Properties

Label 171.3.p.f.46.3
Level $171$
Weight $3$
Character 171.46
Analytic conductor $4.659$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 171.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.65941252056\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.19163381760000.1
Defining polynomial: \( x^{8} - 14x^{6} + 177x^{4} - 266x^{2} + 361 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 46.3
Root \(1.06868 + 0.617004i\) of defining polynomial
Character \(\chi\) \(=\) 171.46
Dual form 171.3.p.f.145.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.06868 + 0.617004i) q^{2} +(-1.23861 - 2.14534i) q^{4} +(-4.08850 + 7.08149i) q^{5} -10.4772 q^{7} -7.99294i q^{8} +O(q^{10})\) \(q+(1.06868 + 0.617004i) q^{2} +(-1.23861 - 2.14534i) q^{4} +(-4.08850 + 7.08149i) q^{5} -10.4772 q^{7} -7.99294i q^{8} +(-8.73861 + 5.04524i) q^{10} -3.90227 q^{11} +(-2.02277 + 1.16785i) q^{13} +(-11.1968 - 6.46449i) q^{14} +(-0.0227744 + 0.0394465i) q^{16} +(2.13736 - 3.70202i) q^{17} +(-17.4772 + 7.45296i) q^{19} +20.2563 q^{20} +(-4.17029 - 2.40772i) q^{22} +(20.0701 + 34.7623i) q^{23} +(-20.9317 - 36.2547i) q^{25} -2.88227 q^{26} +(12.9772 + 22.4772i) q^{28} +(10.6868 - 6.17004i) q^{29} +22.2148i q^{31} +(-27.7370 + 16.0140i) q^{32} +(4.56832 - 2.63752i) q^{34} +(42.8361 - 74.1944i) q^{35} -62.2749i q^{37} +(-23.2761 - 2.81867i) q^{38} +(56.6020 + 32.6792i) q^{40} +(-44.7873 - 25.8579i) q^{41} +(6.67029 - 11.5533i) q^{43} +(4.83341 + 8.37171i) q^{44} +49.5332i q^{46} +(24.1586 + 41.8438i) q^{47} +60.7723 q^{49} -51.6597i q^{50} +(5.01087 + 2.89303i) q^{52} +(-67.7396 + 39.1095i) q^{53} +(15.9545 - 27.6339i) q^{55} +83.7439i q^{56} +15.2277 q^{58} +(82.7011 + 47.7475i) q^{59} +(18.8861 + 32.7117i) q^{61} +(-13.7066 + 23.7406i) q^{62} -39.3406 q^{64} -19.0990i q^{65} +(-52.6247 + 30.3829i) q^{67} -10.5895 q^{68} +(91.5564 - 52.8601i) q^{70} +(-78.8877 - 45.5459i) q^{71} +(41.7950 - 72.3911i) q^{73} +(38.4239 - 66.5521i) q^{74} +(37.6366 + 28.2633i) q^{76} +40.8850 q^{77} +(0.466357 + 0.269251i) q^{79} +(-0.186227 - 0.322554i) q^{80} +(-31.9089 - 55.2678i) q^{82} -54.0816 q^{83} +(17.4772 + 30.2714i) q^{85} +(14.2568 - 8.23119i) q^{86} +31.1907i q^{88} +(-81.6811 + 47.1586i) q^{89} +(21.1931 - 12.2358i) q^{91} +(49.7180 - 86.1142i) q^{92} +59.6237i q^{94} +(18.6776 - 154.236i) q^{95} +(-126.909 - 73.2709i) q^{97} +(64.9462 + 37.4967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{4} - 40 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{4} - 40 q^{7} - 48 q^{10} - 60 q^{13} - 44 q^{16} - 96 q^{19} + 120 q^{22} - 36 q^{25} + 60 q^{28} + 168 q^{34} + 168 q^{40} - 100 q^{43} + 48 q^{49} - 420 q^{52} + 40 q^{55} + 560 q^{58} - 68 q^{61} - 8 q^{64} - 180 q^{67} + 360 q^{70} - 60 q^{73} + 564 q^{76} + 420 q^{79} - 80 q^{82} + 96 q^{85} + 60 q^{91} - 840 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06868 + 0.617004i 0.534341 + 0.308502i 0.742782 0.669533i \(-0.233506\pi\)
−0.208441 + 0.978035i \(0.566839\pi\)
\(3\) 0 0
\(4\) −1.23861 2.14534i −0.309653 0.536335i
\(5\) −4.08850 + 7.08149i −0.817700 + 1.41630i 0.0896726 + 0.995971i \(0.471418\pi\)
−0.907373 + 0.420327i \(0.861915\pi\)
\(6\) 0 0
\(7\) −10.4772 −1.49675 −0.748373 0.663278i \(-0.769165\pi\)
−0.748373 + 0.663278i \(0.769165\pi\)
\(8\) 7.99294i 0.999118i
\(9\) 0 0
\(10\) −8.73861 + 5.04524i −0.873861 + 0.504524i
\(11\) −3.90227 −0.354752 −0.177376 0.984143i \(-0.556761\pi\)
−0.177376 + 0.984143i \(0.556761\pi\)
\(12\) 0 0
\(13\) −2.02277 + 1.16785i −0.155598 + 0.0898346i −0.575777 0.817607i \(-0.695300\pi\)
0.420179 + 0.907441i \(0.361967\pi\)
\(14\) −11.1968 6.46449i −0.799773 0.461749i
\(15\) 0 0
\(16\) −0.0227744 + 0.0394465i −0.00142340 + 0.00246540i
\(17\) 2.13736 3.70202i 0.125727 0.217766i −0.796290 0.604915i \(-0.793207\pi\)
0.922017 + 0.387149i \(0.126540\pi\)
\(18\) 0 0
\(19\) −17.4772 + 7.45296i −0.919854 + 0.392261i
\(20\) 20.2563 1.01281
\(21\) 0 0
\(22\) −4.17029 2.40772i −0.189559 0.109442i
\(23\) 20.0701 + 34.7623i 0.872611 + 1.51141i 0.859286 + 0.511495i \(0.170908\pi\)
0.0133248 + 0.999911i \(0.495758\pi\)
\(24\) 0 0
\(25\) −20.9317 36.2547i −0.837267 1.45019i
\(26\) −2.88227 −0.110857
\(27\) 0 0
\(28\) 12.9772 + 22.4772i 0.463472 + 0.802758i
\(29\) 10.6868 6.17004i 0.368511 0.212760i −0.304297 0.952577i \(-0.598421\pi\)
0.672808 + 0.739817i \(0.265088\pi\)
\(30\) 0 0
\(31\) 22.2148i 0.716608i 0.933605 + 0.358304i \(0.116645\pi\)
−0.933605 + 0.358304i \(0.883355\pi\)
\(32\) −27.7370 + 16.0140i −0.866783 + 0.500437i
\(33\) 0 0
\(34\) 4.56832 2.63752i 0.134362 0.0775742i
\(35\) 42.8361 74.1944i 1.22389 2.11984i
\(36\) 0 0
\(37\) 62.2749i 1.68311i −0.540174 0.841553i \(-0.681642\pi\)
