Properties

Label 1764.2.b.k.1567.2
Level $1764$
Weight $2$
Character 1764.1567
Analytic conductor $14.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1764.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.0856109166\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1212153856.10
Defining polynomial: \(x^{8} - 4 x^{6} + 10 x^{4} - 16 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 196)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1567.2
Root \(1.07072 - 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.k.1567.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.207107 - 1.39897i) q^{2} +(-1.91421 + 0.579471i) q^{4} +2.61313i q^{5} +(1.20711 + 2.55791i) q^{8} +O(q^{10})\) \(q+(-0.207107 - 1.39897i) q^{2} +(-1.91421 + 0.579471i) q^{4} +2.61313i q^{5} +(1.20711 + 2.55791i) q^{8} +(3.65568 - 0.541196i) q^{10} +3.95687i q^{11} -1.08239i q^{13} +(3.32843 - 2.21846i) q^{16} +0.317025i q^{17} -5.16991 q^{19} +(-1.51423 - 5.00208i) q^{20} +(5.53553 - 0.819496i) q^{22} +2.31788i q^{23} -1.82843 q^{25} +(-1.51423 + 0.224171i) q^{26} +6.82843 q^{29} -6.05692 q^{31} +(-3.79289 - 4.19690i) q^{32} +(0.443508 - 0.0656581i) q^{34} -4.00000 q^{37} +(1.07072 + 7.23252i) q^{38} +(-6.68414 + 3.15432i) q^{40} -2.29610i q^{41} -7.23486i q^{43} +(-2.29289 - 7.57430i) q^{44} +(3.24264 - 0.480049i) q^{46} -4.28289 q^{47} +(0.378680 + 2.55791i) q^{50} +(0.627215 + 2.07193i) q^{52} -10.4853 q^{53} -10.3398 q^{55} +(-1.41421 - 9.55274i) q^{58} -11.2268 q^{59} -5.41196i q^{61} +(1.25443 + 8.47343i) q^{62} +(-5.08579 + 6.17534i) q^{64} +2.82843 q^{65} +3.27798i q^{67} +(-0.183707 - 0.606854i) q^{68} +14.0167i q^{73} +(0.828427 + 5.59587i) q^{74} +(9.89630 - 2.99581i) q^{76} +7.91375i q^{79} +(5.79712 + 8.69760i) q^{80} +(-3.21217 + 0.475538i) q^{82} -9.45280 q^{83} -0.828427 q^{85} +(-10.1213 + 1.49839i) q^{86} +(-10.1213 + 4.77637i) q^{88} +5.99162i q^{89} +(-1.34315 - 4.43692i) q^{92} +(0.887016 + 5.99162i) q^{94} -13.5096i q^{95} -9.23880i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} - 4q^{4} + 4q^{8} + O(q^{10}) \) \( 8q + 4q^{2} - 4q^{4} + 4q^{8} + 4q^{16} + 16q^{22} + 8q^{25} + 32q^{29} - 36q^{32} - 32q^{37} - 24q^{44} - 8q^{46} + 20q^{50} - 16q^{53} - 52q^{64} - 16q^{74} + 16q^{85} - 64q^{86} - 64q^{88} - 56q^{92} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(883\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.207107 1.39897i −0.146447 0.989219i
\(3\) 0 0
\(4\) −1.91421 + 0.579471i −0.957107 + 0.289735i
\(5\) 2.61313i 1.16863i 0.811529 + 0.584313i \(0.198636\pi\)
−0.811529 + 0.584313i \(0.801364\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.20711 + 2.55791i 0.426777 + 0.904357i
\(9\) 0 0
\(10\) 3.65568 0.541196i 1.15603 0.171141i
\(11\) 3.95687i 1.19304i 0.802597 + 0.596521i \(0.203451\pi\)
−0.802597 + 0.596521i \(0.796549\pi\)
\(12\) 0 0
\(13\) 1.08239i 0.300202i −0.988671 0.150101i \(-0.952040\pi\)
0.988671 0.150101i \(-0.0479598\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 3.32843 2.21846i 0.832107 0.554615i
\(17\) 0.317025i 0.0768899i 0.999261 + 0.0384450i \(0.0122404\pi\)
−0.999261 + 0.0384450i \(0.987760\pi\)
\(18\) 0 0
\(19\) −5.16991 −1.18606 −0.593029 0.805181i \(-0.702068\pi\)
−0.593029 + 0.805181i \(0.702068\pi\)
\(20\) −1.51423 5.00208i −0.338592 1.11850i
\(21\) 0 0
\(22\) 5.53553 0.819496i 1.18018 0.174717i
\(23\) 2.31788i 0.483312i 0.970362 + 0.241656i \(0.0776906\pi\)
−0.970362 + 0.241656i \(0.922309\pi\)
\(24\) 0 0
\(25\) −1.82843 −0.365685
\(26\) −1.51423 + 0.224171i −0.296965 + 0.0439635i
\(27\) 0 0
\(28\) 0 0
\(29\) 6.82843 1.26801 0.634004 0.773330i \(-0.281410\pi\)
0.634004 + 0.773330i \(0.281410\pi\)
\(30\) 0 0
\(31\) −6.05692 −1.08786 −0.543928 0.839132i \(-0.683063\pi\)
−0.543928 + 0.839132i \(0.683063\pi\)
\(32\) −3.79289 4.19690i −0.670495 0.741914i
\(33\) 0 0
\(34\) 0.443508 0.0656581i 0.0760610 0.0112603i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 1.07072 + 7.23252i 0.173694 + 1.17327i
\(39\) 0 0
\(40\) −6.68414 + 3.15432i −1.05685 + 0.498742i
\(41\) 2.29610i 0.358591i −0.983795 0.179295i \(-0.942618\pi\)
0.983795 0.179295i \(-0.0573818\pi\)
\(42\) 0 0
\(43\) 7.23486i 1.10331i −0.834074 0.551653i \(-0.813997\pi\)
