Properties

Label 105.3.o.b.44.1
Level 105
Weight 3
Character 105.44
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 44.1
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.85988 + 3.22141i) q^{2} +(-2.47330 + 1.69788i) q^{3} +(-4.91833 - 8.51879i) q^{4} +(4.36624 - 2.43637i) q^{5} +(-0.869509 - 11.1254i) q^{6} +(-4.87678 - 5.02166i) q^{7} +21.7110 q^{8} +(3.23443 - 8.39872i) q^{9} +O(q^{10})\) \(q+(-1.85988 + 3.22141i) q^{2} +(-2.47330 + 1.69788i) q^{3} +(-4.91833 - 8.51879i) q^{4} +(4.36624 - 2.43637i) q^{5} +(-0.869509 - 11.1254i) q^{6} +(-4.87678 - 5.02166i) q^{7} +21.7110 q^{8} +(3.23443 - 8.39872i) q^{9} +(-0.272141 + 18.5968i) q^{10} +(-10.0814 + 5.82052i) q^{11} +(26.6283 + 12.7188i) q^{12} -9.22710i q^{13} +(25.2471 - 6.37041i) q^{14} +(-6.66237 + 13.4392i) q^{15} +(-20.7066 + 35.8648i) q^{16} +(-1.56346 - 2.70799i) q^{17} +(21.0401 + 26.0401i) q^{18} +(5.39398 - 9.34265i) q^{19} +(-42.2296 - 25.2122i) q^{20} +(20.5879 + 4.13990i) q^{21} -43.3019i q^{22} +(2.93334 - 5.08070i) q^{23} +(-53.6978 + 36.8625i) q^{24} +(13.1282 - 21.2756i) q^{25} +(29.7243 + 17.1613i) q^{26} +(6.26026 + 26.2642i) q^{27} +(-18.7929 + 66.2424i) q^{28} -38.3541i q^{29} +(-30.9020 - 46.4576i) q^{30} +(-15.7425 - 27.2669i) q^{31} +(-33.6016 - 58.1996i) q^{32} +(15.0519 - 31.5129i) q^{33} +11.6314 q^{34} +(-33.5278 - 10.0441i) q^{35} +(-87.4549 + 13.7542i) q^{36} +(-20.0791 - 11.5927i) q^{37} +(20.0643 + 34.7525i) q^{38} +(15.6665 + 22.8214i) q^{39} +(94.7954 - 52.8960i) q^{40} +22.7035i q^{41} +(-51.6274 + 58.6223i) q^{42} -29.1447i q^{43} +(99.1676 + 57.2544i) q^{44} +(-6.34009 - 44.5511i) q^{45} +(10.9113 + 18.8990i) q^{46} +(-30.0800 + 52.1000i) q^{47} +(-9.68046 - 123.862i) q^{48} +(-1.43408 + 48.9790i) q^{49} +(44.1206 + 81.8613i) q^{50} +(8.46474 + 4.04312i) q^{51} +(-78.6037 + 45.3819i) q^{52} +(-27.9865 - 48.4740i) q^{53} +(-96.2512 - 28.6815i) q^{54} +(-29.8370 + 49.9760i) q^{55} +(-105.880 - 109.025i) q^{56} +(2.52173 + 32.2655i) q^{57} +(123.554 + 71.3342i) q^{58} +(-23.2367 + 13.4157i) q^{59} +(147.254 - 9.34313i) q^{60} +(-19.8501 + 34.3814i) q^{61} +117.117 q^{62} +(-57.9491 + 24.7165i) q^{63} +84.3274 q^{64} +(-22.4807 - 40.2878i) q^{65} +(73.5213 + 107.099i) q^{66} +(86.4356 - 49.9036i) q^{67} +(-15.3792 + 26.6376i) q^{68} +(1.37136 + 17.5466i) q^{69} +(94.7141 - 89.3260i) q^{70} -62.5979i q^{71} +(70.2227 - 182.344i) q^{72} +(37.5802 - 21.6970i) q^{73} +(74.6895 - 43.1220i) q^{74} +(3.65342 + 74.9110i) q^{75} -106.117 q^{76} +(78.3936 + 22.2401i) q^{77} +(-102.655 + 8.02304i) q^{78} +(15.5064 - 26.8579i) q^{79} +(-3.02981 + 207.043i) q^{80} +(-60.0769 - 54.3302i) q^{81} +(-73.1373 - 42.2259i) q^{82} -93.5855 q^{83} +(-65.9910 - 195.745i) q^{84} +(-13.4241 - 8.01458i) q^{85} +(93.8870 + 54.2057i) q^{86} +(65.1206 + 94.8613i) q^{87} +(-218.878 + 126.369i) q^{88} +(34.2984 + 19.8022i) q^{89} +(155.309 + 62.4358i) q^{90} +(-46.3353 + 44.9985i) q^{91} -57.7086 q^{92} +(85.2318 + 40.7103i) q^{93} +(-111.890 - 193.800i) q^{94} +(0.789255 - 53.9341i) q^{95} +(181.922 + 86.8938i) q^{96} +119.768i q^{97} +(-155.114 - 95.7150i) q^{98} +(16.2772 + 103.497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + O(q^{10}) \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + 62q^{10} + 84q^{15} - 116q^{16} - 56q^{19} + 36q^{21} - 12q^{24} - 6q^{25} - 20q^{30} - 444q^{31} + 256q^{34} - 688q^{36} + 168q^{39} + 54q^{40} - 40q^{45} + 304q^{46} + 156q^{49} + 156q^{51} - 140q^{54} - 500q^{55} - 130q^{60} + 288q^{61} + 472q^{64} + 340q^{66} - 272q^{69} + 710q^{70} - 524q^{75} + 400q^{76} - 340q^{79} + 496q^{84} + 896q^{85} + 1356q^{90} - 656q^{91} - 560q^{94} + 472q^{96} - 336q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.85988 + 3.22141i −0.929941 + 1.61071i −0.146526 + 0.989207i \(0.546809\pi\)
−0.783415 + 0.621499i \(0.786524\pi\)
\(3\) −2.47330 + 1.69788i −0.824434 + 0.565959i
\(4\) −4.91833 8.51879i −1.22958 2.12970i
\(5\) 4.36624 2.43637i 0.873249 0.487275i
\(6\) −0.869509 11.1254i −0.144918 1.85423i
\(7\) −4.87678 5.02166i −0.696682 0.717380i
\(8\) 21.7110 2.71387
\(9\) 3.23443 8.39872i 0.359381 0.933191i
\(10\) −0.272141 + 18.5968i −0.0272141 + 1.85968i
\(11\) −10.0814 + 5.82052i −0.916494 + 0.529138i −0.882515 0.470284i \(-0.844151\pi\)
−0.0339793 + 0.999423i \(0.510818\pi\)
\(12\) 26.6283 + 12.7188i 2.21903 + 1.05990i
\(13\) 9.22710i 0.709777i −0.934909 0.354888i \(-0.884519\pi\)
0.934909 0.354888i \(-0.115481\pi\)
\(14\) 25.2471 6.37041i 1.80336 0.455029i
\(15\) −6.66237 + 13.4392i −0.444158 + 0.895948i
\(16\) −20.7066 + 35.8648i −1.29416 + 2.24155i
\(17\) −1.56346 2.70799i −0.0919682 0.159294i 0.816371 0.577528i \(-0.195982\pi\)
−0.908339 + 0.418234i \(0.862649\pi\)
\(18\) 21.0401 + 26.0401i 1.16889 + 1.44667i
\(19\) 5.39398 9.34265i 0.283894 0.491719i −0.688447 0.725287i \(-0.741707\pi\)
0.972340 + 0.233569i \(0.0750403\pi\)
\(20\) −42.2296 25.2122i −2.11148 1.26061i
\(21\) 20.5879 + 4.13990i 0.980376 + 0.197138i
\(22\) 43.3019i 1.96827i
\(23\) 2.93334 5.08070i 0.127537 0.220900i −0.795185 0.606367i \(-0.792626\pi\)
0.922722 + 0.385467i \(0.125960\pi\)
\(24\) −53.6978 + 36.8625i −2.23741 + 1.53594i
\(25\) 13.1282 21.2756i 0.525127 0.851024i
\(26\) 29.7243 + 17.1613i 1.14324 + 0.660051i
\(27\) 6.26026 + 26.2642i 0.231861 + 0.972749i
\(28\) −18.7929 + 66.2424i −0.671174 + 2.36580i
\(29\) 38.3541i 1.32256i −0.750141 0.661278i \(-0.770014\pi\)
0.750141 0.661278i \(-0.229986\pi\)
\(30\) −30.9020 46.4576i −1.03007 1.54859i
\(31\) −15.7425 27.2669i −0.507824 0.879577i −0.999959 0.00905794i \(-0.997117\pi\)
0.492135 0.870519i \(-0.336217\pi\)
\(32\) −33.6016 58.1996i −1.05005 1.81874i
\(33\) 15.0519 31.5129i 0.456118 0.954937i
\(34\) 11.6314 0.342100
\(35\) −33.5278 10.0441i −0.957938 0.286975i
\(36\) −87.4549 + 13.7542i −2.42930 + 0.382060i
\(37\) −20.0791 11.5927i −0.542678 0.313315i 0.203486 0.979078i \(-0.434773\pi\)
