Properties

 Label 3.19.b.b.2.1 Level $3$ Weight $19$ Character 3.2 Analytic conductor $6.162$ Analytic rank $0$ Dimension $4$ Inner twists $2$

Related objects

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,19,Mod(2,3)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 19, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 19);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$3$$ Weight: $$k$$ $$=$$ $$19$$ Character orbit: $$[\chi]$$ $$=$$ 3.b (of order $$2$$, degree $$1$$, 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: $$6.16158413129$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: 4.0.601940665.1 comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{4} - x^{3} + 123x^{2} - 1744x + 16016$$ x^4 - x^3 + 123*x^2 - 1744*x + 16016 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$2^{11}\cdot 3^{11}$$ Twist minimal: yes Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

 Embedding label 2.1 Root $$-6.07949 - 12.9551i$$ of defining polynomial Character $$\chi$$ $$=$$ 3.2 Dual form 3.19.b.b.2.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q-932.767i q^{2} +(-4234.02 + 19222.2i) q^{3} -607911. q^{4} +1.14247e6i q^{5} +(1.79299e7 + 3.94936e6i) q^{6} -9.81043e6 q^{7} +3.22520e8i q^{8} +(-3.51567e8 - 1.62775e8i) q^{9} +O(q^{10})$$ $$q-932.767i q^{2} +(-4234.02 + 19222.2i) q^{3} -607911. q^{4} +1.14247e6i q^{5} +(1.79299e7 + 3.94936e6i) q^{6} -9.81043e6 q^{7} +3.22520e8i q^{8} +(-3.51567e8 - 1.62775e8i) q^{9} +1.06566e9 q^{10} +2.16393e9i q^{11} +(2.57391e9 - 1.16854e10i) q^{12} -1.47189e10 q^{13} +9.15085e9i q^{14} +(-2.19608e10 - 4.83724e9i) q^{15} +1.41476e11 q^{16} +1.36506e10i q^{17} +(-1.51831e11 + 3.27930e11i) q^{18} -2.38919e11 q^{19} -6.94520e11i q^{20} +(4.15376e10 - 1.88578e11i) q^{21} +2.01844e12 q^{22} -5.70649e11i q^{23} +(-6.19955e12 - 1.36556e12i) q^{24} +2.50946e12 q^{25} +1.37293e13i q^{26} +(4.61743e12 - 6.06870e12i) q^{27} +5.96387e12 q^{28} -1.35326e13i q^{29} +(-4.51202e12 + 2.04843e13i) q^{30} -1.17012e13 q^{31} -4.74176e13i q^{32} +(-4.15954e13 - 9.16211e12i) q^{33} +1.27329e13 q^{34} -1.12081e13i q^{35} +(2.13721e14 + 9.89525e13i) q^{36} -1.26080e14 q^{37} +2.22856e14i q^{38} +(6.23201e13 - 2.82930e14i) q^{39} -3.68470e14 q^{40} +3.28662e14i q^{41} +(-1.75900e14 - 3.87449e13i) q^{42} +8.40904e14 q^{43} -1.31547e15i q^{44} +(1.85965e14 - 4.01654e14i) q^{45} -5.32283e14 q^{46} +9.97479e14i q^{47} +(-5.99013e14 + 2.71948e15i) q^{48} -1.53217e15 q^{49} -2.34074e15i q^{50} +(-2.62395e14 - 5.77971e13i) q^{51} +8.94778e15 q^{52} +5.45882e15i q^{53} +(-5.66068e15 - 4.30699e15i) q^{54} -2.47222e15 q^{55} -3.16406e15i q^{56} +(1.01159e15 - 4.59255e15i) q^{57} -1.26228e16 q^{58} -8.03632e14i q^{59} +(1.33502e16 + 2.94061e15i) q^{60} +1.04106e16 q^{61} +1.09145e16i q^{62} +(3.44902e15 + 1.59689e15i) q^{63} -7.14245e15 q^{64} -1.68159e16i q^{65} +(-8.54612e15 + 3.87989e16i) q^{66} -1.50639e16 q^{67} -8.29836e15i q^{68} +(1.09691e16 + 2.41614e15i) q^{69} -1.04546e16 q^{70} -4.47214e16i q^{71} +(5.24981e16 - 1.13387e17i) q^{72} -3.92287e16 q^{73} +1.17603e17i q^{74} +(-1.06251e16 + 4.82374e16i) q^{75} +1.45241e17 q^{76} -2.12290e16i q^{77} +(-2.63908e17 - 5.81302e16i) q^{78} -7.20817e16 q^{79} +1.61632e17i q^{80} +(9.71035e16 + 1.14452e17i) q^{81} +3.06565e17 q^{82} -1.02835e17i q^{83} +(-2.52512e16 + 1.14639e17i) q^{84} -1.55954e16 q^{85} -7.84368e17i q^{86} +(2.60126e17 + 5.72973e16i) q^{87} -6.97910e17 q^{88} +5.12684e17i q^{89} +(-3.74650e17 - 1.73462e17i) q^{90} +1.44399e17 q^{91} +3.46904e17i q^{92} +(4.95431e16 - 2.24923e17i) q^{93} +9.30416e17 q^{94} -2.72957e17i q^{95} +(9.11471e17 + 2.00767e17i) q^{96} -7.28759e17 q^{97} +1.42916e18i q^{98} +(3.52232e17 - 7.60764e17i) q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q + 15876 q^{3} - 1053536 q^{4} + 22698144 q^{6} - 95744152 q^{7} - 885341340 q^{9}+O(q^{10})$$ 4 * q + 15876 * q^3 - 1053536 * q^4 + 22698144 * q^6 - 95744152 * q^7 - 885341340 * q^9 $$4 q + 15876 q^{3} - 1053536 q^{4} + 22698144 q^{6} - 95744152 q^{7} - 885341340 q^{9} + 1461136320 q^{10} + 7123171104 q^{12} - 5426221528 q^{13} - 68287821120 q^{15} + 201224008192 q^{16} - 624067623360 q^{18} + 191416649480 q^{19} - 843499414296 q^{21} + 6661732766400 q^{22} - 16917300997632 q^{24} + 11407599454180 q^{25} - 4632207691356 q^{27} + 5750860980032 q^{28} - 17181499602240 q^{30} + 35728415085608 q^{31} + 12242871023040 q^{33} - 97283346838272 q^{34} + 412657454022048 q^{36} - 475299833502232 q^{37} + 416909545005096 q^{39} - 967003294602240 q^{40} + 149151729948480 q^{42} + 15\!\cdots\!92 q^{43}+ \cdots + 30\!\cdots\!60 q^{99}+O(q^{100})$$ 4 * q + 15876 * q^3 - 1053536 * q^4 + 22698144 * q^6 - 95744152 * q^7 - 885341340 * q^9 + 1461136320 * q^10 + 7123171104 * q^12 - 5426221528 * q^13 - 68287821120 * q^15 + 201224008192 * q^16 - 624067623360 * q^18 + 191416649480 * q^19 - 843499414296 * q^21 + 6661732766400 * q^22 - 16917300997632 * q^24 + 11407599454180 * q^25 - 4632207691356 * q^27 + 5750860980032 * q^28 - 17181499602240 * q^30 + 35728415085608 * q^31 + 12242871023040 * q^33 - 97283346838272 * q^34 + 412657454022048 * q^36 - 475299833502232 * q^37 + 416909545005096 * q^39 - 967003294602240 * q^40 + 149151729948480 * q^42 + 1599607324574792 * q^43 - 221242601301120 * q^45 + 571461969379968 * q^46 - 2192825065342464 * q^48 - 3423787444328244 * q^49 - 4987666703736576 * q^51 + 19843921097419328 * q^52 - 14022277970462496 * q^54 - 84999034592640 * q^55 + 10169351626464648 * q^57 - 15931261886420160 * q^58 + 24723268055608320 * q^60 - 2207268745883992 * q^61 + 13833182825583912 * q^63 - 53493367589593088 * q^64 + 14857554290281920 * q^66 - 41331536078929912 * q^67 + 81420525478583424 * q^69 + 4599036429482880 * q^70 - 4994921842560000 * q^72 - 45389954762456248 * q^73 + 56512911509383140 * q^75 + 344787912869857856 * q^76 - 685829939469704640 * q^78 - 177365384029892440 * q^79 - 72782527872717756 * q^81 + 887840438080579200 * q^82 - 125687415484822464 * q^84 - 258438267155888640 * q^85 + 858898556077746240 * q^87 - 494740797131842560 * q^88 - 688243478411603520 * q^90 - 625122143135405552 * q^91 + 818827434766827432 * q^93 + 1164172551956805888 * q^94 + 1176359757688184832 * q^96 - 3491564534514760312 * q^97 + 3027708259671116160 * q^99

