LMFDB - Embedded newform 12.19.d.a.7.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [12,19,Mod(7,12)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(12, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("12.7");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 12 = 2^{2} \cdot 3 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	12.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:	$24.6463365252$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 332091 x^{16} - 8722796 x^{15} + 44065046710 x^{14} + 2562387593326 x^{13} + \cdots + 51\!\cdots\!09 $ x^18 - 5x^17 - 332091x^16 - 8722796x^15 + 44065046710x^14 + 2562387593326x^13 - 2939418299568910x^12 - 270086571564720600x^11 + 99892143837893471971x^10 + 13287383366374675095257x^9 - 1404426939389796697311653x^8 - 302846077765145575240351608x^7 - 3048385818268269033396834566x^6 + 2387968325606677017735731037126x^5 + 189341038803558425525784877687654x^4 + 5034939808459428548543033598246780x^3 + 5944618618967029844099743191417597x^2 - 1074790996286169638673503552568280077*x + 5142216036403070733098077860515333409
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{139}\cdot 3^{67}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			7.9
Root			$172.291 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	12.7
Dual form			12.19.d.a.7.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(20.2086 - 511.601i) q^{2} +11364.0i q^{3} +(-261327. - 20677.5i) q^{4} -429789. q^{5} +(5.81383e6 + 229650. i) q^{6} +2.05285e7i q^{7} +(-1.58597e7 + 1.33277e8i) q^{8} -1.29140e8 q^{9} +O(q^{10})$	\(q+(20.2086 - 511.601i) q^{2} +11364.0i q^{3} +(-261327. - 20677.5i) q^{4} -429789. q^{5} +(5.81383e6 + 229650. i) q^{6} +2.05285e7i q^{7} +(-1.58597e7 + 1.33277e8i) q^{8} -1.29140e8 q^{9} +(-8.68544e6 + 2.19881e8i) q^{10} -1.14286e9i q^{11} +(2.34978e8 - 2.96972e9i) q^{12} +3.20144e9 q^{13} +(1.05024e10 + 4.14852e8i) q^{14} -4.88412e9i q^{15} +(6.78644e10 + 1.08072e10i) q^{16} +1.45963e11 q^{17} +(-2.60974e9 + 6.60682e10i) q^{18} -2.89697e11i q^{19} +(1.12316e11 + 8.88696e9i) q^{20} -2.33285e11 q^{21} +(-5.84690e11 - 2.30957e10i) q^{22} -1.92222e12i q^{23} +(-1.51456e12 - 1.80229e11i) q^{24} -3.62998e12 q^{25} +(6.46966e10 - 1.63786e12i) q^{26} -1.46755e12i q^{27} +(4.24477e11 - 5.36465e12i) q^{28} +5.44258e12 q^{29} +(-2.49872e12 - 9.87012e10i) q^{30} -3.60274e13i q^{31} +(6.90040e12 - 3.45011e13i) q^{32} +1.29875e13 q^{33} +(2.94971e12 - 7.46748e13i) q^{34} -8.82293e12i q^{35} +(3.37478e13 + 2.67029e12i) q^{36} +6.53703e13 q^{37} +(-1.48209e14 - 5.85437e12i) q^{38} +3.63811e13i q^{39} +(6.81632e12 - 5.72812e13i) q^{40} -4.53635e13 q^{41} +(-4.71437e12 + 1.19349e14i) q^{42} -5.28307e14i q^{43} +(-2.36315e13 + 2.98661e14i) q^{44} +5.55031e13 q^{45} +(-9.83408e14 - 3.88453e13i) q^{46} +1.17848e15i q^{47} +(-1.22813e14 + 7.71210e14i) q^{48} +1.20699e15 q^{49} +(-7.33567e13 + 1.85710e15i) q^{50} +1.65872e15i q^{51} +(-8.36624e14 - 6.61977e13i) q^{52} +5.32455e15 q^{53} +(-7.50799e14 - 2.96571e13i) q^{54} +4.91191e14i q^{55} +(-2.73598e15 - 3.25575e14i) q^{56} +3.29211e15 q^{57} +(1.09987e14 - 2.78443e15i) q^{58} +1.61178e15i q^{59} +(-1.00991e14 + 1.27635e15i) q^{60} +1.33225e16 q^{61} +(-1.84317e16 - 7.28063e14i) q^{62} -2.65105e15i q^{63} +(-1.75113e16 - 4.22747e15i) q^{64} -1.37595e15 q^{65} +(2.62459e14 - 6.64441e15i) q^{66} -1.51919e16i q^{67} +(-3.81441e16 - 3.01815e15i) q^{68} +2.18441e16 q^{69} +(-4.51382e15 - 1.78299e14i) q^{70} -5.81662e16i q^{71} +(2.04812e15 - 1.72115e16i) q^{72} +9.74662e16 q^{73} +(1.32104e15 - 3.34435e16i) q^{74} -4.12510e16i q^{75} +(-5.99020e15 + 7.57057e16i) q^{76} +2.34613e16 q^{77} +(1.86126e16 + 7.35211e14i) q^{78} +1.13964e17i q^{79} +(-2.91674e16 - 4.64481e15i) q^{80} +1.66772e16 q^{81} +(-9.16733e14 + 2.32080e16i) q^{82} +1.92400e17i q^{83} +(6.09638e16 + 4.82375e15i) q^{84} -6.27334e16 q^{85} +(-2.70282e17 - 1.06763e16i) q^{86} +6.18494e16i q^{87} +(1.52318e17 + 1.81254e16i) q^{88} -6.58097e17 q^{89} +(1.12164e15 - 2.83954e16i) q^{90} +6.57207e16i q^{91} +(-3.97466e16 + 5.02328e17i) q^{92} +4.09415e17 q^{93} +(6.02909e17 + 2.38153e16i) q^{94} +1.24509e17i q^{95} +(3.92070e17 + 7.84161e16i) q^{96} +6.80639e16 q^{97} +(2.43917e16 - 6.17500e17i) q^{98} +1.47590e17i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9}+O(q^{10}) $ 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9	$ 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9} + 1397074644 q^{10} - 6468699852 q^{12} + 1799208612 q^{13} - 48147537912 q^{14} - 119537094672 q^{16} - 282984271180 q^{17} + 21953827710 q^{18} + 491637621128 q^{20} + 254050055640 q^{21} + 272503644408 q^{22} + 4483423343232 q^{24} + 20224739695878 q^{25} - 2765456970196 q^{26} + 27756503338032 q^{28} + 1812741883820 q^{29} - 3579410315772 q^{30} + 216191588070880 q^{32} + 17014318866216 q^{33} - 275796423660708 q^{34} + 56425469699916 q^{36} + 197439381411156 q^{37} - 676030464010008 q^{38} + 19\!\cdots\!68 q^{40}+ \cdots - 37\!\cdots\!22 q^{98}+O(q^{100}) $ 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9 + 1397074644 * q^10 - 6468699852 * q^12 + 1799208612 * q^13 - 48147537912 * q^14 - 119537094672 * q^16 - 282984271180 * q^17 + 21953827710 * q^18 + 491637621128 * q^20 + 254050055640 * q^21 + 272503644408 * q^22 + 4483423343232 * q^24 + 20224739695878 * q^25 - 2765456970196 * q^26 + 27756503338032 * q^28 + 1812741883820 * q^29 - 3579410315772 * q^30 + 216191588070880 * q^32 + 17014318866216 * q^33 - 275796423660708 * q^34 + 56425469699916 * q^36 + 197439381411156 * q^37 - 676030464010008 * q^38 + 1941137842438368 * q^40 - 204669372669676 * q^41 - 1059935698181880 * q^42 + 3599128179401424 * q^44 + 222348883607532 * q^45 - 3847169819651040 * q^46 + 1457367907812912 * q^48 - 3424095824368878 * q^49 - 10192520264009358 * q^50 + 4228291003193208 * q^52 - 14112687314785972 * q^53 + 869318113288518 * q^54 - 6591066595001856 * q^56 - 9662233004693640 * q^57 + 17584741731886020 * q^58 + 193536143011224 * q^60 + 4171094773122132 * q^61 + 77227021488187896 * q^62 - 53424456043095936 * q^64 + 35585253307254712 * q^65 + 40644920520184824 * q^66 - 91403316760947112 * q^68 + 26342656148137824 * q^69 + 264958129332427248 * q^70 - 14019292862113968 * q^72 - 83809473755653692 * q^73 + 55949505142092092 * q^74 - 129026923617832848 * q^76 - 354619239852167328 * q^77 - 34535086926497028 * q^78 + 43257628406200352 * q^80 + 300189270593998242 * q^81 - 458290372754774916 * q^82 + 324078384809786832 * q^84 + 166017223439872920 * q^85 - 975848731010420424 * q^86 + 1151342491040801280 * q^88 - 660650117825905468 * q^89 - 180418447249326972 * q^90 + 1359275349780859584 * q^92 - 447365281400937432 * q^93 - 2087066679318498384 * q^94 + 257905715132447136 * q^96 + 2412557706093917220 * q^97 - 3767017570512990122 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/12\mathbb{Z}\right)^\times$.

