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Properties

Label 71.10.g.a.2.11
Level $71$
Weight $10$
Character 71.2
Analytic conductor $36.568$
Analytic rank $0$
Dimension $1272$
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] = [71,10,Mod(2,71)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(71, base_ring=CyclotomicField(70))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("71.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 71 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 71.g (of order \(35\), degree \(24\), 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: \(36.5675443676\)
Analytic rank: \(0\)
Dimension: \(1272\)
Relative dimension: \(53\) over \(\Q(\zeta_{35})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label 2.11
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.25358 + 27.9132i) q^{2} +(194.677 + 170.084i) q^{3} +(-267.637 - 24.0878i) q^{4} +(-39.4486 - 121.410i) q^{5} +(-4991.64 + 5220.85i) q^{6} +(-6331.96 - 1747.51i) q^{7} +(-912.463 + 6736.08i) q^{8} +(6328.41 + 46718.2i) q^{9} +O(q^{10})\) \(q+(-1.25358 + 27.9132i) q^{2} +(194.677 + 170.084i) q^{3} +(-267.637 - 24.0878i) q^{4} +(-39.4486 - 121.410i) q^{5} +(-4991.64 + 5220.85i) q^{6} +(-6331.96 - 1747.51i) q^{7} +(-912.463 + 6736.08i) q^{8} +(6328.41 + 46718.2i) q^{9} +(3438.41 - 948.939i) q^{10} +(-6394.60 + 11883.2i) q^{11} +(-48005.9 - 50210.3i) q^{12} +(21598.7 + 40137.2i) q^{13} +(56716.3 - 174555. i) q^{14} +(12970.2 - 30345.4i) q^{15} +(-322255. - 58480.6i) q^{16} +(-11243.9 - 8169.15i) q^{17} +(-1.31199e6 + 118081. i) q^{18} +(-18082.8 - 42306.9i) q^{19} +(7633.41 + 33444.2i) q^{20} +(-935464. - 1.41717e6i) q^{21} +(-323681. - 193390. i) q^{22} +(64595.4 + 81000.1i) q^{23} +(-1.32334e6 + 1.15616e6i) q^{24} +(1.56693e6 - 1.13844e6i) q^{25} +(-1.14743e6 + 552575. i) q^{26} +(-3.91092e6 + 5.92479e6i) q^{27} +(1.65258e6 + 620222. i) q^{28} +(1.43194e6 - 855546. i) q^{29} +(830779. + 400082. i) q^{30} +(-8.15843e6 + 1.48054e6i) q^{31} +(1.26190e6 - 5.52875e6i) q^{32} +(-3.26602e6 + 1.22576e6i) q^{33} +(242122. - 303612. i) q^{34} +(37621.3 + 837703. i) q^{35} +(-568380. - 1.26560e7i) q^{36} +(-528439. + 662641. i) q^{37} +(1.20359e6 - 451715. i) q^{38} +(-2.62192e6 + 1.14874e7i) q^{39} +(853825. - 154946. i) q^{40} +(1.68639e7 + 8.12125e6i) q^{41} +(4.07304e7 - 2.43353e7i) q^{42} +(-3.62394e6 - 1.36009e6i) q^{43} +(1.99767e6 - 3.02634e6i) q^{44} +(5.42242e6 - 2.61130e6i) q^{45} +(-2.34195e6 + 1.70152e6i) q^{46} +(1.24423e7 - 1.08705e7i) q^{47} +(-5.27890e7 - 6.61953e7i) q^{48} +(2.39847e6 + 1.43302e6i) q^{49} +(2.98132e7 + 4.51651e7i) q^{50} +(-799481. - 3.50275e6i) q^{51} +(-4.81382e6 - 1.12625e7i) q^{52} +(-8.59277e7 + 7.73363e6i) q^{53} +(-1.60477e8 - 1.16594e8i) q^{54} +(1.69500e6 + 307596. i) q^{55} +(1.75491e7 - 4.10580e7i) q^{56} +(3.67542e6 - 1.13118e7i) q^{57} +(2.20860e7 + 4.10426e7i) q^{58} +(-1.84266e7 - 1.92727e7i) q^{59} +(-4.20228e6 + 7.80914e6i) q^{60} +(2.77776e7 - 7.66612e6i) q^{61} +(-3.10993e7 - 2.29584e8i) q^{62} +(4.15693e7 - 3.06877e8i) q^{63} +(-8.90296e6 - 2.45706e6i) q^{64} +(4.02103e6 - 4.20567e6i) q^{65} +(-3.01206e7 - 9.27017e7i) q^{66} +(2.88107e8 + 2.59301e7i) q^{67} +(2.81250e6 + 2.45721e6i) q^{68} +(-1.20159e6 + 2.67555e7i) q^{69} -2.34301e7 q^{70} +(1.32195e8 + 1.68443e8i) q^{71} -3.20472e8 q^{72} +(-4.97097e6 + 1.10687e8i) q^{73} +(-1.78340e7 - 1.55811e7i) q^{74} +(4.98675e8 + 4.48816e7i) q^{75} +(3.82056e6 + 1.17585e7i) q^{76} +(6.12563e7 - 6.40691e7i) q^{77} +(-3.17364e8 - 8.75868e7i) q^{78} +(-6.81118e7 + 5.02821e8i) q^{79} +(5.61235e6 + 4.14320e7i) q^{80} +(-8.74569e8 + 2.41366e8i) q^{81} +(-2.47830e8 + 4.60546e8i) q^{82} +(1.13814e8 + 1.19040e8i) q^{83} +(2.16229e8 + 4.01820e8i) q^{84} +(-548264. + 1.68738e6i) q^{85} +(4.25073e7 - 9.94508e7i) q^{86} +(4.24281e8 + 7.69957e7i) q^{87} +(-7.42110e7 - 5.39174e7i) q^{88} +(8.24009e8 - 7.41622e7i) q^{89} +(6.60924e7 + 1.54631e8i) q^{90} +(-6.66223e7 - 2.91891e8i) q^{91} +(-1.53370e7 - 2.32346e7i) q^{92} +(-1.84008e9 - 1.09939e9i) q^{93} +(2.87834e8 + 3.60932e8i) q^{94} +(-4.42315e6 + 3.86439e6i) q^{95} +(1.18602e9 - 8.61692e8i) q^{96} +(-4.01642e8 + 1.93420e8i) q^{97} +(-4.30068e7 + 6.51525e7i) q^{98} +(-5.95627e8 - 2.23542e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15} + 4755334 q^{16} + 2558412 q^{17} - 2619769 q^{18} - 172269 q^{19} + 738120 q^{20} + 1797929 q^{21} + 3015622 q^{22} + 6635088 q^{23} + 4803145 q^{24} - 115100016 q^{25} + 19254293 q^{26} - 17686931 q^{27} + 15761532 q^{28} - 10052927 q^{29} + 62637435 q^{30} - 23748991 q^{31} + 10388192 q^{32} - 15097203 q^{33} + 33217854 q^{34} - 24823174 q^{35} + 27856812 q^{36} - 27156308 q^{37} - 43400577 q^{38} + 251072838 q^{39} - 129856160 q^{40} + 62087988 q^{41} - 91873950 q^{42} - 167299067 q^{43} + 60914131 q^{44} - 31536191 q^{45} - 50201490 q^{46} - 23317743 q^{47} + 10641329 q^{48} + 338745866 q^{49} + 303770229 q^{50} + 448039613 q^{51} - 979580293 q^{52} + 12085215 q^{53} - 182583505 q^{54} - 243892552 q^{55} + 30440435 q^{56} + 714581966 q^{57} - 244549660 q^{58} - 859013315 q^{59} - 1894499000 q^{60} - 876373921 q^{61} + 186553636 q^{62} - 196611021 q^{63} + 5528242635 q^{64} + 867018244 q^{65} + 2727701199 q^{66} - 286780089 q^{67} - 1689988351 q^{68} - 3073308182 q^{69} - 41489396 q^{70} - 2538053548 q^{71} - 6821388000 q^{72} + 128479023 q^{73} + 3282772334 q^{74} + 3407782757 q^{75} + 7133788844 q^{76} + 1087098389 q^{77} + 2715049934 q^{78} + 144243625 q^{79} - 7443877603 q^{80} - 4083269278 q^{81} - 10375744380 q^{82} + 1543773955 q^{83} - 4117054288 q^{84} + 7843382686 q^{85} + 3545751759 q^{86} + 5261609811 q^{87} - 818728797 q^{88} - 1369081479 q^{89} + 10041256259 q^{90} - 7299574322 q^{91} + 602797624 q^{92} - 2146129677 q^{93} - 683447510 q^{94} - 7007204038 q^{95} + 6601829126 q^{96} - 10081488030 q^{97} - 5942379880 q^{98} - 4074592265 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{35}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.25358 + 27.9132i −0.0554011 + 1.23360i 0.758139 + 0.652093i \(0.226109\pi\)
−0.813540 + 0.581509i \(0.802463\pi\)
\(3\) 194.677 + 170.084i 1.38762 + 1.21232i 0.949642 + 0.313336i \(0.101447\pi\)
0.437974 + 0.898988i \(0.355696\pi\)
\(4\) −267.637 − 24.0878i −0.522729 − 0.0470465i
\(5\) −39.4486 − 121.410i −0.0282271 − 0.0868742i 0.935950 − 0.352132i \(-0.114543\pi\)
−0.964178 + 0.265257i \(0.914543\pi\)
\(6\) −4991.64 + 5220.85i −1.57240 + 1.64460i
\(7\) −6331.96 − 1747.51i −0.996775 − 0.275092i −0.270667 − 0.962673i \(-0.587244\pi\)
−0.726108 + 0.687581i \(0.758673\pi\)
\(8\) −912.463 + 6736.08i −0.0787609 + 0.581436i
\(9\) 6328.41 + 46718.2i 0.321516 + 2.37353i
\(10\) 3438.41 − 948.939i 0.108732 − 0.0300081i
\(11\) −6394.60 + 11883.2i −0.131688 + 0.244717i −0.937897 − 0.346913i \(-0.887230\pi\)
0.806209 + 0.591630i \(0.201516\pi\)
\(12\) −48005.9 − 50210.3i −0.668312 − 0.698999i
\(13\) 21598.7 + 40137.2i 0.209741 + 0.389764i 0.963631 − 0.267237i \(-0.0861105\pi\)
−0.753890 + 0.657001i \(0.771825\pi\)
\(14\) 56716.3 − 174555.i 0.394577 − 1.21438i
\(15\) 12970.2 − 30345.4i 0.0661512 − 0.154768i
