Properties

Label 105.3.o.b.74.19
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 74.19
Character \(\chi\) \(=\) 105.74
Dual form 105.3.o.b.44.19

$q$-expansion

\(f(q)\) \(=\) \(q+(1.85988 + 3.22141i) q^{2} +(-2.70705 - 1.29300i) q^{3} +(-4.91833 + 8.51879i) q^{4} +(-4.36624 - 2.43637i) q^{5} +(-0.869509 - 11.1254i) q^{6} +(-4.87678 + 5.02166i) q^{7} -21.7110 q^{8} +(5.65629 + 7.00046i) q^{9} +O(q^{10})\) \(q+(1.85988 + 3.22141i) q^{2} +(-2.70705 - 1.29300i) q^{3} +(-4.91833 + 8.51879i) q^{4} +(-4.36624 - 2.43637i) q^{5} +(-0.869509 - 11.1254i) q^{6} +(-4.87678 + 5.02166i) q^{7} -21.7110 q^{8} +(5.65629 + 7.00046i) q^{9} +(-0.272141 - 18.5968i) q^{10} +(10.0814 + 5.82052i) q^{11} +(24.3290 - 16.7014i) 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} +(-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} +(13.1282 + 21.2756i) q^{25} +(-29.7243 + 17.1613i) q^{26} +(-6.26026 - 26.2642i) q^{27} +(-18.7929 - 66.2424i) q^{28} -38.3541i q^{29} +(-23.3091 + 50.6945i) q^{30} +(-15.7425 + 27.2669i) q^{31} +(33.6016 - 58.1996i) q^{32} +(-19.7650 - 28.7918i) q^{33} +11.6314 q^{34} +(33.5278 - 10.0441i) q^{35} +(-87.4549 + 13.7542i) q^{36} +(-20.0791 + 11.5927i) q^{37} +(-20.0643 + 34.7525i) q^{38} +(11.9307 - 24.9783i) q^{39} +(94.7954 + 52.8960i) q^{40} +22.7035i q^{41} +(60.1082 + 49.8896i) q^{42} +29.1447i q^{43} +(-99.1676 + 57.2544i) q^{44} +(-7.64099 - 44.3465i) 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} +(-146.917 + 13.6479i) q^{60} +(-19.8501 - 34.3814i) q^{61} -117.117 q^{62} +(-62.7384 - 5.73575i) q^{63} +84.3274 q^{64} +(22.4807 - 40.2878i) 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} +(94.7141 + 89.3260i) q^{70} -62.5979i q^{71} +(-122.803 - 151.987i) q^{72} +(37.5802 + 21.6970i) q^{73} +(-74.6895 - 43.1220i) q^{74} +(-8.02925 - 74.5690i) q^{75} -106.117 q^{76} +(-78.3936 + 22.2401i) q^{77} +(102.655 - 8.02304i) q^{78} +(15.5064 + 26.8579i) q^{79} +(3.02981 + 207.043i) q^{80} +(-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} +(128.647 - 107.094i) q^{90} +(-46.3353 - 44.9985i) q^{91} +57.7086 q^{92} +(77.8721 - 53.4578i) q^{93} +(-111.890 + 193.800i) q^{94} +(-0.789255 - 53.9341i) 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 \(0.213476\pi\)
0.146526 + 0.989207i \(0.453191\pi\)
\(3\) −2.70705 1.29300i −0.902351 0.431001i
\(4\) −4.91833 + 8.51879i −1.22958 + 2.12970i
\(5\) −4.36624 2.43637i −0.873249 0.487275i
\(6\) −0.869509 11.1254i −0.144918 1.85423i
\(7\) −4.87678 + 5.02166i −0.696682 + 0.717380i
\(8\) −21.7110 −2.71387
\(9\) 5.65629 + 7.00046i 0.628476 + 0.777829i
\(10\) −0.272141 18.5968i −0.0272141 1.85968i
\(11\) 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 \(0.115481\pi\)
−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 −0.816371 0.577528i \(-0.804018\pi\)
0.908339 + 0.418234i \(0.137351\pi\)
\(18\) −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 0.795185 0.606367i \(-0.207374\pi\)
−0.922722 + 0.385467i \(0.874040\pi\)
\(24\) 58.7728 + 28.0724i 2.44887 + 1.16968i
\(25\) 13.1282 + 21.2756i 0.525127 + 0.851024i
\(26\) −29.7243 + 17.1613i −1.14324 + 0.660051i
\(27\) −6.26026 26.2642i −0.231861 0.972749i
\(28\) −18.7929 66.2424i −0.671174 2.36580i
\(29\) 38.3541i 1.32256i −0.750141 0.661278i \(-0.770014\pi\)
0.750141 0.661278i \(-0.229986\pi\)
\(30\) −23.3091 + 50.6945i −0.776969 + 1.68982i
\(31\) −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
\(35\) 33.5278 10.0441i 0.957938 0.286975i
\(36\) −87.4549 + 13.7542i −2.42930 + 0.382060i
\(37\) −20.0791 + 11.5927i −0.542678 + 0.313315i −0.746164 0.665763i \(-0.768106\pi\)
0.203486 + 0.979078i \(0.434773\pi\)
\(38\) −20.0643 + 34.7525i −0.528009 + 0.914539i
\(39\) 11.9307 24.9783i 0.305915 0.640468i
\(40\) 94.7954 + 52.8960i 2.36988 + 1.32240i
