Properties

Label 288.3.u.a.19.3
Level $288$
Weight $3$
Character 288.19
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 19.3
Character \(\chi\) \(=\) 288.19
Dual form 288.3.u.a.91.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.345994 + 1.96984i) q^{2} +(-3.76058 - 1.36311i) q^{4} +(-7.20074 + 2.98264i) q^{5} +(4.26150 + 4.26150i) q^{7} +(3.98625 - 6.93612i) q^{8} +O(q^{10})\) \(q+(-0.345994 + 1.96984i) q^{2} +(-3.76058 - 1.36311i) q^{4} +(-7.20074 + 2.98264i) q^{5} +(4.26150 + 4.26150i) q^{7} +(3.98625 - 6.93612i) q^{8} +(-3.38393 - 15.2163i) q^{10} +(-6.19818 + 2.56737i) q^{11} +(-8.05345 - 3.33585i) q^{13} +(-9.86895 + 6.92004i) q^{14} +(12.2839 + 10.2522i) q^{16} -24.5802i q^{17} +(4.96459 - 11.9856i) q^{19} +(31.1446 - 1.40106i) q^{20} +(-2.91279 - 13.0978i) q^{22} +(9.72199 - 9.72199i) q^{23} +(25.2768 - 25.2768i) q^{25} +(9.35754 - 14.7099i) q^{26} +(-10.2168 - 21.8346i) q^{28} +(5.86371 - 14.1563i) q^{29} -17.5320i q^{31} +(-24.4453 + 20.6501i) q^{32} +(48.4192 + 8.50460i) q^{34} +(-43.3965 - 17.9754i) q^{35} +(-36.0346 + 14.9260i) q^{37} +(21.8920 + 13.9264i) q^{38} +(-8.01597 + 61.8348i) q^{40} +(-10.9784 - 10.9784i) q^{41} +(-22.4024 + 9.27937i) q^{43} +(26.8084 - 1.20599i) q^{44} +(15.7871 + 22.5146i) q^{46} -27.0104 q^{47} -12.6792i q^{49} +(41.0458 + 58.5371i) q^{50} +(25.7385 + 23.5224i) q^{52} +(34.0172 + 82.1247i) q^{53} +(36.9740 - 36.9740i) q^{55} +(46.5457 - 12.5709i) q^{56} +(25.8568 + 16.4486i) q^{58} +(-27.8391 - 67.2095i) q^{59} +(-6.37082 + 15.3805i) q^{61} +(34.5354 + 6.06598i) q^{62} +(-32.2196 - 55.2983i) q^{64} +67.9404 q^{65} +(-99.2165 - 41.0968i) q^{67} +(-33.5055 + 92.4357i) q^{68} +(50.4237 - 79.2650i) q^{70} +(2.55754 + 2.55754i) q^{71} +(30.7498 + 30.7498i) q^{73} +(-16.9342 - 76.1469i) q^{74} +(-35.0074 + 38.3054i) q^{76} +(-37.3544 - 15.4727i) q^{77} -90.6600 q^{79} +(-119.031 - 37.1847i) q^{80} +(25.4241 - 17.8272i) q^{82} +(39.3191 - 94.9247i) q^{83} +(73.3140 + 176.996i) q^{85} +(-10.5278 - 47.3398i) q^{86} +(-6.89991 + 53.2256i) q^{88} +(-109.290 + 109.290i) q^{89} +(-20.1040 - 48.5355i) q^{91} +(-49.8124 + 23.3081i) q^{92} +(9.34545 - 53.2063i) q^{94} +101.113i q^{95} +63.7161 q^{97} +(24.9761 + 4.38694i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.345994 + 1.96984i −0.172997 + 0.984922i
\(3\) 0 0
\(4\) −3.76058 1.36311i −0.940144 0.340777i
\(5\) −7.20074 + 2.98264i −1.44015 + 0.596529i −0.959834 0.280568i \(-0.909477\pi\)
−0.480314 + 0.877097i \(0.659477\pi\)
\(6\) 0 0
\(7\) 4.26150 + 4.26150i 0.608786 + 0.608786i 0.942629 0.333843i \(-0.108346\pi\)
−0.333843 + 0.942629i \(0.608346\pi\)
\(8\) 3.98625 6.93612i 0.498281 0.867015i
\(9\) 0 0
\(10\) −3.38393 15.2163i −0.338393 1.52163i
\(11\) −6.19818 + 2.56737i −0.563471 + 0.233397i −0.646191 0.763175i \(-0.723639\pi\)
0.0827202 + 0.996573i \(0.473639\pi\)
\(12\) 0 0
\(13\) −8.05345 3.33585i −0.619496 0.256604i 0.0507868 0.998710i \(-0.483827\pi\)
−0.670283 + 0.742106i \(0.733827\pi\)
\(14\) −9.86895 + 6.92004i −0.704925 + 0.494288i
\(15\) 0 0
\(16\) 12.2839 + 10.2522i 0.767742 + 0.640760i
\(17\) 24.5802i 1.44589i −0.690904 0.722947i \(-0.742787\pi\)
0.690904 0.722947i \(-0.257213\pi\)
\(18\) 0 0
\(19\) 4.96459 11.9856i 0.261294 0.630820i −0.737725 0.675101i \(-0.764100\pi\)
0.999019 + 0.0442815i \(0.0140998\pi\)
\(20\) 31.1446 1.40106i 1.55723 0.0700532i
\(21\) 0 0
\(22\) −2.91279 13.0978i −0.132399 0.595353i
\(23\) 9.72199 9.72199i 0.422695 0.422695i −0.463435 0.886131i \(-0.653383\pi\)
0.886131 + 0.463435i \(0.153383\pi\)
\(24\) 0 0
\(25\) 25.2768 25.2768i 1.01107 1.01107i
\(26\) 9.35754 14.7099i 0.359906 0.565764i
\(27\) 0 0
\(28\) −10.2168 21.8346i −0.364886 0.779807i
\(29\) 5.86371 14.1563i 0.202197 0.488147i −0.789958 0.613161i \(-0.789898\pi\)
0.992155 + 0.125014i \(0.0398977\pi\)
\(30\) 0 0
\(31\) 17.5320i 0.565550i −0.959186 0.282775i \(-0.908745\pi\)
0.959186 0.282775i \(-0.0912549\pi\)
\(32\) −24.4453 + 20.6501i −0.763915 + 0.645316i
\(33\) 0 0
\(34\) 48.4192 + 8.50460i 1.42409 + 0.250135i
\(35\) −43.3965 17.9754i −1.23990 0.513583i
\(36\) 0 0
\(37\) −36.0346 + 14.9260i −0.973909 + 0.403406i −0.812166 0.583427i \(-0.801712\pi\)
−0.161743 + 0.986833i \(0.551712\pi\)
\(38\) 21.8920 + 13.9264i 0.576106 + 0.366485i
\(39\) 0 0
\(40\) −8.01597 + 61.8348i −0.200399 + 1.54587i
\(41\) −10.9784 10.9784i −0.267765 0.267765i 0.560434 0.828199i \(-0.310634\pi\)
−0.828199 + 0.560434i \(0.810634\pi\)
\(42\) 0 0
\(43\) −22.4024 + 9.27937i −0.520985 + 0.215799i −0.627650 0.778496i \(-0.715983\pi\)
0.106664 + 0.994295i \(0.465983\pi\)
\(44\) 26.8084 1.20599i 0.609281 0.0274090i
\(45\) 0 0
\(46\) 15.7871 + 22.5146i 0.343197 + 0.489447i
\(47\) −27.0104 −0.574690 −0.287345 0.957827i \(-0.592773\pi\)
−0.287345 + 0.957827i \(0.592773\pi\)
\(48\) 0 0
\(49\) 12.6792i 0.258760i
\(50\) 41.0458 + 58.5371i 0.820916 + 1.17074i
\(51\) 0 0