0.540174 0.841553i \(-0.318358\pi\)
\(38\) −23.2761 2.81867i −0.612529 0.0741756i
\(39\) 0 0
\(40\) 56.6020 + 32.6792i 1.41505 + 0.816979i
\(41\) −44.7873 25.8579i −1.09237 0.630682i −0.158166 0.987413i \(-0.550558\pi\)
−0.934207 + 0.356731i \(0.883891\pi\)
\(42\) 0 0
\(43\) 6.67029 11.5533i 0.155123 0.268681i −0.777981 0.628288i \(-0.783756\pi\)
0.933104 + 0.359607i \(0.117089\pi\)
\(44\) 4.83341 + 8.37171i 0.109850 + 0.190266i
\(45\) 0 0
\(46\) 49.5332i 1.07681i
\(47\) 24.1586 + 41.8438i 0.514012 + 0.890294i 0.999868 + 0.0162556i \(0.00517456\pi\)
−0.485856 + 0.874039i \(0.661492\pi\)
\(48\) 0 0
\(49\) 60.7723 1.24025
\(50\) 51.6597i 1.03319i
\(51\) 0 0
\(52\) 5.01087 + 2.89303i 0.0963629 + 0.0556351i
\(53\) −67.7396 + 39.1095i −1.27811 + 0.737915i −0.976500 0.215518i \(-0.930856\pi\)
−0.301606 + 0.953433i \(0.597523\pi\)
\(54\) 0 0
\(55\) 15.9545 27.6339i 0.290081 0.502435i
\(56\) 83.7439i 1.49543i
\(57\) 0 0
\(58\) 15.2277 0.262547
\(59\) 82.7011 + 47.7475i 1.40171 + 0.809280i 0.994569 0.104083i \(-0.0331908\pi\)
0.407146 + 0.913363i \(0.366524\pi\)
\(60\) 0 0
\(61\) 18.8861 + 32.7117i 0.309609 + 0.536258i 0.978277 0.207303i \(-0.0664686\pi\)
−0.668668 + 0.743561i \(0.733135\pi\)
\(62\) −13.7066 + 23.7406i −0.221075 + 0.382913i
\(63\) 0 0
\(64\) −39.3406 −0.614697
\(65\) 19.0990i 0.293831i
\(66\) 0 0
\(67\) −52.6247 + 30.3829i −0.785444 + 0.453476i −0.838356 0.545123i \(-0.816483\pi\)
0.0529122 + 0.998599i \(0.483150\pi\)
\(68\) −10.5895 −0.155727
\(69\) 0 0
\(70\) 91.5564 52.8601i 1.30795 0.755145i
\(71\) −78.8877 45.5459i −1.11110 0.641491i −0.171982 0.985100i \(-0.555017\pi\)
−0.939113 + 0.343609i \(0.888350\pi\)
\(72\) 0 0
\(73\) 41.7950 72.3911i 0.572535 0.991659i −0.423770 0.905770i \(-0.639294\pi\)
0.996305 0.0858893i \(-0.0273731\pi\)
\(74\) 38.4239 66.5521i 0.519241 0.899353i
\(75\) 0 0
\(76\) 37.6366 + 28.2633i 0.495219 + 0.371885i
\(77\) 40.8850 0.530974
\(78\) 0 0
\(79\) 0.466357 + 0.269251i 0.00590325 + 0.00340825i 0.502949 0.864316i \(-0.332248\pi\)
−0.497045 + 0.867724i \(0.665582\pi\)
\(80\) −0.186227 0.322554i −0.00232783 0.00403192i
\(81\) 0 0
\(82\) −31.9089 55.2678i −0.389133 0.673998i
\(83\) −54.0816 −0.651586 −0.325793 0.945441i \(-0.605631\pi\)
−0.325793 + 0.945441i \(0.605631\pi\)
\(84\) 0 0
\(85\) 17.4772 + 30.2714i 0.205614 + 0.356135i
\(86\) 14.2568 8.23119i 0.165777 0.0957115i
\(87\) 0 0
\(88\) 31.1907i 0.354439i
\(89\) −81.6811 + 47.1586i −0.917766 + 0.529872i −0.882922 0.469521i \(-0.844427\pi\)
−0.0348441 + 0.999393i \(0.511093\pi\)
\(90\) 0 0
\(91\) 21.1931 12.2358i 0.232891 0.134460i
\(92\) 49.7180 86.1142i 0.540414 0.936024i
\(93\) 0 0
\(94\) 59.6237i 0.634294i
\(95\) 18.6776 154.236i 0.196606 1.62354i
\(96\) 0 0
\(97\) −126.909 73.2709i −1.30834 0.755370i −0.326520 0.945190i \(-0.605876\pi\)
−0.981819 + 0.189820i \(0.939209\pi\)
\(98\) 64.9462 + 37.4967i 0.662716 + 0.382619i
\(99\) 0 0
\(100\) −51.8525 + 89.8111i −0.518525 + 0.898111i
\(101\) 59.3764 + 102.843i 0.587885 + 1.01825i 0.994509 + 0.104651i \(0.0333725\pi\)
−0.406624 + 0.913596i \(0.633294\pi\)
\(102\) 0 0
\(103\) 26.1248i 0.253639i 0.991926 + 0.126819i \(0.0404769\pi\)
−0.991926 + 0.126819i \(0.959523\pi\)
\(104\) 9.33456 + 16.1679i 0.0897553 + 0.155461i
\(105\) 0 0
\(106\) −96.5228 −0.910592
\(107\) 120.708i 1.12811i 0.825737 + 0.564056i \(0.190760\pi\)
−0.825737 + 0.564056i \(0.809240\pi\)
\(108\) 0 0
\(109\) −91.9545 53.0899i −0.843619 0.487064i 0.0148739 0.999889i \(-0.495265\pi\)
−0.858493 + 0.512826i \(0.828599\pi\)
\(110\) 34.1005 19.6879i 0.310004 0.178981i
\(111\) 0 0
\(112\) 0.238613 0.413289i 0.00213047 0.00369008i
\(113\) 101.609i 0.899194i −0.893232 0.449597i \(-0.851568\pi\)
0.893232 0.449597i \(-0.148432\pi\)
\(114\) 0 0
\(115\) −328.226 −2.85414
\(116\) −26.4737 15.2846i −0.228221 0.131764i
\(117\) 0 0
\(118\) 58.9208 + 102.054i 0.499329 + 0.864863i
\(119\) −22.3936 + 38.7869i −0.188182 + 0.325941i
\(120\) 0 0
\(121\) −105.772 −0.874151
\(122\) 46.6112i 0.382059i
\(123\) 0 0
\(124\) 47.6584 27.5156i 0.384342 0.221900i
\(125\) 137.892 1.10313
\(126\) 0 0
\(127\) 95.7267 55.2678i 0.753754 0.435180i −0.0732950 0.997310i \(-0.523351\pi\)
0.827049 + 0.562130i \(0.190018\pi\)
\(128\) 68.9056 + 39.7827i 0.538325 + 0.310802i
\(129\) 0 0
\(130\) 11.7842 20.4108i 0.0906474 0.157006i
\(131\) −28.1582 + 48.7714i −0.214948 + 0.372301i −0.953256 0.302162i \(-0.902292\pi\)
0.738309 + 0.674463i \(0.235625\pi\)
\(132\) 0 0
\(133\) 183.113 78.0863i 1.37679 0.587115i
\(134\) −74.9855 −0.559593
\(135\) 0 0
\(136\) −29.5901 17.0838i −0.217574 0.125616i
\(137\) −69.9658 121.184i −0.510700 0.884558i −0.999923 0.0123992i \(-0.996053\pi\)
0.489224 0.872158i \(-0.337280\pi\)
\(138\) 0 0
