Properties

Label 16.4.e.a.5.3
Level 16
Weight 4
Character 16.5
Analytic conductor 0.944
Analytic rank 0
Dimension 10
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(0.944030560092\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{10} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.3
Root \(-1.62580 - 1.16481i\)
Character \(\chi\) = 16.5
Dual form 16.4.e.a.13.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.460984 - 2.79061i) q^{2} +(0.756776 - 0.756776i) q^{3} +(-7.57499 - 2.57285i) q^{4} +(8.22587 + 8.22587i) q^{5} +(-1.76300 - 2.46073i) q^{6} +2.67171i q^{7} +(-10.6718 + 19.9528i) q^{8} +25.8546i q^{9} +O(q^{10})\) \(q+(0.460984 - 2.79061i) q^{2} +(0.756776 - 0.756776i) q^{3} +(-7.57499 - 2.57285i) q^{4} +(8.22587 + 8.22587i) q^{5} +(-1.76300 - 2.46073i) q^{6} +2.67171i q^{7} +(-10.6718 + 19.9528i) q^{8} +25.8546i q^{9} +(26.7472 - 19.1632i) q^{10} +(-45.2213 - 45.2213i) q^{11} +(-7.67964 + 3.78550i) q^{12} +(35.3968 - 35.3968i) q^{13} +(7.45568 + 1.23161i) q^{14} +12.4503 q^{15} +(50.7609 + 38.9786i) q^{16} -72.4991 q^{17} +(72.1500 + 11.9185i) q^{18} +(19.4427 - 19.4427i) q^{19} +(-41.1470 - 83.4748i) q^{20} +(2.02188 + 2.02188i) q^{21} +(-147.041 + 105.349i) q^{22} +139.462i q^{23} +(7.02366 + 23.1759i) q^{24} +10.3299i q^{25} +(-82.4612 - 115.096i) q^{26} +(39.9991 + 39.9991i) q^{27} +(6.87389 - 20.2381i) q^{28} +(66.0434 - 66.0434i) q^{29} +(5.73937 - 34.7439i) q^{30} +188.682 q^{31} +(132.174 - 123.685i) q^{32} -68.4447 q^{33} +(-33.4209 + 202.317i) q^{34} +(-21.9771 + 21.9771i) q^{35} +(66.5199 - 195.848i) q^{36} +(-84.0653 - 84.0653i) q^{37} +(-45.2941 - 63.2196i) q^{38} -53.5748i q^{39} +(-251.914 + 76.3445i) q^{40} -104.629i q^{41} +(6.57434 - 4.71023i) q^{42} +(-31.4857 - 31.4857i) q^{43} +(226.203 + 458.898i) q^{44} +(-212.676 + 212.676i) q^{45} +(389.183 + 64.2896i) q^{46} -488.151 q^{47} +(67.9127 - 8.91656i) q^{48} +335.862 q^{49} +(28.8266 + 4.76190i) q^{50} +(-54.8656 + 54.8656i) q^{51} +(-359.201 + 177.060i) q^{52} +(149.560 + 149.560i) q^{53} +(130.061 - 93.1828i) q^{54} -743.968i q^{55} +(-53.3080 - 28.5118i) q^{56} -29.4275i q^{57} +(-153.856 - 214.746i) q^{58} +(284.698 + 284.698i) q^{59} +(-94.3107 - 32.0327i) q^{60} +(-228.069 + 228.069i) q^{61} +(86.9792 - 526.537i) q^{62} -69.0758 q^{63} +(-284.227 - 425.863i) q^{64} +582.338 q^{65} +(-31.5519 + 191.002i) q^{66} +(139.151 - 139.151i) q^{67} +(549.180 + 186.529i) q^{68} +(105.541 + 105.541i) q^{69} +(51.1984 + 71.4606i) q^{70} +453.655i q^{71} +(-515.871 - 275.914i) q^{72} +259.747i q^{73} +(-273.346 + 195.841i) q^{74} +(7.81740 + 7.81740i) q^{75} +(-197.301 + 97.2550i) q^{76} +(120.818 - 120.818i) q^{77} +(-149.506 - 24.6971i) q^{78} +323.190 q^{79} +(96.9197 + 738.185i) q^{80} -637.533 q^{81} +(-291.979 - 48.2323i) q^{82} +(-563.897 + 563.897i) q^{83} +(-10.1137 - 20.5177i) q^{84} +(-596.368 - 596.368i) q^{85} +(-102.379 + 73.3499i) q^{86} -99.9602i q^{87} +(1384.88 - 419.700i) q^{88} -866.853i q^{89} +(495.456 + 691.537i) q^{90} +(94.5697 + 94.5697i) q^{91} +(358.814 - 1056.42i) q^{92} +(142.790 - 142.790i) q^{93} +(-225.030 + 1362.24i) q^{94} +319.866 q^{95} +(6.42400 - 193.628i) q^{96} -936.077 q^{97} +(154.827 - 937.259i) q^{98} +(1169.18 - 1169.18i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} + O(q^{10}) \) \( 10q - 2q^{2} - 2q^{3} + 8q^{4} - 2q^{5} - 32q^{6} - 44q^{8} - 68q^{10} + 18q^{11} + 100q^{12} - 2q^{13} + 188q^{14} - 124q^{15} + 280q^{16} - 4q^{17} + 174q^{18} - 26q^{19} - 196q^{20} + 52q^{21} - 588q^{22} - 848q^{24} - 264q^{26} + 184q^{27} + 280q^{28} - 202q^{29} + 1236q^{30} + 368q^{31} + 968q^{32} - 4q^{33} + 436q^{34} + 476q^{35} - 596q^{36} - 10q^{37} - 1232q^{38} - 1336q^{40} - 680q^{42} - 838q^{43} + 868q^{44} + 194q^{45} + 1132q^{46} - 944q^{47} + 1768q^{48} + 94q^{49} + 726q^{50} - 1500q^{51} - 236q^{52} - 378q^{53} - 1376q^{54} - 488q^{56} + 8q^{58} + 1706q^{59} - 192q^{60} + 910q^{61} - 80q^{62} + 2628q^{63} + 512q^{64} - 492q^{65} - 428q^{66} + 1942q^{67} - 880q^{68} + 580q^{69} + 160q^{70} + 1092q^{72} - 452q^{74} - 2954q^{75} - 1228q^{76} - 268q^{77} - 772q^{78} - 4416q^{79} - 2648q^{80} + 482q^{81} - 704q^{82} - 2562q^{83} + 1960q^{84} - 12q^{85} + 3764q^{86} + 1528q^{88} + 1896q^{90} + 3332q^{91} + 632q^{92} - 2192q^{93} - 3248q^{94} + 6900q^{95} - 4432q^{96} - 4q^{97} + 314q^{98} + 4958q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.460984 2.79061i 0.162982 0.986629i
\(3\) 0.756776 0.756776i 0.145642 0.145642i −0.630526 0.776168i \(-0.717161\pi\)
0.776168 + 0.630526i \(0.217161\pi\)
\(4\) −7.57499 2.57285i −0.946874 0.321606i
\(5\) 8.22587 + 8.22587i 0.735744 + 0.735744i 0.971751 0.236007i \(-0.0758389\pi\)
−0.236007 + 0.971751i \(0.575839\pi\)
\(6\) −1.76300 2.46073i −0.119957 0.167431i
\(7\) 2.67171i 0.144259i 0.997395 + 0.0721293i \(0.0229794\pi\)
−0.997395 + 0.0721293i \(0.977021\pi\)
\(8\) −10.6718 + 19.9528i −0.471630 + 0.881797i
\(9\) 25.8546i 0.957577i
\(10\) 26.7472 19.1632i 0.845820 0.605993i
\(11\) −45.2213 45.2213i −1.23952 1.23952i −0.960197 0.279323i \(-0.909890\pi\)
−0.279323 0.960197i \(-0.590110\pi\)
\(12\) −7.67964 + 3.78550i −0.184743 + 0.0910650i
\(13\) 35.3968 35.3968i 0.755176 0.755176i −0.220264 0.975440i \(-0.570692\pi\)
0.975440 + 0.220264i \(0.0706918\pi\)
\(14\) 7.45568 + 1.23161i 0.142330 + 0.0235116i
\(15\) 12.4503 0.214310
\(16\) 50.7609 + 38.9786i 0.793139 + 0.609041i
\(17\) −72.4991 −1.03433 −0.517165 0.855886i \(-0.673013\pi\)
−0.517165 + 0.855886i \(0.673013\pi\)
\(18\) 72.1500 + 11.9185i 0.944773 + 0.156068i
\(19\) 19.4427 19.4427i 0.234761 0.234761i −0.579916 0.814676i \(-0.696915\pi\)
0.814676 + 0.579916i \(0.196915\pi\)
\(20\) −41.1470 83.4748i −0.460037 0.933277i
\(21\) 2.02188 + 2.02188i 0.0210100 + 0.0210100i
\(22\) −147.041 + 105.349i −1.42497 + 1.02093i
\(23\) 139.462i 1.26434i 0.774830 + 0.632170i \(0.217835\pi\)
−0.774830 + 0.632170i \(0.782165\pi\)
