Properties

Label 819.2.fm.e.622.3
Level $819$
Weight $2$
Character 819.622
Analytic conductor $6.540$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.fm (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 622.3
Character \(\chi\) \(=\) 819.622
Dual form 819.2.fm.e.370.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0578232 + 0.215799i) q^{2} +(1.68883 + 0.975044i) q^{4} +(-1.08760 + 1.08760i) q^{5} +(-0.725943 - 2.54421i) q^{7} +(-0.624019 + 0.624019i) q^{8} +O(q^{10})\) \(q+(-0.0578232 + 0.215799i) q^{2} +(1.68883 + 0.975044i) q^{4} +(-1.08760 + 1.08760i) q^{5} +(-0.725943 - 2.54421i) q^{7} +(-0.624019 + 0.624019i) q^{8} +(-0.171815 - 0.297592i) q^{10} +(-4.17464 - 1.11859i) q^{11} +(-3.01096 + 1.98346i) q^{13} +(0.591015 - 0.00954346i) q^{14} +(1.85151 + 3.20690i) q^{16} +(-3.78401 + 6.55410i) q^{17} +(1.31714 + 4.91565i) q^{19} +(-2.89722 + 0.776309i) q^{20} +(0.482783 - 0.836204i) q^{22} +(1.85976 - 1.07373i) q^{23} +2.63425i q^{25} +(-0.253926 - 0.764453i) q^{26} +(1.25473 - 5.00455i) q^{28} +(2.66646 + 4.61844i) q^{29} +(1.09410 - 1.09410i) q^{31} +(-2.50396 + 0.670934i) q^{32} +(-1.19557 - 1.19557i) q^{34} +(3.55662 + 1.97755i) q^{35} +(-2.82556 - 0.757106i) q^{37} -1.13695 q^{38} -1.35737i q^{40} +(-1.37894 - 0.369486i) q^{41} +(-6.58558 - 3.80219i) q^{43} +(-5.95956 - 5.95956i) q^{44} +(0.124173 + 0.463422i) q^{46} +(-5.26364 - 5.26364i) q^{47} +(-5.94601 + 3.69390i) q^{49} +(-0.568470 - 0.152321i) q^{50} +(-7.01895 + 0.413900i) q^{52} +13.1808 q^{53} +(5.75692 - 3.32376i) q^{55} +(2.04064 + 1.13463i) q^{56} +(-1.15084 + 0.308366i) q^{58} +(8.73809 - 2.34136i) q^{59} +(-10.1891 - 5.88266i) q^{61} +(0.172842 + 0.299371i) q^{62} +6.82688i q^{64} +(1.11751 - 5.43193i) q^{65} +(-1.28138 + 4.78216i) q^{67} +(-12.7811 + 7.37915i) q^{68} +(-0.632408 + 0.653167i) q^{70} +(5.25942 - 1.40926i) q^{71} +(8.04396 + 8.04396i) q^{73} +(0.326766 - 0.565975i) q^{74} +(-2.56854 + 9.58594i) q^{76} +(0.184619 + 11.4332i) q^{77} +9.06635 q^{79} +(-5.50153 - 1.47413i) q^{80} +(0.159469 - 0.276209i) q^{82} +(-1.13072 + 1.13072i) q^{83} +(-3.01275 - 11.2437i) q^{85} +(1.20131 - 1.20131i) q^{86} +(3.30308 - 1.90703i) q^{88} +(0.217351 - 0.811166i) q^{89} +(7.23213 + 6.22064i) q^{91} +4.18775 q^{92} +(1.44025 - 0.831529i) q^{94} +(-6.77878 - 3.91373i) q^{95} +(-4.35890 - 16.2676i) q^{97} +(-0.453324 - 1.49674i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + O(q^{10}) \) \( 32q + 2q^{2} + 6q^{4} - 2q^{5} + 2q^{7} - 2q^{8} + 2q^{10} + 4q^{11} + 6q^{13} - 34q^{14} + 14q^{16} + 8q^{17} + 2q^{19} - 44q^{20} - 4q^{22} + 18q^{23} + 28q^{26} - 32q^{28} + 18q^{29} - 14q^{31} + 8q^{32} - 66q^{34} - 22q^{35} - 24q^{37} - 24q^{38} - 6q^{43} + 20q^{44} - 58q^{46} + 28q^{47} + 8q^{49} - 70q^{50} + 28q^{52} + 80q^{53} + 60q^{55} + 54q^{56} - 4q^{58} + 42q^{59} + 36q^{61} - 52q^{62} - 14q^{65} + 26q^{67} + 72q^{68} - 116q^{70} + 4q^{71} + 12q^{73} + 18q^{74} - 48q^{76} - 28q^{77} - 4q^{79} + 98q^{80} + 20q^{82} + 36q^{83} - 10q^{85} + 40q^{86} + 96q^{88} + 54q^{89} + 148q^{91} + 4q^{92} - 60q^{95} - 40q^{97} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{12}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0578232 + 0.215799i −0.0408872 + 0.152593i −0.983351 0.181714i \(-0.941836\pi\)
0.942464 + 0.334307i \(0.108502\pi\)
\(3\) 0 0
\(4\) 1.68883 + 0.975044i 0.844413 + 0.487522i
\(5\) −1.08760 + 1.08760i −0.486390 + 0.486390i −0.907165 0.420775i \(-0.861758\pi\)
0.420775 + 0.907165i \(0.361758\pi\)
\(6\) 0 0
\(7\) −0.725943 2.54421i −0.274381 0.961621i
\(8\) −0.624019 + 0.624019i −0.220624 + 0.220624i
\(9\) 0 0
\(10\) −0.171815 0.297592i −0.0543326 0.0941068i
\(11\) −4.17464 1.11859i −1.25870 0.337268i −0.433010 0.901389i \(-0.642548\pi\)
−0.825692 + 0.564121i \(0.809215\pi\)
\(12\) 0 0
\(13\) −3.01096 + 1.98346i −0.835090 + 0.550113i
\(14\) 0.591015 0.00954346i 0.157955 0.00255060i
\(15\) 0 0
\(16\) 1.85151 + 3.20690i 0.462877 + 0.801726i
\(17\) −3.78401 + 6.55410i −0.917757 + 1.58960i −0.114944 + 0.993372i \(0.536669\pi\)
−0.802813 + 0.596231i \(0.796664\pi\)
\(18\) 0 0
\(19\) 1.31714 + 4.91565i 0.302173 + 1.12773i 0.935351 + 0.353720i \(0.115084\pi\)
−0.633178 + 0.774006i \(0.718250\pi\)
\(20\) −2.89722 + 0.776309i −0.647839 + 0.173588i
\(21\) 0 0
\(22\) 0.482783 0.836204i 0.102930 0.178279i
\(23\) 1.85976 1.07373i 0.387787 0.223889i −0.293414 0.955985i \(-0.594791\pi\)
0.681201 + 0.732097i \(0.261458\pi\)
\(24\) 0 0
\(25\) 2.63425i 0.526850i
\(26\) −0.253926 0.764453i −0.0497989 0.149922i
\(27\) 0 0
\(28\) 1.25473 5.00455i 0.237121 0.945771i
\(29\) 2.66646 + 4.61844i 0.495148 + 0.857622i 0.999984 0.00559304i \(-0.00178033\pi\)
−0.504836 + 0.863215i \(0.668447\pi\)
\(30\) 0 0
\(31\) 1.09410 1.09410i 0.196507 0.196507i −0.601994 0.798501i \(-0.705627\pi\)
0.798501 + 0.601994i \(0.205627\pi\)
\(32\) −2.50396 + 0.670934i −0.442642 + 0.118605i
\(33\) 0 0
\(34\) −1.19557 1.19557i −0.205038 0.205038i
\(35\) 3.55662 + 1.97755i 0.601178 + 0.334267i
\(36\) 0 0
\(37\) −2.82556 0.757106i −0.464519 0.124467i 0.0189661 0.999820i \(-0.493963\pi\)