\(139\) 85.1475 + 147.480i 0.612572 + 1.06101i 0.990805 + 0.135296i \(0.0431984\pi\)
−0.378233 + 0.925710i \(0.623468\pi\)
\(140\) −212.230 −1.51593
\(141\) 0 0
\(142\) −56.2039 97.3481i −0.395802 0.685550i
\(143\) 7.89342 4.55727i 0.0551987 0.0318690i
\(144\) 0 0
\(145\) 100.905i 0.695895i
\(146\) 89.3312 51.5754i 0.611857 0.353256i
\(147\) 0 0
\(148\) −133.601 + 77.1345i −0.902709 + 0.521179i
\(149\) −59.4652 + 102.997i −0.399096 + 0.691254i −0.993615 0.112828i \(-0.964009\pi\)
0.594519 + 0.804082i \(0.297343\pi\)
\(150\) 0 0
\(151\) 150.898i 0.999322i −0.866221 0.499661i \(-0.833458\pi\)
0.866221 0.499661i \(-0.166542\pi\)
\(152\) 59.5711 + 139.694i 0.391915 + 0.919043i
\(153\) 0 0
\(154\) 43.6931 + 25.2262i 0.283721 + 0.163807i
\(155\) −157.314 90.8254i −1.01493 0.585970i
\(156\) 0 0
\(157\) 5.11387 8.85749i 0.0325724 0.0564171i −0.849280 0.527943i \(-0.822963\pi\)
0.881852 + 0.471526i \(0.156297\pi\)
\(158\) 0.332258 + 0.575488i 0.00210290 + 0.00364233i
\(159\) 0 0
\(160\) 261.893i 1.63683i
\(161\) −210.278 364.213i −1.30608 2.26219i
\(162\) 0 0
\(163\) −42.8851 −0.263099 −0.131549 0.991310i \(-0.541995\pi\)
−0.131549 + 0.991310i \(0.541995\pi\)
\(164\) 128.112i 0.781170i
\(165\) 0 0
\(166\) −57.7961 33.3686i −0.348169 0.201016i
\(167\) −1.48133 + 0.855246i −0.00887024 + 0.00512123i −0.504429 0.863453i \(-0.668297\pi\)
0.495558 + 0.868575i \(0.334963\pi\)
\(168\) 0 0
\(169\) −81.7723 + 141.634i −0.483860 + 0.838069i
\(170\) 43.1341i 0.253730i
\(171\) 0 0
\(172\) −33.0476 −0.192137
\(173\) 176.089 + 101.665i 1.01786 + 0.587660i 0.913482 0.406879i \(-0.133383\pi\)
0.104374 + 0.994538i \(0.466716\pi\)
\(174\) 0 0
\(175\) 219.306 + 379.849i 1.25318 + 2.17057i
\(176\) 0.0888721 0.153931i 0.000504955 0.000874607i
\(177\) 0 0
\(178\) −116.388 −0.653866
\(179\) 34.9725i 0.195377i 0.995217 + 0.0976885i \(0.0311449\pi\)
−0.995217 + 0.0976885i \(0.968855\pi\)
\(180\) 0 0
\(181\) 100.295 57.9054i 0.554116 0.319919i −0.196664 0.980471i \(-0.563011\pi\)
0.750781 + 0.660552i \(0.229678\pi\)
\(182\) 30.1982 0.165924
\(183\) 0 0
\(184\) 277.854 160.419i 1.51007 0.871841i
\(185\) 440.999 + 254.611i 2.38378 + 1.37628i
\(186\) 0 0
\(187\) −8.34058 + 14.4463i −0.0446020 + 0.0772530i
\(188\) 59.8462 103.657i 0.318331 0.551365i
\(189\) 0 0
\(190\) 115.125 153.305i 0.605920 0.806870i
\(191\) −175.247 −0.917523 −0.458761 0.888559i \(-0.651707\pi\)
−0.458761 + 0.888559i \(0.651707\pi\)
\(192\) 0 0
\(193\) 290.884 + 167.942i 1.50717 + 0.870166i 0.999965 + 0.00834091i \(0.00265502\pi\)
0.507206 + 0.861825i \(0.330678\pi\)
\(194\) −90.4168 156.607i −0.466066 0.807250i
\(195\) 0 0
\(196\) −75.2733 130.377i −0.384047 0.665190i
\(197\) 243.998 1.23857 0.619284 0.785167i \(-0.287423\pi\)
0.619284 + 0.785167i \(0.287423\pi\)
\(198\) 0 0
\(199\) 169.738 + 293.994i 0.852953 + 1.47736i 0.878531 + 0.477685i \(0.158524\pi\)
−0.0255788 + 0.999673i \(0.508143\pi\)
\(200\) −289.782 + 167.306i −1.44891 + 0.836529i
\(201\) 0 0
\(202\) 146.542i 0.725454i
\(203\) −111.968 + 64.6449i −0.551568 + 0.318448i
\(204\) 0 0
\(205\) 366.226 211.440i 1.78647 1.03142i
\(206\) −16.1191 + 27.9191i −0.0782481 + 0.135530i
\(207\) 0 0
\(208\) 0.106388i 0.000511483i
\(209\) 68.2009 29.0835i 0.326320 0.139155i
\(210\) 0 0
\(211\) −85.0782 49.1199i −0.403214 0.232796i 0.284656 0.958630i \(-0.408121\pi\)
−0.687870 + 0.725834i \(0.741454\pi\)
\(212\) 167.806 + 96.8830i 0.791539 + 0.456995i
\(213\) 0 0
\(214\) −74.4772 + 128.998i −0.348024 + 0.602796i
\(215\) 54.5430 + 94.4712i 0.253688 + 0.439401i
\(216\) 0 0
\(217\) 232.750i 1.07258i
\(218\) −65.5134 113.472i −0.300520 0.520516i
\(219\) 0 0
\(220\) −79.0455 −0.359298
\(221\) 9.98447i 0.0451786i
\(222\) 0 0
\(223\) 57.3535 + 33.1131i 0.257191 + 0.148489i 0.623052 0.782180i \(-0.285892\pi\)
−0.365862 + 0.930669i \(0.619226\pi\)
\(224\) 290.607 167.782i 1.29735 0.749028i
\(225\) 0 0
\(226\) 62.6931 108.588i 0.277403 0.480476i
\(227\) 375.221i 1.65296i −0.562968 0.826479i \(-0.690341\pi\)
0.562968 0.826479i \(-0.309659\pi\)
\(228\) 0 0
\(229\) 40.4534 0.176652 0.0883262 0.996092i \(-0.471848\pi\)
0.0883262 + 0.996092i \(0.471848\pi\)
\(230\) −350.769 202.516i −1.52508 0.880506i
\(231\) 0 0
\(232\) −49.3168 85.4191i −0.212572 0.368186i
\(233\) 134.459 232.890i 0.577078 0.999529i −0.418734 0.908109i \(-0.637526\pi\)
0.995812 0.0914198i \(-0.0291405\pi\)
\(234\) 0 0
\(235\) −395.089 −1.68123
\(236\) 236.563i 1.00238i
\(237\) 0 0
\(238\) −47.8634 + 27.6339i −0.201107 + 0.116109i
\(239\) 58.1786 0.243425 0.121713 0.992565i \(-0.461161\pi\)
0.121713 + 0.992565i \(0.461161\pi\)
\(240\) 0 0
\(241\) 125.159 72.2608i 0.519334 0.299837i −0.217328 0.976099i \(-0.569734\pi\)
0.736662 + 0.676261i \(0.236401\pi\)
