Properties

Label 100.9.b.c.51.2
Level $100$
Weight $9$
Character 100.51
Analytic conductor $40.738$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [100,9,Mod(51,100)]
 
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, 0]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("100.51");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 100 = 2^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 100.b (of order \(2\), degree \(1\), 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: \(2\)
Coefficient field: \(\Q(\sqrt{-39}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 4)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 51.2
Root \(0.500000 - 3.12250i\) of defining polynomial
Character \(\chi\) \(=\) 100.51
Dual form 100.9.b.c.51.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(10.0000 + 12.4900i) q^{2} +99.9200i q^{3} +(-56.0000 + 249.800i) q^{4} +(-1248.00 + 999.200i) q^{6} +1398.88i q^{7} +(-3680.00 + 1798.56i) q^{8} -3423.00 q^{9} +O(q^{10})\) \(q+(10.0000 + 12.4900i) q^{2} +99.9200i q^{3} +(-56.0000 + 249.800i) q^{4} +(-1248.00 + 999.200i) q^{6} +1398.88i q^{7} +(-3680.00 + 1798.56i) q^{8} -3423.00 q^{9} +18485.2i q^{11} +(-24960.0 - 5595.52i) q^{12} +5470.00 q^{13} +(-17472.0 + 13988.8i) q^{14} +(-59264.0 - 27977.6i) q^{16} -73090.0 q^{17} +(-34230.0 - 42753.3i) q^{18} +19484.4i q^{19} -139776. q^{21} +(-230880. + 184852. i) q^{22} -237210. i q^{23} +(-179712. - 367705. i) q^{24} +(54700.0 + 68320.3i) q^{26} +313549. i q^{27} +(-349440. - 78337.3i) q^{28} -128222. q^{29} +67945.6i q^{31} +(-243200. - 1.01998e6i) q^{32} -1.84704e6 q^{33} +(-730900. - 912894. i) q^{34} +(191688. - 855065. i) q^{36} +3.47203e6 q^{37} +(-243360. + 194844. i) q^{38} +546562. i q^{39} +2.14688e6 q^{41} +(-1.39776e6 - 1.74580e6i) q^{42} -5.92815e6i q^{43} +(-4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 - 2.37210e6i) q^{46} +7.62629e6i q^{47} +(2.79552e6 - 5.92166e6i) q^{48} +3.80794e6 q^{49} -7.30315e6i q^{51} +(-306320. + 1.36641e6i) q^{52} -824290. q^{53} +(-3.91622e6 + 3.13549e6i) q^{54} +(-2.51597e6 - 5.14788e6i) q^{56} -1.94688e6 q^{57} +(-1.28222e6 - 1.60149e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(-848640. + 679456. i) q^{62} -4.78836e6i q^{63} +(1.03076e7 - 1.32374e7i) q^{64} +(-1.84704e7 - 2.30695e7i) q^{66} +1.52567e7i q^{67} +(4.09304e6 - 1.82579e7i) q^{68} +2.37020e7 q^{69} +1.19604e6i q^{71} +(1.25966e7 - 6.15647e6i) q^{72} +5.72563e6 q^{73} +(3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 - 1.09113e6i) q^{76} -2.58586e7 q^{77} +(-6.82656e6 + 5.46562e6i) q^{78} -3.59132e7i q^{79} -5.37881e7 q^{81} +(2.14688e7 + 2.68145e7i) q^{82} -5.19603e7i q^{83} +(7.82746e6 - 3.49160e7i) q^{84} +(7.40426e7 - 5.92815e7i) q^{86} -1.28119e7i q^{87} +(-3.32467e7 - 6.80255e7i) q^{88} -8.33242e7 q^{89} +7.65187e6i q^{91} +(5.92550e7 + 1.32838e7i) q^{92} -6.78912e6 q^{93} +(-9.52524e7 + 7.62629e7i) q^{94} +(1.01917e8 - 2.43005e7i) q^{96} -1.20619e8 q^{97} +(3.80794e7 + 4.75611e7i) q^{98} -6.32748e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 20 q^{2} - 112 q^{4} - 2496 q^{6} - 7360 q^{8} - 6846 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 20 q^{2} - 112 q^{4} - 2496 q^{6} - 7360 q^{8} - 6846 q^{9} - 49920 q^{12} + 10940 q^{13} - 34944 q^{14} - 118528 q^{16} - 146180 q^{17} - 68460 q^{18} - 279552 q^{21} - 461760 q^{22} - 359424 q^{24} + 109400 q^{26} - 698880 q^{28} - 256444 q^{29} - 486400 q^{32} - 3694080 q^{33} - 1461800 q^{34} + 383376 q^{36} + 6944060 q^{37} - 486720 q^{38} + 4293764 q^{41} - 2795520 q^{42} - 9235200 q^{44} + 5925504 q^{46} + 5591040 q^{48} + 7615874 q^{49} - 612640 q^{52} - 1648580 q^{53} - 7832448 q^{54} - 5031936 q^{56} - 3893760 q^{57} - 2564440 q^{58} - 29492156 q^{61} - 1697280 q^{62} + 20615168 q^{64} - 36940800 q^{66} + 8186080 q^{68} + 47404032 q^{69} + 25193280 q^{72} + 11451260 q^{73} + 69440600 q^{74} - 9734400 q^{76} - 51717120 q^{77} - 13653120 q^{78} - 107576190 q^{81} + 42937640 q^{82} + 15654912 q^{84} + 148085184 q^{86} - 66493440 q^{88} - 166648444 q^{89} + 118510080 q^{92} - 13578240 q^{93} - 190504704 q^{94} + 203833344 q^{96} - 241238020 q^{97} + 76158740 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.0000 + 12.4900i 0.625000 + 0.780625i
\(3\) 99.9200i 1.23358i 0.787128 + 0.616790i \(0.211567\pi\)
−0.787128 + 0.616790i \(0.788433\pi\)
\(4\) −56.0000 + 249.800i −0.218750 + 0.975781i
\(5\) 0 0
\(6\) −1248.00 + 999.200i −0.962963 + 0.770987i
\(7\) 1398.88i 0.582624i 0.956628 + 0.291312i \(0.0940917\pi\)
−0.956628 + 0.291312i \(0.905908\pi\)
\(8\) −3680.00 + 1798.56i −0.898438 + 0.439101i
\(9\) −3423.00 −0.521719
\(10\) 0 0
\(11\) 18485.2i 1.26256i 0.775554 + 0.631282i \(0.217471\pi\)
−0.775554 + 0.631282i \(0.782529\pi\)
\(12\) −24960.0 5595.52i −1.20370 0.269846i
\(13\) 5470.00 0.191520 0.0957600 0.995404i \(-0.469472\pi\)
