Properties

Label 224.3.w.a.43.1
Level 224
Weight 3
Character 224.43
Analytic conductor 6.104
Analytic rank 0
Dimension 192
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 43.1
Character \(\chi\) \(=\) 224.43
Dual form 224.3.w.a.99.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.99992 - 0.0176912i) q^{2} +(-0.954366 - 2.30404i) q^{3} +(3.99937 + 0.0707620i) q^{4} +(-0.872291 + 2.10590i) q^{5} +(1.86790 + 4.62479i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(-7.99718 - 0.212272i) q^{8} +(1.96616 - 1.96616i) q^{9} +O(q^{10})\) \(q+(-1.99992 - 0.0176912i) q^{2} +(-0.954366 - 2.30404i) q^{3} +(3.99937 + 0.0707620i) q^{4} +(-0.872291 + 2.10590i) q^{5} +(1.86790 + 4.62479i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(-7.99718 - 0.212272i) q^{8} +(1.96616 - 1.96616i) q^{9} +(1.78177 - 4.19620i) q^{10} +(2.92618 - 7.06442i) q^{11} +(-3.65383 - 9.28227i) q^{12} +(-5.89149 - 14.2233i) q^{13} +(3.77461 - 3.70841i) q^{14} +5.68456 q^{15} +(15.9900 + 0.566008i) q^{16} +17.6716i q^{17} +(-3.96695 + 3.89738i) q^{18} +(-19.0646 + 7.89681i) q^{19} +(-3.63763 + 8.36054i) q^{20} +(6.09593 + 2.52502i) q^{21} +(-5.97710 + 14.0765i) q^{22} +(-29.6806 - 29.6806i) q^{23} +(7.14316 + 18.6284i) q^{24} +(14.0038 + 14.0038i) q^{25} +(11.5309 + 28.5497i) q^{26} +(-27.1429 - 11.2430i) q^{27} +(-7.61453 + 7.34976i) q^{28} +(-45.9685 + 19.0408i) q^{29} +(-11.3687 - 0.100567i) q^{30} -35.6063i q^{31} +(-31.9687 - 1.41485i) q^{32} -19.0694 q^{33} +(0.312631 - 35.3417i) q^{34} +(-2.30786 - 5.57168i) q^{35} +(8.00253 - 7.72427i) q^{36} +(17.8954 - 43.2034i) q^{37} +(38.2674 - 15.4557i) q^{38} +(-27.1485 + 27.1485i) q^{39} +(7.42289 - 16.6561i) q^{40} +(-54.6502 + 54.6502i) q^{41} +(-12.1467 - 5.15768i) q^{42} +(-7.16417 + 17.2958i) q^{43} +(12.2028 - 28.0462i) q^{44} +(2.42546 + 5.85559i) q^{45} +(58.8339 + 59.8840i) q^{46} -26.6258 q^{47} +(-13.9562 - 37.3818i) q^{48} -7.00000i q^{49} +(-27.7587 - 28.2542i) q^{50} +(40.7161 - 16.8651i) q^{51} +(-22.5558 - 57.3013i) q^{52} +(-30.7021 - 12.7172i) q^{53} +(54.0849 + 22.9653i) q^{54} +(12.3245 + 12.3245i) q^{55} +(15.3585 - 14.5642i) q^{56} +(36.3892 + 36.3892i) q^{57} +(92.2702 - 37.2668i) q^{58} +(48.6558 + 20.1539i) q^{59} +(22.7347 + 0.402251i) q^{60} +(48.9618 - 20.2806i) q^{61} +(-0.629917 + 71.2097i) q^{62} +7.35669i q^{63} +(63.9099 + 3.39516i) q^{64} +35.0919 q^{65} +(38.1372 + 0.337360i) q^{66} +(-49.1172 - 118.579i) q^{67} +(-1.25048 + 70.6752i) q^{68} +(-40.0593 + 96.7117i) q^{69} +(4.51698 + 11.1837i) q^{70} +(51.1751 - 51.1751i) q^{71} +(-16.1411 + 15.3064i) q^{72} +(-39.1147 + 39.1147i) q^{73} +(-36.5538 + 86.0868i) q^{74} +(18.9006 - 45.6300i) q^{75} +(-76.8052 + 30.2332i) q^{76} +(7.74194 + 18.6907i) q^{77} +(54.7752 - 53.8146i) q^{78} +75.7855 q^{79} +(-15.1399 + 33.1795i) q^{80} +48.2433i q^{81} +(110.263 - 108.329i) q^{82} +(-8.91279 + 3.69180i) q^{83} +(24.2012 + 10.5298i) q^{84} +(-37.2145 - 15.4147i) q^{85} +(14.6338 - 34.4636i) q^{86} +(87.7415 + 87.7415i) q^{87} +(-24.9008 + 55.8743i) q^{88} +(19.6201 + 19.6201i) q^{89} +(-4.74715 - 11.7536i) q^{90} +(37.6314 + 15.5874i) q^{91} +(-116.604 - 120.804i) q^{92} +(-82.0384 + 33.9814i) q^{93} +(53.2494 + 0.471042i) q^{94} -47.0363i q^{95} +(27.2500 + 75.0076i) q^{96} +113.449 q^{97} +(-0.123838 + 13.9995i) q^{98} +(-8.13643 - 19.6431i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192q + O(q^{10}) \) \( 192q + 80q^{10} + 96q^{12} - 20q^{16} - 60q^{18} - 260q^{22} + 64q^{23} - 144q^{24} - 200q^{26} + 192q^{27} - 40q^{30} + 40q^{32} + 120q^{34} + 464q^{36} + 504q^{38} - 384q^{39} + 360q^{40} - 96q^{43} + 52q^{44} + 64q^{46} - 104q^{48} - 312q^{50} - 384q^{51} - 320q^{52} + 160q^{53} - 576q^{54} - 512q^{55} - 196q^{56} - 360q^{58} - 872q^{60} + 128q^{61} - 408q^{62} + 832q^{66} + 160q^{67} + 856q^{68} - 384q^{69} + 336q^{70} + 1488q^{72} + 308q^{74} + 768q^{75} + 1024q^{76} - 224q^{77} - 408q^{78} + 1024q^{79} - 1040q^{80} - 240q^{82} - 1384q^{86} + 896q^{87} - 560q^{88} - 1320q^{90} - 380q^{92} - 936q^{94} - 1088q^{96} - 512q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99992 0.0176912i −0.999961 0.00884560i
\(3\) −0.954366 2.30404i −0.318122 0.768015i −0.999354 0.0359467i \(-0.988555\pi\)
0.681232 0.732068i \(-0.261445\pi\)
\(4\) 3.99937 + 0.0707620i 0.999844 + 0.0176905i
\(5\) −0.872291 + 2.10590i −0.174458 + 0.421179i −0.986788 0.162020i \(-0.948199\pi\)
0.812329 + 0.583199i \(0.198199\pi\)
\(6\) 1.86790 + 4.62479i 0.311316 + 0.770799i
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) −7.99718 0.212272i −0.999648 0.0265340i
\(9\) 1.96616 1.96616i 0.218462 0.218462i
\(10\) 1.78177 4.19620i 0.178177 0.419620i
\(11\) 2.92618 7.06442i 0.266016 0.642220i −0.733272 0.679935i \(-0.762008\pi\)
0.999289 + 0.0377153i \(0.0120080\pi\)
\(12\) −3.65383 9.28227i −0.304486 0.773522i
\(13\) −5.89149 14.2233i −0.453192 1.09410i −0.971102 0.238666i \(-0.923290\pi\)
0.517910 0.855435i \(-0.326710\pi\)
\(14\) 3.77461 3.70841i 0.269615 0.264887i
\(15\) 5.68456 0.378971
\(16\) 15.9900 + 0.566008i 0.999374 + 0.0353755i
\(17\) 17.6716i 1.03950i 0.854317 + 0.519752i \(0.173976\pi\)
−0.854317 + 0.519752i \(0.826024\pi\)
\(18\) −3.96695 + 3.89738i −0.220386 + 0.216521i
\(19\) −19.0646 + 7.89681i −1.00340 + 0.415621i −0.823042 0.567980i \(-0.807725\pi\)
−0.180356 + 0.983601i \(0.557725\pi\)
\(20\) −3.63763 + 8.36054i −0.181882 + 0.418027i
\(21\) 6.09593 + 2.52502i 0.290282 + 0.120239i
\(22\) −5.97710 + 14.0765i −0.271687 + 0.639842i
\(23\) −29.6806 29.6806i −1.29046 1.29046i −0.934501 0.355962i \(-0.884153\pi\)
−0.355962 0.934501i \(-0.615847\pi\)
\(24\) 7.14316 + 18.6284i 0.297632 + 0.776185i
\(25\) 14.0038 + 14.0038i 0.560150 + 0.560150i
\(26\) 11.5309 + 28.5497i 0.443496 + 1.09807i
\(27\) −27.1429 11.2430i −1.00529 0.416406i
\(28\) −7.61453 + 7.34976i −0.271947 + 0.262491i
\(29\) −45.9685 + 19.0408i −1.58512 + 0.656578i −0.989214 0.146476i \(-0.953207\pi\)
−0.595906 + 0.803054i \(0.703207\pi\)
\(30\) −11.3687 0.100567i −0.378956 0.00335222i
