Properties

Label 288.3.u.a.19.2
Level $288$
Weight $3$
Character 288.19
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 19.2
Character \(\chi\) \(=\) 288.19
Dual form 288.3.u.a.91.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.61758 - 1.17620i) q^{2} +(1.23313 + 3.80518i) q^{4} +(-2.28872 + 0.948019i) q^{5} +(-6.37744 - 6.37744i) q^{7} +(2.48095 - 7.60558i) q^{8} +O(q^{10})\) \(q+(-1.61758 - 1.17620i) q^{2} +(1.23313 + 3.80518i) q^{4} +(-2.28872 + 0.948019i) q^{5} +(-6.37744 - 6.37744i) q^{7} +(2.48095 - 7.60558i) q^{8} +(4.81725 + 1.15849i) q^{10} +(1.79646 - 0.744117i) q^{11} +(16.7036 + 6.91888i) q^{13} +(2.81490 + 17.8171i) q^{14} +(-12.9588 + 9.38456i) q^{16} -6.19811i q^{17} +(-8.50083 + 20.5228i) q^{19} +(-6.42967 - 7.53997i) q^{20} +(-3.78114 - 0.909316i) q^{22} +(-23.6476 + 23.6476i) q^{23} +(-13.3382 + 13.3382i) q^{25} +(-18.8815 - 30.8386i) q^{26} +(16.4031 - 32.1315i) q^{28} +(-14.5725 + 35.1811i) q^{29} +14.1609i q^{31} +(31.9999 + 0.0617869i) q^{32} +(-7.29019 + 10.0259i) q^{34} +(20.6421 + 8.55025i) q^{35} +(-30.0695 + 12.4552i) q^{37} +(37.8896 - 23.1987i) q^{38} +(1.53204 + 19.7590i) q^{40} +(56.9700 + 56.9700i) q^{41} +(54.5034 - 22.5760i) q^{43} +(5.04676 + 5.91825i) q^{44} +(66.0659 - 10.4377i) q^{46} -34.8047 q^{47} +32.3435i q^{49} +(37.2638 - 5.88726i) q^{50} +(-5.72981 + 72.0923i) q^{52} +(-3.92967 - 9.48706i) q^{53} +(-3.40615 + 3.40615i) q^{55} +(-64.3263 + 32.6821i) q^{56} +(64.9521 - 39.7682i) q^{58} +(-9.41777 - 22.7365i) q^{59} +(3.00467 - 7.25391i) q^{61} +(16.6560 - 22.9064i) q^{62} +(-51.6898 - 37.7381i) q^{64} -44.7892 q^{65} +(-55.9040 - 23.1562i) q^{67} +(23.5849 - 7.64307i) q^{68} +(-23.3335 - 38.1099i) q^{70} +(-6.27499 - 6.27499i) q^{71} +(66.4597 + 66.4597i) q^{73} +(63.2896 + 15.2203i) q^{74} +(-88.5756 - 7.03989i) q^{76} +(-16.2024 - 6.71124i) q^{77} -75.8508 q^{79} +(20.7623 - 33.7638i) q^{80} +(-25.1457 - 159.161i) q^{82} +(1.23390 - 2.97891i) q^{83} +(5.87593 + 14.1857i) q^{85} +(-114.717 - 27.5881i) q^{86} +(-1.20252 - 15.5092i) q^{88} +(-36.7030 + 36.7030i) q^{89} +(-62.4018 - 150.651i) q^{91} +(-119.144 - 60.8227i) q^{92} +(56.2994 + 40.9371i) q^{94} -55.0300i q^{95} +90.0528 q^{97} +(38.0423 - 52.3182i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61758 1.17620i −0.808790 0.588098i
\(3\) 0 0
\(4\) 1.23313 + 3.80518i 0.308282 + 0.951295i
\(5\) −2.28872 + 0.948019i −0.457744 + 0.189604i −0.599627 0.800280i \(-0.704684\pi\)
0.141883 + 0.989883i \(0.454684\pi\)
\(6\) 0 0
\(7\) −6.37744 6.37744i −0.911063 0.911063i 0.0852929 0.996356i \(-0.472817\pi\)
−0.996356 + 0.0852929i \(0.972817\pi\)
\(8\) 2.48095 7.60558i 0.310119 0.950698i
\(9\) 0 0
\(10\) 4.81725 + 1.15849i 0.481725 + 0.115849i
\(11\) 1.79646 0.744117i 0.163314 0.0676470i −0.299529 0.954087i \(-0.596829\pi\)
0.462843 + 0.886440i \(0.346829\pi\)
\(12\) 0 0
\(13\) 16.7036 + 6.91888i 1.28490 + 0.532221i 0.917460 0.397827i \(-0.130236\pi\)
0.367436 + 0.930049i \(0.380236\pi\)
\(14\) 2.81490 + 17.8171i 0.201065 + 1.27265i
\(15\) 0 0
\(16\) −12.9588 + 9.38456i −0.809924 + 0.586535i
\(17\) 6.19811i 0.364595i −0.983243 0.182297i \(-0.941647\pi\)
0.983243 0.182297i \(-0.0583533\pi\)
\(18\) 0 0
\(19\) −8.50083 + 20.5228i −0.447412 + 1.08015i 0.525876 + 0.850561i \(0.323738\pi\)
−0.973288 + 0.229587i \(0.926262\pi\)
\(20\) −6.42967 7.53997i −0.321484 0.376998i
\(21\) 0 0
\(22\) −3.78114 0.909316i −0.171870 0.0413325i
\(23\) −23.6476 + 23.6476i −1.02815 + 1.02815i −0.0285625 + 0.999592i \(0.509093\pi\)
−0.999592 + 0.0285625i \(0.990907\pi\)
\(24\) 0 0
\(25\) −13.3382 + 13.3382i −0.533527 + 0.533527i
\(26\) −18.8815 30.8386i −0.726213 1.18610i
\(27\) 0 0
\(28\) 16.4031 32.1315i 0.585825 1.14755i
\(29\) −14.5725 + 35.1811i −0.502500 + 1.21314i 0.445618 + 0.895223i \(0.352984\pi\)
−0.948118 + 0.317919i \(0.897016\pi\)
\(30\) 0 0
\(31\) 14.1609i 0.456803i 0.973567 + 0.228401i \(0.0733498\pi\)
−0.973567 + 0.228401i \(0.926650\pi\)
\(32\) 31.9999 + 0.0617869i 0.999998 + 0.00193084i
\(33\) 0 0
\(34\) −7.29019 + 10.0259i −0.214417 + 0.294880i
\(35\) 20.6421 + 8.55025i 0.589775 + 0.244293i
\(36\) 0 0
\(37\) −30.0695 + 12.4552i −0.812689 + 0.336627i −0.750027 0.661408i \(-0.769959\pi\)
−0.0626629 + 0.998035i \(0.519959\pi\)
\(38\) 37.8896 23.1987i 0.997095 0.610491i
\(39\) 0 0
\(40\) 1.53204 + 19.7590i 0.0383010 + 0.493976i
\(41\) 56.9700 + 56.9700i 1.38951 + 1.38951i 0.826341 + 0.563170i \(0.190418\pi\)
0.563170 + 0.826341i \(0.309582\pi\)
\(42\) 0 0
\(43\) 54.5034 22.5760i 1.26752 0.525024i 0.355310 0.934748i \(-0.384375\pi\)
0.912209 + 0.409724i \(0.134375\pi\)
\(44\) 5.04676 + 5.91825i 0.114699 + 0.134506i
\(45\) 0 0
\(46\) 66.0659 10.4377i 1.43622 0.226906i
\(47\) −34.8047 −0.740525 −0.370263 0.928927i \(-0.620732\pi\)
−0.370263 + 0.928927i \(0.620732\pi\)
\(48\) 0 0
\(49\) 32.3435i 0.660072i
\(50\) 37.2638 5.88726i 0.745277 0.117745i
\(51\) 0 0