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

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 $

$2$	20.2086	−	511.601i	0.0394699	−	0.999221i
$2$	20.2086	−	511.601i	0.0394699	−	0.999221i
$3$			11364.0i			0.577350i
$3$			11364.0i			0.577350i
$4$	−261327.	−	20677.5i	−0.996884	−	0.0788783i
$5$	−429789.			−0.220052			−0.110026	−	0.993929i	$-0.535093\pi$
$5$	−429789.			−0.220052			−0.110026	+	0.993929i	$0.535093\pi$
$6$	5.81383e6	+	229650.i	0.576900	+	0.0227880i
$7$			2.05285e7i			0.508715i	0.967110	+	0.254357i	$0.0818640\pi$
$7$			2.05285e7i			0.508715i	−0.967110	+	0.254357i	$0.918136\pi$
$8$	−1.58597e7	+	1.33277e8i	−0.118164	+	0.992994i
$9$	−1.29140e8			−0.333333
$10$	−8.68544e6	+	2.19881e8i	−0.00868544	+	0.219881i
$11$		−	1.14286e9i		−	0.484686i	−0.970191	−	0.242343i	$-0.922084\pi$
$11$		−	1.14286e9i		−	0.484686i	0.970191	−	0.242343i	$-0.0779159\pi$
$12$	2.34978e8	−	2.96972e9i	0.0455404	−	0.575551i
$13$	3.20144e9			0.301895			0.150947	−	0.988542i	$-0.451768\pi$
$13$	3.20144e9			0.301895			0.150947	+	0.988542i	$0.451768\pi$
$14$	1.05024e10	+	4.14852e8i	0.508319	+	0.0200789i
$15$		−	4.88412e9i		−	0.127047i
$16$	6.78644e10	+	1.08072e10i	0.987556	+	0.157265i
$17$	1.45963e11			1.23084			0.615421	−	0.788198i	$-0.288986\pi$
$17$	1.45963e11			1.23084			0.615421	+	0.788198i	$0.288986\pi$
$18$	−2.60974e9	+	6.60682e10i	−0.0131566	+	0.333074i
$19$		−	2.89697e11i		−	0.897763i	−0.893591	−	0.448881i	$-0.851823\pi$
$19$		−	2.89697e11i		−	0.897763i	0.893591	−	0.448881i	$-0.148177\pi$
$20$	1.12316e11	+	8.88696e9i	0.219367	+	0.0173573i
$21$	−2.33285e11			−0.293707
$22$	−5.84690e11	−	2.30957e10i	−0.484308	−	0.0191305i
$23$		−	1.92222e12i		−	1.06722i	−0.845732	−	0.533608i	$-0.820836\pi$
$23$		−	1.92222e12i		−	1.06722i	0.845732	−	0.533608i	$-0.179164\pi$
$24$	−1.51456e12	−	1.80229e11i	−0.573305	−	0.0682219i
$25$	−3.62998e12			−0.951577
$26$	6.46966e10	−	1.63786e12i	0.0119158	−	0.301659i
$27$		−	1.46755e12i		−	0.192450i
$28$	4.24477e11	−	5.36465e12i	0.0401266	−	0.507130i
$29$	5.44258e12			0.375165			0.187583	−	0.982249i	$-0.439935\pi$
$29$	5.44258e12			0.375165			0.187583	+	0.982249i	$0.439935\pi$
$30$	−2.49872e12	−	9.87012e10i	−0.126948	−	0.00501454i
$31$		−	3.60274e13i		−	1.36263i	−0.731991	−	0.681314i	$-0.761409\pi$
$31$		−	3.60274e13i		−	1.36263i	0.731991	−	0.681314i	$-0.238591\pi$
$32$	6.90040e12	−	3.45011e13i	0.196121	−	0.980580i
$33$	1.29875e13			0.279833
$34$	2.94971e12	−	7.46748e13i	0.0485812	−	1.22988i
$35$		−	8.82293e12i		−	0.111944i
$36$	3.37478e13	+	2.67029e12i	0.332295	+	0.0262928i
$37$	6.53703e13			0.502997			0.251498	−	0.967858i	$-0.419077\pi$
$37$	6.53703e13			0.502997			0.251498	+	0.967858i	$0.419077\pi$
$38$	−1.48209e14	−	5.85437e12i	−0.897063	−	0.0354346i
$39$			3.63811e13i			0.174299i
$40$	6.81632e12	−	5.72812e13i	0.0260022	−	0.218511i
$41$	−4.53635e13			−0.138565			−0.0692823	−	0.997597i	$-0.522071\pi$
$41$	−4.53635e13			−0.138565			−0.0692823	+	0.997597i	$0.522071\pi$
$42$	−4.71437e12	+	1.19349e14i	−0.0115926	+	0.293478i
$43$		−	5.28307e14i		−	1.05116i	−0.850743	−	0.525582i	$-0.823848\pi$
$43$		−	5.28307e14i		−	1.05116i	0.850743	−	0.525582i	$-0.176152\pi$
$44$	−2.36315e13	+	2.98661e14i	−0.0382312	+	0.483176i
$45$	5.55031e13			0.0733507
$46$	−9.83408e14	−	3.88453e13i	−1.06638	−	0.0421229i
$47$			1.17848e15i			1.05303i	0.850166	+	0.526514i	$0.176501\pi$
$47$			1.17848e15i			1.05303i	−0.850166	+	0.526514i	$0.823499\pi$
$48$	−1.22813e14	+	7.71210e14i	−0.0907970	+	0.570166i
$49$	1.20699e15			0.741209
$50$	−7.33567e13	+	1.85710e15i	−0.0375587	+	0.950836i
$51$			1.65872e15i			0.710627i
$52$	−8.36624e14	−	6.61977e13i	−0.300954	−	0.0238129i
$53$	5.32455e15			1.61362			0.806808	−	0.590814i	$-0.201193\pi$
$53$	5.32455e15			1.61362			0.806808	+	0.590814i	$0.201193\pi$
$54$	−7.50799e14	−	2.96571e13i	−0.192300	−	0.00759599i
$55$			4.91191e14i			0.106656i
$56$	−2.73598e15	−	3.25575e14i	−0.505151	−	0.0601117i
$57$	3.29211e15			0.518324
$58$	1.09987e14	−	2.78443e15i	0.0148077	−	0.374873i
$59$			1.61178e15i			0.186054i	0.995664	+	0.0930270i	$0.0296543\pi$
$59$			1.61178e15i			0.186054i	−0.995664	+	0.0930270i	$0.970346\pi$
$60$	−1.00991e14	+	1.27635e15i	−0.0100213	+	0.126651i
$61$	1.33225e16			1.13925			0.569624	−	0.821905i	$-0.307089\pi$
$61$	1.33225e16			1.13925			0.569624	+	0.821905i	$0.307089\pi$
$62$	−1.84317e16	−	7.28063e14i	−1.36157	−	0.0537828i
$63$		−	2.65105e15i		−	0.169572i
$64$	−1.75113e16	−	4.22747e15i	−0.972075	−	0.234672i
$65$	−1.37595e15			−0.0664326
$66$	2.62459e14	−	6.64441e15i	0.0110450	−	0.279615i
$67$		−	1.51919e16i		−	0.558393i	−0.960234	−	0.279197i	$-0.909932\pi$
$67$		−	1.51919e16i		−	0.558393i	0.960234	−	0.279197i	$-0.0900681\pi$
$68$	−3.81441e16	−	3.01815e15i	−1.22701	−	0.0970868i
$69$	2.18441e16			0.616157
$70$	−4.51382e15	−	1.78299e14i	−0.111857	−	0.00441841i
$71$		−	5.81662e16i		−	1.26866i	−0.773062	−	0.634330i	$-0.781276\pi$
$71$		−	5.81662e16i		−	1.26866i	0.773062	−	0.634330i	$-0.218724\pi$
$72$	2.04812e15	−	1.72115e16i	0.0393879	−	0.330998i
$73$	9.74662e16			1.65557			0.827787	−	0.561043i	$-0.189600\pi$
$73$	9.74662e16			1.65557			0.827787	+	0.561043i	$0.189600\pi$
$74$	1.32104e15	−	3.34435e16i	0.0198532	−	0.502605i
$75$		−	4.12510e16i		−	0.549393i
$76$	−5.99020e15	+	7.57057e16i	−0.0708140	+	0.894966i