\(16\) −322255. − 58480.6i −1.22930 − 0.223086i
\(17\) −11243.9 − 8169.15i −0.0326509 − 0.0237223i 0.571340 − 0.820713i \(-0.306424\pi\)
−0.603991 + 0.796991i \(0.706424\pi\)
\(18\) −1.31199e6 + 118081.i −2.94580 + 0.265127i
\(19\) −18082.8 − 42306.9i −0.0318328 − 0.0744766i 0.902857 − 0.429941i \(-0.141466\pi\)
−0.934690 + 0.355464i \(0.884323\pi\)
\(20\) 7633.41 + 33444.2i 0.0106680 + 0.0467397i
\(21\) −935464. − 1.41717e6i −1.04964 − 1.59014i
\(22\) −323681. − 193390.i −0.294588 − 0.176008i
\(23\) 64595.4 + 81000.1i 0.0481312 + 0.0603546i 0.805314 − 0.592848i \(-0.201996\pi\)
−0.757183 + 0.653202i \(0.773425\pi\)
\(24\) −1.32334e6 + 1.15616e6i −0.814179 + 0.711326i
\(25\) 1.56693e6 − 1.13844e6i 0.802267 − 0.582881i
\(26\) −1.14743e6 + 552575.i −0.492434 + 0.237144i
\(27\) −3.91092e6 + 5.92479e6i −1.41626 + 2.14554i
\(28\) 1.65258e6 + 620222.i 0.508101 + 0.190694i
\(29\) 1.43194e6 − 855546.i 0.375954 − 0.224622i −0.312475 − 0.949926i \(-0.601158\pi\)
0.688429 + 0.725304i \(0.258301\pi\)
\(30\) 830779. + 400082.i 0.187258 + 0.0901785i
\(31\) −8.15843e6 + 1.48054e6i −1.58664 + 0.287933i −0.898944 − 0.438064i \(-0.855664\pi\)
−0.687698 + 0.725997i \(0.741379\pi\)
\(32\) 1.26190e6 − 5.52875e6i 0.212741 − 0.932078i
\(33\) −3.26602e6 + 1.22576e6i −0.479409 + 0.179925i
\(34\) 242122. − 303612.i 0.0310728 − 0.0389640i
\(35\) 37621.3 + 837703.i 0.00423767 + 0.0943591i
\(36\) −568380. − 1.26560e7i −0.0563998 − 1.25584i
\(37\) −528439. + 662641.i −0.0463540 + 0.0581260i −0.804468 − 0.593996i \(-0.797550\pi\)
0.758114 + 0.652122i \(0.226121\pi\)
\(38\) 1.20359e6 − 451715.i 0.0936380 − 0.0351429i
\(39\) −2.62192e6 + 1.14874e7i −0.181480 + 0.795117i
\(40\) 853825. − 154946.i 0.0527350 − 0.00956999i
\(41\) 1.68639e7 + 8.12125e6i 0.932034 + 0.448844i 0.837352 − 0.546664i \(-0.184102\pi\)
0.0946817 + 0.995508i \(0.469817\pi\)
\(42\) 4.07304e7 − 2.43353e7i 2.01975 − 1.20674i
\(43\) −3.62394e6 − 1.36009e6i −0.161649 − 0.0606678i 0.269239 − 0.963074i \(-0.413228\pi\)
−0.430887 + 0.902406i \(0.641799\pi\)
\(44\) 1.99767e6 − 3.02634e6i 0.0803502 − 0.121725i
\(45\) 5.42242e6 − 2.61130e6i 0.197123 − 0.0949294i
\(46\) −2.34195e6 + 1.70152e6i −0.0771200 + 0.0560310i
\(47\) 1.24423e7 − 1.08705e7i 0.371930 − 0.324945i −0.451598 − 0.892222i \(-0.649146\pi\)
0.823528 + 0.567276i \(0.192003\pi\)
\(48\) −5.27890e7 − 6.61953e7i −1.43535 − 1.79987i
\(49\) 2.39847e6 + 1.43302e6i 0.0594362 + 0.0355115i
\(50\) 2.98132e7 + 4.51651e7i 0.674596 + 1.02197i
\(51\) −799481. − 3.50275e6i −0.0165479 − 0.0725010i
\(52\) −4.81382e6 − 1.12625e7i −0.0913008 − 0.213609i
\(53\) −8.59277e7 + 7.73363e6i −1.49586 + 0.134630i −0.807125 − 0.590381i \(-0.798978\pi\)
−0.688738 + 0.725011i \(0.741835\pi\)
\(54\) −1.60477e8 − 1.16594e8i −2.56828 − 1.86596i
\(55\) 1.69500e6 + 307596.i 0.0249768 + 0.00453262i
\(56\) 1.75491e7 − 4.10580e7i 0.238456 − 0.557895i
\(57\) 3.67542e6 − 1.13118e7i 0.0461180 − 0.141937i
\(58\) 2.20860e7 + 4.10426e7i 0.256266 + 0.476222i
\(59\) −1.84266e7 − 1.92727e7i −0.197976 − 0.207066i 0.616354 − 0.787470i \(-0.288609\pi\)
−0.814329 + 0.580403i \(0.802895\pi\)
\(60\) −4.20228e6 + 7.80914e6i −0.0418605 + 0.0777898i
\(61\) 2.77776e7 − 7.66612e6i 0.256868 − 0.0708911i −0.135231 − 0.990814i \(-0.543178\pi\)
0.392099 + 0.919923i \(0.371749\pi\)
\(62\) −3.10993e7 − 2.29584e8i −0.267293 − 1.97324i
\(63\) 4.15693e7 − 3.06877e8i 0.332461 − 2.45432i
\(64\) −8.90296e6 − 2.45706e6i −0.0663322 − 0.0183065i
\(65\) 4.02103e6 − 4.20567e6i 0.0279401 − 0.0292230i
\(66\) −3.01206e7 − 9.27017e7i −0.195396 − 0.601367i
\(67\) 2.88107e8 + 2.59301e7i 1.74670 + 0.157206i 0.916439 − 0.400174i \(-0.131050\pi\)
0.830258 + 0.557379i \(0.188193\pi\)
\(68\) 2.81250e6 + 2.45721e6i 0.0159516 + 0.0139365i
\(69\) −1.20159e6 + 2.67555e7i −0.00638170 + 0.142099i
\(70\) −2.34301e7 −0.116636
\(71\) 1.32195e8 + 1.68443e8i 0.617380 + 0.786665i
\(72\) −3.20472e8 −1.40538
\(73\) −4.97097e6 + 1.10687e8i −0.0204875 + 0.456189i 0.962361 + 0.271774i \(0.0876104\pi\)
−0.982848 + 0.184415i \(0.940961\pi\)
\(74\) −1.78340e7 − 1.55811e7i −0.0691363 − 0.0604026i
\(75\) 4.98675e8 + 4.48816e7i 1.81988 + 0.163792i
\(76\) 3.82056e6 + 1.17585e7i 0.0131361 + 0.0404287i
\(77\) 6.12563e7 − 6.40691e7i 0.198583 − 0.207702i
\(78\) −3.17364e8 − 8.75868e7i −0.970804 − 0.267925i
\(79\) −6.81118e7 + 5.02821e8i −0.196743 + 1.45242i 0.575870 + 0.817541i \(0.304663\pi\)
−0.772613 + 0.634877i \(0.781051\pi\)
\(80\) 5.61235e6 + 4.14320e7i 0.0153193 + 0.113092i
\(81\) −8.74569e8 + 2.41366e8i −2.25742 + 0.623007i
\(82\) −2.47830e8 + 4.60546e8i −0.605330 + 1.12489i
\(83\) 1.13814e8 + 1.19040e8i 0.263234 + 0.275321i 0.841182 − 0.540753i \(-0.181860\pi\)
−0.577947 + 0.816074i \(0.696146\pi\)
\(84\) 2.16229e8 + 4.01820e8i 0.473867 + 0.880593i
\(85\) −548264. + 1.68738e6i −0.00113921 + 0.00350614i
\(86\) 4.25073e7 − 9.94508e7i 0.0837955 − 0.196049i
\(87\) 4.24281e8 + 7.69957e7i 0.793994 + 0.144089i
\(88\) −7.42110e7 − 5.39174e7i −0.131916 − 0.0958423i
\(89\) 8.24009e8 − 7.41622e7i 1.39212 − 0.125293i 0.631947 − 0.775012i \(-0.282256\pi\)
0.760175 + 0.649719i \(0.225113\pi\)
\(90\) 6.60924e7 + 1.54631e8i 0.106184 + 0.248430i
\(91\) −6.66223e7 − 2.91891e8i −0.101844 − 0.446206i
\(92\) −1.53370e7 − 2.32346e7i −0.0223201 − 0.0338135i
\(93\) −1.84008e9 − 1.09939e9i −2.55072 − 1.52398i
\(94\) 2.87834e8 + 3.60932e8i 0.380248 + 0.476816i
\(95\) −4.42315e6 + 3.86439e6i −0.00557154 + 0.00486771i
\(96\) 1.18602e9 − 8.61692e8i 1.42518 − 1.03546i
\(97\) −4.01642e8 + 1.93420e8i −0.460645 + 0.221835i −0.649789 − 0.760115i \(-0.725143\pi\)
0.189145 + 0.981949i \(0.439429\pi\)
\(98\) −4.30068e7 + 6.51525e7i −0.0470999 + 0.0713532i
\(99\) −5.95627e8 − 2.23542e8i −0.623183 − 0.233885i
\(100\) −4.46791e8 + 2.66945e8i −0.446791 + 0.266945i
\(101\) 8.65662e8 + 4.16881e8i 0.827756 + 0.398626i 0.799273 − 0.600968i \(-0.205218\pi\)
0.0284829 + 0.999594i \(0.490932\pi\)
\(102\) 9.87753e7 − 1.79251e7i 0.0903541 − 0.0163968i
\(103\) −4.15726e8 + 1.82141e9i −0.363948 + 1.59456i 0.379121 + 0.925347i \(0.376226\pi\)
−0.743069 + 0.669214i \(0.766631\pi\)
\(104\) −2.90075e8 + 1.08867e8i −0.243142 + 0.0912529i
\(105\) −1.35156e8 + 1.69480e8i −0.108513 + 0.136072i
\(106\) −1.08153e8 − 2.40821e9i −0.0832074 − 1.85276i
\(107\) 8.34923e7 + 1.85910e9i 0.0615771 + 1.37112i 0.757421 + 0.652927i \(0.226459\pi\)
−0.695843 + 0.718193i \(0.744969\pi\)
\(108\) 1.18942e9 − 1.49149e9i 0.841259 − 1.05491i
\(109\) −1.07921e9 + 4.05035e8i −0.732298 + 0.274836i −0.689538 − 0.724249i \(-0.742186\pi\)
−0.0427598 + 0.999085i \(0.513615\pi\)
\(110\) −1.07108e7 + 4.69272e7i −0.00697518 + 0.0305603i
\(111\) −2.15580e8 + 3.91220e7i −0.134789 + 0.0244606i
\(112\) 1.93831e9 + 9.33441e8i 1.16397 + 0.560539i
\(113\) −3.37205e8 + 2.01470e8i −0.194554 + 0.116241i −0.606873 − 0.794799i \(-0.707576\pi\)
0.412319 + 0.911040i \(0.364719\pi\)
\(114\) 3.11141e8 + 1.16773e8i 0.172538 + 0.0647547i
\(115\) 7.28605e6 − 1.10379e7i 0.00388465 − 0.00588499i
\(116\) −4.03850e8 + 1.94484e8i −0.207090 + 0.0997292i
\(117\) −1.73845e9 + 1.26306e9i −0.857682 + 0.623142i
\(118\) 5.61064e8 − 4.90187e8i 0.266405 − 0.232751i
