Properties

Label 224.3.w.a.43.6
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 43.6
Character \(\chi\) \(=\) 224.43
Dual form 224.3.w.a.99.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.86483 - 0.722783i) q^{2} +(-1.45943 - 3.52338i) q^{3} +(2.95517 + 2.69573i) q^{4} +(-3.21097 + 7.75196i) q^{5} +(0.174951 + 7.62534i) q^{6} +(1.87083 - 1.87083i) q^{7} +(-3.56245 - 7.16302i) q^{8} +(-3.92028 + 3.92028i) q^{9} +O(q^{10})\) \(q+(-1.86483 - 0.722783i) q^{2} +(-1.45943 - 3.52338i) q^{3} +(2.95517 + 2.69573i) q^{4} +(-3.21097 + 7.75196i) q^{5} +(0.174951 + 7.62534i) q^{6} +(1.87083 - 1.87083i) q^{7} +(-3.56245 - 7.16302i) q^{8} +(-3.92028 + 3.92028i) q^{9} +(11.5909 - 12.1352i) q^{10} +(3.78882 - 9.14701i) q^{11} +(5.18521 - 14.3464i) q^{12} +(6.24954 + 15.0877i) q^{13} +(-4.84098 + 2.13657i) q^{14} +31.9993 q^{15} +(1.46606 + 15.9327i) q^{16} -19.0578i q^{17} +(10.1442 - 4.47713i) q^{18} +(24.1823 - 10.0166i) q^{19} +(-30.3862 + 14.2525i) q^{20} +(-9.32197 - 3.86129i) q^{21} +(-13.6768 + 14.3191i) q^{22} +(-21.8802 - 21.8802i) q^{23} +(-20.0389 + 23.0058i) q^{24} +(-32.1050 - 32.1050i) q^{25} +(-0.749169 - 32.6531i) q^{26} +(-12.1764 - 5.04363i) q^{27} +(10.5719 - 0.485363i) q^{28} +(20.7285 - 8.58602i) q^{29} +(-59.6731 - 23.1285i) q^{30} +13.8010i q^{31} +(8.78194 - 30.7714i) q^{32} -37.7579 q^{33} +(-13.7747 + 35.5396i) q^{34} +(8.49542 + 20.5098i) q^{35} +(-22.1531 + 1.01707i) q^{36} +(-1.32733 + 3.20446i) q^{37} +(-52.3357 + 1.20075i) q^{38} +(44.0389 - 44.0389i) q^{39} +(66.9664 - 4.61578i) q^{40} +(31.4208 - 31.4208i) q^{41} +(14.5930 + 13.9384i) q^{42} +(22.9809 - 55.4808i) q^{43} +(35.8545 - 16.8173i) q^{44} +(-17.8020 - 42.9777i) q^{45} +(24.9882 + 56.6176i) q^{46} -16.2865 q^{47} +(53.9972 - 28.4181i) q^{48} -7.00000i q^{49} +(36.6653 + 83.0751i) q^{50} +(-67.1479 + 27.8136i) q^{51} +(-22.2040 + 61.4339i) q^{52} +(-0.763626 - 0.316304i) q^{53} +(19.0615 + 18.2064i) q^{54} +(58.7415 + 58.7415i) q^{55} +(-20.0655 - 6.73605i) q^{56} +(-70.5847 - 70.5847i) q^{57} +(-44.8609 + 1.02926i) q^{58} +(70.5577 + 29.2260i) q^{59} +(94.5632 + 86.2614i) q^{60} +(83.2949 - 34.5019i) q^{61} +(9.97509 - 25.7364i) q^{62} +14.6683i q^{63} +(-38.6178 + 51.0359i) q^{64} -137.027 q^{65} +(70.4119 + 27.2907i) q^{66} +(4.73420 + 11.4294i) q^{67} +(51.3748 - 56.3191i) q^{68} +(-45.1596 + 109.025i) q^{69} +(-1.01840 - 44.3875i) q^{70} +(-4.10594 + 4.10594i) q^{71} +(42.0468 + 14.1152i) q^{72} +(55.6784 - 55.6784i) q^{73} +(4.79137 - 5.01639i) q^{74} +(-66.2629 + 159.973i) q^{75} +(98.4650 + 35.5881i) q^{76} +(-10.0243 - 24.2007i) q^{77} +(-113.956 + 50.2945i) q^{78} -44.2539 q^{79} +(-128.217 - 39.7946i) q^{80} +100.160i q^{81} +(-81.3047 + 35.8839i) q^{82} +(29.0804 - 12.0455i) q^{83} +(-17.1390 - 36.5403i) q^{84} +(147.736 + 61.1941i) q^{85} +(-82.9560 + 86.8520i) q^{86} +(-60.5035 - 60.5035i) q^{87} +(-79.0177 + 5.44643i) q^{88} +(-103.429 - 103.429i) q^{89} +(2.13403 + 93.0130i) q^{90} +(39.9184 + 16.5347i) q^{91} +(-5.67655 - 123.643i) q^{92} +(48.6259 - 20.1415i) q^{93} +(30.3716 + 11.7716i) q^{94} +219.623i q^{95} +(-121.236 + 13.9666i) q^{96} +134.846 q^{97} +(-5.05948 + 13.0538i) q^{98} +(21.0056 + 50.7120i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.86483 0.722783i −0.932414 0.361391i
\(3\) −1.45943 3.52338i −0.486477 1.17446i −0.956481 0.291794i \(-0.905748\pi\)
0.470004 0.882664i \(-0.344252\pi\)
\(4\) 2.95517 + 2.69573i 0.738792 + 0.673933i
\(5\) −3.21097 + 7.75196i −0.642194 + 1.55039i 0.181520 + 0.983387i \(0.441898\pi\)
−0.823714 + 0.567006i \(0.808102\pi\)
\(6\) 0.174951 + 7.62534i 0.0291584 + 1.27089i
\(7\) 1.87083 1.87083i 0.267261 0.267261i
\(8\) −3.56245 7.16302i −0.445307 0.895378i
\(9\) −3.92028 + 3.92028i −0.435586 + 0.435586i
\(10\) 11.5909 12.1352i 1.15909 1.21352i
\(11\) 3.78882 9.14701i 0.344438 0.831546i −0.652818 0.757515i \(-0.726413\pi\)
0.997256 0.0740316i \(-0.0235866\pi\)
\(12\) 5.18521 14.3464i 0.432101 1.19553i
\(13\) 6.24954 + 15.0877i 0.480734 + 1.16059i 0.959261 + 0.282521i \(0.0911707\pi\)
−0.478527 + 0.878073i \(0.658829\pi\)
\(14\) −4.84098 + 2.13657i −0.345784 + 0.152612i
\(15\) 31.9993 2.13328
\(16\) 1.46606 + 15.9327i 0.0916284 + 0.995793i
\(17\) 19.0578i 1.12105i −0.828138 0.560524i \(-0.810600\pi\)
0.828138 0.560524i \(-0.189400\pi\)
\(18\) 10.1442 4.47713i 0.563564 0.248730i
\(19\) 24.1823 10.0166i 1.27275 0.527191i 0.358953 0.933356i \(-0.383134\pi\)
0.913800 + 0.406164i \(0.133134\pi\)
\(20\) −30.3862 + 14.2525i −1.51931 + 0.712623i
\(21\) −9.32197 3.86129i −0.443904 0.183871i
\(22\) −13.6768 + 14.3191i −0.621672 + 0.650869i
\(23\) −21.8802 21.8802i −0.951315 0.951315i 0.0475535 0.998869i \(-0.484858\pi\)
−0.998869 + 0.0475535i \(0.984858\pi\)
\(24\) −20.0389 + 23.0058i −0.834953 + 0.958575i
\(25\) −32.1050 32.1050i −1.28420 1.28420i
\(26\) −0.749169 32.6531i −0.0288142 1.25589i
\(27\) −12.1764 5.04363i −0.450978 0.186801i
\(28\) 10.5719 0.485363i 0.377567 0.0173344i
\(29\) 20.7285 8.58602i 0.714775 0.296069i 0.00449611 0.999990i \(-0.498569\pi\)
0.710279 + 0.703920i \(0.248569\pi\)
\(30\) −59.6731 23.1285i −1.98910 0.770951i
\(31\) 13.8010i 0.445192i 0.974911 + 0.222596i \(0.0714531\pi\)
−0.974911 + 0.222596i \(0.928547\pi\)
\(32\) 8.78194 30.7714i 0.274436 0.961606i
\(33\) −37.7579 −1.14418
\(34\) −13.7747 + 35.5396i −0.405137 + 1.04528i
\(35\) 8.49542 + 20.5098i 0.242726 + 0.585993i
\(36\) −22.1531 + 1.01707i −0.615364 + 0.0282518i
\(37\) −1.32733 + 3.20446i −0.0358738 + 0.0866069i −0.940801 0.338959i \(-0.889925\pi\)
0.904927 + 0.425566i \(0.139925\pi\)
\(38\) −52.3357 + 1.20075i −1.37726 + 0.0315988i
\(39\) 44.0389 44.0389i 1.12920 1.12920i
\(40\) 66.9664 4.61578i 1.67416 0.115394i
\(41\) 31.4208 31.4208i 0.766360 0.766360i −0.211104 0.977464i \(-0.567706\pi\)
0.977464 + 0.211104i \(0.0677058\pi\)
\(42\) 14.5930 + 13.9384i 0.347453 + 0.331867i
