Properties

Label 108.5.f.a.19.7
Level 108
Weight 5
Character 108.19
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.7
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.58866 - 3.04940i) q^{2} +(-2.59770 + 15.7877i) q^{4} +(5.51579 + 9.55363i) q^{5} +(10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +O(q^{10})\) \(q+(-2.58866 - 3.04940i) q^{2} +(-2.59770 + 15.7877i) q^{4} +(5.51579 + 9.55363i) q^{5} +(10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +(14.8544 - 41.5509i) q^{10} +(-189.995 - 109.694i) q^{11} +(18.5350 + 32.1036i) q^{13} +(-8.54488 - 46.8884i) q^{14} +(-242.504 - 82.0235i) q^{16} -284.021 q^{17} +45.4901i q^{19} +(-165.158 + 62.2643i) q^{20} +(157.332 + 863.330i) q^{22} +(-174.319 + 100.643i) q^{23} +(251.652 - 435.874i) q^{25} +(49.9160 - 139.626i) q^{26} +(-120.862 + 147.435i) q^{28} +(-614.153 + 1063.74i) q^{29} +(-1311.83 + 757.384i) q^{31} +(377.637 + 951.823i) q^{32} +(735.233 + 866.094i) q^{34} +131.443i q^{35} -1521.29 q^{37} +(138.718 - 117.758i) q^{38} +(617.407 + 342.453i) q^{40} +(-1316.97 - 2281.07i) q^{41} +(-34.6057 - 19.9796i) q^{43} +(2225.36 - 2714.63i) q^{44} +(758.153 + 271.038i) q^{46} +(2498.36 + 1442.43i) q^{47} +(-1129.51 - 1956.38i) q^{49} +(-1980.60 + 360.941i) q^{50} +(-554.991 + 209.230i) q^{52} -1415.13 q^{53} -2420.19i q^{55} +(762.458 - 13.1019i) q^{56} +(4833.61 - 880.870i) q^{58} +(-2453.33 + 1416.43i) q^{59} +(2628.64 - 4552.93i) q^{61} +(5705.44 + 2039.68i) q^{62} +(1924.92 - 3615.51i) q^{64} +(-204.471 + 354.154i) q^{65} +(805.917 - 465.296i) q^{67} +(737.801 - 4484.04i) q^{68} +(400.823 - 340.261i) q^{70} -1162.75i q^{71} -2162.87 q^{73} +(3938.11 + 4639.03i) q^{74} +(-718.185 - 118.170i) q^{76} +(-1307.02 - 2263.82i) q^{77} +(6482.54 + 3742.70i) q^{79} +(-553.978 - 2769.22i) q^{80} +(-3546.69 + 9920.88i) q^{82} +(966.756 + 558.157i) q^{83} +(-1566.60 - 2713.43i) q^{85} +(28.6565 + 157.247i) q^{86} +(-14038.7 + 241.238i) q^{88} +6739.71 q^{89} +441.696i q^{91} +(-1136.10 - 3013.54i) q^{92} +(-2068.85 - 11352.5i) q^{94} +(-434.596 + 250.914i) q^{95} +(-6023.28 + 10432.6i) q^{97} +(-3041.85 + 8508.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58866 3.04940i −0.647164 0.762350i
\(3\) 0 0
\(4\) −2.59770 + 15.7877i −0.162356 + 0.986732i
\(5\) 5.51579 + 9.55363i 0.220632 + 0.382145i 0.955000 0.296606i \(-0.0958548\pi\)
−0.734368 + 0.678751i \(0.762521\pi\)
\(6\) 0 0
\(7\) 10.3188 + 5.95759i 0.210589 + 0.121583i 0.601585 0.798809i \(-0.294536\pi\)
−0.390996 + 0.920392i \(0.627869\pi\)
\(8\) 54.8676 32.9476i 0.857307 0.514806i
\(9\) 0 0
\(10\) 14.8544 41.5509i 0.148544 0.415509i
\(11\) −189.995 109.694i −1.57021 0.906559i −0.996143 0.0877473i \(-0.972033\pi\)
−0.574063 0.818811i \(1.30537\pi\)
\(12\) 0 0
\(13\) 18.5350 + 32.1036i 0.109675 + 0.189962i 0.915639 0.402003i \(-0.131686\pi\)
−0.805964 + 0.591965i \(0.798352\pi\)
\(14\) −8.54488 46.8884i −0.0435963 0.239227i
\(15\) 0 0
\(16\) −242.504 82.0235i −0.947281 0.320404i
\(17\) −284.021 −0.982771 −0.491386 0.870942i \(-0.663509\pi\)
−0.491386 + 0.870942i \(0.663509\pi\)
\(18\) 0 0
\(19\) 45.4901i 0.126011i 0.998013 + 0.0630057i \(0.0200686\pi\)
−0.998013 + 0.0630057i \(0.979931\pi\)
\(20\) −165.158 + 62.2643i −0.412896 + 0.155661i
\(21\) 0 0
\(22\) 157.332 + 863.330i 0.325066 + 1.78374i
\(23\) −174.319 + 100.643i −0.329525 + 0.190252i −0.655630 0.755082i \(-0.727597\pi\)
0.326105 + 0.945334i \(0.394264\pi\)
\(24\) 0 0
\(25\) 251.652 435.874i 0.402643 0.697399i
\(26\) 49.9160 139.626i 0.0738402 0.206547i
\(27\) 0 0
\(28\) −120.862 + 147.435i −0.154161 + 0.188055i
\(29\) −614.153 + 1063.74i −0.730265 + 1.26486i 0.226505 + 0.974010i \(0.427270\pi\)
−0.956770 + 0.290846i \(0.906063\pi\)
\(30\) 0 0
\(31\) −1311.83 + 757.384i −1.36507 + 0.788121i −0.990293 0.138996i \(-0.955613\pi\)
−0.374773 + 0.927117i \(0.622279\pi\)
\(32\) 377.637 + 951.823i 0.368786 + 0.929514i
\(33\) 0 0
\(34\) 735.233 + 866.094i 0.636015 + 0.749216i
\(35\) 131.443i 0.107301i
\(36\) 0 0
\(37\) −1521.29 −1.11124 −0.555622 0.831435i \(-0.687520\pi\)
−0.555622 + 0.831435i \(0.687520\pi\)
\(38\) 138.718 117.758i 0.0960648 0.0815501i
\(39\) 0 0
\(40\) 617.407 + 342.453i 0.385879 + 0.214033i
\(41\) −1316.97 2281.07i −0.783447 1.35697i −0.929923 0.367755i \(-0.880126\pi\)
0.146476 0.989214i \(-0.453207\pi\)
\(42\) 0 0
\(43\) −34.6057 19.9796i −0.0187159 0.0108056i 0.490613 0.871378i \(-0.336773\pi\)
−0.509329 + 0.860572i \(0.670106\pi\)
\(44\) 2225.36 2714.63i 1.14946 1.40219i
\(45\) 0 0
\(46\) 758.153 + 271.038i 0.358295 + 0.128090i
\(47\) 2498.36 + 1442.43i 1.13099 + 0.652978i 0.944184 0.329419i \(-0.106853\pi\)
0.186807 + 0.982397i \(0.440186\pi\)
\(48\) 0 0
\(49\) −1129.51 1956.38i −0.470435 0.814817i
\(50\) −1980.60 + 360.941i −0.792239 + 0.144376i
\(51\) 0 0
