Properties

Label 177.5.b.a.119.61
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [177,5,Mod(119,177)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(177, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("177.119");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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 119.61
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.04906i q^{2} +(-3.85410 + 8.13301i) q^{3} -9.49305 q^{4} -33.9624i q^{5} +(-41.0641 - 19.4596i) q^{6} +88.4932 q^{7} +32.8540i q^{8} +(-51.2919 - 62.6909i) q^{9} +O(q^{10})\) \(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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 78 q - 612 q^{4} + 64 q^{6} + 76 q^{7} - 100 q^{9} - 156 q^{10} - 4 q^{13} + 13 q^{15} + 4948 q^{16} + 22 q^{18} + 812 q^{19} - 173 q^{21} - 1644 q^{22} - 678 q^{24} - 8238 q^{25} + 777 q^{27} - 3764 q^{28} + 1374 q^{30} + 4664 q^{31} - 1042 q^{33} + 3244 q^{34} + 3648 q^{36} - 3960 q^{37} - 7078 q^{39} - 1576 q^{40} + 4934 q^{42} - 1492 q^{43} - 2063 q^{45} - 2036 q^{46} - 2620 q^{48} + 24274 q^{49} + 7300 q^{51} + 8408 q^{52} - 14766 q^{54} + 9780 q^{55} + 6939 q^{57} - 3856 q^{58} + 4712 q^{60} - 212 q^{61} - 7438 q^{63} - 45760 q^{64} + 3048 q^{66} - 12972 q^{67} + 21672 q^{69} + 5828 q^{70} - 866 q^{72} - 5240 q^{73} - 20922 q^{75} + 12368 q^{76} - 16508 q^{78} - 14976 q^{79} + 25524 q^{81} - 14484 q^{82} + 9540 q^{84} + 11572 q^{85} + 5695 q^{87} + 62160 q^{88} - 31672 q^{90} + 8284 q^{91} - 9590 q^{93} - 10992 q^{94} + 34102 q^{96} - 55000 q^{97} - 14254 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(0.217410\pi\)
−0.775675 + 0.631133i \(0.782590\pi\)
\(3\) −3.85410 + 8.13301i −0.428233 + 0.903668i
\(4\) −9.49305 −0.593316
\(5\) 33.9624i 1.35850i −0.733909 0.679248i \(-0.762306\pi\)
0.733909 0.679248i \(-0.237694\pi\)
\(6\) −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 \(0.152313\pi\)
−0.887684 + 0.460453i \(0.847687\pi\)
\(12\) 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 \(0.166482\pi\)
−0.866315 + 0.499498i \(0.833518\pi\)
\(18\) 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 \(0.123951\pi\)
−0.925136 + 0.379636i \(0.876049\pi\)
\(24\) −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 \(0.135799\pi\)
−0.910367 + 0.413801i \(0.864201\pi\)
\(30\) −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 \(-0.851766\pi\)
0.893511 0.449040i \(-0.148234\pi\)
\(42\) −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 \(-0.989263\pi\)
0.999431 0.0337244i \(-0.0107369\pi\)
\(48\) 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 \(0.345769\pi\)
−0.465792 + 0.884894i \(0.654231\pi\)
\(54\) 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 \(0.271468\pi\)
−0.657846 + 0.753152i \(0.728532\pi\)
\(72\) 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 \(-0.806489\pi\)
0.820830 0.571173i \(-0.193511\pi\)
\(84\) 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 \(-0.890314\pi\)
0.941214 0.337810i \(-0.109686\pi\)
\(90\) −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 \(0.0513580\pi\)
−0.987012 + 0.160647i \(0.948642\pi\)
\(102\) 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 \(-0.947335\pi\)
0.986344 0.164699i \(-0.0526653\pi\)
\(108\) −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 \(0.0301051\pi\)
