Properties

Label 45.4.e.c.16.7
Level $45$
Weight $4$
Character 45.16
Analytic conductor $2.655$
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] = [45,4,Mod(16,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, 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("45.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.e (of order \(3\), 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: \(2.65508595026\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.7
Root \(2.65775 + 4.60336i\) of defining polynomial
Character \(\chi\) \(=\) 45.16
Dual form 45.4.e.c.31.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.65775 - 4.60336i) q^{2} +(-5.19389 + 0.153351i) q^{3} +(-10.1273 - 17.5410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-13.0981 + 24.3169i) q^{6} +(6.71686 - 11.6339i) q^{7} -65.1396 q^{8} +(26.9530 - 1.59298i) q^{9} +O(q^{10})\) \(q+(2.65775 - 4.60336i) q^{2} +(-5.19389 + 0.153351i) q^{3} +(-10.1273 - 17.5410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-13.0981 + 24.3169i) q^{6} +(6.71686 - 11.6339i) q^{7} -65.1396 q^{8} +(26.9530 - 1.59298i) q^{9} +26.5775 q^{10} +(23.4628 - 40.6388i) q^{11} +(55.2901 + 89.5531i) q^{12} +(18.0673 + 31.2935i) q^{13} +(-35.7035 - 61.8403i) q^{14} +(-13.6488 - 22.1068i) q^{15} +(-92.1064 + 159.533i) q^{16} -54.6071 q^{17} +(64.3013 - 128.308i) q^{18} +111.339 q^{19} +(50.6366 - 87.7051i) q^{20} +(-33.1026 + 61.4555i) q^{21} +(-124.717 - 216.016i) q^{22} +(17.9870 + 31.1544i) q^{23} +(338.328 - 9.98925i) q^{24} +(-12.5000 + 21.6506i) q^{25} +192.074 q^{26} +(-139.746 + 12.4070i) q^{27} -272.095 q^{28} +(-29.0588 + 50.3312i) q^{29} +(-138.041 + 4.07570i) q^{30} +(147.833 + 256.055i) q^{31} +(229.034 + 396.699i) q^{32} +(-115.631 + 214.671i) q^{33} +(-145.132 + 251.377i) q^{34} +67.1686 q^{35} +(-300.904 - 456.650i) q^{36} -53.0417 q^{37} +(295.911 - 512.533i) q^{38} +(-98.6386 - 159.765i) q^{39} +(-162.849 - 282.063i) q^{40} +(-64.1795 - 111.162i) q^{41} +(194.924 + 315.717i) q^{42} +(82.0858 - 142.177i) q^{43} -950.461 q^{44} +(74.2802 + 112.727i) q^{45} +191.220 q^{46} +(-43.9159 + 76.0646i) q^{47} +(453.926 - 842.721i) q^{48} +(81.2675 + 140.759i) q^{49} +(66.4439 + 115.084i) q^{50} +(283.623 - 8.37409i) q^{51} +(365.947 - 633.839i) q^{52} -479.247 q^{53} +(-314.297 + 676.279i) q^{54} +234.628 q^{55} +(-437.533 + 757.830i) q^{56} +(-578.281 + 17.0739i) q^{57} +(154.462 + 267.536i) q^{58} +(-317.807 - 550.458i) q^{59} +(-249.551 + 463.296i) q^{60} +(-24.0128 + 41.5915i) q^{61} +1571.62 q^{62} +(162.507 - 324.269i) q^{63} +961.163 q^{64} +(-90.3367 + 156.468i) q^{65} +(680.892 + 1102.84i) q^{66} +(14.4592 + 25.0440i) q^{67} +(553.024 + 957.865i) q^{68} +(-98.2001 - 159.054i) q^{69} +(178.518 - 309.202i) q^{70} +576.183 q^{71} +(-1755.70 + 103.766i) q^{72} +835.057 q^{73} +(-140.972 + 244.170i) q^{74} +(61.6035 - 114.368i) q^{75} +(-1127.56 - 1952.99i) q^{76} +(-315.193 - 545.930i) q^{77} +(-997.612 + 29.4548i) q^{78} +(101.869 - 176.442i) q^{79} -921.064 q^{80} +(723.925 - 85.8711i) q^{81} -682.294 q^{82} +(-232.239 + 402.249i) q^{83} +(1413.23 - 41.7262i) q^{84} +(-136.518 - 236.456i) q^{85} +(-436.328 - 755.742i) q^{86} +(143.210 - 265.871i) q^{87} +(-1528.36 + 2647.19i) q^{88} +993.782 q^{89} +(716.344 - 42.3375i) q^{90} +485.423 q^{91} +(364.320 - 631.021i) q^{92} +(-807.097 - 1307.25i) q^{93} +(233.435 + 404.322i) q^{94} +(278.347 + 482.111i) q^{95} +(-1250.41 - 2025.29i) q^{96} +(-440.708 + 763.328i) q^{97} +863.956 q^{98} +(567.656 - 1132.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 2 q^{2} - 5 q^{3} - 36 q^{4} + 35 q^{5} - 31 q^{6} - 22 q^{7} - 36 q^{8} + 17 q^{9} + 20 q^{10} + 23 q^{11} + 287 q^{12} - 96 q^{13} - 21 q^{14} - 20 q^{15} - 324 q^{16} - 322 q^{17} - 89 q^{18} + 558 q^{19} + 180 q^{20} + 180 q^{21} - 311 q^{22} + 96 q^{23} + 48 q^{24} - 175 q^{25} + 716 q^{26} - 470 q^{27} + 674 q^{28} - 296 q^{29} + 80 q^{30} - 244 q^{31} - 314 q^{32} - 211 q^{33} - 125 q^{34} - 220 q^{35} - 2399 q^{36} + 808 q^{37} + 305 q^{38} + 634 q^{39} - 90 q^{40} - 47 q^{41} + 1941 q^{42} - 525 q^{43} - 110 q^{44} + 185 q^{45} + 1434 q^{46} + 164 q^{47} + 2051 q^{48} - 1225 q^{49} + 50 q^{50} + 1517 q^{51} - 1682 q^{52} - 1012 q^{53} - 4066 q^{54} + 230 q^{55} - 981 q^{56} + 337 q^{57} - 1183 q^{58} - 85 q^{59} + 65 q^{60} - 828 q^{61} + 1572 q^{62} - 828 q^{63} + 4472 q^{64} + 480 q^{65} + 4930 q^{66} - 1093 q^{67} + 2473 q^{68} - 822 q^{69} + 105 q^{70} - 656 q^{71} - 4626 q^{72} + 4170 q^{73} - 1316 q^{74} + 25 q^{75} - 2789 q^{76} + 24 q^{77} - 5314 q^{78} - 2110 q^{79} - 3240 q^{80} - 2167 q^{81} - 124 q^{82} + 1290 q^{83} + 5775 q^{84} - 805 q^{85} - 2569 q^{86} + 3604 q^{87} - 2271 q^{88} + 6096 q^{89} + 730 q^{90} + 6676 q^{91} + 2763 q^{92} - 696 q^{93} + 517 q^{94} + 1395 q^{95} - 593 q^{96} - 1787 q^{97} - 2558 q^{98} + 2320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.173548 0.984825i \(-0.444477\pi\)
0.766110 0.642710i \(-0.222190\pi\)
\(3\) −5.19389 + 0.153351i −0.999564 + 0.0295125i
\(4\) −10.1273 17.5410i −1.26591 2.19263i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) −13.0981 + 24.3169i −0.891216 + 1.65456i
\(7\) 6.71686 11.6339i 0.362676 0.628174i −0.625724 0.780045i \(-0.715196\pi\)
0.988400 + 0.151871i \(0.0485297\pi\)
\(8\) −65.1396 −2.87879
\(9\) 26.9530 1.59298i 0.998258 0.0589993i
\(10\) 26.5775 0.840456
\(11\) 23.4628 40.6388i 0.643119 1.11391i −0.341614 0.939840i \(-0.610974\pi\)
0.984733 0.174074i \(-0.0556932\pi\)
\(12\) 55.2901 + 89.5531i 1.33007 + 2.15431i
\(13\) 18.0673 + 31.2935i 0.385460 + 0.667636i 0.991833 0.127544i \(-0.0407095\pi\)
−0.606373 + 0.795180i \(0.707376\pi\)
\(14\) −35.7035 61.8403i −0.681584 1.18054i
\(15\) −13.6488 22.1068i −0.234940 0.380530i
\(16\) −92.1064 + 159.533i −1.43916 + 2.49270i
\(17\) −54.6071 −0.779069 −0.389535 0.921012i \(-0.627364\pi\)
−0.389535 + 0.921012i \(0.627364\pi\)
\(18\) 64.3013 128.308i 0.841998 1.68014i
\(19\) 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
\(21\) −33.1026 + 61.4555i −0.343980 + 0.638604i
\(22\) −124.717 216.016i −1.20862 2.09340i
\(23\) 17.9870 + 31.1544i 0.163067 + 0.282441i 0.935967 0.352087i \(-0.114528\pi\)
−0.772900 + 0.634528i \(0.781195\pi\)
\(24\) 338.328 9.98925i 2.87754 0.0849603i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) 192.074 1.44880
\(27\) −139.746 + 12.4070i −0.996082 + 0.0884347i
\(28\) −272.095 −1.83647
\(29\) −29.0588 + 50.3312i −0.186072 + 0.322285i −0.943937 0.330125i \(-0.892909\pi\)
0.757866 + 0.652411i \(0.226242\pi\)
\(30\) −138.041 + 4.07570i −0.840090 + 0.0248039i
\(31\) 147.833 + 256.055i 0.856506 + 1.48351i 0.875241 + 0.483687i \(0.160703\pi\)
−0.0187353 + 0.999824i \(0.505964\pi\)
\(32\) 229.034 + 396.699i 1.26525 + 2.19147i
\(33\) −115.631 + 214.671i −0.609964 + 1.13241i
\(34\) −145.132 + 251.377i −0.732059 + 1.26796i
\(35\) 67.1686 0.324388
\(36\) −300.904 456.650i −1.39307 2.11412i
\(37\) −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
\(39\) −98.6386 159.765i −0.404995 0.655969i
\(40\) −162.849 282.063i −0.643717 1.11495i
\(41\) −64.1795 111.162i −0.244467 0.423430i 0.717514 0.696544i \(-0.245280\pi\)
−0.961982 + 0.273114i \(0.911946\pi\)
\(42\) 194.924 + 315.717i 0.716127 + 1.15991i
\(43\) 82.0858 142.177i 0.291116 0.504227i −0.682958 0.730457i \(-0.739307\pi\)
