LMFDB - Embedded newform 8.19.d.b.3.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,19,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$16.4308910168$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 56971 x^{14} - 14457953 x^{13} + 5222713963 x^{12} - 1887111404561 x^{11} + \cdots + 32\!\cdots\!30 $ x^16 - 5x^15 + 56971x^14 - 14457953x^13 + 5222713963x^12 - 1887111404561x^11 + 551417417640415x^10 - 120118761233202509x^9 + 30966377422568512537x^8 - 9791029903061915769567x^7 + 2760409144896820517353041x^6 - 573126276959276881630152915x^5 + 113556201106829558152115445753x^4 - 24602953293990202118839424410059x^3 + 5109186069446462658360003036354309x^2 - 959560421721305781394985245626434751*x + 326887106263049715278881269448539579330
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{120}\cdot 3^{13}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.15
Root			$237.992 - 50.3904i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.19.d.b.3.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(501.983 - 100.781i) q^{2} -12665.3 q^{3} +(241830. - 101181. i) q^{4} -2.68543e6i q^{5} +(-6.35775e6 + 1.27642e6i) q^{6} +4.44900e7i q^{7} +(1.11198e8 - 7.51629e7i) q^{8} -2.27011e8 q^{9} +O(q^{10})$	\(q+(501.983 - 100.781i) q^{2} -12665.3 q^{3} +(241830. - 101181. i) q^{4} -2.68543e6i q^{5} +(-6.35775e6 + 1.27642e6i) q^{6} +4.44900e7i q^{7} +(1.11198e8 - 7.51629e7i) q^{8} -2.27011e8 q^{9} +(-2.70640e8 - 1.34804e9i) q^{10} -2.94342e9 q^{11} +(-3.06285e9 + 1.28148e9i) q^{12} -2.11268e10i q^{13} +(4.48374e9 + 2.23333e10i) q^{14} +3.40116e10i q^{15} +(4.82444e10 - 4.89371e10i) q^{16} -8.60555e10 q^{17} +(-1.13956e11 + 2.28784e10i) q^{18} -1.59334e11 q^{19} +(-2.71713e11 - 6.49418e11i) q^{20} -5.63478e11i q^{21} +(-1.47755e12 + 2.96640e11i) q^{22} -8.84583e11i q^{23} +(-1.40835e12 + 9.51958e11i) q^{24} -3.39681e12 q^{25} +(-2.12917e12 - 1.06053e13i) q^{26} +7.78195e12 q^{27} +(4.50153e12 + 1.07590e13i) q^{28} +1.10369e13i q^{29} +(3.42772e12 + 1.70733e13i) q^{30} +9.18771e12i q^{31} +(1.92860e13 - 2.94277e13i) q^{32} +3.72792e13 q^{33} +(-4.31984e13 + 8.67275e12i) q^{34} +1.19475e14 q^{35} +(-5.48983e13 + 2.29692e13i) q^{36} -1.80274e13i q^{37} +(-7.99833e13 + 1.60579e13i) q^{38} +2.67576e14i q^{39} +(-2.01844e14 - 2.98613e14i) q^{40} +4.66778e14 q^{41} +(-5.67878e13 - 2.82857e14i) q^{42} +1.02857e14 q^{43} +(-7.11809e14 + 2.97817e14i) q^{44} +6.09622e14i q^{45} +(-8.91491e13 - 4.44046e14i) q^{46} -1.49713e15i q^{47} +(-6.11029e14 + 6.19802e14i) q^{48} -3.50949e14 q^{49} +(-1.70514e15 + 3.42334e14i) q^{50} +1.08992e15 q^{51} +(-2.13762e15 - 5.10909e15i) q^{52} -4.93584e14i q^{53} +(3.90641e15 - 7.84271e14i) q^{54} +7.90434e15i q^{55} +(3.34400e15 + 4.94719e15i) q^{56} +2.01801e15 q^{57} +(1.11231e15 + 5.54032e15i) q^{58} +1.08985e16 q^{59} +(3.44132e15 + 8.22505e15i) q^{60} -7.51024e15i q^{61} +(9.25946e14 + 4.61208e15i) q^{62} -1.00997e16i q^{63} +(6.71549e15 - 1.67159e16i) q^{64} -5.67343e16 q^{65} +(1.87135e16 - 3.75703e15i) q^{66} -1.79279e16 q^{67} +(-2.08108e16 + 8.70715e15i) q^{68} +1.12035e16i q^{69} +(5.99743e16 - 1.20408e16i) q^{70} -4.48026e16i q^{71} +(-2.52432e16 + 1.70628e16i) q^{72} -5.61569e16 q^{73} +(-1.81681e15 - 9.04944e15i) q^{74} +4.30216e16 q^{75} +(-3.85319e16 + 1.61216e16i) q^{76} -1.30953e17i q^{77} +(2.69665e16 + 1.34319e17i) q^{78} +2.04851e17i q^{79} +(-1.31417e17 - 1.29557e17i) q^{80} -1.06116e16 q^{81} +(2.34315e17 - 4.70423e16i) q^{82} +2.79240e17 q^{83} +(-5.70131e16 - 1.36266e17i) q^{84} +2.31096e17i q^{85} +(5.16327e16 - 1.03661e16i) q^{86} -1.39785e17i q^{87} +(-3.27302e17 + 2.21236e17i) q^{88} -3.39490e17 q^{89} +(6.14383e16 + 3.06020e17i) q^{90} +9.39930e17 q^{91} +(-8.95027e16 - 2.13919e17i) q^{92} -1.16365e17i q^{93} +(-1.50882e17 - 7.51533e17i) q^{94} +4.27881e17i q^{95} +(-2.44262e17 + 3.72710e17i) q^{96} -3.43690e17 q^{97} +(-1.76171e17 + 3.53690e16i) q^{98} +6.68190e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9}+O(q^{10}) $ 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9	$ 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9} - 1569837600 q^{10} - 2471571264 q^{11} + 4764364056 q^{12} + 26163923904 q^{14} - 192320075504 q^{16} - 176439301344 q^{17} - 1044291511122 q^{18} - 833365634368 q^{19} + 1256486405760 q^{20} + 59927319356 q^{22} - 1968891910512 q^{24} - 15320509140080 q^{25} + 4184514840864 q^{26} + 11565649473408 q^{27} - 12301604294400 q^{28} - 36336510039360 q^{30} + 141481742931936 q^{32} - 900457491648 q^{33} + 80653465357268 q^{34} + 20487495736320 q^{35} + 277183098847068 q^{36} + 493456694265564 q^{38} - 519930573603840 q^{40} - 594931562445024 q^{41} - 222362598288000 q^{42} - 25\!\cdots\!92 q^{43}+ \cdots - 81\!\cdots\!68 q^{99}+O(q^{100}) $ 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9 - 1569837600 * q^10 - 2471571264 * q^11 + 4764364056 * q^12 + 26163923904 * q^14 - 192320075504 * q^16 - 176439301344 * q^17 - 1044291511122 * q^18 - 833365634368 * q^19 + 1256486405760 * q^20 + 59927319356 * q^22 - 1968891910512 * q^24 - 15320509140080 * q^25 + 4184514840864 * q^26 + 11565649473408 * q^27 - 12301604294400 * q^28 - 36336510039360 * q^30 + 141481742931936 * q^32 - 900457491648 * q^33 + 80653465357268 * q^34 + 20487495736320 * q^35 + 277183098847068 * q^36 + 493456694265564 * q^38 - 519930573603840 * q^40 - 594931562445024 * q^41 - 222362598288000 * q^42 - 2540155017577792 * q^43 + 73781630442072 * q^44 + 153882272211264 * q^46 + 897135071530464 * q^48 - 3186415704132848 * q^49 + 5668141028706330 * q^50 + 2916050119466880 * q^51 - 4594372123628160 * q^52 - 1377307163285640 * q^54 + 8184134137073664 * q^56 + 9540488340840768 * q^57 - 10505700099162720 * q^58 + 556807886314176 * q^59 + 29677718651516160 * q^60 + 6212402633091840 * q^62 - 56432885385732032 * q^64 - 21153177930524160 * q^65 - 23515570511959320 * q^66 + 162428574934613696 * q^67 - 70717864614203736 * q^68 + 4248100663257600 * q^70 - 36801123950767128 * q^72 - 7655712852492256 * q^73 + 9613779604149984 * q^74 - 384388788469704000 * q^75 - 151130166278324584 * q^76 - 93022771634070720 * q^78 + 26870186366192640 * q^80 + 99506910981790800 * q^81 + 329788507250077556 * q^82 + 866357336138514624 * q^83 + 451843591950574080 * q^84 + 1269201398006865468 * q^86 - 758460699051663856 * q^88 - 883646550464284128 * q^89 - 1227675520905095520 * q^90 - 379834560933460992 * q^91 + 1413121475102841600 * q^92 + 671428514272869504 * q^94 - 483149691255826368 * q^96 - 2614894858526780128 * q^97 - 81635840192738166 * q^98 - 816916348833567168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	501.983	−	100.781i	0.980436	−	0.196838i
$2$	501.983	−	100.781i	0.980436	−	0.196838i
$3$	−12665.3			−0.643462			−0.321731	−	0.946831i	$-0.604265\pi$
$3$	−12665.3			−0.643462			−0.321731	+	0.946831i	$0.604265\pi$
$4$	241830.	−	101181.i	0.922510	−	0.385973i
$5$		−	2.68543e6i		−	1.37494i	−0.726214	−	0.687469i	$-0.758722\pi$
$5$		−	2.68543e6i		−	1.37494i	0.726214	−	0.687469i	$-0.241278\pi$
$6$	−6.35775e6	+	1.27642e6i	−0.630874	+	0.126658i
$7$			4.44900e7i			1.10250i	0.834339	+	0.551252i	$0.185850\pi$
$7$			4.44900e7i			1.10250i	−0.834339	+	0.551252i	$0.814150\pi$
$8$	1.11198e8	−	7.51629e7i	0.828488	−	0.560007i
$9$	−2.27011e8			−0.585956
$10$	−2.70640e8	−	1.34804e9i	−0.270640	−	1.34804i
$11$	−2.94342e9			−1.24830			−0.624149	−	0.781306i	$-0.714554\pi$
$11$	−2.94342e9			−1.24830			−0.624149	+	0.781306i	$0.714554\pi$
$12$	−3.06285e9	+	1.28148e9i	−0.593600	+	0.248359i
$13$		−	2.11268e10i		−	1.99224i	−0.0879818	−	0.996122i	$-0.528042\pi$
$13$		−	2.11268e10i		−	1.99224i	0.0879818	−	0.996122i	$-0.471958\pi$
$14$	4.48374e9	+	2.23333e10i	0.217014	+	1.08094i
$15$			3.40116e10i			0.884721i
$16$	4.82444e10	−	4.89371e10i	0.702049	−	0.712129i
$17$	−8.60555e10			−0.725669			−0.362834	−	0.931854i	$-0.618191\pi$
$17$	−8.60555e10			−0.725669			−0.362834	+	0.931854i	$0.618191\pi$
$18$	−1.13956e11	+	2.28784e10i	−0.574492	+	0.115338i
$19$	−1.59334e11			−0.493773			−0.246887	−	0.969044i	$-0.579407\pi$
$19$	−1.59334e11			−0.493773			−0.246887	+	0.969044i	$0.579407\pi$
$20$	−2.71713e11	−	6.49418e11i	−0.530690	−	1.26839i
$21$		−	5.63478e11i		−	0.709420i
$22$	−1.47755e12	+	2.96640e11i	−1.22388	+	0.245712i
$23$		−	8.84583e11i		−	0.491121i	−0.969381	−	0.245560i	$-0.921028\pi$
$23$		−	8.84583e11i		−	0.491121i	0.969381	−	0.245560i	$-0.0789719\pi$
$24$	−1.40835e12	+	9.51958e11i	−0.533101	+	0.360343i
$25$	−3.39681e12			−0.890455
$26$	−2.12917e12	−	1.06053e13i	−0.392149	−	1.95327i
$27$	7.78195e12			1.02050
$28$	4.50153e12	+	1.07590e13i	0.425537	+	1.01707i
$29$			1.10369e13i			0.760789i	0.924824	+	0.380394i	$0.124212\pi$
$29$			1.10369e13i			0.760789i	−0.924824	+	0.380394i	$0.875788\pi$
$30$	3.42772e12	+	1.70733e13i	0.174146	+	0.867412i
$31$			9.18771e12i			0.347498i	0.984790	+	0.173749i	$0.0555881\pi$
$31$			9.18771e12i			0.347498i	−0.984790	+	0.173749i	$0.944412\pi$
$32$	1.92860e13	−	2.94277e13i	0.548141	−	0.836386i
$33$	3.72792e13			0.803233
$34$	−4.31984e13	+	8.67275e12i	−0.711472	+	0.142839i
$35$	1.19475e14			1.51588
