Properties

Label 105.3.o.b.44.20
Level 105
Weight 3
Character 105.44
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 44.20
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.20

$q$-expansion

\(f(q)\) \(=\) \(q+(1.85988 - 3.22141i) q^{2} +(2.47330 - 1.69788i) q^{3} +(-4.91833 - 8.51879i) q^{4} +(0.0731607 + 4.99946i) q^{5} +(-0.869509 - 11.1254i) q^{6} +(4.87678 + 5.02166i) q^{7} -21.7110 q^{8} +(3.23443 - 8.39872i) q^{9} +O(q^{10})\) \(q+(1.85988 - 3.22141i) q^{2} +(2.47330 - 1.69788i) q^{3} +(-4.91833 - 8.51879i) q^{4} +(0.0731607 + 4.99946i) q^{5} +(-0.869509 - 11.1254i) q^{6} +(4.87678 + 5.02166i) q^{7} -21.7110 q^{8} +(3.23443 - 8.39872i) q^{9} +(16.2414 + 9.06274i) q^{10} +(-10.0814 + 5.82052i) q^{11} +(-26.6283 - 12.7188i) q^{12} +9.22710i q^{13} +(25.2471 - 6.37041i) q^{14} +(8.66942 + 12.2410i) q^{15} +(-20.7066 + 35.8648i) q^{16} +(1.56346 + 2.70799i) q^{17} +(-21.0401 - 26.0401i) q^{18} +(5.39398 - 9.34265i) q^{19} +(42.2296 - 25.2122i) q^{20} +(20.5879 + 4.13990i) q^{21} +43.3019i q^{22} +(-2.93334 + 5.08070i) q^{23} +(-53.6978 + 36.8625i) q^{24} +(-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} +(55.5573 - 5.16102i) q^{30} +(-15.7425 - 27.2669i) q^{31} +(33.6016 + 58.1996i) q^{32} +(-15.0519 + 31.5129i) 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} +(15.6665 + 22.8214i) q^{39} +(-1.58839 - 108.543i) q^{40} +22.7035i q^{41} +(51.6274 - 58.6223i) q^{42} +29.1447i q^{43} +(99.1676 + 57.2544i) q^{44} +(42.2257 + 15.5560i) q^{45} +(10.9113 + 18.8990i) q^{46} +(30.0800 - 52.1000i) q^{47} +(9.68046 + 123.862i) q^{48} +(-1.43408 + 48.9790i) q^{49} +(-44.1206 + 81.8613i) q^{50} +(8.46474 + 4.04312i) q^{51} +(78.6037 - 45.3819i) q^{52} +(27.9865 + 48.4740i) q^{53} +(-96.2512 - 28.6815i) q^{54} +(-29.8370 - 49.9760i) q^{55} +(-105.880 - 109.025i) q^{56} +(-2.52173 - 32.2655i) q^{57} +(-123.554 - 71.3342i) q^{58} +(-23.2367 + 13.4157i) q^{59} +(61.6391 - 134.058i) q^{60} +(-19.8501 + 34.3814i) q^{61} -117.117 q^{62} +(57.9491 - 24.7165i) q^{63} +84.3274 q^{64} +(-46.1306 + 0.675061i) q^{65} +(73.5213 + 107.099i) q^{66} +(-86.4356 + 49.9036i) q^{67} +(15.3792 - 26.6376i) q^{68} +(1.37136 + 17.5466i) q^{69} +(33.6957 + 125.756i) q^{70} -62.5979i q^{71} +(-70.2227 + 182.344i) q^{72} +(-37.5802 + 21.6970i) q^{73} +(74.6895 - 43.1220i) q^{74} +(-60.5640 + 44.2380i) 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} +(-60.0769 - 54.3302i) q^{81} +(73.1373 + 42.2259i) q^{82} +93.5855 q^{83} +(-65.9910 - 195.745i) q^{84} +(-13.4241 + 8.01458i) q^{85} +(93.8870 + 54.2057i) q^{86} +(-65.1206 - 94.8613i) q^{87} +(218.878 - 126.369i) q^{88} +(34.2984 + 19.8022i) q^{89} +(128.647 - 107.094i) q^{90} +(-46.3353 + 44.9985i) q^{91} +57.7086 q^{92} +(-85.2318 - 40.7103i) q^{93} +(-111.890 - 193.800i) q^{94} +(47.1029 + 26.2835i) q^{95} +(181.922 + 86.8938i) q^{96} -119.768i q^{97} +(155.114 + 95.7150i) q^{98} +(16.2772 + 103.497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + O(q^{10}) \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + 62q^{10} + 84q^{15} - 116q^{16} - 56q^{19} + 36q^{21} - 12q^{24} - 6q^{25} - 20q^{30} - 444q^{31} + 256q^{34} - 688q^{36} + 168q^{39} + 54q^{40} - 40q^{45} + 304q^{46} + 156q^{49} + 156q^{51} - 140q^{54} - 500q^{55} - 130q^{60} + 288q^{61} + 472q^{64} + 340q^{66} - 272q^{69} + 710q^{70} - 524q^{75} + 400q^{76} - 340q^{79} + 496q^{84} + 896q^{85} + 1356q^{90} - 656q^{91} - 560q^{94} + 472q^{96} - 336q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.85988 3.22141i 0.929941 1.61071i 0.146526 0.989207i \(-0.453191\pi\)
0.783415 0.621499i \(-0.213476\pi\)
\(3\) 2.47330 1.69788i 0.824434 0.565959i
\(4\) −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
\(9\) 3.23443 8.39872i 0.359381 0.933191i
\(10\) 16.2414 + 9.06274i 1.62414 + 0.906274i
\(11\) −10.0814 + 5.82052i −0.916494 + 0.529138i −0.882515 0.470284i \(-0.844151\pi\)
−0.0339793 + 0.999423i \(0.510818\pi\)
\(12\) −26.6283 12.7188i −2.21903 1.05990i
\(13\) 9.22710i 0.709777i 0.934909 + 0.354888i \(0.115481\pi\)
−0.934909 + 0.354888i \(0.884519\pi\)
\(14\) 25.2471 6.37041i 1.80336 0.455029i
\(15\) 8.66942 + 12.2410i 0.577961 + 0.816064i
\(16\) −20.7066 + 35.8648i −1.29416 + 2.24155i
\(17\) 1.56346 + 2.70799i 0.0919682 + 0.159294i 0.908339 0.418234i \(-0.137351\pi\)
−0.816371 + 0.577528i \(0.804018\pi\)
\(18\) −21.0401 26.0401i −1.16889 1.44667i
\(19\) 5.39398 9.34265i 0.283894 0.491719i −0.688447 0.725287i \(-0.741707\pi\)
0.972340 + 0.233569i \(0.0750403\pi\)
\(20\) 42.2296 25.2122i 2.11148 1.26061i
\(21\) 20.5879 + 4.13990i 0.980376 + 0.197138i
\(22\) 43.3019i 1.96827i
\(23\) −2.93334 + 5.08070i −0.127537 + 0.220900i −0.922722 0.385467i \(-0.874040\pi\)
0.795185 + 0.606367i \(0.207374\pi\)
\(24\) −53.6978 + 36.8625i −2.23741 + 1.53594i
\(25\) −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 \(-0.229986\pi\)
\(30\) 55.5573 5.16102i 1.85191 0.172034i
\(31\) −15.7425 27.2669i −0.507824 0.879577i −0.999959 0.00905794i \(-0.997117\pi\)
0.492135 0.870519i \(-0.336217\pi\)