$77$	2.34613e16			0.246567
$78$	1.86126e16	+	7.35211e14i	0.174163	+	0.00687956i
$79$			1.13964e17i			0.950879i	0.879748	+	0.475440i	$0.157711\pi$
$79$			1.13964e17i			0.950879i	−0.879748	+	0.475440i	$0.842289\pi$
$80$	−2.91674e16	−	4.64481e15i	−0.217314	−	0.0346065i
$81$	1.66772e16			0.111111
$82$	−9.16733e14	+	2.32080e16i	−0.00546913	+	0.138457i
$83$			1.92400e17i			1.02920i	0.857429	+	0.514602i	$0.172060\pi$
$83$			1.92400e17i			1.02920i	−0.857429	+	0.514602i	$0.827940\pi$
$84$	6.09638e16	+	4.82375e15i	0.292792	+	0.0231671i
$85$	−6.27334e16			−0.270850
$86$	−2.70282e17	−	1.06763e16i	−1.05034	−	0.0414893i
$87$			6.18494e16i			0.216602i
$88$	1.52318e17	+	1.81254e16i	0.481290	+	0.0572723i
$89$	−6.58097e17			−1.87836			−0.939182	−	0.343419i	$-0.888415\pi$
$89$	−6.58097e17			−1.87836			−0.939182	+	0.343419i	$0.888415\pi$
$90$	1.12164e15	−	2.83954e16i	0.00289515	−	0.0732936i
$91$			6.57207e16i			0.153578i
$92$	−3.97466e16	+	5.02328e17i	−0.0841801	+	1.06389i
$93$	4.09415e17			0.786714
$94$	6.02909e17	+	2.38153e16i	1.05221	+	0.0415629i
$95$			1.24509e17i			0.197555i
$96$	3.92070e17	+	7.84161e16i	0.566138	+	0.113231i
$97$	6.80639e16			0.0895306			0.0447653	−	0.998998i	$-0.485746\pi$
$97$	6.80639e16			0.0895306			0.0447653	+	0.998998i	$0.485746\pi$
$98$	2.43917e16	−	6.17500e17i	0.0292555	−	0.740632i
$99$			1.47590e17i			0.161562i
$100$	9.48612e17	+	7.50588e16i	0.948612	+	0.0750588i
$101$	−2.01274e18			−1.84033			−0.920165	−	0.391532i	$-0.871945\pi$
$101$	−2.01274e18			−1.84033			−0.920165	+	0.391532i	$0.871945\pi$
$102$	8.48604e17	+	3.35204e16i	0.710074	+	0.0280484i
$103$		−	2.25384e18i		−	1.72738i	−0.504022	−	0.863691i	$-0.668147\pi$
$103$		−	2.25384e18i		−	1.72738i	0.504022	−	0.863691i	$-0.331853\pi$
$104$	−5.07738e16	+	4.26680e17i	−0.0356730	+	0.299780i
$105$	1.00264e17			0.0646308
$106$	1.07602e17	−	2.72405e18i	0.0636892	−	1.61236i
$107$		−	6.45937e17i		−	0.351347i	−0.984448	−	0.175674i	$-0.943790\pi$
$107$		−	6.45937e17i		−	0.351347i	0.984448	−	0.175674i	$-0.0562103\pi$
$108$	−3.03452e16	+	3.83510e17i	−0.0151801	+	0.191850i
$109$	−1.57691e18			−0.726051			−0.363025	−	0.931779i	$-0.618256\pi$
$109$	−1.57691e18			−0.726051			−0.363025	+	0.931779i	$0.618256\pi$
$110$	2.51294e17	+	9.92627e15i	0.106573	+	0.00420971i
$111$			7.42867e17i			0.290405i
$112$	−2.21855e17	+	1.39315e18i	−0.0800031	+	0.502385i
$113$	−1.73056e18			−0.576079			−0.288039	−	0.957619i	$-0.593003\pi$
$113$	−1.73056e18			−0.576079			−0.288039	+	0.957619i	$0.593003\pi$
$114$	6.65290e16	−	1.68425e18i	0.0204582	−	0.517920i
$115$			8.26149e17i			0.234843i
$116$	−1.42229e18	−	1.12539e17i	−0.373996	−	0.0295924i
$117$	−4.13435e17			−0.100632
$118$	8.24591e17	+	3.25719e16i	0.185909	+	0.00734353i
$119$			2.99640e18i			0.626148i
$120$	6.50943e17	+	7.74606e16i	0.126157	+	0.0150124i
$121$	4.25378e18			0.765080
$122$	2.69230e17	−	6.81583e18i	0.0449660	−	1.13836i
$123$		−	5.15511e17i		−	0.0800003i
$124$	−7.44955e17	+	9.41494e18i	−0.107482	+	1.35838i
$125$	3.19964e18			0.429449
$126$	−1.35628e18	−	5.35740e16i	−0.169440	−	0.00669298i
$127$			3.14194e18i			0.365565i	0.983153	+	0.182782i	$0.0585104\pi$
$127$			3.14194e18i			0.365565i	−0.983153	+	0.182782i	$0.941490\pi$
$128$	−2.51666e18	+	8.87339e18i	−0.272857	+	0.962055i
$129$	6.00367e18			0.606889
$130$	−2.78059e16	+	7.03935e17i	−0.00262209	+	0.0663808i
$131$			2.09941e18i			0.184780i	0.995723	+	0.0923900i	$0.0294507\pi$
$131$			2.09941e18i			0.184780i	−0.995723	+	0.0923900i	$0.970549\pi$
$132$	−3.39398e18	−	2.68548e17i	−0.278962	−	0.0220728i
$133$	5.94704e18			0.456705
$134$	−7.77222e18	−	3.07008e17i	−0.557958	−	0.0220397i
$135$			6.30736e17i			0.0423491i
$136$	−2.31493e18	+	1.94536e19i	−0.145441	+	1.22222i
$137$	2.49200e19			1.46576			0.732881	−	0.680357i	$-0.238175\pi$
$137$	2.49200e19			1.46576			0.732881	+	0.680357i	$0.238175\pi$
$138$	4.41438e17	−	1.11754e19i	0.0243197	−	0.615677i
$139$		−	8.47044e18i		−	0.437293i	−0.975804	−	0.218647i	$-0.929836\pi$
$139$		−	8.47044e18i		−	0.437293i	0.975804	−	0.218647i	$-0.0701642\pi$
$140$	−1.82436e17	+	2.30567e18i	−0.00882994	+	0.111595i
$141$	−1.33922e19			−0.607966
$142$	−2.97579e19	−	1.17546e18i	−1.26767	−	0.0500739i
$143$		−	3.65881e18i		−	0.146324i
$144$	−8.76401e18	−	1.39564e18i	−0.329185	−	0.0524217i
$145$	−2.33916e18			−0.0825559
$146$	1.96966e18	−	4.98638e19i	0.0653453	−	1.65428i
$147$			1.37163e19i			0.427937i
$148$	−1.70830e19	−	1.35169e18i	−0.501429	−	0.0396755i
$149$	3.11216e19			0.859776			0.429888	−	0.902882i	$-0.358553\pi$
$149$	3.11216e19			0.859776			0.429888	+	0.902882i	$0.358553\pi$
$150$	−2.11041e19	−	8.33625e17i	−0.548965	−	0.0216845i
$151$		−	6.13728e19i		−	1.50378i	−0.659291	−	0.751888i	$-0.729143\pi$
$151$		−	6.13728e19i		−	1.50378i	0.659291	−	0.751888i	$-0.270857\pi$
$152$	3.86101e19	+	4.59450e18i	0.891473	+	0.106083i
$153$	−1.88497e19			−0.410281
$154$	4.74119e17	−	1.20028e19i	0.00973197	−	0.246375i
$155$			1.54842e19i			0.299849i
$156$	7.52270e17	−	9.50738e18i	0.0137484	−	0.173756i
$157$	−2.83011e19			−0.488322			−0.244161	−	0.969735i	$-0.578512\pi$
$157$	−2.83011e19			−0.488322			−0.244161	+	0.969735i	$0.578512\pi$
$158$	5.83043e19	+	2.30306e18i	0.950138	+	0.0375311i
$159$			6.05081e19i			0.931621i
$160$	−2.96572e18	+	1.48282e19i	−0.0431569	+	0.215779i
