Properties

Label 224.3.w.a.43.2
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 43.2
Character \(\chi\) \(=\) 224.43
Dual form 224.3.w.a.99.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.99845 - 0.0786486i) q^{2} +(1.73419 + 4.18671i) q^{3} +(3.98763 + 0.314351i) q^{4} +(-2.33059 + 5.62654i) q^{5} +(-3.13642 - 8.50332i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(-7.94437 - 0.941838i) q^{8} +(-8.15712 + 8.15712i) q^{9} +O(q^{10})\) \(q+(-1.99845 - 0.0786486i) q^{2} +(1.73419 + 4.18671i) q^{3} +(3.98763 + 0.314351i) q^{4} +(-2.33059 + 5.62654i) q^{5} +(-3.13642 - 8.50332i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(-7.94437 - 0.941838i) q^{8} +(-8.15712 + 8.15712i) q^{9} +(5.10010 - 11.0611i) q^{10} +(-3.50516 + 8.46221i) q^{11} +(5.59921 + 17.2402i) q^{12} +(0.514028 + 1.24097i) q^{13} +(3.88590 - 3.59163i) q^{14} -27.5984 q^{15} +(15.8024 + 2.50703i) q^{16} -23.8792i q^{17} +(16.9432 - 15.6601i) q^{18} +(17.2181 - 7.13196i) q^{19} +(-11.0622 + 21.7039i) q^{20} +(-11.0770 - 4.58824i) q^{21} +(7.67044 - 16.6356i) q^{22} +(2.59794 + 2.59794i) q^{23} +(-9.83384 - 34.8940i) q^{24} +(-8.54866 - 8.54866i) q^{25} +(-0.929661 - 2.52046i) q^{26} +(-10.6171 - 4.39776i) q^{27} +(-8.04827 + 6.87207i) q^{28} +(-20.4589 + 8.47437i) q^{29} +(55.1540 + 2.17057i) q^{30} -4.26728i q^{31} +(-31.3831 - 6.25302i) q^{32} -41.5074 q^{33} +(-1.87806 + 47.7214i) q^{34} +(-6.16616 - 14.8864i) q^{35} +(-35.0918 + 29.9634i) q^{36} +(-10.6032 + 25.5984i) q^{37} +(-34.9704 + 12.8987i) q^{38} +(-4.30417 + 4.30417i) q^{39} +(23.8144 - 42.5043i) q^{40} +(-52.9347 + 52.9347i) q^{41} +(21.7760 + 10.0406i) q^{42} +(18.1278 - 43.7645i) q^{43} +(-16.6374 + 32.6423i) q^{44} +(-26.8855 - 64.9073i) q^{45} +(-4.98754 - 5.39618i) q^{46} -51.5941 q^{47} +(16.9081 + 70.5075i) q^{48} -7.00000i q^{49} +(16.4118 + 17.7564i) q^{50} +(99.9751 - 41.4110i) q^{51} +(1.65965 + 5.11013i) q^{52} +(77.9122 + 32.2723i) q^{53} +(20.8719 + 9.62373i) q^{54} +(-39.4439 - 39.4439i) q^{55} +(16.6246 - 13.1005i) q^{56} +(59.7188 + 59.7188i) q^{57} +(41.5527 - 15.3266i) q^{58} +(31.3508 + 12.9859i) q^{59} +(-110.052 - 8.67558i) q^{60} +(-83.6089 + 34.6319i) q^{61} +(-0.335616 + 8.52796i) q^{62} -30.5212i q^{63} +(62.2259 + 14.9646i) q^{64} -8.18038 q^{65} +(82.9505 + 3.26450i) q^{66} +(22.4005 + 54.0795i) q^{67} +(7.50645 - 95.2213i) q^{68} +(-6.37149 + 15.3821i) q^{69} +(11.1520 + 30.2348i) q^{70} +(-30.7353 + 30.7353i) q^{71} +(72.4859 - 57.1205i) q^{72} +(100.199 - 100.199i) q^{73} +(23.2033 - 50.3232i) q^{74} +(20.9657 - 50.6157i) q^{75} +(70.9013 - 23.0271i) q^{76} +(-9.27378 - 22.3889i) q^{77} +(8.94020 - 8.26316i) q^{78} -11.7979 q^{79} +(-50.9348 + 83.0698i) q^{80} +51.7459i q^{81} +(109.951 - 101.624i) q^{82} +(51.4495 - 21.3111i) q^{83} +(-42.7286 - 21.7782i) q^{84} +(134.357 + 55.6526i) q^{85} +(-39.6696 + 86.0355i) q^{86} +(-70.9594 - 70.9594i) q^{87} +(35.8163 - 63.9256i) q^{88} +(124.312 + 124.312i) q^{89} +(48.6245 + 131.829i) q^{90} +(-3.28331 - 1.35999i) q^{91} +(9.54295 + 11.1763i) q^{92} +(17.8658 - 7.40028i) q^{93} +(103.108 + 4.05781i) q^{94} +113.500i q^{95} +(-28.2447 - 142.236i) q^{96} -150.538 q^{97} +(-0.550540 + 13.9892i) q^{98} +(-40.4352 - 97.6193i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99845 0.0786486i −0.999226 0.0393243i
\(3\) 1.73419 + 4.18671i 0.578063 + 1.39557i 0.894549 + 0.446971i \(0.147497\pi\)
−0.316485 + 0.948597i \(0.602503\pi\)
\(4\) 3.98763 + 0.314351i 0.996907 + 0.0785878i
\(5\) −2.33059 + 5.62654i −0.466118 + 1.12531i 0.499726 + 0.866184i \(0.333434\pi\)
−0.965844 + 0.259125i \(0.916566\pi\)
\(6\) −3.13642 8.50332i −0.522736 1.41722i
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) −7.94437 0.941838i −0.993046 0.117730i
\(9\) −8.15712 + 8.15712i −0.906347 + 0.906347i
\(10\) 5.10010 11.0611i 0.510010 1.10611i
\(11\) −3.50516 + 8.46221i −0.318651 + 0.769292i 0.680675 + 0.732585i \(0.261687\pi\)
−0.999326 + 0.0367061i \(0.988313\pi\)
\(12\) 5.59921 + 17.2402i 0.466601 + 1.43668i
\(13\) 0.514028 + 1.24097i 0.0395406 + 0.0954595i 0.942416 0.334443i \(-0.108548\pi\)
−0.902875 + 0.429902i \(0.858548\pi\)
\(14\) 3.88590 3.59163i 0.277564 0.256545i
\(15\) −27.5984 −1.83989
\(16\) 15.8024 + 2.50703i 0.987648 + 0.156689i
\(17\) 23.8792i 1.40466i −0.711853 0.702329i \(-0.752144\pi\)
0.711853 0.702329i \(-0.247856\pi\)
\(18\) 16.9432 15.6601i 0.941287 0.870004i
\(19\) 17.2181 7.13196i 0.906215 0.375366i 0.119608 0.992821i \(-0.461836\pi\)
0.786606 + 0.617455i \(0.211836\pi\)
\(20\) −11.0622 + 21.7039i −0.553112 + 1.08520i
\(21\) −11.0770 4.58824i −0.527475 0.218487i
\(22\) 7.67044 16.6356i 0.348656 0.756166i
\(23\) 2.59794 + 2.59794i 0.112954 + 0.112954i 0.761325 0.648371i \(-0.224549\pi\)
−0.648371 + 0.761325i \(0.724549\pi\)
\(24\) −9.83384 34.8940i −0.409743 1.45392i
\(25\) −8.54866 8.54866i −0.341947 0.341947i
\(26\) −0.929661 2.52046i −0.0357562 0.0969406i
\(27\) −10.6171 4.39776i −0.393227 0.162880i
\(28\) −8.04827 + 6.87207i −0.287438 + 0.245431i
\(29\) −20.4589 + 8.47437i −0.705481 + 0.292220i −0.706433 0.707780i \(-0.749697\pi\)
0.000952287 1.00000i \(0.499697\pi\)
\(30\) 55.1540 + 2.17057i 1.83847 + 0.0723524i
\(31\) 4.26728i 0.137654i −0.997629 0.0688271i \(-0.978074\pi\)
0.997629 0.0688271i \(-0.0219257\pi\)
\(32\) −31.3831 6.25302i −0.980722 0.195407i
\(33\) −41.5074 −1.25780
\(34\) −1.87806 + 47.7214i −0.0552372 + 1.40357i
\(35\) −6.16616 14.8864i −0.176176 0.425327i
\(36\) −35.0918 + 29.9634i −0.974772 + 0.832316i
\(37\) −10.6032 + 25.5984i −0.286573 + 0.691848i −0.999960 0.00892210i \(-0.997160\pi\)
0.713388 + 0.700770i \(0.247160\pi\)
\(38\) −34.9704 + 12.8987i −0.920275 + 0.339440i
\(39\) −4.30417 + 4.30417i −0.110363 + 0.110363i
\(40\) 23.8144 42.5043i 0.595359 1.06261i
\(41\) −52.9347 + 52.9347i −1.29109 + 1.29109i −0.356978 + 0.934113i \(0.616193\pi\)
−0.934113 + 0.356978i \(0.883807\pi\)