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$-1$$

Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 932.767i 1.82181i −0.412615 0.910906i $$-0.635384\pi$$
0.412615 0.910906i $$-0.364616\pi$$
$$3$$ −4234.02 + 19222.2i −0.215111 + 0.976590i
$$4$$ −607911. −2.31900
$$5$$ 1.14247e6i 0.584944i 0.956274 + 0.292472i $$0.0944779\pi$$
−0.956274 + 0.292472i $$0.905522\pi$$
$$6$$ 1.79299e7 + 3.94936e6i 1.77916 + 0.391891i
$$7$$ −9.81043e6 −0.243112 −0.121556 0.992585i $$-0.538788\pi$$
−0.121556 + 0.992585i $$0.538788\pi$$
$$8$$ 3.22520e8i 2.40296i
$$9$$ −3.51567e8 1.62775e8i −0.907455 0.420150i
$$10$$ 1.06566e9 1.06566
$$11$$ 2.16393e9i 0.917716i 0.888510 + 0.458858i $$0.151741\pi$$
−0.888510 + 0.458858i $$0.848259\pi$$
$$12$$ 2.57391e9 1.16854e10i 0.498841 2.26471i
$$13$$ −1.47189e10 −1.38799 −0.693993 0.719982i $$-0.744150\pi$$
−0.693993 + 0.719982i $$0.744150\pi$$
$$14$$ 9.15085e9i 0.442903i
$$15$$ −2.19608e10 4.83724e9i −0.571251 0.125828i
$$16$$ 1.41476e11 2.05875
$$17$$ 1.36506e10i 0.115110i 0.998342 + 0.0575549i $$0.0183304\pi$$
−0.998342 + 0.0575549i $$0.981670\pi$$
$$18$$ −1.51831e11 + 3.27930e11i −0.765434 + 1.65321i
$$19$$ −2.38919e11 −0.740402 −0.370201 0.928952i $$-0.620711\pi$$
−0.370201 + 0.928952i $$0.620711\pi$$
$$20$$ 6.94520e11i 1.35648i
$$21$$ 4.15376e10 1.88578e11i 0.0522959 0.237420i
$$22$$ 2.01844e12 1.67190
$$23$$ 5.70649e11i 0.316824i −0.987373 0.158412i $$-0.949363\pi$$
0.987373 0.158412i $$-0.0506375\pi$$
$$24$$ −6.19955e12 1.36556e12i −2.34671 0.516903i
$$25$$ 2.50946e12 0.657840
$$26$$ 1.37293e13i 2.52865i
$$27$$ 4.61743e12 6.06870e12i 0.605517 0.795832i
$$28$$ 5.96387e12 0.563775
$$29$$ 1.35326e13i 0.932823i −0.884568 0.466411i $$-0.845547\pi$$
0.884568 0.466411i $$-0.154453\pi$$
$$30$$ −4.51202e12 + 2.04843e13i −0.229235 + 1.04071i
$$31$$ −1.17012e13 −0.442562 −0.221281 0.975210i $$-0.571024\pi$$
−0.221281 + 0.975210i $$0.571024\pi$$
$$32$$ 4.74176e13i 1.34769i
$$33$$ −4.15954e13 9.16211e12i −0.896232 0.197410i
$$34$$ 1.27329e13 0.209708
$$35$$ 1.12081e13i 0.142207i
$$36$$ 2.13721e14 + 9.89525e13i 2.10438 + 0.974326i
$$37$$ −1.26080e14 −0.970132 −0.485066 0.874478i $$-0.661204\pi$$
−0.485066 + 0.874478i $$0.661204\pi$$
$$38$$ 2.22856e14i 1.34887i
$$39$$ 6.23201e13 2.82930e14i 0.298571 1.35549i
$$40$$ −3.68470e14 −1.40560
$$41$$ 3.28662e14i 1.00391i 0.864894 + 0.501955i $$0.167386\pi$$
−0.864894 + 0.501955i $$0.832614\pi$$
$$42$$ −1.75900e14 3.87449e13i −0.432535 0.0952733i
$$43$$ 8.40904e14 1.67313 0.836566 0.547866i $$-0.184560\pi$$
0.836566 + 0.547866i $$0.184560\pi$$
$$44$$ 1.31547e15i 2.12818i
$$45$$ 1.85965e14 4.01654e14i 0.245764 0.530811i
$$46$$ −5.32283e14 −0.577194
$$47$$ 9.97479e14i 0.891298i 0.895208 + 0.445649i $$0.147027\pi$$
−0.895208 + 0.445649i $$0.852973\pi$$
$$48$$ −5.99013e14 + 2.71948e15i −0.442859 + 2.01055i
$$49$$ −1.53217e15 −0.940897
$$50$$ 2.34074e15i 1.19846i
$$51$$ −2.62395e14 5.77971e13i −0.112415 0.0247613i
$$52$$ 8.94778e15 3.21873
$$53$$ 5.45882e15i 1.65431i 0.561977 + 0.827153i $$0.310041\pi$$
−0.561977 + 0.827153i $$0.689959\pi$$
$$54$$ −5.66068e15 4.30699e15i −1.44986 1.10314i
$$55$$ −2.47222e15 −0.536813
$$56$$ 3.16406e15i 0.584188i
$$57$$ 1.01159e15 4.59255e15i 0.159268 0.723069i
$$58$$ −1.26228e16 −1.69943
$$59$$ 8.03632e14i 0.0927660i −0.998924 0.0463830i $$-0.985231\pi$$
0.998924 0.0463830i $$-0.0147695\pi$$
$$60$$ 1.33502e16 + 2.94061e15i 1.32473 + 0.291794i
$$61$$ 1.04106e16 0.890243 0.445121 0.895470i $$-0.353161\pi$$
0.445121 + 0.895470i $$0.353161\pi$$
$$62$$ 1.09145e16i 0.806265i
$$63$$ 3.44902e15 + 1.59689e15i 0.220613 + 0.102143i
$$64$$ −7.14245e15 −0.396486
$$65$$ 1.68159e16i 0.811894i
$$66$$ −8.54612e15 + 3.87989e16i −0.359645 + 1.63276i
$$67$$ −1.50639e16 −0.553685 −0.276843 0.960915i $$-0.589288\pi$$
−0.276843 + 0.960915i $$0.589288\pi$$
$$68$$ 8.29836e15i 0.266939i
$$69$$ 1.09691e16 + 2.41614e15i 0.309407 + 0.0681523i
$$70$$ −1.04546e16 −0.259074
$$71$$ 4.47214e16i 0.975417i −0.873007 0.487709i $$-0.837833\pi$$
0.873007 0.487709i $$-0.162167\pi$$
$$72$$ 5.24981e16 1.13387e17i 1.00960 2.18058i
$$73$$ −3.92287e16 −0.666344 −0.333172 0.942866i $$-0.608119\pi$$
−0.333172 + 0.942866i $$0.608119\pi$$
$$74$$ 1.17603e17i 1.76740i
$$75$$ −1.06251e16 + 4.82374e16i −0.141508 + 0.642440i
$$76$$ 1.45241e17 1.71699
$$77$$ 2.12290e16i 0.223107i
$$78$$ −2.63908e17 5.81302e16i −2.46945 0.543939i
$$79$$ −7.20817e16 −0.601425 −0.300712 0.953715i $$-0.597224\pi$$
−0.300712 + 0.953715i $$0.597224\pi$$
$$80$$ 1.61632e17i 1.20425i
$$81$$ 9.71035e16 + 1.14452e17i 0.646948 + 0.762534i
$$82$$ 3.06565e17 1.82893
$$83$$ 1.02835e17i 0.550093i −0.961431 0.275047i $$-0.911307\pi$$
0.961431 0.275047i $$-0.0886933\pi$$
$$84$$ −2.52512e16 + 1.14639e17i −0.121274 + 0.550577i
$$85$$ −1.55954e16 −0.0673328
$$86$$ 7.84368e17i 3.04813i