0.0957600 + 0.995404i \(0.469472\pi\)
\(14\) −17472.0 + 13988.8i −0.454810 + 0.364140i
\(15\) 0 0
\(16\) −59264.0 27977.6i −0.904297 0.426904i
\(17\) −73090.0 −0.875109 −0.437555 0.899192i \(-0.644155\pi\)
−0.437555 + 0.899192i \(0.644155\pi\)
\(18\) −34230.0 42753.3i −0.326075 0.407267i
\(19\) 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
\(22\) −230880. + 184852.i −0.985588 + 0.789102i
\(23\) 237210.i 0.847660i −0.905742 0.423830i \(-0.860685\pi\)
0.905742 0.423830i \(-0.139315\pi\)
\(24\) −179712. 367705.i −0.541667 1.10829i
\(25\) 0 0
\(26\) 54700.0 + 68320.3i 0.119700 + 0.149505i
\(27\) 313549.i 0.589997i
\(28\) −349440. 78337.3i −0.568513 0.127449i
\(29\) −128222. −0.181289 −0.0906443 0.995883i \(-0.528893\pi\)
−0.0906443 + 0.995883i \(0.528893\pi\)
\(30\) 0 0
\(31\) 67945.6i 0.0735723i 0.999323 + 0.0367862i \(0.0117120\pi\)
−0.999323 + 0.0367862i \(0.988288\pi\)
\(32\) −243200. 1.01998e6i −0.231934 0.972732i
\(33\) −1.84704e6 −1.55747
\(34\) −730900. 912894.i −0.546943 0.683132i
\(35\) 0 0
\(36\) 191688. 855065.i 0.114126 0.509084i
\(37\) 3.47203e6 1.85258 0.926289 0.376813i \(-0.122980\pi\)
0.926289 + 0.376813i \(0.122980\pi\)
\(38\) −243360. + 194844.i −0.116712 + 0.0934442i
\(39\) 546562.i 0.236255i
\(40\) 0 0
\(41\) 2.14688e6 0.759754 0.379877 0.925037i \(-0.375966\pi\)
0.379877 + 0.925037i \(0.375966\pi\)
\(42\) −1.39776e6 1.74580e6i −0.449196 0.561045i
\(43\) 5.92815e6i 1.73399i −0.498321 0.866993i \(-0.666050\pi\)
0.498321 0.866993i \(-0.333950\pi\)
\(44\) −4.61760e6 1.03517e6i −1.23199 0.276186i
\(45\) 0 0
\(46\) 2.96275e6 2.37210e6i 0.661704 0.529787i
\(47\) 7.62629e6i 1.56287i 0.623989 + 0.781433i \(0.285511\pi\)
−0.623989 + 0.781433i \(0.714489\pi\)
\(48\) 2.79552e6 5.92166e6i 0.526620 1.11552i
\(49\) 3.80794e6 0.660550
\(50\) 0 0
\(51\) 7.30315e6i 1.07952i
\(52\) −306320. + 1.36641e6i −0.0418950 + 0.186881i
\(53\) −824290. −0.104466 −0.0522332 0.998635i \(-0.516634\pi\)
−0.0522332 + 0.998635i \(0.516634\pi\)
\(54\) −3.91622e6 + 3.13549e6i −0.460567 + 0.368748i
\(55\) 0 0
\(56\) −2.51597e6 5.14788e6i −0.255831 0.523451i
\(57\) −1.94688e6 −0.184433
\(58\) −1.28222e6 1.60149e6i −0.113305 0.141518i
\(59\) 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 \(0.678751\pi\)
\(62\) −848640. + 679456.i −0.0574324 + 0.0459827i
\(63\) 4.78836e6i 0.303966i
\(64\) 1.03076e7 1.32374e7i 0.614380 0.789010i
\(65\) 0 0
\(66\) −1.84704e7 2.30695e7i −0.973421 1.21580i
\(67\) 1.52567e7i 0.757113i 0.925578 + 0.378557i \(0.123579\pi\)
−0.925578 + 0.378557i \(0.876421\pi\)
\(68\) 4.09304e6 1.82579e7i 0.191430 0.853915i
\(69\) 2.37020e7 1.04566
\(70\) 0 0
\(71\) 1.19604e6i 0.0470666i 0.999723 + 0.0235333i \(0.00749158\pi\)
−0.999723 + 0.0235333i \(0.992508\pi\)
\(72\) 1.25966e7 6.15647e6i 0.468732 0.229088i
\(73\) 5.72563e6 0.201619 0.100810 0.994906i \(-0.467857\pi\)
0.100810 + 0.994906i \(0.467857\pi\)
\(74\) 3.47203e7 + 4.33656e7i 1.15786 + 1.44617i
\(75\) 0 0
\(76\) −4.86720e6 1.09113e6i −0.145890 0.0327055i
\(77\) −2.58586e7 −0.735600
\(78\) −6.82656e6 + 5.46562e6i −0.184427 + 0.147659i
\(79\) 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
\(82\) 2.14688e7 + 2.68145e7i 0.474846 + 0.593082i
\(83\) 5.19603e7i 1.09486i −0.836851 0.547431i \(-0.815606\pi\)
0.836851 0.547431i \(-0.184394\pi\)
\(84\) 7.82746e6 3.49160e7i 0.157218 0.701306i
\(85\) 0 0
\(86\) 7.40426e7 5.92815e7i 1.35359 1.08374i
\(87\) 1.28119e7i 0.223634i
\(88\) −3.32467e7 6.80255e7i −0.554393 1.13433i
\(89\) −8.33242e7 −1.32804 −0.664020 0.747715i \(-0.731151\pi\)
−0.664020 + 0.747715i \(0.731151\pi\)
\(90\) 0 0
\(91\) 7.65187e6i 0.111584i
\(92\) 5.92550e7 + 1.32838e7i 0.827130 + 0.185426i
\(93\) −6.78912e6 −0.0907573
\(94\) −9.52524e7 + 7.62629e7i −1.22001 + 0.976792i
\(95\) 0 0
\(96\) 1.01917e8 2.43005e7i 1.19994 0.286109i
\(97\) −1.20619e8 −1.36248 −0.681238 0.732062i \(-0.738558\pi\)
−0.681238 + 0.732062i \(0.738558\pi\)
\(98\) 3.80794e7 + 4.75611e7i 0.412844 + 0.515641i
\(99\) 6.32748e7i 0.658704i
\(100\) 0 0
\(101\) 2.77246e7 0.266428 0.133214 0.991087i \(-0.457470\pi\)
0.133214 + 0.991087i \(0.457470\pi\)
\(102\) 9.12163e7 7.30315e7i 0.842698 0.674698i
\(103\) 1.04501e8i 0.928477i 0.885710 + 0.464238i \(0.153672\pi\)
−0.885710 + 0.464238i \(0.846328\pi\)
\(104\) −2.01296e7 + 9.83812e6i −0.172069 + 0.0840967i
\(105\) 0 0
\(106\) −8.24290e6 1.02954e7i −0.0652915 0.0815490i
\(107\) 1.00328e8i 0.765394i 0.923874 + 0.382697i \(0.125005\pi\)
−0.923874 + 0.382697i \(0.874995\pi\)
\(108\) −7.83245e7 1.75587e7i −0.575708 0.129062i
\(109\) −5.90716e7 −0.418478 −0.209239 0.977865i \(-0.567099\pi\)
−0.209239 + 0.977865i \(0.567099\pi\)
\(110\) 0 0
\(111\) 3.46925e8i 2.28530i
\(112\) 3.91373e7 8.29032e7i 0.248724 0.526865i
\(113\) −5.50849e7 −0.337846 −0.168923 0.985629i \(-0.554029\pi\)
−0.168923 + 0.985629i \(0.554029\pi\)
\(114\) −1.94688e7 2.43165e7i −0.115271 0.143973i
