Properties

Label 177.5.b.a.119.3
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.3
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.76

$q$-expansion

\(f(q)\) \(=\) \(q-7.49534i q^{2} +(-6.13251 + 6.58728i) q^{3} -40.1801 q^{4} -24.9668i q^{5} +(49.3739 + 45.9653i) q^{6} -52.3496 q^{7} +181.238i q^{8} +(-5.78454 - 80.7932i) q^{9} +O(q^{10})\) \(q-7.49534i q^{2} +(-6.13251 + 6.58728i) q^{3} -40.1801 q^{4} -24.9668i q^{5} +(49.3739 + 45.9653i) q^{6} -52.3496 q^{7} +181.238i q^{8} +(-5.78454 - 80.7932i) q^{9} -187.134 q^{10} +127.308i q^{11} +(246.405 - 264.678i) q^{12} -56.9103 q^{13} +392.378i q^{14} +(164.463 + 153.109i) q^{15} +715.561 q^{16} +227.481i q^{17} +(-605.572 + 43.3571i) q^{18} -187.501 q^{19} +1003.17i q^{20} +(321.035 - 344.841i) q^{21} +954.213 q^{22} -905.445i q^{23} +(-1193.87 - 1111.45i) q^{24} +1.66106 q^{25} +426.562i q^{26} +(567.681 + 457.361i) q^{27} +2103.41 q^{28} -1371.77i q^{29} +(1147.60 - 1232.71i) q^{30} +812.896 q^{31} -2463.56i q^{32} +(-838.610 - 780.715i) q^{33} +1705.05 q^{34} +1307.00i q^{35} +(232.424 + 3246.28i) q^{36} +253.452 q^{37} +1405.38i q^{38} +(349.003 - 374.884i) q^{39} +4524.93 q^{40} +1746.31i q^{41} +(-2584.70 - 2406.26i) q^{42} +1428.74 q^{43} -5115.23i q^{44} +(-2017.14 + 144.421i) q^{45} -6786.61 q^{46} +1935.60i q^{47} +(-4388.19 + 4713.60i) q^{48} +339.479 q^{49} -12.4502i q^{50} +(-1498.48 - 1395.03i) q^{51} +2286.66 q^{52} +4446.72i q^{53} +(3428.08 - 4254.96i) q^{54} +3178.46 q^{55} -9487.75i q^{56} +(1149.85 - 1235.12i) q^{57} -10281.8 q^{58} -453.188i q^{59} +(-6608.15 - 6151.94i) q^{60} -2336.04 q^{61} -6092.93i q^{62} +(302.819 + 4229.49i) q^{63} -7016.24 q^{64} +1420.86i q^{65} +(-5851.73 + 6285.67i) q^{66} +4913.00 q^{67} -9140.23i q^{68} +(5964.42 + 5552.65i) q^{69} +9796.41 q^{70} +8307.66i q^{71} +(14642.8 - 1048.38i) q^{72} -3769.78 q^{73} -1899.71i q^{74} +(-10.1865 + 10.9419i) q^{75} +7533.80 q^{76} -6664.50i q^{77} +(-2809.88 - 2615.90i) q^{78} +2128.79 q^{79} -17865.2i q^{80} +(-6494.08 + 934.704i) q^{81} +13089.2 q^{82} +7492.96i q^{83} +(-12899.2 + 13855.8i) q^{84} +5679.47 q^{85} -10708.9i q^{86} +(9036.20 + 8412.37i) q^{87} -23073.0 q^{88} -10955.2i q^{89} +(1082.49 + 15119.2i) q^{90} +2979.23 q^{91} +36380.9i q^{92} +(-4985.09 + 5354.77i) q^{93} +14508.0 q^{94} +4681.28i q^{95} +(16228.2 + 15107.8i) q^{96} -16012.3 q^{97} -2544.51i q^{98} +(10285.6 - 736.416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.49534i 1.87384i −0.349550 0.936918i \(-0.613666\pi\)
0.349550 0.936918i \(-0.386334\pi\)
\(3\) −6.13251 + 6.58728i −0.681390 + 0.731920i
\(4\) −40.1801 −2.51126
\(5\) 24.9668i 0.998670i −0.866409 0.499335i \(-0.833578\pi\)
0.866409 0.499335i \(-0.166422\pi\)
\(6\) 49.3739 + 45.9653i 1.37150 + 1.27681i
\(7\) −52.3496 −1.06836 −0.534179 0.845371i \(-0.679379\pi\)
−0.534179 + 0.845371i \(0.679379\pi\)
\(8\) 181.238i 2.83185i
\(9\) −5.78454 80.7932i −0.0714141 0.997447i
\(10\) −187.134 −1.87134
\(11\) 127.308i 1.05213i 0.850445 + 0.526064i \(0.176333\pi\)
−0.850445 + 0.526064i \(0.823667\pi\)
\(12\) 246.405 264.678i 1.71115 1.83804i
\(13\) −56.9103 −0.336747 −0.168374 0.985723i \(-0.553851\pi\)
−0.168374 + 0.985723i \(0.553851\pi\)
\(14\) 392.378i 2.00193i
\(15\) 164.463 + 153.109i 0.730947 + 0.680484i
\(16\) 715.561 2.79516
\(17\) 227.481i 0.787133i 0.919296 + 0.393566i \(0.128759\pi\)
−0.919296 + 0.393566i \(0.871241\pi\)
\(18\) −605.572 + 43.3571i −1.86905 + 0.133818i
\(19\) −187.501 −0.519392 −0.259696 0.965690i \(-0.583622\pi\)
−0.259696 + 0.965690i \(0.583622\pi\)
\(20\) 1003.17i 2.50792i
\(21\) 321.035 344.841i 0.727970 0.781953i
\(22\) 954.213 1.97151
\(23\) 905.445i 1.71162i −0.517294 0.855808i \(-0.673061\pi\)
0.517294 0.855808i \(-0.326939\pi\)
\(24\) −1193.87 1111.45i −2.07269 1.92959i
\(25\) 1.66106 0.00265769
\(26\) 426.562i 0.631009i
\(27\) 567.681 + 457.361i 0.778712 + 0.627381i
\(28\) 2103.41 2.68293
\(29\) 1371.77i 1.63111i −0.578678 0.815556i \(-0.696431\pi\)
0.578678 0.815556i \(-0.303569\pi\)
\(30\) 1147.60 1232.71i 1.27512 1.36967i
\(31\) 812.896 0.845885 0.422943 0.906157i \(-0.360997\pi\)
0.422943 + 0.906157i \(0.360997\pi\)
\(32\) 2463.56i 2.40582i
\(33\) −838.610 780.715i −0.770074 0.716910i
\(34\) 1705.05 1.47496
\(35\) 1307.00i 1.06694i
\(36\) 232.424 + 3246.28i 0.179339 + 2.50485i
\(37\) 253.452 0.185136 0.0925682 0.995706i \(-0.470492\pi\)
0.0925682 + 0.995706i \(0.470492\pi\)
\(38\) 1405.38i 0.973255i
\(39\) 349.003 374.884i 0.229456 0.246472i
\(40\) 4524.93 2.82808
\(41\) 1746.31i 1.03885i 0.854515 + 0.519427i \(0.173854\pi\)
−0.854515 + 0.519427i \(0.826146\pi\)
\(42\) −2584.70 2406.26i −1.46525 1.36409i
\(43\) 1428.74 0.772708 0.386354 0.922350i \(-0.373734\pi\)
0.386354 + 0.922350i \(0.373734\pi\)
\(44\) 5115.23i 2.64217i
\(45\) −2017.14 + 144.421i −0.996120 + 0.0713192i
