Properties

Label 16.12.e.a.13.21
Level $16$
Weight $12$
Character 16.13
Analytic conductor $12.293$
Analytic rank $0$
Dimension $42$
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] = [16,12,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 16.e (of order \(4\), 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: \(12.2934908890\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 13.21
Character \(\chi\) \(=\) 16.13
Dual form 16.12.e.a.5.21

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(45.2548 - 0.00312776i) q^{2} +(457.250 + 457.250i) q^{3} +(2048.00 - 0.283093i) q^{4} +(5575.43 - 5575.43i) q^{5} +(20694.2 + 20691.3i) q^{6} -55452.7i q^{7} +(92681.9 - 19.2170i) q^{8} +241008. i q^{9} +O(q^{10})\) \(q+(45.2548 - 0.00312776i) q^{2} +(457.250 + 457.250i) q^{3} +(2048.00 - 0.283093i) q^{4} +(5575.43 - 5575.43i) q^{5} +(20694.2 + 20691.3i) q^{6} -55452.7i q^{7} +(92681.9 - 19.2170i) q^{8} +241008. i q^{9} +(252298. - 252332. i) q^{10} +(-593916. + 593916. i) q^{11} +(936577. + 936318. i) q^{12} +(-320484. - 320484. i) q^{13} +(-173.443 - 2.50950e6i) q^{14} +5.09873e6 q^{15} +(4.19430e6 - 1159.55i) q^{16} -9.66759e6 q^{17} +(753.816 + 1.09068e7i) q^{18} +(6.35824e6 + 6.35824e6i) q^{19} +(1.14169e7 - 1.14201e7i) q^{20} +(2.53557e7 - 2.53557e7i) q^{21} +(-2.68757e7 + 2.68794e7i) q^{22} +1.96028e7i q^{23} +(4.23876e7 + 4.23700e7i) q^{24} -1.33426e7i q^{25} +(-1.45044e7 - 1.45024e7i) q^{26} +(-2.92004e7 + 2.92004e7i) q^{27} +(-15698.3 - 1.13567e8i) q^{28} +(-7.64662e7 - 7.64662e7i) q^{29} +(2.30742e8 - 15947.6i) q^{30} -1.66832e8 q^{31} +(1.89813e8 - 65593.9i) q^{32} -5.43136e8 q^{33} +(-4.37505e8 + 30237.9i) q^{34} +(-3.09173e8 - 3.09173e8i) q^{35} +(68227.6 + 4.93584e8i) q^{36} +(2.74973e7 - 2.74973e7i) q^{37} +(2.87761e8 + 2.87721e8i) q^{38} -2.93082e8i q^{39} +(5.16634e8 - 5.16848e8i) q^{40} +6.15454e8i q^{41} +(1.14739e9 - 1.14755e9i) q^{42} +(8.26623e8 - 8.26623e8i) q^{43} +(-1.21617e9 + 1.21651e9i) q^{44} +(1.34372e9 + 1.34372e9i) q^{45} +(61312.9 + 8.87121e8i) q^{46} +1.20677e9 q^{47} +(1.91838e9 + 1.91731e9i) q^{48} -1.09768e9 q^{49} +(-41732.6 - 6.03819e8i) q^{50} +(-4.42051e9 - 4.42051e9i) q^{51} +(-6.56441e8 - 6.56260e8i) q^{52} +(6.02601e8 - 6.02601e8i) q^{53} +(-1.32137e9 + 1.32155e9i) q^{54} +6.62267e9i q^{55} +(-1.06563e6 - 5.13946e9i) q^{56} +5.81461e9i q^{57} +(-3.46071e9 - 3.46023e9i) q^{58} +(3.88524e9 - 3.88524e9i) q^{59} +(1.04422e10 - 1.44341e6i) q^{60} +(-2.43319e9 - 2.43319e9i) q^{61} +(-7.54996e9 + 521811. i) q^{62} +1.33645e10 q^{63} +(8.58993e9 - 3.56213e6i) q^{64} -3.57367e9 q^{65} +(-2.45795e10 + 1.69880e6i) q^{66} +(8.86750e9 + 8.86750e9i) q^{67} +(-1.97992e10 + 2.73683e6i) q^{68} +(-8.96337e9 + 8.96337e9i) q^{69} +(-1.39925e10 - 1.39906e10i) q^{70} -2.93481e10i q^{71} +(4.63144e6 + 2.23371e10i) q^{72} -7.45154e9i q^{73} +(1.24430e9 - 1.24447e9i) q^{74} +(6.10092e9 - 6.10092e9i) q^{75} +(1.30235e10 + 1.30199e10i) q^{76} +(3.29342e10 + 3.29342e10i) q^{77} +(-916692. - 1.32634e10i) q^{78} -2.31480e10 q^{79} +(2.33786e10 - 2.33915e10i) q^{80} +1.59901e10 q^{81} +(1.92499e6 + 2.78523e10i) q^{82} +(4.40857e9 + 4.40857e9i) q^{83} +(5.19214e10 - 5.19358e10i) q^{84} +(-5.39010e10 + 5.39010e10i) q^{85} +(3.74061e10 - 3.74113e10i) q^{86} -6.99284e10i q^{87} +(-5.50338e10 + 5.50566e10i) q^{88} +4.82749e10i q^{89} +(6.08141e10 + 6.08057e10i) q^{90} +(-1.77717e10 + 1.77717e10i) q^{91} +(5.54941e6 + 4.01465e10i) q^{92} +(-7.62839e10 - 7.62839e10i) q^{93} +(5.46122e10 - 3.77449e6i) q^{94} +7.08998e10 q^{95} +(8.68217e10 + 8.67618e10i) q^{96} +9.19031e10 q^{97} +(-4.96752e10 + 3.43328e6i) q^{98} +(-1.43138e11 - 1.43138e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 42 q - 2 q^{2} - 2 q^{3} + 3080 q^{4} - 2 q^{5} + 30352 q^{6} + 74836 q^{8} - 988948 q^{10} - 540846 q^{11} + 2300260 q^{12} - 2 q^{13} - 1829956 q^{14} - 6075004 q^{15} - 3721448 q^{16} - 4 q^{17} - 32219106 q^{18} - 11291290 q^{19} + 68655164 q^{20} + 354292 q^{21} - 85011388 q^{22} - 66180944 q^{24} + 305685384 q^{26} - 66463304 q^{27} - 322075880 q^{28} + 77673206 q^{29} + 290643636 q^{30} + 343549808 q^{31} + 404698568 q^{32} - 4 q^{33} - 882461836 q^{34} - 434731684 q^{35} + 1854387628 q^{36} - 522762058 q^{37} - 1276252832 q^{38} - 483241016 q^{40} + 2372079160 q^{42} + 3824193658 q^{43} - 2657283740 q^{44} + 97301954 q^{45} - 1032658964 q^{46} - 4586900144 q^{47} - 1058870552 q^{48} - 8474257474 q^{49} + 6515930886 q^{50} + 7074245796 q^{51} - 13915491564 q^{52} - 2100608058 q^{53} + 4385621536 q^{54} + 12910845976 q^{56} - 21491153128 q^{58} + 955824746 q^{59} + 25615752768 q^{60} + 2150827022 q^{61} - 15814519760 q^{62} + 27758037828 q^{63} + 9674332160 q^{64} - 1884965292 q^{65} + 10932459412 q^{66} - 3186519018 q^{67} + 13817664656 q^{68} - 16193060732 q^{69} - 27206453120 q^{70} - 20773133628 q^{72} + 14141420908 q^{74} + 28890034486 q^{75} - 11786004940 q^{76} - 22711870540 q^{77} + 37031200508 q^{78} + 48011833792 q^{79} - 8952586328 q^{80} - 90656394430 q^{81} - 81555388352 q^{82} + 55713221118 q^{83} + 61178517160 q^{84} - 84575506252 q^{85} + 10047297860 q^{86} - 162855622152 q^{88} + 160133627736 q^{90} - 147369662716 q^{91} - 169766721928 q^{92} - 69689773328 q^{93} + 160320530128 q^{94} + 375702304500 q^{95} + 230764310192 q^{96} - 4 q^{97} - 108887063494 q^{98} - 286271331106 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 45.2548 0.00312776i 1.00000 6.91145e-5i
\(3\) 457.250 + 457.250i 1.08639 + 1.08639i 0.995897 + 0.0904954i \(0.0288451\pi\)
0.0904954 + 0.995897i \(0.471155\pi\)
\(4\) 2048.00 0.283093i 1.00000 0.000138229i
\(5\) 5575.43 5575.43i 0.797890 0.797890i −0.184872 0.982763i \(-0.559187\pi\)
0.982763 + 0.184872i \(0.0591872\pi\)
\(6\) 20694.2 + 20691.3i 1.08647 + 1.08632i
\(7\) 55452.7i 1.24705i −0.781804 0.623525i \(-0.785700\pi\)
0.781804 0.623525i \(-0.214300\pi\)
\(8\) 92681.9 19.2170i 1.00000 0.000207343i
\(9\) 241008.i 1.36050i
\(10\) 252298. 252332.i 0.797835 0.797945i
\(11\) −593916. + 593916.i −1.11190 + 1.11190i −0.119004 + 0.992894i \(0.537970\pi\)
−0.992894 + 0.119004i \(0.962030\pi\)
\(12\) 936577. + 936318.i 1.08654 + 1.08624i
\(13\) −320484. 320484.i −0.239396 0.239396i 0.577204 0.816600i \(-0.304144\pi\)
−0.816600 + 0.577204i \(0.804144\pi\)
\(14\) −173.443 2.50950e6i −8.61891e−5 1.24705i
\(15\) 5.09873e6 1.73364
\(16\) 4.19430e6 1159.55i 1.00000 0.000276458i
\(17\) −9.66759e6 −1.65139 −0.825694 0.564118i \(-0.809216\pi\)
−0.825694 + 0.564118i \(0.809216\pi\)
\(18\) 753.816 + 1.09068e7i 9.40300e−5 + 1.36050i
\(19\) 6.35824e6 + 6.35824e6i 0.589104 + 0.589104i 0.937389 0.348285i \(-0.113236\pi\)
−0.348285 + 0.937389i \(0.613236\pi\)
\(20\) 1.14169e7 1.14201e7i 0.797780 0.798000i
\(21\) 2.53557e7 2.53557e7i 1.35478 1.35478i
\(22\) −2.68757e7 + 2.68794e7i −1.11182 + 1.11197i
\(23\) 1.96028e7i 0.635060i 0.948248 + 0.317530i \(0.102853\pi\)
−0.948248 + 0.317530i \(0.897147\pi\)
\(24\) 4.23876e7 + 4.23700e7i 1.08662 + 1.08617i
\(25\) 1.33426e7i 0.273257i
\(26\) −1.45044e7 1.45024e7i −0.239413 0.239380i
\(27\) −2.92004e7 + 2.92004e7i −0.391641 + 0.391641i
\(28\) −15698.3 1.13567e8i −0.000172378 1.24705i
\(29\) −7.64662e7 7.64662e7i −0.692278 0.692278i 0.270454 0.962733i \(-0.412826\pi\)
−0.962733 + 0.270454i \(0.912826\pi\)
\(30\) 2.30742e8 15947.6i 1.73364 0.000119820i
\(31\) −1.66832e8 −1.04662 −0.523311 0.852142i \(-0.675304\pi\)
−0.523311 + 0.852142i \(0.675304\pi\)
\(32\) 1.89813e8 65593.9i 1.00000 0.000345572i
\(33\) −5.43136e8 −2.41591
\(34\) −4.37505e8 + 30237.9i −1.65139 + 0.000114135i
\(35\) −3.09173e8 3.09173e8i −0.995008 0.995008i
\(36\) 68227.6 + 4.93584e8i 0.000188060 + 1.36050i
\(37\) 2.74973e7 2.74973e7i 0.0651899 0.0651899i −0.673760 0.738950i \(-0.735322\pi\)
0.738950 + 0.673760i \(0.235322\pi\)
\(38\) 2.87761e8 + 2.87721e8i 0.589145 + 0.589064i
\(39\) 2.93082e8i 0.520157i
\(40\) 5.16634e8 5.16848e8i 0.797725 0.798056i
\(41\) 6.15454e8i 0.829630i 0.909906 + 0.414815i \(0.136154\pi\)
−0.909906 + 0.414815i \(0.863846\pi\)
\(42\) 1.14739e9 1.14755e9i 1.35469 1.35488i
\(43\) 8.26623e8 8.26623e8i 0.857493 0.857493i −0.133549 0.991042i \(-0.542637\pi\)
0.991042 + 0.133549i \(0.0426373\pi\)
\(44\) −1.21617e9 + 1.21651e9i −1.11174 + 1.11205i