−0.995531 + 0.0944370i \(0.969895\pi\)
\(114\) −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 \(-0.752775\pi\)
0.713245 0.700915i \(-0.247225\pi\)
\(132\) 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 \(-0.862934\pi\)
0.908713 0.417422i \(-0.137066\pi\)
\(138\) 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 \(0.0106526\pi\)
−0.999440 + 0.0334600i \(0.989347\pi\)
\(150\) 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 \(0.197385\pi\)
−0.813819 + 0.581118i \(0.802615\pi\)
\(168\) −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 \(-0.625153\pi\)
0.383126 0.923696i \(-0.374847\pi\)
\(174\) 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 \(0.0855295\pi\)
−0.964117 + 0.265477i \(0.914470\pi\)
\(180\) 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 \(-0.768077\pi\)
0.746103 0.665830i \(-0.231923\pi\)
\(192\) −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 \(0.100507\pi\)
−0.950563 + 0.310533i \(0.899493\pi\)
\(198\) 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 \(0.320308\pi\)
−0.535009 + 0.844846i \(0.679692\pi\)
\(228\) 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 \(-0.922023\pi\)
0.970144 0.242529i \(-0.0779771\pi\)
\(234\) 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 \(-0.802323\pi\)
0.813285 0.581865i \(-0.197677\pi\)
\(240\) −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 \(-0.840944\pi\)
0.877732 0.479153i \(-0.159056\pi\)
\(252\) 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 \(-0.895572\pi\)
0.946666 0.322217i \(-0.104428\pi\)
\(258\) 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 \(-0.815317\pi\)
0.836353 0.548191i \(-0.184683\pi\)
\(264\) 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 \(0.266494\pi\)
−0.669533 + 0.742783i \(0.733506\pi\)
\(270\) 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 \(-0.736132\pi\)
0.675638 0.737233i \(-0.263868\pi\)
\(282\) −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 \(-0.707402\pi\)
0.606439 0.795130i \(-0.292598\pi\)
\(294\) −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 \(0.00354872\pi\)
−0.999938 + 0.0111484i \(0.996451\pi\)
\(312\) −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 \(-0.832268\pi\)
0.864346 0.502897i \(-0.167732\pi\)
\(318\) 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 \(-0.951401\pi\)
0.988367 0.152085i \(-0.0485989\pi\)
\(348\) 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 \(-0.827582\pi\)
0.856850 0.515565i \(-0.172418\pi\)
\(354\) 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 \(0.297124\pi\)
−0.595071 + 0.803673i \(0.702876\pi\)
\(360\) −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 \(-0.955181\pi\)
0.990104 0.140337i \(-0.0448187\pi\)
\(384\) 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 \(-0.987383\pi\)
0.999215 0.0396276i \(-0.0126172\pi\)
\(390\) −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 \(-0.839447\pi\)
0.875468 0.483275i \(-0.160553\pi\)
\(402\) 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 \(-0.988088\pi\)
0.999300 0.0374141i \(-0.0119120\pi\)
\(420\) −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 \(-0.971905\pi\)
0.996107 0.0881483i \(-0.0280949\pi\)
\(432\) −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 \(-0.757134\pi\)