\(52\) −554.991 + 209.230i −0.205248 + 0.0773780i
\(53\) −1415.13 −0.503783 −0.251892 0.967755i \(-0.581053\pi\)
−0.251892 + 0.967755i \(0.581053\pi\)
\(54\) 0 0
\(55\) 2420.19i 0.800062i
\(56\) 762.458 13.1019i 0.243131 0.00417791i
\(57\) 0 0
\(58\) 4833.61 880.870i 1.43686 0.261852i
\(59\) −2453.33 + 1416.43i −0.704778 + 0.406904i −0.809125 0.587637i \(-0.800058\pi\)
0.104346 + 0.994541i \(0.466725\pi\)
\(60\) 0 0
\(61\) 2628.64 4552.93i 0.706433 1.22358i −0.259739 0.965679i \(-0.583637\pi\)
0.966172 0.257899i \(-0.0830300\pi\)
\(62\) 5705.44 + 2039.68i 1.48425 + 0.530614i
\(63\) 0 0
\(64\) 1924.92 3615.51i 0.469950 0.882693i
\(65\) −204.471 + 354.154i −0.0483954 + 0.0838233i
\(66\) 0 0
\(67\) 805.917 465.296i 0.179531 0.103653i −0.407541 0.913187i \(-0.633614\pi\)
0.587073 + 0.809534i \(0.300280\pi\)
\(68\) 737.801 4484.04i 0.159559 0.969732i
\(69\) 0 0
\(70\) 400.823 340.261i 0.0818006 0.0694411i
\(71\) 1162.75i 0.230659i −0.993327 0.115329i \(-0.963208\pi\)
0.993327 0.115329i \(-0.0367923\pi\)
\(72\) 0 0
\(73\) −2162.87 −0.405867 −0.202934 0.979192i \(-0.565048\pi\)
−0.202934 + 0.979192i \(0.565048\pi\)
\(74\) 3938.11 + 4639.03i 0.719158 + 0.847157i
\(75\) 0 0
\(76\) −718.185 118.170i −0.124339 0.0204587i
\(77\) −1307.02 2263.82i −0.220445 0.381822i
\(78\) 0 0
\(79\) 6482.54 + 3742.70i 1.03870 + 0.599695i 0.919466 0.393171i \(-0.128622\pi\)
0.119237 + 0.992866i \(0.461955\pi\)
\(80\) −553.978 2769.22i −0.0865591 0.432690i
\(81\) 0 0
\(82\) −3546.69 + 9920.88i −0.527467 + 1.47544i
\(83\) 966.756 + 558.157i 0.140333 + 0.0810215i 0.568523 0.822667i \(-0.307515\pi\)
−0.428190 + 0.903689i \(0.640848\pi\)
\(84\) 0 0
\(85\) −1566.60 2713.43i −0.216830 0.375561i
\(86\) 28.6565 + 157.247i 0.00387459 + 0.0212611i
\(87\) 0 0
\(88\) −14038.7 + 241.238i −1.81285 + 0.0311516i
\(89\) 6739.71 0.850866 0.425433 0.904990i \(-0.360122\pi\)
0.425433 + 0.904990i \(0.360122\pi\)
\(90\) 0 0
\(91\) 441.696i 0.0533385i
\(92\) −1136.10 3013.54i −0.134227 0.356042i
\(93\) 0 0
\(94\) −2068.85 11352.5i −0.234139 1.28480i
\(95\) −434.596 + 250.914i −0.0481546 + 0.0278021i
\(96\) 0 0
\(97\) −6023.28 + 10432.6i −0.640161 + 1.10879i 0.345235 + 0.938516i \(0.387799\pi\)
−0.985396 + 0.170276i \(0.945534\pi\)
\(98\) −3041.85 + 8508.73i −0.316727 + 0.885957i
\(99\) 0 0
\(100\) 6227.74 + 5105.28i 0.622774 + 0.510528i
\(101\) −4777.60 + 8275.04i −0.468346 + 0.811199i −0.999346 0.0361728i \(-0.988483\pi\)
0.530999 + 0.847372i \(0.321817\pi\)
\(102\) 0 0
\(103\) −9962.26 + 5751.71i −0.939039 + 0.542154i −0.889659 0.456626i \(-0.849058\pi\)
−0.0493798 + 0.998780i \(0.515724\pi\)
\(104\) 2074.71 + 1150.77i 0.191819 + 0.106395i
\(105\) 0 0
\(106\) 3663.28 + 4315.29i 0.326031 + 0.384059i
\(107\) 6602.72i 0.576707i −0.957524 0.288353i \(-0.906892\pi\)
0.957524 0.288353i \(-0.0931078\pi\)
\(108\) 0 0
\(109\) 12045.3 1.01383 0.506913 0.861997i \(-0.330786\pi\)
0.506913 + 0.861997i \(0.330786\pi\)
\(110\) −7380.12 + 6265.04i −0.609928 + 0.517772i
\(111\) 0 0
\(112\) −2013.70 2291.13i −0.160531 0.182647i
\(113\) 1865.35 + 3230.88i 0.146084 + 0.253025i 0.929777 0.368124i \(-0.120000\pi\)
−0.783693 + 0.621149i \(0.786666\pi\)
\(114\) 0 0
\(115\) −1923.01 1110.25i −0.145407 0.0839510i
\(116\) −15198.7 12459.4i −1.12951 0.925933i
\(117\) 0 0
\(118\) 10670.1 + 3814.54i 0.766311 + 0.273954i
\(119\) −2930.77 1692.08i −0.206960 0.119489i
\(120\) 0 0
\(121\) 16744.9 + 29003.0i 1.14370 + 1.98094i
\(122\) −20688.4 + 3770.21i −1.38997 + 0.253307i
\(123\) 0 0
\(124\) −8549.63 22678.2i −0.556037 1.47491i
\(125\) 12447.0 0.796607
\(126\) 0 0
\(127\) 26549.7i 1.64608i −0.567980 0.823042i \(-0.692275\pi\)
0.567980 0.823042i \(-0.307725\pi\)
\(128\) −16008.1 + 3489.47i −0.977056 + 0.212981i
\(129\) 0 0
\(130\) 1609.26 293.269i 0.0952226 0.0173532i
\(131\) 1142.84 659.821i 0.0665954 0.0384489i −0.466333 0.884609i \(-0.654425\pi\)
0.532928 + 0.846161i \(0.321092\pi\)
\(132\) 0 0
\(133\) −271.011 + 469.405i −0.0153209 + 0.0265366i
\(134\) −3505.12 1253.07i −0.195206 0.0697856i
\(135\) 0 0
\(136\) −15583.6 + 9357.79i −0.842537 + 0.505936i
\(137\) 12906.5 22354.7i 0.687648 1.19104i −0.284949 0.958543i \(-0.591977\pi\)
0.972597 0.232499i \(-0.0746901\pi\)
\(138\) 0 0
\(139\) −11377.8 + 6569.00i −0.588885 + 0.339993i −0.764656 0.644438i \(-0.777091\pi\)
0.175772 + 0.984431i \(0.443758\pi\)
\(140\) −2075.19 341.450i −0.105877 0.0174209i
\(141\) 0 0
\(142\) −3545.69 + 3009.96i −0.175843 + 0.149274i
\(143\) 8132.70i 0.397706i
\(144\) 0 0
\(145\) −13550.2 −0.644478
\(146\) 5598.92 + 6595.45i 0.262663 + 0.309413i
\(147\) 0 0
\(148\) 3951.86 24017.7i 0.180417 1.09650i
\(149\) 12968.2 + 22461.6i 0.584128 + 1.01174i 0.994984 + 0.100038i \(0.0318965\pi\)
−0.410856 + 0.911700i \(0.634770\pi\)
\(150\) 0 0