\(45\) 1.34372e9 + 1.34372e9i 1.08553 + 1.08553i
\(46\) 61312.9 + 8.87121e8i 4.38918e−5 + 0.635060i
\(47\) 1.20677e9 0.767514 0.383757 0.923434i \(-0.374630\pi\)
0.383757 + 0.923434i \(0.374630\pi\)
\(48\) 1.91838e9 + 1.91731e9i 1.08669 + 1.08609i
\(49\) −1.09768e9 −0.555132
\(50\) −41732.6 6.03819e8i −1.88860e−5 0.273257i
\(51\) −4.42051e9 4.42051e9i −1.79406 1.79406i
\(52\) −6.56441e8 6.56260e8i −0.239429 0.239363i
\(53\) 6.02601e8 6.02601e8i 0.197930 0.197930i −0.601182 0.799112i \(-0.705303\pi\)
0.799112 + 0.601182i \(0.205303\pi\)
\(54\) −1.32137e9 + 1.32155e9i −0.391614 + 0.391668i
\(55\) 6.62267e9i 1.77435i
\(56\) −1.06563e6 5.13946e9i −0.000258567 1.24705i
\(57\) 5.81461e9i 1.28000i
\(58\) −3.46071e9 3.46023e9i −0.692326 0.692231i
\(59\) 3.88524e9 3.88524e9i 0.707508 0.707508i −0.258502 0.966011i \(-0.583229\pi\)
0.966011 + 0.258502i \(0.0832290\pi\)
\(60\) 1.04422e10 1.44341e6i 1.73364 0.000239640i
\(61\) −2.43319e9 2.43319e9i −0.368861 0.368861i 0.498201 0.867062i \(-0.333994\pi\)
−0.867062 + 0.498201i \(0.833994\pi\)
\(62\) −7.54996e9 + 521811.i −1.04662 + 7.23368e-5i
\(63\) 1.33645e10 1.69661
\(64\) 8.58993e9 3.56213e6i 1.00000 0.000414687i
\(65\) −3.57367e9 −0.382024
\(66\) −2.45795e10 + 1.69880e6i −2.41591 + 0.000166975i
\(67\) 8.86750e9 + 8.86750e9i 0.802398 + 0.802398i 0.983470 0.181072i \(-0.0579567\pi\)
−0.181072 + 0.983470i \(0.557957\pi\)
\(68\) −1.97992e10 + 2.73683e6i −1.65139 + 0.000228270i
\(69\) −8.96337e9 + 8.96337e9i −0.689924 + 0.689924i
\(70\) −1.39925e10 1.39906e10i −0.995077 0.994940i
\(71\) 2.93481e10i 1.93045i −0.261418 0.965226i \(-0.584190\pi\)
0.261418 0.965226i \(-0.415810\pi\)
\(72\) 4.63144e6 + 2.23371e10i 0.000282090 + 1.36050i
\(73\) 7.45154e9i 0.420698i −0.977626 0.210349i \(-0.932540\pi\)
0.977626 0.210349i \(-0.0674600\pi\)
\(74\) 1.24430e9 1.24447e9i 0.0651854 0.0651944i
\(75\) 6.10092e9 6.10092e9i 0.296865 0.296865i
\(76\) 1.30235e10 + 1.30199e10i 0.589186 + 0.589023i
\(77\) 3.29342e10 + 3.29342e10i 1.38659 + 1.38659i
\(78\) −916692. 1.32634e10i −3.59503e−5 0.520157i
\(79\) −2.31480e10 −0.846378 −0.423189 0.906042i \(-0.639089\pi\)
−0.423189 + 0.906042i \(0.639089\pi\)
\(80\) 2.33786e10 2.33915e10i 0.797670 0.798111i
\(81\) 1.59901e10 0.509546
\(82\) 1.92499e6 + 2.78523e10i 5.73394e−5 + 0.829630i
\(83\) 4.40857e9 + 4.40857e9i 0.122848 + 0.122848i 0.765858 0.643010i \(-0.222315\pi\)
−0.643010 + 0.765858i \(0.722315\pi\)
\(84\) 5.19214e10 5.19358e10i 1.35460 1.35497i
\(85\) −5.39010e10 + 5.39010e10i −1.31763 + 1.31763i
\(86\) 3.74061e10 3.74113e10i 0.857434 0.857553i
\(87\) 6.99284e10i 1.50417i
\(88\) −5.50338e10 + 5.50566e10i −1.11167 + 1.11213i
\(89\) 4.82749e10i 0.916382i 0.888854 + 0.458191i \(0.151502\pi\)
−0.888854 + 0.458191i \(0.848498\pi\)
\(90\) 6.08141e10 + 6.08057e10i 1.08560 + 1.08545i
\(91\) −1.77717e10 + 1.77717e10i −0.298539 + 0.298539i
\(92\) 5.54941e6 + 4.01465e10i 8.77836e−5 + 0.635060i
\(93\) −7.62839e10 7.62839e10i −1.13704 1.13704i
\(94\) 5.46122e10 3.77449e6i 0.767514 5.30463e-5i
\(95\) 7.08998e10 0.940081
\(96\) 8.68217e10 + 8.67618e10i 1.08677 + 1.08602i
\(97\) 9.19031e10 1.08664 0.543320 0.839526i \(-0.317167\pi\)
0.543320 + 0.839526i \(0.317167\pi\)
\(98\) −4.96752e10 + 3.43328e6i −0.555132 + 3.83677e-5i
\(99\) −1.43138e11 1.43138e11i −1.51273 1.51273i
\(100\) −3.77721e6 2.73257e10i −3.77721e−5 0.273257i
\(101\) −8.97475e10 + 8.97475e10i −0.849679 + 0.849679i −0.990093 0.140414i \(-0.955157\pi\)
0.140414 + 0.990093i \(0.455157\pi\)
\(102\) −2.00063e11 2.00035e11i −1.79418 1.79393i
\(103\) 1.00244e11i 0.852031i 0.904716 + 0.426015i \(0.140083\pi\)
−0.904716 + 0.426015i \(0.859917\pi\)
\(104\) −2.97092e10 2.96969e10i −0.239446 0.239347i
\(105\) 2.82738e11i 2.16194i
\(106\) 2.72687e10 2.72725e10i 0.197917 0.197944i
\(107\) −2.34076e10 + 2.34076e10i −0.161341 + 0.161341i −0.783161 0.621819i \(-0.786394\pi\)
0.621819 + 0.783161i \(0.286394\pi\)
\(108\) −5.97941e10 + 5.98106e10i −0.391586 + 0.391695i
\(109\) 4.45007e10 + 4.45007e10i 0.277026 + 0.277026i 0.831921 0.554894i \(-0.187241\pi\)
−0.554894 + 0.831921i \(0.687241\pi\)
\(110\) 2.07141e7 + 2.99708e11i 0.000122633 + 1.77435i
\(111\) 2.51463e10 0.141644
\(112\) −6.43001e7 2.32586e11i −0.000344757 1.24705i
\(113\) −2.35044e11 −1.20010 −0.600049 0.799963i \(-0.704852\pi\)
−0.600049 + 0.799963i \(0.704852\pi\)
\(114\) 1.81867e7 + 2.63139e11i 8.84663e−5 + 1.28000i
\(115\) 1.09294e11 + 1.09294e11i 0.506708 + 0.506708i
\(116\) −1.56625e11 1.56581e11i −0.692374 0.692183i
\(117\) 7.72391e10 7.72391e10i 0.325698 0.325698i
\(118\) 1.75814e11 1.75838e11i 0.707459 0.707557i
\(119\) 5.36094e11i 2.05936i
\(120\) 4.72560e11 9.79821e7i 1.73364 0.000359459i
\(121\) 4.20160e11i 1.47263i
\(122\) −1.10121e11 1.10106e11i −0.368887 0.368836i
\(123\) −2.81416e11 + 2.81416e11i −0.901304 + 0.901304i
\(124\) −3.41672e11 + 4.72290e7i −1.04662 + 0.000144674i
\(125\) 1.97847e11 + 1.97847e11i 0.579861 + 0.579861i
\(126\) 6.04810e11 4.18011e7i 1.69661 0.000117260i
\(127\) 6.24519e11 1.67736 0.838678 0.544628i \(-0.183329\pi\)
0.838678 + 0.544628i \(0.183329\pi\)
\(128\) 3.88736e11 1.88071e8i 1.00000 0.000483801i
\(129\) 7.55946e11 1.86315
\(130\) −1.61726e11 + 1.11776e7i −0.382024 + 2.64034e-5i
\(131\) −4.84655e11 4.84655e11i −1.09759 1.09759i −0.994692 0.102900i \(-0.967188\pi\)
−0.102900 0.994692i \(-0.532812\pi\)
\(132\) −1.11234e12 + 1.53758e8i −2.41591 + 0.000333949i
\(133\) 3.52582e11 3.52582e11i 0.734642 0.734642i
\(134\) 4.01325e11 + 4.01270e11i 0.802453 + 0.802343i
\(135\) 3.25609e11i 0.624972i
\(136\) −8.96011e11 + 1.85782e8i −1.65139 + 0.000342404i
\(137\) 5.03802e11i 0.891860i 0.895068 + 0.445930i \(0.147127\pi\)
−0.895068 + 0.445930i \(0.852873\pi\)
\(138\) −4.05608e11 + 4.05664e11i −0.689876 + 0.689972i
\(139\) 2.16836e11 2.16836e11i 0.354446 0.354446i −0.507315 0.861761i \(-0.669362\pi\)
0.861761 + 0.507315i \(0.169362\pi\)
\(140\) −6.33273e11 6.33098e11i −0.995146 0.994871i
\(141\) 5.51796e11 + 5.51796e11i 0.833822 + 0.833822i
\(142\) −9.17939e7 1.32814e12i −0.000133422 1.93045i
\(143\) 3.80681e11 0.532369
\(144\) 2.79460e8 + 1.01086e12i 0.000376120 + 1.36050i
\(145\) −8.52664e11 −1.10472
\(146\) −2.33067e7 3.37218e11i −2.90763e−5 0.420698i
\(147\) −5.01913e11 5.01913e11i −0.603091 0.603091i
\(148\) 5.63066e10 5.63222e10i 0.0651809 0.0651989i
\(149\) −4.15167e11 + 4.15167e11i −0.463126 + 0.463126i −0.899679 0.436553i \(-0.856199\pi\)
0.436553 + 0.899679i \(0.356199\pi\)
\(150\) 2.76077e11 2.76115e11i 0.296844 0.296885i
\(151\) 3.26377e11i 0.338334i 0.985587 + 0.169167i \(0.0541078\pi\)
−0.985587 + 0.169167i \(0.945892\pi\)
\(152\) 5.89416e11 + 5.89172e11i 0.589226 + 0.588982i
\(153\) 2.32997e12i 2.24671i
\(154\) 1.49054e12 + 1.49033e12i 1.38669 + 1.38650i
\(155\) −9.30160e11 + 9.30160e11i −0.835090 + 0.835090i
\(156\) −8.29695e7 6.00233e11i −7.19007e−5 0.520157i
\(157\) −7.29021e11 7.29021e11i −0.609947 0.609947i 0.332985 0.942932i \(-0.391944\pi\)
−0.942932 + 0.332985i \(0.891944\pi\)
\(158\) −1.04756e12 + 7.24014e7i −0.846378 + 5.84969e-5i
\(159\) 5.51078e11 0.430060
\(160\) 1.05792e12 1.05865e12i 0.797614 0.798166i
\(161\) 1.08703e12 0.791951
\(162\) 7.23629e11 5.00132e7i 0.509546 3.52170e-5i
\(163\) −8.04342e11 8.04342e11i −0.547531 0.547531i 0.378195 0.925726i \(-0.376545\pi\)
−0.925726 + 0.378195i \(0.876545\pi\)
\(164\) 1.74231e8 + 1.26045e12i 0.000114679 + 0.829630i
\(165\) −3.02821e12 + 3.02821e12i −1.92763 + 1.92763i
\(166\) 1.99523e11 + 1.99495e11i 0.122857 + 0.122840i
\(167\) 5.08675e11i 0.303040i −0.988454 0.151520i \(-0.951583\pi\)
0.988454 0.151520i \(-0.0484168\pi\)
\(168\) 2.34953e12 2.35051e12i 1.35450 1.35507i
\(169\) 1.58674e12i 0.885379i
\(170\) −2.43911e12 + 2.43945e12i −1.31754 + 1.31772i
\(171\) −1.53239e12 + 1.53239e12i −0.801474 + 0.801474i
\(172\) 1.69269e12 1.69316e12i 0.857375 0.857612i
\(173\) −8.77981e11 8.77981e11i −0.430756 0.430756i 0.458129 0.888886i \(-0.348520\pi\)
−0.888886 + 0.458129i \(0.848520\pi\)
\(174\) −2.18719e8 3.16460e12i −0.000103960 1.50417i
\(175\) −7.39886e11 −0.340766
\(176\) −2.49037e12 + 2.49175e12i −1.11159 + 1.11221i
\(177\) 3.55305e12 1.53726
\(178\) 1.50993e8 + 2.18467e12i 6.33352e−5 + 0.916382i