\(46\) −6786.61 −3.20728
\(47\) 1935.60i 0.876233i 0.898918 + 0.438117i \(0.144354\pi\)
−0.898918 + 0.438117i \(0.855646\pi\)
\(48\) −4388.19 + 4713.60i −1.90459 + 2.04583i
\(49\) 339.479 0.141391
\(50\) 12.4502i 0.00498008i
\(51\) −1498.48 1395.03i −0.576118 0.536345i
\(52\) 2286.66 0.845659
\(53\) 4446.72i 1.58303i 0.611152 + 0.791513i \(0.290706\pi\)
−0.611152 + 0.791513i \(0.709294\pi\)
\(54\) 3428.08 4254.96i 1.17561 1.45918i
\(55\) 3178.46 1.05073
\(56\) 9487.75i 3.02543i
\(57\) 1149.85 1235.12i 0.353909 0.380154i
\(58\) −10281.8 −3.05644
\(59\) 453.188i 0.130189i
\(60\) −6608.15 6151.94i −1.83560 1.70887i
\(61\) −2336.04 −0.627798 −0.313899 0.949456i \(-0.601635\pi\)
−0.313899 + 0.949456i \(0.601635\pi\)
\(62\) 6092.93i 1.58505i
\(63\) 302.819 + 4229.49i 0.0762959 + 1.06563i
\(64\) −7016.24 −1.71295
\(65\) 1420.86i 0.336299i
\(66\) −5851.73 + 6285.67i −1.34337 + 1.44299i
\(67\) 4913.00 1.09445 0.547227 0.836984i \(-0.315683\pi\)
0.547227 + 0.836984i \(0.315683\pi\)
\(68\) 9140.23i 1.97669i
\(69\) 5964.42 + 5552.65i 1.25277 + 1.16628i
\(70\) 9796.41 1.99927
\(71\) 8307.66i 1.64802i 0.566577 + 0.824009i \(0.308267\pi\)
−0.566577 + 0.824009i \(0.691733\pi\)
\(72\) 14642.8 1048.38i 2.82462 0.202234i
\(73\) −3769.78 −0.707408 −0.353704 0.935357i \(-0.615078\pi\)
−0.353704 + 0.935357i \(0.615078\pi\)
\(74\) 1899.71i 0.346915i
\(75\) −10.1865 + 10.9419i −0.00181093 + 0.00194522i
\(76\) 7533.80 1.30433
\(77\) 6664.50i 1.12405i
\(78\) −2809.88 2615.90i −0.461848 0.429963i
\(79\) 2128.79 0.341097 0.170549 0.985349i \(-0.445446\pi\)
0.170549 + 0.985349i \(0.445446\pi\)
\(80\) 17865.2i 2.79144i
\(81\) −6494.08 + 934.704i −0.989800 + 0.142464i
\(82\) 13089.2 1.94664
\(83\) 7492.96i 1.08767i 0.839192 + 0.543835i \(0.183028\pi\)
−0.839192 + 0.543835i \(0.816972\pi\)
\(84\) −12899.2 + 13855.8i −1.82812 + 1.96369i
\(85\) 5679.47 0.786086
\(86\) 10708.9i 1.44793i
\(87\) 9036.20 + 8412.37i 1.19384 + 1.11142i
\(88\) −23073.0 −2.97947
\(89\) 10955.2i 1.38306i −0.722349 0.691529i \(-0.756937\pi\)
0.722349 0.691529i \(-0.243063\pi\)
\(90\) 1082.49 + 15119.2i 0.133640 + 1.86657i
\(91\) 2979.23 0.359767
\(92\) 36380.9i 4.29831i
\(93\) −4985.09 + 5354.77i −0.576378 + 0.619120i
\(94\) 14508.0 1.64192
\(95\) 4681.28i 0.518702i
\(96\) 16228.2 + 15107.8i 1.76087 + 1.63930i
\(97\) −16012.3 −1.70181 −0.850906 0.525318i \(-0.823946\pi\)
−0.850906 + 0.525318i \(0.823946\pi\)
\(98\) 2544.51i 0.264943i
\(99\) 10285.6 736.416i 1.04944 0.0751368i
\(100\) −66.7416 −0.00667416
\(101\) 13426.8i 1.31622i 0.752920 + 0.658112i \(0.228645\pi\)
−0.752920 + 0.658112i \(0.771355\pi\)
\(102\) −10456.2 + 11231.6i −1.00502 + 1.07955i
\(103\) 16881.8 1.59127 0.795635 0.605777i \(-0.207138\pi\)
0.795635 + 0.605777i \(0.207138\pi\)
\(104\) 10314.3i 0.953617i
\(105\) −8609.57 8015.19i −0.780914 0.727002i
\(106\) 33329.7 2.96633
\(107\) 8103.84i 0.707820i 0.935279 + 0.353910i \(0.115148\pi\)
−0.935279 + 0.353910i \(0.884852\pi\)
\(108\) −22809.5 18376.8i −1.95555 1.57552i
\(109\) 4896.71 0.412146 0.206073 0.978537i \(-0.433932\pi\)
0.206073 + 0.978537i \(0.433932\pi\)
\(110\) 23823.6i 1.96889i
\(111\) −1554.30 + 1669.56i −0.126150 + 0.135505i
\(112\) −37459.3 −2.98623
\(113\) 11924.9i 0.933897i 0.884284 + 0.466949i \(0.154647\pi\)
−0.884284 + 0.466949i \(0.845353\pi\)
\(114\) −9257.64 8618.52i −0.712345 0.663167i
\(115\) −22606.0 −1.70934
\(116\) 55117.7i 4.09614i
\(117\) 329.200 + 4597.96i 0.0240485 + 0.335887i
\(118\) −3396.80 −0.243953
\(119\) 11908.6i 0.840940i
\(120\) −27749.2 + 29807.0i −1.92703 + 2.06993i
\(121\) −1566.21 −0.106974
\(122\) 17509.4i 1.17639i
\(123\) −11503.4 10709.3i −0.760357 0.707865i
\(124\) −32662.2 −2.12424
\(125\) 15645.7i 1.00132i
\(126\) 31701.5 2269.73i 1.99682 0.142966i
\(127\) 22268.1 1.38063 0.690313 0.723510i \(-0.257473\pi\)
0.690313 + 0.723510i \(0.257473\pi\)
\(128\) 13172.2i 0.803965i
\(129\) −8761.76 + 9411.50i −0.526516 + 0.565561i
\(130\) 10649.9 0.630169
\(131\) 13648.9i 0.795343i −0.917528 0.397672i \(-0.869818\pi\)
0.917528 0.397672i \(-0.130182\pi\)
\(132\) 33695.5 + 31369.2i 1.93385 + 1.80035i
\(133\) 9815.58 0.554897
\(134\) 36824.6i 2.05083i
\(135\) 11418.8 14173.2i 0.626547 0.777677i
\(136\) −41228.3 −2.22904
\(137\) 33762.7i 1.79885i −0.437070 0.899427i \(-0.643984\pi\)
0.437070 0.899427i \(-0.356016\pi\)
\(138\) 41619.0 44705.3i 2.18541 2.34748i
\(139\) 9781.52 0.506264 0.253132 0.967432i \(-0.418539\pi\)
0.253132 + 0.967432i \(0.418539\pi\)
\(140\) 52515.4i 2.67936i
\(141\) −12750.3 11870.1i −0.641333 0.597057i
\(142\) 62268.7 3.08811
\(143\) 7245.10i 0.354301i
\(144\) −4139.19 57812.4i −0.199614 2.78802i
\(145\) −34248.5 −1.62894
\(146\) 28255.8i 1.32557i
\(147\) −2081.86 + 2236.25i −0.0963424 + 0.103487i
\(148\) −10183.7 −0.464925
