Properties

Label 1050.3.q.e.649.5
Level $1050$
Weight $3$
Character 1050.649
Analytic conductor $28.610$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.6104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 649.5
Character \(\chi\) \(=\) 1050.649
Dual form 1050.3.q.e.199.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(5.56601 - 4.24494i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +2.44949i q^{6} +(5.56601 - 4.24494i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(5.42967 + 9.40447i) q^{11} +(1.73205 - 3.00000i) q^{12} +0.772061 q^{13} +(-9.81857 + 1.26320i) q^{14} +(-2.00000 + 3.46410i) q^{16} +(-9.68565 - 16.7760i) q^{17} +(3.67423 - 2.12132i) q^{18} +(-22.5766 - 13.0346i) q^{19} +(-11.1877 - 4.67280i) q^{21} -15.3574i q^{22} +(11.8599 + 6.84734i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-0.945577 - 0.545929i) q^{26} +5.19615 q^{27} +(12.9185 + 5.39568i) q^{28} +6.99131 q^{29} +(22.7559 - 13.1381i) q^{31} +(4.89898 - 2.82843i) q^{32} +(9.40447 - 16.2890i) q^{33} +27.3952i q^{34} -6.00000 q^{36} +(55.9459 + 32.3004i) q^{37} +(18.4337 + 31.9281i) q^{38} +(-0.668624 - 1.15809i) q^{39} +5.54839i q^{41} +(10.3979 + 13.6339i) q^{42} -68.9320i q^{43} +(-10.8593 + 18.8089i) q^{44} +(-9.68361 - 16.7725i) q^{46} +(-11.3055 + 19.5817i) q^{47} +6.92820 q^{48} +(12.9610 - 47.2548i) q^{49} +(-16.7760 + 29.0570i) q^{51} +(0.772061 + 1.33725i) q^{52} +(64.5742 - 37.2820i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(-12.0065 - 15.7431i) q^{56} +45.1532i q^{57} +(-8.56257 - 4.94360i) q^{58} +(-96.6595 + 55.8064i) q^{59} +(-46.9572 - 27.1108i) q^{61} -37.1603 q^{62} +(2.67965 + 20.8283i) q^{63} -8.00000 q^{64} +(-23.0362 + 13.2999i) q^{66} +(38.3255 - 22.1273i) q^{67} +(19.3713 - 33.5521i) q^{68} -23.7199i q^{69} +31.9550 q^{71} +(7.34847 + 4.24264i) q^{72} +(-53.4812 - 92.6322i) q^{73} +(-45.6797 - 79.1195i) q^{74} -52.1384i q^{76} +(70.1430 + 29.2968i) q^{77} +1.89115i q^{78} +(14.8408 - 25.7050i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(3.92330 - 6.79536i) q^{82} +15.8151 q^{83} +(-3.09419 - 24.0505i) q^{84} +(-48.7423 + 84.4242i) q^{86} +(-6.05465 - 10.4870i) q^{87} +(26.5999 - 15.3574i) q^{88} +(31.8358 + 18.3804i) q^{89} +(4.29730 - 3.27735i) q^{91} +27.3894i q^{92} +(-39.4144 - 22.7559i) q^{93} +(27.6926 - 15.9884i) q^{94} +(-8.48528 - 4.89898i) q^{96} -134.212 q^{97} +(-49.2881 + 48.7102i) q^{98} -32.5780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) −0.866025 1.50000i −0.288675 0.500000i
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 2.44949i 0.408248i
\(7\) 5.56601 4.24494i 0.795145 0.606420i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 + 2.59808i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 5.42967 + 9.40447i 0.493607 + 0.854952i 0.999973 0.00736658i \(-0.00234488\pi\)
−0.506366 + 0.862319i \(0.669012\pi\)
\(12\) 1.73205 3.00000i 0.144338 0.250000i
\(13\) 0.772061 0.0593893 0.0296946 0.999559i \(-0.490547\pi\)
0.0296946 + 0.999559i \(0.490547\pi\)
\(14\) −9.81857 + 1.26320i −0.701326 + 0.0902284i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −9.68565 16.7760i −0.569744 0.986826i −0.996591 0.0825021i \(-0.973709\pi\)
0.426847 0.904324i \(-0.359624\pi\)
\(18\) 3.67423 2.12132i 0.204124 0.117851i
\(19\) −22.5766 13.0346i −1.18824 0.686032i −0.230335 0.973111i \(-0.573982\pi\)
−0.957907 + 0.287079i \(0.907316\pi\)
\(20\) 0 0
\(21\) −11.1877 4.67280i −0.532748 0.222514i
\(22\) 15.3574i 0.698065i
\(23\) 11.8599 + 6.84734i 0.515650 + 0.297711i 0.735153 0.677901i \(-0.237110\pi\)
−0.219503 + 0.975612i \(0.570444\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) −0.945577 0.545929i −0.0363684 0.0209973i
\(27\) 5.19615 0.192450
\(28\) 12.9185 + 5.39568i 0.461374 + 0.192703i
\(29\) 6.99131 0.241080 0.120540 0.992708i \(-0.461537\pi\)
0.120540 + 0.992708i \(0.461537\pi\)
\(30\) 0 0
\(31\) 22.7559 13.1381i 0.734062 0.423811i −0.0858441 0.996309i \(-0.527359\pi\)
0.819906 + 0.572497i \(0.194025\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) 9.40447 16.2890i 0.284984 0.493607i
\(34\) 27.3952i 0.805740i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 55.9459 + 32.3004i 1.51205 + 0.872984i 0.999901 + 0.0140890i \(0.00448483\pi\)
0.512152 + 0.858895i \(0.328849\pi\)
\(38\) 18.4337 + 31.9281i 0.485098 + 0.840214i
\(39\) −0.668624 1.15809i −0.0171442 0.0296946i
\(40\) 0 0
\(41\) 5.54839i 0.135327i 0.997708 + 0.0676633i \(0.0215544\pi\)
−0.997708 + 0.0676633i \(0.978446\pi\)
\(42\) 10.3979 + 13.6339i 0.247570 + 0.324617i
\(43\) 68.9320i 1.60307i −0.597948 0.801535i \(-0.704017\pi\)
0.597948 0.801535i \(-0.295983\pi\)
\(44\) −10.8593 + 18.8089i −0.246803 + 0.427476i
\(45\) 0 0
\(46\) −9.68361 16.7725i −0.210513 0.364620i
\(47\) −11.3055 + 19.5817i −0.240542 + 0.416631i −0.960869 0.277004i \(-0.910658\pi\)
0.720327 + 0.693635i \(0.243992\pi\)
\(48\) 6.92820 0.144338
\(49\) 12.9610 47.2548i 0.264511 0.964383i
\(50\) 0 0
\(51\) −16.7760 + 29.0570i −0.328942 + 0.569744i
\(52\) 0.772061 + 1.33725i 0.0148473 + 0.0257163i
