Properties

Label 4.9.b.b.3.1
Level $4$
Weight $9$
Character 4.3
Analytic conductor $1.630$
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] = [4,9,Mod(3,4)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4.3");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 4.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: \(1.62951444024\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.1
Root \(0.500000 + 3.12250i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.9.b.b.3.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.0000 - 12.4900i) q^{2} -99.9200i q^{3} +(-56.0000 + 249.800i) q^{4} +610.000 q^{5} +(-1248.00 + 999.200i) q^{6} -1398.88i q^{7} +(3680.00 - 1798.56i) q^{8} -3423.00 q^{9} +O(q^{10})\) \(q+(-10.0000 - 12.4900i) q^{2} -99.9200i q^{3} +(-56.0000 + 249.800i) q^{4} +610.000 q^{5} +(-1248.00 + 999.200i) q^{6} -1398.88i q^{7} +(3680.00 - 1798.56i) q^{8} -3423.00 q^{9} +(-6100.00 - 7618.90i) q^{10} +18485.2i q^{11} +(24960.0 + 5595.52i) q^{12} -5470.00 q^{13} +(-17472.0 + 13988.8i) q^{14} -60951.2i q^{15} +(-59264.0 - 27977.6i) q^{16} +73090.0 q^{17} +(34230.0 + 42753.3i) q^{18} +19484.4i q^{19} +(-34160.0 + 152378. i) q^{20} -139776. q^{21} +(230880. - 184852. i) q^{22} +237210. i q^{23} +(-179712. - 367705. i) q^{24} -18525.0 q^{25} +(54700.0 + 68320.3i) q^{26} -313549. i q^{27} +(349440. + 78337.3i) q^{28} -128222. q^{29} +(-761280. + 609512. i) q^{30} +67945.6i q^{31} +(243200. + 1.01998e6i) q^{32} +1.84704e6 q^{33} +(-730900. - 912894. i) q^{34} -853317. i q^{35} +(191688. - 855065. i) q^{36} -3.47203e6 q^{37} +(243360. - 194844. i) q^{38} +546562. i q^{39} +(2.24480e6 - 1.09712e6i) q^{40} +2.14688e6 q^{41} +(1.39776e6 + 1.74580e6i) q^{42} +5.92815e6i q^{43} +(-4.61760e6 - 1.03517e6i) q^{44} -2.08803e6 q^{45} +(2.96275e6 - 2.37210e6i) q^{46} -7.62629e6i q^{47} +(-2.79552e6 + 5.92166e6i) q^{48} +3.80794e6 q^{49} +(185250. + 231377. i) q^{50} -7.30315e6i q^{51} +(306320. - 1.36641e6i) q^{52} +824290. q^{53} +(-3.91622e6 + 3.13549e6i) q^{54} +1.12760e7i q^{55} +(-2.51597e6 - 5.14788e6i) q^{56} +1.94688e6 q^{57} +(1.28222e6 + 1.60149e6i) q^{58} +3.72552e6i q^{59} +(1.52256e7 + 3.41327e6i) q^{60} -1.47461e7 q^{61} +(848640. - 679456. i) q^{62} +4.78836e6i q^{63} +(1.03076e7 - 1.32374e7i) q^{64} -3.33670e6 q^{65} +(-1.84704e7 - 2.30695e7i) q^{66} -1.52567e7i q^{67} +(-4.09304e6 + 1.82579e7i) q^{68} +2.37020e7 q^{69} +(-1.06579e7 + 8.53317e6i) q^{70} +1.19604e6i q^{71} +(-1.25966e7 + 6.15647e6i) q^{72} -5.72563e6 q^{73} +(3.47203e7 + 4.33656e7i) q^{74} +1.85102e6i q^{75} +(-4.86720e6 - 1.09113e6i) q^{76} +2.58586e7 q^{77} +(6.82656e6 - 5.46562e6i) q^{78} -3.59132e7i q^{79} +(-3.61510e7 - 1.70663e7i) q^{80} -5.37881e7 q^{81} +(-2.14688e7 - 2.68145e7i) q^{82} +5.19603e7i q^{83} +(7.82746e6 - 3.49160e7i) q^{84} +4.45849e7 q^{85} +(7.40426e7 - 5.92815e7i) q^{86} +1.28119e7i q^{87} +(3.32467e7 + 6.80255e7i) q^{88} -8.33242e7 q^{89} +(2.08803e7 + 2.60795e7i) q^{90} +7.65187e6i q^{91} +(-5.92550e7 - 1.32838e7i) q^{92} +6.78912e6 q^{93} +(-9.52524e7 + 7.62629e7i) q^{94} +1.18855e7i q^{95} +(1.01917e8 - 2.43005e7i) q^{96} +1.20619e8 q^{97} +(-3.80794e7 - 4.75611e7i) q^{98} -6.32748e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 20 q^{2} - 112 q^{4} + 1220 q^{5} - 2496 q^{6} + 7360 q^{8} - 6846 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 20 q^{2} - 112 q^{4} + 1220 q^{5} - 2496 q^{6} + 7360 q^{8} - 6846 q^{9} - 12200 q^{10} + 49920 q^{12} - 10940 q^{13} - 34944 q^{14} - 118528 q^{16} + 146180 q^{17} + 68460 q^{18} - 68320 q^{20} - 279552 q^{21} + 461760 q^{22} - 359424 q^{24} - 37050 q^{25} + 109400 q^{26} + 698880 q^{28} - 256444 q^{29} - 1522560 q^{30} + 486400 q^{32} + 3694080 q^{33} - 1461800 q^{34} + 383376 q^{36} - 6944060 q^{37} + 486720 q^{38} + 4489600 q^{40} + 4293764 q^{41} + 2795520 q^{42} - 9235200 q^{44} - 4176060 q^{45} + 5925504 q^{46} - 5591040 q^{48} + 7615874 q^{49} + 370500 q^{50} + 612640 q^{52} + 1648580 q^{53} - 7832448 q^{54} - 5031936 