Properties

Label 1520.2.d.i.609.2
Level $1520$
Weight $2$
Character 1520.609
Analytic conductor $12.137$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1520.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1372611072\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.14077504.2
Defining polynomial: \( x^{6} + 9x^{4} + 14x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 609.2
Root \(-1.23277i\) of defining polynomial
Character \(\chi\) \(=\) 1520.609
Dual form 1520.2.d.i.609.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.62236i q^{3} +(-1.92411 - 1.13921i) q^{5} +4.74397i q^{7} +0.367938 q^{9} +O(q^{10})\) \(q-1.62236i q^{3} +(-1.92411 - 1.13921i) q^{5} +4.74397i q^{7} +0.367938 q^{9} -4.48028 q^{11} +0.843176i q^{13} +(-1.84822 + 3.12160i) q^{15} -5.52315i q^{17} +1.00000 q^{19} +7.69643 q^{21} +0.779187i q^{23} +(2.40439 + 4.38394i) q^{25} -5.46402i q^{27} +10.6570 q^{29} +8.65699 q^{31} +7.26864i q^{33} +(5.40439 - 9.12790i) q^{35} -1.62236i q^{37} +1.36794 q^{39} +4.73588 q^{41} +9.67504i q^{43} +(-0.707953 - 0.419160i) q^{45} +3.18559i q^{47} -15.5052 q^{49} -8.96056 q^{51} -6.17922i q^{53} +(8.62054 + 5.10399i) q^{55} -1.62236i q^{57} +11.6964 q^{59} +6.48028 q^{61} +1.74549i q^{63} +(0.960558 - 1.62236i) q^{65} -14.8880i q^{67} +1.26412 q^{69} -0.303566 q^{71} +10.0800i q^{73} +(7.11234 - 3.90079i) q^{75} -21.2543i q^{77} +4.00000 q^{79} -7.76081 q^{81} -0.779187i q^{83} +(-6.29205 + 10.6271i) q^{85} -17.2895i q^{87} +5.69643 q^{89} -4.00000 q^{91} -14.0448i q^{93} +(-1.92411 - 1.13921i) q^{95} +6.17922i q^{97} -1.64847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{5} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{5} - 10 q^{9} - 18 q^{11} + 10 q^{15} + 6 q^{19} + 4 q^{21} - 5 q^{25} + 4 q^{29} - 8 q^{31} + 13 q^{35} - 4 q^{39} + 4 q^{41} - 27 q^{45} - 12 q^{49} - 36 q^{51} - q^{55} + 28 q^{59} + 30 q^{61} - 12 q^{65} + 32 q^{69} - 44 q^{71} + 46 q^{75} + 24 q^{79} + 50 q^{81} - 15 q^{85} - 8 q^{89} - 24 q^{91} - q^{95} + 90 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(401\) \(1141\) \(1217\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 1.62236i 0.936672i −0.883551 0.468336i \(-0.844854\pi\)
0.883551 0.468336i \(-0.155146\pi\)
\(4\) 0 0
\(5\) −1.92411 1.13921i −0.860487 0.509472i
\(6\) 0 0
\(7\) 4.74397i 1.79305i 0.442993 + 0.896525i \(0.353917\pi\)
−0.442993 + 0.896525i \(0.646083\pi\)
\(8\) 0 0
\(9\) 0.367938 0.122646
\(10\) 0 0
\(11\) −4.48028 −1.35085 −0.675427 0.737426i \(-0.736041\pi\)
−0.675427 + 0.737426i \(0.736041\pi\)
\(12\) 0 0
\(13\) 0.843176i 0.233855i 0.993140 + 0.116928i \(0.0373045\pi\)
−0.993140 + 0.116928i \(0.962695\pi\)
\(14\) 0 0
\(15\) −1.84822 + 3.12160i −0.477208 + 0.805994i
\(16\) 0 0
\(17\) 5.52315i 1.33956i −0.742559 0.669781i \(-0.766388\pi\)
0.742559 0.669781i \(-0.233612\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 7.69643 1.67950
\(22\) 0 0
\(23\) 0.779187i 0.162472i 0.996695 + 0.0812358i \(0.0258867\pi\)
−0.996695 + 0.0812358i \(0.974113\pi\)
\(24\) 0 0
\(25\) 2.40439 + 4.38394i 0.480877 + 0.876788i
\(26\) 0 0
\(27\) 5.46402i 1.05155i
\(28\) 0 0
\(29\) 10.6570 1.97895 0.989477 0.144691i \(-0.0462189\pi\)
0.989477 + 0.144691i \(0.0462189\pi\)
\(30\) 0 0
\(31\) 8.65699 1.55484 0.777421 0.628981i \(-0.216528\pi\)
0.777421 + 0.628981i \(0.216528\pi\)
\(32\) 0 0
\(33\) 7.26864i 1.26531i
\(34\) 0 0
\(35\) 5.40439 9.12790i 0.913508 1.54290i
\(36\) 0 0
\(37\) 1.62236i 0.266715i −0.991068 0.133357i \(-0.957424\pi\)
0.991068 0.133357i \(-0.0425758\pi\)
\(38\) 0 0
\(39\) 1.36794 0.219045
\(40\) 0 0
\(41\) 4.73588 0.739620 0.369810 0.929107i \(-0.379423\pi\)
