(477\) 0.531313i 0.0243272i
\(478\) 0 0
\(479\) 11.9574 0.546349 0.273174 0.961965i \(-0.411926\pi\)
0.273174 + 0.961965i \(0.411926\pi\)
\(480\) 0 0
\(481\) −11.8192 −0.538911
\(482\) 0 0
\(483\) 3.13696i 0.142737i
\(484\) 0 0
\(485\) 26.8434 23.1650i 1.21889 1.05187i
\(486\) 0 0
\(487\) 1.19495i 0.0541484i 0.999633 + 0.0270742i \(0.00861904\pi\)
−0.999633 + 0.0270742i \(0.991381\pi\)
\(488\) 0 0
\(489\) −9.80982 −0.443616
\(490\) 0 0
\(491\) 13.6912 0.617874 0.308937 0.951083i \(-0.400027\pi\)
0.308937 + 0.951083i \(0.400027\pi\)
\(492\) 0 0
\(493\) 61.4406i 2.76714i
\(494\) 0 0
\(495\) −1.34036 1.55319i −0.0602447 0.0698109i
\(496\) 0 0
\(497\) 23.5227i 1.05514i
\(498\) 0 0
\(499\) 11.9774 0.536184 0.268092 0.963393i \(-0.413607\pi\)
0.268092 + 0.963393i \(0.413607\pi\)
\(500\) 0 0
\(501\) −12.9877 −0.580249
\(502\) 0 0
\(503\) 32.3666i 1.44316i −0.692333 0.721578i \(-0.743417\pi\)
0.692333 0.721578i \(-0.256583\pi\)
\(504\) 0 0
\(505\) 22.9341 + 26.5758i 1.02056 + 1.18261i
\(506\) 0 0
\(507\) 17.8812i 0.794133i
\(508\) 0 0
\(509\) −15.6507 −0.693706 −0.346853 0.937919i \(-0.612750\pi\)
−0.346853 + 0.937919i \(0.612750\pi\)
\(510\) 0 0
\(511\) −0.0196185 −0.000867872
\(512\) 0 0
\(513\) 12.2393i 0.540377i
\(514\) 0 0
\(515\) 14.1772 12.2345i 0.624721 0.539116i
\(516\) 0 0
\(517\) 40.4261i 1.77794i
\(518\) 0 0
\(519\) −13.4158 −0.588889
\(520\) 0 0
\(521\) 21.7184 0.951499 0.475749 0.879581i \(-0.342177\pi\)
0.475749 + 0.879581i \(0.342177\pi\)
\(522\) 0 0
\(523\) 8.89014i 0.388739i −0.980928 0.194369i \(-0.937734\pi\)
0.980928 0.194369i \(-0.0622660\pi\)
\(524\) 0 0
\(525\) −2.29496 + 15.5160i −0.100160 + 0.677174i
\(526\) 0 0
\(527\) 47.9981i 2.09083i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) −0.368297 −0.0159827
\(532\) 0 0
\(533\) 4.33137i 0.187613i
\(534\) 0 0
\(535\) 11.0419 9.52884i 0.477384 0.411968i
\(536\) 0 0
\(537\) 10.2449i 0.442100i
\(538\) 0 0
\(539\) 18.7077 0.805798
\(540\) 0 0
\(541\) −29.0112 −1.24729 −0.623645 0.781708i \(-0.714349\pi\)
−0.623645 + 0.781708i \(0.714349\pi\)
\(542\) 0 0
\(543\) 45.0703i 1.93415i
\(544\) 0 0
\(545\) 11.8548 + 13.7372i 0.507802 + 0.588436i
\(546\) 0 0
\(547\) 24.9089i 1.06503i 0.846421 + 0.532514i \(0.178753\pi\)
−0.846421 + 0.532514i \(0.821247\pi\)
\(548\) 0 0
\(549\) 0.673103 0.0287273
\(550\) 0 0
\(551\) 19.1818 0.817172
\(552\) 0 0
\(553\) 29.3145i 1.24658i
\(554\) 0 0
\(555\) 17.8355 + 20.6675i 0.757073 + 0.877287i
\(556\) 0 0
\(557\) 15.3536i 0.650552i −0.945619 0.325276i \(-0.894543\pi\)
0.945619 0.325276i \(-0.105457\pi\)
\(558\) 0 0
\(559\) −5.65178 −0.239045
\(560\) 0 0
\(561\) 66.6781 2.81515
\(562\) 0 0