0.722775 0.691083i \(-0.242866\pi\)
\(444\) −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 \(0.00966321\pi\)
−0.999539 + 0.0303532i \(0.990337\pi\)
\(450\) −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 \(-0.827024\pi\)
0.855945 0.517066i \(-0.172976\pi\)
\(462\) 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 \(0.438111\pi\)
−0.193207 + 0.981158i \(0.561889\pi\)
\(468\) 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 \(-0.956569\pi\)
0.990706 0.136021i \(-0.0434315\pi\)
\(480\) 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 \(0.0706168\pi\)
−0.975492 + 0.220034i \(0.929383\pi\)
\(492\) −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 \(-0.912920\pi\)
0.962812 0.270172i \(-0.0870804\pi\)
\(504\) 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 \(-0.816604\pi\)
0.838563 0.544805i \(-0.183396\pi\)
\(510\) −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 \(0.213589\pi\)
−0.783195 + 0.621776i \(0.786411\pi\)
\(522\) 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 \(0.161933\pi\)
−0.873364 + 0.487068i \(0.838067\pi\)
\(558\) 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 \(0.0167730\pi\)
−0.998612 + 0.0526697i \(0.983227\pi\)
\(564\) −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 \(-0.746658\pi\)
0.699644 0.714491i \(-0.253342\pi\)
\(570\) −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 \(-0.923585\pi\)
0.971322 0.237766i \(-0.0764153\pi\)
\(588\) 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 \(0.174333\pi\)
−0.853733 + 0.520712i \(0.825667\pi\)
\(594\) −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 \(-0.658670\pi\)
0.478087 0.878313i \(-0.341330\pi\)
\(600\) 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 \(0.167661\pi\)
−0.864459 + 0.502703i \(0.832339\pi\)
\(618\) −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 \(0.0857759\pi\)
−0.963911 + 0.266223i \(0.914224\pi\)
\(642\) −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 \(0.154492\pi\)
−0.884512 + 0.466518i \(0.845508\pi\)
\(648\) −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 \(0.389499\pi\)
−0.340219 + 0.940346i \(0.610501\pi\)
\(654\) −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 \(0.000327069\pi\)
−0.999999 + 0.00102752i \(0.999673\pi\)
\(660\) 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 \(-0.962853\pi\)
0.993198 0.116435i \(-0.0371468\pi\)
\(678\) 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 \(0.0394140\pi\)
−0.992344 + 0.123507i \(0.960586\pi\)
\(684\) 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 \(0.00417067\pi\)
−0.999914 + 0.0131022i \(0.995829\pi\)
\(702\) 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 \(-0.775347\pi\)
0.761113 0.648619i \(-0.224653\pi\)
\(720\) 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 \(-0.899810\pi\)
0.950872 0.309584i \(-0.100190\pi\)
\(744\) −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 \(0.0528983\pi\)
−0.986223 + 0.165421i \(0.947102\pi\)
\(762\) −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 \(-0.887674\pi\)
0.938380 0.345605i \(-0.112326\pi\)
\(774\) −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
\(783\) 122179. + 492464.i 0.199284 + 0.803251i
\(784\) −1.72551e6 −2.80728
\(785\) 1.56024e6i 2.53194i