0.974074 + 0.226230i \(0.0726402\pi\)
\(44\) −950.461 −3.25653
\(45\) 74.2802 + 112.727i 0.246068 + 0.373431i
\(46\) 191.220 0.612910
\(47\) −43.9159 + 76.0646i −0.136294 + 0.236067i −0.926091 0.377301i \(-0.876852\pi\)
0.789797 + 0.613368i \(0.210186\pi\)
\(48\) 453.926 842.721i 1.36497 2.53409i
\(49\) 81.2675 + 140.759i 0.236932 + 0.410378i
\(50\) 66.4439 + 115.084i 0.187932 + 0.325507i
\(51\) 283.623 8.37409i 0.778730 0.0229923i
\(52\) 365.947 633.839i 0.975918 1.69034i
\(53\) −479.247 −1.24207 −0.621035 0.783783i \(-0.713287\pi\)
−0.621035 + 0.783783i \(0.713287\pi\)
\(54\) −314.297 + 676.279i −0.792046 + 1.70426i
\(55\) 234.628 0.575223
\(56\) −437.533 + 757.830i −1.04407 + 1.80838i
\(57\) −578.281 + 17.0739i −1.34377 + 0.0396754i
\(58\) 154.462 + 267.536i 0.349687 + 0.605676i
\(59\) −317.807 550.458i −0.701271 1.21464i −0.968021 0.250871i \(-0.919283\pi\)
0.266750 0.963766i \(-0.414050\pi\)
\(60\) −249.551 + 463.296i −0.536948 + 0.996854i
\(61\) −24.0128 + 41.5915i −0.0504021 + 0.0872990i −0.890126 0.455715i \(-0.849384\pi\)
0.839724 + 0.543014i \(0.182717\pi\)
\(62\) 1571.62 3.21929
\(63\) 162.507 324.269i 0.324983 0.648477i
\(64\) 961.163 1.87727
\(65\) −90.3367 + 156.468i −0.172383 + 0.298576i
\(66\) 680.892 + 1102.84i 1.26988 + 2.05682i
\(67\) 14.4592 + 25.0440i 0.0263652 + 0.0456658i 0.878907 0.476993i \(-0.158273\pi\)
−0.852542 + 0.522659i \(0.824940\pi\)
\(68\) 553.024 + 957.865i 0.986235 + 1.70821i
\(69\) −98.2001 159.054i −0.171332 0.277505i
\(70\) 178.518 309.202i 0.304813 0.527952i
\(71\) 576.183 0.963103 0.481552 0.876418i \(-0.340073\pi\)
0.481552 + 0.876418i \(0.340073\pi\)
\(72\) −1755.70 + 103.766i −2.87377 + 0.169847i
\(73\) 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
\(75\) 61.6035 114.368i 0.0948447 0.176081i
\(76\) −1127.56 1952.99i −1.70184 2.94768i
\(77\) −315.193 545.930i −0.466488 0.807981i
\(78\) −997.612 + 29.4548i −1.44817 + 0.0427577i
\(79\) 101.869 176.442i 0.145078 0.251282i −0.784324 0.620351i \(-0.786990\pi\)
0.929402 + 0.369069i \(0.120324\pi\)
\(80\) −921.064 −1.28723
\(81\) 723.925 85.8711i 0.993038 0.117793i
\(82\) −682.294 −0.918863
\(83\) −232.239 + 402.249i −0.307127 + 0.531959i −0.977733 0.209855i \(-0.932701\pi\)
0.670606 + 0.741814i \(0.266034\pi\)
\(84\) 1413.23 41.7262i 1.83567 0.0541988i
\(85\) −136.518 236.456i −0.174205 0.301732i
\(86\) −436.328 755.742i −0.547098 0.947602i
\(87\) 143.210 265.871i 0.176479 0.327636i
\(88\) −1528.36 + 2647.19i −1.85140 + 3.20672i
\(89\) 993.782 1.18360 0.591801 0.806084i \(-0.298417\pi\)
0.591801 + 0.806084i \(0.298417\pi\)
\(90\) 716.344 42.3375i 0.838992 0.0495863i
\(91\) 485.423 0.559189
\(92\) 364.320 631.021i 0.412859 0.715092i
\(93\) −807.097 1307.25i −0.899915 1.45759i
\(94\) 233.435 + 404.322i 0.256139 + 0.443645i
\(95\) 278.347 + 482.111i 0.300608 + 0.520668i
\(96\) −1250.41 2025.29i −1.32937 2.15318i
\(97\) −440.708 + 763.328i −0.461310 + 0.799012i −0.999027 0.0441134i \(-0.985954\pi\)
0.537717 + 0.843126i \(0.319287\pi\)
\(98\) 863.956 0.890538
\(99\) 567.656 1132.71i 0.576278 1.14992i
\(100\) 506.366 0.506366
\(101\) −604.869 + 1047.66i −0.595909 + 1.03214i 0.397509 + 0.917598i \(0.369875\pi\)
−0.993418 + 0.114546i \(0.963459\pi\)
\(102\) 715.252 1327.88i 0.694319 1.28902i
\(103\) −372.421 645.053i −0.356270 0.617077i 0.631065 0.775730i \(-0.282618\pi\)
−0.987334 + 0.158653i \(0.949285\pi\)
\(104\) −1176.90 2038.45i −1.10966 1.92198i
\(105\) −348.866 + 10.3004i −0.324246 + 0.00957349i
\(106\) −1273.72 + 2206.15i −1.16712 + 2.02151i
\(107\) −1000.14 −0.903622 −0.451811 0.892114i \(-0.649222\pi\)
−0.451811 + 0.892114i \(0.649222\pi\)
\(108\) 1632.89 + 2325.65i 1.45486 + 2.07209i
\(109\) −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
\(111\) 275.493 8.13403i 0.235573 0.00695538i
\(112\) 1237.33 + 2143.12i 1.04390 + 1.80809i
\(113\) 662.451 + 1147.40i 0.551488 + 0.955206i 0.998168 + 0.0605114i \(0.0192732\pi\)
−0.446679 + 0.894694i \(0.647394\pi\)
\(114\) −1458.33 + 2707.42i −1.19812 + 2.22432i
\(115\) −89.9350 + 155.772i −0.0729260 + 0.126311i
\(116\) 1177.15 0.942202
\(117\) 536.818 + 814.673i 0.424178 + 0.643731i
\(118\) −3378.61 −2.63582
\(119\) −366.789 + 635.297i −0.282550 + 0.489391i
\(120\) 889.074 + 1440.03i 0.676341 + 1.09547i
\(121\) −435.508 754.321i −0.327203 0.566733i
\(122\) 127.640 + 221.080i 0.0947215 + 0.164062i
\(123\) 350.388 + 567.522i 0.256857 + 0.416030i
\(124\) 2994.31 5186.30i 2.16853 3.75600i
\(125\) −125.000 −0.0894427
\(126\) −1060.83 1609.91i −0.750047 1.13827i
\(127\) −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
\(129\) −404.542 + 751.039i −0.276108 + 0.512599i
\(130\) 480.185 + 831.705i 0.323962 + 0.561118i
\(131\) −691.995 1198.57i −0.461526 0.799386i 0.537512 0.843256i \(-0.319364\pi\)
−0.999037 + 0.0438704i \(0.986031\pi\)
\(132\) 4936.59 145.755i 3.25511 0.0961084i
\(133\) 747.847 1295.31i 0.487568 0.844492i
\(134\) 153.715 0.0990970
\(135\) −403.090 574.102i −0.256981 0.366006i
\(136\) 3557.09 2.24278
\(137\) −773.568 + 1339.86i −0.482411 + 0.835561i −0.999796 0.0201918i \(-0.993572\pi\)
0.517385 + 0.855753i \(0.326906\pi\)
\(138\) −993.176 + 29.3239i −0.612643 + 0.0180885i
\(139\) 269.752 + 467.225i 0.164605 + 0.285104i 0.936515 0.350628i \(-0.114032\pi\)
−0.771910 + 0.635732i \(0.780698\pi\)
\(140\) −680.238 1178.21i −0.410647 0.711261i
\(141\) 216.430 401.806i 0.129267 0.239987i
\(142\) 1531.35 2652.38i 0.904988 1.56748i
\(143\) 1695.64 0.991586
\(144\) −2228.41 + 4446.61i −1.28959 + 2.57327i
\(145\) −290.588 −0.166427
\(146\) 2219.38 3844.07i 1.25806 2.17902i
\(147\) −443.680 718.627i −0.248940 0.403206i
\(148\) 537.170 + 930.406i 0.298345 + 0.516749i
\(149\) 602.335 + 1043.27i 0.331176 + 0.573613i 0.982743 0.184978i \(-0.0592214\pi\)
−0.651567 + 0.758591i \(0.725888\pi\)
\(150\) −362.750 587.545i −0.197456 0.319819i
\(151\) −1486.46 + 2574.62i −0.801100 + 1.38755i 0.117793 + 0.993038i \(0.462418\pi\)
−0.918893 + 0.394508i \(0.870915\pi\)
\(152\) −7252.55 −3.87013
\(153\) −1471.82 + 86.9881i −0.777712 + 0.0459645i
\(154\) −3350.82 −1.75336
\(155\) −739.167 + 1280.28i −0.383041 + 0.663446i
\(156\) −1803.49 + 3348.21i −0.925607 + 1.71840i
\(157\) 197.880 + 342.739i 0.100590 + 0.174226i 0.911928 0.410351i \(-0.134594\pi\)
−0.811338 + 0.584577i \(0.801260\pi\)
\(158\) −541.484 937.877i −0.272646 0.472238i
\(159\) 2489.16 73.4932i 1.24153 0.0366566i
\(160\) −1145.17 + 1983.49i −0.565836 + 0.980056i
\(161\) 483.265 0.236563
\(162\) 1528.72 3560.71i 0.741404 1.72689i
\(163\) 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
\(165\) −1218.63 + 35.9806i −0.574972 + 0.0169763i
\(166\) 1234.47 + 2138.16i 0.577188 + 0.999719i
\(167\) −1017.49 1762.34i −0.471470 0.816609i 0.527998 0.849246i \(-0.322943\pi\)
−0.999467 + 0.0326366i \(0.989610\pi\)
\(168\) 2156.29 4003.18i 0.990244 1.83841i
\(169\) 445.643 771.876i 0.202842 0.351332i
\(170\) −1451.32 −0.654773
\(171\) 3000.91 177.360i 1.34202 0.0793163i
\(172\) −3325.24 −1.47411
\(173\) −773.458 + 1339.67i −0.339913 + 0.588746i −0.984416 0.175855i \(-0.943731\pi\)
0.644503 + 0.764602i \(0.277064\pi\)
\(174\) −843.286 1365.87i −0.367410 0.595092i
\(175\) 167.922 + 290.849i 0.0725353 + 0.125635i
\(176\) 4322.15 + 7486.19i 1.85111 + 3.20621i
