Properties

Label 108.5.f.a.91.21
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 91.21
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.21

$q$-expansion

\(f(q)\) \(=\) \(q+(3.93519 - 0.717143i) q^{2} +(14.9714 - 5.64418i) q^{4} +(5.51579 - 9.55363i) q^{5} +(-10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +O(q^{10})\) \(q+(3.93519 - 0.717143i) q^{2} +(14.9714 - 5.64418i) q^{4} +(5.51579 - 9.55363i) q^{5} +(-10.3188 + 5.95759i) q^{7} +(54.8676 - 32.9476i) q^{8} +(14.8544 - 41.5509i) q^{10} +(189.995 - 109.694i) q^{11} +(18.5350 - 32.1036i) q^{13} +(-36.3341 + 30.8443i) q^{14} +(192.286 - 169.003i) q^{16} -284.021 q^{17} +45.4901i q^{19} +(28.6568 - 174.163i) q^{20} +(669.000 - 567.918i) q^{22} +(174.319 + 100.643i) q^{23} +(251.652 + 435.874i) q^{25} +(49.9160 - 139.626i) q^{26} +(-120.862 + 147.435i) q^{28} +(-614.153 - 1063.74i) q^{29} +(1311.83 + 757.384i) q^{31} +(635.484 - 802.954i) q^{32} +(-1117.68 + 203.683i) q^{34} +131.443i q^{35} -1521.29 q^{37} +(32.6229 + 179.012i) q^{38} +(-12.1303 - 705.917i) q^{40} +(-1316.97 + 2281.07i) q^{41} +(34.6057 - 19.9796i) q^{43} +(2225.36 - 2714.63i) q^{44} +(758.153 + 271.038i) q^{46} +(-2498.36 + 1442.43i) q^{47} +(-1129.51 + 1956.38i) q^{49} +(1302.88 + 1534.78i) q^{50} +(96.2969 - 585.252i) q^{52} -1415.13 q^{53} -2420.19i q^{55} +(-369.883 + 666.859i) q^{56} +(-3179.66 - 3745.60i) q^{58} +(2453.33 + 1416.43i) q^{59} +(2628.64 + 4552.93i) q^{61} +(5705.44 + 2039.68i) q^{62} +(1924.92 - 3615.51i) q^{64} +(-204.471 - 354.154i) q^{65} +(-805.917 - 465.296i) q^{67} +(-4252.19 + 1603.07i) q^{68} +(94.2635 + 517.254i) q^{70} -1162.75i q^{71} -2162.87 q^{73} +(-5986.57 + 1090.98i) q^{74} +(256.754 + 681.051i) q^{76} +(-1307.02 + 2263.82i) q^{77} +(-6482.54 + 3742.70i) q^{79} +(-553.978 - 2769.22i) q^{80} +(-3546.69 + 9920.88i) q^{82} +(-966.756 + 558.157i) q^{83} +(-1566.60 + 2713.43i) q^{85} +(121.852 - 103.441i) q^{86} +(6810.44 - 12278.5i) q^{88} +6739.71 q^{89} +441.696i q^{91} +(3177.85 + 522.881i) q^{92} +(-8797.09 + 7467.91i) q^{94} +(434.596 + 250.914i) q^{95} +(-6023.28 - 10432.6i) q^{97} +(-3041.85 + 8508.73i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.93519 0.717143i 0.983797 0.179286i
\(3\) 0 0
\(4\) 14.9714 5.64418i 0.935713 0.352761i
\(5\) 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 −0.601585 0.798809i \(-0.705464\pi\)
0.390996 + 0.920392i \(0.372131\pi\)
\(8\) 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 \(-0.305367\pi\)
0.996143 0.0877473i \(-0.0279668\pi\)
\(12\) 0 0
\(13\) 18.5350 32.1036i 0.109675 0.189962i −0.805964 0.591965i \(-0.798352\pi\)
0.915639 + 0.402003i \(0.131686\pi\)
\(14\) −36.3341 + 30.8443i −0.185378 + 0.157369i
\(15\) 0 0
\(16\) 192.286 169.003i 0.751119 0.660167i
\(17\) −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 \(0.979931\pi\)
\(20\) 28.6568 174.163i 0.0716419 0.435409i
\(21\) 0 0
\(22\) 669.000 567.918i 1.38223 1.17338i
\(23\) 174.319 + 100.643i 0.329525 + 0.190252i 0.655630 0.755082i \(-0.272403\pi\)