\(42\) 21.7760 + 10.0406i 0.518475 + 0.239061i
\(43\) 18.1278 43.7645i 0.421578 1.01778i −0.560305 0.828287i \(-0.689316\pi\)
0.981882 0.189492i \(-0.0606841\pi\)
\(44\) −16.6374 + 32.6423i −0.378122 + 0.741870i
\(45\) −26.8855 64.9073i −0.597455 1.44238i
\(46\) −4.98754 5.39618i −0.108425 0.117308i
\(47\) −51.5941 −1.09775 −0.548874 0.835905i \(-0.684943\pi\)
−0.548874 + 0.835905i \(0.684943\pi\)
\(48\) 16.9081 + 70.5075i 0.352252 + 1.46891i
\(49\) 7.00000i 0.142857i
\(50\) 16.4118 + 17.7564i 0.328235 + 0.355129i
\(51\) 99.9751 41.4110i 1.96030 0.811981i
\(52\) 1.65965 + 5.11013i 0.0319164 + 0.0982717i
\(53\) 77.9122 + 32.2723i 1.47004 + 0.608911i 0.966868 0.255275i \(-0.0821661\pi\)
0.503172 + 0.864186i \(0.332166\pi\)
\(54\) 20.8719 + 9.62373i 0.386518 + 0.178217i
\(55\) −39.4439 39.4439i −0.717161 0.717161i
\(56\) 16.6246 13.1005i 0.296867 0.233938i
\(57\) 59.7188 + 59.7188i 1.04770 + 1.04770i
\(58\) 41.5527 15.3266i 0.716426 0.264251i
\(59\) 31.3508 + 12.9859i 0.531370 + 0.220101i 0.632203 0.774803i \(-0.282151\pi\)
−0.100833 + 0.994903i \(0.532151\pi\)
\(60\) −110.052 8.67558i −1.83420 0.144593i
\(61\) −83.6089 + 34.6319i −1.37064 + 0.567737i −0.941961 0.335721i \(-0.891020\pi\)
−0.428677 + 0.903458i \(0.641020\pi\)
\(62\) −0.335616 + 8.52796i −0.00541316 + 0.137548i
\(63\) 30.5212i 0.484463i
\(64\) 62.2259 + 14.9646i 0.972279 + 0.233822i
\(65\) −8.18038 −0.125852
\(66\) 82.9505 + 3.26450i 1.25683 + 0.0494621i
\(67\) 22.4005 + 54.0795i 0.334335 + 0.807157i 0.998238 + 0.0593381i \(0.0188990\pi\)
−0.663902 + 0.747819i \(0.731101\pi\)
\(68\) 7.50645 95.2213i 0.110389 1.40031i
\(69\) −6.37149 + 15.3821i −0.0923404 + 0.222929i
\(70\) 11.1520 + 30.2348i 0.159314 + 0.431926i
\(71\) −30.7353 + 30.7353i −0.432891 + 0.432891i −0.889611 0.456720i \(-0.849024\pi\)
0.456720 + 0.889611i \(0.349024\pi\)
\(72\) 72.4859 57.1205i 1.00675 0.793340i
\(73\) 100.199 100.199i 1.37259 1.37259i 0.516002 0.856587i \(-0.327420\pi\)
0.856587 0.516002i \(-0.172580\pi\)
\(74\) 23.2033 50.3232i 0.313557 0.680043i
\(75\) 20.9657 50.6157i 0.279543 0.674877i
\(76\) 70.9013 23.0271i 0.932911 0.302988i
\(77\) −9.27378 22.3889i −0.120439 0.290765i
\(78\) 8.94020 8.26316i 0.114618 0.105938i
\(79\) −11.7979 −0.149341 −0.0746706 0.997208i \(-0.523791\pi\)
−0.0746706 + 0.997208i \(0.523791\pi\)
\(80\) −50.9348 + 83.0698i −0.636685 + 1.03837i
\(81\) 51.7459i 0.638838i
\(82\) 109.951 101.624i 1.34086 1.23932i
\(83\) 51.4495 21.3111i 0.619873 0.256760i −0.0505702 0.998721i \(-0.516104\pi\)
0.670444 + 0.741961i \(0.266104\pi\)
\(84\) −42.7286 21.7782i −0.508673 0.259265i
\(85\) 134.357 + 55.6526i 1.58067 + 0.654736i
\(86\) −39.6696 + 86.0355i −0.461275 + 1.00041i
\(87\) −70.9594 70.9594i −0.815625 0.815625i
\(88\) 35.8163 63.9256i 0.407003 0.726427i
\(89\) 124.312 + 124.312i 1.39676 + 1.39676i 0.809129 + 0.587631i \(0.199939\pi\)
0.587631 + 0.809129i \(0.300061\pi\)
\(90\) 48.6245 + 131.829i 0.540272 + 1.46476i
\(91\) −3.28331 1.35999i −0.0360803 0.0149450i
\(92\) 9.54295 + 11.1763i 0.103728 + 0.121481i
\(93\) 17.8658 7.40028i 0.192106 0.0795729i
\(94\) 103.108 + 4.05781i 1.09690 + 0.0431682i
\(95\) 113.500i 1.19474i
\(96\) −28.2447 142.236i −0.294216 1.48162i
\(97\) −150.538 −1.55194 −0.775971 0.630768i \(-0.782740\pi\)
−0.775971 + 0.630768i \(0.782740\pi\)
\(98\) −0.550540 + 13.9892i −0.00561776 + 0.142747i
\(99\) −40.4352 97.6193i −0.408437 0.986053i
\(100\) −31.4016 36.7762i −0.314016 0.367762i
\(101\) −45.2067 + 109.139i −0.447591 + 1.08058i 0.525630 + 0.850713i \(0.323830\pi\)
−0.973222 + 0.229868i \(0.926170\pi\)
\(102\) −203.052 + 74.8951i −1.99071 + 0.734266i
\(103\) 58.1668 58.1668i 0.564727 0.564727i −0.365920 0.930646i \(-0.619246\pi\)
0.930646 + 0.365920i \(0.119246\pi\)
\(104\) −2.91483 10.3429i −0.0280272 0.0994508i
\(105\) 51.6318 51.6318i 0.491732 0.491732i
\(106\) −153.166 70.6223i −1.44496 0.666248i
\(107\) 65.4262 157.953i 0.611460 1.47619i −0.249937 0.968262i \(-0.580410\pi\)
0.861397 0.507933i \(-0.169590\pi\)
\(108\) −40.9547 20.8741i −0.379210 0.193279i
\(109\) 29.7319 + 71.7792i 0.272770 + 0.658525i 0.999600 0.0282928i \(-0.00900708\pi\)
−0.726830 + 0.686818i \(0.759007\pi\)
\(110\) 75.7245 + 81.9289i 0.688405 + 0.744809i
\(111\) −125.561 −1.13118
\(112\) −34.2537 + 24.8733i −0.305837 + 0.222083i
\(113\) 66.5732i 0.589143i 0.955629 + 0.294572i \(0.0951770\pi\)
−0.955629 + 0.294572i \(0.904823\pi\)
\(114\) −114.649 124.042i −1.00569 1.08809i
\(115\) −20.6721 + 8.56268i −0.179758 + 0.0744581i
\(116\) −84.2466 + 27.3614i −0.726264 + 0.235874i
\(117\) −14.3158 5.92979i −0.122357 0.0506819i
\(118\) −61.6318 28.4175i −0.522303 0.240826i
\(119\) 44.6739 + 44.6739i 0.375411 + 0.375411i
\(120\) 219.251 + 25.9932i 1.82710 + 0.216610i
\(121\) 26.2371 + 26.2371i 0.216836 + 0.216836i
\(122\) 169.812 62.6346i 1.39190 0.513398i
\(123\) −313.421 129.823i −2.54814 1.05547i
\(124\) 1.34142 17.0163i 0.0108179 0.137228i
\(125\) −72.6407 + 30.0888i −0.581126 + 0.240710i
\(126\) −2.40045 + 60.9951i −0.0190512 + 0.484088i
\(127\) 90.2134i 0.710342i 0.934801 + 0.355171i \(0.115577\pi\)
−0.934801 + 0.355171i \(0.884423\pi\)
\(128\) −123.179 34.8000i −0.962332 0.271875i
\(129\) 214.666 1.66408
\(130\) 16.3481 + 0.643376i 0.125755 + 0.00494905i
\(131\) −9.28956 22.4270i −0.0709126 0.171198i 0.884449 0.466636i \(-0.154534\pi\)
−0.955362 + 0.295438i \(0.904534\pi\)
\(132\) −165.516 13.0479i −1.25391 0.0988477i
\(133\) −18.8694 + 45.5548i −0.141875 + 0.342517i
\(134\) −40.5130 109.837i −0.302336 0.819680i
\(135\) 49.4883 49.4883i 0.366580 0.366580i
\(136\) −22.4903 + 189.705i −0.165370 + 1.39489i
\(137\) −116.363 + 116.363i −0.849361 + 0.849361i −0.990053 0.140692i \(-0.955067\pi\)
0.140692 + 0.990053i \(0.455067\pi\)
\(138\) 13.9429 30.2393i 0.101035 0.219126i
\(139\) −19.4593 + 46.9788i −0.139995 + 0.337977i −0.978290 0.207239i \(-0.933552\pi\)