\(43\) 22.9809 55.4808i 0.534440 1.29025i −0.394117 0.919060i \(-0.628950\pi\)
0.928557 0.371191i \(-0.121050\pi\)
\(44\) 35.8545 16.8173i 0.814875 0.382212i
\(45\) −17.8020 42.9777i −0.395599 0.955061i
\(46\) 24.9882 + 56.6176i 0.543223 + 1.23082i
\(47\) −16.2865 −0.346522 −0.173261 0.984876i \(-0.555430\pi\)
−0.173261 + 0.984876i \(0.555430\pi\)
\(48\) 53.9972 28.4181i 1.12494 0.592044i
\(49\) 7.00000i 0.142857i
\(50\) 36.6653 + 83.0751i 0.733306 + 1.66150i
\(51\) −67.1479 + 27.8136i −1.31662 + 0.545364i
\(52\) −22.2040 + 61.4339i −0.427000 + 1.18142i
\(53\) −0.763626 0.316304i −0.0144080 0.00596800i 0.375468 0.926835i \(-0.377482\pi\)
−0.389876 + 0.920867i \(0.627482\pi\)
\(54\) 19.0615 + 18.2064i 0.352990 + 0.337156i
\(55\) 58.7415 + 58.7415i 1.06803 + 1.06803i
\(56\) −20.0655 6.73605i −0.358313 0.120287i
\(57\) −70.5847 70.5847i −1.23833 1.23833i
\(58\) −44.8609 + 1.02926i −0.773463 + 0.0177458i
\(59\) 70.5577 + 29.2260i 1.19589 + 0.495355i 0.889670 0.456604i \(-0.150935\pi\)
0.306223 + 0.951960i \(0.400935\pi\)
\(60\) 94.5632 + 86.2614i 1.57605 + 1.43769i
\(61\) 83.2949 34.5019i 1.36549 0.565604i 0.424928 0.905227i \(-0.360299\pi\)
0.940562 + 0.339623i \(0.110299\pi\)
\(62\) 9.97509 25.7364i 0.160889 0.415103i
\(63\) 14.6683i 0.232831i
\(64\) −38.6178 + 51.0359i −0.603404 + 0.797436i
\(65\) −137.027 −2.10810
\(66\) 70.4119 + 27.2907i 1.06685 + 0.413496i
\(67\) 4.73420 + 11.4294i 0.0706597 + 0.170588i 0.955264 0.295755i \(-0.0955713\pi\)
−0.884604 + 0.466343i \(0.845571\pi\)
\(68\) 51.3748 56.3191i 0.755512 0.828222i
\(69\) −45.1596 + 109.025i −0.654488 + 1.58007i
\(70\) −1.01840 44.3875i −0.0145485 0.634108i
\(71\) −4.10594 + 4.10594i −0.0578301 + 0.0578301i −0.735430 0.677600i \(-0.763020\pi\)
0.677600 + 0.735430i \(0.263020\pi\)
\(72\) 42.0468 + 14.1152i 0.583984 + 0.196045i
\(73\) 55.6784 55.6784i 0.762717 0.762717i −0.214095 0.976813i \(-0.568680\pi\)
0.976813 + 0.214095i \(0.0686803\pi\)
\(74\) 4.79137 5.01639i 0.0647482 0.0677891i
\(75\) −66.2629 + 159.973i −0.883505 + 2.13297i
\(76\) 98.4650 + 35.5881i 1.29559 + 0.468265i
\(77\) −10.0243 24.2007i −0.130185 0.314295i
\(78\) −113.956 + 50.2945i −1.46097 + 0.644801i
\(79\) −44.2539 −0.560176 −0.280088 0.959974i \(-0.590364\pi\)
−0.280088 + 0.959974i \(0.590364\pi\)
\(80\) −128.217 39.7946i −1.60271 0.497432i
\(81\) 100.160i 1.23654i
\(82\) −81.3047 + 35.8839i −0.991521 + 0.437609i
\(83\) 29.0804 12.0455i 0.350367 0.145127i −0.200558 0.979682i \(-0.564275\pi\)
0.550924 + 0.834555i \(0.314275\pi\)
\(84\) −17.1390 36.5403i −0.204036 0.435004i
\(85\) 147.736 + 61.1941i 1.73807 + 0.719930i
\(86\) −82.9560 + 86.8520i −0.964605 + 1.00991i
\(87\) −60.5035 60.5035i −0.695443 0.695443i
\(88\) −79.0177 + 5.44643i −0.897929 + 0.0618913i
\(89\) −103.429 103.429i −1.16212 1.16212i −0.984011 0.178108i \(-0.943002\pi\)
−0.178108 0.984011i \(-0.556998\pi\)
\(90\) 2.13403 + 93.0130i 0.0237114 + 1.03348i
\(91\) 39.9184 + 16.5347i 0.438663 + 0.181700i
\(92\) −5.67655 123.643i −0.0617017 1.34395i
\(93\) 48.6259 20.1415i 0.522859 0.216575i
\(94\) 30.3716 + 11.7716i 0.323102 + 0.125230i
\(95\) 219.623i 2.31183i
\(96\) −121.236 + 13.9666i −1.26287 + 0.145485i
\(97\) 134.846 1.39016 0.695081 0.718931i \(-0.255368\pi\)
0.695081 + 0.718931i \(0.255368\pi\)
\(98\) −5.05948 + 13.0538i −0.0516274 + 0.133202i
\(99\) 21.0056 + 50.7120i 0.212178 + 0.512242i
\(100\) −8.32922 181.422i −0.0832922 1.81422i
\(101\) −18.1092 + 43.7195i −0.179299 + 0.432866i −0.987820 0.155601i \(-0.950269\pi\)
0.808521 + 0.588468i \(0.200269\pi\)
\(102\) 145.322 3.33418i 1.42473 0.0326880i
\(103\) −11.7674 + 11.7674i −0.114247 + 0.114247i −0.761919 0.647672i \(-0.775743\pi\)
0.647672 + 0.761919i \(0.275743\pi\)
\(104\) 85.8100 98.5149i 0.825096 0.947259i
\(105\) 59.8651 59.8651i 0.570144 0.570144i
\(106\) 1.19541 + 1.14179i 0.0112775 + 0.0107716i
\(107\) 33.7372 81.4487i 0.315301 0.761203i −0.684190 0.729303i \(-0.739844\pi\)
0.999491 0.0318997i \(-0.0101557\pi\)
\(108\) −22.3871 47.7291i −0.207288 0.441936i
\(109\) −40.7389 98.3524i −0.373752 0.902316i −0.993108 0.117206i \(-0.962606\pi\)
0.619356 0.785110i \(-0.287394\pi\)
\(110\) −67.0855 152.000i −0.609868 1.38182i
\(111\) 13.2276 0.119168
\(112\) 32.5501 + 27.0646i 0.290626 + 0.241648i
\(113\) 182.177i 1.61218i 0.591790 + 0.806092i \(0.298421\pi\)
−0.591790 + 0.806092i \(0.701579\pi\)
\(114\) 80.6110 + 182.646i 0.707114 + 1.60216i
\(115\) 239.872 99.3581i 2.08584 0.863984i
\(116\) 84.4018 + 30.5053i 0.727601 + 0.262977i
\(117\) −83.6479 34.6481i −0.714940 0.296138i
\(118\) −110.454 105.499i −0.936051 0.894062i
\(119\) −35.6539 35.6539i −0.299613 0.299613i
\(120\) −113.996 229.211i −0.949966 1.91010i
\(121\) 16.2473 + 16.2473i 0.134275 + 0.134275i
\(122\) −180.268 + 4.13594i −1.47761 + 0.0339012i
\(123\) −156.564 64.8507i −1.27287 0.527242i
\(124\) −37.2037 + 40.7842i −0.300030 + 0.328904i
\(125\) 158.165 65.5142i 1.26532 0.524114i
\(126\) 10.6020 27.3539i 0.0841430 0.217095i
\(127\) 169.657i 1.33588i −0.744216 0.667939i \(-0.767177\pi\)
0.744216 0.667939i \(-0.232823\pi\)
\(128\) 108.904 67.2609i 0.850809 0.525476i
\(129\) −229.019 −1.77534
\(130\) 255.531 + 99.0404i 1.96562 + 0.761850i
\(131\) 97.2077 + 234.680i 0.742043 + 1.79145i 0.597360 + 0.801973i \(0.296216\pi\)
0.144684 + 0.989478i \(0.453784\pi\)
\(132\) −111.581 101.785i −0.845310 0.771099i
\(133\) 26.5015 63.9804i 0.199260 0.481055i
\(134\) −0.567517 24.7356i −0.00423520 0.184594i
\(135\) 78.1961 78.1961i 0.579230 0.579230i
\(136\) −136.512 + 67.8926i −1.00376 + 0.499210i
\(137\) −133.020 + 133.020i −0.970950 + 0.970950i −0.999590 0.0286394i \(-0.990883\pi\)
0.0286394 + 0.999590i \(0.490883\pi\)
\(138\) 163.016 170.672i 1.18128 1.23676i
\(139\) −75.2362 + 181.636i −0.541268 + 1.30674i 0.382561 + 0.923930i \(0.375042\pi\)
−0.923829 + 0.382806i \(0.874958\pi\)
\(140\) −30.1834 + 83.5112i −0.215596 + 0.596509i
