Properties

Label 1840.2.e.f.369.9
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 369.9
Root \(-0.420790i\) of defining polynomial
Character \(\chi\) \(=\) 1840.369
Dual form 1840.2.e.f.369.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.73961i q^{3} +(1.77747 - 1.35668i) q^{5} -3.32224i q^{7} -0.0262434 q^{9} +O(q^{10})\) \(q+1.73961i q^{3} +(1.77747 - 1.35668i) q^{5} -3.32224i q^{7} -0.0262434 q^{9} -5.77103 q^{11} -1.10197i q^{13} +(2.36010 + 3.09211i) q^{15} +0.893847i q^{17} +2.42839 q^{19} +5.77940 q^{21} +1.00000i q^{23} +(1.31882 - 4.82294i) q^{25} +5.17318i q^{27} -4.11268 q^{29} +9.54624 q^{31} -10.0393i q^{33} +(-4.50722 - 5.90519i) q^{35} -7.69904i q^{37} +1.91700 q^{39} +0.00418347 q^{41} -9.97045i q^{43} +(-0.0466469 + 0.0356040i) q^{45} -10.0079i q^{47} -4.03726 q^{49} -1.55495 q^{51} -6.25169i q^{53} +(-10.2579 + 7.82946i) q^{55} +4.22445i q^{57} -10.7764 q^{59} +10.5929 q^{61} +0.0871868i q^{63} +(-1.49502 - 1.95872i) q^{65} -10.9529i q^{67} -1.73961 q^{69} +12.9170 q^{71} -1.89943i q^{73} +(8.39003 + 2.29423i) q^{75} +19.1727i q^{77} -0.216085 q^{79} -9.07804 q^{81} -5.38967i q^{83} +(1.21267 + 1.58879i) q^{85} -7.15446i q^{87} -6.00657 q^{89} -3.66100 q^{91} +16.6067i q^{93} +(4.31640 - 3.29456i) q^{95} +2.08104i q^{97} +0.151451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 20q^{9} + O(q^{10}) \) \( 12q - 20q^{9} - 4q^{11} - 2q^{15} + 8q^{19} + 8q^{25} - 10q^{29} - 18q^{31} + 10q^{35} - 16q^{39} - 2q^{41} + 2q^{45} - 38q^{49} + 24q^{51} - 16q^{55} - 22q^{59} - 8q^{61} + 38q^{65} - 8q^{69} + 34q^{71} - 16q^{75} + 20q^{79} + 28q^{81} + 6q^{85} + 48q^{89} + 8q^{91} - 12q^{95} - 32q^{99} + O(q^{100}) \)

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
\(3\) 1.73961i 1.00436i 0.864762 + 0.502182i \(0.167469\pi\)
−0.864762 + 0.502182i \(0.832531\pi\)
\(4\) 0 0
\(5\) 1.77747 1.35668i 0.794910 0.606727i
\(6\) 0 0
\(7\) 3.32224i 1.25569i −0.778339 0.627844i \(-0.783938\pi\)
0.778339 0.627844i \(-0.216062\pi\)
\(8\) 0 0
\(9\) −0.0262434 −0.00874780
\(10\) 0 0
\(11\) −5.77103 −1.74003 −0.870016 0.493024i \(-0.835891\pi\)
−0.870016 + 0.493024i \(0.835891\pi\)
\(12\) 0 0
\(13\) 1.10197i 0.305631i −0.988255 0.152816i \(-0.951166\pi\)
0.988255 0.152816i \(-0.0488341\pi\)
\(14\) 0 0
\(15\) 2.36010 + 3.09211i 0.609375 + 0.798379i
\(16\) 0 0
\(17\) 0.893847i 0.216790i 0.994108 + 0.108395i \(0.0345711\pi\)
−0.994108 + 0.108395i \(0.965429\pi\)
\(18\) 0 0
\(19\) 2.42839 0.557111 0.278555 0.960420i \(-0.410144\pi\)
0.278555 + 0.960420i \(0.410144\pi\)
\(20\) 0 0
\(21\) 5.77940 1.26117
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 1.31882 4.82294i 0.263764 0.964587i
\(26\) 0 0
\(27\) 5.17318i 0.995578i
\(28\) 0 0
\(29\) −4.11268 −0.763705 −0.381853 0.924223i \(-0.624714\pi\)
−0.381853 + 0.924223i \(0.624714\pi\)
\(30\) 0 0
\(31\) 9.54624 1.71456 0.857278 0.514854i \(-0.172154\pi\)
0.857278 + 0.514854i \(0.172154\pi\)
\(32\) 0 0
\(33\) 10.0393i 1.74763i
\(34\) 0 0
\(35\) −4.50722 5.90519i −0.761860 0.998159i
\(36\) 0 0
\(37\) 7.69904i 1.26572i −0.774268 0.632858i \(-0.781882\pi\)
0.774268 0.632858i \(-0.218118\pi\)
\(38\) 0 0
\(39\) 1.91700 0.306965
\(40\) 0 0
\(41\) 0.00418347 0.000653348 0.000326674 1.00000i \(-0.499896\pi\)
0.000326674 1.00000i \(0.499896\pi\)
\(42\) 0 0
\(43\) 9.97045i 1.52048i −0.649643 0.760240i \(-0.725081\pi\)
0.649643 0.760240i \(-0.274919\pi\)
\(44\) 0 0
\(45\) −0.0466469 + 0.0356040i −0.00695371 + 0.00530753i
\(46\) 0 0
\(47\) 10.0079i 1.45981i −0.683551 0.729903i \(-0.739565\pi\)
0.683551 0.729903i \(-0.260435\pi\)
\(48\) 0 0
\(49\) −4.03726 −0.576751
\(50\) 0 0
\(51\) −1.55495 −0.217736
