Properties

Label 162.8.c.q.109.2
Level $162$
Weight $8$
Character 162.109
Analytic conductor $50.606$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,8,Mod(55,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.55");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 162.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(50.6063741284\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 2x^{6} + 518x^{5} + 53377x^{4} + 11940x^{3} + 3528x^{2} + 1563408x + 346406544 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{18} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.2
Root \(-9.64382 - 9.64382i\) of defining polynomial
Character \(\chi\) \(=\) 162.109
Dual form 162.8.c.q.55.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(-162.750 + 281.891i) q^{5} +(725.227 + 1256.13i) q^{7} +512.000 q^{8} +2604.00 q^{10} +(2777.90 + 4811.46i) q^{11} +(-6751.86 + 11694.6i) q^{13} +(5801.82 - 10049.0i) q^{14} +(-2048.00 - 3547.24i) q^{16} +11828.7 q^{17} +44544.0 q^{19} +(-10416.0 - 18041.0i) q^{20} +(22223.2 - 38491.7i) q^{22} +(-13403.3 + 23215.2i) q^{23} +(-13912.6 - 24097.3i) q^{25} +108030. q^{26} -92829.0 q^{28} +(-70432.1 - 121992. i) q^{29} +(-82846.2 + 143494. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-47314.8 - 81951.7i) q^{34} -472122. q^{35} +36343.3 q^{37} +(-178176. - 308610. i) q^{38} +(-83328.0 + 144328. i) q^{40} +(239035. - 414020. i) q^{41} +(302108. + 523266. i) q^{43} -355571. q^{44} +214453. q^{46} +(-251533. - 435667. i) q^{47} +(-640137. + 1.10875e6i) q^{49} +(-111301. + 192778. i) q^{50} +(-432119. - 748452. i) q^{52} +1.99651e6 q^{53} -1.80841e6 q^{55} +(371316. + 643138. i) q^{56} +(-563457. + 975935. i) q^{58} +(-304536. + 527472. i) q^{59} +(-950933. - 1.64706e6i) q^{61} +1.32554e6 q^{62} +262144. q^{64} +(-2.19773e6 - 3.80658e6i) q^{65} +(-886834. + 1.53604e6i) q^{67} +(-378519. + 655614. i) q^{68} +(1.88849e6 + 3.27096e6i) q^{70} +1.00843e6 q^{71} +146188. q^{73} +(-145373. - 251794. i) q^{74} +(-1.42541e6 + 2.46888e6i) q^{76} +(-4.02921e6 + 6.97880e6i) q^{77} +(3.63689e6 + 6.29928e6i) q^{79} +1.33325e6 q^{80} -3.82456e6 q^{82} +(2.68846e6 + 4.65655e6i) q^{83} +(-1.92512e6 + 3.33441e6i) q^{85} +(2.41686e6 - 4.18613e6i) q^{86} +(1.42228e6 + 2.46347e6i) q^{88} -2.94159e6 q^{89} -1.95865e7 q^{91} +(-857812. - 1.48577e6i) q^{92} +(-2.01226e6 + 3.48534e6i) q^{94} +(-7.24953e6 + 1.25566e7i) q^{95} +(3.95734e6 + 6.85431e6i) q^{97} +1.02422e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 32 q^{2} - 256 q^{4} - 528 q^{5} - 560 q^{7} + 4096 q^{8} + 8448 q^{10} - 2160 q^{11} - 13460 q^{13} - 4480 q^{14} - 16384 q^{16} + 45120 q^{17} + 73408 q^{19} - 33792 q^{20} - 17280 q^{22} - 62640 q^{23}+ \cdots + 23190336 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 6.92820i −0.353553 0.612372i
\(3\) 0 0
\(4\) −32.0000 + 55.4256i −0.250000 + 0.433013i
\(5\) −162.750 + 281.891i −0.582272 + 1.00852i 0.412938 + 0.910759i \(0.364503\pi\)
−0.995210 + 0.0977650i \(0.968831\pi\)
\(6\) 0 0
\(7\) 725.227 + 1256.13i 0.799155 + 1.38418i 0.920167 + 0.391525i \(0.128052\pi\)
−0.121013 + 0.992651i \(0.538614\pi\)
\(8\) 512.000 0.353553
\(9\) 0 0
\(10\) 2604.00 0.823457
\(11\) 2777.90 + 4811.46i 0.629277 + 1.08994i 0.987697 + 0.156380i \(0.0499823\pi\)
−0.358420 + 0.933560i \(0.616684\pi\)
\(12\) 0 0
\(13\) −6751.86 + 11694.6i −0.852357 + 1.47633i 0.0267188 + 0.999643i \(0.491494\pi\)
−0.879076 + 0.476682i \(0.841839\pi\)
\(14\) 5801.82 10049.0i 0.565088 0.978760i
\(15\) 0 0
\(16\) −2048.00 3547.24i −0.125000 0.216506i
\(17\) 11828.7 0.583937 0.291969 0.956428i \(-0.405690\pi\)
0.291969 + 0.956428i \(0.405690\pi\)
\(18\) 0 0
\(19\) 44544.0 1.48988 0.744940 0.667131i \(-0.232478\pi\)
0.744940 + 0.667131i \(0.232478\pi\)
\(20\) −10416.0 18041.0i −0.291136 0.504262i
\(21\) 0 0
\(22\) 22223.2 38491.7i 0.444966 0.770704i
\(23\) −13403.3 + 23215.2i −0.229702 + 0.397855i −0.957720 0.287703i \(-0.907108\pi\)
0.728018 + 0.685558i \(0.240442\pi\)
\(24\) 0 0
\(25\) −13912.6 24097.3i −0.178081 0.308445i
\(26\) 108030. 1.20541
\(27\) 0 0
\(28\) −92829.0 −0.799155
\(29\) −70432.1 121992.i −0.536263 0.928834i −0.999101 0.0423914i \(-0.986502\pi\)
0.462838 0.886443i \(-0.346831\pi\)
\(30\) 0 0
\(31\) −82846.2 + 143494.i −0.499467 + 0.865102i −1.00000 0.000615720i \(-0.999804\pi\)
0.500533 + 0.865717i \(0.333137\pi\)
\(32\) −16384.0 + 28377.9i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −47314.8 81951.7i −0.206453 0.357587i
\(35\) −472122. −1.86130
\(36\) 0 0
\(37\) 36343.3 0.117956 0.0589778 0.998259i \(-0.481216\pi\)
0.0589778 + 0.998259i \(0.481216\pi\)
\(38\) −178176. 308610.i −0.526752 0.912362i
\(39\) 0 0
\(40\) −83328.0 + 144328.i −0.205864 + 0.356567i
\(41\) 239035. 414020.i 0.541648 0.938163i −0.457161 0.889384i \(-0.651134\pi\)
0.998810 0.0487788i \(-0.0155329\pi\)
\(42\) 0 0
\(43\) 302108. + 523266.i 0.579458 + 1.00365i 0.995541 + 0.0943248i \(0.0300692\pi\)
−0.416083 + 0.909327i \(0.636597\pi\)
\(44\) −355571. −0.629277
\(45\) 0 0
\(46\) 214453. 0.324848
\(47\) −251533. 435667.i −0.353388 0.612086i 0.633453 0.773781i \(-0.281637\pi\)
−0.986841 + 0.161695i \(0.948304\pi\)
\(48\) 0 0
\(49\) −640137. + 1.10875e6i −0.777296 + 1.34632i
\(50\) −111301. + 192778.i −0.125922 + 0.218104i
\(51\) 0 0
\(52\) −432119. 748452.i −0.426178 0.738163i
\(53\) 1.99651e6 1.84207 0.921036 0.389477i \(-0.127344\pi\)
0.921036 + 0.389477i \(0.127344\pi\)
\(54\) 0 0
\(55\) −1.80841e6 −1.46564
\(56\) 371316. + 643138.i 0.282544 + 0.489380i
\(57\) 0 0
\(58\) −563457. + 975935.i −0.379195 + 0.656785i
\(59\) −304536. + 527472.i −0.193044 + 0.334362i −0.946258 0.323414i \(-0.895169\pi\)
0.753214 + 0.657776i \(0.228503\pi\)
\(60\) 0 0
\(61\) −950933. 1.64706e6i −0.536408 0.929087i −0.999094 0.0425640i \(-0.986447\pi\)
0.462685 0.886523i \(-0.346886\pi\)
\(62\) 1.32554e6 0.706353
\(63\) 0 0
\(64\) 262144. 0.125000
\(65\) −2.19773e6 3.80658e6i −0.992607 1.71925i
\(66\) 0 0
\(67\) −886834. + 1.53604e6i −0.360231 + 0.623938i −0.987999 0.154463i \(-0.950635\pi\)
0.627768 + 0.778401i \(0.283969\pi\)
\(68\) −378519. + 655614.i −0.145984 + 0.252852i
