Properties

Label 171.3.p.f.145.3
Level $171$
Weight $3$
Character 171.145
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 145.3
Root \(1.06868 - 0.617004i\) of defining polynomial
Character \(\chi\) \(=\) 171.145
Dual form 171.3.p.f.46.3

$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(154\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.06868 0.617004i 0.534341 0.308502i −0.208441 0.978035i \(-0.566839\pi\)
0.742782 + 0.669533i \(0.233506\pi\)
\(3\) 0 0
\(4\) −1.23861 + 2.14534i −0.309653 + 0.536335i
\(5\) −4.08850 7.08149i −0.817700 1.41630i −0.907373 0.420327i \(-0.861915\pi\)
0.0896726 0.995971i \(-0.471418\pi\)
\(6\) 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 0.420179 0.907441i \(-0.361967\pi\)
−0.575777 + 0.817607i \(0.695300\pi\)
\(14\) −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 0.922017 0.387149i \(-0.126540\pi\)
−0.796290 + 0.604915i \(0.793207\pi\)
\(18\) 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 0.0133248 0.999911i \(-0.495758\pi\)
0.859286 0.511495i \(-0.170908\pi\)
\(24\) 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 0.672808 0.739817i \(-0.265088\pi\)
−0.304297 + 0.952577i \(0.598421\pi\)
\(30\) 0 0
\(31\) 22.2148i 0.716608i −0.933605 0.358304i \(-0.883355\pi\)
0.933605 0.358304i \(-0.116645\pi\)
\(32\) −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 \(0.318358\pi\)
−0.540174 + 0.841553i \(0.681642\pi\)
\(38\) −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 −0.934207 0.356731i \(-0.883891\pi\)
−0.158166 + 0.987413i \(0.550558\pi\)
\(42\) 0 0
\(43\) 6.67029 + 11.5533i 0.155123 + 0.268681i 0.933104 0.359607i \(-0.117089\pi\)
−0.777981 + 0.628288i \(0.783756\pi\)
\(44\) 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 −0.485856 0.874039i \(-0.661492\pi\)
0.999868 0.0162556i \(-0.00517456\pi\)
\(48\) 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 −0.301606 0.953433i \(-0.597523\pi\)
−0.976500 + 0.215518i \(0.930856\pi\)
\(54\) 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 0.407146 0.913363i \(-0.366524\pi\)
0.994569 + 0.104083i \(0.0331908\pi\)
\(60\) 0 0
\(61\) 18.8861 32.7117i 0.309609 0.536258i −0.668668 0.743561i \(-0.733135\pi\)
0.978277 + 0.207303i \(0.0664686\pi\)
\(62\) −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 0.0529122 0.998599i \(-0.483150\pi\)
−0.838356 + 0.545123i \(0.816483\pi\)
\(68\) −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 −0.939113 0.343609i \(-0.888350\pi\)
−0.171982 + 0.985100i \(0.555017\pi\)
\(72\) 0 0
\(73\) 41.7950 + 72.3911i 0.572535 + 0.991659i 0.996305 + 0.0858893i \(0.0273731\pi\)
−0.423770 + 0.905770i \(0.639294\pi\)
\(74\) 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 −0.497045 0.867724i \(-0.665582\pi\)
0.502949 + 0.864316i \(0.332248\pi\)
\(80\) −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 −0.0348441 0.999393i \(-0.511093\pi\)
−0.882922 + 0.469521i \(0.844427\pi\)
\(90\) 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 −0.981819 0.189820i \(-0.939209\pi\)
−0.326520 + 0.945190i \(0.605876\pi\)
\(98\) 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 −0.406624 0.913596i \(-0.633294\pi\)
0.994509 0.104651i \(-0.0333725\pi\)
\(102\) 0 0
\(103\) 26.1248i 0.253639i −0.991926 0.126819i \(-0.959523\pi\)
0.991926 0.126819i \(-0.0404769\pi\)
\(104\) 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 \(-0.809240\pi\)
0.825737 0.564056i \(-0.190760\pi\)
\(108\) 0 0
\(109\) −91.9545 + 53.0899i −0.843619 + 0.487064i −0.858493 0.512826i \(-0.828599\pi\)
0.0148739 + 0.999889i \(0.495265\pi\)
\(110\) 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 \(0.148432\pi\)
−0.893232 + 0.449597i \(0.851568\pi\)
\(114\) 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 0.827049 0.562130i \(-0.190018\pi\)
−0.0732950 + 0.997310i \(0.523351\pi\)