0.369810 + 0.929107i \(0.379423\pi\)
\(42\) 0 0
\(43\) 9.67504i 1.47543i 0.675112 + 0.737715i \(0.264095\pi\)
−0.675112 + 0.737715i \(0.735905\pi\)
\(44\) 0 0
\(45\) −0.707953 0.419160i −0.105535 0.0624847i
\(46\) 0 0
\(47\) 3.18559i 0.464666i 0.972636 + 0.232333i \(0.0746360\pi\)
−0.972636 + 0.232333i \(0.925364\pi\)
\(48\) 0 0
\(49\) −15.5052 −2.21503
\(50\) 0 0
\(51\) −8.96056 −1.25473
\(52\) 0 0
\(53\) 6.17922i 0.848780i −0.905479 0.424390i \(-0.860488\pi\)
0.905479 0.424390i \(-0.139512\pi\)
\(54\) 0 0
\(55\) 8.62054 + 5.10399i 1.16239 + 0.688222i
\(56\) 0 0
\(57\) 1.62236i 0.214887i
\(58\) 0 0
\(59\) 11.6964 1.52275 0.761373 0.648314i \(-0.224526\pi\)
0.761373 + 0.648314i \(0.224526\pi\)
\(60\) 0 0
\(61\) 6.48028 0.829715 0.414857 0.909886i \(-0.363831\pi\)
0.414857 + 0.909886i \(0.363831\pi\)
\(62\) 0 0
\(63\) 1.74549i 0.219911i
\(64\) 0 0
\(65\) 0.960558 1.62236i 0.119143 0.201229i
\(66\) 0 0
\(67\) 14.8880i 1.81885i −0.415864 0.909427i \(-0.636521\pi\)
0.415864 0.909427i \(-0.363479\pi\)
\(68\) 0 0
\(69\) 1.26412 0.152183
\(70\) 0 0
\(71\) −0.303566 −0.0360266 −0.0180133 0.999838i \(-0.505734\pi\)
−0.0180133 + 0.999838i \(0.505734\pi\)
\(72\) 0 0
\(73\) 10.0800i 1.17978i 0.807485 + 0.589888i \(0.200828\pi\)
−0.807485 + 0.589888i \(0.799172\pi\)
\(74\) 0 0
\(75\) 7.11234 3.90079i 0.821262 0.450424i
\(76\) 0 0
\(77\) 21.2543i 2.42215i
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) −7.76081 −0.862312
\(82\) 0 0
\(83\) 0.779187i 0.0855268i −0.999085 0.0427634i \(-0.986384\pi\)
0.999085 0.0427634i \(-0.0136162\pi\)
\(84\) 0 0
\(85\) −6.29205 + 10.6271i −0.682468 + 1.15268i
\(86\) 0 0
\(87\) 17.2895i 1.85363i
\(88\) 0 0
\(89\) 5.69643 0.603821 0.301910 0.953336i \(-0.402376\pi\)
0.301910 + 0.953336i \(0.402376\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) 14.0448i 1.45638i
\(94\) 0 0
\(95\) −1.92411 1.13921i −0.197409 0.116881i
\(96\) 0 0
\(97\) 6.17922i 0.627404i 0.949521 + 0.313702i \(0.101569\pi\)
−0.949521 + 0.313702i \(0.898431\pi\)
\(98\) 0 0
\(99\) −1.64847 −0.165677
\(100\) 0 0
\(101\) 3.36794 0.335122 0.167561 0.985862i \(-0.446411\pi\)
0.167561 + 0.985862i \(0.446411\pi\)
\(102\) 0 0
\(103\) 3.71368i 0.365919i −0.983120 0.182960i \(-0.941432\pi\)
0.983120 0.182960i \(-0.0585678\pi\)
\(104\) 0 0
\(105\) −14.8088 8.76788i −1.44519 0.855657i
\(106\) 0 0
\(107\) 10.2031i 0.986374i −0.869923 0.493187i \(-0.835832\pi\)
0.869923 0.493187i \(-0.164168\pi\)
\(108\) 0 0
\(109\) −2.96056 −0.283570 −0.141785 0.989897i \(-0.545284\pi\)
−0.141785 + 0.989897i \(0.545284\pi\)
\(110\) 0 0
\(111\) −2.63206 −0.249824
\(112\) 0 0
\(113\) 7.08638i 0.666631i 0.942815 + 0.333315i \(0.108167\pi\)
−0.942815 + 0.333315i \(0.891833\pi\)
\(114\) 0 0
\(115\) 0.887659 1.49924i 0.0827747 0.139805i
\(116\) 0 0
\(117\) 0.310237i 0.0286814i
\(118\) 0 0
\(119\) 26.2016 2.40190
\(120\) 0 0
\(121\) 9.07290 0.824809
\(122\) 0 0
\(123\) 7.68331i 0.692781i
\(124\) 0 0
\(125\) 0.367938 11.1743i 0.0329094 0.999458i
\(126\) 0 0
\(127\) 9.79817i 0.869447i −0.900564 0.434723i \(-0.856846\pi\)
0.900564 0.434723i \(-0.143154\pi\)
\(128\) 0 0
\(129\) 15.6964 1.38199
\(130\) 0 0
\(131\) −12.5841 −1.09948 −0.549739 0.835337i \(-0.685273\pi\)
−0.549739 + 0.835337i \(0.685273\pi\)
\(132\) 0 0
\(133\) 4.74397i 0.411354i
\(134\) 0 0
\(135\) −6.22468 + 10.5134i −0.535735 + 0.904846i
\(136\) 0 0
\(137\) 8.89586i 0.760024i 0.924981 + 0.380012i \(0.124080\pi\)
−0.924981 + 0.380012i \(0.875920\pi\)
\(138\) 0 0
\(139\) 6.25560 0.530593 0.265296 0.964167i \(-0.414530\pi\)
0.265296 + 0.964167i \(0.414530\pi\)
\(140\) 0 0
\(141\) 5.16819 0.435240
\(142\) 0 0
\(143\) 3.77767i 0.315904i