−0.326105 + 0.945334i \(0.605736\pi\)
\(24\) 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 0.990293 0.138996i \(-0.0443875\pi\)
0.374773 + 0.927117i \(0.377721\pi\)
\(32\) 635.484 802.954i 0.620590 0.784135i
\(33\) 0 0
\(34\) −1117.68 + 203.683i −0.966847 + 0.176197i
\(35\) 131.443i 0.107301i
\(36\) 0 0
\(37\) −1521.29 −1.11124 −0.555622 0.831435i \(-0.687520\pi\)
−0.555622 + 0.831435i \(0.687520\pi\)
\(38\) 32.6229 + 179.012i 0.0225920 + 0.123970i
\(39\) 0 0
\(40\) −12.1303 705.917i −0.00758145 0.441198i
\(41\) −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 −0.490613 0.871378i \(-0.663227\pi\)
0.509329 + 0.860572i \(0.329894\pi\)
\(44\) 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 \(-0.893147\pi\)
−0.186807 + 0.982397i \(0.559814\pi\)
\(48\) 0 0
\(49\) −1129.51 + 1956.38i −0.470435 + 0.814817i
\(50\) 1302.88 + 1534.78i 0.521153 + 0.613911i
\(51\) 0 0
\(52\) 96.2969 585.252i 0.0356128 0.216439i
\(53\) −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
\(56\) −369.883 + 666.859i −0.117947 + 0.212646i
\(57\) 0 0
\(58\) −3179.66 3745.60i −0.945203 1.11344i
\(59\) 2453.33 + 1416.43i 0.704778 + 0.406904i 0.809125 0.587637i \(-0.199942\pi\)
−0.104346 + 0.994541i \(0.533275\pi\)
\(60\) 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 0.407541 0.913187i \(-0.366386\pi\)
−0.587073 + 0.809534i \(0.699720\pi\)
\(68\) −4252.19 + 1603.07i −0.919592 + 0.346684i
\(69\) 0 0
\(70\) 94.2635 + 517.254i 0.0192375 + 0.105562i
\(71\) 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 \(0.565048\pi\)
\(74\) −5986.57 + 1090.98i −1.09324 + 0.199230i
\(75\) 0 0
\(76\) 256.754 + 681.051i 0.0444519 + 0.117911i
\(77\) −1307.02 + 2263.82i −0.220445 + 0.381822i
\(78\) 0 0
\(79\) −6482.54 + 3742.70i −1.03870 + 0.599695i −0.919466 0.393171i \(-0.871378\pi\)
−0.119237 + 0.992866i \(0.538045\pi\)
\(80\) −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 \(-0.692485\pi\)
0.428190 + 0.903689i \(0.359152\pi\)
\(84\) 0 0
\(85\) −1566.60 + 2713.43i −0.216830 + 0.375561i
\(86\) 121.852 103.441i 0.0164754 0.0139861i
\(87\) 0 0
\(88\) 6810.44 12278.5i 0.879447 1.58555i
\(89\) 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
\(92\) 3177.85 + 522.881i 0.375455 + 0.0617771i
\(93\) 0 0
\(94\) −8797.09 + 7467.91i −0.995596 + 0.845168i
\(95\) 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 0.889659 0.456626i \(-0.150942\pi\)
0.0493798 + 0.998780i \(0.484276\pi\)
\(104\) −40.7622 2372.13i −0.00376870 0.219317i
\(105\) 0 0
\(106\) −5568.79 + 1014.85i −0.495620 + 0.0903211i
\(107\) 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 \(0.330786\pi\)
\(110\) −1735.62 9523.89i −0.143440 0.787099i
\(111\) 0 0
\(112\) −977.325 + 2889.48i −0.0779117 + 0.230347i
\(113\) 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
\(122\) 13609.3 + 16031.5i 0.914356 + 1.07710i
\(123\) 0 0
\(124\) 23914.7 + 3934.92i 1.55533 + 0.255913i
\(125\) 12447.0 0.796607
\(126\) 0 0
\(127\) 26549.7i 1.64608i −0.567980 0.823042i \(-0.692275\pi\)