q^{56} + 3893760 q^{57} + 2564440 q^{58} + 30451200 q^{60} - 29492156 q^{61} + 1697280 q^{62} + 20615168 q^{64} - 6673400 q^{65} - 36940800 q^{66} - 8186080 q^{68} + 47404032 q^{69} - 21315840 q^{70} - 25193280 q^{72} - 11451260 q^{73} + 69440600 q^{74} - 9734400 q^{76} + 51717120 q^{77} + 13653120 q^{78} - 72302080 q^{80} - 107576190 q^{81} - 42937640 q^{82} + 15654912 q^{84} + 89169800 q^{85} + 148085184 q^{86} + 66493440 q^{88} - 166648444 q^{89} + 41760600 q^{90} - 118510080 q^{92} + 13578240 q^{93} - 190504704 q^{94} + 203833344 q^{96} + 241238020 q^{97} - 76158740 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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 \(-0.788433\pi\)
0.787128 0.616790i \(-0.211567\pi\)
\(4\) −56.0000 + 249.800i −0.218750 + 0.975781i
\(5\) 610.000 0.976000 0.488000 0.872844i \(-0.337727\pi\)
0.488000 + 0.872844i \(0.337727\pi\)
\(6\) −1248.00 + 999.200i −0.962963 + 0.770987i
\(7\) 1398.88i 0.582624i −0.956628 0.291312i \(-0.905908\pi\)
0.956628 0.291312i \(-0.0940917\pi\)
\(8\) 3680.00 1798.56i 0.898438 0.439101i
\(9\) −3423.00 −0.521719
\(10\) −6100.00 7618.90i −0.610000 0.761890i
\(11\) 18485.2i 1.26256i 0.775554 + 0.631282i \(0.217471\pi\)
−0.775554 + 0.631282i \(0.782529\pi\)
\(12\) 24960.0 + 5595.52i 1.20370 + 0.269846i
\(13\) −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
\(15\) 60951.2i 1.20397i
\(16\) −59264.0 27977.6i −0.904297 0.426904i
\(17\) 73090.0 0.875109 0.437555 0.899192i \(-0.355845\pi\)
0.437555 + 0.899192i \(0.355845\pi\)
\(18\) 34230.0 + 42753.3i 0.326075 + 0.407267i
\(19\) 19484.4i 0.149511i 0.997202 + 0.0747554i \(0.0238176\pi\)
−0.997202 + 0.0747554i \(0.976182\pi\)
\(20\) −34160.0 + 152378.i −0.213500 + 0.952362i
\(21\) −139776. −0.718713
\(22\) 230880. 184852.i 0.985588 0.789102i
\(23\) 237210.i 0.847660i 0.905742 + 0.423830i \(0.139315\pi\)
−0.905742 + 0.423830i \(0.860685\pi\)
\(24\) −179712. 367705.i −0.541667 1.10829i
\(25\) −18525.0 −0.0474240
\(26\) 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 \(0.528893\pi\)
\(30\) −761280. + 609512.i −0.939852 + 0.752484i
\(31\) 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
\(35\) 853317.i 0.568641i
\(36\) 191688. 855065.i 0.114126 0.509084i
\(37\) −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
\(39\) 546562.i 0.236255i
\(40\) 2.24480e6 1.09712e6i 0.876875 0.428563i
\(41\) 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 \(0.333950\pi\)
−0.498321 + 0.866993i \(0.666050\pi\)
\(44\) −4.61760e6 1.03517e6i −1.23199 0.276186i
\(45\) −2.08803e6 −0.509198
\(46\) 2.96275e6 2.37210e6i 0.661704 0.529787i
\(47\) 7.62629e6i 1.56287i −0.623989 0.781433i \(-0.714489\pi\)
0.623989 0.781433i \(-0.285511\pi\)
\(48\) −2.79552e6 + 5.92166e6i −0.526620 + 1.11552i
\(49\) 3.80794e6 0.660550
\(50\) 185250. + 231377.i 0.0296400 + 0.0370203i
\(51\) 7.30315e6i 1.07952i
\(52\) 306320. 1.36641e6i 0.0418950 0.186881i
\(53\) 824290. 0.104466 0.0522332 0.998635i \(-0.483366\pi\)
0.0522332 + 0.998635i \(0.483366\pi\)
\(54\) −3.91622e6 + 3.13549e6i −0.460567 + 0.368748i
\(55\) 1.12760e7i 1.23226i
\(56\) −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 \(0.950873\pi\)
\(60\) 1.52256e7 + 3.41327e6i 1.17481 + 0.263369i
\(61\) −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
\(65\) −3.33670e6 −0.186923
\(66\) −1.84704e7 2.30695e7i −0.973421 1.21580i
\(67\) 1.52567e7i 0.757113i −0.925578 0.378557i \(-0.876421\pi\)
0.925578 0.378557i \(-0.123579\pi\)
\(68\) −4.09304e6 + 1.82579e7i −0.191430 + 0.853915i
\(69\) 2.37020e7 1.04566
\(70\) −1.06579e7 + 8.53317e6i −0.443895 + 0.355400i
\(71\) 1.19604e6i 0.0470666i 0.999723 + 0.0235333i \(0.00749158\pi\)
−0.999723 + 0.0235333i \(0.992508\pi\)
\(72\) −1.25966e7 + 6.15647e6i −0.468732 + 0.229088i
\(73\) −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
\(75\) 1.85102e6i 0.0585013i
\(76\) −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 \(-0.152515\pi\)
\(80\) −3.61510e7 1.70663e7i −0.882594 0.416658i
\(81\) −5.37881e7 −1.24953