\(141\) 23.7690 + 57.3835i 0.168575 + 0.406975i
\(142\) 10.6246 4.68917i 0.0748210 0.0330223i
\(143\) 161.686 1.13067
\(144\) −68.2079 56.7132i −0.473666 0.393842i
\(145\) 188.256i 1.29832i
\(146\) −144.074 + 63.5872i −0.986808 + 0.435529i
\(147\) −24.6636 + 10.2160i −0.167780 + 0.0694967i
\(148\) −12.5608 + 5.89159i −0.0848705 + 0.0398080i
\(149\) −77.6057 32.1453i −0.520843 0.215740i 0.106744 0.994287i \(-0.465957\pi\)
−0.627587 + 0.778546i \(0.715957\pi\)
\(150\) 239.194 250.428i 1.59463 1.66952i
\(151\) −67.8854 67.8854i −0.449572 0.449572i 0.445640 0.895212i \(-0.352976\pi\)
−0.895212 + 0.445640i \(0.852976\pi\)
\(152\) −157.898 137.535i −1.03880 0.904833i
\(153\) 74.7119 + 74.7119i 0.488313 + 0.488313i
\(154\) 1.20167 + 52.3755i 0.00780304 + 0.340101i
\(155\) −106.984 44.3144i −0.690222 0.285899i
\(156\) 248.860 11.4253i 1.59525 0.0732394i
\(157\) −249.997 + 103.552i −1.59234 + 0.659567i −0.990306 0.138905i \(-0.955642\pi\)
−0.602031 + 0.798473i \(0.705642\pi\)
\(158\) 82.5259 + 31.9860i 0.522316 + 0.202443i
\(159\) 3.15216i 0.0198249i
\(160\) 210.340 + 166.883i 1.31463 + 1.04302i
\(161\) −81.8684 −0.508499
\(162\) 72.3938 186.781i 0.446875 1.15297i
\(163\) −18.4172 44.4631i −0.112989 0.272780i 0.857262 0.514880i \(-0.172164\pi\)
−0.970251 + 0.242100i \(0.922164\pi\)
\(164\) 177.556 8.15172i 1.08266 0.0497056i
\(165\) 121.239 292.698i 0.734784 1.77392i
\(166\) −62.9363 + 1.44397i −0.379134 + 0.00869859i
\(167\) 71.2060 71.2060i 0.426383 0.426383i −0.461011 0.887394i \(-0.652513\pi\)
0.887394 + 0.461011i \(0.152513\pi\)
\(168\) 5.55061 + 80.5292i 0.0330394 + 0.479340i
\(169\) −69.0815 + 69.0815i −0.408766 + 0.408766i
\(170\) −231.271 220.897i −1.36042 1.29939i
\(171\) −55.5333 + 134.069i −0.324756 + 0.784031i
\(172\) 217.474 102.005i 1.26438 0.593051i
\(173\) −58.9432 142.301i −0.340712 0.822551i −0.997644 0.0686017i \(-0.978146\pi\)
0.656932 0.753950i \(-0.271854\pi\)
\(174\) 69.0978 + 156.560i 0.397114 + 0.899768i
\(175\) −120.126 −0.686433
\(176\) 151.291 + 46.9560i 0.859608 + 0.266795i
\(177\) 291.254i 1.64551i
\(178\) 118.120 + 267.633i 0.663596 + 1.50356i
\(179\) −193.675 + 80.2229i −1.08198 + 0.448172i −0.851205 0.524834i \(-0.824128\pi\)
−0.230779 + 0.973006i \(0.574128\pi\)
\(180\) 63.2486 174.996i 0.351381 0.972199i
\(181\) 29.6971 + 12.3010i 0.164072 + 0.0679611i 0.463208 0.886250i \(-0.346698\pi\)
−0.299136 + 0.954211i \(0.596698\pi\)
\(182\) −62.4899 59.6867i −0.343351 0.327949i
\(183\) −243.126 243.126i −1.32856 1.32856i
\(184\) −78.7814 + 234.676i −0.428160 + 1.27541i
\(185\) −20.5788 20.5788i −0.111237 0.111237i
\(186\) −105.237 + 2.41448i −0.565790 + 0.0129811i
\(187\) −174.322 72.2066i −0.932203 0.386131i
\(188\) −48.1294 43.9041i −0.256008 0.233533i
\(189\) −32.2157 + 13.3442i −0.170454 + 0.0706042i
\(190\) 158.740 409.560i 0.835474 2.15558i
\(191\) 320.041i 1.67561i −0.545973 0.837803i \(-0.683840\pi\)
0.545973 0.837803i \(-0.316160\pi\)
\(192\) 236.179 + 61.5818i 1.23010 + 0.320739i
\(193\) −23.5234 −0.121883 −0.0609415 0.998141i \(-0.519410\pi\)
−0.0609415 + 0.998141i \(0.519410\pi\)
\(194\) −251.464 97.4642i −1.29621 0.502393i
\(195\) 199.981 + 482.796i 1.02554 + 2.47588i
\(196\) 18.8701 20.6862i 0.0962762 0.105542i
\(197\) −135.676 + 327.551i −0.688712 + 1.66270i 0.0586492 + 0.998279i \(0.481321\pi\)
−0.747361 + 0.664418i \(0.768679\pi\)
\(198\) −2.51807 109.752i −0.0127175 0.554301i
\(199\) −94.9246 + 94.9246i −0.477008 + 0.477008i −0.904173 0.427165i \(-0.859512\pi\)
0.427165 + 0.904173i \(0.359512\pi\)
\(200\) −115.596 + 344.341i −0.577981 + 1.72171i
\(201\) 33.3607 33.3607i 0.165974 0.165974i
\(202\) 65.3703 68.4403i 0.323615 0.338814i
\(203\) 22.7165 54.8424i 0.111904 0.270160i
\(204\) −273.411 98.8189i −1.34025 0.484406i
\(205\) 142.682 + 344.464i 0.696007 + 1.68031i
\(206\) 30.4495 13.4389i 0.147813 0.0652375i
\(207\) 171.553 0.828760
\(208\) −231.226 + 121.691i −1.11166 + 0.585055i
\(209\) 259.147i 1.23994i
\(210\) −154.908 + 68.3687i −0.737656 + 0.325565i
\(211\) 89.6556 37.1366i 0.424908 0.176003i −0.159974 0.987121i \(-0.551141\pi\)
0.584882 + 0.811119i \(0.301141\pi\)
\(212\) −1.40397 2.99326i −0.00662251 0.0141192i
\(213\) 20.4591 + 8.47443i 0.0960521 + 0.0397861i
\(214\) −121.784 + 127.503i −0.569083 + 0.595810i
\(215\) 356.294 + 356.294i 1.65718 + 1.65718i
\(216\) 7.25023 + 105.188i 0.0335659 + 0.486980i
\(217\) 25.8192 + 25.8192i 0.118983 + 0.118983i
\(218\) 4.88362 + 212.856i 0.0224019 + 0.976403i
\(219\) −277.434 114.917i −1.26682 0.524736i
\(220\) 15.2397 + 331.943i 0.0692716 + 1.50883i
\(221\) 287.539 119.103i 1.30108 0.538926i
\(222\) −24.6673 9.56072i −0.111114 0.0430663i
\(223\) 389.765i 1.74783i −0.486082 0.873913i \(-0.661574\pi\)
0.486082 0.873913i \(-0.338426\pi\)
\(224\) −41.1385 73.9975i −0.183654 0.330346i
\(225\) 251.721 1.11876
\(226\) 131.674 339.729i 0.582630 1.50322i
\(227\) 114.807 + 277.168i 0.505757 + 1.22101i 0.946304 + 0.323277i \(0.104784\pi\)
−0.440547 + 0.897729i \(0.645216\pi\)
\(228\) −18.3123 398.867i −0.0803172 1.74942i
\(229\) −75.7429 + 182.860i −0.330755 + 0.798514i 0.667778 + 0.744361i \(0.267246\pi\)
−0.998533 + 0.0541526i \(0.982754\pi\)
\(230\) −519.134 + 11.9107i −2.25710 + 0.0517854i
\(231\) −70.6385 + 70.6385i −0.305794 + 0.305794i
\(232\) −135.346 117.891i −0.583388 0.508152i
\(233\) 199.254 199.254i 0.855168 0.855168i −0.135596 0.990764i \(-0.543295\pi\)
0.990764 + 0.135596i \(0.0432950\pi\)
\(234\) 130.946 + 125.072i 0.559598 + 0.534496i
\(235\) 52.2955 126.253i 0.222534 0.537245i
\(236\) 129.725 + 276.572i 0.549681 + 1.17192i
\(237\) 64.5854 + 155.923i 0.272512 + 0.657903i
\(238\) 40.7184 + 92.2585i 0.171086 + 0.387641i
\(239\) 358.693 1.50081 0.750404 0.660979i \(-0.229859\pi\)
0.750404 + 0.660979i \(0.229859\pi\)
\(240\) 46.9127 + 509.834i 0.195469 + 2.12431i
\(241\) 297.392i 1.23399i 0.786967 + 0.616995i \(0.211650\pi\)
