Properties

Label 108.5.f.a.91.7
Level 108
Weight 5
Character 108.91
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

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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 91.7
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.7

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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 −0.734368 0.678751i \(-0.762521\pi\)
0.955000 + 0.296606i \(0.0958548\pi\)
\(6\) 0 0
\(7\) 10.3188 5.95759i 0.210589 0.121583i −0.390996 0.920392i \(-0.627869\pi\)
0.601585 + 0.798809i \(0.294536\pi\)
\(8\) 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 −0.574063 + 0.818811i \(0.694633\pi\)
−0.996143 + 0.0877473i \(0.972033\pi\)
\(12\) 0 0
\(13\) 18.5350 32.1036i 0.109675 0.189962i −0.805964 0.591965i \(-0.798352\pi\)
0.915639 + 0.402003i \(0.131686\pi\)
\(14\) −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 \(-0.979931\pi\)
0.998013 0.0630057i \(-0.0200686\pi\)
\(20\) −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 0.326105 0.945334i \(-0.394264\pi\)
−0.655630 + 0.755082i \(0.727597\pi\)
\(24\) 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 −0.956770 0.290846i \(-0.906063\pi\)
0.226505 0.974010i \(-0.427270\pi\)
\(30\) 0 0
\(31\) −1311.83 757.384i −1.36507 0.788121i −0.374773 0.927117i \(-0.622279\pi\)
−0.990293 + 0.138996i \(0.955613\pi\)
\(32\) 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 0.146476 + 0.989214i \(0.453207\pi\)
−0.929923 + 0.367755i \(0.880126\pi\)
\(42\) 0 0
\(43\) −34.6057 + 19.9796i −0.0187159 + 0.0108056i −0.509329 0.860572i \(-0.670106\pi\)
0.490613 + 0.871378i \(0.336773\pi\)
\(44\) 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 0.186807 0.982397i \(-0.440186\pi\)
0.944184 + 0.329419i \(0.106853\pi\)
\(48\) 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 0.104346 0.994541i \(-0.466725\pi\)
−0.809125 + 0.587637i \(0.800058\pi\)
\(60\) 0 0
\(61\) 2628.64 + 4552.93i 0.706433 + 1.22358i 0.966172 + 0.257899i \(0.0830300\pi\)
−0.259739 + 0.965679i \(0.583637\pi\)
\(62\) 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 0.587073 0.809534i \(-0.300280\pi\)
−0.407541 + 0.913187i \(0.633614\pi\)
\(68\) 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 \(0.0367923\pi\)
−0.993327 + 0.115329i \(0.963208\pi\)
\(72\) 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 0.119237 0.992866i \(-0.461955\pi\)
0.919466 + 0.393171i \(0.128622\pi\)
\(80\) −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 −0.428190 0.903689i \(-0.640848\pi\)
0.568523 + 0.822667i \(0.307515\pi\)
\(84\) 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 −0.985396 0.170276i \(-0.945534\pi\)
0.345235 0.938516i \(-0.387799\pi\)
\(98\) −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 0.530999 0.847372i \(-0.321817\pi\)
−0.999346 + 0.0361728i \(0.988483\pi\)
\(102\) 0 0
\(103\) −9962.26 5751.71i −0.939039 0.542154i −0.0493798 0.998780i \(-0.515724\pi\)
−0.889659 + 0.456626i \(0.849058\pi\)
\(104\) 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 \(0.0931078\pi\)
−0.957524 + 0.288353i \(0.906892\pi\)
\(108\) 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 −0.783693 0.621149i \(-0.786666\pi\)
0.929777 + 0.368124i \(0.120000\pi\)
\(114\) 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 \(0.307725\pi\)
−0.567980 + 0.823042i \(0.692275\pi\)
\(128\) −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 0.532928 0.846161i \(-0.321092\pi\)
−0.466333 + 0.884609i \(0.654425\pi\)
\(132\) 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 0.972597 + 0.232499i \(0.0746901\pi\)
−0.284949 + 0.958543i \(0.591977\pi\)
\(138\) 0 0
\(139\) −11377.8 6569.00i −0.588885 0.339993i 0.175772 0.984431i \(-0.443758\pi\)
−0.764656 + 0.644438i \(0.777091\pi\)
\(140\) −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 −0.410856 0.911700i \(-0.634770\pi\)
