Properties

Label 1840.2.e.f.369.7
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 369.7
Root \(-0.116918i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.f.369.6

$q$-expansion

\(f(q)\) \(=\) \(q+0.486391i q^{3} +(1.52160 + 1.63852i) q^{5} -1.80495i q^{7} +2.76342 q^{9} +O(q^{10})\) \(q+0.486391i q^{3} +(1.52160 + 1.63852i) q^{5} -1.80495i q^{7} +2.76342 q^{9} +2.90652 q^{11} +2.25256i q^{13} +(-0.796959 + 0.740092i) q^{15} +2.14477i q^{17} +0.339824 q^{19} +0.877911 q^{21} -1.00000i q^{23} +(-0.369473 + 4.98633i) q^{25} +2.80328i q^{27} +5.60395 q^{29} -5.92083 q^{31} +1.41371i q^{33} +(2.95744 - 2.74641i) q^{35} -8.98088i q^{37} -1.09562 q^{39} +1.89222 q^{41} -9.47322i q^{43} +(4.20482 + 4.52792i) q^{45} +7.83384i q^{47} +3.74216 q^{49} -1.04320 q^{51} -6.47764i q^{53} +(4.42256 + 4.76239i) q^{55} +0.165287i q^{57} +5.17914 q^{59} -9.12565 q^{61} -4.98784i q^{63} +(-3.69085 + 3.42749i) q^{65} +9.25423i q^{67} +0.486391 q^{69} +4.60255 q^{71} +11.3300i q^{73} +(-2.42531 - 0.179708i) q^{75} -5.24613i q^{77} +7.94972 q^{79} +6.92678 q^{81} +5.37849i q^{83} +(-3.51425 + 3.26348i) q^{85} +2.72571i q^{87} -12.9258 q^{89} +4.06575 q^{91} -2.87984i q^{93} +(0.517076 + 0.556807i) q^{95} -2.43210i q^{97} +8.03196 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 20q^{9} + O(q^{10}) \) \( 12q - 20q^{9} - 4q^{11} - 2q^{15} + 8q^{19} + 8q^{25} - 10q^{29} - 18q^{31} + 10q^{35} - 16q^{39} - 2q^{41} + 2q^{45} - 38q^{49} + 24q^{51} - 16q^{55} - 22q^{59} - 8q^{61} + 38q^{65} - 8q^{69} + 34q^{71} - 16q^{75} + 20q^{79} + 28q^{81} + 6q^{85} + 48q^{89} + 8q^{91} - 12q^{95} - 32q^{99} + O(q^{100}) \)

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
\(3\) 0.486391i 0.280818i 0.990094 + 0.140409i \(0.0448417\pi\)
−0.990094 + 0.140409i \(0.955158\pi\)
\(4\) 0 0
\(5\) 1.52160 + 1.63852i 0.680480 + 0.732767i
\(6\) 0 0
\(7\) 1.80495i 0.682207i −0.940026 0.341103i \(-0.889199\pi\)
0.940026 0.341103i \(-0.110801\pi\)
\(8\) 0 0
\(9\) 2.76342 0.921141
\(10\) 0 0
\(11\) 2.90652 0.876350 0.438175 0.898890i \(-0.355625\pi\)
0.438175 + 0.898890i \(0.355625\pi\)
\(12\) 0 0
\(13\) 2.25256i 0.624747i 0.949959 + 0.312373i \(0.101124\pi\)
−0.949959 + 0.312373i \(0.898876\pi\)
\(14\) 0 0
\(15\) −0.796959 + 0.740092i −0.205774 + 0.191091i
\(16\) 0 0
\(17\) 2.14477i 0.520184i 0.965584 + 0.260092i \(0.0837529\pi\)
−0.965584 + 0.260092i \(0.916247\pi\)
\(18\) 0 0
\(19\) 0.339824 0.0779610 0.0389805 0.999240i \(-0.487589\pi\)
0.0389805 + 0.999240i \(0.487589\pi\)
\(20\) 0 0
\(21\) 0.877911 0.191576
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) −0.369473 + 4.98633i −0.0738946 + 0.997266i
\(26\) 0 0
\(27\) 2.80328i 0.539491i
\(28\) 0 0
\(29\) 5.60395 1.04063 0.520313 0.853975i \(-0.325815\pi\)
0.520313 + 0.853975i \(0.325815\pi\)
\(30\) 0 0
\(31\) −5.92083 −1.06341 −0.531706 0.846929i \(-0.678449\pi\)
−0.531706 + 0.846929i \(0.678449\pi\)
\(32\) 0 0
\(33\) 1.41371i 0.246095i
\(34\) 0 0
\(35\) 2.95744 2.74641i 0.499898 0.464228i
\(36\) 0 0
\(37\) 8.98088i 1.47645i −0.674556 0.738224i \(-0.735665\pi\)
0.674556 0.738224i \(-0.264335\pi\)
\(38\) 0 0
\(39\) −1.09562 −0.175440
\(40\) 0 0
\(41\) 1.89222 0.295515 0.147757 0.989024i \(-0.452795\pi\)
0.147757 + 0.989024i \(0.452795\pi\)
\(42\) 0 0
\(43\) 9.47322i 1.44465i −0.691552 0.722327i \(-0.743073\pi\)
0.691552 0.722327i \(-0.256927\pi\)
\(44\) 0 0
\(45\) 4.20482 + 4.52792i 0.626818 + 0.674982i
\(46\) 0 0
\(47\) 7.83384i 1.14268i 0.820712 + 0.571342i \(0.193577\pi\)
−0.820712 + 0.571342i \(0.806423\pi\)
\(48\) 0 0
\(49\) 3.74216 0.534594
\(50\) 0 0
\(51\) −1.04320 −0.146077
\(52\) 0 0