−0.746164 + 0.665763i \(0.768106\pi\)
\(38\) 20.0643 + 34.7525i 0.528009 + 0.914539i
\(39\) 15.6665 + 22.8214i 0.401704 + 0.585164i
\(40\) 94.7954 52.8960i 2.36988 1.32240i
\(41\) 22.7035i 0.553744i 0.960907 + 0.276872i \(0.0892978\pi\)
−0.960907 + 0.276872i \(0.910702\pi\)
\(42\) −51.6274 + 58.6223i −1.22922 + 1.39577i
\(43\) 29.1447i 0.677784i −0.940825 0.338892i \(-0.889948\pi\)
0.940825 0.338892i \(-0.110052\pi\)
\(44\) 99.1676 + 57.2544i 2.25381 + 1.30124i
\(45\) −6.34009 44.5511i −0.140891 0.990025i
\(46\) 10.9113 + 18.8990i 0.237203 + 0.410848i
\(47\) −30.0800 + 52.1000i −0.639999 + 1.10851i 0.345433 + 0.938443i \(0.387732\pi\)
−0.985432 + 0.170068i \(0.945601\pi\)
\(48\) −9.68046 123.862i −0.201676 2.58045i
\(49\) −1.43408 + 48.9790i −0.0292670 + 0.999572i
\(50\) 44.1206 + 81.8613i 0.882412 + 1.63723i
\(51\) 8.46474 + 4.04312i 0.165975 + 0.0792768i
\(52\) −78.6037 + 45.3819i −1.51161 + 0.872728i
\(53\) −27.9865 48.4740i −0.528047 0.914604i −0.999465 0.0326945i \(-0.989591\pi\)
0.471418 0.881910i \(-0.343742\pi\)
\(54\) −96.2512 28.6815i −1.78243 0.531139i
\(55\) −29.8370 + 49.9760i −0.542492 + 0.908654i
\(56\) −105.880 109.025i −1.89071 1.94688i
\(57\) 2.52173 + 32.2655i 0.0442408 + 0.566061i
\(58\) 123.554 + 71.3342i 2.13025 + 1.22990i
\(59\) −23.2367 + 13.4157i −0.393843 + 0.227385i −0.683824 0.729647i \(-0.739684\pi\)
0.289981 + 0.957032i \(0.406351\pi\)
\(60\) 147.254 9.34313i 2.45423 0.155719i
\(61\) −19.8501 + 34.3814i −0.325412 + 0.563630i −0.981596 0.190971i \(-0.938836\pi\)
0.656184 + 0.754601i \(0.272170\pi\)
\(62\) 117.117 1.88899
\(63\) −57.9491 + 24.7165i −0.919827 + 0.392325i
\(64\) 84.3274 1.31762
\(65\) −22.4807 40.2878i −0.345856 0.619812i
\(66\) 73.5213 + 107.099i 1.11396 + 1.62271i
\(67\) 86.4356 49.9036i 1.29008 0.744830i 0.311414 0.950274i \(-0.399197\pi\)
0.978669 + 0.205444i \(0.0658639\pi\)
\(68\) −15.3792 + 26.6376i −0.226165 + 0.391729i
\(69\) 1.37136 + 17.5466i 0.0198748 + 0.254298i
\(70\) 94.7141 89.3260i 1.35306 1.27609i
\(71\) 62.5979i 0.881661i −0.897590 0.440830i \(-0.854684\pi\)
0.897590 0.440830i \(-0.145316\pi\)
\(72\) 70.2227 182.344i 0.975315 2.53256i
\(73\) 37.5802 21.6970i 0.514798 0.297219i −0.220006 0.975499i \(-0.570608\pi\)
0.734804 + 0.678280i \(0.237274\pi\)
\(74\) 74.6895 43.1220i 1.00932 0.582730i
\(75\) 3.65342 + 74.9110i 0.0487123 + 0.998813i
\(76\) −106.117 −1.39628
\(77\) 78.3936 + 22.2401i 1.01810 + 0.288833i
\(78\) −102.655 + 8.02304i −1.31609 + 0.102859i
\(79\) 15.5064 26.8579i 0.196284 0.339974i −0.751037 0.660260i \(-0.770446\pi\)
0.947321 + 0.320287i \(0.103779\pi\)
\(80\) −3.02981 + 207.043i −0.0378726 + 2.58804i
\(81\) −60.0769 54.3302i −0.741690 0.670743i
\(82\) −73.1373 42.2259i −0.891919 0.514949i
\(83\) −93.5855 −1.12754 −0.563768 0.825933i \(-0.690649\pi\)
−0.563768 + 0.825933i \(0.690649\pi\)
\(84\) −65.9910 195.745i −0.785607 2.33030i
\(85\) −13.4241 8.01458i −0.157931 0.0942891i
\(86\) 93.8870 + 54.2057i 1.09171 + 0.630299i
\(87\) 65.1206 + 94.8613i 0.748512 + 1.09036i
\(88\) −218.878 + 126.369i −2.48725 + 1.43601i
\(89\) 34.2984 + 19.8022i 0.385375 + 0.222496i 0.680154 0.733069i \(-0.261913\pi\)
−0.294779 + 0.955565i \(0.595246\pi\)
\(90\) 155.309 + 62.4358i 1.72566 + 0.693731i
\(91\) −46.3353 + 44.9985i −0.509179 + 0.494489i
\(92\) −57.7086 −0.627267
\(93\) 85.2318 + 40.7103i 0.916471 + 0.437745i
\(94\) −111.890 193.800i −1.19032 2.06170i
\(95\) 0.789255 53.9341i 0.00830795 0.567727i
\(96\) 181.922 + 86.8938i 1.89503 + 0.905144i
\(97\) 119.768i 1.23472i 0.786679 + 0.617362i \(0.211799\pi\)
−0.786679 + 0.617362i \(0.788201\pi\)
\(98\) −155.114 95.7150i −1.58280 0.976683i
\(99\) 16.2772 + 103.497i 0.164416 + 1.04543i
\(100\) −245.811 7.19579i −2.45811 0.0719579i
\(101\) −13.8956 + 8.02263i −0.137580 + 0.0794320i −0.567210 0.823573i \(-0.691977\pi\)
0.429630 + 0.903005i \(0.358644\pi\)
\(102\) −28.7680 + 19.7487i −0.282039 + 0.193615i
\(103\) −111.510 64.3802i −1.08262 0.625051i −0.151018 0.988531i \(-0.548255\pi\)
−0.931602 + 0.363480i \(0.881588\pi\)
\(104\) 200.329i 1.92624i
\(105\) 99.9781 32.0840i 0.952172 0.305561i
\(106\) 208.206 1.96421
\(107\) −79.6491 + 137.956i −0.744384 + 1.28931i 0.206099 + 0.978531i \(0.433923\pi\)
−0.950482 + 0.310779i \(0.899410\pi\)
\(108\) 192.949 182.506i 1.78657 1.68987i
\(109\) −12.9451 22.4216i −0.118762 0.205702i 0.800515 0.599313i \(-0.204559\pi\)
−0.919277 + 0.393610i \(0.871226\pi\)
\(110\) −105.500 189.067i −0.959088 1.71879i
\(111\) 69.3445 5.41965i 0.624725 0.0488257i
\(112\) 281.082 70.9234i 2.50966 0.633245i
\(113\) 127.653 1.12967 0.564836 0.825203i \(-0.308940\pi\)
0.564836 + 0.825203i \(0.308940\pi\)
\(114\) −108.631 51.8865i −0.952900 0.455145i
\(115\) 0.429211 29.3303i 0.00373227 0.255046i
\(116\) −326.731 + 188.638i −2.81664 + 1.62619i
\(117\) −77.4958 29.8444i −0.662357 0.255081i
\(118\) 99.8067i 0.845819i
\(119\) −5.97396 + 21.0574i −0.0502013 + 0.176953i
\(120\) −144.647 + 291.779i −1.20539 + 2.43149i
\(121\) 7.25691 12.5693i 0.0599744 0.103879i
\(122\) −73.8378 127.891i −0.605228 1.04829i
\(123\) −38.5477 56.1526i −0.313396 0.456525i
\(124\) −154.854 + 268.215i −1.24882 + 2.16302i
\(125\) 5.48548 124.880i 0.0438839 0.999037i
\(126\) 28.1566 232.648i 0.223465 1.84641i
\(127\) 47.1857i 0.371541i −0.982593 0.185770i \(-0.940522\pi\)
0.982593 0.185770i \(-0.0594781\pi\)
\(128\) −22.4328 + 38.8548i −0.175256 + 0.303553i
\(129\) 49.4841 + 72.0836i 0.383598 + 0.558788i
\(130\) 171.595 + 2.51107i 1.31996 + 0.0193159i
\(131\) 126.778 + 73.1955i 0.967773 + 0.558744i 0.898557 0.438857i \(-0.144617\pi\)
0.0692166 + 0.997602i \(0.477950\pi\)
\(132\) −342.482 + 26.7669i −2.59456 + 0.202779i
\(133\) −73.2208 + 18.4753i −0.550533 + 0.138912i
\(134\) 371.259i 2.77059i
\(135\) 91.3233 + 99.4237i 0.676469 + 0.736472i
\(136\) −33.9442 58.7931i −0.249590 0.432302i