\(24\) 7.02366 + 23.1759i 0.0597374 + 0.197115i
\(25\) 10.3299i 0.0826390i
\(26\) −82.4612 115.096i −0.621999 0.868159i
\(27\) 39.9991 + 39.9991i 0.285105 + 0.285105i
\(28\) 6.87389 20.2381i 0.0463944 0.136595i
\(29\) 66.0434 66.0434i 0.422895 0.422895i −0.463304 0.886199i \(-0.653336\pi\)
0.886199 + 0.463304i \(0.153336\pi\)
\(30\) 5.73937 34.7439i 0.0349287 0.211444i
\(31\) 188.682 1.09317 0.546584 0.837404i \(-0.315928\pi\)
0.546584 + 0.837404i \(0.315928\pi\)
\(32\) 132.174 123.685i 0.730165 0.683271i
\(33\) −68.4447 −0.361051
\(34\) −33.4209 + 202.317i −0.168577 + 1.02050i
\(35\) −21.9771 + 21.9771i −0.106137 + 0.106137i
\(36\) 66.5199 195.848i 0.307963 0.906704i
\(37\) −84.0653 84.0653i −0.373520 0.373520i 0.495237 0.868758i \(-0.335081\pi\)
−0.868758 + 0.495237i \(0.835081\pi\)
\(38\) −45.2941 63.2196i −0.193360 0.269884i
\(39\) 53.5748i 0.219970i
\(40\) −251.914 + 76.3445i −0.995776 + 0.301778i
\(41\) 104.629i 0.398545i −0.979944 0.199272i \(-0.936142\pi\)
0.979944 0.199272i \(-0.0638578\pi\)
\(42\) 6.57434 4.71023i 0.0241534 0.0173049i
\(43\) −31.4857 31.4857i −0.111663 0.111663i 0.649067 0.760731i \(-0.275159\pi\)
−0.760731 + 0.649067i \(0.775159\pi\)
\(44\) 226.203 + 458.898i 0.775032 + 1.57231i
\(45\) −212.676 + 212.676i −0.704532 + 0.704532i
\(46\) 389.183 + 64.2896i 1.24743 + 0.206065i
\(47\) −488.151 −1.51498 −0.757491 0.652846i \(-0.773575\pi\)
−0.757491 + 0.652846i \(0.773575\pi\)
\(48\) 67.9127 8.91656i 0.204216 0.0268124i
\(49\) 335.862 0.979189
\(50\) 28.8266 + 4.76190i 0.0815341 + 0.0134687i
\(51\) −54.8656 + 54.8656i −0.150641 + 0.150641i
\(52\) −359.201 + 177.060i −0.957926 + 0.472187i
\(53\) 149.560 + 149.560i 0.387617 + 0.387617i 0.873837 0.486220i \(-0.161624\pi\)
−0.486220 + 0.873837i \(0.661624\pi\)
\(54\) 130.061 93.1828i 0.327760 0.234826i
\(55\) 743.968i 1.82394i
\(56\) −53.3080 28.5118i −0.127207 0.0680366i
\(57\) 29.4275i 0.0683819i
\(58\) −153.856 214.746i −0.348316 0.486165i
\(59\) 284.698 + 284.698i 0.628212 + 0.628212i 0.947618 0.319406i \(-0.103483\pi\)
−0.319406 + 0.947618i \(0.603483\pi\)
\(60\) −94.3107 32.0327i −0.202924 0.0689234i
\(61\) −228.069 + 228.069i −0.478709 + 0.478709i −0.904719 0.426010i \(-0.859919\pi\)
0.426010 + 0.904719i \(0.359919\pi\)
\(62\) 86.9792 526.537i 0.178167 1.07855i
\(63\) −69.0758 −0.138139
\(64\) −284.227 425.863i −0.555131 0.831763i
\(65\) 582.338 1.11123
\(66\) −31.5519 + 191.002i −0.0588450 + 0.356224i
\(67\) 139.151 139.151i 0.253730 0.253730i −0.568768 0.822498i \(-0.692580\pi\)
0.822498 + 0.568768i \(0.192580\pi\)
\(68\) 549.180 + 186.529i 0.979380 + 0.332647i
\(69\) 105.541 + 105.541i 0.184140 + 0.184140i
\(70\) 51.1984 + 71.4606i 0.0874197 + 0.122017i
\(71\) 453.655i 0.758294i 0.925336 + 0.379147i \(0.123783\pi\)
−0.925336 + 0.379147i \(0.876217\pi\)
\(72\) −515.871 275.914i −0.844388 0.451622i
\(73\) 259.747i 0.416454i 0.978081 + 0.208227i \(0.0667692\pi\)
−0.978081 + 0.208227i \(0.933231\pi\)
\(74\) −273.346 + 195.841i −0.429403 + 0.307649i
\(75\) 7.81740 + 7.81740i 0.0120357 + 0.0120357i
\(76\) −197.301 + 97.2550i −0.297789 + 0.146788i
\(77\) 120.818 120.818i 0.178811 0.178811i
\(78\) −149.506 24.6971i −0.217029 0.0358512i
\(79\) 323.190 0.460275 0.230138 0.973158i \(-0.426082\pi\)
0.230138 + 0.973158i \(0.426082\pi\)
\(80\) 96.9197 + 738.185i 0.135449 + 1.03165i
\(81\) −637.533 −0.874531
\(82\) −291.979 48.2323i −0.393216 0.0649557i
\(83\) −563.897 + 563.897i −0.745732 + 0.745732i −0.973674 0.227943i \(-0.926800\pi\)
0.227943 + 0.973674i \(0.426800\pi\)
\(84\) −10.1137 20.5177i −0.0131369 0.0266508i
\(85\) −596.368 596.368i −0.761002 0.761002i
\(86\) −102.379 + 73.3499i −0.128369 + 0.0919711i
\(87\) 99.9602i 0.123182i
\(88\) 1384.88 419.700i 1.67760 0.508411i
\(89\) 866.853i 1.03243i −0.856459 0.516215i \(-0.827341\pi\)
0.856459 0.516215i \(-0.172659\pi\)
\(90\) 495.456 + 691.537i 0.580285 + 0.809938i
\(91\) 94.5697 + 94.5697i 0.108941 + 0.108941i
\(92\) 358.814 1056.42i 0.406619 1.19717i
\(93\) 142.790 142.790i 0.159211 0.159211i
\(94\) −225.030 + 1362.24i −0.246915 + 1.49472i
\(95\) 319.866 0.345448
\(96\) 6.42400 193.628i 0.00682966 0.205855i
\(97\) −936.077 −0.979837 −0.489919 0.871768i \(-0.662974\pi\)
−0.489919 + 0.871768i \(0.662974\pi\)
\(98\) 154.827 937.259i 0.159591 0.966097i
\(99\) 1169.18 1169.18i 1.18694 1.18694i
\(100\) 26.5772 78.2487i 0.0265772 0.0782487i
\(101\) −1.58844 1.58844i −0.00156491 0.00156491i 0.706324 0.707889i \(-0.250352\pi\)
−0.707889 + 0.706324i \(0.750352\pi\)
\(102\) 127.816 + 178.400i 0.124075 + 0.173179i
\(103\) 1388.28i 1.32807i 0.747700 + 0.664036i \(0.231158\pi\)
−0.747700 + 0.664036i \(0.768842\pi\)
\(104\) 328.518 + 1084.01i 0.309749 + 1.02208i
\(105\) 33.2635i 0.0309160i
\(106\) 486.310 348.420i 0.445609 0.319260i
\(107\) −821.526 821.526i −0.742243 0.742243i 0.230767 0.973009i \(-0.425877\pi\)
−0.973009 + 0.230767i \(0.925877\pi\)
\(108\) −200.081 405.904i −0.178267 0.361649i
\(109\) 532.797 532.797i 0.468190 0.468190i −0.433138 0.901328i \(-0.642594\pi\)
0.901328 + 0.433138i \(0.142594\pi\)
\(110\) −2076.12 342.957i −1.79955 0.297270i
\(111\) −127.237 −0.108800
\(112\) −104.139 + 135.618i −0.0878593 + 0.114417i
\(113\) −67.2680 −0.0560003 −0.0280002 0.999608i \(-0.508914\pi\)
−0.0280002 + 0.999608i \(0.508914\pi\)
\(114\) −82.1206 13.5656i −0.0674675 0.0111450i
\(115\) −1147.19 + 1147.19i −0.930230 + 0.930230i
\(116\) −670.198 + 330.359i −0.536434 + 0.264423i
\(117\) 915.168 + 915.168i 0.723140 + 0.723140i
\(118\) 925.722 663.240i 0.722200 0.517425i
\(119\) 193.696i 0.149211i
\(120\) −132.866 + 248.418i −0.101075 + 0.188978i
\(121\) 2758.92i 2.07282i
\(122\) 531.315 + 741.587i 0.394287 + 0.550329i
\(123\) −79.1808 79.1808i −0.0580447 0.0580447i
\(124\) −1429.26 485.449i −1.03509 0.351570i
\(125\) 943.262 943.262i 0.674943 0.674943i
\(126\) −31.8428 + 192.764i −0.0225142 + 0.136292i
\(127\) 1903.59 1.33005 0.665026 0.746820i \(-0.268421\pi\)
