Properties

Label 76.4.f.a.27.1
Level $76$
Weight $4$
Character 76.27
Analytic conductor $4.484$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,4,Mod(27,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.27");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 76.f (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.48414516044\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 27.1
Character \(\chi\) \(=\) 76.27
Dual form 76.4.f.a.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.82835 - 0.0213793i) q^{2} +(0.662470 - 1.14743i) q^{3} +(7.99909 + 0.120936i) q^{4} +(0.369055 - 0.639222i) q^{5} +(-1.89823 + 3.23117i) q^{6} -4.50637i q^{7} +(-22.6216 - 0.513064i) q^{8} +(12.6223 + 21.8624i) q^{9} +O(q^{10})\) \(q+(-2.82835 - 0.0213793i) q^{2} +(0.662470 - 1.14743i) q^{3} +(7.99909 + 0.120936i) q^{4} +(0.369055 - 0.639222i) q^{5} +(-1.89823 + 3.23117i) q^{6} -4.50637i q^{7} +(-22.6216 - 0.513064i) q^{8} +(12.6223 + 21.8624i) q^{9} +(-1.05748 + 1.80005i) q^{10} -49.6710i q^{11} +(5.43792 - 9.09829i) q^{12} +(73.2720 - 42.3036i) q^{13} +(-0.0963431 + 12.7456i) q^{14} +(-0.488976 - 0.846931i) q^{15} +(63.9707 + 1.93476i) q^{16} +(17.3122 - 29.9855i) q^{17} +(-35.2327 - 62.1043i) q^{18} +(-11.1774 - 82.0614i) q^{19} +(3.02941 - 5.06856i) q^{20} +(-5.17076 - 2.98534i) q^{21} +(-1.06193 + 140.487i) q^{22} +(73.7917 - 42.6037i) q^{23} +(-15.5748 + 25.6168i) q^{24} +(62.2276 + 107.781i) q^{25} +(-208.143 + 118.083i) q^{26} +69.2209 q^{27} +(0.544983 - 36.0469i) q^{28} +(-138.595 + 80.0179i) q^{29} +(1.36489 + 2.40587i) q^{30} -134.491 q^{31} +(-180.890 - 6.83981i) q^{32} +(-56.9941 - 32.9056i) q^{33} +(-49.6059 + 84.4394i) q^{34} +(-2.88058 - 1.66310i) q^{35} +(98.3226 + 176.406i) q^{36} +79.1323i q^{37} +(29.8592 + 232.337i) q^{38} -112.100i q^{39} +(-8.67658 + 14.2709i) q^{40} +(-198.231 - 114.449i) q^{41} +(14.5609 + 8.55411i) q^{42} +(355.124 + 205.031i) q^{43} +(6.00702 - 397.323i) q^{44} +18.6333 q^{45} +(-209.619 + 118.920i) q^{46} +(-249.877 + 144.266i) q^{47} +(44.5987 - 72.1203i) q^{48} +322.693 q^{49} +(-173.697 - 306.173i) q^{50} +(-22.9376 - 39.7290i) q^{51} +(591.225 - 329.529i) q^{52} +(134.834 - 77.8462i) q^{53} +(-195.781 - 1.47989i) q^{54} +(-31.7508 - 18.3313i) q^{55} +(-2.31206 + 101.941i) q^{56} +(-101.564 - 41.5379i) q^{57} +(393.705 - 223.355i) q^{58} +(-340.388 + 589.569i) q^{59} +(-3.80894 - 6.83381i) q^{60} +(-103.732 - 179.668i) q^{61} +(380.387 + 2.87532i) q^{62} +(98.5202 - 56.8806i) q^{63} +(511.474 + 23.2127i) q^{64} -62.4495i q^{65} +(160.496 + 94.2868i) q^{66} +(-152.027 - 263.319i) q^{67} +(142.108 - 237.763i) q^{68} -112.895i q^{69} +(8.11171 + 4.76541i) q^{70} +(265.767 - 460.321i) q^{71} +(-274.319 - 501.039i) q^{72} +(20.3869 - 35.3111i) q^{73} +(1.69179 - 223.814i) q^{74} +164.896 q^{75} +(-79.4850 - 657.768i) q^{76} -223.836 q^{77} +(-2.39661 + 317.056i) q^{78} +(-522.516 + 905.025i) q^{79} +(24.8455 - 40.1775i) q^{80} +(-294.944 + 510.859i) q^{81} +(558.220 + 327.939i) q^{82} +723.982i q^{83} +(-41.0003 - 24.5053i) q^{84} +(-12.7783 - 22.1326i) q^{85} +(-1000.03 - 587.491i) q^{86} +212.038i q^{87} +(-25.4844 + 1123.64i) q^{88} +(-383.737 + 221.551i) q^{89} +(-52.7013 - 0.398366i) q^{90} +(-190.636 - 330.191i) q^{91} +(595.419 - 331.866i) q^{92} +(-89.0962 + 154.319i) q^{93} +(709.822 - 402.693i) q^{94} +(-56.5805 - 23.1403i) q^{95} +(-127.682 + 203.028i) q^{96} +(646.872 + 373.472i) q^{97} +(-912.686 - 6.89894i) q^{98} +(1085.93 - 626.961i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 3 q^{2} + 5 q^{4} - 2 q^{5} + 21 q^{6} - 228 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 3 q^{2} + 5 q^{4} - 2 q^{5} + 21 q^{6} - 228 q^{9} + 96 q^{10} + 102 q^{13} - 78 q^{14} - 67 q^{16} + 74 q^{17} - 276 q^{20} - 24 q^{21} + 21 q^{22} - 79 q^{24} - 502 q^{25} + 492 q^{26} + 412 q^{28} - 6 q^{29} + 928 q^{30} + 147 q^{32} + 558 q^{33} - 1170 q^{34} + 70 q^{36} - 1066 q^{38} + 336 q^{40} + 588 q^{41} - 368 q^{42} + 443 q^{44} + 600 q^{45} + 1353 q^{48} - 2552 q^{49} - 1086 q^{52} - 594 q^{53} + 21 q^{54} + 574 q^{57} + 1564 q^{58} - 2826 q^{60} + 2262 q^{61} - 456 q^{62} - 2098 q^{64} - 2609 q^{66} - 1612 q^{68} + 3402 q^{70} + 7350 q^{72} - 92 q^{73} - 62 q^{74} + 667 q^{76} + 1168 q^{77} - 666 q^{78} - 1558 q^{80} - 2144 q^{81} - 2113 q^{82} + 1974 q^{85} + 1590 q^{86} + 258 q^{89} + 294 q^{90} - 3016 q^{92} + 1780 q^{93} + 158 q^{96} - 792 q^{97} + 3819 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82835 0.0213793i −0.999971 0.00755872i
\(3\) 0.662470 1.14743i 0.127492 0.220823i −0.795212 0.606331i \(-0.792640\pi\)
0.922704 + 0.385508i \(0.125974\pi\)
\(4\) 7.99909 + 0.120936i 0.999886 + 0.0151170i
\(5\) 0.369055 0.639222i 0.0330093 0.0571738i −0.849049 0.528314i \(-0.822824\pi\)
0.882058 + 0.471141i \(0.156158\pi\)
\(6\) −1.89823 + 3.23117i −0.129158 + 0.219853i
\(7\) 4.50637i 0.243321i −0.992572 0.121661i \(-0.961178\pi\)
0.992572 0.121661i \(-0.0388220\pi\)
\(8\) −22.6216 0.513064i −0.999743 0.0226744i
\(9\) 12.6223 + 21.8624i 0.467491 + 0.809719i
\(10\) −1.05748 + 1.80005i −0.0334405 + 0.0569227i
\(11\) 49.6710i 1.36149i −0.732521 0.680744i \(-0.761657\pi\)
0.732521 0.680744i \(-0.238343\pi\)
\(12\) 5.43792 9.09829i 0.130816 0.218871i
\(13\) 73.2720 42.3036i 1.56323 0.902532i 0.566304 0.824196i \(-0.308373\pi\)
0.996927 0.0783358i \(-0.0249606\pi\)
\(14\) −0.0963431 + 12.7456i −0.00183920 + 0.243314i
\(15\) −0.488976 0.846931i −0.00841687 0.0145784i
\(16\) 63.9707 + 1.93476i 0.999543 + 0.0302306i
\(17\) 17.3122 29.9855i 0.246989 0.427798i −0.715700 0.698408i \(-0.753892\pi\)
0.962689 + 0.270610i \(0.0872255\pi\)
\(18\) −35.2327 62.1043i −0.461358 0.813229i
\(19\) −11.1774 82.0614i −0.134962 0.990851i
\(20\) 3.02941 5.06856i 0.0338698 0.0566683i
\(21\) −5.17076 2.98534i −0.0537310 0.0310216i
\(22\) −1.06193 + 140.487i −0.0102911 + 1.36145i
\(23\) 73.7917 42.6037i 0.668984 0.386238i −0.126707 0.991940i \(-0.540441\pi\)
0.795692 + 0.605702i \(0.207108\pi\)
\(24\) −15.5748 + 25.6168i −0.132467 + 0.217876i
\(25\) 62.2276 + 107.781i 0.497821 + 0.862251i
\(26\) −208.143 + 118.083i −1.57001 + 0.890690i
\(27\) 69.2209 0.493391
\(28\) 0.544983 36.0469i 0.00367829 0.243293i
\(29\) −138.595 + 80.0179i −0.887464 + 0.512377i −0.873112 0.487520i \(-0.837902\pi\)
−0.0143516 + 0.999897i \(0.504568\pi\)
\(30\) 1.36489 + 2.40587i 0.00830644 + 0.0146417i
\(31\) −134.491 −0.779202 −0.389601 0.920984i \(-0.627387\pi\)
−0.389601 + 0.920984i \(0.627387\pi\)
\(32\) −180.890 6.83981i −0.999286 0.0377850i
\(33\) −56.9941 32.9056i −0.300648 0.173579i
\(34\) −49.6059 + 84.4394i −0.250216 + 0.425919i
\(35\) −2.88058 1.66310i −0.0139116 0.00803187i
\(36\) 98.3226 + 176.406i 0.455197 + 0.816693i
\(37\) 79.1323i 0.351602i 0.984426 + 0.175801i \(0.0562515\pi\)
−0.984426 + 0.175801i \(0.943748\pi\)
\(38\) 29.8592 + 232.337i 0.127468 + 0.991843i
\(39\) 112.100i 0.460264i
\(40\) −8.67658 + 14.2709i −0.0342972 + 0.0564106i
\(41\) −198.231 114.449i −0.755086 0.435949i 0.0724427 0.997373i \(-0.476921\pi\)
−0.827529 + 0.561423i \(0.810254\pi\)
\(42\) 14.5609 + 8.55411i 0.0534950 + 0.0314269i
\(43\) 355.124 + 205.031i 1.25944 + 0.727138i 0.972965 0.230951i \(-0.0741836\pi\)
0.286474 + 0.958088i \(0.407517\pi\)
\(44\) 6.00702 397.323i 0.0205816 1.36133i
\(45\) 18.6333 0.0617263
\(46\) −209.619 + 118.920i −0.671885 + 0.381171i
\(47\) −249.877 + 144.266i −0.775495 + 0.447732i −0.834831 0.550506i \(-0.814435\pi\)
0.0593363 + 0.998238i \(0.481102\pi\)
\(48\) 44.5987 72.1203i 0.134110 0.216868i
\(49\) 322.693 0.940795
\(50\) −173.697 306.173i −0.491289 0.865989i
\(51\) −22.9376 39.7290i −0.0629785 0.109082i
\(52\) 591.225 329.529i 1.57670 0.878797i
\(53\) 134.834 77.8462i 0.349449 0.201755i −0.314993 0.949094i \(-0.602002\pi\)
