Properties

Label 100.9.d.b.99.1
Level $100$
Weight $9$
Character 100.99
Analytic conductor $40.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [100,9,Mod(99,100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("100.99");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 100.d (of order \(2\), degree \(1\), 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: \(40.7378610061\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{39})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 19x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 5^{2} \)
Twist minimal: no (minimal twist has level 4)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 99.1
Root \(-3.12250 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 100.99
Dual form 100.9.d.b.99.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-12.4900 - 10.0000i) q^{2} +99.9200 q^{3} +(56.0000 + 249.800i) q^{4} +(-1248.00 - 999.200i) q^{6} -1398.88 q^{7} +(1798.56 - 3680.00i) q^{8} +3423.00 q^{9} +O(q^{10})\) \(q+(-12.4900 - 10.0000i) q^{2} +99.9200 q^{3} +(56.0000 + 249.800i) q^{4} +(-1248.00 - 999.200i) q^{6} -1398.88 q^{7} +(1798.56 - 3680.00i) q^{8} +3423.00 q^{9} -18485.2i q^{11} +(5595.52 + 24960.0i) q^{12} +5470.00i q^{13} +(17472.0 + 13988.8i) q^{14} +(-59264.0 + 27977.6i) q^{16} +73090.0i q^{17} +(-42753.3 - 34230.0i) q^{18} +19484.4i q^{19} -139776. q^{21} +(-184852. + 230880. i) q^{22} -237210. q^{23} +(179712. - 367705. i) q^{24} +(54700.0 - 68320.3i) q^{26} -313549. q^{27} +(-78337.3 - 349440. i) q^{28} +128222. q^{29} -67945.6i q^{31} +(1.01998e6 + 243200. i) q^{32} -1.84704e6i q^{33} +(730900. - 912894. i) q^{34} +(191688. + 855065. i) q^{36} -3.47203e6i q^{37} +(194844. - 243360. i) q^{38} +546562. i q^{39} +2.14688e6 q^{41} +(1.74580e6 + 1.39776e6i) q^{42} -5.92815e6 q^{43} +(4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 + 2.37210e6i) q^{46} -7.62629e6 q^{47} +(-5.92166e6 + 2.79552e6i) q^{48} -3.80794e6 q^{49} +7.30315e6i q^{51} +(-1.36641e6 + 306320. i) q^{52} -824290. i q^{53} +(3.91622e6 + 3.13549e6i) q^{54} +(-2.51597e6 + 5.14788e6i) q^{56} +1.94688e6i q^{57} +(-1.60149e6 - 1.28222e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(-679456. + 848640. i) q^{62} -4.78836e6 q^{63} +(-1.03076e7 - 1.32374e7i) q^{64} +(-1.84704e7 + 2.30695e7i) q^{66} -1.52567e7 q^{67} +(-1.82579e7 + 4.09304e6i) q^{68} -2.37020e7 q^{69} -1.19604e6i q^{71} +(6.15647e6 - 1.25966e7i) q^{72} +5.72563e6i q^{73} +(-3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 + 1.09113e6i) q^{76} +2.58586e7i q^{77} +(5.46562e6 - 6.82656e6i) q^{78} -3.59132e7i q^{79} -5.37881e7 q^{81} +(-2.68145e7 - 2.14688e7i) q^{82} -5.19603e7 q^{83} +(-7.82746e6 - 3.49160e7i) q^{84} +(7.40426e7 + 5.92815e7i) q^{86} +1.28119e7 q^{87} +(-6.80255e7 - 3.32467e7i) q^{88} +8.33242e7 q^{89} -7.65187e6i q^{91} +(-1.32838e7 - 5.92550e7i) q^{92} -6.78912e6i q^{93} +(9.52524e7 + 7.62629e7i) q^{94} +(1.01917e8 + 2.43005e7i) q^{96} +1.20619e8i q^{97} +(4.75611e7 + 3.80794e7i) q^{98} -6.32748e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 224 q^{4} - 4992 q^{6} + 13692 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 224 q^{4} - 4992 q^{6} + 13692 q^{9} + 69888 q^{14} - 237056 q^{16} - 559104 q^{21} + 718848 q^{24} + 218800 q^{26} + 512888 q^{29} + 2923600 q^{34} + 766752 q^{36} + 8587528 q^{41} + 18470400 q^{44} + 11851008 q^{46} - 15231748 q^{49} + 15664896 q^{54} - 10063872 q^{56} - 58984312 q^{61} - 41230336 q^{64} - 73881600 q^{66} - 94808064 q^{69} - 138881200 q^{74} - 19468800 q^{76} - 215152380 q^{81} - 31309824 q^{84} + 296170368 q^{86} + 333296888 q^{89} + 381009408 q^{94} + 407666688 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/100\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(77\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −12.4900 10.0000i −0.780625 0.625000i
\(3\) 99.9200 1.23358 0.616790 0.787128i \(-0.288433\pi\)
0.616790 + 0.787128i \(0.288433\pi\)
\(4\) 56.0000 + 249.800i 0.218750 + 0.975781i
\(5\) 0 0
\(6\) −1248.00 999.200i −0.962963 0.770987i
\(7\) −1398.88 −0.582624 −0.291312 0.956628i \(-0.594092\pi\)
−0.291312 + 0.956628i \(0.594092\pi\)
\(8\) 1798.56 3680.00i 0.439101 0.898438i
\(9\) 3423.00 0.521719
\(10\) 0 0
\(11\) 18485.2i 1.26256i −0.775554 0.631282i \(-0.782529\pi\)
0.775554 0.631282i \(-0.217471\pi\)
\(12\) 5595.52 + 24960.0i 0.269846 + 1.20370i
\(13\) 5470.00i 0.191520i 0.995404 + 0.0957600i \(0.0305281\pi\)
−0.995404 + 0.0957600i \(0.969472\pi\)
\(14\) 17472.0 + 13988.8i 0.454810 + 0.364140i
\(15\) 0 0
\(16\) −59264.0 + 27977.6i −0.904297 + 0.426904i
\(17\) 73090.0i 0.875109i 0.899192 + 0.437555i \(0.144155\pi\)
−0.899192 + 0.437555i \(0.855845\pi\)
\(18\) −42753.3 34230.0i −0.407267 0.326075i
\(19\) 19484.4i 0.149511i 0.997202 + 0.0747554i \(0.0238176\pi\)
−0.997202 + 0.0747554i \(0.976182\pi\)
\(20\) 0 0
\(21\) −139776. −0.718713
\(22\) −184852. + 230880.i −0.789102 + 0.985588i
\(23\) −237210. −0.847660 −0.423830 0.905742i \(-0.639315\pi\)
−0.423830 + 0.905742i \(0.639315\pi\)
\(24\) 179712. 367705.i 0.541667 1.10829i
