Properties

Label 36.9.d.b.19.1
Level $36$
Weight $9$
Character 36.19
Analytic conductor $14.666$
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] = [36,9,Mod(19,36)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(36, 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("36.19");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 36.d (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: \(14.6656299622\)
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 19.1
Root \(0.500000 + 3.12250i\) of defining polynomial
Character \(\chi\) \(=\) 36.19
Dual form 36.9.d.b.19.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(10.0000 - 12.4900i) q^{2} +(-56.0000 - 249.800i) q^{4} -610.000 q^{5} +1398.88i q^{7} +(-3680.00 - 1798.56i) q^{8} +O(q^{10})\) \(q+(10.0000 - 12.4900i) q^{2} +(-56.0000 - 249.800i) q^{4} -610.000 q^{5} +1398.88i q^{7} +(-3680.00 - 1798.56i) q^{8} +(-6100.00 + 7618.90i) q^{10} +18485.2i q^{11} -5470.00 q^{13} +(17472.0 + 13988.8i) q^{14} +(-59264.0 + 27977.6i) q^{16} -73090.0 q^{17} -19484.4i q^{19} +(34160.0 + 152378. i) q^{20} +(230880. + 184852. i) q^{22} +237210. i q^{23} -18525.0 q^{25} +(-54700.0 + 68320.3i) q^{26} +(349440. - 78337.3i) q^{28} +128222. q^{29} -67945.6i q^{31} +(-243200. + 1.01998e6i) q^{32} +(-730900. + 912894. i) q^{34} -853317. i q^{35} -3.47203e6 q^{37} +(-243360. - 194844. i) q^{38} +(2.24480e6 + 1.09712e6i) q^{40} -2.14688e6 q^{41} -5.92815e6i q^{43} +(4.61760e6 - 1.03517e6i) q^{44} +(2.96275e6 + 2.37210e6i) q^{46} -7.62629e6i q^{47} +3.80794e6 q^{49} +(-185250. + 231377. i) q^{50} +(306320. + 1.36641e6i) q^{52} -824290. q^{53} -1.12760e7i q^{55} +(2.51597e6 - 5.14788e6i) q^{56} +(1.28222e6 - 1.60149e6i) q^{58} +3.72552e6i q^{59} -1.47461e7 q^{61} +(-848640. - 679456. i) q^{62} +(1.03076e7 + 1.32374e7i) q^{64} +3.33670e6 q^{65} +1.52567e7i q^{67} +(4.09304e6 + 1.82579e7i) q^{68} +(-1.06579e7 - 8.53317e6i) q^{70} +1.19604e6i q^{71} -5.72563e6 q^{73} +(-3.47203e7 + 4.33656e7i) q^{74} +(-4.86720e6 + 1.09113e6i) q^{76} -2.58586e7 q^{77} +3.59132e7i q^{79} +(3.61510e7 - 1.70663e7i) q^{80} +(-2.14688e7 + 2.68145e7i) q^{82} +5.19603e7i q^{83} +4.45849e7 q^{85} +(-7.40426e7 - 5.92815e7i) q^{86} +(3.32467e7 - 6.80255e7i) q^{88} +8.33242e7 q^{89} -7.65187e6i q^{91} +(5.92550e7 - 1.32838e7i) q^{92} +(-9.52524e7 - 7.62629e7i) q^{94} +1.18855e7i q^{95} +1.20619e8 q^{97} +(3.80794e7 - 4.75611e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 20 q^{2} - 112 q^{4} - 1220 q^{5} - 7360 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 20 q^{2} - 112 q^{4} - 1220 q^{5} - 7360 q^{8} - 12200 q^{10} - 10940 q^{13} + 34944 q^{14} - 118528 q^{16} - 146180 q^{17} + 68320 q^{20} + 461760 q^{22} - 37050 q^{25} - 109400 q^{26} + 698880 q^{28} + 256444 q^{29} - 486400 q^{32} - 1461800 q^{34} - 6944060 q^{37} - 486720 q^{38} + 4489600 q^{40} - 4293764 q^{41} + 9235200 q^{44} + 5925504 q^{46} + 7615874 q^{49} - 370500 q^{50} + 612640 q^{52} - 1648580 q^{53} + 5031936 q^{56} + 2564440 q^{58} - 29492156 q^{61} - 1697280 q^{62} + 20615168 q^{64} + 6673400 q^{65} + 8186080 q^{68} - 21315840 q^{70} - 11451260 q^{73} - 69440600 q^{74} - 9734400 q^{76} - 51717120 q^{77} + 72302080 q^{80} - 42937640 q^{82} + 89169800 q^{85} - 148085184 q^{86} + 66493440 q^{88} + 166648444 q^{89} + 118510080 q^{92} - 190504704 q^{94} + 241238020 q^{97} + 76158740 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(-1\) \(1\)

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
\(3\) 0 0
\(4\) −56.0000 249.800i −0.218750 0.975781i
\(5\) −610.000 −0.976000 −0.488000 0.872844i \(-0.662273\pi\)
