Properties

Label 135.4.e.c.91.1
Level $135$
Weight $4$
Character 135.91
Analytic conductor $7.965$
Analytic rank $0$
Dimension $14$
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] = [135,4,Mod(46,135)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(135, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("135.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 135.e (of order \(3\), 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: \(7.96525785077\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + 209529 x^{6} - 55412 x^{5} + 765088 x^{4} + 276096 x^{3} + 1572480 x^{2} + \cdots + 82944 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{13} \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 91.1
Root \(2.65775 - 4.60336i\) of defining polynomial
Character \(\chi\) \(=\) 135.91
Dual form 135.4.e.c.46.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.65775 - 4.60336i) q^{2} +(-10.1273 + 17.5410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(6.71686 + 11.6339i) q^{7} +65.1396 q^{8} +O(q^{10})\) \(q+(-2.65775 - 4.60336i) q^{2} +(-10.1273 + 17.5410i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(6.71686 + 11.6339i) q^{7} +65.1396 q^{8} +26.5775 q^{10} +(-23.4628 - 40.6388i) q^{11} +(18.0673 - 31.2935i) q^{13} +(35.7035 - 61.8403i) q^{14} +(-92.1064 - 159.533i) q^{16} +54.6071 q^{17} +111.339 q^{19} +(-50.6366 - 87.7051i) q^{20} +(-124.717 + 216.016i) q^{22} +(-17.9870 + 31.1544i) q^{23} +(-12.5000 - 21.6506i) q^{25} -192.074 q^{26} -272.095 q^{28} +(29.0588 + 50.3312i) q^{29} +(147.833 - 256.055i) q^{31} +(-229.034 + 396.699i) q^{32} +(-145.132 - 251.377i) q^{34} -67.1686 q^{35} -53.0417 q^{37} +(-295.911 - 512.533i) q^{38} +(-162.849 + 282.063i) q^{40} +(64.1795 - 111.162i) q^{41} +(82.0858 + 142.177i) q^{43} +950.461 q^{44} +191.220 q^{46} +(43.9159 + 76.0646i) q^{47} +(81.2675 - 140.759i) q^{49} +(-66.4439 + 115.084i) q^{50} +(365.947 + 633.839i) q^{52} +479.247 q^{53} +234.628 q^{55} +(437.533 + 757.830i) q^{56} +(154.462 - 267.536i) q^{58} +(317.807 - 550.458i) q^{59} +(-24.0128 - 41.5915i) q^{61} -1571.62 q^{62} +961.163 q^{64} +(90.3367 + 156.468i) q^{65} +(14.4592 - 25.0440i) q^{67} +(-553.024 + 957.865i) q^{68} +(178.518 + 309.202i) q^{70} -576.183 q^{71} +835.057 q^{73} +(140.972 + 244.170i) q^{74} +(-1127.56 + 1952.99i) q^{76} +(315.193 - 545.930i) q^{77} +(101.869 + 176.442i) q^{79} +921.064 q^{80} -682.294 q^{82} +(232.239 + 402.249i) q^{83} +(-136.518 + 236.456i) q^{85} +(436.328 - 755.742i) q^{86} +(-1528.36 - 2647.19i) q^{88} -993.782 q^{89} +485.423 q^{91} +(-364.320 - 631.021i) q^{92} +(233.435 - 404.322i) q^{94} +(-278.347 + 482.111i) q^{95} +(-440.708 - 763.328i) q^{97} -863.956 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 2 q^{2} - 36 q^{4} - 35 q^{5} - 22 q^{7} + 36 q^{8} + 20 q^{10} - 23 q^{11} - 96 q^{13} + 21 q^{14} - 324 q^{16} + 322 q^{17} + 558 q^{19} - 180 q^{20} - 311 q^{22} - 96 q^{23} - 175 q^{25} - 716 q^{26} + 674 q^{28} + 296 q^{29} - 244 q^{31} + 314 q^{32} - 125 q^{34} + 220 q^{35} + 808 q^{37} - 305 q^{38} - 90 q^{40} + 47 q^{41} - 525 q^{43} + 110 q^{44} + 1434 q^{46} - 164 q^{47} - 1225 q^{49} - 50 q^{50} - 1682 q^{52} + 1012 q^{53} + 230 q^{55} + 981 q^{56} - 1183 q^{58} + 85 q^{59} - 828 q^{61} - 1572 q^{62} + 4472 q^{64} - 480 q^{65} - 1093 q^{67} - 2473 q^{68} + 105 q^{70} + 656 q^{71} + 4170 q^{73} + 1316 q^{74} - 2789 q^{76} - 24 q^{77} - 2110 q^{79} + 3240 q^{80} - 124 q^{82} - 1290 q^{83} - 805 q^{85} + 2569 q^{86} - 2271 q^{88} - 6096 q^{89} + 6676 q^{91} - 2763 q^{92} + 517 q^{94} - 1395 q^{95} - 1787 q^{97} + 2558 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).

\(n\) \(56\) \(82\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65775 4.60336i −0.939658 1.62754i −0.766110 0.642710i \(-0.777810\pi\)
−0.173548 0.984825i \(-0.555523\pi\)
\(3\) 0 0
\(4\) −10.1273 + 17.5410i −1.26591 + 2.19263i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 6.71686 + 11.6339i 0.362676 + 0.628174i 0.988400 0.151871i \(-0.0485297\pi\)
−0.625724 + 0.780045i \(0.715196\pi\)
\(8\) 65.1396 2.87879
\(9\) 0 0
\(10\) 26.5775 0.840456
\(11\) −23.4628 40.6388i −0.643119 1.11391i −0.984733 0.174074i \(-0.944307\pi\)
0.341614 0.939840i \(-0.389026\pi\)
\(12\) 0 0
\(13\) 18.0673 31.2935i 0.385460 0.667636i −0.606373 0.795180i \(-0.707376\pi\)
0.991833 + 0.127544i \(0.0407095\pi\)
\(14\) 35.7035 61.8403i 0.681584 1.18054i
\(15\) 0 0
\(16\) −92.1064 159.533i −1.43916 2.49270i
\(17\) 54.6071 0.779069 0.389535 0.921012i \(-0.372636\pi\)
0.389535 + 0.921012i \(0.372636\pi\)
\(18\) 0 0
\(19\) 111.339 1.34436 0.672180 0.740388i \(-0.265358\pi\)
0.672180 + 0.740388i \(0.265358\pi\)
\(20\) −50.6366 87.7051i −0.566134 0.980573i
\(21\) 0 0
\(22\) −124.717 + 216.016i −1.20862 + 2.09340i
\(23\) −17.9870 + 31.1544i −0.163067 + 0.282441i −0.935967 0.352087i \(-0.885472\pi\)
0.772900 + 0.634528i \(0.218805\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −192.074 −1.44880
\(27\) 0 0
\(28\) −272.095 −1.83647
\(29\) 29.0588 + 50.3312i 0.186072 + 0.322285i 0.943937 0.330125i \(-0.107091\pi\)
−0.757866 + 0.652411i \(0.773758\pi\)
\(30\) 0 0
\(31\) 147.833 256.055i 0.856506 1.48351i −0.0187353 0.999824i \(-0.505964\pi\)
0.875241 0.483687i \(-0.160703\pi\)
\(32\) −229.034 + 396.699i −1.26525 + 2.19147i
\(33\) 0 0
\(34\) −145.132 251.377i −0.732059 1.26796i
\(35\) −67.1686 −0.324388
\(36\) 0 0
\(37\) −53.0417 −0.235676 −0.117838 0.993033i \(-0.537596\pi\)
−0.117838 + 0.993033i \(0.537596\pi\)
\(38\) −295.911 512.533i −1.26324 2.18799i
\(39\) 0 0
\(40\) −162.849 + 282.063i −0.643717 + 1.11495i
\(41\) 64.1795 111.162i 0.244467 0.423430i −0.717514 0.696544i \(-0.754720\pi\)
0.961982 + 0.273114i \(0.0880536\pi\)
\(42\) 0 0
\(43\) 82.0858 + 142.177i 0.291116 + 0.504227i 0.974074 0.226230i \(-0.0726402\pi\)
−0.682958 + 0.730457i \(0.739307\pi\)
\(44\) 950.461 3.25653
\(45\) 0 0
\(46\) 191.220 0.612910
