Properties

Label 1050.3.q.e.199.11
Level $1050$
Weight $3$
Character 1050.199
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 199.11
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.e.649.11

$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

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

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 −0.506366 0.862319i \(-0.669012\pi\)
0.999973 + 0.00736658i \(0.00234488\pi\)
\(12\) −1.73205 3.00000i −0.144338 0.250000i
\(13\) −0.772061 −0.0593893 −0.0296946 0.999559i \(-0.509453\pi\)
−0.0296946 + 0.999559i \(0.509453\pi\)
\(14\) −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 −0.426847 0.904324i \(-0.640376\pi\)
0.996591 0.0825021i \(-0.0262911\pi\)
\(18\) −3.67423 2.12132i −0.204124 0.117851i
\(19\) −22.5766 + 13.0346i −1.18824 + 0.686032i −0.957907 0.287079i \(-0.907316\pi\)
−0.230335 + 0.973111i \(0.573982\pi\)
\(20\) 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 \(-0.762890\pi\)
0.219503 + 0.975612i \(0.429556\pi\)
\(24\) −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 0.819906 0.572497i \(-0.194025\pi\)
−0.0858441 + 0.996309i \(0.527359\pi\)
\(32\) −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 −0.512152 + 0.858895i \(0.671151\pi\)
−0.999901 + 0.0140890i \(0.995515\pi\)
\(38\) −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 \(-0.978446\pi\)
0.997708 0.0676633i \(-0.0215544\pi\)
\(42\) −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 \(-0.0893415\pi\)
−0.720327 + 0.693635i \(0.756008\pi\)
\(48\) −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 \(-0.581684\pi\)
−0.964572 + 0.263821i \(0.915017\pi\)
\(54\) −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 −0.981420 0.191874i \(-0.938543\pi\)
−0.656878 0.753997i \(-0.728123\pi\)
\(60\) 0 0
\(61\) −46.9572 + 27.1108i −0.769790 + 0.444439i −0.832800 0.553574i \(-0.813263\pi\)
0.0630096 + 0.998013i \(0.479930\pi\)
\(62\) 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 \(-0.440469\pi\)
−0.757957 + 0.652305i \(0.773802\pi\)
\(68\) −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 −0.223141 0.974786i \(-0.571631\pi\)
0.955760 0.294147i \(-0.0950357\pi\)
\(74\) −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 0.944536 0.328408i \(-0.106512\pi\)
−0.756678 + 0.653788i \(0.773179\pi\)
\(80\) 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 \(-0.530372\pi\)
−0.0952717 + 0.995451i \(0.530372\pi\)
\(84\) −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 −0.310368 0.950616i \(-0.600452\pi\)
0.668074 + 0.744095i \(0.267119\pi\)
\(90\) 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 \(-0.256812\pi\)
0.691813 + 0.722077i \(0.256812\pi\)
\(98\) 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 0.982830 0.184511i \(-0.0590702\pi\)
0.331624 + 0.943412i \(0.392404\pi\)
\(102\) −41.0927 23.7249i −0.402870 0.232597i
\(103\) −31.6679 54.8504i −0.307456 0.532529i 0.670349 0.742046i \(-0.266144\pi\)
−0.977805 + 0.209517i \(0.932811\pi\)
\(104\) 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 \(-0.600969\pi\)
0.666865 + 0.745179i \(0.267636\pi\)
\(108\) −5.19615 + 9.00000i −0.0481125 + 0.0833333i
\(109\) 2.64166 4.57549i 0.0242354 0.0419770i −0.853653 0.520842i \(-0.825618\pi\)
0.877889 + 0.478865i \(0.158952\pi\)
\(110\) 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 −0.734304 0.678820i \(-0.762491\pi\)
0.220724 + 0.975336i \(0.429158\pi\)
\(132\) −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 \(-0.0183411\pi\)
0.449297 + 0.893382i \(0.351674\pi\)
\(138\) 16.7725 + 29.0508i 0.121540 + 0.210513i
\(139\) 61.7421i 0.444188i 0.975025 + 0.222094i \(0.0712892\pi\)
−0.975025 + 0.222094i \(0.928711\pi\)
