Properties

Label 1764.2.b.k.1567.7
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 1567.7
Root \(1.36145 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 1764.1567
Dual form 1764.2.b.k.1567.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.20711 + 0.736813i) q^{2} +(0.914214 + 1.77882i) q^{4} -1.08239i q^{5} +(-0.207107 + 2.82083i) q^{8} +O(q^{10})\) \(q+(1.20711 + 0.736813i) q^{2} +(0.914214 + 1.77882i) q^{4} -1.08239i q^{5} +(-0.207107 + 2.82083i) q^{8} +(0.797521 - 1.30656i) q^{10} +2.08402i q^{11} -2.61313i q^{13} +(-2.32843 + 3.25245i) q^{16} +4.46088i q^{17} +1.12786 q^{19} +(1.92538 - 0.989538i) q^{20} +(-1.53553 + 2.51564i) q^{22} +7.11529i q^{23} +3.82843 q^{25} +(1.92538 - 3.15432i) q^{26} +1.17157 q^{29} +7.70154 q^{31} +(-5.20711 + 2.21044i) q^{32} +(-3.28684 + 5.38476i) q^{34} -4.00000 q^{37} +(1.36145 + 0.831025i) q^{38} +(3.05325 + 0.224171i) q^{40} +5.54328i q^{41} +7.97852i q^{43} +(-3.70711 + 1.90524i) q^{44} +(-5.24264 + 8.58892i) q^{46} -5.44581 q^{47} +(4.62132 + 2.82083i) q^{50} +(4.64829 - 2.38896i) q^{52} +6.48528 q^{53} +2.25573 q^{55} +(1.41421 + 0.863230i) q^{58} +8.82940 q^{59} -13.0656i q^{61} +(9.29658 + 5.67459i) q^{62} +(-7.91421 - 1.16843i) q^{64} -2.82843 q^{65} -10.0625i q^{67} +(-7.93513 + 4.07820i) q^{68} +7.97069i q^{73} +(-4.82843 - 2.94725i) q^{74} +(1.03111 + 2.00627i) q^{76} +4.16804i q^{79} +(3.52043 + 2.52027i) q^{80} +(-4.08436 + 6.69133i) q^{82} -4.31795 q^{83} +4.82843 q^{85} +(-5.87868 + 9.63093i) q^{86} +(-5.87868 - 0.431615i) q^{88} -4.01254i q^{89} +(-12.6569 + 6.50490i) q^{92} +(-6.57368 - 4.01254i) q^{94} -1.22079i q^{95} -3.82683i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{2} - 4q^{4} + 4q^{8} + O(q^{10}) \) \( 8q + 4q^{2} - 4q^{4} + 4q^{8} + 4q^{16} + 16q^{22} + 8q^{25} + 32q^{29} - 36q^{32} - 32q^{37} - 24q^{44} - 8q^{46} + 20q^{50} - 16q^{53} - 52q^{64} - 16q^{74} + 16q^{85} - 64q^{86} - 64q^{88} - 56q^{92} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.20711 + 0.736813i 0.853553 + 0.521005i
\(3\) 0 0
\(4\) 0.914214 + 1.77882i 0.457107 + 0.889412i
\(5\) 1.08239i 0.484061i −0.970269 0.242030i \(-0.922187\pi\)
0.970269 0.242030i \(-0.0778133\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −0.207107 + 2.82083i −0.0732233 + 0.997316i
\(9\) 0 0
\(10\) 0.797521 1.30656i 0.252198 0.413171i
\(11\) 2.08402i 0.628356i 0.949364 + 0.314178i \(0.101729\pi\)
−0.949364 + 0.314178i \(0.898271\pi\)
\(12\) 0 0
\(13\) 2.61313i 0.724751i −0.932032 0.362375i \(-0.881966\pi\)
0.932032 0.362375i \(-0.118034\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.32843 + 3.25245i −0.582107 + 0.813112i
\(17\) 4.46088i 1.08192i 0.841047 + 0.540962i \(0.181940\pi\)
−0.841047 + 0.540962i \(0.818060\pi\)
\(18\) 0 0
\(19\) 1.12786 0.258750 0.129375 0.991596i \(-0.458703\pi\)
0.129375 + 0.991596i \(0.458703\pi\)
\(20\) 1.92538 0.989538i 0.430529 0.221267i
\(21\) 0 0
\(22\) −1.53553 + 2.51564i −0.327377 + 0.536336i
\(23\) 7.11529i 1.48364i 0.670598 + 0.741821i \(0.266037\pi\)
−0.670598 + 0.741821i \(0.733963\pi\)
\(24\) 0 0
\(25\) 3.82843 0.765685
\(26\) 1.92538 3.15432i 0.377599 0.618613i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.17157 0.217556 0.108778 0.994066i \(-0.465306\pi\)
0.108778 + 0.994066i \(0.465306\pi\)
\(30\) 0 0
\(31\) 7.70154 1.38324 0.691619 0.722263i \(-0.256898\pi\)
0.691619 + 0.722263i \(0.256898\pi\)
\(32\) −5.20711 + 2.21044i −0.920495 + 0.390754i
\(33\) 0 0
\(34\) −3.28684 + 5.38476i −0.563688 + 0.923479i
\(35\) 0 0
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 1.36145 + 0.831025i 0.220857 + 0.134810i
\(39\) 0 0
\(40\) 3.05325 + 0.224171i 0.482761 + 0.0354445i
\(41\) 5.54328i 0.865714i 0.901462 + 0.432857i \(0.142495\pi\)
−0.901462 + 0.432857i \(0.857505\pi\)
\(42\) 0 0
\(43\) 7.97852i 1.21671i 0.793664 + 0.608357i \(0.208171\pi\)
−0.793664 + 0.608357i \(0.791829\pi\)
\(44\) −3.70711 + 1.90524i −0.558867 + 0.287226i
\(45\) 0 0
\(46\) −5.24264 + 8.58892i −0.772985 + 1.26637i
\(47\) −5.44581 −0.794353 −0.397177 0.917742i \(-0.630010\pi\)
−0.397177 + 0.917742i \(0.630010\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 4.62132 + 2.82083i 0.653553 + 0.398926i