\(69\) 0 0
\(70\) 1.88849e6 + 3.27096e6i 0.658069 + 1.13981i
\(71\) 1.00843e6 0.334380 0.167190 0.985925i \(-0.446531\pi\)
0.167190 + 0.985925i \(0.446531\pi\)
\(72\) 0 0
\(73\) 146188. 0.0439825 0.0219913 0.999758i \(-0.492999\pi\)
0.0219913 + 0.999758i \(0.492999\pi\)
\(74\) −145373. 251794.i −0.0417036 0.0722327i
\(75\) 0 0
\(76\) −1.42541e6 + 2.46888e6i −0.372470 + 0.645137i
\(77\) −4.02921e6 + 6.97880e6i −1.00578 + 1.74206i
\(78\) 0 0
\(79\) 3.63689e6 + 6.29928e6i 0.829919 + 1.43746i 0.898101 + 0.439788i \(0.144947\pi\)
−0.0681828 + 0.997673i \(0.521720\pi\)
\(80\) 1.33325e6 0.291136
\(81\) 0 0
\(82\) −3.82456e6 −0.766007
\(83\) 2.68846e6 + 4.65655e6i 0.516096 + 0.893905i 0.999825 + 0.0186871i \(0.00594865\pi\)
−0.483729 + 0.875218i \(0.660718\pi\)
\(84\) 0 0
\(85\) −1.92512e6 + 3.33441e6i −0.340010 + 0.588915i
\(86\) 2.41686e6 4.18613e6i 0.409739 0.709689i
\(87\) 0 0
\(88\) 1.42228e6 + 2.46347e6i 0.222483 + 0.385352i
\(89\) −2.94159e6 −0.442301 −0.221150 0.975240i \(-0.570981\pi\)
−0.221150 + 0.975240i \(0.570981\pi\)
\(90\) 0 0
\(91\) −1.95865e7 −2.72466
\(92\) −857812. 1.48577e6i −0.114851 0.198928i
\(93\) 0 0
\(94\) −2.01226e6 + 3.48534e6i −0.249883 + 0.432810i
\(95\) −7.24953e6 + 1.25566e7i −0.867515 + 1.50258i
\(96\) 0 0
\(97\) 3.95734e6 + 6.85431e6i 0.440253 + 0.762540i 0.997708 0.0676669i \(-0.0215555\pi\)
−0.557455 + 0.830207i \(0.688222\pi\)
\(98\) 1.02422e7 1.09926
\(99\) 0 0
\(100\) 1.78081e6 0.178081
\(101\) −9.25788e6 1.60351e7i −0.894101 1.54863i −0.834913 0.550382i \(-0.814482\pi\)
−0.0591886 0.998247i \(-0.518851\pi\)
\(102\) 0 0
\(103\) −5.02032e6 + 8.69546e6i −0.452691 + 0.784083i −0.998552 0.0537923i \(-0.982869\pi\)
0.545862 + 0.837875i \(0.316202\pi\)
\(104\) −3.45695e6 + 5.98761e6i −0.301354 + 0.521960i
\(105\) 0 0
\(106\) −7.98606e6 1.38323e7i −0.651271 1.12803i
\(107\) 1.26542e7 0.998601 0.499300 0.866429i \(-0.333590\pi\)
0.499300 + 0.866429i \(0.333590\pi\)
\(108\) 0 0
\(109\) −1.26740e6 −0.0937388 −0.0468694 0.998901i \(-0.514924\pi\)
−0.0468694 + 0.998901i \(0.514924\pi\)
\(110\) 7.23364e6 + 1.25290e7i 0.518182 + 0.897518i
\(111\) 0 0
\(112\) 2.97053e6 5.14511e6i 0.199789 0.346044i
\(113\) 7.42101e6 1.28536e7i 0.483825 0.838010i −0.516002 0.856587i \(-0.672580\pi\)
0.999827 + 0.0185773i \(0.00591367\pi\)
\(114\) 0 0
\(115\) −4.36278e6 7.55655e6i −0.267498 0.463320i
\(116\) 9.01531e6 0.536263
\(117\) 0 0
\(118\) 4.87257e6 0.273005
\(119\) 8.57850e6 + 1.48584e7i 0.466656 + 0.808272i
\(120\) 0 0
\(121\) −5.68985e6 + 9.85512e6i −0.291979 + 0.505723i
\(122\) −7.60747e6 + 1.31765e7i −0.379298 + 0.656963i
\(123\) 0 0
\(124\) −5.30216e6 9.18360e6i −0.249733 0.432551i
\(125\) −1.63726e7 −0.749778
\(126\) 0 0
\(127\) −9.71798e6 −0.420982 −0.210491 0.977596i \(-0.567506\pi\)
−0.210491 + 0.977596i \(0.567506\pi\)
\(128\) −1.04858e6 1.81619e6i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −1.75818e7 + 3.04526e7i −0.701879 + 1.21569i
\(131\) 9.15312e6 1.58537e7i 0.355729 0.616141i −0.631513 0.775365i \(-0.717566\pi\)
0.987242 + 0.159224i \(0.0508992\pi\)
\(132\) 0 0
\(133\) 3.23045e7 + 5.59530e7i 1.19064 + 2.06226i
\(134\) 1.41893e7 0.509443
\(135\) 0 0
\(136\) 6.05630e6 0.206453
\(137\) −2.42286e7 4.19652e7i −0.805019 1.39433i −0.916278 0.400543i \(-0.868821\pi\)
0.111258 0.993792i \(-0.464512\pi\)
\(138\) 0 0
\(139\) 1.89915e7 3.28943e7i 0.599802 1.03889i −0.393048 0.919518i \(-0.628579\pi\)
0.992850 0.119370i \(-0.0380875\pi\)
\(140\) 1.51079e7 2.61677e7i 0.465325 0.805967i
\(141\) 0 0
\(142\) −4.03371e6 6.98658e6i −0.118221 0.204765i
\(143\) −7.50239e7 −2.14547
\(144\) 0 0
\(145\) 4.58513e7 1.24900
\(146\) −584750. 1.01282e6i −0.0155502 0.0269337i
\(147\) 0 0
\(148\) −1.16299e6 + 2.01435e6i −0.0294889 + 0.0510762i
\(149\) −1.79041e7 + 3.10108e7i −0.443405 + 0.768000i −0.997940 0.0641605i \(-0.979563\pi\)
0.554534 + 0.832161i \(0.312896\pi\)
\(150\) 0 0
\(151\) −2.40510e7 4.16575e7i −0.568478 0.984632i −0.996717 0.0809668i \(-0.974199\pi\)
0.428239 0.903665i \(-0.359134\pi\)
\(152\) 2.28065e7 0.526752
\(153\) 0 0
\(154\) 6.44674e7 1.42239
\(155\) −2.69664e7 4.67072e7i −0.581651 1.00745i
\(156\) 0 0
\(157\) 3.97645e7 6.88742e7i 0.820062 1.42039i −0.0855727 0.996332i \(-0.527272\pi\)
0.905635 0.424058i \(-0.139395\pi\)
\(158\) 2.90951e7 5.03942e7i 0.586841 1.01644i
\(159\) 0 0
\(160\) −5.33299e6 9.23701e6i −0.102932 0.178284i
\(161\) −3.88818e7 −0.734269
\(162\) 0 0
\(163\) −4.46340e7 −0.807252 −0.403626 0.914924i \(-0.632250\pi\)
−0.403626 + 0.914924i \(0.632250\pi\)
\(164\) 1.52982e7 + 2.64973e7i 0.270824 + 0.469081i
\(165\) 0 0
\(166\) 2.15077e7 3.72524e7i 0.364935 0.632086i
\(167\) 3.54323e6 6.13706e6i 0.0588697 0.101965i −0.835089 0.550115i \(-0.814584\pi\)
0.893958 + 0.448150i \(0.147917\pi\)
\(168\) 0 0
\(169\) −5.98009e7 1.03578e8i −0.953024 1.65069i
\(170\) 3.08019e7 0.480847
\(171\) 0 0
\(172\) −3.86698e7 −0.579458
\(173\) 3.44494e7 + 5.96681e7i 0.505848 + 0.876154i 0.999977 + 0.00676581i \(0.00215364\pi\)
−0.494129 + 0.869388i \(0.664513\pi\)
\(174\) 0 0
\(175\) 2.01795e7 3.49520e7i 0.284628 0.492991i
\(176\) 1.13783e7 1.97077e7i 0.157319 0.272485i
\(177\) 0 0
\(178\) 1.17664e7 + 2.03800e7i 0.156377 + 0.270853i
\(179\) −8.88821e7 −1.15832 −0.579161 0.815214i \(-0.696620\pi\)
−0.579161 + 0.815214i \(0.696620\pi\)
\(180\) 0 0
\(181\) 7.42211e7 0.930363 0.465182 0.885215i \(-0.345989\pi\)
0.465182 + 0.885215i \(0.345989\pi\)
\(182\) 7.83460e7 + 1.35699e8i 0.963313 + 1.66851i
\(183\) 0 0
\(184\) −6.86250e6 + 1.18862e7i −0.0812119 + 0.140663i
\(185\) −5.91487e6 + 1.02449e7i −0.0686822 + 0.118961i
\(186\) 0 0
\(187\) 3.28589e7 + 5.69134e7i 0.367458 + 0.636456i
\(188\) 3.21962e7 0.353388
\(189\) 0 0
\(190\) 1.15992e8 1.22685
\(191\) −1.27812e7 2.21377e7i −0.132726 0.229888i 0.792001 0.610520i \(-0.209040\pi\)
−0.924726 + 0.380632i \(0.875706\pi\)
\(192\) 0 0
\(193\) 4.91854e7 8.51916e7i 0.492477 0.852994i −0.507486 0.861660i \(-0.669425\pi\)
0.999962 + 0.00866567i \(0.00275840\pi\)
\(194\) 3.16587e7 5.48345e7i 0.311306 0.539197i
\(195\) 0 0
\(196\) −4.09687e7 7.09599e7i −0.388648 0.673158i