−0.786967 + 0.616995i \(0.788350\pi\)
\(242\) −18.5551 42.0416i −0.0766741 0.173726i
\(243\) 243.313 100.784i 1.00129 0.414747i
\(244\) 339.158 + 122.582i 1.38999 + 0.502384i
\(245\) 54.2637 + 22.4768i 0.221485 + 0.0917420i
\(246\) 245.091 + 234.097i 0.996305 + 0.951614i
\(247\) 302.256 + 302.256i 1.22371 + 1.22371i
\(248\) 98.8565 49.1653i 0.398615 0.198247i
\(249\) −84.8817 84.8817i −0.340890 0.340890i
\(250\) −342.304 + 7.85358i −1.36922 + 0.0314143i
\(251\) −159.044 65.8783i −0.633642 0.262463i 0.0426575 0.999090i \(-0.486418\pi\)
−0.676300 + 0.736627i \(0.736418\pi\)
\(252\) −39.5419 + 43.3474i −0.156912 + 0.172014i
\(253\) −283.039 + 117.239i −1.11873 + 0.463394i
\(254\) −122.625 + 316.380i −0.482775 + 1.24559i
\(255\) 609.836i 2.39151i
\(256\) −251.701 + 46.7164i −0.983208 + 0.182486i
\(257\) 35.7404 0.139068 0.0695338 0.997580i \(-0.477849\pi\)
0.0695338 + 0.997580i \(0.477849\pi\)
\(258\) 427.081 + 165.531i 1.65535 + 0.641592i
\(259\) 3.51178 + 8.47819i 0.0135590 + 0.0327343i
\(260\) −404.937 369.387i −1.55745 1.42072i
\(261\) −47.6018 + 114.921i −0.182382 + 0.440310i
\(262\) −11.6529 507.898i −0.0444766 1.93854i
\(263\) 83.8716 83.8716i 0.318904 0.318904i −0.529442 0.848346i \(-0.677599\pi\)
0.848346 + 0.529442i \(0.177599\pi\)
\(264\) 134.511 + 270.460i 0.509510 + 1.02447i
\(265\) 4.90396 4.90396i 0.0185055 0.0185055i
\(266\) −95.6647 + 100.158i −0.359642 + 0.376532i
\(267\) −213.471 + 515.364i −0.799517 + 1.93020i
\(268\) −16.8202 + 46.5379i −0.0627618 + 0.173649i
\(269\) 92.3785 + 223.022i 0.343415 + 0.829076i 0.997366 + 0.0725394i \(0.0231103\pi\)
−0.653951 + 0.756537i \(0.726890\pi\)
\(270\) −202.341 + 89.3035i −0.749412 + 0.330754i
\(271\) −3.17334 −0.0117098 −0.00585488 0.999983i \(-0.501864\pi\)
−0.00585488 + 0.999983i \(0.501864\pi\)
\(272\) 303.642 27.9398i 1.11633 0.102720i
\(273\) 164.779i 0.603585i
\(274\) 344.205 151.915i 1.25622 0.554435i
\(275\) −415.304 + 172.025i −1.51020 + 0.625544i
\(276\) −427.357 + 200.449i −1.54839 + 0.726265i
\(277\) −66.3442 27.4807i −0.239510 0.0992082i 0.259700 0.965689i \(-0.416376\pi\)
−0.499210 + 0.866481i \(0.666376\pi\)
\(278\) 271.586 284.341i 0.976929 1.02281i
\(279\) −54.1035 54.1035i −0.193920 0.193920i
\(280\) 116.647 133.918i 0.416598 0.478279i
\(281\) −111.165 111.165i −0.395604 0.395604i 0.481075 0.876679i \(-0.340246\pi\)
−0.876679 + 0.481075i \(0.840246\pi\)
\(282\) −2.84934 124.190i −0.0101040 0.440391i
\(283\) −156.594 64.8632i −0.553334 0.229199i 0.0884543 0.996080i \(-0.471807\pi\)
−0.641788 + 0.766882i \(0.721807\pi\)
\(284\) −23.2023 + 1.06523i −0.0816981 + 0.00375082i
\(285\) 773.816 320.525i 2.71514 1.12465i
\(286\) −301.516 116.864i −1.05425 0.408615i
\(287\) 117.566i 0.409637i
\(288\) 86.2047 + 155.060i 0.299322 + 0.538402i
\(289\) −74.2005 −0.256749
\(290\) 136.068 351.065i 0.469200 1.21057i
\(291\) −196.798 475.112i −0.676281 1.63269i
\(292\) 314.633 14.4451i 1.07751 0.0494693i
\(293\) 10.0354 24.2276i 0.0342505 0.0826880i −0.905829 0.423644i \(-0.860751\pi\)
0.940079 + 0.340956i \(0.110751\pi\)
\(294\) 53.3774 1.22465i 0.181556 0.00416549i
\(295\) −453.117 + 453.117i −1.53599 + 1.53599i
\(296\) 27.6821 1.90804i 0.0935208 0.00644608i
\(297\) −92.2683 + 92.2683i −0.310668 + 0.310668i
\(298\) 121.487 + 116.038i 0.407675 + 0.389388i
\(299\) 193.382 466.865i 0.646761 1.56142i
\(300\) −627.062 + 294.120i −2.09021 + 0.980399i
\(301\) −60.8018 146.788i −0.201999 0.487669i
\(302\) 77.5282 + 175.661i 0.256716 + 0.581659i
\(303\) 180.469 0.595608
\(304\) 195.045 + 370.604i 0.641594 + 1.21909i
\(305\) 756.483i 2.48027i
\(306\) −85.3244 193.325i −0.278838 0.631782i
\(307\) −345.866 + 143.262i −1.12660 + 0.466652i −0.866623 0.498963i \(-0.833714\pi\)
−0.259975 + 0.965615i \(0.583714\pi\)
\(308\) 35.6152 98.5399i 0.115634 0.319935i
\(309\) 58.6347 + 24.2873i 0.189756 + 0.0785997i
\(310\) 167.478 + 159.965i 0.540252 + 0.516017i
\(311\) −152.858 152.858i −0.491506 0.491506i 0.417274 0.908781i \(-0.362985\pi\)
−0.908781 + 0.417274i \(0.862985\pi\)
\(312\) −472.339 158.565i −1.51391 0.508222i
\(313\) 348.270 + 348.270i 1.11269 + 1.11269i 0.992786 + 0.119899i \(0.0382571\pi\)
0.119899 + 0.992786i \(0.461743\pi\)
\(314\) 541.047 12.4134i 1.72308 0.0395331i
\(315\) −113.708 47.0995i −0.360979 0.149522i
\(316\) −130.778 119.297i −0.413854 0.377521i
\(317\) 85.1857 35.2851i 0.268724 0.111309i −0.244253 0.969712i \(-0.578543\pi\)
0.512977 + 0.858402i \(0.328543\pi\)
\(318\) 2.27833 5.87824i 0.00716456 0.0184850i
\(319\) 222.134i 0.696346i
\(320\) −271.628 463.239i −0.848837 1.44762i
\(321\) −336.211 −1.04739
\(322\) 152.671 + 59.1731i 0.474132 + 0.183767i
\(323\) −190.895 460.862i −0.591007 1.42682i
\(324\) −270.004 + 295.989i −0.833346 + 0.913547i
\(325\) 283.749 685.032i 0.873075 2.10779i
\(326\) 2.20778 + 96.2277i 0.00677234 + 0.295177i
\(327\) −287.077 + 287.077i −0.877911 + 0.877911i
\(328\) −337.003 113.133i −1.02745 0.344917i
\(329\) −30.4693 + 30.4693i −0.0926119 + 0.0926119i
\(330\) −437.647 + 458.201i −1.32620 + 1.38849i
\(331\) 118.078 285.067i 0.356733 0.861229i −0.639023 0.769188i \(-0.720661\pi\)
0.995755 0.0920407i \(-0.0293390\pi\)
\(332\) 118.409 + 42.7965i 0.356654 + 0.128905i
\(333\) −7.35886 17.7659i −0.0220987 0.0533509i
\(334\) −184.253 + 81.3205i −0.551657 + 0.243475i
\(335\) −103.801 −0.309855
\(336\) 47.8542 154.185i 0.142423 0.458884i
\(337\) 111.788i 0.331715i −0.986150 0.165857i \(-0.946961\pi\)
0.986150 0.165857i \(-0.0530391\pi\)
\(338\) 178.756 78.8942i 0.528864 0.233415i
\(339\) 641.877 265.874i 1.89344 0.784290i
\(340\) 271.621 + 579.094i 0.798885 + 1.70322i
\(341\) 126.237 + 52.2893i 0.370198 + 0.153341i
\(342\) 200.463 209.878i 0.586149 0.613677i
\(343\) −13.0958 13.0958i −0.0381802 0.0381802i
\(344\) −479.279 + 33.0351i −1.39325 + 0.0960323i
\(345\) −700.152 700.152i −2.02943 2.02943i
