Properties

Label 224.3.w.a.43.7
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 43.7
Character \(\chi\) \(=\) 224.43
Dual form 224.3.w.a.99.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.80532 + 0.860701i) q^{2} +(1.98167 + 4.78418i) q^{3} +(2.51839 - 3.10769i) q^{4} +(1.28939 - 3.11286i) q^{5} +(-7.69530 - 6.93136i) q^{6} +(1.87083 - 1.87083i) q^{7} +(-1.87171 + 7.77796i) q^{8} +(-12.5974 + 12.5974i) q^{9} +O(q^{10})\) \(q+(-1.80532 + 0.860701i) q^{2} +(1.98167 + 4.78418i) q^{3} +(2.51839 - 3.10769i) q^{4} +(1.28939 - 3.11286i) q^{5} +(-7.69530 - 6.93136i) q^{6} +(1.87083 - 1.87083i) q^{7} +(-1.87171 + 7.77796i) q^{8} +(-12.5974 + 12.5974i) q^{9} +(0.351479 + 6.72950i) q^{10} +(-2.68304 + 6.47744i) q^{11} +(19.8583 + 5.88999i) q^{12} +(4.80288 + 11.5952i) q^{13} +(-1.76723 + 4.98768i) q^{14} +17.4476 q^{15} +(-3.31546 - 15.6527i) q^{16} +32.2298i q^{17} +(11.8997 - 33.5849i) q^{18} +(-2.14744 + 0.889498i) q^{19} +(-6.42663 - 11.8464i) q^{20} +(12.6577 + 5.24301i) q^{21} +(-0.731379 - 14.0032i) q^{22} +(-20.4827 - 20.4827i) q^{23} +(-40.9202 + 6.45877i) q^{24} +(9.65028 + 9.65028i) q^{25} +(-18.6507 - 16.7992i) q^{26} +(-42.1742 - 17.4691i) q^{27} +(-1.10248 - 10.5254i) q^{28} +(6.33351 - 2.62343i) q^{29} +(-31.4986 + 15.0172i) q^{30} +2.54417i q^{31} +(19.4578 + 25.4046i) q^{32} -36.3061 q^{33} +(-27.7402 - 58.1852i) q^{34} +(-3.41140 - 8.23586i) q^{35} +(7.42365 + 70.8737i) q^{36} +(2.41415 - 5.82827i) q^{37} +(3.11123 - 3.45414i) q^{38} +(-45.9557 + 45.9557i) q^{39} +(21.7984 + 15.8552i) q^{40} +(-23.5727 + 23.5727i) q^{41} +(-27.3640 + 1.42921i) q^{42} +(22.2031 - 53.6031i) q^{43} +(13.3729 + 24.6508i) q^{44} +(22.9709 + 55.4567i) q^{45} +(54.6074 + 19.3484i) q^{46} +79.1930 q^{47} +(68.3152 - 46.8803i) q^{48} -7.00000i q^{49} +(-25.7279 - 9.11587i) q^{50} +(-154.193 + 63.8688i) q^{51} +(48.1297 + 14.2753i) q^{52} +(-4.48196 - 1.85649i) q^{53} +(91.1738 - 4.76196i) q^{54} +(16.7039 + 16.7039i) q^{55} +(11.0496 + 18.0529i) q^{56} +(-8.51103 - 8.51103i) q^{57} +(-9.17605 + 10.1874i) q^{58} +(-7.84916 - 3.25123i) q^{59} +(43.9399 - 54.2218i) q^{60} +(-25.7364 + 10.6604i) q^{61} +(-2.18977 - 4.59306i) q^{62} +47.1350i q^{63} +(-56.9934 - 29.1162i) q^{64} +42.2870 q^{65} +(65.5443 - 31.2487i) q^{66} +(-43.4366 - 104.865i) q^{67} +(100.160 + 81.1671i) q^{68} +(57.4028 - 138.583i) q^{69} +(13.2473 + 11.9322i) q^{70} +(-44.8731 + 44.8731i) q^{71} +(-74.4032 - 121.560i) q^{72} +(90.7952 - 90.7952i) q^{73} +(0.658081 + 12.5998i) q^{74} +(-27.0450 + 65.2923i) q^{75} +(-2.64380 + 8.91367i) q^{76} +(7.09866 + 17.1377i) q^{77} +(43.4107 - 122.519i) q^{78} +133.148 q^{79} +(-52.9997 - 9.86189i) q^{80} -76.0486i q^{81} +(22.2673 - 62.8455i) q^{82} +(76.7072 - 31.7732i) q^{83} +(48.1707 - 26.1324i) q^{84} +(100.327 + 41.5568i) q^{85} +(6.05242 + 115.881i) q^{86} +(25.1019 + 25.1019i) q^{87} +(-45.3594 - 32.9925i) q^{88} +(-42.5804 - 42.5804i) q^{89} +(-89.2017 - 80.3462i) q^{90} +(30.6780 + 12.7072i) q^{91} +(-115.237 + 12.0705i) q^{92} +(-12.1718 + 5.04171i) q^{93} +(-142.969 + 68.1615i) q^{94} +7.83159i q^{95} +(-82.9812 + 143.433i) q^{96} +158.380 q^{97} +(6.02491 + 12.6373i) q^{98} +(-47.7994 - 115.398i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80532 + 0.860701i −0.902662 + 0.430351i
\(3\) 1.98167 + 4.78418i 0.660557 + 1.59473i 0.796933 + 0.604068i \(0.206454\pi\)
−0.136376 + 0.990657i \(0.543546\pi\)
\(4\) 2.51839 3.10769i 0.629597 0.776922i
\(5\) 1.28939 3.11286i 0.257878 0.622572i −0.740920 0.671594i \(-0.765610\pi\)
0.998798 + 0.0490211i \(0.0156101\pi\)
\(6\) −7.69530 6.93136i −1.28255 1.15523i
\(7\) 1.87083 1.87083i 0.267261 0.267261i
\(8\) −1.87171 + 7.77796i −0.233964 + 0.972245i
\(9\) −12.5974 + 12.5974i −1.39971 + 1.39971i
\(10\) 0.351479 + 6.72950i 0.0351479 + 0.672950i
\(11\) −2.68304 + 6.47744i −0.243913 + 0.588858i −0.997665 0.0683012i \(-0.978242\pi\)
0.753752 + 0.657159i \(0.228242\pi\)
\(12\) 19.8583 + 5.88999i 1.65486 + 0.490832i
\(13\) 4.80288 + 11.5952i 0.369452 + 0.891937i 0.993840 + 0.110823i \(0.0353485\pi\)
−0.624388 + 0.781115i \(0.714651\pi\)
\(14\) −1.76723 + 4.98768i −0.126230 + 0.356263i
\(15\) 17.4476 1.16317
\(16\) −3.31546 15.6527i −0.207216 0.978295i
\(17\) 32.2298i 1.89587i 0.318463 + 0.947935i \(0.396833\pi\)
−0.318463 + 0.947935i \(0.603167\pi\)
\(18\) 11.8997 33.5849i 0.661097 1.86583i
\(19\) −2.14744 + 0.889498i −0.113023 + 0.0468157i −0.438478 0.898742i \(-0.644482\pi\)
0.325455 + 0.945557i \(0.394482\pi\)
\(20\) −6.42663 11.8464i −0.321331 0.592321i
\(21\) 12.6577 + 5.24301i 0.602749 + 0.249667i
\(22\) −0.731379 14.0032i −0.0332445 0.636508i
\(23\) −20.4827 20.4827i −0.890552 0.890552i 0.104023 0.994575i \(-0.466828\pi\)
−0.994575 + 0.104023i \(0.966828\pi\)
\(24\) −40.9202 + 6.45877i −1.70501 + 0.269115i
\(25\) 9.65028 + 9.65028i 0.386011 + 0.386011i
\(26\) −18.6507 16.7992i −0.717336 0.646124i
\(27\) −42.1742 17.4691i −1.56201 0.647004i
\(28\) −1.10248 10.5254i −0.0393744 0.375908i
\(29\) 6.33351 2.62343i 0.218397 0.0904630i −0.270803 0.962635i \(-0.587289\pi\)
0.489199 + 0.872172i \(0.337289\pi\)
\(30\) −31.4986 + 15.0172i −1.04995 + 0.500573i
\(31\) 2.54417i 0.0820701i 0.999158 + 0.0410351i \(0.0130655\pi\)
−0.999158 + 0.0410351i \(0.986934\pi\)
\(32\) 19.4578 + 25.4046i 0.608056 + 0.793894i
\(33\) −36.3061 −1.10019
\(34\) −27.7402 58.1852i −0.815889 1.71133i
\(35\) −3.41140 8.23586i −0.0974687 0.235310i
\(36\) 7.42365 + 70.8737i 0.206213 + 1.96871i
\(37\) 2.41415 5.82827i 0.0652473 0.157521i −0.887893 0.460051i \(-0.847831\pi\)
0.953140 + 0.302530i \(0.0978312\pi\)
\(38\) 3.11123 3.45414i 0.0818745 0.0908983i
\(39\) −45.9557 + 45.9557i −1.17835 + 1.17835i
\(40\) 21.7984 + 15.8552i 0.544959 + 0.396380i
\(41\) −23.5727 + 23.5727i −0.574945 + 0.574945i −0.933506 0.358561i \(-0.883267\pi\)
0.358561 + 0.933506i \(0.383267\pi\)
