Properties

Label 225.4.e.d.76.1
Level $225$
Weight $4$
Character 225.76
Analytic conductor $13.275$
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] = [225,4,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.76");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.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: \(13.2754297513\)
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: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.1
Root \(2.65775 - 4.60336i\) of defining polynomial
Character \(\chi\) \(=\) 225.76
Dual form 225.4.e.d.151.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65775 4.60336i −0.939658 1.62754i −0.766110 0.642710i \(-0.777810\pi\)
−0.173548 0.984825i \(-0.555523\pi\)
\(3\) 5.19389 + 0.153351i 0.999564 + 0.0295125i
\(4\) −10.1273 + 17.5410i −1.26591 + 2.19263i
\(5\) 0 0
\(6\) −13.0981 24.3169i −0.891216 1.65456i
\(7\) −6.71686 11.6339i −0.362676 0.628174i 0.625724 0.780045i \(-0.284804\pi\)
−0.988400 + 0.151871i \(0.951470\pi\)
\(8\) 65.1396 2.87879
\(9\) 26.9530 + 1.59298i 0.998258 + 0.0589993i
\(10\) 0 0
\(11\) 23.4628 + 40.6388i 0.643119 + 1.11391i 0.984733 + 0.174074i \(0.0556932\pi\)
−0.341614 + 0.939840i \(0.610974\pi\)
\(12\) −55.2901 + 89.5531i −1.33007 + 2.15431i
\(13\) −18.0673 + 31.2935i −0.385460 + 0.667636i −0.991833 0.127544i \(-0.959290\pi\)
0.606373 + 0.795180i \(0.292624\pi\)
\(14\) −35.7035 + 61.8403i −0.681584 + 1.18054i
\(15\) 0 0
\(16\) −92.1064 159.533i −1.43916 2.49270i
\(17\) 54.6071 0.779069 0.389535 0.921012i \(-0.372636\pi\)
0.389535 + 0.921012i \(0.372636\pi\)
\(18\) −64.3013 128.308i −0.841998 1.68014i
\(19\) 111.339 1.34436 0.672180 0.740388i \(-0.265358\pi\)
0.672180 + 0.740388i \(0.265358\pi\)
\(20\) 0 0
\(21\) −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 \(-0.885472\pi\)
0.772900 + 0.634528i \(0.218805\pi\)
\(24\) 338.328 + 9.98925i 2.87754 + 0.0849603i
\(25\) 0 0
\(26\) 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 0.757866 0.652411i \(-0.226242\pi\)
−0.943937 + 0.330125i \(0.892909\pi\)
\(30\) 0 0
\(31\) 147.833 256.055i 0.856506 1.48351i −0.0187353 0.999824i \(-0.505964\pi\)
0.875241 0.483687i \(-0.160703\pi\)
\(32\) −229.034 + 396.699i −1.26525 + 2.19147i
\(33\) 115.631 + 214.671i 0.609964 + 1.13241i
\(34\) −145.132 251.377i −0.732059 1.26796i
\(35\) 0 0
\(36\) −300.904 + 456.650i −1.39307 + 2.11412i
\(37\) 53.0417 0.235676 0.117838 0.993033i \(-0.462404\pi\)
0.117838 + 0.993033i \(0.462404\pi\)
\(38\) −295.911 512.533i −1.26324 2.18799i
\(39\) −98.6386 + 159.765i −0.404995 + 0.655969i
\(40\) 0 0
\(41\) −64.1795 + 111.162i −0.244467 + 0.423430i −0.961982 0.273114i \(-0.911946\pi\)
0.717514 + 0.696544i \(0.245280\pi\)
\(42\) −194.924 + 315.717i −0.716127 + 1.15991i
\(43\) −82.0858 142.177i −0.291116 0.504227i 0.682958 0.730457i \(-0.260693\pi\)
−0.974074 + 0.226230i \(0.927360\pi\)
\(44\) −950.461 −3.25653
\(45\) 0 0
\(46\) 191.220 0.612910
\(47\) 43.9159 + 76.0646i 0.136294 + 0.236067i 0.926091 0.377301i \(-0.123148\pi\)
−0.789797 + 0.613368i \(0.789814\pi\)
\(48\) −453.926 842.721i −1.36497 2.53409i
\(49\) 81.2675 140.759i 0.236932 0.410378i
\(50\) 0 0
\(51\) 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 \(-0.286713\pi\)
0.621035 + 0.783783i \(0.286713\pi\)
\(54\) −314.297 676.279i −0.792046 1.70426i
\(55\) 0 0
\(56\) −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 0.266750 + 0.963766i \(0.414050\pi\)
−0.968021 + 0.250871i \(0.919283\pi\)
\(60\) 0 0
\(61\) −24.0128 41.5915i −0.0504021 0.0872990i 0.839724 0.543014i \(-0.182717\pi\)
−0.890126 + 0.455715i \(0.849384\pi\)
\(62\) −1571.62 −3.21929
\(63\) −162.507 324.269i −0.324983 0.648477i
\(64\) 961.163 1.87727
\(65\) 0 0
\(66\) 680.892 1102.84i 1.26988 2.05682i
\(67\) −14.4592 + 25.0440i −0.0263652 + 0.0456658i −0.878907 0.476993i \(-0.841727\pi\)
0.852542 + 0.522659i \(0.175060\pi\)
\(68\) −553.024 + 957.865i −0.986235 + 1.70821i
\(69\) −98.2001 + 159.054i −0.171332 + 0.277505i
\(70\) 0 0
\(71\) 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 \(-0.733459\pi\)
−0.669425 + 0.742880i \(0.733459\pi\)
\(74\) −140.972 244.170i −0.221455 0.383571i
\(75\) 0 0
\(76\) −1127.56 + 1952.99i −1.70184 + 2.94768i
\(77\) 315.193 545.930i 0.466488 0.807981i
\(78\) 997.612 + 29.4548i 1.44817 + 0.0427577i
\(79\) 101.869 + 176.442i 0.145078 + 0.251282i 0.929402 0.369069i \(-0.120324\pi\)
−0.784324 + 0.620351i \(0.786990\pi\)
\(80\) 0 0
\(81\) 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 \(-0.0672991\pi\)
−0.670606 + 0.741814i \(0.733966\pi\)
\(84\) 1413.23 + 41.7262i 1.83567 + 0.0541988i
\(85\) 0 0
\(86\) −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 \(0.298417\pi\)
\(90\) 0 0
\(91\) 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
\(95\) 0 0
