Properties

Label 36.5.f.a.31.12
Level $36$
Weight $5$
Character 36.31
Analytic conductor $3.721$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [36,5,Mod(7,36)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(36, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("36.7");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 36.f (of order \(6\), degree \(2\), 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: \(3.72131867102\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.12
Character \(\chi\) \(=\) 36.31
Dual form 36.5.f.a.7.12

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0678484 + 3.99942i) q^{2} +(-2.72970 - 8.57606i) q^{3} +(-15.9908 + 0.542709i) q^{4} +(16.6139 - 28.7760i) q^{5} +(34.1141 - 11.4991i) q^{6} +(39.9759 - 23.0801i) q^{7} +(-3.25547 - 63.9171i) q^{8} +(-66.0975 + 46.8201i) q^{9} +O(q^{10})\) \(q+(0.0678484 + 3.99942i) q^{2} +(-2.72970 - 8.57606i) q^{3} +(-15.9908 + 0.542709i) q^{4} +(16.6139 - 28.7760i) q^{5} +(34.1141 - 11.4991i) q^{6} +(39.9759 - 23.0801i) q^{7} +(-3.25547 - 63.9171i) q^{8} +(-66.0975 + 46.8201i) q^{9} +(116.215 + 64.4935i) q^{10} +(-63.6109 + 36.7258i) q^{11} +(48.3044 + 135.657i) q^{12} +(151.520 - 262.440i) q^{13} +(95.0195 + 158.315i) q^{14} +(-292.136 - 63.9314i) q^{15} +(255.411 - 17.3567i) q^{16} -182.019 q^{17} +(-191.738 - 261.175i) q^{18} +314.215i q^{19} +(-250.052 + 469.168i) q^{20} +(-307.059 - 279.834i) q^{21} +(-151.198 - 251.915i) q^{22} +(-290.919 - 167.962i) q^{23} +(-539.271 + 202.394i) q^{24} +(-239.540 - 414.896i) q^{25} +(1059.89 + 588.185i) q^{26} +(581.958 + 439.051i) q^{27} +(-626.721 + 390.765i) q^{28} +(357.370 + 618.983i) q^{29} +(235.868 - 1172.71i) q^{30} +(985.186 + 568.798i) q^{31} +(86.7460 + 1020.32i) q^{32} +(488.601 + 445.280i) q^{33} +(-12.3497 - 727.971i) q^{34} -1533.80i q^{35} +(1031.54 - 784.562i) q^{36} +1008.45 q^{37} +(-1256.68 + 21.3190i) q^{38} +(-2664.30 - 583.059i) q^{39} +(-1893.37 - 968.231i) q^{40} +(-557.553 + 965.709i) q^{41} +(1098.34 - 1247.04i) q^{42} +(2182.06 - 1259.82i) q^{43} +(997.257 - 621.796i) q^{44} +(249.164 + 2679.89i) q^{45} +(652.014 - 1174.90i) q^{46} +(980.476 - 566.078i) q^{47} +(-846.047 - 2143.04i) q^{48} +(-135.117 + 234.029i) q^{49} +(1643.09 - 986.173i) q^{50} +(496.857 + 1561.00i) q^{51} +(-2280.49 + 4278.85i) q^{52} -1057.77 q^{53} +(-1716.47 + 2357.29i) q^{54} +2440.63i q^{55} +(-1605.36 - 2480.01i) q^{56} +(2694.73 - 857.713i) q^{57} +(-2451.33 + 1471.27i) q^{58} +(878.476 + 507.188i) q^{59} +(4706.18 + 863.769i) q^{60} +(-430.304 - 745.308i) q^{61} +(-2208.02 + 3978.77i) q^{62} +(-1561.69 + 3397.22i) q^{63} +(-4074.80 + 416.161i) q^{64} +(-5034.65 - 8720.27i) q^{65} +(-1747.71 + 1984.33i) q^{66} +(559.041 + 322.762i) q^{67} +(2910.63 - 98.7833i) q^{68} +(-646.331 + 2953.42i) q^{69} +(6134.31 - 104.066i) q^{70} -9567.89i q^{71} +(3207.79 + 4072.34i) q^{72} +1899.10 q^{73} +(68.4216 + 4033.22i) q^{74} +(-2904.30 + 3186.85i) q^{75} +(-170.527 - 5024.55i) q^{76} +(-1695.27 + 2936.29i) q^{77} +(2151.13 - 10695.2i) q^{78} +(-6768.11 + 3907.57i) q^{79} +(3743.90 - 7638.08i) q^{80} +(2176.75 - 6189.38i) q^{81} +(-3900.11 - 2164.37i) q^{82} +(-7052.56 + 4071.80i) q^{83} +(5061.98 + 4308.12i) q^{84} +(-3024.04 + 5237.78i) q^{85} +(5186.58 + 8641.52i) q^{86} +(4332.92 - 4754.46i) q^{87} +(2554.49 + 3946.27i) q^{88} +7653.39 q^{89} +(-10701.1 + 1178.34i) q^{90} -13988.4i q^{91} +(4743.18 + 2527.96i) q^{92} +(2188.78 - 10001.7i) q^{93} +(2330.51 + 3882.93i) q^{94} +(9041.87 + 5220.33i) q^{95} +(8513.52 - 3529.10i) q^{96} +(-6366.75 - 11027.5i) q^{97} +(-945.149 - 524.510i) q^{98} +(2485.01 - 5405.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0678484 + 3.99942i 0.0169621 + 0.999856i
\(3\) −2.72970 8.57606i −0.303300 0.952895i
\(4\) −15.9908 + 0.542709i −0.999425 + 0.0339193i
\(5\) 16.6139 28.7760i 0.664554 1.15104i −0.314852 0.949141i \(-0.601955\pi\)
0.979406 0.201901i \(-0.0647118\pi\)
\(6\) 34.1141 11.4991i 0.947613 0.319419i
\(7\) 39.9759 23.0801i 0.815835 0.471023i −0.0331429 0.999451i \(-0.510552\pi\)
0.848978 + 0.528428i \(0.177218\pi\)
\(8\) −3.25547 63.9171i −0.0508667 0.998705i
\(9\) −66.0975 + 46.8201i −0.816018 + 0.578026i
\(10\) 116.215 + 64.4935i 1.16215 + 0.644935i
\(11\) −63.6109 + 36.7258i −0.525710 + 0.303519i −0.739268 0.673412i \(-0.764828\pi\)
0.213558 + 0.976930i \(0.431495\pi\)
\(12\) 48.3044 + 135.657i 0.335447 + 0.942059i
\(13\) 151.520 262.440i 0.896566 1.55290i 0.0647110 0.997904i \(-0.479387\pi\)
0.831855 0.554993i \(-0.187279\pi\)
\(14\) 95.0195 + 158.315i 0.484793 + 0.807728i
\(15\) −292.136 63.9314i −1.29838 0.284140i
\(16\) 255.411 17.3567i 0.997699 0.0677996i
\(17\) −182.019 −0.629823 −0.314912 0.949121i \(-0.601975\pi\)
−0.314912 + 0.949121i \(0.601975\pi\)
\(18\) −191.738 261.175i −0.591784 0.806096i
\(19\) 314.215i 0.870402i 0.900333 + 0.435201i \(0.143323\pi\)
−0.900333 + 0.435201i \(0.856677\pi\)
\(20\) −250.052 + 469.168i −0.625129 + 1.17292i
\(21\) −307.059 279.834i −0.696278 0.634544i
\(22\) −151.198 251.915i −0.312392 0.520486i
\(23\) −290.919 167.962i −0.549941 0.317509i 0.199157 0.979968i \(-0.436180\pi\)
−0.749098 + 0.662459i \(0.769513\pi\)
\(24\) −539.271 + 202.394i −0.936234 + 0.351378i
\(25\) −239.540 414.896i −0.383265 0.663834i
\(26\) 1059.89 + 588.185i 1.56788 + 0.870096i
\(27\) 581.958 + 439.051i 0.798297 + 0.602265i
\(28\) −626.721 + 390.765i −0.799389 + 0.498424i
\(29\) 357.370 + 618.983i 0.424935 + 0.736008i 0.996414 0.0846079i \(-0.0269638\pi\)
−0.571480 + 0.820616i \(0.693630\pi\)
\(30\) 235.868 1172.71i 0.262075 1.30301i
\(31\) 985.186 + 568.798i 1.02517 + 0.591881i 0.915597 0.402098i \(-0.131719\pi\)
0.109571 + 0.993979i \(0.465052\pi\)
\(32\) 86.7460 + 1020.32i 0.0847129 + 0.996405i
\(33\) 488.601 + 445.280i 0.448669 + 0.408889i
\(34\) −12.3497 727.971i −0.0106831 0.629733i
\(35\) 1533.80i 1.25208i
\(36\) 1031.54 784.562i 0.795942 0.605372i
\(37\) 1008.45 0.736632 0.368316 0.929701i \(-0.379934\pi\)
0.368316 + 0.929701i \(0.379934\pi\)
\(38\) −1256.68 + 21.3190i −0.870277 + 0.0147638i
\(39\) −2664.30 583.059i −1.75168 0.383339i
\(40\) −1893.37 968.231i −1.18336 0.605144i
\(41\) −557.553 + 965.709i −0.331679 + 0.574485i −0.982841 0.184454i \(-0.940948\pi\)
0.651162 + 0.758939i \(0.274282\pi\)
\(42\) 1098.34 1247.04i 0.622643 0.706941i
\(43\) 2182.06 1259.82i 1.18013 0.681349i 0.224087 0.974569i \(-0.428060\pi\)
0.956045 + 0.293220i \(0.0947268\pi\)
\(44\) 997.257 621.796i 0.515112 0.321176i
\(45\) 249.164 + 2679.89i 0.123044 + 1.32340i
\(46\) 652.014 1174.90i 0.308135 0.555248i
\(47\) 980.476 566.078i 0.443855 0.256260i −0.261376 0.965237i \(-0.584176\pi\)
0.705232 + 0.708977i \(0.250843\pi\)
\(48\) −846.047 2143.04i −0.367208 0.930139i
\(49\) −135.117 + 234.029i −0.0562752 + 0.0974714i
\(50\) 1643.09 986.173i 0.657237 0.394469i
\(51\) 496.857 + 1561.00i 0.191025 + 0.600156i
\(52\) −2280.49 + 4278.85i −0.843377 + 1.58241i
\(53\) −1057.77 −0.376566 −0.188283 0.982115i \(-0.560292\pi\)
−0.188283 + 0.982115i \(0.560292\pi\)
\(54\) −1716.47 + 2357.29i −0.588637 + 0.808397i
\(55\) 2440.63i 0.806818i
\(56\) −1605.36 2480.01i −0.511912 0.790820i
\(57\) 2694.73 857.713i 0.829402 0.263993i
\(58\) −2451.33 + 1471.27i −0.728695 + 0.437358i
\(59\) 878.476 + 507.188i 0.252363 + 0.145702i 0.620846 0.783933i \(-0.286789\pi\)
−0.368483 + 0.929635i \(0.620123\pi\)
\(60\) 4706.18 + 863.769i 1.30727 + 0.239936i
\(61\) −430.304 745.308i −0.115642 0.200298i 0.802394 0.596794i \(-0.203559\pi\)
−0.918036 + 0.396497i \(0.870226\pi\)
\(62\) −2208.02 + 3978.77i −0.574407 + 1.03506i
\(63\) −1561.69 + 3397.22i −0.393473 + 0.855937i
\(64\) −4074.80 + 416.161i −0.994825 + 0.101602i
\(65\) −5034.65 8720.27i −1.19163 2.06397i
\(66\) −1747.71 + 1984.33i −0.401220 + 0.455540i
