Properties

Label 2646.2.t.a.1979.1
Level $2646$
Weight $2$
Character 2646.1979
Analytic conductor $21.128$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1979.1
Root \(-1.62181 + 0.608059i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1979
Dual form 2646.2.t.a.2285.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.89111 q^{5} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.89111 q^{5} +1.00000i q^{8} +(3.36980 - 1.94556i) q^{10} +3.94462i q^{11} +(-2.46687 + 1.42425i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.371058 - 0.642692i) q^{17} +(1.54563 + 0.892369i) q^{19} +(-1.94556 + 3.36980i) q^{20} +(-1.97231 - 3.41614i) q^{22} +6.25311i q^{23} +10.1408 q^{25} +(1.42425 - 2.46687i) q^{26} +(2.50079 + 1.44383i) q^{29} +(3.04125 + 1.75587i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.642692 + 0.371058i) q^{34} +(-1.50079 + 2.59944i) q^{37} -1.78474 q^{38} -3.89111i q^{40} +(-5.24705 - 9.08816i) q^{41} +(0.471521 - 0.816699i) q^{43} +(3.41614 + 1.97231i) q^{44} +(-3.12656 - 5.41535i) q^{46} +(1.09263 + 1.89248i) q^{47} +(-8.78217 + 5.07039i) q^{50} +2.84849i q^{52} -15.3490i q^{55} -2.88766 q^{58} +(0.0105673 - 0.0183031i) q^{59} +(-2.13832 + 1.23456i) q^{61} -3.51174 q^{62} -1.00000 q^{64} +(9.59886 - 5.54191i) q^{65} +(-6.72463 + 11.6474i) q^{67} -0.742117 q^{68} -1.94304i q^{71} +(4.20443 - 2.42743i) q^{73} -3.00158i q^{74} +(1.54563 - 0.892369i) q^{76} +(-1.81806 - 3.14898i) q^{79} +(1.94556 + 3.36980i) q^{80} +(9.08816 + 5.24705i) q^{82} +(-4.02998 + 6.98012i) q^{83} +(1.44383 + 2.50079i) q^{85} +0.943042i q^{86} -3.94462 q^{88} +(4.63323 - 8.02499i) q^{89} +(5.41535 + 3.12656i) q^{92} +(-1.89248 - 1.09263i) q^{94} +(-6.01422 - 3.47231i) q^{95} +(-16.2983 - 9.40980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 8 q^{16} + 16 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} - 60 q^{50} + 24 q^{58} - 16 q^{64} + 84 q^{65} - 28 q^{67} - 4 q^{79} - 12 q^{85} + 48 q^{92} + 12 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −3.89111 −1.74016 −0.870080 0.492911i \(-0.835933\pi\)
−0.870080 + 0.492911i \(0.835933\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 3.36980 1.94556i 1.06563 0.615239i
\(11\) 3.94462i 1.18935i 0.803967 + 0.594674i \(0.202719\pi\)
−0.803967 + 0.594674i \(0.797281\pi\)
\(12\) 0 0
\(13\) −2.46687 + 1.42425i −0.684186 + 0.395015i −0.801430 0.598088i \(-0.795927\pi\)
0.117244 + 0.993103i \(0.462594\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.371058 0.642692i −0.0899949 0.155876i 0.817514 0.575909i \(-0.195352\pi\)
−0.907509 + 0.420033i \(0.862018\pi\)
\(18\) 0 0
\(19\) 1.54563 + 0.892369i 0.354591 + 0.204723i 0.666706 0.745321i \(-0.267704\pi\)
−0.312114 + 0.950045i \(0.601037\pi\)
\(20\) −1.94556 + 3.36980i −0.435040 + 0.753511i
\(21\) 0 0
\(22\) −1.97231 3.41614i −0.420498 0.728324i
\(23\) 6.25311i 1.30386i 0.758278 + 0.651932i \(0.226041\pi\)
−0.758278 + 0.651932i \(0.773959\pi\)
\(24\) 0 0
\(25\) 10.1408 2.02815
\(26\) 1.42425 2.46687i 0.279318 0.483793i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.50079 + 1.44383i 0.464385 + 0.268113i 0.713886 0.700262i \(-0.246933\pi\)
−0.249501 + 0.968374i \(0.580267\pi\)
\(30\) 0 0
\(31\) 3.04125 + 1.75587i 0.546225 + 0.315363i 0.747598 0.664152i \(-0.231207\pi\)
−0.201373 + 0.979515i \(0.564540\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 0.642692 + 0.371058i 0.110221 + 0.0636360i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.50079 + 2.59944i −0.246728 + 0.427346i −0.962616 0.270870i \(-0.912689\pi\)
0.715888 + 0.698215i \(0.246022\pi\)
\(38\) −1.78474 −0.289523
\(39\) 0 0
\(40\) 3.89111i 0.615239i
\(41\) −5.24705 9.08816i −0.819452 1.41933i −0.906087 0.423092i \(-0.860945\pi\)
0.0866345 0.996240i \(-0.472389\pi\)
\(42\) 0 0
\(43\) 0.471521 0.816699i 0.0719063 0.124545i −0.827830 0.560978i \(-0.810425\pi\)
0.899737 + 0.436433i \(0.143758\pi\)
\(44\) 3.41614 + 1.97231i 0.515003 + 0.297337i
\(45\) 0 0
\(46\) −3.12656 5.41535i −0.460985 0.798450i
\(47\) 1.09263 + 1.89248i 0.159376 + 0.276047i 0.934644 0.355585i \(-0.115718\pi\)
−0.775268 + 0.631633i \(0.782385\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −8.78217 + 5.07039i −1.24199 + 0.717061i
\(51\) 0 0
\(52\) 2.84849i 0.395015i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 15.3490i 2.06965i
\(56\) 0 0