\(197\) 1.40581e7 0.131007 0.0655036 0.997852i \(-0.479135\pi\)
0.0655036 + 0.997852i \(0.479135\pi\)
\(198\) 0 0
\(199\) 2.87427e7 0.258548 0.129274 0.991609i \(-0.458735\pi\)
0.129274 + 0.991609i \(0.458735\pi\)
\(200\) −7.12323e6 1.23378e7i −0.0629611 0.109052i
\(201\) 0 0
\(202\) −7.40630e7 + 1.28281e8i −0.632225 + 1.09505i
\(203\) 1.02158e8 1.76944e8i 0.857113 1.48456i
\(204\) 0 0
\(205\) 7.78058e7 + 1.34764e8i 0.630773 + 1.09253i
\(206\) 8.03252e7 0.640201
\(207\) 0 0
\(208\) 5.53112e7 0.426178
\(209\) 1.23739e8 + 2.14322e8i 0.937548 + 1.62388i
\(210\) 0 0
\(211\) 9.86546e7 1.70875e8i 0.722984 1.25224i −0.236815 0.971555i \(-0.576103\pi\)
0.959798 0.280690i \(-0.0905633\pi\)
\(212\) −6.38884e7 + 1.10658e8i −0.460518 + 0.797641i
\(213\) 0 0
\(214\) −5.06169e7 8.76710e7i −0.353059 0.611516i
\(215\) −1.96672e8 −1.34961
\(216\) 0 0
\(217\) −2.40329e8 −1.59660
\(218\) 5.06958e6 + 8.78078e6i 0.0331417 + 0.0574031i
\(219\) 0 0
\(220\) 5.78691e7 1.00232e8i 0.366410 0.634641i
\(221\) −7.98657e7 + 1.38332e8i −0.497723 + 0.862081i
\(222\) 0 0
\(223\) 3.74143e7 + 6.48035e7i 0.225928 + 0.391319i 0.956598 0.291412i \(-0.0941252\pi\)
−0.730669 + 0.682732i \(0.760792\pi\)
\(224\) −4.75285e7 −0.282544
\(225\) 0 0
\(226\) −1.18736e8 −0.684232
\(227\) −3.61741e7 6.26554e7i −0.205261 0.355523i 0.744955 0.667115i \(-0.232471\pi\)
−0.950216 + 0.311592i \(0.899138\pi\)
\(228\) 0 0
\(229\) 1.52392e8 2.63951e8i 0.838567 1.45244i −0.0525253 0.998620i \(-0.516727\pi\)
0.891093 0.453822i \(-0.149940\pi\)
\(230\) −3.49022e7 + 6.04524e7i −0.189150 + 0.327617i
\(231\) 0 0
\(232\) −3.60612e7 6.24599e7i −0.189597 0.328392i
\(233\) −2.36334e7 −0.122400 −0.0612000 0.998126i \(-0.519493\pi\)
−0.0612000 + 0.998126i \(0.519493\pi\)
\(234\) 0 0
\(235\) 1.63748e8 0.823072
\(236\) −1.94903e7 3.37582e7i −0.0965220 0.167181i
\(237\) 0 0
\(238\) 6.86280e7 1.18867e8i 0.329976 0.571535i
\(239\) −1.15507e8 + 2.00064e8i −0.547288 + 0.947931i 0.451171 + 0.892438i \(0.351007\pi\)
−0.998459 + 0.0554937i \(0.982327\pi\)
\(240\) 0 0
\(241\) 2.96906e7 + 5.14256e7i 0.136634 + 0.236657i 0.926220 0.376982i \(-0.123038\pi\)
−0.789586 + 0.613639i \(0.789705\pi\)
\(242\) 9.10377e7 0.412921
\(243\) 0 0
\(244\) 1.21719e8 0.536408
\(245\) −2.08364e8 3.60898e8i −0.905195 1.56784i
\(246\) 0 0
\(247\) −3.00755e8 + 5.20922e8i −1.26991 + 2.19955i
\(248\) −4.24172e7 + 7.34688e7i −0.176588 + 0.305860i
\(249\) 0 0
\(250\) 6.54904e7 + 1.13433e8i 0.265086 + 0.459143i
\(251\) 3.16166e8 1.26199 0.630997 0.775785i \(-0.282646\pi\)
0.630997 + 0.775785i \(0.282646\pi\)
\(252\) 0 0
\(253\) −1.48932e8 −0.578185
\(254\) 3.88719e7 + 6.73282e7i 0.148839 + 0.257798i
\(255\) 0 0
\(256\) −8.38861e6 + 1.45295e7i −0.0312500 + 0.0541266i
\(257\) 2.83155e7 4.90438e7i 0.104054 0.180226i −0.809297 0.587399i \(-0.800152\pi\)
0.913351 + 0.407173i \(0.133485\pi\)
\(258\) 0 0
\(259\) 2.63571e7 + 4.56519e7i 0.0942647 + 0.163271i
\(260\) 2.81309e8 0.992607
\(261\) 0 0
\(262\) −1.46450e8 −0.503077
\(263\) −1.20320e7 2.08400e7i −0.0407842 0.0706404i 0.844913 0.534904i \(-0.179652\pi\)
−0.885697 + 0.464264i \(0.846319\pi\)
\(264\) 0 0
\(265\) −3.24932e8 + 5.62799e8i −1.07259 + 1.85778i
\(266\) 2.58436e8 4.47624e8i 0.841913 1.45824i
\(267\) 0 0
\(268\) −5.67574e7 9.83067e7i −0.180115 0.311969i
\(269\) −4.42132e8 −1.38490 −0.692451 0.721465i \(-0.743469\pi\)
−0.692451 + 0.721465i \(0.743469\pi\)
\(270\) 0 0
\(271\) 1.81928e8 0.555272 0.277636 0.960686i \(-0.410449\pi\)
0.277636 + 0.960686i \(0.410449\pi\)
\(272\) −2.42252e7 4.19593e7i −0.0729921 0.126426i
\(273\) 0 0
\(274\) −1.93829e8 + 3.35721e8i −0.569235 + 0.985943i
\(275\) 7.72954e7 1.33880e8i 0.224124 0.388195i
\(276\) 0 0
\(277\) −1.30393e8 2.25847e8i −0.368617 0.638463i 0.620733 0.784022i \(-0.286835\pi\)
−0.989350 + 0.145559i \(0.953502\pi\)
\(278\) −3.03864e8 −0.848249
\(279\) 0 0
\(280\) −2.41727e8 −0.658069
\(281\) 1.77884e8 + 3.08105e8i 0.478261 + 0.828373i 0.999689 0.0249221i \(-0.00793379\pi\)
−0.521428 + 0.853295i \(0.674600\pi\)
\(282\) 0 0
\(283\) 7.52802e7 1.30389e8i 0.197437 0.341971i −0.750260 0.661143i \(-0.770072\pi\)
0.947697 + 0.319172i \(0.103405\pi\)
\(284\) −3.22697e7 + 5.58927e7i −0.0835950 + 0.144791i
\(285\) 0 0
\(286\) 3.00096e8 + 5.19781e8i 0.758540 + 1.31383i
\(287\) 6.93418e8 1.73144
\(288\) 0 0
\(289\) −2.70420e8 −0.659017
\(290\) −1.83405e8 3.17667e8i −0.441589 0.764855i
\(291\) 0 0
\(292\) −4.67800e6 + 8.10254e6i −0.0109956 + 0.0190450i
\(293\) −1.09451e8 + 1.89574e8i −0.254204 + 0.440294i −0.964679 0.263429i \(-0.915147\pi\)
0.710475 + 0.703722i \(0.248480\pi\)
\(294\) 0 0
\(295\) −9.91264e7 1.71692e8i −0.224808 0.389379i
\(296\) 1.86078e7 0.0417036
\(297\) 0 0
\(298\) 2.86466e8 0.627070
\(299\) −1.80994e8 3.13492e8i −0.391576 0.678230i
\(300\) 0 0
\(301\) −4.38193e8 + 7.58973e8i −0.926154 + 1.60415i
\(302\) −1.92408e8 + 3.33260e8i −0.401974 + 0.696240i
\(303\) 0 0
\(304\) −9.12261e7 1.58008e8i −0.186235 0.322569i
\(305\) 6.19057e8 1.24934
\(306\) 0 0
\(307\) −5.49207e8 −1.08331 −0.541654 0.840602i \(-0.682202\pi\)
−0.541654 + 0.840602i \(0.682202\pi\)
\(308\) −2.57870e8 4.46643e8i −0.502890 0.871030i
\(309\) 0 0
\(310\) −2.15731e8 + 3.73658e8i −0.411289 + 0.712374i
\(311\) −2.54600e8 + 4.40980e8i −0.479951 + 0.831299i −0.999736 0.0229982i \(-0.992679\pi\)
0.519785 + 0.854297i \(0.326012\pi\)
\(312\) 0 0
\(313\) −2.80921e8 4.86569e8i −0.517819 0.896889i −0.999786 0.0206997i \(-0.993411\pi\)
0.481966 0.876190i \(-0.339923\pi\)
\(314\) −6.36232e8 −1.15974
\(315\) 0 0
\(316\) −4.65522e8 −0.829919
\(317\) −4.47978e8 7.75921e8i −0.789859 1.36808i −0.926053 0.377394i \(-0.876820\pi\)
0.136194 0.990682i \(-0.456513\pi\)
\(318\) 0 0
\(319\) 3.91306e8 6.77762e8i 0.674916 1.16899i
\(320\) −4.26639e7 + 7.38961e7i −0.0727840 + 0.126066i
\(321\) 0 0
\(322\) 1.55527e8 + 2.69381e8i 0.259603 + 0.449646i
\(323\) 5.26898e8 0.869997
\(324\) 0 0
\(325\) 3.75743e8 0.607154
\(326\) 1.78536e8 + 3.09233e8i 0.285407 + 0.494339i
\(327\) 0 0
\(328\) 1.22386e8 2.11978e8i 0.191502 0.331691i
\(329\) 3.64836e8 6.31915e8i 0.564823 0.978303i