\(96\) −1250.41 + 2025.29i −1.32937 + 2.15318i
\(97\) 440.708 + 763.328i 0.461310 + 0.799012i 0.999027 0.0441134i \(-0.0140463\pi\)
−0.537717 + 0.843126i \(0.680713\pi\)
\(98\) −863.956 −0.890538
\(99\) 567.656 + 1132.71i 0.576278 + 1.14992i
\(100\) 0 0
\(101\) −604.869 1047.66i −0.595909 1.03214i −0.993418 0.114546i \(-0.963459\pi\)
0.397509 0.917598i \(-0.369875\pi\)
\(102\) −715.252 1327.88i −0.694319 1.28902i
\(103\) 372.421 645.053i 0.356270 0.617077i −0.631065 0.775730i \(-0.717382\pi\)
0.987334 + 0.158653i \(0.0507151\pi\)
\(104\) −1176.90 + 2038.45i −1.10966 + 1.92198i
\(105\) 0 0
\(106\) −1273.72 2206.15i −1.16712 2.02151i
\(107\) 1000.14 0.903622 0.451811 0.892114i \(-0.350778\pi\)
0.451811 + 0.892114i \(0.350778\pi\)
\(108\) −1632.89 + 2325.65i −1.45486 + 2.07209i
\(109\) −915.517 −0.804502 −0.402251 0.915530i \(-0.631772\pi\)
−0.402251 + 0.915530i \(0.631772\pi\)
\(110\) 0 0
\(111\) 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 0.446679 + 0.894694i \(0.352606\pi\)
−0.998168 + 0.0605114i \(0.980727\pi\)
\(114\) −1458.33 2707.42i −1.19812 2.22432i
\(115\) 0 0
\(116\) 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
\(120\) 0 0
\(121\) −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
\(125\) 0 0
\(126\) −1060.83 + 1609.91i −0.750047 + 1.13827i
\(127\) 993.635 0.694259 0.347129 0.937817i \(-0.387157\pi\)
0.347129 + 0.937817i \(0.387157\pi\)
\(128\) −722.262 1251.00i −0.498747 0.863855i
\(129\) −404.542 751.039i −0.276108 0.512599i
\(130\) 0 0
\(131\) −691.995 + 1198.57i −0.461526 + 0.799386i −0.999037 0.0438704i \(-0.986031\pi\)
0.537512 + 0.843256i \(0.319364\pi\)
\(132\) −4936.59 145.755i −3.25511 0.0961084i
\(133\) −747.847 1295.31i −0.487568 0.844492i
\(134\) 153.715 0.0990970
\(135\) 0 0
\(136\) 3557.09 2.24278
\(137\) 773.568 + 1339.86i 0.482411 + 0.835561i 0.999796 0.0201918i \(-0.00642770\pi\)
−0.517385 + 0.855753i \(0.673094\pi\)
\(138\) 993.176 + 29.3239i 0.612643 + 0.0180885i
\(139\) 269.752 467.225i 0.164605 0.285104i −0.771910 0.635732i \(-0.780698\pi\)
0.936515 + 0.350628i \(0.114032\pi\)
\(140\) 0 0
\(141\) 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
\(145\) 0 0
\(146\) 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 −0.651567 0.758591i \(-0.725888\pi\)
0.982743 + 0.184978i \(0.0592214\pi\)
\(150\) 0 0
\(151\) −1486.46 2574.62i −0.801100 1.38755i −0.918893 0.394508i \(-0.870915\pi\)
0.117793 0.993038i \(-0.462418\pi\)
\(152\) 7252.55 3.87013
\(153\) 1471.82 + 86.9881i 0.777712 + 0.0459645i
\(154\) −3350.82 −1.75336
\(155\) 0 0
\(156\) −1803.49 3348.21i −0.925607 1.71840i
\(157\) −197.880 + 342.739i −0.100590 + 0.174226i −0.911928 0.410351i \(-0.865406\pi\)
0.811338 + 0.584577i \(0.198740\pi\)
\(158\) 541.484 937.877i 0.272646 0.472238i
\(159\) 2489.16 + 73.4932i 1.24153 + 0.0366566i
\(160\) 0 0
\(161\) 483.265 0.236563
\(162\) −1528.72 3560.71i −0.741404 1.72689i
\(163\) −3861.43 −1.85553 −0.927764 0.373169i \(-0.878271\pi\)
−0.927764 + 0.373169i \(0.878271\pi\)
\(164\) −1299.93 2251.55i −0.618949 1.07205i
\(165\) 0 0
\(166\) 1234.47 2138.16i 0.577188 0.999719i
\(167\) 1017.49 1762.34i 0.471470 0.816609i −0.527998 0.849246i \(-0.677057\pi\)
0.999467 + 0.0326366i \(0.0103904\pi\)
\(168\) −2156.29 4003.18i −0.990244 1.83841i
\(169\) 445.643 + 771.876i 0.202842 + 0.351332i
\(170\) 0 0
\(171\) 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 \(-0.0562691\pi\)
−0.644503 + 0.764602i \(0.722936\pi\)
\(174\) −843.286 + 1365.87i −0.367410 + 0.595092i
\(175\) 0 0
\(176\) 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 \(0.555033\pi\)
\(180\) 0 0
\(181\) −4403.55 −1.80836 −0.904180 0.427152i \(-0.859517\pi\)
−0.904180 + 0.427152i \(0.859517\pi\)
\(182\) −1290.14 2234.58i −0.525446 0.910099i
\(183\) −118.342 219.704i −0.0478037 0.0887485i
\(184\) −1171.67 + 2029.38i −0.469437 + 0.813088i
\(185\) 0 0
\(186\) −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
\(190\) 0 0
\(191\) 1523.46 + 2638.72i 0.577141 + 0.999637i 0.995805 + 0.0914964i \(0.0291650\pi\)
−0.418664 + 0.908141i \(0.637502\pi\)
\(192\) 4992.18 + 147.396i 1.87645 + 0.0554030i
\(193\) 945.452 1637.57i 0.352617 0.610751i −0.634090 0.773259i \(-0.718625\pi\)
0.986707 + 0.162508i \(0.0519584\pi\)
\(194\) 2342.58 4057.48i 0.866947 1.50160i
\(195\) 0 0
\(196\) 1646.04 + 2851.03i 0.599870 + 1.03901i
\(197\) −3652.00 −1.32078 −0.660392 0.750921i \(-0.729610\pi\)
−0.660392 + 0.750921i \(0.729610\pi\)
\(198\) 3705.60 5623.60i 1.33003 2.01844i
\(199\) 3217.26 1.14606 0.573029 0.819535i \(-0.305768\pi\)
0.573029 + 0.819535i \(0.305768\pi\)
\(200\) 0 0
\(201\) −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
\(205\) 0 0
\(206\) −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
\(210\) 0 0
