Properties

Label 1050.3.q.b.199.6
Level $1050$
Weight $3$
Character 1050.199
Analytic conductor $28.610$
Analytic rank $0$
Dimension $16$
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: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.22986704741655040229376.1
Defining polynomial: \( x^{16} - 31x^{12} + 880x^{8} - 2511x^{4} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.6
Root \(1.25838 - 0.337183i\) of defining polynomial
Character \(\chi\) \(=\) 1050.199
Dual form 1050.3.q.b.649.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.98615 - 0.440173i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +2.44949i q^{6} +(6.98615 - 0.440173i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-3.76860 + 6.52741i) q^{11} +(1.73205 + 3.00000i) q^{12} -21.3906 q^{13} +(8.24500 - 5.47905i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-10.4937 + 18.1757i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(-20.8728 + 12.0509i) q^{19} +(-5.38992 + 10.8604i) q^{21} +10.6592i q^{22} +(4.83250 - 2.79005i) q^{23} +(4.24264 + 2.44949i) q^{24} +(-26.1981 + 15.1255i) q^{26} +5.19615 q^{27} +(6.22374 - 12.5405i) q^{28} +9.96625 q^{29} +(5.70073 + 3.29132i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-6.52741 - 11.3058i) q^{33} +29.6807i q^{34} -6.00000 q^{36} +(-19.3960 + 11.1983i) q^{37} +(-17.0426 + 29.5187i) q^{38} +(18.5248 - 32.0860i) q^{39} -51.0827i q^{41} +(1.07820 + 17.1125i) q^{42} +34.7656i q^{43} +(7.53720 + 13.0548i) q^{44} +(3.94572 - 6.83419i) q^{46} +(38.8246 + 67.2462i) q^{47} +6.92820 q^{48} +(48.6125 - 6.15023i) q^{49} +(-18.1757 - 31.4812i) q^{51} +(-21.3906 + 37.0497i) q^{52} +(-43.1262 - 24.8989i) q^{53} +(6.36396 - 3.67423i) q^{54} +(-1.24500 - 19.7598i) q^{56} -41.7457i q^{57} +(12.2061 - 7.04720i) q^{58} +(-72.9362 - 42.1098i) q^{59} +(-72.4404 + 41.8235i) q^{61} +9.30925 q^{62} +(-11.6228 - 17.4903i) q^{63} -8.00000 q^{64} +(-15.9888 - 9.23115i) q^{66} +(57.6618 + 33.2911i) q^{67} +(20.9874 + 36.3513i) q^{68} +9.66501i q^{69} -68.1049 q^{71} +(-7.34847 + 4.24264i) q^{72} +(-43.8283 + 75.9128i) q^{73} +(-15.8368 + 27.4301i) q^{74} +48.2038i q^{76} +(-23.4548 + 47.2603i) q^{77} -52.3962i q^{78} +(49.3730 + 85.5165i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-36.1209 - 62.5632i) q^{82} -26.9448 q^{83} +(13.4209 + 20.1960i) q^{84} +(24.5830 + 42.5790i) q^{86} +(-8.63103 + 14.9494i) q^{87} +(18.4623 + 10.6592i) q^{88} +(-12.0453 + 6.95436i) q^{89} +(-149.438 + 9.41559i) q^{91} -11.1602i q^{92} +(-9.87395 + 5.70073i) q^{93} +(95.1005 + 54.9063i) q^{94} +(8.48528 - 4.89898i) q^{96} +3.69132 q^{97} +(55.1890 - 41.9067i) q^{98} +22.6116 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 16 q^{4} - 24 q^{9} - 8 q^{11} + 32 q^{14} - 32 q^{16} - 144 q^{19} - 144 q^{26} + 48 q^{29} + 192 q^{31} - 96 q^{36} + 24 q^{39} + 16 q^{44} + 64 q^{46} + 528 q^{49} + 48 q^{51} + 80 q^{56} - 624 q^{59} - 408 q^{61} - 128 q^{64} - 72 q^{66} - 128 q^{71} + 32 q^{74} + 288 q^{79} - 72 q^{81} + 352 q^{86} + 672 q^{89} - 592 q^{91} - 72 q^{94} + 48 q^{99}+O(q^{100}) \) 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
\(7\) 6.98615 0.440173i 0.998021 0.0628819i
\(8\) 2.82843i 0.353553i
\(9\) −1.50000 2.59808i −0.166667 0.288675i
\(10\) 0 0
\(11\) −3.76860 + 6.52741i −0.342600 + 0.593401i −0.984915 0.173040i \(-0.944641\pi\)
0.642315 + 0.766441i \(0.277974\pi\)
\(12\) 1.73205 + 3.00000i 0.144338 + 0.250000i
\(13\) −21.3906 −1.64543 −0.822717 0.568451i \(-0.807543\pi\)
−0.822717 + 0.568451i \(0.807543\pi\)
\(14\) 8.24500 5.47905i 0.588928 0.391361i
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −10.4937 + 18.1757i −0.617278 + 1.06916i 0.372703 + 0.927951i \(0.378431\pi\)
−0.989980 + 0.141205i \(0.954902\pi\)
\(18\) −3.67423 2.12132i −0.204124 0.117851i
\(19\) −20.8728 + 12.0509i −1.09857 + 0.634260i −0.935845 0.352411i \(-0.885362\pi\)
−0.162726 + 0.986671i \(0.552029\pi\)
\(20\) 0 0
\(21\) −5.38992 + 10.8604i −0.256663 + 0.517163i
\(22\) 10.6592i 0.484510i
\(23\) 4.83250 2.79005i 0.210109 0.121306i −0.391253 0.920283i \(-0.627958\pi\)
0.601362 + 0.798977i \(0.294625\pi\)
\(24\) 4.24264 + 2.44949i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −26.1981 + 15.1255i −1.00762 + 0.581749i
\(27\) 5.19615 0.192450
\(28\) 6.22374 12.5405i 0.222277 0.447876i
\(29\) 9.96625 0.343664 0.171832 0.985126i \(-0.445031\pi\)
0.171832 + 0.985126i \(0.445031\pi\)
\(30\) 0 0
\(31\) 5.70073 + 3.29132i 0.183894 + 0.106171i 0.589121 0.808045i \(-0.299474\pi\)
−0.405227 + 0.914216i \(0.632807\pi\)
\(32\) −4.89898 2.82843i −0.153093 0.0883883i
\(33\) −6.52741 11.3058i −0.197800 0.342600i
\(34\) 29.6807i 0.872962i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −19.3960 + 11.1983i −0.524216 + 0.302656i −0.738658 0.674080i \(-0.764540\pi\)
0.214442 + 0.976737i \(0.431207\pi\)
\(38\) −17.0426 + 29.5187i −0.448490 + 0.776807i
\(39\) 18.5248 32.0860i 0.474996 0.822717i
\(40\) 0 0
\(41\) 51.0827i 1.24592i −0.782254 0.622959i \(-0.785930\pi\)
0.782254 0.622959i \(-0.214070\pi\)
\(42\) 1.07820 + 17.1125i 0.0256714 + 0.407440i
