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Properties

Label 74.8.f.b.9.5
Level $74$
Weight $8$
Character 74.9
Analytic conductor $23.116$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,8,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), 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: \(23.1164918858\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.5
Character \(\chi\) \(=\) 74.9
Dual form 74.8.f.b.33.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38919 - 7.87846i) q^{2} +(-2.39984 + 13.6102i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-34.7022 - 29.1186i) q^{5} +110.561 q^{6} +(-140.013 - 117.485i) q^{7} +(256.000 + 443.405i) q^{8} +(1875.63 + 682.674i) q^{9} +O(q^{10})\) \(q+(-1.38919 - 7.87846i) q^{2} +(-2.39984 + 13.6102i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(-34.7022 - 29.1186i) q^{5} +110.561 q^{6} +(-140.013 - 117.485i) q^{7} +(256.000 + 443.405i) q^{8} +(1875.63 + 682.674i) q^{9} +(-181.202 + 313.852i) q^{10} +(-242.862 - 420.649i) q^{11} +(-153.590 - 871.051i) q^{12} +(381.274 - 138.772i) q^{13} +(-731.095 + 1266.29i) q^{14} +(479.590 - 402.424i) q^{15} +(3137.72 - 2632.86i) q^{16} +(-12523.2 - 4558.08i) q^{17} +(2772.82 - 15725.4i) q^{18} +(1371.19 - 7776.41i) q^{19} +(2724.39 + 991.597i) q^{20} +(1935.00 - 1623.66i) q^{21} +(-2976.68 + 2497.73i) q^{22} +(34537.2 - 59820.2i) q^{23} +(-6649.18 + 2420.10i) q^{24} +(-13209.9 - 74917.1i) q^{25} +(-1622.97 - 2811.07i) q^{26} +(-28904.8 + 50064.7i) q^{27} +(10992.1 + 4000.79i) q^{28} +(-67531.8 - 116969. i) q^{29} +(-3836.72 - 3219.39i) q^{30} -168321. q^{31} +(-25101.7 - 21062.9i) q^{32} +(6307.93 - 2295.90i) q^{33} +(-18513.6 + 104996. i) q^{34} +(1437.76 + 8153.97i) q^{35} -127744. q^{36} +(109883. - 287850. i) q^{37} -63171.0 q^{38} +(973.720 + 5522.24i) q^{39} +(4027.58 - 22841.5i) q^{40} +(-524509. + 190906. i) q^{41} +(-15480.0 - 12989.2i) q^{42} -632169. q^{43} +(23813.5 + 19981.9i) q^{44} +(-45210.0 - 78306.1i) q^{45} +(-519270. - 188999. i) q^{46} +(161379. - 279516. i) q^{47} +(28303.6 + 49023.3i) q^{48} +(-137206. - 778133. i) q^{49} +(-571881. + 208148. i) q^{50} +(92090.0 - 159505. i) q^{51} +(-19892.3 + 16691.6i) q^{52} +(-391642. + 328626. i) q^{53} +(434587. + 158177. i) q^{54} +(-3820.87 + 21669.2i) q^{55} +(16250.0 - 92158.5i) q^{56} +(102548. + 37324.3i) q^{57} +(-827718. + 694538. i) q^{58} +(1.70627e6 - 1.43173e6i) q^{59} +(-20033.9 + 34699.8i) q^{60} +(2.30063e6 - 837362. i) q^{61} +(233829. + 1.32611e6i) q^{62} +(-182409. - 315941. i) q^{63} +(-131072. + 227023. i) q^{64} +(-17271.9 - 6286.47i) q^{65} +(-26851.0 - 46507.4i) q^{66} +(-251802. - 211287. i) q^{67} +852924. q^{68} +(731280. + 613616. i) q^{69} +(62243.4 - 22654.8i) q^{70} +(56594.4 - 320963. i) q^{71} +(177460. + 1.00643e6i) q^{72} +3.75445e6 q^{73} +(-2.42046e6 - 465835. i) q^{74} +1.05134e6 q^{75} +(87756.2 + 497690. i) q^{76} +(-15416.0 + 87428.7i) q^{77} +(42154.1 - 15342.8i) q^{78} +(-1.50336e6 - 1.26147e6i) q^{79} -185551. q^{80} +(2.73196e6 + 2.29239e6i) q^{81} +(2.23268e6 + 3.86712e6i) q^{82} +(2.60792e6 + 949206. i) q^{83} +(-80830.7 + 140003. i) q^{84} +(301859. + 522835. i) q^{85} +(878200. + 4.98052e6i) q^{86} +(1.75403e6 - 638414. i) q^{87} +(124345. - 215372. i) q^{88} +(-770543. + 646562. i) q^{89} +(-554127. + 464967. i) q^{90} +(-69686.9 - 25364.0i) q^{91} +(-767657. + 4.35360e6i) q^{92} +(403944. - 2.29088e6i) q^{93} +(-2.42634e6 - 883116. i) q^{94} +(-274022. + 229932. i) q^{95} +(346910. - 291092. i) q^{96} +(160227. - 277521. i) q^{97} +(-5.93989e6 + 2.16194e6i) q^{98} +(-168353. - 954776. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38919 − 7.87846i −0.122788 − 0.696364i
\(3\) −2.39984 + 13.6102i −0.0513166 + 0.291031i −0.999656 − 0.0262265i \(-0.991651\pi\)
0.948339 + 0.317258i \(0.102762\pi\)
\(4\) −60.1403 + 21.8893i −0.469846 + 0.171010i
\(5\) −34.7022 − 29.1186i −0.124155 − 0.104178i 0.578596 − 0.815614i \(-0.303601\pi\)
−0.702751 + 0.711436i \(0.748045\pi\)
\(6\) 110.561 0.208965
\(7\) −140.013 − 117.485i −0.154285 − 0.129461i 0.562377 − 0.826881i \(-0.309887\pi\)
−0.716663 + 0.697420i \(0.754331\pi\)
\(8\) 256.000 + 443.405i 0.176777 + 0.306186i
\(9\) 1875.63 + 682.674i 0.857627 + 0.312151i
\(10\) −181.202 + 313.852i −0.0573012 + 0.0992486i
\(11\) −242.862 − 420.649i −0.0550154 − 0.0952895i 0.837206 − 0.546887i \(-0.184187\pi\)
−0.892222 + 0.451598i \(0.850854\pi\)
\(12\) −153.590 − 871.051i −0.0256583 − 0.145516i
\(13\) 381.274 − 138.772i 0.0481322 − 0.0175187i −0.317842 − 0.948144i \(-0.602958\pi\)
0.365974 + 0.930625i \(0.380736\pi\)
\(14\) −731.095 + 1266.29i −0.0712075 + 0.123335i
\(15\) 479.590 − 402.424i 0.0366902 − 0.0307868i
\(16\) 3137.72 − 2632.86i 0.191511 − 0.160697i
\(17\) −12523.2 − 4558.08i −0.618223 − 0.225015i 0.0138746 − 0.999904i \(-0.495583\pi\)
−0.632097 + 0.774889i \(0.717806\pi\)
\(18\) 2772.82 − 15725.4i 0.112064 − 0.635549i
\(19\) 1371.19 − 7776.41i 0.0458628 − 0.260101i −0.953252 − 0.302178i \(-0.902286\pi\)
0.999114 + 0.0420770i \(0.0133975\pi\)
\(20\) 2724.39 + 991.597i 0.0761490 + 0.0277160i
\(21\) 1935.00 − 1623.66i 0.0455945 − 0.0382584i
\(22\) −2976.68 + 2497.73i −0.0596010 + 0.0500112i
\(23\) 34537.2 − 59820.2i 0.591888 − 1.02518i −0.402090 − 0.915600i \(-0.631716\pi\)
0.993978 − 0.109580i \(-0.0349506\pi\)
\(24\) −6649.18 + 2420.10i −0.0981813 + 0.0357351i
\(25\) −13209.9 − 74917.1i −0.169087 − 0.958939i
\(26\) −1622.97 − 2811.07i −0.0181094 − 0.0313664i
\(27\) −28904.8 + 50064.7i −0.282616 + 0.489506i
\(28\) 10992.1 + 4000.79i 0.0946295 + 0.0344423i
\(29\) −67531.8 − 116969.i −0.514181 − 0.890587i −0.999865 − 0.0164524i \(-0.994763\pi\)
0.485684 − 0.874134i \(-0.338571\pi\)
\(30\) −3836.72 − 3219.39i −0.0259439 − 0.0217695i
\(31\) −168321. −1.01478 −0.507391 − 0.861716i \(-0.669390\pi\)
−0.507391 + 0.861716i \(0.669390\pi\)
\(32\) −25101.7 − 21062.9i −0.135419 − 0.113630i
\(33\) 6307.93 − 2295.90i 0.0305554 − 0.0111213i
\(34\) −18513.6 + 104996.i −0.0807819 + 0.458137i
\(35\) 1437.76 + 8153.97i 0.00566826 + 0.0321463i
\(36\) −127744. −0.456334
\(37\) 109883. − 287850.i 0.356637 − 0.934243i
\(38\) −63171.0 −0.186756
\(39\) 973.720 + 5522.24i 0.00262850 + 0.0149070i
\(40\) 4027.58 − 22841.5i 0.00995025 − 0.0564307i
\(41\) −524509. + 190906.i −1.18853 + 0.432589i −0.859206 − 0.511629i \(-0.829042\pi\)
−0.329321 + 0.944218i \(0.606820\pi\)
\(42\) −15480.0 − 12989.2i −0.0322402 − 0.0270527i
\(43\) −632169. −1.21253 −0.606267 − 0.795261i \(-0.707334\pi\)
−0.606267 + 0.795261i \(0.707334\pi\)