\(211\) −2473.90 + 4284.92i −0.807159 + 1.39804i 0.107666 + 0.994187i \(0.465662\pi\)
−0.914824 + 0.403853i \(0.867671\pi\)
\(212\) −4853.49 + 8406.48i −1.57235 + 2.72339i
\(213\) 2992.63 + 88.3585i 0.962684 + 0.0284236i
\(214\) −2658.14 4604.03i −0.849096 1.47068i
\(215\) 0 0
\(216\) 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
\(220\) 0 0
\(221\) −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 \(-0.113653\pi\)
−0.771154 + 0.636649i \(0.780320\pi\)
\(224\) 6153.56 1.83550
\(225\) 0 0
\(226\) 7042.53 2.07284
\(227\) −1910.12 3308.43i −0.558498 0.967348i −0.997622 0.0689210i \(-0.978044\pi\)
0.439124 0.898427i \(-0.355289\pi\)
\(228\) −6155.92 + 9970.72i −1.78810 + 2.89617i
\(229\) −72.3848 + 125.374i −0.0208879 + 0.0361788i −0.876280 0.481801i \(-0.839983\pi\)
0.855393 + 0.517980i \(0.173316\pi\)
\(230\) 0 0
\(231\) 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 \(-0.557880\pi\)
−0.180835 + 0.983513i \(0.557880\pi\)
\(234\) 5176.97 + 305.970i 1.44628 + 0.0854782i
\(235\) 0 0
\(236\) −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 0.425473 + 0.904971i \(0.360108\pi\)
−0.996465 + 0.0840147i \(0.973226\pi\)
\(240\) 0 0
\(241\) −1141.57 1977.25i −0.305124 0.528490i 0.672165 0.740401i \(-0.265364\pi\)
−0.977289 + 0.211912i \(0.932031\pi\)
\(242\) 4629.89 1.22984
\(243\) 3746.82 + 557.020i 0.989129 + 0.147049i
\(244\) 972.742 0.255219
\(245\) 0 0
\(246\) 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
\(250\) 0 0
\(251\) −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
\(255\) 0 0
\(256\) 5.46197 9.46041i 0.00133349 0.00230967i
\(257\) 1131.09 1959.10i 0.274535 0.475508i −0.695483 0.718542i \(-0.744810\pi\)
0.970018 + 0.243035i \(0.0781429\pi\)
\(258\) −2382.13 + 3858.33i −0.574826 + 0.931043i
\(259\) −356.274 617.085i −0.0854741 0.148045i
\(260\) 0 0
\(261\) −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 \(-0.160566\pi\)
−0.856285 + 0.516504i \(0.827233\pi\)
\(264\) 7532.17 + 13983.6i 1.75596 + 3.25997i
\(265\) 0 0
\(266\) −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 \(0.377830\pi\)
\(270\) 0 0
\(271\) −1954.96 −0.438212 −0.219106 0.975701i \(-0.570314\pi\)
−0.219106 + 0.975701i \(0.570314\pi\)
\(272\) −5029.67 8711.64i −1.12121 1.94199i
\(273\) 2521.23 + 74.4403i 0.558945 + 0.0165031i
\(274\) 4111.91 7122.03i 0.906603 1.57028i
\(275\) 0 0
\(276\) −1795.47 3333.32i −0.391575 0.726965i
\(277\) −2121.67 3674.85i −0.460213 0.797112i 0.538758 0.842460i \(-0.318894\pi\)
−0.998971 + 0.0453482i \(0.985560\pi\)
\(278\) −2867.74 −0.618689
\(279\) 4392.44 6665.95i 0.942540 1.43039i
\(280\) 0 0
\(281\) 1311.15 + 2270.97i 0.278350 + 0.482117i 0.970975 0.239181i \(-0.0768791\pi\)
−0.692625 + 0.721298i \(0.743546\pi\)
\(282\) 1274.44 2064.21i 0.269120 0.435893i
\(283\) −3.53735 + 6.12688i −0.000743017 + 0.00128694i −0.866397 0.499356i \(-0.833570\pi\)
0.865654 + 0.500643i \(0.166903\pi\)
\(284\) −5835.18 + 10106.8i −1.21921 + 2.11173i
\(285\) 0 0
\(286\) 4506.60 + 7805.66i 0.931751 + 1.61384i
\(287\) 1724.34 0.354650
\(288\) −6805.08 + 10327.4i −1.39234 + 2.11301i
\(289\) −1931.06 −0.393051
\(290\) 0 0
\(291\) 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 \(-0.980620\pi\)
0.551769 + 0.833997i \(0.313953\pi\)
\(294\) −4487.29 132.489i −0.890151 0.0262820i
\(295\) 0 0
\(296\) 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
\(300\) 0 0
\(301\) −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
\(305\) 0 0
\(306\) −3511.31 7006.54i −0.655975 1.30895i
\(307\) 3889.78 0.723132 0.361566 0.932347i \(-0.382242\pi\)
0.361566 + 0.932347i \(0.382242\pi\)
\(308\) 6384.12 + 11057.6i 1.18107 + 2.04567i
\(309\) 2033.24 3293.22i 0.374326 0.606294i
\(310\) 0 0
\(311\) 3647.83 6318.23i 0.665111 1.15201i −0.314145 0.949375i \(-0.601718\pi\)
0.979255 0.202630i \(-0.0649490\pi\)
\(312\) −6425.28 + 10407.0i −1.16590 + 1.88840i
\(313\) −318.036 550.854i −0.0574328 0.0994765i 0.835880 0.548913i \(-0.184958\pi\)
−0.893312 + 0.449436i \(0.851625\pi\)
\(314\) 2103.67 0.378080
\(315\) 0 0
\(316\) −4126.62 −0.734623
\(317\) −3073.18 5322.90i −0.544501 0.943104i −0.998638 0.0521721i \(-0.983386\pi\)
0.454137 0.890932i \(-0.349948\pi\)
\(318\) −6277.25 11653.8i −1.10695 2.05508i
\(319\) 1363.60 2361.83i 0.239332 0.414536i
\(320\) 0 0
\(321\) 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
\(325\) 0 0
\(326\) 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
\(330\) 0 0
\(331\) −5867.20 10162.3i −0.974291 1.68752i −0.682255 0.731114i \(-0.739001\pi\)
−0.292036 0.956407i \(-0.594333\pi\)
\(332\) −9407.82 −1.55518
\(333\) 1429.63 + 84.4945i 0.235265 + 0.0139047i
\(334\) −10816.9 −1.77208
\(335\) 0 0
\(336\) −6755.22 + 10941.4i −1.09681 + 1.77649i
\(337\) 3141.65 5441.49i 0.507823 0.879575i −0.492136 0.870518i \(-0.663784\pi\)