0.567980 0.823042i \(-0.307725\pi\)
\(128\) 4982.07 15608.2i 0.304082 0.952646i
\(129\) 0 0
\(130\) −1058.61 1247.03i −0.0626396 0.0737886i
\(131\) −1142.84 659.821i −0.0665954 0.0384489i 0.466333 0.884609i \(-0.345575\pi\)
−0.532928 + 0.846161i \(0.678908\pi\)
\(132\) 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 0.764656 0.644438i \(-0.222909\pi\)
−0.175772 + 0.984431i \(0.556242\pi\)
\(140\) 741.889 + 1967.89i 0.0378515 + 0.100403i
\(141\) 0 0
\(142\) −833.858 4575.64i −0.0413538 0.226921i
\(143\) 8132.70i 0.397706i
\(144\) 0 0
\(145\) −13550.2 −0.644478
\(146\) −8511.29 + 1551.08i −0.399291 + 0.0727662i
\(147\) 0 0
\(148\) −22775.9 + 8586.46i −1.03981 + 0.392004i
\(149\) 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 −0.930496 0.366303i \(-0.880623\pi\)
−0.148020 + 0.988984i \(0.547290\pi\)
\(152\) 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 \(0.130948\pi\)
\(158\) −22826.0 + 19377.1i −0.914356 + 0.776203i
\(159\) 0 0
\(160\) −4165.93 10500.1i −0.162732 0.410161i
\(161\) −2398.36 −0.0925257
\(162\) 0 0
\(163\) 407.281i 0.0153292i 0.999971 + 0.00766459i \(0.00243974\pi\)
−0.999971 + 0.00766459i \(0.997560\pi\)
\(164\) −6842.21 + 41584.0i −0.254395 + 1.54610i
\(165\) 0 0
\(166\) −3404.09 + 2889.76i −0.123534 + 0.104868i
\(167\) −20561.9 11871.4i −0.737277 0.425667i 0.0838016 0.996482i \(-0.473294\pi\)
−0.821078 + 0.570816i \(0.806627\pi\)
\(168\) 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
\(176\) 17994.9 53202.2i 0.580931 1.71753i
\(177\) 0 0
\(178\) 26522.0 4833.34i 0.837080 0.152548i
\(179\) 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 \(0.620554\pi\)
\(182\) 316.759 + 1738.16i 0.00956283 + 0.0524743i
\(183\) 0 0
\(184\) 12880.4 221.334i 0.380447 0.00653752i
\(185\) −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 \(-0.766554\pi\)
0.208257 + 0.978074i \(0.433221\pi\)
\(192\) 0 0
\(193\) −9144.35 + 15838.5i −0.245493 + 0.425205i −0.962270 0.272097i \(-0.912283\pi\)
0.716777 + 0.697302i \(0.245616\pi\)
\(194\) −31184.4 36734.8i −0.828579 0.976055i
\(195\) 0 0
\(196\) −5868.28 + 35664.9i −0.152756 + 0.928387i
\(197\) −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 \(-0.203906\pi\)
\(200\) 28168.6 + 15624.1i 0.704214 + 0.390602i
\(201\) 0 0
\(202\) −24735.1 29137.6i −0.606194 0.714088i
\(203\) 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 \(-0.158476\pi\)
0.0257275 + 0.999669i \(0.491810\pi\)
\(212\) −21186.5 + 7987.24i −0.471397 + 0.177715i
\(213\) 0 0
\(214\) −4735.09 25982.9i −0.103395 0.567363i
\(215\) 440.814i 0.00953626i
\(216\) 0 0
\(217\) −18048.7 −0.383290
\(218\) 47400.4 8638.18i 0.997400 0.181765i
\(219\) 0 0
\(220\) −13660.0 36233.6i −0.282231 0.748629i
\(221\) −5264.34 + 9118.10i −0.107785 + 0.186689i
\(222\) 0 0
\(223\) 71531.9 41298.9i 1.43843 0.830480i 0.440693 0.897658i \(-0.354733\pi\)
0.997741 + 0.0671780i \(0.0213996\pi\)
\(224\) −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 \(-0.573609\pi\)
0.728376 + 0.685178i \(0.240276\pi\)