\(43\) 34.7656i 0.808503i 0.914648 + 0.404252i \(0.132468\pi\)
−0.914648 + 0.404252i \(0.867532\pi\)
\(44\) 7.53720 + 13.0548i 0.171300 + 0.296700i
\(45\) 0 0
\(46\) 3.94572 6.83419i 0.0857766 0.148569i
\(47\) 38.8246 + 67.2462i 0.826056 + 1.43077i 0.901110 + 0.433591i \(0.142754\pi\)
−0.0750536 + 0.997179i \(0.523913\pi\)
\(48\) 6.92820 0.144338
\(49\) 48.6125 6.15023i 0.992092 0.125515i
\(50\) 0 0
\(51\) −18.1757 31.4812i −0.356385 0.617278i
\(52\) −21.3906 + 37.0497i −0.411359 + 0.712494i
\(53\) −43.1262 24.8989i −0.813703 0.469791i 0.0345374 0.999403i \(-0.489004\pi\)
−0.848240 + 0.529612i \(0.822338\pi\)
\(54\) 6.36396 3.67423i 0.117851 0.0680414i
\(55\) 0 0
\(56\) −1.24500 19.7598i −0.0222321 0.352854i
\(57\) 41.7457i 0.732381i
\(58\) 12.2061 7.04720i 0.210450 0.121504i
\(59\) −72.9362 42.1098i −1.23621 0.713725i −0.267890 0.963449i \(-0.586327\pi\)
−0.968317 + 0.249725i \(0.919660\pi\)
\(60\) 0 0
\(61\) −72.4404 + 41.8235i −1.18755 + 0.685631i −0.957749 0.287607i \(-0.907140\pi\)
−0.229799 + 0.973238i \(0.573807\pi\)
\(62\) 9.30925 0.150149
\(63\) −11.6228 17.4903i −0.184489 0.277624i
\(64\) −8.00000 −0.125000
\(65\) 0 0
\(66\) −15.9888 9.23115i −0.242255 0.139866i
\(67\) 57.6618 + 33.2911i 0.860625 + 0.496882i 0.864221 0.503112i \(-0.167812\pi\)
−0.00359682 + 0.999994i \(0.501145\pi\)
\(68\) 20.9874 + 36.3513i 0.308639 + 0.534578i
\(69\) 9.66501i 0.140073i
\(70\) 0 0
\(71\) −68.1049 −0.959224 −0.479612 0.877481i \(-0.659223\pi\)
−0.479612 + 0.877481i \(0.659223\pi\)
\(72\) −7.34847 + 4.24264i −0.102062 + 0.0589256i
\(73\) −43.8283 + 75.9128i −0.600387 + 1.03990i 0.392375 + 0.919805i \(0.371654\pi\)
−0.992762 + 0.120096i \(0.961680\pi\)
\(74\) −15.8368 + 27.4301i −0.214010 + 0.370677i
\(75\) 0 0
\(76\) 48.2038i 0.634260i
\(77\) −23.4548 + 47.2603i −0.304608 + 0.613770i
\(78\) 52.3962i 0.671746i
\(79\) 49.3730 + 85.5165i 0.624974 + 1.08249i 0.988546 + 0.150921i \(0.0482238\pi\)
−0.363572 + 0.931566i \(0.618443\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −36.1209 62.5632i −0.440499 0.762966i
\(83\) −26.9448 −0.324636 −0.162318 0.986739i \(-0.551897\pi\)
−0.162318 + 0.986739i \(0.551897\pi\)
\(84\) 13.4209 + 20.1960i 0.159772 + 0.240429i
\(85\) 0 0
\(86\) 24.5830 + 42.5790i 0.285849 + 0.495105i
\(87\) −8.63103 + 14.9494i −0.0992072 + 0.171832i
\(88\) 18.4623 + 10.6592i 0.209799 + 0.121127i
\(89\) −12.0453 + 6.95436i −0.135341 + 0.0781389i −0.566142 0.824308i \(-0.691564\pi\)
0.430801 + 0.902447i \(0.358231\pi\)
\(90\) 0 0
\(91\) −149.438 + 9.41559i −1.64218 + 0.103468i
\(92\) 11.1602i 0.121306i
\(93\) −9.87395 + 5.70073i −0.106171 + 0.0612981i
\(94\) 95.1005 + 54.9063i 1.01171 + 0.584110i
\(95\) 0 0
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 3.69132 0.0380549 0.0190274 0.999819i \(-0.493943\pi\)
0.0190274 + 0.999819i \(0.493943\pi\)
\(98\) 55.1890 41.9067i 0.563153 0.427619i
\(99\) 22.6116 0.228400
\(100\) 0 0
\(101\) −158.170 91.3195i −1.56604 0.904154i −0.996624 0.0821041i \(-0.973836\pi\)
−0.569416 0.822049i \(-0.692831\pi\)
\(102\) −44.5211 25.7043i −0.436481 0.252003i
\(103\) 45.5253 + 78.8521i 0.441993 + 0.765555i 0.997837 0.0657318i \(-0.0209382\pi\)
−0.555844 + 0.831287i \(0.687605\pi\)
\(104\) 60.5019i 0.581749i
\(105\) 0 0
\(106\) −70.4249 −0.664385
\(107\) 44.6318 25.7682i 0.417120 0.240824i −0.276724 0.960949i \(-0.589249\pi\)
0.693844 + 0.720125i \(0.255916\pi\)
\(108\) 5.19615 9.00000i 0.0481125 0.0833333i
\(109\) 19.1807 33.2219i 0.175970 0.304788i −0.764527 0.644592i \(-0.777027\pi\)
0.940496 + 0.339804i \(0.110361\pi\)
\(110\) 0 0
\(111\) 38.7920i 0.349477i
\(112\) −15.4971 23.3204i −0.138367 0.208218i
\(113\) 198.558i 1.75715i 0.477608 + 0.878573i \(0.341504\pi\)
−0.477608 + 0.878573i \(0.658496\pi\)
\(114\) −29.5187 51.1278i −0.258936 0.448490i
\(115\) 0 0
\(116\) 9.96625 17.2621i 0.0859160 0.148811i
\(117\) 32.0860 + 55.5745i 0.274239 + 0.474996i
\(118\) −119.104 −1.00936
\(119\) −65.3102 + 131.597i −0.548825 + 1.10586i
\(120\) 0 0
\(121\) 32.0953 + 55.5907i 0.265250 + 0.459427i
\(122\) −59.1474 + 102.446i −0.484814 + 0.839723i
\(123\) 76.6240 + 44.2389i 0.622959 + 0.359666i
\(124\) 11.4015 6.58263i 0.0919472 0.0530857i
\(125\) 0 0
\(126\) −26.6025 13.2026i −0.211131 0.104782i
\(127\) 74.1132i 0.583569i −0.956484 0.291784i \(-0.905751\pi\)
0.956484 0.291784i \(-0.0942490\pi\)
\(128\) −9.79796 + 5.65685i −0.0765466 + 0.0441942i
\(129\) −52.1485 30.1079i −0.404252 0.233395i
\(130\) 0 0
\(131\) 17.3500 10.0170i 0.132443 0.0764657i −0.432315 0.901723i \(-0.642303\pi\)
0.564757 + 0.825257i \(0.308970\pi\)
\(132\) −26.1096 −0.197800
\(133\) −140.516 + 93.3773i −1.05651 + 0.702085i
\(134\) 94.1614 0.702697
\(135\) 0 0
\(136\) 51.4085 + 29.6807i 0.378004 + 0.218241i
\(137\) 74.6259 + 43.0853i 0.544715 + 0.314491i 0.746988 0.664838i \(-0.231499\pi\)
−0.202273 + 0.979329i \(0.564833\pi\)
\(138\) 6.83419 + 11.8372i 0.0495231 + 0.0857766i
\(139\) 232.502i 1.67268i −0.548213 0.836339i \(-0.684692\pi\)
0.548213 0.836339i \(-0.315308\pi\)
\(140\) 0 0
\(141\) −134.492 −0.953847
\(142\) −83.4111 + 48.1574i −0.587402 + 0.339137i
\(143\) 80.6128 139.625i 0.563726 0.976402i