$$87$$ 2.60126e17 + 5.72973e16i 0.910985 + 0.200660i
$$88$$ −6.97910e17 −2.20524
$$89$$ 5.12684e17i 1.46332i 0.681669 + 0.731661i $$0.261254\pi$$
−0.681669 + 0.731661i $$0.738746\pi$$
$$90$$ −3.74650e17 1.73462e17i −0.967037 0.447736i
$$91$$ 1.44399e17 0.337435
$$92$$ 3.46904e17i 0.734715i
$$93$$ 4.95431e16 2.24923e17i 0.0951999 0.432202i
$$94$$ 9.30416e17 1.62378
$$95$$ 2.72957e17i 0.433094i
$$96$$ 9.11471e17 + 2.00767e17i 1.31614 + 0.289902i
$$97$$ −7.28759e17 −0.958602 −0.479301 0.877651i $$-0.659110\pi$$
−0.479301 + 0.877651i $$0.659110\pi$$
$$98$$ 1.42916e18i 1.71414i
$$99$$ 3.52232e17 7.60764e17i 0.385578 0.832785i
$$100$$ −1.52553e18 −1.52553
$$101$$ 1.15126e18i 1.05264i 0.850286 + 0.526321i $$0.176429\pi$$
−0.850286 + 0.526321i $$0.823571\pi$$
$$102$$ −5.39112e16 + 2.44754e17i −0.0451105 + 0.204799i
$$103$$ −1.83618e18 −1.40728 −0.703638 0.710559i $$-0.748442\pi$$
−0.703638 + 0.710559i $$0.748442\pi$$
$$104$$ 4.74714e18i 3.33528i
$$105$$ 2.15445e17 + 4.74554e16i 0.138878 + 0.0305902i
$$106$$ 5.09181e18 3.01383
$$107$$ 1.30924e18i 0.712140i −0.934459 0.356070i $$-0.884117\pi$$
0.934459 0.356070i $$-0.115883\pi$$
$$108$$ −2.80699e18 + 3.68923e18i −1.40419 + 1.84553i
$$109$$ 9.37377e17 0.431594 0.215797 0.976438i $$-0.430765\pi$$
0.215797 + 0.976438i $$0.430765\pi$$
$$110$$ 2.30601e18i 0.977971i
$$111$$ 5.33826e17 2.42354e18i 0.208686 0.947420i
$$112$$ −1.38794e18 −0.500506
$$113$$ 5.05201e17i 0.168174i −0.996458 0.0840868i $$-0.973203\pi$$
0.996458 0.0840868i $$-0.0267973\pi$$
$$114$$ −4.28378e18 9.43576e17i −1.31730 0.290157i
$$115$$ 6.51949e17 0.185325
$$116$$ 8.22661e18i 2.16321i
$$117$$ 5.17467e18 + 2.39586e18i 1.25953 + 0.583162i
$$118$$ −7.49601e17 −0.169002
$$119$$ 1.33918e17i 0.0279845i
$$120$$ 1.56011e18 7.08280e18i 0.302360 1.37269i
$$121$$ 8.77344e17 0.157798
$$122$$ 9.71069e18i 1.62185i
$$123$$ −6.31761e18 1.39156e18i −0.980408 0.215952i
$$124$$ 7.11328e18 1.02630
$$125$$ 7.22516e18i 0.969744i
$$126$$ 1.48953e18 3.21713e18i 0.186086 0.401915i
$$127$$ −8.86372e18 −1.03129 −0.515647 0.856801i $$-0.672448\pi$$
−0.515647 + 0.856801i $$0.672448\pi$$
$$128$$ 5.76799e18i 0.625366i
$$129$$ −3.56041e18 + 1.61640e19i −0.359909 + 1.63396i
$$130$$ −1.56853e19 −1.47912
$$131$$ 1.50395e19i 1.32371i −0.749632 0.661855i $$-0.769769\pi$$
0.749632 0.661855i $$-0.230231\pi$$
$$132$$ 2.52863e19 + 5.56975e18i 2.07836 + 0.457794i
$$133$$ 2.34389e18 0.180000
$$134$$ 1.40511e19i 1.00871i
$$135$$ 6.93330e18 + 5.27527e18i 0.465518 + 0.354194i
$$136$$ −4.40260e18 −0.276604
$$137$$ 7.91047e18i 0.465283i 0.972563 + 0.232641i $$0.0747369\pi$$
−0.972563 + 0.232641i $$0.925263\pi$$
$$138$$ 2.25370e18 1.02317e19i 0.124161 0.563682i
$$139$$ 2.96560e19 1.53102 0.765508 0.643426i $$-0.222488\pi$$
0.765508 + 0.643426i $$0.222488\pi$$
$$140$$ 6.81354e18i 0.329777i
$$141$$ −1.91738e19 4.22335e18i −0.870433 0.191728i
$$142$$ −4.17147e19 −1.77703
$$143$$ 3.18506e19i 1.27378i
$$144$$ −4.97383e19 2.30287e19i −1.86822 0.864983i
$$145$$ 1.54606e19 0.545649
$$146$$ 3.65913e19i 1.21395i
$$147$$ 6.48724e18 2.94517e19i 0.202397 0.918870i
$$148$$ 7.66454e19 2.24973
$$149$$ 3.76072e19i 1.03895i 0.854486 + 0.519475i $$0.173872\pi$$
−0.854486 + 0.519475i $$0.826128\pi$$
$$150$$ 4.49943e19 + 9.91076e18i 1.17040 + 0.257802i
$$151$$ −3.02438e19 −0.741044 −0.370522 0.928824i $$-0.620821\pi$$
−0.370522 + 0.928824i $$0.620821\pi$$
$$152$$ 7.70561e19i 1.77916i
$$153$$ 2.22198e18 4.79910e18i 0.0483633 0.104457i
$$154$$ −1.98018e19 −0.406459
$$155$$ 1.33682e19i 0.258874i
$$156$$ −3.78851e19 + 1.71996e20i −0.692384 + 3.14338i
$$157$$ −1.60317e19 −0.276620 −0.138310 0.990389i $$-0.544167\pi$$
−0.138310 + 0.990389i $$0.544167\pi$$
$$158$$ 6.72354e19i 1.09568i
$$159$$ −1.04931e20 2.31128e19i −1.61558 0.355859i
$$160$$ 5.41731e19 0.788323
$$161$$ 5.59831e18i 0.0770237i
$$162$$ 1.06757e20 9.05749e19i 1.38919 1.17862i
$$163$$ 4.78329e19 0.588895 0.294448 0.955668i $$-0.404864\pi$$
0.294448 + 0.955668i $$0.404864\pi$$
$$164$$ 1.99797e20i 2.32806i
$$165$$ 1.04674e19 4.75215e19i 0.115474 0.524246i
$$166$$ −9.59207e19 −1.00217
$$167$$ 1.25413e20i 1.24135i 0.784067 + 0.620676i $$0.213142\pi$$
−0.784067 + 0.620676i $$0.786858\pi$$
$$168$$ 6.08203e19 + 1.33967e19i 0.570512 + 0.125665i
$$169$$ 1.04190e20 0.926503
$$170$$ 1.45469e19i 0.122668i
$$171$$ 8.39958e19 + 3.88899e19i 0.671881 + 0.311080i
$$172$$ −5.11195e20 −3.87999
$$173$$ 1.32712e19i 0.0956085i 0.998857 + 0.0478042i $$0.0152224\pi$$
−0.998857 + 0.0478042i $$0.984778\pi$$
$$174$$ 5.34451e19 2.42637e20i 0.365565 1.65964i
$$175$$ −2.46189e19 −0.159929
$$176$$ 3.06144e20i 1.88935i
$$177$$ 1.54476e19 + 3.40260e18i 0.0905943 + 0.0199550i
$$178$$ 4.78215e20 2.66590
$$179$$ 3.08776e19i 0.163669i −0.996646 0.0818345i $$-0.973922\pi$$
0.996646 0.0818345i $$-0.0260779\pi$$
$$180$$ −1.13050e20 + 2.44170e20i −0.569927 + 1.23095i
$$181$$ 6.94280e18 0.0332987 0.0166494 0.999861i $$-0.494700\pi$$
0.0166494 + 0.999861i $$0.494700\pi$$
$$182$$ 1.34690e20i 0.614743i
$$183$$ −4.40789e19 + 2.00115e20i −0.191501 + 0.869402i
$$184$$ 1.84046e20 0.761317
$$185$$ 1.44043e20i 0.567473i
$$186$$ −2.09800e20 4.62122e19i −0.787390 0.173436i
$$187$$ −2.95389e19 −0.105638
$$188$$ 6.06379e20i 2.06692i
$$189$$ −4.52990e19 + 5.95365e19i −0.147208 + 0.193476i
$$190$$ −2.54606e20 −0.789016
$$191$$ 3.84936e19i 0.113786i 0.998380 + 0.0568930i $$0.0181194\pi$$
−0.998380 + 0.0568930i $$0.981881\pi$$
$$192$$ 3.02413e19 1.37294e20i 0.0852884 0.387204i
$$193$$ −5.08300e20 −1.36806 −0.684028 0.729455i $$-0.739774\pi$$