\(346\) 7.06587 + 307.971i 0.0204216 + 0.890089i
\(347\) 50.4661 + 20.9038i 0.145436 + 0.0602414i 0.454214 0.890893i \(-0.349920\pi\)
−0.308778 + 0.951134i \(0.599920\pi\)
\(348\) −15.6969 341.899i −0.0451060 0.982469i
\(349\) 306.851 127.102i 0.879229 0.364189i 0.103031 0.994678i \(-0.467146\pi\)
0.776198 + 0.630489i \(0.217146\pi\)
\(350\) 224.014 + 86.8248i 0.640040 + 0.248071i
\(351\) 215.235i 0.613204i
\(352\) −248.193 196.916i −0.705093 0.559419i
\(353\) 378.182 1.07134 0.535669 0.844428i \(-0.320060\pi\)
0.535669 + 0.844428i \(0.320060\pi\)
\(354\) −210.514 + 543.140i −0.594672 + 1.53429i
\(355\) −18.6451 45.0131i −0.0525213 0.126798i
\(356\) −26.8332 584.465i −0.0753743 1.64176i
\(357\) −73.5877 + 177.657i −0.206128 + 0.497637i
\(358\) 419.155 9.61679i 1.17082 0.0268626i
\(359\) 54.9945 54.9945i 0.153188 0.153188i −0.626352 0.779540i \(-0.715453\pi\)
0.779540 + 0.626352i \(0.215453\pi\)
\(360\) −244.432 + 280.622i −0.678977 + 0.779506i
\(361\) 229.185 229.185i 0.634862 0.634862i
\(362\) −46.4891 44.4037i −0.128423 0.122662i
\(363\) 33.5335 80.9570i 0.0923787 0.223022i
\(364\) 73.3923 + 156.472i 0.201627 + 0.429868i
\(365\) 252.835 + 610.398i 0.692699 + 1.67232i
\(366\) 277.661 + 629.116i 0.758636 + 1.71889i
\(367\) −292.612 −0.797308 −0.398654 0.917101i \(-0.630523\pi\)
−0.398654 + 0.917101i \(0.630523\pi\)
\(368\) 316.534 380.689i 0.860146 1.03448i
\(369\) 246.356i 0.667632i
\(370\) 23.5019 + 53.2500i 0.0635188 + 0.143919i
\(371\) −2.02036 + 0.836862i −0.00544572 + 0.00225569i
\(372\) 197.994 + 71.5609i 0.532242 + 0.192368i
\(373\) −65.5558 27.1541i −0.175753 0.0727992i 0.293072 0.956090i \(-0.405322\pi\)
−0.468825 + 0.883291i \(0.655322\pi\)
\(374\) 272.891 + 260.650i 0.729655 + 0.696925i
\(375\) −461.662 461.662i −1.23110 1.23110i
\(376\) 58.0200 + 116.661i 0.154309 + 0.310268i
\(377\) 259.087 + 259.087i 0.687233 + 0.687233i
\(378\) 69.7218 1.59965i 0.184449 0.00423187i
\(379\) 118.105 + 48.9206i 0.311622 + 0.129078i 0.533013 0.846107i \(-0.321060\pi\)
−0.221391 + 0.975185i \(0.571060\pi\)
\(380\) −592.046 + 649.024i −1.55802 + 1.70796i
\(381\) −597.764 + 247.602i −1.56893 + 0.649874i
\(382\) −231.320 + 596.821i −0.605550 + 1.56236i
\(383\) 526.878i 1.37566i 0.725872 + 0.687830i \(0.241436\pi\)
−0.725872 + 0.687830i \(0.758564\pi\)
\(384\) −395.922 285.545i −1.03105 0.743608i
\(385\) 219.791 0.570885
\(386\) 43.8671 + 17.0023i 0.113645 + 0.0440475i
\(387\) 127.409 + 307.592i 0.329221 + 0.794810i
\(388\) 398.492 + 363.508i 1.02704 + 0.936876i
\(389\) −62.8626 + 151.764i −0.161601 + 0.390138i −0.983851 0.178987i \(-0.942718\pi\)
0.822251 + 0.569125i \(0.192718\pi\)
\(390\) −23.9729 1044.87i −0.0614689 2.67916i
\(391\) −416.990 + 416.990i −1.06647 + 1.06647i
\(392\) −50.1412 + 24.9372i −0.127911 + 0.0636153i
\(393\) 684.998 684.998i 1.74300 1.74300i
\(394\) 489.761 512.763i 1.24305 1.30143i
\(395\) 142.098 343.055i 0.359741 0.868492i
\(396\) −74.6309 + 206.488i −0.188462 + 0.521434i
\(397\) 100.139 + 241.756i 0.252239 + 0.608958i 0.998384 0.0568251i \(-0.0180978\pi\)
−0.746146 + 0.665783i \(0.768098\pi\)
\(398\) 245.628 108.408i 0.617156 0.272382i
\(399\) −264.104 −0.661915
\(400\) 464.451 558.586i 1.16113 1.39646i
\(401\) 134.292i 0.334893i −0.985881 0.167446i \(-0.946448\pi\)
0.985881 0.167446i \(-0.0535521\pi\)
\(402\) −86.3246 + 38.0995i −0.214738 + 0.0947748i
\(403\) −208.225 + 86.2496i −0.516687 + 0.214019i
\(404\) −171.372 + 80.3809i −0.424188 + 0.198963i
\(405\) −776.435 321.610i −1.91712 0.794099i
\(406\) −82.0014 + 85.8526i −0.201974 + 0.211460i
\(407\) 24.2822 + 24.2822i 0.0596614 + 0.0596614i
\(408\) 438.440 + 381.897i 1.07461 + 0.936022i
\(409\) −167.303 167.303i −0.409054 0.409054i 0.472355 0.881409i \(-0.343404\pi\)
−0.881409 + 0.472355i \(0.843404\pi\)
\(410\) −17.1041 745.493i −0.0417173 1.81828i
\(411\) 662.814 + 274.546i 1.61269 + 0.667996i
\(412\) −66.4965 + 3.05291i −0.161399 + 0.00740997i
\(413\) 186.678 77.3246i 0.452005 0.187227i
\(414\) −319.917 123.996i −0.772747 0.299507i
\(415\) 264.108i 0.636405i
\(416\) 519.153 59.8075i 1.24796 0.143768i
\(417\) 749.775 1.79802
\(418\) −187.307 + 483.264i −0.448103 + 1.15614i
\(419\) 30.6971 + 74.1094i 0.0732628 + 0.176872i 0.956269 0.292490i \(-0.0944839\pi\)
−0.883006 + 0.469362i \(0.844484\pi\)
\(420\) 338.292 15.5313i 0.805457 0.0369792i
\(421\) 234.474 566.070i 0.556945 1.34458i −0.355229 0.934779i \(-0.615597\pi\)
0.912174 0.409804i \(-0.134403\pi\)
\(422\) −194.034 + 4.45178i −0.459796 + 0.0105493i
\(423\) 63.8477 63.8477i 0.150940 0.150940i
\(424\) 0.454688 + 6.59669i 0.00107238 + 0.0155582i
\(425\) −611.850 + 611.850i −1.43965 + 1.43965i
\(426\) −32.0275 30.5909i −0.0751820 0.0718095i
\(427\) 91.2833 220.377i 0.213778 0.516106i
\(428\) 319.263 149.748i 0.745942 0.349880i
\(429\) −235.969 569.680i −0.550045 1.32793i
\(430\) −406.904 921.951i −0.946289 2.14407i
\(431\) 179.915 0.417437 0.208718 0.977976i \(-0.433071\pi\)
0.208718 + 0.977976i \(0.433071\pi\)
\(432\) 62.5074 201.397i 0.144693 0.466197i
\(433\) 458.444i 1.05876i −0.848384 0.529381i \(-0.822424\pi\)
0.848384 0.529381i \(-0.177576\pi\)
\(434\) −29.4867 66.8101i −0.0679417 0.153940i
\(435\) 663.296 274.746i 1.52482 0.631600i
\(436\) 144.741 400.469i 0.331976 0.918508i
\(437\) −748.281 309.948i −1.71231 0.709264i
\(438\) 434.308 + 414.826i 0.991570 + 0.947090i
\(439\) −322.678 322.678i −0.735031 0.735031i 0.236581 0.971612i \(-0.423973\pi\)
−0.971612 + 0.236581i \(0.923973\pi\)
\(440\) 211.503 630.031i 0.480688 1.43189i
\(441\) 27.4419 + 27.4419i 0.0622266 + 0.0622266i
\(442\) −622.296 + 14.2775i −1.40791 + 0.0323021i
\(443\) 520.748 + 215.701i 1.17550 + 0.486910i 0.883008 0.469357i \(-0.155514\pi\)
0.292496 + 0.956267i \(0.405514\pi\)
\(444\) 39.0899 + 35.6582i 0.0880404 + 0.0803112i
\(445\) 1133.88 469.669i 2.54805 1.05544i
\(446\) −281.716 + 726.846i −0.631650 + 1.62970i
\(447\) 320.348i 0.716661i