0.834074 0.551653i \(-0.186003\pi\)
\(44\) −2.29289 7.57430i −0.345667 1.14187i
\(45\) 0 0
\(46\) 3.24264 0.480049i 0.478101 0.0707794i
\(47\) −4.28289 −0.624724 −0.312362 0.949963i \(-0.601120\pi\)
−0.312362 + 0.949963i \(0.601120\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.378680 + 2.55791i 0.0535534 + 0.361743i
\(51\) 0 0
\(52\) 0.627215 + 2.07193i 0.0869790 + 0.287325i
\(53\) −10.4853 −1.44026 −0.720132 0.693837i \(-0.755919\pi\)
−0.720132 + 0.693837i \(0.755919\pi\)
\(54\) 0 0
\(55\) −10.3398 −1.39422
\(56\) 0 0
\(57\) 0 0
\(58\) −1.41421 9.55274i −0.185695 1.25434i
\(59\) −11.2268 −1.46161 −0.730804 0.682587i \(-0.760855\pi\)
−0.730804 + 0.682587i \(0.760855\pi\)
\(60\) 0 0
\(61\) 5.41196i 0.692931i −0.938063 0.346465i \(-0.887382\pi\)
0.938063 0.346465i \(-0.112618\pi\)
\(62\) 1.25443 + 8.47343i 0.159313 + 1.07613i
\(63\) 0 0
\(64\) −5.08579 + 6.17534i −0.635723 + 0.771917i
\(65\) 2.82843 0.350823
\(66\) 0 0
\(67\) 3.27798i 0.400469i 0.979748 + 0.200235i \(0.0641704\pi\)
−0.979748 + 0.200235i \(0.935830\pi\)
\(68\) −0.183707 0.606854i −0.0222777 0.0735919i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 14.0167i 1.64053i 0.571983 + 0.820266i \(0.306174\pi\)
−0.571983 + 0.820266i \(0.693826\pi\)
\(74\) 0.828427 + 5.59587i 0.0963027 + 0.650506i
\(75\) 0 0
\(76\) 9.89630 2.99581i 1.13518 0.343643i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.91375i 0.890366i 0.895440 + 0.445183i \(0.146861\pi\)
−0.895440 + 0.445183i \(0.853139\pi\)
\(80\) 5.79712 + 8.69760i 0.648138 + 0.972421i
\(81\) 0 0
\(82\) −3.21217 + 0.475538i −0.354725 + 0.0525144i
\(83\) −9.45280 −1.03758 −0.518790 0.854902i \(-0.673617\pi\)
−0.518790 + 0.854902i \(0.673617\pi\)
\(84\) 0 0
\(85\) −0.828427 −0.0898555
\(86\) −10.1213 + 1.49839i −1.09141 + 0.161575i
\(87\) 0 0
\(88\) −10.1213 + 4.77637i −1.07894 + 0.509163i
\(89\) 5.99162i 0.635110i 0.948240 + 0.317555i \(0.102862\pi\)
−0.948240 + 0.317555i \(0.897138\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.34315 4.43692i −0.140033 0.462581i
\(93\) 0 0
\(94\) 0.887016 + 5.99162i 0.0914887 + 0.617988i
\(95\) 13.5096i 1.38606i
\(96\) 0 0
\(97\) 9.23880i 0.938058i −0.883183 0.469029i \(-0.844604\pi\)
0.883183 0.469029i \(-0.155396\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 3.50000 1.05952i 0.350000 0.105952i
\(101\) 15.2304i 1.51548i 0.652555 + 0.757741i \(0.273697\pi\)
−0.652555 + 0.757741i \(0.726303\pi\)
\(102\) 0 0
\(103\) 12.1138 1.19361 0.596806 0.802385i \(-0.296436\pi\)
0.596806 + 0.802385i \(0.296436\pi\)
\(104\) 2.76866 1.30656i 0.271489 0.128119i
\(105\) 0 0
\(106\) 2.17157 + 14.6686i 0.210922 + 1.42474i
\(107\) 2.31788i 0.224078i 0.993704 + 0.112039i \(0.0357382\pi\)
−0.993704 + 0.112039i \(0.964262\pi\)
\(108\) 0 0
\(109\) −5.65685 −0.541828 −0.270914 0.962604i \(-0.587326\pi\)
−0.270914 + 0.962604i \(0.587326\pi\)
\(110\) 2.14144 + 14.4650i 0.204179 + 1.37919i
\(111\) 0 0
\(112\) 0 0
\(113\) 4.24264 0.399114 0.199557 0.979886i \(-0.436050\pi\)
0.199557 + 0.979886i \(0.436050\pi\)
\(114\) 0 0
\(115\) −6.05692 −0.564811
\(116\) −13.0711 + 3.95687i −1.21362 + 0.367387i
\(117\) 0 0
\(118\) 2.32515 + 15.7060i 0.214048 + 1.44585i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.65685 −0.423350
\(122\) −7.57115 + 1.12085i −0.685460 + 0.101477i
\(123\) 0 0
\(124\) 11.5942 3.50981i 1.04119 0.315190i
\(125\) 8.28772i 0.741276i
\(126\) 0 0
\(127\) 10.2316i 0.907911i −0.891024 0.453955i \(-0.850013\pi\)
0.891024 0.453955i \(-0.149987\pi\)
\(128\) 9.69239 + 5.83589i 0.856694 + 0.515825i
\(129\) 0 0
\(130\) −0.585786 3.95687i −0.0513769 0.347041i
\(131\) −0.367414 −0.0321011 −0.0160505 0.999871i \(-0.505109\pi\)
−0.0160505 + 0.999871i \(0.505109\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.58579 0.678892i 0.396152 0.0586474i
\(135\) 0 0
\(136\) −0.810922 + 0.382683i −0.0695360 + 0.0328148i
\(137\) 8.24264 0.704216 0.352108 0.935959i \(-0.385465\pi\)
0.352108 + 0.935959i \(0.385465\pi\)
\(138\) 0 0
\(139\) −22.8211 −1.93566 −0.967829 0.251610i \(-0.919040\pi\)
−0.967829 + 0.251610i \(0.919040\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.28289 0.358153
\(144\) 0 0
\(145\) 17.8435i 1.48183i