\(47\) 43.9159 + 76.0646i 0.136294 + 0.236067i 0.926091 0.377301i \(-0.123148\pi\)
−0.789797 + 0.613368i \(0.789814\pi\)
\(48\) 0 0
\(49\) 81.2675 140.759i 0.236932 0.410378i
\(50\) −66.4439 + 115.084i −0.187932 + 0.325507i
\(51\) 0 0
\(52\) 365.947 + 633.839i 0.975918 + 1.69034i
\(53\) 479.247 1.24207 0.621035 0.783783i \(-0.286713\pi\)
0.621035 + 0.783783i \(0.286713\pi\)
\(54\) 0 0
\(55\) 234.628 0.575223
\(56\) 437.533 + 757.830i 1.04407 + 1.80838i
\(57\) 0 0
\(58\) 154.462 267.536i 0.349687 0.605676i
\(59\) 317.807 550.458i 0.701271 1.21464i −0.266750 0.963766i \(-0.585950\pi\)
0.968021 0.250871i \(-0.0807169\pi\)
\(60\) 0 0
\(61\) −24.0128 41.5915i −0.0504021 0.0872990i 0.839724 0.543014i \(-0.182717\pi\)
−0.890126 + 0.455715i \(0.849384\pi\)
\(62\) −1571.62 −3.21929
\(63\) 0 0
\(64\) 961.163 1.87727
\(65\) 90.3367 + 156.468i 0.172383 + 0.298576i
\(66\) 0 0
\(67\) 14.4592 25.0440i 0.0263652 0.0456658i −0.852542 0.522659i \(-0.824940\pi\)
0.878907 + 0.476993i \(0.158273\pi\)
\(68\) −553.024 + 957.865i −0.986235 + 1.70821i
\(69\) 0 0
\(70\) 178.518 + 309.202i 0.304813 + 0.527952i
\(71\) −576.183 −0.963103 −0.481552 0.876418i \(-0.659927\pi\)
−0.481552 + 0.876418i \(0.659927\pi\)
\(72\) 0 0
\(73\) 835.057 1.33885 0.669425 0.742880i \(-0.266541\pi\)
0.669425 + 0.742880i \(0.266541\pi\)
\(74\) 140.972 + 244.170i 0.221455 + 0.383571i
\(75\) 0 0
\(76\) −1127.56 + 1952.99i −1.70184 + 2.94768i
\(77\) 315.193 545.930i 0.466488 0.807981i
\(78\) 0 0
\(79\) 101.869 + 176.442i 0.145078 + 0.251282i 0.929402 0.369069i \(-0.120324\pi\)
−0.784324 + 0.620351i \(0.786990\pi\)
\(80\) 921.064 1.28723
\(81\) 0 0
\(82\) −682.294 −0.918863
\(83\) 232.239 + 402.249i 0.307127 + 0.531959i 0.977733 0.209855i \(-0.0672991\pi\)
−0.670606 + 0.741814i \(0.733966\pi\)
\(84\) 0 0
\(85\) −136.518 + 236.456i −0.174205 + 0.301732i
\(86\) 436.328 755.742i 0.547098 0.947602i
\(87\) 0 0
\(88\) −1528.36 2647.19i −1.85140 3.20672i
\(89\) −993.782 −1.18360 −0.591801 0.806084i \(-0.701583\pi\)
−0.591801 + 0.806084i \(0.701583\pi\)
\(90\) 0 0
\(91\) 485.423 0.559189
\(92\) −364.320 631.021i −0.412859 0.715092i
\(93\) 0 0
\(94\) 233.435 404.322i 0.256139 0.443645i
\(95\) −278.347 + 482.111i −0.300608 + 0.520668i
\(96\) 0 0
\(97\) −440.708 763.328i −0.461310 0.799012i 0.537717 0.843126i \(-0.319287\pi\)
−0.999027 + 0.0441134i \(0.985954\pi\)
\(98\) −863.956 −0.890538
\(99\) 0 0
\(100\) 506.366 0.506366
\(101\) 604.869 + 1047.66i 0.595909 + 1.03214i 0.993418 + 0.114546i \(0.0365412\pi\)
−0.397509 + 0.917598i \(0.630125\pi\)
\(102\) 0 0
\(103\) −372.421 + 645.053i −0.356270 + 0.617077i −0.987334 0.158653i \(-0.949285\pi\)
0.631065 + 0.775730i \(0.282618\pi\)
\(104\) 1176.90 2038.45i 1.10966 1.92198i
\(105\) 0 0
\(106\) −1273.72 2206.15i −1.16712 2.02151i
\(107\) 1000.14 0.903622 0.451811 0.892114i \(-0.350778\pi\)
0.451811 + 0.892114i \(0.350778\pi\)
\(108\) 0 0
\(109\) −915.517 −0.804502 −0.402251 0.915530i \(-0.631772\pi\)
−0.402251 + 0.915530i \(0.631772\pi\)
\(110\) −623.584 1080.08i −0.540513 0.936196i
\(111\) 0 0
\(112\) 1237.33 2143.12i 1.04390 1.80809i
\(113\) −662.451 + 1147.40i −0.551488 + 0.955206i 0.446679 + 0.894694i \(0.352606\pi\)
−0.998168 + 0.0605114i \(0.980727\pi\)
\(114\) 0 0
\(115\) −89.9350 155.772i −0.0729260 0.126311i
\(116\) −1177.15 −0.942202
\(117\) 0 0
\(118\) −3378.61 −2.63582
\(119\) 366.789 + 635.297i 0.282550 + 0.489391i
\(120\) 0 0
\(121\) −435.508 + 754.321i −0.327203 + 0.566733i
\(122\) −127.640 + 221.080i −0.0947215 + 0.164062i
\(123\) 0 0
\(124\) 2994.31 + 5186.30i 2.16853 + 3.75600i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −993.635 −0.694259 −0.347129 0.937817i \(-0.612843\pi\)
−0.347129 + 0.937817i \(0.612843\pi\)
\(128\) −722.262 1251.00i −0.498747 0.863855i
\(129\) 0 0
\(130\) 480.185 831.705i 0.323962 0.561118i
\(131\) 691.995 1198.57i 0.461526 0.799386i −0.537512 0.843256i \(-0.680636\pi\)
0.999037 + 0.0438704i \(0.0139689\pi\)
\(132\) 0 0
\(133\) 747.847 + 1295.31i 0.487568 + 0.844492i
\(134\) −153.715 −0.0990970
\(135\) 0 0
\(136\) 3557.09 2.24278
\(137\) 773.568 + 1339.86i 0.482411 + 0.835561i 0.999796 0.0201918i \(-0.00642770\pi\)
−0.517385 + 0.855753i \(0.673094\pi\)
\(138\) 0 0
\(139\) 269.752 467.225i 0.164605 0.285104i −0.771910 0.635732i \(-0.780698\pi\)
0.936515 + 0.350628i \(0.114032\pi\)
\(140\) 680.238 1178.21i 0.410647 0.711261i
\(141\) 0 0
\(142\) 1531.35 + 2652.38i 0.904988 + 1.56748i
\(143\) −1695.64 −0.991586
\(144\) 0 0
\(145\) −290.588 −0.166427
\(146\) −2219.38 3844.07i −1.25806 2.17902i
\(147\) 0 0
\(148\) 537.170 930.406i 0.298345 0.516749i
\(149\) −602.335 + 1043.27i −0.331176 + 0.573613i −0.982743 0.184978i \(-0.940779\pi\)
0.651567 + 0.758591i \(0.274112\pi\)
\(150\) 0 0
\(151\) −1486.46 2574.62i −0.801100 1.38755i −0.918893 0.394508i \(-0.870915\pi\)
0.117793 0.993038i \(-0.462418\pi\)
\(152\) 7252.55 3.87013
\(153\) 0 0
\(154\) −3350.82 −1.75336
\(155\) 739.167 + 1280.28i 0.383041 + 0.663446i
\(156\) 0 0
\(157\) 197.880 342.739i 0.100590 0.174226i −0.811338 0.584577i \(-0.801260\pi\)
0.911928 + 0.410351i \(0.134594\pi\)
\(158\) 541.484 937.877i 0.272646 0.472238i
\(159\) 0 0
\(160\) −1145.17 1983.49i −0.565836 0.980056i
\(161\) −483.265 −0.236563
\(162\) 0 0
\(163\) 3861.43 1.85553 0.927764 0.373169i \(-0.121729\pi\)
0.927764 + 0.373169i \(0.121729\pi\)
\(164\) 1299.93 + 2251.55i 0.618949 + 1.07205i
\(165\) 0 0
\(166\) 1234.47 2138.16i 0.577188 0.999719i
\(167\) 1017.49 1762.34i 0.471470 0.816609i −0.527998 0.849246i \(-0.677057\pi\)
0.999467 + 0.0326366i \(0.0103904\pi\)
\(168\) 0 0
\(169\) 445.643 + 771.876i 0.202842 + 0.351332i
\(170\) 1451.32 0.654773
\(171\) 0 0
\(172\) −3325.24 −1.47411
\(173\) 773.458 + 1339.67i 0.339913 + 0.588746i 0.984416 0.175855i \(-0.0562691\pi\)
−0.644503 + 0.764602i \(0.722936\pi\)
\(174\) 0 0
\(175\) 167.922 290.849i 0.0725353 0.125635i
\(176\) −4322.15 + 7486.19i −1.85111 + 3.20621i
\(177\) 0 0
\(178\) 2641.23 + 4574.74i 1.11218 + 1.92636i