\(42\) −27.3640 + 1.42921i −0.651523 + 0.0340288i
\(43\) 22.2031 53.6031i 0.516352 1.24658i −0.423778 0.905766i \(-0.639296\pi\)
0.940130 0.340817i \(-0.110704\pi\)
\(44\) 13.3729 + 24.6508i 0.303930 + 0.560244i
\(45\) 22.9709 + 55.4567i 0.510465 + 1.23237i
\(46\) 54.6074 + 19.3484i 1.18712 + 0.420618i
\(47\) 79.1930 1.68496 0.842479 0.538730i \(-0.181096\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(48\) 68.3152 46.8803i 1.42323 0.976672i
\(49\) 7.00000i 0.142857i
\(50\) −25.7279 9.11587i −0.514558 0.182317i
\(51\) −154.193 + 63.8688i −3.02339 + 1.25233i
\(52\) 48.1297 + 14.2753i 0.925572 + 0.274525i
\(53\) −4.48196 1.85649i −0.0845653 0.0350281i 0.340000 0.940426i \(-0.389573\pi\)
−0.424565 + 0.905397i \(0.639573\pi\)
\(54\) 91.1738 4.76196i 1.68840 0.0881845i
\(55\) 16.7039 + 16.7039i 0.303707 + 0.303707i
\(56\) 11.0496 + 18.0529i 0.197314 + 0.322373i
\(57\) −8.51103 8.51103i −0.149316 0.149316i
\(58\) −9.17605 + 10.1874i −0.158208 + 0.175645i
\(59\) −7.84916 3.25123i −0.133037 0.0551056i 0.315172 0.949035i \(-0.397938\pi\)
−0.448209 + 0.893929i \(0.647938\pi\)
\(60\) 43.9399 54.2218i 0.732331 0.903696i
\(61\) −25.7364 + 10.6604i −0.421909 + 0.174760i −0.583528 0.812093i \(-0.698328\pi\)
0.161620 + 0.986853i \(0.448328\pi\)
\(62\) −2.18977 4.59306i −0.0353189 0.0740816i
\(63\) 47.1350i 0.748174i
\(64\) −56.9934 29.1162i −0.890522 0.454940i
\(65\) 42.2870 0.650569
\(66\) 65.5443 31.2487i 0.993095 0.473465i
\(67\) −43.4366 104.865i −0.648308 1.56515i −0.815201 0.579178i \(-0.803373\pi\)
0.166893 0.985975i \(-0.446627\pi\)
\(68\) 100.160 + 81.1671i 1.47294 + 1.19363i
\(69\) 57.4028 138.583i 0.831925 2.00845i
\(70\) 13.2473 + 11.9322i 0.189247 + 0.170460i
\(71\) −44.8731 + 44.8731i −0.632015 + 0.632015i −0.948573 0.316558i \(-0.897473\pi\)
0.316558 + 0.948573i \(0.397473\pi\)
\(72\) −74.4032 121.560i −1.03338 1.68834i
\(73\) 90.7952 90.7952i 1.24377 1.24377i 0.285345 0.958425i \(-0.407892\pi\)
0.958425 0.285345i \(-0.0921081\pi\)
\(74\) 0.658081 + 12.5998i 0.00889299 + 0.170267i
\(75\) −27.0450 + 65.2923i −0.360600 + 0.870564i
\(76\) −2.64380 + 8.91367i −0.0347868 + 0.117285i
\(77\) 7.09866 + 17.1377i 0.0921905 + 0.222567i
\(78\) 43.4107 122.519i 0.556548 1.57076i
\(79\) 133.148 1.68542 0.842710 0.538367i \(-0.180959\pi\)
0.842710 + 0.538367i \(0.180959\pi\)
\(80\) −52.9997 9.86189i −0.662496 0.123274i
\(81\) 76.0486i 0.938871i
\(82\) 22.2673 62.8455i 0.271553 0.766409i
\(83\) 76.7072 31.7732i 0.924183 0.382809i 0.130714 0.991420i \(-0.458273\pi\)
0.793469 + 0.608611i \(0.208273\pi\)
\(84\) 48.1707 26.1324i 0.573461 0.311100i
\(85\) 100.327 + 41.5568i 1.18032 + 0.488903i
\(86\) 6.05242 + 115.881i 0.0703770 + 1.34746i
\(87\) 25.1019 + 25.1019i 0.288527 + 0.288527i
\(88\) −45.3594 32.9925i −0.515448 0.374915i
\(89\) −42.5804 42.5804i −0.478432 0.478432i 0.426198 0.904630i \(-0.359853\pi\)
−0.904630 + 0.426198i \(0.859853\pi\)
\(90\) −89.2017 80.3462i −0.991129 0.892736i
\(91\) 30.6780 + 12.7072i 0.337121 + 0.139640i
\(92\) −115.237 + 12.0705i −1.25258 + 0.131201i
\(93\) −12.1718 + 5.04171i −0.130879 + 0.0542120i
\(94\) −142.969 + 68.1615i −1.52095 + 0.725123i
\(95\) 7.83159i 0.0824378i
\(96\) −82.9812 + 143.433i −0.864387 + 1.49409i
\(97\) 158.380 1.63279 0.816393 0.577497i \(-0.195970\pi\)
0.816393 + 0.577497i \(0.195970\pi\)
\(98\) 6.02491 + 12.6373i 0.0614787 + 0.128952i
\(99\) −47.7994 115.398i −0.482822 1.16563i
\(100\) 54.2932 5.68694i 0.542932 0.0568694i
\(101\) 4.69082 11.3246i 0.0464438 0.112125i −0.898955 0.438041i \(-0.855673\pi\)
0.945399 + 0.325916i \(0.105673\pi\)
\(102\) 223.396 248.018i 2.19016 2.43155i
\(103\) −100.291 + 100.291i −0.973697 + 0.973697i −0.999663 0.0259659i \(-0.991734\pi\)
0.0259659 + 0.999663i \(0.491734\pi\)
\(104\) −99.1765 + 15.6538i −0.953620 + 0.150517i
\(105\) 32.6415 32.6415i 0.310872 0.310872i
\(106\) 9.68927 0.506066i 0.0914082 0.00477421i
\(107\) −77.6109 + 187.369i −0.725335 + 1.75111i −0.0677887 + 0.997700i \(0.521594\pi\)
−0.657546 + 0.753414i \(0.728406\pi\)
\(108\) −160.499 + 87.0703i −1.48611 + 0.806206i
\(109\) 16.1607 + 39.0154i 0.148263 + 0.357939i 0.980511 0.196465i \(-0.0629462\pi\)
−0.832248 + 0.554404i \(0.812946\pi\)
\(110\) −44.5330 15.7789i −0.404845 0.143444i
\(111\) 32.6675 0.294302
\(112\) −35.4862 23.0809i −0.316841 0.206080i
\(113\) 40.8893i 0.361853i 0.983497 + 0.180926i \(0.0579096\pi\)
−0.983497 + 0.180926i \(0.942090\pi\)
\(114\) 22.6906 + 8.03971i 0.199041 + 0.0705238i
\(115\) −90.1700 + 37.3496i −0.784087 + 0.324779i
\(116\) 7.79743 26.2894i 0.0672193 0.226633i
\(117\) −206.572 85.5650i −1.76557 0.731325i
\(118\) 16.9686 0.886263i 0.143802 0.00751070i
\(119\) 60.2964 + 60.2964i 0.506693 + 0.506693i
\(120\) −32.6569 + 135.707i −0.272141 + 1.13089i
\(121\) 50.8014 + 50.8014i 0.419846 + 0.419846i
\(122\) 37.2872 41.3968i 0.305633 0.339318i
\(123\) −159.490 66.0627i −1.29666 0.537095i
\(124\) 7.90650 + 6.40721i 0.0637621 + 0.0516711i
\(125\) 120.305 49.8318i 0.962436 0.398654i
\(126\) −40.5691 85.0939i −0.321977 0.675348i
\(127\) 235.921i 1.85764i −0.370527 0.928822i \(-0.620823\pi\)
0.370527 0.928822i \(-0.379177\pi\)
\(128\) 127.952 + 3.50985i 0.999624 + 0.0274207i
\(129\) 300.446 2.32904
\(130\) −76.3417 + 36.3965i −0.587244 + 0.279973i
\(131\) −1.45053 3.50189i −0.0110728 0.0267320i 0.918246 0.396009i \(-0.129605\pi\)
−0.929319 + 0.369277i \(0.879605\pi\)
\(132\) −91.4328 + 112.828i −0.692673 + 0.854758i
\(133\) −2.35339 + 5.68159i −0.0176947 + 0.0427187i
\(134\) 168.675 + 151.930i 1.25877 + 1.13380i
\(135\) −108.758 + 108.758i −0.805614 + 0.805614i
\(136\) −250.682 60.3248i −1.84325 0.443565i
\(137\) −64.4425 + 64.4425i −0.470383 + 0.470383i −0.902039 0.431655i \(-0.857930\pi\)
0.431655 + 0.902039i \(0.357930\pi\)
\(138\) 15.6476 + 299.593i 0.113389 + 2.17097i
\(139\) 63.2937 152.805i 0.455351 1.09931i −0.514909 0.857245i \(-0.672174\pi\)