\(146\) 19.6089 2.90295i 1.62284 0.240250i
\(147\) 0 0
\(148\) 7.65685 2.31788i 0.629390 0.190529i
\(149\) −4.82843 −0.395560 −0.197780 0.980246i \(-0.563373\pi\)
−0.197780 + 0.980246i \(0.563373\pi\)
\(150\) 0 0
\(151\) 21.4234i 1.74341i −0.490032 0.871704i \(-0.663015\pi\)
0.490032 0.871704i \(-0.336985\pi\)
\(152\) −6.24063 13.2241i −0.506182 1.07262i
\(153\) 0 0
\(154\) 0 0
\(155\) 15.8275i 1.27130i
\(156\) 0 0
\(157\) 19.1886i 1.53141i −0.643189 0.765707i \(-0.722389\pi\)
0.643189 0.765707i \(-0.277611\pi\)
\(158\) 11.0711 1.63899i 0.880767 0.130391i
\(159\) 0 0
\(160\) 10.9670 9.91131i 0.867019 0.783558i
\(161\) 0 0
\(162\) 0 0
\(163\) 15.1486i 1.18653i 0.805007 + 0.593265i \(0.202161\pi\)
−0.805007 + 0.593265i \(0.797839\pi\)
\(164\) 1.33052 + 4.39523i 0.103896 + 0.343210i
\(165\) 0 0
\(166\) 1.95774 + 13.2241i 0.151950 + 1.02639i
\(167\) −7.83095 −0.605977 −0.302989 0.952994i \(-0.597984\pi\)
−0.302989 + 0.952994i \(0.597984\pi\)
\(168\) 0 0
\(169\) 11.8284 0.909879
\(170\) 0.171573 + 1.15894i 0.0131590 + 0.0888868i
\(171\) 0 0
\(172\) 4.19239 + 13.8491i 0.319667 + 1.05598i
\(173\) 6.57128i 0.499605i 0.968297 + 0.249802i \(0.0803657\pi\)
−0.968297 + 0.249802i \(0.919634\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 8.77817 + 13.1702i 0.661680 + 0.992739i
\(177\) 0 0
\(178\) 8.38207 1.24090i 0.628263 0.0930098i
\(179\) 13.5096i 1.00976i −0.863191 0.504878i \(-0.831537\pi\)
0.863191 0.504878i \(-0.168463\pi\)
\(180\) 0 0
\(181\) 21.9874i 1.63431i 0.576418 + 0.817155i \(0.304450\pi\)
−0.576418 + 0.817155i \(0.695550\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −5.92893 + 2.79793i −0.437087 + 0.206266i
\(185\) 10.4525i 0.768483i
\(186\) 0 0
\(187\) −1.25443 −0.0917330
\(188\) 8.19837 2.48181i 0.597927 0.181005i
\(189\) 0 0
\(190\) −18.8995 + 2.79793i −1.37111 + 0.202983i
\(191\) 6.55596i 0.474373i 0.971464 + 0.237186i \(0.0762252\pi\)
−0.971464 + 0.237186i \(0.923775\pi\)
\(192\) 0 0
\(193\) 14.5858 1.04991 0.524954 0.851131i \(-0.324083\pi\)
0.524954 + 0.851131i \(0.324083\pi\)
\(194\) −12.9248 + 1.91342i −0.927944 + 0.137375i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) −17.1316 −1.21442 −0.607212 0.794540i \(-0.707712\pi\)
−0.607212 + 0.794540i \(0.707712\pi\)
\(200\) −2.20711 4.67695i −0.156066 0.330710i
\(201\) 0 0
\(202\) 21.3068 3.15432i 1.49914 0.221937i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 0.419058
\(206\) −2.50886 16.9469i −0.174800 1.18074i
\(207\) 0 0
\(208\) −2.40125 3.60266i −0.166496 0.249800i
\(209\) 20.4567i 1.41502i
\(210\) 0 0
\(211\) 14.4697i 0.996136i 0.867138 + 0.498068i \(0.165957\pi\)
−0.867138 + 0.498068i \(0.834043\pi\)
\(212\) 20.0711 6.07591i 1.37849 0.417296i
\(213\) 0 0
\(214\) 3.24264 0.480049i 0.221662 0.0328155i
\(215\) 18.9056 1.28935
\(216\) 0 0
\(217\) 0 0
\(218\) 1.17157 + 7.91375i 0.0793489 + 0.535987i
\(219\) 0 0
\(220\) 19.7926 5.99162i 1.33442 0.403955i
\(221\) 0.343146 0.0230825
\(222\) 0 0
\(223\) 7.83095 0.524399 0.262200 0.965014i \(-0.415552\pi\)
0.262200 + 0.965014i \(0.415552\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −0.878680 5.93531i −0.0584489 0.394811i
\(227\) 9.97240 0.661891 0.330946 0.943650i \(-0.392632\pi\)
0.330946 + 0.943650i \(0.392632\pi\)
\(228\) 0 0
\(229\) 1.34502i 0.0888817i 0.999012 + 0.0444409i \(0.0141506\pi\)
−0.999012 + 0.0444409i \(0.985849\pi\)
\(230\) 1.25443 + 8.47343i 0.0827146 + 0.558721i
\(231\) 0 0
\(232\) 8.24264 + 17.4665i 0.541156 + 1.14673i
\(233\) −16.2426 −1.06409 −0.532045 0.846716i \(-0.678576\pi\)
−0.532045 + 0.846716i \(0.678576\pi\)
\(234\) 0 0
\(235\) 11.1917i 0.730068i
\(236\) 21.4905 6.50562i 1.39892 0.423480i
\(237\) 0 0
\(238\) 0 0
\(239\) 10.2316i 0.661829i 0.943661 + 0.330915i \(0.107357\pi\)
−0.943661 + 0.330915i \(0.892643\pi\)
\(240\) 0 0
\(241\) 5.09494i 0.328194i −0.986444 0.164097i \(-0.947529\pi\)
0.986444 0.164097i \(-0.0524710\pi\)
\(242\) 0.964466 + 6.51478i 0.0619982 + 0.418786i
\(243\) 0 0
\(244\) 3.13607 + 10.3596i 0.200767 + 0.663209i
\(245\) 0 0
\(246\) 0 0
\(247\) 5.59587i 0.356056i
\(248\) −7.31135 15.4930i −0.464271 0.983809i
\(249\) 0 0
\(250\) 11.5942 1.71644i 0.733284 0.108557i
\(251\) 3.91548 0.247143 0.123571 0.992336i \(-0.460565\pi\)