0.999959 0.00905696i \(-0.00288296\pi\)
\(338\) 2368.82 4102.91i 0.381203 0.660264i
\(339\) −3616.65 + 5857.88i −0.579438 + 0.938514i
\(340\) 0 0
\(341\) 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
\(345\) 0 0
\(346\) 4111.32 7121.02i 0.638803 1.10644i
\(347\) 2400.41 4157.63i 0.371357 0.643209i −0.618418 0.785849i \(-0.712226\pi\)
0.989775 + 0.142641i \(0.0455594\pi\)
\(348\) 6113.98 + 180.517i 0.941792 + 0.0278068i
\(349\) 1946.23 + 3370.97i 0.298508 + 0.517031i 0.975795 0.218688i \(-0.0701778\pi\)
−0.677287 + 0.735719i \(0.736844\pi\)
\(350\) 0 0
\(351\) −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 \(-0.238456\pi\)
−0.955906 + 0.293673i \(0.905122\pi\)
\(354\) 17548.1 + 518.115i 2.63467 + 0.0777896i
\(355\) 0 0
\(356\) −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 \(0.748854\pi\)
\(360\) 0 0
\(361\) 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
\(365\) 0 0
\(366\) −696.853 + 1128.69i −0.0995221 + 0.161195i
\(367\) 2268.59 + 3929.31i 0.322669 + 0.558879i 0.981038 0.193817i \(-0.0620867\pi\)
−0.658369 + 0.752695i \(0.728753\pi\)
\(368\) 6626.88 0.938722
\(369\) −1906.91 + 2893.91i −0.269023 + 0.408269i
\(370\) 0 0
\(371\) −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 0.0993385 0.995054i \(-0.468327\pi\)
0.812073 0.583557i \(-0.198339\pi\)
\(374\) 6810.43 11796.0i 0.941601 1.63090i
\(375\) 0 0
\(376\) 2860.66 + 4954.82i 0.392360 + 0.679588i
\(377\) 2100.06 0.286892
\(378\) −5756.70 + 8198.99i −0.783314 + 1.11564i
\(379\) −9451.10 −1.28092 −0.640462 0.767990i \(-0.721257\pi\)
−0.640462 + 0.767990i \(0.721257\pi\)
\(380\) 0 0
\(381\) 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 0.422722 + 0.906260i \(0.361075\pi\)
−0.996205 + 0.0870420i \(0.972259\pi\)
\(384\) −3559.51 6608.29i −0.473035 0.878198i
\(385\) 0 0
\(386\) −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 0.684199 0.729295i \(-0.260152\pi\)
−0.973688 + 0.227886i \(0.926819\pi\)
\(390\) 0 0
\(391\) −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
\(395\) 0 0
\(396\) −25617.7 1514.07i −3.25086 0.192133i
\(397\) −10445.6 −1.32053 −0.660265 0.751033i \(-0.729556\pi\)
−0.660265 + 0.751033i \(0.729556\pi\)
\(398\) −8550.68 14810.2i −1.07690 1.86525i
\(399\) −3685.59 6842.37i −0.462432 0.858514i
\(400\) 0 0
\(401\) 6341.72 10984.2i 0.789751 1.36789i −0.136368 0.990658i \(-0.543543\pi\)
0.926119 0.377231i \(-0.123124\pi\)
\(402\) 798.381 + 23.5725i 0.0990538 + 0.00292460i
\(403\) 5341.91 + 9252.47i 0.660297 + 1.14367i
\(404\) 24502.8 3.01748
\(405\) 0 0
\(406\) 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 −0.305671 0.952137i \(-0.598881\pi\)
0.977411 0.211349i \(-0.0677858\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) −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 −0.918846 0.394617i \(-0.870877\pi\)
0.801171 + 0.598435i \(0.204211\pi\)
\(420\) 0 0
\(421\) 5478.85 + 9489.65i 0.634259 + 1.09857i 0.986672 + 0.162724i \(0.0520280\pi\)
−0.352413 + 0.935845i \(0.614639\pi\)
\(422\) 26300.1 3.03381
\(423\) 1062.49 + 2120.12i 0.122128 + 0.243697i
\(424\) 31218.0 3.57565
\(425\) 0 0
\(426\) −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
\(430\) 0 0
\(431\) −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 \(-0.145540\pi\)
0.897279 + 0.441463i \(0.145540\pi\)
\(434\) 10556.4 + 18284.1i 1.16756 + 2.02227i
\(435\) 0 0
\(436\) 9271.73 16059.1i 1.01843 1.76397i
\(437\) −2002.65 + 3468.69i −0.219221 + 0.379702i
\(438\) 10937.7 + 20306.0i 1.19320 + 2.21520i
\(439\) −346.098 599.460i −0.0376273 0.0651724i 0.846598 0.532232i \(-0.178647\pi\)
−0.884226 + 0.467060i \(0.845313\pi\)
\(440\) 0 0
\(441\) 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 \(-0.283107\pi\)
−0.987577 + 0.157137i \(0.949774\pi\)
\(444\) −2932.68 + 4750.05i −0.313466 + 0.507719i
\(445\) 0 0
\(446\) 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 \(0.671109\pi\)
\(450\) 0 0
\(451\) −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
\(455\) 0 0
\(456\) 37669.0 + 1112.19i 3.86844 + 0.114217i
\(457\) 2221.36 + 3847.51i 0.227376 + 0.393827i 0.957030 0.289990i \(-0.0936520\pi\)
−0.729654 + 0.683817i \(0.760319\pi\)
\(458\) 769.524 0.0785098
\(459\) 7631.15 + 677.513i 0.776017 + 0.0688967i
\(460\) 0 0
\(461\) −9469.70 16402.0i −0.956720 1.65709i −0.730383 0.683038i \(-0.760658\pi\)
−0.226337 0.974049i \(-0.572675\pi\)
\(462\) −17403.8 513.853i −1.75259 0.0517459i
\(463\) −8396.10 + 14542.5i −0.842764 + 1.45971i 0.0447846 + 0.998997i \(0.485740\pi\)
−0.887549 + 0.460714i \(0.847593\pi\)
\(464\) −5353.00 + 9271.66i −0.535575 + 0.927642i
\(465\) 0 0
\(466\) 3418.70 + 5921.36i 0.339846 + 0.588630i
\(467\) −1367.93 −0.135547 −0.0677735 0.997701i \(-0.521590\pi\)
−0.0677735 + 0.997701i \(0.521590\pi\)