\(51\) 0 0
\(52\) 4.64829 2.38896i 0.644602 0.331288i
\(53\) 6.48528 0.890822 0.445411 0.895326i \(-0.353058\pi\)
0.445411 + 0.895326i \(0.353058\pi\)
\(54\) 0 0
\(55\) 2.25573 0.304162
\(56\) 0 0
\(57\) 0 0
\(58\) 1.41421 + 0.863230i 0.185695 + 0.113348i
\(59\) 8.82940 1.14949 0.574745 0.818332i \(-0.305101\pi\)
0.574745 + 0.818332i \(0.305101\pi\)
\(60\) 0 0
\(61\) 13.0656i 1.67288i −0.548057 0.836441i \(-0.684632\pi\)
0.548057 0.836441i \(-0.315368\pi\)
\(62\) 9.29658 + 5.67459i 1.18067 + 0.720674i
\(63\) 0 0
\(64\) −7.91421 1.16843i −0.989277 0.146053i
\(65\) −2.82843 −0.350823
\(66\) 0 0
\(67\) 10.0625i 1.22934i −0.788786 0.614668i \(-0.789290\pi\)
0.788786 0.614668i \(-0.210710\pi\)
\(68\) −7.93513 + 4.07820i −0.962276 + 0.494555i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 7.97069i 0.932899i 0.884548 + 0.466450i \(0.154467\pi\)
−0.884548 + 0.466450i \(0.845533\pi\)
\(74\) −4.82843 2.94725i −0.561293 0.342611i
\(75\) 0 0
\(76\) 1.03111 + 2.00627i 0.118276 + 0.230135i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.16804i 0.468941i 0.972123 + 0.234471i \(0.0753357\pi\)
−0.972123 + 0.234471i \(0.924664\pi\)
\(80\) 3.52043 + 2.52027i 0.393596 + 0.281775i
\(81\) 0 0
\(82\) −4.08436 + 6.69133i −0.451042 + 0.738934i
\(83\) −4.31795 −0.473956 −0.236978 0.971515i \(-0.576157\pi\)
−0.236978 + 0.971515i \(0.576157\pi\)
\(84\) 0 0
\(85\) 4.82843 0.523716
\(86\) −5.87868 + 9.63093i −0.633914 + 1.03853i
\(87\) 0 0
\(88\) −5.87868 0.431615i −0.626669 0.0460103i
\(89\) 4.01254i 0.425329i −0.977125 0.212664i \(-0.931786\pi\)
0.977125 0.212664i \(-0.0682141\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −12.6569 + 6.50490i −1.31957 + 0.678183i
\(93\) 0 0
\(94\) −6.57368 4.01254i −0.678023 0.413862i
\(95\) 1.22079i 0.125251i
\(96\) 0 0
\(97\) 3.82683i 0.388556i −0.980946 0.194278i \(-0.937764\pi\)
0.980946 0.194278i \(-0.0622364\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 3.50000 + 6.81010i 0.350000 + 0.681010i
\(101\) 0.185709i 0.0184788i −0.999957 0.00923938i \(-0.997059\pi\)
0.999957 0.00923938i \(-0.00294103\pi\)
\(102\) 0 0
\(103\) −15.4031 −1.51771 −0.758855 0.651259i \(-0.774241\pi\)
−0.758855 + 0.651259i \(0.774241\pi\)
\(104\) 7.37120 + 0.541196i 0.722805 + 0.0530686i
\(105\) 0 0
\(106\) 7.82843 + 4.77844i 0.760364 + 0.464123i
\(107\) 7.11529i 0.687861i 0.938995 + 0.343931i \(0.111759\pi\)
−0.938995 + 0.343931i \(0.888241\pi\)
\(108\) 0 0
\(109\) 5.65685 0.541828 0.270914 0.962604i \(-0.412674\pi\)
0.270914 + 0.962604i \(0.412674\pi\)
\(110\) 2.72291 + 1.66205i 0.259619 + 0.158470i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.24264 −0.399114 −0.199557 0.979886i \(-0.563950\pi\)
−0.199557 + 0.979886i \(0.563950\pi\)
\(114\) 0 0
\(115\) 7.70154 0.718172
\(116\) 1.07107 + 2.08402i 0.0994461 + 0.193497i
\(117\) 0 0
\(118\) 10.6580 + 6.50562i 0.981151 + 0.598891i
\(119\) 0 0
\(120\) 0 0
\(121\) 6.65685 0.605169
\(122\) 9.62692 15.7716i 0.871581 1.42789i
\(123\) 0 0
\(124\) 7.04085 + 13.6997i 0.632287 + 1.23027i
\(125\) 9.55582i 0.854699i
\(126\) 0 0
\(127\) 11.2833i 1.00123i −0.865669 0.500617i \(-0.833106\pi\)
0.865669 0.500617i \(-0.166894\pi\)
\(128\) −8.69239 7.24171i −0.768306 0.640083i
\(129\) 0 0
\(130\) −3.41421 2.08402i −0.299446 0.182781i
\(131\) −15.8703 −1.38659 −0.693295 0.720654i \(-0.743842\pi\)
−0.693295 + 0.720654i \(0.743842\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 7.41421 12.1466i 0.640490 1.04930i
\(135\) 0 0
\(136\) −12.5834 0.923880i −1.07902 0.0792220i
\(137\) −0.242641 −0.0207302 −0.0103651 0.999946i \(-0.503299\pi\)
−0.0103651 + 0.999946i \(0.503299\pi\)
\(138\) 0 0
\(139\) 1.78855 0.151703 0.0758515 0.997119i \(-0.475833\pi\)
0.0758515 + 0.997119i \(0.475833\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.44581 0.455402
\(144\) 0 0
\(145\) 1.26810i 0.105310i
\(146\) −5.87291 + 9.62148i −0.486045 + 0.796279i
\(147\) 0 0
\(148\) −3.65685 7.11529i −0.300592 0.584874i
\(149\) 0.828427 0.0678674 0.0339337 0.999424i \(-0.489196\pi\)
0.0339337 + 0.999424i \(0.489196\pi\)
\(150\) 0 0
\(151\) 5.38883i 0.438537i −0.975665 0.219269i \(-0.929633\pi\)