\(179\) 1.50802e12 + 1.50802e12i 0.613360 + 0.613360i 0.943820 0.330460i \(-0.107204\pi\)
−0.330460 + 0.943820i \(0.607204\pi\)
\(180\) 2.75232e12 + 2.75156e12i 1.08568 + 1.08538i
\(181\) −4.49068e11 + 4.49068e11i −0.171822 + 0.171822i −0.787780 0.615957i \(-0.788769\pi\)
0.615957 + 0.787780i \(0.288769\pi\)
\(182\) −8.04200e11 + 8.04311e11i −0.298518 + 0.298560i
\(183\) 2.22516e12i 0.801456i
\(184\) 3.76706e8 + 1.81682e12i 0.000131675 + 0.635060i
\(185\) 3.06618e11i 0.104029i
\(186\) −3.45246e12 3.45198e12i −1.13712 1.13696i
\(187\) 5.74173e12 5.74173e12i 1.83618 1.83618i
\(188\) 2.47147e12 3.41628e8i 0.767514 0.000106093i
\(189\) 1.61924e12 + 1.61924e12i 0.488395 + 0.488395i
\(190\) 3.20856e12 2.21758e8i 0.940081 6.49732e-5i
\(191\) 4.96899e12 1.41444 0.707220 0.706993i \(-0.249949\pi\)
0.707220 + 0.706993i \(0.249949\pi\)
\(192\) 3.92937e12 + 3.92612e12i 1.08684 + 1.08594i
\(193\) −2.71012e12 −0.728489 −0.364244 0.931303i \(-0.618673\pi\)
−0.364244 + 0.931303i \(0.618673\pi\)
\(194\) 4.15906e12 2.87451e8i 1.08664 7.51025e-5i
\(195\) −1.63406e12 1.63406e12i −0.415028 0.415028i
\(196\) −2.24804e12 + 3.10745e8i −0.555132 + 7.67353e-5i
\(197\) −5.19796e12 + 5.19796e12i −1.24816 + 1.24816i −0.291623 + 0.956533i \(0.594195\pi\)
−0.956533 + 0.291623i \(0.905805\pi\)
\(198\) −6.47815e12 6.47725e12i −1.51284 1.51263i
\(199\) 1.24035e12i 0.281742i −0.990028 0.140871i \(-0.955010\pi\)
0.990028 0.140871i \(-0.0449903\pi\)
\(200\) −2.56405e8 1.23662e12i −5.66581e−5 0.273257i
\(201\) 8.10933e12i 1.74344i
\(202\) −4.06123e12 + 4.06179e12i −0.849620 + 0.849738i
\(203\) −4.24026e12 + 4.24026e12i −0.863305 + 0.863305i
\(204\) −9.05445e12 9.05194e12i −1.79430 1.79381i
\(205\) 3.43142e12 + 3.43142e12i 0.661954 + 0.661954i
\(206\) 3.13541e8 + 4.53654e12i 5.88876e−5 + 0.852031i
\(207\) −4.72443e12 −0.863997
\(208\) −1.34458e12 1.34383e12i −0.239463 0.239330i
\(209\) −7.55252e12 −1.31005
\(210\) −8.84338e8 1.27953e13i −0.000149421 2.16194i
\(211\) −2.59805e12 2.59805e12i −0.427656 0.427656i 0.460173 0.887829i \(-0.347787\pi\)
−0.887829 + 0.460173i \(0.847787\pi\)
\(212\) 1.23396e12 1.23430e12i 0.197903 0.197958i
\(213\) 1.34194e13 1.34194e13i 2.09723 2.09723i
\(214\) −1.05923e12 + 1.05938e12i −0.161330 + 0.161353i
\(215\) 9.21755e12i 1.36837i
\(216\) −2.70578e12 + 2.70691e12i −0.391559 + 0.391722i
\(217\) 9.25129e12i 1.30519i
\(218\) 2.01401e12 + 2.01373e12i 0.277046 + 0.277007i
\(219\) 3.40722e12 3.40722e12i 0.457043 0.457043i
\(220\) 1.87483e9 + 1.35632e13i 0.000245266 + 1.77435i
\(221\) 3.09831e12 + 3.09831e12i 0.395336 + 0.395336i
\(222\) 1.13799e12 7.86515e7i 0.141644 9.78962e-6i
\(223\) 3.31901e12 0.403025 0.201512 0.979486i \(-0.435414\pi\)
0.201512 + 0.979486i \(0.435414\pi\)
\(224\) −3.63736e9 1.05256e13i −0.000430946 1.24705i
\(225\) 3.21568e12 0.371766
\(226\) −1.06369e13 + 7.35161e8i −1.20010 + 8.29442e-5i
\(227\) 2.66770e12 + 2.66770e12i 0.293762 + 0.293762i 0.838564 0.544803i \(-0.183395\pi\)
−0.544803 + 0.838564i \(0.683395\pi\)
\(228\) 1.64607e9 + 1.19083e13i 0.000176933 + 1.28000i
\(229\) 5.06633e12 5.06633e12i 0.531616 0.531616i −0.389437 0.921053i \(-0.627330\pi\)
0.921053 + 0.389437i \(0.127330\pi\)
\(230\) 4.94642e12 + 4.94574e12i 0.506743 + 0.506673i
\(231\) 3.01184e13i 3.01277i
\(232\) −7.08851e12 7.08557e12i −0.692422 0.692135i
\(233\) 1.26560e13i 1.20737i −0.797224 0.603683i \(-0.793699\pi\)
0.797224 0.603683i \(-0.206301\pi\)
\(234\) 3.49520e12 3.49568e12i 0.325675 0.325720i
\(235\) 6.72826e12 6.72826e12i 0.612392 0.612392i
\(236\) 7.95587e12 7.95807e12i 0.707410 0.707606i
\(237\) −1.05844e13 1.05844e13i −0.919498 0.919498i
\(238\) 1.67678e9 + 2.42609e13i 0.000142332 + 2.05936i
\(239\) 3.75926e12 0.311828 0.155914 0.987771i \(-0.450168\pi\)
0.155914 + 0.987771i \(0.450168\pi\)
\(240\) 2.13856e13 5.91222e9i 1.73364 0.000479279i
\(241\) −5.53115e12 −0.438250 −0.219125 0.975697i \(-0.570320\pi\)
−0.219125 + 0.975697i \(0.570320\pi\)
\(242\) −1.31416e9 1.90143e13i −0.000101780 1.47263i
\(243\) 1.24842e13 + 1.24842e13i 0.945207 + 0.945207i
\(244\) −4.98387e12 4.98249e12i −0.368912 0.368810i
\(245\) −6.12002e12 + 6.12002e12i −0.442934 + 0.442934i
\(246\) −1.27346e13 + 1.27363e13i −0.901241 + 0.901366i
\(247\) 4.07543e12i 0.282059i
\(248\) −1.54623e13 + 3.20601e9i −1.04662 + 0.000217010i
\(249\) 4.03164e12i 0.266922i
\(250\) 8.95414e12 + 8.95290e12i 0.579901 + 0.579821i
\(251\) −3.06972e12 + 3.06972e12i −0.194488 + 0.194488i −0.797632 0.603144i \(-0.793914\pi\)
0.603144 + 0.797632i \(0.293914\pi\)
\(252\) 2.73706e13 3.78341e9i 1.69661 0.000234520i
\(253\) −1.16424e13 1.16424e13i −0.706122 0.706122i
\(254\) 2.82625e13 1.95335e9i 1.67736 0.000115930i
\(255\) −4.92924e13 −2.86292
\(256\) 1.75922e13 9.72699e9i 1.00000 0.000552916i
\(257\) 1.71375e12 0.0953489 0.0476745 0.998863i \(-0.484819\pi\)
0.0476745 + 0.998863i \(0.484819\pi\)
\(258\) 3.42102e13 2.36442e9i 1.86315 0.000128770i
\(259\) −1.52480e12 1.52480e12i −0.0812950 0.0812950i
\(260\) −7.31887e12 + 1.01168e9i −0.382024 + 5.28068e-5i
\(261\) 1.84290e13 1.84290e13i 0.941842 0.941842i
\(262\) −2.19345e13 2.19315e13i −1.09767 1.09752i
\(263\) 1.01496e13i 0.497384i −0.968583 0.248692i \(-0.919999\pi\)
0.968583 0.248692i \(-0.0800007\pi\)
\(264\) −5.03388e13 + 1.04374e10i −2.41591 + 0.000500924i
\(265\) 6.71951e12i 0.315853i
\(266\) 1.59549e13 1.59571e13i 0.734591 0.734693i
\(267\) −2.20737e13 + 2.20737e13i −0.995550 + 0.995550i
\(268\) 1.81632e13 + 1.81581e13i 0.802509 + 0.802287i
\(269\) −1.30252e13 1.30252e13i −0.563828 0.563828i 0.366564 0.930393i \(-0.380534\pi\)
−0.930393 + 0.366564i \(0.880534\pi\)
\(270\) 1.01843e9 + 1.47354e13i 4.31946e−5 + 0.624972i
\(271\) −1.84540e13 −0.766934 −0.383467 0.923554i \(-0.625270\pi\)
−0.383467 + 0.923554i \(0.625270\pi\)
\(272\) −4.05488e13 + 1.12100e10i −1.65139 + 0.000456539i
\(273\) −1.62522e13 −0.648661
\(274\) 1.57577e9 + 2.27995e13i 6.16404e−5 + 0.891860i
\(275\) 7.92441e12 + 7.92441e12i 0.303834 + 0.303834i
\(276\) −1.83544e13 + 1.83595e13i −0.689829 + 0.690019i
\(277\) 1.56562e13 1.56562e13i 0.576828 0.576828i −0.357200 0.934028i \(-0.616268\pi\)
0.934028 + 0.357200i \(0.116268\pi\)
\(278\) 9.81220e12 9.81356e12i 0.354421 0.354470i
\(279\) 4.02078e13i 1.42393i
\(280\) −2.86606e13 2.86488e13i −0.995215 0.994802i
\(281\) 5.12053e13i 1.74353i 0.489922 + 0.871766i \(0.337025\pi\)
−0.489922 + 0.871766i \(0.662975\pi\)
\(282\) 2.49732e13 + 2.49697e13i 0.833879 + 0.833764i
\(283\) 3.68160e10 3.68160e10i 0.00120562 0.00120562i −0.706504 0.707709i \(-0.749729\pi\)
0.707709 + 0.706504i \(0.249729\pi\)
\(284\) −8.30823e9 6.01049e13i −0.000266844 1.93045i
\(285\) 3.24189e13 + 3.24189e13i 1.02130 + 1.02130i
\(286\) 1.72276e13 1.19068e9i 0.532369 3.67944e-5i
\(287\) 3.41286e13 1.03459
\(288\) 1.58087e10 + 4.57463e13i 0.000470150 + 1.36050i
\(289\) 5.91905e13 1.72708
\(290\) −3.85872e13 + 2.66693e9i −1.10472 + 7.63524e-5i
\(291\) 4.20227e13 + 4.20227e13i 1.18052 + 1.18052i
\(292\) −2.10948e9 1.52608e13i −5.81526e−5 0.420698i
\(293\) 7.30934e12 7.30934e12i 0.197745 0.197745i −0.601287 0.799033i \(-0.705345\pi\)
0.799033 + 0.601287i \(0.205345\pi\)
\(294\) −2.27156e13 2.27124e13i −0.603133 0.603050i
\(295\) 4.33237e13i 1.12903i
\(296\) 2.54797e12 2.54903e12i 0.0651764 0.0652034i
\(297\) 3.46851e13i 0.870929i
\(298\) −1.87870e13 + 1.87896e13i −0.463094 + 0.463158i
\(299\) 6.28237e12 6.28237e12i 0.152031 0.152031i
\(300\) 1.24930e13 1.24964e13i 0.296824 0.296906i
\(301\) −4.58385e13 4.58385e13i −1.06934 1.06934i
\(302\) 1.02083e9 + 1.47701e13i 2.33838e−5 + 0.338334i
\(303\) −8.20741e13 −1.84617
\(304\) 2.66758e13 + 2.66610e13i 0.589267 + 0.588941i
\(305\) −2.71322e13 −0.588621
\(306\) −7.28758e9 1.05442e14i −0.000155280 2.24671i
\(307\) 5.00023e13 + 5.00023e13i 1.04648 + 1.04648i 0.998866 + 0.0476101i \(0.0151605\pi\)
0.0476101 + 0.998866i \(0.484840\pi\)
\(308\) 6.74586e13 + 6.74400e13i 1.38678 + 1.38640i
\(309\) −4.58367e13 + 4.58367e13i −0.925639 + 0.925639i
\(310\) −4.20913e13 + 4.20971e13i −0.835032 + 0.835148i
\(311\) 8.72624e13i 1.70077i 0.526163 + 0.850384i \(0.323630\pi\)
−0.526163 + 0.850384i \(0.676370\pi\)
\(312\) −5.63216e9 2.71634e13i −0.000107851 0.520157i
\(313\) 5.00784e13i 0.942229i 0.882072 + 0.471114i \(0.156148\pi\)