\(31\) 35.6063i 1.14859i −0.818649 0.574295i \(-0.805276\pi\)
0.818649 0.574295i \(-0.194724\pi\)
\(32\) −31.9687 1.41485i −0.999022 0.0442142i
\(33\) −19.0694 −0.577860
\(34\) 0.312631 35.3417i 0.00919503 1.03946i
\(35\) −2.30786 5.57168i −0.0659390 0.159191i
\(36\) 8.00253 7.72427i 0.222293 0.214563i
\(37\) 17.8954 43.2034i 0.483660 1.16766i −0.474198 0.880418i \(-0.657262\pi\)
0.957858 0.287241i \(-0.0927380\pi\)
\(38\) 38.2674 15.4557i 1.00704 0.406729i
\(39\) −27.1485 + 27.1485i −0.696115 + 0.696115i
\(40\) 7.42289 16.6561i 0.185572 0.416402i
\(41\) −54.6502 + 54.6502i −1.33293 + 1.33293i −0.430197 + 0.902735i \(0.641556\pi\)
−0.902735 + 0.430197i \(0.858444\pi\)
\(42\) −12.1467 5.15768i −0.289207 0.122802i
\(43\) −7.16417 + 17.2958i −0.166609 + 0.402229i −0.985028 0.172392i \(-0.944850\pi\)
0.818420 + 0.574621i \(0.194850\pi\)
\(44\) 12.2028 28.0462i 0.277336 0.637413i
\(45\) 2.42546 + 5.85559i 0.0538992 + 0.130124i
\(46\) 58.8339 + 59.8840i 1.27900 + 1.30183i
\(47\) −26.6258 −0.566506 −0.283253 0.959045i \(-0.591414\pi\)
−0.283253 + 0.959045i \(0.591414\pi\)
\(48\) −13.9562 37.3818i −0.290754 0.778788i
\(49\) 7.00000i 0.142857i
\(50\) −27.7587 28.2542i −0.555174 0.565083i
\(51\) 40.7161 16.8651i 0.798354 0.330689i
\(52\) −22.5558 57.3013i −0.433765 1.10195i
\(53\) −30.7021 12.7172i −0.579286 0.239948i 0.0737480 0.997277i \(-0.476504\pi\)
−0.653034 + 0.757329i \(0.726504\pi\)
\(54\) 54.0849 + 22.9653i 1.00157 + 0.425283i
\(55\) 12.3245 + 12.3245i 0.224081 + 0.224081i
\(56\) 15.3585 14.5642i 0.274259 0.260076i
\(57\) 36.3892 + 36.3892i 0.638407 + 0.638407i
\(58\) 92.2702 37.2668i 1.59087 0.642531i
\(59\) 48.6558 + 20.1539i 0.824675 + 0.341592i 0.754793 0.655964i \(-0.227738\pi\)
0.0698826 + 0.997555i \(0.477738\pi\)
\(60\) 22.7347 + 0.402251i 0.378912 + 0.00670419i
\(61\) 48.9618 20.2806i 0.802652 0.332469i 0.0566337 0.998395i \(-0.481963\pi\)
0.746018 + 0.665926i \(0.231963\pi\)
\(62\) −0.629917 + 71.2097i −0.0101600 + 1.14854i
\(63\) 7.35669i 0.116773i
\(64\) 63.9099 + 3.39516i 0.998592 + 0.0530494i
\(65\) 35.0919 0.539876
\(66\) 38.1372 + 0.337360i 0.577837 + 0.00511151i
\(67\) −49.1172 118.579i −0.733093 1.76984i −0.632005 0.774964i \(-0.717768\pi\)
−0.101088 0.994878i \(-0.532232\pi\)
\(68\) −1.25048 + 70.6752i −0.0183893 + 1.03934i
\(69\) −40.0593 + 96.7117i −0.580569 + 1.40162i
\(70\) 4.51698 + 11.1837i 0.0645283 + 0.159768i
\(71\) 51.1751 51.1751i 0.720776 0.720776i −0.247988 0.968763i \(-0.579769\pi\)
0.968763 + 0.247988i \(0.0797692\pi\)
\(72\) −16.1411 + 15.3064i −0.224182 + 0.212588i
\(73\) −39.1147 + 39.1147i −0.535818 + 0.535818i −0.922298 0.386480i \(-0.873691\pi\)
0.386480 + 0.922298i \(0.373691\pi\)
\(74\) −36.5538 + 86.0868i −0.493970 + 1.16333i
\(75\) 18.9006 45.6300i 0.252008 0.608400i
\(76\) −76.8052 + 30.2332i −1.01059 + 0.397806i
\(77\) 7.74194 + 18.6907i 0.100545 + 0.242736i
\(78\) 54.7752 53.8146i 0.702246 0.689931i
\(79\) 75.7855 0.959311 0.479655 0.877457i \(-0.340762\pi\)
0.479655 + 0.877457i \(0.340762\pi\)
\(80\) −15.1399 + 33.1795i −0.189248 + 0.414744i
\(81\) 48.2433i 0.595597i
\(82\) 110.263 108.329i 1.34467 1.32109i
\(83\) −8.91279 + 3.69180i −0.107383 + 0.0444795i −0.435728 0.900078i \(-0.643509\pi\)
0.328345 + 0.944558i \(0.393509\pi\)
\(84\) 24.2012 + 10.5298i 0.288110 + 0.125355i
\(85\) −37.2145 15.4147i −0.437817 0.181350i
\(86\) 14.6338 34.4636i 0.170160 0.400739i
\(87\) 87.7415 + 87.7415i 1.00852 + 1.00852i
\(88\) −24.9008 + 55.8743i −0.282963 + 0.634935i
\(89\) 19.6201 + 19.6201i 0.220451 + 0.220451i 0.808688 0.588237i \(-0.200178\pi\)
−0.588237 + 0.808688i \(0.700178\pi\)
\(90\) −4.74715 11.7536i −0.0527461 0.130596i
\(91\) 37.6314 + 15.5874i 0.413531 + 0.171290i
\(92\) −116.604 120.804i −1.26743 1.31309i
\(93\) −82.0384 + 33.9814i −0.882133 + 0.365392i
\(94\) 53.2494 + 0.471042i 0.566483 + 0.00501108i
\(95\) 47.0363i 0.495119i
\(96\) 27.2500 + 75.0076i 0.283854 + 0.781329i
\(97\) 113.449 1.16958 0.584790 0.811185i \(-0.301177\pi\)
0.584790 + 0.811185i \(0.301177\pi\)
\(98\) −0.123838 + 13.9995i −0.00126366 + 0.142852i
\(99\) −8.13643 19.6431i −0.0821862 0.198415i
\(100\) 55.0153 + 56.9972i 0.550153 + 0.569972i
\(101\) 67.6028 163.208i 0.669335 1.61592i −0.113390 0.993551i \(-0.536171\pi\)
0.782725 0.622367i \(-0.213829\pi\)
\(102\) −81.7273 + 33.0086i −0.801248 + 0.323614i
\(103\) −59.0984 + 59.0984i −0.573771 + 0.573771i −0.933180 0.359409i \(-0.882978\pi\)
0.359409 + 0.933180i \(0.382978\pi\)
\(104\) 44.0961 + 114.997i 0.424001 + 1.10574i
\(105\) −10.6348 + 10.6348i −0.101284 + 0.101284i
\(106\) 61.1769 + 25.9766i 0.577140 + 0.245063i
\(107\) 44.1507 106.589i 0.412624 0.996162i −0.571807 0.820388i \(-0.693757\pi\)
0.984431 0.175773i \(-0.0562426\pi\)
\(108\) −107.759 46.8856i −0.997770 0.434125i
\(109\) −30.3328 73.2298i −0.278282 0.671833i 0.721506 0.692408i \(-0.243450\pi\)
−0.999788 + 0.0205754i \(0.993450\pi\)
\(110\) −24.4299 24.8660i −0.222090 0.226054i
\(111\) −116.621 −1.05064
\(112\) −30.9734 + 28.8556i −0.276548 + 0.257639i
\(113\) 45.6347i 0.403847i 0.979401 + 0.201924i \(0.0647192\pi\)
−0.979401 + 0.201924i \(0.935281\pi\)
\(114\) −72.1317 73.4193i −0.632735 0.644029i
\(115\) 88.3945 36.6142i 0.768648 0.318384i
\(116\) −185.193 + 72.8983i −1.59649 + 0.628434i
\(117\) −39.5489 16.3817i −0.338025 0.140014i
\(118\) −96.9513 41.1670i −0.821621 0.348873i
\(119\) −33.0605 33.0605i −0.277819 0.277819i
\(120\) −45.4605 1.20667i −0.378837 0.0100556i
\(121\) 44.2164 + 44.2164i 0.365425 + 0.365425i
\(122\) −98.2785 + 39.6935i −0.805561 + 0.325356i
\(123\) 178.073 + 73.7602i 1.44775 + 0.599676i
\(124\) 2.51957 142.403i 0.0203191 1.14841i
\(125\) −94.3532 + 39.0824i −0.754826 + 0.312659i
\(126\) 0.130149 14.7128i 0.00103293 0.116768i
\(127\) 3.08313i 0.0242766i −0.999926 0.0121383i \(-0.996136\pi\)
0.999926 0.0121383i \(-0.00386384\pi\)
\(128\) −127.755 7.92070i −0.998084 0.0618804i
\(129\) 46.6876 0.361919
\(130\) −70.1811 0.620818i −0.539855 0.00477552i
