LMFDB - Embedded newform 8.19.d.b.3.1

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			3.1
Root			$-226.199 - 141.712i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.19.d.b.3.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-426.398 - 283.424i) q^{2} +35846.9 q^{3} +(101486. + 241703. i) q^{4} -3.47680e6i q^{5} +(-1.52851e7 - 1.01599e7i) q^{6} +1.08296e7i q^{7} +(2.52310e7 - 1.31825e8i) q^{8} +8.97583e8 q^{9} +O(q^{10})$	\(q+(-426.398 - 283.424i) q^{2} +35846.9 q^{3} +(101486. + 241703. i) q^{4} -3.47680e6i q^{5} +(-1.52851e7 - 1.01599e7i) q^{6} +1.08296e7i q^{7} +(2.52310e7 - 1.31825e8i) q^{8} +8.97583e8 q^{9} +(-9.85407e8 + 1.48250e9i) q^{10} -1.36275e8 q^{11} +(3.63796e9 + 8.66430e9i) q^{12} -2.80141e9i q^{13} +(3.06936e9 - 4.61771e9i) q^{14} -1.24633e11i q^{15} +(-4.81207e10 + 4.90587e10i) q^{16} +2.99849e10 q^{17} +(-3.82727e11 - 2.54397e11i) q^{18} -5.03309e10 q^{19} +(8.40350e11 - 3.52845e11i) q^{20} +3.88208e11i q^{21} +(5.81073e10 + 3.86236e10i) q^{22} -1.64351e12i q^{23} +(9.04453e11 - 4.72552e12i) q^{24} -8.27341e12 q^{25} +(-7.93988e11 + 1.19452e12i) q^{26} +1.82878e13 q^{27} +(-2.61754e12 + 1.09905e12i) q^{28} -5.13731e12i q^{29} +(-3.53238e13 + 5.31430e13i) q^{30} -3.37595e13i q^{31} +(3.44230e13 - 7.27996e12i) q^{32} -4.88504e12 q^{33} +(-1.27855e13 - 8.49843e12i) q^{34} +3.76523e13 q^{35} +(9.10919e13 + 2.16948e14i) q^{36} +1.22733e14i q^{37} +(2.14610e13 + 1.42650e13i) q^{38} -1.00422e14i q^{39} +(-4.58328e14 - 8.77229e13i) q^{40} +4.29547e14 q^{41} +(1.10027e14 - 1.65531e14i) q^{42} -5.15040e14 q^{43} +(-1.38300e13 - 3.29380e13i) q^{44} -3.12071e15i q^{45} +(-4.65809e14 + 7.00787e14i) q^{46} -4.52697e14i q^{47} +(-1.72498e15 + 1.75861e15i) q^{48} +1.51113e15 q^{49} +(3.52776e15 + 2.34488e15i) q^{50} +1.07487e15 q^{51} +(6.77109e14 - 2.84304e14i) q^{52} +3.85227e15i q^{53} +(-7.79786e15 - 5.18319e15i) q^{54} +4.73800e14i q^{55} +(1.42761e15 + 2.73241e14i) q^{56} -1.80421e15 q^{57} +(-1.45604e15 + 2.19054e15i) q^{58} -8.14938e15 q^{59} +(3.01240e16 - 1.26484e16i) q^{60} +1.63847e16i q^{61} +(-9.56825e15 + 1.43950e16i) q^{62} +9.72046e15i q^{63} +(-1.67412e16 - 6.65214e15i) q^{64} -9.73995e15 q^{65} +(2.08297e15 + 1.38454e15i) q^{66} +3.10380e16 q^{67} +(3.04304e15 + 7.24742e15i) q^{68} -5.89147e16i q^{69} +(-1.60548e16 - 1.06716e16i) q^{70} +4.98018e16i q^{71} +(2.26469e16 - 1.18324e17i) q^{72} +7.59692e16 q^{73} +(3.47854e16 - 5.23330e16i) q^{74} -2.96577e17 q^{75} +(-5.10788e15 - 1.21651e16i) q^{76} -1.47580e15i q^{77} +(-2.84620e16 + 4.28198e16i) q^{78} +1.64362e17i q^{79} +(1.70567e17 + 1.67306e17i) q^{80} +3.07819e17 q^{81} +(-1.83158e17 - 1.21744e17i) q^{82} +4.04293e16 q^{83} +(-9.38308e16 + 3.93976e16i) q^{84} -1.04251e17i q^{85} +(2.19612e17 + 1.45975e17i) q^{86} -1.84157e17i q^{87} +(-3.43835e15 + 1.79644e16i) q^{88} +1.65081e17 q^{89} +(-8.84485e17 + 1.33066e18i) q^{90} +3.03382e16 q^{91} +(3.97240e17 - 1.66793e17i) q^{92} -1.21017e18i q^{93} +(-1.28305e17 + 1.93029e17i) q^{94} +1.74990e17i q^{95} +(1.23396e18 - 2.60964e17i) q^{96} -4.02901e17 q^{97} +(-6.44344e17 - 4.28291e17i) q^{98} -1.22318e17 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 $

$2$	−426.398	−	283.424i	−0.832808	−	0.553562i
$2$	−426.398	−	283.424i	−0.832808	−	0.553562i
$3$	35846.9			1.82121			0.910607	−	0.413274i	$-0.135615\pi$
$3$	35846.9			1.82121			0.910607	+	0.413274i	$0.135615\pi$
$4$	101486.	+	241703.i	0.387138	+	0.922022i
$5$		−	3.47680e6i		−	1.78012i	−0.455844	−	0.890060i	$-0.650663\pi$
$5$		−	3.47680e6i		−	1.78012i	0.455844	−	0.890060i	$-0.349337\pi$
$6$	−1.52851e7	−	1.01599e7i	−1.51672	−	1.00816i
$7$			1.08296e7i			0.268367i	0.990956	+	0.134184i	$0.0428412\pi$
$7$			1.08296e7i			0.268367i	−0.990956	+	0.134184i	$0.957159\pi$
$8$	2.52310e7	−	1.31825e8i	0.187985	−	0.982172i
$9$	8.97583e8			2.31682
$10$	−9.85407e8	+	1.48250e9i	−0.985407	+	1.48250i
$11$	−1.36275e8			−0.0577939			−0.0288970	−	0.999582i	$-0.509199\pi$
$11$	−1.36275e8			−0.0577939			−0.0288970	+	0.999582i	$0.509199\pi$
$12$	3.63796e9	+	8.66430e9i	0.705060	+	1.67920i
$13$		−	2.80141e9i		−	0.264172i	−0.991238	−	0.132086i	$-0.957832\pi$
$13$		−	2.80141e9i		−	0.264172i	0.991238	−	0.132086i	$-0.0421675\pi$
$14$	3.06936e9	−	4.61771e9i	0.148558	−	0.223498i
$15$		−	1.24633e11i		−	3.24198i
$16$	−4.81207e10	+	4.90587e10i	−0.700249	+	0.713899i
$17$	2.99849e10			0.252849			0.126425	−	0.991976i	$-0.459650\pi$
$17$	2.99849e10			0.252849			0.126425	+	0.991976i	$0.459650\pi$
$18$	−3.82727e11	−	2.54397e11i	−1.92946	−	1.28250i
$19$	−5.03309e10			−0.155974			−0.0779871	−	0.996954i	$-0.524849\pi$
$19$	−5.03309e10			−0.155974			−0.0779871	+	0.996954i	$0.524849\pi$
$20$	8.40350e11	−	3.52845e11i	1.64131	−	0.689151i
$21$			3.88208e11i			0.488754i
$22$	5.81073e10	+	3.86236e10i	0.0481312	+	0.0319925i
$23$		−	1.64351e12i		−	0.912475i	−0.889858	−	0.456237i	$-0.849197\pi$
$23$		−	1.64351e12i		−	0.912475i	0.889858	−	0.456237i	$-0.150803\pi$
$24$	9.04453e11	−	4.72552e12i	0.342362	−	1.78874i
$25$	−8.27341e12			−2.16883
$26$	−7.93988e11	+	1.19452e12i	−0.146236	+	0.220005i
$27$	1.82878e13			2.39821
$28$	−2.61754e12	+	1.09905e12i	−0.247441	+	0.103895i
$29$		−	5.13731e12i		−	0.354123i	−0.984200	−	0.177061i	$-0.943341\pi$
$29$		−	5.13731e12i		−	0.354123i	0.984200	−	0.177061i	$-0.0566591\pi$
$30$	−3.53238e13	+	5.31430e13i	−1.79464	+	2.69994i
$31$		−	3.37595e13i		−	1.27685i	−0.769683	−	0.638426i	$-0.779586\pi$
$31$		−	3.37595e13i		−	1.27685i	0.769683	−	0.638426i	$-0.220414\pi$
$32$	3.44230e13	−	7.27996e12i	0.978360	−	0.206909i
$33$	−4.88504e12			−0.105255
$34$	−1.27855e13	−	8.49843e12i	−0.210575	−	0.139968i
$35$	3.76523e13			0.477726
$36$	9.10919e13	+	2.16948e14i	0.896928	+	2.13616i
$37$			1.22733e14i			0.944376i	0.881498	+	0.472188i	$0.156536\pi$
$37$			1.22733e14i			0.944376i	−0.881498	+	0.472188i	$0.843464\pi$
$38$	2.14610e13	+	1.42650e13i	0.129896	+	0.0863414i
$39$		−	1.00422e14i		−	0.481114i
$40$	−4.58328e14	−	8.77229e13i	−1.74838	−	0.334636i
$41$	4.29547e14			1.31207			0.656033	−	0.754732i	$-0.272233\pi$
$41$	4.29547e14			1.31207			0.656033	+	0.754732i	$0.272233\pi$
$42$	1.10027e14	−	1.65531e14i	0.270556	−	0.407038i
$43$	−5.15040e14			−1.02477			−0.512383	−	0.858757i	$-0.671237\pi$
$43$	−5.15040e14			−1.02477			−0.512383	+	0.858757i	$0.671237\pi$
$44$	−1.38300e13	−	3.29380e13i	−0.0223742	−	0.0532873i
$45$		−	3.12071e15i		−	4.12421i
$46$	−4.65809e14	+	7.00787e14i	−0.505112	+	0.759916i
$47$		−	4.52697e14i		−	0.404508i	−0.979333	−	0.202254i	$-0.935173\pi$
$47$		−	4.52697e14i		−	0.404508i	0.979333	−	0.202254i	$-0.0648266\pi$
$48$	−1.72498e15	+	1.75861e15i	−1.27530	+	1.30016i
$49$	1.51113e15			0.927979
$50$	3.52776e15	+	2.34488e15i	1.80621	+	1.20058i
$51$	1.07487e15			0.460493
$52$	6.77109e14	−	2.84304e14i	0.243573	−	0.102271i
$53$			3.85227e15i			1.16744i	0.811956	+	0.583719i	$0.198403\pi$
$53$			3.85227e15i			1.16744i	−0.811956	+	0.583719i	$0.801597\pi$
$54$	−7.79786e15	−	5.18319e15i	−1.99725	−	1.32756i
$55$			4.73800e14i			0.102880i
$56$	1.42761e15	+	2.73241e14i	0.263583	+	0.0504492i
$57$	−1.80421e15			−0.284062
$58$	−1.45604e15	+	2.19054e15i	−0.196029	+	0.294916i
$59$	−8.14938e15			−0.940711			−0.470356	−	0.882477i	$-0.655874\pi$
$59$	−8.14938e15			−0.940711			−0.470356	+	0.882477i	$0.655874\pi$
$60$	3.01240e16	−	1.26484e16i	2.98917	−	1.25509i
$61$			1.63847e16i			1.40110i	0.713603	+	0.700551i	$0.247062\pi$
$61$			1.63847e16i			1.40110i	−0.713603	+	0.700551i	$0.752938\pi$
$62$	−9.56825e15	+	1.43950e16i	−0.706817	+	1.06337i
$63$			9.72046e15i			0.621759i
$64$	−1.67412e16	−	6.65214e15i	−0.929323	−	0.369268i
$65$	−9.73995e15			−0.470258
$66$	2.08297e15	+	1.38454e15i	0.0876572	+	0.0582652i
$67$	3.10380e16			1.14083			0.570414	−	0.821357i	$-0.306783\pi$
$67$	3.10380e16			1.14083			0.570414	+	0.821357i	$0.306783\pi$
$68$	3.04304e15	+	7.24742e15i	0.0978875	+	0.233133i
$69$		−	5.89147e16i		−	1.66181i
$70$	−1.60548e16	−	1.06716e16i	−0.397854	−	0.264451i
$71$			4.98018e16i			1.08623i	0.839660	+	0.543113i	$0.182755\pi$
$71$			4.98018e16i			1.08623i	−0.839660	+	0.543113i	$0.817245\pi$
$72$	2.26469e16	−	1.18324e17i	0.435528	−	2.27551i
$73$	7.59692e16			1.29042			0.645211	−	0.764005i	$-0.276770\pi$
$73$	7.59692e16			1.29042			0.645211	+	0.764005i	$0.276770\pi$
$74$	3.47854e16	−	5.23330e16i	0.522771	−	0.786484i
$75$	−2.96577e17			−3.94989