\(242\) −113.037 65.2619i −0.467095 0.269677i
\(243\) 0 0
\(244\) 46.7852 81.0343i 0.191743 0.332108i
\(245\) −248.467 + 430.358i −1.01415 + 1.75656i
\(246\) 0 0
\(247\) 26.6486 35.4864i 0.107889 0.143670i
\(248\) 177.562 0.715976
\(249\) 0 0
\(250\) 147.362 + 85.0797i 0.589449 + 0.340319i
\(251\) 46.8273 + 81.1072i 0.186563 + 0.323136i 0.944102 0.329653i \(-0.106932\pi\)
−0.757539 + 0.652790i \(0.773599\pi\)
\(252\) 0 0
\(253\) −78.3188 135.652i −0.309561 0.536175i
\(254\) 136.402 0.537015
\(255\) 0 0
\(256\) 127.773 + 221.310i 0.499114 + 0.864492i
\(257\) −358.565 + 207.018i −1.39519 + 0.805516i −0.993884 0.110427i \(-0.964778\pi\)
−0.401310 + 0.915942i \(0.631445\pi\)
\(258\) 0 0
\(259\) 652.469i 2.51918i
\(260\) −40.9739 + 23.6563i −0.157592 + 0.0909857i
\(261\) 0 0
\(262\) −60.1843 + 34.7474i −0.229711 + 0.132624i
\(263\) −85.7696 + 148.557i −0.326120 + 0.564857i −0.981738 0.190236i \(-0.939075\pi\)
0.655618 + 0.755093i \(0.272408\pi\)
\(264\) 0 0
\(265\) 639.597i 2.41357i
\(266\) 243.869 + 29.5319i 0.916800 + 0.111022i
\(267\) 0 0
\(268\) 130.363 + 75.2653i 0.486430 + 0.280841i
\(269\) −5.85341 3.37947i −0.0217599 0.0125631i 0.489081 0.872239i \(-0.337332\pi\)
−0.510840 + 0.859676i \(0.670666\pi\)
\(270\) 0 0
\(271\) −123.499 + 213.906i −0.455716 + 0.789323i −0.998729 0.0504013i \(-0.983950\pi\)
0.543013 + 0.839724i \(0.317283\pi\)
\(272\) 0.0973545 + 0.168623i 0.000357921 + 0.000619937i
\(273\) 0 0
\(274\) 172.677i 0.630207i
\(275\) 81.6811 + 141.476i 0.297022 + 0.514458i
\(276\) 0 0
\(277\) 67.6356 0.244172 0.122086 0.992520i \(-0.461042\pi\)
0.122086 + 0.992520i \(0.461042\pi\)
\(278\) 210.145i 0.755918i
\(279\) 0 0
\(280\) −593.032 342.387i −2.11797 1.22281i
\(281\) −22.1270 + 12.7750i −0.0787439 + 0.0454628i −0.538855 0.842399i \(-0.681143\pi\)
0.460111 + 0.887861i \(0.347810\pi\)
\(282\) 0 0
\(283\) 0.477226 0.826579i 0.00168631 0.00292077i −0.865181 0.501460i \(-0.832797\pi\)
0.866867 + 0.498539i \(0.166130\pi\)
\(284\) 225.655i 0.794559i
\(285\) 0 0
\(286\) 11.2474 0.0393266
\(287\) 469.246 + 270.920i 1.63501 + 0.943971i
\(288\) 0 0
\(289\) 135.363 + 234.456i 0.468385 + 0.811267i
\(290\) −62.2586 + 107.835i −0.214685 + 0.371845i
\(291\) 0 0
\(292\) −207.071 −0.709149
\(293\) 297.002i 1.01366i −0.862046 0.506830i \(-0.830817\pi\)
0.862046 0.506830i \(-0.169183\pi\)
\(294\) 0 0
\(295\) −676.247 + 390.432i −2.29236 + 1.32350i
\(296\) −497.760 −1.68162
\(297\) 0 0
\(298\) −127.099 + 73.3806i −0.426506 + 0.246243i
\(299\) −81.1944 46.8776i −0.271553 0.156781i
\(300\) 0 0
\(301\) −69.8861 + 121.046i −0.232180 + 0.402147i
\(302\) 93.1044 161.262i 0.308293 0.533979i
\(303\) 0 0
\(304\) 0.104041 0.859152i 0.000342240 0.00282616i
\(305\) −308.864 −1.01267
\(306\) 0 0
\(307\) 47.8634 + 27.6339i 0.155907 + 0.0900128i 0.575924 0.817503i \(-0.304643\pi\)
−0.420017 + 0.907516i \(0.637976\pi\)
\(308\) −50.6407 87.7123i −0.164418 0.284780i
\(309\) 0 0
\(310\) −112.079 194.127i −0.361546 0.626216i
\(311\) −110.770 −0.356175 −0.178088 0.984015i \(-0.556991\pi\)
−0.178088 + 0.984015i \(0.556991\pi\)
\(312\) 0 0
\(313\) −105.727 183.124i −0.337785 0.585061i 0.646231 0.763142i \(-0.276344\pi\)
−0.984016 + 0.178081i \(0.943011\pi\)
\(314\) 10.9302 6.31056i 0.0348096 0.0200973i
\(315\) 0 0
\(316\) 1.33399i 0.00422150i
\(317\) 143.470 82.8324i 0.452587 0.261301i −0.256335 0.966588i \(-0.582515\pi\)
0.708922 + 0.705287i \(0.249182\pi\)
\(318\) 0 0
\(319\) −41.7029 + 24.0772i −0.130730 + 0.0754770i
\(320\) 160.844 278.590i 0.502637 0.870594i
\(321\) 0 0
\(322\) 518.970i 1.61171i
\(323\) −9.76417 + 80.6308i −0.0302296 + 0.249631i
\(324\) 0 0
\(325\) 84.6801 + 48.8901i 0.260554 + 0.150431i
\(326\) −45.8305 26.4603i −0.140584 0.0811664i
\(327\) 0 0
\(328\) −206.681 + 357.982i −0.630125 + 1.09141i
\(329\) −253.115 438.407i −0.769345 1.33255i
\(330\) 0 0
\(331\) 358.233i 1.08227i 0.840934 + 0.541137i \(0.182006\pi\)
−0.840934 + 0.541137i \(0.817994\pi\)
\(332\) 66.9862 + 116.024i 0.201766 + 0.349468i
\(333\) 0 0
\(334\) −2.11076 −0.00631964
\(335\) 496.882i 1.48323i
\(336\) 0 0
\(337\) −550.179 317.646i −1.63258 0.942570i −0.983294 0.182025i \(-0.941735\pi\)
−0.649285 0.760545i \(-0.724932\pi\)
\(338\) −174.777 + 100.908i −0.517092 + 0.298543i
\(339\) 0 0
\(340\) 43.2950 74.9892i 0.127338 0.220556i
\(341\) 86.6884i 0.254218i
\(342\) 0 0
\(343\) −123.341 −0.359594
\(344\) −92.3447 53.3153i −0.268444 0.154986i
\(345\) 0 0
\(346\) 125.455 + 217.295i 0.362588 + 0.628021i
\(347\) −74.7992 + 129.556i −0.215560 + 0.373360i −0.953446 0.301565i \(-0.902491\pi\)
0.737886 + 0.674926i \(0.235824\pi\)
\(348\) 0 0
\(349\) 211.863 0.607058 0.303529 0.952822i \(-0.401835\pi\)
0.303529 + 0.952822i \(0.401835\pi\)