0.970259 0.242068i \(-0.0778258\pi\)
\(140\) −34.1857 10.1395i −0.244184 0.0724249i
\(141\) 156.934 + 378.873i 1.11301 + 2.68704i
\(142\) 42.3881 119.633i 0.298508 0.842485i
\(143\) −87.9934 −0.615339
\(144\) 238.949 + 155.417i 1.65937 + 1.07928i
\(145\) 23.0980i 0.159296i
\(146\) −85.7672 + 242.062i −0.587446 + 1.65796i
\(147\) 33.4892 13.8717i 0.227818 0.0943653i
\(148\) −12.0327 22.1803i −0.0813020 0.149867i
\(149\) 118.011 + 48.8816i 0.792017 + 0.328064i 0.741754 0.670672i \(-0.233994\pi\)
0.0502630 + 0.998736i \(0.483994\pi\)
\(150\) −7.37228 141.151i −0.0491485 0.941010i
\(151\) −39.2703 39.2703i −0.260068 0.260068i 0.565014 0.825082i \(-0.308871\pi\)
−0.825082 + 0.565014i \(0.808871\pi\)
\(152\) −2.89910 18.3676i −0.0190730 0.120839i
\(153\) −406.010 406.010i −2.65366 2.65366i
\(154\) −27.5658 24.8293i −0.178999 0.161229i
\(155\) 7.91966 + 3.28043i 0.0510946 + 0.0211641i
\(156\) 27.0818 + 258.550i 0.173601 + 1.65737i
\(157\) −132.470 + 54.8707i −0.843756 + 0.349495i −0.762333 0.647185i \(-0.775946\pi\)
−0.0814224 + 0.996680i \(0.525946\pi\)
\(158\) −240.376 + 114.601i −1.52137 + 0.725322i
\(159\) 25.1214i 0.157996i
\(160\) 104.170 27.8130i 0.651061 0.173831i
\(161\) −76.6392 −0.476020
\(162\) 65.4551 + 137.292i 0.404044 + 0.847483i
\(163\) 44.4880 + 107.404i 0.272933 + 0.658917i 0.999606 0.0280655i \(-0.00893471\pi\)
−0.726674 + 0.686983i \(0.758935\pi\)
\(164\) 13.8915 + 132.622i 0.0847041 + 0.808671i
\(165\) −46.8127 + 113.016i −0.283714 + 0.684945i
\(166\) −111.134 + 123.383i −0.669483 + 0.743270i
\(167\) 112.957 112.957i 0.676388 0.676388i −0.282793 0.959181i \(-0.591261\pi\)
0.959181 + 0.282793i \(0.0912609\pi\)
\(168\) −64.4715 + 88.6380i −0.383759 + 0.527607i
\(169\) 8.12044 8.12044i 0.0480500 0.0480500i
\(170\) −216.891 + 11.3281i −1.27583 + 0.0666358i
\(171\) 15.8467 38.2574i 0.0926709 0.223727i
\(172\) −110.666 203.994i −0.643405 1.18601i
\(173\) −114.799 277.148i −0.663575 1.60201i −0.792159 0.610314i \(-0.791043\pi\)
0.128584 0.991699i \(-0.458957\pi\)
\(174\) −66.9222 23.7118i −0.384610 0.136275i
\(175\) 36.1081 0.206332
\(176\) 110.285 + 20.5212i 0.626620 + 0.116598i
\(177\) 43.9946i 0.248557i
\(178\) 113.520 + 40.2224i 0.637755 + 0.225969i
\(179\) 66.7089 27.6317i 0.372675 0.154367i −0.188481 0.982077i \(-0.560357\pi\)
0.561157 + 0.827710i \(0.310357\pi\)
\(180\) 230.192 + 68.2750i 1.27884 + 0.379305i
\(181\) −150.490 62.3352i −0.831439 0.344393i −0.0739668 0.997261i \(-0.523566\pi\)
−0.757472 + 0.652867i \(0.773566\pi\)
\(182\) −66.3208 + 3.46391i −0.364400 + 0.0190324i
\(183\) −102.002 102.002i −0.557389 0.557389i
\(184\) 197.651 120.976i 1.07419 0.657478i
\(185\) −15.0298 15.0298i −0.0812423 0.0812423i
\(186\) 17.6346 19.5782i 0.0948096 0.105259i
\(187\) −208.767 86.4739i −1.11640 0.462427i
\(188\) 199.439 246.107i 1.06084 1.30908i
\(189\) −111.582 + 46.2189i −0.590383 + 0.244545i
\(190\) −6.74066 14.1386i −0.0354772 0.0744135i
\(191\) 300.865i 1.57521i −0.616182 0.787604i \(-0.711322\pi\)
0.616182 0.787604i \(-0.288678\pi\)
\(192\) 26.3548 330.365i 0.137265 1.72065i
\(193\) −38.0955 −0.197386 −0.0986931 0.995118i \(-0.531466\pi\)
−0.0986931 + 0.995118i \(0.531466\pi\)
\(194\) −285.928 + 136.318i −1.47385 + 0.702671i
\(195\) 83.7989 + 202.308i 0.429738 + 1.03748i
\(196\) −21.7538 17.6287i −0.110989 0.0899424i
\(197\) −86.4792 + 208.779i −0.438981 + 1.05979i 0.537321 + 0.843378i \(0.319436\pi\)
−0.976301 + 0.216415i \(0.930564\pi\)
\(198\) 185.616 + 167.189i 0.937457 + 0.844391i
\(199\) 186.158 186.158i 0.935466 0.935466i −0.0625744 0.998040i \(-0.519931\pi\)
0.998040 + 0.0625744i \(0.0199311\pi\)
\(200\) −93.1221 + 56.9970i −0.465610 + 0.284985i
\(201\) 415.617 415.617i 2.06775 2.06775i
\(202\) 1.27869 + 24.4820i 0.00633013 + 0.121198i
\(203\) 6.94093 16.7569i 0.0341918 0.0825463i
\(204\) −189.833 + 640.030i −0.930554 + 3.13740i
\(205\) 42.9842 + 103.773i 0.209679 + 0.506211i
\(206\) 94.7369 267.378i 0.459888 1.29795i
\(207\) 516.056 2.49302
\(208\) 165.572 113.622i 0.796021 0.546257i
\(209\) 16.2965i 0.0779735i
\(210\) −30.8339 + 87.0231i −0.146828 + 0.414396i
\(211\) −118.757 + 49.1906i −0.562828 + 0.233131i −0.645912 0.763412i \(-0.723523\pi\)
0.0830846 + 0.996542i \(0.473523\pi\)
\(212\) −17.0567 + 9.25318i −0.0804561 + 0.0436471i
\(213\) −303.604 125.757i −1.42537 0.590409i
\(214\) −21.1562 405.062i −0.0988607 1.89281i
\(215\) −138.231 138.231i −0.642933 0.642933i
\(216\) 214.812 295.332i 0.994500 1.36728i
\(217\) 4.75971 + 4.75971i 0.0219342 + 0.0219342i
\(218\) −62.7559 56.5259i −0.287871 0.259293i
\(219\) 614.306 + 254.454i 2.80505 + 1.16189i
\(220\) 93.9773 9.84364i 0.427170 0.0447438i
\(221\) −373.710 + 154.796i −1.69100 + 0.700434i
\(222\) −58.9755 + 28.1170i −0.265655 + 0.126653i
\(223\) 214.882i 0.963598i 0.876282 + 0.481799i \(0.160016\pi\)
−0.876282 + 0.481799i \(0.839984\pi\)
\(224\) 83.9299 + 11.1255i 0.374687 + 0.0496673i
\(225\) −243.136 −1.08061
\(226\) −35.1935 73.8185i −0.155724 0.326631i
\(227\) −56.0179 135.239i −0.246775 0.595767i 0.751152 0.660129i \(-0.229499\pi\)
−0.997927 + 0.0643625i \(0.979499\pi\)
\(228\) −47.8837 + 5.01557i −0.210016 + 0.0219981i
\(229\) −47.1058 + 113.724i −0.205702 + 0.496609i −0.992738 0.120298i \(-0.961615\pi\)
0.787035 + 0.616908i \(0.211615\pi\)
\(230\) 130.639 145.038i 0.567996 0.630598i
\(231\) −67.9225 + 67.9225i −0.294037 + 0.294037i
\(232\) 8.55041 + 54.1721i 0.0368552 + 0.233500i
\(233\) 159.124 159.124i 0.682934 0.682934i −0.277726 0.960660i \(-0.589581\pi\)
0.960660 + 0.277726i \(0.0895807\pi\)
\(234\) 446.576 23.3245i 1.90844 0.0996771i
\(235\) 102.111 246.517i 0.434513 1.04901i
\(236\) −29.8710 + 16.2049i −0.126572 + 0.0686648i
\(237\) 263.856 + 637.005i 1.11332 + 2.68778i
\(238\) −160.752 56.9573i −0.675428 0.239317i
\(239\) −59.6502 −0.249582 −0.124791 0.992183i \(-0.539826\pi\)
−0.124791 + 0.992183i \(0.539826\pi\)