\(144\) −6.00000 + 10.3923i −0.0416667 + 0.0721688i
\(145\) 0 0
\(146\) 123.965i 0.849076i
\(147\) −32.8743 + 78.2450i −0.223635 + 0.532279i
\(148\) 44.7931i 0.302656i
\(149\) −109.963 190.462i −0.738008 1.27827i −0.953391 0.301738i \(-0.902433\pi\)
0.215383 0.976530i \(-0.430900\pi\)
\(150\) 0 0
\(151\) 130.461 225.965i 0.863980 1.49646i −0.00407633 0.999992i \(-0.501298\pi\)
0.868056 0.496466i \(-0.165369\pi\)
\(152\) 34.0852 + 59.0373i 0.224245 + 0.388403i
\(153\) 62.9623 0.411518
\(154\) 4.69190 + 74.4668i 0.0304669 + 0.483551i
\(155\) 0 0
\(156\) −37.0497 64.1719i −0.237498 0.411359i
\(157\) 57.0954 98.8921i 0.363665 0.629886i −0.624896 0.780708i \(-0.714859\pi\)
0.988561 + 0.150822i \(0.0481920\pi\)
\(158\) 120.939 + 69.8239i 0.765434 + 0.441923i
\(159\) 74.6968 43.1262i 0.469791 0.271234i
\(160\) 0 0
\(161\) 32.5325 21.6188i 0.202065 0.134278i
\(162\) 12.7279i 0.0785674i
\(163\) −42.1894 + 24.3581i −0.258831 + 0.149436i −0.623801 0.781583i \(-0.714412\pi\)
0.364970 + 0.931019i \(0.381079\pi\)
\(164\) −88.4777 51.0827i −0.539498 0.311480i
\(165\) 0 0
\(166\) −33.0005 + 19.0528i −0.198798 + 0.114776i
\(167\) −49.6127 −0.297082 −0.148541 0.988906i \(-0.547458\pi\)
−0.148541 + 0.988906i \(0.547458\pi\)
\(168\) 30.7179 + 15.2450i 0.182845 + 0.0907440i
\(169\) 288.560 1.70745
\(170\) 0 0
\(171\) 62.6185 + 36.1528i 0.366190 + 0.211420i
\(172\) 60.2159 + 34.7656i 0.350092 + 0.202126i
\(173\) 117.670 + 203.811i 0.680176 + 1.17810i 0.974927 + 0.222525i \(0.0714298\pi\)
−0.294751 + 0.955574i \(0.595237\pi\)
\(174\) 24.4122i 0.140300i
\(175\) 0 0
\(176\) 30.1488 0.171300
\(177\) 126.329 72.9362i 0.713725 0.412069i
\(178\) −9.83495 + 17.0346i −0.0552525 + 0.0957002i
\(179\) −22.1049 + 38.2868i −0.123491 + 0.213893i −0.921142 0.389226i \(-0.872742\pi\)
0.797651 + 0.603119i \(0.206076\pi\)
\(180\) 0 0
\(181\) 117.049i 0.646679i 0.946283 + 0.323340i \(0.104806\pi\)
−0.946283 + 0.323340i \(0.895194\pi\)
\(182\) −176.366 + 117.200i −0.969043 + 0.643958i
\(183\) 144.881i 0.791699i
\(184\) −7.89145 13.6684i −0.0428883 0.0742847i
\(185\) 0 0
\(186\) −8.06204 + 13.9639i −0.0433443 + 0.0750746i
\(187\) −79.0933 136.994i −0.422959 0.732586i
\(188\) 155.299 0.826056
\(189\) 36.3011 2.28721i 0.192069 0.0121016i
\(190\) 0 0
\(191\) −117.156 202.920i −0.613383 1.06241i −0.990666 0.136313i \(-0.956475\pi\)
0.377283 0.926098i \(-0.376858\pi\)
\(192\) 6.92820 12.0000i 0.0360844 0.0625000i
\(193\) −16.9438 9.78252i −0.0877918 0.0506866i 0.455461 0.890256i \(-0.349474\pi\)
−0.543253 + 0.839569i \(0.682808\pi\)
\(194\) 4.52093 2.61016i 0.0233037 0.0134544i
\(195\) 0 0
\(196\) 37.9600 90.3495i 0.193673 0.460967i
\(197\) 179.443i 0.910877i −0.890267 0.455438i \(-0.849483\pi\)
0.890267 0.455438i \(-0.150517\pi\)
\(198\) 27.6934 15.9888i 0.139866 0.0807516i
\(199\) 221.630 + 127.958i 1.11372 + 0.643006i 0.939790 0.341753i \(-0.111021\pi\)
0.173928 + 0.984758i \(0.444354\pi\)
\(200\) 0 0
\(201\) −99.8732 + 57.6618i −0.496882 + 0.286875i
\(202\) −258.291 −1.27867
\(203\) 69.6257 4.38688i 0.342984 0.0216102i
\(204\) −72.7026 −0.356385
\(205\) 0 0
\(206\) 111.514 + 64.3825i 0.541329 + 0.312536i
\(207\) −14.4975 8.37014i −0.0700363 0.0404355i
\(208\) 42.7813 + 74.0994i 0.205679 + 0.356247i
\(209\) 181.661i 0.869190i
\(210\) 0 0
\(211\) 196.891 0.933132 0.466566 0.884486i \(-0.345491\pi\)
0.466566 + 0.884486i \(0.345491\pi\)
\(212\) −86.2525 + 49.7979i −0.406851 + 0.234896i
\(213\) 58.9806 102.157i 0.276904 0.479612i
\(214\) 36.4417 63.1189i 0.170288 0.294948i
\(215\) 0 0
\(216\) 14.6969i 0.0680414i
\(217\) 41.2749 + 20.4843i 0.190207 + 0.0943977i
\(218\) 54.2512i 0.248859i
\(219\) −75.9128 131.485i −0.346634 0.600387i
\(220\) 0 0
\(221\) 224.467 388.789i 1.01569 1.75923i
\(222\) −27.4301 47.5103i −0.123559 0.214010i
\(223\) −431.015 −1.93280 −0.966401 0.257039i \(-0.917253\pi\)
−0.966401 + 0.257039i \(0.917253\pi\)
\(224\) −35.4700 17.6034i −0.158348 0.0785866i
\(225\) 0 0
\(226\) 140.401 + 243.182i 0.621245 + 1.07603i
\(227\) −87.5479 + 151.637i −0.385673 + 0.668006i −0.991862 0.127315i \(-0.959364\pi\)
0.606189 + 0.795321i \(0.292698\pi\)
\(228\) −72.3057 41.7457i −0.317130 0.183095i
\(229\) −29.0717 + 16.7846i −0.126951 + 0.0732951i −0.562131 0.827048i \(-0.690018\pi\)
0.435180 + 0.900344i \(0.356685\pi\)
\(230\) 0 0
\(231\) −50.5779 76.1108i −0.218952 0.329484i
\(232\) 28.1888i 0.121504i
\(233\) 134.159 77.4567i 0.575790 0.332432i −0.183669 0.982988i \(-0.558797\pi\)
0.759458 + 0.650556i \(0.225464\pi\)
\(234\) 78.5942 + 45.3764i 0.335873 + 0.193916i
\(235\) 0 0
\(236\) −145.872 + 84.2195i −0.618104 + 0.356862i
\(237\) −171.033 −0.721658
\(238\) 13.0647 + 207.354i 0.0548935 + 0.871235i
\(239\) −316.591 −1.32465 −0.662325 0.749217i \(-0.730430\pi\)
−0.662325 + 0.749217i \(0.730430\pi\)
\(240\) 0 0
\(241\) 202.219 + 116.751i 0.839084 + 0.484446i 0.856953 0.515395i \(-0.172355\pi\)
−0.0178685 + 0.999840i \(0.505688\pi\)
\(242\) 78.6171 + 45.3896i 0.324864 + 0.187560i
\(243\) −7.79423 13.5000i −0.0320750 0.0555556i
\(244\) 167.294i 0.685631i
\(245\) 0 0
\(246\) 125.126 0.508644