\(52\) −5.72981 + 72.0923i −0.110189 + 1.38639i
\(53\) −3.92967 9.48706i −0.0741447 0.179001i 0.882462 0.470384i \(-0.155885\pi\)
−0.956606 + 0.291383i \(0.905885\pi\)
\(54\) 0 0
\(55\) −3.40615 + 3.40615i −0.0619300 + 0.0619300i
\(56\) −64.3263 + 32.6821i −1.14868 + 0.583608i
\(57\) 0 0
\(58\) 64.9521 39.7682i 1.11986 0.685658i
\(59\) −9.41777 22.7365i −0.159623 0.385365i 0.823752 0.566951i \(-0.191877\pi\)
−0.983375 + 0.181586i \(0.941877\pi\)
\(60\) 0 0
\(61\) 3.00467 7.25391i 0.0492568 0.118916i −0.897336 0.441348i \(-0.854500\pi\)
0.946593 + 0.322432i \(0.104500\pi\)
\(62\) 16.6560 22.9064i 0.268644 0.369457i
\(63\) 0 0
\(64\) −51.6898 37.7381i −0.807653 0.589658i
\(65\) −44.7892 −0.689065
\(66\) 0 0
\(67\) −55.9040 23.1562i −0.834388 0.345615i −0.0757497 0.997127i \(-0.524135\pi\)
−0.758638 + 0.651512i \(0.774135\pi\)
\(68\) 23.5849 7.64307i 0.346837 0.112398i
\(69\) 0 0
\(70\) −23.3335 38.1099i −0.333336 0.544427i
\(71\) −6.27499 6.27499i −0.0883801 0.0883801i 0.661535 0.749915i \(-0.269905\pi\)
−0.749915 + 0.661535i \(0.769905\pi\)
\(72\) 0 0
\(73\) 66.4597 + 66.4597i 0.910406 + 0.910406i 0.996304 0.0858977i \(-0.0273758\pi\)
−0.0858977 + 0.996304i \(0.527376\pi\)
\(74\) 63.2896 + 15.2203i 0.855265 + 0.205680i
\(75\) 0 0
\(76\) −88.5756 7.03989i −1.16547 0.0926301i
\(77\) −16.2024 6.71124i −0.210420 0.0871589i
\(78\) 0 0
\(79\) −75.8508 −0.960136 −0.480068 0.877231i \(-0.659388\pi\)
−0.480068 + 0.877231i \(0.659388\pi\)
\(80\) 20.7623 33.7638i 0.259529 0.422048i
\(81\) 0 0
\(82\) −25.1457 159.161i −0.306654 1.94099i
\(83\) 1.23390 2.97891i 0.0148663 0.0358905i −0.916272 0.400556i \(-0.868817\pi\)
0.931138 + 0.364666i \(0.118817\pi\)
\(84\) 0 0
\(85\) 5.87593 + 14.1857i 0.0691286 + 0.166891i
\(86\) −114.717 27.5881i −1.33392 0.320791i
\(87\) 0 0
\(88\) −1.20252 15.5092i −0.0136651 0.176241i
\(89\) −36.7030 + 36.7030i −0.412393 + 0.412393i −0.882572 0.470178i \(-0.844190\pi\)
0.470178 + 0.882572i \(0.344190\pi\)
\(90\) 0 0
\(91\) −62.4018 150.651i −0.685734 1.65551i
\(92\) −119.144 60.8227i −1.29504 0.661116i
\(93\) 0 0
\(94\) 56.2994 + 40.9371i 0.598929 + 0.435501i
\(95\) 55.0300i 0.579263i
\(96\) 0 0
\(97\) 90.0528 0.928379 0.464189 0.885736i \(-0.346346\pi\)
0.464189 + 0.885736i \(0.346346\pi\)
\(98\) 38.0423 52.3182i 0.388187 0.533859i
\(99\) 0 0
\(100\) −67.2018 34.3064i −0.672018 0.343064i
\(101\) 20.0870 8.32031i 0.198881 0.0823793i −0.281020 0.959702i \(-0.590673\pi\)
0.479901 + 0.877323i \(0.340673\pi\)
\(102\) 0 0
\(103\) 4.88882 + 4.88882i 0.0474642 + 0.0474642i 0.730441 0.682976i \(-0.239315\pi\)
−0.682976 + 0.730441i \(0.739315\pi\)
\(104\) 94.0630 109.876i 0.904452 1.05650i
\(105\) 0 0
\(106\) −4.80208 + 19.9681i −0.0453027 + 0.188379i
\(107\) 51.9710 21.5271i 0.485710 0.201188i −0.126371 0.991983i \(-0.540333\pi\)
0.612080 + 0.790795i \(0.290333\pi\)
\(108\) 0 0
\(109\) −49.8054 20.6301i −0.456931 0.189267i 0.142333 0.989819i \(-0.454540\pi\)
−0.599263 + 0.800552i \(0.704540\pi\)
\(110\) 9.51602 1.50342i 0.0865093 0.0136675i
\(111\) 0 0
\(112\) 142.493 + 22.7944i 1.27226 + 0.203522i
\(113\) 62.0870i 0.549442i 0.961524 + 0.274721i \(0.0885855\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(114\) 0 0
\(115\) 31.7043 76.5410i 0.275690 0.665574i
\(116\) −151.840 12.0681i −1.30897 0.104035i
\(117\) 0 0
\(118\) −11.5086 + 47.8553i −0.0975304 + 0.405553i
\(119\) −39.5281 + 39.5281i −0.332169 + 0.332169i
\(120\) 0 0
\(121\) −82.8864 + 82.8864i −0.685011 + 0.685011i
\(122\) −13.3923 + 8.19970i −0.109773 + 0.0672106i
\(123\) 0 0
\(124\) −53.8847 + 17.4622i −0.434554 + 0.140824i
\(125\) 41.5830 100.390i 0.332664 0.803122i
\(126\) 0 0
\(127\) 177.045i 1.39406i −0.717043 0.697029i \(-0.754505\pi\)
0.717043 0.697029i \(-0.245495\pi\)
\(128\) 39.2250 + 121.842i 0.306445 + 0.951888i
\(129\) 0 0
\(130\) 72.4502 + 52.6809i 0.557309 + 0.405238i
\(131\) −88.7654 36.7678i −0.677598 0.280670i 0.0172241 0.999852i \(-0.494517\pi\)
−0.694823 + 0.719181i \(0.744517\pi\)
\(132\) 0 0
\(133\) 185.097 76.6695i 1.39170 0.576462i
\(134\) 63.1930 + 103.211i 0.471589 + 0.770231i
\(135\) 0 0
\(136\) −47.1402 15.3772i −0.346619 0.113068i
\(137\) 58.5583 + 58.5583i 0.427433 + 0.427433i 0.887753 0.460320i \(-0.152265\pi\)
−0.460320 + 0.887753i \(0.652265\pi\)
\(138\) 0 0
\(139\) −166.832 + 69.1039i −1.20023 + 0.497151i −0.891072 0.453861i \(-0.850046\pi\)
−0.309155 + 0.951012i \(0.600046\pi\)
\(140\) −7.08082 + 89.0906i −0.0505773 + 0.636361i
\(141\) 0 0
\(142\) 2.76968 + 17.5309i 0.0195048 + 0.123457i
\(143\) 35.1558 0.245845
\(144\) 0 0
\(145\) 94.3348i 0.650585i
\(146\) −29.3343 185.673i −0.200920 1.27174i
\(147\) 0 0
\(148\) −84.4739 99.0610i −0.570769 0.669331i
\(149\) −18.0040 43.4655i −0.120832 0.291715i 0.851877 0.523742i \(-0.175464\pi\)
−0.972709 + 0.232027i \(0.925464\pi\)
\(150\) 0 0
\(151\) −68.3596 + 68.3596i −0.452713 + 0.452713i −0.896254 0.443541i \(-0.853722\pi\)
