Properties

Label 38.8.c.a.7.2
Level $38$
Weight $8$
Character 38.7
Analytic conductor $11.871$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [38,8,Mod(7,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 38.c (of order \(3\), degree \(2\), 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: \(11.8706309684\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 10165 x^{10} - 228496 x^{9} + 79937698 x^{8} - 1362528496 x^{7} + 222057453949 x^{6} - 1418140039384 x^{5} + 423936076682002 x^{4} + \cdots + 20\!\cdots\!25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 7.2
Root \(-21.5062 - 37.2499i\) of defining polynomial
Character \(\chi\) \(=\) 38.7
Dual form 38.8.c.a.11.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.00000 - 6.92820i) q^{2} +(-20.5062 - 35.5178i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-273.130 - 473.076i) q^{5} +(-164.050 + 284.143i) q^{6} -154.247 q^{7} +512.000 q^{8} +(252.489 - 437.324i) q^{9} +O(q^{10})\) \(q+(-4.00000 - 6.92820i) q^{2} +(-20.5062 - 35.5178i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-273.130 - 473.076i) q^{5} +(-164.050 + 284.143i) q^{6} -154.247 q^{7} +512.000 q^{8} +(252.489 - 437.324i) q^{9} +(-2185.04 + 3784.60i) q^{10} -4153.91 q^{11} +2624.80 q^{12} +(4201.88 - 7277.88i) q^{13} +(616.990 + 1068.66i) q^{14} +(-11201.7 + 19402.0i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(16175.7 + 28017.1i) q^{17} -4039.83 q^{18} +(6628.11 + 29153.7i) q^{19} +34960.7 q^{20} +(3163.03 + 5478.53i) q^{21} +(16615.6 + 28779.1i) q^{22} +(32161.4 - 55705.2i) q^{23} +(-10499.2 - 18185.1i) q^{24} +(-110138. + 190764. i) q^{25} -67230.1 q^{26} -110405. q^{27} +(4935.92 - 8549.26i) q^{28} +(101353. - 175549. i) q^{29} +179228. q^{30} -132507. q^{31} +(-16384.0 + 28377.9i) q^{32} +(85180.9 + 147538. i) q^{33} +(129406. - 224137. i) q^{34} +(42129.6 + 72970.7i) q^{35} +(16159.3 + 27988.8i) q^{36} +93680.1 q^{37} +(175471. - 162536. i) q^{38} -344659. q^{39} +(-139843. - 242215. i) q^{40} +(-248414. - 430265. i) q^{41} +(25304.3 - 43828.3i) q^{42} +(-172620. - 298987. i) q^{43} +(132925. - 230233. i) q^{44} -275850. q^{45} -514583. q^{46} +(-20822.9 + 36066.4i) q^{47} +(-83993.5 + 145481. i) q^{48} -799751. q^{49} +1.76221e6 q^{50} +(663405. - 1.14905e6i) q^{51} +(268921. + 465784. i) q^{52} +(164905. - 285623. i) q^{53} +(441619. + 764906. i) q^{54} +(1.13456e6 + 1.96511e6i) q^{55} -78974.7 q^{56} +(899560. - 833249. i) q^{57} -1.62165e6 q^{58} +(815192. + 1.41195e6i) q^{59} +(-716912. - 1.24173e6i) q^{60} +(-13024.4 + 22558.9i) q^{61} +(530026. + 918032. i) q^{62} +(-38945.8 + 67456.1i) q^{63} +262144. q^{64} -4.59065e6 q^{65} +(681448. - 1.18030e6i) q^{66} +(-1.61635e6 + 2.79960e6i) q^{67} -2.07049e6 q^{68} -2.63804e6 q^{69} +(337037. - 583765. i) q^{70} +(819449. + 1.41933e6i) q^{71} +(129275. - 223910. i) q^{72} +(938190. + 1.62499e6i) q^{73} +(-374720. - 649035. i) q^{74} +9.03405e6 q^{75} +(-1.82796e6 - 565552. i) q^{76} +640729. q^{77} +(1.37864e6 + 2.38787e6i) q^{78} +(-304783. - 527899. i) q^{79} +(-1.11874e6 + 1.93772e6i) q^{80} +(1.71179e6 + 2.96491e6i) q^{81} +(-1.98731e6 + 3.44212e6i) q^{82} -2.79851e6 q^{83} -404868. q^{84} +(8.83615e6 - 1.53047e7i) q^{85} +(-1.38096e6 + 2.39190e6i) q^{86} -8.31348e6 q^{87} -2.12680e6 q^{88} +(1.68177e6 - 2.91292e6i) q^{89} +(1.10340e6 + 1.91114e6i) q^{90} +(-648130. + 1.12259e6i) q^{91} +(2.05833e6 + 3.56513e6i) q^{92} +(2.71721e6 + 4.70634e6i) q^{93} +333167. q^{94} +(1.19816e7 - 1.10984e7i) q^{95} +1.34390e6 q^{96} +(-3.68140e6 - 6.37637e6i) q^{97} +(3.19900e6 + 5.54084e6i) q^{98} +(-1.04882e6 + 1.81660e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 48 q^{2} + 12 q^{3} - 384 q^{4} + 124 q^{5} + 96 q^{6} - 1036 q^{7} + 6144 q^{8} - 7232 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 48 q^{2} + 12 q^{3} - 384 q^{4} + 124 q^{5} + 96 q^{6} - 1036 q^{7} + 6144 q^{8} - 7232 q^{9} + 992 q^{10} - 11760 q^{11} - 1536 q^{12} + 17390 q^{13} + 4144 q^{14} - 4062 q^{15} - 24576 q^{16} + 45254 q^{17} + 115712 q^{18} - 26264 q^{19} - 15872 q^{20} + 46034 q^{21} + 47040 q^{22} + 76554 q^{23} + 6144 q^{24} - 233468 q^{25} - 278240 q^{26} + 546408 q^{27} + 33152 q^{28} + 109808 q^{29} + 64992 q^{30} - 367004 q^{31} - 196608 q^{32} - 50480 q^{33} + 362032 q^{34} - 531444 q^{35} - 462848 q^{36} + 922140 q^{37} + 517760 q^{38} - 2676440 q^{39} + 63488 q^{40} + 489142 q^{41} + 368272 q^{42} + 1781092 q^{43} + 376320 q^{44} - 3827592 q^{45} - 1224864 q^{46} + 178950 q^{47} + 49152 q^{48} + 96332 q^{49} + 3735488 q^{50} + 1520200 q^{51} + 1112960 q^{52} + 939902 q^{53} - 2185632 q^{54} - 2722538 q^{55} - 530432 q^{56} + 1773906 q^{57} - 1756928 q^{58} + 1874564 q^{59} - 259968 q^{60} - 1791828 q^{61} + 1468016 q^{62} + 2212152 q^{63} + 3145728 q^{64} + 2592956 q^{65} - 403840 q^{66} + 5363976 q^{67} - 5792512 q^{68} - 15864224 q^{69} - 4251552 q^{70} + 3980204 q^{71} - 3702784 q^{72} + 15279830 q^{73} - 3688560 q^{74} + 11837664 q^{75} - 2461184 q^{76} - 2416228 q^{77} + 10705760 q^{78} - 7164236 q^{79} + 507904 q^{80} - 5997626 q^{81} + 3913136 q^{82} - 12916808 q^{83} - 5892352 q^{84} + 18415506 q^{85} + 14248736 q^{86} + 15255300 q^{87} - 6021120 q^{88} + 4966022 q^{89} + 15310368 q^{90} - 37018212 q^{91} + 4899456 q^{92} - 31429094 q^{93} - 2863200 q^{94} + 15365984 q^{95} - 786432 q^{96} - 10277950 q^{97} - 385328 q^{98} + 1480976 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 6.92820i −0.353553 0.612372i
\(3\) −20.5062 35.5178i −0.438492 0.759490i 0.559082 0.829113i \(-0.311154\pi\)
−0.997573 + 0.0696227i \(0.977820\pi\)
\(4\) −32.0000 + 55.4256i −0.250000 + 0.433013i
\(5\) −273.130 473.076i −0.977181 1.69253i −0.672543 0.740058i \(-0.734798\pi\)
−0.304638 0.952468i \(-0.598536\pi\)
\(6\) −164.050 + 284.143i −0.310060 + 0.537040i
\(7\) −154.247 −0.169971 −0.0849855 0.996382i \(-0.527084\pi\)
−0.0849855 + 0.996382i \(0.527084\pi\)
\(8\) 512.000 0.353553
\(9\) 252.489 437.324i 0.115450 0.199965i
\(10\) −2185.04 + 3784.60i −0.690971 + 1.19680i
\(11\) −4153.91 −0.940984 −0.470492 0.882404i \(-0.655924\pi\)
−0.470492 + 0.882404i \(0.655924\pi\)
\(12\) 2624.80 0.438492
\(13\) 4201.88 7277.88i 0.530447 0.918762i −0.468921 0.883240i \(-0.655357\pi\)
0.999369 0.0355220i \(-0.0113094\pi\)
\(14\) 616.990 + 1068.66i 0.0600938 + 0.104086i
\(15\) −11201.7 + 19402.0i −0.856971 + 1.48432i
\(16\) −2048.00 3547.24i −0.125000 0.216506i
\(17\) 16175.7 + 28017.1i 0.798531 + 1.38310i 0.920573 + 0.390572i \(0.127723\pi\)
−0.122041 + 0.992525i \(0.538944\pi\)
\(18\) −4039.83 −0.163271
\(19\) 6628.11 + 29153.7i 0.221693 + 0.975117i
\(20\) 34960.7 0.977181
\(21\) 3163.03 + 5478.53i 0.0745309 + 0.129091i
\(22\) 16615.6 + 28779.1i 0.332688 + 0.576233i
\(23\) 32161.4 55705.2i 0.551173 0.954659i −0.447018 0.894525i \(-0.647514\pi\)
0.998190 0.0601338i \(-0.0191527\pi\)
\(24\) −10499.2 18185.1i −0.155030 0.268520i
\(25\) −110138. + 190764.i −1.40976 + 2.44178i
\(26\) −67230.1 −0.750166
\(27\) −110405. −1.07948
\(28\) 4935.92 8549.26i 0.0424927 0.0735996i
\(29\) 101353. 175549.i 0.771693 1.33661i −0.164942 0.986303i \(-0.552744\pi\)
0.936635 0.350307i \(-0.113923\pi\)
\(30\) 179228. 1.21194
\(31\) −132507. −0.798861 −0.399431 0.916763i \(-0.630792\pi\)
−0.399431 + 0.916763i \(0.630792\pi\)
\(32\) −16384.0 + 28377.9i −0.0883883 + 0.153093i
\(33\) 85180.9 + 147538.i 0.412614 + 0.714668i
\(34\) 129406. 224137.i 0.564647 0.977997i
\(35\) 42129.6 + 72970.7i 0.166092 + 0.287680i
\(36\) 16159.3 + 27988.8i 0.0577250 + 0.0999827i
\(37\) 93680.1 0.304047 0.152024 0.988377i \(-0.451421\pi\)
0.152024 + 0.988377i \(0.451421\pi\)
\(38\) 175471. 162536.i 0.518754 0.480514i
\(39\) −344659. −0.930387
\(40\) −139843. 242215.i −0.345486 0.598399i