\(330\) 0 0
\(331\) 3.52581e8 + 6.10688e8i 0.534393 + 0.925595i 0.999192 + 0.0401795i \(0.0127930\pi\)
−0.464800 + 0.885416i \(0.653874\pi\)
\(332\) −3.44123e8 −0.516096
\(333\) 0 0
\(334\) −5.66917e7 −0.0832543
\(335\) −2.88664e8 4.99981e8i −0.419504 0.726603i
\(336\) 0 0
\(337\) −4.97208e8 + 8.61189e8i −0.707674 + 1.22573i 0.258044 + 0.966133i \(0.416922\pi\)
−0.965718 + 0.259594i \(0.916411\pi\)
\(338\) −4.78407e8 + 8.28625e8i −0.673890 + 1.16721i
\(339\) 0 0
\(340\) −1.23208e8 2.13402e8i −0.170005 0.294457i
\(341\) −9.20553e8 −1.25721
\(342\) 0 0
\(343\) −6.62466e8 −0.886409
\(344\) 1.54679e8 + 2.67912e8i 0.204869 + 0.354844i
\(345\) 0 0
\(346\) 2.75595e8 4.77345e8i 0.357688 0.619535i
\(347\) −8.19608e6 + 1.41960e7i −0.0105306 + 0.0182395i −0.871243 0.490853i \(-0.836685\pi\)
0.860712 + 0.509092i \(0.170019\pi\)
\(348\) 0 0
\(349\) 2.13389e8 + 3.69600e8i 0.268709 + 0.465418i 0.968529 0.248902i \(-0.0800695\pi\)
−0.699819 + 0.714320i \(0.746736\pi\)
\(350\) −3.22873e8 −0.402525
\(351\) 0 0
\(352\) −1.82052e8 −0.222483
\(353\) 8.02765e8 + 1.39043e9i 0.971353 + 1.68243i 0.691480 + 0.722396i \(0.256959\pi\)
0.279873 + 0.960037i \(0.409708\pi\)
\(354\) 0 0
\(355\) −1.64121e8 + 2.84267e8i −0.194700 + 0.337230i
\(356\) 9.41310e7 1.63040e8i 0.110575 0.191522i
\(357\) 0 0
\(358\) 3.55529e8 + 6.15794e8i 0.409528 + 0.709324i
\(359\) 1.39612e9 1.59255 0.796276 0.604934i \(-0.206801\pi\)
0.796276 + 0.604934i \(0.206801\pi\)
\(360\) 0 0
\(361\) 1.09029e9 1.21974
\(362\) −2.96885e8 5.14219e8i −0.328933 0.569729i
\(363\) 0 0
\(364\) 6.26768e8 1.08559e9i 0.681165 1.17981i
\(365\) −2.37920e7 + 4.12090e7i −0.0256098 + 0.0443575i
\(366\) 0 0
\(367\) 7.53807e8 + 1.30563e9i 0.796029 + 1.37876i 0.922184 + 0.386752i \(0.126403\pi\)
−0.126154 + 0.992011i \(0.540264\pi\)
\(368\) 1.09800e8 0.114851
\(369\) 0 0
\(370\) 9.46379e7 0.0971313
\(371\) 1.44793e9 + 2.50788e9i 1.47210 + 2.54975i
\(372\) 0 0
\(373\) 3.86590e8 6.69593e8i 0.385718 0.668083i −0.606151 0.795350i \(-0.707287\pi\)
0.991868 + 0.127267i \(0.0406206\pi\)
\(374\) 2.62872e8 4.55307e8i 0.259832 0.450043i
\(375\) 0 0
\(376\) −1.28785e8 2.23062e8i −0.124942 0.216405i
\(377\) 1.90219e9 1.82835
\(378\) 0 0
\(379\) 1.65039e9 1.55722 0.778610 0.627508i \(-0.215925\pi\)
0.778610 + 0.627508i \(0.215925\pi\)
\(380\) −4.63970e8 8.03619e8i −0.433758 0.751290i
\(381\) 0 0
\(382\) −1.02250e8 + 1.77102e8i −0.0938514 + 0.162555i
\(383\) 3.25719e8 5.64162e8i 0.296242 0.513107i −0.679031 0.734110i \(-0.737600\pi\)
0.975273 + 0.221003i \(0.0709331\pi\)
\(384\) 0 0
\(385\) −1.31151e9 2.27160e9i −1.17127 2.02871i
\(386\) −7.86966e8 −0.696467
\(387\) 0 0
\(388\) −5.06539e8 −0.440253
\(389\) 4.36384e8 + 7.55840e8i 0.375877 + 0.651038i 0.990458 0.137816i \(-0.0440082\pi\)
−0.614581 + 0.788854i \(0.710675\pi\)
\(390\) 0 0
\(391\) −1.58544e8 + 2.74606e8i −0.134131 + 0.232323i
\(392\) −3.27750e8 + 5.67680e8i −0.274816 + 0.475995i
\(393\) 0 0
\(394\) −5.62324e7 9.73974e7i −0.0463180 0.0802252i
\(395\) −2.36761e9 −1.93295
\(396\) 0 0
\(397\) 3.62633e8 0.290871 0.145436 0.989368i \(-0.453542\pi\)
0.145436 + 0.989368i \(0.453542\pi\)
\(398\) −1.14971e8 1.99135e8i −0.0914107 0.158328i
\(399\) 0 0
\(400\) −5.69859e7 + 9.87024e7i −0.0445202 + 0.0771113i
\(401\) −3.49199e8 + 6.04830e8i −0.270438 + 0.468412i −0.968974 0.247163i \(-0.920502\pi\)
0.698536 + 0.715575i \(0.253835\pi\)
\(402\) 0 0
\(403\) −1.11873e9 1.93770e9i −0.851448 1.47475i
\(404\) 1.18501e9 0.894101
\(405\) 0 0
\(406\) −1.63454e9 −1.21214
\(407\) 1.00958e8 + 1.74864e8i 0.0742267 + 0.128564i
\(408\) 0 0
\(409\) 6.15434e8 1.06596e9i 0.444785 0.770390i −0.553252 0.833014i \(-0.686613\pi\)
0.998037 + 0.0626235i \(0.0199467\pi\)
\(410\) 6.22446e8 1.07811e9i 0.446024 0.772536i
\(411\) 0 0
\(412\) −3.21301e8 5.56509e8i −0.226345 0.392042i
\(413\) −8.83430e8 −0.617088
\(414\) 0 0
\(415\) −1.75019e9 −1.20203
\(416\) −2.21245e8 3.83207e8i −0.150677 0.260980i
\(417\) 0 0
\(418\) 9.89909e8 1.71457e9i 0.662946 1.14826i
\(419\) 7.98065e8 1.38229e9i 0.530016 0.918015i −0.469371 0.883001i \(-0.655519\pi\)
0.999387 0.0350135i \(-0.0111474\pi\)
\(420\) 0 0
\(421\) 3.86456e8 + 6.69362e8i 0.252414 + 0.437194i 0.964190 0.265213i \(-0.0854422\pi\)
−0.711776 + 0.702407i \(0.752109\pi\)
\(422\) −1.57847e9 −1.02245
\(423\) 0 0
\(424\) 1.02222e9 0.651271
\(425\) −1.64568e8 2.85040e8i −0.103988 0.180113i
\(426\) 0 0
\(427\) 1.37928e9 2.38899e9i 0.857346 1.48497i
\(428\) −4.04935e8 + 7.01368e8i −0.249650 + 0.432407i
\(429\) 0 0
\(430\) 7.86688e8 + 1.36258e9i 0.477159 + 0.826463i
\(431\) 2.41483e8 0.145284 0.0726418 0.997358i \(-0.476857\pi\)
0.0726418 + 0.997358i \(0.476857\pi\)
\(432\) 0 0
\(433\) 2.85764e9 1.69161 0.845805 0.533493i \(-0.179121\pi\)
0.845805 + 0.533493i \(0.179121\pi\)
\(434\) 9.61316e8 + 1.66505e9i 0.564485 + 0.977716i
\(435\) 0 0
\(436\) 4.05567e7 7.02462e7i 0.0234347 0.0405901i
\(437\) −5.97037e8 + 1.03410e9i −0.342228 + 0.592757i
\(438\) 0 0
\(439\) −1.63501e8 2.83192e8i −0.0922347 0.159755i 0.816216 0.577746i \(-0.196068\pi\)
−0.908451 + 0.417991i \(0.862734\pi\)
\(440\) −9.25906e8 −0.518182
\(441\) 0 0
\(442\) 1.27785e9 0.703886
\(443\) −3.98605e8 6.90404e8i −0.217836 0.377303i 0.736310 0.676644i \(-0.236566\pi\)
−0.954146 + 0.299341i \(0.903233\pi\)
\(444\) 0 0
\(445\) 4.78744e8 8.29209e8i 0.257539 0.446071i
\(446\) 2.99314e8 5.18428e8i 0.159755 0.276704i
\(447\) 0 0
\(448\) 1.90114e8 + 3.29287e8i 0.0998943 + 0.173022i
\(449\) −1.41817e9 −0.739378 −0.369689 0.929155i \(-0.620536\pi\)
−0.369689 + 0.929155i \(0.620536\pi\)
\(450\) 0 0
\(451\) 2.65606e9 1.36339
\(452\) 4.74945e8 + 8.22628e8i 0.241913 + 0.419005i
\(453\) 0 0
\(454\) −2.89393e8 + 5.01243e8i −0.145142 + 0.251393i
\(455\) 3.18770e9 5.52126e9i 1.58649 2.74789i
\(456\) 0 0
\(457\) 4.87453e8 + 8.44293e8i 0.238905 + 0.413796i 0.960400 0.278623i \(-0.0898781\pi\)
−0.721495 + 0.692420i \(0.756545\pi\)
\(458\) −2.43827e9 −1.18591
\(459\) 0 0
\(460\) 5.58435e8 0.267498
\(461\) −6.86431e8 1.18893e9i −0.326320 0.565203i 0.655459 0.755231i \(-0.272475\pi\)
−0.981779 + 0.190028i \(0.939142\pi\)
\(462\) 0 0
