Properties

Label 189.4.i.a.143.17
Level $189$
Weight $4$
Character 189.143
Analytic conductor $11.151$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,4,Mod(143,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.143");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.i (of order \(6\), degree \(2\), not 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: \(11.1513609911\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 143.17
Character \(\chi\) \(=\) 189.143
Dual form 189.4.i.a.152.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.46625i q^{2} -4.01488 q^{4} +(-9.02701 + 15.6352i) q^{5} +(-18.1650 - 3.61017i) q^{7} +13.8134i q^{8} +O(q^{10})\) \(q+3.46625i q^{2} -4.01488 q^{4} +(-9.02701 + 15.6352i) q^{5} +(-18.1650 - 3.61017i) q^{7} +13.8134i q^{8} +(-54.1956 - 31.2898i) q^{10} +(10.2147 - 5.89746i) q^{11} +(45.9746 - 26.5435i) q^{13} +(12.5137 - 62.9644i) q^{14} -79.9998 q^{16} +(-5.93967 + 10.2878i) q^{17} +(-12.1984 + 7.04273i) q^{19} +(36.2423 - 62.7736i) q^{20} +(20.4421 + 35.4067i) q^{22} +(-139.665 - 80.6357i) q^{23} +(-100.474 - 174.026i) q^{25} +(92.0062 + 159.359i) q^{26} +(72.9302 + 14.4944i) q^{28} +(-131.443 - 75.8889i) q^{29} -90.1597i q^{31} -166.792i q^{32} +(-35.6601 - 20.5884i) q^{34} +(220.421 - 251.425i) q^{35} +(185.189 + 320.757i) q^{37} +(-24.4119 - 42.2826i) q^{38} +(-215.976 - 124.694i) q^{40} +(129.206 + 223.791i) q^{41} +(-173.288 + 300.144i) q^{43} +(-41.0108 + 23.6776i) q^{44} +(279.503 - 484.114i) q^{46} +71.6618 q^{47} +(316.933 + 131.157i) q^{49} +(603.216 - 348.267i) q^{50} +(-184.583 + 106.569i) q^{52} +(-143.612 - 82.9146i) q^{53} +212.946i q^{55} +(49.8687 - 250.921i) q^{56} +(263.050 - 455.616i) q^{58} -575.335 q^{59} -496.392i q^{61} +312.516 q^{62} -61.8567 q^{64} +958.432i q^{65} -700.848 q^{67} +(23.8471 - 41.3043i) q^{68} +(871.501 + 764.035i) q^{70} +1134.69i q^{71} +(281.645 + 162.608i) q^{73} +(-1111.82 + 641.911i) q^{74} +(48.9750 - 28.2757i) q^{76} +(-206.841 + 70.2505i) q^{77} -523.879 q^{79} +(722.159 - 1250.82i) q^{80} +(-775.717 + 447.860i) q^{82} +(-410.436 + 710.896i) q^{83} +(-107.235 - 185.736i) q^{85} +(-1040.37 - 600.661i) q^{86} +(81.4641 + 141.100i) q^{88} +(181.259 + 313.950i) q^{89} +(-930.955 + 316.186i) q^{91} +(560.739 + 323.743i) q^{92} +248.398i q^{94} -254.299i q^{95} +(273.568 + 157.944i) q^{97} +(-454.624 + 1098.57i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - 162 q^{4} + 3 q^{5} + 5 q^{7} - 6 q^{10} - 9 q^{11} - 36 q^{13} - 54 q^{14} + 526 q^{16} + 72 q^{17} - 6 q^{19} - 24 q^{20} + 14 q^{22} + 285 q^{23} - 349 q^{25} + 96 q^{26} - 156 q^{28} + 132 q^{29} + 24 q^{34} - 765 q^{35} + 82 q^{37} + 873 q^{38} + 420 q^{40} - 618 q^{41} + 82 q^{43} - 603 q^{44} + 266 q^{46} + 402 q^{47} - 79 q^{49} + 1845 q^{50} + 189 q^{52} - 564 q^{53} - 66 q^{56} + 269 q^{58} - 1494 q^{59} + 2904 q^{62} - 1144 q^{64} - 590 q^{67} - 3504 q^{68} - 105 q^{70} - 6 q^{73} - 1515 q^{74} - 144 q^{76} + 4443 q^{77} + 1102 q^{79} + 4239 q^{80} + 18 q^{82} - 1830 q^{83} - 237 q^{85} - 1209 q^{86} - 623 q^{88} - 4266 q^{89} - 1140 q^{91} - 7896 q^{92} - 792 q^{97} - 5667 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.46625i 1.22550i 0.790275 + 0.612752i \(0.209938\pi\)
−0.790275 + 0.612752i \(0.790062\pi\)
\(3\) 0 0
\(4\) −4.01488 −0.501860
\(5\) −9.02701 + 15.6352i −0.807400 + 1.39846i 0.107259 + 0.994231i \(0.465793\pi\)
−0.914659 + 0.404227i \(0.867541\pi\)
\(6\) 0 0
\(7\) −18.1650 3.61017i −0.980817 0.194931i
\(8\) 13.8134i 0.610473i
\(9\) 0 0
\(10\) −54.1956 31.2898i −1.71382 0.989472i
\(11\) 10.2147 5.89746i 0.279986 0.161650i −0.353431 0.935461i \(-0.614985\pi\)
0.633417 + 0.773810i \(0.281652\pi\)
\(12\) 0 0
\(13\) 45.9746 26.5435i 0.980851 0.566295i 0.0783244 0.996928i \(-0.475043\pi\)
0.902527 + 0.430633i \(0.141710\pi\)
\(14\) 12.5137 62.9644i 0.238888 1.20200i
\(15\) 0 0
\(16\) −79.9998 −1.25000
\(17\) −5.93967 + 10.2878i −0.0847401 + 0.146774i −0.905280 0.424814i \(-0.860339\pi\)
0.820540 + 0.571589i \(0.193673\pi\)
\(18\) 0 0
\(19\) −12.1984 + 7.04273i −0.147289 + 0.0850376i −0.571834 0.820370i \(-0.693768\pi\)
0.424544 + 0.905407i \(0.360434\pi\)
\(20\) 36.2423 62.7736i 0.405202 0.701830i
\(21\) 0 0
\(22\) 20.4421 + 35.4067i 0.198103 + 0.343124i
\(23\) −139.665 80.6357i −1.26618 0.731031i −0.291919 0.956443i \(-0.594294\pi\)
−0.974263 + 0.225412i \(0.927627\pi\)
\(24\) 0 0
\(25\) −100.474 174.026i −0.803790 1.39220i
\(26\) 92.0062 + 159.359i 0.693997 + 1.20204i
\(27\) 0 0
\(28\) 72.9302 + 14.4944i 0.492233 + 0.0978278i
\(29\) −131.443 75.8889i −0.841670 0.485939i 0.0161612 0.999869i \(-0.494855\pi\)
−0.857832 + 0.513931i \(0.828189\pi\)
\(30\) 0 0
\(31\) 90.1597i 0.522360i −0.965290 0.261180i \(-0.915888\pi\)
0.965290 0.261180i \(-0.0841116\pi\)
\(32\) 166.792i 0.921403i
\(33\) 0 0
\(34\) −35.6601 20.5884i −0.179872 0.103849i
\(35\) 220.421 251.425i 1.06451 1.21424i
\(36\) 0 0
\(37\) 185.189 + 320.757i 0.822835 + 1.42519i 0.903563 + 0.428456i \(0.140942\pi\)
−0.0807273 + 0.996736i \(0.525724\pi\)
\(38\) −24.4119 42.2826i −0.104214 0.180504i
\(39\) 0 0
\(40\) −215.976 124.694i −0.853721 0.492896i
\(41\) 129.206 + 223.791i 0.492161 + 0.852447i 0.999959 0.00902843i \(-0.00287388\pi\)
−0.507798 + 0.861476i \(0.669541\pi\)
\(42\) 0 0
\(43\) −173.288 + 300.144i −0.614563 + 1.06446i 0.375897 + 0.926661i \(0.377334\pi\)
−0.990461 + 0.137794i \(0.955999\pi\)
\(44\) −41.0108 + 23.6776i −0.140514 + 0.0811257i
\(45\) 0 0
\(46\) 279.503 484.114i 0.895881 1.55171i
\(47\) 71.6618 0.222403 0.111202 0.993798i \(-0.464530\pi\)
0.111202 + 0.993798i \(0.464530\pi\)
\(48\) 0 0
\(49\) 316.933 + 131.157i 0.924004 + 0.382383i
\(50\) 603.216 348.267i 1.70615 0.985047i
\(51\) 0 0
\(52\) −184.583 + 106.569i −0.492250 + 0.284201i
\(53\) −143.612 82.9146i −0.372201 0.214890i 0.302219 0.953239i \(-0.402273\pi\)
−0.674420 + 0.738348i \(0.735606\pi\)
\(54\) 0 0
\(55\) 212.946i 0.522065i
\(56\) 49.8687 250.921i 0.119000 0.598762i
\(57\) 0 0