\(52\) 25.7385 + 23.5224i 0.494971 + 0.452354i
\(53\) 34.0172 + 82.1247i 0.641833 + 1.54952i 0.824204 + 0.566293i \(0.191623\pi\)
−0.182371 + 0.983230i \(0.558377\pi\)
\(54\) 0 0
\(55\) 36.9740 36.9740i 0.672254 0.672254i
\(56\) 46.5457 12.5709i 0.831173 0.224480i
\(57\) 0 0
\(58\) 25.8568 + 16.4486i 0.445807 + 0.283596i
\(59\) −27.8391 67.2095i −0.471849 1.13914i −0.963345 0.268264i \(-0.913550\pi\)
0.491497 0.870879i \(-0.336450\pi\)
\(60\) 0 0
\(61\) −6.37082 + 15.3805i −0.104440 + 0.252140i −0.967457 0.253034i \(-0.918572\pi\)
0.863018 + 0.505174i \(0.168572\pi\)
\(62\) 34.5354 + 6.06598i 0.557022 + 0.0978384i
\(63\) 0 0
\(64\) −32.2196 55.2983i −0.503431 0.864035i
\(65\) 67.9404 1.04524
\(66\) 0 0
\(67\) −99.2165 41.0968i −1.48084 0.613386i −0.511542 0.859258i \(-0.670925\pi\)
−0.969302 + 0.245873i \(0.920925\pi\)
\(68\) −33.5055 + 92.4357i −0.492728 + 1.35935i
\(69\) 0 0
\(70\) 50.4237 79.2650i 0.720339 1.13236i
\(71\) 2.55754 + 2.55754i 0.0360217 + 0.0360217i 0.724888 0.688867i \(-0.241891\pi\)
−0.688867 + 0.724888i \(0.741891\pi\)
\(72\) 0 0
\(73\) 30.7498 + 30.7498i 0.421230 + 0.421230i 0.885627 0.464397i \(-0.153729\pi\)
−0.464397 + 0.885627i \(0.653729\pi\)
\(74\) −16.9342 76.1469i −0.228840 1.02901i
\(75\) 0 0
\(76\) −35.0074 + 38.3054i −0.460623 + 0.504019i
\(77\) −37.3544 15.4727i −0.485122 0.200944i
\(78\) 0 0
\(79\) −90.6600 −1.14759 −0.573797 0.818997i \(-0.694530\pi\)
−0.573797 + 0.818997i \(0.694530\pi\)
\(80\) −119.031 37.1847i −1.48789 0.464809i
\(81\) 0 0
\(82\) 25.4241 17.8272i 0.310051 0.217405i
\(83\) 39.3191 94.9247i 0.473724 1.14367i −0.488781 0.872407i \(-0.662558\pi\)
0.962505 0.271264i \(-0.0874417\pi\)
\(84\) 0 0
\(85\) 73.3140 + 176.996i 0.862517 + 2.08230i
\(86\) −10.5278 47.3398i −0.122417 0.550463i
\(87\) 0 0
\(88\) −6.89991 + 53.2256i −0.0784081 + 0.604836i
\(89\) −109.290 + 109.290i −1.22798 + 1.22798i −0.263248 + 0.964728i \(0.584794\pi\)
−0.964728 + 0.263248i \(0.915206\pi\)
\(90\) 0 0
\(91\) −20.1040 48.5355i −0.220924 0.533357i
\(92\) −49.8124 + 23.3081i −0.541439 + 0.253349i
\(93\) 0 0
\(94\) 9.34545 53.2063i 0.0994196 0.566025i
\(95\) 101.113i 1.06434i
\(96\) 0 0
\(97\) 63.7161 0.656867 0.328433 0.944527i \(-0.393479\pi\)
0.328433 + 0.944527i \(0.393479\pi\)
\(98\) 24.9761 + 4.38694i 0.254859 + 0.0447647i
\(99\) 0 0
\(100\) −129.511 + 60.6004i −1.29511 + 0.606004i
\(101\) 14.4312 5.97761i 0.142883 0.0591842i −0.310096 0.950705i \(-0.600361\pi\)
0.452979 + 0.891521i \(0.350361\pi\)
\(102\) 0 0
\(103\) −9.69681 9.69681i −0.0941438 0.0941438i 0.658466 0.752610i \(-0.271205\pi\)
−0.752610 + 0.658466i \(0.771205\pi\)
\(104\) −55.2409 + 42.5622i −0.531163 + 0.409252i
\(105\) 0 0
\(106\) −173.543 + 38.5939i −1.63719 + 0.364093i
\(107\) −138.127 + 57.2140i −1.29091 + 0.534710i −0.919255 0.393662i \(-0.871208\pi\)
−0.371650 + 0.928373i \(0.621208\pi\)
\(108\) 0 0
\(109\) −32.0941 13.2938i −0.294442 0.121962i 0.230573 0.973055i \(-0.425940\pi\)
−0.525014 + 0.851093i \(0.675940\pi\)
\(110\) 60.0402 + 85.6257i 0.545820 + 0.778416i
\(111\) 0 0
\(112\) 8.65814 + 96.0372i 0.0773048 + 0.857475i
\(113\) 125.923i 1.11436i −0.830392 0.557180i \(-0.811883\pi\)
0.830392 0.557180i \(-0.188117\pi\)
\(114\) 0 0
\(115\) −41.0083 + 99.0028i −0.356594 + 0.860894i
\(116\) −41.3475 + 45.2428i −0.356444 + 0.390024i
\(117\) 0 0
\(118\) 142.024 31.5846i 1.20360 0.267666i
\(119\) 104.748 104.748i 0.880239 0.880239i
\(120\) 0 0
\(121\) −53.7338 + 53.7338i −0.444081 + 0.444081i
\(122\) −28.0930 17.8711i −0.230270 0.146484i
\(123\) 0 0
\(124\) −23.8981 + 65.9306i −0.192727 + 0.531698i
\(125\) −32.0540 + 77.3852i −0.256432 + 0.619081i
\(126\) 0 0
\(127\) 79.4160i 0.625322i −0.949865 0.312661i \(-0.898780\pi\)
0.949865 0.312661i \(-0.101220\pi\)
\(128\) 120.077 44.3347i 0.938100 0.346365i
\(129\) 0 0
\(130\) −23.5070 + 133.832i −0.180823 + 1.02948i
\(131\) −53.2656 22.0633i −0.406608 0.168422i 0.169999 0.985444i \(-0.445624\pi\)
−0.576607 + 0.817022i \(0.695624\pi\)
\(132\) 0 0
\(133\) 72.2331 29.9199i 0.543106 0.224962i
\(134\) 115.283 181.222i 0.860319 1.35240i
\(135\) 0 0
\(136\) −170.491 97.9828i −1.25361 0.720462i
\(137\) −50.7359 50.7359i −0.370335 0.370335i 0.497264 0.867599i \(-0.334338\pi\)
−0.867599 + 0.497264i \(0.834338\pi\)
\(138\) 0 0
\(139\) 133.213 55.1786i 0.958366 0.396968i 0.151997 0.988381i \(-0.451430\pi\)
0.806369 + 0.591413i \(0.201430\pi\)
\(140\) 138.693 + 126.752i 0.990667 + 0.905372i
\(141\) 0 0
\(142\) −5.92286 + 4.15307i −0.0417102 + 0.0292469i
\(143\) 58.4811 0.408959
\(144\) 0 0
\(145\) 119.425i 0.823620i
\(146\) −71.2116 + 49.9331i −0.487751 + 0.342007i
\(147\) 0 0
\(148\) 155.857 7.01134i 1.05309 0.0473739i
\(149\) −5.00779 12.0899i −0.0336093 0.0811401i 0.906184 0.422884i \(-0.138982\pi\)
−0.939793 + 0.341744i \(0.888982\pi\)
\(150\) 0 0
\(151\) −17.6867 + 17.6867i −0.117130 + 0.117130i −0.763243 0.646112i \(-0.776394\pi\)
