Properties

Label 48.9.l.a.19.2
Level $48$
Weight $9$
Character 48.19
Analytic conductor $19.554$
Analytic rank $0$
Dimension $64$
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] = [48,9,Mod(19,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.19");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 48.l (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: \(19.5541732829\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 19.2
Character \(\chi\) \(=\) 48.19
Dual form 48.9.l.a.43.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-15.6102 + 3.51009i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(231.359 - 109.587i) q^{4} +(801.254 - 801.254i) q^{5} +(400.129 - 632.273i) q^{6} +3981.15 q^{7} +(-3226.90 + 2522.76i) q^{8} -2187.00i q^{9} +O(q^{10})\) \(q+(-15.6102 + 3.51009i) q^{2} +(-33.0681 + 33.0681i) q^{3} +(231.359 - 109.587i) q^{4} +(801.254 - 801.254i) q^{5} +(400.129 - 632.273i) q^{6} +3981.15 q^{7} +(-3226.90 + 2522.76i) q^{8} -2187.00i q^{9} +(-9695.29 + 15320.2i) q^{10} +(-11803.7 - 11803.7i) q^{11} +(-4026.77 + 11274.4i) q^{12} +(-9800.60 - 9800.60i) q^{13} +(-62146.7 + 13974.2i) q^{14} +52991.9i q^{15} +(41517.5 - 50707.6i) q^{16} +65409.7 q^{17} +(7676.57 + 34139.6i) q^{18} +(-66925.9 + 66925.9i) q^{19} +(97570.3 - 273184. i) q^{20} +(-131649. + 131649. i) q^{21} +(225690. + 142826. i) q^{22} +171177. q^{23} +(23284.5 - 190130. i) q^{24} -893392. i q^{25} +(187391. + 118589. i) q^{26} +(72320.0 + 72320.0i) q^{27} +(921073. - 436281. i) q^{28} +(-841274. - 841274. i) q^{29} +(-186007. - 827216. i) q^{30} +729280. i q^{31} +(-470110. + 937288. i) q^{32} +780650. q^{33} +(-1.02106e6 + 229594. i) q^{34} +(3.18991e6 - 3.18991e6i) q^{35} +(-239666. - 505981. i) q^{36} +(-722145. + 722145. i) q^{37} +(809812. - 1.27964e6i) q^{38} +648175. q^{39} +(-564194. + 4.60694e6i) q^{40} -3.36723e6i q^{41} +(1.59297e6 - 2.51717e6i) q^{42} +(2.22438e6 + 2.22438e6i) q^{43} +(-4.02440e6 - 1.43735e6i) q^{44} +(-1.75234e6 - 1.75234e6i) q^{45} +(-2.67212e6 + 600848. i) q^{46} -6.58869e6i q^{47} +(303898. + 3.04971e6i) q^{48} +1.00848e7 q^{49} +(3.13589e6 + 1.39461e7i) q^{50} +(-2.16297e6 + 2.16297e6i) q^{51} +(-3.34147e6 - 1.19344e6i) q^{52} +(-4.27914e6 + 4.27914e6i) q^{53} +(-1.38278e6 - 875082. i) q^{54} -1.89155e7 q^{55} +(-1.28468e7 + 1.00435e7i) q^{56} -4.42622e6i q^{57} +(1.60854e7 + 1.01795e7i) q^{58} +(-444418. - 444418. i) q^{59} +(5.80721e6 + 1.22601e7i) q^{60} +(5.73465e6 + 5.73465e6i) q^{61} +(-2.55984e6 - 1.13842e7i) q^{62} -8.70678e6i q^{63} +(4.04856e6 - 1.62814e7i) q^{64} -1.57056e7 q^{65} +(-1.21861e7 + 2.74015e6i) q^{66} +(9.61269e6 - 9.61269e6i) q^{67} +(1.51331e7 - 7.16803e6i) q^{68} +(-5.66051e6 + 5.66051e6i) q^{69} +(-3.85984e7 + 6.09922e7i) q^{70} +3.11414e7 q^{71} +(5.51728e6 + 7.05723e6i) q^{72} -8.30428e6i q^{73} +(8.73806e6 - 1.38076e7i) q^{74} +(2.95428e7 + 2.95428e7i) q^{75} +(-8.14969e6 + 2.28180e7i) q^{76} +(-4.69922e7 - 4.69922e7i) q^{77} +(-1.01182e7 + 2.27515e6i) q^{78} -1.13422e7i q^{79} +(-7.36359e6 - 7.38958e7i) q^{80} -4.78297e6 q^{81} +(1.18193e7 + 5.25633e7i) q^{82} +(4.19151e7 - 4.19151e7i) q^{83} +(-1.60312e7 + 4.48851e7i) q^{84} +(5.24098e7 - 5.24098e7i) q^{85} +(-4.25309e7 - 2.69153e7i) q^{86} +5.56387e7 q^{87} +(6.78671e7 + 8.31142e6i) q^{88} +1.99621e7i q^{89} +(3.35054e7 + 2.12036e7i) q^{90} +(-3.90177e7 - 3.90177e7i) q^{91} +(3.96033e7 - 1.87587e7i) q^{92} +(-2.41159e7 - 2.41159e7i) q^{93} +(2.31269e7 + 1.02851e8i) q^{94} +1.07249e8i q^{95} +(-1.54487e7 - 4.65400e7i) q^{96} -1.50732e8 q^{97} +(-1.57425e8 + 3.53984e7i) q^{98} +(-2.58146e7 + 2.58146e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −15.6102 + 3.51009i −0.975639 + 0.219381i
\(3\) −33.0681 + 33.0681i −0.408248 + 0.408248i
\(4\) 231.359 109.587i 0.903744 0.428073i
\(5\) 801.254 801.254i 1.28201 1.28201i 0.342483 0.939524i \(-0.388732\pi\)
0.939524 0.342483i \(-0.111268\pi\)
\(6\) 400.129 632.273i 0.308741 0.487865i
\(7\) 3981.15 1.65812 0.829061 0.559158i \(-0.188876\pi\)
0.829061 + 0.559158i \(0.188876\pi\)
\(8\) −3226.90 + 2522.76i −0.787818 + 0.615909i
\(9\) 2187.00i 0.333333i
\(10\) −9695.29 + 15320.2i −0.969529 + 1.53202i
\(11\) −11803.7 11803.7i −0.806206 0.806206i 0.177851 0.984057i \(-0.443085\pi\)
−0.984057 + 0.177851i \(0.943085\pi\)
\(12\) −4026.77 + 11274.4i −0.194192 + 0.543712i
\(13\) −9800.60 9800.60i −0.343146 0.343146i 0.514402 0.857549i \(-0.328014\pi\)
−0.857549 + 0.514402i \(0.828014\pi\)
\(14\) −62146.7 + 13974.2i −1.61773 + 0.363760i
\(15\) 52991.9i 1.04675i
\(16\) 41517.5 50707.6i 0.633507 0.773737i
\(17\) 65409.7 0.783153 0.391576 0.920146i \(-0.371930\pi\)
0.391576 + 0.920146i \(0.371930\pi\)
\(18\) 7676.57 + 34139.6i 0.0731269 + 0.325213i
\(19\) −66925.9 + 66925.9i −0.513546 + 0.513546i −0.915611 0.402065i \(-0.868293\pi\)
0.402065 + 0.915611i \(0.368293\pi\)
\(20\) 97570.3 273184.i 0.609814 1.70740i
\(21\) −131649. + 131649.i −0.676925 + 0.676925i
\(22\) 225690. + 142826.i 0.963432 + 0.609700i
\(23\) 171177. 0.611695 0.305847 0.952081i \(-0.401060\pi\)
0.305847 + 0.952081i \(0.401060\pi\)
\(24\) 23284.5 190130.i 0.0701815 0.573069i
\(25\) 893392.i 2.28708i
\(26\) 187391. + 118589.i 0.410067 + 0.259507i
\(27\) 72320.0 + 72320.0i 0.136083 + 0.136083i
\(28\) 921073. 436281.i 1.49852 0.709797i
\(29\) −841274. 841274.i −1.18945 1.18945i −0.977220 0.212229i \(-0.931928\pi\)
−0.212229 0.977220i \(-0.568072\pi\)
\(30\) −186007. 827216.i −0.229638 1.02125i
\(31\) 729280.i 0.789674i 0.918751 + 0.394837i \(0.129199\pi\)
−0.918751 + 0.394837i \(0.870801\pi\)
\(32\) −470110. + 937288.i −0.448332 + 0.893867i
\(33\) 780650. 0.658265
\(34\) −1.02106e6 + 229594.i −0.764074 + 0.171809i
\(35\) 3.18991e6 3.18991e6i 2.12572 2.12572i
\(36\) −239666. 505981.i −0.142691 0.301248i
\(37\) −722145. + 722145.i −0.385316 + 0.385316i −0.873013 0.487697i \(-0.837837\pi\)
0.487697 + 0.873013i \(0.337837\pi\)
\(38\) 809812. 1.27964e6i 0.388374 0.613698i
\(39\) 648175. 0.280178
\(40\) −564194. + 4.60694e6i −0.220388 + 1.79959i
\(41\) 3.36723e6i 1.19162i −0.803125 0.595810i \(-0.796831\pi\)
0.803125 0.595810i \(-0.203169\pi\)
\(42\) 1.59297e6 2.51717e6i 0.511931 0.808939i
\(43\) 2.22438e6 + 2.22438e6i 0.650632 + 0.650632i 0.953145 0.302513i \(-0.0978256\pi\)
−0.302513 + 0.953145i \(0.597826\pi\)
\(44\) −4.02440e6 1.43735e6i −1.07372 0.383489i
\(45\) −1.75234e6 1.75234e6i −0.427336 0.427336i
\(46\) −2.67212e6 + 600848.i −0.596794 + 0.134194i
\(47\) 6.58869e6i 1.35023i −0.737713 0.675114i \(-0.764094\pi\)
0.737713 0.675114i \(-0.235906\pi\)
\(48\) 303898. + 3.04971e6i 0.0572484 + 0.574505i
\(49\) 1.00848e7 1.74937
\(50\) 3.13589e6 + 1.39461e7i 0.501742 + 2.23137i
\(51\) −2.16297e6 + 2.16297e6i −0.319721 + 0.319721i
\(52\) −3.34147e6 1.19344e6i −0.457008 0.163225i
\(53\) −4.27914e6 + 4.27914e6i −0.542316 + 0.542316i −0.924207 0.381891i \(-0.875273\pi\)
0.381891 + 0.924207i \(0.375273\pi\)
\(54\) −1.38278e6 875082.i −0.162622 0.102914i
\(55\) −1.89155e7 −2.06712
\(56\) −1.28468e7 + 1.00435e7i −1.30630 + 1.02125i
\(57\) 4.42622e6i 0.419309i
\(58\) 1.60854e7 + 1.01795e7i 1.42141 + 0.899531i
\(59\) −444418. 444418.i −0.0366761 0.0366761i 0.688531 0.725207i \(-0.258256\pi\)
−0.725207 + 0.688531i \(0.758256\pi\)
\(60\) 5.80721e6 + 1.22601e7i 0.448087 + 0.945998i
\(61\) 5.73465e6 + 5.73465e6i 0.414179 + 0.414179i 0.883191 0.469013i \(-0.155390\pi\)
−0.469013 + 0.883191i \(0.655390\pi\)
\(62\) −2.55984e6 1.13842e7i −0.173239 0.770437i
\(63\) 8.70678e6i 0.552707i
\(64\) 4.04856e6 1.62814e7i 0.241313 0.970447i
\(65\) −1.57056e7 −0.879832
\(66\) −1.21861e7 + 2.74015e6i −0.642229 + 0.144411i
\(67\) 9.61269e6 9.61269e6i 0.477030 0.477030i −0.427150 0.904181i \(-0.640483\pi\)
0.904181 + 0.427150i \(0.140483\pi\)
\(68\) 1.51331e7 7.16803e6i 0.707770 0.335246i
\(69\) −5.66051e6 + 5.66051e6i −0.249723 + 0.249723i