$76$	−5.10788e15	−	1.21651e16i	−0.0603835	−	0.143812i
$77$		−	1.47580e15i		−	0.0155100i
$78$	−2.84620e16	+	4.28198e16i	−0.266327	+	0.400676i
$79$			1.64362e17i			1.37138i	0.727893	+	0.685690i	$0.240500\pi$
$79$			1.64362e17i			1.37138i	−0.727893	+	0.685690i	$0.759500\pi$
$80$	1.70567e17	+	1.67306e17i	1.27082	+	1.24653i
$81$	3.07819e17			2.05083
$82$	−1.83158e17	−	1.21744e17i	−1.09270	−	0.726310i
$83$	4.04293e16			0.216268			0.108134	−	0.994136i	$-0.465512\pi$
$83$	4.04293e16			0.216268			0.108134	+	0.994136i	$0.465512\pi$
$84$	−9.38308e16	+	3.93976e16i	−0.450642	+	0.189215i
$85$		−	1.04251e17i		−	0.450102i
$86$	2.19612e17	+	1.45975e17i	0.853433	+	0.567272i
$87$		−	1.84157e17i		−	0.644933i
$88$	−3.43835e15	+	1.79644e16i	−0.0108644	+	0.0567636i
$89$	1.65081e17			0.471182			0.235591	−	0.971852i	$-0.424298\pi$
$89$	1.65081e17			0.471182			0.235591	+	0.971852i	$0.424298\pi$
$90$	−8.84485e17	+	1.33066e18i	−2.28301	+	3.43468i
$91$	3.03382e16			0.0708952
$92$	3.97240e17	−	1.66793e17i	0.841322	−	0.353253i
$93$		−	1.21017e18i		−	2.32542i
$94$	−1.28305e17	+	1.93029e17i	−0.223920	+	0.336877i
$95$			1.74990e17i			0.277653i
$96$	1.23396e18	−	2.60964e17i	1.78180	−	0.376825i
$97$	−4.02901e17			−0.529972			−0.264986	−	0.964252i	$-0.585367\pi$
$97$	−4.02901e17			−0.529972			−0.264986	+	0.964252i	$0.585367\pi$
$98$	−6.44344e17	−	4.28291e17i	−0.772828	−	0.513694i
$99$	−1.22318e17			−0.133898
$100$	−8.39634e17	−	1.99970e18i	−0.839634	−	1.99970i
$101$			1.24060e18i			1.13433i	0.823606	+	0.567163i	$0.191959\pi$
$101$			1.24060e18i			1.13433i	−0.823606	+	0.567163i	$0.808041\pi$
$102$	−4.58320e17	−	3.04643e17i	−0.383502	−	0.254911i
$103$		−	1.12022e18i		−	0.858556i	−0.903172	−	0.429278i	$-0.858768\pi$
$103$		−	1.12022e18i		−	0.858556i	0.903172	−	0.429278i	$-0.141232\pi$
$104$	−3.69296e17	−	7.06824e16i	−0.259463	−	0.0496605i
$105$	1.34972e18			0.870041
$106$	1.09183e18	−	1.64260e18i	0.646250	−	0.972252i
$107$	−1.14037e18			−0.620287			−0.310144	−	0.950690i	$-0.600377\pi$
$107$	−1.14037e18			−0.620287			−0.310144	+	0.950690i	$0.600377\pi$
$108$	1.85595e18	+	4.42020e18i	0.928437	+	2.21120i
$109$			2.82963e16i			0.0130284i	0.999979	+	0.00651419i	$0.00207355\pi$
$109$			2.82963e16i			0.0130284i	−0.999979	+	0.00651419i	$0.997926\pi$
$110$	1.34286e17	−	2.02027e17i	0.0569505	−	0.0856793i
$111$			4.39960e18i			1.71991i
$112$	−5.31286e17	−	5.21128e17i	−0.191587	−	0.187924i
$113$	2.32500e18			0.773956			0.386978	−	0.922089i	$-0.373519\pi$
$113$	2.32500e18			0.773956			0.386978	+	0.922089i	$0.373519\pi$
$114$	7.69311e17	+	5.11356e17i	0.236569	+	0.157246i
$115$	−5.71413e18			−1.62431
$116$	1.24170e18	−	5.21364e17i	0.326509	−	0.137094i
$117$		−	2.51450e18i		−	0.612039i
$118$	3.47487e18	+	2.30973e18i	0.783432	+	0.520742i
$119$			3.24724e17i			0.0678565i
$120$	−1.64297e19	−	3.14460e18i	−3.18418	−	0.609445i
$121$	−5.54135e18			−0.996660
$122$	4.64381e18	−	6.98639e18i	0.775597	−	1.16685i
$123$	1.53979e19			2.38955
$124$	8.15975e18	−	3.42611e18i	1.17729	−	0.494317i
$125$			1.55020e19i			2.08065i
$126$	2.75501e18	−	4.14478e18i	0.344182	−	0.517805i
$127$			9.14710e18i			1.06427i	0.846661	+	0.532133i	$0.178609\pi$
$127$			9.14710e18i			1.06427i	−0.846661	+	0.532133i	$0.821391\pi$
$128$	5.25303e18	+	7.58131e18i	0.569535	+	0.821967i
$129$	−1.84626e19			−1.86632
$130$	4.15309e18	+	2.76053e18i	0.391635	+	0.260317i
$131$	1.00187e18			0.0881796			0.0440898	−	0.999028i	$-0.485961\pi$
$131$	1.00187e18			0.0881796			0.0440898	+	0.999028i	$0.485961\pi$
$132$	−4.95763e17	−	1.18073e18i	−0.0407482	−	0.0970475i
$133$		−	5.45064e17i		−	0.0418584i
$134$	−1.32345e19	−	8.79691e18i	−0.950091	−	0.631520i
$135$		−	6.35828e19i		−	4.26910i
$136$	7.56548e17	−	3.95275e18i	0.0475320	−	0.248342i
$137$	3.46626e18			0.203881			0.101940	−	0.994791i	$-0.467495\pi$
$137$	3.46626e18			0.203881			0.101940	+	0.994791i	$0.467495\pi$
$138$	−1.66978e19	+	2.51211e19i	−0.919916	+	1.38397i
$139$	2.01094e19			1.03817			0.519083	−	0.854724i	$-0.326274\pi$
$139$	2.01094e19			1.03817			0.519083	+	0.854724i	$0.326274\pi$
$140$	3.82117e18	+	9.10065e18i	0.184946	+	0.440474i
$141$		−	1.62278e19i		−	0.736695i
$142$	1.41150e19	−	2.12354e19i	0.601294	−	0.904618i
$143$			3.81763e17i			0.0152675i
$144$	−4.31924e19	+	4.40343e19i	−1.62235	+	1.65397i
$145$	−1.78614e19			−0.630381
$146$	−3.23931e19	−	2.15315e19i	−1.07467	−	0.714329i
$147$	5.41695e19			1.69005
$148$	−2.96648e19	+	1.24556e19i	−0.870736	+	0.365604i
$149$			2.79939e19i			0.773369i	0.922212	+	0.386684i	$0.126380\pi$
$149$			2.79939e19i			0.773369i	−0.922212	+	0.386684i	$0.873620\pi$
$150$	1.26460e20	+	8.40569e19i	3.28950	+	2.18651i
$151$			3.64407e19i			0.892882i	0.894813	+	0.446441i	$0.147309\pi$
$151$			3.64407e19i			0.892882i	−0.894813	+	0.446441i	$0.852691\pi$
$152$	−1.26990e18	+	6.63487e18i	−0.0293209	+	0.153193i
$153$	2.69139e19			0.585806
$154$	−4.18278e17	+	6.29279e17i	−0.00858575	+	0.0129168i
$155$	−1.17375e20			−2.27295
$156$	2.42723e19	−	1.01914e19i	0.443598	−	0.186257i
$157$		−	5.65222e19i		−	0.975264i	−0.873049	−	0.487632i	$-0.837861\pi$
$157$		−	5.65222e19i		−	0.975264i	0.873049	−	0.487632i	$-0.162139\pi$
$158$	4.65842e19	−	7.00836e19i	0.759145	−	1.14210i
$159$			1.38092e20i			2.12615i
$160$	−2.53109e19	−	1.19682e20i	−0.368323	−	1.74160i
$161$	1.77985e19			0.244878
$162$	−1.31253e20	−	8.72432e19i	−1.70795	−	1.13526i
$163$	2.32565e18			0.0286323			0.0143161	−	0.999898i	$-0.495443\pi$
$163$	2.32565e18			0.0286323			0.0143161	+	0.999898i	$0.495443\pi$
$164$	4.35929e19	+	1.03823e20i	0.507950	+	1.20975i
$165$			1.69843e19i			0.187367i
$166$	−1.72389e19	−	1.14586e19i	−0.180110	−	0.119718i
$167$		−	1.78856e20i		−	1.77033i	−0.465274	−	0.885167i	$-0.654044\pi$
$167$		−	1.78856e20i		−	1.77033i	0.465274	−	0.885167i	$-0.345956\pi$
$168$	5.11754e19	+	9.79486e18i	0.480041	+	0.0918787i
$169$	1.04607e20			0.930213
$170$	−2.95473e19	+	4.44525e19i	−0.249160	+	0.374849i
$171$	−4.51762e19			−0.361364
$172$	−5.22692e19	−	1.24486e20i	−0.396725	−	0.944857i
$173$			1.63126e20i			1.17519i	0.809154	+	0.587597i	$0.199926\pi$
$173$			1.63126e20i			1.17519i	−0.809154	+	0.587597i	$0.800074\pi$
$174$	−5.21945e19	+	7.85241e19i	−0.357011	+	0.537105i
$175$		−	8.95977e19i		−	0.582042i
$176$	6.55766e18	−	6.68548e18i	0.0404701	−	0.0412590i
$177$	−2.92130e20			−1.71324
$178$	−7.03903e19	−	4.67880e19i	−0.392404	−	0.260828i
$179$	−2.69767e19			−0.142992			−0.0714961	−	0.997441i	$-0.522777\pi$
$179$	−2.69767e19			−0.142992			−0.0714961	+	0.997441i	$0.522777\pi$
$180$	7.54284e20	−	3.16708e20i	3.80262	−	1.59664i
$181$		−	2.69695e20i		−	1.29350i	−0.762703	−	0.646749i	$-0.776128\pi$
$181$		−	2.69695e20i		−	1.29350i	0.762703	−	0.646749i	$-0.223872\pi$
$182$	−1.29361e19	−	8.59856e18i	−0.0590421	−	0.0392449i
$183$			5.87341e20i			2.55171i
$184$	−2.16655e20	−	4.14673e19i	−0.896207	−	0.171532i
$185$	4.26717e20			1.68110
$186$	−3.42992e20	+	5.16016e20i	−1.28727	+	1.93663i
$187$	−4.08619e18			−0.0146132
$188$	1.09418e20	−	4.59423e19i	0.372965	−	0.156600i
$189$			1.98049e20i			0.643601i
$190$	4.95965e19	−	7.46155e19i	0.153698	−	0.231231i
$191$			1.48397e20i			0.438658i	0.975651	+	0.219329i	$0.0703867\pi$
$191$			1.48397e20i			0.438658i	−0.975651	+	0.219329i	$0.929613\pi$
$192$	−6.00121e20	−	2.38459e20i	−1.69250	−	0.672516i
$193$	−1.72513e20			−0.464309			−0.232154	−	0.972679i	$-0.574577\pi$
$193$	−1.72513e20			−0.464309			−0.232154	+	0.972679i	$0.574577\pi$
$194$	1.71796e20	+	1.14192e20i	0.441365	+	0.293372i
$195$	−3.49147e20			−0.856440
$196$	1.53359e20	+	3.65245e20i	0.359256	+	0.855617i
$197$		−	3.97468e20i		−	0.889418i	−0.895675	−	0.444709i	$-0.853307\pi$
$197$		−	3.97468e20i		−	0.889418i	0.895675	−	0.444709i	$-0.146693\pi$
$198$	5.21562e19	+	3.46679e19i	0.111511	+	0.0741209i
$199$		−	3.99187e20i		−	0.815640i	−0.913062	−	0.407820i	$-0.866289\pi$
$199$		−	3.99187e20i		−	0.815640i	0.913062	−	0.407820i	$-0.133711\pi$
$200$	−2.08746e20	+	1.09064e21i	−0.407707	+	2.13016i
$201$	1.11262e21			2.07769
$202$	3.51614e20	−	5.28987e20i	0.627920	−	0.944675i
$203$	5.56350e19			0.0950350
$204$	1.09084e20	+	2.59798e20i	0.178274	+	0.424585i
$205$		−	1.49345e21i		−	2.33563i
$206$	−3.17497e20	+	4.77660e20i	−0.475264	+	0.715012i
$207$		−	1.47518e21i		−	2.11404i
$208$	1.37434e20	+	1.34806e20i	0.188592	+	0.184986i
$209$	6.85885e18			0.00901436