0.975665 0.219269i \(-0.0703671\pi\)
\(152\) −0.233588 + 3.18152i −0.0189465 + 0.258055i
\(153\) 0 0
\(154\) 0 0
\(155\) 8.33609i 0.669571i
\(156\) 0 0
\(157\) 20.1940i 1.61166i 0.592147 + 0.805830i \(0.298280\pi\)
−0.592147 + 0.805830i \(0.701720\pi\)
\(158\) −3.07107 + 5.03127i −0.244321 + 0.400267i
\(159\) 0 0
\(160\) 2.39256 + 5.63613i 0.189149 + 0.445575i
\(161\) 0 0
\(162\) 0 0
\(163\) 3.81048i 0.298460i −0.988803 0.149230i \(-0.952321\pi\)
0.988803 0.149230i \(-0.0476795\pi\)
\(164\) −9.86051 + 5.06774i −0.769977 + 0.395724i
\(165\) 0 0
\(166\) −5.21222 3.18152i −0.404547 0.246934i
\(167\) 20.8489 1.61334 0.806668 0.591005i \(-0.201269\pi\)
0.806668 + 0.591005i \(0.201269\pi\)
\(168\) 0 0
\(169\) 6.17157 0.474736
\(170\) 5.82843 + 3.55765i 0.447020 + 0.272859i
\(171\) 0 0
\(172\) −14.1924 + 7.29408i −1.08216 + 0.556168i
\(173\) 21.0907i 1.60350i −0.597661 0.801749i \(-0.703903\pi\)
0.597661 0.801749i \(-0.296097\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.77817 4.85249i −0.510924 0.365770i
\(177\) 0 0
\(178\) 2.95649 4.84357i 0.221599 0.363041i
\(179\) 1.22079i 0.0912462i −0.998959 0.0456231i \(-0.985473\pi\)
0.998959 0.0456231i \(-0.0145273\pi\)
\(180\) 0 0
\(181\) 6.04601i 0.449397i −0.974428 0.224698i \(-0.927860\pi\)
0.974428 0.224698i \(-0.0721396\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −20.0711 1.47363i −1.47966 0.108637i
\(185\) 4.32957i 0.318316i
\(186\) 0 0
\(187\) −9.29658 −0.679833
\(188\) −4.97863 9.68714i −0.363104 0.706507i
\(189\) 0 0
\(190\) 0.899495 1.47363i 0.0652562 0.106908i
\(191\) 20.1251i 1.45620i −0.685471 0.728100i \(-0.740404\pi\)
0.685471 0.728100i \(-0.259596\pi\)
\(192\) 0 0
\(193\) 17.4142 1.25350 0.626751 0.779219i \(-0.284384\pi\)
0.626751 + 0.779219i \(0.284384\pi\)
\(194\) 2.81966 4.61940i 0.202440 0.331653i
\(195\) 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
\(199\) −21.7832 −1.54417 −0.772087 0.635517i \(-0.780787\pi\)
−0.772087 + 0.635517i \(0.780787\pi\)
\(200\) −0.792893 + 10.7994i −0.0560660 + 0.763630i
\(201\) 0 0
\(202\) 0.136833 0.224171i 0.00962753 0.0157726i
\(203\) 0 0
\(204\) 0 0
\(205\) 6.00000 0.419058
\(206\) −18.5932 11.3492i −1.29545 0.790735i
\(207\) 0 0
\(208\) 8.49906 + 6.08447i 0.589304 + 0.421882i
\(209\) 2.35049i 0.162587i
\(210\) 0 0
\(211\) 15.9570i 1.09853i −0.835649 0.549264i \(-0.814908\pi\)
0.835649 0.549264i \(-0.185092\pi\)
\(212\) 5.92893 + 11.5362i 0.407201 + 0.792308i
\(213\) 0 0
\(214\) −5.24264 + 8.58892i −0.358380 + 0.587127i
\(215\) 8.63589 0.588963
\(216\) 0 0
\(217\) 0 0
\(218\) 6.82843 + 4.16804i 0.462479 + 0.282295i
\(219\) 0 0
\(220\) 2.06222 + 4.01254i 0.139035 + 0.270526i
\(221\) 11.6569 0.784125
\(222\) 0 0
\(223\) −20.8489 −1.39614 −0.698072 0.716027i \(-0.745959\pi\)
−0.698072 + 0.716027i \(0.745959\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −5.12132 3.12603i −0.340665 0.207941i
\(227\) −18.1260 −1.20306 −0.601532 0.798849i \(-0.705443\pi\)
−0.601532 + 0.798849i \(0.705443\pi\)
\(228\) 0 0
\(229\) 18.9259i 1.25066i −0.780360 0.625330i \(-0.784964\pi\)
0.780360 0.625330i \(-0.215036\pi\)
\(230\) 9.29658 + 5.67459i 0.612998 + 0.374172i
\(231\) 0 0
\(232\) −0.242641 + 3.30481i −0.0159301 + 0.216972i
\(233\) −7.75736 −0.508202 −0.254101 0.967178i \(-0.581779\pi\)
−0.254101 + 0.967178i \(0.581779\pi\)
\(234\) 0 0
\(235\) 5.89450i 0.384515i
\(236\) 8.07196 + 15.7060i 0.525440 + 1.02237i
\(237\) 0 0
\(238\) 0 0
\(239\) 11.2833i 0.729858i 0.931035 + 0.364929i \(0.118907\pi\)
−0.931035 + 0.364929i \(0.881093\pi\)
\(240\) 0 0
\(241\) 8.60474i 0.554280i −0.960830 0.277140i \(-0.910613\pi\)
0.960830 0.277140i \(-0.0893866\pi\)
\(242\) 8.03553 + 4.90486i 0.516544 + 0.315296i
\(243\) 0 0
\(244\) 23.2415 11.9448i 1.48788 0.764686i
\(245\) 0 0
\(246\) 0 0
\(247\) 2.94725i 0.187529i
\(248\) −1.59504 + 21.7248i −0.101285 + 1.37952i
\(249\) 0 0
\(250\) 7.04085 11.5349i 0.445303 0.729531i
\(251\) −10.4244 −0.657985 −0.328993 0.944333i \(-0.606709\pi\)
−0.328993 + 0.944333i \(0.606709\pi\)
\(252\) 0 0
\(253\) −14.8284 −0.932255
\(254\) 8.31371 13.6202i 0.521648 0.854607i
\(255\) 0 0