0.646112 + 0.763243i \(0.276394\pi\)
\(152\) −63.3434 82.2125i −0.416733 0.540872i
\(153\) 0 0
\(154\) 43.4032 68.2289i 0.281839 0.443045i
\(155\) 52.2918 + 126.244i 0.337367 + 0.814475i
\(156\) 0 0
\(157\) 73.8536 178.298i 0.470405 1.13566i −0.493580 0.869701i \(-0.664312\pi\)
0.963985 0.265958i \(-0.0856882\pi\)
\(158\) 31.3678 178.586i 0.198531 1.13029i
\(159\) 0 0
\(160\) 114.432 221.608i 0.715202 1.38505i
\(161\) 82.8605 0.514662
\(162\) 0 0
\(163\) −132.246 54.7779i −0.811322 0.336061i −0.0618408 0.998086i \(-0.519697\pi\)
−0.749481 + 0.662025i \(0.769697\pi\)
\(164\) 26.3203 + 56.2497i 0.160490 + 0.342986i
\(165\) 0 0
\(166\) 173.383 + 110.296i 1.04447 + 0.664433i
\(167\) 109.750 + 109.750i 0.657187 + 0.657187i 0.954714 0.297526i \(-0.0961616\pi\)
−0.297526 + 0.954714i \(0.596162\pi\)
\(168\) 0 0
\(169\) −65.7709 65.7709i −0.389177 0.389177i
\(170\) −374.020 + 83.1777i −2.20012 + 0.489281i
\(171\) 0 0
\(172\) 96.8946 4.35888i 0.563341 0.0253423i
\(173\) 287.188 + 118.957i 1.66005 + 0.687613i 0.998081 0.0619221i \(-0.0197230\pi\)
0.661964 + 0.749535i \(0.269723\pi\)
\(174\) 0 0
\(175\) 215.434 1.23105
\(176\) −102.459 32.0075i −0.582152 0.181861i
\(177\) 0 0
\(178\) −177.470 253.098i −0.997025 1.42190i
\(179\) −48.9443 + 118.162i −0.273432 + 0.660122i −0.999625 0.0273677i \(-0.991288\pi\)
0.726194 + 0.687490i \(0.241288\pi\)
\(180\) 0 0
\(181\) 38.9220 + 93.9660i 0.215039 + 0.519149i 0.994184 0.107694i \(-0.0343466\pi\)
−0.779145 + 0.626843i \(0.784347\pi\)
\(182\) 102.563 22.8089i 0.563534 0.125323i
\(183\) 0 0
\(184\) −28.6786 106.187i −0.155862 0.577104i
\(185\) 214.957 214.957i 1.16193 1.16193i
\(186\) 0 0
\(187\) 63.1065 + 152.353i 0.337468 + 0.814719i
\(188\) 101.575 + 36.8182i 0.540291 + 0.195841i
\(189\) 0 0
\(190\) −199.176 34.9844i −1.04830 0.184128i
\(191\) 66.5635i 0.348500i 0.984701 + 0.174250i \(0.0557500\pi\)
−0.984701 + 0.174250i \(0.944250\pi\)
\(192\) 0 0
\(193\) 275.880 1.42943 0.714714 0.699417i \(-0.246557\pi\)
0.714714 + 0.699417i \(0.246557\pi\)
\(194\) −22.0454 + 125.511i −0.113636 + 0.646962i
\(195\) 0 0
\(196\) −17.2832 + 47.6813i −0.0881796 + 0.243272i
\(197\) −167.300 + 69.2980i −0.849240 + 0.351767i −0.764490 0.644636i \(-0.777009\pi\)
−0.0847497 + 0.996402i \(0.527009\pi\)
\(198\) 0 0
\(199\) −233.526 233.526i −1.17350 1.17350i −0.981370 0.192125i \(-0.938462\pi\)
−0.192125 0.981370i \(-0.561538\pi\)
\(200\) −74.5634 276.083i −0.372817 1.38041i
\(201\) 0 0
\(202\) 6.78184 + 30.4955i 0.0335735 + 0.150968i
\(203\) 85.3151 35.3387i 0.420271 0.174082i
\(204\) 0 0
\(205\) 111.797 + 46.3078i 0.545351 + 0.225892i
\(206\) 22.4562 15.7462i 0.109011 0.0764377i
\(207\) 0 0
\(208\) −64.7278 123.542i −0.311192 0.593953i
\(209\) 87.0348i 0.416434i
\(210\) 0 0
\(211\) 32.7097 78.9682i 0.155022 0.374257i −0.827219 0.561880i \(-0.810078\pi\)
0.982241 + 0.187623i \(0.0600783\pi\)
\(212\) −15.9792 355.205i −0.0753735 1.67550i
\(213\) 0 0
\(214\) −64.9117 291.884i −0.303325 1.36394i
\(215\) 133.637 133.637i 0.621566 0.621566i
\(216\) 0 0
\(217\) 74.7128 74.7128i 0.344298 0.344298i
\(218\) 37.2912 58.6209i 0.171060 0.268903i
\(219\) 0 0
\(220\) −189.443 + 88.6438i −0.861104 + 0.402927i
\(221\) −81.9957 + 197.955i −0.371021 + 0.895725i
\(222\) 0 0
\(223\) 373.446i 1.67465i 0.546708 + 0.837323i \(0.315881\pi\)
−0.546708 + 0.837323i \(0.684119\pi\)
\(224\) −192.174 16.1731i −0.857920 0.0722015i
\(225\) 0 0
\(226\) 248.048 + 43.5685i 1.09756 + 0.192781i
\(227\) −7.71962 3.19757i −0.0340071 0.0140862i 0.365615 0.930766i \(-0.380859\pi\)
−0.399622 + 0.916680i \(0.630859\pi\)
\(228\) 0 0
\(229\) −165.203 + 68.4293i −0.721410 + 0.298818i −0.713017 0.701147i \(-0.752672\pi\)
−0.00839310 + 0.999965i \(0.502672\pi\)
\(230\) −180.831 115.034i −0.786224 0.500149i
\(231\) 0 0
\(232\) −74.8153 97.1018i −0.322480 0.418542i
\(233\) −14.0197 14.0197i −0.0601703 0.0601703i 0.676381 0.736552i \(-0.263547\pi\)
−0.736552 + 0.676381i \(0.763547\pi\)
\(234\) 0 0
\(235\) 194.495 80.5625i 0.827638 0.342819i
\(236\) 13.0771 + 290.694i 0.0554114 + 1.23175i
\(237\) 0 0
\(238\) 170.096 + 242.581i 0.714688 + 1.01925i
\(239\) 230.951 0.966321 0.483161 0.875532i \(-0.339489\pi\)
0.483161 + 0.875532i \(0.339489\pi\)
\(240\) 0 0
\(241\) 111.407i 0.462269i 0.972922 + 0.231135i \(0.0742438\pi\)
−0.972922 + 0.231135i \(0.925756\pi\)
\(242\) −87.2557 124.439i −0.360561 0.514210i
\(243\) 0 0
\(244\) 44.9233 49.1555i 0.184112 0.201457i
\(245\) 37.8177 + 91.3000i 0.154358 + 0.372653i
\(246\) 0 0
\(247\) −79.9641 + 79.9641i −0.323741 + 0.323741i
\(248\) −121.604 69.8871i −0.490340 0.281803i
\(249\) 0 0
\(250\) −141.346 89.9162i −0.565385 0.359665i
\(251\) −93.4234 225.544i −0.372205 0.898581i −0.993376 0.114907i \(-0.963343\pi\)
0.621172 0.783675i \(-0.286657\pi\)
\(252\) 0 0
\(253\) −35.2987 + 85.2186i −0.139521 + 0.336833i