−0.882072 + 0.471114i \(0.843852\pi\)
\(314\) −3.29940e13 3.29895e13i −0.609989 0.609905i
\(315\) 7.45130e13 7.45130e13i 1.35371 1.35371i
\(316\) −4.74071e13 + 6.55303e9i −0.846378 + 0.000116994i
\(317\) 5.46587e13 + 5.46587e13i 0.959033 + 0.959033i 0.999193 0.0401607i \(-0.0127870\pi\)
−0.0401607 + 0.999193i \(0.512787\pi\)
\(318\) 2.49390e13 1.72364e9i 0.430060 2.97234e-5i
\(319\) 9.08290e13 1.53949
\(320\) 4.78727e13 4.79124e13i 0.797559 0.798221i
\(321\) −2.14062e13 −0.350560
\(322\) 4.91933e13 3.39997e9i 0.791951 5.47353e-5i
\(323\) −6.14689e13 6.14689e13i −0.972840 0.972840i
\(324\) 3.27477e13 4.52668e9i 0.509546 7.04340e-5i
\(325\) −4.27610e12 + 4.27610e12i −0.0654168 + 0.0654168i
\(326\) −3.64029e13 3.63979e13i −0.547569 0.547494i
\(327\) 4.06959e13i 0.601919i
\(328\) 1.18272e10 + 5.70415e13i 0.000172018 + 0.829630i
\(329\) 6.69187e13i 0.957128i
\(330\) −1.37032e14 + 1.37051e14i −1.92750 + 1.92777i
\(331\) −1.49745e13 + 1.49745e13i −0.207156 + 0.207156i −0.803058 0.595901i \(-0.796795\pi\)
0.595901 + 0.803058i \(0.296795\pi\)
\(332\) 9.03000e12 + 9.02751e12i 0.122865 + 0.122831i
\(333\) 6.62706e12 + 6.62706e12i 0.0886906 + 0.0886906i
\(334\) −1.59102e9 2.30200e13i −2.09444e−5 0.303040i
\(335\) 9.88802e13 1.28045
\(336\) 1.06320e14 1.06379e14i 1.35441 1.35516i
\(337\) −6.74796e12 −0.0845684 −0.0422842 0.999106i \(-0.513463\pi\)
−0.0422842 + 0.999106i \(0.513463\pi\)
\(338\) −4.96295e9 7.18077e13i −6.11925e−5 0.885379i
\(339\) −1.07474e14 1.07474e14i −1.30378 1.30378i
\(340\) −1.10374e14 + 1.10404e14i −1.31744 + 1.31781i
\(341\) 9.90842e13 9.90842e13i 1.16374 1.16374i
\(342\) −6.93431e13 + 6.93527e13i −0.801419 + 0.801530i
\(343\) 4.87789e13i 0.554772i
\(344\) 7.65971e13 7.66288e13i 0.857315 0.857671i
\(345\) 9.99492e13i 1.10097i
\(346\) −3.97356e13 3.97301e13i −0.430786 0.430727i
\(347\) −9.73980e13 + 9.73980e13i −1.03929 + 1.03929i −0.0400971 + 0.999196i \(0.512767\pi\)
−0.999196 + 0.0400971i \(0.987233\pi\)
\(348\) −1.97962e10 1.43213e14i −0.000207920 1.50417i
\(349\) −8.34720e12 8.34720e12i −0.0862980 0.0862980i 0.662640 0.748938i \(-0.269436\pi\)
−0.748938 + 0.662640i \(0.769436\pi\)
\(350\) −3.34834e13 + 2.31419e9i −0.340766 + 2.35518e-5i
\(351\) 1.87165e13 0.187515
\(352\) −1.12694e14 + 1.12772e14i −1.11151 + 1.11228i
\(353\) −9.06184e13 −0.879945 −0.439973 0.898011i \(-0.645012\pi\)
−0.439973 + 0.898011i \(0.645012\pi\)
\(354\) 1.60793e14 1.11131e10i 1.53726 0.000106247i
\(355\) −1.63628e14 1.63628e14i −1.54029 1.54029i
\(356\) 1.36663e10 + 9.88670e13i 0.000126670 + 0.916382i
\(357\) −2.45129e14 + 2.45129e14i −2.23728 + 2.23728i
\(358\) 6.82499e13 + 6.82405e13i 0.613403 + 0.613318i
\(359\) 7.14917e13i 0.632756i −0.948633 0.316378i \(-0.897533\pi\)
0.948633 0.316378i \(-0.102467\pi\)
\(360\) 1.24565e14 + 1.24513e14i 1.08575 + 1.08530i
\(361\) 3.56358e13i 0.305912i
\(362\) −2.03211e13 + 2.03239e13i −0.171811 + 0.171834i
\(363\) 1.92118e14 1.92118e14i 1.59986 1.59986i
\(364\) −3.63914e13 + 3.64015e13i −0.298498 + 0.298580i
\(365\) −4.15455e13 4.15455e13i −0.335671 0.335671i
\(366\) −6.95976e9 1.00699e14i −5.53922e−5 0.801456i
\(367\) 4.19051e12 0.0328552 0.0164276 0.999865i \(-0.494771\pi\)
0.0164276 + 0.999865i \(0.494771\pi\)
\(368\) 2.27304e10 + 8.22200e13i 0.000175567 + 0.635060i
\(369\) −1.48329e14 −1.12871
\(370\) −9.59029e8 1.38760e13i −7.18989e−6 0.104029i
\(371\) −3.34159e13 3.34159e13i −0.246829 0.246829i
\(372\) −1.56251e14 1.56208e14i −1.13720 1.13689i
\(373\) 1.12134e14 1.12134e14i 0.804153 0.804153i −0.179589 0.983742i \(-0.557477\pi\)
0.983742 + 0.179589i \(0.0574768\pi\)
\(374\) 2.59823e14 2.59859e14i 1.83605 1.83630i
\(375\) 1.80931e14i 1.25991i
\(376\) 1.11846e14 2.31905e10i 0.767514 0.000159139i
\(377\) 4.90124e13i 0.331458i
\(378\) 7.32835e13 + 7.32734e13i 0.488429 + 0.488361i
\(379\) −1.04153e14 + 1.04153e14i −0.684154 + 0.684154i −0.960934 0.276779i \(-0.910733\pi\)
0.276779 + 0.960934i \(0.410733\pi\)
\(380\) 1.45203e14 2.00712e10i 0.940081 0.000129946i
\(381\) 2.85561e14 + 2.85561e14i 1.82227 + 1.82227i
\(382\) 2.24871e14 1.55418e10i 1.41444 9.77583e-5i
\(383\) −1.29233e14 −0.801274 −0.400637 0.916237i \(-0.631211\pi\)
−0.400637 + 0.916237i \(0.631211\pi\)
\(384\) 1.77835e14 + 1.77663e14i 1.08692 + 1.08587i
\(385\) 3.67245e14 2.21270
\(386\) −1.22646e14 + 8.47660e9i −0.728489 + 5.03491e-5i
\(387\) 1.99223e14 + 1.99223e14i 1.16662 + 1.16662i
\(388\) 1.88218e14 2.60171e10i 1.08664 0.000150205i
\(389\) −2.24630e14 + 2.24630e14i −1.27863 + 1.27863i −0.337198 + 0.941434i \(0.609479\pi\)
−0.941434 + 0.337198i \(0.890521\pi\)
\(390\) −7.39542e13 7.39440e13i −0.415057 0.414999i
\(391\) 1.89512e14i 1.04873i
\(392\) −1.01735e14 + 2.10940e10i −0.555132 + 0.000115103i
\(393\) 4.43217e14i 2.38483i
\(394\) −2.35217e14 + 2.35249e14i −1.24807 + 1.24824i
\(395\) −1.29060e14 + 1.29060e14i −0.675316 + 0.675316i
\(396\) −2.93188e14 2.93107e14i −1.51294 1.51252i
\(397\) −2.06448e14 2.06448e14i −1.05066 1.05066i −0.998646 0.0520169i \(-0.983435\pi\)
−0.0520169 0.998646i \(-0.516565\pi\)
\(398\) −3.87952e9 5.61318e13i −1.94725e−5 0.281742i
\(399\) 3.22436e14 1.59622
\(400\) −1.54714e10 5.59631e13i −7.55442e−5 0.273257i
\(401\) 1.77354e14 0.854177 0.427089 0.904210i \(-0.359539\pi\)
0.427089 + 0.904210i \(0.359539\pi\)
\(402\) 2.53641e10 + 3.66986e14i 0.000120497 + 1.74344i
\(403\) 5.34670e13 + 5.34670e13i 0.250558 + 0.250558i
\(404\) −1.83777e14 + 1.83828e14i −0.849561 + 0.849796i
\(405\) 8.91516e13 8.91516e13i 0.406562 0.406562i
\(406\) −1.91879e14 + 1.91906e14i −0.863246 + 0.863365i
\(407\) 3.26621e13i 0.144969i
\(408\) −4.09786e14 4.09616e14i −1.79443 1.79368i
\(409\) 3.56385e14i 1.53972i −0.638213 0.769860i \(-0.720326\pi\)
0.638213 0.769860i \(-0.279674\pi\)
\(410\) 1.55299e14 + 1.55278e14i 0.661999 + 0.661908i
\(411\) −2.30363e14 + 2.30363e14i −0.968910 + 0.968910i
\(412\) 2.83785e10 + 2.05300e14i 0.000117775 + 0.852031i
\(413\) −2.15447e14 2.15447e14i −0.882298 0.882298i
\(414\) −2.13803e14 + 1.47769e10i −0.863997 + 5.97147e-5i
\(415\) 4.91593e13 0.196039
\(416\) −6.08528e13 6.08108e13i −0.239479 0.239314i
\(417\) 1.98296e14 0.770135
\(418\) −3.41788e14 + 2.36225e10i −1.31005 + 9.05433e-5i
\(419\) 2.71801e14 + 2.71801e14i 1.02819 + 1.02819i 0.999591 + 0.0286012i \(0.00910529\pi\)
0.0286012 + 0.999591i \(0.490895\pi\)
\(420\) −8.00412e10 5.79048e14i −0.000298842 2.16194i
\(421\) 5.71653e13 5.71653e13i 0.210660 0.210660i −0.593888 0.804548i \(-0.702408\pi\)
0.804548 + 0.593888i \(0.202408\pi\)
\(422\) −1.17583e14 1.17566e14i −0.427686 0.427626i
\(423\) 2.90841e14i 1.04420i
\(424\) 5.58386e13 5.58618e13i 0.197889 0.197971i
\(425\) 1.28991e14i 0.451254i
\(426\) 6.07251e14 6.07335e14i 2.09708 2.09737i
\(427\) −1.34927e14 + 1.34927e14i −0.459988 + 0.459988i
\(428\) −4.79321e13 + 4.79454e13i −0.161319 + 0.161364i
\(429\) 1.74066e14 + 1.74066e14i 0.578361 + 0.578361i
\(430\) −2.88303e10 4.17139e14i −9.45742e−5 1.36837i
\(431\) 4.62177e13 0.149687 0.0748434 0.997195i \(-0.476154\pi\)
0.0748434 + 0.997195i \(0.476154\pi\)
\(432\) −1.22441e14 + 1.22509e14i −0.391532 + 0.391749i
\(433\) −2.17070e14 −0.685356 −0.342678 0.939453i \(-0.611334\pi\)
−0.342678 + 0.939453i \(0.611334\pi\)
\(434\) 2.89358e10 + 4.18666e14i 9.02075e−5 + 1.30519i
\(435\) −3.89880e14 3.89880e14i −1.20016 1.20016i
\(436\) 9.11500e13 + 9.11248e13i 0.277065 + 0.276988i
\(437\) −1.24639e14 + 1.24639e14i −0.374117 + 0.374117i
\(438\) 1.54182e14 1.54204e14i 0.457011 0.457075i
\(439\) 2.67074e14i 0.781766i 0.920440 + 0.390883i \(0.127830\pi\)
−0.920440 + 0.390883i \(0.872170\pi\)
\(440\) 1.27268e11 + 6.13801e14i 0.000367899 + 1.77435i
\(441\) 2.64549e14i 0.755255i
\(442\) 1.40223e14 + 1.40204e14i 0.395364 + 0.395309i
\(443\) 2.39831e14 2.39831e14i 0.667858 0.667858i −0.289362 0.957220i \(-0.593443\pi\)
0.957220 + 0.289362i \(0.0934431\pi\)
\(444\) 5.14995e13 7.11872e9i 0.141644 1.95792e-5i
\(445\) 2.69153e14 + 2.69153e14i 0.731172 + 0.731172i
\(446\) 1.50201e14 1.03811e10i 0.403025 2.78548e-5i
\(447\) −3.79670e14 −1.00627
\(448\) −1.97530e11 4.76335e14i −0.000517135 1.24705i
\(449\) 5.87700e14 1.51985 0.759925 0.650011i \(-0.225236\pi\)
0.759925 + 0.650011i \(0.225236\pi\)
\(450\) 1.45525e14 1.00579e10i 0.371766 2.56944e-5i