0.123571 + 0.992336i \(0.460565\pi\)
\(252\) 0 0
\(253\) −9.17157 −0.576612
\(254\) −14.3137 + 2.11904i −0.898122 + 0.132960i
\(255\) 0 0
\(256\) 6.15685 14.7680i 0.384803 0.922999i
\(257\) 19.0572i 1.18876i −0.804185 0.594379i \(-0.797398\pi\)
0.804185 0.594379i \(-0.202602\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −5.41421 + 1.63899i −0.335775 + 0.101646i
\(261\) 0 0
\(262\) 0.0760939 + 0.514000i 0.00470110 + 0.0317550i
\(263\) 25.6614i 1.58235i 0.611588 + 0.791176i \(0.290531\pi\)
−0.611588 + 0.791176i \(0.709469\pi\)
\(264\) 0 0
\(265\) 27.3994i 1.68313i
\(266\) 0 0
\(267\) 0 0
\(268\) −1.89949 6.27476i −0.116030 0.383292i
\(269\) 5.04054i 0.307327i −0.988123 0.153664i \(-0.950893\pi\)
0.988123 0.153664i \(-0.0491072\pi\)
\(270\) 0 0
\(271\) 4.28289 0.260167 0.130084 0.991503i \(-0.458475\pi\)
0.130084 + 0.991503i \(0.458475\pi\)
\(272\) 0.703309 + 1.05520i 0.0426443 + 0.0639806i
\(273\) 0 0
\(274\) −1.70711 11.5312i −0.103130 0.696624i
\(275\) 7.23486i 0.436278i
\(276\) 0 0
\(277\) −4.14214 −0.248877 −0.124438 0.992227i \(-0.539713\pi\)
−0.124438 + 0.992227i \(0.539713\pi\)
\(278\) 4.72640 + 31.9259i 0.283470 + 1.91479i
\(279\) 0 0
\(280\) 0 0
\(281\) −10.3848 −0.619504 −0.309752 0.950817i \(-0.600246\pi\)
−0.309752 + 0.950817i \(0.600246\pi\)
\(282\) 0 0
\(283\) 3.39587 0.201864 0.100932 0.994893i \(-0.467818\pi\)
0.100932 + 0.994893i \(0.467818\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −0.887016 5.99162i −0.0524503 0.354292i
\(287\) 0 0
\(288\) 0 0
\(289\) 16.8995 0.994088
\(290\) 24.9625 3.69552i 1.46585 0.217008i
\(291\) 0 0
\(292\) −8.12227 26.8310i −0.475320 1.57016i
\(293\) 11.7975i 0.689219i 0.938746 + 0.344609i \(0.111989\pi\)
−0.938746 + 0.344609i \(0.888011\pi\)
\(294\) 0 0
\(295\) 29.3371i 1.70807i
\(296\) −4.82843 10.2316i −0.280647 0.594702i
\(297\) 0 0
\(298\) 1.00000 + 6.75481i 0.0579284 + 0.391295i
\(299\) 2.50886 0.145091
\(300\) 0 0
\(301\) 0 0
\(302\) −29.9706 + 4.43692i −1.72461 + 0.255316i
\(303\) 0 0
\(304\) −17.2077 + 11.4692i −0.986927 + 0.657806i
\(305\) 14.1421 0.809776
\(306\) 0 0
\(307\) −3.91548 −0.223468 −0.111734 0.993738i \(-0.535640\pi\)
−0.111734 + 0.993738i \(0.535640\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −22.1421 + 3.27798i −1.25759 + 0.186177i
\(311\) −20.6796 −1.17263 −0.586317 0.810082i \(-0.699423\pi\)
−0.586317 + 0.810082i \(0.699423\pi\)
\(312\) 0 0
\(313\) 12.7486i 0.720594i −0.932838 0.360297i \(-0.882675\pi\)
0.932838 0.360297i \(-0.117325\pi\)
\(314\) −26.8442 + 3.97408i −1.51490 + 0.224270i
\(315\) 0 0
\(316\) −4.58579 15.1486i −0.257971 0.852176i
\(317\) 5.51472 0.309737 0.154869 0.987935i \(-0.450505\pi\)
0.154869 + 0.987935i \(0.450505\pi\)
\(318\) 0 0
\(319\) 27.0192i 1.51279i
\(320\) −16.1369 13.2898i −0.902082 0.742922i
\(321\) 0 0
\(322\) 0 0
\(323\) 1.63899i 0.0911959i
\(324\) 0 0
\(325\) 1.97908i 0.109779i
\(326\) 21.1924 3.13738i 1.17374 0.173763i
\(327\) 0 0
\(328\) 5.87321 2.77164i 0.324294 0.153038i
\(329\) 0 0
\(330\) 0 0
\(331\) 15.1486i 0.832643i 0.909218 + 0.416321i \(0.136681\pi\)
−0.909218 + 0.416321i \(0.863319\pi\)
\(332\) 18.0947 5.47762i 0.993074 0.300623i
\(333\) 0 0
\(334\) 1.62184 + 10.9552i 0.0887433 + 0.599444i
\(335\) −8.56578 −0.467999
\(336\) 0 0
\(337\) 10.8284 0.589862 0.294931 0.955519i \(-0.404703\pi\)
0.294931 + 0.955519i \(0.404703\pi\)
\(338\) −2.44975 16.5476i −0.133249 0.900069i
\(339\) 0 0
\(340\) 1.58579 0.480049i 0.0860013 0.0260343i
\(341\) 23.9665i 1.29786i
\(342\) 0 0
\(343\) 0 0
\(344\) 18.5061 8.73324i 0.997782 0.470865i
\(345\) 0 0
\(346\) 9.19299 1.36096i 0.494218 0.0731654i
\(347\) 3.95687i 0.212416i 0.994344 + 0.106208i \(0.0338710\pi\)
−0.994344 + 0.106208i \(0.966129\pi\)
\(348\) 0 0
\(349\) 8.47343i 0.453572i 0.973945 + 0.226786i \(0.0728218\pi\)
−0.973945 + 0.226786i \(0.927178\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 16.6066 15.0080i 0.885135 0.799929i
\(353\) 10.0586i 0.535363i −0.963507 0.267681i \(-0.913743\pi\)
0.963507 0.267681i \(-0.0862575\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −3.47197 11.4692i −0.184014 0.607868i
\(357\) 0 0
\(358\) −18.8995 + 2.79793i −0.998869 + 0.147875i