\(25\) 0 0
\(26\) 54700.0 68320.3i 0.119700 0.149505i
\(27\) −313549. −0.589997
\(28\) −78337.3 349440.i −0.127449 0.568513i
\(29\) 128222. 0.181289 0.0906443 0.995883i \(-0.471107\pi\)
0.0906443 + 0.995883i \(0.471107\pi\)
\(30\) 0 0
\(31\) 67945.6i 0.0735723i −0.999323 0.0367862i \(-0.988288\pi\)
0.999323 0.0367862i \(-0.0117120\pi\)
\(32\) 1.01998e6 + 243200.i 0.972732 + 0.231934i
\(33\) 1.84704e6i 1.55747i
\(34\) 730900. 912894.i 0.546943 0.683132i
\(35\) 0 0
\(36\) 191688. + 855065.i 0.114126 + 0.509084i
\(37\) 3.47203e6i 1.85258i −0.376813 0.926289i \(-0.622980\pi\)
0.376813 0.926289i \(-0.377020\pi\)
\(38\) 194844. 243360.i 0.0934442 0.116712i
\(39\) 546562.i 0.236255i
\(40\) 0 0
\(41\) 2.14688e6 0.759754 0.379877 0.925037i \(-0.375966\pi\)
0.379877 + 0.925037i \(0.375966\pi\)
\(42\) 1.74580e6 + 1.39776e6i 0.561045 + 0.449196i
\(43\) −5.92815e6 −1.73399 −0.866993 0.498321i \(-0.833950\pi\)
−0.866993 + 0.498321i \(0.833950\pi\)
\(44\) 4.61760e6 1.03517e6i 1.23199 0.276186i
\(45\) 0 0
\(46\) 2.96275e6 + 2.37210e6i 0.661704 + 0.529787i
\(47\) −7.62629e6 −1.56287 −0.781433 0.623989i \(-0.785511\pi\)
−0.781433 + 0.623989i \(0.785511\pi\)
\(48\) −5.92166e6 + 2.79552e6i −1.11552 + 0.526620i
\(49\) −3.80794e6 −0.660550
\(50\) 0 0
\(51\) 7.30315e6i 1.07952i
\(52\) −1.36641e6 + 306320.i −0.186881 + 0.0418950i
\(53\) 824290.i 0.104466i −0.998635 0.0522332i \(-0.983366\pi\)
0.998635 0.0522332i \(-0.0166339\pi\)
\(54\) 3.91622e6 + 3.13549e6i 0.460567 + 0.368748i
\(55\) 0 0
\(56\) −2.51597e6 + 5.14788e6i −0.255831 + 0.523451i
\(57\) 1.94688e6i 0.184433i
\(58\) −1.60149e6 1.28222e6i −0.141518 0.113305i
\(59\) 3.72552e6i 0.307453i 0.988113 + 0.153726i \(0.0491274\pi\)
−0.988113 + 0.153726i \(0.950873\pi\)
\(60\) 0 0
\(61\) −1.47461e7 −1.06502 −0.532509 0.846424i \(-0.678751\pi\)
−0.532509 + 0.846424i \(0.678751\pi\)
\(62\) −679456. + 848640.i −0.0459827 + 0.0574324i
\(63\) −4.78836e6 −0.303966
\(64\) −1.03076e7 1.32374e7i −0.614380 0.789010i
\(65\) 0 0
\(66\) −1.84704e7 + 2.30695e7i −0.973421 + 1.21580i
\(67\) −1.52567e7 −0.757113 −0.378557 0.925578i \(-0.623579\pi\)
−0.378557 + 0.925578i \(0.623579\pi\)
\(68\) −1.82579e7 + 4.09304e6i −0.853915 + 0.191430i
\(69\) −2.37020e7 −1.04566
\(70\) 0 0
\(71\) 1.19604e6i 0.0470666i −0.999723 0.0235333i \(-0.992508\pi\)
0.999723 0.0235333i \(-0.00749158\pi\)
\(72\) 6.15647e6 1.25966e7i 0.229088 0.468732i
\(73\) 5.72563e6i 0.201619i 0.994906 + 0.100810i \(0.0321433\pi\)
−0.994906 + 0.100810i \(0.967857\pi\)
\(74\) −3.47203e7 + 4.33656e7i −1.15786 + 1.44617i
\(75\) 0 0
\(76\) −4.86720e6 + 1.09113e6i −0.145890 + 0.0327055i
\(77\) 2.58586e7i 0.735600i
\(78\) 5.46562e6 6.82656e6i 0.147659 0.184427i
\(79\) 3.59132e7i 0.922032i −0.887392 0.461016i \(-0.847485\pi\)
0.887392 0.461016i \(-0.152515\pi\)
\(80\) 0 0
\(81\) −5.37881e7 −1.24953
\(82\) −2.68145e7 2.14688e7i −0.593082 0.474846i
\(83\) −5.19603e7 −1.09486 −0.547431 0.836851i \(-0.684394\pi\)
−0.547431 + 0.836851i \(0.684394\pi\)
\(84\) −7.82746e6 3.49160e7i −0.157218 0.701306i
\(85\) 0 0
\(86\) 7.40426e7 + 5.92815e7i 1.35359 + 1.08374i
\(87\) 1.28119e7 0.223634
\(88\) −6.80255e7 3.32467e7i −1.13433 0.554393i
\(89\) 8.33242e7 1.32804 0.664020 0.747715i \(-0.268849\pi\)
0.664020 + 0.747715i \(0.268849\pi\)
\(90\) 0 0
\(91\) 7.65187e6i 0.111584i
\(92\) −1.32838e7 5.92550e7i −0.185426 0.827130i
\(93\) 6.78912e6i 0.0907573i
\(94\) 9.52524e7 + 7.62629e7i 1.22001 + 0.976792i
\(95\) 0 0
\(96\) 1.01917e8 + 2.43005e7i 1.19994 + 0.286109i
\(97\) 1.20619e8i 1.36248i 0.732062 + 0.681238i \(0.238558\pi\)
−0.732062 + 0.681238i \(0.761442\pi\)
\(98\) 4.75611e7 + 3.80794e7i 0.515641 + 0.412844i
\(99\) 6.32748e7i 0.658704i
\(100\) 0 0
\(101\) 2.77246e7 0.266428 0.133214 0.991087i \(-0.457470\pi\)
0.133214 + 0.991087i \(0.457470\pi\)
\(102\) 7.30315e7 9.12163e7i 0.674698 0.842698i
\(103\) 1.04501e8 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(104\) 2.01296e7 + 9.83812e6i 0.172069 + 0.0840967i
\(105\) 0 0
\(106\) −8.24290e6 + 1.02954e7i −0.0652915 + 0.0815490i
\(107\) −1.00328e8 −0.765394 −0.382697 0.923874i \(-0.625005\pi\)
−0.382697 + 0.923874i \(0.625005\pi\)
\(108\) −1.75587e7 7.83245e7i −0.129062 0.575708i
\(109\) 5.90716e7 0.418478 0.209239 0.977865i \(-0.432901\pi\)
0.209239 + 0.977865i \(0.432901\pi\)
\(110\) 0 0
\(111\) 3.46925e8i 2.28530i
\(112\) 8.29032e7 3.91373e7i 0.526865 0.248724i
\(113\) 5.50849e7i 0.337846i −0.985629 0.168923i \(-0.945971\pi\)
0.985629 0.168923i \(-0.0540290\pi\)
\(114\) 1.94688e7 2.43165e7i 0.115271 0.143973i
\(115\) 0 0
\(116\) 7.18043e6 + 3.20298e7i 0.0396569 + 0.176898i
\(117\) 1.87238e7i 0.0999196i
\(118\) 3.72552e7 4.65317e7i 0.192158 0.240005i
\(119\) 1.02244e8i 0.509859i
\(120\) 0 0
\(121\) −1.27344e8 −0.594067
\(122\) 1.84178e8 + 1.47461e8i 0.831380 + 0.665637i
\(123\) 2.14516e8 0.937217
\(124\) 1.69728e7 3.80495e6i 0.0717905 0.0160939i
\(125\) 0 0
\(126\) 5.98067e7 + 4.78836e7i 0.237283 + 0.189979i
\(127\) −2.57160e8 −0.988529 −0.494264 0.869312i \(-0.664562\pi\)
−0.494264 + 0.869312i \(0.664562\pi\)