\(468\) −8853.67 17666.8i −0.874489 1.74497i
\(469\) 388.480 0.0382481
\(470\) 0 0
\(471\) −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
\(475\) 0 0
\(476\) 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 0.861150 0.508351i \(-0.169745\pi\)
−0.870820 + 0.491603i \(0.836411\pi\)
\(480\) 0 0
\(481\) −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
\(485\) 0 0
\(486\) −7393.95 18728.4i −0.690116 1.74802i
\(487\) −18961.3 −1.76431 −0.882153 0.470964i \(-0.843906\pi\)
−0.882153 + 0.470964i \(0.843906\pi\)
\(488\) −1564.19 2709.25i −0.145097 0.251315i
\(489\) −20055.9 592.157i −1.85472 0.0547612i
\(490\) 0 0
\(491\) −5856.15 + 10143.1i −0.538257 + 0.932289i 0.460741 + 0.887535i \(0.347584\pi\)
−0.998998 + 0.0447541i \(0.985750\pi\)
\(492\) −6406.43 11893.6i −0.587041 1.08985i
\(493\) −1586.82 2748.45i −0.144963 0.251083i
\(494\) 21385.3 1.94771
\(495\) 0 0
\(496\) −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 −0.992028 0.126021i \(-0.959779\pi\)
0.605151 + 0.796110i \(0.293113\pi\)
\(500\) 0 0
\(501\) 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 \(-0.569051\pi\)
−0.215232 + 0.976563i \(0.569051\pi\)
\(504\) −10585.6 21122.8i −0.935557 1.86683i
\(505\) 0 0
\(506\) 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 −0.527073 0.849820i \(-0.676711\pi\)
0.999502 + 0.0315486i \(0.0100439\pi\)
\(510\) 0 0
\(511\) 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
\(515\) 0 0
\(516\) 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
\(520\) 0 0
\(521\) 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 \(-0.878219\pi\)
−0.927702 + 0.373321i \(0.878219\pi\)
\(524\) −14016.1 24276.6i −1.16850 2.02391i
\(525\) 0 0
\(526\) 434.463 752.511i 0.0360142 0.0623784i
\(527\) 8072.77 13982.4i 0.667277 1.15576i
\(528\) 23596.8 38219.6i 1.94492 3.15018i
\(529\) 5436.44 + 9416.18i 0.446818 + 0.773912i
\(530\) 0 0
\(531\) −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
\(535\) 0 0
\(536\) −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
\(540\) 0 0
\(541\) 4257.08 0.338311 0.169155 0.985589i \(-0.445896\pi\)
0.169155 + 0.985589i \(0.445896\pi\)
\(542\) 5195.81 + 8999.40i 0.411770 + 0.713206i
\(543\) −22871.5 675.290i −1.80757 0.0533692i
\(544\) −12506.9 + 21662.6i −0.985715 + 1.70731i
\(545\) 0 0
\(546\) −6358.14 11804.0i −0.498358 0.925210i
\(547\) −10609.1 18375.5i −0.829272 1.43634i −0.898610 0.438748i \(-0.855422\pi\)
0.0693385 0.997593i \(-0.477911\pi\)
\(548\) −31336.7 −2.44277
\(549\) −580.963 1159.27i −0.0451637 0.0901206i
\(550\) 0 0
\(551\) −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
\(555\) 0 0
\(556\) 5463.73 + 9463.46i 0.416752 + 0.721835i
\(557\) −2506.42 −0.190665 −0.0953324 0.995445i \(-0.530391\pi\)
−0.0953324 + 0.995445i \(0.530391\pi\)
\(558\) −42359.8 2503.56i −3.21368 0.189936i
\(559\) 5932.29 0.448854
\(560\) 0 0
\(561\) 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 −0.337136 0.941456i \(-0.609458\pi\)
0.983893 0.178759i \(-0.0572084\pi\)
\(564\) −9239.93 272.812i −0.689843 0.0203679i
\(565\) 0 0
\(566\) 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 0.945132 + 0.326689i \(0.105933\pi\)
−0.189645 + 0.981853i \(0.560734\pi\)
\(570\) 0 0
\(571\) −3412.53 + 5910.68i −0.250105 + 0.433195i −0.963555 0.267512i \(-0.913799\pi\)
0.713449 + 0.700707i \(0.247132\pi\)
\(572\) 17172.3 29743.3i 1.25526 2.17418i
\(573\) 7508.05 + 13938.8i 0.547388 + 1.01623i
\(574\) −4582.87 7937.77i −0.333250 0.577206i
\(575\) 0 0
\(576\) 25906.2 + 1531.11i 1.87400 + 0.110758i
\(577\) −4249.00 −0.306565 −0.153283 0.988182i \(-0.548984\pi\)
−0.153283 + 0.988182i \(0.548984\pi\)
\(578\) 5132.28 + 8889.37i 0.369333 + 0.639704i
\(579\) 5161.70 8360.38i 0.370489 0.600079i
\(580\) 0 0
\(581\) 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
\(585\) 0 0
\(586\) 23800.1 1.67777
\(587\) 9344.04 + 16184.3i 0.657018 + 1.13799i 0.981384 + 0.192057i \(0.0615159\pi\)
−0.324365 + 0.945932i \(0.605151\pi\)
\(588\) 8112.16 + 15060.4i 0.568945 + 1.05626i
\(589\) 16459.6 28508.8i 1.15145 1.99437i
\(590\) 0 0
\(591\) −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 \(-0.358322\pi\)
0.430542 + 0.902570i \(0.358322\pi\)
\(594\) 20108.8 28640.1i 1.38902 1.97831i
\(595\) 0 0
\(596\) 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 −0.744380 0.667756i \(-0.767255\pi\)
0.950484 + 0.310774i \(0.100588\pi\)
\(600\) 0 0
\(601\) 315.654 + 546.729i 0.0214239 + 0.0371074i 0.876539 0.481332i \(-0.159847\pi\)
−0.855115 + 0.518439i \(0.826513\pi\)
\(602\) 11723.0 0.793679
\(603\) −429.612 + 651.977i −0.0290135 + 0.0440307i
\(604\) 60215.2 4.05649
\(605\) 0 0
\(606\) −17553.3 + 28431.0i −1.17666 + 1.90583i
\(607\) −4727.43 + 8188.16i −0.316113 + 0.547524i −0.979673 0.200599i \(-0.935711\pi\)