\(359\) 31.2573i 1.64970i 0.565353 + 0.824849i \(0.308740\pi\)
−0.565353 + 0.824849i \(0.691260\pi\)
\(360\) 0 0
\(361\) 7.72792 0.406733
\(362\) 30.7596 4.55374i 1.61669 0.239339i
\(363\) 0 0
\(364\) 0 0
\(365\) −36.6274 −1.91717
\(366\) 0 0
\(367\) 12.8487 0.670695 0.335348 0.942094i \(-0.391146\pi\)
0.335348 + 0.942094i \(0.391146\pi\)
\(368\) 5.14214 + 7.71491i 0.268052 + 0.402167i
\(369\) 0 0
\(370\) −14.6227 + 2.16478i −0.760198 + 0.112542i
\(371\) 0 0
\(372\) 0 0
\(373\) −20.1421 −1.04292 −0.521460 0.853276i \(-0.674612\pi\)
−0.521460 + 0.853276i \(0.674612\pi\)
\(374\) 0.259801 + 1.75490i 0.0134340 + 0.0907440i
\(375\) 0 0
\(376\) −5.16991 10.9552i −0.266618 0.564973i
\(377\) 7.39104i 0.380658i
\(378\) 0 0
\(379\) 21.7046i 1.11489i −0.830214 0.557444i \(-0.811782\pi\)
0.830214 0.557444i \(-0.188218\pi\)
\(380\) 7.82843 + 25.8603i 0.401590 + 1.32660i
\(381\) 0 0
\(382\) 9.17157 1.35778i 0.469258 0.0694703i
\(383\) −31.0194 −1.58502 −0.792509 0.609860i \(-0.791226\pi\)
−0.792509 + 0.609860i \(0.791226\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3.02082 20.4050i −0.153755 1.03859i
\(387\) 0 0
\(388\) 5.35361 + 17.6850i 0.271788 + 0.897821i
\(389\) −14.1421 −0.717035 −0.358517 0.933523i \(-0.616718\pi\)
−0.358517 + 0.933523i \(0.616718\pi\)
\(390\) 0 0
\(391\) −0.734828 −0.0371618
\(392\) 0 0
\(393\) 0 0
\(394\) 0.414214 + 2.79793i 0.0208678 + 0.140958i
\(395\) −20.6796 −1.04050
\(396\) 0 0
\(397\) 16.1271i 0.809396i −0.914450 0.404698i \(-0.867377\pi\)
0.914450 0.404698i \(-0.132623\pi\)
\(398\) 3.54806 + 23.9665i 0.177848 + 1.20133i
\(399\) 0 0
\(400\) −6.08579 + 4.05630i −0.304289 + 0.202815i
\(401\) 12.8284 0.640621 0.320311 0.947313i \(-0.396213\pi\)
0.320311 + 0.947313i \(0.396213\pi\)
\(402\) 0 0
\(403\) 6.55596i 0.326576i
\(404\) −8.82558 29.1543i −0.439089 1.45048i
\(405\) 0 0
\(406\) 0 0
\(407\) 15.8275i 0.784540i
\(408\) 0 0
\(409\) 13.8310i 0.683899i −0.939718 0.341949i \(-0.888913\pi\)
0.939718 0.341949i \(-0.111087\pi\)
\(410\) −1.24264 8.39380i −0.0613696 0.414540i
\(411\) 0 0
\(412\) −23.1885 + 7.01962i −1.14241 + 0.345832i
\(413\) 0 0
\(414\) 0 0
\(415\) 24.7013i 1.21254i
\(416\) −4.54269 + 4.10540i −0.222724 + 0.201284i
\(417\) 0 0
\(418\) −28.6182 + 4.23671i −1.39976 + 0.207224i
\(419\) 17.2837 0.844366 0.422183 0.906511i \(-0.361264\pi\)
0.422183 + 0.906511i \(0.361264\pi\)
\(420\) 0 0
\(421\) −10.4853 −0.511021 −0.255511 0.966806i \(-0.582244\pi\)
−0.255511 + 0.966806i \(0.582244\pi\)
\(422\) 20.2426 2.99678i 0.985396 0.145881i
\(423\) 0 0
\(424\) −12.6569 26.8204i −0.614671 1.30251i
\(425\) 0.579658i 0.0281175i
\(426\) 0 0
\(427\) 0 0
\(428\) −1.34315 4.43692i −0.0649234 0.214467i
\(429\) 0 0
\(430\) −3.91548 26.4483i −0.188821 1.27545i
\(431\) 0.960099i 0.0462463i 0.999733 + 0.0231232i \(0.00736099\pi\)
−0.999733 + 0.0231232i \(0.992639\pi\)
\(432\) 0 0
\(433\) 26.1857i 1.25840i 0.777243 + 0.629201i \(0.216618\pi\)
−0.777243 + 0.629201i \(0.783382\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 10.8284 3.27798i 0.518588 0.156987i
\(437\) 11.9832i 0.573236i
\(438\) 0 0
\(439\) −22.4537 −1.07165 −0.535827 0.844328i \(-0.680000\pi\)
−0.535827 + 0.844328i \(0.680000\pi\)
\(440\) −12.4813 26.4483i −0.595021 1.26087i
\(441\) 0 0
\(442\) −0.0710678 0.480049i −0.00338035 0.0228336i
\(443\) 28.3770i 1.34823i −0.738625 0.674116i \(-0.764525\pi\)
0.738625 0.674116i \(-0.235475\pi\)
\(444\) 0 0
\(445\) −15.6569 −0.742206
\(446\) −1.62184 10.9552i −0.0767965 0.518746i
\(447\) 0 0
\(448\) 0 0
\(449\) 16.2843 0.768502 0.384251 0.923229i \(-0.374460\pi\)
0.384251 + 0.923229i \(0.374460\pi\)
\(450\) 0 0
\(451\) 9.08538 0.427814
\(452\) −8.12132 + 2.45849i −0.381995 + 0.115637i
\(453\) 0 0
\(454\) −2.06535 13.9510i −0.0969317 0.654755i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.727922 0.0340508 0.0170254 0.999855i \(-0.494580\pi\)
0.0170254 + 0.999855i \(0.494580\pi\)
\(458\) 1.88164 0.278564i 0.0879235 0.0130164i
\(459\) 0 0
\(460\) 11.5942 3.50981i 0.540584 0.163646i
\(461\) 29.7499i 1.38559i 0.721135 + 0.692794i \(0.243621\pi\)
−0.721135 + 0.692794i \(0.756379\pi\)
\(462\) 0 0
\(463\) 34.9330i 1.62347i 0.584024 + 0.811737i \(0.301477\pi\)