0.838296 + 0.545216i \(0.183552\pi\)
\(140\) −19.9088 61.2999i −0.142206 0.437857i
\(141\) −89.4740 216.009i −0.634568 1.53198i
\(142\) 63.8403 59.0057i 0.449579 0.415533i
\(143\) −12.3031 −0.0860359
\(144\) −149.352 + 108.452i −1.03717 + 0.753137i
\(145\) 134.863i 0.930092i
\(146\) −208.124 + 192.363i −1.42550 + 1.31755i
\(147\) 29.3069 12.1393i 0.199367 0.0825805i
\(148\) −50.3285 + 98.7436i −0.340057 + 0.667187i
\(149\) 40.8212 + 16.9087i 0.273968 + 0.113481i 0.515437 0.856927i \(-0.327629\pi\)
−0.241470 + 0.970408i \(0.577629\pi\)
\(150\) −45.8799 + 99.5043i −0.305866 + 0.663362i
\(151\) 190.030 + 190.030i 1.25847 + 1.25847i 0.951821 + 0.306654i \(0.0992093\pi\)
0.306654 + 0.951821i \(0.400791\pi\)
\(152\) −143.504 + 40.4423i −0.944104 + 0.266068i
\(153\) 194.785 + 194.785i 1.27311 + 1.27311i
\(154\) 16.7724 + 45.4725i 0.108911 + 0.295276i
\(155\) 24.0100 + 9.94528i 0.154903 + 0.0641631i
\(156\) −18.5165 + 15.8104i −0.118695 + 0.101349i
\(157\) −11.0655 + 4.58347i −0.0704807 + 0.0291941i −0.417645 0.908610i \(-0.637145\pi\)
0.347165 + 0.937804i \(0.387145\pi\)
\(158\) 23.5776 + 0.927892i 0.149226 + 0.00587274i
\(159\) 382.161i 2.40353i
\(160\) 108.324 162.005i 0.677025 1.01253i
\(161\) −9.72060 −0.0603764
\(162\) 4.06975 103.412i 0.0251219 0.638344i
\(163\) 24.7816 + 59.8282i 0.152035 + 0.367044i 0.981486 0.191535i \(-0.0613467\pi\)
−0.829451 + 0.558579i \(0.811347\pi\)
\(164\) −227.724 + 194.444i −1.38856 + 1.18563i
\(165\) 96.7367 233.543i 0.586283 1.41541i
\(166\) −104.495 + 38.5427i −0.629491 + 0.232185i
\(167\) 214.447 214.447i 1.28411 1.28411i 0.345806 0.938306i \(-0.387606\pi\)
0.938306 0.345806i \(-0.112394\pi\)
\(168\) 83.6782 + 46.8833i 0.498085 + 0.279067i
\(169\) 118.225 118.225i 0.699558 0.699558i
\(170\) −264.130 121.786i −1.55370 0.716389i
\(171\) −82.2737 + 198.626i −0.481133 + 1.16156i
\(172\) 86.0445 168.818i 0.500259 0.981500i
\(173\) −19.2082 46.3727i −0.111030 0.268050i 0.858591 0.512660i \(-0.171340\pi\)
−0.969622 + 0.244610i \(0.921340\pi\)
\(174\) 136.228 + 147.390i 0.782920 + 0.847068i
\(175\) 31.9862 0.182778
\(176\) −76.6049 + 124.935i −0.435255 + 0.709860i
\(177\) 153.777i 0.868795i
\(178\) −238.654 258.208i −1.34075 1.45061i
\(179\) 220.508 91.3372i 1.23189 0.510264i 0.330716 0.943730i \(-0.392710\pi\)
0.901170 + 0.433466i \(0.142710\pi\)
\(180\) −86.8057 267.278i −0.482254 1.48488i
\(181\) −308.500 127.785i −1.70442 0.705994i −0.704427 0.709776i \(-0.748796\pi\)
−0.999993 + 0.00378209i \(0.998796\pi\)
\(182\) 6.45458 + 2.97611i 0.0354647 + 0.0163522i
\(183\) −289.987 289.987i −1.58463 1.58463i
\(184\) −18.1921 23.0858i −0.0988703 0.125466i
\(185\) −119.319 119.319i −0.644965 0.644965i
\(186\) −36.2861 + 13.3840i −0.195086 + 0.0719569i
\(187\) 202.071 + 83.7004i 1.08059 + 0.447596i
\(188\) −205.738 16.2187i −1.09435 0.0862696i
\(189\) 28.0903 11.6354i 0.148626 0.0615628i
\(190\) 8.92662 226.824i 0.0469822 1.19381i
\(191\) 356.257i 1.86522i −0.360888 0.932609i \(-0.617526\pi\)
0.360888 0.932609i \(-0.382474\pi\)
\(192\) 45.2591 + 286.473i 0.235725 + 1.49205i
\(193\) 175.565 0.909663 0.454832 0.890577i \(-0.349699\pi\)
0.454832 + 0.890577i \(0.349699\pi\)
\(194\) 300.844 + 11.8396i 1.55074 + 0.0610291i
\(195\) −14.1863 34.2489i −0.0727505 0.175635i
\(196\) 2.20046 27.9134i 0.0112268 0.142415i
\(197\) 67.7147 163.478i 0.343729 0.829836i −0.653603 0.756838i \(-0.726743\pi\)
0.997332 0.0729980i \(-0.0232567\pi\)
\(198\) 73.1303 + 198.268i 0.369345 + 1.00135i
\(199\) 96.1252 96.1252i 0.483041 0.483041i −0.423060 0.906102i \(-0.639044\pi\)
0.906102 + 0.423060i \(0.139044\pi\)
\(200\) 59.8623 + 75.9652i 0.299311 + 0.379826i
\(201\) −187.568 + 187.568i −0.933176 + 0.933176i
\(202\) 98.9271 214.553i 0.489738 1.06214i
\(203\) 22.4211 54.1293i 0.110449 0.266647i
\(204\) 411.681 133.705i 2.01804 0.655414i
\(205\) −174.470 421.209i −0.851075 2.05468i
\(206\) −120.818 + 111.669i −0.586497 + 0.542082i
\(207\) −42.3834 −0.204751
\(208\) 5.01170 + 20.8990i 0.0240947 + 0.100476i
\(209\) 170.702i 0.816754i
\(210\) −107.245 + 99.1230i −0.510688 + 0.472014i
\(211\) −150.258 + 62.2390i −0.712124 + 0.294971i −0.709183 0.705024i \(-0.750936\pi\)
−0.00294072 + 0.999996i \(0.500936\pi\)
\(212\) 300.540 + 153.182i 1.41764 + 0.722555i
\(213\) −181.980 75.3787i −0.854367 0.353891i
\(214\) −143.174 + 310.516i −0.669037 + 1.45101i
\(215\) 203.994 + 203.994i 0.948810 + 0.948810i
\(216\) 80.2043 + 44.9370i 0.371316 + 0.208042i
\(217\) 7.98335 + 7.98335i 0.0367896 + 0.0367896i
\(218\) −53.7725 145.786i −0.246663 0.668742i
\(219\) 593.268 + 245.740i 2.70899 + 1.12210i
\(220\) −144.888 169.687i −0.658583 0.771304i
\(221\) 29.6334 12.2746i 0.134088 0.0555411i
\(222\) 250.927 + 9.87518i 1.13030 + 0.0444828i
\(223\) 201.113i 0.901853i 0.892561 + 0.450926i \(0.148906\pi\)
−0.892561 + 0.450926i \(0.851094\pi\)
\(224\) 70.4108 47.0141i 0.314334 0.209884i
\(225\) 139.465 0.619844
\(226\) 5.23589 133.043i 0.0231677 0.588688i
\(227\) −20.9871 50.6674i −0.0924542 0.223204i 0.870887 0.491483i \(-0.163545\pi\)
−0.963341 + 0.268279i \(0.913545\pi\)
\(228\) 219.364 + 256.909i 0.962122 + 1.12680i
\(229\) −8.50384 + 20.5301i −0.0371347 + 0.0896511i −0.941359 0.337407i \(-0.890450\pi\)
0.904224 + 0.427058i \(0.140450\pi\)
\(230\) 41.9858 15.4863i 0.182547 0.0673317i
\(231\) 77.6532 77.6532i 0.336161 0.336161i
\(232\) 170.515 48.0545i 0.734978 0.207131i
\(233\) −70.1185 + 70.1185i −0.300938 + 0.300938i −0.841381 0.540443i \(-0.818257\pi\)
0.540443 + 0.841381i \(0.318257\pi\)
\(234\) 28.1430 + 12.9763i 0.120269 + 0.0554543i
\(235\) 120.245 290.297i 0.511680 1.23530i
\(236\) 120.933 + 61.6383i 0.512429 + 0.261179i
\(237\) −20.4599 49.3945i −0.0863286 0.208416i
\(238\) −85.7651 92.7921i −0.360357 0.389883i
\(239\) −291.950 −1.22155 −0.610774 0.791805i \(-0.709142\pi\)
−0.610774 + 0.791805i \(0.709142\pi\)
\(240\) −436.119 69.1900i −1.81716 0.288292i
