Properties

Label 16.8.e.a.5.8
Level $16$
Weight $8$
Character 16.5
Analytic conductor $4.998$
Analytic rank $0$
Dimension $26$
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] = [16,8,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, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 8 \)
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: \(4.99816040775\)
Analytic rank: \(0\)
Dimension: \(26\)
Relative dimension: \(13\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.8
Character \(\chi\) \(=\) 16.5
Dual form 16.8.e.a.13.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.26019 - 10.4810i) q^{2} +(61.7547 - 61.7547i) q^{3} +(-91.7015 - 89.3019i) q^{4} +(160.824 + 160.824i) q^{5} +(-384.163 - 910.337i) q^{6} +1202.46i q^{7} +(-1326.64 + 580.677i) q^{8} -5440.30i q^{9} +O(q^{10})\) \(q+(4.26019 - 10.4810i) q^{2} +(61.7547 - 61.7547i) q^{3} +(-91.7015 - 89.3019i) q^{4} +(160.824 + 160.824i) q^{5} +(-384.163 - 910.337i) q^{6} +1202.46i q^{7} +(-1326.64 + 580.677i) q^{8} -5440.30i q^{9} +(2370.74 - 1000.45i) q^{10} +(313.790 + 313.790i) q^{11} +(-11177.8 + 148.186i) q^{12} +(-2231.18 + 2231.18i) q^{13} +(12603.0 + 5122.73i) q^{14} +19863.3 q^{15} +(434.333 + 16378.2i) q^{16} +21041.2 q^{17} +(-57019.6 - 23176.7i) q^{18} +(-17903.6 + 17903.6i) q^{19} +(-385.912 - 29109.8i) q^{20} +(74257.9 + 74257.9i) q^{21} +(4625.62 - 1952.02i) q^{22} -33619.9i q^{23} +(-46066.5 + 117786. i) q^{24} -26396.1i q^{25} +(13879.7 + 32890.2i) q^{26} +(-200907. - 200907. i) q^{27} +(107382. - 110268. i) q^{28} +(-4104.39 + 4104.39i) q^{29} +(84621.6 - 208187. i) q^{30} +9133.16 q^{31} +(173510. + 65222.2i) q^{32} +38756.0 q^{33} +(89639.6 - 220532. i) q^{34} +(-193385. + 193385. i) q^{35} +(-485829. + 498883. i) q^{36} +(-104557. - 104557. i) q^{37} +(111375. + 263921. i) q^{38} +275572. i q^{39} +(-306743. - 119968. i) q^{40} +599792. i q^{41} +(1.09465e6 - 461942. i) q^{42} +(79842.5 + 79842.5i) q^{43} +(-752.965 - 56797.0i) q^{44} +(874932. - 874932. i) q^{45} +(-352369. - 143227. i) q^{46} -1.24454e6 q^{47} +(1.03826e6 + 984612. i) q^{48} -622377. q^{49} +(-276657. - 112452. i) q^{50} +(1.29939e6 - 1.29939e6i) q^{51} +(403852. - 5353.91i) q^{52} +(274857. + 274857. i) q^{53} +(-2.96160e6 + 1.24979e6i) q^{54} +100930. i q^{55} +(-698244. - 1.59523e6i) q^{56} +2.21127e6i q^{57} +(25532.5 + 60503.5i) q^{58} +(-1.13722e6 - 1.13722e6i) q^{59} +(-1.82150e6 - 1.77383e6i) q^{60} +(984936. - 984936. i) q^{61} +(38909.0 - 95724.4i) q^{62} +6.54176e6 q^{63} +(1.42278e6 - 1.54070e6i) q^{64} -717657. q^{65} +(165108. - 406201. i) q^{66} +(-2.25153e6 + 2.25153e6i) q^{67} +(-1.92951e6 - 1.87902e6i) q^{68} +(-2.07619e6 - 2.07619e6i) q^{69} +(1.20301e6 + 2.85073e6i) q^{70} +5.48968e6i q^{71} +(3.15906e6 + 7.21730e6i) q^{72} -4.23698e6i q^{73} +(-1.54129e6 + 650425. i) q^{74} +(-1.63008e6 - 1.63008e6i) q^{75} +(3.24062e6 - 42961.3i) q^{76} +(-377321. + 377321. i) q^{77} +(2.88826e6 + 1.17399e6i) q^{78} +3.54577e6 q^{79} +(-2.56417e6 + 2.70387e6i) q^{80} -1.29159e7 q^{81} +(6.28640e6 + 2.55523e6i) q^{82} +(179482. - 179482. i) q^{83} +(-178188. - 1.34409e7i) q^{84} +(3.38394e6 + 3.38394e6i) q^{85} +(1.17697e6 - 496683. i) q^{86} +506931. i q^{87} +(-598496. - 234074. i) q^{88} -262425. i q^{89} +(-5.44276e6 - 1.28975e7i) q^{90} +(-2.68292e6 - 2.68292e6i) q^{91} +(-3.00232e6 + 3.08299e6i) q^{92} +(564016. - 564016. i) q^{93} +(-5.30199e6 + 1.30440e7i) q^{94} -5.75868e6 q^{95} +(1.47429e7 - 6.68730e6i) q^{96} +1.53573e7 q^{97} +(-2.65145e6 + 6.52312e6i) q^{98} +(1.70711e6 - 1.70711e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 26 q - 2 q^{2} - 2 q^{3} - 184 q^{4} - 2 q^{5} - 176 q^{6} - 1004 q^{8} + 12972 q^{10} + 1202 q^{11} - 27356 q^{12} - 2 q^{13} + 22268 q^{14} - 27004 q^{15} + 13336 q^{16} - 4 q^{17} - 29346 q^{18} + 60582 q^{19} + 46204 q^{20} + 4372 q^{21} - 44348 q^{22} - 59216 q^{24} - 35960 q^{26} - 233672 q^{27} + 220312 q^{28} - 51690 q^{29} + 27636 q^{30} + 357488 q^{31} - 248632 q^{32} - 4 q^{33} + 924660 q^{34} - 252004 q^{35} - 1015508 q^{36} + 415574 q^{37} - 5472 q^{38} - 1121976 q^{40} + 124600 q^{42} + 569754 q^{43} - 758620 q^{44} + 151874 q^{45} + 2335660 q^{46} - 2076464 q^{47} + 4141288 q^{48} - 1647090 q^{49} - 787194 q^{50} + 2609508 q^{51} + 410324 q^{52} + 907814 q^{53} - 7404512 q^{54} - 4093160 q^{56} - 1860712 q^{58} - 4865142 q^{59} + 5147328 q^{60} + 2279886 q^{61} + 6274096 q^{62} + 8295108 q^{63} + 10452224 q^{64} - 1426892 q^{65} + 10937812 q^{66} - 5564458 q^{67} - 7403760 q^{68} - 4786076 q^{69} - 22140800 q^{70} - 25293948 q^{72} - 13177044 q^{74} + 6212566 q^{75} + 17814260 q^{76} + 7604308 q^{77} + 37993916 q^{78} - 9598912 q^{79} + 40047272 q^{80} - 5314414 q^{81} + 22858240 q^{82} + 4531198 q^{83} - 30159704 q^{84} + 7377748 q^{85} - 54129468 q^{86} - 59216392 q^{88} - 33515304 q^{90} + 2587652 q^{91} + 21810936 q^{92} - 14504144 q^{93} + 77196112 q^{94} - 4900620 q^{95} + 116940464 q^{96} - 4 q^{97} + 21823866 q^{98} + 18815006 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.26019 10.4810i 0.376551 0.926396i
\(3\) 61.7547 61.7547i 1.32052 1.32052i 0.407171 0.913352i \(-0.366515\pi\)
0.913352 0.407171i \(-0.133485\pi\)
\(4\) −91.7015 89.3019i −0.716418 0.697671i
\(5\) 160.824 + 160.824i 0.575383 + 0.575383i 0.933628 0.358245i \(-0.116625\pi\)
−0.358245 + 0.933628i \(0.616625\pi\)
\(6\) −384.163 910.337i −0.726082 1.72057i
\(7\) 1202.46i 1.32504i 0.749044 + 0.662520i \(0.230513\pi\)
−0.749044 + 0.662520i \(0.769487\pi\)
\(8\) −1326.64 + 580.677i −0.916088 + 0.400977i
\(9\) 5440.30i 2.48756i
\(10\) 2370.74 1000.45i 0.749693 0.316371i
\(11\) 313.790 + 313.790i 0.0710827 + 0.0710827i 0.741754 0.670672i \(-0.233994\pi\)
−0.670672 + 0.741754i \(0.733994\pi\)
\(12\) −11177.8 + 148.186i −1.86734 + 0.0247555i
\(13\) −2231.18 + 2231.18i −0.281665 + 0.281665i −0.833773 0.552108i \(-0.813824\pi\)
0.552108 + 0.833773i \(0.313824\pi\)
\(14\) 12603.0 + 5122.73i 1.22751 + 0.498946i
\(15\) 19863.3 1.51961
\(16\) 434.333 + 16378.2i 0.0265096 + 0.999649i
\(17\) 21041.2 1.03872 0.519361 0.854555i \(-0.326170\pi\)
0.519361 + 0.854555i \(0.326170\pi\)
\(18\) −57019.6 23176.7i −2.30447 0.936695i
\(19\) −17903.6 + 17903.6i −0.598830 + 0.598830i −0.940001 0.341171i \(-0.889177\pi\)
0.341171 + 0.940001i \(0.389177\pi\)
\(20\) −385.912 29109.8i −0.0107866 0.813642i
\(21\) 74257.9 + 74257.9i 1.74975 + 1.74975i
\(22\) 4625.62 1952.02i 0.0926171 0.0390844i
\(23\) 33619.9i 0.576167i −0.957605 0.288084i \(-0.906982\pi\)
0.957605 0.288084i \(-0.0930181\pi\)
\(24\) −46066.5 + 117786.i −0.680215 + 1.73922i
\(25\) 26396.1i 0.337870i
\(26\) 13879.7 + 32890.2i 0.154872 + 0.366995i
\(27\) −200907. 200907.i −1.96436 1.96436i
\(28\) 107382. 110268.i 0.924442 0.949283i
\(29\) −4104.39 + 4104.39i −0.0312504 + 0.0312504i −0.722559 0.691309i \(-0.757034\pi\)
0.691309 + 0.722559i \(0.257034\pi\)
\(30\) 84621.6 208187.i 0.572212 1.40776i
\(31\) 9133.16 0.0550624 0.0275312 0.999621i \(-0.491235\pi\)
0.0275312 + 0.999621i \(0.491235\pi\)
\(32\) 173510. + 65222.2i 0.936052 + 0.351861i
\(33\) 38756.0 0.187733
\(34\) 89639.6 220532.i 0.391132 0.962267i
\(35\) −193385. + 193385.i −0.762405 + 0.762405i
\(36\) −485829. + 498883.i −1.73550 + 1.78213i
\(37\) −104557. 104557.i −0.339349 0.339349i 0.516773 0.856122i \(-0.327133\pi\)
−0.856122 + 0.516773i \(0.827133\pi\)
\(38\) 111375. + 263921.i 0.329263 + 0.780244i
\(39\) 275572.i 0.743891i
\(40\) −306743. 119968.i −0.757816 0.296386i
\(41\) 599792.i 1.35912i 0.733621 + 0.679559i \(0.237829\pi\)
−0.733621 + 0.679559i \(0.762171\pi\)
\(42\) 1.09465e6 461942.i 2.27983 0.962088i
\(43\) 79842.5 + 79842.5i 0.153142 + 0.153142i 0.779520 0.626378i \(-0.215463\pi\)
−0.626378 + 0.779520i \(0.715463\pi\)
\(44\) −752.965 56797.0i −0.00133257 0.100517i
\(45\) 874932. 874932.i 1.43130 1.43130i
\(46\) −352369. 143227.i −0.533759 0.216957i
\(47\) −1.24454e6 −1.74851 −0.874254 0.485469i \(-0.838649\pi\)
−0.874254 + 0.485469i \(0.838649\pi\)