\(67\) 559.041 + 322.762i 0.124536 + 0.0719008i 0.560974 0.827834i \(-0.310427\pi\)
−0.436438 + 0.899734i \(0.643760\pi\)
\(68\) 2910.63 98.7833i 0.629461 0.0213632i
\(69\) −646.331 + 2953.42i −0.135755 + 0.620337i
\(70\) 6134.31 104.066i 1.25190 0.0212379i
\(71\) 9567.89i 1.89801i −0.315254 0.949007i \(-0.602090\pi\)
0.315254 0.949007i \(-0.397910\pi\)
\(72\) 3207.79 + 4072.34i 0.618786 + 0.785560i
\(73\) 1899.10 0.356372 0.178186 0.983997i \(-0.442977\pi\)
0.178186 + 0.983997i \(0.442977\pi\)
\(74\) 68.4216 + 4033.22i 0.0124948 + 0.736526i
\(75\) −2904.30 + 3186.85i −0.516320 + 0.566552i
\(76\) −170.527 5024.55i −0.0295234 0.869902i
\(77\) −1695.27 + 2936.29i −0.285928 + 0.495242i
\(78\) 2151.13 10695.2i 0.353572 1.75793i
\(79\) −6768.11 + 3907.57i −1.08446 + 0.626113i −0.932096 0.362212i \(-0.882022\pi\)
−0.152363 + 0.988325i \(0.548688\pi\)
\(80\) 3743.90 7638.08i 0.584985 1.19345i
\(81\) 2176.75 6189.38i 0.331772 0.943360i
\(82\) −3900.11 2164.37i −0.580028 0.321887i
\(83\) −7052.56 + 4071.80i −1.02374 + 0.591058i −0.915186 0.403032i \(-0.867956\pi\)
−0.108556 + 0.994090i \(0.534623\pi\)
\(84\) 5061.98 + 4308.12i 0.717401 + 0.610562i
\(85\) −3024.04 + 5237.78i −0.418552 + 0.724953i
\(86\) 5186.58 + 8641.52i 0.701269 + 1.16840i
\(87\) 4332.92 4754.46i 0.572456 0.628149i
\(88\) 2554.49 + 3946.27i 0.329867 + 0.509590i
\(89\) 7653.39 0.966215 0.483107 0.875561i \(-0.339508\pi\)
0.483107 + 0.875561i \(0.339508\pi\)
\(90\) −10701.1 + 1178.34i −1.32112 + 0.145474i
\(91\) 13988.4i 1.68921i
\(92\) 4743.18 + 2527.96i 0.560395 + 0.298673i
\(93\) 2188.78 10001.7i 0.253067 1.15640i
\(94\) 2330.51 + 3882.93i 0.263752 + 0.439445i
\(95\) 9041.87 + 5220.33i 1.00187 + 0.578430i
\(96\) 8513.52 3529.10i 0.923776 0.382932i
\(97\) −6366.75 11027.5i −0.676666 1.17202i −0.975979 0.217865i \(-0.930091\pi\)
0.299313 0.954155i \(-0.403243\pi\)
\(98\) −945.149 524.510i −0.0984120 0.0546137i
\(99\) 2485.01 5405.75i 0.253547 0.551551i
\(100\) 4055.61 + 6504.52i 0.405561 + 0.650452i
\(101\) 6873.20 + 11904.7i 0.673777 + 1.16702i 0.976825 + 0.214040i \(0.0686624\pi\)
−0.303048 + 0.952975i \(0.598004\pi\)
\(102\) −6209.41 + 2093.05i −0.596829 + 0.201178i
\(103\) 11251.5 + 6496.03i 1.06056 + 0.612313i 0.925587 0.378536i \(-0.123572\pi\)
0.134971 + 0.990850i \(0.456906\pi\)
\(104\) −17267.7 8830.34i −1.59649 0.816414i
\(105\) −13153.9 + 4186.81i −1.19310 + 0.379756i
\(106\) −71.7682 4230.49i −0.00638734 0.376512i
\(107\) 14891.8i 1.30071i 0.759631 + 0.650354i \(0.225379\pi\)
−0.759631 + 0.650354i \(0.774621\pi\)
\(108\) −9544.25 6704.94i −0.818266 0.574840i
\(109\) 7539.02 0.634544 0.317272 0.948335i \(-0.397233\pi\)
0.317272 + 0.948335i \(0.397233\pi\)
\(110\) −9761.10 + 165.592i −0.806702 + 0.0136853i
\(111\) −2752.76 8648.52i −0.223421 0.701933i
\(112\) 9809.70 6588.76i 0.782023 0.525252i
\(113\) 496.140 859.339i 0.0388550 0.0672988i −0.845944 0.533272i \(-0.820962\pi\)
0.884799 + 0.465973i \(0.154296\pi\)
\(114\) 3613.19 + 10719.2i 0.278023 + 0.824805i
\(115\) −9666.57 + 5581.00i −0.730932 + 0.422004i
\(116\) −6050.56 9704.08i −0.449655 0.721171i
\(117\) 2272.39 + 24440.8i 0.166001 + 1.78543i
\(118\) −1968.86 + 3547.81i −0.141400 + 0.254798i
\(119\) −7276.38 + 4201.02i −0.513832 + 0.296661i
\(120\) −3135.27 + 18880.6i −0.217727 + 1.31115i
\(121\) −4622.94 + 8007.16i −0.315753 + 0.546900i
\(122\) 2951.61 1771.54i 0.198307 0.119023i
\(123\) 9803.93 + 2145.51i 0.648022 + 0.141814i
\(124\) −16062.6 8560.86i −1.04465 0.556767i
\(125\) 4848.57 0.310308
\(126\) −13692.9 6015.38i −0.862488 0.378898i
\(127\) 7123.52i 0.441659i −0.975312 0.220829i \(-0.929124\pi\)
0.975312 0.220829i \(-0.0708764\pi\)
\(128\) −1940.87 16268.6i −0.118461 0.992959i
\(129\) −16760.6 15274.6i −1.00719 0.917889i
\(130\) 34534.5 20727.4i 2.04346 1.22647i
\(131\) −6027.16 3479.78i −0.351212 0.202773i 0.314007 0.949421i \(-0.398329\pi\)
−0.665219 + 0.746648i \(0.731662\pi\)
\(132\) −8054.77 6855.22i −0.462280 0.393435i
\(133\) 7252.12 + 12561.0i 0.409979 + 0.710105i
\(134\) −1252.93 + 2257.74i −0.0697780 + 0.125737i
\(135\) 22302.7 9452.13i 1.22374 0.518635i
\(136\) 592.557 + 11634.1i 0.0320371 + 0.629008i
\(137\) 4244.42 + 7351.56i 0.226140 + 0.391686i 0.956661 0.291204i \(-0.0940559\pi\)
−0.730521 + 0.682891i \(0.760723\pi\)
\(138\) −11855.9 2384.57i −0.622550 0.125214i
\(139\) −18483.9 10671.7i −0.956673 0.552335i −0.0615252 0.998106i \(-0.519596\pi\)
−0.895147 + 0.445770i \(0.852930\pi\)
\(140\) 832.406 + 24526.7i 0.0424697 + 1.25136i
\(141\) −7531.12 6863.39i −0.378810 0.345224i
\(142\) 38266.1 649.166i 1.89774 0.0321943i
\(143\) 22258.7i 1.08850i
\(144\) −16069.4 + 13105.6i −0.774951 + 0.632022i
\(145\) 23749.2 1.12957
\(146\) 128.851 + 7595.32i 0.00604481 + 0.356320i
\(147\) 2375.87 + 519.939i 0.109948 + 0.0240612i
\(148\) −16125.9 + 547.294i −0.736208 + 0.0249860i
\(149\) 6366.78 11027.6i 0.286779 0.496716i −0.686260 0.727356i \(-0.740749\pi\)
0.973039 + 0.230640i \(0.0740821\pi\)
\(150\) −12942.6 11399.3i −0.575228 0.506636i
\(151\) −3061.84 + 1767.75i −0.134285 + 0.0775296i −0.565638 0.824654i \(-0.691370\pi\)
0.431352 + 0.902184i \(0.358037\pi\)
\(152\) 20083.7 1022.92i 0.869276 0.0442745i
\(153\) 12031.0 8522.15i 0.513947 0.364054i
\(154\) −11858.5 6580.88i −0.500021 0.277487i
\(155\) 32735.5 18899.8i 1.36256 0.786674i
\(156\) 42920.7 + 7877.64i 1.76367 + 0.323703i
\(157\) −14870.6 + 25756.6i −0.603292 + 1.04493i 0.389027 + 0.921227i \(0.372811\pi\)
−0.992319 + 0.123706i \(0.960522\pi\)
\(158\) −16087.2 26803.4i −0.644417 1.07368i
\(159\) 2887.40 + 9071.53i 0.114212 + 0.358828i
\(160\) 30801.9 + 14455.2i 1.20320 + 0.564657i
\(161\) −15506.3 −0.598216
\(162\) 24901.7 + 8285.82i 0.948852 + 0.315722i
\(163\) 5903.96i 0.222213i 0.993809 + 0.111106i \(0.0354394\pi\)
−0.993809 + 0.111106i \(0.964561\pi\)
\(164\) 8391.61 15745.0i 0.312002 0.585405i
\(165\) 20930.9 6662.18i 0.768813 0.244708i
\(166\) −16763.4 27929.9i −0.608338 1.01357i
\(167\) −17810.7 10283.0i −0.638628 0.368712i 0.145458 0.989364i \(-0.453535\pi\)
−0.784086 + 0.620652i \(0.786868\pi\)
\(168\) −16886.6 + 20537.3i −0.598305 + 0.727654i
\(169\) −31635.9 54795.0i −1.10766 1.91852i
\(170\) −21153.3 11739.0i −0.731948 0.406195i
\(171\) −14711.6 20768.8i −0.503115 0.710264i
\(172\) −34209.2 + 21329.7i −1.15634 + 0.720987i
\(173\) −3054.99 5291.39i −0.102074 0.176798i 0.810465 0.585787i \(-0.199215\pi\)
−0.912539 + 0.408989i \(0.865881\pi\)
\(174\) 19309.1 + 17006.6i 0.637769 + 0.561719i
\(175\) −19151.7 11057.2i −0.625361 0.361053i
\(176\) −15609.5 + 10484.2i −0.503922 + 0.338463i
\(177\) 1951.70 8918.33i 0.0622969 0.284667i
\(178\) 519.270 + 30609.1i 0.0163890 + 0.966076i
\(179\) 11534.8i 0.360001i 0.983667 + 0.180001i \(0.0576099\pi\)
−0.983667 + 0.180001i \(0.942390\pi\)
\(180\) −5438.72 42718.3i −0.167862 1.31847i
\(181\) −25544.2 −0.779713 −0.389857 0.920876i \(-0.627475\pi\)
−0.389857 + 0.920876i \(0.627475\pi\)
\(182\) 55945.4 949.087i 1.68897 0.0286526i
\(183\) −5217.20 + 5724.78i −0.155789 + 0.170945i
\(184\) −9788.59 + 19141.5i −0.289124 + 0.565380i
\(185\) 16754.2 29019.2i 0.489532 0.847894i
\(186\) 40149.4 + 8075.25i 1.16052 + 0.233416i
\(187\) 11578.4 6684.78i 0.331104 0.191163i
\(188\) −15371.4 + 9584.15i −0.434908 + 0.271168i
\(189\) 33397.7 + 4119.80i 0.934959 + 0.115333i
\(190\) −20264.8 + 36516.5i −0.561353 + 1.01154i
\(191\) −33833.7 + 19533.9i −0.927433 + 0.535454i −0.885999 0.463687i \(-0.846526\pi\)
−0.0414344 + 0.999141i \(0.513193\pi\)
\(192\) 14692.0 + 33809.8i 0.398546 + 0.917148i
\(193\) −13915.2 + 24101.8i −0.373572 + 0.647045i −0.990112 0.140278i \(-0.955200\pi\)
0.616541 + 0.787323i \(0.288534\pi\)
\(194\) 43671.8 26211.5i 1.16037 0.696449i
\(195\) −61042.4 + 66981.2i −1.60532 + 1.76150i
