Properties

Label 57.3.g.b.31.3
Level $57$
Weight $3$
Character 57.31
Analytic conductor $1.553$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 57.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.55313750685\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.92607408.1
Defining polynomial: \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.3
Root \(0.500000 - 2.69511i\) of defining polynomial
Character \(\chi\) \(=\) 57.31
Dual form 57.3.g.b.46.3

$q$-expansion

\(f(q)\) \(=\) \(q+(3.08403 - 1.78057i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(4.34085 - 7.51857i) q^{4} +(2.32722 + 4.03087i) q^{5} +(-3.08403 + 5.34170i) q^{6} -10.6817 q^{7} -16.6722i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(3.08403 - 1.78057i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(4.34085 - 7.51857i) q^{4} +(2.32722 + 4.03087i) q^{5} +(-3.08403 + 5.34170i) q^{6} -10.6817 q^{7} -16.6722i q^{8} +(1.50000 - 2.59808i) q^{9} +(14.3545 + 8.28756i) q^{10} -6.37280 q^{11} +15.0371i q^{12} +(15.3770 + 8.87792i) q^{13} +(-32.9427 + 19.0195i) q^{14} +(-6.98167 - 4.03087i) q^{15} +(-12.3225 - 21.3432i) q^{16} +(-5.84976 - 10.1321i) q^{17} -10.6834i q^{18} +(-3.88643 + 18.5983i) q^{19} +40.4085 q^{20} +(16.0225 - 9.25062i) q^{21} +(-19.6539 + 11.3472i) q^{22} +(13.9817 - 24.2170i) q^{23} +(14.4385 + 25.0082i) q^{24} +(1.66807 - 2.88918i) q^{25} +63.2310 q^{26} +5.19615i q^{27} +(-46.3676 + 80.3110i) q^{28} +(-33.2498 - 19.1968i) q^{29} -28.7089 q^{30} -42.9440i q^{31} +(-18.2521 - 10.5379i) q^{32} +(9.55920 - 5.51901i) q^{33} +(-36.0817 - 20.8318i) q^{34} +(-24.8587 - 43.0565i) q^{35} +(-13.0225 - 22.5557i) q^{36} +33.9790i q^{37} +(21.1296 + 64.2778i) q^{38} -30.7540 q^{39} +(67.2032 - 38.7998i) q^{40} +(16.3728 - 9.45284i) q^{41} +(32.9427 - 57.0585i) q^{42} +(26.5089 + 45.9148i) q^{43} +(-27.6634 + 47.9143i) q^{44} +13.9633 q^{45} -99.5813i q^{46} +(-12.0272 + 20.8318i) q^{47} +(36.9675 + 21.3432i) q^{48} +65.0986 q^{49} -11.8804i q^{50} +(17.5493 + 10.1321i) q^{51} +(133.499 - 77.0754i) q^{52} +(-13.3224 - 7.69168i) q^{53} +(9.25210 + 16.0251i) q^{54} +(-14.8309 - 25.6879i) q^{55} +178.087i q^{56} +(-10.2769 - 31.2632i) q^{57} -136.725 q^{58} +(25.6539 - 14.8113i) q^{59} +(-60.6127 + 34.9948i) q^{60} +(-21.3403 + 36.9626i) q^{61} +(-76.4648 - 132.441i) q^{62} +(-16.0225 + 27.7519i) q^{63} +23.5266 q^{64} +82.6436i q^{65} +(19.6539 - 34.0416i) q^{66} +(-15.1585 - 8.75178i) q^{67} -101.572 q^{68} +48.4339i q^{69} +(-153.330 - 88.5252i) q^{70} +(-74.6028 + 43.0719i) q^{71} +(-43.3155 - 25.0082i) q^{72} +(46.2352 + 80.0817i) q^{73} +(60.5019 + 104.792i) q^{74} +5.77836i q^{75} +(122.962 + 109.953i) q^{76} +68.0723 q^{77} +(-94.8465 + 54.7596i) q^{78} +(-26.3908 + 15.2367i) q^{79} +(57.3545 - 99.3409i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(33.6629 - 58.3058i) q^{82} +77.1154 q^{83} -160.622i q^{84} +(27.2274 - 47.1592i) q^{85} +(163.509 + 94.4019i) q^{86} +66.4996 q^{87} +106.248i q^{88} +(-76.8129 - 44.3479i) q^{89} +(43.0634 - 24.8627i) q^{90} +(-164.253 - 94.8312i) q^{91} +(-121.385 - 210.244i) q^{92} +(37.1906 + 64.4160i) q^{93} +85.6613i q^{94} +(-84.0118 + 27.6166i) q^{95} +36.5042 q^{96} +(-1.82351 + 1.05281i) q^{97} +(200.766 - 115.912i) q^{98} +(-9.55920 + 16.5570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} - 9 q^{3} + 5 q^{4} + 4 q^{5} - 3 q^{6} - 22 q^{7} + 9 q^{9} + 54 q^{10} - 36 q^{11} - 3 q^{13} - 57 q^{14} - 12 q^{15} - 23 q^{16} + 38 q^{17} - 10 q^{19} + 32 q^{20} + 33 q^{21} + 36 q^{22} + 54 q^{23} + 39 q^{24} - 21 q^{25} + 118 q^{26} - 101 q^{28} - 102 q^{29} - 108 q^{30} - 63 q^{32} + 54 q^{33} - 150 q^{34} - 24 q^{35} - 15 q^{36} + 119 q^{38} + 6 q^{39} + 30 q^{40} + 96 q^{41} + 57 q^{42} + 107 q^{43} - 94 q^{44} + 24 q^{45} - 50 q^{47} + 69 q^{48} - 48 q^{49} - 114 q^{51} + 399 q^{52} - 90 q^{53} + 9 q^{54} + 148 q^{55} - 3 q^{57} - 116 q^{58} - 48 q^{60} + 27 q^{61} - 121 q^{62} - 33 q^{63} + 46 q^{64} - 36 q^{66} - 39 q^{67} - 388 q^{68} - 354 q^{70} + 84 q^{71} - 117 q^{72} - 77 q^{73} + 219 q^{74} + 215 q^{76} + 260 q^{77} - 177 q^{78} + 9 q^{79} + 312 q^{80} - 27 q^{81} - 4 q^{82} - 348 q^{83} + 68 q^{85} + 249 q^{86} + 204 q^{87} - 72 q^{89} + 162 q^{90} - 393 q^{91} - 118 q^{92} + 129 q^{93} + 104 q^{95} + 126 q^{96} - 228 q^{97} + 540 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).