\(179\) 823.973 0.344059 0.172030 0.985092i \(-0.444967\pi\)
0.172030 + 0.985092i \(0.444967\pi\)
\(180\) 0 0
\(181\) −4403.55 −1.80836 −0.904180 0.427152i \(-0.859517\pi\)
−0.904180 + 0.427152i \(0.859517\pi\)
\(182\) −1290.14 2234.58i −0.525446 0.910099i
\(183\) 0 0
\(184\) −1171.67 + 2029.38i −0.469437 + 0.813088i
\(185\) 132.604 229.677i 0.0526987 0.0912769i
\(186\) 0 0
\(187\) −1281.24 2219.17i −0.501034 0.867816i
\(188\) −1779.00 −0.690144
\(189\) 0 0
\(190\) 2959.11 1.12988
\(191\) −1523.46 2638.72i −0.577141 0.999637i −0.995805 0.0914964i \(-0.970835\pi\)
0.418664 0.908141i \(-0.362498\pi\)
\(192\) 0 0
\(193\) −945.452 + 1637.57i −0.352617 + 0.610751i −0.986707 0.162508i \(-0.948042\pi\)
0.634090 + 0.773259i \(0.281375\pi\)
\(194\) −2342.58 + 4057.48i −0.866947 + 1.50160i
\(195\) 0 0
\(196\) 1646.04 + 2851.03i 0.599870 + 1.03901i
\(197\) −3652.00 −1.32078 −0.660392 0.750921i \(-0.729610\pi\)
−0.660392 + 0.750921i \(0.729610\pi\)
\(198\) 0 0
\(199\) 3217.26 1.14606 0.573029 0.819535i \(-0.305768\pi\)
0.573029 + 0.819535i \(0.305768\pi\)
\(200\) −814.245 1410.31i −0.287879 0.498621i
\(201\) 0 0
\(202\) 3215.19 5568.87i 1.11990 1.93972i
\(203\) −390.367 + 676.136i −0.134968 + 0.233771i
\(204\) 0 0
\(205\) 320.898 + 555.811i 0.109329 + 0.189364i
\(206\) 3959.22 1.33909
\(207\) 0 0
\(208\) −6656.47 −2.21896
\(209\) −2612.32 4524.67i −0.864583 1.49750i
\(210\) 0 0
\(211\) −2473.90 + 4284.92i −0.807159 + 1.39804i 0.107666 + 0.994187i \(0.465662\pi\)
−0.914824 + 0.403853i \(0.867671\pi\)
\(212\) −4853.49 + 8406.48i −1.57235 + 2.72339i
\(213\) 0 0
\(214\) −2658.14 4604.03i −0.849096 1.47068i
\(215\) −820.858 −0.260382
\(216\) 0 0
\(217\) 3971.91 1.24254
\(218\) 2433.22 + 4214.46i 0.755956 + 1.30935i
\(219\) 0 0
\(220\) −2376.15 + 4115.62i −0.728183 + 1.26125i
\(221\) 986.606 1708.85i 0.300300 0.520135i
\(222\) 0 0
\(223\) −552.056 956.189i −0.165778 0.287135i 0.771154 0.636649i \(-0.219680\pi\)
−0.936931 + 0.349514i \(0.886347\pi\)
\(224\) −6153.56 −1.83550
\(225\) 0 0
\(226\) 7042.53 2.07284
\(227\) −1910.12 3308.43i −0.558498 0.967348i −0.997622 0.0689210i \(-0.978044\pi\)
0.439124 0.898427i \(-0.355289\pi\)
\(228\) 0 0
\(229\) −72.3848 + 125.374i −0.0208879 + 0.0361788i −0.876280 0.481801i \(-0.839983\pi\)
0.855393 + 0.517980i \(0.173316\pi\)
\(230\) −478.050 + 828.008i −0.137051 + 0.237379i
\(231\) 0 0
\(232\) 1892.87 + 3278.55i 0.535661 + 0.927792i
\(233\) −1286.31 −0.361670 −0.180835 0.983513i \(-0.557880\pi\)
−0.180835 + 0.983513i \(0.557880\pi\)
\(234\) 0 0
\(235\) −439.159 −0.121905
\(236\) 6437.07 + 11149.3i 1.77550 + 3.07525i
\(237\) 0 0
\(238\) 1949.67 3376.92i 0.531001 0.919721i
\(239\) 2109.73 3654.15i 0.570991 0.988986i −0.425473 0.904971i \(-0.639892\pi\)
0.996465 0.0840147i \(-0.0267743\pi\)
\(240\) 0 0
\(241\) −1141.57 1977.25i −0.305124 0.528490i 0.672165 0.740401i \(-0.265364\pi\)
−0.977289 + 0.211912i \(0.932031\pi\)
\(242\) 4629.89 1.22984
\(243\) 0 0
\(244\) 972.742 0.255219
\(245\) 406.338 + 703.797i 0.105959 + 0.183526i
\(246\) 0 0
\(247\) 2011.59 3484.18i 0.518197 0.897543i
\(248\) 9629.81 16679.3i 2.46570 4.27072i
\(249\) 0 0
\(250\) −332.219 575.421i −0.0840456 0.145571i
\(251\) 7922.23 1.99222 0.996109 0.0881290i \(-0.0280888\pi\)
0.996109 + 0.0881290i \(0.0280888\pi\)
\(252\) 0 0
\(253\) 1688.10 0.419487
\(254\) 2640.84 + 4574.06i 0.652366 + 1.12993i
\(255\) 0 0
\(256\) 5.46197 9.46041i 0.00133349 0.00230967i
\(257\) 1131.09 1959.10i 0.274535 0.475508i −0.695483 0.718542i \(-0.744810\pi\)
0.970018 + 0.243035i \(0.0781429\pi\)
\(258\) 0 0
\(259\) −356.274 617.085i −0.0854741 0.148045i
\(260\) −3659.47 −0.872888
\(261\) 0 0
\(262\) −7356.61 −1.73471
\(263\) 81.7349 + 141.569i 0.0191635 + 0.0331921i 0.875448 0.483312i \(-0.160566\pi\)
−0.856285 + 0.516504i \(0.827233\pi\)
\(264\) 0 0
\(265\) −1198.12 + 2075.20i −0.277735 + 0.481051i
\(266\) 3975.18 6885.22i 0.916294 1.58707i
\(267\) 0 0
\(268\) 292.865 + 507.257i 0.0667521 + 0.115618i
\(269\) −3304.13 −0.748908 −0.374454 0.927246i \(-0.622170\pi\)
−0.374454 + 0.927246i \(0.622170\pi\)
\(270\) 0 0
\(271\) −1954.96 −0.438212 −0.219106 0.975701i \(-0.570314\pi\)
−0.219106 + 0.975701i \(0.570314\pi\)
\(272\) −5029.67 8711.64i −1.12121 1.94199i
\(273\) 0 0
\(274\) 4111.91 7122.03i 0.906603 1.57028i
\(275\) −586.570 + 1015.97i −0.128624 + 0.222783i
\(276\) 0 0
\(277\) 2121.67 + 3674.85i 0.460213 + 0.797112i 0.998971 0.0453482i \(-0.0144397\pi\)
−0.538758 + 0.842460i \(0.681106\pi\)
\(278\) −2867.74 −0.618689
\(279\) 0 0
\(280\) −4375.33 −0.933844
\(281\) −1311.15 2270.97i −0.278350 0.482117i 0.692625 0.721298i \(-0.256454\pi\)
−0.970975 + 0.239181i \(0.923121\pi\)
\(282\) 0 0
\(283\) 3.53735 6.12688i 0.000743017 0.00128694i −0.865654 0.500643i \(-0.833097\pi\)
0.866397 + 0.499356i \(0.166430\pi\)
\(284\) 5835.18 10106.8i 1.21921 2.11173i
\(285\) 0 0
\(286\) 4506.60 + 7805.66i 0.931751 + 1.61384i
\(287\) 1724.34 0.354650
\(288\) 0 0
\(289\) −1931.06 −0.393051
\(290\) 772.310 + 1337.68i 0.156385 + 0.270867i
\(291\) 0 0
\(292\) −8456.88 + 14647.7i −1.69487 + 2.93560i
\(293\) −2238.75 + 3877.62i −0.446378 + 0.773150i −0.998147 0.0608470i \(-0.980620\pi\)
0.551769 + 0.833997i \(0.313953\pi\)
\(294\) 0 0
\(295\) 1589.04 + 2752.29i 0.313618 + 0.543202i
\(296\) −3455.12 −0.678461
\(297\) 0 0
\(298\) 6403.43 1.24477
\(299\) 649.955 + 1125.75i 0.125712 + 0.217739i
\(300\) 0 0
\(301\) −1102.72 + 1909.96i −0.211162 + 0.365743i
\(302\) −7901.27 + 13685.4i −1.50552 + 2.60764i
\(303\) 0 0
\(304\) −10255.0 17762.2i −1.93475 3.35109i
\(305\) 240.128 0.0450810
\(306\) 0 0
\(307\) −3889.78 −0.723132 −0.361566 0.932347i \(-0.617758\pi\)
−0.361566 + 0.932347i \(0.617758\pi\)
\(308\) 6384.12 + 11057.6i 1.18107 + 2.04567i
\(309\) 0 0
\(310\) 3929.05 6805.31i 0.719855 1.24683i
\(311\) −3647.83 + 6318.23i −0.665111 + 1.15201i 0.314145 + 0.949375i \(0.398282\pi\)
−0.979255 + 0.202630i \(0.935051\pi\)
\(312\) 0 0
\(313\) 318.036 + 550.854i 0.0574328 + 0.0994765i 0.893312 0.449436i \(-0.148375\pi\)