\(44\) 23813.5 + 19981.9i 0.0421442 + 0.0353632i
\(45\) −45210.0 − 78306.1i −0.0739590 − 0.128101i
\(46\) −519270. − 188999.i −0.786576 − 0.286290i
\(47\) 161379. − 279516.i 0.226727 − 0.392703i −0.730109 − 0.683331i \(-0.760531\pi\)
0.956836 + 0.290628i \(0.0938641\pi\)
\(48\) 28303.6 + 49023.3i 0.0369401 + 0.0639821i
\(49\) −137206. − 778133.i −0.166604 − 0.944860i
\(50\) −571881. + 208148.i −0.647009 + 0.235492i
\(51\) 92090.0 − 159505.i 0.0972114 − 0.168375i
\(52\) −19892.3 + 16691.6i −0.0196189 + 0.0164622i
\(53\) −391642. + 328626.i −0.361346 + 0.303205i −0.805327 − 0.592831i \(-0.798010\pi\)
0.443981 + 0.896036i \(0.353566\pi\)
\(54\) 434587. + 158177.i 0.375576 + 0.136699i
\(55\) −3820.87 + 21669.2i −0.00309666 + 0.0175620i
\(56\) 16250.0 − 92158.5i 0.0123651 − 0.0701257i
\(57\) 102548. + 37324.3i 0.0733439 + 0.0266950i
\(58\) −827718. + 694538.i −0.557038 + 0.467410i
\(59\) 1.70627e6 − 1.43173e6i 1.08160 − 0.907569i 0.0855457 − 0.996334i \(-0.472737\pi\)
0.996053 + 0.0887656i \(0.0282922\pi\)
\(60\) −20033.9 + 34699.8i −0.0119739 + 0.0207394i
\(61\) 2.30063e6 − 837362.i 1.29775 − 0.472344i 0.401490 − 0.915863i \(-0.368492\pi\)
0.896265 + 0.443519i \(0.146270\pi\)
\(62\) 233829. + 1.32611e6i 0.124603 + 0.706658i
\(63\) −182409. − 315941.i −0.0919080 − 0.159189i
\(64\) −131072. + 227023.i −0.0625000 + 0.108253i
\(65\) −17271.9 − 6286.47i −0.00780089 − 0.00283929i
\(66\) −26851.0 − 46507.4i −0.0114963 − 0.0199121i
\(67\) −251802. − 211287.i −0.102281 − 0.0858243i 0.590213 − 0.807248i \(-0.299044\pi\)
−0.692494 + 0.721423i \(0.743488\pi\)
\(68\) 852924. 0.328949
\(69\) 731280. + 613616.i 0.267986 + 0.224867i
\(70\) 62243.4 − 22654.8i 0.0216895 − 0.00789435i
\(71\) 56594.4 − 320963.i 0.0187659 − 0.106427i −0.973986 − 0.226608i \(-0.927236\pi\)
0.992752 + 0.120181i \(0.0383475\pi\)
\(72\) 177460. + 1.00643e6i 0.0560322 + 0.317775i
\(73\) 3.75445e6 1.12958 0.564790 − 0.825235i \(-0.308957\pi\)
0.564790 + 0.825235i \(0.308957\pi\)
\(74\) −2.42046e6 − 465835.i −0.694364 − 0.133635i
\(75\) 1.05134e6 0.287758
\(76\) 87756.2 + 497690.i 0.0229314 + 0.130050i
\(77\) −15416.0 + 87428.7i −0.00384818 + 0.0218241i
\(78\) 42154.1 − 15342.8i 0.0100579 − 0.00366079i
\(79\) −1.50336e6 − 1.26147e6i −0.343059 − 0.287860i 0.454937 − 0.890524i \(-0.349662\pi\)
−0.797996 + 0.602663i \(0.794106\pi\)
\(80\) −185551. −0.0405181
\(81\) 2.73196e6 + 2.29239e6i 0.571185 + 0.479281i
\(82\) 2.23268e6 + 3.86712e6i 0.447176 + 0.774531i
\(83\) 2.60792e6 + 949206.i 0.500635 + 0.182216i 0.579980 − 0.814631i \(-0.303061\pi\)
−0.0793446 + 0.996847i \(0.525283\pi\)
\(84\) −80830.7 + 140003.i −0.0148799 + 0.0257727i
\(85\) 301859. + 522835.i 0.0533136 + 0.0923418i
\(86\) 878200. + 4.98052e6i 0.148884 + 0.844365i
\(87\) 1.75403e6 − 638414.i 0.285574 − 0.103941i
\(88\) 124345. − 215372.i 0.0194509 − 0.0336899i
\(89\) −770543. + 646562.i −0.115859 + 0.0972177i −0.698877 − 0.715242i \(-0.746316\pi\)
0.583017 + 0.812460i \(0.301872\pi\)
\(90\) −554127. + 464967.i −0.0801235 + 0.0672316i
\(91\) −69686.9 − 25364.0i −0.00969408 − 0.00352836i
\(92\) −767657. + 4.35360e6i −0.102780 + 0.582896i
\(93\) 403944. − 2.29088e6i 0.0520752 − 0.295333i
\(94\) −2.42634e6 − 883116.i −0.301304 − 0.109666i
\(95\) −274022. + 229932.i −0.0327908 + 0.0275148i
\(96\) 346910. − 291092.i 0.0400191 − 0.0335800i
\(97\) 160227. − 277521.i 0.0178252 − 0.0308741i −0.856975 − 0.515358i \(-0.827659\pi\)
0.874800 + 0.484484i \(0.160992\pi\)
\(98\) −5.93989e6 + 2.16194e6i −0.637510 + 0.232035i
\(99\) −168353. − 954776.i −0.0174380 − 0.0988959i
\(100\) 2.43433e6 + 4.21639e6i 0.243433 + 0.421639i
\(101\) −217811. + 377259.i −0.0210356 + 0.0364347i −0.876352 − 0.481672i \(-0.840030\pi\)
0.855316 + 0.518107i \(0.173363\pi\)
\(102\) −1.38458e6 − 503946.i −0.129187 − 0.0470201i
\(103\) 3.79704e6 + 6.57666e6i 0.342385 + 0.593028i 0.984875 − 0.173266i \(-0.0554320\pi\)
−0.642490 + 0.766294i \(0.722099\pi\)
\(104\) 159139. + 133533.i 0.0138726 + 0.0116405i
\(105\) −114427. −0.00964645
\(106\) 3.13313e6 + 2.62901e6i 0.255510 + 0.214399i
\(107\) −8.91289e6 + 3.24403e6i −0.703356 + 0.256001i −0.668843 − 0.743404i \(-0.733210\pi\)
−0.0345131 + 0.999404i \(0.510988\pi\)
\(108\) 642467. − 3.64361e6i 0.0490758 − 0.278323i
\(109\) −1.53050e6 − 8.67987e6i −0.113198 − 0.641978i −0.987627 − 0.156824i \(-0.949874\pi\)
0.874428 − 0.485154i \(-0.161237\pi\)
\(110\) 176028. 0.0126098
\(111\) 3.65399e6 + 2.18633e6i 0.253592 + 0.151735i
\(112\) −748642. −0.0503513
\(113\) −279562. − 1.58547e6i −0.0182265 − 0.103368i 0.974337 − 0.225093i \(-0.0722685\pi\)
−0.992564 + 0.121725i \(0.961157\pi\)
\(114\) 151600. − 859768.i 0.00958370 − 0.0543519i
\(115\) −2.94040e6 + 1.07022e6i −0.180287 + 0.0656191i
\(116\) 6.62175e6 + 5.55630e6i 0.393885 + 0.330509i
\(117\) 809865. 0.0467479
\(118\) −1.36502e7 − 1.14539e7i −0.764805 − 0.641748i
\(119\) 1.21791e6 + 2.10948e6i 0.0662521 + 0.114752i
\(120\) 301212. + 109632.i 0.0159125 + 0.00579166i
\(121\) 9.62562e6 − 1.66721e7i 0.493947 − 0.855541i
\(122\) −9.79312e6 − 1.69622e7i −0.488272 − 0.845712i
\(123\) −1.33952e6 − 7.59680e6i −0.0649055 − 0.368097i
\(124\) 1.01229e7 − 3.68443e6i 0.476792 − 0.173538i
\(125\) −3.49262e6 + 6.04940e6i −0.159944 + 0.277030i
\(126\) −2.23573e6 + 1.87600e6i −0.0995686 + 0.0835480i
\(127\) 5.65418e6 − 4.74442e6i 0.244938 − 0.205528i −0.512051 − 0.858955i \(-0.671114\pi\)
0.756989 + 0.653428i \(0.226670\pi\)
\(128\) 1.97068e6 + 717268.i 0.0830579 + 0.0302306i
\(129\) 1.51711e6 − 8.60394e6i 0.0622231 − 0.352885i
\(130\) −25533.8 + 144809.i −0.00101933 + 0.00578089i
\(131\) −3.15569e7 − 1.14858e7i −1.22644 − 0.446387i −0.354061 − 0.935222i \(-0.615200\pi\)
−0.872376 + 0.488836i \(0.837422\pi\)
\(132\) −329105. + 276152.i −0.0124545 + 0.0104506i
\(133\) −1.10559e6 + 927704.i −0.0407488 + 0.0341923i
\(134\) −1.31481e6 + 2.27733e6i −0.0472061 + 0.0817633i
\(135\) 2.46088e6 − 895686.i 0.0860839 − 0.0313320i
\(136\) −1.18487e6 − 6.71973e6i −0.0403910 − 0.229069i
\(137\) −1.22199e7 − 2.11654e7i −0.406017 − 0.703242i 0.588422 − 0.808554i \(-0.299749\pi\)
−0.994439 + 0.105312i \(0.966416\pi\)
\(138\) 3.81847e6 − 6.61379e6i 0.123684 − 0.214227i
\(139\) −1.72113e7 − 6.26442e6i −0.543579 − 0.197847i 0.0556121 − 0.998452i \(-0.482289\pi\)
−0.599192 + 0.800606i \(0.704511\pi\)
\(140\) −264952. − 458911.i −0.00816055 − 0.0141345i
\(141\) 3.41698e6 + 2.86719e6i 0.102654 + 0.0861369i
\(142\) −2.60732e6 −0.0764160
\(143\) −150971. − 126680.i −0.00431736 − 0.00362269i
\(144\) 7.68258e6 − 2.79623e6i 0.214407 − 0.0780377i
\(145\) −1.06246e6 + 6.02551e6i −0.0289417 + 0.164137i