0.443541 + 0.896254i \(0.353722\pi\)
\(152\) 134.998 + 115.570i 0.888144 + 0.760328i
\(153\) 0 0
\(154\) 18.3149 + 29.9131i 0.118928 + 0.194241i
\(155\) −13.4248 32.4103i −0.0866115 0.209099i
\(156\) 0 0
\(157\) −74.5650 + 180.016i −0.474936 + 1.14660i 0.487020 + 0.873391i \(0.338084\pi\)
−0.961956 + 0.273206i \(0.911916\pi\)
\(158\) 122.695 + 89.2153i 0.776549 + 0.564654i
\(159\) 0 0
\(160\) −73.2975 + 30.1952i −0.458110 + 0.188720i
\(161\) 301.622 1.87343
\(162\) 0 0
\(163\) 267.123 + 110.646i 1.63879 + 0.678811i 0.996175 0.0873756i \(-0.0278480\pi\)
0.642619 + 0.766186i \(0.277848\pi\)
\(164\) −146.530 + 287.032i −0.893473 + 1.75020i
\(165\) 0 0
\(166\) −5.49972 + 3.36731i −0.0331308 + 0.0202850i
\(167\) −99.3059 99.3059i −0.594646 0.594646i 0.344237 0.938883i \(-0.388138\pi\)
−0.938883 + 0.344237i \(0.888138\pi\)
\(168\) 0 0
\(169\) 111.640 + 111.640i 0.660592 + 0.660592i
\(170\) 7.18042 29.8578i 0.0422378 0.175634i
\(171\) 0 0
\(172\) 153.116 + 179.556i 0.890207 + 1.04393i
\(173\) −187.259 77.5652i −1.08242 0.448354i −0.231063 0.972939i \(-0.574220\pi\)
−0.851358 + 0.524585i \(0.824220\pi\)
\(174\) 0 0
\(175\) 170.127 0.972153
\(176\) −16.2967 + 26.5018i −0.0925948 + 0.150578i
\(177\) 0 0
\(178\) 102.540 16.2001i 0.576067 0.0910121i
\(179\) 101.230 244.390i 0.565528 1.36531i −0.339761 0.940512i \(-0.610346\pi\)
0.905290 0.424795i \(-0.139654\pi\)
\(180\) 0 0
\(181\) 6.07796 + 14.6735i 0.0335799 + 0.0810690i 0.939780 0.341780i \(-0.111030\pi\)
−0.906200 + 0.422849i \(0.861030\pi\)
\(182\) −76.2554 + 317.087i −0.418986 + 1.74224i
\(183\) 0 0
\(184\) 121.185 + 238.522i 0.658614 + 1.29631i
\(185\) 57.0130 57.0130i 0.308178 0.308178i
\(186\) 0 0
\(187\) −4.61212 11.1346i −0.0246637 0.0595435i
\(188\) −42.9187 132.438i −0.228291 0.704458i
\(189\) 0 0
\(190\) −64.7260 + 89.0154i −0.340663 + 0.468502i
\(191\) 370.577i 1.94019i 0.242716 + 0.970097i \(0.421962\pi\)
−0.242716 + 0.970097i \(0.578038\pi\)
\(192\) 0 0
\(193\) −132.679 −0.687456 −0.343728 0.939069i \(-0.611690\pi\)
−0.343728 + 0.939069i \(0.611690\pi\)
\(194\) −145.668 105.920i −0.750864 0.545977i
\(195\) 0 0
\(196\) −123.073 + 39.8837i −0.627923 + 0.203488i
\(197\) −116.390 + 48.2104i −0.590814 + 0.244723i −0.658001 0.753017i \(-0.728598\pi\)
0.0671870 + 0.997740i \(0.478598\pi\)
\(198\) 0 0
\(199\) −89.9950 89.9950i −0.452236 0.452236i 0.443860 0.896096i \(-0.353609\pi\)
−0.896096 + 0.443860i \(0.853609\pi\)
\(200\) 68.3532 + 134.536i 0.341766 + 0.672679i
\(201\) 0 0
\(202\) −42.2786 10.1675i −0.209300 0.0503340i
\(203\) 317.301 131.430i 1.56306 0.647440i
\(204\) 0 0
\(205\) −184.397 76.3797i −0.899498 0.372584i
\(206\) −2.15785 13.6582i −0.0104750 0.0663022i
\(207\) 0 0
\(208\) −281.390 + 67.0961i −1.35283 + 0.322578i
\(209\) 43.1940i 0.206670i
\(210\) 0 0
\(211\) 20.9287 50.5264i 0.0991883 0.239462i −0.866494 0.499187i \(-0.833632\pi\)
0.965683 + 0.259725i \(0.0836321\pi\)
\(212\) 31.2542 26.6519i 0.147425 0.125716i
\(213\) 0 0
\(214\) −109.387 26.3062i −0.511155 0.122926i
\(215\) −103.340 + 103.340i −0.480653 + 0.480653i
\(216\) 0 0
\(217\) 90.3102 90.3102i 0.416176 0.416176i
\(218\) 56.2993 + 91.9518i 0.258254 + 0.421797i
\(219\) 0 0
\(220\) −17.1612 8.76079i −0.0780057 0.0398218i
\(221\) 42.8840 103.531i 0.194045 0.468466i
\(222\) 0 0
\(223\) 52.7540i 0.236565i 0.992980 + 0.118283i \(0.0377388\pi\)
−0.992980 + 0.118283i \(0.962261\pi\)
\(224\) −203.684 204.472i −0.909302 0.912820i
\(225\) 0 0
\(226\) 73.0264 100.431i 0.323126 0.444383i
\(227\) 327.101 + 135.490i 1.44097 + 0.596871i 0.960034 0.279883i \(-0.0902957\pi\)
0.480939 + 0.876754i \(0.340296\pi\)
\(228\) 0 0
\(229\) 245.430 101.660i 1.07175 0.443932i 0.224139 0.974557i \(-0.428043\pi\)
0.847606 + 0.530625i \(0.178043\pi\)
\(230\) −141.311 + 86.5207i −0.614398 + 0.376177i
\(231\) 0 0
\(232\) 231.419 + 198.115i 0.997497 + 0.853944i
\(233\) 31.8772 + 31.8772i 0.136812 + 0.136812i 0.772196 0.635384i \(-0.219158\pi\)
−0.635384 + 0.772196i \(0.719158\pi\)
\(234\) 0 0
\(235\) 79.6582 32.9955i 0.338971 0.140406i
\(236\) 74.9032 63.8734i 0.317386 0.270650i
\(237\) 0 0
\(238\) 110.433 17.4471i 0.464002 0.0733071i
\(239\) −90.0511 −0.376783 −0.188391 0.982094i \(-0.560327\pi\)
−0.188391 + 0.982094i \(0.560327\pi\)
\(240\) 0 0
\(241\) 20.9972i 0.0871252i 0.999051 + 0.0435626i \(0.0138708\pi\)
−0.999051 + 0.0435626i \(0.986129\pi\)
\(242\) 231.566 36.5848i 0.956884 0.151177i
\(243\) 0 0
\(244\) 31.3076 + 2.48829i 0.128310 + 0.0101979i
\(245\) −30.6623 74.0253i −0.125152 0.302144i
\(246\) 0 0
\(247\) −283.990 + 283.990i −1.14976 + 1.14976i
\(248\) 107.702 + 35.1324i 0.434281 + 0.141663i
\(249\) 0 0
\(250\) −185.342 + 113.479i −0.741369 + 0.453918i
\(251\) −105.207 253.991i −0.419150 1.01192i −0.982594 0.185764i \(-0.940524\pi\)
0.563444 0.826154i \(-0.309476\pi\)
\(252\) 0 0
\(253\) −24.8853 + 60.0783i −0.0983607 + 0.237464i