\(53\) 6.47764i 0.889772i −0.895587 0.444886i \(-0.853244\pi\)
0.895587 0.444886i \(-0.146756\pi\)
\(54\) 0 0
\(55\) 4.42256 + 4.76239i 0.596338 + 0.642160i
\(56\) 0 0
\(57\) 0.165287i 0.0218928i
\(58\) 0 0
\(59\) 5.17914 0.674267 0.337134 0.941457i \(-0.390543\pi\)
0.337134 + 0.941457i \(0.390543\pi\)
\(60\) 0 0
\(61\) −9.12565 −1.16842 −0.584210 0.811602i \(-0.698596\pi\)
−0.584210 + 0.811602i \(0.698596\pi\)
\(62\) 0 0
\(63\) 4.98784i 0.628409i
\(64\) 0 0
\(65\) −3.69085 + 3.42749i −0.457794 + 0.425127i
\(66\) 0 0
\(67\) 9.25423i 1.13058i 0.824891 + 0.565292i \(0.191236\pi\)
−0.824891 + 0.565292i \(0.808764\pi\)
\(68\) 0 0
\(69\) 0.486391 0.0585546
\(70\) 0 0
\(71\) 4.60255 0.546222 0.273111 0.961982i \(-0.411947\pi\)
0.273111 + 0.961982i \(0.411947\pi\)
\(72\) 0 0
\(73\) 11.3300i 1.32608i 0.748585 + 0.663038i \(0.230733\pi\)
−0.748585 + 0.663038i \(0.769267\pi\)
\(74\) 0 0
\(75\) −2.42531 0.179708i −0.280050 0.0207509i
\(76\) 0 0
\(77\) 5.24613i 0.597852i
\(78\) 0 0
\(79\) 7.94972 0.894414 0.447207 0.894431i \(-0.352419\pi\)
0.447207 + 0.894431i \(0.352419\pi\)
\(80\) 0 0
\(81\) 6.92678 0.769643
\(82\) 0 0
\(83\) 5.37849i 0.590366i 0.955441 + 0.295183i \(0.0953806\pi\)
−0.955441 + 0.295183i \(0.904619\pi\)
\(84\) 0 0
\(85\) −3.51425 + 3.26348i −0.381174 + 0.353975i
\(86\) 0 0
\(87\) 2.72571i 0.292227i
\(88\) 0 0
\(89\) −12.9258 −1.37014 −0.685069 0.728479i \(-0.740228\pi\)
−0.685069 + 0.728479i \(0.740228\pi\)
\(90\) 0 0
\(91\) 4.06575 0.426206
\(92\) 0 0
\(93\) 2.87984i 0.298625i
\(94\) 0 0
\(95\) 0.517076 + 0.556807i 0.0530508 + 0.0571272i
\(96\) 0 0
\(97\) 2.43210i 0.246942i −0.992348 0.123471i \(-0.960597\pi\)
0.992348 0.123471i \(-0.0394026\pi\)
\(98\) 0 0
\(99\) 8.03196 0.807242
\(100\) 0 0
\(101\) 2.89635 0.288198 0.144099 0.989563i \(-0.453972\pi\)
0.144099 + 0.989563i \(0.453972\pi\)
\(102\) 0 0
\(103\) 10.3524i 1.02005i 0.860159 + 0.510027i \(0.170364\pi\)
−0.860159 + 0.510027i \(0.829636\pi\)
\(104\) 0 0
\(105\) 1.33583 + 1.43847i 0.130363 + 0.140380i
\(106\) 0 0
\(107\) 15.2395i 1.47326i 0.676296 + 0.736630i \(0.263584\pi\)
−0.676296 + 0.736630i \(0.736416\pi\)
\(108\) 0 0
\(109\) 7.00555 0.671010 0.335505 0.942038i \(-0.391093\pi\)
0.335505 + 0.942038i \(0.391093\pi\)
\(110\) 0 0
\(111\) 4.36822 0.414613
\(112\) 0 0
\(113\) 6.48460i 0.610020i −0.952349 0.305010i \(-0.901340\pi\)
0.952349 0.305010i \(-0.0986597\pi\)
\(114\) 0 0
\(115\) 1.63852 1.52160i 0.152792 0.141890i
\(116\) 0 0
\(117\) 6.22477i 0.575480i
\(118\) 0 0
\(119\) 3.87121 0.354873
\(120\) 0 0
\(121\) −2.55212 −0.232011
\(122\) 0 0
\(123\) 0.920357i 0.0829858i
\(124\) 0 0
\(125\) −8.73237 + 6.98181i −0.781047 + 0.624472i
\(126\) 0 0
\(127\) 6.28324i 0.557547i 0.960357 + 0.278774i \(0.0899279\pi\)
−0.960357 + 0.278774i \(0.910072\pi\)
\(128\) 0 0
\(129\) 4.60769 0.405684
\(130\) 0 0
\(131\) 7.90426 0.690598 0.345299 0.938493i \(-0.387777\pi\)
0.345299 + 0.938493i \(0.387777\pi\)
\(132\) 0 0
\(133\) 0.613365i 0.0531855i
\(134\) 0 0
\(135\) −4.59321 + 4.26546i −0.395321 + 0.367113i
\(136\) 0 0
\(137\) 8.28955i 0.708224i −0.935203 0.354112i \(-0.884783\pi\)
0.935203 0.354112i \(-0.115217\pi\)
\(138\) 0 0
\(139\) −8.97515 −0.761262 −0.380631 0.924727i \(-0.624293\pi\)
−0.380631 + 0.924727i \(0.624293\pi\)
\(140\) 0 0
\(141\) −3.81031 −0.320886
\(142\) 0 0
\(143\) 6.54711i 0.547497i
\(144\) 0 0
\(145\) 8.52696 + 9.18216i 0.708125 + 0.762537i
\(146\) 0 0
\(147\) 1.82015i 0.150124i
\(148\) 0 0
\(149\) −5.39792 −0.442215 −0.221107 0.975249i \(-0.570967\pi\)
−0.221107 + 0.975249i \(0.570967\pi\)
\(150\) 0 0
\(151\) −22.6083 −1.83984 −0.919919 0.392108i \(-0.871746\pi\)