−0.684028 + 0.729455i $$0.739774\pi$$
$$194$$ 6.79762e20i 1.74639i
$$195$$ 3.23238e20 + 7.11989e19i 0.792887 + 0.174647i
$$196$$ 9.31422e20 2.18194
$$197$$ 6.30050e20i 1.40987i −0.709272 0.704935i $$-0.750976\pi$$
0.709272 0.704935i $$-0.249024\pi$$
$$198$$ −7.09616e20 3.28551e20i −1.51718 0.702451i
$$199$$ 1.14335e19 0.0233615 0.0116807 0.999932i $$-0.496282\pi$$
0.0116807 + 0.999932i $$0.496282\pi$$
$$200$$ 8.09352e20i 1.58077i
$$201$$ 6.37807e19 2.89561e20i 0.119104 0.540723i
$$202$$ 1.07386e21 1.91771
$$203$$ 1.32761e20i 0.226780i
$$204$$ 1.59513e20 + 3.51355e19i 0.260690 + 0.0574215i
$$205$$ −3.75486e20 −0.587231
$$206$$ 1.71272e21i 2.56379i
$$207$$ −9.28872e19 + 2.00621e20i −0.133114 + 0.287504i
$$208$$ −2.08237e21 −2.85751
$$209$$ 5.17002e20i 0.679479i
$$210$$ 4.42649e19 2.00960e20i 0.0557296 0.253009i
$$211$$ 6.41724e20 0.774117 0.387058 0.922055i $$-0.373491\pi$$
0.387058 + 0.922055i $$0.373491\pi$$
$$212$$ 3.31847e21i 3.83633i
$$213$$ 8.59645e20 + 1.89352e20i 0.952582 + 0.209823i
$$214$$ −1.22122e21 −1.29738
$$215$$ 9.60707e20i 0.978690i
$$216$$ 1.95728e21 + 1.48921e21i 1.91236 + 1.45504i
$$217$$ 1.14794e20 0.107592
$$218$$ 8.74355e20i 0.786284i
$$219$$ 1.66095e20 7.54063e20i 0.143338 0.650744i
$$220$$ 1.50289e21 1.24487
$$221$$ 2.00922e20i 0.159771i
$$222$$ −2.26060e21 4.97935e20i −1.72602 0.380186i
$$223$$ −8.65729e20 −0.634802 −0.317401 0.948291i $$-0.602810\pi$$
−0.317401 + 0.948291i $$0.602810\pi$$
$$224$$ 4.65187e20i 0.327639i
$$225$$ −8.82242e20 4.08477e20i −0.596960 0.276391i
$$226$$ −4.71235e20 −0.306381
$$227$$ 2.48692e21i 1.55392i 0.629547 + 0.776962i $$0.283240\pi$$
−0.629547 + 0.776962i $$0.716760\pi$$
$$228$$ −6.14955e20 + 2.79186e21i −0.369343 + 1.67679i
$$229$$ −4.47185e20 −0.258207 −0.129103 0.991631i $$-0.541210\pi$$
−0.129103 + 0.991631i $$0.541210\pi$$
$$230$$ 6.08117e20i 0.337627i
$$231$$ 4.08069e20 + 8.98843e19i 0.217884 + 0.0479928i
$$232$$ 4.36454e21 2.24154
$$233$$ 2.20802e21i 1.09094i 0.838131 + 0.545468i $$0.183648\pi$$
−0.838131 + 0.545468i $$0.816352\pi$$
$$234$$ 2.23478e21 4.82676e21i 1.06241 2.29463i
$$235$$ −1.13959e21 −0.521360
$$236$$ 4.88537e20i 0.215124i
$$237$$ 3.05196e20 1.38557e21i 0.129373 0.587345i
$$238$$ −1.24915e20 −0.0509825
$$239$$ 1.30522e21i 0.512983i −0.966547 0.256491i $$-0.917434\pi$$
0.966547 0.256491i $$-0.0825665\pi$$
$$240$$ −3.10693e21 6.84355e20i −1.17606 0.259048i
$$241$$ 1.77386e21 0.646795 0.323398 0.946263i $$-0.395175\pi$$
0.323398 + 0.946263i $$0.395175\pi$$
$$242$$ 8.18358e20i 0.287478i
$$243$$ −2.61116e21 + 1.38195e21i −0.883848 + 0.467774i
$$244$$ −6.32874e21 −2.06447
$$245$$ 1.75046e21i 0.550372i
$$246$$ −1.29800e21 + 5.89286e21i −0.393423 + 1.78612i
$$247$$ 3.51662e21 1.02767
$$248$$ 3.77387e21i 1.06346i
$$249$$ 1.97671e21 + 4.35404e20i 0.537215 + 0.118331i
$$250$$ 6.73939e21 1.76669
$$251$$ 4.95925e21i 1.25416i −0.778956 0.627079i $$-0.784250\pi$$
0.778956 0.627079i $$-0.215750\pi$$
$$252$$ −2.09670e21 9.70767e20i −0.511600 0.236870i
$$253$$ 1.23484e21 0.290755
$$254$$ 8.26779e21i 1.87882i
$$255$$ 6.60314e19 2.99778e20i 0.0144840 0.0657565i
$$256$$ −7.25254e21 −1.53579
$$257$$ 7.24122e20i 0.148052i 0.997256 + 0.0740259i $$0.0235847\pi$$
−0.997256 + 0.0740259i $$0.976415\pi$$
$$258$$ 1.50773e22 + 3.32103e21i 2.97677 + 0.655686i
$$259$$ 1.23690e21 0.235850
$$260$$ 1.02226e22i 1.88278i
$$261$$ −2.20276e21 + 4.75761e21i −0.391925 + 0.846494i
$$262$$ −1.40284e22 −2.41155
$$263$$ 1.13671e22i 1.88821i −0.329650 0.944103i $$-0.606931\pi$$
0.329650 0.944103i $$-0.393069\pi$$
$$264$$ 2.95497e21 1.34154e22i 0.474370 2.15361i
$$265$$ −6.23653e21 −0.967676
$$266$$ 2.18631e21i 0.327927i
$$267$$ −9.85492e21 2.17072e21i −1.42906 0.314776i
$$268$$ 9.15748e21 1.28399
$$269$$ 9.09091e21i 1.23264i 0.787495 + 0.616321i $$0.211377\pi$$
−0.787495 + 0.616321i $$0.788623\pi$$
$$270$$ 4.92060e21 6.46716e21i 0.645275 0.848085i
$$271$$ 5.59132e21 0.709235 0.354618 0.935011i $$-0.384611\pi$$
0.354618 + 0.935011i $$0.384611\pi$$
$$272$$ 1.93124e21i 0.236982i
$$273$$ −6.11387e20 + 2.77566e21i −0.0725860 + 0.329536i
$$274$$ 7.37863e21 0.847658
$$275$$ 5.43029e21i 0.603710i
$$276$$ −6.66826e21 1.46880e21i −0.717515 0.158045i
$$277$$ −3.61235e21 −0.376246 −0.188123 0.982145i $$-0.560240\pi$$
−0.188123 + 0.982145i $$0.560240\pi$$
$$278$$ 2.76622e22i 2.78922i
$$279$$ 4.11374e21 + 1.90466e21i 0.401605 + 0.185942i
$$280$$ 3.61484e21 0.341718
$$281$$ 3.75694e20i 0.0343936i 0.999852 + 0.0171968i $$0.00547418\pi$$
−0.999852 + 0.0171968i $$0.994526\pi$$
$$282$$ −3.93940e21 + 1.78847e22i −0.349292 + 1.58576i
$$283$$ 4.33569e21 0.372375 0.186187 0.982514i $$-0.440387\pi$$
0.186187 + 0.982514i $$0.440387\pi$$
$$284$$ 2.71866e22i 2.26199i
$$285$$ 5.24684e21 + 1.15571e21i 0.422955 + 0.0931632i
$$286$$ −2.97092e22 −2.32058
$$287$$ 3.22431e21i 0.244062i
$$288$$ −7.71838e21 + 1.66704e22i −0.566231 + 1.22297i
$$289$$ 1.38767e22 0.986750
$$290$$ 1.44211e22i 0.994070i
$$291$$ 3.08558e21 1.40084e22i 0.206205 0.936160i
$$292$$ 2.38476e22 1.54525
$$293$$ 1.01590e22i 0.638326i 0.947700 + 0.319163i $$0.103402\pi$$
−0.947700 + 0.319163i $$0.896598\pi$$
$$294$$ −2.74716e22 6.05109e21i −1.67401 0.368729i
$$295$$ 9.18125e20 0.0542630
$$296$$ 4.06633e22i 2.33119i
$$297$$ 1.31322e22 + 9.99178e21i 0.730348 + 0.555693i
$$298$$ 3.50788e22 1.89277
$$299$$ 8.39932e21i 0.439748i
$$300$$ 6.45913e21 2.93240e22i 0.328158 1.48982i
$$301$$ −8.24963e21 −0.406758
$$302$$ 2.82105e22i 1.35004i
$$303$$ −2.21297e22 4.87446e21i −1.02800 0.226434i
$$304$$ −3.38013e22 −1.52430
$$305$$ 1.18938e22i 0.520742i