\(140\) 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 0.812659 0.582739i \(-0.198019\pi\)
−0.910997 + 0.412414i \(0.864686\pi\)
\(150\) 0 0
\(151\) −81.8479 + 141.765i −0.542039 + 0.938839i 0.456748 + 0.889596i \(0.349014\pi\)
−0.998787 + 0.0492431i \(0.984319\pi\)
\(152\) 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 −0.314722 0.949184i \(-0.601911\pi\)
0.979378 0.202035i \(-0.0647555\pi\)
\(158\) 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 \(-0.526274\pi\)
0.821853 + 0.569699i \(0.192940\pi\)
\(164\) −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 \(-0.447921\pi\)
0.162881 + 0.986646i \(0.447921\pi\)
\(168\) 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 \(-0.108586\pi\)
−0.760921 + 0.648845i \(0.775252\pi\)
\(174\) 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 −0.992880 0.119115i \(-0.961994\pi\)
0.599597 + 0.800302i \(0.295328\pi\)
\(180\) 0 0
\(181\) 222.987i 1.23197i −0.787757 0.615986i \(-0.788758\pi\)
0.787757 0.615986i \(-0.211242\pi\)
\(182\) 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 0.637727 0.770263i \(-0.279875\pi\)
−0.985930 + 0.167156i \(0.946542\pi\)
\(192\) −6.92820 + 12.0000i −0.0360844 + 0.0625000i
\(193\) −247.010 142.611i −1.27984 0.738919i −0.303025 0.952983i \(-0.597997\pi\)
−0.976820 + 0.214064i \(0.931330\pi\)
\(194\) 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 0.520936 0.853595i \(-0.325583\pi\)
−0.478767 + 0.877942i \(0.658916\pi\)
\(200\) 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 \(-0.535822\pi\)
−0.112299 + 0.993674i \(0.535822\pi\)
\(224\) 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 −0.305052 0.952336i \(-0.598674\pi\)
0.977273 0.211985i \(-0.0679927\pi\)
\(228\) 78.2076 + 45.1532i 0.343016 + 0.198040i
\(229\) 353.428 204.052i 1.54335 0.891055i 0.544728 0.838613i \(-0.316633\pi\)
0.998624 0.0524421i \(-0.0167005\pi\)
\(230\) 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 \(-0.512629\pi\)
0.845511 + 0.533958i \(0.179296\pi\)
\(234\) 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 0.619419 0.785060i \(-0.287368\pi\)
−0.370172 + 0.928963i \(0.620701\pi\)
\(242\) 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 \(-0.829195\pi\)
0.859451 0.511218i \(-0.170805\pi\)
\(252\) 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 \(-0.0388355\pi\)
−0.601681 + 0.798737i \(0.705502\pi\)
\(258\) −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 −0.974408 0.224787i \(-0.927831\pi\)
−0.681875 0.731469i \(-0.738835\pi\)
\(264\) −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 0.708934 0.705275i \(-0.249176\pi\)
−0.256318 + 0.966592i \(0.582510\pi\)
\(270\) 0 0
\(271\) 103.808 59.9334i 0.383054 0.221157i −0.296092 0.955159i \(-0.595684\pi\)
0.679146 + 0.734003i \(0.262350\pi\)
\(272\) −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 \(-0.395205\pi\)
−0.657860 + 0.753140i \(0.728538\pi\)
\(278\) 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 −0.278358 0.960477i \(-0.589790\pi\)
0.970977 0.239173i \(-0.0768765\pi\)
\(284\) 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 \(-0.174012\pi\)
0.854257 + 0.519850i \(0.174012\pi\)
\(294\) 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 \(-0.724598\pi\)
−0.648488 + 0.761225i \(0.724598\pi\)
\(308\) −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 0.918616 0.395151i \(-0.129308\pi\)
0.117097 + 0.993120i \(0.462641\pi\)
\(312\) 3.27558 + 1.89115i 0.0104986 + 0.00606139i
\(313\) 211.243 + 365.884i 0.674899 + 1.16896i 0.976499 + 0.215524i \(0.0691460\pi\)
−0.301600 + 0.953435i \(0.597521\pi\)
\(314\) 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 \(-0.777426\pi\)
0.174737 + 0.984615i \(0.444093\pi\)
\(318\) −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 0.660942 0.750437i \(-0.270157\pi\)