\(128\) 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 0.738309 0.674463i \(-0.235625\pi\)
−0.953256 + 0.302162i \(0.902292\pi\)
\(132\) 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 0.489224 + 0.872158i \(0.337280\pi\)
−0.999923 + 0.0123992i \(0.996053\pi\)
\(138\) 0 0
\(139\) 85.1475 147.480i 0.612572 1.06101i −0.378233 0.925710i \(-0.623468\pi\)
0.990805 0.135296i \(-0.0431984\pi\)
\(140\) −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 0.594519 0.804082i \(-0.297343\pi\)
−0.993615 + 0.112828i \(0.964009\pi\)
\(150\) 0 0
\(151\) 150.898i 0.999322i 0.866221 + 0.499661i \(0.166542\pi\)
−0.866221 + 0.499661i \(0.833458\pi\)
\(152\) 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 0.881852 0.471526i \(-0.156297\pi\)
−0.849280 + 0.527943i \(0.822963\pi\)
\(158\) 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 0.495558 0.868575i \(-0.334963\pi\)
−0.504429 + 0.863453i \(0.668297\pi\)
\(168\) 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 0.104374 0.994538i \(-0.466716\pi\)
0.913482 + 0.406879i \(0.133383\pi\)
\(174\) 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 \(-0.968855\pi\)
0.995217 0.0976885i \(-0.0311449\pi\)
\(180\) 0 0
\(181\) 100.295 + 57.9054i 0.554116 + 0.319919i 0.750781 0.660552i \(-0.229678\pi\)
−0.196664 + 0.980471i \(0.563011\pi\)
\(182\) 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 0.507206 0.861825i \(-0.330678\pi\)
0.999965 0.00834091i \(-0.00265502\pi\)
\(194\) −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 −0.0255788 0.999673i \(-0.508143\pi\)
0.878531 0.477685i \(-0.158524\pi\)
\(200\) −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 −0.687870 0.725834i \(-0.741454\pi\)
0.284656 + 0.958630i \(0.408121\pi\)
\(212\) 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 −0.365862 0.930669i \(-0.619226\pi\)
0.623052 + 0.782180i \(0.285892\pi\)
\(224\) 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 \(0.309659\pi\)
−0.562968 + 0.826479i \(0.690341\pi\)
\(228\) 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 0.995812 + 0.0914198i \(0.0291405\pi\)
−0.418734 + 0.908109i \(0.637526\pi\)
\(234\) 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 0.736662 0.676261i \(-0.236401\pi\)
−0.217328 + 0.976099i \(0.569734\pi\)
\(242\) −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 −0.757539 0.652790i \(-0.773599\pi\)
0.944102 + 0.329653i \(0.106932\pi\)
\(252\) 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 −0.401310 0.915942i \(-0.631445\pi\)
−0.993884 + 0.110427i \(0.964778\pi\)
\(258\) 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 0.655618 0.755093i \(-0.272408\pi\)
−0.981738 + 0.190236i \(0.939075\pi\)
\(264\) 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 −0.510840 0.859676i \(-0.670666\pi\)
0.489081 + 0.872239i \(0.337332\pi\)
\(270\) 0 0
\(271\) −123.499 213.906i −0.455716 0.789323i 0.543013 0.839724i \(-0.317283\pi\)
−0.998729 + 0.0504013i \(0.983950\pi\)
\(272\) 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 0.460111 0.887861i \(-0.347810\pi\)
−0.538855 + 0.842399i \(0.681143\pi\)
\(282\) 0 0
\(283\) 0.477226 + 0.826579i 0.00168631 + 0.00292077i 0.866867 0.498539i \(-0.166130\pi\)
−0.865181 + 0.501460i \(0.832797\pi\)
\(284\) 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 \(0.169183\pi\)
−0.862046 + 0.506830i \(0.830817\pi\)
\(294\) 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 −0.420017 0.907516i \(-0.637976\pi\)
0.575924 + 0.817503i \(0.304643\pi\)
\(308\) −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 −0.984016 0.178081i \(-0.943011\pi\)
0.646231 + 0.763142i \(0.276344\pi\)
\(314\) 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 0.708922 0.705287i \(-0.249182\pi\)
−0.256335 + 0.966588i \(0.582515\pi\)
\(318\) 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 \(-0.817994\pi\)