−0.488000 + 0.872844i \(0.662273\pi\)
\(6\) 0 0
\(7\) 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
\(9\) 0 0
\(10\) −6100.00 + 7618.90i −0.610000 + 0.761890i
\(11\) 18485.2i 1.26256i 0.775554 + 0.631282i \(0.217471\pi\)
−0.775554 + 0.631282i \(0.782529\pi\)
\(12\) 0 0
\(13\) −5470.00 −0.191520 −0.0957600 0.995404i \(-0.530528\pi\)
−0.0957600 + 0.995404i \(0.530528\pi\)
\(14\) 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 \(0.644155\pi\)
\(18\) 0 0
\(19\) 19484.4i 0.149511i −0.997202 0.0747554i \(-0.976182\pi\)
0.997202 0.0747554i \(-0.0238176\pi\)
\(20\) 34160.0 + 152378.i 0.213500 + 0.952362i
\(21\) 0 0
\(22\) 230880. + 184852.i 0.985588 + 0.789102i
\(23\) 237210.i 0.847660i 0.905742 + 0.423830i \(0.139315\pi\)
−0.905742 + 0.423830i \(0.860685\pi\)
\(24\) 0 0
\(25\) −18525.0 −0.0474240
\(26\) −54700.0 + 68320.3i −0.119700 + 0.149505i
\(27\) 0 0
\(28\) 349440. 78337.3i 0.568513 0.127449i
\(29\) 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 \(-0.0117120\pi\)
\(32\) −243200. + 1.01998e6i −0.231934 + 0.972732i
\(33\) 0 0
\(34\) −730900. + 912894.i −0.546943 + 0.683132i
\(35\) 853317.i 0.568641i
\(36\) 0 0
\(37\) −3.47203e6 −1.85258 −0.926289 0.376813i \(-0.877020\pi\)
−0.926289 + 0.376813i \(0.877020\pi\)
\(38\) −243360. 194844.i −0.116712 0.0934442i
\(39\) 0 0
\(40\) 2.24480e6 + 1.09712e6i 0.876875 + 0.428563i
\(41\) −2.14688e6 −0.759754 −0.379877 0.925037i \(-0.624034\pi\)
−0.379877 + 0.925037i \(0.624034\pi\)
\(42\) 0 0
\(43\) 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 \(-0.714489\pi\)
0.623989 0.781433i \(-0.285511\pi\)
\(48\) 0 0
\(49\) 3.80794e6 0.660550
\(50\) −185250. + 231377.i −0.0296400 + 0.0370203i
\(51\) 0 0
\(52\) 306320. + 1.36641e6i 0.0418950 + 0.186881i
\(53\) −824290. −0.104466 −0.0522332 0.998635i \(-0.516634\pi\)
−0.0522332 + 0.998635i \(0.516634\pi\)
\(54\) 0 0
\(55\) 1.12760e7i 1.23226i
\(56\) 2.51597e6 5.14788e6i 0.255831 0.523451i
\(57\) 0 0
\(58\) 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
\(63\) 0 0
\(64\) 1.03076e7 + 1.32374e7i 0.614380 + 0.789010i
\(65\) 3.33670e6 0.186923
\(66\) 0 0
\(67\) 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
\(69\) 0 0
\(70\) −1.06579e7 8.53317e6i −0.443895 0.355400i
\(71\) 1.19604e6i 0.0470666i 0.999723 + 0.0235333i \(0.00749158\pi\)
−0.999723 + 0.0235333i \(0.992508\pi\)
\(72\) 0 0
\(73\) −5.72563e6 −0.201619 −0.100810 0.994906i \(-0.532143\pi\)
−0.100810 + 0.994906i \(0.532143\pi\)
\(74\) −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
\(78\) 0 0
\(79\) 3.59132e7i 0.922032i 0.887392 + 0.461016i \(0.152515\pi\)
−0.887392 + 0.461016i \(0.847485\pi\)
\(80\) 3.61510e7 1.70663e7i 0.882594 0.416658i
\(81\) 0 0
\(82\) −2.14688e7 + 2.68145e7i −0.474846 + 0.593082i
\(83\) 5.19603e7i 1.09486i 0.836851 + 0.547431i \(0.184394\pi\)
−0.836851 + 0.547431i \(0.815606\pi\)
\(84\) 0 0
\(85\) 4.45849e7 0.854107
\(86\) −7.40426e7 5.92815e7i −1.35359 1.08374i
\(87\) 0 0
\(88\) 3.32467e7 6.80255e7i 0.554393 1.13433i
\(89\) 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
\(92\) 5.92550e7 1.32838e7i 0.827130 0.185426i
\(93\) 0 0
\(94\) −9.52524e7 7.62629e7i −1.22001 0.976792i
\(95\) 1.18855e7i 0.145923i
\(96\) 0 0
\(97\) 1.20619e8 1.36248 0.681238 0.732062i \(-0.261442\pi\)
0.681238 + 0.732062i \(0.261442\pi\)
\(98\) 3.80794e7 4.75611e7i 0.412844 0.515641i
\(99\) 0 0
\(100\) 1.03740e6 + 4.62754e6i 0.0103740 + 0.0462754i
\(101\) −2.77246e7 −0.266428 −0.133214 0.991087i \(-0.542530\pi\)
−0.133214 + 0.991087i \(0.542530\pi\)
\(102\) 0 0
\(103\) 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 \(-0.874995\pi\)