\(151\) 24591.2 + 14197.8i 1.07852 + 0.622681i 0.930496 0.366303i \(-0.119377\pi\)
0.148020 + 0.988984i \(0.452710\pi\)
\(152\) 1498.79 + 2495.93i 0.0648714 + 0.108030i
\(153\) 0 0
\(154\) −3519.88 + 9845.88i −0.148418 + 0.415158i
\(155\) −14471.5 8355.15i −0.602353 0.347769i
\(156\) 0 0
\(157\) 2760.19 + 4780.78i 0.111980 + 0.193954i 0.916568 0.399878i \(-0.130948\pi\)
−0.804589 + 0.593832i \(0.797614\pi\)
\(158\) −5368.10 29456.4i −0.215033 1.17996i
\(159\) 0 0
\(160\) −7010.39 + 8857.86i −0.273844 + 0.346010i
\(161\) −2398.36 −0.0925257
\(162\) 0 0
\(163\) 407.281i 0.0153292i 0.999971 + 0.00766459i \(0.00243974\pi\)
−0.999971 + 0.00766459i \(0.997560\pi\)
\(164\) 39433.9 14866.5i 1.46616 0.552739i
\(165\) 0 0
\(166\) −800.556 4392.91i −0.0290520 0.159417i
\(167\) 20561.9 11871.4i 0.737277 0.425667i −0.0838016 0.996482i \(-0.526706\pi\)
0.821078 + 0.570816i \(0.193373\pi\)
\(168\) 0 0
\(169\) 13593.4 23544.5i 0.475943 0.824357i
\(170\) −4218.95 + 11801.3i −0.145984 + 0.408351i
\(171\) 0 0
\(172\) 405.328 494.444i 0.0137009 0.0167132i
\(173\) −1413.25 + 2447.82i −0.0472200 + 0.0817874i −0.888669 0.458549i \(-0.848370\pi\)
0.841449 + 0.540336i \(0.181703\pi\)
\(174\) 0 0
\(175\) 5193.52 2998.48i 0.169584 0.0979095i
\(176\) 37077.0 + 42185.2i 1.19696 + 1.36187i
\(177\) 0 0
\(178\) −17446.8 20552.1i −0.550650 0.648658i
\(179\) 45743.4i 1.42765i 0.700323 + 0.713826i \(0.253039\pi\)
−0.700323 + 0.713826i \(0.746961\pi\)
\(180\) 0 0
\(181\) −24226.2 −0.739483 −0.369742 0.929135i \(-0.620554\pi\)
−0.369742 + 0.929135i \(0.620554\pi\)
\(182\) 1346.91 1143.40i 0.0406626 0.0345188i
\(183\) 0 0
\(184\) −6248.52 + 11265.4i −0.184562 + 0.332745i
\(185\) −8391.13 14533.9i −0.245176 0.424657i
\(186\) 0 0
\(187\) 53962.5 + 31155.3i 1.54315 + 0.890940i
\(188\) −29262.6 + 35696.4i −0.827938 + 1.00997i
\(189\) 0 0
\(190\) 1890.16 + 675.726i 0.0523589 + 0.0187182i
\(191\) 19504.6 + 11261.0i 0.534651 + 0.308681i 0.742908 0.669393i \(-0.233446\pi\)
−0.208257 + 0.978074i \(0.566779\pi\)
\(192\) 0 0
\(193\) −9144.35 15838.5i −0.245493 0.425205i 0.716777 0.697302i \(-0.245616\pi\)
−0.962270 + 0.272097i \(0.912283\pi\)
\(194\) 47405.5 8639.10i 1.25958 0.229544i
\(195\) 0 0
\(196\) 33820.9 12750.4i 0.880385 0.331903i
\(197\) −36300.2 −0.935356 −0.467678 0.883899i \(-0.654909\pi\)
−0.467678 + 0.883899i \(0.654909\pi\)
\(198\) 0 0
\(199\) 47336.5i 1.19533i −0.801744 0.597667i \(-0.796094\pi\)
0.801744 0.597667i \(-0.203906\pi\)
\(200\) −553.433 32206.7i −0.0138358 0.805168i
\(201\) 0 0
\(202\) 37601.5 6852.44i 0.921515 0.167935i
\(203\) −12674.7 + 7317.73i −0.307571 + 0.177576i
\(204\) 0 0
\(205\) 14528.3 25163.8i 0.345706 0.598781i
\(206\) 43328.2 + 15489.7i 1.02102 + 0.365014i
\(207\) 0 0
\(208\) −1861.57 9305.56i −0.0430280 0.215088i
\(209\) 4989.97 8642.89i 0.114237 0.197864i
\(210\) 0 0
\(211\) −40261.7 + 23245.1i −0.904330 + 0.522115i −0.878602 0.477554i \(-0.841524\pi\)
−0.0257275 + 0.999669i \(0.508190\pi\)
\(212\) 3676.08 22341.6i 0.0817924 0.497099i
\(213\) 0 0
\(214\) −20134.3 + 17092.2i −0.439653 + 0.373224i
\(215\) 440.814i 0.00953626i
\(216\) 0 0
\(217\) −18048.7 −0.383290
\(218\) −31181.1 36730.9i −0.656113 0.772891i
\(219\) 0 0
\(220\) 38209.2 + 6286.92i 0.789447 + 0.129895i
\(221\) −5264.34 9118.10i −0.107785 0.186689i
\(222\) 0 0
\(223\) −71531.9 41298.9i −1.43843 0.830480i −0.440693 0.897658i \(-0.645267\pi\)
−0.997741 + 0.0671780i \(0.978600\pi\)
\(224\) −1773.79 + 12071.5i −0.0353514 + 0.240583i
\(225\) 0 0
\(226\) 5023.49 14051.8i 0.0983533 0.275116i
\(227\) −25722.3 14850.8i −0.499182 0.288203i 0.229194 0.973381i \(-0.426391\pi\)
−0.728376 + 0.685178i \(0.759724\pi\)
\(228\) 0 0
\(229\) −22667.9 39262.0i −0.432256 0.748690i 0.564811 0.825220i \(-0.308949\pi\)
−0.997067 + 0.0765307i \(0.975616\pi\)
\(230\) 1592.42 + 8738.10i 0.0301024 + 0.165182i
\(231\) 0 0
\(232\) 1350.64 + 78599.9i 0.0250937 + 1.46031i
\(233\) −50931.3 −0.938151 −0.469075 0.883158i \(-0.655413\pi\)
−0.469075 + 0.883158i \(0.655413\pi\)
\(234\) 0 0
\(235\) 31824.5i 0.576270i
\(236\) −15989.2 42412.0i −0.287080 0.761491i
\(237\) 0 0
\(238\) 2426.92 + 13317.3i 0.0428452 + 0.235105i
\(239\) 31946.2 18444.1i 0.559272 0.322896i −0.193581 0.981084i \(-0.562010\pi\)
0.752853 + 0.658188i \(0.228677\pi\)
\(240\) 0 0
\(241\) −4193.64 + 7263.59i −0.0722033 + 0.125060i −0.899867 0.436165i \(-0.856336\pi\)
0.827663 + 0.561225i \(0.189670\pi\)
\(242\) 45094.9 126141.i 0.770011 2.15389i
\(243\) 0 0
\(244\) 65052.0 + 53327.3i 1.09265 + 0.895715i
\(245\) 12460.3 21581.9i 0.207586 0.359549i
\(246\) 0 0
\(247\) −1460.40 + 843.160i −0.0239374 + 0.0138203i
\(248\) −47023.0 + 84777.4i −0.764551 + 1.37840i
\(249\) 0 0
\(250\) −32221.0 37955.8i −0.515536 0.607293i
\(251\) 1475.47i 0.0234198i 0.999931 + 0.0117099i \(0.00372746\pi\)