\(82\) −2.14688e7 2.68145e7i −0.474846 0.593082i
\(83\) 5.19603e7i 1.09486i 0.836851 + 0.547431i \(0.184394\pi\)
−0.836851 + 0.547431i \(0.815606\pi\)
\(84\) 7.82746e6 3.49160e7i 0.157218 0.701306i
\(85\) 4.45849e7 0.854107
\(86\) 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 \(0.731151\pi\)
\(90\) 2.08803e7 + 2.60795e7i 0.318249 + 0.397493i
\(91\) 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
\(95\) 1.18855e7i 0.145923i
\(96\) 1.01917e8 2.43005e7i 1.19994 0.286109i
\(97\) 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
\(99\) 6.32748e7i 0.658704i
\(100\) 1.03740e6 4.62754e6i 0.0103740 0.0462754i
\(101\) 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 \(-0.846328\pi\)
0.885710 0.464238i \(-0.153672\pi\)
\(104\) −2.01296e7 + 9.83812e6i −0.172069 + 0.0840967i
\(105\) −8.52634e7 −0.701464
\(106\) −8.24290e6 1.02954e7i −0.0652915 0.0815490i
\(107\) 1.00328e8i 0.765394i −0.923874 0.382697i \(-0.874995\pi\)
0.923874 0.382697i \(-0.125005\pi\)
\(108\) 7.83245e7 + 1.75587e7i 0.575708 + 0.129062i
\(109\) −5.90716e7 −0.418478 −0.209239 0.977865i \(-0.567099\pi\)
−0.209239 + 0.977865i \(0.567099\pi\)
\(110\) 1.40837e8 1.12760e8i 0.961934 0.770164i
\(111\) 3.46925e8i 2.28530i
\(112\) −3.91373e7 + 8.29032e7i −0.248724 + 0.526865i
\(113\) 5.50849e7 0.337846 0.168923 0.985629i \(-0.445971\pi\)
0.168923 + 0.985629i \(0.445971\pi\)
\(114\) −1.94688e7 2.43165e7i −0.115271 0.143973i
\(115\) 1.44698e8i 0.827316i
\(116\) 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
\(120\) −1.09624e8 2.24300e8i −0.528667 1.08170i
\(121\) −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
\(125\) −2.49581e8 −1.02229
\(126\) 5.98067e7 4.78836e7i 0.237283 0.189979i
\(127\) 2.57160e8i 0.988529i −0.869312 0.494264i \(-0.835438\pi\)
0.869312 0.494264i \(-0.164562\pi\)
\(128\) −2.68411e8 + 3.63229e6i −0.999908 + 0.0135313i
\(129\) 5.92341e8 2.13901
\(130\) 3.33670e7 + 4.16754e7i 0.116827 + 0.145917i
\(131\) 3.12175e8i 1.06002i 0.847992 + 0.530009i \(0.177812\pi\)
−0.847992 + 0.530009i \(0.822188\pi\)
\(132\) −1.03434e8 + 4.61390e8i −0.340697 + 1.51975i
\(133\) 2.72563e7 0.0871085
\(134\) −1.90556e8 + 1.52567e8i −0.591021 + 0.473196i
\(135\) 1.91265e8i 0.575838i
\(136\) 2.68971e8 1.31457e8i 0.786231 0.384262i
\(137\) 2.21980e8 0.630132 0.315066 0.949070i \(-0.397973\pi\)
0.315066 + 0.949070i \(0.397973\pi\)
\(138\) −2.37020e8 2.96038e8i −0.653535 0.816265i
\(139\) 2.95030e8i 0.790328i 0.918611 + 0.395164i \(0.129312\pi\)
−0.918611 + 0.395164i \(0.870688\pi\)
\(140\) 2.13158e8 + 4.77857e7i 0.554869 + 0.124390i
\(141\) −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
\(145\) −7.82154e7 −0.176938
\(146\) 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 \(0.365728\pi\)
\(150\) 2.31192e7 1.85102e7i 0.0456676 0.0365633i
\(151\) 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
\(155\) 4.14468e7i 0.0718066i
\(156\) −1.36531e8 3.06075e7i −0.230533 0.0516808i
\(157\) −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
\(159\) 8.23630e7i 0.128868i
\(160\) 1.48352e8 + 6.22190e8i 0.226367 + 0.949386i
\(161\) 3.31828e8 0.493867
\(162\) 5.37881e8 + 6.71813e8i 0.780955 + 0.975413i
\(163\) 5.78509e8i 0.819520i −0.912193 0.409760i \(-0.865612\pi\)
0.912193 0.409760i \(-0.134388\pi\)
\(164\) −1.20225e8 + 5.36291e8i −0.166196 + 0.741353i
\(165\) 1.12669e9 1.52009
\(166\) 6.48984e8 5.19603e8i 0.854676 0.684288i
\(167\) 4.68118e8i 0.601852i −0.953647 0.300926i \(-0.902704\pi\)
0.953647 0.300926i \(-0.0972958\pi\)
\(168\) −5.14376e8 + 2.51395e8i −0.645719 + 0.315588i
\(169\) −7.85810e8 −0.963320
\(170\) −4.45849e8 5.56865e8i −0.533817 0.666737i
\(171\) 6.66951e7i 0.0780026i
\(172\) −1.48085e9 3.31976e8i −1.69199 0.379309i
\(173\) −2.06197e8 −0.230196 −0.115098 0.993354i \(-0.536718\pi\)
−0.115098 + 0.993354i \(0.536718\pi\)
\(174\) 1.60021e8 1.28119e8i 0.174574 0.139771i
\(175\) 2.59142e7i 0.0276303i
\(176\) 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 \(-0.0220176\pi\)
