Properties

Label 2646.2.t.a.1979.4
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 1979.4
Root \(1.62181 - 0.608059i\) of defining polynomial
Character \(\chi\) \(=\) 2646.1979
Dual form 2646.2.t.a.2285.4

$q$-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 \(-0.164067\pi\)
0.870080 + 0.492911i \(0.164067\pi\)
\(6\) 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 −0.117244 0.993103i \(-0.537406\pi\)
0.801430 + 0.598088i \(0.204073\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.371058 + 0.642692i 0.0899949 + 0.155876i 0.907509 0.420033i \(-0.137982\pi\)
−0.817514 + 0.575909i \(0.804648\pi\)
\(18\) 0 0
\(19\) −1.54563 0.892369i −0.354591 0.204723i 0.312114 0.950045i \(-0.398963\pi\)
−0.666706 + 0.745321i \(0.732296\pi\)
\(20\) 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 0.201373 0.979515i \(-0.435460\pi\)
−0.747598 + 0.664152i \(0.768793\pi\)
\(32\) 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 \(0.139055\pi\)
−0.0866345 + 0.996240i \(0.527611\pi\)
\(42\) 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 0.775268 0.631633i \(-0.217615\pi\)
−0.934644 + 0.355585i \(0.884282\pi\)
\(48\) 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 −0.866712 0.498808i \(-0.833771\pi\)
0.865337 + 0.501191i \(0.167105\pi\)
\(60\) 0 0
\(61\) 2.13832 1.23456i 0.273783 0.158069i −0.356822 0.934172i \(-0.616140\pi\)
0.630606 + 0.776103i \(0.282807\pi\)
\(62\) 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 −0.725442 0.688284i \(-0.758364\pi\)
0.233350 + 0.972393i \(0.425031\pi\)
\(74\) 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 −0.555516 0.831506i \(-0.687479\pi\)
0.997863 + 0.0653378i \(0.0208125\pi\)
\(84\) 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 −0.999948 0.0102218i \(-0.996746\pi\)
0.508826 + 0.860869i \(0.330080\pi\)
\(90\) 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 \(0.0712643\pi\)
0.679794 + 0.733403i \(0.262069\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 5.07039 8.78217i 0.507039 0.878217i
\(101\) 8.28158 0.824048 0.412024 0.911173i \(-0.364822\pi\)
0.412024 + 0.911173i \(0.364822\pi\)
\(102\) 0 0
\(103\) 17.0487i 1.67986i −0.542697 0.839929i \(-0.682597\pi\)
0.542697 0.839929i \(-0.317403\pi\)
\(104\) 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 \(-0.271351\pi\)
0.658122 + 0.752911i \(0.271351\pi\)
\(132\) 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 −0.373610 0.927586i \(-0.621880\pi\)
0.616508 + 0.787349i \(0.288547\pi\)
\(140\) 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 −0.199465 0.979905i \(-0.563921\pi\)
−0.948355 + 0.317210i \(0.897254\pi\)
\(158\) 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 0.998602 0.0528541i \(-0.0168318\pi\)
−0.545074 + 0.838388i \(0.683498\pi\)
\(168\) 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 \(0.0533798\pi\)
−0.348435 + 0.937333i \(0.613287\pi\)
\(174\) 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 \(-0.934074\pi\)
0.978629 0.205636i \(-0.0659263\pi\)
\(182\) 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 −0.554588 0.832125i \(-0.687124\pi\)
0.443347 + 0.896350i \(0.353791\pi\)
\(200\) 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 0.822451 0.568836i \(-0.192606\pi\)
−0.0814006 + 0.996681i \(0.525939\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.91614 + 8.51501i −0.327017 + 0.566410i
\(227\) −19.9822 −1.32627 −0.663133 0.748502i \(-0.730773\pi\)
−0.663133 + 0.748502i \(0.730773\pi\)
\(228\) 0 0
\(229\) 10.1314i 0.669500i 0.942307 + 0.334750i \(0.108652\pi\)
−0.942307 + 0.334750i \(0.891348\pi\)
\(230\) −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 \(0.0930996\pi\)
−0.957531 + 0.288329i \(0.906900\pi\)
\(242\) 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 \(-0.630648\pi\)
−0.399017 + 0.916944i \(0.630648\pi\)
\(252\) 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 \(-0.669832\pi\)
−0.508588 + 0.861010i \(0.669832\pi\)
\(258\) 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 0.955422 0.295244i \(-0.0954009\pi\)
−0.733400 + 0.679798i \(0.762068\pi\)
\(270\) 0 0
\(271\) 19.6483 + 11.3440i 1.19355 + 0.689097i 0.959110 0.283033i \(-0.0913407\pi\)
0.234441 + 0.972130i \(0.424674\pi\)
\(272\) 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 \(0.00474785\pi\)
0.512861 + 0.858471i \(0.328585\pi\)
\(284\) −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 0.752913 0.658121i \(-0.228648\pi\)
−0.946405 + 0.322981i \(0.895315\pi\)
\(294\) 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 \(0.212840\pi\)
−0.784655 + 0.619933i \(0.787160\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 13.6646 0.776095
\(311\) −3.14900 + 5.45422i −0.178563 + 0.309281i −0.941389 0.337324i \(-0.890478\pi\)
0.762825 + 0.646605i \(0.223812\pi\)