\(451\) −3.65528e14 3.65528e14i −0.922464 0.922464i
\(452\) −4.81369e14 + 6.65391e10i −1.20010 + 0.000165888i
\(453\) −1.49236e14 + 1.49236e14i −0.367564 + 0.367564i
\(454\) 1.20735e14 + 1.20718e14i 0.293782 + 0.293742i
\(455\) 1.98170e14i 0.476403i
\(456\) 1.11739e11 + 5.38909e14i 0.000265399 + 1.28000i
\(457\) 4.52197e14i 1.06118i 0.847629 + 0.530589i \(0.178029\pi\)
−0.847629 + 0.530589i \(0.821971\pi\)
\(458\) 2.29260e14 2.29292e14i 0.531580 0.531653i
\(459\) 2.82297e14 2.82297e14i 0.646751 0.646751i
\(460\) 2.23865e14 + 2.23803e14i 0.506778 + 0.506638i
\(461\) −5.12674e14 5.12674e14i −1.14680 1.14680i −0.987179 0.159616i \(-0.948974\pi\)
−0.159616 0.987179i \(-0.551026\pi\)
\(462\) 9.42031e10 + 1.36300e15i 0.000208226 + 3.01277i
\(463\) 2.55229e14 0.557486 0.278743 0.960366i \(-0.410082\pi\)
0.278743 + 0.960366i \(0.410082\pi\)
\(464\) −3.20811e14 3.20634e14i −0.692470 0.692087i
\(465\) −8.50631e14 −1.81447
\(466\) −3.95850e10 5.72745e14i −8.34465e−5 1.20737i
\(467\) 1.22952e14 + 1.22952e14i 0.256148 + 0.256148i 0.823485 0.567337i \(-0.192026\pi\)
−0.567337 + 0.823485i \(0.692026\pi\)
\(468\) 1.58164e14 1.58208e14i 0.325653 0.325743i
\(469\) 4.91727e14 4.91727e14i 1.00063 1.00063i
\(470\) 3.04465e14 3.04507e14i 0.612350 0.612435i
\(471\) 6.66690e14i 1.32528i
\(472\) 3.60017e14 3.60166e14i 0.707362 0.707655i
\(473\) 9.81888e14i 1.90689i
\(474\) −4.79029e14 4.78963e14i −0.919562 0.919435i
\(475\) 8.48358e13 8.48358e13i 0.160977 0.160977i
\(476\) 1.51764e11 + 1.09792e15i 0.000284664 + 2.05936i
\(477\) 1.45232e14 + 1.45232e14i 0.269284 + 0.269284i
\(478\) 1.70125e14 1.17581e10i 0.311828 2.15518e-5i
\(479\) 2.71050e14 0.491139 0.245569 0.969379i \(-0.421025\pi\)
0.245569 + 0.969379i \(0.421025\pi\)
\(480\) 9.67802e14 3.34446e11i 1.73364 0.000599099i
\(481\) −1.76249e13 −0.0312124
\(482\) −2.50311e14 + 1.73001e10i −0.438250 + 3.02894e-5i
\(483\) 4.97043e14 + 4.97043e14i 0.860369 + 0.860369i
\(484\) −1.18944e11 8.60487e14i −0.000203561 1.47263i
\(485\) 5.12399e14 5.12399e14i 0.867019 0.867019i
\(486\) 5.65011e14 + 5.64932e14i 0.945273 + 0.945142i
\(487\) 3.77246e14i 0.624045i −0.950075 0.312022i \(-0.898994\pi\)
0.950075 0.312022i \(-0.101006\pi\)
\(488\) −2.25560e14 2.25466e14i −0.368938 0.368785i
\(489\) 7.35571e14i 1.18967i
\(490\) −2.76941e14 + 2.76980e14i −0.442904 + 0.442965i
\(491\) −4.41994e14 + 4.41994e14i −0.698985 + 0.698985i −0.964192 0.265207i \(-0.914560\pi\)
0.265207 + 0.964192i \(0.414560\pi\)
\(492\) −5.76261e14 + 5.76420e14i −0.901179 + 0.901428i
\(493\) 7.39245e14 + 7.39245e14i 1.14322 + 1.14322i
\(494\) −1.27470e10 1.84433e14i −1.94943e−5 0.282059i
\(495\) −1.59611e15 −2.41399
\(496\) −6.99744e14 + 1.93450e11i −1.04662 + 0.000289347i
\(497\) −1.62743e15 −2.40737
\(498\) 1.26100e10 + 1.82451e14i 1.84482e−5 + 0.266922i
\(499\) −5.44840e14 5.44840e14i −0.788344 0.788344i 0.192878 0.981223i \(-0.438218\pi\)
−0.981223 + 0.192878i \(0.938218\pi\)
\(500\) 4.05246e14 + 4.05134e14i 0.579941 + 0.579781i
\(501\) 2.32592e14 2.32592e14i 0.329220 0.329220i
\(502\) −1.38910e14 + 1.38929e14i −0.194475 + 0.194502i
\(503\) 3.71015e14i 0.513768i 0.966442 + 0.256884i \(0.0826958\pi\)
−0.966442 + 0.256884i \(0.917304\pi\)
\(504\) 1.23865e15 2.56826e11i 1.69661 0.000351780i
\(505\) 1.00076e15i 1.35590i
\(506\) −5.26911e14 5.26838e14i −0.706171 0.706073i
\(507\) 7.25537e14 7.25537e14i 0.961869 0.961869i
\(508\) 1.27902e15 1.76797e11i 1.67736 0.000231859i
\(509\) −7.69790e14 7.69790e14i −0.998676 0.998676i 0.00132283 0.999999i \(-0.499579\pi\)
−0.999999 + 0.00132283i \(0.999579\pi\)
\(510\) −2.23072e15 + 1.54175e11i −2.86292 + 0.000197869i
\(511\) −4.13208e14 −0.524631
\(512\) 7.96131e14 4.95218e11i 1.00000 0.000622030i
\(513\) −3.71326e14 −0.461434
\(514\) 7.75556e13 5.36021e9i 0.0953489 6.58999e-6i
\(515\) 5.58905e14 + 5.58905e14i 0.679827 + 0.679827i
\(516\) 1.54818e15 2.14003e11i 1.86315 0.000257541i
\(517\) −7.16720e14 + 7.16720e14i −0.853398 + 0.853398i
\(518\) −6.90093e13 6.89998e13i −0.0813006 0.0812894i
\(519\) 8.02914e14i 0.935941i
\(520\) −3.31214e14 + 6.86751e10i −0.382024 + 7.92101e-5i
\(521\) 1.01193e14i 0.115489i 0.998331 + 0.0577447i \(0.0183909\pi\)
−0.998331 + 0.0577447i \(0.981609\pi\)
\(522\) 8.33942e14 8.34058e14i 0.941777 0.941907i
\(523\) 2.30526e14 2.30526e14i 0.257608 0.257608i −0.566472 0.824081i \(-0.691692\pi\)
0.824081 + 0.566472i \(0.191692\pi\)
\(524\) −9.92711e14 9.92437e14i −1.09774 1.09744i
\(525\) −3.38313e14 3.38313e14i −0.370205 0.370205i
\(526\) −3.17455e10 4.59318e14i −3.43764e−5 0.497384i
\(527\) 1.61286e15 1.72838
\(528\) −2.27808e15 + 6.29792e11i −2.41591 + 0.000667899i
\(529\) 5.68541e14 0.596699
\(530\) −2.10170e10 3.04090e14i −2.18300e−5 0.315853i
\(531\) 9.36373e14 + 9.36373e14i 0.962562 + 0.962562i
\(532\) 7.21988e14 7.22187e14i 0.734541 0.734744i
\(533\) 1.97243e14 1.97243e14i 0.198610 0.198610i
\(534\) −9.98873e14 + 9.99011e14i −0.995481 + 0.995619i
\(535\) 2.61015e14i 0.257465i
\(536\) 8.22027e14 + 8.21686e14i 0.802564 + 0.802232i
\(537\) 1.37908e15i 1.33270i
\(538\) −5.89494e14 5.89413e14i −0.563867 0.563790i
\(539\) 6.51928e14 6.51928e14i 0.617250 0.617250i
\(540\) 9.21776e10 + 6.66847e14i 8.63892e−5 + 0.624972i
\(541\) −3.94835e14 3.94835e14i −0.366295 0.366295i 0.499829 0.866124i \(-0.333396\pi\)
−0.866124 + 0.499829i \(0.833396\pi\)
\(542\) −8.35130e14 + 5.77196e10i −0.766934 + 5.30063e-5i
\(543\) −4.10672e14 −0.373333
\(544\) −1.83503e15 + 6.34136e11i −1.65139 + 0.000570674i
\(545\) 4.96221e14 0.442073
\(546\) −7.35491e14 + 5.08331e10i −0.648661 + 4.48319e-5i
\(547\) 2.85865e14 + 2.85865e14i 0.249592 + 0.249592i 0.820803 0.571211i \(-0.193526\pi\)
−0.571211 + 0.820803i \(0.693526\pi\)
\(548\) 1.42623e11 + 1.03179e15i 0.000123281 + 0.891860i
\(549\) 5.86419e14 5.86419e14i 0.501834 0.501834i
\(550\) 3.58643e14 + 3.58593e14i 0.303855 + 0.303813i
\(551\) 9.72382e14i 0.815648i
\(552\) −8.30570e14 + 8.30914e14i −0.689781 + 0.690067i
\(553\) 1.28362e15i 1.05547i
\(554\) 7.08468e14 7.08566e14i 0.576789 0.576868i
\(555\) 1.40201e14 1.40201e14i 0.113016 0.113016i
\(556\) 4.44019e14 4.44142e14i 0.354397 0.354495i
\(557\) 6.89000e13 + 6.89000e13i 0.0544522 + 0.0544522i 0.733809 0.679356i \(-0.237741\pi\)
−0.679356 + 0.733809i \(0.737741\pi\)
\(558\) −1.25761e11 1.81960e15i −9.84139e−5 1.42393i
\(559\) −5.29838e14 −0.410562
\(560\) −1.29712e15 1.29641e15i −0.995283 0.994733i
\(561\) 5.25081e15 3.98961
\(562\) 1.60158e11 + 2.31729e15i 0.000120503 + 1.74353i
\(563\) 2.79657e14 + 2.79657e14i 0.208367 + 0.208367i 0.803573 0.595206i \(-0.202930\pi\)
−0.595206 + 0.803573i \(0.702930\pi\)
\(564\) 1.13023e15 + 1.12992e15i 0.833937 + 0.833707i
\(565\) −1.31047e15 + 1.31047e15i −0.957547 + 0.957547i
\(566\) 1.66599e12 1.66622e12i 0.00120554 0.00120570i
\(567\) 8.86694e14i 0.635429i
\(568\) −5.63982e11 2.72004e15i −0.000400266 1.93045i
\(569\) 1.64126e15i 1.15361i −0.816881 0.576807i \(-0.804299\pi\)
0.816881 0.576807i \(-0.195701\pi\)
\(570\) 1.46721e15 + 1.46701e15i 1.02137 + 1.02123i
\(571\) −1.29829e15 + 1.29829e15i −0.895100 + 0.895100i −0.994998 0.0998976i \(-0.968148\pi\)
0.0998976 + 0.994998i \(0.468148\pi\)
\(572\) 7.79634e14 1.07768e11i 0.532369 7.35887e-5i
\(573\) 2.27207e15 + 2.27207e15i 1.53664 + 1.53664i
\(574\) 1.54448e15 1.06746e11i 1.03459 7.15051e-5i
\(575\) 2.61553e14 0.173535
\(576\) 8.58502e11 + 2.07024e15i 0.000564180 + 1.36050i
\(577\) −1.84725e15 −1.20242 −0.601212 0.799089i \(-0.705315\pi\)
−0.601212 + 0.799089i \(0.705315\pi\)
\(578\) 2.67865e15 1.85134e11i 1.72708 0.000119367i
\(579\) −1.23920e15 1.23920e15i −0.791424 0.791424i
\(580\) −1.74626e15 + 2.41383e11i −1.10472 + 0.000152705i
\(581\) 2.44467e14 2.44467e14i 0.153198 0.153198i
\(582\) 1.90186e15 + 1.90160e15i 1.18060 + 1.18044i
\(583\) 7.15788e14i 0.440157i
\(584\) −1.43196e11 6.90623e14i −8.72289e−5 0.420698i
\(585\) 8.61282e14i 0.519742i
\(586\) 3.30760e14 3.30806e14i 0.197732 0.197759i
\(587\) 7.54803e14 7.54803e14i 0.447017 0.447017i −0.447345 0.894362i \(-0.647630\pi\)
0.894362 + 0.447345i \(0.147630\pi\)
\(588\) −1.02806e15 1.02778e15i −0.603175 0.603008i
\(589\) −1.06076e15 1.06076e15i −0.616570 0.616570i
\(590\) −1.35506e11 1.96061e15i −7.80321e−5 1.12903i
\(591\) −4.75354e15 −2.71198