$$306$$ −4.47645e21 2.07259e21i −0.190301 0.0881089i
$$307$$ −3.56186e22 −1.47039 −0.735194 0.677857i $$-0.762909\pi$$
−0.735194 + 0.677857i $$0.762909\pi$$
$$308$$ 1.29054e22i 0.517385i
$$309$$ 7.77441e21 3.52954e22i 0.302720 1.37433i
$$310$$ −1.24695e22 −0.471620
$$311$$ 9.62119e21i 0.353497i 0.984256 + 0.176748i $$0.0565579\pi$$
−0.984256 + 0.176748i $$0.943442\pi$$
$$312$$ 9.12505e22 + 2.00995e22i 3.25720 + 0.717454i
$$313$$ −2.06842e22 −0.717364 −0.358682 0.933460i $$-0.616774\pi$$
−0.358682 + 0.933460i $$0.616774\pi$$
$$314$$ 1.49539e22i 0.503949i
$$315$$ −1.82440e21 + 3.94040e21i −0.0597481 + 0.129046i
$$316$$ 4.38193e22 1.39470
$$317$$ 4.70774e22i 1.45640i −0.685367 0.728198i $$-0.740358\pi$$
0.685367 0.728198i $$-0.259642\pi$$
$$318$$ −2.15588e22 + 9.78758e22i −0.648308 + 2.94328i
$$319$$ 2.92835e22 0.856066
$$320$$ 8.16003e21i 0.231922i
$$321$$ 2.51665e22 + 5.54335e21i 0.695468 + 0.153189i
$$322$$ 5.22192e21 0.140323
$$323$$ 3.26139e21i 0.0852275i
$$324$$ −5.90303e22 6.95768e22i −1.50027 1.76831i
$$325$$ −3.69365e22 −0.913072
$$326$$ 4.46170e22i 1.07286i
$$327$$ −3.96888e21 + 1.80185e22i −0.0928406 + 0.421491i
$$328$$ −1.06000e23 −2.41236
$$329$$ 9.78570e21i 0.216685i
$$330$$ −4.43265e22 9.76368e21i −0.955077 0.210372i
$$331$$ 6.94207e22 1.45558 0.727791 0.685799i $$-0.240547\pi$$
0.727791 + 0.685799i $$0.240547\pi$$
$$332$$ 6.25143e22i 1.27566i
$$333$$ 4.43255e22 + 2.05226e22i 0.880350 + 0.407601i
$$334$$ 1.16981e23 2.26151
$$335$$ 1.72100e22i 0.323875i
$$336$$ 5.87658e21 2.66793e22i 0.107664 0.488789i
$$337$$ −7.20588e22 −1.28534 −0.642670 0.766143i $$-0.722173\pi$$
−0.642670 + 0.766143i $$0.722173\pi$$
$$338$$ 9.71853e22i 1.68791i
$$339$$ 9.71107e21 + 2.13903e21i 0.164237 + 0.0361759i
$$340$$ 9.48063e21 0.156145
$$341$$ 2.53205e22i 0.406146i
$$342$$ 3.62752e22 7.83486e22i 0.566729 1.22404i
$$343$$ 3.10067e22 0.471854
$$344$$ 2.71209e23i 4.02048i
$$345$$ −2.76037e21 + 1.25319e22i −0.0398653 + 0.180986i
$$346$$ 1.23790e22 0.174181
$$347$$ 7.97053e22i 1.09275i 0.837540 + 0.546376i $$0.183993\pi$$
−0.837540 + 0.546376i $$0.816007\pi$$
$$348$$ −1.58134e23 3.48317e22i −2.11257 0.465330i
$$349$$ −2.86134e22 −0.372513 −0.186256 0.982501i $$-0.559635\pi$$
−0.186256 + 0.982501i $$0.559635\pi$$
$$350$$ 2.29637e22i 0.291360i
$$351$$ −6.79635e22 + 8.93245e22i −0.840449 + 1.10460i
$$352$$ 1.02608e23 1.23679
$$353$$ 4.43974e22i 0.521657i −0.965385 0.260829i $$-0.916004\pi$$
0.965385 0.260829i $$-0.0839957\pi$$
$$354$$ 3.17383e21 1.44090e22i 0.0363542 0.165046i
$$355$$ 5.10928e22 0.570565
$$356$$ 3.11666e23i 3.39344i
$$357$$ 2.57421e21 + 5.67014e20i 0.0273294 + 0.00601977i
$$358$$ −2.88016e22 −0.298174
$$359$$ 4.97330e22i 0.502105i 0.967973 + 0.251052i $$0.0807767\pi$$
−0.967973 + 0.251052i $$0.919223\pi$$
$$360$$ 1.29542e23 + 5.99775e22i 1.27552 + 0.590563i
$$361$$ −4.70452e22 −0.451805
$$362$$ 6.47602e21i 0.0606640i
$$363$$ −3.71470e21 + 1.68645e22i −0.0339441 + 0.154104i
$$364$$ −8.77815e22 −0.782511
$$365$$ 4.48176e22i 0.389774i
$$366$$ 1.86661e23 + 4.11153e22i 1.58389 + 0.348878i
$$367$$ −6.92177e22 −0.573090 −0.286545 0.958067i $$-0.592507\pi$$
−0.286545 + 0.958067i $$0.592507\pi$$
$$368$$ 8.07332e22i 0.652262i
$$369$$ 5.34978e22 1.15547e23i 0.421792 0.911003i
$$370$$ −1.34358e23 −1.03383
$$371$$ 5.35533e22i 0.402181i
$$372$$ −3.01178e22 + 1.36733e23i −0.220768 + 1.00227i
$$373$$ 8.88028e22 0.635400 0.317700 0.948191i $$-0.397090\pi$$
0.317700 + 0.948191i $$0.397090\pi$$
$$374$$ 2.75529e22i 0.192453i
$$375$$ −1.38884e23 3.05915e22i −0.947042 0.208602i
$$376$$ −3.21707e23 −2.14176
$$377$$ 1.99185e23i 1.29474i
$$378$$ 5.55337e22 + 4.22534e22i 0.352477 + 0.268186i
$$379$$ 2.92079e23 1.81028 0.905142 0.425109i $$-0.139764\pi$$
0.905142 + 0.425109i $$0.139764\pi$$
$$380$$ 1.65934e23i 1.00434i
$$381$$ 3.75292e22 1.70380e23i 0.221842 1.00715i
$$382$$ 3.59056e22 0.207297
$$383$$ 1.19044e23i 0.671306i 0.941986 + 0.335653i $$0.108957\pi$$
−0.941986 + 0.335653i $$0.891043\pi$$
$$384$$ 1.10873e23 + 2.44218e22i 0.610726 + 0.134523i
$$385$$ 2.42535e22 0.130505
$$386$$ 4.74126e23i 2.49234i
$$387$$ −2.95634e23 1.36878e23i −1.51829 0.702966i
$$388$$ 4.43020e23 2.22299
$$389$$ 3.20490e23i 1.57133i −0.618650 0.785666i $$-0.712320\pi$$
0.618650 0.785666i $$-0.287680\pi$$
$$390$$ 6.64120e22 3.01506e23i 0.318174 1.44449i
$$391$$ 7.78971e21 0.0364696
$$392$$ 4.94156e23i 2.26094i
$$393$$ 2.89093e23 + 6.36778e22i 1.29272 + 0.284744i
$$394$$ −5.87690e23 −2.56852
$$395$$ 8.23511e22i 0.351800i
$$396$$ −2.14126e23 + 4.62477e23i −0.894154 + 1.93123i
$$397$$ −3.68991e23 −1.50626 −0.753132 0.657870i $$-0.771458\pi$$
−0.753132 + 0.657870i $$0.771458\pi$$
$$398$$ 1.06648e22i 0.0425602i
$$399$$ −9.92411e21 + 4.50548e22i −0.0387200 + 0.175786i
$$400$$ 3.55029e23 1.35433
$$401$$ 4.34713e23i 1.62145i 0.585429 + 0.810724i $$0.300926\pi$$
−0.585429 + 0.810724i $$0.699074\pi$$
$$402$$ −2.70093e23 5.94926e22i −0.985096 0.216984i
$$403$$ 1.72228e23 0.614270
$$404$$ 6.99863e23i 2.44107i
$$405$$ −1.30758e23 + 1.10938e23i −0.446040 + 0.378429i
$$406$$ 1.23835e23 0.413150
$$407$$ 2.72828e23i 0.890305i
$$408$$ 1.86407e22 8.46277e22i 0.0595006 0.270129i
$$409$$ 1.61875e22 0.0505440 0.0252720 0.999681i $$-0.491955\pi$$
0.0252720 + 0.999681i $$0.491955\pi$$
$$410$$ 3.50241e23i 1.06982i
$$411$$ −1.52057e23 3.34931e22i −0.454391 0.100087i
$$412$$ 1.11623e24 3.26347
$$413$$ 7.88397e21i 0.0225525i
$$414$$ 1.87133e23 + 8.66422e22i 0.523778 + 0.242508i
$$415$$ 1.17485e23 0.321774
$$416$$ 6.97934e23i 1.87057i
$$417$$ −1.25564e23 + 5.70055e23i −0.329338 + 1.49518i