\(70\) −3.85984e7 + 6.09922e7i −1.60760 + 2.54028i
\(71\) 3.11414e7 1.22547 0.612737 0.790287i \(-0.290068\pi\)
0.612737 + 0.790287i \(0.290068\pi\)
\(72\) 5.51728e6 + 7.05723e6i 0.205303 + 0.262606i
\(73\) 8.30428e6i 0.292422i −0.989253 0.146211i \(-0.953292\pi\)
0.989253 0.146211i \(-0.0467079\pi\)
\(74\) 8.73806e6 1.38076e7i 0.291399 0.460461i
\(75\) 2.95428e7 + 2.95428e7i 0.933698 + 0.933698i
\(76\) −8.14969e6 + 2.28180e7i −0.244279 + 0.683950i
\(77\) −4.69922e7 4.69922e7i −1.33679 1.33679i
\(78\) −1.01182e7 + 2.27515e6i −0.273353 + 0.0614656i
\(79\) 1.13422e7i 0.291198i −0.989344 0.145599i \(-0.953489\pi\)
0.989344 0.145599i \(-0.0465110\pi\)
\(80\) −7.36359e6 7.38958e7i −0.179775 1.80410i
\(81\) −4.78297e6 −0.111111
\(82\) 1.18193e7 + 5.25633e7i 0.261418 + 1.16259i
\(83\) 4.19151e7 4.19151e7i 0.883199 0.883199i −0.110660 0.993858i \(-0.535296\pi\)
0.993858 + 0.110660i \(0.0352964\pi\)
\(84\) −1.60312e7 + 4.48851e7i −0.321994 + 0.901541i
\(85\) 5.24098e7 5.24098e7i 1.00401 1.00401i
\(86\) −4.25309e7 2.69153e7i −0.777518 0.492046i
\(87\) 5.56387e7 0.971181
\(88\) 6.78671e7 + 8.31142e6i 1.13169 + 0.138594i
\(89\) 1.99621e7i 0.318160i 0.987266 + 0.159080i \(0.0508528\pi\)
−0.987266 + 0.159080i \(0.949147\pi\)
\(90\) 3.35054e7 + 2.12036e7i 0.510675 + 0.323176i
\(91\) −3.90177e7 3.90177e7i −0.568978 0.568978i
\(92\) 3.96033e7 1.87587e7i 0.552816 0.261850i
\(93\) −2.41159e7 2.41159e7i −0.322383 0.322383i
\(94\) 2.31269e7 + 1.02851e8i 0.296214 + 1.31734i
\(95\) 1.07249e8i 1.31674i
\(96\) −1.54487e7 4.65400e7i −0.181889 0.547950i
\(97\) −1.50732e8 −1.70263 −0.851313 0.524658i \(-0.824193\pi\)
−0.851313 + 0.524658i \(0.824193\pi\)
\(98\) −1.57425e8 + 3.53984e7i −1.70675 + 0.383777i
\(99\) −2.58146e7 + 2.58146e7i −0.268735 + 0.268735i
\(100\) −9.79039e7 2.06694e8i −0.979039 2.06694i
\(101\) −2.47390e7 + 2.47390e7i −0.237737 + 0.237737i −0.815912 0.578176i \(-0.803765\pi\)
0.578176 + 0.815912i \(0.303765\pi\)
\(102\) 2.61723e7 4.13568e7i 0.241792 0.382073i
\(103\) 5.01910e7 0.445941 0.222970 0.974825i \(-0.428425\pi\)
0.222970 + 0.974825i \(0.428425\pi\)
\(104\) 5.63502e7 + 6.90098e6i 0.481684 + 0.0589899i
\(105\) 2.10969e8i 1.73565i
\(106\) 5.17782e7 8.18185e7i 0.410131 0.648079i
\(107\) −1.36696e8 1.36696e8i −1.04285 1.04285i −0.999040 0.0438074i \(-0.986051\pi\)
−0.0438074 0.999040i \(-0.513949\pi\)
\(108\) 2.46571e7 + 8.80654e6i 0.181237 + 0.0647307i
\(109\) 3.22422e7 + 3.22422e7i 0.228412 + 0.228412i 0.812029 0.583617i \(-0.198363\pi\)
−0.583617 + 0.812029i \(0.698363\pi\)
\(110\) 2.95275e8 6.63950e7i 2.01677 0.453487i
\(111\) 4.77599e7i 0.314610i
\(112\) 1.65288e8 2.01875e8i 1.05043 1.28295i
\(113\) 2.56528e8 1.57334 0.786668 0.617376i \(-0.211804\pi\)
0.786668 + 0.617376i \(0.211804\pi\)
\(114\) 1.55364e7 + 6.90944e7i 0.0919882 + 0.409094i
\(115\) 1.37157e8 1.37157e8i 0.784197 0.784197i
\(116\) −2.86828e8 1.02444e8i −1.58413 0.565787i
\(117\) −2.14339e7 + 2.14339e7i −0.114382 + 0.114382i
\(118\) 8.49741e6 + 5.37752e6i 0.0438287 + 0.0277366i
\(119\) 2.60406e8 1.29856
\(120\) −1.33686e8 1.71000e8i −0.644705 0.824651i
\(121\) 6.42941e7i 0.299937i
\(122\) −1.09648e8 6.93901e7i −0.494952 0.313226i
\(123\) 1.11348e8 + 1.11348e8i 0.486477 + 0.486477i
\(124\) 7.99194e7 + 1.68725e8i 0.338038 + 0.713663i
\(125\) −4.02844e8 4.02844e8i −1.65005 1.65005i
\(126\) 3.05616e7 + 1.35915e8i 0.121253 + 0.539243i
\(127\) 3.16547e8i 1.21681i 0.793626 + 0.608406i \(0.208191\pi\)
−0.793626 + 0.608406i \(0.791809\pi\)
\(128\) −6.04973e6 + 2.68367e8i −0.0225370 + 0.999746i
\(129\) −1.47112e8 −0.531239
\(130\) 2.45167e8 5.51279e7i 0.858399 0.193018i
\(131\) −1.55206e8 + 1.55206e8i −0.527017 + 0.527017i −0.919682 0.392665i \(-0.871553\pi\)
0.392665 + 0.919682i \(0.371553\pi\)
\(132\) 1.80610e8 8.55488e7i 0.594903 0.281785i
\(133\) −2.66442e8 + 2.66442e8i −0.851522 + 0.851522i
\(134\) −1.16315e8 + 1.83798e8i −0.360758 + 0.570061i
\(135\) 1.15893e8 0.348918
\(136\) −2.11071e8 + 1.65013e8i −0.616981 + 0.482350i
\(137\) 8.99216e7i 0.255259i 0.991822 + 0.127630i \(0.0407369\pi\)
−0.991822 + 0.127630i \(0.959263\pi\)
\(138\) 6.84930e7 1.08231e8i 0.188855 0.298424i
\(139\) 3.42205e8 + 3.42205e8i 0.916699 + 0.916699i 0.996788 0.0800887i \(-0.0255203\pi\)
−0.0800887 + 0.996788i \(0.525520\pi\)
\(140\) 3.88442e8 1.08759e9i 1.01115 2.83108i
\(141\) 2.17875e8 + 2.17875e8i 0.551229 + 0.551229i
\(142\) −4.86124e8 + 1.09309e8i −1.19562 + 0.268845i
\(143\) 2.31366e8i 0.553293i
\(144\) −1.10898e8 9.07989e7i −0.257912 0.211169i
\(145\) −1.34815e9 −3.04976
\(146\) 2.91488e7 + 1.29632e8i 0.0641518 + 0.285299i
\(147\) −3.33484e8 + 3.33484e8i −0.714176 + 0.714176i
\(148\) −8.79370e7 + 2.46212e8i −0.183284 + 0.513171i
\(149\) −6.36434e8 + 6.36434e8i −1.29124 + 1.29124i −0.357227 + 0.934018i \(0.616278\pi\)
−0.934018 + 0.357227i \(0.883722\pi\)
\(150\) −5.64868e8 3.57472e8i −1.11579 0.706117i
\(151\) 5.09050e8 0.979157 0.489579 0.871959i \(-0.337151\pi\)
0.489579 + 0.871959i \(0.337151\pi\)
\(152\) 4.71251e7 3.84801e8i 0.0882831 0.720878i
\(153\) 1.43051e8i 0.261051i
\(154\) 8.98505e8 + 5.68612e8i 1.59749 + 1.01096i
\(155\) 5.84339e8 + 5.84339e8i 1.01237 + 1.01237i
\(156\) 1.49961e8 7.10313e7i 0.253209 0.119937i
\(157\) −4.61395e8 4.61395e8i −0.759407 0.759407i 0.216808 0.976214i \(-0.430436\pi\)
−0.976214 + 0.216808i \(0.930436\pi\)
\(158\) 3.98121e7 + 1.77054e8i 0.0638833 + 0.284104i
\(159\) 2.83006e8i 0.442799i
\(160\) 3.74328e8 + 1.12768e9i 0.571180 + 1.72071i
\(161\) 6.81483e8 1.01426
\(162\) 7.46632e7 1.67887e7i 0.108404 0.0243756i
\(163\) −1.97899e8 + 1.97899e8i −0.280345 + 0.280345i −0.833247 0.552902i \(-0.813521\pi\)
0.552902 + 0.833247i \(0.313521\pi\)
\(164\) −3.69004e8 7.79038e8i −0.510100 1.07692i
\(165\) 6.25499e8 6.25499e8i 0.843900 0.843900i
\(166\) −5.07179e8 + 8.01431e8i −0.667927 + 1.05544i
\(167\) 2.82528e8 0.363241 0.181621 0.983369i \(-0.441866\pi\)
0.181621 + 0.983369i \(0.441866\pi\)
\(168\) 9.26992e7 7.56938e8i 0.116369 0.950218i
\(169\) 6.23627e8i 0.764501i
\(170\) −6.34166e8 + 1.00209e9i −0.759289 + 1.19981i
\(171\) 1.46367e8 + 1.46367e8i 0.171182 + 0.171182i
\(172\) 7.58392e8 + 2.70867e8i 0.866523 + 0.309487i
\(173\) 6.03265e8 + 6.03265e8i 0.673479 + 0.673479i 0.958516 0.285038i \(-0.0920061\pi\)
−0.285038 + 0.958516i \(0.592006\pi\)
\(174\) −8.68533e8 + 1.95297e8i −0.947522 + 0.213058i
\(175\) 3.55673e9i 3.79226i
\(176\) −1.08859e9 + 1.08477e8i −1.13453 + 0.113054i
\(177\) 2.93921e7 0.0299459
\(178\) −7.00687e7 3.11613e8i −0.0697982 0.310410i
\(179\) 7.84663e7 7.84663e7i 0.0764313 0.0764313i −0.667858 0.744289i \(-0.732789\pi\)
0.744289 + 0.667858i \(0.232789\pi\)
\(180\) −5.97453e8 2.13386e8i −0.569133 0.203271i
\(181\) 1.46128e9 1.46128e9i 1.36150 1.36150i 0.489497 0.872005i \(-0.337180\pi\)
0.872005 0.489497i \(-0.162820\pi\)
\(182\) 7.46030e8 + 4.72119e8i 0.679941 + 0.430295i
\(183\) −3.79268e8 −0.338175
\(184\) −5.52372e8 + 4.31840e8i −0.481904 + 0.376748i
\(185\) 1.15724e9i 0.987957i
\(186\) 4.61104e8 + 2.91806e8i 0.385254 + 0.243805i
\(187\) −7.72074e8 7.72074e8i −0.631382 0.631382i
\(188\) −7.22032e8 1.52435e9i −0.577996 1.22026i
\(189\) 2.87917e8 + 2.87917e8i 0.225642 + 0.225642i
\(190\) −3.76455e8 1.67419e9i −0.288867 1.28466i
\(191\) 1.69151e9i 1.27099i 0.772105 + 0.635495i \(0.219204\pi\)
−0.772105 + 0.635495i \(0.780796\pi\)
\(192\) 4.04517e8 + 6.72274e8i 0.297668 + 0.494699i
\(193\) 1.07898e9 0.777650 0.388825 0.921312i \(-0.372881\pi\)
0.388825 + 0.921312i \(0.372881\pi\)
\(194\) 2.35297e9 5.29084e8i 1.66115 0.373523i
\(195\) 5.19353e8 5.19353e8i 0.359190 0.359190i
\(196\) 2.33319e9 1.10515e9i 1.58098 0.748857i
\(197\) 4.34821e8 4.34821e8i 0.288699 0.288699i −0.547867 0.836566i \(-0.684560\pi\)
0.836566 + 0.547867i \(0.184560\pi\)
\(198\) 3.12360e8 4.93584e8i 0.203233 0.321144i
\(199\) 6.10853e8 0.389515 0.194758 0.980851i \(-0.437608\pi\)
0.194758 + 0.980851i \(0.437608\pi\)