\(53\) 64.5742 37.2820i 1.21838 0.703433i 0.253810 0.967254i \(-0.418316\pi\)
0.964572 + 0.263821i \(0.0849828\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) 0 0
\(56\) −12.0065 15.7431i −0.214402 0.281126i
\(57\) 45.1532i 0.792161i
\(58\) −8.56257 4.94360i −0.147631 0.0852345i
\(59\) −96.6595 + 55.8064i −1.63830 + 0.945871i −0.656878 + 0.753997i \(0.728123\pi\)
−0.981420 + 0.191874i \(0.938543\pi\)
\(60\) 0 0
\(61\) −46.9572 27.1108i −0.769790 0.444439i 0.0630096 0.998013i \(-0.479930\pi\)
−0.832800 + 0.553574i \(0.813263\pi\)
\(62\) −37.1603 −0.599359
\(63\) 2.67965 + 20.8283i 0.0425341 + 0.330608i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −23.0362 + 13.2999i −0.349033 + 0.201514i
\(67\) 38.3255 22.1273i 0.572023 0.330258i −0.185934 0.982562i \(-0.559531\pi\)
0.757957 + 0.652305i \(0.226198\pi\)
\(68\) 19.3713 33.5521i 0.284872 0.493413i
\(69\) 23.7199i 0.343767i
\(70\) 0 0
\(71\) 31.9550 0.450071 0.225035 0.974351i \(-0.427750\pi\)
0.225035 + 0.974351i \(0.427750\pi\)
\(72\) 7.34847 + 4.24264i 0.102062 + 0.0589256i
\(73\) −53.4812 92.6322i −0.732619 1.26893i −0.955760 0.294147i \(-0.904964\pi\)
0.223141 0.974786i \(-0.428369\pi\)
\(74\) −45.6797 79.1195i −0.617293 1.06918i
\(75\) 0 0
\(76\) 52.1384i 0.686032i
\(77\) 70.1430 + 29.2968i 0.910949 + 0.380478i
\(78\) 1.89115i 0.0242456i
\(79\) 14.8408 25.7050i 0.187858 0.325380i −0.756678 0.653788i \(-0.773179\pi\)
0.944536 + 0.328408i \(0.106512\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 3.92330 6.79536i 0.0478451 0.0828702i
\(83\) 15.8151 0.190543 0.0952717 0.995451i \(-0.469628\pi\)
0.0952717 + 0.995451i \(0.469628\pi\)
\(84\) −3.09419 24.0505i −0.0368356 0.286315i
\(85\) 0 0
\(86\) −48.7423 + 84.4242i −0.566771 + 0.981676i
\(87\) −6.05465 10.4870i −0.0695937 0.120540i
\(88\) 26.5999 15.3574i 0.302271 0.174516i
\(89\) 31.8358 + 18.3804i 0.357706 + 0.206521i 0.668074 0.744095i \(-0.267119\pi\)
−0.310368 + 0.950616i \(0.600452\pi\)
\(90\) 0 0
\(91\) 4.29730 3.27735i 0.0472231 0.0360148i
\(92\) 27.3894i 0.297711i
\(93\) −39.4144 22.7559i −0.423811 0.244687i
\(94\) 27.6926 15.9884i 0.294603 0.170089i
\(95\) 0 0
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) −134.212 −1.38363 −0.691813 0.722077i \(-0.743188\pi\)
−0.691813 + 0.722077i \(0.743188\pi\)
\(98\) −49.2881 + 48.7102i −0.502940 + 0.497043i
\(99\) −32.5780 −0.329071
\(100\) 0 0
\(101\) 132.760 76.6490i 1.31445 0.758901i 0.331624 0.943412i \(-0.392404\pi\)
0.982830 + 0.184511i \(0.0590702\pi\)
\(102\) 41.0927 23.7249i 0.402870 0.232597i
\(103\) 31.6679 54.8504i 0.307456 0.532529i −0.670349 0.742046i \(-0.733856\pi\)
0.977805 + 0.209517i \(0.0671891\pi\)
\(104\) 2.18372i 0.0209973i
\(105\) 0 0
\(106\) −105.449 −0.994805
\(107\) −37.9800 21.9277i −0.354953 0.204932i 0.311912 0.950111i \(-0.399031\pi\)
−0.666865 + 0.745179i \(0.732364\pi\)
\(108\) 5.19615 + 9.00000i 0.0481125 + 0.0833333i
\(109\) 2.64166 + 4.57549i 0.0242354 + 0.0419770i 0.877889 0.478865i \(-0.158952\pi\)
−0.853653 + 0.520842i \(0.825618\pi\)
\(110\) 0 0
\(111\) 111.892i 1.00804i
\(112\) 3.57286 + 27.7711i 0.0319006 + 0.247956i
\(113\) 106.725i 0.944469i −0.881473 0.472234i \(-0.843448\pi\)
0.881473 0.472234i \(-0.156552\pi\)
\(114\) 31.9281 55.3011i 0.280071 0.485098i
\(115\) 0 0
\(116\) 6.99131 + 12.1093i 0.0602699 + 0.104391i
\(117\) −1.15809 + 2.00587i −0.00989821 + 0.0171442i
\(118\) 157.844 1.33766
\(119\) −125.124 52.2607i −1.05146 0.439166i
\(120\) 0 0
\(121\) 1.53727 2.66262i 0.0127047 0.0220051i
\(122\) 38.3404 + 66.4075i 0.314266 + 0.544324i
\(123\) 8.32258 4.80504i 0.0676633 0.0390654i
\(124\) 45.5119 + 26.2763i 0.367031 + 0.211906i
\(125\) 0 0
\(126\) 11.4460 27.4042i 0.0908410 0.217494i
\(127\) 203.641i 1.60348i −0.597676 0.801738i \(-0.703909\pi\)
0.597676 0.801738i \(-0.296091\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) −103.398 + 59.6969i −0.801535 + 0.462767i
\(130\) 0 0
\(131\) −67.2791 38.8436i −0.513581 0.296516i 0.220724 0.975336i \(-0.429158\pi\)
−0.734304 + 0.678820i \(0.762491\pi\)
\(132\) 37.6179 0.284984
\(133\) −180.993 + 23.2854i −1.36085 + 0.175078i
\(134\) −62.5853 −0.467055
\(135\) 0 0
\(136\) −47.4498 + 27.3952i −0.348896 + 0.201435i
\(137\) −198.326 + 114.504i −1.44764 + 0.835794i −0.998340 0.0575883i \(-0.981659\pi\)
−0.449297 + 0.893382i \(0.648326\pi\)
\(138\) −16.7725 + 29.0508i −0.121540 + 0.210513i
\(139\) 61.7421i 0.444188i −0.975025 0.222094i \(-0.928711\pi\)
0.975025 0.222094i \(-0.0712892\pi\)
\(140\) 0 0
\(141\) 39.1633 0.277754
\(142\) −39.1368 22.5956i −0.275611 0.159124i
\(143\) 4.19204 + 7.26082i 0.0293149 + 0.0507750i
\(144\) −6.00000 10.3923i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) 151.268i 1.03608i
\(147\) −82.1067 + 21.4823i −0.558549 + 0.146138i
\(148\) 129.202i 0.872984i
\(149\) −14.6523 + 25.3785i −0.0983373 + 0.170325i −0.910997 0.412414i \(-0.864686\pi\)
0.812659 + 0.582739i \(0.198019\pi\)
\(150\) 0 0
\(151\) −81.8479 141.765i −0.542039 0.938839i −0.998787 0.0492431i \(-0.984319\pi\)
0.456748 0.889596i \(-0.349014\pi\)