\(57\) 0 0
\(58\) −2.88766 −0.379169
\(59\) 0.0105673 0.0183031i 0.00137575 0.00238286i −0.865337 0.501191i \(-0.832895\pi\)
0.866712 + 0.498808i \(0.166229\pi\)
\(60\) 0 0
\(61\) −2.13832 + 1.23456i −0.273783 + 0.158069i −0.630606 0.776103i \(-0.717193\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(62\) −3.51174 −0.445991
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 9.59886 5.54191i 1.19059 0.687389i
\(66\) 0 0
\(67\) −6.72463 + 11.6474i −0.821544 + 1.42296i 0.0829874 + 0.996551i \(0.473554\pi\)
−0.904532 + 0.426406i \(0.859779\pi\)
\(68\) −0.742117 −0.0899949
\(69\) 0 0
\(70\) 0 0
\(71\) 1.94304i 0.230597i −0.993331 0.115298i \(-0.963218\pi\)
0.993331 0.115298i \(-0.0367824\pi\)
\(72\) 0 0
\(73\) 4.20443 2.42743i 0.492092 0.284109i −0.233350 0.972393i \(-0.574969\pi\)
0.725442 + 0.688284i \(0.241636\pi\)
\(74\) 3.00158i 0.348926i
\(75\) 0 0
\(76\) 1.54563 0.892369i 0.177296 0.102362i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.81806 3.14898i −0.204548 0.354288i 0.745440 0.666572i \(-0.232239\pi\)
−0.949989 + 0.312284i \(0.898906\pi\)
\(80\) 1.94556 + 3.36980i 0.217520 + 0.376756i
\(81\) 0 0
\(82\) 9.08816 + 5.24705i 1.00362 + 0.579440i
\(83\) −4.02998 + 6.98012i −0.442347 + 0.766168i −0.997863 0.0653378i \(-0.979188\pi\)
0.555516 + 0.831506i \(0.312521\pi\)
\(84\) 0 0
\(85\) 1.44383 + 2.50079i 0.156605 + 0.271249i
\(86\) 0.943042i 0.101691i
\(87\) 0 0
\(88\) −3.94462 −0.420498
\(89\) 4.63323 8.02499i 0.491122 0.850647i −0.508826 0.860869i \(-0.669920\pi\)
0.999948 + 0.0102218i \(0.00325375\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.41535 + 3.12656i 0.564589 + 0.325966i
\(93\) 0 0
\(94\) −1.89248 1.09263i −0.195195 0.112696i
\(95\) −6.01422 3.47231i −0.617046 0.356251i
\(96\) 0 0
\(97\) −16.2983 9.40980i −1.65484 0.955421i −0.975043 0.222018i \(-0.928736\pi\)
−0.679794 0.733403i \(-0.737931\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 5.07039 8.78217i 0.507039 0.878217i
\(101\) −8.28158 −0.824048 −0.412024 0.911173i \(-0.635178\pi\)
−0.412024 + 0.911173i \(0.635178\pi\)
\(102\) 0 0
\(103\) 17.0487i 1.67986i 0.542697 + 0.839929i \(0.317403\pi\)
−0.542697 + 0.839929i \(0.682597\pi\)
\(104\) −1.42425 2.46687i −0.139659 0.241896i
\(105\) 0 0
\(106\) 0 0
\(107\) −12.4161 7.16846i −1.20031 0.693001i −0.239689 0.970850i \(-0.577045\pi\)
−0.960625 + 0.277848i \(0.910379\pi\)
\(108\) 0 0
\(109\) −5.63998 9.76874i −0.540212 0.935675i −0.998891 0.0470733i \(-0.985011\pi\)
0.458679 0.888602i \(-0.348323\pi\)
\(110\) 7.67448 + 13.2926i 0.731733 + 1.26740i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.51501 4.91614i 0.801024 0.462472i −0.0428049 0.999083i \(-0.513629\pi\)
0.843829 + 0.536612i \(0.180296\pi\)
\(114\) 0 0
\(115\) 24.3316i 2.26893i
\(116\) 2.50079 1.44383i 0.232192 0.134056i
\(117\) 0 0
\(118\) 0.0211346i 0.00194560i
\(119\) 0 0
\(120\) 0 0
\(121\) −4.56002 −0.414548
\(122\) 1.23456 2.13832i 0.111772 0.193594i
\(123\) 0 0
\(124\) 3.04125 1.75587i 0.273112 0.157682i
\(125\) −20.0033 −1.78915
\(126\) 0 0
\(127\) 2.94462 0.261293 0.130646 0.991429i \(-0.458295\pi\)
0.130646 + 0.991429i \(0.458295\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −5.54191 + 9.59886i −0.486057 + 0.841876i
\(131\) −15.0651 −1.31624 −0.658122 0.752911i \(-0.728649\pi\)
−0.658122 + 0.752911i \(0.728649\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 13.4493i 1.16184i
\(135\) 0 0
\(136\) 0.642692 0.371058i 0.0551104 0.0318180i
\(137\) 15.7199i 1.34305i −0.740984 0.671523i \(-0.765641\pi\)
0.740984 0.671523i \(-0.234359\pi\)
\(138\) 0 0
\(139\) −2.86373 + 1.65337i −0.242898 + 0.140237i −0.616508 0.787349i \(-0.711453\pi\)
0.373610 + 0.927586i \(0.378120\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.971521 + 1.68272i 0.0815282 + 0.141211i
\(143\) −5.61811 9.73085i −0.469810 0.813735i
\(144\) 0 0
\(145\) −9.73085 5.61811i −0.808103 0.466559i
\(146\) −2.42743 + 4.20443i −0.200896 + 0.347961i
\(147\) 0 0
\(148\) 1.50079 + 2.59944i 0.123364 + 0.213673i
\(149\) 11.0016i 0.901284i −0.892705 0.450642i \(-0.851195\pi\)
0.892705 0.450642i \(-0.148805\pi\)
\(150\) 0 0
\(151\) −1.43998 −0.117184 −0.0585918 0.998282i \(-0.518661\pi\)
−0.0585918 + 0.998282i \(0.518661\pi\)
\(152\) −0.892369 + 1.54563i −0.0723807 + 0.125367i
\(153\) 0 0
\(154\) 0 0
\(155\) −11.8339 6.83228i −0.950518 0.548782i