\(119\) 5.69201e7 + 7.13756e7i 0.0260198 + 0.0326278i
\(120\) 1.92574e8 + 1.15058e8i 0.0847778 + 0.0506524i
\(121\) 1.19867e9 + 1.81590e9i 0.508352 + 0.770121i
\(122\) 1.79165e8 + 7.84971e8i 0.0732205 + 0.320800i
\(123\) 1.90173e9 + 4.44931e9i 0.749161 + 1.75275i
\(124\) 2.21916e9 − 1.99728e8i 0.842930 − 0.0758651i
\(125\) −4.01746e8 − 2.91885e8i −0.147183 − 0.106934i
\(126\) 8.51381e9 + 1.54503e9i 3.00924 + 0.546096i
\(127\) 6.71971e8 − 1.57215e9i 0.229210 − 0.536264i −0.764961 − 0.644077i \(-0.777242\pi\)
0.994171 + 0.107813i \(0.0343847\pi\)
\(128\) 9.76981e8 − 3.00684e9i 0.321693 − 0.990069i
\(129\) −4.74169e8 − 8.81153e8i −0.150758 − 0.280154i
\(130\) 1.12353e8 + 1.17512e8i 0.0345016 + 0.0360859i
\(131\) 2.22440e9 − 4.13363e9i 0.659922 − 1.22634i −0.302076 − 0.953284i \(-0.597680\pi\)
0.961998 − 0.273056i \(-0.0880345\pi\)
\(132\) 9.03635e8 − 2.49387e8i 0.259066 − 0.0714976i
\(133\) 4.05681e7 + 2.99486e8i 0.0112422 + 0.0829934i
\(134\) −1.08496e9 + 8.00950e9i −0.290698 + 2.14602i
\(135\) 8.73611e8 + 2.41101e8i 0.226369 + 0.0624738i
\(136\) 6.52877e7 − 6.82855e7i 0.0163646 − 0.0171161i
\(137\) 2.32565e8 + 7.15760e8i 0.0564028 + 0.173590i 0.975289 − 0.220932i \(-0.0709100\pi\)
−0.918886 + 0.394522i \(0.870910\pi\)
\(138\) −7.45326e8 − 6.70806e7i −0.174941 − 0.0157449i
\(139\) −5.88267e9 − 5.13953e9i −1.33662 − 1.16777i −0.971562 − 0.236784i \(-0.923907\pi\)
−0.365057 − 0.930985i \(-0.618951\pi\)
\(140\) 1.01096e7 − 2.25107e8i 0.00222411 − 0.0495236i
\(141\) 4.27114e9 0.910035
\(142\) −4.86750e9 + 3.47883e9i −1.00464 + 0.718018i
\(143\) −6.15072e8 −0.123002
\(144\) 6.92749e8 − 1.54252e10i 0.134259 − 2.98952i
\(145\) −1.60360e8 − 1.40103e8i −0.0301260 − 0.0263203i
\(146\) −3.08341e9 − 2.77512e8i −0.561621 − 0.0505468i
\(147\) 2.23193e8 + 6.86917e8i 0.0394232 + 0.121332i
\(148\) 1.57391e8 − 1.64619e8i 0.0269652 − 0.0282034i
\(149\) −7.75209e9 − 2.13944e9i −1.28849 − 0.355600i −0.446348 − 0.894859i \(-0.647276\pi\)
−0.842140 + 0.539259i \(0.818704\pi\)
\(150\) −1.87792e9 + 1.38634e10i −0.302877 + 2.23593i
\(151\) 4.20304e8 + 3.10281e9i 0.0657911 + 0.485690i 0.993629 + 0.112705i \(0.0359514\pi\)
−0.927837 + 0.372985i \(0.878334\pi\)
\(152\) 3.01482e8 − 8.32038e7i 0.0458106 − 0.0126429i
\(153\) 3.10492e8 − 5.76991e8i 0.0458078 − 0.0851251i
\(154\) 1.71158e9 + 1.79018e9i 0.245219 + 0.256479i
\(155\) 5.01591e8 + 9.32112e8i 0.0698003 + 0.129711i
\(156\) 9.78431e8 − 3.01130e9i 0.132273 − 0.407093i
\(157\) −4.15139e9 + 9.71265e9i −0.545312 + 1.27582i 0.389615 + 0.920978i \(0.372608\pi\)
−0.934926 + 0.354842i \(0.884535\pi\)
\(158\) −1.39500e10 − 2.53155e9i −1.78081 − 0.323169i
\(159\) −1.80435e10 − 1.31094e10i −2.23890 − 1.62665i
\(160\) −7.21028e8 + 6.48937e7i −0.0869785 + 0.00782821i
\(161\) −2.67467e8 − 6.25771e8i −0.0313729 − 0.0734005i
\(162\) −5.64095e9 − 2.47146e10i −0.643479 − 2.81927i
\(163\) 4.81953e9 + 7.30127e9i 0.534762 + 0.810129i 0.997062 − 0.0765939i \(-0.0244045\pi\)
−0.462301 + 0.886723i \(0.652976\pi\)
\(164\) −4.31780e9 − 2.57976e9i −0.466085 − 0.278473i
\(165\) 2.77659e8 + 3.48174e8i 0.0291632 + 0.0365695i
\(166\) −3.46545e9 + 3.02768e9i −0.354220 + 0.309473i
\(167\) −8.57311e9 + 6.22873e9i −0.852932 + 0.619691i −0.925953 − 0.377639i \(-0.876736\pi\)
0.0730209 + 0.997330i \(0.476736\pi\)
\(168\) 1.03997e10 − 5.00824e9i 1.00723 − 0.485058i
\(169\) 4.69750e9 − 7.11640e9i 0.442972 − 0.671074i
\(170\) −4.64130e7 − 1.74191e7i −0.00426206 − 0.00159958i
\(171\) 1.86207e9 − 1.11253e9i 0.166538 − 0.0995016i
\(172\) 9.37140e8 + 4.51303e8i 0.0816444 + 0.0393179i
\(173\) −1.60377e10 + 2.91041e9i −1.36124 + 0.247028i −0.809564 − 0.587032i \(-0.800296\pi\)
−0.551673 + 0.834060i \(0.686010\pi\)
\(174\) −2.68107e9 + 1.17465e10i −0.221736 + 0.971490i
\(175\) −1.19112e10 + 4.47033e9i −0.960026 + 0.360304i
\(176\) 2.75562e9 − 3.45544e9i 0.216478 − 0.271454i
\(177\) −3.09253e8 − 6.88604e9i −0.0236828 − 0.527339i
\(178\) 1.03714e9 + 2.30937e10i 0.0774368 + 1.72426i
\(179\) 6.04756e9 − 7.58340e9i 0.440293 − 0.552109i −0.511328 − 0.859386i \(-0.670846\pi\)
0.951620 + 0.307276i \(0.0994176\pi\)
\(180\) −1.51414e9 + 5.68268e8i −0.107508 + 0.0403484i
\(181\) 5.41490e9 − 2.37242e10i 0.375005 − 1.64300i −0.337492 − 0.941328i \(-0.609579\pi\)
0.712497 − 0.701675i \(-0.247564\pi\)
\(182\) 8.23114e9 − 1.49373e9i 0.556082 − 0.100914i
\(183\) 6.71154e9 + 3.23211e9i 0.442377 + 0.213038i
\(184\) −6.04563e8 + 3.61210e8i −0.0388832 + 0.0232316i
\(185\) 1.01298e8 + 3.80176e7i 0.00635809 + 0.00238623i
\(186\) 3.29943e10 − 4.99842e10i 2.02130 − 3.06214i
\(187\) 1.68975e8 − 8.13742e7i 0.0101050 − 0.00486631i
\(188\) −3.59188e9 + 2.60965e9i −0.209706 + 0.152360i
\(189\) 3.51174e10 − 3.06812e10i 2.00191 − 1.74902i
\(190\) −1.02323e8 − 1.28309e8i −0.00569615 − 0.00714274i
\(191\) 3.90148e9 + 2.33103e9i 0.212119 + 0.126735i 0.615029 − 0.788504i \(-0.289144\pi\)
−0.402910 + 0.915239i \(0.632001\pi\)
\(192\) −1.31529e9 − 1.99259e9i −0.0698502 − 0.105819i
\(193\) 4.60759e9 + 2.01872e10i 0.239037 + 1.04729i 0.941881 + 0.335947i \(0.109056\pi\)
−0.702844 + 0.711344i \(0.748087\pi\)
\(194\) −4.89549e9 − 1.14536e10i −0.248135 − 0.580542i
\(195\) 1.49812e9 − 1.34833e8i 0.0741978 − 0.00667792i
\(196\) −6.07401e8 − 4.41303e8i −0.0293984 − 0.0213592i
\(197\) 2.72407e10 + 4.94345e9i 1.28860 + 0.233847i 0.779252 − 0.626711i \(-0.215599\pi\)
0.509353 + 0.860558i \(0.329885\pi\)
\(198\) 6.98646e9 − 1.63456e10i 0.323045 − 0.755802i
\(199\) −1.07364e10 + 3.30431e10i −0.485309 + 1.49363i 0.346225 + 0.938151i \(0.387463\pi\)
−0.831534 + 0.555475i \(0.812537\pi\)
\(200\) 6.23885e9 + 1.15937e10i 0.275721 + 0.512375i
\(201\) 5.16776e10 + 5.40505e10i 2.23316 + 2.33570i
\(202\) −1.27217e10 + 2.36408e10i −0.537605 + 0.999037i
\(203\) −1.05621e10 + 2.91495e9i −0.436534 + 0.120476i
\(204\) 1.29597e8 + 9.56725e8i 0.00523914 + 0.0386769i
\(205\) 3.20744e8 − 2.36783e9i 0.0126843 − 0.0936392i
\(206\) −5.03204e10 − 1.38875e10i −1.94689 − 0.537308i
\(207\) −3.37539e9 + 3.53038e9i −0.127778 + 0.133646i
\(208\) −4.61305e9 − 1.41975e10i −0.170885 − 0.525929i
\(209\) 6.18371e8 + 5.56544e7i 0.0224177 + 0.00201763i
\(210\) −4.56131e9 − 3.98510e9i −0.161846 − 0.141401i
\(211\) 1.16556e9 − 2.59531e10i 0.0404820 − 0.901402i −0.871306 − 0.490740i \(-0.836726\pi\)
0.911788 − 0.410661i \(-0.134702\pi\)
\(212\) 2.31837e10 0.788265
\(213\) −2.91415e9 + 5.52763e10i −0.0970071 + 1.84005i
\(214\) −5.19981e10 −1.69483
\(215\) −2.21693e7 + 4.93637e8i −0.000707584 + 0.0157556i
\(216\) −3.63413e10 − 3.17504e10i −1.13595 − 0.992447i
\(217\) 5.42461e10 + 4.88224e9i 1.66073 + 0.149469i
\(218\) −9.95296e9 − 3.06320e10i −0.298468 − 0.918590i
\(219\) −1.97939e10 + 2.07028e10i −0.581478 + 0.608178i
\(220\) −4.46235e8 − 1.23153e8i −0.0128428 − 0.00354440i
\(221\) 8.50333e7 − 6.27741e8i 0.00239786 − 0.0177017i
\(222\) −8.21772e8 − 6.06657e9i −0.0227072 − 0.167631i
\(223\) 3.18725e10 − 8.79625e9i 0.863066 − 0.238191i 0.193643 − 0.981072i \(-0.437970\pi\)
0.669424 + 0.742881i \(0.266541\pi\)
\(224\) −1.76519e10 + 3.28027e10i −0.468462 + 0.870549i
\(225\) 6.31020e10 + 6.59995e10i 1.64143 + 1.71680i