\(200\) 2.25382e9 + 2.88289e9i 1.40864 + 1.80180i
\(201\) 6.35747e8i 0.389493i
\(202\) 2.99345e8 4.73017e8i 0.179790 0.284100i
\(203\) −3.34924e9 3.34924e9i −1.97225 1.97225i
\(204\) −2.63390e8 + 7.37456e8i −0.152082 + 0.425809i
\(205\) −2.69801e9 2.69801e9i −1.52767 1.52767i
\(206\) −7.83493e8 + 1.76175e8i −0.435077 + 0.0978308i
\(207\) 3.74365e8i 0.203898i
\(208\) −9.03862e8 + 9.00683e7i −0.482891 + 0.0481192i
\(209\) 1.57994e9 0.828048
\(210\) −7.40520e8 3.29327e9i −0.380767 1.69336i
\(211\) −1.69822e9 + 1.69822e9i −0.856772 + 0.856772i −0.990956 0.134184i \(-0.957159\pi\)
0.134184 + 0.990956i \(0.457159\pi\)
\(212\) −5.21079e8 + 1.45895e9i −0.257964 + 0.722266i
\(213\) −1.02979e9 + 1.02979e9i −0.500298 + 0.500298i
\(214\) 2.61367e9 + 1.65404e9i 1.24622 + 0.788662i
\(215\) 3.56459e9 1.66823
\(216\) −4.15815e8 5.09233e7i −0.191023 0.0233938i
\(217\) 2.90337e9i 1.30937i
\(218\) −6.16481e8 3.90135e8i −0.272957 0.172738i
\(219\) 2.74607e8 + 2.74607e8i 0.119381 + 0.119381i
\(220\) −4.37626e9 + 2.07288e9i −1.86815 + 0.884880i
\(221\) −6.41054e8 6.41054e8i −0.268736 0.268736i
\(222\) 1.67642e8 + 7.45544e8i 0.0690193 + 0.306945i
\(223\) 2.40180e8i 0.0971219i 0.998820 + 0.0485609i \(0.0154635\pi\)
−0.998820 + 0.0485609i \(0.984536\pi\)
\(224\) −1.87158e9 + 3.73148e9i −0.743389 + 1.48214i
\(225\) −1.95385e9 −0.762361
\(226\) −4.00447e9 + 9.00438e8i −1.53501 + 0.345160i
\(227\) −1.64734e9 + 1.64734e9i −0.620412 + 0.620412i −0.945637 0.325225i \(-0.894560\pi\)
0.325225 + 0.945637i \(0.394560\pi\)
\(228\) −4.85055e8 1.02404e9i −0.179495 0.378948i
\(229\) 8.03016e8 8.03016e8i 0.292000 0.292000i −0.545870 0.837870i \(-0.683801\pi\)
0.837870 + 0.545870i \(0.183801\pi\)
\(230\) −1.65961e9 + 2.62248e9i −0.593056 + 0.937131i
\(231\) 3.10788e9 1.09148
\(232\) 4.83704e9 + 5.92374e8i 1.66966 + 0.204477i
\(233\) 3.15782e8i 0.107143i −0.998564 0.0535715i \(-0.982940\pi\)
0.998564 0.0535715i \(-0.0170605\pi\)
\(234\) 2.59353e8 4.09823e8i 0.0865025 0.136689i
\(235\) −5.27921e9 5.27921e9i −1.73100 1.73100i
\(236\) −1.51522e8 5.41176e7i −0.0488459 0.0174458i
\(237\) 3.75065e8 + 3.75065e8i 0.118881 + 0.118881i
\(238\) −4.06499e9 + 9.14048e8i −1.26693 + 0.284879i
\(239\) 5.17402e9i 1.58576i 0.609379 + 0.792879i \(0.291419\pi\)
−0.609379 + 0.792879i \(0.708581\pi\)
\(240\) 2.68709e9 + 2.20009e9i 0.809912 + 0.663127i
\(241\) 4.88631e9 1.44848 0.724241 0.689547i \(-0.242190\pi\)
0.724241 + 0.689547i \(0.242190\pi\)
\(242\) −2.25678e8 1.00365e9i −0.0658003 0.292630i
\(243\) 1.58164e8 1.58164e8i 0.0453609 0.0453609i
\(244\) 1.95520e9 + 6.98319e8i 0.551610 + 0.197013i
\(245\) 8.08045e9 8.08045e9i 2.24270 2.24270i
\(246\) −2.12901e9 1.34733e9i −0.581350 0.367902i
\(247\) 1.31183e9 0.352443
\(248\) −1.83980e9 2.35331e9i −0.486367 0.622119i
\(249\) 2.77211e9i 0.721129i
\(250\) 7.70252e9 + 4.87447e9i 1.97184 + 1.24787i
\(251\) 3.13700e9 + 3.13700e9i 0.790351 + 0.790351i 0.981551 0.191200i \(-0.0612380\pi\)
−0.191200 + 0.981551i \(0.561238\pi\)
\(252\) −9.54146e8 2.01439e9i −0.236599 0.499506i
\(253\) −2.02052e9 2.02052e9i −0.493152 0.493152i
\(254\) −1.11111e9 4.94138e9i −0.266945 1.18717i
\(255\) 3.46619e9i 0.819768i
\(256\) −8.47556e8 4.21051e9i −0.197337 0.980336i
\(257\) −1.34595e9 −0.308529 −0.154264 0.988030i \(-0.549301\pi\)
−0.154264 + 0.988030i \(0.549301\pi\)
\(258\) 2.29646e9 5.16377e8i 0.518298 0.116544i
\(259\) −2.87497e9 + 2.87497e9i −0.638902 + 0.638902i
\(260\) −3.63361e9 + 1.72112e9i −0.795143 + 0.376632i
\(261\) −1.83987e9 + 1.83987e9i −0.396483 + 0.396483i
\(262\) 1.87802e9 2.96759e9i 0.398561 0.629795i
\(263\) −8.67333e9 −1.81285 −0.906427 0.422362i \(-0.861201\pi\)
−0.906427 + 0.422362i \(0.861201\pi\)
\(264\) −2.51908e9 + 1.96939e9i −0.518592 + 0.405431i
\(265\) 6.85736e9i 1.39051i
\(266\) 3.22398e9 5.09445e9i 0.643971 1.01759i
\(267\) −6.60109e8 6.60109e8i −0.129888 0.129888i
\(268\) 1.17056e9 3.27740e9i 0.226910 0.635317i
\(269\) −2.42919e8 2.42919e8i −0.0463929 0.0463929i 0.683530 0.729923i \(-0.260444\pi\)
−0.729923 + 0.683530i \(0.760444\pi\)
\(270\) −1.80912e9 + 4.06796e8i −0.340418 + 0.0765459i
\(271\) 4.03223e9i 0.747599i −0.927510 0.373799i \(-0.878055\pi\)
0.927510 0.373799i \(-0.121945\pi\)
\(272\) 2.71565e9 3.31677e9i 0.496133 0.605954i
\(273\) 2.58048e9 0.464569
\(274\) −3.15633e8 1.40370e9i −0.0559990 0.249041i
\(275\) −1.05453e10 + 1.05453e10i −1.84386 + 1.84386i
\(276\) −6.89291e8 + 1.92992e9i −0.118786 + 0.332586i
\(277\) 6.68880e7 6.68880e7i 0.0113613 0.0113613i −0.701403 0.712765i \(-0.747443\pi\)
0.712765 + 0.701403i \(0.247443\pi\)
\(278\) −6.54306e9 4.14072e9i −1.09547 0.693262i
\(279\) 1.59494e9 0.263225
\(280\) −2.24614e9 + 1.83409e10i −0.365431 + 2.98393i
\(281\) 9.74132e9i 1.56240i 0.624280 + 0.781201i \(0.285392\pi\)
−0.624280 + 0.781201i \(0.714608\pi\)
\(282\) −4.16585e9 2.63632e9i −0.658729 0.416871i
\(283\) 2.81827e9 + 2.81827e9i 0.439377 + 0.439377i 0.891802 0.452426i \(-0.149441\pi\)
−0.452426 + 0.891802i \(0.649441\pi\)
\(284\) 7.20482e9 3.41268e9i 1.10752 0.524592i
\(285\) −3.54653e9 3.54653e9i −0.537557 0.537557i
\(286\) −8.12116e8 3.61168e9i −0.121382 0.539815i
\(287\) 1.34055e10i 1.97585i
\(288\) 2.04985e9 + 1.02813e9i 0.297956 + 0.149444i
\(289\) −2.69733e9 −0.386672
\(290\) 2.10449e10 4.73213e9i 2.97547 0.669059i
\(291\) 4.98443e9 4.98443e9i 0.695094 0.695094i
\(292\) −9.10038e8 1.92127e9i −0.125178 0.264275i
\(293\) −3.44523e8 + 3.44523e8i −0.0467463 + 0.0467463i −0.730094 0.683347i \(-0.760524\pi\)
0.683347 + 0.730094i \(0.260524\pi\)
\(294\) 4.03520e9 6.37632e9i 0.540102 0.853455i
\(295\) −7.12183e8 −0.0940381
\(296\) 5.08490e8 4.15209e9i 0.0662393 0.540879i
\(297\) 1.70728e9i 0.219422i
\(298\) 7.70094e9 1.21688e10i 0.976515 1.54306i
\(299\) −1.67764e9 1.67764e9i −0.209901 0.209901i
\(300\) 1.00725e10 + 3.59748e9i 1.24352 + 0.444134i
\(301\) 8.85560e9 + 8.85560e9i 1.07883 + 1.07883i
\(302\) −7.94638e9 + 1.78681e9i −0.955304 + 0.214808i
\(303\) 1.63614e9i 0.194111i
\(304\) 6.15054e8 + 6.17225e9i 0.0720143 + 0.722685i
\(305\) 9.18983e9 1.06196
\(306\) 5.02122e8 + 2.23306e9i 0.0572695 + 0.254691i
\(307\) 2.08118e9 2.08118e9i 0.234291 0.234291i −0.580190 0.814481i \(-0.697022\pi\)
0.814481 + 0.580190i \(0.197022\pi\)
\(308\) −1.60217e10 5.72232e9i −1.78036 0.635872i
\(309\) −1.65972e9 + 1.65972e9i −0.182055 + 0.182055i
\(310\) −1.11727e10 7.07058e9i −1.20980 0.765611i
\(311\) 8.49196e8 0.0907751 0.0453875 0.998969i \(-0.485548\pi\)
0.0453875 + 0.998969i \(0.485548\pi\)
\(312\) −2.09160e9 + 1.63519e9i −0.220729 + 0.172564i
\(313\) 4.51783e9i 0.470710i 0.971910 + 0.235355i \(0.0756252\pi\)
−0.971910 + 0.235355i \(0.924375\pi\)
\(314\) 8.82202e9 + 5.58295e9i 0.907506 + 0.574308i
\(315\) −6.97634e9 6.97634e9i −0.708575 0.708575i
\(316\) −1.24295e9 2.62411e9i −0.124654 0.263169i
\(317\) −1.62586e9 1.62586e9i −0.161007 0.161007i 0.622006 0.783013i \(-0.286318\pi\)
−0.783013 + 0.622006i \(0.786318\pi\)
\(318\) 9.93377e8 + 4.41779e9i 0.0971416 + 0.432013i
\(319\) 1.98602e10i 1.91788i
\(320\) −9.80162e9 1.62895e10i −0.934755 1.55349i
\(321\) 9.04056e9 0.851481
\(322\) −1.06381e10 + 2.39207e9i −0.989556 + 0.222510i
\(323\) −4.37760e9 + 4.37760e9i −0.402185 + 0.402185i
\(324\) −1.10658e9 + 5.24150e8i −0.100416 + 0.0475636i
\(325\) −8.75578e9 + 8.75578e9i −0.784805 + 0.784805i
\(326\) 2.39460e9 3.78389e9i 0.212013 0.335018i
\(327\) −2.13238e9 −0.186497
\(328\) 8.49473e9 + 1.08657e10i 0.733929 + 0.938779i
\(329\) 2.62305e10i 2.23884i
\(330\) −7.56863e9 + 1.19597e10i −0.638207 + 1.00848i
\(331\) 2.41258e9 + 2.41258e9i 0.200987 + 0.200987i 0.800423 0.599436i \(-0.204608\pi\)
−0.599436 + 0.800423i \(0.704608\pi\)
\(332\) 5.10408e9 1.42908e10i 0.420112 1.17626i
\(333\) 1.57933e9 + 1.57933e9i 0.128439 + 0.128439i
\(334\) −4.41033e9 + 9.91699e8i −0.354393 + 0.0796882i
\(335\) 1.54044e10i 1.22311i