\(48\) 1.03826e6 + 984612.i 1.35507 + 1.28505i
\(49\) −622377. −0.755732
\(50\) −276657. 112452.i −0.313001 0.127225i
\(51\) 1.29939e6 1.29939e6i 1.37166 1.37166i
\(52\) 403852. 5353.91i 0.398300 0.00528031i
\(53\) 274857. + 274857.i 0.253596 + 0.253596i 0.822443 0.568847i \(-0.192610\pi\)
−0.568847 + 0.822443i \(0.692610\pi\)
\(54\) −2.96160e6 + 1.24979e6i −2.55946 + 1.08009i
\(55\) 100930.i 0.0817995i
\(56\) −698244. 1.59523e6i −0.531311 1.21385i
\(57\) 2.21127e6i 1.58154i
\(58\) 25532.5 + 60503.5i 0.0171829 + 0.0407176i
\(59\) −1.13722e6 1.13722e6i −0.720876 0.720876i 0.247908 0.968784i \(-0.420257\pi\)
−0.968784 + 0.247908i \(0.920257\pi\)
\(60\) −1.82150e6 1.77383e6i −1.08868 1.06019i
\(61\) 984936. 984936.i 0.555589 0.555589i −0.372459 0.928048i \(-0.621485\pi\)
0.928048 + 0.372459i \(0.121485\pi\)
\(62\) 38909.0 95724.4i 0.0207338 0.0510096i
\(63\) 6.54176e6 3.29612
\(64\) 1.42278e6 1.54070e6i 0.678434 0.734661i
\(65\) −717657. −0.324131
\(66\) 165108. 406201.i 0.0706911 0.173915i
\(67\) −2.25153e6 + 2.25153e6i −0.914570 + 0.914570i −0.996628 0.0820580i \(-0.973851\pi\)
0.0820580 + 0.996628i \(0.473851\pi\)
\(68\) −1.92951e6 1.87902e6i −0.744159 0.724686i
\(69\) −2.07619e6 2.07619e6i −0.760842 0.760842i
\(70\) 1.20301e6 + 2.85073e6i 0.419204 + 0.993373i
\(71\) 5.48968e6i 1.82030i 0.414278 + 0.910150i \(0.364034\pi\)
−0.414278 + 0.910150i \(0.635966\pi\)
\(72\) 3.15906e6 + 7.21730e6i 0.997456 + 2.27883i
\(73\) 4.23698e6i 1.27476i −0.770552 0.637378i \(-0.780019\pi\)
0.770552 0.637378i \(-0.219981\pi\)
\(74\) −1.54129e6 + 650425.i −0.442153 + 0.186589i
\(75\) −1.63008e6 1.63008e6i −0.446165 0.446165i
\(76\) 3.24062e6 42961.3i 0.846800 0.0112261i
\(77\) −377321. + 377321.i −0.0941875 + 0.0941875i
\(78\) 2.88826e6 + 1.17399e6i 0.689137 + 0.280113i
\(79\) 3.54577e6 0.809125 0.404563 0.914510i \(-0.367424\pi\)
0.404563 + 0.914510i \(0.367424\pi\)
\(80\) −2.56417e6 + 2.70387e6i −0.559927 + 0.590433i
\(81\) −1.29159e7 −2.70040
\(82\) 6.28640e6 + 2.55523e6i 1.25908 + 0.511778i
\(83\) 179482. 179482.i 0.0344546 0.0344546i −0.689670 0.724124i \(-0.742244\pi\)
0.724124 + 0.689670i \(0.242244\pi\)
\(84\) −178188. 1.34409e7i −0.0328021 2.47430i
\(85\) 3.38394e6 + 3.38394e6i 0.597662 + 0.597662i
\(86\) 1.17697e6 496683.i 0.199536 0.0842043i
\(87\) 506931.i 0.0825337i
\(88\) −598496. 234074.i −0.0936206 0.0366155i
\(89\) 262425.i 0.0394584i −0.999805 0.0197292i \(-0.993720\pi\)
0.999805 0.0197292i \(-0.00628041\pi\)
\(90\) −5.44276e6 1.28975e7i −0.786992 1.86491i
\(91\) −2.68292e6 2.68292e6i −0.373218 0.373218i
\(92\) −3.00232e6 + 3.08299e6i −0.401975 + 0.412776i
\(93\) 564016. 564016.i 0.0727112 0.0727112i
\(94\) −5.30199e6 + 1.30440e7i −0.658403 + 1.61981i
\(95\) −5.75868e6 −0.689113
\(96\) 1.47429e7 6.68730e6i 1.70072 0.771438i
\(97\) 1.53573e7 1.70849 0.854247 0.519867i \(-0.174018\pi\)
0.854247 + 0.519867i \(0.174018\pi\)
\(98\) −2.65145e6 + 6.52312e6i −0.284572 + 0.700106i
\(99\) 1.70711e6 1.70711e6i 0.176823 0.176823i
\(100\) −2.35722e6 + 2.42056e6i −0.235722 + 0.242056i
\(101\) −4.25472e6 4.25472e6i −0.410910 0.410910i 0.471146 0.882055i \(-0.343841\pi\)
−0.882055 + 0.471146i \(0.843841\pi\)
\(102\) −8.08324e6 1.91546e7i −0.754197 1.78720i
\(103\) 1.37835e7i 1.24288i −0.783463 0.621438i \(-0.786549\pi\)
0.783463 0.621438i \(-0.213451\pi\)
\(104\) 1.66437e6 4.25557e6i 0.145089 0.370972i
\(105\) 2.38849e7i 2.01355i
\(106\) 4.05172e6 1.70983e6i 0.330422 0.139438i
\(107\) −4.13797e6 4.13797e6i −0.326546 0.326546i 0.524726 0.851271i \(-0.324168\pi\)
−0.851271 + 0.524726i \(0.824168\pi\)
\(108\) 482092. + 3.63648e7i 0.0368254 + 2.77778i
\(109\) 5.14000e6 5.14000e6i 0.380163 0.380163i −0.490998 0.871161i \(-0.663368\pi\)
0.871161 + 0.490998i \(0.163368\pi\)
\(110\) 1.05784e6 + 429981.i 0.0757787 + 0.0308017i
\(111\) −1.29138e7 −0.896236
\(112\) −1.96943e7 + 522270.i −1.32457 + 0.0351263i
\(113\) 1.07199e7 0.698899 0.349449 0.936955i \(-0.386369\pi\)
0.349449 + 0.936955i \(0.386369\pi\)
\(114\) 2.31763e7 + 9.42044e6i 1.46513 + 0.595531i
\(115\) 5.40689e6 5.40689e6i 0.331516 0.331516i
\(116\) 742909. 9848.83i 0.0441909 0.000585844i
\(117\) 1.21383e7 + 1.21383e7i 0.700660 + 0.700660i
\(118\) −1.67639e7 + 7.07436e6i −0.939263 + 0.396370i
\(119\) 2.53013e7i 1.37635i
\(120\) −2.63514e7 + 1.15342e7i −1.39210 + 0.609330i
\(121\) 1.92902e7i 0.989894i
\(122\) −6.12707e6 1.45191e7i −0.305487 0.723903i
\(123\) 3.70400e7 + 3.70400e7i 1.79475 + 1.79475i
\(124\) −837525. 815609.i −0.0394477 0.0384155i
\(125\) 1.68095e7 1.68095e7i 0.769787 0.769787i
\(126\) 2.78692e7 6.85640e7i 1.24116 3.05351i
\(127\) −2.14599e7 −0.929640 −0.464820 0.885405i \(-0.653881\pi\)
−0.464820 + 0.885405i \(0.653881\pi\)
\(128\) −1.00867e7 2.14758e7i −0.425122 0.905136i
\(129\) 9.86131e6 0.404455
\(130\) −3.05736e6 + 7.52174e6i −0.122052 + 0.300273i
\(131\) −1.95903e6 + 1.95903e6i −0.0761361 + 0.0761361i −0.744149 0.668013i \(-0.767145\pi\)
0.668013 + 0.744149i \(0.267145\pi\)
\(132\) −3.55398e6 3.46099e6i −0.134495 0.130976i
\(133\) −2.15285e7 2.15285e7i −0.793474 0.793474i
\(134\) 1.40063e7 + 3.31902e7i 0.502871 + 1.19164i
\(135\) 6.46213e7i 2.26052i
\(136\) −2.79140e7 + 1.22181e7i −0.951561 + 0.416504i
\(137\) 3.21454e6i 0.106806i −0.998573 0.0534031i \(-0.982993\pi\)
0.998573 0.0534031i \(-0.0170068\pi\)
\(138\) −3.06054e7 + 1.29155e7i −0.991337 + 0.418344i
\(139\) −2.99300e7 2.99300e7i −0.945267 0.945267i 0.0533107 0.998578i \(-0.483023\pi\)
−0.998578 + 0.0533107i \(0.983023\pi\)
\(140\) 3.50034e7 464045.i 1.07811 0.0142926i
\(141\) −7.68565e7 + 7.68565e7i −2.30894 + 2.30894i
\(142\) 5.75372e7 + 2.33871e7i 1.68632 + 0.685437i
\(143\) −1.40024e6 −0.0400431
\(144\) 8.91025e7 2.36290e6i 2.48669 0.0659443i
\(145\) −1.32017e6 −0.0359619
\(146\) −4.44077e7 1.80504e7i −1.18093 0.480011i
\(147\) −3.84348e7 + 3.84348e7i −0.997961 + 0.997961i
\(148\) 250893. + 1.89251e7i 0.00636169 + 0.479869i
\(149\) 3.53474e7 + 3.53474e7i 0.875397 + 0.875397i 0.993054 0.117657i \(-0.0375385\pi\)
−0.117657 + 0.993054i \(0.537538\pi\)
\(150\) −2.40293e7 + 1.01404e7i −0.581329 + 0.245321i
\(151\) 1.10574e7i 0.261356i −0.991425 0.130678i \(-0.958285\pi\)
0.991425 0.130678i \(-0.0417153\pi\)
\(152\) 1.33554e7 3.41479e7i 0.308464 0.788699i
\(153\) 1.14470e8i 2.58388i
\(154\) 2.34723e6 + 5.56215e6i 0.0517885 + 0.122721i
\(155\) 1.46883e6 + 1.46883e6i 0.0316819 + 0.0316819i
\(156\) 2.46091e7 2.52704e7i 0.518991 0.532937i
\(157\) −2.40003e7 + 2.40003e7i −0.494958 + 0.494958i −0.909864 0.414906i \(-0.863814\pi\)
0.414906 + 0.909864i \(0.363814\pi\)
\(158\) 1.51057e7 3.71631e7i 0.304677 0.749570i
\(159\) 3.39475e7 0.669758
\(160\) 1.74153e7 + 3.83940e7i 0.336134 + 0.741043i
\(161\) 4.04267e7 0.763444
\(162\) −5.50244e7 + 1.35372e8i −1.01684 + 2.50164i
\(163\) 3.75312e7 3.75312e7i 0.678791 0.678791i −0.280936 0.959727i \(-0.590645\pi\)
0.959727 + 0.280936i \(0.0906447\pi\)
\(164\) 5.35626e7 5.50019e7i 0.948218 0.973697i
\(165\) 6.23291e6 + 6.23291e6i 0.108018 + 0.108018i
\(166\) −1.11652e6 2.64577e6i −0.0189446 0.0448925i
\(167\) 9.47634e7i 1.57447i 0.616656 + 0.787233i \(0.288487\pi\)
−0.616656 + 0.787233i \(0.711513\pi\)
\(168\) −1.41633e8 5.53934e7i −2.30453 0.901312i
\(169\) 5.27922e7i 0.841329i
\(170\) 4.98832e7 2.10507e7i 0.778722 0.328621i
\(171\) 9.74012e7 + 9.74012e7i 1.48963 + 1.48963i
\(172\) −191589. 1.44518e7i −0.00287092 0.216557i
\(173\) −3.79692e7 + 3.79692e7i −0.557532 + 0.557532i −0.928604 0.371072i \(-0.878990\pi\)
0.371072 + 0.928604i \(0.378990\pi\)
\(174\) 5.31313e6 + 2.15962e6i 0.0764589 + 0.0310782i
\(175\) 3.17404e7 0.447691
\(176\) −5.00303e6 + 5.27561e6i −0.0691734 + 0.0729421i
\(177\) −1.40457e8 −1.90387
\(178\) −2.75047e6 1.11798e6i −0.0365541 0.0148581i
\(179\) 2.43266e7 2.43266e7i 0.317026 0.317026i −0.530598 0.847624i \(-0.678032\pi\)
0.847624 + 0.530598i \(0.178032\pi\)
\(180\) −1.58366e8 + 2.09947e6i −2.02399 + 0.0268322i
\(181\) −9.65728e7 9.65728e7i −1.21054 1.21054i −0.970849 0.239693i \(-0.922953\pi\)