\(180\) 1.16930e8 5.21590e8i 0.111387 0.496866i
\(181\) 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
\(185\) −2.11794e9 −1.80812
\(186\) −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
\(190\) 1.48450e8 1.18855e8i 0.113911 0.0912016i
\(191\) 9.92461e8i 0.745727i −0.927886 0.372864i \(-0.878376\pi\)
0.927886 0.372864i \(-0.121624\pi\)
\(192\) −1.32268e9 1.02993e9i −0.973307 0.757887i
\(193\) 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
\(195\) 3.33403e8i 0.230585i
\(196\) −2.13244e8 + 9.51222e8i −0.144495 + 0.644552i
\(197\) 1.70538e9 1.13229 0.566144 0.824306i \(-0.308435\pi\)
0.566144 + 0.824306i \(0.308435\pi\)
\(198\) −7.90302e8 + 6.32748e8i −0.514200 + 0.411690i
\(199\) 2.49036e9i 1.58800i −0.607919 0.793999i \(-0.707996\pi\)
0.607919 0.793999i \(-0.292004\pi\)
\(200\) −6.81720e7 + 3.33183e7i −0.0426075 + 0.0208239i
\(201\) −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
\(205\) 1.30960e9 0.741519
\(206\) −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
\(210\) 8.52634e8 + 1.06494e9i 0.438415 + 0.547580i
\(211\) 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
\(215\) 3.61617e9i 1.69237i
\(216\) −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
\(220\) −2.81674e9 6.31454e8i −1.20242 0.269557i
\(221\) −3.99802e8 −0.167601
\(222\) 4.33309e9 3.46925e9i 1.78396 1.42831i
\(223\) 1.47920e9i 0.598147i 0.954230 + 0.299073i \(0.0966776\pi\)
−0.954230 + 0.299073i \(0.903322\pi\)
\(224\) 1.42683e9 3.40208e8i 0.566737 0.135130i
\(225\) 6.34111e7 0.0247420
\(226\) −5.50849e8 6.88011e8i −0.211154 0.263731i
\(227\) 7.50054e8i 0.282481i 0.989975 + 0.141241i \(0.0451091\pi\)
−0.989975 + 0.141241i \(0.954891\pi\)
\(228\) −1.09025e8 + 4.86330e8i −0.0403448 + 0.179967i
\(229\) −2.84784e9 −1.03556 −0.517778 0.855515i \(-0.673241\pi\)
−0.517778 + 0.855515i \(0.673241\pi\)
\(230\) 1.80728e9 1.44698e9i 0.645823 0.517073i
\(231\) 2.58379e9i 0.907421i
\(232\) −4.71857e8 + 2.30615e8i −0.162876 + 0.0796041i
\(233\) 2.20621e8 0.0748553 0.0374276 0.999299i \(-0.488084\pi\)
0.0374276 + 0.999299i \(0.488084\pi\)
\(234\) −1.87238e8 2.33860e8i −0.0624498 0.0779997i
\(235\) 4.65204e9i 1.52536i
\(236\) −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 \(0.787192\pi\)
\(240\) −1.70527e9 + 3.61221e9i −0.513981 + 1.08875i
\(241\) 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
\(245\) 2.32284e9 0.644696
\(246\) −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
\(250\) 2.49582e9 + 3.11727e9i 0.638929 + 0.798022i
\(251\) 5.21367e9i 1.31356i −0.754084 0.656778i \(-0.771919\pi\)
0.754084 0.656778i \(-0.228081\pi\)
\(252\) −1.19613e9 2.68148e8i −0.296604 0.0664926i
\(253\) −4.38487e9 −1.07022
\(254\) −3.21193e9 + 2.57160e9i −0.771670 + 0.617830i
\(255\) 4.45492e9i 1.05361i
\(256\) 2.72948e9 + 3.31613e9i 0.635506 + 0.772096i
\(257\) −6.13693e9 −1.40676 −0.703378 0.710816i \(-0.748326\pi\)
−0.703378 + 0.710816i \(0.748326\pi\)
\(258\) −5.92341e9 7.39833e9i −1.33688 1.66976i
\(259\) 4.85695e9i 1.07936i
\(260\) 1.86855e8 8.33507e8i 0.0408895 0.182396i
\(261\) 4.38904e8 0.0945818
\(262\) 3.89907e9 3.12175e9i 0.827477 0.662512i
\(263\) 6.96916e9i 1.45666i −0.685228 0.728329i \(-0.740297\pi\)
0.685228 0.728329i \(-0.259703\pi\)
\(264\) 6.79711e9 3.32201e9i 1.39929 0.683889i
\(265\) 5.02817e8 0.101959
\(266\) −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 \(0.416768\pi\)
\(270\) −2.38890e9 + 1.91265e9i −0.449513 + 0.359898i
\(271\) 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
\(275\) 3.42438e8i 0.0598758i
\(276\) −1.32731e9 + 5.92076e9i −0.228737 + 1.02033i
\(277\) −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
\(279\) 2.32578e8i 0.0383841i
\(280\) −1.53474e9 3.14020e9i −0.249691 0.510888i
\(281\) 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 \(-0.970901\pi\)
0.995824 0.0912908i \(-0.0290993\pi\)
\(284\) −2.98771e8 6.69784e7i −0.0459267 0.0102958i
\(285\) 1.18760e9 0.180007
\(286\) −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
\(290\) 7.82154e8 + 9.76910e8i 0.110586 + 0.138122i