\(41\) 22.7035i 0.553744i 0.960907 + 0.276872i \(0.0892978\pi\)
−0.960907 + 0.276872i \(0.910702\pi\)
\(42\) 60.1082 + 49.8896i 1.43115 + 1.18785i
\(43\) 29.1447i 0.677784i 0.940825 + 0.338892i \(0.110052\pi\)
−0.940825 + 0.338892i \(0.889948\pi\)
\(44\) −99.1676 + 57.2544i −2.25381 + 1.30124i
\(45\) −7.64099 44.3465i −0.169800 0.985479i
\(46\) 10.9113 18.8990i 0.237203 0.410848i
\(47\) 30.0800 + 52.1000i 0.639999 + 1.10851i 0.985432 + 0.170068i \(0.0543987\pi\)
−0.345433 + 0.938443i \(0.612268\pi\)
\(48\) 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 \(-0.656258\pi\)
0.999465 0.0326945i \(-0.0104088\pi\)
\(54\) 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 \(0.593649\pi\)
\(60\) −146.917 + 13.6479i −2.44862 + 0.227466i
\(61\) −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
\(65\) 22.4807 40.2878i 0.345856 0.619812i
\(66\) 55.9895 117.221i 0.848326 1.77607i
\(67\) 86.4356 + 49.9036i 1.29008 + 0.744830i 0.978669 0.205444i \(-0.0658639\pi\)
0.311414 + 0.950274i \(0.399197\pi\)
\(68\) 15.3792 + 26.6376i 0.226165 + 0.391729i
\(69\) 1.37136 + 17.5466i 0.0198748 + 0.254298i
\(70\) 94.7141 + 89.3260i 1.35306 + 1.27609i
\(71\) 62.5979i 0.881661i −0.897590 0.440830i \(-0.854684\pi\)
0.897590 0.440830i \(-0.145316\pi\)
\(72\) −122.803 151.987i −1.70560 2.11093i
\(73\) 37.5802 + 21.6970i 0.514798 + 0.297219i 0.734804 0.678280i \(-0.237274\pi\)
−0.220006 + 0.975499i \(0.570608\pi\)
\(74\) −74.6895 43.1220i −1.00932 0.582730i
\(75\) −8.02925 74.5690i −0.107057 0.994253i
\(76\) −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 \(0.770446\pi\)
\(80\) 3.02981 + 207.043i 0.0378726 + 2.58804i
\(81\) −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 \(-0.309351\pi\)
0.563768 + 0.825933i \(0.309351\pi\)
\(84\) −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 \(0.404754\pi\)
\(90\) 128.647 107.094i 1.42941 1.18993i
\(91\) −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
\(95\) −0.789255 53.9341i −0.00830795 0.567727i
\(96\) −166.214 + 114.103i −1.73139 + 1.18857i
\(97\) 119.768i 1.23472i −0.786679 0.617362i \(-0.788201\pi\)
0.786679 0.617362i \(-0.211799\pi\)
\(98\) 155.114 95.7150i 1.58280 0.976683i
\(99\) 16.2772 + 103.497i 0.164416 + 1.04543i
\(100\) −245.811 + 7.19579i −2.45811 + 0.0719579i
\(101\) 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 −0.931602 0.363480i \(-0.881588\pi\)
−0.151018 + 0.988531i \(0.548255\pi\)
\(104\) 200.329i 1.92624i
\(105\) −103.749 16.1616i −0.988083 0.153920i
\(106\) 208.206 1.96421
\(107\) 79.6491 + 137.956i 0.744384 + 1.28931i 0.950482 + 0.310779i \(0.100590\pi\)
−0.206099 + 0.978531i \(0.566077\pi\)
\(108\) 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 \(0.204559\pi\)
\(110\) 105.500 189.067i 0.959088 1.71879i
\(111\) 69.3445 5.41965i 0.624725 0.0488257i
\(112\) 281.082 + 70.9234i 2.50966 + 0.633245i
\(113\) −127.653 −1.12967 −0.564836 0.825203i \(-0.691060\pi\)
−0.564836 + 0.825203i \(0.691060\pi\)
\(114\) 99.2503 68.1336i 0.870617 0.597663i
\(115\) 0.429211 + 29.3303i 0.00373227 + 0.255046i
\(116\) 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
\(120\) −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
\(123\) 29.3557 61.4596i 0.238664 0.499672i
\(124\) −154.854 268.215i −1.24882 2.16302i
\(125\) −5.48548 124.880i −0.0438839 0.999037i
\(126\) −98.2088 212.774i −0.779435 1.68868i
\(127\) 47.1857i 0.371541i 0.982593 + 0.185770i \(0.0594781\pi\)
−0.982593 + 0.185770i \(0.940522\pi\)
\(128\) 22.4328 + 38.8548i 0.175256 + 0.303553i
\(129\) 37.6842 78.8963i 0.292125 0.611599i
\(130\) 171.595 2.51107i 1.31996 0.0193159i
\(131\) −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
\(135\) −36.6556 + 129.928i −0.271523 + 0.962432i
\(136\) −33.9442 + 58.7931i −0.249590 + 0.432302i
\(137\) −82.4265 + 142.767i −0.601653 + 1.04209i 0.390917 + 0.920426i \(0.372158\pi\)