\(58\) 263.050 455.616i 0.595520 1.03147i
\(59\) −575.335 −1.26953 −0.634765 0.772706i \(-0.718903\pi\)
−0.634765 + 0.772706i \(0.718903\pi\)
\(60\) 0 0
\(61\) 496.392i 1.04191i −0.853585 0.520954i \(-0.825576\pi\)
0.853585 0.520954i \(-0.174424\pi\)
\(62\) 312.516 0.640154
\(63\) 0 0
\(64\) −61.8567 −0.120814
\(65\) 958.432i 1.82891i
\(66\) 0 0
\(67\) −700.848 −1.27794 −0.638971 0.769231i \(-0.720640\pi\)
−0.638971 + 0.769231i \(0.720640\pi\)
\(68\) 23.8471 41.3043i 0.0425276 0.0736600i
\(69\) 0 0
\(70\) 871.501 + 764.035i 1.48806 + 1.30457i
\(71\) 1134.69i 1.89666i 0.317289 + 0.948329i \(0.397228\pi\)
−0.317289 + 0.948329i \(0.602772\pi\)
\(72\) 0 0
\(73\) 281.645 + 162.608i 0.451563 + 0.260710i 0.708490 0.705721i \(-0.249377\pi\)
−0.256927 + 0.966431i \(0.582710\pi\)
\(74\) −1111.82 + 641.911i −1.74658 + 1.00839i
\(75\) 0 0
\(76\) 48.9750 28.2757i 0.0739186 0.0426769i
\(77\) −206.841 + 70.2505i −0.306126 + 0.103971i
\(78\) 0 0
\(79\) −523.879 −0.746088 −0.373044 0.927814i \(-0.621686\pi\)
−0.373044 + 0.927814i \(0.621686\pi\)
\(80\) 722.159 1250.82i 1.00925 1.74807i
\(81\) 0 0
\(82\) −775.717 + 447.860i −1.04468 + 0.603145i
\(83\) −410.436 + 710.896i −0.542786 + 0.940133i 0.455957 + 0.890002i \(0.349297\pi\)
−0.998743 + 0.0501309i \(0.984036\pi\)
\(84\) 0 0
\(85\) −107.235 185.736i −0.136838 0.237011i
\(86\) −1040.37 600.661i −1.30449 0.753150i
\(87\) 0 0
\(88\) 81.4641 + 141.100i 0.0986830 + 0.170924i
\(89\) 181.259 + 313.950i 0.215881 + 0.373917i 0.953545 0.301251i \(-0.0974043\pi\)
−0.737664 + 0.675168i \(0.764071\pi\)
\(90\) 0 0
\(91\) −930.955 + 316.186i −1.07242 + 0.364234i
\(92\) 560.739 + 323.743i 0.635446 + 0.366875i
\(93\) 0 0
\(94\) 248.398i 0.272556i
\(95\) 254.299i 0.274637i
\(96\) 0 0
\(97\) 273.568 + 157.944i 0.286357 + 0.165328i 0.636298 0.771444i \(-0.280465\pi\)
−0.349941 + 0.936772i \(0.613798\pi\)
\(98\) −454.624 + 1098.57i −0.468611 + 1.13237i
\(99\) 0 0
\(100\) 403.390 + 698.691i 0.403390 + 0.698691i
\(101\) −376.181 651.565i −0.370608 0.641912i 0.619051 0.785351i \(-0.287517\pi\)
−0.989659 + 0.143439i \(0.954184\pi\)
\(102\) 0 0
\(103\) 1521.17 + 878.247i 1.45520 + 0.840158i 0.998769 0.0496033i \(-0.0157957\pi\)
0.456427 + 0.889761i \(0.349129\pi\)
\(104\) 366.656 + 635.067i 0.345708 + 0.598783i
\(105\) 0 0
\(106\) 287.402 497.796i 0.263349 0.456134i
\(107\) −1162.99 + 671.452i −1.05075 + 0.606652i −0.922860 0.385137i \(-0.874154\pi\)
−0.127892 + 0.991788i \(0.540821\pi\)
\(108\) 0 0
\(109\) −40.4130 + 69.9973i −0.0355125 + 0.0615094i −0.883235 0.468930i \(-0.844640\pi\)
0.847723 + 0.530439i \(0.177973\pi\)
\(110\) −738.123 −0.639793
\(111\) 0 0
\(112\) 1453.19 + 288.812i 1.22602 + 0.243663i
\(113\) 1113.30 642.766i 0.926821 0.535100i 0.0410161 0.999158i \(-0.486941\pi\)
0.885805 + 0.464058i \(0.153607\pi\)
\(114\) 0 0
\(115\) 2521.52 1455.80i 2.04463 1.18047i
\(116\) 527.730 + 304.685i 0.422401 + 0.243873i
\(117\) 0 0
\(118\) 1994.25i 1.55581i
\(119\) 145.035 165.435i 0.111725 0.127440i
\(120\) 0 0
\(121\) −595.940 + 1032.20i −0.447738 + 0.775506i
\(122\) 1720.62 1.27686
\(123\) 0 0
\(124\) 361.980i 0.262151i
\(125\) 1371.16 0.981119
\(126\) 0 0
\(127\) −817.285 −0.571042 −0.285521 0.958372i \(-0.592167\pi\)
−0.285521 + 0.958372i \(0.592167\pi\)
\(128\) 1548.74i 1.06946i
\(129\) 0 0
\(130\) −3322.16 −2.24133
\(131\) 457.664 792.697i 0.305239 0.528689i −0.672076 0.740482i \(-0.734597\pi\)
0.977314 + 0.211793i \(0.0679304\pi\)
\(132\) 0 0
\(133\) 247.009 83.8930i 0.161040 0.0546951i
\(134\) 2429.31i 1.56612i
\(135\) 0 0
\(136\) −142.110 82.0472i −0.0896016 0.0517315i
\(137\) −641.359 + 370.289i −0.399963 + 0.230919i −0.686468 0.727160i \(-0.740840\pi\)
0.286505 + 0.958079i \(0.407507\pi\)
\(138\) 0 0
\(139\) 106.660 61.5800i 0.0650846 0.0375766i −0.467105 0.884202i \(-0.654703\pi\)
0.532189 + 0.846625i \(0.321370\pi\)
\(140\) −884.964 + 1009.44i −0.534237 + 0.609380i
\(141\) 0 0
\(142\) −3933.11 −2.32436
\(143\) 313.078 542.267i 0.183083 0.317110i
\(144\) 0 0
\(145\) 2373.08 1370.10i 1.35913 0.784694i
\(146\) −563.640 + 976.252i −0.319501 + 0.553392i
\(147\) 0 0
\(148\) −743.512 1287.80i −0.412948 0.715247i
\(149\) 355.076 + 205.003i 0.195228 + 0.112715i 0.594428 0.804149i \(-0.297379\pi\)
−0.399200 + 0.916864i \(0.630712\pi\)
\(150\) 0 0
\(151\) 163.759 + 283.639i 0.0882550 + 0.152862i 0.906774 0.421618i \(-0.138538\pi\)
−0.818519 + 0.574480i \(0.805204\pi\)
\(152\) −97.2842 168.501i −0.0519131 0.0899162i
\(153\) 0 0
\(154\) −243.506 716.961i −0.127417 0.375158i
\(155\) 1409.67 + 813.872i 0.730499 + 0.421754i
\(156\) 0 0
\(157\) 1445.64i 0.734869i 0.930049 + 0.367435i \(0.119764\pi\)
−0.930049 + 0.367435i \(0.880236\pi\)
\(158\) 1815.89i 0.914334i
\(159\) 0 0
\(160\) 2607.83 + 1505.63i 1.28854 + 0.743941i
\(161\) 2245.91 + 1968.96i 1.09939 + 0.963825i
\(162\) 0 0
\(163\) −66.7405 115.598i −0.0320707 0.0555481i 0.849545 0.527517i \(-0.176877\pi\)
−0.881615 + 0.471969i \(0.843544\pi\)
\(164\) −518.746 898.495i −0.246996 0.427809i
\(165\) 0 0
\(166\) −2464.14 1422.67i −1.15214 0.665186i
\(167\) −1258.17 2179.21i −0.582994 1.00978i −0.995122 0.0986499i \(-0.968548\pi\)
0.412128 0.911126i \(-0.364786\pi\)
\(168\) 0 0
\(169\) 310.611 537.994i 0.141380 0.244877i
\(170\) 643.808 371.703i 0.290458 0.167696i
\(171\) 0 0
\(172\) 695.732 1205.04i 0.308425 0.534207i
\(173\) 3687.50 1.62055 0.810275 0.586050i \(-0.199318\pi\)
0.810275 + 0.586050i \(0.199318\pi\)
\(174\) 0 0
\(175\) 1196.84 + 3523.90i 0.516987 + 1.52218i
\(176\) −817.174 + 471.796i −0.349982 + 0.202062i
\(177\) 0 0
\(178\) −1088.23 + 628.289i −0.458237 + 0.264563i
\(179\) −1545.34 892.205i −0.645276 0.372550i 0.141368 0.989957i \(-0.454850\pi\)
−0.786644 + 0.617407i \(0.788183\pi\)
\(180\) 0 0
\(181\) 1168.16i 0.479717i −0.970808 0.239859i \(-0.922899\pi\)
0.970808 0.239859i \(-0.0771011\pi\)
\(182\) −1095.98 3226.92i −0.446370 1.31426i
\(183\) 0 0
\(184\) 1113.86 1929.25i 0.446274 0.772970i
\(185\) −6686.81 −2.65743
\(186\) 0 0
\(187\) 140.116i 0.0547930i
