Properties

Label 105.3.o.b.44.2
Level 105
Weight 3
Character 105.44
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

Related objects

Downloads

Learn more about

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 44.2
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.85988 + 3.22141i) q^{2} +(2.70705 - 1.29300i) q^{3} +(-4.91833 - 8.51879i) q^{4} +(-0.0731607 - 4.99946i) q^{5} +(-0.869509 + 11.1254i) q^{6} +(4.87678 + 5.02166i) q^{7} +21.7110 q^{8} +(5.65629 - 7.00046i) q^{9} +O(q^{10})\) \(q+(-1.85988 + 3.22141i) q^{2} +(2.70705 - 1.29300i) q^{3} +(-4.91833 - 8.51879i) q^{4} +(-0.0731607 - 4.99946i) q^{5} +(-0.869509 + 11.1254i) q^{6} +(4.87678 + 5.02166i) q^{7} +21.7110 q^{8} +(5.65629 - 7.00046i) q^{9} +(16.2414 + 9.06274i) q^{10} +(10.0814 - 5.82052i) q^{11} +(-24.3290 - 16.7014i) 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} +(12.0313 + 31.2413i) q^{18} +(5.39398 - 9.34265i) q^{19} +(-42.2296 + 25.2122i) q^{20} +(19.6947 + 7.28821i) q^{21} +43.3019i q^{22} +(2.93334 - 5.08070i) q^{23} +(58.7728 - 28.0724i) q^{24} +(-24.9893 + 0.731528i) q^{25} +(-29.7243 - 17.1613i) q^{26} +(6.26026 - 26.2642i) q^{27} +(18.7929 - 66.2424i) q^{28} +38.3541i q^{29} +(55.6845 + 3.53314i) q^{30} +(-15.7425 - 27.2669i) q^{31} +(-33.6016 - 58.1996i) q^{32} +(19.7650 - 28.7918i) q^{33} +11.6314 q^{34} +(24.7488 - 24.7487i) q^{35} +(-87.4549 - 13.7542i) q^{36} +(20.0791 + 11.5927i) q^{37} +(20.0643 + 34.7525i) q^{38} +(11.9307 + 24.9783i) q^{39} +(-1.58839 - 108.543i) q^{40} -22.7035i q^{41} +(-60.1082 + 49.8896i) q^{42} +29.1447i q^{43} +(-99.1676 - 57.2544i) q^{44} +(-35.4124 - 27.7662i) 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} +(-7.73381 - 5.30912i) q^{51} +(78.6037 - 45.3819i) q^{52} +(-27.9865 - 48.4740i) q^{53} +(72.9645 + 69.0152i) 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} +(-81.7182 + 122.854i) q^{60} +(-19.8501 + 34.3814i) q^{61} +117.117 q^{62} +(62.7384 - 5.73575i) q^{63} +84.3274 q^{64} +(46.1306 - 0.675061i) q^{65} +(55.9895 + 117.221i) q^{66} +(-86.4356 + 49.9036i) q^{67} +(-15.3792 + 26.6376i) q^{68} +(1.37136 - 17.5466i) q^{69} +(33.6957 + 125.756i) q^{70} +62.5979i q^{71} +(122.803 - 151.987i) q^{72} +(-37.5802 + 21.6970i) q^{73} +(-74.6895 + 43.1220i) q^{74} +(-66.7015 + 34.2915i) q^{75} -106.117 q^{76} +(78.3936 + 22.2401i) q^{77} +(-102.655 - 8.02304i) q^{78} +(15.5064 - 26.8579i) q^{79} +(180.820 + 100.898i) q^{80} +(-17.0129 - 79.1932i) q^{81} +(73.1373 + 42.2259i) q^{82} -93.5855 q^{83} +(-34.7783 - 203.621i) q^{84} +(-13.4241 + 8.01458i) q^{85} +(-93.8870 - 54.2057i) q^{86} +(49.5920 + 103.827i) 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} +(-77.8721 - 53.4578i) q^{93} +(-111.890 - 193.800i) q^{94} +(-47.1029 - 26.2835i) q^{95} +(-166.214 - 114.103i) 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 \(0.786524\pi\)
\(3\) 2.70705 1.29300i 0.902351 0.431001i
\(4\) −4.91833 8.51879i −1.22958 2.12970i
\(5\) −0.0731607 4.99946i −0.0146321 0.999893i
\(6\) −0.869509 + 11.1254i −0.144918 + 1.85423i
\(7\) 4.87678 + 5.02166i 0.696682 + 0.717380i
\(8\) 21.7110 2.71387
\(9\) 5.65629 7.00046i 0.628476 0.777829i
\(10\) 16.2414 + 9.06274i 1.62414 + 0.906274i
\(11\) 10.0814 5.82052i 0.916494 0.529138i 0.0339793 0.999423i \(-0.489182\pi\)
0.882515 + 0.470284i \(0.155849\pi\)
\(12\) −24.3290 16.7014i −2.02742 1.39178i
\(13\) 9.22710i 0.709777i 0.934909 + 0.354888i \(0.115481\pi\)
−0.934909 + 0.354888i \(0.884519\pi\)
\(14\) −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 \(0.862649\pi\)
\(18\) 12.0313 + 31.2413i 0.668407 + 1.73563i
\(19\) 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
\(21\) 19.6947 + 7.28821i 0.937844 + 0.347058i
\(22\) 43.3019i 1.96827i
\(23\) 2.93334 5.08070i 0.127537 0.220900i −0.795185 0.606367i \(-0.792626\pi\)
0.922722 + 0.385467i \(0.125960\pi\)
\(24\) 58.7728 28.0724i 2.44887 1.16968i
\(25\) −24.9893 + 0.731528i −0.999572 + 0.0292611i
\(26\) −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 \(0.229986\pi\)
−0.750141 + 0.661278i \(0.770014\pi\)
\(30\) 55.6845 + 3.53314i 1.85615 + 0.117771i
\(31\) −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
\(33\) 19.7650 28.7918i 0.598941 0.872479i
\(34\) 11.6314 0.342100
\(35\) 24.7488 24.7487i 0.707109 0.707105i
\(36\) −87.4549 13.7542i −2.42930 0.382060i
\(37\) 20.0791 + 11.5927i 0.542678 + 0.313315i 0.746164 0.665763i \(-0.231894\pi\)
−0.203486 + 0.979078i \(0.565227\pi\)
\(38\) 20.0643 + 34.7525i 0.528009 + 0.914539i
\(39\) 11.9307 + 24.9783i 0.305915 + 0.640468i