\(241\) 102.739i 0.426301i −0.977019 0.213150i \(-0.931628\pi\)
0.977019 0.213150i \(-0.0683724\pi\)
\(242\) −50.3701 54.4972i −0.208141 0.225195i
\(243\) −312.199 + 129.317i −1.28477 + 0.532169i
\(244\) −344.288 + 111.817i −1.41102 + 0.458265i
\(245\) 39.3858 + 16.3141i 0.160758 + 0.0665883i
\(246\) 616.146 + 284.096i 2.50466 + 1.15486i
\(247\) 17.7012 + 17.7012i 0.0716646 + 0.0716646i
\(248\) −4.01909 + 33.9008i −0.0162060 + 0.136697i
\(249\) 178.446 + 178.446i 0.716652 + 0.716652i
\(250\) 147.535 54.4179i 0.590142 0.217672i
\(251\) 247.590 + 102.555i 0.986413 + 0.408586i 0.816797 0.576925i \(-0.195747\pi\)
0.169616 + 0.985510i \(0.445747\pi\)
\(252\) 9.59436 121.707i 0.0380729 0.482965i
\(253\) −31.0905 + 12.8781i −0.122887 + 0.0509016i
\(254\) 7.09516 180.287i 0.0279337 0.709792i
\(255\) 659.026i 2.58442i
\(256\) 243.430 + 79.2341i 0.950897 + 0.309508i
\(257\) −284.088 −1.10540 −0.552699 0.833381i \(-0.686402\pi\)
−0.552699 + 0.833381i \(0.686402\pi\)
\(258\) −429.000 16.8832i −1.66279 0.0654387i
\(259\) −28.0534 67.7269i −0.108314 0.261494i
\(260\) −32.6203 2.57151i −0.125463 0.00989044i
\(261\) 97.7596 236.013i 0.374558 0.904263i
\(262\) 16.8009 + 45.5499i 0.0641255 + 0.173854i
\(263\) −80.9875 + 80.9875i −0.307937 + 0.307937i −0.844109 0.536172i \(-0.819870\pi\)
0.536172 + 0.844109i \(0.319870\pi\)
\(264\) 329.750 + 39.0932i 1.24905 + 0.148080i
\(265\) −363.163 + 363.163i −1.37043 + 1.37043i
\(266\) 41.2924 89.5550i 0.155235 0.336673i
\(267\) −304.876 + 736.036i −1.14186 + 2.75669i
\(268\) 72.3248 + 222.691i 0.269869 + 0.830936i
\(269\) −100.809 243.374i −0.374754 0.904735i −0.992931 0.118696i \(-0.962129\pi\)
0.618177 0.786039i \(-0.287871\pi\)
\(270\) −102.792 + 95.0079i −0.380712 + 0.351881i
\(271\) −33.1880 −0.122465 −0.0612326 0.998124i \(-0.519503\pi\)
−0.0612326 + 0.998124i \(0.519503\pi\)
\(272\) 59.8659 377.348i 0.220095 1.38731i
\(273\) 16.1047i 0.0589917i
\(274\) 241.697 223.393i 0.882105 0.815304i
\(275\) 102.305 42.3761i 0.372018 0.154095i
\(276\) −30.2425 + 59.3353i −0.109574 + 0.214983i
\(277\) 264.549 + 109.580i 0.955052 + 0.395595i 0.805127 0.593102i \(-0.202097\pi\)
0.149924 + 0.988697i \(0.452097\pi\)
\(278\) 42.5833 92.3546i 0.153177 0.332211i
\(279\) 34.8087 + 34.8087i 0.124762 + 0.124762i
\(280\) 34.9656 + 124.071i 0.124877 + 0.443110i
\(281\) 57.6627 + 57.6627i 0.205205 + 0.205205i 0.802226 0.597021i \(-0.203649\pi\)
−0.597021 + 0.802226i \(0.703649\pi\)
\(282\) 161.821 + 438.722i 0.573833 + 1.55575i
\(283\) 196.091 + 81.2237i 0.692902 + 0.287009i 0.701209 0.712956i \(-0.252644\pi\)
−0.00830663 + 0.999965i \(0.502644\pi\)
\(284\) −132.222 + 112.899i −0.465572 + 0.397532i
\(285\) −475.191 + 196.830i −1.66734 + 0.690633i
\(286\) 24.5872 + 0.967624i 0.0859693 + 0.00338330i
\(287\) 198.064i 0.690117i
\(288\) 307.003 204.989i 1.06598 0.711768i
\(289\) −281.215 −0.973063
\(290\) −10.6068 + 269.518i −0.0365753 + 0.929373i
\(291\) −261.062 630.260i −0.897121 2.16584i
\(292\) 431.054 368.059i 1.47621 1.26048i
\(293\) 34.0186 82.1281i 0.116104 0.280301i −0.855135 0.518405i \(-0.826526\pi\)
0.971240 + 0.238104i \(0.0765260\pi\)
\(294\) −59.5233 + 21.9549i −0.202460 + 0.0746766i
\(295\) −146.132 + 146.132i −0.495362 + 0.495362i
\(296\) 108.345 193.376i 0.366031 0.653298i
\(297\) 74.4295 74.4295i 0.250604 0.250604i
\(298\) −80.2494 37.0018i −0.269293 0.124167i
\(299\) −1.88856 + 4.55939i −0.00631626 + 0.0152488i
\(300\) 99.5147 195.246i 0.331716 0.650821i
\(301\) 47.9618 + 115.790i 0.159341 + 0.384684i
\(302\) −364.820 394.711i −1.20801 1.30699i
\(303\) −535.329 −1.76676
\(304\) 289.966 69.5356i 0.953837 0.228736i
\(305\) 551.142i 1.80702i
\(306\) −373.950 404.589i −1.22206 1.32219i
\(307\) −219.422 + 90.8874i −0.714728 + 0.296050i −0.710260 0.703940i \(-0.751422\pi\)
−0.00446871 + 0.999990i \(0.501422\pi\)
\(308\) −29.9424 92.1938i −0.0972157 0.299331i
\(309\) 344.400 + 142.655i 1.11456 + 0.461667i
\(310\) −47.2008 21.7635i −0.152260 0.0702050i
\(311\) 234.549 + 234.549i 0.754178 + 0.754178i 0.975256 0.221078i \(-0.0709576\pi\)
−0.221078 + 0.975256i \(0.570958\pi\)
\(312\) 38.2477 30.1401i 0.122589 0.0966028i
\(313\) −248.600 248.600i −0.794249 0.794249i 0.187933 0.982182i \(-0.439821\pi\)
−0.982182 + 0.187933i \(0.939821\pi\)
\(314\) 22.4743 8.28956i 0.0715742 0.0263999i
\(315\) 171.729 + 71.1323i 0.545170 + 0.225817i
\(316\) −47.0458 3.70870i −0.148879 0.0117364i
\(317\) 260.242 107.796i 0.820953 0.340050i 0.0676380 0.997710i \(-0.478454\pi\)
0.753315 + 0.657660i \(0.228454\pi\)
\(318\) 30.0565 763.732i 0.0945172 2.40167i
\(319\) 202.832i 0.635837i
\(320\) −229.222 + 315.240i −0.716319 + 0.985126i
\(321\) 774.763 2.41359
\(322\) 19.4262 + 0.764512i 0.0603297 + 0.00237426i
\(323\) −170.305 411.154i −0.527261 1.27292i
\(324\) −16.2664 + 206.343i −0.0502049 + 0.636863i
\(325\) 6.21442 15.0029i 0.0191213 0.0461628i
\(326\) −44.8195 121.513i −0.137483 0.372739i
\(327\) −248.958 + 248.958i −0.761338 + 0.761338i
\(328\) 470.389 370.677i 1.43411 1.13011i
\(329\) 96.5238 96.5238i 0.293385 0.293385i
\(330\) −211.692 + 459.117i −0.641490 + 1.39126i
\(331\) −70.9958 + 171.399i −0.214489 + 0.517822i −0.994103 0.108438i \(-0.965415\pi\)
0.779614 + 0.626260i \(0.215415\pi\)
\(332\) 211.861 68.8074i 0.638134 0.207251i
\(333\) −122.317 295.301i −0.367320 0.886788i
\(334\) −445.428 + 411.696i −1.33362 + 1.23262i
\(335\) −356.487 −1.06414
\(336\) −163.540 100.275i −0.486725 0.298438i
\(337\) 157.758i 0.468125i 0.972222 + 0.234063i \(0.0752020\pi\)
−0.972222 + 0.234063i \(0.924798\pi\)
\(338\) −245.566 + 226.969i −0.726526 + 0.671507i
\(339\) −278.722 + 115.451i −0.822190 + 0.340562i
\(340\) 518.272 + 264.157i 1.52433 + 0.776933i
\(341\) 36.1106 + 14.9575i 0.105896 + 0.0438637i
\(342\) 180.042 390.475i 0.526438 1.14174i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) −185.233 + 330.607i −0.538469 + 0.961068i