−0.584024 + 0.811737i \(0.698523\pi\)
\(464\) 22.7279 15.1486i 1.05512 0.703256i
\(465\) 0 0
\(466\) 3.36396 + 22.7229i 0.155832 + 1.05262i
\(467\) 24.0755 1.11408 0.557041 0.830485i \(-0.311937\pi\)
0.557041 + 0.830485i \(0.311937\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −15.6569 + 2.31788i −0.722197 + 0.106916i
\(471\) 0 0
\(472\) −13.5520 28.7172i −0.623780 1.32182i
\(473\) 28.6274 1.31629
\(474\) 0 0
\(475\) 9.45280 0.433724
\(476\) 0 0
\(477\) 0 0
\(478\) 14.3137 2.11904i 0.654694 0.0969226i
\(479\) 32.7935 1.49837 0.749186 0.662360i \(-0.230445\pi\)
0.749186 + 0.662360i \(0.230445\pi\)
\(480\) 0 0
\(481\) 4.32957i 0.197411i
\(482\) −7.12764 + 1.05520i −0.324655 + 0.0480628i
\(483\) 0 0
\(484\) 8.91421 2.69851i 0.405192 0.122660i
\(485\) 24.1421 1.09624
\(486\) 0 0
\(487\) 19.5032i 0.883773i 0.897071 + 0.441886i \(0.145691\pi\)
−0.897071 + 0.441886i \(0.854309\pi\)
\(488\) 13.8433 6.53281i 0.626657 0.295727i
\(489\) 0 0
\(490\) 0 0
\(491\) 14.4697i 0.653009i 0.945196 + 0.326504i \(0.105871\pi\)
−0.945196 + 0.326504i \(0.894129\pi\)
\(492\) 0 0
\(493\) 2.16478i 0.0974970i
\(494\) 7.82843 1.15894i 0.352218 0.0521433i
\(495\) 0 0
\(496\) −20.1600 + 13.4370i −0.905212 + 0.603341i
\(497\) 0 0
\(498\) 0 0
\(499\) 12.5495i 0.561793i −0.959738 0.280897i \(-0.909368\pi\)
0.959738 0.280897i \(-0.0906318\pi\)
\(500\) −4.80249 15.8645i −0.214774 0.709480i
\(501\) 0 0
\(502\) −0.810922 5.47762i −0.0361932 0.244478i
\(503\) 7.83095 0.349165 0.174582 0.984643i \(-0.444142\pi\)
0.174582 + 0.984643i \(0.444142\pi\)
\(504\) 0 0
\(505\) −39.7990 −1.77103
\(506\) 1.89949 + 12.8307i 0.0844428 + 0.570395i
\(507\) 0 0
\(508\) 5.92893 + 19.5855i 0.263054 + 0.868967i
\(509\) 6.57128i 0.291267i 0.989339 + 0.145633i \(0.0465220\pi\)
−0.989339 + 0.145633i \(0.953478\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −21.9350 5.55468i −0.969400 0.245485i
\(513\) 0 0
\(514\) −26.6604 + 3.94689i −1.17594 + 0.174090i
\(515\) 31.6550i 1.39489i
\(516\) 0 0
\(517\) 16.9469i 0.745322i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.41421 + 7.23486i 0.149723 + 0.317269i
\(521\) 12.0376i 0.527378i −0.964608 0.263689i \(-0.915061\pi\)
0.964608 0.263689i \(-0.0849393\pi\)
\(522\) 0 0
\(523\) −7.46354 −0.326358 −0.163179 0.986597i \(-0.552175\pi\)
−0.163179 + 0.986597i \(0.552175\pi\)
\(524\) 0.703309 0.212906i 0.0307242 0.00930083i
\(525\) 0 0
\(526\) 35.8995 5.31466i 1.56529 0.231730i
\(527\) 1.92020i 0.0836451i
\(528\) 0 0
\(529\) 17.6274 0.766409
\(530\) −38.3308 + 5.67459i −1.66498 + 0.246489i
\(531\) 0 0
\(532\) 0 0
\(533\) −2.48528 −0.107649
\(534\) 0 0
\(535\) −6.05692 −0.261864
\(536\) −8.38478 + 3.95687i −0.362167 + 0.170911i
\(537\) 0 0
\(538\) −7.05155 + 1.04393i −0.304014 + 0.0450070i
\(539\) 0 0
\(540\) 0 0
\(541\) 45.3137 1.94819 0.974094 0.226142i \(-0.0726115\pi\)
0.974094 + 0.226142i \(0.0726115\pi\)
\(542\) −0.887016 5.99162i −0.0381006 0.257362i
\(543\) 0 0
\(544\) 1.33052 1.20244i 0.0570457 0.0515543i
\(545\) 14.7821i 0.633194i
\(546\) 0 0
\(547\) 27.6981i 1.18429i 0.805833 + 0.592143i \(0.201718\pi\)
−0.805833 + 0.592143i \(0.798282\pi\)
\(548\) −15.7782 + 4.77637i −0.674010 + 0.204036i
\(549\) 0 0
\(550\) −10.1213 + 1.49839i −0.431575 + 0.0638915i
\(551\) −35.3023 −1.50393
\(552\) 0 0
\(553\) 0 0
\(554\) 0.857864 + 5.79471i 0.0364472 + 0.246194i
\(555\) 0 0
\(556\) 43.6844 13.2241i 1.85263 0.560829i
\(557\) 19.6569 0.832888 0.416444 0.909161i \(-0.363276\pi\)
0.416444 + 0.909161i \(0.363276\pi\)
\(558\) 0 0
\(559\) −7.83095 −0.331214
\(560\) 0 0
\(561\) 0 0
\(562\) 2.15076 + 14.5280i 0.0907242 + 0.612825i
\(563\) 21.0470 0.887027 0.443513 0.896268i \(-0.353732\pi\)
0.443513 + 0.896268i \(0.353732\pi\)
\(564\) 0 0
\(565\) 11.0866i 0.466415i
\(566\) −0.703309 4.75071i −0.0295623 0.199687i
\(567\) 0 0
\(568\) 0 0
\(569\) −18.8284 −0.789329 −0.394664 0.918825i \(-0.629139\pi\)
−0.394664 + 0.918825i \(0.629139\pi\)
\(570\) 0 0
\(571\) 9.95043i 0.416412i −0.978085 0.208206i \(-0.933237\pi\)
0.978085 0.208206i \(-0.0667625\pi\)
\(572\) −8.19837 + 2.48181i −0.342791 + 0.103770i
\(573\) 0 0
\(574\) 0 0
\(575\) 4.23808i 0.176740i
\(576\) 0 0
\(577\) 0.842290i 0.0350650i 0.999846 + 0.0175325i \(0.00558105\pi\)