\(n\) \(20\) \(40\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.08403 1.78057i 1.54202 0.890284i 0.543306 0.839535i \(-0.317172\pi\)
0.998711 0.0507494i \(-0.0161610\pi\)
\(3\) −1.50000 + 0.866025i −0.500000 + 0.288675i
\(4\) 4.34085 7.51857i 1.08521 1.87964i
\(5\) 2.32722 + 4.03087i 0.465445 + 0.806174i 0.999221 0.0394517i \(-0.0125611\pi\)
−0.533777 + 0.845625i \(0.679228\pi\)
\(6\) −3.08403 + 5.34170i −0.514006 + 0.890284i
\(7\) −10.6817 −1.52596 −0.762978 0.646424i \(-0.776264\pi\)
−0.762978 + 0.646424i \(0.776264\pi\)
\(8\) 16.6722i 2.08402i
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 14.3545 + 8.28756i 1.43545 + 0.828756i
\(11\) −6.37280 −0.579346 −0.289673 0.957126i \(-0.593547\pi\)
−0.289673 + 0.957126i \(0.593547\pi\)
\(12\) 15.0371i 1.25309i
\(13\) 15.3770 + 8.87792i 1.18285 + 0.682917i 0.956671 0.291170i \(-0.0940444\pi\)
0.226176 + 0.974087i \(0.427378\pi\)
\(14\) −32.9427 + 19.0195i −2.35305 + 1.35853i
\(15\) −6.98167 4.03087i −0.465445 0.268725i
\(16\) −12.3225 21.3432i −0.770157 1.33395i
\(17\) −5.84976 10.1321i −0.344104 0.596005i 0.641087 0.767468i \(-0.278484\pi\)
−0.985191 + 0.171463i \(0.945151\pi\)
\(18\) 10.6834i 0.593523i
\(19\) −3.88643 + 18.5983i −0.204549 + 0.978856i
\(20\) 40.4085 2.02042
\(21\) 16.0225 9.25062i 0.762978 0.440506i
\(22\) −19.6539 + 11.3472i −0.893361 + 0.515782i
\(23\) 13.9817 24.2170i 0.607899 1.05291i −0.383688 0.923463i \(-0.625346\pi\)
0.991586 0.129448i \(-0.0413206\pi\)
\(24\) 14.4385 + 25.0082i 0.601604 + 1.04201i
\(25\) 1.66807 2.88918i 0.0667228 0.115567i
\(26\) 63.2310 2.43196
\(27\) 5.19615i 0.192450i
\(28\) −46.3676 + 80.3110i −1.65599 + 2.86825i
\(29\) −33.2498 19.1968i −1.14655 0.661958i −0.198502 0.980100i \(-0.563608\pi\)
−0.948043 + 0.318142i \(0.896941\pi\)
\(30\) −28.7089 −0.956965
\(31\) 42.9440i 1.38529i −0.721278 0.692645i \(-0.756445\pi\)
0.721278 0.692645i \(-0.243555\pi\)
\(32\) −18.2521 10.5379i −0.570378 0.329308i
\(33\) 9.55920 5.51901i 0.289673 0.167243i
\(34\) −36.0817 20.8318i −1.06123 0.612700i
\(35\) −24.8587 43.0565i −0.710248 1.23019i
\(36\) −13.0225 22.5557i −0.361737 0.626547i
\(37\) 33.9790i 0.918351i 0.888346 + 0.459176i \(0.151855\pi\)
−0.888346 + 0.459176i \(0.848145\pi\)
\(38\) 21.1296 + 64.2778i 0.556043 + 1.69152i
\(39\) −30.7540 −0.788565
\(40\) 67.2032 38.7998i 1.68008 0.969995i
\(41\) 16.3728 9.45284i 0.399337 0.230557i −0.286861 0.957972i \(-0.592612\pi\)
0.686198 + 0.727415i \(0.259278\pi\)
\(42\) 32.9427 57.0585i 0.784350 1.35853i
\(43\) 26.5089 + 45.9148i 0.616486 + 1.06779i 0.990122 + 0.140210i \(0.0447778\pi\)
−0.373635 + 0.927576i \(0.621889\pi\)
\(44\) −27.6634 + 47.9143i −0.628713 + 1.08896i
\(45\) 13.9633 0.310296
\(46\) 99.5813i 2.16481i
\(47\) −12.0272 + 20.8318i −0.255899 + 0.443230i −0.965139 0.261737i \(-0.915705\pi\)
0.709240 + 0.704967i \(0.249038\pi\)
\(48\) 36.9675 + 21.3432i 0.770157 + 0.444650i
\(49\) 65.0986 1.32854
\(50\) 11.8804i 0.237609i
\(51\) 17.5493 + 10.1321i 0.344104 + 0.198668i
\(52\) 133.499 77.0754i 2.56728 1.48222i
\(53\) −13.3224 7.69168i −0.251366 0.145126i 0.369024 0.929420i \(-0.379692\pi\)
−0.620389 + 0.784294i \(0.713025\pi\)
\(54\) 9.25210 + 16.0251i 0.171335 + 0.296761i
\(55\) −14.8309 25.6879i −0.269653 0.467053i
\(56\) 178.087i 3.18012i
\(57\) −10.2769 31.2632i −0.180297 0.548476i
\(58\) −136.725 −2.35732
\(59\) 25.6539 14.8113i 0.434813 0.251039i −0.266582 0.963812i \(-0.585894\pi\)
0.701395 + 0.712773i \(0.252561\pi\)
\(60\) −60.6127 + 34.9948i −1.01021 + 0.583246i
\(61\) −21.3403 + 36.9626i −0.349842 + 0.605944i −0.986221 0.165433i \(-0.947098\pi\)
0.636379 + 0.771376i \(0.280431\pi\)
\(62\) −76.4648 132.441i −1.23330 2.13614i
\(63\) −16.0225 + 27.7519i −0.254326 + 0.440506i
\(64\) 23.5266 0.367603
\(65\) 82.6436i 1.27144i
\(66\) 19.6539 34.0416i 0.297787 0.515782i
\(67\) −15.1585 8.75178i −0.226247 0.130624i 0.382593 0.923917i \(-0.375031\pi\)
−0.608839 + 0.793294i \(0.708365\pi\)
\(68\) −101.572 −1.49370
\(69\) 48.4339i 0.701941i
\(70\) −153.330 88.5252i −2.19043 1.26465i
\(71\) −74.6028 + 43.0719i −1.05074 + 0.606647i −0.922857 0.385142i \(-0.874153\pi\)
−0.127886 + 0.991789i \(0.540819\pi\)
\(72\) −43.3155 25.0082i −0.601604 0.347336i
\(73\) 46.2352 + 80.0817i 0.633359 + 1.09701i 0.986860 + 0.161576i \(0.0516576\pi\)
−0.353502 + 0.935434i \(0.615009\pi\)
\(74\) 60.5019 + 104.792i 0.817593 + 1.41611i
\(75\) 5.77836i 0.0770448i
\(76\) 122.962 + 109.953i 1.61792 + 1.44674i
\(77\) 68.0723 0.884056
\(78\) −94.8465 + 54.7596i −1.21598 + 0.702047i
\(79\) −26.3908 + 15.2367i −0.334060 + 0.192870i −0.657642 0.753330i \(-0.728446\pi\)
0.323582 + 0.946200i \(0.395113\pi\)
\(80\) 57.3545 99.3409i 0.716931 1.24176i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 33.6629 58.3058i 0.410523 0.711046i
\(83\) 77.1154 0.929101 0.464551 0.885547i \(-0.346216\pi\)
0.464551 + 0.885547i \(0.346216\pi\)
\(84\) 160.622i 1.91217i
\(85\) 27.2274 47.1592i 0.320322 0.554815i
\(86\) 163.509 + 94.4019i 1.90127 + 1.09770i
\(87\) 66.4996 0.764364
\(88\) 106.248i 1.20737i
\(89\) −76.8129 44.3479i −0.863066 0.498291i 0.00197195 0.999998i \(-0.499372\pi\)
−0.865038 + 0.501707i \(0.832706\pi\)
\(90\) 43.0634 24.8627i 0.478482 0.276252i
\(91\) −164.253 94.8312i −1.80497 1.04210i
\(92\) −121.385 210.244i −1.31940 2.28526i
\(93\) 37.1906 + 64.4160i 0.399899 + 0.692645i
\(94\) 85.6613i 0.911291i
\(95\) −84.0118 + 27.6166i −0.884334 + 0.290702i
\(96\) 36.5042 0.380252
\(97\) −1.82351 + 1.05281i −0.0187991 + 0.0108537i −0.509370 0.860548i \(-0.670122\pi\)
0.490571 + 0.871401i \(0.336788\pi\)
\(98\) 200.766 115.912i 2.04864 1.18278i
\(99\) −9.55920 + 16.5570i −0.0965576 + 0.167243i
\(100\) −14.4817 25.0830i −0.144817 0.250830i
\(101\) −13.7690 + 23.8486i −0.136327 + 0.236125i −0.926104 0.377269i \(-0.876863\pi\)
0.789777 + 0.613395i \(0.210196\pi\)
\(102\) 72.1635 0.707485
\(103\) 102.351i 0.993696i 0.867837 + 0.496848i \(0.165509\pi\)