\(228\) 0 0
\(229\) −22667.9 + 39262.0i −0.432256 + 0.748690i −0.997067 0.0765307i \(-0.975616\pi\)
0.564811 + 0.825220i \(0.308949\pi\)
\(230\) 6771.21 5748.13i 0.128000 0.108660i
\(231\) 0 0
\(232\) −68744.9 38130.3i −1.27722 0.708425i
\(233\) −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
\(236\) 44724.5 + 7358.94i 0.803010 + 0.132127i
\(237\) 0 0
\(238\) 10319.7 8760.43i 0.182184 0.154658i
\(239\) −31946.2 18444.1i −0.559272 0.322896i 0.193581 0.981084i \(-0.437990\pi\)
−0.752853 + 0.658188i \(0.771323\pi\)
\(240\) 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
\(248\) 96930.9 1665.64i 1.57601 0.0270818i
\(249\) 0 0
\(250\) 48981.2 8926.26i 0.783699 0.142820i
\(251\) 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
\(254\) −19039.9 104478.i −0.295119 1.61941i
\(255\) 0 0
\(256\) 8412.13 64993.9i 0.128359 0.991728i
\(257\) 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 −0.614392 0.789001i \(-0.710599\pi\)
0.376099 + 0.926580i \(0.377265\pi\)
\(264\) 0 0
\(265\) −7805.54 + 13519.6i −0.111151 + 0.192518i
\(266\) −1403.11 1652.84i −0.0198303 0.0233598i
\(267\) 0 0
\(268\) −14691.9 2417.40i −0.204555 0.0336573i
\(269\) −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 \(0.931259\pi\)
\(272\) −54613.4 + 48000.3i −0.738178 + 0.648793i
\(273\) 0 0
\(274\) 66820.8 + 78714.0i 0.890043 + 1.04846i
\(275\) 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 0.765835 0.643038i \(-0.222326\pi\)
−0.173970 + 0.984751i \(0.555659\pi\)
\(284\) −6562.78 17408.0i −0.0813675 0.215830i
\(285\) 0 0
\(286\) −5832.30 32003.7i −0.0713030 0.391262i
\(287\) 31383.9i 0.381016i
\(288\) 0 0
\(289\) −2853.15 −0.0341609
\(290\) −53322.4 + 9717.39i −0.634036 + 0.115546i
\(291\) 0 0
\(292\) −32381.2 + 12207.6i −0.379776 + 0.143174i
\(293\) −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
\(302\) −86589.3 + 73506.3i −0.949403 + 0.805955i
\(303\) 0 0
\(304\) 7687.95 + 8747.13i 0.0831886 + 0.0946495i
\(305\) 57996.0 0.623446
\(306\) 0 0
\(307\) 123447.i 1.30980i 0.755716 + 0.654900i \(0.227289\pi\)
−0.755716 + 0.654900i \(0.772711\pi\)
\(308\) −6790.48 + 41269.7i −0.0715813 + 0.435040i
\(309\) 0 0
\(310\) 50956.4 43257.2i 0.530243 0.450127i
\(311\) −52431.9 30271.6i −0.542094 0.312978i 0.203833 0.979006i \(-0.434660\pi\)
−0.745927 + 0.666027i \(0.767993\pi\)
\(312\) 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
\(320\) −23923.8 38332.3i −0.233631 0.374339i
\(321\) 0 0
\(322\) −9437.99 + 1719.97i −0.0910265 + 0.0165885i
\(323\) 12920.1i 0.123840i
\(324\) 0 0
\(325\) 18657.5 0.176639
\(326\) 292.079 + 1602.73i 0.00274830 + 0.0150808i
\(327\) 0 0
\(328\) 2896.29 + 168548.i 0.0269212 + 1.56666i
\(329\) 17186.8 29768.4i 0.158783 0.275019i
\(330\) 0 0
\(331\) −37439.2 + 21615.5i −0.341720 + 0.197292i −0.661032 0.750357i \(-0.729881\pi\)
0.319312 + 0.947650i \(0.396548\pi\)
\(332\) −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 \(0.183285\pi\)
\(338\) 70377.3 + 82903.5i 0.616027 + 0.725671i
\(339\) 0 0