\(196\) 2033.61 3815.64i 0.0529366 0.0993242i
\(197\) −21103.0 −0.543765 −0.271883 0.962330i \(-0.587646\pi\)
−0.271883 + 0.962330i \(0.587646\pi\)
\(198\) 21788.5 + 9571.86i 0.555772 + 0.244155i
\(199\) 5447.97i 0.137572i 0.997631 + 0.0687858i \(0.0219125\pi\)
−0.997631 + 0.0687858i \(0.978087\pi\)
\(200\) −25739.2 + 16661.4i −0.643479 + 0.416535i
\(201\) 1242.02 5675.41i 0.0307422 0.140477i
\(202\) −47145.7 + 28296.5i −1.15542 + 0.693475i
\(203\) 28572.4 + 16496.3i 0.693353 + 0.400308i
\(204\) −8792.31 24692.1i −0.211272 0.593331i
\(205\) 18526.2 + 32088.3i 0.440837 + 0.763553i
\(206\) −25217.0 + 45440.1i −0.594236 + 1.07079i
\(207\) 27093.0 2518.99i 0.632291 0.0587875i
\(208\) 34144.7 69659.8i 0.789217 1.61011i
\(209\) −11539.8 19987.5i −0.264183 0.457579i
\(210\) −17637.3 52324.1i −0.399939 1.18649i
\(211\) 59935.1 + 34603.5i 1.34622 + 0.777241i 0.987712 0.156286i \(-0.0499520\pi\)
0.358509 + 0.933526i \(0.383285\pi\)
\(212\) 16914.6 574.063i 0.376349 0.0127729i
\(213\) −82054.8 + 26117.5i −1.80861 + 0.575668i
\(214\) −59558.7 + 1010.38i −1.30052 + 0.0220627i
\(215\) 83721.5i 1.81117i
\(216\) 26168.3 38626.4i 0.560878 0.827898i
\(217\) 52511.7 1.11516
\(218\) 511.510 + 30151.8i 0.0107632 + 0.634453i
\(219\) −5183.98 16286.8i −0.108088 0.339585i
\(220\) −1324.55 39027.5i −0.0273667 0.806354i
\(221\) −27579.4 + 47769.0i −0.564678 + 0.978051i
\(222\) 34402.3 11596.3i 0.698043 0.235295i
\(223\) −21934.5 + 12663.9i −0.441080 + 0.254658i −0.704056 0.710145i \(-0.748629\pi\)
0.262976 + 0.964802i \(0.415296\pi\)
\(224\) 27016.8 + 38786.1i 0.538441 + 0.773001i
\(225\) 35258.5 + 16208.3i 0.696464 + 0.320163i
\(226\) 3470.52 + 1925.97i 0.0679482 + 0.0377079i
\(227\) 84184.1 48603.7i 1.63372 0.943230i 0.650792 0.759256i \(-0.274437\pi\)
0.982931 0.183975i \(-0.0588964\pi\)
\(228\) −42625.3 + 15178.0i −0.819971 + 0.291974i
\(229\) 42946.4 74385.3i 0.818947 1.41846i −0.0875119 0.996163i \(-0.527892\pi\)
0.906459 0.422294i \(-0.138775\pi\)
\(230\) −22976.6 38282.1i −0.434341 0.723669i
\(231\) 29809.4 + 6523.53i 0.558636 + 0.122253i
\(232\) 38400.2 24857.2i 0.713440 0.461823i
\(233\) −12774.0 −0.235297 −0.117649 0.993055i \(-0.537536\pi\)
−0.117649 + 0.993055i \(0.537536\pi\)
\(234\) −97594.8 + 10746.5i −1.78236 + 0.196262i
\(235\) 37619.0i 0.681194i
\(236\) −14322.8 7633.59i −0.257160 0.137058i
\(237\) 51986.4 + 47377.2i 0.925536 + 0.843476i
\(238\) −17295.3 28816.3i −0.305334 0.508726i
\(239\) −91748.4 52971.0i −1.60621 0.927347i −0.990207 0.139605i \(-0.955417\pi\)
−0.616005 0.787742i \(-0.711250\pi\)
\(240\) −75724.3 11258.3i −1.31466 0.195456i
\(241\) 5089.73 + 8815.67i 0.0876316 + 0.151782i 0.906510 0.422185i \(-0.138737\pi\)
−0.818878 + 0.573968i \(0.805404\pi\)
\(242\) −32337.7 17945.8i −0.552177 0.306431i
\(243\) −59022.4 1772.80i −0.999549 0.0300225i
\(244\) 7285.38 + 11684.5i 0.122369 + 0.196260i
\(245\) 4489.62 + 7776.25i 0.0747958 + 0.129550i
\(246\) −7915.61 + 39355.6i −0.130802 + 0.650334i
\(247\) 82462.6 + 47609.8i 1.35165 + 0.780373i
\(248\) 33148.7 64822.0i 0.538968 1.05395i
\(249\) 54171.3 + 49368.4i 0.873717 + 0.796251i
\(250\) 328.967 + 19391.5i 0.00526347 + 0.310264i
\(251\) 21848.1i 0.346790i 0.984852 + 0.173395i \(0.0554738\pi\)
−0.984852 + 0.173395i \(0.944526\pi\)
\(252\) 23129.0 55171.7i 0.364214 0.868791i
\(253\) 24674.2 0.385479
\(254\) 28490.0 483.319i 0.441595 0.00749146i
\(255\) 53174.2 + 11636.7i 0.817751 + 0.178958i
\(256\) 64933.5 8866.17i 0.990806 0.135287i
\(257\) −27780.7 + 48117.6i −0.420608 + 0.728514i −0.995999 0.0893643i \(-0.971516\pi\)
0.575391 + 0.817878i \(0.304850\pi\)
\(258\) 59952.4 68069.2i 0.900673 1.02261i
\(259\) 40313.7 23275.1i 0.600971 0.346971i
\(260\) 85240.6 + 136712.i 1.26096 + 2.02236i
\(261\) −52602.1 24181.1i −0.772186 0.354973i
\(262\) 13508.2 24341.3i 0.196786 0.354601i
\(263\) −21792.0 + 12581.6i −0.315055 + 0.181897i −0.649186 0.760629i \(-0.724890\pi\)
0.334131 + 0.942527i \(0.391557\pi\)
\(264\) 26870.4 32679.6i 0.385537 0.468887i
\(265\) −17573.7 + 30438.5i −0.250248 + 0.433443i
\(266\) −49744.9 + 29856.6i −0.703049 + 0.421965i
\(267\) −20891.4 65635.9i −0.293053 0.920701i
\(268\) −9114.67 4857.83i −0.126903 0.0676352i
\(269\) 54154.0 0.748386 0.374193 0.927351i \(-0.377920\pi\)
0.374193 + 0.927351i \(0.377920\pi\)
\(270\) 39316.3 + 88556.7i 0.539318 + 1.21477i
\(271\) 94942.5i 1.29277i 0.763011 + 0.646386i \(0.223720\pi\)
−0.763011 + 0.646386i \(0.776280\pi\)
\(272\) −46489.6 + 3159.25i −0.628374 + 0.0427017i
\(273\) −119965. + 38184.0i −1.60964 + 0.512338i
\(274\) −29114.0 + 17474.0i −0.387794 + 0.232751i
\(275\) 30474.7 + 17594.6i 0.402972 + 0.232656i
\(276\) 8732.50 47578.4i 0.114636 0.624585i
\(277\) −54019.7 93564.9i −0.704033 1.21942i −0.967039 0.254627i \(-0.918047\pi\)
0.263006 0.964794i \(-0.415286\pi\)
\(278\) 41426.4 74648.9i 0.536029 0.965904i
\(279\) −91749.5 + 8530.45i −1.17868 + 0.109588i
\(280\) −98036.0 + 4993.24i −1.25046 + 0.0636893i
\(281\) 34463.0 + 59691.7i 0.436456 + 0.755964i 0.997413 0.0718805i \(-0.0229000\pi\)
−0.560957 + 0.827845i \(0.689567\pi\)
\(282\) 26938.7 30585.8i 0.338749 0.384611i
\(283\) −39154.2 22605.7i −0.488884 0.282257i 0.235228 0.971940i \(-0.424416\pi\)
−0.724111 + 0.689683i \(0.757750\pi\)
\(284\) 5192.58 + 152998.i 0.0643793 + 1.89692i
\(285\) 20088.2 91793.5i 0.247316 1.13011i
\(286\) −89022.0 + 1510.22i −1.08834 + 0.0184632i
\(287\) 51473.5i 0.624914i
\(288\) −53505.2 63379.1i −0.645076 0.764119i
\(289\) −50390.1 −0.603323
\(290\) 1611.34 + 94983.0i 0.0191598 + 1.12941i
\(291\) −77193.4 + 84703.5i −0.911579 + 1.00027i
\(292\) −30368.2 + 1030.66i −0.356167 + 0.0120879i
\(293\) 35853.6 62100.3i 0.417636 0.723366i −0.578065 0.815990i \(-0.696192\pi\)
0.995701 + 0.0926242i \(0.0295255\pi\)
\(294\) −1918.26 + 9537.40i −0.0221928 + 0.110341i
\(295\) 29189.7 16852.7i 0.335418 0.193654i
\(296\) −3282.98 64457.2i −0.0374701 0.735679i
\(297\) −53143.3 6555.55i −0.602471 0.0743184i
\(298\) 44536.0 + 24715.3i 0.501509 + 0.278313i
\(299\) −88159.9 + 50899.1i −0.986117 + 0.569335i
\(300\) 44712.5 52536.5i 0.496806 0.583739i
\(301\) 58153.4 100725.i 0.641862 1.11174i
\(302\) −7277.73 12125.6i −0.0797962 0.132951i
\(303\) 83333.8 91441.2i 0.907687 0.995994i
\(304\) 5453.74 + 80254.0i 0.0590129 + 0.868400i
\(305\) −28596.0 −0.307401
\(306\) 34900.0 + 47538.8i 0.372720 + 0.507698i
\(307\) 95866.9i 1.01717i −0.861013 0.508583i \(-0.830170\pi\)
0.861013 0.508583i \(-0.169830\pi\)
\(308\) 25515.2 47873.7i 0.268966 0.504656i
\(309\) 24997.2 114225.i 0.261803 1.19632i
\(310\) 77809.5 + 129641.i 0.809673 + 1.34902i
\(311\) 20844.0 + 12034.3i 0.215506 + 0.124423i 0.603868 0.797085i \(-0.293626\pi\)
−0.388362 + 0.921507i \(0.626959\pi\)
\(312\) −28593.9 + 172193.i −0.293741 + 1.76891i
\(313\) 49654.5 + 86004.2i 0.506839 + 0.877871i 0.999969 + 0.00791525i \(0.00251953\pi\)
−0.493130 + 0.869956i \(0.664147\pi\)
\(314\) −104020. 57726.1i −1.05502 0.585481i
\(315\) 71812.6 + 101380.i 0.723735 + 1.02172i
\(316\) 106107. 66158.2i 1.06260 0.662536i
\(317\) −29720.5 51477.4i −0.295759 0.512269i 0.679402 0.733766i \(-0.262239\pi\)
−0.975161 + 0.221497i \(0.928906\pi\)
\(318\) −36085.0 + 12163.4i −0.356839 + 0.120282i
\(319\) −45465.2 26249.4i −0.446785 0.257951i
\(320\) −55722.7 + 124171.i −0.544167 + 1.21261i
\(321\) 127713. 40650.2i 1.23944 0.394505i
\(322\) −1052.08 62016.5i −0.0101470 0.598129i
\(323\) 57193.1i 0.548200i
\(324\) −31449.0 + 100154.i −0.299583 + 0.954070i
\(325\) −145180. −1.37449
\(326\) −23612.5 + 400.574i −0.222181 + 0.00376919i
\(327\) −20579.3 64655.1i −0.192457 0.604654i
\(328\) 63540.5 + 32493.3i 0.590613 + 0.302028i
\(329\) 26130.3 45259.0i 0.241408 0.418132i
\(330\) 28065.0 + 83259.7i 0.257713 + 0.764552i