\(291\) 1.20522e10i 1.68072i
\(292\) 3.20635e8 1.43026e9i 0.0441042 0.196736i
\(293\) 4.80980e9 0.652614 0.326307 0.945264i \(-0.394196\pi\)
0.326307 + 0.945264i \(0.394196\pi\)
\(294\) −4.75231e9 + 3.80489e9i −0.636085 + 0.509275i
\(295\) 2.27256e9i 0.300074i
\(296\) −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
\(300\) −4.62384e8 1.03657e8i −0.0570844 0.0127972i
\(301\) 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
\(305\) −8.99511e9 −1.03946
\(306\) 2.50187e9 + 3.12484e9i 0.285351 + 0.356403i
\(307\) 3.49176e9i 0.393089i 0.980495 + 0.196545i \(0.0629721\pi\)
−0.980495 + 0.196545i \(0.937028\pi\)
\(308\) −1.44808e9 + 6.45947e9i −0.160912 + 0.717784i
\(309\) −1.04417e10 −1.14535
\(310\) 5.17670e8 4.14468e8i 0.0560540 0.0448791i
\(311\) 1.29807e10i 1.38757i 0.720182 + 0.693785i \(0.244058\pi\)
−0.720182 + 0.693785i \(0.755942\pi\)
\(312\) 9.83025e8 + 2.01135e9i 0.103740 + 0.212260i
\(313\) −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
\(315\) 2.92090e9i 0.296671i
\(316\) 8.97112e9 + 2.01114e9i 0.899702 + 0.201695i
\(317\) 1.65902e10 1.64291 0.821455 0.570273i \(-0.193163\pi\)
0.821455 + 0.570273i \(0.193163\pi\)
\(318\) −1.02871e9 + 8.23630e8i −0.100597 + 0.0805423i
\(319\) 2.37021e9i 0.228888i
\(320\) 6.28763e9 8.07481e9i 0.599635 0.770074i
\(321\) −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
\(325\) 1.01332e8 0.00908264
\(326\) −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
\(330\) −1.12669e10 1.40724e10i −0.950059 1.18662i
\(331\) 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
\(335\) 9.30657e9i 0.738942i
\(336\) 8.28368e9 + 3.91060e9i 0.649930 + 0.306822i
\(337\) −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
\(339\) 5.50408e9i 0.416760i
\(340\) −2.49675e9 + 1.11373e10i −0.186836 + 0.833421i
\(341\) −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
\(345\) 1.44582e10 1.02056
\(346\) 2.06197e9 + 2.57540e9i 0.143872 + 0.179697i
\(347\) 1.59731e10i 1.10172i 0.834599 + 0.550859i \(0.185700\pi\)
−0.834599 + 0.550859i \(0.814300\pi\)
\(348\) −3.20042e9 7.17469e8i −0.218218 0.0489199i
\(349\) 1.03634e10 0.698553 0.349277 0.937020i \(-0.386427\pi\)
0.349277 + 0.937020i \(0.386427\pi\)
\(350\) 3.23669e8 2.59142e8i 0.0215689 0.0172690i
\(351\) 1.71511e9i 0.112996i
\(352\) −1.88546e10 + 4.49560e9i −1.22814 + 0.292831i
\(353\) −1.30979e10 −0.843536 −0.421768 0.906704i \(-0.638590\pi\)
−0.421768 + 0.906704i \(0.638590\pi\)
\(354\) −3.72253e9 4.64944e9i −0.237042 0.296066i
\(355\) 7.29586e8i 0.0459370i
\(356\) 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 \(-0.0318119\pi\)
\(360\) −7.68395e9 + 3.75545e9i −0.457483 + 0.223590i
\(361\) 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
\(365\) −3.49263e9 −0.196780
\(366\) 1.84031e10 1.47343e10i 1.02557 0.821116i
\(367\) 1.96628e10i 1.08388i −0.840418 0.541939i \(-0.817691\pi\)
0.840418 0.541939i \(-0.182309\pi\)
\(368\) 6.63656e9 1.40580e10i 0.361870 0.766536i
\(369\) −7.34878e9 −0.396378
\(370\) 2.11794e10 + 2.64530e10i 1.13007 + 1.41146i
\(371\) 1.15308e9i 0.0608646i
\(372\) −3.80191e8 + 1.69592e9i −0.0198532 + 0.0885593i
\(373\) −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
\(375\) 2.49382e10i 1.26107i
\(376\) −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 \(-0.0235340\pi\)
\(380\) −2.96899e9 6.65587e8i −0.142388 0.0319206i
\(381\) −2.56955e10 −1.21943
\(382\) −1.23958e10 + 9.92461e9i −0.582133 + 0.466080i
\(383\) 2.23357e10i 1.03802i 0.854770 + 0.519008i \(0.173698\pi\)
−0.854770 + 0.519008i \(0.826302\pi\)
\(384\) 3.62938e8 + 2.68196e10i 0.0166920 + 1.23347i
\(385\) 1.57737e10 0.717945
\(386\) −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 \(0.259825\pi\)
\(390\) 4.16420e9 3.33403e9i 0.180000 0.144116i
\(391\) 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
\(395\) 2.19071e10i 0.899904i
\(396\) 1.58060e10 + 3.54339e9i 0.642751 + 0.144091i
\(397\) 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
\(399\) 2.72345e9i 0.107455i