\(32\) 33.6016 + 58.1996i 1.05005 + 1.81874i
\(33\) −15.0519 + 31.5129i −0.456118 + 0.954937i
\(34\) 11.6314 0.342100
\(35\) −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
\(39\) 15.6665 + 22.8214i 0.401704 + 0.585164i
\(40\) −1.58839 108.543i −0.0397097 2.71358i
\(41\) 22.7035i 0.553744i 0.960907 + 0.276872i \(0.0892978\pi\)
−0.960907 + 0.276872i \(0.910702\pi\)
\(42\) 51.6274 58.6223i 1.22922 1.39577i
\(43\) 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
\(45\) 42.2257 + 15.5560i 0.938349 + 0.345688i
\(46\) 10.9113 + 18.8990i 0.237203 + 0.410848i
\(47\) 30.0800 52.1000i 0.639999 1.10851i −0.345433 0.938443i \(-0.612268\pi\)
0.985432 0.170068i \(-0.0543987\pi\)
\(48\) 9.68046 + 123.862i 0.201676 + 2.58045i
\(49\) −1.43408 + 48.9790i −0.0292670 + 0.999572i
\(50\) −44.1206 + 81.8613i −0.882412 + 1.63723i
\(51\) 8.46474 + 4.04312i 0.165975 + 0.0792768i
\(52\) 78.6037 45.3819i 1.51161 0.872728i
\(53\) 27.9865 + 48.4740i 0.528047 + 0.914604i 0.999465 + 0.0326945i \(0.0104088\pi\)
−0.471418 + 0.881910i \(0.656258\pi\)
\(54\) −96.2512 28.6815i −1.78243 0.531139i
\(55\) −29.8370 49.9760i −0.542492 0.908654i
\(56\) −105.880 109.025i −1.89071 1.94688i
\(57\) −2.52173 32.2655i −0.0442408 0.566061i
\(58\) −123.554 71.3342i −2.13025 1.22990i
\(59\) −23.2367 + 13.4157i −0.393843 + 0.227385i −0.683824 0.729647i \(-0.739684\pi\)
0.289981 + 0.957032i \(0.406351\pi\)
\(60\) 61.6391 134.058i 1.02732 2.23430i
\(61\) −19.8501 + 34.3814i −0.325412 + 0.563630i −0.981596 0.190971i \(-0.938836\pi\)
0.656184 + 0.754601i \(0.272170\pi\)
\(62\) −117.117 −1.88899
\(63\) 57.9491 24.7165i 0.919827 0.392325i
\(64\) 84.3274 1.31762
\(65\) −46.1306 + 0.675061i −0.709701 + 0.0103856i
\(66\) 73.5213 + 107.099i 1.11396 + 1.62271i
\(67\) −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 \(-0.854684\pi\)
0.897590 0.440830i \(-0.145316\pi\)
\(72\) −70.2227 + 182.344i −0.975315 + 2.53256i
\(73\) −37.5802 + 21.6970i −0.514798 + 0.297219i −0.734804 0.678280i \(-0.762726\pi\)
0.220006 + 0.975499i \(0.429392\pi\)
\(74\) 74.6895 43.1220i 1.00932 0.582730i
\(75\) −60.5640 + 44.2380i −0.807520 + 0.589840i
\(76\) −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
\(81\) −60.0769 54.3302i −0.741690 0.670743i
\(82\) 73.1373 + 42.2259i 0.891919 + 0.514949i
\(83\) 93.5855 1.12754 0.563768 0.825933i \(-0.309351\pi\)
0.563768 + 0.825933i \(0.309351\pi\)
\(84\) −65.9910 195.745i −0.785607 2.33030i
\(85\) −13.4241 + 8.01458i −0.157931 + 0.0942891i
\(86\) 93.8870 + 54.2057i 1.09171 + 0.630299i
\(87\) −65.1206 94.8613i −0.748512 1.09036i
\(88\) 218.878 126.369i 2.48725 1.43601i
\(89\) 34.2984 + 19.8022i 0.385375 + 0.222496i 0.680154 0.733069i \(-0.261913\pi\)
−0.294779 + 0.955565i \(0.595246\pi\)
\(90\) 128.647 107.094i 1.42941 1.18993i
\(91\) −46.3353 + 44.9985i −0.509179 + 0.494489i
\(92\) 57.7086 0.627267
\(93\) −85.2318 40.7103i −0.916471 0.437745i
\(94\) −111.890 193.800i −1.19032 2.06170i
\(95\) 47.1029 + 26.2835i 0.495820 + 0.276669i
\(96\) 181.922 + 86.8938i 1.89503 + 0.905144i
\(97\) 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 −0.567210 0.823573i \(-0.691977\pi\)
0.429630 + 0.903005i \(0.358644\pi\)
\(102\) 28.7680 19.7487i 0.282039 0.193615i
\(103\) 111.510 + 64.3802i 1.08262 + 0.625051i 0.931602 0.363480i \(-0.118412\pi\)
0.151018 + 0.988531i \(0.451745\pi\)
\(104\) 200.329i 1.92624i
\(105\) −19.1911 + 103.231i −0.182772 + 0.983155i
\(106\) 208.206 1.96421
\(107\) 79.6491 137.956i 0.744384 1.28931i −0.206099 0.978531i \(-0.566077\pi\)
0.950482 0.310779i \(-0.100590\pi\)
\(108\) −192.949 + 182.506i −1.78657 + 1.68987i
\(109\) −12.9451 22.4216i −0.118762 0.205702i 0.800515 0.599313i \(-0.204559\pi\)
−0.919277 + 0.393610i \(0.871226\pi\)
\(110\) −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 \(-0.691060\pi\)
−0.564836 + 0.825203i \(0.691060\pi\)
\(114\) −108.631 51.8865i −0.952900 0.455145i
\(115\) −25.6154 14.2934i −0.222742 0.124291i
\(116\) −326.731 + 188.638i −2.81664 + 1.62619i
\(117\) 77.4958 + 29.8444i 0.662357 + 0.255081i
\(118\) 99.8067i 0.845819i
\(119\) −5.97396 + 21.0574i −0.0502013 + 0.176953i
\(120\) −188.222 265.763i −1.56851 2.21469i
\(121\) 7.25691 12.5693i 0.0599744 0.103879i
\(122\) 73.8378 + 127.891i 0.605228 + 1.04829i
\(123\) 38.5477 + 56.1526i 0.313396 + 0.456525i
\(124\) −154.854 + 268.215i −1.24882 + 2.16302i
\(125\) −5.48548 124.880i −0.0438839 0.999037i
\(126\) 28.1566 232.648i 0.223465 1.84641i
\(127\) 47.1857i 0.371541i 0.982593 + 0.185770i \(0.0594781\pi\)
−0.982593 + 0.185770i \(0.940522\pi\)
\(128\) 22.4328 38.8548i 0.175256 0.303553i
\(129\) 49.4841 + 72.0836i 0.383598 + 0.558788i
\(130\) −83.6228 + 149.861i −0.643252 + 1.15278i
\(131\) 126.778 + 73.1955i 0.967773 + 0.558744i 0.898557 0.438857i \(-0.144617\pi\)
0.0692166 + 0.997602i \(0.477950\pi\)
\(132\) 342.482 26.7669i 2.59456 0.202779i
\(133\) 73.2208 18.4753i 0.550533 0.138912i
\(134\) 371.259i 2.77059i
\(135\) 130.849 33.2194i 0.969252 0.246070i
\(136\) −33.9442 58.7931i −0.249590 0.432302i