\(131\) −21.8182 52.6738i −0.166551 0.402090i 0.818464 0.574558i \(-0.194826\pi\)
−0.985015 + 0.172468i \(0.944826\pi\)
\(132\) −76.2655 1.34939i −0.577769 0.0102226i
\(133\) 20.8930 50.4401i 0.157090 0.379249i
\(134\) 96.1327 + 238.018i 0.717409 + 1.77626i
\(135\) 47.3531 47.3531i 0.350764 0.350764i
\(136\) 3.75118 141.323i 0.0275822 1.03914i
\(137\) −55.3500 + 55.3500i −0.404014 + 0.404014i −0.879645 0.475631i \(-0.842220\pi\)
0.475631 + 0.879645i \(0.342220\pi\)
\(138\) 81.8264 192.707i 0.592945 1.39643i
\(139\) −30.5863 + 73.8418i −0.220045 + 0.531236i −0.994896 0.100908i \(-0.967825\pi\)
0.774851 + 0.632144i \(0.217825\pi\)
\(140\) −8.83575 22.4465i −0.0631125 0.160332i
\(141\) 25.4107 + 61.3469i 0.180218 + 0.435085i
\(142\) −103.251 + 101.441i −0.727123 + 0.714372i
\(143\) −117.719 −0.823210
\(144\) 32.5517 30.3260i 0.226053 0.210597i
\(145\) 113.414i 0.782165i
\(146\) 78.9183 77.5344i 0.540537 0.531057i
\(147\) −16.1283 + 6.68056i −0.109716 + 0.0454460i
\(148\) 74.6277 171.520i 0.504241 1.15892i
\(149\) 160.274 + 66.3876i 1.07566 + 0.445555i 0.848986 0.528415i \(-0.177214\pi\)
0.226678 + 0.973970i \(0.427214\pi\)
\(150\) −38.6069 + 90.9220i −0.257379 + 0.606147i
\(151\) −31.0048 31.0048i −0.205330 0.205330i 0.596949 0.802279i \(-0.296379\pi\)
−0.802279 + 0.596949i \(0.796379\pi\)
\(152\) 154.139 59.1053i 1.01407 0.388851i
\(153\) 34.7451 + 34.7451i 0.227092 + 0.227092i
\(154\) −15.1526 37.5169i −0.0983936 0.243616i
\(155\) 74.9831 + 31.0590i 0.483762 + 0.200381i
\(156\) −110.498 + 106.656i −0.708321 + 0.683692i
\(157\) −171.959 + 71.2278i −1.09528 + 0.453680i −0.855845 0.517232i \(-0.826962\pi\)
−0.239436 + 0.970912i \(0.576962\pi\)
\(158\) −151.565 1.34074i −0.959273 0.00848568i
\(159\) 82.8760i 0.521233i
\(160\) 30.8655 66.0886i 0.192910 0.413054i
\(161\) 111.055 0.689781
\(162\) 0.853482 96.4829i 0.00526841 0.595573i
\(163\) −55.6080 134.250i −0.341153 0.823617i −0.997600 0.0692444i \(-0.977941\pi\)
0.656446 0.754373i \(-0.272059\pi\)
\(164\) −222.434 + 214.699i −1.35630 + 1.30914i
\(165\) 16.6340 40.1581i 0.100812 0.243383i
\(166\) 17.8902 7.22563i 0.107772 0.0435279i
\(167\) −93.7705 + 93.7705i −0.561500 + 0.561500i −0.929733 0.368233i \(-0.879963\pi\)
0.368233 + 0.929733i \(0.379963\pi\)
\(168\) −48.2143 21.4870i −0.286990 0.127899i
\(169\) −48.0920 + 48.0920i −0.284568 + 0.284568i
\(170\) 74.1533 + 31.4866i 0.436196 + 0.185216i
\(171\) −21.9576 + 53.0103i −0.128407 + 0.310002i
\(172\) −29.8761 + 68.6656i −0.173698 + 0.399218i
\(173\) 11.2153 + 27.0761i 0.0648283 + 0.156509i 0.952974 0.303054i \(-0.0980061\pi\)
−0.888145 + 0.459563i \(0.848006\pi\)
\(174\) −173.924 177.028i −0.999563 1.01740i
\(175\) −52.3973 −0.299413
\(176\) 50.7880 111.304i 0.288568 0.632407i
\(177\) 131.339i 0.742030i
\(178\) −38.8917 39.5859i −0.218492 0.222392i
\(179\) −4.66222 + 1.93115i −0.0260459 + 0.0107886i −0.395668 0.918393i \(-0.629487\pi\)
0.369622 + 0.929182i \(0.379487\pi\)
\(180\) 9.28598 + 23.5903i 0.0515888 + 0.131057i
\(181\) 111.613 + 46.2314i 0.616644 + 0.255422i 0.669066 0.743203i \(-0.266694\pi\)
−0.0524222 + 0.998625i \(0.516694\pi\)
\(182\) −74.9840 31.8394i −0.412000 0.174942i
\(183\) −93.4549 93.4549i −0.510682 0.510682i
\(184\) 231.061 + 243.662i 1.25577 + 1.32425i
\(185\) 75.3718 + 75.3718i 0.407415 + 0.407415i
\(186\) 164.672 66.5088i 0.885331 0.357574i
\(187\) 124.839 + 51.7101i 0.667590 + 0.276525i
\(188\) −106.486 1.88409i −0.566417 0.0100218i
\(189\) 71.8135 29.7461i 0.379965 0.157387i
\(190\) −0.832129 + 94.0690i −0.00437963 + 0.495100i
\(191\) 252.094i 1.31986i 0.751326 + 0.659931i \(0.229414\pi\)
−0.751326 + 0.659931i \(0.770586\pi\)
\(192\) −53.1708 150.491i −0.276931 0.783809i
\(193\) 26.6322 0.137991 0.0689954 0.997617i \(-0.478021\pi\)
0.0689954 + 0.997617i \(0.478021\pi\)
\(194\) −226.890 2.00705i −1.16953 0.0103456i
\(195\) −33.4905 80.8533i −0.171746 0.414632i
\(196\) 0.495334 27.9956i 0.00252721 0.142835i
\(197\) −18.5181 + 44.7067i −0.0940006 + 0.226938i −0.963885 0.266317i \(-0.914193\pi\)
0.869885 + 0.493255i \(0.164193\pi\)
\(198\) 15.9247 + 39.4286i 0.0804279 + 0.199134i
\(199\) −19.8123 + 19.8123i −0.0995595 + 0.0995595i −0.755132 0.655573i \(-0.772427\pi\)
0.655573 + 0.755132i \(0.272427\pi\)
\(200\) −109.018 114.963i −0.545090 0.574816i
\(201\) −226.336 + 226.336i −1.12605 + 1.12605i
\(202\) −138.088 + 325.207i −0.683603 + 1.60993i
\(203\) 50.3771 121.621i 0.248163 0.599119i
\(204\) 164.032 64.5689i 0.804079 0.316514i
\(205\) −67.4168 162.759i −0.328862 0.793944i
\(206\) 119.238 117.147i 0.578824 0.568674i
\(207\) −116.714 −0.563834
\(208\) −86.1543 230.765i −0.414204 1.10945i
\(209\) 157.788i 0.754964i
\(210\) 21.4570 21.0807i 0.102176 0.100384i
\(211\) 268.135 111.065i 1.27078 0.526374i 0.357579 0.933883i \(-0.383602\pi\)
0.913201 + 0.407509i \(0.133602\pi\)
\(212\) −121.889 53.0336i −0.574950 0.250158i
\(213\) −166.749 69.0698i −0.782861 0.324272i
\(214\) −90.1837 + 212.389i −0.421419 + 0.992473i
\(215\) −30.1740 30.1740i −0.140344 0.140344i
\(216\) 214.681 + 95.6738i 0.993891 + 0.442934i
\(217\) 66.6132 + 66.6132i 0.306973 + 0.306973i
\(218\) 59.3676 + 146.990i 0.272329 + 0.674268i
\(219\) 127.452 + 52.7922i 0.581971 + 0.241060i
\(220\) 48.4180 + 50.1622i 0.220082 + 0.228010i
\(221\) 251.348 104.112i 1.13732 0.471094i
\(222\) 233.233 + 2.06317i 1.05060 + 0.00929356i
\(223\) 177.960i 0.798027i 0.916945 + 0.399014i \(0.130647\pi\)
−0.916945 + 0.399014i \(0.869353\pi\)
\(224\) 62.4549 57.1610i 0.278817 0.255183i
\(225\) 55.0672 0.244743
\(226\) 0.807333 91.2659i 0.00357227 0.403831i
\(227\) 47.5042 + 114.685i 0.209270 + 0.505221i 0.993309 0.115490i \(-0.0368438\pi\)
−0.784039 + 0.620712i \(0.786844\pi\)
\(228\) 142.959 + 148.109i 0.627013 + 0.649600i
\(229\) −4.37726 + 10.5676i −0.0191147 + 0.0461469i −0.933149 0.359491i \(-0.882950\pi\)
0.914034 + 0.405638i \(0.132950\pi\)
\(230\) −177.430 + 71.6617i −0.771434 + 0.311573i
\(231\) 35.6755 35.6755i 0.154440 0.154440i
\(232\) 371.660 142.515i 1.60198 0.614287i