\(115\) 0 0
\(116\) 7.18043e6 3.20298e7i 0.0396569 0.176898i
\(117\) −1.87238e7 −0.0999196
\(118\) −4.65317e7 + 3.72552e7i −0.240005 + 0.192158i
\(119\) 1.02244e8i 0.509859i
\(120\) 0 0
\(121\) −1.27344e8 −0.594067
\(122\) −1.47461e8 1.84178e8i −0.665637 0.831380i
\(123\) 2.14516e8i 0.937217i
\(124\) −1.69728e7 3.80495e6i −0.0717905 0.0160939i
\(125\) 0 0
\(126\) 5.98067e7 4.78836e7i 0.237283 0.189979i
\(127\) 2.57160e8i 0.988529i 0.869312 + 0.494264i \(0.164562\pi\)
−0.869312 + 0.494264i \(0.835438\pi\)
\(128\) 2.68411e8 3.63229e6i 0.999908 0.0135313i
\(129\) 5.92341e8 2.13901
\(130\) 0 0
\(131\) 3.12175e8i 1.06002i 0.847992 + 0.530009i \(0.177812\pi\)
−0.847992 + 0.530009i \(0.822188\pi\)
\(132\) 1.03434e8 4.61390e8i 0.340697 1.51975i
\(133\) −2.72563e7 −0.0871085
\(134\) −1.90556e8 + 1.52567e8i −0.591021 + 0.473196i
\(135\) 0 0
\(136\) 2.68971e8 1.31457e8i 0.786231 0.384262i
\(137\) −2.21980e8 −0.630132 −0.315066 0.949070i \(-0.602027\pi\)
−0.315066 + 0.949070i \(0.602027\pi\)
\(138\) 2.37020e8 + 2.96038e8i 0.653535 + 0.816265i
\(139\) 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
\(142\) −1.49386e7 + 1.19604e7i −0.0367414 + 0.0294166i
\(143\) 1.01114e8i 0.241806i
\(144\) 2.02861e8 + 9.57673e7i 0.471789 + 0.222724i
\(145\) 0 0
\(146\) 5.72563e7 + 7.15131e7i 0.126012 + 0.157389i
\(147\) 3.80489e8i 0.814841i
\(148\) −1.94434e8 + 8.67313e8i −0.405252 + 1.80771i
\(149\) 4.03603e8 0.818859 0.409429 0.912342i \(-0.365728\pi\)
0.409429 + 0.912342i \(0.365728\pi\)
\(150\) 0 0
\(151\) 8.36985e8i 1.60994i 0.593316 + 0.804970i \(0.297819\pi\)
−0.593316 + 0.804970i \(0.702181\pi\)
\(152\) −3.50438e7 7.17026e7i −0.0656504 0.134326i
\(153\) 2.50187e8 0.456561
\(154\) −2.58586e8 3.22973e8i −0.459750 0.574227i
\(155\) 0 0
\(156\) −1.36531e8 3.06075e7i −0.230533 0.0516808i
\(157\) 2.71319e8 0.446561 0.223281 0.974754i \(-0.428323\pi\)
0.223281 + 0.974754i \(0.428323\pi\)
\(158\) 4.48556e8 3.59132e8i 0.719761 0.576270i
\(159\) 8.23630e7i 0.128868i
\(160\) 0 0
\(161\) 3.31828e8 0.493867
\(162\) −5.37881e8 6.71813e8i −0.780955 0.975413i
\(163\) 5.78509e8i 0.819520i 0.912193 + 0.409760i \(0.134388\pi\)
−0.912193 + 0.409760i \(0.865612\pi\)
\(164\) −1.20225e8 + 5.36291e8i −0.166196 + 0.741353i
\(165\) 0 0
\(166\) 6.48984e8 5.19603e8i 0.854676 0.684288i
\(167\) 4.68118e8i 0.601852i 0.953647 + 0.300926i \(0.0972958\pi\)
−0.953647 + 0.300926i \(0.902704\pi\)
\(168\) 5.14376e8 2.51395e8i 0.645719 0.315588i
\(169\) −7.85810e8 −0.963320
\(170\) 0 0
\(171\) 6.66951e7i 0.0780026i
\(172\) 1.48085e9 + 3.31976e8i 1.69199 + 0.379309i
\(173\) 2.06197e8 0.230196 0.115098 0.993354i \(-0.463282\pi\)
0.115098 + 0.993354i \(0.463282\pi\)
\(174\) 1.60021e8 1.28119e8i 0.174574 0.139771i
\(175\) 0 0
\(176\) 5.17171e8 1.09551e9i 0.538994 1.14173i
\(177\) −3.72253e8 −0.379268
\(178\) −8.33242e8 1.04072e9i −0.830025 1.03670i
\(179\) 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 \(0.427824\pi\)
\(182\) −9.55718e7 + 7.65187e7i −0.0871053 + 0.0697400i
\(183\) 1.47343e9i 1.31379i
\(184\) 4.26636e8 + 8.72933e8i 0.372209 + 0.761569i
\(185\) 0 0
\(186\) −6.78912e7 8.47961e7i −0.0567233 0.0708474i
\(187\) 1.35108e9i 1.10488i
\(188\) −1.90505e9 4.27072e8i −1.52502 0.341877i
\(189\) −4.38617e8 −0.343747
\(190\) 0 0
\(191\) 9.92461e8i 0.745727i −0.927886 0.372864i \(-0.878376\pi\)
0.927886 0.372864i \(-0.121624\pi\)
\(192\) 1.32268e9 + 1.02993e9i 0.973307 + 0.757887i
\(193\) −1.17593e9 −0.847526 −0.423763 0.905773i \(-0.639291\pi\)
−0.423763 + 0.905773i \(0.639291\pi\)
\(194\) −1.20619e9 1.50653e9i −0.851547 1.06358i
\(195\) 0 0
\(196\) −2.13244e8 + 9.51222e8i −0.144495 + 0.644552i
\(197\) −1.70538e9 −1.13229 −0.566144 0.824306i \(-0.691565\pi\)
−0.566144 + 0.824306i \(0.691565\pi\)
\(198\) 7.90302e8 6.32748e8i 0.514200 0.411690i
\(199\) 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
\(202\) 2.77246e8 + 3.46281e8i 0.166518 + 0.207981i
\(203\) 1.79367e8i 0.105623i
\(204\) 1.82433e9 + 4.08976e8i 1.05337 + 0.236144i
\(205\) 0 0
\(206\) −1.30522e9 + 1.04501e9i −0.724792 + 0.580298i
\(207\) 8.11970e8i 0.442241i
\(208\) −3.24174e8 1.53037e8i −0.173191 0.0817606i
\(209\) −3.60173e8 −0.188767
\(210\) 0 0
\(211\) 1.46774e9i 0.740491i −0.928934 0.370245i \(-0.879274\pi\)
0.928934 0.370245i \(-0.120726\pi\)
\(212\) 4.61602e7 2.05908e8i 0.0228520 0.101936i
\(213\) −1.19508e8 −0.0580604
\(214\) −1.25309e9 + 1.00328e9i −0.597486 + 0.478371i
\(215\) 0 0
\(216\) −5.63936e8 1.15386e9i −0.259069 0.530076i
\(217\) −9.50477e7 −0.0428650
\(218\) −5.90716e8 7.37804e8i −0.261549 0.326674i
\(219\) 5.72105e8i 0.248713i
\(220\) 0 0
\(221\) −3.99802e8 −0.167601
\(222\) −4.33309e9 + 3.46925e9i −1.78396 + 1.42831i
\(223\) 1.47920e9i 0.598147i −0.954230 0.299073i \(-0.903322\pi\)
0.954230 0.299073i \(-0.0966776\pi\)
\(224\) 1.42683e9 3.40208e8i 0.566737 0.135130i
\(225\) 0 0