\(463\) −8.93573e8 + 1.54771e9i −0.418405 + 0.724698i −0.995779 0.0917813i \(-0.970744\pi\)
0.577375 + 0.816479i \(0.304077\pi\)
\(464\) −2.88490e8 + 4.99679e8i −0.134066 + 0.232209i
\(465\) 0 0
\(466\) 9.45338e7 + 1.63737e8i 0.0432749 + 0.0749544i
\(467\) 2.25768e9 1.02578 0.512889 0.858455i \(-0.328575\pi\)
0.512889 + 0.858455i \(0.328575\pi\)
\(468\) 0 0
\(469\) −2.57262e9 −1.15152
\(470\) −6.54991e8 1.13448e9i −0.291000 0.504026i
\(471\) 0 0
\(472\) −1.55922e8 + 2.70065e8i −0.0682514 + 0.118215i
\(473\) −1.67845e9 + 2.90716e9i −0.729280 + 1.26315i
\(474\) 0 0
\(475\) −6.19721e8 1.07339e9i −0.265319 0.459546i
\(476\) −1.09805e9 −0.466656
\(477\) 0 0
\(478\) 1.84811e9 0.773983
\(479\) −8.71334e8 1.50919e9i −0.362252 0.627438i 0.626080 0.779759i \(-0.284659\pi\)
−0.988331 + 0.152321i \(0.951325\pi\)
\(480\) 0 0
\(481\) −2.45385e8 + 4.25019e8i −0.100540 + 0.174141i
\(482\) 2.37525e8 4.11405e8i 0.0966149 0.167342i
\(483\) 0 0
\(484\) −3.64151e8 6.30727e8i −0.145990 0.252862i
\(485\) −2.57623e9 −1.02539
\(486\) 0 0
\(487\) −2.68849e9 −1.05477 −0.527384 0.849627i \(-0.676827\pi\)
−0.527384 + 0.849627i \(0.676827\pi\)
\(488\) −4.86878e8 8.43297e8i −0.189649 0.328482i
\(489\) 0 0
\(490\) −1.66691e9 + 2.88718e9i −0.640070 + 1.10863i
\(491\) 1.17441e9 2.03413e9i 0.447747 0.775521i −0.550492 0.834841i \(-0.685560\pi\)
0.998239 + 0.0593196i \(0.0188931\pi\)
\(492\) 0 0
\(493\) −8.33120e8 1.44301e9i −0.313144 0.542381i
\(494\) 4.81207e9 1.79592
\(495\) 0 0
\(496\) 6.78676e8 0.249733
\(497\) 7.31338e8 + 1.26671e9i 0.267221 + 0.462841i
\(498\) 0 0
\(499\) 8.33712e8 1.44403e9i 0.300375 0.520265i −0.675846 0.737043i \(-0.736221\pi\)
0.976221 + 0.216778i \(0.0695547\pi\)
\(500\) 5.23923e8 9.07461e8i 0.187444 0.324663i
\(501\) 0 0
\(502\) −1.26467e9 2.19046e9i −0.446182 0.772811i
\(503\) 3.41605e9 1.19684 0.598419 0.801183i \(-0.295796\pi\)
0.598419 + 0.801183i \(0.295796\pi\)
\(504\) 0 0
\(505\) 6.02688e9 2.08244
\(506\) 5.95729e8 + 1.03183e9i 0.204419 + 0.354064i
\(507\) 0 0
\(508\) 3.10975e8 5.38625e8i 0.105245 0.182290i
\(509\) −2.52319e9 + 4.37030e9i −0.848083 + 1.46892i 0.0348342 + 0.999393i \(0.488910\pi\)
−0.882917 + 0.469529i \(0.844424\pi\)
\(510\) 0 0
\(511\) 1.06019e8 + 1.83631e8i 0.0351489 + 0.0608796i
\(512\) 1.34218e8 0.0441942
\(513\) 0 0
\(514\) −4.53047e8 −0.147154
\(515\) −1.63411e9 2.83037e9i −0.527178 0.913099i
\(516\) 0 0
\(517\) 1.39746e9 2.42048e9i 0.444758 0.770344i
\(518\) 2.10857e8 3.65215e8i 0.0666552 0.115450i
\(519\) 0 0
\(520\) −1.12524e9 1.94897e9i −0.350939 0.607845i
\(521\) 2.07610e9 0.643156 0.321578 0.946883i \(-0.395787\pi\)
0.321578 + 0.946883i \(0.395787\pi\)
\(522\) 0 0
\(523\) −2.82869e9 −0.864627 −0.432314 0.901723i \(-0.642303\pi\)
−0.432314 + 0.901723i \(0.642303\pi\)
\(524\) 5.85800e8 + 1.01463e9i 0.177865 + 0.308071i
\(525\) 0 0
\(526\) −9.62559e7 + 1.66720e8i −0.0288388 + 0.0499503i
\(527\) −9.79963e8 + 1.69735e9i −0.291657 + 0.505165i
\(528\) 0 0
\(529\) 1.34312e9 + 2.32634e9i 0.394474 + 0.683249i
\(530\) 5.19892e9 1.51687
\(531\) 0 0
\(532\) −4.13498e9 −1.19064
\(533\) 3.22786e9 + 5.59081e9i 0.923356 + 1.59930i
\(534\) 0 0
\(535\) −2.05947e9 + 3.56711e9i −0.581457 + 1.00711i
\(536\) −4.54059e8 + 7.86454e8i −0.127361 + 0.220595i
\(537\) 0 0
\(538\) 1.76853e9 + 3.06318e9i 0.489637 + 0.848076i
\(539\) −7.11294e9 −1.95654
\(540\) 0 0
\(541\) −3.38888e9 −0.920166 −0.460083 0.887876i \(-0.652180\pi\)
−0.460083 + 0.887876i \(0.652180\pi\)
\(542\) −7.27710e8 1.26043e9i −0.196318 0.340033i
\(543\) 0 0
\(544\) −1.93802e8 + 3.35674e8i −0.0516132 + 0.0893967i
\(545\) 2.06269e8 3.57268e8i 0.0545815 0.0945379i
\(546\) 0 0
\(547\) 8.30774e8 + 1.43894e9i 0.217034 + 0.375913i 0.953900 0.300125i \(-0.0970285\pi\)
−0.736866 + 0.676039i \(0.763695\pi\)
\(548\) 3.10126e9 0.805019
\(549\) 0 0
\(550\) −1.23673e9 −0.316960
\(551\) −3.13733e9 5.43401e9i −0.798967 1.38385i
\(552\) 0 0
\(553\) −5.27514e9 + 9.13682e9i −1.32647 + 2.29751i
\(554\) −1.04314e9 + 1.80678e9i −0.260651 + 0.451462i
\(555\) 0 0
\(556\) 1.21546e9 + 2.10523e9i 0.299901 + 0.519444i
\(557\) −6.21412e9 −1.52365 −0.761827 0.647780i \(-0.775697\pi\)
−0.761827 + 0.647780i \(0.775697\pi\)
\(558\) 0 0
\(559\) −8.15915e9 −1.97562
\(560\) 9.66907e8 + 1.67473e9i 0.232663 + 0.402983i
\(561\) 0 0
\(562\) 1.42307e9 2.46484e9i 0.338182 0.585748i
\(563\) 3.04740e8 5.27825e8i 0.0719697 0.124655i −0.827795 0.561031i \(-0.810405\pi\)
0.899765 + 0.436376i \(0.143738\pi\)
\(564\) 0 0
\(565\) 2.41554e9 + 4.18383e9i 0.563436 + 0.975899i
\(566\) −1.20448e9 −0.279218
\(567\) 0 0
\(568\) 5.16314e8 0.118221
\(569\) −2.27558e9 3.94141e9i −0.517844 0.896931i −0.999785 0.0207280i \(-0.993402\pi\)
0.481942 0.876203i \(-0.339932\pi\)
\(570\) 0 0
\(571\) 1.66501e9 2.88388e9i 0.374275 0.648262i −0.615944 0.787790i \(-0.711225\pi\)
0.990218 + 0.139528i \(0.0445584\pi\)
\(572\) 2.40076e9 4.15825e9i 0.536369 0.929018i
\(573\) 0 0
\(574\) −2.77367e9 4.80414e9i −0.612158 1.06029i
\(575\) 7.45898e8 0.163622
\(576\) 0 0
\(577\) −1.26141e9 −0.273363 −0.136682 0.990615i \(-0.543644\pi\)
−0.136682 + 0.990615i \(0.543644\pi\)
\(578\) 1.08168e9 + 1.87353e9i 0.232998 + 0.403564i
\(579\) 0 0
\(580\) −1.46724e9 + 2.54133e9i −0.312251 + 0.540834i
\(581\) −3.89949e9 + 6.75412e9i −0.824881 + 1.42874i
\(582\) 0 0
\(583\) 5.54611e9 + 9.60615e9i 1.15917 + 2.00775i
\(584\) 7.48480e7 0.0155502
\(585\) 0 0
\(586\) 1.75121e9 0.359498
\(587\) 2.15884e9 + 3.73921e9i 0.440541 + 0.763039i 0.997730 0.0673465i \(-0.0214533\pi\)
−0.557189 + 0.830386i \(0.688120\pi\)
\(588\) 0 0
\(589\) −3.69030e9 + 6.39178e9i −0.744146 + 1.28890i
\(590\) −7.93011e8 + 1.37354e9i −0.158963 + 0.275333i
\(591\) 0 0
\(592\) −7.44311e7 1.28918e8i −0.0147444 0.0255381i
\(593\) 2.64830e9 0.521525 0.260762 0.965403i \(-0.416026\pi\)
0.260762 + 0.965403i \(0.416026\pi\)
\(594\) 0 0
\(595\) −5.58460e9 −1.08688
\(596\) −1.14586e9 1.98469e9i −0.221703 0.384000i
\(597\) 0 0
\(598\) −1.44796e9 + 2.50793e9i −0.276886 + 0.479581i
\(599\) −3.56231e9 + 6.17011e9i −0.677233 + 1.17300i 0.298577 + 0.954385i \(0.403488\pi\)
−0.975811 + 0.218617i \(0.929845\pi\)