\(336\) 1.20986e9 + 1.21414e10i 0.0949248 + 0.952599i
\(337\) 5.07050e9 0.393125 0.196563 0.980491i \(-0.437022\pi\)
0.196563 + 0.980491i \(0.437022\pi\)
\(338\) 2.18899e9 + 9.73496e9i 0.167717 + 0.745877i
\(339\) −8.48291e9 + 8.48291e9i −0.642312 + 0.642312i
\(340\) 6.38204e9 1.78689e10i 0.477577 1.33715i
\(341\) 8.60818e9 8.60818e9i 0.636640 0.636640i
\(342\) −2.79858e9 1.77106e9i −0.204566 0.129458i
\(343\) 1.71984e10 1.24254
\(344\) −1.27894e10 1.56627e9i −0.913309 0.111849i
\(345\) 9.07102e9i 0.640294i
\(346\) −1.15346e10 7.29959e9i −0.804820 0.509324i
\(347\) −1.66552e9 1.66552e9i −0.114876 0.114876i 0.647332 0.762208i \(-0.275885\pi\)
−0.762208 + 0.647332i \(0.775885\pi\)
\(348\) 1.28725e10 6.09726e9i 0.877699 0.415736i
\(349\) −2.04594e10 2.04594e10i −1.37909 1.37909i −0.846166 0.532919i \(-0.821095\pi\)
−0.532919 0.846166i \(-0.678905\pi\)
\(350\) 1.24844e10 + 5.55213e10i 0.831949 + 3.69988i
\(351\) 1.41756e9i 0.0933926i
\(352\) 1.66124e10 5.51441e9i 1.08209 0.359193i
\(353\) −2.96196e9 −0.190757 −0.0953785 0.995441i \(-0.530406\pi\)
−0.0953785 + 0.995441i \(0.530406\pi\)
\(354\) −4.58818e8 + 1.03169e8i −0.0292164 + 0.00656956i
\(355\) 2.49522e10 2.49522e10i 1.57107 1.57107i
\(356\) 2.18758e9 + 4.61840e9i 0.136196 + 0.287536i
\(357\) −8.61113e9 + 8.61113e9i −0.530136 + 0.530136i
\(358\) −9.49454e8 + 1.50030e9i −0.0578018 + 0.0913369i
\(359\) 3.43100e9 0.206558 0.103279 0.994652i \(-0.467066\pi\)
0.103279 + 0.994652i \(0.467066\pi\)
\(360\) 1.00754e10 + 1.23389e9i 0.599862 + 0.0734628i
\(361\) 8.02542e9i 0.472541i
\(362\) −1.76817e10 + 2.79401e10i −1.02965 + 1.62702i
\(363\) −2.12608e9 2.12608e9i −0.122449 0.122449i
\(364\) −1.33029e10 4.75126e9i −0.757775 0.270647i
\(365\) −6.65384e9 6.65384e9i −0.374888 0.374888i
\(366\) 5.92046e9 1.33127e9i 0.329937 0.0741892i
\(367\) 5.38362e9i 0.296763i 0.988930 + 0.148382i \(0.0474064\pi\)
−0.988930 + 0.148382i \(0.952594\pi\)
\(368\) 7.10686e9 8.67999e9i 0.387513 0.473291i
\(369\) −7.36414e9 −0.397207
\(370\) −4.06203e9 1.80648e10i −0.216739 0.963889i
\(371\) −1.70359e10 + 1.70359e10i −0.899227 + 0.899227i
\(372\) −8.22221e9 2.93664e9i −0.429355 0.153348i
\(373\) 9.61558e9 9.61558e9i 0.496753 0.496753i −0.413673 0.910426i \(-0.635754\pi\)
0.910426 + 0.413673i \(0.135754\pi\)
\(374\) 1.47623e10 + 9.34220e9i 0.754515 + 0.477488i
\(375\) 2.66426e10 1.34726
\(376\) 1.66217e10 + 2.12610e10i 0.831618 + 1.06373i
\(377\) 1.64900e10i 0.816310i
\(378\) −5.50506e9 3.48383e9i −0.269646 0.170644i
\(379\) 1.19771e10 + 1.19771e10i 0.580489 + 0.580489i 0.935038 0.354548i \(-0.115365\pi\)
−0.354548 + 0.935038i \(0.615365\pi\)
\(380\) 1.17531e10 + 2.48130e10i 0.563661 + 1.19000i
\(381\) −1.04676e10 1.04676e10i −0.496762 0.496762i
\(382\) −5.93737e9 2.64049e10i −0.278831 1.24003i
\(383\) 2.81705e10i 1.30918i 0.755983 + 0.654591i \(0.227159\pi\)
−0.755983 + 0.654591i \(0.772841\pi\)
\(384\) −8.67435e9 9.07445e9i −0.398944 0.417345i
\(385\) −7.53053e10 −3.42754
\(386\) −1.68431e10 + 3.78732e9i −0.758706 + 0.170601i
\(387\) 4.86472e9 4.86472e9i 0.216877 0.216877i
\(388\) −3.48732e10 + 1.65182e10i −1.53874 + 0.728848i
\(389\) 2.49827e10 2.49827e10i 1.09104 1.09104i 0.0956224 0.995418i \(-0.469516\pi\)
0.995418 0.0956224i \(-0.0304841\pi\)
\(390\) −6.28424e9 + 9.93020e9i −0.271641 + 0.429239i
\(391\) 1.11967e10 0.479050
\(392\) −3.25425e10 + 2.54414e10i −1.37818 + 1.07745i
\(393\) 1.02648e10i 0.430307i
\(394\) −5.26139e9 + 8.31391e9i −0.218331 + 0.345001i
\(395\) −9.08798e9 9.08798e9i −0.373318 0.373318i
\(396\) −3.14349e9 + 8.80137e9i −0.127830 + 0.357906i
\(397\) 3.05393e10 + 3.05393e10i 1.22941 + 1.22941i 0.964186 + 0.265226i \(0.0854467\pi\)
0.265226 + 0.964186i \(0.414553\pi\)
\(398\) −9.53555e9 + 2.14415e9i −0.380026 + 0.0854521i
\(399\) 1.76215e10i 0.695265i
\(400\) −4.53018e10 3.70914e10i −1.76960 1.44888i
\(401\) −3.52622e9 −0.136374 −0.0681870 0.997673i \(-0.521721\pi\)
−0.0681870 + 0.997673i \(0.521721\pi\)
\(402\) −2.23153e9 9.92416e9i −0.0854473 0.380005i
\(403\) 7.14739e9 7.14739e9i 0.270974 0.270974i
\(404\) −3.01251e9 + 8.43463e9i −0.113085 + 0.316622i
\(405\) −3.83237e9 + 3.83237e9i −0.142445 + 0.142445i
\(406\) 6.40385e10 + 4.05263e10i 2.35688 + 1.49153i
\(407\) 1.70479e10 0.621289
\(408\) 1.52303e9 1.24364e10i 0.0549628 0.448800i
\(409\) 8.42907e9i 0.301222i 0.988593 + 0.150611i \(0.0481240\pi\)
−0.988593 + 0.150611i \(0.951876\pi\)
\(410\) 5.15868e10 + 3.26463e10i 1.82559 + 1.15531i
\(411\) −2.97354e9 2.97354e9i −0.104209 0.104209i
\(412\) 1.16121e10 5.50027e9i 0.403016 0.190895i
\(413\) −1.76929e9 1.76929e9i −0.0608135 0.0608135i
\(414\) 1.31405e9 + 5.84392e9i 0.0447313 + 0.198931i
\(415\) 6.71694e10i 2.26453i
\(416\) 1.37933e10 4.57862e9i 0.460571 0.152884i
\(417\) −2.26321e10 −0.748482
\(418\) −2.46632e10 + 5.54574e9i −0.807876 + 0.181658i
\(419\) 2.03465e9 2.03465e9i 0.0660135 0.0660135i −0.673329 0.739343i \(-0.735136\pi\)
0.739343 + 0.673329i \(0.235136\pi\)
\(420\) 2.31194e10 + 4.88094e10i 0.742983 + 1.56858i
\(421\) −1.91783e10 + 1.91783e10i −0.610495 + 0.610495i −0.943075 0.332580i \(-0.892081\pi\)
0.332580 + 0.943075i \(0.392081\pi\)
\(422\) 2.05488e10 3.24706e10i 0.647941 1.02386i
\(423\) −1.44095e10 −0.450076
\(424\) 3.01311e9 2.46036e10i 0.0932290 0.761264i
\(425\) 5.84365e10i 1.79114i
\(426\) 1.24606e10 1.96898e10i 0.378355 0.597866i
\(427\) 2.28305e10 + 2.28305e10i 0.686759 + 0.686759i
\(428\) −4.66058e10 1.66457e10i −1.38888 0.496053i
\(429\) −7.65084e9 7.65084e9i −0.225881 0.225881i
\(430\) −5.56441e10 + 1.25120e10i −1.62759 + 0.365977i
\(431\) 5.40991e10i 1.56777i 0.620909 + 0.783883i \(0.286764\pi\)
−0.620909 + 0.783883i \(0.713236\pi\)
\(432\) 6.66972e9 6.64626e8i 0.191502 0.0190828i
\(433\) 4.69626e10 1.33598 0.667991 0.744169i \(-0.267154\pi\)
0.667991 + 0.744169i \(0.267154\pi\)
\(434\) −1.01911e10 4.53223e10i −0.287252 1.27748i
\(435\) 4.45808e10 4.45808e10i 1.24506 1.24506i
\(436\) 1.09928e10 + 3.92619e9i 0.304203 + 0.108649i
\(437\) −1.14562e10 + 1.14562e10i −0.314134 + 0.314134i
\(438\) −5.25057e9 3.32278e9i −0.142663 0.0902829i
\(439\) −8.46085e9 −0.227801 −0.113901 0.993492i \(-0.536335\pi\)
−0.113901 + 0.993492i \(0.536335\pi\)
\(440\) 6.10384e10 4.77192e10i 1.62852 1.27316i
\(441\) 2.20554e10i 0.583122i
\(442\) 1.22572e10 + 7.75685e9i 0.321145 + 0.203234i
\(443\) 3.27403e9 + 3.27403e9i 0.0850096 + 0.0850096i 0.748333 0.663323i \(-0.230855\pi\)
−0.663323 + 0.748333i \(0.730855\pi\)
\(444\) −5.23385e9 1.10497e10i −0.134676 0.284327i
\(445\) 1.59947e10 + 1.59947e10i 0.407884 + 0.407884i
\(446\) −8.43053e8 3.74926e9i −0.0213067 0.0947559i
\(447\) 4.20914e10i 1.05430i
\(448\) 1.61179e10 6.48187e10i 0.400126 1.60912i
\(449\) 6.59472e9 0.162260 0.0811300 0.996704i \(-0.474147\pi\)
0.0811300 + 0.996704i \(0.474147\pi\)
\(450\) 3.05000e10 6.85819e9i 0.743790 0.167247i
\(451\) −3.97457e10 + 3.97457e10i −0.960692 + 0.960692i
\(452\) 5.93500e10 2.81121e10i 1.42189 0.673503i
\(453\) −1.68333e10 + 1.68333e10i −0.399739 + 0.399739i
\(454\) 1.99331e10 3.14977e10i 0.469192 0.741405i
\(455\) −6.25262e10 −1.45887
\(456\) 1.11663e10 + 1.42830e10i 0.258256 + 0.330339i
\(457\) 1.98110e10i 0.454194i 0.973872 + 0.227097i \(0.0729234\pi\)
−0.973872 + 0.227097i \(0.927077\pi\)
\(458\) −9.71661e9 + 1.53539e10i −0.220827 + 0.348946i
\(459\) 4.73043e9 + 4.73043e9i 0.106574 + 0.106574i
\(460\) 1.67018e10 4.67629e10i 0.373020 1.04441i
\(461\) 3.16400e10 + 3.16400e10i 0.700541 + 0.700541i 0.964527 0.263986i \(-0.0850372\pi\)
−0.263986 + 0.964527i \(0.585037\pi\)
\(462\) −4.85148e10 + 1.09090e10i −1.06489 + 0.239450i
\(463\) 6.36842e9i 0.138582i 0.997596 + 0.0692912i \(0.0220738\pi\)
−0.997596 + 0.0692912i \(0.977926\pi\)
\(464\) −7.75867e10 + 7.73137e9i −1.67384 + 0.166796i
\(465\) −3.86460e10 −0.826594
\(466\) 1.10842e9 + 4.92943e9i 0.0235051 + 0.104533i
\(467\) 4.74631e10 4.74631e10i 0.997904 0.997904i −0.00209338 0.999998i \(-0.500666\pi\)
