Properties

Label 177.5.b.a.119.18
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 119.18
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.61

$q$-expansion

\(f(q)\) \(=\) \(q-5.04906i q^{2} +(-3.85410 - 8.13301i) q^{3} -9.49305 q^{4} +33.9624i q^{5} +(-41.0641 + 19.4596i) q^{6} +88.4932 q^{7} -32.8540i q^{8} +(-51.2919 + 62.6909i) q^{9} +O(q^{10})\) \(q-5.04906i q^{2} +(-3.85410 - 8.13301i) q^{3} -9.49305 q^{4} +33.9624i q^{5} +(-41.0641 + 19.4596i) q^{6} +88.4932 q^{7} -32.8540i q^{8} +(-51.2919 + 62.6909i) q^{9} +171.478 q^{10} -111.430i q^{11} +(36.5871 + 77.2071i) q^{12} +6.16984 q^{13} -446.808i q^{14} +(276.217 - 130.894i) q^{15} -317.771 q^{16} -288.710i q^{17} +(316.530 + 258.976i) q^{18} +261.438 q^{19} -322.407i q^{20} +(-341.062 - 719.717i) q^{21} -562.615 q^{22} -401.655i q^{23} +(-267.202 + 126.623i) q^{24} -528.444 q^{25} -31.1519i q^{26} +(707.550 + 175.541i) q^{27} -840.071 q^{28} -696.014i q^{29} +(-660.894 - 1394.64i) q^{30} +1230.65 q^{31} +1078.78i q^{32} +(-906.259 + 429.461i) q^{33} -1457.71 q^{34} +3005.44i q^{35} +(486.916 - 595.128i) q^{36} -1133.89 q^{37} -1320.02i q^{38} +(-23.7791 - 50.1794i) q^{39} +1115.80 q^{40} +1509.67i q^{41} +(-3633.90 + 1722.04i) q^{42} -1234.10 q^{43} +1057.81i q^{44} +(-2129.13 - 1741.99i) q^{45} -2027.98 q^{46} +148.995i q^{47} +(1224.72 + 2584.43i) q^{48} +5430.05 q^{49} +2668.15i q^{50} +(-2348.08 + 1112.72i) q^{51} -58.5706 q^{52} -4971.34i q^{53} +(886.317 - 3572.46i) q^{54} +3784.42 q^{55} -2907.36i q^{56} +(-1007.61 - 2126.28i) q^{57} -3514.22 q^{58} -453.188i q^{59} +(-2622.14 + 1242.59i) q^{60} +2566.52 q^{61} -6213.62i q^{62} +(-4538.98 + 5547.72i) q^{63} +362.503 q^{64} +209.542i q^{65} +(2168.37 + 4575.76i) q^{66} -7694.85 q^{67} +2740.74i q^{68} +(-3266.67 + 1548.02i) q^{69} +15174.7 q^{70} -7593.28i q^{71} +(2059.65 + 1685.14i) q^{72} -4759.98 q^{73} +5725.10i q^{74} +(2036.68 + 4297.84i) q^{75} -2481.85 q^{76} -9860.77i q^{77} +(-253.359 + 120.062i) q^{78} +8166.54 q^{79} -10792.3i q^{80} +(-1299.29 - 6431.06i) q^{81} +7622.44 q^{82} +7869.62i q^{83} +(3237.71 + 6832.31i) q^{84} +9805.27 q^{85} +6231.06i q^{86} +(-5660.69 + 2682.50i) q^{87} -3660.91 q^{88} +5351.59i q^{89} +(-8795.44 + 10750.1i) q^{90} +545.989 q^{91} +3812.94i q^{92} +(-4743.04 - 10008.9i) q^{93} +752.283 q^{94} +8879.07i q^{95} +(8773.74 - 4157.73i) q^{96} -7987.92 q^{97} -27416.7i q^{98} +(6985.62 + 5715.43i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.04906i 1.26227i −0.775675 0.631133i \(-0.782590\pi\)
0.775675 0.631133i \(-0.217410\pi\)
\(3\) −3.85410 8.13301i −0.428233 0.903668i
\(4\) −9.49305 −0.593316
\(5\) 33.9624i 1.35850i 0.733909 + 0.679248i \(0.237694\pi\)
−0.733909 + 0.679248i \(0.762306\pi\)
\(6\) −41.0641 + 19.4596i −1.14067 + 0.540544i
\(7\) 88.4932 1.80598 0.902992 0.429657i \(-0.141366\pi\)
0.902992 + 0.429657i \(0.141366\pi\)
\(8\) 32.8540i 0.513344i
\(9\) −51.2919 + 62.6909i −0.633233 + 0.773961i
\(10\) 171.478 1.71478
\(11\) 111.430i 0.920906i −0.887684 0.460453i \(-0.847687\pi\)
0.887684 0.460453i \(-0.152313\pi\)
\(12\) 36.5871 + 77.2071i 0.254077 + 0.536161i
\(13\) 6.16984 0.0365079 0.0182539 0.999833i \(-0.494189\pi\)
0.0182539 + 0.999833i \(0.494189\pi\)
\(14\) 446.808i 2.27963i
\(15\) 276.217 130.894i 1.22763 0.581753i
\(16\) −317.771 −1.24129
\(17\) 288.710i 0.998996i −0.866315 0.499498i \(-0.833518\pi\)
0.866315 0.499498i \(-0.166482\pi\)
\(18\) 316.530 + 258.976i 0.976945 + 0.799308i
\(19\) 261.438 0.724205 0.362103 0.932138i \(-0.382059\pi\)
0.362103 + 0.932138i \(0.382059\pi\)
\(20\) 322.407i 0.806017i
\(21\) −341.062 719.717i −0.773382 1.63201i
\(22\) −562.615 −1.16243
\(23\) 401.655i 0.759273i −0.925136 0.379636i \(-0.876049\pi\)
0.925136 0.379636i \(-0.123951\pi\)
\(24\) −267.202 + 126.623i −0.463893 + 0.219831i
\(25\) −528.444 −0.845511
\(26\) 31.1519i 0.0460827i
\(27\) 707.550 + 175.541i 0.970576 + 0.240797i
\(28\) −840.071 −1.07152
\(29\) 696.014i 0.827603i −0.910367 0.413801i \(-0.864201\pi\)
0.910367 0.413801i \(-0.135799\pi\)
\(30\) −660.894 1394.64i −0.734327 1.54960i
\(31\) 1230.65 1.28059 0.640295 0.768129i \(-0.278812\pi\)
0.640295 + 0.768129i \(0.278812\pi\)
\(32\) 1078.78i 1.05350i
\(33\) −906.259 + 429.461i −0.832194 + 0.394362i
\(34\) −1457.71 −1.26100
\(35\) 3005.44i 2.45342i
\(36\) 486.916 595.128i 0.375707 0.459203i
\(37\) −1133.89 −0.828264 −0.414132 0.910217i \(-0.635915\pi\)
−0.414132 + 0.910217i \(0.635915\pi\)
\(38\) 1320.02i 0.914140i
\(39\) −23.7791 50.1794i −0.0156339 0.0329910i
\(40\) 1115.80 0.697375
\(41\) 1509.67i 0.898081i 0.893511 + 0.449040i \(0.148234\pi\)
−0.893511 + 0.449040i \(0.851766\pi\)
\(42\) −3633.90 + 1722.04i −2.06003 + 0.976214i
\(43\) −1234.10 −0.667443 −0.333722 0.942672i \(-0.608305\pi\)
−0.333722 + 0.942672i \(0.608305\pi\)
\(44\) 1057.81i 0.546388i