\(152\) −36.8674 + 63.8563i −0.242549 + 0.420107i
\(153\) 58.1139 0.379830
\(154\) −65.1914 85.4797i −0.423320 0.555063i
\(155\) 0 0
\(156\) 1.33725 2.31618i 0.00857210 0.0148473i
\(157\) −104.351 180.741i −0.664657 1.15122i −0.979378 0.202035i \(-0.935245\pi\)
0.314722 0.949184i \(-0.398089\pi\)
\(158\) −36.3524 + 20.9880i −0.230078 + 0.132836i
\(159\) −111.846 64.5742i −0.703433 0.406127i
\(160\) 0 0
\(161\) 95.0792 12.2323i 0.590554 0.0759771i
\(162\) 12.7279i 0.0785674i
\(163\) −120.523 69.5841i −0.739406 0.426896i 0.0824475 0.996595i \(-0.473726\pi\)
−0.821853 + 0.569699i \(0.807060\pi\)
\(164\) −9.61009 + 5.54839i −0.0585981 + 0.0338316i
\(165\) 0 0
\(166\) −19.3695 11.1830i −0.116683 0.0673672i
\(167\) −54.4023 −0.325762 −0.162881 0.986646i \(-0.552079\pi\)
−0.162881 + 0.986646i \(0.552079\pi\)
\(168\) −13.2167 + 31.6436i −0.0786707 + 0.188355i
\(169\) −168.404 −0.996473
\(170\) 0 0
\(171\) 67.7298 39.1038i 0.396081 0.228677i
\(172\) 119.394 68.9320i 0.694150 0.400768i
\(173\) −31.3918 + 54.3723i −0.181456 + 0.314291i −0.942376 0.334554i \(-0.891414\pi\)
0.760921 + 0.648845i \(0.224748\pi\)
\(174\) 17.1251i 0.0984203i
\(175\) 0 0
\(176\) −43.4374 −0.246803
\(177\) 167.419 + 96.6595i 0.945871 + 0.546099i
\(178\) −25.9938 45.0226i −0.146033 0.252936i
\(179\) −70.3978 121.933i −0.393284 0.681187i 0.599597 0.800302i \(-0.295328\pi\)
−0.992880 + 0.119115i \(0.961994\pi\)
\(180\) 0 0
\(181\) 222.987i 1.23197i 0.787757 + 0.615986i \(0.211242\pi\)
−0.787757 + 0.615986i \(0.788758\pi\)
\(182\) −7.58053 + 0.975265i −0.0416513 + 0.00535860i
\(183\) 93.9144i 0.513193i
\(184\) 19.3672 33.5450i 0.105257 0.182310i
\(185\) 0 0
\(186\) 32.1817 + 55.7404i 0.173020 + 0.299680i
\(187\) 105.180 182.177i 0.562459 0.974208i
\(188\) −45.2219 −0.240542
\(189\) 28.9219 22.0573i 0.153026 0.116705i
\(190\) 0 0
\(191\) −66.5069 + 115.193i −0.348204 + 0.603106i −0.985930 0.167156i \(-0.946542\pi\)
0.637727 + 0.770263i \(0.279875\pi\)
\(192\) 6.92820 + 12.0000i 0.0360844 + 0.0625000i
\(193\) 247.010 142.611i 1.27984 0.738919i 0.303025 0.952983i \(-0.402003\pi\)
0.976820 + 0.214064i \(0.0686700\pi\)
\(194\) 164.375 + 94.9020i 0.847295 + 0.489186i
\(195\) 0 0
\(196\) 94.8087 24.8056i 0.483718 0.126559i
\(197\) 307.784i 1.56236i 0.624309 + 0.781178i \(0.285381\pi\)
−0.624309 + 0.781178i \(0.714619\pi\)
\(198\) 39.8998 + 23.0362i 0.201514 + 0.116344i
\(199\) 8.39167 4.84493i 0.0421692 0.0243464i −0.478767 0.877942i \(-0.658916\pi\)
0.520936 + 0.853595i \(0.325583\pi\)
\(200\) 0 0
\(201\) −66.3818 38.3255i −0.330258 0.190674i
\(202\) −216.796 −1.07325
\(203\) 38.9137 29.6777i 0.191693 0.146195i
\(204\) −67.1042 −0.328942
\(205\) 0 0
\(206\) −77.5702 + 44.7852i −0.376555 + 0.217404i
\(207\) −35.5798 + 20.5420i −0.171883 + 0.0992369i
\(208\) −1.54412 + 2.67450i −0.00742366 + 0.0128582i
\(209\) 283.095i 1.35452i
\(210\) 0 0
\(211\) 175.954 0.833903 0.416952 0.908929i \(-0.363098\pi\)
0.416952 + 0.908929i \(0.363098\pi\)
\(212\) 129.148 + 74.5639i 0.609191 + 0.351717i
\(213\) −27.6739 47.9326i −0.129924 0.225035i
\(214\) 31.0105 + 53.7118i 0.144909 + 0.250990i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 70.8893 169.725i 0.326679 0.782141i
\(218\) 7.47174i 0.0342740i
\(219\) −92.6322 + 160.444i −0.422978 + 0.732619i
\(220\) 0 0
\(221\) −7.47791 12.9521i −0.0338367 0.0586069i
\(222\) −79.1195 + 137.039i −0.356394 + 0.617293i
\(223\) 50.0854 0.224598 0.112299 0.993674i \(-0.464178\pi\)
0.112299 + 0.993674i \(0.464178\pi\)
\(224\) 15.2613 36.5389i 0.0681308 0.163120i
\(225\) 0 0
\(226\) −75.4659 + 130.711i −0.333920 + 0.578366i
\(227\) −152.594 264.301i −0.672221 1.16432i −0.977273 0.211985i \(-0.932007\pi\)
0.305052 0.952336i \(-0.401326\pi\)
\(228\) −78.2076 + 45.1532i −0.343016 + 0.198040i
\(229\) 353.428 + 204.052i 1.54335 + 0.891055i 0.998624 + 0.0524421i \(0.0167005\pi\)
0.544728 + 0.838613i \(0.316633\pi\)
\(230\) 0 0
\(231\) −16.8004 130.586i −0.0727292 0.565309i
\(232\) 19.7744i 0.0852345i
\(233\) −187.762 108.404i −0.805846 0.465255i 0.0396654 0.999213i \(-0.487371\pi\)
−0.845511 + 0.533958i \(0.820704\pi\)
\(234\) 2.83673 1.63779i 0.0121228 0.00699909i
\(235\) 0 0
\(236\) −193.319 111.613i −0.819149 0.472936i
\(237\) −51.4100 −0.216920
\(238\) 116.291 + 152.482i 0.488617 + 0.640680i
\(239\) 389.739 1.63071 0.815354 0.578963i \(-0.196543\pi\)
0.815354 + 0.578963i \(0.196543\pi\)
\(240\) 0 0
\(241\) 60.0686 34.6806i 0.249247 0.143903i −0.370172 0.928963i \(-0.620701\pi\)
0.619419 + 0.785060i \(0.287368\pi\)
\(242\) −3.76552 + 2.17402i −0.0155600 + 0.00898356i
\(243\) −7.79423 + 13.5000i −0.0320750 + 0.0555556i
\(244\) 108.443i 0.444439i
\(245\) 0 0
\(246\) −13.5907 −0.0552468
\(247\) −17.4305 10.0635i −0.0705688 0.0407429i
\(248\) −37.1603 64.3635i −0.149840 0.259530i
\(249\) −13.6963 23.7226i −0.0550051 0.0952717i
\(250\) 0 0
\(251\) 256.631i 1.02244i 0.859451 + 0.511218i \(0.170805\pi\)
−0.859451 + 0.511218i \(0.829195\pi\)
\(252\) −33.3961 + 25.4696i −0.132524 + 0.101070i
\(253\) 148.715i 0.587808i