\(448\) 23.2321 + 167.727i 0.0518573 + 0.374390i
\(449\) 323.979 0.721556 0.360778 0.932652i \(-0.382511\pi\)
0.360778 + 0.932652i \(0.382511\pi\)
\(450\) −469.416 181.939i −1.04315 0.404310i
\(451\) −168.359 406.453i −0.373300 0.901227i
\(452\) −491.100 + 538.363i −1.08650 + 1.19107i
\(453\) −140.112 + 338.260i −0.309298 + 0.746710i
\(454\) −13.7626 599.852i −0.0303141 1.32126i
\(455\) −256.353 + 256.353i −0.563414 + 0.563414i
\(456\) −254.145 + 757.055i −0.557336 + 1.66021i
\(457\) −259.533 + 259.533i −0.567906 + 0.567906i −0.931541 0.363635i \(-0.881535\pi\)
0.363635 + 0.931541i \(0.381535\pi\)
\(458\) 273.415 286.256i 0.596977 0.625013i
\(459\) −96.1206 + 232.056i −0.209413 + 0.505568i
\(460\) 976.704 + 353.010i 2.12327 + 0.767413i
\(461\) 48.2981 + 116.602i 0.104768 + 0.252933i 0.967567 0.252615i \(-0.0812906\pi\)
−0.862799 + 0.505547i \(0.831291\pi\)
\(462\) 182.785 80.6723i 0.395638 0.174615i
\(463\) −226.906 −0.490077 −0.245039 0.969513i \(-0.578801\pi\)
−0.245039 + 0.969513i \(0.578801\pi\)
\(464\) 167.187 + 317.673i 0.360318 + 0.684640i
\(465\) 441.620i 0.949721i
\(466\) −515.592 + 227.557i −1.10642 + 0.488320i
\(467\) −244.027 + 101.079i −0.522542 + 0.216444i −0.628333 0.777944i \(-0.716263\pi\)
0.105791 + 0.994388i \(0.466263\pi\)
\(468\) −153.792 327.884i −0.328615 0.700606i
\(469\) 30.2393 + 12.5255i 0.0644761 + 0.0267069i
\(470\) −188.775 + 197.641i −0.401650 + 0.420513i
\(471\) 729.706 + 729.706i 1.54927 + 1.54927i
\(472\) −42.0124 609.523i −0.0890093 1.29136i
\(473\) −420.413 420.413i −0.888822 0.888822i
\(474\) −7.74224 337.451i −0.0163338 0.711922i
\(475\) −1097.96 454.788i −2.31148 0.957448i
\(476\) −9.24996 201.477i −0.0194327 0.423271i
\(477\) 4.23362 1.75362i 0.00887552 0.00367636i
\(478\) −668.901 259.257i −1.39937 0.542379i
\(479\) 24.8680i 0.0519165i 0.999663 + 0.0259583i \(0.00826370\pi\)
−0.999663 + 0.0259583i \(0.991736\pi\)
\(480\) 281.015 984.661i 0.585449 2.05138i
\(481\) −56.6431 −0.117761
\(482\) 214.950 554.584i 0.445953 1.15059i
\(483\) 119.481 + 288.453i 0.247373 + 0.597211i
\(484\) 4.21515 + 91.8117i 0.00870899 + 0.189694i
\(485\) −432.985 + 1045.32i −0.892753 + 2.15530i
\(486\) −526.582 + 12.0815i −1.08350 + 0.0248591i
\(487\) −277.431 + 277.431i −0.569673 + 0.569673i −0.932037 0.362364i \(-0.881970\pi\)
0.362364 + 0.932037i \(0.381970\pi\)
\(488\) −543.872 473.732i −1.11449 0.970762i
\(489\) −129.782 + 129.782i −0.265402 + 0.265402i
\(490\) −84.9467 81.1362i −0.173361 0.165584i
\(491\) −85.4108 + 206.200i −0.173953 + 0.419959i −0.986677 0.162689i \(-0.947983\pi\)
0.812725 + 0.582648i \(0.197983\pi\)
\(492\) −287.852 613.698i −0.585064 1.24735i
\(493\) −163.631 395.040i −0.331908 0.801297i
\(494\) −345.191 782.122i −0.698766 1.58324i
\(495\) −460.566 −0.930436
\(496\) −219.886 + 20.2330i −0.443319 + 0.0407923i
\(497\) 15.3630i 0.0309115i
\(498\) 96.9387 + 219.641i 0.194656 + 0.441046i
\(499\) 369.856 153.199i 0.741195 0.307013i 0.0200516 0.999799i \(-0.493617\pi\)
0.721143 + 0.692786i \(0.243617\pi\)
\(500\) 644.014 + 232.766i 1.28803 + 0.465531i
\(501\) −354.806 146.965i −0.708195 0.293344i
\(502\) 248.974 + 237.806i 0.495965 + 0.473717i
\(503\) 225.545 + 225.545i 0.448400 + 0.448400i 0.894822 0.446422i \(-0.147302\pi\)
−0.446422 + 0.894822i \(0.647302\pi\)
\(504\) 105.070 52.2553i 0.208471 0.103681i
\(505\) −280.764 280.764i −0.555968 0.555968i
\(506\) 612.557 14.0541i 1.21059 0.0277749i
\(507\) 344.220 + 142.580i 0.678934 + 0.281224i
\(508\) 457.349 501.364i 0.900293 0.986937i
\(509\) −343.754 + 142.388i −0.675352 + 0.279740i −0.693882 0.720088i \(-0.744101\pi\)
0.0185304 + 0.999828i \(0.494101\pi\)
\(510\) −440.779 + 1137.24i −0.864273 + 2.22988i
\(511\) 208.329i 0.407690i
\(512\) 503.146 + 94.8074i 0.982706 + 0.185171i
\(513\) −344.974 −0.672463
\(514\) −66.6497 25.8325i −0.129669 0.0502578i
\(515\) −53.4358 129.005i −0.103759 0.250496i
\(516\) −676.789 617.373i −1.31161 1.19646i
\(517\) −61.7066 + 148.973i −0.119355 + 0.288149i
\(518\) −0.420978 18.3486i −0.000812700 0.0354221i
\(519\) −415.358 + 415.358i −0.800304 + 0.800304i
\(520\) 488.151 + 981.524i 0.938752 + 1.88755i
\(521\) −575.156 + 575.156i −1.10395 + 1.10395i −0.110016 + 0.993930i \(0.535090\pi\)
−0.993930 + 0.110016i \(0.964910\pi\)
\(522\) 171.832 179.902i 0.329180 0.344640i
\(523\) 240.564 580.772i 0.459968 1.11046i −0.508441 0.861097i \(-0.669778\pi\)
0.968409 0.249365i \(-0.0802220\pi\)
\(524\) −345.370 + 955.565i −0.659102 + 1.82360i
\(525\) 175.315 + 423.248i 0.333933 + 0.806187i
\(526\) −217.027 + 95.7852i −0.412599 + 0.182101i
\(527\) 263.016 0.499082
\(528\) −55.3551 601.584i −0.104839 1.13936i
\(529\) 428.491i 0.810001i
\(530\) −12.6895 + 5.60054i −0.0239425 + 0.0105671i
\(531\) −391.180 + 162.032i −0.736685 + 0.305145i
\(532\) 250.790 117.632i 0.471411 0.221112i
\(533\) 670.433 + 277.702i 1.25785 + 0.521018i
\(534\) 770.583 806.773i 1.44304 1.51081i
\(535\) 523.059 + 523.059i 0.977680 + 0.977680i
\(536\) 65.0035 74.6278i 0.121275 0.139231i
\(537\) 565.311 + 565.311i 1.05272 + 1.05272i
\(538\) −11.0740 482.667i −0.0205836 0.897150i
\(539\) −64.0291 26.5217i −0.118792 0.0492054i
\(540\) 441.878 20.2870i 0.818294 0.0375685i
\(541\) 307.544 127.389i 0.568472 0.235469i −0.0798863 0.996804i \(-0.525456\pi\)
0.648359 + 0.761335i \(0.275456\pi\)
\(542\) 5.91774 + 2.29364i 0.0109183 + 0.00423181i
\(543\) 122.586i 0.225758i
\(544\) −586.435 167.365i −1.07801 0.307655i
\(545\) 893.236 1.63896
\(546\) −119.099 + 307.284i −0.218130 + 0.562791i
\(547\) 47.4221 + 114.487i 0.0866948 + 0.209300i 0.961281 0.275571i \(-0.0888668\pi\)
−0.874586 + 0.484870i \(0.838867\pi\)
\(548\) −751.684 + 34.5104i −1.37169 + 0.0629752i
\(549\) −191.282 + 461.796i −0.348419 + 0.841158i
\(550\) 898.807 20.6216i 1.63419 0.0374938i
\(551\) 415.259 415.259i 0.753646 0.753646i
\(552\) 941.828 64.9171i 1.70621 0.117603i
