Properties

Label 224.3.w.a.99.1
Level 224
Weight 3
Character 224.99
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 99.1
Character \(\chi\) \(=\) 224.99
Dual form 224.3.w.a.43.1

$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\)

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 0.681232 + 0.732068i \(0.261445\pi\)
−0.999354 + 0.0359467i \(0.988555\pi\)
\(4\) 3.99937 0.0707620i 0.999844 0.0176905i
\(5\) −0.872291 2.10590i −0.174458 0.421179i 0.812329 0.583199i \(-0.198199\pi\)
−0.986788 + 0.162020i \(0.948199\pi\)
\(6\) 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 0.999289 0.0377153i \(-0.0120080\pi\)
−0.733272 + 0.679935i \(0.762008\pi\)
\(12\) −3.65383 + 9.28227i −0.304486 + 0.773522i
\(13\) −5.89149 + 14.2233i −0.453192 + 1.09410i 0.517910 + 0.855435i \(0.326710\pi\)
−0.971102 + 0.238666i \(0.923290\pi\)
\(14\) 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 \(-0.826024\pi\)
0.854317 0.519752i \(-0.173976\pi\)
\(18\) −3.96695 3.89738i −0.220386 0.216521i
\(19\) −19.0646 7.89681i −1.00340 0.415621i −0.180356 0.983601i \(-0.557725\pi\)
−0.823042 + 0.567980i \(0.807725\pi\)
\(20\) −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 −0.355962 + 0.934501i \(0.615847\pi\)
−0.934501 + 0.355962i \(0.884153\pi\)
\(24\) 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 −0.595906 0.803054i \(-0.703207\pi\)
−0.989214 + 0.146476i \(0.953207\pi\)
\(30\) −11.3687 + 0.100567i −0.378956 + 0.00335222i
\(31\) 35.6063i 1.14859i 0.818649 + 0.574295i \(0.194724\pi\)
−0.818649 + 0.574295i \(0.805276\pi\)
\(32\) −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 0.957858 + 0.287241i \(0.0927380\pi\)
−0.474198 + 0.880418i \(0.657262\pi\)
\(38\) 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 −0.902735 0.430197i \(-0.858444\pi\)
−0.430197 0.902735i \(-0.641556\pi\)
\(42\) −12.1467 + 5.15768i −0.289207 + 0.122802i
\(43\) −7.16417 17.2958i −0.166609 0.402229i 0.818420 0.574621i \(-0.194850\pi\)
−0.985028 + 0.172392i \(0.944850\pi\)
\(44\) 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 −0.653034 0.757329i \(-0.726504\pi\)
0.0737480 + 0.997277i \(0.476504\pi\)
\(54\) 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 0.0698826 0.997555i \(-0.477738\pi\)
0.754793 + 0.655964i \(0.227738\pi\)
\(60\) 22.7347 0.402251i 0.378912 0.00670419i
\(61\) 48.9618 + 20.2806i 0.802652 + 0.332469i 0.746018 0.665926i \(-0.231963\pi\)
0.0566337 + 0.998395i \(0.481963\pi\)
\(62\) −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 −0.101088 + 0.994878i \(0.532232\pi\)
−0.632005 + 0.774964i \(0.717768\pi\)
\(68\) −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 0.968763 0.247988i \(-0.0797692\pi\)
−0.247988 + 0.968763i \(0.579769\pi\)
\(72\) −16.1411 15.3064i −0.224182 0.212588i
\(73\) −39.1147 39.1147i −0.535818 0.535818i 0.386480 0.922298i \(-0.373691\pi\)
−0.922298 + 0.386480i \(0.873691\pi\)
\(74\) −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 0.328345 0.944558i \(-0.393509\pi\)
−0.435728 + 0.900078i \(0.643509\pi\)
\(84\) 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 −0.588237 0.808688i \(-0.700178\pi\)
0.808688 + 0.588237i \(0.200178\pi\)
\(90\) −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 0.782725 + 0.622367i \(0.213829\pi\)
−0.113390 + 0.993551i \(0.536171\pi\)
\(102\) −81.7273 33.0086i −0.801248 0.323614i
\(103\) −59.0984 59.0984i −0.573771 0.573771i 0.359409 0.933180i \(-0.382978\pi\)
−0.933180 + 0.359409i \(0.882978\pi\)
\(104\) 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 0.984431 + 0.175773i \(0.0562426\pi\)
−0.571807 + 0.820388i \(0.693757\pi\)
\(108\) −107.759 + 46.8856i −0.997770 + 0.434125i
\(109\) −30.3328 + 73.2298i −0.278282 + 0.671833i −0.999788 0.0205754i \(-0.993450\pi\)
0.721506 + 0.692408i \(0.243450\pi\)
\(110\) −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 \(-0.935281\pi\)
0.979401 0.201924i \(-0.0647192\pi\)
\(114\) −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 \(0.00386384\pi\)
−0.999926 + 0.0121383i \(0.996136\pi\)
\(128\) −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 −0.985015 0.172468i \(-0.944826\pi\)
0.818464 + 0.574558i \(0.194826\pi\)