\(254\) −143.996 + 249.409i −0.566914 + 0.981924i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −100.458 + 173.998i −0.390886 + 0.677034i −0.992567 0.121703i \(-0.961165\pi\)
0.601681 + 0.798737i \(0.294498\pi\)
\(258\) 168.848 0.654451
\(259\) 448.509 57.7025i 1.73170 0.222789i
\(260\) 0 0
\(261\) −10.4870 + 18.1640i −0.0401799 + 0.0695937i
\(262\) 54.9331 + 95.1470i 0.209668 + 0.363156i
\(263\) 435.602 251.495i 1.65628 0.956256i 0.681875 0.731469i \(-0.261165\pi\)
0.974408 0.224787i \(-0.0721686\pi\)
\(264\) −46.0723 26.5999i −0.174516 0.100757i
\(265\) 0 0
\(266\) 238.135 + 99.4625i 0.895245 + 0.373919i
\(267\) 63.6716i 0.238470i
\(268\) 76.6511 + 44.2545i 0.286012 + 0.165129i
\(269\) 121.754 70.2945i 0.452616 0.261318i −0.256318 0.966592i \(-0.582510\pi\)
0.708934 + 0.705275i \(0.249176\pi\)
\(270\) 0 0
\(271\) 103.808 + 59.9334i 0.383054 + 0.221157i 0.679146 0.734003i \(-0.262350\pi\)
−0.296092 + 0.955159i \(0.595684\pi\)
\(272\) 77.4852 0.284872
\(273\) −8.63759 3.60768i −0.0316395 0.0132150i
\(274\) 323.866 1.18199
\(275\) 0 0
\(276\) 41.0841 23.7199i 0.148855 0.0859416i
\(277\) 92.6706 53.5034i 0.334551 0.193153i −0.323309 0.946293i \(-0.604795\pi\)
0.657860 + 0.753140i \(0.271462\pi\)
\(278\) −43.6583 + 75.6183i −0.157044 + 0.272008i
\(279\) 78.8289i 0.282541i
\(280\) 0 0
\(281\) −85.5187 −0.304337 −0.152169 0.988355i \(-0.548626\pi\)
−0.152169 + 0.988355i \(0.548626\pi\)
\(282\) −47.9651 27.6926i −0.170089 0.0982008i
\(283\) −196.011 339.501i −0.692619 1.19965i −0.970977 0.239173i \(-0.923124\pi\)
0.278358 0.960477i \(-0.410210\pi\)
\(284\) 31.9550 + 55.3477i 0.112518 + 0.194886i
\(285\) 0 0
\(286\) 11.8569i 0.0414576i
\(287\) 23.5526 + 30.8824i 0.0820646 + 0.107604i
\(288\) 16.9706i 0.0589256i
\(289\) −43.1238 + 74.6926i −0.149217 + 0.258452i
\(290\) 0 0
\(291\) 116.231 + 201.318i 0.399419 + 0.691813i
\(292\) 106.962 185.264i 0.366310 0.634467i
\(293\) −500.595 −1.70851 −0.854257 0.519850i \(-0.825988\pi\)
−0.854257 + 0.519850i \(0.825988\pi\)
\(294\) 115.750 + 31.7479i 0.393708 + 0.107986i
\(295\) 0 0
\(296\) 91.3593 158.239i 0.308646 0.534591i
\(297\) 28.2134 + 48.8671i 0.0949947 + 0.164536i
\(298\) 35.8906 20.7214i 0.120438 0.0695350i
\(299\) 9.15660 + 5.28656i 0.0306241 + 0.0176808i
\(300\) 0 0
\(301\) −292.612 383.677i −0.972133 1.27467i
\(302\) 231.501i 0.766559i
\(303\) −229.947 132.760i −0.758901 0.438151i
\(304\) 90.3064 52.1384i 0.297061 0.171508i
\(305\) 0 0
\(306\) −71.1747 41.0927i −0.232597 0.134290i
\(307\) 398.171 1.29698 0.648488 0.761225i \(-0.275402\pi\)
0.648488 + 0.761225i \(0.275402\pi\)
\(308\) 19.3995 + 150.788i 0.0629853 + 0.489572i
\(309\) −109.701 −0.355019
\(310\) 0 0
\(311\) 322.107 185.968i 1.03571 0.597969i 0.117097 0.993120i \(-0.462641\pi\)
0.918616 + 0.395151i \(0.129308\pi\)
\(312\) −3.27558 + 1.89115i −0.0104986 + 0.00606139i
\(313\) −211.243 + 365.884i −0.674899 + 1.16896i 0.301600 + 0.953435i \(0.402479\pi\)
−0.976499 + 0.215524i \(0.930854\pi\)
\(314\) 295.149i 0.939966i
\(315\) 0 0
\(316\) 59.3632 0.187858
\(317\) 187.219 + 108.091i 0.590597 + 0.340981i 0.765333 0.643634i \(-0.222574\pi\)
−0.174737 + 0.984615i \(0.555907\pi\)
\(318\) 91.3218 + 158.174i 0.287175 + 0.497402i
\(319\) 37.9605 + 65.7496i 0.118999 + 0.206112i
\(320\) 0 0
\(321\) 75.9599i 0.236635i
\(322\) −125.097 52.2497i −0.388501 0.162266i
\(323\) 504.995i 1.56345i
\(324\) 9.00000 15.5885i 0.0277778 0.0481125i
\(325\) 0 0
\(326\) 98.4067 + 170.445i 0.301861 + 0.522839i
\(327\) 4.57549 7.92498i 0.0139923 0.0242354i
\(328\) 15.6932 0.0478451
\(329\) 20.1965 + 156.983i 0.0613874 + 0.477151i
\(330\) 0 0
\(331\) −105.730 + 183.130i −0.319426 + 0.553262i −0.980368 0.197175i \(-0.936823\pi\)
0.660942 + 0.750437i \(0.270157\pi\)
\(332\) 15.8151 + 27.3926i 0.0476358 + 0.0825077i
\(333\) −167.838 + 96.9012i −0.504018 + 0.290995i
\(334\) 66.6289 + 38.4682i 0.199488 + 0.115174i
\(335\) 0 0
\(336\) 38.5625 29.4098i 0.114769 0.0875291i
\(337\) 260.379i 0.772639i −0.922365 0.386319i \(-0.873746\pi\)
0.922365 0.386319i \(-0.126254\pi\)
\(338\) 206.252 + 119.080i 0.610213 + 0.352306i
\(339\) −160.087 + 92.4265i −0.472234 + 0.272645i
\(340\) 0 0
\(341\) 247.115 + 142.672i 0.724676 + 0.418392i
\(342\) −110.602 −0.323399
\(343\) −128.452 318.039i −0.374496 0.927228i
\(344\) −194.969 −0.566771
\(345\) 0 0
\(346\) 76.8940 44.3948i 0.222237 0.128309i
\(347\) 443.350 255.968i 1.27767 0.737661i 0.301247 0.953546i \(-0.402597\pi\)
0.976419 + 0.215885i \(0.0692636\pi\)
\(348\) 12.1093 20.9739i 0.0347968 0.0602699i
\(349\) 527.872i 1.51253i 0.654266 + 0.756264i \(0.272978\pi\)
−0.654266 + 0.756264i \(0.727022\pi\)
\(350\) 0 0
\(351\) 4.01174 0.0114295
\(352\) 53.1997 + 30.7149i 0.151136 + 0.0872582i
\(353\) 68.2579 + 118.226i 0.193365 + 0.334918i 0.946363 0.323104i \(-0.104726\pi\)
−0.752998 + 0.658023i \(0.771393\pi\)
\(354\) −136.697 236.767i −0.386150 0.668832i
\(355\) 0 0
\(356\) 73.5216i 0.206521i
\(357\) 29.9693 + 232.945i 0.0839475 + 0.652506i
\(358\) 199.115i 0.556187i
\(359\) −278.525 + 482.419i −0.775835 + 1.34379i 0.158490 + 0.987361i \(0.449338\pi\)