0.663560 + 0.748123i \(0.269045\pi\)
\(608\) −25500.4 + 44167.9i −1.70095 + 2.94613i
\(609\) −2131.21 + 3451.91i −0.141808 + 0.229686i
\(610\) 0 0
\(611\) −3173.77 −0.210143
\(612\) −16431.5 + 24936.3i −1.08530 + 1.64705i
\(613\) 2682.66 0.176757 0.0883783 0.996087i \(-0.471832\pi\)
0.0883783 + 0.996087i \(0.471832\pi\)
\(614\) −10338.1 17906.1i −0.679497 1.17692i
\(615\) 0 0
\(616\) 20531.5 35561.7i 1.34292 2.32601i
\(617\) −1169.26 + 2025.22i −0.0762930 + 0.132143i −0.901648 0.432471i \(-0.857642\pi\)
0.825355 + 0.564614i \(0.190975\pi\)
\(618\) −20563.7 607.152i −1.33850 0.0395198i
\(619\) 5965.11 + 10331.9i 0.387331 + 0.670878i 0.992090 0.125531i \(-0.0400636\pi\)
−0.604758 + 0.796409i \(0.706730\pi\)
\(620\) 0 0
\(621\) −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
\(625\) 0 0
\(626\) −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
\(630\) 0 0
\(631\) 4106.81 0.259096 0.129548 0.991573i \(-0.458647\pi\)
0.129548 + 0.991573i \(0.458647\pi\)
\(632\) 6635.68 + 11493.3i 0.417648 + 0.723387i
\(633\) −13506.3 + 21876.0i −0.848067 + 1.37361i
\(634\) −16335.5 + 28293.9i −1.02329 + 1.77239i
\(635\) 0 0
\(636\) −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
\(640\) 0 0
\(641\) −7462.65 12925.7i −0.459839 0.796465i 0.539113 0.842234i \(-0.318760\pi\)
−0.998952 + 0.0457684i \(0.985426\pi\)
\(642\) −13100.0 24320.4i −0.805323 1.49510i
\(643\) 9502.84 16459.4i 0.582823 1.00948i −0.412319 0.911039i \(-0.635281\pi\)
0.995143 0.0984406i \(-0.0313854\pi\)
\(644\) −4894.18 + 8476.96i −0.299468 + 0.518694i
\(645\) 0 0
\(646\) −16158.8 27987.9i −0.984151 1.70460i
\(647\) −9252.81 −0.562234 −0.281117 0.959673i \(-0.590705\pi\)
−0.281117 + 0.959673i \(0.590705\pi\)
\(648\) 47156.1 + 5593.61i 2.85875 + 0.339101i
\(649\) −29826.6 −1.80400
\(650\) 0 0
\(651\) −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 −0.284887 0.958561i \(-0.591956\pi\)
0.972582 0.232561i \(-0.0747105\pi\)
\(654\) 11991.6 + 22262.6i 0.716985 + 1.33109i
\(655\) 0 0
\(656\) 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 0.753500 0.657448i \(-0.228364\pi\)
−0.946117 + 0.323826i \(0.895031\pi\)
\(660\) 0 0
\(661\) 2598.16 4500.15i 0.152885 0.264804i −0.779402 0.626524i \(-0.784477\pi\)
0.932287 + 0.361720i \(0.117810\pi\)
\(662\) −31187.1 + 54017.7i −1.83100 + 3.17139i
\(663\) −5386.37 + 8724.29i −0.315520 + 0.511045i
\(664\) 15127.9 + 26202.3i 0.884153 + 1.53140i
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) 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 0.914718 + 0.404093i \(0.132413\pi\)
−0.107405 + 0.994215i \(0.534254\pi\)
\(674\) −33398.9 −1.90872
\(675\) 0 0
\(676\) −18052.7 −1.02712
\(677\) 4338.44 + 7514.40i 0.246292 + 0.426590i 0.962494 0.271303i \(-0.0874544\pi\)
−0.716202 + 0.697893i \(0.754121\pi\)
\(678\) 36578.1 + 1079.98i 2.07194 + 0.0611747i
\(679\) 5920.34 10254.3i 0.334613 0.579566i
\(680\) 0 0
\(681\) −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 \(-0.696055\pi\)
−0.577714 + 0.816239i \(0.696055\pi\)
\(684\) −33502.2 + 50842.8i −1.87279 + 2.84214i
\(685\) 0 0
\(686\) 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
\(690\) 0 0
\(691\) −3493.03 6050.10i −0.192303 0.333078i 0.753710 0.657207i \(-0.228262\pi\)
−0.946013 + 0.324129i \(0.894929\pi\)
\(692\) −31332.2 −1.72120
\(693\) 9365.04 14212.3i 0.513346 0.779051i
\(694\) −25518.8 −1.39579
\(695\) 0 0
\(696\) −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
\(700\) 0 0
\(701\) 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
\(705\) 0 0
\(706\) −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 0.976942 + 0.213504i \(0.0684876\pi\)
−0.303571 + 0.952809i \(0.598179\pi\)
\(710\) 0 0
\(711\) 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
\(715\) 0 0
\(716\) 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 \(0.357352\pi\)
\(720\) 0 0
\(721\) −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
\(725\) 0 0
\(726\) 24047.1 + 710.000i 1.22930 + 0.0362956i
\(727\) 718.240 + 1244.03i 0.0366410 + 0.0634642i 0.883764 0.467932i \(-0.155001\pi\)
−0.847123 + 0.531396i \(0.821668\pi\)
\(728\) 31620.3 1.60979
\(729\) 19375.1 + 3467.68i 0.984359 + 0.176176i
\(730\) 0 0
\(731\) −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 \(-0.739421\pi\)
0.973993 + 0.226580i \(0.0727544\pi\)
\(734\) 12058.7 20886.3i 0.606397 1.05031i
\(735\) 0 0
\(736\) −8239.28 14270.9i −0.412641 0.714715i
\(737\) −1357.01 −0.0678237
\(738\) 18389.8 + 1086.88i 0.917262 + 0.0542122i
\(739\) 4127.87 0.205475 0.102737 0.994709i \(-0.467240\pi\)
0.102737 + 0.994709i \(0.467240\pi\)
\(740\) 0 0
\(741\) −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 0.296482 + 0.955038i \(0.404186\pi\)
−0.975329 + 0.220758i \(0.929147\pi\)
\(744\) 52574.0 85153.8i 2.59066 4.19609i