0.665026 + 0.746820i \(0.268421\pi\)
\(128\) −1319.44 + 596.851i −0.911118 + 0.412146i
\(129\) −47.6552 −0.0325257
\(130\) 268.448 1625.08i 0.181111 1.09638i
\(131\) 918.430 918.430i 0.612546 0.612546i −0.331062 0.943609i \(-0.607407\pi\)
0.943609 + 0.331062i \(0.107407\pi\)
\(132\) 518.468 + 176.098i 0.341870 + 0.116116i
\(133\) 51.9451 + 51.9451i 0.0338662 + 0.0338662i
\(134\) −324.169 452.461i −0.208984 0.291691i
\(135\) 658.054i 0.419528i
\(136\) 773.693 1446.56i 0.487821 0.912069i
\(137\) 477.234i 0.297612i −0.988866 0.148806i \(-0.952457\pi\)
0.988866 0.148806i \(-0.0475430\pi\)
\(138\) 343.177 245.872i 0.211690 0.151667i
\(139\) −1513.89 1513.89i −0.923788 0.923788i 0.0735064 0.997295i \(-0.476581\pi\)
−0.997295 + 0.0735064i \(0.976581\pi\)
\(140\) 223.020 109.933i 0.134633 0.0663642i
\(141\) −369.421 + 369.421i −0.220644 + 0.220644i
\(142\) 1265.97 + 209.127i 0.748155 + 0.123589i
\(143\) −3201.37 −1.87211
\(144\) −1007.78 + 1312.40i −0.583203 + 0.759492i
\(145\) 1086.53 0.622285
\(146\) 724.853 + 119.739i 0.410885 + 0.0678746i
\(147\) 254.172 254.172i 0.142611 0.142611i
\(148\) 420.507 + 853.081i 0.233550 + 0.473803i
\(149\) 375.353 + 375.353i 0.206377 + 0.206377i 0.802725 0.596349i \(-0.203382\pi\)
−0.596349 + 0.802725i \(0.703382\pi\)
\(150\) 25.4190 18.2116i 0.0138364 0.00991315i
\(151\) 2997.52i 1.61546i −0.589553 0.807730i \(-0.700696\pi\)
0.589553 0.807730i \(-0.299304\pi\)
\(152\) 180.448 + 595.423i 0.0962912 + 0.317731i
\(153\) 1874.43i 0.990451i
\(154\) −281.460 392.850i −0.147277 0.205564i
\(155\) 1552.07 + 1552.07i 0.804293 + 0.804293i
\(156\) −137.840 + 405.829i −0.0707438 + 0.208284i
\(157\) −1509.01 + 1509.01i −0.767082 + 0.767082i −0.977592 0.210510i \(-0.932488\pi\)
0.210510 + 0.977592i \(0.432488\pi\)
\(158\) 148.985 901.897i 0.0750167 0.454121i
\(159\) 226.368 0.112906
\(160\) 2104.66 + 69.8265i 1.03993 + 0.0345017i
\(161\) −372.601 −0.182392
\(162\) −293.892 + 1779.10i −0.142533 + 0.862837i
\(163\) −1425.19 + 1425.19i −0.684844 + 0.684844i −0.961088 0.276244i \(-0.910910\pi\)
0.276244 + 0.961088i \(0.410910\pi\)
\(164\) −269.195 + 792.565i −0.128174 + 0.377371i
\(165\) −563.017 563.017i −0.265641 0.265641i
\(166\) 1313.67 + 1833.56i 0.614219 + 0.857301i
\(167\) 792.415i 0.367179i 0.983003 + 0.183590i \(0.0587717\pi\)
−0.983003 + 0.183590i \(0.941228\pi\)
\(168\) −61.9192 + 18.7651i −0.0284355 + 0.00861763i
\(169\) 308.861i 0.140583i
\(170\) −1939.15 + 1389.31i −0.874857 + 0.626797i
\(171\) 502.682 + 502.682i 0.224802 + 0.224802i
\(172\) 157.496 + 319.512i 0.0698195 + 0.141643i
\(173\) −773.594 + 773.594i −0.339972 + 0.339972i −0.856357 0.516384i \(-0.827278\pi\)
0.516384 + 0.856357i \(0.327278\pi\)
\(174\) −278.950 46.0800i −0.121535 0.0200765i
\(175\) −27.5984 −0.0119214
\(176\) −532.810 4058.13i −0.228194 1.73803i
\(177\) 430.905 0.182988
\(178\) −2419.05 399.605i −1.01862 0.168268i
\(179\) 426.050 426.050i 0.177902 0.177902i −0.612539 0.790441i \(-0.709852\pi\)
0.790441 + 0.612539i \(0.209852\pi\)
\(180\) 2158.21 1063.84i 0.893684 0.440521i
\(181\) −2618.06 2618.06i −1.07513 1.07513i −0.996938 0.0781951i \(-0.975084\pi\)
−0.0781951 0.996938i \(-0.524916\pi\)
\(182\) 307.502 220.312i 0.125239 0.0897286i
\(183\) 345.194i 0.139440i
\(184\) −2782.65 1488.30i −1.11489 0.596300i
\(185\) 1383.02i 0.549631i
\(186\) −332.647 464.294i −0.131134 0.183031i
\(187\) 3278.50 + 3278.50i 1.28207 + 1.28207i
\(188\) 3697.74 + 1255.94i 1.43450 + 0.487227i
\(189\) −106.866 + 106.866i −0.0411288 + 0.0411288i
\(190\) 147.453 892.620i 0.0563019 0.340829i
\(191\) 3216.39 1.21848 0.609240 0.792986i \(-0.291475\pi\)
0.609240 + 0.792986i \(0.291475\pi\)
\(192\) −537.379 107.186i −0.201989 0.0402891i
\(193\) 2852.57 1.06390 0.531950 0.846776i \(-0.321459\pi\)
0.531950 + 0.846776i \(0.321459\pi\)
\(194\) −431.516 + 2612.22i −0.159696 + 0.966736i
\(195\) 440.700 440.700i 0.161842 0.161842i
\(196\) −2544.15 864.122i −0.927169 0.314913i
\(197\) 1609.02 + 1609.02i 0.581918 + 0.581918i 0.935430 0.353512i \(-0.115013\pi\)
−0.353512 + 0.935430i \(0.615013\pi\)
\(198\) −2723.74 3801.68i −0.977616 1.36451i
\(199\) 747.136i 0.266146i −0.991106 0.133073i \(-0.957516\pi\)
0.991106 0.133073i \(-0.0424845\pi\)
\(200\) −206.110 110.238i −0.0728708 0.0389750i
\(201\) 210.612i 0.0739074i
\(202\) −5.16496 + 3.70047i −0.00179904 + 0.00128893i
\(203\) 176.449 + 176.449i 0.0610062 + 0.0610062i
\(204\) 556.767 274.445i 0.191086 0.0941912i
\(205\) 860.666 860.666i 0.293227 0.293227i
\(206\) 3874.15 + 639.975i 1.31032 + 0.216452i
\(207\) −3605.73 −1.21070
\(208\) 3176.49 417.055i 1.05889 0.139027i
\(209\) −1758.44 −0.581981
\(210\) 92.8254 + 15.3339i 0.0305027 + 0.00503877i
\(211\) −2227.13 + 2227.13i −0.726645 + 0.726645i −0.969950 0.243305i \(-0.921769\pi\)
0.243305 + 0.969950i \(0.421769\pi\)
\(212\) −748.122 1517.72i −0.242364 0.491684i
\(213\) 343.315 + 343.315i 0.110439 + 0.110439i
\(214\) −2671.27 + 1913.85i −0.853290 + 0.611346i
\(215\) 517.995i 0.164311i
\(216\) −1224.95 + 371.232i −0.385868 + 0.116941i
\(217\) 504.102i 0.157699i
\(218\) −1241.22 1732.44i −0.385623 0.538237i
\(219\) 196.570 + 196.570i 0.0606530 + 0.0606530i
\(220\) −1914.12 + 5635.55i −0.586590 + 1.72704i
\(221\) −2566.23 + 2566.23i −0.781102 + 0.781102i
\(222\) −58.6543 + 355.069i −0.0177325 + 0.107345i
\(223\) −358.053 −0.107520 −0.0537601 0.998554i \(-0.517121\pi\)
−0.0537601 + 0.998554i \(0.517121\pi\)
\(224\) 330.451 + 353.130i 0.0985677 + 0.105332i
\(225\) −267.075 −0.0791332
\(226\) −31.0094 + 187.719i −0.00912706 + 0.0552516i
\(227\) 3455.40 3455.40i 1.01032 1.01032i 0.0103741 0.999946i \(-0.496698\pi\)
0.999946 0.0103741i \(-0.00330223\pi\)
\(228\) −75.7125 + 222.913i −0.0219920 + 0.0647490i
\(229\) −1430.03 1430.03i −0.412659 0.412659i 0.470005 0.882664i \(-0.344252\pi\)
−0.882664 + 0.470005i \(0.844252\pi\)
\(230\) 2672.53 + 3730.21i 0.766181 + 1.06940i
\(231\) 182.864i 0.0520847i