\(226\) −5.20097e9 − 9.66503e9i −0.132616 − 0.246442i
\(227\) 9.72863e9 − 2.99417e10i 0.243184 − 0.748444i −0.752746 − 0.658312i \(-0.771271\pi\)
0.995930 − 0.0901326i \(-0.0287291\pi\)
\(228\) −1.25616e9 + 2.93892e9i −0.0307848 + 0.0720247i
\(229\) 6.40129e10 + 1.16166e10i 1.53818 + 0.279139i 0.880460 − 0.474121i \(-0.157234\pi\)
0.657723 + 0.753260i \(0.271520\pi\)
\(230\) 2.98969e8 + 2.17214e8i 0.00704452 + 0.00511814i
\(231\) 2.28223e10 − 2.05405e9i 0.527359 − 0.0474632i
\(232\) 4.45643e9 + 1.04263e10i 0.100993 + 0.236285i
\(233\) −1.27730e10 − 5.59621e10i −0.283916 − 1.24392i −0.892725 − 0.450602i \(-0.851209\pi\)
0.608809 − 0.793317i \(-0.291648\pi\)
\(234\) −3.30767e10 − 5.01091e10i −0.721193 − 1.09256i
\(235\) −1.81063e9 − 1.08180e9i −0.0387279 − 0.0231388i
\(236\) 4.46742e9 + 5.60196e9i 0.0937460 + 0.117554i
\(237\) −9.87818e10 + 8.63030e10i −2.03381 + 1.77688i
\(238\) −2.06368e9 + 1.49935e9i −0.0416913 + 0.0302905i
\(239\) 7.75511e9 − 3.73466e9i 0.153744 − 0.0740390i −0.355430 − 0.934703i \(-0.615665\pi\)
0.509173 + 0.860664i \(0.329951\pi\)
\(240\) −5.95434e9 + 9.02045e9i −0.115847 + 0.175500i
\(241\) 4.84261e10 + 1.81746e10i 0.924705 + 0.347048i 0.767891 − 0.640581i \(-0.221306\pi\)
0.156814 + 0.987628i \(0.449878\pi\)
\(242\) −5.21904e10 + 3.11823e10i −0.978185 + 0.584439i
\(243\) −8.54158e10 − 4.11341e10i −1.57148 − 0.756787i
\(244\) −7.61897e9 + 1.38264e9i −0.137608 + 0.0249721i
\(245\) 7.93669e7 − 3.47729e8i 0.00140732 − 0.00616586i
\(246\) −1.26579e11 + 4.75057e10i −2.20370 + 0.827062i
\(247\) 1.30751e9 − 1.63957e9i 0.0223517 − 0.0280281i
\(248\) −2.52874e9 − 5.63067e10i −0.0424494 − 0.945209i
\(249\) 1.91012e9 + 4.25322e10i 0.0314894 + 0.701166i
\(250\) 8.65108e9 − 1.08481e10i 0.140068 − 0.175640i
\(251\) −1.11212e11 + 4.17387e10i −1.76857 + 0.663755i −0.768864 + 0.639412i \(0.779178\pi\)
−0.999704 + 0.0243424i \(0.992251\pi\)
\(252\) −1.85175e10 + 8.11304e10i −0.289254 + 1.26730i
\(253\) −1.37560e9 + 2.49634e8i −0.0211081 + 0.00383055i
\(254\) 4.30415e10 + 2.07277e10i 0.648838 + 0.312464i
\(255\) −3.93732e8 + 2.35244e8i −0.00583136 + 0.00348408i
\(256\) 7.82786e10 + 2.93785e10i 1.13910 + 0.427513i
\(257\) −6.63199e9 + 1.00470e10i −0.0948298 + 0.143661i −0.878891 − 0.477022i \(-0.841716\pi\)
0.784061 + 0.620683i \(0.213145\pi\)
\(258\) 2.51902e10 − 1.21310e10i 0.353951 − 0.170454i
\(259\) 4.50403e9 − 3.27237e9i 0.0621945 − 0.0451870i
\(260\) −1.17748e9 + 1.02874e9i −0.0159799 + 0.0139612i
\(261\) 4.90315e10 + 6.14835e10i 0.654022 + 0.820118i
\(262\) 1.12594e11 + 6.72721e10i 1.47625 + 0.882021i
\(263\) −2.35022e8 − 3.56043e8i −0.00302906 − 0.00458883i 0.833056 − 0.553189i \(-0.186589\pi\)
−0.836085 + 0.548600i \(0.815161\pi\)
\(264\) −5.27667e9 − 2.31186e10i −0.0668563 − 0.292917i
\(265\) 4.32867e9 + 1.01274e10i 0.0539198 + 0.126152i
\(266\) −8.41046e9 + 7.56955e8i −0.103004 + 0.00927049i
\(267\) 1.73030e11 + 1.25713e11i 2.08363 + 1.51384i
\(268\) −7.64837e10 − 1.38797e10i −0.905654 − 0.164352i
\(269\) 3.07889e10 − 7.20343e10i 0.358517 − 0.838792i −0.639056 − 0.769160i \(-0.720675\pi\)
0.997573 − 0.0696315i \(-0.0221824\pi\)
\(270\) −7.82506e9 + 2.40831e10i −0.0896088 + 0.275788i
\(271\) 1.83142e10 + 3.40335e10i 0.206266 + 0.383306i 0.962620 − 0.270857i \(-0.0873070\pi\)
−0.756354 + 0.654162i \(0.773021\pi\)
\(272\) 3.14566e9 + 3.29010e9i 0.0348459 + 0.0364459i
\(273\) 3.66763e10 − 6.81560e10i 0.399626 − 0.742629i
\(274\) −2.02707e10 + 5.59436e9i −0.217266 + 0.0599615i
\(275\) 3.50838e9 + 2.58999e10i 0.0369921 + 0.273087i
\(276\) 9.66073e8 − 7.13183e9i 0.0100212 − 0.0739793i
\(277\) 9.46901e10 + 2.61328e10i 0.966375 + 0.266702i 0.713390 − 0.700768i \(-0.247159\pi\)
0.252985 + 0.967470i \(0.418588\pi\)
\(278\) 1.50835e11 − 1.57761e11i 1.51461 − 1.58416i
\(279\) −1.20798e11 − 3.71778e11i −1.19355 − 3.67337i
\(280\) −5.67716e9 − 5.10953e8i −0.0551975 − 0.00496787i
\(281\) 6.55030e10 + 5.72283e10i 0.626734 + 0.547561i 0.911637 − 0.410995i \(-0.134819\pi\)
−0.284904 + 0.958556i \(0.591962\pi\)
\(282\) −5.35424e9 + 1.19221e11i −0.0504169 + 1.12262i
\(283\) 3.72318e10 0.345045 0.172522 − 0.985006i \(-0.444808\pi\)
0.172522 + 0.985006i \(0.444808\pi\)
\(284\) −3.13229e10 − 4.82659e10i −0.285713 − 0.440259i
\(285\) −1.51836e9 −0.0136324
\(286\) 7.71044e8 − 1.71686e10i 0.00681447 − 0.151736i
\(287\) −9.25899e10 − 8.08934e10i −0.805555 − 0.703792i
\(288\) 2.66279e11 + 2.39655e10i 2.28071 + 0.205268i
\(289\) −3.65860e10 − 1.12600e11i −0.308514 − 0.949507i
\(290\) 4.11174e9 − 4.30054e9i 0.0341377 − 0.0357053i
\(291\) −1.11088e11 − 3.06584e10i −0.908133 − 0.250629i
\(292\) 3.99663e9 − 2.95043e10i 0.0321715 − 0.237500i
\(293\) 1.48085e9 + 1.09321e10i 0.0117383 + 0.0866560i 0.995871 − 0.0907769i \(-0.0289350\pi\)
−0.984133 + 0.177433i \(0.943221\pi\)
\(294\) −1.94539e10 + 5.36892e9i −0.151860 + 0.0419106i
\(295\) −1.61301e9 + 2.99747e9i −0.0124004 + 0.0230439i
\(296\) −3.98142e9 − 4.16424e9i −0.0301457 − 0.0315299i
\(297\) −4.53964e10 − 8.43607e10i −0.338546 − 0.629124i
\(298\) 6.94365e10 − 2.13704e11i 0.510052 − 1.56978i
\(299\) −1.85594e9 + 4.34218e9i −0.0134290 + 0.0314186i
\(300\) −1.32383e11 − 2.40240e10i −0.943598 − 0.171238i
\(301\) 2.05699e10 + 1.49449e10i 0.144438 + 0.104941i
\(302\) −8.71363e10 + 7.84241e9i −0.602792 + 0.0542523i
\(303\) 9.76197e10 + 2.28393e11i 0.665343 + 1.55665i
\(304\) 3.35315e9 + 1.46911e10i 0.0225176 + 0.0986559i
\(305\) −2.02653e9 − 3.07007e9i −0.0134092 − 0.0203141i
\(306\) 1.57164e10 + 9.39014e9i 0.102473 + 0.0612246i
\(307\) −8.57260e10 − 1.07497e11i −0.550795 − 0.690675i 0.426032 − 0.904708i \(-0.359911\pi\)
−0.976826 + 0.214033i \(0.931340\pi\)
\(308\) −1.79378e10 + 1.56717e10i −0.113577 + 0.0992291i
\(309\) −3.90726e11 + 2.83879e11i −2.43814 + 1.77142i
\(310\) −2.66470e10 + 1.28325e10i −0.163878 + 0.0789196i
\(311\) 7.03377e10 − 1.06557e11i 0.426350 − 0.645893i −0.556382 − 0.830927i \(-0.687811\pi\)
0.982732 + 0.185034i \(0.0592395\pi\)
\(312\) −7.49876e10 − 2.81433e10i −0.448016 − 0.168143i
\(313\) 2.76736e11 − 1.65342e11i 1.62973 − 0.973718i 0.653514 − 0.756915i \(-0.273294\pi\)
0.976215 − 0.216803i \(-0.0695630\pi\)
\(314\) −2.65907e11 − 1.28054e11i −1.54364 − 0.743379i
\(315\) −3.88979e10 + 7.05892e9i −0.222602 + 0.0403962i
\(316\) 3.03411e10 − 1.32933e11i 0.171175 − 0.749965i
\(317\) −1.46666e11 + 5.50445e10i −0.815758 + 0.306159i −0.724156 − 0.689636i \(-0.757770\pi\)
−0.0916025 + 0.995796i \(0.529199\pi\)
\(318\) 3.88544e11 − 4.87219e11i 2.13068 − 2.67179i
\(319\) 1.00989e9 + 2.24869e10i 0.00546027 + 0.121582i
\(320\) 5.28968e7 + 1.17784e9i 0.000282003 + 0.00627929i
\(321\) −2.99950e11 + 3.76125e11i −1.57680 + 1.97724i
\(322\) 1.78026e10 − 6.68141e9i 0.0922850 − 0.0346351i
\(323\) −1.42290e8 + 6.23415e8i −0.000727384 + 0.00318688i
\(324\) 2.39881e11 − 4.35320e10i 1.20933 − 0.219461i
\(325\) 7.95374e10 + 3.83032e10i 0.395454 + 0.190441i
\(326\) −2.09844e11 + 1.25376e11i −1.02900 + 0.614801i
\(327\) −2.78988e11 − 1.04706e11i −1.34934 − 0.506415i
\(328\) −7.00931e10 + 1.06186e11i −0.334382 + 0.506567i
\(329\) −9.77807e10 + 4.70887e10i −0.460121 + 0.221582i