\(156\) 0 0
\(157\) 14.3822 + 8.30354i 1.14782 + 0.662695i 0.948355 0.317210i \(-0.102746\pi\)
0.199465 + 0.979905i \(0.436079\pi\)
\(158\) 3.14898 + 1.81806i 0.250519 + 0.144637i
\(159\) 0 0
\(160\) −3.36980 1.94556i −0.266406 0.153810i
\(161\) 0 0
\(162\) 0 0
\(163\) 6.19773 10.7348i 0.485444 0.840813i −0.514416 0.857541i \(-0.671991\pi\)
0.999860 + 0.0167274i \(0.00532476\pi\)
\(164\) −10.4941 −0.819452
\(165\) 0 0
\(166\) 8.05995i 0.625574i
\(167\) −5.86087 10.1513i −0.453528 0.785534i 0.545074 0.838388i \(-0.316502\pi\)
−0.998602 + 0.0528541i \(0.983168\pi\)
\(168\) 0 0
\(169\) −2.44304 + 4.23147i −0.187926 + 0.325498i
\(170\) −2.50079 1.44383i −0.191802 0.110737i
\(171\) 0 0
\(172\) −0.471521 0.816699i −0.0359532 0.0622727i
\(173\) −8.38548 14.5241i −0.637536 1.10425i −0.985972 0.166913i \(-0.946620\pi\)
0.348435 0.937333i \(-0.386713\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 3.41614 1.97231i 0.257501 0.148668i
\(177\) 0 0
\(178\) 9.26646i 0.694551i
\(179\) −5.00158 + 2.88766i −0.373835 + 0.215834i −0.675133 0.737696i \(-0.735914\pi\)
0.301297 + 0.953530i \(0.402580\pi\)
\(180\) 0 0
\(181\) 5.53310i 0.411272i 0.978629 + 0.205636i \(0.0659263\pi\)
−0.978629 + 0.205636i \(0.934074\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.25311 −0.460985
\(185\) 5.83974 10.1147i 0.429346 0.743649i
\(186\) 0 0
\(187\) 2.53518 1.46368i 0.185390 0.107035i
\(188\) 2.18525 0.159376
\(189\) 0 0
\(190\) 6.94462 0.503816
\(191\) −5.38124 + 3.10686i −0.389373 + 0.224805i −0.681888 0.731456i \(-0.738841\pi\)
0.292515 + 0.956261i \(0.405508\pi\)
\(192\) 0 0
\(193\) 3.90271 6.75970i 0.280923 0.486574i −0.690689 0.723152i \(-0.742693\pi\)
0.971612 + 0.236578i \(0.0760260\pi\)
\(194\) 18.8196 1.35117
\(195\) 0 0
\(196\) 0 0
\(197\) 12.7737i 0.910092i 0.890468 + 0.455046i \(0.150377\pi\)
−0.890468 + 0.455046i \(0.849623\pi\)
\(198\) 0 0
\(199\) 1.56925 0.906005i 0.111241 0.0642250i −0.443347 0.896350i \(-0.646209\pi\)
0.554588 + 0.832125i \(0.312876\pi\)
\(200\) 10.1408i 0.717061i
\(201\) 0 0
\(202\) 7.17206 4.14079i 0.504624 0.291345i
\(203\) 0 0
\(204\) 0 0
\(205\) 20.4169 + 35.3631i 1.42598 + 2.46986i
\(206\) −8.52435 14.7646i −0.593919 1.02870i
\(207\) 0 0
\(208\) 2.46687 + 1.42425i 0.171047 + 0.0987537i
\(209\) −3.52006 + 6.09692i −0.243487 + 0.421732i
\(210\) 0 0
\(211\) −1.88766 3.26953i −0.129952 0.225083i 0.793706 0.608302i \(-0.208149\pi\)
−0.923658 + 0.383218i \(0.874816\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 14.3369 0.980052
\(215\) −1.83474 + 3.17787i −0.125128 + 0.216729i
\(216\) 0 0
\(217\) 0 0
\(218\) 9.76874 + 5.63998i 0.661622 + 0.381988i
\(219\) 0 0
\(220\) −13.2926 7.67448i −0.896187 0.517414i
\(221\) 1.83070 + 1.05696i 0.123146 + 0.0710987i
\(222\) 0 0
\(223\) −11.0662 6.38910i −0.741051 0.427846i 0.0814006 0.996681i \(-0.474061\pi\)
−0.822451 + 0.568836i \(0.807394\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.91614 + 8.51501i −0.327017 + 0.566410i
\(227\) 19.9822 1.32627 0.663133 0.748502i \(-0.269227\pi\)
0.663133 + 0.748502i \(0.269227\pi\)
\(228\) 0 0
\(229\) 10.1314i 0.669500i −0.942307 0.334750i \(-0.891348\pi\)
0.942307 0.334750i \(-0.108652\pi\)
\(230\) 12.1658 + 21.0718i 0.802188 + 1.38943i
\(231\) 0 0
\(232\) −1.44383 + 2.50079i −0.0947921 + 0.164185i
\(233\) −6.33070 3.65503i −0.414738 0.239449i 0.278085 0.960556i \(-0.410300\pi\)
−0.692824 + 0.721107i \(0.743634\pi\)
\(234\) 0 0
\(235\) −4.25153 7.36387i −0.277339 0.480366i
\(236\) −0.0105673 0.0183031i −0.000687873 0.00119143i
\(237\) 0 0
\(238\) 0 0
\(239\) −7.28317 + 4.20494i −0.471109 + 0.271995i −0.716704 0.697378i \(-0.754350\pi\)
0.245595 + 0.969373i \(0.421017\pi\)
\(240\) 0 0
\(241\) 8.95213i 0.576657i −0.957531 0.288329i \(-0.906900\pi\)
0.957531 0.288329i \(-0.0930996\pi\)
\(242\) 3.94910 2.28001i 0.253858 0.146565i
\(243\) 0 0
\(244\) 2.46911i 0.158069i
\(245\) 0 0
\(246\) 0 0
\(247\) −5.08381 −0.323475
\(248\) −1.75587 + 3.04125i −0.111498 + 0.193120i
\(249\) 0 0
\(250\) 17.3234 10.0017i 1.09563 0.632561i
\(251\) 12.6432 0.798033 0.399017 0.916944i \(-0.369352\pi\)
0.399017 + 0.916944i \(0.369352\pi\)
\(252\) 0 0
\(253\) −24.6661 −1.55075
\(254\) −2.55012 + 1.47231i −0.160008 + 0.0923809i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 16.3066 1.01718 0.508588 0.861010i \(-0.330168\pi\)