0.999998 + 0.00209338i \(0.000666344\pi\)
\(468\) −2.61005e9 + 7.30779e9i −0.0544083 + 0.152336i
\(469\) 3.82696e10 3.82696e10i 0.790974 0.790974i
\(470\) 1.00940e11 + 6.38792e10i 2.06858 + 1.30909i
\(471\) 3.05149e10 0.620053
\(472\) 2.55525e9 + 3.12932e8i 0.0514832 + 0.00630495i
\(473\) 5.25117e10i 1.04909i
\(474\) −7.17136e9 4.53834e9i −0.142065 0.0899049i
\(475\) 5.97910e10 + 5.97910e10i 1.17452 + 1.17452i
\(476\) 6.02471e10 2.85370e10i 1.17357 0.555879i
\(477\) 9.35847e9 + 9.35847e9i 0.180772 + 0.180772i
\(478\) −1.81613e10 8.07677e10i −0.347885 1.54713i
\(479\) 8.21950e10i 1.56136i 0.624931 + 0.780680i \(0.285127\pi\)
−0.624931 + 0.780680i \(0.714873\pi\)
\(480\) −4.96687e10 2.49120e10i −0.935659 0.469293i
\(481\) 1.41549e10 0.264440
\(482\) −7.62764e10 + 1.71514e10i −1.41320 + 0.317769i
\(483\) −2.25353e10 + 2.25353e10i −0.414072 + 0.414072i
\(484\) 7.04577e9 + 1.48750e10i 0.128395 + 0.271066i
\(485\) −1.20775e11 + 1.20775e11i −2.18278 + 2.18278i
\(486\) −1.91380e9 + 3.02414e9i −0.0343046 + 0.0542072i
\(487\) −8.52282e10 −1.51519 −0.757596 0.652724i \(-0.773626\pi\)
−0.757596 + 0.652724i \(0.773626\pi\)
\(488\) −3.29723e10 4.03799e9i −0.581393 0.0712010i
\(489\) 1.30883e10i 0.228901i
\(490\) −9.77746e10 + 1.54501e11i −1.69606 + 2.68007i
\(491\) 2.99337e10 + 2.99337e10i 0.515033 + 0.515033i 0.916064 0.401031i \(-0.131348\pi\)
−0.401031 + 0.916064i \(0.631348\pi\)
\(492\) 3.79636e10 + 1.35591e10i 0.647898 + 0.231403i
\(493\) −5.50275e10 5.50275e10i −0.931520 0.931520i
\(494\) −2.04779e10 + 4.60463e9i −0.343857 + 0.0773192i
\(495\) 4.13681e10i 0.689041i
\(496\) 3.69801e10 + 3.02779e10i 0.610999 + 0.500264i
\(497\) 1.23978e11 2.03199
\(498\) −9.73035e9 4.32732e10i −0.158202 0.703561i
\(499\) 4.51980e10 4.51980e10i 0.728983 0.728983i −0.241434 0.970417i \(-0.577618\pi\)
0.970417 + 0.241434i \(0.0776179\pi\)
\(500\) −1.37348e11 4.90551e10i −2.19757 0.784882i
\(501\) −9.34266e9 + 9.34266e9i −0.148293 + 0.148293i
\(502\) −5.99805e10 3.79582e10i −0.944485 0.597710i
\(503\) −8.12674e10 −1.26953 −0.634767 0.772704i \(-0.718904\pi\)
−0.634767 + 0.772704i \(0.718904\pi\)
\(504\) 2.19651e10 + 2.80959e10i 0.340417 + 0.435432i
\(505\) 3.96444e10i 0.609560i
\(506\) 3.86330e10 + 2.44486e10i 0.589327 + 0.372951i
\(507\) 2.06222e10 + 2.06222e10i 0.312106 + 0.312106i
\(508\) 3.46894e10 + 7.32359e10i 0.520884 + 1.09969i
\(509\) −2.96439e10 2.96439e10i −0.441635 0.441635i 0.450926 0.892561i \(-0.351094\pi\)
−0.892561 + 0.450926i \(0.851094\pi\)
\(510\) −1.21666e10 5.41080e10i −0.179841 0.799798i
\(511\) 3.30606e10i 0.484872i
\(512\) 2.80098e10 + 6.27520e10i 0.407596 + 0.913162i
\(513\) −9.68015e9 −0.139770
\(514\) 2.10106e10 4.72440e9i 0.301013 0.0676853i
\(515\) 4.02158e10 4.02158e10i 0.571699 0.571699i
\(516\) −3.40357e10 + 1.61215e10i −0.480104 + 0.227409i
\(517\) −7.77706e10 + 7.77706e10i −1.08856 + 1.08856i
\(518\) 3.47875e10 5.49703e10i 0.483175 0.763500i
\(519\) −3.98977e10 −0.549893
\(520\) 5.06803e10 3.96214e10i 0.693147 0.541896i
\(521\) 4.69200e10i 0.636806i −0.947955 0.318403i \(-0.896853\pi\)
0.947955 0.318403i \(-0.103147\pi\)
\(522\) 2.22626e10 3.51788e10i 0.299844 0.473805i
\(523\) 1.29871e10 + 1.29871e10i 0.173582 + 0.173582i 0.788551 0.614969i \(-0.210832\pi\)
−0.614969 + 0.788551i \(0.710832\pi\)
\(524\) −1.88998e10 + 5.29169e10i −0.250687 + 0.701890i
\(525\) 1.17614e11 + 1.17614e11i 1.54819 + 1.54819i
\(526\) 1.35393e11 3.04442e10i 1.76869 0.397705i
\(527\) 4.77020e10i 0.618435i
\(528\) 3.24107e10 3.95849e10i 0.417015 0.509323i
\(529\) −4.90093e10 −0.625829
\(530\) −2.40699e10 1.07045e11i −0.305050 1.35663i
\(531\) −9.71942e8 + 9.71942e8i −0.0122254 + 0.0122254i
\(532\) −3.24451e10 + 9.08421e10i −0.405045 + 1.13407i
\(533\) −3.30009e10 + 3.30009e10i −0.408900 + 0.408900i
\(534\) 1.26215e10 + 7.98741e9i 0.155219 + 0.0982292i
\(535\) −2.19057e11 −2.67388
\(536\) −6.76867e9 + 5.52697e10i −0.0820057 + 0.669620i
\(537\) 5.18947e9i 0.0624059i
\(538\) 4.64468e9 + 2.93935e9i 0.0554405 + 0.0350851i
\(539\) −1.19037e11 1.19037e11i −1.41035 1.41035i
\(540\) 2.68129e10 1.27004e10i 0.315333 0.149362i
\(541\) 9.11939e10 + 9.11939e10i 1.06458 + 1.06458i 0.997766 + 0.0668108i \(0.0212824\pi\)
0.0668108 + 0.997766i \(0.478718\pi\)
\(542\) 1.41535e10 + 6.29441e10i 0.164009 + 0.729387i
\(543\) 9.66434e10i 1.11166i
\(544\) −3.07497e10 + 6.13077e10i −0.351112 + 0.700034i
\(545\) 5.16684e10 0.585651
\(546\) −4.02819e10 + 9.05773e9i −0.453252 + 0.101917i
\(547\) −3.56651e10 + 3.56651e10i −0.398377 + 0.398377i −0.877660 0.479283i \(-0.840897\pi\)
0.479283 + 0.877660i \(0.340897\pi\)
\(548\) 9.85420e9 + 2.08041e10i 0.109270 + 0.230689i
\(549\) 1.25417e10 1.25417e10i 0.138060 0.138060i
\(550\) 1.27600e11 2.01630e11i 1.39444 2.20345i
\(551\) 1.12606e11 1.22167
\(552\) 3.98578e9 3.25460e10i 0.0429297 0.350543i
\(553\) 4.51550e10i 0.482842i
\(554\) −8.09354e8 + 1.27892e9i −0.00859210 + 0.0135770i
\(555\) −3.82679e10 3.82679e10i −0.403332 0.403332i
\(556\) 1.16673e11 + 4.16709e10i 1.22088 + 0.436048i
\(557\) 7.92797e10 + 7.92797e10i 0.823648 + 0.823648i 0.986629 0.162982i \(-0.0521111\pi\)
−0.162982 + 0.986629i \(0.552111\pi\)
\(558\) −2.48973e10 + 5.59837e9i −0.256812 + 0.0577464i
\(559\) 4.36006e10i 0.446524i
\(560\) −2.93155e10 2.94190e11i −0.298089 2.99141i
\(561\) 5.10621e10 0.515522
\(562\) −3.41929e10 1.52064e11i −0.342761 1.52434i
\(563\) −4.39922e10 + 4.39922e10i −0.437867 + 0.437867i −0.891294 0.453427i \(-0.850201\pi\)
0.453427 + 0.891294i \(0.350201\pi\)
\(564\) 7.42836e10 + 2.65311e10i 0.734136 + 0.262204i
\(565\) 2.05544e11 2.05544e11i 2.01703 2.01703i
\(566\) −5.38862e10 3.41015e10i −0.525064 0.332282i
\(567\) −1.90417e10 −0.184236
\(568\) −1.00490e11 + 7.85622e10i −0.965450 + 0.754780i
\(569\) 6.41694e9i 0.0612180i −0.999531 0.0306090i \(-0.990255\pi\)
0.999531 0.0306090i \(-0.00974467\pi\)
\(570\) 6.78108e10 + 4.29135e10i 0.642391 + 0.406532i
\(571\) −1.40094e10 1.40094e10i −0.131788 0.131788i 0.638136 0.769924i \(-0.279706\pi\)
−0.769924 + 0.638136i \(0.779706\pi\)
\(572\) 2.53546e10 + 5.35285e10i 0.236850 + 0.500036i
\(573\) −5.59352e10 5.59352e10i −0.518879 0.518879i
\(574\) 4.70544e10 + 2.09262e11i 0.433464 + 1.92772i
\(575\) 1.52928e11i 1.39900i
\(576\) −3.56074e10 8.85420e9i −0.323482 0.0804376i
\(577\) −9.70585e10 −0.875650 −0.437825 0.899060i \(-0.644251\pi\)
−0.437825 + 0.899060i \(0.644251\pi\)
\(578\) 4.21059e10 9.46787e9i 0.377252 0.0848284i
\(579\) −3.56798e10 + 3.56798e10i −0.317474 + 0.317474i
\(580\) −3.11906e11 + 1.47739e11i −2.75621 + 1.30552i
\(581\) 1.66870e11 1.66870e11i 1.46445 1.46445i
\(582\) −6.03123e10 + 9.53039e10i −0.525671 + 0.830651i
\(583\) 1.01019e11 0.874438
\(584\) 2.09497e10 + 2.67971e10i 0.180106 + 0.230376i
\(585\) 3.43480e10i 0.293277i
\(586\) 4.16877e9 6.58739e9i 0.0353523 0.0558628i
\(587\) −7.24852e10 7.24852e10i −0.610516 0.610516i 0.332565 0.943080i \(-0.392086\pi\)
−0.943080 + 0.332565i \(0.892086\pi\)
\(588\) −4.06090e10 + 1.13700e11i −0.339713 + 0.951152i
\(589\) −4.88077e10 4.88077e10i −0.405534 0.405534i
\(590\) 1.11173e10 2.49983e9i 0.0917473 0.0206301i
\(591\) 2.87574e10i 0.235722i
\(592\) 6.63657e9 + 6.65999e10i 0.0540327 + 0.542234i
\(593\) 4.74436e10 0.383671 0.191835 0.981427i \(-0.438556\pi\)
0.191835 + 0.981427i \(0.438556\pi\)
\(594\) 5.99271e9 + 2.66510e10i 0.0481368 + 0.214076i
\(595\) 2.08651e11 2.08651e11i 1.66477 1.66477i
\(596\) −7.74998e10 + 2.16989e11i −0.614208 + 1.71970i
\(597\) −2.01997e10 + 2.01997e10i −0.159019 + 0.159019i
\(598\) 3.20770e10 + 2.02997e10i 0.250836 + 0.158739i
\(599\) −1.68278e11 −1.30714 −0.653568 0.756867i \(-0.726729\pi\)
−0.653568 + 0.756867i \(0.726729\pi\)
\(600\) −1.69861e11 2.08022e10i −1.31066 0.160511i
\(601\) 1.94924e10i 0.149406i −0.997206 0.0747030i \(-0.976199\pi\)
0.997206 0.0747030i \(-0.0238009\pi\)