−0.999846 + 0.0175325i \(0.994419\pi\)
\(578\) −3.50000 23.6418i −0.145581 0.983370i
\(579\) 0 0
\(580\) −10.3398 34.1563i −0.429337 1.41827i
\(581\) 0 0
\(582\) 0 0
\(583\) 41.4889i 1.71830i
\(584\) −35.8534 + 16.9197i −1.48363 + 0.700141i
\(585\) 0 0
\(586\) 16.5043 2.44335i 0.681788 0.100934i
\(587\) −22.8211 −0.941926 −0.470963 0.882153i \(-0.656094\pi\)
−0.470963 + 0.882153i \(0.656094\pi\)
\(588\) 0 0
\(589\) 31.3137 1.29026
\(590\) −41.0416 + 6.07591i −1.68966 + 0.250141i
\(591\) 0 0
\(592\) −13.3137 + 8.87385i −0.547190 + 0.364713i
\(593\) 37.4579i 1.53821i 0.639121 + 0.769106i \(0.279298\pi\)
−0.639121 + 0.769106i \(0.720702\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.24264 2.79793i 0.378593 0.114608i
\(597\) 0 0
\(598\) −0.519602 3.50981i −0.0212481 0.143527i
\(599\) 32.2174i 1.31637i −0.752857 0.658184i \(-0.771325\pi\)
0.752857 0.658184i \(-0.228675\pi\)
\(600\) 0 0
\(601\) 25.5516i 1.04227i −0.853474 0.521136i \(-0.825509\pi\)
0.853474 0.521136i \(-0.174491\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 12.4142 + 41.0089i 0.505127 + 1.66863i
\(605\) 12.1689i 0.494738i
\(606\) 0 0
\(607\) 12.1138 0.491686 0.245843 0.969310i \(-0.420935\pi\)
0.245843 + 0.969310i \(0.420935\pi\)
\(608\) 19.6089 + 21.6976i 0.795246 + 0.879953i
\(609\) 0 0
\(610\) −2.92893 19.7844i −0.118589 0.801046i
\(611\) 4.63577i 0.187543i
\(612\) 0 0
\(613\) −8.68629 −0.350836 −0.175418 0.984494i \(-0.556128\pi\)
−0.175418 + 0.984494i \(0.556128\pi\)
\(614\) 0.810922 + 5.47762i 0.0327261 + 0.221059i
\(615\) 0 0
\(616\) 0 0
\(617\) 35.4558 1.42740 0.713699 0.700452i \(-0.247018\pi\)
0.713699 + 0.700452i \(0.247018\pi\)
\(618\) 0 0
\(619\) 13.5205 0.543433 0.271717 0.962377i \(-0.412409\pi\)
0.271717 + 0.962377i \(0.412409\pi\)
\(620\) 9.17157 + 30.2972i 0.368339 + 1.21677i
\(621\) 0 0
\(622\) 4.28289 + 28.9301i 0.171728 + 1.15999i
\(623\) 0 0
\(624\) 0 0
\(625\) −30.7990 −1.23196
\(626\) −17.8349 + 2.64032i −0.712825 + 0.105529i
\(627\) 0 0
\(628\) 11.1192 + 36.7310i 0.443705 + 1.46573i
\(629\) 1.26810i 0.0505625i
\(630\) 0 0
\(631\) 20.4633i 0.814630i 0.913288 + 0.407315i \(0.133535\pi\)
−0.913288 + 0.407315i \(0.866465\pi\)
\(632\) −20.2426 + 9.55274i −0.805209 + 0.379988i
\(633\) 0 0
\(634\) −1.14214 7.71491i −0.0453600 0.306398i
\(635\) 26.7365 1.06101
\(636\) 0 0
\(637\) 0 0
\(638\) 37.7990 5.59587i 1.49648 0.221542i
\(639\) 0 0
\(640\) −15.2499 + 25.3274i −0.602806 + 1.00115i
\(641\) −49.4558 −1.95339 −0.976694 0.214636i \(-0.931144\pi\)
−0.976694 + 0.214636i \(0.931144\pi\)
\(642\) 0 0
\(643\) 41.7267 1.64554 0.822769 0.568375i \(-0.192428\pi\)
0.822769 + 0.568375i \(0.192428\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.29289 + 0.339446i −0.0902127 + 0.0133553i
\(647\) 43.8681 1.72463 0.862317 0.506370i \(-0.169013\pi\)
0.862317 + 0.506370i \(0.169013\pi\)
\(648\) 0 0
\(649\) 44.4231i 1.74376i
\(650\) 2.76866 0.409880i 0.108596 0.0160768i
\(651\) 0 0
\(652\) −8.77817 28.9977i −0.343780 1.13564i
\(653\) 23.7990 0.931326 0.465663 0.884962i \(-0.345816\pi\)
0.465663 + 0.884962i \(0.345816\pi\)
\(654\) 0 0
\(655\) 0.960099i 0.0375142i
\(656\) −5.09381 7.64240i −0.198880 0.298386i
\(657\) 0 0
\(658\) 0 0
\(659\) 13.2284i 0.515306i −0.966238 0.257653i \(-0.917051\pi\)
0.966238 0.257653i \(-0.0829491\pi\)
\(660\) 0 0
\(661\) 37.6662i 1.46504i 0.680744 + 0.732522i \(0.261657\pi\)
−0.680744 + 0.732522i \(0.738343\pi\)
\(662\) 21.1924 3.13738i 0.823666 0.121938i
\(663\) 0 0
\(664\) −11.4105 24.1794i −0.442815 0.938342i
\(665\) 0 0
\(666\) 0 0
\(667\) 15.8275i 0.612843i
\(668\) 14.9901 4.53781i 0.579985 0.175573i
\(669\) 0 0
\(670\) 1.77403 + 11.9832i 0.0685368 + 0.462953i
\(671\) 21.4144 0.826696
\(672\) 0 0
\(673\) 10.3848 0.400304 0.200152 0.979765i \(-0.435856\pi\)
0.200152 + 0.979765i \(0.435856\pi\)
\(674\) −2.24264 15.1486i −0.0863833 0.583502i
\(675\) 0 0
\(676\) −22.6421 + 6.85423i −0.870851 + 0.263624i
\(677\) 28.8532i 1.10892i −0.832211 0.554459i \(-0.812925\pi\)
0.832211 0.554459i \(-0.187075\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.00000 2.11904i −0.0383482 0.0812615i
\(681\) 0 0
\(682\) −33.5283 + 4.96362i −1.28386 + 0.190067i