\(330\) −1.00667e10 + 7.31390e9i −0.0467278 + 0.0339497i
\(331\) 1.46878e10 − 1.28323e10i 0.0672558 − 0.0587596i −0.623655 − 0.781700i \(-0.714353\pi\)
0.690910 + 0.722940i \(0.257210\pi\)
\(332\) −2.75933e10 − 3.46010e10i −0.124647 − 0.156303i
\(333\) −3.43016e10 − 2.04942e10i −0.152867 − 0.0913340i
\(334\) −1.63117e11 − 2.47111e11i −0.717199 − 1.08651i
\(335\) −8.21725e9 − 3.60021e10i −0.0356471 − 0.156180i
\(336\) 2.18581e11 + 5.11396e11i 0.935590 + 2.18892i
\(337\) 7.57179e10 − 6.81473e9i 0.319789 − 0.0287816i 0.0714181 − 0.997446i \(-0.477248\pi\)
0.248371 + 0.968665i \(0.420105\pi\)
\(338\) 1.92753e11 + 1.40043e11i 0.803297 + 0.583629i
\(339\) −9.99130e10 − 1.81315e10i −0.410888 − 0.0745651i
\(340\) 1.87381e8 − 4.38401e8i 0.000760451 − 0.00177916i
\(341\) 3.45764e10 − 1.06415e11i 0.138479 − 0.426196i
\(342\) 2.87201e10 + 5.33709e10i 0.113519 + 0.210954i
\(343\) 1.70497e11 + 1.78326e11i 0.665110 + 0.695651i
\(344\) 1.24684e10 − 2.31701e10i 0.0480061 − 0.0892103i
\(345\) 3.29580e9 − 9.09582e8i 0.0125249 − 0.00345666i
\(346\) −6.11343e10 − 4.51311e11i −0.229320 − 1.69291i
\(347\) 2.80934e10 − 2.07394e11i 0.104021 − 0.767915i −0.861531 − 0.507705i \(-0.830494\pi\)
0.965552 − 0.260210i \(-0.0837917\pi\)
\(348\) −1.11699e11 − 3.08269e10i −0.408265 − 0.112674i
\(349\) −1.20859e11 + 1.26409e11i −0.436078 + 0.456102i −0.903915 − 0.427713i \(-0.859319\pi\)
0.467836 + 0.883815i \(0.345034\pi\)
\(350\) −1.09850e11 − 3.38083e11i −0.391285 − 1.20425i
\(351\) −3.22275e11 − 2.90053e10i −1.13330 − 0.101999i
\(352\) 5.76296e10 + 5.03495e10i 0.200080 + 0.174805i
\(353\) 1.18113e10 − 2.62999e11i 0.0404865 − 0.901503i −0.871278 − 0.490790i \(-0.836708\pi\)
0.911765 − 0.410713i \(-0.134720\pi\)
\(354\) 1.92599e11 0.651839
\(355\) 1.52358e10 − 2.26947e10i 0.0509140 − 0.0758396i
\(356\) −2.22322e11 −0.733597
\(357\) −1.05882e9 + 2.35764e10i −0.00344996 + 0.0768194i
\(358\) 2.04096e11 + 1.78313e11i 0.656690 + 0.573733i
\(359\) −5.74647e11 − 5.17192e10i −1.82590 − 0.164334i −0.877119 − 0.480274i \(-0.840537\pi\)
−0.948779 + 0.315940i \(0.897680\pi\)
\(360\) 1.26422e10 + 3.89086e10i 0.0396698 + 0.122091i
\(361\) 2.21535e11 − 2.31707e11i 0.686529 − 0.718053i
\(362\) 6.55432e11 + 1.80888e11i 2.00604 + 0.553631i
\(363\) −7.55035e10 + 5.57390e11i −0.228238 + 1.68492i
\(364\) 1.07996e10 + 7.97258e10i 0.0322442 + 0.238036i
\(365\) 1.36347e10 − 3.76293e9i 0.0402094 − 0.0110971i
\(366\) −9.86320e10 + 1.83289e11i −0.287312 + 0.533914i
\(367\) −1.31874e11 − 1.37929e11i −0.379457 − 0.396881i 0.505292 − 0.862948i \(-0.331385\pi\)
−0.884749 + 0.466068i \(0.845670\pi\)
\(368\) −1.60792e10 − 2.98802e10i −0.0457036 − 0.0849315i
\(369\) −2.72688e11 + 8.39247e11i −0.765680 + 2.35652i
\(370\) −1.18818e9 + 2.77988e9i −0.00329590 + 0.00771115i
\(371\) 5.57606e11 + 1.01191e11i 1.52807 + 0.277305i
\(372\) 4.65991e11 + 3.38562e11i 1.26164 + 0.916633i
\(373\) −3.70786e11 + 3.33714e10i −0.991822 + 0.0892656i −0.573649 − 0.819101i \(-0.694473\pi\)
−0.418174 + 0.908367i \(0.637330\pi\)
\(374\) 2.05959e9 + 4.81865e9i 0.00544326 + 0.0127351i
\(375\) −2.85656e10 − 1.25154e11i −0.0745938 − 0.326817i
\(376\) 6.18716e10 + 9.37314e10i 0.159641 + 0.241846i
\(377\) 6.52674e10 + 3.89955e10i 0.166403 + 0.0994210i
\(378\) 8.12388e11 + 1.01870e12i 2.04668 + 2.56646i
\(379\) 7.50099e9 − 6.55341e9i 0.0186742 − 0.0163152i −0.648551 − 0.761171i \(-0.724625\pi\)
0.667225 + 0.744856i \(0.267482\pi\)
\(380\) 1.27689e9 − 9.27711e8i 0.00314142 − 0.00228237i
\(381\) 3.98216e11 − 1.91771e11i 0.968181 − 0.466251i
\(382\) −6.99573e10 + 1.05981e11i −0.168092 + 0.254649i
\(383\) −2.04869e11 − 7.68884e10i −0.486498 − 0.182586i 0.0960591 − 0.995376i \(-0.469376\pi\)
−0.582557 + 0.812790i \(0.697948\pi\)
\(384\) 7.01612e11 − 4.19194e11i 1.64667 − 0.983839i
\(385\) −1.01951e10 − 4.90971e9i −0.0236493 − 0.0113889i
\(386\) −5.69265e11 + 1.03306e11i −1.30518 + 0.236856i
\(387\) 4.06070e10 − 1.77911e11i 0.0920241 − 0.403184i
\(388\) 1.12153e11 − 4.20919e10i 0.251229 − 0.0942878i
\(389\) −1.29088e11 + 1.61872e11i −0.285834 + 0.358425i −0.903932 − 0.427677i \(-0.859332\pi\)
0.618098 + 0.786101i \(0.287904\pi\)
\(390\) 1.88561e9 + 4.19864e10i 0.00412726 + 0.0919005i
\(391\) −6.46006e7 − 1.43844e9i −0.000139779 − 0.00311242i
\(392\) −1.18414e10 + 1.48487e10i −0.0253289 + 0.0317615i
\(393\) 1.13611e12 − 4.26388e11i 2.40244 − 0.901650i
\(394\) −1.72136e11 + 7.54178e11i −0.359864 + 1.57667i
\(395\) 6.37346e10 − 1.15661e10i 0.131731 − 0.0239057i
\(396\) 1.54027e11 + 7.41757e10i 0.314753 + 0.151577i
\(397\) 5.20195e11 − 3.10802e11i 1.05102 − 0.627952i 0.119940 − 0.992781i \(-0.461730\pi\)
0.931075 + 0.364829i \(0.118872\pi\)
\(398\) −9.08880e11 − 3.41108e11i −1.81565 − 0.681426i
\(399\) −4.30401e10 + 6.52030e10i −0.0850150 + 0.128792i
\(400\) −5.71527e11 + 2.75233e11i −1.11626 + 0.537564i
\(401\) 5.00367e11 − 3.63538e11i 0.966359 − 0.702101i 0.0117403 − 0.999931i \(-0.496263\pi\)
0.954619 + 0.297830i \(0.0962629\pi\)
\(402\) −1.57351e12 + 1.37473e12i −3.00505 + 2.62543i
\(403\) −2.35636e11 − 2.95479e11i −0.445010 − 0.558025i
\(404\) −2.21642e11 − 1.32425e11i −0.413938 − 0.247317i
\(405\) 6.38048e10 + 9.66602e10i 0.117844 + 0.178525i
\(406\) −6.81252e10 − 2.98476e11i −0.124434 − 0.545183i
\(407\) −4.49511e9 − 1.05168e10i −0.00812018 − 0.0189981i
\(408\) 2.43243e10 − 2.18923e9i 0.0434580 − 0.00391129i
\(409\) 4.04884e11 + 2.94165e11i 0.715444 + 0.519800i 0.884925 − 0.465733i \(-0.154209\pi\)
−0.169481 + 0.985533i \(0.554209\pi\)
\(410\) 6.56916e10 + 1.19213e10i 0.114811 + 0.0208351i
\(411\) −7.64645e10 + 1.78898e11i −0.132182 + 0.309255i
\(412\) 1.55138e11 − 4.77465e11i 0.265265 − 0.816401i
\(413\) 8.29974e10 + 1.54235e11i 0.140375 + 0.260860i
\(414\) −9.43129e10 − 9.86436e10i −0.157786 − 0.165032i
\(415\) 9.96285e9 − 1.85141e10i 0.0164880 − 0.0306398i
\(416\) 2.49164e11 − 6.87649e10i 0.407911 − 0.112576i
\(417\) −2.71067e11 − 2.00110e12i −0.439000 − 3.24083i
\(418\) −2.32868e9 + 1.71910e10i −0.00373092 + 0.0275427i
\(419\) −4.73647e10 − 1.30718e10i −0.0750744 − 0.0207192i 0.228298 − 0.973591i \(-0.426684\pi\)
−0.303372 + 0.952872i \(0.598113\pi\)
\(420\) 4.02552e10 − 4.21037e10i 0.0631249 − 0.0660234i
\(421\) −2.16875e11 − 6.67472e11i −0.336465 − 1.03553i −0.965996 − 0.258557i \(-0.916753\pi\)
0.629531 − 0.776975i \(-0.283247\pi\)
\(422\) 7.22974e11 + 6.50688e10i 1.10973 + 0.0998773i
\(423\) 5.86591e11 + 5.12490e11i 0.890849 + 0.778311i
\(424\) 2.63115e10 − 5.85872e11i 0.0395367 − 0.880352i
\(425\) −2.69184e10 −0.0400220
\(426\) −1.53929e12 − 1.50637e11i −2.26452 − 0.221609i
\(427\) −1.89283e11 −0.275541
\(428\) 2.24360e10 − 4.99576e11i 0.0323183 − 0.719622i
\(429\) −1.19740e11 − 1.04614e11i −0.170680 − 0.149119i
\(430\) −1.37512e10 − 1.23763e9i −0.0193969 − 0.00174575i
\(431\) 5.55696e10 + 1.71026e11i 0.0775692 + 0.238733i 0.982321 − 0.187207i \(-0.0599434\pi\)
−0.904751 + 0.425940i \(0.859943\pi\)
\(432\) 1.60680e12 − 1.68058e12i 2.21965 − 2.32157i
\(433\) 1.01781e12 + 2.80898e11i 1.39146 + 0.384019i 0.879872 − 0.475210i \(-0.157628\pi\)
0.511590 + 0.859229i \(0.329057\pi\)
\(434\) −2.04281e11 + 1.50806e12i −0.276391 + 2.04040i