$36$	−5.48983e13	+	2.29692e13i	−0.540550	+	0.226163i
$37$		−	1.80274e13i		−	0.138713i	−0.997592	−	0.0693565i	$-0.977905\pi$
$37$		−	1.80274e13i		−	0.138713i	0.997592	−	0.0693565i	$-0.0220946\pi$
$38$	−7.99833e13	+	1.60579e13i	−0.484113	+	0.0971931i
$39$			2.67576e14i			1.28193i
$40$	−2.01844e14	−	2.98613e14i	−0.769975	−	1.13912i
$41$	4.66778e14			1.42579			0.712896	−	0.701270i	$-0.247383\pi$
$41$	4.66778e14			1.42579			0.712896	+	0.701270i	$0.247383\pi$
$42$	−5.67878e13	−	2.82857e14i	−0.139641	−	0.695541i
$43$	1.02857e14			0.204653			0.102327	−	0.994751i	$-0.467371\pi$
$43$	1.02857e14			0.204653			0.102327	+	0.994751i	$0.467371\pi$
$44$	−7.11809e14	+	2.97817e14i	−1.15157	+	0.481810i
$45$			6.09622e14i			0.805653i
$46$	−8.91491e13	−	4.44046e14i	−0.0966710	−	0.481512i
$47$		−	1.49713e15i		−	1.33776i	−0.743370	−	0.668880i	$-0.766774\pi$
$47$		−	1.49713e15i		−	1.33776i	0.743370	−	0.668880i	$-0.233226\pi$
$48$	−6.11029e14	+	6.19802e14i	−0.451742	+	0.458228i
$49$	−3.50949e14			−0.215516
$50$	−1.70514e15	+	3.42334e14i	−0.873034	+	0.175275i
$51$	1.08992e15			0.466941
$52$	−2.13762e15	−	5.10909e15i	−0.768953	−	1.83786i
$53$		−	4.93584e14i		−	0.149582i	−0.997199	−	0.0747908i	$-0.976171\pi$
$53$		−	4.93584e14i		−	0.149582i	0.997199	−	0.0747908i	$-0.0238289\pi$
$54$	3.90641e15	−	7.84271e14i	1.00054	−	0.200873i
$55$			7.90434e15i			1.71633i
$56$	3.34400e15	+	4.94719e15i	0.617410	+	0.913412i
$57$	2.01801e15			0.317724
$58$	1.11231e15	+	5.54032e15i	0.149752	+	0.745905i
$59$	1.08985e16			1.25805			0.629024	−	0.777386i	$-0.283455\pi$
$59$	1.08985e16			1.25805			0.629024	+	0.777386i	$0.283455\pi$
$60$	3.44132e15	+	8.22505e15i	0.341479	+	0.816164i
$61$		−	7.51024e15i		−	0.642222i	−0.947042	−	0.321111i	$-0.895944\pi$
$61$		−	7.51024e15i		−	0.642222i	0.947042	−	0.321111i	$-0.104056\pi$
$62$	9.25946e14	+	4.61208e15i	0.0684007	+	0.340699i
$63$		−	1.00997e16i		−	0.646019i
$64$	6.71549e15	−	1.67159e16i	0.372784	−	0.927918i
$65$	−5.67343e16			−2.73921
$66$	1.87135e16	−	3.75703e15i	0.787518	−	0.158106i
$67$	−1.79279e16			−0.658957			−0.329478	−	0.944163i	$-0.606873\pi$
$67$	−1.79279e16			−0.658957			−0.329478	+	0.944163i	$0.606873\pi$
$68$	−2.08108e16	+	8.70715e15i	−0.669436	+	0.280089i
$69$			1.12035e16i			0.316018i
$70$	5.99743e16	−	1.20408e16i	1.48622	−	0.298381i
$71$		−	4.48026e16i		−	0.977187i	−0.872511	−	0.488594i	$-0.837510\pi$
$71$		−	4.48026e16i		−	0.977187i	0.872511	−	0.488594i	$-0.162490\pi$
$72$	−2.52432e16	+	1.70628e16i	−0.485458	+	0.328139i
$73$	−5.61569e16			−0.953888			−0.476944	−	0.878934i	$-0.658255\pi$
$73$	−5.61569e16			−0.953888			−0.476944	+	0.878934i	$0.658255\pi$
$74$	−1.81681e15	−	9.04944e15i	−0.0273039	−	0.135999i
$75$	4.30216e16			0.572974
$76$	−3.85319e16	+	1.61216e16i	−0.455511	+	0.190583i
$77$		−	1.30953e17i		−	1.37625i
$78$	2.69665e16	+	1.34319e17i	0.252333	+	1.25685i
$79$			2.04851e17i			1.70921i	0.519282	+	0.854603i	$0.326199\pi$
$79$			2.04851e17i			1.70921i	−0.519282	+	0.854603i	$0.673801\pi$
$80$	−1.31417e17	−	1.29557e17i	−0.979133	−	0.965274i
$81$	−1.06116e16			−0.0706994
$82$	2.34315e17	−	4.70423e16i	1.39790	−	0.280649i
$83$	2.79240e17			1.49374			0.746869	−	0.664971i	$-0.231556\pi$
$83$	2.79240e17			1.49374			0.746869	+	0.664971i	$0.231556\pi$
$84$	−5.70131e16	−	1.36266e17i	−0.273817	−	0.654447i
$85$			2.31096e17i			0.997749i
$86$	5.16327e16	−	1.03661e16i	0.200650	−	0.0402835i
$87$		−	1.39785e17i		−	0.489539i
$88$	−3.27302e17	+	2.21236e17i	−1.03420	+	0.699055i
$89$	−3.39490e17			−0.968986			−0.484493	−	0.874795i	$-0.660996\pi$
$89$	−3.39490e17			−0.968986			−0.484493	+	0.874795i	$0.660996\pi$
$90$	6.14383e16	+	3.06020e17i	0.158583	+	0.789892i
$91$	9.39930e17			2.19646
$92$	−8.95027e16	−	2.13919e17i	−0.189560	−	0.453064i
$93$		−	1.16365e17i		−	0.223602i
$94$	−1.50882e17	−	7.51533e17i	−0.263322	−	1.31159i
$95$			4.27881e17i			0.678907i
$96$	−2.44262e17	+	3.72710e17i	−0.352708	+	0.538183i
$97$	−3.43690e17			−0.452086			−0.226043	−	0.974117i	$-0.572579\pi$
$97$	−3.43690e17			−0.452086			−0.226043	+	0.974117i	$0.572579\pi$
$98$	−1.76171e17	+	3.53690e16i	−0.211300	+	0.0424217i
$99$	6.68190e17			0.731448
$100$	−8.21453e17	+	3.43692e17i	−0.821453	+	0.343692i
$101$		−	7.98203e16i		−	0.0729828i	−0.999334	−	0.0364914i	$-0.988382\pi$
$101$		−	7.98203e16i		−	0.0729828i	0.999334	−	0.0364914i	$-0.0116182\pi$
$102$	5.47120e17	−	1.09843e17i	0.457805	−	0.0919115i
$103$		−	1.40625e17i		−	0.107777i	−0.998547	−	0.0538887i	$-0.982838\pi$
$103$		−	1.40625e17i		−	0.107777i	0.998547	−	0.0538887i	$-0.0171616\pi$
$104$	−1.58795e18	−	2.34925e18i	−1.11567	−	1.65055i
$105$	−1.51318e18			−0.975409
$106$	−4.97438e16	−	2.47771e17i	−0.0294433	−	0.146655i
$107$	−1.37814e18			−0.749617			−0.374809	−	0.927102i	$-0.622292\pi$
$107$	−1.37814e18			−0.749617			−0.374809	+	0.927102i	$0.622292\pi$
$108$	1.88191e18	−	7.87382e17i	0.941424	−	0.393887i
$109$		−	2.21708e18i		−	1.02080i	−0.859936	−	0.510402i	$-0.829496\pi$
$109$		−	2.21708e18i		−	1.02080i	0.859936	−	0.510402i	$-0.170504\pi$
$110$	7.96606e17	+	3.96784e18i	0.337839	+	1.68275i
$111$			2.28322e17i			0.0892566i
$112$	2.17721e18	+	2.14640e18i	0.785125	+	0.774012i
$113$	1.42945e18			0.475841			0.237920	−	0.971285i	$-0.423534\pi$
$113$	1.42945e18			0.475841			0.237920	+	0.971285i	$0.423534\pi$
$114$	1.01301e18	−	2.03377e17i	0.311509	−	0.0625401i
$115$	−2.37548e18			−0.675261
$116$	1.11672e18	+	2.66905e18i	0.293644	+	0.701835i
$117$			4.79601e18i			1.16737i
$118$	5.47084e18	−	1.09836e18i	1.23343	−	0.247631i
$119$		−	3.82861e18i		−	0.800053i
$120$	2.55641e18	+	3.78202e18i	0.495450	+	0.732981i
$121$	3.10381e18			0.558247
$122$	−7.56888e17	−	3.77001e18i	−0.126413	−	0.629658i
$123$	−5.91188e18			−0.917443
$124$	9.29618e17	+	2.22187e18i	0.134125	+	0.320570i
$125$		−	1.12219e18i		−	0.150618i
$126$	−1.01786e18	−	5.06990e18i	−0.127161	−	0.633381i
$127$			4.50211e18i			0.523821i	0.965092	+	0.261910i	$0.0843525\pi$
$127$			4.50211e18i			0.523821i	−0.965092	+	0.261910i	$0.915648\pi$
$128$	1.68642e18	−	9.06789e18i	0.182842	−	0.983142i
$129$	−1.30272e18			−0.131687
$130$	−2.84797e19	+	5.71773e18i	−2.68562	+	0.539180i
$131$	−3.38528e18			−0.297957			−0.148978	−	0.988840i	$-0.547598\pi$
$131$	−3.38528e18			−0.297957			−0.148978	+	0.988840i	$0.547598\pi$
$132$	9.01525e18	−	3.77193e18i	0.740990	−	0.310026i
$133$		−	7.08880e18i		−	0.544387i
$134$	−8.99952e18	+	1.80679e18i	−0.646065	+	0.129708i
$135$		−	2.08978e19i		−	1.40313i
$136$	−9.56918e18	+	6.46818e18i	−0.601208	+	0.406379i
$137$	2.39494e19			1.40867			0.704335	−	0.709868i	$-0.251245\pi$
$137$	2.39494e19			1.40867			0.704335	+	0.709868i	$0.251245\pi$
$138$	1.12910e18	+	5.62396e18i	0.0622042	+	0.309835i
$139$	−1.06784e19			−0.551280			−0.275640	−	0.961261i	$-0.588890\pi$
$139$	−1.06784e19			−0.551280			−0.275640	+	0.961261i	$0.588890\pi$
$140$	2.88926e19	−	1.20885e19i	1.39841	−	0.585088i
$141$			1.89615e19i			0.860798i
$142$	−4.51524e18	−	2.24901e19i	−0.192347	−	0.958070i
$143$			6.21849e19i			2.48691i
$144$	−1.09520e19	+	1.11093e19i	−0.411370	+	0.417276i
$145$	2.96387e19			1.04604
$146$	−2.81898e19	+	5.65954e18i	−0.935226	+	0.187761i
$147$	4.44487e18			0.138676
$148$	−1.82402e18	−	4.35957e18i	−0.0535395	−	0.127964i
$149$		−	9.35207e18i		−	0.258364i	−0.991621	−	0.129182i	$-0.958765\pi$
$149$		−	9.35207e18i		−	0.258364i	0.991621	−	0.129182i	$-0.0412351\pi$
$150$	2.15961e19	−	4.33575e18i	0.561764	−	0.112783i
$151$		−	8.06556e19i		−	1.97625i	−0.153653	−	0.988125i	$-0.549104\pi$
$151$		−	8.06556e19i		−	1.97625i	0.153653	−	0.988125i	$-0.450896\pi$
$152$	−1.77176e19	+	1.19760e19i	−0.409085	+	0.276516i
$153$	1.95356e19			0.425210
$154$	−1.31975e19	−	6.57361e19i	−0.270898	−	1.34933i
$155$	2.46729e19			0.477788
$156$	2.70735e19	+	6.47080e19i	0.494793	+	1.18260i
$157$			8.10808e19i			1.39901i	0.714628	+	0.699505i	$0.246596\pi$
$157$			8.10808e19i			1.39901i	−0.714628	+	0.699505i	$0.753404\pi$
$158$	2.06451e19	+	1.02832e20i	0.336436	+	1.67577i
$159$			6.25138e18i			0.0962502i
$160$	−7.90260e19	−	5.17911e19i	−1.14998	−	0.753659i
$161$	3.93551e19			0.541463
$162$	−5.32685e18	+	1.06945e18i	−0.0693162	+	0.0139163i
$163$	−9.02626e19			−1.11127			−0.555635	−	0.831426i	$-0.687525\pi$
$163$	−9.02626e19			−1.11127			−0.555635	+	0.831426i	$0.687525\pi$
$164$	1.12881e20	−	4.72289e19i	1.31531	−	0.550318i
$165$		−	1.00111e20i		−	1.10440i
$166$	1.40174e20	−	2.81420e19i	1.46451	−	0.294024i
$167$			1.06287e20i			1.05204i	0.850472	+	0.526020i	$0.176316\pi$
$167$			1.06287e20i			1.05204i	−0.850472	+	0.526020i	$0.823684\pi$
$168$	−4.23526e19	−	6.26575e19i	−0.397280	−	0.587746i
$169$	−3.33884e20			−2.96904
$170$	2.32900e19	+	1.16006e20i	0.196395	+	0.978230i
$171$	3.61707e19			0.289329
$172$	2.48740e19	−	1.04072e19i	0.188795	−	0.0789908i
$173$		−	2.24021e20i		−	1.61389i	−0.590625	−	0.806946i	$-0.701119\pi$
$173$		−	2.24021e20i		−	1.61389i	0.590625	−	0.806946i	$-0.298881\pi$
$174$	−1.40876e19	−	7.01697e19i	−0.0963597	−	0.479962i
$175$		−	1.51124e20i		−	0.981730i
$176$	−1.42004e20	+	1.44042e20i	−0.876366	+	0.888948i
$177$	−1.38032e20			−0.809506
$178$	−1.70418e20	+	3.42141e19i	−0.950028	+	0.190733i