\(137\) 82.4265 + 142.767i 0.601653 + 1.04209i 0.992571 + 0.121668i \(0.0388245\pi\)
−0.390917 + 0.920426i \(0.627842\pi\)
\(138\) −59.0752 28.2168i −0.428081 0.204470i
\(139\) 251.524 1.80953 0.904763 0.425915i \(-0.140048\pi\)
0.904763 + 0.425915i \(0.140048\pi\)
\(140\) 79.3370 + 335.017i 0.566693 + 2.39298i
\(141\) −14.0626 179.931i −0.0997348 1.27611i
\(142\) 201.654 + 116.425i 1.42010 + 0.819893i
\(143\) 53.7065 + 93.0224i 0.375570 + 0.650506i
\(144\) 234.244 + 289.911i 1.62670 + 2.01327i
\(145\) −93.4450 167.463i −0.644448 1.15492i
\(146\) 161.415i 1.10558i
\(147\) −79.6134 123.575i −0.541588 0.840644i
\(148\) 228.066i 1.54099i
\(149\) −208.574 120.420i −1.39983 0.808189i −0.405451 0.914117i \(-0.632886\pi\)
−0.994374 + 0.105927i \(0.966219\pi\)
\(150\) −248.114 127.556i −1.65409 0.850376i
\(151\) −22.6110 39.1633i −0.149741 0.259360i 0.781390 0.624042i \(-0.214511\pi\)
−0.931132 + 0.364683i \(0.881177\pi\)
\(152\) 117.109 202.838i 0.770451 1.33446i
\(153\) −27.8006 + 4.37224i −0.181703 + 0.0285767i
\(154\) −217.447 + 211.174i −1.41200 + 1.37126i
\(155\) −135.168 80.6991i −0.872052 0.520640i
\(156\) 117.358 245.702i 0.752294 1.57502i
\(157\) −1.63878 + 0.946152i −0.0104381 + 0.00602645i −0.505210 0.862996i \(-0.668585\pi\)
0.494772 + 0.869023i \(0.335252\pi\)
\(158\) 57.6803 + 99.9052i 0.365065 + 0.632311i
\(159\) 151.522 + 72.3732i 0.952968 + 0.455178i
\(160\) −288.509 172.248i −1.80318 1.07655i
\(161\) −39.8188 + 10.0472i −0.247322 + 0.0624050i
\(162\) 286.756 92.4846i 1.77010 0.570893i
\(163\) 115.997 + 66.9711i 0.711640 + 0.410865i 0.811668 0.584119i \(-0.198560\pi\)
−0.100028 + 0.994985i \(0.531893\pi\)
\(164\) 193.406 111.663i 1.17931 0.680873i
\(165\) −11.0570 174.265i −0.0670120 1.05615i
\(166\) 174.058 301.477i 1.04854 1.81613i
\(167\) 23.6454 0.141589 0.0707945 0.997491i \(-0.477447\pi\)
0.0707945 + 0.997491i \(0.477447\pi\)
\(168\) 446.983 + 89.8813i 2.66061 + 0.535008i
\(169\) 83.8607 0.496217
\(170\) 50.7855 28.3384i 0.298738 0.166697i
\(171\) −61.0198 75.5207i −0.356841 0.441642i
\(172\) −248.278 + 143.343i −1.44347 + 0.833390i
\(173\) 32.5846 56.4382i 0.188350 0.326232i −0.756350 0.654167i \(-0.773019\pi\)
0.944700 + 0.327935i \(0.106353\pi\)
\(174\) −426.704 + 33.3492i −2.45232 + 0.191662i
\(175\) −170.862 + 37.8312i −0.976354 + 0.216178i
\(176\) 482.092i 2.73916i
\(177\) 34.6931 72.6342i 0.196006 0.410363i
\(178\) −127.582 + 73.6595i −0.716752 + 0.413817i
\(179\) 140.927 81.3643i 0.787302 0.454549i −0.0517096 0.998662i \(-0.516467\pi\)
0.839012 + 0.544113i \(0.183134\pi\)
\(180\) −348.339 + 273.127i −1.93522 + 1.51737i
\(181\) 152.677 0.843519 0.421759 0.906708i \(-0.361413\pi\)
0.421759 + 0.906708i \(0.361413\pi\)
\(182\) −58.7804 232.957i −0.322969 1.27998i
\(183\) −9.28008 118.739i −0.0507108 0.648845i
\(184\) 63.6857 110.307i 0.346118 0.599494i
\(185\) −115.914 1.69625i −0.626563 0.00916894i
\(186\) −289.666 + 198.850i −1.55734 + 1.06909i
\(187\) 31.5238 + 18.2003i 0.168577 + 0.0973278i
\(188\) 591.772 3.14773
\(189\) 101.360 159.522i 0.536296 0.844030i
\(190\) 172.276 + 102.854i 0.906715 + 0.541334i
\(191\) 181.527 + 104.805i 0.950403 + 0.548716i 0.893206 0.449647i \(-0.148450\pi\)
0.0571970 + 0.998363i \(0.481784\pi\)
\(192\) −208.567 + 143.177i −1.08629 + 0.745716i
\(193\) 102.657 59.2693i 0.531904 0.307095i −0.209888 0.977725i \(-0.567310\pi\)
0.741791 + 0.670631i \(0.233977\pi\)
\(194\) −385.823 222.755i −1.98878 1.14822i
\(195\) 124.005 + 61.4744i 0.635923 + 0.315253i
\(196\) 424.295 228.678i 2.16477 1.16672i
\(197\) −159.912 −0.811735 −0.405868 0.913932i \(-0.633031\pi\)
−0.405868 + 0.913932i \(0.633031\pi\)
\(198\) −363.681 140.057i −1.83677 0.707359i
\(199\) 43.3843 + 75.1437i 0.218011 + 0.377607i 0.954200 0.299170i \(-0.0967097\pi\)
−0.736189 + 0.676776i \(0.763376\pi\)
\(200\) 285.025 461.914i 1.42513 2.30957i
\(201\) −129.051 + 270.184i −0.642045 + 1.34420i
\(202\) 59.6846i 0.295468i
\(203\) −192.601 + 187.045i −0.948775 + 0.921402i
\(204\) −7.18989 91.9947i −0.0352446 0.450954i
\(205\) 55.3142 + 99.1290i 0.269825 + 0.483556i
\(206\) 414.790 239.479i 2.01355 1.16252i
\(207\) −33.1837 41.0695i −0.160308 0.198403i
\(208\) 330.928 + 191.061i 1.59100 + 0.918564i
\(209\) 125.583i 0.600876i
\(210\) −82.5919 + 381.743i −0.393295 + 1.81782i
\(211\) −291.368 −1.38089 −0.690445 0.723385i \(-0.742585\pi\)
−0.690445 + 0.723385i \(0.742585\pi\)
\(212\) −275.293 + 476.822i −1.29855 + 2.24916i
\(213\) 106.284 + 154.823i 0.498984 + 0.726871i
\(214\) −296.276 513.165i −1.38447 2.39797i
\(215\) −71.0074 127.253i −0.330267 0.591874i
\(216\) 135.916 + 570.222i 0.629242 + 2.63992i
\(217\) −60.1521 + 212.028i −0.277198 + 0.977088i
\(218\) 96.3055 0.441768
\(219\) −56.1085 + 117.470i −0.256203 + 0.536391i
\(220\) 572.483 + 8.37755i 2.60220 + 0.0380798i
\(221\) −24.9869 + 14.4262i −0.113063 + 0.0652769i
\(222\) −111.514 + 233.467i −0.502314 + 1.05165i
\(223\) 317.534i 1.42392i 0.702220 + 0.711960i \(0.252192\pi\)
−0.702220 + 0.711960i \(0.747808\pi\)
\(224\) −128.391 + 452.562i −0.573175 + 2.02037i
\(225\) −136.226 179.074i −0.605447 0.795886i
\(226\) −237.419 + 411.222i −1.05053 + 1.81957i
\(227\) −55.2662 95.7238i −0.243463 0.421691i 0.718235 0.695800i \(-0.244950\pi\)
−0.961698 + 0.274110i \(0.911617\pi\)
\(228\) 262.460 180.174i 1.15114 0.790238i
\(229\) −47.1716 + 81.7037i −0.205990 + 0.356785i −0.950448 0.310885i \(-0.899375\pi\)
0.744458 + 0.667669i \(0.232708\pi\)
\(230\) 93.6867 + 55.9336i 0.407333 + 0.243189i
\(231\) −231.652 + 78.0960i −1.00282 + 0.338078i
\(232\) 832.705i 3.58925i
\(233\) 112.336 194.572i 0.482131 0.835075i −0.517659 0.855587i \(-0.673196\pi\)
0.999790 + 0.0205124i \(0.00652977\pi\)
\(234\) 240.274 194.139i 1.02681 0.829652i
\(235\) −4.40134 + 300.767i −0.0187291 + 1.27986i
\(236\) 228.571 + 131.966i 0.968523 + 0.559177i
\(237\) 7.24937 + 92.7557i 0.0305881 + 0.391374i
\(238\) −56.7238 58.4089i −0.238335 0.245416i