\(144\) 0 0
\(145\) −20.5052 12.1406i −1.70286 1.00822i
\(146\) 0 0
\(147\) 25.1551i 2.07476i
\(148\) 0 0
\(149\) −2.48028 −0.203192 −0.101596 0.994826i \(-0.532395\pi\)
−0.101596 + 0.994826i \(0.532395\pi\)
\(150\) 0 0
\(151\) −3.69643 −0.300812 −0.150406 0.988624i \(-0.548058\pi\)
−0.150406 + 0.988624i \(0.548058\pi\)
\(152\) 0 0
\(153\) 2.03218i 0.164292i
\(154\) 0 0
\(155\) −16.6570 9.86216i −1.33792 0.792148i
\(156\) 0 0
\(157\) 18.8479i 1.50422i 0.659035 + 0.752112i \(0.270965\pi\)
−0.659035 + 0.752112i \(0.729035\pi\)
\(158\) 0 0
\(159\) −10.0249 −0.795029
\(160\) 0 0
\(161\) −3.69643 −0.291320
\(162\) 0 0
\(163\) 2.46554i 0.193116i 0.995327 + 0.0965580i \(0.0307833\pi\)
−0.995327 + 0.0965580i \(0.969217\pi\)
\(164\) 0 0
\(165\) 8.28053 13.9856i 0.644638 1.08878i
\(166\) 0 0
\(167\) 7.49134i 0.579697i 0.957072 + 0.289849i \(0.0936050\pi\)
−0.957072 + 0.289849i \(0.906395\pi\)
\(168\) 0 0
\(169\) 12.2891 0.945312
\(170\) 0 0
\(171\) 0.367938 0.0281369
\(172\) 0 0
\(173\) 20.0653i 1.52554i 0.646673 + 0.762768i \(0.276160\pi\)
−0.646673 + 0.762768i \(0.723840\pi\)
\(174\) 0 0
\(175\) −20.7973 + 11.4063i −1.57212 + 0.862238i
\(176\) 0 0
\(177\) 18.9759i 1.42631i
\(178\) 0 0
\(179\) −3.69643 −0.276284 −0.138142 0.990412i \(-0.544113\pi\)
−0.138142 + 0.990412i \(0.544113\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 10.5134i 0.777170i
\(184\) 0 0
\(185\) −1.84822 + 3.12160i −0.135884 + 0.229505i
\(186\) 0 0
\(187\) 24.7453i 1.80955i
\(188\) 0 0
\(189\) 25.9211 1.88548
\(190\) 0 0
\(191\) −0.887659 −0.0642288 −0.0321144 0.999484i \(-0.510224\pi\)
−0.0321144 + 0.999484i \(0.510224\pi\)
\(192\) 0 0
\(193\) 19.1581i 1.37903i −0.724271 0.689516i \(-0.757823\pi\)
0.724271 0.689516i \(-0.242177\pi\)
\(194\) 0 0
\(195\) −2.63206 1.55837i −0.188486 0.111597i
\(196\) 0 0
\(197\) 3.37271i 0.240295i 0.992756 + 0.120148i \(0.0383368\pi\)
−0.992756 + 0.120148i \(0.961663\pi\)
\(198\) 0 0
\(199\) 4.58409 0.324958 0.162479 0.986712i \(-0.448051\pi\)
0.162479 + 0.986712i \(0.448051\pi\)
\(200\) 0 0
\(201\) −24.1537 −1.70367
\(202\) 0 0
\(203\) 50.5564i 3.54836i
\(204\) 0 0
\(205\) −9.11234 5.39517i −0.636433 0.376815i
\(206\) 0 0
\(207\) 0.286693i 0.0199265i
\(208\) 0 0
\(209\) −4.48028 −0.309907
\(210\) 0 0
\(211\) 14.8817 1.02450 0.512248 0.858837i \(-0.328813\pi\)
0.512248 + 0.858837i \(0.328813\pi\)
\(212\) 0 0
\(213\) 0.492494i 0.0337451i
\(214\) 0 0
\(215\) 11.0219 18.6158i 0.751690 1.26959i
\(216\) 0 0
\(217\) 41.0685i 2.78791i
\(218\) 0 0
\(219\) 16.3534 1.10506
\(220\) 0 0
\(221\) 4.65699 0.313263
\(222\) 0 0
\(223\) 18.7839i 1.25786i 0.777461 + 0.628931i \(0.216507\pi\)
−0.777461 + 0.628931i \(0.783493\pi\)
\(224\) 0 0
\(225\) 0.884666 + 1.61302i 0.0589777 + 0.107535i
\(226\) 0 0
\(227\) 0.843176i 0.0559636i 0.999608 + 0.0279818i \(0.00890804\pi\)
−0.999608 + 0.0279818i \(0.991092\pi\)
\(228\) 0 0
\(229\) 4.86273 0.321338 0.160669 0.987008i \(-0.448635\pi\)
0.160669 + 0.987008i \(0.448635\pi\)
\(230\) 0 0
\(231\) −34.4822 −2.26876
\(232\) 0 0
\(233\) 4.90268i 0.321185i 0.987021 + 0.160593i \(0.0513405\pi\)
−0.987021 + 0.160593i \(0.948659\pi\)
\(234\) 0 0
\(235\) 3.62907 6.12943i 0.236734 0.399840i
\(236\) 0 0
\(237\) 6.48945i 0.421535i
\(238\) 0 0
\(239\) −6.20164 −0.401151 −0.200575 0.979678i \(-0.564281\pi\)
−0.200575 + 0.979678i \(0.564281\pi\)
\(240\) 0 0
\(241\) −3.26412 −0.210261 −0.105130 0.994458i \(-0.533526\pi\)
−0.105130 + 0.994458i \(0.533526\pi\)
\(242\) 0 0
\(243\) 3.80121i 0.243848i
\(244\) 0 0
\(245\) 29.8337 + 17.6637i 1.90601 + 1.12849i
\(246\) 0 0
\(247\) 0.843176i 0.0536500i
\(248\) 0 0
\(249\) −1.26412 −0.0801106