$179$	1.56197e20			0.827933			0.413966	−	0.910292i	$-0.364143\pi$
$179$	1.56197e20			0.827933			0.413966	+	0.910292i	$0.364143\pi$
$180$	6.16820e19	+	1.47425e20i	0.310961	+	0.743223i
$181$			1.17040e20i			0.561340i	0.959804	+	0.280670i	$0.0905567\pi$
$181$			1.17040e20i			0.561340i	−0.959804	+	0.280670i	$0.909443\pi$
$182$	4.71829e20	−	9.47269e19i	2.15349	−	0.432346i
$183$			9.51192e19i			0.413246i
$184$	−6.64878e19	−	9.83637e19i	−0.275031	−	0.406888i
$185$	−4.84112e19			−0.190722
$186$	−1.17274e19	−	5.84132e19i	−0.0440133	−	0.219227i
$187$	2.53298e20			0.905850
$188$	−1.51480e20	−	3.62051e20i	−0.516340	−	1.23410i
$189$			3.46219e20i			1.12511i
$190$	4.31222e19	+	2.14789e20i	0.133635	+	0.665625i
$191$		−	3.58893e18i		−	0.0106088i	−0.999986	−	0.00530438i	$-0.998312\pi$
$191$		−	3.58893e18i		−	0.0106088i	0.999986	−	0.00530438i	$-0.00168844\pi$
$192$	−8.50535e19	+	2.11711e20i	−0.239873	+	0.597080i
$193$	1.20630e20			0.324667			0.162333	−	0.986736i	$-0.448098\pi$
$193$	1.20630e20			0.324667			0.162333	+	0.986736i	$0.448098\pi$
$194$	−1.72526e20	+	3.46373e19i	−0.443241	+	0.0889875i
$195$	7.18556e20			1.76258
$196$	−8.48702e19	+	3.55093e19i	−0.198816	+	0.0831835i
$197$			1.51447e20i			0.338895i	0.985539	+	0.169448i	$0.0541983\pi$
$197$			1.51447e20i			0.338895i	−0.985539	+	0.169448i	$0.945802\pi$
$198$	3.35420e20	−	6.73408e19i	0.717138	−	0.143976i
$199$			3.00723e20i			0.614453i	0.951636	+	0.307227i	$0.0994009\pi$
$199$			3.00723e20i			0.614453i	−0.951636	+	0.307227i	$0.900599\pi$
$200$	−3.77718e20	+	2.55314e20i	−0.737731	+	0.498661i
$201$	2.27062e20			0.424014
$202$	−8.04435e18	−	4.00684e19i	−0.0143658	−	0.0715550i
$203$	−4.91031e20			−0.838773
$204$	2.63575e20	−	1.10278e20i	0.430757	−	0.180227i
$205$		−	1.25350e21i		−	1.96037i
$206$	−1.41723e19	−	7.05915e19i	−0.0212147	−	0.105669i
$207$			2.00810e20i			0.287775i
$208$	−1.03388e21	−	1.01925e21i	−1.41873	−	1.39865i
$209$	4.68988e20			0.616376
$210$	−7.59591e20	+	1.52500e20i	−0.956326	+	0.191997i
$211$	−1.12875e21			−1.36162			−0.680809	−	0.732461i	$-0.738372\pi$
$211$	−1.12875e21			−1.36162			−0.680809	+	0.732461i	$0.738372\pi$
$212$	−4.99411e19	−	1.19364e20i	−0.0577345	−	0.137991i
$213$			5.67437e20i			0.628783i
$214$	−6.91804e20	+	1.38890e20i	−0.734952	+	0.147553i
$215$		−	2.76216e20i		−	0.281386i
$216$	8.65335e20	−	5.84913e20i	0.845475	−	0.571489i
$217$	−4.08762e20			−0.383118
$218$	−2.23439e20	−	1.11294e21i	−0.200933	−	1.00083i
$219$	7.11242e20			0.613791
$220$	7.99766e20	+	1.91151e21i	0.662458	+	1.58333i
$221$			1.81807e21i			1.44571i
$222$	2.30104e19	+	1.14614e20i	0.0175690	+	0.0875104i
$223$		−	1.82552e21i		−	1.33857i	−0.743004	−	0.669287i	$-0.766600\pi$
$223$		−	1.82552e21i		−	1.33857i	0.743004	−	0.669287i	$-0.233400\pi$
$224$	1.30924e21	+	8.58034e20i	0.922120	+	0.604327i
$225$	7.71116e20			0.521767
$226$	7.17558e20	−	1.44061e20i	0.466531	−	0.0936634i
$227$	−2.05517e20			−0.128415			−0.0642074	−	0.997937i	$-0.520452\pi$
$227$	−2.05517e20			−0.128415			−0.0642074	+	0.997937i	$0.520452\pi$
$228$	4.88017e20	−	2.04184e20i	0.293104	−	0.122633i
$229$		−	6.25364e20i		−	0.361088i	−0.983567	−	0.180544i	$-0.942214\pi$
$229$		−	6.25364e20i		−	0.361088i	0.983567	−	0.180544i	$-0.0577859\pi$
$230$	−1.19245e21	+	2.39403e20i	−0.662050	+	0.132917i
$231$			1.65855e21i			0.885567i
$232$	8.29563e20	+	1.22728e21i	0.426047	+	0.630304i
$233$	−2.31164e20			−0.114213			−0.0571067	−	0.998368i	$-0.518188\pi$
$233$	−2.31164e20			−0.114213			−0.0571067	+	0.998368i	$0.518188\pi$
$234$	4.83346e20	+	2.40752e21i	0.229782	+	1.14453i
$235$	−4.02043e21			−1.83934
$236$	2.63558e21	−	1.10271e21i	1.16056	−	0.485573i
$237$		−	2.59449e21i		−	1.09981i
$238$	−3.85851e20	−	1.92190e21i	−0.157481	−	0.784401i
$239$		−	1.72110e21i		−	0.676434i	−0.941068	−	0.338217i	$-0.890176\pi$
$239$		−	1.72110e21i		−	0.676434i	0.941068	−	0.338217i	$-0.109824\pi$
$240$	1.66443e21	+	1.64087e21i	0.630035	+	0.621118i
$241$	2.95295e21			1.07672			0.538361	−	0.842714i	$-0.319044\pi$
$241$	2.95295e21			1.07672			0.538361	+	0.842714i	$0.319044\pi$
$242$	1.55806e21	−	3.12804e20i	0.547325	−	0.109884i
$243$	−2.88049e21			−0.975011
$244$	−7.59890e20	−	1.81620e21i	−0.247881	−	0.592456i
$245$			9.42448e20i			0.296321i
$246$	−2.96766e21	+	5.95804e20i	−0.899495	+	0.180587i
$247$			3.36622e21i			0.983717i
$248$	6.90575e20	+	1.02165e21i	0.194601	+	0.287898i
$249$	−3.53665e21			−0.961164
$250$	−1.13096e20	−	5.63322e20i	−0.0296473	−	0.147672i
$251$	2.14776e21			0.543152			0.271576	−	0.962417i	$-0.412455\pi$
$251$	2.14776e21			0.543152			0.271576	+	0.962417i	$0.412455\pi$
$252$	−1.02190e21	−	2.44243e21i	−0.249346	−	0.595959i
$253$			2.60370e21i			0.613065i
$254$	4.53727e20	+	2.25998e21i	0.103108	+	0.513573i
$255$		−	2.92689e21i		−	0.642014i
$256$	−6.73142e19	−	4.72189e21i	−0.0142543	−	0.999898i
$257$	7.99301e21			1.63423			0.817113	−	0.576477i	$-0.195573\pi$
$257$	7.99301e21			1.63423			0.817113	+	0.576477i	$0.195573\pi$
$258$	−6.53942e20	+	1.31289e20i	−0.129111	+	0.0259209i
$259$	8.02038e20			0.152932
$260$	−1.37201e22	+	5.74041e21i	−2.52695	+	1.05726i
$261$		−	2.50550e21i		−	0.445789i
$262$	−1.69935e21	+	3.41172e20i	−0.292128	+	0.0586491i
$263$		−	6.40199e21i		−	1.06344i	−0.846920	−	0.531720i	$-0.821546\pi$
$263$		−	6.40199e21i		−	1.06344i	0.846920	−	0.531720i	$-0.178454\pi$
$264$	4.14537e21	−	2.80201e21i	0.665468	−	0.449816i
$265$	−1.32548e21			−0.205666
$266$	−7.14415e20	−	3.55846e21i	−0.107156	−	0.533737i
$267$	4.29974e21			0.623506
$268$	−4.33552e21	+	1.81396e21i	−0.607894	+	0.254340i
$269$			7.41151e21i			1.00493i	0.864597	+	0.502466i	$0.167574\pi$
$269$			7.41151e21i			1.00493i	−0.864597	+	0.502466i	$0.832426\pi$
$270$	−2.10610e21	−	1.04904e22i	−0.276189	−	1.37568i
$271$			1.26338e22i			1.60254i	0.598303	+	0.801270i	$0.295842\pi$
$271$			1.26338e22i			1.60254i	−0.598303	+	0.801270i	$0.704158\pi$
$272$	−4.15170e21	+	4.21131e21i	−0.509455	+	0.516769i
$273$	−1.19045e22			−1.41334
$274$	1.20222e22	−	2.41364e21i	1.38111	−	0.277279i
$275$	9.99825e21			1.11155
$276$	1.13358e21	+	2.70934e21i	0.121974	+	0.291529i
$277$		−	5.91364e21i		−	0.615938i	−0.951396	−	0.307969i	$-0.900351\pi$
$277$		−	5.91364e21i		−	0.615938i	0.951396	−	0.307969i	$-0.0996493\pi$
$278$	−5.36037e21	+	1.07618e21i	−0.540495	+	0.108513i
$279$		−	2.08572e21i		−	0.203618i
$280$	1.32853e22	−	8.98006e21i	1.25588	−	0.848901i
$281$	2.61871e21			0.239735			0.119867	−	0.992790i	$-0.461753\pi$
$281$	2.61871e21			0.239735			0.119867	+	0.992790i	$0.461753\pi$
$282$	1.91096e21	+	9.51837e21i	0.169438	+	0.843958i
$283$	1.68013e22			1.44299			0.721496	−	0.692419i	$-0.243455\pi$
$283$	1.68013e22			1.44299			0.721496	+	0.692419i	$0.243455\pi$
$284$	−4.53315e21	−	1.08346e22i	−0.377168	−	0.901465i
$285$		−	5.41923e21i		−	0.436851i
$286$	6.26705e21	+	3.12158e22i	0.489518	+	2.43826i
$287$			2.07670e22i			1.57194i
$288$	−4.37814e21	+	6.68043e21i	−0.321186	+	0.490086i
$289$	−6.65753e21			−0.473405
$290$	1.48781e22	−	2.98701e21i	1.02557	−	0.205899i
$291$	4.35292e21			0.290900
$292$	−1.35804e22	+	5.68199e21i	−0.879971	+	0.368175i
$293$		−	4.39868e21i		−	0.276384i	−0.990405	−	0.138192i	$-0.955871\pi$
$293$		−	4.39868e21i		−	0.276384i	0.990405	−	0.138192i	$-0.0441292\pi$
$294$	2.23125e21	−	4.47958e20i	0.135963	−	0.0272968i
$295$		−	2.92670e22i		−	1.72974i
$296$	−1.35499e21	−	2.00460e21i	−0.0776802	−	0.114922i
$297$	−2.29055e22			−1.27389
$298$	−9.42510e20	−	4.69459e21i	−0.0508557	−	0.253309i
$299$	−1.86884e22			−0.978432
$300$	1.04039e22	−	4.35295e21i	0.528574	−	0.221153i
$301$			4.57613e21i			0.225631i
$302$	−8.12854e21	−	4.04877e22i	−0.389000	−	1.93759i
$303$			1.01095e21i			0.0469617i
$304$	−7.68700e21	+	7.79737e21i	−0.346653	+	0.351630i
$305$	−2.01682e22			−0.883015
$306$	9.80653e21	−	1.96881e21i	0.416891	−	0.0836973i
$307$	−1.52880e22			−0.631111			−0.315556	−	0.948907i	$-0.602191\pi$
$307$	−1.52880e22			−0.631111			−0.315556	+	0.948907i	$0.602191\pi$
$308$	−1.32499e22	−	3.16684e22i	−0.531197	−	1.26961i
$309$			1.78106e21i			0.0693508i
$310$	1.23854e22	−	2.48656e21i	0.468441	−	0.0940467i
$311$			9.54897e20i			0.0350843i	0.999846	+	0.0175422i	$0.00558413\pi$
$311$			9.54897e20i			0.0350843i	−0.999846	+	0.0175422i	$0.994416\pi$
$312$	2.01118e22	+	2.97539e22i	0.717892	+	1.06207i
$313$	1.37281e22			0.476113			0.238056	−	0.971251i	$-0.423490\pi$
$313$	1.37281e22			0.476113			0.238056	+	0.971251i	$0.423490\pi$
$314$	8.17139e21	+	4.07012e22i	0.275378	+	1.37164i
$315$	−2.71221e22			−0.888236
$316$	2.07270e22	+	4.95392e22i	0.659708	+	1.57676i
$317$		−	4.06545e22i		−	1.25769i	−0.777529	−	0.628847i	$-0.783527\pi$
$317$		−	4.06545e22i		−	1.25769i	0.777529	−	0.628847i	$-0.216473\pi$
$318$	6.30019e20	+	3.13809e21i	0.0189457	+	0.0943672i
$319$		−	3.24862e22i		−	0.949691i
$320$	−4.48893e22	−	1.80339e22i	−1.27583	−	0.512556i
$321$	1.74545e22			0.482351
$322$	1.97556e22	−	3.96625e21i	0.530870	−	0.106580i
$323$	1.37116e22			0.358316
$324$	−2.56621e21	+	1.07369e21i	−0.0652209	+	0.0272881i
$325$			7.17637e22i			1.77400i
$326$	−4.53103e22	+	9.09674e21i	−1.08953	+	0.218740i
$327$			2.80799e22i			0.656849i
$328$	5.19047e22	−	3.50844e22i	1.18125	−	0.798453i