0.923874 0.382697i \(-0.125005\pi\)
\(108\) 0 0
\(109\) −5.90716e7 −0.418478 −0.209239 0.977865i \(-0.567099\pi\)
−0.209239 + 0.977865i \(0.567099\pi\)
\(110\) −1.40837e8 1.12760e8i −0.961934 0.770164i
\(111\) 0 0
\(112\) −3.91373e7 8.29032e7i −0.248724 0.526865i
\(113\) −5.50849e7 −0.337846 −0.168923 0.985629i \(-0.554029\pi\)
−0.168923 + 0.985629i \(0.554029\pi\)
\(114\) 0 0
\(115\) 1.44698e8i 0.827316i
\(116\) −7.18043e6 3.20298e7i −0.0396569 0.176898i
\(117\) 0 0
\(118\) 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
\(123\) 0 0
\(124\) −1.69728e7 + 3.80495e6i −0.0717905 + 0.0160939i
\(125\) 2.49581e8 1.02229
\(126\) 0 0
\(127\) 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
\(129\) 0 0
\(130\) 3.33670e7 4.16754e7i 0.116827 0.145917i
\(131\) 3.12175e8i 1.06002i 0.847992 + 0.530009i \(0.177812\pi\)
−0.847992 + 0.530009i \(0.822188\pi\)
\(132\) 0 0
\(133\) 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 \(0.602027\pi\)
\(138\) 0 0
\(139\) 2.95030e8i 0.790328i −0.918611 0.395164i \(-0.870688\pi\)
0.918611 0.395164i \(-0.129312\pi\)
\(140\) −2.13158e8 + 4.77857e7i −0.554869 + 0.124390i
\(141\) 0 0
\(142\) 1.49386e7 + 1.19604e7i 0.0367414 + 0.0294166i
\(143\) 1.01114e8i 0.241806i
\(144\) 0 0
\(145\) −7.82154e7 −0.176938
\(146\) −5.72563e7 + 7.15131e7i −0.126012 + 0.157389i
\(147\) 0 0
\(148\) 1.94434e8 + 8.67313e8i 0.405252 + 1.80771i
\(149\) −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 \(-0.297819\pi\)
\(152\) −3.50438e7 + 7.17026e7i −0.0656504 + 0.134326i
\(153\) 0 0
\(154\) −2.58586e8 + 3.22973e8i −0.459750 + 0.574227i
\(155\) 4.14468e7i 0.0718066i
\(156\) 0 0
\(157\) −2.71319e8 −0.446561 −0.223281 0.974754i \(-0.571677\pi\)
−0.223281 + 0.974754i \(0.571677\pi\)
\(158\) 4.48556e8 + 3.59132e8i 0.719761 + 0.576270i
\(159\) 0 0
\(160\) 1.48352e8 6.22190e8i 0.226367 0.949386i
\(161\) −3.31828e8 −0.493867
\(162\) 0 0
\(163\) 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 \(-0.902704\pi\)
0.953647 0.300926i \(-0.0972958\pi\)
\(168\) 0 0
\(169\) −7.85810e8 −0.963320
\(170\) 4.45849e8 5.56865e8i 0.533817 0.666737i
\(171\) 0 0
\(172\) −1.48085e9 + 3.31976e8i −1.69199 + 0.379309i
\(173\) 2.06197e8 0.230196 0.115098 0.993354i \(-0.463282\pi\)
0.115098 + 0.993354i \(0.463282\pi\)
\(174\) 0 0
\(175\) 2.59142e7i 0.0276303i
\(176\) −5.17171e8 1.09551e9i −0.538994 1.14173i
\(177\) 0 0
\(178\) 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
\(183\) 0 0
\(184\) 4.26636e8 8.72933e8i 0.372209 0.761569i
\(185\) 2.11794e9 1.80812
\(186\) 0 0
\(187\) 1.35108e9i 1.10488i
\(188\) −1.90505e9 + 4.27072e8i −1.52502 + 0.341877i
\(189\) 0 0
\(190\) 1.48450e8 + 1.18855e8i 0.113911 + 0.0912016i
\(191\) 9.92461e8i 0.745727i −0.927886 0.372864i \(-0.878376\pi\)
0.927886 0.372864i \(-0.121624\pi\)
\(192\) 0 0
\(193\) 1.17593e9 0.847526 0.423763 0.905773i \(-0.360709\pi\)
0.423763 + 0.905773i \(0.360709\pi\)
\(194\) 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 \(0.691565\pi\)
\(198\) 0 0
\(199\) 2.49036e9i 1.58800i 0.607919 + 0.793999i \(0.292004\pi\)
−0.607919 + 0.793999i \(0.707996\pi\)
\(200\) 6.81720e7 + 3.33183e7i 0.0426075 + 0.0208239i
\(201\) 0 0
\(202\) −2.77246e8 + 3.46281e8i −0.166518 + 0.207981i
\(203\) 1.79367e8i 0.105623i
\(204\) 0 0
\(205\) 1.30960e9 0.741519
\(206\) 1.30522e9 + 1.04501e9i 0.724792 + 0.580298i
\(207\) 0 0
\(208\) 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 \(0.120726\pi\)
−0.928934 + 0.370245i \(0.879274\pi\)
\(212\) 4.61602e7 + 2.05908e8i 0.0228520 + 0.101936i
\(213\) 0 0
\(214\) −1.25309e9 1.00328e9i −0.597486 0.478371i
\(215\) 3.61617e9i 1.69237i