\(52\) 0 0
\(53\) 6.25169i 0.858735i −0.903130 0.429368i \(-0.858736\pi\)
0.903130 0.429368i \(-0.141264\pi\)
\(54\) 0 0
\(55\) −10.2579 + 7.82946i −1.38317 + 1.05572i
\(56\) 0 0
\(57\) 4.22445i 0.559542i
\(58\) 0 0
\(59\) −10.7764 −1.40297 −0.701486 0.712684i \(-0.747480\pi\)
−0.701486 + 0.712684i \(0.747480\pi\)
\(60\) 0 0
\(61\) 10.5929 1.35628 0.678140 0.734932i \(-0.262786\pi\)
0.678140 + 0.734932i \(0.262786\pi\)
\(62\) 0 0
\(63\) 0.0871868i 0.0109845i
\(64\) 0 0
\(65\) −1.49502 1.95872i −0.185435 0.242949i
\(66\) 0 0
\(67\) 10.9529i 1.33811i −0.743213 0.669055i \(-0.766699\pi\)
0.743213 0.669055i \(-0.233301\pi\)
\(68\) 0 0
\(69\) −1.73961 −0.209424
\(70\) 0 0
\(71\) 12.9170 1.53296 0.766481 0.642267i \(-0.222006\pi\)
0.766481 + 0.642267i \(0.222006\pi\)
\(72\) 0 0
\(73\) 1.89943i 0.222311i −0.993803 0.111156i \(-0.964545\pi\)
0.993803 0.111156i \(-0.0354552\pi\)
\(74\) 0 0
\(75\) 8.39003 + 2.29423i 0.968797 + 0.264915i
\(76\) 0 0
\(77\) 19.1727i 2.18494i
\(78\) 0 0
\(79\) −0.216085 −0.0243114 −0.0121557 0.999926i \(-0.503869\pi\)
−0.0121557 + 0.999926i \(0.503869\pi\)
\(80\) 0 0
\(81\) −9.07804 −1.00867
\(82\) 0 0
\(83\) 5.38967i 0.591593i −0.955251 0.295796i \(-0.904415\pi\)
0.955251 0.295796i \(-0.0955850\pi\)
\(84\) 0 0
\(85\) 1.21267 + 1.58879i 0.131532 + 0.172328i
\(86\) 0 0
\(87\) 7.15446i 0.767038i
\(88\) 0 0
\(89\) −6.00657 −0.636696 −0.318348 0.947974i \(-0.603128\pi\)
−0.318348 + 0.947974i \(0.603128\pi\)
\(90\) 0 0
\(91\) −3.66100 −0.383777
\(92\) 0 0
\(93\) 16.6067i 1.72204i
\(94\) 0 0
\(95\) 4.31640 3.29456i 0.442853 0.338014i
\(96\) 0 0
\(97\) 2.08104i 0.211297i 0.994404 + 0.105649i \(0.0336919\pi\)
−0.994404 + 0.105649i \(0.966308\pi\)
\(98\) 0 0
\(99\) 0.151451 0.0152214
\(100\) 0 0
\(101\) −13.1576 −1.30923 −0.654617 0.755961i \(-0.727170\pi\)
−0.654617 + 0.755961i \(0.727170\pi\)
\(102\) 0 0
\(103\) 18.0956i 1.78301i 0.453008 + 0.891507i \(0.350351\pi\)
−0.453008 + 0.891507i \(0.649649\pi\)
\(104\) 0 0
\(105\) 10.2727 7.84081i 1.00252 0.765185i
\(106\) 0 0
\(107\) 6.97263i 0.674069i −0.941492 0.337035i \(-0.890576\pi\)
0.941492 0.337035i \(-0.109424\pi\)
\(108\) 0 0
\(109\) −10.2873 −0.985344 −0.492672 0.870215i \(-0.663980\pi\)
−0.492672 + 0.870215i \(0.663980\pi\)
\(110\) 0 0
\(111\) 13.3933 1.27124
\(112\) 0 0
\(113\) 5.53454i 0.520646i 0.965522 + 0.260323i \(0.0838290\pi\)
−0.965522 + 0.260323i \(0.916171\pi\)
\(114\) 0 0
\(115\) 1.35668 + 1.77747i 0.126511 + 0.165750i
\(116\) 0 0
\(117\) 0.0289194i 0.00267360i
\(118\) 0 0
\(119\) 2.96957 0.272220
\(120\) 0 0
\(121\) 22.3048 2.02771
\(122\) 0 0
\(123\) 0.00727760i 0.000656199i
\(124\) 0 0
\(125\) −4.19903 10.3619i −0.375573 0.926793i
\(126\) 0 0
\(127\) 11.1580i 0.990110i −0.868862 0.495055i \(-0.835148\pi\)
0.868862 0.495055i \(-0.164852\pi\)
\(128\) 0 0
\(129\) 17.3447 1.52712
\(130\) 0 0
\(131\) 15.0421 1.31423 0.657117 0.753789i \(-0.271776\pi\)
0.657117 + 0.753789i \(0.271776\pi\)
\(132\) 0 0
\(133\) 8.06769i 0.699557i
\(134\) 0 0
\(135\) 7.01836 + 9.19518i 0.604045 + 0.791395i
\(136\) 0 0
\(137\) 2.21231i 0.189010i 0.995524 + 0.0945050i \(0.0301268\pi\)
−0.995524 + 0.0945050i \(0.969873\pi\)
\(138\) 0 0
\(139\) −6.53729 −0.554486 −0.277243 0.960800i \(-0.589421\pi\)
−0.277243 + 0.960800i \(0.589421\pi\)
\(140\) 0 0
\(141\) 17.4099 1.46618
\(142\) 0 0
\(143\) 6.35950i 0.531808i
\(144\) 0 0
\(145\) −7.31017 + 5.57960i −0.607077 + 0.463361i
\(146\) 0 0
\(147\) 7.02326i 0.579269i
\(148\) 0 0
\(149\) 11.1844 0.916263 0.458131 0.888884i \(-0.348519\pi\)
0.458131 + 0.888884i \(0.348519\pi\)
\(150\) 0 0
\(151\) 1.29176 0.105122 0.0525610 0.998618i \(-0.483262\pi\)