$161$	3.94602e19			0.542908
$162$	3.37022e17	−	8.53206e18i	0.00438554	−	0.111025i
$163$		−	1.05705e20i		−	1.30138i	−0.759342	−	0.650691i	$-0.774479\pi$
$163$		−	1.05705e20i		−	1.30138i	0.759342	−	0.650691i	$-0.225521\pi$
$164$	1.18547e19	+	9.38003e17i	0.138133	+	0.0109297i
$165$	−5.58188e18			−0.0615780
$166$	9.84319e19	+	3.88813e18i	1.02840	+	0.0406226i
$167$			8.44405e19i			0.835801i	0.908493	+	0.417900i	$0.137234\pi$
$167$			8.44405e19i			0.835801i	−0.908493	+	0.417900i	$0.862766\pi$
$168$	3.69983e18	−	3.10917e19i	0.0347055	−	0.291649i
$169$	−1.02206e20			−0.908860
$170$	−1.26775e18	+	3.20945e19i	−0.0106904	+	0.270639i
$171$			3.74115e19i			0.299254i
$172$	−1.09240e19	+	1.38061e20i	−0.0829140	+	1.04789i
$173$	−1.83892e20			−1.32479			−0.662397	−	0.749153i	$-0.730461\pi$
$173$	−1.83892e20			−1.32479			−0.662397	+	0.749153i	$0.730461\pi$
$174$	3.16422e19	+	1.24989e18i	0.216433	+	0.00854925i
$175$		−	7.45179e19i		−	0.484081i
$176$	1.23511e19	−	7.75597e19i	0.0762241	−	0.478654i
$177$	−1.83163e19			−0.107418
$178$	−1.32992e19	+	3.36683e20i	−0.0741389	+	1.87690i
$179$			2.13427e20i			1.13129i	0.824650	+	0.565644i	$0.191372\pi$
$179$			2.13427e20i			1.13129i	−0.824650	+	0.565644i	$0.808628\pi$
$180$	−1.45045e19	−	1.14766e18i	−0.0731222	−	0.00578578i
$181$	−2.07064e20			−0.993109			−0.496554	−	0.868006i	$-0.665402\pi$
$181$	−2.07064e20			−0.993109			−0.496554	+	0.868006i	$0.665402\pi$
$182$	3.36228e19	+	1.32812e18i	0.153459	+	0.00606172i
$183$			1.51397e20i			0.657746i
$184$	2.56188e20	+	3.04857e19i	1.05974	+	0.126106i
$185$	−2.80955e19			−0.110685
$186$	8.27370e18	−	2.09457e20i	0.0310515	−	0.786101i
$187$		−	1.66816e20i		−	0.596572i
$188$	2.43679e19	−	3.07968e20i	0.0830611	−	1.04975i
$189$	3.01265e19			0.0979022
$190$	6.36988e19	+	2.51615e18i	0.197401	+	0.00779746i
$191$		−	7.94768e19i		−	0.234931i	−0.993077	−	0.117466i	$-0.962523\pi$
$191$		−	7.94768e19i		−	0.234931i	0.993077	−	0.117466i	$-0.0374770\pi$
$192$	4.80409e19	−	1.98999e20i	0.135488	−	0.561228i
$193$	6.05565e20			1.62984			0.814920	−	0.579573i	$-0.196781\pi$
$193$	6.05565e20			1.62984			0.814920	+	0.579573i	$0.196781\pi$
$194$	1.37548e18	−	3.48216e19i	0.00353376	−	0.0894608i
$195$		−	1.56362e19i		−	0.0383549i
$196$	−3.15421e20	−	2.49576e19i	−0.738900	−	0.0584653i
$197$	−1.13283e20			−0.253494			−0.126747	−	0.991935i	$-0.540454\pi$
$197$	−1.13283e20			−0.253494			−0.126747	+	0.991935i	$0.540454\pi$
$198$	7.55070e19	+	2.98258e18i	0.161436	+	0.00637683i
$199$		−	4.79477e20i		−	0.979694i	−0.871809	−	0.489847i	$-0.837053\pi$
$199$		−	4.79477e20i		−	0.979694i	0.871809	−	0.489847i	$-0.162947\pi$
$200$	5.75703e19	−	4.83794e20i	0.112442	−	0.944910i
$201$	1.72641e20			0.322389
$202$	−4.06747e19	+	1.02972e21i	−0.0726376	+	1.83890i
$203$			1.11728e20i			0.190852i
$204$	3.42982e19	−	4.33469e20i	0.0560531	−	0.708413i
$205$	1.94968e19			0.0304914
$206$	−1.15307e21	−	4.55470e19i	−1.72604	−	0.0681796i
$207$			2.48235e20i			0.355738i
$208$	2.17264e20	+	3.45985e19i	0.298138	+	0.0474775i
$209$	−3.31084e20			−0.435133
$210$	2.02619e18	−	5.12950e19i	0.00255097	−	0.0645804i
$211$		−	1.36049e21i		−	1.64117i	−0.571523	−	0.820586i	$-0.693647\pi$
$211$		−	1.36049e21i		−	1.64117i	0.571523	−	0.820586i	$-0.306353\pi$
$212$	−1.39145e21	−	1.10098e20i	−1.60859	−	0.127279i
$213$	6.60999e20			0.732461
$214$	−3.30462e20	−	1.30535e19i	−0.351073	−	0.0138676i
$215$			2.27061e20i			0.231311i
$216$	1.95591e20	+	2.32748e19i	0.191102	+	0.0227406i
$217$	7.39588e20			0.693190
$218$	−3.18670e19	+	8.06746e20i	−0.0286572	+	0.725485i
$219$			1.10760e21i			0.955846i
$220$	1.01566e19	−	1.28361e20i	0.00841286	−	0.106324i
$221$	4.67292e20			0.371585
$222$	3.80052e20	+	1.50123e19i	0.290179	+	0.0114623i
$223$		−	3.87312e20i		−	0.283999i	−0.989867	−	0.142000i	$-0.954647\pi$
$223$		−	3.87312e20i		−	0.283999i	0.989867	−	0.142000i	$-0.0453532\pi$
$224$	7.08255e20	+	1.41655e20i	0.498836	+	0.0997698i
$225$	4.68776e20			0.317192
$226$	−3.49723e19	+	8.85359e20i	−0.0227378	+	0.575630i
$227$			2.52047e21i			1.57488i	0.616389	+	0.787442i	$0.288595\pi$
$227$			2.52047e21i			1.57488i	−0.616389	+	0.787442i	$0.711405\pi$
$228$	−8.60319e20	−	6.80726e19i	−0.516709	−	0.0408845i
$229$	1.36886e21			0.790385			0.395192	−	0.918598i	$-0.370678\pi$
$229$	1.36886e21			0.790385			0.395192	+	0.918598i	$0.370678\pi$
$230$	4.22659e20	+	1.66953e19i	0.234660	+	0.00926923i
$231$			2.66613e20i			0.142355i
$232$	−8.63175e19	+	7.25373e20i	−0.0443309	+	0.372537i
$233$	1.00096e21			0.494554			0.247277	−	0.968945i	$-0.420464\pi$
$233$	1.00096e21			0.494554			0.247277	+	0.968945i	$0.420464\pi$
$234$	−8.35493e18	+	2.11514e20i	−0.00397192	+	0.100553i
$235$		−	5.06496e20i		−	0.231721i
$236$	3.33276e19	−	4.21203e20i	0.0146756	−	0.185474i
$237$	−1.29509e21			−0.548990
$238$	1.53296e21	+	6.05530e19i	0.625660	+	0.0247140i
$239$			1.68872e20i			0.0663709i	0.999449	+	0.0331854i	$0.0105652\pi$
$239$			1.68872e20i			0.0663709i	−0.999449	+	0.0331854i	$0.989435\pi$
$240$	5.27835e19	−	3.31458e20i	0.0199801	−	0.125466i
$241$	−4.22813e21			−1.54168			−0.770841	−	0.637027i	$-0.780164\pi$
$241$	−4.22813e21			−1.54168			−0.770841	+	0.637027i	$0.780164\pi$
$242$	8.59629e19	−	2.17624e21i	0.0301976	−	0.764484i
$243$			1.89519e20i			0.0641500i
$244$	−3.48154e21	−	2.75477e20i	−1.13570	−	0.0898620i