\(146\) −5.21563e6 − 2.95793e7i −0.138699 − 0.786598i
\(147\) 1.09198e7 0.283533
\(148\) −307593. + 1.97167e7i −0.00779938 + 0.499939i
\(149\) −2.05803e7 −0.509683 −0.254842 − 0.966983i \(-0.582023\pi\)
−0.254842 + 0.966983i \(0.582023\pi\)
\(150\) −1.46050e6 − 8.28292e6i −0.0353332 − 0.200385i
\(151\) −1.10921e7 + 6.29066e7i −0.262178 + 1.48688i 0.514775 + 0.857325i \(0.327875\pi\)
−0.776953 + 0.629559i \(0.783236\pi\)
\(152\) 3.79912e6 − 1.38277e6i 0.0877467 − 0.0319372i
\(153\) −2.03773e7 − 1.70985e7i −0.459966 − 0.385957i
\(154\) 710220. 0.0156700
\(155\) 5.84112e6 + 4.90129e6i 0.125990 + 0.105718i
\(156\) −179438. − 310795.i −0.00378423 − 0.00655448i
\(157\) 4.73490e6 + 1.72336e6i 0.0976476 + 0.0355408i 0.390382 − 0.920653i \(-0.372343\pi\)
−0.292734 + 0.956194i \(0.594565\pi\)
\(158\) −7.84999e6 + 1.35966e7i −0.158332 + 0.274240i
\(159\) −3.53279e6 − 6.11896e6i −0.0696991 − 0.120722i
\(160\) 257765. + 1.46186e6i 0.00497512 + 0.0282153i
\(161\) −1.18636e7 + 4.31800e6i −0.224040 + 0.0815440i
\(162\) 1.42653e7 − 2.47082e7i 0.263620 − 0.456603i
\(163\) 1.20341e7 − 1.00978e7i 0.217648 − 0.182629i −0.527444 − 0.849590i \(-0.676850\pi\)
0.745093 + 0.666961i \(0.232405\pi\)
\(164\) 2.73653e7 − 2.29622e7i 0.484448 − 0.406500i
\(165\) −285753. − 104006.i −0.00495218 − 0.00180245i
\(166\) 3.85539e6 − 2.18650e7i 0.0654170 − 0.370998i
\(167\) −1.66383e7 + 9.43603e7i −0.276440 + 1.56777i 0.457911 + 0.888998i \(0.348598\pi\)
−0.734351 + 0.678770i \(0.762513\pi\)
\(168\) 1.21530e6 + 442332.i 0.0197742 + 0.00719723i
\(169\) −4.79420e7 + 4.02281e7i −0.764035 + 0.641101i
\(170\) 3.69980e6 − 3.10450e6i 0.0577573 − 0.0484641i
\(171\) 7.88060e6 − 1.36496e7i 0.120524 − 0.208753i
\(172\) 3.80189e7 − 1.38377e7i 0.569704 − 0.207355i
\(173\) 6.19760e6 + 3.51483e7i 0.0910044 + 0.516111i 0.995899 + 0.0904751i \(0.0288386\pi\)
−0.904894 + 0.425636i \(0.860050\pi\)
\(174\) −7.46639e6 − 1.29322e7i −0.107446 − 0.186101i
\(175\) −6.95206e6 + 1.20413e7i −0.0980575 + 0.169840i
\(176\) −1.86954e6 − 680457.i −0.0258488 − 0.00940819i
\(177\) 1.53913e7 + 2.66586e7i 0.208627 + 0.361352i
\(178\) 6.16434e6 + 5.17250e6i 0.0819250 + 0.0687433i
\(179\) −2.74684e7 −0.357972 −0.178986 − 0.983852i \(-0.557282\pi\)
−0.178986 + 0.983852i \(0.557282\pi\)
\(180\) 4.43301e6 + 3.71974e6i 0.0566559 + 0.0475399i
\(181\) 9.33830e7 − 3.39886e7i 1.17056 − 0.426048i 0.317700 − 0.948191i \(-0.397090\pi\)
0.852858 + 0.522143i \(0.174867\pi\)
\(182\) −103021. + 584261.i −0.00126671 + 0.00718385i
\(183\) 5.87549e6 + 3.33215e7i 0.0708704 + 0.401926i
\(184\) 3.53661e7 0.418528
\(185\) −1.21950e7 + 6.78938e6i −0.141606 + 0.0788368i
\(186\) −1.86098e7 −0.212054
\(187\) 1.12406e6 + 6.37486e6i 0.0125702 + 0.0712894i
\(188\) −3.58696e6 + 2.03427e7i −0.0393708 + 0.223283i
\(189\) 9.92889e6 − 3.61382e6i 0.106975 − 0.0389359i
\(190\) 2.19218e6 + 1.83945e6i 0.0231866 + 0.0194559i
\(191\) −2.87035e7 −0.298069 −0.149035 − 0.988832i \(-0.547617\pi\)
−0.149035 + 0.988832i \(0.547617\pi\)
\(192\) −2.77528e6 − 2.32873e6i −0.0282978 − 0.0237446i
\(193\) 5.07668e7 + 8.79306e7i 0.508310 + 0.880419i 0.999954 + 0.00962258i \(0.00306301\pi\)
−0.491643 + 0.870797i \(0.663604\pi\)
\(194\) −2.40902e6 − 876811.i −0.0236883 − 0.00862184i
\(195\) 127010. − 219988.i 0.00122664 − 0.00212460i
\(196\) 2.52844e7 + 4.37938e7i 0.239859 + 0.415448i
\(197\) −1.98035e7 − 1.12311e8i −0.184549 − 1.04663i −0.926534 − 0.376211i \(-0.877227\pi\)
0.741985 − 0.670416i \(-0.233884\pi\)
\(198\) −7.28829e6 + 2.65272e6i −0.0667264 + 0.0242864i
\(199\) −1.04095e7 + 1.80298e7i −0.0936362 + 0.162183i −0.909039 − 0.416712i \(-0.863182\pi\)
0.815402 + 0.578895i \(0.196516\pi\)
\(200\) 2.98369e7 − 2.50361e7i 0.263723 − 0.221290i
\(201\) 3.47993e6 − 2.92001e6i 0.0302263 − 0.0253629i
\(202\) 3.27480e6 + 1.19193e6i 0.0279547 + 0.0101747i
\(203\) −4.28670e6 + 2.43111e7i −0.0359656 + 0.203971i
\(204\) −2.04688e6 + 1.16084e7i −0.0168806 + 0.0957345i
\(205\) 2.37605e7 + 8.64813e6i 0.192627 + 0.0701106i
\(206\) 4.65392e7 − 3.90510e7i 0.370923 − 0.311241i
\(207\) 1.05617e8 − 8.86229e7i 0.827630 − 0.694464i
\(208\) 830962. − 1.43927e6i 0.00640265 − 0.0110897i
\(209\) −3.60414e6 + 1.31180e6i −0.0273080 + 0.00993931i
\(210\) 158961. + 901512.i 0.00118447 + 0.00671744i
\(211\) 1.33835e8 + 2.31810e8i 0.980804 + 1.69880i 0.659274 + 0.751903i \(0.270864\pi\)
0.321530 + 0.946899i \(0.395803\pi\)
\(212\) 1.63601e7 − 2.83365e7i 0.117926 − 0.204254i
\(213\) 4.23255e6 + 1.54052e6i 0.0300105 + 0.0109229i
\(214\) 3.79396e7 + 6.57133e7i 0.264633 + 0.458358i
\(215\) 2.19377e7 + 1.84079e7i 0.150542 + 0.126319i
\(216\) −2.95986e7 −0.199840
\(217\) 2.35671e7 + 1.97752e7i 0.156566 + 0.131375i
\(218\) −6.62579e7 + 2.41159e7i −0.433151 + 0.157654i
\(219\) −9.01009e6 + 5.10988e7i −0.0579662 + 0.328743i
\(220\) −244536. − 1.38683e6i −0.00154833 − 0.00878101i
\(221\) −5.40732e6 −0.0336984
\(222\) 1.21488e7 − 3.18250e7i 0.0745245 − 0.195224i
\(223\) 9.62882e7 0.581441 0.290721 − 0.956808i \(-0.406105\pi\)
0.290721 + 0.956808i \(0.406105\pi\)
\(224\) 1.04000e6 + 5.89814e6i 0.00618253 + 0.0350629i
\(225\) 2.63670e7 − 1.49535e8i 0.154320 − 0.875193i
\(226\) −1.21027e7 + 4.40503e6i −0.0697435 + 0.0253846i
\(227\) −3.35258e7 − 2.81315e7i −0.190234 − 0.159625i 0.542696 − 0.839929i \(-0.317403\pi\)
−0.732930 + 0.680304i \(0.761848\pi\)
\(228\) −6.98425e6 −0.0390255
\(229\) −3.91250e7 − 3.28298e7i −0.215293 − 0.180653i 0.528763 − 0.848770i \(-0.322656\pi\)
−0.744056 + 0.668117i \(0.767101\pi\)
\(230\) 1.25164e7 + 2.16791e7i 0.0678318 + 0.117488i
\(231\) −1.15292e6 − 419630.i −0.00615402 − 0.00223988i
\(232\) 3.45763e7 − 5.98879e7i 0.181790 − 0.314870i
\(233\) −4.23574e7 − 7.33652e7i −0.219373 − 0.379966i 0.735243 − 0.677803i \(-0.237068\pi\)
−0.954617 + 0.297838i \(0.903735\pi\)
\(234\) −1.12505e6 − 6.38049e6i −0.00574007 − 0.0325536i
\(235\) −1.37393e7 + 5.00071e6i −0.0690602 + 0.0251359i
\(236\) −7.12761e7 + 1.23454e8i −0.352982 + 0.611382i
\(237\) 2.07767e7 − 1.74337e7i 0.101381 − 0.0850687i
\(238\) 1.49275e7 − 1.25257e7i 0.0717743 − 0.0602258i
\(239\) −8.08403e7 − 2.94235e7i −0.383032 − 0.139412i 0.143325 − 0.989676i \(-0.454220\pi\)
−0.526358 + 0.850263i \(0.676443\pi\)
\(240\) 445293. − 2.52538e6i 0.00207925 − 0.0117920i
\(241\) 6.34093e7 − 3.59612e8i 0.291805 − 1.65491i −0.388106 − 0.921615i \(-0.626871\pi\)
0.679911 − 0.733295i \(-0.262018\pi\)
\(242\) −1.44722e8 − 5.26745e7i −0.656419 − 0.238917i
\(243\) −1.34607e8 + 1.12949e8i −0.601791 + 0.504962i
\(244\) −1.20032e8 + 1.00718e8i −0.528970 + 0.443858i