−0.980368 + 0.197175i \(0.936823\pi\)
\(332\) −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 \(-0.597403\pi\)
−0.976419 + 0.215885i \(0.930736\pi\)
\(348\) −12.1093 20.9739i −0.0347968 0.0602699i
\(349\) 527.872i 1.51253i −0.654266 0.756264i \(-0.727022\pi\)
0.654266 0.756264i \(-0.272978\pi\)
\(350\) 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 \(-0.895274\pi\)
0.752998 + 0.658023i \(0.228607\pi\)
\(354\) −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 −0.934324 0.356424i \(-0.883996\pi\)
0.158490 0.987361i \(-0.449338\pi\)
\(360\) 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 \(-0.781928\pi\)
0.935153 + 0.354243i \(0.115262\pi\)
\(368\) 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 \(-0.807016\pi\)
0.0825840 + 0.996584i \(0.473683\pi\)
\(374\) −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 0.923605 + 0.383346i \(0.125228\pi\)
−0.129815 + 0.991538i \(0.541438\pi\)
\(384\) 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 −0.782592 0.622535i \(-0.786103\pi\)
0.930427 + 0.366476i \(0.119436\pi\)
\(390\) 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 \(-0.101758\pi\)
−0.746829 + 0.665016i \(0.768425\pi\)
\(398\) 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 0.900356 0.435154i \(-0.143306\pi\)
−0.827032 + 0.562154i \(0.809973\pi\)
\(402\) −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 0.260650 0.965433i \(-0.416063\pi\)
−0.705765 + 0.708446i \(0.749396\pi\)
\(410\) 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 \(0.308133\pi\)
−0.566924 + 0.823770i \(0.691867\pi\)
\(420\) 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 −0.831701 0.555224i \(-0.812633\pi\)
0.896688 + 0.442662i \(0.145966\pi\)
\(432\) 10.3923 + 18.0000i 0.0240563 + 0.0416667i
\(433\) −71.4593 −0.165033 −0.0825165 0.996590i \(-0.526296\pi\)
−0.0825165 + 0.996590i \(0.526296\pi\)
\(434\) −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 0.580878 0.813991i \(-0.302710\pi\)
0.995376 0.0960592i \(-0.0306238\pi\)
\(440\) 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 −0.594561 + 0.804051i \(0.702674\pi\)
−0.993609 + 0.112879i \(0.963993\pi\)
\(444\) 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 \(-0.363320\pi\)
0.995566 + 0.0940682i \(0.0299872\pi\)
\(458\) 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 \(0.189381\pi\)
−0.828172 + 0.560474i \(0.810619\pi\)
\(462\) 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 −0.975052 0.221977i \(-0.928749\pi\)
0.295288 0.955408i \(-0.404584\pi\)
\(468\) 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 0.874809 0.484469i \(-0.160987\pi\)
0.0178420 + 0.999841i \(0.494320\pi\)
\(480\) 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 \(-0.443964\pi\)
−0.765074 + 0.643942i \(0.777298\pi\)
\(488\) 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 −0.999977 0.00675693i \(-0.997849\pi\)
0.494137 0.869384i \(-0.335484\pi\)
\(500\) 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 \(-0.630994\pi\)
−0.400012 + 0.916510i \(0.630994\pi\)
\(504\) 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 −0.844856 0.534994i \(-0.820314\pi\)
0.0408910 + 0.999164i \(0.486980\pi\)
\(510\) 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 0.545578 0.838060i \(-0.316310\pi\)
−0.452993 + 0.891514i \(0.649644\pi\)
\(522\) −25.6877 14.8308i −0.0492102 0.0284115i
\(523\) 265.238 + 459.405i 0.507146 + 0.878403i 0.999966 + 0.00827171i \(0.00263300\pi\)
−0.492819 + 0.870132i \(0.664034\pi\)
\(524\) 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 0.584462 0.811421i \(-0.301306\pi\)
−0.994942 + 0.100449i \(0.967972\pi\)
\(542\) 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 \(-0.201695\pi\)