$210$	−5.75517e20	−	3.82543e20i	−0.724577	−	0.481622i
$211$	−1.19555e21			−1.44220			−0.721100	−	0.692831i	$-0.756363\pi$
$211$	−1.19555e21			−1.44220			−0.721100	+	0.692831i	$0.756363\pi$
$212$	−9.31104e20	+	3.90951e20i	−1.07640	+	0.451959i
$213$			1.78524e21i			1.97825i
$214$	4.86252e20	+	3.23209e20i	0.516580	+	0.343368i
$215$			1.79069e21i			1.82421i
$216$	4.61418e20	−	2.41078e21i	0.450828	−	2.35545i
$217$	3.65601e20			0.342665
$218$	8.01984e18	−	1.20655e19i	0.00721202	−	0.0108501i
$219$	2.72326e21			2.35013
$220$	−1.14519e20	+	4.80840e19i	−0.0948577	+	0.0398287i
$221$		−	8.40001e19i		−	0.0667958i
$222$	1.24695e21	−	1.87598e21i	0.952078	−	1.43236i
$223$		−	9.47274e20i		−	0.694595i	−0.937755	−	0.347298i	$-0.887099\pi$
$223$		−	9.47274e20i		−	0.694595i	0.937755	−	0.347298i	$-0.112901\pi$
$224$	7.88390e19	+	3.72787e20i	0.0555276	+	0.262560i
$225$	−7.42607e21			−5.02477
$226$	−9.91373e20	−	6.58960e20i	−0.644557	−	0.428433i
$227$	2.11701e21			1.32279			0.661395	−	0.750038i	$-0.269965\pi$
$227$	2.11701e21			1.32279			0.661395	+	0.750038i	$0.269965\pi$
$228$	−1.83102e20	−	4.36082e20i	−0.109971	−	0.261912i
$229$			1.70342e21i			0.983561i	0.870719	+	0.491781i	$0.163654\pi$
$229$			1.70342e21i			0.983561i	−0.870719	+	0.491781i	$0.836346\pi$
$230$	2.43649e21	+	1.61952e21i	1.35274	+	0.899159i
$231$		−	5.29030e19i		−	0.0282470i
$232$	−6.77225e20	−	1.29619e20i	−0.347809	−	0.0665699i
$233$	2.47054e21			1.22064			0.610321	−	0.792154i	$-0.291040\pi$
$233$	2.47054e21			1.22064			0.610321	+	0.792154i	$0.291040\pi$
$234$	−7.12670e20	+	1.07218e21i	−0.338802	+	0.509711i
$235$	−1.57393e21			−0.720072
$236$	−8.27046e20	−	1.96973e21i	−0.364185	−	0.867356i
$237$			5.89188e21i			2.49758i
$238$	9.20345e19	−	1.38462e20i	0.0375628	−	0.0565115i
$239$		−	2.48664e20i		−	0.0977307i	−0.998805	−	0.0488654i	$-0.984439\pi$
$239$		−	2.48664e20i		−	0.0977307i	0.998805	−	0.0488654i	$-0.0155605\pi$
$240$	6.11431e21	+	5.99741e21i	2.31444	+	2.27019i
$241$	1.90611e21			0.695016			0.347508	−	0.937677i	$-0.387028\pi$
$241$	1.90611e21			0.695016			0.347508	+	0.937677i	$0.387028\pi$
$242$	2.36282e21	+	1.57055e21i	0.830026	+	0.551713i
$243$	3.94930e21			1.33679
$244$	−3.96022e21	+	1.66281e21i	−1.29185	+	0.542419i
$245$		−	5.25390e21i		−	1.65191i
$246$	−6.56564e21	−	4.36414e21i	−1.99004	−	1.32277i
$247$			1.40998e20i			0.0412040i
$248$	−4.45034e21	−	8.51785e20i	−1.25409	−	0.240030i
$249$	1.44927e21			0.393871
$250$	4.39365e21	−	6.61003e21i	1.15177	−	1.73278i
$251$	−7.71308e21			−1.95058			−0.975292	−	0.220921i	$-0.929094\pi$
$251$	−7.71308e21			−1.95058			−0.975292	+	0.220921i	$0.929094\pi$
$252$	−2.34946e21	+	9.86488e20i	−0.573275	+	0.240706i
$253$			2.23969e20i			0.0527355i
$254$	2.59251e21	−	3.90030e21i	0.589137	−	0.886329i
$255$		−	3.73709e21i		−	0.819732i
$256$	−9.11542e19	−	4.72149e21i	−0.0193027	−	0.999814i
$257$	−7.58318e21			−1.55043			−0.775217	−	0.631695i	$-0.782359\pi$
$257$	−7.58318e21			−1.55043			−0.775217	+	0.631695i	$0.782359\pi$
$258$	7.87241e21	+	5.23274e21i	1.55428	+	1.03312i
$259$	−1.32915e21			−0.253440
$260$	−9.88466e20	−	2.35417e21i	−0.182055	−	0.433588i
$261$		−	4.61116e21i		−	0.820438i
$262$	−4.27193e20	−	2.83953e20i	−0.0734366	−	0.0488129i
$263$			3.30248e21i			0.548578i	0.961647	+	0.274289i	$0.0884425\pi$
$263$			3.30248e21i			0.548578i	−0.961647	+	0.274289i	$0.911558\pi$
$264$	−1.23254e20	+	6.43970e20i	−0.0197864	+	0.103379i
$265$	1.33936e22			2.07818
$266$	−1.54484e20	+	2.32414e20i	−0.0231712	+	0.0348600i
$267$	5.91767e21			0.858122
$268$	3.14992e21	+	7.50196e21i	0.441658	+	1.05187i
$269$		−	1.42430e22i		−	1.93122i	−0.259994	−	0.965610i	$-0.583721\pi$
$269$		−	1.42430e22i		−	1.93122i	0.259994	−	0.965610i	$-0.416279\pi$
$270$	−1.80209e22	+	2.71116e22i	−2.36321	+	3.55534i
$271$			1.37402e22i			1.74289i	0.490491	+	0.871446i	$0.336817\pi$
$271$			1.37402e22i			1.74289i	−0.490491	+	0.871446i	$0.663183\pi$
$272$	−1.44289e21	+	1.47102e21i	−0.177058	+	0.180509i
$273$	1.08753e21			0.129115
$274$	−1.47801e21	−	9.82422e20i	−0.169794	−	0.112861i
$275$	1.12746e21			0.125345
$276$	1.42398e22	−	5.97900e21i	1.53223	−	0.643350i
$277$			9.97314e21i			1.03876i	0.854544	+	0.519379i	$0.173837\pi$
$277$			9.97314e21i			1.03876i	−0.854544	+	0.519379i	$0.826163\pi$
$278$	−8.57461e21	−	5.69949e21i	−0.864592	−	0.574689i
$279$		−	3.03020e22i		−	2.95824i
$280$	9.50004e20	−	4.96351e21i	0.0898055	−	0.469209i
$281$	4.87172e21			0.445990			0.222995	−	0.974820i	$-0.428417\pi$
$281$	4.87172e21			0.445990			0.222995	+	0.974820i	$0.428417\pi$
$282$	−4.59935e21	+	6.91949e21i	−0.407806	+	0.613525i
$283$	−2.09871e21			−0.180249			−0.0901247	−	0.995930i	$-0.528727\pi$
$283$	−2.09871e21			−0.180249			−0.0901247	+	0.995930i	$0.528727\pi$
$284$	−1.20372e22	+	5.05418e21i	−1.00152	+	0.420519i
$285$			6.27287e21i			0.505665i
$286$	1.08201e20	−	1.62783e20i	0.00845154	−	0.0127149i
$287$			4.65181e21i			0.352116i
$288$	3.08975e22	−	6.53437e21i	2.26668	−	0.479370i
$289$	−1.31640e22			−0.936067
$290$	7.61605e21	+	5.06234e21i	0.524986	+	0.348955i
$291$	−1.44428e22			−0.965192
$292$	7.70979e21	+	1.83619e22i	0.499571	+	1.18980i
$293$			1.17383e22i			0.737557i	0.929517	+	0.368779i	$0.120224\pi$
$293$			1.17383e22i			0.737557i	−0.929517	+	0.368779i	$0.879776\pi$
$294$	−2.30978e22	−	1.53529e22i	−1.40749	−	0.935547i
$295$			2.83337e22i			1.67458i
$296$	1.61792e22	+	3.09667e21i	0.927540	+	0.177529i
$297$	−2.49217e21			−0.138602
$298$	7.93413e21	−	1.19365e22i	0.428108	−	0.644068i
$299$	−4.60414e21			−0.241050
$300$	−3.00983e22	−	7.16833e22i	−1.52915	−	3.64189i
$301$		−	5.57767e21i		−	0.275014i
$302$	1.03282e22	−	1.55382e22i	0.494266	−	0.743599i
$303$			4.44715e22i			2.06585i
$304$	2.42196e21	−	2.46917e21i	0.109221	−	0.111350i
$305$	5.69662e22			2.49413
$306$	−1.14760e22	−	7.62805e21i	−0.487864	−	0.324280i
$307$	−3.79319e22			−1.56588			−0.782941	−	0.622096i	$-0.786282\pi$
$307$	−3.79319e22			−1.56588			−0.782941	+	0.622096i	$0.786282\pi$
$308$	3.56705e20	−	1.49773e20i	0.0143006	−	0.00600450i
$309$		−	4.01565e22i		−	1.56361i
$310$	5.00484e22	+	3.32668e22i	1.89293	+	1.25822i
$311$		−	3.70263e22i		−	1.36040i	−0.733026	−	0.680201i	$-0.761893\pi$
$311$		−	3.70263e22i		−	1.36040i	0.733026	−	0.680201i	$-0.238107\pi$
$312$	−1.32381e22	−	2.53375e21i	−0.472537	−	0.0904424i
$313$	−2.78803e22			−0.966938			−0.483469	−	0.875361i	$-0.660623\pi$
$313$	−2.78803e22			−0.966938			−0.483469	+	0.875361i	$0.660623\pi$
$314$	−1.60197e22	+	2.41009e22i	−0.539870	+	0.812208i
$315$	3.37960e22			1.10680
$316$	−3.97268e22	+	1.66804e22i	−1.26444	+	0.530913i
$317$		−	8.83287e21i		−	0.273255i	−0.990622	−	0.136628i	$-0.956374\pi$
$317$		−	8.83287e21i		−	0.273255i	0.990622	−	0.136628i	$-0.0436264\pi$
$318$	3.91386e22	−	5.88822e22i	1.17696	−	1.77068i
$319$			7.00087e20i			0.0204661i
$320$	−2.31281e22	+	5.82057e22i	−0.657341	+	1.65431i
$321$	−4.08789e22			−1.12968
$322$	−7.58924e21	−	5.04452e21i	−0.203937	−	0.135555i
$323$	−1.50917e21			−0.0394380
$324$	3.12392e22	+	7.44006e22i	0.793954	+	1.89091i
$325$			2.31773e22i			0.572943i
$326$	−9.91651e20	−	6.59144e20i	−0.0238452	−	0.0158497i
$327$			1.01433e21i			0.0237275i
$328$	1.08379e22	−	5.66249e22i	0.246649	−	1.28867i
$329$	4.90252e21			0.108557
$330$	4.81376e21	−	7.24206e21i	0.103719	−	0.156040i
$331$	2.27336e22			0.476669			0.238335	−	0.971183i	$-0.423399\pi$
$331$	2.27336e22			0.476669			0.238335	+	0.971183i	$0.423399\pi$
$332$	4.10300e21	+	9.77186e21i	0.0837256	+	0.199404i
$333$			1.10163e23i			2.18795i
$334$	−5.06920e22	+	7.62637e22i	−0.979990	+	1.47435i
$335$		−	1.07913e23i		−	2.03081i
$336$	−1.90450e22	−	1.86808e22i	−0.348921	−	0.342250i
$337$	6.91628e22			1.23368			0.616842	−	0.787087i	$-0.288412\pi$
$337$	6.91628e22			1.23368			0.616842	+	0.787087i	$0.288412\pi$
$338$	−4.46044e22	−	2.96483e22i	−0.774689	−	0.514931i
$339$	8.33440e22			1.40954
$340$	2.51978e22	−	1.05800e22i	0.415004	−	0.174251i
$341$			4.60058e21i			0.0737943i
$342$	1.92630e22	+	1.28040e22i	0.300947	+	0.200037i
$343$			3.40000e22i			0.517407i
$344$	−1.29950e22	+	6.78950e22i	−0.192641	+	1.00650i
$345$	−2.04834e23			−2.95822
$346$	4.62339e22	−	6.95567e22i	0.650543	−	0.978710i
$347$	3.56633e22			0.488941			0.244471	−	0.969657i	$-0.421386\pi$
$347$	3.56633e22			0.488941			0.244471	+	0.969657i	$0.421386\pi$
$348$	4.45112e22	−	1.86893e22i	0.594643	−	0.249678i