0.0525610 + 0.998618i \(0.483262\pi\)
\(152\) 0 0
\(153\) 0.0234576i 0.00189643i
\(154\) 0 0
\(155\) 16.9682 12.9512i 1.36292 1.04027i
\(156\) 0 0
\(157\) 11.0465i 0.881609i 0.897603 + 0.440805i \(0.145307\pi\)
−0.897603 + 0.440805i \(0.854693\pi\)
\(158\) 0 0
\(159\) 10.8755 0.862483
\(160\) 0 0
\(161\) 3.32224 0.261829
\(162\) 0 0
\(163\) 5.04265i 0.394971i 0.980306 + 0.197485i \(0.0632775\pi\)
−0.980306 + 0.197485i \(0.936723\pi\)
\(164\) 0 0
\(165\) −13.6202 17.8447i −1.06033 1.38921i
\(166\) 0 0
\(167\) 1.20759i 0.0934465i −0.998908 0.0467232i \(-0.985122\pi\)
0.998908 0.0467232i \(-0.0148779\pi\)
\(168\) 0 0
\(169\) 11.7857 0.906590
\(170\) 0 0
\(171\) −0.0637292 −0.00487349
\(172\) 0 0
\(173\) 15.7392i 1.19663i 0.801262 + 0.598313i \(0.204162\pi\)
−0.801262 + 0.598313i \(0.795838\pi\)
\(174\) 0 0
\(175\) −16.0229 4.38143i −1.21122 0.331205i
\(176\) 0 0
\(177\) 18.7468i 1.40909i
\(178\) 0 0
\(179\) 6.61963 0.494774 0.247387 0.968917i \(-0.420428\pi\)
0.247387 + 0.968917i \(0.420428\pi\)
\(180\) 0 0
\(181\) −16.0433 −1.19249 −0.596245 0.802803i \(-0.703341\pi\)
−0.596245 + 0.802803i \(0.703341\pi\)
\(182\) 0 0
\(183\) 18.4275i 1.36220i
\(184\) 0 0
\(185\) −10.4452 13.6848i −0.767944 1.00613i
\(186\) 0 0
\(187\) 5.15842i 0.377221i
\(188\) 0 0
\(189\) 17.1865 1.25014
\(190\) 0 0
\(191\) −0.295590 −0.0213881 −0.0106941 0.999943i \(-0.503404\pi\)
−0.0106941 + 0.999943i \(0.503404\pi\)
\(192\) 0 0
\(193\) 1.42564i 0.102620i 0.998683 + 0.0513101i \(0.0163397\pi\)
−0.998683 + 0.0513101i \(0.983660\pi\)
\(194\) 0 0
\(195\) 3.40741 2.60076i 0.244010 0.186244i
\(196\) 0 0
\(197\) 8.60107i 0.612801i −0.951903 0.306401i \(-0.900875\pi\)
0.951903 0.306401i \(-0.0991247\pi\)
\(198\) 0 0
\(199\) 3.81515 0.270449 0.135224 0.990815i \(-0.456824\pi\)
0.135224 + 0.990815i \(0.456824\pi\)
\(200\) 0 0
\(201\) 19.0538 1.34395
\(202\) 0 0
\(203\) 13.6633i 0.958975i
\(204\) 0 0
\(205\) 0.00743600 0.00567564i 0.000519353 0.000396404i
\(206\) 0 0
\(207\) 0.0262434i 0.00182404i
\(208\) 0 0
\(209\) −14.0143 −0.969390
\(210\) 0 0
\(211\) −1.32370 −0.0911273 −0.0455637 0.998961i \(-0.514508\pi\)
−0.0455637 + 0.998961i \(0.514508\pi\)
\(212\) 0 0
\(213\) 22.4705i 1.53965i
\(214\) 0 0
\(215\) −13.5267 17.7222i −0.922516 1.20864i
\(216\) 0 0
\(217\) 31.7149i 2.15295i
\(218\) 0 0
\(219\) 3.30427 0.223282
\(220\) 0 0
\(221\) 0.984992 0.0662577
\(222\) 0 0
\(223\) 25.1286i 1.68274i 0.540462 + 0.841368i \(0.318249\pi\)
−0.540462 + 0.841368i \(0.681751\pi\)
\(224\) 0 0
\(225\) −0.0346103 + 0.126570i −0.00230736 + 0.00843802i
\(226\) 0 0
\(227\) 23.8021i 1.57980i 0.613236 + 0.789900i \(0.289867\pi\)
−0.613236 + 0.789900i \(0.710133\pi\)
\(228\) 0 0
\(229\) 0.789351 0.0521618 0.0260809 0.999660i \(-0.491697\pi\)
0.0260809 + 0.999660i \(0.491697\pi\)
\(230\) 0 0
\(231\) −33.3531 −2.19447
\(232\) 0 0
\(233\) 20.8101i 1.36331i 0.731672 + 0.681656i \(0.238740\pi\)
−0.731672 + 0.681656i \(0.761260\pi\)
\(234\) 0 0
\(235\) −13.5776 17.7888i −0.885704 1.16041i
\(236\) 0 0
\(237\) 0.375903i 0.0244175i
\(238\) 0 0
\(239\) −25.2398 −1.63262 −0.816312 0.577611i \(-0.803985\pi\)
−0.816312 + 0.577611i \(0.803985\pi\)
\(240\) 0 0
\(241\) 5.27710 0.339928 0.169964 0.985450i \(-0.445635\pi\)
0.169964 + 0.985450i \(0.445635\pi\)
\(242\) 0 0
\(243\) 0.272722i 0.0174951i
\(244\) 0 0
\(245\) −7.17612 + 5.47728i −0.458466 + 0.349931i
\(246\) 0 0
\(247\) 2.67601i 0.170270i
\(248\) 0 0
\(249\) 9.37592 0.594175
\(250\) 0 0
\(251\) 10.8439 0.684461 0.342230 0.939616i \(-0.388818\pi\)
0.342230 + 0.939616i \(0.388818\pi\)
\(252\) 0 0
\(253\) 5.77103i 0.362822i
\(254\) 0 0