−0.483485 + 0.875353i \(0.660629\pi\)
\(38\) −1.13695 −0.184438
\(39\) 0 0
\(40\) 1.35737i 0.214618i
\(41\) −1.37894 0.369486i −0.215354 0.0577039i 0.149529 0.988757i \(-0.452224\pi\)
−0.364883 + 0.931053i \(0.618891\pi\)
\(42\) 0 0
\(43\) −6.58558 3.80219i −1.00429 0.579828i −0.0947764 0.995499i \(-0.530214\pi\)
−0.909515 + 0.415671i \(0.863547\pi\)
\(44\) −5.95956 5.95956i −0.898438 0.898438i
\(45\) 0 0
\(46\) 0.124173 + 0.463422i 0.0183084 + 0.0683278i
\(47\) −5.26364 5.26364i −0.767781 0.767781i 0.209934 0.977716i \(-0.432675\pi\)
−0.977716 + 0.209934i \(0.932675\pi\)
\(48\) 0 0
\(49\) −5.94601 + 3.69390i −0.849431 + 0.527700i
\(50\) −0.568470 0.152321i −0.0803937 0.0215414i
\(51\) 0 0
\(52\) −7.01895 + 0.413900i −0.973353 + 0.0573976i
\(53\) 13.1808 1.81053 0.905263 0.424851i \(-0.139673\pi\)
0.905263 + 0.424851i \(0.139673\pi\)
\(54\) 0 0
\(55\) 5.75692 3.32376i 0.776263 0.448176i
\(56\) 2.04064 + 1.13463i 0.272692 + 0.151622i
\(57\) 0 0
\(58\) −1.15084 + 0.308366i −0.151112 + 0.0404905i
\(59\) 8.73809 2.34136i 1.13760 0.304820i 0.359616 0.933101i \(-0.382908\pi\)
0.777987 + 0.628281i \(0.216241\pi\)
\(60\) 0 0
\(61\) −10.1891 5.88266i −1.30458 0.753197i −0.323391 0.946266i \(-0.604823\pi\)
−0.981185 + 0.193068i \(0.938156\pi\)
\(62\) 0.172842 + 0.299371i 0.0219510 + 0.0380202i
\(63\) 0 0
\(64\) 6.82688i 0.853360i
\(65\) 1.11751 5.43193i 0.138610 0.673748i
\(66\) 0 0
\(67\) −1.28138 + 4.78216i −0.156545 + 0.584234i 0.842423 + 0.538817i \(0.181128\pi\)
−0.998968 + 0.0454175i \(0.985538\pi\)
\(68\) −12.7811 + 7.37915i −1.54993 + 0.894854i
\(69\) 0 0
\(70\) −0.632408 + 0.653167i −0.0755873 + 0.0780684i
\(71\) 5.25942 1.40926i 0.624179 0.167248i 0.0671520 0.997743i \(-0.478609\pi\)
0.557027 + 0.830495i \(0.311942\pi\)
\(72\) 0 0
\(73\) 8.04396 + 8.04396i 0.941474 + 0.941474i 0.998380 0.0569055i \(-0.0181234\pi\)
−0.0569055 + 0.998380i \(0.518123\pi\)
\(74\) 0.326766 0.565975i 0.0379857 0.0657932i
\(75\) 0 0
\(76\) −2.56854 + 9.58594i −0.294632 + 1.09958i
\(77\) 0.184619 + 11.4332i 0.0210392 + 1.30293i
\(78\) 0 0
\(79\) 9.06635 1.02004 0.510022 0.860161i \(-0.329637\pi\)
0.510022 + 0.860161i \(0.329637\pi\)
\(80\) −5.50153 1.47413i −0.615090 0.164813i
\(81\) 0 0
\(82\) 0.159469 0.276209i 0.0176104 0.0305022i
\(83\) −1.13072 + 1.13072i −0.124113 + 0.124113i −0.766435 0.642322i \(-0.777971\pi\)
0.642322 + 0.766435i \(0.277971\pi\)
\(84\) 0 0
\(85\) −3.01275 11.2437i −0.326778 1.21955i
\(86\) 1.20131 1.20131i 0.129540 0.129540i
\(87\) 0 0
\(88\) 3.30308 1.90703i 0.352109 0.203290i
\(89\) 0.217351 0.811166i 0.0230392 0.0859834i −0.953449 0.301554i \(-0.902495\pi\)
0.976488 + 0.215571i \(0.0691612\pi\)
\(90\) 0 0
\(91\) 7.23213 + 6.22064i 0.758133 + 0.652100i
\(92\) 4.18775 0.436603
\(93\) 0 0
\(94\) 1.44025 0.831529i 0.148551 0.0857657i
\(95\) −6.77878 3.91373i −0.695488 0.401540i
\(96\) 0 0
\(97\) −4.35890 16.2676i −0.442579 1.65173i −0.722251 0.691631i \(-0.756892\pi\)
0.279672 0.960096i \(-0.409774\pi\)
\(98\) −0.453324 1.49674i −0.0457926 0.151193i
\(99\) 0 0
\(100\) −2.56851 + 4.44879i −0.256851 + 0.444879i
\(101\) 5.48585 + 9.50177i 0.545863 + 0.945462i 0.998552 + 0.0537934i \(0.0171313\pi\)
−0.452690 + 0.891668i \(0.649535\pi\)
\(102\) 0 0
\(103\) −4.70231 −0.463332 −0.231666 0.972795i \(-0.574418\pi\)
−0.231666 + 0.972795i \(0.574418\pi\)
\(104\) 0.641180 3.11661i 0.0628728 0.305609i
\(105\) 0 0
\(106\) −0.762158 + 2.84441i −0.0740274 + 0.276274i
\(107\) −6.55307 11.3502i −0.633509 1.09727i −0.986829 0.161767i \(-0.948281\pi\)
0.353320 0.935503i \(-0.385053\pi\)
\(108\) 0 0
\(109\) −0.872057 0.872057i −0.0835279 0.0835279i 0.664108 0.747636i \(-0.268811\pi\)
−0.747636 + 0.664108i \(0.768811\pi\)
\(110\) 0.384381 + 1.43453i 0.0366493 + 0.136777i
\(111\) 0 0
\(112\) 6.81495 7.03865i 0.643952 0.665090i
\(113\) −6.21370 + 10.7625i −0.584536 + 1.01245i 0.410397 + 0.911907i \(0.365390\pi\)
−0.994933 + 0.100539i \(0.967943\pi\)
\(114\) 0 0
\(115\) −0.854883 + 3.19047i −0.0797183 + 0.297513i
\(116\) 10.3996i 0.965583i
\(117\) 0 0
\(118\) 2.02106i 0.186053i
\(119\) 19.4220 + 4.86942i 1.78041 + 0.446379i
\(120\) 0 0
\(121\) 6.65011 + 3.83944i 0.604556 + 0.349040i
\(122\) 1.85864 1.85864i 0.168273 0.168273i
\(123\) 0 0
\(124\) 2.91455 0.780950i 0.261734 0.0701314i
\(125\) −8.30301 8.30301i −0.742644 0.742644i
\(126\) 0 0
\(127\) 5.51334 3.18313i 0.489230 0.282457i −0.235025 0.971989i \(-0.575517\pi\)
0.724255 + 0.689532i \(0.242184\pi\)
\(128\) −6.48115 1.73662i −0.572858 0.153497i
\(129\) 0 0
\(130\) 1.10759 + 0.555250i 0.0971420 + 0.0486986i
\(131\) 3.73498i 0.326327i −0.986599 0.163163i \(-0.947830\pi\)
0.986599 0.163163i \(-0.0521698\pi\)
\(132\) 0 0
\(133\) 11.5503 6.91957i 1.00154 0.600003i
\(134\) −0.957894 0.553040i −0.0827494 0.0477754i
\(135\) 0 0
\(136\) −1.72859 6.45118i −0.148225 0.553184i
\(137\) −0.00793713 0.0296218i −0.000678115 0.00253076i 0.965586 0.260084i \(-0.0837503\pi\)
−0.966264 + 0.257553i \(0.917084\pi\)
\(138\) 0 0