\(256\) −5.15685 15.1462i −0.322303 0.946636i
\(257\) 9.42450i 0.587884i 0.955823 + 0.293942i \(0.0949673\pi\)
−0.955823 + 0.293942i \(0.905033\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.58579 5.03127i −0.160364 0.312026i
\(261\) 0 0
\(262\) −19.1571 11.6934i −1.18353 0.722421i
\(263\) 21.8516i 1.34742i −0.738994 0.673712i \(-0.764699\pi\)
0.738994 0.673712i \(-0.235301\pi\)
\(264\) 0 0
\(265\) 7.01962i 0.431212i
\(266\) 0 0
\(267\) 0 0
\(268\) 17.8995 9.19932i 1.09339 0.561938i
\(269\) 17.3952i 1.06060i 0.847809 + 0.530302i \(0.177921\pi\)
−0.847809 + 0.530302i \(0.822079\pi\)
\(270\) 0 0
\(271\) 5.44581 0.330809 0.165405 0.986226i \(-0.447107\pi\)
0.165405 + 0.986226i \(0.447107\pi\)
\(272\) −14.5088 10.3868i −0.879725 0.629795i
\(273\) 0 0
\(274\) −0.292893 0.178781i −0.0176943 0.0108005i
\(275\) 7.97852i 0.481123i
\(276\) 0 0
\(277\) 24.1421 1.45056 0.725280 0.688454i \(-0.241710\pi\)
0.725280 + 0.688454i \(0.241710\pi\)
\(278\) 2.15897 + 1.31783i 0.129487 + 0.0790381i
\(279\) 0 0
\(280\) 0 0
\(281\) 26.3848 1.57398 0.786992 0.616963i \(-0.211637\pi\)
0.786992 + 0.616963i \(0.211637\pi\)
\(282\) 0 0
\(283\) 12.0195 0.714484 0.357242 0.934012i \(-0.383717\pi\)
0.357242 + 0.934012i \(0.383717\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 6.57368 + 4.01254i 0.388710 + 0.237267i
\(287\) 0 0
\(288\) 0 0
\(289\) −2.89949 −0.170559
\(290\) 0.934353 1.53073i 0.0548671 0.0898878i
\(291\) 0 0
\(292\) −14.1785 + 7.28692i −0.829732 + 0.426435i
\(293\) 23.2555i 1.35860i −0.733860 0.679300i \(-0.762283\pi\)
0.733860 0.679300i \(-0.237717\pi\)
\(294\) 0 0
\(295\) 9.55688i 0.556423i
\(296\) 0.828427 11.2833i 0.0481513 0.655831i
\(297\) 0 0
\(298\) 1.00000 + 0.610396i 0.0579284 + 0.0353593i
\(299\) 18.5932 1.07527
\(300\) 0 0
\(301\) 0 0
\(302\) 3.97056 6.50490i 0.228480 0.374315i
\(303\) 0 0
\(304\) −2.62615 + 3.66832i −0.150620 + 0.210393i
\(305\) −14.1421 −0.809776
\(306\) 0 0
\(307\) 10.4244 0.594954 0.297477 0.954729i \(-0.403855\pi\)
0.297477 + 0.954729i \(0.403855\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 6.14214 10.0625i 0.348850 0.571514i
\(311\) 4.51146 0.255821 0.127911 0.991786i \(-0.459173\pi\)
0.127911 + 0.991786i \(0.459173\pi\)
\(312\) 0 0
\(313\) 9.87285i 0.558046i 0.960284 + 0.279023i \(0.0900106\pi\)
−0.960284 + 0.279023i \(0.909989\pi\)
\(314\) −14.8792 + 24.3764i −0.839683 + 1.37564i
\(315\) 0 0
\(316\) −7.41421 + 3.81048i −0.417082 + 0.214356i
\(317\) 22.4853 1.26290 0.631450 0.775417i \(-0.282460\pi\)
0.631450 + 0.775417i \(0.282460\pi\)
\(318\) 0 0
\(319\) 2.44158i 0.136702i
\(320\) −1.26470 + 8.56628i −0.0706987 + 0.478870i
\(321\) 0 0
\(322\) 0 0
\(323\) 5.03127i 0.279948i
\(324\) 0 0
\(325\) 10.0042i 0.554931i
\(326\) 2.80761 4.59966i 0.155499 0.254751i
\(327\) 0 0
\(328\) −15.6367 1.14805i −0.863391 0.0633905i
\(329\) 0 0
\(330\) 0 0
\(331\) 3.81048i 0.209443i −0.994502 0.104722i \(-0.966605\pi\)
0.994502 0.104722i \(-0.0333951\pi\)
\(332\) −3.94753 7.68087i −0.216649 0.421542i
\(333\) 0 0
\(334\) 25.1668 + 15.3617i 1.37707 + 0.840556i
\(335\) −10.8916 −0.595073
\(336\) 0 0
\(337\) 5.17157 0.281714 0.140857 0.990030i \(-0.455014\pi\)
0.140857 + 0.990030i \(0.455014\pi\)
\(338\) 7.44975 + 4.54729i 0.405213 + 0.247340i
\(339\) 0 0
\(340\) 4.41421 + 8.58892i 0.239394 + 0.465800i
\(341\) 16.0502i 0.869166i
\(342\) 0 0
\(343\) 0 0
\(344\) −22.5061 1.65241i −1.21345 0.0890918i
\(345\) 0 0
\(346\) 15.5399 25.4587i 0.835431 1.36867i
\(347\) 2.08402i 0.111876i 0.998434 + 0.0559381i \(0.0178149\pi\)
−0.998434 + 0.0559381i \(0.982185\pi\)
\(348\) 0 0
\(349\) 5.67459i 0.303754i 0.988399 + 0.151877i \(0.0485318\pi\)
−0.988399 + 0.151877i \(0.951468\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.60660 10.8517i −0.245533 0.578399i
\(353\) 27.9790i 1.48917i −0.667526 0.744586i \(-0.732647\pi\)
0.667526 0.744586i \(-0.267353\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 7.13761 3.66832i 0.378292 0.194421i
\(357\) 0 0
\(358\) 0.899495 1.47363i 0.0475398 0.0778835i
\(359\) 24.7988i 1.30883i −0.756135 0.654415i \(-0.772915\pi\)
0.756135 0.654415i \(-0.227085\pi\)
\(360\) 0 0
\(361\) −17.7279 −0.933049