−0.919919 + 0.392108i \(0.871746\pi\)
\(152\) 0 0
\(153\) 5.92692i 0.479163i
\(154\) 0 0
\(155\) −9.00913 9.70138i −0.723631 0.779234i
\(156\) 0 0
\(157\) 8.00033i 0.638496i 0.947671 + 0.319248i \(0.103430\pi\)
−0.947671 + 0.319248i \(0.896570\pi\)
\(158\) 0 0
\(159\) 3.15066 0.249864
\(160\) 0 0
\(161\) −1.80495 −0.142250
\(162\) 0 0
\(163\) 18.6504i 1.46081i −0.683015 0.730404i \(-0.739332\pi\)
0.683015 0.730404i \(-0.260668\pi\)
\(164\) 0 0
\(165\) −2.31638 + 2.15109i −0.180330 + 0.167462i
\(166\) 0 0
\(167\) 3.13547i 0.242630i 0.992614 + 0.121315i \(0.0387111\pi\)
−0.992614 + 0.121315i \(0.961289\pi\)
\(168\) 0 0
\(169\) 7.92599 0.609692
\(170\) 0 0
\(171\) 0.939078 0.0718131
\(172\) 0 0
\(173\) 7.56301i 0.575005i −0.957780 0.287503i \(-0.907175\pi\)
0.957780 0.287503i \(-0.0928250\pi\)
\(174\) 0 0
\(175\) 9.00007 + 0.666880i 0.680342 + 0.0504114i
\(176\) 0 0
\(177\) 2.51909i 0.189346i
\(178\) 0 0
\(179\) 9.73608 0.727709 0.363855 0.931456i \(-0.381461\pi\)
0.363855 + 0.931456i \(0.381461\pi\)
\(180\) 0 0
\(181\) 0.260581 0.0193688 0.00968440 0.999953i \(-0.496917\pi\)
0.00968440 + 0.999953i \(0.496917\pi\)
\(182\) 0 0
\(183\) 4.43863i 0.328113i
\(184\) 0 0
\(185\) 14.7153 13.6653i 1.08189 1.00469i
\(186\) 0 0
\(187\) 6.23384i 0.455863i
\(188\) 0 0
\(189\) 5.05977 0.368044
\(190\) 0 0
\(191\) 18.1730 1.31495 0.657476 0.753475i \(-0.271624\pi\)
0.657476 + 0.753475i \(0.271624\pi\)
\(192\) 0 0
\(193\) 2.15073i 0.154813i 0.997000 + 0.0774063i \(0.0246639\pi\)
−0.997000 + 0.0774063i \(0.975336\pi\)
\(194\) 0 0
\(195\) −1.66710 1.79520i −0.119383 0.128557i
\(196\) 0 0
\(197\) 27.0886i 1.92998i −0.262279 0.964992i \(-0.584474\pi\)
0.262279 0.964992i \(-0.415526\pi\)
\(198\) 0 0
\(199\) −14.2178 −1.00787 −0.503937 0.863741i \(-0.668116\pi\)
−0.503937 + 0.863741i \(0.668116\pi\)
\(200\) 0 0
\(201\) −4.50117 −0.317488
\(202\) 0 0
\(203\) 10.1148i 0.709922i
\(204\) 0 0
\(205\) 2.87920 + 3.10043i 0.201092 + 0.216543i
\(206\) 0 0
\(207\) 2.76342i 0.192071i
\(208\) 0 0
\(209\) 0.987706 0.0683211
\(210\) 0 0
\(211\) −1.89855 −0.130701 −0.0653506 0.997862i \(-0.520817\pi\)
−0.0653506 + 0.997862i \(0.520817\pi\)
\(212\) 0 0
\(213\) 2.23864i 0.153389i
\(214\) 0 0
\(215\) 15.5220 14.4144i 1.05859 0.983057i
\(216\) 0 0
\(217\) 10.6868i 0.725467i
\(218\) 0 0
\(219\) −5.51081 −0.372386
\(220\) 0 0
\(221\) −4.83122 −0.324983
\(222\) 0 0
\(223\) 20.5574i 1.37663i −0.725414 0.688313i \(-0.758352\pi\)
0.725414 0.688313i \(-0.241648\pi\)
\(224\) 0 0
\(225\) −1.02101 + 13.7793i −0.0680674 + 0.918623i
\(226\) 0 0
\(227\) 7.67464i 0.509384i −0.967022 0.254692i \(-0.918026\pi\)
0.967022 0.254692i \(-0.0819740\pi\)
\(228\) 0 0
\(229\) −8.50379 −0.561946 −0.280973 0.959716i \(-0.590657\pi\)
−0.280973 + 0.959716i \(0.590657\pi\)
\(230\) 0 0
\(231\) 2.55167 0.167887
\(232\) 0 0
\(233\) 2.37058i 0.155302i 0.996981 + 0.0776511i \(0.0247420\pi\)
−0.996981 + 0.0776511i \(0.975258\pi\)
\(234\) 0 0
\(235\) −12.8359 + 11.9200i −0.837320 + 0.777573i
\(236\) 0 0
\(237\) 3.86667i 0.251167i
\(238\) 0 0
\(239\) −0.298079 −0.0192811 −0.00964057 0.999954i \(-0.503069\pi\)
−0.00964057 + 0.999954i \(0.503069\pi\)
\(240\) 0 0
\(241\) 29.7779 1.91817 0.959083 0.283126i \(-0.0913714\pi\)
0.959083 + 0.283126i \(0.0913714\pi\)
\(242\) 0 0
\(243\) 11.7790i 0.755620i
\(244\) 0 0
\(245\) 5.69406 + 6.13159i 0.363780 + 0.391733i
\(246\) 0 0
\(247\) 0.765472i 0.0487058i
\(248\) 0 0
\(249\) −2.61605 −0.165785
\(250\) 0 0
\(251\) −10.1766 −0.642341 −0.321171 0.947021i \(-0.604076\pi\)
−0.321171 + 0.947021i \(0.604076\pi\)
\(252\) 0 0
\(253\) 2.90652i 0.182732i
\(254\) 0 0
\(255\) −1.58733 1.70930i −0.0994024 0.107040i