\(245\) −1.78968e7 + 3.09982e7i −0.0777490 + 0.134665i
\(246\) −5.79903e7 + 2.11067e7i −0.248360 + 0.0903957i
\(247\) −556352. − 3.15523e6i −0.00234915 − 0.0133227i
\(248\) −4.30902e7 − 7.46345e7i −0.179390 − 0.310712i
\(249\) −1.91775e7 + 3.32163e7i −0.0787215 + 0.136350i
\(250\) 5.25119e7 + 1.91128e7i 0.212553 + 0.0773631i
\(251\) −8.21534e7 − 1.42294e8i −0.327920 − 0.567973i 0.654179 − 0.756339i \(-0.273014\pi\)
−0.982099 + 0.188366i \(0.939681\pi\)
\(252\) 1.78858e7 + 1.50080e7i 0.0704056 + 0.0590773i
\(253\) −3.35510e7 −0.130252
\(254\) −4.52334e7 − 3.79554e7i −0.173198 − 0.145330i
\(255\) −7.84029e6 + 2.85363e6i −0.0296102 + 0.0107772i
\(256\) 2.91333e6 − 1.65223e7i 0.0108530 − 0.0615505i
\(257\) −6.95974e7 − 3.94706e8i −0.255757 − 1.45047i −0.794123 − 0.607757i \(-0.792069\pi\)
0.538366 − 0.842711i \(-0.319042\pi\)
\(258\) −6.98933e7 −0.253377
\(259\) −4.92031e7 + 2.73931e7i −0.175972 + 0.0979696i
\(260\) 1.17635e6 0.00415077
\(261\) −4.68134e7 − 2.65492e8i −0.162978 − 0.924293i
\(262\) −4.66519e7 + 2.64576e8i −0.160256 + 0.908858i
\(263\) −1.54464e8 + 5.62203e7i −0.523578 + 0.190567i −0.590269 − 0.807207i \(-0.700978\pi\)
0.0666903 + 0.997774i \(0.478756\pi\)
\(264\) 2.63284e6 + 2.20922e6i 0.00880666 + 0.00738967i
\(265\) 2.31600e7 0.0764501
\(266\) 8.84475e6 + 7.42163e6i 0.0288138 + 0.0241776i
\(267\) −6.95064e6 − 1.20389e7i −0.0223478 − 0.0387076i
\(268\) 1.97683e7 + 7.19509e6i 0.0627334 + 0.0228331i
\(269\) −1.05940e7 + 1.83493e7i −0.0331838 + 0.0574761i −0.882140 − 0.470987i \(-0.843898\pi\)
0.848957 + 0.528463i \(0.177231\pi\)
\(270\) −1.04752e7 − 1.81437e7i −0.0323885 − 0.0560986i
\(271\) 5.48428e7 + 3.11029e8i 0.167389 + 0.949310i 0.946567 + 0.322507i \(0.104526\pi\)
−0.779178 + 0.626803i \(0.784363\pi\)
\(272\) −5.12951e7 + 1.86699e7i −0.154556 + 0.0562537i
\(273\) 512446. − 887582.i 0.00152433 − 0.00264021i
\(274\) −1.49775e8 + 1.25676e8i −0.439859 + 0.369085i
\(275\) −2.83056e7 + 2.37512e7i −0.0820745 + 0.0688686i
\(276\) −5.74110e7 − 2.08959e7i −0.164367 − 0.0598245i
\(277\) 2.44231e7 − 1.38510e8i 0.0690433 − 0.391564i −0.930629 − 0.365964i \(-0.880739\pi\)
0.999672 − 0.0255999i \(-0.00814959\pi\)
\(278\) −2.54442e7 + 1.44301e8i −0.0710285 + 0.402822i
\(279\) −3.15708e8 − 1.14908e8i −0.870305 − 0.316765i
\(280\) −3.24744e6 + 2.72493e6i −0.00884074 + 0.00741826i
\(281\) −5.45865e7 + 4.58035e7i −0.146762 + 0.123148i −0.713213 − 0.700948i \(-0.752761\pi\)
0.566451 + 0.824096i \(0.308316\pi\)
\(282\) 1.78422e7 − 3.09036e7i 0.0473780 − 0.0820611i
\(283\) 2.56694e8 − 9.34291e7i 0.673231 − 0.245036i 0.0172923 − 0.999850i \(-0.494495\pi\)
0.655938 + 0.754815i \(0.272273\pi\)
\(284\) 3.62204e6 + 2.05416e7i 0.00938295 + 0.0532134i
\(285\) −2.47180e6 − 4.28129e6i −0.00632494 − 0.0109551i
\(286\) −788316. + 1.36540e6i −0.00199260 + 0.00345128i
\(287\) 9.58665e7 + 3.48925e7i 0.239376 + 0.0871256i
\(288\) −3.27025e7 − 5.66424e7i −0.0806692 − 0.139723i
\(289\) −1.78283e8 − 1.49597e8i −0.434477 − 0.364569i
\(290\) 4.89477e7 0.117853
\(291\) 3.39259e6 + 2.84672e6i 0.00807059 + 0.00677203i
\(292\) −2.25794e8 + 8.21823e7i −0.530729 + 0.193169i
\(293\) 4.42363e7 − 2.50877e8i 0.102741 − 0.582671i −0.889358 − 0.457211i \(-0.848848\pi\)
0.992099 − 0.125460i \(-0.0400406\pi\)
\(294\) −1.51696e7 − 8.60312e7i −0.0348144 − 0.197442i
\(295\) −1.00902e8 −0.228834
\(296\) 1.55764e8 − 2.49667e7i 0.349097 − 0.0559552i
\(297\) 2.80795e7 0.0621930
\(298\) 2.85899e7 + 1.62141e8i 0.0625829 + 0.354925i
\(299\) 4.86675e6 − 2.76007e7i 0.0105291 − 0.0597133i
\(300\) −6.32278e7 + 2.30130e7i −0.135202 + 0.0492095i
\(301\) 8.85118e7 + 7.42702e7i 0.187076 + 0.156976i
\(302\) 5.11017e8 1.06761
\(303\) −4.61185e6 − 3.86980e6i −0.00952415 − 0.00799171i
\(304\) −1.61718e7 − 2.80103e7i −0.0330141 − 0.0571822i
\(305\) −1.04220e8 − 3.79329e7i −0.210330 − 0.0765539i
\(306\) −1.06402e8 + 1.84294e8i −0.212289 + 0.367695i
\(307\) 1.90959e8 + 3.30751e8i 0.376666 + 0.652405i 0.990575 − 0.136972i \(-0.0437371\pi\)
−0.613909 + 0.789377i \(0.710404\pi\)
\(308\) −986627. − 5.59544e6i −0.00192409 − 0.0109121i
\(309\) −9.86218e7 + 3.58954e7i −0.190160 + 0.0692124i
\(310\) 3.05002e7 − 5.28279e7i 0.0581482 − 0.100716i
\(311\) 2.97564e8 − 2.49686e8i 0.560943 − 0.470687i −0.317684 − 0.948197i \(-0.602905\pi\)
0.878626 + 0.477510i \(0.158461\pi\)
\(312\) −2.19932e6 + 1.84545e6i −0.00409965 + 0.00344001i
\(313\) 6.04405e8 + 2.19985e8i 1.11410 + 0.405498i 0.832495 − 0.554033i \(-0.186912\pi\)
0.281602 + 0.959531i \(0.409134\pi\)
\(314\) 6.99979e6 − 3.96978e7i 0.0127594 − 0.0723623i
\(315\) −2.86978e6 + 1.62754e7i −0.00517324 + 0.0293389i
\(316\) 1.18025e8 + 4.29577e7i 0.210412 + 0.0765837i
\(317\) 6.74598e8 − 5.66055e8i 1.18943 − 0.998047i 0.189557 − 0.981870i \(-0.439295\pi\)
0.999869 − 0.0161776i \(-0.00514970\pi\)
\(318\) −4.33003e7 + 3.63333e7i −0.0755086 + 0.0633592i
\(319\) −3.28018e7 + 5.68143e7i −0.0565757 + 0.0979920i
\(320\) 1.11591e7 − 4.06158e6i 0.0190373 − 0.00692900i
\(321\) −2.27623e7 − 1.29091e8i −0.0384103 − 0.217836i
\(322\) 5.05000e7 + 8.74685e7i 0.0842938 + 0.146001i
\(323\) −5.26172e7 + 9.11357e7i −0.0868799 + 0.150480i
\(324\) −2.14480e8 − 7.80643e7i −0.350331 − 0.127510i
\(325\) −1.54330e7 − 2.67308e7i −0.0249379 − 0.0431937i
\(326\) −9.62725e7 − 8.07822e7i −0.153901 − 0.129138i
\(327\) 1.21808e8 0.192645
\(328\) −2.18923e8 − 1.83698e8i −0.342557 − 0.287439i
\(329\) −5.54340e7 + 2.01763e7i −0.0858204 + 0.0312361i
\(330\) −422440. + 2.39578e6i −0.000647092 + 0.00366984i
\(331\) 1.61341e8 + 9.15009e8i 0.244538 + 1.38684i 0.821563 + 0.570117i \(0.193102\pi\)
−0.577025 + 0.816726i \(0.695787\pi\)
\(332\) −1.77619e8 −0.266382
\(333\) 4.02608e8 − 4.64885e8i 0.597486 − 0.689908i
\(334\) 7.66528e8 1.12568
\(335\) 2.58570e6 + 1.46642e7i 0.00375769 + 0.0213109i
\(336\) 1.79662e6 − 1.01891e7i 0.00258386 − 0.0146538i
\(337\) −2.84824e8 + 1.03667e8i −0.405389 + 0.147549i −0.536663 − 0.843797i \(-0.680315\pi\)
0.131274 + 0.991346i \(0.458093\pi\)
\(338\) 3.83536e8 + 3.21825e8i 0.540254 + 0.453327i
\(339\) 2.22495e7 0.0310185
\(340\) −2.95984e7 − 2.48360e7i −0.0408406 − 0.0342693i
\(341\) 4.08788e7 + 7.08041e7i 0.0558287 + 0.0966981i
\(342\) −1.18485e8 − 4.31252e7i −0.160167 − 0.0582961i
\(343\) −1.47469e8 + 2.55424e8i −0.197320 + 0.341769i
\(344\) −1.61835e8 − 2.80307e8i −0.214348 − 0.371261i
\(345\) −7.50937e6 − 4.25877e7i −0.00984547 − 0.0558364i
\(346\) 2.68305e8 − 9.76551e7i 0.348227 − 0.126744i
\(347\) −5.00948e8 + 8.67667e8i −0.643635 + 1.11481i 0.340980 + 0.940070i \(0.389241\pi\)
−0.984615 + 0.174738i \(0.944092\pi\)