$245$	−5.18754e20			−0.163105
$246$	−2.63736e20	−	1.04177e19i	−0.0799379	−	0.00315760i
$247$		−	9.27448e20i		−	0.271030i
$248$	4.80164e21	+	5.71383e20i	1.35308	+	0.161013i
$249$	−2.18643e21			−0.594212
$250$	6.46603e19	−	1.63694e21i	0.0169503	−	0.429114i
$251$		−	3.57247e21i		−	0.903453i	−0.892157	−	0.451726i	$-0.850808\pi$
$251$		−	3.57247e21i		−	0.903453i	0.892157	−	0.451726i	$-0.149192\pi$
$252$	−5.48170e19	+	6.92792e20i	−0.0133755	+	0.169043i
$253$	−2.19683e21			−0.517264
$254$	1.60742e21	+	6.34942e19i	0.365280	+	0.0144288i
$255$		−	7.12901e20i		−	0.156375i
$256$	4.48878e21	+	1.46684e21i	0.950535	+	0.310616i
$257$	−2.73651e21			−0.559498			−0.279749	−	0.960073i	$-0.590251\pi$
$257$	−2.73651e21			−0.559498			−0.279749	+	0.960073i	$0.590251\pi$
$258$	1.21326e20	−	3.07148e21i	0.0239539	−	0.606416i
$259$			1.34195e21i			0.255882i
$260$	3.59572e20	+	2.84511e19i	0.0662256	+	0.00524009i
$261$	−7.02855e20			−0.125055
$262$	1.07406e21	+	4.24261e19i	0.184636	+	0.00729325i
$263$		−	5.80712e21i		−	0.964626i	−0.875999	−	0.482313i	$-0.839797\pi$
$263$		−	5.80712e21i		−	0.964626i	0.875999	−	0.482313i	$-0.160203\pi$
$264$	−2.05977e20	+	1.73094e21i	−0.0330662	+	0.277873i
$265$	−2.28844e21			−0.355080
$266$	1.20181e20	−	3.04251e21i	0.0180261	−	0.456349i
$267$		−	7.47861e21i		−	1.08447i
$268$	−3.14131e20	+	3.97007e21i	−0.0440451	+	0.556653i
$269$	5.46197e21			0.740591			0.370296	−	0.928914i	$-0.379256\pi$
$269$	5.46197e21			0.740591			0.370296	+	0.928914i	$0.379256\pi$
$270$	3.22685e20	+	1.27463e19i	0.0423161	+	0.00167151i
$271$			9.90330e21i			1.25619i	0.778135	+	0.628097i	$0.216166\pi$
$271$			9.90330e21i			1.25619i	−0.778135	+	0.628097i	$0.783834\pi$
$272$	9.90569e21	+	1.57745e21i	1.21553	+	0.193569i
$273$	−7.46849e20			−0.0886685
$274$	5.03598e20	−	1.27491e22i	0.0578535	−	1.46462i
$275$			4.14857e21i			0.461216i
$276$	−5.70845e21	−	4.51680e20i	−0.614237	−	0.0486014i
$277$	−2.53208e21			−0.263730			−0.131865	−	0.991268i	$-0.542097\pi$
$277$	−2.53208e21			−0.263730			−0.131865	+	0.991268i	$0.542097\pi$
$278$	−4.33348e21	−	1.71176e20i	−0.436952	−	0.0172599i
$279$			4.65258e21i			0.454210i
$280$	1.17590e21	+	1.39929e20i	0.111160	+	0.0132277i
$281$	1.43811e21			0.131655			0.0658274	−	0.997831i	$-0.479031\pi$
$281$	1.43811e21			0.131655			0.0658274	+	0.997831i	$0.479031\pi$
$282$	−2.70637e20	+	6.85145e21i	−0.0239964	+	0.607492i
$283$			1.47642e22i			1.26803i	0.773319	+	0.634017i	$0.218595\pi$
$283$			1.47642e22i			1.26803i	−0.773319	+	0.634017i	$0.781405\pi$
$284$	−1.20273e21	+	1.52004e22i	−0.100070	+	1.26471i
$285$	−1.41492e21			−0.114058
$286$	−1.87185e21	−	7.39394e19i	−0.146210	−	0.00577539i
$287$		−	9.31245e20i		−	0.0704899i
$288$	−8.91119e20	+	4.45547e21i	−0.0653738	+	0.326860i
$289$	7.24212e21			0.514973
$290$	−4.72712e19	+	1.19672e21i	−0.00325848	+	0.0824916i
$291$			7.73477e20i			0.0516905i
$292$	−2.54706e22	−	2.01536e21i	−1.65042	−	0.130589i
$293$	1.37021e22			0.860950			0.430475	−	0.902603i	$-0.358346\pi$
$293$	1.37021e22			0.860950			0.430475	+	0.902603i	$0.358346\pi$
$294$	7.01726e21	+	2.77187e20i	0.427604	+	0.0168906i
$295$		−	6.92728e20i		−	0.0409416i
$296$	−1.03675e21	+	8.71238e21i	−0.0594360	+	0.499473i
$297$	−1.67721e21			−0.0932778
$298$	6.28923e20	−	1.59218e22i	0.0339353	−	0.859106i
$299$		−	6.15387e21i		−	0.322187i
$300$	−8.52967e20	+	1.07800e22i	−0.0433352	+	0.547681i
$301$	1.08453e22			0.534742
$302$	−3.13984e22	−	1.24026e21i	−1.50260	−	0.0593539i
$303$		−	2.28728e22i		−	1.06251i
$304$	3.13081e21	−	1.96601e22i	0.141187	−	0.886591i
$305$	−5.72589e21			−0.250694
$306$	−3.80926e20	+	9.64352e21i	−0.0161937	+	0.409961i
$307$			4.71504e21i			0.194644i	0.995253	+	0.0973218i	$0.0310276\pi$
$307$			4.71504e21i			0.194644i	−0.995253	+	0.0973218i	$0.968972\pi$
$308$	−6.13106e21	−	4.85119e20i	−0.245799	−	0.0194488i
$309$	2.56126e22			0.997305
$310$	7.92173e21	+	3.12914e20i	0.299616	+	0.0118350i
$311$		−	6.22919e21i		−	0.228870i	−0.993431	−	0.114435i	$-0.963494\pi$
$311$		−	6.22919e21i		−	0.228870i	0.993431	−	0.114435i	$-0.0365057\pi$
$312$	−4.84878e21	−	5.76993e20i	−0.173078	−	0.0205958i
$313$	4.47470e22			1.55190			0.775952	−	0.630792i	$-0.217270\pi$
$313$	4.47470e22			1.55190			0.775952	+	0.630792i	$0.217270\pi$
$314$	−5.71925e20	+	1.44789e22i	−0.0192740	+	0.487941i
$315$			1.13939e21i			0.0373146i
$316$	2.35650e21	−	2.97820e22i	0.0750037	−	0.947916i
$317$	−2.90175e22			−0.897689			−0.448845	−	0.893610i	$-0.648164\pi$
$317$	−2.90175e22			−0.897689			−0.448845	+	0.893610i	$0.648164\pi$
$318$	3.09560e22	+	1.22278e21i	0.930895	+	0.0367710i
$319$		−	6.22012e21i		−	0.181837i
$320$	7.52619e21	+	1.81692e21i	0.213907	+	0.0516401i
$321$	7.34042e21			0.202850
$322$	7.97435e20	−	2.01879e22i	0.0214285	−	0.542485i
$323$		−	4.22850e22i		−	1.10500i
$324$	−4.35820e21	−	3.44842e20i	−0.110765	−	0.00876426i
$325$	−1.16212e22			−0.287276
$326$	−5.40785e22	−	2.13614e21i	−1.30037	−	0.0513655i
$327$		−	1.79199e22i		−	0.419186i
$328$	7.19451e20	−	6.04593e21i	0.0163733	−	0.137594i
$329$	−2.41923e22			−0.535691
$330$	−1.12802e20	+	2.85570e21i	−0.00243048	+	0.0615300i
$331$			7.42751e22i			1.55737i	0.627416	+	0.778685i	$0.284113\pi$
$331$			7.42751e22i			1.55737i	−0.627416	+	0.778685i	$0.715887\pi$
$332$	3.97834e21	−	5.02793e22i	0.0811819	−	1.02600i