\(592\) 1.15300e14 1.15364e14i 0.0651719 0.0652079i
\(593\) −2.83705e15 −1.58879 −0.794393 0.607404i \(-0.792211\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(594\) −1.08487e11 1.56967e15i −6.01938e−5 0.870929i
\(595\) 2.98896e15 + 2.98896e15i 1.64315 + 1.64315i
\(596\) −8.50145e14 + 8.50380e14i −0.463062 + 0.463190i
\(597\) 5.67150e14 5.67150e14i 0.306083 0.306083i
\(598\) 2.84288e14 2.84327e14i 0.152021 0.152042i
\(599\) 1.42147e15i 0.753167i −0.926383 0.376584i \(-0.877099\pi\)
0.926383 0.376584i \(-0.122901\pi\)
\(600\) 5.65328e14 5.65562e14i 0.296803 0.296926i
\(601\) 1.37212e15i 0.713810i −0.934141 0.356905i \(-0.883832\pi\)
0.934141 0.356905i \(-0.116168\pi\)
\(602\) −2.07456e15 2.07427e15i −1.06941 1.06926i
\(603\) −2.13714e15 + 2.13714e15i −1.09166 + 1.09166i
\(604\) 9.23949e10 + 6.68420e14i 4.67676e−5 + 0.338334i
\(605\) −2.34257e15 2.34257e15i −1.17500 1.17500i
\(606\) −3.71425e15 + 2.56708e11i −1.84617 + 0.000127597i
\(607\) 9.58569e14 0.472156 0.236078 0.971734i \(-0.424138\pi\)
0.236078 + 0.971734i \(0.424138\pi\)
\(608\) 1.20729e15 + 1.20646e15i 0.589308 + 0.588901i
\(609\) −3.87772e15 −1.87578
\(610\) −1.22786e15 + 8.48631e10i −0.588621 + 4.06822e-5i
\(611\) −3.86750e14 3.86750e14i −0.183740 0.183740i
\(612\) −6.59597e11 4.77177e15i −0.000310560 2.24671i
\(613\) 1.16692e15 1.16692e15i 0.544512 0.544512i −0.380336 0.924848i \(-0.624192\pi\)
0.924848 + 0.380336i \(0.124192\pi\)
\(614\) 2.26300e15 + 2.26269e15i 1.04655 + 1.04640i
\(615\) 3.13803e15i 1.43828i
\(616\) 3.05304e15 + 3.05177e15i 1.38688 + 1.38630i
\(617\) 1.66121e15i 0.747920i −0.927445 0.373960i \(-0.878000\pi\)
0.927445 0.373960i \(-0.122000\pi\)
\(618\) −2.07419e15 + 2.07448e15i −0.925576 + 0.925703i
\(619\) −1.32258e15 + 1.32258e15i −0.584958 + 0.584958i −0.936262 0.351304i \(-0.885738\pi\)
0.351304 + 0.936262i \(0.385738\pi\)
\(620\) −1.90470e15 + 1.90523e15i −0.834975 + 0.835205i
\(621\) −5.72409e14 5.72409e14i −0.248715 0.248715i
\(622\) 2.72936e11 + 3.94905e15i 0.000117548 + 1.70077i
\(623\) 2.67698e15 1.14277
\(624\) −3.39843e11 1.22928e15i −0.000143801 0.520157i
\(625\) 2.85766e15 1.19859
\(626\) 1.56633e11 + 2.26629e15i 6.51216e−5 + 0.942229i
\(627\) −3.45339e15 3.45339e15i −1.42323 1.42323i
\(628\) −1.49324e15 1.49283e15i −0.610031 0.609863i
\(629\) −2.65832e14 + 2.65832e14i −0.107654 + 0.107654i
\(630\) 3.37184e15 3.37231e15i 1.35361 1.35380i
\(631\) 3.87984e15i 1.54402i 0.635612 + 0.772009i \(0.280748\pi\)
−0.635612 + 0.772009i \(0.719252\pi\)
\(632\) −2.14540e15 + 4.44834e11i −0.846378 + 0.000175491i
\(633\) 2.37592e15i 0.929204i
\(634\) 2.47374e15 + 2.47340e15i 0.959099 + 0.958966i
\(635\) 3.48196e15 3.48196e15i 1.33835 1.33835i
\(636\) 1.12861e15 1.56006e11i 0.430060 5.94467e-5i
\(637\) 3.51788e14 + 3.51788e14i 0.132897 + 0.132897i
\(638\) 4.11045e15 2.84092e11i 1.53949 0.000106401i
\(639\) 7.07312e15 2.62637
\(640\) 2.16632e15 2.16842e15i 0.797504 0.798276i
\(641\) −5.57445e14 −0.203462 −0.101731 0.994812i \(-0.532438\pi\)
−0.101731 + 0.994812i \(0.532438\pi\)
\(642\) −9.68736e14 + 6.69536e10i −0.350560 + 2.42288e-5i
\(643\) −3.17954e15 3.17954e15i −1.14079 1.14079i −0.988307 0.152480i \(-0.951274\pi\)
−0.152480 0.988307i \(-0.548726\pi\)
\(644\) 2.22623e15 3.07730e11i 0.791951 0.000109471i
\(645\) 4.21472e15 4.21472e15i 1.48659 1.48659i
\(646\) −2.78196e15 2.78157e15i −0.972908 0.972773i
\(647\) 2.20708e15i 0.765324i 0.923888 + 0.382662i \(0.124993\pi\)
−0.923888 + 0.382662i \(0.875007\pi\)
\(648\) 1.48199e15 3.07281e11i 0.509546 0.000105651i
\(649\) 4.61501e15i 1.57335i
\(650\) −1.93501e14 + 1.93528e14i −0.0654123 + 0.0654214i
\(651\) −4.23015e15 + 4.23015e15i −1.41795 + 1.41795i
\(652\) −1.64752e15 1.64707e15i −0.547607 0.547456i
\(653\) 2.46010e15 + 2.46010e15i 0.810832 + 0.810832i 0.984759 0.173926i \(-0.0556455\pi\)
−0.173926 + 0.984759i \(0.555645\pi\)
\(654\) 1.27287e11 + 1.84169e15i 4.16013e−5 + 0.601919i
\(655\) −5.40432e15 −1.75152
\(656\) 7.13649e11 + 2.58140e15i 0.000229358 + 0.829630i
\(657\) 1.79588e15 0.572358
\(658\) −2.09306e11 3.02840e15i −6.61514e−5 0.957128i
\(659\) 9.41322e13 + 9.41322e13i 0.0295032 + 0.0295032i 0.721704 0.692201i \(-0.243359\pi\)
−0.692201 + 0.721704i \(0.743359\pi\)
\(660\) −6.20092e15 + 6.20264e15i −1.92737 + 1.92790i
\(661\) −1.97944e15 + 1.97944e15i −0.610148 + 0.610148i −0.942984 0.332837i \(-0.891994\pi\)
0.332837 + 0.942984i \(0.391994\pi\)
\(662\) −6.77622e14 + 6.77716e14i −0.207142 + 0.207171i
\(663\) 2.83340e15i 0.858981i
\(664\) 4.08679e14 + 4.08510e14i 0.122874 + 0.122823i
\(665\) 3.93159e15i 1.17233i
\(666\) 2.99927e14 + 2.99886e14i 0.0886967 + 0.0886845i
\(667\) 1.49895e15 1.49895e15i 0.439638 0.439638i
\(668\) −1.44002e11 1.04177e15i −4.18889e−5 0.303040i
\(669\) 1.51762e15 + 1.51762e15i 0.437843 + 0.437843i
\(670\) 4.47481e15 3.09274e11i 1.28045 8.84977e-5i
\(671\) 2.89022e15 0.820272
\(672\) 4.81118e15 4.81450e15i 1.35432 1.35525i
\(673\) 1.41200e15 0.394231 0.197116 0.980380i \(-0.436843\pi\)
0.197116 + 0.980380i \(0.436843\pi\)
\(674\) −3.05378e14 + 2.11060e10i −0.0845684 + 5.84490e-6i
\(675\) 3.89610e14 + 3.89610e14i 0.107019 + 0.107019i
\(676\) −4.49195e11 3.24965e15i −0.000122385 0.885379i
\(677\) −4.85721e15 + 4.85721e15i −1.31265 + 1.31265i −0.393194 + 0.919456i \(0.628630\pi\)
−0.919456 + 0.393194i \(0.871370\pi\)
\(678\) −4.86404e15 4.86337e15i −1.30387 1.30369i
\(679\) 5.09628e15i 1.35509i
\(680\) −4.99461e15 + 4.99668e15i −1.31735 + 1.31790i
\(681\) 2.43961e15i 0.638281i
\(682\) 4.48373e15 4.48435e15i 1.16366 1.16382i
\(683\) −8.68637e14 + 8.68637e14i −0.223627 + 0.223627i −0.810024 0.586397i \(-0.800546\pi\)
0.586397 + 0.810024i \(0.300546\pi\)
\(684\) −3.13789e15 + 3.13876e15i −0.801364 + 0.801585i
\(685\) 2.80891e15 + 2.80891e15i 0.711606 + 0.711606i
\(686\) −1.52569e11 2.20748e15i −3.83428e−5 0.554772i
\(687\) 4.63316e15 1.15509
\(688\) 3.46615e15 3.46806e15i 0.857256 0.857730i
\(689\) −3.86248e14 −0.0947676
\(690\) 3.12618e11 + 4.52319e15i 7.60928e−5 + 1.10097i
\(691\) −4.10027e15 4.10027e15i −0.990110 0.990110i 0.00984162 0.999952i \(-0.496867\pi\)
−0.999952 + 0.00984162i \(0.996867\pi\)
\(692\) −1.79835e15 1.79786e15i −0.430816 0.430697i
\(693\) −7.93741e15 + 7.93741e15i −1.88645 + 1.88645i
\(694\) −4.40743e15 + 4.40804e15i −1.03922 + 1.03936i
\(695\) 2.41791e15i 0.565618i
\(696\) −1.34381e12 6.48109e15i −0.000311880 1.50417i
\(697\) 5.94996e15i 1.37004i
\(698\) −3.77777e14 3.77725e14i −0.0863040 0.0862921i
\(699\) 5.78696e15 5.78696e15i 1.31167 1.31167i
\(700\) −1.51529e15 + 2.09456e11i −0.340766 + 4.71036e-5i
\(701\) 4.09473e14 + 4.09473e14i 0.0913643 + 0.0913643i 0.751312 0.659947i \(-0.229421\pi\)
−0.659947 + 0.751312i \(0.729421\pi\)
\(702\) 8.47012e14 5.85407e10i 0.187515 1.29600e-5i
\(703\) 3.49669e14 0.0768073
\(704\) −5.09958e15 + 5.10381e15i −1.11144 + 1.11236i
\(705\) 6.15299e15 1.33060
\(706\) −4.10092e15 + 2.83433e11i −0.879945 + 6.08169e-5i
\(707\) 4.97674e15 + 4.97674e15i 1.05959 + 1.05959i
\(708\) 7.27664e15 1.00584e12i 1.53726 0.000212494i
\(709\) −4.23628e13 + 4.23628e13i −0.00888035 + 0.00888035i −0.711533 0.702653i \(-0.751999\pi\)
0.702653 + 0.711533i \(0.251999\pi\)
\(710\) −7.40548e15 7.40445e15i −1.54039 1.54018i
\(711\) 5.57885e15i 1.15149i
\(712\) 9.27698e11 + 4.47421e15i 0.000190006 + 0.916382i
\(713\) 3.27037e15i 0.664668i
\(714\) −1.10925e16 + 1.10940e16i −2.23712 + 2.23743i
\(715\) 2.12246e15 2.12246e15i 0.424772 0.424772i
\(716\) 3.08885e15 + 3.08800e15i 0.613445 + 0.613275i
\(717\) 1.71892e15 + 1.71892e15i 0.338767 + 0.338767i
\(718\) −2.23609e11 3.23534e15i −4.37326e−5 0.632756i
\(719\) 3.44205e15 0.668049 0.334025 0.942564i \(-0.391593\pi\)
0.334025 + 0.942564i \(0.391593\pi\)
\(720\) 5.63754e15 + 5.63442e15i 1.08583 + 1.08523i
\(721\) 5.55882e15 1.06252
\(722\) −1.11460e11 1.61269e15i −2.11429e−5 0.305912i
\(723\) −2.52912e15 2.52912e15i −0.476111 0.476111i
\(724\) −9.19564e14 + 9.19818e14i −0.171799 + 0.171846i
\(725\) −1.02026e15 + 1.02026e15i −0.189170 + 0.189170i
\(726\) 8.69367e15 8.69487e15i 1.59975 1.59997i
\(727\) 8.86644e14i 0.161924i 0.996717 + 0.0809618i \(0.0257992\pi\)
−0.996717 + 0.0809618i \(0.974201\pi\)
\(728\) −1.64677e15 + 1.64746e15i −0.298477 + 0.298601i