−0.835880 + 0.548913i \(0.815042\pi\)
\(314\) −2103.67 −0.378080
\(315\) 0 0
\(316\) −4126.62 −0.734623
\(317\) −3073.18 5322.90i −0.544501 0.943104i −0.998638 0.0521721i \(-0.983386\pi\)
0.454137 0.890932i \(-0.349948\pi\)
\(318\) 0 0
\(319\) 1363.60 2361.83i 0.239332 0.414536i
\(320\) −2402.91 + 4161.96i −0.419771 + 0.727064i
\(321\) 0 0
\(322\) 1284.40 + 2224.65i 0.222288 + 0.385014i
\(323\) 6079.89 1.04735
\(324\) 0 0
\(325\) −903.367 −0.154184
\(326\) −10262.7 17775.6i −1.74356 3.01994i
\(327\) 0 0
\(328\) 4180.63 7241.06i 0.703770 1.21897i
\(329\) −589.954 + 1021.83i −0.0988609 + 0.171232i
\(330\) 0 0
\(331\) −5867.20 10162.3i −0.974291 1.68752i −0.682255 0.731114i \(-0.739001\pi\)
−0.292036 0.956407i \(-0.594333\pi\)
\(332\) −9407.82 −1.55518
\(333\) 0 0
\(334\) −10816.9 −1.77208
\(335\) 72.2958 + 125.220i 0.0117909 + 0.0204224i
\(336\) 0 0
\(337\) −3141.65 + 5441.49i −0.507823 + 0.879575i 0.492136 + 0.870518i \(0.336216\pi\)
−0.999959 + 0.00905696i \(0.997117\pi\)
\(338\) 2368.82 4102.91i 0.381203 0.660264i
\(339\) 0 0
\(340\) −2765.12 4789.33i −0.441058 0.763934i
\(341\) −13874.4 −2.20334
\(342\) 0 0
\(343\) 6791.22 1.06907
\(344\) 5347.04 + 9261.34i 0.838061 + 1.45156i
\(345\) 0 0
\(346\) 4111.32 7121.02i 0.638803 1.10644i
\(347\) 2400.41 4157.63i 0.371357 0.643209i −0.618418 0.785849i \(-0.712226\pi\)
0.989775 + 0.142641i \(0.0455594\pi\)
\(348\) 0 0
\(349\) 1946.23 + 3370.97i 0.298508 + 0.517031i 0.975795 0.218688i \(-0.0701778\pi\)
−0.677287 + 0.735719i \(0.736844\pi\)
\(350\) −1785.18 −0.272633
\(351\) 0 0
\(352\) 21495.2 3.25482
\(353\) −1483.14 2568.87i −0.223624 0.387329i 0.732281 0.681002i \(-0.238456\pi\)
−0.955906 + 0.293673i \(0.905122\pi\)
\(354\) 0 0
\(355\) 1440.46 2494.94i 0.215356 0.373008i
\(356\) 10064.3 17431.9i 1.49834 2.59520i
\(357\) 0 0
\(358\) −2189.92 3793.05i −0.323298 0.559969i
\(359\) 9584.91 1.40911 0.704557 0.709647i \(-0.251146\pi\)
0.704557 + 0.709647i \(0.251146\pi\)
\(360\) 0 0
\(361\) 5537.30 0.807304
\(362\) 11703.5 + 20271.1i 1.69924 + 2.94317i
\(363\) 0 0
\(364\) −4916.03 + 8514.82i −0.707885 + 1.22609i
\(365\) −2087.64 + 3615.90i −0.299376 + 0.518534i
\(366\) 0 0
\(367\) −2268.59 3929.31i −0.322669 0.558879i 0.658369 0.752695i \(-0.271247\pi\)
−0.981038 + 0.193817i \(0.937913\pi\)
\(368\) 6626.88 0.938722
\(369\) 0 0
\(370\) −1409.72 −0.198075
\(371\) 3219.04 + 5575.54i 0.450469 + 0.780236i
\(372\) 0 0
\(373\) −6565.65 + 11372.0i −0.911411 + 1.57861i −0.0993385 + 0.995054i \(0.531673\pi\)
−0.812073 + 0.583557i \(0.801661\pi\)
\(374\) −6810.43 + 11796.0i −0.941601 + 1.63090i
\(375\) 0 0
\(376\) 2860.66 + 4954.82i 0.392360 + 0.679588i
\(377\) 2100.06 0.286892
\(378\) 0 0
\(379\) −9451.10 −1.28092 −0.640462 0.767990i \(-0.721257\pi\)
−0.640462 + 0.767990i \(0.721257\pi\)
\(380\) −5637.81 9764.97i −0.761088 1.31824i
\(381\) 0 0
\(382\) −8097.98 + 14026.1i −1.08463 + 1.87863i
\(383\) −4298.52 + 7445.25i −0.573483 + 0.993301i 0.422722 + 0.906260i \(0.361075\pi\)
−0.996205 + 0.0870420i \(0.972259\pi\)
\(384\) 0 0
\(385\) 1575.97 + 2729.65i 0.208620 + 0.361340i
\(386\) 10051.1 1.32536
\(387\) 0 0
\(388\) 17852.7 2.33592
\(389\) 2221.04 + 3846.95i 0.289489 + 0.501410i 0.973688 0.227886i \(-0.0731813\pi\)
−0.684199 + 0.729295i \(0.739848\pi\)
\(390\) 0 0
\(391\) −982.219 + 1701.25i −0.127041 + 0.220041i
\(392\) 5293.73 9169.01i 0.682076 1.18139i
\(393\) 0 0
\(394\) 9706.13 + 16811.5i 1.24109 + 2.14962i
\(395\) −1018.69 −0.129761
\(396\) 0 0
\(397\) 10445.6 1.32053 0.660265 0.751033i \(-0.270444\pi\)
0.660265 + 0.751033i \(0.270444\pi\)
\(398\) −8550.68 14810.2i −1.07690 1.86525i
\(399\) 0 0
\(400\) −2302.66 + 3988.33i −0.287833 + 0.498541i
\(401\) −6341.72 + 10984.2i −0.789751 + 1.36789i 0.136368 + 0.990658i \(0.456457\pi\)
−0.926119 + 0.377231i \(0.876876\pi\)
\(402\) 0 0
\(403\) −5341.91 9252.47i −0.660297 1.14367i
\(404\) −24502.8 −3.01748
\(405\) 0 0
\(406\) 4150.00 0.507293
\(407\) 1244.51 + 2155.55i 0.151568 + 0.262523i
\(408\) 0 0
\(409\) 5556.30 9623.79i 0.671739 1.16349i −0.305671 0.952137i \(-0.598881\pi\)
0.977411 0.211349i \(-0.0677858\pi\)
\(410\) 1705.73 2954.42i 0.205464 0.355874i
\(411\) 0 0
\(412\) −7543.26 13065.3i −0.902014 1.56233i
\(413\) 8538.67 1.01734
\(414\) 0 0
\(415\) −2322.39 −0.274702
\(416\) 8276.08 + 14334.6i 0.975404 + 1.68945i
\(417\) 0 0
\(418\) −13885.8 + 24050.9i −1.62482 + 2.81428i
\(419\) 1009.26 1748.09i 0.117675 0.203818i −0.801171 0.598435i \(-0.795789\pi\)
0.918846 + 0.394617i \(0.129123\pi\)
\(420\) 0 0
\(421\) 5478.85 + 9489.65i 0.634259 + 1.09857i 0.986672 + 0.162724i \(0.0520280\pi\)
−0.352413 + 0.935845i \(0.614639\pi\)
\(422\) 26300.1 3.03381
\(423\) 0 0
\(424\) 31218.0 3.57565
\(425\) −682.589 1182.28i −0.0779069 0.134939i
\(426\) 0 0
\(427\) 322.582 558.728i 0.0365593 0.0633226i
\(428\) −10128.8 + 17543.5i −1.14391 + 1.98131i
\(429\) 0 0
\(430\) 2181.64 + 3778.71i 0.244670 + 0.423781i
\(431\) 2124.75 0.237460 0.118730 0.992927i \(-0.462118\pi\)
0.118730 + 0.992927i \(0.462118\pi\)
\(432\) 0 0
\(433\) −16169.2 −1.79456 −0.897279 0.441463i \(-0.854460\pi\)
−0.897279 + 0.441463i \(0.854460\pi\)
\(434\) −10556.4 18284.1i −1.16756 2.02227i
\(435\) 0 0
\(436\) 9271.73 16059.1i 1.01843 1.76397i
\(437\) −2002.65 + 3468.69i −0.219221 + 0.379702i
\(438\) 0 0
\(439\) −346.098 599.460i −0.0376273 0.0651724i 0.846598 0.532232i \(-0.178647\pi\)
−0.884226 + 0.467060i \(0.845313\pi\)
\(440\) 15283.6 1.65595
\(441\) 0 0
\(442\) −10488.6 −1.12872
\(443\) −3335.26 5776.83i −0.357704 0.619561i 0.629873 0.776698i \(-0.283107\pi\)
−0.987577 + 0.157137i \(0.949774\pi\)
\(444\) 0 0
\(445\) 2484.45 4303.20i 0.264662 0.458407i
\(446\) −2934.46 + 5082.63i −0.311549 + 0.539618i
\(447\) 0 0
\(448\) 6456.00 + 11182.1i 0.680843 + 1.17925i
\(449\) 9743.18 1.02407 0.512037 0.858964i \(-0.328891\pi\)
0.512037 + 0.858964i \(0.328891\pi\)
\(450\) 0 0
\(451\) −6023.33 −0.628886
\(452\) −13417.7 23240.1i −1.39627 2.41842i