\(340\) −8139.12 + 49466.1i −0.0704076 + 0.427907i
\(341\) 332321. 2.85791
\(342\) 0 0
\(343\) 55525.0i 0.471955i
\(344\) 1240.45 2236.41i 0.0104825 0.0188988i
\(345\) 0 0
\(346\) −7316.83 8619.12i −0.0611182 0.0719964i
\(347\) 25222.5 + 14562.2i 0.209473 + 0.120940i 0.601067 0.799199i \(-0.294743\pi\)
−0.391593 + 0.920138i \(0.628076\pi\)
\(348\) 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
\(356\) 100903. 38040.2i 0.796167 0.300153i
\(357\) 0 0
\(358\) 32804.5 + 180009.i 0.255957 + 1.40452i
\(359\) 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
\(362\) −95334.7 + 17373.6i −0.727501 + 0.132579i
\(363\) 0 0
\(364\) 2493.01 + 6612.82i 0.0188158 + 0.0499096i
\(365\) −11929.9 + 20663.2i −0.0895472 + 0.155100i
\(366\) 0 0
\(367\) 81901.3 47285.7i 0.608077 0.351073i −0.164136 0.986438i \(-0.552483\pi\)
0.772212 + 0.635364i \(0.219150\pi\)
\(368\) 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 \(-0.0588554\pi\)
\(374\) −190010. + 161301.i −1.35842 + 1.15317i
\(375\) 0 0
\(376\) −89554.6 + 161457.i −0.633450 + 1.14204i
\(377\) −45533.4 −0.320366
\(378\) 0 0
\(379\) 51191.3i 0.356384i −0.983996 0.178192i \(-0.942975\pi\)
0.983996 0.178192i \(-0.0570248\pi\)
\(380\) 7922.71 + 1303.60i 0.0548664 + 0.00902769i
\(381\) 0 0
\(382\) −68678.6 + 58301.7i −0.470646 + 0.399535i
\(383\) −132128. 76284.0i −0.900734 0.520039i −0.0232957 0.999729i \(-0.507416\pi\)
−0.877438 + 0.479690i \(0.840749\pi\)
\(384\) 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
\(392\) 2484.03 + 144556.i 0.0161653 + 0.940731i
\(393\) 0 0
\(394\) −142848. + 26032.5i −0.920201 + 0.167696i
\(395\) 82575.7i 0.529247i
\(396\) 0 0
\(397\) −126087. −0.799998 −0.399999 0.916516i \(-0.630990\pi\)
−0.399999 + 0.916516i \(0.630990\pi\)
\(398\) −33947.0 186278.i −0.214306 1.17597i
\(399\) 0 0
\(400\) 122053. + 41282.8i 0.762833 + 0.258017i
\(401\) 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 \(0.208214\pi\)
\(410\) 75217.6 + 88605.3i 0.447458 + 0.527099i
\(411\) 0 0
\(412\) 181613. + 29882.5i 1.06992 + 0.176044i
\(413\) −33754.1 −0.197891
\(414\) 0 0
\(415\) 12314.7i 0.0715036i
\(416\) −13999.0 35284.1i −0.0808930 0.203888i
\(417\) 0 0
\(418\) 25834.7 + 30432.9i 0.147860 + 0.174177i
\(419\) 182385. + 105300.i 1.03887 + 0.599792i 0.919513 0.393060i \(-0.128583\pi\)
0.119357 + 0.992851i \(0.461917\pi\)
\(420\) 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
\(428\) −37266.9 98852.0i −0.203440 0.539632i
\(429\) 0 0
\(430\) −316.126 1734.69i −0.00170972 0.00938175i
\(431\) 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 \(0.439172\pi\)
\(434\) −71025.1 + 12943.5i −0.377079 + 0.0687183i
\(435\) 0 0
\(436\) 180335. 67985.7i 0.948651 0.357639i
\(437\) −4578.26 + 7929.78i −0.0239739 + 0.0415239i
\(438\) 0 0
\(439\) 94609.3 54622.7i 0.490913 0.283429i −0.234040 0.972227i \(-0.575195\pi\)
0.724953 + 0.688798i \(0.241861\pi\)
\(440\) −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 \(-0.466713\pi\)
0.913486 + 0.406871i \(0.133380\pi\)
\(444\) 0 0