\(240\) −57.8469 273.103i −0.241029 1.13793i
\(241\) 128.088i 0.531487i 0.964044 + 0.265743i \(0.0856174\pi\)
−0.964044 + 0.265743i \(0.914383\pi\)
\(242\) −135.438 47.9882i −0.559661 0.198298i
\(243\) −15.7379 + 6.51886i −0.0647651 + 0.0268266i
\(244\) −31.6851 + 106.828i −0.129857 + 0.437819i
\(245\) −21.7900 9.02573i −0.0889389 0.0368397i
\(246\) 344.791 18.0083i 1.40159 0.0732043i
\(247\) −20.6278 20.6278i −0.0835133 0.0835133i
\(248\) −19.7885 4.76196i −0.0797923 0.0192014i
\(249\) 304.017 + 304.017i 1.22095 + 1.22095i
\(250\) −174.298 + 193.509i −0.697193 + 0.774035i
\(251\) −238.863 98.9402i −0.951644 0.394184i −0.147796 0.989018i \(-0.547218\pi\)
−0.803849 + 0.594834i \(0.797218\pi\)
\(252\) 146.481 + 118.704i 0.581273 + 0.471048i
\(253\) 187.631 77.7194i 0.741626 0.307191i
\(254\) 203.057 + 425.913i 0.799438 + 1.67682i
\(255\) 562.333i 2.20523i
\(256\) −234.015 + 103.792i −0.914123 + 0.405437i
\(257\) 168.260 0.654710 0.327355 0.944901i \(-0.393843\pi\)
0.327355 + 0.944901i \(0.393843\pi\)
\(258\) −542.402 + 258.594i −2.10233 + 1.00230i
\(259\) −6.38724 15.4202i −0.0246612 0.0595373i
\(260\) 106.495 131.415i 0.409596 0.505442i
\(261\) −46.7372 + 112.834i −0.179070 + 0.432313i
\(262\) 5.63276 + 5.07357i 0.0214991 + 0.0193648i
\(263\) 22.3135 22.3135i 0.0848423 0.0848423i −0.663412 0.748254i \(-0.730892\pi\)
0.748254 + 0.663412i \(0.230892\pi\)
\(264\) 67.9545 282.388i 0.257404 1.06965i
\(265\) −11.5580 + 11.5580i −0.0436150 + 0.0436150i
\(266\) −0.641519 12.2827i −0.00241172 0.0461755i
\(267\) 119.332 288.093i 0.446936 1.07900i
\(268\) −435.279 129.104i −1.62417 0.481731i
\(269\) 49.4575 + 119.401i 0.183857 + 0.443869i 0.988755 0.149543i \(-0.0477803\pi\)
−0.804898 + 0.593413i \(0.797780\pi\)
\(270\) 102.735 289.951i 0.380501 1.07389i
\(271\) 442.683 1.63352 0.816759 0.576980i \(-0.195769\pi\)
0.816759 + 0.576980i \(0.195769\pi\)
\(272\) 504.484 106.857i 1.85472 0.392855i
\(273\) 171.950i 0.629855i
\(274\) 60.8738 171.805i 0.222167 0.627027i
\(275\) −88.4013 + 36.6170i −0.321459 + 0.133153i
\(276\) −286.109 527.395i −1.03663 1.91085i
\(277\) 58.8645 + 24.3825i 0.212507 + 0.0880234i 0.486398 0.873738i \(-0.338311\pi\)
−0.273891 + 0.961761i \(0.588311\pi\)
\(278\) 17.2534 + 330.339i 0.0620627 + 1.18827i
\(279\) −32.0499 32.0499i −0.114874 0.114874i
\(280\) 70.4434 11.1186i 0.251583 0.0397094i
\(281\) 140.937 + 140.937i 0.501555 + 0.501555i 0.911921 0.410366i \(-0.134599\pi\)
−0.410366 + 0.911921i \(0.634599\pi\)
\(282\) −609.414 548.915i −2.16104 1.94651i
\(283\) −210.747 87.2944i −0.744690 0.308461i −0.0221171 0.999755i \(-0.507041\pi\)
−0.722573 + 0.691295i \(0.757041\pi\)
\(284\) 26.4438 + 252.459i 0.0931121 + 0.888942i
\(285\) −37.4677 + 15.5196i −0.131466 + 0.0544549i
\(286\) 158.857 75.7361i 0.555443 0.264811i
\(287\) 88.2011i 0.307321i
\(288\) −565.148 74.9141i −1.96232 0.260118i
\(289\) −749.760 −2.59432
\(290\) 19.8804 + 41.6993i 0.0685533 + 0.143791i
\(291\) 313.857 + 757.719i 1.07855 + 2.60384i
\(292\) −53.5058 510.821i −0.183239 1.74939i
\(293\) 172.468 416.374i 0.588628 1.42107i −0.296187 0.955130i \(-0.595715\pi\)
0.884815 0.465943i \(-0.154285\pi\)
\(294\) −48.5195 + 53.8671i −0.165032 + 0.183221i
\(295\) −20.2413 + 20.2413i −0.0686144 + 0.0686144i
\(296\) 40.8135 + 29.6860i 0.137883 + 0.100291i
\(297\) 226.310 226.310i 0.761988 0.761988i
\(298\) −255.120 + 13.3248i −0.856107 + 0.0447141i
\(299\) 139.125 335.877i 0.465300 1.12333i
\(300\) 134.799 + 248.479i 0.449329 + 0.828262i
\(301\) −58.7440 141.820i −0.195163 0.471164i
\(302\) 104.696 + 37.0956i 0.346674 + 0.122833i
\(303\) 63.4748 0.209488
\(304\) 21.0428 + 30.6642i 0.0692198 + 0.100869i
\(305\) 93.8594i 0.307736i
\(306\) 1082.43 + 383.526i 3.53736 + 1.25335i
\(307\) 76.2417 31.5803i 0.248344 0.102868i −0.255039 0.966931i \(-0.582088\pi\)
0.503383 + 0.864063i \(0.332088\pi\)
\(308\) 71.1358 + 21.0989i 0.230960 + 0.0685029i
\(309\) −678.552 281.065i −2.19596 0.909597i
\(310\) −17.1210 + 0.894223i −0.0552291 + 0.00288459i
\(311\) 72.2275 + 72.2275i 0.232243 + 0.232243i 0.813628 0.581385i \(-0.197489\pi\)
−0.581385 + 0.813628i \(0.697489\pi\)
\(312\) −271.426 443.457i −0.869954 1.42134i
\(313\) 70.7113 + 70.7113i 0.225915 + 0.225915i 0.810984 0.585069i \(-0.198933\pi\)
−0.585069 + 0.810984i \(0.698933\pi\)
\(314\) 191.923 213.076i 0.611221 0.678587i
\(315\) 146.725 + 60.7754i 0.465793 + 0.192938i
\(316\) 335.319 413.783i 1.06114 1.30944i
\(317\) 478.850 198.346i 1.51057 0.625697i 0.534892 0.844920i \(-0.320352\pi\)
0.975675 + 0.219223i \(0.0703522\pi\)
\(318\) 21.6220 + 45.3523i 0.0679938 + 0.142617i
\(319\) 48.0637i 0.150670i
\(320\) −164.121 + 139.870i −0.512879 + 0.437095i
\(321\) −1050.21 −3.27167
\(322\) 138.359 65.9635i 0.429685 0.204856i
\(323\) −28.6684 69.2115i −0.0887565 0.214277i
\(324\) −236.335 191.520i −0.729430 0.591110i
\(325\) −65.5476 + 158.246i −0.201685 + 0.486911i
\(326\) −172.758 155.607i −0.529931 0.477323i
\(327\) −154.631 + 154.631i −0.472879 + 0.472879i
\(328\) −139.227 227.469i −0.424471 0.693504i
\(329\) 148.157 148.157i 0.450324 0.450324i
\(330\) −12.7608 244.322i −0.0386692 0.740370i
\(331\) −145.551 + 351.391i −0.439731 + 1.06161i 0.536310 + 0.844021i \(0.319818\pi\)
−0.976042 + 0.217584i \(0.930182\pi\)
\(332\) 94.4373 318.399i 0.284450 0.959034i
\(333\) 43.0089 + 103.833i 0.129156 + 0.311810i
\(334\) −106.702 + 301.146i −0.319466 + 0.901634i
\(335\) −382.438 −1.14161
\(336\) 40.1011 215.511i 0.119349 0.641402i
\(337\) 390.349i 1.15831i 0.815219 + 0.579153i \(0.196617\pi\)
−0.815219 + 0.579153i \(0.803383\pi\)
\(338\) −7.67075 + 21.6493i −0.0226945 + 0.0640512i
\(339\) −195.622 + 81.0292i −0.577056 + 0.239024i
\(340\) 381.807 207.129i 1.12296 0.609202i
\(341\) −16.4797 6.82613i −0.0483276 0.0200180i
\(342\) 4.31971 + 82.7063i 0.0126307 + 0.241831i
\(343\) −13.0958 13.0958i −0.0381802 0.0381802i