\(137\) −82.4265 142.767i −0.601653 1.04209i −0.992571 0.121668i \(-0.961176\pi\)
0.390917 0.920426i \(-0.372158\pi\)
\(138\) 59.0752 + 28.2168i 0.428081 + 0.204470i
\(139\) 251.524 1.80953 0.904763 0.425915i \(-0.140048\pi\)
0.904763 + 0.425915i \(0.140048\pi\)
\(140\) 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
\(144\) 234.244 + 289.911i 1.62670 + 2.01327i
\(145\) 191.750 2.80601i 1.32241 0.0193518i
\(146\) 161.415i 1.10558i
\(147\) 79.6134 + 123.575i 0.541588 + 0.840644i
\(148\) 228.066i 1.54099i
\(149\) −208.574 120.420i −1.39983 0.808189i −0.405451 0.914117i \(-0.632886\pi\)
−0.994374 + 0.105927i \(0.966219\pi\)
\(150\) 29.8669 + 277.379i 0.199113 + 1.84919i
\(151\) −22.6110 39.1633i −0.149741 0.259360i 0.781390 0.624042i \(-0.214511\pi\)
−0.931132 + 0.364683i \(0.881177\pi\)
\(152\) −117.109 + 202.838i −0.770451 + 1.33446i
\(153\) 27.8006 4.37224i 0.181703 0.0285767i
\(154\) −217.447 + 211.174i −1.41200 + 1.37126i
\(155\) 135.168 80.6991i 0.872052 0.520640i
\(156\) 117.358 245.702i 0.752294 1.57502i
\(157\) 1.63878 0.946152i 0.0104381 0.00602645i −0.494772 0.869023i \(-0.664748\pi\)
0.505210 + 0.862996i \(0.331415\pi\)
\(158\) −57.6803 99.9052i −0.365065 0.632311i
\(159\) 151.522 + 72.3732i 0.952968 + 0.455178i
\(160\) −288.509 + 172.248i −1.80318 + 1.07655i
\(161\) −39.8188 + 10.0472i −0.247322 + 0.0624050i
\(162\) −286.756 + 92.4846i −1.77010 + 0.570893i
\(163\) −115.997 66.9711i −0.711640 0.410865i 0.100028 0.994985i \(-0.468107\pi\)
−0.811668 + 0.584119i \(0.801440\pi\)
\(164\) 193.406 111.663i 1.17931 0.680873i
\(165\) −158.649 72.9459i −0.961509 0.442097i
\(166\) 174.058 301.477i 1.04854 1.81613i
\(167\) −23.6454 −0.141589 −0.0707945 0.997491i \(-0.522553\pi\)
−0.0707945 + 0.997491i \(0.522553\pi\)
\(168\) −446.983 89.8813i −2.66061 0.535008i
\(169\) 83.8607 0.496217
\(170\) 0.850961 + 58.1508i 0.00500565 + 0.342063i
\(171\) −61.0198 75.5207i −0.356841 0.441642i
\(172\) 248.278 143.343i 1.44347 0.833390i
\(173\) −32.5846 + 56.4382i −0.188350 + 0.326232i −0.944700 0.327935i \(-0.893647\pi\)
0.756350 + 0.654167i \(0.226981\pi\)
\(174\) −426.704 + 33.3492i −2.45232 + 0.191662i
\(175\) −125.541 121.920i −0.717376 0.696687i
\(176\) 482.092i 2.73916i
\(177\) −34.6931 + 72.6342i −0.196006 + 0.410363i
\(178\) 127.582 73.6595i 0.716752 0.413817i
\(179\) 140.927 81.3643i 0.787302 0.454549i −0.0517096 0.998662i \(-0.516467\pi\)
0.839012 + 0.544113i \(0.183134\pi\)
\(180\) −75.1618 436.221i −0.417565 2.42345i
\(181\) 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
\(186\) −289.666 + 198.850i −1.55734 + 1.06909i
\(187\) −31.5238 18.2003i −0.168577 0.0973278i
\(188\) −591.772 −3.14773
\(189\) 101.360 159.522i 0.536296 0.844030i
\(190\) 172.276 102.854i 0.906715 0.541334i
\(191\) 181.527 + 104.805i 0.950403 + 0.548716i 0.893206 0.449647i \(-0.148450\pi\)
0.0571970 + 0.998363i \(0.481784\pi\)
\(192\) 208.567 143.177i 1.08629 0.745716i
\(193\) −102.657 + 59.2693i −0.531904 + 0.307095i −0.741791 0.670631i \(-0.766023\pi\)
0.209888 + 0.977725i \(0.432690\pi\)
\(194\) −385.823 222.755i −1.98878 1.14822i
\(195\) −112.949 + 79.9936i −0.579223 + 0.410224i
\(196\) 424.295 228.678i 2.16477 1.16672i
\(197\) 159.912 0.811735 0.405868 0.913932i \(-0.366969\pi\)
0.405868 + 0.913932i \(0.366969\pi\)
\(198\) 363.681 + 140.057i 1.83677 + 0.707359i
\(199\) 43.3843 + 75.1437i 0.218011 + 0.377607i 0.954200 0.299170i \(-0.0967097\pi\)
−0.736189 + 0.676776i \(0.763376\pi\)
\(200\) 542.542 15.8822i 2.71271 0.0794110i
\(201\) −129.051 + 270.184i −0.642045 + 1.34420i
\(202\) 59.6846i 0.295468i
\(203\) 192.601 187.045i 0.948775 0.921402i
\(204\) −7.18989 91.9947i −0.0352446 0.450954i
\(205\) −113.505 + 1.66100i −0.553685 + 0.00810246i
\(206\) 414.790 239.479i 2.01355 1.16252i
\(207\) 33.1837 + 41.0695i 0.160308 + 0.198403i
\(208\) −330.928 191.061i −1.59100 0.918564i
\(209\) 125.583i 0.600876i
\(210\) 296.857 + 253.820i 1.41361 + 1.20867i
\(211\) −291.368 −1.38089 −0.690445 0.723385i \(-0.742585\pi\)
−0.690445 + 0.723385i \(0.742585\pi\)
\(212\) 275.293 476.822i 1.29855 2.24916i
\(213\) −106.284 154.823i −0.498984 0.726871i
\(214\) −296.276 513.165i −1.38447 2.39797i
\(215\) −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
\(219\) −56.1085 + 117.470i −0.256203 + 0.536391i
\(220\) −278.986 + 499.974i −1.26812 + 2.27261i
\(221\) −24.9869 + 14.4262i −0.113063 + 0.0652769i
\(222\) 111.514 233.467i 0.502314 1.05165i
\(223\) 317.534i 1.42392i −0.702220 0.711960i \(-0.747808\pi\)
0.702220 0.711960i \(-0.252192\pi\)
\(224\) −128.391 + 452.562i −0.573175 + 2.02037i
\(225\) −74.6823 + 212.244i −0.331921 + 0.943307i
\(226\) −237.419 + 411.222i −1.05053 + 1.81957i
\(227\) 55.2662 + 95.7238i 0.243463 + 0.421691i 0.961698 0.274110i \(-0.0883831\pi\)
−0.718235 + 0.695800i \(0.755050\pi\)
\(228\) −262.460 + 180.174i −1.15114 + 0.790238i
\(229\) −47.1716 + 81.7037i −0.205990 + 0.356785i −0.950448 0.310885i \(-0.899375\pi\)
0.744458 + 0.667669i \(0.232708\pi\)
\(230\) −93.6867 + 55.9336i −0.407333 + 0.243189i