$$418$$ −4.82243e23 −1.23788
$$419$$ 1.48601e23i 0.373333i 0.982423 + 0.186666i $$0.0597684\pi$$
−0.982423 + 0.186666i $$0.940232\pi$$
$$420$$ −1.30971e23 2.88487e22i −0.322057 0.0709386i
$$421$$ −2.10694e23 −0.507123 −0.253562 0.967319i $$-0.581602\pi$$
−0.253562 + 0.967319i $$0.581602\pi$$
$$422$$ 5.98580e23i 1.41029i
$$423$$ 1.62364e23 3.50680e23i 0.374479 0.808813i
$$424$$ −1.76058e24 −3.97523
$$425$$ 3.42557e22i 0.0757238i
$$426$$ 1.76621e23 8.01848e23i 0.382257 1.73543i
$$427$$ −1.02133e23 −0.216428
$$428$$ 7.95901e23i 1.65145i
$$429$$ 6.12239e23 + 1.34856e23i 1.24396 + 0.274003i
$$430$$ 8.96116e23 1.78299
$$431$$ 1.45530e23i 0.283567i −0.989898 0.141783i $$-0.954716\pi$$
0.989898 0.141783i $$-0.0452837\pi$$
$$432$$ 6.53256e23 8.58576e23i 1.24661 1.63842i
$$433$$ 2.76937e23 0.517594 0.258797 0.965932i $$-0.416674\pi$$
0.258797 + 0.965932i $$0.416674\pi$$
$$434$$ 1.07076e23i 0.196012i
$$435$$ −6.54605e22 + 2.97187e23i −0.117375 + 0.532876i
$$436$$ −5.69842e23 −1.00087
$$437$$ 1.36339e23i 0.234577i
$$438$$ −7.03365e23 1.54928e23i −1.18553 0.261134i
$$439$$ 7.04854e23 1.16391 0.581954 0.813222i $$-0.302288\pi$$
0.581954 + 0.813222i $$0.302288\pi$$
$$440$$ 7.97341e23i 1.28994i
$$441$$ 5.38659e23 + 2.49398e23i 0.853821 + 0.395318i
$$442$$ −1.87413e23 −0.291072
$$443$$ 1.22387e24i 1.86252i −0.364351 0.931262i $$-0.618709\pi$$
0.364351 0.931262i $$-0.381291\pi$$
$$444$$ −3.24519e23 + 1.47329e24i −0.483941 + 2.19706i
$$445$$ −5.85726e23 −0.855962
$$446$$ 8.07524e23i 1.15649i
$$447$$ −7.22894e23 1.59230e23i −1.01463 0.223489i
$$448$$ 7.00705e22 0.0963903
$$449$$ 4.92165e23i 0.663580i 0.943353 + 0.331790i $$0.107653\pi$$
−0.943353 + 0.331790i $$0.892347\pi$$
$$450$$ −3.81014e23 + 8.22927e23i −0.503533 + 1.08755i
$$451$$ −7.11200e23 −0.921304
$$452$$ 3.07117e23i 0.389994i
$$453$$ 1.28053e23 5.81353e23i 0.159407 0.723696i
$$454$$ 2.31972e24 2.83096
$$455$$ 1.64971e23i 0.197381i
$$456$$ 1.48119e24 + 3.26257e23i 1.73751 + 0.382716i
$$457$$ −1.39981e24 −1.60999 −0.804994 0.593284i $$-0.797831\pi$$
−0.804994 + 0.593284i $$0.797831\pi$$
$$458$$ 4.17120e23i 0.470404i
$$459$$ 8.28415e22 + 6.30308e22i 0.0916080 + 0.0697009i
$$460$$ −3.96327e23 −0.429767
$$461$$ 1.15752e24i 1.23090i −0.788177 0.615449i $$-0.788975\pi$$
0.788177 0.615449i $$-0.211025\pi$$
$$462$$ 8.38411e22 3.80634e23i 0.0874338 0.396944i
$$463$$ 1.06888e23 0.109320 0.0546602 0.998505i $$-0.482592\pi$$
0.0546602 + 0.998505i $$0.482592\pi$$
$$464$$ 1.91454e24i 1.92045i
$$465$$ 2.56967e23 + 5.66015e22i 0.252814 + 0.0556867i
$$466$$ 2.05957e24 1.98748
$$467$$ 1.19933e24i 1.13524i 0.823291 + 0.567619i $$0.192135\pi$$
−0.823291 + 0.567619i $$0.807865\pi$$
$$468$$ −3.14574e24 1.45647e24i −2.92085 1.35235i
$$469$$ 1.47783e23 0.134607
$$470$$ 1.06297e24i 0.949819i
$$471$$ 6.78788e22 3.08165e23i 0.0595039 0.270144i
$$472$$ 2.59187e23 0.222913
$$473$$ 1.81965e24i 1.53546i
$$474$$ −1.29241e24 2.84677e23i −1.07003 0.235693i
$$475$$ −5.99557e23 −0.487066
$$476$$ 8.14105e22i 0.0648960i
$$477$$ 8.88557e23 1.91914e24i 0.695056 1.50121i
$$478$$ −1.21747e24 −0.934557
$$479$$ 8.59327e23i 0.647350i −0.946168 0.323675i $$-0.895082\pi$$
0.946168 0.323675i $$-0.104918\pi$$
$$480$$ −2.29370e23 + 1.04133e24i −0.169577 + 0.769868i
$$481$$ 1.85576e24 1.34653
$$482$$ 1.65460e24i 1.17834i
$$483$$ −1.07612e23 2.37034e22i −0.0752205 0.0165686i
$$484$$ −5.33347e23 −0.365933
$$485$$ 8.32585e23i 0.560729i
$$486$$ 1.28904e24 + 2.43561e24i 0.852195 + 1.61020i
$$487$$ 9.68317e23 0.628430 0.314215 0.949352i $$-0.398259\pi$$
0.314215 + 0.949352i $$0.398259\pi$$
$$488$$ 3.35764e24i 2.13922i
$$489$$ −2.02526e23 + 9.19454e23i −0.126678 + 0.575109i
$$490$$ −1.63277e24 −1.00267
$$491$$ 1.67063e24i 1.00727i 0.863916 + 0.503635i $$0.168004\pi$$
−0.863916 + 0.503635i $$0.831996\pi$$
$$492$$ 3.84054e24 + 8.45946e23i 2.27356 + 0.500791i
$$493$$ 1.84728e23 0.107377
$$494$$ 3.28019e24i 1.87222i
$$495$$ 8.69149e23 + 4.02415e23i 0.487133 + 0.225542i
$$496$$ −1.65544e24 −0.911125
$$497$$ 4.38736e23i 0.237135i
$$498$$ 4.06131e23 1.84381e24i 0.215577 0.978705i
$$499$$ 3.00033e23 0.156410 0.0782050 0.996937i $$-0.475081\pi$$
0.0782050 + 0.996937i $$0.475081\pi$$
$$500$$ 4.39225e24i 2.24883i
$$501$$ −2.41072e24 5.31002e23i −1.21229 0.267028i
$$502$$ −4.62582e24 −2.28484
$$503$$ 3.08864e24i 1.49850i 0.662289 + 0.749248i $$0.269585\pi$$
−0.662289 + 0.749248i $$0.730415\pi$$
$$504$$ −5.15029e23 + 1.11238e24i −0.245447 + 0.530124i
$$505$$ −1.31528e24 −0.615737
$$506$$ 1.15182e24i 0.529700i
$$507$$ −4.41144e23 + 2.00277e24i −0.199301 + 0.904813i
$$508$$ 5.38835e24 2.39157
$$509$$ 3.85870e24i 1.68260i −0.540569 0.841299i $$-0.681791\pi$$
0.540569 0.841299i $$-0.318209\pi$$
$$510$$ −2.79624e23 6.15919e22i −0.119796 0.0263871i
$$511$$ 3.84851e23 0.161996
$$512$$ 5.25289e24i 2.17254i
$$513$$ −1.10319e24 + 1.44992e24i −0.448326 + 0.589236i
$$514$$ 6.75437e23 0.269722
$$515$$ 2.09777e24i 0.823178i
$$516$$ 2.16441e24 9.82630e24i 0.834627 3.78916i
$$517$$ −2.15847e24 −0.817958
$$518$$ 1.15374e24i 0.429675i
$$519$$ −2.55103e23 5.61907e22i −0.0933702 0.0205664i
$$520$$ 5.42346e24 1.95095
$$521$$ 1.16274e24i 0.411097i 0.978647 + 0.205549i $$0.0658979\pi$$
−0.978647 + 0.205549i $$0.934102\pi$$
$$522$$ 4.43774e24 + 2.05467e24i 1.54215 + 0.714014i
$$523$$ 1.12148e24 0.383069 0.191534 0.981486i $$-0.438654\pi$$
0.191534 + 0.981486i $$0.438654\pi$$
$$524$$ 9.14270e24i 3.06968i
$$525$$ 1.04237e23 4.73230e23i 0.0344023 0.156185i
$$526$$ −1.06029e25 −3.43996
$$527$$ 1.59728e23i 0.0509432i
$$528$$ −5.88476e24 1.29622e24i −1.84512 0.406419i