\(41\) −248414. 430265.i −0.562901 0.974973i −0.997242 0.0742246i \(-0.976352\pi\)
0.434340 0.900749i \(-0.356982\pi\)
\(42\) 25304.3 43828.3i 0.0527013 0.0912813i
\(43\) −172620. 298987.i −0.331095 0.573473i 0.651632 0.758535i \(-0.274085\pi\)
−0.982727 + 0.185062i \(0.940751\pi\)
\(44\) 132925. 230233.i 0.235246 0.407458i
\(45\) −275850. −0.451262
\(46\) −514583. −0.779476
\(47\) −20822.9 + 36066.4i −0.0292549 + 0.0506711i −0.880282 0.474450i \(-0.842647\pi\)
0.851027 + 0.525122i \(0.175980\pi\)
\(48\) −83993.5 + 145481.i −0.109623 + 0.189872i
\(49\) −799751. −0.971110
\(50\) 1.76221e6 1.99371
\(51\) 663405. 1.14905e6i 0.700299 1.21295i
\(52\) 268921. + 465784.i 0.265224 + 0.459381i
\(53\) 164905. 285623.i 0.152148 0.263529i −0.779869 0.625943i \(-0.784714\pi\)
0.932017 + 0.362414i \(0.118047\pi\)
\(54\) 441619. + 764906.i 0.381653 + 0.661043i
\(55\) 1.13456e6 + 1.96511e6i 0.919512 + 1.59264i
\(56\) −78974.7 −0.0600938
\(57\) 899560. 833249.i 0.643381 0.595954i
\(58\) −1.62165e6 −1.09134
\(59\) 815192. + 1.41195e6i 0.516747 + 0.895032i 0.999811 + 0.0194470i \(0.00619057\pi\)
−0.483064 + 0.875585i \(0.660476\pi\)
\(60\) −716912. 1.24173e6i −0.428486 0.742159i
\(61\) −13024.4 + 22558.9i −0.00734688 + 0.0127252i −0.869675 0.493624i \(-0.835672\pi\)
0.862329 + 0.506349i \(0.169005\pi\)
\(62\) 530026. + 918032.i 0.282440 + 0.489201i
\(63\) −38945.8 + 67456.1i −0.0196232 + 0.0339883i
\(64\) 262144. 0.125000
\(65\) −4.59065e6 −2.07337
\(66\) 681448. 1.18030e6i 0.291762 0.505347i
\(67\) −1.61635e6 + 2.79960e6i −0.656559 + 1.13719i 0.324941 + 0.945734i \(0.394656\pi\)
−0.981500 + 0.191460i \(0.938678\pi\)
\(68\) −2.07049e6 −0.798531
\(69\) −2.63804e6 −0.966738
\(70\) 337037. 583765.i 0.117445 0.203421i
\(71\) 819449. + 1.41933e6i 0.271718 + 0.470629i 0.969302 0.245874i \(-0.0790750\pi\)
−0.697584 + 0.716503i \(0.745742\pi\)
\(72\) 129275. 223910.i 0.0408178 0.0706984i
\(73\) 938190. + 1.62499e6i 0.282267 + 0.488902i 0.971943 0.235217i \(-0.0755801\pi\)
−0.689675 + 0.724119i \(0.742247\pi\)
\(74\) −374720. 649035.i −0.107497 0.186190i
\(75\) 9.03405e6 2.47268
\(76\) −1.82796e6 565552.i −0.477661 0.147783i
\(77\) 640729. 0.159940
\(78\) 1.37864e6 + 2.38787e6i 0.328942 + 0.569743i
\(79\) −304783. 527899.i −0.0695497 0.120464i 0.829153 0.559021i \(-0.188823\pi\)
−0.898703 + 0.438557i \(0.855490\pi\)
\(80\) −1.11874e6 + 1.93772e6i −0.244295 + 0.423132i
\(81\) 1.71179e6 + 2.96491e6i 0.357892 + 0.619888i
\(82\) −1.98731e6 + 3.44212e6i −0.398031 + 0.689410i
\(83\) −2.79851e6 −0.537222 −0.268611 0.963249i \(-0.586565\pi\)
−0.268611 + 0.963249i \(0.586565\pi\)
\(84\) −404868. −0.0745309
\(85\) 8.83615e6 1.53047e7i 1.56062 2.70307i
\(86\) −1.38096e6 + 2.39190e6i −0.234119 + 0.405507i
\(87\) −8.31348e6 −1.35352
\(88\) −2.12680e6 −0.332688
\(89\) 1.68177e6 2.91292e6i 0.252873 0.437989i −0.711442 0.702744i \(-0.751958\pi\)
0.964316 + 0.264755i \(0.0852911\pi\)
\(90\) 1.10340e6 + 1.91114e6i 0.159545 + 0.276341i
\(91\) −648130. + 1.12259e6i −0.0901607 + 0.156163i
\(92\) 2.05833e6 + 3.56513e6i 0.275586 + 0.477329i
\(93\) 2.71721e6 + 4.70634e6i 0.350294 + 0.606727i
\(94\) 333167. 0.0413727
\(95\) 1.19816e7 1.10984e7i 1.43378 1.32809i
\(96\) 1.34390e6 0.155030
\(97\) −3.68140e6 6.37637e6i −0.409555 0.709369i 0.585285 0.810827i \(-0.300983\pi\)
−0.994840 + 0.101458i \(0.967649\pi\)
\(98\) 3.19900e6 + 5.54084e6i 0.343339 + 0.594681i
\(99\) −1.04882e6 + 1.81660e6i −0.108637 + 0.188164i
\(100\) −7.04882e6 1.22089e7i −0.704882 1.22089i
\(101\) 238004. 412235.i 0.0229858 0.0398126i −0.854304 0.519774i \(-0.826016\pi\)
0.877289 + 0.479962i \(0.159349\pi\)
\(102\) −1.06145e7 −0.990372
\(103\) −6.44953e6 −0.581564 −0.290782 0.956789i \(-0.593915\pi\)
−0.290782 + 0.956789i \(0.593915\pi\)
\(104\) 2.15136e6 3.72627e6i 0.187541 0.324831i
\(105\) 1.72784e6 2.99271e6i 0.145660 0.252291i
\(106\) −2.63848e6 −0.215170
\(107\) 5.75553e6 0.454195 0.227098 0.973872i \(-0.427076\pi\)
0.227098 + 0.973872i \(0.427076\pi\)
\(108\) 3.53295e6 6.11925e6i 0.269870 0.467428i
\(109\) 4.69049e6 + 8.12417e6i 0.346917 + 0.600878i 0.985700 0.168509i \(-0.0538951\pi\)
−0.638783 + 0.769387i \(0.720562\pi\)
\(110\) 9.07646e6 1.57209e7i 0.650193 1.12617i
\(111\) −1.92103e6 3.32731e6i −0.133322 0.230921i
\(112\) 315899. + 547153.i 0.0212464 + 0.0367998i
\(113\) −9.60445e6 −0.626178 −0.313089 0.949724i \(-0.601364\pi\)
−0.313089 + 0.949724i \(0.601364\pi\)
\(114\) −9.37116e6 2.89934e6i −0.592415 0.183287i
\(115\) −3.51370e7 −2.15438
\(116\) 6.48660e6 + 1.12351e7i 0.385846 + 0.668305i
\(117\) −2.12186e6 3.67517e6i −0.122480 0.212142i
\(118\) 6.52154e6 1.12956e7i 0.365395 0.632883i
\(119\) −2.49506e6 4.32157e6i −0.135727 0.235086i
\(120\) −5.73529e6 + 9.93382e6i −0.302985 + 0.524786i
\(121\) −2.23223e6 −0.114549
\(122\) 208390. 0.0103901
\(123\) −1.01881e7 + 1.76462e7i −0.493655 + 0.855036i
\(124\) 4.24021e6 7.34426e6i 0.199715 0.345917i
\(125\) 7.76513e7 3.55602
\(126\) 623133. 0.0277513
\(127\) −2.26623e7 + 3.92523e7i −0.981728 + 1.70040i −0.326067 + 0.945346i \(0.605724\pi\)
−0.655660 + 0.755056i \(0.727610\pi\)
\(128\) −1.04858e6 1.81619e6i −0.0441942 0.0765466i
\(129\) −7.07958e6 + 1.22622e7i −0.290365 + 0.502926i
\(130\) 1.83626e7 + 3.18049e7i 0.733048 + 1.26968i
\(131\) −1.10278e7 1.91007e7i −0.428587 0.742334i 0.568161 0.822917i \(-0.307655\pi\)
−0.996748 + 0.0805833i \(0.974322\pi\)
\(132\) −1.09032e7 −0.412614
\(133\) −1.02237e6 4.49689e6i −0.0376814 0.165741i
\(134\) 2.58616e7 0.928515
\(135\) 3.01549e7 + 5.22297e7i 1.05485 + 1.82705i
\(136\) 8.28196e6 + 1.43448e7i 0.282323 + 0.488999i
\(137\) −9.51577e6 + 1.64818e7i −0.316171 + 0.547624i −0.979686 0.200539i \(-0.935731\pi\)
0.663515 + 0.748163i \(0.269064\pi\)
\(138\) 1.05521e7 + 1.82769e7i 0.341794 + 0.592004i
\(139\) 2.80421e7 4.85704e7i 0.885644 1.53398i 0.0406699 0.999173i \(-0.487051\pi\)
0.844974 0.534807i \(-0.179616\pi\)
\(140\) −5.39259e6 −0.166092
\(141\) 1.70800e6 0.0513122
\(142\) 6.55560e6 1.13546e7i 0.192133 0.332785i
\(143\) −1.74542e7 + 3.02316e7i −0.499143 + 0.864540i
\(144\) −2.06839e6 −0.0577250
\(145\) −1.10730e8 −3.01633
\(146\) 7.50552e6 1.29999e7i 0.199593 0.345706i
\(147\) 1.63999e7 + 2.84054e7i 0.425824 + 0.737548i
\(148\) −2.99776e6 + 5.19228e6i −0.0760119 + 0.131656i
\(149\) −2.94438e7 5.09982e7i −0.729192 1.26300i −0.957225 0.289344i \(-0.906563\pi\)
0.228033 0.973653i \(-0.426771\pi\)
\(150\) −3.61362e7 6.25897e7i −0.874224 1.51420i
\(151\) 7.76266e6 0.183481 0.0917405 0.995783i \(-0.470757\pi\)
0.0917405 + 0.995783i \(0.470757\pi\)
\(152\) 3.39359e6 + 1.49267e7i 0.0783803 + 0.344756i
\(153\) 1.63368e7 0.368762
\(154\) −2.56292e6 4.43910e6i −0.0565473 0.0979428i
\(155\) 3.61916e7 + 6.26856e7i 0.780632 + 1.35209i
\(156\) 1.10291e7 1.91029e7i 0.232597 0.402869i
\(157\) −4.46555e7 7.73456e7i −0.920929 1.59510i −0.797980 0.602683i \(-0.794098\pi\)
−0.122949 0.992413i \(-0.539235\pi\)
\(158\) −2.43826e6 + 4.22319e6i −0.0491791 + 0.0851807i
\(159\) −1.35263e7 −0.266863
\(160\) 1.78999e7 0.345486
\(161\) −4.96081e6 + 8.59238e6i −0.0936833 + 0.162264i
\(162\) 1.36943e7 2.37192e7i 0.253068 0.438327i
\(163\) 3.48661e7 0.630589 0.315294 0.948994i \(-0.397897\pi\)
0.315294 + 0.948994i \(0.397897\pi\)
\(164\) 3.17970e7 0.562901
\(165\) 4.65310e7 8.05940e7i 0.806396 1.39672i
\(166\) 1.11940e7 + 1.93887e7i 0.189937 + 0.328980i
\(167\) −4.69765e7 + 8.13658e7i −0.780501 + 1.35187i 0.151149 + 0.988511i \(0.451703\pi\)
−0.931650 + 0.363356i \(0.881631\pi\)
\(168\) 1.61947e6 + 2.80501e6i 0.0263506 + 0.0456406i
\(169\) −3.93740e6 6.81978e6i −0.0627489 0.108684i
\(170\) −1.41378e8 −2.20705
\(171\) 1.44232e7 + 4.46237e6i 0.220584 + 0.0682464i
\(172\) 2.20954e7 0.331095
\(173\) −2.32466e7 4.02642e7i −0.341348 0.591232i 0.643335 0.765585i \(-0.277550\pi\)
−0.984683 + 0.174352i \(0.944217\pi\)