−0.992571 + 0.121668i \(0.961176\pi\)
\(138\) −53.9741 + 37.0522i −0.391117 + 0.268494i
\(139\) 251.524 1.80953 0.904763 0.425915i \(-0.140048\pi\)
0.904763 + 0.425915i \(0.140048\pi\)
\(140\) −79.3370 + 335.017i −0.566693 + 2.39298i
\(141\) −14.0626 179.931i −0.0997348 1.27611i
\(142\) 201.654 116.425i 1.42010 0.819893i
\(143\) −53.7065 + 93.0224i −0.375570 + 0.650506i
\(144\) 133.948 347.817i 0.930194 2.41540i
\(145\) −93.4450 + 167.463i −0.644448 + 1.15492i
\(146\) 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 \(0.0337811\pi\)
\(150\) 225.284 164.555i 1.50189 1.09703i
\(151\) −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 0.494772 0.869023i \(-0.335252\pi\)
−0.505210 + 0.862996i \(0.668585\pi\)
\(158\) −57.6803 + 99.9052i −0.365065 + 0.632311i
\(159\) −138.438 + 95.0352i −0.870679 + 0.597706i
\(160\) −288.509 + 172.248i −1.80318 + 1.07655i
\(161\) 39.8188 + 10.0472i 0.247322 + 0.0624050i
\(162\) −286.756 + 92.4846i −1.77010 + 0.570893i
\(163\) 115.997 66.9711i 0.711640 0.410865i −0.100028 0.994985i \(-0.531893\pi\)
0.811668 + 0.584119i \(0.198560\pi\)
\(164\) −193.406 111.663i −1.17931 0.680873i
\(165\) 16.1515 + 173.867i 0.0978876 + 1.05374i
\(166\) 174.058 + 301.477i 1.04854 + 1.81613i
\(167\) −23.6454 −0.141589 −0.0707945 0.997491i \(-0.522553\pi\)
−0.0707945 + 0.997491i \(0.522553\pi\)
\(168\) −427.591 + 158.234i −2.54519 + 0.941870i
\(169\) 83.8607 0.496217
\(170\) −50.7855 28.3384i −0.298738 0.166697i
\(171\) −34.8929 + 90.6051i −0.204052 + 0.529854i
\(172\) −248.278 143.343i −1.44347 0.833390i
\(173\) −32.5846 56.4382i −0.188350 0.326232i 0.756350 0.654167i \(-0.226981\pi\)
−0.944700 + 0.327935i \(0.893647\pi\)
\(174\) −426.704 + 33.3492i −2.45232 + 0.191662i
\(175\) −170.862 37.8312i −0.976354 0.216178i
\(176\) 482.092i 2.73916i
\(177\) −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 \(0.816866\pi\)
\(180\) 415.360 + 153.019i 2.30755 + 0.850104i
\(181\) 152.677 0.843519 0.421759 0.906708i \(-0.361413\pi\)
0.421759 + 0.906708i \(0.361413\pi\)
\(182\) 58.7804 232.957i 0.322969 1.27998i
\(183\) 9.28008 + 118.739i 0.0507108 + 0.648845i
\(184\) 63.6857 + 110.307i 0.346118 + 0.599494i
\(185\) 115.914 1.69625i 0.626563 0.00916894i
\(186\) 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 0.741791 0.670631i \(-0.233977\pi\)
−0.209888 + 0.977725i \(0.567310\pi\)
\(194\) 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 \(0.366969\pi\)
\(198\) −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 \(0.0967097\pi\)
\(200\) −285.025 461.914i −1.42513 2.30957i
\(201\) −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
\(205\) 55.3142 99.1290i 0.269825 0.483556i
\(206\) −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
\(210\) −140.897 364.276i −0.670940 1.73465i
\(211\) −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
\(215\) 71.0074 127.253i 0.330267 0.591874i
\(216\) 135.916 + 570.222i 0.629242 + 2.63992i
\(217\) −60.1521 212.028i −0.277198 0.977088i
\(218\) −96.3055 −0.441768
\(219\) −73.6775 107.326i −0.336427 0.490074i
\(220\) 572.483 8.37755i 2.60220 0.0380798i
\(221\) 24.9869 + 14.4262i 0.113063 + 0.0652769i
\(222\) 146.432 + 213.307i 0.659602 + 0.960844i
\(223\) 317.534i 1.42392i −0.702220 0.711960i \(-0.747808\pi\)
0.702220 0.711960i \(-0.252192\pi\)
\(224\) 128.391 + 452.562i 0.573175 + 2.02037i
\(225\) −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 −0.718235 0.695800i \(-0.755050\pi\)
0.961698 + 0.274110i \(0.0883831\pi\)
\(228\) 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 0.517659 0.855587i \(-0.326804\pi\)
−0.999790 + 0.0205124i \(0.993470\pi\)
\(234\) −288.266 111.014i −1.23191 0.474420i
\(235\) −4.40134 300.767i −0.0187291 1.27986i
\(236\) −228.571 + 131.966i −0.968523 + 0.559177i