\(331\) −79852.0 + 46102.6i −0.728836 + 0.420794i −0.817996 0.575223i \(-0.804915\pi\)
0.0891599 + 0.996017i \(0.471582\pi\)
\(332\) 110566. 68938.8i 1.00310 0.625442i
\(333\) −66656.0 + 47215.7i −0.601105 + 0.425793i
\(334\) 39917.7 71930.3i 0.357827 0.644791i
\(335\) 18575.7 10724.7i 0.165522 0.0955639i
\(336\) −83283.1 66143.2i −0.737698 0.585877i
\(337\) −22954.2 + 39757.8i −0.202117 + 0.350076i −0.949210 0.314643i \(-0.898115\pi\)
0.747094 + 0.664719i \(0.231449\pi\)
\(338\) 217002. 130243.i 1.89946 1.14004i
\(339\) −8724.05 1909.18i −0.0759135 0.0166130i
\(340\) 45514.1 85397.5i 0.393721 0.738733i
\(341\) −83558.1 −0.718588
\(342\) 82065.2 60247.1i 0.701628 0.515091i
\(343\) 123305.i 1.04807i
\(344\) −87627.4 135370.i −0.740497 1.14395i
\(345\) 74249.8 + 67666.6i 0.623817 + 0.568508i
\(346\) 20955.3 12577.2i 0.175041 0.105059i
\(347\) 131615. + 75987.9i 1.09306 + 0.631081i 0.934391 0.356250i \(-0.115945\pi\)
0.158674 + 0.987331i \(0.449278\pi\)
\(348\) −66706.5 + 78379.1i −0.550820 + 0.647205i
\(349\) 93645.6 + 162199.i 0.768841 + 1.33167i 0.938192 + 0.346116i \(0.112500\pi\)
−0.169350 + 0.985556i \(0.554167\pi\)
\(350\) 42923.2 77346.0i 0.350393 0.631396i
\(351\) 203402. 86204.1i 1.65098 0.699703i
\(352\) −42990.0 61717.6i −0.346962 0.498108i
\(353\) −22707.8 39331.1i −0.182232 0.315636i 0.760408 0.649446i \(-0.224999\pi\)
−0.942640 + 0.333810i \(0.891666\pi\)
\(354\) 35800.6 + 7200.58i 0.285683 + 0.0574594i
\(355\) −275326. 158960.i −2.18469 1.26133i
\(356\) −122384. + 4153.56i −0.965659 + 0.0327733i
\(357\) 55890.5 + 50935.1i 0.438532 + 0.399651i
\(358\) −46132.5 + 782.617i −0.359949 + 0.00610637i
\(359\) 71504.2i 0.554808i −0.960753 0.277404i \(-0.910526\pi\)
0.960753 0.277404i \(-0.0894740\pi\)
\(360\) 170480. 24650.1i 1.31543 0.190202i
\(361\) 31589.8 0.242400
\(362\) −1733.13 102162.i −0.0132256 0.779601i
\(363\) 81289.1 + 17789.4i 0.616906 + 0.135005i
\(364\) 7591.61 + 223685.i 0.0572969 + 1.68824i
\(365\) 31551.4 54648.7i 0.236828 0.410199i
\(366\) −23249.8 20477.4i −0.173563 0.152867i
\(367\) −57406.0 + 33143.4i −0.426211 + 0.246073i −0.697731 0.716360i \(-0.745807\pi\)
0.271520 + 0.962433i \(0.412474\pi\)
\(368\) −77219.2 37850.0i −0.570203 0.279492i
\(369\) −8361.81 89935.6i −0.0614112 0.660509i
\(370\) 117197. + 65038.4i 0.856076 + 0.475080i
\(371\) −42285.5 + 24413.5i −0.307216 + 0.177371i
\(372\) −29572.3 + 161122.i −0.213697 + 1.16431i
\(373\) −71784.3 + 124334.i −0.515955 + 0.893660i 0.483873 + 0.875138i \(0.339229\pi\)
−0.999828 + 0.0185223i \(0.994104\pi\)
\(374\) 27520.9 + 45853.3i 0.196752 + 0.327814i
\(375\) −13235.1 41581.6i −0.0941165 0.295691i
\(376\) −39374.0 60826.4i −0.278506 0.430245i
\(377\) 216594. 1.52393
\(378\) −14210.9 + 133851.i −0.0994574 + 0.936781i
\(379\) 183178.i 1.27525i −0.770348 0.637624i \(-0.779917\pi\)
0.770348 0.637624i \(-0.220083\pi\)
\(380\) −147420. 78570.1i −1.02091 0.544114i
\(381\) −61091.7 + 19445.1i −0.420855 + 0.133955i
\(382\) −80419.9 133990.i −0.551108 0.918218i
\(383\) 15175.9 + 8761.79i 0.103456 + 0.0597303i 0.550835 0.834614i \(-0.314309\pi\)
−0.447379 + 0.894344i \(0.647643\pi\)
\(384\) −134223. + 61053.5i −0.910256 + 0.414046i
\(385\) 56329.9 + 97566.3i 0.380030 + 0.658231i
\(386\) −97337.4 54017.4i −0.653288 0.362543i
\(387\) −85244.2 + 185435.i −0.569171 + 1.23814i
\(388\) 107794. + 172884.i 0.716031 + 1.14839i
\(389\) −38430.8 66564.0i −0.253968 0.439886i 0.710646 0.703549i \(-0.248403\pi\)
−0.964615 + 0.263663i \(0.915069\pi\)
\(390\) −272028. 239590.i −1.78848 1.57521i
\(391\) 52952.8 + 30572.3i 0.346366 + 0.199974i
\(392\) 15398.3 + 7874.40i 0.100208 + 0.0512443i
\(393\) −13390.5 + 61188.0i −0.0866983 + 0.396169i
\(394\) −1431.80 84399.8i −0.00922340 0.543687i
\(395\) 259679.i 1.66434i
\(396\) −36803.6 + 87790.9i −0.234693 + 0.559834i
\(397\) −73295.7 −0.465047 −0.232524 0.972591i \(-0.574698\pi\)
−0.232524 + 0.972591i \(0.574698\pi\)
\(398\) −21788.8 + 369.636i −0.137552 + 0.00233350i
\(399\) 87928.1 96482.5i 0.552309 0.606042i
\(400\) −68382.4 101811.i −0.427390 0.636321i
\(401\) −142274. + 246426.i −0.884784 + 1.53249i −0.0388226 + 0.999246i \(0.512361\pi\)
−0.845961 + 0.533244i \(0.820973\pi\)
\(402\) 22782.6 + 4582.28i 0.140978 + 0.0283550i
\(403\) 298550. 172368.i 1.83826 1.06132i
\(404\) −116369. 186636.i −0.712973 1.14349i
\(405\) −141942. 165468.i −0.865366 1.00880i
\(406\) −64037.0 + 115392.i −0.388489 + 0.700044i
\(407\) −64148.4 + 37036.1i −0.387255 + 0.223582i
\(408\) 98157.5 36839.5i 0.589662 0.221306i
\(409\) 56577.0 97994.2i 0.338215 0.585806i −0.645882 0.763437i \(-0.723510\pi\)
0.984097 + 0.177632i \(0.0568435\pi\)
\(410\) −127078. + 76271.3i −0.755965 + 0.453725i
\(411\) 51461.4 56468.0i 0.304648 0.334286i
\(412\) −183445. 97770.4i −1.08072 0.575988i
\(413\) 46823.9 0.274516
\(414\) 11912.7 + 108186.i 0.0695040 + 0.631203i
\(415\) 270593.i 1.57116i
\(416\) 280916. + 131833.i 1.62327 + 0.761793i
\(417\) −41065.4 + 187649.i −0.236159 + 1.07913i
\(418\) 79155.6 47508.7i 0.453032 0.271907i
\(419\) 237314. + 137013.i 1.35175 + 0.780431i 0.988494 0.151260i \(-0.0483331\pi\)
0.363252 + 0.931691i \(0.381666\pi\)
\(420\) 208070. 74089.2i 1.17953 0.420007i
\(421\) −6241.89 10811.3i −0.0352170 0.0609976i 0.847880 0.530189i \(-0.177879\pi\)
−0.883097 + 0.469191i \(0.844546\pi\)
\(422\) −134328. + 242054.i −0.754294 + 1.35921i
\(423\) −38303.1 + 83322.3i −0.214069 + 0.465673i
\(424\) 3443.55 + 67609.9i 0.0191547 + 0.376078i
\(425\) 43600.9 + 75518.9i 0.241389 + 0.418098i
\(426\) −110022. 326400.i −0.606263 1.79858i
\(427\) −34403.6 19862.9i −0.188690 0.108940i
\(428\) −8081.91 238132.i −0.0441191 1.29996i
\(429\) 190892. 60759.5i 1.03722 0.330141i
\(430\) 334838. 5680.37i 1.81091 0.0307213i
\(431\) 119855.i 0.645211i −0.946533 0.322606i \(-0.895441\pi\)
0.946533 0.322606i \(-0.104559\pi\)
\(432\) 156259. + 102038.i 0.837293 + 0.546755i
\(433\) −282465. −1.50657 −0.753284 0.657696i \(-0.771531\pi\)
−0.753284 + 0.657696i \(0.771531\pi\)
\(434\) 3562.83 + 210016.i 0.0189154 + 1.11500i
\(435\) −64828.1 203674.i −0.342598 1.07636i
\(436\) −120555. + 4091.49i −0.634179 + 0.0215233i
\(437\) 52776.3 91411.2i 0.276360 0.478670i
\(438\) 64786.2 21838.0i 0.337703 0.113832i
\(439\) −148459. + 85712.8i −0.770331 + 0.444751i −0.832993 0.553284i \(-0.813374\pi\)
0.0626618 + 0.998035i \(0.480041\pi\)
\(440\) 155998. 7945.39i 0.805774 0.0410402i
\(441\) −2026.39 21794.9i −0.0104195 0.112067i
\(442\) −192920. 107061.i −0.987488 0.548007i
\(443\) −71888.2 + 41504.7i −0.366311 + 0.211490i −0.671846 0.740691i \(-0.734498\pi\)
0.305535 + 0.952181i \(0.401165\pi\)
\(444\) 48712.5 + 136803.i 0.247101 + 0.693951i
\(445\) 127152. 220234.i 0.642102 1.11215i
\(446\) −52136.4 86866.0i −0.262103 0.436697i
\(447\) −111953. 24499.9i −0.560298 0.122616i
\(448\) −153289. + 110683.i −0.763757 + 0.551476i
\(449\) 252767. 1.25380 0.626898 0.779101i \(-0.284324\pi\)
0.626898 + 0.779101i \(0.284324\pi\)
\(450\) −62431.5 + 142113.i −0.308304 + 0.701794i
\(451\) 81906.2i 0.402683i
\(452\) −7467.29 + 14010.8i −0.0365499 + 0.0685780i
\(453\) 23518.2 + 21433.1i 0.114606 + 0.104445i
\(454\) 200099. + 333390.i 0.970806 + 1.61749i
\(455\) −402530. 232401.i −1.94435 1.12257i
\(456\) −63595.2 169447.i −0.305840 0.814900i
\(457\) 9489.80 + 16436.8i 0.0454386 + 0.0787019i 0.887850 0.460133i \(-0.152198\pi\)
−0.842412 + 0.538835i \(0.818865\pi\)
\(458\) 300412. + 166714.i 1.43214 + 0.794769i
\(459\) −105927. 79915.6i −0.502786 0.379320i
\(460\) 151547. 94490.7i 0.716197 0.446554i
\(461\) 97075.9 + 168140.i 0.456783 + 0.791171i 0.998789 0.0492038i \(-0.0156684\pi\)
−0.542006 + 0.840375i \(0.682335\pi\)
\(462\) −24067.8 + 119663.i −0.112760 + 0.560630i
\(463\) −86227.9 49783.7i −0.402240 0.232234i 0.285210 0.958465i \(-0.407937\pi\)
