Properties

Label 108.5.f.a.19.21
Level 108
Weight 5
Character 108.19
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 19.21
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.21

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 0.955000 0.296606i \(-0.0958548\pi\)
−0.734368 + 0.678751i \(0.762521\pi\)
\(6\) 0 0
\(7\) −10.3188 5.95759i −0.210589 0.121583i 0.390996 0.920392i \(-0.372131\pi\)
−0.601585 + 0.798809i \(0.705464\pi\)
\(8\) 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 \(0.0279668\pi\)
0.574063 + 0.818811i \(0.305367\pi\)
\(12\) 0 0
\(13\) 18.5350 + 32.1036i 0.109675 + 0.189962i 0.915639 0.402003i \(-0.131686\pi\)
−0.805964 + 0.591965i \(0.798352\pi\)
\(14\) −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 \(-0.979931\pi\)
0.998013 0.0630057i \(-0.0200686\pi\)
\(20\) 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 −0.326105 0.945334i \(-0.605736\pi\)
0.655630 + 0.755082i \(0.272403\pi\)
\(24\) 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 0.374773 0.927117i \(-0.377721\pi\)
0.990293 + 0.138996i \(0.0443875\pi\)
\(32\) 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 −0.929923 0.367755i \(-0.880126\pi\)
0.146476 0.989214i \(-0.453207\pi\)
\(42\) 0 0
\(43\) 34.6057 + 19.9796i 0.0187159 + 0.0108056i 0.509329 0.860572i \(-0.329894\pi\)
−0.490613 + 0.871378i \(0.663227\pi\)
\(44\) 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 \(-0.559814\pi\)
−0.944184 + 0.329419i \(0.893147\pi\)
\(48\) 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 −0.104346 0.994541i \(-0.533275\pi\)
0.809125 + 0.587637i \(0.199942\pi\)
\(60\) 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 −0.587073 0.809534i \(-0.699720\pi\)
0.407541 + 0.913187i \(0.366386\pi\)
\(68\) −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 \(0.0367923\pi\)
−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 \(0.565048\pi\)
\(74\) −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 −0.119237 0.992866i \(-0.538045\pi\)
−0.919466 + 0.393171i \(0.871378\pi\)
\(80\) −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 \(-0.359152\pi\)
−0.568523 + 0.822667i \(0.692485\pi\)
\(84\) 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 0.345235 + 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 0.0493798 0.998780i \(-0.484276\pi\)
0.889659 + 0.456626i \(0.150942\pi\)
\(104\) −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 \(0.0931078\pi\)
−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 \(0.330786\pi\)
\(110\) −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 0.929777 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
\(122\) 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 \(0.307725\pi\)
−0.567980 + 0.823042i \(0.692275\pi\)
\(128\) 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 −0.532928 0.846161i \(-0.678908\pi\)
0.466333 + 0.884609i \(0.345575\pi\)
\(132\) 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 −0.175772 0.984431i \(-0.556242\pi\)
0.764656 + 0.644438i \(0.222909\pi\)
\(140\) 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 0.994984 + 0.100038i \(0.0318965\pi\)
−0.410856 + 0.911700i \(0.634770\pi\)
\(150\) 0 0
\(151\) −24591.2 14197.8i −1.07852 0.622681i −0.148020 0.988984i \(-0.547290\pi\)
−0.930496 + 0.366303i \(0.880623\pi\)
\(152\) 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 \(0.797614\pi\)
\(158\) −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 \(-0.997560\pi\)
0.999971 0.00766459i \(-0.00243974\pi\)
\(164\) −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 −0.821078 0.570816i \(-0.806627\pi\)
0.0838016 + 0.996482i \(0.473294\pi\)
\(168\) 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
\(176\) 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 \(-0.746961\pi\)
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 \(0.620554\pi\)
\(182\) 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 0.208257 0.978074i \(-0.433221\pi\)
−0.742908 + 0.669393i \(0.766554\pi\)
\(192\) 0 0
\(193\) −9144.35 15838.5i −0.245493 0.425205i 0.716777 0.697302i \(-0.245616\pi\)
−0.962270 + 0.272097i \(0.912283\pi\)