\(45\) −2129.13 1741.99i −1.05142 0.860244i
\(46\) −2027.98 −0.958405
\(47\) 148.995i 0.0674489i 0.999431 + 0.0337244i \(0.0107369\pi\)
−0.999431 + 0.0337244i \(0.989263\pi\)
\(48\) 1224.72 + 2584.43i 0.531562 + 1.12172i
\(49\) 5430.05 2.26158
\(50\) 2668.15i 1.06726i
\(51\) −2348.08 + 1112.72i −0.902761 + 0.427803i
\(52\) −58.5706 −0.0216607
\(53\) 4971.34i 1.76979i −0.465792 0.884894i \(-0.654231\pi\)
0.465792 0.884894i \(-0.345769\pi\)
\(54\) 886.317 3572.46i 0.303950 1.22512i
\(55\) 3784.42 1.25105
\(56\) 2907.36i 0.927091i
\(57\) −1007.61 2126.28i −0.310129 0.654441i
\(58\) −3514.22 −1.04465
\(59\) 453.188i 0.130189i
\(60\) −2622.14 + 1242.59i −0.728372 + 0.345163i
\(61\) 2566.52 0.689740 0.344870 0.938651i \(-0.387923\pi\)
0.344870 + 0.938651i \(0.387923\pi\)
\(62\) 6213.62i 1.61645i
\(63\) −4538.98 + 5547.72i −1.14361 + 1.39776i
\(64\) 362.503 0.0885017
\(65\) 209.542i 0.0495958i
\(66\) 2168.37 + 4575.76i 0.497790 + 1.05045i
\(67\) −7694.85 −1.71416 −0.857079 0.515185i \(-0.827723\pi\)
−0.857079 + 0.515185i \(0.827723\pi\)
\(68\) 2740.74i 0.592720i
\(69\) −3266.67 + 1548.02i −0.686131 + 0.325146i
\(70\) 15174.7 3.09687
\(71\) 7593.28i 1.50630i −0.657846 0.753152i \(-0.728532\pi\)
0.657846 0.753152i \(-0.271468\pi\)
\(72\) 2059.65 + 1685.14i 0.397308 + 0.325066i
\(73\) −4759.98 −0.893221 −0.446611 0.894728i \(-0.647369\pi\)
−0.446611 + 0.894728i \(0.647369\pi\)
\(74\) 5725.10i 1.04549i
\(75\) 2036.68 + 4297.84i 0.362076 + 0.764061i
\(76\) −2481.85 −0.429682
\(77\) 9860.77i 1.66314i
\(78\) −253.359 + 120.062i −0.0416435 + 0.0197341i
\(79\) 8166.54 1.30853 0.654266 0.756265i \(-0.272978\pi\)
0.654266 + 0.756265i \(0.272978\pi\)
\(80\) 10792.3i 1.68629i
\(81\) −1299.29 6431.06i −0.198032 0.980196i
\(82\) 7622.44 1.13362
\(83\) 7869.62i 1.14235i 0.820830 + 0.571173i \(0.193511\pi\)
−0.820830 + 0.571173i \(0.806489\pi\)
\(84\) 3237.71 + 6832.31i 0.458860 + 0.968298i
\(85\) 9805.27 1.35713
\(86\) 6231.06i 0.842491i
\(87\) −5660.69 + 2682.50i −0.747878 + 0.354407i
\(88\) −3660.91 −0.472741
\(89\) 5351.59i 0.675620i 0.941214 + 0.337810i \(0.109686\pi\)
−0.941214 + 0.337810i \(0.890314\pi\)
\(90\) −8795.44 + 10750.1i −1.08586 + 1.32718i
\(91\) 545.989 0.0659327
\(92\) 3812.94i 0.450489i
\(93\) −4743.04 10008.9i −0.548391 1.15723i
\(94\) 752.283 0.0851384
\(95\) 8879.07i 0.983830i
\(96\) 8773.74 4157.73i 0.952012 0.451142i
\(97\) −7987.92 −0.848966 −0.424483 0.905436i \(-0.639544\pi\)
−0.424483 + 0.905436i \(0.639544\pi\)
\(98\) 27416.7i 2.85472i
\(99\) 6985.62 + 5715.43i 0.712746 + 0.583148i
\(100\) 5016.55 0.501655
\(101\) 3277.52i 0.321294i −0.987012 0.160647i \(-0.948642\pi\)
0.987012 0.160647i \(-0.0513580\pi\)
\(102\) 5618.17 + 11855.6i 0.540001 + 1.13952i
\(103\) 14838.0 1.39862 0.699310 0.714819i \(-0.253491\pi\)
0.699310 + 0.714819i \(0.253491\pi\)
\(104\) 202.704i 0.0187411i
\(105\) 24443.3 11583.3i 2.21708 1.05064i
\(106\) −25100.6 −2.23394
\(107\) 3771.28i 0.329398i 0.986344 + 0.164699i \(0.0526653\pi\)
−0.986344 + 0.164699i \(0.947335\pi\)
\(108\) −6716.80 1666.42i −0.575858 0.142868i
\(109\) 17882.7 1.50515 0.752577 0.658504i \(-0.228810\pi\)
0.752577 + 0.658504i \(0.228810\pi\)
\(110\) 19107.8i 1.57915i
\(111\) 4370.14 + 9221.97i 0.354690 + 0.748476i
\(112\) −28120.6 −2.24175
\(113\) 2411.73i 0.188874i −0.995531 0.0944370i \(-0.969895\pi\)
0.995531 0.0944370i \(-0.0301051\pi\)
\(114\) −10735.7 + 5087.48i −0.826079 + 0.391465i
\(115\) 13641.2 1.03147
\(116\) 6607.29i 0.491030i
\(117\) −316.462 + 386.792i −0.0231180 + 0.0282557i
\(118\) −2288.17 −0.164333
\(119\) 25548.9i 1.80417i
\(120\) −4300.40 9074.82i −0.298639 0.630196i
\(121\) 2224.44 0.151932
\(122\) 12958.5i 0.870635i
\(123\) 12278.2 5818.43i 0.811567 0.384588i
\(124\) −11682.6 −0.759794
\(125\) 3279.27i 0.209873i
\(126\) 28010.8 + 22917.6i 1.76435 + 1.44354i
\(127\) 3307.85 0.205087 0.102543 0.994729i \(-0.467302\pi\)
0.102543 + 0.994729i \(0.467302\pi\)
\(128\) 15430.2i 0.941785i
\(129\) 4756.35 + 10037.0i 0.285821 + 0.603147i
\(130\) 1057.99 0.0626031
\(131\) 24056.8i 1.40183i 0.713245 + 0.700915i \(0.247225\pi\)
−0.713245 + 0.700915i \(0.752775\pi\)
\(132\) 8603.16 4076.89i 0.493754 0.233981i
\(133\) 23135.5 1.30790
\(134\) 38851.8i 2.16372i
\(135\) −5961.79 + 24030.1i −0.327121 + 1.31852i
\(136\) −9485.27 −0.512828
\(137\) 15669.2i 0.834845i 0.908713 + 0.417422i \(0.137066\pi\)
−0.908713 + 0.417422i \(0.862934\pi\)
\(138\) 7816.05 + 16493.6i 0.410421 + 0.866080i
\(139\) 22577.2 1.16853 0.584267 0.811562i \(-0.301382\pi\)
0.584267 + 0.811562i \(0.301382\pi\)
\(140\) 28530.8i 1.45565i
\(141\) 1211.77 574.239i 0.0609514 0.0288838i
\(142\) −38339.0 −1.90136
\(143\) 687.502i 0.0336203i
\(144\) 16299.1 19921.3i 0.786027 0.960712i
\(145\) 23638.3 1.12429
\(146\) 24033.4i 1.12748i
\(147\) −20928.0 44162.7i −0.968483 2.04372i
\(148\) 10764.1 0.491422