\(188\) −287.713 −0.111615
\(189\) 0 0
\(190\) 881.464 0.336569
\(191\) 1054.37i 0.399434i −0.979854 0.199717i \(-0.935998\pi\)
0.979854 0.199717i \(-0.0640022\pi\)
\(192\) 0 0
\(193\) 1225.74 0.457155 0.228578 0.973526i \(-0.426593\pi\)
0.228578 + 0.973526i \(0.426593\pi\)
\(194\) −547.475 + 948.254i −0.202610 + 0.350931i
\(195\) 0 0
\(196\) −1272.45 526.580i −0.463720 0.191902i
\(197\) 799.520i 0.289155i −0.989494 0.144577i \(-0.953818\pi\)
0.989494 0.144577i \(-0.0461822\pi\)
\(198\) 0 0
\(199\) −2275.00 1313.47i −0.810406 0.467888i 0.0366911 0.999327i \(-0.488318\pi\)
−0.847097 + 0.531439i \(0.821652\pi\)
\(200\) 2403.89 1387.89i 0.849903 0.490692i
\(201\) 0 0
\(202\) 2258.49 1303.94i 0.786666 0.454182i
\(203\) 2113.70 + 1853.05i 0.730800 + 0.640684i
\(204\) 0 0
\(205\) −4665.37 −1.58948
\(206\) −3044.22 + 5272.75i −1.02962 + 1.78335i
\(207\) 0 0
\(208\) −3677.96 + 2123.47i −1.22606 + 0.707867i
\(209\) −83.0685 + 143.879i −0.0274927 + 0.0476187i
\(210\) 0 0
\(211\) −1004.95 1740.62i −0.327883 0.567911i 0.654208 0.756315i \(-0.273002\pi\)
−0.982092 + 0.188404i \(0.939669\pi\)
\(212\) 576.586 + 332.892i 0.186793 + 0.107845i
\(213\) 0 0
\(214\) −2327.42 4031.21i −0.743454 1.28770i
\(215\) −3128.55 5418.81i −0.992397 1.71888i
\(216\) 0 0
\(217\) −325.492 + 1637.75i −0.101824 + 0.512340i
\(218\) −242.628 140.081i −0.0753800 0.0435207i
\(219\) 0 0
\(220\) 854.951i 0.262004i
\(221\) 630.638i 0.191952i
\(222\) 0 0
\(223\) 3897.23 + 2250.07i 1.17030 + 0.675676i 0.953752 0.300595i \(-0.0971854\pi\)
0.216553 + 0.976271i \(0.430519\pi\)
\(224\) −602.146 + 3029.77i −0.179610 + 0.903728i
\(225\) 0 0
\(226\) 2227.99 + 3858.98i 0.655767 + 1.13582i
\(227\) 1637.48 + 2836.19i 0.478780 + 0.829271i 0.999704 0.0243318i \(-0.00774581\pi\)
−0.520924 + 0.853603i \(0.674412\pi\)
\(228\) 0 0
\(229\) −1155.01 666.848i −0.333299 0.192430i 0.324006 0.946055i \(-0.394970\pi\)
−0.657305 + 0.753625i \(0.728304\pi\)
\(230\) 5046.16 + 8740.20i 1.44667 + 2.50570i
\(231\) 0 0
\(232\) 1048.29 1815.68i 0.296652 0.513817i
\(233\) −678.031 + 391.461i −0.190641 + 0.110066i −0.592282 0.805730i \(-0.701773\pi\)
0.401642 + 0.915797i \(0.368440\pi\)
\(234\) 0 0
\(235\) −646.892 + 1120.45i −0.179568 + 0.311022i
\(236\) 2309.90 0.637126
\(237\) 0 0
\(238\) 573.438 + 502.726i 0.156178 + 0.136920i
\(239\) 4512.91 2605.53i 1.22141 0.705179i 0.256188 0.966627i \(-0.417534\pi\)
0.965217 + 0.261449i \(0.0842002\pi\)
\(240\) 0 0
\(241\) −2328.71 + 1344.48i −0.622428 + 0.359359i −0.777814 0.628495i \(-0.783671\pi\)
0.155386 + 0.987854i \(0.450338\pi\)
\(242\) −3577.86 2065.68i −0.950385 0.548705i
\(243\) 0 0
\(244\) 1992.95i 0.522892i
\(245\) −4911.63 + 3771.37i −1.28079 + 0.983445i
\(246\) 0 0
\(247\) −373.877 + 647.574i −0.0963127 + 0.166818i
\(248\) 1245.41 0.318887
\(249\) 0 0
\(250\) 4752.77i 1.20237i
\(251\) 2540.09 0.638762 0.319381 0.947626i \(-0.396525\pi\)
0.319381 + 0.947626i \(0.396525\pi\)
\(252\) 0 0
\(253\) −1902.18 −0.472685
\(254\) 2832.91i 0.699814i
\(255\) 0 0
\(256\) 4873.48 1.18981
\(257\) −1934.85 + 3351.25i −0.469620 + 0.813406i −0.999397 0.0347315i \(-0.988942\pi\)
0.529777 + 0.848137i \(0.322276\pi\)
\(258\) 0 0
\(259\) −2205.97 6495.11i −0.529237 1.55825i
\(260\) 3847.99i 0.917854i
\(261\) 0 0
\(262\) 2747.68 + 1586.38i 0.647910 + 0.374071i
\(263\) 1965.36 1134.70i 0.460796 0.266041i −0.251583 0.967836i \(-0.580951\pi\)
0.712379 + 0.701795i \(0.247618\pi\)
\(264\) 0 0
\(265\) 2592.78 1496.94i 0.601030 0.347005i
\(266\) 290.794 + 856.193i 0.0670290 + 0.197356i
\(267\) 0 0
\(268\) 2813.82 0.641348
\(269\) 1363.14 2361.02i 0.308967 0.535146i −0.669170 0.743109i \(-0.733350\pi\)
0.978137 + 0.207964i \(0.0666836\pi\)
\(270\) 0 0
\(271\) 5611.15 3239.60i 1.25776 0.726168i 0.285122 0.958491i \(-0.407966\pi\)
0.972639 + 0.232323i \(0.0746326\pi\)
\(272\) 475.172 823.023i 0.105925 0.183467i
\(273\) 0 0
\(274\) −1283.51 2223.11i −0.282992 0.490157i
\(275\) −2052.62 1185.08i −0.450100 0.259865i
\(276\) 0 0
\(277\) 4101.30 + 7103.66i 0.889615 + 1.54086i 0.840331 + 0.542074i \(0.182361\pi\)
0.0492841 + 0.998785i \(0.484306\pi\)
\(278\) 213.452 + 369.709i 0.0460503 + 0.0797614i
\(279\) 0 0
\(280\) 3473.04 + 3044.77i 0.741263 + 0.649857i
\(281\) −586.668 338.713i −0.124547 0.0719072i 0.436432 0.899737i \(-0.356242\pi\)
−0.560979 + 0.827830i \(0.689575\pi\)
\(282\) 0 0
\(283\) 2464.61i 0.517688i 0.965919 + 0.258844i \(0.0833415\pi\)
−0.965919 + 0.258844i \(0.916658\pi\)
\(284\) 4555.63i 0.951856i
\(285\) 0 0
\(286\) 1879.63 + 1085.21i 0.388619 + 0.224369i
\(287\) −1539.10 4531.62i −0.316552 0.932032i
\(288\) 0 0
\(289\) 2385.94 + 4132.57i 0.485638 + 0.841150i
\(290\) 4749.11 + 8225.69i 0.961645 + 1.66562i
\(291\) 0 0
\(292\) −1130.77 652.851i −0.226621 0.130840i
\(293\) 3122.10 + 5407.64i 0.622510 + 1.07822i 0.989017 + 0.147803i \(0.0472202\pi\)
−0.366507 + 0.930415i \(0.619446\pi\)
\(294\) 0 0
\(295\) 5193.55 8995.49i 1.02502 1.77538i
\(296\) −4430.75 + 2558.10i −0.870041 + 0.502319i
\(297\) 0 0
\(298\) −710.591 + 1230.78i −0.138132 + 0.239252i
\(299\) −8561.41 −1.65592
\(300\) 0 0
\(301\) 4231.35 4826.52i 0.810269 0.924238i
\(302\) −983.162 + 567.629i −0.187333 + 0.108157i
\(303\) 0 0
\(304\) 975.867 563.417i 0.184111 0.106297i
\(305\) 7761.20 + 4480.93i 1.45707 + 0.841237i
\(306\) 0 0
\(307\) 6996.15i 1.30062i 0.759667 + 0.650312i \(0.225362\pi\)
−0.759667 + 0.650312i \(0.774638\pi\)
\(308\) 830.440 282.047i 0.153632 0.0521790i
\(309\) 0 0
\(310\) −2821.08 + 4886.26i −0.516861 + 0.895229i
\(311\) −2141.91 −0.390535 −0.195268 0.980750i \(-0.562558\pi\)
−0.195268 + 0.980750i \(0.562558\pi\)
\(312\) 0 0
\(313\) 5422.41i 0.979210i 0.871944 + 0.489605i \(0.162859\pi\)
−0.871944 + 0.489605i \(0.837141\pi\)
\(314\) −5010.94 −0.900585
\(315\) 0 0
\(316\) 2103.31 0.374432
\(317\) 1525.39i 0.270266i −0.990827 0.135133i \(-0.956854\pi\)
0.990827 0.135133i \(-0.0431461\pi\)
\(318\) 0 0
\(319\) −1790.21 −0.314208
\(320\) 558.381 967.144i 0.0975451 0.168953i