\(174\) 3.32539e7 + 5.75975e7i 0.478543 + 0.828860i
\(175\) 1.69885e7 2.94249e7i 0.239619 0.415032i
\(176\) 8.50720e6 + 1.47349e7i 0.117623 + 0.203729i
\(177\) 3.34330e7 5.79077e7i 0.453179 0.784928i
\(178\) −2.69084e7 −0.357617
\(179\) 1.07319e8 1.39859 0.699293 0.714835i \(-0.253498\pi\)
0.699293 + 0.714835i \(0.253498\pi\)
\(180\) 8.82720e6 1.52892e7i 0.112816 0.195402i
\(181\) 6.67351e6 1.15589e7i 0.0836526 0.144891i −0.821164 0.570693i \(-0.806675\pi\)
0.904816 + 0.425802i \(0.140008\pi\)
\(182\) 1.03701e7 0.127506
\(183\) 1.06832e6 0.0128862
\(184\) 1.64666e7 2.85211e7i 0.194869 0.337523i
\(185\) −2.55869e7 4.43178e7i −0.297109 0.514608i
\(186\) 2.17377e7 3.76508e7i 0.247695 0.429021i
\(187\) −6.71924e7 1.16381e8i −0.751405 1.30147i
\(188\) −1.33267e6 2.30825e6i −0.0146275 0.0253355i
\(189\) 1.70296e7 0.183480
\(190\) −1.24818e8 3.86174e7i −1.32020 0.408456i
\(191\) −6.55337e7 −0.680531 −0.340266 0.940329i \(-0.610517\pi\)
−0.340266 + 0.940329i \(0.610517\pi\)
\(192\) −5.37558e6 9.31079e6i −0.0548115 0.0949362i
\(193\) 4.82731e6 + 8.36115e6i 0.0483342 + 0.0837173i 0.889180 0.457557i \(-0.151275\pi\)
−0.840846 + 0.541274i \(0.817942\pi\)
\(194\) −2.94512e7 + 5.10110e7i −0.289599 + 0.501600i
\(195\) 9.41369e7 + 1.63050e8i 0.909156 + 1.57470i
\(196\) 2.55920e7 4.43267e7i 0.242777 0.420503i
\(197\) 5.35511e7 0.499042 0.249521 0.968369i \(-0.419727\pi\)
0.249521 + 0.968369i \(0.419727\pi\)
\(198\) 1.67811e7 0.153635
\(199\) 4.51927e7 7.82760e7i 0.406520 0.704114i −0.587977 0.808878i \(-0.700075\pi\)
0.994497 + 0.104764i \(0.0334087\pi\)
\(200\) −5.63906e7 + 9.76713e7i −0.498427 + 0.863301i
\(201\) 1.32581e8 1.15158
\(202\) −3.80807e6 −0.0325068
\(203\) −1.56335e7 + 2.70780e7i −0.131165 + 0.227185i
\(204\) 4.24579e7 + 7.35393e7i 0.350149 + 0.606476i
\(205\) −1.35699e8 + 2.35037e8i −1.10011 + 1.90545i
\(206\) 2.57981e7 + 4.46836e7i 0.205614 + 0.356134i
\(207\) −1.62408e7 2.81299e7i −0.127266 0.220431i
\(208\) −3.44218e7 −0.265224
\(209\) −2.75325e7 1.21102e8i −0.208610 0.917569i
\(210\) −2.76454e7 −0.205995
\(211\) 7.82087e7 + 1.35461e8i 0.573148 + 0.992721i 0.996240 + 0.0866345i \(0.0276112\pi\)
−0.423092 + 0.906087i \(0.639055\pi\)
\(212\) 1.05539e7 + 1.82799e7i 0.0760742 + 0.131764i
\(213\) 3.36076e7 5.82101e7i 0.238292 0.412734i
\(214\) −2.30221e7 3.98755e7i −0.160582 0.278137i
\(215\) −9.42957e7 + 1.63325e8i −0.647079 + 1.12077i
\(216\) −5.65272e7 −0.381653
\(217\) 2.04388e7 0.135783
\(218\) 3.75240e7 6.49934e7i 0.245308 0.424885i
\(219\) 3.84775e7 6.66449e7i 0.247544 0.428759i
\(220\) −1.45223e8 −0.919512
\(221\) 2.71874e8 1.69432
\(222\) −1.53682e7 + 2.66185e7i −0.0942731 + 0.163286i
\(223\) −7.08858e7 1.22778e8i −0.428047 0.741400i 0.568652 0.822578i \(-0.307465\pi\)
−0.996700 + 0.0811782i \(0.974132\pi\)
\(224\) 2.52719e6 4.37722e6i 0.0150235 0.0260214i
\(225\) 5.56172e7 + 9.63319e7i 0.325515 + 0.563808i
\(226\) 3.84178e7 + 6.65416e7i 0.221387 + 0.383454i
\(227\) −1.90775e8 −1.08251 −0.541253 0.840860i \(-0.682050\pi\)
−0.541253 + 0.840860i \(0.682050\pi\)
\(228\) 1.73974e7 + 7.65226e7i 0.0972105 + 0.427581i
\(229\) −2.83164e8 −1.55816 −0.779082 0.626922i \(-0.784315\pi\)
−0.779082 + 0.626922i \(0.784315\pi\)
\(230\) 1.40548e8 + 2.43436e8i 0.761689 + 1.31928i
\(231\) −1.31389e7 2.27573e7i −0.0701323 0.121473i
\(232\) 5.18928e7 8.98810e7i 0.272835 0.472563i
\(233\) −7.81310e7 1.35327e8i −0.404648 0.700872i 0.589632 0.807672i \(-0.299273\pi\)
−0.994280 + 0.106800i \(0.965939\pi\)
\(234\) −1.69749e7 + 2.94014e7i −0.0866067 + 0.150007i
\(235\) 2.27495e7 0.114349
\(236\) −1.04345e8 −0.516747
\(237\) −1.24999e7 + 2.16504e7i −0.0609940 + 0.105645i
\(238\) −1.99605e7 + 3.45726e7i −0.0959736 + 0.166231i
\(239\) −1.41308e7 −0.0669536 −0.0334768 0.999439i \(-0.510658\pi\)
−0.0334768 + 0.999439i \(0.510658\pi\)
\(240\) 9.17647e7 0.428486
\(241\) 1.69877e8 2.94236e8i 0.781763 1.35405i −0.149151 0.988814i \(-0.547654\pi\)
0.930914 0.365238i \(-0.119012\pi\)
\(242\) 8.92894e6 + 1.54654e7i 0.0404992 + 0.0701466i
\(243\) −5.05228e7 + 8.75081e7i −0.225874 + 0.391225i
\(244\) −833561. 1.44377e6i −0.00367344 0.00636259i
\(245\) 2.18436e8 + 3.78343e8i 0.948950 + 1.64363i
\(246\) 1.63009e8 0.698134
\(247\) 2.40028e8 + 7.42621e7i 1.01350 + 0.313565i
\(248\) −6.78434e7 −0.282440
\(249\) 5.73869e7 + 9.93971e7i 0.235567 + 0.408015i
\(250\) −3.10605e8 5.37984e8i −1.25724 2.17761i
\(251\) 1.57767e8 2.73260e8i 0.629734 1.09073i −0.357871 0.933771i \(-0.616497\pi\)
0.987605 0.156960i \(-0.0501693\pi\)
\(252\) −2.49253e6 4.31719e6i −0.00981158 0.0169942i
\(253\) −1.33595e8 + 2.31394e8i −0.518645 + 0.898319i
\(254\) 3.62597e8 1.38837
\(255\) −7.24784e8 −2.73727
\(256\) −8.38861e6 + 1.45295e7i −0.0312500 + 0.0541266i
\(257\) −2.82821e6 + 4.89860e6i −0.0103931 + 0.0180014i −0.871175 0.490972i \(-0.836642\pi\)
0.860782 + 0.508974i \(0.169975\pi\)
\(258\) 1.13273e8 0.410638
\(259\) −1.44499e7 −0.0516792
\(260\) 1.46901e8 2.54440e8i 0.518343 0.897796i
\(261\) −5.11812e7 8.86484e7i −0.178184 0.308624i
\(262\) −8.82223e7 + 1.52805e8i −0.303057 + 0.524909i
\(263\) 1.93484e7 + 3.35125e7i 0.0655844 + 0.113596i 0.896953 0.442126i \(-0.145775\pi\)
−0.831369 + 0.555721i \(0.812442\pi\)
\(264\) 4.36126e7 + 7.55393e7i 0.145881 + 0.252673i
\(265\) −1.80162e8 −0.594706
\(266\) −2.70659e7 + 2.50707e7i −0.0881732 + 0.0816735i
\(267\) −1.37947e8 −0.443531
\(268\) −1.03447e8 1.79175e8i −0.328280 0.568597i
\(269\) −1.10064e8 1.90637e8i −0.344757 0.597137i 0.640553 0.767914i \(-0.278705\pi\)
−0.985310 + 0.170778i \(0.945372\pi\)
\(270\) 2.41239e8 4.17838e8i 0.745889 1.29192i
\(271\) 2.74339e8 + 4.75170e8i 0.837328 + 1.45030i 0.892121 + 0.451797i \(0.149217\pi\)
−0.0547924 + 0.998498i \(0.517450\pi\)
\(272\) 6.62557e7 1.14758e8i 0.199633 0.345774i
\(273\) 5.31628e7 0.158139
\(274\) 1.52252e8 0.447133
\(275\) 4.57502e8 7.92417e8i 1.32657 2.29768i
\(276\) 8.44172e7 1.46215e8i 0.241685 0.418610i
\(277\) −1.26285e7 −0.0357004 −0.0178502 0.999841i \(-0.505682\pi\)
−0.0178502 + 0.999841i \(0.505682\pi\)
\(278\) −4.48674e8 −1.25249
\(279\) −3.34565e7 + 5.79483e7i −0.0922286 + 0.159745i
\(280\) 2.15704e7 + 3.73610e7i 0.0587225 + 0.101710i
\(281\) 1.06204e8 1.83951e8i 0.285542 0.494573i −0.687198 0.726470i \(-0.741160\pi\)
0.972741 + 0.231896i \(0.0744930\pi\)
\(282\) −6.83200e6 1.18334e7i −0.0181416 0.0314222i
\(283\) 1.33394e8 + 2.31045e8i 0.349851 + 0.605960i 0.986223 0.165423i \(-0.0528989\pi\)
−0.636372 + 0.771383i \(0.719566\pi\)
\(284\) −1.04890e8 −0.271718
\(285\) −6.39887e8 1.97974e8i −1.63737 0.506584i
\(286\) 2.79268e8 0.705894
\(287\) 3.83172e7 + 6.63673e7i 0.0956769 + 0.165717i
\(288\) 8.27357e6 + 1.43302e7i 0.0204089 + 0.0353492i
\(289\) −3.18137e8 + 5.51030e8i −0.775304 + 1.34287i
\(290\) 4.42922e8 + 7.67163e8i 1.06643 + 1.84712i
\(291\) −1.50983e8 + 2.61511e8i −0.359173 + 0.622105i
\(292\) −1.20088e8 −0.282267
\(293\) −1.33760e8 −0.310663 −0.155331 0.987862i \(-0.549645\pi\)
−0.155331 + 0.987862i \(0.549645\pi\)
\(294\) 1.31199e8 2.27243e8i 0.301103 0.521525i
\(295\) 4.45307e8 7.71295e8i 1.00991 1.74922i
\(296\) 4.79642e7 0.107497
\(297\) 4.58611e8 1.01577
\(298\) −2.35550e8 + 4.07985e8i −0.515617 + 0.893074i
\(299\) −2.70277e8 4.68134e8i −0.584736 1.01279i
\(300\) −2.89089e8 + 5.00718e8i −0.618170 + 1.07070i
\(301\) 2.66262e7 + 4.61180e7i 0.0562765 + 0.0974738i
\(302\) −3.10506e7 5.37813e7i −0.0648704 0.112359i
\(303\) −1.95223e7 −0.0403163
\(304\) 8.98409e7 8.32183e7i 0.183407 0.169887i
\(305\) 1.42294e7 0.0287169
\(306\) −6.53471e7 1.13184e8i −0.130377 0.225820i
\(307\) −3.21992e8 5.57706e8i −0.635126 1.10007i −0.986488 0.163831i \(-0.947615\pi\)
0.351362 0.936240i \(-0.385719\pi\)
\(308\) −2.05033e7 + 3.55128e7i −0.0399850 + 0.0692560i
\(309\) 1.32255e8 + 2.29073e8i 0.255011 + 0.441692i