−0.867837 + 0.496848i \(0.834491\pi\)
\(104\) 148.014 256.368i 1.42321 2.46508i
\(105\) 74.5760 + 43.0565i 0.710248 + 0.410062i
\(106\) −54.7823 −0.516814
\(107\) 0.549592i 0.00513638i 0.999997 + 0.00256819i \(0.000817481\pi\)
−0.999997 + 0.00256819i \(0.999183\pi\)
\(108\) 39.0676 + 22.5557i 0.361737 + 0.208849i
\(109\) 80.7219 46.6048i 0.740568 0.427567i −0.0817076 0.996656i \(-0.526037\pi\)
0.822276 + 0.569089i \(0.192704\pi\)
\(110\) −91.4782 52.8150i −0.831620 0.480136i
\(111\) −29.4267 50.9685i −0.265105 0.459176i
\(112\) 131.625 + 227.982i 1.17523 + 2.03555i
\(113\) 55.4186i 0.490430i −0.969469 0.245215i \(-0.921141\pi\)
0.969469 0.245215i \(-0.0788586\pi\)
\(114\) −87.3606 78.1179i −0.766321 0.685244i
\(115\) 130.154 1.13177
\(116\) −288.665 + 166.661i −2.48849 + 1.43673i
\(117\) 46.1310 26.6338i 0.394282 0.227639i
\(118\) 52.7451 91.3572i 0.446992 0.774214i
\(119\) 62.4854 + 108.228i 0.525087 + 0.909478i
\(120\) −67.2032 + 116.399i −0.560027 + 0.969995i
\(121\) −80.3874 −0.664359
\(122\) 151.992i 1.24583i
\(123\) −16.3728 + 28.3585i −0.133112 + 0.230557i
\(124\) −322.877 186.413i −2.60385 1.50333i
\(125\) 131.889 1.05511
\(126\) 114.117i 0.905690i
\(127\) −82.7181 47.7573i −0.651324 0.376042i 0.137640 0.990482i \(-0.456048\pi\)
−0.788963 + 0.614441i \(0.789382\pi\)
\(128\) 145.565 84.0422i 1.13723 0.656580i
\(129\) −79.5267 45.9148i −0.616486 0.355929i
\(130\) 147.153 + 254.876i 1.13194 + 1.96058i
\(131\) −84.0762 145.624i −0.641803 1.11164i −0.985030 0.172383i \(-0.944853\pi\)
0.343227 0.939252i \(-0.388480\pi\)
\(132\) 95.8287i 0.725975i
\(133\) 41.5136 198.661i 0.312133 1.49369i
\(134\) −62.3326 −0.465168
\(135\) −20.9450 + 12.0926i −0.155148 + 0.0895748i
\(136\) −168.924 + 97.5281i −1.24209 + 0.717119i
\(137\) 59.3774 102.845i 0.433412 0.750691i −0.563753 0.825943i \(-0.690643\pi\)
0.997165 + 0.0752526i \(0.0239763\pi\)
\(138\) 86.2399 + 149.372i 0.624927 + 1.08240i
\(139\) −55.1822 + 95.5784i −0.396994 + 0.687614i −0.993354 0.115104i \(-0.963280\pi\)
0.596359 + 0.802718i \(0.296613\pi\)
\(140\) −431.631 −3.08308
\(141\) 41.6636i 0.295487i
\(142\) −153.385 + 265.671i −1.08018 + 1.87092i
\(143\) −97.9947 56.5772i −0.685277 0.395645i
\(144\) −73.9351 −0.513438
\(145\) 178.701i 1.23242i
\(146\) 285.182 + 164.650i 1.95330 + 1.12774i
\(147\) −97.6479 + 56.3770i −0.664271 + 0.383517i
\(148\) 255.473 + 147.498i 1.72617 + 0.996605i
\(149\) 28.8719 + 50.0077i 0.193771 + 0.335622i 0.946497 0.322712i \(-0.104595\pi\)
−0.752726 + 0.658334i \(0.771261\pi\)
\(150\) 10.2888 + 17.8207i 0.0685918 + 0.118804i
\(151\) 205.459i 1.36066i −0.732908 0.680328i \(-0.761837\pi\)
0.732908 0.680328i \(-0.238163\pi\)
\(152\) 310.073 + 64.7951i 2.03996 + 0.426284i
\(153\) −35.0986 −0.229402
\(154\) 209.937 121.207i 1.36323 0.787061i
\(155\) 173.102 99.9403i 1.11678 0.644776i
\(156\) −133.499 + 231.226i −0.855760 + 1.48222i
\(157\) −55.6080 96.3159i −0.354191 0.613477i 0.632788 0.774325i \(-0.281910\pi\)
−0.986979 + 0.160848i \(0.948577\pi\)
\(158\) −54.2600 + 93.9811i −0.343418 + 0.594817i
\(159\) 26.6448 0.167577
\(160\) 98.0958i 0.613099i
\(161\) −149.348 + 258.678i −0.927627 + 1.60670i
\(162\) −27.7563 16.0251i −0.171335 0.0989205i
\(163\) 69.1905 0.424481 0.212241 0.977217i \(-0.431924\pi\)
0.212241 + 0.977217i \(0.431924\pi\)
\(164\) 164.133i 1.00081i
\(165\) 44.4928 + 25.6879i 0.269653 + 0.155684i
\(166\) 237.827 137.309i 1.43269 0.827164i
\(167\) 181.817 + 104.972i 1.08873 + 0.628577i 0.933237 0.359261i \(-0.116971\pi\)
0.155490 + 0.987837i \(0.450304\pi\)
\(168\) −154.228 267.130i −0.918022 1.59006i
\(169\) 73.1350 + 126.674i 0.432751 + 0.749547i
\(170\) 193.921i 1.14071i
\(171\) 42.4901 + 37.9946i 0.248480 + 0.222191i
\(172\) 460.285 2.67607
\(173\) −264.781 + 152.871i −1.53053 + 0.883649i −0.531188 + 0.847254i \(0.678254\pi\)
−0.999337 + 0.0363949i \(0.988413\pi\)
\(174\) 205.087 118.407i 1.17866 0.680501i
\(175\) −17.8178 + 30.8613i −0.101816 + 0.176351i
\(176\) 78.5290 + 136.016i 0.446187 + 0.772819i
\(177\) −25.6539 + 44.4339i −0.144938 + 0.251039i
\(178\) −315.858 −1.77448
\(179\) 303.001i 1.69274i −0.532593 0.846371i \(-0.678782\pi\)
0.532593 0.846371i \(-0.321218\pi\)
\(180\) 60.6127 104.984i 0.336737 0.583246i
\(181\) −62.8763 36.3016i −0.347383 0.200561i 0.316149 0.948709i \(-0.397610\pi\)
−0.663532 + 0.748148i \(0.730943\pi\)
\(182\) −675.414 −3.71107
\(183\) 73.9251i 0.403962i
\(184\) −403.749 233.104i −2.19429 1.26687i
\(185\) −136.965 + 79.0767i −0.740350 + 0.427442i
\(186\) 229.394 + 132.441i 1.23330 + 0.712048i
\(187\) 37.2794 + 64.5698i 0.199355 + 0.345293i
\(188\) 104.417 + 180.855i 0.555409 + 0.961997i
\(189\) 55.5037i 0.293670i
\(190\) −209.922 + 234.759i −1.10485 + 1.23558i
\(191\) −48.5734 −0.254311 −0.127156 0.991883i \(-0.540585\pi\)
−0.127156 + 0.991883i \(0.540585\pi\)
\(192\) −35.2899 + 20.3747i −0.183802 + 0.106118i
\(193\) 9.48401 5.47559i 0.0491399 0.0283710i −0.475229 0.879862i \(-0.657635\pi\)
0.524369 + 0.851491i \(0.324301\pi\)
\(194\) −3.74919 + 6.49378i −0.0193257 + 0.0334731i
\(195\) −71.5715 123.965i −0.367033 0.635720i
\(196\) 282.583 489.448i 1.44175 2.49718i
\(197\) 104.442 0.530163 0.265082 0.964226i \(-0.414601\pi\)
0.265082 + 0.964226i \(0.414601\pi\)
\(198\) 68.0833i 0.343855i
\(199\) −140.643 + 243.602i −0.706751 + 1.22413i 0.259305 + 0.965795i \(0.416506\pi\)
−0.966056 + 0.258333i \(0.916827\pi\)
\(200\) −48.1689 27.8103i −0.240844 0.139052i
\(201\) 30.3171 0.150831
\(202\) 98.0667i 0.485479i
\(203\) 355.164 + 205.054i 1.74958 + 1.01012i
\(204\) 152.358 87.9637i 0.746851 0.431194i
\(205\) 76.2063 + 43.9977i 0.371738 + 0.214623i
\(206\) 182.242 + 315.653i 0.884672 + 1.53230i
\(207\) −41.9450 72.6509i −0.202633 0.350970i
\(208\) 437.593i 2.10381i
\(209\) 24.7674 118.523i 0.118504 0.567096i
\(210\) 306.660 1.46029
\(211\) 89.2808 51.5463i 0.423132 0.244295i −0.273285 0.961933i \(-0.588110\pi\)