\(40\) −1.58839 108.543i −0.0397097 2.71358i
\(41\) 22.7035i 0.553744i −0.960907 0.276872i \(-0.910702\pi\)
0.960907 0.276872i \(-0.0892978\pi\)
\(42\) −60.1082 + 49.8896i −1.43115 + 1.18785i
\(43\) 29.1447i 0.677784i 0.940825 + 0.338892i \(0.110052\pi\)
−0.940825 + 0.338892i \(0.889948\pi\)
\(44\) −99.1676 57.2544i −2.25381 1.30124i
\(45\) −35.4124 27.7662i −0.786941 0.617028i
\(46\) 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
\(51\) −7.73381 5.30912i −0.151643 0.104100i
\(52\) 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 \(-0.343742\pi\)
\(54\) 72.9645 + 69.0152i 1.35119 + 1.27806i
\(55\) −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 −0.289981 0.957032i \(-0.593649\pi\)
0.683824 + 0.729647i \(0.260316\pi\)
\(60\) −81.7182 + 122.854i −1.36197 + 2.04756i
\(61\) −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
\(63\) 62.7384 5.73575i 0.995847 0.0910437i
\(64\) 84.3274 1.31762
\(65\) 46.1306 0.675061i 0.709701 0.0103856i
\(66\) 55.9895 + 117.221i 0.848326 + 1.77607i
\(67\) −86.4356 + 49.9036i −1.29008 + 0.744830i −0.978669 0.205444i \(-0.934136\pi\)
−0.311414 + 0.950274i \(0.600803\pi\)
\(68\) −15.3792 + 26.6376i −0.226165 + 0.391729i
\(69\) 1.37136 17.5466i 0.0198748 0.254298i
\(70\) 33.6957 + 125.756i 0.481368 + 1.79651i
\(71\) 62.5979i 0.881661i 0.897590 + 0.440830i \(0.145316\pi\)
−0.897590 + 0.440830i \(0.854684\pi\)
\(72\) 122.803 151.987i 1.70560 2.11093i
\(73\) −37.5802 + 21.6970i −0.514798 + 0.297219i −0.734804 0.678280i \(-0.762726\pi\)
0.220006 + 0.975499i \(0.429392\pi\)
\(74\) −74.6895 + 43.1220i −1.00932 + 0.582730i
\(75\) −66.7015 + 34.2915i −0.889353 + 0.457220i
\(76\) −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 \(0.103779\pi\)
\(80\) 180.820 + 100.898i 2.26025 + 1.26122i
\(81\) −17.0129 79.1932i −0.210035 0.977694i
\(82\) 73.1373 + 42.2259i 0.891919 + 0.514949i
\(83\) −93.5855 −1.12754 −0.563768 0.825933i \(-0.690649\pi\)
−0.563768 + 0.825933i \(0.690649\pi\)
\(84\) −34.7783 203.621i −0.414028 2.42406i
\(85\) −13.4241 + 8.01458i −0.157931 + 0.0942891i
\(86\) −93.8870 54.2057i −1.09171 0.630299i
\(87\) 49.5920 + 103.827i 0.570023 + 1.19341i
\(88\) 218.878 126.369i 2.48725 1.43601i
\(89\) −34.2984 19.8022i −0.385375 0.222496i 0.294779 0.955565i \(-0.404754\pi\)
−0.680154 + 0.733069i \(0.738087\pi\)
\(90\) 155.309 62.4358i 1.72566 0.693731i
\(91\) −46.3353 + 44.9985i −0.509179 + 0.494489i
\(92\) −57.7086 −0.627267
\(93\) −77.8721 53.4578i −0.837334 0.574815i
\(94\) −111.890 193.800i −1.19032 2.06170i
\(95\) −47.1029 26.2835i −0.495820 0.276669i
\(96\) −166.214 114.103i −1.73139 1.18857i
\(97\) 119.768i 1.23472i −0.786679 0.617362i \(-0.788201\pi\)
0.786679 0.617362i \(-0.211799\pi\)
\(98\) −155.114 95.7150i −1.58280 0.976683i
\(99\) 16.2772 103.497i 0.164416 1.04543i
\(100\) 129.137 + 209.281i 1.29137 + 2.09281i
\(101\) 13.8956 8.02263i 0.137580 0.0794320i −0.429630 0.903005i \(-0.641356\pi\)
0.567210 + 0.823573i \(0.308023\pi\)
\(102\) 31.4868 15.0394i 0.308694 0.147445i
\(103\) 111.510 + 64.3802i 1.08262 + 0.625051i 0.931602 0.363480i \(-0.118412\pi\)
0.151018 + 0.988531i \(0.451745\pi\)
\(104\) 200.329i 1.92624i
\(105\) 34.9963 98.9963i 0.333298 0.942822i
\(106\) 208.206 1.96421
\(107\) −79.6491 + 137.956i −0.744384 + 1.28931i 0.206099 + 0.978531i \(0.433923\pi\)
−0.950482 + 0.310779i \(0.899410\pi\)
\(108\) −254.529 + 75.8462i −2.35675 + 0.702279i
\(109\) −12.9451 22.4216i −0.118762 0.205702i 0.800515 0.599313i \(-0.204559\pi\)
−0.919277 + 0.393610i \(0.871226\pi\)
\(110\) 216.486 3.16800i 1.96806 0.0288000i
\(111\) 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 \(0.308940\pi\)
\(114\) 99.2503 + 68.1336i 0.870617 + 0.597663i
\(115\) −25.6154 14.2934i −0.222742 0.124291i
\(116\) 326.731 188.638i 2.81664 1.62619i
\(117\) 64.5939 + 52.1911i 0.552085 + 0.446078i
\(118\) 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
\(123\) −29.3557 61.4596i −0.238664 0.499672i
\(124\) −154.854 + 268.215i −1.24882 + 2.16302i
\(125\) 5.48548 + 124.880i 0.0438839 + 0.999037i
\(126\) −98.2088 + 212.774i −0.779435 + 1.68868i
\(127\) 47.1857i 0.371541i 0.982593 + 0.185770i \(0.0594781\pi\)
−0.982593 + 0.185770i \(0.940522\pi\)
\(128\) −22.4328 + 38.8548i −0.175256 + 0.303553i
\(129\) 37.6842 + 78.8963i 0.292125 + 0.611599i
\(130\) −83.6228 + 149.861i −0.643252 + 1.15278i
\(131\) −126.778 73.1955i −0.967773 0.558744i −0.0692166 0.997602i \(-0.522050\pi\)
−0.898557 + 0.438857i \(0.855383\pi\)
\(132\) −342.482 26.7669i −2.59456 0.202779i
\(133\) 73.2208 18.4753i 0.550533 0.138912i