\(149\) 1485.69i 0.0669201i −0.999440 0.0334600i \(-0.989347\pi\)
0.999440 0.0334600i \(-0.0106526\pi\)
\(150\) 21700.1 10283.3i 0.964449 0.457036i
\(151\) −20410.8 −0.895170 −0.447585 0.894241i \(-0.647716\pi\)
−0.447585 + 0.894241i \(0.647716\pi\)
\(152\) 8589.29i 0.371766i
\(153\) 18099.5 + 14808.5i 0.773184 + 0.632597i
\(154\) −49787.7 −2.09933
\(155\) 41795.7i 1.73968i
\(156\) 225.737 + 476.355i 0.00927583 + 0.0195741i
\(157\) −45940.4 −1.86378 −0.931891 0.362738i \(-0.881842\pi\)
−0.931891 + 0.362738i \(0.881842\pi\)
\(158\) 41233.4i 1.65171i
\(159\) −40431.9 + 19160.0i −1.59930 + 0.757882i
\(160\) −36638.0 −1.43117
\(161\) 35543.8i 1.37124i
\(162\) −32470.9 + 6560.19i −1.23727 + 0.249969i
\(163\) 25058.4 0.943145 0.471573 0.881827i \(-0.343687\pi\)
0.471573 + 0.881827i \(0.343687\pi\)
\(164\) 14331.4i 0.532846i
\(165\) −14585.5 30778.7i −0.535740 1.13053i
\(166\) 39734.2 1.44194
\(167\) 32413.6i 1.16224i −0.813819 0.581118i \(-0.802615\pi\)
0.813819 0.581118i \(-0.197385\pi\)
\(168\) −23645.6 + 11205.2i −0.837783 + 0.397011i
\(169\) −28522.9 −0.998667
\(170\) 49507.5i 1.71306i
\(171\) −13409.7 + 16389.8i −0.458591 + 0.560507i
\(172\) 11715.4 0.396005
\(173\) 55290.6i 1.84739i 0.383126 + 0.923696i \(0.374847\pi\)
−0.383126 + 0.923696i \(0.625153\pi\)
\(174\) 13544.1 + 28581.2i 0.447356 + 0.944021i
\(175\) −46763.7 −1.52698
\(176\) 35409.1i 1.14311i
\(177\) −3685.78 + 1746.63i −0.117648 + 0.0557512i
\(178\) 27020.5 0.852812
\(179\) 17012.3i 0.530955i −0.964117 0.265477i \(-0.914470\pi\)
0.964117 0.265477i \(-0.0855295\pi\)
\(180\) 20212.0 + 16536.8i 0.623826 + 0.510396i
\(181\) 17714.0 0.540703 0.270352 0.962762i \(-0.412860\pi\)
0.270352 + 0.962762i \(0.412860\pi\)
\(182\) 2756.73i 0.0832246i
\(183\) −9891.62 20873.6i −0.295369 0.623296i
\(184\) −13196.0 −0.389768
\(185\) 38509.7i 1.12519i
\(186\) −50535.5 + 23947.9i −1.46073 + 0.692216i
\(187\) −32170.8 −0.919981
\(188\) 1414.41i 0.0400185i
\(189\) 62613.4 + 15534.2i 1.75284 + 0.434875i
\(190\) 44831.0 1.24186
\(191\) 48580.3i 1.33166i 0.746103 + 0.665830i \(0.231923\pi\)
−0.746103 + 0.665830i \(0.768077\pi\)
\(192\) −1397.12 2948.24i −0.0378993 0.0799761i
\(193\) 32320.8 0.867697 0.433848 0.900986i \(-0.357155\pi\)
0.433848 + 0.900986i \(0.357155\pi\)
\(194\) 40331.5i 1.07162i
\(195\) 1704.21 807.597i 0.0448182 0.0212386i
\(196\) −51547.8 −1.34183
\(197\) 24102.9i 0.621066i −0.950563 0.310533i \(-0.899493\pi\)
0.950563 0.310533i \(-0.100507\pi\)
\(198\) 28857.6 35270.8i 0.736088 0.899675i
\(199\) 42180.4 1.06513 0.532567 0.846388i \(-0.321228\pi\)
0.532567 + 0.846388i \(0.321228\pi\)
\(200\) 17361.5i 0.434038i
\(201\) 29656.7 + 62582.4i 0.734059 + 1.54903i
\(202\) −16548.4 −0.405558
\(203\) 61592.5i 1.49464i
\(204\) 22290.5 10563.1i 0.535622 0.253822i
\(205\) −51272.1 −1.22004
\(206\) 74917.8i 1.76543i
\(207\) 25180.1 + 20601.7i 0.587648 + 0.480797i
\(208\) −1960.59 −0.0453170
\(209\) 29132.0i 0.666925i
\(210\) −58484.7 123416.i −1.32618 2.79854i
\(211\) −40533.0 −0.910425 −0.455212 0.890383i \(-0.650437\pi\)
−0.455212 + 0.890383i \(0.650437\pi\)
\(212\) 47193.1i 1.05004i
\(213\) −61756.3 + 29265.2i −1.36120 + 0.645049i
\(214\) 19041.4 0.415788
\(215\) 41913.1i 0.906719i
\(216\) 5767.22 23245.8i 0.123611 0.498239i
\(217\) 108904. 2.31273
\(218\) 90291.1i 1.89991i
\(219\) 18345.4 + 38713.0i 0.382507 + 0.807176i
\(220\) −35925.7 −0.742266
\(221\) 1781.29i 0.0364712i
\(222\) 46562.3 22065.1i 0.944776 0.447713i
\(223\) 16360.3 0.328989 0.164494 0.986378i \(-0.447401\pi\)
0.164494 + 0.986378i \(0.447401\pi\)
\(224\) 95464.8i 1.90260i
\(225\) 27104.9 33128.6i 0.535405 0.654393i
\(226\) −12177.0 −0.238409
\(227\) 87068.2i 1.68969i −0.535009 0.844846i \(-0.679692\pi\)
0.535009 0.844846i \(-0.320308\pi\)
\(228\) 9565.28 + 20184.9i 0.184004 + 0.388290i
\(229\) −16660.9 −0.317707 −0.158854 0.987302i \(-0.550780\pi\)
−0.158854 + 0.987302i \(0.550780\pi\)
\(230\) 68875.2i 1.30199i
\(231\) −80197.8 + 38004.4i −1.50293 + 0.712212i
\(232\) −22866.8 −0.424845
\(233\) 26333.3i 0.485059i 0.970144 + 0.242529i \(0.0779771\pi\)
−0.970144 + 0.242529i \(0.922023\pi\)
\(234\) 1952.94 + 1597.84i 0.0356662 + 0.0291811i
\(235\) −5060.21 −0.0916290
\(236\) 4302.13i 0.0772431i
\(237\) −31474.7 66418.6i −0.560356 1.18248i
\(238\) −128998. −2.27734
\(239\) 66473.4i 1.16373i 0.813285 + 0.581865i \(0.197677\pi\)
−0.813285 + 0.581865i \(0.802323\pi\)
\(240\) −87773.6 + 41594.4i −1.52385 + 0.722125i
\(241\) 15975.1 0.275048 0.137524 0.990498i \(-0.456086\pi\)
0.137524 + 0.990498i \(0.456086\pi\)
\(242\) 11231.3i 0.191779i
\(243\) −47296.3 + 35353.1i −0.800968 + 0.598708i
\(244\) −24364.1 −0.409233
\(245\) 184418.i 3.07235i
\(246\) −29377.6 61993.4i −0.485452 1.02441i
\(247\) 1613.03 0.0264392
\(248\) 40431.7i 0.657383i
\(249\) 64003.7 30330.3i 1.03230 0.489190i