\(194\) −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 \(0.203906\pi\)
−0.801744 + 0.597667i \(0.796094\pi\)
\(200\) 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 0.0257275 0.999669i \(-0.491810\pi\)
0.878602 + 0.477554i \(0.158476\pi\)
\(212\) −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 0.997741 0.0671780i \(-0.0213996\pi\)
0.440693 + 0.897658i \(0.354733\pi\)
\(224\) −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 \(-0.240276\pi\)
−0.229194 + 0.973381i \(0.573609\pi\)
\(228\) 0 0
\(229\) −22667.9 39262.0i −0.432256 0.748690i 0.564811 0.825220i \(-0.308949\pi\)
−0.997067 + 0.0765307i \(0.975616\pi\)
\(230\) 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 −0.752853 0.658188i \(-0.771323\pi\)
0.193581 + 0.981084i \(0.437990\pi\)
\(240\) 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
\(248\) 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 \(-0.996273\pi\)
0.999931 0.0117099i \(-0.00372746\pi\)
\(252\) 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 0.966900 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 0.376099 0.926580i \(-0.377265\pi\)
−0.614392 + 0.789001i \(0.710599\pi\)
\(264\) 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 \(-0.931259\pi\)
0.976772 0.214281i \(-0.0687409\pi\)
\(272\) −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 −0.997176 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 −0.173970 0.984751i \(-0.555659\pi\)
0.765835 + 0.643038i \(0.222326\pi\)
\(284\) −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 −0.999825 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
\(302\) −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 \(-0.772711\pi\)
0.755716 0.654900i \(-0.227289\pi\)
\(308\) −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 −0.745927 0.666027i \(-0.767993\pi\)
0.203833 + 0.979006i \(0.434660\pi\)
\(312\) 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
\(320\) −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 0.319312 0.947650i \(-0.396548\pi\)
−0.661032 + 0.750357i \(0.729881\pi\)
\(332\) −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 \(0.849951\pi\)
\(338\) 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 −0.391593 0.920138i \(-0.628076\pi\)
0.601067 + 0.799199i \(0.294743\pi\)
\(348\) 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
\(356\) 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 \(0.0834942\pi\)
−0.965795 + 0.259307i \(0.916506\pi\)
\(360\) 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 0.772212 0.635364i \(-0.219150\pi\)
−0.164136 + 0.986438i \(0.552483\pi\)
\(368\) 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 \(0.607811\pi\)
\(374\) −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 \(0.0570248\pi\)
−0.983996 + 0.178192i \(0.942975\pi\)
\(380\) 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 −0.877438 0.479690i \(-0.840749\pi\)
−0.0232957 + 0.999729i \(0.507416\pi\)
\(384\) 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
\(392\) 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 0.954939 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 \(0.874880\pi\)
\(410\) 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 0.119357 0.992851i \(-0.461917\pi\)
0.919513 + 0.393060i \(0.128583\pi\)
\(420\) 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
\(428\) −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 \(0.132369\pi\)
−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 \(0.439172\pi\)
\(434\) −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 0.724953 0.688798i \(-0.241861\pi\)
−0.234040 + 0.972227i \(0.575195\pi\)
\(440\) −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 \(-0.133380\pi\)
0.104382 + 0.994537i \(0.466713\pi\)
\(444\) 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 −0.934271 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 −0.105521 0.994417i \(-0.533651\pi\)
0.808430 + 0.588592i \(0.200318\pi\)
\(464\) −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 \(0.129096\pi\)
−0.918879 + 0.394540i \(0.870904\pi\)
\(468\) 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 0.851912 0.523685i \(-0.175443\pi\)