\(134\) 371.259i 2.77059i
\(135\) −131.765 29.3764i −0.976037 0.217603i
\(136\) −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 \(0.627842\pi\)
\(138\) 53.9741 + 37.0522i 0.391117 + 0.268494i
\(139\) 251.524 1.80953 0.904763 0.425915i \(-0.140048\pi\)
0.904763 + 0.425915i \(0.140048\pi\)
\(140\) −332.551 89.1079i −2.37537 0.636485i
\(141\) −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
\(144\) 133.948 + 347.817i 0.930194 + 2.41540i
\(145\) 191.750 2.80601i 1.32241 0.0193518i
\(146\) 161.415i 1.10558i
\(147\) 59.4479 + 134.443i 0.404407 + 0.914579i
\(148\) 228.066i 1.54099i
\(149\) 208.574 + 120.420i 1.39983 + 0.808189i 0.994374 0.105927i \(-0.0337811\pi\)
0.405451 + 0.914117i \(0.367114\pi\)
\(150\) 13.5899 278.651i 0.0905992 1.85767i
\(151\) −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
\(156\) 154.106 224.486i 0.987856 1.43901i
\(157\) 1.63878 0.946152i 0.0104381 0.00602645i −0.494772 0.869023i \(-0.664748\pi\)
0.505210 + 0.862996i \(0.331415\pi\)
\(158\) 57.6803 + 99.9052i 0.365065 + 0.632311i
\(159\) −138.438 95.0352i −0.870679 0.597706i
\(160\) −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 0.100028 0.994985i \(-0.468107\pi\)
−0.811668 + 0.584119i \(0.801440\pi\)
\(164\) −193.406 + 111.663i −1.17931 + 0.680873i
\(165\) −145.390 96.7082i −0.881149 0.586110i
\(166\) 174.058 301.477i 1.04854 1.81613i
\(167\) 23.6454 0.141589 0.0707945 0.997491i \(-0.477447\pi\)
0.0707945 + 0.997491i \(0.477447\pi\)
\(168\) 427.591 + 158.234i 2.54519 + 0.941870i
\(169\) 83.8607 0.496217
\(170\) −0.850961 58.1508i −0.00500565 0.342063i
\(171\) −34.8929 90.6051i −0.204052 0.529854i
\(172\) 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
\(175\) −125.541 121.920i −0.717376 0.696687i
\(176\) 482.092i 2.73916i
\(177\) 45.5565 66.3622i 0.257381 0.374928i
\(178\) 127.582 73.6595i 0.716752 0.413817i
\(179\) −140.927 + 81.3643i −0.787302 + 0.454549i −0.839012 0.544113i \(-0.816866\pi\)
0.0517096 + 0.998662i \(0.483533\pi\)
\(180\) −62.3652 + 438.234i −0.346474 + 2.43463i
\(181\) 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
\(185\) 56.4881 101.233i 0.305341 0.547204i
\(186\) 317.042 151.433i 1.70453 0.814155i
\(187\) −31.5238 18.2003i −0.168577 0.0973278i
\(188\) 591.772 3.14773
\(189\) 162.420 96.6479i 0.859364 0.511364i
\(190\) 172.276 102.854i 0.906715 0.541334i
\(191\) −181.527 104.805i −0.950403 0.548716i −0.0571970 0.998363i \(-0.518216\pi\)
−0.893206 + 0.449647i \(0.851550\pi\)
\(192\) 228.279 109.036i 1.18895 0.567894i
\(193\) −102.657 + 59.2693i −0.531904 + 0.307095i −0.741791 0.670631i \(-0.766023\pi\)
0.209888 + 0.977725i \(0.432690\pi\)
\(194\) 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 \(0.633031\pi\)
\(198\) 303.133 + 244.928i 1.53098 + 1.23701i
\(199\) 43.3843 + 75.1437i 0.218011 + 0.377607i 0.954200 0.299170i \(-0.0967097\pi\)
−0.736189 + 0.676776i \(0.763376\pi\)
\(200\) −542.542 + 15.8822i −2.71271 + 0.0794110i
\(201\) −169.460 + 246.853i −0.843086 + 1.22813i
\(202\) 59.6846i 0.295468i
\(203\) −192.601 + 187.045i −0.948775 + 0.921402i
\(204\) −7.18989 + 91.9947i −0.0352446 + 0.450954i
\(205\) −113.505 + 1.66100i −0.553685 + 0.00810246i
\(206\) −414.790 + 239.479i −2.01355 + 1.16252i
\(207\) −18.9754 49.2726i −0.0916686 0.238032i
\(208\) −330.928 191.061i −1.59100 0.918564i
\(209\) 125.583i 0.600876i
\(210\) 253.819 + 296.859i 1.20866 + 1.41361i
\(211\) −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
\(213\) 80.9393 + 169.456i 0.379997 + 0.795568i
\(214\) −296.276 513.165i −1.38447 2.39797i
\(215\) 145.708 2.13225i 0.677711 0.00991742i
\(216\) 135.916 570.222i 0.629242 2.63992i
\(217\) 60.1521 212.028i 0.277198 0.977088i
\(218\) 96.3055 0.441768
\(219\) −73.6775 + 107.326i −0.336427 + 0.490074i
\(220\) −278.986 + 499.974i −1.26812 + 2.27261i
\(221\) 24.9869 14.4262i 0.113063 0.0652769i
\(222\) −146.432 + 213.307i −0.659602 + 0.960844i
\(223\) 317.534i 1.42392i −0.702220 0.711960i \(-0.747808\pi\)
0.702220 0.711960i \(-0.252192\pi\)
\(224\) 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 \(0.911617\pi\)
\(228\) −287.266 + 137.210i −1.25994 + 0.601799i
\(229\) −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
\(231\) 240.972 41.1579i 1.04317 0.178173i
\(232\) 832.705i 3.58925i
\(233\) 112.336 194.572i 0.482131 0.835075i −0.517659 0.855587i \(-0.673196\pi\)
0.999790 + 0.0205124i \(0.00652977\pi\)
\(234\) −288.266 + 111.014i −1.23191 + 0.474420i
\(235\) 262.673 + 146.572i 1.11776 + 0.623711i
\(236\) −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 \(0.191478\pi\)