0.664443 + 0.747339i \(0.268669\pi\)
\(54\) −195.781 1.47989i −0.493377 0.00372941i
\(55\) −31.7508 18.3313i −0.0778415 0.0449418i
\(56\) −2.31206 + 101.941i −0.00551718 + 0.243259i
\(57\) −101.564 41.5379i −0.236010 0.0965232i
\(58\) 393.705 223.355i 0.891311 0.505655i
\(59\) −340.388 + 589.569i −0.751097 + 1.30094i 0.196194 + 0.980565i \(0.437142\pi\)
−0.947291 + 0.320373i \(0.896192\pi\)
\(60\) −3.80894 6.83381i −0.00819553 0.0147040i
\(61\) −103.732 179.668i −0.217729 0.377118i 0.736384 0.676563i \(-0.236532\pi\)
−0.954113 + 0.299446i \(0.903198\pi\)
\(62\) 380.387 + 2.87532i 0.779180 + 0.00588978i
\(63\) 98.5202 56.8806i 0.197022 0.113751i
\(64\) 511.474 + 23.2127i 0.998972 + 0.0453372i
\(65\) 62.4495i 0.119168i
\(66\) 160.496 + 94.2868i 0.299328 + 0.175847i
\(67\) −152.027 263.319i −0.277211 0.480143i 0.693480 0.720476i \(-0.256077\pi\)
−0.970690 + 0.240333i \(0.922743\pi\)
\(68\) 142.108 237.763i 0.253428 0.424015i
\(69\) 112.895i 0.196970i
\(70\) 8.11171 + 4.76541i 0.0138505 + 0.00813679i
\(71\) 265.767 460.321i 0.444235 0.769438i −0.553764 0.832674i \(-0.686809\pi\)
0.997999 + 0.0632363i \(0.0201422\pi\)
\(72\) −274.319 501.039i −0.449011 0.820111i
\(73\) 20.3869 35.3111i 0.0326864 0.0566144i −0.849219 0.528040i \(-0.822927\pi\)
0.881906 + 0.471426i \(0.156260\pi\)
\(74\) 1.69179 223.814i 0.00265766 0.351592i
\(75\) 164.896 0.253873
\(76\) −79.4850 657.768i −0.119968 0.992778i
\(77\) −223.836 −0.331279
\(78\) −2.39661 + 317.056i −0.00347901 + 0.460251i
\(79\) −522.516 + 905.025i −0.744148 + 1.28890i 0.206444 + 0.978458i \(0.433811\pi\)
−0.950592 + 0.310444i \(0.899522\pi\)
\(80\) 24.8455 40.1775i 0.0347226 0.0561498i
\(81\) −294.944 + 510.859i −0.404588 + 0.700767i
\(82\) 558.220 + 327.939i 0.751769 + 0.441644i
\(83\) 723.982i 0.957438i 0.877968 + 0.478719i \(0.158899\pi\)
−0.877968 + 0.478719i \(0.841101\pi\)
\(84\) −41.0003 24.5053i −0.0532559 0.0318303i
\(85\) −12.7783 22.1326i −0.0163059 0.0282426i
\(86\) −1000.03 587.491i −1.25391 0.736637i
\(87\) 212.038i 0.261297i
\(88\) −25.4844 + 1123.64i −0.0308710 + 1.36114i
\(89\) −383.737 + 221.551i −0.457034 + 0.263869i −0.710796 0.703398i \(-0.751665\pi\)
0.253762 + 0.967267i \(0.418332\pi\)
\(90\) −52.7013 0.398366i −0.0617245 0.000466572i
\(91\) −190.636 330.191i −0.219605 0.380367i
\(92\) 595.419 331.866i 0.674747 0.376081i
\(93\) −89.0962 + 154.319i −0.0993424 + 0.172066i
\(94\) 709.822 402.693i 0.778857 0.441858i
\(95\) −56.5805 23.1403i −0.0611057 0.0249910i
\(96\) −127.682 + 203.028i −0.135745 + 0.215848i
\(97\) 646.872 + 373.472i 0.677113 + 0.390931i 0.798766 0.601642i \(-0.205486\pi\)
−0.121654 + 0.992573i \(0.538820\pi\)
\(98\) −912.686 6.89894i −0.940768 0.00711121i
\(99\) 1085.93 626.961i 1.10242 0.636484i
\(100\) 484.729 + 869.678i 0.484729 + 0.869678i
\(101\) −646.936 1120.53i −0.637352 1.10393i −0.986012 0.166677i \(-0.946696\pi\)
0.348659 0.937250i \(-0.386637\pi\)
\(102\) 64.0260 + 112.858i 0.0621522 + 0.109555i
\(103\) −1326.23 −1.26871 −0.634354 0.773043i \(-0.718734\pi\)
−0.634354 + 0.773043i \(0.718734\pi\)
\(104\) −1679.24 + 919.383i −1.58329 + 0.866855i
\(105\) −3.81659 + 2.20351i −0.00354725 + 0.00204800i
\(106\) −383.020 + 217.293i −0.350964 + 0.199108i
\(107\) 1319.98 1.19259 0.596295 0.802765i \(-0.296639\pi\)
0.596295 + 0.802765i \(0.296639\pi\)
\(108\) 553.704 + 8.37130i 0.493335 + 0.00745860i
\(109\) −64.6250 37.3113i −0.0567886 0.0327869i 0.471337 0.881953i \(-0.343772\pi\)
−0.528125 + 0.849166i \(0.677105\pi\)
\(110\) 89.4104 + 52.5262i 0.0774995 + 0.0455289i
\(111\) 90.7989 + 52.4228i 0.0776419 + 0.0448266i
\(112\) 8.71874 288.276i 0.00735574 0.243210i
\(113\) 786.249i 0.654549i −0.944929 0.327275i \(-0.893870\pi\)
0.944929 0.327275i \(-0.106130\pi\)
\(114\) 286.372 + 119.655i 0.235273 + 0.0983044i
\(115\) 62.8925i 0.0509978i
\(116\) −1118.31 + 623.309i −0.895108 + 0.498903i
\(117\) 1849.72 + 1067.94i 1.46159 + 0.843852i
\(118\) 975.339 1660.23i 0.760909 1.29522i
\(119\) −135.126 78.0151i −0.104092 0.0600977i
\(120\) 10.6269 + 19.4098i 0.00808415 + 0.0147655i
\(121\) −1136.21 −0.853651
\(122\) 289.548 + 510.382i 0.214872 + 0.378753i
\(123\) −262.645 + 151.638i −0.192535 + 0.111160i
\(124\) −1075.80 16.2648i −0.779113 0.0117792i
\(125\) 184.126 0.131749
\(126\) −279.865 + 158.772i −0.197876 + 0.112258i
\(127\) −552.637 957.195i −0.386131 0.668798i 0.605795 0.795621i \(-0.292855\pi\)
−0.991925 + 0.126823i \(0.959522\pi\)
\(128\) −1446.13 76.5884i −0.998601 0.0528869i
\(129\) 470.518 271.654i 0.321138 0.185409i
\(130\) −1.33513 + 176.629i −0.000900757 + 0.119164i
\(131\) 1054.72 + 608.945i 0.703448 + 0.406136i 0.808630 0.588317i \(-0.200209\pi\)
−0.105182 + 0.994453i \(0.533543\pi\)
\(132\) −451.921 270.107i −0.297990 0.178105i
\(133\) −369.799 + 50.3696i −0.241095 + 0.0328391i
\(134\) 424.357 + 748.008i 0.273573 + 0.482224i
\(135\) 25.5463 44.2475i 0.0162865 0.0282090i
\(136\) −407.013 + 669.439i −0.256626 + 0.422087i
\(137\) 707.565 + 1225.54i 0.441251 + 0.764269i 0.997783 0.0665575i \(-0.0212016\pi\)
−0.556532 + 0.830826i \(0.687868\pi\)
\(138\) −2.41361 + 319.305i −0.00148884 + 0.196964i
\(139\) 2333.04 1346.98i 1.42364 0.821938i 0.427031 0.904237i \(-0.359560\pi\)
0.996608 + 0.0822989i \(0.0262262\pi\)
\(140\) −22.8408 13.6517i −0.0137886 0.00824125i
\(141\) 382.289i 0.228330i
\(142\) −761.521 + 1296.27i −0.450038 + 0.766058i
\(143\) −2101.26 3639.50i −1.22879 2.12832i
\(144\) 765.157 + 1422.98i 0.442799 + 0.823481i
\(145\) 118.124i 0.0676529i
\(146\) −58.4161 + 99.4362i −0.0331134 + 0.0563657i
\(147\) 213.774 370.268i 0.119944 0.207749i
\(148\) −9.56995 + 632.986i −0.00531517 + 0.351562i
\(149\) −591.567 + 1024.62i −0.325255 + 0.563359i −0.981564 0.191134i \(-0.938784\pi\)
0.656309 + 0.754493i \(0.272117\pi\)
\(150\) −466.382 3.52535i −0.253866 0.00191896i
\(151\) −1594.75 −0.859463 −0.429732 0.902957i \(-0.641392\pi\)
−0.429732 + 0.902957i \(0.641392\pi\)
\(152\) 210.748 + 1862.09i 0.112460 + 0.993656i
\(153\) 874.075 0.461861
\(154\) 633.086 + 4.78546i 0.331270 + 0.00250405i
\(155\) −49.6346 + 85.9696i −0.0257209 + 0.0445500i
\(156\) 13.5569 896.694i 0.00695782 0.460211i
\(157\) 664.438 1150.84i 0.337758 0.585013i −0.646253 0.763123i \(-0.723665\pi\)
0.984011 + 0.178110i \(0.0569982\pi\)
\(158\) 1497.21 2548.55i 0.753869 1.28324i
\(159\) 206.283i 0.102889i
\(160\) −71.1306 + 113.105i −0.0351460 + 0.0558857i
\(161\) −191.988 332.533i −0.0939800 0.162778i
\(162\) 845.127 1438.58i 0.409873 0.697688i
\(163\) 2556.53i 1.22848i 0.789118 + 0.614241i \(0.210538\pi\)
−0.789118 + 0.614241i \(0.789462\pi\)
\(164\) −1571.83 939.460i −0.748409 0.447314i
\(165\) −42.0679 + 24.2879i −0.0198484 + 0.0114595i
\(166\) 15.4782 2047.67i 0.00723701 0.957411i
\(167\) 239.494 + 414.816i 0.110974 + 0.192212i 0.916163 0.400806i \(-0.131270\pi\)
−0.805189 + 0.593018i \(0.797936\pi\)
\(168\) 115.439 + 70.1860i 0.0530138 + 0.0322320i
\(169\) 2480.69 4296.69i 1.12913 1.95571i
\(170\) 35.6682 + 62.8720i 0.0160919 + 0.0283651i
\(171\) 1652.97 1280.17i 0.739217 0.572495i
\(172\) 2815.87 + 1683.01i 1.24830 + 0.746093i
\(173\) 1959.77 + 1131.47i 0.861262 + 0.497250i 0.864435 0.502745i \(-0.167677\pi\)
−0.00317273 + 0.999995i \(0.501010\pi\)
\(174\) 4.53322 599.716i 0.00197507 0.261289i
\(175\) 485.703 280.421i 0.209804 0.121130i
\(176\) 96.1013 3177.49i 0.0411586 1.36087i
\(177\) 450.994 + 781.144i 0.191518 + 0.331720i
\(178\) 1090.08 618.418i 0.459015 0.260407i
\(179\) 353.630 0.147662 0.0738311 0.997271i \(-0.476477\pi\)
0.0738311 + 0.997271i \(0.476477\pi\)
\(180\) 149.049 + 2.25343i 0.0617192 + 0.000933117i
\(181\) −2979.93 + 1720.46i −1.22374 + 0.706525i −0.965713 0.259613i \(-0.916405\pi\)
−0.258025 + 0.966138i \(0.583072\pi\)
\(182\) 532.125 + 937.971i 0.216724 + 0.382017i