\(231\) −231.652 + 78.0960i −1.00282 + 0.338078i
\(232\) 832.705i 3.58925i
\(233\) −112.336 + 194.572i −0.482131 + 0.835075i −0.999790 0.0205124i \(-0.993470\pi\)
0.517659 + 0.855587i \(0.326804\pi\)
\(234\) 240.274 194.139i 1.02681 0.829652i
\(235\) 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 \(-0.191478\pi\)
\(240\) −618.533 + 57.4589i −2.57722 + 0.239412i
\(241\) 29.4855 + 51.0703i 0.122346 + 0.211910i 0.920693 0.390289i \(-0.127625\pi\)
−0.798346 + 0.602199i \(0.794291\pi\)
\(242\) −26.9940 46.7549i −0.111545 0.193202i
\(243\) −240.834 32.3717i −0.991087 0.133217i
\(244\) 390.517 1.60048
\(245\) −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
\(249\) 231.465 158.897i 0.929579 0.638139i
\(250\) −412.491 214.590i −1.64996 0.858361i
\(251\) 38.0046i 0.151413i 0.997130 + 0.0757064i \(0.0241212\pi\)
−0.997130 + 0.0757064i \(0.975879\pi\)
\(252\) −495.567 372.092i −1.96653 1.47656i
\(253\) 68.2943i 0.269938i
\(254\) 152.004 + 87.7598i 0.598443 + 0.345511i
\(255\) −19.5941 + 42.6150i −0.0768397 + 0.167117i
\(256\) 85.2100 + 147.588i 0.332852 + 0.576516i
\(257\) −213.944 + 370.562i −0.832467 + 1.44188i 0.0636088 + 0.997975i \(0.479739\pi\)
−0.896076 + 0.443901i \(0.853594\pi\)
\(258\) 324.245 25.3416i 1.25677 0.0982231i
\(259\) 39.7068 + 157.365i 0.153308 + 0.607587i
\(260\) 232.636 + 389.656i 0.894753 + 1.49868i
\(261\) −322.125 124.054i −1.23420 0.475302i
\(262\) 471.585 272.270i 1.79994 1.03920i
\(263\) 17.1949 + 29.7824i 0.0653797 + 0.113241i 0.896862 0.442310i \(-0.145841\pi\)
−0.831483 + 0.555551i \(0.812507\pi\)
\(264\) 326.791 684.176i 1.23785 2.59158i
\(265\) −240.297 + 143.464i −0.906780 + 0.541373i
\(266\) 76.6656 270.236i 0.288217 1.01593i
\(267\) 118.452 9.25766i 0.443640 0.0346729i
\(268\) 850.237 + 490.884i 3.17252 + 1.83166i
\(269\) −390.528 + 225.472i −1.45178 + 0.838185i −0.998582 0.0532259i \(-0.983050\pi\)
−0.453196 + 0.891411i \(0.649716\pi\)
\(270\) 136.350 483.303i 0.505001 1.79001i
\(271\) 112.662 195.136i 0.415727 0.720060i −0.579778 0.814775i \(-0.696861\pi\)
0.995504 + 0.0947148i \(0.0301939\pi\)
\(272\) −129.495 −0.476086
\(273\) −38.1993 + 189.966i −0.139924 + 0.695848i
\(274\) −613.214 −2.23801
\(275\) 247.670 152.826i 0.900619 0.555729i
\(276\) 142.731 97.9820i 0.517140 0.355007i
\(277\) −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 \(0.156324\pi\)
−0.881812 + 0.471602i \(0.843676\pi\)
\(282\) −605.787 289.349i −2.14818 1.02606i
\(283\) 182.790 105.534i 0.645901 0.372911i −0.140983 0.990012i \(-0.545026\pi\)
0.786884 + 0.617101i \(0.211693\pi\)
\(284\) −533.258 + 307.877i −1.87767 + 1.08407i
\(285\) 161.126 14.9678i 0.565354 0.0525188i
\(286\) −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
\(291\) −203.352 296.223i −0.698803 1.01795i
\(292\) 369.664 + 213.425i 1.26597 + 0.730909i
\(293\) 241.372 0.823795 0.411898 0.911230i \(-0.364866\pi\)
0.411898 + 0.911230i \(0.364866\pi\)
\(294\) 546.156 26.6330i 1.85768 0.0905883i
\(295\) −68.7715 115.190i −0.233124 0.390473i
\(296\) −435.936 251.688i −1.47276 0.850297i
\(297\) 215.984 + 228.343i 0.727218 + 0.768832i
\(298\) −775.846 + 447.935i −2.60351 + 1.50314i
\(299\) −46.8801 27.0662i −0.156790 0.0905226i
\(300\) 674.728 + 298.355i 2.24909 + 0.994517i
\(301\) −146.355 + 142.132i −0.486228 + 0.472200i
\(302\) −168.215 −0.557003
\(303\) −20.7466 + 43.4354i −0.0684706 + 0.143351i
\(304\) 223.382 + 386.908i 0.734808 + 1.27272i
\(305\) −173.341 96.7246i −0.568331 0.317130i
\(306\) 37.6210 97.6888i 0.122944 0.319245i
\(307\) 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 −0.315944 0.948778i \(-0.602321\pi\)
0.663694 + 0.748004i \(0.268988\pi\)
\(312\) −340.134 495.474i −1.09017 1.58806i
\(313\) −200.253 115.616i −0.639786 0.369380i 0.144746 0.989469i \(-0.453763\pi\)
−0.784532 + 0.620088i \(0.787097\pi\)
\(314\) 7.03893i 0.0224170i
\(315\) 127.809 + 287.906i 0.405742 + 0.913988i
\(316\) −305.063 −0.965388
\(317\) −80.4184 + 139.289i −0.253686 + 0.439397i −0.964538 0.263945i \(-0.914976\pi\)
0.710852 + 0.703342i \(0.248310\pi\)
\(318\) 514.957 353.509i 1.61936 1.11166i
\(319\) 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
\(324\) −167.350 + 778.996i −0.516511 + 2.40431i
\(325\) −6.74989 230.579i −0.0207689 0.709473i
\(326\) −431.483 + 249.117i −1.32357 + 0.764161i
\(327\) −70.0862 33.4761i −0.214331 0.102373i
\(328\) 492.915i 1.50279i
\(329\) 408.322 103.029i 1.24110 0.313158i
\(330\) −530.057 + 375.403i −1.60623 + 1.13758i
\(331\) 229.247 397.068i 0.692590 1.19960i −0.278396 0.960466i \(-0.589803\pi\)
0.970986 0.239135i \(-0.0768640\pi\)
\(332\) −460.284 797.235i −1.38640 2.40131i
\(333\) 162.308 131.143i 0.487411 0.393822i
\(334\) −43.9776 + 76.1714i −0.131669 + 0.228058i
\(335\) −255.815 428.481i −0.763627 1.27905i
\(336\) −574.781 + 652.657i −1.71066 + 1.94243i
\(337\) 170.410i 0.505667i −0.967510 0.252834i \(-0.918637\pi\)
0.967510 0.252834i \(-0.0813625\pi\)
\(338\) 155.971 270.150i 0.461453 0.799259i
\(339\) −315.724 + 216.739i −0.931339 + 0.639347i
\(340\) 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