−0.824462 + 0.565918i \(0.808522\pi\)
\(240\) 619.950 + 39.3353i 2.58312 + 0.163897i
\(241\) 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
\(243\) −148.452 192.383i −0.610913 0.791698i
\(244\) 390.517 1.60048
\(245\) 244.974 + 3.58631i 0.999893 + 0.0146380i
\(246\) 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
\(249\) −253.341 + 121.006i −1.01743 + 0.485969i
\(250\) −412.491 214.590i −1.64996 0.858361i
\(251\) 38.0046i 0.151413i −0.997130 0.0757064i \(-0.975879\pi\)
0.997130 0.0757064i \(-0.0241212\pi\)
\(252\) −357.429 506.245i −1.41837 2.00891i
\(253\) 68.2943i 0.269938i
\(254\) −152.004 87.7598i −0.598443 0.345511i
\(255\) −25.9769 + 39.0533i −0.101870 + 0.153150i
\(256\) 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
\(261\) 268.496 + 216.942i 1.02872 + 0.831195i
\(262\) 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 \(0.854159\pi\)
\(264\) 429.118 625.098i 1.62545 2.36779i
\(265\) −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 0.453196 0.891411i \(-0.350284\pi\)
0.998582 + 0.0532259i \(0.0169503\pi\)
\(270\) 339.701 369.833i 1.25815 1.36975i
\(271\) 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
\(273\) −67.2490 + 181.725i −0.246333 + 0.665660i
\(274\) −613.214 −2.23801
\(275\) −247.670 + 152.826i −0.900619 + 0.555729i
\(276\) −156.220 + 74.6173i −0.566015 + 0.270353i
\(277\) −227.641 + 131.429i −0.821810 + 0.474472i −0.851040 0.525101i \(-0.824028\pi\)
0.0292305 + 0.999573i \(0.490694\pi\)
\(278\) −467.805 + 810.263i −1.68275 + 2.91461i
\(279\) −279.925 44.0243i −1.00332 0.157793i
\(280\) 537.321 537.318i 1.91900 1.91899i
\(281\) 265.040i 0.943204i −0.881812 0.471602i \(-0.843676\pi\)
0.881812 0.471602i \(-0.156324\pi\)
\(282\) −553.477 379.952i −1.96269 1.34735i
\(283\) 182.790 105.534i 0.645901 0.372911i −0.140983 0.990012i \(-0.545026\pi\)
0.786884 + 0.617101i \(0.211693\pi\)
\(284\) 533.258 307.877i 1.87767 1.08407i
\(285\) −161.495 10.2467i −0.566648 0.0359534i
\(286\) −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
\(290\) −347.593 + 622.925i −1.19860 + 2.14802i
\(291\) −154.861 324.219i −0.532167 1.11415i
\(292\) 369.664 + 213.425i 1.26597 + 0.730909i
\(293\) −241.372 −0.823795 −0.411898 0.911230i \(-0.635134\pi\)
−0.411898 + 0.911230i \(0.635134\pi\)
\(294\) −543.663 58.5424i −1.84919 0.199124i
\(295\) −68.7715 115.190i −0.233124 0.390473i
\(296\) 435.936 + 251.688i 1.47276 + 0.850297i
\(297\) −89.7590 301.219i −0.302219 1.01421i
\(298\) −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
\(303\) 27.2429 39.6848i 0.0899105 0.130973i
\(304\) 223.382 + 386.908i 0.734808 + 1.27272i
\(305\) 173.341 + 96.7246i 0.568331 + 0.317130i
\(306\) 65.7905 81.4252i 0.215002 0.266095i
\(307\) 378.511i 1.23293i 0.787381 + 0.616467i \(0.211437\pi\)
−0.787381 + 0.616467i \(0.788563\pi\)
\(308\) −196.106 777.203i −0.636708 2.52339i
\(309\) 385.107 + 30.0982i 1.24630 + 0.0974053i
\(310\) −8.56837 585.523i −0.0276399 1.88878i
\(311\) −108.150 + 62.4406i −0.347750 + 0.200774i −0.663694 0.748004i \(-0.731012\pi\)
0.315944 + 0.948778i \(0.397679\pi\)
\(312\) 259.026 + 542.302i 0.830213 + 1.73815i
\(313\) −200.253 115.616i −0.639786 0.369380i 0.144746 0.989469i \(-0.453763\pi\)
−0.784532 + 0.620088i \(0.787097\pi\)
\(314\) 7.03893i 0.0224170i
\(315\) −33.2657 313.239i −0.105605 0.994408i
\(316\) −305.063 −0.965388
\(317\) 80.4184 139.289i 0.253686 0.439397i −0.710852 0.703342i \(-0.751690\pi\)
0.964538 + 0.263945i \(0.0850237\pi\)
\(318\) 563.626 269.211i 1.77241 0.846577i
\(319\) 223.241 + 386.665i 0.699815 + 1.21211i
\(320\) −6.16945 421.592i −0.0192795 1.31747i
\(321\) −37.2365 + 476.441i −0.116002 + 1.48424i
\(322\) −41.6921 + 146.959i −0.129479 + 0.456395i
\(323\) −33.7331 −0.104437
\(324\) −590.955 + 534.427i −1.82394 + 1.64947i
\(325\) −6.74989 230.579i −0.0207689 0.709473i
\(326\) 431.483 249.117i 1.32357 0.764161i
\(327\) −64.0343 43.9584i −0.195823 0.134429i
\(328\) 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
\(333\) 194.727 74.9914i 0.584766 0.225199i
\(334\) −43.9776 + 76.1714i −0.131669 + 0.228058i
\(335\) 255.815 + 428.481i 0.763627 + 1.27905i
\(336\) −669.200 + 555.433i −1.99167 + 1.65308i
\(337\) 170.410i 0.505667i −0.967510 0.252834i \(-0.918637\pi\)
0.967510 0.252834i \(-0.0813625\pi\)
\(338\) −155.971 + 270.150i −0.461453 + 0.799259i
\(339\) 345.563 165.056i 1.01936 0.486889i
\(340\) 134.299 + 74.9390i 0.394996 + 0.220409i
\(341\) −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
\(345\) −87.8237 5.57234i −0.254561 0.0161517i