\(254\) −208.240 + 286.385i −0.819842 + 1.12750i
\(255\) 0 0
\(256\) 79.8601 243.225i 0.311954 0.950097i
\(257\) −236.584 −0.920561 −0.460281 0.887773i \(-0.652251\pi\)
−0.460281 + 0.887773i \(0.652251\pi\)
\(258\) 0 0
\(259\) 271.199 + 112.334i 1.04710 + 0.433723i
\(260\) −55.2309 170.431i −0.212427 0.655504i
\(261\) 0 0
\(262\) 100.339 + 163.880i 0.382973 + 0.625498i
\(263\) −32.0070 32.0070i −0.121700 0.121700i 0.643634 0.765334i \(-0.277426\pi\)
−0.765334 + 0.643634i \(0.777426\pi\)
\(264\) 0 0
\(265\) 17.9878 + 17.9878i 0.0678786 + 0.0678786i
\(266\) −389.587 93.6906i −1.46461 0.352220i
\(267\) 0 0
\(268\) 19.1766 241.279i 0.0715545 0.900296i
\(269\) −115.344 47.7769i −0.428787 0.177609i 0.157844 0.987464i \(-0.449546\pi\)
−0.586630 + 0.809855i \(0.699546\pi\)
\(270\) 0 0
\(271\) −55.4325 −0.204548 −0.102274 0.994756i \(-0.532612\pi\)
−0.102274 + 0.994756i \(0.532612\pi\)
\(272\) 58.1665 + 80.3199i 0.213847 + 0.295294i
\(273\) 0 0
\(274\) −25.8468 163.599i −0.0943312 0.597076i
\(275\) −14.0363 + 33.8866i −0.0510410 + 0.123224i
\(276\) 0 0
\(277\) −35.7881 86.4001i −0.129199 0.311914i 0.846022 0.533148i \(-0.178991\pi\)
−0.975221 + 0.221235i \(0.928991\pi\)
\(278\) 351.143 + 84.4454i 1.26310 + 0.303761i
\(279\) 0 0
\(280\) 116.242 135.783i 0.415149 0.484938i
\(281\) −13.8509 + 13.8509i −0.0492914 + 0.0492914i −0.731323 0.682031i \(-0.761097\pi\)
0.682031 + 0.731323i \(0.261097\pi\)
\(282\) 0 0
\(283\) −135.615 327.403i −0.479205 1.15690i −0.959982 0.280060i \(-0.909646\pi\)
0.480778 0.876843i \(-0.340354\pi\)
\(284\) 16.1396 31.6153i 0.0568295 0.111322i
\(285\) 0 0
\(286\) −56.8674 41.3501i −0.198837 0.144581i
\(287\) 726.645i 2.53186i
\(288\) 0 0
\(289\) 250.583 0.867071
\(290\) −110.956 + 152.594i −0.382608 + 0.526187i
\(291\) 0 0
\(292\) −170.938 + 334.844i −0.585403 + 1.14673i
\(293\) 412.791 170.984i 1.40884 0.583562i 0.456811 0.889564i \(-0.348991\pi\)
0.952031 + 0.306002i \(0.0989914\pi\)
\(294\) 0 0
\(295\) 43.1093 + 43.1093i 0.146133 + 0.146133i
\(296\) 20.1281 + 259.597i 0.0680005 + 0.877016i
\(297\) 0 0
\(298\) −22.0010 + 91.4851i −0.0738289 + 0.306997i
\(299\) −558.615 + 231.386i −1.86828 + 0.773866i
\(300\) 0 0
\(301\) −491.569 203.615i −1.63312 0.676461i
\(302\) 190.981 30.1729i 0.632389 0.0999102i
\(303\) 0 0
\(304\) −82.4372 345.727i −0.271175 1.13726i
\(305\) 19.4507i 0.0637726i
\(306\) 0 0
\(307\) −42.3557 + 102.256i −0.137967 + 0.333081i −0.977728 0.209874i \(-0.932695\pi\)
0.839762 + 0.542955i \(0.182695\pi\)
\(308\) 5.55785 69.9287i 0.0180450 0.227041i
\(309\) 0 0
\(310\) −16.4052 + 68.2164i −0.0529199 + 0.220053i
\(311\) −337.326 + 337.326i −1.08465 + 1.08465i −0.0885790 + 0.996069i \(0.528233\pi\)
−0.996069 + 0.0885790i \(0.971767\pi\)
\(312\) 0 0
\(313\) −70.0735 + 70.0735i −0.223877 + 0.223877i −0.810129 0.586252i \(-0.800603\pi\)
0.586252 + 0.810129i \(0.300603\pi\)
\(314\) 332.348 203.487i 1.05843 0.648047i
\(315\) 0 0
\(316\) −93.5338 288.626i −0.295993 0.913373i
\(317\) −32.8632 + 79.3388i −0.103669 + 0.250280i −0.967200 0.254017i \(-0.918248\pi\)
0.863530 + 0.504297i \(0.168248\pi\)
\(318\) 0 0
\(319\) 74.0450i 0.232116i
\(320\) 154.080 + 37.3691i 0.481500 + 0.116779i
\(321\) 0 0
\(322\) −487.897 354.766i −1.51521 1.10176i
\(323\) 127.203 + 52.6891i 0.393816 + 0.163124i
\(324\) 0 0
\(325\) −315.081 + 130.511i −0.969480 + 0.401572i
\(326\) −301.952 493.168i −0.926233 1.51279i
\(327\) 0 0
\(328\) 574.629 291.950i 1.75192 0.890092i
\(329\) 221.965 + 221.965i 0.674665 + 0.674665i
\(330\) 0 0
\(331\) 124.865 51.7206i 0.377234 0.156256i −0.186006 0.982549i \(-0.559554\pi\)
0.563240 + 0.826293i \(0.309554\pi\)
\(332\) 12.8568 + 1.02185i 0.0387254 + 0.00307785i
\(333\) 0 0
\(334\) 43.8321 + 277.438i 0.131234 + 0.830654i
\(335\) 149.901 0.447466
\(336\) 0 0
\(337\) 323.529i 0.960027i −0.877261 0.480014i \(-0.840632\pi\)
0.877261 0.480014i \(-0.159368\pi\)
\(338\) −49.2762 311.897i −0.145787 0.922772i
\(339\) 0 0
\(340\) −46.7335 + 39.8518i −0.137452 + 0.117211i
\(341\) 10.5373 + 25.4394i 0.0309013 + 0.0746024i
\(342\) 0 0
\(343\) −106.226 + 106.226i −0.309696 + 0.309696i
\(344\) −36.4838 470.540i −0.106058 1.36785i
\(345\) 0 0
\(346\) 211.674 + 345.721i 0.611776 + 0.999193i
\(347\) 135.065 + 326.076i 0.389236 + 0.939700i 0.990102 + 0.140350i \(0.0448226\pi\)
−0.600866 + 0.799350i \(0.705177\pi\)
\(348\) 0 0
\(349\) 187.869 453.555i 0.538305 1.29958i −0.387600 0.921828i \(-0.626696\pi\)
0.925905 0.377756i \(-0.123304\pi\)
\(350\) −275.194 200.102i −0.786267 0.571721i
\(351\) 0 0
\(352\) 57.5325 23.7007i 0.163445 0.0673315i
\(353\) 70.5556 0.199874 0.0999372 0.994994i \(-0.468136\pi\)
0.0999372 + 0.994994i \(0.468136\pi\)
\(354\) 0 0
\(355\) 20.3105 + 8.41289i 0.0572127 + 0.0236983i
\(356\) −184.921 94.4020i −0.519441 0.265174i
\(357\) 0 0
\(358\) −451.197 + 276.254i −1.26033 + 0.771660i