\(239\) 270.509i 1.13184i −0.824462 0.565918i \(-0.808522\pi\)
0.824462 0.565918i \(-0.191478\pi\)
\(240\) −344.040 517.225i −1.43350 2.15510i
\(241\) 29.4855 + 51.0703i 0.122346 + 0.211910i 0.920693 0.390289i \(-0.127625\pi\)
−0.798346 + 0.602199i \(0.794291\pi\)
\(242\) 26.9940 + 46.7549i 0.111545 + 0.193202i
\(243\) 240.834 + 32.3717i 0.991087 + 0.133217i
\(244\) 390.517 1.60048
\(245\) 113.070 + 217.348i 0.461509 + 0.887136i
\(246\) 252.585 19.7409i 1.02677 0.0802475i
\(247\) −86.2056 49.7708i −0.349010 0.201501i
\(248\) −341.786 591.990i −1.37817 2.38706i
\(249\) 231.465 158.897i 0.929579 0.638139i
\(250\) 392.086 + 249.932i 1.56834 + 0.999729i
\(251\) 38.0046i 0.151413i 0.997130 + 0.0757064i \(0.0241212\pi\)
−0.997130 + 0.0757064i \(0.975879\pi\)
\(252\) 495.567 + 372.092i 1.96653 + 1.47656i
\(253\) 68.2943i 0.269938i
\(254\) 152.004 + 87.7598i 0.598443 + 0.345511i
\(255\) 46.8096 2.97004i 0.183567 0.0116472i
\(256\) 85.2100 + 147.588i 0.332852 + 0.576516i
\(257\) 213.944 370.562i 0.832467 1.44188i −0.0636088 0.997975i \(-0.520261\pi\)
0.896076 0.443901i \(-0.146406\pi\)
\(258\) −324.245 + 25.3416i −1.25677 + 0.0982231i
\(259\) 39.7068 + 157.365i 0.153308 + 0.607587i
\(260\) −232.636 + 389.656i −0.894753 + 1.49868i
\(261\) −322.125 124.054i −1.23420 0.475302i
\(262\) −471.585 + 272.270i −1.79994 + 1.03920i
\(263\) −17.1949 29.7824i −0.0653797 0.113241i 0.831483 0.555551i \(-0.187493\pi\)
−0.896862 + 0.442310i \(0.854159\pi\)
\(264\) 326.791 684.176i 1.23785 2.59158i
\(265\) −240.297 143.464i −0.906780 0.541373i
\(266\) 76.6656 270.236i 0.288217 1.01593i
\(267\) −118.452 + 9.25766i −0.443640 + 0.0346729i
\(268\) −850.237 490.884i −3.17252 1.83166i
\(269\) −390.528 + 225.472i −1.45178 + 0.838185i −0.998582 0.0532259i \(-0.983050\pi\)
−0.453196 + 0.891411i \(0.649716\pi\)
\(270\) −490.135 + 109.273i −1.81531 + 0.404716i
\(271\) 112.662 195.136i 0.415727 0.720060i −0.579778 0.814775i \(-0.696861\pi\)
0.995504 + 0.0947148i \(0.0301939\pi\)
\(272\) 129.495 0.476086
\(273\) 38.1993 189.966i 0.139924 0.695848i
\(274\) −613.214 −2.23801
\(275\) −8.51575 + 290.901i −0.0309664 + 1.05782i
\(276\) 142.731 97.9820i 0.517140 0.355007i
\(277\) 227.641 131.429i 0.821810 0.474472i −0.0292305 0.999573i \(-0.509306\pi\)
0.851040 + 0.525101i \(0.175972\pi\)
\(278\) −467.805 + 810.263i −1.68275 + 2.91461i
\(279\) −279.925 + 44.0243i −1.00332 + 0.157793i
\(280\) −727.922 218.068i −2.59972 0.778814i
\(281\) 265.040i 0.943204i 0.881812 + 0.471602i \(0.156324\pi\)
−0.881812 + 0.471602i \(0.843676\pi\)
\(282\) 605.787 + 289.349i 2.14818 + 1.02606i
\(283\) −182.790 + 105.534i −0.645901 + 0.372911i −0.786884 0.617101i \(-0.788307\pi\)
0.140983 + 0.990012i \(0.454974\pi\)
\(284\) −533.258 + 307.877i −1.87767 + 1.08407i
\(285\) 89.6213 + 134.735i 0.314461 + 0.472755i
\(286\) −399.551 −1.39703
\(287\) 114.009 110.720i 0.397245 0.385784i
\(288\) −597.484 + 93.9673i −2.07460 + 0.326275i
\(289\) 139.611 241.814i 0.483084 0.836726i
\(290\) 713.265 + 10.4377i 2.45954 + 0.0359921i
\(291\) −203.352 296.223i −0.698803 1.01795i
\(292\) −369.664 213.425i −1.26597 0.730909i
\(293\) −241.372 −0.823795 −0.411898 0.911230i \(-0.635134\pi\)
−0.411898 + 0.911230i \(0.635134\pi\)
\(294\) 546.156 26.6330i 1.85768 0.0905883i
\(295\) −68.7715 + 115.190i −0.233124 + 0.390473i
\(296\) −435.936 251.688i −1.47276 0.850297i
\(297\) −215.984 228.343i −0.727218 0.768832i
\(298\) 775.846 447.935i 2.60351 1.50314i
\(299\) −46.8801 27.0662i −0.156790 0.0905226i
\(300\) 620.182 399.559i 2.06727 1.33186i
\(301\) −146.355 + 142.132i −0.486228 + 0.472200i
\(302\) 168.215 0.557003
\(303\) 20.7466 43.4354i 0.0684706 0.143351i
\(304\) 223.382 + 386.908i 0.734808 + 1.27272i
\(305\) −2.90450 + 198.480i −0.00952294 + 0.650754i
\(306\) 37.6210 97.6888i 0.122944 0.319245i
\(307\) 378.511i 1.23293i −0.787381 0.616467i \(-0.788563\pi\)
0.787381 0.616467i \(-0.211437\pi\)
\(308\) −196.106 777.203i −0.636708 2.52339i
\(309\) 385.107 30.0982i 1.24630 0.0974053i
\(310\) 511.362 285.341i 1.64955 0.920455i
\(311\) 108.150 62.4406i 0.347750 0.200774i −0.315944 0.948778i \(-0.602321\pi\)
0.663694 + 0.748004i \(0.268988\pi\)
\(312\) 340.134 + 495.474i 1.09017 + 1.58806i
\(313\) 200.253 + 115.616i 0.639786 + 0.369380i 0.784532 0.620088i \(-0.212903\pi\)
−0.144746 + 0.989469i \(0.546237\pi\)
\(314\) 7.03893i 0.0224170i
\(315\) −192.801 + 249.104i −0.612068 + 0.790805i
\(316\) −305.063 −0.965388
\(317\) 80.4184 139.289i 0.253686 0.439397i −0.710852 0.703342i \(-0.751690\pi\)
0.964538 + 0.263945i \(0.0850237\pi\)
\(318\) −514.957 + 353.509i −1.61936 + 1.11166i
\(319\) 223.241 + 386.665i 0.699815 + 1.21211i
\(320\) 368.194 205.453i 1.15061 0.642041i
\(321\) −37.2365 476.441i −0.116002 1.48424i
\(322\) 41.6921 146.959i 0.129479 0.456395i
\(323\) −33.7331 −0.104437
\(324\) −167.350 + 778.996i −0.516511 + 2.40431i
\(325\) −196.312 121.135i −0.604037 0.372723i
\(326\) −431.483 + 249.117i −1.32357 + 0.764161i
\(327\) 70.0862 + 33.4761i 0.214331 + 0.102373i
\(328\) 492.915i 1.50279i
\(329\) 408.322 103.029i 1.24110 0.313158i
\(330\) 581.944 + 288.494i 1.76347 + 0.874223i
\(331\) 229.247 397.068i 0.692590 1.19960i −0.278396 0.960466i \(-0.589803\pi\)
0.970986 0.239135i \(-0.0768640\pi\)
\(332\) 460.284 + 797.235i 1.38640 + 2.40131i
\(333\) −162.308 + 131.143i −0.487411 + 0.393822i
\(334\) −43.9776 + 76.1714i −0.131669 + 0.228058i
\(335\) 255.815 428.481i 0.763627 1.27905i
\(336\) −574.781 + 652.657i −1.71066 + 1.94243i
\(337\) 170.410i 0.505667i 0.967510 + 0.252834i \(0.0813625\pi\)
−0.967510 + 0.252834i \(0.918637\pi\)
\(338\) −155.971 + 270.150i −0.461453 + 0.799259i
\(339\) −315.724 + 216.739i −0.931339 + 0.639347i
\(340\) −2.25031 + 153.776i −0.00661855 + 0.452281i
\(341\) 317.415 + 183.260i 0.930835 + 0.537418i
\(342\) 356.773 56.1103i 1.04320 0.164065i
\(343\) 252.950 231.658i 0.737462 0.675388i