$329$	6.66073e22			1.47489
$330$	−1.00892e22	−	5.02538e22i	−0.217386	−	1.08279i
$331$	2.00289e22			0.419957			0.209978	−	0.977706i	$-0.432661\pi$
$331$	2.00289e22			0.419957			0.209978	+	0.977706i	$0.432661\pi$
$332$	6.75287e22	−	2.82536e22i	1.37799	−	0.576543i
$333$			4.09242e21i			0.0812797i
$334$	1.07117e22	+	5.33544e22i	0.207081	+	1.03146i
$335$			4.81441e22i			0.906025i
$336$	−2.75750e22	−	2.71847e22i	−0.505198	−	0.498048i
$337$	4.06151e22			0.724467			0.362233	−	0.932087i	$-0.382014\pi$
$337$	4.06151e22			0.724467			0.362233	+	0.932087i	$0.382014\pi$
$338$	−1.67604e23	+	3.36491e22i	−2.91095	+	0.584418i
$339$	−1.81043e22			−0.306186
$340$	2.33824e22	+	5.58860e22i	0.385105	+	0.920434i
$341$		−	2.70433e22i		−	0.433781i
$342$	1.81571e22	−	3.64532e21i	0.283669	−	0.0569509i
$343$			5.68344e22i			0.864897i
$344$	1.14375e22	−	7.73105e21i	0.169553	−	0.114607i
$345$	3.00861e22			0.434505
$346$	−2.25771e22	−	1.12455e23i	−0.317675	−	1.58232i
$347$	3.95355e22			0.542029			0.271014	−	0.962575i	$-0.412641\pi$
$347$	3.95355e22			0.542029			0.271014	+	0.962575i	$0.412641\pi$
$348$	−1.41435e22	−	3.38043e22i	−0.188949	−	0.451604i
$349$		−	1.46940e22i		−	0.191299i	−0.995415	−	0.0956494i	$-0.969507\pi$
$349$		−	1.46940e22i		−	0.191299i	0.995415	−	0.0956494i	$-0.0304928\pi$
$350$	−1.52304e22	−	7.58619e22i	−0.193241	−	0.962524i
$351$		−	1.64407e23i		−	2.03309i
$352$	−5.67667e22	+	8.66182e22i	−0.684242	+	1.04406i
$353$	5.44723e22			0.640035			0.320017	−	0.947412i	$-0.396311\pi$
$353$	5.44723e22			0.640035			0.320017	+	0.947412i	$0.396311\pi$
$354$	−6.92897e22	+	1.39110e22i	−0.793669	+	0.159341i
$355$	−1.20314e23			−1.34357
$356$	−8.20991e22	+	3.43498e22i	−0.893899	+	0.374003i
$357$			4.84904e22i			0.514804i
$358$	7.84082e22	−	1.57417e22i	0.811735	−	0.162968i
$359$		−	2.10530e22i		−	0.212551i	−0.994337	−	0.106276i	$-0.966107\pi$
$359$		−	2.10530e22i		−	0.212551i	0.994337	−	0.106276i	$-0.0338926\pi$
$360$	4.58210e22	+	6.77886e22i	0.451171	+	0.667474i
$361$	−7.87399e22			−0.756188
$362$	1.17954e22	+	5.87520e22i	0.110493	+	0.550358i
$363$	−3.93105e22			−0.359211
$364$	2.27304e23	−	9.51027e22i	2.02625	−	0.847774i
$365$			1.50805e23i			1.31154i
$366$	9.58619e21	+	4.77482e22i	0.0813423	+	0.405161i
$367$			4.38943e22i			0.363424i	0.983352	+	0.181712i	$0.0581639\pi$
$367$			4.38943e22i			0.363424i	−0.983352	+	0.181712i	$0.941836\pi$
$368$	−4.32889e22	−	4.26762e22i	−0.349741	−	0.344791i
$369$	−1.05964e23			−0.835451
$370$	−2.43016e22	+	4.87892e21i	−0.186990	+	0.0375412i
$371$	2.19596e22			0.164914
$372$	−1.17739e22	−	2.81406e22i	−0.0863044	−	0.206275i
$373$		−	2.58068e23i		−	1.84652i	−0.384172	−	0.923262i	$-0.625513\pi$
$373$		−	2.58068e23i		−	1.84652i	0.384172	−	0.923262i	$-0.374487\pi$
$374$	1.27151e23	−	2.55275e22i	0.888128	−	0.178305i
$375$			1.42129e22i			0.0969172i
$376$	−1.12528e23	−	1.66477e23i	−0.749155	−	1.10832i
$377$	2.33173e23			1.51568
$378$	3.48923e22	+	1.73796e23i	0.221464	+	1.10310i
$379$	−1.19927e23			−0.743303			−0.371651	−	0.928372i	$-0.621208\pi$
$379$	−1.19927e23			−0.743303			−0.371651	+	0.928372i	$0.621208\pi$
$380$	4.32933e22	+	1.03475e23i	0.262040	+	0.626299i
$381$		−	5.70204e22i		−	0.337059i
$382$	−3.61696e20	−	1.80158e21i	−0.00208820	−	0.0104012i
$383$			1.31343e22i			0.0740656i	0.999314	+	0.0370328i	$0.0117906\pi$
$383$			1.31343e22i			0.0740656i	−0.999314	+	0.0370328i	$0.988209\pi$
$384$	−2.13590e22	+	1.14847e23i	−0.117652	+	0.632615i
$385$	−3.51664e23			−1.89226
$386$	6.05540e22	−	1.21572e22i	0.318315	−	0.0639067i
$387$	−2.33498e22			−0.119918
$388$	−8.31146e22	+	3.47747e22i	−0.417054	+	0.174493i
$389$			9.26572e22i			0.454289i	0.973861	+	0.227145i	$0.0729390\pi$
$389$			9.26572e22i			0.454289i	−0.973861	+	0.227145i	$0.927061\pi$
$390$	3.60703e23	−	7.24167e22i	1.72810	−	0.346942i
$391$			7.61233e22i			0.356391i
$392$	−3.90248e22	+	2.63784e22i	−0.178552	+	0.120690i
$393$	4.28755e22			0.191724
$394$	1.52630e22	+	7.60240e22i	0.0667073	+	0.332265i
$395$	5.50112e23			2.35005
$396$	1.61589e23	−	6.76079e22i	0.674768	−	0.282319i
$397$		−	1.32229e23i		−	0.539774i	−0.962892	−	0.269887i	$-0.913014\pi$
$397$		−	1.32229e23i		−	0.539774i	0.962892	−	0.269887i	$-0.0869864\pi$
$398$	3.03071e22	+	1.50958e23i	0.120947	+	0.602432i
$399$			8.97815e22i			0.350293i
$400$	−1.63877e23	+	1.66230e23i	−0.625143	+	0.634118i
$401$	−2.14899e23			−0.801558			−0.400779	−	0.916175i	$-0.631260\pi$
$401$	−2.14899e23			−0.801558			−0.400779	+	0.916175i	$0.631260\pi$
$402$	1.13981e23	−	2.28835e22i	0.415719	−	0.0834619i
$403$	1.94107e23			0.692301
$404$	−8.07626e21	−	1.93030e22i	−0.0281694	−	0.0673274i
$405$			2.84967e22i			0.0972073i
$406$	−2.46489e23	+	4.94865e22i	−0.822363	+	0.165102i
$407$			5.30621e22i			0.173155i
$408$	1.21196e23	−	8.19212e22i	0.386855	−	0.261490i
$409$	−5.51664e23			−1.72252			−0.861261	−	0.508163i	$-0.830325\pi$
$409$	−5.51664e23			−1.72252			−0.861261	+	0.508163i	$0.830325\pi$
$410$	−1.26329e23	−	6.29235e23i	−0.385876	−	1.92202i
$411$	−3.03325e23			−0.906426
$412$	−1.42285e22	−	3.40074e22i	−0.0415992	−	0.0994258i
$413$			4.84873e23i			1.38700i
$414$	2.02379e22	+	1.00804e23i	0.0566450	+	0.282145i
$415$		−	7.49877e23i		−	2.05380i
$416$	−6.21712e23	−	4.07450e23i	−1.66629	−	1.09203i
$417$	1.35245e23			0.354728
$418$	2.35424e23	−	4.72651e22i	0.604317	−	0.121326i
$419$	4.60477e23			1.15686			0.578432	−	0.815731i	$-0.303665\pi$
$419$	4.60477e23			1.15686			0.578432	+	0.815731i	$0.303665\pi$
$420$	−3.65933e23	+	1.53104e23i	−0.899824	+	0.376482i
$421$		−	2.24835e23i		−	0.541160i	−0.962698	−	0.270580i	$-0.912785\pi$
$421$		−	2.24835e23i		−	0.541160i	0.962698	−	0.270580i	$-0.0872154\pi$
$422$	−5.66613e23	+	1.13756e23i	−1.33498	+	0.268018i
$423$			3.39865e23i			0.783869i
$424$	−3.70992e22	−	5.48855e22i	−0.0837668	−	0.123927i
$425$	2.92315e23			0.646175
$426$	5.71868e22	+	2.84844e23i	0.123768	+	0.616482i
$427$	3.34131e23			0.708052
$428$	−3.33276e23	+	1.39441e23i	−0.691529	+	0.289332i
$429$		−	7.87589e23i		−	1.60024i
$430$	−2.78373e22	−	1.38656e23i	−0.0553873	−	0.275881i
$431$			9.35443e23i			1.82273i	0.411602	+	0.911364i	$0.364969\pi$
$431$			9.35443e23i			1.82273i	−0.411602	+	0.911364i	$0.635031\pi$
$432$	3.75436e23	−	3.80826e23i	0.716443	−	0.726730i
$433$	6.55984e23			1.22603			0.613017	−	0.790070i	$-0.289956\pi$
$433$	6.55984e23			1.22603			0.613017	+	0.790070i	$0.289956\pi$
$434$	−2.05191e23	+	4.11953e22i	−0.375623	+	0.0754120i
$435$	−3.75382e23			−0.673086
$436$	−2.24325e23	−	5.36157e23i	−0.394003	−	0.941702i
$437$			1.40945e23i			0.242502i
$438$	3.57032e23	−	7.16796e22i	0.601783	−	0.120817i
$439$			2.24151e23i			0.370135i	0.982726	+	0.185068i	$0.0592504\pi$
$439$			2.24151e23i			0.370135i	−0.982726	+	0.185068i	$0.940750\pi$
$440$	5.94113e23	+	8.78945e23i	0.961158	+	1.42196i
$441$	7.96695e22			0.126283
$442$	1.83227e23	+	9.12642e23i	0.284570	+	1.41743i
$443$	3.38076e23			0.514494			0.257247	−	0.966346i	$-0.417185\pi$
$443$	3.38076e23			0.514494			0.257247	+	0.966346i	$0.417185\pi$
$444$	2.31017e22	+	5.52151e22i	0.0344507	+	0.0823401i
$445$			9.11676e23i			1.33230i
$446$	−1.83977e23	−	9.16379e23i	−0.263482	−	1.31239i
$447$			1.18447e23i			0.166247i
$448$	7.43690e23	+	2.98772e23i	1.02303	+	0.410997i
$449$	8.42932e23			1.13652			0.568258	−	0.822850i	$-0.307618\pi$
$449$	8.42932e23			1.13652			0.568258	+	0.822850i	$0.307618\pi$
$450$	3.87087e23	−	7.77137e22i	0.511559	−	0.102703i
$451$	−1.37392e24			−1.77981
$452$	3.45683e23	−	1.44632e23i	0.438968	−	0.183662i
$453$			1.02152e24i			1.27164i
$454$	−1.03166e23	+	2.07122e22i	−0.125903	+	0.0252769i
$455$		−	2.52411e24i		−	3.01999i
$456$	2.24399e23	−	1.51680e23i	0.263231	−	0.177928i
$457$	−5.29783e23			−0.609330			−0.304665	−	0.952460i	$-0.598544\pi$
$457$	−5.29783e23			−0.609330			−0.304665	+	0.952460i	$0.598544\pi$
$458$	−6.30247e22	−	3.13922e23i	−0.0710758	−	0.354024i
$459$	−6.69679e23			−0.740547
$460$	−5.74464e23	+	2.40353e23i	−0.622934	+	0.260633i
$461$		−	1.21831e24i		−	1.29554i	−0.761837	−	0.647768i	$-0.775703\pi$
$461$		−	1.21831e24i		−	1.29554i	0.761837	−	0.647768i	$-0.224297\pi$
$462$	1.67150e23	+	8.32566e23i	0.174313	+	0.868242i
$463$			5.81872e23i			0.595112i	0.954704	+	0.297556i	$0.0961715\pi$
$463$			5.81872e23i			0.595112i	−0.954704	+	0.297556i	$0.903829\pi$
$464$	5.40113e23	+	5.32468e23i	0.541779	+	0.534111i
$465$	−3.12489e23			−0.307439
$466$	−1.16041e23	+	2.32969e22i	−0.111979	+	0.0224815i
$467$	−1.20522e24			−1.14082			−0.570408	−	0.821361i	$-0.693215\pi$
$467$	−1.20522e24			−1.14082			−0.570408	+	0.821361i	$0.693215\pi$
$468$	4.85264e23	+	1.15982e24i	0.450573	+	1.07691i
$469$		−	7.97614e23i		−	0.726503i
$470$	−2.01819e24	+	4.05182e23i	−1.80335	+	0.362051i
$471$		−	1.02691e24i		−	0.900211i
$472$	1.21188e24	−	8.19159e23i	1.04228	−	0.704515i
$473$	−3.02752e23			−0.255468
$474$	−2.61475e23	−	1.30239e24i	−0.216484	−	1.07829i
$475$	5.41230e23			0.439682
$476$	−3.87381e23	−	9.25875e23i	−0.308799	−	0.738057i
$477$			1.12049e23i			0.0876483i
$478$	−1.73454e23	−	8.63965e23i	−0.133148	−	0.663201i
$479$			2.05745e24i			1.54992i	0.632011	+	0.774959i	$0.282230\pi$