\(250\) 0 0
\(251\) −28.4263 −1.79425 −0.897127 0.441773i \(-0.854350\pi\)
−0.897127 + 0.441773i \(0.854350\pi\)
\(252\) 0 0
\(253\) 3.49097i 0.219476i
\(254\) 0 0
\(255\) 17.2411 + 10.2080i 1.07968 + 0.639249i
\(256\) 0 0
\(257\) 9.55192i 0.595832i −0.954592 0.297916i \(-0.903708\pi\)
0.954592 0.297916i \(-0.0962916\pi\)
\(258\) 0 0
\(259\) 7.69643 0.478233
\(260\) 0 0
\(261\) 3.92112 0.242711
\(262\) 0 0
\(263\) 9.54706i 0.588697i −0.955698 0.294349i \(-0.904897\pi\)
0.955698 0.294349i \(-0.0951027\pi\)
\(264\) 0 0
\(265\) −7.03944 + 11.8895i −0.432430 + 0.730365i
\(266\) 0 0
\(267\) 9.24168i 0.565582i
\(268\) 0 0
\(269\) 14.3534 0.875144 0.437572 0.899183i \(-0.355839\pi\)
0.437572 + 0.899183i \(0.355839\pi\)
\(270\) 0 0
\(271\) 12.1038 0.735254 0.367627 0.929973i \(-0.380170\pi\)
0.367627 + 0.929973i \(0.380170\pi\)
\(272\) 0 0
\(273\) 6.48945i 0.392760i
\(274\) 0 0
\(275\) −10.7723 19.6413i −0.649596 1.18441i
\(276\) 0 0
\(277\) 3.59055i 0.215735i 0.994165 + 0.107868i \(0.0344023\pi\)
−0.994165 + 0.107868i \(0.965598\pi\)
\(278\) 0 0
\(279\) 3.18524 0.190695
\(280\) 0 0
\(281\) 26.7069 1.59320 0.796599 0.604509i \(-0.206631\pi\)
0.796599 + 0.604509i \(0.206631\pi\)
\(282\) 0 0
\(283\) 20.4751i 1.21712i −0.793508 0.608559i \(-0.791748\pi\)
0.793508 0.608559i \(-0.208252\pi\)
\(284\) 0 0
\(285\) −1.84822 + 3.12160i −0.109479 + 0.184908i
\(286\) 0 0
\(287\) 22.4668i 1.32618i
\(288\) 0 0
\(289\) −13.5052 −0.794424
\(290\) 0 0
\(291\) 10.0249 0.587672
\(292\) 0 0
\(293\) 19.1581i 1.11923i −0.828753 0.559615i \(-0.810949\pi\)
0.828753 0.559615i \(-0.189051\pi\)
\(294\) 0 0
\(295\) −22.5052 13.3247i −1.31030 0.775796i
\(296\) 0 0
\(297\) 24.4803i 1.42049i
\(298\) 0 0
\(299\) −0.656992 −0.0379948
\(300\) 0 0
\(301\) −45.8981 −2.64552
\(302\) 0 0
\(303\) 5.46402i 0.313900i
\(304\) 0 0
\(305\) −12.4688 7.38242i −0.713959 0.422716i
\(306\) 0 0
\(307\) 32.0495i 1.82916i 0.404404 + 0.914580i \(0.367479\pi\)
−0.404404 + 0.914580i \(0.632521\pi\)
\(308\) 0 0
\(309\) −6.02493 −0.342746
\(310\) 0 0
\(311\) 20.5301 1.16416 0.582079 0.813132i \(-0.302240\pi\)
0.582079 + 0.813132i \(0.302240\pi\)
\(312\) 0 0
\(313\) 14.7932i 0.836163i −0.908409 0.418082i \(-0.862703\pi\)
0.908409 0.418082i \(-0.137297\pi\)
\(314\) 0 0
\(315\) 1.98848 3.35851i 0.112038 0.189230i
\(316\) 0 0
\(317\) 16.9485i 0.951925i 0.879466 + 0.475962i \(0.157900\pi\)
−0.879466 + 0.475962i \(0.842100\pi\)
\(318\) 0 0
\(319\) −47.7463 −2.67328
\(320\) 0 0
\(321\) −16.5532 −0.923908
\(322\) 0 0
\(323\) 5.52315i 0.307316i
\(324\) 0 0
\(325\) −3.69643 + 2.02732i −0.205041 + 0.112456i
\(326\) 0 0
\(327\) 4.80310i 0.265612i
\(328\) 0 0
\(329\) −15.1123 −0.833170
\(330\) 0 0
\(331\) 22.1287 1.21631 0.608153 0.793820i \(-0.291911\pi\)
0.608153 + 0.793820i \(0.291911\pi\)
\(332\) 0 0
\(333\) 0.596929i 0.0327115i
\(334\) 0 0
\(335\) −16.9606 + 28.6461i −0.926654 + 1.56510i
\(336\) 0 0
\(337\) 27.9948i 1.52498i −0.647002 0.762488i \(-0.723978\pi\)
0.647002 0.762488i \(-0.276022\pi\)
\(338\) 0 0
\(339\) 11.4967 0.624414
\(340\) 0 0
\(341\) −38.7857 −2.10037
\(342\) 0 0
\(343\) 40.3484i 2.17861i
\(344\) 0 0
\(345\) −2.43231 1.44011i −0.130951 0.0775327i
\(346\) 0 0
\(347\) 17.1024i 0.918105i −0.888409 0.459052i \(-0.848189\pi\)
0.888409 0.459052i \(-0.151811\pi\)
\(348\) 0 0
\(349\) 19.2411 1.02995 0.514976 0.857205i \(-0.327801\pi\)
0.514976 + 0.857205i \(0.327801\pi\)
\(350\) 0 0
\(351\) 4.60713 0.245910
\(352\) 0 0
\(353\) 7.42735i 0.395318i 0.980271 + 0.197659i \(0.0633339\pi\)
−0.980271 + 0.197659i \(0.936666\pi\)
\(354\) 0 0
\(355\) 0.584094 + 0.345826i 0.0310005 + 0.0183545i
\(356\) 0 0