\(139\) 2.85559 + 1.64867i 0.242208 + 0.139839i 0.616191 0.787597i \(-0.288675\pi\)
−0.373983 + 0.927435i \(0.622008\pi\)
\(140\) 4.07831 + 6.80759i 0.344680 + 0.575346i
\(141\) 0 0
\(142\) 1.21647i 0.102084i
\(143\) 14.7884 4.91220i 1.23667 0.410779i
\(144\) 0 0
\(145\) −7.92305 2.12297i −0.657974 0.176303i
\(146\) −2.20101 + 1.27075i −0.182157 + 0.105168i
\(147\) 0 0
\(148\) −4.03366 4.03366i −0.331565 0.331565i
\(149\) −4.52646 + 1.21286i −0.370822 + 0.0993615i −0.439417 0.898283i \(-0.644815\pi\)
0.0685950 + 0.997645i \(0.478148\pi\)
\(150\) 0 0
\(151\) −4.74970 + 4.74970i −0.386525 + 0.386525i −0.873446 0.486921i \(-0.838120\pi\)
0.486921 + 0.873446i \(0.338120\pi\)
\(152\) −3.88938 2.24553i −0.315470 0.182137i
\(153\) 0 0
\(154\) −2.47795 0.621264i −0.199679 0.0500629i
\(155\) 2.37989i 0.191158i
\(156\) 0 0
\(157\) 17.1115i 1.36565i 0.730584 + 0.682823i \(0.239248\pi\)
−0.730584 + 0.682823i \(0.760752\pi\)
\(158\) −0.524246 + 1.95651i −0.0417068 + 0.155652i
\(159\) 0 0
\(160\) 1.99360 3.45301i 0.157608 0.272985i
\(161\) −4.08188 3.95215i −0.321697 0.311473i
\(162\) 0 0
\(163\) 5.05271 + 18.8570i 0.395759 + 1.47699i 0.820484 + 0.571669i \(0.193704\pi\)
−0.424726 + 0.905322i \(0.639630\pi\)
\(164\) −1.96852 1.96852i −0.153716 0.153716i
\(165\) 0 0
\(166\) −0.178627 0.309390i −0.0138641 0.0240134i
\(167\) 3.66374 13.6733i 0.283508 1.05807i −0.666414 0.745582i \(-0.732172\pi\)
0.949922 0.312486i \(-0.101162\pi\)
\(168\) 0 0
\(169\) 5.13177 11.9442i 0.394751 0.918788i
\(170\) 2.60060 0.199457
\(171\) 0 0
\(172\) −7.41460 12.8425i −0.565358 0.979228i
\(173\) 9.66072 16.7329i 0.734491 1.27218i −0.220456 0.975397i \(-0.570754\pi\)
0.954946 0.296778i \(-0.0959122\pi\)
\(174\) 0 0
\(175\) 6.70209 1.91232i 0.506631 0.144558i
\(176\) −4.14216 15.4588i −0.312227 1.16525i
\(177\) 0 0
\(178\) 0.162481 + 0.0938085i 0.0121785 + 0.00703124i
\(179\) −3.56116 + 2.05604i −0.266173 + 0.153675i −0.627147 0.778901i \(-0.715778\pi\)
0.360974 + 0.932576i \(0.382444\pi\)
\(180\) 0 0
\(181\) 2.09652 0.155833 0.0779165 0.996960i \(-0.475173\pi\)
0.0779165 + 0.996960i \(0.475173\pi\)
\(182\) −1.76059 + 1.20099i −0.130504 + 0.0890233i
\(183\) 0 0
\(184\) −0.490496 + 1.83056i −0.0361598 + 0.134950i
\(185\) 3.89650 2.24965i 0.286477 0.165397i
\(186\) 0 0
\(187\) 23.1283 23.1283i 1.69131 1.69131i
\(188\) −3.75709 14.0217i −0.274014 1.02263i
\(189\) 0 0
\(190\) 1.23655 1.23655i 0.0897089 0.0897089i
\(191\) −4.22074 + 7.31054i −0.305402 + 0.528972i −0.977351 0.211626i \(-0.932124\pi\)
0.671949 + 0.740598i \(0.265458\pi\)
\(192\) 0 0
\(193\) 1.96647 + 0.526915i 0.141550 + 0.0379282i 0.328898 0.944365i \(-0.393323\pi\)
−0.187348 + 0.982294i \(0.559989\pi\)
\(194\) 3.76259 0.270138
\(195\) 0 0
\(196\) −13.6435 + 0.440734i −0.974535 + 0.0314810i
\(197\) −3.46988 + 12.9498i −0.247219 + 0.922632i 0.725037 + 0.688710i \(0.241823\pi\)
−0.972255 + 0.233922i \(0.924844\pi\)
\(198\) 0 0
\(199\) 3.76822 6.52675i 0.267122 0.462669i −0.700995 0.713166i \(-0.747261\pi\)
0.968117 + 0.250497i \(0.0805940\pi\)
\(200\) −1.64382 1.64382i −0.116236 0.116236i
\(201\) 0 0
\(202\) −2.36768 + 0.634419i −0.166590 + 0.0446376i
\(203\) 9.81458 10.1367i 0.688849 0.711460i
\(204\) 0 0
\(205\) 1.90159 1.09788i 0.132813 0.0766794i
\(206\) 0.271903 1.01475i 0.0189444 0.0707013i
\(207\) 0 0
\(208\) −11.9356 5.98347i −0.827584 0.414879i
\(209\) 21.9944i 1.52139i
\(210\) 0 0
\(211\) 8.48310 + 14.6932i 0.584001 + 1.01152i 0.994999 + 0.0998830i \(0.0318469\pi\)
−0.410998 + 0.911636i \(0.634820\pi\)
\(212\) 22.2601 + 12.8519i 1.52883 + 0.882671i
\(213\) 0 0
\(214\) 2.82829 0.757839i 0.193338 0.0518048i
\(215\) 11.2977 3.02722i 0.770499 0.206455i
\(216\) 0 0
\(217\) −3.57788 1.98937i −0.242883 0.135047i
\(218\) 0.238614 0.137764i 0.0161610 0.00933056i
\(219\) 0 0
\(220\) 12.9632 0.873982
\(221\) −1.60629 27.2396i −0.108051 1.83233i
\(222\) 0 0
\(223\) −12.1895 3.26617i −0.816269 0.218719i −0.173555 0.984824i \(-0.555525\pi\)
−0.642715 + 0.766106i \(0.722192\pi\)
\(224\) 3.52473 + 5.88354i 0.235506 + 0.393111i
\(225\) 0 0
\(226\) −1.96323 1.96323i −0.130592 0.130592i
\(227\) 5.09212 + 19.0040i 0.337976 + 1.26134i 0.900607 + 0.434635i \(0.143122\pi\)
−0.562631 + 0.826708i \(0.690211\pi\)
\(228\) 0 0
\(229\) 19.8246 + 19.8246i 1.31004 + 1.31004i 0.921379 + 0.388666i \(0.127064\pi\)
0.388666 + 0.921379i \(0.372936\pi\)
\(230\) −0.639068 0.368966i −0.0421389 0.0243289i
\(231\) 0 0
\(232\) −4.54591 1.21807i −0.298454 0.0799704i
\(233\) 10.8900i 0.713427i 0.934214 + 0.356714i \(0.116103\pi\)
−0.934214 + 0.356714i \(0.883897\pi\)
\(234\) 0 0
\(235\) 11.4495 0.746882
\(236\) 17.0400 + 4.56586i 1.10921 + 0.297212i
\(237\) 0 0
\(238\) −2.17386 + 3.90968i −0.140910 + 0.253427i
\(239\) 10.0403 + 10.0403i 0.649451 + 0.649451i 0.952860 0.303409i \(-0.0981250\pi\)
−0.303409 + 0.952860i \(0.598125\pi\)
\(240\) 0 0
\(241\) 15.1305 4.05421i 0.974642 0.261155i 0.263856 0.964562i \(-0.415006\pi\)
0.710787 + 0.703408i \(0.248339\pi\)
\(242\) −1.21308 + 1.21308i −0.0779797 + 0.0779797i
\(243\) 0 0