\(453\) 0 0
\(454\) −10153.3 + 17586.0i −1.04959 + 1.81795i
\(455\) −1213.56 + 2101.94i −0.125038 + 0.216573i
\(456\) 0 0
\(457\) −2221.36 3847.51i −0.227376 0.393827i 0.729654 0.683817i \(-0.239681\pi\)
−0.957030 + 0.289990i \(0.906348\pi\)
\(458\) 769.524 0.0785098
\(459\) 0 0
\(460\) 3643.20 0.369272
\(461\) 9469.70 + 16402.0i 0.956720 + 1.65709i 0.730383 + 0.683038i \(0.239342\pi\)
0.226337 + 0.974049i \(0.427325\pi\)
\(462\) 0 0
\(463\) 8396.10 14542.5i 0.842764 1.45971i −0.0447846 0.998997i \(-0.514260\pi\)
0.887549 0.460714i \(-0.152407\pi\)
\(464\) 5353.00 9271.66i 0.535575 0.927642i
\(465\) 0 0
\(466\) 3418.70 + 5921.36i 0.339846 + 0.588630i
\(467\) −1367.93 −0.135547 −0.0677735 0.997701i \(-0.521590\pi\)
−0.0677735 + 0.997701i \(0.521590\pi\)
\(468\) 0 0
\(469\) 388.480 0.0382481
\(470\) 1167.18 + 2021.61i 0.114549 + 0.198404i
\(471\) 0 0
\(472\) 20701.8 35856.6i 2.01881 3.49668i
\(473\) 3851.93 6671.74i 0.374444 0.648556i
\(474\) 0 0
\(475\) −1391.73 2410.55i −0.134436 0.232850i
\(476\) −14858.3 −1.43074
\(477\) 0 0
\(478\) −22428.5 −2.14615
\(479\) 101.371 + 175.579i 0.00966960 + 0.0167482i 0.870820 0.491603i \(-0.163589\pi\)
−0.861150 + 0.508351i \(0.830255\pi\)
\(480\) 0 0
\(481\) −958.323 + 1659.86i −0.0908436 + 0.157346i
\(482\) −6068.01 + 10510.1i −0.573424 + 0.993199i
\(483\) 0 0
\(484\) −8821.04 15278.5i −0.828423 1.43487i
\(485\) 4407.08 0.412608
\(486\) 0 0
\(487\) 18961.3 1.76431 0.882153 0.470964i \(-0.156094\pi\)
0.882153 + 0.470964i \(0.156094\pi\)
\(488\) −1564.19 2709.25i −0.145097 0.251315i
\(489\) 0 0
\(490\) 2159.89 3741.04i 0.199130 0.344904i
\(491\) 5856.15 10143.1i 0.538257 0.932289i −0.460741 0.887535i \(-0.652416\pi\)
0.998998 0.0447541i \(-0.0142504\pi\)
\(492\) 0 0
\(493\) 1586.82 + 2748.45i 0.144963 + 0.251083i
\(494\) −21385.3 −1.94771
\(495\) 0 0
\(496\) −54465.7 −4.93061
\(497\) −3870.14 6703.28i −0.349295 0.604996i
\(498\) 0 0
\(499\) −4312.44 + 7469.36i −0.386876 + 0.670089i −0.992028 0.126021i \(-0.959779\pi\)
0.605151 + 0.796110i \(0.293113\pi\)
\(500\) −1265.91 + 2192.63i −0.113227 + 0.196115i
\(501\) 0 0
\(502\) −21055.3 36468.9i −1.87200 3.24241i
\(503\) −4856.12 −0.430465 −0.215232 0.976563i \(-0.569051\pi\)
−0.215232 + 0.976563i \(0.569051\pi\)
\(504\) 0 0
\(505\) −6048.69 −0.532997
\(506\) −4486.56 7770.96i −0.394174 0.682730i
\(507\) 0 0
\(508\) 10062.9 17429.4i 0.878872 1.52225i
\(509\) −5425.17 + 9396.67i −0.472429 + 0.818271i −0.999502 0.0315486i \(-0.989956\pi\)
0.527073 + 0.849820i \(0.323289\pi\)
\(510\) 0 0
\(511\) 5608.96 + 9715.01i 0.485569 + 0.841030i
\(512\) −11614.3 −1.00251
\(513\) 0 0
\(514\) −12024.6 −1.03187
\(515\) −1862.11 3225.26i −0.159329 0.275965i
\(516\) 0 0
\(517\) 2060.78 3569.38i 0.175306 0.303639i
\(518\) −1893.78 + 3280.12i −0.160633 + 0.278224i
\(519\) 0 0
\(520\) 5884.49 + 10192.2i 0.496254 + 0.859537i
\(521\) −3559.30 −0.299301 −0.149651 0.988739i \(-0.547815\pi\)
−0.149651 + 0.988739i \(0.547815\pi\)
\(522\) 0 0
\(523\) 22191.7 1.85540 0.927702 0.373321i \(-0.121781\pi\)
0.927702 + 0.373321i \(0.121781\pi\)
\(524\) 14016.1 + 24276.6i 1.16850 + 2.02391i
\(525\) 0 0
\(526\) 434.463 752.511i 0.0360142 0.0623784i
\(527\) 8072.77 13982.4i 0.667277 1.15576i
\(528\) 0 0
\(529\) 5436.44 + 9416.18i 0.446818 + 0.773912i
\(530\) 12737.2 1.04390
\(531\) 0 0
\(532\) −30294.7 −2.46888
\(533\) −2319.11 4016.81i −0.188465 0.326430i
\(534\) 0 0
\(535\) −2500.36 + 4330.75i −0.202056 + 0.349971i
\(536\) 941.863 1631.35i 0.0758998 0.131462i
\(537\) 0 0
\(538\) 8781.56 + 15210.1i 0.703717 + 1.21887i
\(539\) −7627.06 −0.609500
\(540\) 0 0
\(541\) 4257.08 0.338311 0.169155 0.985589i \(-0.445896\pi\)
0.169155 + 0.985589i \(0.445896\pi\)
\(542\) 5195.81 + 8999.40i 0.411770 + 0.713206i
\(543\) 0 0
\(544\) −12506.9 + 21662.6i −0.985715 + 1.70731i
\(545\) 2288.79 3964.31i 0.179892 0.311582i
\(546\) 0 0
\(547\) 10609.1 + 18375.5i 0.829272 + 1.43634i 0.898610 + 0.438748i \(0.144578\pi\)
−0.0693385 + 0.997593i \(0.522089\pi\)
\(548\) −31336.7 −2.44277
\(549\) 0 0
\(550\) 6235.84 0.483449
\(551\) 3235.36 + 5603.81i 0.250147 + 0.433268i
\(552\) 0 0
\(553\) −1368.48 + 2370.27i −0.105232 + 0.182268i
\(554\) 11277.8 19533.7i 0.864885 1.49803i
\(555\) 0 0
\(556\) 5463.73 + 9463.46i 0.416752 + 0.721835i
\(557\) −2506.42 −0.190665 −0.0953324 0.995445i \(-0.530391\pi\)
−0.0953324 + 0.995445i \(0.530391\pi\)
\(558\) 0 0
\(559\) 5932.29 0.448854
\(560\) 6186.66 + 10715.6i 0.466847 + 0.808602i
\(561\) 0 0
\(562\) −6969.41 + 12071.4i −0.523108 + 0.906050i
\(563\) 8639.80 14964.6i 0.646757 1.12022i −0.337136 0.941456i \(-0.609458\pi\)
0.983893 0.178759i \(-0.0572084\pi\)
\(564\) 0 0
\(565\) −3312.26 5737.00i −0.246633 0.427181i
\(566\) −37.6057 −0.00279273
\(567\) 0 0
\(568\) −37532.3 −2.77257
\(569\) −10254.1 17760.5i −0.755487 1.30854i −0.945132 0.326689i \(-0.894067\pi\)
0.189645 0.981853i \(-0.439266\pi\)
\(570\) 0 0
\(571\) −3412.53 + 5910.68i −0.250105 + 0.433195i −0.963555 0.267512i \(-0.913799\pi\)
0.713449 + 0.700707i \(0.247132\pi\)
\(572\) 17172.3 29743.3i 1.25526 2.17418i
\(573\) 0 0
\(574\) −4582.87 7937.77i −0.333250 0.577206i
\(575\) 899.350 0.0652270
\(576\) 0 0
\(577\) 4249.00 0.306565 0.153283 0.988182i \(-0.451016\pi\)
0.153283 + 0.988182i \(0.451016\pi\)
\(578\) 5132.28 + 8889.37i 0.369333 + 0.639704i
\(579\) 0 0
\(580\) 2942.87 5097.20i 0.210683 0.364913i
\(581\) −3119.83 + 5403.71i −0.222775 + 0.385858i
\(582\) 0 0
\(583\) −11244.5 19476.0i −0.798798 1.38356i
\(584\) 54395.2 3.85426
\(585\) 0 0
\(586\) 23800.1 1.67777
\(587\) 9344.04 + 16184.3i 0.657018 + 1.13799i 0.981384 + 0.192057i \(0.0615159\pi\)
−0.324365 + 0.945932i \(0.605151\pi\)
\(588\) 0 0
\(589\) 16459.6 28508.8i 1.15145 1.99437i
\(590\) 8446.53 14629.8i 0.589387 1.02085i
\(591\) 0 0
\(592\) 4885.48 + 8461.91i 0.339176 + 0.587470i
\(593\) 12434.5 0.861084 0.430542 0.902570i \(-0.358322\pi\)
0.430542 + 0.902570i \(0.358322\pi\)
\(594\) 0 0