\(216\) 0 0
\(217\) 9.50477e7 0.0428650
\(218\) −5.90716e8 + 7.37804e8i −0.261549 + 0.326674i
\(219\) 0 0
\(220\) −2.81674e9 + 6.31454e8i −1.20242 + 0.269557i
\(221\) 3.99802e8 0.167601
\(222\) 0 0
\(223\) 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 \(0.0451091\pi\)
−0.989975 + 0.141241i \(0.954891\pi\)
\(228\) 0 0
\(229\) −2.84784e9 −1.03556 −0.517778 0.855515i \(-0.673241\pi\)
−0.517778 + 0.855515i \(0.673241\pi\)
\(230\) −1.80728e9 1.44698e9i −0.645823 0.517073i
\(231\) 0 0
\(232\) −4.71857e8 2.30615e8i −0.162876 0.0796041i
\(233\) −2.20621e8 −0.0748553 −0.0374276 0.999299i \(-0.511916\pi\)
−0.0374276 + 0.999299i \(0.511916\pi\)
\(234\) 0 0
\(235\) 4.65204e9i 1.52536i
\(236\) 9.30634e8 2.08629e8i 0.300007 0.0672553i
\(237\) 0 0
\(238\) −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
\(243\) 0 0
\(244\) 8.25780e8 + 3.68357e9i 0.232973 + 1.03922i
\(245\) −2.32284e9 −0.644696
\(246\) 0 0
\(247\) 1.06580e8i 0.0286343i
\(248\) −1.22204e8 + 2.50040e8i −0.0323057 + 0.0661001i
\(249\) 0 0
\(250\) 2.49582e9 3.11727e9i 0.638929 0.798022i
\(251\) 5.21367e9i 1.31356i −0.754084 0.656778i \(-0.771919\pi\)
0.754084 0.656778i \(-0.228081\pi\)
\(252\) 0 0
\(253\) −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 \(0.251674\pi\)
\(258\) 0 0
\(259\) 4.85695e9i 1.07936i
\(260\) −1.86855e8 8.33507e8i −0.0408895 0.182396i
\(261\) 0 0
\(262\) 3.89907e9 + 3.12175e9i 0.827477 + 0.662512i
\(263\) 6.96916e9i 1.45666i −0.685228 0.728329i \(-0.740297\pi\)
0.685228 0.728329i \(-0.259703\pi\)
\(264\) 0 0
\(265\) 5.02817e8 0.101959
\(266\) 2.72563e8 3.40431e8i 0.0544428 0.0679991i
\(267\) 0 0
\(268\) 3.81112e9 8.54374e8i 0.738777 0.165619i
\(269\) −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 \(-0.265518\pi\)
\(272\) 4.33161e9 2.04488e9i 0.791359 0.373588i
\(273\) 0 0
\(274\) −2.21980e9 + 2.77253e9i −0.393832 + 0.491897i
\(275\) 3.42438e8i 0.0598758i
\(276\) 0 0
\(277\) −8.22965e9 −1.39786 −0.698928 0.715192i \(-0.746339\pi\)
−0.698928 + 0.715192i \(0.746339\pi\)
\(278\) −3.68493e9 2.95030e9i −0.616949 0.493955i
\(279\) 0 0
\(280\) −1.53474e9 + 3.14020e9i −0.249691 + 0.510888i
\(281\) −3.08105e9 −0.494167 −0.247083 0.968994i \(-0.579472\pi\)
−0.247083 + 0.968994i \(0.579472\pi\)
\(282\) 0 0
\(283\) 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
\(288\) 0 0
\(289\) −1.63361e9 −0.234184
\(290\) −7.82154e8 + 9.76910e8i −0.110586 + 0.138122i
\(291\) 0 0
\(292\) 3.20635e8 + 1.43026e9i 0.0441042 + 0.196736i
\(293\) −4.80980e9 −0.652614 −0.326307 0.945264i \(-0.605804\pi\)
−0.326307 + 0.945264i \(0.605804\pi\)
\(294\) 0 0
\(295\) 2.27256e9i 0.300074i
\(296\) 1.27771e10 + 6.24465e9i 1.66443 + 0.813470i
\(297\) 0 0
\(298\) −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
\(303\) 0 0
\(304\) 5.45126e8 + 1.15472e9i 0.0638268 + 0.135202i
\(305\) 8.99511e9 1.03946
\(306\) 0 0
\(307\) 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
\(309\) 0 0
\(310\) 5.17670e8 + 4.14468e8i 0.0560540 + 0.0448791i
\(311\) 1.29807e10i 1.38757i 0.720182 + 0.693785i \(0.244058\pi\)
−0.720182 + 0.693785i \(0.755942\pi\)
\(312\) 0 0
\(313\) −6.31165e9 −0.657606 −0.328803 0.944399i \(-0.606645\pi\)
−0.328803 + 0.944399i \(0.606645\pi\)
\(314\) −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 \(0.806837\pi\)
\(318\) 0 0
\(319\) 2.37021e9i 0.228888i
\(320\) −6.28763e9 8.07481e9i −0.599635 0.770074i
\(321\) 0 0
\(322\) −3.31828e9 + 4.14453e9i −0.308667 + 0.385525i
\(323\) 1.42411e9i 0.130838i
\(324\) 0 0
\(325\) 1.01332e8 0.00908264
\(326\) 7.22557e9 + 5.78509e9i 0.639738 + 0.512200i
\(327\) 0 0