\(237\) −7.24937 92.7557i −0.0305881 0.391374i
\(238\) −56.7238 + 58.4089i −0.238335 + 0.245416i
\(239\) 270.509i 1.13184i −0.824462 0.565918i \(-0.808522\pi\)
0.824462 0.565918i \(-0.191478\pi\)
\(240\) 259.506 564.395i 1.08127 2.35165i
\(241\) 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
\(245\) −113.070 + 217.348i −0.461509 + 0.887136i
\(246\) 252.585 19.7409i 1.02677 0.0802475i
\(247\) −86.2056 + 49.7708i −0.349010 + 0.201501i
\(248\) 341.786 591.990i 1.37817 2.38706i
\(249\) −253.341 121.006i −1.01743 0.485969i
\(250\) 392.086 249.932i 1.56834 0.999729i
\(251\) 38.0046i 0.151413i 0.997130 + 0.0757064i \(0.0241212\pi\)
−0.997130 + 0.0757064i \(0.975879\pi\)
\(252\) 357.429 506.245i 1.41837 2.00891i
\(253\) 68.2943i 0.269938i
\(254\) −152.004 + 87.7598i −0.598443 + 0.345511i
\(255\) 46.7027 4.33847i 0.183148 0.0170136i
\(256\) 85.2100 147.588i 0.332852 0.576516i
\(257\) −213.944 370.562i −0.832467 1.44188i −0.896076 0.443901i \(-0.853594\pi\)
0.0636088 0.997975i \(-0.479739\pi\)
\(258\) 324.245 25.3416i 1.25677 0.0982231i
\(259\) 39.7068 157.365i 0.153308 0.607587i
\(260\) 232.636 + 389.656i 0.894753 + 1.49868i
\(261\) 268.496 216.942i 1.02872 0.831195i
\(262\) −471.585 272.270i −1.79994 1.03920i
\(263\) 17.1949 29.7824i 0.0653797 0.113241i −0.831483 0.555551i \(-0.812507\pi\)
0.896862 + 0.442310i \(0.145841\pi\)
\(264\) 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 \(0.350284\pi\)
\(270\) −486.728 + 123.569i −1.80269 + 0.457661i
\(271\) 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
\(275\) 8.51575 + 290.901i 0.0309664 + 1.05782i
\(276\) −156.220 74.6173i −0.566015 0.270353i
\(277\) 227.641 + 131.429i 0.821810 + 0.474472i 0.851040 0.525101i \(-0.175972\pi\)
−0.0292305 + 0.999573i \(0.509306\pi\)
\(278\) 467.805 + 810.263i 1.68275 + 2.91461i
\(279\) −279.925 + 44.0243i −1.00332 + 0.157793i
\(280\) −727.922 + 218.068i −2.59972 + 0.778814i
\(281\) 265.040i 0.943204i 0.881812 + 0.471602i \(0.156324\pi\)
−0.881812 + 0.471602i \(0.843676\pi\)
\(282\) 553.477 379.952i 1.96269 1.34735i
\(283\) −182.790 105.534i −0.645901 0.372911i 0.140983 0.990012i \(-0.454974\pi\)
−0.786884 + 0.617101i \(0.788307\pi\)
\(284\) 533.258 + 307.877i 1.87767 + 1.08407i
\(285\) −67.6003 + 147.023i −0.237194 + 0.515870i
\(286\) −399.551 −1.39703
\(287\) −114.009 110.720i −0.397245 0.385784i
\(288\) 597.484 93.9673i 2.07460 0.326275i
\(289\) 139.611 + 241.814i 0.483084 + 0.836726i
\(290\) −713.265 + 10.4377i −2.45954 + 0.0359921i
\(291\) −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 \(-0.364866\pi\)
0.411898 + 0.911230i \(0.364866\pi\)
\(294\) −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
\(300\) 674.728 + 298.355i 2.24909 + 0.994517i
\(301\) −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
\(305\) 2.90450 + 198.480i 0.00952294 + 0.650754i
\(306\) 65.7905 + 81.4252i 0.215002 + 0.266095i
\(307\) 378.511i 1.23293i 0.787381 + 0.616467i \(0.211437\pi\)
−0.787381 + 0.616467i \(0.788563\pi\)
\(308\) 196.106 777.203i 0.636708 2.52339i
\(309\) 385.107 30.0982i 1.24630 0.0974053i
\(310\) 511.362 + 285.341i 1.64955 + 0.920455i
\(311\) −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 −0.144746 0.989469i \(-0.546237\pi\)
0.784532 + 0.620088i \(0.212903\pi\)
\(314\) 7.03893i 0.0224170i
\(315\) 259.957 + 177.898i 0.825259 + 0.564755i
\(316\) −305.063 −0.965388
\(317\) −80.4184 139.289i −0.253686 0.439397i 0.710852 0.703342i \(-0.248310\pi\)
−0.964538 + 0.263945i \(0.914976\pi\)
\(318\) −563.626 269.211i −1.77241 0.846577i
\(319\) 223.241 386.665i 0.699815 1.21211i
\(320\) −368.194 205.453i −1.15061 0.642041i
\(321\) −37.2365 476.441i −0.116002 1.48424i
\(322\) 41.6921 + 146.959i 0.129479 + 0.456395i
\(323\) 33.7331 0.104437
\(324\) −590.955 534.427i −1.82394 1.64947i