\(348\) −9.15134e7 + 7.67889e7i −0.116401 + 0.0976722i
\(349\) 1.63182e8 − 1.36926e8i 0.205486 − 0.172424i −0.534237 − 0.845335i \(-0.679401\pi\)
0.739723 + 0.672911i \(0.234956\pi\)
\(350\) 1.04525e8 + 3.80439e7i 0.130311 + 0.0474294i
\(351\) −4.07307e6 + 2.30995e7i −0.00502745 + 0.0285121i
\(352\) −2.76381e6 + 1.56744e7i −0.00337761 + 0.0191554i
\(353\) 4.47076e8 + 1.62722e8i 0.540966 + 0.196896i 0.598028 − 0.801475i \(-0.295951\pi\)
−0.0570620 + 0.998371i \(0.518173\pi\)
\(354\) 1.88647e8 − 1.58294e8i 0.226016 − 0.189650i
\(355\) −1.13100e7 + 9.49019e6i −0.0134172 + 0.0112584i
\(356\) 3.21879e7 − 5.57511e7i 0.0378110 − 0.0654905i
\(357\) −3.16332e7 + 1.15135e7i −0.0367963 + 0.0133927i
\(358\) 3.81588e7 + 2.16409e8i 0.0439545 + 0.249279i
\(359\) 4.48559e8 + 7.76926e8i 0.511668 + 0.886236i 0.999909 + 0.0135262i \(0.00430566\pi\)
−0.488240 + 0.872709i \(0.662361\pi\)
\(360\) 2.31475e7 − 4.00927e7i 0.0261485 − 0.0452905i
\(361\) 7.81372e8 + 2.84396e8i 0.874144 + 0.318162i
\(362\) −3.97504e8 − 6.88498e8i −0.440415 − 0.762821i
\(363\) 2.03810e8 + 1.71017e8i 0.223641 + 0.187657i
\(364\) 4.74619e6 0.00515811
\(365\) −1.30288e8 − 1.09325e8i −0.140242 − 0.117677i
\(366\) 2.54360e8 − 9.25796e7i 0.271185 − 0.0987033i
\(367\) −2.34881e8 + 1.33208e9i −0.248038 + 1.40669i 0.565293 + 0.824890i \(0.308763\pi\)
−0.813331 + 0.581801i \(0.802348\pi\)
\(368\) −4.91301e7 − 2.78630e8i −0.0513902 − 0.291448i
\(369\) −1.11411e9 −1.15435
\(370\) 7.04310e7 + 8.66461e7i 0.0722866 + 0.0889289i
\(371\) 9.34435e7 0.0950037
\(372\) 2.58524e7 + 1.46616e8i 0.0260376 + 0.147667i
\(373\) −1.74483e8 + 9.89540e8i −0.174089 + 0.987308i 0.765101 + 0.643910i \(0.222689\pi\)
−0.939190 + 0.343398i \(0.888422\pi\)
\(374\) 4.86625e7 − 1.77117e7i 0.0480999 − 0.0175069i
\(375\) −7.39517e7 − 6.20529e7i −0.0724167 − 0.0607648i
\(376\) 1.65252e8 0.160320
\(377\) −4.19802e7 − 3.52255e7i −0.0403505 − 0.0338581i
\(378\) −4.22644e7 − 7.32041e7i −0.0402488 − 0.0697130i
\(379\) 2.99306e8 + 1.08938e8i 0.282409 + 0.102788i 0.479341 − 0.877629i \(-0.340876\pi\)
−0.196932 + 0.980417i \(0.563098\pi\)
\(380\) 1.14467e7 − 1.98263e7i 0.0107014 − 0.0185353i
\(381\) 5.10033e7 + 8.83403e7i 0.0472455 + 0.0818316i
\(382\) 3.98744e7 + 2.26139e8i 0.0365993 + 0.207565i
\(383\) −9.80168e8 + 3.56752e8i −0.891466 + 0.324467i −0.746828 − 0.665017i \(-0.768424\pi\)
−0.144638 + 0.989485i \(0.546202\pi\)
\(384\) −1.44915e7 + 2.51000e7i −0.0130603 + 0.0226211i
\(385\) 3.08078e6 − 2.58508e6i 0.00275136 − 0.00230867i
\(386\) 6.22234e8 − 5.22116e8i 0.550678 − 0.462074i
\(387\) −1.18572e9 − 4.31565e8i −1.03990 − 0.378493i
\(388\) −3.56135e6 + 2.01974e7i −0.00309531 + 0.0175544i
\(389\) 3.11851e8 − 1.76860e9i 0.268611 − 1.52337i −0.489941 − 0.871756i \(-0.662982\pi\)
0.758552 − 0.651613i \(-0.225907\pi\)
\(390\) −1.90960e6 − 695039.i −0.00163011 − 0.000593312i
\(391\) −7.05182e8 + 5.91718e8i −0.596599 + 0.500606i
\(392\) 3.09903e8 − 2.60040e8i 0.259851 − 0.218041i
\(393\) 2.32055e8 − 4.01932e8i 0.192849 − 0.334024i
\(394\) −8.57330e8 + 3.12043e8i −0.706173 + 0.257026i
\(395\) 1.54377e7 + 8.75517e7i 0.0126036 + 0.0714784i
\(396\) 3.10242e7 + 5.37354e7i 0.0251054 + 0.0434838i
\(397\) −2.91620e8 + 5.05101e8i −0.233911 + 0.405146i −0.958956 − 0.283556i \(-0.908486\pi\)
0.725045 + 0.688702i \(0.241819\pi\)
\(398\) 1.56508e8 + 5.69641e7i 0.124436 + 0.0452909i
\(399\) −9.97296e6 − 1.72737e7i −0.00785994 − 0.0136138i
\(400\) −2.38695e8 − 2.00289e8i −0.186481 − 0.156476i
\(401\) −1.26568e9 −0.980212 −0.490106 − 0.871663i \(-0.663042\pi\)
−0.490106 + 0.871663i \(0.663042\pi\)
\(402\) −2.78395e7 − 2.33601e7i −0.0213732 − 0.0179342i
\(403\) −6.41765e7 + 2.33583e7i −0.0488437 + 0.0177776i
\(404\) 4.84127e6 − 2.74562e7i 0.00365279 − 0.0207160i
\(405\) −2.80540e7 − 1.59102e8i −0.0209847 − 0.119010i
\(406\) 1.97489e8 0.146454
\(407\) −1.47770e8 + 2.36854e7i −0.108644 + 0.0174141i
\(408\) 9.43002e7 0.0687388
\(409\) −2.14290e8 − 1.21530e9i −0.154871 − 0.878319i −0.958903 − 0.283733i \(-0.908427\pi\)
0.804032 − 0.594586i \(-0.202684\pi\)
\(410\) 3.51262e7 − 1.99210e8i 0.0251702 − 0.142747i
\(411\) 3.17391e8 − 1.15521e8i 0.225501 − 0.0820756i
\(412\) −3.72313e8 − 3.12408e8i −0.262282 − 0.220081i
\(413\) −4.07107e8 −0.284369
\(414\) −8.44933e8 − 7.08983e8i −0.585223 − 0.491060i
\(415\) −6.28611e7 − 1.08879e8i −0.0431732 − 0.0747781i
\(416\) −1.24936e7 − 4.54729e6i −0.00850865 − 0.00309689i
\(417\) 1.26564e8 − 2.19216e8i 0.0854742 − 0.148046i
\(418\) 1.53418e7 + 2.65728e7i 0.0102745 + 0.0177959i
\(419\) −2.90365e8 − 1.64674e9i −0.192839 − 1.09364i −0.915463 − 0.402403i \(-0.868175\pi\)
0.722623 − 0.691242i \(-0.242936\pi\)
\(420\) 6.88170e6 − 2.50473e6i 0.00453235 − 0.00164964i
\(421\) 1.19815e8 − 2.07526e8i 0.0782573 − 0.135546i −0.824241 − 0.566239i \(-0.808398\pi\)
0.902498 + 0.430694i \(0.141731\pi\)
\(422\) 1.64038e9 − 1.37644e9i 1.06255 − 0.891589i
\(423\) 4.93505e8 − 4.14100e8i 0.317030 − 0.266020i
\(424\) −2.45975e8 − 8.95275e7i −0.156715 − 0.0570396i
\(425\) −1.76048e8 + 9.98416e8i −0.111242 + 0.630885i
\(426\) 6.25714e6 − 3.54860e7i 0.00392141 − 0.0222394i
\(427\) −4.20495e8 − 1.53048e8i −0.261375 − 0.0951326i
\(428\) 4.65015e8 − 3.90194e8i 0.286691 − 0.240562i
\(429\) 2.08644e6 − 1.75073e6i 0.00127587 − 0.00107058i
\(430\) 1.14550e8 − 1.98407e8i 0.0694796 − 0.120342i
\(431\) 5.60264e8 − 2.03920e8i 0.337072 − 0.122684i −0.167938 − 0.985797i \(-0.553711\pi\)
0.505010 + 0.863113i \(0.331489\pi\)
\(432\) 4.11179e7 + 2.33191e8i 0.0245379 + 0.139161i
\(433\) 9.85561e8 + 1.70704e9i 0.583413 + 1.01050i 0.995071 + 0.0991624i \(0.0316163\pi\)
−0.411658 + 0.911338i \(0.635050\pi\)
\(434\) 1.23059e8 − 2.13144e8i 0.0722602 − 0.125158i
\(435\) −7.94585e7 − 2.89205e7i −0.0462837 − 0.0168459i
\(436\) 2.82041e8 + 4.88509e8i 0.162970 + 0.282273i
\(437\) −4.17829e8 − 3.50600e8i −0.239505 − 0.200968i
\(438\) 4.15096e8 0.236042
\(439\) 2.85035e7 + 2.39173e7i 0.0160795 + 0.0134923i 0.650792 − 0.759256i \(-0.274437\pi\)
−0.634712 + 0.772748i \(0.718881\pi\)
\(440\) −1.05864e7 + 3.85313e6i −0.00592466 + 0.00215640i
\(441\) 2.73863e8 − 1.55316e9i 0.152054 − 0.862343i
\(442\) 7.51176e6 + 4.26013e7i 0.00413775 + 0.0234663i
\(443\) −1.73770e9 −0.949648 −0.474824 − 0.880081i \(-0.657488\pi\)
−0.474824 + 0.880081i \(0.657488\pi\)
\(444\) −2.67609e8 − 5.15032e7i −0.145098 − 0.0279251i
\(445\) 4.55666e7 0.0245124
\(446\) −1.33762e8 − 7.58603e8i −0.0713939 − 0.404895i
\(447\) 4.93895e7 − 2.80102e8i 0.0261552 − 0.148334i
\(448\) 4.50236e7 − 1.63872e7i 0.0236574 − 0.00861058i