\(149\) 43389.2i 1.95438i 0.212363 + 0.977191i \(0.431884\pi\)
−0.212363 + 0.977191i \(0.568116\pi\)
\(150\) 82.0130 + 76.3511i 0.00364502 + 0.00339338i
\(151\) −15713.3 −0.689148 −0.344574 0.938759i \(-0.611977\pi\)
−0.344574 + 0.938759i \(0.611977\pi\)
\(152\) 33982.3i 1.47084i
\(153\) 18378.9 1315.88i 0.785123 0.0562124i
\(154\) −49952.7 −2.10629
\(155\) 20295.4i 0.844760i
\(156\) −14023.0 + 15062.9i −0.576224 + 0.618955i
\(157\) −14305.3 −0.580361 −0.290181 0.956972i \(-0.593715\pi\)
−0.290181 + 0.956972i \(0.593715\pi\)
\(158\) 15956.0i 0.639160i
\(159\) −29291.8 27269.6i −1.15865 1.07866i
\(160\) −61507.1 −2.40262
\(161\) 47399.6i 1.82862i
\(162\) 7005.92 + 48675.3i 0.266953 + 1.85472i
\(163\) −11045.1 −0.415713 −0.207857 0.978159i \(-0.566649\pi\)
−0.207857 + 0.978159i \(0.566649\pi\)
\(164\) 70167.0i 2.60883i
\(165\) −19491.9 + 20937.4i −0.715957 + 0.769050i
\(166\) 56162.3 2.03812
\(167\) 36094.9i 1.29424i 0.762390 + 0.647118i \(0.224026\pi\)
−0.762390 + 0.647118i \(0.775974\pi\)
\(168\) 62498.5 + 58183.8i 2.21437 + 2.06150i
\(169\) −25322.2 −0.886601
\(170\) 42569.6i 1.47300i
\(171\) 1084.61 + 15148.8i 0.0370919 + 0.518066i
\(172\) −57406.9 −1.94047
\(173\) 36096.8i 1.20608i 0.797711 + 0.603040i \(0.206044\pi\)
−0.797711 + 0.603040i \(0.793956\pi\)
\(174\) 63053.6 67729.4i 2.08263 2.23707i
\(175\) −86.9558 −0.00283937
\(176\) 91096.3i 2.94087i
\(177\) 2985.27 + 2779.18i 0.0952879 + 0.0887095i
\(178\) −82113.0 −2.59162
\(179\) 4409.95i 0.137635i 0.997629 + 0.0688174i \(0.0219226\pi\)
−0.997629 + 0.0688174i \(0.978077\pi\)
\(180\) 81049.1 5802.87i 2.50152 0.179101i
\(181\) −43407.5 −1.32497 −0.662487 0.749074i \(-0.730499\pi\)
−0.662487 + 0.749074i \(0.730499\pi\)
\(182\) 22330.3i 0.674144i
\(183\) 14325.8 15388.1i 0.427776 0.459498i
\(184\) 164101. 4.84704
\(185\) 6327.87i 0.184890i
\(186\) 40135.8 + 37365.0i 1.16013 + 1.08004i
\(187\) −28960.1 −0.828165
\(188\) 77772.6i 2.20045i
\(189\) −29717.9 23942.7i −0.831944 0.670268i
\(190\) 35087.8 0.971961
\(191\) 40966.2i 1.12295i 0.827495 + 0.561473i \(0.189765\pi\)
−0.827495 + 0.561473i \(0.810235\pi\)
\(192\) 43027.2 46217.9i 1.16719 1.25374i
\(193\) 37461.5 1.00571 0.502853 0.864372i \(-0.332284\pi\)
0.502853 + 0.864372i \(0.332284\pi\)
\(194\) 120018.i 3.18891i
\(195\) −9359.63 8713.47i −0.246144 0.229151i
\(196\) −13640.3 −0.355069
\(197\) 60634.8i 1.56239i −0.624287 0.781195i \(-0.714611\pi\)
0.624287 0.781195i \(-0.285389\pi\)
\(198\) −5519.69 77093.9i −0.140794 1.96648i
\(199\) −37712.7 −0.952317 −0.476159 0.879359i \(-0.657971\pi\)
−0.476159 + 0.879359i \(0.657971\pi\)
\(200\) 301.048i 0.00752619i
\(201\) −30129.1 + 32363.3i −0.745751 + 0.801053i
\(202\) 100638. 2.46639
\(203\) 71811.4i 1.74261i
\(204\) 60209.3 + 56052.6i 1.44678 + 1.34690i
\(205\) 43599.7 1.03747
\(206\) 126535.i 2.98178i
\(207\) −73153.7 + 5237.58i −1.70725 + 0.122234i
\(208\) −40722.7 −0.941262
\(209\) 23870.2i 0.546467i
\(210\) −60076.6 + 64531.7i −1.36228 + 1.46330i
\(211\) 44136.4 0.991362 0.495681 0.868505i \(-0.334919\pi\)
0.495681 + 0.868505i \(0.334919\pi\)
\(212\) 178670.i 3.97539i
\(213\) −54724.9 50946.8i −1.20622 1.12294i
\(214\) 60741.0 1.32634
\(215\) 35671.0i 0.771681i
\(216\) −82891.3 + 102886.i −1.77665 + 2.20520i
\(217\) −42554.7 −0.903709
\(218\) 36702.5i 0.772293i
\(219\) 23118.2 24832.6i 0.482021 0.517767i
\(220\) −127711. −2.63865
\(221\) 12946.0i 0.265065i
\(222\) 12513.9 + 11650.0i 0.253914 + 0.236385i
\(223\) 44232.6 0.889473 0.444736 0.895662i \(-0.353297\pi\)
0.444736 + 0.895662i \(0.353297\pi\)
\(224\) 128966.i 2.57028i
\(225\) −9.60847 134.202i −0.000189797 0.00265091i
\(226\) 89381.4 1.74997
\(227\) 18920.9i 0.367190i −0.983002 0.183595i \(-0.941227\pi\)
0.983002 0.183595i \(-0.0587735\pi\)
\(228\) −46201.1 + 49627.2i −0.888757 + 0.954664i
\(229\) 32265.4 0.615271 0.307635 0.951504i \(-0.400462\pi\)
0.307635 + 0.951504i \(0.400462\pi\)
\(230\) 169440.i 3.20302i
\(231\) 43900.9 + 40870.1i 0.822715 + 0.765917i
\(232\) 248616. 4.61906
\(233\) 22096.7i 0.407019i −0.979073 0.203509i \(-0.934765\pi\)
0.979073 0.203509i \(-0.0652348\pi\)
\(234\) 34463.3 2467.47i 0.629397 0.0450629i
\(235\) 48325.6 0.875068
\(236\) 18209.1i 0.326938i
\(237\) −13054.8 + 14022.9i −0.232420 + 0.249656i
\(238\) −89258.7 −1.57578
\(239\) 24979.4i 0.437307i −0.975803 0.218654i \(-0.929834\pi\)
0.975803 0.218654i \(-0.0701665\pi\)
\(240\) 117683. + 109559.i 2.04311 + 1.90206i
\(241\) 32935.6 0.567064 0.283532 0.958963i \(-0.408494\pi\)
0.283532 + 0.958963i \(0.408494\pi\)
\(242\) 11739.2i 0.200452i
\(243\) 33667.9 48510.4i 0.570168 0.821528i
\(244\) 93862.3 1.57656
\(245\) 8475.70i 0.141203i
\(246\) −80269.7 + 86222.3i −1.32642 + 1.42478i
\(247\) 10670.7 0.174904
\(248\) 147328.i 2.39542i
\(249\) −49358.3 45950.7i −0.796088 0.741128i
\(250\) −117270. −1.87632