\(128\) −3.63229e6 + 2.68411e8i −0.0135313 + 0.999908i
\(129\) −5.92341e8 −2.13901
\(130\) 0 0
\(131\) 3.12175e8i 1.06002i −0.847992 0.530009i \(-0.822188\pi\)
0.847992 0.530009i \(-0.177812\pi\)
\(132\) 4.61390e8 1.03434e8i 1.51975 0.340697i
\(133\) 2.72563e7i 0.0871085i
\(134\) 1.90556e8 + 1.52567e8i 0.591021 + 0.473196i
\(135\) 0 0
\(136\) 2.68971e8 + 1.31457e8i 0.786231 + 0.384262i
\(137\) 2.21980e8i 0.630132i 0.949070 + 0.315066i \(0.102027\pi\)
−0.949070 + 0.315066i \(0.897973\pi\)
\(138\) 2.96038e8 + 2.37020e8i 0.816265 + 0.653535i
\(139\) 2.95030e8i 0.790328i 0.918611 + 0.395164i \(0.129312\pi\)
−0.918611 + 0.395164i \(0.870688\pi\)
\(140\) 0 0
\(141\) −7.62019e8 −1.92792
\(142\) −1.19604e7 + 1.49386e7i −0.0294166 + 0.0367414i
\(143\) 1.01114e8 0.241806
\(144\) −2.02861e8 + 9.57673e7i −0.471789 + 0.222724i
\(145\) 0 0
\(146\) 5.72563e7 7.15131e7i 0.126012 0.157389i
\(147\) −3.80489e8 −0.814841
\(148\) 8.67313e8 1.94434e8i 1.80771 0.405252i
\(149\) −4.03603e8 −0.818859 −0.409429 0.912342i \(-0.634272\pi\)
−0.409429 + 0.912342i \(0.634272\pi\)
\(150\) 0 0
\(151\) 8.36985e8i 1.60994i −0.593316 0.804970i \(-0.702181\pi\)
0.593316 0.804970i \(-0.297819\pi\)
\(152\) 7.17026e7 + 3.50438e7i 0.134326 + 0.0656504i
\(153\) 2.50187e8i 0.456561i
\(154\) 2.58586e8 3.22973e8i 0.459750 0.574227i
\(155\) 0 0
\(156\) −1.36531e8 + 3.06075e7i −0.230533 + 0.0516808i
\(157\) 2.71319e8i 0.446561i −0.974754 0.223281i \(-0.928323\pi\)
0.974754 0.223281i \(-0.0716767\pi\)
\(158\) −3.59132e8 + 4.48556e8i −0.576270 + 0.719761i
\(159\) 8.23630e7i 0.128868i
\(160\) 0 0
\(161\) 3.31828e8 0.493867
\(162\) 6.71813e8 + 5.37881e8i 0.975413 + 0.780955i
\(163\) 5.78509e8 0.819520 0.409760 0.912193i \(-0.365612\pi\)
0.409760 + 0.912193i \(0.365612\pi\)
\(164\) 1.20225e8 + 5.36291e8i 0.166196 + 0.741353i
\(165\) 0 0
\(166\) 6.48984e8 + 5.19603e8i 0.854676 + 0.684288i
\(167\) −4.68118e8 −0.601852 −0.300926 0.953647i \(-0.597296\pi\)
−0.300926 + 0.953647i \(0.597296\pi\)
\(168\) −2.51395e8 + 5.14376e8i −0.315588 + 0.645719i
\(169\) 7.85810e8 0.963320
\(170\) 0 0
\(171\) 6.66951e7i 0.0780026i
\(172\) −3.31976e8 1.48085e9i −0.379309 1.69199i
\(173\) 2.06197e8i 0.230196i 0.993354 + 0.115098i \(0.0367182\pi\)
−0.993354 + 0.115098i \(0.963282\pi\)
\(174\) −1.60021e8 1.28119e8i −0.174574 0.139771i
\(175\) 0 0
\(176\) 5.17171e8 + 1.09551e9i 0.538994 + 1.14173i
\(177\) 3.72253e8i 0.379268i
\(178\) −1.04072e9 8.33242e8i −1.03670 0.830025i
\(179\) 1.41911e8i 0.138230i −0.997609 0.0691152i \(-0.977982\pi\)
0.997609 0.0691152i \(-0.0220176\pi\)
\(180\) 0 0
\(181\) 4.82566e8 0.449616 0.224808 0.974403i \(-0.427824\pi\)
0.224808 + 0.974403i \(0.427824\pi\)
\(182\) −7.65187e7 + 9.55718e7i −0.0697400 + 0.0871053i
\(183\) −1.47343e9 −1.31379
\(184\) −4.26636e8 + 8.72933e8i −0.372209 + 0.761569i
\(185\) 0 0
\(186\) −6.78912e7 + 8.47961e7i −0.0567233 + 0.0708474i
\(187\) 1.35108e9 1.10488
\(188\) −4.27072e8 1.90505e9i −0.341877 1.52502i
\(189\) 4.38617e8 0.343747
\(190\) 0 0
\(191\) 9.92461e8i 0.745727i 0.927886 + 0.372864i \(0.121624\pi\)
−0.927886 + 0.372864i \(0.878376\pi\)
\(192\) −1.02993e9 1.32268e9i −0.757887 0.973307i
\(193\) 1.17593e9i 0.847526i −0.905773 0.423763i \(-0.860709\pi\)
0.905773 0.423763i \(-0.139291\pi\)
\(194\) 1.20619e9 1.50653e9i 0.851547 1.06358i
\(195\) 0 0
\(196\) −2.13244e8 9.51222e8i −0.144495 0.644552i
\(197\) 1.70538e9i 1.13229i 0.824306 + 0.566144i \(0.191565\pi\)
−0.824306 + 0.566144i \(0.808435\pi\)
\(198\) −6.32748e8 + 7.90302e8i −0.411690 + 0.514200i
\(199\) 2.49036e9i 1.58800i −0.607919 0.793999i \(-0.707996\pi\)
0.607919 0.793999i \(-0.292004\pi\)
\(200\) 0 0
\(201\) −1.52445e9 −0.933960
\(202\) −3.46281e8 2.77246e8i −0.207981 0.166518i
\(203\) −1.79367e8 −0.105623
\(204\) −1.82433e9 + 4.08976e8i −1.05337 + 0.236144i
\(205\) 0 0
\(206\) −1.30522e9 1.04501e9i −0.724792 0.580298i
\(207\) −8.11970e8 −0.442241
\(208\) −1.53037e8 3.24174e8i −0.0817606 0.173191i
\(209\) 3.60173e8 0.188767
\(210\) 0 0
\(211\) 1.46774e9i 0.740491i 0.928934 + 0.370245i \(0.120726\pi\)
−0.928934 + 0.370245i \(0.879274\pi\)
\(212\) 2.05908e8 4.61602e7i 0.101936 0.0228520i
\(213\) 1.19508e8i 0.0580604i
\(214\) 1.25309e9 + 1.00328e9i 0.597486 + 0.478371i
\(215\) 0 0
\(216\) −5.63936e8 + 1.15386e9i −0.259069 + 0.530076i
\(217\) 9.50477e7i 0.0428650i
\(218\) −7.37804e8 5.90716e8i −0.326674 0.261549i
\(219\) 5.72105e8i 0.248713i
\(220\) 0 0
\(221\) −3.99802e8 −0.167601
\(222\) −3.46925e9 + 4.33309e9i −1.42831 + 1.78396i
\(223\) −1.47920e9 −0.598147 −0.299073 0.954230i \(-0.596678\pi\)
−0.299073 + 0.954230i \(0.596678\pi\)
\(224\) −1.42683e9 3.40208e8i −0.566737 0.135130i
\(225\) 0 0
\(226\) −5.50849e8 + 6.88011e8i −0.211154 + 0.263731i
\(227\) 7.50054e8 0.282481 0.141241 0.989975i \(-0.454891\pi\)
0.141241 + 0.989975i \(0.454891\pi\)
\(228\) −4.86330e8 + 1.09025e8i −0.179967 + 0.0403448i
\(229\) 2.84784e9 1.03556 0.517778 0.855515i \(-0.326759\pi\)
0.517778 + 0.855515i \(0.326759\pi\)
\(230\) 0 0
\(231\) 2.58379e9i 0.907421i
\(232\) 2.30615e8 4.71857e8i 0.0796041 0.162876i