$349$		−	6.57517e22i		−	0.856008i	−0.903777	−	0.428004i	$-0.859217\pi$
$349$		−	6.57517e22i		−	0.856008i	0.903777	−	0.428004i	$-0.140783\pi$
$350$	−2.53941e22	+	3.82042e22i	−0.322196	+	0.484729i
$351$		−	5.12316e22i		−	0.633540i
$352$	−4.69099e21	+	9.92077e20i	−0.0565433	+	0.0119581i
$353$	−2.20900e22			−0.259552			−0.129776	−	0.991543i	$-0.541426\pi$
$353$	−2.20900e22			−0.259552			−0.129776	+	0.991543i	$0.541426\pi$
$354$	1.24564e23	+	8.27967e22i	1.42680	+	0.948383i
$355$	1.73151e23			1.93361
$356$	1.67534e22	+	3.99006e22i	0.182412	+	0.434440i
$357$			1.16404e22i			0.123581i
$358$	1.15028e22	+	7.64585e21i	0.119085	+	0.0791551i
$359$		−	1.38349e23i		−	1.39678i	−0.715719	−	0.698389i	$-0.753901\pi$
$359$		−	1.38349e23i		−	1.39678i	0.715719	−	0.698389i	$-0.246099\pi$
$360$	−4.11388e23	−	7.87386e22i	−4.05069	−	0.775292i
$361$	−1.01594e23			−0.975672
$362$	−7.64380e22	+	1.14997e23i	−0.716032	+	1.07723i
$363$	−1.98640e23			−1.81513
$364$	3.07889e21	+	7.33281e21i	0.0274462	+	0.0653669i
$365$		−	2.64129e23i		−	2.29710i
$366$	1.66466e23	−	2.50441e23i	1.41253	−	2.12508i
$367$		−	2.17842e22i		−	0.180363i	−0.995925	−	0.0901813i	$-0.971255\pi$
$367$		−	2.17842e22i		−	0.180363i	0.995925	−	0.0901813i	$-0.0287447\pi$
$368$	8.06283e22	+	7.90867e22i	0.651414	+	0.638959i
$369$	3.85554e23			3.03982
$370$	−1.81951e23	−	1.20942e23i	−1.40004	−	0.930595i
$371$	−4.17185e22			−0.313302
$372$	2.92502e23	−	1.22816e23i	2.14409	−	0.900258i
$373$			1.59981e23i			1.14469i	0.820013	+	0.572345i	$0.193966\pi$
$373$			1.59981e23i			1.14469i	−0.820013	+	0.572345i	$0.806034\pi$
$374$	1.74234e21	+	1.15812e21i	0.0121700	+	0.00808929i
$375$			5.55701e23i			3.78930i
$376$	−5.96767e22	−	1.14220e22i	−0.397296	−	0.0760415i
$377$	−1.43917e22			−0.0935494
$378$	5.61318e22	−	8.44477e22i	0.356273	−	0.535996i
$379$	−1.69897e23			−1.05301			−0.526506	−	0.850171i	$-0.676498\pi$
$379$	−1.69897e23			−1.05301			−0.526506	+	0.850171i	$0.676498\pi$
$380$	−4.22956e22	+	1.77590e22i	−0.256002	+	0.107490i
$381$			3.27896e23i			1.93825i
$382$	4.20593e22	−	6.32762e22i	0.242824	−	0.365317i
$383$		−	1.52269e22i		−	0.0858665i	−0.999078	−	0.0429333i	$-0.986330\pi$
$383$		−	1.52269e22i		−	0.0858665i	0.999078	−	0.0429333i	$-0.0136703\pi$
$384$	1.88305e23	+	2.71767e23i	1.03724	+	1.49698i
$385$	−5.13106e21			−0.0276097
$386$	7.35593e22	+	4.88944e22i	0.386680	+	0.257024i
$387$	−4.62291e23			−2.37420
$388$	−4.08887e22	−	9.73822e22i	−0.205172	−	0.488646i
$389$			8.21497e22i			0.402772i	0.979512	+	0.201386i	$0.0645446\pi$
$389$			8.21497e22i			0.402772i	−0.979512	+	0.201386i	$0.935455\pi$
$390$	1.48876e23	+	9.89567e22i	0.713250	+	0.474093i
$391$		−	4.92803e22i		−	0.230719i
$392$	3.81274e22	−	1.99205e23i	0.174447	−	0.911435i
$393$	3.59138e22			0.160594
$394$	−1.12652e23	+	1.69479e23i	−0.492348	+	0.740714i
$395$	5.71454e23			2.44122
$396$	−1.24136e22	−	2.95646e22i	−0.0518370	−	0.123457i
$397$			7.33206e22i			0.299303i	0.988739	+	0.149652i	$0.0478152\pi$
$397$			7.33206e22i			0.299303i	−0.988739	+	0.149652i	$0.952185\pi$
$398$	−1.13139e23	+	1.70212e23i	−0.451508	+	0.679272i
$399$		−	1.95389e22i		−	0.0762330i
$400$	3.98123e23	−	4.05883e23i	1.51872	−	1.54832i
$401$	−1.38921e23			−0.518167			−0.259083	−	0.965855i	$-0.583420\pi$
$401$	−1.38921e23			−0.518167			−0.259083	+	0.965855i	$0.583420\pi$
$402$	−4.74417e23	−	3.15342e23i	−1.73032	−	1.15013i
$403$	−9.45743e22			−0.337309
$404$	−2.99855e23	+	1.25903e23i	−1.04587	+	0.439140i
$405$		−	1.07022e24i		−	3.65072i
$406$	−2.37226e22	−	1.57683e22i	−0.0791459	−	0.0526078i
$407$		−	1.67254e22i		−	0.0545792i
$408$	2.71199e22	−	1.41694e23i	0.0865659	−	0.452283i
$409$	−9.61573e22			−0.300243			−0.150121	−	0.988668i	$-0.547966\pi$
$409$	−9.61573e22			−0.300243			−0.150121	+	0.988668i	$0.547966\pi$
$410$	−4.23278e23	+	6.36802e23i	−1.29292	+	1.94513i
$411$	1.24255e23			0.371311
$412$	2.70760e23	−	1.13687e23i	0.791608	−	0.332379i
$413$		−	8.82544e22i		−	0.252456i
$414$	−4.18102e23	+	6.29015e23i	−1.17025	+	1.76059i
$415$		−	1.40564e23i		−	0.384984i
$416$	−2.03942e22	−	9.64331e22i	−0.0546596	−	0.258456i
$417$	7.20862e23			1.89072
$418$	−2.92460e21	−	1.94396e21i	−0.00750723	−	0.00499001i
$419$	−3.85125e22			−0.0967554			−0.0483777	−	0.998829i	$-0.515405\pi$
$419$	−3.85125e22			−0.0967554			−0.0483777	+	0.998829i	$0.515405\pi$
$420$	1.36977e23	+	3.26231e23i	0.336826	+	0.802197i
$421$			4.63719e23i			1.11613i	0.829796	+	0.558066i	$0.188457\pi$
$421$			4.63719e23i			1.11613i	−0.829796	+	0.558066i	$0.811543\pi$
$422$	5.09780e23	+	3.38847e23i	1.20108	+	0.798348i
$423$		−	4.06333e23i		−	0.937171i
$424$	5.07825e23	+	9.71966e22i	1.14663	+	0.219461i
$425$	−2.48077e23			−0.548386
$426$	5.05981e23	−	7.61224e23i	1.09508	−	1.64750i
$427$	−1.77439e23			−0.376010
$428$	−1.15732e23	−	2.75631e23i	−0.240137	−	0.571919i
$429$			1.36850e22i			0.0278055i
$430$	5.07524e23	−	7.63545e23i	1.00981	−	1.51921i
$431$			2.54794e23i			0.496471i	0.968700	+	0.248235i	$0.0798507\pi$
$431$			2.54794e23i			0.496471i	−0.968700	+	0.248235i	$0.920149\pi$
$432$	−8.80021e23	+	8.97175e23i	−1.67934	+	1.71208i
$433$	−5.45490e23			−1.01952			−0.509760	−	0.860316i	$-0.670266\pi$
$433$	−5.45490e23			−1.01952			−0.509760	+	0.860316i	$0.670266\pi$
$434$	−1.55892e23	−	1.03620e23i	−0.285374	−	0.189687i
$435$	−6.40276e23			−1.14806
$436$	−6.83928e21	+	2.87167e21i	−0.0120125	+	0.00504378i
$437$			8.27192e22i			0.142322i
$438$	−1.16119e24	−	7.71838e23i	−1.95721	−	1.30095i
$439$		−	3.40557e23i		−	0.562352i	−0.959656	−	0.281176i	$-0.909275\pi$
$439$		−	3.40557e23i		−	0.562352i	0.959656	−	0.281176i	$-0.0907245\pi$
$440$	6.24587e22	+	1.19544e22i	0.101046	+	0.0193400i
$441$	1.35637e24			2.14996
$442$	−2.38076e22	+	3.58174e22i	−0.0369756	+	0.0556281i
$443$	3.64770e23			0.555118			0.277559	−	0.960709i	$-0.410475\pi$
$443$	3.64770e23			0.555118			0.277559	+	0.960709i	$0.410475\pi$
$444$	−1.06339e24	+	4.46496e23i	−1.58580	+	0.665842i
$445$		−	5.73955e23i		−	0.838759i
$446$	−2.68480e23	+	4.03915e23i	−0.384502	+	0.578465i
$447$			1.00350e24i			1.40847i
$448$	7.20400e22	−	1.81300e23i	0.0990995	−	0.249400i
$449$	1.21112e23			0.163294			0.0816468	−	0.996661i	$-0.473982\pi$
$449$	1.21112e23			0.163294			0.0816468	+	0.996661i	$0.473982\pi$
$450$	3.16646e24	+	2.10473e24i	4.18467	+	2.78153i
$451$	−5.85365e22			−0.0758294
$452$	2.35954e23	+	5.61958e23i	0.299628	+	0.713605i
$453$			1.30629e24i			1.62613i
$454$	−9.02689e23	−	6.00012e23i	−1.10163	−	0.732246i
$455$		−	1.05480e23i		−	0.126202i
$456$	−4.55220e22	+	2.37840e23i	−0.0533996	+	0.278998i
$457$	−1.16172e23			−0.133615			−0.0668077	−	0.997766i	$-0.521281\pi$
$457$	−1.16172e23			−0.133615			−0.0668077	+	0.997766i	$0.521281\pi$
$458$	4.82789e23	−	7.26332e23i	0.544462	−	0.819117i
$459$	5.48357e23			0.606386
$460$	−5.79904e23	−	1.38112e24i	−0.628833	−	1.49765i
$461$		−	1.17462e24i		−	1.24908i	−0.780992	−	0.624541i	$-0.785286\pi$
$461$		−	1.17462e24i		−	1.24908i	0.780992	−	0.624541i	$-0.214714\pi$
$462$	−1.49940e22	+	2.25577e22i	−0.0156365	+	0.0235243i
$463$			7.75697e23i			0.793347i	0.917960	+	0.396673i	$0.129835\pi$
$463$			7.75697e23i			0.793347i	−0.917960	+	0.396673i	$0.870165\pi$
$464$	2.52030e23	+	2.47211e23i	0.252808	+	0.247974i
$465$	−4.20753e24			−4.13953
$466$	−1.05343e24	−	7.00210e23i	−1.01656	−	0.675701i
$467$	1.68463e24			1.59460			0.797300	−	0.603584i	$-0.206261\pi$
$467$	1.68463e24			1.59460			0.797300	+	0.603584i	$0.206261\pi$
$468$	6.07762e23	−	2.55186e23i	0.564314	−	0.236943i
$469$			3.36129e23i			0.306161i
$470$	6.71122e23	+	4.46091e23i	0.599681	+	0.398605i
$471$		−	2.02615e24i		−	1.77616i
$472$	−2.05617e23	+	1.07429e24i	−0.176840	+	0.923940i
$473$	7.01871e22			0.0592252
$474$	1.66990e24	−	2.51228e24i	1.38256	−	2.08000i
$475$	4.16409e23			0.338281
$476$	−7.84866e22	+	3.29549e22i	−0.0625652	+	0.0262698i
$477$			3.45773e24i			2.70474i
$478$	−7.04772e22	+	1.06030e23i	−0.0541000	+	0.0813909i
$479$		−	1.30173e24i		−	0.980619i	−0.871548	−	0.490310i	$-0.836884\pi$
$479$		−	1.30173e24i		−	0.980619i	0.871548	−	0.490310i	$-0.163116\pi$
$480$	−9.07320e23	−	4.29022e24i	−0.670794	−	3.17182i
$481$	3.43825e23			0.249478
$482$	−8.12761e23	−	5.40237e23i	−0.578814	−	0.384734i
$483$	6.38022e23			0.445976
$484$	−5.62368e23	−	1.33936e24i	−0.385844	−	0.918942i
$485$			1.40080e24i			0.943413i
$486$	−1.68397e24	−	1.11933e24i	−1.11329	−	0.739998i