\(226\) −5.50849e8 6.88011e8i −0.211154 0.263731i
\(227\) 7.50054e8i 0.282481i −0.989975 0.141241i \(-0.954891\pi\)
0.989975 0.141241i \(-0.0451091\pi\)
\(228\) 1.09025e8 4.86330e8i 0.0403448 0.179967i
\(229\) −2.84784e9 −1.03556 −0.517778 0.855515i \(-0.673241\pi\)
−0.517778 + 0.855515i \(0.673241\pi\)
\(230\) 0 0
\(231\) 2.58379e9i 0.907421i
\(232\) 4.71857e8 2.30615e8i 0.162876 0.0796041i
\(233\) −2.20621e8 −0.0748553 −0.0374276 0.999299i \(-0.511916\pi\)
−0.0374276 + 0.999299i \(0.511916\pi\)
\(234\) −1.87238e8 2.33860e8i −0.0624498 0.0779997i
\(235\) 0 0
\(236\) −9.30634e8 2.08629e8i −0.300007 0.0672553i
\(237\) 3.58845e9 1.13740
\(238\) 1.27703e9 1.02244e9i 0.398009 0.318662i
\(239\) 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 \(0.131427\pi\)
\(242\) −1.27344e9 1.59052e9i −0.371292 0.463743i
\(243\) 3.31731e9i 0.951395i
\(244\) 8.25780e8 3.68357e9i 0.232973 1.03922i
\(245\) 0 0
\(246\) −2.67931e9 + 2.14516e9i −0.731615 + 0.585760i
\(247\) 1.06580e8i 0.0286343i
\(248\) −1.22204e8 2.50040e8i −0.0323057 0.0661001i
\(249\) 5.19187e9 1.35060
\(250\) 0 0
\(251\) 5.21367e9i 1.31356i −0.754084 0.656778i \(-0.771919\pi\)
0.754084 0.656778i \(-0.228081\pi\)
\(252\) 1.19613e9 + 2.68148e8i 0.296604 + 0.0664926i
\(253\) 4.38487e9 1.07022
\(254\) −3.21193e9 + 2.57160e9i −0.771670 + 0.617830i
\(255\) 0 0
\(256\) 2.72948e9 + 3.31613e9i 0.635506 + 0.772096i
\(257\) 6.13693e9 1.40676 0.703378 0.710816i \(-0.251674\pi\)
0.703378 + 0.710816i \(0.251674\pi\)
\(258\) 5.92341e9 + 7.39833e9i 1.33688 + 1.66976i
\(259\) 4.85695e9i 1.07936i
\(260\) 0 0
\(261\) 4.38904e8 0.0945818
\(262\) −3.89907e9 + 3.12175e9i −0.827477 + 0.662512i
\(263\) 6.96916e9i 1.45666i 0.685228 + 0.728329i \(0.259703\pi\)
−0.685228 + 0.728329i \(0.740297\pi\)
\(264\) 6.79711e9 3.32201e9i 1.39929 0.683889i
\(265\) 0 0
\(266\) −2.72563e8 3.40431e8i −0.0544428 0.0679991i
\(267\) 8.32575e9i 1.63824i
\(268\) −3.81112e9 8.54374e8i −0.738777 0.165619i
\(269\) 2.70720e9 0.517025 0.258513 0.966008i \(-0.416768\pi\)
0.258513 + 0.966008i \(0.416768\pi\)
\(270\) 0 0
\(271\) 7.99032e9i 1.48145i 0.671808 + 0.740725i \(0.265518\pi\)
−0.671808 + 0.740725i \(0.734482\pi\)
\(272\) 4.33161e9 + 2.04488e9i 0.791359 + 0.373588i
\(273\) −7.64575e8 −0.137648
\(274\) −2.21980e9 2.77253e9i −0.393832 0.491897i
\(275\) 0 0
\(276\) −1.32731e9 + 5.92076e9i −0.228737 + 1.02033i
\(277\) 8.22965e9 1.39786 0.698928 0.715192i \(-0.253661\pi\)
0.698928 + 0.715192i \(0.253661\pi\)
\(278\) −3.68493e9 + 2.95030e9i −0.616949 + 0.493955i
\(279\) 2.32578e8i 0.0383841i
\(280\) 0 0
\(281\) 3.08105e9 0.494167 0.247083 0.968994i \(-0.420528\pi\)
0.247083 + 0.968994i \(0.420528\pi\)
\(282\) −7.62019e9 9.51761e9i −1.20495 1.50498i
\(283\) 1.17112e9i 0.182582i 0.995824 + 0.0912908i \(0.0290993\pi\)
−0.995824 + 0.0912908i \(0.970901\pi\)
\(284\) −2.98771e8 6.69784e7i −0.0459267 0.0102958i
\(285\) 0 0
\(286\) −1.26291e9 + 1.01114e9i −0.188760 + 0.151129i
\(287\) 3.00323e9i 0.442650i
\(288\) 8.32474e8 + 3.49140e9i 0.121004 + 0.507493i
\(289\) −1.63361e9 −0.234184
\(290\) 0 0
\(291\) 1.20522e10i 1.68072i
\(292\) −3.20635e8 + 1.43026e9i −0.0441042 + 0.196736i
\(293\) −4.80980e9 −0.652614 −0.326307 0.945264i \(-0.605804\pi\)
−0.326307 + 0.945264i \(0.605804\pi\)
\(294\) −4.75231e9 + 3.80489e9i −0.636085 + 0.509275i
\(295\) 0 0
\(296\) −1.27771e10 + 6.24465e9i −1.66443 + 0.813470i
\(297\) −5.79601e9 −0.744909
\(298\) 4.03603e9 + 5.04100e9i 0.511787 + 0.639221i
\(299\) 1.29754e9i 0.162344i
\(300\) 0 0
\(301\) 8.29277e9 1.01026
\(302\) −1.04539e10 + 8.36985e9i −1.25676 + 1.00621i
\(303\) 2.77025e9i 0.328661i
\(304\) 5.45126e8 1.15472e9i 0.0638268 0.135202i
\(305\) 0 0
\(306\) 2.50187e9 + 3.12484e9i 0.285351 + 0.356403i
\(307\) 3.49176e9i 0.393089i −0.980495 0.196545i \(-0.937028\pi\)
0.980495 0.196545i \(-0.0629721\pi\)
\(308\) 1.44808e9 6.45947e9i 0.160912 0.717784i
\(309\) −1.04417e10 −1.14535
\(310\) 0 0
\(311\) 1.29807e10i 1.38757i 0.720182 + 0.693785i \(0.244058\pi\)
−0.720182 + 0.693785i \(0.755942\pi\)
\(312\) −9.83025e8 2.01135e9i −0.103740 0.212260i
\(313\) 6.31165e9 0.657606 0.328803 0.944399i \(-0.393355\pi\)
0.328803 + 0.944399i \(0.393355\pi\)
\(314\) 2.71319e9 + 3.38877e9i 0.279101 + 0.348597i
\(315\) 0 0
\(316\) 8.97112e9 + 2.01114e9i 0.899702 + 0.201695i
\(317\) −1.65902e10 −1.64291 −0.821455 0.570273i \(-0.806837\pi\)
−0.821455 + 0.570273i \(0.806837\pi\)
\(318\) 1.02871e9 8.23630e8i 0.100597 0.0805423i
\(319\) 2.37021e9i 0.228888i
\(320\) 0 0
\(321\) −1.00247e10 −0.944175
\(322\) 3.31828e9 + 4.14453e9i 0.308667 + 0.385525i
\(323\) 1.42411e9i 0.130838i
\(324\) 3.01213e9 1.34363e10i 0.273334 1.21927i
\(325\) 0 0
\(326\) −7.22557e9 + 5.78509e9i −0.639738 + 0.512200i
\(327\) 5.90243e9i 0.516226i
\(328\) −7.90053e9 + 3.86129e9i −0.682591 + 0.333609i
\(329\) −1.06683e10 −0.910563
\(330\) 0 0