\(786\) −468135. + 987871.i −0.757751 + 1.59903i
\(787\) 682596. 1.10208 0.551041 0.834478i \(-0.314231\pi\)
0.551041 + 0.834478i \(0.314231\pi\)
\(788\) 228810.i 0.368488i
\(789\) 616773. + 292278.i 0.990767 + 0.469507i
\(790\) 1.40038e6 2.24385
\(791\) 213422.i 0.341104i
\(792\) 187775. + 229506.i 0.299355 + 0.365884i
\(793\) 15835.0 0.0251809
\(794\) 331155.i 0.525279i
\(795\) −650720. + 1.37317e6i −1.02958 + 2.17264i
\(796\) −400420. −0.631960
\(797\) 753632.i 1.18643i −0.805043 0.593216i \(-0.797858\pi\)
0.805043 0.593216i \(-0.202142\pi\)
\(798\) −950039. 450207.i −1.49189 0.706980i
\(799\) 43016.2 0.0673811
\(800\) 570076.i 0.890743i
\(801\) −335496. + 274493.i −0.522904 + 0.427825i
\(802\) 784737. 1.22004
\(803\) 530402.i 0.822573i
\(804\) −281533. + 594098.i −0.435529 + 0.919064i
\(805\) 1.20715e6 1.86282
\(806\) 38337.0i 0.0590130i
\(807\) −874275. 414304.i −1.34246 0.636168i
\(808\) −107680. −0.164934
\(809\) 682052.i 1.04213i 0.853518 + 0.521063i \(0.174464\pi\)
−0.853518 + 0.521063i \(0.825536\pi\)
\(810\) −222800. + 1.10279e6i −0.339582 + 1.68082i
\(811\) 784718. 1.19309 0.596543 0.802581i \(-0.296541\pi\)
0.596543 + 0.802581i \(0.296541\pi\)
\(812\) 584701.i 0.886792i
\(813\) −50369.5 + 106291.i −0.0762055 + 0.160811i
\(814\) 637946. 0.962798
\(815\) 851044.i 1.28126i
\(816\) 746152. + 353589.i 1.12059 + 0.531028i
\(817\) −322642. −0.483366
\(818\) 20697.6i 0.0309324i
\(819\) −28004.8 34228.5i −0.0417508 0.0510294i
\(820\) 486729. 0.723868
\(821\) 579986.i 0.860461i 0.902719 + 0.430231i \(0.141568\pi\)
−0.902719 + 0.430231i \(0.858432\pi\)
\(822\) −304916. + 643442.i −0.451270 + 0.952282i
\(823\) −1.12641e6 −1.66302 −0.831512 0.555507i \(-0.812524\pi\)
−0.831512 + 0.555507i \(0.812524\pi\)
\(824\) 487486.i 0.717973i
\(825\) 478907. + 226946.i 0.703629 + 0.333438i
\(826\) −202488. −0.296783
\(827\) 380772.i 0.556743i −0.960474 0.278371i \(-0.910205\pi\)
0.960474 0.278371i \(-0.0897946\pi\)
\(828\) −239036. + 195573.i −0.348661 + 0.285264i
\(829\) 292205. 0.425186 0.212593 0.977141i \(-0.431809\pi\)
0.212593 + 0.977141i \(0.431809\pi\)
\(830\) 1.34947e6i 1.95887i
\(831\) −141799. + 299228.i −0.205339 + 0.433311i
\(832\) 2236.58 0.00323101
\(833\) 1.56771e6i 2.25931i
\(834\) −927114. 439344.i −1.33291 0.631644i
\(835\) 1.10084e6 1.57889
\(836\) 276551.i 0.395697i
\(837\) 870744. 216029.i 1.24291 0.308362i
\(838\) 66329.0 0.0944530
\(839\) 546728.i 0.776689i 0.921514 + 0.388344i \(0.126953\pi\)
−0.921514 + 0.388344i \(0.873047\pi\)
\(840\) −380557. + 803060.i −0.539338 + 1.13812i
\(841\) 222846. 0.315074
\(842\) 440149.i 0.620833i
\(843\) 946889. + 448715.i 1.33243 + 0.631415i
\(844\) 384782. 0.540169
\(845\) 968707.i 1.35669i
\(846\) −38586.0 47161.3i −0.0539124 0.0658938i
\(847\) 196848. 0.274387
\(848\) 1.57975e6i 2.19682i
\(849\) 291561. 615260.i 0.404496 0.853578i
\(850\) 770321. 1.06619
\(851\) 455434.i 0.628879i
\(852\) 586255. + 277816.i 0.807621 + 0.382718i
\(853\) −474069. −0.651543 −0.325772 0.945449i \(-0.605624\pi\)
−0.325772 + 0.945449i \(0.605624\pi\)
\(854\) 1.14674e6i 1.57235i
\(855\) −556636. + 455424.i −0.761446 + 0.622994i
\(856\) 123902. 0.169095
\(857\) 686889.i 0.935245i −0.883928 0.467622i \(-0.845111\pi\)
0.883928 0.467622i \(-0.154889\pi\)