0.994984 0.100038i \(-0.0318965\pi\)
\(150\) 0 0
\(151\) 24591.2 14197.8i 1.07852 0.622681i 0.148020 0.988984i \(-0.452710\pi\)
0.930496 + 0.366303i \(0.119377\pi\)
\(152\) 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 −0.804589 0.593832i \(-0.797614\pi\)
0.916568 + 0.399878i \(0.130948\pi\)
\(158\) −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 \(-0.997560\pi\)
0.999971 0.00766459i \(-0.00243974\pi\)
\(164\) 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 0.821078 0.570816i \(-0.193373\pi\)
−0.0838016 + 0.996482i \(0.526706\pi\)
\(168\) 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 0.841449 0.540336i \(-0.181703\pi\)
−0.888669 + 0.458549i \(0.848370\pi\)
\(174\) 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 \(-0.746961\pi\)
0.700323 0.713826i \(-0.253039\pi\)
\(180\) 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 −0.208257 0.978074i \(-0.566779\pi\)
0.742908 + 0.669393i \(0.233446\pi\)
\(192\) 0 0
\(193\) −9144.35 + 15838.5i −0.245493 + 0.425205i −0.962270 0.272097i \(-0.912283\pi\)
0.716777 + 0.697302i \(0.245616\pi\)
\(194\) 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 \(0.203906\pi\)
−0.801744 + 0.597667i \(0.796094\pi\)
\(200\) −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 −0.0257275 0.999669i \(-0.508190\pi\)
−0.878602 + 0.477554i \(0.841524\pi\)
\(212\) 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 −0.997741 0.0671780i \(-0.978600\pi\)
−0.440693 + 0.897658i \(0.645267\pi\)
\(224\) −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 −0.728376 0.685178i \(-0.759724\pi\)
0.229194 + 0.973381i \(0.426391\pi\)
\(228\) 0 0
\(229\) −22667.9 + 39262.0i −0.432256 + 0.748690i −0.997067 0.0765307i \(-0.975616\pi\)
0.564811 + 0.825220i \(0.308949\pi\)
\(230\) 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 0.752853 0.658188i \(-0.228677\pi\)
−0.193581 + 0.981084i \(0.562010\pi\)
\(240\) 0 0
\(241\) −4193.64 7263.59i −0.0722033 0.125060i 0.827663 0.561225i \(-0.189670\pi\)
−0.899867 + 0.436165i \(0.856336\pi\)
\(242\) 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 \(-0.996273\pi\)
0.999931 0.0117099i \(-0.00372746\pi\)
\(252\) 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 −0.704420 0.709783i \(-0.748793\pi\)
0.966900 + 0.255154i \(0.0821263\pi\)
\(258\) 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 −0.376099 0.926580i \(-0.622735\pi\)
0.614392 + 0.789001i \(0.289401\pi\)
\(264\) 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 \(-0.931259\pi\)
0.976772 0.214281i \(-0.0687409\pi\)
\(272\) 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 0.563627 0.826029i \(-0.309405\pi\)
−0.997176 + 0.0751008i \(0.976072\pi\)
\(278\) 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 −0.929936 0.367721i \(-0.880138\pi\)
0.146512 0.989209i \(-0.453195\pi\)
\(282\) 0 0
\(283\) −47401.9 27367.5i −0.591865 0.341713i 0.173970 0.984751i \(-0.444341\pi\)
−0.765835 + 0.643038i \(0.777674\pi\)
\(284\) 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 0.483698 + 0.875235i \(0.339293\pi\)
−0.999825 + 0.0187226i \(0.994040\pi\)
\(294\) 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 \(-0.772711\pi\)
0.755716 0.654900i \(-0.227289\pi\)
\(308\) 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 0.745927 0.666027i \(-0.232007\pi\)
−0.203833 + 0.979006i \(0.565340\pi\)
\(312\) 0 0
\(313\) 26193.1 + 45367.8i 0.267361 + 0.463083i 0.968180 0.250257i \(-0.0805150\pi\)
−0.700818 + 0.713340i \(0.747182\pi\)
\(314\) 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 0.794072 0.607823i \(-0.207957\pi\)
−0.923427 + 0.383775i \(0.874624\pi\)
\(318\) 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 −0.319312 0.947650i \(-0.603452\pi\)
0.661032 + 0.750357i \(0.270119\pi\)
\(332\) −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 −0.890937 0.454127i \(-0.849951\pi\)