0.508588 + 0.861010i \(0.330168\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 11.0838i 0.687389i
\(261\) 0 0
\(262\) 13.0468 7.53255i 0.806032 0.465363i
\(263\) 23.7215i 1.46273i 0.681985 + 0.731366i \(0.261117\pi\)
−0.681985 + 0.731366i \(0.738883\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 6.72463 + 11.6474i 0.410772 + 0.711478i
\(269\) −3.64144 6.30716i −0.222022 0.384554i 0.733400 0.679798i \(-0.237932\pi\)
−0.955422 + 0.295244i \(0.904599\pi\)
\(270\) 0 0
\(271\) −19.6483 11.3440i −1.19355 0.689097i −0.234441 0.972130i \(-0.575326\pi\)
−0.959110 + 0.283033i \(0.908659\pi\)
\(272\) −0.371058 + 0.642692i −0.0224987 + 0.0389689i
\(273\) 0 0
\(274\) 7.85997 + 13.6139i 0.474838 + 0.822444i
\(275\) 40.0015i 2.41218i
\(276\) 0 0
\(277\) 24.1676 1.45209 0.726046 0.687646i \(-0.241356\pi\)
0.726046 + 0.687646i \(0.241356\pi\)
\(278\) 1.65337 2.86373i 0.0991628 0.171755i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.11229 + 2.37423i 0.245319 + 0.141635i 0.617619 0.786478i \(-0.288097\pi\)
−0.372300 + 0.928112i \(0.621431\pi\)
\(282\) 0 0
\(283\) −25.4484 14.6926i −1.51275 0.873387i −0.999889 0.0149153i \(-0.995252\pi\)
−0.512861 0.858471i \(-0.671415\pi\)
\(284\) −1.68272 0.971521i −0.0998513 0.0576492i
\(285\) 0 0
\(286\) 9.73085 + 5.61811i 0.575398 + 0.332206i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.22463 14.2455i 0.483802 0.837969i
\(290\) 11.2362 0.659814
\(291\) 0 0
\(292\) 4.85486i 0.284109i
\(293\) 3.31206 + 5.73666i 0.193493 + 0.335139i 0.946405 0.322981i \(-0.104685\pi\)
−0.752913 + 0.658121i \(0.771352\pi\)
\(294\) 0 0
\(295\) −0.0411186 + 0.0712195i −0.00239402 + 0.00414656i
\(296\) −2.59944 1.50079i −0.151090 0.0872316i
\(297\) 0 0
\(298\) 5.50079 + 9.52765i 0.318652 + 0.551922i
\(299\) −8.90597 15.4256i −0.515046 0.892085i
\(300\) 0 0
\(301\) 0 0
\(302\) 1.24706 0.719988i 0.0717600 0.0414307i
\(303\) 0 0
\(304\) 1.78474i 0.102362i
\(305\) 8.32043 4.80380i 0.476426 0.275065i
\(306\) 0 0
\(307\) 21.7242i 1.23987i −0.784655 0.619933i \(-0.787160\pi\)
0.784655 0.619933i \(-0.212840\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 13.6646 0.776095
\(311\) 3.14900 5.45422i 0.178563 0.309281i −0.762825 0.646605i \(-0.776188\pi\)
0.941389 + 0.337324i \(0.109522\pi\)
\(312\) 0 0
\(313\) −19.2423 + 11.1095i −1.08764 + 0.627948i −0.932946 0.360015i \(-0.882771\pi\)
−0.154691 + 0.987963i \(0.549438\pi\)
\(314\) −16.6071 −0.937192
\(315\) 0 0
\(316\) −3.63613 −0.204548
\(317\) 13.5632 7.83070i 0.761784 0.439816i −0.0681519 0.997675i \(-0.521710\pi\)
0.829936 + 0.557859i \(0.188377\pi\)
\(318\) 0 0
\(319\) −5.69536 + 9.86466i −0.318879 + 0.552315i
\(320\) 3.89111 0.217520
\(321\) 0 0
\(322\) 0 0
\(323\) 1.32448i 0.0736963i
\(324\) 0 0
\(325\) −25.0159 + 14.4430i −1.38763 + 0.801151i
\(326\) 12.3955i 0.686521i
\(327\) 0 0
\(328\) 9.08816 5.24705i 0.501810 0.289720i
\(329\) 0 0
\(330\) 0 0
\(331\) −0.636129 1.10181i −0.0349648 0.0605608i 0.848013 0.529975i \(-0.177799\pi\)
−0.882978 + 0.469414i \(0.844465\pi\)
\(332\) 4.02998 + 6.98012i 0.221174 + 0.383084i
\(333\) 0 0
\(334\) 10.1513 + 5.86087i 0.555456 + 0.320693i
\(335\) 26.1663 45.3214i 1.42962 2.47617i
\(336\) 0 0
\(337\) −3.78001 6.54717i −0.205910 0.356647i 0.744512 0.667609i \(-0.232682\pi\)
−0.950422 + 0.310962i \(0.899349\pi\)
\(338\) 4.88608i 0.265768i
\(339\) 0 0
\(340\) 2.88766 0.156605
\(341\) −6.92623 + 11.9966i −0.375076 + 0.649651i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.816699 + 0.471521i 0.0440334 + 0.0254227i
\(345\) 0 0
\(346\) 14.5241 + 8.38548i 0.780820 + 0.450806i
\(347\) 19.1470 + 11.0545i 1.02787 + 0.593439i 0.916373 0.400326i \(-0.131103\pi\)
0.111494 + 0.993765i \(0.464436\pi\)
\(348\) 0 0
\(349\) 12.7682 + 7.37173i 0.683467 + 0.394600i 0.801160 0.598450i \(-0.204217\pi\)
−0.117693 + 0.993050i \(0.537550\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.97231 + 3.41614i −0.105124 + 0.182081i
\(353\) −17.2776 −0.919595 −0.459798 0.888024i \(-0.652078\pi\)
−0.459798 + 0.888024i \(0.652078\pi\)
\(354\) 0 0
\(355\) 7.56060i 0.401275i
\(356\) −4.63323 8.02499i −0.245561 0.425324i
\(357\) 0 0
\(358\) 2.88766 5.00158i 0.152618 0.264342i
\(359\) −9.45088 5.45647i −0.498799 0.287982i 0.229419 0.973328i \(-0.426318\pi\)
−0.728217 + 0.685346i \(0.759651\pi\)
\(360\) 0 0