\(345\) −71.6989 71.6989i −0.207823 0.207823i
\(346\) 34.7395 + 94.1844i 0.100403 + 0.272209i
\(347\) −442.736 183.387i −1.27590 0.528494i −0.361145 0.932510i \(-0.617614\pi\)
−0.914752 + 0.404016i \(0.867614\pi\)
\(348\) −260.654 305.266i −0.749004 0.877201i
\(349\) 396.276 164.143i 1.13546 0.470323i 0.265827 0.964021i \(-0.414355\pi\)
0.869634 + 0.493697i \(0.164355\pi\)
\(350\) −63.9229 2.51567i −0.182637 0.00718762i
\(351\) 15.4361i 0.0439776i
\(352\) 162.917 243.653i 0.462833 0.692195i
\(353\) 197.940 0.560736 0.280368 0.959893i \(-0.409544\pi\)
0.280368 + 0.959893i \(0.409544\pi\)
\(354\) 12.0943 307.316i 0.0341648 0.868123i
\(355\) −101.302 244.565i −0.285358 0.688914i
\(356\) 456.631 + 534.786i 1.28267 + 1.50221i
\(357\) −109.563 + 264.509i −0.306900 + 0.740922i
\(358\) −447.858 + 165.191i −1.25100 + 0.461426i
\(359\) −222.920 + 222.920i −0.620947 + 0.620947i −0.945774 0.324826i \(-0.894694\pi\)
0.324826 + 0.945774i \(0.394694\pi\)
\(360\) 152.456 + 540.969i 0.423489 + 1.50269i
\(361\) −9.66811 + 9.66811i −0.0267815 + 0.0267815i
\(362\) 606.473 + 279.635i 1.67534 + 0.772473i
\(363\) −64.3469 + 155.347i −0.177264 + 0.427954i
\(364\) −12.6651 6.45525i −0.0347942 0.0177342i
\(365\) 330.251 + 797.297i 0.904798 + 2.18438i
\(366\) 556.719 + 602.333i 1.52109 + 1.64572i
\(367\) 367.464 1.00126 0.500632 0.865660i \(-0.333101\pi\)
0.500632 + 0.865660i \(0.333101\pi\)
\(368\) 34.5405 + 47.5667i 0.0938600 + 0.129257i
\(369\) 863.590i 2.34035i
\(370\) 229.068 + 247.837i 0.619104 + 0.669829i
\(371\) −206.136 + 85.3844i −0.555623 + 0.230147i
\(372\) 73.5687 23.8934i 0.197765 0.0642296i
\(373\) 220.315 + 91.2575i 0.590657 + 0.244658i 0.657933 0.753076i \(-0.271431\pi\)
−0.0672763 + 0.997734i \(0.521431\pi\)
\(374\) −397.246 183.164i −1.06215 0.489743i
\(375\) −251.946 251.946i −0.671855 0.671855i
\(376\) 409.883 + 48.5933i 1.09011 + 0.129237i
\(377\) −21.0330 21.0330i −0.0557903 0.0557903i
\(378\) −57.0522 + 21.0435i −0.150932 + 0.0556706i
\(379\) 569.858 + 236.043i 1.50358 + 0.622804i 0.974222 0.225592i \(-0.0724316\pi\)
0.529361 + 0.848397i \(0.322432\pi\)
\(380\) −35.6788 + 452.596i −0.0938917 + 1.19104i
\(381\) −377.697 + 156.447i −0.991331 + 0.410623i
\(382\) −28.0191 + 711.962i −0.0733484 + 1.86378i
\(383\) 606.614i 1.58385i −0.610619 0.791924i \(-0.709079\pi\)
0.610619 0.791924i \(-0.290921\pi\)
\(384\) −67.9175 576.062i −0.176869 1.50016i
\(385\) 147.585 0.383339
\(386\) −350.858 13.8080i −0.908960 0.0357719i
\(387\) 209.121 + 504.863i 0.540365 + 1.30456i
\(388\) −600.291 47.3219i −1.54714 0.121964i
\(389\) 195.027 470.836i 0.501354 1.21038i −0.447392 0.894338i \(-0.647647\pi\)
0.948746 0.316038i \(-0.102353\pi\)
\(390\) 25.6571 + 69.5605i 0.0657875 + 0.178360i
\(391\) 62.0367 62.0367i 0.158662 0.158662i
\(392\) −6.59286 + 55.6106i −0.0168185 + 0.141864i
\(393\) 77.7853 77.7853i 0.197927 0.197927i
\(394\) −148.182 + 321.377i −0.376096 + 0.815677i
\(395\) 27.4962 66.3817i 0.0696106 0.168055i
\(396\) −130.554 401.980i −0.329682 1.01510i
\(397\) 141.703 + 342.101i 0.356934 + 0.861715i 0.995728 + 0.0923372i \(0.0294338\pi\)
−0.638794 + 0.769378i \(0.720566\pi\)
\(398\) −199.662 + 184.542i −0.501663 + 0.463672i
\(399\) −223.447 −0.560019
\(400\) −113.657 156.521i −0.284143 0.391302i
\(401\) 591.998i 1.47630i −0.674635 0.738152i \(-0.735699\pi\)
0.674635 0.738152i \(-0.264301\pi\)
\(402\) 389.599 360.095i 0.969151 0.895758i
\(403\) 5.29559 2.19350i 0.0131404 0.00544294i
\(404\) −214.576 + 420.994i −0.531128 + 1.04206i
\(405\) −291.151 120.599i −0.718890 0.297774i
\(406\) −49.0647 + 106.411i −0.120849 + 0.262097i
\(407\) −179.453 179.453i −0.440916 0.440916i
\(408\) −833.241 + 234.824i −2.04226 + 0.575549i
\(409\) −449.198 449.198i −1.09828 1.09828i −0.994611 0.103673i \(-0.966940\pi\)
−0.103673 0.994611i \(-0.533060\pi\)
\(410\) 315.543 + 855.487i 0.769618 + 2.08655i
\(411\) −688.970 285.381i −1.67633 0.694357i
\(412\) 250.233 213.663i 0.607361 0.518599i
\(413\) −82.9465 + 34.3576i −0.200839 + 0.0831902i
\(414\) 84.7013 + 3.33340i 0.204592 + 0.00805169i
\(415\) 339.150i 0.817229i
\(416\) −8.37197 42.1599i −0.0201249 0.101346i
\(417\) −230.433 −0.552596
\(418\) 13.4255 341.139i 0.0321183 0.816123i
\(419\) 51.8940 + 125.283i 0.123852 + 0.299005i 0.973629 0.228137i \(-0.0732635\pi\)
−0.849777 + 0.527142i \(0.823263\pi\)
\(420\) 222.119 189.658i 0.528855 0.451567i
\(421\) −67.8514 + 163.808i −0.161167 + 0.389092i −0.983748 0.179557i \(-0.942534\pi\)
0.822580 + 0.568649i \(0.192534\pi\)
\(422\) 305.179 112.564i 0.723173 0.266739i
\(423\) 420.860 420.860i 0.994940 0.994940i
\(424\) −588.567 329.763i −1.38813 0.777744i
\(425\) −204.135 + 204.135i −0.480318 + 0.480318i
\(426\) 357.751 + 164.953i 0.839790 + 0.387214i
\(427\) 91.6275 221.208i 0.214584 0.518052i
\(428\) 310.548 609.291i 0.725580 1.42358i
\(429\) −21.3360 51.5096i −0.0497342 0.120069i
\(430\) −391.629 423.717i −0.910765 0.985387i
\(431\) 841.384 1.95217 0.976084 0.217393i \(-0.0697554\pi\)
0.976084 + 0.217393i \(0.0697554\pi\)
\(432\) −156.750 96.1124i −0.362848 0.222482i
\(433\) 277.875i 0.641743i −0.947123 0.320872i \(-0.896024\pi\)
0.947123 0.320872i \(-0.103976\pi\)
\(434\) −15.3265 16.5822i −0.0353145 0.0382079i
\(435\) 564.633 233.879i 1.29801 0.537652i
\(436\) 95.9960 + 295.575i 0.220174 + 0.677925i
\(437\) 63.2599 + 26.2031i 0.144760 + 0.0599614i
\(438\) −1166.29 537.759i −2.66276 1.22776i
\(439\) 125.112 + 125.112i 0.284993 + 0.284993i 0.835097 0.550103i \(-0.185412\pi\)
−0.550103 + 0.835097i \(0.685412\pi\)
\(440\) 276.207 + 350.506i 0.627743 + 0.796605i
\(441\) 57.0999 + 57.0999i 0.129478 + 0.129478i
\(442\) −60.1864 + 22.1995i −0.136168 + 0.0502252i
\(443\) 554.215 + 229.563i 1.25105 + 0.518202i 0.907151 0.420805i \(-0.138252\pi\)
0.343899 + 0.939007i \(0.388252\pi\)
\(444\) −500.690 39.4702i −1.12768 0.0888968i
\(445\) −989.164 + 409.725i −2.22284 + 0.920731i