\(233\) 2.20621e8i 0.0748553i −0.999299 0.0374276i \(-0.988084\pi\)
0.999299 0.0374276i \(-0.0119164\pi\)
\(234\) 1.87238e8 2.33860e8i 0.0624498 0.0779997i
\(235\) 0 0
\(236\) −9.30634e8 + 2.08629e8i −0.300007 + 0.0672553i
\(237\) 3.58845e9i 1.13740i
\(238\) −1.02244e9 + 1.27703e9i −0.318662 + 0.398009i
\(239\) 4.04493e9i 1.23971i 0.784717 + 0.619855i \(0.212808\pi\)
−0.784717 + 0.619855i \(0.787192\pi\)
\(240\) 0 0
\(241\) 6.17983e9 1.83193 0.915964 0.401260i \(-0.131427\pi\)
0.915964 + 0.401260i \(0.131427\pi\)
\(242\) 1.59052e9 + 1.27344e9i 0.463743 + 0.371292i
\(243\) −3.31731e9 −0.951395
\(244\) −8.25780e8 3.68357e9i −0.232973 1.03922i
\(245\) 0 0
\(246\) −2.67931e9 2.14516e9i −0.731615 0.585760i
\(247\) −1.06580e8 −0.0286343
\(248\) −2.50040e8 1.22204e8i −0.0661001 0.0323057i
\(249\) −5.19187e9 −1.35060
\(250\) 0 0
\(251\) 5.21367e9i 1.31356i 0.754084 + 0.656778i \(0.228081\pi\)
−0.754084 + 0.656778i \(0.771919\pi\)
\(252\) −2.68148e8 1.19613e9i −0.0664926 0.296604i
\(253\) 4.38487e9i 1.07022i
\(254\) 3.21193e9 + 2.57160e9i 0.771670 + 0.617830i
\(255\) 0 0
\(256\) 2.72948e9 3.31613e9i 0.635506 0.772096i
\(257\) 6.13693e9i 1.40676i −0.710816 0.703378i \(-0.751674\pi\)
0.710816 0.703378i \(-0.248326\pi\)
\(258\) 7.39833e9 + 5.92341e9i 1.66976 + 1.33688i
\(259\) 4.85695e9i 1.07936i
\(260\) 0 0
\(261\) 4.38904e8 0.0945818
\(262\) −3.12175e9 + 3.89907e9i −0.662512 + 0.827477i
\(263\) 6.96916e9 1.45666 0.728329 0.685228i \(-0.240297\pi\)
0.728329 + 0.685228i \(0.240297\pi\)
\(264\) −6.79711e9 3.32201e9i −1.39929 0.683889i
\(265\) 0 0
\(266\) −2.72563e8 + 3.40431e8i −0.0544428 + 0.0679991i
\(267\) 8.32575e9 1.63824
\(268\) −8.54374e8 3.81112e9i −0.165619 0.738777i
\(269\) −2.70720e9 −0.517025 −0.258513 0.966008i \(-0.583232\pi\)
−0.258513 + 0.966008i \(0.583232\pi\)
\(270\) 0 0
\(271\) 7.99032e9i 1.48145i −0.671808 0.740725i \(-0.734482\pi\)
0.671808 0.740725i \(-0.265518\pi\)
\(272\) −2.04488e9 4.33161e9i −0.373588 0.791359i
\(273\) 7.64575e8i 0.137648i
\(274\) 2.21980e9 2.77253e9i 0.393832 0.491897i
\(275\) 0 0
\(276\) −1.32731e9 5.92076e9i −0.228737 1.02033i
\(277\) 8.22965e9i 1.39786i −0.715192 0.698928i \(-0.753661\pi\)
0.715192 0.698928i \(-0.246339\pi\)
\(278\) 2.95030e9 3.68493e9i 0.493955 0.616949i
\(279\) 2.32578e8i 0.0383841i
\(280\) 0 0
\(281\) 3.08105e9 0.494167 0.247083 0.968994i \(-0.420528\pi\)
0.247083 + 0.968994i \(0.420528\pi\)
\(282\) 9.51761e9 + 7.62019e9i 1.50498 + 1.20495i
\(283\) 1.17112e9 0.182582 0.0912908 0.995824i \(-0.470901\pi\)
0.0912908 + 0.995824i \(0.470901\pi\)
\(284\) 2.98771e8 6.69784e7i 0.0459267 0.0102958i
\(285\) 0 0
\(286\) −1.26291e9 1.01114e9i −0.188760 0.151129i
\(287\) −3.00323e9 −0.442650
\(288\) 3.49140e9 + 8.32474e8i 0.507493 + 0.121004i
\(289\) 1.63361e9 0.234184
\(290\) 0 0
\(291\) 1.20522e10i 1.68072i
\(292\) −1.43026e9 + 3.20635e8i −0.196736 + 0.0441042i
\(293\) 4.80980e9i 0.652614i −0.945264 0.326307i \(-0.894196\pi\)
0.945264 0.326307i \(-0.105804\pi\)
\(294\) 4.75231e9 + 3.80489e9i 0.636085 + 0.509275i
\(295\) 0 0
\(296\) −1.27771e10 6.24465e9i −1.66443 0.813470i
\(297\) 5.79601e9i 0.744909i
\(298\) 5.04100e9 + 4.03603e9i 0.639221 + 0.511787i
\(299\) 1.29754e9i 0.162344i
\(300\) 0 0
\(301\) 8.29277e9 1.01026
\(302\) −8.36985e9 + 1.04539e10i −1.00621 + 1.25676i
\(303\) 2.77025e9 0.328661
\(304\) −5.45126e8 1.15472e9i −0.0638268 0.135202i
\(305\) 0 0
\(306\) 2.50187e9 3.12484e9i 0.285351 0.356403i
\(307\) 3.49176e9 0.393089 0.196545 0.980495i \(-0.437028\pi\)
0.196545 + 0.980495i \(0.437028\pi\)
\(308\) −6.45947e9 + 1.44808e9i −0.717784 + 0.160912i
\(309\) 1.04417e10 1.14535
\(310\) 0 0
\(311\) 1.29807e10i 1.38757i −0.720182 0.693785i \(-0.755942\pi\)
0.720182 0.693785i \(-0.244058\pi\)
\(312\) 2.01135e9 + 9.83025e8i 0.212260 + 0.103740i
\(313\) 6.31165e9i 0.657606i 0.944399 + 0.328803i \(0.106645\pi\)
−0.944399 + 0.328803i \(0.893355\pi\)
\(314\) −2.71319e9 + 3.38877e9i −0.279101 + 0.348597i
\(315\) 0 0
\(316\) 8.97112e9 2.01114e9i 0.899702 0.201695i
\(317\) 1.65902e10i 1.64291i 0.570273 + 0.821455i \(0.306837\pi\)
−0.570273 + 0.821455i \(0.693163\pi\)
\(318\) −8.23630e8 + 1.02871e9i −0.0805423 + 0.100597i
\(319\) 2.37021e9i 0.228888i
\(320\) 0 0
\(321\) −1.00247e10 −0.944175
\(322\) −4.14453e9 3.31828e9i −0.385525 0.308667i
\(323\) −1.42411e9 −0.130838
\(324\) −3.01213e9 1.34363e10i −0.273334 1.21927i
\(325\) 0 0
\(326\) −7.22557e9 5.78509e9i −0.639738 0.512200i
\(327\) 5.90243e9 0.516226
\(328\) 3.86129e9 7.90053e9i 0.333609 0.682591i
\(329\) 1.06683e10 0.910563
\(330\) 0 0
\(331\) 5.48640e9i 0.457062i 0.973537 + 0.228531i \(0.0733922\pi\)
−0.973537 + 0.228531i \(0.926608\pi\)
\(332\) −2.90978e9 1.29797e10i −0.239501 1.06834i
\(333\) 1.18848e10i 0.966526i
\(334\) 5.84680e9 + 4.68118e9i 0.469821 + 0.376158i
\(335\) 0 0
\(336\) 8.28368e9 3.91060e9i 0.649930 0.306822i
\(337\) 3.56226e8i 0.0276189i −0.999905 0.0138095i \(-0.995604\pi\)
0.999905 0.0138095i \(-0.00439583\pi\)
\(338\) −9.81476e9 7.85810e9i −0.751992 0.602075i
\(339\) 5.50408e9i 0.416760i
\(340\) 0 0