\(449\) −1.87670e9 − 1.57474e9i −0.978435 − 0.821004i 0.00541783 − 0.999985i \(-0.498275\pi\)
−0.983853 + 0.178981i \(0.942720\pi\)
\(450\) −1.21473e9 −0.628402
\(451\) 2.07687e8 + 1.74270e8i 0.106608 + 0.0894551i
\(452\) 5.15178e7 + 8.92315e7i 0.0262406 + 0.0454500i
\(453\) −8.29551e8 − 3.01932e8i −0.419276 − 0.152604i
\(454\) −1.75059e8 + 3.03211e8i −0.0877990 + 0.152072i
\(455\) 1.67973e6 + 2.90938e6i 0.000835986 + 0.00144797i
\(456\) 9.70242e6 + 5.50252e7i 0.00479185 + 0.0271759i
\(457\) 1.84784e9 − 6.72558e8i 0.905643 − 0.329627i 0.153131 − 0.988206i \(-0.451064\pi\)
0.752512 + 0.658579i \(0.228842\pi\)
\(458\) −2.04296e8 + 3.53852e8i −0.0993646 + 0.172105i
\(459\) 5.90181e8 − 4.95220e8i 0.284866 − 0.239031i
\(460\) 1.53410e8 − 1.28727e8i 0.0734856 − 0.0616617i
\(461\) 1.52383e9 + 5.54627e8i 0.724406 + 0.263662i 0.677795 − 0.735251i \(-0.262936\pi\)
0.0466109 + 0.998913i \(0.485158\pi\)
\(462\) −1.70442e6 + 9.66622e6i −0.000804134 + 0.00456047i
\(463\) −1.81875e8 + 1.03147e9i −0.0851610 + 0.482972i 0.912161 + 0.409833i \(0.134413\pi\)
−0.997322 + 0.0731393i \(0.976698\pi\)
\(464\) −5.19858e8 − 1.89213e8i −0.241586 − 0.0879300i
\(465\) −8.07251e7 + 6.77364e7i −0.0372326 + 0.0312419i
\(466\) −5.19162e8 + 4.35629e8i −0.237658 + 0.199419i
\(467\) −4.74078e8 + 8.21128e8i −0.215398 + 0.373080i −0.953396 − 0.301723i \(-0.902438\pi\)
0.737998 + 0.674803i \(0.235771\pi\)
\(468\) −4.87056e7 + 1.77274e7i −0.0219643 + 0.00799436i
\(469\) 1.04325e7 + 5.91657e7i 0.00466964 + 0.0264829i
\(470\) 5.84844e7 + 1.01298e8i 0.0259835 + 0.0450047i
\(471\) −3.48183e7 + 6.03070e7i −0.0153544 + 0.0265947i
\(472\) 1.07164e9 + 3.90046e8i 0.469086 + 0.170733i
\(473\) 1.53530e8 + 2.65921e8i 0.0667080 + 0.115542i
\(474\) −1.66213e8 − 1.39469e8i −0.0716872 − 0.0601527i
\(475\) −6.00700e8 −0.257176
\(476\) −1.19420e8 − 1.00206e8i −0.0507521 − 0.0425861i
\(477\) −9.58919e8 + 3.49018e8i −0.404546 + 0.147243i
\(478\) −1.19509e8 + 6.77772e8i −0.0500501 + 0.283848i
\(479\) 1.60637e8 + 9.11015e8i 0.0667837 + 0.378749i 0.999820 + 0.0189671i \(0.00603777\pi\)
−0.933036 + 0.359782i \(0.882851\pi\)
\(480\) −2.05147e7 −0.00846684
\(481\) 1.95006e6 − 1.24998e8i 0.000798987 − 0.0512150i
\(482\) −2.92127e9 −1.18825
\(483\) −3.02980e7 − 1.71828e8i −0.0122349 − 0.0693873i
\(484\) −2.13948e8 + 1.21336e9i −0.0857729 + 0.486442i
\(485\) −1.36412e7 + 4.96501e6i −0.00542948 + 0.00197617i
\(486\) 1.07686e9 + 9.03589e8i 0.425530 + 0.357062i
\(487\) 2.68749e9 1.05438 0.527188 − 0.849749i \(-0.323246\pi\)
0.527188 + 0.849749i \(0.323246\pi\)
\(488\) 9.60252e8 + 8.05747e8i 0.374038 + 0.313855i
\(489\) 1.08553e8 + 1.88019e8i 0.0419817 + 0.0727144i
\(490\) 2.69080e8 + 9.79372e7i 0.103323 + 0.0376064i
\(491\) 8.49150e8 − 1.47077e9i 0.323742 − 0.560738i −0.657515 − 0.753442i \(-0.728392\pi\)
0.981257 + 0.192704i \(0.0617256\pi\)
\(492\) 2.46848e8 + 4.27553e8i 0.0934440 + 0.161850i
\(493\) 3.12564e8 + 1.77264e9i 0.117483 + 0.666279i
\(494\) −2.40855e7 + 8.76639e6i −0.00898898 + 0.00327172i
\(495\) −2.19596e7 + 3.80351e7i −0.00813777 + 0.0140950i
\(496\) −5.28145e8 + 4.43166e8i −0.194342 + 0.163072i
\(497\) −4.56322e7 + 3.82900e7i −0.0166734 + 0.0139906i
\(498\) 2.88335e8 + 1.04945e8i 0.104615 + 0.0380768i
\(499\) 1.50579e8 − 8.53977e8i 0.0542516 − 0.307676i −0.945592 − 0.325355i \(-0.894516\pi\)
0.999844 + 0.0176782i \(0.00562745\pi\)
\(500\) 7.76305e7 − 4.40264e8i 0.0277739 − 0.157514i
\(501\) −1.24433e9 − 4.52900e8i −0.442083 − 0.160905i
\(502\) −1.00693e9 + 8.44915e8i −0.355252 + 0.298092i
\(503\) 1.25129e9 − 1.04996e9i 0.438401 − 0.367862i −0.396710 − 0.917944i \(-0.629848\pi\)
0.835111 + 0.550082i \(0.185404\pi\)
\(504\) 9.33932e7 − 1.61762e8i 0.0324944 − 0.0562819i
\(505\) 1.85438e7 − 6.74939e6i 0.00640735 − 0.00233209i
\(506\) 4.66086e7 + 2.64331e8i 0.0159933 + 0.0907028i
\(507\) −4.32459e8 − 7.49041e8i −0.147373 − 0.255257i
\(508\) −2.36192e8 + 4.09097e8i −0.0799361 + 0.138453i
\(509\) 1.05418e9 + 3.83691e8i 0.354327 + 0.128964i 0.513050 − 0.858359i \(-0.328516\pi\)
−0.158723 + 0.987323i \(0.550738\pi\)
\(510\) 3.33738e7 + 5.78052e7i 0.0111407 + 0.0192962i
\(511\) −5.25672e8 − 4.41091e8i −0.174278 − 0.146236i
\(512\) −1.34218e8 −0.0441942
\(513\) 3.49689e8 + 2.93424e8i 0.114359 + 0.0959588i
\(514\) −3.01300e9 + 1.09664e9i −0.978650 + 0.356200i
\(515\) 5.97377e7 − 3.38789e8i 0.0192718 − 0.109296i
\(516\) 9.70948e7 + 5.50652e8i 0.0311116 + 0.176442i
\(517\) −1.56771e8 −0.0498940
\(518\) 2.84167e8 + 3.49590e8i 0.0898297 + 0.110511i
\(519\) −4.93248e8 −0.154875
\(520\) −1.63416e6 − 9.26780e6i −0.000509663 − 0.00289045i
\(521\) −9.99177e8 + 5.66661e9i −0.309535 + 1.75546i 0.291813 + 0.956475i \(0.405742\pi\)
−0.601348 + 0.798987i \(0.705370\pi\)
\(522\) −2.02664e9 + 7.37635e8i −0.623633 + 0.226984i
\(523\) 2.64276e9 + 2.21754e9i 0.807797 + 0.677822i 0.950081 − 0.312003i \(-0.101000\pi\)
−0.142284 + 0.989826i \(0.545445\pi\)
\(524\) 2.14926e9 0.652574
\(525\) −1.47201e8 − 1.23516e8i −0.0443969 − 0.0372534i
\(526\) 6.57508e8 + 1.13884e9i 0.196993 + 0.341202i
\(527\) 2.10792e9 + 7.67222e8i 0.627361 + 0.228341i
\(528\) 1.37477e7 − 2.38118e7i 0.00406455 − 0.00704001i
\(529\) −6.83224e8 − 1.18338e9i −0.200663 − 0.347559i
\(530\) −3.21735e7 − 1.82465e8i −0.00938714 − 0.0532371i
\(531\) 4.17774e9 − 1.52057e9i 1.21091 − 0.440734i
\(532\) 4.61840e7 − 7.99931e7i 0.0132984 − 0.0230336i
\(533\) −1.73489e8 + 1.45575e8i −0.0496280 + 0.0416429i
\(534\) −8.51920e7 + 7.14846e7i −0.0242105 + 0.0203151i
\(535\) 4.03759e8 + 1.46956e8i 0.113995 + 0.0414906i
\(536\) 2.92243e7 − 1.65739e8i 0.00819725 − 0.0464889i
\(537\) 6.59199e7 − 3.73850e8i 0.0183699 − 0.104181i
\(538\) 1.59282e8 + 5.79737e7i 0.0440989 + 0.0160507i
\(539\) −2.93998e8 + 2.46694e8i −0.0808694 + 0.0678575i
\(540\) −1.28392e8 + 1.07734e8i −0.0350881 + 0.0294424i
\(541\) 2.50436e9 − 4.33768e9i 0.679996 − 1.17779i −0.294985 − 0.955502i \(-0.595315\pi\)
0.974981 − 0.222286i \(-0.0713519\pi\)
\(542\) 2.37424e9 − 8.64154e8i 0.640512 − 0.233127i
\(543\) 2.38487e8 + 1.35253e9i 0.0639242 + 0.362532i
\(544\) 2.18348e8 + 3.78191e8i 0.0581506 + 0.100720i
\(545\) −1.99634e8 + 3.45777e8i −0.0528260 + 0.0914973i
\(546\) −7.70466e6 − 2.80427e6i −0.00202572 − 0.000737302i
\(547\) −1.12673e9 − 1.95156e9i −0.294350 − 0.509830i 0.680483 − 0.732764i \(-0.261770\pi\)
−0.974834 + 0.222934i \(0.928437\pi\)
\(548\) 1.19820e9 + 1.00541e9i 0.311027 + 0.260983i
\(549\) 4.88678e9 1.26043
\(550\) 2.26445e8 + 1.90010e8i 0.0580354 + 0.0486975i
\(551\) −1.00219e9 + 3.64769e8i −0.255224 + 0.0928939i
\(552\) −8.48730e7 + 4.81339e8i −0.0214775 + 0.121805i