\(255\) −2.76387 + 2.10957i −0.173081 + 0.132106i
\(256\) 0 0
\(257\) 18.6238i 1.16172i 0.814004 + 0.580859i \(0.197283\pi\)
−0.814004 + 0.580859i \(0.802717\pi\)
\(258\) 0 0
\(259\) −25.5781 −1.58934
\(260\) 0 0
\(261\) 0.107931 0.00668074
\(262\) 0 0
\(263\) 19.4370i 1.19854i −0.800548 0.599269i \(-0.795458\pi\)
0.800548 0.599269i \(-0.204542\pi\)
\(264\) 0 0
\(265\) −8.48156 11.1122i −0.521018 0.682617i
\(266\) 0 0
\(267\) 10.4491i 0.639474i
\(268\) 0 0
\(269\) 3.80493 0.231991 0.115995 0.993250i \(-0.462994\pi\)
0.115995 + 0.993250i \(0.462994\pi\)
\(270\) 0 0
\(271\) 18.2100 1.10618 0.553089 0.833122i \(-0.313449\pi\)
0.553089 + 0.833122i \(0.313449\pi\)
\(272\) 0 0
\(273\) 6.36872i 0.385452i
\(274\) 0 0
\(275\) −7.61095 + 27.8333i −0.458958 + 1.67841i
\(276\) 0 0
\(277\) 14.7624i 0.886988i 0.896277 + 0.443494i \(0.146261\pi\)
−0.896277 + 0.443494i \(0.853739\pi\)
\(278\) 0 0
\(279\) −0.250526 −0.0149986
\(280\) 0 0
\(281\) −6.29738 −0.375670 −0.187835 0.982201i \(-0.560147\pi\)
−0.187835 + 0.982201i \(0.560147\pi\)
\(282\) 0 0
\(283\) 28.4443i 1.69084i 0.534105 + 0.845418i \(0.320649\pi\)
−0.534105 + 0.845418i \(0.679351\pi\)
\(284\) 0 0
\(285\) 5.73124 + 7.50885i 0.339490 + 0.444786i
\(286\) 0 0
\(287\) 0.0138985i 0.000820401i
\(288\) 0 0
\(289\) 16.2010 0.953002
\(290\) 0 0
\(291\) −3.62020 −0.212220
\(292\) 0 0
\(293\) 14.4907i 0.846556i −0.906000 0.423278i \(-0.860879\pi\)
0.906000 0.423278i \(-0.139121\pi\)
\(294\) 0 0
\(295\) −19.1548 + 14.6202i −1.11524 + 0.851221i
\(296\) 0 0
\(297\) 29.8546i 1.73234i
\(298\) 0 0
\(299\) 1.10197 0.0637285
\(300\) 0 0
\(301\) −33.1242 −1.90925
\(302\) 0 0
\(303\) 22.8892i 1.31495i
\(304\) 0 0
\(305\) 18.8286 14.3712i 1.07812 0.822893i
\(306\) 0 0
\(307\) 30.4707i 1.73905i 0.493885 + 0.869527i \(0.335576\pi\)
−0.493885 + 0.869527i \(0.664424\pi\)
\(308\) 0 0
\(309\) −31.4793 −1.79080
\(310\) 0 0
\(311\) −20.9031 −1.18531 −0.592654 0.805457i \(-0.701920\pi\)
−0.592654 + 0.805457i \(0.701920\pi\)
\(312\) 0 0
\(313\) 14.3614i 0.811757i −0.913927 0.405878i \(-0.866966\pi\)
0.913927 0.405878i \(-0.133034\pi\)
\(314\) 0 0
\(315\) 0.118285 + 0.154972i 0.00666460 + 0.00873169i
\(316\) 0 0
\(317\) 33.6939i 1.89244i 0.323525 + 0.946220i \(0.395132\pi\)
−0.323525 + 0.946220i \(0.604868\pi\)
\(318\) 0 0
\(319\) 23.7344 1.32887
\(320\) 0 0
\(321\) 12.1297 0.677011
\(322\) 0 0
\(323\) 2.17061i 0.120776i
\(324\) 0 0
\(325\) −5.31473 1.45330i −0.294808 0.0806146i
\(326\) 0 0
\(327\) 17.8959i 0.989644i
\(328\) 0 0
\(329\) −33.2487 −1.83306
\(330\) 0 0
\(331\) −9.82292 −0.539917 −0.269958 0.962872i \(-0.587010\pi\)
−0.269958 + 0.962872i \(0.587010\pi\)
\(332\) 0 0
\(333\) 0.202049i 0.0110722i
\(334\) 0 0
\(335\) −14.8596 19.4685i −0.811868 1.06368i
\(336\) 0 0
\(337\) 13.2410i 0.721286i −0.932704 0.360643i \(-0.882557\pi\)
0.932704 0.360643i \(-0.117443\pi\)
\(338\) 0 0
\(339\) −9.62795 −0.522918
\(340\) 0 0
\(341\) −55.0917 −2.98338
\(342\) 0 0
\(343\) 9.84292i 0.531468i
\(344\) 0 0
\(345\) −3.09211 + 2.36010i −0.166474 + 0.127064i
\(346\) 0 0
\(347\) 9.15627i 0.491534i 0.969329 + 0.245767i \(0.0790399\pi\)
−0.969329 + 0.245767i \(0.920960\pi\)
\(348\) 0 0
\(349\) −25.7744 −1.37967 −0.689836 0.723966i \(-0.742317\pi\)
−0.689836 + 0.723966i \(0.742317\pi\)
\(350\) 0 0
\(351\) 5.70068 0.304280
\(352\) 0 0
\(353\) 2.40654i 0.128087i 0.997947 + 0.0640436i \(0.0203997\pi\)
−0.997947 + 0.0640436i \(0.979600\pi\)
\(354\) 0 0
\(355\) 22.9596 17.5242i 1.21857 0.930090i
\(356\) 0 0
\(357\) 5.16590i 0.273408i
\(358\) 0 0
\(359\) 21.5236 1.13597 0.567985 0.823039i \(-0.307723\pi\)
0.567985 + 0.823039i \(0.307723\pi\)
\(360\) 0 0