\(251\) 15587.0i 0.247409i 0.992319 + 0.123705i \(0.0394776\pi\)
−0.992319 + 0.123705i \(0.960522\pi\)
\(252\) −12167.3 169941.i −0.191599 2.67607i
\(253\) 115270. 1.80084
\(254\) 166907.i 2.58707i
\(255\) −34829.4 + 37412.3i −0.535631 + 0.575352i
\(256\) −13530.0 −0.206451
\(257\) 7399.34i 0.112028i 0.998430 + 0.0560140i \(0.0178392\pi\)
−0.998430 + 0.0560140i \(0.982161\pi\)
\(258\) 70542.4 + 65672.3i 1.05977 + 0.986604i
\(259\) −13268.1 −0.197792
\(260\) 57090.5i 0.844534i
\(261\) −110829. + 7935.04i −1.62695 + 0.116484i
\(262\) −102303. −1.49034
\(263\) 111995.i 1.61916i 0.587013 + 0.809578i \(0.300304\pi\)
−0.587013 + 0.809578i \(0.699696\pi\)
\(264\) 141495. 151988.i 2.03018 2.18073i
\(265\) 111020. 1.58092
\(266\) 73571.1i 1.03979i
\(267\) 72165.0 + 67182.9i 1.01229 + 0.942403i
\(268\) −197405. −2.74846
\(269\) 21091.5i 0.291475i −0.989323 0.145738i \(-0.953444\pi\)
0.989323 0.145738i \(-0.0465556\pi\)
\(270\) −106233. 85587.9i −1.45724 1.17405i
\(271\) −71615.9 −0.975148 −0.487574 0.873082i \(-0.662118\pi\)
−0.487574 + 0.873082i \(0.662118\pi\)
\(272\) 162777.i 2.20016i
\(273\) −18270.2 + 19625.0i −0.245142 + 0.263321i
\(274\) −253063. −3.37076
\(275\) 211.465i 0.00279624i
\(276\) −239651. 223106.i −3.14602 2.92883i
\(277\) 90722.5 1.18238 0.591188 0.806534i \(-0.298659\pi\)
0.591188 + 0.806534i \(0.298659\pi\)
\(278\) 73315.8i 0.948655i
\(279\) −4702.23 65676.4i −0.0604081 0.843725i
\(280\) −236878. −3.02141
\(281\) 44079.6i 0.558246i −0.960255 0.279123i \(-0.909956\pi\)
0.960255 0.279123i \(-0.0900436\pi\)
\(282\) −88970.4 + 95568.1i −1.11879 + 1.20175i
\(283\) 4240.96 0.0529530 0.0264765 0.999649i \(-0.491571\pi\)
0.0264765 + 0.999649i \(0.491571\pi\)
\(284\) 333803.i 4.13860i
\(285\) −30836.9 28708.0i −0.379648 0.353438i
\(286\) −54304.5 −0.663902
\(287\) 91418.7i 1.10987i
\(288\) −199039. + 14250.6i −2.39968 + 0.171809i
\(289\) 31773.2 0.380422
\(290\) 256704.i 3.05237i
\(291\) 98195.9 105478.i 1.15960 1.24559i
\(292\) 151470. 1.77649
\(293\) 11551.5i 0.134556i 0.997734 + 0.0672778i \(0.0214314\pi\)
−0.997734 + 0.0672778i \(0.978569\pi\)
\(294\) 16761.4 + 15604.3i 0.193917 + 0.180530i
\(295\) −11314.6 −0.130016
\(296\) 45935.2i 0.524278i
\(297\) −58225.5 + 72270.1i −0.660086 + 0.819305i
\(298\) 325217. 3.66219
\(299\) 51529.1i 0.576381i
\(300\) 409.294 439.646i 0.00454771 0.00488495i
\(301\) −74793.8 −0.825530
\(302\) 117776.i 1.29135i
\(303\) −88446.1 82340.1i −0.963371 0.896863i
\(304\) −134168. −1.45178
\(305\) 58323.3i 0.626964i
\(306\) −9862.94 137756.i −0.105333 1.47119i
\(307\) −13202.7 −0.140084 −0.0700418 0.997544i \(-0.522313\pi\)
−0.0700418 + 0.997544i \(0.522313\pi\)
\(308\) 267780.i 2.82278i
\(309\) −103528. + 111205.i −1.08428 + 1.16468i
\(310\) −152121. −1.58294
\(311\) 68017.1i 0.703230i −0.936145 0.351615i \(-0.885633\pi\)
0.936145 0.351615i \(-0.114367\pi\)
\(312\) 67943.3 + 63252.7i 0.697971 + 0.649785i
\(313\) 10627.8 0.108481 0.0542404 0.998528i \(-0.482726\pi\)
0.0542404 + 0.998528i \(0.482726\pi\)
\(314\) 107223.i 1.08750i
\(315\) 105597. 7560.40i 1.06421 0.0761945i
\(316\) −85534.9 −0.856583
\(317\) 123218.i 1.22619i 0.790010 + 0.613094i \(0.210075\pi\)
−0.790010 + 0.613094i \(0.789925\pi\)
\(318\) −204395. + 219552.i −2.02123 + 2.17112i
\(319\) 174636. 1.71614
\(320\) 175173.i 1.71067i
\(321\) −53382.3 49696.9i −0.518068 0.482302i
\(322\) 355277. 3.42653
\(323\) 42652.9i 0.408831i
\(324\) 260933. 37556.5i 2.48564 0.357763i
\(325\) −94.5313 −0.000894971
\(326\) 82786.7i 0.778978i
\(327\) −30029.1 + 32256.0i −0.280832 + 0.301658i
\(328\) −316499. −2.94187
\(329\) 101328.i 0.936132i
\(330\) 156933. + 146099.i 1.44107 + 1.34159i
\(331\) −142152. −1.29747 −0.648734 0.761015i \(-0.724701\pi\)
−0.648734 + 0.761015i \(0.724701\pi\)
\(332\) 301068.i 2.73142i
\(333\) −1466.10 20477.2i −0.0132214 0.184664i
\(334\) 270544. 2.42518
\(335\) 122662.i 1.09300i
\(336\) 229720. 246755.i 2.03479 2.18568i
\(337\) −115078. −1.01328 −0.506642 0.862156i \(-0.669114\pi\)
−0.506642 + 0.862156i \(0.669114\pi\)
\(338\) 189799.i 1.66134i
\(339\) −78552.9 73129.8i −0.683538 0.636349i
\(340\) −228202. −1.97406
\(341\) 103488.i 0.889980i
\(342\) 113545. 8129.49i 0.970770 0.0695042i
\(343\) 107920. 0.917303
\(344\) 258942.i 2.18819i
\(345\) 138632. 148912.i 1.16473 1.25110i
\(346\) 270558. 2.26000
\(347\) 155553.i 1.29188i 0.763390 + 0.645938i \(0.223533\pi\)
−0.763390 + 0.645938i \(0.776467\pi\)
\(348\) −363076. 338010.i −2.99805 2.79107i
\(349\) −71293.8 −0.585330 −0.292665 0.956215i \(-0.594542\pi\)
−0.292665 + 0.956215i \(0.594542\pi\)
\(350\) 651.763i 0.00532052i
\(351\) −32306.9 26028.5i −0.262229 0.211269i
\(352\) 313630. 2.53123
\(353\) 64338.5i 0.516323i 0.966102 + 0.258162i \(0.0831167\pi\)
−0.966102 + 0.258162i \(0.916883\pi\)
\(354\) 20830.9 22375.6i 0.166227 0.178554i