\(341\) −1.25599e9 −0.0928897
\(342\) 6.66951e8 8.33021e8i 0.0487517 0.0608908i
\(343\) 1.33911e10 0.967476
\(344\) −1.06621e10 + 2.18156e10i −0.761396 + 1.55788i
\(345\) 0 0
\(346\) 2.06197e9 2.57540e9i 0.143872 0.179697i
\(347\) 1.59731e10 1.10172 0.550859 0.834599i \(-0.314300\pi\)
0.550859 + 0.834599i \(0.314300\pi\)
\(348\) 7.17469e8 + 3.20042e9i 0.0489199 + 0.218218i
\(349\) −1.03634e10 −0.698553 −0.349277 0.937020i \(-0.613573\pi\)
−0.349277 + 0.937020i \(0.613573\pi\)
\(350\) 0 0
\(351\) 1.71511e9i 0.112996i
\(352\) 4.49560e9 1.88546e10i 0.292831 1.22814i
\(353\) 1.30979e10i 0.843536i 0.906704 + 0.421768i \(0.138590\pi\)
−0.906704 + 0.421768i \(0.861410\pi\)
\(354\) 3.72253e9 4.64944e9i 0.237042 0.296066i
\(355\) 0 0
\(356\) 4.66616e9 + 2.08144e10i 0.290509 + 1.29588i
\(357\) 1.02162e10i 0.628952i
\(358\) −1.41911e9 + 1.77247e9i −0.0863940 + 0.107906i
\(359\) 3.31454e9i 0.199547i −0.995010 0.0997737i \(-0.968188\pi\)
0.995010 0.0997737i \(-0.0318119\pi\)
\(360\) 0 0
\(361\) 1.66039e10 0.977647
\(362\) −6.02724e9 4.82566e9i −0.350982 0.281010i
\(363\) −1.27242e10 −0.732829
\(364\) 1.91144e9 4.28505e8i 0.108882 0.0244090i
\(365\) 0 0
\(366\) 1.84031e10 + 1.47343e10i 1.02557 + 0.821116i
\(367\) −1.96628e10 −1.08388 −0.541939 0.840418i \(-0.682309\pi\)
−0.541939 + 0.840418i \(0.682309\pi\)
\(368\) 1.40580e10 6.63656e9i 0.766536 0.361870i
\(369\) 7.34878e9 0.396378
\(370\) 0 0
\(371\) 1.15308e9i 0.0608646i
\(372\) 1.69592e9 3.80191e8i 0.0885593 0.0198532i
\(373\) 2.10063e10i 1.08521i 0.839987 + 0.542606i \(0.182562\pi\)
−0.839987 + 0.542606i \(0.817438\pi\)
\(374\) −1.68750e10 1.35108e10i −0.862498 0.690551i
\(375\) 0 0
\(376\) −1.37163e10 + 2.80648e10i −0.686257 + 1.40414i
\(377\) 7.01374e8i 0.0347204i
\(378\) −5.47833e9 4.38617e9i −0.268337 0.214842i
\(379\) 3.04816e9i 0.147734i −0.997268 0.0738670i \(-0.976466\pi\)
0.997268 0.0738670i \(-0.0235340\pi\)
\(380\) 0 0
\(381\) −2.56955e10 −1.21943
\(382\) 9.92461e9 1.23958e10i 0.466080 0.582133i
\(383\) −2.23357e10 −1.03802 −0.519008 0.854770i \(-0.673698\pi\)
−0.519008 + 0.854770i \(0.673698\pi\)
\(384\) −3.62938e8 + 2.68196e10i −0.0166920 + 1.23347i
\(385\) 0 0
\(386\) −1.17593e10 + 1.46874e10i −0.529704 + 0.661599i
\(387\) −2.02921e10 −0.904654
\(388\) −3.01306e10 + 6.75466e9i −1.32948 + 0.298042i
\(389\) −3.13680e10 −1.36990 −0.684948 0.728592i \(-0.740175\pi\)
−0.684948 + 0.728592i \(0.740175\pi\)
\(390\) 0 0
\(391\) 1.73377e10i 0.741795i
\(392\) −6.84880e9 + 1.40132e10i −0.290048 + 0.593463i
\(393\) 3.11926e10i 1.30762i
\(394\) 1.70538e10 2.13002e10i 0.707680 0.883892i
\(395\) 0 0
\(396\) 1.58060e10 3.54339e9i 0.642751 0.144091i
\(397\) 7.65788e9i 0.308281i 0.988049 + 0.154140i \(0.0492608\pi\)
−0.988049 + 0.154140i \(0.950739\pi\)
\(398\) −2.49036e10 + 3.11046e10i −0.992499 + 1.23963i
\(399\) 2.72345e9i 0.107455i
\(400\) 0 0
\(401\) −3.26120e10 −1.26125 −0.630623 0.776089i \(-0.717201\pi\)
−0.630623 + 0.776089i \(0.717201\pi\)
\(402\) 1.90403e10 + 1.52445e10i 0.729072 + 0.583725i
\(403\) 3.71662e8 0.0140906
\(404\) 1.55258e9 + 6.92561e9i 0.0582812 + 0.259976i
\(405\) 0 0
\(406\) 2.24029e9 + 1.79367e9i 0.0824520 + 0.0660144i
\(407\) −6.41811e10 −2.33900
\(408\) 2.68756e10 + 1.31352e10i 0.969879 + 0.474018i
\(409\) −2.26168e10 −0.808236 −0.404118 0.914707i \(-0.632422\pi\)
−0.404118 + 0.914707i \(0.632422\pi\)
\(410\) 0 0
\(411\) 2.21802e10i 0.777318i
\(412\) 5.85205e9 + 2.61043e10i 0.203104 + 0.905990i
\(413\) 5.21155e9i 0.179129i
\(414\) 1.01415e10 + 8.11970e9i 0.345224 + 0.276400i
\(415\) 0 0
\(416\) −1.33030e9 + 5.57931e9i −0.0444199 + 0.186297i
\(417\) 2.94794e10i 0.974932i
\(418\) −4.49856e9 3.60173e9i −0.147356 0.117979i
\(419\) 4.94503e10i 1.60440i 0.597054 + 0.802201i \(0.296338\pi\)
−0.597054 + 0.802201i \(0.703662\pi\)
\(420\) 0 0
\(421\) −3.34077e10 −1.06345 −0.531726 0.846916i \(-0.678457\pi\)
−0.531726 + 0.846916i \(0.678457\pi\)
\(422\) 1.46774e10 1.83321e10i 0.462807 0.578045i
\(423\) −2.61048e10 −0.815378
\(424\) −3.03339e9 1.48253e9i −0.0938565 0.0458713i
\(425\) 0 0
\(426\) −1.19508e9 + 1.49266e9i −0.0362878 + 0.0453234i
\(427\) 2.06280e10 0.620505
\(428\) −5.61834e9 2.50618e10i −0.167430 0.746857i
\(429\) 1.01033e10 0.298287
\(430\) 0 0
\(431\) 3.06956e10i 0.889544i −0.895644 0.444772i \(-0.853285\pi\)
0.895644 0.444772i \(-0.146715\pi\)
\(432\) 1.85822e10 8.77234e9i 0.533533 0.251872i
\(433\) 2.88433e9i 0.0820529i −0.999158 0.0410265i \(-0.986937\pi\)
0.999158 0.0410265i \(-0.0130628\pi\)
\(434\) 9.50477e8 1.18715e9i 0.0267906 0.0334615i
\(435\) 0 0
\(436\) 3.30801e9 + 1.47561e10i 0.0915421 + 0.408343i
\(437\) 4.62189e9i 0.126734i
\(438\) 5.72105e9 7.14559e9i 0.155446 0.194152i
\(439\) 6.92422e10i 1.86429i −0.362088 0.932144i \(-0.617936\pi\)
0.362088 0.932144i \(-0.382064\pi\)
\(440\) 0 0
\(441\) −1.30346e10 −0.344621
\(442\) 4.99353e9 + 3.99802e9i 0.130833 + 0.104751i
\(443\) 2.06609e10 0.536455 0.268228 0.963356i \(-0.413562\pi\)
0.268228 + 0.963356i \(0.413562\pi\)
\(444\) 8.66619e10 1.94278e10i 2.22996 0.499910i
\(445\) 0 0
\(446\) 1.84752e10 + 1.47920e10i 0.466928 + 0.373842i