\(553\) 6.22865e7 + 3.53244e8i 0.0156623 + 0.0888253i
\(554\) −1.12518e9 −0.281149
\(555\) −6.31386e7 − 1.82270e8i −0.0156772 − 0.0452573i
\(556\) 1.17222e9 0.289233
\(557\) 2.48070e8 + 1.40688e9i 0.0608249 + 0.344955i 0.999999 + 0.00151344i \(0.000481742\pi\)
−0.939174 + 0.343442i \(0.888407\pi\)
\(558\) −4.66724e8 + 2.64693e9i −0.113721 + 0.644944i
\(559\) −2.41030e8 + 8.77276e7i −0.0583619 + 0.0212420i
\(560\) 2.59795e7 + 2.17994e7i 0.00625135 + 0.00524550i
\(561\) −8.94605e7 −0.0213925
\(562\) 4.36692e8 + 3.66428e8i 0.103776 + 0.0870787i
\(563\) 2.22455e9 + 3.85303e9i 0.525366 + 0.909961i 0.999564 + 0.0295423i \(0.00940499\pi\)
−0.474197 + 0.880419i \(0.657262\pi\)
\(564\) −2.68259e8 − 9.76383e7i −0.0629618 − 0.0229162i
\(565\) −3.64654e7 + 6.31600e7i −0.00850573 + 0.0147324i
\(566\) −1.09267e9 − 1.89257e9i −0.253299 − 0.438726i
\(567\) −1.13189e8 − 6.41928e8i −0.0260774 − 0.147892i
\(568\) 1.56805e8 − 5.70723e7i 0.0359038 − 0.0130679i
\(569\) 9.04629e6 − 1.56686e7i 0.00205863 − 0.00356565i −0.864994 − 0.501782i \(-0.832678\pi\)
0.867053 + 0.498216i \(0.166011\pi\)
\(570\) −3.02962e7 + 2.54215e7i −0.00685213 + 0.00574962i
\(571\) 5.44287e9 − 4.56711e9i 1.22349 − 1.02663i 0.224860 − 0.974391i \(-0.427808\pi\)
0.998634 − 0.0522425i \(-0.0166369\pi\)
\(572\) 1.18524e7 + 4.31392e6i 0.00264801 + 0.000963797i
\(573\) 6.88837e7 − 3.90659e8i 0.0152959 − 0.0867475i
\(574\) 1.41723e8 − 8.03752e8i 0.0312788 − 0.177391i
\(575\) −4.93779e9 − 1.79721e9i −1.08317 − 0.394240i
\(576\) −4.00825e8 + 3.36332e8i −0.0873930 + 0.0733314i
\(577\) 3.97074e9 − 3.33184e9i 0.860509 − 0.722053i −0.101568 − 0.994829i \(-0.532386\pi\)
0.962078 + 0.272775i \(0.0879416\pi\)
\(578\) −9.30926e8 + 1.61241e9i −0.200525 + 0.347319i
\(579\) −1.31858e9 + 4.79925e8i −0.282314 + 0.102754i
\(580\) −6.79974e7 − 3.85633e8i −0.0144709 − 0.0820683i
\(581\) −2.53625e8 − 4.39292e8i −0.0536508 − 0.0929259i
\(582\) 1.77148e7 − 3.06830e7i 0.00372483 − 0.00645159i
\(583\) 2.33351e8 + 8.49328e7i 0.0487719 + 0.0177515i
\(584\) 9.61140e8 + 1.66474e9i 0.199683 + 0.345862i
\(585\) −2.81041e7 − 2.35822e7i −0.00580397 − 0.00487011i
\(586\) −2.03797e9 −0.418367
\(587\) −6.47657e9 − 5.43449e9i −1.32164 − 1.10898i −0.985955 − 0.167009i \(-0.946589\pi\)
−0.335681 − 0.941976i \(-0.608966\pi\)
\(588\) −6.56720e8 + 2.39027e8i −0.133217 + 0.0484870i
\(589\) −2.30801e8 + 1.30893e9i −0.0465407 + 0.263946i
\(590\) 1.40171e8 + 7.94949e8i 0.0280980 + 0.159352i
\(591\) 1.57610e9 0.314072
\(592\) −4.13085e8 − 1.19250e9i −0.0818301 − 0.236228i
\(593\) −4.40529e9 −0.867528 −0.433764 − 0.901026i \(-0.642815\pi\)
−0.433764 + 0.901026i \(0.642815\pi\)
\(594\) −3.90076e7 − 2.21223e8i −0.00763655 − 0.0433090i
\(595\) 1.91610e7 − 1.08667e8i 0.00372914 − 0.0211490i
\(596\) 1.23771e9 − 4.50489e8i 0.239473 − 0.0871610i
\(597\) −2.20407e8 − 1.84944e8i −0.0423951 − 0.0355737i
\(598\) −2.24212e8 −0.0428750
\(599\) −2.02663e9 − 1.70054e9i −0.385283 − 0.323291i 0.429489 − 0.903072i \(-0.358694\pi\)
−0.814772 + 0.579781i \(0.803138\pi\)
\(600\) 2.69142e8 + 4.66168e8i 0.0508689 + 0.0881076i
\(601\) −5.88708e9 − 2.14272e9i −1.10621 − 0.402629i −0.276611 − 0.960982i \(-0.589211\pi\)
−0.829603 + 0.558353i \(0.811433\pi\)
\(602\) 4.62176e8 − 8.00512e8i 0.0863415 − 0.149548i
\(603\) −3.28047e8 − 5.68194e8i −0.0609292 − 0.105532i
\(604\) −7.09897e8 − 4.02602e9i −0.131089 − 0.743442i
\(605\) −8.19499e8 + 2.98273e8i −0.150454 + 0.0547609i
\(606\) −2.40814e7 + 4.17102e7i −0.00439569 + 0.00761356i
\(607\) 2.63733e9 − 2.21298e9i 0.478634 − 0.401621i −0.371298 − 0.928514i \(-0.621087\pi\)
0.849932 + 0.526892i \(0.176643\pi\)
\(608\) −1.98213e8 + 1.66320e8i −0.0357659 + 0.0300111i
\(609\) −3.20591e8 − 1.16685e8i −0.0575162 − 0.0209342i
\(610\) −1.54072e8 + 8.73789e8i −0.0274834 + 0.155866i
\(611\) 2.27404e7 − 1.28967e8i 0.00403324 − 0.0228736i
\(612\) 1.59977e9 + 5.82268e8i 0.282116 + 0.102682i
\(613\) −3.35733e9 + 2.81714e9i −0.588685 + 0.493965i −0.887786 − 0.460256i \(-0.847758\pi\)
0.299101 + 0.954221i \(0.403313\pi\)
\(614\) 2.34053e9 − 1.96394e9i 0.408061 − 0.342404i
\(615\) −1.74724e8 + 3.02631e8i −0.0302893 + 0.0524627i
\(616\) −4.27129e7 + 1.55462e7i −0.00736251 + 0.00267974i
\(617\) 1.36147e9 + 7.72127e9i 0.233351 + 1.32340i 0.846059 + 0.533089i \(0.178969\pi\)
−0.612708 + 0.790309i \(0.709920\pi\)
\(618\) 4.19805e8 + 7.27123e8i 0.0715464 + 0.123922i
\(619\) 3.05348e9 − 5.28878e9i 0.517461 − 0.896269i −0.482333 − 0.875988i \(-0.660211\pi\)
0.999794 − 0.0202812i \(-0.00645615\pi\)
\(620\) −4.58573e8 − 1.66907e8i −0.0772747 − 0.0281257i
\(621\) 1.99658e9 + 3.45819e9i 0.334555 + 0.579466i
\(622\) −2.38051e9 − 1.99748e9i −0.396646 − 0.332826i
\(623\) 1.83847e8 0.0304613
\(624\) 1.75945e7 + 1.47636e7i 0.00289889 + 0.00243246i
\(625\) −5.28742e9 + 1.92446e9i −0.866291 + 0.315304i
\(626\) 8.93516e8 − 5.06738e9i 0.145577 − 0.825607i
\(627\) −9.20448e6 − 5.22012e7i −0.00149129 − 0.00845754i
\(628\) −3.22481e8 −0.0519572
\(629\) −2.68814e9 + 3.10395e9i −0.430699 + 0.497322i
\(630\) 1.32211e8 0.0210658
\(631\) −1.17719e9 − 6.67619e9i −0.186528 − 1.05785i −0.923976 − 0.382450i \(-0.875080\pi\)
0.737448 − 0.675404i \(-0.236031\pi\)
\(632\) 1.74482e8 − 9.89534e8i 0.0274941 − 0.155927i
\(633\) −3.47615e9 + 1.26522e9i −0.544736 + 0.198268i
\(634\) −5.39678e9 − 4.52844e9i −0.841051 − 0.705726i
\(635\) −3.34364e8 −0.0518217
\(636\) 3.46403e8 + 2.90666e8i 0.0533926 + 0.0448017i
\(637\) −1.60296e8 − 2.77641e8i −0.0245717 − 0.0425595i
\(638\) 4.93177e8 + 1.79502e8i 0.0751849 + 0.0273651i
\(639\) 3.25263e8 − 5.63372e8i 0.0493153 − 0.0854167i
\(640\) −4.75011e7 − 8.22743e7i −0.00716265 − 0.0124061i
\(641\) 5.42874e7 + 3.07879e8i 0.00814135 + 0.0461719i 0.988608 − 0.150515i \(-0.0480930\pi\)
−0.980466 + 0.196686i \(0.936982\pi\)
\(642\) −9.85419e8 + 3.58663e8i −0.146977 + 0.0534951i
\(643\) −1.26024e9 + 2.18280e9i −0.186945 + 0.323798i −0.944230 − 0.329286i \(-0.893192\pi\)
0.757285 + 0.653084i \(0.226525\pi\)
\(644\) 6.18964e8 − 5.19372e8i 0.0913197 − 0.0766263i
\(645\) −3.03182e8 + 2.54400e8i −0.0444881 + 0.0373300i
\(646\) 7.91104e8 + 2.87938e8i 0.115457 + 0.0420229i
\(647\) −1.40600e9 + 7.97381e9i −0.204089 + 1.15745i 0.694778 + 0.719224i \(0.255503\pi\)
−0.898867 + 0.438222i \(0.855608\pi\)
\(648\) −3.17074e8 + 1.79822e9i −0.0457771 + 0.259615i
\(649\) −1.01664e9 − 3.70028e8i −0.145986 − 0.0531347i
\(650\) −1.89158e8 + 1.58723e8i −0.0270165 + 0.0226695i
\(651\) −3.25701e8 + 2.73296e8i −0.0462685 + 0.0388239i
\(652\) −5.02699e8 + 8.70701e8i −0.0710300 + 0.123028i