\(331\) 5.48640e9i 0.457062i −0.973537 0.228531i \(-0.926608\pi\)
0.973537 0.228531i \(-0.0733922\pi\)
\(332\) 1.29797e10 + 2.90978e9i 1.06834 + 0.239501i
\(333\) −1.18848e10 −0.966526
\(334\) −5.84680e9 + 4.68118e9i −0.469821 + 0.376158i
\(335\) 0 0
\(336\) 8.28368e9 + 3.91060e9i 0.649930 + 0.306822i
\(337\) 3.56226e8 0.0276189 0.0138095 0.999905i \(-0.495604\pi\)
0.0138095 + 0.999905i \(0.495604\pi\)
\(338\) −7.85810e9 9.81476e9i −0.602075 0.751992i
\(339\) 5.50408e9i 0.416760i
\(340\) 0 0
\(341\) −1.25599e9 −0.0928897
\(342\) 8.33021e8 6.66951e8i 0.0608908 0.0487517i
\(343\) 1.33911e10i 0.967476i
\(344\) 1.06621e10 + 2.18156e10i 0.761396 + 1.55788i
\(345\) 0 0
\(346\) 2.06197e9 + 2.57540e9i 0.143872 + 0.179697i
\(347\) 1.59731e10i 1.10172i −0.834599 0.550859i \(-0.814300\pi\)
0.834599 0.550859i \(-0.185700\pi\)
\(348\) 3.20042e9 + 7.17469e8i 0.218218 + 0.0489199i
\(349\) 1.03634e10 0.698553 0.349277 0.937020i \(-0.386427\pi\)
0.349277 + 0.937020i \(0.386427\pi\)
\(350\) 0 0
\(351\) 1.71511e9i 0.112996i
\(352\) 1.88546e10 4.49560e9i 1.22814 0.292831i
\(353\) 1.30979e10 0.843536 0.421768 0.906704i \(-0.361410\pi\)
0.421768 + 0.906704i \(0.361410\pi\)
\(354\) −3.72253e9 4.64944e9i −0.237042 0.296066i
\(355\) 0 0
\(356\) 4.66616e9 2.08144e10i 0.290509 1.29588i
\(357\) 1.02162e10 0.628952
\(358\) 1.77247e9 1.41911e9i 0.107906 0.0863940i
\(359\) 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
\(362\) 4.82566e9 + 6.02724e9i 0.281010 + 0.350982i
\(363\) 1.27242e10i 0.732829i
\(364\) −1.91144e9 4.28505e8i −0.108882 0.0244090i
\(365\) 0 0
\(366\) 1.84031e10 1.47343e10i 1.02557 0.821116i
\(367\) 1.96628e10i 1.08388i 0.840418 + 0.541939i \(0.182309\pi\)
−0.840418 + 0.541939i \(0.817691\pi\)
\(368\) −6.63656e9 + 1.40580e10i −0.361870 + 0.766536i
\(369\) −7.34878e9 −0.396378
\(370\) 0 0
\(371\) 1.15308e9i 0.0608646i
\(372\) 3.80191e8 1.69592e9i 0.0198532 0.0885593i
\(373\) 2.10063e10 1.08521 0.542606 0.839987i \(-0.317438\pi\)
0.542606 + 0.839987i \(0.317438\pi\)
\(374\) 1.68750e10 1.35108e10i 0.862498 0.690551i
\(375\) 0 0
\(376\) −1.37163e10 2.80648e10i −0.686257 1.40414i
\(377\) −7.01374e8 −0.0347204
\(378\) −4.38617e9 5.47833e9i −0.214842 0.268337i
\(379\) 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
\(382\) 1.23958e10 9.92461e9i 0.582133 0.466080i
\(383\) 2.23357e10i 1.03802i −0.854770 0.519008i \(-0.826302\pi\)
0.854770 0.519008i \(-0.173698\pi\)
\(384\) 3.62938e8 + 2.68196e10i 0.0166920 + 1.23347i
\(385\) 0 0
\(386\) −1.17593e10 1.46874e10i −0.529704 0.661599i
\(387\) 2.02921e10i 0.904654i
\(388\) 6.75466e9 3.01306e10i 0.298042 1.32948i
\(389\) 3.13680e10 1.36990 0.684948 0.728592i \(-0.259825\pi\)
0.684948 + 0.728592i \(0.259825\pi\)
\(390\) 0 0
\(391\) 1.73377e10i 0.741795i
\(392\) −1.40132e10 + 6.84880e9i −0.593463 + 0.290048i
\(393\) −3.11926e10 −1.30762
\(394\) −1.70538e10 2.13002e10i −0.707680 0.883892i
\(395\) 0 0
\(396\) 1.58060e10 + 3.54339e9i 0.642751 + 0.144091i
\(397\) −7.65788e9 −0.308281 −0.154140 0.988049i \(-0.549261\pi\)
−0.154140 + 0.988049i \(0.549261\pi\)
\(398\) 3.11046e10 2.49036e10i 1.23963 0.992499i
\(399\) 2.72345e9i 0.107455i
\(400\) 0 0
\(401\) −3.26120e10 −1.26125 −0.630623 0.776089i \(-0.717201\pi\)
−0.630623 + 0.776089i \(0.717201\pi\)
\(402\) −1.52445e10 1.90403e10i −0.583725 0.729072i
\(403\) 3.71662e8i 0.0140906i
\(404\) −1.55258e9 + 6.92561e9i −0.0582812 + 0.259976i
\(405\) 0 0
\(406\) 2.24029e9 1.79367e9i 0.0824520 0.0660144i
\(407\) 6.41811e10i 2.33900i
\(408\) 1.31352e10 + 2.68756e10i 0.474018 + 0.969879i
\(409\) 2.26168e10 0.808236 0.404118 0.914707i \(-0.367578\pi\)
0.404118 + 0.914707i \(0.367578\pi\)
\(410\) 0 0
\(411\) 2.21802e10i 0.777318i
\(412\) −2.61043e10 5.85205e9i −0.905990 0.203104i
\(413\) −5.21155e9 −0.179129
\(414\) −1.01415e10 + 8.11970e9i −0.345224 + 0.276400i
\(415\) 0 0
\(416\) −1.33030e9 5.57931e9i −0.0444199 0.186297i
\(417\) −2.94794e10 −0.974932
\(418\) −3.60173e9 4.49856e9i −0.117979 0.147356i
\(419\) 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 \(0.678457\pi\)
\(422\) 1.83321e10 1.46774e10i 0.578045 0.462807i
\(423\) 2.61048e10i 0.815378i
\(424\) 3.03339e9 1.48253e9i 0.0938565 0.0458713i
\(425\) 0 0
\(426\) −1.19508e9 1.49266e9i −0.0362878 0.0453234i
\(427\) 2.06280e10i 0.620505i
\(428\) −2.50618e10 5.61834e9i −0.746857 0.167430i
\(429\) −1.01033e10 −0.298287
\(430\) 0 0
\(431\) 3.06956e10i 0.889544i 0.895644 + 0.444772i \(0.146715\pi\)
−0.895644 + 0.444772i \(0.853285\pi\)
\(432\) 8.77234e9 1.85822e10i 0.251872 0.533533i
\(433\) −2.88433e9 −0.0820529 −0.0410265 0.999158i \(-0.513063\pi\)
−0.0410265 + 0.999158i \(0.513063\pi\)
\(434\) −9.50477e8 1.18715e9i −0.0267906 0.0334615i
\(435\) 0 0
\(436\) 3.30801e9 1.47561e10i 0.0915421 0.408343i
\(437\) 4.62189e9 0.126734
\(438\) −7.14559e9 + 5.72105e9i −0.194152 + 0.155446i
\(439\) 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