\(359\) 409.567 + 409.567i 1.14086 + 1.14086i 0.988294 + 0.152561i \(0.0487522\pi\)
0.152561 + 0.988294i \(0.451248\pi\)
\(360\) 0 0
\(361\) −93.6563 93.6563i −0.259436 0.259436i
\(362\) 7.42731 30.8844i 0.0205174 0.0853161i
\(363\) 0 0
\(364\) 496.306 423.223i 1.36348 1.16270i
\(365\) −215.113 89.1026i −0.589350 0.244117i
\(366\) 0 0
\(367\) 513.680 1.39967 0.699837 0.714303i \(-0.253256\pi\)
0.699837 + 0.714303i \(0.253256\pi\)
\(368\) 84.5217 528.365i 0.229678 1.43578i
\(369\) 0 0
\(370\) −159.281 + 25.1646i −0.430490 + 0.0680126i
\(371\) −35.4419 + 85.5644i −0.0955308 + 0.230632i
\(372\) 0 0
\(373\) −46.5164 112.301i −0.124709 0.301074i 0.849178 0.528106i \(-0.177098\pi\)
−0.973887 + 0.227032i \(0.927098\pi\)
\(374\) −5.63604 + 23.4359i −0.0150696 + 0.0626629i
\(375\) 0 0
\(376\) −86.3486 + 264.710i −0.229651 + 0.704016i
\(377\) −486.828 + 486.828i −1.29132 + 1.29132i
\(378\) 0 0
\(379\) 172.090 + 415.462i 0.454064 + 1.09621i 0.970763 + 0.240040i \(0.0771604\pi\)
−0.516699 + 0.856167i \(0.672840\pi\)
\(380\) 209.399 67.8591i 0.551050 0.178576i
\(381\) 0 0
\(382\) 435.871 599.438i 1.14102 1.56921i
\(383\) 430.627i 1.12435i 0.827017 + 0.562177i \(0.190036\pi\)
−0.827017 + 0.562177i \(0.809964\pi\)
\(384\) 0 0
\(385\) 43.4451 0.112844
\(386\) 214.619 + 156.056i 0.556008 + 0.404291i
\(387\) 0 0
\(388\) 111.047 + 342.667i 0.286203 + 0.883162i
\(389\) −55.8615 + 23.1386i −0.143603 + 0.0594823i −0.453327 0.891344i \(-0.649763\pi\)
0.309725 + 0.950826i \(0.399763\pi\)
\(390\) 0 0
\(391\) 146.570 + 146.570i 0.374860 + 0.374860i
\(392\) 245.991 + 80.2426i 0.627529 + 0.204701i
\(393\) 0 0
\(394\) 244.975 + 58.9135i 0.621765 + 0.149527i
\(395\) 173.601 71.9080i 0.439497 0.182046i
\(396\) 0 0
\(397\) −67.6641 28.0274i −0.170439 0.0705979i 0.295833 0.955240i \(-0.404403\pi\)
−0.466271 + 0.884642i \(0.654403\pi\)
\(398\) 39.7224 + 251.426i 0.0998051 + 0.631723i
\(399\) 0 0
\(400\) 47.6736 298.019i 0.119184 0.745048i
\(401\) 536.024i 1.33672i −0.743839 0.668359i \(-0.766997\pi\)
0.743839 0.668359i \(-0.233003\pi\)
\(402\) 0 0
\(403\) −97.9774 + 236.538i −0.243120 + 0.586944i
\(404\) 56.4301 + 66.1746i 0.139679 + 0.163799i
\(405\) 0 0
\(406\) −667.847 160.609i −1.64494 0.395588i
\(407\) −44.7505 + 44.7505i −0.109952 + 0.109952i
\(408\) 0 0
\(409\) −540.379 + 540.379i −1.32122 + 1.32122i −0.408430 + 0.912790i \(0.633923\pi\)
−0.912790 + 0.408430i \(0.866077\pi\)
\(410\) 208.439 + 340.437i 0.508389 + 0.830335i
\(411\) 0 0
\(412\) −12.5743 + 24.6314i −0.0305201 + 0.0597849i
\(413\) −84.9395 + 205.062i −0.205665 + 0.496518i
\(414\) 0 0
\(415\) 7.98765i 0.0192474i
\(416\) 534.088 + 222.436i 1.28387 + 0.534701i
\(417\) 0 0
\(418\) 50.8045 69.8697i 0.121542 0.167152i
\(419\) 341.184 + 141.323i 0.814281 + 0.337286i 0.750661 0.660688i \(-0.229735\pi\)
0.0636205 + 0.997974i \(0.479735\pi\)
\(420\) 0 0
\(421\) 339.196 140.500i 0.805692 0.333728i 0.0584581 0.998290i \(-0.481382\pi\)
0.747234 + 0.664561i \(0.231382\pi\)
\(422\) −93.2828 + 57.1142i −0.221049 + 0.135342i
\(423\) 0 0
\(424\) −81.9039 + 6.35051i −0.193170 + 0.0149776i
\(425\) 82.6714 + 82.6714i 0.194521 + 0.194521i
\(426\) 0 0
\(427\) −65.4234 + 27.0993i −0.153216 + 0.0634643i
\(428\) 146.001 + 171.213i 0.341125 + 0.400031i
\(429\) 0 0
\(430\) 288.710 45.6129i 0.671419 0.106077i
\(431\) −154.504 −0.358478 −0.179239 0.983806i \(-0.557363\pi\)
−0.179239 + 0.983806i \(0.557363\pi\)
\(432\) 0 0
\(433\) 506.808i 1.17046i −0.810868 0.585228i \(-0.801005\pi\)
0.810868 0.585228i \(-0.198995\pi\)
\(434\) −252.306 + 39.8615i −0.581351 + 0.0918468i
\(435\) 0 0
\(436\) 17.0846 214.958i 0.0391850 0.493023i
\(437\) −284.291 686.338i −0.650550 1.57057i
\(438\) 0 0
\(439\) −144.746 + 144.746i −0.329718 + 0.329718i −0.852479 0.522761i \(-0.824902\pi\)
0.522761 + 0.852479i \(0.324902\pi\)
\(440\) 17.4553 + 34.3563i 0.0396711 + 0.0780824i
\(441\) 0 0
\(442\) −191.141 + 117.030i −0.432446 + 0.264773i
\(443\) −230.959 557.584i −0.521351 1.25865i −0.937064 0.349158i \(-0.886468\pi\)
0.415713 0.909496i \(-0.363532\pi\)
\(444\) 0 0
\(445\) 49.2078 118.798i 0.110579 0.266962i
\(446\) 62.0490 85.3338i 0.139123 0.191331i
\(447\) 0 0
\(448\) 88.9759 + 570.321i 0.198607 + 1.27304i
\(449\) 0.201052 0.000447778 0.000223889 1.00000i \(-0.499929\pi\)
0.000223889 1.00000i \(0.499929\pi\)
\(450\) 0 0
\(451\) 144.736 + 59.9518i 0.320923 + 0.132931i
\(452\) −236.252 + 76.5613i −0.522681 + 0.169383i
\(453\) 0 0
\(454\) −369.750 603.900i −0.814427 1.33018i
\(455\) 285.641 + 285.641i 0.627782 + 0.627782i
\(456\) 0 0
\(457\) 226.835 + 226.835i 0.496358 + 0.496358i 0.910302 0.413944i \(-0.135849\pi\)
−0.413944 + 0.910302i \(0.635849\pi\)
\(458\) −516.575 124.230i −1.12789 0.271244i
\(459\) 0 0
\(460\) 330.348 + 26.2557i 0.718147 + 0.0570775i
\(461\) −496.600 205.699i −1.07722 0.446201i −0.227690 0.973734i \(-0.573117\pi\)
−0.849535 + 0.527533i \(0.823117\pi\)
\(462\) 0 0