0.840934 0.541137i \(-0.182006\pi\)
\(332\) 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 −0.649285 + 0.760545i \(0.724932\pi\)
−0.983294 + 0.182025i \(0.941735\pi\)
\(338\) −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 0.737886 0.674926i \(-0.235824\pi\)
−0.953446 + 0.301565i \(0.902491\pi\)
\(348\) 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 0.985776 0.168064i \(-0.0537517\pi\)
−0.638436 + 0.769675i \(0.720418\pi\)
\(360\) 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 −0.0506268 + 0.998718i \(0.516122\pi\)
−0.839601 + 0.543203i \(0.817211\pi\)
\(368\) −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 \(-0.856756\pi\)
0.900441 0.434978i \(-0.143244\pi\)
\(374\) −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 \(-0.990990\pi\)
0.999599 0.0283026i \(-0.00901021\pi\)
\(380\) −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 −0.721892 0.692006i \(-0.756727\pi\)
0.238348 + 0.971180i \(0.423394\pi\)
\(384\) 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 −0.514695 0.857373i \(-0.672095\pi\)
0.999855 + 0.0170523i \(0.00542818\pi\)
\(390\) 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 0.983144 0.182833i \(-0.0585267\pi\)
−0.649910 + 0.760011i \(0.725193\pi\)
\(398\) 418.915i 1.05255i
\(399\) 0 0
\(400\) 1.90683 0.00476707
\(401\) −424.726 + 245.216i −1.05917 + 0.611510i −0.925202 0.379476i \(-0.876104\pi\)
−0.133965 + 0.990986i \(0.542771\pi\)
\(402\) 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 −0.0161160 0.999870i \(-0.505130\pi\)
−0.873971 + 0.485978i \(0.838463\pi\)
\(410\) 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 0.172584 0.984995i \(-0.444788\pi\)
0.939323 + 0.343035i \(0.111455\pi\)
\(422\) −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 0.251745 0.967794i \(-0.418996\pi\)
−0.712262 + 0.701914i \(0.752329\pi\)
\(432\) 0 0
\(433\) 238.975 + 137.972i 0.551906 + 0.318643i 0.749890 0.661562i \(-0.230106\pi\)
−0.197985 + 0.980205i \(0.563440\pi\)
\(434\) 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 −0.487823 0.872943i \(-0.662209\pi\)
0.512079 + 0.858938i \(0.328875\pi\)
\(440\) −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 −0.828289 0.560301i \(-0.810685\pi\)
0.899380 + 0.437168i \(0.144019\pi\)
\(444\) 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 \(-0.726583\pi\)
0.653222 0.757167i \(-0.273417\pi\)
\(450\) 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 −0.996039 0.0889223i \(-0.971658\pi\)
0.421010 0.907056i \(-0.361676\pi\)
\(462\) 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 −0.970099 0.242708i \(-0.921964\pi\)
0.695241 + 0.718777i \(0.255298\pi\)
\(480\) 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 \(0.102328\pi\)
−0.948771 + 0.315964i \(0.897672\pi\)
\(488\) 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 −0.992107 0.125393i \(-0.959981\pi\)
0.387460 0.921887i \(-0.373353\pi\)
\(492\) 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 0.981524 + 0.191340i \(0.0612833\pi\)
−0.325057 + 0.945695i \(0.605383\pi\)
\(500\) −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 −0.180315 0.983609i \(-0.557712\pi\)
0.941988 0.335647i \(-0.108955\pi\)
\(504\) 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 −0.488955 0.872309i \(-0.662622\pi\)
−0.999919 + 0.0127070i \(0.995955\pi\)
\(510\) 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 \(0.140698\pi\)
−0.903891 + 0.427762i \(0.859302\pi\)
\(522\) 0 0
\(523\) 764.415 + 441.335i 1.46160 + 0.843853i 0.999085 0.0427611i \(-0.0136154\pi\)
0.462510 + 0.886614i \(0.346949\pi\)
\(524\) 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 −0.925124 0.379665i \(-0.876039\pi\)
0.791362 + 0.611348i \(0.209373\pi\)
\(542\) −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 0.414300 0.910140i \(-0.364026\pi\)
−0.581055 + 0.813865i \(0.697360\pi\)