\(256\) 0 0
\(257\) 28.2919i 1.76480i 0.470501 + 0.882400i \(0.344073\pi\)
−0.470501 + 0.882400i \(0.655927\pi\)
\(258\) 0 0
\(259\) −16.2100 −1.00724
\(260\) 0 0
\(261\) 15.4861 0.958564
\(262\) 0 0
\(263\) 24.9182i 1.53652i −0.640138 0.768260i \(-0.721123\pi\)
0.640138 0.768260i \(-0.278877\pi\)
\(264\) 0 0
\(265\) 10.6137 9.85637i 0.651996 0.605472i
\(266\) 0 0
\(267\) 6.28701i 0.384759i
\(268\) 0 0
\(269\) −25.8948 −1.57883 −0.789416 0.613859i \(-0.789616\pi\)
−0.789416 + 0.613859i \(0.789616\pi\)
\(270\) 0 0
\(271\) −3.49603 −0.212369 −0.106184 0.994346i \(-0.533863\pi\)
−0.106184 + 0.994346i \(0.533863\pi\)
\(272\) 0 0
\(273\) 1.97754i 0.119686i
\(274\) 0 0
\(275\) −1.07388 + 14.4929i −0.0647576 + 0.873954i
\(276\) 0 0
\(277\) 1.38317i 0.0831064i −0.999136 0.0415532i \(-0.986769\pi\)
0.999136 0.0415532i \(-0.0132306\pi\)
\(278\) 0 0
\(279\) −16.3618 −0.979553
\(280\) 0 0
\(281\) 15.3144 0.913582 0.456791 0.889574i \(-0.348999\pi\)
0.456791 + 0.889574i \(0.348999\pi\)
\(282\) 0 0
\(283\) 11.8266i 0.703019i −0.936184 0.351510i \(-0.885668\pi\)
0.936184 0.351510i \(-0.114332\pi\)
\(284\) 0 0
\(285\) −0.270826 + 0.251501i −0.0160423 + 0.0148976i
\(286\) 0 0
\(287\) 3.41536i 0.201602i
\(288\) 0 0
\(289\) 12.3999 0.729409
\(290\) 0 0
\(291\) 1.18295 0.0693458
\(292\) 0 0
\(293\) 31.4274i 1.83601i −0.396569 0.918005i \(-0.629799\pi\)
0.396569 0.918005i \(-0.370201\pi\)
\(294\) 0 0
\(295\) 7.88058 + 8.48611i 0.458825 + 0.494081i
\(296\) 0 0
\(297\) 8.14779i 0.472783i
\(298\) 0 0
\(299\) 2.25256 0.130269
\(300\) 0 0
\(301\) −17.0987 −0.985552
\(302\) 0 0
\(303\) 1.40876i 0.0809311i
\(304\) 0 0
\(305\) −13.8856 14.9525i −0.795086 0.856180i
\(306\) 0 0
\(307\) 1.43504i 0.0819018i 0.999161 + 0.0409509i \(0.0130387\pi\)
−0.999161 + 0.0409509i \(0.986961\pi\)
\(308\) 0 0
\(309\) −5.03532 −0.286449
\(310\) 0 0
\(311\) −20.9698 −1.18909 −0.594544 0.804063i \(-0.702667\pi\)
−0.594544 + 0.804063i \(0.702667\pi\)
\(312\) 0 0
\(313\) 0.535929i 0.0302925i 0.999885 + 0.0151463i \(0.00482139\pi\)
−0.999885 + 0.0151463i \(0.995179\pi\)
\(314\) 0 0
\(315\) 8.17266 7.58949i 0.460477 0.427619i
\(316\) 0 0
\(317\) 6.61790i 0.371698i 0.982578 + 0.185849i \(0.0595036\pi\)
−0.982578 + 0.185849i \(0.940496\pi\)
\(318\) 0 0
\(319\) 16.2880 0.911953
\(320\) 0 0
\(321\) −7.41236 −0.413718
\(322\) 0 0
\(323\) 0.728845i 0.0405540i
\(324\) 0 0
\(325\) −11.2320 0.832259i −0.623038 0.0461654i
\(326\) 0 0
\(327\) 3.40744i 0.188432i
\(328\) 0 0
\(329\) 14.1397 0.779546
\(330\) 0 0
\(331\) 1.81617 0.0998255 0.0499127 0.998754i \(-0.484106\pi\)
0.0499127 + 0.998754i \(0.484106\pi\)
\(332\) 0 0
\(333\) 24.8180i 1.36002i
\(334\) 0 0
\(335\) −15.1632 + 14.0812i −0.828454 + 0.769339i
\(336\) 0 0
\(337\) 16.3308i 0.889593i 0.895632 + 0.444796i \(0.146724\pi\)
−0.895632 + 0.444796i \(0.853276\pi\)
\(338\) 0 0
\(339\) 3.15405 0.171304
\(340\) 0 0
\(341\) −17.2090 −0.931922
\(342\) 0 0
\(343\) 19.3891i 1.04691i
\(344\) 0 0
\(345\) 0.740092 + 0.796959i 0.0398452 + 0.0429069i
\(346\) 0 0
\(347\) 12.1771i 0.653700i 0.945076 + 0.326850i \(0.105987\pi\)
−0.945076 + 0.326850i \(0.894013\pi\)
\(348\) 0 0
\(349\) −12.0364 −0.644293 −0.322147 0.946690i \(-0.604404\pi\)
−0.322147 + 0.946690i \(0.604404\pi\)
\(350\) 0 0
\(351\) −6.31454 −0.337045
\(352\) 0 0
\(353\) 30.0447i 1.59912i −0.600588 0.799559i \(-0.705067\pi\)
0.600588 0.799559i \(-0.294933\pi\)
\(354\) 0 0
\(355\) 7.00324 + 7.54135i 0.371693 + 0.400254i
\(356\) 0 0
\(357\) 1.88292i 0.0996547i
\(358\) 0 0
\(359\) −29.6859 −1.56676 −0.783380 0.621543i \(-0.786506\pi\)
−0.783380 + 0.621543i \(0.786506\pi\)
\(360\) 0 0