0.838754 + 0.544511i \(0.183285\pi\)
\(338\) −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 0.391593 0.920138i \(-0.371924\pi\)
−0.601067 + 0.799199i \(0.705257\pi\)
\(348\) 0 0
\(349\) −59988.4 103903.i −0.492512 0.853055i 0.507451 0.861681i \(-0.330588\pi\)
−0.999963 + 0.00862528i \(0.997254\pi\)
\(350\) −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 0.989305 + 0.145865i \(0.0465964\pi\)
−0.368330 + 0.929695i \(0.620070\pi\)
\(354\) 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 \(0.0834942\pi\)
−0.965795 + 0.259307i \(0.916506\pi\)
\(360\) 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 −0.772212 0.635364i \(-0.780850\pi\)
0.164136 + 0.986438i \(0.447517\pi\)
\(368\) 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 −0.332260 0.943188i \(-0.607811\pi\)
0.982955 0.183848i \(-0.0588554\pi\)
\(374\) −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 \(0.0570248\pi\)
−0.983996 + 0.178192i \(0.942975\pi\)
\(380\) −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 0.877438 0.479690i \(-0.159251\pi\)
0.0232957 + 0.999729i \(0.492584\pi\)
\(384\) 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 0.956123 0.292965i \(-0.0946418\pi\)
−0.731776 + 0.681545i \(0.761308\pi\)
\(390\) 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 −0.734509 0.678599i \(-0.762587\pi\)
0.954939 + 0.296803i \(0.0959206\pi\)
\(402\) 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 −0.923735 0.383031i \(-0.874880\pi\)
0.793582 + 0.608463i \(0.208214\pi\)
\(410\) −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 −0.119357 0.992851i \(-0.538083\pi\)
−0.919513 + 0.393060i \(0.871417\pi\)
\(420\) 0 0
\(421\) −42063.0 72855.3i −0.237321 0.411052i 0.722624 0.691242i \(-0.242936\pi\)
−0.959945 + 0.280190i \(0.909603\pi\)
\(422\) 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 \(0.132369\pi\)
−0.914774 + 0.403967i \(0.867631\pi\)
\(432\) 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 −0.724953 0.688798i \(-0.758139\pi\)
0.234040 + 0.972227i \(0.424805\pi\)
\(440\) −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 −0.913486 0.406871i \(-0.866620\pi\)
−0.104382 + 0.994537i \(0.533287\pi\)
\(444\) 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 0.775929 0.630820i \(-0.217281\pi\)
−0.934271 + 0.356564i \(0.883948\pi\)
\(458\) −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 0.585471 0.810694i \(-0.300910\pi\)
−0.994817 + 0.101686i \(0.967576\pi\)
\(462\) 0 0
\(463\) −150682. 86996.3i −0.702909 0.405825i 0.105521 0.994417i \(-0.466349\pi\)
−0.808430 + 0.588592i \(0.799682\pi\)
\(464\) 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 \(0.129096\pi\)
−0.918879 + 0.394540i \(0.870904\pi\)
\(468\) 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 −0.851912 0.523685i \(-0.824557\pi\)
0.0275690 + 0.999620i \(0.491223\pi\)
\(480\) 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 \(0.309757\pi\)
−0.562716 + 0.826650i \(0.690243\pi\)
\(488\) −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 0.0735480 0.997292i \(-0.476568\pi\)
−0.826906 + 0.562340i \(0.809901\pi\)
\(492\) 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 0.717332 0.696731i \(-0.245363\pi\)
−0.244721 + 0.969594i \(0.578696\pi\)
\(500\) −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 \(-0.848159\pi\)
0.888365 0.459137i \(-0.151841\pi\)
\(504\) 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 −0.971496 0.237057i \(-0.923817\pi\)
0.691045 + 0.722812i \(0.257151\pi\)
\(510\) 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 \(-0.957278\pi\)
0.991007 0.133811i \(-0.0427215\pi\)
\(524\) 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 −0.878211 0.478274i \(-0.841263\pi\)
−0.0249077 + 0.999690i \(0.507929\pi\)
\(548\) 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 0.613302 0.789849i \(-0.289841\pi\)
