Properties

Label 105.3.o.b.74.2
Level 105
Weight 3
Character 105.74
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 74.2
Character \(\chi\) \(=\) 105.74
Dual form 105.3.o.b.44.2

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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 −0.783415 0.621499i \(-0.786524\pi\)
−0.146526 0.989207i \(-0.546809\pi\)
\(3\) 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 0.882515 0.470284i \(-0.155849\pi\)
0.0339793 + 0.999423i \(0.489182\pi\)
\(12\) −24.3290 + 16.7014i −2.02742 + 1.39178i
\(13\) 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 −0.908339 0.418234i \(-0.862649\pi\)
0.816371 + 0.577528i \(0.195982\pi\)
\(18\) 12.0313 31.2413i 0.668407 1.73563i
\(19\) 5.39398 + 9.34265i 0.283894 + 0.491719i 0.972340 0.233569i \(-0.0750403\pi\)
−0.688447 + 0.725287i \(0.741707\pi\)
\(20\) −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 0.922722 0.385467i \(-0.125960\pi\)
−0.795185 + 0.606367i \(0.792626\pi\)
\(24\) 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 \(-0.770014\pi\)
0.750141 0.661278i \(-0.229986\pi\)
\(30\) 55.6845 3.53314i 1.85615 0.117771i
\(31\) −15.7425 + 27.2669i −0.507824 + 0.879577i 0.492135 + 0.870519i \(0.336217\pi\)
−0.999959 + 0.00905794i \(0.997117\pi\)
\(32\) −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 −0.203486 0.979078i \(-0.565227\pi\)
0.746164 + 0.665763i \(0.231894\pi\)
\(38\) 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 \(0.0892978\pi\)
−0.960907 + 0.276872i \(0.910702\pi\)
\(42\) −60.1082 49.8896i −1.43115 1.18785i
\(43\) 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
\(45\) −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 −0.985432 0.170068i \(-0.945601\pi\)
0.345433 0.938443i \(-0.387732\pi\)
\(48\) −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 0.471418 + 0.881910i \(0.343742\pi\)
−0.999465 + 0.0326945i \(0.989591\pi\)
\(54\) 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 0.683824 0.729647i \(-0.260316\pi\)
−0.289981 + 0.957032i \(0.593649\pi\)
\(60\) −81.7182 122.854i −1.36197 2.04756i
\(61\) −19.8501 34.3814i −0.325412 0.563630i 0.656184 0.754601i \(-0.272170\pi\)
−0.981596 + 0.190971i \(0.938836\pi\)
\(62\) 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 −0.311414 0.950274i \(-0.600803\pi\)
−0.978669 + 0.205444i \(0.934136\pi\)
\(68\) −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 \(-0.854684\pi\)
0.897590 0.440830i \(-0.145316\pi\)
\(72\) 122.803 + 151.987i 1.70560 + 2.11093i
\(73\) −37.5802 21.6970i −0.514798 0.297219i 0.220006 0.975499i \(-0.429392\pi\)
−0.734804 + 0.678280i \(0.762726\pi\)
\(74\) −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 0.947321 0.320287i \(-0.103779\pi\)
−0.751037 + 0.660260i \(0.770446\pi\)
\(80\) 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 −0.680154 0.733069i \(-0.738087\pi\)
0.294779 + 0.955565i \(0.404754\pi\)
\(90\) 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 \(0.211799\pi\)
−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
\(100\) 129.137 209.281i 1.29137 2.09281i
\(101\) 13.8956 + 8.02263i 0.137580 + 0.0794320i 0.567210 0.823573i \(-0.308023\pi\)
−0.429630 + 0.903005i \(0.641356\pi\)
\(102\) 31.4868 + 15.0394i 0.308694 + 0.147445i
\(103\) 111.510 64.3802i 1.08262 0.625051i 0.151018 0.988531i \(-0.451745\pi\)
0.931602 + 0.363480i \(0.118412\pi\)
\(104\) 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 −0.950482 0.310779i \(-0.899410\pi\)
0.206099 0.978531i \(-0.433923\pi\)
\(108\) −254.529 75.8462i −2.35675 0.702279i
\(109\) −12.9451 + 22.4216i −0.118762 + 0.205702i −0.919277 0.393610i \(-0.871226\pi\)
0.800515 + 0.599313i \(0.204559\pi\)
\(110\) 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 \(-0.940522\pi\)
0.982593 0.185770i \(-0.0594781\pi\)
\(128\) −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 −0.898557 0.438857i \(-0.855383\pi\)
−0.0692166 + 0.997602i \(0.522050\pi\)
\(132\) −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 −0.390917 0.920426i \(-0.627842\pi\)