\(600\) 0 0
\(601\) −1.04714e8 1.81369e8i −0.0196762 0.0340803i 0.856020 0.516943i \(-0.172930\pi\)
−0.875696 + 0.482863i \(0.839597\pi\)
\(602\) 7.01109e9 1.30978
\(603\) 0 0
\(604\) 3.07853e9 0.568478
\(605\) −1.85205e9 3.20784e9i −0.340023 0.588937i
\(606\) 0 0
\(607\) 3.89744e9 6.75057e9i 0.707326 1.22512i −0.258520 0.966006i \(-0.583235\pi\)
0.965846 0.259118i \(-0.0834319\pi\)
\(608\) −7.29809e8 + 1.26407e9i −0.131688 + 0.228090i
\(609\) 0 0
\(610\) −2.47623e9 4.28895e9i −0.441709 0.765063i
\(611\) 6.79325e9 1.20485
\(612\) 0 0
\(613\) −9.11476e8 −0.159821 −0.0799105 0.996802i \(-0.525463\pi\)
−0.0799105 + 0.996802i \(0.525463\pi\)
\(614\) 2.19683e9 + 3.80502e9i 0.383007 + 0.663388i
\(615\) 0 0
\(616\) −2.06296e9 + 3.57315e9i −0.355597 + 0.615912i
\(617\) −1.17581e9 + 2.03657e9i −0.201530 + 0.349061i −0.949022 0.315211i \(-0.897925\pi\)
0.747491 + 0.664271i \(0.231258\pi\)
\(618\) 0 0
\(619\) 8.76271e8 + 1.51775e9i 0.148498 + 0.257206i 0.930673 0.365853i \(-0.119223\pi\)
−0.782174 + 0.623060i \(0.785889\pi\)
\(620\) 3.45170e9 0.581651
\(621\) 0 0
\(622\) 4.07360e9 0.678753
\(623\) −2.13332e9 3.69502e9i −0.353467 0.612222i
\(624\) 0 0
\(625\) 3.75156e9 6.49789e9i 0.614655 1.06461i
\(626\) −2.24736e9 + 3.89255e9i −0.366154 + 0.634197i
\(627\) 0 0
\(628\) 2.54493e9 + 4.40795e9i 0.410031 + 0.710195i
\(629\) 4.29894e8 0.0688786
\(630\) 0 0
\(631\) 1.95065e9 0.309084 0.154542 0.987986i \(-0.450610\pi\)
0.154542 + 0.987986i \(0.450610\pi\)
\(632\) 1.86209e9 + 3.22523e9i 0.293421 + 0.508219i
\(633\) 0 0
\(634\) −3.58383e9 + 6.20737e9i −0.558515 + 0.967376i
\(635\) 1.58160e9 2.73941e9i 0.245126 0.424570i
\(636\) 0 0
\(637\) −8.64422e9 1.49722e10i −1.32507 2.29508i
\(638\) −6.26090e9 −0.954475
\(639\) 0 0
\(640\) 6.82623e8 0.102932
\(641\) 6.82635e8 + 1.18236e9i 0.102373 + 0.177315i 0.912662 0.408715i \(-0.134023\pi\)
−0.810289 + 0.586031i \(0.800690\pi\)
\(642\) 0 0
\(643\) 3.85524e9 6.67747e9i 0.571891 0.990544i −0.424481 0.905437i \(-0.639543\pi\)
0.996372 0.0851072i \(-0.0271233\pi\)
\(644\) 1.24422e9 2.15505e9i 0.183567 0.317948i
\(645\) 0 0
\(646\) −2.10759e9 3.65045e9i −0.307590 0.532762i
\(647\) 1.07543e10 1.56106 0.780529 0.625120i \(-0.214950\pi\)
0.780529 + 0.625120i \(0.214950\pi\)
\(648\) 0 0
\(649\) −3.38388e9 −0.485913
\(650\) −1.50297e9 2.60322e9i −0.214661 0.371804i
\(651\) 0 0
\(652\) 1.42829e9 2.47387e9i 0.201813 0.349550i
\(653\) 6.41419e9 1.11097e10i 0.901458 1.56137i 0.0758554 0.997119i \(-0.475831\pi\)
0.825603 0.564252i \(-0.190835\pi\)
\(654\) 0 0
\(655\) 2.97934e9 + 5.16037e9i 0.414262 + 0.717523i
\(656\) −1.95817e9 −0.270824
\(657\) 0 0
\(658\) −5.83738e9 −0.798781
\(659\) −4.04554e9 7.00708e9i −0.550652 0.953758i −0.998228 0.0595117i \(-0.981046\pi\)
0.447575 0.894246i \(-0.352288\pi\)
\(660\) 0 0
\(661\) −5.42598e9 + 9.39806e9i −0.730756 + 1.26571i 0.225804 + 0.974173i \(0.427499\pi\)
−0.956560 + 0.291535i \(0.905834\pi\)
\(662\) 2.82065e9 4.88550e9i 0.377873 0.654495i
\(663\) 0 0
\(664\) 1.37649e9 + 2.38416e9i 0.182468 + 0.316043i
\(665\) −2.10302e10 −2.77312
\(666\) 0 0
\(667\) 3.77609e9 0.492722
\(668\) 2.26767e8 + 3.92772e8i 0.0294348 + 0.0509827i
\(669\) 0 0
\(670\) −2.30932e9 + 3.99985e9i −0.296634 + 0.513786i
\(671\) 5.28319e9 9.15076e9i 0.675099 1.16931i
\(672\) 0 0
\(673\) −4.23340e9 7.33246e9i −0.535348 0.927250i −0.999146 0.0413095i \(-0.986847\pi\)
0.463798 0.885941i \(-0.346486\pi\)
\(674\) 7.95532e9 1.00080
\(675\) 0 0
\(676\) 7.65451e9 0.953024
\(677\) −3.69685e9 6.40313e9i −0.457901 0.793108i 0.540949 0.841056i \(-0.318065\pi\)
−0.998850 + 0.0479477i \(0.984732\pi\)
\(678\) 0 0
\(679\) −5.73994e9 + 9.94186e9i −0.703660 + 1.21877i
\(680\) −9.85662e8 + 1.70722e9i −0.120212 + 0.208213i
\(681\) 0 0
\(682\) 3.68221e9 + 6.37778e9i 0.444492 + 0.769882i
\(683\) 4.64936e9 0.558368 0.279184 0.960238i \(-0.409936\pi\)
0.279184 + 0.960238i \(0.409936\pi\)
\(684\) 0 0
\(685\) 1.57728e10 1.87496
\(686\) 2.64986e9 + 4.58970e9i 0.313393 + 0.542813i
\(687\) 0 0
\(688\) 1.23743e9 2.14330e9i 0.144865 0.250913i
\(689\) −1.34802e10 + 2.33483e10i −1.57010 + 2.71950i
\(690\) 0 0
\(691\) 5.83835e9 + 1.01123e10i 0.673158 + 1.16594i 0.977004 + 0.213223i \(0.0683959\pi\)
−0.303846 + 0.952721i \(0.598271\pi\)
\(692\) −4.40952e9 −0.505848
\(693\) 0 0
\(694\) 1.31137e8 0.0148925
\(695\) 6.18174e9 + 1.07071e10i 0.698496 + 1.20983i
\(696\) 0 0
\(697\) 2.82747e9 4.89733e9i 0.316289 0.547828i
\(698\) 1.70711e9 2.95680e9i 0.190006 0.329100i
\(699\) 0 0
\(700\) 1.29149e9 + 2.23693e9i 0.142314 + 0.246495i
\(701\) −1.48274e10 −1.62575 −0.812873 0.582441i \(-0.802098\pi\)
−0.812873 + 0.582441i \(0.802098\pi\)
\(702\) 0 0
\(703\) 1.61888e9 0.175740
\(704\) 7.28209e8 + 1.26130e9i 0.0786596 + 0.136242i
\(705\) 0 0
\(706\) 6.42212e9 1.11234e10i 0.686850 1.18966i
\(707\) 1.34281e10 2.32582e10i 1.42905 2.47519i
\(708\) 0 0
\(709\) −3.08325e9 5.34034e9i −0.324898 0.562739i 0.656594 0.754244i \(-0.271996\pi\)
−0.981492 + 0.191505i \(0.938663\pi\)
\(710\) 2.62594e9 0.275347
\(711\) 0 0
\(712\) −1.50610e9 −0.156377
\(713\) −2.22083e9 3.84658e9i −0.229457 0.397431i
\(714\) 0 0
\(715\) 1.22101e10 2.11486e10i 1.24925 2.16376i
\(716\) 2.84423e9 4.92635e9i 0.289580 0.501568i
\(717\) 0 0
\(718\) −5.58450e9 9.67263e9i −0.563052 0.975234i
\(719\) −1.31343e10 −1.31782 −0.658912 0.752220i \(-0.728983\pi\)
−0.658912 + 0.752220i \(0.728983\pi\)
\(720\) 0 0
\(721\) −1.45635e10 −1.44708
\(722\) −4.36118e9 7.55378e9i −0.431245 0.746938i
\(723\) 0 0
\(724\) −2.37508e9 + 4.11375e9i −0.232591 + 0.402859i
\(725\) −1.95978e9 + 3.39444e9i −0.190996 + 0.330815i
\(726\) 0 0
\(727\) −2.22778e9 3.85863e9i −0.215031 0.372445i 0.738251 0.674526i \(-0.235652\pi\)
−0.953282 + 0.302081i \(0.902319\pi\)
\(728\) −1.00283e10 −0.963313
\(729\) 0 0
\(730\) 3.80672e8 0.0362177
\(731\) 3.57354e9 + 6.18956e9i 0.338367 + 0.586069i
\(732\) 0 0
\(733\) −1.49868e9 + 2.59579e9i −0.140555 + 0.243448i −0.927706 0.373313i \(-0.878222\pi\)
0.787151 + 0.616760i \(0.211555\pi\)
\(734\) 6.03046e9 1.04451e10i 0.562878 0.974933i
\(735\) 0 0
\(736\) −4.39200e8 7.60716e8i −0.0406060 0.0703316i