\(328\) 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 \(0.0733922\pi\)
−0.973537 + 0.228531i \(0.926608\pi\)
\(332\) 1.29797e10 2.90978e9i 1.06834 0.239501i
\(333\) 0 0
\(334\) −5.84680e9 4.68118e9i −0.469821 0.376158i
\(335\) 9.30657e9i 0.738942i
\(336\) 0 0
\(337\) −3.56226e8 −0.0276189 −0.0138095 0.999905i \(-0.504396\pi\)
−0.0138095 + 0.999905i \(0.504396\pi\)
\(338\) −7.85810e9 + 9.81476e9i −0.602075 + 0.751992i
\(339\) 0 0
\(340\) −2.49675e9 1.11373e10i −0.186836 0.833421i
\(341\) 1.25599e9 0.0928897
\(342\) 0 0
\(343\) 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 \(0.185700\pi\)
−0.834599 + 0.550859i \(0.814300\pi\)
\(348\) 0 0
\(349\) 1.03634e10 0.698553 0.349277 0.937020i \(-0.386427\pi\)
0.349277 + 0.937020i \(0.386427\pi\)
\(350\) −3.23669e8 2.59142e8i −0.0215689 0.0172690i
\(351\) 0 0
\(352\) −1.88546e10 4.49560e9i −1.22814 0.292831i
\(353\) 1.30979e10 0.843536 0.421768 0.906704i \(-0.361410\pi\)
0.421768 + 0.906704i \(0.361410\pi\)
\(354\) 0 0
\(355\) 7.29586e8i 0.0459370i
\(356\) −4.66616e9 2.08144e10i −0.290509 1.29588i
\(357\) 0 0
\(358\) −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
\(363\) 0 0
\(364\) −1.91144e9 + 4.28505e8i −0.108882 + 0.0244090i
\(365\) 3.49263e9 0.196780
\(366\) 0 0
\(367\) 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
\(369\) 0 0
\(370\) 2.11794e10 2.64530e10i 1.13007 1.41146i
\(371\) 1.15308e9i 0.0608646i
\(372\) 0 0
\(373\) −2.10063e10 −1.08521 −0.542606 0.839987i \(-0.682562\pi\)
−0.542606 + 0.839987i \(0.682562\pi\)
\(374\) −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
\(378\) 0 0
\(379\) 3.04816e9i 0.147734i 0.997268 + 0.0738670i \(0.0235340\pi\)
−0.997268 + 0.0738670i \(0.976466\pi\)
\(380\) 2.96899e9 6.65587e8i 0.142388 0.0319206i
\(381\) 0 0
\(382\) −1.23958e10 9.92461e9i −0.582133 0.466080i
\(383\) 2.23357e10i 1.03802i 0.854770 + 0.519008i \(0.173698\pi\)
−0.854770 + 0.519008i \(0.826302\pi\)
\(384\) 0 0
\(385\) 1.57737e10 0.717945
\(386\) 1.17593e10 1.46874e10i 0.529704 0.661599i
\(387\) 0 0
\(388\) −6.75466e9 3.01306e10i −0.298042 1.32948i
\(389\) −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
\(392\) −1.40132e10 6.84880e9i −0.593463 0.290048i
\(393\) 0 0
\(394\) −1.70538e10 + 2.13002e10i −0.707680 + 0.883892i
\(395\) 2.19071e10i 0.899904i
\(396\) 0 0
\(397\) 7.65788e9 0.308281 0.154140 0.988049i \(-0.450739\pi\)
0.154140 + 0.988049i \(0.450739\pi\)
\(398\) 3.11046e10 + 2.49036e10i 1.23963 + 0.992499i
\(399\) 0 0
\(400\) 1.09787e9 5.18285e8i 0.0428854 0.0202455i
\(401\) 3.26120e10 1.26125 0.630623 0.776089i \(-0.282799\pi\)
0.630623 + 0.776089i \(0.282799\pi\)
\(402\) 0 0
\(403\) 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
\(408\) 0 0
\(409\) 2.26168e10 0.808236 0.404118 0.914707i \(-0.367578\pi\)
0.404118 + 0.914707i \(0.367578\pi\)
\(410\) 1.30960e10 1.63569e10i 0.463450 0.578848i
\(411\) 0 0
\(412\) 2.61043e10 5.85205e9i 0.905990 0.203104i
\(413\) −5.21155e9 −0.179129
\(414\) 0 0
\(415\) 3.16958e10i 1.06858i
\(416\) 1.33030e9 5.57931e9i 0.0444199 0.186297i
\(417\) 0 0
\(418\) 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
\(423\) 0 0
\(424\) 3.03339e9 + 1.48253e9i 0.0938565 + 0.0458713i
\(425\) 1.35399e9 0.0415012
\(426\) 0 0
\(427\) 2.06280e10i 0.620505i
\(428\) −2.50618e10 + 5.61834e9i −0.746857 + 0.167430i
\(429\) 0 0
\(430\) 4.51660e10 + 3.61617e10i 1.32111 + 1.05773i
\(431\) 3.06956e10i 0.889544i 0.895644 + 0.444772i \(0.146715\pi\)
−0.895644 + 0.444772i \(0.853285\pi\)
\(432\) 0 0
\(433\) 2.88433e9 0.0820529 0.0410265 0.999158i \(-0.486937\pi\)
0.0410265 + 0.999158i \(0.486937\pi\)
\(434\) 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