\(548\) −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 0.463454 + 0.886121i \(0.346610\pi\)
−0.999130 + 0.0416975i \(0.986723\pi\)
\(558\) 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 \(0.217008\pi\)
−0.776471 + 0.630153i \(0.782992\pi\)
\(564\) 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 \(-0.922291\pi\)
0.970348 0.241712i \(-0.0777090\pi\)
\(570\) 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 0.562580 0.826743i \(-0.309809\pi\)
−0.997270 + 0.0738374i \(0.976475\pi\)
\(588\) 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 −0.813807 0.581135i \(-0.802609\pi\)
0.910181 + 0.414210i \(0.135942\pi\)
\(594\) 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 −0.0126651 0.999920i \(-0.504032\pi\)
−0.872288 + 0.488992i \(0.837365\pi\)
\(600\) 0 0
\(601\) 46.8204i 0.0779041i −0.999241 0.0389520i \(-0.987598\pi\)
0.999241 0.0389520i \(-0.0124020\pi\)
\(602\) −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 \(-0.953259\pi\)
0.989238 0.146315i \(-0.0467412\pi\)
\(608\) 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 0.663187 0.748454i \(-0.269203\pi\)
−0.979773 + 0.200110i \(0.935870\pi\)
\(614\) 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 −0.759618 0.650369i \(-0.774614\pi\)
0.943045 + 0.332664i \(0.107948\pi\)
\(618\) 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 0.434063 + 0.900883i \(0.357080\pi\)
−0.997219 + 0.0745321i \(0.976254\pi\)
\(632\) 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 0.411122 0.911580i \(-0.365137\pi\)
0.995013 + 0.0997480i \(0.0318037\pi\)
\(642\) 0 0
\(643\) 7.89596 + 13.6762i 0.0122799 + 0.0212694i 0.872100 0.489328i \(-0.162758\pi\)
−0.859820 + 0.510597i \(0.829424\pi\)
\(644\) −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 0.411603 0.911363i \(-0.364969\pi\)
−0.583462 + 0.812140i \(0.698302\pi\)
\(660\) 0 0
\(661\) −194.222 112.134i −0.293830 0.169643i 0.345838 0.938294i \(-0.387595\pi\)
−0.639668 + 0.768652i \(0.720928\pi\)
\(662\) −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 \(0.0239964\pi\)
−0.997160 + 0.0753154i \(0.976004\pi\)
\(674\) −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 \(0.0143249\pi\)
−0.998988 + 0.0449878i \(0.985675\pi\)
\(678\) 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 \(0.0277118\pi\)
−0.996213 + 0.0869492i \(0.972288\pi\)
\(684\) 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 0.853987 0.520295i \(-0.174178\pi\)
−0.877582 + 0.479427i \(0.840845\pi\)
\(702\) 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 −0.476299 0.879283i \(-0.658022\pi\)
0.999631 0.0271545i \(-0.00864459\pi\)
\(710\) 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 −0.773894 0.633315i \(-0.781694\pi\)
−0.161520 0.986869i \(-0.551640\pi\)
\(720\) 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 0.930237 0.366958i \(-0.119601\pi\)
−0.782914 + 0.622130i \(0.786268\pi\)
\(728\) −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 0.725713 + 0.687997i \(0.241510\pi\)
0.232966 + 0.972485i \(0.425157\pi\)
\(740\) 1261.46i 1.70467i
\(741\) 0 0
\(742\) 1011.29 1.36293
\(743\) −539.026 + 311.207i −0.725472 + 0.418852i −0.816764 0.576973i \(-0.804234\pi\)
0.0912911 + 0.995824i \(0.470901\pi\)
\(744\) 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 0.141052 0.990002i \(-0.454951\pi\)
−0.786841 + 0.617156i \(0.788285\pi\)
\(752\) −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 −0.817738 0.575591i \(-0.804772\pi\)
−0.0896071 0.995977i \(-0.528561\pi\)
\(758\) −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 −0.814580 0.580051i \(-0.803033\pi\)
0.909629 + 0.415422i \(0.136366\pi\)
\(770\) −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 0.151109 0.988517i \(-0.451716\pi\)
−0.780527 + 0.625123i \(0.785049\pi\)
\(774\) 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