\(683\) 32.2174i 1.23276i −0.787447 0.616382i \(-0.788598\pi\)
0.787447 0.616382i \(-0.211402\pi\)
\(684\) 0 0
\(685\) 21.5391i 0.822965i
\(686\) 0 0
\(687\) 0 0
\(688\) −16.0503 24.0807i −0.611910 0.918068i
\(689\) 11.3492i 0.432370i
\(690\) 0 0
\(691\) 8.19837 0.311881 0.155940 0.987766i \(-0.450159\pi\)
0.155940 + 0.987766i \(0.450159\pi\)
\(692\) −3.80786 12.5788i −0.144753 0.478175i
\(693\) 0 0
\(694\) 5.53553 0.819496i 0.210126 0.0311076i
\(695\) 59.6343i 2.26206i
\(696\) 0 0
\(697\) 0.727922 0.0275720
\(698\) 11.8540 1.75490i 0.448682 0.0664241i
\(699\) 0 0
\(700\) 0 0
\(701\) −16.0000 −0.604312 −0.302156 0.953259i \(-0.597706\pi\)
−0.302156 + 0.953259i \(0.597706\pi\)
\(702\) 0 0
\(703\) 20.6796 0.779947
\(704\) −24.4350 20.1238i −0.920930 0.758445i
\(705\) 0 0
\(706\) −14.0716 + 2.08319i −0.529591 + 0.0784021i
\(707\) 0 0
\(708\) 0 0
\(709\) −46.6274 −1.75113 −0.875565 0.483101i \(-0.839510\pi\)
−0.875565 + 0.483101i \(0.839510\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −15.3260 + 7.23252i −0.574366 + 0.271050i
\(713\) 14.0392i 0.525774i
\(714\) 0 0
\(715\) 11.1917i 0.418547i
\(716\) 7.82843 + 25.8603i 0.292562 + 0.966444i
\(717\) 0 0
\(718\) 43.7279 6.47360i 1.63191 0.241593i
\(719\) 33.5283 1.25039 0.625197 0.780467i \(-0.285019\pi\)
0.625197 + 0.780467i \(0.285019\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.60051 10.8111i −0.0595646 0.402348i
\(723\) 0 0
\(724\) −12.7411 42.0886i −0.473518 1.56421i
\(725\) −12.4853 −0.463692
\(726\) 0 0
\(727\) 29.9802 1.11191 0.555953 0.831214i \(-0.312354\pi\)
0.555953 + 0.831214i \(0.312354\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7.58579 + 51.2405i 0.280763 + 1.89650i
\(731\) 2.29363 0.0848331
\(732\) 0 0
\(733\) 20.4567i 0.755584i 0.925890 + 0.377792i \(0.123317\pi\)
−0.925890 + 0.377792i \(0.876683\pi\)
\(734\) −2.66105 17.9749i −0.0982210 0.663464i
\(735\) 0 0
\(736\) 9.72792 8.79148i 0.358576 0.324058i
\(737\) −12.9706 −0.477777
\(738\) 0 0
\(739\) 12.4330i 0.457357i −0.973502 0.228678i \(-0.926560\pi\)
0.973502 0.228678i \(-0.0734404\pi\)
\(740\) 6.05692 + 20.0083i 0.222657 + 0.735521i
\(741\) 0 0
\(742\) 0 0
\(743\) 45.1646i 1.65693i 0.560042 + 0.828464i \(0.310785\pi\)
−0.560042 + 0.828464i \(0.689215\pi\)
\(744\) 0 0
\(745\) 12.6173i 0.462262i
\(746\) 4.17157 + 28.1782i 0.152732 + 1.03168i
\(747\) 0 0
\(748\) 2.40125 0.726905i 0.0877982 0.0265783i
\(749\) 0 0
\(750\) 0 0
\(751\) 37.2509i 1.35930i −0.733535 0.679652i \(-0.762131\pi\)
0.733535 0.679652i \(-0.237869\pi\)
\(752\) −14.2553 + 9.50143i −0.519837 + 0.346481i
\(753\) 0 0
\(754\) −10.3398 + 1.53073i −0.376554 + 0.0557460i
\(755\) 55.9819 2.03739
\(756\) 0 0
\(757\) −44.2843 −1.60954 −0.804770 0.593587i \(-0.797711\pi\)
−0.804770 + 0.593587i \(0.797711\pi\)
\(758\) −30.3640 + 4.49516i −1.10287 + 0.163272i
\(759\) 0 0
\(760\) 34.5563 16.3075i 1.25349 0.591537i
\(761\) 0.0543929i 0.00197174i 1.00000 0.000985871i \(0.000313813\pi\)
−1.00000 0.000985871i \(0.999686\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −3.79899 12.5495i −0.137443 0.454026i
\(765\) 0 0
\(766\) 6.42433 + 43.3951i 0.232121 + 1.56793i
\(767\) 12.1518i 0.438777i
\(768\) 0 0
\(769\) 19.1342i 0.689996i −0.938603 0.344998i \(-0.887880\pi\)
0.938603 0.344998i \(-0.112120\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −27.9203 + 8.45204i −1.00487 + 0.304195i
\(773\) 49.4955i 1.78023i 0.455735 + 0.890116i \(0.349376\pi\)
−0.455735 + 0.890116i \(0.650624\pi\)
\(774\) 0 0
\(775\) 11.0746 0.397813
\(776\) 23.6320 11.1522i 0.848339 0.400341i
\(777\) 0 0
\(778\) 2.92893 + 19.7844i 0.105007 + 0.709304i
\(779\) 11.8706i 0.425309i
\(780\) 0 0
\(781\) 0 0
\(782\) 0.152188 + 1.02800i 0.00544222 + 0.0367612i
\(783\) 0 0
\(784\) 0 0
\(785\) 50.1421 1.78965
\(786\) 0 0
\(787\) 41.2071 1.46887 0.734436 0.678677i \(-0.237447\pi\)
0.734436 + 0.678677i \(0.237447\pi\)
\(788\) 3.82843 1.15894i 0.136382 0.0412856i
\(789\) 0 0
\(790\) 4.28289 + 28.9301i 0.152378 + 1.02929i
\(791\) 0 0
\(792\) 0 0
\(793\) −5.85786 −0.208019
\(794\) −22.5613 + 3.34003i −0.800669 + 0.118533i
\(795\) 0 0
\(796\) 32.7935 9.92724i 1.16233 0.351862i
\(797\) 20.1940i 0.715309i 0.933854 + 0.357655i \(0.116424\pi\)