\(737\) −9.85414e9 −0.906740
\(738\) 0 0
\(739\) 8.82559e9 0.804429 0.402215 0.915545i \(-0.368241\pi\)
0.402215 + 0.915545i \(0.368241\pi\)
\(740\) −3.78552e8 6.55671e8i −0.0343411 0.0594805i
\(741\) 0 0
\(742\) 1.15834e10 2.00630e10i 1.04093 1.80295i
\(743\) −1.00349e10 + 1.73809e10i −0.897534 + 1.55457i −0.0668969 + 0.997760i \(0.521310\pi\)
−0.830637 + 0.556814i \(0.812023\pi\)
\(744\) 0 0
\(745\) −5.82778e9 1.00940e10i −0.516365 0.894370i
\(746\) −6.18544e9 −0.545487
\(747\) 0 0
\(748\) −4.20595e9 −0.367458
\(749\) 9.17718e9 + 1.58953e10i 0.798036 + 1.38224i
\(750\) 0 0
\(751\) 1.97123e9 3.41427e9i 0.169824 0.294143i −0.768534 0.639809i \(-0.779014\pi\)
0.938358 + 0.345666i \(0.112347\pi\)
\(752\) −1.03028e9 + 1.78449e9i −0.0883470 + 0.153022i
\(753\) 0 0
\(754\) −7.60876e9 1.31788e10i −0.646419 1.11963i
\(755\) 1.56572e10 1.32403
\(756\) 0 0
\(757\) 1.54038e10 1.29060 0.645301 0.763928i \(-0.276732\pi\)
0.645301 + 0.763928i \(0.276732\pi\)
\(758\) −6.60157e9 1.14343e10i −0.550561 0.953599i
\(759\) 0 0
\(760\) −3.71176e9 + 6.42896e9i −0.306713 + 0.531243i
\(761\) 9.60848e9 1.66424e10i 0.790330 1.36889i −0.135433 0.990787i \(-0.543243\pi\)
0.925763 0.378105i \(-0.123424\pi\)
\(762\) 0 0
\(763\) −9.19149e8 1.59201e9i −0.0749118 0.129751i
\(764\) 1.63600e9 0.132726
\(765\) 0 0
\(766\) −5.21150e9 −0.418950
\(767\) −4.11236e9 7.12282e9i −0.329085 0.569992i
\(768\) 0 0
\(769\) 6.02623e7 1.04377e8i 0.00477863 0.00827683i −0.863626 0.504133i \(-0.831812\pi\)
0.868405 + 0.495856i \(0.165146\pi\)
\(770\) −1.04921e10 + 1.81728e10i −0.828216 + 1.43451i
\(771\) 0 0
\(772\) 3.14786e9 + 5.45226e9i 0.246238 + 0.426497i
\(773\) 2.06347e10 1.60683 0.803415 0.595420i \(-0.203014\pi\)
0.803415 + 0.595420i \(0.203014\pi\)
\(774\) 0 0
\(775\) 4.61041e9 0.355782
\(776\) 2.02616e9 + 3.50941e9i 0.155653 + 0.269599i
\(777\) 0 0
\(778\) 3.49107e9 6.04672e9i 0.265785 0.460353i
\(779\) 1.06476e10 1.84421e10i 0.806992 1.39775i
\(780\) 0 0
\(781\) 2.80131e9 + 4.85201e9i 0.210418 + 0.364454i
\(782\) 2.53670e9 0.189691
\(783\) 0 0
\(784\) 5.24400e9 0.388648
\(785\) 1.29433e10 + 2.24185e10i 0.954998 + 1.65411i
\(786\) 0 0
\(787\) −8.45354e8 + 1.46420e9i −0.0618197 + 0.107075i −0.895279 0.445506i \(-0.853024\pi\)
0.833459 + 0.552581i \(0.186357\pi\)
\(788\) −4.49859e8 + 7.79179e8i −0.0327518 + 0.0567278i
\(789\) 0 0
\(790\) 9.47046e9 + 1.64033e10i 0.683402 + 1.18369i
\(791\) 2.15277e10 1.54660
\(792\) 0 0
\(793\) 2.56823e10 1.82885
\(794\) −1.45053e9 2.51239e9i −0.102838 0.178121i
\(795\) 0 0
\(796\) −9.19767e8 + 1.59308e9i −0.0646371 + 0.111955i
\(797\) 6.79877e8 1.17758e9i 0.0475692 0.0823923i −0.841260 0.540630i \(-0.818186\pi\)
0.888830 + 0.458238i \(0.151519\pi\)
\(798\) 0 0
\(799\) −2.97531e9 5.15338e9i −0.206356 0.357420i
\(800\) 9.11774e8 0.0629611
\(801\) 0 0
\(802\) 5.58718e9 0.382457
\(803\) 4.06094e8 + 7.03376e8i 0.0276772 + 0.0479383i
\(804\) 0 0
\(805\) 6.32800e9 1.09604e10i 0.427544 0.740529i
\(806\) −8.94985e9 + 1.55016e10i −0.602064 + 1.04281i
\(807\) 0 0
\(808\) −4.74004e9 8.20998e9i −0.316113 0.547523i
\(809\) −1.53965e10 −1.02235 −0.511177 0.859475i \(-0.670790\pi\)
−0.511177 + 0.859475i \(0.670790\pi\)
\(810\) 0 0
\(811\) −9.67476e9 −0.636894 −0.318447 0.947941i \(-0.603161\pi\)
−0.318447 + 0.947941i \(0.603161\pi\)
\(812\) 6.53814e9 + 1.13244e10i 0.428557 + 0.742282i
\(813\) 0 0
\(814\) 8.07664e8 1.39891e9i 0.0524862 0.0909088i
\(815\) 7.26417e9 1.25819e10i 0.470040 0.814133i
\(816\) 0 0
\(817\) 1.34571e10 + 2.33083e10i 0.863324 + 1.49532i
\(818\) −9.84695e9 −0.629021
\(819\) 0 0
\(820\) −9.95914e9 −0.630773
\(821\) 1.23171e10 + 2.13339e10i 0.776799 + 1.34546i 0.933778 + 0.357853i \(0.116491\pi\)
−0.156979 + 0.987602i \(0.550176\pi\)
\(822\) 0 0
\(823\) 1.07424e9 1.86064e9i 0.0671743 0.116349i −0.830482 0.557045i \(-0.811935\pi\)
0.897656 + 0.440696i \(0.145268\pi\)
\(824\) −2.57041e9 + 4.45207e9i −0.160050 + 0.277215i
\(825\) 0 0
\(826\) 3.53372e9 + 6.12058e9i 0.218174 + 0.377888i
\(827\) −1.31873e10 −0.810751 −0.405375 0.914150i \(-0.632859\pi\)
−0.405375 + 0.914150i \(0.632859\pi\)
\(828\) 0 0
\(829\) 6.41872e8 0.0391298 0.0195649 0.999809i \(-0.493772\pi\)
0.0195649 + 0.999809i \(0.493772\pi\)
\(830\) 7.00075e9 + 1.21257e10i 0.424983 + 0.736092i
\(831\) 0 0
\(832\) −1.76996e9 + 3.06566e9i −0.106545 + 0.184541i
\(833\) −7.57199e9 + 1.31151e10i −0.453892 + 0.786164i
\(834\) 0 0
\(835\) 1.15332e9 + 1.99761e9i 0.0685563 + 0.118743i
\(836\) −1.58385e10 −0.937548
\(837\) 0 0
\(838\) −1.27690e10 −0.749556
\(839\) −5.06722e9 8.77669e9i −0.296212 0.513055i 0.679054 0.734088i \(-0.262390\pi\)
−0.975266 + 0.221034i \(0.929057\pi\)
\(840\) 0 0
\(841\) −1.29642e9 + 2.24546e9i −0.0751551 + 0.130173i
\(842\) 3.09165e9 5.35490e9i 0.178484 0.309143i
\(843\) 0 0
\(844\) 6.31389e9 + 1.09360e10i 0.361492 + 0.626122i
\(845\) 3.89303e10 2.21968
\(846\) 0 0
\(847\) −1.65057e10 −0.933347
\(848\) −4.08886e9 7.08211e9i −0.230259 0.398820i
\(849\) 0 0
\(850\) −1.31654e9 + 2.28032e9i −0.0735306 + 0.127359i
\(851\) −4.87121e8 + 8.43718e8i −0.0270946 + 0.0469292i
\(852\) 0 0
\(853\) −6.75163e9 1.16942e10i −0.372467 0.645131i 0.617478 0.786588i \(-0.288155\pi\)
−0.989944 + 0.141457i \(0.954821\pi\)
\(854\) −2.20686e10 −1.21247
\(855\) 0 0
\(856\) 6.47896e9 0.353059
\(857\) 2.75769e9 + 4.77646e9i 0.149662 + 0.259223i 0.931103 0.364757i \(-0.118848\pi\)
−0.781440 + 0.623980i \(0.785515\pi\)
\(858\) 0 0
\(859\) −6.06756e9 + 1.05093e10i −0.326617 + 0.565717i −0.981838 0.189720i \(-0.939242\pi\)
0.655222 + 0.755437i \(0.272575\pi\)
\(860\) 6.29350e9 1.09007e10i 0.337402 0.584398i
\(861\) 0 0
\(862\) −9.65934e8 1.67305e9i −0.0513655 0.0889677i
\(863\) 2.09525e9 0.110968 0.0554839 0.998460i \(-0.482330\pi\)
0.0554839 + 0.998460i \(0.482330\pi\)
\(864\) 0 0
\(865\) −2.24265e10 −1.17816
\(866\) −1.14306e10 1.97983e10i −0.598074 1.03589i
\(867\) 0 0
\(868\) 7.69053e9 1.33204e10i 0.399151 0.691350i
\(869\) −2.02058e10 + 3.49975e10i −1.04450 + 1.80912i
\(870\) 0 0
\(871\) −1.19756e10 2.07423e10i −0.614090 1.06364i
\(872\) −6.48907e8 −0.0331417