\(321\) 0 0
\(322\) −6824.91 + 7784.87i −1.18117 + 1.34731i
\(323\) 167.326i 0.0288244i
\(324\) 0 0
\(325\) −9238.48 5333.84i −1.57680 0.910364i
\(326\) 400.691 231.339i 0.0680744 0.0393027i
\(327\) 0 0
\(328\) −3091.33 + 1784.78i −0.520396 + 0.300451i
\(329\) −1301.74 258.711i −0.218137 0.0433532i
\(330\) 0 0
\(331\) 178.450 0.0296330 0.0148165 0.999890i \(-0.495284\pi\)
0.0148165 + 0.999890i \(0.495284\pi\)
\(332\) 1647.85 2854.16i 0.272402 0.471815i
\(333\) 0 0
\(334\) 7553.69 4361.13i 1.23748 0.714462i
\(335\) 6326.56 10957.9i 1.03181 1.78715i
\(336\) 0 0
\(337\) −1570.00 2719.33i −0.253779 0.439558i 0.710784 0.703410i \(-0.248340\pi\)
−0.964563 + 0.263852i \(0.915007\pi\)
\(338\) 1864.82 + 1076.66i 0.300098 + 0.173261i
\(339\) 0 0
\(340\) 430.535 + 745.708i 0.0686736 + 0.118946i
\(341\) −531.713 920.955i −0.0844396 0.146254i
\(342\) 0 0
\(343\) −5283.59 3526.65i −0.831741 0.555164i
\(344\) −4146.02 2393.71i −0.649821 0.375174i
\(345\) 0 0
\(346\) 12781.8i 1.98599i
\(347\) 3602.36i 0.557305i 0.960392 + 0.278653i \(0.0898878\pi\)
−0.960392 + 0.278653i \(0.910112\pi\)
\(348\) 0 0
\(349\) −4656.87 2688.64i −0.714259 0.412378i 0.0983769 0.995149i \(-0.468635\pi\)
−0.812636 + 0.582772i \(0.801968\pi\)
\(350\) −12214.7 + 4148.55i −1.86544 + 0.633570i
\(351\) 0 0
\(352\) −983.648 1703.73i −0.148945 0.257980i
\(353\) 2022.86 + 3503.70i 0.305003 + 0.528281i 0.977262 0.212035i \(-0.0680091\pi\)
−0.672259 + 0.740316i \(0.734676\pi\)
\(354\) 0 0
\(355\) −17741.1 10242.8i −2.65240 1.53136i
\(356\) −727.733 1260.47i −0.108342 0.187654i
\(357\) 0 0
\(358\) 3092.60 5356.55i 0.456562 0.790788i
\(359\) −254.213 + 146.770i −0.0373729 + 0.0215772i −0.518570 0.855035i \(-0.673535\pi\)
0.481197 + 0.876612i \(0.340202\pi\)
\(360\) 0 0
\(361\) −3330.30 + 5768.25i −0.485537 + 0.840975i
\(362\) 4049.14 0.587896
\(363\) 0 0
\(364\) 3737.67 1269.45i 0.538206 0.182794i
\(365\) −5084.83 + 2935.73i −0.729184 + 0.420994i
\(366\) 0 0
\(367\) −6468.89 + 3734.81i −0.920090 + 0.531214i −0.883664 0.468122i \(-0.844931\pi\)
−0.0364264 + 0.999336i \(0.511597\pi\)
\(368\) 11173.2 + 6450.84i 1.58272 + 0.913786i
\(369\) 0 0
\(370\) 23178.2i 3.25669i
\(371\) 2309.38 + 2024.61i 0.323172 + 0.283322i
\(372\) 0 0
\(373\) 6519.35 11291.8i 0.904984 1.56748i 0.0840463 0.996462i \(-0.473216\pi\)
0.820938 0.571017i \(-0.193451\pi\)
\(374\) −485.676 −0.0671490
\(375\) 0 0
\(376\) 989.895i 0.135771i
\(377\) −8057.42 −1.10074
\(378\) 0 0
\(379\) −8544.38 −1.15803 −0.579017 0.815315i \(-0.696564\pi\)
−0.579017 + 0.815315i \(0.696564\pi\)
\(380\) 1020.98i 0.137829i
\(381\) 0 0
\(382\) 3654.72 0.489508
\(383\) 4417.82 7651.89i 0.589400 1.02087i −0.404911 0.914356i \(-0.632698\pi\)
0.994311 0.106514i \(-0.0339690\pi\)
\(384\) 0 0
\(385\) 768.769 3868.16i 0.101767 0.512051i
\(386\) 4248.73i 0.560246i
\(387\) 0 0
\(388\) −1098.34 634.128i −0.143711 0.0829716i
\(389\) −5438.84 + 3140.11i −0.708895 + 0.409281i −0.810652 0.585529i \(-0.800887\pi\)
0.101757 + 0.994809i \(0.467554\pi\)
\(390\) 0 0
\(391\) 1659.13 957.899i 0.214593 0.123895i
\(392\) −1811.73 + 4377.94i −0.233434 + 0.564079i
\(393\) 0 0
\(394\) 2771.34 0.354360
\(395\) 4729.06 8190.96i 0.602391 1.04337i
\(396\) 0 0
\(397\) 10068.6 5813.13i 1.27287 0.734893i 0.297345 0.954770i \(-0.403899\pi\)
0.975528 + 0.219877i \(0.0705655\pi\)
\(398\) 4552.83 7885.73i 0.573398 0.993155i
\(399\) 0 0
\(400\) 8037.87 + 13922.0i 1.00473 + 1.74025i
\(401\) −9999.11 5772.99i −1.24522 0.718926i −0.275064 0.961426i \(-0.588699\pi\)
−0.970151 + 0.242500i \(0.922032\pi\)
\(402\) 0 0
\(403\) −2393.15 4145.06i −0.295810 0.512358i
\(404\) 1510.32 + 2615.95i 0.185993 + 0.322150i
\(405\) 0 0
\(406\) −6423.15 + 7326.60i −0.785161 + 0.895599i
\(407\) 3783.30 + 2184.29i 0.460765 + 0.266023i
\(408\) 0 0
\(409\) 10939.3i 1.32253i 0.750154 + 0.661263i \(0.229979\pi\)
−0.750154 + 0.661263i \(0.770021\pi\)
\(410\) 16171.3i 1.94792i
\(411\) 0 0
\(412\) −6107.31 3526.05i −0.730304 0.421641i
\(413\) 10450.9 + 2077.05i 1.24518 + 0.247470i
\(414\) 0 0
\(415\) −7410.02 12834.5i −0.876491 1.51813i
\(416\) −4427.23 7668.19i −0.521786 0.903759i
\(417\) 0 0
\(418\) −498.720 287.936i −0.0583569 0.0336924i
\(419\) 236.117 + 408.966i 0.0275300 + 0.0476833i 0.879462 0.475969i \(-0.157902\pi\)
−0.851932 + 0.523652i \(0.824569\pi\)
\(420\) 0 0
\(421\) −8133.40 + 14087.5i −0.941562 + 1.63083i −0.179070 + 0.983836i \(0.557309\pi\)
−0.762492 + 0.646998i \(0.776024\pi\)
\(422\) 6033.42 3483.40i 0.695977 0.401822i
\(423\) 0 0
\(424\) 1145.33 1983.78i 0.131185 0.227219i
\(425\) 2387.12 0.272453
\(426\) 0 0
\(427\) −1792.06 + 9016.95i −0.203100 + 1.02192i
\(428\) 4669.26 2695.80i 0.527330 0.304454i
\(429\) 0 0
\(430\) 18782.9 10844.3i 2.10650 1.21619i
\(431\) 7130.94 + 4117.05i 0.796949 + 0.460119i 0.842403 0.538847i \(-0.181140\pi\)
−0.0454539 + 0.998966i \(0.514473\pi\)
\(432\) 0 0
\(433\) 8661.16i 0.961268i 0.876921 + 0.480634i \(0.159593\pi\)
−0.876921 + 0.480634i \(0.840407\pi\)
\(434\) −5676.85 1128.23i −0.627874 0.124786i
\(435\) 0 0
\(436\) 162.253 281.031i 0.0178223 0.0308691i
\(437\) 2271.58 0.248660
\(438\) 0 0
\(439\) 12326.7i 1.34014i −0.742299 0.670069i \(-0.766264\pi\)
0.742299 0.670069i \(-0.233736\pi\)
\(440\) −2941.51 −0.318707
\(441\) 0 0
\(442\) −2185.95 −0.235237
\(443\) 4487.07i 0.481236i 0.970620 + 0.240618i \(0.0773500\pi\)
−0.970620 + 0.240618i \(0.922650\pi\)
\(444\) 0 0
\(445\) −6544.91 −0.697210
\(446\) −7799.29 + 13508.8i −0.828043 + 1.43421i
\(447\) 0 0
\(448\) 1123.63 + 223.313i 0.118496 + 0.0235503i
\(449\) 14430.4i 1.51674i −0.651827 0.758368i \(-0.725997\pi\)
0.651827 0.758368i \(-0.274003\pi\)
\(450\) 0 0
\(451\) 2639.60 + 1523.98i 0.275596 + 0.159116i
\(452\) −4469.78 + 2580.63i −0.465134 + 0.268545i
\(453\) 0 0
\(454\) −9830.94 + 5675.90i −1.01628 + 0.586747i
\(455\) 3460.10 17409.9i 0.356510 1.79382i
\(456\) 0 0
\(457\) 11998.9 1.22820 0.614099 0.789229i \(-0.289519\pi\)
0.614099 + 0.789229i \(0.289519\pi\)