\(177\) 1735.07 + 2810.28i 0.736812 + 1.19341i
\(178\) 2641.23 4574.74i 1.11218 1.92636i
\(179\) −823.973 −0.344059 −0.172030 0.985092i \(-0.555033\pi\)
−0.172030 + 0.985092i \(0.555033\pi\)
\(180\) 1225.09 2444.58i 0.507295 1.01227i
\(181\) −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
\(183\) 118.342 219.704i 0.0478037 0.0887485i
\(184\) −1171.67 2029.38i −0.469437 0.813088i
\(185\) −132.604 229.677i −0.0526987 0.0912769i
\(186\) −8162.82 + 241.010i −3.21789 + 0.0950093i
\(187\) −1281.24 + 2219.17i −0.501034 + 0.867816i
\(188\) 1779.00 0.690144
\(189\) −794.315 + 1709.14i −0.305703 + 0.657786i
\(190\) 2959.11 1.12988
\(191\) 1523.46 2638.72i 0.577141 0.999637i −0.418664 0.908141i \(-0.637502\pi\)
0.995805 0.0914964i \(-0.0291650\pi\)
\(192\) −4992.18 + 147.396i −1.87645 + 0.0554030i
\(193\) −945.452 1637.57i −0.352617 0.610751i 0.634090 0.773259i \(-0.281375\pi\)
−0.986707 + 0.162508i \(0.948042\pi\)
\(194\) 2342.58 + 4057.48i 0.866947 + 1.50160i
\(195\) 445.204 826.529i 0.163496 0.303533i
\(196\) 1646.04 2851.03i 0.599870 1.03901i
\(197\) 3652.00 1.32078 0.660392 0.750921i \(-0.270390\pi\)
0.660392 + 0.750921i \(0.270390\pi\)
\(198\) −3705.60 5623.60i −1.33003 2.01844i
\(199\) 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
\(201\) −78.9398 127.858i −0.0277014 0.0448678i
\(202\) 3215.19 + 5568.87i 1.11990 + 1.93972i
\(203\) 390.367 + 676.136i 0.134968 + 0.233771i
\(204\) −3019.23 4890.24i −1.03622 1.67836i
\(205\) 320.898 555.811i 0.109329 0.189364i
\(206\) −3959.22 −1.33909
\(207\) 534.432 + 811.051i 0.179447 + 0.272328i
\(208\) −6656.47 −2.21896
\(209\) 2612.32 4524.67i 0.864583 1.49750i
\(210\) −879.784 + 1633.34i −0.289100 + 0.536718i
\(211\) −2473.90 4284.92i −0.807159 1.39804i −0.914824 0.403853i \(-0.867671\pi\)
0.107666 0.994187i \(-0.465662\pi\)
\(212\) 4853.49 + 8406.48i 1.57235 + 2.72339i
\(213\) −2992.63 + 88.3585i −0.962684 + 0.0284236i
\(214\) −2658.14 + 4604.03i −0.849096 + 1.47068i
\(215\) 820.858 0.260382
\(216\) 9103.02 808.189i 2.86751 0.254585i
\(217\) 3971.91 1.24254
\(218\) −2433.22 + 4214.46i −0.755956 + 1.30935i
\(219\) −4337.19 + 128.057i −1.33827 + 0.0395128i
\(220\) −2376.15 4115.62i −0.728183 1.26125i
\(221\) −986.606 1708.85i −0.300300 0.520135i
\(222\) 694.748 1289.81i 0.210038 0.389939i
\(223\) −552.056 + 956.189i −0.165778 + 0.287135i −0.936931 0.349514i \(-0.886347\pi\)
0.771154 + 0.636649i \(0.219680\pi\)
\(224\) 6153.56 1.83550
\(225\) −302.423 + 603.461i −0.0896068 + 0.178803i
\(226\) 7042.53 2.07284
\(227\) 1910.12 3308.43i 0.558498 0.967348i −0.439124 0.898427i \(-0.644711\pi\)
0.997622 0.0689210i \(-0.0219556\pi\)
\(228\) 6155.92 + 9970.72i 1.78810 + 2.89617i
\(229\) −72.3848 125.374i −0.0208879 0.0361788i 0.855393 0.517980i \(-0.173316\pi\)
−0.876280 + 0.481801i \(0.839983\pi\)
\(230\) 478.050 + 828.008i 0.137051 + 0.237379i
\(231\) 1720.80 + 2787.17i 0.490130 + 0.793862i
\(232\) 1892.87 3278.55i 0.535661 0.927792i
\(233\) 1286.31 0.361670 0.180835 0.983513i \(-0.442120\pi\)
0.180835 + 0.983513i \(0.442120\pi\)
\(234\) 5176.97 305.970i 1.44628 0.0854782i
\(235\) −439.159 −0.121905
\(236\) −6437.07 + 11149.3i −1.77550 + 3.07525i
\(237\) −502.037 + 932.041i −0.137598 + 0.255454i
\(238\) 1949.67 + 3376.92i 0.531001 + 0.919721i
\(239\) −2109.73 3654.15i −0.570991 0.988986i −0.996465 0.0840147i \(-0.973226\pi\)
0.425473 0.904971i \(-0.360108\pi\)
\(240\) 4783.91 141.247i 1.28667 0.0379893i
\(241\) −1141.57 + 1977.25i −0.305124 + 0.528490i −0.977289 0.211912i \(-0.932031\pi\)
0.672165 + 0.740401i \(0.265364\pi\)
\(242\) −4629.89 −1.22984
\(243\) −3746.82 + 557.020i −0.989129 + 0.147049i
\(244\) 972.742 0.255219
\(245\) −406.338 + 703.797i −0.105959 + 0.183526i
\(246\) 3543.76 104.631i 0.918462 0.0271179i
\(247\) 2011.59 + 3484.18i 0.518197 + 0.897543i
\(248\) −9629.81 16679.3i −2.46570 4.27072i
\(249\) 1144.54 2124.85i 0.291293 0.540791i
\(250\) −332.219 + 575.421i −0.0840456 + 0.145571i
\(251\) −7922.23 −1.99222 −0.996109 0.0881290i \(-0.971911\pi\)
−0.996109 + 0.0881290i \(0.971911\pi\)
\(252\) −7333.77 + 433.442i −1.83327 + 0.108350i
\(253\) 1688.10 0.419487
\(254\) −2640.84 + 4574.06i −0.652366 + 1.12993i
\(255\) 745.320 + 1207.19i 0.183034 + 0.296460i
\(256\) 5.46197 + 9.46041i 0.00133349 + 0.00230967i
\(257\) −1131.09 1959.10i −0.274535 0.475508i 0.695483 0.718542i \(-0.255190\pi\)
−0.970018 + 0.243035i \(0.921857\pi\)
\(258\) 2382.13 + 3858.33i 0.574826 + 0.931043i
\(259\) −356.274 + 617.085i −0.0854741 + 0.148045i
\(260\) 3659.47 0.872888
\(261\) −703.043 + 1402.87i −0.166733 + 0.332702i
\(262\) −7356.61 −1.73471
\(263\) −81.7349 + 141.569i −0.0191635 + 0.0331921i −0.875448 0.483312i \(-0.839434\pi\)
0.856285 + 0.516504i \(0.172767\pi\)
\(264\) 7532.17 13983.6i 1.75596 3.25997i
\(265\) −1198.12 2075.20i −0.277735 0.481051i
\(266\) −3975.18 6885.22i −0.916294 1.58707i
\(267\) −5161.59 + 152.398i −1.18309 + 0.0349311i
\(268\) 292.865 507.257i 0.0667521 0.115618i
\(269\) 3304.13 0.748908 0.374454 0.927246i \(-0.377830\pi\)
0.374454 + 0.927246i \(0.377830\pi\)
\(270\) −3714.12 + 329.749i −0.837163 + 0.0743254i
\(271\) −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
\(273\) −2521.23 + 74.4403i −0.558945 + 0.0165031i
\(274\) 4111.91 + 7122.03i 0.906603 + 1.57028i
\(275\) 586.570 + 1015.97i 0.128624 + 0.222783i
\(276\) −1795.47 + 3333.32i −0.391575 + 0.726965i
\(277\) 2121.67 3674.85i 0.460213 0.797112i −0.538758 0.842460i \(-0.681106\pi\)
0.998971 + 0.0453482i \(0.0144397\pi\)
\(278\) 2867.74 0.618689
\(279\) 4392.44 + 6665.95i 0.942540 + 1.43039i
\(280\) −4375.33 −0.933844
\(281\) 1311.15 2270.97i 0.278350 0.482117i −0.692625 0.721298i \(-0.743546\pi\)
0.970975 + 0.239181i \(0.0768791\pi\)
\(282\) −1274.44 2064.21i −0.269120 0.435893i
\(283\) 3.53735 + 6.12688i 0.000743017 + 0.00128694i 0.866397 0.499356i \(-0.166430\pi\)
−0.865654 + 0.500643i \(0.833097\pi\)
\(284\) −5835.18 10106.8i −1.21921 2.11173i
\(285\) −1519.63 2461.34i −0.315843 0.511570i
\(286\) 4506.60 7805.66i 0.931751 1.61384i
\(287\) −1724.34 −0.354650
\(288\) 6805.08 + 10327.4i 1.39234 + 2.11301i
\(289\) −1931.06 −0.393051
\(290\) −772.310 + 1337.68i −0.156385 + 0.270867i
\(291\) 2171.93 4032.22i 0.437528 0.812279i
\(292\) −8456.88 14647.7i −1.69487 2.93560i
\(293\) 2238.75 + 3877.62i 0.446378 + 0.773150i 0.998147 0.0608470i \(-0.0193802\pi\)
−0.551769 + 0.833997i \(0.686047\pi\)
\(294\) −4487.29 + 132.489i −0.890151 + 0.0262820i
\(295\) 1589.04 2752.29i 0.313618 0.543202i
\(296\) 3455.12 0.678461
\(297\) −2774.64 + 5970.23i −0.542090 + 1.16642i
\(298\) 6403.43 1.24477
\(299\) −649.955 + 1125.75i −0.125712 + 0.217739i
\(300\) −2630.01 + 77.6519i −0.506145 + 0.0149441i
\(301\) −1102.72 1909.96i −0.211162 0.365743i
\(302\) 7901.27 + 13685.4i 1.50552 + 2.60764i
\(303\) 2980.96 5534.21i 0.565188 1.04928i
\(304\) −10255.0 + 17762.2i −1.93475 + 3.35109i
\(305\) −240.128 −0.0450810
\(306\) −3511.31 + 7006.54i −0.655975 + 1.30895i
\(307\) −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
\(309\) 2033.24 + 3293.22i 0.374326 + 0.606294i
\(310\) 3929.05 + 6805.31i 0.719855 + 1.24683i
\(311\) 3647.83 + 6318.23i 0.665111 + 1.15201i 0.979255 + 0.202630i \(0.0649490\pi\)
−0.314145 + 0.949375i \(0.601718\pi\)
\(312\) 6425.28 + 10407.0i 1.16590 + 1.88840i