−0.239693 0.970849i \(-0.577047\pi\)
\(182\) −3.95493e7 + 1.66898e7i −0.486283 + 0.205212i
\(183\) 1.21649e8i 1.46734i
\(184\) 1.95223e7 + 4.46013e7i 0.231030 + 0.527820i
\(185\) 3.36305e7i 0.390511i
\(186\) −3.50862e6 8.31425e6i −0.0399798 0.0947388i
\(187\) 6.60251e6 + 6.60251e6i 0.0738352 + 0.0738352i
\(188\) 1.14126e8 + 1.11140e8i 1.25266 + 1.21988i
\(189\) 2.41583e8 2.41583e8i 2.60285 2.60285i
\(190\) −2.45331e7 + 6.03566e7i −0.259487 + 0.638391i
\(191\) 8.94372e6 0.0928756 0.0464378 0.998921i \(-0.485213\pi\)
0.0464378 + 0.998921i \(0.485213\pi\)
\(192\) −7.28192e6 1.83009e8i −0.0742492 1.86602i
\(193\) 1.39431e8 1.39607 0.698037 0.716062i \(-0.254057\pi\)
0.698037 + 0.716062i \(0.254057\pi\)
\(194\) 6.54251e7 1.60959e8i 0.643336 1.58274i
\(195\) −4.43187e7 + 4.43187e7i −0.428022 + 0.428022i
\(196\) 5.70729e7 + 5.55795e7i 0.541420 + 0.527252i
\(197\) −1.05806e8 1.05806e8i −0.986004 0.986004i 0.0138997 0.999903i \(-0.495575\pi\)
−0.999903 + 0.0138997i \(0.995575\pi\)
\(198\) −1.06195e7 2.51648e7i −0.0972250 0.230391i
\(199\) 1.09713e8i 0.986899i 0.869774 + 0.493449i \(0.164264\pi\)
−0.869774 + 0.493449i \(0.835736\pi\)
\(200\) 1.53276e7 + 3.50180e7i 0.135478 + 0.309519i
\(201\) 2.78086e8i 2.41542i
\(202\) −6.27196e7 + 2.64677e7i −0.535394 + 0.225936i
\(203\) −4.93538e6 4.93538e6i −0.0414080 0.0414080i
\(204\) −2.35195e8 + 3.11801e6i −1.93964 + 0.0257141i
\(205\) −9.64612e7 + 9.64612e7i −0.782013 + 0.782013i
\(206\) −1.44464e8 5.87202e7i −1.15140 0.468007i
\(207\) −1.82902e8 −1.43325
\(208\) −3.75119e7 3.55738e7i −0.289033 0.274099i
\(209\) −1.12360e7 −0.0851330
\(210\) 2.50337e8 + 1.01754e8i 1.86534 + 0.758204i
\(211\) 1.50429e8 1.50429e8i 1.10241 1.10241i 0.108288 0.994120i \(-0.465463\pi\)
0.994120 0.108288i \(-0.0345370\pi\)
\(212\) −659544. 4.97501e7i −0.00475410 0.358607i
\(213\) 3.39014e8 + 3.39014e8i 2.40375 + 2.40375i
\(214\) −6.09985e7 + 2.57414e7i −0.425472 + 0.179549i
\(215\) 2.56812e7i 0.176231i
\(216\) 3.83192e8 + 1.49868e8i 2.58719 + 1.01186i
\(217\) 1.09823e7i 0.0729599i
\(218\) −3.19748e7 7.57695e7i −0.209031 0.495333i
\(219\) −2.61654e8 2.61654e8i −1.68334 1.68334i
\(220\) 9.01324e6 9.25543e6i 0.0570692 0.0586027i
\(221\) −4.69467e7 + 4.69467e7i −0.292572 + 0.292572i
\(222\) −5.50151e7 + 1.35349e8i −0.337479 + 0.830269i
\(223\) 2.61269e7 0.157768 0.0788842 0.996884i \(-0.474864\pi\)
0.0788842 + 0.996884i \(0.474864\pi\)
\(224\) −7.84274e7 + 2.08640e8i −0.466230 + 1.24031i
\(225\) −1.43603e8 −0.840472
\(226\) 4.56686e7 1.12354e8i 0.263171 0.647457i
\(227\) −8.25829e7 + 8.25829e7i −0.468597 + 0.468597i −0.901460 0.432863i \(-0.857504\pi\)
0.432863 + 0.901460i \(0.357504\pi\)
\(228\) 1.97471e8 2.02777e8i 1.10339 1.13304i
\(229\) −6.46397e7 6.46397e7i −0.355693 0.355693i 0.506530 0.862223i \(-0.330928\pi\)
−0.862223 + 0.506530i \(0.830928\pi\)
\(230\) −3.36351e7 7.97038e7i −0.182282 0.431948i
\(231\) 4.66027e7i 0.248754i
\(232\) 3.06171e6 7.82836e6i 0.0160974 0.0411588i
\(233\) 1.31897e8i 0.683109i −0.939862 0.341555i \(-0.889047\pi\)
0.939862 0.341555i \(-0.110953\pi\)
\(234\) 1.78933e8 7.55096e7i 0.912922 0.385254i
\(235\) −2.00153e8 2.00153e8i −1.00606 1.00606i
\(236\) 2.72884e6 + 2.05840e8i 0.0135141 + 1.01938i
\(237\) 2.18968e8 2.18968e8i 1.06847 1.06847i
\(238\) 2.65182e8 + 1.07788e8i 1.27504 + 0.518266i
\(239\) 1.29899e8 0.615478 0.307739 0.951471i \(-0.400428\pi\)
0.307739 + 0.951471i \(0.400428\pi\)
\(240\) 8.62730e6 + 3.25326e8i 0.0402843 + 1.51908i
\(241\) −1.44120e8 −0.663233 −0.331616 0.943414i \(-0.607594\pi\)
−0.331616 + 0.943414i \(0.607594\pi\)
\(242\) −2.02180e8 8.21802e7i −0.917034 0.372746i
\(243\) −3.58238e8 + 3.58238e8i −1.60158 + 1.60158i
\(244\) −1.78277e8 + 2.36344e6i −0.785653 + 0.0104155i
\(245\) −1.00093e8 1.00093e8i −0.434835 0.434835i
\(246\) 5.46013e8 2.30418e8i 2.33846 0.986831i
\(247\) 7.98926e7i 0.337339i
\(248\) −1.21164e7 + 5.30342e6i −0.0504420 + 0.0220788i
\(249\) 2.21677e7i 0.0909961i
\(250\) −1.04568e8 2.47792e8i −0.423263 1.00299i
\(251\) 3.49428e7 + 3.49428e7i 0.139476 + 0.139476i 0.773398 0.633921i \(-0.218556\pi\)
−0.633921 + 0.773398i \(0.718556\pi\)
\(252\) −5.99890e8 5.84192e8i −2.36140 2.29961i
\(253\) 1.05496e7 1.05496e7i 0.0409555 0.0409555i
\(254\) −9.14234e7 + 2.24921e8i −0.350057 + 0.861215i
\(255\) 4.17948e8 1.57845
\(256\) −2.68058e8 + 1.42272e7i −0.998594 + 0.0530006i
\(257\) 3.00776e8 1.10529 0.552647 0.833416i \(-0.313618\pi\)
0.552647 + 0.833416i \(0.313618\pi\)
\(258\) 4.20111e7 1.03356e8i 0.152298 0.374686i
\(259\) 1.25726e8 1.25726e8i 0.449651 0.449651i
\(260\) 6.58102e7 + 6.40881e7i 0.232213 + 0.226137i
\(261\) 2.23291e7 + 2.23291e7i 0.0777373 + 0.0777373i
\(262\) 1.21867e7 + 2.88783e7i 0.0418630 + 0.0992013i
\(263\) 3.76784e8i 1.27716i 0.769553 + 0.638582i \(0.220479\pi\)
−0.769553 + 0.638582i \(0.779521\pi\)
\(264\) −5.14151e7 + 2.25047e7i −0.171980 + 0.0752766i
\(265\) 8.84075e7i 0.291829i
\(266\) −3.17355e8 + 1.33924e8i −1.03386 + 0.436287i
\(267\) −1.62060e7 1.62060e7i −0.0521058 0.0521058i
\(268\) 4.07535e8 5.40275e6i 1.29328 0.0171452i
\(269\) 1.16914e8 1.16914e8i 0.366214 0.366214i −0.499881 0.866094i \(-0.666623\pi\)
0.866094 + 0.499881i \(0.166623\pi\)
\(270\) −6.77294e8 2.75299e8i −2.09413 0.851201i
\(271\) 4.28052e8 1.30648 0.653242 0.757149i \(-0.273408\pi\)
0.653242 + 0.757149i \(0.273408\pi\)
\(272\) 9.13889e6 + 3.44618e8i 0.0275361 + 1.03836i
\(273\) −3.31366e8 −0.985685
\(274\) −3.36915e7 1.36945e7i −0.0989448 0.0402180i
\(275\) 8.28282e6 8.28282e6i 0.0240167 0.0240167i
\(276\) 4.98198e6 + 3.75797e8i 0.0142633 + 1.07590i
\(277\) 2.81665e8 + 2.81665e8i 0.796259 + 0.796259i 0.982503 0.186245i \(-0.0596317\pi\)
−0.186245 + 0.982503i \(0.559632\pi\)
\(278\) −4.41203e8 + 1.86188e8i −1.23163 + 0.519750i
\(279\) 4.96871e7i 0.136971i
\(280\) 1.44258e8 3.68847e8i 0.392723 1.00414i
\(281\) 1.55429e7i 0.0417888i −0.999782 0.0208944i \(-0.993349\pi\)
0.999782 0.0208944i \(-0.00665138\pi\)
\(282\) 4.78107e8 + 1.13295e9i 1.26956 + 3.00843i
\(283\) 2.73861e8 + 2.73861e8i 0.718253 + 0.718253i 0.968247 0.249994i \(-0.0804287\pi\)
−0.249994 + 0.968247i \(0.580429\pi\)
\(284\) 4.90239e8 5.03412e8i 1.26997 1.30410i
\(285\) −3.55626e8 + 3.55626e8i −0.909990 + 0.909990i
\(286\) −5.96531e6 + 1.46759e7i −0.0150783 + 0.0370957i
\(287\) −7.21229e8 −1.80089
\(288\) 3.54828e8 9.43947e8i 0.875275 2.32849i
\(289\) 3.23934e7 0.0789430
\(290\) −5.62418e6 + 1.38367e7i −0.0135415 + 0.0333149i
\(291\) 9.48386e8 9.48386e8i 2.25611 2.25611i
\(292\) −3.78371e8 + 3.88538e8i −0.889360 + 0.913258i
\(293\) −2.08481e8 2.08481e8i −0.484206 0.484206i 0.422266 0.906472i \(-0.361235\pi\)
−0.906472 + 0.422266i \(0.861235\pi\)
\(294\) 2.39094e8 + 5.66573e8i 0.548723 + 1.30029i
\(295\) 3.65784e8i 0.829559i
\(296\) 1.99423e8 + 7.79951e7i 0.446944 + 0.174802i
\(297\) 1.26085e8i 0.279264i
\(298\) 5.21061e8 2.19888e8i 1.14060 0.481332i
\(299\) 7.50120e7 + 7.50120e7i 0.162286 + 0.162286i
\(300\) 3.91153e6 + 2.95051e8i 0.00836415 + 0.630917i
\(301\) −9.60078e7 + 9.60078e7i −0.202919 + 0.202919i
\(302\) −1.15892e8 4.71065e7i −0.242119 0.0984138i
\(303\) −5.25499e8 −1.08523
\(304\) −3.01006e8 2.85454e8i −0.614495 0.582745i
\(305\) 3.16803e8 0.639352
\(306\) −1.19976e9 4.87666e8i −2.39370 0.972965i
\(307\) −6.18048e8 + 6.18048e8i −1.21910 + 1.21910i −0.251148 + 0.967949i \(0.580808\pi\)
−0.967949 + 0.251148i \(0.919192\pi\)
\(308\) 6.82964e7 905414.i 0.133190 0.00176571i
\(309\) −8.51194e8 8.51194e8i −1.64125 1.64125i
\(310\) 2.16523e7 9.13729e6i 0.0412799 0.0174201i
\(311\) 5.41827e7i 0.102141i 0.998695 + 0.0510704i \(0.0162633\pi\)
−0.998695 + 0.0510704i \(0.983737\pi\)
\(312\) −1.60019e8 3.65584e8i −0.298283 0.681469i
\(313\) 9.15920e8i 1.68831i 0.536099 + 0.844155i \(0.319898\pi\)
−0.536099 + 0.844155i \(0.680102\pi\)
\(314\) 1.49301e8 + 3.53793e8i 0.272150 + 0.644904i
\(315\) 1.05207e9 + 1.05207e9i 1.89653 + 1.89653i
\(316\) −3.25153e8 3.16644e8i −0.579672 0.564504i