\(310\) 2.89532e8 5.01485e8i 0.551990 0.956075i
\(311\) −6.34581e8 −1.19626 −0.598130 0.801399i \(-0.704089\pi\)
−0.598130 + 0.801399i \(0.704089\pi\)
\(312\) −1.76465e8 −0.328942
\(313\) 1.79090e8 3.10194e8i 0.330116 0.571778i −0.652418 0.757859i \(-0.726245\pi\)
0.982534 + 0.186081i \(0.0595787\pi\)
\(314\) −3.57244e8 + 6.18765e8i −0.651195 + 1.12790i
\(315\) 4.25491e7 0.0767015
\(316\) 3.90122e7 0.0695497
\(317\) −2.59766e8 + 4.49928e8i −0.458011 + 0.793297i −0.998856 0.0478246i \(-0.984771\pi\)
0.540845 + 0.841122i \(0.318104\pi\)
\(318\) 5.41052e7 + 9.37129e7i 0.0943504 + 0.163420i
\(319\) −4.21012e8 + 7.29213e8i −0.726150 + 1.25773i
\(320\) −7.15995e7 1.24014e8i −0.122148 0.211566i
\(321\) −1.18024e8 2.04424e8i −0.199161 0.344957i
\(322\) 7.93730e7 0.132488
\(323\) −7.09590e8 + 6.57283e8i −1.17165 + 1.08528i
\(324\) −2.19109e8 −0.357892
\(325\) 9.25573e8 + 1.60314e9i 1.49561 + 2.59048i
\(326\) −1.39464e8 2.41559e8i −0.222947 0.386155i
\(327\) 1.92369e8 3.33192e8i 0.304241 0.526960i
\(328\) −1.27188e8 2.20296e8i −0.199016 0.344705i
\(329\) 3.21188e6 5.56314e6i 0.00497249 0.00861261i
\(330\) −7.44496e8 −1.14042
\(331\) 9.98621e8 1.51357 0.756785 0.653663i \(-0.226769\pi\)
0.756785 + 0.653663i \(0.226769\pi\)
\(332\) 8.95524e7 1.55109e8i 0.134306 0.232624i
\(333\) 2.36532e7 4.09686e7i 0.0351023 0.0607990i
\(334\) 7.51625e8 1.10379
\(335\) 1.76590e9 2.56631
\(336\) 1.29558e7 2.24401e7i 0.0186327 0.0322728i
\(337\) −1.79876e8 3.11555e8i −0.256017 0.443435i 0.709154 0.705054i \(-0.249077\pi\)
−0.965171 + 0.261619i \(0.915744\pi\)
\(338\) −3.14992e7 + 5.45582e7i −0.0443702 + 0.0768514i
\(339\) 1.96951e8 + 3.41129e8i 0.274574 + 0.475576i
\(340\) 5.65514e8 + 9.79498e8i 0.780309 + 1.35154i
\(341\) 5.50420e8 0.751716
\(342\) −2.67764e7 1.17776e8i −0.0361960 0.159208i
\(343\) 2.50389e8 0.335031
\(344\) −8.83816e7 1.53081e8i −0.117060 0.202753i
\(345\) 7.20528e8 + 1.24799e9i 0.944678 + 1.63623i
\(346\) −1.85973e8 + 3.22114e8i −0.241370 + 0.418064i
\(347\) −2.63938e8 4.57153e8i −0.339116 0.587366i 0.645151 0.764055i \(-0.276795\pi\)
−0.984267 + 0.176689i \(0.943461\pi\)
\(348\) 2.66031e8 4.60780e8i 0.338381 0.586093i
\(349\) −9.05796e8 −1.14062 −0.570311 0.821429i \(-0.693177\pi\)
−0.570311 + 0.821429i \(0.693177\pi\)
\(350\) −2.71816e8 −0.338872
\(351\) −4.63908e8 + 8.03511e8i −0.572607 + 0.991784i
\(352\) 6.80576e7 1.17879e8i 0.0831720 0.144058i
\(353\) 5.07191e8 0.613705 0.306853 0.951757i \(-0.400724\pi\)
0.306853 + 0.951757i \(0.400724\pi\)
\(354\) −5.34929e8 −0.640891
\(355\) 4.47633e8 7.75323e8i 0.531035 0.919779i
\(356\) 1.07634e8 + 1.86427e8i 0.126437 + 0.218995i
\(357\) −1.02329e8 + 1.77238e8i −0.119030 + 0.206167i
\(358\) −4.29274e8 7.43524e8i −0.494475 0.856455i
\(359\) −8.67693e8 1.50289e9i −0.989773 1.71434i −0.618426 0.785843i \(-0.712229\pi\)
−0.371347 0.928494i \(-0.621104\pi\)
\(360\) −1.41235e8 −0.159545
\(361\) −8.06008e8 + 3.86468e8i −0.901705 + 0.432353i
\(362\) −1.06776e8 −0.118303
\(363\) 4.57747e7 + 7.92841e7i 0.0502288 + 0.0869988i
\(364\) −4.14803e7 7.18460e7i −0.0450803 0.0780814i
\(365\) 5.12496e8 8.87670e8i 0.551653 0.955490i
\(366\) −4.27330e6 7.40157e6i −0.00455596 0.00789115i
\(367\) 5.98701e8 1.03698e9i 0.632235 1.09506i −0.354858 0.934920i \(-0.615471\pi\)
0.987094 0.160144i \(-0.0511957\pi\)
\(368\) −2.63466e8 −0.275586
\(369\) −2.50887e8 −0.259948
\(370\) −2.04695e8 + 3.54542e8i −0.210088 + 0.363883i
\(371\) −2.54361e7 + 4.40567e7i −0.0258608 + 0.0447922i
\(372\) −3.47803e8 −0.350294
\(373\) −1.27457e9 −1.27170 −0.635849 0.771813i \(-0.719350\pi\)
−0.635849 + 0.771813i \(0.719350\pi\)
\(374\) −5.37539e8 + 9.31045e8i −0.531324 + 0.920280i
\(375\) −1.59234e9 2.75801e9i −1.55928 2.70076i
\(376\) −1.06613e7 + 1.84660e7i −0.0103432 + 0.0179149i
\(377\) −8.51748e8 1.47527e9i −0.818685 1.41800i
\(378\) −6.81185e7 1.17985e8i −0.0648700 0.112358i
\(379\) −7.81768e8 −0.737634 −0.368817 0.929502i \(-0.620237\pi\)
−0.368817 + 0.929502i \(0.620237\pi\)
\(380\) 2.31723e8 + 1.01923e9i 0.216634 + 0.952865i
\(381\) 1.85887e9 1.72192
\(382\) 2.62135e8 + 4.54031e8i 0.240604 + 0.416739i
\(383\) 2.04803e8 + 3.54730e8i 0.186269 + 0.322628i 0.944004 0.329935i \(-0.107027\pi\)
−0.757734 + 0.652563i \(0.773694\pi\)
\(384\) −4.30047e7 + 7.44863e7i −0.0387576 + 0.0671301i
\(385\) −1.75003e8 3.03113e8i −0.156290 0.270703i
\(386\) 3.86185e7 6.68892e7i 0.0341775 0.0591971i
\(387\) −1.74339e8 −0.152900
\(388\) 4.71219e8 0.409555
\(389\) 8.21227e8 1.42241e9i 0.707359 1.22518i −0.258475 0.966018i \(-0.583220\pi\)
0.965834 0.259163i \(-0.0834468\pi\)
\(390\) 7.53095e8 1.30440e9i 0.642871 1.11348i
\(391\) 2.08093e9 1.76051
\(392\) −4.09472e8 −0.343339
\(393\) −4.52277e8 + 7.83366e8i −0.375863 + 0.651015i
\(394\) −2.14205e8 3.71013e8i −0.176438 0.305599i
\(395\) −1.66491e8 + 2.88370e8i −0.135925 + 0.235430i
\(396\) −6.71243e7 1.16263e8i −0.0543183 0.0940821i
\(397\) 8.91669e8 + 1.54442e9i 0.715215 + 1.23879i 0.962877 + 0.269942i \(0.0870046\pi\)
−0.247661 + 0.968847i \(0.579662\pi\)
\(398\) −7.23083e8 −0.574907
\(399\) −1.38755e8 + 1.28526e8i −0.109356 + 0.101295i
\(400\) 9.02249e8 0.704882
\(401\) 8.19592e8 + 1.41958e9i 0.634735 + 1.09939i 0.986571 + 0.163332i \(0.0522241\pi\)
−0.351836 + 0.936062i \(0.614443\pi\)
\(402\) −5.30324e8 9.18549e8i −0.407146 0.705198i
\(403\) −5.56777e8 + 9.64366e8i −0.423754 + 0.733963i
\(404\) 1.52323e7 + 2.63831e7i 0.0114929 + 0.0199063i
\(405\) 9.35083e8 1.61961e9i 0.699451 1.21149i
\(406\) 2.50135e8 0.185496
\(407\) −3.89138e8 −0.286104
\(408\) 3.39663e8 5.88314e8i 0.247593 0.428844i
\(409\) −4.30118e7 + 7.44986e7i −0.0310854 + 0.0538414i −0.881150 0.472838i \(-0.843230\pi\)
0.850064 + 0.526679i \(0.176563\pi\)
\(410\) 2.17118e9 1.55579
\(411\) 7.80530e8 0.554553
\(412\) 2.06385e8 3.57469e8i 0.145391 0.251825i
\(413\) −1.25741e8 2.17790e8i −0.0878320 0.152129i
\(414\) −1.29927e8 + 2.25039e8i −0.0899905 + 0.155868i
\(415\) 7.64359e8 + 1.32391e9i 0.524963 + 0.909263i
\(416\) 1.37687e8 + 2.38481e8i 0.0937707 + 0.162416i
\(417\) −2.30015e9 −1.55339
\(418\) −7.28888e8 + 6.75158e8i −0.488139 + 0.452156i
\(419\) −2.62562e8 −0.174374 −0.0871871 0.996192i \(-0.527788\pi\)
−0.0871871 + 0.996192i \(0.527788\pi\)
\(420\) 1.10582e8 + 1.91533e8i 0.0728301 + 0.126145i
\(421\) 9.44601e8 + 1.63610e9i 0.616966 + 1.06862i 0.990036 + 0.140813i \(0.0449716\pi\)
−0.373071 + 0.927803i \(0.621695\pi\)
\(422\) 6.25670e8 1.08369e9i 0.405277 0.701960i
\(423\) 1.05151e7 + 1.82127e7i 0.00675497 + 0.0117000i
\(424\) 8.44312e7 1.46239e8i 0.0537926 0.0931715i
\(425\) −7.12623e9 −4.50296
\(426\) −5.37722e8 −0.336996
\(427\) 2.00898e6 3.47965e6i 0.00124876 0.00216291i
\(428\) −1.84177e8 + 3.19004e8i −0.113549 + 0.196672i
\(429\) 1.43168e9 0.875479
\(430\) 1.50873e9 0.915108
\(431\) −1.21752e8 + 2.10881e8i −0.0732499 + 0.126873i −0.900324 0.435220i \(-0.856670\pi\)
0.827074 + 0.562093i \(0.190004\pi\)
\(432\) 2.26109e8 + 3.91632e8i 0.134935 + 0.233714i
\(433\) −1.51328e6 + 2.62109e6i −0.000895804 + 0.00155158i −0.866473 0.499224i \(-0.833618\pi\)
0.865577 + 0.500776i \(0.166952\pi\)
\(434\) −8.17552e7 1.41604e8i −0.0480066 0.0831499i
\(435\) 2.27066e9 + 3.93291e9i 1.32264 + 2.29087i
\(436\) −6.00383e8 −0.346917
\(437\) 1.83718e9 + 5.68405e8i 1.05309 + 0.325816i
\(438\) −6.15640e8 −0.350080
\(439\) −7.63105e8 1.32174e9i −0.430485 0.745623i 0.566430 0.824110i \(-0.308324\pi\)
−0.996915 + 0.0784875i \(0.974991\pi\)
\(440\) 5.80894e8 + 1.00614e9i 0.325096 + 0.563083i
\(441\) −2.01929e8 + 3.49750e8i −0.112115 + 0.194188i
\(442\) −1.08749e9 1.88360e9i −0.599031 1.03755i
\(443\) 9.06404e8 1.56994e9i 0.495346 0.857964i −0.504640 0.863330i \(-0.668375\pi\)
0.999986 + 0.00536571i \(0.00170797\pi\)
\(444\) 2.45891e8 0.133322
\(445\) −1.83737e9 −0.988411