\(858\) 13378.5 28231.7i 0.0181733 0.0383497i
\(859\) −251544. −0.340900 −0.170450 0.985366i \(-0.554522\pi\)
−0.170450 + 0.985366i \(0.554522\pi\)
\(860\) 397883.i 0.537971i
\(861\) 1.08654e6 + 514892.i 1.46568 + 0.694560i
\(862\) 165352. 0.222533
\(863\) 779321.i 1.04639i −0.852212 0.523196i \(-0.824740\pi\)
0.852212 0.523196i \(-0.175260\pi\)
\(864\) −189370. 763291.i −0.253679 1.02250i
\(865\) −1.87780e6 −2.50967
\(866\) 246.972i 0.000329315i
\(867\) −646.240 + 1363.71i −0.000859717 + 0.00181420i
\(868\) −1.03383e6 −1.37218
\(869\) 909995.i 1.20503i
\(870\) −970686. 459991.i −1.28245 0.607731i
\(871\) −47476.0 −0.0625803
\(872\) 587520.i 0.772662i
\(873\) 409715. + 500770.i 0.537593 + 0.657067i
\(874\) −530192. −0.694082
\(875\) 290193.i 0.379027i
\(876\) −174154. + 367504.i −0.226947 + 0.478910i
\(877\) −1.13477e6 −1.47540 −0.737698 0.675131i \(-0.764087\pi\)
−0.737698 + 0.675131i \(0.764087\pi\)
\(878\) 1.81749e6i 2.35767i
\(879\) 1.11034e6 + 526170.i 1.43707 + 0.681002i
\(880\) −1.20258e6 −1.55291
\(881\) 651746.i 0.839705i −0.907592 0.419853i \(-0.862082\pi\)
0.907592 0.419853i \(-0.137918\pi\)
\(882\) 1.71878e6 1.40625e6i 2.20944 1.80770i
\(883\) −740498. −0.949736 −0.474868 0.880057i \(-0.657504\pi\)
−0.474868 + 0.880057i \(0.657504\pi\)
\(884\) 16909.9i 0.0216390i
\(885\) −59319.7 + 125178.i −0.0757378 + 0.159824i
\(886\) 1.36955e6 1.74466
\(887\) 846445.i 1.07585i 0.842993 + 0.537925i \(0.180792\pi\)
−0.842993 + 0.537925i \(0.819208\pi\)
\(888\) 302979. + 143576.i 0.384226 + 0.182078i
\(889\) 292722. 0.370384
\(890\) 917681.i 1.15854i
\(891\) −716611. 144779.i −0.902668 0.182369i
\(892\) −155309. −0.195194
\(893\) 38952.9i 0.0488468i
\(894\) 28911.0 61008.7i 0.0361732 0.0763337i
\(895\) 577779. 0.721300
\(896\) 1.36547e6i 1.70085i
\(897\) −20154.8 9551.02i −0.0250492 0.0118704i
\(898\) −61792.8 −0.0766276
\(899\) 856548.i 1.05982i
\(900\) −257308. 314492.i −0.317664 0.388261i
\(901\) −1.43527e6 −1.76801
\(902\) 849366.i 1.04395i
\(903\) 420905. 888204.i 0.516189 1.08927i
\(904\) −79235.1 −0.0969573
\(905\) 601609.i 0.734543i
\(906\) 838151. + 397185.i 1.02109 + 0.483879i
\(907\) −1.01416e6 −1.23280 −0.616402 0.787432i \(-0.711410\pi\)
−0.616402 + 0.787432i \(0.711410\pi\)
\(908\) 826543.i 1.00252i
\(909\) 205470. 168110.i 0.248669 0.203454i
\(910\) 93625.2 0.113060
\(911\) 353146.i 0.425518i 0.977105 + 0.212759i \(0.0682449\pi\)
−0.977105 + 0.212759i \(0.931755\pi\)
\(912\) 320188. 675670.i 0.384960 0.812353i
\(913\) 876908. 1.05199
\(914\) 1.84213e6i 2.20510i
\(915\) 708916. + 335943.i 0.846745 + 0.401258i
\(916\) 158163. 0.188501
\(917\) 2.12886e6i 2.53168i
\(918\) −1.03141e6 + 255888.i −1.22389 + 0.303644i
\(919\) 571593. 0.676793 0.338396 0.941004i \(-0.390116\pi\)
0.338396 + 0.941004i \(0.390116\pi\)
\(920\) 448167.i 0.529498i
\(921\) −155483. + 328104.i −0.183301 + 0.386806i
\(922\) 1.10966e6 1.30535
\(923\) 46849.3i 0.0549920i
\(924\) 761322. + 360777.i 0.891711 + 0.422567i
\(925\) 599200. 0.700306
\(926\) 959750.i 1.11927i
\(927\) −761067. 930204.i −0.885652 1.08248i
\(928\) 750847. 0.871877
\(929\) 613192.i 0.710502i 0.934771 + 0.355251i \(0.115605\pi\)
−0.934771 + 0.355251i \(0.884395\pi\)
\(930\) −813328. + 1.71630e6i −0.940372 + 1.98440i
\(931\) 1.41962e6 1.63785
\(932\) 249984.i 0.287793i