\(357\) 42.5086i 2.24979i
\(358\) 0 0
\(359\) 28.1767 1.48711 0.743555 0.668675i \(-0.233138\pi\)
0.743555 + 0.668675i \(0.233138\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 14.7195i 0.772575i
\(364\) 0 0
\(365\) 11.4833 19.3950i 0.601062 1.01518i
\(366\) 0 0
\(367\) 26.1165i 1.36327i −0.731692 0.681636i \(-0.761269\pi\)
0.731692 0.681636i \(-0.238731\pi\)
\(368\) 0 0
\(369\) 1.74251 0.0907115
\(370\) 0 0
\(371\) 29.3140 1.52191
\(372\) 0 0
\(373\) 0.438217i 0.0226900i −0.999936 0.0113450i \(-0.996389\pi\)
0.999936 0.0113450i \(-0.00361130\pi\)
\(374\) 0 0
\(375\) −18.1287 0.596929i −0.936164 0.0308253i
\(376\) 0 0
\(377\) 8.98572i 0.462788i
\(378\) 0 0
\(379\) −13.7753 −0.707591 −0.353795 0.935323i \(-0.615109\pi\)
−0.353795 + 0.935323i \(0.615109\pi\)
\(380\) 0 0
\(381\) −15.8962 −0.814386
\(382\) 0 0
\(383\) 22.3153i 1.14026i 0.821555 + 0.570130i \(0.193107\pi\)
−0.821555 + 0.570130i \(0.806893\pi\)
\(384\) 0 0
\(385\) −24.2132 + 40.8956i −1.23402 + 2.08423i
\(386\) 0 0
\(387\) 3.55982i 0.180956i
\(388\) 0 0
\(389\) −14.4263 −0.731444 −0.365722 0.930724i \(-0.619178\pi\)
−0.365722 + 0.930724i \(0.619178\pi\)
\(390\) 0 0
\(391\) 4.30357 0.217641
\(392\) 0 0
\(393\) 20.4160i 1.02985i
\(394\) 0 0
\(395\) −7.69643 4.55685i −0.387250 0.229280i
\(396\) 0 0
\(397\) 16.4512i 0.825662i 0.910808 + 0.412831i \(0.135460\pi\)
−0.910808 + 0.412831i \(0.864540\pi\)
\(398\) 0 0
\(399\) 7.69643 0.385304
\(400\) 0 0
\(401\) 2.96056 0.147843 0.0739216 0.997264i \(-0.476449\pi\)
0.0739216 + 0.997264i \(0.476449\pi\)
\(402\) 0 0
\(403\) 7.29937i 0.363608i
\(404\) 0 0
\(405\) 14.9326 + 8.84121i 0.742009 + 0.439323i
\(406\) 0 0
\(407\) 7.26864i 0.360293i
\(408\) 0 0
\(409\) −17.0893 −0.845012 −0.422506 0.906360i \(-0.638849\pi\)
−0.422506 + 0.906360i \(0.638849\pi\)
\(410\) 0 0
\(411\) 14.4323 0.711893
\(412\) 0 0
\(413\) 55.4875i 2.73036i
\(414\) 0 0
\(415\) −0.887659 + 1.49924i −0.0435735 + 0.0735948i
\(416\) 0 0
\(417\) 10.1489i 0.496991i
\(418\) 0 0
\(419\) −15.3929 −0.751991 −0.375995 0.926622i \(-0.622699\pi\)
−0.375995 + 0.926622i \(0.622699\pi\)
\(420\) 0 0
\(421\) −16.4323 −0.800862 −0.400431 0.916327i \(-0.631140\pi\)
−0.400431 + 0.916327i \(0.631140\pi\)
\(422\) 0 0
\(423\) 1.17210i 0.0569895i
\(424\) 0 0
\(425\) 24.2132 13.2798i 1.17451 0.644165i
\(426\) 0 0
\(427\) 30.7422i 1.48772i
\(428\) 0 0
\(429\) −6.12874 −0.295899
\(430\) 0 0
\(431\) −15.1852 −0.731447 −0.365724 0.930724i \(-0.619178\pi\)
−0.365724 + 0.930724i \(0.619178\pi\)
\(432\) 0 0
\(433\) 23.4380i 1.12636i 0.826335 + 0.563179i \(0.190422\pi\)
−0.826335 + 0.563179i \(0.809578\pi\)
\(434\) 0 0
\(435\) −19.6964 + 33.2669i −0.944372 + 1.59503i
\(436\) 0 0
\(437\) 0.779187i 0.0372735i
\(438\) 0 0
\(439\) 0.511196 0.0243980 0.0121990 0.999926i \(-0.496117\pi\)
0.0121990 + 0.999926i \(0.496117\pi\)
\(440\) 0 0
\(441\) −5.70496 −0.271665
\(442\) 0 0
\(443\) 19.7834i 0.939940i 0.882682 + 0.469970i \(0.155735\pi\)
−0.882682 + 0.469970i \(0.844265\pi\)
\(444\) 0 0
\(445\) −10.9606 6.48945i −0.519580 0.307630i
\(446\) 0 0
\(447\) 4.02391i 0.190325i
\(448\) 0 0
\(449\) −31.1682 −1.47092 −0.735459 0.677569i \(-0.763033\pi\)
−0.735459 + 0.677569i \(0.763033\pi\)
\(450\) 0 0
\(451\) −21.2180 −0.999119
\(452\) 0 0
\(453\) 5.99696i 0.281762i
\(454\) 0 0
\(455\) 7.69643 + 4.55685i 0.360814 + 0.213629i
\(456\) 0 0
\(457\) 7.20950i 0.337246i 0.985681 + 0.168623i \(0.0539321\pi\)
−0.985681 + 0.168623i \(0.946068\pi\)
\(458\) 0 0
\(459\) −30.1786 −1.40862
\(460\) 0 0
\(461\) −5.41591 −0.252244 −0.126122 0.992015i \(-0.540253\pi\)
−0.126122 + 0.992015i \(0.540253\pi\)
\(462\) 0 0
\(463\) 8.73715i 0.406050i −0.979174 0.203025i \(-0.934923\pi\)