\(254\) 156.437 + 27.4775i 0.615894 + 0.108179i
\(255\) 0 0
\(256\) 45.7867 + 251.872i 0.178854 + 0.983876i
\(257\) 278.684 1.08437 0.542187 0.840258i \(-0.317597\pi\)
0.542187 + 0.840258i \(0.317597\pi\)
\(258\) 0 0
\(259\) −217.169 89.9543i −0.838490 0.347314i
\(260\) −255.495 92.6102i −0.982674 0.356193i
\(261\) 0 0
\(262\) 61.8909 97.2912i 0.236225 0.371340i
\(263\) −271.210 271.210i −1.03122 1.03122i −0.999497 0.0317197i \(-0.989902\pi\)
−0.0317197 0.999497i \(-0.510098\pi\)
\(264\) 0 0
\(265\) −489.898 489.898i −1.84867 1.84867i
\(266\) 33.9454 + 152.640i 0.127614 + 0.573835i
\(267\) 0 0
\(268\) 317.092 + 289.791i 1.18318 + 1.08131i
\(269\) −54.9518 22.7618i −0.204282 0.0846163i 0.278197 0.960524i \(-0.410263\pi\)
−0.482478 + 0.875908i \(0.660263\pi\)
\(270\) 0 0
\(271\) 443.976 1.63829 0.819143 0.573589i \(-0.194449\pi\)
0.819143 + 0.573589i \(0.194449\pi\)
\(272\) 252.000 301.940i 0.926470 1.11007i
\(273\) 0 0
\(274\) 117.496 82.3875i 0.428818 0.300684i
\(275\) −91.7754 + 221.565i −0.333729 + 0.805693i
\(276\) 0 0
\(277\) 23.1329 + 55.8478i 0.0835124 + 0.201617i 0.960119 0.279590i \(-0.0901986\pi\)
−0.876607 + 0.481207i \(0.840199\pi\)
\(278\) 62.6023 + 281.500i 0.225188 + 1.01259i
\(279\) 0 0
\(280\) −297.669 + 229.349i −1.06310 + 0.819103i
\(281\) 159.772 159.772i 0.568582 0.568582i −0.363149 0.931731i \(-0.618298\pi\)
0.931731 + 0.363149i \(0.118298\pi\)
\(282\) 0 0
\(283\) −185.468 447.761i −0.655366 1.58219i −0.804883 0.593434i \(-0.797772\pi\)
0.149517 0.988759i \(-0.452228\pi\)
\(284\) −6.13162 13.1040i −0.0215902 0.0461410i
\(285\) 0 0
\(286\) −20.2341 + 115.199i −0.0707487 + 0.402793i
\(287\) 93.5687i 0.326023i
\(288\) 0 0
\(289\) −315.186 −1.09061
\(290\) −235.249 41.3203i −0.811202 0.142484i
\(291\) 0 0
\(292\) −73.7216 157.552i −0.252471 0.539563i
\(293\) −476.574 + 197.403i −1.62653 + 0.673732i −0.994837 0.101485i \(-0.967641\pi\)
−0.631696 + 0.775216i \(0.717641\pi\)
\(294\) 0 0
\(295\) 400.924 + 400.924i 1.35906 + 1.35906i
\(296\) −40.1143 + 309.439i −0.135521 + 1.04540i
\(297\) 0 0
\(298\) 25.5479 5.68155i 0.0857310 0.0190656i
\(299\) −110.727 + 45.8645i −0.370323 + 0.153393i
\(300\) 0 0
\(301\) −135.012 55.9237i −0.448544 0.185793i
\(302\) −28.7206 40.9595i −0.0951012 0.135628i
\(303\) 0 0
\(304\) 183.862 96.3315i 0.604810 0.316880i
\(305\) 129.753i 0.425420i
\(306\) 0 0
\(307\) −196.212 + 473.698i −0.639127 + 1.54299i 0.188716 + 0.982032i \(0.439567\pi\)
−0.827844 + 0.560959i \(0.810433\pi\)
\(308\) 119.383 + 109.104i 0.387608 + 0.354235i
\(309\) 0 0
\(310\) −266.773 + 59.3272i −0.860558 + 0.191378i
\(311\) −386.346 + 386.346i −1.24227 + 1.24227i −0.283215 + 0.959057i \(0.591401\pi\)
−0.959057 + 0.283215i \(0.908599\pi\)
\(312\) 0 0
\(313\) 127.090 127.090i 0.406038 0.406038i −0.474316 0.880354i \(-0.657305\pi\)
0.880354 + 0.474316i \(0.157305\pi\)
\(314\) 325.667 + 207.170i 1.03716 + 0.659778i
\(315\) 0 0
\(316\) 340.934 + 123.579i 1.07890 + 0.391074i
\(317\) 24.4377 58.9979i 0.0770906 0.186113i −0.880636 0.473794i \(-0.842884\pi\)
0.957726 + 0.287681i \(0.0928842\pi\)
\(318\) 0 0
\(319\) 102.797i 0.322249i
\(320\) 396.940 + 302.089i 1.24044 + 0.944027i
\(321\) 0 0
\(322\) −28.6693 + 163.222i −0.0890349 + 0.506902i
\(323\) −294.608 122.031i −0.912099 0.377804i
\(324\) 0 0
\(325\) −287.885 + 119.246i −0.885801 + 0.366911i
\(326\) 153.660 241.550i 0.471350 0.740952i
\(327\) 0 0
\(328\) −119.910 + 32.3848i −0.365579 + 0.0987341i
\(329\) −115.105 115.105i −0.349863 0.349863i
\(330\) 0 0
\(331\) 53.7512 22.2645i 0.162390 0.0672643i −0.300007 0.953937i \(-0.596989\pi\)
0.462398 + 0.886673i \(0.346989\pi\)
\(332\) −277.255 + 303.375i −0.835106 + 0.913781i
\(333\) 0 0
\(334\) −254.164 + 178.218i −0.760970 + 0.533587i
\(335\) 837.010 2.49854
\(336\) 0 0
\(337\) 368.803i 1.09437i −0.837012 0.547185i \(-0.815700\pi\)
0.837012 0.547185i \(-0.184300\pi\)
\(338\) 152.315 106.802i 0.450636 0.315983i
\(339\) 0 0
\(340\) −34.4384 765.540i −0.101289 2.25159i
\(341\) 45.0113 + 108.667i 0.131998 + 0.318671i
\(342\) 0 0
\(343\) 262.846 262.846i 0.766315 0.766315i
\(344\) −24.9387 + 192.376i −0.0724961 + 0.559231i
\(345\) 0 0
\(346\) −333.692 + 524.557i −0.964429 + 1.51606i
\(347\) −166.265 401.400i −0.479151 1.15677i −0.960008 0.279973i \(-0.909675\pi\)
0.480857 0.876799i \(-0.340325\pi\)
\(348\) 0 0
\(349\) −24.6685 + 59.5550i −0.0706833 + 0.170645i −0.955273 0.295726i \(-0.904439\pi\)
0.884590 + 0.466370i \(0.154439\pi\)
\(350\) −74.5390 + 424.372i −0.212969 + 1.21249i
\(351\) 0 0
\(352\) 98.4999 190.753i 0.279829 0.541913i
\(353\) −245.534 −0.695563 −0.347782 0.937576i \(-0.613065\pi\)
−0.347782 + 0.937576i \(0.613065\pi\)
\(354\) 0 0
\(355\) −26.0444 10.7880i −0.0733646 0.0303886i
\(356\) 559.967 262.019i 1.57294 0.736008i
\(357\) 0 0
\(358\) −215.826 137.296i −0.602866 0.383508i
\(359\) −61.7019 61.7019i −0.171872 0.171872i 0.615930 0.787801i \(-0.288781\pi\)