\(446\) 15.8173 401.915i 0.0354647 0.901155i
\(447\) 200.229i 0.447940i
\(448\) −144.410 + 88.4178i −0.322344 + 0.197361i
\(449\) 157.741 0.351315 0.175658 0.984451i \(-0.443795\pi\)
0.175658 + 0.984451i \(0.443795\pi\)
\(450\) −278.714 10.9687i −0.619365 0.0243750i
\(451\) −262.400 633.489i −0.581818 1.40463i
\(452\) −20.9274 + 265.469i −0.0462995 + 0.587321i
\(453\) −466.051 + 1125.15i −1.02881 + 2.48377i
\(454\) 37.9568 + 102.907i 0.0836054 + 0.226667i
\(455\) 15.3041 15.3041i 0.0336354 0.0336354i
\(456\) −418.183 530.674i −0.917068 1.16376i
\(457\) −387.593 + 387.593i −0.848124 + 0.848124i −0.989899 0.141775i \(-0.954719\pi\)
0.141775 + 0.989899i \(0.454719\pi\)
\(458\) 18.6092 40.3596i 0.0406314 0.0881214i
\(459\) −105.015 + 253.528i −0.228790 + 0.552349i
\(460\) −85.1245 + 27.6465i −0.185053 + 0.0601011i
\(461\) 156.971 + 378.962i 0.340502 + 0.822044i 0.997665 + 0.0682959i \(0.0217562\pi\)
−0.657163 + 0.753748i \(0.728244\pi\)
\(462\) −161.294 + 149.079i −0.349120 + 0.322682i
\(463\) −44.5642 −0.0962509 −0.0481254 0.998841i \(-0.515325\pi\)
−0.0481254 + 0.998841i \(0.515325\pi\)
\(464\) −344.545 + 82.6239i −0.742554 + 0.178069i
\(465\) 117.770i 0.253269i
\(466\) 145.643 134.614i 0.312539 0.288871i
\(467\) 208.678 86.4375i 0.446849 0.185091i −0.147900 0.989002i \(-0.547251\pi\)
0.594749 + 0.803911i \(0.297251\pi\)
\(468\) −55.2219 28.1460i −0.117996 0.0601410i
\(469\) −143.081 59.2661i −0.305077 0.126367i
\(470\) −263.135 + 570.687i −0.559862 + 1.21423i
\(471\) −38.3792 38.3792i −0.0814846 0.0814846i
\(472\) −236.832 132.692i −0.501762 0.281128i
\(473\) 306.803 + 306.803i 0.648632 + 0.648632i
\(474\) 37.0033 + 100.322i 0.0780660 + 0.211649i
\(475\) −208.160 86.2228i −0.438232 0.181522i
\(476\) 164.099 + 192.186i 0.344747 + 0.403752i
\(477\) −898.788 + 372.290i −1.88425 + 0.780482i
\(478\) 583.448 + 22.9615i 1.22060 + 0.0480365i
\(479\) 56.9433i 0.118879i 0.998232 + 0.0594397i \(0.0189314\pi\)
−0.998232 + 0.0594397i \(0.981069\pi\)
\(480\) 866.123 + 172.573i 1.80442 + 0.359527i
\(481\) −37.2172 −0.0773747
\(482\) −8.08024 + 205.318i −0.0167640 + 0.425971i
\(483\) −16.8574 40.6973i −0.0349014 0.0842594i
\(484\) 96.3762 + 112.872i 0.199124 + 0.233206i
\(485\) 350.843 847.011i 0.723389 1.74641i
\(486\) 634.086 233.880i 1.30470 0.481235i
\(487\) −112.925 + 112.925i −0.231878 + 0.231878i −0.813476 0.581598i \(-0.802428\pi\)
0.581598 + 0.813476i \(0.302428\pi\)
\(488\) 696.837 196.383i 1.42795 0.402424i
\(489\) −207.507 + 207.507i −0.424349 + 0.424349i
\(490\) −77.4276 35.7007i −0.158015 0.0728585i
\(491\) 19.4012 46.8387i 0.0395137 0.0953946i −0.902891 0.429870i \(-0.858559\pi\)
0.942404 + 0.334476i \(0.108559\pi\)
\(492\) −1209.00 616.211i −2.45731 1.25246i
\(493\) 202.361 + 488.543i 0.410469 + 0.990959i
\(494\) −33.9828 36.7671i −0.0687910 0.0744274i
\(495\) 643.497 1.29999
\(496\) 10.6982 67.4331i 0.0215690 0.135954i
\(497\) 115.001i 0.231390i
\(498\) −342.582 370.651i −0.687916 0.744280i
\(499\) −284.672 + 117.915i −0.570484 + 0.236302i −0.649230 0.760593i \(-0.724909\pi\)
0.0787455 + 0.996895i \(0.474909\pi\)
\(500\) −299.123 + 97.1481i −0.598245 + 0.194296i
\(501\) 1269.72 + 525.934i 2.53436 + 1.04977i
\(502\) −486.731 224.424i −0.969583 0.447060i
\(503\) −232.889 232.889i −0.462999 0.462999i 0.436638 0.899637i \(-0.356169\pi\)
−0.899637 + 0.436638i \(0.856169\pi\)
\(504\) −28.7460 + 242.471i −0.0570357 + 0.481094i
\(505\) −508.715 508.715i −1.00736 1.00736i
\(506\) 63.1457 23.2911i 0.124794 0.0460298i
\(507\) 699.999 + 289.949i 1.38067 + 0.571892i
\(508\) −28.3587 + 359.738i −0.0558242 + 0.708145i
\(509\) 609.065 252.283i 1.19659 0.495645i 0.306696 0.951808i \(-0.400777\pi\)
0.889896 + 0.456163i \(0.150777\pi\)
\(510\) 51.8315 1317.03i 0.101630 2.58242i
\(511\) 374.910i 0.733680i
\(512\) −480.251 177.491i −0.937990 0.346662i
\(513\) −214.171 −0.417488
\(514\) 567.736 + 22.3431i 1.10454 + 0.0434691i
\(515\) 191.715 + 462.841i 0.372262 + 0.898721i
\(516\) 856.009 + 67.4805i 1.65893 + 0.130776i
\(517\) 180.846 436.600i 0.349798 0.844488i
\(518\) 50.7368 + 137.555i 0.0979474 + 0.265551i
\(519\) 160.838 160.838i 0.309900 0.309900i
\(520\) 64.9880 + 7.70459i 0.124977 + 0.0148165i
\(521\) 162.426 162.426i 0.311759 0.311759i −0.533832 0.845591i \(-0.679248\pi\)
0.845591 + 0.533832i \(0.179248\pi\)
\(522\) −213.930 + 463.971i −0.409828 + 0.888834i
\(523\) −78.7324 + 190.077i −0.150540 + 0.363436i −0.981102 0.193490i \(-0.938019\pi\)
0.830562 + 0.556926i \(0.188019\pi\)
\(524\) −29.9934 92.3506i −0.0572392 0.176242i
\(525\) 55.4701 + 133.917i 0.105657 + 0.255079i
\(526\) 168.219 155.480i 0.319808 0.295590i
\(527\) −101.899 −0.193357
\(528\) −655.915 104.060i −1.24226 0.197084i
\(529\) 515.501i 0.974483i
\(530\) 754.326 697.201i 1.42326 1.31547i
\(531\) −361.660 + 149.805i −0.681093 + 0.282118i
\(532\) −89.5644 + 175.724i −0.168354 + 0.330308i
\(533\) −92.9005 38.4807i −0.174297 0.0721964i
\(534\) 667.169 1446.96i 1.24938 2.70965i
\(535\) 736.247 + 736.247i 1.37616 + 1.37616i
\(536\) −127.023 450.725i −0.236984 0.840905i
\(537\) 764.804 + 764.804i 1.42422 + 1.42422i
\(538\) 182.320 + 494.300i 0.338886 + 0.918772i
\(539\) 59.2355 + 24.5361i 0.109899 + 0.0455216i
\(540\) 212.898 181.784i 0.394255 0.336638i
\(541\) −154.262 + 63.8974i −0.285142 + 0.118110i −0.520670 0.853758i \(-0.674318\pi\)
0.235528 + 0.971867i \(0.424318\pi\)
\(542\) 66.3247 + 2.61019i 0.122370 + 0.00481586i
\(543\) 1513.20i 2.78674i
\(544\) −149.317 + 749.403i −0.274480 + 1.37758i
\(545\) −473.162 −0.868187
\(546\) −1.26661 + 32.1845i −0.00231981 + 0.0589461i
\(547\) 73.2921 + 176.943i 0.133989 + 0.323478i 0.976606 0.215034i \(-0.0689864\pi\)
−0.842617 + 0.538513i \(0.818986\pi\)
\(548\) −500.589 + 427.432i −0.913484 + 0.779985i
\(549\) 399.511 964.505i 0.727707 1.75684i
\(550\) −207.785 + 76.6405i −0.377790 + 0.139346i