\(183\) −274.876 −0.111035
\(184\) −1691.15 + 925.903i −0.677570 + 0.370970i
\(185\) 50.5831 + 29.2042i 0.0201024 + 0.0116061i
\(186\) 255.294 434.563i 0.100640 0.171310i
\(187\) −1489.41 859.913i −0.582442 0.336273i
\(188\) −2016.23 + 1123.78i −0.782175 + 0.435958i
\(189\) 311.935i 0.120053i
\(190\) 159.535 + 66.6585i 0.0609151 + 0.0254522i
\(191\) 2214.92i 0.839088i 0.907735 + 0.419544i \(0.137810\pi\)
−0.907735 + 0.419544i \(0.862190\pi\)
\(192\) 365.471 571.503i 0.137373 0.214816i
\(193\) −2298.46 1327.02i −0.857238 0.494927i 0.00584807 0.999983i \(-0.498138\pi\)
−0.863087 + 0.505056i \(0.831472\pi\)
\(194\) −1821.59 1070.14i −0.674138 0.396038i
\(195\) −71.6565 41.3709i −0.0263150 0.0151930i
\(196\) 2581.25 + 39.0252i 0.940687 + 0.0142220i
\(197\) 2067.70 0.747805 0.373903 0.927468i \(-0.378019\pi\)
0.373903 + 0.927468i \(0.378019\pi\)
\(198\) −3084.78 + 1750.05i −1.10720 + 0.628133i
\(199\) −2688.65 + 1552.29i −0.957755 + 0.552960i −0.895481 0.445099i \(-0.853168\pi\)
−0.0622735 + 0.998059i \(0.519835\pi\)
\(200\) −1352.39 2470.11i −0.478142 0.873317i
\(201\) −402.854 −0.141369
\(202\) 1805.80 + 3183.07i 0.628990 + 1.10871i
\(203\) 360.590 + 624.561i 0.124672 + 0.215939i
\(204\) −178.675 320.570i −0.0613223 0.110022i
\(205\) −146.317 + 84.4759i −0.0498497 + 0.0287808i
\(206\) 3751.02 + 28.3538i 1.26867 + 0.00958981i
\(207\) 1862.84 + 1075.51i 0.625489 + 0.361126i
\(208\) 4769.11 2564.43i 1.58980 0.854862i
\(209\) −4076.07 + 555.194i −1.34903 + 0.183749i
\(210\) 10.8417 6.15069i 0.00356263 0.00202113i
\(211\) −2780.73 + 4816.37i −0.907269 + 1.57144i −0.0894259 + 0.995993i \(0.528503\pi\)
−0.817843 + 0.575442i \(0.804830\pi\)
\(212\) 1087.96 606.392i 0.352459 0.196449i
\(213\) −352.125 609.898i −0.113273 0.196195i
\(214\) −3733.36 28.2202i −1.19256 0.00901446i
\(215\) 262.121 151.335i 0.0831464 0.0480046i
\(216\) −1565.89 35.5147i −0.493264 0.0111874i
\(217\) 606.066i 0.189597i
\(218\) 181.984 + 106.911i 0.0565391 + 0.0332152i
\(219\) −27.0114 46.7851i −0.00833452 0.0144358i
\(220\) −251.761 150.474i −0.0771532 0.0461134i
\(221\) 2929.47i 0.891662i
\(222\) −255.690 150.211i −0.0773008 0.0454122i
\(223\) −1420.79 + 2460.88i −0.426652 + 0.738982i −0.996573 0.0827169i \(-0.973640\pi\)
0.569922 + 0.821699i \(0.306974\pi\)
\(224\) −30.8228 + 815.158i −0.00919389 + 0.243148i
\(225\) −1570.91 + 2720.89i −0.465454 + 0.806190i
\(226\) −16.8095 + 2223.78i −0.00494756 + 0.654531i
\(227\) 6747.68 1.97295 0.986474 0.163918i \(-0.0524132\pi\)
0.986474 + 0.163918i \(0.0524132\pi\)
\(228\) −807.400 344.548i −0.234523 0.100080i
\(229\) −5819.92 −1.67944 −0.839719 0.543022i \(-0.817280\pi\)
−0.839719 + 0.543022i \(0.817280\pi\)
\(230\) −1.34460 + 177.882i −0.000385479 + 0.0509964i
\(231\) −148.285 + 256.837i −0.0422356 + 0.0731542i
\(232\) 3176.29 1739.02i 0.898853 0.492123i
\(233\) −2388.43 + 4136.88i −0.671550 + 1.16316i 0.305914 + 0.952059i \(0.401038\pi\)
−0.977464 + 0.211100i \(0.932295\pi\)
\(234\) −5208.81 3060.04i −1.45517 0.854876i
\(235\) 212.969i 0.0591173i
\(236\) −2794.09 + 4674.85i −0.770678 + 1.28944i
\(237\) 692.303 + 1199.10i 0.189746 + 0.328650i
\(238\) 380.515 + 223.542i 0.103635 + 0.0608828i
\(239\) 2200.76i 0.595630i 0.954624 + 0.297815i \(0.0962578\pi\)
−0.954624 + 0.297815i \(0.903742\pi\)
\(240\) −29.6416 55.1249i −0.00797231 0.0148262i
\(241\) 2267.70 1309.25i 0.606121 0.349944i −0.165325 0.986239i \(-0.552867\pi\)
0.771446 + 0.636295i \(0.219534\pi\)
\(242\) 3213.59 + 24.2914i 0.853626 + 0.00645251i
\(243\) 1325.27 + 2295.43i 0.349859 + 0.605974i
\(244\) −808.029 1449.73i −0.212003 0.380366i
\(245\) 119.091 206.272i 0.0310550 0.0537888i
\(246\) 746.092 423.269i 0.193370 0.109702i
\(247\) −4290.49 5539.96i −1.10525 1.42712i
\(248\) 3042.40 + 69.0024i 0.779002 + 0.0176680i
\(249\) 830.720 + 479.617i 0.211425 + 0.122066i
\(250\) −520.771 3.93647i −0.131746 0.000995858i
\(251\) −2025.28 + 1169.30i −0.509302 + 0.294046i −0.732547 0.680717i \(-0.761668\pi\)
0.223245 + 0.974762i \(0.428335\pi\)
\(252\) 794.950 443.079i 0.198719 0.110759i
\(253\) −2116.17 3665.31i −0.525859 0.910815i
\(254\) 1542.58 + 2719.09i 0.381064 + 0.671697i
\(255\) −33.8609 −0.00831550
\(256\) 4088.51 + 247.536i 0.998172 + 0.0604335i
\(257\) −869.787 + 502.172i −0.211112 + 0.121886i −0.601828 0.798626i \(-0.705561\pi\)
0.390716 + 0.920511i \(0.372227\pi\)
\(258\) −1336.60 + 758.271i −0.322530 + 0.182976i
\(259\) 356.600 0.0855522
\(260\) 7.55240 499.539i 0.00180146 0.119154i
\(261\) −3498.77 2020.01i −0.829763 0.479064i
\(262\) −2970.11 1744.86i −0.700358 0.411442i
\(263\) −1845.24 1065.35i −0.432632 0.249780i 0.267835 0.963465i \(-0.413692\pi\)
−0.700467 + 0.713684i \(0.747025\pi\)
\(264\) 1272.41 + 773.618i 0.296635 + 0.180352i
\(265\) 114.918i 0.0266391i
\(266\) 1047.00 134.557i 0.241336 0.0310158i
\(267\) 587.082i 0.134565i
\(268\) −1184.24 2124.70i −0.269921 0.484279i
\(269\) 6843.59 + 3951.15i 1.55116 + 0.895561i 0.998048 + 0.0624516i \(0.0198919\pi\)
0.553109 + 0.833109i \(0.313441\pi\)
\(270\) −73.1998 + 124.601i −0.0164993 + 0.0280851i
\(271\) −2528.33 1459.73i −0.566735 0.327204i 0.189110 0.981956i \(-0.439440\pi\)
−0.755844 + 0.654752i \(0.772773\pi\)
\(272\) 1165.49 1884.70i 0.259809 0.420136i
\(273\) −505.162 −0.111992
\(274\) −1975.04 3481.37i −0.435461 0.767582i
\(275\) 5353.61 3090.91i 1.17394 0.677777i
\(276\) 13.6530 903.054i 0.00297760 0.196947i
\(277\) 7348.21 1.59390 0.796952 0.604043i \(-0.206444\pi\)
0.796952 + 0.604043i \(0.206444\pi\)
\(278\) −6627.44 + 3759.85i −1.42981 + 0.811154i
\(279\) −1697.58 2940.29i −0.364270 0.630935i
\(280\) 64.3099 + 39.0999i 0.0137259 + 0.00834524i
\(281\) 7853.37 4534.15i 1.66723 0.962578i 0.698115 0.715986i \(-0.254023\pi\)
0.969119 0.246592i \(-0.0793108\pi\)
\(282\) 8.17306 1081.24i 0.00172588 0.228323i
\(283\) 1365.03 + 788.098i 0.286722 + 0.165539i 0.636463 0.771308i \(-0.280397\pi\)
−0.349741 + 0.936847i \(0.613730\pi\)
\(284\) 2181.56 3650.01i 0.455816 0.762634i
\(285\) −64.0348 + 49.5925i −0.0133091 + 0.0103074i
\(286\) 5865.29 + 10338.7i 1.21266 + 2.13755i
\(287\) −515.749 + 893.304i −0.106076 + 0.183728i
\(288\) −2133.71 4041.03i −0.436562 0.826805i
\(289\) 1857.08 + 3216.55i 0.377993 + 0.654703i
\(290\) 2.52541 334.096i 0.000511370 0.0676510i
\(291\) 857.067 494.828i 0.172653 0.0996815i
\(292\) 167.347 279.991i 0.0335385 0.0561138i
\(293\) 2462.12i 0.490916i −0.969407 0.245458i \(-0.921062\pi\)
0.969407 0.245458i \(-0.0789384\pi\)
\(294\) −612.543 + 1042.67i −0.121511 + 0.206837i
\(295\) 251.244 + 435.167i 0.0495864 + 0.0858861i
\(296\) 40.5999 1790.10i 0.00797238 0.351511i
\(297\) 3438.27i 0.671746i
\(298\) 1695.06 2885.35i 0.329504 0.560884i
\(299\) 3604.58 6243.32i 0.697185 1.20756i
\(300\) 1319.01 + 19.9418i 0.253844 + 0.00383781i
\(301\) 923.946 1600.32i 0.176928 0.306448i
\(302\) 4510.51 + 34.0947i 0.859439 + 0.00649645i
\(303\) −1714.30 −0.325030
\(304\) −556.259 5271.15i −0.104946 0.994478i
\(305\) −153.131 −0.0287483
\(306\) −2472.19 18.6871i −0.461848 0.00349108i
\(307\) 1493.35 2586.56i 0.277622 0.480856i −0.693171 0.720773i \(-0.743787\pi\)
0.970793 + 0.239917i \(0.0771203\pi\)
\(308\) −1790.48 27.0699i −0.331241 0.00500795i
\(309\) −878.584 + 1521.75i −0.161751 + 0.280160i
\(310\) 142.222 242.091i 0.0260569 0.0443543i
\(311\) 7918.77i 1.44383i −0.691980 0.721917i \(-0.743261\pi\)
0.691980 0.721917i \(-0.256739\pi\)
\(312\) −57.5143 + 2535.87i −0.0104362 + 0.460146i
\(313\) −1893.92 3280.37i −0.342015 0.592388i 0.642791 0.766041i \(-0.277776\pi\)
−0.984807 + 0.173653i \(0.944443\pi\)
\(314\) −1903.87 + 3240.77i −0.342170 + 0.582444i
\(315\) 83.9684i 0.0150193i
\(316\) −4289.10 + 7176.18i −0.763547 + 1.27751i
\(317\) −5247.03 + 3029.38i −0.929662 + 0.536740i −0.886705 0.462337i \(-0.847011\pi\)