$487$			1.08221e24i			0.702348i	0.936310	+	0.351174i	$0.114217\pi$
$487$			1.08221e24i			0.702348i	−0.936310	+	0.351174i	$0.885783\pi$
$488$	2.15991e24	+	4.13402e23i	1.37612	+	0.263387i
$489$	8.33674e22			0.0521455
$490$	−1.48908e24	+	2.24025e24i	−0.914437	+	1.37573i
$491$	−2.27518e24			−1.37177			−0.685887	−	0.727708i	$-0.740586\pi$
$491$	−2.27518e24			−1.37177			−0.685887	+	0.727708i	$0.740586\pi$
$492$	1.56267e24	+	3.72172e24i	0.925085	+	2.20322i
$493$		−	1.54042e23i		−	0.0895398i
$494$	3.99622e22	−	6.01211e22i	0.0228090	−	0.0343150i
$495$			4.25275e23i			0.238354i
$496$	1.65620e24	+	1.62453e24i	0.911543	+	0.894115i
$497$	−5.39334e23			−0.291508
$498$	−6.17964e23	−	4.10757e23i	−0.328019	−	0.218032i
$499$	−7.54183e23			−0.393162			−0.196581	−	0.980488i	$-0.562984\pi$
$499$	−7.54183e23			−0.393162			−0.196581	+	0.980488i	$0.562984\pi$
$500$	−3.74688e24	+	1.57324e24i	−1.91840	+	0.805497i
$501$		−	6.41144e24i		−	3.22415i
$502$	3.28884e24	+	2.18607e24i	1.62446	+	1.07977i
$503$		−	2.48165e24i		−	1.20401i	−0.798494	−	0.602003i	$-0.794370\pi$
$503$		−	2.48165e24i		−	1.20401i	0.798494	−	0.602003i	$-0.205630\pi$
$504$	1.28140e24	+	2.45257e23i	0.610674	+	0.116882i
$505$	4.31330e24			2.01923
$506$	6.34781e22	−	9.54998e22i	0.0291924	−	0.0439185i
$507$	3.74986e24			1.69412
$508$	−2.21088e24	+	9.28301e23i	−0.981276	+	0.412017i
$509$			2.65070e23i			0.115585i	0.998329	+	0.0577925i	$0.0184062\pi$
$509$			2.65070e23i			0.115585i	−0.998329	+	0.0577925i	$0.981594\pi$
$510$	−1.05918e24	+	1.59349e24i	−0.453773	+	0.682679i
$511$			8.22715e23i			0.346307i
$512$	−1.29931e24	+	2.03907e24i	−0.537384	+	0.843338i
$513$	−9.20441e23			−0.374059
$514$	3.23345e24	+	2.14925e24i	1.29121	+	0.858262i
$515$	−3.89478e24			−1.52833
$516$	−1.87369e24	−	4.46246e24i	−0.722522	−	1.72079i
$517$			6.16913e22i			0.0233781i
$518$	5.66745e23	+	3.76712e23i	0.211067	+	0.140295i
$519$			5.84758e24i			2.14028i
$520$	−2.45748e23	+	1.28397e24i	−0.0884017	+	0.461874i
$521$	4.48105e24			1.58431			0.792155	−	0.610320i	$-0.208959\pi$
$521$	4.48105e24			1.58431			0.792155	+	0.610320i	$0.208959\pi$
$522$	−1.30691e24	+	1.96619e24i	−0.454164	+	0.683267i
$523$	1.94656e24			0.664895			0.332448	−	0.943122i	$-0.392126\pi$
$523$	1.94656e24			0.664895			0.332448	+	0.943122i	$0.392126\pi$
$524$	1.01675e23	+	2.42154e23i	0.0341376	+	0.0813035i
$525$		−	3.21180e24i		−	1.06002i
$526$	9.36002e23	−	1.40817e24i	0.303672	−	0.456860i
$527$		−	1.01227e24i		−	0.322851i
$528$	2.35072e23	−	2.39654e23i	0.0737048	−	0.0751415i
$529$	5.43039e23			0.167390
$530$	−5.71098e24	−	3.79605e24i	−1.73072	−	1.15040i
$531$	−7.31474e24			−2.17946
$532$	1.31743e23	−	5.53162e22i	0.0385943	−	0.0162049i
$533$		−	1.20334e24i		−	0.346611i
$534$	−2.52328e24	−	1.67721e24i	−0.714651	−	0.475024i
$535$			3.96484e24i			1.10419i
$536$	7.83119e23	−	4.09158e24i	0.214459	−	1.12049i
$537$	−9.67034e23			−0.260419
$538$	−4.03681e24	+	6.07319e24i	−1.06905	+	1.60834i
$539$	−2.05930e23			−0.0536315
$540$	1.53681e25	−	6.45276e24i	3.93620	−	1.65273i
$541$		−	3.82714e24i		−	0.964050i	−0.876158	−	0.482025i	$-0.839901\pi$
$541$		−	3.82714e24i		−	0.964050i	0.876158	−	0.482025i	$-0.160099\pi$
$542$	3.89431e24	−	5.85880e24i	0.964799	−	1.45149i
$543$		−	9.66774e24i		−	2.35574i
$544$	1.03217e24	−	2.18289e23i	0.247378	−	0.0523168i
$545$	9.83803e22			0.0231921
$546$	−4.63721e23	−	3.08232e23i	−0.107528	−	0.0714734i
$547$	−8.31133e24			−1.89577			−0.947883	−	0.318620i	$-0.896781\pi$
$547$	−8.31133e24			−1.89577			−0.947883	+	0.318620i	$0.896781\pi$
$548$	3.51777e23	+	8.37805e23i	0.0789300	+	0.187983i
$549$			1.47066e25i			3.24610i
$550$	−4.80746e23	−	3.19549e23i	−0.104388	−	0.0693862i
$551$			2.58566e23i			0.0552340i
$552$	−7.76642e24	−	1.48647e24i	−1.63218	−	0.312396i
$553$	−1.77998e24			−0.368034
$554$	2.82663e24	−	4.25252e24i	0.575017	−	0.865085i
$555$	1.52965e25			3.06165
$556$	2.04082e24	+	4.86050e24i	0.401913	+	0.957211i
$557$			8.43060e23i			0.163366i	0.996658	+	0.0816830i	$0.0260295\pi$
$557$			8.43060e23i			0.163366i	−0.996658	+	0.0816830i	$0.973970\pi$
$558$	−8.58830e24	+	1.29207e25i	−1.63757	+	2.46364i
$559$			1.44284e24i			0.270715i
$560$	−1.81186e24	+	1.84717e24i	−0.334527	+	0.341048i
$561$	−1.46477e23			−0.0266137
$562$	−2.07729e24	−	1.38076e24i	−0.371424	−	0.246883i
$563$	5.66512e24			0.996858			0.498429	−	0.866930i	$-0.333910\pi$
$563$	5.66512e24			0.996858			0.498429	+	0.866930i	$0.333910\pi$
$564$	3.92230e24	−	1.64689e24i	0.679249	−	0.285202i
$565$		−	8.08354e24i		−	1.37773i
$566$	8.94884e23	+	5.94824e23i	0.150113	+	0.0997793i
$567$			3.33355e24i			0.550376i
$568$	6.56512e24	+	1.25655e24i	1.06686	+	0.204195i
$569$	−7.57789e24			−1.21210			−0.606049	−	0.795427i	$-0.707246\pi$
$569$	−7.57789e24			−1.21210			−0.606049	+	0.795427i	$0.707246\pi$
$570$	1.77788e24	−	2.67474e24i	0.279917	−	0.421122i
$571$	−5.34260e24			−0.827995			−0.413997	−	0.910278i	$-0.635868\pi$
$571$	−5.34260e24			−0.827995			−0.413997	+	0.910278i	$0.635868\pi$
$572$	−9.22730e22	+	3.87435e22i	−0.0140770	+	0.00591064i
$573$			5.31959e24i			0.798889i
$574$	1.31844e24	−	1.98352e24i	0.194918	−	0.293245i
$575$			1.35974e25i			1.97900i
$576$	−1.50266e25	−	5.97085e24i	−2.15307	−	0.855527i
$577$	8.76279e24			1.23612			0.618059	−	0.786132i	$-0.287919\pi$
$577$	8.76279e24			1.23612			0.618059	+	0.786132i	$0.287919\pi$
$578$	5.61309e24	+	3.73099e24i	0.779564	+	0.518171i
$579$	−6.18408e24			−0.845605
$580$	−1.81268e24	−	4.31714e24i	−0.244044	−	0.581225i
$581$			4.37833e23i			0.0580394i
$582$	6.15836e24	+	4.09343e24i	0.803819	+	0.534294i
$583$		−	5.24968e23i		−	0.0674708i
$584$	1.91678e24	−	1.00146e25i	0.242580	−	1.26742i
$585$	−8.74241e24			−1.08950
$586$	3.32691e24	−	5.00517e24i	0.408284	−	0.614244i
$587$	−7.96895e24			−0.963071			−0.481535	−	0.876427i	$-0.659921\pi$
$587$	−7.96895e24			−0.963071			−0.481535	+	0.876427i	$0.659921\pi$
$588$	5.49744e24	+	1.30929e25i	0.654281	+	1.55826i
$589$			1.69915e24i			0.199156i
$590$	8.03045e24	−	1.20814e25i	0.926983	−	1.39460i
$591$		−	1.42480e25i		−	1.61982i
$592$	−6.02112e24	−	5.90599e24i	−0.674189	−	0.661299i
$593$	3.11221e24			0.343224			0.171612	−	0.985165i	$-0.445103\pi$
$593$	3.11221e24			0.343224			0.171612	+	0.985165i	$0.445103\pi$
$594$	1.06265e24	+	7.06340e23i	0.115429	+	0.0767248i
$595$	1.12900e24			0.120793
$596$	−6.76619e24	+	2.84098e24i	−0.713063	+	0.299400i
$597$		−	1.43096e25i		−	1.48546i
$598$	1.96319e24	+	1.30492e24i	0.200749	+	0.133436i
$599$			1.18101e25i			1.18963i	0.803864	+	0.594814i	$0.202774\pi$
$599$			1.18101e25i			1.18963i	−0.803864	+	0.594814i	$0.797226\pi$
$600$	−7.48292e24	+	3.90962e25i	−0.742522	+	3.87947i
$601$	4.63978e24			0.453552			0.226776	−	0.973947i	$-0.427182\pi$
$601$	4.63978e24			0.453552			0.226776	+	0.973947i	$0.427182\pi$
$602$	−1.58084e24	+	2.37830e24i	−0.152237	+	0.229034i
$603$	2.78592e25			2.64309
$604$	−8.80781e24	+	3.69821e24i	−0.823257	+	0.345668i
$605$			1.92661e25i			1.77417i
$606$	1.26043e25	−	1.89626e25i	1.14358	−	1.72045i
$607$		−	7.64084e24i		−	0.683035i	−0.939875	−	0.341518i	$-0.889059\pi$
$607$		−	7.64084e24i		−	0.683035i	0.939875	−	0.341518i	$-0.110941\pi$
$608$	−1.73254e24	+	3.66407e23i	−0.152599	+	0.0322724i
$609$	1.99434e24			0.173079
$610$	−2.42903e25	−	1.61456e25i	−2.07713	−	1.38066i
$611$	−1.26819e24			−0.106860
$612$	2.73138e24	+	6.50516e24i	0.226788	+	0.540126i
$613$			1.33533e24i			0.109255i	0.998507	+	0.0546277i	$0.0173972\pi$
$613$			1.33533e24i			0.109255i	−0.998507	+	0.0546277i	$0.982603\pi$
$614$	1.61741e25	+	1.07508e25i	1.30408	+	0.866814i
$615$		−	5.35355e25i		−	4.25369i
$616$	−1.94548e23	−	3.72359e22i	−0.0152335	−	0.00291565i
$617$	−1.43061e25			−1.10396			−0.551982	−	0.833856i	$-0.686128\pi$
$617$	−1.43061e25			−1.10396			−0.551982	+	0.833856i	$0.686128\pi$
$618$	−1.13813e25	+	1.71226e25i	−0.865558	+	1.30219i
$619$	−7.11980e24			−0.533644			−0.266822	−	0.963746i	$-0.585974\pi$
$619$	−7.11980e24			−0.533644			−0.266822	+	0.963746i	$0.585974\pi$
$620$	−1.19119e25	−	2.83698e25i	−0.879944	−	2.09571i
$621$		−	3.00561e25i		−	2.18830i
$622$	−1.04941e25	+	1.57879e25i	−0.753067	+	1.13295i
$623$			1.78776e24i			0.126450i
$624$	4.92658e24	+	4.83239e24i	0.343467	+	0.336900i
$625$	2.23369e25			1.53498
$626$	1.18881e25	+	7.90195e24i	0.805273	+	0.535260i
$627$	2.45869e23			0.0164171
$628$	1.36616e25	−	5.73620e24i	0.899215	−	0.377561i
$629$			3.68013e24i			0.238785i