−0.687450 + 0.726232i \(0.741270\pi\)
\(464\) 102020. + 151892.i 0.473858 + 0.705504i
\(465\) −251444. 229150.i −1.16288 1.05978i
\(466\) −866.698 51088.8i −0.00399113 0.235263i
\(467\) 126990.i 0.582287i −0.956679 0.291144i \(-0.905964\pi\)
0.956679 0.291144i \(-0.0940358\pi\)
\(468\) −49601.6 389594.i −0.226466 1.77877i
\(469\) 29797.6 0.135468
\(470\) 150454. 2552.38i 0.681096 0.0115545i
\(471\) 261482. + 57223.0i 1.17869 + 0.257946i
\(472\) 29558.2 57800.8i 0.132676 0.259448i
\(473\) −92535.3 + 160276.i −0.413605 + 0.716384i
\(474\) −185954. + 211130.i −0.827655 + 0.939710i
\(475\) 130367. 75267.2i 0.577802 0.333594i
\(476\) 114075. 71126.6i 0.503474 0.313919i
\(477\) 69916.2 49525.1i 0.307285 0.217665i
\(478\) 205628. 370535.i 0.899969 1.62171i
\(479\) 48437.8 27965.6i 0.211112 0.121886i −0.390716 0.920511i \(-0.627773\pi\)
0.601828 + 0.798626i \(0.294439\pi\)
\(480\) 39888.8 303618.i 0.173129 1.31778i
\(481\) 152800. 264657.i 0.660439 1.14391i
\(482\) −34912.3 + 20954.1i −0.150274 + 0.0901935i
\(483\) 42327.7 + 132983.i 0.181439 + 0.570037i
\(484\) 69578.9 130550.i 0.297021 0.557295i
\(485\) −423105. −1.79872
\(486\) 3085.61 236176.i 0.0130638 0.999915i
\(487\) 274913.i 1.15914i 0.814921 + 0.579572i \(0.196780\pi\)
−0.814921 + 0.579572i \(0.803220\pi\)
\(488\) −46237.1 + 29930.1i −0.194156 + 0.125681i
\(489\) 50632.7 16116.1i 0.211745 0.0673971i
\(490\) −30795.9 + 18483.5i −0.128263 + 0.0769825i
\(491\) −28037.6 16187.5i −0.116299 0.0671455i 0.440722 0.897644i \(-0.354723\pi\)
−0.557021 + 0.830498i \(0.688056\pi\)
\(492\) −157937. 28987.7i −0.652460 0.119752i
\(493\) −65048.1 112667.i −0.267634 0.463555i
\(494\) −184817. + 333033.i −0.757334 + 1.36469i
\(495\) −114270. 161319.i −0.466362 0.658379i
\(496\) 261500. + 128178.i 1.06294 + 0.521013i
\(497\) −220828. 382485.i −0.894008 1.54847i
\(498\) −193770. + 220004.i −0.781316 + 0.887097i
\(499\) 251446. + 145172.i 1.00982 + 0.583019i 0.911139 0.412100i \(-0.135204\pi\)
0.0986806 + 0.995119i \(0.468538\pi\)
\(500\) −77532.4 + 2631.36i −0.310130 + 0.0105254i
\(501\) −39569.8 + 180815.i −0.157648 + 0.720376i
\(502\) −87380.0 + 1482.36i −0.346740 + 0.00588229i
\(503\) 9486.90i 0.0374963i 0.999824 + 0.0187481i \(0.00596807\pi\)
−0.999824 + 0.0187481i \(0.994032\pi\)
\(504\) 222224. + 88759.5i 0.874844 + 0.349425i
\(505\) 456761. 1.79104
\(506\) 1674.10 + 98682.4i 0.00653854 + 0.385424i
\(507\) −383568. + 420885.i −1.49220 + 1.63737i
\(508\) 3865.99 + 113911.i 0.0149808 + 0.441405i
\(509\) 146376. 253530.i 0.564980 0.978575i −0.432071 0.901839i \(-0.642217\pi\)
0.997052 0.0767350i \(-0.0244496\pi\)
\(510\) −42932.4 + 213456.i −0.165061 + 0.820669i
\(511\) 75918.5 43831.5i 0.290741 0.167859i
\(512\) 39865.2 + 259095.i 0.152074 + 0.988369i
\(513\) −137956. + 182860.i −0.524213 + 0.694839i
\(514\) −194328. 107842.i −0.735544 0.408190i
\(515\) 373860. 215848.i 1.40960 0.813831i
\(516\) 276305. + 235157.i 1.03774 + 0.883197i
\(517\) −41579.3 + 72017.4i −0.155559 + 0.269437i
\(518\) 95822.3 + 159652.i 0.357114 + 0.594999i
\(519\) −37040.1 + 40643.7i −0.137511 + 0.150889i
\(520\) −540985. + 350189.i −2.00068 + 1.29508i
\(521\) −344253. −1.26824 −0.634120 0.773234i \(-0.718638\pi\)
−0.634120 + 0.773234i \(0.718638\pi\)
\(522\) 93141.6 212019.i 0.341824 0.778096i
\(523\) 79326.1i 0.290010i 0.989431 + 0.145005i \(0.0463198\pi\)
−0.989431 + 0.145005i \(0.953680\pi\)
\(524\) 98267.5 + 52373.4i 0.357888 + 0.190743i
\(525\) −42549.1 + 194429.i −0.154373 + 0.705411i
\(526\) −51797.9 86302.0i −0.187215 0.311924i
\(527\) −179323. 103532.i −0.645675 0.372780i
\(528\) 132523. + 105249.i 0.475359 + 0.377529i
\(529\) −83497.9 144623.i −0.298376 0.516803i
\(530\) −122929. 68219.5i −0.437625 0.242860i
\(531\) −81811.7 + 7606.48i −0.290152 + 0.0269771i
\(532\) −122784. 196925.i −0.433830 0.695790i
\(533\) 168960. + 292648.i 0.594744 + 1.03013i
\(534\) 261088. 88007.0i 0.915598 0.308628i
\(535\) 428527. + 247410.i 1.49717 + 0.864391i
\(536\) 18810.1 36783.1i 0.0654729 0.128032i
\(537\) 98923.0 31486.5i 0.343043 0.109188i
\(538\) 3674.26 + 216585.i 0.0126942 + 0.748278i
\(539\) 19849.0i 0.0683223i
\(540\) −351508. + 163251.i −1.20545 + 0.559845i
\(541\) 167330. 0.571715 0.285857 0.958272i \(-0.407722\pi\)
0.285857 + 0.958272i \(0.407722\pi\)
\(542\) −379715. + 6441.69i −1.29259 + 0.0219281i
\(543\) 69728.0 + 219068.i 0.236487 + 0.742985i
\(544\) −15789.4 185717.i −0.0533541 0.627559i
\(545\) 125252. 216943.i 0.421689 0.730387i
\(546\) −160854. 477200.i −0.539567 1.60072i
\(547\) −246877. + 142535.i −0.825100 + 0.476372i −0.852172 0.523262i \(-0.824715\pi\)
0.0270722 + 0.999633i \(0.491382\pi\)
\(548\) −71861.5 115254.i −0.239296 0.383790i
\(549\) 63337.4 + 29116.1i 0.210143 + 0.0966026i
\(550\) −68300.6 + 123075.i −0.225787 + 0.406860i
\(551\) −194494. + 112291.i −0.640623 + 0.369864i
\(552\) 190879. + 31696.9i 0.626439 + 0.104025i
\(553\) −180374. + 312417.i −0.589827 + 1.02161i
\(554\) 370541. 222396.i 1.20730 0.724616i
\(555\) −294604. 64471.6i −0.956429 0.209306i
\(556\) 301363. + 160617.i 0.974857 + 0.519568i
\(557\) 51271.9 0.165260 0.0826302 0.996580i \(-0.473668\pi\)
0.0826302 + 0.996580i \(0.473668\pi\)
\(558\) −40342.0 366366.i −0.129565 1.17665i
\(559\) 763547.i 2.44350i
\(560\) −26621.7 391749.i −0.0848905 1.24920i
\(561\) −88934.6 81049.4i −0.282582 0.257528i
\(562\) −236394. + 141882.i −0.748452 + 0.449216i
\(563\) −2488.80 1436.91i −0.00785187 0.00453328i 0.496069 0.868283i \(-0.334776\pi\)
−0.503921 + 0.863750i \(0.668110\pi\)
\(564\) 124153. + 105664.i 0.390302 + 0.332176i
\(565\) −16485.6 28553.9i −0.0516425 0.0894474i
\(566\) 87753.2 158128.i 0.273924 0.493601i
\(567\) −55833.9 297666.i −0.173673 0.925898i
\(568\) −611552. + 31148.0i −1.89556 + 0.0965458i
\(569\) 56876.7 + 98513.3i 0.175675 + 0.304278i 0.940395 0.340085i \(-0.110456\pi\)
−0.764720 + 0.644363i \(0.777123\pi\)
\(570\) 368484. + 74113.3i 1.13415 + 0.228111i
\(571\) −27258.4 15737.7i −0.0836043 0.0482689i 0.457615 0.889150i \(-0.348704\pi\)
−0.541219 + 0.840881i \(0.682037\pi\)
\(572\) −12080.0 355934.i −0.0369211 1.08787i
\(573\) 259880. + 236838.i 0.791522 + 0.721344i
\(574\) −205864. + 3492.39i −0.624824 + 0.0105998i
\(575\) 160935.i 0.486760i
\(576\) 249850. 218290.i 0.753067 0.657944i
\(577\) −654654. −1.96635 −0.983174 0.182671i \(-0.941526\pi\)
−0.983174 + 0.182671i \(0.941526\pi\)
\(578\) −3418.89 201531.i −0.0102336 0.603236i
\(579\) 244682. + 53546.6i 0.729870 + 0.159726i
\(580\) −379768. + 12888.9i −1.12892 + 0.0383142i
\(581\) −187955. + 325548.i −0.556803 + 0.964412i
\(582\) −344003. 302982.i −1.01558 0.894482i
\(583\) 67285.9 38847.5i 0.197964 0.114295i
\(584\) −6182.48 121385.i −0.0181275 0.355910i
\(585\) 741062. + 340665.i 2.16542 + 0.995441i
\(586\) 250798. + 139180.i 0.730346 + 0.405306i
\(587\) 557280. 321746.i 1.61732 0.933763i 0.629716 0.776825i \(-0.283171\pi\)
0.987609 0.156937i \(-0.0501620\pi\)
\(588\) −38274.3 7024.84i −0.110701 0.0203180i
\(589\) −178725. + 309561.i −0.515175 + 0.892309i
\(590\) 69381.6 + 115599.i 0.199315 + 0.332085i
\(591\) 57604.8 + 180980.i 0.164924 + 0.518151i
\(592\) 257569. 17503.3i 0.734937 0.0499433i
\(593\) −183090. −0.520661 −0.260330 0.965520i \(-0.583831\pi\)
−0.260330 + 0.965520i \(0.583831\pi\)
\(594\) 22612.7 212988.i 0.0640886 0.603645i
\(595\) 279180.i 0.788589i
\(596\) −95825.2 + 179795.i −0.269766 + 0.506158i
\(597\) 46722.1 14871.3i 0.131091 0.0417255i
\(598\) −209549. 349135.i −0.585980 0.976318i
\(599\) 24104.3 + 13916.6i 0.0671800 + 0.0387864i 0.533214 0.845981i \(-0.320984\pi\)
−0.466034 + 0.884767i \(0.654317\pi\)
\(600\) 213149. + 175260.i 0.592082 + 0.486833i
\(601\) 135764. + 235150.i 0.375868 + 0.651022i 0.990457 0.137826i \(-0.0440113\pi\)