−0.934324 + 0.356424i \(0.883996\pi\)
\(360\) 0 0
\(361\) 159.302 + 275.919i 0.441279 + 0.764318i
\(362\) 157.676 273.102i 0.435568 0.754426i
\(363\) −5.32525 −0.0146701
\(364\) 9.97383 + 4.16579i 0.0274006 + 0.0114445i
\(365\) 0 0
\(366\) 66.4075 115.021i 0.181441 0.314266i
\(367\) −59.0110 102.210i −0.160793 0.278502i 0.774360 0.632745i \(-0.218072\pi\)
−0.935153 + 0.354243i \(0.884738\pi\)
\(368\) −47.4398 + 27.3894i −0.128912 + 0.0744276i
\(369\) −14.4151 8.32258i −0.0390654 0.0225544i
\(370\) 0 0
\(371\) 201.162 481.625i 0.542215 1.29818i
\(372\) 91.0237i 0.244687i
\(373\) 275.718 + 159.186i 0.739191 + 0.426772i 0.821775 0.569812i \(-0.192984\pi\)
−0.0825840 + 0.996584i \(0.526317\pi\)
\(374\) −257.637 + 148.747i −0.688869 + 0.397719i
\(375\) 0 0
\(376\) 55.3853 + 31.9767i 0.147301 + 0.0850444i
\(377\) 5.39771 0.0143175
\(378\) −51.0188 + 6.56377i −0.134970 + 0.0173645i
\(379\) 579.699 1.52955 0.764774 0.644299i \(-0.222851\pi\)
0.764774 + 0.644299i \(0.222851\pi\)
\(380\) 0 0
\(381\) −305.462 + 176.359i −0.801738 + 0.462883i
\(382\) 162.908 94.0549i 0.426461 0.246217i
\(383\) −304.022 + 526.581i −0.793790 + 1.37488i 0.129815 + 0.991538i \(0.458562\pi\)
−0.923605 + 0.383346i \(0.874772\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −403.366 −1.04499
\(387\) 179.091 + 103.398i 0.462767 + 0.267178i
\(388\) −134.212 232.462i −0.345907 0.599128i
\(389\) 57.5081 + 99.6069i 0.147836 + 0.256059i 0.930427 0.366476i \(-0.119436\pi\)
−0.782592 + 0.622535i \(0.786103\pi\)
\(390\) 0 0
\(391\) 265.284i 0.678476i
\(392\) −133.657 36.6593i −0.340961 0.0935187i
\(393\) 134.558i 0.342387i
\(394\) 217.636 376.957i 0.552376 0.956744i
\(395\) 0 0
\(396\) −32.5780 56.4268i −0.0822678 0.142492i
\(397\) −80.3952 + 139.249i −0.202507 + 0.350752i −0.949336 0.314264i \(-0.898242\pi\)
0.746829 + 0.665016i \(0.231575\pi\)
\(398\) −13.7035 −0.0344310
\(399\) 191.672 + 251.323i 0.480382 + 0.629883i
\(400\) 0 0
\(401\) 29.4028 50.9272i 0.0733238 0.127000i −0.827032 0.562154i \(-0.809973\pi\)
0.900356 + 0.435154i \(0.143306\pi\)
\(402\) 54.2005 + 93.8780i 0.134827 + 0.233527i
\(403\) 17.5690 10.1434i 0.0435954 0.0251698i
\(404\) 265.520 + 153.298i 0.657227 + 0.379450i
\(405\) 0 0
\(406\) −68.6447 + 8.83141i −0.169076 + 0.0217522i
\(407\) 701.523i 1.72364i
\(408\) 82.1855 + 47.4498i 0.201435 + 0.116299i
\(409\) −182.052 + 105.108i −0.445114 + 0.256987i −0.705765 0.708446i \(-0.749396\pi\)
0.260650 + 0.965433i \(0.416063\pi\)
\(410\) 0 0
\(411\) 343.511 + 198.326i 0.835794 + 0.482546i
\(412\) 126.672 0.307456
\(413\) −301.114 + 720.933i −0.729089 + 1.74560i
\(414\) 58.1016 0.140342
\(415\) 0 0
\(416\) 3.78231 2.18372i 0.00909209 0.00524932i
\(417\) −92.6132 + 53.4702i −0.222094 + 0.128226i
\(418\) −200.178 + 346.719i −0.478895 + 0.829471i
\(419\) 690.319i 1.64754i −0.566924 0.823770i \(-0.691867\pi\)
0.566924 0.823770i \(-0.308133\pi\)
\(420\) 0 0
\(421\) 407.084 0.966945 0.483472 0.875360i \(-0.339375\pi\)
0.483472 + 0.875360i \(0.339375\pi\)
\(422\) −215.498 124.418i −0.510659 0.294829i
\(423\) −33.9164 58.7450i −0.0801807 0.138877i
\(424\) −105.449 182.644i −0.248701 0.430763i
\(425\) 0 0
\(426\) 78.2735i 0.183741i
\(427\) −376.448 + 48.4315i −0.881611 + 0.113423i
\(428\) 87.7110i 0.204932i
\(429\) 7.26082 12.5761i 0.0169250 0.0293149i
\(430\) 0 0
\(431\) 28.0096 + 48.5141i 0.0649875 + 0.112562i 0.896688 0.442662i \(-0.145966\pi\)
−0.831701 + 0.555224i \(0.812633\pi\)
\(432\) −10.3923 + 18.0000i −0.0240563 + 0.0416667i
\(433\) 71.4593 0.165033 0.0825165 0.996590i \(-0.473704\pi\)
0.0825165 + 0.996590i \(0.473704\pi\)
\(434\) −206.835 + 157.743i −0.476578 + 0.363463i
\(435\) 0 0
\(436\) −5.28332 + 9.15098i −0.0121177 + 0.0209885i
\(437\) −178.505 309.179i −0.408478 0.707504i
\(438\) 226.902 131.002i 0.518040 0.299091i
\(439\) 691.975 + 399.512i 1.57625 + 0.910050i 0.995376 + 0.0960592i \(0.0306238\pi\)
0.580878 + 0.813991i \(0.302710\pi\)
\(440\) 0 0
\(441\) 103.330 + 104.556i 0.234308 + 0.237088i
\(442\) 21.1507i 0.0478523i
\(443\) 703.559 + 406.200i 1.58817 + 0.916930i 0.993609 + 0.112879i \(0.0360073\pi\)
0.594561 + 0.804051i \(0.297326\pi\)
\(444\) 193.802 111.892i 0.436492 0.252009i
\(445\) 0 0
\(446\) −61.3419 35.4157i −0.137538 0.0794075i
\(447\) 50.7569 0.113550
\(448\) −44.5281 + 33.9595i −0.0993931 + 0.0758024i
\(449\) −434.785 −0.968340 −0.484170 0.874974i \(-0.660878\pi\)
−0.484170 + 0.874974i \(0.660878\pi\)
\(450\) 0 0
\(451\) −52.1797 + 30.1259i −0.115698 + 0.0667981i
\(452\) 184.853 106.725i 0.408967 0.236117i
\(453\) −141.765 + 245.544i −0.312946 + 0.542039i
\(454\) 431.601i 0.950663i
\(455\) 0 0
\(456\) 127.713 0.280071
\(457\) −645.231 372.524i −1.41188 0.815151i −0.416317 0.909219i \(-0.636680\pi\)
−0.995566 + 0.0940682i \(0.970013\pi\)
\(458\) −288.572 499.822i −0.630071 1.09131i
\(459\) −50.3281 87.1709i −0.109647 0.189915i
\(460\) 0 0
\(461\) 516.757i 1.12095i −0.828172 0.560474i \(-0.810619\pi\)
0.828172 0.560474i \(-0.189381\pi\)
\(462\) −71.7622 + 171.815i −0.155329 + 0.371893i