\(317\) 3.83951e8 3.83951e8i 0.676968 0.676968i −0.282345 0.959313i \(-0.591112\pi\)
0.959313 + 0.282345i \(0.0911122\pi\)
\(318\) 1.44623e8 3.55803e8i 0.252198 0.620461i
\(319\) −2.57583e6 −0.00444273
\(320\) 4.76599e8 1.89639e7i 0.813070 0.0323521i
\(321\) −5.11079e8 −0.862423
\(322\) 1.72225e8 4.23711e8i 0.287476 0.707252i
\(323\) −3.76714e8 + 3.76714e8i −0.622018 + 0.622018i
\(324\) 1.18441e9 + 1.15342e9i 1.93462 + 1.88399i
\(325\) 5.88945e7 + 5.88945e7i 0.0951662 + 0.0951662i
\(326\) −2.33473e8 5.53254e8i −0.373229 0.884429i
\(327\) 6.34838e8i 1.00403i
\(328\) −3.48286e8 7.95707e8i −0.544976 1.24507i
\(329\) 1.49652e9i 2.31684i
\(330\) 9.18803e7 3.87735e7i 0.140742 0.0593932i
\(331\) −1.82269e8 1.82269e8i −0.276258 0.276258i 0.555355 0.831613i \(-0.312582\pi\)
−0.831613 + 0.555355i \(0.812582\pi\)
\(332\) −3.24868e7 + 430682.i −0.0487218 + 0.000645911i
\(333\) −5.68820e8 + 5.68820e8i −0.844151 + 0.844151i
\(334\) 9.93213e8 + 4.03710e8i 1.45858 + 0.592867i
\(335\) −7.24203e8 −1.05245
\(336\) −1.18396e9 + 1.24847e9i −1.70275 + 1.79552i
\(337\) 4.15826e8 0.591843 0.295921 0.955212i \(-0.404373\pi\)
0.295921 + 0.955212i \(0.404373\pi\)
\(338\) 5.53313e8 + 2.24905e8i 0.779404 + 0.316804i
\(339\) 6.62002e8 6.62002e8i 0.922912 0.922912i
\(340\) −8.12004e6 6.12504e8i −0.0112042 0.845148i
\(341\) 2.86589e6 + 2.86589e6i 0.00391399 + 0.00391399i
\(342\) 1.43581e9 6.05911e8i 1.94091 0.819063i
\(343\) 2.41894e8i 0.323666i
\(344\) −1.52285e8 5.95593e7i −0.201698 0.0788851i
\(345\) 6.67802e8i 0.875550i
\(346\) 2.36198e8 + 5.59710e8i 0.306556 + 0.726435i
\(347\) −1.16993e8 1.16993e8i −0.150316 0.150316i 0.627943 0.778259i \(-0.283897\pi\)
−0.778259 + 0.627943i \(0.783897\pi\)
\(348\) 4.52699e7 4.64863e7i 0.0575814 0.0591287i
\(349\) −9.43121e8 + 9.43121e8i −1.18762 + 1.18762i −0.209900 + 0.977723i \(0.567314\pi\)
−0.977723 + 0.209900i \(0.932686\pi\)
\(350\) 1.35220e8 3.32670e8i 0.168579 0.414739i
\(351\) 8.96518e8 1.10658
\(352\) 3.39796e7 + 7.49118e7i 0.0415259 + 0.0915484i
\(353\) −2.66226e8 −0.322136 −0.161068 0.986943i \(-0.551494\pi\)
−0.161068 + 0.986943i \(0.551494\pi\)
\(354\) −5.98373e8 + 1.47212e9i −0.716904 + 1.76373i
\(355\) −8.82875e8 + 8.82875e8i −1.04737 + 1.04737i
\(356\) −2.34350e7 + 2.40648e7i −0.0275290 + 0.0282687i
\(357\) 1.56247e9 + 1.56247e9i 1.81750 + 1.81750i
\(358\) −1.51330e8 3.58602e8i −0.174315 0.413068i
\(359\) 6.82905e8i 0.778987i 0.921029 + 0.389493i \(0.127350\pi\)
−0.921029 + 0.389493i \(0.872650\pi\)
\(360\) −6.52664e8 + 1.66877e9i −0.737277 + 1.88511i
\(361\) 2.52791e8i 0.282804i
\(362\) −1.42359e9 + 6.00758e8i −1.57727 + 0.665609i
\(363\) −1.19126e9 1.19126e9i −1.30718 1.30718i
\(364\) 6.43789e6 + 4.85617e8i 0.00699662 + 0.527763i
\(365\) 6.81410e8 6.81410e8i 0.733472 0.733472i
\(366\) −1.27500e9 5.18248e8i −1.35933 0.552528i
\(367\) −2.05790e8 −0.217316 −0.108658 0.994079i \(-0.534655\pi\)
−0.108658 + 0.994079i \(0.534655\pi\)
\(368\) 5.50634e8 1.46022e7i 0.575965 0.0152740i
\(369\) 3.26305e9 3.38089
\(370\) −3.52481e8 1.43273e8i −0.361767 0.147047i
\(371\) −3.30506e8 + 3.30506e8i −0.336025 + 0.336025i
\(372\) −1.02089e8 + 1.35340e6i −0.102820 + 0.00136310i
\(373\) 1.39903e8 + 1.39903e8i 0.139588 + 0.139588i 0.773448 0.633860i \(-0.218530\pi\)
−0.633860 + 0.773448i \(0.718530\pi\)
\(374\) 9.73287e7 4.10728e7i 0.0962034 0.0405979i
\(375\) 2.07614e9i 2.03304i
\(376\) 1.65106e9 7.22678e8i 1.60179 0.701112i
\(377\) 1.83153e7i 0.0176043i
\(378\) −1.50283e9 3.56121e9i −1.43116 3.39138i
\(379\) 3.01841e7 + 3.01841e7i 0.0284801 + 0.0284801i 0.721203 0.692723i \(-0.243589\pi\)
−0.692723 + 0.721203i \(0.743589\pi\)
\(380\) 5.28080e8 + 5.14261e8i 0.493693 + 0.480774i
\(381\) −1.32525e9 + 1.32525e9i −1.22761 + 1.22761i
\(382\) 3.81020e7 9.37389e7i 0.0349724 0.0860396i
\(383\) 1.42433e9 1.29543 0.647717 0.761881i \(-0.275724\pi\)
0.647717 + 0.761881i \(0.275724\pi\)
\(384\) −1.94913e9 7.03331e8i −1.75664 0.633870i
\(385\) −1.21365e8 −0.108388
\(386\) 5.94002e8 1.46137e9i 0.525694 1.29332i
\(387\) 4.34367e8 4.34367e8i 0.380950 0.380950i
\(388\) −1.40829e9 1.37144e9i −1.22400 1.19197i
\(389\) 1.23137e9 + 1.23137e9i 1.06063 + 1.06063i 0.998039 + 0.0625913i \(0.0199365\pi\)
0.0625913 + 0.998039i \(0.480064\pi\)
\(390\) 2.75697e8 + 6.53309e8i 0.235345 + 0.557690i
\(391\) 7.07402e8i 0.598477i
\(392\) 8.25669e8 3.61400e8i 0.692316 0.303031i
\(393\) 2.41958e8i 0.201079i
\(394\) −1.55970e9 + 6.58196e8i −1.28471 + 0.542148i
\(395\) 5.70246e8 + 5.70246e8i 0.465557 + 0.465557i
\(396\) −3.08993e8 + 4.09635e6i −0.250043 + 0.00331485i
\(397\) 1.48636e9 1.48636e9i 1.19223 1.19223i 0.215784 0.976441i \(-0.430769\pi\)
0.976441 0.215784i \(-0.0692308\pi\)
\(398\) 1.14990e9 + 4.67399e8i 0.914259 + 0.371618i
\(399\) −2.65897e9 −2.09560
\(400\) 4.32322e8 1.14647e7i 0.337751 0.00895680i
\(401\) −1.01690e9 −0.787544 −0.393772 0.919208i \(-0.628830\pi\)
−0.393772 + 0.919208i \(0.628830\pi\)
\(402\) 2.91461e9 + 1.18470e9i 2.23763 + 0.909530i
\(403\) −2.03777e7 + 2.03777e7i −0.0155092 + 0.0155092i
\(404\) 1.02096e7 + 7.70119e8i 0.00770323 + 0.581063i
\(405\) −2.07720e9 2.07720e9i −1.55376 1.55376i
\(406\) −7.27533e7 + 3.07019e7i −0.0539525 + 0.0227680i
\(407\) 6.56177e7i 0.0482437i
\(408\) −9.69295e8 + 2.47835e9i −0.706554 + 1.80656i
\(409\) 5.67432e8i 0.410093i 0.978752 + 0.205046i \(0.0657345\pi\)
−0.978752 + 0.205046i \(0.934266\pi\)
\(410\) 6.00063e8 + 1.42195e9i 0.429985 + 1.01892i
\(411\) −1.98513e8 1.98513e8i −0.141040 0.141040i
\(412\) −1.23089e9 + 1.26396e9i −0.867119 + 0.890419i
\(413\) 1.36746e9 1.36746e9i 0.955190 0.955190i
\(414\) −7.79198e8 + 1.91699e9i −0.539693 + 1.32776i
\(415\) 5.77300e7 0.0396491
\(416\) −5.32656e8 + 2.41610e8i −0.362760 + 0.164546i
\(417\) −3.69664e9 −2.49649
\(418\) −4.78673e7 + 1.17764e8i −0.0320570 + 0.0788669i
\(419\) 1.16751e9 1.16751e9i 0.775372 0.775372i −0.203668 0.979040i \(-0.565286\pi\)
0.979040 + 0.203668i \(0.0652863\pi\)
\(420\) 2.13297e9 2.19029e9i 1.40479 1.44254i
\(421\) −1.41024e9 1.41024e9i −0.921096 0.921096i 0.0760111 0.997107i \(-0.475782\pi\)
−0.997107 + 0.0760111i \(0.975782\pi\)
\(422\) −9.35784e8 2.21750e9i −0.606153 1.43638i
\(423\) 6.77069e9i 4.34952i
\(424\) −5.24240e8 2.05033e8i −0.334002 0.130630i
\(425\) 5.55405e8i 0.350953i
\(426\) 4.99746e9 2.10893e9i 3.13196 1.32169i
\(427\) 1.18435e9 + 1.18435e9i 0.736178 + 0.736178i
\(428\) 9.92941e6 + 7.48987e8i 0.00612168 + 0.461765i
\(429\) −8.64717e7 + 8.64717e7i −0.0528778 + 0.0528778i
\(430\) 2.69164e8 + 1.09407e8i 0.163259 + 0.0663599i
\(431\) −1.12113e9 −0.674503 −0.337252 0.941415i \(-0.609497\pi\)
−0.337252 + 0.941415i \(0.609497\pi\)
\(432\) 3.20324e9 3.37776e9i 1.91159 2.01574i
\(433\) 2.87439e8 0.170153 0.0850763 0.996374i \(-0.472887\pi\)
0.0850763 + 0.996374i \(0.472887\pi\)
\(434\) 1.15105e8 + 4.67867e7i 0.0675897 + 0.0274732i
\(435\) −8.15268e7 + 8.15268e7i −0.0474885 + 0.0474885i
\(436\) −9.30357e8 + 1.23339e7i −0.537585 + 0.00712683i
\(437\) 6.01918e8 + 6.01918e8i 0.345026 + 0.345026i
\(438\) −3.85708e9 + 1.62769e9i −2.19331 + 0.925577i
\(439\) 2.85117e9i 1.60841i −0.594349 0.804207i \(-0.702590\pi\)
0.594349 0.804207i \(-0.297410\pi\)
\(440\) −5.86078e7 1.33897e8i −0.0327998 0.0749356i
\(441\) 3.38592e9i 1.87993i
\(442\) 2.92045e8 + 6.92050e8i 0.160869 + 0.381206i
\(443\) 4.04267e8 + 4.04267e8i 0.220930 + 0.220930i 0.808890 0.587960i \(-0.200069\pi\)
−0.587960 + 0.808890i \(0.700069\pi\)
\(444\) 1.18421e9 + 1.15322e9i 0.642079 + 0.625278i
\(445\) 4.22043e7 4.22043e7i 0.0227037 0.0227037i
\(446\) 1.11305e8 2.73835e8i 0.0594079 0.146156i
\(447\) 4.36573e9 2.31196
\(448\) 1.85263e9 + 1.71084e9i 0.973456 + 0.898952i
\(449\) −7.72327e8 −0.402660 −0.201330 0.979523i \(-0.564526\pi\)
−0.201330 + 0.979523i \(0.564526\pi\)
\(450\) −6.11775e8 + 1.50509e9i −0.316481 + 0.778610i
\(451\) −1.88209e8 + 1.88209e8i −0.0966099 + 0.0966099i
\(452\) −9.83027e8 9.57303e8i −0.500704 0.487602i
\(453\) −6.82844e8 6.82844e8i −0.345126 0.345126i
\(454\) 5.13730e8 + 1.21737e9i 0.257656 + 0.610557i