\(345\) −87.6230 + 8.13978i −0.253980 + 0.0235936i
\(346\) 121.207 + 209.937i 0.350310 + 0.606754i
\(347\) 311.981 + 540.367i 0.899080 + 1.55725i 0.828672 + 0.559735i \(0.189097\pi\)
0.0704086 + 0.997518i \(0.477570\pi\)
\(348\) −487.819 + 1021.31i −1.40178 + 2.93479i
\(349\) −25.5776 −0.0732883 −0.0366442 0.999328i \(-0.511667\pi\)
−0.0366442 + 0.999328i \(0.511667\pi\)
\(350\) −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 \(-0.256721\pi\)
−0.971175 + 0.238367i \(0.923388\pi\)
\(354\) 169.459 + 246.852i 0.478699 + 0.697322i
\(355\) 312.956 4.57971i 0.881566 0.0129006i
\(356\) 389.574i 1.09431i
\(357\) 20.9775 + 62.2244i 0.0587605 + 0.174298i
\(358\) 605.312i 1.69082i
\(359\) −402.581 232.430i −1.12140 0.647438i −0.179639 0.983733i \(-0.557493\pi\)
−0.941757 + 0.336294i \(0.890826\pi\)
\(360\) −916.761 337.735i −2.54656 0.938154i
\(361\) 122.310 + 211.847i 0.338809 + 0.586834i
\(362\) 283.961 491.835i 0.784423 1.35866i
\(363\) −3.39266 43.4091i −0.00934616 0.119584i
\(364\) 611.225 + 173.404i 1.67919 + 0.476384i
\(365\) −111.223 186.294i −0.304719 0.510394i
\(366\) 399.766 + 190.945i 1.09226 + 0.521708i
\(367\) −353.989 + 204.375i −0.964547 + 0.556881i −0.897569 0.440873i \(-0.854669\pi\)
−0.0669775 + 0.997754i \(0.521336\pi\)
\(368\) −121.479 210.408i −0.330106 0.571760i
\(369\) 190.680 + 73.4330i 0.516749 + 0.199005i
\(370\) 221.051 + 370.253i 0.597436 + 1.00068i
\(371\) −106.936 + 376.936i −0.288237 + 1.01600i
\(372\) 72.3953 + 926.299i 0.194611 + 2.49005i
\(373\) 629.997 + 363.729i 1.68900 + 0.975144i 0.955286 + 0.295685i \(0.0955478\pi\)
0.733713 + 0.679459i \(0.237786\pi\)
\(374\) −117.261 + 67.7008i −0.313533 + 0.181018i
\(375\) −225.597 299.551i −0.601593 0.798803i
\(376\) −653.065 + 1131.14i −1.73688 + 3.00836i
\(377\) 353.897 0.938720
\(378\) −325.367 623.214i −0.860759 1.64871i
\(379\) −257.337 −0.678989 −0.339494 0.940608i \(-0.610256\pi\)
−0.339494 + 0.940608i \(0.610256\pi\)
\(380\) −7.76362 530.530i −0.0204306 1.39613i
\(381\) 80.1154 + 116.704i 0.210277 + 0.306311i
\(382\) 675.238 389.849i 1.76764 1.02055i
\(383\) −63.6145 + 110.184i −0.166095 + 0.287685i −0.937044 0.349212i \(-0.886449\pi\)
0.770948 + 0.636898i \(0.219783\pi\)
\(384\) −10.4875 134.188i −0.0273112 0.349447i
\(385\) 105.453 393.553i 0.273905 1.02222i
\(386\) 440.935i 1.14232i
\(387\) 244.778 + 94.2666i 0.632501 + 0.243583i
\(388\) −1020.28 + 589.059i −2.62959 + 1.51819i
\(389\) 92.0153 53.1250i 0.236543 0.136568i −0.377044 0.926195i \(-0.623059\pi\)
0.613587 + 0.789627i \(0.289726\pi\)
\(390\) 47.6212 + 512.632i 0.122106 + 1.31444i
\(391\) −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
\(396\) 801.615 647.695i 2.02428 1.63559i
\(397\) −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
\(399\) 149.728 170.015i 0.375259 0.426103i
\(400\) 491.206 911.383i 1.22801 2.27846i
\(401\) 378.110 + 218.302i 0.942918 + 0.544394i 0.890874 0.454251i \(-0.150093\pi\)
0.0520445 + 0.998645i \(0.483426\pi\)
\(402\) 630.352 + 918.236i 1.56804 + 2.28417i
\(403\) 251.594 145.258i 0.624303 0.360442i
\(404\) 136.686 + 78.9158i 0.338332 + 0.195336i
\(405\) 267.226 304.327i 0.659818 0.751425i
\(406\) −244.332 968.329i −0.601802 2.38505i
\(407\) −269.901 −0.663148
\(408\) −183.778 87.7800i −0.450435 0.215147i
\(409\) −225.188 390.037i −0.550581 0.953635i −0.998233 0.0594267i \(-0.981073\pi\)
0.447651 0.894208i \(-0.352261\pi\)
\(410\) −205.756 + 368.737i −0.501844 + 0.899358i
\(411\) −446.266 213.155i −1.08581 0.518626i
\(412\) 1266.57i 3.07420i
\(413\) −180.689 51.2613i −0.437505 0.124119i
\(414\) 194.019 30.5138i 0.468646 0.0737047i
\(415\) 6.84678 + 467.877i 0.0164983 + 1.12742i
\(416\) −537.014 + 310.045i −1.29090 + 0.745300i
\(417\) 622.095 427.057i 1.49183 1.02412i
\(418\) 404.555 + 233.570i 0.967835 + 0.558780i
\(419\) 694.997i 1.65870i 0.558727 + 0.829352i \(0.311290\pi\)
−0.558727 + 0.829352i \(0.688710\pi\)
\(420\) 973.794 344.240i 2.31856 0.819620i
\(421\) 114.851 0.272805 0.136403 0.990653i \(-0.456446\pi\)
0.136403 + 0.990653i \(0.456446\pi\)
\(422\) −541.910 + 938.615i −1.28415 + 2.22421i
\(423\) −340.282 421.147i −0.804449 0.995620i
\(424\) −607.614 1052.42i −1.43305 2.48212i
\(425\) −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
\(429\) −290.773 138.885i −0.677792 0.323742i
\(430\) −264.131 + 473.351i −0.614257 + 1.10082i
\(431\) 312.237 180.270i 0.724448 0.418260i −0.0919394 0.995765i \(-0.529307\pi\)
0.816388 + 0.577504i \(0.195973\pi\)
\(432\) 1071.59 + 319.318i 2.48053 + 0.739163i
\(433\) 590.764i 1.36435i 0.731188 + 0.682176i \(0.238966\pi\)
−0.731188 + 0.682176i \(0.761034\pi\)
\(434\) −571.154 588.122i −1.31602 1.35512i
\(435\) 469.491 332.508i 1.07929 0.764386i
\(436\) −127.336 + 220.553i −0.292056 + 0.505856i
\(437\) 31.6448 + 54.8104i 0.0724138 + 0.125424i
\(438\) 274.063 + 399.228i 0.625715 + 0.911480i
\(439\) 235.149 407.290i 0.535647 0.927769i −0.463484 0.886105i \(-0.653401\pi\)
0.999132 0.0416635i \(-0.0132657\pi\)
\(440\) 647.791 + 1085.03i 1.47225 + 2.46597i