\(344\) 632.760i 1.83942i
\(345\) 48.7376 + 73.2714i 0.141269 + 0.212381i
\(346\) 121.207 + 209.937i 0.350310 + 0.606754i
\(347\) −311.981 540.367i −0.899080 1.55725i −0.828672 0.559735i \(-0.810903\pi\)
−0.0704086 0.997518i \(-0.522430\pi\)
\(348\) 487.819 1021.31i 1.40178 2.93479i
\(349\) −25.5776 −0.0732883 −0.0366442 0.999328i \(-0.511667\pi\)
−0.0366442 + 0.999328i \(0.511667\pi\)
\(350\) 195.913 620.778i 0.559752 1.77365i
\(351\) 242.343 57.7640i 0.690435 0.164570i
\(352\) 677.504 + 391.157i 1.92473 + 1.11124i
\(353\) 98.5420 + 170.680i 0.279156 + 0.483512i 0.971175 0.238367i \(-0.0766121\pi\)
−0.692019 + 0.721879i \(0.743279\pi\)
\(354\) 169.459 + 246.852i 0.478699 + 0.697322i
\(355\) −152.512 273.318i −0.429611 0.769909i
\(356\) 389.574i 1.09431i
\(357\) −20.9775 62.2244i −0.0587605 0.174298i
\(358\) 605.312i 1.69082i
\(359\) −402.581 232.430i −1.12140 0.647438i −0.179639 0.983733i \(-0.557493\pi\)
−0.941757 + 0.336294i \(0.890826\pi\)
\(360\) −137.649 967.248i −0.382360 2.68680i
\(361\) 122.310 + 211.847i 0.338809 + 0.586834i
\(362\) −283.961 + 491.835i −0.784423 + 1.35866i
\(363\) 3.39266 + 43.4091i 0.00934616 + 0.119584i
\(364\) 611.225 + 173.404i 1.67919 + 0.476384i
\(365\) 111.223 186.294i 0.304719 0.510394i
\(366\) 399.766 + 190.945i 1.09226 + 0.521708i
\(367\) 353.989 204.375i 0.964547 0.556881i 0.0669775 0.997754i \(-0.478664\pi\)
0.897569 + 0.440873i \(0.145331\pi\)
\(368\) 121.479 + 210.408i 0.330106 + 0.571760i
\(369\) 190.680 + 73.4330i 0.516749 + 0.199005i
\(370\) 221.051 370.253i 0.597436 1.00068i
\(371\) −106.936 + 376.936i −0.288237 + 1.01600i
\(372\) −72.3953 926.299i −0.194611 2.49005i
\(373\) −629.997 363.729i −1.68900 0.975144i −0.955286 0.295685i \(-0.904452\pi\)
−0.733713 0.679459i \(-0.762214\pi\)
\(374\) −117.261 + 67.7008i −0.313533 + 0.181018i
\(375\) 198.463 + 318.178i 0.529234 + 0.848476i
\(376\) −653.065 + 1131.14i −1.73688 + 3.00836i
\(377\) −353.897 −0.938720
\(378\) 325.367 + 623.214i 0.860759 + 1.64871i
\(379\) −257.337 −0.678989 −0.339494 0.940608i \(-0.610256\pi\)
−0.339494 + 0.940608i \(0.610256\pi\)
\(380\) −463.335 + 258.542i −1.21930 + 0.680373i
\(381\) 80.1154 + 116.704i 0.210277 + 0.306311i
\(382\) −675.238 + 389.849i −1.76764 + 1.02055i
\(383\) 63.6145 110.184i 0.166095 0.287685i −0.770948 0.636898i \(-0.780217\pi\)
0.937044 + 0.349212i \(0.113551\pi\)
\(384\) −10.4875 134.188i −0.0273112 0.349447i
\(385\) 396.471 93.8902i 1.02979 0.243871i
\(386\) 440.935i 1.14232i
\(387\) −244.778 94.2666i −0.632501 0.243583i
\(388\) 1020.28 589.059i 2.62959 1.51819i
\(389\) 92.0153 53.1250i 0.236543 0.136568i −0.377044 0.926195i \(-0.623059\pi\)
0.613587 + 0.789627i \(0.289726\pi\)
\(390\) −428.669 + 285.136i −1.09915 + 0.731118i
\(391\) −18.3447 −0.0469173
\(392\) −31.1353 + 1063.38i −0.0794269 + 2.71271i
\(393\) −437.838 + 34.2194i −1.11409 + 0.0870723i
\(394\) 297.417 515.142i 0.754866 1.30747i
\(395\) 2.26892 155.048i 0.00574411 0.392526i
\(396\) 801.615 647.695i 2.02428 1.63559i
\(397\) 116.882 + 67.4818i 0.294413 + 0.169979i 0.639930 0.768433i \(-0.278963\pi\)
−0.345517 + 0.938412i \(0.612297\pi\)
\(398\) −322.758 −0.810951
\(399\) 149.728 170.015i 0.375259 0.426103i
\(400\) 491.206 + 911.383i 1.22801 + 2.27846i
\(401\) 378.110 + 218.302i 0.942918 + 0.544394i 0.890874 0.454251i \(-0.150093\pi\)
0.0520445 + 0.998645i \(0.483426\pi\)
\(402\) −630.352 918.236i −1.56804 2.28417i
\(403\) −251.594 + 145.258i −0.624303 + 0.360442i
\(404\) 136.686 + 78.9158i 0.338332 + 0.195336i
\(405\) −394.679 90.8490i −0.974516 0.224319i
\(406\) −244.332 968.329i −0.601802 2.38505i
\(407\) 269.901 0.663148
\(408\) 183.778 + 87.7800i 0.450435 + 0.215147i
\(409\) −225.188 390.037i −0.550581 0.953635i −0.998233 0.0594267i \(-0.981073\pi\)
0.447651 0.894208i \(-0.352261\pi\)
\(410\) −422.213 6.17854i −1.02979 0.0150696i
\(411\) −446.266 213.155i −1.08581 0.518626i
\(412\) 1266.57i 3.07420i
\(413\) 180.689 + 51.2613i 0.437505 + 0.124119i
\(414\) 194.019 30.5138i 0.468646 0.0737047i
\(415\) −408.617 + 228.009i −0.984620 + 0.549420i
\(416\) −537.014 + 310.045i −1.29090 + 0.745300i
\(417\) −622.095 + 427.057i −1.49183 + 1.02412i
\(418\) −404.555 233.570i −0.967835 0.558780i
\(419\) 694.997i 1.65870i 0.558727 + 0.829352i \(0.311290\pi\)
−0.558727 + 0.829352i \(0.688710\pi\)
\(420\) −765.041 693.893i −1.82153 1.65213i
\(421\) 114.851 0.272805 0.136403 0.990653i \(-0.456446\pi\)
0.136403 + 0.990653i \(0.456446\pi\)
\(422\) 541.910 938.615i 1.28415 2.22421i
\(423\) 340.282 + 421.147i 0.804449 + 0.995620i
\(424\) −607.614 1052.42i −1.43305 2.48212i
\(425\) −78.1395 2.28743i −0.183858 0.00538219i
\(426\) −696.425 + 54.4294i −1.63480 + 0.127769i
\(427\) 269.456 67.9900i 0.631045 0.159227i
\(428\) 1566.96 3.66112
\(429\) −290.773 138.885i −0.677792 0.323742i
\(430\) 541.999 + 7.93145i 1.26046 + 0.0184452i
\(431\) 312.237 180.270i 0.724448 0.418260i −0.0919394 0.995765i \(-0.529307\pi\)
0.816388 + 0.577504i \(0.195973\pi\)
\(432\) −1071.59 319.318i −2.48053 0.739163i
\(433\) 590.764i 1.36435i −0.731188 0.682176i \(-0.761034\pi\)
0.731188 0.682176i \(-0.238966\pi\)
\(434\) −571.154 588.122i −1.31602 1.35512i
\(435\) 515.450 + 255.530i 1.18494 + 0.587424i
\(436\) −127.336 + 220.553i −0.292056 + 0.505856i
\(437\) −31.6448 54.8104i −0.0724138 0.125424i
\(438\) −274.063 399.228i −0.625715 0.911480i
\(439\) 235.149 407.290i 0.535647 0.927769i −0.463484 0.886105i \(-0.653401\pi\)
0.999132 0.0416635i \(-0.0132657\pi\)
\(440\) −647.791 + 1085.03i −1.47225 + 2.46597i
\(441\) 406.722 + 170.464i 0.922273 + 0.386539i
\(442\) 107.324i 0.242815i
\(443\) −99.6641 + 172.623i −0.224975 + 0.389669i −0.956312 0.292348i \(-0.905564\pi\)
0.731337 + 0.682017i \(0.238897\pi\)
\(444\) −387.228 564.076i −0.872135 1.27044i
\(445\) 198.001 + 2.89748i 0.444945 + 0.00651120i
\(446\) −1022.91 590.576i −2.29352 1.32416i