\(232\) 612.951 + 2022.55i 0.173458 + 0.572357i
\(233\) 926.479i 0.260496i 0.991481 + 0.130248i \(0.0415774\pi\)
−0.991481 + 0.130248i \(0.958423\pi\)
\(234\) 2975.75 2132.00i 0.831330 0.595612i
\(235\) −4015.47 4015.47i −1.11464 1.11464i
\(236\) −1424.10 2889.07i −0.392801 0.796875i
\(237\) 244.583 244.583i 0.0670352 0.0670352i
\(238\) −540.530 89.2908i −0.147216 0.0243187i
\(239\) −792.472 −0.214480 −0.107240 0.994233i \(-0.534201\pi\)
−0.107240 + 0.994233i \(0.534201\pi\)
\(240\) 631.987 + 485.295i 0.169978 + 0.130523i
\(241\) 1449.01 0.387299 0.193650 0.981071i \(-0.437967\pi\)
0.193650 + 0.981071i \(0.437967\pi\)
\(242\) 7699.07 + 1271.82i 2.04510 + 0.337833i
\(243\) −1562.44 + 1562.44i −0.412473 + 0.412473i
\(244\) 2314.41 1140.83i 0.607233 0.299321i
\(245\) 2762.76 + 2762.76i 0.720433 + 0.720433i
\(246\) −257.464 + 184.462i −0.0667288 + 0.0478083i
\(247\) 1376.42i 0.354572i
\(248\) −2013.57 + 3764.73i −0.515571 + 0.963953i
\(249\) 853.487i 0.217219i
\(250\) −2197.45 3067.10i −0.555915 0.775922i
\(251\) −3580.04 3580.04i −0.900280 0.900280i 0.0951802 0.995460i \(-0.469657\pi\)
−0.995460 + 0.0951802i \(0.969657\pi\)
\(252\) 523.249 + 177.722i 0.130800 + 0.0444262i
\(253\) 6306.64 6306.64i 1.56717 1.56717i
\(254\) 877.525 5312.18i 0.216775 1.31227i
\(255\) −902.634 −0.221667
\(256\) 1057.34 + 3957.18i 0.258139 + 0.966108i
\(257\) −4708.87 −1.14292 −0.571461 0.820629i \(-0.693623\pi\)
−0.571461 + 0.820629i \(0.693623\pi\)
\(258\) −21.9683 + 132.987i −0.00530111 + 0.0320908i
\(259\) 224.598 224.598i 0.0538835 0.0538835i
\(260\) −4411.21 1498.27i −1.05220 0.357379i
\(261\) 1707.53 + 1707.53i 0.404955 + 0.404955i
\(262\) −2139.60 2986.36i −0.504522 0.704190i
\(263\) 2967.82i 0.695830i 0.937526 + 0.347915i \(0.113110\pi\)
−0.937526 + 0.347915i \(0.886890\pi\)
\(264\) 730.425 1365.66i 0.170282 0.318374i
\(265\) 2460.53i 0.570374i
\(266\) 168.904 121.013i 0.0389330 0.0278938i
\(267\) −656.013 656.013i −0.150365 0.150365i
\(268\) −1412.08 + 696.050i −0.321852 + 0.158649i
\(269\) −663.633 + 663.633i −0.150418 + 0.150418i −0.778305 0.627887i \(-0.783920\pi\)
0.627887 + 0.778305i \(0.283920\pi\)
\(270\) 1836.37 + 303.352i 0.413919 + 0.0683757i
\(271\) 8058.74 1.80640 0.903199 0.429223i \(-0.141212\pi\)
0.903199 + 0.429223i \(0.141212\pi\)
\(272\) −3680.12 2825.91i −0.820368 0.629949i
\(273\) 143.136 0.0317326
\(274\) −1331.77 219.997i −0.293633 0.0485055i
\(275\) 467.130 467.130i 0.102433 0.102433i
\(276\) −527.933 1071.02i −0.115137 0.233578i
\(277\) 482.477 + 482.477i 0.104654 + 0.104654i 0.757495 0.652841i \(-0.226423\pi\)
−0.652841 + 0.757495i \(0.726423\pi\)
\(278\) −4922.56 + 3526.80i −1.06200 + 0.760875i
\(279\) 4878.29i 1.04679i
\(280\) −203.970 673.039i −0.0435341 0.143649i
\(281\) 5899.10i 1.25235i 0.779682 + 0.626175i \(0.215381\pi\)
−0.779682 + 0.626175i \(0.784619\pi\)
\(282\) 860.612 + 1201.21i 0.181733 + 0.253655i
\(283\) −679.897 679.897i −0.142812 0.142812i 0.632086 0.774898i \(-0.282199\pi\)
−0.774898 + 0.632086i \(0.782199\pi\)
\(284\) 1167.18 3436.43i 0.243872 0.718009i
\(285\) 242.067 242.067i 0.0503116 0.0503116i
\(286\) −1475.78 + 8933.77i −0.305121 + 1.84708i
\(287\) 279.538 0.0574935
\(288\) 3197.83 + 3417.30i 0.654285 + 0.699189i
\(289\) 343.118 0.0698388
\(290\) 500.872 3032.08i 0.101421 0.613965i
\(291\) −708.401 + 708.401i −0.142705 + 0.142705i
\(292\) 668.290 1967.58i 0.133934 0.394329i
\(293\) −3552.87 3552.87i −0.708398 0.708398i 0.257800 0.966198i \(-0.417002\pi\)
−0.966198 + 0.257800i \(0.917002\pi\)
\(294\) −592.126 826.464i −0.117461 0.163947i
\(295\) 4683.78i 0.924407i
\(296\) 2574.46 780.213i 0.505532 0.153206i
\(297\) 3617.62i 0.706786i
\(298\) 1220.49 874.432i 0.237253 0.169981i
\(299\) 4936.50 + 4936.50i 0.954799 + 0.954799i
\(300\) −39.1037 79.3297i −0.00752552 0.0152670i
\(301\) 84.1205 84.1205i 0.0161084 0.0161084i
\(302\) −8364.89 1381.81i −1.59386 0.263291i
\(303\) −2.40419 −0.000455831
\(304\) 1744.78 229.079i 0.329177 0.0432191i
\(305\) −3752.13 −0.704415
\(306\) −5230.81 864.083i −0.977207 0.161426i
\(307\) 2735.56 2735.56i 0.508556 0.508556i −0.405527 0.914083i \(-0.632912\pi\)
0.914083 + 0.405527i \(0.132912\pi\)
\(308\) −1226.04 + 604.348i −0.226819 + 0.111805i
\(309\) 1050.62 + 1050.62i 0.193423 + 0.193423i
\(310\) 5046.70 3615.74i 0.924624 0.662453i
\(311\) 5796.70i 1.05692i −0.848960 0.528458i \(-0.822771\pi\)
0.848960 0.528458i \(-0.177229\pi\)
\(312\) 1068.97 + 571.738i 0.193969 + 0.103744i
\(313\) 8362.62i 1.51017i −0.655627 0.755085i \(-0.727596\pi\)
0.655627 0.755085i \(-0.272404\pi\)
\(314\) 3515.42 + 4906.67i 0.631804 + 0.881846i
\(315\) −568.209 568.209i −0.101635 0.101635i
\(316\) −2448.16 831.519i −0.435822 0.148027i
\(317\) −344.406 + 344.406i −0.0610214 + 0.0610214i −0.736959 0.675938i \(-0.763739\pi\)
0.675938 + 0.736959i \(0.263739\pi\)
\(318\) 104.352 631.703i 0.0184017 0.111397i
\(319\) −5973.13 −1.04837
\(320\) 1165.07 5841.11i 0.203530 1.02040i
\(321\) −1243.42 −0.216203
\(322\) −171.763 + 1039.78i −0.0297266 + 0.179953i
\(323\) −1409.58 + 1409.58i −0.242820 + 0.242820i
\(324\) 4829.30 + 1640.28i 0.828070 + 0.281254i
\(325\) 365.644 + 365.644i 0.0624071 + 0.0624071i
\(326\) 3320.16 + 4634.14i 0.564069 + 0.787304i
\(327\) 806.416i 0.136376i
\(328\) 2087.64 + 1116.58i 0.351435 + 0.187965i
\(329\) 1304.20i 0.218549i
\(330\) −1830.70 + 1311.62i −0.305384 + 0.218795i
\(331\) 2687.86 + 2687.86i 0.446339 + 0.446339i 0.894135 0.447797i \(-0.147791\pi\)
−0.447797 + 0.894135i \(0.647791\pi\)
\(332\) 5722.33 2820.69i 0.945945 0.466282i
\(333\) 2173.47 2173.47i 0.357675 0.357675i
\(334\) 2211.32 + 365.290i 0.362270 + 0.0598437i
\(335\) 2289.27 0.373361
\(336\) 23.8224 + 181.443i 0.00386792 + 0.0294599i
\(337\) −1795.31 −0.290199 −0.145099 0.989417i \(-0.546350\pi\)
−0.145099 + 0.989417i \(0.546350\pi\)
\(338\) −861.910 142.380i −0.138703 0.0229125i
\(339\) −50.9068 + 50.9068i −0.00815598 + 0.00815598i