\(361\) −13.1029 −0.689628
\(362\) 0 0
\(363\) 38.8016i 2.03656i
\(364\) 0 0
\(365\) −2.57692 3.37618i −0.134882 0.176717i
\(366\) 0 0
\(367\) 6.47203i 0.337837i 0.985630 + 0.168919i \(0.0540275\pi\)
−0.985630 + 0.168919i \(0.945972\pi\)
\(368\) 0 0
\(369\) −0.000109788 0 −5.71536e−6 0
\(370\) 0 0
\(371\) −20.7696 −1.07830
\(372\) 0 0
\(373\) 27.7866i 1.43874i 0.694629 + 0.719368i \(0.255569\pi\)
−0.694629 + 0.719368i \(0.744431\pi\)
\(374\) 0 0
\(375\) 18.0256 7.30467i 0.930838 0.377212i
\(376\) 0 0
\(377\) 4.53204i 0.233412i
\(378\) 0 0
\(379\) 7.63904 0.392391 0.196196 0.980565i \(-0.437141\pi\)
0.196196 + 0.980565i \(0.437141\pi\)
\(380\) 0 0
\(381\) 19.4105 0.994432
\(382\) 0 0
\(383\) 19.4206i 0.992348i −0.868223 0.496174i \(-0.834738\pi\)
0.868223 0.496174i \(-0.165262\pi\)
\(384\) 0 0
\(385\) 26.0113 + 34.0790i 1.32566 + 1.73683i
\(386\) 0 0
\(387\) 0.261659i 0.0133009i
\(388\) 0 0
\(389\) 26.1255 1.32461 0.662306 0.749233i \(-0.269578\pi\)
0.662306 + 0.749233i \(0.269578\pi\)
\(390\) 0 0
\(391\) −0.893847 −0.0452038
\(392\) 0 0
\(393\) 26.1674i 1.31997i
\(394\) 0 0
\(395\) −0.384085 + 0.293158i −0.0193254 + 0.0147504i
\(396\) 0 0
\(397\) 11.5388i 0.579117i −0.957160 0.289558i \(-0.906492\pi\)
0.957160 0.289558i \(-0.0935085\pi\)
\(398\) 0 0
\(399\) 14.0346 0.702610
\(400\) 0 0
\(401\) −0.188549 −0.00941568 −0.00470784 0.999989i \(-0.501499\pi\)
−0.00470784 + 0.999989i \(0.501499\pi\)
\(402\) 0 0
\(403\) 10.5197i 0.524022i
\(404\) 0 0
\(405\) −16.1360 + 12.3160i −0.801803 + 0.611988i
\(406\) 0 0
\(407\) 44.4314i 2.20238i
\(408\) 0 0
\(409\) 8.48327 0.419471 0.209735 0.977758i \(-0.432740\pi\)
0.209735 + 0.977758i \(0.432740\pi\)
\(410\) 0 0
\(411\) −3.84855 −0.189835
\(412\) 0 0
\(413\) 35.8018i 1.76169i
\(414\) 0 0
\(415\) −7.31207 9.57999i −0.358935 0.470263i
\(416\) 0 0
\(417\) 11.3723i 0.556906i
\(418\) 0 0
\(419\) −2.15604 −0.105329 −0.0526647 0.998612i \(-0.516771\pi\)
−0.0526647 + 0.998612i \(0.516771\pi\)
\(420\) 0 0
\(421\) 8.01842 0.390794 0.195397 0.980724i \(-0.437400\pi\)
0.195397 + 0.980724i \(0.437400\pi\)
\(422\) 0 0
\(423\) 0.262642i 0.0127701i
\(424\) 0 0
\(425\) 4.31097 + 1.17882i 0.209113 + 0.0571814i
\(426\) 0 0
\(427\) 35.1921i 1.70307i
\(428\) 0 0
\(429\) −11.0630 −0.534129
\(430\) 0 0
\(431\) 15.3343 0.738629 0.369315 0.929304i \(-0.379592\pi\)
0.369315 + 0.929304i \(0.379592\pi\)
\(432\) 0 0
\(433\) 16.3093i 0.783777i −0.920013 0.391888i \(-0.871822\pi\)
0.920013 0.391888i \(-0.128178\pi\)
\(434\) 0 0
\(435\) −9.70633 12.7169i −0.465383 0.609726i
\(436\) 0 0
\(437\) 2.42839i 0.116166i
\(438\) 0 0
\(439\) −23.9534 −1.14323 −0.571617 0.820520i \(-0.693684\pi\)
−0.571617 + 0.820520i \(0.693684\pi\)
\(440\) 0 0
\(441\) 0.105951 0.00504531
\(442\) 0 0
\(443\) 29.2360i 1.38905i −0.719471 0.694523i \(-0.755616\pi\)
0.719471 0.694523i \(-0.244384\pi\)
\(444\) 0 0
\(445\) −10.6765 + 8.14902i −0.506116 + 0.386301i
\(446\) 0 0
\(447\) 19.4565i 0.920262i
\(448\) 0 0
\(449\) 21.2244 1.00164 0.500822 0.865550i \(-0.333031\pi\)
0.500822 + 0.865550i \(0.333031\pi\)
\(450\) 0 0
\(451\) −0.0241429 −0.00113685
\(452\) 0 0
\(453\) 2.24716i 0.105581i
\(454\) 0 0
\(455\) −6.50733 + 4.96682i −0.305069 + 0.232848i
\(456\) 0 0
\(457\) 31.5959i 1.47799i −0.673710 0.738996i \(-0.735300\pi\)
0.673710 0.738996i \(-0.264700\pi\)
\(458\) 0 0
\(459\) −4.62403 −0.215831
\(460\) 0 0
\(461\) 16.4858 0.767820 0.383910 0.923370i \(-0.374577\pi\)
0.383910 + 0.923370i \(0.374577\pi\)
\(462\) 0 0
\(463\) 30.1555i 1.40144i 0.713435 + 0.700722i \(0.247139\pi\)
−0.713435 + 0.700722i \(0.752861\pi\)
\(464\) 0 0
\(465\) 22.5301 + 29.5180i 1.04481 + 1.36887i