\(445\) 37174.8 64388.7i 0.187728 0.325154i
\(446\) 251874. 213818.i 1.26623 1.07491i
\(447\) 0 0
\(448\) 1676.80 + 48775.7i 0.00835458 + 0.243023i
\(449\) 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
\(452\) 9691.23 58899.1i 0.0474353 0.288292i
\(453\) 0 0
\(454\) 90572.1 76887.2i 0.439423 0.373029i
\(455\) 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 0.808430 0.588592i \(-0.200318\pi\)
−0.105521 + 0.994417i \(0.533651\pi\)
\(464\) −297869. 100750.i −1.38353 0.467960i
\(465\) 0 0
\(466\) −200424. + 36525.0i −0.922950 + 0.168197i
\(467\) 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
\(470\) 22822.7 + 125236.i 0.103317 + 0.566933i
\(471\) 0 0
\(472\) 181277. 3115.02i 0.813688 0.0139822i
\(473\) 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 \(-0.508777\pi\)
0.851912 + 0.523685i \(0.175443\pi\)
\(480\) 0 0
\(481\) −28197.2 + 48839.0i −0.121875 + 0.211094i
\(482\) −21711.8 25576.2i −0.0934548 0.110088i
\(483\) 0 0
\(484\) 86996.3 528726.i 0.371373 2.25705i
\(485\) −132893. −0.564959
\(486\) 0 0
\(487\) 392112.i 1.65330i −0.562716 0.826650i \(-0.690243\pi\)
0.562716 0.826650i \(-0.309757\pi\)
\(488\) 294235. + 163201.i 1.23553 + 0.685306i
\(489\) 0 0
\(490\) 64511.1 + 75993.1i 0.268684 + 0.316506i
\(491\) 181620. + 104859.i 0.753358 + 0.434951i 0.826906 0.562340i \(-0.190099\pi\)
−0.0735480 + 0.997292i \(0.523432\pi\)
\(492\) 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 \(-0.421304\pi\)
−0.717332 + 0.696731i \(0.754637\pi\)
\(500\) 186349. 70253.0i 0.745395 0.281012i
\(501\) 0 0
\(502\) 1058.12 + 5806.24i 0.00419883 + 0.0230403i
\(503\) 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
\(506\) 173776. 31668.7i 0.678718 0.123689i
\(507\) 0 0
\(508\) −149851. 397486.i −0.580675 1.54026i
\(509\) −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
\(518\) 55274.9 46923.2i 0.206001 0.174875i
\(519\) 0 0
\(520\) −22887.3 12694.8i −0.0846425 0.0469481i
\(521\) −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 \(0.957278\pi\)
\(524\) −20834.1 3428.04i −0.0758775 0.0124848i
\(525\) 0 0
\(526\) −58037.4 + 49268.3i −0.209767 + 0.178072i
\(527\) −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
\(536\) −59549.1 + 1023.28i −0.207274 + 0.00356176i
\(537\) 0 0
\(538\) −231090. + 42113.6i −0.798394 + 0.145498i
\(539\) 495602.i 1.70591i
\(540\) 0 0
\(541\) 438165. 1.49707 0.748536 0.663094i \(-0.230757\pi\)
0.748536 + 0.663094i \(0.230757\pi\)
\(542\) 22571.4 + 123856.i 0.0768351 + 0.421619i
\(543\) 0 0
\(544\) −180491. + 228056.i −0.609898 + 0.770625i
\(545\) 66439.2 115076.i 0.223682 0.387429i
\(546\) 0 0
\(547\) 270221. 156012.i 0.903118 0.521416i 0.0249077 0.999690i \(-0.492071\pi\)
0.878211 + 0.478274i \(0.158737\pi\)
\(548\) 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
\(554\) −172227. 202881.i −0.561155 0.661032i
\(555\) 0 0
\(556\) 207419. + 34128.6i 0.670963 + 0.110400i
\(557\) −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
\(560\) 22214.3 + 25274.7i 0.0708363 + 0.0805955i