\(132\) −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 0.475631 0.879645i \(-0.342220\pi\)
−0.879645 + 0.475631i \(0.842220\pi\)
\(138\) 81.8264 + 192.707i 0.592945 + 1.39643i
\(139\) −30.5863 73.8418i −0.220045 0.531236i 0.774851 0.632144i \(-0.217825\pi\)
−0.994896 + 0.100908i \(0.967825\pi\)
\(140\) −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 0.226678 0.973970i \(-0.427214\pi\)
0.848986 + 0.528415i \(0.177214\pi\)
\(150\) −38.6069 90.9220i −0.257379 0.606147i
\(151\) −31.0048 + 31.0048i −0.205330 + 0.205330i −0.802279 0.596949i \(-0.796379\pi\)
0.596949 + 0.802279i \(0.296379\pi\)
\(152\) 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 −0.239436 0.970912i \(-0.576962\pi\)
−0.855845 + 0.517232i \(0.826962\pi\)
\(158\) −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 0.656446 + 0.754373i \(0.272059\pi\)
−0.997600 + 0.0692444i \(0.977941\pi\)
\(164\) −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 0.368233 0.929733i \(-0.379963\pi\)
−0.929733 + 0.368233i \(0.879963\pi\)
\(168\) −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 −0.888145 0.459563i \(-0.848006\pi\)
0.952974 + 0.303054i \(0.0980061\pi\)
\(174\) −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 0.369622 0.929182i \(-0.379487\pi\)
−0.395668 + 0.918393i \(0.629487\pi\)
\(180\) 9.28598 23.5903i 0.0515888 0.131057i
\(181\) 111.613 46.2314i 0.616644 0.255422i −0.0524222 0.998625i \(-0.516694\pi\)
0.669066 + 0.743203i \(0.266694\pi\)
\(182\) −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 \(-0.770586\pi\)
0.751326 0.659931i \(-0.229414\pi\)
\(192\) −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 0.869885 0.493255i \(-0.164193\pi\)
−0.963885 + 0.266317i \(0.914193\pi\)
\(198\) 15.9247 39.4286i 0.0804279 0.199134i
\(199\) −19.8123 19.8123i −0.0995595 0.0995595i 0.655573 0.755132i \(-0.272427\pi\)
−0.755132 + 0.655573i \(0.772427\pi\)
\(200\) −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 0.913201 0.407509i \(-0.133602\pi\)
0.357579 + 0.933883i \(0.383602\pi\)
\(212\) −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 \(-0.869353\pi\)
0.916945 0.399014i \(-0.130647\pi\)
\(224\) 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 −0.784039 0.620712i \(-0.786844\pi\)
0.993309 + 0.115490i \(0.0368438\pi\)
\(228\) 142.959 148.109i 0.627013 0.649600i
\(229\) −4.37726 10.5676i −0.0191147 0.0461469i 0.914034 0.405638i \(-0.132950\pi\)
−0.933149 + 0.359491i \(0.882950\pi\)
\(230\) −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 0.962850 + 0.270037i \(0.0870360\pi\)
0.270037 + 0.962850i \(0.412964\pi\)
\(234\) 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 \(0.246985\pi\)
−0.713773 + 0.700377i \(0.753015\pi\)
\(242\) −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 −0.646512 0.762904i \(-0.723773\pi\)
0.0823014 + 0.996607i \(0.473773\pi\)
\(252\) −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 0.999926 + 0.0122044i \(0.00388487\pi\)
0.0122044 + 0.999926i \(0.496115\pi\)
\(264\) 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 0.404964 + 0.914333i \(0.367284\pi\)
−0.932883 + 0.360178i \(0.882716\pi\)
\(270\) −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 0.289691 0.957120i \(-0.406447\pi\)
0.881629 + 0.471944i \(0.156447\pi\)
\(278\) 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 −0.905810 0.423685i \(-0.860736\pi\)
0.423685 + 0.905810i \(0.360736\pi\)
\(282\) −49.7342 + 123.139i −0.176362 + 0.436662i
\(283\) 299.230 123.945i 1.05735 0.437969i 0.214840 0.976649i \(-0.431077\pi\)
0.842510 + 0.538681i \(0.181077\pi\)
\(284\) 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 0.945791 + 0.324775i \(0.105289\pi\)
−0.439125 + 0.898426i \(0.644711\pi\)
\(294\) 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 −0.585881 0.810397i \(-0.699251\pi\)
−0.987318 + 0.158757i \(0.949251\pi\)
\(308\) 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 −0.690915 0.722936i \(-0.742792\pi\)
0.722936 + 0.690915i \(0.242792\pi\)
\(312\) 222.874 + 211.349i 0.714341 + 0.677400i
\(313\) 45.2106 45.2106i 0.144443 0.144443i −0.631188 0.775630i \(-0.717432\pi\)