\(247\) 446.484 257.777i 1.80763 1.04363i
\(248\) 9.30925 16.1241i 0.0375373 0.0650165i
\(249\) 23.3349 40.4172i 0.0937143 0.162318i
\(250\) 0 0
\(251\) 56.6879i 0.225848i −0.993604 0.112924i \(-0.963978\pi\)
0.993604 0.112924i \(-0.0360217\pi\)
\(252\) −41.9169 + 2.64104i −0.166337 + 0.0104803i
\(253\) 42.0583i 0.166238i
\(254\) −52.4060 90.7698i −0.206323 0.357361i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 145.219 + 251.528i 0.565056 + 0.978706i 0.997044 + 0.0768270i \(0.0244789\pi\)
−0.431988 + 0.901879i \(0.642188\pi\)
\(258\) −85.1581 −0.330070
\(259\) −130.574 + 86.7704i −0.504147 + 0.335021i
\(260\) 0 0
\(261\) −14.9494 25.8931i −0.0572773 0.0992072i
\(262\) 14.1662 24.5366i 0.0540694 0.0936510i
\(263\) −385.031 222.298i −1.46399 0.845238i −0.464802 0.885415i \(-0.653875\pi\)
−0.999193 + 0.0401768i \(0.987208\pi\)
\(264\) −31.9776 + 18.4623i −0.121127 + 0.0699329i
\(265\) 0 0
\(266\) −106.069 + 213.723i −0.398755 + 0.803471i
\(267\) 24.0906i 0.0902270i
\(268\) 115.324 66.5822i 0.430312 0.248441i
\(269\) 144.956 + 83.6902i 0.538869 + 0.311116i 0.744620 0.667488i \(-0.232631\pi\)
−0.205752 + 0.978604i \(0.565964\pi\)
\(270\) 0 0
\(271\) 2.24099 1.29384i 0.00826933 0.00477430i −0.495860 0.868403i \(-0.665147\pi\)
0.504129 + 0.863628i \(0.331814\pi\)
\(272\) 83.9498 0.308639
\(273\) 115.294 232.311i 0.422322 0.850957i
\(274\) 121.864 0.444758
\(275\) 0 0
\(276\) 16.7403 + 9.66501i 0.0606532 + 0.0350181i
\(277\) 440.903 + 254.556i 1.59171 + 0.918973i 0.993014 + 0.117996i \(0.0376468\pi\)
0.598694 + 0.800978i \(0.295686\pi\)
\(278\) −164.404 284.756i −0.591381 1.02430i
\(279\) 19.7479i 0.0707810i
\(280\) 0 0
\(281\) 210.688 0.749779 0.374890 0.927069i \(-0.377681\pi\)
0.374890 + 0.927069i \(0.377681\pi\)
\(282\) −164.719 + 95.1005i −0.584110 + 0.337236i
\(283\) 19.7433 34.1964i 0.0697643 0.120835i −0.829033 0.559199i \(-0.811109\pi\)
0.898797 + 0.438364i \(0.144442\pi\)
\(284\) −68.1049 + 117.961i −0.239806 + 0.415356i
\(285\) 0 0
\(286\) 228.007i 0.797229i
\(287\) −22.4852 356.871i −0.0783457 1.24345i
\(288\) 16.9706i 0.0589256i
\(289\) −75.7363 131.179i −0.262063 0.453907i
\(290\) 0 0
\(291\) −3.19678 + 5.53698i −0.0109855 + 0.0190274i
\(292\) 87.6565 + 151.826i 0.300194 + 0.519951i
\(293\) −89.6023 −0.305810 −0.152905 0.988241i \(-0.548863\pi\)
−0.152905 + 0.988241i \(0.548863\pi\)
\(294\) 15.0649 + 119.076i 0.0512412 + 0.405020i
\(295\) 0 0
\(296\) 31.6735 + 54.8602i 0.107005 + 0.185338i
\(297\) −19.5822 + 33.9174i −0.0659334 + 0.114200i
\(298\) −269.354 155.511i −0.903871 0.521850i
\(299\) −103.370 + 59.6809i −0.345720 + 0.199602i
\(300\) 0 0
\(301\) 15.3029 + 242.878i 0.0508402 + 0.806903i
\(302\) 368.999i 1.22185i
\(303\) 273.959 158.170i 0.904154 0.522013i
\(304\) 83.4914 + 48.2038i 0.274643 + 0.158565i
\(305\) 0 0
\(306\) 77.1128 44.5211i 0.252003 0.145494i
\(307\) 470.478 1.53250 0.766251 0.642542i \(-0.222120\pi\)
0.766251 + 0.642542i \(0.222120\pi\)
\(308\) 58.4024 + 87.8852i 0.189618 + 0.285341i
\(309\) −157.704 −0.510370
\(310\) 0 0
\(311\) 217.631 + 125.649i 0.699778 + 0.404017i 0.807265 0.590189i \(-0.200947\pi\)
−0.107487 + 0.994207i \(0.534280\pi\)
\(312\) −90.7528 52.3962i −0.290874 0.167936i
\(313\) 194.231 + 336.417i 0.620545 + 1.07482i 0.989384 + 0.145322i \(0.0464219\pi\)
−0.368839 + 0.929493i \(0.620245\pi\)
\(314\) 161.490i 0.514300i
\(315\) 0 0
\(316\) 197.492 0.624974
\(317\) 129.366 74.6898i 0.408096 0.235614i −0.281875 0.959451i \(-0.590956\pi\)
0.689971 + 0.723837i \(0.257623\pi\)
\(318\) 60.9897 105.637i 0.191792 0.332193i
\(319\) −37.5588 + 65.0538i −0.117739 + 0.203930i
\(320\) 0 0
\(321\) 89.2636i 0.278080i
\(322\) 24.5572 49.4815i 0.0762645 0.153669i
\(323\) 505.837i 1.56606i
\(324\) 9.00000 + 15.5885i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) −34.4475 + 59.6648i −0.105667 + 0.183021i
\(327\) 33.2219 + 57.5420i 0.101596 + 0.175970i
\(328\) −144.484 −0.440499
\(329\) 300.835 + 452.702i 0.914391 + 1.37600i
\(330\) 0 0
\(331\) 235.465 + 407.838i 0.711375 + 1.23214i 0.964341 + 0.264663i \(0.0852607\pi\)
−0.252966 + 0.967475i \(0.581406\pi\)
\(332\) −26.9448 + 46.6697i −0.0811590 + 0.140571i
\(333\) 58.1880 + 33.5948i 0.174739 + 0.100885i
\(334\) −60.7628 + 35.0814i −0.181925 + 0.105034i
\(335\) 0 0
\(336\) 48.4014 3.04961i 0.144052 0.00907622i
\(337\) 532.478i 1.58005i −0.613072 0.790027i \(-0.710066\pi\)
0.613072 0.790027i \(-0.289934\pi\)
\(338\) 353.412 204.042i 1.04560 0.603676i
\(339\) −297.836 171.956i −0.878573 0.507244i
\(340\) 0 0
\(341\) −42.9675 + 24.8073i −0.126004 + 0.0727487i
\(342\) 102.256 0.298993
\(343\) 336.907 64.3643i 0.982236 0.187651i
\(344\) 98.3321 0.285849
\(345\) 0 0
\(346\) 288.232 + 166.411i 0.833042 + 0.480957i
\(347\) −389.385 224.812i −1.12215 0.647872i −0.180199 0.983630i \(-0.557674\pi\)
−0.941948 + 0.335758i \(0.891008\pi\)
\(348\) 17.2621 + 29.8988i 0.0496036 + 0.0859160i
\(349\) 330.676i 0.947495i 0.880661 + 0.473747i \(0.157099\pi\)
−0.880661 + 0.473747i \(0.842901\pi\)
\(350\) 0 0
\(351\) −111.149 −0.316664
\(352\) 36.9246 21.3184i 0.104899 0.0605637i