\(873\) 0 0
\(874\) 9.55259e9 0.483984
\(875\) −1.18738e10 2.05661e10i −0.599188 1.03782i
\(876\) 0 0
\(877\) −1.76793e10 + 3.06214e10i −0.885045 + 1.53294i −0.0393839 + 0.999224i \(0.512540\pi\)
−0.845662 + 0.533719i \(0.820794\pi\)
\(878\) −1.30801e9 + 2.26554e9i −0.0652198 + 0.112964i
\(879\) 0 0
\(880\) 3.70363e9 + 6.41487e9i 0.183205 + 0.317321i
\(881\) −7.96497e8 −0.0392436 −0.0196218 0.999807i \(-0.506246\pi\)
−0.0196218 + 0.999807i \(0.506246\pi\)
\(882\) 0 0
\(883\) −4.24897e9 −0.207693 −0.103846 0.994593i \(-0.533115\pi\)
−0.103846 + 0.994593i \(0.533115\pi\)
\(884\) −5.11141e9 8.85322e9i −0.248861 0.431041i
\(885\) 0 0
\(886\) −3.18884e9 + 5.52323e9i −0.154033 + 0.266793i
\(887\) 8.84899e9 1.53269e10i 0.425756 0.737431i −0.570735 0.821135i \(-0.693341\pi\)
0.996491 + 0.0837033i \(0.0266748\pi\)
\(888\) 0 0
\(889\) −7.04774e9 1.22070e10i −0.336429 0.582713i
\(890\) −7.65991e9 −0.364215
\(891\) 0 0
\(892\) −4.78903e9 −0.225928
\(893\) −1.12043e10 1.94064e10i −0.526506 0.911935i
\(894\) 0 0
\(895\) 1.44656e10 2.50551e10i 0.674458 1.16819i
\(896\) 1.52091e9 2.63430e9i 0.0706359 0.122345i
\(897\) 0 0
\(898\) 5.67269e9 + 9.82538e9i 0.261410 + 0.452775i
\(899\) 2.33401e10 1.07138
\(900\) 0 0
\(901\) 2.36162e10 1.07565
\(902\) −1.06242e10 1.84017e10i −0.482030 0.834901i
\(903\) 0 0
\(904\) 3.79956e9 6.58103e9i 0.171058 0.296281i
\(905\) −1.20795e10 + 2.09223e10i −0.541724 + 0.938294i
\(906\) 0 0
\(907\) 5.75478e8 + 9.96758e8i 0.0256096 + 0.0443572i 0.878546 0.477657i \(-0.158514\pi\)
−0.852937 + 0.522015i \(0.825181\pi\)
\(908\) 4.63029e9 0.205261
\(909\) 0 0
\(910\) −5.10032e10 −2.24364
\(911\) 5.73328e9 + 9.93034e9i 0.251240 + 0.435161i 0.963868 0.266382i \(-0.0858283\pi\)
−0.712627 + 0.701543i \(0.752495\pi\)
\(912\) 0 0
\(913\) −1.49366e10 + 2.58709e10i −0.649535 + 1.12503i
\(914\) 3.89962e9 6.75435e9i 0.168932 0.292598i
\(915\) 0 0
\(916\) 9.75309e9 + 1.68928e10i 0.419284 + 0.726221i
\(917\) 2.65524e10 1.13713
\(918\) 0 0
\(919\) −3.59560e10 −1.52815 −0.764076 0.645126i \(-0.776805\pi\)
−0.764076 + 0.645126i \(0.776805\pi\)
\(920\) −2.23374e9 3.86895e9i −0.0945748 0.163808i
\(921\) 0 0
\(922\) −5.49145e9 + 9.51147e9i −0.230743 + 0.399659i
\(923\) −6.80875e9 + 1.17931e10i −0.285011 + 0.493653i
\(924\) 0 0
\(925\) −5.05629e8 8.75774e8i −0.0210056 0.0363828i
\(926\) 1.42972e10 0.591714
\(927\) 0 0
\(928\) 4.61584e9 0.189597
\(929\) −2.86558e9 4.96333e9i −0.117262 0.203104i 0.801420 0.598102i \(-0.204078\pi\)
−0.918682 + 0.394999i \(0.870745\pi\)
\(930\) 0 0
\(931\) −2.85142e10 + 4.93881e10i −1.15808 + 2.00585i
\(932\) 7.56270e8 1.30990e9i 0.0306000 0.0530008i
\(933\) 0 0
\(934\) −9.03071e9 1.56417e10i −0.362667 0.628158i
\(935\) −2.13912e10 −0.855842
\(936\) 0 0
\(937\) −1.02489e10 −0.406995 −0.203497 0.979076i \(-0.565231\pi\)
−0.203497 + 0.979076i \(0.565231\pi\)
\(938\) 1.02905e10 + 1.78237e10i 0.407124 + 0.705159i
\(939\) 0 0
\(940\) −5.23993e9 + 9.07582e9i −0.205768 + 0.356400i
\(941\) −5.69738e9 + 9.86815e9i −0.222901 + 0.386075i −0.955688 0.294383i \(-0.904886\pi\)
0.732787 + 0.680458i \(0.238219\pi\)
\(942\) 0 0
\(943\) 6.40771e9 + 1.10985e10i 0.248835 + 0.430996i
\(944\) 2.49476e9 0.0965220
\(945\) 0 0
\(946\) 2.68552e10 1.03136
\(947\) −1.20000e10 2.07846e10i −0.459151 0.795273i 0.539765 0.841816i \(-0.318513\pi\)
−0.998916 + 0.0465423i \(0.985180\pi\)
\(948\) 0 0
\(949\) −9.87037e8 + 1.70960e9i −0.0374888 + 0.0649326i
\(950\) −4.95777e9 + 8.58711e9i −0.187609 + 0.324948i
\(951\) 0 0
\(952\) 4.39219e9 + 7.60750e9i 0.164988 + 0.285767i
\(953\) −1.56339e10 −0.585117 −0.292558 0.956248i \(-0.594507\pi\)
−0.292558 + 0.956248i \(0.594507\pi\)
\(954\) 0 0
\(955\) 8.32058e9 0.309130
\(956\) −7.39246e9 1.28041e10i −0.273644 0.473966i
\(957\) 0 0
\(958\) −6.97067e9 + 1.20736e10i −0.256150 + 0.443666i
\(959\) 3.51425e10 6.08685e10i 1.28667 2.22858i
\(960\) 0 0
\(961\) 2.93306e7 + 5.08021e7i 0.00106608 + 0.00184650i
\(962\) 3.92616e9 0.142185
\(963\) 0 0
\(964\) −3.80039e9 −0.136634
\(965\) 1.60098e10 + 2.77298e10i 0.573510 + 0.993349i
\(966\) 0 0
\(967\) −2.10964e10 + 3.65401e10i −0.750268 + 1.29950i 0.197425 + 0.980318i \(0.436742\pi\)
−0.947693 + 0.319184i \(0.896591\pi\)
\(968\) −2.91320e9 + 5.04582e9i −0.103230 + 0.178800i
\(969\) 0 0
\(970\) 1.03049e10 + 1.78486e10i 0.362529 + 0.627919i
\(971\) 8.93754e9 0.313293 0.156646 0.987655i \(-0.449932\pi\)
0.156646 + 0.987655i \(0.449932\pi\)
\(972\) 0 0
\(973\) 5.50927e10 1.91734
\(974\) 1.07540e10 + 1.86264e10i 0.372917 + 0.645911i
\(975\) 0 0
\(976\) −3.89502e9 + 6.74638e9i −0.134102 + 0.232272i
\(977\) 1.06289e10 1.84097e10i 0.364633 0.631563i −0.624084 0.781357i \(-0.714528\pi\)
0.988717 + 0.149794i \(0.0478611\pi\)
\(978\) 0 0
\(979\) −8.17145e9 1.41534e10i −0.278330 0.482081i
\(980\) 2.66706e10 0.905195
\(981\) 0 0
\(982\) −1.87905e10 −0.633210
\(983\) 5.16755e9 + 8.95046e9i 0.173519 + 0.300544i 0.939648 0.342143i \(-0.111153\pi\)
−0.766129 + 0.642687i \(0.777819\pi\)
\(984\) 0 0
\(985\) −2.28796e9 + 3.96285e9i −0.0762818 + 0.132124i
\(986\) −6.66496e9 + 1.15441e10i −0.221426 + 0.383521i
\(987\) 0 0
\(988\) −1.92483e10 3.33390e10i −0.634955 1.09977i
\(989\) −1.61970e10 −0.532411
\(990\) 0 0
\(991\) 5.00170e10 1.63253 0.816263 0.577681i \(-0.196042\pi\)
0.816263 + 0.577681i \(0.196042\pi\)
\(992\) −2.71470e9 4.70200e9i −0.0882941 0.152930i
\(993\) 0 0
\(994\) 5.85071e9 1.01337e10i 0.188954 0.327278i
\(995\) −4.67787e9 + 8.10231e9i −0.150545 + 0.260752i
\(996\) 0 0
\(997\) 1.69044e10 + 2.92792e10i 0.540214 + 0.935678i 0.998891 + 0.0470752i \(0.0149901\pi\)
−0.458677 + 0.888603i \(0.651677\pi\)
\(998\) −1.33394e10 −0.424795
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 162.8.c.q.109.2 8
3.2 odd 2 162.8.c.r.109.3 8
9.2 odd 6 162.8.c.r.55.3 8
9.4 even 3 162.8.a.j.1.3 yes 4
9.5 odd 6 162.8.a.g.1.2 4
9.7 even 3 inner 162.8.c.q.55.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
162.8.a.g.1.2 4 9.5 odd 6
162.8.a.j.1.3 yes 4 9.4 even 3
162.8.c.q.55.2 8 9.7 even 3 inner
162.8.c.q.109.2 8 1.1 even 1 trivial
162.8.c.r.55.3 8 9.2 odd 6
162.8.c.r.109.3 8 3.2 odd 2