−0.0275690 + 0.999620i \(0.508777\pi\)
\(480\) 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 \(0.309757\pi\)
−0.562716 + 0.826650i \(0.690243\pi\)
\(488\) 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 −0.0735480 0.997292i \(-0.523432\pi\)
0.826906 + 0.562340i \(0.190099\pi\)
\(492\) 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 \(-0.754637\pi\)
0.244721 + 0.969594i \(0.421304\pi\)
\(500\) 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 \(-0.848159\pi\)
0.888365 0.459137i \(-0.151841\pi\)
\(504\) 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 0.691045 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
\(518\) 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 \(-0.957278\pi\)
0.991007 0.133811i \(-0.0427215\pi\)
\(524\) −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 0.878211 0.478274i \(-0.158737\pi\)
0.0249077 + 0.999690i \(0.492071\pi\)
\(548\) 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 −0.613302 0.789849i \(-0.710159\pi\)
0.377378 + 0.926059i \(0.376826\pi\)
\(564\) 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 −0.0394467 0.999222i \(-0.512560\pi\)
0.845628 + 0.533773i \(0.179226\pi\)
\(572\) −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 −0.448666 0.893699i \(-0.648101\pi\)
−0.998300 + 0.0582932i \(0.981434\pi\)
\(588\) 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 −0.712767 0.701401i \(-0.752558\pi\)
0.251048 + 0.967975i \(0.419225\pi\)
\(600\) 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 −0.578523 0.815666i \(-0.696371\pi\)
0.417126 + 0.908849i \(0.363038\pi\)
\(608\) 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 0.879099 0.476639i \(-0.158145\pi\)
−0.852331 + 0.523003i \(0.824812\pi\)
\(618\) 0 0
\(619\) −388604. 224361.i −1.01421 0.585552i −0.101786 0.994806i \(-0.532456\pi\)
−0.912420 + 0.409254i \(0.865789\pi\)
\(620\) 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 \(0.168687\pi\)
−0.862835 + 0.505486i \(0.831313\pi\)
\(632\) −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 −0.566367 0.824153i \(-0.691652\pi\)
0.996921 + 0.0784117i \(0.0249849\pi\)
\(642\) 0 0
\(643\) 227886. 131570.i 0.551184 0.318226i −0.198415 0.980118i \(-0.563580\pi\)
0.749599 + 0.661892i \(0.230246\pi\)
\(644\) −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 \(0.102586\pi\)
−0.948515 + 0.316732i \(0.897414\pi\)
\(648\) 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 0.862559 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 0.937802 0.347171i \(-0.112858\pi\)
0.168242 + 0.985746i \(0.446191\pi\)
\(660\) 0 0
\(661\) 410614. + 711204.i 0.939789 + 1.62776i 0.765863 + 0.643004i \(0.222312\pi\)
0.173926 + 0.984759i \(0.444355\pi\)
\(662\) −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 0.425926 + 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
\(680\) 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 \(0.305734\pi\)
−0.573117 + 0.819474i \(0.694266\pi\)
\(684\) 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 0.179659 0.983729i \(-0.442500\pi\)
−0.762105 + 0.647454i \(0.775834\pi\)
\(692\) −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 −0.477600 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
\(716\) 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 \(0.109486\pi\)
−0.941426 + 0.337219i \(0.890514\pi\)
\(720\) 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 −0.0854497 0.996342i \(-0.527233\pi\)
−0.905583 + 0.424170i \(0.860566\pi\)
\(728\) 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 \(0.687389\pi\)
\(734\) 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 \(0.281312\pi\)
−0.634244 + 0.773133i \(0.718688\pi\)
\(740\) −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 −0.900189 0.435499i \(-0.856572\pi\)
−0.0729415 + 0.997336i \(0.523239\pi\)
\(744\) 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 \(-0.442345\pi\)
0.941928 + 0.335816i \(0.109012\pi\)
\(752\) −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 0.960074 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 \(0.819107\pi\)
\(770\) 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