$333$	−8.44193e21			−0.167666
$334$	4.31999e22	+	1.70642e21i	0.835149	+	0.0329890i
$335$			6.52934e21i			0.122876i
$336$	−1.58318e22	−	2.52116e21i	−0.290052	−	0.0461898i
$337$	−7.15250e22			−1.27582			−0.637909	−	0.770112i	$-0.720200\pi$
$337$	−7.15250e22			−1.27582			−0.637909	+	0.770112i	$0.720200\pi$
$338$	−2.06544e21	+	5.22888e22i	−0.0358726	+	0.908151i
$339$		−	1.96661e22i		−	0.332599i
$340$	1.63939e22	+	1.29717e21i	0.270006	+	0.0213642i
$341$	−4.11744e22			−0.660447
$342$	1.91398e22	+	7.56034e20i	0.299021	+	0.0118115i
$343$			5.82066e22i			0.885779i
$344$	7.04114e22	+	8.37877e21i	1.04380	+	0.124209i
$345$	−9.38834e21			−0.135587
$346$	−3.71620e21	+	9.40794e22i	−0.0522895	+	1.32376i
$347$			5.21016e22i			0.714309i	0.934045	+	0.357154i	$0.116253\pi$
$347$			5.21016e22i			0.714309i	−0.934045	+	0.357154i	$0.883747\pi$
$348$	1.27889e21	−	1.61629e22i	0.0170852	−	0.215927i
$349$	5.20990e21			0.0678266			0.0339133	−	0.999425i	$-0.489203\pi$
$349$	5.20990e21			0.0678266			0.0339133	+	0.999425i	$0.489203\pi$
$350$	−3.81235e22	−	1.50590e21i	−0.483704	−	0.0191066i
$351$		−	4.69827e21i		−	0.0580996i
$352$	−3.94300e22	−	7.88622e21i	−0.475273	−	0.0950572i
$353$	3.03078e22			0.356108			0.178054	−	0.984021i	$-0.443020\pi$
$353$	3.03078e22			0.356108			0.178054	+	0.984021i	$0.443020\pi$
$354$	−3.70147e20	+	9.37064e21i	−0.00423979	+	0.107335i
$355$			2.49992e22i			0.279171i
$356$	1.71979e23	+	1.36078e22i	1.87251	+	0.148162i
$357$	−3.40510e22			−0.361507
$358$	1.09190e23	+	4.31307e21i	1.13041	+	0.0446518i
$359$		−	9.92056e22i		−	1.00158i	−0.865568	−	0.500791i	$-0.833043\pi$
$359$		−	9.92056e22i		−	1.00158i	0.865568	−	0.500791i	$-0.166957\pi$
$360$	−8.80261e20	+	7.39731e21i	−0.00866740	+	0.0728368i
$361$	2.02030e22			0.194022
$362$	−4.18447e21	+	1.05934e23i	−0.0391979	+	0.992335i
$363$			4.83399e22i			0.441719i
$364$	1.35894e21	−	1.71746e22i	0.0121140	−	0.153100i
$365$	−4.18900e22			−0.364313
$366$	7.74550e22	+	3.05952e21i	0.657233	+	0.0259612i
$367$		−	1.60760e23i		−	1.33101i	−0.746392	−	0.665506i	$-0.768216\pi$
$367$		−	1.60760e23i		−	1.33101i	0.746392	−	0.665506i	$-0.231784\pi$
$368$	2.07737e22	−	1.30450e23i	0.167836	−	1.05394i
$369$	5.85825e21			0.0461882
$370$	−5.67770e20	+	1.43737e22i	−0.00436875	+	0.110599i
$371$			1.09305e23i			0.820870i
$372$	−1.06991e23	−	8.46566e21i	−0.784263	−	0.0620547i
$373$	−9.66463e22			−0.691522			−0.345761	−	0.938323i	$-0.612379\pi$
$373$	−9.66463e22			−0.691522			−0.345761	+	0.938323i	$0.612379\pi$
$374$	−8.53431e22	−	3.37111e21i	−0.596107	−	0.0235466i
$375$			3.63607e22i			0.247942i
$376$	−1.57064e23	−	1.86902e22i	−1.04565	−	0.124430i
$377$	1.74241e22			0.113260
$378$	6.08814e20	−	1.54128e22i	0.00386419	−	0.0978259i
$379$		−	1.30208e23i		−	0.807020i	−0.914975	−	0.403510i	$-0.867790\pi$
$379$		−	1.30208e23i		−	0.807020i	0.914975	−	0.403510i	$-0.132210\pi$
$380$	2.57453e21	−	3.25375e22i	0.0155828	−	0.196939i
$381$	−3.57049e22			−0.211059
$382$	−4.06604e22	−	1.60612e21i	−0.234748	−	0.00927270i
$383$			1.19611e23i			0.674499i	0.941415	+	0.337250i	$0.109497\pi$
$383$			1.19611e23i			0.674499i	−0.941415	+	0.337250i	$0.890503\pi$
$384$	−1.00837e23	−	2.85993e22i	−0.555443	−	0.157534i
$385$	−1.00834e22			−0.0542576
$386$	1.22376e22	−	3.09808e23i	0.0643297	−	1.62857i
$387$			6.82256e22i			0.350388i
$388$	−1.77870e22	−	1.40739e21i	−0.0892516	−	0.00706202i
$389$	3.36618e23			1.65041			0.825204	−	0.564835i	$-0.191060\pi$
$389$	3.36618e23			1.65041			0.825204	+	0.564835i	$0.191060\pi$
$390$	−7.99951e21	−	3.15986e20i	−0.0383250	−	0.00151386i
$391$		−	2.80573e23i		−	1.31357i
$392$	−1.91425e22	+	1.60865e23i	−0.0875841	+	0.736016i
$393$	−2.38576e22			−0.106683
$394$	−2.28928e21	+	5.79555e22i	−0.0100054	+	0.253296i
$395$		−	4.89807e22i		−	0.209243i
$396$	3.05178e21	−	3.85692e22i	0.0127437	−	0.161059i
$397$	5.00389e21			0.0204265			0.0102132	−	0.999948i	$-0.496749\pi$
$397$	5.00389e21			0.0204265			0.0102132	+	0.999948i	$0.496749\pi$
$398$	−2.45301e23	−	9.68956e21i	−0.978930	−	0.0386684i
$399$			6.75821e22i			0.263679i
$400$	−2.46346e23	−	3.92298e22i	−0.939736	−	0.149650i
$401$	4.23136e23			1.57827			0.789134	−	0.614221i	$-0.210530\pi$
$401$	4.23136e23			1.57827			0.789134	+	0.614221i	$0.210530\pi$
$402$	3.48883e21	−	8.83233e22i	0.0127246	−	0.322137i
$403$		−	1.15340e23i		−	0.411370i
$404$	5.25984e23	+	4.16184e22i	1.83460	+	0.145162i
$405$	−7.16768e21			−0.0244502
$406$	5.71601e22	+	2.25786e21i	0.190703	+	0.00753292i
$407$		−	7.47093e22i		−	0.243795i
$408$	−2.21070e23	−	2.63068e22i	−0.705649	−	0.0839704i
$409$	3.02501e23			0.944533			0.472266	−	0.881456i	$-0.343436\pi$
$409$	3.02501e23			0.944533			0.472266	+	0.881456i	$0.343436\pi$
$410$	3.94002e20	−	9.97457e21i	0.00120349	−	0.0304677i
$411$			2.83191e23i			0.846258i
$412$	−4.66038e22	+	5.88990e23i	−0.136253	+	1.72200i
$413$	−3.30875e22			−0.0946484
$414$	1.26998e23	+	5.01649e21i	0.355461	+	0.0140410i
$415$		−	8.26914e22i		−	0.226479i
$416$	2.20912e22	−	1.10453e23i	0.0592080	−	0.296032i
$417$	9.62579e22			0.252471
$418$	−6.69074e21	+	1.69383e23i	−0.0171746	+	0.434794i
$419$			6.76895e23i			1.70057i	0.526321	+	0.850286i	$0.323571\pi$
$419$			6.76895e23i			1.70057i	−0.526321	+	0.850286i	$0.676429\pi$
$420$	−2.62016e22	−	2.07320e21i	−0.0644294	−	0.00509797i