\(350\) 541.250i 1.54643i
\(351\) 0 0
\(352\) 108.238 62.4910i 0.307493 0.177531i
\(353\) 154.974 0.439019 0.219509 0.975610i \(-0.429554\pi\)
0.219509 + 0.975610i \(0.429554\pi\)
\(354\) 0 0
\(355\) 645.065 372.429i 1.81709 1.04909i
\(356\) 202.343 + 116.823i 0.568378 + 0.328153i
\(357\) 0 0
\(358\) −21.5782 + 37.3745i −0.0602742 + 0.104398i
\(359\) 124.695 215.978i 0.347340 0.601610i −0.638436 0.769675i \(-0.720418\pi\)
0.985776 + 0.168064i \(0.0537517\pi\)
\(360\) 0 0
\(361\) 249.907 260.514i 0.692263 0.721646i
\(362\) 142.911 0.394783
\(363\) 0 0
\(364\) −52.5000 30.3109i −0.144231 0.0832717i
\(365\) 341.758 + 591.942i 0.936323 + 1.62176i
\(366\) 0 0
\(367\) −326.714 565.885i −0.890228 1.54192i −0.839601 0.543203i \(-0.817211\pi\)
−0.0506268 0.998718i \(-0.516122\pi\)
\(368\) −1.82834 −0.00496830
\(369\) 0 0
\(370\) 314.192 + 544.197i 0.849168 + 1.47080i
\(371\) 709.723 409.759i 1.91300 1.10447i
\(372\) 0 0
\(373\) 324.494i 0.869956i 0.900441 + 0.434978i \(0.143244\pi\)
−0.900441 + 0.434978i \(0.856756\pi\)
\(374\) −17.8269 + 10.2923i −0.0476654 + 0.0275196i
\(375\) 0 0
\(376\) 334.455 193.098i 0.889509 0.513558i
\(377\) −14.4113 + 24.9612i −0.0382264 + 0.0662100i
\(378\) 0 0
\(379\) 21.4534i 0.0566053i 0.999599 + 0.0283026i \(0.00901021\pi\)
−0.999599 + 0.0283026i \(0.990990\pi\)
\(380\) −354.024 + 150.969i −0.931641 + 0.397287i
\(381\) 0 0
\(382\) −187.283 108.128i −0.490270 0.283057i
\(383\) −185.197 106.924i −0.483544 0.279174i 0.238348 0.971180i \(-0.423394\pi\)
−0.721892 + 0.692006i \(0.756727\pi\)
\(384\) 0 0
\(385\) −167.158 + 289.527i −0.434178 + 0.752018i
\(386\) 207.242 + 358.953i 0.536896 + 0.929930i
\(387\) 0 0
\(388\) 363.017i 0.935611i
\(389\) 188.727 + 326.885i 0.485160 + 0.840321i 0.999855 0.0170523i \(-0.00542818\pi\)
−0.514695 + 0.857373i \(0.672095\pi\)
\(390\) 0 0
\(391\) 171.588 0.438844
\(392\) 485.749i 1.23916i
\(393\) 0 0
\(394\) 260.756 + 150.548i 0.661818 + 0.382101i
\(395\) −3.81340 + 2.20167i −0.00965418 + 0.00557385i
\(396\) 0 0
\(397\) 132.294 229.140i 0.333234 0.577179i −0.649910 0.760011i \(-0.725193\pi\)
0.983144 + 0.182833i \(0.0585267\pi\)
\(398\) 418.915i 1.05255i
\(399\) 0 0
\(400\) 1.90683 0.00476707
\(401\) −424.726 245.216i −1.05917 0.611510i −0.133965 0.990986i \(-0.542771\pi\)
−0.925202 + 0.379476i \(0.876104\pi\)
\(402\) 0 0
\(403\) −25.9436 44.9356i −0.0643761 0.111503i
\(404\) 147.089 254.765i 0.364081 0.630607i
\(405\) 0 0
\(406\) −159.545 −0.392967
\(407\) 243.014i 0.597086i
\(408\) 0 0
\(409\) −364.046 + 210.182i −0.890087 + 0.513892i −0.873971 0.485978i \(-0.838463\pi\)
−0.0161160 + 0.999870i \(0.505130\pi\)
\(410\) 521.838 1.27278
\(411\) 0 0
\(412\) 56.0466 32.3585i 0.136035 0.0785401i
\(413\) −866.479 500.262i −2.09801 1.21129i
\(414\) 0 0
\(415\) 221.113 382.979i 0.532802 0.922840i
\(416\) 37.4039 64.7854i 0.0899131 0.155734i
\(417\) 0 0
\(418\) 90.8297 + 10.9992i 0.217296 + 0.0263140i
\(419\) 646.178 1.54219 0.771095 0.636720i \(-0.219709\pi\)
0.771095 + 0.636720i \(0.219709\pi\)
\(420\) 0 0
\(421\) 468.113 + 270.265i 1.11191 + 0.641960i 0.939323 0.343035i \(-0.111455\pi\)
0.172584 + 0.984995i \(0.444788\pi\)
\(422\) −60.6143 104.987i −0.143636 0.248785i
\(423\) 0 0
\(424\) 312.600 + 541.439i 0.737264 + 1.27698i
\(425\) −178.954 −0.421069
\(426\) 0 0
\(427\) −197.874 342.728i −0.463406 0.802642i
\(428\) 258.960 149.510i 0.605046 0.349323i
\(429\) 0 0
\(430\) 134.613i 0.313053i
\(431\) −198.483 + 114.594i −0.460517 + 0.265880i −0.712262 0.701914i \(-0.752329\pi\)
0.251745 + 0.967794i \(0.418996\pi\)
\(432\) 0 0
\(433\) 238.975 137.972i 0.551906 0.318643i −0.197985 0.980205i \(-0.563440\pi\)
0.749890 + 0.661562i \(0.230106\pi\)
\(434\) 143.608 248.736i 0.330893 0.573123i
\(435\) 0 0
\(436\) 263.031i 0.603283i
\(437\) −609.851 457.968i −1.39554 1.04798i
\(438\) 0 0
\(439\) 10.6486 + 6.14794i 0.0242564 + 0.0140044i 0.512079 0.858938i \(-0.328875\pi\)
−0.487823 + 0.872943i \(0.662209\pi\)
\(440\) −220.876 127.523i −0.501992 0.289825i
\(441\) 0 0
\(442\) −6.16046 + 10.6702i −0.0139377 + 0.0241408i
\(443\) 31.4933 + 54.5480i 0.0710910 + 0.123133i 0.899380 0.437168i \(-0.144019\pi\)
−0.828289 + 0.560301i \(0.810685\pi\)
\(444\) 0 0
\(445\) 771.232i 1.73311i
\(446\) 40.8618 + 70.7747i 0.0916183 + 0.158688i
\(447\) 0 0
\(448\) 412.180 0.920045
\(449\) 679.936i 1.51433i 0.653222 + 0.757167i \(0.273417\pi\)
−0.653222 + 0.757167i \(0.726583\pi\)
\(450\) 0 0
\(451\) 174.772 + 100.905i 0.387522 + 0.223736i
\(452\) −217.986 + 125.854i −0.482269 + 0.278438i
\(453\) 0 0
\(454\) 231.513 400.992i 0.509940 0.883243i
\(455\) 200.105i 0.439790i
\(456\) 0 0
\(457\) −434.089 −0.949867 −0.474933 0.880022i \(-0.657528\pi\)