$$529$$ 2.91851e24 0.899622
$$530$$ 5.81723e24i 1.76292i
$$531$$ −1.30811e23 + 2.82530e23i −0.0389756 + 0.0841810i
$$532$$ −1.42488e24 −0.417420
$$533$$ 4.83754e24i 1.39341i
$$534$$ −2.02477e24 + 9.19235e24i −0.573463 + 2.60349i
$$535$$ 1.49577e24 0.416562
$$536$$ 4.85840e24i 1.33049i
$$537$$ 5.93536e23 + 1.30737e23i 0.159837 + 0.0352070i
$$538$$ 8.47970e24 2.24564
$$539$$ 3.31550e24i 0.863476i
$$540$$ −4.21483e24 3.20690e24i −1.07953 0.821375i
$$541$$ 2.23337e24 0.562582 0.281291 0.959622i $$-0.409237\pi$$
0.281291 + 0.959622i $$0.409237\pi$$
$$542$$ 5.21540e24i 1.29209i
$$543$$ −2.93960e22 + 1.33456e23i −0.00716291 + 0.0325192i
$$544$$ 6.47279e23 0.155132
$$545$$ 1.07092e24i 0.252459i
$$546$$ 2.58905e24 + 5.70282e23i 0.600352 + 0.132238i
$$547$$ 2.13233e24 0.486372 0.243186 0.969980i $$-0.421808\pi$$
0.243186 + 0.969980i $$0.421808\pi$$
$$548$$ 4.80886e24i 1.07899i
$$549$$ −3.66003e24 1.69459e24i −0.807855 0.374035i
$$550$$ 5.06519e24 1.09985
$$551$$ 3.23319e24i 0.690664i
$$552$$ −7.79255e23 + 3.53777e24i −0.163768 + 0.743495i
$$553$$ 7.07152e23 0.146213
$$554$$ 3.36949e24i 0.685450i
$$555$$ 2.76882e24 + 6.09880e23i 0.554188 + 0.122070i
$$556$$ −1.80282e25 −3.55042
$$557$$ 4.28440e24i 0.830221i −0.909771 0.415111i $$-0.863743\pi$$
0.909771 0.415111i $$-0.136257\pi$$
$$558$$ 1.77660e24 3.83717e24i 0.338752 0.731649i
$$559$$ −1.23772e25 −2.32228
$$560$$ 1.58568e24i 0.292768i
$$561$$ 1.25069e23 5.67804e23i 0.0227239 0.103165i
$$562$$ 3.50435e23 0.0626587
$$563$$ 6.48683e24i 1.14145i 0.821141 + 0.570725i $$0.193338\pi$$
−0.821141 + 0.570725i $$0.806662\pi$$
$$564$$ 1.16559e25 + 2.56742e24i 2.01853 + 0.444616i
$$565$$ 5.77176e23 0.0983722
$$566$$ 4.04419e24i 0.678396i
$$567$$ −9.52627e23 1.12283e24i −0.157281 0.185381i
$$568$$ 1.44236e25 2.34389
$$569$$ 1.13256e25i 1.81155i 0.423762 + 0.905774i $$0.360709\pi$$
−0.423762 + 0.905774i $$0.639291\pi$$
$$570$$ 1.07801e24 4.89409e24i 0.169726 0.770545i
$$571$$ 3.22177e23 0.0499309 0.0249654 0.999688i $$-0.492052\pi$$
0.0249654 + 0.999688i $$0.492052\pi$$
$$572$$ 1.93623e25i 2.95388i
$$573$$ −7.39933e23 1.62983e23i −0.111122 0.0244766i
$$574$$ −3.00754e24 −0.444635
$$575$$ 1.43202e24i 0.208420i
$$576$$ 2.51105e24 + 1.16261e24i 0.359793 + 0.166583i
$$577$$ 1.04474e25 1.47375 0.736877 0.676027i $$-0.236300\pi$$
0.736877 + 0.676027i $$0.236300\pi$$
$$578$$ 1.29438e25i 1.79767i
$$579$$ 2.15215e24 9.77065e24i 0.294284 1.33603i
$$580$$ −9.39866e24 −1.26536
$$581$$ 1.00885e24i 0.133734i
$$582$$ −1.30665e25 2.87813e24i −1.70551 0.375667i
$$583$$ −1.18125e25 −1.51818
$$584$$ 1.26521e25i 1.60120i
$$585$$ −2.73720e24 + 5.91190e24i −0.341117 + 0.736757i
$$586$$ 9.47598e24 1.16291
$$587$$ 1.94521e24i 0.235084i −0.993068 0.117542i $$-0.962498\pi$$
0.993068 0.117542i $$-0.0375015\pi$$
$$588$$ −3.94367e24 + 1.79040e25i −0.469358 + 2.13086i
$$589$$ 2.79563e24 0.327674
$$590$$ 8.56397e23i 0.0988569i
$$591$$ 1.21110e25 + 2.66765e24i 1.37686 + 0.303278i
$$592$$ −1.78373e25 −1.99726
$$593$$ 1.02435e25i 1.12968i 0.825200 + 0.564841i $$0.191063\pi$$
−0.825200 + 0.564841i $$0.808937\pi$$
$$594$$ 9.32000e24 1.22493e25i 1.01237 1.33056i
$$595$$ 1.52998e23 0.0163694
$$596$$ 2.28618e25i 2.40932i
$$597$$ −4.84096e22 + 2.19777e23i −0.00502531 + 0.0228146i
$$598$$ 7.83461e24 0.801137
$$599$$ 8.10173e24i 0.816086i −0.912963 0.408043i $$-0.866211\pi$$
0.912963 0.408043i $$-0.133789\pi$$
$$600$$ −1.55575e25 3.42682e24i −1.54376 0.340040i
$$601$$ −4.00759e24 −0.391754 −0.195877 0.980628i $$-0.562755\pi$$
−0.195877 + 0.980628i $$0.562755\pi$$
$$602$$ 7.69499e24i 0.741036i
$$603$$ 5.29595e24 + 2.45201e24i 0.502444 + 0.232631i
$$604$$ 1.83856e25 1.71848
$$605$$ 1.00234e24i 0.0923031i
$$606$$ −4.54673e24 + 2.06419e25i −0.412521 + 1.87282i
$$607$$ 1.18663e25 1.06076 0.530378 0.847761i $$-0.322050\pi$$
0.530378 + 0.847761i $$0.322050\pi$$
$$608$$ 1.13289e25i 0.997832i
$$609$$ −2.55195e24 5.62112e23i −0.221471 0.0487828i
$$610$$ 1.10942e25 0.948695
$$611$$ 1.46818e25i 1.23711i
$$612$$ −1.35076e24 + 2.91743e24i −0.112154 + 0.242235i
$$613$$ −1.12607e25 −0.921345 −0.460673 0.887570i $$-0.652392\pi$$
−0.460673 + 0.887570i $$0.652392\pi$$
$$614$$ 3.32239e25i 2.67877i
$$615$$ 1.58982e24 7.21768e24i 0.126320 0.573484i
$$616$$ 6.84679e24 0.536119
$$617$$ 2.90545e23i 0.0224206i 0.999937 + 0.0112103i $$0.00356842\pi$$
−0.999937 + 0.0112103i $$0.996432\pi$$
$$618$$ −3.29224e25 7.25172e24i −2.50377 0.551499i
$$619$$ −1.42594e25 −1.06877 −0.534385 0.845241i $$-0.679457\pi$$
−0.534385 + 0.845241i $$0.679457\pi$$
$$620$$ 8.12670e24i 0.600329i
$$621$$ −3.46310e24 2.63493e24i −0.252139 0.191843i
$$622$$ 8.97433e24 0.644004
$$623$$ 5.02965e24i 0.355750i
$$624$$ 8.81681e24 4.00278e25i 0.614682 2.79062i
$$625$$ 1.31831e24 0.0905936
$$626$$ 1.92935e25i 1.30690i
$$627$$ 9.93793e24 + 2.18900e24i 0.663572 + 0.146163i
$$628$$ 9.74587e24 0.641481
$$629$$ 1.72107e24i 0.111672i
$$630$$ 3.67548e24 + 1.70174e24i 0.235098 + 0.108850i
$$631$$ −1.34151e25 −0.845923 −0.422961 0.906148i $$-0.639009\pi$$
−0.422961 + 0.906148i $$0.639009\pi$$
$$632$$ 2.32478e25i 1.44520i
$$633$$ −2.71708e24 + 1.23354e25i −0.166521 + 0.755995i
$$634$$ −4.39123e25 −2.65328
$$635$$ 1.01265e25i 0.603249i
$$636$$ 6.37884e25 + 1.40505e25i 3.74652 + 0.825235i
$$637$$ 2.25518e25 1.30595
$$638$$ 2.73147e25i 1.55959i
$$639$$ −7.27951e24 + 1.57226e25i −0.409821 + 0.885147i
$$640$$ 6.58975e24 0.365805
$$641$$ 5.98895e24i 0.327815i 0.986476 + 0.163907i $$0.0524098\pi$$
−0.986476 + 0.163907i $$0.947590\pi$$
$$642$$ 5.17066e24 2.34745e25i 0.279081 1.26701i