\(463\) 538.823i 1.16376i −0.813273 0.581882i \(-0.802316\pi\)
0.813273 0.581882i \(-0.197684\pi\)
\(464\) −13.9826 + 24.2186i −0.0301350 + 0.0521953i
\(465\) 0 0
\(466\) 153.307 + 265.536i 0.328985 + 0.569819i
\(467\) 317.450 549.839i 0.679764 1.17739i −0.295288 0.955408i \(-0.595416\pi\)
0.975052 0.221977i \(-0.0712510\pi\)
\(468\) −4.63236 −0.00989821
\(469\) 119.392 285.850i 0.254566 0.609489i
\(470\) 0 0
\(471\) −180.741 + 313.053i −0.383740 + 0.664657i
\(472\) 157.844 + 273.394i 0.334416 + 0.579226i
\(473\) 648.269 374.279i 1.37055 0.791286i
\(474\) 62.9641 + 36.3524i 0.132836 + 0.0766928i
\(475\) 0 0
\(476\) −34.6055 268.981i −0.0727007 0.565087i
\(477\) 223.692i 0.468955i
\(478\) −477.331 275.587i −0.998600 0.576542i
\(479\) 427.580 246.863i 0.892650 0.515372i 0.0178420 0.999841i \(-0.494320\pi\)
0.874809 + 0.484469i \(0.160987\pi\)
\(480\) 0 0
\(481\) 43.1937 + 24.9379i 0.0897997 + 0.0518459i
\(482\) −98.0915 −0.203509
\(483\) −100.689 132.025i −0.208467 0.273344i
\(484\) 6.14906 0.0127047
\(485\) 0 0
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) 287.301 165.873i 0.589941 0.340603i −0.175133 0.984545i \(-0.556036\pi\)
0.765074 + 0.643942i \(0.222702\pi\)
\(488\) −76.6808 + 132.815i −0.157133 + 0.272162i
\(489\) 241.046i 0.492937i
\(490\) 0 0
\(491\) −744.294 −1.51587 −0.757937 0.652328i \(-0.773793\pi\)
−0.757937 + 0.652328i \(0.773793\pi\)
\(492\) 16.6452 + 9.61009i 0.0338316 + 0.0195327i
\(493\) −67.7154 117.287i −0.137354 0.237904i
\(494\) 14.2319 + 24.6505i 0.0288096 + 0.0498997i
\(495\) 0 0
\(496\) 105.105i 0.211906i
\(497\) 177.862 135.647i 0.357872 0.272932i
\(498\) 38.7389i 0.0777890i
\(499\) −252.414 + 437.194i −0.505840 + 0.876141i 0.494137 + 0.869384i \(0.335484\pi\)
−0.999977 + 0.00675693i \(0.997849\pi\)
\(500\) 0 0
\(501\) 47.1138 + 81.6034i 0.0940394 + 0.162881i
\(502\) 181.466 314.308i 0.361486 0.626111i
\(503\) 402.412 0.800024 0.400012 0.916510i \(-0.369006\pi\)
0.400012 + 0.916510i \(0.369006\pi\)
\(504\) 58.9114 7.57919i 0.116888 0.0150381i
\(505\) 0 0
\(506\) 105.158 182.138i 0.207821 0.359957i
\(507\) 145.842 + 252.606i 0.287657 + 0.498236i
\(508\) 352.717 203.641i 0.694325 0.400869i
\(509\) −409.218 236.262i −0.803965 0.464169i 0.0408910 0.999164i \(-0.486980\pi\)
−0.844856 + 0.534994i \(0.820314\pi\)
\(510\) 0 0
\(511\) −690.895 288.568i −1.35204 0.564712i
\(512\) 22.6274i 0.0441942i
\(513\) −117.311 67.7298i −0.228677 0.132027i
\(514\) 246.070 142.069i 0.478735 0.276398i
\(515\) 0 0
\(516\) −206.796 119.394i −0.400768 0.231383i
\(517\) −245.540 −0.474933
\(518\) −590.111 246.473i −1.13921 0.475817i
\(519\) 108.745 0.209527
\(520\) 0 0
\(521\) 48.2368 27.8496i 0.0925851 0.0534540i −0.452993 0.891514i \(-0.649644\pi\)
0.545578 + 0.838060i \(0.316310\pi\)
\(522\) 25.6877 14.8308i 0.0492102 0.0284115i
\(523\) −265.238 + 459.405i −0.507146 + 0.878403i 0.492819 + 0.870132i \(0.335966\pi\)
−0.999966 + 0.00827171i \(0.997367\pi\)
\(524\) 155.374i 0.296516i
\(525\) 0 0
\(526\) −711.336 −1.35235
\(527\) −440.812 254.503i −0.836456 0.482928i
\(528\) 37.6179 + 65.1561i 0.0712460 + 0.123402i
\(529\) −170.728 295.709i −0.322737 0.558997i
\(530\) 0 0
\(531\) 334.838i 0.630581i
\(532\) −221.324 290.203i −0.416023 0.545495i
\(533\) 4.28369i 0.00803694i
\(534\) −45.0226 + 77.9815i −0.0843120 + 0.146033i
\(535\) 0 0
\(536\) −62.5853 108.401i −0.116764 0.202241i
\(537\) −121.933 + 211.193i −0.227062 + 0.393284i
\(538\) −198.823 −0.369559
\(539\) 514.780 134.686i 0.955065 0.249882i
\(540\) 0 0
\(541\) −222.070 + 384.636i −0.410480 + 0.710972i −0.994942 0.100449i \(-0.967972\pi\)
0.584462 + 0.811421i \(0.301306\pi\)
\(542\) −84.7586 146.806i −0.156381 0.270860i
\(543\) 334.480 193.112i 0.615986 0.355640i
\(544\) −94.8996 54.7903i −0.174448 0.100718i
\(545\) 0 0
\(546\) 8.02783 + 10.5262i 0.0147030 + 0.0192787i
\(547\) 308.345i 0.563702i 0.959458 + 0.281851i \(0.0909484\pi\)
−0.959458 + 0.281851i \(0.909052\pi\)
\(548\) −396.653 229.008i −0.723819 0.417897i
\(549\) 140.872 81.3323i 0.256597 0.148146i
\(550\) 0 0
\(551\) −157.840 91.1289i −0.286461 0.165388i
\(552\) −67.0900 −0.121540
\(553\) −26.5121 206.073i −0.0479422 0.372645i
\(554\) −151.330 −0.273160
\(555\) 0 0
\(556\) 106.940 61.7421i 0.192339 0.111047i
\(557\) −387.702 + 223.840i −0.696054 + 0.401867i −0.805876 0.592084i \(-0.798305\pi\)
0.109822 + 0.993951i \(0.464972\pi\)
\(558\) 55.7404 96.5452i 0.0998932 0.173020i
\(559\) 53.2197i 0.0952052i
\(560\) 0 0
\(561\) −364.354 −0.649472
\(562\) 104.739 + 60.4709i 0.186368 + 0.107599i
\(563\) −423.248 733.087i −0.751773 1.30211i −0.946963 0.321343i \(-0.895866\pi\)
0.195190 0.980765i \(-0.437468\pi\)
\(564\) 39.1633 + 67.8328i 0.0694385 + 0.120271i
\(565\) 0 0
\(566\) 554.403i 0.979511i
\(567\) −58.1331 24.2806i −0.102527 0.0428229i
\(568\) 90.3825i 0.159124i
\(569\) 175.038 303.174i 0.307623 0.532819i −0.670219 0.742164i \(-0.733800\pi\)
0.977842 + 0.209345i \(0.0671331\pi\)
\(570\) 0 0
\(571\) 382.891 + 663.186i 0.670562 + 1.16145i 0.977745 + 0.209797i \(0.0672803\pi\)