\(438\) 0 0
\(439\) 6.92422e10i 1.86429i 0.362088 + 0.932144i \(0.382064\pi\)
−0.362088 + 0.932144i \(0.617936\pi\)
\(440\) −2.02805e10 + 4.14956e10i −0.541088 + 1.10711i
\(441\) 0 0
\(442\) 3.99802e9 4.99353e9i 0.104751 0.130833i
\(443\) 2.06609e10i 0.536455i −0.963356 0.268228i \(-0.913562\pi\)
0.963356 0.268228i \(-0.0864379\pi\)
\(444\) 0 0
\(445\) −5.08278e10 −1.29617
\(446\) −1.84752e10 1.47920e10i −0.466928 0.373842i
\(447\) 0 0
\(448\) −1.85175e10 + 1.44191e10i −0.459696 + 0.357952i
\(449\) −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
\(452\) 3.08476e9 + 1.37602e10i 0.0739039 + 0.329664i
\(453\) 0 0
\(454\) 9.36818e9 + 7.50054e9i 0.220512 + 0.176551i
\(455\) 4.66764e9i 0.108906i
\(456\) 0 0
\(457\) −2.06831e10 −0.474188 −0.237094 0.971487i \(-0.576195\pi\)
−0.237094 + 0.971487i \(0.576195\pi\)
\(458\) −2.84784e10 + 3.55695e10i −0.647223 + 0.808381i
\(459\) 0 0
\(460\) −3.61456e10 + 8.10309e9i −0.807279 + 0.180975i
\(461\) −7.65072e10 −1.69394 −0.846971 0.531640i \(-0.821576\pi\)
−0.846971 + 0.531640i \(0.821576\pi\)
\(462\) 0 0
\(463\) 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 \(-0.935000\pi\)
0.979223 0.202788i \(-0.0650002\pi\)
\(468\) 0 0
\(469\) −2.13423e10 −0.441112
\(470\) 5.81039e10 + 4.65204e10i 1.19073 + 0.953349i
\(471\) 0 0
\(472\) 6.70056e9 1.37099e10i 0.135003 0.276227i
\(473\) 1.09583e11 2.18927
\(474\) 0 0
\(475\) 3.60948e8i 0.00709040i
\(476\) −2.55406e10 + 5.72567e9i −0.497511 + 0.111532i
\(477\) 0 0
\(478\) 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
\(483\) 0 0
\(484\) 7.13124e9 + 3.18104e10i 0.129952 + 0.579679i
\(485\) −7.35776e10 −1.32978
\(486\) 0 0
\(487\) 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
\(489\) 0 0
\(490\) −2.32284e10 + 2.90123e10i −0.402935 + 0.503266i
\(491\) 2.12850e9i 0.0366225i 0.999832 + 0.0183113i \(0.00582898\pi\)
−0.999832 + 0.0183113i \(0.994171\pi\)
\(492\) 0 0
\(493\) −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
\(498\) 0 0
\(499\) 1.04101e10i 0.167901i 0.996470 + 0.0839503i \(0.0267537\pi\)
−0.996470 + 0.0839503i \(0.973246\pi\)
\(500\) −1.39766e10 6.23454e10i −0.223625 0.997527i
\(501\) 0 0
\(502\) −6.51187e10 5.21367e10i −1.02539 0.820973i
\(503\) 3.93019e10i 0.613962i −0.951716 0.306981i \(-0.900681\pi\)
0.951716 0.306981i \(-0.0993188\pi\)
\(504\) 0 0
\(505\) 1.69120e10 0.260034
\(506\) −4.38487e10 + 5.47670e10i −0.668890 + 0.835444i
\(507\) 0 0
\(508\) 6.42387e10 1.44010e10i 0.964587 0.216241i
\(509\) 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
\(512\) −1.41237e10 6.72524e10i −0.205526 0.978652i
\(513\) 0 0
\(514\) 6.13693e10 7.66503e10i 0.879223 1.09815i
\(515\) 6.37455e10i 0.906194i
\(516\) 0 0
\(517\) 1.40973e11 1.97322
\(518\) −6.06633e10 4.85695e10i −0.842572 0.674598i
\(519\) 0 0
\(520\) −1.22791e10 6.00125e9i −0.167939 0.0820783i
\(521\) −1.84550e9 −0.0250475 −0.0125237 0.999922i \(-0.503987\pi\)
−0.0125237 + 0.999922i \(0.503987\pi\)
\(522\) 0 0
\(523\) 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
\(528\) 0 0
\(529\) 2.20424e10 0.281473
\(530\) 5.02817e9 6.28018e9i 0.0637245 0.0795919i
\(531\) 0 0
\(532\) −1.52635e9 6.80863e9i −0.0190550 0.0849988i
\(533\) 1.17434e10 0.145508
\(534\) 0 0
\(535\) 6.11998e10i 0.747025i
\(536\) 2.74400e10 5.61446e10i 0.332449 0.680219i
\(537\) 0 0
\(538\) −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
\(543\) 0 0
\(544\) 1.77755e10 7.45506e10i 0.202967 0.851246i
\(545\) 3.60337e10 0.408435
\(546\) 0 0
\(547\) 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
\(549\) 0 0
\(550\) −4.27705e9 3.42438e9i −0.0467405 0.0374224i