−0.787801 + 0.615930i \(0.788781\pi\)
\(360\) 0 0
\(361\) 136.259 + 136.259i 0.377448 + 0.377448i
\(362\) −198.565 + 44.1586i −0.548523 + 0.121985i
\(363\) 0 0
\(364\) 9.44365 + 209.925i 0.0259441 + 0.576718i
\(365\) −313.137 129.706i −0.857910 0.355358i
\(366\) 0 0
\(367\) 123.349 0.336102 0.168051 0.985778i \(-0.446253\pi\)
0.168051 + 0.985778i \(0.446253\pi\)
\(368\) 219.095 19.7523i 0.595367 0.0536747i
\(369\) 0 0
\(370\) 349.058 + 497.806i 0.943400 + 1.34542i
\(371\) −205.010 + 494.939i −0.552588 + 1.33407i
\(372\) 0 0
\(373\) −11.5942 27.9909i −0.0310836 0.0750425i 0.907575 0.419889i \(-0.137931\pi\)
−0.938659 + 0.344846i \(0.887931\pi\)
\(374\) −321.945 + 71.5969i −0.860816 + 0.191436i
\(375\) 0 0
\(376\) −107.670 + 187.348i −0.286357 + 0.498265i
\(377\) −94.4462 + 94.4462i −0.250520 + 0.250520i
\(378\) 0 0
\(379\) 205.083 + 495.114i 0.541115 + 1.30637i 0.923937 + 0.382546i \(0.124953\pi\)
−0.382821 + 0.923823i \(0.625047\pi\)
\(380\) 137.828 380.242i 0.362704 1.00064i
\(381\) 0 0
\(382\) −131.120 23.0306i −0.343245 0.0602894i
\(383\) 605.809i 1.58175i 0.611979 + 0.790874i \(0.290374\pi\)
−0.611979 + 0.790874i \(0.709626\pi\)
\(384\) 0 0
\(385\) 315.129 0.818517
\(386\) −95.4528 + 543.440i −0.247287 + 1.40788i
\(387\) 0 0
\(388\) −239.609 86.8519i −0.617549 0.223845i
\(389\) 426.567 176.690i 1.09657 0.454215i 0.240279 0.970704i \(-0.422761\pi\)
0.856294 + 0.516489i \(0.172761\pi\)
\(390\) 0 0
\(391\) −238.968 238.968i −0.611172 0.611172i
\(392\) −87.9448 50.5427i −0.224349 0.128935i
\(393\) 0 0
\(394\) −78.6214 353.532i −0.199547 0.897290i
\(395\) 652.819 270.407i 1.65271 0.684573i
\(396\) 0 0
\(397\) 294.458 + 121.969i 0.741708 + 0.307226i 0.721353 0.692567i \(-0.243520\pi\)
0.0203548 + 0.999793i \(0.493520\pi\)
\(398\) 540.808 379.211i 1.35881 0.952791i
\(399\) 0 0
\(400\) 569.639 51.3552i 1.42410 0.128388i
\(401\) 48.4544i 0.120834i 0.998173 + 0.0604169i \(0.0192430\pi\)
−0.998173 + 0.0604169i \(0.980757\pi\)
\(402\) 0 0
\(403\) −58.4842 + 141.193i −0.145122 + 0.350356i
\(404\) −62.4178 + 2.80791i −0.154500 + 0.00695028i
\(405\) 0 0
\(406\) 40.0932 + 180.284i 0.0987516 + 0.444050i
\(407\) 185.029 185.029i 0.454616 0.454616i
\(408\) 0 0
\(409\) −242.037 + 242.037i −0.591778 + 0.591778i −0.938111 0.346334i \(-0.887427\pi\)
0.346334 + 0.938111i \(0.387427\pi\)
\(410\) −129.900 + 204.201i −0.316830 + 0.498050i
\(411\) 0 0
\(412\) 23.2478 + 49.6834i 0.0564266 + 0.120591i
\(413\) 167.777 405.049i 0.406239 0.980749i
\(414\) 0 0
\(415\) 800.803i 1.92965i
\(416\) 265.755 84.7589i 0.638833 0.203747i
\(417\) 0 0
\(418\) −171.445 30.1135i −0.410155 0.0720419i
\(419\) −163.261 67.6248i −0.389644 0.161396i 0.179256 0.983802i \(-0.442631\pi\)
−0.568900 + 0.822407i \(0.692631\pi\)
\(420\) 0 0
\(421\) −624.400 + 258.635i −1.48314 + 0.614335i −0.969810 0.243860i \(-0.921586\pi\)
−0.513325 + 0.858195i \(0.671586\pi\)
\(422\) 144.238 + 91.7555i 0.341795 + 0.217430i
\(423\) 0 0
\(424\) 705.228 + 91.4225i 1.66327 + 0.215619i
\(425\) −621.309 621.309i −1.46190 1.46190i
\(426\) 0 0
\(427\) −92.6933 + 38.3948i −0.217080 + 0.0899176i
\(428\) 597.426 26.8757i 1.39585 0.0627936i
\(429\) 0 0
\(430\) 217.006 + 309.481i 0.504665 + 0.719723i
\(431\) −606.510 −1.40722 −0.703608 0.710588i \(-0.748429\pi\)
−0.703608 + 0.710588i \(0.748429\pi\)
\(432\) 0 0
\(433\) 3.82972i 0.00884462i −0.999990 0.00442231i \(-0.998592\pi\)
0.999990 0.00442231i \(-0.00140767\pi\)
\(434\) 121.322 + 173.023i 0.279545 + 0.398670i
\(435\) 0 0
\(436\) 102.572 + 93.7403i 0.235256 + 0.215001i
\(437\) −68.2580 164.789i −0.156197 0.377092i
\(438\) 0 0
\(439\) −36.3389 + 36.3389i −0.0827765 + 0.0827765i −0.747283 0.664506i \(-0.768642\pi\)
0.664506 + 0.747283i \(0.268642\pi\)
\(440\) −109.068 403.843i −0.247883 0.917826i
\(441\) 0 0
\(442\) −361.571 230.010i −0.818034 0.520385i
\(443\) 208.435 + 503.207i 0.470508 + 1.13591i 0.963939 + 0.266122i \(0.0857425\pi\)
−0.493431 + 0.869785i \(0.664258\pi\)
\(444\) 0 0
\(445\) 460.995 1112.94i 1.03594 2.50099i
\(446\) −735.631 129.210i −1.64940 0.289709i
\(447\) 0 0
\(448\) 98.3497 372.957i 0.219530 0.832494i
\(449\) −431.670 −0.961402 −0.480701 0.876884i \(-0.659618\pi\)
−0.480701 + 0.876884i \(0.659618\pi\)
\(450\) 0 0
\(451\) 96.2316 + 39.8604i 0.213374 + 0.0883823i
\(452\) −171.646 + 473.542i −0.379749 + 1.04766i
\(453\) 0 0
\(454\) 8.96966 14.1001i 0.0197570 0.0310575i
\(455\) 289.528 + 289.528i 0.636325 + 0.636325i
\(456\) 0 0
\(457\) −187.054 187.054i −0.409309 0.409309i 0.472189 0.881497i \(-0.343464\pi\)
−0.881497 + 0.472189i \(0.843464\pi\)
\(458\) −77.6358 349.100i −0.169510 0.762227i
\(459\) 0 0
\(460\) 289.166 316.409i 0.628623 0.687845i
\(461\) −253.784 105.121i −0.550508 0.228028i 0.0900508 0.995937i \(-0.471297\pi\)
−0.640558 + 0.767909i \(0.721297\pi\)
\(462\) 0 0
\(463\) −765.246 −1.65280 −0.826400 0.563084i \(-0.809615\pi\)