\(344\) 375.365 + 273.025i 1.09118 + 0.793676i
\(345\) −357.374 357.374i −1.03587 1.03587i
\(346\) 445.790 + 401.535i 1.28841 + 1.16051i
\(347\) −369.864 153.203i −1.06589 0.441506i −0.220351 0.975421i \(-0.570720\pi\)
−0.845538 + 0.533915i \(0.820720\pi\)
\(348\) 141.225 14.7926i 0.405819 0.0425074i
\(349\) −21.1755 + 8.77119i −0.0606749 + 0.0251324i −0.412814 0.910815i \(-0.635454\pi\)
0.352140 + 0.935947i \(0.385454\pi\)
\(350\) −65.1867 + 31.0783i −0.186248 + 0.0887950i
\(351\) 572.920i 1.63225i
\(352\) −216.763 + 57.8750i −0.615804 + 0.164418i
\(353\) −289.867 −0.821152 −0.410576 0.911826i \(-0.634672\pi\)
−0.410576 + 0.911826i \(0.634672\pi\)
\(354\) 37.8662 + 79.4245i 0.106967 + 0.224363i
\(355\) 81.8249 + 197.543i 0.230493 + 0.556458i
\(356\) −239.561 + 25.0927i −0.672923 + 0.0704852i
\(357\) −168.981 + 407.956i −0.473336 + 1.14273i
\(358\) −96.6485 + 107.301i −0.269968 + 0.299722i
\(359\) −35.2788 + 35.2788i −0.0982697 + 0.0982697i −0.754532 0.656263i \(-0.772136\pi\)
0.656263 + 0.754532i \(0.272136\pi\)
\(360\) −474.335 + 74.8681i −1.31760 + 0.207967i
\(361\) −251.445 + 251.445i −0.696524 + 0.696524i
\(362\) 325.336 16.9922i 0.898718 0.0469396i
\(363\) −142.371 + 343.715i −0.392207 + 0.946872i
\(364\) 116.749 63.3359i 0.320739 0.174000i
\(365\) −165.563 399.703i −0.453596 1.09508i
\(366\) 271.941 + 96.3536i 0.743007 + 0.263261i
\(367\) −109.584 −0.298594 −0.149297 0.988792i \(-0.547701\pi\)
−0.149297 + 0.988792i \(0.547701\pi\)
\(368\) −252.700 + 388.519i −0.686686 + 1.05576i
\(369\) 593.908i 1.60951i
\(370\) 40.0699 + 14.1975i 0.108297 + 0.0383717i
\(371\) −11.8581 + 4.91181i −0.0319627 + 0.0132394i
\(372\) −14.9851 + 50.5231i −0.0402827 + 0.135815i
\(373\) 260.099 + 107.736i 0.697315 + 0.288838i 0.703044 0.711146i \(-0.251824\pi\)
−0.00572885 + 0.999984i \(0.501824\pi\)
\(374\) 451.319 23.5722i 1.20674 0.0630273i
\(375\) 476.808 + 476.808i 1.27149 + 1.27149i
\(376\) −148.226 + 615.960i −0.394219 + 1.63819i
\(377\) 60.8382 + 60.8382i 0.161375 + 0.161375i
\(378\) 161.662 179.479i 0.427676 0.474813i
\(379\) −36.0680 14.9399i −0.0951663 0.0394192i 0.334592 0.942363i \(-0.391401\pi\)
−0.429759 + 0.902944i \(0.641401\pi\)
\(380\) 24.3382 + 19.7230i 0.0640478 + 0.0519026i
\(381\) 1128.69 467.517i 2.96243 1.22708i
\(382\) 258.955 + 543.158i 0.677891 + 1.42188i
\(383\) 331.350i 0.865144i 0.901599 + 0.432572i \(0.142394\pi\)
−0.901599 + 0.432572i \(0.857606\pi\)
\(384\) 236.767 + 619.100i 0.616580 + 1.61224i
\(385\) 62.5002 0.162338
\(386\) 68.7748 32.7889i 0.178173 0.0849453i
\(387\) 395.557 + 954.958i 1.02211 + 2.46759i
\(388\) 398.863 492.196i 1.02800 1.26855i
\(389\) 163.551 394.846i 0.420439 1.01503i −0.561780 0.827287i \(-0.689883\pi\)
0.982218 0.187742i \(-0.0601169\pi\)
\(390\) −325.411 293.106i −0.834388 0.751555i
\(391\) 660.153 660.153i 1.68837 1.68837i
\(392\) 54.4457 + 13.1020i 0.138892 + 0.0334234i
\(393\) 13.8792 13.8792i 0.0353160 0.0353160i
\(394\) −23.5736 451.347i −0.0598316 1.14555i
\(395\) 171.680 414.472i 0.434633 1.04930i
\(396\) −478.998 142.071i −1.20959 0.358765i
\(397\) −154.885 373.925i −0.390138 0.941876i −0.989909 0.141704i \(-0.954742\pi\)
0.599771 0.800172i \(-0.295258\pi\)
\(398\) −175.849 + 496.301i −0.441831 + 1.24699i
\(399\) −31.8454 −0.0798130
\(400\) 119.058 183.048i 0.297645 0.457621i
\(401\) 360.839i 0.899848i 0.893067 + 0.449924i \(0.148549\pi\)
−0.893067 + 0.449924i \(0.851451\pi\)
\(402\) −392.601 + 1108.04i −0.976619 + 2.75633i
\(403\) −29.5002 + 12.2194i −0.0732014 + 0.0303210i
\(404\) −23.3802 43.0974i −0.0578717 0.106677i
\(405\) −236.729 98.0563i −0.584515 0.242114i
\(406\) 1.89205 + 36.2257i 0.00466022 + 0.0892258i
\(407\) 31.2750 + 31.2750i 0.0768428 + 0.0768428i
\(408\) −208.165 1318.85i −0.510208 3.23248i
\(409\) 129.110 + 129.110i 0.315673 + 0.315673i 0.847103 0.531429i \(-0.178345\pi\)
−0.531429 + 0.847103i \(0.678345\pi\)
\(410\) −166.918 150.348i −0.407117 0.366701i
\(411\) −436.008 180.600i −1.06085 0.439417i
\(412\) 59.1016 + 564.243i 0.143450 + 1.36952i
\(413\) −20.7669 + 8.60194i −0.0502831 + 0.0208280i
\(414\) −931.647 + 444.170i −2.25036 + 1.07287i
\(415\) 279.747i 0.674089i
\(416\) −201.118 + 347.632i −0.483456 + 0.835654i
\(417\) 856.471 2.05389
\(418\) 14.0264 + 29.4204i 0.0335560 + 0.0703837i
\(419\) −142.795 344.738i −0.340800 0.822764i −0.997635 0.0687297i \(-0.978105\pi\)
0.656835 0.754034i \(-0.271895\pi\)
\(420\) −19.2357 183.644i −0.0457993 0.437247i
\(421\) −183.539 + 443.102i −0.435959 + 1.05250i 0.541372 + 0.840783i \(0.317905\pi\)
−0.977331 + 0.211716i \(0.932095\pi\)
\(422\) 172.056 191.019i 0.407715 0.452652i
\(423\) −997.622 + 997.622i −2.35845 + 2.35845i
\(424\) 22.8286 31.3857i 0.0538411 0.0740229i
\(425\) −311.027 + 311.027i −0.731827 + 0.731827i
\(426\) 656.344 34.2805i 1.54071 0.0804707i
\(427\) −28.2047 + 68.0922i −0.0660532 + 0.159467i
\(428\) 386.831 + 713.058i 0.903811 + 1.66602i
\(429\) −174.374 420.976i −0.406466 0.981296i
\(430\) 368.526 + 130.576i 0.857037 + 0.303664i
\(431\) 226.936 0.526534 0.263267 0.964723i \(-0.415200\pi\)
0.263267 + 0.964723i \(0.415200\pi\)
\(432\) −133.612 + 718.059i −0.309288 + 1.66217i
\(433\) 629.109i 1.45291i 0.687215 + 0.726454i \(0.258833\pi\)
−0.687215 + 0.726454i \(0.741167\pi\)
\(434\) −12.6895 4.49613i −0.0292385 0.0103597i
\(435\) 110.505 45.7725i 0.254034 0.105224i
\(436\) 161.947 + 48.0334i 0.371437 + 0.110168i
\(437\) 62.2047 + 25.7660i 0.142345 + 0.0589611i
\(438\) −1328.03 + 69.3624i −3.03203 + 0.158362i
\(439\) 85.0117 + 85.0117i 0.193648 + 0.193648i 0.797271 0.603622i \(-0.206276\pi\)
−0.603622 + 0.797271i \(0.706276\pi\)
\(440\) −161.187 + 98.6574i −0.366334 + 0.224221i
\(441\) 88.1815 + 88.1815i 0.199958 + 0.199958i
\(442\) 541.435 601.110i 1.22497 1.35998i
\(443\) −665.919 275.833i −1.50320 0.622647i −0.529061 0.848584i \(-0.677456\pi\)
−0.974142 + 0.225937i \(0.927456\pi\)