\(346\) 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 \(-0.522430\pi\)
\(348\) 640.568 933.117i 1.84071 2.68137i
\(349\) −25.5776 −0.0732883 −0.0366442 0.999328i \(-0.511667\pi\)
−0.0366442 + 0.999328i \(0.511667\pi\)
\(350\) 626.246 177.661i 1.78927 0.507603i
\(351\) 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 \(0.743279\pi\)
\(354\) 129.050 + 270.182i 0.364549 + 0.763226i
\(355\) 312.956 4.57971i 0.881566 0.0129006i
\(356\) 389.574i 1.09431i
\(357\) −11.0555 64.7279i −0.0309677 0.181311i
\(358\) 605.312i 1.69082i
\(359\) 402.581 + 232.430i 1.12140 + 0.647438i 0.941757 0.336294i \(-0.109174\pi\)
0.179639 + 0.983733i \(0.442507\pi\)
\(360\) −768.837 602.832i −2.13566 1.67453i
\(361\) 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
\(366\) −365.246 250.735i −0.997940 0.685068i
\(367\) −353.989 + 204.375i −0.964547 + 0.556881i −0.897569 0.440873i \(-0.854669\pi\)
−0.0669775 + 0.997754i \(0.521336\pi\)
\(368\) 121.479 + 210.408i 0.330106 + 0.571760i
\(369\) −158.935 128.418i −0.430718 0.348015i
\(370\) 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 \(0.0955478\pi\)
0.733713 + 0.679459i \(0.237786\pi\)
\(374\) 117.261 67.7008i 0.313533 0.181018i
\(375\) 176.319 + 330.963i 0.470185 + 0.882568i
\(376\) −653.065 + 1131.14i −1.73688 + 3.00836i
\(377\) −353.897 −0.938720
\(378\) 9.26082 + 702.975i 0.0244995 + 1.85972i
\(379\) −257.337 −0.678989 −0.339494 0.940608i \(-0.610256\pi\)
−0.339494 + 0.940608i \(0.610256\pi\)
\(380\) 7.76362 + 530.530i 0.0204306 + 1.39613i
\(381\) 61.0112 + 127.734i 0.160134 + 0.335260i
\(382\) 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
\(385\) 105.453 393.553i 0.273905 1.02222i
\(386\) 440.935i 1.14232i
\(387\) 204.026 + 164.851i 0.527200 + 0.425971i
\(388\) −1020.28 + 589.059i −2.62959 + 1.51819i
\(389\) −92.0153 + 53.1250i −0.236543 + 0.136568i −0.613587 0.789627i \(-0.710274\pi\)
0.377044 + 0.926195i \(0.376941\pi\)
\(390\) −32.6006 + 513.806i −0.0835913 + 1.31745i
\(391\) −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
\(395\) −135.410 75.5589i −0.342809 0.191288i
\(396\) −961.727 + 370.371i −2.42860 + 0.935281i
\(397\) −116.882 67.4818i −0.294413 0.169979i 0.345517 0.938412i \(-0.387703\pi\)
−0.639930 + 0.768433i \(0.721037\pi\)
\(398\) −322.758 −0.810951
\(399\) 174.324 144.688i 0.436903 0.362628i
\(400\) 491.206 911.383i 1.22801 2.27846i
\(401\) −378.110 218.302i −0.942918 0.544394i −0.0520445 0.998645i \(-0.516574\pi\)
−0.890874 + 0.454251i \(0.849907\pi\)
\(402\) −480.039 1005.02i −1.19413 2.50005i
\(403\) 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
\(408\) −167.909 115.266i −0.411540 0.282515i
\(409\) −225.188 390.037i −0.550581 0.953635i −0.998233 0.0594267i \(-0.981073\pi\)
0.447651 0.894208i \(-0.352261\pi\)
\(410\) 205.756 368.737i 0.501844 0.899358i
\(411\) 407.731 + 279.900i 0.992046 + 0.681022i
\(412\) 1266.57i 3.07420i
\(413\) 180.689 + 51.2613i 0.437505 + 0.124119i
\(414\) 194.019 + 30.5138i 0.468646 + 0.0737047i
\(415\) 6.84678 + 467.877i 0.0164983 + 1.12742i
\(416\) 537.014 310.045i 1.29090 0.745300i
\(417\) 680.889 325.221i 1.63283 0.779908i
\(418\) 404.555 + 233.570i 0.967835 + 0.558780i
\(419\) 694.997i 1.65870i −0.558727 0.829352i \(-0.688710\pi\)
0.558727 0.829352i \(-0.311290\pi\)
\(420\) −1015.45 + 188.770i −2.41774 + 0.449452i
\(421\) 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
\(423\) 194.583 + 505.266i 0.460008 + 1.19448i
\(424\) −607.614 1052.42i −1.43305 2.48212i
\(425\) 41.0507 + 66.5271i 0.0965899 + 0.156534i
\(426\) −696.425 54.4294i −1.63480 0.127769i
\(427\) −269.456 + 67.9900i −0.631045 + 0.159227i
\(428\) 1566.96 3.66112
\(429\) 265.665 + 182.374i 0.619265 + 0.425114i
\(430\) −264.131 + 473.351i −0.614257 + 1.10082i
\(431\) −312.237 + 180.270i −0.724448 + 0.418260i −0.816388 0.577504i \(-0.804027\pi\)
0.0919394 + 0.995765i \(0.470693\pi\)
\(432\) 812.333 + 768.364i 1.88040 + 1.77862i
\(433\) 590.764i 1.36435i 0.731188 + 0.682176i \(0.238966\pi\)
−0.731188 + 0.682176i \(0.761034\pi\)
\(434\) 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
\(438\) −208.710 436.960i −0.476508 0.997625i
\(439\) 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
\(441\) 334.764 + 287.079i 0.759102 + 0.650972i
\(442\) 107.324i 0.242815i
\(443\) −99.6641 + 172.623i −0.224975 + 0.389669i −0.956312 0.292348i \(-0.905564\pi\)
0.731337 + 0.682017i \(0.238897\pi\)
\(444\) −294.890 617.387i −0.664167 1.39051i
\(445\) −96.4910 + 172.922i −0.216834 + 0.388589i
\(446\) 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 \(-0.844845\pi\)