0.979174 0.203025i \(-0.0650772\pi\)
\(464\) 0 0
\(465\) −16.0000 + 27.0237i −0.741982 + 1.25319i
\(466\) 0 0
\(467\) 17.3584i 0.803249i −0.915804 0.401624i \(-0.868446\pi\)
0.915804 0.401624i \(-0.131554\pi\)
\(468\) 0 0
\(469\) 70.6280 3.26130
\(470\) 0 0
\(471\) 30.5781 1.40896
\(472\) 0 0
\(473\) 43.3469i 1.99309i
\(474\) 0 0
\(475\) 2.40439 + 4.38394i 0.110321 + 0.201149i
\(476\) 0 0
\(477\) 2.27357i 0.104100i
\(478\) 0 0
\(479\) 7.44682 0.340254 0.170127 0.985422i \(-0.445582\pi\)
0.170127 + 0.985422i \(0.445582\pi\)
\(480\) 0 0
\(481\) 1.36794 0.0623726
\(482\) 0 0
\(483\) 5.99696i 0.272871i
\(484\) 0 0
\(485\) 7.03944 11.8895i 0.319645 0.539874i
\(486\) 0 0
\(487\) 2.15530i 0.0976661i 0.998807 + 0.0488330i \(0.0155502\pi\)
−0.998807 + 0.0488330i \(0.984450\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) −29.3140 −1.32292 −0.661461 0.749980i \(-0.730063\pi\)
−0.661461 + 0.749980i \(0.730063\pi\)
\(492\) 0 0
\(493\) 58.8602i 2.65093i
\(494\) 0 0
\(495\) 3.17183 + 1.87795i 0.142563 + 0.0844078i
\(496\) 0 0
\(497\) 1.44011i 0.0645976i
\(498\) 0 0
\(499\) −23.5696 −1.05512 −0.527560 0.849518i \(-0.676893\pi\)
−0.527560 + 0.849518i \(0.676893\pi\)
\(500\) 0 0
\(501\) 12.1537 0.542986
\(502\) 0 0
\(503\) 9.08297i 0.404990i 0.979283 + 0.202495i \(0.0649049\pi\)
−0.979283 + 0.202495i \(0.935095\pi\)
\(504\) 0 0
\(505\) −6.48028 3.83680i −0.288369 0.170735i
\(506\) 0 0
\(507\) 19.9373i 0.885447i
\(508\) 0 0
\(509\) 18.5112 0.820494 0.410247 0.911974i \(-0.365442\pi\)
0.410247 + 0.911974i \(0.365442\pi\)
\(510\) 0 0
\(511\) −47.8192 −2.11540
\(512\) 0 0
\(513\) 5.46402i 0.241242i
\(514\) 0 0
\(515\) −4.23067 + 7.14552i −0.186425 + 0.314869i
\(516\) 0 0
\(517\) 14.2723i 0.627697i
\(518\) 0 0
\(519\) 32.5532 1.42893
\(520\) 0 0
\(521\) −25.0893 −1.09918 −0.549591 0.835434i \(-0.685216\pi\)
−0.549591 + 0.835434i \(0.685216\pi\)
\(522\) 0 0
\(523\) 28.5181i 1.24701i −0.781820 0.623504i \(-0.785708\pi\)
0.781820 0.623504i \(-0.214292\pi\)
\(524\) 0 0
\(525\) 18.5052 + 33.7407i 0.807634 + 1.47256i
\(526\) 0 0
\(527\) 47.8139i 2.08281i
\(528\) 0 0
\(529\) 22.3929 0.973603
\(530\) 0 0
\(531\) 4.30357 0.186759
\(532\) 0 0
\(533\) 3.99318i 0.172964i
\(534\) 0 0
\(535\) −11.6235 + 19.6319i −0.502529 + 0.848762i
\(536\) 0 0
\(537\) 5.99696i 0.258788i
\(538\) 0 0
\(539\) 69.4677 2.99218
\(540\) 0 0
\(541\) −15.6485 −0.672780 −0.336390 0.941723i \(-0.609206\pi\)
−0.336390 + 0.941723i \(0.609206\pi\)
\(542\) 0 0
\(543\) 3.24473i 0.139245i
\(544\) 0 0
\(545\) 5.69643 + 3.37271i 0.244008 + 0.144471i
\(546\) 0 0
\(547\) 10.8543i 0.464098i 0.972704 + 0.232049i \(0.0745429\pi\)
−0.972704 + 0.232049i \(0.925457\pi\)
\(548\) 0 0
\(549\) 2.38434 0.101761
\(550\) 0 0
\(551\) 10.6570 0.454003
\(552\) 0 0
\(553\) 18.9759i 0.806936i
\(554\) 0 0
\(555\) 5.06437 + 2.99848i 0.214971 + 0.127278i
\(556\) 0 0
\(557\) 18.8763i 0.799814i 0.916556 + 0.399907i \(0.130958\pi\)
−0.916556 + 0.399907i \(0.869042\pi\)
\(558\) 0 0
\(559\) −8.15777 −0.345037
\(560\) 0 0
\(561\) 40.1458 1.69496
\(562\) 0 0
\(563\) 22.2846i 0.939183i −0.882884 0.469591i \(-0.844401\pi\)
0.882884 0.469591i \(-0.155599\pi\)
\(564\) 0 0
\(565\) 8.07290 13.6350i 0.339629 0.573627i
\(566\) 0 0
\(567\) 36.8170i 1.54617i
\(568\) 0 0
\(569\) 7.11833 0.298416 0.149208 0.988806i \(-0.452328\pi\)
0.149208 + 0.988806i \(0.452328\pi\)
\(570\) 0 0
\(571\) −1.21017 −0.0506440 −0.0253220 0.999679i \(-0.508061\pi\)
−0.0253220 + 0.999679i \(0.508061\pi\)
\(572\) 0 0
\(573\) 1.44011i 0.0601613i
\(574\) 0 0
\(575\) −3.41591 + 1.87347i −0.142453 + 0.0781289i
\(576\) 0 0