\(446\) −5.67086e8 + 9.82222e8i −0.302675 + 0.524249i
\(447\) −1.20756e9 + 2.09156e9i −0.639489 + 1.10763i
\(448\) −4.04350e7 −0.0212464
\(449\) −9.74366e8 −0.507996 −0.253998 0.967205i \(-0.581746\pi\)
−0.253998 + 0.967205i \(0.581746\pi\)
\(450\) 4.44938e8 7.70655e8i 0.230174 0.398673i
\(451\) 1.03189e9 + 1.78728e9i 0.529681 + 0.917435i
\(452\) 3.07342e8 5.32332e8i 0.156545 0.271143i
\(453\) −1.59183e8 2.75713e8i −0.0804549 0.139352i
\(454\) 7.63099e8 + 1.32173e9i 0.382724 + 0.662897i
\(455\) 7.08095e8 0.352413
\(456\) 4.60575e8 4.26623e8i 0.227469 0.210702i
\(457\) 1.03143e9 0.505514 0.252757 0.967530i \(-0.418663\pi\)
0.252757 + 0.967530i \(0.418663\pi\)
\(458\) 1.13265e9 + 1.96182e9i 0.550894 + 0.954177i
\(459\) −1.78587e9 3.09322e9i −0.861998 1.49302i
\(460\) 1.12438e9 1.94749e9i 0.538595 0.932874i
\(461\) 6.79120e8 + 1.17627e9i 0.322844 + 0.559183i 0.981074 0.193635i \(-0.0620277\pi\)
−0.658229 + 0.752817i \(0.728694\pi\)
\(462\) −1.05112e8 + 1.82058e8i −0.0495911 + 0.0858942i
\(463\) 2.58298e9 1.20945 0.604725 0.796435i \(-0.293283\pi\)
0.604725 + 0.796435i \(0.293283\pi\)
\(464\) −8.30285e8 −0.385846
\(465\) 1.48430e9 2.57089e9i 0.684601 1.18576i
\(466\) −6.25048e8 + 1.08262e9i −0.286130 + 0.495591i
\(467\) −3.30929e9 −1.50358 −0.751788 0.659405i \(-0.770808\pi\)
−0.751788 + 0.659405i \(0.770808\pi\)
\(468\) 2.71598e8 0.122480
\(469\) 2.49318e8 4.31832e8i 0.111596 0.193290i
\(470\) −9.09980e7 1.57613e8i −0.0404286 0.0700245i
\(471\) −1.83143e9 + 3.17213e9i −0.807640 + 1.39887i
\(472\) 4.17378e8 + 7.22921e8i 0.182698 + 0.316442i
\(473\) 7.17049e8 + 1.24196e9i 0.311555 + 0.539629i
\(474\) 1.99998e8 0.0862585
\(475\) −6.29150e9 1.94652e9i −2.69356 0.833358i
\(476\) 3.19368e8 0.135727
\(477\) −8.32733e7 1.44234e8i −0.0351311 0.0608488i
\(478\) 5.65232e7 + 9.79010e7i 0.0236717 + 0.0410005i
\(479\) −4.67315e8 + 8.09413e8i −0.194283 + 0.336508i −0.946665 0.322219i \(-0.895571\pi\)
0.752382 + 0.658727i \(0.228905\pi\)
\(480\) −3.67059e8 6.35764e8i −0.151493 0.262393i
\(481\) 3.93633e8 6.81792e8i 0.161281 0.279347i
\(482\) −2.71803e9 −1.10558
\(483\) 4.06910e8 0.164317
\(484\) 7.14315e7 1.23723e8i 0.0286372 0.0496011i
\(485\) −2.01100e9 + 3.48316e9i −0.800418 + 1.38636i
\(486\) 8.08365e8 0.319434
\(487\) 1.86460e9 0.731532 0.365766 0.930707i \(-0.380807\pi\)
0.365766 + 0.930707i \(0.380807\pi\)
\(488\) −6.66849e6 + 1.15502e7i −0.00259752 + 0.00449903i
\(489\) −7.14971e8 1.23837e9i −0.276508 0.478926i
\(490\) 1.74749e9 3.02674e9i 0.671009 1.16222i
\(491\) −2.50220e9 4.33394e9i −0.953974 1.65233i −0.736698 0.676222i \(-0.763616\pi\)
−0.217276 0.976110i \(-0.569717\pi\)
\(492\) −6.52036e8 1.12936e9i −0.246827 0.427518i
\(493\) 6.55783e9 2.46488
\(494\) −4.45608e8 1.96001e9i −0.166306 0.731499i
\(495\) 1.14585e9 0.424631
\(496\) 2.71373e8 + 4.70033e8i 0.0998577 + 0.172959i
\(497\) −1.26398e8 2.18928e8i −0.0461841 0.0799932i
\(498\) 4.59095e8 7.95177e8i 0.166571 0.288510i
\(499\) 2.13293e9 + 3.69435e9i 0.768468 + 1.33103i 0.938394 + 0.345568i \(0.112314\pi\)
−0.169926 + 0.985457i \(0.554353\pi\)
\(500\) −2.48484e9 + 4.30387e9i −0.889004 + 1.53980i
\(501\) 3.85325e9 1.36897
\(502\) −2.52427e9 −0.890578
\(503\) 1.88365e9 3.26257e9i 0.659951 1.14307i −0.320676 0.947189i \(-0.603910\pi\)
0.980628 0.195880i \(-0.0627564\pi\)
\(504\) −1.99403e7 + 3.45375e7i −0.00693783 + 0.0120167i
\(505\) −2.60025e8 −0.0898451
\(506\) 2.13753e9 0.733474
\(507\) −1.61482e8 + 2.79696e8i −0.0550298 + 0.0953143i
\(508\) −1.45039e9 2.51215e9i −0.490864 0.850201i
\(509\) 1.79550e9 3.10990e9i 0.603495 1.04528i −0.388792 0.921325i \(-0.627108\pi\)
0.992287 0.123959i \(-0.0395591\pi\)
\(510\) 2.89914e9 + 5.02145e9i 0.967772 + 1.67623i
\(511\) −1.44713e8 2.50651e8i −0.0479773 0.0830991i
\(512\) 1.34218e8 0.0441942
\(513\) −7.31774e8 3.21871e9i −0.239313 1.05262i
\(514\) 4.52513e7 0.0146981
\(515\) 1.76156e9 + 3.05111e9i 0.568293 + 0.984313i
\(516\) −4.53093e8 7.84781e8i −0.145182 0.251463i
\(517\) 8.64965e7 1.49816e8i 0.0275284 0.0476807i
\(518\) 5.77997e7 + 1.00112e8i 0.0182714 + 0.0316469i
\(519\) −9.53399e8 + 1.65134e9i −0.299357 + 0.518501i
\(520\) −2.35041e9 −0.733048
\(521\) 1.62650e8 0.0503874 0.0251937 0.999683i \(-0.491980\pi\)
0.0251937 + 0.999683i \(0.491980\pi\)
\(522\) −4.09449e8 + 7.09187e8i −0.125995 + 0.218230i
\(523\) 1.55375e9 2.69118e9i 0.474926 0.822596i −0.524662 0.851311i \(-0.675808\pi\)
0.999588 + 0.0287151i \(0.00914155\pi\)
\(524\) 1.41156e9 0.428587
\(525\) −1.39348e9 −0.420284
\(526\) 1.54788e8 2.68100e8i 0.0463752 0.0803242i
\(527\) −2.14339e9 3.71245e9i −0.637916 1.10490i
\(528\) 3.48901e8 6.04315e8i 0.103153 0.178667i
\(529\) −3.66299e8 6.34449e8i −0.107582 0.186338i
\(530\) 7.20648e8 + 1.24820e9i 0.210260 + 0.364182i
\(531\) 8.23309e8 0.238634
\(532\) 2.81959e8 + 8.72350e7i 0.0811885 + 0.0251189i
\(533\) −4.17522e9 −1.19436
\(534\) 5.51790e8 + 9.55728e8i 0.156812 + 0.271606i
\(535\) −1.57201e9 2.72280e9i −0.443831 0.768737i
\(536\) −8.27572e8 + 1.43340e9i −0.232129 + 0.402059i
\(537\) −2.20070e9 3.81172e9i −0.613268 1.06221i
\(538\) −8.80514e8 + 1.52509e9i −0.243780 + 0.422239i
\(539\) 3.32209e9 0.913799
\(540\) −3.85982e9 −1.05485
\(541\) 2.41634e9 4.18523e9i 0.656098 1.13639i −0.325520 0.945535i \(-0.605539\pi\)
0.981617 0.190859i \(-0.0611274\pi\)
\(542\) 2.19472e9 3.80136e9i 0.592080 1.02551i
\(543\) −5.47394e8 −0.146724
\(544\) −1.06009e9 −0.282323
\(545\) 2.56223e9 4.43792e9i 0.678002 1.17433i
\(546\) −2.12651e8 3.68323e8i −0.0559105 0.0968398i
\(547\) −3.80472e9 + 6.58996e9i −0.993955 + 1.72158i −0.401900 + 0.915684i \(0.631650\pi\)
−0.592055 + 0.805897i \(0.701683\pi\)
\(548\) −6.09009e8 1.05484e9i −0.158085 0.273812i
\(549\) 6.57704e6 + 1.13918e7i 0.00169640 + 0.00293824i
\(550\) −7.32004e9 −1.87605
\(551\) 5.78968e9 + 1.79127e9i 1.47443 + 0.456173i
\(552\) −1.35067e9 −0.341794
\(553\) 4.70119e7 + 8.14271e7i 0.0118214 + 0.0204753i
\(554\) 5.05140e7 + 8.74929e7i 0.0126220 + 0.0218619i
\(555\) −1.04938e9 + 1.81758e9i −0.260560 + 0.451303i
\(556\) 1.79470e9 + 3.10850e9i 0.442822 + 0.766990i
\(557\) 1.66736e9 2.88795e9i 0.408824 0.708104i −0.585934 0.810359i \(-0.699272\pi\)
0.994758 + 0.102254i \(0.0326056\pi\)
\(558\) 5.35304e8 0.130431
\(559\) −2.90132e9 −0.702514
\(560\) 1.72563e8 2.98888e8i 0.0415231 0.0719201i
\(561\) −2.75572e9 + 4.77305e9i −0.658970 + 1.14137i
\(562\) −1.69927e9 −0.403818
\(563\) −2.13639e9 −0.504546 −0.252273 0.967656i \(-0.581178\pi\)
−0.252273 + 0.967656i \(0.581178\pi\)
\(564\) −5.46560e7 + 9.46669e7i −0.0128281 + 0.0222188i
\(565\) 2.62327e9 + 4.54363e9i 0.611889 + 1.05982i
\(566\) 1.06715e9 1.84836e9i 0.247382 0.428478i
\(567\) −2.64039e8 4.57329e8i −0.0608313 0.105363i
\(568\) 4.19558e8 + 7.26696e8i 0.0960667 + 0.166392i
\(569\) 3.31529e9 0.754448 0.377224 0.926122i \(-0.376879\pi\)
0.377224 + 0.926122i \(0.376879\pi\)
\(570\) 1.18794e9 + 5.22516e9i 0.268679 + 1.18178i
\(571\) 1.96490e9 0.441686 0.220843 0.975309i \(-0.429119\pi\)
0.220843 + 0.975309i \(0.429119\pi\)
\(572\) −1.11707e9 1.93482e9i −0.249571 0.432270i
\(573\) 1.34385e9 + 2.32762e9i 0.298407 + 0.516857i
\(574\) 3.06537e8 5.30938e8i 0.0676538 0.117180i
\(575\) 7.08438e9 + 1.22705e10i 1.55405 + 2.69169i
\(576\) 6.61886e7 1.14642e8i 0.0144313 0.0249957i
\(577\) −7.08114e9 −1.53458 −0.767288 0.641303i \(-0.778394\pi\)
−0.767288 + 0.641303i \(0.778394\pi\)
\(578\) 5.09020e9 1.09645
\(579\) 1.97980e8 3.42911e8i 0.0423883 0.0734187i
\(580\) 3.54338e9 6.13731e9i 0.754083 1.30611i
\(581\) 4.31663e8 0.0913122
\(582\) 2.41573e9 0.507947
\(583\) −6.84999e8 + 1.18645e9i −0.143169 + 0.247976i
\(584\) 4.80353e8 + 8.31996e8i 0.0997966 + 0.172853i
\(585\) −1.15909e9 + 2.00760e9i −0.239371 + 0.414603i
\(586\) 5.35040e8 + 9.26716e8i 0.109836 + 0.190241i