\(729\) 8.58422e15i 1.54419i
\(730\) −1.88027e15 1.88001e15i −0.335694 0.335647i
\(731\) −7.99145e15 + 7.99145e15i −1.41605 + 1.41605i
\(732\) −6.29926e11 4.55712e15i −0.000110784 0.801456i
\(733\) −7.89968e15 7.89968e15i −1.37892 1.37892i −0.846455 0.532461i \(-0.821267\pi\)
−0.532461 0.846455i \(-0.678733\pi\)
\(734\) 1.89641e14 1.31069e10i 0.0328552 2.27077e-6i
\(735\) −5.59676e15 −0.962401
\(736\) 1.28582e12 + 3.72085e15i 0.000219459 + 0.635060i
\(737\) −1.05331e16 −1.78437
\(738\) −6.71262e15 + 4.63939e11i −1.12871 + 7.80101e-5i
\(739\) 3.16961e15 + 3.16961e15i 0.529007 + 0.529007i 0.920276 0.391269i \(-0.127964\pi\)
−0.391269 + 0.920276i \(0.627964\pi\)
\(740\) −8.68014e10 6.27954e14i −1.43798e−5 0.104029i
\(741\) 1.86349e15 1.86349e15i 0.306427 0.306427i
\(742\) −1.51233e15 1.51212e15i −0.246846 0.246812i
\(743\) 1.94649e15i 0.315364i 0.987490 + 0.157682i \(0.0504022\pi\)
−0.987490 + 0.157682i \(0.949598\pi\)
\(744\) −7.07161e15 7.06867e15i −1.13728 1.13681i
\(745\) 4.62947e15i 0.739047i
\(746\) 5.07425e15 5.07495e15i 0.804097 0.804208i
\(747\) −1.06250e15 + 1.06250e15i −0.167134 + 0.167134i
\(748\) 1.17574e16 1.17607e16i 1.83592 1.83643i
\(749\) 1.29801e15 + 1.29801e15i 0.201201 + 0.201201i
\(750\) 5.65909e11 + 8.18799e15i 8.70782e−5 + 1.25991i
\(751\) −8.22162e14 −0.125585 −0.0627925 0.998027i \(-0.520001\pi\)
−0.0627925 + 0.998027i \(0.520001\pi\)
\(752\) 5.06156e15 1.39931e12i 0.767514 0.000212185i
\(753\) −2.80726e15 −0.422581
\(754\) 1.53299e11 + 2.21805e15i 2.29085e−5 + 0.331458i
\(755\) 1.81969e15 + 1.81969e15i 0.269954 + 0.269954i
\(756\) 3.31666e15 + 3.31575e15i 0.488463 + 0.488328i
\(757\) 1.22234e15 1.22234e15i 0.178716 0.178716i −0.612080 0.790796i \(-0.709667\pi\)
0.790796 + 0.612080i \(0.209667\pi\)
\(758\) −4.71308e15 + 4.71373e15i −0.684107 + 0.684202i
\(759\) 1.06470e16i 1.53425i
\(760\) 6.57113e15 1.36248e12i 0.940081 0.000194920i
\(761\) 7.64079e15i 1.08523i −0.839981 0.542616i \(-0.817434\pi\)
0.839981 0.542616i \(-0.182566\pi\)
\(762\) 1.29239e16 + 1.29221e16i 1.82239 + 1.82214i
\(763\) 2.46768e15 2.46768e15i 0.345466 0.345466i
\(764\) 1.01765e16 1.40669e12i 1.41444 0.000195517i
\(765\) −1.29906e16 1.29906e16i −1.79263 1.79263i
\(766\) −5.84843e15 + 4.04211e11i −0.801274 + 5.53796e-5i
\(767\) −2.49031e15 −0.338750
\(768\) 8.04847e15 + 8.03958e15i 1.08699 + 1.08579i
\(769\) 4.51581e15 0.605537 0.302768 0.953064i \(-0.402089\pi\)
0.302768 + 0.953064i \(0.402089\pi\)
\(770\) 1.66196e16 1.14865e12i 2.21270 0.000152929i
\(771\) 7.83613e14 + 7.83613e14i 0.103586 + 0.103586i
\(772\) −5.55032e15 + 7.67215e11i −0.728489 + 0.000100698i
\(773\) −1.07717e15 + 1.07717e15i −0.140377 + 0.140377i −0.773803 0.633426i \(-0.781648\pi\)
0.633426 + 0.773803i \(0.281648\pi\)
\(774\) 9.01641e15 + 9.01516e15i 1.16670 + 1.16654i
\(775\) 2.22598e15i 0.285997i
\(776\) 8.51775e15 1.76610e12i 1.08664 0.000225308i
\(777\) 1.39443e15i 0.176637i
\(778\) −1.01649e16 + 1.01663e16i −1.27854 + 1.27872i
\(779\) −3.91321e15 + 3.91321e15i −0.488739 + 0.488739i
\(780\) −3.34702e15 3.34609e15i −0.415085 0.414971i
\(781\) 1.74303e16 + 1.74303e16i 2.14647 + 2.14647i
\(782\) −5.92748e11 8.57632e15i −7.24824e−5 1.04873i
\(783\) 4.46569e15 0.542249
\(784\) −4.60399e15 + 1.27281e12i −0.555132 + 0.000153471i
\(785\) −8.12921e15 −0.973342
\(786\) −1.38628e12 2.00577e16i −0.000164826 2.38483i
\(787\) −4.70724e15 4.70724e15i −0.555783 0.555783i 0.372321 0.928104i \(-0.378562\pi\)
−0.928104 + 0.372321i \(0.878562\pi\)
\(788\) −1.06440e16 + 1.06469e16i −1.24798 + 1.24833i
\(789\) 4.64090e15 4.64090e15i 0.540354 0.540354i
\(790\) −5.84018e15 + 5.84099e15i −0.675270 + 0.675363i
\(791\) 1.30338e16i 1.49658i
\(792\) −1.32691e16 1.32636e16i −1.51305 1.51242i
\(793\) 1.55960e15i 0.176608i
\(794\) −9.34343e15 9.34214e15i −1.05074 1.05059i
\(795\) 3.07250e15 3.07250e15i 0.343141 0.343141i
\(796\) −3.51134e11 2.54024e15i −3.89449e−5 0.281742i
\(797\) 7.24872e15 + 7.24872e15i 0.798436 + 0.798436i 0.982849 0.184412i \(-0.0590382\pi\)
−0.184412 + 0.982849i \(0.559038\pi\)
\(798\) 1.45918e16 1.00850e12i 1.59622 0.000110322i
\(799\) −1.16666e16 −1.26746
\(800\) −8.75197e11 2.53260e15i −9.44302e−5 0.273257i
\(801\) −1.16346e16 −1.24673
\(802\) 8.02614e15 5.54723e11i 0.854177 5.90360e-5i
\(803\) 4.42559e15 + 4.42559e15i 0.467773 + 0.467773i
\(804\) 2.29569e12 + 1.66079e16i 0.000240994 + 1.74344i
\(805\) 6.06064e15 6.06064e15i 0.631890 0.631890i
\(806\) 2.41981e15 + 2.41947e15i 0.250575 + 0.250540i
\(807\) 1.19115e16i 1.22508i
\(808\) −8.31625e15 + 8.31969e15i −0.849503 + 0.849855i
\(809\) 1.03410e16i 1.04917i 0.851360 + 0.524583i \(0.175779\pi\)
−0.851360 + 0.524583i \(0.824221\pi\)
\(810\) 4.03426e15 4.03482e15i 0.406533 0.406590i
\(811\) 1.11196e16 1.11196e16i 1.11295 1.11295i 0.120200 0.992750i \(-0.461646\pi\)
0.992750 0.120200i \(-0.0383536\pi\)
\(812\) −8.68286e15 + 8.68526e15i −0.863186 + 0.863425i
\(813\) −8.43807e15 8.43807e15i −0.833192 0.833192i
\(814\) 1.02159e11 + 1.47812e15i 1.00195e−5 + 0.144969i
\(815\) −8.96910e15 −0.873740
\(816\) −1.85461e16 1.85358e16i −1.79455 1.79356i
\(817\) 1.05117e16 1.01031
\(818\) −1.11469e12 1.61282e16i −0.000106417 1.53972i
\(819\) −4.28312e15 4.28312e15i −0.406161 0.406161i
\(820\) 7.02852e15 + 7.02658e15i 0.662045 + 0.661862i
\(821\) 7.05917e15 7.05917e15i 0.660490 0.660490i −0.295005 0.955496i \(-0.595321\pi\)
0.955496 + 0.295005i \(0.0953215\pi\)
\(822\) −1.04243e16 + 1.04258e16i −0.968843 + 0.968977i
\(823\) 1.30797e16i 1.20753i 0.797163 + 0.603764i \(0.206333\pi\)
−0.797163 + 0.603764i \(0.793667\pi\)
\(824\) 1.92639e12 + 9.29084e15i 0.000176663 + 0.852031i
\(825\) 7.24687e15i 0.660167i
\(826\) −9.75069e15 9.74934e15i −0.882359 0.882237i
\(827\) 8.30624e15 8.30624e15i 0.746662 0.746662i −0.227189 0.973851i \(-0.572953\pi\)
0.973851 + 0.227189i \(0.0729534\pi\)
\(828\) −9.67562e15 + 1.33745e12i −0.863997 + 0.000119429i
\(829\) −1.07494e16 1.07494e16i −0.953531 0.953531i 0.0454367 0.998967i \(-0.485532\pi\)
−0.998967 + 0.0454367i \(0.985532\pi\)
\(830\) 2.22470e15 1.53759e11i 0.196039 1.35491e-5i
\(831\) 1.43176e16 1.25332
\(832\) −2.75408e15 2.75179e15i −0.239496 0.239297i
\(833\) 1.06119e16 0.916739
\(834\) 8.97387e15 6.20224e11i 0.770135 5.32274e-5i
\(835\) −2.83608e15 2.83608e15i −0.241793 0.241793i
\(836\) −1.54676e16 + 2.13806e12i −1.31005 + 0.000181087i
\(837\) 4.87156e15 4.87156e15i 0.409900 0.409900i
\(838\) 1.23012e16 + 1.22995e16i 1.02826 + 1.02812i
\(839\) 7.21546e15i 0.599202i 0.954065 + 0.299601i \(0.0968535\pi\)
−0.954065 + 0.299601i \(0.903146\pi\)
\(840\) −5.43337e12 2.62047e16i −0.000448264 2.16194i
\(841\) 5.06335e14i 0.0415011i
\(842\) 2.58683e15 2.58719e15i 0.210645 0.210674i
\(843\) −2.34136e16 + 2.34136e16i −1.89416 + 1.89416i
\(844\) −5.32155e15 5.32008e15i −0.427715 0.427597i
\(845\) −8.84676e15 8.84676e15i −0.706435 0.706435i
\(846\) 9.09683e11 + 1.31620e16i 7.21694e−5 + 1.04420i
\(847\) −2.32990e16 −1.83645
\(848\) 2.52679e15 2.52819e15i 0.197876 0.197985i
\(849\) 3.36682e13 0.00261956
\(850\) 4.03454e11 + 5.83748e15i 3.11882e−5 + 0.451254i
\(851\) 5.39023e14 + 5.39023e14i 0.0413995 + 0.0413995i
\(852\) 2.74792e16 2.74868e16i 2.09694 2.09752i
\(853\) 2.11551e15 2.11551e15i 0.160397 0.160397i −0.622346 0.782742i \(-0.713820\pi\)
0.782742 + 0.622346i \(0.213820\pi\)
\(854\) −6.10569e15 + 6.10653e15i −0.459956 + 0.460020i
\(855\) 1.70874e16i 1.27898i
\(856\) −2.16901e15 + 2.16991e15i −0.161308 + 0.161375i
\(857\) 5.60408e15i 0.414104i −0.978330 0.207052i \(-0.933613\pi\)
0.978330 0.207052i \(-0.0663870\pi\)
\(858\) 7.87788e15 + 7.87679e15i 0.578401 + 0.578321i
\(859\) −2.84823e14 + 2.84823e14i −0.0207784 + 0.0207784i −0.717420 0.696641i \(-0.754677\pi\)
0.696641 + 0.717420i \(0.254677\pi\)
\(860\) −2.60942e12 1.88775e16i −0.000189148 1.36837i
\(861\) 1.56053e16 + 1.56053e16i 1.12397 + 1.12397i
\(862\) 2.09158e15 1.44558e11i 0.149687 1.03455e-5i
\(863\) 2.14058e15 0.152220 0.0761102 0.997099i \(-0.475750\pi\)
0.0761102 + 0.997099i \(0.475750\pi\)
\(864\) −5.54068e15 + 5.54451e15i −0.391505 + 0.391776i
\(865\) −9.79024e15 −0.687392
\(866\) −9.82347e15 + 6.78944e11i −0.685356 + 4.73680e-5i
\(867\) 2.70648e16 + 2.70648e16i 1.87629 + 1.87629i
\(868\) 2.61897e12 + 1.89466e16i 0.000180415 + 1.30519i