\(361\) −7.90736 13.6959i −0.416177 0.720839i
\(362\) −2.76655 4.79180i −0.145407 0.251852i
\(363\) 0 0
\(364\) 0 0
\(365\) −16.3599 + 9.44541i −0.856318 + 0.494395i
\(366\) 0 0
\(367\) 35.7272i 1.86494i 0.361242 + 0.932472i \(0.382353\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(368\) 5.41535 3.12656i 0.282295 0.162983i
\(369\) 0 0
\(370\) 11.6795i 0.607187i
\(371\) 0 0
\(372\) 0 0
\(373\) −32.0600 −1.66001 −0.830003 0.557760i \(-0.811661\pi\)
−0.830003 + 0.557760i \(0.811661\pi\)
\(374\) −1.46368 + 2.53518i −0.0756853 + 0.131091i
\(375\) 0 0
\(376\) −1.89248 + 1.09263i −0.0975974 + 0.0563479i
\(377\) −8.22549 −0.423634
\(378\) 0 0
\(379\) 34.8891 1.79214 0.896068 0.443918i \(-0.146412\pi\)
0.896068 + 0.443918i \(0.146412\pi\)
\(380\) −6.01422 + 3.47231i −0.308523 + 0.178126i
\(381\) 0 0
\(382\) 3.10686 5.38124i 0.158961 0.275328i
\(383\) 17.5342 0.895957 0.447978 0.894044i \(-0.352144\pi\)
0.447978 + 0.894044i \(0.352144\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 7.80542i 0.397286i
\(387\) 0 0
\(388\) −16.2983 + 9.40980i −0.827418 + 0.477710i
\(389\) 7.62171i 0.386436i −0.981156 0.193218i \(-0.938108\pi\)
0.981156 0.193218i \(-0.0618925\pi\)
\(390\) 0 0
\(391\) 4.01882 2.32027i 0.203241 0.117341i
\(392\) 0 0
\(393\) 0 0
\(394\) −6.38687 11.0624i −0.321766 0.557315i
\(395\) 7.07430 + 12.2530i 0.355947 + 0.616517i
\(396\) 0 0
\(397\) 32.6032 + 18.8234i 1.63631 + 0.944722i 0.982090 + 0.188414i \(0.0603348\pi\)
0.654216 + 0.756307i \(0.272999\pi\)
\(398\) −0.906005 + 1.56925i −0.0454139 + 0.0786592i
\(399\) 0 0
\(400\) −5.07039 8.78217i −0.253519 0.439108i
\(401\) 21.4415i 1.07074i −0.844619 0.535368i \(-0.820173\pi\)
0.844619 0.535368i \(-0.179827\pi\)
\(402\) 0 0
\(403\) −10.0032 −0.498293
\(404\) −4.14079 + 7.17206i −0.206012 + 0.356823i
\(405\) 0 0
\(406\) 0 0
\(407\) −10.2538 5.92004i −0.508262 0.293445i
\(408\) 0 0
\(409\) −25.6086 14.7851i −1.26627 0.731079i −0.291986 0.956423i \(-0.594316\pi\)
−0.974279 + 0.225344i \(0.927649\pi\)
\(410\) −35.3631 20.4169i −1.74646 1.00832i
\(411\) 0 0
\(412\) 14.7646 + 8.52435i 0.727400 + 0.419964i
\(413\) 0 0
\(414\) 0 0
\(415\) 15.6811 27.1605i 0.769755 1.33325i
\(416\) −2.84849 −0.139659
\(417\) 0 0
\(418\) 7.04011i 0.344343i
\(419\) 3.56481 + 6.17443i 0.174152 + 0.301641i 0.939868 0.341539i \(-0.110948\pi\)
−0.765715 + 0.643180i \(0.777615\pi\)
\(420\) 0 0
\(421\) −2.31007 + 4.00115i −0.112586 + 0.195004i −0.916812 0.399319i \(-0.869247\pi\)
0.804226 + 0.594323i \(0.202580\pi\)
\(422\) 3.26953 + 1.88766i 0.159158 + 0.0918899i
\(423\) 0 0
\(424\) 0 0
\(425\) −3.76282 6.51739i −0.182524 0.316140i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.4161 + 7.16846i −0.600157 + 0.346501i
\(429\) 0 0
\(430\) 3.66949i 0.176958i
\(431\) −3.47078 + 2.00385i −0.167181 + 0.0965223i −0.581256 0.813721i \(-0.697439\pi\)
0.414075 + 0.910243i \(0.364105\pi\)
\(432\) 0 0
\(433\) 29.4125i 1.41348i 0.707475 + 0.706738i \(0.249834\pi\)
−0.707475 + 0.706738i \(0.750166\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −11.2800 −0.540212
\(437\) −5.58008 + 9.66498i −0.266931 + 0.462339i
\(438\) 0 0
\(439\) 18.5130 10.6885i 0.883575 0.510133i 0.0117398 0.999931i \(-0.496263\pi\)
0.871836 + 0.489799i \(0.162930\pi\)
\(440\) 15.3490 0.731733
\(441\) 0 0
\(442\) −2.11392 −0.100549
\(443\) 5.05227 2.91693i 0.240041 0.138587i −0.375155 0.926962i \(-0.622410\pi\)
0.615195 + 0.788375i \(0.289077\pi\)
\(444\) 0 0
\(445\) −18.0284 + 31.2262i −0.854630 + 1.48026i
\(446\) 12.7782 0.605065
\(447\) 0 0
\(448\) 0 0
\(449\) 22.5823i 1.06573i −0.846202 0.532863i \(-0.821116\pi\)
0.846202 0.532863i \(-0.178884\pi\)
\(450\) 0 0
\(451\) 35.8493 20.6976i 1.68808 0.974613i
\(452\) 9.83228i 0.462472i
\(453\) 0 0
\(454\) −17.3051 + 9.99110i −0.812168 + 0.468906i
\(455\) 0 0
\(456\) 0 0
\(457\) −19.9311 34.5218i −0.932340 1.61486i −0.779310 0.626638i \(-0.784430\pi\)
−0.153029 0.988222i \(-0.548903\pi\)
\(458\) 5.06568 + 8.77402i 0.236704 + 0.409983i
\(459\) 0 0
\(460\) −21.0718 12.1658i −0.982476 0.567233i
\(461\) 3.68254 6.37834i 0.171513 0.297069i −0.767436 0.641125i \(-0.778468\pi\)
0.938949 + 0.344056i \(0.111801\pi\)
\(462\) 0 0
\(463\) −14.3457 24.8475i −0.666702 1.15476i −0.978821 0.204718i \(-0.934372\pi\)
0.312119 0.950043i \(-0.398961\pi\)
\(464\) 2.88766i 0.134056i
\(465\) 0 0
\(466\) 7.31007 0.338632