0.883537 0.468361i \(-0.155155\pi\)
\(450\) −323.508 771.896i −0.718907 1.71532i
\(451\) −132.146 228.884i −0.293007 0.507503i
\(452\) −627.838 1087.45i −1.38902 2.40586i
\(453\) −111.847 76.7812i −0.246904 0.169495i
\(454\) 411.154 0.905626
\(455\) 228.358 + 228.360i 0.501887 + 0.501889i
\(456\) 54.7491 700.515i 0.120064 1.53622i
\(457\) −433.751 250.426i −0.949127 0.547979i −0.0563173 0.998413i \(-0.517936\pi\)
−0.892810 + 0.450434i \(0.851269\pi\)
\(458\) −175.467 303.918i −0.383117 0.663577i
\(459\) −80.9109 + 24.1103i −0.176277 + 0.0525279i
\(460\) 4.22200 + 288.512i 0.00917825 + 0.627200i
\(461\) 68.9132i 0.149486i −0.997203 0.0747432i \(-0.976186\pi\)
0.997203 0.0747432i \(-0.0238137\pi\)
\(462\) −315.594 + 852.819i −0.683103 + 1.84593i
\(463\) 72.6957i 0.157010i 0.996914 + 0.0785051i \(0.0250147\pi\)
−0.996914 + 0.0785051i \(0.974985\pi\)
\(464\) −1375.56 794.182i −2.96458 1.71160i
\(465\) −261.563 + 393.230i −0.562501 + 0.845655i
\(466\) 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
\(471\) 3.21290 4.68024i 0.00682144 0.00993681i
\(472\) 504.492 291.268i 1.06884 0.617094i
\(473\) 169.637 + 293.820i 0.358641 + 0.621185i
\(474\) 285.321 + 195.868i 0.601944 + 0.413223i
\(475\) −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 −0.860868 0.508828i \(-0.830079\pi\)
0.0102233 + 0.999948i \(0.496746\pi\)
\(480\) −558.292 + 839.326i −1.16311 + 1.74860i
\(481\) −106.967 + 185.272i −0.222384 + 0.385180i
\(482\) −219.358 −0.455100
\(483\) 94.8006 78.6841i 0.196275 0.162907i
\(484\) −142.767 −0.294974
\(485\) −598.777 + 8.76232i −1.23459 + 0.0180666i
\(486\) 895.846 120.415i 1.84331 0.247768i
\(487\) −173.689 + 100.280i −0.356651 + 0.205913i −0.667611 0.744510i \(-0.732683\pi\)
0.310959 + 0.950423i \(0.399350\pi\)
\(488\) −430.965 + 746.454i −0.883126 + 1.52962i
\(489\) −400.605 31.3095i −0.819232 0.0640275i
\(490\) −467.175 + 782.491i −0.953419 + 1.59692i
\(491\) 744.767i 1.51684i 0.651768 + 0.758418i \(0.274027\pi\)
−0.651768 + 0.758418i \(0.725973\pi\)
\(492\) −379.181 + 552.354i −0.770693 + 1.12267i
\(493\) 103.863 59.9651i 0.210675 0.121633i
\(494\) −320.664 + 185.136i −0.649118 + 0.374769i
\(495\) −518.621 73.8052i −1.04772 0.149101i
\(496\) 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 \(0.986006\pi\)
\(500\) 1036.84 660.928i 2.07369 1.32186i
\(501\) 64.0093 30.5735i 0.127763 0.0610250i
\(502\) 122.428 + 70.6841i 0.243881 + 0.140805i
\(503\) 924.410 1.83779 0.918897 0.394499i \(-0.129082\pi\)
0.918897 + 0.394499i \(0.129082\pi\)
\(504\) 1362.11 124.529i 2.70260 0.247081i
\(505\) −41.1255 68.8837i −0.0814366 0.136403i
\(506\) 220.004 + 127.019i 0.434791 + 0.251027i
\(507\) 227.015 108.432i 0.447762 0.213870i
\(508\) 401.965 232.075i 0.791269 0.456840i
\(509\) −821.002 474.006i −1.61297 0.931249i −0.988677 0.150059i \(-0.952054\pi\)
−0.624293 0.781190i \(-0.714613\pi\)
\(510\) −77.4927 156.317i −0.151947 0.306504i
\(511\) −292.225 82.9038i −0.571869 0.162238i
\(512\) −813.385 −1.58864
\(513\) −211.610 200.156i −0.412495 0.390168i
\(514\) 795.822 + 1378.40i 1.54829 + 2.68172i
\(515\) 313.709 562.200i 0.609143 1.09165i
\(516\) 486.758 709.061i 0.943329 1.37415i
\(517\) 700.324i 1.35459i
\(518\) −580.788 164.769i −1.12121 0.318086i
\(519\) 15.2335 194.913i 0.0293517 0.375556i
\(520\) 1001.54 14.6562i 1.92604 0.0281850i
\(521\) 511.768 295.469i 0.982280 0.567120i 0.0793222 0.996849i \(-0.474724\pi\)
0.902958 + 0.429729i \(0.141391\pi\)
\(522\) −1198.23 + 461.451i −2.29546 + 0.884006i
\(523\) −152.158 87.8483i −0.290933 0.167970i 0.347430 0.937706i \(-0.387055\pi\)
−0.638362 + 0.769736i \(0.720388\pi\)
\(524\) 1440.00i 2.74809i
\(525\) −497.489 167.720i −0.947598 0.319467i
\(526\) 127.922 0.243197
\(527\) −49.2256 + 85.2613i −0.0934073 + 0.161786i
\(528\) 623.346 + 1305.05i 1.18058 + 2.47168i
\(529\) 247.291 + 428.321i 0.467469 + 0.809680i
\(530\) −15.2325 1040.92i −0.0287406 1.96400i
\(531\) 37.5173 238.551i 0.0706540 0.449248i
\(532\) −517.511 532.885i −0.972765 1.00166i
\(533\) 209.487 0.393035
\(534\) 250.129 364.364i 0.468407 0.682330i
\(535\) 695.534 + 388.110i 1.30006 + 0.725439i
\(536\) −1876.60 + 1083.46i −3.50112 + 2.02137i
\(537\) −276.293 + 402.477i −0.514512 + 0.749491i
\(538\) 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
\(543\) 413.305 197.412i 0.761151 0.363558i
\(544\) −105.069 + 181.985i −0.193142 + 0.334532i
\(545\) −111.149 + 66.3589i −0.203943 + 0.121760i
\(546\) −460.336 554.624i −0.843106 1.01580i
\(547\) 760.168i 1.38970i −0.719153 0.694852i \(-0.755470\pi\)