\(745\) 0 0
\(746\) −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
\(750\) 0 0
\(751\) −17197.1 + 29786.2i −0.835592 + 1.44729i 0.0579559 + 0.998319i \(0.481542\pi\)
−0.893548 + 0.448968i \(0.851792\pi\)
\(752\) 8089.88 14012.1i 0.392297 0.679479i
\(753\) −41147.2 1214.89i −1.99135 0.0587953i
\(754\) −5581.44 9667.33i −0.269581 0.466928i
\(755\) 0 0
\(756\) 38024.3 + 3375.89i 1.82927 + 0.162408i
\(757\) 30459.8 1.46246 0.731229 0.682132i \(-0.238947\pi\)
0.731229 + 0.682132i \(0.238947\pi\)
\(758\) 25118.7 + 43506.8i 1.20363 + 2.08475i
\(759\) −8767.82 258.873i −0.419304 0.0123801i
\(760\) 0 0
\(761\) −223.584 + 387.259i −0.0106504 + 0.0184469i −0.871301 0.490748i \(-0.836724\pi\)
0.860651 + 0.509195i \(0.170057\pi\)
\(762\) −13014.8 24162.2i −0.618734 1.14869i
\(763\) 6149.40 + 10651.1i 0.291774 + 0.505367i
\(764\) −61714.3 −2.92244
\(765\) 0 0
\(766\) 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 −0.755975 0.654601i \(-0.772837\pi\)
0.944888 + 0.327393i \(0.106170\pi\)
\(770\) 0 0
\(771\) 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 \(-0.349282\pi\)
0.456000 + 0.889980i \(0.349282\pi\)
\(774\) −12964.2 + 19674.4i −0.602053 + 0.913673i
\(775\) 0 0
\(776\) 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
\(780\) 0 0
\(781\) 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
\(785\) 0 0
\(786\) 38209.4 + 1128.15i 1.73395 + 0.0511955i
\(787\) 8968.18 15533.3i 0.406202 0.703563i −0.588258 0.808673i \(-0.700186\pi\)
0.994461 + 0.105110i \(0.0335196\pi\)
\(788\) 36985.0 64059.9i 1.67200 2.89599i
\(789\) 402.812 + 747.828i 0.0181755 + 0.0337432i
\(790\) 0 0
\(791\) 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
\(795\) 0 0
\(796\) −32582.2 + 56434.0i −1.45081 + 2.51288i
\(797\) −8971.31 + 15538.8i −0.398720 + 0.690604i −0.993568 0.113235i \(-0.963879\pi\)
0.594848 + 0.803838i \(0.297212\pi\)
\(798\) −21702.5 + 35151.5i −0.962733 + 1.55933i
\(799\) 2398.12 + 4153.67i 0.106182 + 0.183913i
\(800\) 0 0
\(801\) 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
\(805\) 0 0
\(806\) 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 \(0.282152\pi\)
\(810\) 0 0
\(811\) 1438.31 0.0622760 0.0311380 0.999515i \(-0.490087\pi\)
0.0311380 + 0.999515i \(0.490087\pi\)
\(812\) −7906.74 13694.9i −0.341715 0.591867i
\(813\) −10153.9 299.796i −0.438021 0.0129327i
\(814\) 6615.19 11457.9i 0.284843 0.493363i
\(815\) 0 0
\(816\) −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
\(820\) 0 0
\(821\) 121.415 + 210.297i 0.00516128 + 0.00893959i 0.868595 0.495524i \(-0.165024\pi\)
−0.863433 + 0.504463i \(0.831690\pi\)
\(822\) 22449.0 36360.5i 0.952552 1.54284i
\(823\) 9085.50 15736.5i 0.384812 0.666515i −0.606931 0.794755i \(-0.707599\pi\)
0.991743 + 0.128240i \(0.0409328\pi\)
\(824\) 24259.4 42018.5i 1.02563 1.77644i
\(825\) 0 0
\(826\) −22693.7 39306.6i −0.955949 1.65575i
\(827\) −12181.7 −0.512213 −0.256107 0.966649i \(-0.582440\pi\)
−0.256107 + 0.966649i \(0.582440\pi\)
\(828\) −8814.30 17588.2i −0.369950 0.738205i
\(829\) −17370.0 −0.727724 −0.363862 0.931453i \(-0.618542\pi\)
−0.363862 + 0.931453i \(0.618542\pi\)
\(830\) 0 0
\(831\) −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
\(835\) 0 0
\(836\) −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 −0.984238 0.176849i \(-0.943409\pi\)
0.338963 0.940800i \(-0.389924\pi\)
\(840\) 0 0
\(841\) 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
\(845\) 0 0
\(846\) 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
\(850\) 0 0
\(851\) −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 −0.921993 0.387205i \(-0.873440\pi\)
0.125667 0.992072i \(-0.459893\pi\)
\(854\) 3429.37 0.137413
\(855\) 0 0
\(856\) 65149.0 2.60134
\(857\) 16604.7 + 28760.1i 0.661849 + 1.14636i 0.980129 + 0.198360i \(0.0635614\pi\)
−0.318280 + 0.947997i \(0.603105\pi\)
\(858\) 22209.8 + 41232.8i 0.883717 + 1.64064i
\(859\) −17202.4 + 29795.5i −0.683282 + 1.18348i 0.290691 + 0.956817i \(0.406115\pi\)
−0.973973 + 0.226663i \(0.927219\pi\)
\(860\) 0 0
\(861\) 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 \(-0.582531\pi\)
−0.256382 + 0.966575i \(0.582531\pi\)
\(864\) −36928.6 + 52595.6i −1.45409 + 2.07099i
\(865\) 0 0
\(866\) −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
\(870\) 0 0
\(871\) −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
\(875\) 0 0
\(876\) 46170.4 74781.9i 1.78077 2.88430i
\(877\) −11415.7 + 19772.6i −0.439546 + 0.761317i −0.997654 0.0684517i \(-0.978194\pi\)
0.558108 + 0.829768i \(0.311527\pi\)
\(878\) −1839.69 + 3186.43i −0.0707135 + 0.122479i
\(879\) −12222.4 + 19796.6i −0.469002 + 0.759640i
\(880\) 0 0
\(881\) −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 \(-0.489211\pi\)
0.0338884 + 0.999426i \(0.489211\pi\)