\(250\) 16557.2 0.264916
\(251\) 60374.2i 0.958306i 0.877732 + 0.479153i \(0.159056\pi\)
−0.877732 + 0.479153i \(0.840944\pi\)
\(252\) 43088.8 52664.8i 0.678521 0.829314i
\(253\) −44756.3 −0.699219
\(254\) 16701.5i 0.258874i
\(255\) −37790.5 79746.4i −0.581169 1.22640i
\(256\) 83708.1 1.27728
\(257\) 42564.2i 0.644434i 0.946666 + 0.322217i \(0.104428\pi\)
−0.946666 + 0.322217i \(0.895572\pi\)
\(258\) 50677.3 24015.1i 0.761333 0.360783i
\(259\) −100342. −1.49583
\(260\) 1989.20i 0.0294260i
\(261\) 43633.7 + 35699.8i 0.640532 + 0.524065i
\(262\) 121464. 1.76948
\(263\) 75835.7i 1.09638i 0.836353 + 0.548191i \(0.184683\pi\)
−0.836353 + 0.548191i \(0.815317\pi\)
\(264\) 14109.5 + 29774.2i 0.202444 + 0.427201i
\(265\) 168838. 2.40425
\(266\) 116813.i 1.65092i
\(267\) 43524.5 20625.5i 0.610536 0.289323i
\(268\) 73047.6 1.01704
\(269\) 107497.i 1.48557i −0.669533 0.742783i \(-0.733506\pi\)
0.669533 0.742783i \(-0.266494\pi\)
\(270\) 121329. + 30101.4i 1.66433 + 0.412914i
\(271\) 13069.1 0.177953 0.0889767 0.996034i \(-0.471640\pi\)
0.0889767 + 0.996034i \(0.471640\pi\)
\(272\) 91743.5i 1.24005i
\(273\) −2104.29 4440.53i −0.0282346 0.0595813i
\(274\) 79114.8 1.05380
\(275\) 58884.3i 0.778636i
\(276\) 31010.7 14695.4i 0.407092 0.192914i
\(277\) 36791.8 0.479503 0.239751 0.970834i \(-0.422934\pi\)
0.239751 + 0.970834i \(0.422934\pi\)
\(278\) 113994.i 1.47500i
\(279\) −63122.2 + 77150.4i −0.810912 + 0.991127i
\(280\) 98740.8 1.25945
\(281\) 116425.i 1.47447i 0.675638 + 0.737233i \(0.263868\pi\)
−0.675638 + 0.737233i \(0.736132\pi\)
\(282\) −2899.37 6118.33i −0.0364591 0.0769369i
\(283\) −75649.7 −0.944570 −0.472285 0.881446i \(-0.656571\pi\)
−0.472285 + 0.881446i \(0.656571\pi\)
\(284\) 72083.4i 0.893714i
\(285\) 72213.6 34220.8i 0.889056 0.421309i
\(286\) −3471.24 −0.0424378
\(287\) 133596.i 1.62192i
\(288\) −67629.7 55332.7i −0.815366 0.667109i
\(289\) 167.676 0.00200759
\(290\) 119351.i 1.41916i
\(291\) 30786.2 + 64965.9i 0.363555 + 0.767184i
\(292\) 45186.7 0.529962
\(293\) 136522.i 1.59026i 0.606439 + 0.795130i \(0.292598\pi\)
−0.606439 + 0.795130i \(0.707402\pi\)
\(294\) −222980. + 105667.i −2.57972 + 1.22248i
\(295\) 15391.3 0.176861
\(296\) 37252.9i 0.425184i
\(297\) 19560.4 78842.0i 0.221751 0.893809i
\(298\) −7501.36 −0.0844709
\(299\) 2478.15i 0.0277195i
\(300\) −19334.3 40799.7i −0.214825 0.453330i
\(301\) −109210. −1.20539
\(302\) 103055.i 1.12994i
\(303\) −26656.1 + 12631.9i −0.290343 + 0.137589i
\(304\) −83077.4 −0.898951
\(305\) 87165.2i 0.937008i
\(306\) 74768.9 91385.4i 0.798506 0.975964i
\(307\) 40342.3 0.428039 0.214020 0.976829i \(-0.431344\pi\)
0.214020 + 0.976829i \(0.431344\pi\)
\(308\) 93608.8i 0.986768i
\(309\) −57186.9 120677.i −0.598935 1.26389i
\(310\) 211029. 2.19594
\(311\) 2156.57i 0.0222968i −0.999938 0.0111484i \(-0.996451\pi\)
0.999938 0.0111484i \(-0.00354872\pi\)
\(312\) −1648.59 + 781.240i −0.0169357 + 0.00802556i
\(313\) 140844. 1.43763 0.718817 0.695199i \(-0.244684\pi\)
0.718817 + 0.695199i \(0.244684\pi\)
\(314\) 231956.i 2.35259i
\(315\) −188414. 154155.i −1.89885 1.55359i
\(316\) −77525.4 −0.776372
\(317\) 101071.i 1.00579i 0.864346 + 0.502897i \(0.167732\pi\)
−0.864346 + 0.502897i \(0.832268\pi\)
\(318\) 96740.1 + 204143.i 0.956649 + 2.01874i
\(319\) −77556.6 −0.762144
\(320\) 12311.5i 0.120229i
\(321\) 30671.9 14534.9i 0.297667 0.141059i
\(322\) −179463. −1.73086
\(323\) 75479.7i 0.723478i
\(324\) 12334.2 + 61050.4i 0.117496 + 0.581565i
\(325\) −3260.41 −0.0308678
\(326\) 126522.i 1.19050i
\(327\) −68921.8 145441.i −0.644557 1.36016i
\(328\) 49598.8 0.461024
\(329\) 13185.0i 0.121812i
\(330\) −155404. + 73643.2i −1.42703 + 0.676246i
\(331\) 40959.7 0.373853 0.186926 0.982374i \(-0.440147\pi\)
0.186926 + 0.982374i \(0.440147\pi\)
\(332\) 74706.7i 0.677771i
\(333\) 58159.5 71084.8i 0.524484 0.641044i
\(334\) −163658. −1.46705
\(335\) 261336.i 2.32868i
\(336\) 108379. + 228705.i 0.959993 + 2.02580i
\(337\) −105275. −0.926965 −0.463483 0.886106i \(-0.653400\pi\)
−0.463483 + 0.886106i \(0.653400\pi\)
\(338\) 144014.i 1.26058i
\(339\) −19614.7 + 9295.06i −0.170680 + 0.0808821i
\(340\) −93082.0 −0.805207
\(341\) 137131.i 1.17930i
\(342\) 82753.1 + 67706.2i 0.707509 + 0.578863i
\(343\) 268051. 2.27839
\(344\) 40545.2i 0.342628i
\(345\) −52574.4 110944.i −0.441709 0.932106i
\(346\) 279166. 2.33190
\(347\) 36624.9i 0.304171i 0.988367 + 0.152085i \(0.0485989\pi\)
−0.988367 + 0.152085i \(0.951401\pi\)
\(348\) 53737.2 25465.2i 0.443728 0.210275i
\(349\) 11886.3 0.0975879 0.0487939 0.998809i \(-0.484462\pi\)
0.0487939 + 0.998809i \(0.484462\pi\)
\(350\) 236113.i 1.92745i
\(351\) 4365.46 + 1083.06i 0.0354337 + 0.00879098i
\(352\) 120208. 0.970172
\(353\) 128488.i 1.03113i 0.856850 + 0.515565i \(0.172418\pi\)
−0.856850 + 0.515565i \(0.827582\pi\)
\(354\) 8818.84 + 18609.7i 0.0703728 + 0.148503i