\(444\) 82.2695 101.521i 0.185292 0.228650i
\(445\) −187.450 + 77.6442i −0.421235 + 0.174481i
\(446\) −184.949 387.932i −0.414685 0.869803i
\(447\) 661.451i 1.47976i
\(448\) −161.096 + 52.1535i −0.359590 + 0.116414i
\(449\) −326.908 −0.728079 −0.364040 0.931383i \(-0.618603\pi\)
−0.364040 + 0.931383i \(0.618603\pi\)
\(450\) 438.939 209.268i 0.975421 0.465039i
\(451\) −89.4443 215.938i −0.198324 0.478798i
\(452\) 127.071 + 102.975i 0.281131 + 0.227821i
\(453\) 110.055 265.697i 0.242947 0.586527i
\(454\) 217.531 + 195.936i 0.479143 + 0.431576i
\(455\) 79.1117 79.1117i 0.173872 0.173872i
\(456\) 82.1287 50.2683i 0.180107 0.110238i
\(457\) −62.1035 + 62.1035i −0.135894 + 0.135894i −0.771782 0.635888i \(-0.780634\pi\)
0.635888 + 0.771782i \(0.280634\pi\)
\(458\) −12.8407 245.852i −0.0280365 0.536795i
\(459\) 563.026 1359.27i 1.22664 2.96136i
\(460\) −111.012 + 374.281i −0.241330 + 0.813654i
\(461\) −166.562 402.116i −0.361306 0.872269i −0.995110 0.0987754i \(-0.968507\pi\)
0.633804 0.773494i \(-0.281493\pi\)
\(462\) 64.1611 181.083i 0.138877 0.391955i
\(463\) 185.627 0.400923 0.200461 0.979702i \(-0.435756\pi\)
0.200461 + 0.979702i \(0.435756\pi\)
\(464\) −62.0622 90.4388i −0.133755 0.194911i
\(465\) 44.3898i 0.0954619i
\(466\) −150.312 + 424.228i −0.322558 + 0.910360i
\(467\) 633.772 262.517i 1.35711 0.562135i 0.418850 0.908055i \(-0.362433\pi\)
0.938264 + 0.345920i \(0.112433\pi\)
\(468\) −786.138 + 426.477i −1.67978 + 0.911275i
\(469\) −277.447 114.922i −0.591572 0.245037i
\(470\) 27.8347 + 532.930i 0.0592227 + 1.13389i
\(471\) −525.022 525.022i −1.11470 1.11470i
\(472\) 39.9793 54.9651i 0.0847019 0.116452i
\(473\) 287.639 + 287.639i 0.608116 + 0.608116i
\(474\) −1024.62 922.898i −2.16164 1.94704i
\(475\) −29.3073 12.1395i −0.0616996 0.0255568i
\(476\) 339.232 35.5328i 0.712673 0.0746488i
\(477\) 79.8477 33.0740i 0.167396 0.0693375i
\(478\) 107.688 51.3410i 0.225288 0.107408i
\(479\) 697.602i 1.45637i 0.685379 + 0.728186i \(0.259636\pi\)
−0.685379 + 0.728186i \(0.740364\pi\)
\(480\) 339.492 + 443.250i 0.707276 + 0.923438i
\(481\) 79.1748 0.164605
\(482\) −110.246 231.241i −0.228726 0.479753i
\(483\) −151.874 366.655i −0.314438 0.759121i
\(484\) 285.813 29.9374i 0.590522 0.0618541i
\(485\) 204.214 493.016i 0.421059 1.01653i
\(486\) 22.8012 25.3143i 0.0469161 0.0520870i
\(487\) −354.807 + 354.807i −0.728556 + 0.728556i −0.970332 0.241776i \(-0.922270\pi\)
0.241776 + 0.970332i \(0.422270\pi\)
\(488\) −34.7449 220.130i −0.0711985 0.451086i
\(489\) −425.677 + 425.677i −0.870505 + 0.870505i
\(490\) 47.1065 2.46035i 0.0961358 0.00502113i
\(491\) −186.386 + 449.975i −0.379605 + 0.916447i 0.612435 + 0.790521i \(0.290190\pi\)
−0.992040 + 0.125926i \(0.959810\pi\)
\(492\) −606.959 + 329.272i −1.23366 + 0.669253i
\(493\) 84.5525 + 204.128i 0.171506 + 0.414052i
\(494\) 54.9942 + 19.4855i 0.111324 + 0.0394443i
\(495\) −420.850 −0.850201
\(496\) 39.8232 8.43510i 0.0802888 0.0170063i
\(497\) 167.900i 0.337826i
\(498\) −810.516 287.181i −1.62754 0.576669i
\(499\) 123.894 51.3186i 0.248285 0.102843i −0.255071 0.966922i \(-0.582099\pi\)
0.503355 + 0.864080i \(0.332099\pi\)
\(500\) 148.112 499.365i 0.296223 0.998729i
\(501\) 764.248 + 316.562i 1.52545 + 0.631860i
\(502\) 516.382 26.9704i 1.02865 0.0537259i
\(503\) −237.562 237.562i −0.472291 0.472291i 0.430364 0.902655i \(-0.358385\pi\)
−0.902655 + 0.430364i \(0.858385\pi\)
\(504\) −366.614 88.2231i −0.727409 0.175046i
\(505\) −29.2038 29.2038i −0.0578292 0.0578292i
\(506\) −271.842 + 301.803i −0.537237 + 0.596449i
\(507\) 54.9417 + 22.7576i 0.108366 + 0.0448867i
\(508\) −733.168 594.139i −1.44324 1.16957i
\(509\) −878.817 + 364.018i −1.72656 + 0.715163i −0.726962 + 0.686677i \(0.759069\pi\)
−0.999594 + 0.0284860i \(0.990931\pi\)
\(510\) −484.001 1015.19i −0.949022 1.99058i
\(511\) 339.724i 0.664823i
\(512\) 333.140 388.795i 0.650664 0.759366i
\(513\) 106.105 0.206833
\(514\) −303.764 + 144.822i −0.590981 + 0.281755i
\(515\) 182.877 + 441.505i 0.355102 + 0.857292i
\(516\) 756.639 933.692i 1.46635 1.80948i
\(517\) −212.478 + 512.968i −0.410983 + 0.992201i
\(518\) 24.8032 + 22.3409i 0.0478826 + 0.0431291i
\(519\) 1098.43 1098.43i 2.11644 2.11644i
\(520\) −79.1490 + 328.907i −0.152210 + 0.632513i
\(521\) 592.661 592.661i 1.13754 1.13754i 0.148655 0.988889i \(-0.452505\pi\)
0.988889 0.148655i \(-0.0474945\pi\)
\(522\) −12.7403 243.928i −0.0244066 0.467295i
\(523\) 236.359 570.622i 0.451930 1.09106i −0.519658 0.854375i \(-0.673940\pi\)
0.971587 0.236681i \(-0.0760595\pi\)
\(524\) −14.5358 4.31132i −0.0277401 0.00822771i
\(525\) 71.5543 + 172.747i 0.136294 + 0.329042i
\(526\) −21.0779 + 59.4884i −0.0400720 + 0.113096i
\(527\) −81.9982 −0.155594
\(528\) 120.371 + 568.289i 0.227976 + 1.07631i
\(529\) 310.081i 0.586165i
\(530\) 10.9179 30.8139i 0.0205999 0.0581394i
\(531\) 139.836 57.9218i 0.263344 0.109081i
\(532\) 11.7299 + 21.6220i 0.0220486 + 0.0406429i
\(533\) −386.547 160.113i −0.725230 0.300400i
\(534\) 32.5291 + 622.809i 0.0609158 + 1.16631i
\(535\) 483.184 + 483.184i 0.903147 + 0.903147i
\(536\) 896.939 141.571i 1.67339 0.264125i
\(537\) 264.390 + 264.390i 0.492346 + 0.492346i
\(538\) −192.055 172.989i −0.356980 0.321541i
\(539\) 45.3421 + 18.7813i 0.0841226 + 0.0348447i
\(540\) 64.0913 + 611.880i 0.118688 + 1.13311i
\(541\) 344.547 142.716i 0.636870 0.263800i −0.0407988 0.999167i \(-0.512990\pi\)
0.677669 + 0.735367i \(0.262990\pi\)
\(542\) −799.186 + 381.018i −1.47451 + 0.702985i
\(543\) 843.501i 1.55341i
\(544\) −818.785 + 627.121i −1.50512 + 1.15280i
\(545\) 142.287 0.261077
\(546\) −147.998 310.426i −0.271058 0.568546i
\(547\) 168.470 + 406.722i 0.307989 + 0.743551i 0.999770 + 0.0214438i \(0.00682630\pi\)
−0.691781 + 0.722107i \(0.743174\pi\)
\(548\) 37.9761 + 362.558i 0.0692995 + 0.661603i
\(549\) 189.918 458.504i 0.345935 0.835161i
\(550\) 128.077 142.193i 0.232866 0.258532i