$479$			2.05745e24i			1.54992i	−0.632011	+	0.774959i	$0.717770\pi$
$480$	1.00089e24	+	6.55948e23i	0.739968	+	0.484951i
$481$	−3.80860e23			−0.276350
$482$	1.48233e24	−	2.97601e23i	1.05566	−	0.211939i
$483$	−4.98444e23			−0.348411
$484$	7.50595e23	−	3.14045e23i	0.514988	−	0.215468i
$485$			9.22953e23i			0.621590i
$486$	−1.44596e24	+	2.90298e23i	−0.955936	+	0.191919i
$487$			9.26185e23i			0.601087i	0.953768	+	0.300543i	$0.0971680\pi$
$487$			9.26185e23i			0.601087i	−0.953768	+	0.300543i	$0.902832\pi$
$488$	−5.64491e23	−	8.35122e23i	−0.359649	−	0.532073i
$489$	1.14320e24			0.715060
$490$	9.49807e22	+	4.73093e23i	0.0583272	+	0.290524i
$491$	−1.07494e24			−0.648110			−0.324055	−	0.946038i	$-0.605046\pi$
$491$	−1.07494e24			−0.648110			−0.324055	+	0.946038i	$0.605046\pi$
$492$	−1.42967e24	+	5.98167e23i	−0.846351	+	0.354109i
$493$		−	9.49783e23i		−	0.552080i
$494$	3.39251e23	+	1.68979e24i	0.193632	+	0.964471i
$495$		−	1.79437e24i		−	1.00570i
$496$	4.49620e23	+	4.43256e23i	0.247463	+	0.243961i
$497$	1.99327e24			1.07735
$498$	−1.77534e24	+	3.56426e23i	−0.942360	+	0.189193i
$499$	6.31275e23			0.329089			0.164545	−	0.986370i	$-0.447385\pi$
$499$	6.31275e23			0.329089			0.164545	+	0.986370i	$0.447385\pi$
$500$	−1.13544e23	−	2.71380e23i	−0.0581346	−	0.138947i
$501$		−	1.34616e24i		−	0.676949i
$502$	1.07814e24	−	2.16453e23i	0.532526	−	0.106913i
$503$			1.31652e24i			0.638727i	0.947632	+	0.319364i	$0.103469\pi$
$503$			1.31652e24i			0.638727i	−0.947632	+	0.319364i	$0.896531\pi$
$504$	−7.59126e23	−	1.12307e24i	−0.361775	−	0.535219i
$505$	−2.14351e23			−0.100347
$506$	2.62403e23	+	1.30701e24i	0.120674	+	0.601071i
$507$	4.22873e24			1.91046
$508$	4.55526e23	+	1.08875e24i	0.202181	+	0.483230i
$509$			2.08067e24i			0.907284i	0.891184	+	0.453642i	$0.149876\pi$
$509$			2.08067e24i			0.907284i	−0.891184	+	0.453642i	$0.850124\pi$
$510$	−2.94974e23	−	1.46925e24i	−0.126373	−	0.629454i
$511$		−	2.49842e24i		−	1.05167i
$512$	−5.09666e23	−	2.36352e24i	−0.210793	−	0.977531i
$513$	−1.23993e24			−0.503897
$514$	4.01236e24	−	8.05543e23i	1.60225	−	0.321677i
$515$	−3.77638e23			−0.148187
$516$	−3.15036e23	+	1.31810e23i	−0.121482	+	0.0508276i
$517$			4.40668e24i			1.66992i
$518$	4.02610e23	−	8.08301e22i	0.149940	−	0.0301027i
$519$			2.83729e24i			1.03848i
$520$	−6.30873e24	+	4.26431e24i	−2.26940	+	1.53398i
$521$	−1.09641e24			−0.387644			−0.193822	−	0.981037i	$-0.562088\pi$
$521$	−1.09641e24			−0.387644			−0.193822	+	0.981037i	$0.562088\pi$
$522$	−2.52506e23	−	1.25772e24i	−0.0877480	−	0.437067i
$523$	4.21318e24			1.43911			0.719557	−	0.694434i	$-0.244345\pi$
$523$	4.21318e24			1.43911			0.719557	+	0.694434i	$0.244345\pi$
$524$	−8.18664e23	+	3.42525e23i	−0.274868	+	0.115003i
$525$			1.91403e24i			0.631706i
$526$	−6.45198e23	−	3.21369e24i	−0.209325	−	1.04264i
$527$		−	7.90653e23i		−	0.252168i
$528$	1.79851e24	−	1.82434e24i	0.563909	−	0.572005i
$529$	2.46166e24			0.758800
$530$	−6.65371e23	+	1.33583e23i	−0.201642	+	0.0404827i
$531$	−2.47407e24			−0.737160
$532$	−7.17249e23	−	1.71429e24i	−0.210119	−	0.502202i
$533$		−	9.86151e24i		−	2.84052i
$534$	2.15840e24	−	4.33331e23i	0.611308	−	0.122729i
$535$			3.70089e24i			1.03068i
$536$	−1.99355e24	+	1.34751e24i	−0.545938	+	0.369020i
$537$	−1.97828e24			−0.532744
$538$	7.46939e23	+	3.72046e24i	0.197808	+	0.985271i
$539$	1.03299e24			0.269028
$540$	−2.11446e24	−	5.05373e24i	−0.541570	−	1.29440i
$541$		−	1.86780e24i		−	0.470496i	−0.971935	−	0.235248i	$-0.924410\pi$
$541$		−	1.86780e24i		−	0.470496i	0.971935	−	0.235248i	$-0.0755902\pi$
$542$	1.27324e24	+	6.34194e24i	0.315440	+	1.57119i
$543$		−	1.48234e24i		−	0.361201i
$544$	−1.65966e24	+	2.53242e24i	−0.397768	+	0.606939i
$545$	−5.95380e24			−1.40354
$546$	−5.97584e24	+	1.19974e24i	−1.38569	+	0.278198i
$547$	3.24479e24			0.740116			0.370058	−	0.929009i	$-0.379338\pi$
$547$	3.24479e24			0.740116			0.370058	+	0.929009i	$0.379338\pi$
$548$	5.79169e24	−	2.42321e24i	1.29951	−	0.543709i
$549$			1.70491e24i			0.376314i
$550$	5.01896e24	−	1.00763e24i	1.08981	−	0.218795i
$551$		−	1.75855e24i		−	0.375657i
$552$	8.42086e23	+	1.24580e24i	0.176972	+	0.261817i
$553$	−9.11383e24			−1.88441
$554$	−5.95982e23	−	2.96855e24i	−0.121240	−	0.603888i
$555$	6.13141e23			0.122722
$556$	−2.58236e24	+	1.08044e24i	−0.508561	+	0.212779i
$557$			2.05823e24i			0.398838i	0.979914	+	0.199419i	$0.0639055\pi$
$557$			2.05823e24i			0.398838i	−0.979914	+	0.199419i	$0.936095\pi$
$558$	−2.10200e23	−	1.04699e24i	−0.0400798	−	0.199635i
$559$		−	2.17304e24i		−	0.407720i
$560$	5.76399e24	−	5.84674e24i	1.06422	−	1.07950i
$561$	−3.20808e24			−0.582881
$562$	1.31455e24	−	2.63916e23i	0.235044	−	0.0471888i
$563$	−9.33242e24			−1.64217			−0.821086	−	0.570804i	$-0.806632\pi$
$563$	−9.33242e24			−1.64217			−0.821086	+	0.570804i	$0.806632\pi$
$564$	1.91854e24	+	4.58548e24i	0.332245	+	0.794095i
$565$		−	3.83867e24i		−	0.654252i
$566$	8.43395e24	−	1.69324e24i	1.41476	−	0.284035i
$567$		−	4.72110e23i		−	0.0779464i
$568$	−3.36749e24	−	4.98195e24i	−0.547232	−	0.809588i
$569$	3.07545e24			0.491925			0.245962	−	0.969279i	$-0.420896\pi$
$569$	3.07545e24			0.491925			0.245962	+	0.969279i	$0.420896\pi$
$570$	−5.46155e23	−	2.72036e24i	−0.0859888	−	0.428305i
$571$	4.81777e24			0.746657			0.373329	−	0.927699i	$-0.378216\pi$
$571$	4.81777e24			0.746657			0.373329	+	0.927699i	$0.378216\pi$
$572$	6.29191e24	+	1.50382e25i	0.959883	+	2.29420i
$573$			4.54548e22i			0.00682634i
$574$	2.09291e24	+	1.04247e25i	0.309417	+	1.54119i
$575$			3.00477e24i			0.437321i
$576$	−1.52449e24	+	3.79470e24i	−0.218435	+	0.543719i
$577$	1.06763e25			1.50605			0.753026	−	0.657991i	$-0.228594\pi$
$577$	1.06763e25			1.50605			0.753026	+	0.657991i	$0.228594\pi$
$578$	−3.34197e24	+	6.70952e23i	−0.464143	+	0.0931839i
$579$	−1.52781e24			−0.208911
$580$	7.16754e24	−	2.99886e24i	0.964980	−	0.403743i
$581$			1.24234e25i			1.64685i
$582$	2.18509e24	−	4.38691e23i	0.285209	−	0.0572601i
$583$			1.45283e24i			0.186722i
$584$	−6.24452e24	+	4.22091e24i	−0.790284	+	0.534184i
$585$	1.28793e25			1.60506
$586$	−4.43303e23	−	2.20806e24i	−0.0544029	−	0.270977i
$587$	1.28364e24			0.155132			0.0775661	−	0.996987i	$-0.475285\pi$
$587$	1.28364e24			0.155132			0.0775661	+	0.996987i	$0.475285\pi$
$588$	1.07490e24	−	4.49734e23i	0.127930	−	0.0535254i
$589$		−	1.46392e24i		−	0.171585i
$590$	−2.94955e24	−	1.46915e25i	−0.340477	−	1.69590i
$591$		−	1.91812e24i		−	0.218066i
$592$	−8.82207e23	−	8.69721e23i	−0.0987814	−	0.0973833i
$593$	−5.48333e24			−0.604717			−0.302359	−	0.953194i	$-0.597774\pi$
$593$	−5.48333e24			−0.604717			−0.302359	+	0.953194i	$0.597774\pi$
$594$	−1.14982e25	+	2.30844e24i	−1.24897	+	0.250750i
$595$	−1.02815e25			−1.10002
$596$	−9.46249e23	−	2.26162e24i	−0.0997215	−	0.238343i
$597$		−	3.80874e24i		−	0.395377i
$598$	−9.38125e24	+	1.88343e24i	−0.959290	+	0.192592i
$599$		−	1.41388e25i		−	1.42420i	−0.702076	−	0.712102i	$-0.747744\pi$
$599$		−	1.41388e25i		−	1.42420i	0.702076	−	0.712102i	$-0.252256\pi$
$600$	4.78390e24	−	3.23362e24i	0.474702	−	0.320869i
$601$	5.10304e24			0.498837			0.249419	−	0.968396i	$-0.419761\pi$
$601$	5.10304e24			0.498837			0.249419	+	0.968396i	$0.419761\pi$
$602$	4.61186e23	+	2.29714e24i	0.0444127	+	0.221217i
$603$	4.06985e24			0.386120
$604$	−8.16078e24	−	1.95050e25i	−0.762780	−	1.82311i
$605$		−	8.33504e24i		−	0.767555i
$606$	1.01884e23	+	5.07478e23i	0.00924383	+	0.0460430i
$607$			1.21595e25i			1.08697i	0.839420	+	0.543483i	$0.182895\pi$
$607$			1.21595e25i			1.08697i	−0.839420	+	0.543483i	$0.817105\pi$
$608$	−3.07292e24	+	4.68885e24i	−0.270657	+	0.412985i
$609$	6.21904e24			0.539719
$610$	−1.01241e25	+	2.03257e24i	−0.865740	+	0.173811i
$611$	−3.16295e25			−2.66514
$612$	4.72430e24	−	1.97662e24i	0.392260	−	0.164120i
$613$			1.36944e25i			1.12046i	0.828336	+	0.560231i	$0.189288\pi$
$613$			1.36944e25i			1.12046i	−0.828336	+	0.560231i	$0.810712\pi$
$614$	−7.67433e24	+	1.54074e24i	−0.618764	+	0.124226i
$615$			1.58759e25i			1.26143i
$616$	−9.84279e24	−	1.45617e25i	−0.770712	−	1.14021i
$617$	2.04414e25			1.57741			0.788703	−	0.614774i	$-0.210753\pi$
$617$	2.04414e25			1.57741			0.788703	+	0.614774i	$0.210753\pi$
$618$	1.79496e23	+	8.94060e23i	0.0136508	+	0.0679940i
$619$	2.43775e25			1.82715			0.913574	−	0.406674i	$-0.133311\pi$
$619$	2.43775e25			1.82715			0.913574	+	0.406674i	$0.133311\pi$
$620$	5.96666e24	−	2.49642e24i	0.440764	−	0.184413i
$621$		−	6.88378e24i		−	0.501190i
$622$	9.62354e22	+	4.79343e23i	0.00690592	+	0.0343979i
$623$		−	1.51039e25i		−	1.06831i
$624$	1.30944e25	+	1.29091e25i	0.912902	+	0.899981i
$625$	−1.59714e25			−1.09755
$626$	6.89125e24	−	1.38352e24i	0.466798	−	0.0937169i
$627$	−5.93987e24			−0.396615
$628$	8.20380e24	+	1.96078e25i	0.539981	+	1.29060i
$629$			1.55135e24i			0.100660i
$630$	−1.36148e25	+	2.73339e24i	−0.870859	+	0.174838i
$631$		−	8.94379e24i		−	0.563971i	−0.959419	−	0.281986i	$-0.909007\pi$
$631$		−	8.94379e24i		−	0.563971i	0.959419	−	0.281986i	$-0.0909931\pi$
$632$	1.53972e25	+	2.27790e25i	0.957167	+	1.41606i
$633$	1.42959e25			0.876150
$634$	−4.09719e24	−	2.04079e25i	−0.247562	−	1.23309i
$635$	1.20901e25			0.720221