0.696416 + 0.717638i \(0.254777\pi\)
\(212\) −115.661 + 66.7768i −0.545570 + 0.314985i
\(213\) 74.6028 129.216i 0.350248 0.606647i
\(214\) 0.978587 + 1.69496i 0.00457284 + 0.00792038i
\(215\) −123.384 + 213.708i −0.573880 + 0.993990i
\(216\) 86.6310 0.401070
\(217\) 458.715i 2.11389i
\(218\) 165.966 287.462i 0.761313 1.31863i
\(219\) −138.706 80.0817i −0.633359 0.365670i
\(220\) −257.515 −1.17052
\(221\) 207.735i 0.939977i
\(222\) −181.506 104.792i −0.817593 0.472038i
\(223\) −68.9560 + 39.8118i −0.309220 + 0.178528i −0.646577 0.762848i \(-0.723800\pi\)
0.337357 + 0.941377i \(0.390467\pi\)
\(224\) 194.963 + 112.562i 0.870372 + 0.502510i
\(225\) −5.00421 8.66754i −0.0222409 0.0385224i
\(226\) −98.6766 170.913i −0.436622 0.756252i
\(227\) 131.031i 0.577228i −0.957446 0.288614i \(-0.906806\pi\)
0.957446 0.288614i \(-0.0931944\pi\)
\(228\) −279.665 58.4407i −1.22660 0.256319i
\(229\) 30.3537 0.132549 0.0662745 0.997801i \(-0.478889\pi\)
0.0662745 + 0.997801i \(0.478889\pi\)
\(230\) 401.399 231.748i 1.74521 1.00760i
\(231\) −102.108 + 58.9524i −0.442028 + 0.255205i
\(232\) −320.052 + 554.346i −1.37953 + 2.38942i
\(233\) −47.0484 81.4902i −0.201924 0.349743i 0.747224 0.664572i \(-0.231386\pi\)
−0.949148 + 0.314829i \(0.898053\pi\)
\(234\) 94.8465 164.279i 0.405327 0.702047i
\(235\) −111.960 −0.476427
\(236\) 257.175i 1.08972i
\(237\) 26.3908 45.7101i 0.111353 0.192870i
\(238\) 385.414 + 222.519i 1.61939 + 0.934954i
\(239\) 375.297 1.57028 0.785141 0.619317i \(-0.212591\pi\)
0.785141 + 0.619317i \(0.212591\pi\)
\(240\) 198.682i 0.827840i
\(241\) 0.482424 + 0.278528i 0.00200176 + 0.00115572i 0.501001 0.865447i \(-0.332965\pi\)
−0.498999 + 0.866603i \(0.666299\pi\)
\(242\) −247.917 + 143.135i −1.02445 + 0.591468i
\(243\) 13.5000 + 7.79423i 0.0555556 + 0.0320750i
\(244\) 185.270 + 320.898i 0.759305 + 1.31515i
\(245\) 151.499 + 262.404i 0.618363 + 1.07104i
\(246\) 116.612i 0.474031i
\(247\) −224.876 + 251.482i −0.910428 + 1.01815i
\(248\) −715.969 −2.88697
\(249\) −115.673 + 66.7839i −0.464551 + 0.268208i
\(250\) 406.750 234.837i 1.62700 0.939350i
\(251\) 117.309 203.185i 0.467367 0.809504i −0.531938 0.846783i \(-0.678536\pi\)
0.999305 + 0.0372799i \(0.0118693\pi\)
\(252\) 139.103 + 240.933i 0.551995 + 0.956084i
\(253\) −89.1024 + 154.330i −0.352183 + 0.610000i
\(254\) −340.141 −1.33914
\(255\) 94.3185i 0.369876i
\(256\) 252.232 436.879i 0.985283 1.70656i
\(257\) −11.0702 6.39141i −0.0430749 0.0248693i 0.478308 0.878192i \(-0.341250\pi\)
−0.521383 + 0.853323i \(0.674584\pi\)
\(258\) −327.018 −1.26751
\(259\) 362.953i 1.40136i
\(260\) 621.361 + 358.743i 2.38985 + 1.37978i
\(261\) −99.7494 + 57.5904i −0.382182 + 0.220653i
\(262\) −518.588 299.407i −1.97934 1.14277i
\(263\) 106.457 + 184.389i 0.404780 + 0.701099i 0.994296 0.106657i \(-0.0340148\pi\)
−0.589516 + 0.807757i \(0.700681\pi\)
\(264\) −92.0138 159.372i −0.348537 0.603684i
\(265\) 71.6010i 0.270193i
\(266\) −225.700 686.595i −0.848497 2.58119i
\(267\) 153.626 0.575377
\(268\) −131.602 + 75.9803i −0.491051 + 0.283508i
\(269\) −438.717 + 253.293i −1.63092 + 0.941610i −0.647106 + 0.762400i \(0.724021\pi\)
−0.983811 + 0.179211i \(0.942646\pi\)
\(270\) −43.0634 + 74.5880i −0.159494 + 0.276252i
\(271\) 110.063 + 190.635i 0.406136 + 0.703449i 0.994453 0.105182i \(-0.0335425\pi\)
−0.588317 + 0.808631i \(0.700209\pi\)
\(272\) −144.168 + 249.706i −0.530028 + 0.918035i
\(273\) 328.505 1.20332
\(274\) 422.902i 1.54344i
\(275\) −10.6303 + 18.4122i −0.0386556 + 0.0669534i
\(276\) 364.154 + 210.244i 1.31940 + 0.761754i
\(277\) 262.083 0.946148 0.473074 0.881023i \(-0.343144\pi\)
0.473074 + 0.881023i \(0.343144\pi\)
\(278\) 393.023i 1.41375i
\(279\) −111.572 64.4160i −0.399899 0.230882i
\(280\) −717.844 + 414.448i −2.56373 + 1.48017i
\(281\) −346.203 199.880i −1.23204 0.711317i −0.264583 0.964363i \(-0.585234\pi\)
−0.967454 + 0.253046i \(0.918568\pi\)
\(282\) −74.1849 128.492i −0.263067 0.455645i
\(283\) 41.2358 + 71.4225i 0.145710 + 0.252376i 0.929637 0.368475i \(-0.120120\pi\)
−0.783928 + 0.620852i \(0.786787\pi\)
\(284\) 747.875i 2.63336i
\(285\) 102.101 114.181i 0.358249 0.400636i
\(286\) −402.959 −1.40895
\(287\) −174.889 + 100.972i −0.609370 + 0.351820i
\(288\) −54.7563 + 31.6136i −0.190126 + 0.109769i
\(289\) 76.0605 131.741i 0.263185 0.455850i
\(290\) −318.189 551.120i −1.09720 1.90041i
\(291\) 1.82351 3.15842i 0.00626637 0.0108537i
\(292\) 802.800 2.74931
\(293\) 223.552i 0.762977i 0.924374 + 0.381489i \(0.124588\pi\)
−0.924374 + 0.381489i \(0.875412\pi\)
\(294\) −200.766 + 347.737i −0.682878 + 1.18278i
\(295\) 119.405 + 68.9384i 0.404762 + 0.233690i
\(296\) 566.503 1.91386
\(297\) 33.1141i 0.111495i
\(298\) 178.084 + 102.817i 0.597598 + 0.345023i
\(299\) 429.993 248.256i 1.43810 0.830289i
\(300\) 43.4450 + 25.0830i 0.144817 + 0.0836099i
\(301\) −283.160 490.448i −0.940731 1.62939i
\(302\) −365.834 633.643i −1.21137 2.09816i
\(303\) 47.6973i 0.157417i
\(304\) 444.838 146.229i 1.46328 0.481015i
\(305\) −198.655 −0.651328
\(306\) −108.245 + 62.4954i −0.353743 + 0.204233i
\(307\) 339.034 195.741i 1.10434 0.637594i 0.166986 0.985959i \(-0.446597\pi\)
0.937359 + 0.348366i \(0.113263\pi\)
\(308\) 295.492 511.806i 0.959388 1.66171i
\(309\) −88.6383 153.526i −0.286855 0.496848i
\(310\) 355.901 616.439i 1.14807 1.98851i
\(311\) 375.828 1.20845 0.604224 0.796814i \(-0.293483\pi\)
0.604224 + 0.796814i \(0.293483\pi\)
\(312\) 512.736i 1.64338i
\(313\) 75.3935 130.585i 0.240874 0.417206i −0.720090 0.693881i \(-0.755899\pi\)
0.960963 + 0.276675i \(0.0892327\pi\)
\(314\) −342.994 198.028i −1.09234 0.630661i
\(315\) −149.152 −0.473499
\(316\) 264.561i 0.837218i
\(317\) −438.163 252.973i −1.38222 0.798024i −0.389796 0.920901i \(-0.627454\pi\)
−0.992422 + 0.122878i \(0.960788\pi\)
\(318\) 82.1734 47.4428i 0.258407 0.149191i
\(319\) 211.895 + 122.337i 0.664246 + 0.383503i
\(320\) 54.7517 + 94.8327i 0.171099 + 0.296352i