−0.999931 + 0.0117099i \(0.996273\pi\)
\(252\) 0 0
\(253\) 44159.6 0.689897
\(254\) −80960.7 + 68728.1i −1.25489 + 1.06529i
\(255\) 0 0
\(256\) 52080.3 + 39782.1i 0.794682 + 0.607026i
\(257\) 17336.5 + 30027.8i 0.262480 + 0.454629i 0.966900 0.255154i \(-0.0821263\pi\)
−0.704420 + 0.709783i \(0.748793\pi\)
\(258\) 0 0
\(259\) −15698.0 9063.23i −0.234015 0.135109i
\(260\) −5060.12 4148.11i −0.0748539 0.0613626i
\(261\) 0 0
\(262\) −4970.49 1776.94i −0.0724097 0.0258863i
\(263\) 16482.5 + 9516.19i 0.238294 + 0.137579i 0.614392 0.789001i \(-0.289401\pi\)
−0.376099 + 0.926580i \(0.622735\pi\)
\(264\) 0 0
\(265\) −7805.54 13519.6i −0.111151 0.192518i
\(266\) 2132.96 388.707i 0.0301453 0.00549363i
\(267\) 0 0
\(268\) 5252.43 + 13932.3i 0.0731292 + 0.193978i
\(269\) −58724.1 −0.811544 −0.405772 0.913974i \(-0.632997\pi\)
−0.405772 + 0.913974i \(0.632997\pi\)
\(270\) 0 0
\(271\) 31474.1i 0.428563i 0.976772 + 0.214281i \(0.0687409\pi\)
−0.976772 + 0.214281i \(0.931259\pi\)
\(272\) 68876.2 + 23296.4i 0.930960 + 0.314884i
\(273\) 0 0
\(274\) −101579. + 18511.6i −1.35301 + 0.246571i
\(275\) −95625.2 + 55209.2i −1.26447 + 0.730040i
\(276\) 0 0
\(277\) −33265.8 + 57618.0i −0.433549 + 0.750929i −0.997176 0.0751008i \(-0.976072\pi\)
0.563627 + 0.826029i \(0.309405\pi\)
\(278\) 49484.8 + 17690.7i 0.640299 + 0.228905i
\(279\) 0 0
\(280\) 4330.73 + 7211.98i 0.0552389 + 0.0919895i
\(281\) −61859.9 + 107145.i −0.783424 + 1.35693i 0.146512 + 0.989209i \(0.453195\pi\)
−0.929936 + 0.367721i \(0.880138\pi\)
\(282\) 0 0
\(283\) −47401.9 + 27367.5i −0.591865 + 0.341713i −0.765835 0.643038i \(-0.777674\pi\)
0.173970 + 0.984751i \(0.444341\pi\)
\(284\) 18357.2 + 3020.48i 0.227598 + 0.0374489i
\(285\) 0 0
\(286\) −24799.9 + 21052.8i −0.303192 + 0.257381i
\(287\) 31383.9i 0.381016i
\(288\) 0 0
\(289\) −2853.15 −0.0341609
\(290\) 35076.7 + 41319.9i 0.417083 + 0.491318i
\(291\) 0 0
\(292\) 5618.48 34146.7i 0.0658951 0.400482i
\(293\) −44309.0 76745.4i −0.516127 0.893958i −0.999825 0.0187226i \(-0.994040\pi\)
0.483698 0.875235i \(-0.339293\pi\)
\(294\) 0 0
\(295\) −27064.1 15625.5i −0.310993 0.179552i
\(296\) −83469.8 + 50122.9i −0.952677 + 0.572075i
\(297\) 0 0
\(298\) 34924.2 97690.7i 0.393273 1.10007i
\(299\) −6462.01 3730.84i −0.0722812 0.0417316i
\(300\) 0 0
\(301\) −238.061 412.333i −0.00262757 0.00455109i
\(302\) −20363.6 111742.i −0.223276 1.22518i
\(303\) 0 0
\(304\) 3731.26 11031.5i 0.0403746 0.119368i
\(305\) 57996.0 0.623446
\(306\) 0 0
\(307\) 123447.i 1.30980i 0.755716 + 0.654900i \(0.227289\pi\)
−0.755716 + 0.654900i \(0.772711\pi\)
\(308\) 39135.8 14754.1i 0.412547 0.155529i
\(309\) 0 0
\(310\) 11983.7 + 65758.1i 0.124700 + 0.684268i
\(311\) 52431.9 30271.6i 0.542094 0.312978i −0.203833 0.979006i \(-0.565340\pi\)
0.745927 + 0.666027i \(0.232007\pi\)
\(312\) 0 0
\(313\) 26193.1 45367.8i 0.267361 0.463083i −0.700818 0.713340i \(-0.747182\pi\)
0.968180 + 0.250257i \(0.0805150\pi\)
\(314\) 7433.35 20792.7i 0.0753920 0.210888i
\(315\) 0 0
\(316\) −75928.4 + 92622.1i −0.760378 + 0.927557i
\(317\) −12998.7 + 22514.4i −0.129354 + 0.224048i −0.923427 0.383775i \(-0.874624\pi\)
0.794072 + 0.607823i \(0.207957\pi\)
\(318\) 0 0
\(319\) 233372. 134737.i 2.29333 1.32406i
\(320\) 45158.7 1552.45i 0.441003 0.0151607i
\(321\) 0 0
\(322\) 6208.53 + 7313.56i 0.0598794 + 0.0705370i
\(323\) 12920.1i 0.123840i
\(324\) 0 0
\(325\) 18657.5 0.176639
\(326\) 1241.96 1054.31i 0.0116862 0.00992050i
\(327\) 0 0
\(328\) −147415. 81765.6i −1.37023 0.760017i
\(329\) 17186.8 + 29768.4i 0.158783 + 0.275019i
\(330\) 0 0
\(331\) 37439.2 + 21615.5i 0.341720 + 0.197292i 0.661032 0.750357i \(-0.270119\pi\)
−0.319312 + 0.947650i \(0.603452\pi\)
\(332\) −11323.4 + 13812.9i −0.102731 + 0.125317i
\(333\) 0 0
\(334\) −89428.5 31970.5i −0.801647 0.286587i
\(335\) 8890.54 + 5132.95i 0.0792206 + 0.0457381i
\(336\) 0 0
\(337\) −5926.38 10264.8i −0.0521831 0.0903837i 0.838754 0.544511i \(-0.183285\pi\)
−0.890937 + 0.454127i \(0.849951\pi\)
\(338\) −106985. + 19496.8i −0.936462 + 0.170659i
\(339\) 0 0
\(340\) 46908.4 17684.3i 0.405782 0.152979i
\(341\) 332321. 2.85791
\(342\) 0 0
\(343\) 55525.0i 0.471955i
\(344\) −2557.01 + 43.9392i −0.0216081 + 0.000371309i
\(345\) 0 0
\(346\) 11122.8 2027.00i 0.0929098 0.0169317i
\(347\) −25222.5 + 14562.2i −0.209473 + 0.120940i −0.601067 0.799199i \(-0.705257\pi\)
0.391593 + 0.920138i \(0.371924\pi\)
\(348\) 0 0
\(349\) −59988.4 + 103903.i −0.492512 + 0.853055i −0.999963 0.00862528i \(-0.997254\pi\)
0.507451 + 0.861681i \(0.330588\pi\)
\(350\) −22587.8 8075.08i −0.184390 0.0659191i
\(351\) 0 0
\(352\) 32659.8 222266.i 0.263589 1.79385i
\(353\) 77379.0 134024.i 0.620975 1.07556i −0.368330 0.929695i \(-0.620070\pi\)
0.989305 0.145865i \(-0.0465964\pi\)
\(354\) 0 0