\(340\) 2983.12 + 6051.85i 0.475830 + 0.965316i
\(341\) −8532.42 8532.42i −1.35500 1.35500i
\(342\) 1634.52 1171.06i 0.258434 0.185157i
\(343\) 1813.72i 0.285515i
\(344\) 964.235 292.220i 0.151128 0.0458007i
\(345\) 1736.34i 0.270960i
\(346\) 1802.18 + 2515.41i 0.280017 + 0.390836i
\(347\) −1967.33 1967.33i −0.304357 0.304357i 0.538359 0.842716i \(-0.319045\pi\)
−0.842716 + 0.538359i \(0.819045\pi\)
\(348\) −257.182 + 757.197i −0.0396162 + 0.116638i
\(349\) −7363.37 + 7363.37i −1.12938 + 1.12938i −0.139097 + 0.990279i \(0.544420\pi\)
−0.990279 + 0.139097i \(0.955580\pi\)
\(350\) −12.7224 + 77.0163i −0.00194297 + 0.0117620i
\(351\) 2831.68 0.430609
\(352\) −11570.3 383.867i −1.75198 0.0581255i
\(353\) 10644.3 1.60493 0.802466 0.596698i \(-0.203521\pi\)
0.802466 + 0.596698i \(0.203521\pi\)
\(354\) 198.640 1202.49i 0.0298238 0.180541i
\(355\) −3731.70 + 3731.70i −0.557911 + 0.557911i
\(356\) −2230.28 + 6566.40i −0.332036 + 0.977580i
\(357\) −146.585 146.585i −0.0217313 0.0217313i
\(358\) −992.537 1385.34i −0.146529 0.204518i
\(359\) 7459.42i 1.09664i −0.836269 0.548319i \(-0.815268\pi\)
0.836269 0.548319i \(-0.184732\pi\)
\(360\) −1973.86 6513.12i −0.288976 0.953532i
\(361\) 6102.96i 0.889775i
\(362\) −8512.87 + 6099.10i −1.23599 + 0.885530i
\(363\) 2087.89 + 2087.89i 0.301889 + 0.301889i
\(364\) −473.051 959.678i −0.0681170 0.138189i
\(365\) −2136.65 + 2136.65i −0.306403 + 0.306403i
\(366\) 963.302 + 159.129i 0.137575 + 0.0227262i
\(367\) −6251.35 −0.889149 −0.444574 0.895742i \(-0.646645\pi\)
−0.444574 + 0.895742i \(0.646645\pi\)
\(368\) −5436.03 + 7079.21i −0.770034 + 1.00280i
\(369\) 2705.14 0.381637
\(370\) −3859.47 637.550i −0.542282 0.0895801i
\(371\) −399.582 + 399.582i −0.0559171 + 0.0559171i
\(372\) −1449.01 + 714.254i −0.201956 + 0.0995494i
\(373\) 8911.86 + 8911.86i 1.23710 + 1.23710i 0.961180 + 0.275921i \(0.0889827\pi\)
0.275921 + 0.961180i \(0.411017\pi\)
\(374\) 10660.3 7637.67i 1.47389 1.05598i
\(375\) 1427.68i 0.196600i
\(376\) 5209.43 9739.97i 0.714510 1.33591i
\(377\) 4675.45i 0.638721i
\(378\) 248.957 + 347.484i 0.0338756 + 0.0472821i
\(379\) 1184.03 + 1184.03i 0.160473 + 0.160473i 0.782776 0.622303i \(-0.213803\pi\)
−0.622303 + 0.782776i \(0.713803\pi\)
\(380\) −2422.98 822.966i −0.327095 0.111098i
\(381\) 1440.59 1440.59i 0.193711 0.193711i
\(382\) 1482.70 8975.67i 0.198591 1.20219i
\(383\) −2880.38 −0.384283 −0.192142 0.981367i \(-0.561543\pi\)
−0.192142 + 0.981367i \(0.561543\pi\)
\(384\) −546.838 + 1450.20i −0.0726711 + 0.192722i
\(385\) 1987.66 0.263119
\(386\) 1314.99 7960.42i 0.173397 1.04968i
\(387\) 814.050 814.050i 0.106926 0.106926i
\(388\) 7090.77 + 2408.38i 0.927782 + 0.315122i
\(389\) 9244.24 + 9244.24i 1.20489 + 1.20489i 0.972662 + 0.232226i \(0.0746009\pi\)
0.232226 + 0.972662i \(0.425399\pi\)
\(390\) −1026.66 1432.98i −0.133300 0.186055i
\(391\) 10110.9i 1.30774i
\(392\) −3584.24 + 6701.38i −0.461815 + 0.863446i
\(393\) 1390.09i 0.178424i
\(394\) 5231.87 3748.41i 0.668979 0.479295i
\(395\) 2658.52 + 2658.52i 0.338645 + 0.338645i
\(396\) −11864.6 + 5848.38i −1.50560 + 0.742152i
\(397\) −4257.80 + 4257.80i −0.538270 + 0.538270i −0.923020 0.384751i \(-0.874287\pi\)
0.384751 + 0.923020i \(0.374287\pi\)
\(398\) −2084.96 344.417i −0.262587 0.0433771i
\(399\) 78.6216 0.00986467
\(400\) −402.644 + 524.354i −0.0503305 + 0.0655442i
\(401\) 12722.6 1.58437 0.792187 0.610278i \(-0.208942\pi\)
0.792187 + 0.610278i \(0.208942\pi\)
\(402\) −587.734 97.0884i −0.0729192 0.0120456i
\(403\) 6678.72 6678.72i 0.825535 0.825535i
\(404\) 7.94560 + 16.1192i 0.000978486 + 0.00198505i
\(405\) −5244.26 5244.26i −0.643431 0.643431i
\(406\) 573.739 411.059i 0.0701335 0.0502476i
\(407\) 7603.08i 0.925972i
\(408\) −509.209 1680.23i −0.0617882 0.203882i
\(409\) 232.991i 0.0281678i −0.999901 0.0140839i \(-0.995517\pi\)
0.999901 0.0140839i \(-0.00448320\pi\)
\(410\) −2005.03 2798.53i −0.241515 0.337097i
\(411\) −361.159 361.159i −0.0433447 0.0433447i
\(412\) 3571.84 10516.2i 0.427116 1.25752i
\(413\) −760.629 + 760.629i −0.0906250 + 0.0906250i
\(414\) −1662.18 + 10062.2i −0.197323 + 1.19451i
\(415\) −9277.08 −1.09734
\(416\) 300.471 9056.59i 0.0354129 1.06739i
\(417\) −2291.35 −0.269084
\(418\) −810.614 + 4907.13i −0.0948527 + 0.574200i
\(419\) −6125.69 + 6125.69i −0.714223 + 0.714223i −0.967416 0.253193i \(-0.918519\pi\)
0.253193 + 0.967416i \(0.418519\pi\)
\(420\) 85.5819 251.971i 0.00994279 0.0292736i
\(421\) −8308.44 8308.44i −0.961825 0.961825i 0.0374725 0.999298i \(-0.488069\pi\)
−0.999298 + 0.0374725i \(0.988069\pi\)
\(422\) 5188.38 + 7241.73i 0.598499 + 0.835360i
\(423\) 12620.9i 1.45071i
\(424\) −4580.22 + 1388.07i −0.524611 + 0.158988i
\(425\) 748.907i 0.0854760i
\(426\) 1116.32 799.795i 0.126962 0.0909629i
\(427\) −609.333 609.333i −0.0690579 0.0690579i
\(428\) 4109.39 + 8336.72i 0.464100 + 0.941520i
\(429\) −2422.72 + 2422.72i −0.272657 + 0.272657i
\(430\) −1445.52 238.787i −0.162114 0.0267798i
\(431\) 8737.57 0.976506 0.488253 0.872702i \(-0.337634\pi\)
0.488253 + 0.872702i \(0.337634\pi\)
\(432\) 471.281 + 3589.50i 0.0524873 + 0.399768i
\(433\) −11627.5 −1.29049 −0.645247 0.763974i \(-0.723245\pi\)
−0.645247 + 0.763974i \(0.723245\pi\)
\(434\) 1406.75 + 232.383i 0.155590 + 0.0257021i
\(435\) 822.260 822.260i 0.0906306 0.0906306i
\(436\) −5406.74 + 2665.13i −0.593890 + 0.292744i
\(437\) 2711.51 + 2711.51i 0.296817 + 0.296817i
\(438\) 639.167 457.935i 0.0697273 0.0499566i
\(439\) 17631.8i 1.91690i 0.285261 + 0.958450i \(0.407920\pi\)
−0.285261 + 0.958450i \(0.592080\pi\)
\(440\) 14844.2 + 7939.45i 1.60834 + 0.860224i
\(441\) 8683.57i 0.937649i
\(442\) 5978.36 + 8344.34i 0.643352 + 0.897963i
\(443\) −4549.81 4549.81i −0.487964 0.487964i 0.419699 0.907663i \(-0.362136\pi\)
−0.907663 + 0.419699i \(0.862136\pi\)
\(444\) 963.821 + 327.362i 0.103020 + 0.0349908i
\(445\) 7130.62 7130.62i 0.759604 0.759604i