\(400\) 1.09787e9 + 5.18285e8i 0.0428854 + 0.0202455i
\(401\) −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
\(405\) −3.28107e10 −1.21954
\(406\) 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 \(0.367578\pi\)
\(410\) −1.30960e10 1.63569e10i −0.463450 0.578848i
\(411\) 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
\(415\) 3.16958e10i 1.06858i
\(416\) −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 \(0.703662\pi\)
\(420\) 4.77475e9 2.12988e10i 0.153445 0.684475i
\(421\) −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
\(425\) −1.35399e9 −0.0415012
\(426\) −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
\(430\) 4.51660e10 3.61617e10i 1.32111 1.05773i
\(431\) 3.06956e10i 0.889544i 0.895644 + 0.444772i \(0.146715\pi\)
−0.895644 + 0.444772i \(0.853285\pi\)
\(432\) −8.77234e9 + 1.85822e10i −0.251872 + 0.533533i
\(433\) 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
\(435\) 7.81528e9i 0.218267i
\(436\) 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 \(-0.382064\pi\)
\(440\) 2.02805e10 + 4.14956e10i 0.541088 + 1.10711i
\(441\) −1.30346e10 −0.344621
\(442\) 3.99802e9 + 4.99353e9i 0.104751 + 0.130833i
\(443\) 2.06609e10i 0.536455i −0.963356 0.268228i \(-0.913562\pi\)
0.963356 0.268228i \(-0.0864379\pi\)
\(444\) −8.66619e10 1.94278e10i −2.22996 0.499910i
\(445\) −5.08278e10 −1.29617
\(446\) 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 \(0.416379\pi\)
\(450\) −6.34111e8 7.92004e8i −0.0154638 0.0193142i
\(451\) 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
\(455\) 4.66764e9i 0.108906i
\(456\) 7.16452e9 3.50158e9i 0.165702 0.0809850i
\(457\) −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
\(459\) 2.29173e10i 0.516312i
\(460\) −3.61456e10 8.10309e9i −0.807279 0.180975i
\(461\) 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 \(-0.988177\pi\)
0.999310 0.0371352i \(-0.0118232\pi\)
\(464\) 7.59895e9 + 3.58734e9i 0.163939 + 0.0773929i
\(465\) 4.14136e9 0.0885791
\(466\) −2.20621e9 2.75555e9i −0.0467845 0.0584339i
\(467\) 1.92903e10i 0.405576i −0.979223 0.202788i \(-0.935000\pi\)
0.979223 0.202788i \(-0.0650002\pi\)
\(468\) −1.04853e9 + 4.67721e9i −0.0218574 + 0.0974997i
\(469\) −2.13423e10 −0.441112
\(470\) −5.81039e10 + 4.65204e10i −1.19073 + 0.953349i
\(471\) 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
\(475\) 3.60948e8i 0.00709040i
\(476\) 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 \(0.925590\pi\)
\(480\) 6.21692e10 1.48233e10i 1.17114 0.279242i
\(481\) 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
\(485\) 7.35776e10 1.32978
\(486\) 4.14332e10 3.31731e10i 0.742683 0.594622i
\(487\) 9.30801e10i 1.65478i 0.561626 + 0.827391i \(0.310176\pi\)
−0.561626 + 0.827391i \(0.689824\pi\)
\(488\) −5.42656e10 + 2.65217e10i −0.956853 + 0.467651i
\(489\) −5.78046e10 −1.01094
\(490\) −2.32284e10 2.90123e10i −0.402935 0.503266i
\(491\) 2.12850e9i 0.0366225i 0.999832 + 0.0183113i \(0.00582898\pi\)
−0.999832 + 0.0183113i \(0.994171\pi\)
\(492\) 5.35862e10 + 1.20129e10i 0.914518 + 0.205016i
\(493\) −9.37175e9 −0.158647
\(494\) −1.33118e9 + 1.06580e9i −0.0223526 + 0.0178964i
\(495\) 3.85976e10i 0.642895i
\(496\) 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 \(-0.0267537\pi\)
\(500\) 1.39766e10 6.23454e10i 0.223625 0.997527i
\(501\) −4.67744e10 −0.742433
\(502\) −6.51187e10 + 5.21367e10i −1.02539 + 0.820973i
\(503\) 3.93019e10i 0.613962i −0.951716 0.306981i \(-0.900681\pi\)
0.951716 0.306981i \(-0.0993188\pi\)
\(504\) 8.61216e9 + 1.76212e10i 0.133472 + 0.273094i
\(505\) 1.69120e10 0.260034
\(506\) 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 \(0.577861\pi\)
\(510\) −5.56420e10 + 4.45492e10i −0.822473 + 0.658505i
\(511\) 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
\(515\) 6.37455e10i 0.906194i
\(516\) −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
\(520\) −1.22791e10 + 6.00125e9i −0.167939 + 0.0820783i
\(521\) 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 \(-0.863131\pi\)