\(355\) 257886. 2.04631
\(356\) 50802.9i 0.400856i
\(357\) −207789. + 98467.8i −1.63037 + 0.772605i
\(358\) −85896.3 −0.670206
\(359\) 207156.i 1.60735i −0.595071 0.803673i \(-0.702876\pi\)
0.595071 0.803673i \(-0.297124\pi\)
\(360\) −57231.5 + 69950.5i −0.441601 + 0.539742i
\(361\) −61971.1 −0.475527
\(362\) 89439.0i 0.682511i
\(363\) −8573.19 18091.4i −0.0650623 0.137296i
\(364\) −5183.10 −0.0391189
\(365\) 161660.i 1.21344i
\(366\) −105392. + 49943.4i −0.786765 + 0.372835i
\(367\) −123091. −0.913892 −0.456946 0.889494i \(-0.651057\pi\)
−0.456946 + 0.889494i \(0.651057\pi\)
\(368\) 127634.i 0.942480i
\(369\) −94642.8 77434.0i −0.695080 0.568694i
\(370\) −194438. −1.42029
\(371\) 439930.i 3.19621i
\(372\) 45025.9 + 95014.8i 0.325369 + 0.686602i
\(373\) −215834. −1.55132 −0.775662 0.631149i \(-0.782584\pi\)
−0.775662 + 0.631149i \(0.782584\pi\)
\(374\) 162433.i 1.16126i
\(375\) 26670.3 12638.6i 0.189656 0.0898745i
\(376\) 4895.07 0.0346245
\(377\) 4294.29i 0.0302140i
\(378\) 78433.0 316139.i 0.548928 2.21256i
\(379\) 170916. 1.18988 0.594942 0.803769i \(-0.297175\pi\)
0.594942 + 0.803769i \(0.297175\pi\)
\(380\) 84289.4i 0.583722i
\(381\) −12748.8 26902.8i −0.0878250 0.185331i
\(382\) 245285. 1.68091
\(383\) 41171.9i 0.280675i 0.990104 + 0.140337i \(0.0448187\pi\)
−0.990104 + 0.140337i \(0.955181\pi\)
\(384\) 125494. 59469.5i 0.851061 0.403303i
\(385\) 334895. 2.25937
\(386\) 163190.i 1.09526i
\(387\) 63299.4 77367.0i 0.422647 0.516575i
\(388\) 75829.8 0.503705
\(389\) 11993.0i 0.0792552i 0.999215 + 0.0396276i \(0.0126172\pi\)
−0.999215 + 0.0396276i \(0.987383\pi\)
\(390\) −4077.61 8604.67i −0.0268087 0.0565725i
\(391\) −115962. −0.758510
\(392\) 178399.i 1.16097i
\(393\) 195654. 92717.3i 1.26679 0.600310i
\(394\) −121697. −0.783950
\(395\) 277355.i 1.77763i
\(396\) −66314.9 54256.9i −0.422883 0.345991i
\(397\) −65587.3 −0.416139 −0.208070 0.978114i \(-0.566718\pi\)
−0.208070 + 0.978114i \(0.566718\pi\)
\(398\) 212971.i 1.34448i
\(399\) −89166.5 188161.i −0.560088 1.18191i
\(400\) 167924. 1.04953
\(401\) 155422.i 0.966551i 0.875468 + 0.483275i \(0.160553\pi\)
−0.875468 + 0.483275i \(0.839447\pi\)
\(402\) 315982. 149739.i 1.95529 0.926578i
\(403\) 7592.89 0.0467517
\(404\) 31113.6i 0.190629i
\(405\) 218414. 44127.0i 1.33159 0.269026i
\(406\) −310985. −1.88663
\(407\) 126349.i 0.762753i
\(408\) 36557.2 + 77143.9i 0.219610 + 0.463427i
\(409\) −4099.29 −0.0245054 −0.0122527 0.999925i \(-0.503900\pi\)
−0.0122527 + 0.999925i \(0.503900\pi\)
\(410\) 258876.i 1.54001i
\(411\) 127438. 60390.6i 0.754423 0.357508i
\(412\) −140857. −0.829823
\(413\) 40104.0i 0.235119i
\(414\) 104019. 127136.i 0.606893 0.741768i
\(415\) −267271. −1.55187
\(416\) 6655.90i 0.0384610i
\(417\) −87014.9 183621.i −0.500405 1.05597i
\(418\) −147089. −0.841837
\(419\) 13136.9i 0.0748281i 0.999300 + 0.0374141i \(0.0119120\pi\)
−0.999300 + 0.0374141i \(0.988088\pi\)
\(420\) −232042. + 109961.i −1.31543 + 0.623359i
\(421\) 87174.3 0.491840 0.245920 0.969290i \(-0.420910\pi\)
0.245920 + 0.969290i \(0.420910\pi\)
\(422\) 204654.i 1.14920i
\(423\) −9340.60 7642.21i −0.0522028 0.0427108i
\(424\) −163328. −0.908510
\(425\) 152567.i 0.844662i
\(426\) 147762. + 311811.i 0.814224 + 1.71820i
\(427\) 227120. 1.24566
\(428\) 35800.9i 0.195437i
\(429\) −5591.47 + 2649.70i −0.0303816 + 0.0143973i
\(430\) −211622. −1.14452
\(431\) 32749.0i 0.176297i 0.996107 + 0.0881483i \(0.0280949\pi\)
−0.996107 + 0.0881483i \(0.971905\pi\)
\(432\) −224839. 55781.7i −1.20477 0.298899i
\(433\) −48.9144 −0.000260892 −0.000130446 1.00000i \(-0.500042\pi\)
−0.000130446 1.00000i \(0.500042\pi\)
\(434\) 549863.i 2.91928i
\(435\) −91104.3 192251.i −0.481460 1.01599i
\(436\) −169762. −0.893032
\(437\) 105008.i 0.549870i
\(438\) 195464. 92627.2i 1.01887 0.482825i
\(439\) −359966. −1.86781 −0.933905 0.357522i \(-0.883622\pi\)
−0.933905 + 0.357522i \(0.883622\pi\)
\(440\) 124333.i 0.642217i
\(441\) −278518. + 340415.i −1.43211 + 1.75038i
\(442\) −8993.86 −0.0460364
\(443\) 271249.i 1.38217i 0.722775 + 0.691083i \(0.242866\pi\)
−0.722775 + 0.691083i \(0.757134\pi\)
\(444\) −41485.9 87544.7i −0.210443 0.444083i
\(445\) −181753. −0.917827
\(446\) 82604.1i 0.415271i
\(447\) −12083.2 + 5726.00i −0.0604736 + 0.0286574i
\(448\) 32079.0 0.159833
\(449\) 12238.5i 0.0607064i −0.999539 0.0303532i \(-0.990337\pi\)
0.999539 0.0303532i \(-0.00966321\pi\)
\(450\) −167269. 136854.i −0.826018 0.675824i
\(451\) 168222. 0.827048
\(452\) 22894.7i 0.112062i
\(453\) 78665.1 + 166001.i 0.383341 + 0.808937i
\(454\) −439613. −2.13284
\(455\) 18543.1i 0.0895693i
\(456\) −69856.8 + 33104.0i −0.335953 + 0.159203i
\(457\) −364846. −1.74694 −0.873469 0.486879i \(-0.838135\pi\)
−0.873469 + 0.486879i \(0.838135\pi\)
\(458\) 84121.9i 0.401031i
\(459\) 50680.3 204276.i 0.240555 0.969601i
\(460\) −129496. −0.611987