\(362\) 4.45478 7.29818i 0.234138 0.383584i
\(363\) 0 0
\(364\) 0 0
\(365\) 8.62742 0.451580
\(366\) 0 0
\(367\) 16.3374 0.852807 0.426404 0.904533i \(-0.359780\pi\)
0.426404 + 0.904533i \(0.359780\pi\)
\(368\) −23.1421 16.5674i −1.20637 0.863638i
\(369\) 0 0
\(370\) −3.19008 + 5.22625i −0.165844 + 0.271700i
\(371\) 0 0
\(372\) 0 0
\(373\) 8.14214 0.421584 0.210792 0.977531i \(-0.432396\pi\)
0.210792 + 0.977531i \(0.432396\pi\)
\(374\) −11.2220 6.84984i −0.580274 0.354197i
\(375\) 0 0
\(376\) 1.12786 15.3617i 0.0581652 0.792221i
\(377\) 3.06147i 0.157674i
\(378\) 0 0
\(379\) 23.9356i 1.22949i 0.788727 + 0.614744i \(0.210741\pi\)
−0.788727 + 0.614744i \(0.789259\pi\)
\(380\) 2.17157 1.11606i 0.111399 0.0572529i
\(381\) 0 0
\(382\) 14.8284 24.2931i 0.758688 1.24294i
\(383\) 6.76719 0.345787 0.172894 0.984941i \(-0.444688\pi\)
0.172894 + 0.984941i \(0.444688\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 21.0208 + 12.8310i 1.06993 + 0.653082i
\(387\) 0 0
\(388\) 6.80726 3.49854i 0.345586 0.177612i
\(389\) 14.1421 0.717035 0.358517 0.933523i \(-0.383282\pi\)
0.358517 + 0.933523i \(0.383282\pi\)
\(390\) 0 0
\(391\) −31.7405 −1.60519
\(392\) 0 0
\(393\) 0 0
\(394\) −2.41421 1.47363i −0.121626 0.0742402i
\(395\) 4.51146 0.226996
\(396\) 0 0
\(397\) 12.8030i 0.642564i 0.946984 + 0.321282i \(0.104114\pi\)
−0.946984 + 0.321282i \(0.895886\pi\)
\(398\) −26.2947 16.0502i −1.31803 0.804523i
\(399\) 0 0
\(400\) −8.91421 + 12.4518i −0.445711 + 0.622588i
\(401\) 7.17157 0.358131 0.179066 0.983837i \(-0.442693\pi\)
0.179066 + 0.983837i \(0.442693\pi\)
\(402\) 0 0
\(403\) 20.1251i 1.00250i
\(404\) 0.330344 0.169778i 0.0164352 0.00844676i
\(405\) 0 0
\(406\) 0 0
\(407\) 8.33609i 0.413204i
\(408\) 0 0
\(409\) 7.25972i 0.358970i 0.983761 + 0.179485i \(0.0574431\pi\)
−0.983761 + 0.179485i \(0.942557\pi\)
\(410\) 7.24264 + 4.42088i 0.357689 + 0.218332i
\(411\) 0 0
\(412\) −14.0817 27.3994i −0.693756 1.34987i
\(413\) 0 0
\(414\) 0 0
\(415\) 4.67371i 0.229423i
\(416\) 5.77615 + 13.6068i 0.283199 + 0.667130i
\(417\) 0 0
\(418\) −1.73187 + 2.83730i −0.0847087 + 0.138777i
\(419\) −16.5309 −0.807589 −0.403795 0.914850i \(-0.632309\pi\)
−0.403795 + 0.914850i \(0.632309\pi\)
\(420\) 0 0
\(421\) 6.48528 0.316073 0.158037 0.987433i \(-0.449484\pi\)
0.158037 + 0.987433i \(0.449484\pi\)
\(422\) 11.7574 19.2619i 0.572339 0.937653i
\(423\) 0 0
\(424\) −1.34315 + 18.2939i −0.0652289 + 0.888431i
\(425\) 17.0782i 0.828413i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.6569 + 6.50490i −0.611792 + 0.314426i
\(429\) 0 0
\(430\) 10.4244 + 6.36304i 0.502711 + 0.306853i
\(431\) 17.1778i 0.827427i −0.910407 0.413714i \(-0.864231\pi\)
0.910407 0.413714i \(-0.135769\pi\)
\(432\) 0 0
\(433\) 15.1760i 0.729313i 0.931142 + 0.364657i \(0.118814\pi\)
−0.931142 + 0.364657i \(0.881186\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.17157 + 10.0625i 0.247673 + 0.481909i
\(437\) 8.02509i 0.383892i
\(438\) 0 0
\(439\) 17.6588 0.842809 0.421404 0.906873i \(-0.361537\pi\)
0.421404 + 0.906873i \(0.361537\pi\)
\(440\) −0.467177 + 6.36304i −0.0222718 + 0.303346i
\(441\) 0 0
\(442\) 14.0711 + 8.58892i 0.669292 + 0.408533i
\(443\) 26.7347i 1.27020i −0.772428 0.635102i \(-0.780958\pi\)
0.772428 0.635102i \(-0.219042\pi\)
\(444\) 0 0
\(445\) −4.34315 −0.205885
\(446\) −25.1668 15.3617i −1.19168 0.727399i
\(447\) 0 0
\(448\) 0 0
\(449\) −40.2843 −1.90113 −0.950566 0.310522i \(-0.899496\pi\)
−0.950566 + 0.310522i \(0.899496\pi\)
\(450\) 0 0
\(451\) −11.5523 −0.543977
\(452\) −3.87868 7.54691i −0.182438 0.354977i
\(453\) 0 0
\(454\) −21.8800 13.3555i −1.02688 0.626803i
\(455\) 0 0
\(456\) 0 0
\(457\) −24.7279 −1.15672 −0.578362 0.815780i \(-0.696308\pi\)
−0.578362 + 0.815780i \(0.696308\pi\)
\(458\) 13.9449 22.8456i 0.651601 1.06751i
\(459\) 0 0
\(460\) 7.04085 + 13.6997i 0.328281 + 0.638751i
\(461\) 27.4763i 1.27970i 0.768501 + 0.639849i \(0.221003\pi\)
−0.768501 + 0.639849i \(0.778997\pi\)
\(462\) 0 0
\(463\) 6.60963i 0.307175i 0.988135 + 0.153588i \(0.0490828\pi\)
−0.988135 + 0.153588i \(0.950917\pi\)
\(464\) −2.72792 + 3.81048i −0.126641 + 0.176897i
\(465\) 0 0