\(455\) 8.62956e8i 0.429486i
\(456\) −1.28403e9 2.93355e9i −0.634161 1.44883i
\(457\) 1.74188e9i 0.853714i 0.904319 + 0.426857i \(0.140379\pi\)
−0.904319 + 0.426857i \(0.859621\pi\)
\(458\) −9.52865e8 + 4.02109e8i −0.463449 + 0.195576i
\(459\) −4.22731e9 4.22731e9i −2.04042 2.04042i
\(460\) −9.78666e8 + 1.29743e7i −0.468794 + 0.00621486i
\(461\) 3.94690e8 3.94690e8i 0.187630 0.187630i −0.607041 0.794671i \(-0.707644\pi\)
0.794671 + 0.607041i \(0.207644\pi\)
\(462\) 4.88442e8 + 1.98537e8i 0.230444 + 0.0936685i
\(463\) 1.89577e9 0.887671 0.443835 0.896108i \(-0.353618\pi\)
0.443835 + 0.896108i \(0.353618\pi\)
\(464\) −6.90054e7 6.54400e7i −0.0320679 0.0304110i
\(465\) 1.81415e8 0.0836735
\(466\) −1.38241e9 5.61908e8i −0.632829 0.257226i
\(467\) −1.55488e9 + 1.55488e9i −0.706459 + 0.706459i −0.965789 0.259330i \(-0.916498\pi\)
0.259330 + 0.965789i \(0.416498\pi\)
\(468\) −2.91269e7 2.19707e9i −0.0131351 0.990795i
\(469\) −2.70739e9 2.70739e9i −1.21184 1.21184i
\(470\) −2.95049e9 + 1.24511e9i −1.31084 + 0.553177i
\(471\) 2.96427e9i 1.30721i
\(472\) 2.16903e9 + 8.48316e8i 0.949441 + 0.371331i
\(473\) 5.01075e7i 0.0217715i
\(474\) −1.36215e9 3.22785e9i −0.587491 1.39216i
\(475\) 4.72586e8 + 4.72586e8i 0.202327 + 0.202327i
\(476\) 2.25945e9 2.32017e9i 0.960239 0.986041i
\(477\) 1.49531e9 1.49531e9i 0.630835 0.630835i
\(478\) 5.53394e8 1.36147e9i 0.231759 0.570176i
\(479\) −9.27374e8 −0.385550 −0.192775 0.981243i \(-0.561749\pi\)
−0.192775 + 0.981243i \(0.561749\pi\)
\(480\) 3.44649e9 + 1.29553e9i 1.42244 + 0.534692i
\(481\) 4.66570e8 0.191165
\(482\) −6.13981e8 + 1.51052e9i −0.249741 + 0.614416i
\(483\) 2.49654e9 2.49654e9i 1.00815 1.00815i
\(484\) −1.72266e9 + 1.76894e9i −0.690621 + 0.709178i
\(485\) 2.46983e9 + 2.46983e9i 0.983038 + 0.983038i
\(486\) 2.22852e9 + 5.28084e9i 0.880621 + 2.08678i
\(487\) 3.35907e9i 1.31786i −0.752206 0.658929i \(-0.771010\pi\)
0.752206 0.658929i \(-0.228990\pi\)
\(488\) −7.34723e8 + 1.87858e9i −0.286190 + 0.731747i
\(489\) 4.63546e9i 1.79272i
\(490\) −1.47549e9 + 6.22659e8i −0.566567 + 0.239091i
\(491\) −6.58146e8 6.58146e8i −0.250921 0.250921i 0.570427 0.821348i \(-0.306778\pi\)
−0.821348 + 0.570427i \(0.806778\pi\)
\(492\) −8.88807e7 6.70437e9i −0.0336457 2.53793i
\(493\) −8.63613e7 + 8.63613e7i −0.0324605 + 0.0324605i
\(494\) −8.37352e8 3.40358e8i −0.312510 0.127026i
\(495\) 5.49089e8 0.203481
\(496\) 3.96683e6 + 1.49585e8i 0.00145968 + 0.0550430i
\(497\) −6.60115e9 −2.41197
\(498\) −2.32339e8 9.44386e7i −0.0842984 0.0342647i
\(499\) −1.16527e9 + 1.16527e9i −0.419830 + 0.419830i −0.885145 0.465315i \(-0.845941\pi\)
0.465315 + 0.885145i \(0.345941\pi\)
\(500\) −3.04258e9 + 4.03359e7i −1.08855 + 0.0144310i
\(501\) 5.85209e9 + 5.85209e9i 2.07912 + 2.07912i
\(502\) 5.15098e8 2.17372e8i 0.181730 0.0766902i
\(503\) 8.09330e8i 0.283555i 0.989899 + 0.141778i \(0.0452818\pi\)
−0.989899 + 0.141778i \(0.954718\pi\)
\(504\) −8.67855e9 + 3.79865e9i −3.01953 + 1.32167i
\(505\) 1.36853e9i 0.472861i
\(506\) −6.56265e7 1.55513e8i −0.0225192 0.0533629i
\(507\) 3.26017e9 + 3.26017e9i 1.11099 + 1.11099i
\(508\) 1.96791e9 + 1.91641e9i 0.666011 + 0.648583i
\(509\) −3.64859e9 + 3.64859e9i −1.22635 + 1.22635i −0.261011 + 0.965336i \(0.584056\pi\)
−0.965336 + 0.261011i \(0.915944\pi\)
\(510\) 1.78054e9 4.38050e9i 0.594369 1.46227i
\(511\) 5.09482e9 1.68910
\(512\) −9.92864e8 + 2.87012e9i −0.326923 + 0.945051i
\(513\) 7.19392e9 2.35264
\(514\) 1.28136e9 3.15243e9i 0.416200 1.02394i
\(515\) 2.21671e9 2.21671e9i 0.715129 0.715129i
\(516\) −9.04297e8 8.80634e8i −0.289759 0.282177i
\(517\) −3.90525e8 3.90525e8i −0.124289 0.124289i
\(518\) −7.82112e8 1.85334e9i −0.247238 0.585871i
\(519\) 4.68956e9i 1.47247i
\(520\) 9.52070e8 4.16727e8i 0.296932 0.129969i
\(521\) 5.31090e7i 0.0164527i 0.999966 + 0.00822633i \(0.00261855\pi\)
−0.999966 + 0.00822633i \(0.997381\pi\)
\(522\) 3.29157e8 1.38904e8i 0.101288 0.0427434i
\(523\) −1.99031e9 1.99031e9i −0.608364 0.608364i 0.334154 0.942518i \(-0.391549\pi\)
−0.942518 + 0.334154i \(0.891549\pi\)
\(524\) 3.54590e8 4.70085e6i 0.107663 0.00142730i
\(525\) 1.96012e9 1.96012e9i 0.591187 0.591187i
\(526\) 3.94906e9 + 1.60517e9i 1.18316 + 0.480918i
\(527\) 1.92173e8 0.0571945
\(528\) 1.68330e7 + 6.34755e8i 0.00497672 + 0.187667i
\(529\) 2.27453e9 0.668032
\(530\) 9.26597e8 + 3.76633e8i 0.270349 + 0.109889i
\(531\) −6.18679e9 + 6.18679e9i −1.79322 + 1.79322i
\(532\) 5.16595e7 + 3.89673e9i 0.0148751 + 1.12204i
\(533\) −1.33825e9 1.33825e9i −0.382816 0.382816i
\(534\) −2.38895e8 + 1.00814e8i −0.0678911 + 0.0286501i
\(535\) 1.33097e9i 0.375778i
\(536\) 1.67955e9 4.29438e9i 0.471104 1.20455i
\(537\) 3.00456e9i 0.837281i
\(538\) −7.27298e8 1.72345e9i −0.201361 0.477157i
\(539\) −1.95296e8 1.95296e8i −0.0537195 0.0537195i
\(540\) −5.77081e9 + 5.92587e9i −1.57710 + 1.61947i
\(541\) 1.46358e9 1.46358e9i 0.397398 0.397398i −0.479916 0.877314i \(-0.659333\pi\)
0.877314 + 0.479916i \(0.159333\pi\)
\(542\) 1.82359e9 4.48640e9i 0.491959 1.21032i
\(543\) −1.19277e10 −3.19710
\(544\) 3.65086e9 + 1.37235e9i 0.972298 + 0.365485i
\(545\) 1.65327e9 0.437479
\(546\) −1.41168e9 + 3.47303e9i −0.371161 + 0.913135i
\(547\) −1.11429e9 + 1.11429e9i −0.291101 + 0.291101i −0.837515 0.546414i \(-0.815993\pi\)
0.546414 + 0.837515i \(0.315993\pi\)
\(548\) −2.87064e8 + 2.94778e8i −0.0745156 + 0.0765179i
\(549\) −5.35835e9 5.35835e9i −1.38206 1.38206i
\(550\) −5.15256e7 1.22098e8i −0.0132055 0.0312925i
\(551\) 1.46967e8i 0.0374274i
\(552\) 3.95994e9 + 1.54875e9i 1.00208 + 0.391918i
\(553\) 4.26366e9i 1.07212i
\(554\) 4.15207e9 1.75218e9i 1.03748 0.437818i
\(555\) −2.07685e9 2.07685e9i −0.515678 0.515678i
\(556\) 7.18195e7 + 5.41743e9i 0.0177207 + 1.33669i
\(557\) −4.33757e9 + 4.33757e9i −1.06354 + 1.06354i −0.0656996 + 0.997839i \(0.520928\pi\)
−0.997839 + 0.0656996i \(0.979072\pi\)
\(558\) −5.20769e8 2.11677e8i −0.126889 0.0515767i
\(559\) −3.56286e8 −0.0862696
\(560\) −3.25131e9 3.08332e9i −0.782348 0.741926i
\(561\) 8.15473e8 0.195002
\(562\) −1.62905e8 6.62158e7i −0.0387130 0.0157356i
\(563\) 1.49585e9 1.49585e9i 0.353271 0.353271i −0.508054 0.861325i \(-0.669635\pi\)
0.861325 + 0.508054i \(0.169635\pi\)
\(564\) 1.39113e10 1.84424e8i 3.26505 0.0432852i
\(565\) 1.72401e9 + 1.72401e9i 0.402134 + 0.402134i
\(566\) 4.03703e9 1.70363e9i 0.935846 0.394927i
\(567\) 1.55310e10i 3.57814i
\(568\) −3.18774e9 7.28282e9i −0.729900 1.66756i
\(569\) 5.13775e9i 1.16918i 0.811330 + 0.584588i \(0.198744\pi\)
−0.811330 + 0.584588i \(0.801256\pi\)
\(570\) 2.21227e9 + 5.24234e9i 0.500353 + 1.18567i
\(571\) −1.26567e9 1.26567e9i −0.284508 0.284508i 0.550396 0.834904i \(-0.314477\pi\)
−0.834904 + 0.550396i \(0.814477\pi\)
\(572\) 1.28404e8 + 1.25044e8i 0.0286876 + 0.0279369i
\(573\) 5.52317e8 5.52317e8i 0.122644 0.122644i
\(574\) −3.07257e9 + 7.55918e9i −0.678126 + 1.66833i
\(575\) −8.87433e8 −0.194670
\(576\) −8.38185e9 7.74034e9i −1.82752 1.68765i
\(577\) −5.72767e8 −0.124126 −0.0620630 0.998072i \(-0.519768\pi\)
−0.0620630 + 0.998072i \(0.519768\pi\)
\(578\) 1.38002e8 3.39514e8i 0.0297261 0.0731325i
\(579\) 8.61052e9 8.61052e9i 1.84355 1.84355i
\(580\) 1.21062e8 + 1.17894e8i 0.0257637 + 0.0250896i
\(581\) 2.15820e8 + 2.15820e8i 0.0456537 + 0.0456537i
\(582\) −5.89970e9 1.39803e10i −1.24051 2.93959i
\(583\) 1.72495e8i 0.0360526i
\(584\) 2.46032e9 + 5.62094e9i 0.511148 + 1.16779i
\(585\) 3.90426e9i 0.806295i
\(586\) −3.07326e9 + 1.29692e9i −0.630895 + 0.266238i
\(587\) 4.64216e9 + 4.64216e9i 0.947298 + 0.947298i 0.998679 0.0513812i \(-0.0163624\pi\)
−0.0513812 + 0.998679i \(0.516362\pi\)
\(588\) 6.95682e9 9.22275e7i 1.41121 0.0187085i
\(589\) −1.63517e8 + 1.63517e8i −0.0329730 + 0.0329730i
\(590\) −3.83377e9 1.55831e9i −0.768500 0.312372i
\(591\) −1.30680e10 −2.60408
\(592\) 1.66704e9 1.75787e9i 0.330233 0.348225i
\(593\) 6.95056e8 0.136876 0.0684382 0.997655i \(-0.478198\pi\)
0.0684382 + 0.997655i \(0.478198\pi\)
\(594\) −1.32149e9 5.37146e8i −0.258709 0.105157i