\(361\) −18.8845 −0.993922
\(362\) 0 0
\(363\) 1.24133i 0.0651527i
\(364\) 0 0
\(365\) −18.5644 + 17.2397i −0.971705 + 0.902368i
\(366\) 0 0
\(367\) 12.4413i 0.649428i −0.945812 0.324714i \(-0.894732\pi\)
0.945812 0.324714i \(-0.105268\pi\)
\(368\) 0 0
\(369\) 5.22900 0.272211
\(370\) 0 0
\(371\) −11.6918 −0.607008
\(372\) 0 0
\(373\) 28.5580i 1.47867i −0.673335 0.739337i \(-0.735139\pi\)
0.673335 0.739337i \(-0.264861\pi\)
\(374\) 0 0
\(375\) −3.39589 4.24735i −0.175363 0.219332i
\(376\) 0 0
\(377\) 12.6232i 0.650128i
\(378\) 0 0
\(379\) 14.8436 0.762465 0.381233 0.924479i \(-0.375500\pi\)
0.381233 + 0.924479i \(0.375500\pi\)
\(380\) 0 0
\(381\) −3.05611 −0.156569
\(382\) 0 0
\(383\) 7.00776i 0.358080i 0.983842 + 0.179040i \(0.0572991\pi\)
−0.983842 + 0.179040i \(0.942701\pi\)
\(384\) 0 0
\(385\) 8.59587 7.98250i 0.438086 0.406826i
\(386\) 0 0
\(387\) 26.1785i 1.33073i
\(388\) 0 0
\(389\) −29.2715 −1.48413 −0.742063 0.670330i \(-0.766153\pi\)
−0.742063 + 0.670330i \(0.766153\pi\)
\(390\) 0 0
\(391\) 2.14477 0.108466
\(392\) 0 0
\(393\) 3.84456i 0.193932i
\(394\) 0 0
\(395\) 12.0963 + 13.0258i 0.608630 + 0.655397i
\(396\) 0 0
\(397\) 32.9288i 1.65265i −0.563196 0.826324i \(-0.690428\pi\)
0.563196 0.826324i \(-0.309572\pi\)
\(398\) 0 0
\(399\) 0.298335 0.0149354
\(400\) 0 0
\(401\) −24.3403 −1.21550 −0.607749 0.794129i \(-0.707927\pi\)
−0.607749 + 0.794129i \(0.707927\pi\)
\(402\) 0 0
\(403\) 13.3370i 0.664363i
\(404\) 0 0
\(405\) 10.5398 + 11.3497i 0.523726 + 0.563969i
\(406\) 0 0
\(407\) 26.1031i 1.29389i
\(408\) 0 0
\(409\) 5.84661 0.289096 0.144548 0.989498i \(-0.453827\pi\)
0.144548 + 0.989498i \(0.453827\pi\)
\(410\) 0 0
\(411\) 4.03196 0.198882
\(412\) 0 0
\(413\) 9.34809i 0.459990i
\(414\) 0 0
\(415\) −8.81274 + 8.18390i −0.432600 + 0.401732i
\(416\) 0 0
\(417\) 4.36543i 0.213776i
\(418\) 0 0
\(419\) −28.0557 −1.37061 −0.685304 0.728257i \(-0.740331\pi\)
−0.685304 + 0.728257i \(0.740331\pi\)
\(420\) 0 0
\(421\) −30.0719 −1.46561 −0.732807 0.680437i \(-0.761790\pi\)
−0.732807 + 0.680437i \(0.761790\pi\)
\(422\) 0 0
\(423\) 21.6482i 1.05257i
\(424\) 0 0
\(425\) −10.6945 0.792436i −0.518762 0.0384388i
\(426\) 0 0
\(427\) 16.4713i 0.797104i
\(428\) 0 0
\(429\) −3.18445 −0.153747
\(430\) 0 0
\(431\) 9.92111 0.477883 0.238941 0.971034i \(-0.423200\pi\)
0.238941 + 0.971034i \(0.423200\pi\)
\(432\) 0 0
\(433\) 9.82152i 0.471992i 0.971754 + 0.235996i \(0.0758353\pi\)
−0.971754 + 0.235996i \(0.924165\pi\)
\(434\) 0 0
\(435\) −4.46612 + 4.14743i −0.214134 + 0.198854i
\(436\) 0 0
\(437\) 0.339824i 0.0162560i
\(438\) 0 0
\(439\) 24.4026 1.16467 0.582336 0.812948i \(-0.302139\pi\)
0.582336 + 0.812948i \(0.302139\pi\)
\(440\) 0 0
\(441\) 10.3412 0.492437
\(442\) 0 0
\(443\) 8.35646i 0.397027i 0.980098 + 0.198514i \(0.0636114\pi\)
−0.980098 + 0.198514i \(0.936389\pi\)
\(444\) 0 0
\(445\) −19.6680 21.1792i −0.932351 1.00399i
\(446\) 0 0
\(447\) 2.62550i 0.124182i
\(448\) 0 0
\(449\) −15.4109 −0.727286 −0.363643 0.931538i \(-0.618467\pi\)
−0.363643 + 0.931538i \(0.618467\pi\)
\(450\) 0 0
\(451\) 5.49978 0.258974
\(452\) 0 0
\(453\) 10.9965i 0.516659i
\(454\) 0 0
\(455\) 6.18644 + 6.66180i 0.290025 + 0.312310i
\(456\) 0 0
\(457\) 22.9314i 1.07269i 0.844000 + 0.536343i \(0.180195\pi\)
−0.844000 + 0.536343i \(0.819805\pi\)
\(458\) 0 0
\(459\) −6.01239 −0.280634
\(460\) 0 0
\(461\) −9.71207 −0.452336 −0.226168 0.974088i \(-0.572620\pi\)
−0.226168 + 0.974088i \(0.572620\pi\)
\(462\) 0 0
\(463\) 13.6091i 0.632469i 0.948681 + 0.316234i \(0.102419\pi\)
−0.948681 + 0.316234i \(0.897581\pi\)
\(464\) 0 0
\(465\) 4.71866 4.38196i 0.218823 0.203208i
\(466\) 0 0