$421$	−5.28240e22			−0.127143			−0.0635714	−	0.997977i	$-0.520249\pi$
$421$	−5.28240e22			−0.127143			−0.0635714	+	0.997977i	$0.520249\pi$
$422$	−6.96029e23	−	2.74936e22i	−1.63989	−	0.0647769i
$423$		−	1.52189e23i		−	0.351009i
$424$	−8.44456e22	+	7.09642e23i	−0.190671	+	1.60231i
$425$	−5.29843e23			−1.17124
$426$	1.33579e22	−	3.38168e23i	0.0289102	−	0.731890i
$427$			2.73492e23i			0.579553i
$428$	−1.33563e22	+	1.68801e23i	−0.0277137	+	0.350252i
$429$	4.15787e22			0.0844802
$430$	1.16164e23	+	4.58858e21i	0.231130	+	0.00912981i
$431$		−	5.20442e23i		−	1.01409i	−0.861920	−	0.507045i	$-0.830738\pi$
$431$		−	5.20442e23i		−	1.01409i	0.861920	−	0.507045i	$-0.169262\pi$
$432$	1.58600e22	−	9.95941e22i	0.0302657	−	0.190055i
$433$	1.87005e22			0.0349512			0.0174756	−	0.999847i	$-0.494437\pi$
$433$	1.87005e22			0.0349512			0.0174756	+	0.999847i	$0.494437\pi$
$434$	1.49460e22	−	3.78374e23i	0.0273601	−	0.692650i
$435$		−	2.65822e22i		−	0.0476637i
$436$	4.12088e23	+	3.26064e22i	0.723789	+	0.0572697i
$437$	−5.56861e23			−0.958106
$438$	5.66652e23	+	2.23831e22i	0.955101	+	0.0377271i
$439$		−	3.48990e23i		−	0.576279i	−0.957589	−	0.288139i	$-0.906963\pi$
$439$		−	3.48990e23i		−	0.576279i	0.957589	−	0.288139i	$-0.0930366\pi$
$440$	−6.54646e22	−	7.79012e21i	−0.105909	−	0.0126029i
$441$	−1.55872e23			−0.247070
$442$	9.44331e21	−	2.39067e23i	0.0146664	−	0.371295i
$443$			4.85746e23i			0.739223i	0.929186	+	0.369612i	$0.120509\pi$
$443$			4.85746e23i			0.739223i	−0.929186	+	0.369612i	$0.879491\pi$
$444$	1.53606e22	−	1.94131e23i	0.0229067	−	0.289500i
$445$	2.82843e23			0.413338
$446$	−1.98149e23	−	7.82703e21i	−0.283778	−	0.0112094i
$447$			3.53665e23i			0.496392i
$448$	8.67836e22	−	3.59481e23i	0.119381	−	0.494509i
$449$	−6.03263e23			−0.813373			−0.406686	−	0.913568i	$-0.633316\pi$
$449$	−6.03263e23			−0.813373			−0.406686	+	0.913568i	$0.633316\pi$
$450$	9.47330e21	−	2.39826e23i	0.0125196	−	0.316945i
$451$			5.18443e22i			0.0671603i
$452$	4.52244e23	+	3.57837e22i	0.574284	+	0.0454401i
$453$	6.97439e23			0.868206
$454$	1.28947e24	+	5.09351e22i	1.57366	+	0.0621605i
$455$		−	2.82461e22i		−	0.0337952i
$456$	−5.22118e22	+	4.38764e23i	−0.0612471	+	0.514692i
$457$	−1.35080e24			−1.55362			−0.776811	−	0.629734i	$-0.783164\pi$
$457$	−1.35080e24			−1.55362			−0.776811	+	0.629734i	$0.783164\pi$
$458$	2.76627e22	−	7.00308e23i	0.0311964	−	0.789769i
$459$		−	2.14208e23i		−	0.236876i
$460$	1.70827e22	−	2.15895e23i	0.0185240	−	0.234111i
$461$	−9.61566e22			−0.102252			−0.0511259	−	0.998692i	$-0.516281\pi$
$461$	−9.61566e22			−0.102252			−0.0511259	+	0.998692i	$0.516281\pi$
$462$	1.36400e23	+	5.38788e21i	0.142245	+	0.00561876i
$463$		−	1.59244e24i		−	1.62867i	−0.580394	−	0.814336i	$-0.697101\pi$
$463$		−	1.59244e24i		−	1.62867i	0.580394	−	0.814336i	$-0.302899\pi$
$464$	3.69357e23	+	5.88189e22i	0.370497	+	0.0590004i
$465$	−1.75962e23			−0.173118
$466$	2.02280e22	−	5.12093e23i	0.0195200	−	0.494169i
$467$		−	4.89998e23i		−	0.463813i	−0.972738	−	0.231906i	$-0.925504\pi$
$467$		−	4.89998e23i		−	0.463813i	0.972738	−	0.231906i	$-0.0744963\pi$
$468$	1.08042e23	+	8.54878e21i	0.100318	+	0.00793764i
$469$	3.11868e23			0.284063
$470$	−2.59124e23	−	1.02356e22i	−0.231541	−	0.00914601i
$471$		−	3.21613e23i		−	0.281933i
$472$	−2.14814e23	−	2.55624e22i	−0.184750	−	0.0219848i
$473$	−6.03783e23			−0.509484
$474$	−2.61719e22	+	6.62569e23i	−0.0216686	+	0.548563i
$475$			1.05159e24i			0.854290i
$476$	6.19580e22	−	7.83041e23i	0.0493895	−	0.624197i
$477$	−6.87613e23			−0.537872
$478$	8.63953e22	+	3.41267e21i	0.0663191	+	0.00261965i
$479$		−	6.01368e23i		−	0.453024i	−0.974008	−	0.226512i	$-0.927268\pi$
$479$		−	6.01368e23i		−	0.453024i	0.974008	−	0.226512i	$-0.0727322\pi$
$480$	−1.68507e23	−	3.37024e22i	−0.124580	−	0.0249167i
$481$	2.09279e23			0.151852
$482$	−8.54446e22	+	2.16312e24i	−0.0608501	+	1.54048i
$483$			4.48425e23i			0.313448i
$484$	−1.11163e24	−	8.79574e22i	−0.762696	−	0.0603482i
$485$	−2.92532e22			−0.0197014
$486$	9.69582e22	+	3.82992e21i	0.0641000	+	0.00253200i
$487$		−	3.29448e23i		−	0.213809i	−0.994269	−	0.106905i	$-0.965906\pi$
$487$		−	3.29448e23i		−	0.213809i	0.994269	−	0.106905i	$-0.0340939\pi$
$488$	−2.11291e23	+	1.77559e24i	−0.134618	+	1.13127i
$489$	1.20122e24			0.751354
$490$	−1.04833e22	+	2.65395e23i	−0.00643773	+	0.162978i
$491$			2.68621e24i			1.61960i	0.586709	+	0.809798i	$0.300423\pi$
$491$			2.68621e24i			1.61960i	−0.586709	+	0.809798i	$0.699577\pi$
$492$	−1.06595e22	+	1.34717e23i	−0.00631029	+	0.0797510i
$493$	7.94415e23			0.461769
$494$	−4.74483e23	−	1.87424e22i	−0.270819	−	0.0106975i
$495$		−	6.34324e22i		−	0.0355520i
$496$	3.89354e23	−	2.44498e24i	0.214294	−	1.34567i
$497$	1.19406e24			0.645386
$498$	−4.41846e22	+	1.11858e24i	−0.0234535	+	0.593748i
$499$			3.57997e24i			1.86627i	0.359525	+	0.933136i	$0.382939\pi$
$499$			3.57997e24i			1.86627i	−0.359525	+	0.933136i	$0.617061\pi$
$500$	−8.36154e23	−	6.61605e22i	−0.428111	−	0.0338742i
$501$	−9.59581e23			−0.482550
$502$	−1.82768e24	−	7.21946e22i	−0.902749	−	0.0356592i
$503$		−	3.18575e24i		−	1.54561i	−0.634644	−	0.772805i	$-0.718853\pi$
$503$		−	3.18575e24i		−	1.54561i	0.634644	−	0.772805i	$-0.281147\pi$
$504$	3.53325e23	+	4.20448e22i	0.168384	+	0.0200372i
$505$	8.65055e23			0.404968
$506$	−4.43949e22	+	1.12390e24i	−0.0204164	+	0.516861i