\(321\) −0.475961 0.824389i −0.00148274 0.00256819i
\(322\) 1063.70i 3.30341i
\(323\) 211.174 69.4179i 0.653789 0.214916i
\(324\) −78.1352 −0.241158
\(325\) 51.2998 29.6180i 0.157846 0.0911322i
\(326\) 213.386 123.198i 0.654558 0.377909i
\(327\) −80.7219 + 139.814i −0.246856 + 0.427567i
\(328\) −157.599 272.970i −0.480485 0.832225i
\(329\) 128.471 222.519i 0.390491 0.676349i
\(330\) 182.956 0.554413
\(331\) 443.028i 1.33845i 0.743058 + 0.669227i \(0.233374\pi\)
−0.743058 + 0.669227i \(0.766626\pi\)
\(332\) 334.746 579.797i 1.00827 1.74638i
\(333\) 88.2800 + 50.9685i 0.265105 + 0.153059i
\(334\) 747.642 2.23845
\(335\) 81.4694i 0.243192i
\(336\) −394.876 227.982i −1.17523 0.678517i
\(337\) 168.764 97.4357i 0.500782 0.289127i −0.228254 0.973602i \(-0.573302\pi\)
0.729037 + 0.684475i \(0.239968\pi\)
\(338\) 451.102 + 260.444i 1.33462 + 0.770543i
\(339\) 47.9939 + 83.1279i 0.141575 + 0.245215i
\(340\) −236.380 409.422i −0.695235 1.20418i
\(341\) 273.674i 0.802562i
\(342\) 198.693 + 41.5203i 0.580974 + 0.121404i
\(343\) −171.960 −0.501341
\(344\) 765.498 441.961i 2.22529 1.28477i
\(345\) −195.231 + 112.717i −0.565886 + 0.326715i
\(346\) −544.396 + 942.921i −1.57340 + 2.72520i
\(347\) 262.446 + 454.570i 0.756329 + 1.31000i 0.944711 + 0.327905i \(0.106342\pi\)
−0.188382 + 0.982096i \(0.560324\pi\)
\(348\) 288.665 499.982i 0.829496 1.43673i
\(349\) −369.064 −1.05749 −0.528745 0.848781i \(-0.677337\pi\)
−0.528745 + 0.848781i \(0.677337\pi\)
\(350\) 126.903i 0.362581i
\(351\) −46.1310 + 79.9013i −0.131427 + 0.227639i
\(352\) 116.317 + 67.1557i 0.330446 + 0.190783i
\(353\) 323.725 0.917067 0.458533 0.888677i \(-0.348375\pi\)
0.458533 + 0.888677i \(0.348375\pi\)
\(354\) 182.714i 0.516142i
\(355\) −347.235 200.476i −0.978126 0.564721i
\(356\) −666.866 + 385.015i −1.87322 + 1.08150i
\(357\) −187.456 108.228i −0.525087 0.303159i
\(358\) −539.514 934.465i −1.50702 2.61024i
\(359\) −6.25614 10.8359i −0.0174266 0.0301837i 0.857181 0.515016i \(-0.172214\pi\)
−0.874607 + 0.484832i \(0.838881\pi\)
\(360\) 232.799i 0.646663i
\(361\) −330.791 144.562i −0.916320 0.400448i
\(362\) −258.550 −0.714227
\(363\) 120.581 69.6175i 0.332179 0.191784i
\(364\) −1425.99 + 823.296i −3.91756 + 2.26180i
\(365\) −215.199 + 372.736i −0.589587 + 1.02119i
\(366\) −131.629 227.988i −0.359641 0.622917i
\(367\) −44.3159 + 76.7574i −0.120752 + 0.209148i −0.920064 0.391767i \(-0.871864\pi\)
0.799313 + 0.600916i \(0.205197\pi\)
\(368\) −689.157 −1.87271
\(369\) 56.7171i 0.153705i
\(370\) −281.603 + 487.750i −0.761089 + 1.31824i
\(371\) 142.306 + 82.1602i 0.383573 + 0.221456i
\(372\) 645.755 1.73590
\(373\) 406.489i 1.08978i 0.838507 + 0.544892i \(0.183429\pi\)
−0.838507 + 0.544892i \(0.816571\pi\)
\(374\) 229.942 + 132.757i 0.614818 + 0.354965i
\(375\) −197.834 + 114.219i −0.527556 + 0.304585i
\(376\) 347.311 + 200.520i 0.923699 + 0.533298i
\(377\) −340.855 590.378i −0.904125 1.56599i
\(378\) −98.8281 171.175i −0.261450 0.452845i
\(379\) 433.800i 1.14459i −0.820047 0.572296i \(-0.806053\pi\)
0.820047 0.572296i \(-0.193947\pi\)
\(380\) −157.045 + 751.528i −0.413275 + 1.97770i
\(381\) 165.436 0.434216
\(382\) −149.802 + 86.4883i −0.392152 + 0.226409i
\(383\) −355.819 + 205.432i −0.929031 + 0.536377i −0.886505 0.462719i \(-0.846874\pi\)
−0.0425263 + 0.999095i \(0.513541\pi\)
\(384\) −145.565 + 252.127i −0.379076 + 0.656580i
\(385\) 158.419 + 274.391i 0.411479 + 0.712703i
\(386\) 19.4993 33.7738i 0.0505164 0.0874970i
\(387\) 159.053 0.410991
\(388\) 18.2803i 0.0471141i
\(389\) −94.6013 + 163.854i −0.243191 + 0.421219i −0.961621 0.274380i \(-0.911528\pi\)
0.718430 + 0.695599i \(0.244861\pi\)
\(390\) −441.458 254.876i −1.13194 0.653528i
\(391\) −327.158 −0.836721
\(392\) 1085.33i 2.76871i
\(393\) 252.228 + 145.624i 0.641803 + 0.370545i
\(394\) 322.103 185.966i 0.817521 0.471996i
\(395\) −122.834 70.9185i −0.310973 0.179540i
\(396\) 82.9901 + 143.743i 0.209571 + 0.362987i
\(397\) −220.839 382.504i −0.556269 0.963487i −0.997804 0.0662425i \(-0.978899\pi\)
0.441534 0.897244i \(-0.354434\pi\)
\(398\) 1001.70i 2.51684i
\(399\) 109.775 + 333.943i 0.275125 + 0.836951i
\(400\) −82.2192 −0.205548
\(401\) 320.526 185.056i 0.799316 0.461485i −0.0439159 0.999035i \(-0.513983\pi\)
0.843232 + 0.537550i \(0.180650\pi\)
\(402\) 93.4988 53.9816i 0.232584 0.134283i
\(403\) 381.254 660.351i 0.946039 1.63859i
\(404\) 119.538 + 207.047i 0.295887 + 0.512491i
\(405\) 20.9450 36.2778i 0.0517161 0.0895748i
\(406\) 1460.45 3.59717
\(407\) 216.541i 0.532043i
\(408\) 168.924 292.584i 0.414029 0.717119i
\(409\) 418.387 + 241.556i 1.02295 + 0.590602i 0.914958 0.403550i \(-0.132224\pi\)
0.107995 + 0.994151i \(0.465557\pi\)
\(410\) 313.364 0.764302
\(411\) 205.689i 0.500461i
\(412\) 769.531 + 444.289i 1.86779 + 1.07837i
\(413\) −274.028 + 158.210i −0.663505 + 0.383075i
\(414\) −258.720 149.372i −0.624927 0.360802i
\(415\) 179.465 + 310.842i 0.432445 + 0.749017i
\(416\) −187.109 324.082i −0.449780 0.779042i
\(417\) 191.157i 0.458409i
\(418\) −134.655 409.630i −0.322141 0.979975i
\(419\) −295.264 −0.704687 −0.352344 0.935871i \(-0.614615\pi\)
−0.352344 + 0.935871i \(0.614615\pi\)
\(420\) 647.446 373.803i 1.54154 0.890008i
\(421\) −449.581 + 259.566i −1.06789 + 0.616545i −0.927604 0.373566i \(-0.878135\pi\)
−0.140284 + 0.990111i \(0.544802\pi\)
\(422\) 183.563 317.941i 0.434984 0.753415i
\(423\) 36.0817 + 62.4954i 0.0852996 + 0.147743i
\(424\) −128.237 + 222.113i −0.302446 + 0.523851i
\(425\) −39.0312 −0.0918382
\(426\) 531.341i 1.24728i
\(427\) 227.951 394.823i 0.533843 0.924644i
\(428\) 4.13215 + 2.38570i 0.00965455 + 0.00557406i
\(429\) 195.989 0.456852
\(430\) 878.777i 2.04367i
\(431\) −195.895 113.100i −0.454514 0.262414i 0.255221 0.966883i \(-0.417852\pi\)
−0.709735 + 0.704469i \(0.751185\pi\)
\(432\) 110.903 64.0297i 0.256719 0.148217i
\(433\) −251.769 145.359i −0.581452 0.335702i 0.180258 0.983619i \(-0.442307\pi\)
