Properties

Label 171.3.p.f.46.2
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 46.2
Root \(-1.06868 - 0.617004i\) of defining polynomial
Character \(\chi\) \(=\) 171.46
Dual form 171.3.p.f.145.2

$q$-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 0.208441 0.978035i \(-0.433161\pi\)
−0.742782 + 0.669533i \(0.766494\pi\)
\(3\) 0 0
\(4\) −1.23861 2.14534i −0.309653 0.536335i
\(5\) 4.08850 7.08149i 0.817700 1.41630i −0.0896726 0.995971i \(-0.528582\pi\)
0.907373 0.420327i \(-0.138085\pi\)
\(6\) 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 \(-0.443239\pi\)
0.177376 + 0.984143i \(0.443239\pi\)
\(12\) 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 −0.922017 0.387149i \(-0.873460\pi\)
0.796290 + 0.604915i \(0.206793\pi\)
\(18\) 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 \(-0.829092\pi\)
−0.0133248 0.999911i \(-0.504242\pi\)
\(24\) 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 \(-0.734912\pi\)
0.304297 + 0.952577i \(0.401579\pi\)
\(30\) 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 0.934207 0.356731i \(-0.116109\pi\)
0.158166 + 0.987413i \(0.449442\pi\)
\(42\) 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 \(-0.994825\pi\)
0.485856 0.874039i \(-0.338508\pi\)
\(48\) 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 \(-0.402477\pi\)
0.976500 + 0.215518i \(0.0691440\pi\)
\(54\) 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 \(-0.633476\pi\)
−0.994569 + 0.104083i \(0.966809\pi\)
\(60\) 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 0.939113 0.343609i \(-0.111650\pi\)
0.171982 + 0.985100i \(0.444983\pi\)
\(72\) 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 \(-0.394369\pi\)
0.325793 + 0.945441i \(0.394369\pi\)
\(84\) 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 \(-0.488907\pi\)
0.882922 + 0.469521i \(0.155573\pi\)
\(90\) 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 \(-0.966627\pi\)
0.406624 0.913596i \(-0.366706\pi\)
\(102\) 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 \(-0.809240\pi\)
0.825737 0.564056i \(-0.190760\pi\)
\(108\) 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 \(0.148432\pi\)
−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 −0.0732950 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 −0.738309 0.674463i \(-0.764375\pi\)
0.953256 + 0.302162i \(0.0977085\pi\)
\(132\) 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 \(0.00394687\pi\)
−0.489224 + 0.872158i \(0.662720\pi\)
\(138\) 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 −0.594519 0.804082i \(-0.702657\pi\)
0.993615 + 0.112828i \(0.0359908\pi\)
\(150\) 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 −0.495558 0.868575i \(-0.665037\pi\)
0.504429 + 0.863453i \(0.331703\pi\)
\(168\) 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 \(-0.533284\pi\)
−0.913482 + 0.406879i \(0.866617\pi\)
\(174\) 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 −0.196664 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 \(-0.348293\pi\)
0.458761 + 0.888559i \(0.348293\pi\)
\(192\) 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 \(-0.712577\pi\)
−0.619284 + 0.785167i \(0.712577\pi\)
\(198\) 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 \(0.309659\pi\)
−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 0.418734 + 0.908109i \(0.362474\pi\)
−0.995812 + 0.0914198i \(0.970859\pi\)
\(234\) 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 \(-0.538839\pi\)
−0.121713 + 0.992565i \(0.538839\pi\)
\(240\) 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 0.757539 0.652790i \(-0.226401\pi\)
−0.944102 + 0.329653i \(0.893068\pi\)
\(252\) 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 \(-0.368555\pi\)
0.993884 + 0.110427i \(0.0352218\pi\)
\(258\) 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 \(-0.727592\pi\)
0.981738 + 0.190236i \(0.0609252\pi\)
\(264\) 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 \(-0.329334\pi\)
−0.489081 + 0.872239i \(0.662668\pi\)
\(270\) 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 −0.460111 0.887861i \(-0.652190\pi\)
0.538855 + 0.842399i \(0.318857\pi\)