−0.0429571 + 0.999077i \(0.513678\pi\)
\(318\) −4.41019 + 583.440i −0.000777708 + 0.102886i
\(319\) 3974.57 + 6884.15i 0.697596 + 1.20827i
\(320\) 203.600 318.379i 0.0355675 0.0556185i
\(321\) 874.446 1514.59i 0.152046 0.263352i
\(322\) 535.899 + 944.623i 0.0927469 + 0.163484i
\(323\) −2654.16 1085.50i −0.457218 0.186993i
\(324\) −2421.07 + 4050.73i −0.415135 + 0.694570i
\(325\) 9119.09 + 5264.91i 1.55642 + 0.898598i
\(326\) 54.6568 7230.74i 0.00928576 1.22845i
\(327\) −85.6243 + 49.4352i −0.0144802 + 0.00836016i
\(328\) 4425.59 + 2690.72i 0.745007 + 0.452958i
\(329\) 650.118 + 1126.04i 0.108943 + 0.188694i
\(330\) 119.502 67.7953i 0.0199344 0.0113091i
\(331\) −3679.62 −0.611027 −0.305514 0.952188i \(-0.598828\pi\)
−0.305514 + 0.952188i \(0.598828\pi\)
\(332\) −87.5556 + 5791.20i −0.0144736 + 0.957329i
\(333\) −1730.02 + 998.829i −0.284699 + 0.164371i
\(334\) −668.504 1178.36i −0.109518 0.193046i
\(335\) −224.426 −0.0366021
\(336\) −325.001 200.978i −0.0527687 0.0326318i
\(337\) 3642.41 + 2102.94i 0.588767 + 0.339925i 0.764610 0.644493i \(-0.222932\pi\)
−0.175843 + 0.984418i \(0.556265\pi\)
\(338\) −7108.12 + 12099.5i −1.14388 + 1.94712i
\(339\) −902.167 520.866i −0.144540 0.0834501i
\(340\) −99.5380 178.586i −0.0158771 0.0284859i
\(341\) 6680.30i 1.06088i
\(342\) −4702.55 + 3585.41i −0.743523 + 0.566891i
\(343\) 2999.86i 0.472237i
\(344\) −7928.28 4820.33i −1.24263 0.755508i
\(345\) −72.1648 41.6644i −0.0112615 0.00650184i
\(346\) −5518.71 3242.09i −0.857479 0.503746i
\(347\) −6827.50 3941.86i −1.05625 0.609828i −0.131859 0.991268i \(-0.542095\pi\)
−0.924393 + 0.381441i \(0.875428\pi\)
\(348\) −25.6430 + 1696.11i −0.00395003 + 0.261267i
\(349\) −8924.22 −1.36877 −0.684387 0.729119i \(-0.739930\pi\)
−0.684387 + 0.729119i \(0.739930\pi\)
\(350\) −1379.73 + 782.743i −0.210714 + 0.119541i
\(351\) 5071.95 2928.29i 0.771285 0.445301i
\(352\) −339.740 + 8984.99i −0.0514438 + 1.36052i
\(353\) 2456.42 0.370375 0.185187 0.982703i \(-0.440711\pi\)
0.185187 + 0.982703i \(0.440711\pi\)
\(354\) −1258.87 2218.99i −0.189005 0.333158i
\(355\) −196.165 339.768i −0.0293278 0.0507972i
\(356\) −3096.34 + 1725.79i −0.460971 + 0.256930i
\(357\) −179.034 + 103.365i −0.0265420 + 0.0153240i
\(358\) −1000.19 7.56036i −0.147658 0.00111614i
\(359\) 9703.78 + 5602.48i 1.42659 + 0.823642i 0.996850 0.0793100i \(-0.0252717\pi\)
0.429740 + 0.902952i \(0.358605\pi\)
\(360\) −421.514 9.56006i −0.0617104 0.00139961i
\(361\) −6609.13 + 1834.47i −0.963571 + 0.267454i
\(362\) 8465.06 4802.36i 1.22904 0.697255i
\(363\) −752.705 + 1303.72i −0.108834 + 0.188506i
\(364\) −1484.98 2664.28i −0.213830 0.383644i
\(365\) −15.0478 26.0635i −0.00215791 0.00373761i
\(366\) 777.445 + 5.87666i 0.111032 + 0.000839284i
\(367\) 1927.88 1113.06i 0.274208 0.158314i −0.356591 0.934261i \(-0.616061\pi\)
0.630798 + 0.775947i \(0.282728\pi\)
\(368\) 4802.94 2582.62i 0.680355 0.365838i
\(369\) 5778.42i 0.815210i
\(370\) −142.442 83.6810i −0.0200141 0.0117578i
\(371\) −350.804 607.610i −0.0490912 0.0850285i
\(372\) −731.351 + 1223.64i −0.101932 + 0.170545i
\(373\) 12573.6i 1.74541i −0.488250 0.872704i \(-0.662364\pi\)
0.488250 0.872704i \(-0.337636\pi\)
\(374\) 4194.19 + 2463.97i 0.579883 + 0.340666i
\(375\) 121.978 211.271i 0.0167971 0.0290934i
\(376\) 5726.63 3135.33i 0.785448 0.430033i
\(377\) −6770.09 + 11726.1i −0.924874 + 1.60193i
\(378\) −6.66895 + 882.260i −0.000907444 + 0.120049i
\(379\) 2056.69 0.278747 0.139374 0.990240i \(-0.455491\pi\)
0.139374 + 0.990240i \(0.455491\pi\)
\(380\) −449.794 191.944i −0.0607209 0.0259119i
\(381\) −1464.42 −0.196915
\(382\) 47.3534 6264.55i 0.00634243 0.839064i
\(383\) −4006.80 + 6939.98i −0.534563 + 0.925891i 0.464621 + 0.885510i \(0.346191\pi\)
−0.999184 + 0.0403812i \(0.987143\pi\)
\(384\) −1045.90 + 1608.60i −0.138993 + 0.213772i
\(385\) −82.6079 + 143.081i −0.0109353 + 0.0189405i
\(386\) 6472.48 + 3802.41i 0.853473 + 0.501392i
\(387\) 10351.8i 1.35972i
\(388\) 5129.22 + 3065.66i 0.671125 + 0.401122i
\(389\) −2349.43 4069.33i −0.306223 0.530394i 0.671310 0.741177i \(-0.265732\pi\)
−0.977533 + 0.210783i \(0.932399\pi\)
\(390\) 201.785 + 118.543i 0.0261994 + 0.0153915i
\(391\) 2950.25i 0.381587i
\(392\) −7299.82 165.562i −0.940553 0.0213320i
\(393\) 1397.45 806.816i 0.179369 0.103559i
\(394\) −5848.17 44.2060i −0.747784 0.00565245i
\(395\) 385.675 + 668.008i 0.0491276 + 0.0850915i
\(396\) 8762.25 4883.79i 1.11192 0.619746i
\(397\) 2830.35 4902.32i 0.357812 0.619749i −0.629783 0.776771i \(-0.716856\pi\)
0.987595 + 0.157022i \(0.0501895\pi\)
\(398\) 7637.61 4332.94i 0.961907 0.545705i
\(399\) −187.185 + 457.688i −0.0234862 + 0.0574262i
\(400\) 3772.22 + 7015.25i 0.471527 + 0.876906i
\(401\) 1563.86 + 902.893i 0.194751 + 0.112440i 0.594205 0.804314i \(-0.297467\pi\)
−0.399454 + 0.916753i \(0.630800\pi\)
\(402\) 1139.41 + 8.61275i 0.141365 + 0.00106857i
\(403\) −9854.42 + 5689.45i −1.21807 + 0.703255i
\(404\) −5039.39 9041.43i −0.620591 1.11344i
\(405\) 217.702 + 377.070i 0.0267103 + 0.0462636i
\(406\) −1006.52 1774.18i −0.123037 0.216875i
\(407\) 3930.58 0.478702
\(408\) 498.501 + 910.503i 0.0604889 + 0.110482i
\(409\) −2607.64 + 1505.52i −0.315256 + 0.182013i −0.649276 0.760553i \(-0.724928\pi\)
0.334020 + 0.942566i \(0.391595\pi\)
\(410\) 415.640 235.799i 0.0500659 0.0284031i
\(411\) 1874.96 0.225024
\(412\) −10608.6 160.389i −1.26856 0.0191791i
\(413\) 2656.82 + 1533.91i 0.316546 + 0.182758i
\(414\) −5245.76 3081.74i −0.622741 0.365844i
\(415\) 462.786 + 267.189i 0.0547404 + 0.0316044i
\(416\) −13543.5 + 7151.14i −1.59622 + 0.842821i
\(417\) 3569.34i 0.419163i
\(418\) 11540.4 1483.14i 1.35038 0.173547i
\(419\) 7760.36i 0.904817i −0.891811 0.452408i \(-0.850565\pi\)
0.891811 0.452408i \(-0.149435\pi\)
\(420\) −30.7957 + 17.1645i −0.00357780 + 0.00199415i
\(421\) 5746.84 + 3317.94i 0.665282 + 0.384101i 0.794287 0.607543i \(-0.207845\pi\)
−0.129005 + 0.991644i \(0.541178\pi\)
\(422\) 7967.85 13562.9i 0.919121 1.56453i
\(423\) −6308.02 3641.94i −0.725075 0.418622i
\(424\) −3090.09 + 1691.83i −0.353934 + 0.193779i
\(425\) 4309.18 0.491825
\(426\) 982.891 + 1732.53i 0.111787 + 0.197046i
\(427\) −809.652 + 467.453i −0.0917607 + 0.0529781i
\(428\) 10558.6 + 159.633i 1.19245 + 0.0180284i
\(429\) −5568.10 −0.626644
\(430\) −744.604 + 422.425i −0.0835069 + 0.0473748i
\(431\) 6953.65 + 12044.1i 0.777136 + 1.34604i 0.933586 + 0.358353i \(0.116662\pi\)
−0.156450 + 0.987686i \(0.550005\pi\)
\(432\) 4428.11 + 133.926i 0.493166 + 0.0149155i
\(433\) −2510.54 + 1449.46i −0.278635 + 0.160870i −0.632805 0.774311i \(-0.718097\pi\)
0.354170 + 0.935181i \(0.384763\pi\)
\(434\) 12.9573 1714.16i 0.00143311 0.189591i
\(435\) 135.539 + 78.2536i 0.0149393 + 0.00862523i
\(436\) −512.429 306.272i −0.0562864 0.0336416i
\(437\) −4320.92 5579.25i −0.472992 0.610736i
\(438\) 75.3973 + 132.902i 0.00822517 + 0.0144984i
\(439\) 429.671 744.212i 0.0467132 0.0809096i −0.841723 0.539909i \(-0.818459\pi\)
0.888437 + 0.458999i \(0.151792\pi\)
\(440\) 708.849 + 430.975i 0.0768024 + 0.0466952i
\(441\) 4073.11 + 7054.84i 0.439813 + 0.761779i
\(442\) −62.6300 + 8285.55i −0.00673983 + 0.891637i
\(443\) −8117.63 + 4686.71i −0.870610 + 0.502647i −0.867551 0.497349i \(-0.834307\pi\)
−0.00305877 + 0.999995i \(0.500974\pi\)
\(444\) 719.968 + 430.315i 0.0769554 + 0.0459952i
\(445\) 327.058i 0.0348405i
\(446\) 4071.11 6929.86i 0.432225 0.735736i
\(447\) 783.791 + 1357.57i 0.0829352 + 0.143648i
\(448\) 104.605 2304.89i 0.0110315 0.243071i
\(449\) 46.9376i 0.00493346i 0.999997 + 0.00246673i \(0.000785185\pi\)
−0.999997 + 0.00246673i \(0.999215\pi\)
\(450\) 4501.24 7662.03i 0.471534 0.802648i
\(451\) −5684.79 + 9846.35i −0.593540 + 1.02804i