\(355\) 11108.5 6413.49i 0.0881451 0.0508906i
\(356\) −17507.8 + 106405.i −0.138144 + 0.839577i
\(357\) 0 0
\(358\) 139490. 118414.i 1.08837 0.923925i
\(359\) 66839.6i 0.518615i −0.965795 0.259307i \(-0.916506\pi\)
0.965795 0.259307i \(-0.0834942\pi\)
\(360\) 0 0
\(361\) 128252. 0.984121
\(362\) 62713.4 + 73875.4i 0.478567 + 0.563745i
\(363\) 0 0
\(364\) −6973.37 1147.39i −0.0526308 0.00865984i
\(365\) −11929.9 20663.2i −0.0895472 0.155100i
\(366\) 0 0
\(367\) −81901.3 47285.7i −0.608077 0.351073i 0.164136 0.986438i \(-0.447517\pi\)
−0.772212 + 0.635364i \(0.780850\pi\)
\(368\) 50528.1 10108.1i 0.373110 0.0746403i
\(369\) 0 0
\(370\) −22597.8 + 63211.2i −0.165068 + 0.461732i
\(371\) −14602.5 8430.74i −0.106091 0.0612517i
\(372\) 0 0
\(373\) 90530.4 + 156803.i 0.650694 + 1.12704i 0.982955 + 0.183848i \(0.0588554\pi\)
−0.332260 + 0.943188i \(0.607811\pi\)
\(374\) −44685.5 245204.i −0.319465 1.75301i
\(375\) 0 0
\(376\) 184604. 3172.19i 1.30576 0.0224379i
\(377\) −45533.4 −0.320366
\(378\) 0 0
\(379\) 51191.3i 0.356384i −0.983996 0.178192i \(-0.942975\pi\)
0.983996 0.178192i \(-0.0570248\pi\)
\(380\) −2832.41 7513.07i −0.0196150 0.0520296i
\(381\) 0 0
\(382\) −16151.5 88628.2i −0.110684 0.607359i
\(383\) 132128. 76284.0i 0.900734 0.520039i 0.0232957 0.999729i \(-0.492584\pi\)
0.877438 + 0.479690i \(0.159251\pi\)
\(384\) 0 0
\(385\) 14418.5 24973.5i 0.0972742 0.168484i
\(386\) −24626.3 + 68885.2i −0.165282 + 0.462329i
\(387\) 0 0
\(388\) −149061. 122195.i −0.990147 0.811687i
\(389\) 33948.4 58800.3i 0.224347 0.388580i −0.731776 0.681545i \(-0.761308\pi\)
0.956123 + 0.292965i \(0.0946418\pi\)
\(390\) 0 0
\(391\) 49510.2 28584.7i 0.323848 0.186974i
\(392\) −126432. 70127.0i −0.822780 0.456366i
\(393\) 0 0
\(394\) 93968.9 + 110694.i 0.605329 + 0.713069i
\(395\) 82575.7i 0.529247i
\(396\) 0 0
\(397\) −126087. −0.799998 −0.399999 0.916516i \(-0.630990\pi\)
−0.399999 + 0.916516i \(0.630990\pi\)
\(398\) −144348. + 122538.i −0.911264 + 0.773578i
\(399\) 0 0
\(400\) −96778.6 + 85059.8i −0.604866 + 0.531624i
\(401\) 35445.4 + 61393.2i 0.220430 + 0.381796i 0.954939 0.296803i \(-0.0959206\pi\)
−0.734509 + 0.678599i \(0.762587\pi\)
\(402\) 0 0
\(403\) −48629.5 28076.3i −0.299426 0.172874i
\(404\) −118233. 96923.5i −0.724398 0.593836i
\(405\) 0 0
\(406\) 55125.1 + 19707.1i 0.334424 + 0.119556i
\(407\) 289038. + 166876.i 1.74488 + 1.00741i
\(408\) 0 0
\(409\) −21772.1 37710.4i −0.130153 0.225432i 0.793582 0.608463i \(-0.208214\pi\)
−0.923735 + 0.383031i \(0.874880\pi\)
\(410\) −114343. + 20837.7i −0.680209 + 0.123960i
\(411\) 0 0
\(412\) −64927.4 172223.i −0.382502 1.01460i
\(413\) −33754.1 −0.197891
\(414\) 0 0
\(415\) 12314.7i 0.0715036i
\(416\) −23557.4 + 29765.6i −0.136126 + 0.172000i
\(417\) 0 0
\(418\) −39273.0 + 7157.04i −0.224771 + 0.0409620i
\(419\) −182385. + 105300.i −1.03887 + 0.599792i −0.919513 0.393060i \(-0.871417\pi\)
−0.119357 + 0.992851i \(0.538083\pi\)
\(420\) 0 0
\(421\) −42063.0 + 72855.3i −0.237321 + 0.411052i −0.959945 0.280190i \(-0.909603\pi\)
0.722624 + 0.691242i \(0.242936\pi\)
\(422\) 175107. + 62600.4i 0.983285 + 0.351522i
\(423\) 0 0
\(424\) −77644.7 + 46625.0i −0.431897 + 0.259350i
\(425\) −71474.4 + 123797.i −0.395706 + 0.685383i
\(426\) 0 0
\(427\) 54249.0 31320.7i 0.297533 0.171781i
\(428\) 104242. + 17151.9i 0.569055 + 0.0936320i
\(429\) 0 0
\(430\) −1344.22 + 1141.12i −0.00726997 + 0.00617153i
\(431\) 150083.i 0.807933i −0.914774 0.403967i \(-0.867631\pi\)
0.914774 0.403967i \(-0.132369\pi\)
\(432\) 0 0
\(433\) 71221.5 0.379871 0.189935 0.981797i \(-0.439172\pi\)
0.189935 + 0.981797i \(0.439172\pi\)
\(434\) 46722.0 + 55037.8i 0.248051 + 0.292201i
\(435\) 0 0
\(436\) −31290.0 + 190167.i −0.164601 + 1.00038i
\(437\) −4578.26 7929.78i −0.0239739 0.0415239i
\(438\) 0 0
\(439\) −94609.3 54622.7i −0.490913 0.283429i 0.234040 0.972227i \(-0.424805\pi\)
−0.724953 + 0.688798i \(0.758139\pi\)
\(440\) −79739.3 132790.i −0.411876 0.685899i
\(441\) 0 0
\(442\) −14177.2 + 39656.7i −0.0725680 + 0.202989i
\(443\) −199756. 115329.i −1.01787 0.587666i −0.104382 0.994537i \(-0.533287\pi\)
−0.913486 + 0.406871i \(0.866620\pi\)
\(444\) 0 0
\(445\) 37174.8 + 64388.7i 0.187728 + 0.325154i
\(446\) 59234.5 + 325038.i 0.297786 + 1.63405i
\(447\) 0 0
\(448\) 41402.6 25840.0i 0.206287 0.128747i
\(449\) 9751.64 0.0483710 0.0241855 0.999707i \(-0.492301\pi\)
0.0241855 + 0.999707i \(0.492301\pi\)
\(450\) 0 0
\(451\) 577854.i 2.84096i
\(452\) −55853.8 + 21056.7i −0.273386 + 0.103066i
\(453\) 0 0
\(454\) 21300.3 + 116881.i 0.103341 + 0.567066i
\(455\) −4219.80 + 2436.30i −0.0203831 + 0.0117682i
\(456\) 0 0
\(457\) −33069.5 + 57278.1i −0.158342 + 0.274256i −0.934271 0.356564i \(-0.883948\pi\)
0.775929 + 0.630820i \(0.217281\pi\)
\(458\) −61046.1 + 170760.i −0.291023 + 0.814056i