\(587\) 2.63789e9 + 4.56896e9i 0.538299 + 0.932361i 0.998996 + 0.0448032i \(0.0142661\pi\)
−0.460697 + 0.887557i \(0.652401\pi\)
\(588\) −2.09918e9 −0.425824
\(589\) −8.78267e8 3.86306e9i −0.177102 0.778983i
\(590\) −7.12492e9 −1.42823
\(591\) −1.09813e9 1.90202e9i −0.218826 0.379017i
\(592\) −1.91857e8 3.32306e8i −0.0380059 0.0658282i
\(593\) 5.72443e8 9.91501e8i 0.112730 0.195255i −0.804140 0.594440i \(-0.797374\pi\)
0.916870 + 0.399185i \(0.130707\pi\)
\(594\) −1.83444e9 3.17735e9i −0.359130 0.622031i
\(595\) −1.36295e9 + 2.36070e9i −0.265260 + 0.459444i
\(596\) 3.76881e9 0.729192
\(597\) −3.70693e9 −0.713023
\(598\) −2.16222e9 + 3.74507e9i −0.413471 + 0.716153i
\(599\) 1.24639e9 2.15880e9i 0.236951 0.410411i −0.722887 0.690966i \(-0.757185\pi\)
0.959838 + 0.280555i \(0.0905185\pi\)
\(600\) 4.62543e9 0.874224
\(601\) 6.02681e8 0.113247 0.0566235 0.998396i \(-0.481967\pi\)
0.0566235 + 0.998396i \(0.481967\pi\)
\(602\) 2.13010e8 3.68944e8i 0.0397935 0.0689244i
\(603\) 8.16223e8 + 1.41374e9i 0.151600 + 0.262578i
\(604\) −2.48405e8 + 4.30250e8i −0.0458703 + 0.0794496i
\(605\) 6.09691e8 + 1.05602e9i 0.111935 + 0.193877i
\(606\) 7.80891e7 + 1.35254e8i 0.0142540 + 0.0246886i
\(607\) −6.23151e9 −1.13092 −0.565461 0.824775i \(-0.691302\pi\)
−0.565461 + 0.824775i \(0.691302\pi\)
\(608\) −9.35917e8 2.89563e8i −0.168879 0.0522493i
\(609\) 1.28233e9 0.230060
\(610\) −5.69177e7 9.85844e7i −0.0101530 0.0175855i
\(611\) 1.74991e8 + 3.03093e8i 0.0310364 + 0.0537567i
\(612\) −5.22777e8 + 9.05476e8i −0.0921905 + 0.159679i
\(613\) −3.30404e9 5.72276e9i −0.579340 1.00345i −0.995555 0.0941796i \(-0.969977\pi\)
0.416216 0.909266i \(-0.363356\pi\)
\(614\) −2.57593e9 + 4.46165e9i −0.449102 + 0.777868i
\(615\) 1.11307e10 1.92956
\(616\) 3.28053e8 0.0565473
\(617\) −2.51081e9 + 4.34886e9i −0.430345 + 0.745379i −0.996903 0.0786427i \(-0.974941\pi\)
0.566558 + 0.824022i \(0.308275\pi\)
\(618\) 1.05804e9 1.83259e9i 0.180320 0.312323i
\(619\) −5.27733e9 −0.894328 −0.447164 0.894452i \(-0.647566\pi\)
−0.447164 + 0.894452i \(0.647566\pi\)
\(620\) −4.63252e9 −0.780632
\(621\) −3.55077e9 + 6.15011e9i −0.594979 + 1.03053i
\(622\) 2.53832e9 + 4.39650e9i 0.422942 + 0.732557i
\(623\) −2.59409e8 + 4.49310e8i −0.0429811 + 0.0744455i
\(624\) 7.05862e8 + 1.22259e9i 0.116298 + 0.201435i
\(625\) −1.26044e10 2.18315e10i −2.06511 3.57687i
\(626\) −2.86545e9 −0.466855
\(627\) −3.73669e9 + 3.46124e9i −0.605411 + 0.560783i
\(628\) 5.71591e9 0.920929
\(629\) 1.51534e9 + 2.62465e9i 0.242791 + 0.420527i
\(630\) −1.70197e8 2.94789e8i −0.0271181 0.0469699i
\(631\) 1.29310e9 2.23971e9i 0.204894 0.354887i −0.745205 0.666835i \(-0.767648\pi\)
0.950099 + 0.311949i \(0.100982\pi\)
\(632\) −1.56049e8 2.70284e8i −0.0245895 0.0425903i
\(633\) 3.20753e9 5.55561e9i 0.502641 0.870600i
\(634\) 4.15626e9 0.647725
\(635\) 2.47591e10 3.83730
\(636\) 4.32841e8 7.49703e8i 0.0667158 0.115555i
\(637\) −3.36046e9 + 5.82049e9i −0.515123 + 0.892219i
\(638\) 6.73618e9 1.02693
\(639\) 8.27609e8 0.125479
\(640\) −5.72796e8 + 9.92111e8i −0.0863714 + 0.149600i
\(641\) −9.35551e8 1.62042e9i −0.140302 0.243010i 0.787308 0.616560i \(-0.211474\pi\)
−0.927610 + 0.373549i \(0.878141\pi\)
\(642\) −9.44194e8 + 1.63539e9i −0.140828 + 0.243921i
\(643\) 1.16439e8 + 2.01678e8i 0.0172726 + 0.0299171i 0.874533 0.484967i \(-0.161168\pi\)
−0.857260 + 0.514884i \(0.827835\pi\)
\(644\) −3.17492e8 5.49912e8i −0.0468417 0.0811321i
\(645\) 7.73460e9 1.13495
\(646\) 7.39215e9 + 2.28705e9i 1.07884 + 0.333781i
\(647\) −1.01186e10 −1.46877 −0.734385 0.678733i \(-0.762529\pi\)
−0.734385 + 0.678733i \(0.762529\pi\)
\(648\) 8.76436e8 + 1.51803e9i 0.126534 + 0.219163i
\(649\) −3.38623e9 5.86513e9i −0.486251 0.842211i
\(650\) 7.40458e9 1.28251e10i 1.05756 1.83174i
\(651\) −4.19123e8 7.25942e8i −0.0595398 0.103126i
\(652\) −1.11571e9 + 1.93247e9i −0.157647 + 0.273053i
\(653\) 8.66788e8 0.121819 0.0609097 0.998143i \(-0.480600\pi\)
0.0609097 + 0.998143i \(0.480600\pi\)
\(654\) −3.07790e9 −0.430261
\(655\) −6.02404e9 + 1.04340e10i −0.837613 + 1.45079i
\(656\) −1.01750e9 + 1.76237e9i −0.140725 + 0.243743i
\(657\) 9.47532e8 0.130351
\(658\) −5.13901e7 −0.00703216
\(659\) −2.28489e9 + 3.95755e9i −0.311004 + 0.538676i −0.978580 0.205866i \(-0.933999\pi\)
0.667576 + 0.744542i \(0.267332\pi\)
\(660\) 2.97798e9 + 5.15802e9i 0.403198 + 0.698360i
\(661\) −6.10131e9 + 1.05678e10i −0.821709 + 1.42324i 0.0826998 + 0.996575i \(0.473646\pi\)
−0.904409 + 0.426667i \(0.859688\pi\)
\(662\) −3.99448e9 6.91865e9i −0.535128 0.926869i
\(663\) −5.57510e9 9.65636e9i −0.742943 1.28682i
\(664\) −1.43284e9 −0.189937
\(665\) −1.84813e9 + 1.71189e9i −0.243700 + 0.225736i
\(666\) −3.78452e8 −0.0496422
\(667\) −6.51932e9 1.12918e10i −0.850672 1.47341i
\(668\) −3.00650e9 5.20741e9i −0.390250 0.675934i
\(669\) −2.90720e9 + 5.03542e9i −0.375391 + 0.650195i
\(670\) −7.06359e9 1.22345e10i −0.907327 1.57154i
\(671\) 5.41021e7 9.37076e7i 0.00691330 0.0119742i
\(672\) −2.07292e8 −0.0263506
\(673\) 9.89747e9 1.25162 0.625809 0.779977i \(-0.284769\pi\)
0.625809 + 0.779977i \(0.284769\pi\)
\(674\) −1.43901e9 + 2.49244e9i −0.181032 + 0.313556i
\(675\) 1.21597e10 2.10613e10i 1.52181 2.63585i
\(676\) 5.03987e8 0.0627489
\(677\) −2.44937e9 −0.303385 −0.151692 0.988428i \(-0.548472\pi\)
−0.151692 + 0.988428i \(0.548472\pi\)
\(678\) 1.57561e9 2.72903e9i 0.194153 0.336283i
\(679\) 5.67846e8 + 9.83538e8i 0.0696124 + 0.120572i
\(680\) 4.52411e9 7.83599e9i 0.551762 0.955680i
\(681\) 3.91207e9 + 6.77590e9i 0.474670 + 0.822152i
\(682\) −2.20168e9 3.81342e9i −0.265772 0.460330i
\(683\) −1.25074e10 −1.50208 −0.751040 0.660256i \(-0.770448\pi\)
−0.751040 + 0.660256i \(0.770448\pi\)
\(684\) −7.08871e8 + 6.56617e8i −0.0846975 + 0.0784541i
\(685\) 1.03962e10 1.23582
\(686\) −1.00156e9 1.73474e9i −0.118452 0.205164i
\(687\) 5.80662e9 + 1.00574e10i 0.683242 + 1.18341i
\(688\) −7.07053e8 + 1.22465e9i −0.0827737 + 0.143368i
\(689\) −1.38582e9 2.40031e9i −0.161413 0.279576i
\(690\) 5.76422e9 9.98392e9i 0.667988 1.15699i
\(691\) −2.95176e9 −0.340336 −0.170168 0.985415i \(-0.554431\pi\)
−0.170168 + 0.985415i \(0.554431\pi\)
\(692\) 2.97556e9 0.341348
\(693\) 1.61777e8 2.80206e8i 0.0184651 0.0319825i
\(694\) −2.11150e9 + 3.65723e9i −0.239791 + 0.415330i
\(695\) −3.06366e10 −3.46174
\(696\) −4.25650e9 −0.478543
\(697\) 8.03653e9 1.39197e10i 0.898988 1.55709i
\(698\) 3.62318e9 + 6.27554e9i 0.403270 + 0.698485i
\(699\) −3.20435e9 + 5.55009e9i −0.354870 + 0.614653i
\(700\) 1.08726e9 + 1.88319e9i 0.119809 + 0.207516i
\(701\) 9.07691e8 + 1.57217e9i 0.0995234 + 0.172380i 0.911487 0.411328i \(-0.134935\pi\)
−0.811964 + 0.583707i \(0.801602\pi\)
\(702\) 7.42252e9 0.809788
\(703\) 6.20922e8 + 2.73112e9i 0.0674052 + 0.296482i
\(704\) −1.08892e9 −0.117623
\(705\) −4.66506e8 8.08012e8i −0.0501413 0.0868473i
\(706\) −2.02876e9 3.51392e9i −0.216978 0.375816i
\(707\) −3.67115e7 + 6.35862e7i −0.00390692 + 0.00676698i
\(708\) 2.13971e9 + 3.70609e9i 0.226589 + 0.392464i
\(709\) 9.88791e8 1.71264e9i 0.104194 0.180469i −0.809215 0.587513i \(-0.800107\pi\)
0.913409 + 0.407044i \(0.133440\pi\)
\(710\) −7.16213e9 −0.750996
\(711\) −3.07817e8 −0.0321181
\(712\) 8.61069e8 1.49141e9i 0.0894042 0.154853i
\(713\) −4.26160e9 + 7.38130e9i −0.440311 + 0.762640i
\(714\) 1.63726e9 0.168334
\(715\) 1.90691e10 1.95101
\(716\) −3.43419e9 + 5.94820e9i −0.349646 + 0.605605i
\(717\) 2.89769e8 + 5.01895e8i 0.0293586 + 0.0508506i
\(718\) −6.94155e9 + 1.20231e10i −0.699875 + 1.21222i
\(719\) −3.55313e9 6.15420e9i −0.356500 0.617476i 0.630873 0.775886i \(-0.282697\pi\)
−0.987374 + 0.158409i \(0.949363\pi\)
\(720\) 5.64941e8 + 9.78506e8i 0.0564078 + 0.0977012i
\(721\) 9.94823e8 0.0988490
\(722\) 5.90156e9 + 4.03832e9i 0.583562 + 0.399319i
\(723\) −1.39341e10 −1.37119
\(724\) 4.27105e8 + 7.39767e8i 0.0418263 + 0.0724453i