−0.761710 + 0.647918i \(0.775640\pi\)
\(434\) 816.773 + 1414.69i 1.88197 + 3.25966i
\(435\) 154.759 + 268.051i 0.355769 + 0.616210i
\(436\) 809.218i 1.85600i
\(437\) 396.055 + 354.152i 0.906304 + 0.810417i
\(438\) −570.364 −1.30220
\(439\) 251.921 145.447i 0.573852 0.331314i −0.184834 0.982770i \(-0.559175\pi\)
0.758686 + 0.651456i \(0.225842\pi\)
\(440\) −428.273 + 247.264i −0.973348 + 0.561963i
\(441\) 97.6479 169.131i 0.221424 0.383517i
\(442\) −369.886 640.662i −0.836847 1.44946i
\(443\) −217.722 + 377.106i −0.491473 + 0.851256i −0.999952 0.00981853i \(-0.996875\pi\)
0.508479 + 0.861074i \(0.330208\pi\)
\(444\) −510.947 −1.15078
\(445\) 412.830i 0.927708i
\(446\) −141.775 + 245.562i −0.317882 + 0.550587i
\(447\) −86.6158 50.0077i −0.193771 0.111874i
\(448\) −251.304 −0.560947
\(449\) 263.736i 0.587385i −0.955900 0.293692i \(-0.905116\pi\)
0.955900 0.293692i \(-0.0948842\pi\)
\(450\) −30.8663 17.8207i −0.0685918 0.0396015i
\(451\) −104.341 + 60.2411i −0.231354 + 0.133572i
\(452\) −416.669 240.564i −0.921833 0.532221i
\(453\) 177.933 + 308.189i 0.392788 + 0.680328i
\(454\) −233.309 404.103i −0.513897 0.890096i
\(455\) 882.774i 1.94016i
\(456\) −521.224 + 171.339i −1.14303 + 0.375743i
\(457\) 641.042 1.40272 0.701359 0.712809i \(-0.252577\pi\)
0.701359 + 0.712809i \(0.252577\pi\)
\(458\) 93.6119 54.0469i 0.204393 0.118006i
\(459\) 52.6479 30.3963i 0.114701 0.0662228i
\(460\) 564.978 978.570i 1.22821 2.12733i
\(461\) −323.490 560.302i −0.701714 1.21540i −0.967864 0.251473i \(-0.919085\pi\)
0.266150 0.963932i \(-0.414248\pi\)
\(462\) −209.937 + 363.622i −0.454410 + 0.787061i
\(463\) −407.362 −0.879831 −0.439916 0.898039i \(-0.644992\pi\)
−0.439916 + 0.898039i \(0.644992\pi\)
\(464\) 946.211i 2.03925i
\(465\) −173.102 + 299.821i −0.372262 + 0.644776i
\(466\) −290.198 167.546i −0.622742 0.359540i
\(467\) 146.962 0.314694 0.157347 0.987543i \(-0.449706\pi\)
0.157347 + 0.987543i \(0.449706\pi\)
\(468\) 462.452i 0.988146i
\(469\) 161.919 + 93.4838i 0.345242 + 0.199326i
\(470\) −345.290 + 199.353i −0.734659 + 0.424155i
\(471\) 166.824 + 96.3159i 0.354191 + 0.204492i
\(472\) −246.936 427.706i −0.523170 0.906158i
\(473\) −168.936 292.606i −0.357159 0.618617i
\(474\) 187.962i 0.396545i
\(475\) 47.2509 + 42.2518i 0.0994757 + 0.0889512i
\(476\) 1084.96 2.27932
\(477\) −39.9672 + 23.0751i −0.0837886 + 0.0483754i
\(478\) 1157.43 668.242i 2.42140 1.39800i
\(479\) −309.698 + 536.413i −0.646552 + 1.11986i 0.337389 + 0.941365i \(0.390456\pi\)
−0.983941 + 0.178495i \(0.942877\pi\)
\(480\) 84.9534 + 147.144i 0.176986 + 0.306549i
\(481\) −301.663 + 522.495i −0.627158 + 1.08627i
\(482\) 1.98375 0.00411566
\(483\) 517.356i 1.07113i
\(484\) −348.949 + 604.398i −0.720970 + 1.24876i
\(485\) −8.48745 4.90023i −0.0174999 0.0101036i
\(486\) 55.5126 0.114224
\(487\) 343.861i 0.706080i −0.935608 0.353040i \(-0.885148\pi\)
0.935608 0.353040i \(-0.114852\pi\)
\(488\) 616.245 + 355.789i 1.26280 + 0.729077i
\(489\) −103.786 + 59.9207i −0.212241 + 0.122537i
\(490\) 934.456 + 539.508i 1.90705 + 1.10104i
\(491\) −250.993 434.733i −0.511187 0.885402i −0.999916 0.0129665i \(-0.995873\pi\)
0.488729 0.872436i \(-0.337461\pi\)
\(492\) 142.144 + 246.200i 0.288910 + 0.500407i
\(493\) 449.187i 0.911129i
\(494\) −245.743 + 1175.99i −0.497455 + 2.38054i
\(495\) −88.9856 −0.179769
\(496\) −916.564 + 529.178i −1.84791 + 1.06689i
\(497\) 796.884 460.081i 1.60339 0.925717i
\(498\) −237.827 + 411.928i −0.477563 + 0.827164i
\(499\) 453.717 + 785.861i 0.909253 + 1.57487i 0.815105 + 0.579314i \(0.196679\pi\)
0.0941479 + 0.995558i \(0.469987\pi\)
\(500\) 572.510 991.616i 1.14502 1.98323i
\(501\) −363.635 −0.725818
\(502\) 835.508i 1.66436i
\(503\) 183.800 318.352i 0.365408 0.632906i −0.623433 0.781877i \(-0.714263\pi\)
0.988842 + 0.148971i \(0.0475960\pi\)
\(504\) 462.683 + 267.130i 0.918022 + 0.530020i
\(505\) −128.174 −0.253810
\(506\) 634.612i 1.25417i
\(507\) −219.405 126.674i −0.432751 0.249849i
\(508\) −718.133 + 414.614i −1.41365 + 0.816170i
\(509\) 406.585 + 234.742i 0.798791 + 0.461182i 0.843048 0.537838i \(-0.180759\pi\)
−0.0442573 + 0.999020i \(0.514092\pi\)
\(510\) 167.941 + 290.881i 0.329295 + 0.570356i
\(511\) −493.870 855.408i −0.966478 1.67399i
\(512\) 1124.13i 2.19557i
\(513\) −96.6395 20.1945i −0.188381 0.0393654i
\(514\) −45.5214 −0.0885630
\(515\) −412.562 + 238.193i −0.801092 + 0.462511i
\(516\) −690.427 + 398.618i −1.33804 + 0.772516i
\(517\) 76.6473 132.757i 0.148254 0.256783i
\(518\) −646.263 1119.36i −1.24761 2.16093i
\(519\) 264.781 458.614i 0.510175 0.883649i
\(520\) 1377.85 2.64970
\(521\) 691.695i 1.32763i 0.747897 + 0.663815i \(0.231064\pi\)
−0.747897 + 0.663815i \(0.768936\pi\)
\(522\) −205.087 + 355.221i −0.392887 + 0.680501i
\(523\) −70.7545 40.8501i −0.135286 0.0781073i 0.430830 0.902433i \(-0.358221\pi\)
−0.566115 + 0.824326i \(0.691554\pi\)
\(524\) −1459.85 −2.78597
\(525\) 61.7227i 0.117567i
\(526\) 656.635 + 379.108i 1.24836 + 0.720738i
\(527\) −435.113 + 251.212i −0.825640 + 0.476684i
\(528\) −235.587 136.016i −0.446187 0.257606i
\(529\) −126.474 219.060i −0.239081 0.414101i
\(530\) −127.491 220.820i −0.240548 0.416642i
\(531\) 88.8679i 0.167359i
\(532\) −1313.44 1174.48i −2.46888 2.20767i
\(533\) 335.686 0.629806
\(534\) 473.787 273.541i 0.887242 0.512249i
\(535\) −2.21533 + 1.27902i −0.00414081 + 0.00239070i
\(536\) −145.911 + 252.725i −0.272222 + 0.471502i
\(537\) 262.406 + 454.501i 0.488653 + 0.846371i
\(538\) −902.012 + 1562.33i −1.67660 + 2.90396i
\(539\) −414.860 −0.769685
\(540\) 209.969i 0.388831i
\(541\) 373.182 646.370i 0.689800 1.19477i −0.282102 0.959384i \(-0.591032\pi\)
0.971902 0.235384i \(-0.0756349\pi\)
\(542\) 678.876 + 391.949i 1.25254 + 0.723153i
\(543\) 125.753 0.231588
\(544\) 246.576i 0.453264i
\(545\) 375.716 + 216.920i 0.689387 + 0.398018i
\(546\) 1013.12 584.926i 1.85553 1.07129i