\(442\) −3.99802e9 4.99353e9i −0.104751 0.130833i
\(443\) 2.06609e10i 0.536455i 0.963356 + 0.268228i \(0.0864379\pi\)
−0.963356 + 0.268228i \(0.913562\pi\)
\(444\) −8.66619e10 1.94278e10i −2.22996 0.499910i
\(445\) 0 0
\(446\) 1.84752e10 1.47920e10i 0.466928 0.373842i
\(447\) 4.03280e10i 1.01013i
\(448\) 1.85175e10 + 1.44191e10i 0.459696 + 0.357952i
\(449\) 2.11092e10 0.519382 0.259691 0.965692i \(-0.416379\pi\)
0.259691 + 0.965692i \(0.416379\pi\)
\(450\) 0 0
\(451\) 3.96855e10i 0.959237i
\(452\) 3.08476e9 1.37602e10i 0.0739039 0.329664i
\(453\) −8.36315e10 −1.98599
\(454\) 9.36818e9 7.50054e9i 0.220512 0.176551i
\(455\) 0 0
\(456\) 7.16452e9 3.50158e9i 0.165702 0.0809850i
\(457\) 2.06831e10 0.474188 0.237094 0.971487i \(-0.423805\pi\)
0.237094 + 0.971487i \(0.423805\pi\)
\(458\) −2.84784e10 3.55695e10i −0.647223 0.808381i
\(459\) 2.29173e10i 0.516312i
\(460\) 0 0
\(461\) 7.65072e10 1.69394 0.846971 0.531640i \(-0.178424\pi\)
0.846971 + 0.531640i \(0.178424\pi\)
\(462\) 3.22715e10 2.58379e10i 0.708355 0.567138i
\(463\) 3.41303e9i 0.0742704i 0.999310 + 0.0371352i \(0.0118232\pi\)
−0.999310 + 0.0371352i \(0.988177\pi\)
\(464\) 7.59895e9 + 3.58734e9i 0.163939 + 0.0773929i
\(465\) 0 0
\(466\) −2.20621e9 2.75555e9i −0.0467845 0.0584339i
\(467\) 1.92903e10i 0.405576i 0.979223 + 0.202788i \(0.0650002\pi\)
−0.979223 + 0.202788i \(0.935000\pi\)
\(468\) 1.04853e9 4.67721e9i 0.0218574 0.0974997i
\(469\) −2.13423e10 −0.441112
\(470\) 0 0
\(471\) 2.71102e10i 0.550869i
\(472\) −6.70056e9 1.37099e10i −0.135003 0.276227i
\(473\) 1.09583e11 2.18927
\(474\) 3.58845e10 + 4.48197e10i 0.710875 + 0.887883i
\(475\) 0 0
\(476\) 2.55406e10 + 5.72567e9i 0.497511 + 0.111532i
\(477\) 2.82154e9 0.0545021
\(478\) −5.05212e10 + 4.04493e10i −0.967748 + 0.774818i
\(479\) 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
\(482\) 6.17983e10 + 7.71861e10i 1.14496 + 1.43005i
\(483\) 3.31563e10i 0.609224i
\(484\) 7.13124e9 3.18104e10i 0.129952 0.579679i
\(485\) 0 0
\(486\) 4.14332e10 3.31731e10i 0.742683 0.594622i
\(487\) 9.30801e10i 1.65478i −0.561626 0.827391i \(-0.689824\pi\)
0.561626 0.827391i \(-0.310176\pi\)
\(488\) 5.42656e10 2.65217e10i 0.956853 0.467651i
\(489\) −5.78046e10 −1.01094
\(490\) 0 0
\(491\) 2.12850e9i 0.0366225i 0.999832 + 0.0183113i \(0.00582898\pi\)
−0.999832 + 0.0183113i \(0.994171\pi\)
\(492\) −5.35862e10 1.20129e10i −0.914518 0.205016i
\(493\) 9.37175e9 0.158647
\(494\) −1.33118e9 + 1.06580e9i −0.0223526 + 0.0178964i
\(495\) 0 0
\(496\) 1.90095e9 4.02673e9i 0.0314083 0.0665312i
\(497\) −1.67312e9 −0.0274221
\(498\) 5.19187e10 + 6.48464e10i 0.844124 + 1.05431i
\(499\) 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
\(502\) 6.51187e10 5.21367e10i 1.02539 0.820973i
\(503\) 3.93019e10i 0.613962i 0.951716 + 0.306981i \(0.0993188\pi\)
−0.951716 + 0.306981i \(0.900681\pi\)
\(504\) 8.61216e9 + 1.76212e10i 0.133472 + 0.273094i
\(505\) 0 0
\(506\) 4.38487e10 + 5.47670e10i 0.668890 + 0.835444i
\(507\) 7.85181e10i 1.18833i
\(508\) −6.42387e10 1.44010e10i −0.964587 0.216241i
\(509\) −3.25113e10 −0.484354 −0.242177 0.970232i \(-0.577861\pi\)
−0.242177 + 0.970232i \(0.577861\pi\)
\(510\) 0 0
\(511\) 8.00947e9i 0.117468i
\(512\) −1.41237e10 + 6.72524e10i −0.205526 + 0.978652i
\(513\) −6.10931e9 −0.0882110
\(514\) 6.13693e10 + 7.66503e10i 0.879223 + 1.09815i
\(515\) 0 0
\(516\) −3.31711e10 + 1.47967e11i −0.467908 + 2.08720i
\(517\) −1.40973e11 −1.97322
\(518\) −6.06633e10 + 4.85695e10i −0.842572 + 0.674598i
\(519\) 2.06032e10i 0.283965i
\(520\) 0 0
\(521\) 1.84550e9 0.0250475 0.0125237 0.999922i \(-0.496013\pi\)
0.0125237 + 0.999922i \(0.496013\pi\)
\(522\) 4.38904e9 + 5.48191e9i 0.0591136 + 0.0738329i
\(523\) 6.23770e10i 0.833715i 0.908972 + 0.416858i \(0.136869\pi\)
−0.908972 + 0.416858i \(0.863131\pi\)
\(524\) −7.79814e10 1.74818e10i −1.03435 0.231879i
\(525\) 0 0
\(526\) −8.70448e10 + 6.96916e10i −1.13710 + 0.910411i
\(527\) 4.96614e9i 0.0643838i
\(528\) 1.09463e11 + 5.16757e10i 1.40842 + 0.664892i
\(529\) 2.20424e10 0.281473
\(530\) 0 0
\(531\) 1.27524e10i 0.160404i
\(532\) 1.52635e9 6.80863e9i 0.0190550 0.0849988i
\(533\) 1.17434e10 0.145508
\(534\) 1.03989e11 8.32575e10i 1.27885 1.02390i
\(535\) 0 0
\(536\) −2.74400e10 5.61446e10i −0.332449 0.680219i
\(537\) 1.41797e10 0.170518
\(538\) 2.70720e10 + 3.38130e10i 0.323141 + 0.403603i
\(539\) 7.03905e10i 0.833986i
\(540\) 0 0
\(541\) −7.45917e10 −0.870766 −0.435383 0.900245i \(-0.643387\pi\)
−0.435383 + 0.900245i \(0.643387\pi\)
\(542\) −9.97991e10 + 7.99032e10i −1.15646 + 0.925907i
\(543\) 4.82179e10i 0.554638i
\(544\) 1.77755e10 + 7.45506e10i 0.202967 + 0.851246i
\(545\) 0 0
\(546\) −7.64575e9 9.54954e9i −0.0860299 0.107451i
\(547\) 1.41531e9i 0.0158089i 0.999969 + 0.00790445i \(0.00251609\pi\)
−0.999969 + 0.00790445i \(0.997484\pi\)
\(548\) 1.24309e10 5.54506e10i 0.137841 0.614871i
\(549\) 5.04758e10 0.555641