\(353\) 135.686 235.014i 0.384379 0.665763i −0.607304 0.794469i \(-0.707749\pi\)
0.991683 + 0.128706i \(0.0410824\pi\)
\(354\) 103.147 178.657i 0.291377 0.504680i
\(355\) 0 0
\(356\) 27.8174i 0.0781389i
\(357\) −140.835 211.932i −0.394496 0.593646i
\(358\) 62.5221i 0.174643i
\(359\) −3.79200 6.56794i −0.0105627 0.0182951i 0.860696 0.509120i \(-0.170029\pi\)
−0.871258 + 0.490825i \(0.836696\pi\)
\(360\) 0 0
\(361\) 109.950 190.440i 0.304572 0.527534i
\(362\) 82.7661 + 143.355i 0.228636 + 0.396009i
\(363\) −111.181 −0.306285
\(364\) −133.130 + 268.250i −0.365741 + 0.736951i
\(365\) 0 0
\(366\) −102.446 177.442i −0.279908 0.484814i
\(367\) −265.706 + 460.216i −0.723995 + 1.25400i 0.235392 + 0.971901i \(0.424363\pi\)
−0.959386 + 0.282095i \(0.908971\pi\)
\(368\) −19.3300 11.1602i −0.0525272 0.0303266i
\(369\) −132.717 + 76.6240i −0.359666 + 0.207653i
\(370\) 0 0
\(371\) −312.246 154.965i −0.841634 0.417695i
\(372\) 22.8029i 0.0612981i
\(373\) −497.937 + 287.484i −1.33495 + 0.770734i −0.986054 0.166427i \(-0.946777\pi\)
−0.348897 + 0.937161i \(0.613444\pi\)
\(374\) −193.738 111.855i −0.518016 0.299077i
\(375\) 0 0
\(376\) 190.201 109.813i 0.505854 0.292055i
\(377\) −213.185 −0.565476
\(378\) 42.8423 28.4700i 0.113339 0.0753174i
\(379\) −627.464 −1.65558 −0.827789 0.561040i \(-0.810402\pi\)
−0.827789 + 0.561040i \(0.810402\pi\)
\(380\) 0 0
\(381\) 111.170 + 64.1839i 0.291784 + 0.168462i
\(382\) −286.973 165.684i −0.751238 0.433727i
\(383\) −33.3056 57.6870i −0.0869597 0.150619i 0.819265 0.573415i \(-0.194382\pi\)
−0.906225 + 0.422797i \(0.861048\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −27.6691 −0.0716817
\(387\) 90.3238 52.1485i 0.233395 0.134751i
\(388\) 3.69132 6.39356i 0.00951372 0.0164782i
\(389\) 274.525 475.491i 0.705719 1.22234i −0.260713 0.965416i \(-0.583957\pi\)
0.966431 0.256925i \(-0.0827092\pi\)
\(390\) 0 0
\(391\) 117.112i 0.299519i
\(392\) −17.3955 137.497i −0.0443762 0.350757i
\(393\) 34.7000i 0.0882950i
\(394\) −126.885 219.772i −0.322044 0.557796i
\(395\) 0 0
\(396\) 22.6116 39.1644i 0.0571000 0.0989001i
\(397\) −259.283 449.091i −0.653106 1.13121i −0.982365 0.186973i \(-0.940132\pi\)
0.329259 0.944240i \(-0.393201\pi\)
\(398\) 361.920 0.909347
\(399\) −18.3753 291.642i −0.0460535 0.730931i
\(400\) 0 0
\(401\) 238.149 + 412.486i 0.593888 + 1.02864i 0.993703 + 0.112048i \(0.0357411\pi\)
−0.399815 + 0.916596i \(0.630926\pi\)
\(402\) −81.5462 + 141.242i −0.202851 + 0.351349i
\(403\) −121.942 70.4033i −0.302586 0.174698i
\(404\) −316.340 + 182.639i −0.783020 + 0.452077i
\(405\) 0 0
\(406\) 82.1717 54.6056i 0.202393 0.134497i
\(407\) 168.807i 0.414760i
\(408\) −89.0422 + 51.4085i −0.218241 + 0.126001i
\(409\) 93.2552 + 53.8409i 0.228008 + 0.131640i 0.609653 0.792669i \(-0.291309\pi\)
−0.381645 + 0.924309i \(0.624642\pi\)
\(410\) 0 0
\(411\) −129.256 + 74.6259i −0.314491 + 0.181572i
\(412\) 182.101 0.441993
\(413\) −528.079 262.080i −1.27864 0.634577i
\(414\) −23.6743 −0.0571844
\(415\) 0 0
\(416\) 104.792 + 60.5019i 0.251905 + 0.145437i
\(417\) 348.753 + 201.353i 0.836339 + 0.482861i
\(418\) −128.454 222.488i −0.307305 0.532268i
\(419\) 323.811i 0.772818i −0.922328 0.386409i \(-0.873715\pi\)
0.922328 0.386409i \(-0.126285\pi\)
\(420\) 0 0
\(421\) −238.957 −0.567595 −0.283797 0.958884i \(-0.591594\pi\)
−0.283797 + 0.958884i \(0.591594\pi\)
\(422\) 241.141 139.223i 0.571424 0.329912i
\(423\) 116.474 201.739i 0.275352 0.476924i
\(424\) −70.4249 + 121.979i −0.166096 + 0.287687i
\(425\) 0 0
\(426\) 166.822i 0.391601i
\(427\) −487.670 + 324.071i −1.14208 + 0.758950i
\(428\) 103.073i 0.240824i
\(429\) 139.625 + 241.838i 0.325467 + 0.563726i
\(430\) 0 0
\(431\) 95.8960 166.097i 0.222497 0.385375i −0.733069 0.680154i \(-0.761913\pi\)
0.955565 + 0.294779i \(0.0952461\pi\)
\(432\) −10.3923 18.0000i −0.0240563 0.0416667i
\(433\) −122.083 −0.281946 −0.140973 0.990013i \(-0.545023\pi\)
−0.140973 + 0.990013i \(0.545023\pi\)
\(434\) 65.0358 4.09768i 0.149852 0.00944166i
\(435\) 0 0
\(436\) −38.3614 66.4438i −0.0879848 0.152394i
\(437\) −67.2454 + 116.472i −0.153880 + 0.266527i
\(438\) −185.948 107.357i −0.424538 0.245107i
\(439\) 217.656 125.664i 0.495800 0.286250i −0.231177 0.972912i \(-0.574258\pi\)
0.726978 + 0.686661i \(0.240924\pi\)
\(440\) 0 0
\(441\) −88.8975 117.074i −0.201582 0.265473i
\(442\) 634.890i 1.43640i
\(443\) 95.0802 54.8946i 0.214628 0.123916i −0.388832 0.921309i \(-0.627121\pi\)
0.603460 + 0.797393i \(0.293788\pi\)
\(444\) −67.1897 38.7920i −0.151328 0.0873693i
\(445\) 0 0
\(446\) −527.883 + 304.773i −1.18359 + 0.683349i
\(447\) 380.924 0.852178
\(448\) −55.8892 + 3.52139i −0.124753 + 0.00786024i
\(449\) −806.490 −1.79619 −0.898095 0.439801i \(-0.855049\pi\)
−0.898095 + 0.439801i \(0.855049\pi\)
\(450\) 0 0
\(451\) 333.437 + 192.510i 0.739329 + 0.426852i
\(452\) 343.912 + 198.558i 0.760867 + 0.439287i
\(453\) 225.965 + 391.383i 0.498819 + 0.863980i
\(454\) 247.623i 0.545425i
\(455\) 0 0
\(456\) −118.075 −0.258936
\(457\) 668.964 386.226i 1.46382 0.845135i 0.464631 0.885504i \(-0.346187\pi\)
0.999185 + 0.0403698i \(0.0128536\pi\)
\(458\) −23.7370 + 41.1137i −0.0518275 + 0.0897678i