\(447\) −4.03280e10 −1.01013
\(448\) 1.44191e10 + 1.85175e10i 0.357952 + 0.459696i
\(449\) −2.11092e10 −0.519382 −0.259691 0.965692i \(-0.583621\pi\)
−0.259691 + 0.965692i \(0.583621\pi\)
\(450\) 0 0
\(451\) 3.96855e10i 0.959237i
\(452\) 1.37602e10 3.08476e9i 0.329664 0.0739039i
\(453\) 8.36315e10i 1.98599i
\(454\) −9.36818e9 7.50054e9i −0.220512 0.176551i
\(455\) 0 0
\(456\) 7.16452e9 + 3.50158e9i 0.165702 + 0.0809850i
\(457\) 2.06831e10i 0.474188i −0.971487 0.237094i \(-0.923805\pi\)
0.971487 0.237094i \(-0.0761950\pi\)
\(458\) −3.55695e10 2.84784e10i −0.808381 0.647223i
\(459\) 2.29173e10i 0.516312i
\(460\) 0 0
\(461\) 7.65072e10 1.69394 0.846971 0.531640i \(-0.178424\pi\)
0.846971 + 0.531640i \(0.178424\pi\)
\(462\) 2.58379e10 3.22715e10i 0.567138 0.708355i
\(463\) 3.41303e9 0.0742704 0.0371352 0.999310i \(-0.488177\pi\)
0.0371352 + 0.999310i \(0.488177\pi\)
\(464\) −7.59895e9 + 3.58734e9i −0.163939 + 0.0773929i
\(465\) 0 0
\(466\) −2.20621e9 + 2.75555e9i −0.0467845 + 0.0584339i
\(467\) −1.92903e10 −0.405576 −0.202788 0.979223i \(-0.565000\pi\)
−0.202788 + 0.979223i \(0.565000\pi\)
\(468\) −4.67721e9 + 1.04853e9i −0.0974997 + 0.0218574i
\(469\) 2.13423e10 0.441112
\(470\) 0 0
\(471\) 2.71102e10i 0.550869i
\(472\) 1.37099e10 + 6.70056e9i 0.276227 + 0.135003i
\(473\) 1.09583e11i 2.18927i
\(474\) −3.58845e10 + 4.48197e10i −0.710875 + 0.887883i
\(475\) 0 0
\(476\) 2.55406e10 5.72567e9i 0.497511 0.111532i
\(477\) 2.82154e9i 0.0545021i
\(478\) 4.04493e10 5.05212e10i 0.774818 0.967748i
\(479\) 2.43887e10i 0.463282i 0.972801 + 0.231641i \(0.0744095\pi\)
−0.972801 + 0.231641i \(0.925590\pi\)
\(480\) 0 0
\(481\) 1.89920e10 0.354806
\(482\) −7.71861e10 6.17983e10i −1.43005 1.14496i
\(483\) 3.31563e10 0.609224
\(484\) −7.13124e9 3.18104e10i −0.129952 0.579679i
\(485\) 0 0
\(486\) 4.14332e10 + 3.31731e10i 0.742683 + 0.594622i
\(487\) 9.30801e10 1.65478 0.827391 0.561626i \(-0.189824\pi\)
0.827391 + 0.561626i \(0.189824\pi\)
\(488\) −2.65217e10 + 5.42656e10i −0.467651 + 0.956853i
\(489\) 5.78046e10 1.01094
\(490\) 0 0
\(491\) 2.12850e9i 0.0366225i −0.999832 0.0183113i \(-0.994171\pi\)
0.999832 0.0183113i \(-0.00582898\pi\)
\(492\) 1.20129e10 + 5.35862e10i 0.205016 + 0.914518i
\(493\) 9.37175e9i 0.158647i
\(494\) 1.33118e9 + 1.06580e9i 0.0223526 + 0.0178964i
\(495\) 0 0
\(496\) 1.90095e9 + 4.02673e9i 0.0314083 + 0.0665312i
\(497\) 1.67312e9i 0.0274221i
\(498\) 6.48464e10 + 5.19187e10i 1.05431 + 0.844124i
\(499\) 1.04101e10i 0.167901i −0.996470 0.0839503i \(-0.973246\pi\)
0.996470 0.0839503i \(-0.0267537\pi\)
\(500\) 0 0
\(501\) −4.67744e10 −0.742433
\(502\) 5.21367e10 6.51187e10i 0.820973 1.02539i
\(503\) 3.93019e10 0.613962 0.306981 0.951716i \(-0.400681\pi\)
0.306981 + 0.951716i \(0.400681\pi\)
\(504\) −8.61216e9 + 1.76212e10i −0.133472 + 0.273094i
\(505\) 0 0
\(506\) 4.38487e10 5.47670e10i 0.668890 0.835444i
\(507\) 7.85181e10 1.18833
\(508\) −1.44010e10 6.42387e10i −0.216241 0.964587i
\(509\) 3.25113e10 0.484354 0.242177 0.970232i \(-0.422139\pi\)
0.242177 + 0.970232i \(0.422139\pi\)
\(510\) 0 0
\(511\) 8.00947e9i 0.117468i
\(512\) −6.72524e10 + 1.41237e10i −0.978652 + 0.205526i
\(513\) 6.10931e9i 0.0882110i
\(514\) −6.13693e10 + 7.66503e10i −0.879223 + 1.09815i
\(515\) 0 0
\(516\) −3.31711e10 1.47967e11i −0.467908 2.08720i
\(517\) 1.40973e11i 1.97322i
\(518\) 4.85695e10 6.06633e10i 0.674598 0.842572i
\(519\) 2.06032e10i 0.283965i
\(520\) 0 0
\(521\) 1.84550e9 0.0250475 0.0125237 0.999922i \(-0.496013\pi\)
0.0125237 + 0.999922i \(0.496013\pi\)
\(522\) −5.48191e9 4.38904e9i −0.0738329 0.0591136i
\(523\) 6.23770e10 0.833715 0.416858 0.908972i \(-0.363131\pi\)
0.416858 + 0.908972i \(0.363131\pi\)
\(524\) 7.79814e10 1.74818e10i 1.03435 0.231879i
\(525\) 0 0
\(526\) −8.70448e10 6.96916e10i −1.13710 0.910411i
\(527\) 4.96614e9 0.0643838
\(528\) 5.16757e10 + 1.09463e11i 0.664892 + 1.40842i
\(529\) −2.20424e10 −0.281473
\(530\) 0 0
\(531\) 1.27524e10i 0.160404i
\(532\) 6.80863e9 1.52635e9i 0.0849988 0.0190550i
\(533\) 1.17434e10i 0.145508i
\(534\) −1.03989e11 8.32575e10i −1.27885 1.02390i
\(535\) 0 0
\(536\) −2.74400e10 + 5.61446e10i −0.332449 + 0.680219i
\(537\) 1.41797e10i 0.170518i
\(538\) 3.38130e10 + 2.70720e10i 0.403603 + 0.323141i
\(539\) 7.03905e10i 0.833986i
\(540\) 0 0
\(541\) −7.45917e10 −0.870766 −0.435383 0.900245i \(-0.643387\pi\)
−0.435383 + 0.900245i \(0.643387\pi\)
\(542\) −7.99032e10 + 9.97991e10i −0.925907 + 1.15646i
\(543\) 4.82179e10 0.554638
\(544\) −1.77755e10 + 7.45506e10i −0.202967 + 0.851246i
\(545\) 0 0
\(546\) −7.64575e9 + 9.54954e9i −0.0860299 + 0.107451i
\(547\) −1.41531e9 −0.0158089 −0.00790445 0.999969i \(-0.502516\pi\)
−0.00790445 + 0.999969i \(0.502516\pi\)
\(548\) −5.54506e10 + 1.24309e10i −0.614871 + 0.137841i
\(549\) −5.04758e10 −0.555641
\(550\) 0 0
\(551\) 2.49833e9i 0.0271046i
\(552\) −4.26295e10 + 8.72234e10i −0.459149 + 0.939457i
\(553\) 5.02383e10i 0.537198i
\(554\) −8.22965e10 + 1.02788e11i −0.873660 + 1.09120i
\(555\) 0 0
\(556\) −7.36985e10 + 1.65217e10i −0.771187 + 0.172884i