\(463\) −520.019 −1.12315 −0.561576 0.827425i \(-0.689805\pi\)
−0.561576 + 0.827425i \(0.689805\pi\)
\(464\) −141.317 592.661i −0.304564 1.27729i
\(465\) 0 0
\(466\) −14.0701 89.0576i −0.0301933 0.191111i
\(467\) −35.4966 + 85.6964i −0.0760099 + 0.183504i −0.957317 0.289040i \(-0.906664\pi\)
0.881307 + 0.472544i \(0.156664\pi\)
\(468\) 0 0
\(469\) 208.847 + 504.202i 0.445303 + 1.07506i
\(470\) −167.663 40.3207i −0.356729 0.0857888i
\(471\) 0 0
\(472\) −196.289 + 15.2195i −0.415868 + 0.0322448i
\(473\) 81.1137 81.1137i 0.171488 0.171488i
\(474\) 0 0
\(475\) −160.351 387.122i −0.337582 0.814994i
\(476\) −199.155 101.668i −0.418392 0.213589i
\(477\) 0 0
\(478\) 145.665 + 105.918i 0.304738 + 0.221585i
\(479\) 163.116i 0.340535i 0.985398 + 0.170268i \(0.0544632\pi\)
−0.985398 + 0.170268i \(0.945537\pi\)
\(480\) 0 0
\(481\) −588.447 −1.22338
\(482\) 24.6968 33.9646i 0.0512381 0.0704660i
\(483\) 0 0
\(484\) −417.607 213.188i −0.862825 0.440471i
\(485\) −206.106 + 85.3718i −0.424960 + 0.176024i
\(486\) 0 0
\(487\) 371.724 + 371.724i 0.763294 + 0.763294i 0.976916 0.213622i \(-0.0685262\pi\)
−0.213622 + 0.976916i \(0.568526\pi\)
\(488\) −47.7158 40.8488i −0.0977782 0.0837066i
\(489\) 0 0
\(490\) −37.4695 + 155.807i −0.0764684 + 0.317973i
\(491\) −281.201 + 116.477i −0.572710 + 0.237224i −0.650193 0.759769i \(-0.725312\pi\)
0.0774824 + 0.996994i \(0.475312\pi\)
\(492\) 0 0
\(493\) 218.056 + 90.3220i 0.442305 + 0.183209i
\(494\) 793.403 125.349i 1.60608 0.253742i
\(495\) 0 0
\(496\) −132.894 183.508i −0.267931 0.369975i
\(497\) 80.0367i 0.161040i
\(498\) 0 0
\(499\) −236.126 + 570.059i −0.473199 + 1.14240i 0.489542 + 0.871980i \(0.337164\pi\)
−0.962741 + 0.270424i \(0.912836\pi\)
\(500\) 433.280 + 34.4366i 0.866560 + 0.0688732i
\(501\) 0 0
\(502\) −128.563 + 534.595i −0.256102 + 1.06493i
\(503\) −12.8902 + 12.8902i −0.0256266 + 0.0256266i −0.719804 0.694177i \(-0.755768\pi\)
0.694177 + 0.719804i \(0.255768\pi\)
\(504\) 0 0
\(505\) −38.0857 + 38.0857i −0.0754173 + 0.0754173i
\(506\) 110.918 67.9116i 0.219205 0.134213i
\(507\) 0 0
\(508\) 673.690 218.320i 1.32616 0.429764i
\(509\) −59.1272 + 142.746i −0.116163 + 0.280443i −0.971258 0.238028i \(-0.923499\pi\)
0.855095 + 0.518472i \(0.173499\pi\)
\(510\) 0 0
\(511\) 847.685i 1.65888i
\(512\) −415.260 + 299.505i −0.811055 + 0.584970i
\(513\) 0 0
\(514\) 382.694 + 278.269i 0.744541 + 0.541380i
\(515\) −15.8238 6.55444i −0.0307259 0.0127271i
\(516\) 0 0
\(517\) −62.5251 + 25.8988i −0.120938 + 0.0500943i
\(518\) −306.559 500.692i −0.591812 0.966588i
\(519\) 0 0
\(520\) −111.120 + 340.648i −0.213692 + 0.655093i
\(521\) −119.838 119.838i −0.230015 0.230015i 0.582684 0.812699i \(-0.302003\pi\)
−0.812699 + 0.582684i \(0.802003\pi\)
\(522\) 0 0
\(523\) −689.004 + 285.395i −1.31741 + 0.545688i −0.927037 0.374970i \(-0.877653\pi\)
−0.390370 + 0.920658i \(0.627653\pi\)
\(524\) 30.4490 383.108i 0.0581087 0.731122i
\(525\) 0 0
\(526\) 14.1274 + 89.4203i 0.0268582 + 0.170001i
\(527\) 87.7707 0.166548
\(528\) 0 0
\(529\) 589.413i 1.11420i
\(530\) −7.93955 50.2540i −0.0149803 0.0948188i
\(531\) 0 0
\(532\) 519.989 + 609.782i 0.977423 + 1.14621i
\(533\) 557.438 + 1345.77i 1.04585 + 2.52490i
\(534\) 0 0
\(535\) −98.5390 + 98.5390i −0.184185 + 0.184185i
\(536\) −314.811 + 367.733i −0.587334 + 0.686069i
\(537\) 0 0
\(538\) 130.383 + 212.950i 0.242347 + 0.395817i
\(539\) 24.0673 + 58.1037i 0.0446519 + 0.107799i
\(540\) 0 0
\(541\) −294.810 + 711.735i −0.544936 + 1.31559i 0.376267 + 0.926511i \(0.377207\pi\)
−0.921204 + 0.389081i \(0.872793\pi\)
\(542\) 89.6665 + 65.1995i 0.165436 + 0.120294i
\(543\) 0 0
\(544\) 0.382962 198.339i 0.000703974 0.364594i
\(545\) 133.549 0.245043
\(546\) 0 0
\(547\) 518.930 + 214.948i 0.948683 + 0.392957i 0.802736 0.596335i \(-0.203377\pi\)
0.145948 + 0.989292i \(0.453377\pi\)
\(548\) −150.615 + 295.035i −0.274845 + 0.538385i
\(549\) 0 0
\(550\) 62.5621 38.3049i 0.113749 0.0696452i
\(551\) −598.138 598.138i −1.08555 1.08555i
\(552\) 0 0
\(553\) 483.734 + 483.734i 0.874745 + 0.874745i
\(554\) −43.7333 + 181.853i −0.0789410 + 0.328254i
\(555\) 0 0
\(556\) −468.678 549.610i −0.842946 0.988508i
\(557\) 883.511 + 365.962i 1.58620 + 0.657024i 0.989380 0.145355i \(-0.0464323\pi\)
0.596816 + 0.802378i \(0.296432\pi\)
\(558\) 0 0
\(559\) 1066.61 1.90806
\(560\) −347.737 + 82.9164i −0.620959 + 0.148065i
\(561\) 0 0
\(562\) 38.6963 6.11357i 0.0688546 0.0108782i
\(563\) −385.055 + 929.606i −0.683935 + 1.65117i 0.0727214 + 0.997352i \(0.476832\pi\)
−0.756656 + 0.653813i \(0.773168\pi\)
\(564\) 0 0
\(565\) −58.8596 142.100i −0.104176 0.251504i
\(566\) −165.722 + 689.111i −0.292796 + 1.21751i
\(567\) 0 0
\(568\) −63.2928 + 32.1570i −0.111431 + 0.0566145i
\(569\) 503.029 503.029i 0.884058 0.884058i −0.109886 0.993944i \(-0.535049\pi\)
0.993944 + 0.109886i \(0.0350485\pi\)
\(570\) 0 0
\(571\) −48.1525 116.250i −0.0843301 0.203591i 0.876089 0.482149i \(-0.160144\pi\)