\(355\) 207415. 1.64583
\(356\) 440182.i 3.47322i
\(357\) 78445.0 + 73029.4i 0.615501 + 0.573009i
\(358\) 33054.1 0.257905
\(359\) 38102.5i 0.295641i −0.989014 0.147821i \(-0.952774\pi\)
0.989014 0.147821i \(-0.0472258\pi\)
\(360\) −26174.7 365584.i −0.201965 2.82086i
\(361\) −95164.5 −0.730232
\(362\) 325354.i 2.48278i
\(363\) 9604.78 10317.0i 0.0728910 0.0782964i
\(364\) −119706. −0.903467
\(365\) 94119.2i 0.706468i
\(366\) −115339. 107377.i −0.861024 0.801582i
\(367\) 170699. 1.26736 0.633679 0.773596i \(-0.281544\pi\)
0.633679 + 0.773596i \(0.281544\pi\)
\(368\) 647901.i 4.78424i
\(369\) 141090. 10101.6i 1.03620 0.0741888i
\(370\) −47429.5 −0.346454
\(371\) 232784.i 1.69124i
\(372\) 200302. 215155.i 1.44743 1.55477i
\(373\) 63737.6 0.458118 0.229059 0.973412i \(-0.426435\pi\)
0.229059 + 0.973412i \(0.426435\pi\)
\(374\) 217066.i 1.55184i
\(375\) 103063. + 95947.4i 0.732889 + 0.682293i
\(376\) −350805. −2.48136
\(377\) 78067.5i 0.549272i
\(378\) −179458. + 222746.i −1.25597 + 1.55893i
\(379\) −278735. −1.94050 −0.970249 0.242111i \(-0.922160\pi\)
−0.970249 + 0.242111i \(0.922160\pi\)
\(380\) 188095.i 1.30259i
\(381\) −136560. + 146686.i −0.940746 + 1.01051i
\(382\) 307056. 2.10422
\(383\) 82161.9i 0.560110i 0.959984 + 0.280055i \(0.0903527\pi\)
−0.959984 + 0.280055i \(0.909647\pi\)
\(384\) −86768.8 80778.5i −0.588438 0.547814i
\(385\) −166391. −1.12256
\(386\) 280787.i 1.88453i
\(387\) −8264.60 115432.i −0.0551823 0.770736i
\(388\) 643378. 4.27369
\(389\) 101073.i 0.667939i −0.942584 0.333969i \(-0.891612\pi\)
0.942584 0.333969i \(-0.108388\pi\)
\(390\) −65310.4 + 70153.6i −0.429391 + 0.461234i
\(391\) 205972. 1.34727
\(392\) 61526.7i 0.400398i
\(393\) 89909.0 + 83702.0i 0.582128 + 0.541939i
\(394\) −454478. −2.92766
\(395\) 53148.9i 0.340643i
\(396\) −413276. + 29589.3i −2.63542 + 0.188688i
\(397\) 60367.3 0.383019 0.191510 0.981491i \(-0.438662\pi\)
0.191510 + 0.981491i \(0.438662\pi\)
\(398\) 282670.i 1.78449i
\(399\) −60194.2 + 64658.0i −0.378102 + 0.406141i
\(400\) 1188.59 0.00742868
\(401\) 91315.9i 0.567881i −0.958842 0.283941i \(-0.908358\pi\)
0.958842 0.283941i \(-0.0916419\pi\)
\(402\) 242574. + 225828.i 1.50104 + 1.39741i
\(403\) −46262.1 −0.284849
\(404\) 539491.i 3.30538i
\(405\) 23336.5 + 162136.i 0.142274 + 0.988484i
\(406\) 538251. 3.26537
\(407\) 32266.3i 0.194787i
\(408\) 252833. 271583.i 1.51885 1.63148i
\(409\) 23670.6 0.141502 0.0707510 0.997494i \(-0.477460\pi\)
0.0707510 + 0.997494i \(0.477460\pi\)
\(410\) 326795.i 1.94405i
\(411\) 222404. + 207050.i 1.31662 + 1.22572i
\(412\) −678312. −3.99609
\(413\) 23724.2i 0.139088i
\(414\) 39257.5 + 548312.i 0.229045 + 3.19910i
\(415\) 187075. 1.08622
\(416\) 140202.i 0.810153i
\(417\) −59985.3 + 64433.6i −0.344963 + 0.370545i
\(418\) −178916. −1.02399
\(419\) 116387.i 0.662946i 0.943465 + 0.331473i \(0.107546\pi\)
−0.943465 + 0.331473i \(0.892454\pi\)
\(420\) 345934. + 322051.i 1.96108 + 1.82569i
\(421\) 321783. 1.81551 0.907755 0.419500i \(-0.137795\pi\)
0.907755 + 0.419500i \(0.137795\pi\)
\(422\) 330818.i 1.85765i
\(423\) 156383. 11196.6i 0.873996 0.0625754i
\(424\) −805916. −4.48289
\(425\) 377.860i 0.00209196i
\(426\) −381864. + 410182.i −2.10421 + 2.26025i
\(427\) 122291. 0.670714
\(428\) 325613.i 1.77752i
\(429\) 47725.5 + 44430.7i 0.259320 + 0.241417i
\(430\) −267366. −1.44600
\(431\) 300041.i 1.61520i 0.589732 + 0.807599i \(0.299233\pi\)
−0.589732 + 0.807599i \(0.700767\pi\)
\(432\) 406210. + 327270.i 2.17662 + 1.75363i
\(433\) 41166.3 0.219566 0.109783 0.993956i \(-0.464984\pi\)
0.109783 + 0.993956i \(0.464984\pi\)
\(434\) 318962.i 1.69340i
\(435\) 210030. 225605.i 1.10995 1.19226i
\(436\) −196750. −1.03500
\(437\) 169771.i 0.889000i
\(438\) −186129. 173279.i −0.970209 0.903229i
\(439\) −132293. −0.686450 −0.343225 0.939253i \(-0.611519\pi\)
−0.343225 + 0.939253i \(0.611519\pi\)
\(440\) 576058.i 2.97551i
\(441\) −1963.73 27427.6i −0.0100973 0.141030i
\(442\) −97034.8 −0.496687
\(443\) 125977.i 0.641926i 0.947092 + 0.320963i \(0.104007\pi\)
−0.947092 + 0.320963i \(0.895993\pi\)
\(444\) 62451.8 67083.0i 0.316796 0.340288i
\(445\) −273516. −1.38122
\(446\) 331538.i 1.66673i
\(447\) −285817. 266085.i −1.43045 1.33170i
\(448\) 367297. 1.83004
\(449\) 129881.i 0.644246i −0.946698 0.322123i \(-0.895604\pi\)
0.946698 0.322123i \(-0.104396\pi\)
\(450\) −1005.89 + 72.0188i −0.00496737 + 0.000355648i
\(451\) −222319. −1.09301
\(452\) 479145.i 2.34526i
\(453\) 96361.8 103508.i 0.469579 0.504401i
\(454\) −141819. −0.688053
\(455\) 74381.7i 0.359288i
\(456\) 223851. + 208397.i 1.07654 + 1.00222i
\(457\) −63515.2 −0.304120 −0.152060 0.988371i \(-0.548591\pi\)
−0.152060 + 0.988371i \(0.548591\pi\)
\(458\) 241840.i 1.15292i
\(459\) −104041. + 129137.i −0.493832 + 0.612950i
\(460\) 908313. 4.29259