\(602\) −1.69322e11 1.07154e11i −1.28922 0.815873i
\(603\) −2.10230e10 2.10230e10i −0.159010 0.159010i
\(604\) 1.17773e11 5.57851e10i 0.884908 0.419151i
\(605\) 5.15159e10 + 5.15159e10i 0.384521 + 0.384521i
\(606\) 5.74301e9 + 2.55406e10i 0.0425842 + 0.189382i
\(607\) 1.90357e11i 1.40221i −0.713058 0.701105i \(-0.752690\pi\)
0.713058 0.701105i \(-0.247310\pi\)
\(608\) −3.12663e10 9.41913e10i −0.228803 0.689281i
\(609\) 2.21506e11 1.61034
\(610\) −1.43455e11 + 3.22571e10i −1.03609 + 0.232973i
\(611\) −6.45731e10 + 6.45731e10i −0.463326 + 0.463326i
\(612\) −1.56765e10 3.30961e10i −0.111749 0.235923i
\(613\) 9.96007e10 9.96007e10i 0.705376 0.705376i −0.260183 0.965559i \(-0.583783\pi\)
0.965559 + 0.260183i \(0.0837830\pi\)
\(614\) −2.51825e10 + 3.97927e10i −0.177184 + 0.279982i
\(615\) 1.78436e11 1.24733
\(616\) 2.70189e11 + 3.30890e10i 1.87648 + 0.229806i
\(617\) 2.24596e11i 1.54975i −0.632114 0.774875i \(-0.717813\pi\)
0.632114 0.774875i \(-0.282187\pi\)
\(618\) 2.00829e10 3.17344e10i 0.137680 0.217559i
\(619\) 1.11621e11 + 1.11621e11i 0.760298 + 0.760298i 0.976376 0.216078i \(-0.0693266\pi\)
−0.216078 + 0.976376i \(0.569327\pi\)
\(620\) 1.99228e11 + 7.11561e10i 1.34829 + 0.481554i
\(621\) 1.23795e10 + 1.23795e10i 0.0832411 + 0.0832411i
\(622\) −1.32561e10 + 2.98076e9i −0.0885637 + 0.0199143i
\(623\) 7.94721e10i 0.527548i
\(624\) 2.69106e10 3.28674e10i 0.177495 0.216784i
\(625\) −2.96580e11 −1.94367
\(626\) −1.58580e10 7.05244e10i −0.103265 0.459243i
\(627\) −5.22457e10 + 5.22457e10i −0.338049 + 0.338049i
\(628\) −1.57310e11 5.61850e10i −1.01139 0.361228i
\(629\) −4.72353e10 + 4.72353e10i −0.301762 + 0.301762i
\(630\) 1.33390e11 + 8.44147e10i 0.846761 + 0.535866i
\(631\) 1.57220e10 0.0991724 0.0495862 0.998770i \(-0.484210\pi\)
0.0495862 + 0.998770i \(0.484210\pi\)
\(632\) 2.86137e10 + 3.66001e10i 0.179352 + 0.229411i
\(633\) 1.12314e11i 0.699551i
\(634\) 3.10869e10 + 1.96731e10i 0.192407 + 0.121763i
\(635\) 2.53635e11 + 2.53635e11i 1.55996 + 1.55996i
\(636\) −3.10137e10 6.54758e10i −0.189550 0.400177i
\(637\) −9.88367e10 9.88367e10i −0.600289 0.600289i
\(638\) −6.97112e10 3.10023e11i −0.420746 1.87116i
\(639\) 6.81062e10i 0.408491i
\(640\) 2.10183e11 + 2.19878e11i 1.25279 + 1.31057i
\(641\) −2.97629e11 −1.76296 −0.881482 0.472218i \(-0.843453\pi\)
−0.881482 + 0.472218i \(0.843453\pi\)
\(642\) −1.41125e11 + 3.17332e10i −0.830739 + 0.186799i
\(643\) −8.65912e10 + 8.65912e10i −0.506559 + 0.506559i −0.913468 0.406910i \(-0.866606\pi\)
0.406910 + 0.913468i \(0.366606\pi\)
\(644\) 1.57667e11 7.46814e10i 0.916636 0.434179i
\(645\) −1.17874e11 + 1.17874e11i −0.681052 + 0.681052i
\(646\) 5.29696e10 8.37011e10i 0.304156 0.480619i
\(647\) 1.13405e11 0.647165 0.323582 0.946200i \(-0.395113\pi\)
0.323582 + 0.946200i \(0.395113\pi\)
\(648\) 1.54342e10 1.20663e10i 0.0875353 0.0684343i
\(649\) 1.04915e10i 0.0591370i
\(650\) 1.05946e11 1.67413e11i 0.593515 0.937857i
\(651\) −9.60091e10 9.60091e10i −0.534550 0.534550i
\(652\) −2.40985e10 + 6.74727e10i −0.133352 + 0.373368i
\(653\) −3.13157e10 3.13157e10i −0.172230 0.172230i 0.615728 0.787959i \(-0.288862\pi\)
−0.787959 + 0.615728i \(0.788862\pi\)
\(654\) 3.32869e10 7.48483e9i 0.181954 0.0409139i
\(655\) 2.48720e11i 1.35128i
\(656\) −1.70744e11 1.39799e11i −0.922000 0.754900i
\(657\) −1.81615e10 −0.0974741
\(658\) 9.20716e10 + 4.09465e11i 0.491159 + 2.18430i
\(659\) −1.43093e10 + 1.43093e10i −0.0758713 + 0.0758713i −0.744024 0.668153i \(-0.767085\pi\)
0.668153 + 0.744024i \(0.267085\pi\)
\(660\) 7.61682e10 2.13261e11i 0.401419 1.12392i
\(661\) −1.06672e11 + 1.06672e11i −0.558787 + 0.558787i −0.928962 0.370175i \(-0.879298\pi\)
0.370175 + 0.928962i \(0.379298\pi\)
\(662\) −4.61292e10 2.91925e10i −0.240184 0.151999i
\(663\) 4.23969e10 0.219422
\(664\) −2.95141e10 + 2.40998e11i −0.151830 + 1.23977i
\(665\) 4.26975e11i 2.18331i
\(666\) −3.01973e10 1.91101e10i −0.153487 0.0971330i
\(667\) −1.44007e11 1.44007e11i −0.727580 0.727580i
\(668\) 6.53652e10 3.09613e10i 0.328277 0.155494i
\(669\) −7.94229e9 7.94229e9i −0.0396498 0.0396498i
\(670\) 5.40709e10 + 2.40467e11i 0.268327 + 1.19332i
\(671\) 1.35380e11i 0.667827i
\(672\) −6.15035e10 1.85283e11i −0.301594 0.908569i
\(673\) 3.05808e11 1.49070 0.745348 0.666676i \(-0.232283\pi\)
0.745348 + 0.666676i \(0.232283\pi\)
\(674\) −7.91516e10 + 1.77979e10i −0.383548 + 0.0862441i
\(675\) 6.46101e10 6.46101e10i 0.311233 0.311233i
\(676\) −6.83412e10 1.44281e11i −0.327262 0.690913i
\(677\) 8.02090e10 8.02090e10i 0.381829 0.381829i −0.489932 0.871761i \(-0.662978\pi\)
0.871761 + 0.489932i \(0.162978\pi\)
\(678\) 1.02644e11 1.62196e11i 0.485754 0.767576i
\(679\) −6.00088e11 −2.82316
\(680\) −3.69038e10 + 3.01339e11i −0.172598 + 1.40935i
\(681\) 1.08949e11i 0.506564i
\(682\) −1.04160e11 + 1.64591e11i −0.481464 + 0.760797i
\(683\) −2.01790e11 2.01790e11i −0.927295 0.927295i 0.0702357 0.997530i \(-0.477625\pi\)
−0.997530 + 0.0702357i \(0.977625\pi\)
\(684\) 4.99031e10 + 1.78234e10i 0.227983 + 0.0814264i
\(685\) 7.20500e10 + 7.20500e10i 0.327244 + 0.327244i
\(686\) −2.68471e11 + 6.03679e10i −1.21227 + 0.272590i
\(687\) 5.31085e10i 0.238417i
\(688\) 2.05144e11 2.04422e10i 0.915598 0.0912377i
\(689\) 8.38763e10 0.372188
\(690\) −3.18401e10 1.41601e11i −0.140468 0.624696i
\(691\) 5.60772e10 5.60772e10i 0.245966 0.245966i −0.573347 0.819313i \(-0.694355\pi\)
0.819313 + 0.573347i \(0.194355\pi\)
\(692\) 2.05680e11 + 7.34607e10i 0.896950 + 0.320355i
\(693\) −1.02772e11 + 1.02772e11i −0.445596 + 0.445596i
\(694\) 3.18452e10 + 2.01530e10i 0.137280 + 0.0868763i
\(695\) 5.48386e11 2.35043
\(696\) −1.79541e11 + 1.40363e11i −0.765113 + 0.598159i
\(697\) 2.20250e11i 0.933220i
\(698\) 3.91190e11 + 2.47562e11i 1.64803 + 1.04295i
\(699\) 1.04423e10 + 1.04423e10i 0.0437409 + 0.0437409i
\(700\) −3.89770e11 8.22879e11i −1.62337 3.42724i
\(701\) 2.91810e11 + 2.91810e11i 1.20845 + 1.20845i 0.971529 + 0.236922i \(0.0761385\pi\)
0.236922 + 0.971529i \(0.423862\pi\)
\(702\) 4.97576e9 + 2.21284e10i 0.0204885 + 0.0911175i
\(703\) 9.66604e10i 0.395756i
\(704\) −2.39968e11 + 1.44392e11i −0.976929 + 0.587833i
\(705\) 3.49147e11 1.41336
\(706\) 4.62369e10 1.03968e10i 0.186110 0.0418484i
\(707\) −9.84895e10 + 9.84895e10i −0.394196 + 0.394196i
\(708\) 6.80012e9 3.22098e9i 0.0270635 0.0128190i
\(709\) 1.27769e11 1.27769e11i 0.505641 0.505641i −0.407545 0.913185i \(-0.633615\pi\)
0.913185 + 0.407545i \(0.133615\pi\)
\(710\) −3.01925e11 + 4.77093e11i −1.18813 + 1.87746i
\(711\) −2.48054e10 −0.0970661
\(712\) −5.03596e10 6.44157e10i −0.195958 0.250652i
\(713\) 1.24836e11i 0.483039i
\(714\) 1.04196e11 1.64648e11i 0.400920 0.633523i
\(715\) 1.85383e11 + 1.85383e11i 0.709326 + 0.709326i
\(716\) 9.55499e9 2.67527e10i 0.0363562 0.101793i
\(717\) −1.71095e11 1.71095e11i −0.647383 0.647383i
\(718\) −5.35587e10 + 1.20431e10i −0.201527 + 0.0453149i
\(719\) 2.93251e11i 1.09730i −0.836053 0.548649i \(-0.815142\pi\)
0.836053 0.548649i \(-0.184858\pi\)
\(720\) −1.61610e11 + 1.61042e10i −0.601366 + 0.0599250i
\(721\) 1.99818e11 0.739424
\(722\) −2.81700e10 1.25279e11i −0.103666 0.461029i
\(723\) −1.61581e11 + 1.61581e11i −0.591340 + 0.591340i
\(724\) 1.77942e11 4.98215e11i 0.647628 1.81327i
\(725\) −7.51588e11 + 7.51588e11i −2.72037 + 2.72037i
\(726\) 4.06514e10 + 2.57259e10i 0.146329 + 0.0926028i
\(727\) −2.13676e11 −0.764922 −0.382461 0.923972i \(-0.624923\pi\)
−0.382461 + 0.923972i \(0.624923\pi\)
\(728\) 2.24338e11 + 2.74739e10i 0.798690 + 0.0978124i
\(729\) 1.04604e10i 0.0370370i
\(730\) 1.27224e11 + 8.05124e10i 0.447998 + 0.283512i
\(731\) 1.45496e11 + 1.45496e11i 0.509544 + 0.509544i
\(732\) −8.77469e10 + 4.15627e10i −0.305624 + 0.144764i
\(733\) 7.06655e10 + 7.06655e10i 0.244789 + 0.244789i 0.818828 0.574039i \(-0.194624\pi\)
−0.574039 + 0.818828i \(0.694624\pi\)
\(734\) −1.88970e10 8.40396e10i −0.0651041 0.289534i
\(735\) 5.34411e11i 1.83116i