\(325\) −196.312 + 121.135i −0.604037 + 0.372723i
\(326\) 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
\(330\) −530.057 + 375.403i −1.60623 + 1.13758i
\(331\) 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 \(-0.918637\pi\)
0.967510 0.252834i \(-0.0813625\pi\)
\(338\) 155.971 + 270.150i 0.461453 + 0.799259i
\(339\) 345.563 + 165.056i 1.01936 + 0.486889i
\(340\) −2.25031 153.776i −0.00661855 0.452281i
\(341\) −317.415 + 183.260i −0.930835 + 0.537418i
\(342\) −356.773 + 56.1103i −1.04320 + 0.164065i
\(343\) 252.950 + 231.658i 0.737462 + 0.675388i
\(344\) 632.760i 1.83942i
\(345\) 36.7623 79.9537i 0.106557 0.231750i
\(346\) 121.207 209.937i 0.350310 0.606754i
\(347\) 311.981 540.367i 0.899080 1.55725i 0.0704086 0.997518i \(-0.477570\pi\)
0.828672 0.559735i \(-0.189097\pi\)
\(348\) −640.568 933.117i −1.84071 2.68137i
\(349\) −25.5776 −0.0732883 −0.0366442 0.999328i \(-0.511667\pi\)
−0.0366442 + 0.999328i \(0.511667\pi\)
\(350\) −195.913 620.778i −0.559752 1.77365i
\(351\) 242.343 57.7640i 0.690435 0.164570i
\(352\) 677.504 391.157i 1.92473 1.11124i
\(353\) −98.5420 + 170.680i −0.279156 + 0.483512i −0.971175 0.238367i \(-0.923388\pi\)
0.692019 + 0.721879i \(0.256721\pi\)
\(354\) 129.050 270.182i 0.364549 0.763226i
\(355\) −152.512 + 273.318i −0.429611 + 0.769909i
\(356\) 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 \(0.109174\pi\)
\(360\) 165.893 + 962.806i 0.460815 + 2.67446i
\(361\) 122.310 211.847i 0.338809 0.586834i
\(362\) 283.961 + 491.835i 0.784423 + 1.35866i
\(363\) −3.39266 43.4091i −0.00934616 0.119584i
\(364\) 611.225 173.404i 1.67919 0.476384i
\(365\) −111.223 186.294i −0.304719 0.510394i
\(366\) −365.246 + 250.735i −0.997940 + 0.685068i
\(367\) 353.989 + 204.375i 0.964547 + 0.556881i 0.897569 0.440873i \(-0.145331\pi\)
0.0669775 + 0.997754i \(0.478664\pi\)
\(368\) −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 \(0.762214\pi\)
−0.955286 + 0.295685i \(0.904452\pi\)
\(374\) 117.261 + 67.7008i 0.313533 + 0.181018i
\(375\) −146.620 + 345.149i −0.390987 + 0.920396i
\(376\) −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 \(0.610256\pi\)
\(380\) 463.335 + 258.542i 1.21930 + 0.680373i
\(381\) 61.0112 127.734i 0.160134 0.335260i
\(382\) −675.238 389.849i −1.76764 1.02055i
\(383\) −63.6145 110.184i −0.166095 0.287685i 0.770948 0.636898i \(-0.219783\pi\)
−0.937044 + 0.349212i \(0.886449\pi\)
\(384\) −10.4875 134.188i −0.0273112 0.349447i
\(385\) 396.471 + 93.8902i 1.02979 + 0.243871i
\(386\) 440.935i 1.14232i
\(387\) −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 \(0.710274\pi\)
\(390\) −467.763 215.075i −1.19939 0.551474i
\(391\) −18.3447 −0.0469173
\(392\) 31.1353 + 1063.38i 0.0794269 + 2.71271i
\(393\) 437.838 34.2194i 1.11409 0.0870723i
\(394\) 297.417 + 515.142i 0.754866 + 1.30747i
\(395\) −2.26892 155.048i −0.00574411 0.392526i
\(396\) −961.727 370.371i −2.42860 0.935281i
\(397\) 116.882 67.4818i 0.294413 0.169979i −0.345517 0.938412i \(-0.612297\pi\)
0.639930 + 0.768433i \(0.278963\pi\)
\(398\) 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
\(405\) 267.226 304.327i 0.659818 0.751425i
\(406\) −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 \(0.981073\pi\)
\(410\) 422.213 6.17854i 1.02979 0.0150696i
\(411\) 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
\(415\) −408.617 228.009i −0.984620 0.549420i
\(416\) 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 \(0.688710\pi\)
\(420\) 647.947 804.326i 1.54273 1.91506i
\(421\) 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
\(425\) 78.1395 2.28743i 0.183858 0.00538219i
\(426\) −696.425 + 54.4294i −1.63480 + 0.127769i
\(427\) 269.456 + 67.9900i 0.631045 + 0.159227i
\(428\) −1566.96 −3.66112
\(429\) 265.665 182.374i 0.619265 0.425114i
\(430\) 541.999 7.93145i 1.26046 0.0184452i