\(233\) 287.263 287.263i 1.23289 1.23289i 0.270037 0.962850i \(-0.412964\pi\)
0.962850 0.270037i \(-0.0870360\pi\)
\(234\) 78.8049 + 33.4618i 0.336773 + 0.142999i
\(235\) 23.2254 56.0711i 0.0988315 0.238600i
\(236\) 193.167 + 84.0460i 0.818503 + 0.356127i
\(237\) −72.3271 174.613i −0.305178 0.736764i
\(238\) 65.5335 + 66.7032i 0.275351 + 0.280266i
\(239\) −106.925 −0.447386 −0.223693 0.974660i \(-0.571811\pi\)
−0.223693 + 0.974660i \(0.571811\pi\)
\(240\) 90.8961 + 3.21751i 0.378734 + 0.0134063i
\(241\) 337.582i 1.40075i −0.713773 0.700377i \(-0.753015\pi\)
0.713773 0.700377i \(-0.246985\pi\)
\(242\) −87.6472 89.2117i −0.362178 0.368643i
\(243\) −133.132 + 55.1450i −0.547867 + 0.226934i
\(244\) 197.251 77.6452i 0.808408 0.318218i
\(245\) 14.7413 + 6.10604i 0.0601685 + 0.0249226i
\(246\) −354.827 150.665i −1.44238 0.612459i
\(247\) 224.638 + 224.638i 0.909464 + 0.909464i
\(248\) −7.55822 + 284.750i −0.0304767 + 1.14818i
\(249\) 17.0121 + 17.0121i 0.0683218 + 0.0683218i
\(250\) 189.391 76.4925i 0.757562 0.305970i
\(251\) −141.617 58.6596i −0.564211 0.233704i 0.0823014 0.996607i \(-0.473773\pi\)
−0.646512 + 0.762904i \(0.723773\pi\)
\(252\) −0.520574 + 29.4222i −0.00206577 + 0.116755i
\(253\) −296.527 + 122.826i −1.17204 + 0.485477i
\(254\) −0.0545443 + 6.16602i −0.000214741 + 0.0242757i
\(255\) 100.455i 0.393942i
\(256\) 255.359 + 18.1009i 0.997497 + 0.0707067i
\(257\) 137.099 0.533461 0.266731 0.963771i \(-0.414057\pi\)
0.266731 + 0.963771i \(0.414057\pi\)
\(258\) −93.3715 0.825959i −0.361905 0.00320139i
\(259\) 47.3468 + 114.305i 0.182806 + 0.441334i
\(260\) 140.346 + 2.48318i 0.539791 + 0.00955067i
\(261\) −52.9441 + 127.818i −0.202851 + 0.489726i
\(262\) 42.7028 + 105.729i 0.162988 + 0.403547i
\(263\) 266.190 266.190i 1.01213 1.01213i 0.0122044 0.999926i \(-0.496115\pi\)
0.999926 0.0122044i \(-0.00388487\pi\)
\(264\) 152.501 + 4.04790i 0.577656 + 0.0153329i
\(265\) 53.5624 53.5624i 0.202122 0.202122i
\(266\) −42.6767 + 100.507i −0.160439 + 0.377845i
\(267\) 26.4809 63.9305i 0.0991793 0.239440i
\(268\) −188.047 477.719i −0.701668 1.78253i
\(269\) −142.010 342.844i −0.527920 1.27451i −0.932883 0.360178i \(-0.882716\pi\)
0.404964 0.914333i \(-0.367284\pi\)
\(270\) −95.5402 + 93.8647i −0.353853 + 0.347647i
\(271\) −510.501 −1.88377 −0.941883 0.335940i \(-0.890946\pi\)
−0.941883 + 0.335940i \(0.890946\pi\)
\(272\) −10.0022 + 282.568i −0.0367729 + 1.03885i
\(273\) 101.580i 0.372089i
\(274\) 111.675 109.716i 0.407572 0.400425i
\(275\) 139.906 57.9509i 0.508749 0.210731i
\(276\) −167.056 + 383.951i −0.605274 + 1.39113i
\(277\) 324.456 + 134.394i 1.17132 + 0.485177i 0.881629 0.471944i \(-0.156447\pi\)
0.289691 + 0.957120i \(0.406447\pi\)
\(278\) 62.4765 147.137i 0.224736 0.529269i
\(279\) −70.0076 70.0076i −0.250923 0.250923i
\(280\) 17.2737 + 45.0476i 0.0616918 + 0.160884i
\(281\) −135.477 135.477i −0.482125 0.482125i 0.423685 0.905810i \(-0.360736\pi\)
−0.905810 + 0.423685i \(0.860736\pi\)
\(282\) −49.7342 123.139i −0.176362 0.436662i
\(283\) 299.230 + 123.945i 1.05735 + 0.437969i 0.842510 0.538681i \(-0.181077\pi\)
0.214840 + 0.976649i \(0.431077\pi\)
\(284\) 208.289 201.047i 0.733414 0.707912i
\(285\) −108.374 + 44.8899i −0.380259 + 0.157508i
\(286\) 235.429 + 2.08259i 0.823177 + 0.00728178i
\(287\) 204.482i 0.712482i
\(288\) −65.6374 + 60.0737i −0.227907 + 0.208589i
\(289\) −23.2842 −0.0805680
\(290\) −2.00643 + 226.819i −0.00691872 + 0.782135i
\(291\) −108.272 261.392i −0.372069 0.898255i
\(292\) −159.202 + 153.666i −0.545213 + 0.526255i
\(293\) 148.453 358.398i 0.506666 1.22320i −0.439125 0.898426i \(-0.644711\pi\)
0.945791 0.324775i \(-0.105289\pi\)
\(294\) 32.3735 13.0753i 0.110114 0.0444737i
\(295\) −84.8841 + 84.8841i −0.287743 + 0.287743i
\(296\) −152.284 + 341.707i −0.514473 + 1.15441i
\(297\) −158.850 + 158.850i −0.534849 + 0.534849i
\(298\) −319.361 135.606i −1.07168 0.455052i
\(299\) −247.294 + 597.020i −0.827070 + 1.99672i
\(300\) 78.8193 181.154i 0.262731 0.603847i
\(301\) −18.9546 45.7605i −0.0629721 0.152028i
\(302\) 61.4587 + 62.5558i 0.203506 + 0.207138i
\(303\) −440.556 −1.45398
\(304\) −309.312 + 115.479i −1.01747 + 0.379866i
\(305\) 120.799i 0.396062i
\(306\) −68.8728 70.1021i −0.225074 0.229092i
\(307\) −482.972 + 200.054i −1.57320 + 0.651640i −0.987318 0.158757i \(-0.949251\pi\)
−0.585881 + 0.810397i \(0.699251\pi\)
\(308\) 29.6403 + 75.2989i 0.0962348 + 0.244477i
\(309\) 192.567 + 79.7638i 0.623194 + 0.258135i
\(310\) −149.411 63.4422i −0.481971 0.204652i
\(311\) 9.95863 + 9.95863i 0.0320213 + 0.0320213i 0.722936 0.690915i \(-0.242792\pi\)
−0.690915 + 0.722936i \(0.742792\pi\)
\(312\) 222.874 211.349i 0.714341 0.677400i
\(313\) 45.2106 + 45.2106i 0.144443 + 0.144443i 0.775630 0.631188i \(-0.217432\pi\)
−0.631188 + 0.775630i \(0.717432\pi\)
\(314\) 345.165 139.408i 1.09925 0.443974i
\(315\) −15.4924 6.41717i −0.0491823 0.0203720i
\(316\) 303.095 + 5.36274i 0.959160 + 0.0169707i
\(317\) 62.7896 26.0083i 0.198075 0.0820452i −0.281441 0.959579i \(-0.590812\pi\)
0.479516 + 0.877533i \(0.340812\pi\)
\(318\) 1.46618 165.745i 0.00461061 0.521212i
\(319\) 380.457i 1.19266i
\(320\) −62.8979 + 131.626i −0.196556 + 0.411331i
\(321\) −287.722 −0.896331
\(322\) −222.101 1.96469i −0.689754 0.00610153i
\(323\) −139.549 336.901i −0.432040 1.04304i
\(324\) −3.41380 + 192.943i −0.0105364 + 0.595504i
\(325\) 116.677 281.683i 0.359006 0.866717i
\(326\) 108.837 + 269.472i 0.333855 + 0.826603i
\(327\) −139.776 + 139.776i −0.427450 + 0.427450i
\(328\) 448.648 425.447i 1.36783 1.29709i
\(329\) 49.8122 49.8122i 0.151405 0.151405i
\(330\) −33.9772 + 80.0188i −0.102961 + 0.242481i
\(331\) −153.798 + 371.301i −0.464647 + 1.12176i 0.501822 + 0.864971i \(0.332663\pi\)
−0.966468 + 0.256785i \(0.917337\pi\)
\(332\) −35.9068 + 14.1342i −0.108153 + 0.0425729i
\(333\) −49.7594 120.130i −0.149428 0.360750i
\(334\) 189.193 185.875i 0.566445 0.556511i
\(335\) 292.560 0.873315
\(336\) 96.0446 + 43.8253i 0.285847 + 0.130432i