\(467\) −6.83519 + 11.8389i −0.316295 + 0.547839i −0.979712 0.200411i \(-0.935772\pi\)
0.663417 + 0.748250i \(0.269106\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.36387 + 4.25153i 0.339670 + 0.196109i
\(471\) 0 0
\(472\) 0.0183031 + 0.0105673i 0.000842469 + 0.000486400i
\(473\) 3.22157 + 1.85997i 0.148128 + 0.0855216i
\(474\) 0 0
\(475\) 15.6739 + 9.04931i 0.719166 + 0.415211i
\(476\) 0 0
\(477\) 0 0
\(478\) 4.20494 7.28317i 0.192329 0.333124i
\(479\) 10.4107 0.475679 0.237839 0.971304i \(-0.423561\pi\)
0.237839 + 0.971304i \(0.423561\pi\)
\(480\) 0 0
\(481\) 8.54997i 0.389845i
\(482\) 4.47607 + 7.75277i 0.203879 + 0.353129i
\(483\) 0 0
\(484\) −2.28001 + 3.94910i −0.103637 + 0.179504i
\(485\) 63.4184 + 36.6146i 2.87968 + 1.66258i
\(486\) 0 0
\(487\) −1.16925 2.02520i −0.0529838 0.0917707i 0.838317 0.545183i \(-0.183540\pi\)
−0.891301 + 0.453412i \(0.850207\pi\)
\(488\) −1.23456 2.13832i −0.0558858 0.0967970i
\(489\) 0 0
\(490\) 0 0
\(491\) 29.3448 16.9422i 1.32431 0.764591i 0.339898 0.940462i \(-0.389608\pi\)
0.984413 + 0.175871i \(0.0562742\pi\)
\(492\) 0 0
\(493\) 2.14298i 0.0965151i
\(494\) 4.40271 2.54191i 0.198087 0.114366i
\(495\) 0 0
\(496\) 3.51174i 0.157682i
\(497\) 0 0
\(498\) 0 0
\(499\) −16.6045 −0.743317 −0.371659 0.928369i \(-0.621211\pi\)
−0.371659 + 0.928369i \(0.621211\pi\)
\(500\) −10.0017 + 17.3234i −0.447288 + 0.774726i
\(501\) 0 0
\(502\) −10.9494 + 6.32161i −0.488694 + 0.282147i
\(503\) 35.3661 1.57690 0.788449 0.615100i \(-0.210885\pi\)
0.788449 + 0.615100i \(0.210885\pi\)
\(504\) 0 0
\(505\) 32.2246 1.43398
\(506\) 21.3615 12.3331i 0.949635 0.548272i
\(507\) 0 0
\(508\) 1.47231 2.55012i 0.0653232 0.113143i
\(509\) −37.0582 −1.64257 −0.821287 0.570515i \(-0.806744\pi\)
−0.821287 + 0.570515i \(0.806744\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −14.1219 + 8.15329i −0.622891 + 0.359626i
\(515\) 66.3384i 2.92322i
\(516\) 0 0
\(517\) −7.46513 + 4.30999i −0.328316 + 0.189553i
\(518\) 0 0
\(519\) 0 0
\(520\) 5.54191 + 9.59886i 0.243029 + 0.420938i
\(521\) 0.891547 + 1.54420i 0.0390594 + 0.0676528i 0.884894 0.465792i \(-0.154231\pi\)
−0.845835 + 0.533445i \(0.820897\pi\)
\(522\) 0 0
\(523\) −20.8312 12.0269i −0.910886 0.525901i −0.0301702 0.999545i \(-0.509605\pi\)
−0.880716 + 0.473644i \(0.842938\pi\)
\(524\) −7.53255 + 13.0468i −0.329061 + 0.569950i
\(525\) 0 0
\(526\) −11.8608 20.5434i −0.517154 0.895737i
\(527\) 2.60612i 0.113524i
\(528\) 0 0
\(529\) −16.1014 −0.700060
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 25.8876 + 14.9462i 1.12132 + 0.647392i
\(534\) 0 0
\(535\) 48.3126 + 27.8933i 2.08874 + 1.20593i
\(536\) −11.6474 6.72463i −0.503091 0.290460i
\(537\) 0 0
\(538\) 6.30716 + 3.64144i 0.271921 + 0.156994i
\(539\) 0 0
\(540\) 0 0
\(541\) −15.0016 + 25.9835i −0.644968 + 1.11712i 0.339341 + 0.940664i \(0.389796\pi\)
−0.984309 + 0.176454i \(0.943537\pi\)
\(542\) 22.6879 0.974530
\(543\) 0 0
\(544\) 0.742117i 0.0318180i
\(545\) 21.9458 + 38.0113i 0.940056 + 1.62822i
\(546\) 0 0
\(547\) −10.7816 + 18.6743i −0.460987 + 0.798454i −0.999010 0.0444765i \(-0.985838\pi\)
0.538023 + 0.842930i \(0.319171\pi\)
\(548\) −13.6139 7.85997i −0.581556 0.335761i
\(549\) 0 0
\(550\) −20.0007 34.6423i −0.852835 1.47715i
\(551\) 2.57686 + 4.46325i 0.109778 + 0.190141i
\(552\) 0 0
\(553\) 0 0
\(554\) −20.9298 + 12.0838i −0.889221 + 0.513392i
\(555\) 0 0
\(556\) 3.30675i 0.140237i
\(557\) −31.9976 + 18.4738i −1.35578 + 0.782762i −0.989052 0.147565i \(-0.952856\pi\)
−0.366731 + 0.930327i \(0.619523\pi\)
\(558\) 0 0
\(559\) 2.68625i 0.113616i
\(560\) 0 0
\(561\) 0 0
\(562\) −4.74847 −0.200302
\(563\) −7.58422 + 13.1363i −0.319637 + 0.553627i −0.980412 0.196957i \(-0.936894\pi\)
0.660776 + 0.750584i \(0.270228\pi\)
\(564\) 0 0
\(565\) −33.1329 + 19.1293i −1.39391 + 0.804774i
\(566\) 29.3853 1.23516
\(567\) 0 0
\(568\) 1.94304 0.0815282
\(569\) −31.8084 + 18.3646i −1.33348 + 0.769885i −0.985831 0.167740i \(-0.946353\pi\)
−0.347648 + 0.937625i \(0.613020\pi\)
\(570\) 0 0
\(571\) −5.61387 + 9.72351i −0.234933 + 0.406916i −0.959253 0.282548i \(-0.908820\pi\)
0.724320 + 0.689464i \(0.242154\pi\)
\(572\) −11.2362 −0.469810
\(573\) 0 0
\(574\) 0 0
\(575\) 63.4114i 2.64444i
\(576\) 0 0
\(577\) −31.6545 + 18.2757i −1.31780 + 0.760829i −0.983374 0.181594i \(-0.941874\pi\)
−0.334422 + 0.942424i \(0.608541\pi\)