\(431\) −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 \(0.238966\pi\)
−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
\(438\) 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 0.956312 0.292348i \(-0.0944365\pi\)
−0.731337 + 0.682017i \(0.761103\pi\)
\(444\) −294.890 + 617.387i −0.664167 + 1.39051i
\(445\) 198.001 2.89748i 0.444945 0.00651120i
\(446\) 1022.91 590.576i 2.29352 1.32416i
\(447\) −720.325 + 56.2973i −1.61146 + 0.125945i
\(448\) −411.246 + 423.463i −0.917960 + 0.945231i
\(449\) 420.588i 0.936722i 0.883537 + 0.468361i \(0.155155\pi\)
−0.883537 + 0.468361i \(0.844845\pi\)
\(450\) −822.626 + 154.167i −1.82806 + 0.342593i
\(451\) −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
\(455\) 92.6782 + 309.365i 0.203688 + 0.679922i
\(456\) 54.7491 + 700.515i 0.120064 + 1.53622i
\(457\) 433.751 250.426i 0.949127 0.547979i 0.0563173 0.998413i \(-0.482064\pi\)
0.892810 + 0.450434i \(0.148731\pi\)
\(458\) 175.467 303.918i 0.383117 0.663577i
\(459\) −80.9109 24.1103i −0.176277 0.0525279i
\(460\) −251.970 140.600i −0.547760 0.305651i
\(461\) 68.9132i 0.149486i 0.997203 + 0.0747432i \(0.0238137\pi\)
−0.997203 + 0.0747432i \(0.976186\pi\)
\(462\) 315.594 + 852.819i 0.683103 + 1.84593i
\(463\) 72.6957i 0.157010i 0.996914 + 0.0785051i \(0.0250147\pi\)
−0.996914 + 0.0785051i \(0.974985\pi\)
\(464\) −1375.56 + 794.182i −2.96458 + 1.71160i
\(465\) −470.252 + 43.6842i −1.01129 + 0.0939446i
\(466\) 417.865 723.763i 0.896706 1.55314i
\(467\) −67.4292 116.791i −0.144388 0.250087i 0.784756 0.619804i \(-0.212788\pi\)
−0.929144 + 0.369717i \(0.879455\pi\)
\(468\) −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 \(0.830079\pi\)
\(480\) 1003.73 93.2415i 2.09109 0.194253i
\(481\) −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
\(485\) −291.800 + 522.937i −0.601650 + 1.07822i
\(486\) 895.846 + 120.415i 1.84331 + 0.247768i
\(487\) 173.689 + 100.280i 0.356651 + 0.205913i 0.667611 0.744510i \(-0.267317\pi\)
−0.310959 + 0.950423i \(0.600650\pi\)
\(488\) 430.965 + 746.454i 0.883126 + 1.52962i
\(489\) −400.605 + 31.3095i −0.819232 + 0.0640275i
\(490\) −910.464 + 39.9986i −1.85809 + 0.0816298i
\(491\) 744.767i 1.51684i −0.651768 0.758418i \(-0.725973\pi\)
0.651768 0.758418i \(-0.274027\pi\)
\(492\) 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
\(495\) 181.088 491.551i 0.365834 0.993033i
\(496\) 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 \(-0.347328\pi\)
\(500\) 1090.80 + 567.469i 2.18160 + 1.13494i
\(501\) 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 \(-0.870918\pi\)
−0.918897 + 0.394499i \(0.870918\pi\)
\(504\) 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 \(0.952054\pi\)
\(510\) 100.838 + 142.380i 0.197721 + 0.279176i
\(511\) −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
\(515\) 643.734 9.42020i 1.24997 0.0182917i
\(516\) 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
\(520\) −488.077 + 874.686i −0.938609 + 1.68209i
\(521\) 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 −0.347430 0.937706i \(-0.612945\pi\)
0.638362 + 0.769736i \(0.279612\pi\)
\(524\) 1440.00i 2.74809i
\(525\) 413.617 + 323.336i 0.787841 + 0.615878i
\(526\) 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
\(530\) −909.080 507.268i −1.71524 0.957110i
\(531\) 37.5173 + 238.551i 0.0706540 + 0.449248i
\(532\) 517.511 532.885i 0.972765 1.00166i
\(533\) −209.487 −0.393035
\(534\) 250.129 + 364.364i 0.468407 + 0.682330i
\(535\) −11.6544 796.405i −0.0217838 1.48861i
\(536\) −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
\(540\) −926.548 951.291i −1.71583 1.76165i
\(541\) −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 \(-0.755470\pi\)
0.719153 0.694852i \(-0.244530\pi\)
\(548\) −810.801 1404.35i −1.47956 2.56268i
\(549\) 128.408 333.431i 0.233894 0.607343i