\(933\) −17539.4 8311.63i −0.0201489 0.00954823i
\(934\) −2.16080e6 −2.47697
\(935\) 1.09260e6i 1.24979i
\(936\) 12707.7 10397.1i 0.0145049 0.0118675i
\(937\) 1.14653e6 1.30589 0.652944 0.757406i \(-0.273534\pi\)
0.652944 + 0.757406i \(0.273534\pi\)
\(938\) 3.43812e6i 3.90765i
\(939\) −542825. + 1.14548e6i −0.615642 + 1.29914i
\(940\) 48036.8 0.0543649
\(941\) 1.17604e6i 1.32814i 0.747670 + 0.664070i \(0.231172\pi\)
−0.747670 + 0.664070i \(0.768828\pi\)
\(942\) 1.88650e6 + 893981.i 2.12596 + 1.00746i
\(943\) 606369. 0.681889
\(944\) 144010.i 0.161602i
\(945\) −527578. 2.12650e6i −0.590776 2.38123i
\(946\) 694325. 0.775855
\(947\) 777766.i 0.867259i 0.901091 + 0.433629i \(0.142767\pi\)
−0.901091 + 0.433629i \(0.857233\pi\)
\(948\) 298790. 630515.i 0.332468 0.701583i
\(949\) −29368.3 −0.0326096
\(950\) 697556.i 0.772915i
\(951\) 822014. + 389538.i 0.908904 + 0.430714i
\(952\) −839382. −0.926160
\(953\) 1840.55i 0.00202657i −0.999999 0.00101329i \(-0.999677\pi\)
0.999999 0.00101329i \(-0.000322539\pi\)
\(954\) 1.28746e6 + 1.57358e6i 1.41461 + 1.72899i
\(955\) −1.64990e6 −1.80906
\(956\) 631036.i 0.690459i
\(957\) 298911. 630769.i 0.326375 0.688726i
\(958\) 315151. 0.343390
\(959\) 1.38662e6i 1.50772i
\(960\) 100129. + 47449.6i 0.108647 + 0.0514861i
\(961\) 590972. 0.639912
\(962\) 35322.9i 0.0381686i
\(963\) −236425. + 193436.i −0.254941 + 0.208586i
\(964\) −151652. −0.163190
\(965\) 1.09769e6i 1.17876i
\(966\) 691667. 1.45957e6i 0.741213 1.56413i
\(967\) 408089. 0.436417 0.218209 0.975902i \(-0.429979\pi\)
0.218209 + 0.975902i \(0.429979\pi\)
\(968\) 73081.6i 0.0779933i
\(969\) −613878. 290906.i −0.653784 0.309817i
\(970\) −1.36976e6 −1.45579
\(971\) 109032.i 0.115642i −0.998327 0.0578209i \(-0.981585\pi\)
0.998327 0.0578209i \(-0.0184152\pi\)
\(972\) 448987. + 335609.i 0.475227 + 0.355223i
\(973\) 1.99793e6 2.11035
\(974\) 2.36880e6i 2.49696i
\(975\) 12566.0 26517.0i 0.0132186 0.0278943i
\(976\) −815566. −0.856168
\(977\) 874095.i 0.915735i 0.889020 + 0.457867i \(0.151387\pi\)
−0.889020 + 0.457867i \(0.848613\pi\)
\(978\) −1.02900e6 487627.i −1.07582 0.509811i
\(979\) 596325. 0.622183
\(980\) 1.75069e6i 1.82287i
\(981\) −917239. 1.12108e6i −0.953114 1.16493i
\(982\) −535665. −0.555482
\(983\) 641128.i 0.663495i 0.943368 + 0.331747i \(0.107638\pi\)
−0.943368 + 0.331747i \(0.892362\pi\)
\(984\) −191159. + 403388.i −0.197426 + 0.416613i
\(985\) 818593. 0.843715
\(986\) 1.01459e6i 1.04361i
\(987\) 107234. + 50816.3i 0.110077 + 0.0521637i
\(988\) −15312.6 −0.0156868
\(989\) 495684.i 0.506772i
\(990\) 1.19788e6 980073.i 1.22220 0.999972i
\(991\) −290313. −0.295610 −0.147805 0.989017i \(-0.547221\pi\)
−0.147805 + 0.989017i \(0.547221\pi\)
\(992\) 1.32760e6i 1.34910i
\(993\) −157863. + 333126.i −0.160096 + 0.337839i
\(994\) −3.39274e6 −3.43382
\(995\) 1.43255e6i 1.44698i
\(996\) −607590. 287927.i −0.612480 0.290244i
\(997\) 996017. 1.00202 0.501010 0.865442i \(-0.332962\pi\)
0.501010 + 0.865442i \(0.332962\pi\)
\(998\) 1.93928e6i 1.94706i
\(999\) −802286. + 199045.i −0.803893 + 0.199443i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 177.5.b.a.119.61 yes 78
3.2 odd 2 inner 177.5.b.a.119.18 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
177.5.b.a.119.18 78 3.2 odd 2 inner
177.5.b.a.119.61 yes 78 1.1 even 1 trivial