\(578\) 16.4493i 0.684199i
\(579\) 0 0
\(580\) −9.73085 + 5.61811i −0.404052 + 0.233279i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 2.42743 + 4.20443i 0.100448 + 0.173981i
\(585\) 0 0
\(586\) −5.73666 3.31206i −0.236979 0.136820i
\(587\) −4.99738 + 8.65571i −0.206264 + 0.357259i −0.950535 0.310619i \(-0.899464\pi\)
0.744271 + 0.667878i \(0.232797\pi\)
\(588\) 0 0
\(589\) 3.13376 + 5.42784i 0.129124 + 0.223650i
\(590\) 0.0822372i 0.00338565i
\(591\) 0 0
\(592\) 3.00158 0.123364
\(593\) 3.89111 6.73961i 0.159789 0.276763i −0.775004 0.631957i \(-0.782252\pi\)
0.934792 + 0.355194i \(0.115585\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −9.52765 5.50079i −0.390268 0.225321i
\(597\) 0 0
\(598\) 15.4256 + 8.90597i 0.630800 + 0.364192i
\(599\) 21.6614 + 12.5062i 0.885061 + 0.510990i 0.872324 0.488929i \(-0.162612\pi\)
0.0127373 + 0.999919i \(0.495945\pi\)
\(600\) 0 0
\(601\) 25.9925 + 15.0068i 1.06026 + 0.612139i 0.925503 0.378740i \(-0.123643\pi\)
0.134753 + 0.990879i \(0.456976\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.719988 + 1.24706i −0.0292959 + 0.0507420i
\(605\) 17.7436 0.721379
\(606\) 0 0
\(607\) 4.58280i 0.186010i 0.995666 + 0.0930050i \(0.0296473\pi\)
−0.995666 + 0.0930050i \(0.970353\pi\)
\(608\) 0.892369 + 1.54563i 0.0361903 + 0.0626835i
\(609\) 0 0
\(610\) −4.80380 + 8.32043i −0.194500 + 0.336884i
\(611\) −5.39073 3.11234i −0.218085 0.125912i
\(612\) 0 0
\(613\) −15.2761 26.4590i −0.616996 1.06867i −0.990031 0.140852i \(-0.955016\pi\)
0.373034 0.927818i \(-0.378317\pi\)
\(614\) 10.8621 + 18.8137i 0.438359 + 0.759259i
\(615\) 0 0
\(616\) 0 0
\(617\) 28.2484 16.3092i 1.13724 0.656585i 0.191493 0.981494i \(-0.438667\pi\)
0.945745 + 0.324909i \(0.105334\pi\)
\(618\) 0 0
\(619\) 20.0045i 0.804049i 0.915629 + 0.402024i \(0.131693\pi\)
−0.915629 + 0.402024i \(0.868307\pi\)
\(620\) −11.8339 + 6.83228i −0.475259 + 0.274391i
\(621\) 0 0
\(622\) 6.29800i 0.252527i
\(623\) 0 0
\(624\) 0 0
\(625\) 27.1314 1.08526
\(626\) 11.1095 19.2423i 0.444026 0.769076i
\(627\) 0 0
\(628\) 14.3822 8.30354i 0.573910 0.331347i
\(629\) 2.22752 0.0888171
\(630\) 0 0
\(631\) 6.09634 0.242692 0.121346 0.992610i \(-0.461279\pi\)
0.121346 + 0.992610i \(0.461279\pi\)
\(632\) 3.14898 1.81806i 0.125260 0.0723187i
\(633\) 0 0
\(634\) −7.83070 + 13.5632i −0.310997 + 0.538663i
\(635\) −11.4579 −0.454691
\(636\) 0 0
\(637\) 0 0
\(638\) 11.3907i 0.450963i
\(639\) 0 0
\(640\) −3.36980 + 1.94556i −0.133203 + 0.0769049i
\(641\) 33.4415i 1.32086i 0.750888 + 0.660429i \(0.229626\pi\)
−0.750888 + 0.660429i \(0.770374\pi\)
\(642\) 0 0
\(643\) −16.6022 + 9.58527i −0.654726 + 0.378006i −0.790264 0.612766i \(-0.790057\pi\)
0.135539 + 0.990772i \(0.456724\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.662242 + 1.14704i 0.0260556 + 0.0451296i
\(647\) 22.3025 + 38.6290i 0.876800 + 1.51866i 0.854832 + 0.518904i \(0.173660\pi\)
0.0219681 + 0.999759i \(0.493007\pi\)
\(648\) 0 0
\(649\) 0.0721988 + 0.0416840i 0.00283405 + 0.00163624i
\(650\) 14.4430 25.0159i 0.566500 0.981206i
\(651\) 0 0
\(652\) −6.19773 10.7348i −0.242722 0.420407i
\(653\) 0.652123i 0.0255195i 0.999919 + 0.0127598i \(0.00406167\pi\)
−0.999919 + 0.0127598i \(0.995938\pi\)
\(654\) 0 0
\(655\) 58.6200 2.29047
\(656\) −5.24705 + 9.08816i −0.204863 + 0.354833i
\(657\) 0 0
\(658\) 0 0
\(659\) −26.2738 15.1692i −1.02348 0.590908i −0.108372 0.994110i \(-0.534564\pi\)
−0.915111 + 0.403202i \(0.867897\pi\)
\(660\) 0 0
\(661\) −11.1004 6.40881i −0.431755 0.249274i 0.268339 0.963325i \(-0.413525\pi\)
−0.700094 + 0.714051i \(0.746859\pi\)
\(662\) 1.10181 + 0.636129i 0.0428230 + 0.0247239i
\(663\) 0 0
\(664\) −6.98012 4.02998i −0.270881 0.156393i
\(665\) 0 0
\(666\) 0 0
\(667\) −9.02843 + 15.6377i −0.349582 + 0.605494i
\(668\) −11.7217 −0.453528
\(669\) 0 0
\(670\) 52.3326i 2.02179i
\(671\) −4.86986 8.43484i −0.187999 0.325623i
\(672\) 0 0
\(673\) 11.2246 19.4416i 0.432678 0.749420i −0.564425 0.825484i \(-0.690902\pi\)
0.997103 + 0.0760644i \(0.0242355\pi\)
\(674\) 6.54717 + 3.78001i 0.252188 + 0.145601i
\(675\) 0 0
\(676\) 2.44304 + 4.23147i 0.0939632 + 0.162749i
\(677\) 25.5903 + 44.3237i 0.983516 + 1.70350i 0.648353 + 0.761340i \(0.275458\pi\)
0.335163 + 0.942160i \(0.391209\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.50079 + 1.44383i −0.0959009 + 0.0553684i