−0.474933 + 0.880022i \(0.657528\pi\)
\(458\) 43.2318 + 24.9599i 0.0943926 + 0.0544976i
\(459\) 0 0
\(460\) 406.545 + 704.156i 0.883792 + 1.53077i
\(461\) −265.088 + 459.146i −0.575028 + 0.995978i 0.421010 + 0.907056i \(0.361676\pi\)
−0.996039 + 0.0889223i \(0.971658\pi\)
\(462\) 0 0
\(463\) −450.022 −0.971969 −0.485985 0.873967i \(-0.661539\pi\)
−0.485985 + 0.873967i \(0.661539\pi\)
\(464\) 0.562076i 0.00121137i
\(465\) 0 0
\(466\) 287.388 165.924i 0.616713 0.356059i
\(467\) −733.340 −1.57032 −0.785161 0.619292i \(-0.787420\pi\)
−0.785161 + 0.619292i \(0.787420\pi\)
\(468\) 0 0
\(469\) 551.361 318.329i 1.17561 0.678739i
\(470\) −422.224 243.771i −0.898350 0.518663i
\(471\) 0 0
\(472\) 381.643 661.026i 0.808566 1.40048i
\(473\) −26.0293 + 45.0841i −0.0550302 + 0.0953152i
\(474\) 0 0
\(475\) 636.033 + 477.629i 1.33902 + 1.00554i
\(476\) 110.948 0.233084
\(477\) 0 0
\(478\) 62.1744 + 35.8964i 0.130072 + 0.0750971i
\(479\) −131.657 228.037i −0.274859 0.476069i 0.695241 0.718777i \(-0.255298\pi\)
−0.970099 + 0.242708i \(0.921964\pi\)
\(480\) 0 0
\(481\) 72.7277 + 125.968i 0.151201 + 0.261888i
\(482\) 178.341 0.370002
\(483\) 0 0
\(484\) 131.011 + 226.917i 0.270684 + 0.468838i
\(485\) 1037.73 599.136i 2.13966 1.23533i
\(486\) 0 0
\(487\) 307.749i 0.631929i −0.948771 0.315964i \(-0.897672\pi\)
0.948771 0.315964i \(-0.102328\pi\)
\(488\) 261.463 150.956i 0.535785 0.309336i
\(489\) 0 0
\(490\) −531.065 + 306.611i −1.08381 + 0.625736i
\(491\) −296.882 + 514.214i −0.604647 + 1.04728i 0.387460 + 0.921887i \(0.373353\pi\)
−0.992107 + 0.125393i \(0.959981\pi\)
\(492\) 0 0
\(493\) 52.7505i 0.106999i
\(494\) 50.3741 21.4814i 0.101972 0.0434847i
\(495\) 0 0
\(496\) −0.876297 0.505930i −0.00176673 0.00102002i
\(497\) 826.525 + 477.194i 1.66303 + 0.960149i
\(498\) 0 0
\(499\) 327.577 567.380i 0.656467 1.13703i −0.325057 0.945695i \(-0.605383\pi\)
0.981524 0.191340i \(-0.0612833\pi\)
\(500\) −170.794 295.825i −0.341589 0.591649i
\(501\) 0 0
\(502\) 115.570i 0.230220i
\(503\) 383.121 + 663.586i 0.761673 + 1.31926i 0.941988 + 0.335647i \(0.108955\pi\)
−0.180315 + 0.983609i \(0.557712\pi\)
\(504\) 0 0
\(505\) −971.041 −1.92285
\(506\) 193.292i 0.382000i
\(507\) 0 0
\(508\) −237.137 136.911i −0.466804 0.269510i
\(509\) −757.837 + 437.537i −1.48887 + 0.859602i −0.999919 0.0127070i \(-0.995955\pi\)
−0.488955 + 0.872309i \(0.662622\pi\)
\(510\) 0 0
\(511\) −437.896 + 758.458i −0.856939 + 1.48426i
\(512\) 2.91512i 0.00569359i
\(513\) 0 0
\(514\) −510.922 −0.994012
\(515\) −185.003 106.811i −0.359228 0.207401i
\(516\) 0 0
\(517\) −94.2733 163.286i −0.182347 0.315834i
\(518\) −402.576 + 697.281i −0.777173 + 1.34610i
\(519\) 0 0
\(520\) −152.657 −0.293572
\(521\) 445.728i 0.855525i −0.903891 0.427762i \(-0.859302\pi\)
0.903891 0.427762i \(-0.140698\pi\)
\(522\) 0 0
\(523\) 764.415 441.335i 1.46160 0.843853i 0.462510 0.886614i \(-0.346949\pi\)
0.999085 + 0.0427611i \(0.0136154\pi\)
\(524\) 139.508 0.266237
\(525\) 0 0
\(526\) −183.321 + 105.840i −0.348519 + 0.201217i
\(527\) 82.2398 + 47.4812i 0.156053 + 0.0900971i
\(528\) 0 0
\(529\) −541.114 + 937.237i −1.02290 + 1.77171i
\(530\) 394.633 683.525i 0.744591 1.28967i
\(531\) 0 0
\(532\) −394.328 296.121i −0.741217 0.556618i
\(533\) 120.793 0.226628
\(534\) 0 0
\(535\) −854.792 493.514i −1.59774 0.922457i
\(536\) 242.849 + 420.627i 0.453076 + 0.784751i
\(537\) 0 0
\(538\) −4.17029 7.22315i −0.00775147 0.0134259i
\(539\) −237.150 −0.439981
\(540\) 0 0
\(541\) −72.3654 125.341i −0.133762 0.231683i 0.791362 0.611348i \(-0.209373\pi\)
−0.925124 + 0.379665i \(0.876039\pi\)
\(542\) −263.962 + 152.399i −0.487015 + 0.281178i
\(543\) 0 0
\(544\) 136.911i 0.251674i
\(545\) 751.912 434.116i 1.37965 0.796544i
\(546\) 0 0
\(547\) −91.2148 + 52.6629i −0.166755 + 0.0962758i −0.581055 0.813865i \(-0.697360\pi\)
0.414300 + 0.910140i \(0.364026\pi\)
\(548\) −173.321 + 300.201i −0.316279 + 0.547812i
\(549\) 0 0
\(550\) 201.590i 0.366528i
\(551\) −140.791 + 187.484i −0.255519 + 0.340261i
\(552\) 0 0
\(553\) −4.88613 2.82101i −0.00883567 0.00510128i
\(554\) 72.2809 + 41.7314i 0.130471 + 0.0753275i
\(555\) 0 0
\(556\) 210.930 365.341i 0.379370 0.657088i
\(557\) −298.372 516.795i −0.535676 0.927819i −0.999130 0.0416975i \(-0.986723\pi\)
0.463454 0.886121i \(-0.346610\pi\)
\(558\) 0 0
\(559\) 31.1596i 0.0557416i
\(560\) 1.95114 + 3.37947i 0.00348417 + 0.00603477i
\(561\) 0 0
\(562\) −31.5290 −0.0561014
\(563\) 709.552i 1.26031i −0.776471 0.630153i \(-0.782992\pi\)
0.776471 0.630153i \(-0.217008\pi\)
\(564\) 0 0
\(565\) 719.542 + 415.428i 1.27353 + 0.735271i
\(566\) 1.02000 0.588900i 0.00180213 0.00104046i
\(567\) 0 0
\(568\) −364.046 + 630.545i −0.640925 + 1.11012i