\(467\) 34.9381i 1.61674i −0.588674 0.808371i \(-0.700350\pi\)
0.588674 0.808371i \(-0.299650\pi\)
\(468\) 0 0
\(469\) 16.7034 0.771292
\(470\) 0 0
\(471\) −3.89129 −0.179301
\(472\) 0 0
\(473\) 27.5342i 1.26602i
\(474\) 0 0
\(475\) −0.125556 + 1.69447i −0.00576090 + 0.0777478i
\(476\) 0 0
\(477\) 17.9005i 0.819606i
\(478\) 0 0
\(479\) −6.87962 −0.314338 −0.157169 0.987572i \(-0.550237\pi\)
−0.157169 + 0.987572i \(0.550237\pi\)
\(480\) 0 0
\(481\) 20.2299 0.922406
\(482\) 0 0
\(483\) 0.877911i 0.0399463i
\(484\) 0 0
\(485\) 3.98503 3.70068i 0.180951 0.168039i
\(486\) 0 0
\(487\) 31.8903i 1.44509i 0.691325 + 0.722544i \(0.257027\pi\)
−0.691325 + 0.722544i \(0.742973\pi\)
\(488\) 0 0
\(489\) 9.07136 0.410221
\(490\) 0 0
\(491\) −22.1719 −1.00061 −0.500303 0.865851i \(-0.666778\pi\)
−0.500303 + 0.865851i \(0.666778\pi\)
\(492\) 0 0
\(493\) 12.0192i 0.541317i
\(494\) 0 0
\(495\) 12.2214 + 13.1605i 0.549312 + 0.591520i
\(496\) 0 0
\(497\) 8.30737i 0.372636i
\(498\) 0 0
\(499\) 11.5721 0.518037 0.259019 0.965872i \(-0.416601\pi\)
0.259019 + 0.965872i \(0.416601\pi\)
\(500\) 0 0
\(501\) −1.52506 −0.0681349
\(502\) 0 0
\(503\) 39.2532i 1.75021i −0.483931 0.875106i \(-0.660792\pi\)
0.483931 0.875106i \(-0.339208\pi\)
\(504\) 0 0
\(505\) 4.40709 + 4.74572i 0.196113 + 0.211182i
\(506\) 0 0
\(507\) 3.85513i 0.171212i
\(508\) 0 0
\(509\) 3.61391 0.160184 0.0800919 0.996787i \(-0.474479\pi\)
0.0800919 + 0.996787i \(0.474479\pi\)
\(510\) 0 0
\(511\) 20.4501 0.904658
\(512\) 0 0
\(513\) 0.952620i 0.0420592i
\(514\) 0 0
\(515\) −16.9626 + 15.7522i −0.747461 + 0.694126i
\(516\) 0 0
\(517\) 22.7692i 1.00139i
\(518\) 0 0
\(519\) 3.67858 0.161472
\(520\) 0 0
\(521\) 7.64494 0.334931 0.167465 0.985878i \(-0.446442\pi\)
0.167465 + 0.985878i \(0.446442\pi\)
\(522\) 0 0
\(523\) 5.62852i 0.246118i 0.992399 + 0.123059i \(0.0392704\pi\)
−0.992399 + 0.123059i \(0.960730\pi\)
\(524\) 0 0
\(525\) −0.324364 + 4.37755i −0.0141564 + 0.191052i
\(526\) 0 0
\(527\) 12.6988i 0.553170i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 14.3122 0.621095
\(532\) 0 0
\(533\) 4.26233i 0.184622i
\(534\) 0 0
\(535\) −24.9702 + 23.1884i −1.07956 + 1.00252i
\(536\) 0 0
\(537\) 4.73554i 0.204354i
\(538\) 0 0
\(539\) 10.8767 0.468492
\(540\) 0 0
\(541\) 0.537263 0.0230987 0.0115494 0.999933i \(-0.496324\pi\)
0.0115494 + 0.999933i \(0.496324\pi\)
\(542\) 0 0
\(543\) 0.126744i 0.00543911i
\(544\) 0 0
\(545\) 10.6596 + 11.4787i 0.456609 + 0.491694i
\(546\) 0 0
\(547\) 41.7590i 1.78548i −0.450568 0.892742i \(-0.648778\pi\)
0.450568 0.892742i \(-0.351222\pi\)
\(548\) 0 0
\(549\) −25.2181 −1.07628
\(550\) 0 0
\(551\) 1.90435 0.0811282
\(552\) 0 0
\(553\) 14.3488i 0.610175i
\(554\) 0 0
\(555\) 6.64668 + 7.15740i 0.282136 + 0.303815i
\(556\) 0 0
\(557\) 22.5405i 0.955071i −0.878613 0.477535i \(-0.841530\pi\)
0.878613 0.477535i \(-0.158470\pi\)
\(558\) 0 0
\(559\) 21.3390 0.902542
\(560\) 0 0
\(561\) −3.03208 −0.128015
\(562\) 0 0
\(563\) 31.5366i 1.32911i −0.747240 0.664554i \(-0.768622\pi\)
0.747240 0.664554i \(-0.231378\pi\)
\(564\) 0 0
\(565\) 10.6251 9.86696i 0.447002 0.415106i
\(566\) 0 0
\(567\) 12.5025i 0.525055i
\(568\) 0 0
\(569\) −2.49650 −0.104659 −0.0523294 0.998630i \(-0.516665\pi\)
−0.0523294 + 0.998630i \(0.516665\pi\)
\(570\) 0 0
\(571\) 43.6658 1.82736 0.913678 0.406440i \(-0.133230\pi\)
0.913678 + 0.406440i \(0.133230\pi\)
\(572\) 0 0
\(573\) 8.83919i 0.369262i
\(574\) 0 0
\(575\) 4.98633 + 0.369473i 0.207944 + 0.0154081i
\(576\) 0 0
\(577\) 33.7402i 1.40462i 0.711869 + 0.702312i \(0.247849\pi\)
−0.711869 + 0.702312i \(0.752151\pi\)
\(578\) 0 0
\(579\) −1.04609 −0.0434742
\(580\) 0 0