\(466\) −9.36396 5.71572i −0.433777 0.264776i
\(467\) 7.50803 0.347430 0.173715 0.984796i \(-0.444423\pi\)
0.173715 + 0.984796i \(0.444423\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −4.34315 + 7.11529i −0.200334 + 0.328204i
\(471\) 0 0
\(472\) −1.82863 + 24.9063i −0.0841695 + 1.14640i
\(473\) −16.6274 −0.764529
\(474\) 0 0
\(475\) 4.31795 0.198121
\(476\) 0 0
\(477\) 0 0
\(478\) −8.31371 + 13.6202i −0.380260 + 0.622973i
\(479\) −19.9145 −0.909918 −0.454959 0.890512i \(-0.650346\pi\)
−0.454959 + 0.890512i \(0.650346\pi\)
\(480\) 0 0
\(481\) 10.4525i 0.476593i
\(482\) 6.34009 10.3868i 0.288783 0.473108i
\(483\) 0 0
\(484\) 6.08579 + 11.8414i 0.276627 + 0.538244i
\(485\) −4.14214 −0.188085
\(486\) 0 0
\(487\) 39.7445i 1.80100i 0.434860 + 0.900498i \(0.356798\pi\)
−0.434860 + 0.900498i \(0.643202\pi\)
\(488\) 36.8560 + 2.70598i 1.66839 + 0.122494i
\(489\) 0 0
\(490\) 0 0
\(491\) 15.9570i 0.720132i −0.932927 0.360066i \(-0.882754\pi\)
0.932927 0.360066i \(-0.117246\pi\)
\(492\) 0 0
\(493\) 5.22625i 0.235379i
\(494\) 2.17157 3.55765i 0.0977037 0.160066i
\(495\) 0 0
\(496\) −17.9325 + 25.0489i −0.805192 + 1.12473i
\(497\) 0 0
\(498\) 0 0
\(499\) 18.3986i 0.823636i −0.911266 0.411818i \(-0.864894\pi\)
0.911266 0.411818i \(-0.135106\pi\)
\(500\) 16.9981 8.73606i 0.760179 0.390689i
\(501\) 0 0
\(502\) −12.5834 7.68087i −0.561625 0.342814i
\(503\) −20.8489 −0.929606 −0.464803 0.885414i \(-0.653875\pi\)
−0.464803 + 0.885414i \(0.653875\pi\)
\(504\) 0 0
\(505\) −0.201010 −0.00894483
\(506\) −17.8995 10.9258i −0.795730 0.485710i
\(507\) 0 0
\(508\) 20.0711 10.3154i 0.890510 0.457671i
\(509\) 21.0907i 0.934830i −0.884038 0.467415i \(-0.845185\pi\)
0.884038 0.467415i \(-0.154815\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 4.93503 22.0827i 0.218100 0.975927i
\(513\) 0 0
\(514\) −6.94410 + 11.3764i −0.306291 + 0.501791i
\(515\) 16.6722i 0.734664i
\(516\) 0 0
\(517\) 11.3492i 0.499137i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.585786 7.97852i 0.0256884 0.349881i
\(521\) 17.9749i 0.787493i −0.919219 0.393746i \(-0.871179\pi\)
0.919219 0.393746i \(-0.128821\pi\)
\(522\) 0 0
\(523\) 36.7191 1.60562 0.802808 0.596238i \(-0.203338\pi\)
0.802808 + 0.596238i \(0.203338\pi\)
\(524\) −14.5088 28.2304i −0.633820 1.23325i
\(525\) 0 0
\(526\) 16.1005 26.3772i 0.702015 1.15010i
\(527\) 34.3557i 1.49656i
\(528\) 0 0
\(529\) −27.6274 −1.20119
\(530\) 5.17214 8.47343i 0.224664 0.368062i
\(531\) 0 0
\(532\) 0 0
\(533\) 14.4853 0.627427
\(534\) 0 0
\(535\) 7.70154 0.332967
\(536\) 28.3848 + 2.08402i 1.22604 + 0.0900160i
\(537\) 0 0
\(538\) −12.8170 + 20.9979i −0.552580 + 0.905282i
\(539\) 0 0
\(540\) 0 0
\(541\) 22.6863 0.975360 0.487680 0.873023i \(-0.337843\pi\)
0.487680 + 0.873023i \(0.337843\pi\)
\(542\) 6.57368 + 4.01254i 0.282364 + 0.172353i
\(543\) 0 0
\(544\) −9.86051 23.2283i −0.422766 0.995905i
\(545\) 6.12293i 0.262278i
\(546\) 0 0
\(547\) 14.5882i 0.623744i 0.950124 + 0.311872i \(0.100956\pi\)
−0.950124 + 0.311872i \(0.899044\pi\)
\(548\) −0.221825 0.431615i −0.00947591 0.0184377i
\(549\) 0 0
\(550\) −5.87868 + 9.63093i −0.250668 + 0.410664i
\(551\) 1.32138 0.0562925
\(552\) 0 0
\(553\) 0 0
\(554\) 29.1421 + 17.7882i 1.23813 + 0.755750i
\(555\) 0 0
\(556\) 1.63512 + 3.18152i 0.0693445 + 0.134926i
\(557\) 8.34315 0.353510 0.176755 0.984255i \(-0.443440\pi\)
0.176755 + 0.984255i \(0.443440\pi\)
\(558\) 0 0
\(559\) 20.8489 0.881814
\(560\) 0 0
\(561\) 0 0
\(562\) 31.8492 + 19.4406i 1.34348 + 0.820054i
\(563\) 11.3588 0.478716 0.239358 0.970931i \(-0.423063\pi\)
0.239358 + 0.970931i \(0.423063\pi\)
\(564\) 0 0
\(565\) 4.59220i 0.193195i
\(566\) 14.5088 + 8.85611i 0.609850 + 0.372250i
\(567\) 0 0
\(568\) 0 0
\(569\) −13.1716 −0.552181 −0.276091 0.961132i \(-0.589039\pi\)
−0.276091 + 0.961132i \(0.589039\pi\)
\(570\) 0 0
\(571\) 40.6077i 1.69938i −0.527282 0.849691i \(-0.676789\pi\)
0.527282 0.849691i \(-0.323211\pi\)
\(572\) 4.97863 + 9.68714i 0.208167 + 0.405040i
\(573\) 0 0
\(574\) 0 0
\(575\) 27.2404i 1.13600i
\(576\) 0 0
\(577\) 38.6172i 1.60766i −0.594862 0.803828i \(-0.702793\pi\)
0.594862 0.803828i \(-0.297207\pi\)
\(578\) −3.50000 2.13639i −0.145581 0.0888619i