−0.307183 + 0.951650i \(0.599386\pi\)
\(572\) −8.38408 + 14.5216i −0.0146575 + 0.0253875i
\(573\) 230.387 0.402071
\(574\) −7.00871 54.4772i −0.0122103 0.0949081i
\(575\) 0 0
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 53.0857 + 91.9471i 0.0920029 + 0.159354i 0.908354 0.418203i \(-0.137340\pi\)
−0.816351 + 0.577556i \(0.804006\pi\)
\(578\) 105.631 60.9862i 0.182753 0.105512i
\(579\) −427.834 247.010i −0.738919 0.426615i
\(580\) 0 0
\(581\) 88.0271 67.1341i 0.151510 0.115549i
\(582\) 328.750i 0.564863i
\(583\) 701.234 + 404.858i 1.20280 + 0.694439i
\(584\) −262.003 + 151.268i −0.448636 + 0.259020i
\(585\) 0 0
\(586\) 613.101 + 353.974i 1.04625 + 0.604051i
\(587\) 802.707 1.36747 0.683737 0.729729i \(-0.260354\pi\)
0.683737 + 0.729729i \(0.260354\pi\)
\(588\) −119.315 120.731i −0.202917 0.205324i
\(589\) −685.002 −1.16299
\(590\) 0 0
\(591\) 461.676 266.549i 0.781178 0.451013i
\(592\) −223.784 + 129.202i −0.378013 + 0.218246i
\(593\) 42.5138 73.6360i 0.0716927 0.124175i −0.827951 0.560801i \(-0.810493\pi\)
0.899643 + 0.436626i \(0.143827\pi\)
\(594\) 79.7996i 0.134343i
\(595\) 0 0
\(596\) −58.6090 −0.0983373
\(597\) −14.5348 8.39167i −0.0243464 0.0140564i
\(598\) −7.47633 12.9494i −0.0125022 0.0216545i
\(599\) 185.040 + 320.498i 0.308914 + 0.535055i 0.978125 0.208017i \(-0.0667011\pi\)
−0.669211 + 0.743072i \(0.733368\pi\)
\(600\) 0 0
\(601\) 462.547i 0.769628i 0.922994 + 0.384814i \(0.125734\pi\)
−0.922994 + 0.384814i \(0.874266\pi\)
\(602\) 87.0748 + 676.814i 0.144643 + 1.12428i
\(603\) 132.764i 0.220172i
\(604\) 163.696 283.529i 0.271020 0.469420i
\(605\) 0 0
\(606\) 187.751 + 325.194i 0.309820 + 0.536624i
\(607\) −345.333 + 598.134i −0.568918 + 0.985394i 0.427756 + 0.903894i \(0.359304\pi\)
−0.996673 + 0.0814998i \(0.974029\pi\)
\(608\) −147.470 −0.242549
\(609\) −78.2168 32.6690i −0.128435 0.0536436i
\(610\) 0 0
\(611\) −8.72851 + 15.1182i −0.0142856 + 0.0247434i
\(612\) 58.1139 + 100.656i 0.0949574 + 0.164471i
\(613\) −85.1695 + 49.1726i −0.138939 + 0.0802163i −0.567858 0.823126i \(-0.692228\pi\)
0.428919 + 0.903343i \(0.358894\pi\)
\(614\) −487.658 281.550i −0.794232 0.458550i
\(615\) 0 0
\(616\) 82.8639 198.394i 0.134519 0.322069i
\(617\) 794.667i 1.28795i 0.765045 + 0.643976i \(0.222717\pi\)
−0.765045 + 0.643976i \(0.777283\pi\)
\(618\) 134.356 + 77.5702i 0.217404 + 0.125518i
\(619\) 114.032 65.8365i 0.184220 0.106359i −0.405054 0.914293i \(-0.632747\pi\)
0.589274 + 0.807933i \(0.299414\pi\)
\(620\) 0 0
\(621\) 61.6261 + 35.5798i 0.0992369 + 0.0572944i
\(622\) −525.998 −0.845656
\(623\) 255.222 32.8353i 0.409666 0.0527052i
\(624\) 5.34899 0.00857210
\(625\) 0 0
\(626\) 517.438 298.743i 0.826579 0.477225i
\(627\) −424.642 + 245.167i −0.677260 + 0.391016i
\(628\) 208.702 361.483i 0.332328 0.575609i
\(629\) 1251.40i 1.98951i
\(630\) 0 0
\(631\) −1086.67 −1.72213 −0.861067 0.508492i \(-0.830203\pi\)
−0.861067 + 0.508492i \(0.830203\pi\)
\(632\) −72.7047 41.9761i −0.115039 0.0664179i
\(633\) −152.380 263.930i −0.240727 0.416952i
\(634\) −152.864 264.768i −0.241110 0.417615i
\(635\) 0 0
\(636\) 258.297i 0.406127i
\(637\) 10.0067 36.4835i 0.0157091 0.0572740i
\(638\) 107.369i 0.168289i
\(639\) −47.9326 + 83.0216i −0.0750118 + 0.129924i
\(640\) 0 0
\(641\) 310.496 + 537.795i 0.484393 + 0.838993i 0.999839 0.0179287i \(-0.00570718\pi\)
−0.515446 + 0.856922i \(0.672374\pi\)
\(642\) 53.7118 93.0316i 0.0836632 0.144909i
\(643\) −75.8433 −0.117952 −0.0589761 0.998259i \(-0.518784\pi\)
−0.0589761 + 0.998259i \(0.518784\pi\)
\(644\) 116.266 + 152.450i 0.180538 + 0.236723i
\(645\) 0 0
\(646\) 357.085 618.490i 0.552763 0.957414i
\(647\) −78.8723 136.611i −0.121905 0.211145i 0.798614 0.601843i \(-0.205567\pi\)
−0.920519 + 0.390698i \(0.872234\pi\)
\(648\) −22.0454 + 12.7279i −0.0340207 + 0.0196419i
\(649\) −1049.66 606.021i −1.61735 0.933777i
\(650\) 0 0
\(651\) −315.979 + 40.6519i −0.485374 + 0.0624453i
\(652\) 278.336i 0.426896i
\(653\) 623.004 + 359.691i 0.954064 + 0.550829i 0.894341 0.447386i \(-0.147645\pi\)
0.0597229 + 0.998215i \(0.480978\pi\)
\(654\) −11.2076 + 6.47072i −0.0171370 + 0.00989407i
\(655\) 0 0
\(656\) −19.2202 11.0968i −0.0292991 0.0169158i
\(657\) 320.887 0.488413
\(658\) 86.2681 206.545i 0.131106 0.313898i
\(659\) 10.5090 0.0159469 0.00797343 0.999968i \(-0.497462\pi\)
0.00797343 + 0.999968i \(0.497462\pi\)
\(660\) 0 0
\(661\) 1040.86 600.938i 1.57467 0.909135i 0.579083 0.815268i \(-0.303411\pi\)
0.995585 0.0938667i \(-0.0299227\pi\)
\(662\) 258.985 149.525i 0.391215 0.225868i
\(663\) −12.9521 + 22.4337i −0.0195356 + 0.0338367i
\(664\) 44.7318i 0.0673672i
\(665\) 0 0
\(666\) 274.078 0.411529
\(667\) 82.9166 + 47.8719i 0.124313 + 0.0717720i
\(668\) −54.4023 94.2275i −0.0814405 0.141059i
\(669\) −43.3753 75.1282i −0.0648360 0.112299i
\(670\) 0 0
\(671\) 588.810i 0.877512i
\(672\) −68.0251 + 8.75169i −0.101228 + 0.0130234i
\(673\) 1070.49i 1.59062i 0.606203 + 0.795310i \(0.292692\pi\)
−0.606203 + 0.795310i \(0.707308\pi\)
\(674\) −184.116 + 318.898i −0.273169 + 0.473143i