\(653\) −3.85234e9 + 1.40214e9i −0.541412 + 0.197058i −0.598227 − 0.801327i \(-0.704128\pi\)
0.0568145 + 0.998385i \(0.481906\pi\)
\(654\) −1.69213e8 − 9.59656e8i −0.0236544 − 0.134151i
\(655\) 7.60646e8 + 1.31748e9i 0.105764 + 0.183189i
\(656\) −1.14313e9 + 1.97996e9i −0.158101 + 0.273838i
\(657\) 7.04196e9 + 2.56307e9i 0.968757 + 0.352599i
\(658\) 2.35966e8 + 4.08706e8i 0.0322894 + 0.0559268i
\(659\) −1.00727e10 − 8.45198e9i −1.37103 − 1.15043i −0.972401 − 0.233315i \(-0.925043\pi\)
−0.398626 − 0.917114i \(-0.630513\pi\)
\(660\) 1.94619e7 0.00263500
\(661\) −4.79260e9 − 4.02147e9i −0.645455 − 0.541601i 0.260233 − 0.965546i \(-0.416201\pi\)
−0.905688 + 0.423945i \(0.860645\pi\)
\(662\) 6.98473e9 − 2.54223e9i 0.935722 − 0.340575i
\(663\) 1.29767e7 − 7.35945e7i 0.00172929 − 0.00980727i
\(664\) 2.46745e8 + 1.39936e9i 0.0327085 + 0.185499i
\(665\) 6.53801e7 0.00862124
\(666\) −4.22188e9 − 2.52612e9i −0.553791 − 0.331355i
\(667\) −9.32944e9 −1.21735
\(668\) −1.06485e9 − 6.03906e9i −0.138220 − 0.783884i
\(669\) −2.31076e8 + 1.31050e9i −0.0298376 + 0.169218i
\(670\) 1.11940e8 − 4.07427e7i 0.0143788 − 0.00523345i
\(671\) −9.10970e8 − 7.64395e8i −0.116406 − 0.0976762i
\(672\) −8.27706e7 −0.0105217
\(673\) 2.26172e9 + 1.89781e9i 0.286013 + 0.239994i 0.774494 − 0.632581i \(-0.218004\pi\)
−0.488481 + 0.872574i \(0.662449\pi\)
\(674\) 1.21241e9 + 2.09996e9i 0.152525 + 0.264181i
\(675\) 4.13253e9 + 1.50412e9i 0.517193 + 0.188243i
\(676\) 2.00268e9 − 3.46875e9i 0.249344 − 0.431877i
\(677\) 3.51719e9 + 6.09194e9i 0.435647 + 0.754563i 0.997348 − 0.0727772i \(-0.0231862\pi\)
−0.561701 + 0.827340i \(0.689853\pi\)
\(678\) −3.09087e7 − 1.75292e8i −0.00380870 − 0.0216002i
\(679\) −5.50382e7 + 2.00323e7i −0.00674715 + 0.00245576i
\(680\) −1.54552e8 + 2.67691e8i −0.0188492 + 0.0326478i
\(681\) 4.63331e8 − 3.88781e8i 0.0562181 − 0.0471726i
\(682\) 5.01039e8 − 4.20422e8i 0.0604820 − 0.0507504i
\(683\) 4.11839e9 + 1.49897e9i 0.494601 + 0.180020i 0.577264 − 0.816558i \(-0.304120\pi\)
−0.0826632 + 0.996578i \(0.526343\pi\)
\(684\) −1.75162e8 + 9.93392e8i −0.0209287 + 0.118693i
\(685\) −1.92252e8 + 1.09031e9i −0.0228535 + 0.129609i
\(686\) 2.21721e9 + 8.06999e8i 0.262224 + 0.0954418i
\(687\) 5.40713e8 − 4.53712e8i 0.0636237 − 0.0533866i
\(688\) −1.98357e9 + 1.66441e9i −0.232214 + 0.194850i
\(689\) −1.03719e8 + 1.79646e8i −0.0120806 + 0.0209242i
\(690\) −3.25094e8 + 1.18325e8i −0.0376736 + 0.0137121i
\(691\) −1.86816e9 − 1.05948e10i −0.215397 − 1.22158i −0.880216 − 0.474574i \(-0.842602\pi\)
0.664819 − 0.747005i \(-0.268509\pi\)
\(692\) −1.14210e9 − 1.97817e9i −0.131018 − 0.226930i
\(693\) −8.86001e7 + 1.53460e8i −0.0101127 + 0.0175157i
\(694\) 7.53179e9 + 2.74135e9i 0.855343 + 0.311319i
\(695\) 4.14861e8 + 7.18560e8i 0.0468766 + 0.0811926i
\(696\) 7.32108e8 + 6.14311e8i 0.0823081 + 0.0690647i
\(697\) 7.43870e9 0.832113
\(698\) −1.30546e9 − 1.09541e9i −0.145301 − 0.121922i
\(699\) 1.10016e9 − 4.00427e8i 0.121839 − 0.0443459i
\(700\) 1.54523e8 − 8.76345e8i 0.0170275 − 0.0965677i
\(701\) 2.27870e9 + 1.29231e10i 0.249847 + 1.41695i 0.808962 + 0.587861i \(0.200030\pi\)
−0.559115 + 0.829090i \(0.688859\pi\)
\(702\) 1.87647e8 0.0204721
\(703\) −2.08777e9 − 1.24920e9i −0.226641 − 0.135608i
\(704\) 1.27329e8 0.0137539
\(705\) −3.50883e7 − 1.98996e8i −0.00377138 − 0.0213886i
\(706\) 6.60931e8 − 3.74833e9i 0.0706870 − 0.400886i
\(707\) 7.48185e7 − 2.72317e7i 0.00796234 − 0.00289806i
\(708\) −1.50918e9 − 1.26635e9i −0.159817 − 0.134103i
\(709\) 7.05155e9 0.743058 0.371529 − 0.928421i \(-0.378834\pi\)
0.371529 + 0.928421i \(0.378834\pi\)
\(710\) 9.04797e7 + 7.59215e7i 0.00948739 + 0.00796087i
\(711\) −1.95858e9 − 3.39236e9i −0.204361 − 0.353963i
\(712\) −4.83948e8 − 1.76143e8i −0.0502480 − 0.0182888i
\(713\) −5.81334e9 + 1.00690e10i −0.600638 + 1.04034i
\(714\) 1.34653e8 + 2.33226e8i 0.0138444 + 0.0239791i
\(715\) 1.55029e6 + 8.79215e6i 0.000158614 + 0.000899547i
\(716\) 1.65196e9 − 6.01265e8i 0.168192 − 0.0612167i
\(717\) 5.94462e8 − 1.02964e9i 0.0602292 − 0.104320i
\(718\) 5.49785e9 − 4.61325e9i 0.554316 − 0.465126i
\(719\) 5.78409e9 − 4.85343e9i 0.580342 − 0.486965i −0.304717 − 0.952443i \(-0.598562\pi\)
0.885059 + 0.465478i \(0.154118\pi\)
\(720\) −3.48025e8 − 1.26671e8i −0.0347494 − 0.0126477i
\(721\) 2.41023e8 − 1.36691e9i 0.0239489 − 0.135821i
\(722\) 1.15513e9 − 6.55109e9i 0.114223 − 0.647789i
\(723\) 4.74221e9 + 1.72602e9i 0.466656 + 0.169849i
\(724\) −4.87210e9 + 4.08817e9i −0.477123 + 0.400354i
\(725\) −7.87086e9 + 6.60444e9i −0.767078 + 0.643654i
\(726\) 1.06422e9 − 1.84328e9i 0.103217 − 0.178778i
\(727\) 8.89177e9 − 3.23634e9i 0.858258 − 0.312380i 0.124855 − 0.992175i \(-0.460153\pi\)
0.733402 + 0.679795i \(0.237931\pi\)
\(728\) −6.59334e6 − 3.73927e7i −0.000633353 − 0.00359192i
\(729\) 2.68556e9 + 4.65152e9i 0.256737 + 0.444681i
\(730\) −6.80315e8 + 1.17834e9i −0.0647262 + 0.112109i
\(731\) 7.91680e9 + 2.88148e9i 0.749616 + 0.272838i
\(732\) −1.08274e9 − 1.87536e9i −0.102032 − 0.176724i
\(733\) 1.32544e8 + 1.11218e8i 0.0124307 + 0.0104306i 0.648982 − 0.760804i \(-0.275195\pi\)
−0.636551 + 0.771235i \(0.719640\pi\)
\(734\) 1.08210e10 1.01003
\(735\) −3.78942e8 − 3.17970e8i −0.0352019 − 0.0295379i
\(736\) −2.12693e9 + 7.74139e8i −0.196644 + 0.0715725i
\(737\) −2.77245e7 + 1.57233e8i −0.00255110 + 0.0144680i
\(738\) 1.54771e9 + 8.77748e9i 0.141740 + 0.803845i
\(739\) −1.09005e10 −0.993551 −0.496775 − 0.867879i \(-0.665483\pi\)
−0.496775 + 0.867879i \(0.665483\pi\)
\(740\) 5.84796e8 − 6.75255e8i 0.0530510 − 0.0612572i
\(741\) 4.42784e7 0.00399786
\(742\) −1.29810e8 − 7.36191e8i −0.0116653 − 0.0661571i
\(743\) −2.70469e9 + 1.53391e10i −0.241912 + 1.37195i 0.585645 + 0.810567i \(0.300841\pi\)
−0.827557 + 0.561382i \(0.810270\pi\)
\(744\) 1.11920e9 − 4.07355e8i 0.0996327 − 0.0362633i
\(745\) 7.14184e8 + 5.99271e8i 0.0632795 + 0.0530978i
\(746\) 8.03844e9 0.708902
\(747\) 4.24350e9 + 3.56072e9i 0.372479 + 0.312547i
\(748\) −2.07142e8 − 3.58781e8i −0.0180973 − 0.0313454i
\(749\) 1.62904e9 + 5.92923e8i 0.141660 + 0.0515599i
\(750\) −3.86148e8 + 6.68829e8i −0.0334226 + 0.0578896i
\(751\) 2.06152e8 + 3.57065e8i 0.0177602 + 0.0307615i 0.874769 − 0.484540i \(-0.161013\pi\)
−0.857009 + 0.515302i \(0.827680\pi\)
\(752\) −2.29565e8 − 1.30193e9i −0.0196854 − 0.111641i
\(753\) 2.13380e9 − 7.76639e8i 0.182126 − 0.0662883i
\(754\) −2.19205e8 + 3.79674e8i −0.0186230 + 0.0322560i
\(755\) 2.21668e9 − 1.86001e9i 0.187451 − 0.157290i
\(756\) −5.18022e8 + 4.34672e8i −0.0436036 + 0.0365878i
\(757\) −3.81024e9 − 1.38681e9i −0.319239 − 0.116194i 0.177430