\(458\) 2311.46 4003.57i 0.235824 0.408460i
\(459\) 0 0
\(460\) −10123.6 + 5844.85i −1.02612 + 0.592430i
\(461\) −8143.25 + 14104.5i −0.822709 + 1.42497i 0.0809488 + 0.996718i \(0.474205\pi\)
−0.903658 + 0.428255i \(0.859128\pi\)
\(462\) 0 0
\(463\) 1256.95 + 2177.11i 0.126168 + 0.218529i 0.922189 0.386740i \(-0.126399\pi\)
−0.796021 + 0.605269i \(0.793066\pi\)
\(464\) 10515.4 + 6071.10i 1.05209 + 0.607422i
\(465\) 0 0
\(466\) −1356.90 2350.22i −0.134887 0.233631i
\(467\) 3861.82 + 6688.87i 0.382663 + 0.662793i 0.991442 0.130548i \(-0.0416735\pi\)
−0.608779 + 0.793340i \(0.708340\pi\)
\(468\) 0 0
\(469\) 12730.9 + 2530.18i 1.25343 + 0.249110i
\(470\) −3883.76 2242.29i −0.381158 0.220062i
\(471\) 0 0
\(472\) 7947.34i 0.775013i
\(473\) 4087.85i 0.397377i
\(474\) 0 0
\(475\) 2451.23 + 1415.22i 0.236779 + 0.136705i
\(476\) −582.297 + 664.200i −0.0560704 + 0.0639571i
\(477\) 0 0
\(478\) 9031.41 + 15642.9i 0.864199 + 1.49684i
\(479\) 42.4285 + 73.4883i 0.00404720 + 0.00700995i 0.868042 0.496491i \(-0.165378\pi\)
−0.863995 + 0.503501i \(0.832045\pi\)
\(480\) 0 0
\(481\) 17028.0 + 9831.12i 1.61416 + 0.931935i
\(482\) −4660.30 8071.87i −0.440396 0.762788i
\(483\) 0 0
\(484\) 2392.63 4144.15i 0.224702 0.389195i
\(485\) −4939.00 + 2851.53i −0.462409 + 0.266972i
\(486\) 0 0
\(487\) 2652.69 4594.60i 0.246828 0.427518i −0.715816 0.698289i \(-0.753945\pi\)
0.962644 + 0.270771i \(0.0872785\pi\)
\(488\) 6856.87 0.636057
\(489\) 0 0
\(490\) −13072.5 17024.9i −1.20522 1.56961i
\(491\) −752.365 + 434.378i −0.0691523 + 0.0399251i −0.534177 0.845372i \(-0.679379\pi\)
0.465025 + 0.885297i \(0.346045\pi\)
\(492\) 0 0
\(493\) 1561.46 901.510i 0.142646 0.0823570i
\(494\) −2244.65 1295.95i −0.204437 0.118032i
\(495\) 0 0
\(496\) 7212.76i 0.652948i
\(497\) 4096.41 20611.6i 0.369717 1.86027i
\(498\) 0 0
\(499\) 899.130 1557.34i 0.0806625 0.139712i −0.822872 0.568227i \(-0.807630\pi\)
0.903535 + 0.428515i \(0.140963\pi\)
\(500\) −5505.02 −0.492384
\(501\) 0 0
\(502\) 8804.59i 0.782805i
\(503\) −307.609 −0.0272676 −0.0136338 0.999907i \(-0.504340\pi\)
−0.0136338 + 0.999907i \(0.504340\pi\)
\(504\) 0 0
\(505\) 13583.2 1.19692
\(506\) 6593.44i 0.579277i
\(507\) 0 0
\(508\) 3281.30 0.286583
\(509\) −1405.20 + 2433.88i −0.122367 + 0.211945i −0.920700 0.390270i \(-0.872382\pi\)
0.798334 + 0.602215i \(0.205715\pi\)
\(510\) 0 0
\(511\) −4529.04 3970.56i −0.392080 0.343732i
\(512\) 4502.73i 0.388661i
\(513\) 0 0
\(514\) −11616.3 6706.65i −0.996832 0.575521i
\(515\) −27463.2 + 15855.9i −2.34985 + 1.35669i
\(516\) 0 0
\(517\) 732.004 422.623i 0.0622698 0.0359515i
\(518\) 22513.7 7646.45i 1.90964 0.648582i
\(519\) 0 0
\(520\) −13239.2 −1.11650
\(521\) 2227.32 3857.83i 0.187295 0.324405i −0.757052 0.653354i \(-0.773361\pi\)
0.944348 + 0.328950i \(0.106695\pi\)
\(522\) 0 0
\(523\) 6168.37 3561.31i 0.515724 0.297754i −0.219459 0.975622i \(-0.570429\pi\)
0.735184 + 0.677868i \(0.237096\pi\)
\(524\) −1837.46 + 3182.58i −0.153187 + 0.265328i
\(525\) 0 0
\(526\) 3933.16 + 6812.43i 0.326034 + 0.564708i
\(527\) 927.546 + 535.519i 0.0766690 + 0.0442648i
\(528\) 0 0
\(529\) 6920.74 + 11987.1i 0.568812 + 0.985211i
\(530\) 5188.77 + 8987.21i 0.425256 + 0.736565i
\(531\) 0 0
\(532\) −991.710 + 336.820i −0.0808197 + 0.0274493i
\(533\) 11880.4 + 6859.15i 0.965473 + 0.557416i
\(534\) 0 0
\(535\) 24244.8i 1.95924i
\(536\) 9681.10i 0.780149i
\(537\) 0 0
\(538\) 8183.90 + 4724.98i 0.655823 + 0.378640i
\(539\) 4010.88 529.370i 0.320521 0.0423035i
\(540\) 0 0
\(541\) −4251.18 7363.26i −0.337842 0.585159i 0.646185 0.763181i \(-0.276364\pi\)
−0.984027 + 0.178022i \(0.943030\pi\)
\(542\) 11229.3 + 19449.6i 0.889922 + 1.54139i
\(543\) 0 0
\(544\) 1715.92 + 990.688i 0.135238 + 0.0780798i
\(545\) −729.616 1263.73i −0.0573456 0.0993254i
\(546\) 0 0
\(547\) −9900.32 + 17147.9i −0.773870 + 1.34038i 0.161557 + 0.986863i \(0.448348\pi\)
−0.935427 + 0.353519i \(0.884985\pi\)
\(548\) 2574.98 1486.66i 0.200725 0.115889i
\(549\) 0 0
\(550\) 4107.78 7114.88i 0.318466 0.551599i
\(551\) 2137.86 0.165292
\(552\) 0 0
\(553\) 9516.25 + 1891.29i 0.731776 + 0.145435i
\(554\) −24623.1 + 14216.1i −1.88833 + 1.09023i
\(555\) 0 0
\(556\) −428.226 + 247.236i −0.0326633 + 0.0188582i
\(557\) −1286.96 743.026i −0.0978998 0.0565225i 0.450251 0.892902i \(-0.351335\pi\)
−0.548151 + 0.836380i \(0.684668\pi\)
\(558\) 0 0
\(559\) 18398.7i 1.39210i
\(560\) −17633.7 + 20113.9i −1.33064 + 1.51780i
\(561\) 0 0
\(562\) 1174.06 2033.54i 0.0881226 0.152633i
\(563\) −3428.18 −0.256626 −0.128313 0.991734i \(-0.540956\pi\)
−0.128313 + 0.991734i \(0.540956\pi\)
\(564\) 0 0
\(565\) 23209.0i 1.72816i
\(566\) −8542.94 −0.634428
\(567\) 0 0
\(568\) −15673.9 −1.15786
\(569\) 15518.2i 1.14333i 0.820486 + 0.571667i \(0.193703\pi\)
−0.820486 + 0.571667i \(0.806297\pi\)
\(570\) 0 0
\(571\) −3775.08 −0.276676 −0.138338 0.990385i \(-0.544176\pi\)
−0.138338 + 0.990385i \(0.544176\pi\)
\(572\) −1256.97 + 2177.14i −0.0918821 + 0.159145i
\(573\) 0 0
\(574\) 15707.7 5334.91i 1.14221 0.387935i
\(575\) 32407.1i 2.35038i
\(576\) 0 0
\(577\) 8116.59 + 4686.12i 0.585612 + 0.338103i 0.763361 0.645973i \(-0.223548\pi\)
−0.177748 + 0.984076i \(0.556881\pi\)
\(578\) −14324.5 + 8270.26i −1.03083 + 0.595152i
\(579\) 0 0
\(580\) −9527.64 + 5500.78i −0.682092 + 0.393806i
\(581\) 10022.0 11431.7i 0.715634 0.816293i
\(582\) 0 0
\(583\) −1955.94 −0.138948
\(584\) −2246.17 + 3890.49i −0.159156 + 0.275667i
\(585\) 0 0
\(586\) −18744.2 + 10822.0i −1.32136 + 0.762888i
\(587\) 4412.41 7642.52i 0.310255 0.537377i −0.668162 0.744015i \(-0.732919\pi\)
0.978417 + 0.206638i \(0.0662522\pi\)
\(588\) 0 0
\(589\) 634.971 + 1099.80i 0.0444202 + 0.0769381i
\(590\) 31180.6 + 18002.1i 2.17574 + 1.25616i
\(591\) 0 0
\(592\) −14815.1 25660.5i −1.02854 1.78149i
\(593\) −7130.68 12350.7i −0.493797 0.855282i 0.506177 0.862430i \(-0.331058\pi\)
−0.999974 + 0.00714731i \(0.997725\pi\)
\(594\) 0 0
\(595\) 1277.38 + 3761.03i 0.0880127 + 0.259138i
\(596\) −1425.59 823.062i −0.0979769 0.0565670i