−0.826400 + 0.563084i \(0.809615\pi\)
\(464\) 217.161 113.778i 0.468020 0.245211i
\(465\) 0 0
\(466\) 32.4673 22.7659i 0.0696723 0.0488538i
\(467\) 110.687 267.223i 0.237018 0.572211i −0.759954 0.649977i \(-0.774779\pi\)
0.996972 + 0.0777657i \(0.0247786\pi\)
\(468\) 0 0
\(469\) −247.677 597.945i −0.528096 1.27494i
\(470\) 91.4014 + 410.999i 0.194471 + 0.874466i
\(471\) 0 0
\(472\) −577.147 74.8186i −1.22277 0.158514i
\(473\) 115.030 115.030i 0.243193 0.243193i
\(474\) 0 0
\(475\) −177.468 428.447i −0.373618 0.901993i
\(476\) −536.698 + 251.131i −1.12752 + 0.527586i
\(477\) 0 0
\(478\) −79.9076 + 454.937i −0.167171 + 0.951751i
\(479\) 158.059i 0.329977i −0.986296 0.164988i \(-0.947241\pi\)
0.986296 0.164988i \(-0.0527586\pi\)
\(480\) 0 0
\(481\) 339.994 0.706848
\(482\) −219.454 38.5461i −0.455299 0.0799712i
\(483\) 0 0
\(484\) 275.315 128.825i 0.568833 0.266168i
\(485\) −458.803 + 190.042i −0.945985 + 0.391840i
\(486\) 0 0
\(487\) −675.116 675.116i −1.38628 1.38628i −0.832996 0.553280i \(-0.813376\pi\)
−0.553280 0.832996i \(-0.686624\pi\)
\(488\) 81.2855 + 105.499i 0.166569 + 0.216187i
\(489\) 0 0
\(490\) −192.931 + 42.9057i −0.393738 + 0.0875627i
\(491\) −87.1226 + 36.0874i −0.177439 + 0.0734977i −0.469634 0.882861i \(-0.655614\pi\)
0.292195 + 0.956359i \(0.405614\pi\)
\(492\) 0 0
\(493\) −347.963 144.131i −0.705808 0.292355i
\(494\) −129.850 185.184i −0.262854 0.374866i
\(495\) 0 0
\(496\) 179.741 215.361i 0.362381 0.434196i
\(497\) 21.7979i 0.0438590i
\(498\) 0 0
\(499\) 164.812 397.892i 0.330285 0.797378i −0.668284 0.743906i \(-0.732971\pi\)
0.998569 0.0534724i \(-0.0170289\pi\)
\(500\) 226.026 247.320i 0.452052 0.494640i
\(501\) 0 0
\(502\) 476.610 105.993i 0.949423 0.211141i
\(503\) 270.905 270.905i 0.538578 0.538578i −0.384533 0.923111i \(-0.625638\pi\)
0.923111 + 0.384533i \(0.125638\pi\)
\(504\) 0 0
\(505\) −86.0864 + 86.0864i −0.170468 + 0.170468i
\(506\) −155.654 99.0181i −0.307617 0.195688i
\(507\) 0 0
\(508\) −108.253 + 298.650i −0.213096 + 0.587893i
\(509\) 194.137 468.689i 0.381409 0.920803i −0.610285 0.792182i \(-0.708945\pi\)
0.991694 0.128621i \(-0.0410551\pi\)
\(510\) 0 0
\(511\) 262.081i 0.512878i
\(512\) −511.991 + 3.04640i −0.999982 + 0.00595000i
\(513\) 0 0
\(514\) −96.4230 + 548.964i −0.187593 + 1.06802i
\(515\) 98.7463 + 40.9021i 0.191740 + 0.0794215i
\(516\) 0 0
\(517\) 167.416 69.3458i 0.323821 0.134131i
\(518\) 252.335 396.665i 0.487133 0.765763i
\(519\) 0 0
\(520\) 270.828 471.243i 0.520822 0.906237i
\(521\) 240.434 + 240.434i 0.461486 + 0.461486i 0.899142 0.437656i \(-0.144191\pi\)
−0.437656 + 0.899142i \(0.644191\pi\)
\(522\) 0 0
\(523\) 846.467 350.618i 1.61848 0.670398i 0.624611 0.780936i \(-0.285257\pi\)
0.993872 + 0.110538i \(0.0352574\pi\)
\(524\) 170.235 + 155.578i 0.324875 + 0.296904i
\(525\) 0 0
\(526\) 628.078 440.404i 1.19407 0.837271i
\(527\) −430.941 −0.817725
\(528\) 0 0
\(529\) 339.966i 0.642657i
\(530\) 1134.52 795.521i 2.14061 1.50098i
\(531\) 0 0
\(532\) −312.422 + 14.0546i −0.587260 + 0.0264183i
\(533\) 51.7916 + 125.036i 0.0971699 + 0.234589i
\(534\) 0 0
\(535\) 823.967 823.967i 1.54012 1.54012i
\(536\) −680.555 + 524.356i −1.26969 + 0.978276i
\(537\) 0 0
\(538\) 63.8502 100.371i 0.118681 0.186563i
\(539\) 32.5523 + 78.5883i 0.0603939 + 0.145804i
\(540\) 0 0
\(541\) −6.87337 + 16.5938i −0.0127049 + 0.0306724i −0.930105 0.367294i \(-0.880284\pi\)
0.917400 + 0.397967i \(0.130284\pi\)
\(542\) −153.613 + 874.563i −0.283419 + 1.61358i
\(543\) 0 0
\(544\) 507.584 + 600.870i 0.933059 + 1.10454i
\(545\) 270.752 0.496793
\(546\) 0 0
\(547\) 354.417 + 146.804i 0.647929 + 0.268381i 0.682349 0.731026i \(-0.260958\pi\)
−0.0344200 + 0.999407i \(0.510958\pi\)
\(548\) 121.638 + 259.955i 0.221967 + 0.474370i
\(549\) 0 0
\(550\) −404.696 257.444i −0.735811 0.468079i
\(551\) −140.560 140.560i −0.255100 0.255100i
\(552\) 0 0
\(553\) −386.348 386.348i −0.698639 0.698639i
\(554\) −118.015 + 26.2452i −0.213024 + 0.0473741i
\(555\) 0 0
\(556\) −576.171 + 25.9195i −1.03628 + 0.0466178i
\(557\) 549.588 + 227.647i 0.986692 + 0.408701i 0.816900 0.576779i \(-0.195690\pi\)
0.169792 + 0.985480i \(0.445690\pi\)
\(558\) 0 0
\(559\) 211.371 0.378123
\(560\) −348.790 665.715i −0.622839 1.18878i
\(561\) 0 0
\(562\) 259.445 + 370.005i 0.461646 + 0.658372i
\(563\) 150.445 363.205i 0.267219 0.645125i −0.732131 0.681164i \(-0.761474\pi\)
0.999350 + 0.0360391i \(0.0114741\pi\)
\(564\) 0 0
\(565\) 375.583 + 906.737i 0.664748 + 1.60484i
\(566\) 946.190 210.422i 1.67171 0.371770i
\(567\) 0 0
\(568\) 27.9344 7.54442i 0.0491803 0.0132824i
\(569\) −510.987 + 510.987i −0.898045 + 0.898045i −0.995263 0.0972186i \(-0.969005\pi\)
0.0972186 + 0.995263i \(0.469005\pi\)
\(570\) 0 0
\(571\) 328.247 + 792.459i 0.574864 + 1.38784i 0.897371 + 0.441277i \(0.145474\pi\)
−0.322507 + 0.946567i \(0.604526\pi\)