\(466\) 0 0
\(467\) 7.89645i 0.365404i 0.983168 + 0.182702i \(0.0584844\pi\)
−0.983168 + 0.182702i \(0.941516\pi\)
\(468\) 0 0
\(469\) −36.3882 −1.68025
\(470\) 0 0
\(471\) −19.2167 −0.885457
\(472\) 0 0
\(473\) 57.5398i 2.64568i
\(474\) 0 0
\(475\) 3.20261 11.7120i 0.146946 0.537382i
\(476\) 0 0
\(477\) 0.164066i 0.00751205i
\(478\) 0 0
\(479\) 39.5234 1.80587 0.902935 0.429778i \(-0.141408\pi\)
0.902935 + 0.429778i \(0.141408\pi\)
\(480\) 0 0
\(481\) −8.48411 −0.386842
\(482\) 0 0
\(483\) 5.77940i 0.262972i
\(484\) 0 0
\(485\) 2.82331 + 3.69899i 0.128200 + 0.167962i
\(486\) 0 0
\(487\) 3.20444i 0.145207i −0.997361 0.0726035i \(-0.976869\pi\)
0.997361 0.0726035i \(-0.0231308\pi\)
\(488\) 0 0
\(489\) −8.77224 −0.396695
\(490\) 0 0
\(491\) −34.8865 −1.57441 −0.787203 0.616694i \(-0.788472\pi\)
−0.787203 + 0.616694i \(0.788472\pi\)
\(492\) 0 0
\(493\) 3.67611i 0.165564i
\(494\) 0 0
\(495\) 0.269201 0.205472i 0.0120997 0.00923527i
\(496\) 0 0
\(497\) 42.9132i 1.92492i
\(498\) 0 0
\(499\) 33.1594 1.48442 0.742210 0.670167i \(-0.233778\pi\)
0.742210 + 0.670167i \(0.233778\pi\)
\(500\) 0 0
\(501\) 2.10074 0.0938543
\(502\) 0 0
\(503\) 7.05945i 0.314765i 0.987538 + 0.157383i \(0.0503056\pi\)
−0.987538 + 0.157383i \(0.949694\pi\)
\(504\) 0 0
\(505\) −23.3874 + 17.8508i −1.04072 + 0.794348i
\(506\) 0 0
\(507\) 20.5025i 0.910546i
\(508\) 0 0
\(509\) −16.6812 −0.739382 −0.369691 0.929155i \(-0.620536\pi\)
−0.369691 + 0.929155i \(0.620536\pi\)
\(510\) 0 0
\(511\) −6.31035 −0.279154
\(512\) 0 0
\(513\) 12.5625i 0.554648i
\(514\) 0 0
\(515\) 24.5500 + 32.1645i 1.08180 + 1.41734i
\(516\) 0 0
\(517\) 57.7560i 2.54011i
\(518\) 0 0
\(519\) −27.3800 −1.20185
\(520\) 0 0
\(521\) −24.9941 −1.09501 −0.547507 0.836801i \(-0.684423\pi\)
−0.547507 + 0.836801i \(0.684423\pi\)
\(522\) 0 0
\(523\) 14.3283i 0.626535i −0.949665 0.313267i \(-0.898576\pi\)
0.949665 0.313267i \(-0.101424\pi\)
\(524\) 0 0
\(525\) 7.62199 27.8737i 0.332651 1.21651i
\(526\) 0 0
\(527\) 8.53289i 0.371698i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) 0 0
\(531\) 0.282810 0.0122729
\(532\) 0 0
\(533\) 0.00461005i 0.000199683i
\(534\) 0 0
\(535\) −9.45965 12.3937i −0.408976 0.535824i
\(536\) 0 0
\(537\) 11.5156i 0.496934i
\(538\) 0 0
\(539\) 23.2992 1.00357
\(540\) 0 0
\(541\) 22.0323 0.947244 0.473622 0.880728i \(-0.342946\pi\)
0.473622 + 0.880728i \(0.342946\pi\)
\(542\) 0 0
\(543\) 27.9091i 1.19769i
\(544\) 0 0
\(545\) −18.2854 + 13.9566i −0.783260 + 0.597835i
\(546\) 0 0
\(547\) 21.5194i 0.920104i −0.887892 0.460052i \(-0.847831\pi\)
0.887892 0.460052i \(-0.152169\pi\)
\(548\) 0 0
\(549\) −0.277993 −0.0118645
\(550\) 0 0
\(551\) −9.98719 −0.425468
\(552\) 0 0
\(553\) 0.717884i 0.0305276i
\(554\) 0 0
\(555\) 23.8063 18.1705i 1.01052 0.771295i
\(556\) 0 0
\(557\) 21.1923i 0.897945i −0.893546 0.448972i \(-0.851790\pi\)
0.893546 0.448972i \(-0.148210\pi\)
\(558\) 0 0
\(559\) −10.9871 −0.464706
\(560\) 0 0
\(561\) 8.97364 0.378867
\(562\) 0 0
\(563\) 23.6292i 0.995851i 0.867220 + 0.497925i \(0.165905\pi\)
−0.867220 + 0.497925i \(0.834095\pi\)
\(564\) 0 0
\(565\) 7.50862 + 9.83750i 0.315890 + 0.413867i
\(566\) 0 0
\(567\) 30.1594i 1.26658i
\(568\) 0 0
\(569\) 33.7490 1.41483 0.707415 0.706798i \(-0.249861\pi\)
0.707415 + 0.706798i \(0.249861\pi\)
\(570\) 0 0
\(571\) 25.4667 1.06575 0.532874 0.846194i \(-0.321112\pi\)
0.532874 + 0.846194i \(0.321112\pi\)
\(572\) 0 0
\(573\) 0.514211i 0.0214815i
\(574\) 0 0
\(575\) 4.82294 + 1.31882i 0.201130 + 0.0549986i
\(576\) 0 0
\(577\) 22.7293i 0.946234i −0.881000 0.473117i \(-0.843129\pi\)
0.881000 0.473117i \(-0.156871\pi\)
\(578\) 0 0
\(579\) −2.48006 −0.103068