\(244\) −11.4717 19.8696i −0.734400 1.27202i
\(245\) 2.44940 10.4844i 0.156486 0.669822i
\(246\) 0 0
\(247\) −13.7159 12.1883i −0.872719 0.775524i
\(248\) 1.36548i 0.0867082i
\(249\) 0 0
\(250\) 2.27189 1.31168i 0.143687 0.0829577i
\(251\) −10.7847 + 18.6797i −0.680727 + 1.17905i 0.294033 + 0.955795i \(0.405003\pi\)
−0.974759 + 0.223258i \(0.928331\pi\)
\(252\) 0 0
\(253\) −8.96490 + 2.40214i −0.563619 + 0.151021i
\(254\) 0.368118 + 1.37383i 0.0230977 + 0.0862020i
\(255\) 0 0
\(256\) −6.07736 + 10.5263i −0.379835 + 0.657893i
\(257\) 1.05953 + 1.83517i 0.0660920 + 0.114475i 0.897178 0.441669i \(-0.145614\pi\)
−0.831086 + 0.556144i \(0.812280\pi\)
\(258\) 0 0
\(259\) 0.124957 + 7.73843i 0.00776444 + 0.480843i
\(260\) 7.18365 8.08396i 0.445511 0.501346i
\(261\) 0 0
\(262\) 0.806006 + 0.215969i 0.0497952 + 0.0133426i
\(263\) −5.53188 9.58150i −0.341111 0.590821i 0.643529 0.765422i \(-0.277470\pi\)
−0.984639 + 0.174601i \(0.944136\pi\)
\(264\) 0 0
\(265\) −14.3355 + 14.3355i −0.880621 + 0.880621i
\(266\) 0.825364 + 2.89265i 0.0506063 + 0.177360i
\(267\) 0 0
\(268\) −6.82684 + 6.82684i −0.417016 + 0.417016i
\(269\) 23.8459 + 13.7675i 1.45391 + 0.839416i 0.998700 0.0509670i \(-0.0162303\pi\)
0.455211 + 0.890383i \(0.349564\pi\)
\(270\) 0 0
\(271\) −3.80218 + 14.1899i −0.230966 + 0.861978i 0.748960 + 0.662616i \(0.230554\pi\)
−0.979926 + 0.199362i \(0.936113\pi\)
\(272\) −28.0245 −1.69923
\(273\) 0 0
\(274\) 0.00685131 0.000413903
\(275\) 2.94665 10.9971i 0.177690 0.663148i
\(276\) 0 0
\(277\) 4.50623 + 2.60167i 0.270753 + 0.156319i 0.629230 0.777219i \(-0.283370\pi\)
−0.358477 + 0.933539i \(0.616704\pi\)
\(278\) −0.520902 + 0.520902i −0.0312416 + 0.0312416i
\(279\) 0 0
\(280\) −3.45343 + 0.985370i −0.206382 + 0.0588871i
\(281\) 10.7634 10.7634i 0.642088 0.642088i −0.308980 0.951068i \(-0.599988\pi\)
0.951068 + 0.308980i \(0.0999877\pi\)
\(282\) 0 0
\(283\) 2.03356 + 3.52223i 0.120882 + 0.209375i 0.920116 0.391646i \(-0.128094\pi\)
−0.799233 + 0.601021i \(0.794761\pi\)
\(284\) 10.2563 + 2.74818i 0.608601 + 0.163074i
\(285\) 0 0
\(286\) 0.204938 + 3.47536i 0.0121183 + 0.205502i
\(287\) 0.0609819 + 3.77654i 0.00359965 + 0.222922i
\(288\) 0 0
\(289\) −20.1375 34.8791i −1.18456 2.05171i
\(290\) 0.916273 1.58703i 0.0538054 0.0931937i
\(291\) 0 0
\(292\) 5.74163 + 21.4280i 0.336003 + 1.25398i
\(293\) −21.3183 + 5.71221i −1.24543 + 0.333711i −0.820568 0.571549i \(-0.806343\pi\)
−0.424858 + 0.905260i \(0.639676\pi\)
\(294\) 0 0
\(295\) −6.95708 + 12.0500i −0.405057 + 0.701579i
\(296\) 2.23565 1.29075i 0.129944 0.0750235i
\(297\) 0 0
\(298\) 1.04694i 0.0606475i
\(299\) −3.46996 + 6.92173i −0.200673 + 0.400294i
\(300\) 0 0
\(301\) −4.89281 + 19.5153i −0.282017 + 1.12484i
\(302\) −0.750339 1.29962i −0.0431771 0.0747850i
\(303\) 0 0
\(304\) −13.3253 + 13.3253i −0.764259 + 0.764259i
\(305\) 17.4796 4.68365i 1.00088 0.268185i
\(306\) 0 0
\(307\) −9.60326 9.60326i −0.548087 0.548087i 0.377800 0.925887i \(-0.376681\pi\)
−0.925887 + 0.377800i \(0.876681\pi\)
\(308\) −10.8361 + 19.4887i −0.617443 + 1.11047i
\(309\) 0 0
\(310\) −0.513579 0.137613i −0.0291693 0.00781590i
\(311\) 16.2194 0.919715 0.459858 0.887993i \(-0.347900\pi\)
0.459858 + 0.887993i \(0.347900\pi\)
\(312\) 0 0
\(313\) 24.2234i 1.36919i −0.728926 0.684593i \(-0.759980\pi\)
0.728926 0.684593i \(-0.240020\pi\)
\(314\) −3.69265 0.989442i −0.208388 0.0558375i
\(315\) 0 0
\(316\) 15.3115 + 8.84009i 0.861338 + 0.497294i
\(317\) 18.9182 + 18.9182i 1.06255 + 1.06255i 0.997909 + 0.0646418i \(0.0205905\pi\)
0.0646418 + 0.997909i \(0.479410\pi\)
\(318\) 0 0
\(319\) −5.96535 22.2630i −0.333996 1.24649i
\(320\) −7.42492 7.42492i −0.415065 0.415065i
\(321\) 0 0
\(322\) 1.08890 0.652341i 0.0606820 0.0363535i
\(323\) −37.2017 9.96817i −2.06996 0.554644i
\(324\) 0 0
\(325\) −5.22494 7.93163i −0.289827 0.439968i
\(326\) −4.36148 −0.241560
\(327\) 0 0
\(328\) 1.09105 0.629918i 0.0602432 0.0347814i
\(329\) −9.57071 + 17.2129i −0.527650 + 0.948979i
\(330\) 0 0
\(331\) 13.9589 3.74029i 0.767253 0.205585i 0.146095 0.989271i \(-0.453329\pi\)
0.621157 + 0.783686i \(0.286663\pi\)
\(332\) −3.01209 + 0.807087i −0.165310 + 0.0442947i
\(333\) 0 0
\(334\) 2.73883 + 1.58126i 0.149862 + 0.0865229i
\(335\) −3.80746 6.59471i −0.208024 0.360307i
\(336\) 0 0
\(337\) 5.15524i 0.280824i 0.990093 + 0.140412i \(0.0448426\pi\)
−0.990093 + 0.140412i \(0.955157\pi\)
\(338\) 2.28082 + 1.79809i 0.124060 + 0.0978030i
\(339\) 0 0
\(340\) 5.87512 21.9263i 0.318623 1.18912i
\(341\) −5.79134 + 3.34363i −0.313619 + 0.181068i
\(342\) 0 0
\(343\) 13.7145 + 12.4463i 0.740515 + 0.672040i
\(344\) 6.48216 1.73689i 0.349495 0.0936469i
\(345\) 0 0
\(346\) 3.05232 + 3.05232i 0.164094 + 0.164094i
\(347\) −11.9012 + 20.6134i −0.638888 + 1.10659i 0.346789 + 0.937943i \(0.387272\pi\)
−0.985677 + 0.168643i \(0.946062\pi\)
\(348\) 0 0
\(349\) 3.16538 11.8134i 0.169439 0.632355i −0.827993 0.560738i \(-0.810518\pi\)
0.997432 0.0716166i \(-0.0228158\pi\)
\(350\) 0.0251399 + 1.55688i 0.00134378 + 0.0832189i
\(351\) 0 0