\(577\) 41.4143i 1.72410i −0.506823 0.862050i \(-0.669180\pi\)
0.506823 0.862050i \(-0.330820\pi\)
\(578\) 0 0
\(579\) −31.0814 −1.29170
\(580\) 0 0
\(581\) 3.69643 0.153354
\(582\) 0 0
\(583\) 27.6846i 1.14658i
\(584\) 0 0
\(585\) 0.353426 0.596929i 0.0146124 0.0246800i
\(586\) 0 0
\(587\) 0.0591336i 0.00244071i 0.999999 + 0.00122035i \(0.000388450\pi\)
−0.999999 + 0.00122035i \(0.999612\pi\)
\(588\) 0 0
\(589\) 8.65699 0.356705
\(590\) 0 0
\(591\) 5.47175 0.225078
\(592\) 0 0
\(593\) 42.8828i 1.76099i −0.474059 0.880493i \(-0.657212\pi\)
0.474059 0.880493i \(-0.342788\pi\)
\(594\) 0 0
\(595\) −50.4148 29.8493i −2.06681 1.22370i
\(596\) 0 0
\(597\) 7.43706i 0.304379i
\(598\) 0 0
\(599\) 15.3430 0.626898 0.313449 0.949605i \(-0.398515\pi\)
0.313449 + 0.949605i \(0.398515\pi\)
\(600\) 0 0
\(601\) −12.5781 −0.513072 −0.256536 0.966535i \(-0.582581\pi\)
−0.256536 + 0.966535i \(0.582581\pi\)
\(602\) 0 0
\(603\) 5.47785i 0.223075i
\(604\) 0 0
\(605\) −17.4572 10.3360i −0.709738 0.420217i
\(606\) 0 0
\(607\) 2.65751i 0.107865i −0.998545 0.0539325i \(-0.982824\pi\)
0.998545 0.0539325i \(-0.0171756\pi\)
\(608\) 0 0
\(609\) 82.0208 3.32365
\(610\) 0 0
\(611\) −2.68602 −0.108665
\(612\) 0 0
\(613\) 34.1052i 1.37750i −0.725001 0.688748i \(-0.758161\pi\)
0.725001 0.688748i \(-0.241839\pi\)
\(614\) 0 0
\(615\) −8.75293 + 14.7835i −0.352952 + 0.596129i
\(616\) 0 0
\(617\) 29.9226i 1.20464i 0.798255 + 0.602319i \(0.205756\pi\)
−0.798255 + 0.602319i \(0.794244\pi\)
\(618\) 0 0
\(619\) 17.2102 0.691735 0.345868 0.938283i \(-0.387585\pi\)
0.345868 + 0.938283i \(0.387585\pi\)
\(620\) 0 0
\(621\) 4.25749 0.170847
\(622\) 0 0
\(623\) 27.0237i 1.08268i
\(624\) 0 0
\(625\) −13.4378 + 21.0814i −0.537514 + 0.843255i
\(626\) 0 0
\(627\) 7.26864i 0.290281i
\(628\) 0 0
\(629\) −8.96056 −0.357281
\(630\) 0 0
\(631\) 3.36195 0.133837 0.0669186 0.997758i \(-0.478683\pi\)
0.0669186 + 0.997758i \(0.478683\pi\)
\(632\) 0 0
\(633\) 24.1435i 0.959617i
\(634\) 0 0
\(635\) −11.1622 + 18.8527i −0.442958 + 0.748148i
\(636\) 0 0
\(637\) 13.0736i 0.517996i
\(638\) 0 0
\(639\) −0.111693 −0.00441853
\(640\) 0 0
\(641\) −16.2745 −0.642806 −0.321403 0.946943i \(-0.604154\pi\)
−0.321403 + 0.946943i \(0.604154\pi\)
\(642\) 0 0
\(643\) 35.7040i 1.40803i 0.710185 + 0.704015i \(0.248611\pi\)
−0.710185 + 0.704015i \(0.751389\pi\)
\(644\) 0 0
\(645\) −30.2016 17.8816i −1.18919 0.704087i
\(646\) 0 0
\(647\) 15.2881i 0.601036i −0.953776 0.300518i \(-0.902840\pi\)
0.953776 0.300518i \(-0.0971595\pi\)
\(648\) 0 0
\(649\) −52.4033 −2.05701
\(650\) 0 0
\(651\) 66.6280 2.61136
\(652\) 0 0
\(653\) 16.4512i 0.643785i −0.946776 0.321892i \(-0.895681\pi\)
0.946776 0.321892i \(-0.104319\pi\)
\(654\) 0 0
\(655\) 24.2132 + 14.3360i 0.946087 + 0.560152i
\(656\) 0 0
\(657\) 3.70882i 0.144695i
\(658\) 0 0
\(659\) 7.03944 0.274218 0.137109 0.990556i \(-0.456219\pi\)
0.137109 + 0.990556i \(0.456219\pi\)
\(660\) 0 0
\(661\) 6.35343 0.247120 0.123560 0.992337i \(-0.460569\pi\)
0.123560 + 0.992337i \(0.460569\pi\)
\(662\) 0 0
\(663\) 7.55533i 0.293425i
\(664\) 0 0
\(665\) 5.40439 9.12790i 0.209573 0.353965i
\(666\) 0 0
\(667\) 8.30378i 0.321524i
\(668\) 0 0
\(669\) 30.4743 1.17820
\(670\) 0 0
\(671\) −29.0335 −1.12082
\(672\) 0 0
\(673\) 7.08638i 0.273160i −0.990629 0.136580i \(-0.956389\pi\)
0.990629 0.136580i \(-0.0436111\pi\)
\(674\) 0 0
\(675\) 23.9539 13.1376i 0.921987 0.505667i
\(676\) 0 0
\(677\) 17.6095i 0.676786i −0.941005 0.338393i \(-0.890117\pi\)
0.941005 0.338393i \(-0.109883\pi\)
\(678\) 0 0
\(679\) −29.3140 −1.12497
\(680\) 0 0
\(681\) 1.36794 0.0524195
\(682\) 0 0
\(683\) 26.5855i 1.01726i −0.860984 0.508632i \(-0.830151\pi\)