\(551\) 2.49833e9i 0.0271046i
\(552\) 0 0
\(553\) −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 \(0.246666\pi\)
\(558\) 0 0
\(559\) 3.24270e10i 0.332093i
\(560\) 2.38737e10 + 5.05710e10i 0.242755 + 0.514220i
\(561\) 0 0
\(562\) −3.08105e10 + 3.84823e10i −0.308854 + 0.385759i
\(563\) 1.06415e11i 1.05918i 0.848255 + 0.529589i \(0.177654\pi\)
−0.848255 + 0.529589i \(0.822346\pi\)
\(564\) 0 0
\(565\) 3.36018e10 0.329738
\(566\) 1.46273e10 + 1.17112e10i 0.142528 + 0.114113i
\(567\) 0 0
\(568\) 2.15115e9 4.40143e9i 0.0206670 0.0422864i
\(569\) −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 \(0.749986\pi\)
\(572\) −2.52583e10 + 5.66238e9i −0.235950 + 0.0528951i
\(573\) 0 0
\(574\) −3.75103e10 3.00323e10i −0.345544 0.276657i
\(575\) 4.39432e9i 0.0401994i
\(576\) 0 0
\(577\) 4.96477e9 0.0447915 0.0223958 0.999749i \(-0.492871\pi\)
0.0223958 + 0.999749i \(0.492871\pi\)
\(578\) −1.63361e10 + 2.04038e10i −0.146365 + 0.182810i
\(579\) 0 0
\(580\) 4.38006e9 + 1.95382e10i 0.0387051 + 0.172652i
\(581\) −7.26862e10 −0.637892
\(582\) 0 0
\(583\) 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 \(-0.776363\pi\)
0.763181 0.646185i \(-0.223637\pi\)
\(588\) 0 0
\(589\) −1.32388e9 −0.0109999
\(590\) −2.83843e10 2.27256e10i −0.234245 0.187546i
\(591\) 0 0
\(592\) 2.05766e11 9.71390e10i 1.67528 0.790873i
\(593\) −2.06036e11 −1.66619 −0.833094 0.553131i \(-0.813433\pi\)
−0.833094 + 0.553131i \(0.813433\pi\)
\(594\) 0 0
\(595\) 6.23689e10i 0.497623i
\(596\) 2.26017e10 + 1.00820e11i 0.179125 + 0.799027i
\(597\) 0 0
\(598\) −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
\(603\) 0 0
\(604\) −2.09079e11 + 4.68711e10i −1.57095 + 0.352174i
\(605\) 7.76795e10 0.579809
\(606\) 0 0
\(607\) 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
\(609\) 0 0
\(610\) 8.99511e10 1.12349e11i 0.649661 0.811427i
\(611\) 4.17158e10i 0.299320i
\(612\) 0 0
\(613\) 1.27158e11 0.900538 0.450269 0.892893i \(-0.351328\pi\)
0.450269 + 0.892893i \(0.351328\pi\)
\(614\) −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 \(0.444067\pi\)
\(618\) 0 0
\(619\) 7.06748e10i 0.481395i −0.970600 0.240698i \(-0.922624\pi\)
0.970600 0.240698i \(-0.0773762\pi\)
\(620\) 1.03534e10 2.32102e9i 0.0700675 0.0157077i
\(621\) 0 0
\(622\) 1.62128e11 + 1.29807e11i 1.08317 + 0.867231i
\(623\) 1.16561e11i 0.773748i
\(624\) 0 0
\(625\) −1.45008e11 −0.950327
\(626\) −6.31165e10 + 7.88325e10i −0.411004 + 0.513343i
\(627\) 0 0
\(628\) 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 \(0.174537\pi\)
−0.853399 + 0.521259i \(0.825463\pi\)
\(632\) 6.45921e10 1.32161e11i 0.404866 0.828388i
\(633\) 0 0
\(634\) −1.65902e11 + 2.07211e11i −1.02682 + 1.28250i
\(635\) 1.56868e11i 0.964804i
\(636\) 0 0
\(637\) −2.08294e10 −0.126508
\(638\) 2.96039e10 + 2.37021e10i 0.178676 + 0.143055i
\(639\) 0 0
\(640\) −1.63731e11 2.21570e9i −0.975911 0.0132066i
\(641\) −1.12013e11 −0.663490 −0.331745 0.943369i \(-0.607637\pi\)
−0.331745 + 0.943369i \(0.607637\pi\)
\(642\) 0 0
\(643\) 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 \(-0.717197\pi\)
0.630614 0.776097i \(-0.282803\pi\)
\(648\) 0 0
\(649\) −6.88669e10 −0.388179
\(650\) 1.01332e9 1.26563e9i 0.00567665 0.00709013i
\(651\) 0 0
\(652\) 1.44511e11 3.23965e10i 0.799672 0.179270i
\(653\) −3.03789e11 −1.67078 −0.835391 0.549656i \(-0.814759\pi\)
−0.835391 + 0.549656i \(0.814759\pi\)
\(654\) 0 0
\(655\) 1.90427e11i 1.03458i
\(656\) 1.27233e11 6.00646e10i 0.687043 0.324342i
\(657\) 0 0
\(658\) 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
\(663\) 0 0
\(664\) 9.34537e10 1.91214e11i 0.480755 0.983665i