\(551\) −11.2673 + 11.2673i −0.0204488 + 0.0204488i
\(552\) 970.450 + 705.864i 1.75806 + 1.27874i
\(553\) 249.098 249.098i 0.450448 0.450448i
\(554\) −127.255 + 6.64650i −0.229703 + 0.0119973i
\(555\) 42.1212 101.690i 0.0758940 0.183224i
\(556\) −315.471 581.518i −0.567394 1.04590i
\(557\) −292.899 707.120i −0.525850 1.26951i −0.934220 0.356698i \(-0.883903\pi\)
0.408369 0.912817i \(-0.366097\pi\)
\(558\) 85.4457 + 30.2750i 0.153129 + 0.0542563i
\(559\) 728.177 1.30264
\(560\) −117.603 + 80.7034i −0.210006 + 0.144113i
\(561\) 1170.14i 2.08581i
\(562\) −375.741 133.132i −0.668579 0.236890i
\(563\) −423.908 + 175.588i −0.752945 + 0.311880i −0.725943 0.687755i \(-0.758596\pi\)
−0.0270024 + 0.999635i \(0.508596\pi\)
\(564\) 1572.64 + 466.446i 2.78837 + 0.827032i
\(565\) 127.283 + 52.7223i 0.225279 + 0.0933138i
\(566\) 455.601 23.7959i 0.804950 0.0420422i
\(567\) −142.274 142.274i −0.250924 0.250924i
\(568\) −265.032 433.011i −0.466605 0.762343i
\(569\) 430.439 + 430.439i 0.756484 + 0.756484i 0.975681 0.219197i \(-0.0703437\pi\)
−0.219197 + 0.975681i \(0.570344\pi\)
\(570\) 54.2836 60.2665i 0.0952343 0.105731i
\(571\) −461.909 191.329i −0.808948 0.335077i −0.0604139 0.998173i \(-0.519242\pi\)
−0.748534 + 0.663096i \(0.769242\pi\)
\(572\) −221.601 + 273.456i −0.387415 + 0.478070i
\(573\) 1439.39 596.214i 2.51202 1.04051i
\(574\) −75.9148 159.232i −0.132256 0.277407i
\(575\) 395.328i 0.687526i
\(576\) 1084.75 351.179i 1.88325 0.609686i
\(577\) −138.933 −0.240784 −0.120392 0.992726i \(-0.538415\pi\)
−0.120392 + 0.992726i \(0.538415\pi\)
\(578\) 1353.56 645.319i 2.34180 1.11647i
\(579\) −75.4928 182.256i −0.130385 0.314777i
\(580\) −71.7813 58.1696i −0.123761 0.100292i
\(581\) 84.0639 202.948i 0.144688 0.349308i
\(582\) −1218.78 1097.79i −2.09413 1.88624i
\(583\) 24.0506 24.0506i 0.0412531 0.0412531i
\(584\) 536.259 + 876.144i 0.918252 + 1.50025i
\(585\) −532.704 + 532.704i −0.910606 + 0.910606i
\(586\) 47.0136 + 900.134i 0.0802280 + 1.53606i
\(587\) 104.243 251.665i 0.177586 0.428731i −0.809873 0.586605i \(-0.800464\pi\)
0.987459 + 0.157874i \(0.0504641\pi\)
\(588\) 41.2299 139.008i 0.0701189 0.236409i
\(589\) −2.26304 5.46346i −0.00384217 0.00927582i
\(590\) 19.1203 53.9637i 0.0324074 0.0914639i
\(591\) −1170.21 −1.98005
\(592\) −99.2324 18.4646i −0.167622 0.0311902i
\(593\) 323.479i 0.545496i −0.962086 0.272748i \(-0.912068\pi\)
0.962086 0.272748i \(-0.0879325\pi\)
\(594\) −213.778 + 603.349i −0.359895 + 1.01574i
\(595\) 265.440 109.949i 0.446118 0.184788i
\(596\) 449.105 243.637i 0.753532 0.408788i
\(597\) 1259.51 + 521.708i 2.10974 + 0.873883i
\(598\) 37.9244 + 726.111i 0.0634188 + 1.21423i
\(599\) −531.828 531.828i −0.887860 0.887860i 0.106457 0.994317i \(-0.466049\pi\)
−0.994317 + 0.106457i \(0.966049\pi\)
\(600\) −457.221 332.563i −0.762035 0.554272i
\(601\) 327.104 + 327.104i 0.544266 + 0.544266i 0.924777 0.380511i \(-0.124252\pi\)
−0.380511 + 0.924777i \(0.624252\pi\)
\(602\) 228.117 + 205.471i 0.378932 + 0.341314i
\(603\) 1868.21 + 773.839i 3.09820 + 1.28331i
\(604\) −220.938 + 23.1421i −0.365791 + 0.0383147i
\(605\) 223.641 92.6350i 0.369654 0.153116i
\(606\) −114.592 + 54.6328i −0.189096 + 0.0901531i
\(607\) 66.1212i 0.108931i −0.998516 0.0544656i \(-0.982654\pi\)
0.998516 0.0544656i \(-0.0173455\pi\)
\(608\) −64.3818 37.2472i −0.105891 0.0612618i
\(609\) 93.9225 0.154224
\(610\) −80.7849 169.447i −0.132434 0.277781i
\(611\) 380.355 + 918.257i 0.622512 + 1.50288i
\(612\) −2284.24 + 239.263i −3.73242 + 0.390952i
\(613\) −148.181 + 357.741i −0.241731 + 0.583590i −0.997455 0.0713001i \(-0.977285\pi\)
0.755724 + 0.654890i \(0.227285\pi\)
\(614\) −110.460 + 122.634i −0.179902 + 0.199730i
\(615\) −411.288 + 411.288i −0.668762 + 0.668762i
\(616\) −146.583 + 23.1363i −0.237959 + 0.0375590i
\(617\) 240.725 240.725i 0.390154 0.390154i −0.484588 0.874743i \(-0.661030\pi\)
0.874743 + 0.484588i \(0.161030\pi\)
\(618\) 1466.92 76.6165i 2.37366 0.123975i
\(619\) −347.023 + 837.787i −0.560618 + 1.35345i 0.348654 + 0.937251i \(0.386639\pi\)
−0.909273 + 0.416201i \(0.863361\pi\)
\(620\) 30.1393 16.3504i 0.0486118 0.0263717i
\(621\) 506.026 + 1221.66i 0.814857 + 1.96724i
\(622\) −192.560 68.2277i −0.309583 0.109691i
\(623\) −159.321 −0.255733
\(624\) 871.695 + 566.967i 1.39695 + 0.908601i
\(625\) 97.5550i 0.156088i
\(626\) −188.518 66.7955i −0.301147 0.106702i
\(627\) 77.9652 32.2942i 0.124346 0.0515059i
\(628\) −163.089 + 549.860i −0.259695 + 0.875573i
\(629\) 187.844 + 77.8076i 0.298639 + 0.123700i
\(630\) −317.195 + 16.5670i −0.503484 + 0.0262968i
\(631\) −394.850 394.850i −0.625753 0.625753i 0.321244 0.946997i \(-0.395899\pi\)
−0.946997 + 0.321244i \(0.895899\pi\)
\(632\) −249.215 + 1035.62i −0.394328 + 1.63864i
\(633\) −470.673 470.673i −0.743559 0.743559i
\(634\) −693.762 + 770.225i −1.09426 + 1.21487i
\(635\) −734.389 304.194i −1.15652 0.479045i
\(636\) −78.0696 63.2655i −0.122751 0.0994740i
\(637\) 81.1663 33.6202i 0.127420 0.0527789i
\(638\) −41.3685 86.7705i −0.0648409 0.136004i
\(639\) 1130.56i 1.76927i
\(640\) 175.906 393.771i 0.274852 0.615267i
\(641\) −1205.25 −1.88026 −0.940129 0.340819i \(-0.889296\pi\)
−0.940129 + 0.340819i \(0.889296\pi\)
\(642\) 1895.96 903.914i 2.95321 1.40797i
\(643\) −172.619 416.739i −0.268459 0.648117i 0.730952 0.682429i \(-0.239076\pi\)
−0.999411 + 0.0343114i \(0.989076\pi\)
\(644\) −193.007 + 238.171i −0.299701 + 0.369830i
\(645\) 387.392 935.247i 0.600607 1.44999i
\(646\) 111.326 + 100.274i 0.172331 + 0.155223i
\(647\) −295.241 + 295.241i −0.456323 + 0.456323i −0.897447 0.441123i \(-0.854580\pi\)
0.441123 + 0.897447i \(0.354580\pi\)
\(648\) 591.503 + 142.341i 0.912813 + 0.219662i
\(649\) 42.1193 42.1193i 0.0648987 0.0648987i
\(650\) −17.8678 342.102i −0.0274890 0.526311i
\(651\) −13.3391 + 32.2035i −0.0204902 + 0.0494677i
\(652\) 445.815 + 132.229i 0.683765 + 0.202805i