−0.614589 + 0.788848i \(0.710678\pi\)
\(602\) 406786. + 225746.i 1.12247 + 0.622912i
\(603\) −52063.0 + 4840.58i −0.143184 + 0.0133126i
\(604\) 48001.8 29929.5i 0.131578 0.0820399i
\(605\) 153610. + 266060.i 0.419670 + 0.726889i
\(606\) 371366. + 327083.i 1.01125 + 0.890662i
\(607\) 86991.8 + 50224.8i 0.236103 + 0.136314i 0.613384 0.789785i \(-0.289808\pi\)
−0.377281 + 0.926099i \(0.623141\pi\)
\(608\) −320600. + 27256.9i −0.867274 + 0.0737343i
\(609\) 63479.0 290068.i 0.171157 0.782106i
\(610\) −1940.19 114368.i −0.00521417 0.307357i
\(611\) 343088.i 0.919015i
\(612\) −187760. + 142805.i −0.501303 + 0.381278i
\(613\) 458408. 1.21992 0.609960 0.792432i \(-0.291185\pi\)
0.609960 + 0.792432i \(0.291185\pi\)
\(614\) 383412. 6504.41i 1.01702 0.0172533i
\(615\) 224620. 246473.i 0.593880 0.651657i
\(616\) 193198. + 98797.8i 0.509146 + 0.260367i
\(617\) 237317. 411046.i 0.623389 1.07974i −0.365461 0.930827i \(-0.619089\pi\)
0.988850 0.148915i \(-0.0475781\pi\)
\(618\) 458532. + 92224.6i 1.20058 + 0.241474i
\(619\) −5714.30 + 3299.15i −0.0149136 + 0.00861036i −0.507438 0.861688i \(-0.669407\pi\)
0.492525 + 0.870298i \(0.336074\pi\)
\(620\) −513209. + 319989.i −1.33509 + 0.832438i
\(621\) −95558.8 225475.i −0.247792 0.584676i
\(622\) −46715.9 + 84180.4i −0.120749 + 0.217586i
\(623\) 305951. 176641.i 0.788272 0.455109i
\(624\) −690611. 102676.i −1.77364 0.263694i
\(625\) 230266. 398833.i 0.589481 1.02101i
\(626\) −340598. + 204425.i −0.869148 + 0.521657i
\(627\) −139914. + 153526.i −0.355898 + 0.390523i
\(628\) 223814. 419938.i 0.567502 1.06479i
\(629\) −183557. −0.463948
\(630\) −400590. + 294088.i −1.00930 + 0.740962i
\(631\) 102946.i 0.258553i 0.991609 + 0.129277i \(0.0412655\pi\)
−0.991609 + 0.129277i \(0.958734\pi\)
\(632\) 271794. + 419877.i 0.680465 + 1.05121i
\(633\) 133157. 608464.i 0.332320 1.51854i
\(634\) 203864. 122358.i 0.507179 0.304405i
\(635\) −204987. 118349.i −0.508368 0.293506i
\(636\) −51095.1 143494.i −0.126318 0.354747i
\(637\) 40945.7 + 70919.9i 0.100909 + 0.174779i
\(638\) 101898. 183616.i 0.250336 0.451096i
\(639\) 447970. + 632413.i 1.09710 + 1.54881i
\(640\) −500392. 214434.i −1.22166 0.523521i
\(641\) −202403. 350572.i −0.492607 0.853221i 0.507356 0.861736i \(-0.330623\pi\)
−0.999964 + 0.00851530i \(0.997289\pi\)
\(642\) 171242. + 508020.i 0.415471 + 1.23257i
\(643\) −426111. 246015.i −1.03063 0.595032i −0.113462 0.993542i \(-0.536194\pi\)
−0.917164 + 0.398510i \(0.869527\pi\)
\(644\) 247959. 8415.43i 0.597871 0.0202911i
\(645\) −718001. + 228535.i −1.72586 + 0.549329i
\(646\) 228740. 3880.46i 0.548121 0.00929861i
\(647\) 306912.i 0.733171i 0.930384 + 0.366586i \(0.119473\pi\)
−0.930384 + 0.366586i \(0.880527\pi\)
\(648\) −402694. 118983.i −0.959015 0.283356i
\(649\) −74507.5 −0.176893
\(650\) −9850.24 580637.i −0.0233142 1.37429i
\(651\) −143341. 450343.i −0.338227 1.06263i
\(652\) −3204.13 94409.1i −0.00753729 0.222085i
\(653\) −97661.8 + 169155.i −0.229033 + 0.396697i −0.957522 0.288361i \(-0.906890\pi\)
0.728489 + 0.685058i \(0.240223\pi\)
\(654\) 257187. 86692.0i 0.601303 0.202686i
\(655\) −200269. + 115625.i −0.466799 + 0.269507i
\(656\) −125644. + 256330.i −0.291966 + 0.595651i
\(657\) −125526. + 88916.3i −0.290806 + 0.205992i
\(658\) 182783. + 101435.i 0.422166 + 0.234281i
\(659\) −678872. + 391947.i −1.56321 + 0.902519i −0.566279 + 0.824213i \(0.691618\pi\)
−0.996929 + 0.0783055i \(0.975049\pi\)
\(660\) −331087. + 117893.i −0.760071 + 0.270645i
\(661\) −371075. + 642721.i −0.849295 + 1.47102i 0.0325431 + 0.999470i \(0.489639\pi\)
−0.881838 + 0.471552i \(0.843694\pi\)
\(662\) −189802. 316234.i −0.433096 0.721594i
\(663\) 484953. + 106128.i 1.10325 + 0.241436i
\(664\) 283217. + 437524.i 0.642367 + 0.992352i
\(665\) 481943. 1.08981
\(666\) −193358. 263382.i −0.435927 0.593797i
\(667\) 240099.i 0.539682i
\(668\) 290388. + 154768.i 0.650767 + 0.346838i
\(669\) 168481. + 153543.i 0.376442 + 0.343065i
\(670\) 44152.8 + 73564.3i 0.0983577 + 0.163877i
\(671\) 54744.0 + 31606.5i 0.121588 + 0.0701990i
\(672\) 258884. 337572.i 0.573280 0.747529i
\(673\) −211601. 366503.i −0.467183 0.809185i 0.532114 0.846673i \(-0.321398\pi\)
−0.999297 + 0.0374878i \(0.988064\pi\)
\(674\) −160566. 89106.0i −0.353454 0.196149i
\(675\) 42758.0 346623.i 0.0938447 0.760763i
\(676\) 535621. + 859046.i 1.17210 + 1.87985i
\(677\) −154122. 266947.i −0.336269 0.582435i 0.647459 0.762100i \(-0.275832\pi\)
−0.983728 + 0.179665i \(0.942498\pi\)
\(678\) 7043.72 35020.7i 0.0153230 0.0761843i
\(679\) −509034. 293891.i −1.10410 0.637450i
\(680\) 344629. + 176236.i 0.745305 + 0.381134i
\(681\) −646626. 589294.i −1.39431 1.27069i
\(682\) −5669.28 334184.i −0.0121887 0.718484i
\(683\) 760287.i 1.62981i 0.579597 + 0.814903i \(0.303210\pi\)
−0.579597 + 0.814903i \(0.696790\pi\)
\(684\) 246522. + 324126.i 0.526918 + 0.692790i
\(685\) 282065. 0.601130
\(686\) −493148. + 8366.02i −1.04792 + 0.0177775i
\(687\) −755164. 165261.i −1.60003 0.350152i
\(688\) 535457. 359644.i 1.13122 0.759794i
\(689\) −160273. + 277602.i −0.337616 + 0.584768i
\(690\) −265590. + 301548.i −0.557845 + 0.633370i
\(691\) −313235. + 180846.i −0.656016 + 0.378751i −0.790757 0.612130i \(-0.790313\pi\)
0.134742 + 0.990881i \(0.456980\pi\)
\(692\) 51723.4 + 82955.6i 0.108013 + 0.173234i
\(693\) −25424.5 273454.i −0.0529403 0.569401i
\(694\) −294978. + 531539.i −0.612450 + 1.10361i
\(695\) −614177. + 354595.i −1.27152 + 0.734113i
\(696\) −317997. 261470.i −0.656455 0.539763i
\(697\) 101485. 175777.i 0.208899 0.361824i
\(698\) −642349. + 385534.i −1.31844 + 0.791319i
\(699\) 34869.3 + 109551.i 0.0713656 + 0.224214i
\(700\) 312252. + 166420.i 0.637248 + 0.339633i
\(701\) 878492. 1.78773 0.893864 0.448337i \(-0.147984\pi\)
0.893864 + 0.448337i \(0.147984\pi\)
\(702\) 358567. + 807644.i 0.727606 + 1.63887i
\(703\) 316870.i 0.641167i
\(704\) 243918. 176123.i 0.492151 0.355361i
\(705\) −322622. + 102688.i −0.649107 + 0.206606i
\(706\) 155761. 93486.7i 0.312499 0.187560i
\(707\) 549525. + 317268.i 1.09938 + 0.634728i
\(708\) −26369.2 + 143670.i −0.0526054 + 0.286616i
\(709\) −431190. 746844.i −0.857781 1.48572i −0.874041 0.485853i \(-0.838509\pi\)
0.0162593 0.999868i \(-0.494824\pi\)
\(710\) 617066. 1.11193e6i 1.22409 2.20577i
\(711\) 264402. 575164.i 0.523029 1.13776i
\(712\) −24915.4 489183.i −0.0491482 0.964964i
\(713\) −191073. 330948.i −0.375855 0.651000i
\(714\) −199919. + 226986.i −0.392155 + 0.445248i
\(715\) 640517. + 369803.i 1.25291 + 0.723366i
\(716\) −6260.03 184450.i −0.0122110 0.359794i
\(717\) −203836. + 931435.i −0.396500 + 1.81182i
\(718\) 285976. 4851.44i 0.554728 0.00941070i
\(719\) 424008.i 0.820193i −0.912042 0.410097i \(-0.865495\pi\)
0.912042 0.410097i \(-0.134505\pi\)
\(720\) 110153. + 680148.i 0.212487 + 1.31201i
\(721\) 599717. 1.15365
\(722\) 2143.31 + 126341.i 0.00411160 + 0.242365i
\(723\) 61710.3 67714.0i 0.118054 0.129539i
\(724\) 408472. 13863.1i 0.779265 0.0264473i
\(725\) 171209. 296543.i 0.325725 0.564172i
\(726\) −65632.1 + 326317.i −0.124521 + 0.619107i
\(727\) 78836.8 45516.5i 0.149163 0.0861191i −0.423561 0.905868i \(-0.639220\pi\)
0.572724 + 0.819748i \(0.305887\pi\)
\(728\) −894096. + 45538.7i −1.68702 + 0.0859247i
\(729\) 145910. + 511018.i 0.274555 + 0.961571i
\(730\) 220704. + 122480.i 0.414157 + 0.229836i
\(731\) −397177. + 229310.i −0.743275 + 0.429130i
\(732\) 80320.3 94375.1i 0.149901 0.176131i
\(733\) 6638.99 11499.1i 0.0123565 0.0214020i −0.859781 0.510663i \(-0.829400\pi\)
0.872138 + 0.489261i \(0.162733\pi\)
\(734\) −136449. 227342.i −0.253267 0.421976i
\(735\) 54434.2 59730.0i 0.100762 0.110565i
\(736\) 146139. 311400.i 0.269780 0.574862i
\(737\) −47414.8 −0.0872929
\(738\) 359123. 39544.4i 0.659373 0.0726060i