\(551\) −291.825 + 291.825i −0.529628 + 0.529628i
\(552\) 65.1049 116.200i 0.117944 0.210508i
\(553\) 22.0719 22.0719i 0.0399131 0.0399131i
\(554\) −520.071 239.797i −0.938756 0.432846i
\(555\) 292.631 706.473i 0.527262 1.27292i
\(556\) −92.3642 + 181.217i −0.166123 + 0.325930i
\(557\) 165.983 + 400.718i 0.297995 + 0.719423i 0.999974 + 0.00722522i \(0.00229988\pi\)
−0.701979 + 0.712197i \(0.747700\pi\)
\(558\) −66.8260 72.3013i −0.119760 0.129572i
\(559\) 63.6288 0.113826
\(560\) −60.1192 250.700i −0.107356 0.447678i
\(561\) 991.162i 1.76678i
\(562\) −110.701 119.771i −0.196977 0.213116i
\(563\) 273.769 113.399i 0.486268 0.201419i −0.126060 0.992023i \(-0.540233\pi\)
0.612328 + 0.790604i \(0.290233\pi\)
\(564\) −288.886 889.492i −0.512210 1.57711i
\(565\) −374.577 155.155i −0.662968 0.274610i
\(566\) −385.491 177.744i −0.681080 0.314035i
\(567\) −96.8077 96.8077i −0.170737 0.170737i
\(568\) 273.120 215.225i 0.480845 0.378916i
\(569\) 260.130 + 260.130i 0.457171 + 0.457171i 0.897726 0.440555i \(-0.145218\pi\)
−0.440555 + 0.897726i \(0.645218\pi\)
\(570\) 965.127 355.983i 1.69321 0.624532i
\(571\) 502.521 + 208.151i 0.880071 + 0.364537i 0.776524 0.630087i \(-0.216981\pi\)
0.103547 + 0.994625i \(0.466981\pi\)
\(572\) −49.0603 3.86750i −0.0857698 0.00676137i
\(573\) 1491.54 617.817i 2.60304 1.07821i
\(574\) −15.5774 + 395.821i −0.0271384 + 0.689583i
\(575\) 44.4178i 0.0772484i
\(576\) −629.652 + 385.516i −1.09315 + 0.669299i
\(577\) −508.343 −0.881011 −0.440505 0.897750i \(-0.645201\pi\)
−0.440505 + 0.897750i \(0.645201\pi\)
\(578\) 561.995 + 22.1172i 0.972311 + 0.0382650i
\(579\) 304.463 + 735.039i 0.525843 + 1.26950i
\(580\) 42.3945 537.785i 0.0730939 0.927216i
\(581\) −56.3838 + 136.123i −0.0970461 + 0.234290i
\(582\) 472.152 + 1280.08i 0.811257 + 2.19945i
\(583\) −546.189 + 546.189i −0.936860 + 0.936860i
\(584\) −890.389 + 701.647i −1.52464 + 1.20145i
\(585\) 66.7284 66.7284i 0.114066 0.114066i
\(586\) −74.4438 + 161.454i −0.127037 + 0.275518i
\(587\) 20.7154 50.0114i 0.0352903 0.0851983i −0.905252 0.424876i \(-0.860318\pi\)
0.940542 + 0.339677i \(0.110318\pi\)
\(588\) 120.681 39.1945i 0.205240 0.0666573i
\(589\) −30.4341 73.4744i −0.0516708 0.124744i
\(590\) 303.531 280.545i 0.514459 0.475499i
\(591\) 801.863 1.35679
\(592\) −231.731 + 377.932i −0.391438 + 0.638399i
\(593\) 734.895i 1.23928i −0.784885 0.619641i \(-0.787278\pi\)
0.784885 0.619641i \(-0.212722\pi\)
\(594\) −154.598 + 142.890i −0.260265 + 0.240556i
\(595\) −355.476 + 147.243i −0.597438 + 0.247467i
\(596\) 157.465 + 80.2578i 0.264202 + 0.134661i
\(597\) 569.147 + 235.748i 0.953345 + 0.394889i
\(598\) 4.13279 8.96319i 0.00691102 0.0149886i
\(599\) 535.397 + 535.397i 0.893818 + 0.893818i 0.994880 0.101063i \(-0.0322242\pi\)
−0.101063 + 0.994880i \(0.532224\pi\)
\(600\) −214.231 + 382.364i −0.357052 + 0.637273i
\(601\) −60.7005 60.7005i −0.100999 0.100999i 0.654802 0.755801i \(-0.272752\pi\)
−0.755801 + 0.654802i \(0.772752\pi\)
\(602\) −86.7426 235.173i −0.144091 0.390653i
\(603\) −623.857 258.410i −1.03459 0.428541i
\(604\) 698.032 + 817.504i 1.15568 + 1.35348i
\(605\) −208.772 + 86.4763i −0.345078 + 0.142936i
\(606\) 1069.83 + 42.1029i 1.76539 + 0.0694767i
\(607\) 217.578i 0.358449i −0.983808 0.179224i \(-0.942641\pi\)
0.983808 0.179224i \(-0.0573588\pi\)
\(608\) −584.953 + 116.158i −0.962094 + 0.191050i
\(609\) 265.506 0.435970
\(610\) −43.3466 + 1101.43i −0.0710599 + 1.80563i
\(611\) −26.5208 64.0270i −0.0434056 0.104790i
\(612\) 715.501 + 837.963i 1.16912 + 1.36922i
\(613\) −117.750 + 284.274i −0.192088 + 0.463742i −0.990353 0.138564i \(-0.955751\pi\)
0.798265 + 0.602306i \(0.205751\pi\)
\(614\) 445.652 164.377i 0.725817 0.267715i
\(615\) 1460.91 1460.91i 2.37547 2.37547i
\(616\) 52.5876 + 186.600i 0.0853695 + 0.302922i
\(617\) −178.070 + 178.070i −0.288606 + 0.288606i −0.836529 0.547923i \(-0.815419\pi\)
0.547923 + 0.836529i \(0.315419\pi\)
\(618\) −677.047 312.176i −1.09555 0.505139i
\(619\) −181.083 + 437.172i −0.292541 + 0.706255i −1.00000 0.000498676i \(-0.999841\pi\)
0.707459 + 0.706754i \(0.249841\pi\)
\(620\) 92.6168 + 47.2057i 0.149382 + 0.0761382i
\(621\) −16.1575 39.0077i −0.0260186 0.0628144i
\(622\) −450.289 487.183i −0.723937 0.783252i
\(623\) −465.132 −0.746600
\(624\) −78.8068 + 57.2254i −0.126293 + 0.0917073i
\(625\) 781.082i 1.24973i
\(626\) 477.263 + 516.367i 0.762401 + 0.824868i
\(627\) −714.677 + 296.029i −1.13984 + 0.472136i
\(628\) −45.5658 + 14.7987i −0.0725570 + 0.0235648i
\(629\) 611.268 + 253.195i 0.971809 + 0.402537i
\(630\) −337.597 155.661i −0.535868 0.247081i
\(631\) −655.158 655.158i −1.03828 1.03828i −0.999237 0.0390474i \(-0.987568\pi\)
−0.0390474 0.999237i \(-0.512432\pi\)
\(632\) 93.7272 + 11.1118i 0.148303 + 0.0175819i
\(633\) −521.152 521.152i −0.823305 0.823305i
\(634\) −528.559 + 194.957i −0.833690 + 0.307503i
\(635\) −507.590 210.251i −0.799354 0.331103i
\(636\) −120.133 + 1523.92i −0.188888 + 2.39610i
\(637\) 8.68682 3.59820i 0.0136371 0.00564866i
\(638\) −15.9524 + 405.350i −0.0250038 + 0.635345i
\(639\) 501.423i 0.784699i
\(640\) 482.883 611.965i 0.754504 0.956195i
\(641\) −111.511 −0.173965 −0.0869824 0.996210i \(-0.527722\pi\)
−0.0869824 + 0.996210i \(0.527722\pi\)
\(642\) −1548.33 60.9341i −2.41173 0.0949129i
\(643\) −430.087 1038.32i −0.668876 1.61481i −0.783493 0.621401i \(-0.786564\pi\)
0.114617 0.993410i \(-0.463436\pi\)
\(644\) −38.7621 3.05568i −0.0601897 0.00474485i
\(645\) −500.299 + 1207.83i −0.775657 + 1.87260i
\(646\) 308.011 + 835.066i 0.476797 + 1.29267i
\(647\) 613.865 613.865i 0.948787 0.948787i −0.0499642 0.998751i \(-0.515911\pi\)
0.998751 + 0.0499642i \(0.0159107\pi\)
\(648\) 48.7362 411.088i 0.0752103 0.634396i
\(649\) −219.779 + 219.779i −0.338643 + 0.338643i
\(650\) −13.5992 + 29.4939i −0.0209218 + 0.0453752i
\(651\) −19.5793 + 47.2686i −0.0300757 + 0.0726092i
\(652\) 80.0129 + 246.363i 0.122719 + 0.377857i