0.775630 + 0.631188i \(0.217432\pi\)
\(314\) 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 0.479516 0.877533i \(-0.340812\pi\)
−0.281441 + 0.959579i \(0.590812\pi\)
\(318\) 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 −0.966468 0.256785i \(-0.917337\pi\)
0.501822 0.864971i \(-0.332663\pi\)
\(332\) −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 \(0.0760616\pi\)
−0.971586 + 0.236687i \(0.923938\pi\)
\(338\) 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 −0.170980 0.985275i \(-0.554693\pi\)
0.575794 + 0.817595i \(0.304693\pi\)
\(348\) 344.702 357.120i 0.990524 1.02621i
\(349\) −160.272 66.3867i −0.459231 0.190220i 0.141060 0.990001i \(-0.454949\pi\)
−0.600292 + 0.799781i \(0.704949\pi\)
\(350\) 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 0.964551 0.263898i \(-0.0850082\pi\)
−0.263898 + 0.964551i \(0.585008\pi\)
\(360\) −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 −0.681607 0.731719i \(-0.738718\pi\)
0.0354346 + 0.999372i \(0.488718\pi\)
\(374\) −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 −0.696104 0.717941i \(-0.745085\pi\)
0.0154415 + 0.999881i \(0.495085\pi\)
\(380\) 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 \(-0.898131\pi\)
0.949226 0.314595i \(-0.101869\pi\)
\(384\) 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 0.931354 0.364116i \(-0.118629\pi\)
−0.916035 + 0.401097i \(0.868629\pi\)
\(390\) 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 0.703601 + 0.710595i \(0.251574\pi\)
−0.999988 + 0.00494541i \(0.998426\pi\)
\(398\) 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 \(0.416659\pi\)
−0.258842 + 0.965920i \(0.583341\pi\)
\(402\) 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 −0.800916 0.598777i \(-0.795654\pi\)
0.598777 + 0.800916i \(0.295654\pi\)
\(410\) 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 0.670955 + 0.741498i \(0.265884\pi\)
−0.998755 + 0.0498812i \(0.984116\pi\)
\(420\) −43.2853 41.7802i −0.103060 0.0994766i
\(421\) −193.389 466.882i −0.459356 1.10898i −0.968659 0.248395i \(-0.920097\pi\)
0.509303 0.860587i \(-0.329903\pi\)
\(422\) −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 \(0.284315\pi\)
−0.626920 + 0.779083i \(0.715685\pi\)
\(434\) −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 −0.818509 0.574493i \(-0.805199\pi\)
0.574493 + 0.818509i \(0.305199\pi\)
\(440\) −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 −0.714979 0.699146i \(-0.753564\pi\)
−0.0111960 + 0.999937i \(0.503564\pi\)
\(444\) −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 0.702799 0.711389i \(-0.251933\pi\)
−0.711389 + 0.702799i \(0.751933\pi\)
\(458\) 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 −0.862394 0.506238i \(-0.831036\pi\)
0.967769 + 0.251841i \(0.0810358\pi\)
\(462\) −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 0.811231 0.584726i \(-0.198798\pi\)
0.160164 + 0.987090i \(0.448798\pi\)
\(468\) −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 \(0.105292\pi\)
−0.945788 + 0.324784i \(0.894708\pi\)
\(480\) −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 0.991398 + 0.130882i \(0.0417810\pi\)
0.130882 + 0.991398i \(0.458219\pi\)
\(488\) −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 −0.955497 0.295002i \(-0.904680\pi\)
0.467041 0.884236i \(-0.345320\pi\)
\(492\) 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 −0.00935515 0.999956i \(-0.502978\pi\)
−0.713691 + 0.700461i \(0.752978\pi\)
\(500\) −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 0.0844411 0.996428i \(-0.473090\pi\)
0.996428 0.0844411i \(-0.0269105\pi\)
\(504\) 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 0.583207 0.812324i \(-0.301798\pi\)
−0.162010 + 0.986789i \(0.551798\pi\)
\(510\) 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 0.973276 0.229638i \(-0.0737541\pi\)
−0.229638 + 0.973276i \(0.573754\pi\)
\(522\) 108.145 + 254.690i 0.207175 + 0.487912i
\(523\) 105.605 + 254.953i 0.201922 + 0.487483i 0.992108 0.125384i \(-0.0400163\pi\)
−0.790186 + 0.612867i \(0.790016\pi\)
\(524\) −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 −0.436970 0.899476i \(-0.643949\pi\)
−0.945010 + 0.327041i \(0.893949\pi\)