\(736\) −8.04722e10 + 1.60442e11i −0.274242 + 0.546774i
\(737\) −2.26930e11 −0.769169
\(738\) 1.14956e11 2.58488e10i 0.387531 0.0871395i
\(739\) −1.92162e11 + 1.92162e11i −0.644302 + 0.644302i −0.951610 0.307308i \(-0.900572\pi\)
0.307308 + 0.951610i \(0.400572\pi\)
\(740\) 1.26818e11 + 2.67738e11i 0.422917 + 0.892860i
\(741\) −4.33797e10 + 4.33797e10i −0.143884 + 0.143884i
\(742\) 2.06137e11 3.25732e11i 0.680048 1.07459i
\(743\) 1.66823e11 0.547395 0.273697 0.961816i \(-0.411753\pi\)
0.273697 + 0.961816i \(0.411753\pi\)
\(744\) 1.38658e11 + 1.69809e10i 0.452537 + 0.0554205i
\(745\) 1.01989e12i 3.31077i
\(746\) −1.16350e11 + 1.83853e11i −0.375673 + 0.593629i
\(747\) −9.16684e10 9.16684e10i −0.294400 0.294400i
\(748\) −2.63235e11 9.40169e10i −0.840886 0.300331i
\(749\) −5.44207e11 5.44207e11i −1.72917 1.72917i
\(750\) −4.15897e11 + 9.35180e10i −1.31444 + 0.295563i
\(751\) 8.99062e9i 0.0282638i 0.999900 + 0.0141319i \(0.00449847\pi\)
−0.999900 + 0.0141319i \(0.995502\pi\)
\(752\) −3.34096e11 2.73546e11i −1.04472 0.855380i
\(753\) −2.07469e11 −0.645319
\(754\) −5.78814e10 2.57413e11i −0.179083 0.796424i
\(755\) 4.07878e11 4.07878e11i 1.25529 1.25529i
\(756\) 9.81638e10 + 3.50601e10i 0.300514 + 0.107331i
\(757\) 3.36371e11 3.36371e11i 1.02432 1.02432i 0.0246204 0.999697i \(-0.492162\pi\)
0.999697 0.0246204i \(-0.00783769\pi\)
\(758\) −2.29006e11 1.44924e11i −0.693696 0.439000i
\(759\) 1.33630e11 0.402657
\(760\) −2.70564e11 3.46083e11i −0.810991 1.03735i
\(761\) 2.12823e11i 0.634571i −0.948330 0.317286i \(-0.897229\pi\)
0.948330 0.317286i \(-0.102771\pi\)
\(762\) 2.00144e11 + 1.26660e11i 0.593640 + 0.375680i
\(763\) 1.28361e11 + 1.28361e11i 0.378734 + 0.378734i
\(764\) 1.85367e11 + 3.91346e11i 0.544076 + 1.14865i
\(765\) −1.14620e11 1.14620e11i −0.334669 0.334669i
\(766\) −9.88811e10 4.39748e11i −0.287209 1.27729i
\(767\) 8.71113e9i 0.0251706i
\(768\) 1.67261e11 + 1.11207e11i 0.480783 + 0.319658i
\(769\) −4.57027e11 −1.30688 −0.653442 0.756977i \(-0.726676\pi\)
−0.653442 + 0.756977i \(0.726676\pi\)
\(770\) 1.17553e12 2.64329e11i 3.34405 0.751937i
\(771\) 4.45080e10 4.45080e10i 0.125956 0.125956i
\(772\) 2.49631e11 1.18242e11i 0.702797 0.332891i
\(773\) 1.35987e10 1.35987e10i 0.0380872 0.0380872i −0.687807 0.725894i \(-0.741426\pi\)
0.725894 + 0.687807i \(0.241426\pi\)
\(774\) −5.88638e10 + 9.30151e10i −0.164015 + 0.259173i
\(775\) 6.51533e11 1.80605
\(776\) 4.86398e11 3.80262e11i 1.34136 1.04866i
\(777\) 1.90140e11i 0.521661i
\(778\) −3.02294e11 + 4.77677e11i −0.825109 + 1.30381i
\(779\) 2.25355e11 + 2.25355e11i 0.611952 + 0.611952i
\(780\) 6.32426e10 1.77071e11i 0.170856 0.478375i
\(781\) −3.67582e11 3.67582e11i −0.987985 0.987985i
\(782\) −1.74782e11 + 3.93013e10i −0.467380 + 0.105094i
\(783\) 1.21682e11i 0.323727i
\(784\) 4.18694e11 5.11374e11i 1.10824 1.35355i
\(785\) −7.39390e11 −1.94713
\(786\) 3.60302e10 + 1.60235e11i 0.0944011 + 0.419825i
\(787\) −3.61195e11 + 3.61195e11i −0.941548 + 0.941548i −0.998384 0.0568352i \(-0.981899\pi\)
0.0568352 + 0.998384i \(0.481899\pi\)
\(788\) 5.29489e10 1.48250e11i 0.137326 0.384494i
\(789\) 2.86811e11 2.86811e11i 0.740095 0.740095i
\(790\) 1.73765e11 + 1.09966e11i 0.446123 + 0.282325i
\(791\) 1.02128e12 2.60878
\(792\) 1.81771e10 1.48425e11i 0.0461980 0.377231i
\(793\) 1.12406e11i 0.284248i
\(794\) −5.83922e11 3.69530e11i −1.46917 0.929754i
\(795\) −2.26760e11 2.26760e11i −0.567672 0.567672i
\(796\) 1.41326e11 6.69413e10i 0.352022 0.166741i
\(797\) 1.92548e10 + 1.92548e10i 0.0477206 + 0.0477206i 0.730564 0.682844i \(-0.239257\pi\)
−0.682844 + 0.730564i \(0.739257\pi\)
\(798\) 6.18529e10 + 2.75075e11i 0.152528 + 0.678328i
\(799\) 4.30964e11i 1.05744i
\(800\) 8.37366e11 + 4.19993e11i 2.04435 + 1.02537i
\(801\) 4.36571e10 0.106053
\(802\) 5.50451e10 1.23774e10i 0.133052 0.0299178i
\(803\) −9.80210e10 + 9.80210e10i −0.235753 + 0.235753i
\(804\) 6.96694e10 + 1.47086e11i 0.166732 + 0.352002i
\(805\) 5.46041e11 5.46041e11i 1.30029 1.30029i
\(806\) −8.64844e10 + 1.36660e11i −0.204926 + 0.323819i
\(807\) 1.60657e10 0.0378797
\(808\) 1.74197e10 1.42241e11i 0.0408690 0.333717i
\(809\) 7.16040e11i 1.67164i 0.549002 + 0.835821i \(0.315008\pi\)
−0.549002 + 0.835821i \(0.684992\pi\)
\(810\) 4.63723e10 7.32762e10i 0.107725 0.170225i
\(811\) 4.67294e11 + 4.67294e11i 1.08021 + 1.08021i 0.996490 + 0.0837178i \(0.0266794\pi\)
0.0837178 + 0.996490i \(0.473321\pi\)
\(812\) −1.14191e12 4.07843e11i −2.62668 0.938143i
\(813\) 1.33338e11 + 1.33338e11i 0.305206 + 0.305206i
\(814\) −2.66122e11 + 5.98397e10i −0.606154 + 0.136299i
\(815\) 3.17135e11i 0.718809i
\(816\) 1.98779e10 + 1.99481e11i 0.0448342 + 0.449925i
\(817\) −2.97737e11 −0.668259
\(818\) −2.95868e10 1.31580e11i −0.0660822 0.293884i
\(819\) −8.53317e10 + 8.53317e10i −0.189659 + 0.189659i
\(820\) −9.19874e11 3.28542e11i −2.03457 0.726667i
\(821\) 1.95092e11 1.95092e11i 0.429404 0.429404i −0.459021 0.888425i \(-0.651800\pi\)
0.888425 + 0.459021i \(0.151800\pi\)
\(822\) 5.68550e10 + 3.59802e10i 0.124532 + 0.0788091i
\(823\) 1.72562e11 0.376137 0.188069 0.982156i \(-0.439777\pi\)
0.188069 + 0.982156i \(0.439777\pi\)
\(824\) −1.61961e11 + 1.26620e11i −0.351320 + 0.274659i
\(825\) 6.97426e11i 1.50551i
\(826\) 3.38295e10 + 2.14087e10i 0.0726733 + 0.0459907i
\(827\) −3.54772e11 3.54772e11i −0.758451 0.758451i 0.217590 0.976040i \(-0.430181\pi\)
−0.976040 + 0.217590i \(0.930181\pi\)
\(828\) −4.10254e10 8.66125e10i −0.0872833 0.184272i
\(829\) −6.18736e11 6.18736e11i −1.31005 1.31005i −0.921377 0.388671i \(-0.872934\pi\)
−0.388671 0.921377i \(-0.627066\pi\)
\(830\) 2.35771e11 + 1.04853e12i 0.496795 + 2.20937i
\(831\) 4.42372e9i 0.00927648i
\(832\) −1.99246e11 + 1.19889e11i −0.415811 + 0.250200i
\(833\) 6.59641e11 1.37002
\(834\) 3.53293e11 7.94408e10i 0.730248 0.164202i
\(835\) 2.26377e11 2.26377e11i 0.465678 0.465678i
\(836\) 3.65533e11 1.73140e11i 0.748344 0.354465i
\(837\) −5.27415e10 + 5.27415e10i −0.107461 + 0.107461i
\(838\) −2.46195e10 + 3.89031e10i −0.0499233 + 0.0788875i
\(839\) −3.78850e11 −0.764574 −0.382287 0.924044i \(-0.624863\pi\)
−0.382287 + 0.924044i \(0.624863\pi\)
\(840\) −5.32224e11 6.80776e11i −1.06900 1.36737i
\(841\) 9.15239e11i 1.82958i
\(842\) 2.32060e11 3.66695e11i 0.461692 0.729554i
\(843\) −3.22127e11 3.22127e11i −0.637848 0.637848i
\(844\) −2.06796e11 + 5.79001e11i −0.407542 + 1.14106i
\(845\) −4.99684e11 4.99684e11i −0.980096 0.980096i
\(846\) 2.24935e11 5.05785e10i 0.439112 0.0987380i
\(847\) 2.55964e11i 0.497331i
\(848\) 3.93256e10 + 3.94644e11i 0.0760487 + 0.763171i
\(849\) −1.86390e11 −0.358749
\(850\) 2.05117e11 + 9.12207e11i 0.392941 + 1.74750i
\(851\) −1.23615e11 + 1.23615e11i −0.235696 + 0.235696i
\(852\) −1.25399e11 + 3.51101e11i −0.237977 + 0.666305i
\(853\) 3.72573e11 3.72573e11i 0.703746 0.703746i −0.261467 0.965213i \(-0.584206\pi\)
0.965213 + 0.261467i \(0.0842062\pi\)
\(854\) −4.36527e11 2.76252e11i −0.820690 0.519367i
\(855\) 2.34554e11 0.438913
\(856\) 7.85956e11 + 9.62529e10i 1.46387 + 0.179275i
\(857\) 4.90767e11i 0.909812i 0.890539 + 0.454906i \(0.150327\pi\)
−0.890539 + 0.454906i \(0.849673\pi\)
\(858\) 1.46286e11 + 9.25762e10i 0.269932 + 0.170825i
\(859\) −8.37729e10 8.37729e10i −0.153862 0.153862i 0.625978 0.779840i \(-0.284700\pi\)
−0.779840 + 0.625978i \(0.784700\pi\)
\(860\) 8.24699e11 3.90632e11i 1.50765 0.714124i
\(861\) 4.43293e11 + 4.43293e11i 0.806638 + 0.806638i
\(862\) −1.89893e11 8.44500e11i −0.343938 1.52957i
\(863\) 2.69969e11i 0.486710i 0.969937 + 0.243355i \(0.0782480\pi\)
−0.969937 + 0.243355i \(0.921752\pi\)
\(864\) −1.01783e11 + 3.37863e10i −0.182650 + 0.0606297i
\(865\) 9.66738e11 1.72681
\(866\) −7.33097e11 + 1.64843e11i −1.30344 + 0.293089i
\(867\) 8.91956e10 8.91956e10i 0.157858 0.157858i
\(868\) 3.18171e11 + 6.71720e11i 0.560508 + 1.18334i
\(869\) −1.33879e11 + 1.33879e11i −0.234766 + 0.234766i