\(595\) −4.06906e9 + 4.06906e9i −0.791927 + 0.791927i
\(596\) −8.48190e7 6.39799e9i −0.0164109 1.23789i
\(597\) 6.77530e9 + 6.77530e9i 1.30322 + 1.30322i
\(598\) 1.10576e9 4.66633e8i 0.211450 0.0892321i
\(599\) 4.70981e9i 0.895384i 0.894188 + 0.447692i \(0.147754\pi\)
−0.894188 + 0.447692i \(0.852246\pi\)
\(600\) 3.10908e9 + 1.21598e9i 0.587628 + 0.229824i
\(601\) 7.02648e9i 1.32031i −0.751128 0.660157i \(-0.770490\pi\)
0.751128 0.660157i \(-0.229510\pi\)
\(602\) 5.97243e8 + 1.41527e9i 0.111574 + 0.264393i
\(603\) 1.22490e10 + 1.22490e10i 2.27505 + 2.27505i
\(604\) −9.87443e8 + 1.01398e9i −0.182340 + 0.187240i
\(605\) 3.10234e9 3.10234e9i 0.569568 0.569568i
\(606\) −2.23873e9 + 5.50774e9i −0.408645 + 1.00535i
\(607\) 8.10093e8 0.147019 0.0735096 0.997295i \(-0.476580\pi\)
0.0735096 + 0.997295i \(0.476580\pi\)
\(608\) −4.27418e9 + 1.93875e9i −0.771242 + 0.349832i
\(609\) −6.09567e8 −0.109361
\(610\) 1.34964e9 3.32041e9i 0.240749 0.592293i
\(611\) 2.77680e9 2.77680e9i 0.492494 0.492494i
\(612\) −1.02224e10 + 1.04971e10i −1.80270 + 1.85114i
\(613\) −7.64430e9 7.64430e9i −1.34037 1.34037i −0.895685 0.444689i \(-0.853314\pi\)
−0.444689 0.895685i \(-0.646686\pi\)
\(614\) 3.84474e9 + 9.11075e9i 0.670313 + 1.58842i
\(615\) 1.19139e10i 2.06533i
\(616\) 2.81466e8 7.19669e8i 0.0485170 0.124051i
\(617\) 1.76031e9i 0.301710i 0.988556 + 0.150855i \(0.0482027\pi\)
−0.988556 + 0.150855i \(0.951797\pi\)
\(618\) −1.25476e10 + 5.29509e9i −2.13846 + 0.902430i
\(619\) 5.28896e8 + 5.28896e8i 0.0896299 + 0.0896299i 0.750500 0.660870i \(-0.229813\pi\)
−0.660870 + 0.750500i \(0.729813\pi\)
\(620\) −3.52459e6 2.65864e8i −0.000593934 0.0448011i
\(621\) −6.75445e9 + 6.75445e9i −1.13180 + 1.13180i
\(622\) 5.67887e8 + 2.30829e8i 0.0946228 + 0.0384613i
\(623\) 3.15557e8 0.0522840
\(624\) −4.51339e9 + 1.19690e8i −0.743629 + 0.0197202i
\(625\) 3.34457e9 0.547974
\(626\) 9.59973e9 + 3.90200e9i 1.56404 + 0.635736i
\(627\) −6.93874e8 + 6.93874e8i −0.112420 + 0.112420i
\(628\) 4.34414e9 5.75909e7i 0.699915 0.00927887i
\(629\) −2.20000e9 2.20000e9i −0.352489 0.352489i
\(630\) 1.55088e10 6.54472e9i 2.47108 1.04280i
\(631\) 9.08344e9i 1.43929i −0.694344 0.719644i \(-0.744305\pi\)
0.694344 0.719644i \(-0.255695\pi\)
\(632\) −4.70395e9 + 2.05895e9i −0.741230 + 0.324441i
\(633\) 1.85794e10i 2.91151i
\(634\) −2.38847e9 5.65988e9i −0.372227 0.882054i
\(635\) −3.45128e9 3.45128e9i −0.534899 0.534899i
\(636\) −3.11304e9 3.03158e9i −0.479827 0.467271i
\(637\) 1.38864e9 1.38864e9i 0.212863 0.212863i
\(638\) −1.09735e7 + 2.69972e7i −0.00167292 + 0.00411572i
\(639\) 2.98655e10 4.52811
\(640\) 1.83164e9 5.07601e9i 0.276192 0.765407i
\(641\) 9.60692e9 1.44073 0.720363 0.693598i \(-0.243975\pi\)
0.720363 + 0.693598i \(0.243975\pi\)
\(642\) −2.17729e9 + 5.35660e9i −0.324746 + 0.798945i
\(643\) −9.22467e9 + 9.22467e9i −1.36840 + 1.36840i −0.505672 + 0.862726i \(0.668755\pi\)
−0.862726 + 0.505672i \(0.831245\pi\)
\(644\) −3.70719e9 3.61018e9i −0.546945 0.532633i
\(645\) 1.58594e9 + 1.58594e9i 0.232717 + 0.232717i
\(646\) 2.34346e9 + 5.55321e9i 0.342013 + 0.810457i
\(647\) 7.64371e9i 1.10953i −0.832007 0.554765i \(-0.812808\pi\)
0.832007 0.554765i \(-0.187192\pi\)
\(648\) 1.71348e10 7.49999e9i 2.47380 1.08280i
\(649\) 7.13693e8i 0.102484i
\(650\) 8.68173e8 3.66369e8i 0.123997 0.0523266i
\(651\) 6.78209e8 + 6.78209e8i 0.0963452 + 0.0963452i
\(652\) −6.79328e9 + 9.00594e7i −0.959871 + 0.0127251i
\(653\) −9.00786e9 + 9.00786e9i −1.26598 + 1.26598i −0.317828 + 0.948148i \(0.602954\pi\)
−0.948148 + 0.317828i \(0.897046\pi\)
\(654\) −6.65372e9 2.70453e9i −0.930128 0.378068i
\(655\) −6.30118e8 −0.0876147
\(656\) −9.82354e9 + 2.60510e8i −1.35864 + 0.0360297i
\(657\) −2.30505e10 −3.17103
\(658\) −1.56850e10 6.37546e9i −2.14631 0.872410i
\(659\) 8.58058e9 8.58058e9i 1.16793 1.16793i 0.185239 0.982693i \(-0.440694\pi\)
0.982693 0.185239i \(-0.0593060\pi\)
\(660\) −1.49564e7 1.12818e9i −0.00202499 0.152747i
\(661\) −3.98292e9 3.98292e9i −0.536410 0.536410i 0.386063 0.922472i \(-0.373835\pi\)
−0.922472 + 0.386063i \(0.873835\pi\)
\(662\) −2.68686e9 + 1.13386e9i −0.359950 + 0.151899i
\(663\) 5.79837e9i 0.772696i
\(664\) −1.33886e8 + 3.42328e8i −0.0177479 + 0.0453789i
\(665\) 6.92461e9i 0.913103i
\(666\) 3.53850e9 + 8.38507e9i 0.464152 + 1.09988i
\(667\) 1.37989e8 + 1.37989e8i 0.0180055 + 0.0180055i
\(668\) 8.46256e9 8.68995e9i 1.09846 1.12798i
\(669\) 1.61346e9 1.61346e9i 0.208337 0.208337i
\(670\) −3.08524e9 + 7.59035e9i −0.396303 + 0.974990i
\(671\) 6.18126e8 0.0789856
\(672\) 8.04124e9 + 1.77278e10i 1.02219 + 2.25352i
\(673\) 1.05739e10 1.33716 0.668580 0.743640i \(-0.266902\pi\)
0.668580 + 0.743640i \(0.266902\pi\)
\(674\) 1.77150e9 4.35826e9i 0.222859 0.548281i
\(675\) −5.30315e9 + 5.30315e9i −0.663698 + 0.663698i
\(676\) 4.71444e9 4.84112e9i 0.586971 0.602744i
\(677\) 1.00400e10 + 1.00400e10i 1.24358 + 1.24358i 0.958504 + 0.285078i \(0.0920195\pi\)
0.285078 + 0.958504i \(0.407981\pi\)
\(678\) −4.11817e9 9.75868e9i −0.507458 1.20251i
\(679\) 1.84666e10i 2.26382i
\(680\) −6.45423e9 2.52428e9i −0.787160 0.307862i
\(681\) 1.01998e10i 1.23759i
\(682\) 4.22466e7 1.78281e7i 0.00509972 0.00215208i
\(683\) −1.01009e10 1.01009e10i −1.21307 1.21307i −0.970012 0.243059i \(-0.921849\pi\)
−0.243059 0.970012i \(-0.578151\pi\)
\(684\) −2.33722e8 1.76299e10i −0.0279257 2.10647i
\(685\) 5.16976e8 5.16976e8i 0.0614544 0.0614544i
\(686\) 2.53529e9 + 1.03052e9i 0.299842 + 0.121877i
\(687\) −7.98362e9 −0.939401
\(688\) −1.27300e9 + 1.34236e9i −0.149029 + 0.157148i
\(689\) −1.22651e9 −0.142858
\(690\) −6.99922e9 2.84497e9i −0.811106 0.329690i
\(691\) 8.49939e8 8.49939e8i 0.0979974 0.0979974i −0.656408 0.754406i \(-0.727925\pi\)
0.754406 + 0.656408i \(0.227925\pi\)
\(692\) 6.87256e9 9.11103e7i 0.788401 0.0104519i
\(693\) 2.05274e9 + 2.05274e9i 0.234297 + 0.234297i
\(694\) −1.72461e9 + 7.27786e8i −0.195854 + 0.0826505i
\(695\) 9.62694e9i 1.08778i
\(696\) −2.94363e8 6.72514e8i −0.0330942 0.0756082i
\(697\) 1.26203e10i 1.41175i
\(698\) 5.86695e9 + 1.39027e10i 0.653008 + 1.54741i
\(699\) −8.14528e9 8.14528e9i −0.902061 0.902061i
\(700\) −2.91064e9 2.83447e9i −0.320734 0.312341i
\(701\) 8.49362e9 8.49362e9i 0.931278 0.931278i −0.0665075 0.997786i \(-0.521186\pi\)
0.997786 + 0.0665075i \(0.0211856\pi\)
\(702\) 3.81934e9 9.39638e9i 0.416686 1.02513i
\(703\) 3.74390e9 0.406425
\(704\) 9.29908e8 3.70011e7i 0.100447 0.00399678i
\(705\) −2.47208e10 −2.65705
\(706\) −1.13417e9 + 2.79031e9i −0.121301 + 0.298425i
\(707\) 5.11615e9 5.11615e9i 0.544472 0.544472i
\(708\) 1.28801e10 + 1.25431e10i 1.36396 + 1.32827i
\(709\) −4.58762e9 4.58762e9i −0.483421 0.483421i 0.422801 0.906222i \(-0.361047\pi\)
−0.906222 + 0.422801i \(0.861047\pi\)
\(710\) 5.49217e9 + 1.30146e10i 0.575890 + 1.36467i
\(711\) 1.92900e10i 2.01275i
\(712\) 1.52384e8 + 3.48143e8i 0.0158219 + 0.0361474i
\(713\) 3.07056e8i 0.0317251i
\(714\) 2.30327e10 9.71981e9i 2.36811 0.999342i
\(715\) −2.25193e8 2.25193e8i −0.0230401 0.0230401i
\(716\) −4.40319e9 + 5.83737e7i −0.448303 + 0.00594322i
\(717\) 8.02186e9 8.02186e9i 0.812752 0.812752i
\(718\) 7.15751e9 + 2.90931e9i 0.721650 + 0.293329i
\(719\) −9.61133e9 −0.964345 −0.482172 0.876076i \(-0.660152\pi\)
−0.482172 + 0.876076i \(0.660152\pi\)
\(720\) 1.47099e10 + 1.39498e10i 1.46874 + 1.39285i
\(721\) 1.65741e10 1.64686
\(722\) 2.64949e9 + 1.07694e9i 0.261989 + 0.106490i
\(723\) −8.90012e9 + 8.90012e9i −0.875814 + 0.875814i
\(724\) 2.31735e8 + 1.74800e10i 0.0226937 + 1.71181i
\(725\) 1.08340e8 + 1.08340e8i 0.0105586 + 0.0105586i
\(726\) −1.75606e10 + 7.41059e9i −1.70318 + 0.718745i
\(727\) 1.34243e10i 1.29575i 0.761745 + 0.647877i \(0.224343\pi\)
−0.761745 + 0.647877i \(0.775657\pi\)
\(728\) 5.11717e9 + 2.00135e9i 0.491552 + 0.192248i
\(729\) 1.59986e10i 1.52945i
\(730\) −4.23890e9 1.00448e10i −0.403295 0.955675i
\(731\) 1.67998e9 + 1.67998e9i 0.159072 + 0.159072i
\(732\) −1.08635e10 + 1.11554e10i −1.02372 + 1.05123i