\(550\) 0 0
\(551\) 2.49833e9i 0.0271046i
\(552\) −8.72234e10 + 4.26295e10i −0.939457 + 0.459149i
\(553\) 5.02383e10 0.537198
\(554\) 8.22965e10 + 1.02788e11i 0.873660 + 1.09120i
\(555\) 0 0
\(556\) −7.36985e10 1.65217e10i −0.771187 0.172884i
\(557\) 1.37543e11 1.42895 0.714475 0.699661i \(-0.246666\pi\)
0.714475 + 0.699661i \(0.246666\pi\)
\(558\) 2.90489e9 2.32578e9i 0.0299636 0.0239901i
\(559\) 3.24270e10i 0.332093i
\(560\) 0 0
\(561\) 1.35000e11 1.36296
\(562\) 3.08105e10 + 3.84823e10i 0.308854 + 0.385759i
\(563\) 1.06415e11i 1.05918i −0.848255 0.529589i \(-0.822346\pi\)
0.848255 0.529589i \(-0.177654\pi\)
\(564\) 4.26731e10 1.90352e11i 0.421733 1.88123i
\(565\) 0 0
\(566\) −1.46273e10 + 1.17112e10i −0.142528 + 0.114113i
\(567\) 7.52431e10i 0.728005i
\(568\) −2.15115e9 4.40143e9i −0.0206670 0.0422864i
\(569\) 4.02429e10 0.383919 0.191960 0.981403i \(-0.438516\pi\)
0.191960 + 0.981403i \(0.438516\pi\)
\(570\) 0 0
\(571\) 1.50341e11i 1.41427i −0.707077 0.707137i \(-0.749986\pi\)
0.707077 0.707137i \(-0.250014\pi\)
\(572\) −2.52583e10 5.66238e9i −0.235950 0.0528951i
\(573\) 9.91667e10 0.919914
\(574\) −3.75103e10 + 3.00323e10i −0.345544 + 0.276657i
\(575\) 0 0
\(576\) −3.52829e10 + 4.53116e10i −0.320534 + 0.411642i
\(577\) −4.96477e9 −0.0447915 −0.0223958 0.999749i \(-0.507129\pi\)
−0.0223958 + 0.999749i \(0.507129\pi\)
\(578\) −1.63361e10 2.04038e10i −0.146365 0.182810i
\(579\) 1.17499e11i 1.04549i
\(580\) 0 0
\(581\) 7.26862e10 0.637892
\(582\) 1.50533e11 1.20522e11i 1.31201 1.05045i
\(583\) 1.52372e10i 0.131895i
\(584\) −2.10703e10 + 1.02979e10i −0.181142 + 0.0885313i
\(585\) 0 0
\(586\) −4.80980e10 6.00743e10i −0.407884 0.509446i
\(587\) 1.53440e11i 1.29237i 0.763181 + 0.646185i \(0.223637\pi\)
−0.763181 + 0.646185i \(0.776363\pi\)
\(588\) −9.50461e10 2.13074e10i −0.795106 0.178246i
\(589\) −1.32388e9 −0.0109999
\(590\) 0 0
\(591\) 1.70402e11i 1.39677i
\(592\) −2.05766e11 9.71390e10i −1.67528 0.790873i
\(593\) −2.06036e11 −1.66619 −0.833094 0.553131i \(-0.813433\pi\)
−0.833094 + 0.553131i \(0.813433\pi\)
\(594\) −5.79601e10 7.23922e10i −0.465568 0.581495i
\(595\) 0 0
\(596\) −2.26017e10 + 1.00820e11i −0.179125 + 0.799027i
\(597\) 2.48837e11 1.95892
\(598\) 1.62063e10 1.29754e10i 0.126730 0.101465i
\(599\) 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 \(0.372927\pi\)
\(602\) 8.29277e10 + 1.03577e11i 0.631413 + 0.788635i
\(603\) 5.22236e10i 0.395001i
\(604\) −2.09079e11 4.68711e10i −1.57095 0.352174i
\(605\) 0 0
\(606\) −3.46004e10 + 2.77025e10i −0.256561 + 0.205413i
\(607\) 1.97883e11i 1.45765i −0.684700 0.728825i \(-0.740067\pi\)
0.684700 0.728825i \(-0.259933\pi\)
\(608\) 1.98738e10 4.73860e9i 0.145434 0.0346766i
\(609\) 1.79224e10 0.130294
\(610\) 0 0
\(611\) 4.17158e10i 0.299320i
\(612\) −1.40105e10 + 6.24967e10i −0.0998728 + 0.445504i
\(613\) −1.27158e11 −0.900538 −0.450269 0.892893i \(-0.648672\pi\)
−0.450269 + 0.892893i \(0.648672\pi\)
\(614\) 4.36121e10 3.49176e10i 0.306855 0.245681i
\(615\) 0 0
\(616\) 9.51595e10 4.65082e10i 0.660890 0.323003i
\(617\) 5.06702e10 0.349632 0.174816 0.984601i \(-0.444067\pi\)
0.174816 + 0.984601i \(0.444067\pi\)
\(618\) −1.04417e11 1.30417e11i −0.715844 0.894089i
\(619\) 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
\(622\) −1.62128e11 + 1.29807e11i −1.08317 + 0.867231i
\(623\) 1.16561e11i 0.773748i
\(624\) 1.52915e10 3.23915e10i 0.100858 0.213645i
\(625\) 0 0
\(626\) 6.31165e10 + 7.88325e10i 0.411004 + 0.513343i
\(627\) 3.59885e10i 0.232859i
\(628\) −1.51938e10 + 6.77754e10i −0.0976853 + 0.435746i
\(629\) −2.53771e11 −1.62121
\(630\) 0 0
\(631\) 1.65273e11i 1.04252i −0.853399 0.521259i \(-0.825463\pi\)
0.853399 0.521259i \(-0.174537\pi\)
\(632\) 6.45921e10 + 1.32161e11i 0.404866 + 0.828388i
\(633\) 1.46657e11 0.913454
\(634\) −1.65902e11 2.07211e11i −1.02682 1.28250i
\(635\) 0 0
\(636\) 2.05743e10 + 4.61233e9i 0.125747 + 0.0281898i
\(637\) 2.08294e10 0.126508
\(638\) 2.96039e10 2.37021e10i 0.178676 0.143055i
\(639\) 4.09405e9i 0.0245556i
\(640\) 0 0
\(641\) 1.12013e11 0.663490 0.331745 0.943369i \(-0.392363\pi\)
0.331745 + 0.943369i \(0.392363\pi\)
\(642\) −1.00247e11 1.25209e11i −0.590109 0.737046i
\(643\) 2.65913e11i 1.55559i −0.628518 0.777795i \(-0.716338\pi\)
0.628518 0.777795i \(-0.283662\pi\)
\(644\) −1.85824e10 + 8.28907e10i −0.108033 + 0.481906i
\(645\) 0 0
\(646\) 1.77872e10 1.42411e10i 0.102136 0.0817739i
\(647\) 2.71996e11i 1.55219i 0.630614 + 0.776097i \(0.282803\pi\)
−0.630614 + 0.776097i \(0.717197\pi\)
\(648\) 1.97940e11 9.67411e10i 1.12262 0.548670i
\(649\) −6.88669e10 −0.388179
\(650\) 0 0
\(651\) 9.49716e9i 0.0528774i
\(652\) −1.44511e11 3.23965e10i −0.799672 0.179270i
\(653\) −3.03789e11 −1.67078 −0.835391 0.549656i \(-0.814759\pi\)
−0.835391 + 0.549656i \(0.814759\pi\)
\(654\) 7.37213e10 5.90243e10i 0.402979 0.322641i
\(655\) 0 0