\(352\) 11.2036 0.597156
\(353\) −16.5186 4.42614i −0.879196 0.235580i −0.209136 0.977887i \(-0.567065\pi\)
−0.670060 + 0.742307i \(0.733732\pi\)
\(354\) 0 0
\(355\) −4.18744 + 7.25286i −0.222246 + 0.384942i
\(356\) 1.15799 1.15799i 0.0613734 0.0613734i
\(357\) 0 0
\(358\) −0.237773 0.887382i −0.0125667 0.0468996i
\(359\) −14.6210 + 14.6210i −0.771665 + 0.771665i −0.978397 0.206733i \(-0.933717\pi\)
0.206733 + 0.978397i \(0.433717\pi\)
\(360\) 0 0
\(361\) −5.97423 + 3.44922i −0.314433 + 0.181538i
\(362\) −0.121228 + 0.452427i −0.00637158 + 0.0237790i
\(363\) 0 0
\(364\) 6.14840 + 17.5572i 0.322264 + 0.920248i
\(365\) −17.4972 −0.915846
\(366\) 0 0
\(367\) −0.401157 + 0.231608i −0.0209402 + 0.0120898i −0.510434 0.859917i \(-0.670515\pi\)
0.489493 + 0.872007i \(0.337182\pi\)
\(368\) 6.88672 + 3.97605i 0.358995 + 0.207266i
\(369\) 0 0
\(370\) 0.260164 + 0.970945i 0.0135253 + 0.0504770i
\(371\) −9.56853 33.5348i −0.496774 1.74104i
\(372\) 0 0
\(373\) −0.348917 + 0.604342i −0.0180662 + 0.0312916i −0.874917 0.484273i \(-0.839084\pi\)
0.856851 + 0.515564i \(0.172418\pi\)
\(374\) 3.65371 + 6.32841i 0.188929 + 0.327234i
\(375\) 0 0
\(376\) 6.56923 0.338782
\(377\) −17.1891 8.61712i −0.885283 0.443804i
\(378\) 0 0
\(379\) 1.85118 6.90871i 0.0950889 0.354877i −0.901944 0.431853i \(-0.857860\pi\)
0.997033 + 0.0769763i \(0.0245266\pi\)
\(380\) −7.63212 13.2192i −0.391519 0.678132i
\(381\) 0 0
\(382\) −1.33355 1.33355i −0.0682305 0.0682305i
\(383\) 0.496583 + 1.85327i 0.0253742 + 0.0946979i 0.977452 0.211159i \(-0.0677238\pi\)
−0.952078 + 0.305857i \(0.901057\pi\)
\(384\) 0 0
\(385\) −12.6355 12.2340i −0.643967 0.623500i
\(386\) −0.227416 + 0.393895i −0.0115751 + 0.0200487i
\(387\) 0 0
\(388\) 8.50023 31.7233i 0.431534 1.61051i
\(389\) 6.17075i 0.312870i 0.987688 + 0.156435i \(0.0500001\pi\)
−0.987688 + 0.156435i \(0.950000\pi\)
\(390\) 0 0
\(391\) 16.2521i 0.821903i
\(392\) 1.40536 6.01549i 0.0709814 0.303828i
\(393\) 0 0
\(394\) −2.59391 1.49759i −0.130679 0.0754477i
\(395\) −9.86057 + 9.86057i −0.496139 + 0.496139i
\(396\) 0 0
\(397\) −30.1243 + 8.07177i −1.51189 + 0.405111i −0.917063 0.398741i \(-0.869447\pi\)
−0.594830 + 0.803852i \(0.702780\pi\)
\(398\) 1.19058 + 1.19058i 0.0596782 + 0.0596782i
\(399\) 0 0
\(400\) −8.44780 + 4.87734i −0.422390 + 0.243867i
\(401\) −24.2526 6.49846i −1.21112 0.324517i −0.403916 0.914796i \(-0.632351\pi\)
−0.807199 + 0.590279i \(0.799018\pi\)
\(402\) 0 0
\(403\) −1.12419 + 5.46441i −0.0559999 + 0.272202i
\(404\) 21.3958i 1.06448i
\(405\) 0 0
\(406\) 1.61999 + 2.70412i 0.0803988 + 0.134203i
\(407\) 10.9488 + 6.32129i 0.542712 + 0.313335i
\(408\) 0 0
\(409\) 3.92450 + 14.6464i 0.194054 + 0.724219i 0.992510 + 0.122165i \(0.0389838\pi\)
−0.798456 + 0.602053i \(0.794349\pi\)
\(410\) 0.126966 + 0.473844i 0.00627041 + 0.0234015i
\(411\) 0 0
\(412\) −7.94138 4.58496i −0.391244 0.225885i
\(413\) −12.3003 20.5318i −0.605257 1.01031i
\(414\) 0 0
\(415\) 2.45954i 0.120734i
\(416\) 6.20855 6.98666i 0.304399 0.342549i
\(417\) 0 0
\(418\) 4.74638 + 1.27179i 0.232153 + 0.0622052i
\(419\) −3.99149 + 2.30449i −0.194997 + 0.112582i −0.594320 0.804229i \(-0.702579\pi\)
0.399323 + 0.916810i \(0.369245\pi\)
\(420\) 0 0
\(421\) 12.6437 + 12.6437i 0.616216 + 0.616216i 0.944559 0.328342i \(-0.106490\pi\)
−0.328342 + 0.944559i \(0.606490\pi\)
\(422\) −3.66129 + 0.981041i −0.178229 + 0.0477563i
\(423\) 0 0
\(424\) −8.22509 + 8.22509i −0.399446 + 0.399446i
\(425\) −17.2652 9.96804i −0.837483 0.483521i
\(426\) 0 0
\(427\) −7.57004 + 30.1936i −0.366340 + 1.46117i
\(428\) 25.5581i 1.23540i
\(429\) 0 0
\(430\) 2.61309i 0.126014i
\(431\) −2.12448 + 7.92867i −0.102333 + 0.381911i −0.998029 0.0627557i \(-0.980011\pi\)
0.895696 + 0.444666i \(0.146678\pi\)
\(432\) 0 0
\(433\) 8.67779 15.0304i 0.417028 0.722314i −0.578611 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932901i \(0.0297384\pi\)
\(434\) 0.636190 0.657073i 0.0305381 0.0315405i
\(435\) 0 0
\(436\) −0.622458 2.32305i −0.0298103 0.111254i
\(437\) 7.72766 + 7.72766i 0.369664 + 0.369664i
\(438\) 0 0
\(439\) −7.78946 13.4917i −0.371771 0.643926i 0.618067 0.786125i \(-0.287916\pi\)
−0.989838 + 0.142199i \(0.954583\pi\)
\(440\) −1.51834 + 5.66652i −0.0723840 + 0.270141i
\(441\) 0 0
\(442\) 5.97116 + 1.22844i 0.284019 + 0.0584311i
\(443\) 30.0278 1.42667 0.713333 0.700825i \(-0.247185\pi\)
0.713333 + 0.700825i \(0.247185\pi\)
\(444\) 0 0
\(445\) 0.645833 + 1.11862i 0.0306154 + 0.0530274i
\(446\) 1.40967 2.44162i 0.0667499 0.115614i
\(447\) 0 0
\(448\) 17.3690 4.95593i 0.820609 0.234145i
\(449\) −1.79908 6.71427i −0.0849040 0.316866i 0.910392 0.413747i \(-0.135780\pi\)
−0.995296 + 0.0968807i \(0.969113\pi\)
\(450\) 0 0
\(451\) 5.34327 + 3.08494i 0.251605 + 0.145264i
\(452\) −20.9877 + 12.1173i −0.987179 + 0.569948i
\(453\) 0 0
\(454\) −4.39550 −0.206291
\(455\) −14.6312 + 1.10009i −0.685923 + 0.0515732i
\(456\) 0 0
\(457\) 5.76514 21.5158i 0.269682 1.00647i −0.689640 0.724152i \(-0.742231\pi\)
0.959322 0.282314i \(-0.0911020\pi\)