\(884\) −19983.3 34612.1i −0.760308 1.31689i
\(885\) 0 0
\(886\) −17728.6 + 30706.8i −0.672239 + 1.16435i
\(887\) 11492.1 19904.8i 0.435023 0.753482i −0.562274 0.826951i \(-0.690073\pi\)
0.997298 + 0.0734685i \(0.0234068\pi\)
\(888\) 17945.5 + 529.847i 0.678166 + 0.0200231i
\(889\) −6674.11 11559.9i −0.251791 0.436115i
\(890\) 0 0
\(891\) 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
\(895\) 0 0
\(896\) −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
\(900\) 0 0
\(901\) 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
\(905\) 0 0
\(906\) −43137.0 + 69868.8i −1.58182 + 2.56207i
\(907\) 22705.0 + 39326.3i 0.831211 + 1.43970i 0.897078 + 0.441872i \(0.145685\pi\)
−0.0658671 + 0.997828i \(0.520981\pi\)
\(908\) 77377.5 2.82804
\(909\) −14634.1 29201.2i −0.533975 1.06550i
\(910\) 0 0
\(911\) 15390.9 + 26657.8i 0.559740 + 0.969497i 0.997518 + 0.0704143i \(0.0224321\pi\)
−0.437778 + 0.899083i \(0.644235\pi\)
\(912\) −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
\(915\) 0 0
\(916\) −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 \(0.632049\pi\)
\(920\) 0 0
\(921\) 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
\(925\) 0 0
\(926\) 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 0.937095 + 0.349075i \(0.113504\pi\)
−0.166240 + 0.986085i \(0.553163\pi\)
\(930\) 0 0
\(931\) 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
\(935\) 0 0
\(936\) −34968.1 + 53067.4i −1.22112 + 1.85317i
\(937\) 41123.3 1.43377 0.716884 0.697193i \(-0.245568\pi\)
0.716884 + 0.697193i \(0.245568\pi\)
\(938\) −1032.49 1788.32i −0.0359401 0.0622501i
\(939\) −1567.37 2909.85i −0.0544720 0.101128i
\(940\) 0 0
\(941\) −11038.9 + 19119.9i −0.382419 + 0.662370i −0.991408 0.130810i \(-0.958242\pi\)
0.608988 + 0.793179i \(0.291576\pi\)
\(942\) 10926.2 + 322.601i 0.377915 + 0.0111581i
\(943\) −2308.80 3998.95i −0.0797293 0.138095i
\(944\) 117088. 4.03697
\(945\) 0 0
\(946\) −40949.9 −1.40740
\(947\) 4308.20 + 7462.03i 0.147833 + 0.256054i 0.930426 0.366479i \(-0.119437\pi\)
−0.782593 + 0.622533i \(0.786104\pi\)
\(948\) −21433.2 632.824i −0.734303 0.0216805i
\(949\) 15087.3 26131.9i 0.516073 0.893864i
\(950\) 0 0
\(951\) −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 \(-0.332469\pi\)
0.502350 + 0.864664i \(0.332469\pi\)
\(954\) −30816.2 61491.3i −1.04582 2.08685i
\(955\) 0 0
\(956\) −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
\(960\) 0 0
\(961\) −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
\(965\) 0 0
\(966\) −6329.88 11751.5i −0.210829 0.391407i
\(967\) 22288.0 38603.9i 0.741192 1.28378i −0.210761 0.977538i \(-0.567594\pi\)
0.951953 0.306244i \(-0.0990725\pi\)
\(968\) −28368.8 + 49136.2i −0.941949 + 1.63150i
\(969\) 31578.3 + 932.360i 1.04689 + 0.0309099i
\(970\) 0 0
\(971\) 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
\(975\) 0 0
\(976\) −4423.47 + 7661.68i −0.145074 + 0.251275i
\(977\) 22670.9 39267.1i 0.742381 1.28584i −0.209027 0.977910i \(-0.567030\pi\)
0.951408 0.307932i \(-0.0996369\pi\)
\(978\) 50577.6 + 93898.3i 1.65368 + 3.07008i
\(979\) 23316.9 + 40386.1i 0.761197 + 1.31843i
\(980\) 0 0
\(981\) −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 \(-0.128566\pi\)
−0.800123 + 0.599836i \(0.795232\pi\)
\(984\) −22824.1 + 36968.1i −0.739438 + 1.19766i
\(985\) 0 0
\(986\) −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
\(990\) 0 0
\(991\) 33328.4 1.06833 0.534164 0.845381i \(-0.320627\pi\)
0.534164 + 0.845381i \(0.320627\pi\)
\(992\) 67717.8 + 117291.i 2.16738 + 3.75402i
\(993\) −28915.2 53681.5i −0.924064 1.71554i
\(994\) −20571.8 + 35631.3i −0.656435 + 1.13698i
\(995\) 0 0
\(996\) −48863.2 1442.70i −1.55451 0.0458974i
\(997\) −17665.8 30598.1i −0.561166 0.971968i −0.997395 0.0721326i \(-0.977020\pi\)
0.436229 0.899836i \(-0.356314\pi\)
\(998\) 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 225.4.e.d.76.1 14
5.2 odd 4 225.4.k.d.49.13 28
5.3 odd 4 225.4.k.d.49.2 28
5.4 even 2 45.4.e.c.31.7 yes 14
9.4 even 3 2025.4.a.bb.1.7 7
9.5 odd 6 2025.4.a.ba.1.1 7
9.7 even 3 inner 225.4.e.d.151.1 14
15.14 odd 2 135.4.e.c.91.1 14
45.4 even 6 405.4.a.m.1.1 7
45.7 odd 12 225.4.k.d.124.2 28
45.14 odd 6 405.4.a.n.1.7 7
45.29 odd 6 135.4.e.c.46.1 14
45.34 even 6 45.4.e.c.16.7 14
45.43 odd 12 225.4.k.d.124.13 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.c.16.7 14 45.34 even 6
45.4.e.c.31.7 yes 14 5.4 even 2
135.4.e.c.46.1 14 45.29 odd 6
135.4.e.c.91.1 14 15.14 odd 2
225.4.e.d.76.1 14 1.1 even 1 trivial
225.4.e.d.151.1 14 9.7 even 3 inner
225.4.k.d.49.2 28 5.3 odd 4
225.4.k.d.49.13 28 5.2 odd 4
225.4.k.d.124.2 28 45.7 odd 12
225.4.k.d.124.13 28 45.43 odd 12
405.4.a.m.1.1 7 45.4 even 6
405.4.a.n.1.7 7 45.14 odd 6
2025.4.a.ba.1.1 7 9.5 odd 6
2025.4.a.bb.1.7 7 9.4 even 3