\(547\) 404.687 + 233.646i 0.739830 + 0.427141i 0.822008 0.569476i \(-0.192854\pi\)
−0.0821772 + 0.996618i \(0.526187\pi\)
\(548\) −515.496 892.866i −0.940687 1.62932i
\(549\) 64.0210 + 110.888i 0.116614 + 0.201981i
\(550\) 75.7117i 0.137658i
\(551\) 486.250 543.782i 0.882487 0.986900i
\(552\) 807.498 1.46286
\(553\) 281.898 162.754i 0.509761 0.294311i
\(554\) 808.273 466.657i 1.45898 0.842341i
\(555\) 136.965 237.230i 0.246783 0.427442i
\(556\) 479.075 + 829.782i 0.861645 + 1.49241i
\(557\) 386.099 668.743i 0.693175 1.20061i −0.277617 0.960692i \(-0.589544\pi\)
0.970792 0.239923i \(-0.0771222\pi\)
\(558\) −458.789 −0.822202
\(559\) 941.376i 1.68404i
\(560\) −612.643 + 1061.13i −1.09401 + 1.89487i
\(561\) −111.838 64.5698i −0.199355 0.115098i
\(562\) −1423.60 −2.53310
\(563\) 195.273i 0.346844i 0.984848 + 0.173422i \(0.0554825\pi\)
−0.984848 + 0.173422i \(0.944518\pi\)
\(564\) −313.251 180.855i −0.555409 0.320666i
\(565\) 223.385 128.971i 0.395372 0.228268i
\(566\) 254.345 + 146.846i 0.449373 + 0.259446i
\(567\) 48.0676 + 83.2556i 0.0847753 + 0.146835i
\(568\) 718.102 + 1243.79i 1.26426 + 2.18977i
\(569\) 579.517i 1.01848i 0.860624 + 0.509242i \(0.170074\pi\)
−0.860624 + 0.509242i \(0.829926\pi\)
\(570\) 111.575 533.937i 0.195746 0.936731i
\(571\) −145.886 −0.255492 −0.127746 0.991807i \(-0.540774\pi\)
−0.127746 + 0.991807i \(0.540774\pi\)
\(572\) −850.760 + 491.186i −1.48734 + 0.858717i
\(573\) 72.8602 42.0658i 0.127156 0.0734133i
\(574\) −359.576 + 622.805i −0.626440 + 1.08503i
\(575\) −46.6448 80.7911i −0.0811214 0.140506i
\(576\) 35.2899 61.1240i 0.0612672 0.106118i
\(577\) −1037.54 −1.79817 −0.899084 0.437777i \(-0.855766\pi\)
−0.899084 + 0.437777i \(0.855766\pi\)
\(578\) 541.724i 0.937239i
\(579\) −9.48401 + 16.4268i −0.0163800 + 0.0283710i
\(580\) −1343.57 775.713i −2.31651 1.33744i
\(581\) −823.723 −1.41777
\(582\) 12.9876i 0.0223154i
\(583\) 84.9009 + 49.0176i 0.145628 + 0.0840782i
\(584\) 1335.13 770.840i 2.28619 1.31993i
\(585\) 214.714 + 123.965i 0.367033 + 0.211907i
\(586\) 398.050 + 689.443i 0.679266 + 1.17652i
\(587\) 441.521 + 764.737i 0.752165 + 1.30279i 0.946771 + 0.321907i \(0.104324\pi\)
−0.194606 + 0.980882i \(0.562343\pi\)
\(588\) 978.896i 1.66479i
\(589\) 798.684 + 166.899i 1.35600 + 0.283360i
\(590\) 490.998 0.832201
\(591\) −156.663 + 90.4495i −0.265082 + 0.153045i
\(592\) 725.221 418.707i 1.22504 0.707275i
\(593\) 119.583 207.125i 0.201658 0.349283i −0.747404 0.664369i \(-0.768700\pi\)
0.949063 + 0.315087i \(0.102034\pi\)
\(594\) −58.9618 102.125i −0.0992624 0.171927i
\(595\) −290.835 + 503.741i −0.488798 + 0.846623i
\(596\) 501.315 0.841132
\(597\) 487.203i 0.816086i
\(598\) 884.075 1531.26i 1.47839 2.56064i
\(599\) −793.604 458.187i −1.32488 0.764920i −0.340378 0.940289i \(-0.610555\pi\)
−0.984503 + 0.175368i \(0.943888\pi\)
\(600\) 96.3377 0.160563
\(601\) 789.891i 1.31429i 0.753762 + 0.657147i \(0.228237\pi\)
−0.753762 + 0.657147i \(0.771763\pi\)
\(602\) −1746.55 1008.37i −2.90125 1.67504i
\(603\) −45.4756 + 26.2553i −0.0754155 + 0.0435412i
\(604\) −1544.76 891.867i −2.55755 1.47660i
\(605\) −187.079 324.031i −0.309222 0.535588i
\(606\) −84.9283 147.100i −0.140146 0.242739i
\(607\) 653.712i 1.07696i 0.842640 + 0.538478i \(0.181000\pi\)
−0.842640 + 0.538478i \(0.819000\pi\)
\(608\) 266.921 298.503i 0.439015 0.490959i
\(609\) −710.329 −1.16639
\(610\) −612.659 + 353.719i −1.00436 + 0.579867i
\(611\) −369.886 + 213.554i −0.605379 + 0.349515i
\(612\) −152.358 + 263.891i −0.248950 + 0.431194i
\(613\) 528.343 + 915.118i 0.861898 + 1.49285i 0.870095 + 0.492885i \(0.164057\pi\)
−0.00819687 + 0.999966i \(0.502609\pi\)
\(614\) 697.061 1207.35i 1.13528 1.96636i
\(615\) −152.413 −0.247825
\(616\) 1134.91i 1.84239i
\(617\) −501.032 + 867.813i −0.812045 + 1.40650i 0.0993850 + 0.995049i \(0.468312\pi\)
−0.911430 + 0.411455i \(0.865021\pi\)
\(618\) −546.727 315.653i −0.884672 0.510766i
\(619\) 252.948 0.408640 0.204320 0.978904i \(-0.434502\pi\)
0.204320 + 0.978904i \(0.434502\pi\)
\(620\) 1735.30i 2.79887i
\(621\) 125.835 + 72.6509i 0.202633 + 0.116990i
\(622\) 1159.07 669.187i 1.86345 1.07586i
\(623\) 820.491 + 473.711i 1.31700 + 0.760371i
\(624\) 378.967 + 656.390i 0.607319 + 1.05191i
\(625\) 265.233 + 459.398i 0.424373 + 0.735036i
\(626\) 536.973i 0.857784i
\(627\) 65.4929 + 199.234i 0.104454 + 0.317757i
\(628\) −965.543 −1.53749
\(629\) 344.278 198.769i 0.547342 0.316008i
\(630\) −459.990 + 265.575i −0.730143 + 0.421548i
\(631\) −605.640 + 1049.00i −0.959809 + 1.66244i −0.236853 + 0.971546i \(0.576116\pi\)
−0.722957 + 0.690893i \(0.757217\pi\)
\(632\) 254.029 + 439.991i 0.401944 + 0.696188i
\(633\) −89.2808 + 154.639i −0.141044 + 0.244295i
\(634\) −1801.75 −2.84187
\(635\) 444.568i 0.700107i
\(636\) 115.661 200.331i 0.181857 0.314985i
\(637\) 1001.02 + 577.940i 1.57146 + 0.907284i
\(638\) 871.320 1.36571
\(639\) 258.432i 0.404431i
\(640\) 677.526 + 391.170i 1.05863 + 0.611203i
\(641\) 89.1040 51.4442i 0.139008 0.0802562i −0.428883 0.903360i \(-0.641093\pi\)
0.567891 + 0.823104i \(0.307759\pi\)
\(642\) −2.93576 1.69496i −0.00457284 0.00264013i
\(643\) −384.990 666.822i −0.598740 1.03705i −0.993007 0.118052i \(-0.962335\pi\)
0.394267 0.918996i \(-0.370998\pi\)
\(644\) 1296.59 + 2245.76i 2.01334 + 3.48721i
\(645\) 427.416i 0.662660i
\(646\) 527.665 590.097i 0.816818 0.913463i
\(647\) −790.984 −1.22254 −0.611270 0.791422i \(-0.709341\pi\)
−0.611270 + 0.791422i \(0.709341\pi\)
\(648\) −129.947 + 75.0247i −0.200535 + 0.115779i
\(649\) −163.488 + 94.3896i −0.251907 + 0.145438i
\(650\) 105.474 182.686i 0.162267 0.281055i
\(651\) −397.259 688.072i −0.610228 1.05695i
\(652\) 300.345 520.213i 0.460652 0.797873i
\(653\) 320.503 0.490816 0.245408 0.969420i \(-0.421078\pi\)
0.245408 + 0.969420i \(0.421078\pi\)
\(654\) 574.924i 0.879088i
\(655\) 391.328 677.800i 0.597447 1.03481i
\(656\) −403.508 232.966i −0.615104 0.355130i
\(657\) 277.411 0.422239