\(563\) 16.8264i 0.709146i 0.935028 + 0.354573i \(0.115374\pi\)
−0.935028 + 0.354573i \(0.884626\pi\)
\(564\) 0 0
\(565\) 21.8758 18.8782i 0.920323 0.794212i
\(566\) 0 0
\(567\) 16.7492i 0.703398i
\(568\) 0 0
\(569\) −1.75646 −0.0736344 −0.0368172 0.999322i \(-0.511722\pi\)
−0.0368172 + 0.999322i \(0.511722\pi\)
\(570\) 0 0
\(571\) −13.4273 −0.561913 −0.280956 0.959721i \(-0.590652\pi\)
−0.280956 + 0.959721i \(0.590652\pi\)
\(572\) 0 0
\(573\) 6.48823i 0.271050i
\(574\) 0 0
\(575\) −4.94619 0.731587i −0.206270 0.0305093i
\(576\) 0 0
\(577\) 20.4806i 0.852620i 0.904577 + 0.426310i \(0.140187\pi\)
−0.904577 + 0.426310i \(0.859813\pi\)
\(578\) 0 0
\(579\) 38.7792 1.61161
\(580\) 0 0
\(581\) −4.63781 −0.192409
\(582\) 0 0
\(583\) 13.2078i 0.547010i
\(584\) 0 0
\(585\) 0.562533 0.485449i 0.0232579 0.0200709i
\(586\) 0 0
\(587\) 45.3569i 1.87208i 0.351893 + 0.936040i \(0.385538\pi\)
−0.351893 + 0.936040i \(0.614462\pi\)
\(588\) 0 0
\(589\) 14.9851 0.617449
\(590\) 0 0
\(591\) −12.9805 −0.533945
\(592\) 0 0
\(593\) 28.8520i 1.18481i −0.805641 0.592404i \(-0.798179\pi\)
0.805641 0.592404i \(-0.201821\pi\)
\(594\) 0 0
\(595\) −20.0443 23.2271i −0.821736 0.952219i
\(596\) 0 0
\(597\) 11.6615i 0.477275i
\(598\) 0 0
\(599\) 8.78767 0.359054 0.179527 0.983753i \(-0.442543\pi\)
0.179527 + 0.983753i \(0.442543\pi\)
\(600\) 0 0
\(601\) −44.7810 −1.82665 −0.913327 0.407227i \(-0.866496\pi\)
−0.913327 + 0.407227i \(0.866496\pi\)
\(602\) 0 0
\(603\) 2.45234i 0.0998669i
\(604\) 0 0
\(605\) 17.2498 + 19.9889i 0.701305 + 0.812664i
\(606\) 0 0
\(607\) 6.96387i 0.282655i 0.989963 + 0.141327i \(0.0451370\pi\)
−0.989963 + 0.141327i \(0.954863\pi\)
\(608\) 0 0
\(609\) −24.6639 −0.999432
\(610\) 0 0
\(611\) −14.6414 −0.592329
\(612\) 0 0
\(613\) 30.6214i 1.23679i 0.785869 + 0.618393i \(0.212216\pi\)
−0.785869 + 0.618393i \(0.787784\pi\)
\(614\) 0 0
\(615\) −7.57398 + 6.53612i −0.305412 + 0.263562i
\(616\) 0 0
\(617\) 10.6041i 0.426905i −0.976953 0.213452i \(-0.931529\pi\)
0.976953 0.213452i \(-0.0684709\pi\)
\(618\) 0 0
\(619\) 21.0095 0.844445 0.422223 0.906492i \(-0.361250\pi\)
0.422223 + 0.906492i \(0.361250\pi\)
\(620\) 0 0
\(621\) 5.01670 0.201313
\(622\) 0 0
\(623\) 23.1286i 0.926629i
\(624\) 0 0
\(625\) −23.9296 7.23713i −0.957182 0.289485i
\(626\) 0 0
\(627\) 20.8170i 0.831349i
\(628\) 0 0
\(629\) −53.3985 −2.12914
\(630\) 0 0
\(631\) −5.45489 −0.217156 −0.108578 0.994088i \(-0.534630\pi\)
−0.108578 + 0.994088i \(0.534630\pi\)
\(632\) 0 0
\(633\) 40.7099i 1.61807i
\(634\) 0 0
\(635\) −11.9416 + 10.3052i −0.473887 + 0.408950i
\(636\) 0 0
\(637\) 6.77552i 0.268456i
\(638\) 0 0
\(639\) −2.57383 −0.101819