\(446\) −165.057 + 999.186i −0.0175239 + 0.106083i
\(447\) 568.116 0.0601140
\(448\) 1137.78 759.371i 0.119989 0.0800824i
\(449\) −12926.5 −1.35867 −0.679334 0.733830i \(-0.737731\pi\)
−0.679334 + 0.733830i \(0.737731\pi\)
\(450\) −123.117 + 745.301i −0.0128973 + 0.0780751i
\(451\) −4731.46 + 4731.46i −0.494004 + 0.494004i
\(452\) 509.554 + 173.070i 0.0530252 + 0.0180101i
\(453\) −2268.45 2268.45i −0.235278 0.235278i
\(454\) −8049.78 11235.5i −0.832147 1.16148i
\(455\) 1555.84i 0.160305i
\(456\) 587.160 + 314.043i 0.0602989 + 0.0322509i
\(457\) 9320.32i 0.954018i −0.878898 0.477009i \(-0.841721\pi\)
0.878898 0.477009i \(-0.158279\pi\)
\(458\) −4649.87 + 3331.43i −0.474398 + 0.339886i
\(459\) −2899.90 2899.90i −0.294892 0.294892i
\(460\) 11641.5 5738.43i 1.17998 0.581643i
\(461\) 12885.0 12885.0i 1.30177 1.30177i 0.374566 0.927200i \(-0.377792\pi\)
0.927200 0.374566i \(-0.122208\pi\)
\(462\) −510.302 84.2973i −0.0513883 0.00848889i
\(463\) 7038.37 0.706482 0.353241 0.935532i \(-0.385080\pi\)
0.353241 + 0.935532i \(0.385080\pi\)
\(464\) 5926.71 778.144i 0.592975 0.0778543i
\(465\) 2349.14 0.234277
\(466\) 2585.44 + 427.091i 0.257013 + 0.0424563i
\(467\) 6001.76 6001.76i 0.594707 0.594707i −0.344192 0.938899i \(-0.611847\pi\)
0.938899 + 0.344192i \(0.111847\pi\)
\(468\) −4577.80 9286.98i −0.452156 0.917288i
\(469\) 371.769 + 371.769i 0.0366028 + 0.0366028i
\(470\) −13056.7 + 9354.53i −1.28140 + 0.918069i
\(471\) 2283.96i 0.223438i
\(472\) −8718.75 + 2642.29i −0.850239 + 0.257672i
\(473\) 2847.65i 0.276818i
\(474\) −569.786 795.283i −0.0552133 0.0770644i
\(475\) 200.840 + 200.840i 0.0194004 + 0.0194004i
\(476\) −498.351 + 1467.25i −0.0479872 + 0.141284i
\(477\) −3866.82 + 3866.82i −0.371173 + 0.371173i
\(478\) −365.317 + 2211.48i −0.0349565 + 0.211612i
\(479\) −587.317 −0.0560234 −0.0280117 0.999608i \(-0.508918\pi\)
−0.0280117 + 0.999608i \(0.508918\pi\)
\(480\) 1645.60 1539.92i 0.156482 0.146432i
\(481\) −5951.28 −0.564148
\(482\) 667.971 4043.63i 0.0631229 0.382121i
\(483\) −281.975 + 281.975i −0.0265638 + 0.0265638i
\(484\) 7098.29 20898.8i 0.666631 1.96270i
\(485\) −7700.05 7700.05i −0.720910 0.720910i
\(486\) 3639.91 + 5080.43i 0.339732 + 0.474183i
\(487\) 8366.45i 0.778481i 0.921136 + 0.389240i \(0.127262\pi\)
−0.921136 + 0.389240i \(0.872738\pi\)
\(488\) −2116.71 6984.51i −0.196351 0.647897i
\(489\) 2157.10i 0.199483i
\(490\) 8983.36 6436.19i 0.828218 0.593382i
\(491\) 1529.30 + 1529.30i 0.140563 + 0.140563i 0.773887 0.633324i \(-0.218310\pi\)
−0.633324 + 0.773887i \(0.718310\pi\)
\(492\) 396.074 + 803.514i 0.0362935 + 0.0736285i
\(493\) −4788.09 + 4788.09i −0.437413 + 0.437413i
\(494\) −3841.04 634.505i −0.349831 0.0577889i
\(495\) 19235.0 1.74656
\(496\) 9577.65 + 7354.55i 0.867035 + 0.665784i
\(497\) −1212.03 −0.109390
\(498\) 2381.75 + 393.444i 0.214315 + 0.0354029i
\(499\) 11364.5 11364.5i 1.01952 1.01952i 0.0197191 0.999806i \(-0.493723\pi\)
0.999806 0.0197191i \(-0.00627718\pi\)
\(500\) −9572.06 + 4718.33i −0.856151 + 0.422020i
\(501\) 599.681 + 599.681i 0.0534766 + 0.0534766i
\(502\) −11640.8 + 8340.15i −1.03497 + 0.741513i
\(503\) 12570.2i 1.11427i 0.830421 + 0.557137i \(0.188100\pi\)
−0.830421 + 0.557137i \(0.811900\pi\)
\(504\) 737.160 1378.25i 0.0651503 0.121810i
\(505\) 26.1326i 0.00230274i
\(506\) −14692.1 20506.6i −1.29080 1.80164i
\(507\) −233.738 233.738i −0.0204747 0.0204747i
\(508\) −14419.7 4897.66i −1.25939 0.427753i
\(509\) 11880.4 11880.4i 1.03456 1.03456i 0.0351750 0.999381i \(-0.488801\pi\)
0.999381 0.0351750i \(-0.0111989\pi\)
\(510\) −416.099 + 2518.90i −0.0361278 + 0.218703i
\(511\) −693.968 −0.0600770
\(512\) 11530.3 1126.42i 0.995262 0.0972291i
\(513\) 1555.38 0.133863
\(514\) −2170.71 + 13140.6i −0.186276 + 1.12764i
\(515\) −11419.8 + 11419.8i −0.977122 + 0.977122i
\(516\) 360.988 + 122.610i 0.0307977 + 0.0104604i
\(517\) 22074.8 + 22074.8i 1.87785 + 1.87785i
\(518\) −523.229 730.300i −0.0443810 0.0619451i
\(519\) 1170.87i 0.0990283i
\(520\) −6214.57 + 11619.3i −0.524090 + 0.979882i
\(521\) 6612.98i 0.556085i 0.960569 + 0.278042i \(0.0896856\pi\)
−0.960569 + 0.278042i \(0.910314\pi\)
\(522\) 5552.18 3977.89i 0.465541 0.333540i
\(523\) 5129.30 + 5129.30i 0.428850 + 0.428850i 0.888236 0.459387i \(-0.151931\pi\)
−0.459387 + 0.888236i \(0.651931\pi\)
\(524\) −9320.07 + 4594.11i −0.777003 + 0.383005i
\(525\) −20.8858 + 20.8858i −0.00173625 + 0.00173625i
\(526\) 8282.01 + 1368.11i 0.686526 + 0.113408i
\(527\) −13679.3 −1.13070
\(528\) −3474.32 2667.88i −0.286364 0.219895i
\(529\) −7282.60 −0.598553
\(530\) 6866.38 + 1134.26i 0.562748 + 0.0929609i
\(531\) −7360.75 + 7360.75i −0.601562 + 0.601562i
\(532\) −259.837 527.130i −0.0211755 0.0429586i
\(533\) −3703.53 3703.53i −0.300972 0.300972i
\(534\) −2133.09 + 1528.26i −0.172861 + 0.123847i
\(535\) 13515.5i 1.09220i
\(536\) 1291.46 + 4261.42i 0.104072 + 0.343406i
\(537\) 644.849i 0.0518199i
\(538\) 1546.02 + 2157.86i 0.123891 + 0.172922i
\(539\) −15188.1 15188.1i −1.21372 1.21372i
\(540\) 1693.07 4984.75i 0.134923 0.397240i
\(541\) −10968.5 + 10968.5i −0.871672 + 0.871672i −0.992655 0.120983i \(-0.961395\pi\)
0.120983 + 0.992655i \(0.461395\pi\)
\(542\) 3714.95 22488.8i 0.294411 1.78224i
\(543\) −3962.57 −0.313168
\(544\) −9582.49 + 8967.07i −0.755231 + 0.706728i
\(545\) 8765.44 0.688936
\(546\) 65.9834 399.437i 0.00517185 0.0313083i
\(547\) 13088.8 13088.8i 1.02311 1.02311i 0.0233784 0.999727i \(-0.492558\pi\)
0.999727 0.0233784i \(-0.00744226\pi\)
\(548\) −1227.85 + 3615.04i −0.0957138 + 0.281801i
\(549\) −5896.63 5896.63i −0.458401 0.458401i
\(550\) −1088.24 1518.92i −0.0843684 0.117758i
\(551\) 2568.12i 0.198558i
\(552\) −3232.16 + 979.532i −0.249220 + 0.0755284i
\(553\) 863.469i 0.0663986i
\(554\) 1568.82 1123.99i 0.120312 0.0861981i
\(555\) −1046.64 1046.64i −0.0800491 0.0800491i
\(556\) 7572.70 + 15362.7i 0.577615 + 1.17181i
\(557\) 5049.87 5049.87i 0.384147 0.384147i −0.488447 0.872594i \(-0.662436\pi\)