\(452\) 95.0859 6289.27i 0.00989483 0.654475i
\(453\) −1056.47 + 1829.87i −0.109575 + 0.189790i
\(454\) −19084.8 144.261i −1.97289 0.0149130i
\(455\) −281.421 −0.0289961
\(456\) 2276.24 + 991.762i 0.233760 + 0.101850i
\(457\) −16206.4 −1.65887 −0.829437 0.558600i \(-0.811339\pi\)
−0.829437 + 0.558600i \(0.811339\pi\)
\(458\) 16460.7 + 124.426i 1.67939 + 0.0126944i
\(459\) 1198.36 2075.63i 0.121862 0.211072i
\(460\) 7.60597 503.082i 0.000770935 0.0509920i
\(461\) 1337.04 2315.82i 0.135080 0.233966i −0.790548 0.612400i \(-0.790204\pi\)
0.925628 + 0.378434i \(0.123537\pi\)
\(462\) 424.891 723.253i 0.0427873 0.0728328i
\(463\) 3894.57i 0.390920i −0.980712 0.195460i \(-0.937380\pi\)
0.980712 0.195460i \(-0.0626201\pi\)
\(464\) −9020.84 + 4850.65i −0.902547 + 0.485315i
\(465\) 65.7628 + 113.905i 0.00655845 + 0.0113596i
\(466\) 6843.75 11649.5i 0.680323 1.15805i
\(467\) 5247.43i 0.519962i 0.965614 + 0.259981i \(0.0837162\pi\)
−0.965614 + 0.259981i \(0.916284\pi\)
\(468\) 14666.9 + 8766.21i 1.44867 + 0.865850i
\(469\) −1186.61 + 685.092i −0.116829 + 0.0674512i
\(470\) 4.55313 602.350i 0.000446852 0.0591156i
\(471\) −880.341 1524.80i −0.0861231 0.149170i
\(472\) 8002.61 13162.4i 0.780402 1.28357i
\(473\) 10184.1 17639.4i 0.989989 1.71471i
\(474\) −1932.44 3406.28i −0.187257 0.330075i
\(475\) 8149.14 6311.20i 0.787175 0.609637i
\(476\) −1071.45 640.391i −0.103172 0.0616644i
\(477\) 3403.81 + 1965.19i 0.326729 + 0.188637i
\(478\) 47.0508 6224.52i 0.00450220 0.595613i
\(479\) −5030.07 + 2904.11i −0.479812 + 0.277020i −0.720338 0.693623i \(-0.756013\pi\)
0.240526 + 0.970643i \(0.422680\pi\)
\(480\) 82.6581 + 156.546i 0.00786001 + 0.0148861i
\(481\) 3347.58 + 5798.18i 0.317332 + 0.549635i
\(482\) −6441.82 + 3654.54i −0.608749 + 0.345353i
\(483\) −508.745 −0.0479269
\(484\) −9088.64 137.409i −0.853553 0.0129047i
\(485\) 477.463 275.663i 0.0447020 0.0258087i
\(486\) −3699.23 6520.60i −0.345269 0.608601i
\(487\) 14400.7 1.33995 0.669976 0.742383i \(-0.266304\pi\)
0.669976 + 0.742383i \(0.266304\pi\)
\(488\) 2254.39 + 4117.61i 0.209122 + 0.381957i
\(489\) 2933.44 + 1693.62i 0.271278 + 0.156622i
\(490\) −341.242 + 580.864i −0.0314607 + 0.0535525i
\(491\) −13775.5 7953.26i −1.26615 0.731010i −0.291890 0.956452i \(-0.594284\pi\)
−0.974257 + 0.225442i \(0.927617\pi\)
\(492\) −2119.25 + 1181.20i −0.194194 + 0.108237i
\(493\) 5541.13i 0.506207i
\(494\) 12016.5 + 15760.6i 1.09443 + 1.43544i
\(495\) 925.533i 0.0840396i
\(496\) −8603.48 260.207i −0.778846 0.0235557i
\(497\) −2074.38 1197.64i −0.187221 0.108092i
\(498\) −2339.31 1374.28i −0.210496 0.123661i
\(499\) 11104.9 + 6411.43i 0.996241 + 0.575180i 0.907134 0.420842i \(-0.138265\pi\)
0.0891072 + 0.996022i \(0.471599\pi\)
\(500\) 1472.84 + 22.2674i 0.131734 + 0.00199166i
\(501\) 634.631 0.0565933
\(502\) 5753.21 3263.88i 0.511510 0.290188i
\(503\) −3741.55 + 2160.18i −0.331665 + 0.191487i −0.656580 0.754256i \(-0.727998\pi\)
0.324915 + 0.945743i \(0.394664\pi\)
\(504\) −2257.87 + 1236.18i −0.199550 + 0.109254i
\(505\) −955.021 −0.0841542
\(506\) 5906.89 + 10412.0i 0.518959 + 0.914763i
\(507\) −3286.77 5692.85i −0.287911 0.498676i
\(508\) −4304.83 7723.52i −0.375976 0.674558i
\(509\) 5473.70 3160.24i 0.476655 0.275197i −0.242367 0.970185i \(-0.577924\pi\)
0.719021 + 0.694988i \(0.244590\pi\)
\(510\) 95.7704 + 0.723923i 0.00831527 + 6.28546e-5i
\(511\) −159.125 91.8709i −0.0137755 0.00795329i
\(512\) −11558.4 787.526i −0.997687 0.0679767i
\(513\) −773.711 5680.36i −0.0665890 0.488877i
\(514\) 2470.79 1401.72i 0.212027 0.120286i
\(515\) −489.450 + 847.753i −0.0418791 + 0.0725368i
\(516\) 3796.57 2116.08i 0.323904 0.180533i
\(517\) 7165.86 + 12411.6i 0.609582 + 1.05583i
\(518\) −1008.59 7.62385i −0.0855498 0.000646666i
\(519\) 2596.57 1499.13i 0.219609 0.126791i
\(520\) −32.0406 + 1412.71i −0.00270206 + 0.119137i
\(521\) 8771.99i 0.737635i −0.929502 0.368818i \(-0.879763\pi\)
0.929502 0.368818i \(-0.120237\pi\)
\(522\) 9852.54 + 5788.10i 0.826118 + 0.485322i
\(523\) 276.125 + 478.262i 0.0230862 + 0.0399865i 0.877338 0.479873i \(-0.159317\pi\)
−0.854251 + 0.519860i \(0.825984\pi\)
\(524\) 8363.19 + 4998.56i 0.697228 + 0.416724i
\(525\) 743.081i 0.0617728i
\(526\) 5196.19 + 3052.62i 0.430732 + 0.253043i
\(527\) −2328.33 + 4032.78i −0.192455 + 0.333341i
\(528\) −3582.29 2215.26i −0.295264 0.182589i
\(529\) −2453.35 + 4249.33i −0.201640 + 0.349251i
\(530\) −2.45687 + 325.028i −0.000201358 + 0.0266384i
\(531\) −17185.9 −1.40453
\(532\) −2964.15 + 358.189i −0.241564 + 0.0291907i
\(533\) −19366.4 −1.57383
\(534\) 12.5514 1660.47i 0.00101714 0.134561i
\(535\) 487.145 843.760i 0.0393666 0.0681849i
\(536\) 3304.00 + 6034.70i 0.266252 + 0.486305i
\(537\) 234.269 405.766i 0.0188258 0.0326073i
\(538\) −19271.6 11321.5i −1.54434 0.907260i
\(539\) 16028.5i 1.28088i
\(540\) 209.698 350.850i 0.0167111 0.0279596i
\(541\) −3031.52 5250.75i −0.240915 0.417278i 0.720060 0.693912i \(-0.244114\pi\)
−0.960975 + 0.276634i \(0.910781\pi\)
\(542\) 7119.78 + 4182.68i 0.564245 + 0.331479i
\(543\) 4559.02i 0.360307i
\(544\) −3336.69 + 5305.67i −0.262977 + 0.418160i
\(545\) −47.7004 + 27.5398i −0.00374910 + 0.00216455i
\(546\) 1428.77 + 10.8000i 0.111989 + 0.000846517i
\(547\) −4722.69 8179.93i −0.369154 0.639394i 0.620279 0.784381i \(-0.287019\pi\)
−0.989434 + 0.144987i \(0.953686\pi\)
\(548\) 5511.66 + 9888.76i 0.429647 + 0.770852i
\(549\) 2618.65 4535.64i 0.203573 0.352598i
\(550\) −15207.9 + 8627.70i −1.17903 + 0.668884i
\(551\) 8115.51 + 10478.9i 0.627463 + 0.810193i
\(552\) −57.9222 + 2553.86i −0.00446618 + 0.196919i
\(553\) 4078.38 + 2354.65i 0.313617 + 0.181067i
\(554\) −20783.3 157.100i −1.59386 0.0120479i
\(555\) 67.0196 38.6938i 0.00512581 0.00295939i
\(556\) 18825.1 10492.5i 1.43590 0.800323i
\(557\) 676.733 + 1172.14i 0.0514795 + 0.0891651i 0.890617 0.454754i \(-0.150273\pi\)
−0.839137 + 0.543920i \(0.816940\pi\)
\(558\) 4738.48 + 8352.46i 0.359491 + 0.633670i
\(559\) 34694.2 2.62506
\(560\) −181.055 111.963i −0.0136624 0.00844875i
\(561\) −1973.38 + 1139.33i −0.148514 + 0.0857445i
\(562\) −22309.0 + 12656.2i −1.67446 + 0.949948i
\(563\) 2068.92 0.154875 0.0774373 0.996997i \(-0.475326\pi\)
0.0774373 + 0.996997i \(0.475326\pi\)
\(564\) −46.2325 + 3057.96i −0.00345167 + 0.228304i
\(565\) −502.588 290.169i −0.0374231 0.0216062i
\(566\) −3843.91 2258.20i −0.285463 0.167702i
\(567\) 2302.12 + 1329.13i 0.170511 + 0.0984448i
\(568\) −6248.24 + 10276.8i −0.461567 + 0.759167i
\(569\) 18706.6i 1.37824i 0.724646 + 0.689121i \(0.242003\pi\)
−0.724646 + 0.689121i \(0.757997\pi\)
\(570\) 182.173 138.896i 0.0133866 0.0102065i
\(571\) 14720.6i 1.07887i −0.842027 0.539436i \(-0.818637\pi\)
0.842027 0.539436i \(-0.181363\pi\)
\(572\) −16368.0 29366.8i −1.19647 2.14665i
\(573\) 2541.47 + 1467.32i 0.185290 + 0.106977i
\(574\) 1477.82 2515.55i 0.107461 0.182921i
\(575\) 9183.76 + 5302.25i 0.666069 + 0.384555i
\(576\) 5948.47 + 11475.0i 0.430300 + 0.830081i
\(577\) 4484.35 0.323546 0.161773 0.986828i \(-0.448279\pi\)
0.161773 + 0.986828i \(0.448279\pi\)
\(578\) −5183.69 9137.23i −0.373033 0.657541i
\(579\) −3045.33 + 1758.22i −0.218583 + 0.126199i
\(580\) −14.2855 + 944.884i −0.00102271 + 0.0676452i
\(581\) 3262.53 0.232965
\(582\) −2434.66 + 1381.22i −0.173402 + 0.0983736i
\(583\) −3866.70 6697.32i −0.274687 0.475771i
\(584\) −479.301 + 788.334i −0.0339617 + 0.0558587i
\(585\) 1365.30 788.254i 0.0964924 0.0557099i
\(586\) −52.6383 + 6963.72i −0.00371070 + 0.490902i
\(587\) −15532.6 8967.77i −1.09216 0.630561i −0.158013 0.987437i \(-0.550509\pi\)
−0.934152 + 0.356876i \(0.883842\pi\)
\(588\) 1754.78 2935.95i 0.123071 0.205912i
\(589\) 1503.26 + 11036.5i 0.105163 + 0.772073i
\(590\) −701.301 1236.17i −0.0489358 0.0862585i
\(591\) 1369.79 2372.55i 0.0953395 0.165133i