\(557\) 1.37543e11i 1.42895i −0.699661 0.714475i \(-0.746666\pi\)
0.699661 0.714475i \(-0.253334\pi\)
\(558\) −2.32578e9 + 2.90489e9i −0.0239901 + 0.0299636i
\(559\) 3.24270e10i 0.332093i
\(560\) 0 0
\(561\) 1.35000e11 1.36296
\(562\) −3.84823e10 3.08105e10i −0.385759 0.308854i
\(563\) −1.06415e11 −1.05918 −0.529589 0.848255i \(-0.677654\pi\)
−0.529589 + 0.848255i \(0.677654\pi\)
\(564\) −4.26731e10 1.90352e11i −0.421733 1.88123i
\(565\) 0 0
\(566\) −1.46273e10 1.17112e10i −0.142528 0.114113i
\(567\) 7.52431e10 0.728005
\(568\) −4.40143e9 2.15115e9i −0.0422864 0.0206670i
\(569\) −4.02429e10 −0.383919 −0.191960 0.981403i \(-0.561484\pi\)
−0.191960 + 0.981403i \(0.561484\pi\)
\(570\) 0 0
\(571\) 1.50341e11i 1.41427i 0.707077 + 0.707137i \(0.250014\pi\)
−0.707077 + 0.707137i \(0.749986\pi\)
\(572\) 5.66238e9 + 2.52583e10i 0.0528951 + 0.235950i
\(573\) 9.91667e10i 0.919914i
\(574\) 3.75103e10 + 3.00323e10i 0.345544 + 0.276657i
\(575\) 0 0
\(576\) −3.52829e10 4.53116e10i −0.320534 0.411642i
\(577\) 4.96477e9i 0.0447915i 0.999749 + 0.0223958i \(0.00712939\pi\)
−0.999749 + 0.0223958i \(0.992871\pi\)
\(578\) −2.04038e10 1.63361e10i −0.182810 0.146365i
\(579\) 1.17499e11i 1.04549i
\(580\) 0 0
\(581\) 7.26862e10 0.637892
\(582\) 1.20522e11 1.50533e11i 1.05045 1.31201i
\(583\) −1.52372e10 −0.131895
\(584\) 2.10703e10 + 1.02979e10i 0.181142 + 0.0885313i
\(585\) 0 0
\(586\) −4.80980e10 + 6.00743e10i −0.407884 + 0.509446i
\(587\) −1.53440e11 −1.29237 −0.646185 0.763181i \(-0.723637\pi\)
−0.646185 + 0.763181i \(0.723637\pi\)
\(588\) −2.13074e10 9.50461e10i −0.178246 0.795106i
\(589\) 1.32388e9 0.0109999
\(590\) 0 0
\(591\) 1.70402e11i 1.39677i
\(592\) 9.71390e10 + 2.05766e11i 0.790873 + 1.67528i
\(593\) 2.06036e11i 1.66619i −0.553131 0.833094i \(-0.686567\pi\)
0.553131 0.833094i \(-0.313433\pi\)
\(594\) 5.79601e10 7.23922e10i 0.465568 0.581495i
\(595\) 0 0
\(596\) −2.26017e10 1.00820e11i −0.179125 0.799027i
\(597\) 2.48837e11i 1.95892i
\(598\) −1.29754e10 + 1.62063e10i −0.101465 + 0.126730i
\(599\) 2.30634e11i 1.79150i 0.444558 + 0.895750i \(0.353361\pi\)
−0.444558 + 0.895750i \(0.646639\pi\)
\(600\) 0 0
\(601\) 1.01422e11 0.777382 0.388691 0.921368i \(-0.372927\pi\)
0.388691 + 0.921368i \(0.372927\pi\)
\(602\) −1.03577e11 8.29277e10i −0.788635 0.631413i
\(603\) −5.22236e10 −0.395001
\(604\) 2.09079e11 4.68711e10i 1.57095 0.352174i
\(605\) 0 0
\(606\) −3.46004e10 2.77025e10i −0.256561 0.205413i
\(607\) 1.97883e11 1.45765 0.728825 0.684700i \(-0.240067\pi\)
0.728825 + 0.684700i \(0.240067\pi\)
\(608\) −4.73860e9 + 1.98738e10i −0.0346766 + 0.145434i
\(609\) −1.79224e10 −0.130294
\(610\) 0 0
\(611\) 4.17158e10i 0.299320i
\(612\) −6.24967e10 + 1.40105e10i −0.445504 + 0.0998728i
\(613\) 1.27158e11i 0.900538i −0.892893 0.450269i \(-0.851328\pi\)
0.892893 0.450269i \(-0.148672\pi\)
\(614\) −4.36121e10 3.49176e10i −0.306855 0.245681i
\(615\) 0 0
\(616\) 9.51595e10 + 4.65082e10i 0.660890 + 0.323003i
\(617\) 5.06702e10i 0.349632i −0.984601 0.174816i \(-0.944067\pi\)
0.984601 0.174816i \(-0.0559331\pi\)
\(618\) −1.30417e11 1.04417e11i −0.894089 0.715844i
\(619\) 7.06748e10i 0.481395i 0.970600 + 0.240698i \(0.0773762\pi\)
−0.970600 + 0.240698i \(0.922624\pi\)
\(620\) 0 0
\(621\) 7.43769e10 0.500117
\(622\) −1.29807e11 + 1.62128e11i −0.867231 + 1.08317i
\(623\) −1.16561e11 −0.773748
\(624\) −1.52915e10 3.23915e10i −0.100858 0.213645i
\(625\) 0 0
\(626\) 6.31165e10 7.88325e10i 0.411004 0.513343i
\(627\) 3.59885e10 0.232859
\(628\) 6.77754e10 1.51938e10i 0.435746 0.0976853i
\(629\) 2.53771e11 1.62121
\(630\) 0 0
\(631\) 1.65273e11i 1.04252i 0.853399 + 0.521259i \(0.174537\pi\)
−0.853399 + 0.521259i \(0.825463\pi\)
\(632\) −1.32161e11 6.45921e10i −0.828388 0.404866i
\(633\) 1.46657e11i 0.913454i
\(634\) 1.65902e11 2.07211e11i 1.02682 1.28250i
\(635\) 0 0
\(636\) 2.05743e10 4.61233e9i 0.125747 0.0281898i
\(637\) 2.08294e10i 0.126508i
\(638\) −2.37021e10 + 2.96039e10i −0.143055 + 0.178676i
\(639\) 4.09405e9i 0.0245556i
\(640\) 0 0
\(641\) 1.12013e11 0.663490 0.331745 0.943369i \(-0.392363\pi\)
0.331745 + 0.943369i \(0.392363\pi\)
\(642\) 1.25209e11 + 1.00247e11i 0.737046 + 0.590109i
\(643\) −2.65913e11 −1.55559 −0.777795 0.628518i \(-0.783662\pi\)
−0.777795 + 0.628518i \(0.783662\pi\)
\(644\) 1.85824e10 + 8.28907e10i 0.108033 + 0.481906i
\(645\) 0 0
\(646\) 1.77872e10 + 1.42411e10i 0.102136 + 0.0817739i
\(647\) −2.71996e11 −1.55219 −0.776097 0.630614i \(-0.782803\pi\)
−0.776097 + 0.630614i \(0.782803\pi\)
\(648\) −9.67411e10 + 1.97940e11i −0.548670 + 1.12262i
\(649\) 6.88669e10 0.388179
\(650\) 0 0
\(651\) 9.49716e9i 0.0528774i
\(652\) 3.23965e10 + 1.44511e11i 0.179270 + 0.799672i
\(653\) 3.03789e11i 1.67078i −0.549656 0.835391i \(-0.685241\pi\)
0.549656 0.835391i \(-0.314759\pi\)
\(654\) −7.37213e10 5.90243e10i −0.402979 0.322641i
\(655\) 0 0
\(656\) −1.27233e11 + 6.00646e10i −0.687043 + 0.324342i
\(657\) 1.95988e10i 0.105189i
\(658\) −1.33247e11 1.06683e11i −0.710808 0.569102i
\(659\) 4.18575e10i 0.221938i −0.993824 0.110969i \(-0.964605\pi\)