\(447\) 720.325 56.2973i 1.61146 0.125945i
\(448\) −411.246 423.463i −0.917960 0.945231i
\(449\) 420.588i 0.936722i 0.883537 + 0.468361i \(0.155155\pi\)
−0.883537 + 0.468361i \(0.844845\pi\)
\(450\) 830.235 105.781i 1.84497 0.235070i
\(451\) −132.146 228.884i −0.293007 0.507503i
\(452\) −627.838 1087.45i −1.38902 2.40586i
\(453\) 122.418 + 58.4721i 0.270239 + 0.129077i
\(454\) 411.154 0.905626
\(455\) −92.6782 + 309.365i −0.203688 + 0.679922i
\(456\) 54.7491 + 700.515i 0.120064 + 1.53622i
\(457\) 433.751 + 250.426i 0.949127 + 0.547979i 0.892810 0.450434i \(-0.148731\pi\)
0.0563173 + 0.998413i \(0.482064\pi\)
\(458\) −175.467 303.918i −0.383117 0.663577i
\(459\) 61.3356 58.0158i 0.133629 0.126396i
\(460\) −251.970 + 140.600i −0.547760 + 0.305651i
\(461\) 68.9132i 0.149486i 0.997203 + 0.0747432i \(0.0238137\pi\)
−0.997203 + 0.0747432i \(0.976186\pi\)
\(462\) 179.266 891.495i 0.388021 1.92964i
\(463\) 72.6957i 0.157010i −0.996914 0.0785051i \(-0.974985\pi\)
0.996914 0.0785051i \(-0.0250147\pi\)
\(464\) 1375.56 + 794.182i 2.96458 + 1.71160i
\(465\) 471.328 29.9054i 1.01361 0.0643127i
\(466\) 417.865 + 723.763i 0.896706 + 1.55314i
\(467\) 67.4292 116.791i 0.144388 0.250087i −0.784756 0.619804i \(-0.787212\pi\)
0.929144 + 0.369717i \(0.120545\pi\)
\(468\) 126.911 + 806.955i 0.271178 + 1.72426i
\(469\) −672.126 190.681i −1.43310 0.406569i
\(470\) −960.710 573.571i −2.04406 1.22036i
\(471\) 2.44675 5.12257i 0.00519481 0.0108759i
\(472\) −504.492 + 291.268i −1.06884 + 0.617094i
\(473\) 169.637 + 293.820i 0.358641 + 0.621185i
\(474\) −312.287 149.162i −0.658834 0.314687i
\(475\) −127.957 237.412i −0.269384 0.499815i
\(476\) 208.766 52.6764i 0.438583 0.110665i
\(477\) −497.640 + 78.2646i −1.04327 + 0.164077i
\(478\) 871.419 + 503.114i 1.82305 + 1.05254i
\(479\) 407.459 235.247i 0.850645 0.491120i −0.0102233 0.999948i \(-0.503254\pi\)
0.860868 + 0.508828i \(0.169921\pi\)
\(480\) 1006.02 63.8314i 2.09588 0.132982i
\(481\) −106.967 + 185.272i −0.222384 + 0.385180i
\(482\) −219.358 −0.455100
\(483\) 81.4250 92.4571i 0.168582 0.191423i
\(484\) −142.767 −0.294974
\(485\) 291.800 + 522.937i 0.601650 + 1.07822i
\(486\) −552.206 + 715.618i −1.13623 + 1.47247i
\(487\) 173.689 100.280i 0.356651 0.205913i −0.310959 0.950423i \(-0.600650\pi\)
0.667611 + 0.744510i \(0.267317\pi\)
\(488\) −430.965 + 746.454i −0.883126 + 1.52962i
\(489\) −400.605 + 31.3095i −0.819232 + 0.0640275i
\(490\) −910.464 39.9986i −1.85809 0.0816298i
\(491\) 744.767i 1.51684i −0.651768 0.758418i \(-0.725973\pi\)
0.651768 0.758418i \(-0.274027\pi\)
\(492\) −288.762 + 604.557i −0.586914 + 1.22877i
\(493\) −103.863 + 59.9651i −0.210675 + 0.121633i
\(494\) 320.664 185.136i 0.649118 0.374769i
\(495\) 323.228 + 412.237i 0.652986 + 0.832802i
\(496\) 1303.89 2.62882
\(497\) −314.345 + 305.276i −0.632485 + 0.614238i
\(498\) 81.3734 + 1041.17i 0.163400 + 2.09071i
\(499\) −268.252 + 464.626i −0.537579 + 0.931114i 0.461455 + 0.887164i \(0.347328\pi\)
−0.999034 + 0.0439501i \(0.986006\pi\)
\(500\) −1090.80 + 567.469i −2.18160 + 1.13494i
\(501\) −58.4821 + 40.1469i −0.116731 + 0.0801335i
\(502\) −122.428 70.6841i −0.243881 0.140805i
\(503\) 924.410 1.83779 0.918897 0.394499i \(-0.129082\pi\)
0.918897 + 0.394499i \(0.129082\pi\)
\(504\) −1258.13 + 536.618i −2.49629 + 1.06472i
\(505\) −41.1255 + 68.8837i −0.0814366 + 0.136403i
\(506\) −220.004 127.019i −0.434791 0.251027i
\(507\) −207.413 + 142.385i −0.409098 + 0.280838i
\(508\) −401.965 + 232.075i −0.791269 + 0.456840i
\(509\) 821.002 + 474.006i 1.61297 + 0.931249i 0.988677 + 0.150059i \(0.0479463\pi\)
0.624293 + 0.781190i \(0.285387\pi\)
\(510\) −77.4927 + 156.317i −0.151947 + 0.306504i
\(511\) −292.225 82.9038i −0.571869 0.162238i
\(512\) −813.385 −1.58864
\(513\) 279.145 + 83.1813i 0.544143 + 0.162147i
\(514\) 795.822 + 1378.40i 1.54829 + 2.68172i
\(515\) −643.734 9.42020i −1.24997 0.0182917i
\(516\) 370.686 776.075i 0.718384 1.50402i
\(517\) 700.324i 1.35459i
\(518\) −580.788 164.769i −1.12121 0.318086i
\(519\) 15.2335 + 194.913i 0.0293517 + 0.375556i
\(520\) −488.077 874.686i −0.938609 1.68209i
\(521\) −511.768 + 295.469i −0.982280 + 0.567120i −0.902958 0.429729i \(-0.858609\pi\)
−0.0793222 + 0.996849i \(0.525276\pi\)
\(522\) 998.744 806.973i 1.91330 1.54593i
\(523\) 152.158 + 87.8483i 0.290933 + 0.167970i 0.638362 0.769736i \(-0.279612\pi\)
−0.347430 + 0.937706i \(0.612945\pi\)
\(524\) 1440.00i 2.74809i
\(525\) 358.360 383.670i 0.682591 0.730801i
\(526\) 127.922 0.243197
\(527\) −49.2256 + 85.2613i −0.0934073 + 0.161786i
\(528\) 818.532 + 1192.36i 1.55025 + 2.25825i
\(529\) 247.291 + 428.321i 0.467469 + 0.809680i
\(530\) 909.080 507.268i 1.71524 0.957110i
\(531\) 37.5173 + 238.551i 0.0706540 + 0.449248i
\(532\) 517.511 + 532.885i 0.972765 + 1.00166i
\(533\) 209.487 0.393035
\(534\) 190.484 398.800i 0.356711 0.746817i
\(535\) −11.6544 + 796.405i −0.0217838 + 1.48861i
\(536\) 1876.60 1083.46i 3.50112 2.02137i
\(537\) −210.409 + 440.515i −0.391822 + 0.820326i
\(538\) 1677.40i 3.11785i
\(539\) −270.626 502.126i −0.502088 0.931588i
\(540\) 397.812 1266.96i 0.736688 2.34623i
\(541\) −376.475 + 652.073i −0.695887 + 1.20531i 0.273994 + 0.961731i \(0.411655\pi\)
−0.969881 + 0.243580i \(0.921678\pi\)
\(542\) 419.076 + 725.861i 0.773203 + 1.33923i
\(543\) −377.616 + 259.227i −0.695425 + 0.477397i
\(544\) −105.069 + 181.985i −0.193142 + 0.334532i
\(545\) −111.149 66.3589i −0.203943 0.121760i
\(546\) 540.914 + 476.371i 0.990685 + 0.872474i
\(547\) 760.168i 1.38970i 0.719153 + 0.694852i \(0.244530\pi\)
−0.719153 + 0.694852i \(0.755470\pi\)
\(548\) 810.801 1404.35i 1.47956 2.56268i
\(549\) 224.556 + 277.920i 0.409027 + 0.506229i
\(550\) −921.275 568.475i −1.67504 1.03359i
\(551\) −358.329 206.881i −0.650325 0.375465i
\(552\) 29.7735 + 380.953i 0.0539376 + 0.690132i
\(553\) −210.493 + 53.1121i −0.380638 + 0.0960437i
\(554\) 977.768i 1.76492i