−0.377378 + 0.926059i \(0.623174\pi\)
\(564\) 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 0.874731 + 0.484609i \(0.161038\pi\)
−0.0176822 + 0.999844i \(0.505629\pi\)
\(570\) 0 0
\(571\) −262848. 151755.i −0.806181 0.465449i 0.0394467 0.999222i \(-0.487440\pi\)
−0.845628 + 0.533773i \(0.820774\pi\)
\(572\) 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 0.448666 0.893699i \(-0.351899\pi\)
0.998300 + 0.0582932i \(0.0185658\pi\)
\(588\) 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 0.712767 0.701401i \(-0.247442\pi\)
−0.251048 + 0.967975i \(0.580775\pi\)
\(600\) 0 0
\(601\) 203120. + 351814.i 0.562346 + 0.974012i 0.997291 + 0.0735551i \(0.0234345\pi\)
−0.434945 + 0.900457i \(0.643232\pi\)
\(602\) −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 0.578523 0.815666i \(-0.303629\pi\)
−0.417126 + 0.908849i \(0.636962\pi\)
\(608\) −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 −0.852331 0.523003i \(-0.824812\pi\)
0.879099 + 0.476639i \(0.158145\pi\)
\(618\) 0 0
\(619\) 388604. 224361.i 1.01421 0.585552i 0.101786 0.994806i \(-0.467544\pi\)
0.912420 + 0.409254i \(0.134211\pi\)
\(620\) 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 \(0.168687\pi\)
−0.862835 + 0.505486i \(0.831313\pi\)
\(632\) 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 0.996921 0.0784117i \(-0.0249849\pi\)
−0.566367 + 0.824153i \(0.691652\pi\)
\(642\) 0 0
\(643\) −227886. 131570.i −0.551184 0.318226i 0.198415 0.980118i \(-0.436420\pi\)
−0.749599 + 0.661892i \(0.769754\pi\)
\(644\) 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 \(0.102586\pi\)
−0.948515 + 0.316732i \(0.897414\pi\)
\(648\) 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 −0.869451 0.494019i \(-0.835527\pi\)
0.862559 + 0.505957i \(0.168861\pi\)
\(654\) 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 −0.937802 0.347171i \(-0.887142\pi\)
−0.168242 + 0.985746i \(0.553809\pi\)
\(660\) 0 0
\(661\) 410614. 711204.i 0.939789 1.62776i 0.173926 0.984759i \(-0.444355\pi\)
0.765863 0.643004i \(-0.222312\pi\)
\(662\) −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 −0.996506 0.0835158i \(-0.973385\pi\)
0.425926 0.904758i \(-0.359948\pi\)
\(674\) −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 −0.946125 0.323801i \(-0.895039\pi\)
0.192642 0.981269i \(-0.438294\pi\)
\(678\) 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 \(0.305734\pi\)
−0.573117 + 0.819474i \(0.694266\pi\)
\(684\) 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 −0.179659 0.983729i \(-0.557500\pi\)
0.762105 + 0.647454i \(0.224166\pi\)
\(692\) −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 0.999670 + 0.0256748i \(0.00817343\pi\)
−0.477600 + 0.878577i \(0.658493\pi\)
\(710\) −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 \(0.109486\pi\)
−0.941426 + 0.337219i \(0.890514\pi\)
\(720\) 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 0.0854497 0.996342i \(-0.472767\pi\)
0.905583 + 0.424170i \(0.139434\pi\)
\(728\) 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 −0.555280 0.831664i \(-0.687389\pi\)
0.997882 + 0.0650546i \(0.0207222\pi\)
\(734\) 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 \(0.281312\pi\)
−0.634244 + 0.773133i \(0.718688\pi\)
\(740\) 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 0.900189 0.435499i \(-0.143428\pi\)
0.0729415 + 0.997336i \(0.476761\pi\)
\(744\) 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 −0.180139 0.983641i \(-0.557655\pi\)
−0.941928 + 0.335816i \(0.890988\pi\)
\(752\) −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 −0.722305 0.691575i \(-0.756917\pi\)
0.960074 + 0.279747i \(0.0902505\pi\)
\(762\) 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 −0.842821 0.538193i \(-0.819107\pi\)
0.887500 + 0.460808i \(0.152440\pi\)
\(770\) −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