\(553\) −82.7914 + 82.7914i −0.149713 + 0.149713i
\(554\) 103.858 + 99.1992i 0.187469 + 0.179060i
\(555\) −42.4736 + 102.540i −0.0765289 + 0.184757i
\(556\) −711.978 + 333.949i −1.28054 + 0.600628i
\(557\) −348.410 841.136i −0.625511 1.51012i −0.845146 0.534536i \(-0.820486\pi\)
0.219634 0.975582i \(-0.429514\pi\)
\(558\) 61.7887 + 139.999i 0.110732 + 0.250894i
\(559\) 980.699 1.75438
\(560\) −314.321 + 165.423i −0.561288 + 0.295399i
\(561\) 719.582i 1.28268i
\(562\) 126.955 + 287.651i 0.225899 + 0.511835i
\(563\) −52.7869 + 21.8651i −0.0937601 + 0.0388367i −0.429070 0.903271i \(-0.641159\pi\)
0.335310 + 0.942108i \(0.391159\pi\)
\(564\) −84.4491 + 233.653i −0.149732 + 0.414279i
\(565\) −1412.23 584.964i −2.49952 1.03533i
\(566\) 245.138 + 234.142i 0.433106 + 0.413678i
\(567\) 187.382 + 187.382i 0.330480 + 0.330480i
\(568\) 44.0382 + 14.7837i 0.0775320 + 0.0260277i
\(569\) −600.133 600.133i −1.05472 1.05472i −0.998414 0.0563022i \(-0.982069\pi\)
−0.0563022 0.998414i \(-0.517931\pi\)
\(570\) −1674.70 + 38.4232i −2.93808 + 0.0674092i
\(571\) 671.148 + 277.998i 1.17539 + 0.486862i 0.882971 0.469428i \(-0.155540\pi\)
0.292419 + 0.956290i \(0.405540\pi\)
\(572\) 477.809 + 435.862i 0.835331 + 0.761996i
\(573\) −1127.62 + 467.077i −1.96793 + 0.815143i
\(574\) −84.9745 + 219.240i −0.148039 + 0.381951i
\(575\) 1404.93i 2.44335i
\(576\) −48.6823 351.467i −0.0845178 0.610186i
\(577\) −804.788 −1.39478 −0.697390 0.716692i \(-0.745655\pi\)
−0.697390 + 0.716692i \(0.745655\pi\)
\(578\) 138.371 + 53.6309i 0.239397 + 0.0927870i
\(579\) 34.3308 + 82.8818i 0.0592932 + 0.143147i
\(580\) −507.487 + 556.328i −0.874978 + 0.959186i
\(581\) 31.8694 76.9396i 0.0548527 0.132426i
\(582\) 23.5913 + 1028.24i 0.0405349 + 1.76674i
\(583\) −5.78647 + 5.78647i −0.00992534 + 0.00992534i
\(584\) −597.177 200.474i −1.02256 0.343277i
\(585\) 537.182 537.182i 0.918260 0.918260i
\(586\) −36.2256 + 37.9269i −0.0618184 + 0.0647216i
\(587\) 105.077 253.679i 0.179007 0.432162i −0.808751 0.588151i \(-0.799856\pi\)
0.987759 + 0.155988i \(0.0498562\pi\)
\(588\) −100.425 36.2965i −0.170791 0.0617287i
\(589\) 138.239 + 333.739i 0.234701 + 0.566619i
\(590\) 1172.49 517.480i 1.98727 0.877085i
\(591\) 1352.10 2.28781
\(592\) −53.0016 16.4500i −0.0895297 0.0277872i
\(593\) 770.015i 1.29851i −0.760572 0.649254i \(-0.775081\pi\)
0.760572 0.649254i \(-0.224919\pi\)
\(594\) 238.754 105.375i 0.401944 0.177398i
\(595\) 390.871 161.904i 0.656927 0.272108i
\(596\) −142.683 304.199i −0.239401 0.510401i
\(597\) 472.991 + 195.919i 0.792279 + 0.328173i
\(598\) −698.065 + 730.849i −1.16733 + 1.22216i
\(599\) 702.158 + 702.158i 1.17222 + 1.17222i 0.981680 + 0.190537i \(0.0610228\pi\)
0.190537 + 0.981680i \(0.438977\pi\)
\(600\) 1381.95 95.2531i 2.30324 0.158755i
\(601\) 695.160 + 695.160i 1.15667 + 1.15667i 0.985187 + 0.171486i \(0.0548569\pi\)
0.171486 + 0.985187i \(0.445143\pi\)
\(602\) 7.28867 + 317.682i 0.0121074 + 0.527710i
\(603\) −63.3657 26.2469i −0.105084 0.0435272i
\(604\) −17.6120 383.614i −0.0291590 0.635122i
\(605\) −178.118 + 73.7788i −0.294409 + 0.121948i
\(606\) −336.544 130.440i −0.555354 0.215248i
\(607\) 208.764i 0.343928i 0.985103 + 0.171964i \(0.0550112\pi\)
−0.985103 + 0.171964i \(0.944989\pi\)
\(608\) −95.8583 832.088i −0.157662 1.36857i
\(609\) −226.383 −0.371730
\(610\) 546.773 1410.71i 0.896349 2.31264i
\(611\) −101.783 245.727i −0.166585 0.402171i
\(612\) 19.3831 + 422.190i 0.0316717 + 0.689853i
\(613\) −311.265 + 751.461i −0.507774 + 1.22587i 0.437388 + 0.899273i \(0.355904\pi\)
−0.945162 + 0.326602i \(0.894096\pi\)
\(614\) 748.528 17.1737i 1.21910 0.0279702i
\(615\) 1005.44 1005.44i 1.63486 1.63486i
\(616\) −137.639 + 158.018i −0.223440 + 0.256523i
\(617\) −105.254 + 105.254i −0.170590 + 0.170590i −0.787238 0.616649i \(-0.788490\pi\)
0.616649 + 0.787238i \(0.288490\pi\)
\(618\) −91.7893 87.6718i −0.148526 0.141864i
\(619\) 29.1313 70.3291i 0.0470618 0.113617i −0.898600 0.438768i \(-0.855415\pi\)
0.945662 + 0.325151i \(0.105415\pi\)
\(620\) −196.697 419.358i −0.317254 0.676384i
\(621\) 156.067 + 376.779i 0.251315 + 0.606729i
\(622\) 174.571 + 395.538i 0.280661 + 0.635914i
\(623\) −386.994 −0.621179
\(624\) 766.222 + 637.095i 1.22792 + 1.02099i
\(625\) 301.375i 0.482199i
\(626\) −397.741 901.189i −0.635369 1.43960i
\(627\) −913.072 + 378.207i −1.45625 + 0.603200i
\(628\) −1017.93 367.911i −1.62091 0.585845i
\(629\) 61.0700 + 25.2960i 0.0970905 + 0.0402162i
\(630\) 178.004 + 170.019i 0.282546 + 0.269871i
\(631\) −177.553 177.553i −0.281383 0.281383i 0.552277 0.833661i \(-0.313759\pi\)
−0.833661 + 0.552277i \(0.813759\pi\)
\(632\) 157.652 + 316.992i 0.249450 + 0.501569i
\(633\) −261.692 261.692i −0.413416 0.413416i
\(634\) −184.360 + 4.22983i −0.290789 + 0.00667166i
\(635\) 1315.17 + 544.762i 2.07114 + 0.857893i
\(636\) −8.49739 + 9.31518i −0.0133607 + 0.0146465i
\(637\) 105.614 43.7468i 0.165799 0.0686762i
\(638\) −160.555 + 414.242i −0.251653 + 0.649283i
\(639\) 32.1928i 0.0503800i
\(640\) 171.718 + 1060.19i 0.268310 + 1.65654i
\(641\) 598.704 0.934016 0.467008 0.884253i \(-0.345332\pi\)
0.467008 + 0.884253i \(0.345332\pi\)
\(642\) 626.977 + 243.008i 0.976599 + 0.378517i
\(643\) −107.194 258.789i −0.166709 0.402471i 0.818343 0.574731i \(-0.194893\pi\)
−0.985052 + 0.172260i \(0.944893\pi\)
\(644\) −241.935 220.695i −0.375675 0.342695i
\(645\) 735.372 1775.34i 1.14011 2.75247i
\(646\) 22.8838 + 997.404i 0.0354238 + 1.54397i
\(647\) −506.754 + 506.754i −0.783237 + 0.783237i −0.980376 0.197138i \(-0.936835\pi\)
0.197138 + 0.980376i \(0.436835\pi\)
\(648\) 717.447 356.815i 1.10717 0.550640i
\(649\) 534.660 534.660i 0.823822 0.823822i
\(650\) −1024.27 + 1072.38i −1.57580 + 1.64981i
\(651\) 53.2895 128.652i 0.0818578 0.197622i
\(652\) 65.4346 181.044i 0.100360 0.277675i
\(653\) 306.691 + 740.419i 0.469665 + 1.13387i 0.964310 + 0.264777i \(0.0852983\pi\)