0.992571 0.121668i \(-0.0388245\pi\)
\(138\) 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 0.405451 0.914117i \(-0.367114\pi\)
0.994374 + 0.105927i \(0.0337811\pi\)
\(150\) 13.5899 + 278.651i 0.0905992 + 1.85767i
\(151\) −22.6110 + 39.1633i −0.149741 + 0.259360i −0.931132 0.364683i \(-0.881177\pi\)
0.781390 + 0.624042i \(0.214511\pi\)
\(152\) 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 0.505210 0.862996i \(-0.331415\pi\)
−0.494772 + 0.869023i \(0.664748\pi\)
\(158\) 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 −0.811668 0.584119i \(-0.801440\pi\)
0.100028 + 0.994985i \(0.468107\pi\)
\(164\) −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 0.944700 0.327935i \(-0.106353\pi\)
−0.756350 + 0.654167i \(0.773019\pi\)
\(174\) −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 0.0517096 0.998662i \(-0.483533\pi\)
−0.839012 + 0.544113i \(0.816866\pi\)
\(180\) −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 −0.893206 0.449647i \(-0.851550\pi\)
−0.0571970 + 0.998363i \(0.518216\pi\)
\(192\) 228.279 + 109.036i 1.18895 + 0.567894i
\(193\) −102.657 59.2693i −0.531904 0.307095i 0.209888 0.977725i \(-0.432690\pi\)
−0.741791 + 0.670631i \(0.766023\pi\)
\(194\) 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 −0.736189 0.676776i \(-0.763376\pi\)
0.954200 + 0.299170i \(0.0967097\pi\)
\(200\) −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 \(0.252192\pi\)
−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 −0.961698 0.274110i \(-0.911617\pi\)
0.718235 + 0.695800i \(0.244950\pi\)
\(228\) −287.266 137.210i −1.25994 0.601799i
\(229\) −47.1716 81.7037i −0.205990 0.356785i 0.744458 0.667669i \(-0.232708\pi\)
−0.950448 + 0.310885i \(0.899375\pi\)
\(230\) 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 0.999790 0.0205124i \(-0.00652977\pi\)
−0.517659 + 0.855587i \(0.673196\pi\)
\(234\) −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 \(-0.808522\pi\)
0.824462 0.565918i \(-0.191478\pi\)
\(240\) 619.950 39.3353i 2.58312 0.163897i
\(241\) 29.4855 51.0703i 0.122346 0.211910i −0.798346 0.602199i \(-0.794291\pi\)
0.920693 + 0.390289i \(0.127625\pi\)
\(242\) 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 \(0.0241212\pi\)
−0.997130 + 0.0757064i \(0.975879\pi\)
\(252\) −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 0.896076 + 0.443901i \(0.146406\pi\)
−0.0636088 + 0.997975i \(0.520261\pi\)
\(258\) −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 −0.896862 0.442310i \(-0.854159\pi\)
0.831483 + 0.555551i \(0.187493\pi\)
\(264\) 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 0.998582 0.0532259i \(-0.0169503\pi\)
0.453196 + 0.891411i \(0.350284\pi\)
\(270\) 339.701 + 369.833i 1.25815 + 1.36975i
\(271\) 112.662 + 195.136i 0.415727 + 0.720060i 0.995504 0.0947148i \(-0.0301939\pi\)
−0.579778 + 0.814775i \(0.696861\pi\)
\(272\) 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 0.0292305 0.999573i \(-0.490694\pi\)
−0.851040 + 0.525101i \(0.824028\pi\)
\(278\) −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 \(0.156324\pi\)
−0.881812 + 0.471602i \(0.843676\pi\)
\(282\) −553.477 + 379.952i −1.96269 + 1.34735i
\(283\) 182.790 + 105.534i 0.645901 + 0.372911i 0.786884 0.617101i \(-0.211693\pi\)
−0.140983 + 0.990012i \(0.545026\pi\)
\(284\) 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 \(-0.788563\pi\)
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
\(310\) −8.56837 + 585.523i −0.0276399 + 1.88878i
\(311\) −108.150 62.4406i −0.347750 0.200774i 0.315944 0.948778i \(-0.397679\pi\)
−0.663694 + 0.748004i \(0.731012\pi\)
\(312\) 259.026 542.302i 0.830213 1.73815i
\(313\) −200.253 + 115.616i −0.639786 + 0.369380i −0.784532 0.620088i \(-0.787097\pi\)
0.144746 + 0.989469i \(0.453763\pi\)
\(314\) 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 0.964538 0.263945i \(-0.0850237\pi\)
−0.710852 + 0.703342i \(0.751690\pi\)
\(318\) 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 0.970986 + 0.239135i \(0.0768640\pi\)
−0.278396 + 0.960466i \(0.589803\pi\)