\(313\) 318.036 550.854i 0.0574328 0.0994765i −0.835880 0.548913i \(-0.815042\pi\)
0.893312 + 0.449436i \(0.148375\pi\)
\(314\) 2103.67 0.378080
\(315\) 1810.39 106.998i 0.323823 0.0191386i
\(316\) −4126.62 −0.734623
\(317\) 3073.18 5322.90i 0.544501 0.943104i −0.454137 0.890932i \(-0.650052\pi\)
0.998638 0.0521721i \(-0.0166144\pi\)
\(318\) 6277.25 11653.8i 1.10695 2.05508i
\(319\) 1363.60 + 2361.83i 0.239332 + 0.414536i
\(320\) 2402.91 + 4161.96i 0.419771 + 0.727064i
\(321\) 5194.64 153.374i 0.903229 0.0266682i
\(322\) 1284.40 2224.65i 0.222288 0.385014i
\(323\) −6079.89 −1.04735
\(324\) −8837.68 11828.7i −1.51538 2.02825i
\(325\) −903.367 −0.154184
\(326\) 10262.7 17775.6i 1.74356 3.01994i
\(327\) 4755.10 140.396i 0.804151 0.0237429i
\(328\) 4180.63 + 7241.06i 0.703770 + 1.21897i
\(329\) 589.954 + 1021.83i 0.0988609 + 0.171232i
\(330\) −3073.19 + 5705.44i −0.512648 + 0.951740i
\(331\) −5867.20 + 10162.3i −0.974291 + 1.68752i −0.292036 + 0.956407i \(0.594333\pi\)
−0.682255 + 0.731114i \(0.739001\pi\)
\(332\) 9407.82 1.55518
\(333\) −1429.63 + 84.4945i −0.235265 + 0.0139047i
\(334\) −10816.9 −1.77208
\(335\) −72.2958 + 125.220i −0.0117909 + 0.0204224i
\(336\) −6755.22 10941.4i −1.09681 1.77649i
\(337\) −3141.65 5441.49i −0.507823 0.879575i −0.999959 0.00905696i \(-0.997117\pi\)
0.492136 0.870518i \(-0.336216\pi\)
\(338\) −2368.82 4102.91i −0.381203 0.660264i
\(339\) −3616.65 5857.88i −0.579438 0.938514i
\(340\) −2765.12 + 4789.33i −0.441058 + 0.763934i
\(341\) 13874.4 2.20334
\(342\) 7159.22 14285.7i 1.13195 2.25871i
\(343\) 6791.22 1.06907
\(344\) −5347.04 + 9261.34i −0.838061 + 1.45156i
\(345\) 443.225 822.854i 0.0691664 0.128409i
\(346\) 4111.32 + 7121.02i 0.638803 + 1.10644i
\(347\) −2400.41 4157.63i −0.371357 0.643209i 0.618418 0.785849i \(-0.287774\pi\)
−0.989775 + 0.142641i \(0.954441\pi\)
\(348\) −6113.98 + 180.517i −0.941792 + 0.0278068i
\(349\) 1946.23 3370.97i 0.298508 0.517031i −0.677287 0.735719i \(-0.736844\pi\)
0.975795 + 0.218688i \(0.0701778\pi\)
\(350\) 1785.18 0.272633
\(351\) −2913.11 4149.00i −0.442992 0.630932i
\(352\) 21495.2 3.25482
\(353\) 1483.14 2568.87i 0.223624 0.387329i −0.732281 0.681002i \(-0.761544\pi\)
0.955906 + 0.293673i \(0.0948778\pi\)
\(354\) 17548.1 518.115i 2.63467 0.0777896i
\(355\) 1440.46 + 2494.94i 0.215356 + 0.373008i
\(356\) −10064.3 17431.9i −1.49834 2.59520i
\(357\) 1807.64 3355.91i 0.267984 0.497517i
\(358\) −2189.92 + 3793.05i −0.323298 + 0.559969i
\(359\) −9584.91 −1.40911 −0.704557 0.709647i \(-0.748854\pi\)
−0.704557 + 0.709647i \(0.748854\pi\)
\(360\) −4838.58 7343.01i −0.708377 1.07503i
\(361\) 5537.30 0.807304
\(362\) −11703.5 + 20271.1i −1.69924 + 2.94317i
\(363\) 2377.65 + 3851.08i 0.343787 + 0.556829i
\(364\) −4916.03 8514.82i −0.707885 1.22609i
\(365\) 2087.64 + 3615.90i 0.299376 + 0.518534i
\(366\) −696.853 1128.69i −0.0995221 0.161195i
\(367\) −2268.59 + 3929.31i −0.322669 + 0.558879i −0.981038 0.193817i \(-0.937913\pi\)
0.658369 + 0.752695i \(0.271247\pi\)
\(368\) −6626.88 −0.938722
\(369\) −1906.91 2893.91i −0.269023 0.408269i
\(370\) −1409.72 −0.198075
\(371\) −3219.04 + 5575.54i −0.450469 + 0.780236i
\(372\) −14756.8 + 27396.3i −2.05673 + 3.81836i
\(373\) −6565.65 11372.0i −0.911411 1.57861i −0.812073 0.583557i \(-0.801661\pi\)
−0.0993385 0.995054i \(-0.531673\pi\)
\(374\) 6810.43 + 11796.0i 0.941601 + 1.63090i
\(375\) 649.236 19.1689i 0.0894038 0.00263968i
\(376\) 2860.66 4954.82i 0.392360 0.679588i
\(377\) −2100.06 −0.286892
\(378\) 5756.70 + 8198.99i 0.783314 + 1.11564i
\(379\) −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
\(381\) 5160.83 152.375i 0.693956 0.0204893i
\(382\) −8097.98 14026.1i −1.08463 1.87863i
\(383\) 4298.52 + 7445.25i 0.573483 + 0.993301i 0.996205 + 0.0870420i \(0.0277414\pi\)
−0.422722 + 0.906260i \(0.638925\pi\)
\(384\) −3559.51 + 6608.29i −0.473035 + 0.878198i
\(385\) 1575.97 2729.65i 0.208620 0.361340i
\(386\) −10051.1 −1.32536
\(387\) 1985.97 3962.85i 0.260860 0.520524i
\(388\) 17852.7 2.33592
\(389\) −2221.04 + 3846.95i −0.289489 + 0.501410i −0.973688 0.227886i \(-0.926819\pi\)
0.684199 + 0.729295i \(0.260152\pi\)
\(390\) −2621.57 4246.15i −0.340381 0.551313i
\(391\) −982.219 1701.25i −0.127041 0.220041i
\(392\) −5293.73 9169.01i −0.682076 1.18139i
\(393\) 3777.95 + 6119.12i 0.484917 + 0.785417i
\(394\) 9706.13 16811.5i 1.24109 2.14962i
\(395\) 1018.69 0.129761
\(396\) −25617.7 + 1514.07i −3.25086 + 0.192133i
\(397\) 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
\(399\) −3685.59 + 6842.37i −0.462432 + 0.858514i
\(400\) −2302.66 3988.33i −0.287833 0.498541i
\(401\) 6341.72 + 10984.2i 0.789751 + 1.36789i 0.926119 + 0.377231i \(0.123124\pi\)
−0.136368 + 0.990658i \(0.543543\pi\)
\(402\) −798.381 + 23.5725i −0.0990538 + 0.00292460i
\(403\) −5341.91 + 9252.47i −0.660297 + 1.14367i
\(404\) 24502.8 3.01748
\(405\) 2181.64 + 2920.01i 0.267671 + 0.358263i
\(406\) 4150.00 0.507293
\(407\) −1244.51 + 2155.55i −0.151568 + 0.262523i
\(408\) −18475.1 + 545.484i −2.24180 + 0.0661899i
\(409\) 5556.30 + 9623.79i 0.671739 + 1.16349i 0.977411 + 0.211349i \(0.0677858\pi\)
−0.305671 + 0.952137i \(0.598881\pi\)
\(410\) −1705.73 2954.42i −0.205464 0.355874i
\(411\) 3812.36 7077.71i 0.457542 0.849434i
\(412\) −7543.26 + 13065.3i −0.902014 + 1.56233i
\(413\) −8538.67 −1.01734
\(414\) 5153.95 304.610i 0.611843 0.0361613i
\(415\) −2322.39 −0.274702
\(416\) −8276.08 + 14334.6i −0.975404 + 1.68945i
\(417\) −1472.71 2385.35i −0.172947 0.280122i
\(418\) −13885.8 24050.9i −1.62482 2.81428i
\(419\) −1009.26 1748.09i −0.117675 0.203818i 0.801171 0.598435i \(-0.204211\pi\)
−0.918846 + 0.394617i \(0.870877\pi\)
\(420\) 3713.76 + 6015.16i 0.431459 + 0.698832i
\(421\) 5478.85 9489.65i 0.634259 1.09857i −0.352413 0.935845i \(-0.614639\pi\)
0.986672 0.162724i \(-0.0520280\pi\)
\(422\) −26300.1 −3.03381
\(423\) −1062.49 + 2120.12i −0.122128 + 0.243697i
\(424\) 31218.0 3.57565
\(425\) 682.589 1182.28i 0.0779069 0.134939i
\(426\) −7546.93 + 14011.0i −0.858333 + 1.59351i
\(427\) 322.582 + 558.728i 0.0365593 + 0.0633226i
\(428\) 10128.8 + 17543.5i 1.14391 + 1.98131i
\(429\) −8806.98 + 260.029i −0.991154 + 0.0292642i
\(430\) 2181.64 3778.71i 0.244670 0.423781i
\(431\) −2124.75 −0.237460 −0.118730 0.992927i \(-0.537882\pi\)
−0.118730 + 0.992927i \(0.537882\pi\)
\(432\) 10892.2 23436.9i 1.21308 2.61021i
\(433\) −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
\(435\) 1509.28 44.5620i 0.166355 0.00491169i
\(436\) 9271.73 + 16059.1i 1.01843 + 1.76397i
\(437\) 2002.65 + 3468.69i 0.219221 + 0.379702i
\(438\) −10937.7 + 20306.0i −1.19320 + 2.21520i
\(439\) −346.098 + 599.460i −0.0376273 + 0.0651724i −0.884226 0.467060i \(-0.845313\pi\)
0.846598 + 0.532232i \(0.178647\pi\)
\(440\) −15283.6 −1.65595
\(441\) 2414.63 + 3664.43i 0.260731 + 0.395684i
\(442\) −10488.6 −1.12872
\(443\) 3335.26 5776.83i 0.357704 0.619561i −0.629873 0.776698i \(-0.716893\pi\)
0.987577 + 0.157137i \(0.0502264\pi\)
\(444\) −2932.68 4750.05i −0.313466 0.507719i
\(445\) 2484.45 + 4303.20i 0.264662 + 0.458407i
\(446\) 2934.46 + 5082.63i 0.311549 + 0.539618i
\(447\) −3288.45 5326.28i −0.347960 0.563589i
\(448\) 6456.00 11182.1i 0.680843 1.17925i
\(449\) −9743.18 −1.02407 −0.512037 0.858964i \(-0.671109\pi\)
−0.512037 + 0.858964i \(0.671109\pi\)
\(450\) 1974.19 + 2996.01i 0.206809 + 0.313852i