\(597\) 0 0
\(598\) 29676.0i 2.02933i
\(599\) 6963.46i 0.474991i −0.971389 0.237495i \(-0.923674\pi\)
0.971389 0.237495i \(-0.0763265\pi\)
\(600\) 0 0
\(601\) −17885.4 10326.1i −1.21391 0.700850i −0.250300 0.968168i \(-0.580529\pi\)
−0.963608 + 0.267318i \(0.913863\pi\)
\(602\) 16729.9 + 14666.9i 1.13266 + 0.992988i
\(603\) 0 0
\(604\) −657.472 1138.77i −0.0442916 0.0767154i
\(605\) −10759.1 18635.3i −0.723008 1.25229i
\(606\) 0 0
\(607\) −9603.08 5544.34i −0.642137 0.370738i 0.143300 0.989679i \(-0.454229\pi\)
−0.785437 + 0.618941i \(0.787562\pi\)
\(608\) 1174.67 + 2034.59i 0.0783539 + 0.135713i
\(609\) 0 0
\(610\) −15532.0 + 26902.2i −1.03094 + 1.78564i
\(611\) 3294.63 1902.15i 0.218145 0.125946i
\(612\) 0 0
\(613\) 2166.52 3752.52i 0.142748 0.247248i −0.785782 0.618503i \(-0.787739\pi\)
0.928531 + 0.371256i \(0.121073\pi\)
\(614\) −24250.4 −1.59392
\(615\) 0 0
\(616\) −970.400 2857.18i −0.0634717 0.186882i
\(617\) −17477.3 + 10090.5i −1.14037 + 0.658393i −0.946522 0.322639i \(-0.895430\pi\)
−0.193848 + 0.981032i \(0.562097\pi\)
\(618\) 0 0
\(619\) 1788.20 1032.42i 0.116113 0.0670378i −0.440819 0.897596i \(-0.645312\pi\)
0.556932 + 0.830558i \(0.311979\pi\)
\(620\) −5659.65 3267.60i −0.366608 0.211661i
\(621\) 0 0
\(622\) 7424.39i 0.478603i
\(623\) −2159.16 6357.27i −0.138852 0.408826i
\(624\) 0 0
\(625\) 181.780 314.852i 0.0116339 0.0201505i
\(626\) −18795.4 −1.20003
\(627\) 0 0
\(628\) 5804.06i 0.368801i
\(629\) −4399.85 −0.278909
\(630\) 0 0
\(631\) 21996.0 1.38771 0.693856 0.720114i \(-0.255911\pi\)
0.693856 + 0.720114i \(0.255911\pi\)
\(632\) 7236.56i 0.455466i
\(633\) 0 0
\(634\) 5287.36 0.331211
\(635\) 7377.64 12778.4i 0.461059 0.798578i
\(636\) 0 0
\(637\) 18052.3 2382.61i 1.12285 0.148198i
\(638\) 6205.31i 0.385063i
\(639\) 0 0
\(640\) 24215.0 + 13980.5i 1.49560 + 0.863483i
\(641\) 15031.3 8678.33i 0.926211 0.534748i 0.0405997 0.999175i \(-0.487073\pi\)
0.885611 + 0.464427i \(0.153740\pi\)
\(642\) 0 0
\(643\) −6891.57 + 3978.85i −0.422670 + 0.244029i −0.696219 0.717829i \(-0.745136\pi\)
0.273549 + 0.961858i \(0.411802\pi\)
\(644\) −9017.04 7905.14i −0.551741 0.483705i
\(645\) 0 0
\(646\) 579.994 0.0353244
\(647\) −1066.63 + 1847.45i −0.0648120 + 0.112258i −0.896611 0.442820i \(-0.853978\pi\)
0.831799 + 0.555078i \(0.187311\pi\)
\(648\) 0 0
\(649\) −5876.87 + 3393.01i −0.355451 + 0.205220i
\(650\) 18488.4 32022.9i 1.11565 1.93237i
\(651\) 0 0
\(652\) 267.955 + 464.112i 0.0160950 + 0.0278773i
\(653\) 8113.61 + 4684.40i 0.486233 + 0.280727i 0.723010 0.690837i \(-0.242758\pi\)
−0.236777 + 0.971564i \(0.576091\pi\)
\(654\) 0 0
\(655\) 8262.67 + 14311.4i 0.492899 + 0.853727i
\(656\) −10336.5 17903.3i −0.615199 1.06556i
\(657\) 0 0
\(658\) 896.757 4512.14i 0.0531295 0.267328i
\(659\) 25364.6 + 14644.3i 1.49934 + 0.865645i 1.00000 0.000759530i \(-0.000241766\pi\)
0.499342 + 0.866405i \(0.333575\pi\)
\(660\) 0 0
\(661\) 21972.3i 1.29293i 0.762945 + 0.646464i \(0.223753\pi\)
−0.762945 + 0.646464i \(0.776247\pi\)
\(662\) 618.553i 0.0363153i
\(663\) 0 0
\(664\) −9819.91 5669.53i −0.573926 0.331356i
\(665\) −918.062 + 4619.34i −0.0535352 + 0.269369i
\(666\) 0 0
\(667\) 12238.7 + 21198.1i 0.710472 + 1.23057i
\(668\) 5051.40 + 8749.27i 0.292581 + 0.506766i
\(669\) 0 0
\(670\) 37982.9 + 21929.4i 2.19016 + 1.26449i
\(671\) −2927.45 5070.49i −0.168425 0.291720i
\(672\) 0 0
\(673\) 16676.4 28884.4i 0.955168 1.65440i 0.221184 0.975232i \(-0.429008\pi\)
0.733984 0.679167i \(-0.237659\pi\)
\(674\) 9425.86 5442.03i 0.538681 0.311007i
\(675\) 0 0
\(676\) −1247.07 + 2159.98i −0.0709528 + 0.122894i
\(677\) 16326.4 0.926843 0.463422 0.886138i \(-0.346622\pi\)
0.463422 + 0.886138i \(0.346622\pi\)
\(678\) 0 0
\(679\) −4399.15 3856.68i −0.248636 0.217976i
\(680\) 2565.65 1481.28i 0.144689 0.0835361i
\(681\) 0 0
\(682\) 3192.26 1843.05i 0.179234 0.103481i
\(683\) −8855.85 5112.93i −0.496134 0.286443i 0.230982 0.972958i \(-0.425806\pi\)
−0.727116 + 0.686515i \(0.759140\pi\)
\(684\) 0 0
\(685\) 13370.4i 0.745776i
\(686\) 12224.2 18314.2i 0.680356 1.01930i
\(687\) 0 0
\(688\) 13863.0 24011.5i 0.768202 1.33057i
\(689\) −8803.36 −0.486765
\(690\) 0 0
\(691\) 14449.2i 0.795473i −0.917500 0.397737i \(-0.869796\pi\)
0.917500 0.397737i \(-0.130204\pi\)
\(692\) −14804.8 −0.813289
\(693\) 0 0
\(694\) −12486.7 −0.682980
\(695\) 2223.53i 0.121357i
\(696\) 0 0
\(697\) −3069.76 −0.166823
\(698\) 9319.51 16141.9i 0.505370 0.875327i
\(699\) 0 0
\(700\) −4805.18 14148.0i −0.259455 0.763921i
\(701\) 9044.78i 0.487328i 0.969860 + 0.243664i \(0.0783494\pi\)
−0.969860 + 0.243664i \(0.921651\pi\)
\(702\) 0 0
\(703\) −4518.01 2608.48i −0.242390 0.139944i
\(704\) −631.848 + 364.797i −0.0338262 + 0.0195296i
\(705\) 0 0
\(706\) −12144.7 + 7011.75i −0.647411 + 0.373783i
\(707\) 4481.07 + 13193.7i 0.238370 + 0.701841i
\(708\) 0 0
\(709\) −15902.0 −0.842330 −0.421165 0.906984i \(-0.638379\pi\)
−0.421165 + 0.906984i \(0.638379\pi\)
\(710\) 35504.2 61495.1i 1.87669 3.25052i
\(711\) 0 0
\(712\) −4336.72 + 2503.81i −0.228266 + 0.131790i
\(713\) −7270.09 + 12592.2i −0.381861 + 0.661403i
\(714\) 0 0
\(715\) 5652.32 + 9790.10i 0.295643 + 0.512069i
\(716\) 6204.37 + 3582.09i 0.323838 + 0.186968i
\(717\) 0 0
\(718\) −508.742 881.166i −0.0264430 0.0458006i
\(719\) −5718.63 9904.97i −0.296619 0.513759i 0.678741 0.734378i \(-0.262526\pi\)
−0.975360 + 0.220618i \(0.929192\pi\)
\(720\) 0 0
\(721\) −24461.4 21445.0i −1.26351 1.10770i
\(722\) −19994.2 11543.6i −1.03062 0.595028i
\(723\) 0 0
\(724\) 4690.03i 0.240751i
\(725\) 30499.4i 1.56237i
\(726\) 0 0
\(727\) −18614.6 10747.1i −0.949623 0.548265i −0.0566590 0.998394i \(-0.518045\pi\)
−0.892964 + 0.450129i \(0.851378\pi\)
\(728\) −4367.61 12859.7i −0.222355 0.654686i
\(729\) 0 0
\(730\) −10176.0 17625.3i −0.515930 0.893617i
\(731\) −2058.55 3565.52i −0.104156 0.180404i
\(732\) 0 0
\(733\) 1111.43 + 641.684i 0.0560048 + 0.0323344i 0.527741 0.849405i \(-0.323039\pi\)
−0.471736 + 0.881740i \(0.656373\pi\)