\(579\) 0 0
\(580\) 2.25573 1.15932i 0.0936640 0.0481380i
\(581\) 0 0
\(582\) 0 0
\(583\) 13.5155i 0.559753i
\(584\) −22.4840 1.65078i −0.930395 0.0683100i
\(585\) 0 0
\(586\) 17.1350 28.0719i 0.707838 1.15964i
\(587\) 1.78855 0.0738214 0.0369107 0.999319i \(-0.488248\pi\)
0.0369107 + 0.999319i \(0.488248\pi\)
\(588\) 0 0
\(589\) 8.68629 0.357912
\(590\) 7.04163 11.5362i 0.289899 0.474937i
\(591\) 0 0
\(592\) 9.31371 13.0098i 0.382791 0.534699i
\(593\) 34.9986i 1.43722i 0.695412 + 0.718611i \(0.255222\pi\)
−0.695412 + 0.718611i \(0.744778\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.757359 + 1.47363i 0.0310226 + 0.0603621i
\(597\) 0 0
\(598\) 22.4439 + 13.6997i 0.917801 + 0.560222i
\(599\) 41.9766i 1.71512i 0.514385 + 0.857560i \(0.328020\pi\)
−0.514385 + 0.857560i \(0.671980\pi\)
\(600\) 0 0
\(601\) 6.25425i 0.255116i −0.991831 0.127558i \(-0.959286\pi\)
0.991831 0.127558i \(-0.0407139\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 9.58579 4.92655i 0.390040 0.200458i
\(605\) 7.20533i 0.292938i
\(606\) 0 0
\(607\) −15.4031 −0.625192 −0.312596 0.949886i \(-0.601199\pi\)
−0.312596 + 0.949886i \(0.601199\pi\)
\(608\) −5.87291 + 2.49307i −0.238178 + 0.101108i
\(609\) 0 0
\(610\) −17.0711 10.4201i −0.691187 0.421898i
\(611\) 14.2306i 0.575708i
\(612\) 0 0
\(613\) −31.3137 −1.26475 −0.632374 0.774663i \(-0.717920\pi\)
−0.632374 + 0.774663i \(0.717920\pi\)
\(614\) 12.5834 + 7.68087i 0.507825 + 0.309974i
\(615\) 0 0
\(616\) 0 0
\(617\) −15.4558 −0.622229 −0.311114 0.950372i \(-0.600702\pi\)
−0.311114 + 0.950372i \(0.600702\pi\)
\(618\) 0 0
\(619\) −44.4207 −1.78542 −0.892709 0.450634i \(-0.851198\pi\)
−0.892709 + 0.450634i \(0.851198\pi\)
\(620\) 14.8284 7.62096i 0.595524 0.306065i
\(621\) 0 0
\(622\) 5.44581 + 3.32410i 0.218357 + 0.133284i
\(623\) 0 0
\(624\) 0 0
\(625\) 8.79899 0.351960
\(626\) −7.27444 + 11.9176i −0.290745 + 0.476322i
\(627\) 0 0
\(628\) −35.9216 + 18.4617i −1.43343 + 0.736700i
\(629\) 17.8435i 0.711469i
\(630\) 0 0
\(631\) 22.5667i 0.898365i 0.893440 + 0.449183i \(0.148285\pi\)
−0.893440 + 0.449183i \(0.851715\pi\)
\(632\) −11.7574 0.863230i −0.467683 0.0343374i
\(633\) 0 0
\(634\) 27.1421 + 16.5674i 1.07795 + 0.657977i
\(635\) −12.2130 −0.484658
\(636\) 0 0
\(637\) 0 0
\(638\) −1.79899 + 2.94725i −0.0712227 + 0.116683i
\(639\) 0 0
\(640\) −7.83837 + 9.40857i −0.309839 + 0.371907i
\(641\) 1.45584 0.0575024 0.0287512 0.999587i \(-0.490847\pi\)
0.0287512 + 0.999587i \(0.490847\pi\)
\(642\) 0 0
\(643\) 6.84734 0.270033 0.135016 0.990843i \(-0.456891\pi\)
0.135016 + 0.990843i \(0.456891\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3.70711 + 6.07328i −0.145854 + 0.238950i
\(647\) 9.57025 0.376245 0.188123 0.982146i \(-0.439760\pi\)
0.188123 + 0.982146i \(0.439760\pi\)
\(648\) 0 0
\(649\) 18.4007i 0.722289i
\(650\) 7.37120 12.0761i 0.289122 0.473663i
\(651\) 0 0
\(652\) 6.77817 3.48359i 0.265454 0.136428i
\(653\) −15.7990 −0.618262 −0.309131 0.951019i \(-0.600038\pi\)
−0.309131 + 0.951019i \(0.600038\pi\)
\(654\) 0 0
\(655\) 17.1778i 0.671194i
\(656\) −18.0292 12.9071i −0.703923 0.503938i
\(657\) 0 0
\(658\) 0 0
\(659\) 30.5452i 1.18987i −0.803773 0.594936i \(-0.797177\pi\)
0.803773 0.594936i \(-0.202823\pi\)
\(660\) 0 0
\(661\) 12.5404i 0.487764i −0.969805 0.243882i \(-0.921579\pi\)
0.969805 0.243882i \(-0.0784209\pi\)
\(662\) 2.80761 4.59966i 0.109121 0.178771i
\(663\) 0 0
\(664\) 0.894276 12.1802i 0.0347046 0.472684i
\(665\) 0 0
\(666\) 0 0
\(667\) 8.33609i 0.322775i
\(668\) 19.0603 + 37.0865i 0.737467 + 1.43492i
\(669\) 0 0
\(670\) −13.1474 8.02509i −0.507926 0.310036i
\(671\) 27.2291 1.05117
\(672\) 0 0
\(673\) −26.3848 −1.01706 −0.508529 0.861045i \(-0.669811\pi\)
−0.508529 + 0.861045i \(0.669811\pi\)
\(674\) 6.24264 + 3.81048i 0.240458 + 0.146774i
\(675\) 0 0
\(676\) 5.64214 + 10.9781i 0.217005 + 0.422236i
\(677\) 40.0936i 1.54092i −0.637488 0.770461i \(-0.720026\pi\)
0.637488 0.770461i \(-0.279974\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.00000 + 13.6202i −0.0383482 + 0.522311i
\(681\) 0 0
\(682\) −11.8260 + 19.3743i −0.452840 + 0.741879i