−0.960419 + 0.278558i \(0.910144\pi\)
\(572\) 43.3517 + 133.774i 0.0757897 + 0.233871i
\(573\) 0 0
\(574\) −854.677 + 1175.41i −1.48898 + 2.04775i
\(575\) 630.830i 1.09710i
\(576\) 0 0
\(577\) −11.8629 −0.0205595 −0.0102798 0.999947i \(-0.503272\pi\)
−0.0102798 + 0.999947i \(0.503272\pi\)
\(578\) −405.339 294.735i −0.701278 0.509922i
\(579\) 0 0
\(580\) 358.961 116.327i 0.618898 0.200564i
\(581\) −26.8670 + 11.1287i −0.0462426 + 0.0191543i
\(582\) 0 0
\(583\) −14.1190 14.1190i −0.0242178 0.0242178i
\(584\) 670.347 340.581i 1.14786 0.583187i
\(585\) 0 0
\(586\) −868.832 208.943i −1.48265 0.356558i
\(587\) 496.631 205.711i 0.846049 0.350445i 0.0828132 0.996565i \(-0.473610\pi\)
0.763236 + 0.646120i \(0.223610\pi\)
\(588\) 0 0
\(589\) −290.621 120.379i −0.493414 0.204379i
\(590\) −19.0278 120.438i −0.0322505 0.204132i
\(591\) 0 0
\(592\) 272.778 443.593i 0.460773 0.749313i
\(593\) 410.471i 0.692193i −0.938199 0.346097i \(-0.887507\pi\)
0.938199 0.346097i \(-0.112493\pi\)
\(594\) 0 0
\(595\) 52.9954 127.942i 0.0890678 0.215029i
\(596\) 143.193 122.107i 0.240256 0.204878i
\(597\) 0 0
\(598\) 1175.76 + 282.755i 1.96615 + 0.472835i
\(599\) 565.778 565.778i 0.944537 0.944537i −0.0540033 0.998541i \(-0.517198\pi\)
0.998541 + 0.0540033i \(0.0171982\pi\)
\(600\) 0 0
\(601\) 224.391 224.391i 0.373362 0.373362i −0.495338 0.868700i \(-0.664956\pi\)
0.868700 + 0.495338i \(0.164956\pi\)
\(602\) 555.662 + 907.544i 0.923026 + 1.50755i
\(603\) 0 0
\(604\) −344.417 175.824i −0.570226 0.291100i
\(605\) 111.126 268.282i 0.183679 0.443441i
\(606\) 0 0
\(607\) 19.8654i 0.0327271i −0.999866 0.0163636i \(-0.994791\pi\)
0.999866 0.0163636i \(-0.00520892\pi\)
\(608\) −273.294 + 656.204i −0.449497 + 1.07928i
\(609\) 0 0
\(610\) 22.8778 31.4630i 0.0375045 0.0515787i
\(611\) −581.365 240.809i −0.951498 0.394123i
\(612\) 0 0
\(613\) 905.460 375.054i 1.47710 0.611833i 0.508631 0.860985i \(-0.330152\pi\)
0.968464 + 0.249152i \(0.0801518\pi\)
\(614\) 188.787 115.588i 0.307470 0.188255i
\(615\) 0 0
\(616\) −91.2401 + 106.578i −0.148117 + 0.173016i
\(617\) −673.907 673.907i −1.09223 1.09223i −0.995290 0.0969409i \(-0.969094\pi\)
−0.0969409 0.995290i \(-0.530906\pi\)
\(618\) 0 0
\(619\) 354.963 147.030i 0.573446 0.237529i −0.0770649 0.997026i \(-0.524555\pi\)
0.650511 + 0.759497i \(0.274555\pi\)
\(620\) 106.773 91.0498i 0.172214 0.146855i
\(621\) 0 0
\(622\) 942.412 148.890i 1.51513 0.239374i
\(623\) 468.143 0.751433
\(624\) 0 0
\(625\) 202.389i 0.323822i
\(626\) 195.770 30.9294i 0.312731 0.0494080i
\(627\) 0 0
\(628\) −776.940 61.7503i −1.23717 0.0983286i
\(629\) 77.1987 + 186.374i 0.122732 + 0.296302i
\(630\) 0 0
\(631\) −494.698 + 494.698i −0.783991 + 0.783991i −0.980502 0.196511i \(-0.937039\pi\)
0.196511 + 0.980502i \(0.437039\pi\)
\(632\) −188.182 + 576.889i −0.297756 + 0.912800i
\(633\) 0 0
\(634\) 146.477 89.6833i 0.231036 0.141456i
\(635\) 167.843 + 405.208i 0.264319 + 0.638122i
\(636\) 0 0
\(637\) −223.781 + 540.255i −0.351304 + 0.848124i
\(638\) 87.0914 119.774i 0.136507 0.187733i
\(639\) 0 0
\(640\) −205.283 241.676i −0.320755 0.377618i
\(641\) −440.457 −0.687141 −0.343571 0.939127i \(-0.611636\pi\)
−0.343571 + 0.939127i \(0.611636\pi\)
\(642\) 0 0
\(643\) −211.055 87.4220i −0.328235 0.135960i 0.212479 0.977166i \(-0.431846\pi\)
−0.540715 + 0.841206i \(0.681846\pi\)
\(644\) 371.939 + 1147.72i 0.577545 + 1.78218i
\(645\) 0 0
\(646\) −143.788 234.844i −0.222582 0.363535i
\(647\) −515.935 515.935i −0.797426 0.797426i 0.185263 0.982689i \(-0.440686\pi\)
−0.982689 + 0.185263i \(0.940686\pi\)
\(648\) 0 0
\(649\) −33.8372 33.8372i −0.0521375 0.0521375i
\(650\) 663.175 + 159.485i 1.02027 + 0.245362i
\(651\) 0 0
\(652\) −91.6307 + 1152.89i −0.140538 + 1.76824i
\(653\) 613.161 + 253.980i 0.938991 + 0.388943i 0.799082 0.601222i \(-0.205319\pi\)
0.139909 + 0.990164i \(0.455319\pi\)
\(654\) 0 0
\(655\) 238.016 0.363383
\(656\) −1272.90 203.623i −1.94040 0.310402i
\(657\) 0 0
\(658\) −97.9719 620.120i −0.148893 0.942431i
\(659\) 19.4679 46.9996i 0.0295416 0.0713196i −0.908420 0.418058i \(-0.862711\pi\)
0.937962 + 0.346738i \(0.112711\pi\)
\(660\) 0 0
\(661\) 46.1458 + 111.406i 0.0698122 + 0.168541i 0.954934 0.296817i \(-0.0959253\pi\)
−0.885122 + 0.465359i \(0.845925\pi\)
\(662\) −262.812 63.2029i −0.396997 0.0954726i
\(663\) 0 0
\(664\) −19.5951 16.7751i −0.0295107 0.0252637i
\(665\) −350.950 + 350.950i −0.527745 + 0.527745i
\(666\) 0 0
\(667\) −487.344 1176.55i −0.730650 1.76395i
\(668\) 255.420 500.334i 0.382365 0.749003i
\(669\) 0 0
\(670\) −242.477 176.313i −0.361906 0.263154i
\(671\) 15.2672i 0.0227528i
\(672\) 0 0
\(673\) −352.344 −0.523542 −0.261771 0.965130i \(-0.584306\pi\)
−0.261771 + 0.965130i \(0.584306\pi\)
\(674\) −380.533 + 523.334i −0.564590 + 0.776460i
\(675\) 0 0
\(676\) −287.144 + 562.477i −0.424769 + 0.832066i