\(337\) 159.527i 0.473374i −0.971586 0.236687i \(-0.923938\pi\)
0.971586 0.236687i \(-0.0760616\pi\)
\(338\) 97.0311 95.3295i 0.287074 0.282040i
\(339\) 105.144 43.5522i 0.310160 0.128473i
\(340\) −147.744 64.2827i −0.434541 0.189067i
\(341\) −251.538 104.190i −0.737647 0.305543i
\(342\) 44.8513 105.628i 0.131144 0.308854i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 60.9646 136.797i 0.177223 0.397666i
\(345\) −168.721 168.721i −0.489048 0.489048i
\(346\) −21.9507 54.3485i −0.0634413 0.157077i
\(347\) 140.470 + 58.1848i 0.404814 + 0.167679i 0.575794 0.817595i \(-0.304693\pi\)
−0.170980 + 0.985275i \(0.554693\pi\)
\(348\) 344.702 + 357.120i 0.990524 + 1.02621i
\(349\) −160.272 + 66.3867i −0.459231 + 0.190220i −0.600292 0.799781i \(-0.704949\pi\)
0.141060 + 0.990001i \(0.454949\pi\)
\(350\) 104.790 + 0.926971i 0.299401 + 0.00264849i
\(351\) 452.301i 1.28861i
\(352\) −103.541 + 221.700i −0.294151 + 0.629830i
\(353\) −640.333 −1.81397 −0.906987 0.421159i \(-0.861623\pi\)
−0.906987 + 0.421159i \(0.861623\pi\)
\(354\) −2.32355 + 262.668i −0.00656370 + 0.742001i
\(355\) 63.1298 + 152.409i 0.177831 + 0.429321i
\(356\) 77.0799 + 79.8567i 0.216517 + 0.224316i
\(357\) −44.6210 + 107.725i −0.124989 + 0.301749i
\(358\) 9.35823 3.77968i 0.0261403 0.0105578i
\(359\) 251.534 251.534i 0.700653 0.700653i −0.263898 0.964551i \(-0.585008\pi\)
0.964551 + 0.263898i \(0.0850082\pi\)
\(360\) −18.1539 47.3431i −0.0504275 0.131509i
\(361\) 45.8330 45.8330i 0.126961 0.126961i
\(362\) −222.399 94.4338i −0.614361 0.260867i
\(363\) 59.6779 144.075i 0.164402 0.396902i
\(364\) 149.399 + 65.0028i 0.410436 + 0.178579i
\(365\) −48.2521 116.491i −0.132198 0.319153i
\(366\) 185.249 + 188.556i 0.506145 + 0.515180i
\(367\) 508.040 1.38431 0.692153 0.721751i \(-0.256663\pi\)
0.692153 + 0.721751i \(0.256663\pi\)
\(368\) −457.793 491.392i −1.24400 1.33531i
\(369\) 214.902i 0.582390i
\(370\) −149.404 152.071i −0.403796 0.411003i
\(371\) 81.2302 33.6467i 0.218949 0.0906918i
\(372\) −330.507 + 130.099i −0.888459 + 0.349729i
\(373\) −241.022 99.8347i −0.646172 0.267653i 0.0354346 0.999372i \(-0.488718\pi\)
−0.681607 + 0.731719i \(0.738718\pi\)
\(374\) −248.754 105.625i −0.665118 0.282419i
\(375\) 180.095 + 180.095i 0.480254 + 0.480254i
\(376\) 212.931 + 5.65191i 0.566306 + 0.0150317i
\(377\) 541.646 + 541.646i 1.43673 + 1.43673i
\(378\) −144.148 + 58.2194i −0.381343 + 0.154020i
\(379\) −257.971 106.855i −0.680662 0.281939i 0.0154415 0.999881i \(-0.495085\pi\)
−0.696104 + 0.717941i \(0.745085\pi\)
\(380\) 3.32839 188.116i 0.00875891 0.495042i
\(381\) −7.10367 + 2.94244i −0.0186448 + 0.00772293i
\(382\) 4.45984 504.167i 0.0116750 1.31981i
\(383\) 240.980i 0.629191i 0.949226 + 0.314595i \(0.101869\pi\)
−0.949226 + 0.314595i \(0.898131\pi\)
\(384\) 103.675 + 301.912i 0.269987 + 0.786228i
\(385\) −46.1139 −0.119776
\(386\) −53.2624 0.471156i −0.137985 0.00122061i
\(387\) 19.9205 + 48.0922i 0.0514740 + 0.124269i
\(388\) 453.726 + 8.02790i 1.16940 + 0.0206905i
\(389\) 5.95873 14.3857i 0.0153181 0.0369811i −0.916035 0.401097i \(-0.868629\pi\)
0.931354 + 0.364116i \(0.118629\pi\)
\(390\) 65.5481 + 162.293i 0.168072 + 0.416135i
\(391\) 524.503 524.503i 1.34144 1.34144i
\(392\) −1.48591 + 55.9803i −0.00379058 + 0.142807i
\(393\) −100.540 + 100.540i −0.255827 + 0.255827i
\(394\) 37.8257 89.0823i 0.0960044 0.226097i
\(395\) −66.1070 + 159.596i −0.167360 + 0.404042i
\(396\) −31.1507 79.1358i −0.0786633 0.199838i
\(397\) −117.665 284.070i −0.296387 0.715540i −0.999988 0.00494541i \(-0.998426\pi\)
0.703601 0.710595i \(-0.251574\pi\)
\(398\) 39.9736 39.2726i 0.100436 0.0986750i
\(399\) −136.156 −0.341243
\(400\) 215.994 + 231.846i 0.539984 + 0.579615i
\(401\) 774.668i 1.93184i −0.258842 0.965920i \(-0.583341\pi\)
0.258842 0.965920i \(-0.416659\pi\)
\(402\) 456.659 448.651i 1.13597 1.11605i
\(403\) −506.439 + 209.774i −1.25667 + 0.520531i
\(404\) 281.918 647.945i 0.697817 1.60382i
\(405\) −101.595 42.0822i −0.250853 0.103907i
\(406\) −102.902 + 242.342i −0.253453 + 0.596900i
\(407\) −252.842 252.842i −0.621232 0.621232i
\(408\) −329.194 + 126.231i −0.806847 + 0.309389i
\(409\) −82.6747 82.6747i −0.202139 0.202139i 0.598777 0.800916i \(-0.295654\pi\)
−0.800916 + 0.598777i \(0.795654\pi\)
\(410\) 131.949 + 326.697i 0.321827 + 0.796822i
\(411\) 180.353 + 74.7046i 0.438815 + 0.181763i
\(412\) −240.539 + 232.175i −0.583832 + 0.563531i
\(413\) −128.731 + 53.3222i −0.311698 + 0.129109i
\(414\) 233.418 + 2.06480i 0.563812 + 0.00498745i
\(415\) 21.9897i 0.0529873i
\(416\) 168.219 + 463.037i 0.404374 + 1.11307i
\(417\) 199.325 0.477998
\(418\) 2.79145 315.563i 0.00667811 0.754935i
\(419\) −137.348 331.588i −0.327800 0.791379i −0.998755 0.0498812i \(-0.984116\pi\)
0.670955 0.741498i \(-0.265884\pi\)
\(420\) −43.2853 + 41.7802i −0.103060 + 0.0994766i
\(421\) −193.389 + 466.882i −0.459356 + 1.10898i 0.509303 + 0.860587i \(0.329903\pi\)
−0.968659 + 0.248395i \(0.920097\pi\)
\(422\) −538.213 + 217.378i −1.27539 + 0.515113i
\(423\) −52.3505 + 52.3505i −0.123760 + 0.123760i
\(424\) 242.831 + 108.219i 0.572715 + 0.255234i
\(425\) −247.468 + 247.468i −0.582278 + 0.582278i
\(426\) 332.264 + 141.084i 0.779962 + 0.331184i
\(427\) −53.6575 + 129.541i −0.125662 + 0.303374i
\(428\) 184.118 423.166i 0.430182 0.988706i
\(429\) 112.347 + 271.230i 0.261881 + 0.632237i
\(430\) 59.8118 + 60.8794i 0.139097 + 0.141580i
\(431\) −195.419 −0.453408 −0.226704 0.973964i \(-0.572795\pi\)
−0.226704 + 0.973964i \(0.572795\pi\)
\(432\) −427.652 195.138i −0.989934 0.451709i
\(433\) 674.686i 1.55817i −0.626920 0.779083i \(-0.715685\pi\)
0.626920 0.779083i \(-0.284315\pi\)
\(434\) −132.043 134.400i −0.304246 0.309677i
\(435\) −261.311 + 108.238i −0.600714 + 0.248824i
\(436\) −116.130 295.020i −0.266354 0.676651i
\(437\) 800.231 + 331.466i 1.83119 + 0.758504i
\(438\) −253.960 107.835i −0.579816 0.246199i
\(439\) −107.123 107.123i −0.244016 0.244016i 0.574493 0.818509i \(-0.305199\pi\)
−0.818509 + 0.574493i \(0.805199\pi\)