\(595\) −3667.89 −0.252721
\(596\) −12200.1 21131.1i −0.838480 1.45229i
\(597\) 0 0
\(598\) 3454.84 5983.96i 0.236252 0.409201i
\(599\) −3021.52 + 5233.42i −0.206103 + 0.356981i −0.950484 0.310774i \(-0.899412\pi\)
0.744380 + 0.667756i \(0.232745\pi\)
\(600\) 0 0
\(601\) 315.654 + 546.729i 0.0214239 + 0.0371074i 0.876539 0.481332i \(-0.159847\pi\)
−0.855115 + 0.518439i \(0.826513\pi\)
\(602\) 11723.0 0.793679
\(603\) 0 0
\(604\) 60215.2 4.05649
\(605\) −2177.54 3771.61i −0.146330 0.253451i
\(606\) 0 0
\(607\) 4727.43 8188.16i 0.316113 0.547524i −0.663560 0.748123i \(-0.730955\pi\)
0.979673 + 0.200599i \(0.0642888\pi\)
\(608\) −25500.4 + 44167.9i −1.70095 + 2.94613i
\(609\) 0 0
\(610\) −638.202 1105.40i −0.0423607 0.0733709i
\(611\) 3173.77 0.210143
\(612\) 0 0
\(613\) −2682.66 −0.176757 −0.0883783 0.996087i \(-0.528168\pi\)
−0.0883783 + 0.996087i \(0.528168\pi\)
\(614\) 10338.1 + 17906.1i 0.679497 + 1.17692i
\(615\) 0 0
\(616\) 20531.5 35561.7i 1.34292 2.32601i
\(617\) −1169.26 + 2025.22i −0.0762930 + 0.132143i −0.901648 0.432471i \(-0.857642\pi\)
0.825355 + 0.564614i \(0.190975\pi\)
\(618\) 0 0
\(619\) 5965.11 + 10331.9i 0.387331 + 0.670878i 0.992090 0.125531i \(-0.0400636\pi\)
−0.604758 + 0.796409i \(0.706730\pi\)
\(620\) −29943.1 −1.93959
\(621\) 0 0
\(622\) 38780.1 2.49991
\(623\) −6675.09 11561.6i −0.429265 0.743509i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 1690.52 2928.07i 0.107934 0.186948i
\(627\) 0 0
\(628\) 4008.00 + 6942.05i 0.254676 + 0.441111i
\(629\) −2896.46 −0.183608
\(630\) 0 0
\(631\) 4106.81 0.259096 0.129548 0.991573i \(-0.458647\pi\)
0.129548 + 0.991573i \(0.458647\pi\)
\(632\) 6635.68 + 11493.3i 0.417648 + 0.723387i
\(633\) 0 0
\(634\) −16335.5 + 28293.9i −1.02329 + 1.77239i
\(635\) 2484.09 4302.57i 0.155241 0.268885i
\(636\) 0 0
\(637\) −2936.58 5086.30i −0.182655 0.316368i
\(638\) −14496.5 −0.899562
\(639\) 0 0
\(640\) 7222.62 0.446093
\(641\) 7462.65 + 12925.7i 0.459839 + 0.796465i 0.998952 0.0457684i \(-0.0145736\pi\)
−0.539113 + 0.842234i \(0.681240\pi\)
\(642\) 0 0
\(643\) −9502.84 + 16459.4i −0.582823 + 1.00948i 0.412319 + 0.911039i \(0.364719\pi\)
−0.995143 + 0.0984406i \(0.968615\pi\)
\(644\) 4894.18 8476.96i 0.299468 0.518694i
\(645\) 0 0
\(646\) −16158.8 27987.9i −0.984151 1.70460i
\(647\) −9252.81 −0.562234 −0.281117 0.959673i \(-0.590705\pi\)
−0.281117 + 0.959673i \(0.590705\pi\)
\(648\) 0 0
\(649\) −29826.6 −1.80400
\(650\) 2400.93 + 4158.53i 0.144880 + 0.250940i
\(651\) 0 0
\(652\) −39106.0 + 67733.5i −2.34894 + 4.06848i
\(653\) 11475.3 19875.9i 0.687695 1.19112i −0.284887 0.958561i \(-0.591956\pi\)
0.972582 0.232561i \(-0.0747105\pi\)
\(654\) 0 0
\(655\) 3459.97 + 5992.85i 0.206401 + 0.357496i
\(656\) −23645.4 −1.40731
\(657\) 0 0
\(658\) 6271.81 0.371582
\(659\) 3258.54 + 5643.96i 0.192617 + 0.333623i 0.946117 0.323826i \(-0.104969\pi\)
−0.753500 + 0.657448i \(0.771636\pi\)
\(660\) 0 0
\(661\) 2598.16 4500.15i 0.152885 0.264804i −0.779402 0.626524i \(-0.784477\pi\)
0.932287 + 0.361720i \(0.117810\pi\)
\(662\) −31187.1 + 54017.7i −1.83100 + 3.17139i
\(663\) 0 0
\(664\) 15127.9 + 26202.3i 0.884153 + 1.53140i
\(665\) −7478.47 −0.436094
\(666\) 0 0
\(667\) −2090.72 −0.121369
\(668\) 20608.8 + 35695.5i 1.19368 + 2.06751i
\(669\) 0 0
\(670\) 384.289 665.607i 0.0221588 0.0383801i
\(671\) −1126.82 + 1951.71i −0.0648291 + 0.112287i
\(672\) 0 0
\(673\) −14095.0 24413.2i −0.807313 1.39831i −0.914718 0.404093i \(-0.867587\pi\)
0.107405 0.994215i \(-0.465746\pi\)
\(674\) 33398.9 1.90872
\(675\) 0 0
\(676\) −18052.7 −1.02712
\(677\) 4338.44 + 7514.40i 0.246292 + 0.426590i 0.962494 0.271303i \(-0.0874544\pi\)
−0.716202 + 0.697893i \(0.754121\pi\)
\(678\) 0 0
\(679\) 5920.34 10254.3i 0.334613 0.579566i
\(680\) −8892.71 + 15402.6i −0.501500 + 0.868624i
\(681\) 0 0
\(682\) 36874.6 + 63868.7i 2.07039 + 3.58601i
\(683\) −20624.1 −1.15543 −0.577714 0.816239i \(-0.696055\pi\)
−0.577714 + 0.816239i \(0.696055\pi\)
\(684\) 0 0
\(685\) −7735.68 −0.431482
\(686\) −18049.4 31262.5i −1.00456 1.73995i
\(687\) 0 0
\(688\) 15121.3 26190.8i 0.837926 1.45133i
\(689\) 8658.72 14997.3i 0.478768 0.829250i
\(690\) 0 0
\(691\) −3493.03 6050.10i −0.192303 0.333078i 0.753710 0.657207i \(-0.228262\pi\)
−0.946013 + 0.324129i \(0.894929\pi\)
\(692\) −31332.2 −1.72120
\(693\) 0 0
\(694\) −25518.8 −1.39579
\(695\) 1348.76 + 2336.12i 0.0736136 + 0.127502i
\(696\) 0 0
\(697\) 3504.66 6070.25i 0.190457 0.329881i
\(698\) 10345.2 17918.4i 0.560991 0.971664i
\(699\) 0 0
\(700\) 3401.19 + 5891.03i 0.183647 + 0.318086i
\(701\) −7848.55 −0.422875 −0.211438 0.977391i \(-0.567815\pi\)
−0.211438 + 0.977391i \(0.567815\pi\)
\(702\) 0 0
\(703\) −5905.60 −0.316833
\(704\) −22551.6 39060.5i −1.20731 2.09112i
\(705\) 0 0
\(706\) −7883.63 + 13654.8i −0.420261 + 0.727913i
\(707\) −8125.65 + 14074.0i −0.432244 + 0.748669i
\(708\) 0 0
\(709\) 12712.3 + 22018.3i 0.673371 + 1.16631i 0.976942 + 0.213504i \(0.0684876\pi\)
−0.303571 + 0.952809i \(0.598179\pi\)
\(710\) −15313.5 −0.809445
\(711\) 0 0
\(712\) −64734.5 −3.40734
\(713\) 5318.16 + 9211.33i 0.279336 + 0.483825i
\(714\) 0 0
\(715\) 4239.11 7342.35i 0.221725 0.384039i
\(716\) −8344.63 + 14453.3i −0.435550 + 0.754394i
\(717\) 0 0
\(718\) −25474.3 44122.8i −1.32409 2.29338i
\(719\) −16707.2 −0.866584 −0.433292 0.901254i \(-0.642648\pi\)
−0.433292 + 0.901254i \(0.642648\pi\)
\(720\) 0 0
\(721\) −10006.0 −0.516843
\(722\) −14716.8 25490.2i −0.758590 1.31392i
\(723\) 0 0
\(724\) 44596.1 77242.7i 2.28923 3.96506i
\(725\) 726.469 1258.28i 0.0372143 0.0644571i
\(726\) 0 0
\(727\) −718.240 1244.03i −0.0366410 0.0634642i 0.847123 0.531396i \(-0.178332\pi\)
−0.883764 + 0.467932i \(0.844999\pi\)
\(728\) 31620.3 1.60979
\(729\) 0 0
\(730\) 22193.8 1.12524
\(731\) 4482.47 + 7763.87i 0.226799 + 0.392828i
\(732\) 0 0
\(733\) −5770.44 + 9994.70i −0.290772 + 0.503633i −0.973993 0.226580i \(-0.927246\pi\)
0.683220 + 0.730212i \(0.260579\pi\)
\(734\) −12058.7 + 20886.3i −0.606397 + 1.05031i