\(458\) −5.42445 + 3.13181i −0.253468 + 0.146340i
\(459\) 0 0
\(460\) −4.55459 + 4.55459i −0.212359 + 0.212359i
\(461\) 3.01705 + 11.2598i 0.140518 + 0.524420i 0.999914 + 0.0131099i \(0.00417312\pi\)
−0.859396 + 0.511311i \(0.829160\pi\)
\(462\) 0 0
\(463\) 16.6774 16.6774i 0.775063 0.775063i −0.203924 0.978987i \(-0.565369\pi\)
0.978987 + 0.203924i \(0.0653694\pi\)
\(464\) −9.87392 + 17.1021i −0.458385 + 0.793947i
\(465\) 0 0
\(466\) −2.35005 0.629695i −0.108864 0.0291700i
\(467\) 17.0336 0.788223 0.394111 0.919063i \(-0.371052\pi\)
0.394111 + 0.919063i \(0.371052\pi\)
\(468\) 0 0
\(469\) 13.0970 0.211485i 0.604765 0.00976549i
\(470\) −0.662046 + 2.47079i −0.0305379 + 0.113969i
\(471\) 0 0
\(472\) −3.99168 + 6.91379i −0.183732 + 0.318233i
\(473\) 23.2393 + 23.2393i 1.06855 + 1.06855i
\(474\) 0 0
\(475\) −12.9491 + 3.46969i −0.594143 + 0.159200i
\(476\) 28.0524 + 27.1609i 1.28578 + 1.24492i
\(477\) 0 0
\(478\) −2.74724 + 1.58612i −0.125656 + 0.0725475i
\(479\) −8.69175 + 32.4380i −0.397136 + 1.48213i 0.420976 + 0.907072i \(0.361688\pi\)
−0.818111 + 0.575060i \(0.804979\pi\)
\(480\) 0 0
\(481\) 10.0093 3.32477i 0.456386 0.151596i
\(482\) 3.49958i 0.159402i
\(483\) 0 0
\(484\) 7.48725 + 12.9683i 0.340330 + 0.589468i
\(485\) 22.4334 + 12.9519i 1.01865 + 0.588117i
\(486\) 0 0
\(487\) −3.78357 + 1.01381i −0.171450 + 0.0459399i −0.343523 0.939144i \(-0.611620\pi\)
0.172073 + 0.985084i \(0.444954\pi\)
\(488\) 10.0291 2.68728i 0.453994 0.121647i
\(489\) 0 0
\(490\) 2.12089 + 1.13482i 0.0958119 + 0.0512659i
\(491\) 6.15458 3.55335i 0.277752 0.160360i −0.354653 0.934998i \(-0.615401\pi\)
0.632405 + 0.774638i \(0.282068\pi\)
\(492\) 0 0
\(493\) −40.3596 −1.81770
\(494\) 3.42332 2.25510i 0.154023 0.101462i
\(495\) 0 0
\(496\) 5.53442 + 1.48294i 0.248503 + 0.0665861i
\(497\) −7.40349 12.3580i −0.332092 0.554334i
\(498\) 0 0
\(499\) 5.42530 + 5.42530i 0.242870 + 0.242870i 0.818036 0.575167i \(-0.195063\pi\)
−0.575167 + 0.818036i \(0.695063\pi\)
\(500\) −5.92654 22.1181i −0.265043 0.989153i
\(501\) 0 0
\(502\) −3.40746 3.40746i −0.152082 0.152082i
\(503\) −11.4527 6.61222i −0.510651 0.294824i 0.222450 0.974944i \(-0.428594\pi\)
−0.733101 + 0.680120i \(0.761928\pi\)
\(504\) 0 0
\(505\) −16.3005 4.36772i −0.725364 0.194361i
\(506\) 2.07352i 0.0921792i
\(507\) 0 0
\(508\) 12.4148 0.550816
\(509\) −38.3913 10.2869i −1.70167 0.455960i −0.728308 0.685250i \(-0.759693\pi\)
−0.973358 + 0.229290i \(0.926360\pi\)
\(510\) 0 0
\(511\) 14.6261 26.3050i 0.647019 1.16366i
\(512\) −11.4092 11.4092i −0.504221 0.504221i
\(513\) 0 0
\(514\) −0.457294 + 0.122531i −0.0201704 + 0.00540463i
\(515\) 5.11423 5.11423i 0.225360 0.225360i
\(516\) 0 0
\(517\) 16.0860 + 27.8617i 0.707460 + 1.22536i
\(518\) −1.67717 0.420495i −0.0736907 0.0184755i
\(519\) 0 0
\(520\) 2.69228 + 4.08698i 0.118064 + 0.179226i
\(521\) 9.34550i 0.409434i −0.978821 0.204717i \(-0.934373\pi\)
0.978821 0.204717i \(-0.0656274\pi\)
\(522\) 0 0
\(523\) −16.9149 + 9.76580i −0.739635 + 0.427028i −0.821937 0.569579i \(-0.807106\pi\)
0.0823016 + 0.996607i \(0.473773\pi\)
\(524\) 3.64177 6.30773i 0.159091 0.275554i
\(525\) 0 0
\(526\) 2.38755 0.639743i 0.104102 0.0278941i
\(527\) 3.03076 + 11.3110i 0.132022 + 0.492713i
\(528\) 0 0
\(529\) −9.19419 + 15.9248i −0.399748 + 0.692383i
\(530\) −2.26466 3.92251i −0.0983706 0.170383i
\(531\) 0 0
\(532\) 26.2533 0.423927i 1.13822 0.0183796i
\(533\) 4.88479 1.62256i 0.211584 0.0702811i
\(534\) 0 0
\(535\) 19.4716 + 5.21741i 0.841833 + 0.225568i
\(536\) −2.18456 3.78376i −0.0943585 0.163434i
\(537\) 0 0
\(538\) −4.34985 + 4.34985i −0.187536 + 0.187536i
\(539\) 28.9545 8.76956i 1.24716 0.377732i
\(540\) 0 0
\(541\) −0.184083 + 0.184083i −0.00791436 + 0.00791436i −0.711053 0.703139i \(-0.751781\pi\)
0.703139 + 0.711053i \(0.251781\pi\)
\(542\) −2.84232 1.64102i −0.122088 0.0704877i
\(543\) 0 0
\(544\) 5.07764 18.9500i 0.217702 0.812475i
\(545\) 1.89690 0.0812542
\(546\) 0 0
\(547\) −26.9425 −1.15198 −0.575990 0.817457i \(-0.695383\pi\)
−0.575990 + 0.817457i \(0.695383\pi\)
\(548\) 0.0154781 0.0577651i 0.000661192 0.00246760i
\(549\) 0 0
\(550\) 2.20277 + 1.27177i 0.0939265 + 0.0542285i
\(551\) −19.1905 + 19.1905i −0.817543 + 0.817543i
\(552\) 0 0
\(553\) −6.58166 23.0667i −0.279880 0.980896i
\(554\) −0.822003 + 0.822003i −0.0349236 + 0.0349236i
\(555\) 0 0
\(556\) 3.21506 + 5.56864i 0.136349 + 0.236163i
\(557\) −29.5799 7.92591i −1.25334 0.335832i −0.429715 0.902965i \(-0.641386\pi\)
−0.823626 + 0.567133i \(0.808052\pi\)
\(558\) 0 0
\(559\) 27.3704 1.61400i 1.15765 0.0682651i
\(560\) 0.243299 + 15.0672i 0.0102812 + 0.636705i
\(561\) 0 0
\(562\) 1.70035 + 2.94510i 0.0717250 + 0.124231i
\(563\) 7.49329 12.9788i 0.315804 0.546989i −0.663804 0.747907i \(-0.731059\pi\)
0.979608 + 0.200917i \(0.0643923\pi\)
\(564\) 0 0
\(565\) −4.94722 18.4633i −0.208131 0.776756i
\(566\) −0.877680 + 0.235174i −0.0368917 + 0.00988509i
\(567\) 0 0
\(568\) −2.40258 + 4.16138i −0.100810 + 0.174608i
\(569\) −6.07156 + 3.50542i −0.254533 + 0.146955i −0.621838 0.783146i \(-0.713614\pi\)