\(683\) 41.9766i 1.60619i 0.595850 + 0.803096i \(0.296815\pi\)
−0.595850 + 0.803096i \(0.703185\pi\)
\(684\) 0 0
\(685\) 0.262632i 0.0100347i
\(686\) 0 0
\(687\) 0 0
\(688\) −25.9497 18.5774i −0.989325 0.708257i
\(689\) 16.9469i 0.645624i
\(690\) 0 0
\(691\) −4.97863 −0.189396 −0.0946981 0.995506i \(-0.530189\pi\)
−0.0946981 + 0.995506i \(0.530189\pi\)
\(692\) 37.5167 19.2814i 1.42617 0.732970i
\(693\) 0 0
\(694\) −1.53553 + 2.51564i −0.0582881 + 0.0954923i
\(695\) 1.93591i 0.0734334i
\(696\) 0 0
\(697\) −24.7279 −0.936637
\(698\) −4.18111 + 6.84984i −0.158257 + 0.259270i
\(699\) 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
\(703\) −4.51146 −0.170153
\(704\) 2.43503 16.4934i 0.0917736 0.621618i
\(705\) 0 0
\(706\) 20.6153 33.7737i 0.775867 1.27109i
\(707\) 0 0
\(708\) 0 0
\(709\) −1.37258 −0.0515484 −0.0257742 0.999668i \(-0.508205\pi\)
−0.0257742 + 0.999668i \(0.508205\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 11.3187 + 0.831025i 0.424187 + 0.0311440i
\(713\) 54.7987i 2.05223i
\(714\) 0 0
\(715\) 5.89450i 0.220442i
\(716\) 2.17157 1.11606i 0.0811555 0.0417093i
\(717\) 0 0
\(718\) 18.2721 29.9348i 0.681908 1.11716i
\(719\) 11.8260 0.441034 0.220517 0.975383i \(-0.429225\pi\)
0.220517 + 0.975383i \(0.429225\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −21.3995 13.0622i −0.796407 0.486123i
\(723\) 0 0
\(724\) 10.7548 5.52735i 0.399699 0.205422i
\(725\) 4.48528 0.166579
\(726\) 0 0
\(727\) 38.1207 1.41382 0.706909 0.707305i \(-0.250089\pi\)
0.706909 + 0.707305i \(0.250089\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 10.4142 + 6.35679i 0.385447 + 0.235275i
\(731\) −35.5913 −1.31639
\(732\) 0 0
\(733\) 2.35049i 0.0868175i −0.999057 0.0434087i \(-0.986178\pi\)
0.999057 0.0434087i \(-0.0138218\pi\)
\(734\) 19.7210 + 12.0376i 0.727916 + 0.444317i
\(735\) 0 0
\(736\) −15.7279 37.0501i −0.579739 1.36568i
\(737\) 20.9706 0.772461
\(738\) 0 0
\(739\) 52.3968i 1.92745i 0.266905 + 0.963723i \(0.413999\pi\)
−0.266905 + 0.963723i \(0.586001\pi\)
\(740\) −7.70154 + 3.95815i −0.283114 + 0.145505i
\(741\) 0 0
\(742\) 0 0
\(743\) 17.8930i 0.656429i 0.944603 + 0.328215i \(0.106447\pi\)
−0.944603 + 0.328215i \(0.893553\pi\)
\(744\) 0 0
\(745\) 0.896683i 0.0328519i
\(746\) 9.82843 + 5.99923i 0.359844 + 0.219647i
\(747\) 0 0
\(748\) −8.49906 16.5370i −0.310756 0.604652i
\(749\) 0 0
\(750\) 0 0
\(751\) 13.7249i 0.500829i −0.968139 0.250415i \(-0.919433\pi\)
0.968139 0.250415i \(-0.0805670\pi\)
\(752\) 12.6802 17.7122i 0.462398 0.645898i
\(753\) 0 0
\(754\) 2.25573 3.69552i 0.0821488 0.134583i
\(755\) −5.83283 −0.212279
\(756\) 0 0
\(757\) 12.2843 0.446479 0.223240 0.974764i \(-0.428337\pi\)
0.223240 + 0.974764i \(0.428337\pi\)
\(758\) −17.6360 + 28.8928i −0.640570 + 1.04943i
\(759\) 0 0
\(760\) 3.44365 + 0.252834i 0.124914 + 0.00917126i
\(761\) 25.9999i 0.942497i 0.882000 + 0.471249i \(0.156197\pi\)
−0.882000 + 0.471249i \(0.843803\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 35.7990 18.3986i 1.29516 0.665639i
\(765\) 0 0
\(766\) 8.16872 + 4.98615i 0.295148 + 0.180157i
\(767\) 23.0723i 0.833094i
\(768\) 0 0
\(769\) 46.1940i 1.66580i 0.553425 + 0.832899i \(0.313320\pi\)
−0.553425 + 0.832899i \(0.686680\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 15.9203 + 30.9768i 0.572985 + 1.11488i
\(773\) 52.9735i 1.90532i 0.304031 + 0.952662i \(0.401667\pi\)
−0.304031 + 0.952662i \(0.598333\pi\)
\(774\) 0 0
\(775\) 29.4848 1.05912
\(776\) 10.7949 + 0.792563i 0.387513 + 0.0284514i
\(777\) 0 0
\(778\) 17.0711 + 10.4201i 0.612027 + 0.373579i
\(779\) 6.25206i 0.224003i
\(780\) 0 0
\(781\) 0 0
\(782\) −38.3142 23.3868i −1.37011 0.836311i
\(783\) 0 0
\(784\) 0 0
\(785\) 21.8579 0.780141
\(786\) 0 0
\(787\) 29.2913 1.04412 0.522061 0.852908i \(-0.325164\pi\)
0.522061 + 0.852908i \(0.325164\pi\)
\(788\) −1.82843 3.55765i −0.0651350 0.126736i
\(789\) 0 0
\(790\) 5.44581 + 3.32410i 0.193753 + 0.118266i
\(791\) 0 0
\(792\) 0 0
\(793\) −34.1421 −1.21242
\(794\) −9.43341 + 15.4546i −0.334779 + 0.548463i
\(795\) 0 0
\(796\) −19.9145 38.7485i −0.705852 1.37341i
\(797\) 19.1886i 0.679694i 0.940481 + 0.339847i \(0.110375\pi\)
−0.940481 + 0.339847i