\(653\) 1.76266 + 4.25544i 0.00269933 + 0.00651676i 0.925223 0.379423i \(-0.123877\pi\)
−0.922524 + 0.385939i \(0.873877\pi\)
\(654\) 146.068 412.251i 0.223346 0.630353i
\(655\) −12.7712 −0.0194980
\(656\) 447.132 + 290.823i 0.681604 + 0.443328i
\(657\) 2287.56i 3.48182i
\(658\) −139.952 + 394.989i −0.212693 + 0.600287i
\(659\) −107.602 + 44.5704i −0.163281 + 0.0676333i −0.462827 0.886449i \(-0.653165\pi\)
0.299546 + 0.954082i \(0.403165\pi\)
\(660\) 233.326 + 430.097i 0.353524 + 0.651662i
\(661\) −819.916 339.620i −1.24042 0.513798i −0.336573 0.941657i \(-0.609268\pi\)
−0.903845 + 0.427859i \(0.859268\pi\)
\(662\) −39.6762 759.651i −0.0599339 1.14751i
\(663\) −1481.14 1481.14i −2.23400 2.23400i
\(664\) 103.557 + 656.096i 0.155959 + 0.988096i
\(665\) 14.6516 + 14.6516i 0.0220324 + 0.0220324i
\(666\) −167.014 150.434i −0.250772 0.225877i
\(667\) −183.462 75.9925i −0.275056 0.113932i
\(668\) −66.5657 635.504i −0.0996493 0.951353i
\(669\) −1028.03 + 425.826i −1.53667 + 0.636511i
\(670\) 690.424 329.165i 1.03048 0.491291i
\(671\) 195.308i 0.291071i
\(672\) 113.095 + 423.582i 0.168296 + 0.630331i
\(673\) 314.608 0.467471 0.233736 0.972300i \(-0.424905\pi\)
0.233736 + 0.972300i \(0.424905\pi\)
\(674\) −335.974 704.706i −0.498478 1.04556i
\(675\) −238.411 575.575i −0.353201 0.852704i
\(676\) −4.78540 45.6862i −0.00707899 0.0675832i
\(677\) 231.365 558.565i 0.341751 0.825059i −0.655788 0.754945i \(-0.727664\pi\)
0.997539 0.0701143i \(-0.0223364\pi\)
\(678\) 283.419 314.656i 0.418022 0.464094i
\(679\) 296.302 296.302i 0.436380 0.436380i
\(680\) −511.010 + 702.557i −0.751485 + 1.03317i
\(681\) 535.999 535.999i 0.787076 0.787076i
\(682\) 35.6265 1.86076i 0.0522383 0.00272838i
\(683\) −67.4338 + 162.800i −0.0987318 + 0.238360i −0.965526 0.260306i \(-0.916177\pi\)
0.866794 + 0.498666i \(0.166177\pi\)
\(684\) −78.9839 145.594i −0.115473 0.212856i
\(685\) 117.509 + 283.692i 0.171546 + 0.414149i
\(686\) 34.9137 + 12.3706i 0.0508947 + 0.0180329i
\(687\) −637.422 −0.927834
\(688\) −912.648 169.821i −1.32652 0.246832i
\(689\) 60.8856i 0.0883681i
\(690\) 952.769 + 337.584i 1.38082 + 0.489252i
\(691\) 81.5119 33.7634i 0.117962 0.0488616i −0.322922 0.946426i \(-0.604665\pi\)
0.440884 + 0.897564i \(0.354665\pi\)
\(692\) −1150.40 341.208i −1.66242 0.493075i
\(693\) −305.314 126.465i −0.440569 0.182489i
\(694\) 799.585 41.7620i 1.15214 0.0601758i
\(695\) −394.049 394.049i −0.566977 0.566977i
\(696\) −242.225 + 148.258i −0.348024 + 0.213014i
\(697\) −759.745 759.745i −1.09002 1.09002i
\(698\) 30.6793 34.0606i 0.0439532 0.0487975i
\(699\) 1076.61 + 445.945i 1.54021 + 0.637976i
\(700\) 90.9340 112.213i 0.129906 0.160304i
\(701\) −16.1430 + 6.68667i −0.0230286 + 0.00953875i −0.394168 0.919038i \(-0.628967\pi\)
0.371139 + 0.928577i \(0.378967\pi\)
\(702\) 493.113 + 1034.31i 0.702440 + 1.47337i
\(703\) 14.6632i 0.0208581i
\(704\) 341.514 291.051i 0.485105 0.413425i
\(705\) 1381.73 1.95990
\(706\) 523.303 249.489i 0.741223 0.353383i
\(707\) −12.4107 29.9622i −0.0175541 0.0423793i
\(708\) −136.722 110.795i −0.193110 0.156491i
\(709\) −43.8518 + 105.868i −0.0618502 + 0.149320i −0.951783 0.306772i \(-0.900751\pi\)
0.889933 + 0.456092i \(0.150751\pi\)
\(710\) −317.746 286.202i −0.447529 0.403101i
\(711\) −1677.32 + 1677.32i −2.35909 + 2.35909i
\(712\) 410.887 251.491i 0.577089 0.353217i
\(713\) 52.1115 52.1115i 0.0730877 0.0730877i
\(714\) −46.0631 881.935i −0.0645141 1.23520i
\(715\) −113.458 + 273.911i −0.158682 + 0.383093i
\(716\) 82.1280 276.898i 0.114704 0.386729i
\(717\) −118.207 285.377i −0.164863 0.398015i
\(718\) 33.3252 94.0542i 0.0464139 0.130995i
\(719\) −414.680 −0.576745 −0.288373 0.957518i \(-0.593114\pi\)
−0.288373 + 0.957518i \(0.593114\pi\)
\(720\) 791.890 543.422i 1.09985 0.754753i
\(721\) 375.254i 0.520463i
\(722\) 237.521 670.359i 0.328976 0.928476i
\(723\) −612.797 + 253.829i −0.847575 + 0.351077i
\(724\) −572.711 + 310.693i −0.791038 + 0.429135i
\(725\) 86.4370 + 35.8034i 0.119223 + 0.0493840i
\(726\) −38.8094 743.055i −0.0534565 1.02349i
\(727\) 19.1796 + 19.1796i 0.0263819 + 0.0263819i 0.720175 0.693793i \(-0.244062\pi\)
−0.693793 + 0.720175i \(0.744062\pi\)
\(728\) −156.257 + 214.828i −0.214638 + 0.295093i
\(729\) −546.345 546.345i −0.749444 0.749444i
\(730\) 642.919 + 579.094i 0.880711 + 0.793279i
\(731\) 1727.62 + 715.602i 2.36336 + 0.978936i
\(732\) −573.872 + 60.1102i −0.783979 + 0.0821177i
\(733\) 264.856 109.707i 0.361331 0.149668i −0.194630 0.980877i \(-0.562350\pi\)
0.555961 + 0.831209i \(0.312350\pi\)
\(734\) 197.834 94.3190i 0.269529 0.128500i
\(735\) 122.133i 0.166168i
\(736\) 121.807 918.903i 0.165498 1.24851i
\(737\) 795.801 1.07978
\(738\) 511.178 + 1072.20i 0.692653 + 1.45284i
\(739\) 162.041 + 391.201i 0.219270 + 0.529365i 0.994788 0.101960i \(-0.0325114\pi\)
−0.775518 + 0.631325i \(0.782511\pi\)
\(740\) −84.5590 + 8.85712i −0.114269 + 0.0119691i
\(741\) 57.8095 139.564i 0.0780155 0.188346i
\(742\) 17.1802 19.0737i 0.0231539 0.0257058i
\(743\) −534.670 + 534.670i −0.719610 + 0.719610i −0.968525 0.248915i \(-0.919926\pi\)
0.248915 + 0.968525i \(0.419926\pi\)
\(744\) −16.4322 104.108i −0.0220863 0.139930i
\(745\) 304.323 304.323i 0.408488 0.408488i
\(746\) −562.291 + 29.3682i −0.753741 + 0.0393676i
\(747\) −566.050 + 1366.57i −0.757765 + 1.82941i
\(748\) −794.489 + 431.007i −1.06215 + 0.576212i
\(749\) 205.339 + 495.732i 0.274151 + 0.661859i
\(750\) −1271.18 450.403i −1.69491 0.600538i
\(751\) −479.403 −0.638352 −0.319176 0.947695i \(-0.603406\pi\)
−0.319176 + 0.947695i \(0.603406\pi\)
\(752\) −262.561 1239.59i −0.349151 1.64839i
\(753\) 1338.83i 1.77799i
\(754\) −162.196 57.4691i −0.215114 0.0762190i
\(755\) −172.878 + 71.6083i −0.228977 + 0.0948454i
\(756\) −137.374 + 463.161i −0.181711 + 0.612646i
\(757\) −1195.88 495.352i −1.57977 0.654361i −0.591391 0.806385i \(-0.701421\pi\)
−0.988377 + 0.152023i \(0.951421\pi\)