\(451\) −6023.33 −0.628886
\(452\) 13417.7 23240.1i 1.39627 2.41842i
\(453\) 7325.67 13600.2i 0.759801 1.41058i
\(454\) −10153.3 17586.0i −1.04959 1.81795i
\(455\) 1213.56 + 2101.94i 0.125038 + 0.216573i
\(456\) 37669.0 1112.19i 3.86844 0.114217i
\(457\) −2221.36 + 3847.51i −0.227376 + 0.393827i −0.957030 0.289990i \(-0.906348\pi\)
0.729654 + 0.683817i \(0.239681\pi\)
\(458\) −769.524 −0.0785098
\(459\) 7631.15 677.513i 0.776017 0.0688967i
\(460\) 3643.20 0.369272
\(461\) −9469.70 + 16402.0i −0.956720 + 1.65709i −0.226337 + 0.974049i \(0.572675\pi\)
−0.730383 + 0.683038i \(0.760658\pi\)
\(462\) 17403.8 513.853i 1.75259 0.0517459i
\(463\) 8396.10 + 14542.5i 0.842764 + 1.45971i 0.887549 + 0.460714i \(0.152407\pi\)
−0.0447846 + 0.998997i \(0.514260\pi\)
\(464\) −5353.00 9271.66i −0.535575 0.927642i
\(465\) 3642.82 6762.96i 0.363294 0.674462i
\(466\) 3418.70 5921.36i 0.339846 0.588630i
\(467\) 1367.93 0.135547 0.0677735 0.997701i \(-0.478410\pi\)
0.0677735 + 0.997701i \(0.478410\pi\)
\(468\) 8853.67 17666.8i 0.874489 1.74497i
\(469\) 388.480 0.0382481
\(470\) −1167.18 + 2021.61i −0.114549 + 0.198404i
\(471\) −1080.33 1749.80i −0.105688 0.171182i
\(472\) 20701.8 + 35856.6i 2.01881 + 3.49668i
\(473\) −3851.93 6671.74i −0.374444 0.648556i
\(474\) 2956.23 + 4788.19i 0.286465 + 0.463985i
\(475\) −1391.73 + 2410.55i −0.134436 + 0.232850i
\(476\) 14858.3 1.43074
\(477\) −12917.1 + 763.432i −1.23991 + 0.0732812i
\(478\) −22428.5 −2.14615
\(479\) −101.371 + 175.579i −0.00966960 + 0.0167482i −0.870820 0.491603i \(-0.836411\pi\)
0.861150 + 0.508351i \(0.169745\pi\)
\(480\) 5643.72 10477.7i 0.536665 0.996329i
\(481\) −958.323 1659.86i −0.0908436 0.157346i
\(482\) 6068.01 + 10510.1i 0.573424 + 0.993199i
\(483\) −2510.02 + 74.1094i −0.236460 + 0.00698156i
\(484\) −8821.04 + 15278.5i −0.828423 + 1.43487i
\(485\) −4407.08 −0.412608
\(486\) −7393.95 + 18728.4i −0.690116 + 1.74802i
\(487\) 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
\(489\) −20055.9 + 592.157i −1.85472 + 0.0547612i
\(490\) 2159.89 + 3741.04i 0.199130 + 0.344904i
\(491\) −5856.15 10143.1i −0.538257 0.932289i −0.998998 0.0447541i \(-0.985750\pi\)
0.460741 0.887535i \(-0.347584\pi\)
\(492\) 6406.43 11893.6i 0.587041 1.08985i
\(493\) 1586.82 2748.45i 0.144963 0.251083i
\(494\) 21385.3 1.94771
\(495\) 6323.93 373.758i 0.574221 0.0339377i
\(496\) −54465.7 −4.93061
\(497\) 3870.14 6703.28i 0.349295 0.604996i
\(498\) −6739.57 10916.1i −0.606441 0.982249i
\(499\) −4312.44 7469.36i −0.386876 0.670089i 0.605151 0.796110i \(-0.293113\pi\)
−0.992028 + 0.126021i \(0.959779\pi\)
\(500\) 1265.91 + 2192.63i 0.113227 + 0.196115i
\(501\) 5554.97 + 8997.35i 0.495364 + 0.802339i
\(502\) −21055.3 + 36468.9i −1.87200 + 3.24241i
\(503\) 4856.12 0.430465 0.215232 0.976563i \(-0.430949\pi\)
0.215232 + 0.976563i \(0.430949\pi\)
\(504\) −10585.6 + 21122.8i −0.935557 + 1.86683i
\(505\) −6048.69 −0.532997
\(506\) 4486.56 7770.96i 0.394174 0.682730i
\(507\) −2196.25 + 4077.38i −0.192384 + 0.357165i
\(508\) 10062.9 + 17429.4i 0.878872 + 1.52225i
\(509\) 5425.17 + 9396.67i 0.472429 + 0.818271i 0.999502 0.0315486i \(-0.0100439\pi\)
−0.527073 + 0.849820i \(0.676711\pi\)
\(510\) 7538.01 222.563i 0.654488 0.0193240i
\(511\) 5608.96 9715.01i 0.485569 0.841030i
\(512\) 11614.3 1.00251
\(513\) −15559.2 + 1381.38i −1.33909 + 0.118888i
\(514\) −12024.6 −1.03187
\(515\) 1862.11 3225.26i 0.159329 0.275965i
\(516\) 17270.9 509.930i 1.47347 0.0435047i
\(517\) 2060.78 + 3569.38i 0.175306 + 0.303639i
\(518\) 1893.78 + 3280.12i 0.160633 + 0.278224i
\(519\) 3811.81 7076.70i 0.322389 0.598521i
\(520\) 5884.49 10192.2i 0.496254 0.859537i
\(521\) 3559.30 0.299301 0.149651 0.988739i \(-0.452185\pi\)
0.149651 + 0.988739i \(0.452185\pi\)
\(522\) 4589.39 + 6964.84i 0.384813 + 0.583990i
\(523\) 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
\(525\) −916.768 1484.88i −0.0762115 0.123439i
\(526\) 434.463 + 752.511i 0.0360142 + 0.0623784i
\(527\) −8072.77 13982.4i −0.667277 1.15576i
\(528\) −23596.8 38219.6i −1.94492 3.15018i
\(529\) 5436.44 9416.18i 0.446818 0.773912i
\(530\) −12737.2 −1.04390
\(531\) −9442.72 14330.2i −0.771712 1.17115i
\(532\) −30294.7 −2.46888
\(533\) 2319.11 4016.81i 0.188465 0.326430i
\(534\) −13016.7 + 24165.7i −1.05485 + 1.95834i
\(535\) −2500.36 4330.75i −0.202056 0.349971i
\(536\) −941.863 1631.35i −0.0758998 0.131462i
\(537\) 4279.63 126.357i 0.343910 0.0101541i
\(538\) 8781.56 15210.1i 0.703717 1.21887i
\(539\) 7627.06 0.609500
\(540\) −5988.12 + 12884.7i −0.477199 + 1.02680i
\(541\) 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
\(543\) 22871.5 675.290i 1.80757 0.0533692i
\(544\) −12506.9 21662.6i −0.985715 1.70731i
\(545\) −2288.79 3964.31i −0.179892 0.311582i
\(546\) −6358.14 + 11804.0i −0.498358 + 0.925210i
\(547\) 10609.1 18375.5i 0.829272 1.43634i −0.0693385 0.997593i \(-0.522089\pi\)
0.898610 0.438748i \(-0.144578\pi\)
\(548\) 31336.7 2.44277
\(549\) −580.963 + 1159.27i −0.0451637 + 0.0901206i
\(550\) 6235.84 0.483449
\(551\) −3235.36 + 5603.81i −0.250147 + 0.433268i
\(552\) 6396.71 + 10360.7i 0.493228 + 0.798880i
\(553\) −1368.48 2370.27i −0.105232 0.182268i
\(554\) −11277.8 19533.7i −0.864885 1.49803i
\(555\) 723.954 + 1172.58i 0.0553696 + 0.0896818i
\(556\) 5463.73 9463.46i 0.416752 0.721835i
\(557\) 2506.42 0.190665 0.0953324 0.995445i \(-0.469609\pi\)
0.0953324 + 0.995445i \(0.469609\pi\)
\(558\) 42359.8 2503.56i 3.21368 0.189936i
\(559\) 5932.29 0.448854
\(560\) −6186.66 + 10715.6i −0.466847 + 0.808602i
\(561\) 6314.29 11722.6i 0.475204 0.882225i
\(562\) −6969.41 12071.4i −0.523108 0.906050i
\(563\) −8639.80 14964.6i −0.646757 1.12022i −0.983893 0.178759i \(-0.942792\pi\)
0.337136 0.941456i \(-0.390542\pi\)
\(564\) −9239.93 + 272.812i −0.689843 + 0.0203679i
\(565\) −3312.26 + 5737.00i −0.246633 + 0.427181i
\(566\) 37.6057 0.00279273
\(567\) 3863.48 8998.89i 0.286157 0.666522i
\(568\) −37532.3 −2.77257
\(569\) 10254.1 17760.5i 0.755487 1.30854i −0.189645 0.981853i \(-0.560734\pi\)
0.945132 0.326689i \(-0.105933\pi\)
\(570\) −15369.3 + 453.783i −1.12938 + 0.0333454i
\(571\) −3412.53 5910.68i −0.250105 0.433195i 0.713449 0.700707i \(-0.247132\pi\)
−0.963555 + 0.267512i \(0.913799\pi\)
\(572\) −17172.3 29743.3i −1.25526 2.17418i
\(573\) −7508.05 + 13938.8i −0.547388 + 1.01623i
\(574\) −4582.87 + 7937.77i −0.333250 + 0.577206i
\(575\) −899.350 −0.0652270
\(576\) 25906.2 1531.11i 1.87400 0.110758i
\(577\) 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
\(579\) 5161.70 + 8360.38i 0.370489 + 0.600079i
\(580\) 2942.87 + 5097.20i 0.210683 + 0.364913i
\(581\) 3119.83 + 5403.71i 0.222775 + 0.385858i
\(582\) −12789.3 20714.8i −0.910885 1.47536i
\(583\) −11244.5 + 19476.0i −0.798798 + 1.38356i
\(584\) −54395.2 −3.85426
\(585\) −2185.59 + 4361.17i −0.154467 + 0.308226i
\(586\) 23800.1 1.67777
\(587\) −9344.04 + 16184.3i −0.657018 + 1.13799i 0.324365 + 0.945932i \(0.394849\pi\)
−0.981384 + 0.192057i \(0.938484\pi\)
\(588\) −8112.16 + 15060.4i −0.568945 + 1.05626i
\(589\) 16459.6 + 28508.8i 1.15145 + 1.99437i
\(590\) −8446.53 14629.8i −0.589387 1.02085i
\(591\) −18968.1 + 560.040i −1.32021 + 0.0389797i
\(592\) 4885.48 8461.91i 0.339176 0.587470i
\(593\) −12434.5 −0.861084 −0.430542 0.902570i \(-0.641678\pi\)