\(569\) 275.069i 0.483425i 0.970348 + 0.241712i \(0.0777090\pi\)
−0.970348 + 0.241712i \(0.922291\pi\)
\(570\) 0 0
\(571\) −924.109 −1.61840 −0.809202 0.587531i \(-0.800100\pi\)
−0.809202 + 0.587531i \(0.800100\pi\)
\(572\) −19.5538 11.2894i −0.0341849 0.0197367i
\(573\) 0 0
\(574\) 334.317 + 579.054i 0.582433 + 1.00880i
\(575\) 840.200 1455.27i 1.46122 2.53090i
\(576\) 0 0
\(577\) −443.905 −0.769332 −0.384666 0.923056i \(-0.625683\pi\)
−0.384666 + 0.923056i \(0.625683\pi\)
\(578\) 334.079i 0.577991i
\(579\) 0 0
\(580\) 216.475 124.982i 0.373233 0.215486i
\(581\) 566.626 0.975259
\(582\) 0 0
\(583\) 264.339 152.616i 0.453411 0.261777i
\(584\) −578.618 334.065i −0.990785 0.572030i
\(585\) 0 0
\(586\) 183.252 317.401i 0.312716 0.541640i
\(587\) −255.163 + 441.955i −0.434690 + 0.752905i −0.997270 0.0738374i \(-0.976475\pi\)
0.562580 + 0.826743i \(0.309809\pi\)
\(588\) 0 0
\(589\) −165.566 388.254i −0.281097 0.659174i
\(590\) −963.591 −1.63321
\(591\) 0 0
\(592\) 2.45653 + 1.41828i 0.00414954 + 0.00239574i
\(593\) 57.1501 + 98.9869i 0.0963746 + 0.166926i 0.910181 0.414210i \(-0.135942\pi\)
−0.813807 + 0.581135i \(0.802609\pi\)
\(594\) 0 0
\(595\) −183.113 317.161i −0.307753 0.533043i
\(596\) 294.618 0.494325
\(597\) 0 0
\(598\) −57.8473 100.194i −0.0967346 0.167549i
\(599\) −530.087 + 306.046i −0.884954 + 0.510928i −0.872288 0.488992i \(-0.837365\pi\)
−0.0126651 + 0.999920i \(0.504032\pi\)
\(600\) 0 0
\(601\) 46.8204i 0.0779041i 0.999241 + 0.0389520i \(0.0124020\pi\)
−0.999241 + 0.0389520i \(0.987598\pi\)
\(602\) −149.372 + 86.2400i −0.248126 + 0.143256i
\(603\) 0 0
\(604\) −323.727 + 186.904i −0.535971 + 0.309443i
\(605\) 432.450 749.025i 0.714793 1.23806i
\(606\) 0 0
\(607\) 177.626i 0.292629i 0.989238 + 0.146315i \(0.0467412\pi\)
−0.989238 + 0.146315i \(0.953259\pi\)
\(608\) 365.415 486.603i 0.601012 0.800334i
\(609\) 0 0
\(610\) −330.077 190.570i −0.541110 0.312410i
\(611\) −97.7346 56.4271i −0.159958 0.0923520i
\(612\) 0 0
\(613\) −194.067 + 336.134i −0.316586 + 0.548343i −0.979773 0.200110i \(-0.935870\pi\)
0.663187 + 0.748454i \(0.269203\pi\)
\(614\) 34.1005 + 59.0637i 0.0555382 + 0.0961950i
\(615\) 0 0
\(616\) 326.792i 0.530506i
\(617\) 113.174 + 196.024i 0.183427 + 0.317705i 0.943045 0.332664i \(-0.107948\pi\)
−0.759618 + 0.650369i \(0.774614\pi\)
\(618\) 0 0
\(619\) −168.929 −0.272906 −0.136453 0.990647i \(-0.543570\pi\)
−0.136453 + 0.990647i \(0.543570\pi\)
\(620\) 449.990i 0.725790i
\(621\) 0 0
\(622\) −118.378 68.3458i −0.190319 0.109881i
\(623\) 855.792 494.092i 1.37366 0.793084i
\(624\) 0 0
\(625\) −40.4783 + 70.1104i −0.0647652 + 0.112177i
\(626\) 260.935i 0.416829i
\(627\) 0 0
\(628\) −25.3364 −0.0403446
\(629\) −230.543 133.104i −0.366523 0.211612i
\(630\) 0 0
\(631\) −355.351 615.487i −0.563156 0.975415i −0.997219 0.0745321i \(-0.976254\pi\)
0.434063 0.900883i \(-0.357080\pi\)
\(632\) 2.15211 3.72757i 0.00340524 0.00589805i
\(633\) 0 0
\(634\) 204.432 0.322447
\(635\) 903.850i 1.42339i
\(636\) 0 0
\(637\) −122.929 + 70.9728i −0.192980 + 0.111417i
\(638\) −59.4228 −0.0931392
\(639\) 0 0
\(640\) −563.442 + 325.303i −0.880377 + 0.508286i
\(641\) 901.332 + 520.385i 1.40613 + 0.811832i 0.995013 0.0997480i \(-0.0318037\pi\)
0.411122 + 0.911580i \(0.365137\pi\)
\(642\) 0 0
\(643\) 7.89596 13.6762i 0.0122799 0.0212694i −0.859820 0.510597i \(-0.829424\pi\)
0.872100 + 0.489328i \(0.162758\pi\)
\(644\) −520.907 + 902.238i −0.808862 + 1.40099i
\(645\) 0 0
\(646\) −60.1843 + 80.1441i −0.0931645 + 0.124062i
\(647\) −214.998 −0.332299 −0.166150 0.986101i \(-0.553133\pi\)
−0.166150 + 0.986101i \(0.553133\pi\)
\(648\) 0 0
\(649\) −322.723 186.324i −0.497261 0.287094i
\(650\) 60.3307 + 104.496i 0.0928165 + 0.160763i
\(651\) 0 0
\(652\) 53.1180 + 92.0031i 0.0814694 + 0.141109i
\(653\) 371.833 0.569423 0.284712 0.958613i \(-0.408102\pi\)
0.284712 + 0.958613i \(0.408102\pi\)
\(654\) 0 0
\(655\) −230.249 398.804i −0.351526 0.608861i
\(656\) 2.04001 1.17780i 0.00310977 0.00179543i
\(657\) 0 0
\(658\) 624.691i 0.949378i
\(659\) −113.255 + 65.3877i −0.171859 + 0.0992226i −0.583462 0.812140i \(-0.698302\pi\)
0.411603 + 0.911363i \(0.364969\pi\)
\(660\) 0 0
\(661\) −194.222 + 112.134i −0.293830 + 0.169643i −0.639668 0.768652i \(-0.720928\pi\)
0.345838 + 0.938294i \(0.387595\pi\)
\(662\) −221.031 + 382.837i −0.333884 + 0.578303i
\(663\) 0 0
\(664\) 432.272i 0.651011i
\(665\) −195.689 + 1615.97i −0.294270 + 2.43003i
\(666\) 0 0
\(667\) 428.970 + 247.666i 0.643133 + 0.371313i
\(668\) 3.66959 + 2.11864i 0.00549339 + 0.00317161i
\(669\) 0 0
\(670\) 306.578 531.009i 0.457579 0.792551i
\(671\) −73.6989 127.650i −0.109834 0.190239i
\(672\) 0 0
\(673\) 101.375i 0.150631i −0.997160 0.0753154i \(-0.976004\pi\)