\(640\) 0 0
\(641\) −28.7734 −1.13648 −0.568241 0.822862i \(-0.692376\pi\)
−0.568241 + 0.822862i \(0.692376\pi\)
\(642\) 0 0
\(643\) 11.5319i 0.454775i 0.973804 + 0.227388i \(0.0730185\pi\)
−0.973804 + 0.227388i \(0.926982\pi\)
\(644\) 0 0
\(645\) 8.52864 + 9.88289i 0.335815 + 0.389138i
\(646\) 0 0
\(647\) 3.18564i 0.125240i −0.998037 0.0626202i \(-0.980054\pi\)
0.998037 0.0626202i \(-0.0199457\pi\)
\(648\) 0 0
\(649\) 9.15538 0.359380
\(650\) 0 0
\(651\) −19.2678 −0.755163
\(652\) 0 0
\(653\) 28.6814i 1.12239i −0.827684 0.561194i \(-0.810342\pi\)
0.827684 0.561194i \(-0.189658\pi\)
\(654\) 0 0
\(655\) 16.3014 + 18.8898i 0.636947 + 0.738087i
\(656\) 0 0
\(657\) 0.00214664i 8.37483e-5i
\(658\) 0 0
\(659\) 24.0012 0.934954 0.467477 0.884005i \(-0.345163\pi\)
0.467477 + 0.884005i \(0.345163\pi\)
\(660\) 0 0
\(661\) 31.9043 1.24093 0.620467 0.784232i \(-0.286943\pi\)
0.620467 + 0.784232i \(0.286943\pi\)
\(662\) 0 0
\(663\) 24.1493i 0.937882i
\(664\) 0 0
\(665\) 7.25153 6.25785i 0.281202 0.242669i
\(666\) 0 0
\(667\) 7.86235i 0.304431i
\(668\) 0 0
\(669\) −12.2620 −0.474078
\(670\) 0 0
\(671\) −16.7325 −0.645950
\(672\) 0 0
\(673\) 1.87848i 0.0724101i −0.999344 0.0362051i \(-0.988473\pi\)
0.999344 0.0362051i \(-0.0115269\pi\)
\(674\) 0 0
\(675\) 24.8136 + 3.67016i 0.955075 + 0.141264i
\(676\) 0 0
\(677\) 34.6119i 1.33024i −0.746736 0.665121i \(-0.768380\pi\)
0.746736 0.665121i \(-0.231620\pi\)
\(678\) 0 0
\(679\) 27.8410 1.06844
\(680\) 0 0
\(681\) 31.2665 1.19814
\(682\) 0 0
\(683\) 16.0493i 0.614110i 0.951692 + 0.307055i \(0.0993436\pi\)
−0.951692 + 0.307055i \(0.900656\pi\)
\(684\) 0 0
\(685\) 4.59549 3.96577i 0.175584 0.151524i
\(686\) 0 0
\(687\) 42.6371i 1.62671i
\(688\) 0 0
\(689\) 4.78356 0.182239
\(690\) 0 0
\(691\) 19.5985 0.745564 0.372782 0.927919i \(-0.378404\pi\)
0.372782 + 0.927919i \(0.378404\pi\)
\(692\) 0 0
\(693\) 1.61092i 0.0611937i
\(694\) 0 0
\(695\) 19.1250 + 22.1619i 0.725454 + 0.840648i
\(696\) 0 0
\(697\) 19.5688i 0.741223i
\(698\) 0 0
\(699\) −39.1199 −1.47965
\(700\) 0 0
\(701\) −51.5536 −1.94715 −0.973575 0.228366i \(-0.926662\pi\)
−0.973575 + 0.228366i \(0.926662\pi\)
\(702\) 0 0
\(703\) 16.6711i 0.628761i
\(704\) 0 0
\(705\) 22.0942 + 25.6025i 0.832115 + 0.964245i
\(706\) 0 0
\(707\) 27.5635i 1.03663i
\(708\) 0 0
\(709\) −8.64772 −0.324772 −0.162386 0.986727i \(-0.551919\pi\)
−0.162386 + 0.986727i \(0.551919\pi\)
\(710\) 0 0
\(711\) 3.20756 0.120293
\(712\) 0 0
\(713\) 6.14217i 0.230026i
\(714\) 0 0
\(715\) −13.9838 + 12.0676i −0.522966 + 0.451304i
\(716\) 0 0
\(717\) 34.5615i 1.29072i
\(718\) 0 0
\(719\) −7.50754 −0.279984 −0.139992 0.990153i \(-0.544708\pi\)