0.908972 0.416858i \(-0.136869\pi\)
\(524\) −7.79814e10 1.74818e10i −1.03435 0.231879i
\(525\) 2.58935e9 0.0340842
\(526\) −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
\(530\) −5.02817e9 6.28018e9i −0.0637245 0.0795919i
\(531\) 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
\(535\) 6.11998e10i 0.747025i
\(536\) −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
\(540\) 4.77779e10 + 1.07108e10i 0.561891 + 0.125964i
\(541\) −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
\(545\) −3.60337e10 −0.408435
\(546\) −7.64575e9 9.54954e9i −0.0860299 0.107451i
\(547\) 1.41531e9i 0.0158089i −0.999969 0.00790445i \(-0.997484\pi\)
0.999969 0.00790445i \(-0.00251609\pi\)
\(548\) −1.24309e10 + 5.54506e10i −0.137841 + 0.614871i
\(549\) 5.04758e10 0.555641
\(550\) −4.27705e9 + 3.42438e9i −0.0467405 + 0.0374224i
\(551\) 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
\(555\) 2.11624e11i 2.23046i
\(556\) −7.36985e10 1.65217e10i −0.771187 0.172884i
\(557\) −1.37543e11 −1.42895 −0.714475 0.699661i \(-0.753334\pi\)
−0.714475 + 0.699661i \(0.753334\pi\)
\(558\) −2.90489e9 + 2.32578e9i −0.0299636 + 0.0239901i
\(559\) 3.24270e10i 0.332093i
\(560\) −2.38737e10 + 5.05710e10i −0.242755 + 0.514220i
\(561\) 1.35000e11 1.36296
\(562\) −3.08105e10 3.84823e10i −0.308854 0.385759i
\(563\) 1.06415e11i 1.05918i 0.848255 + 0.529589i \(0.177654\pi\)
−0.848255 + 0.529589i \(0.822346\pi\)
\(564\) 4.26731e10 1.90352e11i 0.421733 1.88123i
\(565\) 3.36018e10 0.329738
\(566\) −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 \(0.438516\pi\)
\(570\) −1.18760e10 1.48331e10i −0.112504 0.140518i
\(571\) 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
\(575\) 4.39432e9i 0.0401994i
\(576\) −3.52829e10 + 4.53116e10i −0.320534 + 0.411642i
\(577\) 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
\(579\) 1.17499e11i 1.04549i
\(580\) 4.38006e9 1.95382e10i 0.0387051 0.172652i
\(581\) 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
\(585\) 1.14215e10 0.0975216
\(586\) −4.80980e10 6.00743e10i −0.407884 0.509446i
\(587\) 1.53440e11i 1.29237i −0.763181 0.646185i \(-0.776363\pi\)
0.763181 0.646185i \(-0.223637\pi\)
\(588\) 9.50461e10 + 2.13074e10i 0.795106 + 0.178246i
\(589\) −1.32388e9 −0.0109999
\(590\) 2.83843e10 2.27256e10i 0.234245 0.187546i
\(591\) 1.70402e11i 1.39677i
\(592\) 2.05766e11 + 9.71390e10i 1.67528 + 0.790873i
\(593\) 2.06036e11 1.66619 0.833094 0.553131i \(-0.186567\pi\)
0.833094 + 0.553131i \(0.186567\pi\)
\(594\) −5.79601e10 7.23922e10i −0.465568 0.581495i
\(595\) 6.23689e10i 0.497623i
\(596\) −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 \(0.646639\pi\)
\(600\) 3.32916e9 + 6.81174e9i 0.0256880 + 0.0525598i
\(601\) 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
\(605\) −7.76795e10 −0.579809
\(606\) −3.46004e10 + 2.77025e10i −0.256561 + 0.205413i
\(607\) 1.97883e11i 1.45765i 0.684700 + 0.728825i \(0.259933\pi\)
−0.684700 + 0.728825i \(0.740067\pi\)
\(608\) −1.98738e10 + 4.73860e9i −0.145434 + 0.0346766i
\(609\) 1.79224e10 0.130294
\(610\) 8.99511e10 + 1.12349e11i 0.649661 + 0.811427i
\(611\) 4.17158e10i 0.299320i
\(612\) 1.40105e10 6.24967e10i 0.0998728 0.445504i
\(613\) 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
\(615\) 1.30855e11i 0.914723i
\(616\) 9.51595e10 4.65082e10i 0.660890 0.323003i
\(617\) −5.06702e10 −0.349632 −0.174816 0.984601i \(-0.555933\pi\)
−0.174816 + 0.984601i \(0.555933\pi\)
\(618\) 1.04417e11 + 1.30417e11i 0.715844 + 0.894089i
\(619\) 7.06748e10i 0.481395i 0.970600 + 0.240698i \(0.0773762\pi\)
−0.970600 + 0.240698i \(0.922624\pi\)
\(620\) −1.03534e10 2.32102e9i −0.0700675 0.0157077i
\(621\) 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
\(625\) −1.45008e11 −0.950327
\(626\) 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
\(630\) 3.64821e10 2.92090e10i 0.231589 0.185419i
\(631\) 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
\(635\) 1.56868e11i 0.964804i
\(636\) 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