\(459\) −54.5270 + 94.4435i −0.118795 + 0.205759i
\(460\) 0 0
\(461\) 793.611i 1.72150i −0.509029 0.860749i \(-0.669995\pi\)
0.509029 0.860749i \(-0.330005\pi\)
\(462\) −115.764 57.4523i −0.250570 0.124356i
\(463\) 274.227i 0.592284i −0.955144 0.296142i \(-0.904300\pi\)
0.955144 0.296142i \(-0.0957001\pi\)
\(464\) −19.9325 34.5241i −0.0429580 0.0744054i
\(465\) 0 0
\(466\) 109.540 189.730i 0.235065 0.407145i
\(467\) −198.815 344.357i −0.425727 0.737381i 0.570761 0.821116i \(-0.306648\pi\)
−0.996488 + 0.0837354i \(0.973315\pi\)
\(468\) 128.344 0.274239
\(469\) 417.488 + 207.195i 0.890166 + 0.441781i
\(470\) 0 0
\(471\) 98.8921 + 171.286i 0.209962 + 0.363665i
\(472\) −119.104 + 206.295i −0.252340 + 0.437065i
\(473\) −226.930 131.018i −0.479766 0.276993i
\(474\) −209.472 + 120.939i −0.441923 + 0.255145i
\(475\) 0 0
\(476\) 162.622 + 244.717i 0.341643 + 0.514112i
\(477\) 149.394i 0.313194i
\(478\) −387.743 + 223.864i −0.811179 + 0.468334i
\(479\) 165.573 + 95.5938i 0.345665 + 0.199570i 0.662774 0.748819i \(-0.269379\pi\)
−0.317110 + 0.948389i \(0.602712\pi\)
\(480\) 0 0
\(481\) 414.893 239.538i 0.862563 0.498001i
\(482\) 330.223 0.685110
\(483\) 4.25428 + 67.5212i 0.00880803 + 0.139795i
\(484\) 128.381 0.265250
\(485\) 0 0
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) −164.561 95.0092i −0.337907 0.195091i 0.321439 0.946930i \(-0.395833\pi\)
−0.659346 + 0.751840i \(0.729167\pi\)
\(488\) 118.295 + 204.892i 0.242407 + 0.419862i
\(489\) 84.3788i 0.172554i
\(490\) 0 0
\(491\) −211.384 −0.430517 −0.215258 0.976557i \(-0.569059\pi\)
−0.215258 + 0.976557i \(0.569059\pi\)
\(492\) 153.248 88.4777i 0.311480 0.179833i
\(493\) −104.583 + 181.143i −0.212136 + 0.367430i
\(494\) 364.552 631.423i 0.737960 1.27818i
\(495\) 0 0
\(496\) 26.3305i 0.0530857i
\(497\) −475.791 + 29.9779i −0.957325 + 0.0603178i
\(498\) 66.0010i 0.132532i
\(499\) −126.864 219.734i −0.254236 0.440349i 0.710452 0.703746i \(-0.248491\pi\)
−0.964688 + 0.263396i \(0.915157\pi\)
\(500\) 0 0
\(501\) 42.9658 74.4190i 0.0857601 0.148541i
\(502\) −40.0844 69.4282i −0.0798494 0.138303i
\(503\) 217.815 0.433033 0.216516 0.976279i \(-0.430531\pi\)
0.216516 + 0.976279i \(0.430531\pi\)
\(504\) −49.4700 + 32.8743i −0.0981547 + 0.0652268i
\(505\) 0 0
\(506\) 29.7397 + 51.5107i 0.0587741 + 0.101800i
\(507\) −249.900 + 432.839i −0.492899 + 0.853727i
\(508\) −128.368 74.1132i −0.252693 0.145892i
\(509\) 24.6582 14.2364i 0.0484444 0.0279694i −0.475582 0.879671i \(-0.657763\pi\)
0.524027 + 0.851702i \(0.324429\pi\)
\(510\) 0 0
\(511\) −272.776 + 549.630i −0.533808 + 1.07560i
\(512\) 22.6274i 0.0441942i
\(513\) −108.458 + 62.6185i −0.211420 + 0.122063i
\(514\) 355.714 + 205.371i 0.692050 + 0.399555i
\(515\) 0 0
\(516\) −104.297 + 60.2159i −0.202126 + 0.116697i
\(517\) −585.258 −1.13203
\(518\) −98.5640 + 198.601i −0.190278 + 0.383400i
\(519\) −407.622 −0.785399
\(520\) 0 0
\(521\) 671.401 + 387.634i 1.28868 + 0.744019i 0.978418 0.206633i \(-0.0662507\pi\)
0.310260 + 0.950652i \(0.399584\pi\)
\(522\) −36.6184 21.1416i −0.0701501 0.0405012i
\(523\) −51.2334 88.7388i −0.0979605 0.169673i 0.812880 0.582431i \(-0.197899\pi\)
−0.910840 + 0.412759i \(0.864565\pi\)
\(524\) 40.0681i 0.0764657i
\(525\) 0 0
\(526\) −628.752 −1.19535
\(527\) −119.644 + 69.0763i −0.227028 + 0.131075i
\(528\) −26.1096 + 45.2232i −0.0494501 + 0.0856500i
\(529\) −248.931 + 431.162i −0.470570 + 0.815050i
\(530\) 0 0
\(531\) 252.659i 0.475816i
\(532\) 21.2180 + 336.759i 0.0398835 + 0.633005i
\(533\) 1092.69i 2.05008i
\(534\) −17.0346 29.5049i −0.0319001 0.0552525i
\(535\) 0 0
\(536\) 94.1614 163.092i 0.175674 0.304277i
\(537\) −38.2868 66.3147i −0.0712976 0.123491i
\(538\) 236.712 0.439984
\(539\) −143.056 + 340.491i −0.265410 + 0.631709i
\(540\) 0 0
\(541\) 408.868 + 708.180i 0.755763 + 1.30902i 0.944994 + 0.327088i \(0.106067\pi\)
−0.189231 + 0.981933i \(0.560599\pi\)
\(542\) 1.82976 3.16924i 0.00337594 0.00584730i
\(543\) −175.573 101.367i −0.323340 0.186680i
\(544\) 102.817 59.3614i 0.189002 0.109120i
\(545\) 0 0
\(546\) −23.0634 366.047i −0.0422406 0.670416i
\(547\) 204.209i 0.373325i 0.982424 + 0.186662i \(0.0597670\pi\)
−0.982424 + 0.186662i \(0.940233\pi\)
\(548\) 149.252 86.1706i 0.272357 0.157246i
\(549\) 217.321 + 125.471i 0.395849 + 0.228544i
\(550\) 0 0
\(551\) −208.024 + 120.103i −0.377539 + 0.217972i
\(552\) 27.3368 0.0495231
\(553\) 382.569 + 575.698i 0.691806 + 1.04105i
\(554\) 719.992 1.29962
\(555\) 0 0
\(556\) −402.706 232.502i −0.724291 0.418169i
\(557\) 464.253 + 268.036i 0.833487 + 0.481214i 0.855045 0.518553i \(-0.173529\pi\)
−0.0215578 + 0.999768i \(0.506863\pi\)
\(558\) −13.9639 24.1861i −0.0250249 0.0433443i
\(559\) 743.660i 1.33034i
\(560\) 0 0
\(561\) 273.987 0.488391
\(562\) 258.039 148.979i 0.459144 0.265087i
\(563\) 494.806 857.029i 0.878874 1.52225i 0.0262960 0.999654i \(-0.491629\pi\)
0.852578 0.522600i \(-0.175038\pi\)
\(564\) −134.492 + 232.948i −0.238462 + 0.413028i
\(565\) 0 0
\(566\) 55.8424i 0.0986616i
\(567\) −28.0068 + 56.4324i −0.0493948 + 0.0995281i
\(568\) 192.630i 0.339137i