0.719153 0.694852i \(-0.244530\pi\)
\(548\) 810.801 1404.35i 1.47956 2.56268i
\(549\) 128.408 + 333.431i 0.233894 + 0.607343i
\(550\) −31.6766 1082.08i −0.0575938 1.96743i
\(551\) 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
\(555\) 22.0221 347.082i 0.0396794 0.625373i
\(556\) −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 \(0.554647\pi\)
\(558\) 662.448 819.873i 1.18718 1.46931i
\(559\) −268.921 −0.481075
\(560\) 375.143 + 1400.07i 0.669899 + 2.50013i
\(561\) −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 \(-0.491327\pi\)
\(564\) 1601.96 765.163i 2.84035 1.35667i
\(565\) −9.33917 638.196i −0.0165295 1.12955i
\(566\) 785.123i 1.38714i
\(567\) 314.713 471.640i 0.555050 0.831817i
\(568\) 1359.06i 2.39271i
\(569\) 888.485 + 512.967i 1.56148 + 0.901523i 0.997107 + 0.0760060i \(0.0242168\pi\)
0.564377 + 0.825517i \(0.309117\pi\)
\(570\) 333.370 501.183i 0.584860 0.879269i
\(571\) −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
\(576\) 476.980 590.331i 0.828090 1.02488i
\(577\) 119.310 68.8835i 0.206776 0.119382i −0.393036 0.919523i \(-0.628575\pi\)
0.599812 + 0.800141i \(0.295242\pi\)
\(578\) 519.321 + 899.490i 0.898479 + 1.55621i
\(579\) −201.264 + 293.181i −0.347606 + 0.506358i
\(580\) −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
\(585\) 256.202 326.753i 0.437952 0.558553i
\(586\) 448.924 777.558i 0.766081 1.32689i
\(587\) −401.054 −0.683227 −0.341614 0.939840i \(-0.610973\pi\)
−0.341614 + 0.939840i \(0.610973\pi\)
\(588\) 852.909 1167.66i 1.45052 1.98581i
\(589\) −339.660 −0.576672
\(590\) 498.980 7.30193i 0.845729 0.0123761i
\(591\) −432.890 + 206.766i −0.732470 + 0.349859i
\(592\) −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
\(595\) −105.713 28.3260i −0.177669 0.0476068i
\(596\) 2369.06i 3.97494i
\(597\) 214.605 + 147.322i 0.359472 + 0.246771i
\(598\) −174.383 + 100.680i −0.291610 + 0.168361i
\(599\) −786.962 + 454.353i −1.31379 + 0.758519i −0.982722 0.185087i \(-0.940743\pi\)
−0.331071 + 0.943606i \(0.607410\pi\)
\(600\) −1448.15 + 744.502i −2.41359 + 1.24084i
\(601\) 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
\(605\) −63.3708 35.3611i −0.104745 0.0584480i
\(606\) 77.1724 + 161.569i 0.127347 + 0.266616i
\(607\) 253.578 + 146.403i 0.417756 + 0.241191i 0.694117 0.719862i \(-0.255795\pi\)
−0.276361 + 0.961054i \(0.589128\pi\)
\(608\) −724.985 −1.19241
\(609\) −279.533 + 755.374i −0.459003 + 1.24035i
\(610\) −633.983 + 378.506i −1.03932 + 0.620502i
\(611\) −480.732 277.551i −0.786796 0.454257i
\(612\) 99.4860 + 258.331i 0.162559 + 0.422110i
\(613\) 733.123 423.269i 1.19596 0.690487i 0.236307 0.971678i \(-0.424063\pi\)
0.959652 + 0.281191i \(0.0907295\pi\)
\(614\) −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 \(0.311230\pi\)
\(618\) −813.213 + 1184.61i −1.31588 + 1.91684i
\(619\) −117.419 203.376i −0.189692 0.328556i 0.755456 0.655200i \(-0.227416\pi\)
−0.945147 + 0.326644i \(0.894082\pi\)
\(620\) 1352.26 + 754.564i 2.18106 + 1.21704i
\(621\) −115.077 108.848i −0.185309 0.175279i
\(622\) 464.529i 0.746831i
\(623\) −67.8258 268.806i −0.108870 0.431470i
\(624\) −1142.88 89.3226i −1.83154 0.143145i
\(625\) 623.930 36.5608i 0.998288 0.0584972i
\(626\) 744.894 430.065i 1.18993 0.687004i
\(627\) −162.379 339.960i −0.258978 0.542202i
\(628\) −16.1201 9.30697i −0.0256690 0.0148200i
\(629\) 72.4986i 0.115260i
\(630\) 1070.94 + 475.425i 1.69991 + 0.754642i
\(631\) 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
\(633\) −788.748 + 376.739i −1.24605 + 0.595165i
\(634\) 299.138 + 518.122i 0.471826 + 0.817226i
\(635\) 235.903 3.45214i 0.371501 0.00543644i
\(636\) −128.702 + 1646.74i −0.202361 + 2.58921i
\(637\) −451.934 13.2324i −0.709473 0.0207730i
\(638\) −1660.81 −2.60315
\(639\) 438.214 + 354.072i 0.685781 + 0.554103i
\(640\) 195.894 + 109.309i 0.306085 + 0.170796i
\(641\) 530.429 306.244i 0.827503 0.477759i −0.0254941 0.999675i \(-0.508116\pi\)
0.852997 + 0.521916i \(0.174783\pi\)
\(642\) −1465.56 1006.08i −2.28280 1.56710i
\(643\) 82.2019i 0.127841i 0.997955 + 0.0639206i \(0.0203604\pi\)
−0.997955 + 0.0639206i \(0.979640\pi\)
\(644\) −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 \(0.671255\pi\)
\(648\) −369.366 1719.36i −0.570009 2.65334i
\(649\) 156.173 270.500i 0.240636 0.416794i
\(650\) 755.343 + 407.105i 1.16207 + 0.626316i
\(651\) −111.318 651.749i −0.170996 1.00115i
\(652\) 1317.54i 2.02077i
\(653\) −155.794 + 269.843i −0.238581 + 0.413235i −0.960307 0.278944i \(-0.910016\pi\)
0.721726 + 0.692179i \(0.243349\pi\)