−0.109822 + 0.993951i \(0.535028\pi\)
\(558\) −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 −0.195190 0.980765i \(-0.562532\pi\)
0.946963 0.321343i \(-0.104134\pi\)
\(564\) 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 0.977842 0.209345i \(-0.0671331\pi\)
−0.670219 + 0.742164i \(0.733800\pi\)
\(570\) 0 0
\(571\) 382.891 663.186i 0.670562 1.16145i −0.307183 0.951650i \(-0.599386\pi\)
0.977745 0.209797i \(-0.0672803\pi\)
\(572\) 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 \(-0.862660\pi\)
0.816351 + 0.577556i \(0.195994\pi\)
\(578\) −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 \(-0.739646\pi\)
−0.683737 + 0.729729i \(0.739646\pi\)
\(588\) 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 \(-0.189507\pi\)
−0.899643 + 0.436626i \(0.856173\pi\)
\(594\) 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 −0.669211 0.743072i \(-0.733368\pi\)
0.978125 + 0.208017i \(0.0667011\pi\)
\(600\) 0 0
\(601\) 462.547i 0.769628i −0.922994 0.384814i \(-0.874266\pi\)
0.922994 0.384814i \(-0.125734\pi\)
\(602\) −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 0.996673 + 0.0814998i \(0.0259710\pi\)
−0.427756 + 0.903894i \(0.640696\pi\)
\(608\) 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 \(-0.307772\pi\)
−0.428919 + 0.903343i \(0.641106\pi\)
\(614\) −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 0.589274 0.807933i \(-0.299414\pi\)
−0.405054 + 0.914293i \(0.632747\pi\)
\(620\) 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 −0.515446 0.856922i \(-0.672374\pi\)
0.999839 + 0.0179287i \(0.00570718\pi\)
\(642\) −53.7118 93.0316i −0.0836632 0.144909i
\(643\) 75.8433 0.117952 0.0589761 0.998259i \(-0.481216\pi\)
0.0589761 + 0.998259i \(0.481216\pi\)
\(644\) 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 \(-0.794433\pi\)
0.920519 + 0.390698i \(0.127766\pi\)
\(648\) 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 \(-0.852355\pi\)
−0.0597229 + 0.998215i \(0.519022\pi\)
\(654\) −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 0.995585 + 0.0938667i \(0.0299227\pi\)
0.579083 + 0.815268i \(0.303411\pi\)
\(662\) −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 \(-0.0211164\pi\)
−0.556309 + 0.830975i \(0.687783\pi\)
\(678\) −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 \(-0.458549\pi\)
−0.793766 + 0.608223i \(0.791883\pi\)
\(684\) 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 −0.371708 0.928350i \(-0.621228\pi\)
0.618120 + 0.786083i \(0.287894\pi\)
\(692\) 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 0.952915 0.303237i \(-0.0980672\pi\)
−0.739068 + 0.673631i \(0.764734\pi\)
\(710\) 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 −0.415116 0.909769i \(-0.636259\pi\)
0.580325 + 0.814385i \(0.302926\pi\)
\(720\) 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 \(-0.670232\pi\)
−0.509669 + 0.860371i \(0.670232\pi\)
\(728\) 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 \(-0.135392\pi\)
−0.812802 + 0.582540i \(0.802059\pi\)
\(734\) 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 0.258505 + 0.966010i \(0.416770\pi\)
−0.965842 + 0.259133i \(0.916563\pi\)
\(740\) 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 0.808246 0.588845i \(-0.200417\pi\)
−0.914078 + 0.405539i \(0.867084\pi\)
\(752\) 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 −0.980401 0.197010i \(-0.936877\pi\)
−0.319585 + 0.947558i \(0.603544\pi\)
\(762\) −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 \(-0.965384\pi\)
0.994093 0.108535i \(-0.0346159\pi\)
\(770\) 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 \(-0.903722\pi\)
0.735269 + 0.677775i \(0.237056\pi\)
\(774\) −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