−0.139992 + 0.990153i \(0.544708\pi\)
\(720\) 0 0
\(721\) 14.7041 0.547608
\(722\) 0 0
\(723\) 20.5037i 0.762543i
\(724\) 0 0
\(725\) 5.75199 38.8887i 0.213624 1.44429i
\(726\) 0 0
\(727\) 2.79852i 0.103791i 0.998653 + 0.0518956i \(0.0165263\pi\)
−0.998653 + 0.0518956i \(0.983474\pi\)
\(728\) 0 0
\(729\) −25.0566 −0.928022
\(730\) 0 0
\(731\) −25.5344 −0.944423
\(732\) 0 0
\(733\) 1.38900i 0.0513038i −0.999671 0.0256519i \(-0.991834\pi\)
0.999671 0.0256519i \(-0.00816615\pi\)
\(734\) 0 0
\(735\) 11.8479 10.2244i 0.437017 0.377132i
\(736\) 0 0
\(737\) 60.9619i 2.24556i
\(738\) 0 0
\(739\) 6.31935 0.232461 0.116230 0.993222i \(-0.462919\pi\)
0.116230 + 0.993222i \(0.462919\pi\)
\(740\) 0 0
\(741\) −7.53944 −0.276968
\(742\) 0 0
\(743\) 39.7611i 1.45869i 0.684144 + 0.729347i \(0.260176\pi\)
−0.684144 + 0.729347i \(0.739824\pi\)
\(744\) 0 0
\(745\) 17.6619 + 20.4664i 0.647082 + 0.749831i
\(746\) 0 0
\(747\) 0.507464i 0.0185671i
\(748\) 0 0
\(749\) 11.4523 0.418457
\(750\) 0 0
\(751\) −7.27267 −0.265384 −0.132692 0.991157i \(-0.542362\pi\)
−0.132692 + 0.991157i \(0.542362\pi\)
\(752\) 0 0
\(753\) 30.3801i 1.10711i
\(754\) 0 0
\(755\) −21.8301 25.2964i −0.794478 0.920632i
\(756\) 0 0
\(757\) 15.8682i 0.576739i −0.957519 0.288369i \(-0.906887\pi\)
0.957519 0.288369i \(-0.0931131\pi\)
\(758\) 0 0
\(759\) 8.53258 0.309713
\(760\) 0 0
\(761\) −4.80457 −0.174166 −0.0870828 0.996201i \(-0.527754\pi\)
−0.0870828 + 0.996201i \(0.527754\pi\)
\(762\) 0 0
\(763\) 14.2477i 0.515801i
\(764\) 0 0
\(765\) 2.54149 2.19323i 0.0918876 0.0792963i
\(766\) 0 0
\(767\) 3.31588i 0.119729i
\(768\) 0 0
\(769\) −30.1358 −1.08673 −0.543363 0.839498i \(-0.682849\pi\)
−0.543363 + 0.839498i \(0.682849\pi\)
\(770\) 0 0
\(771\) 26.1677 0.942406
\(772\) 0 0
\(773\) 3.35253i 0.120582i 0.998181 + 0.0602910i \(0.0192029\pi\)
−0.998181 + 0.0602910i \(0.980797\pi\)
\(774\) 0 0
\(775\) 4.49353 30.3803i 0.161412 1.09129i
\(776\) 0 0
\(777\) 21.4356i 0.768999i
\(778\) 0 0
\(779\) 6.10941 0.218892
\(780\) 0 0
\(781\) 63.9821 2.28946
\(782\) 0 0
\(783\) 39.4431i 1.40958i
\(784\) 0 0
\(785\) 8.09858 6.98883i 0.289051 0.249442i
\(786\) 0 0
\(787\) 2.36807i 0.0844126i 0.999109 + 0.0422063i \(0.0134387\pi\)
−0.999109 + 0.0422063i \(0.986561\pi\)
\(788\) 0 0
\(789\) −18.3384 −0.652863
\(790\) 0 0
\(791\) 22.6888 0.806722
\(792\) 0 0
\(793\) 6.06013i 0.215202i
\(794\) 0 0
\(795\) −7.21848 8.36469i −0.256013 0.296665i
\(796\) 0 0
\(797\) 33.0367i 1.17022i 0.810954 + 0.585110i \(0.198949\pi\)
−0.810954 + 0.585110i \(0.801051\pi\)
\(798\) 0 0
\(799\) −66.1490 −2.34018
\(800\) 0 0
\(801\) −2.53071 −0.0894183
\(802\) 0 0
\(803\) 0.0533626i