\(550\) −921.275 + 568.475i −1.67504 + 1.03359i
\(551\) 358.329 206.881i 0.650325 0.375465i
\(552\) −29.7735 380.953i −0.0539376 0.690132i
\(553\) −210.493 53.1121i −0.380638 0.0960437i
\(554\) 977.768i 1.76492i
\(555\) −315.979 145.286i −0.569332 0.261776i
\(556\) −1237.08 + 2142.68i −2.22496 + 3.85374i
\(557\) −427.707 + 740.811i −0.767877 + 1.33000i 0.170835 + 0.985300i \(0.445353\pi\)
−0.938712 + 0.344702i \(0.887980\pi\)
\(558\) −662.448 819.873i −1.18718 1.46931i
\(559\) −268.921 −0.481075
\(560\) −1054.48 994.490i −1.88299 1.77587i
\(561\) −108.870 + 8.50877i −0.194064 + 0.0151671i
\(562\) −853.804 + 492.944i −1.51922 + 0.877124i
\(563\) 479.723 830.904i 0.852083 1.47585i −0.0272426 0.999629i \(-0.508673\pi\)
0.879325 0.476222i \(-0.157994\pi\)
\(564\) 1601.96 + 765.163i 2.84035 + 1.35667i
\(565\) 557.363 + 311.010i 0.986484 + 0.550460i
\(566\) 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 \(-0.0242168\pi\)
\(570\) −599.350 + 55.6769i −1.05149 + 0.0976787i
\(571\) −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 0.393036 0.919523i \(-0.371425\pi\)
−0.599812 + 0.800141i \(0.704758\pi\)
\(578\) −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
\(585\) 409.190 70.5042i 0.699470 0.120520i
\(586\) 448.924 + 777.558i 0.766081 + 1.32689i
\(587\) 401.054 0.683227 0.341614 0.939840i \(-0.389027\pi\)
0.341614 + 0.939840i \(0.389027\pi\)
\(588\) −852.909 1167.66i −1.45052 1.98581i
\(589\) −339.660 −0.576672
\(590\) 243.166 435.780i 0.412146 0.738611i
\(591\) −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 \(0.0566981\pi\)
−0.338645 + 0.940914i \(0.609969\pi\)
\(594\) 1137.29 271.081i 1.91463 0.456366i
\(595\) 25.2200 106.497i 0.0423865 0.178986i
\(596\) 2369.06i 3.97494i
\(597\) −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 \(0.940743\pi\)
\(600\) 174.323 + 1618.96i 0.290538 + 2.69827i
\(601\) 614.095 1.02179 0.510894 0.859644i \(-0.329314\pi\)
0.510894 + 0.859644i \(0.329314\pi\)
\(602\) 185.664 735.818i 0.308412 1.22229i
\(603\) 139.556 + 887.358i 0.231436 + 1.47157i
\(604\) −222.416 385.236i −0.368239 0.637808i
\(605\) −1.06184 72.5613i −0.00175511 0.119936i
\(606\) 77.1724 161.569i 0.127347 0.266616i
\(607\) −253.578 + 146.403i −0.417756 + 0.241191i −0.694117 0.719862i \(-0.744205\pi\)
0.276361 + 0.961054i \(0.410872\pi\)
\(608\) 724.985 1.19241
\(609\) −279.533 755.374i −0.459003 1.24035i
\(610\) −633.983 + 378.506i −1.03932 + 0.620502i
\(611\) −480.732 + 277.551i −0.786796 + 0.454257i
\(612\) −99.4860 + 258.331i −0.162559 + 0.422110i
\(613\) −733.123 423.269i −1.19596 0.690487i −0.236307 0.971678i \(-0.575937\pi\)
−0.959652 + 0.281191i \(0.909270\pi\)
\(614\) −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 \(0.688770\pi\)
\(618\) 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 \(0.227416\pi\)
\(620\) 22.6584 + 1548.37i 0.0365459 + 2.49738i
\(621\) −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
\(625\) −280.302 + 558.619i −0.448484 + 0.893791i
\(626\) 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
\(630\) −89.5932 + 1168.30i −0.142211 + 1.85444i
\(631\) 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
\(635\) 114.962 206.024i 0.181042 0.324448i
\(636\) −128.702 1646.74i −0.202361 2.58921i
\(637\) 451.934 13.2324i 0.709473 0.0207730i
\(638\) 1660.81 2.60315
\(639\) 438.214 354.072i 0.685781 0.554103i
\(640\) −3.28240 224.304i −0.00512875 0.350475i
\(641\) 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 \(0.0203604\pi\)
−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 −0.999896 0.0144137i \(-0.995412\pi\)
0.512431 + 0.858729i \(0.328745\pi\)
\(648\) 369.366 1719.36i 0.570009 2.65334i
\(649\) 156.173 + 270.500i 0.240636 + 0.416794i
\(650\) −755.343 407.105i −1.16207 0.626316i
\(651\) −111.318 + 651.749i −0.170996 + 1.00115i