\(440\) −95.9448 101.177i −0.218056 0.229948i
\(441\) −13.7631 13.7631i −0.0312089 0.0312089i
\(442\) −504.519 + 203.769i −1.14144 + 0.461016i
\(443\) −321.696 133.251i −0.726175 0.300792i −0.0111960 0.999937i \(-0.503564\pi\)
−0.714979 + 0.699146i \(0.753564\pi\)
\(444\) −466.412 8.25236i −1.05048 0.0185864i
\(445\) −58.4325 + 24.2035i −0.131309 + 0.0543899i
\(446\) 3.14833 355.906i 0.00705903 0.797996i
\(447\) 432.636i 0.967867i
\(448\) −125.916 + 113.213i −0.281063 + 0.252707i
\(449\) 432.034 0.962214 0.481107 0.876662i \(-0.340235\pi\)
0.481107 + 0.876662i \(0.340235\pi\)
\(450\) −110.130 0.974205i −0.244734 0.00216490i
\(451\) 226.156 + 545.988i 0.501454 + 1.21062i
\(452\) −3.22920 + 182.510i −0.00714426 + 0.403784i
\(453\) −41.8465 + 101.026i −0.0923765 + 0.223017i
\(454\) −92.9758 230.202i −0.204792 0.507053i
\(455\) −65.6510 + 65.6510i −0.144288 + 0.144288i
\(456\) −283.286 298.735i −0.621242 0.655121i
\(457\) −3.92569 + 3.92569i −0.00859014 + 0.00859014i −0.711389 0.702799i \(-0.751933\pi\)
0.702799 + 0.711389i \(0.251933\pi\)
\(458\) 8.94112 21.0570i 0.0195221 0.0459760i
\(459\) 198.681 479.658i 0.432856 1.04501i
\(460\) 356.113 140.179i 0.774160 0.304737i
\(461\) 48.5778 + 117.277i 0.105375 + 0.254397i 0.967769 0.251841i \(-0.0810358\pi\)
−0.862394 + 0.506238i \(0.831036\pi\)
\(462\) −71.9794 + 70.7171i −0.155800 + 0.153067i
\(463\) −174.673 −0.377263 −0.188631 0.982048i \(-0.560405\pi\)
−0.188631 + 0.982048i \(0.560405\pi\)
\(464\) −745.813 + 278.443i −1.60735 + 0.600093i
\(465\) 202.406i 0.435282i
\(466\) −579.585 + 569.421i −1.24374 + 1.22193i
\(467\) 453.641 187.904i 0.971395 0.402365i 0.160164 0.987090i \(-0.448798\pi\)
0.811231 + 0.584726i \(0.198798\pi\)
\(468\) −157.012 68.3151i −0.335495 0.145972i
\(469\) 313.732 + 129.952i 0.668937 + 0.277083i
\(470\) −47.4410 + 111.727i −0.100938 + 0.237717i
\(471\) 328.224 + 328.224i 0.696866 + 0.696866i
\(472\) −384.831 171.503i −0.815321 0.363353i
\(473\) 101.221 + 101.221i 0.213999 + 0.213999i
\(474\) 141.560 + 350.492i 0.298649 + 0.739435i
\(475\) −377.561 156.391i −0.794865 0.329244i
\(476\) −129.882 134.561i −0.272861 0.282690i
\(477\) −85.3694 + 35.3611i −0.178971 + 0.0741324i
\(478\) 213.842 + 1.89164i 0.447369 + 0.00395740i
\(479\) 311.143i 0.649568i −0.945788 0.324784i \(-0.894708\pi\)
0.945788 0.324784i \(-0.105292\pi\)
\(480\) −181.728 8.04282i −0.378600 0.0167559i
\(481\) −719.926 −1.49673
\(482\) −5.97222 + 675.137i −0.0123905 + 1.40070i
\(483\) −105.987 255.875i −0.219435 0.529762i
\(484\) 173.709 + 179.967i 0.358903 + 0.371833i
\(485\) −98.9608 + 238.912i −0.204043 + 0.492603i
\(486\) 267.229 107.930i 0.549853 0.222079i
\(487\) 546.550 546.550i 1.12228 1.12228i 0.130882 0.991398i \(-0.458219\pi\)
0.991398 0.130882i \(-0.0417810\pi\)
\(488\) −395.861 + 151.795i −0.811191 + 0.311055i
\(489\) −256.247 + 256.247i −0.524022 + 0.524022i
\(490\) −29.3734 12.4724i −0.0599457 0.0254538i
\(491\) −239.832 + 579.006i −0.488456 + 1.17924i 0.467041 + 0.884236i \(0.345320\pi\)
−0.955497 + 0.295002i \(0.904680\pi\)
\(492\) 706.960 + 307.595i 1.43691 + 0.625194i
\(493\) −336.480 812.335i −0.682515 1.64774i
\(494\) −445.283 453.232i −0.901383 0.917473i
\(495\) 48.4636 0.0979064
\(496\) 20.1534 569.344i 0.0406319 1.14787i
\(497\) 191.480i 0.385271i
\(498\) −33.7220 34.3239i −0.0677148 0.0689235i
\(499\) −360.800 + 149.448i −0.723046 + 0.299495i −0.713691 0.700461i \(-0.752978\pi\)
−0.00935515 + 0.999956i \(0.502978\pi\)
\(500\) −380.119 + 149.628i −0.760239 + 0.299257i
\(501\) 305.543 + 126.560i 0.609866 + 0.252615i
\(502\) 282.185 + 119.820i 0.562121 + 0.238685i
\(503\) 543.677 + 543.677i 1.08087 + 1.08087i 0.996428 + 0.0844411i \(0.0269105\pi\)
0.0844411 + 0.996428i \(0.473090\pi\)
\(504\) 1.56162 58.8328i 0.00309845 0.116732i
\(505\) 284.729 + 284.729i 0.563820 + 0.563820i
\(506\) 595.204 240.396i 1.17629 0.475090i
\(507\) 156.704 + 64.9087i 0.309080 + 0.128025i
\(508\) 0.218169 12.3306i 0.000429466 0.0242728i
\(509\) 214.389 88.8028i 0.421196 0.174465i −0.162010 0.986789i \(-0.551798\pi\)
0.583207 + 0.812324i \(0.301798\pi\)
\(510\) 1.77717 200.902i 0.00348465 0.393926i
\(511\) 146.354i 0.286407i
\(512\) −510.378 40.7180i −0.996833 0.0795274i
\(513\) 606.252 1.18178
\(514\) −274.188 2.42545i −0.533440 0.00471878i
\(515\) −72.9042 176.006i −0.141561 0.341760i
\(516\) 186.721 + 3.30371i 0.361863 + 0.00640254i
\(517\) −77.9117 + 188.096i −0.150700 + 0.363821i
\(518\) −92.6678 229.439i −0.178895 0.442933i
\(519\) 51.6810 51.6810i 0.0995781 0.0995781i
\(520\) −280.637 7.44904i −0.539686 0.0143251i
\(521\) 387.436 387.436i 0.743639 0.743639i −0.229638 0.973276i \(-0.573754\pi\)
0.973276 + 0.229638i \(0.0737541\pi\)
\(522\) 108.145 254.690i 0.207175 0.487912i
\(523\) 105.605 254.953i 0.201922 0.487483i −0.790186 0.612867i \(-0.790016\pi\)
0.992108 + 0.125384i \(0.0400163\pi\)
\(524\) −83.5318 212.206i −0.159412 0.404973i
\(525\) 50.0062 + 120.726i 0.0952499 + 0.229954i
\(526\) −537.069 + 527.650i −1.02104 + 1.00314i
\(527\) 629.218 1.19396
\(528\) −304.919 10.7934i −0.577498 0.0204421i
\(529\) 1232.88i 2.33059i
\(530\) −108.068 + 106.173i −0.203902 + 0.200326i
\(531\) 135.291 56.0393i 0.254785 0.105535i
\(532\) 87.1281 200.251i 0.163775 0.376411i
\(533\) 1099.28 + 455.336i 2.06244 + 0.854289i
\(534\) −54.0907 + 127.387i −0.101293 + 0.238553i
\(535\) 185.954 + 185.954i 0.347577 + 0.347577i
\(536\) 367.628 + 958.727i 0.685873 + 1.78867i
\(537\) 8.89892 + 8.89892i 0.0165716 + 0.0165716i
\(538\) 277.944 + 688.173i 0.516625 + 1.27913i
\(539\) −49.4509 20.4832i −0.0917457 0.0380023i
\(540\) 192.733 186.032i 0.356914 0.344504i
\(541\) −747.652 + 309.687i −1.38198 + 0.572435i −0.945010 0.327041i \(-0.893949\pi\)
−0.436970 + 0.899476i \(0.643949\pi\)
\(542\) 1020.96 + 9.03137i 1.88369 + 0.0166630i
\(543\) 301.282i 0.554847i
\(544\) 25.0027 564.937i 0.0459608 1.03849i
\(545\) 180.673 0.331511
\(546\) −1.79708 + 203.153i −0.00329135 + 0.372075i
\(547\) 104.494 + 252.270i 0.191031 + 0.461189i 0.990155 0.139977i \(-0.0447029\pi\)