\(658\) 915.008i 1.39059i
\(659\) −616.112 355.713i −0.934920 0.539776i −0.0465558 0.998916i \(-0.514825\pi\)
−0.888364 + 0.459139i \(0.848158\pi\)
\(660\) 386.273 223.015i 0.585262 0.337901i
\(661\) −410.779 237.163i −0.621451 0.358795i 0.155983 0.987760i \(-0.450146\pi\)
−0.777434 + 0.628965i \(0.783479\pi\)
\(662\) 788.842 + 1366.31i 1.19160 + 2.06392i
\(663\) 179.904 + 311.602i 0.271348 + 0.469989i
\(664\) 1285.68i 1.93626i
\(665\) 897.388 294.993i 1.34946 0.443598i
\(666\) 363.012 0.545062
\(667\) −929.776 + 536.806i −1.39397 + 0.804807i
\(668\) 1578.48 911.338i 2.36300 1.36428i
\(669\) 68.9560 119.435i 0.103073 0.178528i
\(670\) −145.062 251.254i −0.216510 0.375006i
\(671\) 135.998 235.555i 0.202679 0.351051i
\(672\) −389.927 −0.580248
\(673\) 648.662i 0.963836i −0.876216 0.481918i \(-0.839940\pi\)
0.876216 0.481918i \(-0.160060\pi\)
\(674\) 346.982 600.990i 0.514810 0.891677i
\(675\) 15.0126 + 8.66754i 0.0222409 + 0.0128408i
\(676\) 1269.87 1.87851
\(677\) 860.699i 1.27134i 0.771960 + 0.635671i \(0.219277\pi\)
−0.771960 + 0.635671i \(0.780723\pi\)
\(678\) 296.030 + 170.913i 0.436622 + 0.252084i
\(679\) 19.4782 11.2458i 0.0286866 0.0165622i
\(680\) −786.246 453.939i −1.15624 0.667558i
\(681\) 113.476 + 196.546i 0.166631 + 0.288614i
\(682\) 487.295 + 844.019i 0.714509 + 1.23757i
\(683\) 194.789i 0.285196i 0.989781 + 0.142598i \(0.0455456\pi\)
−0.989781 + 0.142598i \(0.954454\pi\)
\(684\) 470.108 154.536i 0.687293 0.225929i
\(685\) 552.738 0.806916
\(686\) −530.331 + 306.187i −0.773077 + 0.446336i
\(687\) −45.5306 + 26.2871i −0.0662745 + 0.0382636i
\(688\) 653.313 1131.57i 0.949583 1.64473i
\(689\) −136.572 236.550i −0.198218 0.343324i
\(690\) −401.399 + 695.243i −0.581738 + 1.00760i
\(691\) 719.067 1.04062 0.520309 0.853978i \(-0.325817\pi\)
0.520309 + 0.853978i \(0.325817\pi\)
\(692\) 2654.36i 3.83579i
\(693\) 102.108 176.857i 0.147343 0.255205i
\(694\) 1618.79 + 934.607i 2.33255 + 1.34670i
\(695\) −513.685 −0.739115
\(696\) 1108.69i 1.59295i
\(697\) −191.554 110.594i −0.274826 0.158671i
\(698\) −1138.21 + 657.144i −1.63067 + 0.941467i
\(699\) 141.145 + 81.4902i 0.201924 + 0.116581i
\(700\) 154.689 + 267.929i 0.220984 + 0.382755i
\(701\) 242.353 + 419.767i 0.345724 + 0.598812i 0.985485 0.169762i \(-0.0542999\pi\)
−0.639761 + 0.768574i \(0.720967\pi\)
\(702\) 328.558i 0.468031i
\(703\) −631.951 132.057i −0.898934 0.187848i
\(704\) −149.931 −0.212969
\(705\) 167.941 96.9605i 0.238213 0.137533i
\(706\) 998.378 576.414i 1.41413 0.816450i
\(707\) 147.076 254.744i 0.208029 0.360317i
\(708\) 222.720 + 385.762i 0.314576 + 0.544861i
\(709\) 620.485 1074.71i 0.875156 1.51581i 0.0185591 0.999828i \(-0.494092\pi\)
0.856597 0.515987i \(-0.172575\pi\)
\(710\) −1427.84 −2.01105
\(711\) 91.4203i 0.128580i
\(712\) −739.375 + 1280.64i −1.03845 + 1.79865i
\(713\) −1039.97 600.429i −1.45859 0.842116i
\(714\) −770.828 −1.07959
\(715\) 526.671i 0.736603i
\(716\) −2278.13 1315.28i −3.18175 1.83698i
\(717\) −562.946 + 325.017i −0.785141 + 0.453301i
\(718\) −38.5883 22.2790i −0.0537441 0.0310292i
\(719\) 65.3191 + 113.136i 0.0908471 + 0.157352i 0.907868 0.419256i \(-0.137709\pi\)
−0.817021 + 0.576608i \(0.804376\pi\)
\(720\) −172.063 298.023i −0.238977 0.413920i
\(721\) 1093.28i 1.51634i
\(722\) −1277.57 + 143.163i −1.76949 + 0.198287i
\(723\) −0.964848 −0.00133451
\(724\) −545.873 + 315.160i −0.753968 + 0.435303i
\(725\) −110.926 + 64.0432i −0.153001 + 0.0883354i
\(726\) 247.917 429.406i 0.341484 0.591468i
\(727\) −566.505 981.216i −0.779237 1.34968i −0.932382 0.361475i \(-0.882273\pi\)
0.153145 0.988204i \(-0.451060\pi\)
\(728\) −1581.04 + 2738.44i −2.17176 + 3.76160i
\(729\) −27.0000 −0.0370370
\(730\) 1532.71i 2.09960i
\(731\) 310.142 537.181i 0.424271 0.734858i
\(732\) −555.811 320.898i −0.759305 0.438385i
\(733\) −837.144 −1.14208 −0.571040 0.820922i \(-0.693460\pi\)
−0.571040 + 0.820922i \(0.693460\pi\)
\(734\) 315.630i 0.430014i
\(735\) −454.497 262.404i −0.618363 0.357012i
\(736\) −510.390 + 294.674i −0.693464 + 0.400372i
\(737\) 96.6023 + 55.7734i 0.131075 + 0.0756762i
\(738\) −100.989 174.917i −0.136841 0.237015i
\(739\) 144.463 + 250.216i 0.195484 + 0.338588i 0.947059 0.321060i \(-0.104039\pi\)
−0.751575 + 0.659647i \(0.770706\pi\)
\(740\) 1373.04i 1.85546i
\(741\) 119.523 571.972i 0.161300 0.771892i
\(742\) 585.167 0.788635
\(743\) −66.4928 + 38.3896i −0.0894923 + 0.0516684i −0.544078 0.839034i \(-0.683121\pi\)
0.454586 + 0.890703i \(0.349787\pi\)
\(744\) 1073.95 620.047i 1.44349 0.833397i
\(745\) −134.383 + 232.758i −0.180380 + 0.312427i
\(746\) 723.782 + 1253.63i 0.970217 + 1.68046i
\(747\) 115.673 200.352i 0.154850 0.268208i
\(748\) 647.296 0.865370
\(749\) 5.87058i 0.00783789i
\(750\) −406.750 + 704.512i −0.542334 + 0.939350i
\(751\) 923.318 + 533.078i 1.22945 + 0.709824i 0.966915 0.255098i \(-0.0821078\pi\)
0.262536 + 0.964922i \(0.415441\pi\)
\(752\) 592.824 0.788329
\(753\) 406.371i 0.539669i
\(754\) −2102.42 1213.83i −2.78835 1.60986i
\(755\) 828.179 478.149i 1.09693 0.633310i
\(756\) −417.308 240.933i −0.551995 0.318695i
\(757\) 4.94030 + 8.55684i 0.00652615 + 0.0113036i 0.869270 0.494338i \(-0.164589\pi\)
−0.862744 + 0.505641i \(0.831256\pi\)
\(758\) −772.411 1337.85i −1.01901 1.76498i
\(759\) 308.660i 0.406666i
\(760\) 460.429 + 1400.66i 0.605827 + 1.84297i
\(761\) 1147.50 1.50788 0.753940 0.656944i \(-0.228151\pi\)
0.753940 + 0.656944i \(0.228151\pi\)
\(762\) 510.211 294.570i 0.669568 0.386575i
\(763\) −862.247 + 497.819i −1.13007 + 0.652449i
\(764\) −210.850 + 365.203i −0.275982 + 0.478014i
\(765\) −81.6822 141.478i −0.106774 0.184938i
\(766\) −731.572 + 1267.12i −0.955055 + 1.65420i
\(767\) 525.975 0.685756
\(768\) 873.759i 1.13771i
\(769\) 299.227 518.276i 0.389112 0.673961i −0.603218 0.797576i \(-0.706115\pi\)
0.992330 + 0.123615i \(0.0394486\pi\)
\(770\) 977.142 + 564.153i 1.26902 + 0.732667i
\(771\) 22.1405 0.0287166
\(772\)