\(461\) 75639.2i 0.355914i −0.984038 0.177957i \(-0.943051\pi\)
0.984038 0.177957i \(-0.0569488\pi\)
\(462\) 306335. 329052.i 1.43520 1.54163i
\(463\) −180512. −0.842062 −0.421031 0.907046i \(-0.638332\pi\)
−0.421031 + 0.907046i \(0.638332\pi\)
\(464\) 981581.i 4.55922i
\(465\) 133691. + 124462.i 0.618297 + 0.575612i
\(466\) −165622. −0.762686
\(467\) 57521.3i 0.263752i 0.991266 + 0.131876i \(0.0421000\pi\)
−0.991266 + 0.131876i \(0.957900\pi\)
\(468\) −13227.3 184747.i −0.0603920 0.843500i
\(469\) −257194. −1.16927
\(470\) 362217.i 1.63973i
\(471\) 87727.6 94233.2i 0.395453 0.424778i
\(472\) 82135.0 0.368675
\(473\) 181889.i 0.812988i
\(474\) 105107. + 97850.3i 0.467814 + 0.435517i
\(475\) −311.450 −0.00138039
\(476\) 478487.i 2.11182i
\(477\) 359265. 25722.2i 1.57898 0.113050i
\(478\) −187229. −0.819441
\(479\) 337448.i 1.47074i −0.677666 0.735370i \(-0.737008\pi\)
0.677666 0.735370i \(-0.262992\pi\)
\(480\) 377193. 405164.i 1.63712 1.75853i
\(481\) −14424.0 −0.0623441
\(482\) 246864.i 1.06258i
\(483\) −312235. 290679.i −1.33840 1.24600i
\(484\) 62930.4 0.268639
\(485\) 399776.i 1.69955i
\(486\) −363602. 252352.i −1.53941 1.06840i
\(487\) −118967. −0.501615 −0.250807 0.968037i \(-0.580696\pi\)
−0.250807 + 0.968037i \(0.580696\pi\)
\(488\) 423380.i 1.77783i
\(489\) 67734.1 72757.1i 0.283263 0.304269i
\(490\) −63528.3 −0.264591
\(491\) 250334.i 1.03838i −0.854658 0.519191i \(-0.826233\pi\)
0.854658 0.519191i \(-0.173767\pi\)
\(492\) 462210. + 430300.i 1.90945 + 1.77763i
\(493\) 312051. 1.28390
\(494\) 79980.6i 0.327741i
\(495\) −18385.9 256798.i −0.0750369 1.04805i
\(496\) 581676. 2.36438
\(497\) 434902.i 1.76067i
\(498\) −344416. + 369957.i −1.38875 + 1.49174i
\(499\) 163877. 0.658140 0.329070 0.944306i \(-0.393265\pi\)
0.329070 + 0.944306i \(0.393265\pi\)
\(500\) 628646.i 2.51458i
\(501\) −237767. 221353.i −0.947277 0.881879i
\(502\) 116830. 0.463605
\(503\) 151110.i 0.597253i 0.954370 + 0.298626i \(0.0965285\pi\)
−0.954370 + 0.298626i \(0.903472\pi\)
\(504\) −766546. + 54882.3i −3.01771 + 0.216059i
\(505\) 335224. 1.31447
\(506\) 863987.i 3.37448i
\(507\) 155289. 166805.i 0.604122 0.648921i
\(508\) −894736. −3.46711
\(509\) 493716.i 1.90564i 0.303533 + 0.952821i \(0.401834\pi\)
−0.303533 + 0.952821i \(0.598166\pi\)
\(510\) 280418. + 261058.i 1.07812 + 1.00369i
\(511\) 197346. 0.755766
\(512\) 312166.i 1.19082i
\(513\) −106441. 85755.5i −0.404457 0.325857i
\(514\) 55460.6 0.209922
\(515\) 421483.i 1.58915i
\(516\) 352048. 378155.i 1.32222 1.42027i
\(517\) −246416. −0.921910
\(518\) 99448.9i 0.370630i
\(519\) −237780. 221364.i −0.882754 0.821811i
\(520\) −257515. −0.952349
\(521\) 212011.i 0.781056i 0.920591 + 0.390528i \(0.127708\pi\)
−0.920591 + 0.390528i \(0.872292\pi\)
\(522\) 59475.8 + 830703.i 0.218273 + 3.04863i
\(523\) 59345.3 0.216962 0.108481 0.994099i \(-0.465401\pi\)
0.108481 + 0.994099i \(0.465401\pi\)
\(524\) 548414.i 1.99731i
\(525\) 533.257 572.802i 0.00193472 0.00207819i
\(526\) 839443. 3.03403
\(527\) 184919.i 0.665824i
\(528\) −600077. 558649.i −2.15248 2.00388i
\(529\) −539989. −1.92963
\(530\) 832134.i 2.96239i
\(531\) −36614.5 + 2621.48i −0.129857 + 0.00929733i
\(532\) −394391. −1.39349
\(533\) 99383.1i 0.349831i
\(534\) 503559. 540901.i 1.76591 1.89686i
\(535\) 202327. 0.706879
\(536\) 890425.i 3.09933i
\(537\) −29049.6 27044.1i −0.100738 0.0937830i
\(538\) −158088. −0.546177
\(539\) 43218.3i 0.148761i
\(540\) −458810. + 569479.i −1.57342 + 1.95295i
\(541\) 87347.9 0.298440 0.149220 0.988804i \(-0.452324\pi\)
0.149220 + 0.988804i \(0.452324\pi\)
\(542\) 536785.i 1.82727i
\(543\) 266197. 285937.i 0.902824 0.969775i
\(544\) 560414. 1.89370
\(545\) 122255.i 0.411598i
\(546\) 147096. + 136941.i 0.493419 + 0.459355i
\(547\) 224496. 0.750298 0.375149 0.926964i \(-0.377592\pi\)
0.375149 + 0.926964i \(0.377592\pi\)
\(548\) 1.35659e6i 4.51739i
\(549\) 13512.9 + 188736.i 0.0448337 + 0.626196i
\(550\) 1585.00 0.00523969
\(551\) 257207.i 0.847187i
\(552\) −1.00635e6 + 1.08098e6i −3.30272 + 3.54764i
\(553\) −111441. −0.364414
\(554\) 679996.i 2.21558i
\(555\) 41683.4 + 38805.7i 0.135325 + 0.125982i
\(556\) −393023. −1.27136
\(557\) 28993.3i 0.0934518i −0.998908 0.0467259i \(-0.985121\pi\)
0.998908 0.0467259i \(-0.0148787\pi\)
\(558\) −492267. + 35244.8i −1.58100 + 0.113195i
\(559\) −81309.8 −0.260207
\(560\) 935238.i 2.98226i
\(561\) 177598. 190768.i 0.564303 0.606150i
\(562\) −330392. −1.04606
\(563\) 398832.i 1.25827i −0.777297 0.629134i \(-0.783410\pi\)
0.777297 0.629134i \(-0.216590\pi\)
\(564\) 512310. + 476942.i 1.61055 + 1.49936i
\(565\) 297727. 0.932655
\(566\) 31787.4i 0.0992253i
\(567\) 339962. 48931.3i 1.05746 0.152202i
\(568\) −1.50567e6 −4.66694
\(569\) 191717.i 0.592155i 0.955164 + 0.296078i \(0.0956787\pi\)
−0.955164 + 0.296078i \(0.904321\pi\)
\(570\) −215176. + 231133.i −0.662285 + 0.711398i