\(441\) 406.722 + 170.464i 0.922273 + 0.386539i
\(442\) 107.324i 0.242815i
\(443\) 99.6641 172.623i 0.224975 0.389669i −0.731337 0.682017i \(-0.761103\pi\)
0.956312 + 0.292348i \(0.0944365\pi\)
\(444\) −387.228 564.076i −0.872135 1.27044i
\(445\) −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 \(0.844845\pi\)
\(450\) 544.825 + 635.331i 1.21072 + 1.41185i
\(451\) −132.146 228.884i −0.293007 0.507503i
\(452\) 627.838 + 1087.45i 1.38902 + 2.40586i
\(453\) −122.418 58.4721i −0.270239 0.129077i
\(454\) 411.154 0.905626
\(455\) −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
\(459\) 61.3356 58.0158i 0.133629 0.126396i
\(460\) 4.22200 + 288.512i 0.00917825 + 0.627200i
\(461\) 68.9132i 0.149486i 0.997203 + 0.0747432i \(0.0238137\pi\)
−0.997203 + 0.0747432i \(0.976186\pi\)
\(462\) −179.266 + 891.495i −0.388021 + 1.92964i
\(463\) 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
\(465\) 197.294 429.092i 0.424288 0.922778i
\(466\) 417.865 + 723.763i 0.896706 + 1.55314i
\(467\) −67.4292 + 116.791i −0.144388 + 0.250087i −0.929144 0.369717i \(-0.879455\pi\)
0.784756 + 0.619804i \(0.212788\pi\)
\(468\) −126.911 806.955i −0.271178 1.72426i
\(469\) −672.126 190.681i −1.43310 0.406569i
\(470\) 960.710 573.571i 2.04406 1.22036i
\(471\) 2.44675 5.12257i 0.00519481 0.0108759i
\(472\) 504.492 291.268i 1.06884 0.617094i
\(473\) −169.637 293.820i −0.358641 0.621185i
\(474\) −312.287 149.162i −0.658834 0.314687i
\(475\) −127.957 + 237.412i −0.269384 + 0.499815i
\(476\) 208.766 52.6764i 0.438583 0.110665i
\(477\) 497.640 78.2646i 1.04327 0.164077i
\(478\) −871.419 503.114i −1.82305 1.05254i
\(479\) 407.459 235.247i 0.850645 0.491120i −0.0102233 0.999948i \(-0.503254\pi\)
0.860868 + 0.508828i \(0.169921\pi\)
\(480\) −421.113 + 915.872i −0.877319 + 1.90807i
\(481\) −106.967 + 185.272i −0.222384 + 0.385180i
\(482\) 219.358 0.455100
\(483\) −81.4250 + 92.4571i −0.168582 + 0.191423i
\(484\) −142.767 −0.294974
\(485\) 598.777 8.76232i 1.23459 0.0180666i
\(486\) −552.206 + 715.618i −1.13623 + 1.47247i
\(487\) −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 \(-0.725973\pi\)
0.651768 0.758418i \(-0.274027\pi\)
\(492\) 288.762 604.557i 0.586914 1.22877i
\(493\) 103.863 59.9651i 0.210675 0.121633i
\(494\) 320.664 185.136i 0.649118 0.374769i
\(495\) −516.240 + 88.9491i −1.04291 + 0.179695i
\(496\) 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
\(501\) −58.4821 + 40.1469i −0.116731 + 0.0801335i
\(502\) 122.428 + 70.6841i 0.243881 + 0.140805i
\(503\) −924.410 −1.83779 −0.918897 0.394499i \(-0.870918\pi\)
−0.918897 + 0.394499i \(0.870918\pi\)
\(504\) −1258.13 + 536.618i −2.49629 + 1.06472i
\(505\) −41.1255 68.8837i −0.0814366 0.136403i
\(506\) −220.004 127.019i −0.434791 0.251027i
\(507\) 207.413 142.385i 0.409098 0.280838i
\(508\) 401.965 232.075i 0.791269 0.456840i
\(509\) 821.002 + 474.006i 1.61297 + 0.931249i 0.988677 + 0.150059i \(0.0479463\pi\)
0.624293 + 0.781190i \(0.285387\pi\)
\(510\) 100.838 + 142.380i 0.197721 + 0.279176i
\(511\) −292.225 82.9038i −0.571869 0.162238i
\(512\) 813.385 1.58864
\(513\) −279.145 83.1813i −0.544143 0.162147i
\(514\) 795.822 + 1378.40i 1.54829 + 2.68172i
\(515\) −313.709 + 562.200i −0.609143 + 1.09165i
\(516\) 370.686 776.075i 0.718384 1.50402i
\(517\) 700.324i 1.35459i
\(518\) 580.788 + 164.769i 1.12121 + 0.318086i
\(519\) 15.2335 + 194.913i 0.0293517 + 0.375556i
\(520\) 1001.54 14.6562i 1.92604 0.0281850i
\(521\) −511.768 + 295.469i −0.982280 + 0.567120i −0.902958 0.429729i \(-0.858609\pi\)
−0.0793222 + 0.996849i \(0.525276\pi\)
\(522\) −998.744 + 806.973i −1.91330 + 1.54593i
\(523\) −152.158 87.8483i −0.290933 0.167970i 0.347430 0.937706i \(-0.387055\pi\)
−0.638362 + 0.769736i \(0.720388\pi\)
\(524\) 1440.00i 2.74809i
\(525\) −517.505 88.3926i −0.985724 0.168367i
\(526\) 127.922 0.243197
\(527\) 49.2256 85.2613i 0.0934073 0.161786i
\(528\) −818.532 1192.36i −1.55025 2.25825i
\(529\) 247.291 + 428.321i 0.467469 + 0.809680i
\(530\) 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
\(534\) 190.484 398.800i 0.356711 0.746817i
\(535\) 695.534 + 388.110i 1.30006 + 0.725439i
\(536\) 1876.60 1083.46i 3.50112 2.02137i
\(537\) 210.409 440.515i 0.391822 0.820326i
\(538\) 1677.40i 3.11785i
\(539\) −270.626 502.126i −0.502088 0.931588i
\(540\) −926.548 951.291i −1.71583 1.76165i
\(541\) −376.475 + 652.073i −0.695887 + 1.20531i 0.273994 + 0.961731i \(0.411655\pi\)
−0.969881 + 0.243580i \(0.921678\pi\)
\(542\) −419.076 725.861i −0.773203 1.33923i
\(543\) 377.616 259.227i 0.695425 0.477397i
\(544\) −105.069 + 181.985i −0.193142 + 0.334532i
\(545\) 111.149 66.3589i 0.203943 0.121760i
\(546\) 540.914 + 476.371i 0.990685 + 0.872474i
\(547\) 760.168i 1.38970i −0.719153 0.694852i \(-0.755470\pi\)
0.719153 0.694852i \(-0.244530\pi\)
\(548\) −810.801 + 1404.35i −1.47956 + 2.56268i
\(549\) 224.556 + 277.920i 0.409027 + 0.506229i
\(550\) −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
\(555\) 32.1687 + 346.289i 0.0579616 + 0.623944i