0.993824 0.110969i \(-0.0353954\pi\)
\(660\) 0 0
\(661\) −2.46529e11 −1.29141 −0.645703 0.763589i \(-0.723435\pi\)
−0.645703 + 0.763589i \(0.723435\pi\)
\(662\) 5.48640e10 6.85251e10i 0.285664 0.356794i
\(663\) −3.99482e10 −0.206749
\(664\) −9.34537e10 + 1.91214e11i −0.480755 + 0.983665i
\(665\) 0 0
\(666\) −1.18848e11 + 1.48441e11i −0.604079 + 0.754494i
\(667\) −3.04155e10 −0.153671
\(668\) −2.62146e10 1.16936e11i −0.131655 0.587276i
\(669\) −1.47802e11 −0.737862
\(670\) 0 0
\(671\) 2.72584e11i 1.34465i
\(672\) −1.42569e11 3.39935e10i −0.699115 0.166694i
\(673\) 3.15336e11i 1.53714i 0.639767 + 0.768569i \(0.279031\pi\)
−0.639767 + 0.768569i \(0.720969\pi\)
\(674\) −3.56226e9 + 4.44927e9i −0.0172618 + 0.0215600i
\(675\) 0 0
\(676\) 4.40053e10 + 1.96295e11i 0.210726 + 0.939989i
\(677\) 2.47236e10i 0.117695i −0.998267 0.0588475i \(-0.981257\pi\)
0.998267 0.0588475i \(-0.0187426\pi\)
\(678\) −5.50408e10 + 6.87460e10i −0.260475 + 0.325333i
\(679\) 1.68731e11i 0.793811i
\(680\) 0 0
\(681\) 7.49454e10 0.348463
\(682\) 1.56873e10 + 1.25599e10i 0.0725120 + 0.0580561i
\(683\) 7.20843e10 0.331251 0.165626 0.986189i \(-0.447036\pi\)
0.165626 + 0.986189i \(0.447036\pi\)
\(684\) −1.66604e10 + 3.73492e9i −0.0761135 + 0.0170631i
\(685\) 0 0
\(686\) −1.67255e11 1.33911e11i −0.755235 0.604672i
\(687\) 2.84556e11 1.27744
\(688\) 3.51326e11 1.65855e11i 1.56804 0.740246i
\(689\) 4.50887e9 0.0200074
\(690\) 0 0
\(691\) 2.95424e11i 1.29578i −0.761732 0.647892i \(-0.775651\pi\)
0.761732 0.647892i \(-0.224349\pi\)
\(692\) −5.15080e10 + 1.15470e10i −0.224621 + 0.0503554i
\(693\) 8.85139e10i 0.383776i
\(694\) −1.99503e11 1.59731e11i −0.860028 0.688573i
\(695\) 0 0
\(696\) 2.30430e10 4.71479e10i 0.0981980 0.200921i
\(697\) 1.56916e11i 0.664867i
\(698\) 1.29438e11 + 1.03634e11i 0.545308 + 0.436596i
\(699\) 2.20444e10i 0.0923400i
\(700\) 0 0
\(701\) −2.87925e11 −1.19236 −0.596180 0.802851i \(-0.703315\pi\)
−0.596180 + 0.802851i \(0.703315\pi\)
\(702\) −1.71511e10 + 2.14217e10i −0.0706227 + 0.0882077i
\(703\) 6.76504e10 0.276980
\(704\) −2.44696e11 + 1.90538e11i −0.996176 + 0.775694i
\(705\) 0 0
\(706\) 1.30979e11 1.63593e11i 0.527210 0.658485i
\(707\) −3.87834e10 −0.155227
\(708\) −9.29889e10 + 2.08462e10i −0.370082 + 0.0829648i
\(709\) −2.51685e11 −0.996030 −0.498015 0.867168i \(-0.665938\pi\)
−0.498015 + 0.867168i \(0.665938\pi\)
\(710\) 0 0
\(711\) 1.22931e11i 0.481042i
\(712\) 1.49864e11 3.06633e11i 0.583144 1.19316i
\(713\) 1.61174e10i 0.0623643i
\(714\) −1.02162e11 + 1.27601e11i −0.393095 + 0.490976i
\(715\) 0 0
\(716\) 3.54493e10 7.94701e9i 0.134883 0.0302379i
\(717\) 4.04170e11i 1.52928i
\(718\) −3.31454e10 + 4.13986e10i −0.124717 + 0.155772i
\(719\) 1.38856e11i 0.519574i 0.965666 + 0.259787i \(0.0836524\pi\)
−0.965666 + 0.259787i \(0.916348\pi\)
\(720\) 0 0
\(721\) −1.46184e11 −0.540953
\(722\) −2.07383e11 1.66039e11i −0.763175 0.611029i
\(723\) 6.17489e11 2.25983
\(724\) 2.70237e10 + 1.20545e11i 0.0983536 + 0.438727i
\(725\) 0 0
\(726\) 1.58925e11 + 1.27242e11i 0.572064 + 0.458018i
\(727\) 1.79083e11 0.641088 0.320544 0.947234i \(-0.396134\pi\)
0.320544 + 0.947234i \(0.396134\pi\)
\(728\) −2.81589e10 1.37623e10i −0.100251 0.0489967i
\(729\) 2.14381e10 0.0759061
\(730\) 0 0
\(731\) 4.33289e11i 1.51743i
\(732\) −8.25119e10 3.68062e11i −0.287391 1.28197i
\(733\) 2.17618e11i 0.753839i −0.926246 0.376920i \(-0.876983\pi\)
0.926246 0.376920i \(-0.123017\pi\)
\(734\) 2.45588e11 + 1.96628e11i 0.846101 + 0.677423i
\(735\) 0 0
\(736\) −2.41950e11 5.76895e10i −0.824546 0.196601i
\(737\) 2.82023e11i 0.955904i
\(738\) −9.17862e10 7.34878e10i −0.309423 0.247736i
\(739\) 4.84950e11i 1.62599i −0.582268 0.812997i \(-0.697834\pi\)
0.582268 0.812997i \(-0.302166\pi\)
\(740\) 0 0
\(741\) −1.06494e10 −0.0353227
\(742\) 1.15308e10 1.44020e10i 0.0380404 0.0475124i
\(743\) 2.03509e11 0.667771 0.333886 0.942614i \(-0.391640\pi\)
0.333886 + 0.942614i \(0.391640\pi\)
\(744\) −2.49840e10 1.22106e10i −0.0815398 0.0398517i
\(745\) 0 0
\(746\) 2.10063e11 2.62369e11i 0.678258 0.847144i
\(747\) −1.77860e11 −0.571210
\(748\) 7.56606e10 + 3.37500e11i 0.241693 + 1.07812i
\(749\) 1.40346e11 0.445937
\(750\) 0 0
\(751\) 2.34693e11i 0.737804i 0.929468 + 0.368902i \(0.120266\pi\)
−0.929468 + 0.368902i \(0.879734\pi\)
\(752\) 4.51965e11 2.13365e11i 1.41330 0.667194i
\(753\) 5.20950e11i 1.62038i
\(754\) 7.01374e9 8.76016e9i 0.0217002 0.0271036i
\(755\) 0 0
\(756\) 2.45626e10 + 1.09567e11i 0.0751946 + 0.335421i
\(757\) 3.84882e11i 1.17204i −0.810295 0.586022i \(-0.800693\pi\)
0.810295 0.586022i \(-0.199307\pi\)
\(758\) −3.04816e10 + 3.80715e10i −0.0923338 + 0.115325i
\(759\) 4.38136e11i 1.32021i
\(760\) 0 0
\(761\) 2.39209e11 0.713244 0.356622 0.934249i \(-0.383928\pi\)
0.356622 + 0.934249i \(0.383928\pi\)
\(762\) 3.20936e11 + 2.56955e11i 0.951916 + 0.762143i
\(763\) −8.26340e10 −0.243815
\(764\) −2.47917e11 + 5.55778e10i −0.727666 + 0.163128i
\(765\) 0 0
\(766\) 2.78972e11 + 2.23357e11i 0.810301 + 0.648760i
\(767\) −2.03786e10 −0.0588833
\(768\) 2.72729e11 3.31347e11i 0.783947 0.952442i