\(461\) 219775.i 1.03413i 0.855945 + 0.517066i \(0.172976\pi\)
−0.855945 + 0.517066i \(0.827024\pi\)
\(462\) 191886. + 404924.i 0.899002 + 1.89710i
\(463\) 190085. 0.886717 0.443359 0.896344i \(-0.353787\pi\)
0.443359 + 0.896344i \(0.353787\pi\)
\(464\) 221173.i 1.02730i
\(465\) 339925. 161085.i 1.57209 0.744987i
\(466\) 132959. 0.612273
\(467\) 427960.i 1.96232i −0.193207 0.981158i \(-0.561889\pi\)
0.193207 0.981158i \(-0.438111\pi\)
\(468\) 3004.19 3671.84i 0.0137163 0.0167646i
\(469\) −680943. −3.09574
\(470\) 25549.3i 0.115660i
\(471\) 177059. + 373634.i 0.798133 + 1.68424i
\(472\) −14889.0 −0.0668317
\(473\) 137516.i 0.614653i
\(474\) −335352. + 158918.i −1.49260 + 0.707319i
\(475\) −138155. −0.612323
\(476\) 242537.i 1.07044i
\(477\) 311657. + 254989.i 1.36975 + 1.12069i
\(478\) 335629. 1.46894
\(479\) 62417.6i 0.272042i 0.990706 + 0.136021i \(0.0434315\pi\)
−0.990706 + 0.136021i \(0.956569\pi\)
\(480\) 141206. + 297977.i 0.612875 + 1.29330i
\(481\) −6995.94 −0.0302382
\(482\) 80659.2i 0.347184i
\(483\) −289078. + 136989.i −1.23914 + 0.587208i
\(484\) −21116.7 −0.0901436
\(485\) 271289.i 1.15332i
\(486\) 178500. + 238802.i 0.755728 + 1.01103i
\(487\) 469157. 1.97816 0.989078 0.147395i \(-0.0470888\pi\)
0.989078 + 0.147395i \(0.0470888\pi\)
\(488\) 84320.5i 0.354074i
\(489\) −96577.6 203801.i −0.403886 0.852290i
\(490\) 931136. 3.87812
\(491\) 106092.i 0.440068i −0.975492 0.220034i \(-0.929383\pi\)
0.975492 0.220034i \(-0.0706168\pi\)
\(492\) −116558. + 55234.7i −0.481516 + 0.228182i
\(493\) −200946. −0.826771
\(494\) 8144.29i 0.0333733i
\(495\) −194110. + 237248.i −0.792204 + 0.968262i
\(496\) −391064. −1.58959
\(497\) 671954.i 2.72036i
\(498\) −153139. 323159.i −0.617488 1.30304i
\(499\) −384086. −1.54251 −0.771254 0.636527i \(-0.780370\pi\)
−0.771254 + 0.636527i \(0.780370\pi\)
\(500\) 31130.2i 0.124521i
\(501\) −263620. + 124925.i −1.05028 + 0.497708i
\(502\) 304833. 1.20964
\(503\) 136712.i 0.540343i 0.962812 + 0.270172i \(0.0870804\pi\)
−0.962812 + 0.270172i \(0.912920\pi\)
\(504\) 182265. + 149124.i 0.717532 + 0.587064i
\(505\) 111312. 0.436476
\(506\) 225978.i 0.882601i
\(507\) 109930. + 231977.i 0.427662 + 0.902464i
\(508\) −31401.6 −0.121681
\(509\) 282297.i 1.08961i 0.838563 + 0.544805i \(0.183396\pi\)
−0.838563 + 0.544805i \(0.816604\pi\)
\(510\) −402645. + 190807.i −1.54804 + 0.733589i
\(511\) −421226. −1.61314
\(512\) 175764.i 0.670488i
\(513\) 184980. + 45893.1i 0.702896 + 0.174386i
\(514\) 214910. 0.813447
\(515\) 503933.i 1.90002i
\(516\) −45152.3 95281.5i −0.169582 0.357857i
\(517\) 16602.4 0.0621141
\(518\) 506633.i 1.88814i
\(519\) 449679. 213095.i 1.66943 0.791114i
\(520\) 6884.31 0.0254597
\(521\) 337551.i 1.24355i −0.783195 0.621776i \(-0.786411\pi\)
0.783195 0.621776i \(-0.213589\pi\)
\(522\) 180251. 220309.i 0.661510 0.808522i
\(523\) −316302. −1.15637 −0.578187 0.815904i \(-0.696240\pi\)
−0.578187 + 0.815904i \(0.696240\pi\)
\(524\) 228372.i 0.831728i
\(525\) 180232. + 380330.i 0.653903 + 1.37988i
\(526\) 382899. 1.38393
\(527\) 355300.i 1.27930i
\(528\) 287983. 136470.i 1.03300 0.489519i
\(529\) 118514. 0.423505
\(530\) 852476.i 3.03480i
\(531\) 28410.7 + 23244.8i 0.100761 + 0.0824399i
\(532\) −219627. −0.776000
\(533\) 9314.44i 0.0327870i
\(534\) −104140. 219758.i −0.365202 0.770659i
\(535\) −128082. −0.447486
\(536\) 252807.i 0.879952i
\(537\) −138361. + 65567.1i −0.479807 + 0.227372i
\(538\) −542759. −1.87518
\(539\) 605069.i 2.08270i
\(540\) 56595.5 228119.i 0.194086 0.782300i
\(541\) 66158.9 0.226044 0.113022 0.993592i \(-0.463947\pi\)
0.113022 + 0.993592i \(0.463947\pi\)
\(542\) 65986.6i 0.224624i
\(543\) −68271.4 144068.i −0.231547 0.488616i
\(544\) 311455. 1.05244
\(545\) 607341.i 2.04475i
\(546\) −22420.5 + 10624.7i −0.0752074 + 0.0356395i
\(547\) −167080. −0.558407 −0.279204 0.960232i \(-0.590070\pi\)
−0.279204 + 0.960232i \(0.590070\pi\)
\(548\) 148748.i 0.495326i
\(549\) −131642. + 160897.i −0.436766 + 0.533832i
\(550\) 297311. 0.982846
\(551\) 181965.i 0.599354i
\(552\) 50858.6 + 107323.i 0.166912 + 0.352221i
\(553\) 722684. 2.36319
\(554\) 185764.i 0.605260i
\(555\) −313200. + 148420.i −1.01680 + 0.481845i
\(556\) −214327. −0.693309
\(557\) 302225.i 0.974135i −0.873364 0.487068i \(-0.838067\pi\)
0.873364 0.487068i \(-0.161933\pi\)
\(558\) 389537. + 318708.i 1.25107 + 1.02359i
\(559\) −7614.21 −0.0243670
\(560\) 955042.i 3.04541i
\(561\) 123989. + 261646.i 0.393966 + 0.831358i
\(562\) 587839. 1.86117
\(563\) 33389.3i 0.105339i −0.998612 0.0526697i \(-0.983227\pi\)
0.998612 0.0526697i \(-0.0167730\pi\)
\(564\) −11503.4 + 5451.28i −0.0361634 + 0.0171372i
\(565\) 81908.2 0.256585
\(566\) 381960.i 1.19230i
\(567\) −114978. 569106.i −0.357643 1.77022i
\(568\) −249470. −0.773252
\(569\) 462649.i 1.42898i 0.699644 + 0.714491i \(0.253342\pi\)