\(733\) −9.32912e8 + 9.32912e8i −0.0874937 + 0.0874937i −0.749499 0.662005i \(-0.769706\pi\)
0.662005 + 0.749499i \(0.269706\pi\)
\(734\) −8.76704e8 + 2.15688e9i −0.0818308 + 0.201321i
\(735\) −1.23625e10 −1.14842
\(736\) 2.19276e9 5.83339e9i 0.202731 0.539322i
\(737\) −1.41302e9 −0.130020
\(738\) 1.39012e10 3.41999e10i 1.27308 3.13204i
\(739\) −1.69251e9 + 1.69251e9i −0.154268 + 0.154268i −0.780021 0.625753i \(-0.784792\pi\)
0.625753 + 0.780021i \(0.284792\pi\)
\(740\) −3.00327e9 + 3.08397e9i −0.272448 + 0.279769i
\(741\) −4.93375e9 4.93375e9i −0.445464 0.445464i
\(742\) 2.05601e9 + 4.87205e9i 0.184761 + 0.437822i
\(743\) 1.77397e10i 1.58666i 0.608791 + 0.793331i \(0.291655\pi\)
−0.608791 + 0.793331i \(0.708345\pi\)
\(744\) −4.20733e8 + 1.07576e9i −0.0374543 + 0.0957654i
\(745\) 1.13694e10i 1.00738i
\(746\) 2.06234e9 8.70308e8i 0.181875 0.0767515i
\(747\) −9.76433e8 9.76433e8i −0.0857078 0.0857078i
\(748\) −1.58433e7 1.19508e9i −0.00138417 0.104410i
\(749\) 4.97576e9 4.97576e9i 0.432686 0.432686i
\(750\) −2.17599e10 8.84474e9i −1.88340 0.765545i
\(751\) 1.09851e10 0.946375 0.473188 0.880962i \(-0.343103\pi\)
0.473188 + 0.880962i \(0.343103\pi\)
\(752\) −5.40546e8 2.03834e10i −0.0463522 1.74789i
\(753\) 4.31577e9 0.368363
\(754\) −1.91962e8 7.80266e7i −0.0163086 0.00662893i
\(755\) 1.77829e9 1.77829e9i 0.150379 0.150379i
\(756\) −4.37273e10 + 5.79699e8i −3.68067 + 0.0487951i
\(757\) −9.18198e9 9.18198e9i −0.769309 0.769309i 0.208676 0.977985i \(-0.433085\pi\)
−0.977985 + 0.208676i \(0.933085\pi\)
\(758\) 4.44949e8 1.87769e8i 0.0371081 0.0156596i
\(759\) 1.30297e9i 0.108165i
\(760\) 7.63968e9 3.34394e9i 0.631288 0.276319i
\(761\) 1.19466e9i 0.0982647i −0.998792 0.0491324i \(-0.984354\pi\)
0.998792 0.0491324i \(-0.0156456\pi\)
\(762\) 8.24410e9 + 1.95358e10i 0.674995 + 1.59951i
\(763\) 6.18066e9 + 6.18066e9i 0.503732 + 0.503732i
\(764\) −8.20153e8 7.98692e8i −0.0665378 0.0647966i
\(765\) 1.84096e10 1.84096e10i 1.48672 1.48672i
\(766\) 6.06793e9 1.49284e10i 0.487798 1.20009i
\(767\) 5.07467e9 0.406091
\(768\) −1.56753e10 + 1.74325e10i −1.24868 + 1.38866i
\(769\) 8.71208e9 0.690844 0.345422 0.938448i \(-0.387736\pi\)
0.345422 + 0.938448i \(0.387736\pi\)
\(770\) −5.17037e8 + 1.27202e9i −0.0408135 + 0.100410i
\(771\) 1.85744e10 1.85744e10i 1.45957 1.45957i
\(772\) −1.27860e10 1.24514e10i −1.00017 0.974001i
\(773\) 3.31528e9 + 3.31528e9i 0.258162 + 0.258162i 0.824306 0.566144i \(-0.191566\pi\)
−0.566144 + 0.824306i \(0.691566\pi\)
\(774\) −2.70210e9 6.40308e9i −0.209463 0.496358i
\(775\) 2.41080e8i 0.0186039i
\(776\) −2.03736e10 + 8.91764e9i −1.56513 + 0.685068i
\(777\) 1.55283e10i 1.18755i
\(778\) 1.81518e10 7.66006e9i 1.38195 0.583182i
\(779\) −1.07385e10 1.07385e10i −0.813882 0.813882i
\(780\) 8.02184e9 1.06347e8i 0.605261 0.00802402i
\(781\) −1.72261e9 + 1.72261e9i −0.129392 + 0.129392i
\(782\) −7.41426e9 3.01367e9i −0.554427 0.225357i
\(783\) 1.64920e9 0.122774
\(784\) −2.70319e8 1.01934e10i −0.0200341 0.755466i
\(785\) −7.71968e9 −0.569581
\(786\) 2.53596e9 + 1.03079e9i 0.186279 + 0.0757165i
\(787\) 2.66527e8 2.66527e8i 0.0194908 0.0194908i −0.697294 0.716785i \(-0.745613\pi\)
0.716785 + 0.697294i \(0.245613\pi\)
\(788\) 2.53891e8 + 1.91513e10i 0.0184844 + 1.39430i
\(789\) 2.32682e10 + 2.32682e10i 1.68653 + 1.68653i
\(790\) 8.40609e9 3.54737e9i 0.606596 0.255984i
\(791\) 1.28902e10i 0.926069i
\(792\) −1.27343e9 + 3.25599e9i −0.0910832 + 0.232887i
\(793\) 4.39514e9i 0.312980i
\(794\) −9.24634e9 2.19107e10i −0.655538 1.55341i
\(795\) 5.45958e9 + 5.45958e9i 0.385367 + 0.385367i
\(796\) 9.79759e9 1.00609e10i 0.688531 0.707032i
\(797\) −1.91922e10 + 1.91922e10i −1.34283 + 1.34283i −0.449593 + 0.893233i \(0.648431\pi\)
−0.893233 + 0.449593i \(0.851569\pi\)
\(798\) −1.13277e10 + 2.78686e10i −0.789102 + 1.94136i
\(799\) −2.61867e10 −1.81621
\(800\) 1.72161e9 4.57999e9i 0.118883 0.316264i
\(801\) −1.42767e9 −0.0981553
\(802\) −4.33221e9 + 1.06581e10i −0.296551 + 0.729577i
\(803\) 1.32952e9 1.32952e9i 0.0906131 0.0906131i
\(804\) 2.48336e10 2.55009e10i 1.68517 1.73045i
\(805\) 6.50159e9 + 6.50159e9i 0.439273 + 0.439273i
\(806\) 1.26765e8 + 3.00392e8i 0.00852763 + 0.0202076i
\(807\) 1.44400e10i 0.967187i
\(808\) 8.11509e9 + 3.17385e9i 0.541195 + 0.211664i
\(809\) 1.86279e9i 0.123692i −0.998086 0.0618462i \(-0.980301\pi\)
0.998086 0.0618462i \(-0.0196988\pi\)
\(810\) −3.06203e10 + 1.29218e10i −2.02447 + 0.854328i
\(811\) −1.60625e10 1.60625e10i −1.05740 1.05740i −0.998249 0.0591547i \(-0.981159\pi\)
−0.0591547 0.998249i \(-0.518841\pi\)
\(812\) 1.18429e7 + 8.93321e8i 0.000776267 + 0.0585547i
\(813\) 2.64343e10 2.64343e10i 1.72524 1.72524i
\(814\) −6.87737e8 2.79544e8i −0.0446927 0.0181662i
\(815\) 1.20719e10 0.781129
\(816\) 2.18462e10 + 2.07174e10i 1.40754 + 1.33481i
\(817\) −2.85894e9 −0.183412
\(818\) 5.94723e9 + 2.41737e9i 0.379908 + 0.154421i
\(819\) −1.45959e10 + 1.45959e10i −0.928402 + 0.928402i
\(820\) 1.74598e10 2.31467e8i 1.10584 0.0146602i
\(821\) −1.04505e10 1.04505e10i −0.659074 0.659074i 0.296087 0.955161i \(-0.404318\pi\)
−0.955161 + 0.296087i \(0.904318\pi\)
\(822\) −2.92631e9 + 1.23490e9i −0.183768 + 0.0775500i
\(823\) 2.02179e10i 1.26426i −0.774863 0.632129i \(-0.782181\pi\)
0.774863 0.632129i \(-0.217819\pi\)
\(824\) 8.00374e9 + 1.82856e10i 0.498365 + 1.13858i
\(825\) 1.02301e9i 0.0634293i
\(826\) −8.50667e9 2.01580e10i −0.525206 1.24456i
\(827\) 3.41907e9 + 3.41907e9i 0.210203 + 0.210203i 0.804354 0.594151i \(-0.202512\pi\)
−0.594151 + 0.804354i \(0.702512\pi\)
\(828\) 1.67724e10 + 1.63335e10i 1.02681 + 0.999938i
\(829\) −1.87636e10 + 1.87636e10i −1.14387 + 1.14387i −0.156130 + 0.987737i \(0.549902\pi\)
−0.987737 + 0.156130i \(0.950098\pi\)
\(830\) 2.45941e8 6.05067e8i 0.0149299 0.0367308i
\(831\) 3.47883e10 2.10296
\(832\) 2.63094e8 + 6.61205e9i 0.0158372 + 0.398020i
\(833\) −1.30956e10 −0.784995
\(834\) −1.57484e10 + 3.87443e10i −0.940058 + 2.31274i
\(835\) −1.52403e10 + 1.52403e10i −0.905920 + 0.905920i
\(836\) 1.03035e9 + 1.00339e9i 0.0609908 + 0.0593949i
\(837\) −1.83491e9 1.83491e9i −0.108162 0.108162i
\(838\) −7.26280e9 1.72104e10i −0.426334 1.01027i
\(839\) 1.12631e10i 0.658401i −0.944260 0.329201i \(-0.893221\pi\)
0.944260 0.329201i \(-0.106779\pi\)
\(840\) −1.38694e10 3.16866e10i −0.807387 1.84459i
\(841\) 1.72162e10i 0.998047i
\(842\) −2.07885e10 + 8.77277e9i −1.20014 + 0.506459i
\(843\) −9.59848e8 9.59848e8i −0.0551831 0.0551831i
\(844\) −2.72281e10 + 3.60967e8i −1.55890 + 0.0206666i
\(845\) −8.49026e9 + 8.49026e9i −0.484086 + 0.484086i
\(846\) 7.09634e10 + 2.88444e10i 4.02938 + 1.63782i
\(847\) 2.31958e10 1.31165
\(848\) −4.38230e9 + 4.62106e9i −0.246784 + 0.260229i
\(849\) 3.38244e10 1.89694
\(850\) −5.82119e9 2.36613e9i −0.325121 0.132152i
\(851\) −3.51518e9 + 3.51518e9i −0.195522 + 0.195522i
\(852\) −8.13493e8 6.13627e10i −0.0450625 3.39912i
\(853\) −8.00308e9 8.00308e9i −0.441505 0.441505i 0.451012 0.892518i \(-0.351063\pi\)
−0.892518 + 0.451012i \(0.851063\pi\)
\(854\) 1.74587e10 7.36758e9i 0.959201 0.404783i
\(855\) 3.13289e10i 1.71421i
\(856\) 7.89241e9 + 3.08676e9i 0.430082 + 0.168207i
\(857\) 8.36787e9i 0.454132i 0.973879 + 0.227066i \(0.0729133\pi\)
−0.973879 + 0.227066i \(0.927087\pi\)
\(858\) 5.37921e8 + 1.27469e9i 0.0290746 + 0.0688970i
\(859\) 1.16635e10 + 1.16635e10i 0.627847 + 0.627847i 0.947526 0.319679i \(-0.103575\pi\)
−0.319679 + 0.947526i \(0.603575\pi\)
\(860\) 2.29338e9 2.35501e9i 0.122951 0.126255i
\(861\) −4.45393e10 + 4.45393e10i −2.37811 + 2.37811i
\(862\) −4.77622e9 + 1.17505e10i −0.253985 + 0.624857i
\(863\) −8.94130e9 −0.473547 −0.236774 0.971565i \(-0.576090\pi\)
−0.236774 + 0.971565i \(0.576090\pi\)
\(864\) −2.17558e10 4.79629e10i −1.14756 2.52992i
\(865\) −1.22127e10 −0.641589
\(866\) 1.22455e9 3.01264e9i 0.0640712 0.157629i
\(867\) 2.00045e9 2.00045e9i 0.104246 0.104246i
\(868\) 9.80740e8 1.00709e9i 0.0509020 0.0522698i
\(869\) 1.11263e9 + 1.11263e9i 0.0575149 + 0.0575149i
\(870\) 5.07160e8 + 1.20180e9i 0.0261113 + 0.0618750i