\(556\) −1237.08 2142.68i −2.22496 3.85374i
\(557\) −427.707 740.811i −0.767877 1.33000i −0.938712 0.344702i \(-0.887980\pi\)
0.170835 0.985300i \(-0.445353\pi\)
\(558\) −378.807 + 983.633i −0.678866 + 1.76278i
\(559\) −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 \(0.157994\pi\)
−0.0272426 + 0.999629i \(0.508673\pi\)
\(564\) −1463.63 + 1004.76i −2.59509 + 1.78148i
\(565\) −9.33917 638.196i −0.0165295 1.12955i
\(566\) 785.123i 1.38714i
\(567\) −20.1542 566.642i −0.0355453 0.999368i
\(568\) 1359.06i 2.39271i
\(569\) −888.485 512.967i −1.56148 0.901523i −0.997107 0.0760060i \(-0.975783\pi\)
−0.564377 0.825517i \(-0.690883\pi\)
\(570\) 251.457 546.891i 0.441153 0.959457i
\(571\) −190.751 330.391i −0.334065 0.578617i 0.649240 0.760584i \(-0.275087\pi\)
−0.983305 + 0.181966i \(0.941754\pi\)
\(572\) −528.292 + 915.029i −0.923588 + 1.59970i
\(573\) 626.916 48.9969i 1.09409 0.0855095i
\(574\) 144.631 + 573.197i 0.251970 + 0.998600i
\(575\) 69.5855 129.109i 0.121018 0.224537i
\(576\) 272.751 708.242i 0.473527 1.22959i
\(577\) 119.310 68.8835i 0.206776 0.119382i −0.393036 0.919523i \(-0.628575\pi\)
0.599812 + 0.800141i \(0.295242\pi\)
\(578\) −519.321 899.490i −0.898479 1.55621i
\(579\) −153.271 + 320.890i −0.264716 + 0.554215i
\(580\) −966.993 1619.68i −1.66723 2.79255i
\(581\) 456.396 + 469.954i 0.785535 + 0.808872i
\(582\) −1332.47 + 104.139i −2.28946 + 0.178934i
\(583\) −564.288 325.792i −0.967904 0.558820i
\(584\) 815.903 471.062i 1.39709 0.806613i
\(585\) −143.537 + 389.621i −0.245362 + 0.666019i
\(586\) 448.924 777.558i 0.766081 1.32689i
\(587\) 401.054 0.683227 0.341614 0.939840i \(-0.389027\pi\)
0.341614 + 0.939840i \(0.389027\pi\)
\(588\) 661.143 1285.99i 1.12439 2.18706i
\(589\) −339.660 −0.576672
\(590\) −498.980 + 7.30193i −0.845729 + 0.0123761i
\(591\) 395.510 271.510i 0.669222 0.459409i
\(592\) −831.537 + 480.088i −1.40462 + 0.810960i
\(593\) 382.801 663.031i 0.645533 1.11810i −0.338645 0.940914i \(-0.609969\pi\)
0.984178 0.177182i \(-0.0566981\pi\)
\(594\) 1137.29 271.081i 1.91463 0.456366i
\(595\) −105.713 28.3260i −0.177669 0.0476068i
\(596\) 2369.06i 3.97494i
\(597\) 234.887 + 112.192i 0.393446 + 0.187926i
\(598\) −174.383 + 100.680i −0.291610 + 0.168361i
\(599\) 786.962 454.353i 1.31379 0.758519i 0.331071 0.943606i \(-0.392590\pi\)
0.982722 + 0.185087i \(0.0592566\pi\)
\(600\) 1314.90 960.450i 2.19151 1.60075i
\(601\) 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
\(606\) 101.337 + 147.618i 0.167223 + 0.243594i
\(607\) 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
\(609\) 158.782 789.630i 0.260726 1.29660i
\(610\) −633.983 + 378.506i −1.03932 + 0.620502i
\(611\) 480.732 + 277.551i 0.786796 + 0.454257i
\(612\) −173.978 215.323i −0.284278 0.351835i
\(613\) 733.123 423.269i 1.19596 0.690487i 0.236307 0.971678i \(-0.424063\pi\)
0.959652 + 0.281191i \(0.0907295\pi\)
\(614\) 1219.34 + 703.985i 1.98589 + 1.14656i
\(615\) −277.913 + 196.826i −0.451891 + 0.320043i
\(616\) 1702.00 + 482.855i 2.76299 + 0.783855i
\(617\) −689.661 −1.11776 −0.558882 0.829247i \(-0.688770\pi\)
−0.558882 + 0.829247i \(0.688770\pi\)
\(618\) 619.295 1296.57i 1.00210 2.09801i
\(619\) −117.419 203.376i −0.189692 0.328556i 0.755456 0.655200i \(-0.227416\pi\)
−0.945147 + 0.326644i \(0.894082\pi\)
\(620\) −1352.26 754.564i −2.18106 1.21704i
\(621\) 151.804 + 45.2355i 0.244451 + 0.0728430i
\(622\) 464.529i 0.746831i
\(623\) 67.8258 + 268.806i 0.108870 + 0.431470i
\(624\) −1142.88 + 89.3226i −1.83154 + 0.143145i
\(625\) 623.930 36.5608i 0.998288 0.0584972i
\(626\) −744.894 + 430.065i −1.18993 + 0.687004i
\(627\) 213.225 + 310.605i 0.340071 + 0.495383i
\(628\) −16.1201 9.30697i −0.0256690 0.0148200i
\(629\) 72.4986i 0.115260i
\(630\) 1165.17 + 123.747i 1.84948 + 0.196424i
\(631\) 43.4343 0.0688340 0.0344170 0.999408i \(-0.489043\pi\)
0.0344170 + 0.999408i \(0.489043\pi\)
\(632\) −336.660 + 583.112i −0.532689 + 0.922645i
\(633\) −720.640 + 494.706i −1.13845 + 0.781527i
\(634\) 299.138 + 518.122i 0.471826 + 0.817226i
\(635\) −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
\(639\) −525.742 202.469i −0.822758 0.316852i
\(640\) 195.894 + 109.309i 0.306085 + 0.170796i
\(641\) −530.429 + 306.244i −0.827503 + 0.477759i −0.852997 0.521916i \(-0.825217\pi\)
0.0254941 + 0.999675i \(0.491884\pi\)
\(642\) −1604.07 766.171i −2.49855 1.19341i
\(643\) 82.2019i 0.127841i 0.997955 + 0.0639206i \(0.0203604\pi\)
−0.997955 + 0.0639206i \(0.979640\pi\)
\(644\) 281.432 + 289.793i 0.437006 + 0.449988i
\(645\) −356.759 + 252.668i −0.553115 + 0.391733i
\(646\) 62.7396 108.668i 0.0971201 0.168217i
\(647\) −315.390 546.272i −0.487465 0.844315i 0.512431 0.858729i \(-0.328745\pi\)
−0.999896 + 0.0144137i \(0.995412\pi\)
\(648\) 1304.33 + 1179.56i 2.01285 + 1.82031i
\(649\) 156.173 270.500i 0.240636 0.416794i
\(650\) −755.343 407.105i −1.16207 0.626316i
\(651\) −211.223 626.540i −0.324460 0.962427i
\(652\) 1317.54i 2.02077i
\(653\) 155.794 269.843i 0.238581 0.413235i −0.721726 0.692179i \(-0.756651\pi\)
0.960307 + 0.278944i \(0.0899843\pi\)