\(571\) 35119.6 0.107715 0.0538577 0.998549i \(-0.482848\pi\)
0.0538577 + 0.998549i \(0.482848\pi\)
\(572\) 291109.i 0.889742i
\(573\) −269856. 251226.i −0.821907 0.765165i
\(574\) −685214. −2.07971
\(575\) 1504.00i 0.00454895i
\(576\) 40585.7 + 566864.i 0.122329 + 1.70858i
\(577\) −125393. −0.376636 −0.188318 0.982108i \(-0.560303\pi\)
−0.188318 + 0.982108i \(0.560303\pi\)
\(578\) 238151.i 0.712848i
\(579\) −229733. + 246770.i −0.685279 + 0.736097i
\(580\) 1.37611e6 4.09070
\(581\) 392254.i 1.16202i
\(582\) −790592. 736012.i −2.33403 2.17290i
\(583\) −566101. −1.66555
\(584\) 683229.i 2.00327i
\(585\) 114796. 8219.05i 0.335441 0.0240165i
\(586\) 86582.2 0.252135
\(587\) 241835.i 0.701848i 0.936404 + 0.350924i \(0.114133\pi\)
−0.936404 + 0.350924i \(0.885867\pi\)
\(588\) 83649.5 89852.7i 0.241941 0.259882i
\(589\) −152418. −0.439346
\(590\) 84807.0i 0.243628i
\(591\) 399418. + 371844.i 1.14354 + 1.06460i
\(592\) 181360. 0.517486
\(593\) 658549.i 1.87275i 0.351007 + 0.936373i \(0.385839\pi\)
−0.351007 + 0.936373i \(0.614161\pi\)
\(594\) 541689. + 436420.i 1.53524 + 1.23689i
\(595\) −297318. −0.839822
\(596\) 1.74338e6i 4.90796i
\(597\) 231274. 248424.i 0.648900 0.697020i
\(598\) 386228. 1.08004
\(599\) 217294.i 0.605611i 0.953052 + 0.302805i \(0.0979232\pi\)
−0.953052 + 0.302805i \(0.902077\pi\)
\(600\) −1983.08 1846.18i −0.00550857 0.00512827i
\(601\) −103070. −0.285353 −0.142677 0.989769i \(-0.545571\pi\)
−0.142677 + 0.989769i \(0.545571\pi\)
\(602\) 560605.i 1.54691i
\(603\) −28419.5 396937.i −0.0781595 1.09166i
\(604\) 631361. 1.73063
\(605\) 39103.1i 0.106832i
\(606\) −617167. + 662934.i −1.68057 + 1.80520i
\(607\) 405932. 1.10173 0.550866 0.834594i \(-0.314298\pi\)
0.550866 + 0.834594i \(0.314298\pi\)
\(608\) 461919.i 1.24956i
\(609\) −473042. 440384.i −1.27545 1.18740i
\(610\) 437153. 1.17483
\(611\) 110155.i 0.295069i
\(612\) −738468. + 52872.1i −1.97165 + 0.141164i
\(613\) −71073.7 −0.189142 −0.0945710 0.995518i \(-0.530148\pi\)
−0.0945710 + 0.995518i \(0.530148\pi\)
\(614\) 98959.0i 0.262493i
\(615\) −267376. + 287204.i −0.706923 + 0.759346i
\(616\) 1.20786e6 3.18314
\(617\) 442654.i 1.16277i 0.813628 + 0.581386i \(0.197489\pi\)
−0.813628 + 0.581386i \(0.802511\pi\)
\(618\) 833519. + 775975.i 2.18242 + 2.03175i
\(619\) −255374. −0.666493 −0.333246 0.942840i \(-0.608144\pi\)
−0.333246 + 0.942840i \(0.608144\pi\)
\(620\) 815470.i 2.12141i
\(621\) 414115. 514004.i 1.07384 1.33286i
\(622\) −509812. −1.31774
\(623\) 573500.i 1.47760i
\(624\) 249733. 268252.i 0.641367 0.688928i
\(625\) −389584. −0.997335
\(626\) 79658.6i 0.203275i
\(627\) 157240. + 146385.i 0.399970 + 0.372358i
\(628\) 574790. 1.45744
\(629\) 57655.5i 0.145727i
\(630\) −56667.7 791483.i −0.142776 1.99416i
\(631\) 200823. 0.504376 0.252188 0.967678i \(-0.418850\pi\)
0.252188 + 0.967678i \(0.418850\pi\)
\(632\) 385818.i 0.965935i
\(633\) −270667. + 290739.i −0.675505 + 0.725598i
\(634\) 923564. 2.29767
\(635\) 555963.i 1.37879i
\(636\) 1.17695e6 + 1.09569e6i 2.90967 + 2.70879i
\(637\) −19319.9 −0.0476130
\(638\) 1.30896e6i 3.21576i
\(639\) 671202. 48056.0i 1.64381 0.117692i
\(640\) 328866. 0.802896
\(641\) 557807.i 1.35759i −0.734328 0.678794i \(-0.762503\pi\)
0.734328 0.678794i \(-0.237497\pi\)
\(642\) −372495. + 400118.i −0.903755 + 0.970774i
\(643\) 117775. 0.284859 0.142429 0.989805i \(-0.454509\pi\)
0.142429 + 0.989805i \(0.454509\pi\)
\(644\) 1.90452e6i 4.59214i
\(645\) 234975. + 218753.i 0.564809 + 0.525816i
\(646\) −319698. −0.766081
\(647\) 179763.i 0.429430i 0.976677 + 0.214715i \(0.0688823\pi\)
−0.976677 + 0.214715i \(0.931118\pi\)
\(648\) −169404. 1.17698e6i −0.403435 2.80296i
\(649\) 57694.2 0.136975
\(650\) 708.544i 0.00167703i
\(651\) 260968. 280320.i 0.615779 0.661443i
\(652\) 443793. 1.04396
\(653\) 369529.i 0.866608i −0.901248 0.433304i \(-0.857348\pi\)
0.901248 0.433304i \(-0.142652\pi\)
\(654\) 241770. + 225078.i 0.565257 + 0.526233i
\(655\) −340768. −0.794286
\(656\) 1.24959e6i 2.90376i
\(657\) 21806.5 + 304573.i 0.0505190 + 0.705602i
\(658\) −759487. −1.75416
\(659\) 245142.i 0.564477i −0.959344 0.282239i \(-0.908923\pi\)
0.959344 0.282239i \(-0.0910770\pi\)
\(660\) 783188. 841267.i 1.79795 1.93128i
\(661\) −440649. −1.00853 −0.504266 0.863548i \(-0.668237\pi\)
−0.504266 + 0.863548i \(0.668237\pi\)
\(662\) 1.06548e6i 2.43124i
\(663\) 85279.1 + 79391.7i 0.194006 + 0.180613i
\(664\) −1.35801e6 −3.08012
\(665\) 245063.i 0.554160i
\(666\) −153483. + 10988.9i −0.346029 + 0.0247746i
\(667\) −1.24206e6 −2.79184
\(668\) 1.45030e6i 3.25016i
\(669\) −271257. + 291372.i −0.606078 + 0.651023i
\(670\) −919392. −2.04810
\(671\) 297395.i 0.660525i
\(672\) −849537. 790888.i −1.88124 1.75136i
\(673\) 409414. 0.903925 0.451963 0.892037i \(-0.350724\pi\)
0.451963 + 0.892037i \(0.350724\pi\)