\(870\) −5.39433e11 + 8.52398e11i −0.941588 + 1.48787i
\(871\) −1.88420e11 −0.327382
\(872\) −1.85382e11 2.27030e10i −0.320627 0.0392660i
\(873\) 3.29651e11i 0.567542i
\(874\) 1.38621e11 2.19046e11i 0.237566 0.375396i
\(875\) −1.60378e12 1.60378e12i −2.73599 2.73599i
\(876\) 9.36259e10 + 3.34394e10i 0.158994 + 0.0567861i
\(877\) −7.12189e10 7.12189e10i −0.120392 0.120392i 0.644344 0.764736i \(-0.277131\pi\)
−0.764736 + 0.644344i \(0.777131\pi\)
\(878\) 1.32076e11 2.96984e10i 0.222252 0.0499752i
\(879\) 2.27854e10i 0.0381682i
\(880\) −7.85324e11 + 9.59158e11i −1.30954 + 1.59941i
\(881\) 4.16453e11 0.691293 0.345647 0.938365i \(-0.387660\pi\)
0.345647 + 0.938365i \(0.387660\pi\)
\(882\) 7.74163e10 + 3.44289e11i 0.127926 + 0.568917i
\(883\) −1.84941e11 + 1.84941e11i −0.304222 + 0.304222i −0.842663 0.538441i \(-0.819013\pi\)
0.538441 + 0.842663i \(0.319013\pi\)
\(884\) −2.18564e11 7.80624e10i −0.357907 0.127830i
\(885\) 2.35506e10 2.35506e10i 0.0383909 0.0383909i
\(886\) −6.26005e10 3.96162e10i −0.101588 0.0642892i
\(887\) 3.78005e11 0.610665 0.305333 0.952246i \(-0.401232\pi\)
0.305333 + 0.952246i \(0.401232\pi\)
\(888\) 1.20487e11 + 1.54117e11i 0.193771 + 0.247855i
\(889\) 1.26022e12i 2.01762i
\(890\) −3.05824e11 1.93538e11i −0.487429 0.308466i
\(891\) 5.64566e10 + 5.64566e10i 0.0895785 + 0.0895785i
\(892\) 2.63205e10 + 5.55677e10i 0.0415752 + 0.0877734i
\(893\) 4.40953e11 + 4.40953e11i 0.693405 + 0.693405i
\(894\) 1.47744e11 + 6.57056e11i 0.231292 + 1.02861i
\(895\) 1.25743e11i 0.195971i
\(896\) −2.40849e10 + 1.06841e12i −0.0373691 + 1.65770i
\(897\) 1.10953e11 0.171383
\(898\) −1.02945e11 + 2.31481e10i −0.158307 + 0.0355967i
\(899\) 6.13525e11 6.13525e11i 0.939276 0.939276i
\(900\) −4.52040e11 + 2.14116e11i −0.688980 + 0.326346i
\(901\) −2.79897e11 + 2.79897e11i −0.424716 + 0.424716i
\(902\) 4.80928e11 7.59950e11i 0.726531 1.14805i
\(903\) −5.85676e11 −0.880859
\(904\) −8.27792e11 + 6.47160e11i −1.23950 + 0.969032i
\(905\) 2.34171e12i 3.49091i
\(906\) 2.03685e11 3.21858e11i 0.302306 0.477697i
\(907\) 3.65228e11 + 3.65228e11i 0.539678 + 0.539678i 0.923434 0.383756i \(-0.125370\pi\)
−0.383756 + 0.923434i \(0.625370\pi\)
\(908\) −2.00600e11 + 5.61653e11i −0.295112 + 0.826275i
\(909\) 5.41041e10 + 5.41041e10i 0.0792455 + 0.0792455i
\(910\) 9.76048e11 2.19473e11i 1.42333 0.320048i
\(911\) 3.25867e11i 0.473116i −0.971617 0.236558i \(-0.923981\pi\)
0.971617 0.236558i \(-0.0760193\pi\)
\(912\) −2.24443e11 1.83766e11i −0.324435 0.265635i
\(913\) −9.89504e11 −1.42408
\(914\) −6.95383e10 3.09254e11i −0.0996413 0.443129i
\(915\) −3.03890e11 + 3.03890e11i −0.433543 + 0.433543i
\(916\) 9.77848e10 2.73785e11i 0.138896 0.388890i
\(917\) −6.17900e11 + 6.17900e11i −0.873858 + 0.873858i
\(918\) −9.04473e10 5.72388e10i −0.127358 0.0805972i
\(919\) 5.29328e11 0.742101 0.371050 0.928613i \(-0.378998\pi\)
0.371050 + 0.928613i \(0.378998\pi\)
\(920\) −9.65772e10 + 7.88604e11i −0.134810 + 1.10080i
\(921\) 1.37641e11i 0.191298i
\(922\) −6.04968e11 3.82849e11i −0.837160 0.529790i
\(923\) −3.05204e11 3.05204e11i −0.420517 0.420517i
\(924\) 7.19035e11 3.40583e11i 0.986421 0.467234i
\(925\) 6.45159e11 + 6.45159e11i 0.881251 + 0.881251i
\(926\) −2.23537e10 9.94125e10i −0.0304023 0.135206i
\(927\) 1.09768e11i 0.148647i
\(928\) 1.18401e12 3.93025e11i 1.59648 0.529941i
\(929\) 1.24439e12 1.67069 0.835343 0.549729i \(-0.185269\pi\)
0.835343 + 0.549729i \(0.185269\pi\)
\(930\) 6.03272e11 1.35651e11i 0.806458 0.181339i
\(931\) −6.74931e11 + 6.74931e11i −0.898381 + 0.898381i
\(932\) −3.46055e10 7.30588e10i −0.0458650 0.0968298i
\(933\) −2.80813e10 + 2.80813e10i −0.0370588 + 0.0370588i
\(934\) −5.74311e11 + 9.07510e11i −0.754674 + 1.19252i
\(935\) −1.23726e12 −1.61887
\(936\) 1.50925e10 1.23238e11i 0.0196633 0.160561i
\(937\) 3.39899e11i 0.440953i −0.975392 0.220476i \(-0.929239\pi\)
0.975392 0.220476i \(-0.0707612\pi\)
\(938\) −4.63067e11 + 7.31726e11i −0.598181 + 0.945230i
\(939\) −1.49396e11 1.49396e11i −0.192166 0.192166i
\(940\) −1.79992e12 6.42860e11i −2.30538 0.823389i
\(941\) −7.13191e11 7.13191e11i −0.909594 0.909594i 0.0866452 0.996239i \(-0.472385\pi\)
−0.996239 + 0.0866452i \(0.972385\pi\)
\(942\) −4.76345e11 + 1.07110e11i −0.604948 + 0.136028i
\(943\) 5.76394e11i 0.728908i
\(944\) −4.09865e10 + 4.08423e9i −0.0516123 + 0.00514307i
\(945\) 4.61389e11 0.578549
\(946\) 1.84321e11 + 8.19720e11i 0.230149 + 1.02353i
\(947\) −5.92201e10 + 5.92201e10i −0.0736324 + 0.0736324i −0.742964 0.669331i \(-0.766581\pi\)
0.669331 + 0.742964i \(0.266581\pi\)
\(948\) 1.27877e11 + 4.56724e10i 0.158328 + 0.0565484i
\(949\) −8.13870e10 + 8.13870e10i −0.100344 + 0.100344i
\(950\) −1.14322e12 7.23480e11i −1.40358 0.888244i
\(951\) 1.07528e11 0.131462
\(952\) −8.40304e11 + 6.56942e11i −1.02303 + 0.799796i
\(953\) 4.97584e11i 0.603246i −0.953427 0.301623i \(-0.902472\pi\)
0.953427 0.301623i \(-0.0975284\pi\)
\(954\) −1.78937e11 1.13239e11i −0.216026 0.136710i
\(955\) 1.35533e12 + 1.35533e12i 1.62942 + 1.62942i
\(956\) 5.67004e11 + 1.19705e12i 0.678820 + 1.43312i
\(957\) −6.56741e11 6.56741e11i −0.782972 0.782972i
\(958\) −2.88512e11 1.28308e12i −0.342532 1.52332i
\(959\) 3.57991e11i 0.423251i
\(960\) 8.62783e11 + 2.14541e11i 1.01582 + 0.252595i
\(961\) 3.21042e11 0.376416
\(962\) −2.20961e11 + 4.96850e10i −0.257998 + 0.0580130i
\(963\) −2.98954e11 + 2.98954e11i −0.347616 + 0.347616i
\(964\) 1.13049e12 5.35475e11i 1.30906 0.620056i
\(965\) 8.64537e11 8.64537e11i 0.996953 0.996953i
\(966\) 2.72681e11 4.30883e11i 0.313145 0.494824i
\(967\) −2.45981e11 −0.281317 −0.140658 0.990058i \(-0.544922\pi\)
−0.140658 + 0.990058i \(0.544922\pi\)
\(968\) −1.62199e11 2.07471e11i −0.184734 0.236295i
\(969\) 2.89518e11i 0.328383i
\(970\) 1.46139e12 2.30925e12i 1.65075 2.60846i
\(971\) −1.86584e10 1.86584e10i −0.0209892 0.0209892i 0.696534 0.717524i \(-0.254724\pi\)
−0.717524 + 0.696534i \(0.754724\pi\)
\(972\) 1.92599e10 5.39252e10i 0.0215769 0.0604124i
\(973\) 1.36237e12 + 1.36237e12i 1.52000 + 1.52000i
\(974\) 1.33043e12 2.99159e11i 1.47828 0.332404i
\(975\) 5.79074e11i 0.640790i
\(976\) 5.28879e11 5.27019e10i 0.582850 0.0580800i
\(977\) 1.11251e12 1.22103 0.610513 0.792007i \(-0.290963\pi\)
0.610513 + 0.792007i \(0.290963\pi\)
\(978\) 4.59411e10 + 2.04311e11i 0.0502164 + 0.223325i
\(979\) 2.35626e11 2.35626e11i 0.256503 0.256503i
\(980\) 9.83972e11 2.75499e12i 1.06679 2.98687i
\(981\) 7.05136e10 7.05136e10i 0.0761372 0.0761372i
\(982\) −5.72343e11 3.62202e11i −0.615475 0.389498i
\(983\) 1.01320e12 1.08513 0.542563 0.840015i \(-0.317454\pi\)
0.542563 + 0.840015i \(0.317454\pi\)
\(984\) −6.40214e11 7.84045e10i −0.682880 0.0836297i
\(985\) 6.96804e11i 0.740228i
\(986\) 1.05214e12 + 6.65840e11i 1.11318 + 0.704470i
\(987\) 8.67395e11 + 8.67395e11i 0.914004 + 0.914004i
\(988\) 3.03503e11 1.43759e11i 0.318518 0.150871i
\(989\) 3.80764e11 + 3.80764e11i 0.397988 + 0.397988i
\(990\) −1.45206e11 6.45766e11i −0.151162 0.672256i
\(991\) 1.38639e12i 1.43744i −0.695300 0.718719i \(-0.744729\pi\)
0.695300 0.718719i \(-0.255271\pi\)
\(992\) −6.83545e11 3.42842e11i −0.705863 0.354036i
\(993\) −1.59559e11 −0.164106
\(994\) −1.93533e12 + 4.35176e11i −1.98248 + 0.445778i
\(995\) 4.89449e11 4.89449e11i 0.499361 0.499361i
\(996\) 3.03786e11 + 6.41351e11i 0.308696 + 0.651716i
\(997\) 6.11758e11 6.11758e11i 0.619155 0.619155i −0.326160 0.945315i \(-0.605755\pi\)
0.945315 + 0.326160i \(0.105755\pi\)
\(998\) −5.46902e11 + 8.64201e11i −0.551300 + 0.871149i
\(999\) −1.04451e11 −0.104870
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 48.9.l.a.19.2 64
4.3 odd 2 192.9.l.a.175.32 64
16.5 even 4 192.9.l.a.79.32 64
16.11 odd 4 inner 48.9.l.a.43.2 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.9.l.a.19.2 64 1.1 even 1 trivial
48.9.l.a.43.2 yes 64 16.11 odd 4 inner
192.9.l.a.79.32 64 16.5 even 4
192.9.l.a.175.32 64 4.3 odd 2