\(572\) −219.923 79.7161i −0.384480 0.139364i
\(573\) 0 0
\(574\) 184.316 + 32.3742i 0.321108 + 0.0564011i
\(575\) 491.482i 0.854752i
\(576\) 0 0
\(577\) 305.039 0.528663 0.264332 0.964432i \(-0.414849\pi\)
0.264332 + 0.964432i \(0.414849\pi\)
\(578\) 109.052 620.867i 0.188672 1.07416i
\(579\) 0 0
\(580\) 162.789 449.106i 0.280671 0.774322i
\(581\) 572.080 236.963i 0.984647 0.407854i
\(582\) 0 0
\(583\) −421.689 421.689i −0.723309 0.723309i
\(584\) 335.861 90.7080i 0.575104 0.155322i
\(585\) 0 0
\(586\) −223.962 1007.08i −0.382188 1.71856i
\(587\) 388.900 161.088i 0.662521 0.274425i −0.0259780 0.999663i \(-0.508270\pi\)
0.688499 + 0.725237i \(0.258270\pi\)
\(588\) 0 0
\(589\) −210.132 87.0394i −0.356760 0.147775i
\(590\) −928.475 + 651.040i −1.57369 + 1.10346i
\(591\) 0 0
\(592\) −595.668 186.083i −1.00620 0.314330i
\(593\) 1039.64i 1.75319i 0.481228 + 0.876595i \(0.340191\pi\)
−0.481228 + 0.876595i \(0.659809\pi\)
\(594\) 0 0
\(595\) −441.839 + 1066.69i −0.742587 + 1.79276i
\(596\) 2.35235 + 52.2911i 0.00394690 + 0.0877367i
\(597\) 0 0
\(598\) −52.0351 233.983i −0.0870152 0.391276i
\(599\) −22.4929 + 22.4929i −0.0375507 + 0.0375507i −0.725633 0.688082i \(-0.758453\pi\)
0.688082 + 0.725633i \(0.258453\pi\)
\(600\) 0 0
\(601\) −640.653 + 640.653i −1.06598 + 1.06598i −0.0683147 + 0.997664i \(0.521762\pi\)
−0.997664 + 0.0683147i \(0.978238\pi\)
\(602\) 156.874 246.603i 0.260588 0.409639i
\(603\) 0 0
\(604\) 90.6211 42.4033i 0.150035 0.0702041i
\(605\) 226.654 547.192i 0.374636 0.904450i
\(606\) 0 0
\(607\) 860.149i 1.41705i −0.705686 0.708524i \(-0.749361\pi\)
0.705686 0.708524i \(-0.250639\pi\)
\(608\) 126.143 + 395.510i 0.207472 + 0.650511i
\(609\) 0 0
\(610\) 255.593 + 44.8938i 0.419005 + 0.0735964i
\(611\) 217.527 + 90.1026i 0.356018 + 0.147467i
\(612\) 0 0
\(613\) 724.830 300.235i 1.18243 0.489779i 0.297148 0.954831i \(-0.403965\pi\)
0.885283 + 0.465052i \(0.153965\pi\)
\(614\) −865.223 550.404i −1.40916 0.896424i
\(615\) 0 0
\(616\) −256.225 + 197.417i −0.415949 + 0.320482i
\(617\) 704.685 + 704.685i 1.14212 + 1.14212i 0.988063 + 0.154052i \(0.0492324\pi\)
0.154052 + 0.988063i \(0.450768\pi\)
\(618\) 0 0
\(619\) −33.0442 + 13.6874i −0.0533832 + 0.0221121i −0.409215 0.912438i \(-0.634198\pi\)
0.355832 + 0.934550i \(0.384198\pi\)
\(620\) −24.5635 546.028i −0.0396186 0.880691i
\(621\) 0 0
\(622\) −627.369 894.716i −1.00863 1.43845i
\(623\) −931.477 −1.49515
\(624\) 0 0
\(625\) 240.835i 0.385335i
\(626\) 206.375 + 294.320i 0.329673 + 0.470159i
\(627\) 0 0
\(628\) −520.772 + 569.834i −0.829255 + 0.907379i
\(629\) 366.885 + 885.738i 0.583282 + 1.40817i
\(630\) 0 0
\(631\) −718.112 + 718.112i −1.13805 + 1.13805i −0.149255 + 0.988799i \(0.547688\pi\)
−0.988799 + 0.149255i \(0.952312\pi\)
\(632\) −361.393 + 628.829i −0.571825 + 0.994982i
\(633\) 0 0
\(634\) 107.761 + 68.5514i 0.169971 + 0.108125i
\(635\) 236.870 + 571.854i 0.373023 + 0.900557i
\(636\) 0 0
\(637\) −42.2960 + 102.112i −0.0663988 + 0.160301i
\(638\) −202.495 35.5673i −0.317390 0.0557481i
\(639\) 0 0
\(640\) −732.407 + 677.389i −1.14439 + 1.05842i
\(641\) 338.159 0.527549 0.263774 0.964584i \(-0.415033\pi\)
0.263774 + 0.964584i \(0.415033\pi\)
\(642\) 0 0
\(643\) 332.477 + 137.716i 0.517071 + 0.214178i 0.625930 0.779879i \(-0.284720\pi\)
−0.108859 + 0.994057i \(0.534720\pi\)
\(644\) −311.603 112.948i −0.483856 0.175385i
\(645\) 0 0
\(646\) 342.314 538.110i 0.529898 0.832987i
\(647\) 31.2745 + 31.2745i 0.0483377 + 0.0483377i 0.730862 0.682525i \(-0.239118\pi\)
−0.682525 + 0.730862i \(0.739118\pi\)
\(648\) 0 0
\(649\) 345.103 + 345.103i 0.531746 + 0.531746i
\(650\) −135.289 608.348i −0.208138 0.935919i
\(651\) 0 0
\(652\) 422.651 + 386.262i 0.648238 + 0.592426i
\(653\) −355.409 147.215i −0.544271 0.225445i 0.0935696 0.995613i \(-0.470172\pi\)
−0.637841 + 0.770168i \(0.720172\pi\)
\(654\) 0 0
\(655\) 449.359 0.686044
\(656\) −22.3049 247.409i −0.0340014 0.377148i
\(657\) 0 0
\(658\) 266.564 186.913i 0.405113 0.284062i
\(659\) 116.271 280.702i 0.176435 0.425952i −0.810779 0.585352i \(-0.800956\pi\)
0.987214 + 0.159401i \(0.0509562\pi\)
\(660\) 0 0
\(661\) 179.920 + 434.366i 0.272194 + 0.657134i 0.999577 0.0290979i \(-0.00926347\pi\)
−0.727383 + 0.686232i \(0.759263\pi\)
\(662\) 25.2600 + 113.585i 0.0381571 + 0.171579i
\(663\) 0 0
\(664\) −501.673 651.116i −0.755532 0.980596i
\(665\) −430.892 + 430.892i −0.647957 + 0.647957i
\(666\) 0 0
\(667\) −80.6200 194.634i −0.120870 0.291805i
\(668\) −263.123 562.326i −0.393896 0.841805i
\(669\) 0 0
\(670\) −289.600 + 1648.78i −0.432240 + 2.46086i
\(671\) 111.688i 0.166449i
\(672\) 0 0
\(673\) 1168.06 1.73561 0.867803 0.496908i \(-0.165531\pi\)
0.867803 + 0.496908i \(0.165531\pi\)
\(674\) 726.484 + 127.604i 1.07787 + 0.189323i
\(675\) 0 0
\(676\) 157.684 + 336.990i 0.233260 + 0.498505i
\(677\) 604.882 250.550i 0.893474 0.370089i 0.111767 0.993734i \(-0.464349\pi\)