\(569\) 248.330 + 430.120i 0.436432 + 0.755922i 0.997411 0.0719076i \(-0.0229087\pi\)
−0.560979 + 0.827830i \(0.689575\pi\)
\(570\) 0 0
\(571\) 71.0244 123.018i 0.124386 0.215443i −0.797107 0.603838i \(-0.793637\pi\)
0.921493 + 0.388395i \(0.126971\pi\)
\(572\) −161.226 279.251i −0.281863 0.488201i
\(573\) 405.841 0.708274
\(574\) −279.884 421.176i −0.487604 0.733757i
\(575\) 0 0
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −189.689 + 328.551i −0.328751 + 0.569413i −0.982264 0.187502i \(-0.939961\pi\)
0.653514 + 0.756915i \(0.273294\pi\)
\(578\) −185.515 107.107i −0.320961 0.185307i
\(579\) 29.3476 16.9438i 0.0506866 0.0292639i
\(580\) 0 0
\(581\) −188.240 + 11.8604i −0.323993 + 0.0204137i
\(582\) 9.04185i 0.0155358i
\(583\) 325.051 187.668i 0.557549 0.321901i
\(584\) 214.714 + 123.965i 0.367661 + 0.212269i
\(585\) 0 0
\(586\) −109.740 + 63.3584i −0.187269 + 0.108120i
\(587\) −234.204 −0.398984 −0.199492 0.979899i \(-0.563929\pi\)
−0.199492 + 0.979899i \(0.563929\pi\)
\(588\) 102.650 + 135.185i 0.174575 + 0.229906i
\(589\) −158.654 −0.269361
\(590\) 0 0
\(591\) 269.164 + 155.402i 0.455438 + 0.262948i
\(592\) 77.5840 + 44.7931i 0.131054 + 0.0756641i
\(593\) −286.272 495.838i −0.482753 0.836152i 0.517051 0.855954i \(-0.327030\pi\)
−0.999804 + 0.0198023i \(0.993696\pi\)
\(594\) 55.3869i 0.0932439i
\(595\) 0 0
\(596\) −439.853 −0.738008
\(597\) −383.874 + 221.630i −0.643006 + 0.371239i
\(598\) −84.4016 + 146.188i −0.141140 + 0.244461i
\(599\) 46.7105 80.9049i 0.0779807 0.135067i −0.824398 0.566011i \(-0.808486\pi\)
0.902379 + 0.430944i \(0.141819\pi\)
\(600\) 0 0
\(601\) 167.140i 0.278103i 0.990285 + 0.139051i \(0.0444053\pi\)
−0.990285 + 0.139051i \(0.955595\pi\)
\(602\) 190.483 + 286.643i 0.316417 + 0.476151i
\(603\) 199.746i 0.331255i
\(604\) −260.922 451.930i −0.431990 0.748229i
\(605\) 0 0
\(606\) 223.686 387.436i 0.369119 0.639333i
\(607\) 459.572 + 796.002i 0.757120 + 1.31137i 0.944314 + 0.329047i \(0.106727\pi\)
−0.187194 + 0.982323i \(0.559939\pi\)
\(608\) 136.341 0.224245
\(609\) −53.7173 + 108.238i −0.0882058 + 0.177730i
\(610\) 0 0
\(611\) −830.484 1438.44i −1.35922 2.35424i
\(612\) 62.9623 109.054i 0.102880 0.178193i
\(613\) 675.011 + 389.718i 1.10116 + 0.635755i 0.936525 0.350600i \(-0.114022\pi\)
0.164635 + 0.986355i \(0.447356\pi\)
\(614\) 576.215 332.678i 0.938462 0.541821i
\(615\) 0 0
\(616\) 133.672 + 66.3402i 0.217000 + 0.107695i
\(617\) 510.821i 0.827911i −0.910297 0.413956i \(-0.864147\pi\)
0.910297 0.413956i \(-0.135853\pi\)
\(618\) −193.148 + 111.514i −0.312536 + 0.180443i
\(619\) 808.792 + 466.956i 1.30661 + 0.754372i 0.981529 0.191314i \(-0.0612749\pi\)
0.325082 + 0.945686i \(0.394608\pi\)
\(620\) 0 0
\(621\) 25.1104 14.4975i 0.0404355 0.0233454i
\(622\) 355.390 0.571367
\(623\) −81.0892 + 53.8862i −0.130159 + 0.0864947i
\(624\) −148.199 −0.237498
\(625\) 0 0
\(626\) 475.766 + 274.684i 0.760009 + 0.438792i
\(627\) 272.491 + 157.323i 0.434595 + 0.250914i
\(628\) −114.191 197.784i −0.181832 0.314943i
\(629\) 470.047i 0.747292i
\(630\) 0 0
\(631\) −614.861 −0.974423 −0.487212 0.873284i \(-0.661986\pi\)
−0.487212 + 0.873284i \(0.661986\pi\)
\(632\) 241.877 139.648i 0.382717 0.220962i
\(633\) −170.512 + 295.336i −0.269372 + 0.466566i
\(634\) 105.627 182.952i 0.166605 0.288568i
\(635\) 0 0
\(636\) 172.505i 0.271234i
\(637\) −1039.85 + 131.557i −1.63242 + 0.206526i
\(638\) 106.232i 0.166508i
\(639\) 102.157 + 176.942i 0.159871 + 0.276904i
\(640\) 0 0
\(641\) 94.1724 163.111i 0.146915 0.254464i −0.783171 0.621807i \(-0.786399\pi\)
0.930086 + 0.367343i \(0.119732\pi\)
\(642\) 63.1189 + 109.325i 0.0983161 + 0.170288i
\(643\) −23.8831 −0.0371432 −0.0185716 0.999828i \(-0.505912\pi\)
−0.0185716 + 0.999828i \(0.505912\pi\)
\(644\) −4.91242 77.9667i −0.00762798 0.121066i
\(645\) 0 0
\(646\) −357.681 619.521i −0.553685 0.959011i
\(647\) −542.667 + 939.928i −0.838744 + 1.45275i 0.0522010 + 0.998637i \(0.483376\pi\)
−0.890945 + 0.454111i \(0.849957\pi\)
\(648\) 22.0454 + 12.7279i 0.0340207 + 0.0196419i
\(649\) 549.735 317.390i 0.847049 0.489044i
\(650\) 0 0
\(651\) −66.4715 + 44.1724i −0.102107 + 0.0678531i
\(652\) 97.4323i 0.149436i
\(653\) −550.536 + 317.852i −0.843087 + 0.486756i −0.858312 0.513128i \(-0.828487\pi\)
0.0152254 + 0.999884i \(0.495153\pi\)
\(654\) 81.3767 + 46.9829i 0.124429 + 0.0718393i
\(655\) 0 0
\(656\) −176.955 + 102.165i −0.269749 + 0.155740i
\(657\) 262.970 0.400258
\(658\) 688.555 + 341.723i 1.04644 + 0.519336i
\(659\) 888.955 1.34895 0.674473 0.738300i \(-0.264371\pi\)
0.674473 + 0.738300i \(0.264371\pi\)
\(660\) 0 0
\(661\) −656.362 378.951i −0.992983 0.573299i −0.0868187 0.996224i \(-0.527670\pi\)
−0.906165 + 0.422925i \(0.861003\pi\)
\(662\) 576.770 + 332.998i 0.871253 + 0.503018i
\(663\) 388.789 + 673.402i 0.586409 + 1.01569i
\(664\) 76.2114i 0.114776i
\(665\) 0 0
\(666\) 95.0206 0.142674
\(667\) 48.1620 27.8063i 0.0722068 0.0416886i
\(668\) −49.6127 + 85.9316i −0.0742704 + 0.128640i
\(669\) 373.270 646.522i 0.557952 0.966401i
\(670\) 0 0
\(671\) 630.464i 0.939589i
\(672\) 57.1230 37.9600i 0.0850045 0.0564881i