\(734\) −12945.8 22422.8i −0.651005 1.12757i
\(735\) 0 0
\(736\) −13449.4 + 23295.0i −0.673574 + 1.16666i
\(737\) −7158.95 + 4133.22i −0.357806 + 0.206580i
\(738\) 0 0
\(739\) −1436.13 + 2487.45i −0.0714870 + 0.123819i −0.899553 0.436811i \(-0.856108\pi\)
0.828066 + 0.560630i \(0.189441\pi\)
\(740\) 26846.7 1.33366
\(741\) 0 0
\(742\) −7017.79 + 8004.88i −0.347212 + 0.396049i
\(743\) 8010.40 4624.80i 0.395522 0.228355i −0.289028 0.957321i \(-0.593332\pi\)
0.684550 + 0.728966i \(0.259999\pi\)
\(744\) 0 0
\(745\) −6410.54 + 3701.13i −0.315254 + 0.182012i
\(746\) 39140.3 + 22597.7i 1.92095 + 1.10906i
\(747\) 0 0
\(748\) 562.548i 0.0274984i
\(749\) 23549.7 7998.33i 1.14885 0.390191i
\(750\) 0 0
\(751\) −12652.0 + 21913.9i −0.614750 + 1.06478i 0.375678 + 0.926750i \(0.377410\pi\)
−0.990428 + 0.138028i \(0.955923\pi\)
\(752\) −5732.93 −0.278003
\(753\) 0 0
\(754\) 27929.0i 1.34896i
\(755\) −5913.01 −0.285028
\(756\) 0 0
\(757\) 16874.0 0.810166 0.405083 0.914280i \(-0.367243\pi\)
0.405083 + 0.914280i \(0.367243\pi\)
\(758\) 29616.9i 1.41918i
\(759\) 0 0
\(760\) 3512.74 0.167659
\(761\) −18604.3 + 32223.6i −0.886210 + 1.53496i −0.0418900 + 0.999122i \(0.513338\pi\)
−0.844320 + 0.535839i \(0.819995\pi\)
\(762\) 0 0
\(763\) 986.803 1125.60i 0.0468213 0.0534070i
\(764\) 4233.18i 0.200460i
\(765\) 0 0
\(766\) 26523.4 + 15313.3i 1.25108 + 0.722312i
\(767\) −26450.8 + 15271.4i −1.24522 + 0.718928i
\(768\) 0 0
\(769\) 10136.5 5852.32i 0.475335 0.274435i −0.243136 0.969992i \(-0.578176\pi\)
0.718470 + 0.695558i \(0.244843\pi\)
\(770\) 13408.0 + 2664.75i 0.627520 + 0.124715i
\(771\) 0 0
\(772\) −4921.21 −0.229428
\(773\) −8887.85 + 15394.2i −0.413549 + 0.716288i −0.995275 0.0970966i \(-0.969044\pi\)
0.581726 + 0.813385i \(0.302378\pi\)
\(774\) 0 0
\(775\) −15690.1 + 9058.68i −0.727232 + 0.419868i
\(776\) −2181.75 + 3778.91i −0.100928 + 0.174813i
\(777\) 0 0
\(778\) −10884.4 18852.4i −0.501575 0.868753i
\(779\) −3152.21 1819.93i −0.144980 0.0837043i
\(780\) 0 0
\(781\) 6691.78 + 11590.5i 0.306595 + 0.531038i
\(782\) 3320.32 + 5750.96i 0.151834 + 0.262984i
\(783\) 0 0
\(784\) −25354.6 10492.5i −1.15500 0.477977i
\(785\) −22602.9 13049.8i −1.02768 0.593334i
\(786\) 0 0
\(787\) 33310.5i 1.50876i −0.656441 0.754378i \(-0.727939\pi\)
0.656441 0.754378i \(-0.272061\pi\)
\(788\) 3209.98i 0.145115i
\(789\) 0 0
\(790\) 28391.9 + 16392.1i 1.27866 + 0.738233i
\(791\) −22543.6 + 7656.62i −1.01335 + 0.344170i
\(792\) 0 0
\(793\) −13176.0 22821.4i −0.590027 1.02196i
\(794\) 20149.8 + 34900.4i 0.900615 + 1.55991i
\(795\) 0 0
\(796\) 9133.86 + 5273.44i 0.406710 + 0.234814i
\(797\) 10344.8 + 17917.7i 0.459763 + 0.796334i 0.998948 0.0458540i \(-0.0146009\pi\)
−0.539185 + 0.842187i \(0.681268\pi\)
\(798\) 0 0
\(799\) −425.648 + 737.243i −0.0188465 + 0.0326430i
\(800\) −29026.0 + 16758.2i −1.28278 + 0.740614i
\(801\) 0 0
\(802\) 20010.6 34659.4i 0.881046 1.52602i
\(803\) 3835.90 0.168575
\(804\) 0 0
\(805\) −51059.0 + 17341.5i −2.23552 + 0.759262i
\(806\) 14367.8 8295.26i 0.627896 0.362516i
\(807\) 0 0
\(808\) 9000.34 5196.35i 0.391870 0.226246i
\(809\) 17821.9 + 10289.5i 0.774517 + 0.447168i 0.834484 0.551033i \(-0.185766\pi\)
−0.0599663 + 0.998200i \(0.519099\pi\)
\(810\) 0 0
\(811\) 19388.9i 0.839502i −0.907639 0.419751i \(-0.862117\pi\)
0.907639 0.419751i \(-0.137883\pi\)
\(812\) −8486.24 7439.79i −0.366759 0.321534i
\(813\) 0 0
\(814\) −7571.30 + 13113.9i −0.326012 + 0.564669i
\(815\) 2409.87 0.103575
\(816\) 0 0
\(817\) 4881.69i 0.209044i
\(818\) −37918.3 −1.62076
\(819\) 0 0
\(820\) 18730.9 0.797697
\(821\) 18742.9i 0.796751i 0.917222 + 0.398376i \(0.130426\pi\)
−0.917222 + 0.398376i \(0.869574\pi\)
\(822\) 0 0
\(823\) −42.5746 −0.00180323 −0.000901614 1.00000i \(-0.500287\pi\)
−0.000901614 1.00000i \(0.500287\pi\)
\(824\) −12131.6 + 21012.5i −0.512893 + 0.888357i
\(825\) 0 0
\(826\) −7199.59 + 36225.6i −0.303276 + 1.52597i
\(827\) 9687.74i 0.407347i −0.979039 0.203673i \(-0.934712\pi\)
0.979039 0.203673i \(-0.0652880\pi\)
\(828\) 0 0
\(829\) −19027.2 10985.4i −0.797157 0.460239i 0.0453189 0.998973i \(-0.485570\pi\)
−0.842476 + 0.538734i \(0.818903\pi\)
\(830\) 44487.7 25685.0i 1.86047 1.07414i
\(831\) 0 0
\(832\) −2843.84 + 1641.89i −0.118500 + 0.0684163i
\(833\) −3231.80 + 2481.52i −0.134424 + 0.103217i
\(834\) 0 0
\(835\) 45430.0 1.88284
\(836\) 333.510 577.656i 0.0137975 0.0238979i
\(837\) 0 0
\(838\) −1417.58 + 818.439i −0.0584361 + 0.0337381i
\(839\) 24130.1 41794.6i 0.992926 1.71980i 0.393635 0.919267i \(-0.371217\pi\)
0.599291 0.800531i \(-0.295449\pi\)
\(840\) 0 0
\(841\) −676.240 1171.28i −0.0277272 0.0480250i
\(842\) −48830.7 28192.4i −1.99859 1.15389i
\(843\) 0 0
\(844\) 4034.74 + 6988.38i 0.164552 + 0.285012i
\(845\) 5607.78 + 9712.96i 0.228300 + 0.395427i
\(846\) 0 0
\(847\) 14551.6 16598.4i 0.590319 0.673351i
\(848\) 11488.9 + 6633.15i 0.465250 + 0.268612i
\(849\) 0 0
\(850\) 8274.36i 0.333892i
\(851\) 59731.4i 2.40607i
\(852\) 0 0
\(853\) −5301.14 3060.61i −0.212787 0.122853i 0.389819 0.920892i \(-0.372538\pi\)
−0.602606 + 0.798039i \(0.705871\pi\)
\(854\) −31255.0 6211.71i −1.25237 0.248900i
\(855\) 0 0
\(856\) −9275.05 16064.9i −0.370344 0.641455i
\(857\) 1830.74 + 3170.93i 0.0729718 + 0.126391i 0.900202 0.435472i \(-0.143418\pi\)
−0.827231 + 0.561862i \(0.810085\pi\)
\(858\) 0 0
\(859\) 15149.0 + 8746.28i 0.601719 + 0.347403i 0.769718 0.638384i \(-0.220397\pi\)
−0.167998 + 0.985787i \(0.553730\pi\)
\(860\) 12560.7 + 21755.9i 0.498044 + 0.862638i
\(861\) 0 0
\(862\) −14270.7 + 24717.6i −0.563878 + 0.976665i
\(863\) 15522.1 8961.66i 0.612256 0.353486i −0.161592 0.986858i \(-0.551663\pi\)
0.773848 + 0.633371i \(0.218329\pi\)
\(864\) 0 0
\(865\) −33287.1 + 57654.9i −1.30843 + 2.26627i
\(866\) −30021.7 −1.17804
\(867\) 0 0
\(868\) 1306.81 6575.37i 0.0511014 0.257123i
\(869\) −5351.26 + 3089.55i −0.208894 + 0.120605i
\(870\) 0 0
\(871\) −32221.2 + 18602.9i −1.25347 + 0.723692i
\(872\) −966.902 558.241i −0.0375498 0.0216794i
\(873\) 0 0