\(681\) 0 0
\(682\) 13.8525i 0.530438i
\(683\) −12.6107 + 7.28080i −0.482536 + 0.278592i −0.721473 0.692443i \(-0.756534\pi\)
0.238937 + 0.971035i \(0.423201\pi\)
\(684\) 0 0
\(685\) 61.1681i 2.33711i
\(686\) 0 0
\(687\) 0 0
\(688\) −0.943042 −0.0359532
\(689\) 0 0
\(690\) 0 0
\(691\) −21.1757 + 12.2258i −0.805560 + 0.465090i −0.845412 0.534115i \(-0.820645\pi\)
0.0398517 + 0.999206i \(0.487311\pi\)
\(692\) −16.7710 −0.637536
\(693\) 0 0
\(694\) −22.1091 −0.839250
\(695\) 11.1431 6.43347i 0.422682 0.244035i
\(696\) 0 0
\(697\) −3.89393 + 6.74448i −0.147493 + 0.255465i
\(698\) −14.7435 −0.558048
\(699\) 0 0
\(700\) 0 0
\(701\) 2.21697i 0.0837337i −0.999123 0.0418669i \(-0.986669\pi\)
0.999123 0.0418669i \(-0.0133305\pi\)
\(702\) 0 0
\(703\) −4.63932 + 2.67851i −0.174975 + 0.101022i
\(704\) 3.94462i 0.148668i
\(705\) 0 0
\(706\) 14.9629 8.63881i 0.563135 0.325126i
\(707\) 0 0
\(708\) 0 0
\(709\) 12.1962 + 21.1244i 0.458036 + 0.793342i 0.998857 0.0477959i \(-0.0152197\pi\)
−0.540821 + 0.841138i \(0.681886\pi\)
\(710\) −3.78030 6.54767i −0.141872 0.245730i
\(711\) 0 0
\(712\) 8.02499 + 4.63323i 0.300749 + 0.173638i
\(713\) −10.9796 + 19.0173i −0.411190 + 0.712203i
\(714\) 0 0
\(715\) 21.8607 + 37.8639i 0.817544 + 1.41603i
\(716\) 5.77532i 0.215834i
\(717\) 0 0
\(718\) 10.9129 0.407267
\(719\) 1.11376 1.92909i 0.0415363 0.0719429i −0.844510 0.535540i \(-0.820108\pi\)
0.886046 + 0.463597i \(0.153441\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13.6959 + 7.90736i 0.509710 + 0.294281i
\(723\) 0 0
\(724\) 4.79180 + 2.76655i 0.178086 + 0.102818i
\(725\) 25.3599 + 14.6416i 0.941844 + 0.543774i
\(726\) 0 0
\(727\) −10.4880 6.05523i −0.388977 0.224576i 0.292740 0.956192i \(-0.405433\pi\)
−0.681717 + 0.731616i \(0.738766\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 9.44541 16.3599i 0.349590 0.605508i
\(731\) −0.699848 −0.0258848
\(732\) 0 0
\(733\) 15.6661i 0.578641i −0.957232 0.289321i \(-0.906571\pi\)
0.957232 0.289321i \(-0.0934293\pi\)
\(734\) −17.8636 30.9407i −0.659357 1.14204i
\(735\) 0 0
\(736\) −3.12656 + 5.41535i −0.115246 + 0.199613i
\(737\) −45.9446 26.5261i −1.69239 0.977102i
\(738\) 0 0
\(739\) 4.05227 + 7.01874i 0.149065 + 0.258188i 0.930882 0.365319i \(-0.119040\pi\)
−0.781817 + 0.623508i \(0.785707\pi\)
\(740\) −5.83974 10.1147i −0.214673 0.371825i
\(741\) 0 0
\(742\) 0 0
\(743\) 10.5429 6.08697i 0.386783 0.223309i −0.293982 0.955811i \(-0.594981\pi\)
0.680765 + 0.732502i \(0.261647\pi\)
\(744\) 0 0
\(745\) 42.8084i 1.56838i
\(746\) 27.7648 16.0300i 1.01654 0.586900i
\(747\) 0 0
\(748\) 2.92737i 0.107035i
\(749\) 0 0
\(750\) 0 0
\(751\) 34.6123 1.26302 0.631511 0.775367i \(-0.282435\pi\)
0.631511 + 0.775367i \(0.282435\pi\)
\(752\) 1.09263 1.89248i 0.0398440 0.0690118i
\(753\) 0 0
\(754\) 7.12348 4.11274i 0.259422 0.149777i
\(755\) 5.60311 0.203918
\(756\) 0 0
\(757\) −39.0553 −1.41949 −0.709744 0.704459i \(-0.751190\pi\)
−0.709744 + 0.704459i \(0.751190\pi\)
\(758\) −30.2149 + 17.4446i −1.09745 + 0.633615i
\(759\) 0 0
\(760\) 3.47231 6.01422i 0.125954 0.218159i
\(761\) −10.2252 −0.370665 −0.185332 0.982676i \(-0.559336\pi\)
−0.185332 + 0.982676i \(0.559336\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 6.21372i 0.224805i
\(765\) 0 0
\(766\) −15.1851 + 8.76711i −0.548659 + 0.316769i
\(767\) 0.0602018i 0.00217376i
\(768\) 0 0
\(769\) 26.6746 15.4006i 0.961910 0.555359i 0.0651494 0.997876i \(-0.479248\pi\)
0.896760 + 0.442517i \(0.145914\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3.90271 6.75970i −0.140462 0.243287i
\(773\) 17.8916 + 30.9892i 0.643518 + 1.11461i 0.984642 + 0.174587i \(0.0558590\pi\)
−0.341124 + 0.940018i \(0.610808\pi\)
\(774\) 0 0
\(775\) 30.8406 + 17.8059i 1.10783 + 0.639605i
\(776\) 9.40980 16.2983i 0.337792 0.585073i
\(777\) 0 0
\(778\) 3.81086 + 6.60060i 0.136626 + 0.236643i
\(779\) 18.7292i 0.671044i
\(780\) 0 0
\(781\) 7.66456 0.274260
\(782\) −2.32027 + 4.01882i −0.0829727 + 0.143713i
\(783\) 0 0
\(784\) 0 0
\(785\) −55.9626 32.3100i −1.99739 1.15319i
\(786\) 0 0
\(787\) 13.2859 + 7.67064i 0.473592 + 0.273429i 0.717742 0.696309i \(-0.245176\pi\)
−0.244150 + 0.969737i \(0.578509\pi\)
\(788\) 11.0624 + 6.38687i 0.394081 + 0.227523i
\(789\) 0 0
\(790\) −12.2530 7.07430i −0.435944 0.251692i
\(791\) 0 0
\(792\) 0 0
\(793\) 3.51663 6.09098i 0.12