\(725\) 2.23256e10 + 3.86691e10i 2.17581 + 3.76861i
\(726\) 3.66198e8 6.34273e8i 0.0355171 0.0615174i
\(727\) 3.24626e9 + 5.62269e9i 0.313338 + 0.542718i 0.979083 0.203462i \(-0.0652194\pi\)
−0.665745 + 0.746180i \(0.731886\pi\)
\(728\) −3.31842e8 + 5.74768e8i −0.0318766 + 0.0552119i
\(729\) 1.16315e10 1.11196
\(730\) −8.19994e9 −0.780155
\(731\) 5.58451e9 9.67266e9i 0.528779 0.915872i
\(732\) −3.41864e7 + 5.92126e7i −0.00322155 + 0.00557988i
\(733\) 3.30727e9 0.310174 0.155087 0.987901i \(-0.450434\pi\)
0.155087 + 0.987901i \(0.450434\pi\)
\(734\) −9.57922e9 −0.894116
\(735\) 8.95860e9 1.55168e10i 0.832213 1.44144i
\(736\) 1.05386e9 + 1.82535e9i 0.0974345 + 0.168761i
\(737\) 6.71417e9 1.16293e10i 0.617812 1.07008i
\(738\) 1.00355e9 + 1.73820e9i 0.0919055 + 0.159185i
\(739\) −4.58526e9 7.94190e9i −0.417934 0.723884i 0.577797 0.816180i \(-0.303912\pi\)
−0.995732 + 0.0922968i \(0.970579\pi\)
\(740\) 3.27512e9 0.297109
\(741\) −2.28444e9 1.00481e10i −0.206260 0.907236i
\(742\) 4.06978e8 0.0365727
\(743\) −1.75418e9 3.03833e9i −0.156896 0.271753i 0.776852 0.629684i \(-0.216816\pi\)
−0.933748 + 0.357931i \(0.883482\pi\)
\(744\) 1.39121e9 + 2.40965e9i 0.123848 + 0.214510i
\(745\) −1.60840e10 + 2.78583e10i −1.42510 + 2.46835i
\(746\) 5.09829e9 + 8.83051e9i 0.449613 + 0.778753i
\(747\) −7.06594e8 + 1.22386e9i −0.0620223 + 0.107426i
\(748\) 8.60062e9 0.751405
\(749\) −8.87776e8 −0.0772000
\(750\) −1.27387e10 + 2.20640e10i −1.10258 + 1.90972i
\(751\) −2.79200e9 + 4.83589e9i −0.240534 + 0.416617i −0.960866 0.277012i \(-0.910656\pi\)
0.720333 + 0.693629i \(0.243989\pi\)
\(752\) 1.70581e8 0.0146275
\(753\) −1.29408e10 −1.10453
\(754\) −6.81399e9 + 1.18022e10i −0.578897 + 1.00268i
\(755\) −2.12022e9 3.67232e9i −0.179294 0.310547i
\(756\) −5.44948e8 + 9.43878e8i −0.0458700 + 0.0794492i
\(757\) 4.78255e9 + 8.28363e9i 0.400705 + 0.694041i 0.993811 0.111083i \(-0.0354321\pi\)
−0.593107 + 0.805124i \(0.702099\pi\)
\(758\) 3.12707e9 + 5.41625e9i 0.260793 + 0.451707i
\(759\) 1.09582e10 0.909685
\(760\) 6.13457e9 5.68236e9i 0.506917 0.469549i
\(761\) 8.73122e9 0.718172 0.359086 0.933304i \(-0.383088\pi\)
0.359086 + 0.933304i \(0.383088\pi\)
\(762\) −7.43549e9 1.28787e10i −0.608790 1.05446i
\(763\) −7.23497e8 1.25313e9i −0.0589659 0.102132i
\(764\) 2.09708e9 3.63225e9i 0.170133 0.294679i
\(765\) −4.46207e9 7.72853e9i −0.360347 0.624139i
\(766\) 1.63843e9 2.83784e9i 0.131712 0.228132i
\(767\) 1.37014e10 1.09643
\(768\) 6.88075e8 0.0548115
\(769\) 3.33213e9 5.77142e9i 0.264229 0.457658i −0.703132 0.711059i \(-0.748216\pi\)
0.967361 + 0.253401i \(0.0815493\pi\)
\(770\) −1.40002e9 + 2.42491e9i −0.110514 + 0.191416i
\(771\) 2.31983e8 0.0182291
\(772\) −6.17896e8 −0.0483342
\(773\) −1.08342e9 + 1.87654e9i −0.0843661 + 0.146126i −0.905121 0.425154i \(-0.860220\pi\)
0.820755 + 0.571281i \(0.193553\pi\)
\(774\) 6.97357e8 + 1.20786e9i 0.0540582 + 0.0936315i
\(775\) 1.45940e10 2.52775e10i 1.12621 1.95065i
\(776\) −1.88488e9 3.26470e9i −0.144799 0.250800i
\(777\) 2.96313e8 + 5.13230e8i 0.0226609 + 0.0392499i
\(778\) −1.31396e10 −1.00036
\(779\) 1.08973e10 1.00940e10i 0.825922 0.765039i
\(780\) −1.20495e10 −0.909156
\(781\) −3.40392e9 5.89576e9i −0.255682 0.442854i
\(782\) −8.32373e9 1.44171e10i −0.622436 1.07809i
\(783\) −1.11899e10 + 1.93814e10i −0.833026 + 1.44284i
\(784\) 1.63789e9 + 2.83691e9i 0.121389 + 0.210251i
\(785\) −2.43935e10 + 4.22509e10i −1.79983 + 3.11739i
\(786\) 7.23642e9 0.531551
\(787\) −4.05121e9 −0.296260 −0.148130 0.988968i \(-0.547325\pi\)
−0.148130 + 0.988968i \(0.547325\pi\)
\(788\) −1.71364e9 + 2.96811e9i −0.124760 + 0.216091i
\(789\) 7.93527e8 1.37443e9i 0.0575165 0.0996215i
\(790\) 2.66385e9 0.192227
\(791\) 1.48146e9 0.106432
\(792\) −5.36994e8 + 9.30101e8i −0.0384089 + 0.0665261i
\(793\) 1.09454e8 + 1.89580e8i 0.00779427 + 0.0135001i
\(794\) 7.13335e9 1.23553e10i 0.505733 0.875956i
\(795\) 3.69444e9 + 6.39896e9i 0.260774 + 0.451673i
\(796\) 2.89233e9 + 5.00967e9i 0.203260 + 0.352057i
\(797\) 1.32068e10 0.924043 0.462022 0.886869i \(-0.347124\pi\)
0.462022 + 0.886869i \(0.347124\pi\)
\(798\) 1.44548e9 + 4.47215e8i 0.100693 + 0.0311535i
\(799\) −1.34730e9 −0.0934440
\(800\) −3.60900e9 6.25097e9i −0.249213 0.431650i
\(801\) −8.49260e8 1.47096e9i −0.0583885 0.101132i
\(802\) 6.55674e9 1.13566e10i 0.448826 0.777389i
\(803\) −3.89715e9 6.75007e9i −0.265609 0.460049i
\(804\) −4.24260e9 + 7.34839e9i −0.287896 + 0.498650i
\(805\) 5.41979e9 0.366182
\(806\) 8.90844e9 0.599279
\(807\) −4.51400e9 + 7.81848e9i −0.302346 + 0.523679i
\(808\) 1.21858e8 2.11064e8i 0.00812671 0.0140759i
\(809\) −1.65984e10 −1.10217 −0.551083 0.834450i \(-0.685785\pi\)
−0.551083 + 0.834450i \(0.685785\pi\)
\(810\) −1.49613e10 −0.989173
\(811\) −5.60895e9 + 9.71498e9i −0.369240 + 0.639542i −0.989447 0.144896i \(-0.953715\pi\)
0.620207 + 0.784438i \(0.287049\pi\)
\(812\) −1.00054e9 1.73299e9i −0.0655827 0.113593i
\(813\) 1.12513e10 1.94879e10i 0.734323 1.27188i
\(814\) 1.55655e9 + 2.69603e9i 0.101153 + 0.175202i
\(815\) −9.52298e9 1.64943e10i −0.616199 1.06729i
\(816\) −5.43462e9 −0.350149
\(817\) 7.57245e9 7.01425e9i 0.485802 0.449991i
\(818\) 6.88189e8 0.0439613
\(819\) 3.27292e8 + 5.66886e8i 0.0208181 + 0.0360580i
\(820\) −8.68471e9 1.50424e10i −0.550056 0.952725i
\(821\) 1.24209e10 2.15136e10i 0.783342 1.35679i −0.146643 0.989190i \(-0.546847\pi\)
0.929985 0.367598i \(-0.119820\pi\)
\(822\) −3.12212e9 5.40767e9i −0.196064 0.339593i
\(823\) 1.46287e9 2.53377e9i 0.0914760 0.158441i −0.816656 0.577124i \(-0.804175\pi\)
0.908132 + 0.418683i \(0.137508\pi\)
\(824\) −3.30216e9 −0.205614
\(825\) −3.75266e10 −2.32675
\(826\) −1.00593e9 + 1.74232e9i −0.0621066 + 0.107572i
\(827\) −1.06012e10 + 1.83619e10i −0.651759 + 1.12888i 0.330937 + 0.943653i \(0.392635\pi\)
−0.982696 + 0.185227i \(0.940698\pi\)
\(828\) 2.07883e9 0.127266
\(829\) −4.46919e9 −0.272450 −0.136225 0.990678i \(-0.543497\pi\)
−0.136225 + 0.990678i \(0.543497\pi\)
\(830\) 6.11487e9 1.05913e10i 0.371205 0.642946i
\(831\) 2.58963e8 + 4.48537e8i 0.0156543 + 0.0271141i
\(832\) 1.10150e9 1.90785e9i 0.0663059 0.114845i
\(833\) −1.29365e10 2.24067e10i −0.775462 1.34314i
\(834\) 9.20061e9 + 1.59359e10i 0.549206 + 0.951253i
\(835\) 5.13229e10 3.05076
\(836\) 7.59319e9 + 2.34925e9i 0.449471 + 0.139062i
\(837\) 1.46293e10 0.862354
\(838\) 1.05025e9 + 1.81908e9i 0.0616506 + 0.106782i
\(839\) −8.21558e9 1.42298e10i −0.480255 0.831826i 0.519489 0.854477i \(-0.326122\pi\)
−0.999743 + 0.0226518i \(0.992789\pi\)
\(840\) 8.84654e8 1.53227e9i 0.0514987 0.0891983i
\(841\) −1.19200e10 2.06460e10i −0.691019 1.19688i
\(842\) 7.55681e9 1.30888e10i 0.436261 0.755626i
\(843\) −8.71140e9 −0.500831
\(844\) −1.00107e10 −0.573148
\(845\) −2.15085e9 + 3.72538e9i −0.122634 + 0.212408i
\(846\) 8.41211e7 1.45702e8i 0.00477649 0.00827312i
\(847\) 3.44316e8 0.0194700
\(848\) −1.35090e9 −0.0760742
\(849\) 5.47081e9 9.47572e9i 0.306814 0.531417i
\(850\) 2.85049e10 + 4.93720e10i 1.59204 + 2.75749i
\(851\) 3.01288e9 5.21847e9i 0.167583 0.290262i
\(852\) 2.15089e9 + 3.72545e9i 0.119146 + 0.206367i
\(853\) 1.37494e10 + 2.38147e10i 0.758512 + 1.31378i 0.943609 + 0.331062i \(0.107407\pi\)
−0.185097 + 0.982720i \(0.559260\pi\)
\(854\) −3.21437e7 −0.00176601
\(855\) −1.82836e9 8.04205e9i −0.100042 0.440033i
\(856\) 2.94683e9 0.160582
\(857\) 5.93215e9 + 1.02748e10i 0.321943 + 0.557622i 0.980889 0.194569i \(-0.0623307\pi\)
−0.658946 + 0.752190i \(0.728997\pi\)
\(858\) −5.72673e9 9.91898e9i −0.309529 0.536120i
\(859\) 4.09478e9 7.09237e9i 0.220422 0.381782i −0.734514 0.678593i \(-0.762590\pi\)
0.954936 + 0.296811i \(0.0959233\pi\)
\(860\) −6.03492e9 1.04528e10i −0.323539 0.560387i
\(861\) 1.57148e9 2.72189e9i 0.0839070 0.145331i
\(862\) 1.94804e9 0.103591