0.872594 + 0.488447i \(0.162436\pi\)
\(558\) 13613.4 + 2248.81i 1.03280 + 0.170609i
\(559\) −2228.98 −0.168651
\(560\) −1972.21 + 258.941i −0.148824 + 0.0195397i
\(561\) 4962.18 0.373446
\(562\) 16462.1 + 2719.39i 1.23561 + 0.204111i
\(563\) −3249.06 + 3249.06i −0.243217 + 0.243217i −0.818180 0.574962i \(-0.805017\pi\)
0.574962 + 0.818180i \(0.305017\pi\)
\(564\) 3748.82 1847.90i 0.279883 0.137962i
\(565\) −553.338 553.338i −0.0412019 0.0412019i
\(566\) −2210.75 + 1583.90i −0.164178 + 0.117626i
\(567\) 1703.30i 0.126159i
\(568\) −9051.67 4841.29i −0.668661 0.357634i
\(569\) 2806.05i 0.206741i −0.994643 0.103371i \(-0.967037\pi\)
0.994643 0.103371i \(-0.0329628\pi\)
\(570\) −563.925 787.102i −0.0414390 0.0578387i
\(571\) −12038.8 12038.8i −0.882324 0.882324i 0.111446 0.993770i \(-0.464452\pi\)
−0.993770 + 0.111446i \(0.964452\pi\)
\(572\) 24250.3 + 8236.64i 1.77265 + 0.602083i
\(573\) 2434.08 2434.08i 0.177461 0.177461i
\(574\) 128.863 780.082i 0.00937042 0.0567247i
\(575\) −1440.62 −0.104484
\(576\) 11010.5 7348.57i 0.796477 0.531581i
\(577\) 7206.84 0.519973 0.259987 0.965612i \(-0.416282\pi\)
0.259987 + 0.965612i \(0.416282\pi\)
\(578\) 158.172 957.508i 0.0113825 0.0689050i
\(579\) 2158.76 2158.76i 0.154948 0.154948i
\(580\) −8230.45 2795.48i −0.589226 0.200131i
\(581\) −1506.57 1506.57i −0.107578 0.107578i
\(582\) 1650.31 + 2303.43i 0.117539 + 0.164055i
\(583\) 13526.6i 0.960918i
\(584\) −5182.68 2771.96i −0.367227 0.196412i
\(585\) 15056.1i 1.06409i
\(586\) −11552.5 + 8276.84i −0.814382 + 0.583470i
\(587\) 10377.0 + 10377.0i 0.729647 + 0.729647i 0.970549 0.240903i \(-0.0774435\pi\)
−0.240903 + 0.970549i \(0.577443\pi\)
\(588\) −2579.30 + 1271.41i −0.180899 + 0.0891698i
\(589\) 3668.48 3668.48i 0.256633 0.256633i
\(590\) 13070.6 + 2159.14i 0.912047 + 0.150662i
\(591\) 2435.33 0.169503
\(592\) −990.483 7543.98i −0.0687645 0.523743i
\(593\) −4758.60 −0.329531 −0.164766 0.986333i \(-0.552687\pi\)
−0.164766 + 0.986333i \(0.552687\pi\)
\(594\) −10095.4 1667.66i −0.697335 0.115194i
\(595\) 1593.32 1593.32i 0.109781 0.109781i
\(596\) −1877.57 3809.02i −0.129041 0.261785i
\(597\) −565.414 565.414i −0.0387619 0.0387619i
\(598\) 16051.5 11500.2i 1.09765 0.786417i
\(599\) 14256.4i 0.972455i −0.873832 0.486227i \(-0.838373\pi\)
0.873832 0.486227i \(-0.161627\pi\)
\(600\) −239.404 + 72.5535i −0.0162894 + 0.00493664i
\(601\) 10385.2i 0.704862i −0.935838 0.352431i \(-0.885355\pi\)
0.935838 0.352431i \(-0.114645\pi\)
\(602\) −195.969 273.526i −0.0132676 0.0185184i
\(603\) 3597.68 + 3597.68i 0.242966 + 0.242966i
\(604\) −7712.16 + 22706.2i −0.519542 + 1.52964i
\(605\) −22694.5 + 22694.5i −1.52506 + 1.52506i
\(606\) −1.10829 + 6.70914i −7.42924e−5 + 0.000449737i
\(607\) −16243.6 −1.08618 −0.543088 0.839676i \(-0.682745\pi\)
−0.543088 + 0.839676i \(0.682745\pi\)
\(608\) 165.042 4974.59i 0.0110088 0.331819i
\(609\) 267.064 0.0177701
\(610\) −1729.67 + 10470.7i −0.114807 + 0.694996i
\(611\) −17279.0 + 17279.0i −1.14408 + 1.14408i
\(612\) −4822.63 + 14198.8i −0.318535 + 0.937832i
\(613\) −500.502 500.502i −0.0329773 0.0329773i 0.690426 0.723403i \(-0.257423\pi\)
−0.723403 + 0.690426i \(0.757423\pi\)
\(614\) −6372.83 8894.92i −0.418870 0.584642i
\(615\) 1302.66i 0.0854121i
\(616\) 1121.31 + 3699.99i 0.0733426 + 0.242008i
\(617\) 11575.9i 0.755316i −0.925945 0.377658i \(-0.876729\pi\)
0.925945 0.377658i \(-0.123271\pi\)
\(618\) 3416.18 2447.55i 0.222361 0.159312i
\(619\) 18356.1 + 18356.1i 1.19191 + 1.19191i 0.976530 + 0.215380i \(0.0690992\pi\)
0.215380 + 0.976530i \(0.430901\pi\)
\(620\) −7763.68 15750.2i −0.502898 1.02023i
\(621\) −5578.34 + 5578.34i −0.360469 + 0.360469i
\(622\) −16176.3 2672.18i −1.04278 0.172258i
\(623\) 2315.98 0.148937
\(624\) 2088.27 2719.51i 0.133971 0.174467i
\(625\) 16809.5 1.07581
\(626\) −23336.8 3855.03i −1.48998 0.246131i
\(627\) −1330.75 + 1330.75i −0.0847607 + 0.0847607i
\(628\) 15313.2 7548.26i 0.973027 0.479631i
\(629\) 6094.66 + 6094.66i 0.386343 + 0.386343i
\(630\) −1847.58 + 1323.71i −0.116840 + 0.0837111i
\(631\) 10224.8i 0.645079i 0.946556 + 0.322539i \(0.104537\pi\)
−0.946556 + 0.322539i \(0.895463\pi\)
\(632\) −3449.01 + 6448.54i −0.217079 + 0.405869i
\(633\) 3370.88i 0.211660i
\(634\) 802.338 + 1119.87i 0.0502601 + 0.0701509i
\(635\) 15658.7 + 15658.7i 0.978578 + 0.978578i
\(636\) −1714.73 582.409i −0.106908 0.0363114i
\(637\) 11888.4 11888.4i 0.739461 0.739461i
\(638\) −2753.52 + 16668.7i −0.170866 + 1.03436i
\(639\) −11729.0 −0.726125
\(640\) −15763.2 5943.92i −0.973584 0.367116i
\(641\) 19804.4 1.22032 0.610162 0.792277i \(-0.291104\pi\)
0.610162 + 0.792277i \(0.291104\pi\)
\(642\) −573.197 + 3469.91i −0.0352372 + 0.213312i
\(643\) 15680.7 15680.7i 0.961723 0.961723i −0.0375712 0.999294i \(-0.511962\pi\)
0.999294 + 0.0375712i \(0.0119621\pi\)
\(644\) 2822.45 + 958.646i 0.172702 + 0.0586583i
\(645\) −392.006 392.006i −0.0239306 0.0239306i
\(646\) 3283.78 + 4583.37i 0.199998 + 0.279149i
\(647\) 9232.26i 0.560985i 0.959856 + 0.280493i \(0.0904978\pi\)
−0.959856 + 0.280493i \(0.909502\pi\)
\(648\) 6803.60 12720.6i 0.412455 0.771159i
\(649\) 25748.8i 1.55736i
\(650\) 1188.93 851.814i 0.0717438 0.0514014i
\(651\) 381.492 + 381.492i 0.0229675 + 0.0229675i
\(652\) 14462.6 7129.00i 0.868710 0.428210i
\(653\) −19697.9 + 19697.9i −1.18046 + 1.18046i −0.200833 + 0.979626i \(0.564365\pi\)
−0.979626 + 0.200833i \(0.935635\pi\)
\(654\) −2250.39 371.745i −0.134552 0.0222269i
\(655\) 15109.8 0.901355
\(656\) 4078.30 5311.07i 0.242730 0.316101i
\(657\) −6715.66 −0.398786
\(658\) −3639.50 601.213i −0.215627 0.0356196i
\(659\) 3888.06 3888.06i 0.229829 0.229829i −0.582792 0.812621i \(-0.698040\pi\)
0.812621 + 0.582792i \(0.198040\pi\)
\(660\) 2816.29 + 5713.41i 0.166097 + 0.336961i
\(661\) −8110.20 8110.20i −0.477232 0.477232i 0.427013 0.904245i \(-0.359566\pi\)
−0.904245 + 0.427013i \(0.859566\pi\)