\(869\) 1.37479e16 1.37479e16i 0.941086 0.941086i
\(870\) −1.76452e16 1.76428e16i −1.20025 1.20008i
\(871\) 5.68378e15i 0.384182i
\(872\) 4.12526e15 + 4.12355e15i 0.277084 + 0.276969i
\(873\) 2.21494e16i 1.47837i
\(874\) −5.64014e15 + 5.64092e15i −0.374091 + 0.374142i
\(875\) 1.09711e16 1.09711e16i 0.723115 0.723115i
\(876\) 6.97701e15 6.97894e15i 0.456980 0.457106i
\(877\) −6.91657e14 6.91657e14i −0.0450187 0.0450187i 0.684239 0.729258i \(-0.260134\pi\)
−0.729258 + 0.684239i \(0.760134\pi\)
\(878\) 8.35344e11 + 1.20864e16i 5.40313e−5 + 0.781766i
\(879\) 6.68439e15 0.429658
\(880\) 7.67930e12 + 2.77775e16i 0.000490532 + 1.77434i
\(881\) −1.27110e16 −0.806889 −0.403444 0.915004i \(-0.632187\pi\)
−0.403444 + 0.915004i \(0.632187\pi\)
\(882\) −8.27446e11 1.19721e16i −5.21991e−5 0.755255i
\(883\) 1.13706e16 + 1.13706e16i 0.712850 + 0.712850i 0.967131 0.254280i \(-0.0818386\pi\)
−0.254280 + 0.967131i \(0.581839\pi\)
\(884\) 6.34621e15 + 6.34445e15i 0.395391 + 0.395282i
\(885\) 1.98098e16 1.98098e16i 1.22657 1.22657i
\(886\) 1.08527e16 1.08542e16i 0.667812 0.667904i
\(887\) 4.64514e15i 0.284066i 0.989862 + 0.142033i \(0.0453639\pi\)
−0.989862 + 0.142033i \(0.954636\pi\)
\(888\) 2.33060e15 4.83235e11i 0.141644 2.93689e-5i
\(889\) 3.46313e16i 2.09175i
\(890\) 1.21813e16 + 1.21796e16i 0.731223 + 0.731122i
\(891\) −9.49676e15 + 9.49676e15i −0.566563 + 0.566563i
\(892\) 6.79733e15 9.39587e11i 0.403025 5.57096e-5i
\(893\) 7.67294e15 + 7.67294e15i 0.452146 + 0.452146i
\(894\) −1.71819e16 + 1.18752e12i −1.00627 + 6.95480e-5i
\(895\) 1.68157e16 0.978788
\(896\) −1.04290e13 2.15565e16i −0.000603324 1.24705i
\(897\) 5.74523e15 0.330331
\(898\) 2.65963e16 1.83819e12i 1.51985 0.000105044i
\(899\) 1.27570e16 + 1.27570e16i 0.724554 + 0.724554i
\(900\) 6.58572e15 9.10337e11i 0.371766 5.13888e-5i
\(901\) −5.82570e15 + 5.82570e15i −0.326860 + 0.326860i
\(902\) −1.65430e16 1.65408e16i −0.922528 0.922400i
\(903\) 4.19193e16i 2.32344i
\(904\) −2.17843e16 + 4.51683e12i −1.20010 + 0.000248832i
\(905\) 5.00749e15i 0.274191i
\(906\) −6.75317e15 + 6.75411e15i −0.367538 + 0.367589i
\(907\) 1.40963e16 1.40963e16i 0.762543 0.762543i −0.214239 0.976781i \(-0.568727\pi\)
0.976781 + 0.214239i \(0.0687270\pi\)
\(908\) 5.46421e15 + 5.46270e15i 0.293802 + 0.293721i
\(909\) −2.16299e16 2.16299e16i −1.15599 1.15599i
\(910\) 6.19828e11 + 8.96813e15i 3.29263e−5 + 0.476403i
\(911\) −2.45183e16 −1.29461 −0.647305 0.762231i \(-0.724104\pi\)
−0.647305 + 0.762231i \(0.724104\pi\)
\(912\) 6.74232e12 + 2.43882e16i 0.000353865 + 1.28000i
\(913\) −5.23664e15 −0.273189
\(914\) 1.41436e12 + 2.04641e16i 7.33427e−5 + 1.06118i
\(915\) −1.24062e16 1.24062e16i −0.639474 0.639474i
\(916\) 1.03744e16 1.03773e16i 0.531543 0.531690i
\(917\) −2.68755e16 + 2.68755e16i −1.36875 + 1.36875i
\(918\) 1.27744e16 1.27762e16i 0.646706 0.646796i
\(919\) 1.71814e16i 0.864615i −0.901726 0.432307i \(-0.857700\pi\)
0.901726 0.432307i \(-0.142300\pi\)
\(920\) 1.01317e16 + 1.01275e16i 0.506813 + 0.506603i
\(921\) 4.57271e16i 2.27377i
\(922\) −2.32026e16 2.31994e16i −1.14687 1.14672i
\(923\) −9.40559e15 + 9.40559e15i −0.462143 + 0.462143i
\(924\) 8.52629e12 + 6.16824e16i 0.000416451 + 3.01277i
\(925\) −3.66887e14 3.66887e14i −0.0178136 0.0178136i
\(926\) 1.15503e16 7.98295e11i 0.557486 3.85303e-5i
\(927\) −2.41597e16 −1.15918
\(928\) −1.45193e16 1.45092e16i −0.692518 0.692039i
\(929\) 1.37942e16 0.654047 0.327024 0.945016i \(-0.393954\pi\)
0.327024 + 0.945016i \(0.393954\pi\)
\(930\) −3.84952e16 + 2.66057e12i −1.81447 + 0.000125406i
\(931\) −6.97930e15 6.97930e15i −0.327031 0.327031i
\(932\) −3.58282e12 2.59195e16i −0.000166893 1.20737i
\(933\) −3.99007e16 + 3.99007e16i −1.84770 + 1.84770i
\(934\) 5.56453e15 + 5.56377e15i 0.256166 + 0.256130i
\(935\) 6.40252e16i 2.93013i
\(936\) 7.15718e15 7.16015e15i 0.325630 0.325765i
\(937\) 3.53690e16i 1.59976i −0.600160 0.799880i \(-0.704896\pi\)
0.600160 0.799880i \(-0.295104\pi\)
\(938\) 2.22515e16 2.22546e16i 1.00056 1.00070i
\(939\) −2.28983e16 + 2.28983e16i −1.02363 + 1.02363i
\(940\) 1.37776e16 1.37814e16i 0.612308 0.612477i
\(941\) −2.22717e16 2.22717e16i −0.984034 0.984034i 0.0158400 0.999875i \(-0.494958\pi\)
−0.999875 + 0.0158400i \(0.994958\pi\)
\(942\) −2.08525e12 3.01709e16i −9.15963e−5 1.32528i
\(943\) −1.20646e16 −0.526865
\(944\) 1.62914e16 1.63004e16i 0.707313 0.707704i
\(945\) 1.80559e16 0.779371
\(946\) 3.07111e12 + 4.44352e16i 0.000131794 + 1.90689i
\(947\) −2.09342e16 2.09342e16i −0.893163 0.893163i 0.101656 0.994820i \(-0.467586\pi\)
−0.994820 + 0.101656i \(0.967586\pi\)
\(948\) −2.16799e16 2.16739e16i −0.919625 0.919371i
\(949\) −2.38810e15 + 2.38810e15i −0.100714 + 0.100714i
\(950\) 3.83896e15 3.83949e15i 0.160966 0.160988i
\(951\) 4.99854e16i 2.08377i
\(952\) 1.03021e13 + 4.96862e16i 0.000426995 + 2.05936i
\(953\) 2.34667e16i 0.967035i 0.875335 + 0.483517i \(0.160641\pi\)
−0.875335 + 0.483517i \(0.839359\pi\)
\(954\) 6.57288e15 + 6.57198e15i 0.269302 + 0.269265i
\(955\) 2.77043e16 2.77043e16i 1.12857 1.12857i
\(956\) 7.69897e15 1.06422e12i 0.311828 4.31036e-5i
\(957\) 4.15315e16 + 4.15315e16i 1.67249 + 1.67249i
\(958\) 1.22663e16 8.47780e11i 0.491139 3.39448e-5i
\(959\) 2.79372e16 1.11219
\(960\) 4.37977e16 1.81623e13i 1.73364 0.000718919i
\(961\) 2.42445e15 0.0954191
\(962\) −7.97610e14 + 5.51264e10i −0.0312124 + 2.15723e-6i
\(963\) −5.64141e15 5.64141e15i −0.219504 0.219504i
\(964\) −1.13278e16 + 1.56583e12i −0.438250 + 6.05788e-5i
\(965\) −1.51101e16 + 1.51101e16i −0.581254 + 0.581254i
\(966\) 2.24952e16 + 2.24921e16i 0.860429 + 0.860310i
\(967\) 3.94438e16i 1.50014i 0.661357 + 0.750071i \(0.269981\pi\)
−0.661357 + 0.750071i \(0.730019\pi\)
\(968\) −8.07420e12 3.89412e16i −0.000305341 1.47263i
\(969\) 5.62133e16i 2.11377i
\(970\) 2.31869e16 2.31901e16i 0.866959 0.867079i
\(971\) 1.82080e16 1.82080e16i 0.676948 0.676948i −0.282360 0.959308i \(-0.591117\pi\)
0.959308 + 0.282360i \(0.0911174\pi\)
\(972\) 2.55712e16 + 2.55642e16i 0.945338 + 0.945077i
\(973\) −1.20241e16 1.20241e16i −0.442012 0.442012i
\(974\) −1.17994e12 1.70722e16i −4.31305e−5 0.624045i
\(975\) −3.91049e15 −0.142137
\(976\) −1.02084e16 1.02027e16i −0.368963 0.368759i
\(977\) −1.68239e16 −0.604652 −0.302326 0.953205i \(-0.597763\pi\)
−0.302326 + 0.953205i \(0.597763\pi\)
\(978\) −2.30069e12 3.32881e16i −8.22232e−5 1.18967i
\(979\) −2.86712e16 2.86712e16i −1.01892 1.01892i
\(980\) −1.25321e16 + 1.25355e16i −0.442873 + 0.442996i
\(981\) −1.07250e16 + 1.07250e16i −0.376893 + 0.376893i
\(982\) −2.00010e16 + 2.00037e16i −0.698937 + 0.699033i
\(983\) 1.79195e16i 0.622704i −0.950295 0.311352i \(-0.899218\pi\)
0.950295 0.311352i \(-0.100782\pi\)
\(984\) −2.60768e16 + 2.60876e16i −0.901117 + 0.901491i
\(985\) 5.79617e16i 1.99178i
\(986\) 3.34567e16 + 3.34521e16i 1.14330 + 1.14314i
\(987\) 3.05986e16 3.05986e16i 1.03982 1.03982i
\(988\) −1.15372e12 8.34647e15i −3.89887e−5 0.282059i
\(989\) 1.62041e16 + 1.62041e16i 0.544560 + 0.544560i
\(990\) −7.22319e16 + 4.99227e12i −2.41399 + 0.000166842i
\(991\) 5.56476e16 1.84945 0.924723 0.380641i \(-0.124296\pi\)
0.924723 + 0.380641i \(0.124296\pi\)
\(992\) −3.16668e16 + 1.09432e13i −1.04662 + 0.000361684i
\(993\) −1.36942e16 −0.450106
\(994\) −7.36491e16 + 5.09022e12i −2.40737 + 0.000166384i
\(995\) −6.91548e15 6.91548e15i −0.224800 0.224800i
\(996\) 1.14133e12 + 8.25679e15i 3.68964e−5 + 0.266922i
\(997\) 1.04105e16 1.04105e16i 0.334695 0.334695i −0.519671 0.854366i \(-0.673945\pi\)
0.854366 + 0.519671i \(0.173945\pi\)
\(998\) −2.46583e16 2.46549e16i −0.788399 0.788290i
\(999\) 1.60586e15i 0.0510620i
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 16.12.e.a.13.21 yes 42
4.3 odd 2 64.12.e.a.17.2 42
8.3 odd 2 128.12.e.a.33.20 42
8.5 even 2 128.12.e.b.33.2 42
16.3 odd 4 128.12.e.a.97.20 42
16.5 even 4 inner 16.12.e.a.5.21 42
16.11 odd 4 64.12.e.a.49.2 42
16.13 even 4 128.12.e.b.97.2 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.12.e.a.5.21 42 16.5 even 4 inner
16.12.e.a.13.21 yes 42 1.1 even 1 trivial
64.12.e.a.17.2 42 4.3 odd 2
64.12.e.a.49.2 42 16.11 odd 4
128.12.e.a.33.20 42 8.3 odd 2
128.12.e.a.97.20 42 16.3 odd 4
128.12.e.b.33.2 42 8.5 even 2
128.12.e.b.97.2 42 16.13 even 4