\(863\) 2.14665e10 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(864\) 1.80887e9 3.13305e9i 0.0954134 0.165261i
\(865\) −1.26987e10 + 2.19948e10i −0.667118 + 1.15548i
\(866\) 2.42126e7 0.00126686
\(867\) 2.60952e10 1.35986
\(868\) −6.54041e8 + 1.13283e9i −0.0339458 + 0.0587959i
\(869\) 1.26604e9 + 2.19284e9i 0.0654452 + 0.113354i
\(870\) 1.81653e10 3.14632e10i 0.935245 1.61989i
\(871\) 1.35834e10 + 2.35272e10i 0.696541 + 1.20644i
\(872\) 2.40153e9 + 4.15958e9i 0.122654 + 0.212443i
\(873\) −3.71805e9 −0.189132
\(874\) −3.41071e9 1.50020e10i −0.172804 0.760080i
\(875\) −1.19775e10 −0.604420
\(876\) 2.46256e9 + 4.26528e9i 0.123772 + 0.214379i
\(877\) 7.83931e9 + 1.35781e10i 0.392445 + 0.679735i 0.992771 0.120020i \(-0.0382959\pi\)
−0.600326 + 0.799755i \(0.704963\pi\)
\(878\) −6.10484e9 + 1.05739e10i −0.304399 + 0.527235i
\(879\) 2.74291e9 + 4.75086e9i 0.136223 + 0.235945i
\(880\) 4.64715e9 8.04910e9i 0.229878 0.398160i
\(881\) −1.64516e10 −0.810574 −0.405287 0.914190i \(-0.632828\pi\)
−0.405287 + 0.914190i \(0.632828\pi\)
\(882\) 3.23086e9 0.158554
\(883\) −4.22262e9 + 7.31379e9i −0.206405 + 0.357503i −0.950579 0.310482i \(-0.899510\pi\)
0.744175 + 0.667985i \(0.232843\pi\)
\(884\) −8.69996e9 + 1.50688e10i −0.423579 + 0.733660i
\(885\) −3.65263e10 −1.77135
\(886\) −1.45025e10 −0.700525
\(887\) −1.24505e10 + 2.15649e10i −0.599038 + 1.03756i 0.393925 + 0.919143i \(0.371117\pi\)
−0.992963 + 0.118422i \(0.962216\pi\)
\(888\) −9.83565e8 1.70358e9i −0.0471365 0.0816429i
\(889\) 3.49560e9 6.05456e9i 0.166865 0.289019i
\(890\) 7.34950e9 + 1.27297e10i 0.349456 + 0.605276i
\(891\) −7.11061e9 1.23159e10i −0.336771 0.583305i
\(892\) 9.07338e9 0.428047
\(893\) −1.18949e9 3.68014e8i −0.0558958 0.0172936i
\(894\) 1.93210e10 0.904374
\(895\) −2.93119e10 5.07698e10i −1.36667 2.36714i
\(896\) 1.61740e8 + 2.80142e8i 0.00751173 + 0.0130107i
\(897\) −1.10847e10 + 1.91993e10i −0.512804 + 0.888202i
\(898\) 3.89747e9 + 6.75061e9i 0.179604 + 0.311083i
\(899\) −1.34300e10 + 2.32614e10i −0.616475 + 1.06777i
\(900\) −7.11901e9 −0.325515
\(901\) 1.06698e10 0.485981
\(902\) 8.25510e9 1.42983e10i 0.374541 0.648724i
\(903\) 1.09201e9 1.89141e9i 0.0493536 0.0854829i
\(904\) −4.91748e9 −0.221387
\(905\) −7.29095e9 −0.326975
\(906\) −1.27346e9 + 2.20570e9i −0.0568902 + 0.0985368i
\(907\) −1.27383e10 2.20634e10i −0.566873 0.981853i −0.996873 0.0790237i \(-0.974820\pi\)
0.430000 0.902829i \(-0.358514\pi\)
\(908\) 6.10479e9 1.05738e10i 0.270626 0.468739i
\(909\) −1.20187e8 2.08170e8i −0.00530743 0.00919273i
\(910\) −2.83238e9 4.90583e9i −0.124597 0.215808i
\(911\) −1.24205e10 −0.544284 −0.272142 0.962257i \(-0.587732\pi\)
−0.272142 + 0.962257i \(0.587732\pi\)
\(912\) −4.79803e9 1.48446e9i −0.209450 0.0648017i
\(913\) 1.16248e10 0.505518
\(914\) −4.12572e9 7.14595e9i −0.178726 0.309563i
\(915\) −2.91792e8 5.05398e8i −0.0125921 0.0218102i
\(916\) 9.06124e9 1.56945e10i 0.389541 0.674705i
\(917\) 1.70101e9 + 2.94623e9i 0.0728473 + 0.126175i
\(918\) −1.42870e10 + 2.47458e10i −0.609524 + 1.05573i
\(919\) 1.86708e10 0.793523 0.396761 0.917922i \(-0.370134\pi\)
0.396761 + 0.917922i \(0.370134\pi\)
\(920\) −1.79902e10 −0.761689
\(921\) −1.32057e10 + 2.28729e10i −0.556995 + 0.964744i
\(922\) 5.43296e9 9.41016e9i 0.228285 0.395402i
\(923\) 1.37729e10 0.576528
\(924\) 1.68178e9 0.0701323
\(925\) −1.03177e10 + 1.78708e10i −0.428635 + 0.742418i
\(926\) −1.03319e10 1.78954e10i −0.427605 0.740633i
\(927\) −1.62844e9 + 2.82053e9i −0.0671416 + 0.116293i
\(928\) 3.32114e9 + 5.75238e9i 0.136417 + 0.236282i
\(929\) 2.53239e9 + 4.38623e9i 0.103628 + 0.179488i 0.913177 0.407564i \(-0.133622\pi\)
−0.809549 + 0.587052i \(0.800288\pi\)
\(930\) −2.37489e10 −0.968172
\(931\) −5.30083e9 2.33157e10i −0.215288 0.946945i
\(932\) 1.00008e10 0.404648
\(933\) 1.30129e10 + 2.25389e10i 0.524550 + 0.908547i
\(934\) 1.32371e10 + 2.29274e10i 0.531594 + 0.920748i
\(935\) −3.67045e10 + 6.35741e10i −1.46852 + 2.54355i
\(936\) −1.08639e9 1.88169e9i −0.0433034 0.0750036i
\(937\) 4.29832e9 7.44491e9i 0.170691 0.295645i −0.767971 0.640485i \(-0.778733\pi\)
0.938662 + 0.344840i \(0.112067\pi\)
\(938\) −3.98909e9 −0.157821
\(939\) −1.46899e10 −0.579013
\(940\) −7.27984e8 + 1.26090e9i −0.0285874 + 0.0495148i
\(941\) 1.44513e10 2.50304e10i 0.565383 0.979273i −0.431631 0.902050i \(-0.642062\pi\)
0.997014 0.0772222i \(-0.0246051\pi\)
\(942\) 2.93029e10 1.14218
\(943\) −3.19573e10 −1.24102
\(944\) 3.33903e9 5.78337e9i 0.129187 0.223758i
\(945\) −4.65131e9 8.05630e9i −0.179293 0.310545i
\(946\) 5.73639e9 9.93572e9i 0.220303 0.381575i
\(947\) −5.87376e9 1.01737e10i −0.224746 0.389271i 0.731497 0.681844i \(-0.238822\pi\)
−0.956243 + 0.292573i \(0.905489\pi\)
\(948\) −7.99993e8 1.38563e9i −0.0304970 0.0528223i
\(949\) 1.57687e10 0.598912
\(950\) 1.16801e10 + 5.13749e10i 0.441991 + 1.94410i
\(951\) 2.13073e10 0.803335
\(952\) −1.27747e9 2.21264e9i −0.0479868 0.0831156i
\(953\) 1.03182e10 + 1.78716e10i 0.386170 + 0.668866i 0.991931 0.126781i \(-0.0404644\pi\)
−0.605761 + 0.795647i \(0.707131\pi\)
\(954\) −6.66187e8 + 1.15387e9i −0.0248414 + 0.0430266i
\(955\) 1.78992e10 + 3.10024e10i 0.665002 + 1.15182i
\(956\) 4.52185e8 7.83208e8i 0.0167384 0.0289918i
\(957\) 3.45334e10 1.27364
\(958\) 7.47703e9 0.274758
\(959\) 1.46778e9 2.54227e9i 0.0537399 0.0930802i
\(960\) −2.93647e9 + 5.08612e9i −0.107121 + 0.185540i
\(961\) −9.95463e9 −0.361820
\(962\) −6.29813e9 −0.228086
\(963\) 1.45321e9 2.51703e9i 0.0524368 0.0908233i
\(964\) 1.08721e10 + 1.88311e10i 0.390881 + 0.677026i
\(965\) 2.63697e9 4.56737e9i 0.0944625 0.163614i
\(966\) −1.62764e9 2.81916e9i −0.0580950 0.100623i
\(967\) 1.99451e10 + 3.45460e10i 0.709324 + 1.22858i 0.965108 + 0.261851i \(0.0843328\pi\)
−0.255785 + 0.966734i \(0.582334\pi\)
\(968\) −1.14290e9 −0.0404992
\(969\) 3.78963e10 + 1.17247e10i 1.33802 + 0.413970i
\(970\) 3.21760e10 1.13196
\(971\) −1.57109e10 2.72122e10i −0.550725 0.953884i −0.998222 0.0595987i \(-0.981018\pi\)
0.447497 0.894285i \(-0.352315\pi\)
\(972\) −3.23346e9 5.60052e9i −0.112937 0.195612i
\(973\) −4.32542e9 + 7.49186e9i −0.150534 + 0.260732i
\(974\) −7.45838e9 1.29183e10i −0.258636 0.447970i
\(975\) 3.79600e10 6.57487e10i 1.31163 2.27180i
\(976\) 1.06696e8 0.00367344
\(977\) 5.45569e10 1.87163 0.935813 0.352498i \(-0.114668\pi\)
0.935813 + 0.352498i \(0.114668\pi\)
\(978\) −5.71977e9 + 9.90694e9i −0.195521 + 0.338652i
\(979\) −6.98593e9 + 1.21000e10i −0.237950 + 0.412141i
\(980\) −2.79598e10 −0.948950
\(981\) 4.73720e9 0.160206
\(982\) −2.00176e10 + 3.46715e10i −0.674562 + 1.16838i
\(983\) −2.09090e9 3.62155e9i −0.0702096 0.121607i 0.828783 0.559569i \(-0.189033\pi\)
−0.898993 + 0.437963i \(0.855700\pi\)
\(984\) −5.21629e9 + 9.03487e9i −0.174533 + 0.302301i
\(985\) −1.46264e10 2.53337e10i −0.487654 0.844642i
\(986\) −2.62313e10 4.54340e10i −0.871468 1.50943i
\(987\) −2.63454e8 −0.00872158
\(988\) −1.17969e10 + 1.09273e10i −0.389152 + 0.360466i
\(989\) −2.22069e10 −0.729962
\(990\) −4.58342e9 7.93871e9i −0.150130 0.260032i
\(991\) 1.84764e10 + 3.20020e10i 0.603058 + 1.04453i 0.992355 + 0.123415i \(0.0393846\pi\)
−0.389297 + 0.921112i \(0.627282\pi\)
\(992\) 2.17099e9 3.76026e9i 0.0706100 0.122300i
\(993\) −2.04779e10 3.54688e10i −0.663688 1.14954i
\(994\) −1.01118e9 + 1.75142e9i −0.0326571 + 0.0565638i
\(995\) −4.93740e10 −1.58898
\(996\) −7.34553e9 −0.235567
\(997\) −7.50719e9 + 1.30028e10i −0.239908 + 0.415532i −0.960688 0.277632i \(-0.910451\pi\)
0.720780 + 0.693164i \(0.243784\pi\)
\(998\) 1.70635e10 2.95548e10i 0.543389 0.941177i
\(999\) −1.03427e10 −0.328213
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 38.8.c.a.7.2 12
19.11 even 3 inner 38.8.c.a.11.2 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.8.c.a.7.2 12 1.1 even 1 trivial
38.8.c.a.11.2 yes 12 19.11 even 3 inner