# 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 $2$

# Related objects

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})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9}+O(q^{10})$$ 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 $$1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15} + 4755334 q^{16} + 2558412 q^{17} - 2619769 q^{18} - 172269 q^{19} + 738120 q^{20} + 1797929 q^{21} + 3015622 q^{22} + 6635088 q^{23} + 4803145 q^{24} - 115100016 q^{25} + 19254293 q^{26} - 17686931 q^{27} + 15761532 q^{28} - 10052927 q^{29} + 62637435 q^{30} - 23748991 q^{31} + 10388192 q^{32} - 15097203 q^{33} + 33217854 q^{34} - 24823174 q^{35} + 27856812 q^{36} - 27156308 q^{37} - 43400577 q^{38} + 251072838 q^{39} - 129856160 q^{40} + 62087988 q^{41} - 91873950 q^{42} - 167299067 q^{43} + 60914131 q^{44} - 31536191 q^{45} - 50201490 q^{46} - 23317743 q^{47} + 10641329 q^{48} + 338745866 q^{49} + 303770229 q^{50} + 448039613 q^{51} - 979580293 q^{52} + 12085215 q^{53} - 182583505 q^{54} - 243892552 q^{55} + 30440435 q^{56} + 714581966 q^{57} - 244549660 q^{58} - 859013315 q^{59} - 1894499000 q^{60} - 876373921 q^{61} + 186553636 q^{62} - 196611021 q^{63} + 5528242635 q^{64} + 867018244 q^{65} + 2727701199 q^{66} - 286780089 q^{67} - 1689988351 q^{68} - 3073308182 q^{69} - 41489396 q^{70} - 2538053548 q^{71} - 6821388000 q^{72} + 128479023 q^{73} + 3282772334 q^{74} + 3407782757 q^{75} + 7133788844 q^{76} + 1087098389 q^{77} + 2715049934 q^{78} + 144243625 q^{79} - 7443877603 q^{80} - 4083269278 q^{81} - 10375744380 q^{82} + 1543773955 q^{83} - 4117054288 q^{84} + 7843382686 q^{85} + 3545751759 q^{86} + 5261609811 q^{87} - 818728797 q^{88} - 1369081479 q^{89} + 10041256259 q^{90} - 7299574322 q^{91} + 602797624 q^{92} - 2146129677 q^{93} - 683447510 q^{94} - 7007204038 q^{95} + 6601829126 q^{96} - 10081488030 q^{97} - 5942379880 q^{98} - 4074592265 q^{99}+O(q^{100})$$ 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

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −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