−0.494644 + 0.869096i \(0.664702\pi\)
\(654\) 742.844 327.855i 1.13585 0.501307i
\(655\) −2131.36 −3.25399
\(656\) 546.682 + 454.553i 0.833357 + 0.692916i
\(657\) 436.549i 0.664458i
\(658\) 78.8427 34.7973i 0.119822 0.0528835i
\(659\) −144.793 + 59.9752i −0.219716 + 0.0910094i −0.489826 0.871820i \(-0.662940\pi\)
0.270110 + 0.962829i \(0.412940\pi\)
\(660\) 1147.32 538.142i 1.73836 0.815367i
\(661\) −474.566 196.572i −0.717952 0.297385i −0.00636132 0.999980i \(-0.502025\pi\)
−0.711591 + 0.702594i \(0.752025\pi\)
\(662\) −426.237 + 446.255i −0.643863 + 0.674102i
\(663\) −839.286 839.286i −1.26589 1.26589i
\(664\) −189.880 165.392i −0.285964 0.249085i
\(665\) 410.878 + 410.878i 0.617861 + 0.617861i
\(666\) 0.882150 + 38.4491i 0.00132455 + 0.0577314i
\(667\) −641.408 265.680i −0.961632 0.398321i
\(668\) 402.378 18.4735i 0.602362 0.0276549i
\(669\) −1373.29 + 568.835i −2.05275 + 0.850277i
\(670\) 193.572 + 75.0259i 0.288913 + 0.111979i
\(671\) 892.620i 1.33028i
\(672\) −200.682 + 252.940i −0.298634 + 0.376399i
\(673\) 67.5163 0.100321 0.0501607 0.998741i \(-0.484027\pi\)
0.0501607 + 0.998741i \(0.484027\pi\)
\(674\) −80.7983 + 208.465i −0.119879 + 0.309295i
\(675\) 228.997 + 552.848i 0.339255 + 0.819035i
\(676\) −390.373 + 17.9223i −0.577475 + 0.0265123i
\(677\) −473.420 + 1142.94i −0.699291 + 1.68824i 0.0258772 + 0.999665i \(0.491762\pi\)
−0.725168 + 0.688572i \(0.758238\pi\)
\(678\) −1389.16 + 31.8719i −2.04891 + 0.0470088i
\(679\) 252.273 252.273i 0.371536 0.371536i
\(680\) −87.9666 1276.23i −0.129363 1.87682i
\(681\) 809.016 809.016i 1.18798 1.18798i
\(682\) −197.617 188.753i −0.289762 0.276764i
\(683\) 129.144 311.781i 0.189083 0.456487i −0.800701 0.599065i \(-0.795539\pi\)
0.989784 + 0.142578i \(0.0455392\pi\)
\(684\) −525.525 + 246.495i −0.768312 + 0.360372i
\(685\) −604.044 1458.29i −0.881816 2.12889i
\(686\) 14.9560 + 33.8868i 0.0218017 + 0.0493977i
\(687\) 754.824 1.09873
\(688\) 917.650 + 284.810i 1.33379 + 0.413968i
\(689\) 13.4981i 0.0195909i
\(690\) 799.605 + 1811.72i 1.15885 + 2.62568i
\(691\) −579.880 + 240.194i −0.839190 + 0.347604i −0.760534 0.649298i \(-0.775063\pi\)
−0.0786559 + 0.996902i \(0.525063\pi\)
\(692\) 209.419 579.420i 0.302629 0.837312i
\(693\) 134.171 + 55.5756i 0.193609 + 0.0801957i
\(694\) −79.0018 75.4580i −0.113835 0.108729i
\(695\) −1166.46 1166.46i −1.67835 1.67835i
\(696\) −217.847 + 648.929i −0.312999 + 0.932369i
\(697\) −598.811 598.811i −0.859127 0.859127i
\(698\) −664.092 + 15.2365i −0.951421 + 0.0218287i
\(699\) −992.845 411.250i −1.42038 0.588340i
\(700\) −354.992 323.827i −0.507131 0.462610i
\(701\) −371.102 + 153.716i −0.529390 + 0.219281i −0.631336 0.775509i \(-0.717493\pi\)
0.101946 + 0.994790i \(0.467493\pi\)
\(702\) −155.568 + 401.375i −0.221607 + 0.571760i
\(703\) 90.7865i 0.129142i
\(704\) 320.510 + 546.603i 0.455270 + 0.776425i
\(705\) −521.157 −0.739229
\(706\) −705.245 273.344i −0.998930 0.387172i
\(707\) 47.9125 + 115.671i 0.0677687 + 0.163608i
\(708\) 785.144 860.706i 1.10896 1.21569i
\(709\) −126.776 + 306.063i −0.178809 + 0.431683i −0.987717 0.156252i \(-0.950059\pi\)
0.808908 + 0.587935i \(0.200059\pi\)
\(710\) 2.23509 + 97.4181i 0.00314802 + 0.137209i
\(711\) 173.487 173.487i 0.244005 0.244005i
\(712\) −372.402 + 1109.32i −0.523036 + 1.55804i
\(713\) 301.968 301.968i 0.423518 0.423518i
\(714\) 265.636 278.111i 0.372039 0.389511i
\(715\) −519.168 + 1253.38i −0.726109 + 1.75298i
\(716\) −788.602 285.024i −1.10140 0.398078i
\(717\) −523.487 1263.81i −0.730108 1.76264i
\(718\) −142.304 + 62.8062i −0.198196 + 0.0874739i
\(719\) 796.205 1.10738 0.553689 0.832724i \(-0.313220\pi\)
0.553689 + 0.832724i \(0.313220\pi\)
\(720\) 658.652 346.641i 0.914795 0.481446i
\(721\) 44.0296i 0.0610674i
\(722\) −593.042 + 261.740i −0.821388 + 0.362520i
\(723\) 1047.82 434.022i 1.44927 0.600307i
\(724\) 54.6000 + 116.407i 0.0754143 + 0.160783i
\(725\) −941.140 389.833i −1.29812 0.537701i
\(726\) −121.049 + 126.733i −0.166733 + 0.174564i
\(727\) 768.310 + 768.310i 1.05682 + 1.05682i 0.998285 + 0.0585371i \(0.0186436\pi\)
0.0585371 + 0.998285i \(0.481356\pi\)
\(728\) −23.7687 344.840i −0.0326493 0.473682i
\(729\) −72.7833 72.7833i −0.0998399 0.0998399i
\(730\) −30.3089 1321.03i −0.0415190 1.80963i
\(731\) −1057.34 437.966i −1.44643 0.599133i
\(732\) −63.0760 1373.88i −0.0861694 1.87689i
\(733\) 1227.34 508.379i 1.67440 0.693559i 0.675365 0.737484i \(-0.263986\pi\)
0.999035 + 0.0439244i \(0.0139861\pi\)
\(734\) 545.671 + 211.495i 0.743421 + 0.288140i
\(735\) 223.995i 0.304755i
\(736\) −865.436 + 481.134i −1.17586 + 0.653715i
\(737\) 122.482 0.166189
\(738\) 178.062 459.412i 0.241276 0.622509i
\(739\) 134.211 + 324.014i 0.181611 + 0.438449i 0.988299 0.152529i \(-0.0487419\pi\)
−0.806687 + 0.590978i \(0.798742\pi\)
\(740\) −5.33891 116.289i −0.00721475 0.157147i
\(741\) 623.841 1506.08i 0.841890 2.03250i
\(742\) 4.37250 0.100320i 0.00589286 0.000135202i
\(743\) −554.891 + 554.891i −0.746825 + 0.746825i −0.973882 0.227057i \(-0.927090\pi\)
0.227057 + 0.973882i \(0.427090\pi\)
\(744\) −317.502 276.555i −0.426750 0.371714i
\(745\) 498.379 498.379i 0.668965 0.668965i
\(746\) 102.624 + 98.0203i 0.137565 + 0.131394i
\(747\) −66.7816 + 161.225i −0.0893997 + 0.215830i
\(748\) −320.502 683.308i −0.428478 0.913514i
\(749\) −89.2602 215.493i −0.119172 0.287708i
\(750\) 527.239 + 1194.60i 0.702986 + 1.59280i
\(751\) −73.8810 −0.0983769 −0.0491884 0.998790i \(-0.515663\pi\)
−0.0491884 + 0.998790i \(0.515663\pi\)
\(752\) −23.8769 259.488i −0.0317513 0.345064i
\(753\) 656.517i 0.871869i
\(754\) −295.889 670.416i −0.392426 0.889146i
\(755\) 744.223 308.267i 0.985726 0.408301i
\(756\) −131.175 47.4106i −0.173512 0.0627125i
\(757\) 618.004 + 255.986i 0.816386 + 0.338158i 0.751499 0.659734i \(-0.229331\pi\)
0.0648873 + 0.997893i \(0.479331\pi\)
\(758\) −184.886 176.593i −0.243913 0.232972i
\(759\) 826.151 +