\(675\) 0 0
\(676\) −168.404 291.684i −0.249118 0.431485i
\(677\) −298.889 + 517.691i −0.441491 + 0.764685i −0.997800 0.0662906i \(-0.978884\pi\)
0.556309 + 0.830975i \(0.312217\pi\)
\(678\) 261.422 0.385578
\(679\) −747.024 + 569.720i −1.10018 + 0.839058i
\(680\) 0 0
\(681\) −264.301 + 457.782i −0.388107 + 0.672221i
\(682\) −201.768 349.473i −0.295848 0.512424i
\(683\) 453.453 261.801i 0.663913 0.383310i −0.129853 0.991533i \(-0.541451\pi\)
0.793766 + 0.608223i \(0.208117\pi\)
\(684\) 135.460 + 78.2076i 0.198040 + 0.114339i
\(685\) 0 0
\(686\) −67.5667 + 480.346i −0.0984937 + 0.700214i
\(687\) 706.855i 1.02890i
\(688\) 238.788 + 137.864i 0.347075 + 0.200384i
\(689\) 49.8552 28.7839i 0.0723588 0.0417764i
\(690\) 0 0
\(691\) 170.271 + 98.3059i 0.246412 + 0.142266i 0.618120 0.786083i \(-0.287894\pi\)
−0.371708 + 0.928350i \(0.621228\pi\)
\(692\) −125.567 −0.181456
\(693\) −181.330 + 138.292i −0.261659 + 0.199555i
\(694\) −723.988 −1.04321
\(695\) 0 0
\(696\) −29.6616 + 17.1251i −0.0426173 + 0.0246051i
\(697\) 93.0800 53.7398i 0.133544 0.0771015i
\(698\) 373.262 646.509i 0.534760 0.926231i
\(699\) 375.524i 0.537231i
\(700\) 0 0
\(701\) 132.968 0.189683 0.0948414 0.995492i \(-0.469766\pi\)
0.0948414 + 0.995492i \(0.469766\pi\)
\(702\) −4.91336 2.83673i −0.00699909 0.00404093i
\(703\) −842.046 1458.47i −1.19779 2.07463i
\(704\) −43.4374 75.2358i −0.0617008 0.106869i
\(705\) 0 0
\(706\) 193.062i 0.273460i
\(707\) 413.573 990.186i 0.584969 1.40055i
\(708\) 386.638i 0.546099i
\(709\) 151.618 262.609i 0.213847 0.370394i −0.739068 0.673631i \(-0.764734\pi\)
0.952915 + 0.303237i \(0.0980672\pi\)
\(710\) 0 0
\(711\) 44.5224 + 77.1150i 0.0626194 + 0.108460i
\(712\) 51.9877 90.0453i 0.0730164 0.126468i
\(713\) 359.846 0.504692
\(714\) 128.012 306.489i 0.179289 0.429257i
\(715\) 0 0
\(716\) 140.796 243.865i 0.196642 0.340594i
\(717\) −337.524 584.608i −0.470745 0.815354i
\(718\) 682.243 393.893i 0.950200 0.548598i
\(719\) 118.785 + 68.5808i 0.165209 + 0.0953835i 0.580325 0.814385i \(-0.302926\pi\)
−0.415116 + 0.909769i \(0.636259\pi\)
\(720\) 0 0
\(721\) −56.5726 439.727i −0.0784640 0.609884i
\(722\) 450.574i 0.624063i
\(723\) −104.042 60.0686i −0.143903 0.0830824i
\(724\) −386.225 + 222.987i −0.533460 + 0.307993i
\(725\) 0 0
\(726\) 6.52207 + 3.76552i 0.00898356 + 0.00518666i
\(727\) 741.058 1.01934 0.509669 0.860371i \(-0.329768\pi\)
0.509669 + 0.860371i \(0.329768\pi\)
\(728\) −9.26974 12.1546i −0.0127332 0.0166959i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −1156.41 + 667.652i −1.58195 + 0.913340i
\(732\) −162.665 + 93.9144i −0.222219 + 0.128298i
\(733\) −71.9021 + 124.538i −0.0980929 + 0.169902i −0.910895 0.412638i \(-0.864608\pi\)
0.812802 + 0.582540i \(0.197941\pi\)
\(734\) 166.908i 0.227396i
\(735\) 0 0
\(736\) 77.4688 0.105257
\(737\) 416.190 + 240.288i 0.564709 + 0.326035i
\(738\) 11.7699 + 20.3861i 0.0159484 + 0.0276234i
\(739\) −522.722 905.381i −0.707337 1.22514i −0.965842 0.259133i \(-0.916563\pi\)
0.258505 0.966010i \(-0.416770\pi\)
\(740\) 0 0
\(741\) 34.8610i 0.0470459i
\(742\) −586.932 + 447.626i −0.791014 + 0.603269i
\(743\) 660.175i 0.888526i 0.895896 + 0.444263i \(0.146534\pi\)
−0.895896 + 0.444263i \(0.853466\pi\)
\(744\) −64.3635 + 111.481i −0.0865101 + 0.149840i
\(745\) 0 0
\(746\) −225.123 389.925i −0.301774 0.522687i
\(747\) −23.7226 + 41.0888i −0.0317572 + 0.0550051i
\(748\) 420.720 0.562459
\(749\) −304.479 + 39.1724i −0.406514 + 0.0522996i
\(750\) 0 0
\(751\) −79.4795 + 137.663i −0.105832 + 0.183306i −0.914078 0.405539i \(-0.867084\pi\)
0.808246 + 0.588845i \(0.200417\pi\)
\(752\) −45.2219 78.3266i −0.0601355 0.104158i
\(753\) 384.947 222.249i 0.511218 0.295152i
\(754\) −6.61082 3.81676i −0.00876767 0.00506202i
\(755\) 0 0
\(756\) 67.1263 + 28.0368i 0.0887914 + 0.0370857i
\(757\) 777.212i 1.02670i 0.858179 + 0.513350i \(0.171596\pi\)
−0.858179 + 0.513350i \(0.828404\pi\)
\(758\) −709.983 409.909i −0.936653 0.540777i
\(759\) 223.073 128.791i 0.293904 0.169686i
\(760\) 0 0
\(761\) −989.290 571.167i −1.29999 0.750548i −0.319585 0.947558i \(-0.603544\pi\)
−0.980401 + 0.197010i \(0.936877\pi\)
\(762\) 498.817 0.654616
\(763\) 34.1262 + 14.2536i 0.0447263 + 0.0186809i
\(764\) −266.028 −0.348204
\(765\) 0 0
\(766\) 744.698 429.951i 0.972190 0.561294i
\(767\) −74.6270 + 43.0859i −0.0972973 + 0.0561746i
\(768\) −13.8564 + 24.0000i −0.0180422 + 0.0312500i
\(769\) 166.927i 0.217070i 0.994093 + 0.108535i \(0.0346159\pi\)
−0.994093 + 0.108535i \(0.965384\pi\)
\(770\) 0 0
\(771\) 347.995 0.451356
\(772\) 494.020 + 285.223i 0.639922 + 0.369459i
\(773\) 169.546 + 293.663i 0.219336 + 0.379901i 0.954605 0.297874i \(-0.0962777\pi\)
−0.735269 + 0.677775i \(0.762944\pi\)
\(774\) −146.227 253.272i −0.188924 0.327225i
\(775\) 0 0
\(776\) 379.608i 0.489186i
\(777\) −474.974 622.792i −0.611292 0.801534i
\(778\) 162.657i 0.209071i
\(779\) 72.3210 125.264i 0.0928383 0.160801i
\(780\) 0 0
\(781\) 173.505 + 300.520i 0.222158 + 0.384789i
\(782\) −187.584 + 324.905i −0.239877 + 0.415480i
\(783\) 36.3279 0.0463958