0.367305 + 0.930101i \(0.380280\pi\)
\(570\) 0 0
\(571\) 0.237494i 0.00993882i 0.999988 + 0.00496941i \(0.00158182\pi\)
−0.999988 + 0.00496941i \(0.998418\pi\)
\(572\) 29.7646 + 6.12345i 1.24452 + 0.256034i
\(573\) 0 0
\(574\) −0.818500 0.205212i −0.0341635 0.00856537i
\(575\) 2.82848 + 4.89908i 0.117956 + 0.204306i
\(576\) 0 0
\(577\) −3.41695 + 3.41695i −0.142250 + 0.142250i −0.774645 0.632396i \(-0.782072\pi\)
0.632396 + 0.774645i \(0.282072\pi\)
\(578\) 8.69131 2.32883i 0.361511 0.0968665i
\(579\) 0 0
\(580\) −11.3107 11.3107i −0.469649 0.469649i
\(581\) 3.69763 + 2.05595i 0.153403 + 0.0852952i
\(582\) 0 0
\(583\) −55.0253 14.7440i −2.27891 0.610633i
\(584\) −10.0392 −0.415424
\(585\) 0 0
\(586\) 4.93076i 0.203688i
\(587\) 7.16064 + 1.91869i 0.295551 + 0.0791927i 0.403548 0.914959i \(-0.367777\pi\)
−0.107997 + 0.994151i \(0.534444\pi\)
\(588\) 0 0
\(589\) 6.81931 + 3.93713i 0.280985 + 0.162227i
\(590\) −2.19810 2.19810i −0.0904945 0.0904945i
\(591\) 0 0
\(592\) −2.80357 10.4631i −0.115226 0.430030i
\(593\) −20.9219 20.9219i −0.859161 0.859161i 0.132078 0.991239i \(-0.457835\pi\)
−0.991239 + 0.132078i \(0.957835\pi\)
\(594\) 0 0
\(595\) −26.4193 + 15.8274i −1.08309 + 0.648859i
\(596\) −8.82700 2.36519i −0.361568 0.0968818i
\(597\) 0 0
\(598\) −1.29306 1.14905i −0.0528771 0.0469882i
\(599\) 35.0083 1.43040 0.715199 0.698920i \(-0.246336\pi\)
0.715199 + 0.698920i \(0.246336\pi\)
\(600\) 0 0
\(601\) −25.0031 + 14.4355i −1.01990 + 0.588838i −0.914074 0.405547i \(-0.867081\pi\)
−0.105823 + 0.994385i \(0.533748\pi\)
\(602\) −3.92846 2.18430i −0.160112 0.0890254i
\(603\) 0 0
\(604\) −12.6526 + 3.39025i −0.514826 + 0.137947i
\(605\) −11.4084 + 3.05688i −0.463819 + 0.124280i
\(606\) 0 0
\(607\) 22.1458 + 12.7859i 0.898871 + 0.518964i 0.876834 0.480793i \(-0.159651\pi\)
0.0220376 + 0.999757i \(0.492985\pi\)
\(608\) −6.59615 11.4249i −0.267509 0.463339i
\(609\) 0 0
\(610\) 4.04291i 0.163693i
\(611\) 26.2889 + 5.40839i 1.06353 + 0.218800i
\(612\) 0 0
\(613\) −6.84627 + 25.5506i −0.276518 + 1.03198i 0.678299 + 0.734786i \(0.262718\pi\)
−0.954817 + 0.297194i \(0.903949\pi\)
\(614\) 2.62767 1.51708i 0.106044 0.0612245i
\(615\) 0 0
\(616\) −7.24974 7.01933i −0.292100 0.282817i
\(617\) 41.2766 11.0600i 1.66173 0.445260i 0.698870 0.715249i \(-0.253687\pi\)
0.962864 + 0.269988i \(0.0870199\pi\)
\(618\) 0 0
\(619\) 7.36404 + 7.36404i 0.295986 + 0.295986i 0.839439 0.543453i \(-0.182884\pi\)
−0.543453 + 0.839439i \(0.682884\pi\)
\(620\) −2.32050 + 4.01922i −0.0931935 + 0.161416i
\(621\) 0 0
\(622\) −0.937855 + 3.50012i −0.0376046 + 0.140342i
\(623\) −2.22156 + 0.0358728i −0.0890050 + 0.00143722i
\(624\) 0 0
\(625\) 4.88945 0.195578
\(626\) 5.22738 + 1.40067i 0.208928 + 0.0559822i
\(627\) 0 0
\(628\) −16.6845 + 28.8983i −0.665782 + 1.15317i
\(629\) 15.6541 15.6541i 0.624169 0.624169i
\(630\) 0 0
\(631\) −3.47681 12.9756i −0.138410 0.516552i −0.999961 0.00888079i \(-0.997173\pi\)
0.861551 0.507671i \(-0.169494\pi\)
\(632\) −5.65758 + 5.65758i −0.225046 + 0.225046i
\(633\) 0 0
\(634\) −5.17644 + 2.98862i −0.205583 + 0.118693i
\(635\) −2.53434 + 9.45828i −0.100572 + 0.375340i
\(636\) 0 0
\(637\) 10.5765 22.9159i 0.419056 0.907960i
\(638\) 5.14927 0.203862
\(639\) 0 0
\(640\) 8.93765 5.16016i 0.353292 0.203973i
\(641\) 9.03607 + 5.21698i 0.356903 + 0.206058i 0.667722 0.744411i \(-0.267270\pi\)
−0.310818 + 0.950469i \(0.600603\pi\)
\(642\) 0 0
\(643\) −2.33827 8.72656i −0.0922125 0.344142i 0.904370 0.426750i \(-0.140342\pi\)
−0.996582 + 0.0826083i \(0.973675\pi\)
\(644\) −3.04007 10.6545i −0.119795 0.419846i
\(645\) 0 0
\(646\) 4.30225 7.45171i 0.169270 0.293184i
\(647\) 4.86550 + 8.42729i 0.191283 + 0.331311i 0.945676 0.325112i \(-0.105402\pi\)
−0.754393 + 0.656423i \(0.772069\pi\)
\(648\) 0 0
\(649\) −39.0974 −1.53471
\(650\) 2.01376 0.668905i 0.0789863 0.0262366i
\(651\) 0 0
\(652\) −9.85322 + 36.7727i −0.385882 + 1.44013i
\(653\) −19.3917 33.5874i −0.758855 1.31437i −0.943435 0.331557i \(-0.892426\pi\)
0.184580 0.982817i \(-0.440907\pi\)
\(654\) 0 0
\(655\) 4.06217 + 4.06217i 0.158722 + 0.158722i
\(656\) −1.36821 5.10623i −0.0534196 0.199365i
\(657\) 0 0
\(658\) −3.16113 3.06066i −0.123233 0.119317i
\(659\) −16.5452 + 28.6571i −0.644509 + 1.11632i 0.339905 + 0.940460i \(0.389605\pi\)
−0.984415 + 0.175863i \(0.943728\pi\)
\(660\) 0 0
\(661\) 3.34087 12.4683i 0.129945 0.484960i −0.870023 0.493011i \(-0.835896\pi\)
0.999968 + 0.00805129i \(0.00256283\pi\)
\(662\) 3.22860i 0.125483i
\(663\) 0 0
\(664\) 1.41118i 0.0547645i
\(665\) −5.03635 + 20.0878i −0.195301 + 0.778971i
\(666\) 0 0
\(667\) 9.91794 + 5.72612i 0.384024 + 0.221716i
\(668\) 19.5194 19.5194i 0.755229 0.755229i
\(669\) 0 0
\(670\) 1.64329 0.440319i 0.0634859 0.0170110i
\(671\) 35.9554 + 35.9554i 1.38804 + 1.38804i
\(672\) 0 0
\(673\) 22.5255 13.0051i 0.868295 0.501310i 0.00151340 0.999999i \(-0.499518\pi\)
0.866781 + 0.498689i \(0.166185\pi\)
\(674\) −1.11250 0.298092i −0.0428517 0.0114821i
\(675\) 0 0
\(676\) 20.3128 15.1680i 0.781262 0.583386i