0.860984 0.508632i \(-0.169849\pi\)
\(684\) 0 0
\(685\) 10.1343 17.1166i 0.387211 0.653992i
\(686\) 0 0
\(687\) 7.88911i 0.300988i
\(688\) 0 0
\(689\) 5.21017 0.198492
\(690\) 0 0
\(691\) −49.4907 −1.88271 −0.941357 0.337411i \(-0.890449\pi\)
−0.941357 + 0.337411i \(0.890449\pi\)
\(692\) 0 0
\(693\) 7.82027i 0.297067i
\(694\) 0 0
\(695\) −12.0364 7.12646i −0.456569 0.270322i
\(696\) 0 0
\(697\) 26.1570i 0.990766i
\(698\) 0 0
\(699\) 7.95392 0.300845
\(700\) 0 0
\(701\) 29.3389 1.10812 0.554058 0.832478i \(-0.313079\pi\)
0.554058 + 0.832478i \(0.313079\pi\)
\(702\) 0 0
\(703\) 1.62236i 0.0611886i
\(704\) 0 0
\(705\) −9.94415 5.88767i −0.374518 0.221742i
\(706\) 0 0
\(707\) 15.9774i 0.600891i
\(708\) 0 0
\(709\) −24.7359 −0.928975 −0.464488 0.885580i \(-0.653762\pi\)
−0.464488 + 0.885580i \(0.653762\pi\)
\(710\) 0 0
\(711\) 1.47175 0.0551951
\(712\) 0 0
\(713\) 6.74541i 0.252618i
\(714\) 0 0
\(715\) −4.30357 + 7.26864i −0.160944 + 0.271832i
\(716\) 0 0
\(717\) 10.0613i 0.375747i
\(718\) 0 0
\(719\) 26.7548 0.997786 0.498893 0.866663i \(-0.333740\pi\)
0.498893 + 0.866663i \(0.333740\pi\)
\(720\) 0 0
\(721\) 17.6175 0.656112
\(722\) 0 0
\(723\) 5.29559i 0.196945i
\(724\) 0 0
\(725\) 25.6235 + 46.7196i 0.951634 + 1.73512i
\(726\) 0 0
\(727\) 27.2108i 1.00919i −0.863355 0.504596i \(-0.831641\pi\)
0.863355 0.504596i \(-0.168359\pi\)
\(728\) 0 0
\(729\) −29.4494 −1.09072
\(730\) 0 0
\(731\) 53.4367 1.97643
\(732\) 0 0
\(733\) 40.0026i 1.47753i 0.673963 + 0.738765i \(0.264591\pi\)
−0.673963 + 0.738765i \(0.735409\pi\)
\(734\) 0 0
\(735\) 28.6570 48.4011i 1.05703 1.78530i
\(736\) 0 0
\(737\) 66.7022i 2.45701i
\(738\) 0 0
\(739\) 35.1123 1.29163 0.645814 0.763495i \(-0.276518\pi\)
0.645814 + 0.763495i \(0.276518\pi\)
\(740\) 0 0
\(741\) 1.36794 0.0502525
\(742\) 0 0
\(743\) 25.6476i 0.940918i −0.882422 0.470459i \(-0.844088\pi\)
0.882422 0.470459i \(-0.155912\pi\)
\(744\) 0 0
\(745\) 4.77233 + 2.82557i 0.174844 + 0.103521i
\(746\) 0 0
\(747\) 0.286693i 0.0104895i
\(748\) 0 0
\(749\) 48.4033 1.76862
\(750\) 0 0
\(751\) 13.2641 0.484015 0.242007 0.970274i \(-0.422194\pi\)
0.242007 + 0.970274i \(0.422194\pi\)
\(752\) 0 0
\(753\) 46.1178i 1.68063i
\(754\) 0 0
\(755\) 7.11234 + 4.21103i 0.258845 + 0.153255i
\(756\) 0 0
\(757\) 2.77092i 0.100711i −0.998731 0.0503554i \(-0.983965\pi\)
0.998731 0.0503554i \(-0.0160354\pi\)
\(758\) 0 0
\(759\) −5.66363 −0.205577
\(760\) 0 0
\(761\) 10.7838 0.390914 0.195457 0.980712i \(-0.437381\pi\)
0.195457 + 0.980712i \(0.437381\pi\)
\(762\) 0 0
\(763\) 14.0448i 0.508455i
\(764\) 0 0
\(765\) −2.31508 + 3.91013i −0.0837021 + 0.141371i
\(766\) 0 0
\(767\) 9.86216i 0.356102i
\(768\) 0 0
\(769\) 40.6090 1.46440 0.732199 0.681090i \(-0.238494\pi\)
0.732199 + 0.681090i \(0.238494\pi\)
\(770\) 0 0
\(771\) −15.4967 −0.558099
\(772\) 0 0
\(773\) 17.4410i 0.627310i −0.949537 0.313655i \(-0.898446\pi\)
0.949537 0.313655i \(-0.101554\pi\)
\(774\) 0 0
\(775\) 20.8148 + 37.9517i 0.747688 + 1.36327i
\(776\) 0 0
\(777\) 12.4864i 0.447947i
\(778\) 0 0
\(779\) 4.73588 0.169680
\(780\) 0 0
\(781\) 1.36006 0.0486668
\(782\) 0 0
\(783\) 58.2300i 2.08097i
\(784\) 0 0
\(785\) 21.4718 36.2654i 0.766360 1.29437i
\(786\) 0 0
\(787\) 30.8346i 1.09914i 0.835449 + 0.549568i \(0.185208\pi\)
−0.835449 + 0.549568i \(0.814792\pi\)
\(788\) 0 0
\(789\) −15.4888 −0.551416
\(790\) 0 0
\(791\) −33.6175 −1.19530
\(792\) 0 0
\(793\) 5.46402i 0.194033i
\(794\) 0 0
\(795\) 19.2891 + 11.4205i 0.684112 + 0.405044i
\(796\) 0 0
\(797\) 38.1340i 1.35077i 0.737463 + 0.675387i \(0.236024\pi\)
−0.737463 + 0.675387i \(0.763976\pi\)
\(798\) 0 0
\(799\) 17.5945 0.622449
\(800\) 0 0