\(581\) 9.70790 0.402751
\(582\) 0 0
\(583\) 18.8274i 0.779752i
\(584\) 0 0
\(585\) −10.1994 + 9.47160i −0.421693 + 0.391602i
\(586\) 0 0
\(587\) 13.8050i 0.569795i 0.958558 + 0.284898i \(0.0919596\pi\)
−0.958558 + 0.284898i \(0.908040\pi\)
\(588\) 0 0
\(589\) −2.01204 −0.0829047
\(590\) 0 0
\(591\) 13.1757 0.541974
\(592\) 0 0
\(593\) 43.3336i 1.77950i −0.456450 0.889749i \(-0.650879\pi\)
0.456450 0.889749i \(-0.349121\pi\)
\(594\) 0 0
\(595\) 5.89042 + 6.34304i 0.241484 + 0.260039i
\(596\) 0 0
\(597\) 6.91541i 0.283029i
\(598\) 0 0
\(599\) −27.2077 −1.11168 −0.555838 0.831290i \(-0.687603\pi\)
−0.555838 + 0.831290i \(0.687603\pi\)
\(600\) 0 0
\(601\) 39.6299 1.61654 0.808269 0.588813i \(-0.200405\pi\)
0.808269 + 0.588813i \(0.200405\pi\)
\(602\) 0 0
\(603\) 25.5734i 1.04143i
\(604\) 0 0
\(605\) −3.88330 4.18168i −0.157878 0.170010i
\(606\) 0 0
\(607\) 1.10233i 0.0447421i 0.999750 + 0.0223711i \(0.00712152\pi\)
−0.999750 + 0.0223711i \(0.992878\pi\)
\(608\) 0 0
\(609\) 4.91976 0.199359
\(610\) 0 0
\(611\) −17.6462 −0.713887
\(612\) 0 0
\(613\) 13.6705i 0.552145i 0.961137 + 0.276073i \(0.0890331\pi\)
−0.961137 + 0.276073i \(0.910967\pi\)
\(614\) 0 0
\(615\) −1.50802 + 1.40041i −0.0608093 + 0.0564702i
\(616\) 0 0
\(617\) 19.9011i 0.801187i 0.916256 + 0.400594i \(0.131196\pi\)
−0.916256 + 0.400594i \(0.868804\pi\)
\(618\) 0 0
\(619\) −32.1024 −1.29030 −0.645151 0.764055i \(-0.723206\pi\)
−0.645151 + 0.764055i \(0.723206\pi\)
\(620\) 0 0
\(621\) 2.80328 0.112492
\(622\) 0 0
\(623\) 23.3305i 0.934717i
\(624\) 0 0
\(625\) −24.7270 3.68463i −0.989079 0.147385i
\(626\) 0 0
\(627\) 0.480411i 0.0191858i
\(628\) 0 0
\(629\) 19.2620 0.768024
\(630\) 0 0
\(631\) −32.3065 −1.28610 −0.643051 0.765823i \(-0.722332\pi\)
−0.643051 + 0.765823i \(0.722332\pi\)
\(632\) 0 0
\(633\) 0.923435i 0.0367033i
\(634\) 0 0
\(635\) −10.2952 + 9.56057i −0.408552 + 0.379400i
\(636\) 0 0
\(637\) 8.42942i 0.333986i
\(638\) 0 0
\(639\) 12.7188 0.503148
\(640\) 0 0
\(641\) −18.6696 −0.737407 −0.368703 0.929547i \(-0.620198\pi\)
−0.368703 + 0.929547i \(0.620198\pi\)
\(642\) 0 0
\(643\) 19.9459i 0.786590i −0.919412 0.393295i \(-0.871335\pi\)
0.919412 0.393295i \(-0.128665\pi\)
\(644\) 0 0
\(645\) 7.01106 + 7.54978i 0.276060 + 0.297272i
\(646\) 0 0
\(647\) 25.6920i 1.01006i −0.863102 0.505029i \(-0.831482\pi\)
0.863102 0.505029i \(-0.168518\pi\)
\(648\) 0 0
\(649\) 15.0533 0.590894
\(650\) 0 0
\(651\) −5.19796 −0.203724
\(652\) 0 0
\(653\) 14.7648i 0.577791i 0.957361 + 0.288896i \(0.0932880\pi\)
−0.957361 + 0.288896i \(0.906712\pi\)
\(654\) 0 0
\(655\) 12.0271 + 12.9513i 0.469938 + 0.506047i
\(656\) 0 0
\(657\) 31.3096i 1.22150i
\(658\) 0 0
\(659\) 9.53869 0.371574 0.185787 0.982590i \(-0.440516\pi\)
0.185787 + 0.982590i \(0.440516\pi\)
\(660\) 0 0
\(661\) 13.2912 0.516968 0.258484 0.966016i \(-0.416777\pi\)
0.258484 + 0.966016i \(0.416777\pi\)
\(662\) 0 0
\(663\) 2.34986i 0.0912611i
\(664\) 0 0
\(665\) 1.00501 0.933295i 0.0389726 0.0361916i
\(666\) 0 0
\(667\) 5.60395i 0.216986i
\(668\) 0 0
\(669\) 9.99894 0.386581
\(670\) 0 0
\(671\) −26.5239 −1.02395
\(672\) 0 0
\(673\) 11.1517i 0.429868i −0.976629 0.214934i \(-0.931046\pi\)
0.976629 0.214934i \(-0.0689536\pi\)
\(674\) 0 0
\(675\) −13.9781 1.03574i −0.538016 0.0398655i
\(676\) 0 0
\(677\) 27.0771i 1.04066i 0.853966 + 0.520328i \(0.174190\pi\)
−0.853966 + 0.520328i \(0.825810\pi\)
\(678\) 0 0
\(679\) −4.38981 −0.168466
\(680\) 0 0
\(681\) 3.73287 0.143044
\(682\) 0 0
\(683\) 23.8752i 0.913561i −0.889579 0.456780i \(-0.849003\pi\)
0.889579 0.456780i \(-0.150997\pi\)
\(684\) 0 0
\(685\) 13.5826 12.6134i 0.518963 0.481932i