\(739\) 622195.i 1.13930i −0.821888 0.569650i \(-0.807079\pi\)
0.821888 0.569650i \(-0.192921\pi\)
\(740\) −252165. + 473132.i −0.460490 + 0.864011i
\(741\) 183206. 837164.i 0.333660 1.52466i
\(742\) −100509. 167461.i −0.182557 0.304163i
\(743\) 606588. + 350214.i 1.09879 + 0.634389i 0.935904 0.352255i \(-0.114585\pi\)
0.162890 + 0.986644i \(0.447918\pi\)
\(744\) −646403. 107340.i −1.16777 0.193917i
\(745\) −211554. 366422.i −0.381161 0.660189i
\(746\) −502135. 278660.i −0.902283 0.500722i
\(747\) 275514. 599337.i 0.493745 1.07406i
\(748\) −181520. + 113179.i −0.324430 + 0.202284i
\(749\) 343705. + 595314.i 0.612663 + 1.06116i
\(750\) 165404. 55754.1i 0.294052 0.0991185i
\(751\) −73727.4 42566.6i −0.130722 0.0754725i 0.433213 0.901292i \(-0.357380\pi\)
−0.563935 + 0.825819i \(0.690713\pi\)
\(752\) 240599. 161600.i 0.425459 0.285763i
\(753\) 187371. 59638.8i 0.330455 0.105181i
\(754\) 14695.6 + 866252.i 0.0258490 + 1.52371i
\(755\) 117477.i 0.206091i
\(756\) −536291. 47753.7i −0.938333 0.0835533i
\(757\) 319528. 0.557592 0.278796 0.960350i \(-0.410065\pi\)
0.278796 + 0.960350i \(0.410065\pi\)
\(758\) 732606. 12428.3i 1.27506 0.0216309i
\(759\) −67353.0 211607.i −0.116916 0.367321i
\(760\) 304233. 594925.i 0.526719 1.03000i
\(761\) −376888. + 652790.i −0.650794 + 1.12721i 0.332137 + 0.943231i \(0.392230\pi\)
−0.982931 + 0.183977i \(0.941103\pi\)
\(762\) −81914.0 243012.i −0.141074 0.418522i
\(763\) 301379. 174001.i 0.517684 0.298885i
\(764\) 530426. 330724.i 0.908737 0.566604i
\(765\) −45352.5 487790.i −0.0774958 0.833509i
\(766\) −34012.4 + 61289.2i −0.0579669 + 0.104454i
\(767\) 266213. 153698.i 0.452520 0.261263i
\(768\) −253286. 532671.i −0.429426 0.903102i
\(769\) −425156. + 736392.i −0.718945 + 1.24525i 0.242473 + 0.970158i \(0.422041\pi\)
−0.961418 + 0.275091i \(0.911292\pi\)
\(770\) −386387. + 231907.i −0.651690 + 0.391140i
\(771\) 488492. + 106902.i 0.821768 + 0.179837i
\(772\) 209434. 392958.i 0.351409 0.659344i
\(773\) 13034.7 0.0218143 0.0109071 0.999941i \(-0.496528\pi\)
0.0109071 + 0.999941i \(0.496528\pi\)
\(774\) −747417. 328346.i −1.24762 0.548088i
\(775\) 545000.i 0.907388i
\(776\) −684122. + 442844.i −1.13608 + 0.735407i
\(777\) −309653. 282199.i −0.512901 0.467426i
\(778\) 263610. 158217.i 0.435515 0.261393i
\(779\) −303441. 175192.i −0.500033 0.288694i
\(780\) 939766. 1.10421e6i 1.54465 1.81494i
\(781\) 351388. + 608622.i 0.576083 + 0.997805i
\(782\) −118679. + 213855.i −0.194071 + 0.349708i
\(783\) −63790.6 + 517126.i −0.104048 + 0.843476i
\(784\) −30448.3 + 62118.7i −0.0495372 + 0.101063i
\(785\) 494114. + 855831.i 0.801841 + 1.38883i
\(786\) −245625. 49402.6i −0.397583 0.0799659i
\(787\) −473891. 273601.i −0.765120 0.441742i 0.0660112 0.997819i \(-0.478973\pi\)
−0.831131 + 0.556077i \(0.812306\pi\)
\(788\) 337454. 11452.8i 0.543452 0.0184441i
\(789\) 167387. + 152546.i 0.268885 + 0.245045i
\(790\) −1.03857e6 + 17618.8i −1.66410 + 0.0282307i
\(791\) 45803.8i 0.0732064i
\(792\) −353610. 141237.i −0.563734 0.225163i
\(793\) −260798. −0.414723
\(794\) −4972.99 293140.i −0.00788818 0.464981i
\(795\) 309014. + 67624.9i 0.488926 + 0.106997i
\(796\) −2956.66 87117.4i −0.00466633 0.137492i
\(797\) 104227. 180527.i 0.164083 0.284201i −0.772246 0.635324i \(-0.780867\pi\)
0.936329 + 0.351123i \(0.114200\pi\)
\(798\) 391840. + 345116.i 0.615323 + 0.541950i
\(799\) −178465. + 103037.i −0.279550 + 0.161398i
\(800\) 402547. 280398.i 0.628980 0.438122i
\(801\) −505869. + 358332.i −0.788449 + 0.558497i
\(802\) −995215. 552295.i −1.54728 0.858662i
\(803\) −120804. + 69746.0i −0.187348 + 0.108165i
\(804\) −16780.7 + 91428.4i −0.0259596 + 0.141439i
\(805\) −257620. + 446211.i −0.397547 + 0.688571i
\(806\) 709629. + 1.18233e6i 1.09235 + 1.81999i
\(807\) −147824. 464427.i −0.226985 0.713133i
\(808\) 738541. 478071.i 1.13123 0.732267i
\(809\) 844500. 1.29034 0.645168 0.764041i \(-0.276787\pi\)
0.645168 + 0.764041i \(0.276787\pi\)
\(810\) 652146. 578912.i 0.993973 0.882353i
\(811\) 769174.i 1.16945i 0.811230 + 0.584727i \(0.198798\pi\)
−0.811230 + 0.584727i \(0.801202\pi\)
\(812\) −465848. 248282.i −0.706532 0.376559i
\(813\) 814232. 259164.i 1.23188 0.392098i
\(814\) −152475. 254044.i −0.230118 0.383407i
\(815\) 169893. + 98087.6i 0.255776 + 0.147672i
\(816\) 153997. + 390074.i 0.231276 + 0.585823i
\(817\) 395853. + 685638.i 0.593048 + 1.02719i
\(818\) 395759. + 219627.i 0.591458 + 0.328230i
\(819\) 654937. + 924595.i 0.976408 + 1.37843i
\(820\) −313663. 503063.i −0.466483 0.748161i
\(821\) −322867. 559222.i −0.479002 0.829656i 0.520708 0.853735i \(-0.325668\pi\)
−0.999710 + 0.0240788i \(0.992335\pi\)
\(822\) 229331. + 201985.i 0.339406 + 0.298934i
\(823\) −202697. 117027.i −0.299260 0.172778i 0.342851 0.939390i \(-0.388608\pi\)
−0.642110 + 0.766612i \(0.721941\pi\)
\(824\) 378579. 740309.i 0.557574 1.09033i
\(825\) 67705.4 309381.i 0.0994753 0.454554i
\(826\) 3176.92 + 187268.i 0.00465636 + 0.274476i
\(827\) 1.14409e6i 1.67282i −0.548108 0.836408i \(-0.684652\pi\)
0.548108 0.836408i \(-0.315348\pi\)
\(828\) −431872. + 54984.2i −0.629933 + 0.0802005i
\(829\) −563769. −0.820336 −0.410168 0.912010i \(-0.634530\pi\)
−0.410168 + 0.912010i \(0.634530\pi\)
\(830\) −1.08222e6 + 18359.3i −1.57093 + 0.0266502i
\(831\) −654961. + 718681.i −0.948447 + 1.04072i
\(832\) −508196. + 1.13245e6i −0.734149 + 1.63595i
\(833\) 24593.8 42597.7i 0.0354434 0.0613898i
\(834\) −753275. 151506.i −1.08298 0.217820i
\(835\) −591809. + 341681.i −0.848806 + 0.490059i
\(836\) 195378. + 313353.i 0.279552 + 0.448355i
\(837\) 323606. + 763563.i 0.461919 + 1.08992i
\(838\) −531873. + 958415.i −0.757390 + 1.36479i
\(839\) 231599. 133714.i 0.329013 0.189956i −0.326390 0.945235i \(-0.605832\pi\)
0.655403 + 0.755279i \(0.272499\pi\)
\(840\) 310431. + 827133.i 0.439954 + 1.17224i
\(841\) 98213.9 170111.i 0.138861 0.240515i
\(842\) 42815.4 25697.5i 0.0603914 0.0362465i
\(843\) 417846. 458497.i 0.587978 0.645181i
\(844\) −977189. 520811.i −1.37181 0.731131i
\(845\) −2.10238e6 −2.94440
\(846\) −335840. 147537.i −0.469237 0.206139i
\(847\) 426792.i 0.594907i
\(848\) −270167. + 18359.4i −0.375699 + 0.0255310i
\(849\) −86988.4 + 397495.i −0.120683 + 0.551463i
\(850\) −299074. + 179502.i −0.413943 + 0.248446i
\(851\) −293377. 169381.i −0.405105 0.233887i
\(852\) 1.29795e6 462171.i 1.78804 0.636683i
\(853\) −183417. 317688.i −0.252082 0.436619i 0.712017 0.702162i \(-0.247782\pi\)
−0.964099 + 0.265544i \(0.914449\pi\)
\(854\) 77106.0 138942.i 0.105724 0.190510i
\(855\) −842061. + 78291.0i −1.15189 + 0.107098i
\(856\) 951842. 48479.9i 1.29902 0.0661628i
\(857\) −576064. 997772.i −0.784348 1.35853i −0.929388 0.369105i \(-0.879664\pi\)
0.145039 0.989426i \(-0.453669\pi\)
\(858\) 255955. + 759335.i 0.347687 + 1.03148i
\(859\) 1.26237e6 + 728827.i 1.71080 + 0.987730i 0.933486 + 0.358615i \(0.116751\pi\)
0.777313 + 0.629115i \(0.216582\pi\)
\(860\) 45436.4 + 1.33877e6i 0.0614338 + 1.81013i
\(861\) 441440. 140507.i 0.595477 0.189536i
\(862\) 479351. 8131.97i 0.645118 0.0109441i
\(863\) 237901.i 0.319430i −0.987163 0.159715i \(-0.948943\pi\)
0.987163 0.159715i \(-0.0510575\pi\)
\(864\) −397489. + 631869.i −0.532474 + 0.846447i
\(865\) −203020. −0.271336
\(866\) −19164.8 1.12970e6i −0.0255545 1.50635i
\(867\) 137550. + 432148.i 0.182988 + 0.574903i
\(868\) −839703. + 28498.5i −1.11452 + 0.0378254i
\(869\) 287017. 497128.i 0.380074 0.658307i
\(870\) 810181. 273094.i 1.07039 0.360806i
\(871\) 169411. 97809.7i 0.223309 0.128928i
\(872\) −24543.1 481873.i −0.0322772 0.633723i
\(873\) 937137. + 430800.i 1.22963 + 0.565259i
\(874\) 369173. + 204873.i 0.483289 + 0.268201i
\(875\) 193826. 111905.i 0.253160 0.146162i
\(876\) 91735.0 + 257626.i 0.119544 + 0.335723i
\(877\) 331033. 573367.i 0.430400 0.745475i −0.566507 0.824057i \(-0.691706\pi\)