\(665\) −1.66264e10 −0.0850179
\(666\) 0 0
\(667\) 3.04155e10i 0.153671i
\(668\) −1.16936e11 + 2.62146e10i −0.587276 + 0.131655i
\(669\) 0 0
\(670\) −1.16239e11 9.30657e10i −0.576837 0.461839i
\(671\) 2.72584e11i 1.34465i
\(672\) 0 0
\(673\) −3.15336e11 −1.53714 −0.768569 0.639767i \(-0.779031\pi\)
−0.768569 + 0.639767i \(0.779031\pi\)
\(674\) −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 \(0.481257\pi\)
\(678\) 0 0
\(679\) 1.68731e11i 0.793811i
\(680\) −1.64072e11 8.01886e10i −0.767361 0.375039i
\(681\) 0 0
\(682\) 1.25599e10 1.56873e10i 0.0580561 0.0725120i
\(683\) 7.20843e10i 0.331251i −0.986189 0.165626i \(-0.947036\pi\)
0.986189 0.165626i \(-0.0529644\pi\)
\(684\) 0 0
\(685\) 1.35408e11 0.615009
\(686\) 1.67255e11 + 1.33911e11i 0.755235 + 0.604672i
\(687\) 0 0
\(688\) 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 \(-0.775651\pi\)
0.761732 0.647892i \(-0.224349\pi\)
\(692\) −1.15470e10 5.15080e10i −0.0503554 0.224621i
\(693\) 0 0
\(694\) 1.99503e11 + 1.59731e11i 0.860028 + 0.688573i
\(695\) 1.79968e11i 0.771360i
\(696\) 0 0
\(697\) 1.56916e11 0.664867
\(698\) 1.03634e11 1.29438e11i 0.436596 0.545308i
\(699\) 0 0
\(700\) −6.47338e9 + 1.45120e9i −0.0269612 + 0.00604414i
\(701\) 2.87925e11 1.19236 0.596180 0.802851i \(-0.296685\pi\)
0.596180 + 0.802851i \(0.296685\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) 2.51685e11 0.996030 0.498015 0.867168i \(-0.334062\pi\)
0.498015 + 0.867168i \(0.334062\pi\)
\(710\) −9.11252e9 7.29586e9i −0.0358596 0.0287106i
\(711\) 0 0
\(712\) −3.06633e11 1.49864e11i −1.19316 0.583144i
\(713\) 1.61174e10 0.0623643
\(714\) 0 0
\(715\) 6.16795e10i 0.236003i
\(716\) −3.54493e10 + 7.94701e9i −0.134883 + 0.0302379i
\(717\) 0 0
\(718\) −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
\(723\) 0 0
\(724\) −2.70237e10 1.20545e11i −0.0983536 0.438727i
\(725\) −2.37531e9 −0.00859743
\(726\) 0 0
\(727\) 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
\(729\) 0 0
\(730\) 3.49263e10 4.36230e10i 0.122988 0.153612i
\(731\) 4.33289e11i 1.51743i
\(732\) 0 0
\(733\) 2.17618e11 0.753839 0.376920 0.926246i \(-0.376983\pi\)
0.376920 + 0.926246i \(0.376983\pi\)
\(734\) 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
\(738\) 0 0
\(739\) 4.84950e11i 1.62599i 0.582268 + 0.812997i \(0.302166\pi\)
−0.582268 + 0.812997i \(0.697834\pi\)
\(740\) −1.18605e11 5.29061e11i −0.395525 1.76433i
\(741\) 0 0
\(742\) −1.44020e10 1.15308e10i −0.0475124 0.0380404i
\(743\) 2.03509e11i 0.667771i −0.942614 0.333886i \(-0.891640\pi\)
0.942614 0.333886i \(-0.108360\pi\)
\(744\) 0 0
\(745\) 2.46198e11 0.799206
\(746\) −2.10063e11 + 2.62369e11i −0.678258 + 0.847144i
\(747\) 0 0
\(748\) −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 \(0.120266\pi\)
−0.929468 + 0.368902i \(0.879734\pi\)
\(752\) 2.13365e11 + 4.51965e11i 0.667194 + 1.41330i
\(753\) 0 0
\(754\) −7.01374e9 + 8.76016e9i −0.0217002 + 0.0271036i
\(755\) 5.10561e11i 1.57130i
\(756\) 0 0
\(757\) −3.84882e11 −1.17204 −0.586022 0.810295i \(-0.699307\pi\)
−0.586022 + 0.810295i \(0.699307\pi\)
\(758\) 3.80715e10 + 3.04816e10i 0.115325 + 0.0923338i
\(759\) 0 0
\(760\) 2.13767e10 4.37386e10i 0.0640748 0.131102i
\(761\) −2.39209e11 −0.713244 −0.356622 0.934249i \(-0.616072\pi\)
−0.356622 + 0.934249i \(0.616072\pi\)
\(762\) 0 0
\(763\) 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 0.0588833i
\(768\) 0 0
\(769\) 2.08457e11 0.596089 0.298045 0.954552i \(-0.403666\pi\)
0.298045 + 0.954552i \(0.403666\pi\)
\(770\) 1.57737e11 1.97014e11i 0.448716 0.560446i
\(771\) 0 0
\(772\) −6.58522e10 2.93748e11i −0.185396 0.826999i