\(874\) 7873.87i 0.304734i
\(875\) −24907.0 4950.10i −0.962299 0.191250i
\(876\) 0 0
\(877\) −2140.57 + 3707.58i −0.0824196 + 0.142755i −0.904289 0.426921i \(-0.859598\pi\)
0.821869 + 0.569676i \(0.192931\pi\)
\(878\) 42727.4 1.64234
\(879\) 0 0
\(880\) 17035.6i 0.652580i
\(881\) −19495.6 −0.745542 −0.372771 0.927923i \(-0.621592\pi\)
−0.372771 + 0.927923i \(0.621592\pi\)
\(882\) 0 0
\(883\) −6455.82 −0.246043 −0.123021 0.992404i \(-0.539258\pi\)
−0.123021 + 0.992404i \(0.539258\pi\)
\(884\) 2531.93i 0.0963327i
\(885\) 0 0
\(886\) −15553.3 −0.589756
\(887\) −5910.02 + 10236.5i −0.223719 + 0.387493i −0.955934 0.293580i \(-0.905153\pi\)
0.732215 + 0.681073i \(0.238487\pi\)
\(888\) 0 0
\(889\) 14846.0 + 2950.54i 0.560088 + 0.111314i
\(890\) 22686.3i 0.854433i
\(891\) 0 0
\(892\) −15646.9 9033.75i −0.587329 0.339094i
\(893\) −874.157 + 504.695i −0.0327576 + 0.0189126i
\(894\) 0 0
\(895\) 27899.7 16107.9i 1.04199 0.601594i
\(896\) −5591.22 + 28132.9i −0.208471 + 1.04895i
\(897\) 0 0
\(898\) 50019.5 1.85877
\(899\) −6842.12 + 11850.9i −0.253835 + 0.439655i
\(900\) 0 0
\(901\) 1706.02 984.970i 0.0630807 0.0364197i
\(902\) −5282.48 + 9149.52i −0.194997 + 0.337745i
\(903\) 0 0
\(904\) 8878.80 + 15378.5i 0.326664 + 0.565799i
\(905\) 18264.5 + 10545.0i 0.670865 + 0.387324i
\(906\) 0 0
\(907\) 21758.7 + 37687.1i 0.796565 + 1.37969i 0.921841 + 0.387569i \(0.126685\pi\)
−0.125275 + 0.992122i \(0.539981\pi\)
\(908\) −6574.26 11387.0i −0.240280 0.416178i
\(909\) 0 0
\(910\) 60347.1 + 11993.6i 2.19834 + 0.436904i
\(911\) −40124.4 23165.8i −1.45926 0.842501i −0.460280 0.887774i \(-0.652251\pi\)
−0.998975 + 0.0452723i \(0.985584\pi\)
\(912\) 0 0
\(913\) 9682.13i 0.350966i
\(914\) 41591.3i 1.50516i
\(915\) 0 0
\(916\) 4637.24 + 2677.31i 0.167269 + 0.0965731i
\(917\) −11175.2 + 12747.1i −0.402441 + 0.459047i
\(918\) 0 0
\(919\) 13311.5 + 23056.1i 0.477807 + 0.827586i 0.999676 0.0254393i \(-0.00809846\pi\)
−0.521869 + 0.853025i \(0.674765\pi\)
\(920\) 20109.6 + 34830.8i 0.720644 + 1.24819i
\(921\) 0 0
\(922\) −48889.8 28226.5i −1.74631 1.00823i
\(923\) 30118.6 + 52166.9i 1.07407 + 1.86034i
\(924\) 0 0
\(925\) 37213.3 64455.3i 1.32277 2.29111i
\(926\) −7546.40 + 4356.92i −0.267808 + 0.154619i
\(927\) 0 0
\(928\) −12657.6 + 21923.7i −0.447745 + 0.775517i
\(929\) 44617.3 1.57572 0.787862 0.615852i \(-0.211188\pi\)
0.787862 + 0.615852i \(0.211188\pi\)
\(930\) 0 0
\(931\) −4789.78 + 632.173i −0.168613 + 0.0222542i
\(932\) 2722.21 1571.67i 0.0956749 0.0552379i
\(933\) 0 0
\(934\) −23185.3 + 13386.0i −0.812255 + 0.468956i
\(935\) −2190.74 1264.83i −0.0766257 0.0442399i
\(936\) 0 0
\(937\) 37694.9i 1.31423i 0.753789 + 0.657117i \(0.228224\pi\)
−0.753789 + 0.657117i \(0.771776\pi\)
\(938\) −8770.22 + 44128.4i −0.305286 + 1.53608i
\(939\) 0 0
\(940\) 2597.19 4498.47i 0.0901181 0.156089i
\(941\) −26365.3 −0.913373 −0.456686 0.889628i \(-0.650964\pi\)
−0.456686 + 0.889628i \(0.650964\pi\)
\(942\) 0 0
\(943\) 41674.5i 1.43914i
\(944\) 46026.7 1.58691
\(945\) 0 0
\(946\) −14169.5 −0.486987
\(947\) 387.274i 0.0132890i 0.999978 + 0.00664452i \(0.00211503\pi\)
−0.999978 + 0.00664452i \(0.997885\pi\)
\(948\) 0 0
\(949\) 17264.7 0.590555
\(950\) −4905.50 + 8496.58i −0.167532 + 0.290174i
\(951\) 0 0
\(952\) 2285.22 + 2003.43i 0.0777987 + 0.0682053i
\(953\) 33969.5i 1.15465i −0.816514 0.577325i \(-0.804097\pi\)
0.816514 0.577325i \(-0.195903\pi\)
\(954\) 0 0
\(955\) 16485.4 + 9517.85i 0.558591 + 0.322503i
\(956\) −18118.8 + 10460.9i −0.612974 + 0.353901i
\(957\) 0 0
\(958\) −254.729 + 147.068i −0.00859072 + 0.00495985i
\(959\) 12987.1 4410.88i 0.437304 0.148524i
\(960\) 0 0
\(961\) 21662.2 0.727140
\(962\) −34077.1 + 59023.3i −1.14209 + 1.97816i
\(963\) 0 0
\(964\) 9349.47 5397.92i 0.312371 0.180348i
\(965\) −11064.8 + 19164.8i −0.369107 + 0.639312i
\(966\) 0 0
\(967\) 9966.96 + 17263.3i 0.331454 + 0.574095i 0.982797 0.184688i \(-0.0591276\pi\)
−0.651343 + 0.758783i \(0.725794\pi\)
\(968\) −14258.2 8231.97i −0.473425 0.273332i
\(969\) 0 0
\(970\) −9884.12 17119.8i −0.327175 0.566684i
\(971\) −6280.64 10878.4i −0.207575 0.359530i 0.743375 0.668875i \(-0.233224\pi\)
−0.950950 + 0.309344i \(0.899890\pi\)
\(972\) 0 0
\(973\) −2159.79 + 733.541i −0.0711609 + 0.0241688i
\(974\) 15926.0 + 9194.90i 0.523925 + 0.302488i
\(975\) 0 0
\(976\) 39711.2i 1.30238i
\(977\) 22456.1i 0.735348i −0.929955 0.367674i \(-0.880154\pi\)
0.929955 0.367674i \(-0.119846\pi\)
\(978\) 0 0
\(979\) 3703.01 + 2137.94i 0.120888 + 0.0697944i
\(980\) 19719.6 15141.6i 0.642775 0.493552i
\(981\) 0 0
\(982\) −1505.66 2607.88i −0.0489283 0.0847464i
\(983\) −24435.3 42323.2i −0.792844 1.37325i −0.924199 0.381911i \(-0.875266\pi\)
0.131355 0.991335i \(-0.458067\pi\)
\(984\) 0 0
\(985\) 12500.7 + 7217.27i 0.404370 + 0.233463i
\(986\) 3124.86 + 5412.41i 0.100929 + 0.174814i
\(987\) 0 0
\(988\) 1501.07 2599.93i 0.0483355 0.0837195i
\(989\) 48404.7 27946.5i 1.55630 0.898530i
\(990\) 0 0
\(991\) 20255.7 35083.8i 0.649286 1.12460i −0.334008 0.942570i \(-0.608401\pi\)
0.983294 0.182026i \(-0.0582654\pi\)
\(992\) −15037.9 −0.481304
\(993\) 0 0
\(994\) 71444.9 + 14199.2i 2.27977 + 0.453089i
\(995\) 41072.9 23713.5i 1.30864 0.755545i
\(996\) 0 0
\(997\) −52677.3 + 30413.3i −1.67333 + 0.966096i −0.707573 + 0.706640i \(0.750210\pi\)
−0.965755 + 0.259456i \(0.916457\pi\)
\(998\) 5398.13 + 3116.61i 0.171217 + 0.0988522i
\(999\) 0 0
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 189.4.i.a.143.17 44
3.2 odd 2 63.4.i.a.38.6 yes 44
7.5 odd 6 189.4.s.a.89.17 44
9.4 even 3 63.4.s.a.59.6 yes 44
9.5 odd 6 189.4.s.a.17.17 44
21.5 even 6 63.4.s.a.47.6 yes 44
63.5 even 6 inner 189.4.i.a.152.6 44
63.40 odd 6 63.4.i.a.5.17 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.i.a.5.17 44 63.40 odd 6
63.4.i.a.38.6 yes 44 3.2 odd 2
63.4.s.a.47.6 yes 44 21.5 even 6
63.4.s.a.59.6 yes 44 9.4 even 3
189.4.i.a.143.17 44 1.1 even 1 trivial
189.4.i.a.152.6 44 63.5 even 6 inner
189.4.s.a.17.17 44 9.5 odd 6
189.4.s.a.89.17 44 7.5 odd 6