\(435\) −7.38924e9 − 5.45495e10i −0.00989459 − 0.0730448i
\(436\) 2.98594e11 − 8.24067e10i 0.395724 − 0.109213i
\(437\) 2.25879e9 − 4.19754e9i 0.00296285 − 0.00550590i
\(438\) −5.53069e11 − 5.78465e11i −0.718035 − 0.751006i
\(439\) 3.56832e11 + 6.63105e11i 0.458536 + 0.852102i 0.999936 + 0.0113370i \(0.00360877\pi\)
−0.541400 + 0.840765i \(0.682106\pi\)
\(440\) −3.61861e9 + 1.11369e10i −0.00460262 + 0.0141654i
\(441\) −5.17695e10 + 1.21121e11i −0.0651778 + 0.152491i
\(442\) 1.74157e10 + 3.16048e9i 0.0217040 + 0.00393870i
\(443\) 8.75956e11 + 6.36419e11i 1.08060 + 0.785103i 0.977788 − 0.209598i \(-0.0672155\pi\)
0.102814 + 0.994701i \(0.467216\pi\)
\(444\) 5.86396e10 − 5.27766e9i 0.0716090 − 0.00644492i
\(445\) −4.15101e10 − 9.71176e10i −0.0501803 − 0.117403i
\(446\) 2.05577e11 + 9.00691e11i 0.246018 + 1.07788i
\(447\) −1.14527e12 − 1.73501e12i −1.35682 − 2.05550i
\(448\) 5.20795e10 + 3.11160e10i 0.0610823 + 0.0364950i
\(449\) 8.90015e11 + 1.11604e12i 1.03345 + 1.29590i 0.954239 + 0.299045i \(0.0966682\pi\)
0.0792097 + 0.996858i \(0.474760\pi\)
\(450\) −1.92136e12 + 1.67864e12i −2.20878 + 1.92975i
\(451\) −2.04344e11 + 1.48465e11i −0.232577 + 0.168977i
\(452\) 9.51016e10 − 4.57985e10i 0.107168 − 0.0516093i
\(453\) −4.45915e11 + 6.75533e11i −0.497520 + 0.753711i
\(454\) 8.23572e11 + 3.09092e11i 0.909809 + 0.341457i
\(455\) −3.28105e10 + 1.96033e10i −0.0358890 + 0.0214427i
\(456\) 7.28434e10 + 3.50795e10i 0.0788948 + 0.0379937i
\(457\) 3.03114e11 − 5.50071e10i 0.325075 − 0.0589923i −0.0135665 − 0.999908i \(-0.504318\pi\)
0.338641 + 0.940916i \(0.390033\pi\)
\(458\) −4.04503e11 + 1.77224e12i −0.429563 + 1.88204i
\(459\) 9.23744e10 − 3.46687e10i 0.0971392 − 0.0364570i
\(460\) −2.21590e9 + 2.77865e9i −0.00230749 + 0.00289350i
\(461\) 3.84208e10 + 8.55506e11i 0.0396198 + 0.882204i 0.916145 + 0.400848i \(0.131284\pi\)
−0.876525 + 0.481357i \(0.840144\pi\)
\(462\) 2.87254e10 + 6.39620e11i 0.0293344 + 0.653180i
\(463\) 3.68374e11 − 4.61927e11i 0.372542 − 0.467153i −0.559854 − 0.828591i \(-0.689143\pi\)
0.932396 + 0.361439i \(0.117714\pi\)
\(464\) −5.11483e11 + 1.91963e11i −0.512272 + 0.192259i
\(465\) −6.08894e10 + 2.66774e11i −0.0603953 + 0.264609i
\(466\) 1.57809e12 − 2.86382e11i 1.55023 − 0.281325i
\(467\) 5.18601e11 + 2.49745e11i 0.504554 + 0.242980i 0.668804 − 0.743438i \(-0.266806\pi\)
−0.164251 + 0.986419i \(0.552521\pi\)
\(468\) 4.95699e11 − 2.96166e11i 0.477652 − 0.285384i
\(469\) −1.77897e12 − 6.67659e11i −1.69782 − 0.637202i
\(470\) 3.24663e10 − 4.91843e10i 0.0306897 − 0.0464928i
\(471\) −2.46015e12 + 1.18475e12i −2.30339 + 1.10925i
\(472\) 1.46636e11 − 1.06538e11i 0.135989 − 0.0988015i
\(473\) 3.93357e10 − 3.43666e10i 0.0361337 − 0.0315690i
\(474\) −2.28516e12 − 2.86551e12i −2.07929 − 2.60735i
\(475\) −7.64983e10 − 4.57056e10i −0.0689494 − 0.0411953i
\(476\) −1.35147e10 − 2.04739e10i −0.0120663 − 0.0182797i
\(477\) −9.05087e11 − 3.96544e12i −0.800493 − 3.50719i
\(478\) 9.45248e10 + 2.21152e11i 0.0828171 + 0.193760i
\(479\) 1.11999e12 − 1.00801e11i 0.972089 − 0.0874896i 0.407804 − 0.913070i \(-0.366295\pi\)
0.564285 + 0.825580i \(0.309152\pi\)
\(480\) −1.51405e11 − 1.10002e11i −0.130183 − 0.0945836i
\(481\) −3.80102e10 − 6.89783e9i −0.0323778 − 0.00587570i
\(482\) −5.68019e11 + 1.32895e12i −0.479348 + 1.12149i
\(483\) 5.43640e10 − 1.67315e11i 0.0454516 − 0.139886i
\(484\) −2.77067e11 − 5.14877e11i −0.229499 − 0.426481i
\(485\) 3.93274e10 + 4.11333e10i 0.0322744 + 0.0337564i
\(486\) 1.25526e12 − 2.33266e12i 1.02064 − 1.89666i
\(487\) 1.91257e12 − 5.27835e11i 1.54076 − 0.425224i 0.610470 − 0.792039i \(-0.290981\pi\)
0.930294 + 0.366815i \(0.119552\pi\)
\(488\) 2.62936e10 + 1.94107e11i 0.0209875 + 0.154936i
\(489\) −3.03580e11 + 2.24112e12i −0.240095 + 1.77245i
\(490\) 9.60674e9 + 2.65129e9i 0.00752825 + 0.00207766i
\(491\) −1.77293e11 + 1.85434e11i −0.137665 + 0.143987i −0.788033 − 0.615633i \(-0.788900\pi\)
0.650368 + 0.759619i \(0.274615\pi\)
\(492\) −4.01799e11 − 1.23661e12i −0.309148 − 0.951459i
\(493\) −2.30897e10 − 2.07811e9i −0.0176038 − 0.00158437i
\(494\) 4.41266e10 + 3.85522e10i 0.0333372 + 0.0291258i
\(495\) −3.64372e9 + 8.11337e10i −0.00272786 + 0.0607404i
\(496\) 2.71568e12 2.01470
\(497\) −5.42698e11 − 1.29759e12i −0.398983 − 0.953965i
\(498\) −1.18960e12 −0.866703
\(499\) −1.31925e10 + 2.93754e11i −0.00952521 + 0.212095i 0.988586 + 0.150659i \(0.0481395\pi\)
−0.998111 + 0.0614363i \(0.980432\pi\)
\(500\) 1.00491e11 + 8.77966e10i 0.0719057 + 0.0628221i
\(501\) −2.72840e12 − 2.45560e11i −1.93481 − 0.174136i
\(502\) −1.02565e12 − 3.15662e12i −0.720828 − 2.21848i
\(503\) −1.17970e12 + 1.23387e12i −0.821702 + 0.859432i −0.992036 − 0.125954i \(-0.959801\pi\)
0.170335 + 0.985386i \(0.445515\pi\)
\(504\) 2.02921e12 + 5.60028e11i 1.40085 + 0.386609i
\(505\) 1.64645e10 − 1.21546e11i 0.0112652 − 0.0831627i
\(506\) −5.24366e9 − 3.87103e10i −0.00355597 − 0.0262512i
\(507\) 2.12488e12 − 5.86431e11i 1.42823 − 0.394168i
\(508\) −2.17714e11 + 4.04581e11i −0.145044 + 0.269537i
\(509\) −7.38740e11 − 7.72662e11i −0.487822 − 0.510222i 0.432366 − 0.901698i \(-0.357679\pi\)
−0.920188 + 0.391476i \(0.871965\pi\)
\(510\) −6.07284e9 − 1.12852e10i −0.00397490 − 0.00738660i
\(511\) 2.24903e11 − 6.92181e11i 0.145916 − 0.449082i
\(512\) −2.81976e11 + 6.59715e11i −0.181341 + 0.424269i
\(513\) 3.21380e11 + 5.83219e10i 0.204876 + 0.0371795i
\(514\) −2.72131e11 − 1.97715e11i −0.171967 − 0.124941i
\(515\) 2.37538e11 − 2.13788e10i 0.148799 − 0.0133922i
\(516\) 1.05680e11 + 2.47251e11i 0.0656251 + 0.153538i
\(517\) 4.96125e10 + 2.17367e11i 0.0305410 + 0.133809i
\(518\) 8.56961e10 + 1.29824e11i 0.0522970 + 0.0792266i
\(519\) −3.61718e12 − 2.16117e12i −2.18835 − 1.30748i
\(520\) 2.46607e10 + 3.09235e10i 0.0147907 + 0.0185470i
\(521\) 3.31158e11 − 2.89324e11i 0.196909 − 0.172034i −0.553837 − 0.832625i \(-0.686837\pi\)
0.750746 + 0.660591i \(0.229694\pi\)
\(522\) −1.77767e12 + 1.29155e12i −1.04793 + 0.761368i
\(523\) −1.41062e12 + 6.79320e11i −0.824428 + 0.397024i −0.798023 − 0.602627i \(-0.794121\pi\)
−0.0264059 + 0.999651i \(0.508406\pi\)
\(524\) −6.94903e11 + 1.05273e12i −0.402655 + 0.609997i
\(525\) −3.07916e12 − 1.15563e12i −1.76895 − 0.663899i
\(526\) 1.02329e10 − 6.11389e9i 0.00582860 − 0.00348243i
\(527\) 1.03827e11 + 5.00005e10i 0.0586358 + 0.0282375i
\(528\) 1.12417e12 − 2.04007e11i 0.629478 − 0.114233i
\(529\) 3.98406e11 − 1.74553e12i 0.221195 − 0.969118i
\(530\) −2.88115e11 + 1.08132e11i −0.158608 + 0.0595266i
\(531\) 7.83776e11 − 9.82825e11i 0.427826 − 0.536476i
\(532\) −3.64359e9 − 8.11307e10i −0.00197209 − 0.0439120i
\(533\) 3.82759e10 + 8.52280e11i 0.0205425 + 0.457415i
\(534\) −3.72597e12 + 4.67222e12i −1.98291 + 2.48650i
\(535\) 2.22420e11 − 8.34757e10i 0.117377 − 0.0440523i
\(536\) −4.37555e11 + 1.91705e12i −0.228976 + 1.00321i
\(537\) 2.46714e12 − 4.47719e11i 1.28029 − 0.232339i
\(538\) 1.97211e12 + 9.49720e11i 1.01487 + 0.488737i
\(539\) −3.23660e10 + 1.93378e10i −0.0165173 + 0.00986863i
\(540\) −2.28003e11 − 8.55711e10i −0.115390 − 0.0433067i
\(541\) 4.47938e11 − 6.78598e11i 0.224818 − 0.340584i −0.704606 − 0.709599i \(-0.748876\pi\)