\(662\) 8739.82 6261.70i 0.513116 0.367625i
\(663\) 3884.13i 0.227522i
\(664\) −5233.54 17269.1i −0.305875 1.00929i
\(665\) 854.587i 0.0498338i
\(666\) −5063.38 7067.25i −0.294597 0.411187i
\(667\) 9210.54 + 9210.54i 0.534683 + 0.534683i
\(668\) 2038.76 6002.54i 0.118087 0.347672i
\(669\) −270.966 + 270.966i −0.0156594 + 0.0156594i
\(670\) 1055.31 6388.45i 0.0608513 0.368369i
\(671\) 20627.1 1.18674
\(672\) 517.317 + 17.1630i 0.0296964 + 0.000985236i
\(673\) −28428.2 −1.62827 −0.814135 0.580676i \(-0.802788\pi\)
−0.814135 + 0.580676i \(0.802788\pi\)
\(674\) −827.610 + 5010.02i −0.0472972 + 0.286318i
\(675\) −413.186 + 413.186i −0.0235608 + 0.0235608i
\(676\) −794.652 + 2339.62i −0.0452124 + 0.133114i
\(677\) −16967.4 16967.4i −0.963235 0.963235i 0.0361128 0.999348i \(-0.488502\pi\)
−0.999348 + 0.0361128i \(0.988502\pi\)
\(678\) 118.594 + 165.528i 0.00671765 + 0.00937621i
\(679\) 2500.92i 0.141350i
\(680\) 18263.5 5534.91i 1.02996 0.312138i
\(681\) 5229.92i 0.294289i
\(682\) −27744.0 + 19877.3i −1.55773 + 1.11605i
\(683\) −9550.16 9550.16i −0.535032 0.535032i 0.387034 0.922066i \(-0.373500\pi\)
−0.922066 + 0.387034i \(0.873500\pi\)
\(684\) −2514.49 5101.14i −0.140561 0.285156i
\(685\) 3925.66 3925.66i 0.218966 0.218966i
\(686\) 5061.38 + 836.095i 0.281697 + 0.0465339i
\(687\) −2164.42 −0.120201
\(688\) −370.974 2825.51i −0.0205570 0.156572i
\(689\) 10587.9 0.585439
\(690\) 4845.44 + 800.424i 0.267337 + 0.0441617i
\(691\) −20859.7 + 20859.7i −1.14839 + 1.14839i −0.161527 + 0.986868i \(0.551642\pi\)
−0.986868 + 0.161527i \(0.948358\pi\)
\(692\) 7850.30 3869.62i 0.431248 0.212574i
\(693\) 3123.70 + 3123.70i 0.171226 + 0.171226i
\(694\) −6396.96 + 4583.14i −0.349892 + 0.250683i
\(695\) 24906.1i 1.35934i
\(696\) 1994.48 + 1066.75i 0.108622 + 0.0580964i
\(697\) 7585.52i 0.412227i
\(698\) 17153.9 + 23942.7i 0.930207 + 1.29834i
\(699\) 701.137 + 701.137i 0.0379391 + 0.0379391i
\(700\) 209.058 + 71.0065i 0.0112880 + 0.00383399i
\(701\) 23495.4 23495.4i 1.26592 1.26592i 0.317740 0.948178i \(-0.397076\pi\)
0.948178 0.317740i \(-0.102924\pi\)
\(702\) 1305.36 7902.10i 0.0701816 0.424851i
\(703\) −3268.91 −0.175376
\(704\) −6404.93 + 32111.1i −0.342890 + 1.71908i
\(705\) −6077.62 −0.324676
\(706\) 4906.86 29704.2i 0.261575 1.58347i
\(707\) 4.24384 4.24384i 0.000225751 0.000225751i
\(708\) −3264.10 1108.65i −0.173266 0.0588500i
\(709\) 4559.45 + 4559.45i 0.241515 + 0.241515i 0.817477 0.575962i \(-0.195372\pi\)
−0.575962 + 0.817477i \(0.695372\pi\)
\(710\) 8693.47 + 12134.0i 0.459521 + 0.641380i
\(711\) 8355.95i 0.440749i
\(712\) 17296.1 + 9250.84i 0.910393 + 0.486924i
\(713\) 26313.9i 1.38214i
\(714\) −476.633 + 341.487i −0.0249826 + 0.0178989i
\(715\) −26334.1 26334.1i −1.37740 1.37740i
\(716\) −4323.49 + 2131.16i −0.225665 + 0.111236i
\(717\) −599.724 + 599.724i −0.0312372 + 0.0312372i
\(718\) −20816.3 3438.67i −1.08198 0.178733i
\(719\) −6494.67 −0.336871 −0.168436 0.985713i \(-0.553872\pi\)
−0.168436 + 0.985713i \(0.553872\pi\)
\(720\) −19085.5 + 2505.82i −0.987880 + 0.129703i
\(721\) −3709.08 −0.191586
\(722\) 17031.0 + 2813.37i 0.877878 + 0.145018i
\(723\) 1096.58 1096.58i 0.0564069 0.0564069i
\(724\) 13095.9 + 26567.7i 0.672246 + 1.36378i
\(725\) 682.221 + 682.221i 0.0349476 + 0.0349476i
\(726\) 6788.95 4863.99i 0.347055 0.248650i
\(727\) 24866.4i 1.26856i 0.773103 + 0.634280i \(0.218704\pi\)
−0.773103 + 0.634280i \(0.781296\pi\)
\(728\) −2896.15 + 877.704i −0.147443 + 0.0446839i
\(729\) 14848.5i 0.754384i
\(730\) 4977.59 + 6947.50i 0.252368 + 0.352245i
\(731\) 2282.68 + 2282.68i 0.115497 + 0.115497i
\(732\) 888.133 2614.84i 0.0448447 0.132032i
\(733\) −14914.3 + 14914.3i −0.751533 + 0.751533i −0.974765 0.223232i \(-0.928339\pi\)
0.223232 + 0.974765i \(0.428339\pi\)
\(734\) −2881.77 + 17445.1i −0.144916 + 0.877260i
\(735\) 4181.58 0.209850
\(736\) 17249.4 + 18433.2i 0.863886 + 0.923176i
\(737\) −12585.1 −0.629008
\(738\) 1247.03 7548.99i 0.0622001 0.376534i
\(739\) 8451.86 8451.86i 0.420713 0.420713i −0.464737 0.885449i \(-0.653851\pi\)
0.885449 + 0.464737i \(0.153851\pi\)
\(740\) −3558.30 + 10476.4i −0.176765 + 0.520431i
\(741\) −1041.64 1041.64i −0.0516404 0.0516404i
\(742\) 930.875 + 1299.28i 0.0460559 + 0.0642829i
\(743\) 5622.43i 0.277614i 0.990319 + 0.138807i \(0.0443267\pi\)
−0.990319 + 0.138807i \(0.955673\pi\)
\(744\) 1325.24 + 4372.87i 0.0653031 + 0.215480i
\(745\) 6175.21i 0.303681i
\(746\) 28977.7 20761.3i 1.42219 1.01893i
\(747\) −14579.3 14579.3i −0.714095 0.714095i
\(748\) −16399.5 33269.7i −0.801638 1.62628i
\(749\) 2194.88 2194.88i 0.107075 0.107075i
\(750\) −3984.08 658.135i −0.193971 0.0320422i
\(751\) −32314.9 −1.57016 −0.785079 0.619396i \(-0.787378\pi\)
−0.785079 + 0.619396i \(0.787378\pi\)
\(752\) −24779.0 19027.4i −1.20159 0.922685i
\(753\) −5418.58 −0.262236
\(754\) −13047.3 2155.30i −0.630181 0.104100i
\(755\) 24657.2 24657.2i 1.18857 1.18857i
\(756\) 1084.46 534.557i 0.0521710 0.0257165i
\(757\) 12692.8 + 12692.8i 0.609418 + 0.609418i 0.942794 0.333376i \(-0.108188\pi\)
−0.333376 + 0.942794i \(0.608188\pi\)
\(758\) 3849.97 2758.34i 0.184482 0.132173i
\(759\) 9545.42i 0.456491i
\(760\) −3413.53 + 6382.21i −0.162923 + 0.304615i
\(761\) 13108.2i 0.624404i 0.950016 + 0.312202i \(0.101067\pi\)
−0.950016 + 0.312202i \(0.898933\pi\)
\(762\) −3356.04 4684.22i −0.159549 0.222692i
\(763\) 1423.48 + 1423.48i 0.0675404 + 0.0675404i
\(764\) −24364.1 8275.27i −1.15375 0.391870i
\(765\) 15418.8 15418.8i 0.728718 0.728718i
\(766\) −1327.81 + 8038.01i −0.0626314 + 0.379145i
\(767\) 20154.8 0.948822
\(768\) 3794.86 + 2194.53i 0.178301 + 0.103110i
\(769\) 23661.2 1.10955 0.554776 0.832000i \(-0.312804\pi\)
0.554776 + 0.832000i \(0.312804\pi\)
\(770\) 916.280 5546.79i 0.0428837 0.259601i
\(771\) −3563.56 + 3563.56i −0.166457 + 0.166457i
\(772\) −21608.2 7339.24i −1.00738 0.342157i
\(773\) 21370.5 + 21370.5i 0.994362 + 0.994362i 0.999984 0.00562228i \(-0.00178964\pi\)