$$643$$ −1.54893e25 −0.824391 −0.412196 0.911095i $$-0.635238\pi$$
−0.412196 + 0.911095i $$0.635238\pi$$
$$644$$ 3.40328e24i 0.178618i
$$645$$ −1.84669e25 4.06766e24i −0.955778 0.210527i
$$646$$ −3.04212e24 −0.155268
$$647$$ 1.51080e25i 0.760447i −0.924895 0.380223i $$-0.875847\pi$$
0.924895 0.380223i $$-0.124153\pi$$
$$648$$ −3.69132e25 + 3.13178e25i −1.83234 + 1.55459i
$$649$$ 1.73900e24 0.0851328
$$650$$ 3.44531e25i 1.66345i
$$651$$ −4.86039e23 + 2.20659e24i −0.0231442 + 0.105073i
$$652$$ −2.90781e25 −1.36565
$$653$$ 2.12528e25i 0.984457i −0.870466 0.492228i $$-0.836182\pi$$
0.870466 0.492228i $$-0.163818\pi$$
$$654$$ 1.68070e25 + 3.70204e24i 0.767877 + 0.169138i
$$655$$ 1.71822e25 0.774297
$$656$$ 4.64978e25i 2.06680i
$$657$$ 1.37915e25 + 6.38544e24i 0.604677 + 0.279964i
$$658$$ −9.12778e24 −0.394759
$$659$$ 4.11576e25i 1.75583i 0.478820 + 0.877913i $$0.341064\pi$$
−0.478820 + 0.877913i $$0.658936\pi$$
$$660$$ −6.36327e24 + 2.88889e25i −0.267784 + 1.21572i
$$661$$ 3.24714e25 1.34799 0.673996 0.738735i $$-0.264576\pi$$
0.673996 + 0.738735i $$0.264576\pi$$
$$662$$ 6.47533e25i 2.65180i
$$663$$ 3.86217e24 + 8.50709e23i 0.156030 + 0.0343684i
$$664$$ 3.31662e25 1.32185
$$665$$ 2.67783e24i 0.105290i
$$666$$ 1.91428e25 4.13454e25i 0.742571 1.60383i
$$667$$ −7.72236e24 −0.295541
$$668$$ 7.62400e25i 2.87869i
$$669$$ 3.66552e24 1.66412e25i 0.136553 0.619941i
$$670$$ −1.60529e25 −0.590039
$$671$$ 2.25278e25i 0.816990i
$$672$$ −8.94192e24 1.96961e24i −0.319969 0.0704786i
$$673$$ 1.10390e25 0.389758 0.194879 0.980827i $$-0.437569\pi$$
0.194879 + 0.980827i $$0.437569\pi$$
$$674$$ 6.72141e25i 2.34165i
$$675$$ 1.15873e25 1.52292e25i 0.398334 0.523530i
$$676$$ −6.33384e25 −2.14856
$$677$$ 2.74075e25i 0.917427i 0.888584 + 0.458714i $$0.151690\pi$$
−0.888584 + 0.458714i $$0.848310\pi$$
$$678$$ 1.99522e24 9.05817e24i 0.0659058 0.299208i
$$679$$ 7.14944e24 0.233047
$$680$$ 5.02984e24i 0.161798i
$$681$$ −4.78042e25 1.05297e25i −1.51755 0.334266i
$$682$$ −2.36181e25 −0.739922
$$683$$ 3.99739e25i 1.23592i 0.786210 + 0.617960i $$0.212041\pi$$
−0.786210 + 0.617960i $$0.787959\pi$$
$$684$$ −5.10620e25 2.36416e25i −1.55809 0.721393i
$$685$$ −9.03747e24 −0.272165
$$686$$ 2.89220e25i 0.859630i
$$687$$ 1.89339e24 8.59589e24i 0.0555431 0.252162i
$$688$$ 1.18968e26 3.44456
$$689$$ 8.03477e25i 2.29615i
$$690$$ 1.16894e25 + 2.57478e24i 0.329723 + 0.0726271i
$$691$$ −1.02801e25 −0.286218 −0.143109 0.989707i $$-0.545710\pi$$
−0.143109 + 0.989707i $$0.545710\pi$$
$$692$$ 8.06773e24i 0.221716i
$$693$$ −3.45555e24 + 7.46342e24i −0.0937385 + 0.202460i
$$694$$ 7.43465e25 1.99079
$$695$$ 3.38811e25i 0.895560i
$$696$$ −1.84796e25 + 8.38960e25i −0.482179 + 2.18906i
$$697$$ −4.48644e24 −0.115560
$$698$$ 2.66897e25i 0.678648i
$$699$$ −4.24430e25 9.34881e24i −1.06540 0.234672i
$$700$$ 1.49661e25 0.370874
$$701$$ 2.02392e25i 0.495143i 0.968870 + 0.247572i $$0.0796325\pi$$
−0.968870 + 0.247572i $$0.920367\pi$$
$$702$$ 8.33189e25 + 6.33941e25i 2.01238 + 1.53114i
$$703$$ 3.01229e25 0.718288
$$704$$ 1.54557e25i 0.363861i
$$705$$ 4.82505e24 2.19054e25i 0.112150 0.509155i
$$706$$ −4.14124e25 −0.950361
$$707$$ 1.12943e25i 0.255909i
$$708$$ −9.39075e24 2.06848e24i −0.210088 0.0462755i
$$709$$ −8.66215e25 −1.91342 −0.956708 0.291048i $$-0.905996\pi$$
−0.956708 + 0.291048i $$0.905996\pi$$
$$710$$ 4.76577e25i 1.03946i
$$711$$ 2.53415e25 + 1.17331e25i 0.545766 + 0.252688i
$$712$$ −1.65351e26 −3.51631
$$713$$ 6.67727e24i 0.140215i
$$714$$ 5.28892e23 2.40114e24i 0.0109669 0.0497890i
$$715$$ 3.63883e25 0.745088
$$716$$ 1.87708e25i 0.379548i
$$717$$ 2.50892e25 + 5.52633e24i 0.500973 + 0.110348i
$$718$$ 4.63893e25 0.914740
$$719$$ 8.53805e25i 1.66264i −0.555793 0.831320i $$-0.687585\pi$$
0.555793 0.831320i $$-0.312415\pi$$
$$720$$ 2.63096e25 5.68245e25i 0.505967 1.09281i
$$721$$ 1.80137e25 0.342125
$$722$$ 4.38822e25i 0.823103i
$$723$$ −7.51058e24 + 3.40976e25i −0.139133 + 0.631653i
$$724$$ −4.22060e24 −0.0772196
$$725$$ 3.39595e25i 0.613648i
$$726$$ 1.57307e25 + 3.46495e24i 0.280748 + 0.0618397i
$$727$$ 1.83358e25 0.323215 0.161607 0.986855i $$-0.448332\pi$$
0.161607 + 0.986855i $$0.448332\pi$$
$$728$$ 4.65715e25i 0.810845i
$$729$$ −1.55084e25 5.60436e25i −0.266698 0.963780i
$$730$$ −4.18044e25 −0.710095
$$731$$ 1.14789e25i 0.192594i
$$732$$ 2.67960e25 1.21652e26i 0.444090 2.01614i
$$733$$ 9.99901e25 1.63690 0.818449 0.574580i $$-0.194834\pi$$
0.818449 + 0.574580i $$0.194834\pi$$
$$734$$ 6.45640e25i 1.04406i
$$735$$ 3.36476e25 + 7.41148e24i 0.537488 + 0.118391i
$$736$$ −2.70588e25 −0.426981
$$737$$ 3.25971e25i 0.508126i
$$738$$ −1.07778e26 4.99010e25i −1.65967 0.768426i
$$739$$ 7.21830e24 0.109808 0.0549041 0.998492i $$-0.482515\pi$$
0.0549041 + 0.998492i $$0.482515\pi$$
$$740$$ 8.75650e25i 1.31597i
$$741$$ −1.48894e25 + 6.75972e25i −0.221062 + 1.00361i
$$742$$ −4.99528e25 −0.732697
$$743$$ 4.78088e25i 0.692802i 0.938087 + 0.346401i $$0.112596\pi$$
−0.938087 + 0.346401i $$0.887404\pi$$
$$744$$ 7.25421e25 + 1.59786e25i 1.03856 + 0.228762i
$$745$$ −4.29651e25 −0.607728
$$746$$ 8.28324e25i 1.15758i
$$747$$ −1.67389e25 + 3.61532e25i −0.231122 + 0.499185i
$$748$$ 1.79570e25 0.244974
$$749$$ 1.28442e25i 0.173129i
$$750$$ −2.85348e25 + 1.29546e26i −0.380034 + 1.72533i
$$751$$ −1.09528e26 −1.44134 −0.720670 0.693278i $$-0.756166\pi$$
−0.720670 + 0.693278i $$0.756166\pi$$
$$752$$ 1.41119e26i 1.83496i
$$753$$ 9.53277e25 + 2.09976e25i 1.22480 + 0.269783i
$$754$$ 1.85793e26 2.35878
$$755$$ 3.45527e25i 0.433470i
$$756$$ 2.75378e25 3.61929e25i 0.34