\(652\) 1317.54i 2.02077i
\(653\) 155.794 + 269.843i 0.238581 + 0.413235i 0.960307 0.278944i \(-0.0899843\pi\)
−0.721726 + 0.692179i \(0.756651\pi\)
\(654\) 260.704 + 124.523i 0.398630 + 0.190403i
\(655\) 731.876 10.7101i 1.11737 0.0163512i
\(656\) 814.257 470.111i 1.24124 0.716633i
\(657\) 60.6759 + 385.803i 0.0923529 + 0.587219i
\(658\) −427.532 1506.99i −0.649745 2.29026i
\(659\) 436.936i 0.663029i −0.943450 0.331515i \(-0.892440\pi\)
0.943450 0.331515i \(-0.107560\pi\)
\(660\) −1560.57 717.544i −2.36451 1.08719i
\(661\) 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
\(665\) 274.687 + 259.061i 0.413064 + 0.389565i
\(666\) −120.591 766.771i −0.181068 1.15131i
\(667\) −194.866 + 112.506i −0.292153 + 0.168674i
\(668\) 116.296 201.430i 0.174095 0.301542i
\(669\) −410.573 + 859.583i −0.613711 + 1.28488i
\(670\) 904.526 1621.01i 1.35004 2.41942i
\(671\) 462.152i 0.688751i
\(672\) 237.602 1391.12i 0.353575 2.07012i
\(673\) 121.980i 0.181248i 0.995885 + 0.0906240i \(0.0288861\pi\)
−0.995885 + 0.0906240i \(0.971114\pi\)
\(674\) 548.960 316.942i 0.814481 0.470241i
\(675\) 476.601 477.992i 0.706076 0.708136i
\(676\) −412.454 + 714.391i −0.610139 + 1.05679i
\(677\) −238.050 412.314i −0.351624 0.609031i 0.634910 0.772586i \(-0.281037\pi\)
−0.986534 + 0.163555i \(0.947704\pi\)
\(678\) 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 \(-0.548070\pi\)
0.931390 0.364023i \(-0.118597\pi\)
\(684\) −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
\(690\) 325.937 30.2781i 0.472373 0.0438813i
\(691\) 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
\(695\) −1098.22 612.807i −1.58017 0.881736i
\(696\) 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
\(700\) 1162.63 1269.47i 1.66090 1.81353i
\(701\) 189.635i 0.270520i 0.990810 + 0.135260i \(0.0431870\pi\)
−0.990810 + 0.135260i \(0.956813\pi\)
\(702\) 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
\(705\) −376.979 + 819.885i −0.534721 + 1.16296i
\(706\) −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 \(0.731050\pi\)
\(710\) −1164.12 + 17.0354i −1.63961 + 0.0239936i
\(711\) −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 \(0.181871\pi\)
\(720\) −1432.26 + 1192.31i −1.98925 + 1.65598i
\(721\) 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
\(725\) 816.007 503.519i 1.12553 0.694510i
\(726\) 133.528 91.6649i 0.183924 0.126260i
\(727\) 487.145i 0.670075i −0.942205 0.335038i \(-0.891251\pi\)
0.942205 0.335038i \(-0.108749\pi\)
\(728\) 1005.98 + 976.961i 1.38185 + 1.34198i
\(729\) −650.618 + 328.842i −0.892481 + 0.451086i
\(730\) 393.268 704.778i 0.538723 0.965449i
\(731\) 78.9236 + 45.5665i 0.107967 + 0.0623345i
\(732\) −1057.15 504.940i −1.44420 0.689809i
\(733\) 281.918 162.765i 0.384608 0.222054i −0.295213 0.955431i \(-0.595391\pi\)
0.679821 + 0.733378i \(0.262057\pi\)
\(734\) 1520.46i 2.07147i
\(735\) 587.118 442.174i 0.798799 0.601598i
\(736\) −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 \(0.230813\pi\)
\(740\) −555.654 + 995.792i −0.750884 + 1.34566i
\(741\) 297.717 23.2682i 0.401777 0.0314011i
\(742\) −1015.38 + 1045.54i −1.36843 + 1.40908i
\(743\) −509.432 −0.685642 −0.342821 0.939401i \(-0.611382\pi\)
−0.342821 + 0.939401i \(0.611382\pi\)
\(744\) −1690.68 + 1160.62i −2.27242 + 1.55997i
\(745\) −1204.07 + 17.6200i −1.61621 + 0.0236511i
\(746\) −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
\(750\) −1384.56 + 169.612i −1.84608 + 0.226149i
\(751\) 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 \(0.158499\pi\)
−0.878569 + 0.477615i \(0.841501\pi\)
\(758\) −478.616 828.987i −0.631420 1.09365i
\(759\) −88.3048 + 184.876i −0.116344 + 0.243579i
\(760\) 17.1355 + 1170.96i 0.0225467 + 1.54074i
\(761\) 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
\(765\) −132.036 48.6423i −0.172597 0.0635847i