\(332\) 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 \(0.0813625\pi\)
−0.967510 + 0.252834i \(0.918637\pi\)
\(338\) −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 −0.0704086 + 0.997518i \(0.522430\pi\)
−0.828672 + 0.559735i \(0.810903\pi\)
\(348\) 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 −0.692019 0.721879i \(-0.743279\pi\)
0.971175 + 0.238367i \(0.0766121\pi\)
\(354\) 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 0.179639 0.983733i \(-0.442507\pi\)
0.941757 + 0.336294i \(0.109174\pi\)
\(360\) −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 −0.0669775 0.997754i \(-0.521336\pi\)
−0.897569 + 0.440873i \(0.854669\pi\)
\(368\) 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 0.733713 0.679459i \(-0.237786\pi\)
0.955286 0.295685i \(-0.0955478\pi\)
\(374\) 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 0.937044 0.349212i \(-0.113551\pi\)
−0.770948 + 0.636898i \(0.780217\pi\)
\(384\) −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 0.377044 0.926195i \(-0.376941\pi\)
−0.613587 + 0.789627i \(0.710274\pi\)
\(390\) −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 −0.639930 0.768433i \(-0.721037\pi\)
0.345517 + 0.938412i \(0.387703\pi\)
\(398\) −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 −0.890874 0.454251i \(-0.849907\pi\)
−0.0520445 + 0.998645i \(0.516574\pi\)
\(402\) −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 0.447651 + 0.894208i \(0.352261\pi\)
−0.998233 + 0.0594267i \(0.981073\pi\)
\(410\) 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 \(0.311290\pi\)
−0.558727 + 0.829352i \(0.688710\pi\)
\(420\) −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 0.0919394 0.995765i \(-0.470693\pi\)
−0.816388 + 0.577504i \(0.804027\pi\)
\(432\) 812.333 768.364i 1.88040 1.77862i
\(433\) 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
\(438\) −208.710 + 436.960i −0.476508 + 0.997625i
\(439\) 235.149 + 407.290i 0.535647 + 0.927769i 0.999132 + 0.0416635i \(0.0132657\pi\)
−0.463484 + 0.886105i \(0.653401\pi\)
\(440\) −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 0.731337 0.682017i \(-0.238897\pi\)
−0.956312 + 0.292348i \(0.905564\pi\)
\(444\) −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 \(0.155155\pi\)
−0.883537 + 0.468361i \(0.844845\pi\)
\(450\) −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 −0.892810 0.450434i \(-0.851269\pi\)
−0.0563173 + 0.998413i \(0.517936\pi\)
\(458\) −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 \(0.0238137\pi\)
−0.997203 + 0.0747432i \(0.976186\pi\)
\(462\) −315.594 852.819i −0.683103 1.84593i
\(463\) 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
\(465\) −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 0.929144 0.369717i \(-0.120545\pi\)
−0.784756 + 0.619804i \(0.787212\pi\)
\(468\) 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 0.0102233 0.999948i \(-0.496746\pi\)
−0.860868 + 0.508828i \(0.830079\pi\)
\(480\) −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 0.310959 0.950423i \(-0.399350\pi\)
−0.667611 + 0.744510i \(0.732683\pi\)
\(488\) −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 \(-0.725973\pi\)
0.651768 0.758418i \(-0.274027\pi\)
\(492\) −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 −0.999034 0.0439501i \(-0.986006\pi\)
0.461455 0.887164i \(-0.347328\pi\)
\(500\) 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 −0.624293 + 0.781190i \(0.714613\pi\)
−0.988677 + 0.150059i \(0.952054\pi\)
\(510\) −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 0.902958 0.429729i \(-0.141391\pi\)
0.0793222 + 0.996849i \(0.474724\pi\)
\(522\) −1198.23 461.451i −2.29546 0.884006i
\(523\) −152.158 + 87.8483i −0.290933 + 0.167970i −0.638362 0.769736i \(-0.720388\pi\)
0.347430 + 0.937706i \(0.387055\pi\)
\(524\) 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 −0.969881 0.243580i \(-0.921678\pi\)
0.273994 0.961731i \(-0.411655\pi\)
\(542\) 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 \(0.244530\pi\)
−0.719153 + 0.694852i \(0.755470\pi\)