\(459\) 0 0
\(460\) 22523.8 27475.9i 0.106445 0.129848i
\(461\) −86994.6 + 150679.i −0.409346 + 0.709008i −0.994817 0.101686i \(-0.967576\pi\)
0.585471 + 0.810694i \(0.300910\pi\)
\(462\) 0 0
\(463\) −150682. + 86996.3i −0.702909 + 0.405825i −0.808430 0.588592i \(-0.799682\pi\)
0.105521 + 0.994417i \(0.466349\pi\)
\(464\) 236186. 207587.i 1.09703 0.964194i
\(465\) 0 0
\(466\) 131844. + 155310.i 0.607138 + 0.715200i
\(467\) 172090.i 0.789080i −0.918879 0.394540i \(-0.870904\pi\)
0.918879 0.394540i \(-0.129096\pi\)
\(468\) 0 0
\(469\) 11088.2 0.0504097
\(470\) 97045.8 82382.8i 0.439320 0.372942i
\(471\) 0 0
\(472\) −87940.6 + 158548.i −0.394735 + 0.711665i
\(473\) 4383.27 + 7592.05i 0.0195919 + 0.0339341i
\(474\) 0 0
\(475\) 19828.0 + 11447.7i 0.0878802 + 0.0507376i
\(476\) 34327.3 41874.6i 0.151505 0.184815i
\(477\) 0 0
\(478\) −138941. 49671.2i −0.608101 0.217395i
\(479\) −189138. 109199.i −0.824343 0.475935i 0.0275690 0.999620i \(-0.491223\pi\)
−0.851912 + 0.523685i \(0.824557\pi\)
\(480\) 0 0
\(481\) −28197.2 48839.0i −0.121875 0.211094i
\(482\) 33005.5 6014.87i 0.142067 0.0258900i
\(483\) 0 0
\(484\) −501389. + 189022.i −2.14034 + 0.806904i
\(485\) −132893. −0.564959
\(486\) 0 0
\(487\) 392112.i 1.65330i −0.562716 0.826650i \(-0.690243\pi\)
0.562716 0.826650i \(-0.309757\pi\)
\(488\) −5780.89 336416.i −0.0242748 1.41266i
\(489\) 0 0
\(490\) −98067.5 + 17871.7i −0.408444 + 0.0744343i
\(491\) −181620. + 104859.i −0.753358 + 0.434951i −0.826906 0.562340i \(-0.809901\pi\)
0.0735480 + 0.997292i \(0.476568\pi\)
\(492\) 0 0
\(493\) 174432. 302125.i 0.717683 1.24306i
\(494\) 6351.60 + 2270.68i 0.0260273 + 0.00930470i
\(495\) 0 0
\(496\) 380247. 76067.9i 1.54562 0.309199i
\(497\) 6927.19 11998.2i 0.0280443 0.0485741i
\(498\) 0 0
\(499\) 117681. 67943.0i 0.472611 0.272862i −0.244721 0.969594i \(-0.578696\pi\)
0.717332 + 0.696731i \(0.245363\pi\)
\(500\) −32333.5 + 196509.i −0.129334 + 0.786037i
\(501\) 0 0
\(502\) 4499.29 3819.48i 0.0178541 0.0151564i
\(503\) 232332.i 0.918275i 0.888365 + 0.459137i \(0.151841\pi\)
−0.888365 + 0.459137i \(0.848159\pi\)
\(504\) 0 0
\(505\) −105409. −0.413328
\(506\) −114314. 134660.i −0.446477 0.525943i
\(507\) 0 0
\(508\) 419159. + 68968.2i 1.62424 + 0.267252i
\(509\) −72659.4 125850.i −0.280451 0.485755i 0.691045 0.722812i \(-0.257151\pi\)
−0.971496 + 0.237057i \(0.923817\pi\)
\(510\) 0 0
\(511\) −22318.3 12885.5i −0.0854711 0.0493467i
\(512\) −13506.6 261796.i −0.0515234 0.998672i
\(513\) 0 0
\(514\) 46688.3 130598.i 0.176719 0.494321i
\(515\) −109899. 63450.5i −0.414363 0.239233i
\(516\) 0 0
\(517\) −316450. 548108.i −1.18393 2.05062i
\(518\) 12999.3 + 71331.1i 0.0484461 + 0.265839i
\(519\) 0 0
\(520\) 449.672 + 26168.4i 0.00166299 + 0.0967766i
\(521\) −443088. −1.63235 −0.816177 0.577803i \(-0.803910\pi\)
−0.816177 + 0.577803i \(0.803910\pi\)
\(522\) 0 0
\(523\) 73202.4i 0.267622i 0.991007 + 0.133811i \(0.0427215\pi\)
−0.991007 + 0.133811i \(0.957278\pi\)
\(524\) 7448.30 + 19756.9i 0.0271266 + 0.0719543i
\(525\) 0 0
\(526\) −13648.9 74896.0i −0.0493318 0.270699i
\(527\) 372587. 215113.i 1.34155 0.774543i
\(528\) 0 0
\(529\) −119662. + 207261.i −0.427609 + 0.740640i
\(530\) −21020.8 + 58799.9i −0.0748338 + 0.209327i
\(531\) 0 0
\(532\) −6706.83 5498.02i −0.0236970 0.0194260i
\(533\) 48820.3 84559.2i 0.171849 0.297651i
\(534\) 0 0
\(535\) 63079.9 36419.2i 0.220386 0.127240i
\(536\) 28888.4 52082.7i 0.100553 0.181286i
\(537\) 0 0
\(538\) 152017. + 179073.i 0.525202 + 0.618681i
\(539\) 495602.i 1.70591i
\(540\) 0 0
\(541\) 438165. 1.49707 0.748536 0.663094i \(-0.230757\pi\)
0.748536 + 0.663094i \(0.230757\pi\)
\(542\) 95977.1 81475.6i 0.326715 0.277351i
\(543\) 0 0
\(544\) −107257. 270337.i −0.362432 0.913500i
\(545\) 66439.2 + 115076.i 0.223682 + 0.387429i
\(546\) 0 0
\(547\) −270221. 156012.i −0.903118 0.521416i −0.0249077 0.999690i \(-0.507929\pi\)
−0.878211 + 0.478274i \(0.841263\pi\)
\(548\) 319402. + 261834.i 1.06359 + 0.871898i
\(549\) 0 0
\(550\) 415896. + 148682.i 1.37486 + 0.491510i
\(551\) −48389.8 27937.9i −0.159386 0.0920217i
\(552\) 0 0
\(553\) 44594.9 + 77240.6i 0.145826 + 0.252578i
\(554\) 261814. 47712.6i 0.853048 0.155458i
\(555\) 0 0
\(556\) −74153.2 196694.i −0.239873 0.636271i
\(557\) −312549. −1.00741 −0.503707 0.863874i \(-0.668031\pi\)
−0.503707 + 0.863874i \(0.668031\pi\)
\(558\) 0 0
\(559\) 1481.29i 0.00474042i
\(560\) 10781.4 31875.5i 0.0343796 0.101644i
\(561\) 0 0
\(562\) 486861. 88724.8i 1.54146 0.280913i
\(563\) 74780.6 43174.6i 0.235924 0.136211i −0.377378 0.926059i \(-0.623174\pi\)
0.613302 + 0.789849i \(0.289841\pi\)
\(564\) 0 0
\(565\) −20577.7 + 35641.7i −0.0644615 + 0.111651i
\(566\) 206162. + 73702.3i 0.643539 + 0.230064i
\(567\) 0 0
\(568\) −38309.8 63797.4i −0.118744 0.197745i