\(656\) −1.27233e11 6.00646e10i −0.687043 0.324342i
\(657\) −1.95988e10 −0.105189
\(658\) −1.06683e11 1.33247e11i −0.569102 0.710808i
\(659\) 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 \(0.723435\pi\)
\(662\) 6.85251e10 5.48640e10i 0.356794 0.285664i
\(663\) 3.99482e10i 0.206749i
\(664\) 9.34537e10 + 1.91214e11i 0.480755 + 0.983665i
\(665\) 0 0
\(666\) −1.18848e11 1.48441e11i −0.604079 0.754494i
\(667\) 3.04155e10i 0.153671i
\(668\) −1.16936e11 2.62146e10i −0.587276 0.131655i
\(669\) 1.47802e11 0.737862
\(670\) 0 0
\(671\) 2.72584e11i 1.34465i
\(672\) 3.39935e10 + 1.42569e11i 0.166694 + 0.699115i
\(673\) 3.15336e11 1.53714 0.768569 0.639767i \(-0.220969\pi\)
0.768569 + 0.639767i \(0.220969\pi\)
\(674\) 3.56226e9 + 4.44927e9i 0.0172618 + 0.0215600i
\(675\) 0 0
\(676\) 4.40053e10 1.96295e11i 0.210726 0.939989i
\(677\) 2.47236e10 0.117695 0.0588475 0.998267i \(-0.481257\pi\)
0.0588475 + 0.998267i \(0.481257\pi\)
\(678\) 6.87460e10 5.50408e10i 0.325333 0.260475i
\(679\) 1.68731e11i 0.793811i
\(680\) 0 0
\(681\) 7.49454e10 0.348463
\(682\) −1.25599e10 1.56873e10i −0.0580561 0.0725120i
\(683\) 7.20843e10i 0.331251i 0.986189 + 0.165626i \(0.0529644\pi\)
−0.986189 + 0.165626i \(0.947036\pi\)
\(684\) 1.66604e10 + 3.73492e9i 0.0761135 + 0.0170631i
\(685\) 0 0
\(686\) −1.67255e11 + 1.33911e11i −0.755235 + 0.604672i
\(687\) 2.84556e11i 1.27744i
\(688\) −1.65855e11 + 3.51326e11i −0.740246 + 1.56804i
\(689\) −4.50887e9 −0.0200074
\(690\) 0 0
\(691\) 2.95424e11i 1.29578i 0.761732 + 0.647892i \(0.224349\pi\)
−0.761732 + 0.647892i \(0.775651\pi\)
\(692\) −1.15470e10 + 5.15080e10i −0.0503554 + 0.224621i
\(693\) 8.85139e10 0.383776
\(694\) 1.99503e11 1.59731e11i 0.860028 0.688573i
\(695\) 0 0
\(696\) 2.30430e10 + 4.71479e10i 0.0981980 + 0.200921i
\(697\) −1.56916e11 −0.664867
\(698\) 1.03634e11 + 1.29438e11i 0.436596 + 0.545308i
\(699\) 2.20444e10i 0.0923400i
\(700\) 0 0
\(701\) −2.87925e11 −1.19236 −0.596180 0.802851i \(-0.703315\pi\)
−0.596180 + 0.802851i \(0.703315\pi\)
\(702\) −2.14217e10 + 1.71511e10i −0.0882077 + 0.0706227i
\(703\) 6.76504e10i 0.276980i
\(704\) 2.44696e11 + 1.90538e11i 0.996176 + 0.775694i
\(705\) 0 0
\(706\) 1.30979e11 + 1.63593e11i 0.527210 + 0.658485i
\(707\) 3.87834e10i 0.155227i
\(708\) 2.08462e10 9.29889e10i 0.0829648 0.370082i
\(709\) 2.51685e11 0.996030 0.498015 0.867168i \(-0.334062\pi\)
0.498015 + 0.867168i \(0.334062\pi\)
\(710\) 0 0
\(711\) 1.22931e11i 0.481042i
\(712\) 3.06633e11 1.49864e11i 1.19316 0.583144i
\(713\) 1.61174e10 0.0623643
\(714\) 1.02162e11 + 1.27601e11i 0.393095 + 0.490976i
\(715\) 0 0
\(716\) 3.54493e10 + 7.94701e9i 0.134883 + 0.0302379i
\(717\) −4.04170e11 −1.52928
\(718\) 4.13986e10 3.31454e10i 0.155772 0.124717i
\(719\) 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
\(722\) 1.66039e11 + 2.07383e11i 0.611029 + 0.763175i
\(723\) 6.17489e11i 2.25983i
\(724\) −2.70237e10 + 1.20545e11i −0.0983536 + 0.438727i
\(725\) 0 0
\(726\) 1.58925e11 1.27242e11i 0.572064 0.458018i
\(727\) 1.79083e11i 0.641088i −0.947234 0.320544i \(-0.896134\pi\)
0.947234 0.320544i \(-0.103866\pi\)
\(728\) −1.37623e10 2.81589e10i −0.0489967 0.100251i
\(729\) −2.14381e10 −0.0759061
\(730\) 0 0
\(731\) 4.33289e11i 1.51743i
\(732\) 3.68062e11 + 8.25119e10i 1.28197 + 0.287391i
\(733\) −2.17618e11 −0.753839 −0.376920 0.926246i \(-0.623017\pi\)
−0.376920 + 0.926246i \(0.623017\pi\)
\(734\) −2.45588e11 + 1.96628e11i −0.846101 + 0.677423i
\(735\) 0 0
\(736\) −2.41950e11 + 5.76895e10i −0.824546 + 0.196601i
\(737\) −2.82023e11 −0.955904
\(738\) −7.34878e10 9.17862e10i −0.247736 0.309423i
\(739\) 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
\(742\) 1.44020e10 1.15308e10i 0.0475124 0.0380404i
\(743\) 2.03509e11i 0.667771i 0.942614 + 0.333886i \(0.108360\pi\)
−0.942614 + 0.333886i \(0.891640\pi\)
\(744\) 2.49840e10 1.22106e10i 0.0815398 0.0398517i
\(745\) 0 0
\(746\) 2.10063e11 + 2.62369e11i 0.678258 + 0.847144i
\(747\) 1.77860e11i 0.571210i
\(748\) 3.37500e11 + 7.56606e10i 1.07812 + 0.241693i
\(749\) −1.40346e11 −0.445937
\(750\) 0 0
\(751\) 2.34693e11i 0.737804i −0.929468 0.368902i \(-0.879734\pi\)
0.929468 0.368902i \(-0.120266\pi\)
\(752\) 2.13365e11 4.51965e11i 0.667194 1.41330i
\(753\) 5.20950e11 1.62038
\(754\) −7.01374e9 8.76016e9i −0.0217002 0.0271036i
\(755\) 0 0
\(756\) 2.45626e10 1.09567e11i 0.0751946 0.335421i
\(757\) 3.84882e11 1.17204 0.586022 0.810295i \(-0.300693\pi\)
0.586022 + 0.810295i \(0.300693\pi\)
\(758\) 3.80715e10 3.04816e10i 0.115325 0.0923338i
\(759\) 4.38136e11i 1.32021i
\(760\) 0 0
\(761\) 2.39209e11 0.713244 0.356622 0.934249i \(-0.383928\pi\)
0.356622 + 0.934249i \(0.383928\pi\)
\(762\) −2.56955e11 3.20936e11i −0.762143 0.951916i
\(763\) 8.26340e10i 0.243815i
\(764\) 2.47917e11 + 5.55778e10i 0.727666 + 0.163128i
\(765\) 0 0
\(766\) 2.78972e11 2.23357e11i 0.810301 0.648760i
\(767\) 2.03786e10i