\(561\) 0 0
\(562\) −320268. 377272.i −1.01401 1.19449i
\(563\) −74780.6 43174.6i −0.235924 0.136211i 0.377378 0.926059i \(-0.376826\pi\)
−0.613302 + 0.789849i \(0.710159\pi\)
\(564\) 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 0.845628 0.533773i \(-0.179226\pi\)
−0.0394467 + 0.999222i \(0.512560\pi\)
\(572\) −45902.4 121758.i −0.140295 0.372139i
\(573\) 0 0
\(574\) −22506.8 123502.i −0.0683108 0.374843i
\(575\) 101308.i 0.306414i
\(576\) 0 0
\(577\) −500884. −1.50448 −0.752238 0.658892i \(-0.771026\pi\)
−0.752238 + 0.658892i \(0.771026\pi\)
\(578\) −11227.7 + 2046.12i −0.0336074 + 0.00612456i
\(579\) 0 0
\(580\) −202865. + 76479.5i −0.603047 + 0.227347i
\(581\) 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 \(-0.981434\pi\)
−0.448666 + 0.893699i \(0.648101\pi\)
\(588\) 0 0
\(589\) −34453.5 + 59675.2i −0.0993122 + 0.172014i
\(590\) 95296.8 80898.1i 0.273763 0.232399i
\(591\) 0 0
\(592\) −292524. + 257103.i −0.834676 + 0.733607i
\(593\) 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
\(596\) 67375.1 409477.i 0.189674 1.15275i
\(597\) 0 0
\(598\) 22753.7 19315.8i 0.0636282 0.0540144i
\(599\) −165665. 95646.9i −0.461719 0.266574i 0.251048 0.967975i \(-0.419225\pi\)
−0.712767 + 0.701401i \(0.752558\pi\)
\(600\) 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 0.417126 0.908849i \(-0.363038\pi\)
−0.578523 + 0.815666i \(0.696371\pi\)
\(608\) 36526.5 + 28908.2i 0.0988100 + 0.0782014i
\(609\) 0 0
\(610\) 228225. 41591.4i 0.613344 0.111775i
\(611\) 106942.i 0.286461i
\(612\) 0 0
\(613\) −572114. −1.52252 −0.761258 0.648450i \(-0.775418\pi\)
−0.761258 + 0.648450i \(0.775418\pi\)
\(614\) 88529.3 + 485788.i 0.234828 + 1.28858i
\(615\) 0 0
\(616\) 2874.39 + 167274.i 0.00757504 + 0.440825i
\(617\) 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 −0.912420 0.409254i \(-0.865789\pi\)
−0.101786 + 0.994806i \(0.532456\pi\)
\(620\) 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
\(626\) 135610. + 159747.i 0.346053 + 0.407646i
\(627\) 0 0
\(628\) 14340.3 87154.1i 0.0363612 0.220988i
\(629\) 432079. 1.09210
\(630\) 0 0
\(631\) 402529.i 1.01097i −0.862835 0.505486i \(-0.831313\pi\)
0.862835 0.505486i \(-0.168687\pi\)
\(632\) −232369. + 418937.i −0.581760 + 1.04885i
\(633\) 0 0
\(634\) −67298.3 79276.4i −0.167427 0.197227i
\(635\) −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 0.749599 0.661892i \(-0.230246\pi\)
−0.198415 + 0.980118i \(0.563580\pi\)
\(644\) −35906.8 + 13536.8i −0.0865775 + 0.0326395i
\(645\) 0 0
\(646\) −9265.58 50843.2i −0.0222028 0.121834i
\(647\) 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
\(650\) 73420.8 13380.1i 0.173777 0.0316689i
\(651\) 0 0
\(652\) 2298.77 + 6097.57i 0.00540754 + 0.0143437i
\(653\) −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 0.168242 0.985746i \(-0.446191\pi\)
0.937802 + 0.347171i \(0.112858\pi\)
\(660\) 0 0
\(661\) 410614. 711204.i 0.939789 1.62776i 0.173926 0.984759i \(-0.444355\pi\)
0.765863 0.643004i \(-0.222312\pi\)