\(674\) 862547.i 1.89873i
\(675\) 942.952 + 759.704i 0.00206958 + 0.00166739i
\(676\) 1.01745e6 2.22648
\(677\) 877372.i 1.91429i 0.289617 + 0.957143i \(0.406472\pi\)
−0.289617 + 0.957143i \(0.593528\pi\)
\(678\) −548133. + 588781.i −1.19241 + 1.28084i
\(679\) 838240. 1.81815
\(680\) 1.02934e6i 2.22608i
\(681\) 124637. + 116033.i 0.268754 + 0.250200i
\(682\) 775676. 1.66768
\(683\) 170253.i 0.364967i 0.983209 + 0.182483i \(0.0584136\pi\)
−0.983209 + 0.182483i \(0.941586\pi\)
\(684\) −43579.6 608680.i −0.0931474 1.30100i
\(685\) −842945. −1.79646
\(686\) 808895.i 1.71887i
\(687\) −197868. + 212541.i −0.419239 + 0.450329i
\(688\) 1.02235e6 2.15984
\(689\) 253064.i 0.533079i
\(690\) −1.11615e6 1.03909e6i −2.34435 2.18251i
\(691\) −582038. −1.21898 −0.609488 0.792796i \(-0.708625\pi\)
−0.609488 + 0.792796i \(0.708625\pi\)
\(692\) 1.45037e6i 3.02878i
\(693\) −538446. + 38551.1i −1.12118 + 0.0802731i
\(694\) 1.16593e6 2.42076
\(695\) 244213.i 0.505591i
\(696\) −1.52464e6 + 1.63771e6i −3.14739 + 3.38078i
\(697\) −397253. −0.817715
\(698\) 534372.i 1.09681i
\(699\) 145557. + 135508.i 0.297905 + 0.277339i
\(700\) 3493.89 0.00713040
\(701\) 441218.i 0.897877i −0.893563 0.448939i \(-0.851802\pi\)
0.893563 0.448939i \(-0.148198\pi\)
\(702\) −195093. + 242151.i −0.395883 + 0.491374i
\(703\) −47522.3 −0.0961584
\(704\) 893220.i 1.80224i
\(705\) −296358. + 318335.i −0.596263 + 0.640480i
\(706\) 482239. 0.967504
\(707\) 702888.i 1.40620i
\(708\) −119949. 111668.i −0.239292 0.222772i
\(709\) 338754. 0.673895 0.336947 0.941523i \(-0.390606\pi\)
0.336947 + 0.941523i \(0.390606\pi\)
\(710\) 1.55465e6i 3.08401i
\(711\) −12314.1 171991.i −0.0243591 0.340226i
\(712\) 1.98550e6 3.91661
\(713\) 736032.i 1.44783i
\(714\) 547380. 587972.i 1.07372 1.15335i
\(715\) −180887. −0.353830
\(716\) 177193.i 0.345636i
\(717\) 164546. + 153187.i 0.320074 + 0.297977i
\(718\) −285591. −0.553982
\(719\) 380368.i 0.735777i 0.929870 + 0.367889i \(0.119919\pi\)
−0.929870 + 0.367889i \(0.880081\pi\)
\(720\) −1.44339e6 + 103342.i −2.78432 + 0.199348i
\(721\) −883754. −1.70005
\(722\) 713291.i 1.36833i
\(723\) −201978. + 216956.i −0.386392 + 0.415046i
\(724\) 1.74412e6 3.32735
\(725\) 2278.58i 0.00433500i
\(726\) −77329.7 71991.1i −0.146715 0.136586i
\(727\) −698672. −1.32192 −0.660959 0.750422i \(-0.729850\pi\)
−0.660959 + 0.750422i \(0.729850\pi\)
\(728\) 539950.i 1.01881i
\(729\) 113083. + 519270.i 0.212786 + 0.977099i
\(730\) 705455. 1.32380
\(731\) 325011.i 0.608224i
\(732\) −575612. + 618297.i −1.07426 + 1.15392i
\(733\) 633385. 1.17885 0.589427 0.807822i \(-0.299354\pi\)
0.589427 + 0.807822i \(0.299354\pi\)
\(734\) 1.27945e6i 2.37482i
\(735\) 55831.8 + 51977.4i 0.103349 + 0.0962143i
\(736\) −2.23062e6 −4.11784
\(737\) 625462.i 1.15151i
\(738\) −75715.1 1.05752e6i −0.139018 1.94167i
\(739\) 809388. 1.48207 0.741034 0.671468i \(-0.234336\pi\)
0.741034 + 0.671468i \(0.234336\pi\)
\(740\) 254255.i 0.464307i
\(741\) −65438.3 + 70291.0i −0.119178 + 0.128016i
\(742\) −1.74479e6 −3.16910
\(743\) 93385.4i 0.169161i 0.996417 + 0.0845807i \(0.0269551\pi\)
−0.996417 + 0.0845807i \(0.973045\pi\)
\(744\) −970490. 903490.i −1.75325 1.63222i
\(745\) 1.08329e6 1.95178
\(746\) 477735.i 0.858438i
\(747\) 605380. 43343.4i 1.08489 0.0776750i
\(748\) 1.16362e6 2.07973
\(749\) 424233.i 0.756206i
\(750\) 719159. 772489.i 1.27850 1.37331i
\(751\) 728422. 1.29153 0.645763 0.763538i \(-0.276539\pi\)
0.645763 + 0.763538i \(0.276539\pi\)
\(752\) 1.38504e6i 2.44921i
\(753\) −102676. 95587.8i −0.181084 0.168582i
\(754\) 585143. 1.02925
\(755\) 392309.i 0.688232i
\(756\) 1.19407e6 + 962019.i 2.08923 + 1.68322i
\(757\) 625905. 1.09224 0.546118 0.837708i \(-0.316105\pi\)
0.546118 + 0.837708i \(0.316105\pi\)
\(758\) 2.08921e6i 3.63617i
\(759\) −706894. + 759315.i −1.22707 + 1.31807i
\(760\) −848428. −1.46888
\(761\) 545569.i 0.942064i 0.882116 + 0.471032i \(0.156118\pi\)
−0.882116 + 0.471032i \(0.843882\pi\)
\(762\) 1.09946e6 + 1.02356e6i 1.89353 + 1.76280i
\(763\) −256341. −0.440320
\(764\) 1.64603e6i 2.82001i
\(765\) −32853.2 458863.i −0.0561376 0.784079i
\(766\) 615832. 1.04955
\(767\) 25791.0i 0.0438407i
\(768\) 82972.7 89125.7i 0.140674 0.151106i
\(769\) −577208. −0.976066 −0.488033 0.872825i \(-0.662285\pi\)
−0.488033 + 0.872825i \(0.662285\pi\)
\(770\) 1.24716e6i 2.10348i
\(771\) −48741.5 45376.6i −0.0819956 0.0763349i
\(772\) −1.50521e6 −2.52559
\(773\) 1.00968e6i 1.68977i 0.534951 + 0.844883i \(0.320330\pi\)
−0.534951 + 0.844883i \(0.679670\pi\)
\(774\) −865204. + 61946.0i −1.44423 + 0.103403i
\(775\) 1350.27 0.00224810
\(776\) 2.90205e6i 4.81927i
\(777\) 81366.8 87400.7i 0.134774 0.144768i
\(778\) −757578. −1.25161
\(779\) 327435.i 0.539572i
\(780\) 376071. + 350108.i 0.618132 + 0.575458i
\(781\) −1.05763e6 −1.73393
\(782\) 1.54383e6i 2.52456i