\(548\) 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 −0.170835 0.985300i \(-0.554647\pi\)
0.938712 0.344702i \(-0.112020\pi\)
\(558\) 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 0.0272426 + 0.999629i \(0.491327\pi\)
−0.879325 + 0.476222i \(0.842006\pi\)
\(564\) 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 0.564377 0.825517i \(-0.309117\pi\)
0.997107 0.0760060i \(-0.0242168\pi\)
\(570\) 333.370 + 501.183i 0.584860 + 0.879269i
\(571\) −190.751 + 330.391i −0.334065 + 0.578617i −0.983305 0.181966i \(-0.941754\pi\)
0.649240 + 0.760584i \(0.275087\pi\)
\(572\) 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 0.599812 0.800141i \(-0.295242\pi\)
−0.393036 + 0.919523i \(0.628575\pi\)
\(578\) 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 −0.984178 0.177182i \(-0.943302\pi\)
0.338645 0.940914i \(-0.390031\pi\)
\(594\) 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 −0.331071 0.943606i \(-0.607410\pi\)
−0.982722 + 0.185087i \(0.940743\pi\)
\(600\) −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 −0.276361 0.961054i \(-0.589128\pi\)
0.694117 + 0.719862i \(0.255795\pi\)
\(608\) −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 0.959652 0.281191i \(-0.0907295\pi\)
0.236307 + 0.971678i \(0.424063\pi\)
\(614\) −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 −0.945147 0.326644i \(-0.894082\pi\)
0.755456 + 0.655200i \(0.227416\pi\)
\(620\) 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 0.852997 0.521916i \(-0.174783\pi\)
−0.0254941 + 0.999675i \(0.508116\pi\)
\(642\) −1465.56 + 1006.08i −2.28280 + 1.56710i
\(643\) 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 −0.512431 0.858729i \(-0.671255\pi\)
0.999896 + 0.0144137i \(0.00458817\pi\)
\(648\) −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 0.721726 0.692179i \(-0.243349\pi\)
−0.960307 + 0.278944i \(0.910016\pi\)
\(654\) 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 \(-0.892440\pi\)
0.943450 0.331515i \(-0.107560\pi\)
\(660\) −108.764 1714.19i −0.164794 2.59725i
\(661\) 360.203 623.889i 0.544936 0.943857i −0.453675 0.891167i \(-0.649887\pi\)
0.998611 0.0526895i \(-0.0167794\pi\)
\(662\) 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 \(-0.971114\pi\)
0.995885 0.0906240i \(-0.0288861\pi\)
\(674\) 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 0.986534 0.163555i \(-0.0522961\pi\)
−0.634910 + 0.772586i \(0.718963\pi\)
\(678\) −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 0.150442 + 0.988619i \(0.451930\pi\)
−0.931390 + 0.364023i \(0.881403\pi\)
\(684\) −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 0.974004 0.226531i \(-0.0727383\pi\)
−0.683183 + 0.730247i \(0.739405\pi\)
\(692\) −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 \(0.0431870\pi\)
−0.990810 + 0.135260i \(0.956813\pi\)
\(702\) −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 0.979614 0.200891i \(-0.0643836\pi\)
−0.663783 + 0.747925i \(0.731050\pi\)
\(710\) −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 −0.0477467 0.998859i \(-0.515204\pi\)
0.841164 + 0.540780i \(0.181871\pi\)
\(720\) 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 \(0.108749\pi\)
−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
\(730\) −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 −0.679821 0.733378i \(-0.737943\pi\)
0.295213 + 0.955431i \(0.404609\pi\)
\(734\) 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 −0.948580 0.316537i \(-0.897480\pi\)
0.748419 + 0.663226i \(0.230813\pi\)
\(740\) −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 0.995447 + 0.0953188i \(0.0303870\pi\)
−0.415175 + 0.909742i \(0.636280\pi\)
\(752\) −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 \(-0.841501\pi\)
0.878569 0.477615i \(-0.158499\pi\)
\(758\) 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 0.237821 0.971309i \(-0.423567\pi\)
0.960089 + 0.279695i \(0.0902334\pi\)
\(762\) −524.958 + 41.0284i −0.688921 + 0.0538430i
\(763\) 49.4631 + 174.351i 0.0648271 + 0.228507i
\(764\) 2061.85i 2.69876i
\(765\) −19.8249 139.308i −0.0259150 0.182102i