\(569\) 277479. 480608.i 0.857049 1.48445i −0.0176822 0.999844i \(-0.505629\pi\)
0.874731 0.484609i \(-0.161038\pi\)
\(570\) 0 0
\(571\) −262848. + 151755.i −0.806181 + 0.465449i −0.845628 0.533773i \(-0.820774\pi\)
0.0394467 + 0.999222i \(0.487440\pi\)
\(572\) 128397. + 21126.3i 0.392430 + 0.0645701i
\(573\) 0 0
\(574\) −95702.2 + 81242.3i −0.290468 + 0.246580i
\(575\) 101308.i 0.306414i
\(576\) 0 0
\(577\) −500884. −1.50448 −0.752238 0.658892i \(-0.771026\pi\)
−0.752238 + 0.658892i \(0.771026\pi\)
\(578\) 7385.83 + 8700.40i 0.0221077 + 0.0260426i
\(579\) 0 0
\(580\) 35199.2 213926.i 0.104635 0.635927i
\(581\) 6650.54 + 11519.1i 0.0197017 + 0.0341244i
\(582\) 0 0
\(583\) 268867. + 155230.i 0.791043 + 0.456709i
\(584\) −118671. + 71261.2i −0.347953 + 0.208943i
\(585\) 0 0
\(586\) −119327. + 333783.i −0.347490 + 0.972007i
\(587\) 498580. + 287855.i 1.44697 + 0.835406i 0.998300 0.0582932i \(-0.0185658\pi\)
0.448666 + 0.893699i \(0.351899\pi\)
\(588\) 0 0
\(589\) −34453.5 59675.2i −0.0993122 0.172014i
\(590\) 22411.4 + 122978.i 0.0643821 + 0.353285i
\(591\) 0 0
\(592\) 368919. + 124782.i 1.05266 + 0.356048i
\(593\) 138143. 0.392843 0.196421 0.980520i \(-0.437068\pi\)
0.196421 + 0.980520i \(0.437068\pi\)
\(594\) 0 0
\(595\) 37332.6i 0.105452i
\(596\) −388305. + 146390.i −1.09315 + 0.412115i
\(597\) 0 0
\(598\) 5351.10 + 29363.2i 0.0149637 + 0.0821108i
\(599\) 165665. 95646.9i 0.461719 0.266574i −0.251048 0.967975i \(-0.580775\pi\)
0.712767 + 0.701401i \(0.247442\pi\)
\(600\) 0 0
\(601\) 203120. 351814.i 0.562346 0.974012i −0.434945 0.900457i \(-0.643232\pi\)
0.997291 0.0735551i \(-0.0234345\pi\)
\(602\) −641.112 + 1793.33i −0.00176905 + 0.00494843i
\(603\) 0 0
\(604\) −288031. + 351358.i −0.789524 + 0.963110i
\(605\) −184722. + 319948.i −0.504671 + 0.874117i
\(606\) 0 0
\(607\) 59466.9 34333.2i 0.161398 0.0931831i −0.417126 0.908849i \(-0.636962\pi\)
0.578523 + 0.815666i \(0.303629\pi\)
\(608\) −43298.5 + 17178.7i −0.117129 + 0.0464712i
\(609\) 0 0
\(610\) −150132. 176853.i −0.403472 0.475284i
\(611\) 106942.i 0.286461i
\(612\) 0 0
\(613\) −572114. −1.52252 −0.761258 0.648450i \(-0.775418\pi\)
−0.761258 + 0.648450i \(0.775418\pi\)
\(614\) 376440. 319563.i 0.998526 0.847655i
\(615\) 0 0
\(616\) −146300. 81147.5i −0.385553 0.213852i
\(617\) 10190.4 + 17650.3i 0.0267684 + 0.0463642i 0.879099 0.476639i \(-0.158145\pi\)
−0.852331 + 0.523003i \(0.824812\pi\)
\(618\) 0 0
\(619\) 388604. + 224361.i 1.01421 + 0.585552i 0.912420 0.409254i \(-0.134211\pi\)
0.101786 + 0.994806i \(0.467544\pi\)
\(620\) 169501. 206768.i 0.440951 0.537899i
\(621\) 0 0
\(622\) −228038. 81523.2i −0.589423 0.210717i
\(623\) 69546.0 + 40152.4i 0.179183 + 0.103451i
\(624\) 0 0
\(625\) −88627.6 153508.i −0.226887 0.392979i
\(626\) −206150. + 37568.4i −0.526058 + 0.0958680i
\(627\) 0 0
\(628\) −82647.8 + 31158.0i −0.209562 + 0.0790042i
\(629\) 432079. 1.09210
\(630\) 0 0
\(631\) 402529.i 1.01097i −0.862835 0.505486i \(-0.831313\pi\)
0.862835 0.505486i \(-0.168687\pi\)
\(632\) 478995. 8230.94i 1.19921 0.0206070i
\(633\) 0 0
\(634\) 102304. 18643.8i 0.254517 0.0463827i
\(635\) 253646. 146443.i 0.629043 0.363178i
\(636\) 0 0
\(637\) 41871.2 72523.0i 0.103190 0.178730i
\(638\) −1.01499e6 362856.i −2.49356 0.891441i
\(639\) 0 0
\(640\) −121634. 133688.i −0.296959 0.326387i
\(641\) 176906. 306411.i 0.430554 0.745741i −0.566367 0.824153i \(-0.691652\pi\)
0.996921 + 0.0784117i \(0.0249849\pi\)
\(642\) 0 0
\(643\) −227886. + 131570.i −0.551184 + 0.318226i −0.749599 0.661892i \(-0.769754\pi\)
0.198415 + 0.980118i \(0.436420\pi\)
\(644\) 6230.22 37864.6i 0.0150221 0.0912981i
\(645\) 0 0
\(646\) −39398.7 + 33445.8i −0.0944097 + 0.0801451i
\(647\) 265174.i 0.633464i −0.948515 0.316732i \(-0.897414\pi\)
0.948515 0.316732i \(-0.102586\pi\)
\(648\) 0 0
\(649\) 621494. 1.47553
\(650\) −48297.9 56894.3i −0.114315 0.134661i
\(651\) 0 0
\(652\) −6430.04 1057.99i −0.0151258 0.00248879i
\(653\) −2938.96 5090.43i −0.00689235 0.0119379i 0.862559 0.505957i \(-0.168861\pi\)
−0.869451 + 0.494019i \(0.835527\pi\)
\(654\) 0 0
\(655\) 12607.4 + 7278.87i 0.0293861 + 0.0169661i
\(656\) 132270. + 661190.i 0.307365 + 1.53645i
\(657\) 0 0
\(658\) 46285.0 129470.i 0.106903 0.299031i
\(659\) −480334. 277321.i −1.10604 0.638575i −0.168242 0.985746i \(-0.553809\pi\)
−0.937802 + 0.347171i \(0.887142\pi\)
\(660\) 0 0
\(661\) 410614. + 711204.i 0.939789 + 1.62776i 0.765863 + 0.643004i \(0.222312\pi\)
0.173926 + 0.984759i \(0.444355\pi\)
\(662\) −31002.8 170122.i −0.0707433 0.388191i
\(663\) 0 0
\(664\) 71433.6 1227.50i 0.162019 0.00278410i
\(665\) −5979.36 −0.0135211
\(666\) 0 0
\(667\) 247241.i 0.555736i
\(668\) 134009. + 355464.i 0.300318 + 0.796604i
\(669\) 0 0
\(670\) −7362.12 40398.3i −0.0164004 0.0899939i