$630$	−1.44106e25	−	9.57861e24i	−0.921755	−	0.612685i
$631$			4.13788e23i			0.0260924i	0.999915	+	0.0130462i	$0.00415285\pi$
$631$			4.13788e23i			0.0260924i	−0.999915	+	0.0130462i	$0.995847\pi$
$632$	2.16670e25	+	4.14702e24i	1.34693	+	0.257800i
$633$	−4.28568e25			−2.62656
$634$	−2.50345e24	+	3.76632e24i	−0.151264	+	0.227569i
$635$	3.18026e25			1.89452
$636$	−3.33772e25	+	1.40144e25i	−1.96036	+	0.823114i
$637$		−	4.23331e24i		−	0.245146i
$638$	1.98421e23	−	2.98515e23i	0.0113293	−	0.0170444i
$639$			4.47013e25i			2.51659i
$640$	2.63587e25	−	1.82637e25i	1.46320	−	1.01384i
$641$	−2.79818e25			−1.53163			−0.765815	−	0.643061i	$-0.777664\pi$
$641$	−2.79818e25			−1.53163			−0.765815	+	0.643061i	$0.777664\pi$
$642$	1.74307e25	+	1.15861e25i	0.940803	+	0.625346i
$643$	−6.06624e24			−0.322865			−0.161432	−	0.986884i	$-0.551611\pi$
$643$	−6.06624e24			−0.322865			−0.161432	+	0.986884i	$0.551611\pi$
$644$	1.80629e24	+	4.30194e24i	0.0948016	+	0.225783i
$645$			6.41907e25i			3.32227i
$646$	6.43505e23	+	4.27734e23i	0.0328443	+	0.0218314i
$647$			2.42292e25i			1.21955i	0.792574	+	0.609775i	$0.208740\pi$
$647$			2.42292e25i			1.21955i	−0.792574	+	0.609775i	$0.791260\pi$
$648$	7.76657e24	−	4.05782e25i	0.385526	−	2.01427i
$649$	1.11056e24			0.0543674
$650$	6.56899e24	−	9.88272e24i	0.317160	−	0.477152i
$651$	1.31057e25			0.624067
$652$	2.36020e23	+	5.62115e23i	0.0110846	+	0.0263996i
$653$			2.57769e25i			1.19402i	0.802233	+	0.597011i	$0.203645\pi$
$653$			2.57769e25i			1.19402i	−0.802233	+	0.597011i	$0.796355\pi$
$654$	2.87487e23	−	4.32510e23i	0.0131346	−	0.0197604i
$655$		−	3.48328e24i		−	0.156970i
$656$	−2.06701e25	+	2.10730e25i	−0.918773	+	0.936682i
$657$	6.81887e25			2.98967
$658$	−2.09042e24	−	1.38949e24i	−0.0904068	−	0.0600929i
$659$	−2.16127e25			−0.922021			−0.461010	−	0.887395i	$-0.652513\pi$
$659$	−2.16127e25			−0.922021			−0.461010	+	0.887395i	$0.652513\pi$
$660$	−4.10515e24	+	1.72367e24i	−0.172756	+	0.0725366i
$661$		−	3.80929e25i		−	1.58136i	−0.612230	−	0.790680i	$-0.709727\pi$
$661$		−	3.80929e25i		−	1.58136i	0.612230	−	0.790680i	$-0.290273\pi$
$662$	−9.69357e24	−	6.44326e24i	−0.396974	−	0.263866i
$663$		−	3.01115e24i		−	0.121649i
$664$	1.02007e24	−	5.32958e24i	0.0406553	−	0.212413i
$665$	−1.89507e24			−0.0745129
$666$	3.12228e25	−	4.69732e25i	1.21117	−	1.82214i
$667$	−8.44320e24			−0.323128
$668$	4.32299e25	−	1.81513e25i	1.63229	−	0.685362i
$669$		−	3.39569e25i		−	1.26501i
$670$	−3.05851e25	+	4.60137e25i	−1.12418	+	1.69128i
$671$		−	2.23282e24i		−	0.0809751i
$672$	2.82614e24	+	1.33633e25i	0.101128	+	0.478178i
$673$	−1.42553e25			−0.503317			−0.251658	−	0.967816i	$-0.580976\pi$
$673$	−1.42553e25			−0.503317			−0.251658	+	0.967816i	$0.580976\pi$
$674$	−2.94909e25	−	1.96024e25i	−1.02742	−	0.682920i
$675$	−1.51302e26			−5.20129
$676$	1.06162e25	+	2.52839e25i	0.360120	+	0.857677i
$677$		−	3.50982e25i		−	1.17486i	−0.809275	−	0.587430i	$-0.800140\pi$
$677$		−	3.50982e25i		−	1.17486i	0.809275	−	0.587430i	$-0.199860\pi$
$678$	−3.55377e25	−	2.36217e25i	−1.17388	−	0.780268i
$679$		−	4.36325e24i		−	0.142227i
$680$	−1.37429e25	−	2.63036e24i	−0.442078	−	0.0846127i
$681$	7.58884e25			2.40908
$682$	1.30391e24	−	1.96167e24i	0.0408497	−	0.0614565i
$683$	5.18583e25			1.60336			0.801681	−	0.597752i	$-0.203939\pi$
$683$	5.18583e25			1.60336			0.801681	+	0.597752i	$0.203939\pi$
$684$	−4.58474e24	−	1.09192e25i	−0.139898	−	0.333185i
$685$		−	1.20515e25i		−	0.362932i
$686$	9.63642e24	−	1.44975e25i	0.286417	−	0.430900i
$687$			6.10623e25i			1.79127i
$688$	2.47841e25	−	2.52672e25i	0.717591	−	0.731579i
$689$	1.07918e25			0.308405
$690$	8.73408e25	+	5.80549e25i	2.46363	+	1.63756i
$691$	−1.96292e25			−0.546513			−0.273256	−	0.961941i	$-0.588101\pi$
$691$	−1.96292e25			−0.546513			−0.273256	+	0.961941i	$0.588101\pi$
$692$	−3.94281e25	+	1.65550e25i	−1.08355	+	0.454961i
$693$		−	1.32466e24i		−	0.0359339i
$694$	−1.52068e25	−	1.01078e25i	−0.407194	−	0.270659i
$695$		−	6.99164e25i		−	1.84806i
$696$	−2.42765e25	−	4.64646e24i	−0.633435	−	0.121238i
$697$	1.28799e25			0.331755
$698$	−1.86356e25	+	2.80363e25i	−0.473854	+	0.712890i
$699$	8.85613e25			2.22305
$700$	2.16560e25	−	9.09289e24i	0.536655	−	0.225330i
$701$			5.39698e25i			1.32035i	0.751112	+	0.660174i	$0.229518\pi$
$701$			5.39698e25i			1.32035i	−0.751112	+	0.660174i	$0.770482\pi$
$702$	−1.45203e25	+	2.18450e25i	−0.350704	+	0.527617i
$703$		−	6.17726e24i		−	0.147298i
$704$	2.28141e24	+	9.06521e23i	0.0537092	+	0.0213414i
$705$	−5.64207e25			−1.31140
$706$	9.41914e24	+	6.26084e24i	0.216157	+	0.143678i
$707$	−1.34351e25			−0.304416
$708$	−2.96471e25	−	7.06086e25i	−0.663258	−	1.57964i
$709$		−	6.68291e25i		−	1.47622i	−0.674683	−	0.738108i	$-0.735720\pi$
$709$		−	6.68291e25i		−	1.47622i	0.674683	−	0.738108i	$-0.264280\pi$
$710$	−7.38311e25	−	4.90751e25i	−1.61033	−	1.07037i
$711$			1.47529e26i			3.17724i
$712$	4.16517e24	−	2.17618e25i	0.0885753	−	0.462781i
$713$	−5.54839e25			−1.16510
$714$	3.29916e24	−	4.96342e24i	0.0684099	−	0.102919i
$715$	1.32731e24			0.0271781
$716$	−2.73776e24	−	6.52035e24i	−0.0553576	−	0.131842i
$717$		−	8.91383e24i		−	0.177988i
$718$	−3.92115e25	+	5.89919e25i	−0.773204	+	1.16325i
$719$		−	9.75703e25i		−	1.90002i	−0.312222	−	0.950009i	$-0.601073\pi$
$719$		−	9.75703e25i		−	1.90002i	0.312222	−	0.950009i	$-0.398927\pi$
$720$	1.53098e26	+	1.50171e26i	2.94427	+	2.88798i
$721$	1.21315e25			0.230408
$722$	4.33195e25	+	2.87942e25i	0.812547	+	0.540095i
$723$	6.83282e25			1.26577
$724$	6.51860e25	−	2.73702e25i	1.19263	−	0.500762i
$725$			4.25031e25i			0.768030i
$726$	8.46998e25	+	5.62994e25i	1.51165	+	1.00479i
$727$		−	3.21406e24i		−	0.0566558i	−0.999599	−	0.0283279i	$-0.990982\pi$
$727$		−	3.21406e24i		−	0.0566558i	0.999599	−	0.0283279i	$-0.00901825\pi$
$728$	7.65462e23	−	3.99933e24i	0.0133273	−	0.0696313i
$729$	2.23152e25			0.383754
$730$	−7.48606e25	+	1.12624e26i	−1.27159	+	1.91305i
$731$	−1.54434e25			−0.259112
$732$	−1.41962e26	+	5.96068e25i	−2.35273	+	0.987861i
$733$			3.47572e25i			0.568996i	0.958677	+	0.284498i	$0.0918270\pi$
$733$			3.47572e25i			0.568996i	−0.958677	+	0.284498i	$0.908173\pi$
$734$	−6.17415e24	+	9.28872e24i	−0.0998419	+	0.150207i
$735$		−	1.88336e26i		−	3.00849i
$736$	−1.19647e25	−	5.65744e25i	−0.188799	−	0.892729i
$737$	−4.22970e24			−0.0659330
$738$	−1.64399e26	−	1.09275e26i	−2.53158	−	1.68273i
$739$	−3.36930e25			−0.512554			−0.256277	−	0.966603i	$-0.582496\pi$
$739$	−3.36930e25			−0.512554			−0.256277	+	0.966603i	$0.582496\pi$
$740$	4.33057e25	+	1.03139e26i	0.650818	+	1.55001i
$741$			5.05434e24i			0.0750414i
$742$	1.77887e25	+	1.18240e25i	0.260921	+	0.173432i
$743$		−	6.47870e25i		−	0.938833i	−0.882977	−	0.469416i	$-0.844464\pi$
$743$		−	6.47870e25i		−	0.938833i	0.882977	−	0.469416i	$-0.155536\pi$
$744$	−1.59531e26	−	3.05339e25i	−2.28396	−	0.437145i
$745$	9.73290e25			1.37669
$746$	4.53423e25	−	6.82153e25i	0.633657	−	0.953307i
$747$	3.62886e25			0.501055
$748$	−4.14690e23	−	9.87643e23i	−0.00565730	−	0.0134737i
$749$		−	1.23498e25i		−	0.166465i
$750$	1.57499e26	−	2.36949e26i	2.09762	−	3.15576i
$751$			1.29075e26i			1.69856i	0.527939	+	0.849282i	$0.322965\pi$
$751$			1.29075e26i			1.69856i	−0.527939	+	0.849282i	$0.677035\pi$
$752$	2.22087e25	+	2.17841e25i	0.288777	+	0.283256i
$753$	−2.76490e26			−3.55243
$754$	6.13660e24	+	4.07896e24i	0.0779087	+	0.0517854i
$755$	1.26697e26			1.58944
$756$	−4.78690e25	+	2.00992e25i	−0.593414	+	0.249162i
$757$			8.91927e25i			1.09261i	0.837585	+	0.546306i	$0.183967\pi$
$757$			8.91927e25i			1.09261i	−0.837585	+	0.546306i	$0.816033\pi$
$758$	7.24438e25	+	4.81530e25i	0.876957	+	0.582908i
$759$			8.02860e24i			0.0960426i
$760$	2.30681e25	+	4.41518e24i	0.272703	+	0.0521946i
$761$	1.25661e26			1.46804			0.734022	−	0.679125i	$-0.237641\pi$
$761$	1.25661e26			1.46804			0.734022	+	0.679125i	$0.237641\pi$
$762$	9.29335e25	−	1.39814e26i	1.07294	−	1.61419i
$763$	−3.06437e23			−0.00349639
$764$	−3.58680e25	+	1.50602e25i	−0.404452	+	0.169821i
$765$		−	9.35742e25i		−	1.04281i
$766$	−4.31568e24	+	6.49273e24i	−0.0475325	+	0.0715103i
$767$			2.28298e25i			0.248510i
$768$	−3.26760e24	−	1.69251e26i	−0.0351543	−	1.82087i
$769$	3.35301e25			0.356531			0.178266	−	0.983982i	$-0.442951\pi$
$769$	3.35301e25			0.356531			0.178266	+	0.983982i	$0.442951\pi$
$770$	2.18787e24	+	1.45427e24i	0.0229935	+	0.0152837i