\(654\) −238.192 + 163.515i −0.364209 + 0.250023i
\(655\) −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 \(-0.107560\pi\)
\(660\) 158.876 + 1710.27i 0.240721 + 2.59132i
\(661\) 360.203 + 623.889i 0.544936 + 0.943857i 0.998611 + 0.0526895i \(0.0167794\pi\)
−0.453675 + 0.891167i \(0.649887\pi\)
\(662\) −852.747 1477.00i −1.28814 2.23112i
\(663\) −37.3062 + 78.1050i −0.0562688 + 0.117805i
\(664\) −2031.83 −3.05999
\(665\) 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
\(669\) −539.134 785.358i −0.805880 1.17393i
\(670\) −1856.10 + 27.1616i −2.77030 + 0.0405397i
\(671\) 462.152i 0.688751i
\(672\) 450.844 + 1337.31i 0.670899 + 1.99005i
\(673\) 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
\(675\) 175.652 + 651.745i 0.260226 + 0.965548i
\(676\) −412.454 714.391i −0.610139 1.05679i
\(677\) −238.050 + 412.314i −0.351624 + 0.609031i −0.986534 0.163555i \(-0.947704\pi\)
0.634910 + 0.772586i \(0.281037\pi\)
\(678\) 110.995 + 1420.18i 0.163710 + 2.09467i
\(679\) 601.435 584.083i 0.885766 0.860210i
\(680\) 291.451 174.004i 0.428604 0.255889i
\(681\) 299.217 + 142.919i 0.439379 + 0.209866i
\(682\) 1180.71 681.682i 1.73124 0.999534i
\(683\) 533.388 + 923.855i 0.780948 + 1.35264i 0.931390 + 0.364023i \(0.118597\pi\)
−0.150442 + 0.988619i \(0.548070\pi\)
\(684\) −343.230 + 891.250i −0.501798 + 1.30300i
\(685\) 707.728 422.533i 1.03318 0.616837i
\(686\) 275.810 + 1245.71i 0.402056 + 1.81591i
\(687\) 22.0531 + 282.169i 0.0321006 + 0.410727i
\(688\) −1045.27 603.486i −1.51929 0.877160i
\(689\) −447.275 + 258.234i −0.649165 + 0.374795i
\(690\) −136.747 + 297.409i −0.198184 + 0.431027i
\(691\) 200.957 348.068i 0.290821 0.503716i −0.683183 0.730247i \(-0.739405\pi\)
0.974004 + 0.226531i \(0.0727383\pi\)
\(692\) 641.047 0.926369
\(693\) −440.347 + 586.471i −0.635422 + 0.846279i
\(694\) 2320.99 3.34437
\(695\) 18.4017 + 1257.49i 0.0264772 + 1.80933i
\(696\) 1413.83 + 2059.53i 2.03137 + 2.95910i
\(697\) −61.4809 + 35.4960i −0.0882079 + 0.0509268i
\(698\) −47.5714 + 82.3960i −0.0681538 + 0.118046i
\(699\) 52.5181 + 671.969i 0.0751332 + 0.961329i
\(700\) −421.162 + 1669.10i −0.601660 + 2.38443i
\(701\) 189.635i 0.270520i 0.990810 + 0.135260i \(0.0431870\pi\)
−0.990810 + 0.135260i \(0.956813\pi\)
\(702\) 264.647 888.119i 0.376990 1.26513i
\(703\) 216.612 125.061i 0.308126 0.177897i
\(704\) −850.141 + 490.829i −1.20759 + 0.697201i
\(705\) 898.530 83.4694i 1.27451 0.118396i
\(706\) −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
\(711\) −175.418 217.104i −0.246720 0.305351i
\(712\) −744.651 429.925i −1.04586 0.603827i
\(713\) 184.713 0.259065
\(714\) 239.466 + 48.1529i 0.335387 + 0.0674410i
\(715\) 461.133 275.309i 0.644941 0.385048i
\(716\) −1386.25 800.352i −1.93610 1.11781i
\(717\) −459.290 669.049i −0.640572 0.933123i
\(718\) −1497.51 + 864.586i −2.08566 + 1.20416i
\(719\) −570.467 329.359i −0.793418 0.458080i 0.0477467 0.998859i \(-0.484796\pi\)
−0.841164 + 0.540780i \(0.818129\pi\)
\(720\) −1432.26 + 1192.31i −1.98925 + 1.65598i
\(721\) 220.513 + 873.932i 0.305844 + 1.21211i
\(722\) 909.928 1.26029
\(723\) 159.638 + 76.2496i 0.220799 + 0.105463i
\(724\) −750.915 1300.62i −1.03718 1.79644i
\(725\) 28.0571 + 958.443i 0.0386995 + 1.32199i
\(726\) −146.148 69.8066i −0.201306 0.0961523i
\(727\) 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
\(732\) 965.867 663.050i 1.31949 0.905806i
\(733\) −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
\(735\) −611.983 + 407.065i −0.832630 + 0.553830i
\(736\) −394.260 −0.535679
\(737\) 580.930 1006.20i 0.788236 1.36526i
\(738\) 591.201 477.683i 0.801085 0.647267i
\(739\) −147.919 256.204i −0.200161 0.346690i 0.748419 0.663226i \(-0.230813\pi\)
−0.948580 + 0.316537i \(0.897480\pi\)
\(740\) 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 \(-0.611382\pi\)
−0.342821 + 0.939401i \(0.611382\pi\)
\(744\) 1850.47 + 883.860i 2.48718 + 1.18798i
\(745\) 586.777 1051.57i 0.787620 1.41150i
\(746\) 2343.44 1352.99i 3.14134 1.81365i
\(747\) 302.696 785.998i 0.405216 1.05221i
\(748\) 358.060i 0.478690i
\(749\) 1081.20 272.811i 1.44352 0.364234i
\(750\) −1384.56 + 169.612i −1.84608 + 0.226149i
\(751\) 435.784 754.800i 0.580272 1.00506i −0.415175 0.909742i \(-0.636280\pi\)
0.995447 0.0953188i \(-0.0303870\pi\)
\(752\) 1245.70 + 2157.62i 1.65652 + 2.86918i
\(753\) 64.5271 + 93.9968i 0.0856934 + 0.124830i
\(754\) 658.207 1140.05i 0.872954 1.51200i
\(755\) 194.141 115.908i 0.257141 0.153520i
\(756\) −1857.45 78.8855i −2.45695 0.104346i
\(757\) 723.110i 0.955231i 0.878569 + 0.477615i \(0.158499\pi\)
−0.878569 + 0.477615i \(0.841501\pi\)
\(758\) −478.616 + 828.987i −0.631420 + 1.09365i
\(759\) −115.955 168.912i −0.152774 0.222546i
\(760\) −1022.65 570.641i −1.34559 0.750843i
\(761\) −911.610 526.318i −1.19791 0.691614i −0.237821 0.971309i \(-0.576433\pi\)
−0.960089 + 0.279695i \(0.909767\pi\)
\(762\) 524.958 41.0284i 0.688921 0.0538430i
\(763\) 49.4631 174.351i 0.0648271 0.228507i
\(764\) 2061.85i 2.69876i
\(765\) 23.8928 + 138.668i 0.0312324 + 0.181265i