\(662\) −131829. + 111910.i −0.300812 + 0.255361i
\(663\) 0 0
\(664\) −34653.7 + 62477.0i −0.0785984 + 0.141705i
\(665\) −5979.36 −0.0135211
\(666\) 0 0
\(667\) 247241.i 0.555736i
\(668\) −374845. 61676.8i −0.840039 0.138219i
\(669\) 0 0
\(670\) −31304.9 + 26574.9i −0.0697368 + 0.0592001i
\(671\) 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
\(680\) 3445.26 + 200495.i 0.00745083 + 0.433597i
\(681\) 0 0
\(682\) 1.30774e6 238321.i 2.81160 0.512382i
\(683\) 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
\(686\) −39819.4 218502.i −0.0846148 0.464308i
\(687\) 0 0
\(688\) 3277.60 9690.27i 0.00692435 0.0204719i
\(689\) −26229.4 + 45430.7i −0.0552523 + 0.0956998i
\(690\) 0 0
\(691\) −278107. + 160565.i −0.582445 + 0.336275i −0.762105 0.647454i \(-0.775834\pi\)
0.179659 + 0.983729i \(0.442500\pi\)
\(692\) −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
\(698\) −310579. 365858.i −0.637472 0.750933i
\(699\) 0 0
\(700\) −94678.2 15578.3i −0.193221 0.0317925i
\(701\) 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
\(704\) −30873.9 898079.i −0.0622940 1.81205i
\(705\) 0 0
\(706\) 400616. + 471920.i 0.803745 + 0.946801i
\(707\) 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
\(716\) 258184. + 684843.i 0.503620 + 1.33587i
\(717\) 0 0
\(718\) −47933.5 263026.i −0.0929801 0.510211i
\(719\) 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
\(722\) 504694. 91974.7i 0.968175 0.176439i
\(723\) 0 0
\(724\) −362701. + 136737.i −0.691944 + 0.260861i
\(725\) 309106. 535387.i 0.588073 1.01857i
\(726\) 0 0
\(727\) −523789. + 302410.i −0.991032 + 0.572173i −0.905583 0.424170i \(-0.860566\pi\)
−0.0854497 + 0.996342i \(0.527233\pi\)
\(728\) 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 \(0.0207222\pi\)
\(734\) 288386. 244813.i 0.535282 0.454404i
\(735\) 0 0
\(736\) 191589. 76013.1i 0.353683 0.140324i
\(737\) −204160. −0.375868
\(738\) 0 0
\(739\) 844449.i 1.54627i −0.634244 0.773133i \(-0.718688\pi\)
0.634244 0.773133i \(-0.281312\pi\)
\(740\) −43595.3 + 264954.i −0.0796116 + 0.483845i
\(741\) 0 0
\(742\) 51417.4 43648.6i 0.0933905 0.0792798i
\(743\) −537216. 310162.i −0.973131 0.561837i −0.0729415 0.997336i \(-0.523239\pi\)
−0.900189 + 0.435499i \(0.856572\pi\)
\(744\) 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 \(-0.109012\pi\)
0.180139 + 0.983641i \(0.442345\pi\)
\(752\) −236626. + 699589.i −0.418434 + 1.23711i
\(753\) 0 0
\(754\) −179182. + 32653.9i −0.315176 + 0.0574371i
\(755\) 313247.i 0.549533i
\(756\) 0 0
\(757\) −769023. −1.34198 −0.670992 0.741465i \(-0.734132\pi\)
−0.670992 + 0.741465i \(0.734132\pi\)
\(758\) −36711.5 201447.i −0.0638945 0.350609i
\(759\) 0 0
\(760\) 32112.2 551.810i 0.0555960 0.000955349i
\(761\) 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 \(0.152440\pi\)
\(770\) 74649.0 + 87935.4i 0.125905 + 0.148314i
\(771\) 0 0
\(772\) −47508.6 + 288737.i −0.0797145 + 0.484471i
\(773\) 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
\(776\) −674213. 373961.i −1.11963 0.621017i
\(777\) 0 0