\(871\) 1.00472e10i 0.515205i
\(872\) −3.83423e9 + 9.80359e9i −0.195826 + 0.500700i
\(873\) 8.35483e10i 4.24999i
\(874\) 8.87297e9 3.74440e9i 0.449551 0.189711i
\(875\) 2.02129e10 + 2.02129e10i 1.02000 + 1.02000i
\(876\) 6.27861e8 + 4.73603e10i 0.0315572 + 2.38040i
\(877\) 7.31289e9 7.31289e9i 0.366092 0.366092i −0.499958 0.866050i \(-0.666651\pi\)
0.866050 + 0.499958i \(0.166651\pi\)
\(878\) −2.98831e10 1.21466e10i −1.49003 0.605651i
\(879\) −2.57494e10 −1.27881
\(880\) −1.65306e9 + 4.38373e7i −0.0817708 + 0.00216847i
\(881\) −3.54118e10 −1.74474 −0.872372 0.488842i \(-0.837419\pi\)
−0.872372 + 0.488842i \(0.837419\pi\)
\(882\) 3.54877e10 + 1.44247e10i 1.74156 + 0.707890i
\(883\) 9.77015e9 9.77015e9i 0.477572 0.477572i −0.426782 0.904354i \(-0.640353\pi\)
0.904354 + 0.426782i \(0.140353\pi\)
\(884\) 8.49752e9 1.12653e8i 0.413723 0.00548477i
\(885\) −2.25889e10 2.25889e10i −1.09545 1.09545i
\(886\) 5.95936e9 2.51485e9i 0.287860 0.121477i
\(887\) 5.27697e9i 0.253894i 0.991910 + 0.126947i \(0.0405178\pi\)
−0.991910 + 0.126947i \(0.959482\pi\)
\(888\) 1.71319e10 7.49873e9i 0.821031 0.359370i
\(889\) 2.58048e10i 1.23181i
\(890\) −2.62544e8 6.22140e8i −0.0124835 0.0295817i
\(891\) −4.05289e9 4.05289e9i −0.191952 0.191952i
\(892\) −2.39587e9 2.33318e9i −0.113028 0.110070i
\(893\) 2.22819e10 2.22819e10i 1.04706 1.04706i
\(894\) 1.85989e10 4.57571e10i 0.870573 2.14179i
\(895\) 7.82461e9 0.364823
\(896\) 2.58239e10 1.21289e10i 1.19934 0.563303i
\(897\) 9.26469e9 0.428605
\(898\) −3.29026e9 + 8.09474e9i −0.151622 + 0.373023i
\(899\) −3.74860e7 + 3.74860e7i −0.00172072 + 0.00172072i
\(900\) 1.31686e10 + 1.28240e10i 0.602129 + 0.586373i
\(901\) 5.78333e9 + 5.78333e9i 0.263415 + 0.263415i
\(902\) 1.17080e9 + 2.77441e9i 0.0531204 + 0.125878i
\(903\) 1.18579e10i 0.535920i
\(904\) −1.42214e10 + 6.22478e9i −0.640253 + 0.280243i
\(905\) 3.10625e10i 1.39305i
\(906\) −1.00659e10 + 4.24782e9i −0.449681 + 0.189766i
\(907\) 1.84084e10 + 1.84084e10i 0.819203 + 0.819203i 0.985993 0.166789i \(-0.0533400\pi\)
−0.166789 + 0.985993i \(0.553340\pi\)
\(908\) 1.49478e10 1.98165e8i 0.662638 0.00878468i
\(909\) −2.31470e10 + 2.31470e10i −1.02216 + 1.02216i
\(910\) −9.04462e9 3.67636e9i −0.397874 0.161724i
\(911\) −1.76557e10 −0.773697 −0.386848 0.922143i \(-0.626436\pi\)
−0.386848 + 0.922143i \(0.626436\pi\)
\(912\) −3.62167e10 + 9.60428e8i −1.58098 + 0.0419260i
\(913\) 1.12639e8 0.00489825
\(914\) 1.82566e10 + 7.42076e9i 0.790877 + 0.321467i
\(915\) 1.95641e10 1.95641e10i 0.844280 0.844280i
\(916\) 1.55109e8 + 1.17000e10i 0.00666809 + 0.502982i
\(917\) −2.35566e9 2.35566e9i −0.100883 0.100883i
\(918\) −6.23155e10 + 2.62972e10i −2.65856 + 1.12191i
\(919\) 2.50780e10i 1.06583i −0.846169 0.532915i \(-0.821097\pi\)
0.846169 0.532915i \(-0.178903\pi\)
\(920\) −4.03332e9 + 1.03126e10i −0.170768 + 0.436629i
\(921\) 7.63349e10i 3.21969i
\(922\) −2.45528e9 5.81818e9i −0.103167 0.244472i
\(923\) −1.22485e10 1.22485e10i −0.512715 0.512715i
\(924\) 4.16171e9 4.27354e9i 0.173548 0.178211i
\(925\) −2.75989e9 + 2.75989e9i −0.114656 + 0.114656i
\(926\) 8.07634e9 1.98695e10i 0.334254 0.822334i
\(927\) −7.49861e10 −3.09173
\(928\) −9.79851e8 + 4.44456e8i −0.0402478 + 0.0182562i
\(929\) 1.46170e10 0.598140 0.299070 0.954231i \(-0.403324\pi\)
0.299070 + 0.954231i \(0.403324\pi\)
\(930\) 7.72863e8 1.90140e9i 0.0315074 0.0775147i
\(931\) 1.11428e10 1.11428e10i 0.452555 0.452555i
\(932\) −1.17787e10 + 1.20952e10i −0.476586 + 0.489392i
\(933\) 3.34604e9 + 3.34604e9i 0.134879 + 0.134879i
\(934\) 9.67254e9 + 2.29207e10i 0.388442 + 0.920478i
\(935\) 2.12369e9i 0.0849670i
\(936\) −2.31515e10 9.05468e9i −0.922815 0.360917i
\(937\) 1.58555e10i 0.629637i 0.949152 + 0.314818i \(0.101944\pi\)
−0.949152 + 0.314818i \(0.898056\pi\)
\(938\) −3.99101e10 + 1.68421e10i −1.57897 + 0.666324i
\(939\) 5.65624e10 + 5.65624e10i 2.22945 + 2.22945i
\(940\) 4.80284e8 + 3.62283e10i 0.0188604 + 1.42266i
\(941\) 1.71527e10 1.71527e10i 0.671071 0.671071i −0.286892 0.957963i \(-0.592622\pi\)
0.957963 + 0.286892i \(0.0926221\pi\)
\(942\) 3.10684e10 + 1.26284e10i 1.21099 + 0.492231i
\(943\) 2.01649e10 0.783079
\(944\) 1.81317e10 1.91195e10i 0.701513 0.739733i
\(945\) 7.77048e10 2.99527
\(946\) 5.25175e8 + 2.13468e8i 0.0201690 + 0.00819810i
\(947\) 6.39507e9 6.39507e9i 0.244693 0.244693i −0.574096 0.818788i \(-0.694646\pi\)
0.818788 + 0.574096i \(0.194646\pi\)
\(948\) −3.96340e10 + 5.25433e8i −1.51091 + 0.0200303i
\(949\) 9.45348e9 + 9.45348e9i 0.359054 + 0.359054i
\(950\) 6.96647e9 2.93985e9i 0.263621 0.111248i
\(951\) 4.74216e10i 1.78790i
\(952\) −1.46919e10 3.35656e10i −0.551885 1.26086i
\(953\) 3.47793e10i 1.30165i 0.759226 + 0.650827i \(0.225578\pi\)
−0.759226 + 0.650827i \(0.774422\pi\)
\(954\) −9.30197e9 2.20426e10i −0.346861 0.821945i
\(955\) 1.43837e9 + 1.43837e9i 0.0534390 + 0.0534390i
\(956\) −1.19119e10 1.16002e10i −0.440939 0.429401i
\(957\) −1.59070e8 + 1.59070e8i −0.00586673 + 0.00586673i
\(958\) −3.95079e9 + 9.71978e9i −0.145179 + 0.357172i
\(959\) 3.86537e9 0.141522
\(960\) 2.82611e10 3.06034e10i 1.03096 1.11640i
\(961\) −2.74292e10 −0.996968
\(962\) 1.98768e9 4.89011e9i 0.0719836 0.177095i
\(963\) −2.25118e10 + 2.25118e10i −0.812303 + 0.812303i
\(964\) 1.32161e10 + 1.28702e10i 0.475152 + 0.462718i
\(965\) 2.24239e10 + 2.24239e10i 0.803276 + 0.803276i
\(966\) −1.55304e10 3.68019e10i −0.554323 1.31356i
\(967\) 1.12415e10i 0.399790i −0.979817 0.199895i \(-0.935940\pi\)
0.979817 0.199895i \(-0.0640602\pi\)
\(968\) 1.12014e10 + 2.55912e10i 0.396925 + 0.906830i
\(969\) 4.65278e10i 1.64278i
\(970\) 3.64081e10 1.53642e10i 1.28085 0.540518i
\(971\) 1.71514e10 + 1.71514e10i 0.601219 + 0.601219i 0.940636 0.339417i \(-0.110230\pi\)
−0.339417 + 0.940636i \(0.610230\pi\)
\(972\) 6.48423e10 8.59622e8i 2.26478 0.0300245i
\(973\) 3.59897e10 3.59897e10i 1.25252 1.25252i
\(974\) −3.52064e10 1.43103e10i −1.22086 0.496241i
\(975\) 7.27403e9 0.251338
\(976\) 1.65593e10 + 1.57037e10i 0.570122 + 0.540665i
\(977\) 4.79355e10 1.64447 0.822236 0.569147i \(-0.192726\pi\)
0.822236 + 0.569147i \(0.192726\pi\)
\(978\) −4.85842e10 1.97480e10i −1.66077 0.675051i
\(979\) 8.23462e7 8.23462e7i 0.00280481 0.00280481i
\(980\) 2.40183e8 + 1.81173e10i 0.00815174 + 0.614895i
\(981\) −2.79631e10 2.79631e10i −0.945679 0.945679i
\(982\) −9.70184e9 + 4.09418e9i −0.326937 + 0.137968i
\(983\) 4.01721e9i 0.134892i −0.997723 0.0674462i \(-0.978515\pi\)
0.997723 0.0674462i \(-0.0214851\pi\)
\(984\) −7.06470e10 2.76304e10i −2.36380 0.924493i
\(985\) 3.40324e10i 1.13466i
\(986\) 5.37234e8 + 1.27307e9i 0.0178482 + 0.0422943i
\(987\) −9.24171e10 9.24171e10i −3.05944 3.05944i
\(988\) −7.13456e9 + 7.32627e9i −0.235352 + 0.241676i
\(989\) 2.68429e9 2.68429e9i 0.0882354 0.0882354i
\(990\) 2.33923e9 5.75499e9i 0.0766212 0.188504i
\(991\) 6.76525e9 0.220814 0.110407 0.993886i \(-0.464785\pi\)
0.110407 + 0.993886i \(0.464785\pi\)
\(992\) 1.58470e9 + 5.95685e8i 0.0515413 + 0.0193743i
\(993\) −2.25120e10 −0.729610
\(994\) −2.81222e10 + 6.91865e10i −0.908231 + 2.23444i
\(995\) −1.76445e10 + 1.76445e10i −0.567844 + 0.567844i
\(996\) −1.97962e9 + 2.03281e9i −0.0634853 + 0.0651912i
\(997\) 2.14103e10 + 2.14103e10i 0.684212 + 0.684212i 0.960946 0.276735i \(-0.0892523\pi\)
−0.276735 + 0.960946i \(0.589252\pi\)
\(998\) 7.24887e9 + 1.71774e10i 0.230841 + 0.547016i
\(999\) 4.20123e10i 1.33321i
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 16.8.e.a.5.8 26
4.3 odd 2 64.8.e.a.49.1 26
8.3 odd 2 128.8.e.a.97.13 26
8.5 even 2 128.8.e.b.97.1 26
16.3 odd 4 64.8.e.a.17.1 26
16.5 even 4 128.8.e.b.33.1 26
16.11 odd 4 128.8.e.a.33.13 26
16.13 even 4 inner 16.8.e.a.13.8 yes 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.8.e.a.5.8 26 1.1 even 1 trivial
16.8.e.a.13.8 yes 26 16.13 even 4 inner
64.8.e.a.17.1 26 16.3 odd 4
64.8.e.a.49.1 26 4.3 odd 2
128.8.e.a.33.13 26 16.11 odd 4
128.8.e.a.97.13 26 8.3 odd 2
128.8.e.b.33.1 26 16.5 even 4
128.8.e.b.97.1 26 8.5 even 2