−0.799124 + 0.601166i \(0.794703\pi\)
\(548\) −225.282 + 217.449i −0.411098 + 0.396804i
\(549\) 56.3916 136.141i 0.102717 0.247981i
\(550\) −280.826 + 113.422i −0.510593 + 0.206222i
\(551\) 726.008 726.008i 1.31762 1.31762i
\(552\) 340.891 764.917i 0.617555 1.38572i
\(553\) −141.782 + 141.782i −0.256387 + 0.256387i
\(554\) −646.508 274.517i −1.16698 0.495519i
\(555\) 101.728 245.592i 0.183293 0.442509i
\(556\) −127.551 + 293.157i −0.229409 + 0.527260i
\(557\) 217.388 + 524.822i 0.390285 + 0.942230i 0.989877 + 0.141925i \(0.0453292\pi\)
−0.599593 + 0.800305i \(0.704671\pi\)
\(558\) 138.771 + 141.248i 0.248694 + 0.253133i
\(559\) 288.212 0.515585
\(560\) −33.7491 90.3973i −0.0602663 0.161424i
\(561\) 336.986i 0.600687i
\(562\) 268.547 + 273.340i 0.477841 + 0.486370i
\(563\) 162.855 67.4567i 0.289263 0.119816i −0.233334 0.972397i \(-0.574963\pi\)
0.522596 + 0.852580i \(0.324963\pi\)
\(564\) 97.2860 + 247.147i 0.172493 + 0.438205i
\(565\) −96.1020 39.8067i −0.170092 0.0704544i
\(566\) −596.244 253.174i −1.05343 0.447304i
\(567\) −90.2550 90.2550i −0.159180 0.159180i
\(568\) −420.119 + 398.393i −0.739647 + 0.701397i
\(569\) −427.364 427.364i −0.751079 0.751079i 0.223601 0.974681i \(-0.428219\pi\)
−0.974681 + 0.223601i \(0.928219\pi\)
\(570\) 217.533 87.8590i 0.381637 0.154139i
\(571\) −256.927 106.422i −0.449959 0.186379i 0.146184 0.989257i \(-0.453301\pi\)
−0.596143 + 0.802878i \(0.703301\pi\)
\(572\) −470.802 8.33003i −0.823081 0.0145630i
\(573\) 580.835 240.590i 1.01367 0.419877i
\(574\) −3.61754 + 408.949i −0.00630233 + 0.712454i
\(575\) 831.281i 1.44571i
\(576\) 132.332 118.982i 0.229744 0.206565i
\(577\) 427.867 0.741538 0.370769 0.928725i \(-0.379094\pi\)
0.370769 + 0.928725i \(0.379094\pi\)
\(578\) 46.5665 + 0.411925i 0.0805649 + 0.000712672i
\(579\) −25.4169 61.3618i −0.0438979 0.105979i
\(580\) 8.02540 453.585i 0.0138369 0.782043i
\(581\) 9.76758 23.5810i 0.0168117 0.0405869i
\(582\) 211.912 + 524.679i 0.364109 + 0.901511i
\(583\) −179.680 + 179.680i −0.308199 + 0.308199i
\(584\) 321.110 304.504i 0.549847 0.521412i
\(585\) 68.9963 68.9963i 0.117942 0.117942i
\(586\) −303.235 + 714.141i −0.517466 + 1.21867i
\(587\) −81.6568 + 197.137i −0.139109 + 0.335838i −0.978046 0.208390i \(-0.933178\pi\)
0.838937 + 0.544228i \(0.183178\pi\)
\(588\) −64.9759 + 25.5768i −0.110503 + 0.0434980i
\(589\) 281.176 + 678.818i 0.477378 + 1.15249i
\(590\) 171.263 168.260i 0.290277 0.285186i
\(591\) 120.679 0.204195
\(592\) 310.601 680.692i 0.524664 1.14982i
\(593\) 1058.96i 1.78578i −0.450279 0.892888i \(-0.648676\pi\)
0.450279 0.892888i \(-0.351324\pi\)
\(594\) 320.498 314.878i 0.539559 0.530097i
\(595\) 98.4603 40.7836i 0.165479 0.0685438i
\(596\) 636.298 + 276.850i 1.06761 + 0.464514i
\(597\) 64.5567 + 26.7403i 0.108135 + 0.0447911i
\(598\) 505.130 1189.62i 0.844700 1.98933i
\(599\) −545.680 545.680i −0.910986 0.910986i 0.0853641 0.996350i \(-0.472795\pi\)
−0.996350 + 0.0853641i \(0.972795\pi\)
\(600\) −160.837 + 360.899i −0.268062 + 0.601499i
\(601\) 382.967 + 382.967i 0.637216 + 0.637216i 0.949868 0.312652i \(-0.101217\pi\)
−0.312652 + 0.949868i \(0.601217\pi\)
\(602\) 37.0982 + 91.8527i 0.0616249 + 0.152579i
\(603\) −329.718 136.574i −0.546796 0.226490i
\(604\) −121.806 126.194i −0.201666 0.208930i
\(605\) −131.685 + 54.5457i −0.217661 + 0.0901581i
\(606\) 881.077 + 7.79395i 1.45392 + 0.0128613i
\(607\) 1011.18i 1.66587i 0.553373 + 0.832934i \(0.313341\pi\)
−0.553373 + 0.832934i \(0.686659\pi\)
\(608\) 620.643 225.477i 1.02079 0.370851i
\(609\) −328.299 −0.539078
\(610\) 2.13708 241.589i 0.00350341 0.396047i
\(611\) 156.865 + 378.707i 0.256736 + 0.619815i
\(612\) 136.500 + 141.417i 0.223039 + 0.231074i
\(613\) 207.300 500.466i 0.338173 0.816421i −0.659719 0.751513i \(-0.729325\pi\)
0.997891 0.0649081i \(-0.0206754\pi\)
\(614\) 969.445 391.547i 1.57890 0.637699i
\(615\) −310.663 + 310.663i −0.505142 + 0.505142i
\(616\) −57.9462 151.116i −0.0940685 0.245319i
\(617\) −244.957 + 244.957i −0.397013 + 0.397013i −0.877178 0.480165i \(-0.840577\pi\)
0.480165 + 0.877178i \(0.340577\pi\)
\(618\) −383.708 162.928i −0.620886 0.263638i
\(619\) −87.5943 + 211.471i −0.141509 + 0.341634i −0.978706 0.205269i \(-0.934193\pi\)
0.837196 + 0.546902i \(0.184193\pi\)
\(620\) 297.688 + 129.523i 0.480141 + 0.208907i
\(621\) 471.921 + 1139.32i 0.759937 + 1.83465i
\(622\) −19.7403 20.0927i −0.0317368 0.0323033i
\(623\) −73.4119 −0.117836
\(624\) −449.470 + 418.738i −0.720305 + 0.671054i
\(625\) 262.318i 0.419709i
\(626\) −89.6178 91.2174i −0.143159 0.145715i
\(627\) 363.549 150.587i 0.579824 0.240171i
\(628\) −692.769 + 272.698i −1.10314 + 0.434233i
\(629\) 763.471 + 316.240i 1.21379 + 0.502767i
\(630\) 30.8701 + 13.1079i 0.0490002 + 0.0208062i
\(631\) −610.068 610.068i −0.966827 0.966827i 0.0326398 0.999467i \(-0.489609\pi\)
−0.999467 + 0.0326398i \(0.989609\pi\)
\(632\) −606.071 16.0872i −0.958973 0.0254544i
\(633\) −511.797 511.797i −0.808526 0.808526i
\(634\) −126.034 + 50.9038i −0.198793 + 0.0802899i
\(635\) 6.49275 + 2.68939i 0.0102248 + 0.00423526i
\(636\) −5.86447 + 331.452i −0.00922087 + 0.521151i
\(637\) −99.5632 + 41.2404i −0.156300 + 0.0647417i
\(638\) 6.73074 760.885i 0.0105498 1.19261i
\(639\) 201.237i 0.314924i
\(640\) 128.119 262.129i 0.200187 0.409577i
\(641\) 132.131 0.206133 0.103066 0.994674i \(-0.467135\pi\)
0.103066 + 0.994674i \(0.467135\pi\)
\(642\) 575.422 + 5.09015i 0.896296 + 0.00792859i
\(643\) −125.738 303.558i −0.195549 0.472097i 0.795441 0.606031i \(-0.207239\pi\)
−0.990990 + 0.133934i \(0.957239\pi\)
\(644\) 444.149 + 7.85846i 0.689673 + 0.0122026i
\(645\) −40.7252 + 98.3192i −0.0631398 + 0.152433i
\(646\) 273.127 + 676.244i 0.422797 + 1.04682i
\(647\) 533.883 533.883i 0.825167 0.825167i −0.161677 0.986844i \(-0.551690\pi\)
0.986844 + 0.161677i \(0.0516902\pi\)
\(648\) 10.2407 385.811i 0.0158036 0.595387i
\(649\) 284.751 284.751i 0.438754 0.438754i
\(650\) −238.328 + 561.280i −0.366658 + 0.863507i