0.929424 + 0.369015i \(0.120305\pi\)
\(542\) −9.72944e11 + 4.68545e11i −0.484274 + 0.233214i
\(543\) 5.08928e12 − 3.69758e12i 2.51221 − 1.82523i
\(544\) −5.93539e10 + 5.18559e10i −0.0290572 + 0.0253865i
\(545\) 9.17489e10 + 1.15049e11i 0.0445468 + 0.0558599i
\(546\) 1.85648e12 + 1.10919e12i 0.893969 + 0.534122i
\(547\) 7.46958e11 + 1.13159e12i 0.356741 + 0.540440i 0.967987 − 0.251001i \(-0.0807598\pi\)
−0.611246 + 0.791441i \(0.709331\pi\)
\(548\) −4.50019e10 − 1.97166e11i −0.0213166 − 0.0933942i
\(549\) 5.33935e11 + 1.24920e12i 0.250849 + 0.586891i
\(550\) −7.27347e11 + 6.54624e10i −0.338930 + 0.0305042i
\(551\) −6.20891e10 − 4.51104e10i −0.0286968 − 0.0208494i
\(552\) −1.79131e11 − 3.25074e10i −0.0821191 − 0.0149024i
\(553\) 1.30997e12 − 3.06482e12i 0.595658 − 1.39361i
\(554\) −8.48153e11 + 2.61035e12i −0.382543 + 1.17735i
\(555\) 1.32541e10 + 2.46303e10i 0.00592970 + 0.0110192i
\(556\) 1.45062e12 + 1.51723e12i 0.643751 + 0.673310i
\(557\) 8.57252e11 − 1.59304e12i 0.377364 − 0.701259i −0.619098 − 0.785314i \(-0.712501\pi\)
0.996461 + 0.0840552i \(0.0267872\pi\)
\(558\) 1.05289e13 − 2.90580e12i 4.59759 − 1.26886i
\(559\) −2.36825e10 − 1.74831e11i −0.0102583 − 0.0757295i
\(560\) 3.68657e10 − 2.72154e11i 0.0158408 − 0.116941i
\(561\) 4.67361e10 + 1.28983e10i 0.0199214 + 0.00549795i
\(562\) −1.67954e12 + 1.75666e12i −0.710193 + 0.742804i
\(563\) −7.09434e11 − 2.18341e12i −0.297594 − 0.915900i −0.982338 − 0.187116i \(-0.940086\pi\)
0.684744 − 0.728784i \(-0.259914\pi\)
\(564\) −1.14312e12 − 1.02882e11i −0.475702 − 0.0428139i
\(565\) 3.77628e10 + 3.29924e10i 0.0155900 + 0.0136206i
\(566\) −4.66732e10 + 1.03926e12i −0.0191159 + 0.425648i
\(567\) 5.95953e12 2.42152
\(568\) −1.25527e12 + 7.36777e11i −0.506021 + 0.297008i
\(569\) −3.79099e12 −1.51617 −0.758084 − 0.652156i \(-0.773865\pi\)
−0.758084 + 0.652156i \(0.773865\pi\)
\(570\) 1.90339e9 − 4.23823e10i 0.000755250 − 0.0168170i
\(571\) 1.32458e12 + 1.15725e12i 0.521452 + 0.455579i 0.877974 − 0.478708i \(-0.158895\pi\)
−0.356522 + 0.934287i \(0.616037\pi\)
\(572\) 1.64616e11 + 1.48157e10i 0.0642970 + 0.00578683i
\(573\) 3.63058e11 + 1.11738e12i 0.140696 + 0.433017i
\(574\) 2.37406e12 − 2.48308e12i 0.912828 − 0.954743i
\(575\) 1.93430e11 + 5.33833e10i 0.0737935 + 0.0203657i
\(576\) 5.84478e10 − 4.31479e11i 0.0221242 − 0.163327i
\(577\) −4.86544e10 − 3.59182e11i −0.0182739 − 0.134903i 0.979515 − 0.201374i \(-0.0645405\pi\)
−0.997788 + 0.0664702i \(0.978826\pi\)
\(578\) 3.18889e12 − 8.80079e11i 1.18841 − 0.327979i
\(579\) −2.53653e12 + 4.71366e12i −0.937964 + 1.74303i
\(580\) 3.95436e10 + 4.13594e10i 0.0145094 + 0.0151757i
\(581\) −5.12640e11 − 9.52645e11i −0.186647 − 0.346847i
\(582\) 9.95033e11 − 3.06240e12i 0.359488 − 1.10639i
\(583\) 4.57573e11 − 1.07055e12i 0.164041 − 0.383792i
\(584\) −7.41062e11 − 1.34483e11i −0.263631 − 0.0478420i
\(585\) 2.21928e11 + 1.61240e11i 0.0783448 + 0.0569209i
\(586\) −3.07006e11 + 2.76310e10i −0.107549 + 0.00967961i
\(587\) 1.53160e12 + 3.58336e12i 0.532444 + 1.24571i 0.942669 + 0.333730i \(0.108307\pi\)
−0.410225 + 0.911985i \(0.634550\pi\)
\(588\) −4.31884e10 − 1.89221e11i −0.0148994 − 0.0652786i
\(589\) 2.10164e11 + 3.18385e11i 0.0719516 + 0.109002i
\(590\) −8.16469e10 − 4.87818e10i −0.0277399 − 0.0165738i
\(591\) 4.46233e12 + 5.59559e12i 1.50459 + 1.88670i
\(592\) 2.09044e11 − 1.82636e11i 0.0699502 − 0.0611137i
\(593\) −3.46801e12 + 2.51966e12i −1.15169 + 0.836749i −0.988704 − 0.149880i \(-0.952111\pi\)
−0.162982 + 0.986629i \(0.552111\pi\)
\(594\) 2.41169e12 − 1.16141e12i 0.794844 − 0.382777i
\(595\) 6.42031e9 − 9.72636e9i 0.00210005 − 0.00318144i
\(596\) 2.02321e12 + 7.59325e11i 0.656801 + 0.246501i
\(597\) −7.71023e12 + 4.60665e12i −2.48418 + 1.48423i
\(598\) −1.18878e11 − 5.72484e10i −0.0380141 − 0.0183066i
\(599\) −1.70948e12 + 3.10226e11i −0.542556 + 0.0984593i −0.442914 − 0.896564i \(-0.646055\pi\)
−0.0996415 + 0.995023i \(0.531770\pi\)
\(600\) −7.57349e11 + 3.31816e12i −0.238570 + 1.04524i
\(601\) −5.20754e12 + 1.95442e12i −1.62816 + 0.611059i −0.987620 − 0.156864i \(-0.949861\pi\)
−0.640541 + 0.767924i \(0.721290\pi\)
\(602\) −4.42946e11 + 5.55437e11i −0.137457 + 0.172366i
\(603\) 6.11852e11 + 1.36239e13i 0.188460 + 4.19638i
\(604\) −3.77492e10 − 8.40552e11i −0.0115410 − 0.256979i
\(605\) 1.73184e11 − 2.17166e11i 0.0525543 − 0.0659010i
\(606\) −6.49755e12 + 2.43857e12i −1.95714 + 0.734529i
\(607\) 6.73365e11 − 2.95021e12i 0.201327 − 0.882071i −0.768803 − 0.639485i \(-0.779147\pi\)
0.970130 − 0.242585i \(-0.0779954\pi\)
\(608\) −2.56723e11 + 4.65884e10i −0.0761901 + 0.0138265i
\(609\) −2.55198e12 − 1.22897e12i −0.751796 − 0.362046i
\(610\) 8.82358e10 − 5.27185e10i 0.0258024 − 0.0154162i
\(611\) 7.05051e11 + 2.64610e11i 0.204661 + 0.0768106i
\(612\) −9.69977e10 + 1.46945e11i −0.0279499 + 0.0423423i
\(613\) −2.63584e12 + 1.26935e12i −0.753958 + 0.363087i −0.771057 − 0.636767i \(-0.780271\pi\)
0.0170983 + 0.999854i \(0.494557\pi\)
\(614\) 3.10805e12 − 2.25813e12i 0.882532 − 0.641197i
\(615\) 4.65172e11 − 4.06409e11i 0.131122 − 0.114558i
\(616\) 3.75680e11 + 4.71088e11i 0.105125 + 0.131822i
\(617\) −4.73583e11 − 2.82952e11i −0.131557 − 0.0786014i 0.445613 − 0.895226i \(-0.352986\pi\)
−0.577170 + 0.816624i \(0.695843\pi\)
\(618\) −7.43418e12 − 1.12623e13i −2.05015 − 3.10584i
\(619\) 3.41888e11 + 1.49791e12i 0.0936001 + 0.410089i 0.999922 − 0.0124995i \(-0.00397881\pi\)
−0.906322 + 0.422588i \(0.861122\pi\)
\(620\) −1.11792e11 − 2.61550e11i −0.0303842 − 0.0710874i
\(621\) −7.32536e11 + 6.59294e10i −0.197659 + 0.0177896i
\(622\) 2.88618e12 + 2.09693e12i 0.773154 + 0.561729i
\(623\) −5.34720e12 − 9.70373e11i −1.42210 − 0.258073i
\(624\) 1.51672e12 − 3.54854e12i 0.400474 − 0.936956i
\(625\) 1.14938e12 − 3.53743e12i 0.301303 − 0.927316i
\(626\) 4.26831e12 + 7.93185e12i 1.11089 + 2.06438i
\(627\) 1.10917e11 + 1.16010e11i 0.0286611 + 0.0299772i
\(628\) 1.34502e12 − 2.49947e12i 0.345073 − 0.641253i
\(629\) 1.13549e10 − 3.13376e9i 0.00289238 − 0.000798247i
\(630\) −1.48275e11 − 1.09461e12i −0.0375005 − 0.276840i
\(631\) −1.95635e11 + 1.44423e12i −0.0491263 + 0.362665i 0.949655 + 0.313299i \(0.101434\pi\)
−0.998781 + 0.0493656i \(0.984280\pi\)
\(632\) −3.32489e12 − 9.17612e11i −0.828993 − 0.228787i
\(633\) 4.64112e12 − 4.85423e12i 1.14896 − 1.20172i
\(634\) −1.35261e12 − 4.16291e12i −0.332485 − 1.02328i
\(635\) −2.17384e11 − 1.95649e10i −0.0530574 − 0.00477525i
\(636\) 4.51335e12 + 3.94319e12i 1.09381 + 0.955632i
\(637\) −5.71342e9 + 1.27219e11i −0.00137489 + 0.0306143i
\(638\) −6.28947e11 −0.150287
\(639\) −7.03276e12 + 7.24188e12i −1.66868 + 1.71829i
\(640\) −4.03602e11 −0.0950919
\(641\) −1.84906e11 + 4.11726e12i −0.0432604 + 0.963269i 0.853593 + 0.520941i \(0.174419\pi\)
−0.896853 + 0.442328i \(0.854153\pi\)
\(642\) −1.01228e13 − 8.84406e12i −2.35177 − 2.05468i
\(643\) 4.26819e12 + 3.84144e11i 0.984679 + 0.0886227i 0.570261 − 0.821464i \(-0.306842\pi\)
0.414418 + 0.910087i \(0.363985\pi\)
\(644\) 5.65108e10 + 1.73922e11i 0.0129463 + 0.0398445i
\(645\) −8.82758e10 + 9.23292e10i −0.0200827 + 0.0210049i
\(646\) −1.72231e10 − 4.75328e9i −0.00389104 − 0.00107386i