\(555\) 289.571 192.613i 0.521749 0.347050i
\(556\) −1237.08 2142.68i −2.22496 3.85374i
\(557\) 427.707 + 740.811i 0.767877 + 1.33000i 0.938712 + 0.344702i \(0.112020\pi\)
−0.170835 + 0.985300i \(0.554647\pi\)
\(558\) 378.807 983.633i 0.678866 1.76278i
\(559\) −268.921 −0.481075
\(560\) 1054.48 994.490i 1.88299 1.77587i
\(561\) −108.870 + 8.50877i −0.194064 + 0.0151671i
\(562\) −853.804 492.944i −1.51922 0.877124i
\(563\) −479.723 830.904i −0.852083 1.47585i −0.879325 0.476222i \(-0.842006\pi\)
0.0272426 0.999629i \(-0.491327\pi\)
\(564\) −1463.63 + 1004.76i −2.59509 + 1.78148i
\(565\) 557.363 311.010i 0.986484 0.550460i
\(566\) 785.123i 1.38714i
\(567\) 20.1542 + 566.642i 0.0355453 + 0.999368i
\(568\) 1359.06i 2.39271i
\(569\) −888.485 512.967i −1.56148 0.901523i −0.997107 0.0760060i \(-0.975783\pi\)
−0.564377 0.825517i \(-0.690883\pi\)
\(570\) −600.722 + 38.1154i −1.05390 + 0.0668691i
\(571\) −190.751 330.391i −0.334065 0.578617i 0.649240 0.760584i \(-0.275087\pi\)
−0.983305 + 0.181966i \(0.941754\pi\)
\(572\) 528.292 915.029i 0.923588 1.59970i
\(573\) −626.916 + 48.9969i −1.09409 + 0.0855095i
\(574\) 144.631 + 573.197i 0.251970 + 0.998600i
\(575\) −69.5855 129.109i −0.121018 0.224537i
\(576\) 272.751 708.242i 0.473527 1.22959i
\(577\) −119.310 + 68.8835i −0.206776 + 0.119382i −0.599812 0.800141i \(-0.704758\pi\)
0.393036 + 0.919523i \(0.371425\pi\)
\(578\) 519.321 + 899.490i 0.898479 + 1.55621i
\(579\) −153.271 + 320.890i −0.264716 + 0.554215i
\(580\) −966.993 + 1619.68i −1.66723 + 2.79255i
\(581\) 456.396 + 469.954i 0.785535 + 0.808872i
\(582\) 1332.47 104.139i 2.28946 0.178934i
\(583\) 564.288 + 325.792i 0.967904 + 0.558820i
\(584\) 815.903 471.062i 1.39709 0.806613i
\(585\) −411.078 + 58.5006i −0.702697 + 0.100001i
\(586\) 448.924 777.558i 0.766081 1.32689i
\(587\) −401.054 −0.683227 −0.341614 0.939840i \(-0.610973\pi\)
−0.341614 + 0.939840i \(0.610973\pi\)
\(588\) −661.143 + 1285.99i −1.12439 + 2.18706i
\(589\) −339.660 −0.576672
\(590\) −243.166 435.780i −0.412146 0.738611i
\(591\) 395.510 271.510i 0.669222 0.459409i
\(592\) 831.537 480.088i 1.40462 0.810960i
\(593\) −382.801 + 663.031i −0.645533 + 1.11810i 0.338645 + 0.940914i \(0.390031\pi\)
−0.984178 + 0.177182i \(0.943302\pi\)
\(594\) 1137.29 271.081i 1.91463 0.456366i
\(595\) 25.2200 + 106.497i 0.0423865 + 0.178986i
\(596\) 2369.06i 3.97494i
\(597\) −234.887 112.192i −0.393446 0.187926i
\(598\) 174.383 100.680i 0.291610 0.168361i
\(599\) 786.962 454.353i 1.31379 0.758519i 0.331071 0.943606i \(-0.392590\pi\)
0.982722 + 0.185087i \(0.0592566\pi\)
\(600\) 79.3194 + 1626.39i 0.132199 + 2.71065i
\(601\) 614.095 1.02179 0.510894 0.859644i \(-0.329314\pi\)
0.510894 + 0.859644i \(0.329314\pi\)
\(602\) −185.664 735.818i −0.308412 1.22229i
\(603\) −139.556 887.358i −0.231436 1.47157i
\(604\) −222.416 + 385.236i −0.368239 + 0.637808i
\(605\) 1.06184 72.5613i 0.00175511 0.119936i
\(606\) 101.337 + 147.618i 0.167223 + 0.243594i
\(607\) −253.578 146.403i −0.417756 0.241191i 0.276361 0.961054i \(-0.410872\pi\)
−0.694117 + 0.719862i \(0.744205\pi\)
\(608\) −724.985 −1.19241
\(609\) 158.782 789.630i 0.260726 1.29660i
\(610\) −633.983 378.506i −1.03932 0.620502i
\(611\) 480.732 + 277.551i 0.786796 + 0.454257i
\(612\) 173.978 + 215.323i 0.284278 + 0.351835i
\(613\) −733.123 + 423.269i −1.19596 + 0.690487i −0.959652 0.281191i \(-0.909270\pi\)
−0.236307 + 0.971678i \(0.575937\pi\)
\(614\) 1219.34 + 703.985i 1.98589 + 1.14656i
\(615\) −305.118 151.259i −0.496126 0.245950i
\(616\) 1702.00 + 482.855i 2.76299 + 0.783855i
\(617\) 689.661 1.11776 0.558882 0.829247i \(-0.311230\pi\)
0.558882 + 0.829247i \(0.311230\pi\)
\(618\) −619.295 + 1296.57i −1.00210 + 2.09801i
\(619\) −117.419 203.376i −0.189692 0.328556i 0.755456 0.655200i \(-0.227416\pi\)
−0.945147 + 0.326644i \(0.894082\pi\)
\(620\) −22.6584 + 1548.37i −0.0365459 + 2.49738i
\(621\) 151.804 + 45.2355i 0.244451 + 0.0728430i
\(622\) 464.529i 0.746831i
\(623\) −67.8258 268.806i −0.108870 0.431470i
\(624\) −1142.88 + 89.3226i −1.83154 + 0.143145i
\(625\) −280.302 558.619i −0.448484 0.893791i
\(626\) −744.894 + 430.065i −1.18993 + 0.687004i
\(627\) −213.225 310.605i −0.340071 0.495383i
\(628\) 16.1201 + 9.30697i 0.0256690 + 0.0148200i
\(629\) 72.4986i 0.115260i
\(630\) −443.878 1084.40i −0.704568 1.72126i
\(631\) 43.4343 0.0688340 0.0344170 0.999408i \(-0.489043\pi\)
0.0344170 + 0.999408i \(0.489043\pi\)
\(632\) 336.660 583.112i 0.532689 0.922645i
\(633\) 720.640 494.706i 1.13845 0.781527i
\(634\) 299.138 + 518.122i 0.471826 + 0.817226i
\(635\) −114.962 206.024i −0.181042 0.324448i
\(636\) −128.702 1646.74i −0.202361 2.58921i
\(637\) 451.934 + 13.2324i 0.709473 + 0.0207730i
\(638\) −1660.81 −2.60315
\(639\) −525.742 202.469i −0.822758 0.316852i
\(640\) −3.28240 + 224.304i −0.00512875 + 0.350475i
\(641\) −530.429 + 306.244i −0.827503 + 0.477759i −0.852997 0.521916i \(-0.825217\pi\)
0.0254941 + 0.999675i \(0.491884\pi\)
\(642\) 1604.07 + 766.171i 2.49855 + 1.19341i
\(643\) 82.2019i 0.127841i −0.997955 0.0639206i \(-0.979640\pi\)
0.997955 0.0639206i \(-0.0203604\pi\)
\(644\) 281.432 + 289.793i 0.437006 + 0.449988i
\(645\) 391.682 + 194.173i 0.607259 + 0.301043i
\(646\) 62.7396 108.668i 0.0971201 0.168217i
\(647\) 315.390 + 546.272i 0.487465 + 0.844315i 0.999896 0.0144137i \(-0.00458817\pi\)
−0.512431 + 0.858729i \(0.671255\pi\)
\(648\) −1304.33 1179.56i −2.01285 1.82031i
\(649\) 156.173 270.500i 0.240636 0.416794i
\(650\) 755.343 407.105i 1.16207 0.626316i
\(651\) −211.223 626.540i −0.324460 0.962427i
\(652\) 1317.54i 2.02077i
\(653\) −155.794 + 269.843i −0.238581 + 0.413235i −0.960307 0.278944i \(-0.910016\pi\)
0.721726 + 0.692179i \(0.243349\pi\)
\(654\) −238.192 + 163.515i −0.364209 + 0.250023i
\(655\) 731.876 + 10.7101i 1.11737 + 0.0163512i
\(656\) −814.257 470.111i −1.24124 0.716633i
\(657\) −60.6759 385.803i −0.0923529 0.587219i