\(677\) 1178.26 488.051i 1.74041 0.720902i 0.741669 0.670766i \(-0.234035\pi\)
0.998742 0.0501357i \(-0.0159654\pi\)
\(678\) 0 0
\(679\) −574.306 574.306i −0.845812 0.845812i
\(680\) 122.469 9.49575i 0.180101 0.0139643i
\(681\) 0 0
\(682\) 12.8767 53.5443i 0.0188808 0.0785106i
\(683\) 414.446 171.669i 0.606802 0.251346i −0.0580582 0.998313i \(-0.518491\pi\)
0.664861 + 0.746967i \(0.268491\pi\)
\(684\) 0 0
\(685\) −189.538 78.5093i −0.276698 0.114612i
\(686\) 296.771 46.8864i 0.432611 0.0683476i
\(687\) 0 0
\(688\) −494.431 + 804.048i −0.718650 + 1.16867i
\(689\) 185.657i 0.269459i
\(690\) 0 0
\(691\) 268.707 648.715i 0.388866 0.938806i −0.601314 0.799012i \(-0.705356\pi\)
0.990181 0.139794i \(-0.0446439\pi\)
\(692\) 64.2350 808.202i 0.0928251 1.16792i
\(693\) 0 0
\(694\) 165.050 686.316i 0.237825 0.988928i
\(695\) 316.319 316.319i 0.455136 0.455136i
\(696\) 0 0
\(697\) 353.106 353.106i 0.506608 0.506608i
\(698\) −837.361 + 512.691i −1.19966 + 0.734514i
\(699\) 0 0
\(700\) 209.788 + 647.363i 0.299698 + 0.924804i
\(701\) −464.382 + 1121.12i −0.662457 + 1.59931i 0.131484 + 0.991318i \(0.458026\pi\)
−0.793941 + 0.607995i \(0.791974\pi\)
\(702\) 0 0
\(703\) 722.990i 1.02844i
\(704\) −120.940 29.3317i −0.171790 0.0416643i
\(705\) 0 0
\(706\) −114.129 82.9872i −0.161656 0.117546i
\(707\) −181.166 75.0414i −0.256246 0.106141i
\(708\) 0 0
\(709\) 591.984 245.208i 0.834957 0.345850i 0.0760937 0.997101i \(-0.475755\pi\)
0.758863 + 0.651250i \(0.225755\pi\)
\(710\) −22.9587 37.4976i −0.0323362 0.0528136i
\(711\) 0 0
\(712\) 188.090 + 370.206i 0.264171 + 0.519952i
\(713\) −334.870 334.870i −0.469664 0.469664i
\(714\) 0 0
\(715\) −80.4619 + 33.3284i −0.112534 + 0.0466132i
\(716\) 1054.78 + 83.8325i 1.47315 + 0.117084i
\(717\) 0 0
\(718\) −180.777 1144.24i −0.251778 1.59365i
\(719\) 906.230 1.26040 0.630202 0.776432i \(-0.282972\pi\)
0.630202 + 0.776432i \(0.282972\pi\)
\(720\) 0 0
\(721\) 62.3563i 0.0864858i
\(722\) 41.3384 + 261.655i 0.0572555 + 0.362402i
\(723\) 0 0
\(724\) −48.3404 + 41.2220i −0.0667685 + 0.0569365i
\(725\) −274.881 663.622i −0.379147 0.915341i
\(726\) 0 0
\(727\) 317.957 317.957i 0.437355 0.437355i −0.453766 0.891121i \(-0.649920\pi\)
0.891121 + 0.453766i \(0.149920\pi\)
\(728\) −1300.61 + 100.844i −1.78655 + 0.138522i
\(729\) 0 0
\(730\) 243.160 + 397.145i 0.333096 + 0.544034i
\(731\) −139.929 337.818i −0.191421 0.462131i
\(732\) 0 0
\(733\) −159.623 + 385.363i −0.217766 + 0.525734i −0.994577 0.103999i \(-0.966836\pi\)
0.776811 + 0.629734i \(0.216836\pi\)
\(734\) −830.919 604.188i −1.13204 0.823145i
\(735\) 0 0
\(736\) −758.181 + 755.259i −1.03014 + 1.02617i
\(737\) −117.660 −0.159647
\(738\) 0 0
\(739\) −380.514 157.614i −0.514904 0.213280i 0.110073 0.993924i \(-0.464892\pi\)
−0.624977 + 0.780643i \(0.714892\pi\)
\(740\) 287.249 + 146.640i 0.388174 + 0.198162i
\(741\) 0 0
\(742\) 157.971 96.7206i 0.212898 0.130351i
\(743\) −5.76228 5.76228i −0.00775542 0.00775542i 0.703218 0.710974i \(-0.251746\pi\)
−0.710974 + 0.703218i \(0.751746\pi\)
\(744\) 0 0
\(745\) 82.4123 + 82.4123i 0.110620 + 0.110620i
\(746\) −56.8434 + 236.367i −0.0761975 + 0.316847i
\(747\) 0 0
\(748\) 36.6819 31.2804i 0.0490400 0.0418187i
\(749\) −468.729 194.154i −0.625807 0.259218i
\(750\) 0 0
\(751\) −302.377 −0.402632 −0.201316 0.979526i \(-0.564522\pi\)
−0.201316 + 0.979526i \(0.564522\pi\)
\(752\) 451.026 326.627i 0.599769 0.434344i
\(753\) 0 0
\(754\) 1360.09 214.878i 1.80383 0.284985i
\(755\) 91.6499 221.262i 0.121391 0.293063i
\(756\) 0 0
\(757\) −9.31627 22.4915i −0.0123068 0.0297113i 0.917607 0.397490i \(-0.130119\pi\)
−0.929914 + 0.367778i \(0.880119\pi\)
\(758\) 210.295 874.455i 0.277434 1.15363i
\(759\) 0 0
\(760\) −418.535 136.526i −0.550704 0.179640i
\(761\) 163.034 163.034i 0.214236 0.214236i −0.591828 0.806064i \(-0.701594\pi\)
0.806064 + 0.591828i \(0.201594\pi\)
\(762\) 0 0
\(763\) 186.064 + 449.198i 0.243859 + 0.588727i
\(764\) −1410.11 + 456.970i −1.84570 + 0.598128i
\(765\) 0 0
\(766\) 506.502 696.574i 0.661229 0.909365i
\(767\) 444.943i 0.580109i
\(768\) 0 0
\(769\) 180.205 0.234337 0.117168 0.993112i \(-0.462618\pi\)
0.117168 + 0.993112i \(0.462618\pi\)
\(770\) −70.2759 51.0999i −0.0912674 0.0663635i
\(771\) 0 0
\(772\) −163.610 504.868i −0.211931 0.653974i
\(773\) −196.725 + 81.4860i −0.254495 + 0.105415i −0.506284 0.862367i \(-0.668981\pi\)
0.251789 + 0.967782i \(0.418981\pi\)
\(774\) 0 0
\(775\) −188.880 188.880i −0.243716 0.243716i
\(776\) 223.416 684.904i 0.287908 0.882608i
\(777\) 0 0
\(778\) 117.576 + 28.2755i 0.151126 + 0.0363439i
\(779\) −1653.48 + 684.892i −2.12256 + 0.879194i
\(780\) 0 0
\(781\) −15.9421 6.60342i −0.0204124 0.00845508i
\(782\) −64.6938 409.484i −0.0827286 0.523637i
\(783\) 0 0
\(784\) −303.530 419.133i −0.387155 0.534608i
\(785\) 482.695i 0.614898i
\(786\) 0 0
\(787\) 80.6847 194.790i 0.102522 0.247510i −0.864293 0.502990i \(-0.832233\pi\)