\(580\) 0 0
\(581\) −17.9057 −0.742856
\(582\) 0 0
\(583\) 36.0787i 1.49423i
\(584\) 0 0
\(585\) 0.0392345 + 0.0514035i 0.00162215 + 0.00212527i
\(586\) 0 0
\(587\) 35.6609i 1.47188i 0.677045 + 0.735941i \(0.263260\pi\)
−0.677045 + 0.735941i \(0.736740\pi\)
\(588\) 0 0
\(589\) 23.1820 0.955198
\(590\) 0 0
\(591\) 14.9625 0.615476
\(592\) 0 0
\(593\) 20.8412i 0.855845i −0.903815 0.427922i \(-0.859246\pi\)
0.903815 0.427922i \(-0.140754\pi\)
\(594\) 0 0
\(595\) 5.27834 4.02877i 0.216391 0.165163i
\(596\) 0 0
\(597\) 6.63687i 0.271629i
\(598\) 0 0
\(599\) −10.9952 −0.449252 −0.224626 0.974445i \(-0.572116\pi\)
−0.224626 + 0.974445i \(0.572116\pi\)
\(600\) 0 0
\(601\) 2.35032 0.0958714 0.0479357 0.998850i \(-0.484736\pi\)
0.0479357 + 0.998850i \(0.484736\pi\)
\(602\) 0 0
\(603\) 0.287442i 0.0117055i
\(604\) 0 0
\(605\) 39.6462 30.2605i 1.61185 1.23027i
\(606\) 0 0
\(607\) 31.8412i 1.29239i −0.763170 0.646197i \(-0.776358\pi\)
0.763170 0.646197i \(-0.223642\pi\)
\(608\) 0 0
\(609\) −23.7688 −0.963160
\(610\) 0 0
\(611\) −11.0284 −0.446162
\(612\) 0 0
\(613\) 29.0597i 1.17371i −0.809692 0.586856i \(-0.800366\pi\)
0.809692 0.586856i \(-0.199634\pi\)
\(614\) 0 0
\(615\) 0.00987340 + 0.0129357i 0.000398134 + 0.000521619i
\(616\) 0 0
\(617\) 29.9851i 1.20715i −0.797304 0.603577i \(-0.793741\pi\)
0.797304 0.603577i \(-0.206259\pi\)
\(618\) 0 0
\(619\) −16.9204 −0.680089 −0.340045 0.940409i \(-0.610442\pi\)
−0.340045 + 0.940409i \(0.610442\pi\)
\(620\) 0 0
\(621\) −5.17318 −0.207592
\(622\) 0 0
\(623\) 19.9553i 0.799491i
\(624\) 0 0
\(625\) −21.5214 12.7212i −0.860857 0.508847i
\(626\) 0 0
\(627\) 24.3794i 0.973621i
\(628\) 0 0
\(629\) 6.88177 0.274394
\(630\) 0 0
\(631\) 20.4522 0.814188 0.407094 0.913386i \(-0.366542\pi\)
0.407094 + 0.913386i \(0.366542\pi\)
\(632\) 0 0
\(633\) 2.30272i 0.0915250i
\(634\) 0 0
\(635\) −15.1378 19.8330i −0.600727 0.787049i
\(636\) 0 0
\(637\) 4.44894i 0.176273i
\(638\) 0 0
\(639\) −0.338985 −0.0134100
\(640\) 0 0
\(641\) −8.27686 −0.326916 −0.163458 0.986550i \(-0.552265\pi\)
−0.163458 + 0.986550i \(0.552265\pi\)
\(642\) 0 0
\(643\) 0.627685i 0.0247535i 0.999923 + 0.0123767i \(0.00393974\pi\)
−0.999923 + 0.0123767i \(0.996060\pi\)
\(644\) 0 0
\(645\) 30.8297 23.5313i 1.21392 0.926543i
\(646\) 0 0
\(647\) 12.3508i 0.485561i −0.970081 0.242781i \(-0.921940\pi\)
0.970081 0.242781i \(-0.0780596\pi\)
\(648\) 0 0
\(649\) 62.1911 2.44121
\(650\) 0 0
\(651\) 55.1715 2.16234
\(652\) 0 0
\(653\) 18.3211i 0.716959i 0.933538 + 0.358480i \(0.116705\pi\)
−0.933538 + 0.358480i \(0.883295\pi\)
\(654\) 0 0
\(655\) 26.7369 20.4074i 1.04470 0.797381i
\(656\) 0 0
\(657\) 0.0498475i 0.00194473i
\(658\) 0 0
\(659\) −39.1896 −1.52661 −0.763306 0.646038i \(-0.776425\pi\)
−0.763306 + 0.646038i \(0.776425\pi\)
\(660\) 0 0
\(661\) 9.38565 0.365060 0.182530 0.983200i \(-0.441571\pi\)
0.182530 + 0.983200i \(0.441571\pi\)
\(662\) 0 0
\(663\) 1.71350i 0.0665469i
\(664\) 0 0
\(665\) −10.9453 14.3401i −0.424440 0.556085i
\(666\) 0 0
\(667\) 4.11268i 0.159244i
\(668\) 0 0
\(669\) −43.7140 −1.69008
\(670\) 0 0
\(671\) −61.1319 −2.35997
\(672\) 0 0
\(673\) 8.05600i 0.310536i −0.987872 0.155268i \(-0.950376\pi\)
0.987872 0.155268i \(-0.0496241\pi\)
\(674\) 0 0
\(675\) 24.9499 + 6.82249i 0.960322 + 0.262598i
\(676\) 0 0
\(677\) 16.9461i 0.651293i −0.945492 0.325647i \(-0.894418\pi\)
0.945492 0.325647i \(-0.105582\pi\)
\(678\) 0 0
\(679\) 6.91370 0.265324
\(680\) 0 0
\(681\) −41.4063 −1.58669
\(682\) 0 0
\(683\) 0.111363i 0.00426119i −0.999998 0.00213059i \(-0.999322\pi\)
0.999998 0.00213059i \(-0.000678190\pi\)
\(684\) 0 0
\(685\) 3.00140 + 3.93231i 0.114678 + 0.150246i