$771$	−2.71834e26			−2.82367
$772$	−1.75077e25	−	4.16969e25i	−0.179751	−	0.428103i
$773$			6.15259e25i			0.624371i	0.950021	+	0.312185i	$0.101061\pi$
$773$			6.15259e25i			0.624371i	−0.950021	+	0.312185i	$0.898939\pi$
$774$	1.97120e26	+	1.31024e26i	1.97725	+	1.31427i
$775$			2.79306e26i			2.76927i
$776$	−1.01656e25	+	5.31124e25i	−0.0996270	+	0.520523i
$777$	−4.76458e25			−0.461568
$778$	2.32832e25	−	3.50284e25i	0.222960	−	0.335432i
$779$	−2.16195e25			−0.204648
$780$	−3.54335e25	−	8.43898e25i	−0.331560	−	0.789657i
$781$		−	6.78675e24i		−	0.0627773i
$782$	−1.39672e25	+	2.10130e25i	−0.127717	+	0.192144i
$783$		−	9.39500e25i		−	0.849260i
$784$	−7.27169e25	+	7.41343e25i	−0.649816	+	0.662483i
$785$	−1.96516e26			−1.73609
$786$	−1.53136e25	−	1.01788e25i	−0.133744	−	0.0888987i
$787$	−7.75132e24			−0.0669273			−0.0334636	−	0.999440i	$-0.510654\pi$
$787$	−7.75132e24			−0.0669273			−0.0334636	+	0.999440i	$0.510654\pi$
$788$	9.60689e25	−	4.03373e25i	0.820063	−	0.344327i
$789$			1.18384e26i			0.999078i
$790$	−2.43666e26	−	1.61964e26i	−2.03307	−	1.35137i
$791$			2.51788e25i			0.207705i
$792$	−3.08621e24	+	1.61246e25i	−0.0251709	+	0.131511i
$793$	4.59003e25			0.370132
$794$	2.07808e25	−	3.12637e25i	0.165683	−	0.249262i
$795$	4.80118e26			3.78481
$796$	9.64845e25	−	4.05118e25i	0.752038	−	0.315765i
$797$		−	1.14334e26i		−	0.881155i	−0.897715	−	0.440578i	$-0.854774\pi$
$797$		−	1.14334e26i		−	0.881155i	0.897715	−	0.440578i	$-0.145226\pi$
$798$	−5.53778e24	+	8.33132e24i	−0.0421997	+	0.0634875i
$799$		−	1.35741e25i		−	0.102280i
$800$	−2.84796e26	+	6.02301e25i	−2.12189	+	0.448749i
$801$	1.48174e26			1.09164
$802$	5.92357e25	+	3.93736e25i	0.431533	+	0.286838i
$803$	−1.03527e25			−0.0745785
$804$	1.12915e26	+	2.68922e26i	0.804353	+	1.91568i
$805$		−	6.18817e25i		−	0.435913i
$806$	4.03263e25	+	2.68046e25i	0.280914	+	0.186722i
$807$		−	5.10569e26i		−	3.51716i
$808$	1.63541e26	+	3.13014e25i	1.11410	+	0.213237i
$809$	−6.96753e25			−0.469399			−0.234699	−	0.972068i	$-0.575411\pi$
$809$	−6.96753e25			−0.469399			−0.234699	+	0.972068i	$0.575411\pi$
$810$	−3.03327e26	+	4.56340e26i	−2.02090	+	3.04035i
$811$	−2.24307e26			−1.47793			−0.738967	−	0.673741i	$-0.764686\pi$
$811$	−2.24307e26			−1.47793			−0.738967	+	0.673741i	$0.764686\pi$
$812$	5.64616e24	+	1.34471e25i	0.0367916	+	0.0876244i
$813$			4.92545e26i			3.17418i
$814$	−4.74038e24	+	7.13168e24i	−0.0302130	+	0.0454540i
$815$		−	8.08580e24i		−	0.0509688i
$816$	−5.17234e25	+	5.27316e25i	−0.322460	+	0.328745i
$817$	2.59224e25			0.159837
$818$	4.10013e25	+	2.72533e25i	0.250045	+	0.166203i
$819$	2.72310e25			0.164251
$820$	3.60970e26	−	1.51564e26i	2.15351	−	0.904212i
$821$		−	1.51175e26i		−	0.892055i	−0.895019	−	0.446027i	$-0.852838\pi$
$821$		−	1.51175e26i		−	0.892055i	0.895019	−	0.446027i	$-0.147162\pi$
$822$	−5.29820e25	−	3.52168e25i	−0.309230	−	0.205544i
$823$			1.32029e26i			0.762203i	0.924533	+	0.381101i	$0.124455\pi$
$823$			1.32029e26i			0.762203i	−0.924533	+	0.381101i	$0.875545\pi$
$824$	−1.47673e26	−	2.82643e25i	−0.843250	−	0.161396i
$825$	4.04160e25			0.228280
$826$	−2.50134e25	+	3.76315e25i	−0.139750	+	0.210247i
$827$	1.71500e26			0.947797			0.473898	−	0.880580i	$-0.342846\pi$
$827$	1.71500e26			0.947797			0.473898	+	0.880580i	$0.342846\pi$
$828$	3.56556e26	−	1.49710e26i	1.94919	−	0.818424i
$829$		−	1.01192e26i		−	0.547210i	−0.961842	−	0.273605i	$-0.911784\pi$
$829$		−	1.01192e26i		−	0.547210i	0.961842	−	0.273605i	$-0.0882160\pi$
$830$	−3.98393e25	+	5.99363e25i	−0.213112	+	0.320617i
$831$			3.57507e26i			1.89180i
$832$	−1.86354e25	+	4.68990e25i	−0.0975503	+	0.245501i
$833$	4.53112e25			0.234639
$834$	−3.07374e26	−	2.04309e26i	−1.57461	−	1.04663i
$835$	−6.21845e26			−3.15140
$836$	6.96076e23	+	1.65780e24i	0.00348980	+	0.00831144i
$837$		−	6.17386e26i		−	3.06216i
$838$	1.64216e25	+	1.09154e25i	0.0805787	+	0.0535601i
$839$		−	1.53518e26i		−	0.745252i	−0.927982	−	0.372626i	$-0.878458\pi$
$839$		−	1.53518e26i		−	0.745252i	0.927982	−	0.372626i	$-0.121542\pi$
$840$	3.40547e25	−	1.77927e26i	0.163555	−	0.854530i
$841$	1.84065e26			0.874597
$842$	1.31429e26	−	1.97729e26i	0.617849	−	0.929524i
$843$	1.74636e26			0.812244
$844$	−1.21331e26	−	2.88968e26i	−0.558330	−	1.32974i
$845$		−	3.63699e26i		−	1.65589i
$846$	−1.15164e26	+	1.73259e26i	−0.518782	+	0.780483i
$847$		−	6.00105e25i		−	0.267471i
$848$	−1.88988e26	−	1.85374e26i	−0.833433	−	0.817498i
$849$	−7.52322e25			−0.328273
$850$	1.05780e26	+	7.03110e25i	0.456700	+	0.303566i
$851$	2.01712e26			0.861719
$852$	−4.31498e26	+	1.81177e26i	−1.82399	+	0.765855i
$853$			2.05890e26i			0.861178i	0.902548	+	0.430589i	$0.141694\pi$
$853$			2.05890e26i			0.861178i	−0.902548	+	0.430589i	$0.858306\pi$
$854$	7.56598e25	+	5.02906e25i	0.313144	+	0.208145i
$855$			1.57068e26i			0.643271i
$856$	−2.87727e25	+	1.50330e26i	−0.116605	+	0.609229i
$857$	1.36020e26			0.545476			0.272738	−	0.962088i	$-0.412071\pi$
$857$	1.36020e26			0.545476			0.272738	+	0.962088i	$0.412071\pi$
$858$	3.87867e24	−	5.83526e24i	0.0153921	−	0.0231566i
$859$	−1.80946e26			−0.710576			−0.355288	−	0.934757i	$-0.615617\pi$
$859$	−1.80946e26			−0.710576			−0.355288	+	0.934757i	$0.615617\pi$
$860$	−4.32814e26	+	1.81729e26i	−1.68196	+	0.706219i
$861$			1.66753e26i			0.641278i
$862$	7.22147e25	−	1.08644e26i	0.274828	−	0.413465i
$863$			2.20461e26i			0.830298i	0.909754	+	0.415149i	$0.136271\pi$
$863$			2.20461e26i			0.830298i	−0.909754	+	0.415149i	$0.863729\pi$
$864$	6.29520e26	−	1.33134e26i	2.34631	−	0.496211i
$865$	5.67157e26			2.09198
$866$	2.32596e26	+	1.54605e26i	0.849065	+	0.564368i
$867$	−4.71889e26			−1.70478
$868$	3.71034e25	+	8.83668e25i	0.132659	+	0.315945i
$869$		−	2.23985e25i		−	0.0792575i
$870$	2.73012e26	+	1.81470e26i	0.956112	+	0.635522i
$871$		−	8.69503e25i		−	0.301375i
$872$	3.73015e24	+	7.13943e23i	0.0127961	+	0.00244915i
$873$	−3.61637e26			−1.22785
$874$	2.34446e25	−	3.52713e25i	0.0787844	−	0.118527i
$875$	−1.67881e26			−0.558378
$876$	2.76373e26	+	6.58220e26i	0.909825	+	2.16687i
$877$		−	4.77671e26i		−	1.55644i	−0.627991	−	0.778221i	$-0.716123\pi$
$877$		−	4.77671e26i		−	1.55644i	0.627991	−	0.778221i	$-0.283877\pi$
$878$	−9.65219e25	+	1.45212e26i	−0.311297	+	0.468331i
$879$			4.20781e26i			1.34325i
$880$	−2.32441e25	−	2.27996e25i	−0.0734459	−	0.0720417i
$881$	3.98413e26			1.24609			0.623047	−	0.782184i	$-0.285895\pi$
$881$	3.98413e26			1.24609			0.623047	+	0.782184i	$0.285895\pi$
$882$	−5.78352e26	−	3.84427e26i	−1.79050	−	1.19014i
$883$	2.83034e26			0.867346			0.433673	−	0.901070i	$-0.357217\pi$
$883$	2.83034e26			0.867346			0.433673	+	0.901070i	$0.357217\pi$
$884$	2.03030e25	−	8.52481e24i	0.0615872	−	0.0258592i
$885$			1.01568e27i			3.04976i
$886$	−1.55537e26	−	1.03384e26i	−0.462307	−	0.307292i
$887$		−	1.96588e26i		−	0.578422i	−0.957265	−	0.289211i	$-0.906607\pi$
$887$		−	1.96588e26i		−	0.578422i	0.957265	−	0.289211i	$-0.0933929\pi$
$888$	5.79976e26	+	1.11006e26i	1.68925	+	0.323318i
$889$	−9.90594e25			−0.285614
$890$	−1.62672e26	+	2.44733e26i	−0.464306	+	0.698525i
$891$	−4.19480e25			−0.118526
$892$	2.28959e26	−	9.61349e25i	0.640432	−	0.268904i
$893$			2.27847e25i			0.0630927i
$894$	2.84414e26	−	4.27888e26i	0.779676	−	1.17298i
$895$			9.37926e25i			0.254543i
$896$	−8.21025e25	+	5.68882e25i	−0.220589	+	0.152844i
$897$	−1.65044e26			−0.439004
$898$	−5.16418e25	−	3.43260e25i	−0.135992	−	0.0903932i
$899$	−1.73433e26			−0.452162
$900$	−7.53641e26	−	1.79490e27i	−1.94528	−	4.63295i
$901$			1.15510e26i			0.295186i
$902$	2.49598e25	+	1.65906e25i	0.0631513	+	0.0419763i
$903$		−	1.99942e26i		−	0.500859i
$904$	5.86619e25	−	3.06492e26i	0.145492	−	0.760158i
$905$	−9.37674e26			−2.30258
$906$	3.70233e26	−	5.56998e26i	0.900164	−	1.35425i
$907$	−1.92019e26			−0.462252			−0.231126	−	0.972924i	$-0.574241\pi$
$907$	−1.92019e26			−0.462252			−0.231126	+	0.972924i	$0.574241\pi$
$908$	2.14847e26	+	5.11687e26i	0.512102	+	1.21964i
$909$			1.11354e27i			2.62803i
$910$	−2.98954e25	+	4.49763e25i	−0.0698606	+	0.105102i
$911$		−	2.22110e26i		−	0.513927i	−0.966421	−	0.256964i	$-0.917278\pi$
$911$		−	2.22110e26i		−	0.513927i	0.966421	−	0.256964i	$-0.0827221\pi$
$912$	8.68200e25	−	8.85123e25i	0.198914	−	0.202792i
$913$	−5.50950e24			−0.0124990
$914$	4.95355e25	+	3.29260e25i	0.111276	+	0.0739644i
$915$	2.04206e27			4.54234
$916$	−4.11720e26	+	1.72873e26i	−0.906865	+	0.380773i