\(640\) −1.63731e11 + 2.21570e9i −0.975911 + 0.0132066i
\(641\) 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 \(0.283662\pi\)
−0.628518 + 0.777795i \(0.716338\pi\)
\(644\) −1.85824e10 + 8.28907e10i −0.108033 + 0.481906i
\(645\) 3.61328e11 2.08767
\(646\) 1.77872e10 1.42411e10i 0.102136 0.0817739i
\(647\) 2.71996e11i 1.55219i −0.630614 0.776097i \(-0.717197\pi\)
0.630614 0.776097i \(-0.282803\pi\)
\(648\) −1.97940e11 + 9.67411e10i −1.12262 + 0.548670i
\(649\) −6.88669e10 −0.388179
\(650\) −1.01332e9 1.26563e9i −0.00567665 0.00709013i
\(651\) 9.49716e9i 0.0528774i
\(652\) 1.44511e11 + 3.23965e10i 0.799672 + 0.179270i
\(653\) 3.03789e11 1.67078 0.835391 0.549656i \(-0.185241\pi\)
0.835391 + 0.549656i \(0.185241\pi\)
\(654\) 7.37213e10 5.90243e10i 0.402979 0.322641i
\(655\) 1.90427e11i 1.03458i
\(656\) −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 \(-0.0353954\pi\)
\(660\) −6.30949e10 + 2.81448e11i −0.332520 + 1.48328i
\(661\) −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
\(665\) 1.66264e10 0.0850179
\(666\) −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
\(670\) −1.16239e11 + 9.30657e10i −0.576837 + 0.461839i
\(671\) 2.72584e11i 1.34465i
\(672\) −3.39935e10 1.42569e11i −0.166694 0.699115i
\(673\) −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
\(675\) 5.80849e9i 0.0279800i
\(676\) 4.40053e10 1.96295e11i 0.210726 0.939989i
\(677\) −2.47236e10 −0.117695 −0.0588475 0.998267i \(-0.518743\pi\)
−0.0588475 + 0.998267i \(0.518743\pi\)
\(678\) −6.87460e10 + 5.50408e10i −0.325333 + 0.260475i
\(679\) 1.68731e11i 0.793811i
\(680\) 1.64072e11 8.01886e10i 0.767361 0.375039i
\(681\) 7.49454e10 0.348463
\(682\) 1.25599e10 + 1.56873e10i 0.0580561 + 0.0725120i
\(683\) 7.20843e10i 0.331251i −0.986189 0.165626i \(-0.947036\pi\)
0.986189 0.165626i \(-0.0529644\pi\)
\(684\) 1.66604e10 + 3.73492e9i 0.0761135 + 0.0170631i
\(685\) 1.35408e11 0.615009
\(686\) −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
\(690\) −1.44582e11 1.80583e11i −0.637850 0.796675i
\(691\) 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
\(695\) 1.79968e11i 0.771360i
\(696\) 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
\(700\) −6.47338e9 1.45120e9i −0.0269612 0.00604414i
\(701\) −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
\(705\) −4.64831e11 −1.88165
\(706\) 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 \(0.334062\pi\)
\(710\) 9.11252e9 7.29586e9i 0.0358596 0.0287106i
\(711\) 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
\(715\) 6.16795e10i 0.236003i
\(716\) 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 \(0.916348\pi\)
\(720\) 1.23745e11 + 5.84180e10i 0.460466 + 0.217379i
\(721\) −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
\(725\) 2.37531e9 0.00859743
\(726\) 1.58925e11 1.27242e11i 0.572064 0.458018i
\(727\) 1.79083e11i 0.641088i 0.947234 + 0.320544i \(0.103866\pi\)
−0.947234 + 0.320544i \(0.896134\pi\)
\(728\) 1.37623e10 + 2.81589e10i 0.0489967 + 0.100251i
\(729\) −2.14381e10 −0.0759061
\(730\) 3.49263e10 + 4.36230e10i 0.122988 + 0.153612i
\(731\) 4.33289e11i 1.51743i
\(732\) −3.68062e11 8.25119e10i −1.28197 0.287391i
\(733\) 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
\(735\) 2.32098e11i 0.795285i
\(736\) −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 \(-0.302166\pi\)
\(740\) 1.18605e11 5.29061e11i 0.395525 1.76433i
\(741\) −1.06494e10 −0.0353227
\(742\) −1.44020e10 + 1.15308e10i −0.0475124 + 0.0380404i
\(743\) 2.03509e11i 0.667771i −0.942614 0.333886i \(-0.891640\pi\)
0.942614 0.333886i \(-0.108360\pi\)
\(744\) 2.49840e10 1.22106e10i 0.0815398 0.0398517i
\(745\) 2.46198e11 0.799206
\(746\) 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
\(750\) 3.11478e11 2.49382e11i 0.984423 0.788169i
\(751\) 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
\(755\) 5.10561e11i 1.57130i
\(756\) 2.45626e10 1.09567e11i 0.0751946 0.335421i
\(757\) −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
\(759\) 4.38136e11i 1.32021i