\(686\) 0 0
\(687\) 4.13616i 0.157805i
\(688\) 0 0
\(689\) 14.5912 0.555882
\(690\) 0 0
\(691\) −37.5350 −1.42790 −0.713950 0.700197i \(-0.753096\pi\)
−0.713950 + 0.700197i \(0.753096\pi\)
\(692\) 0 0
\(693\) 14.4973i 0.550706i
\(694\) 0 0
\(695\) −13.6566 14.7059i −0.518023 0.557828i
\(696\) 0 0
\(697\) 4.05838i 0.153722i
\(698\) 0 0
\(699\) −1.15303 −0.0436116
\(700\) 0 0
\(701\) 45.8587 1.73206 0.866030 0.499992i \(-0.166664\pi\)
0.866030 + 0.499992i \(0.166664\pi\)
\(702\) 0 0
\(703\) 3.05192i 0.115105i
\(704\) 0 0
\(705\) −5.79776 6.24325i −0.218356 0.235135i
\(706\) 0 0
\(707\) 5.22777i 0.196611i
\(708\) 0 0
\(709\) −10.2917 −0.386515 −0.193257 0.981148i \(-0.561905\pi\)
−0.193257 + 0.981148i \(0.561905\pi\)
\(710\) 0 0
\(711\) 21.9685 0.823881
\(712\) 0 0
\(713\) 5.92083i 0.221737i
\(714\) 0 0
\(715\) −10.7275 + 9.96207i −0.401187 + 0.372560i
\(716\) 0 0
\(717\) 0.144983i 0.00541449i
\(718\) 0 0
\(719\) −15.2862 −0.570080 −0.285040 0.958516i \(-0.592007\pi\)
−0.285040 + 0.958516i \(0.592007\pi\)
\(720\) 0 0
\(721\) 18.6856 0.695887
\(722\) 0 0
\(723\) 14.4837i 0.538655i
\(724\) 0 0
\(725\) −2.07051 + 27.9431i −0.0768967 + 1.03778i
\(726\) 0 0
\(727\) 18.5486i 0.687930i 0.938982 + 0.343965i \(0.111770\pi\)
−0.938982 + 0.343965i \(0.888230\pi\)
\(728\) 0 0
\(729\) 15.0512 0.557451
\(730\) 0 0
\(731\) 20.3179 0.751485
\(732\) 0 0
\(733\) 29.6045i 1.09347i 0.837307 + 0.546734i \(0.184129\pi\)
−0.837307 + 0.546734i \(0.815871\pi\)
\(734\) 0 0
\(735\) −2.98235 + 2.76954i −0.110006 + 0.102156i
\(736\) 0 0
\(737\) 26.8976i 0.990787i
\(738\) 0 0
\(739\) 44.2455 1.62760 0.813799 0.581147i \(-0.197396\pi\)
0.813799 + 0.581147i \(0.197396\pi\)
\(740\) 0 0
\(741\) −0.372319 −0.0136775
\(742\) 0 0
\(743\) 2.33740i 0.0857509i 0.999080 + 0.0428755i \(0.0136519\pi\)
−0.999080 + 0.0428755i \(0.986348\pi\)
\(744\) 0 0
\(745\) −8.21347 8.84458i −0.300918 0.324040i
\(746\) 0 0
\(747\) 14.8630i 0.543810i
\(748\) 0 0
\(749\) 27.5066 1.00507
\(750\) 0 0
\(751\) 34.4606 1.25748 0.628742 0.777614i \(-0.283570\pi\)
0.628742 + 0.777614i \(0.283570\pi\)
\(752\) 0 0
\(753\) 4.94980i 0.180381i
\(754\) 0 0
\(755\) −34.4008 37.0441i −1.25197 1.34817i
\(756\) 0 0
\(757\) 26.5337i 0.964384i −0.876066 0.482192i \(-0.839841\pi\)
0.876066 0.482192i \(-0.160159\pi\)
\(758\) 0 0
\(759\) 1.41371 0.0513143
\(760\) 0 0
\(761\) −48.2585 −1.74937 −0.874685 0.484691i \(-0.838932\pi\)
−0.874685 + 0.484691i \(0.838932\pi\)
\(762\) 0 0
\(763\) 12.6447i 0.457768i
\(764\) 0 0
\(765\) −9.71135 + 9.01839i −0.351115 + 0.326061i
\(766\) 0 0
\(767\) 11.6663i 0.421246i
\(768\) 0 0
\(769\) −31.6874 −1.14268 −0.571338 0.820715i \(-0.693576\pi\)
−0.571338 + 0.820715i \(0.693576\pi\)
\(770\) 0 0
\(771\) −13.7609 −0.495587
\(772\) 0 0
\(773\) 25.7906i 0.927623i 0.885934 + 0.463811i \(0.153519\pi\)
−0.885934 + 0.463811i \(0.846481\pi\)
\(774\) 0 0
\(775\) 2.18759 29.5232i 0.0785805 1.06051i
\(776\) 0 0
\(777\) 7.88441i 0.282852i
\(778\) 0 0
\(779\) 0.643021 0.0230386
\(780\) 0 0
\(781\) 13.3774 0.478682
\(782\) 0 0
\(783\) 15.7094i 0.561408i
\(784\) 0 0
\(785\) −13.1087 + 12.1733i −0.467868 + 0.434483i
\(786\) 0 0
\(787\) 26.2714i 0.936475i 0.883603 + 0.468237i \(0.155111\pi\)
−0.883603 + 0.468237i \(0.844889\pi\)
\(788\) 0 0
\(789\) 12.1200 0.431482
\(790\) 0 0
\(791\) −11.7044 −0.416159
\(792\) 0 0
\(793\) 20.5560i 0.729967i
\(794\) 0 0
\(795\) 4.79405 + 5.16241i 0.170027 + 0.183092i
\(796\) 0 0
\(797\) 5.81284i 0.205901i −0.994686 0.102951i \(-0.967172\pi\)
0.994686 0.102951i \(-0.0328284\pi\)
\(798\) 0 0
\(799\) −16.8018 −0.594405
\(800\) 0 0
\(801\) −35.7196 −1.26209
\(802\) 0 0
\(803\)