\(658\) −427.532 + 1506.99i −0.649745 + 2.29026i
\(659\) 436.936i 0.663029i −0.943450 0.331515i \(-0.892440\pi\)
0.943450 0.331515i \(-0.107560\pi\)
\(660\) −1430.15 + 951.285i −2.16689 + 1.44134i
\(661\) 360.203 + 623.889i 0.544936 + 0.943857i 0.998611 + 0.0526895i \(0.0167794\pi\)
−0.453675 + 0.891167i \(0.649887\pi\)
\(662\) 852.747 + 1477.00i 1.28814 + 2.23112i
\(663\) 37.3062 78.1050i 0.0562688 0.117805i
\(664\) −2031.83 −3.05999
\(665\) −274.687 + 259.061i −0.413064 + 0.389565i
\(666\) −120.591 766.771i −0.181068 1.15131i
\(667\) −194.866 112.506i −0.292153 0.168674i
\(668\) −116.296 201.430i −0.174095 0.301542i
\(669\) −539.134 785.358i −0.805880 1.17393i
\(670\) 904.526 + 1621.01i 1.35004 + 2.41942i
\(671\) 462.152i 0.688751i
\(672\) −450.844 1337.31i −0.670899 1.99005i
\(673\) 121.980i 0.181248i −0.995885 0.0906240i \(-0.971114\pi\)
0.995885 0.0906240i \(-0.0288861\pi\)
\(674\) −548.960 316.942i −0.814481 0.470241i
\(675\) 640.973 + 211.610i 0.949589 + 0.313497i
\(676\) −412.454 714.391i −0.610139 1.05679i
\(677\) 238.050 412.314i 0.351624 0.609031i −0.634910 0.772586i \(-0.718963\pi\)
0.986534 + 0.163555i \(0.0522961\pi\)
\(678\) −110.995 1420.18i −0.163710 2.09467i
\(679\) 601.435 584.083i 0.885766 0.860210i
\(680\) −291.451 174.004i −0.428604 0.255889i
\(681\) 299.217 + 142.919i 0.439379 + 0.209866i
\(682\) −1180.71 + 681.682i −1.73124 + 0.999534i
\(683\) −533.388 923.855i −0.780948 1.35264i −0.931390 0.364023i \(-0.881403\pi\)
0.150442 0.988619i \(-0.451930\pi\)
\(684\) −343.230 + 891.250i −0.501798 + 1.30300i
\(685\) 707.728 + 422.533i 1.03318 + 0.616837i
\(686\) 275.810 + 1245.71i 0.402056 + 1.81591i
\(687\) −22.0531 282.169i −0.0321006 0.410727i
\(688\) 1045.27 + 603.486i 1.51929 + 0.877160i
\(689\) −447.275 + 258.234i −0.649165 + 0.374795i
\(690\) −326.684 + 20.7278i −0.473454 + 0.0300403i
\(691\) 200.957 348.068i 0.290821 0.503716i −0.683183 0.730247i \(-0.739405\pi\)
0.974004 + 0.226531i \(0.0727383\pi\)
\(692\) −641.047 −0.926369
\(693\) 440.347 586.471i 0.635422 0.846279i
\(694\) 2320.99 3.34437
\(695\) 1098.22 612.807i 1.58017 0.881736i
\(696\) 1413.83 + 2059.53i 2.03137 + 2.95910i
\(697\) 61.4809 35.4960i 0.0882079 0.0509268i
\(698\) 47.5714 82.3960i 0.0681538 0.118046i
\(699\) 52.5181 + 671.969i 0.0751332 + 0.961329i
\(700\) 1162.63 + 1269.47i 1.66090 + 1.81353i
\(701\) 189.635i 0.270520i 0.990810 + 0.135260i \(0.0431870\pi\)
−0.990810 + 0.135260i \(0.956813\pi\)
\(702\) −264.647 + 888.119i −0.376990 + 1.26513i
\(703\) −216.612 + 125.061i −0.308126 + 0.177897i
\(704\) −850.141 + 490.829i −1.20759 + 0.697201i
\(705\) −499.780 751.361i −0.708908 1.06576i
\(706\) −733.106 −1.03839
\(707\) 108.053 + 30.6544i 0.152833 + 0.0433584i
\(708\) −789.388 + 61.6950i −1.11495 + 0.0871398i
\(709\) 223.924 387.847i 0.315830 0.547034i −0.663783 0.747925i \(-0.731050\pi\)
0.979614 + 0.200891i \(0.0643836\pi\)
\(710\) 1164.12 + 17.0354i 1.63961 + 0.0239936i
\(711\) −175.418 217.104i −0.246720 0.305351i
\(712\) 744.651 + 429.925i 1.04586 + 0.603827i
\(713\) −184.713 −0.259065
\(714\) 239.466 + 48.1529i 0.335387 + 0.0674410i
\(715\) 461.133 + 275.309i 0.644941 + 0.385048i
\(716\) −1386.25 800.352i −1.93610 1.11781i
\(717\) 459.290 + 669.049i 0.640572 + 0.933123i
\(718\) 1497.51 864.586i 2.08566 1.20416i
\(719\) −570.467 329.359i −0.793418 0.458080i 0.0477467 0.998859i \(-0.484796\pi\)
−0.841164 + 0.540780i \(0.818129\pi\)
\(720\) 1729.10 + 695.114i 2.40153 + 0.965436i
\(721\) 220.513 + 873.932i 0.305844 + 1.21211i
\(722\) −909.928 −1.26029
\(723\) −159.638 76.2496i −0.220799 0.105463i
\(724\) −750.915 1300.62i −1.03718 1.79644i
\(725\) −816.007 503.519i −1.12553 0.694510i
\(726\) −146.148 69.8066i −0.201306 0.0961523i
\(727\) 487.145i 0.670075i 0.942205 + 0.335038i \(0.108749\pi\)
−0.942205 + 0.335038i \(0.891251\pi\)
\(728\) −1005.98 + 976.961i −1.38185 + 1.34198i
\(729\) −650.618 + 328.842i −0.892481 + 0.451086i
\(730\) 393.268 + 704.778i 0.538723 + 0.965449i
\(731\) −78.9236 + 45.5665i −0.107967 + 0.0623345i
\(732\) −965.867 + 663.050i −1.31949 + 0.905806i
\(733\) 281.918 + 162.765i 0.384608 + 0.222054i 0.679821 0.733378i \(-0.262057\pi\)
−0.295213 + 0.955431i \(0.595391\pi\)
\(734\) 1520.46i 2.07147i
\(735\) −648.686 345.589i −0.882565 0.470190i
\(736\) −394.260 −0.535679
\(737\) −580.930 + 1006.20i −0.788236 + 1.36526i
\(738\) −591.201 + 477.683i −0.801085 + 0.647267i
\(739\) −147.919 256.204i −0.200161 0.346690i 0.748419 0.663226i \(-0.230813\pi\)
−0.948580 + 0.316537i \(0.897480\pi\)
\(740\) 555.654 + 995.792i 0.750884 + 1.34566i
\(741\) 297.717 23.2682i 0.401777 0.0314011i
\(742\) −1015.38 1045.54i −1.36843 1.40908i
\(743\) 509.432 0.685642 0.342821 0.939401i \(-0.388618\pi\)
0.342821 + 0.939401i \(0.388618\pi\)
\(744\) 1850.47 + 883.860i 2.48718 + 1.18798i
\(745\) −1204.07 17.6200i −1.61621 0.0236511i
\(746\) 2343.44 1352.99i 3.14134 1.81365i
\(747\) −302.696 + 785.998i −0.405216 + 1.05221i
\(748\) 358.060i 0.478690i
\(749\) 1081.20 272.811i 1.44352 0.364234i
\(750\) −1394.10 + 47.5558i −1.85880 + 0.0634078i
\(751\) 435.784 754.800i 0.580272 1.00506i −0.415175 0.909742i \(-0.636280\pi\)
0.995447 0.0953188i \(-0.0303870\pi\)
\(752\) −1245.70 2157.62i −1.65652 2.86918i
\(753\) −64.5271 93.9968i −0.0856934 0.124830i
\(754\) 658.207 1140.05i 0.872954 1.51200i
\(755\) −194.141 115.908i −0.257141 0.153520i
\(756\) −1857.45 78.8855i −2.45695 0.104346i
\(757\) 723.110i 0.955231i −0.878569 0.477615i \(-0.841501\pi\)
0.878569 0.477615i \(-0.158499\pi\)
\(758\) 478.616 828.987i 0.631420 1.09365i
\(759\) −115.955 168.912i −0.152774 0.222546i
\(760\) 17.1355 1170.96i 0.0225467 1.54074i
\(761\) −911.610 526.318i −1.19791 0.691614i −0.237821 0.971309i \(-0.576433\pi\)
−0.960089 + 0.279695i \(0.909767\pi\)
\(762\) −524.958 + 41.0284i −0.688921 + 0.0538430i
\(763\) −49.4631 + 174.351i −0.0648271 + 0.228507i
\(764\) 2061.85i