\(542\) 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 −0.799124 0.601166i \(-0.794703\pi\)
0.990155 + 0.139977i \(0.0447029\pi\)
\(548\) −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 −0.599593 0.800305i \(-0.704671\pi\)
0.989877 0.141925i \(-0.0453292\pi\)
\(558\) 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 0.522596 0.852580i \(-0.324963\pi\)
−0.233334 + 0.972397i \(0.574963\pi\)
\(564\) 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 −0.974681 0.223601i \(-0.928219\pi\)
0.223601 + 0.974681i \(0.428219\pi\)
\(570\) 217.533 + 87.8590i 0.381637 + 0.154139i
\(571\) −256.927 + 106.422i −0.449959 + 0.186379i −0.596143 0.802878i \(-0.703301\pi\)
0.146184 + 0.989257i \(0.453301\pi\)
\(572\) −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 0.838937 0.544228i \(-0.183178\pi\)
−0.978046 + 0.208390i \(0.933178\pi\)
\(588\) −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 \(0.351324\pi\)
−0.450279 + 0.892888i \(0.648676\pi\)
\(594\) 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 −0.996350 0.0853641i \(-0.972795\pi\)
0.0853641 + 0.996350i \(0.472795\pi\)
\(600\) −160.837 360.899i −0.268062 0.601499i
\(601\) 382.967 382.967i 0.637216 0.637216i −0.312652 0.949868i \(-0.601217\pi\)
0.949868 + 0.312652i \(0.101217\pi\)
\(602\) 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 \(-0.686659\pi\)
0.553373 0.832934i \(-0.313341\pi\)
\(608\) 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 0.997891 + 0.0649081i \(0.0206754\pi\)
−0.659719 + 0.751513i \(0.729325\pi\)
\(614\) 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 0.480165 0.877178i \(-0.340577\pi\)
−0.877178 + 0.480165i \(0.840577\pi\)
\(618\) −383.708 + 162.928i −0.620886 + 0.263638i
\(619\) −87.5943 211.471i −0.141509 0.341634i 0.837196 0.546902i \(-0.184193\pi\)
−0.978706 + 0.205269i \(0.934193\pi\)
\(620\) 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 −0.999467 0.0326398i \(-0.989609\pi\)
0.0326398 + 0.999467i \(0.489609\pi\)
\(632\) −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 −0.990990 0.133934i \(-0.957239\pi\)
0.795441 + 0.606031i \(0.207239\pi\)
\(644\) 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 0.986844 0.161677i \(-0.0516902\pi\)
−0.161677 + 0.986844i \(0.551690\pi\)
\(648\) 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 −0.745081 0.666974i \(-0.767589\pi\)
0.998474 + 0.0552304i \(0.0175893\pi\)
\(654\) 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 0.354445 0.935077i \(-0.384670\pi\)
−0.410569 + 0.911830i \(0.634670\pi\)
\(660\) 69.3674 + 159.430i 0.105102 + 0.241561i
\(661\) −506.247 + 209.695i −0.765881 + 0.317238i −0.731203 0.682160i \(-0.761041\pi\)
−0.0346783 + 0.999399i \(0.511041\pi\)
\(662\) 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 −0.919029 0.394189i \(-0.871026\pi\)
0.371118 0.928586i \(-0.378974\pi\)
\(678\) −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 −0.934653 0.355560i \(-0.884290\pi\)
0.409481 0.912319i \(-0.365710\pi\)
\(684\) −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 0.535536 0.844512i \(-0.320110\pi\)
−0.218479 + 0.975842i \(0.570110\pi\)
\(692\) 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 0.160447 0.987044i \(-0.448706\pi\)
−0.584493 + 0.811399i \(0.698706\pi\)
\(702\) 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 −0.987293 0.158911i \(-0.949202\pi\)
0.585754 0.810489i \(-0.300798\pi\)
\(710\) −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 −0.300095 0.953909i \(-0.597019\pi\)
0.953909 + 0.300095i \(0.0970185\pi\)
\(728\) −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 0.650405 0.759587i \(-0.274599\pi\)
−0.0772034 + 0.997015i \(0.524599\pi\)
\(734\) −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 0.548190 + 0.836354i \(0.315317\pi\)
−0.979020 + 0.203762i \(0.934683\pi\)
\(740\) 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 0.0257993 0.999667i \(-0.491787\pi\)
−0.999667 + 0.0257993i \(0.991787\pi\)
\(744\) 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 −0.896147 0.443758i \(-0.853645\pi\)
−0.319887 + 0.947456i \(0.603645\pi\)
\(758\) 514.031 218.266i 0.678142 0.287949i