$917$			1.08498e25i			0.0236645i
$918$	−2.33818e26	−	1.55417e26i	−0.505003	−	0.335672i
$919$			4.44214e26i			0.950064i	0.879969	+	0.475032i	$0.157563\pi$
$919$			4.44214e26i			0.950064i	−0.879969	+	0.475032i	$0.842437\pi$
$920$	−1.44173e26	+	7.53265e26i	−0.305347	+	1.59536i
$921$	−1.35974e27			−2.85181
$922$	−3.32917e26	+	5.00857e26i	−0.691445	+	1.04025i
$923$	1.39516e26			0.286951
$924$	1.27868e25	−	5.36891e24i	0.0260444	−	0.0109355i
$925$		−	1.01542e27i		−	2.04819i
$926$	2.19851e26	−	3.30755e26i	0.439167	−	0.660705i
$927$		−	1.00549e27i		−	1.98912i
$928$	−3.73994e25	−	1.76842e26i	−0.0732712	−	0.346460i
$929$	9.19897e25			0.178483			0.0892417	−	0.996010i	$-0.471556\pi$
$929$	9.19897e25			0.178483			0.0892417	+	0.996010i	$0.471556\pi$
$930$	1.79408e27	+	1.19251e27i	3.44743	+	2.29149i
$931$	−7.60568e25			−0.144741
$932$	2.50725e26	+	5.97135e26i	0.472556	+	1.12546i
$933$		−	1.32728e27i		−	2.47758i
$934$	−7.18320e26	−	4.77463e26i	−1.32799	−	0.882710i
$935$			1.42068e25i			0.0260132i
$936$	−3.31474e26	−	6.34433e25i	−0.601128	−	0.115054i
$937$	6.97243e26			1.25236			0.626178	−	0.779680i	$-0.284618\pi$
$937$	6.97243e26			1.25236			0.626178	+	0.779680i	$0.284618\pi$
$938$	9.52669e25	−	1.43325e26i	0.169479	−	0.254973i
$939$	−9.99424e26			−1.76100
$940$	−1.59732e26	−	3.80424e26i	−0.278767	−	0.663922i
$941$			7.71125e26i			1.33296i	0.745522	+	0.666481i	$0.232200\pi$
$941$			7.71125e26i			1.33296i	−0.745522	+	0.666481i	$0.767800\pi$
$942$	−5.74259e26	+	8.63945e26i	−0.983218	+	1.47920i
$943$		−	7.05963e26i		−	1.19723i
$944$	3.92154e26	−	3.99798e26i	0.658732	−	0.671573i
$945$	6.88576e26			1.14569
$946$	−2.99276e25	−	1.98927e25i	−0.0493232	−	0.0327849i
$947$	5.01052e26			0.817962			0.408981	−	0.912543i	$-0.365884\pi$
$947$	5.01052e26			0.817962			0.408981	+	0.912543i	$0.365884\pi$
$948$	−1.42408e27	+	5.97942e26i	−2.30282	+	0.966906i
$949$		−	2.12821e26i		−	0.340894i
$950$	−1.77556e26	−	1.18020e26i	−0.281723	−	0.187259i
$951$		−	3.16632e26i		−	0.497656i
$952$	4.28067e25	+	8.19310e24i	0.0666468	+	0.0127560i
$953$	7.95510e26			1.22690			0.613451	−	0.789733i	$-0.289781\pi$
$953$	7.95510e26			1.22690			0.613451	+	0.789733i	$0.289781\pi$
$954$	9.80004e26	−	1.47437e27i	1.49724	−	2.25253i
$955$	5.15947e26			0.780863
$956$	6.01026e25	−	2.52358e25i	0.0901099	−	0.0378352i
$957$			2.50960e25i			0.0372732i
$958$	−3.68941e26	+	5.55053e26i	−0.542834	+	0.816667i
$959$			3.75382e25i			0.0547150i
$960$	−8.29073e26	+	2.08650e27i	−1.19716	+	3.01284i
$961$	−4.40650e26			−0.630352
$962$	−1.46606e26	−	9.74483e25i	−0.207767	−	0.138102i
$963$	−1.02358e27			−1.43709
$964$	1.93443e26	+	4.60712e26i	0.269067	+	0.640820i
$965$			5.99794e26i			0.826525i
$966$	−2.72051e26	−	1.80831e26i	−0.371412	−	0.246875i
$967$			9.39317e26i			1.27050i	0.772307	+	0.635249i	$0.219103\pi$
$967$			9.39317e26i			1.27050i	−0.772307	+	0.635249i	$0.780897\pi$
$968$	−1.39814e26	+	7.30487e26i	−0.187358	+	0.978891i
$969$	−5.40990e25			−0.0718250
$970$	3.97022e26	−	5.97300e26i	0.522238	−	0.785682i
$971$	1.28565e26			0.167551			0.0837757	−	0.996485i	$-0.473302\pi$
$971$	1.28565e26			0.167551			0.0837757	+	0.996485i	$0.473302\pi$
$972$	4.00798e26	+	9.54557e26i	0.517523	+	1.23255i
$973$			2.17777e26i			0.278610i
$974$	3.06725e26	−	4.61453e26i	0.388793	−	0.584921i
$975$			8.30834e26i			1.04345i
$976$	−8.03812e26	−	7.88443e26i	−1.00024	−	0.981120i
$977$	3.96171e26			0.488463			0.244232	−	0.969717i	$-0.421464\pi$
$977$	3.96171e26			0.488463			0.244232	+	0.969717i	$0.421464\pi$
$978$	−3.55477e25	−	2.36283e25i	−0.0434271	−	0.0288658i
$979$	−2.24965e25			−0.0272314
$980$	1.26988e27	−	5.33196e26i	1.52310	−	0.639518i
$981$			2.53983e25i			0.0301844i
$982$	9.70132e26	+	6.44841e26i	1.14242	+	0.759363i
$983$		−	3.94343e26i		−	0.460143i	−0.973174	−	0.230071i	$-0.926104\pi$
$983$		−	3.94343e26i		−	0.460143i	0.973174	−	0.230071i	$-0.0738960\pi$
$984$	3.88505e26	−	2.02983e27i	0.449201	−	2.34695i
$985$	−1.38191e27			−1.58327
$986$	−4.36591e25	+	6.56830e25i	−0.0495658	+	0.0745694i
$987$	1.75740e26			0.197705
$988$	−3.40795e25	+	1.43093e25i	−0.0379910	+	0.0159516i
$989$			8.46471e26i			0.935073i
$990$	1.20533e26	−	1.81336e26i	0.131944	−	0.198503i
$991$		−	1.21537e27i		−	1.31840i	−0.751968	−	0.659200i	$-0.770895\pi$
$991$		−	1.21537e27i		−	1.31840i	0.751968	−	0.659200i	$-0.229105\pi$
$992$	−2.45768e26	−	1.16210e27i	−0.264192	−	1.24922i
$993$	8.14932e26			0.868116
$994$	2.29971e26	+	1.52860e26i	0.242770	+	0.161368i
$995$	−1.38789e27			−1.45194
$996$	1.47080e26	+	3.50291e26i	0.152482	+	0.363158i
$997$			8.41591e25i			0.0864659i	0.999065	+	0.0432330i	$0.0137658\pi$
$997$			8.41591e25i			0.0864659i	−0.999065	+	0.0432330i	$0.986234\pi$
$998$	3.21582e26	+	2.13753e26i	0.327429	+	0.217640i
$999$			2.24451e27i			2.26481i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.19.d.b.3.1	✓	16
3.2	odd	2		72.19.b.b.19.16		16
4.3	odd	2		32.19.d.b.15.1		16
8.3	odd	2	inner	8.19.d.b.3.2	yes	16
8.5	even	2		32.19.d.b.15.2		16
24.11	even	2		72.19.b.b.19.15		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.19.d.b.3.1	✓	16	1.1	even	1	trivial
8.19.d.b.3.2	yes	16	8.3	odd	2	inner
32.19.d.b.15.1		16	4.3	odd	2
32.19.d.b.15.2		16	8.5	even	2
72.19.b.b.19.15		16	24.11	even	2
72.19.b.b.19.16		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)

\(f(q)\)	\(=\)	\(q+(-426.398 - 283.424i) q^{2} +35846.9 q^{3} +(101486. + 241703. i) q^{4} -3.47680e6i q^{5} +(-1.52851e7 - 1.01599e7i) q^{6} +1.08296e7i q^{7} +(2.52310e7 - 1.31825e8i) q^{8} +8.97583e8 q^{9} +O(q^{10})\)	\(q+(-426.398 - 283.424i) q^{2} +35846.9 q^{3} +(101486. + 241703. i) q^{4} -3.47680e6i q^{5} +(-1.52851e7 - 1.01599e7i) q^{6} +1.08296e7i q^{7} +(2.52310e7 - 1.31825e8i) q^{8} +8.97583e8 q^{9} +(-9.85407e8 + 1.48250e9i) q^{10} -1.36275e8 q^{11} +(3.63796e9 + 8.66430e9i) q^{12} -2.80141e9i q^{13} +(3.06936e9 - 4.61771e9i) q^{14} -1.24633e11i q^{15} +(-4.81207e10 + 4.90587e10i) q^{16} +2.99849e10 q^{17} +(-3.82727e11 - 2.54397e11i) q^{18} -5.03309e10 q^{19} +(8.40350e11 - 3.52845e11i) q^{20} +3.88208e11i q^{21} +(5.81073e10 + 3.86236e10i) q^{22} -1.64351e12i q^{23} +(9.04453e11 - 4.72552e12i) q^{24} -8.27341e12 q^{25} +(-7.93988e11 + 1.19452e12i) q^{26} +1.82878e13 q^{27} +(-2.61754e12 + 1.09905e12i) q^{28} -5.13731e12i q^{29} +(-3.53238e13 + 5.31430e13i) q^{30} -3.37595e13i q^{31} +(3.44230e13 - 7.27996e12i) q^{32} -4.88504e12 q^{33} +(-1.27855e13 - 8.49843e12i) q^{34} +3.76523e13 q^{35} +(9.10919e13 + 2.16948e14i) q^{36} +1.22733e14i q^{37} +(2.14610e13 + 1.42650e13i) q^{38} -1.00422e14i q^{39} +(-4.58328e14 - 8.77229e13i) q^{40} +4.29547e14 q^{41} +(1.10027e14 - 1.65531e14i) q^{42} -5.15040e14 q^{43} +(-1.38300e13 - 3.29380e13i) q^{44} -3.12071e15i q^{45} +(-4.65809e14 + 7.00787e14i) q^{46} -4.52697e14i q^{47} +(-1.72498e15 + 1.75861e15i) q^{48} +1.51113e15 q^{49} +(3.52776e15 + 2.34488e15i) q^{50} +1.07487e15 q^{51} +(6.77109e14 - 2.84304e14i) q^{52} +3.85227e15i q^{53} +(-7.79786e15 - 5.18319e15i) q^{54} +4.73800e14i q^{55} +(1.42761e15 + 2.73241e14i) q^{56} -1.80421e15 q^{57} +(-1.45604e15 + 2.19054e15i) q^{58} -8.14938e15 q^{59} +(3.01240e16 - 1.26484e16i) q^{60} +1.63847e16i q^{61} +(-9.56825e15 + 1.43950e16i) q^{62} +9.72046e15i q^{63} +(-1.67412e16 - 6.65214e15i) q^{64} -9.73995e15 q^{65} +(2.08297e15 + 1.38454e15i) q^{66} +3.10380e16 q^{67} +(3.04304e15 + 7.24742e15i) q^{68} -5.89147e16i q^{69} +(-1.60548e16 - 1.06716e16i) q^{70} +4.98018e16i q^{71} +(2.26469e16 - 1.18324e17i) q^{72} +7.59692e16 q^{73} +(3.47854e16 - 5.23330e16i) q^{74} -2.96577e17 q^{75} +(-5.10788e15 - 1.21651e16i) q^{76} -1.47580e15i q^{77} +(-2.84620e16 + 4.28198e16i) q^{78} +1.64362e17i q^{79} +(1.70567e17 + 1.67306e17i) q^{80} +3.07819e17 q^{81} +(-1.83158e17 - 1.21744e17i) q^{82} +4.04293e16 q^{83} +(-9.38308e16 + 3.93976e16i) q^{84} -1.04251e17i q^{85} +(2.19612e17 + 1.45975e17i) q^{86} -1.84157e17i q^{87} +(-3.43835e15 + 1.79644e16i) q^{88} +1.65081e17 q^{89} +(-8.84485e17 + 1.33066e18i) q^{90} +3.03382e16 q^{91} +(3.97240e17 - 1.66793e17i) q^{92} -1.21017e18i q^{93} +(-1.28305e17 + 1.93029e17i) q^{94} +1.74990e17i q^{95} +(1.23396e18 - 2.60964e17i) q^{96} -4.02901e17 q^{97} +(-6.44344e17 - 4.28291e17i) q^{98} -1.22318e17 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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