0.996908 + 0.0785815i \(0.0250391\pi\)
\(878\) −352875. 587935.i −0.457753 0.762676i
\(879\) −630445. 137967.i −0.815961 0.178566i
\(880\) 42361.2 + 623362.i 0.0547019 + 0.804962i
\(881\) 245234. 0.315957 0.157979 0.987443i \(-0.449502\pi\)
0.157979 + 0.987443i \(0.449502\pi\)
\(882\) 87029.6 9583.15i 0.111874 0.0123189i
\(883\) 924835.i 1.18616i −0.805144 0.593079i \(-0.797912\pi\)
0.805144 0.593079i \(-0.202088\pi\)
\(884\) 415092. 778832.i 0.531178 0.996642i
\(885\) −224209. 204330.i −0.286264 0.260883i
\(886\) −170872. 284695.i −0.217673 0.362671i
\(887\) 1.09941e6 + 634747.i 1.39738 + 0.806776i 0.994117 0.108309i \(-0.0345436\pi\)
0.403260 + 0.915085i \(0.367877\pi\)
\(888\) −543827. + 204104.i −0.689660 + 0.258836i
\(889\) −164412. 284769.i −0.208031 0.360321i
\(890\) 889437. + 493593.i 1.12288 + 0.623145i
\(891\) 88844.6 + 473655.i 0.111912 + 0.596632i
\(892\) 343877. 214409.i 0.432188 0.269472i
\(893\) 177870. + 308081.i 0.223049 + 0.386333i
\(894\) 90389.6 449409.i 0.113095 0.562298i
\(895\) 331926. + 191637.i 0.414376 + 0.239240i
\(896\) −453070. 605558.i −0.564351 0.754293i
\(897\) 677164. + 617125.i 0.841606 + 0.766987i
\(898\) 17149.8 + 1.01092e6i 0.0212670 + 1.25362i
\(899\) 813085.i 1.00604i
\(900\) −572608. 240048.i −0.706923 0.296356i
\(901\) 192535. 0.237170
\(902\) 327578. 5557.20i 0.402625 0.00683035i
\(903\) −1.02256e6 223779.i −1.25405 0.274437i
\(904\) −56541.7 28914.3i −0.0691881 0.0353814i
\(905\) −424388. + 735061.i −0.518162 + 0.897483i
\(906\) −84124.2 + 95513.6i −0.102486 + 0.116361i
\(907\) 41146.3 23755.8i 0.0500169 0.0288772i −0.474783 0.880103i \(-0.657473\pi\)
0.524800 + 0.851226i \(0.324140\pi\)
\(908\) −1.31979e6 + 822900.i −1.60079 + 0.998102i
\(909\) −1.01168e6 465068.i −1.22438 0.562845i
\(910\) 902158. 1.62565e6i 1.08943 1.96311i
\(911\) 421729. 243485.i 0.508155 0.293383i −0.223920 0.974608i \(-0.571885\pi\)
0.732075 + 0.681224i \(0.238552\pi\)
\(912\) 673376. 265841.i 0.809595 0.319619i
\(913\) 299080. 518021.i 0.358794 0.621450i
\(914\) −65093.9 + 39068.9i −0.0779198 + 0.0467670i
\(915\) 78058.5 + 245241.i 0.0932349 + 0.292921i
\(916\) −646377. + 1.21279e6i −0.770363 + 1.44542i
\(917\) −321255. −0.382042
\(918\) 312429. 429071.i 0.370737 0.509148i
\(919\) 1.08957e6i 1.29010i −0.764141 0.645049i \(-0.776837\pi\)
0.764141 0.645049i \(-0.223163\pi\)
\(920\) 388191. + 599691.i 0.458637 + 0.708520i
\(921\) −822159. + 261688.i −0.969252 + 0.308506i
\(922\) −665878. + 399656.i −0.783309 + 0.470137i
\(923\) −2.51099e6 1.44972e6i −2.94742 1.70169i
\(924\) −480216. 88138.6i −0.562461 0.103234i
\(925\) −241564. 418402.i −0.282325 0.489001i
\(926\) 193256. 348240.i 0.225377 0.406122i
\(927\) −1.04784e6 + 97423.2i −1.21937 + 0.113371i
\(928\) −600560. + 418326.i −0.697365 + 0.485757i
\(929\) −671427. 1.16295e6i −0.777978 1.34750i −0.933106 0.359603i \(-0.882912\pi\)
0.155128 0.987894i \(-0.450421\pi\)
\(930\) 899410. 1.02118e6i 1.03990 1.18069i
\(931\) −73535.5 42455.7i −0.0848394 0.0489820i
\(932\) 204267. 6932.59i 0.235162 0.00798111i
\(933\) 46308.8 211609.i 0.0531986 0.243092i
\(934\) 507889. 8616.09i 0.582204 0.00987681i
\(935\) 444240.i 0.508153i
\(936\) 1.55479e6 224811.i 1.77468 0.256605i
\(937\) 1.37506e6 1.56618 0.783089 0.621909i \(-0.213643\pi\)
0.783089 + 0.621909i \(0.213643\pi\)
\(938\) 2021.72 + 119173.i 0.00229781 + 0.135448i
\(939\) 602035. 660606.i 0.682795 0.749223i
\(940\) 20416.1 + 601557.i 0.0231056 + 0.680802i
\(941\) 786864. 1.36289e6i 0.888628 1.53915i 0.0471309 0.998889i \(-0.484992\pi\)
0.841498 0.540261i \(-0.181674\pi\)
\(942\) −211118. + 1.04966e6i −0.237916 + 1.18290i
\(943\) 324405. 187295.i 0.364808 0.210622i
\(944\) 233175. + 114294.i 0.261661 + 0.128257i
\(945\) 673416. 892607.i 0.754084 0.999532i
\(946\) −647290. 359214.i −0.723297 0.401394i
\(947\) 938964. 542111.i 1.04701 0.604489i 0.125196 0.992132i \(-0.460044\pi\)
0.921810 + 0.387643i \(0.126711\pi\)
\(948\) −857016. 729385.i −0.953614 0.811597i
\(949\) 287752. 498400.i 0.319511 0.553409i
\(950\) 309871. + 516285.i 0.343347 + 0.572061i
\(951\) −360345. + 395403.i −0.398435 + 0.437198i
\(952\) 292205. + 451409.i 0.322414 + 0.498077i
\(953\) 461469. 0.508108 0.254054 0.967190i \(-0.418236\pi\)
0.254054 + 0.967190i \(0.418236\pi\)
\(954\) 202816. + 276264.i 0.222846 + 0.303548i
\(955\) 1.29813e6i 1.42335i
\(956\) 1.49588e6 + 797255.i 1.63674 + 0.872332i
\(957\) −101010. + 461565.i −0.110291 + 0.503975i
\(958\) 115133. + 191826.i 0.125449 + 0.209014i
\(959\) 339350. + 195924.i 0.368986 + 0.213034i
\(960\) 1.21700e6 + 138932.i 1.32053 + 0.150751i
\(961\) 185301. + 320951.i 0.200646 + 0.347530i
\(962\) 1.06884e6 + 593155.i 1.15495 + 0.640941i
\(963\) −697236. 984311.i −0.751843 1.06140i
\(964\) −86173.2 138207.i −0.0927295 0.148723i
\(965\) 462369. + 800847.i 0.496517 + 0.859993i
\(966\) −528985. + 178309.i −0.566877 + 0.191082i
\(967\) 998780. + 576646.i 1.06811 + 0.616675i 0.927665 0.373413i \(-0.121813\pi\)
0.140447 + 0.990088i \(0.455146\pi\)
\(968\) 526845. + 269418.i 0.562253 + 0.287525i
\(969\) −490491. + 156120.i −0.522377 + 0.166269i
\(970\) −28707.0 1.69218e6i −0.0305101 1.79847i
\(971\) 438562.i 0.465149i −0.972579 0.232575i \(-0.925285\pi\)
0.972579 0.232575i \(-0.0747150\pi\)
\(972\) 944777. 3683.47i 0.999992 0.00389874i
\(973\) −985213. −1.04065
\(974\) −1.09949e6 + 18652.4i −1.15898 + 0.0196615i
\(975\) 396298. + 1.24507e6i 0.416882 + 1.30974i
\(976\) −122840. 182891.i −0.128956 0.191996i
\(977\) −388615. + 673100.i −0.407127 + 0.705165i −0.994566 0.104103i \(-0.966803\pi\)
0.587439 + 0.809268i \(0.300136\pi\)
\(978\) 67890.3 + 201408.i 0.0709790 + 0.210572i
\(979\) −486839. + 281076.i −0.507948 + 0.293264i
\(980\) −76012.8 121912.i −0.0791470 0.126939i
\(981\) −498310. + 352978.i −0.517800 + 0.366783i
\(982\) 62838.4 113233.i 0.0651632 0.117422i
\(983\) −695782. + 401710.i −0.720056 + 0.415724i −0.814773 0.579780i \(-0.803139\pi\)
0.0947175 + 0.995504i \(0.469805\pi\)
\(984\) 105218. 633624.i 0.108668 0.654397i
\(985\) −350602. + 607260.i −0.361362 + 0.625897i
\(986\) 446188. 267799.i 0.458949 0.275458i
\(987\) −459472. 100551.i −0.471655 0.103218i
\(988\) −1.34448e6 716565.i −1.37734 0.734077i
\(989\) −846405. −0.865338
\(990\) 637431. 467961.i 0.650373 0.477462i
\(991\) 206876.i 0.210651i 0.994438 + 0.105325i \(0.0335884\pi\)
−0.994438 + 0.105325i \(0.966412\pi\)
\(992\) −494894. + 1.05455e6i −0.502909 + 1.07162i
\(993\) 613351. + 558969.i 0.622028 + 0.566878i
\(994\) 1.51474e6 909136.i 1.53308 0.920145i
\(995\) 156771. + 90511.8i 0.158351 + 0.0914238i
\(996\) −893035. 760040.i −0.900223 0.766157i
\(997\) 14831.3 + 25688.6i 0.0149207 + 0.0258435i 0.873389 0.487023i \(-0.161917\pi\)
−0.858469 + 0.512866i \(0.828584\pi\)
\(998\) −563546. + 1.01549e6i −0.565807 + 1.01956i
\(999\) 586875. + 442761.i 0.588051 + 0.443647i
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 36.5.f.a.31.12 yes 44
3.2 odd 2 108.5.f.a.91.11 44
4.3 odd 2 inner 36.5.f.a.31.18 yes 44
9.2 odd 6 108.5.f.a.19.5 44
9.4 even 3 324.5.d.f.163.3 22
9.5 odd 6 324.5.d.e.163.20 22
9.7 even 3 inner 36.5.f.a.7.18 yes 44
12.11 even 2 108.5.f.a.91.5 44
36.7 odd 6 inner 36.5.f.a.7.12 44
36.11 even 6 108.5.f.a.19.11 44
36.23 even 6 324.5.d.e.163.19 22
36.31 odd 6 324.5.d.f.163.4 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
36.5.f.a.7.12 44 36.7 odd 6 inner
36.5.f.a.7.18 yes 44 9.7 even 3 inner
36.5.f.a.31.12 yes 44 1.1 even 1 trivial
36.5.f.a.31.18 yes 44 4.3 odd 2 inner
108.5.f.a.19.5 44 9.2 odd 6
108.5.f.a.19.11 44 36.11 even 6
108.5.f.a.91.5 44 12.11 even 2
108.5.f.a.91.11 44 3.2 odd 2
324.5.d.e.163.19 22 36.23 even 6
324.5.d.e.163.20 22 9.5 odd 6
324.5.d.f.163.3 22 9.4 even 3
324.5.d.f.163.4 22 36.31 odd 6