\(592\) −153.102 + 5062.15i −0.0106291 + 0.351441i
\(593\) −3606.72 6247.02i −0.249764 0.432604i 0.713696 0.700456i \(-0.247020\pi\)
−0.963460 + 0.267851i \(0.913686\pi\)
\(594\) −73.5078 + 9724.62i −0.00507755 + 0.671727i
\(595\) −99.7380 + 57.5837i −0.00687203 + 0.00396757i
\(596\) −4855.91 + 8124.52i −0.333735 + 0.558378i
\(597\) 4113.39i 0.281993i
\(598\) −10328.5 + 17581.2i −0.706293 + 1.20226i
\(599\) −2459.33 4259.69i −0.167756 0.290561i 0.769875 0.638195i \(-0.220319\pi\)
−0.937630 + 0.347634i \(0.886985\pi\)
\(600\) −3730.20 84.6020i −0.253808 0.00575644i
\(601\) 14459.6i 0.981396i −0.871330 0.490698i \(-0.836742\pi\)
0.871330 0.490698i \(-0.163258\pi\)
\(602\) −2647.45 + 4506.51i −0.179239 + 0.305102i
\(603\) 3837.86 6647.37i 0.259187 0.448925i
\(604\) −12756.5 192.863i −0.859365 0.0129925i
\(605\) −419.324 + 726.291i −0.0281784 + 0.0488065i
\(606\) 4848.64 + 36.6506i 0.325021 + 0.00245681i
\(607\) −8377.56 −0.560189 −0.280094 0.959972i \(-0.590366\pi\)
−0.280094 + 0.959972i \(0.590366\pi\)
\(608\) 1460.60 + 14920.5i 0.0974262 + 0.995243i
\(609\) 955.521 0.0635791
\(610\) 433.107 + 3.27383i 0.0287475 + 0.000217301i
\(611\) −12206.0 + 21141.4i −0.808185 + 1.39982i
\(612\) 6991.80 + 105.707i 0.461808 + 0.00698196i
\(613\) −8563.84 + 14833.0i −0.564258 + 0.977324i 0.432860 + 0.901461i \(0.357504\pi\)
−0.997118 + 0.0758627i \(0.975829\pi\)
\(614\) −4279.01 + 7283.76i −0.281249 + 0.478744i
\(615\) 223.851i 0.0146773i
\(616\) 5063.53 + 114.842i 0.331194 + 0.00751157i
\(617\) −7713.07 13359.4i −0.503268 0.871687i −0.999993 0.00377819i \(-0.998797\pi\)
0.496724 0.867908i \(-0.334536\pi\)
\(618\) 2517.47 4285.26i 0.163864 0.278930i
\(619\) 19584.9i 1.27170i −0.771812 0.635851i \(-0.780649\pi\)
0.771812 0.635851i \(-0.219351\pi\)
\(620\) −407.428 + 681.675i −0.0263915 + 0.0441560i
\(621\) 5107.93 2949.06i 0.330071 0.190567i
\(622\) −169.298 + 22397.0i −0.0109135 + 1.44379i
\(623\) 998.390 + 1729.26i 0.0642049 + 0.111206i
\(624\) 216.885 7171.09i 0.0139140 0.460054i
\(625\) −7710.50 + 13355.0i −0.493472 + 0.854718i
\(626\) 5286.54 + 9318.51i 0.337528 + 0.594956i
\(627\) −2063.23 + 5044.81i −0.131415 + 0.321324i
\(628\) 5454.08 9125.32i 0.346563 0.579841i
\(629\) 2372.82 + 1369.95i 0.150414 + 0.0868419i
\(630\) −1.79519 + 237.492i −0.000113527 + 0.0150189i
\(631\) 10570.1 6102.64i 0.666859 0.385011i −0.128026 0.991771i \(-0.540864\pi\)
0.794885 + 0.606759i \(0.207531\pi\)
\(632\) 12284.5 20205.0i 0.773182 1.27170i
\(633\) 3684.31 + 6381.41i 0.231340 + 0.400692i
\(634\) 14905.2 8455.95i 0.933692 0.529698i
\(635\) −815.814 −0.0509836
\(636\) 24.9471 1650.08i 0.00155537 0.102877i
\(637\) 23644.3 13651.1i 1.47068 0.849097i
\(638\) −11094.3 19555.7i −0.688443 1.21351i
\(639\) 13418.3 0.830704
\(640\) −582.658 + 896.132i −0.0359869 + 0.0553480i
\(641\) −4287.55 2475.42i −0.264194 0.152532i 0.362052 0.932158i \(-0.382076\pi\)
−0.626246 + 0.779626i \(0.715409\pi\)
\(642\) −2505.62 + 4265.08i −0.154032 + 0.262195i
\(643\) 8459.97 + 4884.37i 0.518863 + 0.299566i 0.736469 0.676471i \(-0.236492\pi\)
−0.217606 + 0.976037i \(0.569825\pi\)
\(644\) −1495.51 2683.18i −0.0915085 0.164180i
\(645\) 401.021i 0.0244809i
\(646\) 7483.67 + 3126.91i 0.455791 + 0.190444i
\(647\) 32532.7i 1.97681i −0.151857 0.988403i \(-0.548525\pi\)
0.151857 0.988403i \(-0.451475\pi\)
\(648\) 6934.22 11405.1i 0.420373 0.691413i
\(649\) 29284.5 + 16907.4i 1.77121 + 1.02261i
\(650\) −25679.4 15085.9i −1.54958 0.910337i
\(651\) 695.419 + 401.501i 0.0418673 + 0.0241721i
\(652\) −309.176 + 20449.9i −0.0185710 + 1.22834i
\(653\) −9833.60 −0.589308 −0.294654 0.955604i \(-0.595204\pi\)
−0.294654 + 0.955604i \(0.595204\pi\)
\(654\) 243.232 137.989i 0.0145430 0.00825047i
\(655\) 778.503 449.469i 0.0464407 0.0268125i
\(656\) −12459.6 7704.91i −0.741562 0.458577i
\(657\) 1029.31 0.0611224
\(658\) −1814.69 3198.72i −0.107513 0.189513i
\(659\) 5862.03 + 10153.3i 0.346513 + 0.600179i 0.985628 0.168933i \(-0.0540322\pi\)
−0.639114 + 0.769112i \(0.720699\pi\)
\(660\) −339.442 + 189.194i −0.0200194 + 0.0111581i
\(661\) 14126.4 8155.87i 0.831245 0.479919i −0.0230339 0.999735i \(-0.507333\pi\)
0.854279 + 0.519815i \(0.173999\pi\)
\(662\) 10407.2 + 78.6676i 0.611010 + 0.00461859i
\(663\) −3361.37 1940.69i −0.196900 0.113680i
\(664\) 371.449 16377.6i 0.0217094 0.957192i
\(665\) −104.279 + 254.973i −0.00608085 + 0.0148683i
\(666\) 4914.46 2788.05i 0.285933 0.162214i
\(667\) −6818.11 + 11809.3i −0.395800 + 0.685545i
\(668\) 1865.57 + 3347.11i 0.108055 + 0.193868i
\(669\) 1882.46 + 3260.52i 0.108790 + 0.188429i
\(670\) 634.755 + 4.79807i 0.0366011 + 0.000276665i
\(671\) −8924.31 + 5152.45i −0.513441 + 0.296435i
\(672\) 914.919 + 575.385i 0.0525205 + 0.0330297i
\(673\) 17591.1i 1.00756i −0.863833 0.503779i \(-0.831943\pi\)
0.863833 0.503779i \(-0.168057\pi\)
\(674\) −10257.0 6025.73i −0.586181 0.344366i
\(675\) 4307.45 + 7460.72i 0.245620 + 0.425427i
\(676\) 20362.9 34069.6i 1.15856 1.93841i
\(677\) 26882.4i 1.52611i −0.646334 0.763054i \(-0.723699\pi\)
0.646334 0.763054i \(-0.276301\pi\)
\(678\) 2540.50 + 1492.48i 0.143905 + 0.0845402i
\(679\) 1683.00 2915.05i 0.0951219 0.164756i
\(680\) 277.710 + 507.232i 0.0156613 + 0.0286051i
\(681\) 4470.13 7742.50i 0.251536 0.435673i
\(682\) 142.820 18894.2i 0.00801886 1.06084i
\(683\) −21470.3 −1.20284 −0.601418 0.798935i \(-0.705397\pi\)
−0.601418 + 0.798935i \(0.705397\pi\)
\(684\) 13377.1 10040.3i 0.747787 0.561255i
\(685\) 1044.52 0.0582615
\(686\) −64.1349 + 8484.64i −0.00356951 + 0.472223i
\(687\) −3855.52 + 6677.96i −0.214115 + 0.370859i
\(688\) 22320.9 + 13803.1i 1.23688 + 0.764879i
\(689\) 6586.35 11407.9i 0.364180 0.630778i
\(690\) 203.216 + 119.384i 0.0112120 + 0.00658677i
\(691\) 50.1397i 0.00276035i 0.999999 + 0.00138018i \(0.000439324\pi\)
−0.999999 + 0.00138018i \(0.999561\pi\)
\(692\) 15539.5 + 9287.75i 0.853647 + 0.510213i
\(693\) −2825.32 4893.60i −0.154870 0.268243i
\(694\) 19226.3 + 11294.9i 1.05161 + 0.617794i
\(695\) 1988.44i 0.108526i
\(696\) 108.789 4796.63i 0.00592476 0.261230i
\(697\) −6863.62 + 3962.71i −0.372996 + 0.215349i
\(698\) 25240.8 + 190.794i 1.36874 + 0.0103462i
\(699\) 3164.53 + 5481.12i 0.171235 + 0.296588i
\(700\) 3919.09 2184.37i 0.211611 0.117945i
\(701\) −11382.0 + 19714.2i −0.613254 + 1.06219i 0.377434 + 0.926037i \(0.376807\pi\)
−0.990688 + 0.136151i \(0.956527\pi\)
\(702\) −14407.8 + 8173.80i −0.774628 + 0.439459i
\(703\) 6493.70 884.495i 0.348385 0.0474529i
\(704\) 1153.00 25405.4i 0.0617261 1.36009i
\(705\) 244.367 + 141.086i 0.0130545 + 0.00753701i
\(706\) −6947.62 52.5167i −0.370364 0.00279956i
\(707\) −5049.51 + 2915.34i −0.268609 + 0.155081i
\(708\) 3513.07 + 6302.98i 0.186482 + 0.334577i
\(709\) 2138.99 + 3704.83i 0.113302 + 0.196245i 0.917100 0.398658i \(-0.130524\pi\)
−0.803798 + 0.594903i \(0.797191\pi\)
\(710\) 547.559 + 965.175i 0.0289430 + 0.0510174i
\(711\) −26381.4 −1.39153
\(712\) 8794.41 4814.95i 0.462900 0.253438i
\(713\) −9924.31 + 5729.81i −0.521274 + 0.300958i
\(714\) 508.580 288.525i 0.0266570 0.0151229i
\(715\) −3101.93 −0.162246
\(716\) 2828.72 + 42.7666i 0.147645 + 0.00223221i
\(717\) 2525.23 + 1457.94i 0.131529 + 0.0759383i
\(718\) −27325.9 16053.2i −1.42032 0.834402i
\(719\) 4380.20 + 2528.91i 0.227196 + 0.131172i 0.609278 0.792957i \(-0.291459\pi\)
−0.382082 + 0.924128i \(0.624793\pi\)
\(720\) 1191.98 + 36.0508i 0.0616981 + 0.00186602i
\(721\) 5976.47i 0.308703i
\(722\) 18732.1 5047.21i 0.965565 0.260163i
\(723\) 3469.37i 0.178461i
\(724\) −24044.8 + 13401.8i −1.23428 + 0.687945i
\(725\) −17248.9 9958.64i −0.883596 0.510144i
\(726\) 2156.78 3671.29i 0.110256 0.187678i
\(727\) 11941.3 + 6894.31i 0.609186 + 0.351714i 0.772647 0.634836i \(-0.218932\pi\)
−0.163461 + 0.986550i \(0.552266\pi\)