−0.699644 + 0.714491i \(0.746658\pi\)
\(570\) −172783. 364611.i −0.531803 1.12223i
\(571\) −149876. −0.459685 −0.229842 0.973228i \(-0.573821\pi\)
−0.229842 + 0.973228i \(0.573821\pi\)
\(572\) 6526.50i 0.0199475i
\(573\) 395104. 187233.i 1.20338 0.570261i
\(574\) 674535. 2.04729
\(575\) 212252.i 0.641973i
\(576\) −18593.4 + 22725.6i −0.0560422 + 0.0684969i
\(577\) −101628. −0.305253 −0.152627 0.988284i \(-0.548773\pi\)
−0.152627 + 0.988284i \(0.548773\pi\)
\(578\) 846.608i 0.00253412i
\(579\) −124568. 262866.i −0.371577 0.784110i
\(580\) −224400. −0.667062
\(581\) 696408.i 2.06306i
\(582\) 328017. 155442.i 0.968390 0.458904i
\(583\) −553954. −1.62981
\(584\) 156384.i 0.458530i
\(585\) −13136.4 10747.8i −0.0383853 0.0314057i
\(586\) 689310. 2.00733
\(587\) 163854.i 0.475533i 0.971322 + 0.237766i \(0.0764153\pi\)
−0.971322 + 0.237766i \(0.923585\pi\)
\(588\) 198670. + 419239.i 0.574616 + 1.21257i
\(589\) 321738. 0.927411
\(590\) 77711.8i 0.223246i
\(591\) −196030. + 92895.1i −0.561237 + 0.265961i
\(592\) 360318. 1.02812
\(593\) 366216.i 1.04142i −0.853733 0.520712i \(-0.825667\pi\)
0.853733 0.520712i \(-0.174333\pi\)
\(594\) −398078. 98762.0i −1.12822 0.279909i
\(595\) 867700. 2.45096
\(596\) 14103.8i 0.0397047i
\(597\) −162567. 343053.i −0.456125 0.962528i
\(598\) −12512.3 −0.0349893
\(599\) 630279.i 1.75663i 0.478087 + 0.878313i \(0.341330\pi\)
−0.478087 + 0.878313i \(0.658670\pi\)
\(600\) 141201. 66912.9i 0.392226 0.185869i
\(601\) 494937. 1.37025 0.685127 0.728424i \(-0.259747\pi\)
0.685127 + 0.728424i \(0.259747\pi\)
\(602\) 551407.i 1.52153i
\(603\) 394683. 482397.i 1.08546 1.32669i
\(604\) 193761. 0.531119
\(605\) 75547.2i 0.206399i
\(606\) 63779.1 + 134588.i 0.173673 + 0.366490i
\(607\) 465849. 1.26435 0.632175 0.774825i \(-0.282162\pi\)
0.632175 + 0.774825i \(0.282162\pi\)
\(608\) 282035.i 0.762948i
\(609\) −500933. + 237384.i −1.35066 + 0.640053i
\(610\) 440103. 1.18275
\(611\) 919.272i 0.00246242i
\(612\) −171819. 140577.i −0.458742 0.375330i
\(613\) 453160. 1.20595 0.602976 0.797759i \(-0.293981\pi\)
0.602976 + 0.797759i \(0.293981\pi\)
\(614\) 203691.i 0.540299i
\(615\) 197608. + 416997.i 0.522461 + 1.10251i
\(616\) −323966. −0.853764
\(617\) 382747.i 1.00541i −0.864459 0.502703i \(-0.832339\pi\)
0.864459 0.502703i \(-0.167661\pi\)
\(618\) −609308. + 288741.i −1.59536 + 0.756016i
\(619\) −514375. −1.34245 −0.671225 0.741253i \(-0.734232\pi\)
−0.671225 + 0.741253i \(0.734232\pi\)
\(620\) 396769.i 1.03218i
\(621\) 70506.9 284191.i 0.182830 0.736932i
\(622\) −10888.7 −0.0281445
\(623\) 473579.i 1.22016i
\(624\) 7556.32 + 15945.5i 0.0194062 + 0.0409515i
\(625\) −441649. −1.13062
\(626\) 711128.i 1.81468i
\(627\) −236931. + 112277.i −0.602679 + 0.285599i
\(628\) 436114. 1.10581
\(629\) 327366.i 0.827432i
\(630\) −778337. + 951313.i −1.96104 + 2.39686i
\(631\) 683875. 1.71758 0.858792 0.512324i \(-0.171215\pi\)
0.858792 + 0.512324i \(0.171215\pi\)
\(632\) 268304.i 0.671726i
\(633\) 156218. + 329656.i 0.389874 + 0.822722i
\(634\) 510315. 1.26958
\(635\) 112342.i 0.278610i
\(636\) 383823. 181887.i 0.948891 0.449663i
\(637\) 33502.5 0.0825655
\(638\) 391588.i 0.962029i
\(639\) 476029. + 389473.i 1.16582 + 0.953841i
\(640\) −524046. −1.27941
\(641\) 218772.i 0.532447i −0.963911 0.266223i \(-0.914224\pi\)
0.963911 0.266223i \(-0.0857759\pi\)
\(642\) −73387.5 154864.i −0.178054 0.375735i
\(643\) −187495. −0.453490 −0.226745 0.973954i \(-0.572808\pi\)
−0.226745 + 0.973954i \(0.572808\pi\)
\(644\) 337419.i 0.813575i
\(645\) −340880. + 161537.i −0.819373 + 0.388287i
\(646\) −381102. −0.913222
\(647\) 390577.i 0.933035i −0.884512 0.466518i \(-0.845508\pi\)
0.884512 0.466518i \(-0.154492\pi\)
\(648\) −211286. + 42686.8i −0.503177 + 0.101659i
\(649\) −50498.5 −0.119892
\(650\) 16462.0i 0.0389634i
\(651\) −419727. 885718.i −0.990386 2.08994i
\(652\) −237881. −0.559583
\(653\) 801944.i 1.88069i −0.340219 0.940346i \(-0.610501\pi\)
0.340219 0.940346i \(-0.389499\pi\)
\(654\) −734339. + 347991.i −1.71688 + 0.813603i
\(655\) −817027. −1.90438
\(656\) 479730.i 1.11478i
\(657\) 244148. 298407.i 0.565617 0.691319i
\(658\) 66571.9 0.153759
\(659\) 892.461i 0.00205503i −0.999999 0.00102752i \(-0.999673\pi\)
0.999999 0.00102752i \(-0.000327069\pi\)
\(660\) 138461. + 292184.i 0.317863 + 0.670762i
\(661\) 610212. 1.39662 0.698309 0.715796i \(-0.253936\pi\)
0.698309 + 0.715796i \(0.253936\pi\)
\(662\) 206808.i 0.471902i
\(663\) −14487.3 + 6865.27i −0.0329579 + 0.0156182i
\(664\) 258548. 0.586416
\(665\) 785737.i 1.77678i
\(666\) −358912. 293651.i −0.809169 0.662038i
\(667\) −279558. −0.628376
\(668\) 307704.i 0.689573i
\(669\) −63054.1 133058.i −0.140884 0.297297i
\(670\) −1.31950e6 −2.93941
\(671\) 285987.i 0.635185i
\(672\) 776417. 367931.i 1.71932 0.814756i
\(673\) 385805. 0.851801 0.425900 0.904770i \(-0.359957\pi\)