\(647\) 7.50821e11 − 5.54279e12i 0.168449 − 1.24354i −0.687388 − 0.726291i \(-0.741243\pi\)
0.855836 − 0.517247i \(-0.173043\pi\)
\(648\) −8.27845e11 − 6.11140e12i −0.184443 − 1.36161i
\(649\) 3.46852e11 − 9.57250e10i 0.0767437 − 0.0211799i
\(650\) −1.16887e12 + 2.17213e12i −0.256837 + 0.477283i
\(651\) 9.73009e12 + 1.01769e13i 2.12326 + 2.22075i
\(652\) −1.11401e12 − 2.07019e12i −0.241422 − 0.448637i
\(653\) 2.30847e12 − 7.10476e12i 0.496839 − 1.52911i −0.317232 − 0.948348i \(-0.602753\pi\)
0.814071 − 0.580766i \(-0.197247\pi\)
\(654\) 3.27242e12 − 7.65620e12i 0.699469 − 1.63649i
\(655\) −5.89615e11 − 1.06999e11i −0.125165 − 0.0227141i
\(656\) −4.95955e12 − 3.60333e12i −1.04562 − 0.759690i
\(657\) −5.20257e12 + 4.68240e11i −1.08937 + 0.0980447i
\(658\) −1.19182e12 − 2.78840e12i −0.247853 − 0.579881i
\(659\) −1.60073e12 − 7.01325e12i −0.330623 − 1.44855i −0.817927 − 0.575322i \(-0.804877\pi\)
0.487304 − 0.873232i \(-0.337980\pi\)
\(660\) −6.59253e10 − 9.98726e10i −0.0135240 − 0.0204880i
\(661\) −6.10940e12 − 3.65020e12i −1.24478 − 0.743720i −0.269139 − 0.963101i \(-0.586739\pi\)
−0.975639 + 0.219381i \(0.929596\pi\)
\(662\) 3.39779e11 + 4.26069e11i 0.0687599 + 0.0862222i
\(663\) 1.23323e11 − 1.07744e11i 0.0247875 − 0.0216562i
\(664\) −9.05710e11 + 6.58037e11i −0.180814 + 0.131369i
\(665\) 3.47603e10 − 1.67397e10i 0.00689265 − 0.00331932i
\(666\) 6.15060e11 − 9.31776e11i 0.121139 − 0.183517i
\(667\) 1.61796e11 + 6.07231e10i 0.0316521 + 0.0118792i
\(668\) 2.44452e12 − 1.46053e12i 0.475007 − 0.283803i
\(669\) 7.70095e12 + 3.70858e12i 1.48637 + 0.715798i
\(670\) 1.01524e12 − 1.84238e11i 0.194639 − 0.0353218i
\(671\) −8.65286e10 + 3.79107e11i −0.0164782 + 0.0721955i
\(672\) −9.01563e12 + 3.38362e12i −1.70543 + 0.640059i
\(673\) −5.01764e12 + 6.29192e12i −0.942826 + 1.18227i 0.0402725 + 0.999189i \(0.487177\pi\)
−0.983098 + 0.183078i \(0.941394\pi\)
\(674\) 9.53024e10 + 2.12207e12i 0.0177883 + 0.396087i
\(675\) 6.16887e11 + 1.37361e13i 0.114377 + 2.54680i
\(676\) −1.42864e12 + 1.79146e12i −0.263126 + 0.329950i
\(677\) 9.67784e12 − 3.63215e12i 1.77064 − 0.664531i 0.771021 − 0.636810i \(-0.219746\pi\)
0.999616 − 0.0277209i \(-0.00882498\pi\)
\(678\) 6.31359e11 − 2.76616e12i 0.114747 − 0.502741i
\(679\) 2.88118e12 − 5.22858e11i 0.520184 − 0.0943995i
\(680\) −1.08661e10 − 5.23283e9i −0.00194887 − 0.000938526i
\(681\) 6.98655e12 − 4.17427e12i 1.24480 − 0.743735i
\(682\) 2.92705e12 + 1.09854e12i 0.518084 + 0.194440i
\(683\) 4.41941e12 − 6.69512e12i 0.777089 − 1.17724i −0.203096 − 0.979159i \(-0.565100\pi\)
0.980186 − 0.198081i \(-0.0634709\pi\)
\(684\) −5.25157e11 + 2.52902e11i −0.0917353 + 0.0441774i
\(685\) 7.77263e10 − 5.64715e10i 0.0134884 − 0.00979990i
\(686\) −5.19139e12 + 4.53558e12i −0.895004 + 0.781941i
\(687\) 1.04860e13 + 1.31491e13i 1.79600 + 2.25211i
\(688\) 1.08829e12 + 6.50225e11i 0.185182 + 0.110641i
\(689\) −2.16634e12 − 3.28186e12i −0.366218 − 0.554796i
\(690\) 2.12578e10 + 9.31366e10i 0.00357024 + 0.0156423i
\(691\) 2.80679e10 + 6.56680e10i 0.00468336 + 0.0109573i 0.921853 − 0.387539i \(-0.126675\pi\)
−0.917170 + 0.398497i \(0.869532\pi\)
\(692\) 4.36238e12 − 3.92622e11i 0.723180 − 0.0650874i
\(693\) 3.38084e12 + 2.45633e12i 0.556834 + 0.404563i
\(694\) 5.75381e12 + 1.04416e12i 0.941538 + 0.170864i
\(695\) −3.91929e11 + 9.16964e11i −0.0637201 + 0.149080i
\(696\) −9.05790e11 + 2.78774e12i −0.146314 + 0.450308i
\(697\) −1.23272e11 − 2.29078e11i −0.0197842 − 0.0367652i
\(698\) −3.37696e12 − 3.53203e12i −0.538489 − 0.563215i
\(699\) 7.03166e12 − 1.30670e13i 1.11407 − 2.07028i
\(700\) 3.29555e12 − 9.09515e11i 0.518785 − 0.143175i
\(701\) −3.84991e11 − 2.84212e12i −0.0602170 − 0.444540i −0.995809 − 0.0914570i \(-0.970848\pi\)
0.935592 − 0.353083i \(-0.114867\pi\)
\(702\) 1.21363e12 − 8.95939e12i 0.188612 − 1.39239i
\(703\) 3.75899e10 + 1.03742e10i 0.00580461 + 0.00160197i
\(704\) 8.61284e10 − 9.00833e10i 0.0132151 − 0.0138219i
\(705\) −1.68491e11 − 5.18561e11i −0.0256877 − 0.0790585i
\(706\) 7.32633e12 + 6.59381e11i 1.10985 + 0.0998885i
\(707\) −4.75284e12 − 4.15243e12i −0.715428 − 0.625050i
\(708\) −8.31021e10 + 1.85041e12i −0.0124297 + 0.276770i
\(709\) 1.23749e13 1.83921 0.919607 − 0.392840i \(-0.128507\pi\)
0.919607 + 0.392840i \(0.128507\pi\)
\(710\) 6.14382e11 + 4.53730e11i 0.0907352 + 0.0670092i
\(711\) −2.39219e13 −3.51061
\(712\) −2.52316e11 + 5.61826e12i −0.0367947 + 0.819298i
\(713\) −6.46921e11 − 5.65197e11i −0.0937450 − 0.0819025i
\(714\) −6.56766e11 − 5.91100e10i −0.0945734 − 0.00851176i
\(715\) 2.42637e10 + 7.46761e10i 0.00347200 + 0.0106857i
\(716\) −1.80122e12 + 1.88393e12i −0.256129 + 0.267890i
\(717\) 2.14495e12 + 5.91968e11i 0.303096 + 0.0836493i
\(718\) 2.16402e12 − 1.59754e13i 0.303879 − 2.24333i
\(719\) −4.30122e11 − 3.17529e12i −0.0600222 − 0.443102i −0.995877 − 0.0907154i \(-0.971085\pi\)
0.935855 − 0.352386i \(-0.114630\pi\)
\(720\) −1.90011e12 + 5.24398e11i −0.263502 + 0.0727218i
\(721\) 5.81530e12 − 1.08066e13i 0.801426 − 1.48930i
\(722\) 6.18997e12 + 6.47421e12i 0.847757 + 0.886684i
\(723\) 6.33624e12 + 1.17747e13i 0.862401 + 1.60261i
\(724\) −2.02069e12 + 6.21906e12i −0.273324 + 0.841203i
\(725\) 1.26976e12 − 2.97076e12i 0.170687 − 0.399343i
\(726\) −1.54639e13 − 2.80628e12i −2.06587 − 0.374901i
\(727\) −4.45492e12 − 3.23669e12i −0.591473 − 0.429730i 0.251369 − 0.967891i \(-0.419119\pi\)
−0.842842 + 0.538161i \(0.819119\pi\)
\(728\) 2.02699e12 − 1.82433e11i 0.267461 − 0.0240720i
\(729\) −2.61372e12 − 6.11511e12i −0.342757 − 0.801919i
\(730\) 8.79434e10 + 3.85305e11i 0.0114617 + 0.0502171i
\(731\) 2.96364e10 + 4.48972e10i 0.00383881 + 0.00581555i
\(732\) −1.71841e12 − 1.02670e12i −0.221221 − 0.132173i
\(733\) 5.68380e12 + 7.12726e12i 0.727228 + 0.911915i 0.998723 − 0.0505248i \(-0.0160894\pi\)
−0.271495 + 0.962440i \(0.587518\pi\)
\(734\) 4.01537e12 − 3.50812e12i 0.510615 − 0.446111i
\(735\) 7.45942e10 − 5.41958e10i 0.00942783 − 0.00684972i
\(736\) 5.29342e11 − 2.54918e11i 0.0664946 − 0.0320221i
\(737\) −2.15046e12 + 3.25781e12i −0.268490 + 0.406745i
\(738\) −2.30843e13 − 8.66366e12i −2.86459 − 1.07510i
\(739\) −4.43445e12 + 2.64946e12i −0.546940 + 0.326782i −0.759648 − 0.650334i \(-0.774629\pi\)
0.212708 + 0.977116i \(0.431772\pi\)
\(740\) −2.61953e10 − 1.26150e10i −0.00321129 − 0.00154648i
\(741\) 5.33408e11 − 9.67993e10i 0.0649947 − 0.0117948i
\(742\) −3.52356e12 + 1.54377e13i −0.426740 + 1.86967i
\(743\) −5.58152e12 + 2.09478e12i −0.671897 + 0.252167i −0.663923 − 0.747801i \(-0.731110\pi\)
−0.00797431 + 0.999968i \(0.502538\pi\)
\(744\) 9.08460e12 − 1.13917e13i 1.08700 − 1.36305i
\(745\) 4.60589e10 + 1.02558e12i 0.00547785 + 0.121974i
\(746\) −4.66691e11 − 1.03917e13i −0.0551702 − 1.22846i
\(747\) −4.84106e12 + 6.07049e12i −0.568849 + 0.713315i
\(748\) −4.71842e10 + 1.77085e10i −0.00551112 + 0.00206836i
\(749\) 2.72013e12 − 1.19177e13i 0.315806 − 1.38364i
\(750\) 3.52926e12 − 6.40467e11i 0.407294 − 0.0739130i
\(751\) −2.29677e12 − 1.10606e12i −0.263474 − 0.126882i 0.297484 − 0.954727i \(-0.403853\pi\)
−0.560957 + 0.827845i \(0.689567\pi\)
\(752\) −4.64531e12 + 2.77545e12i