\(728\) 4143.08 + 7567.26i 0.210924 + 0.385249i
\(729\) −12415.2 −0.630758
\(730\) 42.0031 + 74.0383i 0.00212959 + 0.00375381i
\(731\) 12295.9 7099.05i 0.622136 0.359190i
\(732\) −2198.76 33.2425i −0.111022 0.00167852i
\(733\) −2361.15 −0.118978 −0.0594892 0.998229i \(-0.518947\pi\)
−0.0594892 + 0.998229i \(0.518947\pi\)
\(734\) −5476.50 + 3106.90i −0.275397 + 0.156237i
\(735\) −157.789 273.298i −0.00791855 0.0137153i
\(736\) −13639.6 + 7201.86i −0.683101 + 0.360685i
\(737\) −13079.3 + 7551.36i −0.653709 + 0.377419i
\(738\) −123.539 + 16343.4i −0.00616195 + 0.815186i
\(739\) 6781.05 + 3915.04i 0.337544 + 0.194881i 0.659185 0.751981i \(-0.270901\pi\)
−0.321642 + 0.946862i \(0.604235\pi\)
\(740\) 401.087 + 239.724i 0.0199247 + 0.0119087i
\(741\) −9199.04 + 1252.98i −0.456053 + 0.0621181i
\(742\) 979.205 + 1726.03i 0.0484471 + 0.0853971i
\(743\) 1929.75 3342.43i 0.0952838 0.165036i −0.814443 0.580243i \(-0.802957\pi\)
0.909727 + 0.415207i \(0.136291\pi\)
\(744\) 2094.67 3445.23i 0.103218 0.169769i
\(745\) 436.642 + 756.286i 0.0214729 + 0.0371922i
\(746\) −268.815 + 35562.5i −0.0131931 + 1.74536i
\(747\) −15828.0 + 9138.30i −0.775256 + 0.447594i
\(748\) −11809.9 7058.64i −0.577292 0.345039i
\(749\) 5948.32i 0.290183i
\(750\) −349.512 + 594.941i −0.0170165 + 0.0289656i
\(751\) 14520.5 + 25150.3i 0.705542 + 1.22203i 0.966496 + 0.256683i \(0.0826297\pi\)
−0.260953 + 0.965351i \(0.584037\pi\)
\(752\) −16263.9 + 8745.38i −0.788676 + 0.424084i
\(753\) 3098.50i 0.149954i
\(754\) 19398.9 33020.9i 0.936956 1.59489i
\(755\) −588.551 + 1019.40i −0.0283703 + 0.0491388i
\(756\) 37.7242 2495.20i 0.00181484 0.120039i
\(757\) −16298.5 + 28229.8i −0.782533 + 1.35539i 0.147929 + 0.988998i \(0.452739\pi\)
−0.930462 + 0.366389i \(0.880594\pi\)
\(758\) −5817.04 43.9707i −0.278739 0.00210697i
\(759\) −5607.59 −0.268172
\(760\) 1268.07 + 552.500i 0.0605233 + 0.0263701i
\(761\) −17002.6 −0.809913 −0.404957 0.914336i \(-0.632713\pi\)
−0.404957 + 0.914336i \(0.632713\pi\)
\(762\) 4141.89 + 31.3083i 0.196909 + 0.00148843i
\(763\) −168.139 + 291.224i −0.00797775 + 0.0138179i
\(764\) −267.864 + 17717.3i −0.0126845 + 0.838992i
\(765\) 322.582 558.728i 0.0152457 0.0264064i
\(766\) 11481.0 19543.0i 0.541547 0.921824i
\(767\) 57598.6i 2.71156i
\(768\) 2992.55 4527.30i 0.140605 0.212715i
\(769\) 18030.6 + 31229.9i 0.845514 + 1.46447i 0.885175 + 0.465259i \(0.154039\pi\)
−0.0396610 + 0.999213i \(0.512628\pi\)
\(770\) 236.703 402.917i 0.0110781 0.0188573i
\(771\) 1330.69i 0.0621580i
\(772\) −18225.1 10892.9i −0.849659 0.507829i
\(773\) 18451.8 10653.2i 0.858559 0.495689i −0.00497029 0.999988i \(-0.501582\pi\)
0.863530 + 0.504298i \(0.168249\pi\)
\(774\) 221.315 29278.5i 0.0102778 1.35968i
\(775\) −8369.04 14495.6i −0.387903 0.671868i
\(776\) −14441.7 8780.42i −0.668074 0.406184i
\(777\) 236.237 409.174i 0.0109073 0.0188919i
\(778\) 6558.00 + 11559.7i 0.302205 + 0.532693i
\(779\) −7176.12 + 17546.4i −0.330053 + 0.807014i
\(780\) −568.184 339.595i −0.0260824 0.0155891i
\(781\) −22864.6 13200.9i −1.04758 0.604821i
\(782\) −63.0742 + 8344.32i −0.00288431 + 0.381576i
\(783\) −9593.67 + 5538.91i −0.437867 + 0.252802i
\(784\) 20642.9 + 624.332i 0.940365 + 0.0284408i
\(785\) −490.429 849.448i −0.0222983 0.0386218i
\(786\) −3969.71 + 2252.08i −0.180146 + 0.102200i
\(787\) 31916.2 1.44560 0.722801 0.691056i \(-0.242854\pi\)
0.722801 + 0.691056i \(0.242854\pi\)
\(788\) 16539.7 + 250.060i 0.747720 + 0.0113046i
\(789\) −2444.83 + 1411.52i −0.110315 + 0.0636902i
\(790\) −1076.54 1897.60i −0.0484830 0.0854604i
\(791\) −3543.13 −0.159266
\(792\) −24887.1 + 13625.7i −1.11657 + 0.611324i
\(793\) −15201.2 8776.44i −0.680721 0.393015i
\(794\) −8110.03 + 13804.9i −0.362486 + 0.617026i
\(795\) −131.861 76.1299i −0.00588254 0.00339629i
\(796\) −21694.5 + 12091.8i −0.966004 + 0.538418i
\(797\) 18567.8i 0.825228i −0.910906 0.412614i \(-0.864616\pi\)
0.910906 0.412614i \(-0.135384\pi\)
\(798\) 539.209 1290.50i 0.0239195 0.0572470i
\(799\) 9990.25i 0.442340i
\(800\) −10519.1 19922.2i −0.464885 0.880445i
\(801\) −9687.26 5592.94i −0.427319 0.246713i
\(802\) −4403.83 2587.13i −0.193896 0.113909i
\(803\) −1753.94 1012.64i −0.0770799 0.0445021i
\(804\) −3222.47 48.7197i −0.141353 0.00213708i
\(805\) −283.417 −0.0124089
\(806\) 27993.3 15881.1i 1.22335 0.694028i
\(807\) 9067.35 5235.04i 0.395521 0.228354i
\(808\) 14059.8 + 25680.0i 0.612157 + 1.11809i
\(809\) −5846.62 −0.254087 −0.127043 0.991897i \(-0.540549\pi\)
−0.127043 + 0.991897i \(0.540549\pi\)
\(810\) −607.674 1071.14i −0.0263599 0.0464642i
\(811\) −5472.20 9478.13i −0.236936 0.410385i 0.722898 0.690955i \(-0.242810\pi\)
−0.959834 + 0.280570i \(0.909476\pi\)
\(812\) 2808.86 + 5039.52i 0.121394 + 0.217799i
\(813\) −3349.88 + 1934.06i −0.144509 + 0.0834321i
\(814\) −11117.0 84.0331i −0.478688 0.00361838i
\(815\) 1634.19 + 943.500i 0.0702370 + 0.0405514i
\(816\) −1390.47 2585.88i −0.0596521 0.110936i
\(817\) 12855.7 31433.7i 0.550509 1.34605i
\(818\) 7407.50 4202.39i 0.316623 0.179625i
\(819\) 4812.52 8335.52i 0.205327 0.355637i
\(820\) −1180.62 + 658.035i −0.0502791 + 0.0280239i
\(821\) 9826.49 + 17020.0i 0.417718 + 0.723509i 0.995710 0.0925337i \(-0.0294966\pi\)
−0.577991 + 0.816043i \(0.696163\pi\)
\(822\) −5303.04 40.0854i −0.225018 0.00170090i
\(823\) −23131.5 + 13355.0i −0.979726 + 0.565645i −0.902187 0.431344i \(-0.858039\pi\)
−0.0775386 + 0.996989i \(0.524706\pi\)
\(824\) 30001.3 + 680.439i 1.26838 + 0.0287672i
\(825\) 8190.53i 0.345646i
\(826\) −7481.61 4395.24i −0.315156 0.185145i
\(827\) −9407.85 16294.9i −0.395578 0.685161i 0.597597 0.801797i \(-0.296122\pi\)
−0.993175 + 0.116636i \(0.962789\pi\)
\(828\) 14770.9 + 8828.38i 0.619958 + 0.370540i
\(829\) 42600.5i 1.78477i 0.451271 + 0.892387i \(0.350971\pi\)
−0.451271 + 0.892387i \(0.649029\pi\)
\(830\) −1303.21 765.598i −0.0544999 0.0320172i
\(831\) 4867.97 8431.57i 0.203211 0.351971i
\(832\) 38458.7 19936.3i 1.60254 0.830731i
\(833\) 5586.51 9676.11i 0.232366 0.402470i
\(834\) −76.3099 + 10095.3i −0.00316834 + 0.419151i
\(835\) 353.546 0.0146527
\(836\) −32672.0 + 3948.10i −1.35166 + 0.163335i
\(837\) −9309.57 −0.384452
\(838\) −165.911 + 21949.0i −0.00683926 + 0.904791i
\(839\) 19077.4 33043.0i 0.785011 1.35968i −0.143982 0.989580i \(-0.545991\pi\)
0.928993 0.370098i \(-0.120676\pi\)
\(840\) 87.4679 47.8887i 0.00359277 0.00196705i
\(841\) 611.215 1058.65i 0.0250611 0.0434071i
\(842\) −16183.1 9507.14i −0.662360 0.389118i
\(843\) 12014.9i 0.490886i
\(844\) −22825.8 + 38190.3i −0.930920 + 1.55754i
\(845\) −1831.03 3171.43i −0.0745435 0.129113i
\(846\) 17763.4 + 10435.5i 0.721890 + 0.424091i
\(847\) 5120.18i 0.207711i
\(848\) 8776.02 4719.01i 0.355389 0.191098i
\(849\) 1808.58 1044.18i 0.0731098 0.0422099i
\(850\) −12187.8 92.1272i −0.491811 0.00371757i
\(851\) 3371.33 + 5839.31i 0.135802 + 0.235216i
\(852\) −2742.92 4921.21i −0.110294 0.197885i
\(853\) 20474.0 35461.9i 0.821823 1.42344i −0.0824998 0.996591i \(-0.526290\pi\)
0.904323 0.426849i \(-0.140376\pi\)
\(854\) 2299.97 1304.81i 0.0921585 0.0522830i
\(855\) −208.272 1529.07i −0.00833069 0.0611615i
\(856\) −29860.0 677.234i −1.19228 0.0270413i
\(857\) 18584.3 + 10729.7i 0.740756 + 0.427676i 0.822344 0.568991i \(-0.192666\pi\)
−0.0815882 + 0.996666i \(0.525999\pi\)
\(858\) 15748.5 + 119.042i 0.626626 + 0.00473663i
\(859\) 10176.2 5875.23i 0.404199 0.233365i −0.284095 0.958796i \(-0.591693\pi\)
0.688294 + 0.725432i \(0.258360\pi\)
\(860\) 2115.03 1178.85i 0.0838626 0.0467422i
\(861\) 683.337 + 1183.57i 0.0270477 + 0.0468480i
\(862\) −19409.8 34213.5i −0.766939 1.35187i
\(863\) −14087.7 −0.555677 −0.277839 0.960628i \(-0.589618\pi\)
−0.277839 + 0.960628i \(0.589618\pi\)
\(864\) −12521.4 473.458i −0.493039 0.0186428i