$636$	6.32518e23	+	1.51177e24i	0.0371500	+	0.0887917i
$637$			7.41442e24i			0.429361i
$638$	−3.27398e24	−	1.63075e25i	−0.186935	−	0.931111i
$639$			1.01707e25i			0.572589i
$640$	−2.43511e25	−	4.52876e24i	−1.35176	−	0.251397i
$641$	−6.48273e24			−0.354842			−0.177421	−	0.984135i	$-0.556775\pi$
$641$	−6.48273e24			−0.354842			−0.177421	+	0.984135i	$0.556775\pi$
$642$	8.76188e24	−	1.75908e24i	0.472914	−	0.0949447i
$643$	1.13219e25			0.602589			0.301295	−	0.953531i	$-0.402581\pi$
$643$	1.13219e25			0.602589			0.301295	+	0.953531i	$0.402581\pi$
$644$	9.51727e24	−	3.98198e24i	0.499505	−	0.208990i
$645$			3.49835e24i			0.181061i
$646$	6.88300e24	−	1.38187e24i	0.351306	−	0.0705300i
$647$		−	3.74550e24i		−	0.188526i	−0.995547	−	0.0942631i	$-0.969951\pi$
$647$		−	3.74550e24i		−	0.188526i	0.995547	−	0.0942631i	$-0.0300495\pi$
$648$	−1.17999e24	+	7.97598e23i	−0.0585736	+	0.0395922i
$649$	−3.20787e25			−1.57042
$650$	7.23240e24	+	3.60242e25i	0.349191	+	1.73930i
$651$	5.17708e24			0.246522
$652$	−2.18282e25	+	9.13283e24i	−1.02516	+	0.428921i
$653$			9.80775e24i			0.454308i	0.973859	+	0.227154i	$0.0729421\pi$
$653$			9.80775e24i			0.454308i	−0.973859	+	0.227154i	$0.927058\pi$
$654$	2.82992e24	+	1.40956e25i	0.129293	+	0.643999i
$655$			9.09092e24i			0.409672i
$656$	2.25195e25	−	2.28428e25i	1.00098	−	1.01535i
$657$	1.27482e25			0.558936
$658$	3.34357e25	−	6.71274e24i	1.44603	−	0.290313i
$659$	−2.82374e25			−1.20464			−0.602318	−	0.798256i	$-0.705756\pi$
$659$	−2.82374e25			−1.20464			−0.602318	+	0.798256i	$0.705756\pi$
$660$	−1.01292e25	−	2.42098e25i	−0.426267	−	1.01882i
$661$		−	3.43869e25i		−	1.42751i	−0.700394	−	0.713757i	$-0.746992\pi$
$661$		−	3.43869e25i		−	1.42751i	0.700394	−	0.713757i	$-0.253008\pi$
$662$	1.00542e25	−	2.01853e24i	0.411741	−	0.0826633i
$663$		−	2.30264e25i		−	0.930260i
$664$	3.10508e25	−	2.09885e25i	1.23754	−	0.836503i
$665$	−1.90364e25			−0.748498
$666$	4.12438e23	+	2.05433e24i	0.0159989	+	0.0796895i
$667$	9.76303e24			0.373639
$668$	1.07542e25	+	2.57035e25i	0.406060	+	0.970518i
$669$			2.31207e25i			0.861322i
$670$	4.85201e24	+	2.41676e25i	0.178340	+	0.888300i
$671$			2.21058e25i			0.801684i
$672$	−1.65819e25	−	1.08672e25i	−0.593349	−	0.388862i
$673$	−3.52165e25			−1.24340			−0.621700	−	0.783255i	$-0.713558\pi$
$673$	−3.52165e25			−1.24340			−0.621700	+	0.783255i	$0.713558\pi$
$674$	2.03881e25	−	4.09323e24i	0.710293	−	0.142602i
$675$	−2.64338e25			−0.908712
$676$	−8.07434e25	+	3.37826e25i	−2.73897	+	1.14597i
$677$		−	2.88307e25i		−	0.965066i	−0.875878	−	0.482533i	$-0.839717\pi$
$677$		−	2.88307e25i		−	0.965066i	0.875878	−	0.482533i	$-0.160283\pi$
$678$	−9.08806e24	+	1.82457e24i	−0.300195	+	0.0602689i
$679$		−	1.52908e25i		−	0.498427i
$680$	1.73698e25	+	2.56973e25i	0.558747	+	0.826623i
$681$	2.60293e24			0.0826301
$682$	−2.72545e24	−	1.35753e25i	−0.0853844	−	0.425294i
$683$	4.43549e25			1.37137			0.685686	−	0.727898i	$-0.259502\pi$
$683$	4.43549e25			1.37137			0.685686	+	0.727898i	$0.259502\pi$
$684$	8.74719e24	−	3.65978e24i	0.266909	−	0.111673i
$685$		−	6.43143e25i		−	1.93683i
$686$	5.72782e24	+	2.85299e25i	0.170244	+	0.847976i
$687$			7.92040e24i			0.232347i
$688$	4.96229e24	−	5.03354e24i	0.143677	−	0.145740i
$689$	−1.04278e25			−0.298003
$690$	1.51027e25	−	3.03211e24i	0.426004	−	0.0855269i
$691$	−1.79819e24			−0.0500650			−0.0250325	−	0.999687i	$-0.507969\pi$
$691$	−1.79819e24			−0.0500650			−0.0250325	+	0.999687i	$0.507969\pi$
$692$	−2.26666e25	−	5.41752e25i	−0.622920	−	1.48883i
$693$			2.97278e25i			0.806424i
$694$	1.98462e25	−	3.98443e24i	0.531425	−	0.106692i
$695$			2.86760e25i			0.757975i
$696$	−1.05066e25	−	1.55438e25i	−0.274145	−	0.405577i
$697$	−4.01688e25			−1.03465
$698$	−1.48088e24	−	7.37616e24i	−0.0376548	−	0.187556i
$699$	2.92776e24			0.0734921
$700$	−1.52909e25	−	3.65465e25i	−0.378922	−	0.905656i
$701$			5.90405e25i			1.44440i	0.691683	+	0.722201i	$0.256869\pi$
$701$			5.90405e25i			1.44440i	−0.691683	+	0.722201i	$0.743131\pi$
$702$	−1.65691e25	−	8.25297e25i	−0.400189	−	1.99332i
$703$			2.87238e24i			0.0684927i
$704$	−1.97665e25	+	4.92019e25i	−0.465346	+	1.15832i
$705$	5.09198e25			1.18354
$706$	2.73442e25	−	5.48977e24i	0.627513	−	0.125983i
$707$	3.55121e24			0.0804639
$708$	−3.33803e25	+	1.39662e25i	−0.746777	+	0.312448i
$709$			2.97069e25i			0.656208i	0.944642	+	0.328104i	$0.106410\pi$
$709$			2.97069e25i			0.656208i	−0.944642	+	0.328104i	$0.893590\pi$
$710$	−6.03956e25	+	1.21253e25i	−1.31729	+	0.264466i
$711$		−	4.65035e25i		−	1.00152i
$712$	−3.77506e25	+	2.55171e25i	−0.802793	+	0.542639i
$713$	8.12730e24			0.170663
$714$	4.88691e24	+	2.43414e25i	0.101333	+	0.504732i
$715$	1.66993e26			3.41935
$716$	3.77732e25	−	1.58041e25i	0.763776	−	0.319560i
$717$			2.17982e25i			0.435260i
$718$	−2.12174e24	−	1.05682e25i	−0.0418381	−	0.208393i
$719$		−	3.18331e25i		−	0.619897i	−0.950753	−	0.309948i	$-0.899688\pi$
$719$		−	3.18331e25i		−	0.619897i	0.950753	−	0.309948i	$-0.100312\pi$
$720$	2.98331e25	+	2.94109e25i	0.573729	+	0.565608i
$721$	6.25642e24			0.118825
$722$	−3.95261e25	+	7.93547e24i	−0.741394	+	0.148846i
$723$	−3.74000e25			−0.692830
$724$	1.18422e25	+	2.83038e25i	0.216662	+	0.517842i
$725$		−	3.74902e25i		−	0.677448i
$726$	−1.97332e25	+	3.96175e24i	−0.352183	+	0.0707062i
$727$			8.96430e25i			1.58018i	0.612991	+	0.790090i	$0.289966\pi$
$727$			8.96430e25i			1.58018i	−0.612991	+	0.790090i	$0.710034\pi$
$728$	1.04518e26	−	7.06478e25i	1.81974	−	1.23003i
$729$	4.05933e25			0.698082
$730$	1.51983e25	+	7.57016e25i	0.258160	+	1.28588i
$731$	−8.85144e24			−0.148511
$732$	9.62422e24	+	2.30027e25i	0.159502	+	0.381223i
$733$			2.33821e24i			0.0382779i	0.999817	+	0.0191389i	$0.00609248\pi$
$733$			2.33821e24i			0.0382779i	−0.999817	+	0.0191389i	$0.993908\pi$
$734$	4.42371e24	+	2.20342e25i	0.0715355	+	0.356314i
$735$		−	1.19364e25i		−	0.190672i
$736$	−2.60313e25	−	1.70601e25i	−0.410767	−	0.269203i
$737$	5.27694e25			0.822574
$738$	−5.31922e25	+	1.06791e25i	−0.819107	+	0.164448i
$739$	−6.16334e25			−0.937596			−0.468798	−	0.883305i	$-0.655313\pi$
$739$	−6.16334e25			−0.937596			−0.468798	+	0.883305i	$0.655313\pi$
$740$	−1.17073e25	+	4.89827e24i	−0.175943	+	0.0736135i
$741$		−	4.26341e25i		−	0.632985i
$742$	1.10233e25	−	2.21310e24i	0.161688	−	0.0324614i
$743$			1.15246e26i			1.67004i	0.550216	+	0.835022i	$0.314545\pi$
$743$			1.15246e26i			1.67004i	−0.550216	+	0.835022i	$0.685455\pi$
$744$	−8.74632e24	−	1.29395e25i	−0.125219	−	0.185251i
$745$	−2.51143e25			−0.355234
$746$	−2.60083e25	−	1.29546e26i	−0.363465	−	1.81040i
$747$	−6.33906e25			−0.875265
$748$	6.12550e25	−	2.56288e25i	0.835656	−	0.349634i
$749$		−	6.13135e25i		−	0.826456i
$750$	1.43239e24	+	7.13463e24i	0.0190769	+	0.0950211i
$751$		−	7.26560e25i		−	0.956119i	−0.878327	−	0.478060i	$-0.841340\pi$
$751$		−	7.26560e25i		−	0.956119i	0.878327	−	0.478060i	$-0.158660\pi$
$752$	−7.32651e25	−	7.22281e25i	−0.952657	−	0.939173i
$753$	−2.72019e25			−0.349498
$754$	1.17049e26	−	2.34994e25i	1.48602	−	0.298342i
$755$	−2.16595e26			−2.71722
$756$	3.50307e25	+	8.37263e25i	0.434262	+	1.03792i
$757$			1.13327e26i			1.38825i	0.719852	+	0.694127i	$0.244209\pi$
$757$			1.13327e26i			1.38825i	−0.719852	+	0.694127i	$0.755791\pi$
$758$	−6.02016e25	+	1.20864e25i	−0.728761	+	0.146310i
$759$		−	3.29766e25i		−	0.394484i
$760$	3.21608e25	+	4.75794e25i	0.380193	+	0.562467i
$761$	1.04384e26			1.21947			0.609735	−	0.792605i	$-0.291276\pi$
$761$	1.04384e26			1.21947			0.609735	+	0.792605i	$0.291276\pi$
$762$	−5.74657e24	−	2.86233e25i	−0.0663459	−	0.330465i
$763$	9.86379e25			1.12544
$764$	−3.63130e23	−	8.67913e23i	−0.00409470	−	0.00978669i
$765$		−	5.24613e25i		−	0.584637i
$766$	1.32368e24	+	6.59318e24i	0.0145789	+	0.0726166i
$767$		−	2.30249e26i		−	2.50634i
$768$	8.52553e23	+	5.98040e25i	0.00917213	+	0.643397i
$769$	−8.78575e25			−0.934204			−0.467102	−	0.884203i	$-0.654702\pi$
$769$	−8.78575e25			−0.934204			−0.467102	+	0.884203i	$0.654702\pi$
$770$	−1.76530e26	+	3.54410e25i	−1.85524	+	0.372469i
$771$	−1.01234e26			−1.05156
$772$	2.91719e25	−	1.22054e25i	0.299508	−	0.125313i
$773$		−	3.75016e25i		−	0.380570i	−0.981729	−	0.190285i	$-0.939059\pi$
$773$		−	3.75016e25i		−	0.380570i	0.981729	−	0.190285i	$-0.0609412\pi$
$774$	−1.17212e25	+	2.35321e24i	−0.117572	+	0.0236044i
$775$		−	3.12090e25i		−	0.309431i
$776$	−3.82175e25	+	2.58327e25i	−0.374548	+	0.253171i
$777$	−1.01580e25			−0.0984058
$778$	9.33807e24	+	4.65124e25i	0.0894213	+	0.445402i
$779$	−7.43739e25			−0.704017
$780$	1.73769e26	−	7.27039e25i	1.62600	−	0.680309i
$781$			1.31873e26i			1.21982i
$782$	7.67177e24	+	3.82126e25i	0.0701511	+	0.349418i
$783$			8.58883e25i			0.776387i
$784$	−1.69314e25	+	1.71744e25i	−0.151303	+	0.153475i
$785$	2.17736e26			1.92355
$786$	2.15228e25	−	4.32103e24i	0.187973	−	0.0377385i
$787$	−2.22921e25			−0.192477			−0.0962386	−	0.995358i	$-0.530681\pi$
$787$	−2.22921e25			−0.192477			−0.0962386	+	0.995358i	$0.530681\pi$
$788$	1.53235e25	+	3.66245e25i	0.130804	+	0.312634i
$789$			8.10829e25i			0.684284i
$790$	2.76147e26	−	5.54408e25i	2.30408	−	0.462579i
$791$			6.35961e25i			0.524617i