\(312\) 0 0
\(313\) 19.2423 11.1095i 1.08764 0.627948i 0.154691 0.987963i \(-0.450562\pi\)
0.932946 + 0.360015i \(0.117229\pi\)
\(314\) 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 0.117693 0.993050i \(-0.462450\pi\)
−0.801160 + 0.598450i \(0.795783\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.97231 + 3.41614i −0.105124 + 0.182081i
\(353\) 17.2776 0.919595 0.459798 0.888024i \(-0.347922\pi\)
0.459798 + 0.888024i \(0.347922\pi\)
\(354\) 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 \(-0.617647\pi\)
0.361242 0.932472i \(-0.382353\pi\)
\(368\) 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 \(-0.647856\pi\)
−0.447978 + 0.894044i \(0.647856\pi\)
\(384\) 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 \(-0.939665\pi\)
−0.654216 0.756307i \(-0.727001\pi\)
\(398\) 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 0.974279 0.225344i \(-0.0723506\pi\)
0.291986 + 0.956423i \(0.405684\pi\)
\(410\) −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 0.765715 0.643180i \(-0.222385\pi\)
−0.939868 + 0.341539i \(0.889052\pi\)
\(420\) 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 \(-0.750166\pi\)
0.707475 0.706738i \(-0.249834\pi\)
\(434\) 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 −0.871836 0.489799i \(-0.837070\pi\)
−0.0117398 + 0.999931i \(0.503737\pi\)
\(440\) −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 −0.938949 0.344056i \(-0.888199\pi\)
0.767436 + 0.641125i \(0.221532\pi\)
\(462\) 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 −0.663417 0.748250i \(-0.730894\pi\)
0.979712 + 0.200411i \(0.0642278\pi\)
\(468\) 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 \(-0.576439\pi\)
−0.237839 + 0.971304i \(0.576439\pi\)
\(480\) 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 \(-0.789115\pi\)
−0.788449 + 0.615100i \(0.789115\pi\)
\(504\) 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 \(-0.193256\pi\)
0.821287 + 0.570515i \(0.193256\pi\)
\(510\) 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 0.845835 0.533445i \(-0.179103\pi\)
−0.884894 + 0.465792i \(0.845769\pi\)
\(522\) 0 0
\(523\) 20.8312 + 12.0269i 0.910886 + 0.525901i 0.880716 0.473644i \(-0.157062\pi\)
0.0301702 + 0.999545i \(0.490395\pi\)
\(524\) 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 −0.660776 0.750584i \(-0.729772\pi\)
0.980412 + 0.196957i \(0.0631058\pi\)
\(564\) 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 0.334422 0.942424i \(-0.391459\pi\)
0.983374 + 0.181594i \(0.0581257\pi\)
\(578\) 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 −0.744271 0.667878i \(-0.767203\pi\)
0.950535 + 0.310619i \(0.100536\pi\)
\(588\) 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 −0.934792 0.355194i \(-0.884415\pi\)
0.775004 + 0.631957i \(0.217748\pi\)
\(594\) 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 −0.134753 0.990879i \(-0.543024\pi\)
−0.925503 + 0.378740i \(0.876357\pi\)
\(602\) 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 \(-0.970353\pi\)
0.995666 0.0930050i \(-0.0296473\pi\)
\(608\) −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 \(-0.868307\pi\)
0.915629 0.402024i \(-0.131693\pi\)
\(620\) −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 −0.135539 0.990772i \(-0.543276\pi\)
0.790264 + 0.612766i \(0.209943\pi\)
\(644\) 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 \(-0.826340\pi\)
−0.0219681 0.999759i \(-0.506993\pi\)
\(648\) 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 0.700094 0.714051i \(-0.253141\pi\)
−0.268339 + 0.963325i \(0.586475\pi\)
\(662\) 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 \(-0.724542\pi\)
−0.335163 0.942160i \(-0.608791\pi\)
\(678\) 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 −0.0398517 0.999206i \(-0.512689\pi\)
0.845412 + 0.534115i \(0.179355\pi\)
\(692\) 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 −0.886046 0.463597i \(-0.846559\pi\)
0.844510 + 0.535540i \(0.179892\pi\)
\(720\) 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 0.681717 0.731616i \(-0.261234\pi\)
−0.292740 + 0.956192i \(0.594567\pi\)
\(728\) 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 \(0.0934293\pi\)
−0.957232 + 0.289321i \(0.906571\pi\)
\(734\) 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 \(-0.440664\pi\)
0.185332 + 0.982676i \(0.440664\pi\)
\(762\) 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 −0.896760 0.442517i \(-0.854086\pi\)
−0.0651494 + 0.997876i \(0.520752\pi\)
\(770\) 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 \(-0.944141\pi\)
0.341124 0.940018i \(-0.389192\pi\)
\(774\) 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 0.244150 0.969737i \(-0.421491\pi\)
−0.717742 + 0.696309i \(0.754824\pi\)
\(788\) 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