\(686\) 0 0
\(687\) 1.37316i 0.0523894i
\(688\) 0 0
\(689\) −6.88917 −0.262456
\(690\) 0 0
\(691\) 38.1718 1.45212 0.726062 0.687629i \(-0.241348\pi\)
0.726062 + 0.687629i \(0.241348\pi\)
\(692\) 0 0
\(693\) 0.503158i 0.0191134i
\(694\) 0 0
\(695\) −11.6199 + 8.86903i −0.440766 + 0.336421i
\(696\) 0 0
\(697\) 0.00373938i 0.000141639i
\(698\) 0 0
\(699\) −36.2014 −1.36926
\(700\) 0 0
\(701\) 38.7698 1.46431 0.732157 0.681136i \(-0.238514\pi\)
0.732157 + 0.681136i \(0.238514\pi\)
\(702\) 0 0
\(703\) 18.6963i 0.705144i
\(704\) 0 0
\(705\) 30.9456 23.6197i 1.16548 0.889569i
\(706\) 0 0
\(707\) 43.7128i 1.64399i
\(708\) 0 0
\(709\) 47.4028 1.78025 0.890126 0.455715i \(-0.150617\pi\)
0.890126 + 0.455715i \(0.150617\pi\)
\(710\) 0 0
\(711\) 0.00567080 0.000212671
\(712\) 0 0
\(713\) 9.54624i 0.357510i
\(714\) 0 0
\(715\) 8.62782 + 11.3038i 0.322662 + 0.422739i
\(716\) 0 0
\(717\) 43.9073i 1.63975i
\(718\) 0 0
\(719\) −17.7370 −0.661479 −0.330740 0.943722i \(-0.607298\pi\)
−0.330740 + 0.943722i \(0.607298\pi\)
\(720\) 0 0
\(721\) 60.1179 2.23891
\(722\) 0 0
\(723\) 9.18010i 0.341412i
\(724\) 0 0
\(725\) −5.42388 + 19.8352i −0.201438 + 0.736660i
\(726\) 0 0
\(727\) 50.7341i 1.88163i 0.338927 + 0.940813i \(0.389936\pi\)
−0.338927 + 0.940813i \(0.610064\pi\)
\(728\) 0 0
\(729\) −26.7597 −0.991100
\(730\) 0 0
\(731\) 8.91206 0.329625
\(732\) 0 0
\(733\) 18.9970i 0.701670i 0.936437 + 0.350835i \(0.114102\pi\)
−0.936437 + 0.350835i \(0.885898\pi\)
\(734\) 0 0
\(735\) −9.52834 12.4837i −0.351458 0.460466i
\(736\) 0 0
\(737\) 63.2096i 2.32835i
\(738\) 0 0
\(739\) −44.6999 −1.64431 −0.822156 0.569263i \(-0.807229\pi\)
−0.822156 + 0.569263i \(0.807229\pi\)
\(740\) 0 0
\(741\) 4.65522 0.171014
\(742\) 0 0
\(743\) 38.9841i 1.43019i 0.699029 + 0.715094i \(0.253616\pi\)
−0.699029 + 0.715094i \(0.746384\pi\)
\(744\) 0 0
\(745\) 19.8800 15.1737i 0.728347 0.555922i
\(746\) 0 0
\(747\) 0.141443i 0.00517513i
\(748\) 0 0
\(749\) −23.1647 −0.846421
\(750\) 0 0
\(751\) −3.97027 −0.144877 −0.0724386 0.997373i \(-0.523078\pi\)
−0.0724386 + 0.997373i \(0.523078\pi\)
\(752\) 0 0
\(753\) 18.8641i 0.687448i
\(754\) 0 0
\(755\) 2.29607 1.75251i 0.0835625 0.0637804i
\(756\) 0 0
\(757\) 23.2885i 0.846436i −0.906028 0.423218i \(-0.860900\pi\)
0.906028 0.423218i \(-0.139100\pi\)
\(758\) 0 0
\(759\) 10.0393 0.364405
\(760\) 0 0
\(761\) 5.62214 0.203802 0.101901 0.994795i \(-0.467507\pi\)
0.101901 + 0.994795i \(0.467507\pi\)
\(762\) 0 0
\(763\) 34.1768i 1.23728i
\(764\) 0 0
\(765\) −0.0318245 0.0416952i −0.00115062 0.00150749i
\(766\) 0 0
\(767\) 11.8753i 0.428792i
\(768\) 0 0
\(769\) 33.0457 1.19166 0.595828 0.803112i \(-0.296824\pi\)
0.595828 + 0.803112i \(0.296824\pi\)
\(770\) 0 0
\(771\) −32.3981 −1.16679
\(772\) 0 0
\(773\) 46.8196i 1.68398i 0.539491 + 0.841991i \(0.318617\pi\)
−0.539491 + 0.841991i \(0.681383\pi\)
\(774\) 0 0
\(775\) 12.5898 46.0409i 0.452238 1.65384i
\(776\) 0 0
\(777\) 44.4958i 1.59628i
\(778\) 0 0
\(779\) 0.0101591 0.000363987
\(780\) 0 0
\(781\) −74.5442 −2.66740
\(782\) 0 0
\(783\) 21.2756i 0.760328i
\(784\) 0 0
\(785\) 14.9866 + 19.6349i 0.534896 + 0.700800i
\(786\) 0 0
\(787\) 35.1470i 1.25286i −0.779479 0.626428i \(-0.784516\pi\)
0.779479 0.626428i \(-0.215484\pi\)
\(788\) 0 0
\(789\) 33.8128 1.20377
\(790\) 0 0
\(791\) 18.3871 0.653769
\(792\) 0 0
\(793\) 11.6730i 0.414522i
\(794\) 0 0
\(795\) 19.3309 14.7546i 0.685597 0.523292i
\(796\) 0 0
\(797\) 21.8566i 0.774200i 0.922038 + 0.387100i \(0.126523\pi\)
−0.922038 + 0.387100i \(0.873477\pi\)
\(798\) 0 0
\(799\) 8.94556 0.316471
\(800\) 0 0
\(801\) 0.157633 0.00556969
\(802\) 0 0