$792$	7.43012e25	−	5.02231e25i	0.605995	−	0.409616i
$793$	−1.58667e26			−1.27946
$794$	−1.33262e25	−	6.63768e25i	−0.106248	−	0.529214i
$795$	1.67876e25			0.132338
$796$	3.04273e25	+	7.27239e25i	0.237163	+	0.566839i
$797$		−	5.24200e25i		−	0.403992i	−0.979386	−	0.201996i	$-0.935257\pi$
$797$		−	5.24200e25i		−	0.403992i	0.979386	−	0.201996i	$-0.0647428\pi$
$798$	9.04826e24	+	4.50688e25i	0.0689508	+	0.343440i
$799$			1.28836e26i			0.970771i
$800$	−6.55109e25	+	9.99605e25i	−0.488094	+	0.744764i
$801$	7.70682e25			0.567783
$802$	−1.07876e26	+	2.16577e25i	−0.785876	+	0.157777i
$803$	1.65293e26			1.19074
$804$	5.49105e25	−	2.29743e25i	0.391157	−	0.163658i
$805$		−	1.05685e26i		−	0.744478i
$806$	9.74382e25	−	1.95622e25i	0.678756	−	0.136271i
$807$		−	9.38688e25i		−	0.646636i
$808$	−5.99952e24	−	8.87583e24i	−0.0408709	−	0.0604654i
$809$	−8.63515e25			−0.581746			−0.290873	−	0.956762i	$-0.593946\pi$
$809$	−8.63515e25			−0.581746			−0.290873	+	0.956762i	$0.593946\pi$
$810$	2.87192e24	+	1.43048e25i	0.0191341	+	0.0953055i
$811$	1.82977e26			1.20561			0.602807	−	0.797887i	$-0.294049\pi$
$811$	1.82977e26			1.20561			0.602807	+	0.797887i	$0.294049\pi$
$812$	−1.18746e26	+	4.96828e25i	−0.773776	+	0.323744i
$813$		−	1.60010e26i		−	1.03117i
$814$	5.34765e24	+	2.66363e25i	0.0340834	+	0.169767i
$815$			2.42394e26i			1.52793i
$816$	5.25824e25	−	5.33373e25i	0.327815	−	0.332522i
$817$	−1.63887e25			−0.101052
$818$	−2.76926e26	+	5.55971e25i	−1.68882	+	0.339057i
$819$	−2.13375e26			−1.28703
$820$	−1.26830e26	−	3.03134e26i	−0.756653	−	1.80847i
$821$			1.88566e26i			1.11269i	0.830950	+	0.556347i	$0.187797\pi$
$821$			1.88566e26i			1.11269i	−0.830950	+	0.556347i	$0.812203\pi$
$822$	−1.52264e26	+	3.05694e25i	−0.888693	+	0.178419i
$823$		−	1.24752e26i		−	0.720195i	−0.932915	−	0.360097i	$-0.882743\pi$
$823$		−	1.24752e26i		−	0.720195i	0.932915	−	0.360097i	$-0.117257\pi$
$824$	−1.05698e25	−	1.56372e25i	−0.0603561	−	0.0892923i
$825$	−1.26631e26			−0.715242
$826$	4.88659e25	+	2.43398e26i	0.273014	+	1.35987i
$827$	3.15380e26			1.74295			0.871475	−	0.490440i	$-0.163164\pi$
$827$	3.15380e26			1.74295			0.871475	+	0.490440i	$0.163164\pi$
$828$	2.03181e25	+	4.85621e25i	0.111074	+	0.265475i
$829$		−	3.48340e26i		−	1.88371i	−0.336025	−	0.941853i	$-0.609083\pi$
$829$		−	3.48340e26i		−	1.88371i	0.336025	−	0.941853i	$-0.390917\pi$
$830$	−7.55733e25	−	3.76426e26i	−0.404264	−	2.01362i
$831$			7.48978e25i			0.396333i
$832$	−3.53152e26	−	1.41876e26i	−1.84864	−	0.742678i
$833$	3.02011e25			0.156393
$834$	6.78905e25	−	1.36301e25i	0.347788	−	0.0698238i
$835$	2.85426e26			1.44649
$836$	1.13416e26	−	4.74525e25i	0.568613	−	0.237905i
$837$			7.14983e25i			0.354623i
$838$	2.31152e26	−	4.64073e25i	1.13423	−	0.227714i
$839$		−	2.33731e26i		−	1.13464i	−0.823497	−	0.567321i	$-0.807980\pi$
$839$		−	2.33731e26i		−	1.13464i	0.823497	−	0.567321i	$-0.192020\pi$
$840$	−1.68262e26	+	1.13735e26i	−0.808114	+	0.546236i
$841$	8.86448e25			0.421201
$842$	−2.26591e25	−	1.12864e26i	−0.106521	−	0.530573i
$843$	−3.31667e25			−0.154260
$844$	−2.72966e26	+	1.14207e26i	−1.25611	+	0.525548i
$845$			8.96621e26i			4.08224i
$846$	3.42519e25	+	1.70607e26i	0.154295	+	0.768533i
$847$			1.38088e26i			0.615470i
$848$	−2.41546e25	−	2.38127e25i	−0.106521	−	0.105014i
$849$	−2.12792e26			−0.928511
$850$	1.46737e26	−	2.94597e25i	0.633533	−	0.127192i
$851$	−1.59467e25			−0.0681248
$852$	5.74136e25	+	1.37223e26i	0.242694	+	0.580059i
$853$		−	2.40286e26i		−	1.00505i	−0.864562	−	0.502525i	$-0.832404\pi$
$853$		−	2.40286e26i		−	1.00505i	0.864562	−	0.502525i	$-0.167596\pi$
$854$	1.67728e26	−	3.36740e25i	0.694200	−	0.139371i
$855$		−	9.71339e25i		−	0.397810i
$856$	−1.53246e26	+	1.03585e26i	−0.621049	+	0.419791i
$857$	1.83026e26			0.733981			0.366991	−	0.930225i	$-0.380388\pi$
$857$	1.83026e26			0.733981			0.366991	+	0.930225i	$0.380388\pi$
$858$	−7.93739e25	−	3.95356e26i	−0.314987	−	1.56893i
$859$	−8.35364e25			−0.328048			−0.164024	−	0.986456i	$-0.552447\pi$
$859$	−8.35364e25			−0.328048			−0.164024	+	0.986456i	$0.552447\pi$
$860$	−2.79477e25	−	6.67974e25i	−0.108607	−	0.259581i
$861$		−	2.63020e26i		−	1.01149i
$862$	9.42747e25	+	4.69577e26i	0.358781	+	1.78707i
$863$		−	1.51928e26i		−	0.572192i	−0.958201	−	0.286096i	$-0.907642\pi$
$863$		−	1.51928e26i		−	0.572192i	0.958201	−	0.286096i	$-0.0923576\pi$
$864$	1.50082e26	−	2.29005e26i	0.559379	−	0.853535i
$865$	−6.01593e26			−2.21900
$866$	3.29293e26	−	6.61106e25i	1.20205	−	0.241329i
$867$	8.43195e25			0.304618
$868$	−9.88510e25	+	4.13588e25i	−0.353430	+	0.147873i
$869$		−	6.02963e26i		−	2.13360i
$870$	−1.88436e26	+	3.78313e25i	−0.659917	+	0.132489i
$871$			3.78759e26i			1.31280i
$872$	−1.66642e26	−	2.46534e26i	−0.571658	−	0.845724i
$873$	7.80215e25			0.264902
$874$	1.42045e25	+	7.07519e25i	0.0477336	+	0.237758i
$875$	4.99264e25			0.166057
$876$	1.72000e26	−	7.19639e25i	0.566228	−	0.236907i
$877$		−	1.28874e26i		−	0.419923i	−0.977710	−	0.209962i	$-0.932666\pi$
$877$		−	1.28874e26i		−	0.419923i	0.977710	−	0.209962i	$-0.0673339\pi$
$878$	2.25901e25	+	1.12520e26i	0.0728565	+	0.362894i
$879$			5.57105e25i			0.177843i
$880$	3.86815e26	+	3.81340e26i	1.22225	+	1.20495i
$881$	2.67668e26			0.837169			0.418584	−	0.908178i	$-0.362526\pi$
$881$	2.67668e26			0.837169			0.418584	+	0.908178i	$0.362526\pi$
$882$	3.99927e25	−	8.02916e24i	0.123812	−	0.0248572i
$883$	−4.06826e26			−1.24670			−0.623350	−	0.781943i	$-0.714229\pi$
$883$	−4.06826e26			−1.24670			−0.623350	+	0.781943i	$0.714229\pi$
$884$	1.83954e26	+	4.39665e26i	0.558005	+	1.33368i
$885$			3.70674e26i			1.11302i
$886$	1.69708e26	−	3.40716e25i	0.504429	−	0.101272i
$887$			1.11408e26i			0.327795i	0.986477	+	0.163898i	$0.0524067\pi$
$887$			1.11408e26i			0.327795i	−0.986477	+	0.163898i	$0.947593\pi$
$888$	1.71613e25	+	2.53888e25i	0.0499843	+	0.0739480i
$889$	−2.00299e26			−0.577515
$890$	9.18795e25	+	4.57646e26i	0.262246	+	1.30623i
$891$	3.12344e25			0.0882539
$892$	−1.84707e26	−	4.41466e26i	−0.516654	−	1.23485i
$893$			2.38544e26i			0.660550i
$894$	1.19371e25	+	5.94582e25i	0.0327237	+	0.162995i
$895$		−	4.19455e26i		−	1.13836i
$896$	4.03431e26	+	7.50289e25i	1.08392	+	0.201584i
$897$	2.36693e26			0.629584
$898$	4.23138e26	−	8.49514e25i	1.11428	−	0.223709i
$899$	−1.01404e26			−0.264372
$900$	1.86479e26	−	7.80220e25i	0.481335	−	0.201388i
$901$			4.24756e25i			0.108547i
$902$	−6.89687e26	+	1.38465e26i	−1.74499	+	0.350334i
$903$		−	5.79579e25i		−	0.145185i
$904$	1.58951e26	−	1.07441e26i	0.394228	−	0.266474i
$905$	3.14302e26			0.771808
$906$	1.02950e26	+	5.12788e26i	0.250307	+	1.24676i
$907$	8.43433e25			0.203042			0.101521	−	0.994833i	$-0.467629\pi$
$907$	8.43433e25			0.203042			0.101521	+	0.994833i	$0.467629\pi$
$908$	−4.97003e25	+	2.07943e25i	−0.118464	+	0.0495647i
$909$			1.81201e25i			0.0427647i
$910$	−2.54382e26	−	1.26706e27i	−0.594448	−	2.96091i
$911$			2.61003e26i			0.603921i	0.953320	+	0.301960i	$0.0976410\pi$
$911$			2.61003e26i			0.603921i	−0.953320	+	0.301960i	$0.902359\pi$
$912$	9.73580e25	−	9.87558e25i	0.223058	−	0.226261i
$913$	−8.21920e26			−1.86463
$914$	−2.65942e26	+	5.33920e25i	−0.597409	+	0.119939i
$915$	2.55436e26			0.568187
$916$	−6.32747e25	−	1.51232e26i	−0.139370	−	0.333108i
$917$		−	1.50611e26i		−	0.328499i
$918$	−3.36168e26	+	6.74909e25i	−0.726059	+	0.145768i
$919$		−	2.10185e26i		−	0.449533i	−0.974413	−	0.224767i	$-0.927838\pi$
$919$		−	2.10185e26i		−	0.449533i	0.974413	−	0.224767i	$-0.0721620\pi$
$920$	−2.64148e26	+	1.78548e26i	−0.559445	+	0.378151i
$921$	1.93627e26			0.406096
$922$	−1.22782e26	−	6.11572e26i	−0.255010	−	1.27019i
$923$	−9.46533e26			−1.94680
$924$	1.67813e26	+	4.01089e26i	0.341806	+	0.816945i
$925$			6.12356e25i			0.123518i
$926$	5.86416e25	+	2.92090e26i	0.117140	+	0.583469i
$927$			3.19235e25i			0.0631529i
$928$	3.24790e26	+	2.12857e26i	0.636313	+	0.417019i
$929$	1.52656e26			0.296192			0.148096	−	0.988973i	$-0.452686\pi$
$929$	1.52656e26			0.296192			0.148096	+	0.988973i	$0.452686\pi$
$930$	−1.56864e26	+	3.14929e25i	−0.301424	+	0.0605155i
$931$	5.59183e25			0.106416
$932$	−5.59026e25	+	2.33893e25i	−0.105363	+	0.0440834i
$933$		−	1.20940e25i		−	0.0225754i
$934$	−6.05002e26	+	1.21464e26i	−1.11850	+	0.224556i
$935$		−	6.80212e26i		−	1.24549i
$936$	3.60482e26	+	5.33306e26i	0.653734	+	0.967150i
$937$	5.53624e26			0.994393			0.497197	−	0.867638i	$-0.334363\pi$
$937$	5.53624e26			0.994393			0.497197	+	0.867638i	$0.334363\pi$
$938$	−8.03843e25	−	4.00389e26i	−0.143003	−	0.712290i
$939$	−1.73870e26			−0.306361
$940$	−9.72262e26	+	4.06789e26i	−1.69681	+	0.709935i
$941$		−	6.54807e26i		−	1.13190i	−0.824441	−	0.565949i	$-0.808510\pi$
$941$		−	6.54807e26i		−	1.13190i	0.824441	−	0.565949i	$-0.191490\pi$
$942$	−1.03493e26	−	5.15492e26i	−0.177195	−	0.882599i
$943$		−	4.12904e26i		−	0.700236i
$944$	5.25790e26	−	5.33339e26i	0.883211	−	0.895891i
$945$	9.29746e26			1.54696
$946$	−1.51977e26	+	3.05116e25i	−0.250470	+	0.0502858i
$947$	−3.87834e26			−0.633135			−0.316567	−	0.948570i	$-0.602530\pi$
$947$	−3.87834e26			−0.633135			−0.316567	+	0.948570i	$0.602530\pi$
$948$	−2.62513e26	−	6.27428e26i	−0.424497	−	1.01459i
$949$			1.18641e27i			1.90038i