0.781707 + 0.623645i \(0.214349\pi\)
\(678\) 0 0
\(679\) 271.526 + 271.526i 0.399891 + 0.399891i
\(680\) 1519.91 + 197.034i 2.23516 + 0.289756i
\(681\) 0 0
\(682\) −229.630 + 51.0671i −0.336701 + 0.0748785i
\(683\) 369.863 153.202i 0.541527 0.224308i −0.0951163 0.995466i \(-0.530322\pi\)
0.636644 + 0.771158i \(0.280322\pi\)
\(684\) 0 0
\(685\) 516.663 + 214.009i 0.754253 + 0.312422i
\(686\) 426.823 + 608.709i 0.622191 + 0.887331i
\(687\) 0 0
\(688\) −370.321 115.686i −0.538258 0.168148i
\(689\) 774.863i 1.12462i
\(690\) 0 0
\(691\) 74.8080 180.602i 0.108260 0.261364i −0.860460 0.509518i \(-0.829824\pi\)
0.968721 + 0.248154i \(0.0798239\pi\)
\(692\) −917.840 838.816i −1.32636 1.21216i
\(693\) 0 0
\(694\) 848.222 188.635i 1.22222 0.271808i
\(695\) −794.653 + 794.653i −1.14339 + 1.14339i
\(696\) 0 0
\(697\) −269.851 + 269.851i −0.387160 + 0.387160i
\(698\) −108.779 69.1987i −0.155844 0.0991386i
\(699\) 0 0
\(700\) −810.157 293.661i −1.15737 0.419515i
\(701\) −250.206 + 604.050i −0.356927 + 0.861698i 0.638802 + 0.769371i \(0.279430\pi\)
−0.995729 + 0.0923265i \(0.970570\pi\)
\(702\) 0 0
\(703\) 505.998i 0.719769i
\(704\) 341.674 + 260.029i 0.485333 + 0.369359i
\(705\) 0 0
\(706\) 84.9533 483.663i 0.120330 0.685076i
\(707\) 86.9722 + 36.0251i 0.123016 + 0.0509548i
\(708\) 0 0
\(709\) −771.157 + 319.424i −1.08767 + 0.450527i −0.853193 0.521595i \(-0.825337\pi\)
−0.234476 + 0.972122i \(0.575337\pi\)
\(710\) 30.2618 47.5709i 0.0426223 0.0670013i
\(711\) 0 0
\(712\) 322.391 + 1193.70i 0.452796 + 1.67655i
\(713\) −170.446 170.446i −0.239055 0.239055i
\(714\) 0 0
\(715\) −421.107 + 174.428i −0.588961 + 0.243956i
\(716\) 345.126 377.640i 0.482020 0.527431i
\(717\) 0 0
\(718\) 142.892 100.195i 0.199013 0.139547i
\(719\) −263.077 −0.365893 −0.182947 0.983123i \(-0.558564\pi\)
−0.182947 + 0.983123i \(0.558564\pi\)
\(720\) 0 0
\(721\) 82.6459i 0.114627i
\(722\) −315.553 + 221.264i −0.437054 + 0.306459i
\(723\) 0 0
\(724\) −18.2832 406.421i −0.0252530 0.561355i
\(725\) −209.609 506.041i −0.289116 0.697988i
\(726\) 0 0
\(727\) 320.334 320.334i 0.440625 0.440625i −0.451597 0.892222i \(-0.649146\pi\)
0.892222 + 0.451597i \(0.149146\pi\)
\(728\) −416.788 54.0304i −0.572511 0.0742176i
\(729\) 0 0
\(730\) 363.844 571.954i 0.498416 0.783499i
\(731\) 228.089 + 550.655i 0.312023 + 0.753289i
\(732\) 0 0
\(733\) 119.193 287.758i 0.162610 0.392575i −0.821482 0.570234i \(-0.806852\pi\)
0.984092 + 0.177659i \(0.0568524\pi\)
\(734\) −42.6782 + 242.979i −0.0581446 + 0.331034i
\(735\) 0 0
\(736\) −36.8966 + 438.417i −0.0501313 + 0.595676i
\(737\) 720.473 0.977576
\(738\) 0 0
\(739\) −760.509 315.013i −1.02911 0.426269i −0.196716 0.980461i \(-0.563028\pi\)
−0.832389 + 0.554191i \(0.813028\pi\)
\(740\) −1101.37 + 515.352i −1.48834 + 0.696422i
\(741\) 0 0
\(742\) −904.020 575.084i −1.21836 0.775046i
\(743\) −89.2306 89.2306i −0.120095 0.120095i 0.644505 0.764600i \(-0.277063\pi\)
−0.764600 + 0.644505i \(0.777063\pi\)
\(744\) 0 0
\(745\) 72.1196 + 72.1196i 0.0968049 + 0.0968049i
\(746\) 59.1492 13.1541i 0.0792885 0.0176328i
\(747\) 0 0
\(748\) −29.6436 658.954i −0.0396304 0.880955i
\(749\) −832.445 344.810i −1.11141 0.460361i
\(750\) 0 0
\(751\) −418.271 −0.556953 −0.278476 0.960443i \(-0.589829\pi\)
−0.278476 + 0.960443i \(0.589829\pi\)
\(752\) −331.792 276.915i −0.441213 0.368238i
\(753\) 0 0
\(754\) −153.367 218.722i −0.203404 0.290082i
\(755\) 74.6042 180.110i 0.0988135 0.238557i
\(756\) 0 0
\(757\) −212.675 513.443i −0.280944 0.678260i 0.718914 0.695099i \(-0.244640\pi\)
−0.999858 + 0.0168395i \(0.994640\pi\)
\(758\) −1046.25 + 232.675i −1.38028 + 0.306959i
\(759\) 0 0
\(760\) 701.330 + 403.060i 0.922802 + 0.530343i
\(761\) −60.9342 + 60.9342i −0.0800712 + 0.0800712i −0.746008 0.665937i \(-0.768032\pi\)
0.665937 + 0.746008i \(0.268032\pi\)
\(762\) 0 0
\(763\) −80.1175 193.421i −0.105003 0.253500i
\(764\) 90.7333 250.317i 0.118761 0.327640i
\(765\) 0 0
\(766\) −1193.35 209.607i −1.55790 0.273638i
\(767\) 634.135i 0.826773i
\(768\) 0 0
\(769\) 387.688 0.504146 0.252073 0.967708i \(-0.418888\pi\)
0.252073 + 0.967708i \(0.418888\pi\)
\(770\) −109.033 + 620.755i −0.141601 + 0.806176i
\(771\) 0 0
\(772\) −1037.47 376.054i −1.34387 0.487117i
\(773\) −19.2892 + 7.98984i −0.0249537 + 0.0103361i −0.395125 0.918627i \(-0.629299\pi\)
0.370172 + 0.928963i \(0.379299\pi\)
\(774\) 0 0
\(775\) −443.154 443.154i −0.571812 0.571812i
\(776\) 253.988 441.942i 0.327304 0.569513i
\(777\) 0 0
\(778\) 200.462 + 901.404i 0.257663 + 1.15862i
\(779\) −186.085 + 77.0791i −0.238877 + 0.0989462i
\(780\) 0 0
\(781\) −22.4183 9.28595i −0.0287046 0.0118898i
\(782\) 553.412 388.049i 0.707688 0.496226i
\(783\) 0 0
\(784\) 129.990 155.750i 0.165803 0.198661i
\(785\) 1504.16i 1.91613i
\(786\) 0 0
\(787\) 521.707 1259.51i 0.662906 1.60040i −0.130321 0.991472i \(-0.541601\pi\)
0.793