\(651\) 89.9064 217.053i 0.138105 0.333415i
\(652\) −212.897 540.849i −0.326530 0.829523i
\(653\) 165.465 + 399.468i 0.253392 + 0.611743i 0.998474 0.0552304i \(-0.0175893\pi\)
−0.745081 + 0.666974i \(0.767589\pi\)
\(654\) 282.014 277.068i 0.431214 0.423652i
\(655\) 129.957 0.198408
\(656\) −904.788 + 842.924i −1.37925 + 1.28494i
\(657\) 153.811i 0.234112i
\(658\) −100.502 + 98.7394i −0.152738 + 0.150060i
\(659\) −36.9858 + 15.3200i −0.0561241 + 0.0232474i −0.410569 0.911830i \(-0.634670\pi\)
0.354445 + 0.935077i \(0.384670\pi\)
\(660\) 69.3674 159.430i 0.105102 0.241561i
\(661\) −506.247 209.695i −0.765881 0.317238i −0.0346783 0.999399i \(-0.511041\pi\)
−0.731203 + 0.682160i \(0.761041\pi\)
\(662\) 314.153 739.853i 0.474551 1.11760i
\(663\) −479.757 479.757i −0.723615 0.723615i
\(664\) 72.0609 27.6320i 0.108525 0.0416145i
\(665\) 87.9969 + 87.9969i 0.132326 + 0.132326i
\(666\) 97.3897 + 241.131i 0.146231 + 0.362058i
\(667\) 1929.52 + 799.231i 2.89283 + 1.19825i
\(668\) −381.659 + 368.388i −0.571345 + 0.551479i
\(669\) 410.028 169.839i 0.612897 0.253870i
\(670\) −585.098 5.17574i −0.873281 0.00772499i
\(671\) 405.231i 0.603921i
\(672\) −191.306 89.3463i −0.284682 0.132956i
\(673\) −788.142 −1.17109 −0.585543 0.810641i \(-0.699119\pi\)
−0.585543 + 0.810641i \(0.699119\pi\)
\(674\) −2.82222 + 319.042i −0.00418728 + 0.473355i
\(675\) −222.659 537.547i −0.329866 0.796366i
\(676\) −195.741 + 188.935i −0.289558 + 0.279489i
\(677\) −370.936 + 895.518i −0.547911 + 1.32277i 0.371118 + 0.928586i \(0.378974\pi\)
−0.919029 + 0.394189i \(0.871026\pi\)
\(678\) −211.051 + 85.2409i −0.311285 + 0.125724i
\(679\) −212.244 + 212.244i −0.312584 + 0.312584i
\(680\) 294.339 + 131.174i 0.432851 + 0.192903i
\(681\) 218.904 218.904i 0.321444 0.321444i
\(682\) 501.212 + 212.822i 0.734915 + 0.312056i
\(683\) −358.693 + 865.961i −0.525173 + 1.26788i 0.409481 + 0.912319i \(0.365710\pi\)
−0.934653 + 0.355560i \(0.884290\pi\)
\(684\) −91.5678 + 210.454i −0.133871 + 0.307682i
\(685\) −68.2800 164.843i −0.0996789 0.240646i
\(686\) −25.9589 26.4223i −0.0378410 0.0385164i
\(687\) 28.5258 0.0415223
\(688\) −124.345 + 272.505i −0.180733 + 0.396083i
\(689\) 511.610i 0.742540i
\(690\) 334.445 + 340.414i 0.484702 + 0.493354i
\(691\) 219.087 90.7486i 0.317057 0.131329i −0.218479 0.975842i \(-0.570110\pi\)
0.535536 + 0.844512i \(0.320110\pi\)
\(692\) 42.9382 + 109.081i 0.0620494 + 0.157632i
\(693\) 51.9707 + 21.5270i 0.0749938 + 0.0310635i
\(694\) −279.901 118.850i −0.403315 0.171254i
\(695\) −128.823 128.823i −0.185357 0.185357i
\(696\) −683.060 720.310i −0.981408 1.03493i
\(697\) −965.755 965.755i −1.38559 1.38559i
\(698\) 321.705 129.933i 0.460896 0.186150i
\(699\) −936.020 387.712i −1.33908 0.554667i
\(700\) −209.556 3.70774i −0.299366 0.00529677i
\(701\) −297.256 + 123.127i −0.424045 + 0.175645i −0.584493 0.811399i \(-0.698706\pi\)
0.160447 + 0.987044i \(0.448706\pi\)
\(702\) 8.00174 904.566i 0.0113985 1.28856i
\(703\) 964.971i 1.37265i
\(704\) 210.996 441.551i 0.299711 0.627203i
\(705\) −151.356 −0.214689
\(706\) 1280.62 + 11.3282i 1.81390 + 0.0160457i
\(707\) 178.860 + 431.807i 0.252985 + 0.610760i
\(708\) 9.29384 525.275i 0.0131269 0.741914i
\(709\) −284.691 + 687.304i −0.401538 + 0.969399i 0.585754 + 0.810489i \(0.300798\pi\)
−0.987293 + 0.158911i \(0.949202\pi\)
\(710\) −123.558 305.923i −0.174026 0.430877i
\(711\) 149.006 149.006i 0.209573 0.209573i
\(712\) −152.741 161.071i −0.214524 0.226223i
\(713\) −1056.82 + 1056.82i −1.48221 + 1.48221i
\(714\) 91.1442 214.651i 0.127653 0.300632i
\(715\) 102.685 247.904i 0.143616 0.346719i
\(716\) −18.7826 + 7.39350i −0.0262327 + 0.0103261i
\(717\) 102.046 + 246.361i 0.142323 + 0.343599i
\(718\) −507.499 + 498.599i −0.706823 + 0.694428i
\(719\) −590.658 −0.821499 −0.410749 0.911748i \(-0.634733\pi\)
−0.410749 + 0.911748i \(0.634733\pi\)
\(720\) 35.4688 + 95.0036i 0.0492623 + 0.131949i
\(721\) 221.126i 0.306694i
\(722\) −92.4732 + 90.8515i −0.128079 + 0.125833i
\(723\) −777.803 + 322.177i −1.07580 + 0.445611i
\(724\) 443.109 + 192.795i 0.612029 + 0.266291i
\(725\) −910.374 377.089i −1.25569 0.520123i
\(726\) −121.900 + 287.084i −0.167906 + 0.395432i
\(727\) 475.323 + 475.323i 0.653814 + 0.653814i 0.953909 0.300095i \(-0.0970185\pi\)
−0.300095 + 0.953909i \(0.597019\pi\)
\(728\) −297.636 132.644i −0.408841 0.182203i
\(729\) 561.132 + 561.132i 0.769728 + 0.769728i
\(730\) 94.4396 + 233.826i 0.129369 + 0.320310i
\(731\) −305.644 126.602i −0.418118 0.173190i
\(732\) −367.148 380.374i −0.501568 0.519637i
\(733\) 420.157 174.035i 0.573202 0.237428i −0.0772034 0.997015i \(-0.524599\pi\)
0.650405 + 0.759587i \(0.274599\pi\)
\(734\) −1016.04 8.98784i −1.38425 0.0122450i
\(735\) 39.7919i 0.0541387i
\(736\) 906.858 + 990.845i 1.23214 + 1.34626i
\(737\) −981.420 −1.33164
\(738\) 3.80187 429.787i 0.00515159 0.582367i
\(739\) −318.384 768.646i −0.430830 1.04012i −0.979020 0.203762i \(-0.934683\pi\)
0.548190 0.836354i \(-0.315317\pi\)
\(740\) 296.107 + 306.774i 0.400144 + 0.414559i
\(741\) 303.188 731.961i 0.409161 0.987802i
\(742\) −163.049 + 65.8536i −0.219743 + 0.0887515i
\(743\) −723.584 + 723.584i −0.973868 + 0.973868i −0.999667 0.0257993i \(-0.991787\pi\)
0.0257993 + 0.999667i \(0.491787\pi\)
\(744\) 663.289 254.341i 0.891518 0.341856i
\(745\) −279.611 + 279.611i −0.375317 + 0.375317i
\(746\) 480.259 + 203.925i 0.643779 + 0.273359i
\(747\) −10.2653 + 24.7826i −0.0137420 + 0.0331762i
\(748\) 495.620 + 215.642i 0.662593 + 0.288291i
\(749\) 116.812 + 282.009i 0.155957 + 0.376514i
\(750\) −356.990 363.362i −0.475987 0.484483i
\(751\) −906.745 −1.20738 −0.603691 0.797218i \(-0.706304\pi\)
−0.603691 + 0.797218i \(0.706304\pi\)
\(752\) −425.746 15.0704i −0.566151 0.0200404i
\(753\) 382.274i 0.507668i
\(754\) −1073.67 1092.83i −1.42396 1.44938i
\(755\) 92.3382 38.2477i 0.122302 0.0506593i
\(756\) 289.314 113.884i 0.382690 0.150640i
\(757\) −920.538 381.299i −1.21603 0.503698i −0.319887 0.947456i \(-0.603645\pi\)
−0.896147 + 0.443758i