\(653\) −32.4982 78.4577i −0.0497676 0.120150i 0.897041 0.441948i \(-0.145713\pi\)
−0.946808 + 0.321799i \(0.895713\pi\)
\(654\) 517.110 477.950i 0.790688 0.730810i
\(655\) 147.836 0.225705
\(656\) −969.203 + 703.785i −1.47744 + 1.07284i
\(657\) 1634.67i 2.48808i
\(658\) −200.490 + 185.307i −0.304696 + 0.281621i
\(659\) 449.753 186.294i 0.682477 0.282691i −0.0143847 0.999897i \(-0.504579\pi\)
0.696862 + 0.717205i \(0.254579\pi\)
\(660\) 459.165 900.874i 0.695704 1.36496i
\(661\) −246.333 102.034i −0.372667 0.154364i 0.188486 0.982076i \(-0.439642\pi\)
−0.561153 + 0.827712i \(0.689642\pi\)
\(662\) 155.362 336.949i 0.234686 0.508986i
\(663\) 102.780 + 102.780i 0.155023 + 0.155023i
\(664\) −428.805 + 120.846i −0.645791 + 0.181997i
\(665\) −212.339 212.339i −0.319307 0.319307i
\(666\) 221.221 + 599.764i 0.332163 + 0.900547i
\(667\) −75.1670 31.1352i −0.112694 0.0466794i
\(668\) 922.545 787.722i 1.38106 1.17922i
\(669\) −842.002 + 348.769i −1.25860 + 0.521328i
\(670\) 712.423 + 28.0372i 1.06332 + 0.0418466i
\(671\) 828.906i 1.23533i
\(672\) 318.940 + 213.258i 0.474613 + 0.317348i
\(673\) −7.54613 −0.0112127 −0.00560634 0.999984i \(-0.501785\pi\)
−0.00560634 + 0.999984i \(0.501785\pi\)
\(674\) 12.4075 315.272i 0.0184087 0.467763i
\(675\) 53.1673 + 128.357i 0.0787663 + 0.190159i
\(676\) 508.603 434.274i 0.752371 0.642417i
\(677\) 22.0687 53.2785i 0.0325977 0.0786979i −0.906742 0.421685i \(-0.861439\pi\)
0.939340 + 0.342987i \(0.111439\pi\)
\(678\) 566.093 208.801i 0.834946 0.307967i
\(679\) 281.632 281.632i 0.414774 0.414774i
\(680\) −1014.97 568.667i −1.49260 0.836275i
\(681\) 175.734 175.734i 0.258052 0.258052i
\(682\) −70.9890 32.7319i −0.104089 0.0479940i
\(683\) −24.3820 + 58.8633i −0.0356984 + 0.0861834i −0.940723 0.339175i \(-0.889852\pi\)
0.905025 + 0.425359i \(0.139852\pi\)
\(684\) −390.515 + 766.185i −0.570929 + 1.12015i
\(685\) −383.525 925.912i −0.559891 1.35170i
\(686\) −25.1414 27.2013i −0.0366492 0.0396521i
\(687\) −100.701 −0.146580
\(688\) 396.182 646.135i 0.575845 0.939150i
\(689\) 113.276i 0.164406i
\(690\) 137.648 + 148.926i 0.199490 + 0.215835i
\(691\) 430.109 178.157i 0.622444 0.257825i −0.0490950 0.998794i \(-0.515634\pi\)
0.671539 + 0.740969i \(0.265634\pi\)
\(692\) −62.0179 190.955i −0.0896212 0.275947i
\(693\) 258.276 + 106.982i 0.372693 + 0.154375i
\(694\) 870.364 + 401.312i 1.25413 + 0.578259i
\(695\) −218.977 218.977i −0.315075 0.315075i
\(696\) 496.895 + 630.560i 0.713930 + 0.905976i
\(697\) 1264.04 + 1264.04i 1.81354 + 1.81354i
\(698\) −804.848 + 296.865i −1.15308 + 0.425308i
\(699\) −415.164 171.967i −0.593940 0.246018i
\(700\) 127.549 + 10.0549i 0.182213 + 0.0143641i
\(701\) 1131.33 468.612i 1.61388 0.668491i 0.620589 0.784136i \(-0.286894\pi\)
0.993291 + 0.115646i \(0.0368937\pi\)
\(702\) −1.21403 + 30.8484i −0.00172939 + 0.0439436i
\(703\) 516.376i 0.734532i
\(704\) −344.745 + 474.115i −0.489695 + 0.673459i
\(705\) 1423.91 2.01974
\(706\) −395.573 15.5677i −0.560302 0.0220505i
\(707\) −119.606 288.754i −0.169174 0.408421i
\(708\) −48.3399 + 613.204i −0.0682767 + 0.866108i
\(709\) −362.544 + 875.259i −0.511346 + 1.23450i 0.431755 + 0.901991i \(0.357895\pi\)
−0.943101 + 0.332507i \(0.892105\pi\)
\(710\) 183.213 + 496.718i 0.258046 + 0.699603i
\(711\) 96.2373 96.2373i 0.135355 0.135355i
\(712\) −870.496 1104.66i −1.22261 1.55149i
\(713\) 11.0861 11.0861i 0.0155486 0.0155486i
\(714\) 239.760 519.992i 0.335799 0.728280i
\(715\) 28.6736 69.2241i 0.0401029 0.0968169i
\(716\) 908.014 294.902i 1.26818 0.411874i
\(717\) −506.297 1222.31i −0.706132 1.70475i
\(718\) 463.028 427.963i 0.644885 0.596049i
\(719\) −719.405 −1.00056 −0.500282 0.865863i \(-0.666770\pi\)
−0.500282 + 0.865863i \(0.666770\pi\)
\(720\) −262.130 1093.09i −0.364069 1.51818i
\(721\) 217.640i 0.301859i
\(722\) 20.0816 18.5609i 0.0278139 0.0257076i
\(723\) 430.136 178.168i 0.594932 0.246429i
\(724\) −1190.01 606.536i −1.64367 0.837757i
\(725\) 247.341 + 102.452i 0.341160 + 0.141313i
\(726\) 140.812 305.393i 0.193956 0.420652i
\(727\) 356.221 + 356.221i 0.489988 + 0.489988i 0.908302 0.418315i \(-0.137379\pi\)
−0.418315 + 0.908302i \(0.637379\pi\)
\(728\) 24.8029 + 13.8966i 0.0340699 + 0.0190887i
\(729\) −753.516 753.516i −1.03363 1.03363i
\(730\) −597.285 1619.33i −0.818199 2.21827i
\(731\) −1045.06 432.878i −1.42963 0.592172i
\(732\) −1065.20 1247.52i −1.45520 1.70426i
\(733\) 199.412 82.5992i 0.272049 0.112686i −0.242488 0.970154i \(-0.577964\pi\)
0.514538 + 0.857468i \(0.327964\pi\)
\(734\) −734.359 28.9005i −1.00049 0.0393740i
\(735\) 193.189i 0.262842i
\(736\) −65.2865 97.7764i −0.0887044 0.132848i
\(737\) −536.150 −0.727476
\(738\) −67.9202 + 1725.84i −0.0920327 + 2.33854i
\(739\) 154.012 + 371.818i 0.208406 + 0.503137i 0.993173 0.116655i \(-0.0372171\pi\)
−0.784766 + 0.619792i \(0.787217\pi\)
\(740\) −438.290 513.306i −0.592284 0.693657i
\(741\) −43.4124 + 104.807i −0.0585862 + 0.141440i
\(742\) 418.669 154.424i 0.564244 0.208119i
\(743\) 737.624 737.624i 0.992765 0.992765i −0.00720929 0.999974i \(-0.502295\pi\)
0.999974 + 0.00720929i \(0.00229481\pi\)
\(744\) −148.903 + 41.9638i −0.200138 + 0.0564029i
\(745\) −190.275 + 190.275i −0.255403 + 0.255403i
\(746\) −433.112 199.701i −0.580579 0.267696i
\(747\) −245.843 + 593.517i −0.329107 + 0.794534i
\(748\) 779.471 + 397.287i 1.04207 + 0.531133i
\(749\) 173.101 + 417.904i 0.231110 + 0.557949i
\(750\) 483.686 + 523.317i 0.644915 + 0.697755i
\(751\) −670.743 −0.893133 −0.446566 0.894751i \(-0.647353\pi\)
−0.446566 + 0.894751i \(0.647353\pi\)
\(752\) −815.309 129.348i −1.08419 0.172005i
\(753\) 1214.44i 1.61280i
\(754\) 40.3792 + 43.6876i 0.0535533 + 0.0579411i
\(755\) −1512.09 + 626.329i −2.00277 + 0.829575i
\(756\) 115.671 37.5673i 0.153004 0.0496922i
\(757\) −266.224 110.274i −0.351683 0.145672i 0.199847 0.979827i \(-0.435956\pi\)
−0.551530 + 0.834155i \(0.685956\pi\)