\(654\) 260.704 124.523i 0.398630 0.190403i
\(655\) −356.663 + 639.179i −0.544524 + 0.975845i
\(656\) 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 \(0.107560\pi\)
−0.943450 + 0.331515i \(0.892440\pi\)
\(660\) −108.764 + 1714.19i −0.164794 + 2.59725i
\(661\) 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
\(663\) 48.9878 71.3606i 0.0738880 0.107633i
\(664\) −2031.83 −3.05999
\(665\) −97.7235 364.713i −0.146953 0.548441i
\(666\) −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
\(669\) −410.573 859.583i −0.613711 1.28488i
\(670\) −1856.10 + 27.1616i −2.77030 + 0.0405397i
\(671\) 462.152i 0.688751i
\(672\) −237.602 1391.12i −0.353575 2.07012i
\(673\) 121.980i 0.181248i 0.995885 + 0.0906240i \(0.0288861\pi\)
−0.995885 + 0.0906240i \(0.971114\pi\)
\(674\) 548.960 + 316.942i 0.814481 + 0.470241i
\(675\) −137.226 + 660.904i −0.203298 + 0.979117i
\(676\) −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
\(681\) −273.380 187.670i −0.401439 0.275580i
\(682\) 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 \(-0.451930\pi\)
\(684\) −600.231 + 742.871i −0.877530 + 1.08607i
\(685\) 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
\(690\) 181.293 272.552i 0.262743 0.395003i
\(691\) 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
\(693\) 599.108 422.994i 0.864513 0.610382i
\(694\) 2320.99 3.34437
\(695\) −18.4017 1257.49i −0.0264772 1.80933i
\(696\) 1076.69 + 2254.18i 1.54697 + 3.23876i
\(697\) −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
\(700\) −421.162 + 1669.10i −0.601660 + 2.38443i
\(701\) 189.635i 0.270520i −0.990810 0.135260i \(-0.956813\pi\)
0.990810 0.135260i \(-0.0431870\pi\)
\(702\) −636.810 + 673.251i −0.907137 + 0.959046i
\(703\) 216.612 125.061i 0.308126 0.177897i
\(704\) 850.141 490.829i 1.20759 0.697201i
\(705\) 900.588 + 57.1416i 1.27743 + 0.0810519i
\(706\) −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 \(0.0643836\pi\)
\(710\) −567.308 + 1016.68i −0.799026 + 1.43194i
\(711\) −100.309 260.468i −0.141082 0.366341i
\(712\) −744.651 429.925i −1.04586 0.603827i
\(713\) −184.713 −0.259065
\(714\) 229.077 + 84.7721i 0.320836 + 0.118728i
\(715\) 461.133 275.309i 0.644941 0.385048i
\(716\) 1386.25 + 800.352i 1.93610 + 1.11781i
\(717\) 349.768 + 732.282i 0.487822 + 1.02131i
\(718\) −1497.51 + 864.586i −2.08566 + 1.20416i
\(719\) 570.467 + 329.359i 0.793418 + 0.458080i 0.841164 0.540780i \(-0.181871\pi\)
−0.0477467 + 0.998859i \(0.515204\pi\)
\(720\) 1729.10 695.114i 2.40153 0.965436i
\(721\) 220.513 + 873.932i 0.305844 + 1.21211i
\(722\) −909.928 −1.26029
\(723\) 145.853 + 100.125i 0.201733 + 0.138486i
\(724\) −750.915 1300.62i −1.03718 1.79644i
\(725\) −28.0571 958.443i −0.0386995 1.32199i
\(726\) 133.528 + 91.6649i 0.183924 + 0.126260i
\(727\) 487.145i 0.670075i −0.942205 0.335038i \(-0.891251\pi\)
0.942205 0.335038i \(-0.108749\pi\)
\(728\) −1005.98 + 976.961i −1.38185 + 1.34198i
\(729\) −650.618 328.842i −0.892481 0.451086i
\(730\) −806.989 + 11.8092i −1.10546 + 0.0161770i
\(731\) 78.9236 45.5665i 0.107967 0.0623345i
\(732\) 1057.15 504.940i 1.44420 0.689809i
\(733\) −281.918 162.765i −0.384608 0.222054i 0.295213 0.955431i \(-0.404609\pi\)
−0.679821 + 0.733378i \(0.737943\pi\)
\(734\) 1520.46i 2.07147i
\(735\) 667.794 307.043i 0.908564 0.417746i
\(736\) −394.260 −0.535679
\(737\) −580.930 + 1006.20i −0.788236 + 1.36526i
\(738\) 709.286 273.153i 0.961092 0.370127i
\(739\) −147.919 256.204i −0.200161 0.346690i 0.748419 0.663226i \(-0.230813\pi\)
−0.948580 + 0.316537i \(0.897480\pi\)
\(740\) −1140.21 + 16.6855i −1.54082 + 0.0225479i
\(741\) 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 \(0.388618\pi\)
\(744\) −1690.68 1160.62i −2.27242 1.55997i
\(745\) 586.777 1051.57i 0.787620 1.41150i
\(746\) −2343.44 + 1352.99i −3.14134 + 1.81365i
\(747\) −529.346 + 655.142i −0.708630 + 0.877030i
\(748\) 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
\(753\) −49.1401 102.881i −0.0652591 0.136628i
\(754\) 658.207 1140.05i 0.872954 1.51200i
\(755\) −194.141 + 115.908i −0.257141 + 0.153520i
\(756\) −1622.16 908.274i −2.14571 1.20142i
\(757\) 723.110i 0.955231i 0.878569 + 0.477615i \(0.158499\pi\)
−0.878569 + 0.477615i \(0.841501\pi\)
\(758\) 478.616 828.987i 0.631420 1.09365i
\(759\) −88.3048 184.876i −0.116344 0.243579i
\(760\) −1022.65 570.641i −1.34559 0.750843i
\(761\) 911.610 + 526.318i 1.19791 + 0.691614i 0.960089 0.279695i \(-0.0902334\pi\)
0.237821 + 0.971309i \(0.423567\pi\)
\(762\) −524.958 41.0284i −0.688921 0.0538430i
\(763\) 49.4631 174.351i 0.0648271 0.228507i
\(764\)