$950$	2.71688e26	−	5.45456e25i	0.431081	−	0.0865461i
$951$			5.14900e26i			0.809279i
$952$	−2.87769e26	−	4.25733e26i	−0.448035	−	0.662834i
$953$	3.86859e26			0.596646			0.298323	−	0.954465i	$-0.403573\pi$
$953$	3.86859e26			0.596646			0.298323	+	0.954465i	$0.403573\pi$
$954$	1.12924e25	+	5.62468e25i	0.0172525	+	0.0859335i
$955$	−9.63781e24			−0.0145864
$956$	−1.74142e26	−	4.16215e26i	−0.261086	−	0.624018i
$957$			4.11446e26i			0.611090i
$958$	2.07351e26	+	1.03280e27i	0.305082	+	1.51960i
$959$			1.06551e27i			1.55306i
$960$	5.68535e26	+	2.28405e26i	0.820948	+	0.329810i
$961$	6.14640e26			0.879245
$962$	−1.91185e26	+	3.83834e25i	−0.270944	+	0.0543961i
$963$	3.12854e26			0.439243
$964$	7.14114e26	−	2.98782e26i	0.993286	−	0.415586i
$965$		−	3.23942e26i		−	0.446397i
$966$	−2.50210e26	+	5.02336e25i	−0.341595	+	0.0685804i
$967$			1.18662e27i			1.60499i	0.596658	+	0.802495i	$0.296495\pi$
$967$			1.18662e27i			1.60499i	−0.596658	+	0.802495i	$0.703505\pi$
$968$	3.45136e26	−	2.33291e26i	0.462501	−	0.312622i
$969$	−1.73661e26			−0.230563
$970$	9.30160e25	+	4.63307e26i	0.122352	+	0.609429i
$971$	5.13565e26			0.669302			0.334651	−	0.942342i	$-0.391382\pi$
$971$	5.13565e26			0.669302			0.334651	+	0.942342i	$0.391382\pi$
$972$	−6.96589e26	+	2.91449e26i	−0.899457	+	0.376328i
$973$		−	4.75081e26i		−	0.607788i
$974$	9.33418e25	+	4.64930e26i	0.118317	+	0.589327i
$975$		−	9.08906e26i		−	1.14150i
$976$	−3.67529e26	−	3.62327e26i	−0.457345	−	0.450871i
$977$	5.34565e25			0.0659097			0.0329549	−	0.999457i	$-0.489508\pi$
$977$	5.34565e25			0.0659097			0.0329549	+	0.999457i	$0.489508\pi$
$978$	5.73868e26	−	1.15213e26i	0.701071	−	0.140751i
$979$	9.99263e26			1.20958
$980$	9.53575e25	+	2.27913e26i	0.114372	+	0.273359i
$981$			5.03302e26i			0.598147i
$982$	−5.39599e26	+	1.08333e26i	−0.635431	+	0.127572i
$983$			3.64314e24i			0.00425103i	0.999998	+	0.00212552i	$0.000676573\pi$
$983$			3.64314e24i			0.00425103i	−0.999998	+	0.00212552i	$0.999323\pi$
$984$	−6.57387e26	+	4.44353e26i	−0.760091	+	0.513775i
$985$	4.06700e26			0.465960
$986$	−9.57200e25	−	4.76775e26i	−0.108670	−	0.541280i
$987$	−8.43599e26			−0.949034
$988$	3.40596e26	+	8.14055e26i	0.379688	+	0.907488i
$989$		−	9.09859e25i		−	0.100510i
$990$	−1.80839e26	−	9.00746e26i	−0.197959	−	0.986020i
$991$		−	1.59956e27i		−	1.73515i	−0.497305	−	0.867576i	$-0.665677\pi$
$991$		−	1.59956e27i		−	1.73515i	0.497305	−	0.867576i	$-0.334323\pi$
$992$	2.70373e26	+	1.77194e26i	0.290642	+	0.190478i
$993$	−2.53671e26			−0.270226
$994$	1.00059e27	−	2.00883e26i	1.05628	−	0.212064i
$995$	8.07569e26			0.844835
$996$	−8.55269e26	+	3.57840e26i	−0.886683	+	0.370984i
$997$		−	2.05226e26i		−	0.210851i	−0.994427	−	0.105426i	$-0.966380\pi$
$997$		−	2.05226e26i		−	0.210851i	0.994427	−	0.105426i	$-0.0336205\pi$
$998$	3.16890e26	−	6.36205e25i	0.322651	−	0.0647772i
$999$		−	1.40288e26i		−	0.141557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.19.d.b.3.15	✓	16
3.2	odd	2		72.19.b.b.19.2		16
4.3	odd	2		32.19.d.b.15.11		16
8.3	odd	2	inner	8.19.d.b.3.16	yes	16
8.5	even	2		32.19.d.b.15.12		16
24.11	even	2		72.19.b.b.19.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.19.d.b.3.15	✓	16	1.1	even	1	trivial
8.19.d.b.3.16	yes	16	8.3	odd	2	inner
32.19.d.b.15.11		16	4.3	odd	2
32.19.d.b.15.12		16	8.5	even	2
72.19.b.b.19.1		16	24.11	even	2
72.19.b.b.19.2		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(501.983 - 100.781i) q^{2} -12665.3 q^{3} +(241830. - 101181. i) q^{4} -2.68543e6i q^{5} +(-6.35775e6 + 1.27642e6i) q^{6} +4.44900e7i q^{7} +(1.11198e8 - 7.51629e7i) q^{8} -2.27011e8 q^{9} +O(q^{10})\)	\(q+(501.983 - 100.781i) q^{2} -12665.3 q^{3} +(241830. - 101181. i) q^{4} -2.68543e6i q^{5} +(-6.35775e6 + 1.27642e6i) q^{6} +4.44900e7i q^{7} +(1.11198e8 - 7.51629e7i) q^{8} -2.27011e8 q^{9} +(-2.70640e8 - 1.34804e9i) q^{10} -2.94342e9 q^{11} +(-3.06285e9 + 1.28148e9i) q^{12} -2.11268e10i q^{13} +(4.48374e9 + 2.23333e10i) q^{14} +3.40116e10i q^{15} +(4.82444e10 - 4.89371e10i) q^{16} -8.60555e10 q^{17} +(-1.13956e11 + 2.28784e10i) q^{18} -1.59334e11 q^{19} +(-2.71713e11 - 6.49418e11i) q^{20} -5.63478e11i q^{21} +(-1.47755e12 + 2.96640e11i) q^{22} -8.84583e11i q^{23} +(-1.40835e12 + 9.51958e11i) q^{24} -3.39681e12 q^{25} +(-2.12917e12 - 1.06053e13i) q^{26} +7.78195e12 q^{27} +(4.50153e12 + 1.07590e13i) q^{28} +1.10369e13i q^{29} +(3.42772e12 + 1.70733e13i) q^{30} +9.18771e12i q^{31} +(1.92860e13 - 2.94277e13i) q^{32} +3.72792e13 q^{33} +(-4.31984e13 + 8.67275e12i) q^{34} +1.19475e14 q^{35} +(-5.48983e13 + 2.29692e13i) q^{36} -1.80274e13i q^{37} +(-7.99833e13 + 1.60579e13i) q^{38} +2.67576e14i q^{39} +(-2.01844e14 - 2.98613e14i) q^{40} +4.66778e14 q^{41} +(-5.67878e13 - 2.82857e14i) q^{42} +1.02857e14 q^{43} +(-7.11809e14 + 2.97817e14i) q^{44} +6.09622e14i q^{45} +(-8.91491e13 - 4.44046e14i) q^{46} -1.49713e15i q^{47} +(-6.11029e14 + 6.19802e14i) q^{48} -3.50949e14 q^{49} +(-1.70514e15 + 3.42334e14i) q^{50} +1.08992e15 q^{51} +(-2.13762e15 - 5.10909e15i) q^{52} -4.93584e14i q^{53} +(3.90641e15 - 7.84271e14i) q^{54} +7.90434e15i q^{55} +(3.34400e15 + 4.94719e15i) q^{56} +2.01801e15 q^{57} +(1.11231e15 + 5.54032e15i) q^{58} +1.08985e16 q^{59} +(3.44132e15 + 8.22505e15i) q^{60} -7.51024e15i q^{61} +(9.25946e14 + 4.61208e15i) q^{62} -1.00997e16i q^{63} +(6.71549e15 - 1.67159e16i) q^{64} -5.67343e16 q^{65} +(1.87135e16 - 3.75703e15i) q^{66} -1.79279e16 q^{67} +(-2.08108e16 + 8.70715e15i) q^{68} +1.12035e16i q^{69} +(5.99743e16 - 1.20408e16i) q^{70} -4.48026e16i q^{71} +(-2.52432e16 + 1.70628e16i) q^{72} -5.61569e16 q^{73} +(-1.81681e15 - 9.04944e15i) q^{74} +4.30216e16 q^{75} +(-3.85319e16 + 1.61216e16i) q^{76} -1.30953e17i q^{77} +(2.69665e16 + 1.34319e17i) q^{78} +2.04851e17i q^{79} +(-1.31417e17 - 1.29557e17i) q^{80} -1.06116e16 q^{81} +(2.34315e17 - 4.70423e16i) q^{82} +2.79240e17 q^{83} +(-5.70131e16 - 1.36266e17i) q^{84} +2.31096e17i q^{85} +(5.16327e16 - 1.03661e16i) q^{86} -1.39785e17i q^{87} +(-3.27302e17 + 2.21236e17i) q^{88} -3.39490e17 q^{89} +(6.14383e16 + 3.06020e17i) q^{90} +9.39930e17 q^{91} +(-8.95027e16 - 2.13919e17i) q^{92} -1.16365e17i q^{93} +(-1.50882e17 - 7.51533e17i) q^{94} +4.27881e17i q^{95} +(-2.44262e17 + 3.72710e17i) q^{96} -3.43690e17 q^{97} +(-1.76171e17 + 3.53690e16i) q^{98} +6.68190e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9}+O(q^{10}) \) 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9	\( 16 q + 426 q^{2} + 3264 q^{3} - 444332 q^{4} - 15348708 q^{6} + 304914744 q^{8} + 2313856176 q^{9} - 1569837600 q^{10} - 2471571264 q^{11} + 4764364056 q^{12} + 26163923904 q^{14} - 192320075504 q^{16} - 176439301344 q^{17} - 1044291511122 q^{18} - 833365634368 q^{19} + 1256486405760 q^{20} + 59927319356 q^{22} - 1968891910512 q^{24} - 15320509140080 q^{25} + 4184514840864 q^{26} + 11565649473408 q^{27} - 12301604294400 q^{28} - 36336510039360 q^{30} + 141481742931936 q^{32} - 900457491648 q^{33} + 80653465357268 q^{34} + 20487495736320 q^{35} + 277183098847068 q^{36} + 493456694265564 q^{38} - 519930573603840 q^{40} - 594931562445024 q^{41} - 222362598288000 q^{42} - 25\!\cdots\!92 q^{43}+ \cdots - 81\!\cdots\!68 q^{99}+O(q^{100}) \) 16 * q + 426 * q^2 + 3264 * q^3 - 444332 * q^4 - 15348708 * q^6 + 304914744 * q^8 + 2313856176 * q^9 - 1569837600 * q^10 - 2471571264 * q^11 + 4764364056 * q^12 + 26163923904 * q^14 - 192320075504 * q^16 - 176439301344 * q^17 - 1044291511122 * q^18 - 833365634368 * q^19 + 1256486405760 * q^20 + 59927319356 * q^22 - 1968891910512 * q^24 - 15320509140080 * q^25 + 4184514840864 * q^26 + 11565649473408 * q^27 - 12301604294400 * q^28 - 36336510039360 * q^30 + 141481742931936 * q^32 - 900457491648 * q^33 + 80653465357268 * q^34 + 20487495736320 * q^35 + 277183098847068 * q^36 + 493456694265564 * q^38 - 519930573603840 * q^40 - 594931562445024 * q^41 - 222362598288000 * q^42 - 2540155017577792 * q^43 + 73781630442072 * q^44 + 153882272211264 * q^46 + 897135071530464 * q^48 - 3186415704132848 * q^49 + 5668141028706330 * q^50 + 2916050119466880 * q^51 - 4594372123628160 * q^52 - 1377307163285640 * q^54 + 8184134137073664 * q^56 + 9540488340840768 * q^57 - 10505700099162720 * q^58 + 556807886314176 * q^59 + 29677718651516160 * q^60 + 6212402633091840 * q^62 - 56432885385732032 * q^64 - 21153177930524160 * q^65 - 23515570511959320 * q^66 + 162428574934613696 * q^67 - 70717864614203736 * q^68 + 4248100663257600 * q^70 - 36801123950767128 * q^72 - 7655712852492256 * q^73 + 9613779604149984 * q^74 - 384388788469704000 * q^75 - 151130166278324584 * q^76 - 93022771634070720 * q^78 + 26870186366192640 * q^80 + 99506910981790800 * q^81 + 329788507250077556 * q^82 + 866357336138514624 * q^83 + 451843591950574080 * q^84 + 1269201398006865468 * q^86 - 758460699051663856 * q^88 - 883646550464284128 * q^89 - 1227675520905095520 * q^90 - 379834560933460992 * q^91 + 1413121475102841600 * q^92 + 671428514272869504 * q^94 - 483149691255826368 * q^96 - 2614894858526780128 * q^97 - 81635840192738166 * q^98 - 816916348833567168 * q^99

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