\(735\) 0 0
\(736\) −8239.28 14270.9i −0.412641 0.714715i
\(737\) −1357.01 −0.0678237
\(738\) 0 0
\(739\) 4127.87 0.205475 0.102737 0.994709i \(-0.467240\pi\)
0.102737 + 0.994709i \(0.467240\pi\)
\(740\) 2685.85 + 4652.03i 0.133424 + 0.231097i
\(741\) 0 0
\(742\) 17110.8 29636.8i 0.846574 1.46631i
\(743\) −13748.5 + 23813.1i −0.678846 + 1.17580i 0.296482 + 0.955038i \(0.404186\pi\)
−0.975329 + 0.220758i \(0.929147\pi\)
\(744\) 0 0
\(745\) −3011.67 5216.37i −0.148106 0.256528i
\(746\) 69799.5 3.42566
\(747\) 0 0
\(748\) 51902.0 2.53706
\(749\) 6717.83 + 11635.6i 0.327723 + 0.567632i
\(750\) 0 0
\(751\) −17197.1 + 29786.2i −0.835592 + 1.44729i 0.0579559 + 0.998319i \(0.481542\pi\)
−0.893548 + 0.448968i \(0.851792\pi\)
\(752\) 8089.88 14012.1i 0.392297 0.679479i
\(753\) 0 0
\(754\) −5581.44 9667.33i −0.269581 0.466928i
\(755\) 14864.6 0.716526
\(756\) 0 0
\(757\) −30459.8 −1.46246 −0.731229 0.682132i \(-0.761053\pi\)
−0.731229 + 0.682132i \(0.761053\pi\)
\(758\) 25118.7 + 43506.8i 1.20363 + 2.08475i
\(759\) 0 0
\(760\) −18131.4 + 31404.5i −0.865387 + 1.49889i
\(761\) 223.584 387.259i 0.0106504 0.0184469i −0.860651 0.509195i \(-0.829943\pi\)
0.871301 + 0.490748i \(0.163276\pi\)
\(762\) 0 0
\(763\) −6149.40 10651.1i −0.291774 0.505367i
\(764\) 61714.3 2.92244
\(765\) 0 0
\(766\) 45697.6 2.15551
\(767\) −11483.9 19890.6i −0.540623 0.936387i
\(768\) 0 0
\(769\) 4028.59 6977.71i 0.188914 0.327208i −0.755975 0.654601i \(-0.772837\pi\)
0.944888 + 0.327393i \(0.106170\pi\)
\(770\) 8377.06 14509.5i 0.392062 0.679072i
\(771\) 0 0
\(772\) −19149.8 33168.4i −0.892767 1.54632i
\(773\) 19600.4 0.912001 0.456000 0.889980i \(-0.349282\pi\)
0.456000 + 0.889980i \(0.349282\pi\)
\(774\) 0 0
\(775\) −7391.67 −0.342602
\(776\) −28707.5 49722.8i −1.32801 2.30019i
\(777\) 0 0
\(778\) 11806.0 20448.5i 0.544041 0.942307i
\(779\) 7145.66 12376.7i 0.328652 0.569242i
\(780\) 0 0
\(781\) 13518.9 + 23415.4i 0.619390 + 1.07281i
\(782\) 10442.0 0.477500
\(783\) 0 0
\(784\) −29941.0 −1.36393
\(785\) 989.402 + 1713.70i 0.0449851 + 0.0779164i
\(786\) 0 0
\(787\) −8968.18 + 15533.3i −0.406202 + 0.703563i −0.994461 0.105110i \(-0.966480\pi\)
0.588258 + 0.808673i \(0.299814\pi\)
\(788\) 36985.0 64059.9i 1.67200 2.89599i
\(789\) 0 0
\(790\) 2707.42 + 4689.39i 0.121931 + 0.211191i
\(791\) −17798.4 −0.800047
\(792\) 0 0
\(793\) −1735.39 −0.0777119
\(794\) −27761.9 48085.0i −1.24085 2.14921i
\(795\) 0 0
\(796\) −32582.2 + 56434.0i −1.45081 + 2.51288i
\(797\) −8971.31 + 15538.8i −0.398720 + 0.690604i −0.993568 0.113235i \(-0.963879\pi\)
0.594848 + 0.803838i \(0.297212\pi\)
\(798\) 0 0
\(799\) 2398.12 + 4153.67i 0.106182 + 0.183913i
\(800\) 11451.7 0.506099
\(801\) 0 0
\(802\) 67418.9 2.96838
\(803\) −19592.8 33935.7i −0.861039 1.49136i
\(804\) 0 0
\(805\) 1208.16 2092.60i 0.0528971 0.0916204i
\(806\) −28395.0 + 49181.6i −1.24091 + 2.14931i
\(807\) 0 0
\(808\) 39400.9 + 68244.4i 1.71549 + 2.97132i
\(809\) −29094.2 −1.26440 −0.632200 0.774806i \(-0.717848\pi\)
−0.632200 + 0.774806i \(0.717848\pi\)
\(810\) 0 0
\(811\) 1438.31 0.0622760 0.0311380 0.999515i \(-0.490087\pi\)
0.0311380 + 0.999515i \(0.490087\pi\)
\(812\) −7906.74 13694.9i −0.341715 0.591867i
\(813\) 0 0
\(814\) 6615.19 11457.9i 0.284843 0.493363i
\(815\) −9653.59 + 16720.5i −0.414908 + 0.718643i
\(816\) 0 0
\(817\) 9139.33 + 15829.8i 0.391364 + 0.677863i
\(818\) −59069.1 −2.52482
\(819\) 0 0
\(820\) −12999.3 −0.553605
\(821\) −121.415 210.297i −0.00516128 0.00893959i 0.863433 0.504463i \(-0.168310\pi\)
−0.868595 + 0.495524i \(0.834976\pi\)
\(822\) 0 0
\(823\) −9085.50 + 15736.5i −0.384812 + 0.666515i −0.991743 0.128240i \(-0.959067\pi\)
0.606931 + 0.794755i \(0.292401\pi\)
\(824\) −24259.4 + 42018.5i −1.02563 + 1.77644i
\(825\) 0 0
\(826\) −22693.7 39306.6i −0.955949 1.65575i
\(827\) −12181.7 −0.512213 −0.256107 0.966649i \(-0.582440\pi\)
−0.256107 + 0.966649i \(0.582440\pi\)
\(828\) 0 0
\(829\) −17370.0 −0.727724 −0.363862 0.931453i \(-0.618542\pi\)
−0.363862 + 0.931453i \(0.618542\pi\)
\(830\) 6172.34 + 10690.8i 0.258126 + 0.447088i
\(831\) 0 0
\(832\) 17365.7 30078.2i 0.723613 1.25333i
\(833\) 4437.79 7686.47i 0.184586 0.319713i
\(834\) 0 0
\(835\) 5087.43 + 8811.69i 0.210848 + 0.365199i
\(836\) 105823. 4.37795
\(837\) 0 0
\(838\) −10729.5 −0.442296
\(839\) 15681.5 + 27161.2i 0.645275 + 1.11765i 0.984238 + 0.176849i \(0.0565906\pi\)
−0.338963 + 0.940800i \(0.610076\pi\)
\(840\) 0 0
\(841\) 10505.7 18196.4i 0.430755 0.746089i
\(842\) 29122.9 50442.3i 1.19197 2.06456i
\(843\) 0 0
\(844\) −50108.0 86789.5i −2.04359 3.53960i
\(845\) −4456.43 −0.181427
\(846\) 0 0
\(847\) −11701.0 −0.474676
\(848\) −44141.7 76455.7i −1.78754 3.09611i
\(849\) 0 0
\(850\) −3628.31 + 6284.42i −0.146412 + 0.253593i
\(851\) 954.062 1652.48i 0.0384311 0.0665645i
\(852\) 0 0
\(853\) 19838.8 + 34361.8i 0.796326 + 1.37928i 0.921993 + 0.387205i \(0.126560\pi\)
−0.125667 + 0.992072i \(0.540107\pi\)
\(854\) −3429.37 −0.137413
\(855\) 0 0
\(856\) 65149.0 2.60134
\(857\) 16604.7 + 28760.1i 0.661849 + 1.14636i 0.980129 + 0.198360i \(0.0635614\pi\)
−0.318280 + 0.947997i \(0.603105\pi\)
\(858\) 0 0
\(859\) −17202.4 + 29795.5i −0.683282 + 1.18348i 0.290691 + 0.956817i \(0.406115\pi\)
−0.973973 + 0.226663i \(0.927219\pi\)
\(860\) 8313.09 14398.7i 0.329621 0.570920i
\(861\) 0 0
\(862\) −5647.05 9780.98i −0.223131 0.386475i
\(863\) −12999.7 −0.512765 −0.256382 0.966575i \(-0.582531\pi\)
−0.256382 + 0.966575i \(0.582531\pi\)
\(864\) 0 0
\(865\) −7734.58 −0.304027
\(866\) 42973.9 + 74432.9i 1.68627 + 2.92071i
\(867\) 0 0
\(868\) −40224.8 + 69671.3i −1.57295 + 2.72442i
\(869\) 4780.25 8279.64i 0.186604 0.323208i
\(870\) 0 0
\(871\) −522.477 904.956i −0.0203254 0.0352047i
\(872\) −59636.4 −2.31599
\(873\) 0 0
\(874\) 21290.2 0.823972
\(875\) 839.608 + 1454.24i 0.0324388 + 0.0561856i
\(876\) 0 0
\(877\) 11415.7 19772.6i 0.439546 0.761317i −0.558108 0.829768i \(-0.688473\pi\)
0.997654 + 0.0684517i \(0.0218059\pi\)