−0.430542 + 0.902570i \(0.641678\pi\)
\(594\) 20108.8 + 28640.1i 1.38902 + 1.97831i
\(595\) −3667.89 −0.252721
\(596\) 12200.1 21131.1i 0.838480 1.45229i
\(597\) −16710.1 + 493.371i −1.14556 + 0.0338230i
\(598\) 3454.84 + 5983.96i 0.236252 + 0.409201i
\(599\) 3021.52 + 5233.42i 0.206103 + 0.356981i 0.950484 0.310774i \(-0.100588\pi\)
−0.744380 + 0.667756i \(0.767255\pi\)
\(600\) −4012.82 + 7449.87i −0.273038 + 0.506900i
\(601\) 315.654 546.729i 0.0214239 0.0371074i −0.855115 0.518439i \(-0.826513\pi\)
0.876539 + 0.481332i \(0.159847\pi\)
\(602\) −11723.0 −0.793679
\(603\) 429.612 + 651.977i 0.0290135 + 0.0440307i
\(604\) 60215.2 4.05649
\(605\) 2177.54 3771.61i 0.146330 0.253451i
\(606\) −17553.3 28431.0i −1.17666 1.90583i
\(607\) 4727.43 + 8188.16i 0.316113 + 0.547524i 0.979673 0.200599i \(-0.0642888\pi\)
−0.663560 + 0.748123i \(0.730955\pi\)
\(608\) 25500.4 + 44167.9i 1.70095 + 2.94613i
\(609\) −2131.21 3451.91i −0.141808 0.229686i
\(610\) −638.202 + 1105.40i −0.0423607 + 0.0733709i
\(611\) −3173.77 −0.210143
\(612\) 16431.5 + 24936.3i 1.08530 + 1.64705i
\(613\) −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
\(615\) −1581.47 + 2936.03i −0.103693 + 0.192508i
\(616\) 20531.5 + 35561.7i 1.34292 + 2.32601i
\(617\) 1169.26 + 2025.22i 0.0762930 + 0.132143i 0.901648 0.432471i \(-0.142358\pi\)
−0.825355 + 0.564614i \(0.809025\pi\)
\(618\) 20563.7 607.152i 1.33850 0.0395198i
\(619\) 5965.11 10331.9i 0.387331 0.670878i −0.604758 0.796409i \(-0.706730\pi\)
0.992090 + 0.125531i \(0.0400636\pi\)
\(620\) 29943.1 1.93959
\(621\) −2900.15 4130.55i −0.187406 0.266914i
\(622\) 38780.1 2.49991
\(623\) 6675.09 11561.6i 0.429265 0.743509i
\(624\) 34573.0 1020.78i 2.21799 0.0654870i
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −1690.52 2928.07i −0.107934 0.186948i
\(627\) −12874.2 + 23901.2i −0.820012 + 1.52237i
\(628\) 4008.00 6942.05i 0.254676 0.441111i
\(629\) 2896.46 0.183608
\(630\) 4319.03 8618.28i 0.273134 0.545017i
\(631\) 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
\(633\) 13506.3 + 21876.0i 0.848067 + 1.37361i
\(634\) −16335.5 28293.9i −1.02329 1.77239i
\(635\) −2484.09 4302.57i −0.155241 0.268885i
\(636\) −26497.6 42918.1i −1.65204 2.67580i
\(637\) −2936.58 + 5086.30i −0.182655 + 0.316368i
\(638\) 14496.5 0.899562
\(639\) 15529.8 917.848i 0.961425 0.0568224i
\(640\) 7222.62 0.446093
\(641\) −7462.65 + 12925.7i −0.459839 + 0.796465i −0.998952 0.0457684i \(-0.985426\pi\)
0.539113 + 0.842234i \(0.318760\pi\)
\(642\) 13100.0 24320.4i 0.805323 1.49510i
\(643\) −9502.84 16459.4i −0.582823 1.00948i −0.995143 0.0984406i \(-0.968615\pi\)
0.412319 0.911039i \(-0.364719\pi\)
\(644\) −4894.18 8476.96i −0.299468 0.518694i
\(645\) −4263.45 + 125.880i −0.260268 + 0.00768452i
\(646\) −16158.8 + 27987.9i −0.984151 + 1.70460i
\(647\) 9252.81 0.562234 0.281117 0.959673i \(-0.409295\pi\)
0.281117 + 0.959673i \(0.409295\pi\)
\(648\) −47156.1 + 5593.61i −2.85875 + 0.339101i
\(649\) −29826.6 −1.80400
\(650\) −2400.93 + 4158.53i −0.144880 + 0.250940i
\(651\) −20629.7 + 609.098i −1.24200 + 0.0366704i
\(652\) −39106.0 67733.5i −2.34894 4.06848i
\(653\) −11475.3 19875.9i −0.687695 1.19112i −0.972582 0.232561i \(-0.925289\pi\)
0.284887 0.958561i \(-0.408044\pi\)
\(654\) 11991.6 22262.6i 0.716985 1.33109i
\(655\) 3459.97 5992.85i 0.206401 0.357496i
\(656\) 23645.4 1.40731
\(657\) 22507.3 1330.23i 1.33652 0.0789912i
\(658\) 6271.81 0.371582
\(659\) −3258.54 + 5643.96i −0.192617 + 0.333623i −0.946117 0.323826i \(-0.895031\pi\)
0.753500 + 0.657448i \(0.228364\pi\)
\(660\) 12972.6 + 21011.7i 0.765088 + 1.23921i
\(661\) 2598.16 + 4500.15i 0.152885 + 0.264804i 0.932287 0.361720i \(-0.117810\pi\)
−0.779402 + 0.626524i \(0.784477\pi\)
\(662\) 31187.1 + 54017.7i 1.83100 + 3.17139i
\(663\) 5386.37 + 8724.29i 0.315520 + 0.511045i
\(664\) 15127.9 26202.3i 0.884153 1.53140i
\(665\) 7478.47 0.436094
\(666\) −3410.65 + 6805.68i −0.198439 + 0.395968i
\(667\) −2090.72 −0.121369
\(668\) −20608.8 + 35695.5i −1.19368 + 2.06751i
\(669\) 2720.69 5051.00i 0.157231 0.291903i
\(670\) 384.289 + 665.607i 0.0221588 + 0.0383801i
\(671\) 1126.82 + 1951.71i 0.0648291 + 0.112287i
\(672\) −31960.9 + 943.658i −1.83470 + 0.0541702i
\(673\) −14095.0 + 24413.2i −0.807313 + 1.39831i 0.107405 + 0.994215i \(0.465746\pi\)
−0.914718 + 0.404093i \(0.867587\pi\)
\(674\) −33398.9 −1.90872
\(675\) 1478.21 3180.69i 0.0842909 0.181370i
\(676\) −18052.7 −1.02712
\(677\) −4338.44 + 7514.40i −0.246292 + 0.426590i −0.962494 0.271303i \(-0.912546\pi\)
0.716202 + 0.697893i \(0.245879\pi\)
\(678\) −36578.1 + 1079.98i −2.07194 + 0.0611747i
\(679\) 5920.34 + 10254.3i 0.334613 + 0.579566i
\(680\) 8892.71 + 15402.6i 0.501500 + 0.868624i
\(681\) −9413.60 + 17476.5i −0.529706 + 0.983409i
\(682\) 36874.6 63868.7i 2.07039 3.58601i
\(683\) 20624.1 1.15543 0.577714 0.816239i \(-0.303945\pi\)
0.577714 + 0.816239i \(0.303945\pi\)
\(684\) −33502.2 50842.8i −1.87279 2.84214i
\(685\) −7735.68 −0.431482
\(686\) 18049.4 31262.5i 1.00456 1.73995i
\(687\) 395.185 + 640.079i 0.0219465 + 0.0355466i
\(688\) 15121.3 + 26190.8i 0.837926 + 1.45133i
\(689\) −8658.72 14997.3i −0.478768 0.829250i
\(690\) −2609.92 4227.27i −0.143997 0.233231i
\(691\) −3493.03 + 6050.10i −0.192303 + 0.333078i −0.946013 0.324129i \(-0.894929\pi\)
0.753710 + 0.657207i \(0.228262\pi\)
\(692\) 31332.2 1.72120
\(693\) −9365.04 14212.3i −0.513346 0.779051i
\(694\) −25518.8 −1.39579
\(695\) −1348.76 + 2336.12i −0.0736136 + 0.127502i
\(696\) −9328.61 + 17318.7i −0.508046 + 0.943196i
\(697\) 3504.66 + 6070.25i 0.190457 + 0.329881i
\(698\) −10345.2 17918.4i −0.560991 0.971664i
\(699\) −6680.96 + 197.258i −0.361512 + 0.0106738i
\(700\) 3401.19 5891.03i 0.183647 0.318086i
\(701\) 7848.55 0.422875 0.211438 0.977391i \(-0.432185\pi\)
0.211438 + 0.977391i \(0.432185\pi\)
\(702\) −26841.7 + 2383.07i −1.44312 + 0.128124i
\(703\) −5905.60 −0.316833
\(704\) 22551.6 39060.5i 1.20731 2.09112i
\(705\) 2280.94 67.3457i 0.121852 0.00359771i
\(706\) −7883.63 13654.8i −0.420261 0.727913i
\(707\) 8125.65 + 14074.0i 0.432244 + 0.748669i
\(708\) 31723.6 58895.5i 1.68397 3.12631i
\(709\) 12712.3 22018.3i 0.673371 1.16631i −0.303571 0.952809i \(-0.598179\pi\)
0.976942 0.213504i \(-0.0684876\pi\)
\(710\) 15313.5 0.809445
\(711\) 2464.60 4917.90i 0.129999 0.259403i
\(712\) −64734.5 −3.40734
\(713\) −5318.16 + 9211.33i −0.279336 + 0.483825i
\(714\) −10644.2 17240.4i −0.557913 0.903649i
\(715\) 4239.11 + 7342.35i 0.221725 + 0.384039i
\(716\) 8344.63 + 14453.3i 0.435550 + 0.754394i
\(717\) 11518.1 + 18655.7i 0.599930 + 0.971703i
\(718\) −25474.3 + 44122.8i −1.32409 + 2.29338i
\(719\) 16707.2 0.866584 0.433292 0.901254i \(-0.357352\pi\)
0.433292 + 0.901254i \(0.357352\pi\)
\(720\) −24825.4 + 1467.24i −1.28498 + 0.0759454i
\(721\) −10006.0 −0.516843
\(722\) 14716.8 25490.2i 0.758590 1.31392i
\(723\) 5625.96 10444.7i 0.289394 0.537264i
\(724\) 44596.1 + 77242.7i 2.28923 + 3.96506i
\(725\) −726.469 1258.28i −0.0372143 0.0644571i
\(726\) 24047.1 710.000i 1.22930 0.0362956i
\(727\) −718.240 + 1244.03i −0.0366410 + 0.0634642i −0.883764 0.467932i \(-0.844999\pi\)
0.847123 + 0.531396i \(0.178332\pi\)
\(728\) −31620.3 −1.60979
\(729\) 19375.1 3467.68i 0.984359 0.176176i
\(730\) 22193.8 1.12524
\(731\) −4482.47 + 7763.87i −0.226799 + 0.392828i