\(671\) −998855. + 576689.i −2.21849 + 1.28085i
\(672\) 0 0
\(673\) −258432. + 447618.i −0.570580 + 0.988274i 0.425926 + 0.904758i \(0.359948\pi\)
−0.996506 + 0.0835158i \(0.973385\pi\)
\(674\) −15960.1 + 44643.9i −0.0351330 + 0.0982749i
\(675\) 0 0
\(676\) 336402. + 275770.i 0.736148 + 0.603468i
\(677\) −345343. + 598152.i −0.753483 + 1.30507i 0.192642 + 0.981269i \(0.438294\pi\)
−0.946125 + 0.323801i \(0.895039\pi\)
\(678\) 0 0
\(679\) −124307. + 71768.4i −0.269621 + 0.155666i
\(680\) −175357. 97263.9i −0.379231 0.210346i
\(681\) 0 0
\(682\) −860265. 1.01338e6i −1.84954 2.17873i
\(683\) 764551.i 1.63895i −0.573117 0.819474i \(-0.694266\pi\)
0.573117 0.819474i \(-0.305734\pi\)
\(684\) 0 0
\(685\) 284757. 0.606868
\(686\) −169318. + 143735.i −0.359795 + 0.305433i
\(687\) 0 0
\(688\) 6753.22 + 7683.62i 0.0142671 + 0.0162326i
\(689\) −26229.4 45430.7i −0.0552523 0.0956998i
\(690\) 0 0
\(691\) 278107. + 160565.i 0.582445 + 0.336275i 0.762105 0.647454i \(-0.224166\pi\)
−0.179659 + 0.983729i \(0.557500\pi\)
\(692\) −34974.2 28670.6i −0.0730358 0.0598722i
\(693\) 0 0
\(694\) 109698. + 39216.9i 0.227762 + 0.0814244i
\(695\) −125516. 72466.4i −0.259853 0.150026i
\(696\) 0 0
\(697\) 374048. + 647870.i 0.769949 + 1.33359i
\(698\) 472131. 86040.5i 0.969063 0.176601i
\(699\) 0 0
\(700\) 33847.9 + 89782.9i 0.0690774 + 0.183230i
\(701\) 621799. 1.26536 0.632680 0.774413i \(-0.281955\pi\)
0.632680 + 0.774413i \(0.281955\pi\)
\(702\) 0 0
\(703\) 69203.8i 0.140029i
\(704\) −762323. + 475777.i −1.53813 + 0.959972i
\(705\) 0 0
\(706\) −609002. + 110984.i −1.22183 + 0.222664i
\(707\) −98598.6 + 56925.9i −0.197257 + 0.113886i
\(708\) 0 0
\(709\) 262435. 454550.i 0.522070 0.904252i −0.477600 0.878577i \(-0.658493\pi\)
0.999670 0.0256748i \(-0.00817343\pi\)
\(710\) −48313.4 17271.9i −0.0958409 0.0342629i
\(711\) 0 0
\(712\) 369792. 222057.i 0.729454 0.438031i
\(713\) 152451. 264053.i 0.299882 0.519412i
\(714\) 0 0
\(715\) 77696.8 44858.2i 0.151982 0.0877466i
\(716\) −722183. 118828.i −1.40871 0.231788i
\(717\) 0 0
\(718\) −203821. + 173025.i −0.395366 + 0.335629i
\(719\) 348658.i 0.674438i −0.941426 0.337219i \(-0.890514\pi\)
0.941426 0.337219i \(-0.109486\pi\)
\(720\) 0 0
\(721\) −137065. −0.263668
\(722\) −332000. 391091.i −0.636888 0.750245i
\(723\) 0 0
\(724\) 62932.5 382476.i 0.120060 0.729672i
\(725\) 309106. + 535387.i 0.588073 + 1.01857i
\(726\) 0 0
\(727\) 523789. + 302410.i 0.991032 + 0.572173i 0.905583 0.424170i \(-0.139434\pi\)
0.0854497 + 0.996342i \(0.472767\pi\)
\(728\) 14552.8 + 24234.8i 0.0274590 + 0.0457275i
\(729\) 0 0
\(730\) −32128.0 + 89869.2i −0.0602890 + 0.168642i
\(731\) 9828.75 + 5674.63i 0.0183935 + 0.0106195i
\(732\) 0 0
\(733\) 237805. + 411891.i 0.442602 + 0.766609i 0.997882 0.0650546i \(-0.0207222\pi\)
−0.555280 + 0.831664i \(0.687389\pi\)
\(734\) 67821.2 + 372156.i 0.125885 + 0.690770i
\(735\) 0 0
\(736\) −161624. 127914.i −0.298366 0.236136i
\(737\) −204160. −0.375868
\(738\) 0 0
\(739\) 844449.i 1.54627i −0.634244 0.773133i \(-0.718688\pi\)
0.634244 0.773133i \(-0.281312\pi\)
\(740\) 251254. 94722.2i 0.458828 0.172977i
\(741\) 0 0
\(742\) 12092.1 + 66353.1i 0.0219631 + 0.120518i
\(743\) 537216. 310162.i 0.973131 0.561837i 0.0729415 0.997336i \(-0.476761\pi\)
0.900189 + 0.435499i \(0.143428\pi\)
\(744\) 0 0
\(745\) −143060. + 247787.i −0.257754 + 0.446443i
\(746\) 243804. 681974.i 0.438090 1.22543i
\(747\) 0 0
\(748\) −632049. + 771013.i −1.12966 + 1.37803i
\(749\) 39336.3 68132.4i 0.0701180 0.121448i
\(750\) 0 0
\(751\) −632847. + 365374.i −1.12207 + 0.647825i −0.941928 0.335816i \(-0.890988\pi\)
−0.180139 + 0.983641i \(0.557655\pi\)
\(752\) −487549. 554719.i −0.862149 0.980928i
\(753\) 0 0
\(754\) 117870. + 138849.i 0.207330 + 0.244231i
\(755\) 313247.i 0.549533i
\(756\) 0 0
\(757\) −769023. −1.34198 −0.670992 0.741465i \(-0.734132\pi\)
−0.670992 + 0.741465i \(0.734132\pi\)
\(758\) −156103. + 132517.i −0.271689 + 0.230639i
\(759\) 0 0
\(760\) −15578.2 + 28085.9i −0.0269706 + 0.0486252i
\(761\) 137697. + 238498.i 0.237769 + 0.411828i 0.960074 0.279747i \(-0.0902505\pi\)
−0.722305 + 0.691575i \(0.756917\pi\)
\(762\) 0 0
\(763\) 124293. + 71760.8i 0.213500 + 0.123264i
\(764\) −228452. + 278680.i −0.391389 + 0.477441i
\(765\) 0 0
\(766\) −574654. 205437.i −0.979375 0.350124i
\(767\) −90945.2 52507.2i −0.154593 0.0892541i
\(768\) 0 0
\(769\) 26421.1 + 45762.6i 0.0446784 + 0.0773853i 0.887500 0.460808i \(-0.152440\pi\)
−0.842821 + 0.538193i \(0.819107\pi\)
\(770\) −113479. + 20680.2i −0.191396 + 0.0348798i
\(771\) 0 0
\(772\) 273808. 103225.i 0.459421 0.173201i
\(773\) 195309. 0.326861 0.163430 0.986555i \(-0.447744\pi\)
0.163430 + 0.986555i \(0.447744\pi\)
\(774\) 0 0
\(775\) 762389.i 1.26933i
\(776\) 13246.4 + 770866.i 0.0219975 + 1.28013i
\(777\) 0 0