\(673\) 936.839i 1.39203i 0.718026 + 0.696017i \(0.245046\pi\)
−0.718026 + 0.696017i \(0.754954\pi\)
\(674\) −376.519 652.150i −0.558634 0.967582i
\(675\) 0 0
\(676\) 288.560 499.800i 0.426863 0.739349i
\(677\) −123.589 214.062i −0.182554 0.316192i 0.760196 0.649694i \(-0.225103\pi\)
−0.942749 + 0.333502i \(0.891770\pi\)
\(678\) −486.365 −0.717352
\(679\) 25.7881 1.62482i 0.0379795 0.00239296i
\(680\) 0 0
\(681\) −151.637 262.644i −0.222669 0.385673i
\(682\) −35.0828 + 60.7652i −0.0514411 + 0.0890986i
\(683\) 607.755 + 350.887i 0.889831 + 0.513744i 0.873887 0.486129i \(-0.161591\pi\)
0.0159438 + 0.999873i \(0.494925\pi\)
\(684\) 125.237 72.3057i 0.183095 0.105710i
\(685\) 0 0
\(686\) 367.112 317.059i 0.535149 0.462185i
\(687\) 58.1435i 0.0846339i
\(688\) 120.432 69.5313i 0.175046 0.101063i
\(689\) 922.498 + 532.604i 1.33889 + 0.773011i
\(690\) 0 0
\(691\) −530.850 + 306.486i −0.768234 + 0.443540i −0.832244 0.554409i \(-0.812944\pi\)
0.0640104 + 0.997949i \(0.479611\pi\)
\(692\) 470.682 0.680176
\(693\) 157.968 9.95302i 0.227948 0.0143622i
\(694\) −635.863 −0.916230
\(695\) 0 0
\(696\) 42.2832 + 24.4122i 0.0607518 + 0.0350750i
\(697\) 928.461 + 536.047i 1.33208 + 0.769078i
\(698\) 233.823 + 404.993i 0.334990 + 0.580220i
\(699\) 268.318i 0.383860i
\(700\) 0 0
\(701\) 161.307 0.230110 0.115055 0.993359i \(-0.463296\pi\)
0.115055 + 0.993359i \(0.463296\pi\)
\(702\) −136.129 + 78.5942i −0.193916 + 0.111958i
\(703\) 269.900 467.480i 0.383926 0.664979i
\(704\) 30.1488 52.2193i 0.0428250 0.0741751i
\(705\) 0 0
\(706\) 383.777i 0.543593i
\(707\) −1145.20 568.349i −1.61980 0.803889i
\(708\) 291.745i 0.412069i
\(709\) 285.175 + 493.938i 0.402222 + 0.696669i 0.993994 0.109436i \(-0.0349046\pi\)
−0.591772 + 0.806106i \(0.701571\pi\)
\(710\) 0 0
\(711\) 148.119 256.549i 0.208325 0.360829i
\(712\) 19.6699 + 34.0693i 0.0276263 + 0.0478501i
\(713\) 36.7317 0.0515171
\(714\) −322.345 159.977i −0.451464 0.224057i
\(715\) 0 0
\(716\) 44.2098 + 76.5736i 0.0617455 + 0.106946i
\(717\) 274.176 474.887i 0.382393 0.662325i
\(718\) −9.28847 5.36270i −0.0129366 0.00746894i
\(719\) −431.817 + 249.310i −0.600580 + 0.346745i −0.769270 0.638924i \(-0.779380\pi\)
0.168690 + 0.985669i \(0.446046\pi\)
\(720\) 0 0
\(721\) 352.755 + 530.834i 0.489258 + 0.736246i
\(722\) 310.987i 0.430730i
\(723\) −350.254 + 202.219i −0.484446 + 0.279695i
\(724\) 202.735 + 117.049i 0.280020 + 0.161670i
\(725\) 0 0
\(726\) −136.169 + 78.6171i −0.187560 + 0.108288i
\(727\) −1058.79 −1.45638 −0.728190 0.685375i \(-0.759638\pi\)
−0.728190 + 0.685375i \(0.759638\pi\)
\(728\) 26.6313 + 422.675i 0.0365815 + 0.580597i
\(729\) 27.0000 0.0370370
\(730\) 0 0
\(731\) −631.888 364.821i −0.864416 0.499071i
\(732\) −250.941 144.881i −0.342816 0.197925i
\(733\) 7.56721 + 13.1068i 0.0103236 + 0.0178810i 0.871141 0.491033i \(-0.163380\pi\)
−0.860817 + 0.508914i \(0.830047\pi\)
\(734\) 751.530i 1.02388i
\(735\) 0 0
\(736\) −31.5658 −0.0428883
\(737\) −434.609 + 250.922i −0.589700 + 0.340463i
\(738\) −108.363 + 187.690i −0.146833 + 0.254322i
\(739\) −81.3819 + 140.958i −0.110124 + 0.190741i −0.915820 0.401588i \(-0.868458\pi\)
0.805696 + 0.592329i \(0.201792\pi\)
\(740\) 0 0
\(741\) 892.967i 1.20508i
\(742\) −491.998 + 30.9991i −0.663071 + 0.0417778i
\(743\) 338.071i 0.455009i 0.973777 + 0.227504i \(0.0730566\pi\)
−0.973777 + 0.227504i \(0.926943\pi\)
\(744\) 16.1241 + 27.9277i 0.0216722 + 0.0375373i
\(745\) 0 0
\(746\) −406.564 + 704.189i −0.544991 + 0.943953i
\(747\) 40.4172 + 70.0046i 0.0541060 + 0.0937143i
\(748\) −316.373 −0.422959
\(749\) 300.462 199.666i 0.401151 0.266577i
\(750\) 0 0
\(751\) −239.087 414.111i −0.318359 0.551413i 0.661787 0.749692i \(-0.269798\pi\)
−0.980146 + 0.198279i \(0.936465\pi\)
\(752\) 155.299 268.985i 0.206514 0.357693i
\(753\) 85.0319 + 49.0932i 0.112924 + 0.0651968i
\(754\) −261.097 + 150.744i −0.346282 + 0.199926i
\(755\) 0 0
\(756\) 32.3395 65.1625i 0.0427771 0.0861938i
\(757\) 397.788i 0.525479i 0.964867 + 0.262739i \(0.0846260\pi\)
−0.964867 + 0.262739i \(0.915374\pi\)
\(758\) −768.483 + 443.684i −1.01383 + 0.585335i
\(759\) −63.0874 36.4236i −0.0831192 0.0479889i
\(760\) 0 0
\(761\) −1264.02 + 729.785i −1.66100 + 0.958981i −0.688767 + 0.724983i \(0.741848\pi\)
−0.972237 + 0.233998i \(0.924819\pi\)
\(762\) 181.540 0.238241
\(763\) 119.376 240.536i 0.156456 0.315250i
\(764\) −468.625 −0.613383
\(765\) 0 0
\(766\) −81.5817 47.1012i −0.106503 0.0614898i
\(767\) 1560.15 + 900.755i 2.03410 + 1.17439i
\(768\) −13.8564 24.0000i −0.0180422 0.0312500i
\(769\) 2.10093i 0.00273203i 0.999999 + 0.00136602i \(0.000434817\pi\)
−0.999999 + 0.00136602i \(0.999565\pi\)
\(770\) 0 0
\(771\) −503.055 −0.652471
\(772\) −33.8876 + 19.5650i −0.0438959 + 0.0253433i
\(773\) −226.305 + 391.972i −0.292762 + 0.507079i −0.974462 0.224553i \(-0.927908\pi\)
0.681700 + 0.731632i \(0.261241\pi\)
\(774\) 73.7491 127.737i 0.0952830 0.165035i
\(775\) 0 0
\(776\) 10.4406i 0.0134544i
\(777\) −17.0752 271.007i −0.0219758 0.348786i
\(778\) 776.473i 0.998037i
\(779\) 615.594 + 1066.24i 0.790236 + 1.36873i
\(780\) 0 0
\(781\) 256.660 444.548i 0.328630 0.569204i