\(878\) −1839.69 + 3186.43i −0.0707135 + 0.122479i
\(879\) 0 0
\(880\) −21610.8 37430.9i −0.827839 1.43386i
\(881\) 1889.31 0.0722502 0.0361251 0.999347i \(-0.488499\pi\)
0.0361251 + 0.999347i \(0.488499\pi\)
\(882\) 0 0
\(883\) −1778.37 −0.0677768 −0.0338884 0.999426i \(-0.510789\pi\)
−0.0338884 + 0.999426i \(0.510789\pi\)
\(884\) 19983.3 + 34612.1i 0.760308 + 1.31689i
\(885\) 0 0
\(886\) −17728.6 + 30706.8i −0.672239 + 1.16435i
\(887\) 11492.1 19904.8i 0.435023 0.753482i −0.562274 0.826951i \(-0.690073\pi\)
0.997298 + 0.0734685i \(0.0234068\pi\)
\(888\) 0 0
\(889\) −6674.11 11559.9i −0.251791 0.436115i
\(890\) −26412.3 −0.994766
\(891\) 0 0
\(892\) 22363.4 0.839441
\(893\) 4889.54 + 8468.93i 0.183228 + 0.317359i
\(894\) 0 0
\(895\) −2059.93 + 3567.91i −0.0769340 + 0.133254i
\(896\) 9702.67 16805.5i 0.361767 0.626600i
\(897\) 0 0
\(898\) −25895.0 44851.4i −0.962279 1.66672i
\(899\) 17183.4 0.637485
\(900\) 0 0
\(901\) 26170.3 0.967658
\(902\) 16008.5 + 27727.6i 0.590938 + 1.02353i
\(903\) 0 0
\(904\) −43151.8 + 74741.1i −1.58762 + 2.74984i
\(905\) 11008.9 19067.9i 0.404362 0.700375i
\(906\) 0 0
\(907\) −22705.0 39326.3i −0.831211 1.43970i −0.897078 0.441872i \(-0.854315\pi\)
0.0658671 0.997828i \(-0.479019\pi\)
\(908\) 77377.5 2.82804
\(909\) 0 0
\(910\) 12901.4 0.469973
\(911\) −15390.9 26657.8i −0.559740 0.969497i −0.997518 0.0704143i \(-0.977568\pi\)
0.437778 0.899083i \(-0.355765\pi\)
\(912\) 0 0
\(913\) 10898.0 18875.8i 0.395038 0.684226i
\(914\) −11807.7 + 20451.5i −0.427311 + 0.740125i
\(915\) 0 0
\(916\) −1466.13 2539.41i −0.0528845 0.0915986i
\(917\) 18592.1 0.669538
\(918\) 0 0
\(919\) −22457.3 −0.806093 −0.403046 0.915180i \(-0.632049\pi\)
−0.403046 + 0.915180i \(0.632049\pi\)
\(920\) −5858.33 10146.9i −0.209938 0.363624i
\(921\) 0 0
\(922\) 50336.3 87185.0i 1.79798 3.11419i
\(923\) −10410.1 + 18030.8i −0.371238 + 0.643002i
\(924\) 0 0
\(925\) 663.022 + 1148.39i 0.0235676 + 0.0408203i
\(926\) −89259.1 −3.16764
\(927\) 0 0
\(928\) −26621.8 −0.941706
\(929\) −21827.1 37805.7i −0.770855 1.33516i −0.937095 0.349075i \(-0.886496\pi\)
0.166240 0.986085i \(-0.446837\pi\)
\(930\) 0 0
\(931\) 9048.22 15672.0i 0.318521 0.551695i
\(932\) 13026.9 22563.2i 0.457843 0.793007i
\(933\) 0 0
\(934\) 3635.63 + 6297.10i 0.127368 + 0.220607i
\(935\) 12812.4 0.448138
\(936\) 0 0
\(937\) −41123.3 −1.43377 −0.716884 0.697193i \(-0.754432\pi\)
−0.716884 + 0.697193i \(0.754432\pi\)
\(938\) −1032.49 1788.32i −0.0359401 0.0622501i
\(939\) 0 0
\(940\) 4447.50 7703.30i 0.154321 0.267291i
\(941\) 11038.9 19119.9i 0.382419 0.662370i −0.608988 0.793179i \(-0.708424\pi\)
0.991408 + 0.130810i \(0.0417576\pi\)
\(942\) 0 0
\(943\) 2308.80 + 3998.95i 0.0797293 + 0.138095i
\(944\) −117088. −4.03697
\(945\) 0 0
\(946\) −40949.9 −1.40740
\(947\) 4308.20 + 7462.03i 0.147833 + 0.256054i 0.930426 0.366479i \(-0.119437\pi\)
−0.782593 + 0.622533i \(0.786104\pi\)
\(948\) 0 0
\(949\) 15087.3 26131.9i 0.516073 0.893864i
\(950\) −7397.77 + 12813.3i −0.252648 + 0.437599i
\(951\) 0 0
\(952\) 23892.5 + 41382.9i 0.813402 + 1.40885i
\(953\) 29558.0 1.00470 0.502350 0.864664i \(-0.332469\pi\)
0.502350 + 0.864664i \(0.332469\pi\)
\(954\) 0 0
\(955\) 15234.6 0.516211
\(956\) 42731.7 + 74013.5i 1.44565 + 2.50394i
\(957\) 0 0
\(958\) 538.836 933.291i 0.0181722 0.0314752i
\(959\) −10391.9 + 17999.3i −0.349919 + 0.606077i
\(960\) 0 0
\(961\) −28814.0 49907.3i −0.967204 1.67525i
\(962\) 10187.9 0.341448
\(963\) 0 0
\(964\) 46244.0 1.54504
\(965\) −4727.26 8187.86i −0.157695 0.273136i
\(966\) 0 0
\(967\) −22288.0 + 38603.9i −0.741192 + 1.28378i 0.210761 + 0.977538i \(0.432406\pi\)
−0.951953 + 0.306244i \(0.900928\pi\)
\(968\) −28368.8 + 49136.2i −0.941949 + 1.63150i
\(969\) 0 0
\(970\) −11712.9 20287.4i −0.387711 0.671534i
\(971\) −43702.8 −1.44438 −0.722188 0.691696i \(-0.756864\pi\)
−0.722188 + 0.691696i \(0.756864\pi\)
\(972\) 0 0
\(973\) 7247.56 0.238793
\(974\) −50394.4 87285.6i −1.65784 2.87147i
\(975\) 0 0
\(976\) −4423.47 + 7661.68i −0.145074 + 0.251275i
\(977\) 22670.9 39267.1i 0.742381 1.28584i −0.209027 0.977910i \(-0.567030\pi\)
0.951408 0.307932i \(-0.0996369\pi\)
\(978\) 0 0
\(979\) 23316.9 + 40386.1i 0.761197 + 1.31843i
\(980\) −16460.4 −0.536540
\(981\) 0 0
\(982\) −62256.8 −2.02311
\(983\) 3680.26 + 6374.40i 0.119412 + 0.206828i 0.919535 0.393009i \(-0.128566\pi\)
−0.800123 + 0.599836i \(0.795232\pi\)
\(984\) 0 0
\(985\) 9130.01 15813.6i 0.295336 0.511538i
\(986\) 8434.73 14609.4i 0.272431 0.471864i
\(987\) 0 0
\(988\) 40744.1 + 70570.8i 1.31199 + 2.27242i
\(989\) −5905.91 −0.189886
\(990\) 0 0
\(991\) 33328.4 1.06833 0.534164 0.845381i \(-0.320627\pi\)
0.534164 + 0.845381i \(0.320627\pi\)
\(992\) 67717.8 + 117291.i 2.16738 + 3.75402i
\(993\) 0 0
\(994\) −20571.8 + 35631.3i −0.656435 + 1.13698i
\(995\) −8043.15 + 13931.1i −0.256266 + 0.443866i
\(996\) 0 0
\(997\) 17665.8 + 30598.1i 0.561166 + 0.971968i 0.997395 + 0.0721326i \(0.0229805\pi\)
−0.436229 + 0.899836i \(0.643686\pi\)
\(998\) 45845.6 1.45412
\(999\) 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 135.4.e.c.91.1 14
3.2 odd 2 45.4.e.c.31.7 yes 14
9.2 odd 6 45.4.e.c.16.7 14
9.4 even 3 405.4.a.n.1.7 7
9.5 odd 6 405.4.a.m.1.1 7
9.7 even 3 inner 135.4.e.c.46.1 14
15.2 even 4 225.4.k.d.49.2 28
15.8 even 4 225.4.k.d.49.13 28
15.14 odd 2 225.4.e.d.76.1 14
45.2 even 12 225.4.k.d.124.13 28
45.4 even 6 2025.4.a.ba.1.1 7
45.14 odd 6 2025.4.a.bb.1.7 7
45.29 odd 6 225.4.e.d.151.1 14
45.38 even 12 225.4.k.d.124.2 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.7 14 9.2 odd 6
45.4.e.c.31.7 yes 14 3.2 odd 2
135.4.e.c.46.1 14 9.7 even 3 inner
135.4.e.c.91.1 14 1.1 even 1 trivial
225.4.e.d.76.1 14 15.14 odd 2
225.4.e.d.151.1 14 45.29 odd 6
225.4.k.d.49.2 28 15.2 even 4
225.4.k.d.49.13 28 15.8 even 4
225.4.k.d.124.2 28 45.38 even 12
225.4.k.d.124.13 28 45.2 even 12
405.4.a.m.1.1 7 9.5 odd 6
405.4.a.n.1.7 7 9.4 even 3
2025.4.a.ba.1.1 7 45.4 even 6
2025.4.a.bb.1.7 7 45.14 odd 6