\(732\) −5052.31 + 149.171i −0.255108 + 0.00753215i
\(733\) −5770.44 9994.70i −0.290772 0.503633i 0.683220 0.730212i \(-0.260579\pi\)
−0.973993 + 0.226580i \(0.927246\pi\)
\(734\) 12058.7 + 20886.3i 0.606397 + 1.05031i
\(735\) 2002.54 3717.76i 0.100497 0.186574i
\(736\) −8239.28 + 14270.9i −0.412641 + 0.714715i
\(737\) 1357.01 0.0678237
\(738\) −18389.8 + 1086.88i −0.917262 + 0.0542122i
\(739\) 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
\(741\) −10982.3 17788.0i −0.544460 0.881859i
\(742\) 17110.8 + 29636.8i 0.846574 + 1.46631i
\(743\) 13748.5 + 23813.1i 0.678846 + 1.17580i 0.975329 + 0.220758i \(0.0708530\pi\)
−0.296482 + 0.955038i \(0.595814\pi\)
\(744\) 52574.0 + 85153.8i 2.59066 + 4.19609i
\(745\) −3011.67 + 5216.37i −0.148106 + 0.256528i
\(746\) −69799.5 −3.42566
\(747\) −5618.75 + 11211.8i −0.275207 + 0.549153i
\(748\) 51902.0 2.53706
\(749\) −6717.83 + 11635.6i −0.327723 + 0.567632i
\(750\) 1637.27 3039.62i 0.0797128 0.147988i
\(751\) −17197.1 29786.2i −0.835592 1.44729i −0.893548 0.448968i \(-0.851792\pi\)
0.0579559 0.998319i \(-0.481542\pi\)
\(752\) −8089.88 14012.1i −0.392297 0.679479i
\(753\) 41147.2 1214.89i 1.99135 0.0587953i
\(754\) −5581.44 + 9667.33i −0.269581 + 0.466928i
\(755\) −14864.6 −0.716526
\(756\) 38024.3 3375.89i 1.82927 0.162408i
\(757\) −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
\(759\) −8767.82 + 258.873i −0.419304 + 0.0123801i
\(760\) −18131.4 31404.5i −0.865387 1.49889i
\(761\) −223.584 387.259i −0.0106504 0.0184469i 0.860651 0.509195i \(-0.170057\pi\)
−0.871301 + 0.490748i \(0.836724\pi\)
\(762\) 13014.8 24162.2i 0.618734 1.14869i
\(763\) −6149.40 + 10651.1i −0.291774 + 0.505367i
\(764\) −61714.3 −2.92244
\(765\) −4056.23 6155.72i −0.191704 0.290929i
\(766\) 45697.6 2.15551
\(767\) 11483.9 19890.6i 0.540623 0.936387i
\(768\) −29.8196 48.2987i −0.00140107 0.00226931i
\(769\) 4028.59 + 6977.71i 0.188914 + 0.327208i 0.944888 0.327393i \(-0.106170\pi\)
−0.755975 + 0.654601i \(0.772837\pi\)
\(770\) −8377.06 14509.5i −0.392062 0.679072i
\(771\) 6175.18 + 10001.9i 0.288448 + 0.467198i
\(772\) −19149.8 + 33168.4i −0.892767 + 1.54632i
\(773\) −19600.4 −0.912001 −0.456000 0.889980i \(-0.650718\pi\)
−0.456000 + 0.889980i \(0.650718\pi\)
\(774\) −12964.2 19674.4i −0.602053 0.913673i
\(775\) −7391.67 −0.342602
\(776\) 28707.5 49722.8i 1.32801 2.30019i
\(777\) 1755.82 3259.70i 0.0810677 0.150504i
\(778\) 11806.0 + 20448.5i 0.544041 + 0.942307i
\(779\) −7145.66 12376.7i −0.328652 0.569242i
\(780\) −19006.9 + 561.185i −0.872507 + 0.0257611i
\(781\) 13518.9 23415.4i 0.619390 1.07281i
\(782\) −10442.0 −0.477500
\(783\) 3436.40 7394.14i 0.156841 0.337478i
\(784\) −29941.0 −1.36393
\(785\) −989.402 + 1713.70i −0.0449851 + 0.0779164i
\(786\) 38209.4 1128.15i 1.73395 0.0511955i
\(787\) −8968.18 15533.3i −0.406202 0.703563i 0.588258 0.808673i \(-0.299814\pi\)
−0.994461 + 0.105110i \(0.966480\pi\)
\(788\) −36985.0 64059.9i −1.67200 2.89599i
\(789\) 402.812 747.828i 0.0181755 0.0337432i
\(790\) 2707.42 4689.39i 0.121931 0.211191i
\(791\) 17798.4 0.800047
\(792\) −36976.8 + 73784.4i −1.65898 + 3.31037i
\(793\) −1735.39 −0.0777119
\(794\) 27761.9 48085.0i 1.24085 2.14921i
\(795\) 6541.13 + 10594.6i 0.291811 + 0.472645i
\(796\) −32582.2 56434.0i −1.45081 2.51288i
\(797\) 8971.31 + 15538.8i 0.398720 + 0.690604i 0.993568 0.113235i \(-0.0361211\pi\)
−0.594848 + 0.803838i \(0.702788\pi\)
\(798\) 21702.5 + 35151.5i 0.962733 + 1.55933i
\(799\) 2398.12 4153.67i 0.106182 0.183913i
\(800\) −11451.7 −0.506099
\(801\) 26785.4 1583.08i 1.18154 0.0698317i
\(802\) 67418.9 2.96838
\(803\) 19592.8 33935.7i 0.861039 1.49136i
\(804\) −1443.32 + 2679.55i −0.0633108 + 0.117538i
\(805\) 1208.16 + 2092.60i 0.0528971 + 0.0916204i
\(806\) 28395.0 + 49181.6i 1.24091 + 2.14931i
\(807\) −17161.3 + 506.693i −0.748582 + 0.0221021i
\(808\) 39400.9 68244.4i 1.71549 2.97132i
\(809\) 29094.2 1.26440 0.632200 0.774806i \(-0.282152\pi\)
0.632200 + 0.774806i \(0.282152\pi\)
\(810\) 19240.1 2282.24i 0.834605 0.0989998i
\(811\) 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
\(813\) 10153.9 299.796i 0.438021 0.0129327i
\(814\) 6615.19 + 11457.9i 0.284843 + 0.493363i
\(815\) 9653.59 + 16720.5i 0.414908 + 0.718643i
\(816\) −24787.6 + 46018.6i −1.06341 + 1.97423i
\(817\) 9139.33 15829.8i 0.391364 0.677863i
\(818\) 59069.1 2.52482
\(819\) 13083.6 773.270i 0.558215 0.0329917i
\(820\) −12999.3 −0.553605
\(821\) 121.415 210.297i 0.00516128 0.00893959i −0.863433 0.504463i \(-0.831690\pi\)
0.868595 + 0.495524i \(0.165024\pi\)
\(822\) −22449.0 36360.5i −0.952552 1.54284i
\(823\) −9085.50 15736.5i −0.384812 0.666515i 0.606931 0.794755i \(-0.292401\pi\)
−0.991743 + 0.128240i \(0.959067\pi\)
\(824\) 24259.4 + 42018.5i 1.02563 + 1.77644i
\(825\) −3202.38 5186.88i −0.135143 0.218890i
\(826\) −22693.7 + 39306.6i −0.955949 + 1.65575i
\(827\) 12181.7 0.512213 0.256107 0.966649i \(-0.417560\pi\)
0.256107 + 0.966649i \(0.417560\pi\)
\(828\) 8814.30 17588.2i 0.369950 0.738205i
\(829\) −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
\(831\) −10456.2 + 19412.1i −0.436488 + 0.810347i
\(832\) 17365.7 + 30078.2i 0.723613 + 1.25333i
\(833\) −4437.79 7686.47i −0.184586 0.319713i
\(834\) −14894.7 + 439.772i −0.618420 + 0.0182591i
\(835\) 5087.43 8811.69i 0.210848 0.365199i
\(836\) −105823. −4.37795
\(837\) −23836.1 33948.6i −0.984344 1.40195i
\(838\) −10729.5 −0.442296
\(839\) −15681.5 + 27161.2i −0.645275 + 1.11765i 0.338963 + 0.940800i \(0.389924\pi\)
−0.984238 + 0.176849i \(0.943409\pi\)
\(840\) 22725.0 670.964i 0.933437 0.0275601i
\(841\) 10505.7 + 18196.4i 0.430755 + 0.746089i
\(842\) −29122.9 50442.3i −1.19197 2.06456i
\(843\) −6461.69 + 11996.2i −0.264001 + 0.490122i
\(844\) −50108.0 + 86789.5i −2.04359 + 3.53960i
\(845\) 4456.43 0.181427
\(846\) 6935.85 + 10525.8i 0.281867 + 0.427760i
\(847\) −11701.0 −0.474676
\(848\) 44141.7 76455.7i 1.78754 3.09611i
\(849\) −19.3122 31.2799i −0.000780674 0.00126445i
\(850\) −3628.31 6284.42i −0.146412 0.253593i
\(851\) −954.062 1652.48i −0.0384311 0.0665645i
\(852\) 31857.2 + 51598.9i 1.28100 + 2.07482i
\(853\) 19838.8 34361.8i 0.796326 1.37928i −0.125667 0.992072i \(-0.540107\pi\)
0.921993 0.387205i \(-0.126560\pi\)
\(854\) 3429.37 0.137413
\(855\) 8270.26 + 12550.9i 0.330803 + 0.502026i
\(856\) 65149.0 2.60134
\(857\) −16604.7 + 28760.1i −0.661849 + 1.14636i 0.318280 + 0.947997i \(0.396895\pi\)
−0.980129 + 0.198360i \(0.936439\pi\)
\(858\) −22209.8 + 41232.8i −0.883717 + 1.64064i
\(859\) −17202.4 29795.5i −0.683282 1.18348i −0.973973 0.226663i \(-0.927219\pi\)
0.290691 0.956817i \(-0.406115\pi\)
\(860\) −8313.09 14398.7i −0.329621 0.570920i
\(861\) 8956.03 264.430i 0.354496 0.0104666i
\(862\) −5647.05 + 9780.98i −0.223131 + 0.386475i
\(863\) 12999.7 0.512765 0.256382 0.966575i \(-0.417469\pi\)
0.256382 + 0.966575i \(0.417469\pi\)
\(864\) −36928.6 52595.6i −1.45409 2.07099i
\(865\) −7734.58 −0.304027
\(866\) −42973.9 + 74432.9i −1.68627 + 2.92071i
\(867\) 10029.7 296.131i 0.392880 0.0115999i
\(868\) −40224.8 69671.3i −1.57295 2.72442i
\(869\) −4780.25 8279.64i −0.186604 0.323208i
\(870\) 3806.16 7066.20i 0.148323 0.275364i
\(871\) −522.477 + 904.956i −0.0203254 + 0.0352047i
\(872\) 59636.4 2.31599
\(873\) −10662.4 + 21276.0i −0.413365 + 0.824837i