\(865\) 1446.52 835.151i 0.0568593 0.0328277i
\(866\) 7131.68 4045.91i 0.279843 0.158759i
\(867\) 4921.03 0.192765
\(868\) −73.2953 + 4847.97i −0.00286613 + 0.189575i
\(869\) 44953.5 + 25953.9i 1.75483 + 1.01315i
\(870\) −381.679 224.226i −0.0148737 0.00873790i
\(871\) −22278.7 12862.6i −0.866689 0.500383i
\(872\) 1442.78 + 877.197i 0.0560305 + 0.0340661i
\(873\) 18856.2i 0.731028i
\(874\) 12101.8 + 15872.4i 0.468362 + 0.614294i
\(875\) 829.738i 0.0320575i
\(876\) −210.408 377.505i −0.00811535 0.0145602i
\(877\) −32837.1 18958.5i −1.26434 0.729969i −0.290432 0.956896i \(-0.593799\pi\)
−0.973912 + 0.226926i \(0.927132\pi\)
\(878\) −1231.17 + 2095.70i −0.0473234 + 0.0805542i
\(879\) −2825.11 1631.08i −0.108406 0.0625881i
\(880\) −1995.66 1234.10i −0.0764473 0.0472744i
\(881\) 18862.7 0.721338 0.360669 0.932694i \(-0.382548\pi\)
0.360669 + 0.932694i \(0.382548\pi\)
\(882\) −11369.3 20040.6i −0.434043 0.765082i
\(883\) −5780.61 + 3337.44i −0.220309 + 0.127196i −0.606093 0.795393i \(-0.707264\pi\)
0.385784 + 0.922589i \(0.373931\pi\)
\(884\) 354.279 23433.1i 0.0134793 0.891561i
\(885\) 665.766 0.0252876
\(886\) 23059.7 13082.1i 0.874384 0.496052i
\(887\) −3078.51 5332.14i −0.116535 0.201844i 0.801858 0.597515i \(-0.203845\pi\)
−0.918392 + 0.395671i \(0.870512\pi\)
\(888\) −2027.12 1232.47i −0.0766055 0.0465755i
\(889\) −4313.48 + 2490.39i −0.162733 + 0.0939538i
\(890\) 6.99226 925.032i 0.000263350 0.0348395i
\(891\) 25374.9 + 14650.2i 0.954086 + 0.550842i
\(892\) −11662.7 + 19513.0i −0.437774 + 0.732448i
\(893\) 14631.7 + 18892.7i 0.548298 + 0.707973i
\(894\) −2187.81 3856.42i −0.0818470 0.144271i
\(895\) 130.509 226.048i 0.00487423 0.00844241i
\(896\) −345.136 + 6516.79i −0.0128685 + 0.242981i
\(897\) −4775.85 8272.02i −0.177772 0.307909i
\(898\) 1.00349 132.756i 3.72907e−5 0.00493332i
\(899\) 18639.8 10761.7i 0.691514 0.399246i
\(900\) −12894.9 + 21574.7i −0.477588 + 0.799061i
\(901\) 5390.74i 0.199325i
\(902\) 16289.1 27727.3i 0.601293 1.02353i
\(903\) −1224.17 2120.33i −0.0451140 0.0781397i
\(904\) −403.396 + 17786.2i −0.0148415 + 0.654381i
\(905\) 2539.79i 0.0932877i
\(906\) 3027.20 5152.91i 0.111006 0.188956i
\(907\) −8578.02 + 14857.6i −0.314033 + 0.543922i −0.979232 0.202745i \(-0.935014\pi\)
0.665198 + 0.746667i \(0.268347\pi\)
\(908\) 53975.3 + 816.038i 1.97272 + 0.0298251i
\(909\) 16331.6 28287.2i 0.595913 1.03215i
\(910\) 795.956 + 6.01658i 0.0289952 + 0.000219173i
\(911\) 27397.9 0.996414 0.498207 0.867058i \(-0.333992\pi\)
0.498207 + 0.867058i \(0.333992\pi\)
\(912\) −6416.79 2853.71i −0.232984 0.103614i
\(913\) 35960.9 1.30354
\(914\) 45837.4 + 346.482i 1.65883 + 0.0125390i
\(915\) −101.444 + 175.707i −0.00366519 + 0.00634830i
\(916\) −46554.0 703.839i −1.67925 0.0253881i
\(917\) 2744.14 4752.98i 0.0988215 0.171164i
\(918\) −3433.76 + 5844.97i −0.123454 + 0.210145i
\(919\) 50927.7i 1.82802i −0.405690 0.914011i \(-0.632969\pi\)
0.405690 0.914011i \(-0.367031\pi\)
\(920\) −32.2679 + 1422.73i −0.00115635 + 0.0509847i
\(921\) −1978.60 3427.04i −0.0707895 0.122611i
\(922\) −3831.11 + 6521.34i −0.136845 + 0.232938i
\(923\) 44971.6i 1.60375i
\(924\) −1217.20 + 2036.53i −0.0433366 + 0.0725073i
\(925\) −8528.99 + 4924.21i −0.303169 + 0.175035i
\(926\) −83.2633 + 11015.2i −0.00295486 + 0.390909i
\(927\) −16740.0 28994.5i −0.593110 1.02730i
\(928\) 25617.8 13526.5i 0.906190 0.478479i
\(929\) −10753.0 + 18624.8i −0.379758 + 0.657760i −0.991027 0.133663i \(-0.957326\pi\)
0.611269 + 0.791423i \(0.290659\pi\)
\(930\) −183.565 323.567i −0.00647240 0.0114088i
\(931\) −3606.87 26480.6i −0.126971 0.932187i
\(932\) −19605.6 + 32802.4i −0.689057 + 1.15287i
\(933\) −9086.25 5245.95i −0.318832 0.184078i
\(934\) 112.186 14841.5i 0.00393025 0.519947i
\(935\) −1099.35 + 634.710i −0.0384520 + 0.0222003i
\(936\) −41295.7 25107.4i −1.44208 0.876776i
\(937\) −3417.25 5918.85i −0.119143 0.206361i 0.800286 0.599619i \(-0.204681\pi\)
−0.919428 + 0.393258i \(0.871348\pi\)
\(938\) 3370.80 1912.31i 0.117335 0.0665662i
\(939\) −5018.67 −0.174417
\(940\) −25.7557 + 1703.56i −0.000893678 + 0.0591106i
\(941\) −4239.85 + 2447.88i −0.146881 + 0.0848019i −0.571639 0.820505i \(-0.693692\pi\)
0.424758 + 0.905307i \(0.360359\pi\)
\(942\) 2457.31 + 4331.47i 0.0849931 + 0.149816i
\(943\) −19503.8 −0.673521
\(944\) −22915.5 + 37056.6i −0.790082 + 1.27764i
\(945\) −199.396 115.121i −0.00686386 0.00396285i
\(946\) −29181.3 + 49672.5i −1.00292 + 1.70718i
\(947\) 21112.0 + 12189.0i 0.724442 + 0.418257i 0.816385 0.577508i \(-0.195975\pi\)
−0.0919435 + 0.995764i \(0.529308\pi\)
\(948\) 5392.78 + 9675.46i 0.184757 + 0.331481i
\(949\) 3449.76i 0.118002i
\(950\) −23183.5 + 17676.0i −0.791761 + 0.603670i
\(951\) 8027.48i 0.273721i
\(952\) 3016.74 + 1834.15i 0.102703 + 0.0624425i
\(953\) 34104.1 + 19690.0i 1.15922 + 0.669279i 0.951118 0.308828i \(-0.0999366\pi\)
0.208107 + 0.978106i \(0.433270\pi\)
\(954\) −9585.14 5631.01i −0.325294 0.191101i
\(955\) 1415.82 + 817.427i 0.0479738 + 0.0276977i
\(956\) −266.152 + 17604.1i −0.00900415 + 0.595562i
\(957\) 10532.1 0.355753
\(958\) 14288.9 8106.30i 0.481892 0.273385i
\(959\) 5522.73 3188.55i 0.185963 0.107366i
\(960\) −230.439 444.533i −0.00774727 0.0149451i
\(961\) −11703.2 −0.392844
\(962\) −9344.16 16470.8i −0.313168 0.552018i
\(963\) 16661.1 + 28857.9i 0.557526 + 0.965663i
\(964\) 18297.8 10198.6i 0.611342 0.340741i
\(965\) −1696.52 + 979.486i −0.0565937 + 0.0326744i
\(966\) 1438.91 + 10.8766i 0.0479256 + 0.000362267i
\(967\) −45006.4 25984.5i −1.49670 0.864121i −0.496708 0.867918i \(-0.665458\pi\)
−0.999993 + 0.00379707i \(0.998791\pi\)
\(968\) 25702.9 + 582.948i 0.853431 + 0.0193561i
\(969\) −3003.84 + 2326.36i −0.0995842 + 0.0771242i
\(970\) −1356.32 + 769.464i −0.0448958 + 0.0254701i
\(971\) 22337.6 38689.9i 0.738258 1.27870i −0.215021 0.976610i \(-0.568982\pi\)
0.953279 0.302091i \(-0.0976848\pi\)
\(972\) 10323.3 + 18521.6i 0.340659 + 0.611194i
\(973\) −6070.00 10513.5i −0.199995 0.346402i
\(974\) −40730.1 307.876i −1.33991 0.0101283i
\(975\) 12082.2 6975.68i 0.396863 0.229129i
\(976\) −6288.17 11694.2i −0.206229 0.383527i
\(977\) 48849.3i 1.59962i 0.600253 + 0.799810i \(0.295066\pi\)
−0.600253 + 0.799810i \(0.704934\pi\)
\(978\) −8260.57 4852.86i −0.270086 0.158668i
\(979\) 11004.6 + 19060.6i 0.359254 + 0.622247i
\(980\) 977.568 1635.59i 0.0318646 0.0533132i
\(981\) 1883.81i 0.0613104i
\(982\) 38791.7 + 22789.1i 1.26058 + 0.740559i
\(983\) −19594.1 + 33938.0i −0.635764 + 1.10118i 0.350589 + 0.936530i \(0.385982\pi\)
−0.986353 + 0.164646i \(0.947352\pi\)
\(984\) 6019.24 3295.54i 0.195006 0.106766i
\(985\) 763.096 1321.72i 0.0246845 0.0427549i
\(986\) 118.465 15672.2i 0.00382628 0.506192i
\(987\) 1722.74 0.0555575
\(988\) −33650.0 44833.5i −1.08355 1.44367i
\(989\) 34940.3 1.12339
\(990\) −19.7872 + 2617.73i −0.000635232 + 0.0840372i
\(991\) −5518.01 + 9557.48i −0.176877 + 0.306361i −0.940809 0.338936i \(-0.889933\pi\)
0.763932 + 0.645297i \(0.223266\pi\)
\(992\) 24328.1 + 919.892i 0.778646 + 0.0294422i
\(993\) −2437.64 + 4222.11i −0.0779013 + 0.134929i
\(994\) 5841.46 + 3431.70i 0.186398 + 0.109504i
\(995\) 2291.53i 0.0730113i
\(996\) 6587.00 + 3936.96i 0.209555 + 0.125248i
\(997\) −4004.60 6936.18i −0.127209 0.220332i 0.795385 0.606104i \(-0.207268\pi\)
−0.922594 + 0.385772i \(0.873935\pi\)
\(998\) −31271.5 18371.2i −0.991865 0.582694i
\(999\) 5477.61i 0.173477i
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 76.4.f.a.27.1 56
4.3 odd 2 inner 76.4.f.a.27.10 yes 56
19.12 odd 6 inner 76.4.f.a.31.10 yes 56
76.31 even 6 inner 76.4.f.a.31.1 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.4.f.a.27.1 56 1.1 even 1 trivial
76.4.f.a.27.10 yes 56 4.3 odd 2 inner
76.4.f.a.31.1 yes 56 76.31 even 6 inner
76.4.f.a.31.10 yes 56 19.12 odd 6 inner