0.997160 0.0753154i \(-0.0239964\pi\)
\(674\) −391.978 678.925i −0.581569 1.00731i
\(675\) 0 0
\(676\) 405.137 0.599315
\(677\) 60.9135i 0.0899756i −0.998988 0.0449878i \(-0.985675\pi\)
0.998988 0.0449878i \(-0.0143249\pi\)
\(678\) 0 0
\(679\) 1329.65 + 767.676i 1.95825 + 1.13060i
\(680\) 241.958 139.694i 0.355821 0.205433i
\(681\) 0 0
\(682\) 53.4871 92.6423i 0.0784268 0.135839i
\(683\) 118.773i 0.173898i −0.996213 0.0869492i \(-0.972288\pi\)
0.996213 0.0869492i \(-0.0277118\pi\)
\(684\) 0 0
\(685\) 1144.22 1.67040
\(686\) −131.812 76.1016i −0.192146 0.110935i
\(687\) 0 0
\(688\) 0.303824 + 0.526239i 0.000441605 + 0.000764882i
\(689\) 91.3480 158.219i 0.132580 0.229636i
\(690\) 0 0
\(691\) −55.9089 −0.0809101 −0.0404551 0.999181i \(-0.512881\pi\)
−0.0404551 + 0.999181i \(0.512881\pi\)
\(692\) 503.695i 0.727883i
\(693\) 0 0
\(694\) −159.873 + 92.3028i −0.230365 + 0.133001i
\(695\) −1392.50 −2.00360
\(696\) 0 0
\(697\) −191.453 + 110.536i −0.274682 + 0.158588i
\(698\) 226.415 + 130.720i 0.324376 + 0.187279i
\(699\) 0 0
\(700\) 543.270 940.972i 0.776100 1.34425i
\(701\) −16.5402 + 28.6485i −0.0235952 + 0.0408681i −0.877582 0.479427i \(-0.840845\pi\)
0.853987 + 0.520295i \(0.174178\pi\)
\(702\) 0 0
\(703\) 464.132 + 1088.39i 0.660217 + 1.54821i
\(704\) 153.518 0.218065
\(705\) 0 0
\(706\) 165.617 + 95.6193i 0.234586 + 0.135438i
\(707\) −622.100 1077.51i −0.879915 1.52406i
\(708\) 0 0
\(709\) 371.042 + 642.664i 0.523332 + 0.906438i 0.999631 + 0.0271545i \(0.00864459\pi\)
−0.476299 + 0.879283i \(0.658022\pi\)
\(710\) 919.159 1.29459
\(711\) 0 0
\(712\) 376.936 + 652.873i 0.529405 + 0.916956i
\(713\) −772.240 + 445.853i −1.08309 + 0.625320i
\(714\) 0 0
\(715\) 74.5296i 0.104237i
\(716\) 75.0279 43.3174i 0.104788 0.0604991i
\(717\) 0 0
\(718\) 266.519 153.875i 0.371196 0.214310i
\(719\) −672.563 + 1164.91i −0.935414 + 1.62018i −0.161520 + 0.986869i \(0.551640\pi\)
−0.773894 + 0.633315i \(0.781694\pi\)
\(720\) 0 0
\(721\) 273.715i 0.379633i
\(722\) 427.809 124.213i 0.592533 0.172040i
\(723\) 0 0
\(724\) −248.453 143.445i −0.343168 0.198128i
\(725\) −447.386 258.298i −0.617084 0.356274i
\(726\) 0 0
\(727\) 107.104 185.510i 0.147323 0.255171i −0.782914 0.622130i \(-0.786268\pi\)
0.930237 + 0.366958i \(0.119601\pi\)
\(728\) −97.8002 169.395i −0.134341 0.232685i
\(729\) 0 0
\(730\) 843.464i 1.15543i
\(731\) −28.5137 49.3871i −0.0390064 0.0675610i
\(732\) 0 0
\(733\) 503.818 0.687337 0.343668 0.939091i \(-0.388330\pi\)
0.343668 + 0.939091i \(0.388330\pi\)
\(734\) 806.334i 1.09855i
\(735\) 0 0
\(736\) −1113.37 642.803i −1.51273 0.873374i
\(737\) 205.356 118.562i 0.278638 0.160872i
\(738\) 0 0
\(739\) 708.464 1227.10i 0.958680 1.66048i 0.232966 0.972485i \(-0.425157\pi\)
0.725713 0.687997i \(-0.241510\pi\)
\(740\) 1261.46i 1.70467i
\(741\) 0 0
\(742\) 1011.29 1.36293
\(743\) −539.026 311.207i −0.725472 0.418852i 0.0912911 0.995824i \(-0.470901\pi\)
−0.816764 + 0.576973i \(0.804234\pi\)
\(744\) 0 0
\(745\) −486.247 842.205i −0.652681 1.13048i
\(746\) −200.214 + 346.780i −0.268383 + 0.464853i
\(747\) 0 0
\(748\) 41.3230 0.0552446
\(749\) 1264.68i 1.68850i
\(750\) 0 0
\(751\) −484.987 + 280.007i −0.645788 + 0.372846i −0.786841 0.617156i \(-0.788285\pi\)
0.141052 + 0.990002i \(0.454951\pi\)
\(752\) −2.20079 −0.00292658
\(753\) 0 0
\(754\) −30.8023 + 17.7837i −0.0408518 + 0.0235858i
\(755\) 1068.58 + 616.945i 1.41534 + 0.817146i
\(756\) 0 0
\(757\) −686.860 + 1189.68i −0.907345 + 1.57157i −0.0896071 + 0.995977i \(0.528561\pi\)
−0.817738 + 0.575591i \(0.804772\pi\)
\(758\) −13.2368 + 22.9269i −0.0174628 + 0.0302465i
\(759\) 0 0
\(760\) −1232.80 149.289i −1.62211 0.196433i
\(761\) 1196.22 1.57191 0.785953 0.618286i \(-0.212173\pi\)
0.785953 + 0.618286i \(0.212173\pi\)
\(762\) 0 0
\(763\) 963.428 + 556.235i 1.26268 + 0.729011i
\(764\) 217.063 + 375.964i 0.284114 + 0.492100i
\(765\) 0 0
\(766\) −131.945 228.535i −0.172251 0.298348i
\(767\) −223.048 −0.290805
\(768\) 0 0
\(769\) 73.0921 + 126.599i 0.0950483 + 0.164628i 0.909629 0.415422i \(-0.136366\pi\)
−0.814580 + 0.580051i \(0.803033\pi\)
\(770\) −357.278 + 206.275i −0.463998 + 0.267889i
\(771\) 0 0
\(772\) 832.060i 1.07780i
\(773\) −486.540 + 280.904i −0.629418 + 0.363395i −0.780527 0.625123i \(-0.785049\pi\)
0.151109 + 0.988517i \(0.451716\pi\)
\(774\) 0 0
\(775\) 805.393 464.994i 1.03922 0.599992i
\(776\) −585.650 + 1014.38i −0.754704 + 1.30719i
\(777\) 0 0
\(778\) 465.781i 0.598691i
\(779\) 975.476 + 118.127i 1.25222 + 0.151640i
\(780\) 0 0
\(781\) 307.842 + 177.732i 0.394163 + 0.227570i
\(782\) 183.373 + 105.870i 0.234492 + 0.135384i
\(783\) 0 0
\(784\) −1.38405 + 2.39725i −0.00176537 + 0.00305772i
\(785\) 41.8161 + 72.4277i 0.0532690 + 0.0922646i