\(874\) 21290.2 0.823972
\(875\) −839.608 + 1454.24i −0.0324388 + 0.0561856i
\(876\) 46170.4 + 74781.9i 1.78077 + 2.88430i
\(877\) 11415.7 + 19772.6i 0.439546 + 0.761317i 0.997654 0.0684517i \(-0.0218059\pi\)
−0.558108 + 0.829768i \(0.688473\pi\)
\(878\) 1839.69 + 3186.43i 0.0707135 + 0.122479i
\(879\) −12222.4 19796.6i −0.469002 0.759640i
\(880\) −21610.8 + 37430.9i −0.827839 + 1.43386i
\(881\) −1889.31 −0.0722502 −0.0361251 0.999347i \(-0.511501\pi\)
−0.0361251 + 0.999347i \(0.511501\pi\)
\(882\) 23286.2 1376.27i 0.888987 0.0525411i
\(883\) −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
\(885\) −7831.21 + 14538.8i −0.297450 + 0.552221i
\(886\) −17728.6 30706.8i −0.672239 1.16435i
\(887\) −11492.1 19904.8i −0.435023 0.753482i 0.562274 0.826951i \(-0.309927\pi\)
−0.997298 + 0.0734685i \(0.976593\pi\)
\(888\) −17945.5 + 529.847i −0.678166 + 0.0200231i
\(889\) −6674.11 + 11559.9i −0.251791 + 0.436115i
\(890\) 26412.3 0.994766
\(891\) 13495.6 31434.2i 0.507430 1.18191i
\(892\) 22363.4 0.839441
\(893\) −4889.54 + 8468.93i −0.183228 + 0.317359i
\(894\) −33258.7 + 981.975i −1.24423 + 0.0367362i
\(895\) −2059.93 3567.91i −0.0769340 0.133254i
\(896\) −9702.67 16805.5i −0.361767 0.626600i
\(897\) 3203.16 5946.71i 0.119231 0.221355i
\(898\) −25895.0 + 44851.4i −0.962279 + 1.66672i
\(899\) −17183.4 −0.637485
\(900\) 13648.1 806.631i 0.505484 0.0298752i
\(901\) 26170.3 0.967658
\(902\) −16008.5 + 27727.6i −0.590938 + 1.02353i
\(903\) 6020.29 + 9751.04i 0.221864 + 0.359351i
\(904\) −43151.8 74741.1i −1.58762 2.74984i
\(905\) −11008.9 19067.9i −0.404362 0.700375i
\(906\) −43137.0 69868.8i −1.58182 2.56207i
\(907\) −22705.0 + 39326.3i −0.831211 + 1.43970i 0.0658671 + 0.997828i \(0.479019\pi\)
−0.897078 + 0.441872i \(0.854315\pi\)
\(908\) −77377.5 −2.82804
\(909\) −14634.1 + 29201.2i −0.533975 + 1.06550i
\(910\) 12901.4 0.469973
\(911\) 15390.9 26657.8i 0.559740 0.969497i −0.437778 0.899083i \(-0.644235\pi\)
0.997518 0.0704143i \(-0.0224321\pi\)
\(912\) 50539.5 93827.5i 1.83501 3.40673i
\(913\) 10898.0 + 18875.8i 0.395038 + 0.684226i
\(914\) 11807.7 + 20451.5i 0.427311 + 0.740125i
\(915\) 1247.20 36.8240i 0.0450614 0.00133045i
\(916\) −1466.13 + 2539.41i −0.0528845 + 0.0915986i
\(917\) −18592.1 −0.669538
\(918\) 17162.9 36929.7i 0.617059 1.32773i
\(919\) −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
\(921\) 20203.1 596.503i 0.722817 0.0213414i
\(922\) 50336.3 + 87185.0i 1.79798 + 3.11419i
\(923\) 10410.1 + 18030.8i 0.371238 + 0.643002i
\(924\) 31462.7 58411.0i 1.12018 2.07963i
\(925\) 663.022 1148.39i 0.0235676 0.0408203i
\(926\) 89259.1 3.16764
\(927\) −11065.4 16792.8i −0.392056 0.594983i
\(928\) −26621.8 −0.941706
\(929\) 21827.1 37805.7i 0.770855 1.33516i −0.166240 0.986085i \(-0.553163\pi\)
0.937095 0.349075i \(-0.113504\pi\)
\(930\) −21450.7 34743.5i −0.756338 1.22504i
\(931\) 9048.22 + 15672.0i 0.318521 + 0.551695i
\(932\) −13026.9 22563.2i −0.457843 0.793007i
\(933\) −19915.3 32256.8i −0.698819 1.13187i
\(934\) 3635.63 6297.10i 0.127368 0.220607i
\(935\) −12812.4 −0.448138
\(936\) −34968.1 53067.4i −1.22112 1.85317i
\(937\) −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
\(939\) −1567.37 + 2909.85i −0.0544720 + 0.101128i
\(940\) 4447.50 + 7703.30i 0.154321 + 0.267291i
\(941\) −11038.9 19119.9i −0.382419 0.662370i 0.608988 0.793179i \(-0.291576\pi\)
−0.991408 + 0.130810i \(0.958242\pi\)
\(942\) −10926.2 + 322.601i −0.377915 + 0.0111581i
\(943\) 2308.80 3998.95i 0.0797293 0.138095i
\(944\) 117088. 4.03697
\(945\) −9386.58 + 833.364i −0.323117 + 0.0286871i
\(946\) −40949.9 −1.40740
\(947\) −4308.20 + 7462.03i −0.147833 + 0.256054i −0.930426 0.366479i \(-0.880563\pi\)
0.782593 + 0.622533i \(0.213896\pi\)
\(948\) 21433.2 632.824i 0.734303 0.0216805i
\(949\) 15087.3 + 26131.9i 0.516073 + 0.893864i
\(950\) 7397.77 + 12813.3i 0.252648 + 0.437599i
\(951\) −15145.5 + 28117.8i −0.516431 + 0.958763i
\(952\) 23892.5 41382.9i 0.813402 1.40885i
\(953\) −29558.0 −1.00470 −0.502350 0.864664i \(-0.667531\pi\)
−0.502350 + 0.864664i \(0.667531\pi\)
\(954\) −30816.2 + 61491.3i −1.04582 + 2.08685i
\(955\) 15234.6 0.516211
\(956\) −42731.7 + 74013.5i −1.44565 + 2.50394i
\(957\) −7444.58 12057.9i −0.251462 0.407292i
\(958\) 538.836 + 933.291i 0.0181722 + 0.0314752i
\(959\) 10391.9 + 17999.3i 0.349919 + 0.606077i
\(960\) −13118.7 21248.3i −0.441046 0.714359i
\(961\) −28814.0 + 49907.3i −0.967204 + 1.67525i
\(962\) −10187.9 −0.341448
\(963\) −26956.9 + 1593.21i −0.902048 + 0.0533131i
\(964\) 46244.0 1.54504
\(965\) 4727.26 8187.86i 0.157695 0.273136i
\(966\) −6329.88 + 11751.5i −0.210829 + 0.391407i
\(967\) −22288.0 38603.9i −0.741192 1.28378i −0.951953 0.306244i \(-0.900928\pi\)
0.210761 0.977538i \(-0.432406\pi\)
\(968\) 28368.8 + 49136.2i 0.941949 + 1.63150i
\(969\) 31578.3 932.360i 1.04689 0.0309099i
\(970\) −11712.9 + 20287.4i −0.387711 + 0.671534i
\(971\) 43702.8 1.44438 0.722188 0.691696i \(-0.243136\pi\)
0.722188 + 0.691696i \(0.243136\pi\)
\(972\) 47715.9 + 60081.9i 1.57458 + 1.98264i
\(973\) 7247.56 0.238793
\(974\) 50394.4 87285.6i 1.65784 2.87147i
\(975\) 4691.99 138.533i 0.154117 0.00455035i
\(976\) −4423.47 7661.68i −0.145074 0.251275i
\(977\) −22670.9 39267.1i −0.742381 1.28584i −0.951408 0.307932i \(-0.900363\pi\)
0.209027 0.977910i \(-0.432970\pi\)
\(978\) −50577.6 + 93898.3i −1.65368 + 3.07008i
\(979\) 23316.9 40386.1i 0.761197 1.31843i
\(980\) 16460.4 0.536540
\(981\) −24675.9 + 1458.40i −0.803100 + 0.0474650i
\(982\) −62256.8 −2.02311
\(983\) −3680.26 + 6374.40i −0.119412 + 0.206828i −0.919535 0.393009i \(-0.871434\pi\)
0.800123 + 0.599836i \(0.204768\pi\)
\(984\) −22824.1 36968.1i −0.739438 1.19766i
\(985\) 9130.01 + 15813.6i 0.295336 + 0.511538i
\(986\) −8434.73 14609.4i −0.272431 0.471864i
\(987\) −3220.86 5216.81i −0.103871 0.168240i
\(988\) 40744.1 70570.8i 1.31199 2.27242i
\(989\) 5905.91 0.189886
\(990\) 15086.9 30104.7i 0.484336 0.966455i
\(991\) 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
\(993\) 28915.2 53681.5i 0.924064 1.71554i
\(994\) −20571.8 35631.3i −0.656435 1.13698i
\(995\) 8043.15 + 13931.1i 0.256266 + 0.443866i
\(996\) −48863.2 + 1442.70i −1.55451 + 0.0458974i
\(997\) 17665.8 30598.1i 0.561166 0.971968i −0.436229 0.899836i \(-0.643686\pi\)
0.997395 0.0721326i \(-0.0229805\pi\)
\(998\) −45845.6 −1.45412
\(999\) 7412.39 658.091i 0.234752 0.0208419i
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 45.4.e.c.16.7 14
3.2 odd 2 135.4.e.c.46.1 14
5.2 odd 4 225.4.k.d.124.13 28
5.3 odd 4 225.4.k.d.124.2 28
5.4 even 2 225.4.e.d.151.1 14
9.2 odd 6 405.4.a.n.1.7 7
9.4 even 3 inner 45.4.e.c.31.7 yes 14
9.5 odd 6 135.4.e.c.91.1 14
9.7 even 3 405.4.a.m.1.1 7
45.4 even 6 225.4.e.d.76.1 14
45.13 odd 12 225.4.k.d.49.13 28
45.22 odd 12 225.4.k.d.49.2 28
45.29 odd 6 2025.4.a.ba.1.1 7
45.34 even 6 2025.4.a.bb.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.7 14 1.1 even 1 trivial
45.4.e.c.31.7 yes 14 9.4 even 3 inner
135.4.e.c.46.1 14 3.2 odd 2
135.4.e.c.91.1 14 9.5 odd 6
225.4.e.d.76.1 14 45.4 even 6
225.4.e.d.151.1 14 5.4 even 2
225.4.k.d.49.2 28 45.22 odd 12
225.4.k.d.49.13 28 45.13 odd 12
225.4.k.d.124.2 28 5.3 odd 4
225.4.k.d.124.13 28 5.2 odd 4
405.4.a.m.1.1 7 9.7 even 3
405.4.a.n.1.7 7 9.2 odd 6
2025.4.a.ba.1.1 7 45.29 odd 6
2025.4.a.bb.1.7 7 45.34 even 6