\(677\) 41.0161i 1.57638i 0.615434 + 0.788188i \(0.288981\pi\)
−0.615434 + 0.788188i \(0.711019\pi\)
\(678\) 0 0
\(679\) −38.2240 + 22.8993i −1.46690 + 0.878795i
\(680\) 8.89631 + 5.13629i 0.341158 + 0.196968i
\(681\) 0 0
\(682\) −0.386679 1.44311i −0.0148067 0.0552594i
\(683\) −8.69145 32.4369i −0.332569 1.24116i −0.906481 0.422247i \(-0.861241\pi\)
0.573912 0.818917i \(-0.305425\pi\)
\(684\) 0 0
\(685\) 0.0408491 + 0.0235842i 0.00156076 + 0.000901107i
\(686\) −3.47893 + 2.23990i −0.132826 + 0.0855197i
\(687\) 0 0
\(688\) 28.1591i 1.07356i
\(689\) −39.6870 + 26.1437i −1.51195 + 0.995994i
\(690\) 0 0
\(691\) 33.3878 + 8.94624i 1.27013 + 0.340331i 0.830082 0.557642i \(-0.188294\pi\)
0.440051 + 0.897973i \(0.354960\pi\)
\(692\) 32.6305 18.8392i 1.24043 0.716160i
\(693\) 0 0
\(694\) −3.76020 3.76020i −0.142735 0.142735i
\(695\) −4.89884 + 1.31264i −0.185823 + 0.0497912i
\(696\) 0 0
\(697\) 7.63956 7.63956i 0.289369 0.289369i
\(698\) 2.36628 + 1.36617i 0.0895651 + 0.0517104i
\(699\) 0 0
\(700\) 13.1833 + 3.30526i 0.498280 + 0.124927i
\(701\) 4.79362i 0.181053i 0.995894 + 0.0905263i \(0.0288549\pi\)
−0.995894 + 0.0905263i \(0.971145\pi\)
\(702\) 0 0
\(703\) 14.8867i 0.561461i
\(704\) 7.63649 28.4998i 0.287811 1.07413i
\(705\) 0 0
\(706\) 1.91032 3.30876i 0.0718957 0.124527i
\(707\) 20.1921 20.8549i 0.759402 0.784329i
\(708\) 0 0
\(709\) 2.76549 + 10.3209i 0.103860 + 0.387611i 0.998213 0.0597505i \(-0.0190305\pi\)
−0.894353 + 0.447361i \(0.852364\pi\)
\(710\) −1.32303 1.32303i −0.0496524 0.0496524i
\(711\) 0 0
\(712\) 0.370552 + 0.641814i 0.0138870 + 0.0240530i
\(713\) 0.859994 3.20954i 0.0322070 0.120198i
\(714\) 0 0
\(715\) −10.7413 + 21.4263i −0.401703 + 0.801300i
\(716\) −8.01890 −0.299680
\(717\) 0 0
\(718\) −2.30976 4.00062i −0.0861995 0.149302i
\(719\) 14.9272 25.8547i 0.556690 0.964216i −0.441080 0.897468i \(-0.645404\pi\)
0.997770 0.0667479i \(-0.0212623\pi\)
\(720\) 0 0
\(721\) 3.41361 + 11.9637i 0.127129 + 0.445550i
\(722\) −0.398890 1.48868i −0.0148452 0.0554029i
\(723\) 0 0
\(724\) 3.54065 + 2.04420i 0.131587 + 0.0759720i
\(725\) −12.1661 + 7.02412i −0.451839 + 0.260869i
\(726\) 0 0
\(727\) 41.2241 1.52892 0.764459 0.644672i \(-0.223006\pi\)
0.764459 + 0.644672i \(0.223006\pi\)
\(728\) −8.39478 + 0.631188i −0.311131 + 0.0233934i
\(729\) 0 0
\(730\) 1.01175 3.77589i 0.0374464 0.139752i
\(731\) 49.8398 28.7750i 1.84339 1.06428i
\(732\) 0 0
\(733\) 14.3345 14.3345i 0.529456 0.529456i −0.390954 0.920410i \(-0.627855\pi\)
0.920410 + 0.390954i \(0.127855\pi\)
\(734\) −0.0267847 0.0999617i −0.000988640 0.00368965i
\(735\) 0 0
\(736\) −3.93636 + 3.93636i −0.145096 + 0.145096i
\(737\) 10.6986 18.5305i 0.394087 0.682579i
\(738\) 0 0
\(739\) 24.4381 + 6.54818i 0.898972 + 0.240879i 0.678575 0.734532i \(-0.262598\pi\)
0.220397 + 0.975410i \(0.429265\pi\)
\(740\) 8.77402 0.322539
\(741\) 0 0
\(742\) 7.79007 0.125791i 0.285982 0.00461793i
\(743\) −10.9162 + 40.7397i −0.400476 + 1.49460i 0.411774 + 0.911286i \(0.364909\pi\)
−0.812250 + 0.583310i \(0.801757\pi\)
\(744\) 0 0
\(745\) 3.60387 6.24209i 0.132036 0.228693i
\(746\) −0.110241 0.110241i −0.00403621 0.00403621i
\(747\) 0 0
\(748\) 61.6106 16.5085i 2.25271 0.603611i
\(749\) −24.1203 + 24.9120i −0.881335 + 0.910265i
\(750\) 0 0
\(751\) −6.23654 + 3.60067i −0.227574 + 0.131390i −0.609453 0.792823i \(-0.708611\pi\)
0.381878 + 0.924213i \(0.375277\pi\)
\(752\) 7.13433 26.6257i 0.260162 0.970938i
\(753\) 0 0
\(754\) 2.85350 3.21112i 0.103918 0.116942i
\(755\) 10.3315i 0.376004i
\(756\) 0 0
\(757\) −11.5449 19.9964i −0.419607 0.726780i 0.576293 0.817243i \(-0.304499\pi\)
−0.995900 + 0.0904628i \(0.971165\pi\)
\(758\) 1.38385 + 0.798968i 0.0502638 + 0.0290198i
\(759\) 0 0
\(760\) 6.67233 1.78785i 0.242031 0.0648520i
\(761\) −5.76843 + 1.54565i −0.209105 + 0.0560296i −0.361851 0.932236i \(-0.617855\pi\)
0.152746 + 0.988266i \(0.451188\pi\)
\(762\) 0 0
\(763\) −1.58563 + 2.85176i −0.0574038 + 0.103241i
\(764\) −14.2562 + 8.23082i −0.515771 + 0.297780i
\(765\) 0 0
\(766\) −0.428649 −0.0154877
\(767\) −21.6660 + 24.3814i −0.782315 + 0.880362i
\(768\) 0 0
\(769\) −32.9326 8.82426i −1.18758 0.318211i −0.389650 0.920963i \(-0.627404\pi\)
−0.797929 + 0.602752i \(0.794071\pi\)
\(770\) 3.37071 2.01933i 0.121472 0.0727717i
\(771\) 0 0
\(772\) 2.80726 + 2.80726i 0.101036 + 0.101036i
\(773\) 0.0200118 + 0.0746850i 0.000719774 + 0.00268623i 0.966285 0.257476i \(-0.0828907\pi\)
−0.965565 + 0.260162i \(0.916224\pi\)
\(774\) 0 0
\(775\) 2.88214 + 2.88214i 0.103530 + 0.103530i
\(776\) 12.8713 + 7.43127i 0.462054 + 0.266767i
\(777\) 0 0
\(778\) −1.33164 0.356813i −0.0477417 0.0127924i
\(779\) 7.26504i 0.260297i
\(780\) 0 0
\(781\) −23.5326 −0.842063
\(782\) −3.50718 0.939747i −0.125417 0.0336053i
\(783\) 0 0
\(784\) −22.8551 12.2290i −0.816253 0.436750i
\(785\) −18.6105 18.6105i −0.664236 0.664236i
\(786\) 0 0
\(787\) −13.7109 + 3.67383i −0.488742 + 0.130958i −0.494770 0.869024i \(-0.664748\pi\)
0.00602847 + 0.999982i \(0.498081\pi\)
\(788\) −18.4866 + 18.4866i