0.425900 + 0.904770i \(0.359957\pi\)
\(674\) 531538.i 1.17008i
\(675\) −373901. 92763.5i −0.820632 0.203596i
\(676\) 270770. 0.592525
\(677\) 106731.i 0.232871i 0.993198 + 0.116435i \(0.0371468\pi\)
−0.993198 + 0.116435i \(0.962853\pi\)
\(678\) 46931.3 + 99035.7i 0.102095 + 0.215443i
\(679\) −706877. −1.53322
\(680\) 322143.i 0.696675i
\(681\) −708127. + 335569.i −1.52692 + 0.723582i
\(682\) −692381. −1.48859
\(683\) 115229.i 0.247013i −0.992344 0.123507i \(-0.960586\pi\)
0.992344 0.123507i \(-0.0394140\pi\)
\(684\) 127298. 155589.i 0.272089 0.332558i
\(685\) −532163. −1.13413
\(686\) 1.35340e6i 2.87594i
\(687\) 64212.7 + 135503.i 0.136053 + 0.287102i
\(688\) 392162. 0.828492
\(689\) 30672.3i 0.0646112i
\(690\) −560163. + 265452.i −1.17657 + 0.557555i
\(691\) −735740. −1.54088 −0.770439 0.637513i \(-0.779963\pi\)
−0.770439 + 0.637513i \(0.779963\pi\)
\(692\) 524876.i 1.09609i
\(693\) 618180. + 505777.i 1.28721 + 1.05316i
\(694\) 184922. 0.383945
\(695\) 766777.i 1.58745i
\(696\) 88131.0 + 185976.i 0.181933 + 0.383919i
\(697\) 435858. 0.897179
\(698\) 60014.7i 0.123182i
\(699\) 214169. 101491.i 0.438332 0.207718i
\(700\) 443931. 0.905981
\(701\) 12876.8i 0.0262043i −0.999914 0.0131022i \(-0.995829\pi\)
0.999914 0.0131022i \(-0.00417067\pi\)
\(702\) 5468.43 22041.5i 0.0110966 0.0447267i
\(703\) −296443. −0.599833
\(704\) 40393.6i 0.0815017i
\(705\) 19502.5 + 41154.8i 0.0392386 + 0.0828022i
\(706\) 648745. 1.30156
\(707\) 290038.i 0.580251i
\(708\) 34989.3 16580.8i 0.0698022 0.0330781i
\(709\) 495300. 0.985316 0.492658 0.870223i \(-0.336025\pi\)
0.492658 + 0.870223i \(0.336025\pi\)
\(710\) 1.30208e6i 2.58299i
\(711\) −418877. + 511968.i −0.828605 + 1.01275i
\(712\) 175821. 0.346825
\(713\) 494296.i 0.972318i
\(714\) 497170. + 1.04914e6i 0.975234 + 2.05796i
\(715\) 23349.2 0.0456731
\(716\) 161499.i 0.315024i
\(717\) 540629. 256195.i 1.05163 0.498348i
\(718\) −1.04595e6 −2.02890
\(719\) 670622.i 1.29724i 0.761113 + 0.648619i \(0.224653\pi\)
−0.761113 + 0.648619i \(0.775347\pi\)
\(720\) 676576. + 553555.i 1.30512 + 1.06781i
\(721\) 1.31306e6 2.52589
\(722\) 312896.i 0.600241i
\(723\) −61569.5 129926.i −0.117785 0.248552i
\(724\) −168160. −0.320808
\(725\) 367804.i 0.699747i
\(726\) −91344.5 + 43286.6i −0.173304 + 0.0821259i
\(727\) −191652. −0.362614 −0.181307 0.983427i \(-0.558033\pi\)
−0.181307 + 0.983427i \(0.558033\pi\)
\(728\) 17937.9i 0.0338461i
\(729\) 469812. + 248408.i 0.884034 + 0.467423i
\(730\) −816233. −1.53168
\(731\) 356298.i 0.666773i
\(732\) 93901.7 + 198154.i 0.175247 + 0.369811i
\(733\) −2889.84 −0.00537856 −0.00268928 0.999996i \(-0.500856\pi\)
−0.00268928 + 0.999996i \(0.500856\pi\)
\(734\) 621496.i 1.15358i
\(735\) 1.49987e6 710763.i 2.77638 1.31568i
\(736\) 433298. 0.799892
\(737\) 857435.i 1.57858i
\(738\) −390969. + 477857.i −0.717844 + 0.877376i
\(739\) −779522. −1.42738 −0.713690 0.700462i \(-0.752977\pi\)
−0.713690 + 0.700462i \(0.752977\pi\)
\(740\) 365575.i 0.667595i
\(741\) −6216.78 13118.8i −0.0113221 0.0238923i
\(742\) −2.22123e6 −4.03447
\(743\) 341811.i 0.619168i 0.950872 + 0.309584i \(0.100190\pi\)
−0.950872 + 0.309584i \(0.899810\pi\)
\(744\) −328832. + 155828.i −0.594056 + 0.281513i
\(745\) 50457.7 0.0909106
\(746\) 1.08976e6i 1.95818i
\(747\) −493353. 403647.i −0.884131 0.723371i
\(748\) 305399. 0.545839
\(749\) 333733.i 0.594888i
\(750\) −63813.1 134660.i −0.113446 0.239396i
\(751\) 110915. 0.196658 0.0983290 0.995154i \(-0.468650\pi\)
0.0983290 + 0.995154i \(0.468650\pi\)
\(752\) 47346.1i 0.0837237i
\(753\) 491024. 232688.i 0.865990 0.410378i
\(754\) −21682.1 −0.0381381
\(755\) 693199.i 1.21609i
\(756\) −594392. 147467.i −1.03999 0.258018i
\(757\) −1.02325e6 −1.78563 −0.892813 0.450427i \(-0.851272\pi\)
−0.892813 + 0.450427i \(0.851272\pi\)
\(758\) 862966.i 1.50195i
\(759\) 172495. + 364004.i 0.299429 + 0.631862i
\(760\) 291713. 0.505043
\(761\) 191598.i 0.330842i −0.986223 0.165421i \(-0.947102\pi\)
0.986223 0.165421i \(-0.0528983\pi\)
\(762\) −135834. + 64369.3i −0.233936 + 0.110858i
\(763\) 1.58250e6 2.71829
\(764\) 461175.i 0.790095i
\(765\) −502931. + 614701.i −0.859380 + 1.05037i
\(766\) 207880. 0.354286
\(767\) 2796.09i 0.00475292i
\(768\) −322619. 680799.i −0.546975 1.15424i
\(769\) −423911. −0.716839 −0.358419 0.933561i \(-0.616684\pi\)
−0.358419 + 0.933561i \(0.616684\pi\)
\(770\) 1.69091e6i 2.85193i
\(771\) 346176. 164047.i 0.582355 0.275968i
\(772\) −306823. −0.514818
\(773\) 413018.i 0.691210i 0.938380 + 0.345605i \(0.112326\pi\)
−0.938380 + 0.345605i \(0.887674\pi\)
\(774\) −390631. 319603.i −0.652056 0.533493i
\(775\) −650329. −1.08275
\(776\) 262435.i 0.435812i
\(777\) 386727. + 816082.i 0.640565 + 1.35174i
\(778\) 60553.3 0.100041
\(779\) 394686.i 0.650395i
\(780\) −16178.2 + 7666.56i −0.0265913 + 0.0126012i
\(781\) −846116. −1.38716
\(782\) 585499.i 0.957442i