\(282\) 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 \(0.169183\pi\)
−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 0.575924 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 \(-0.443009\pi\)
0.178088 + 0.984015i \(0.443009\pi\)
\(312\) 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 −0.708922 0.705287i \(-0.750818\pi\)
0.256335 + 0.966588i \(0.417485\pi\)
\(318\) 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 −0.737886 0.674926i \(-0.764176\pi\)
0.953446 + 0.301565i \(0.0975091\pi\)
\(348\) 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 \(-0.570446\pi\)
−0.219509 + 0.975610i \(0.570446\pi\)
\(354\) 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 \(-0.946248\pi\)
0.638436 + 0.769675i \(0.279582\pi\)
\(360\) 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 0.721892 0.692006i \(-0.243273\pi\)
−0.238348 + 0.971180i \(0.576606\pi\)
\(384\) 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 \(-0.327905\pi\)
−0.999855 + 0.0170523i \(0.994572\pi\)
\(390\) 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 0.925202 0.379476i \(-0.123896\pi\)
0.133965 + 0.990986i \(0.457229\pi\)
\(402\) 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 \(-0.780291\pi\)
−0.771095 + 0.636720i \(0.780291\pi\)
\(420\) 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 −0.251745 0.967794i \(-0.581004\pi\)
0.712262 + 0.701914i \(0.247671\pi\)
\(432\) 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 0.828289 0.560301i \(-0.189315\pi\)
−0.899380 + 0.437168i \(0.855981\pi\)
\(444\) 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 −0.421010 0.907056i \(-0.638324\pi\)
0.996039 0.0889223i \(-0.0283423\pi\)
\(462\) 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 \(-0.212580\pi\)
0.785161 + 0.619292i \(0.212580\pi\)
\(468\) 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 \(-0.0780356\pi\)
−0.695241 + 0.718777i \(0.744702\pi\)
\(480\) 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 \(-0.626647\pi\)
0.992107 0.125393i \(-0.0400193\pi\)
\(492\) 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 \(-0.891045\pi\)
0.180315 0.983609i \(-0.442288\pi\)
\(504\) 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 \(-0.337378\pi\)
0.999919 + 0.0127070i \(0.00404489\pi\)
\(510\) 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 0.462510 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 \(0.0132766\pi\)
−0.463454 + 0.886121i \(0.653390\pi\)
\(558\) 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 \(-0.690191\pi\)
0.997270 + 0.0738374i \(0.0235246\pi\)
\(588\) 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 \(-0.197391\pi\)
−0.910181 + 0.414210i \(0.864058\pi\)
\(594\) 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 \(-0.495968\pi\)
0.872288 + 0.488992i \(0.162635\pi\)
\(600\) 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 0.759618 0.650369i \(-0.225386\pi\)
−0.943045 + 0.332664i \(0.892052\pi\)
\(618\) 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 −0.411122 0.911580i \(-0.634863\pi\)
−0.995013 + 0.0997480i \(0.968196\pi\)
\(642\) 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 \(-0.446867\pi\)
0.166150 + 0.986101i \(0.446867\pi\)
\(648\) 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 \(-0.591898\pi\)
−0.284712 + 0.958613i \(0.591898\pi\)
\(654\) 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 \(-0.635031\pi\)
0.583462 + 0.812140i \(0.301698\pi\)
\(660\) 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 \(0.0143249\pi\)
−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 \(-0.825822\pi\)
0.877582 + 0.479427i \(0.159155\pi\)
\(702\) 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 \(-0.448360\pi\)
0.773894 0.633315i \(-0.218306\pi\)
\(720\) 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 0.816764 0.576973i \(-0.195766\pi\)
−0.0912911 + 0.995824i \(0.529099\pi\)
\(744\) 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 \(-0.787827\pi\)
−0.785953 + 0.618286i \(0.787827\pi\)
\(762\) 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 −0.151109 0.988517i \(-0.548284\pi\)
0.780527 + 0.625123i \(0.214951\pi\)
\(774\) 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