$507$		−	1.16147e24i		−	0.524730i
$508$	6.49673e22	−	8.21074e23i	0.0288351	−	0.364426i
$509$	2.21223e24			0.964652			0.482326	−	0.875992i	$-0.339792\pi$
$509$	2.21223e24			0.964652			0.482326	+	0.875992i	$0.339792\pi$
$510$	−3.64721e23	−	1.44067e22i	−0.156253	−	0.00617211i
$511$			2.00083e24i			0.842215i
$512$	8.41151e23	−	2.26682e24i	0.347892	−	0.937535i
$513$	−4.25144e23			−0.172775
$514$	−5.53010e22	+	1.40000e24i	−0.0220833	+	0.559062i
$515$			9.68677e23i			0.380114i
$516$	−1.56892e24	−	1.24141e23i	−0.604998	−	0.0478704i
$517$	1.34684e24			0.510388
$518$	6.86545e23	+	2.71190e22i	0.255682	+	0.0100996i
$519$		−	2.08975e24i		−	0.764870i
$520$	2.18220e22	−	1.83382e23i	0.00784992	−	0.0659672i
$521$	3.91558e24			1.38438			0.692192	−	0.721713i	$-0.256645\pi$
$521$	3.91558e24			1.38438			0.692192	+	0.721713i	$0.256645\pi$
$522$	−1.42037e22	+	3.59582e23i	−0.00493591	+	0.124958i
$523$			2.46165e24i			0.840836i	0.907331	+	0.420418i	$0.138117\pi$
$523$			2.46165e24i			0.840836i	−0.907331	+	0.420418i	$0.861883\pi$
$524$	4.34104e22	−	5.48632e23i	0.0145751	−	0.184204i
$525$	8.46821e23			0.279485
$526$	−2.97093e24	−	1.17354e23i	−0.963875	−	0.0380737i
$527$		−	5.25867e24i		−	1.67718i
$528$	8.81387e23	+	1.40358e23i	0.276351	+	0.0440080i
$529$	−4.50769e23			−0.138948
$530$	−4.62461e22	+	1.17077e24i	−0.0140150	+	0.354803i
$531$		−	2.08146e23i		−	0.0620180i
$532$	−1.55412e24	−	1.22970e23i	−0.455282	−	0.0360241i
$533$	−1.45229e23			−0.0418319
$534$	−3.82606e24	−	1.51132e23i	−1.08363	−	0.0428041i
$535$			2.77617e23i			0.0773147i
$536$	2.02474e24	+	2.40939e23i	0.554481	+	0.0659818i
$537$	−2.42539e24			−0.653149
$538$	1.10379e23	−	2.79435e24i	0.0292311	−	0.740014i
$539$		−	1.37943e24i		−	0.359253i
$540$	1.30420e22	−	1.64829e23i	0.00334042	−	0.0422171i
$541$	−4.54196e24			−1.14411			−0.572055	−	0.820215i	$-0.693854\pi$
$541$	−4.54196e24			−1.14411			−0.572055	+	0.820215i	$0.693854\pi$
$542$	5.06654e24	+	2.00132e23i	1.25521	+	0.0495818i
$543$		−	2.35307e24i		−	0.573372i
$544$	1.00720e24	−	5.03588e24i	0.241394	−	1.20694i
$545$	6.77737e23			0.159769
$546$	−1.50928e22	+	3.82089e23i	−0.00349974	+	0.0885994i
$547$			9.76061e22i			0.0222634i	0.999938	+	0.0111317i	$0.00354340\pi$
$547$			9.76061e22i			0.0222634i	−0.999938	+	0.0111317i	$0.996457\pi$
$548$	−6.51228e24	−	5.15283e23i	−1.46119	−	0.115617i
$549$	−1.72048e24			−0.379750
$550$	2.12241e24	+	8.38367e22i	0.460856	+	0.0182041i
$551$		−	1.57670e24i		−	0.336809i
$552$	−3.46439e23	+	2.91132e24i	−0.0728074	+	0.611840i
$553$	−2.33952e24			−0.483726
$554$	−5.11698e22	+	1.29542e24i	−0.0104094	+	0.263525i
$555$		−	3.19276e23i		−	0.0639043i
$556$	−1.75147e23	+	2.21356e24i	−0.0344929	+	0.435931i
$557$	−2.45261e24			−0.475260			−0.237630	−	0.971356i	$-0.576371\pi$
$557$	−2.45261e24			−0.475260			−0.237630	+	0.971356i	$0.576371\pi$
$558$	2.38027e24	+	9.40222e22i	0.453856	+	0.0179276i
$559$		−	1.69134e24i		−	0.317340i
$560$	9.53509e22	−	5.98762e23i	0.0176049	−	0.110551i
$561$	1.89569e24			0.344431
$562$	2.90623e22	−	7.35741e23i	0.00519640	−	0.131552i
$563$			3.99133e24i			0.702331i	0.936313	+	0.351166i	$0.114215\pi$
$563$			3.99133e24i			0.702331i	−0.936313	+	0.351166i	$0.885785\pi$
$564$	3.49974e24	+	2.76916e23i	0.606072	+	0.0479553i
$565$	7.43778e23			0.126767
$566$	7.55336e24	+	2.98363e23i	1.26705	+	0.0500492i
$567$			3.42357e23i			0.0565239i
$568$	7.75224e24	+	9.22496e23i	1.25977	+	0.149910i
$569$	−7.41215e24			−1.18559			−0.592794	−	0.805354i	$-0.701975\pi$
$569$	−7.41215e24			−1.18559			−0.592794	+	0.805354i	$0.701975\pi$
$570$	−2.85934e22	+	7.23872e23i	−0.00450187	+	0.113969i
$571$			7.23320e24i			1.12100i	0.828155	+	0.560500i	$0.189391\pi$
$571$			7.23320e24i			1.12100i	−0.828155	+	0.560500i	$0.810609\pi$
$572$	−7.56549e22	+	9.56147e23i	−0.0115418	+	0.145868i
$573$	9.03174e23			0.135637
$574$	−4.76426e23	−	1.88191e22i	−0.0704349	−	0.00278223i
$575$			6.97761e24i			1.01554i
$576$	2.26142e24	+	5.45936e23i	0.324025	+	0.0782239i
$577$	8.78495e24			1.23924			0.619622	−	0.784900i	$-0.287286\pi$
$577$	8.78495e24			1.23924			0.619622	+	0.784900i	$0.287286\pi$
$578$	1.46353e23	−	3.70507e24i	0.0203260	−	0.514572i
$579$			6.88164e24i			0.940989i
$580$	6.11287e23	+	4.83680e22i	0.0822987	+	0.00651187i
$581$	−3.94968e24			−0.523572
$582$	3.95712e23	+	1.56309e22i	0.0516502	+	0.00204022i
$583$		−	6.08523e24i		−	0.782096i
$584$	−1.54578e24	+	1.29900e25i	−0.195629	+	1.64397i
$585$	1.77690e23			0.0221442
$586$	2.76900e23	−	7.01000e24i	0.0339816	−	0.860279i
$587$			1.37150e24i			0.165750i	0.996560	+	0.0828748i	$0.0264102\pi$
$587$			1.37150e24i			0.165750i	−0.996560	+	0.0828748i	$0.973590\pi$
$588$	2.83618e23	−	3.58444e24i	0.0337550	−	0.426604i
$589$	−1.04370e25			−1.22332
$590$	−3.54400e23	−	1.39991e22i	−0.0409097	−	0.00161596i
$591$		−	1.28734e24i		−	0.146355i
$592$	4.43631e24	+	7.06468e23i	0.496737	+	0.0791038i
$593$	−6.19848e24			−0.683585			−0.341793	−	0.939775i	$-0.611034\pi$
$593$	−6.19848e24			−0.683585			−0.341793	+	0.939775i	$0.611034\pi$
$594$	−3.38940e22	+	8.58060e23i	−0.00368167	+	0.0932051i
$595$		−	1.28782e24i		−	0.137785i
$596$	−8.13292e24	−	6.43516e23i	−0.857097	−	0.0678177i
$597$	5.44877e24			0.565626
$598$	−3.14832e24	−	1.24361e23i	−0.321935	−	0.0127167i
$599$		−	2.44504e24i		−	0.246289i	−0.992389	−	0.123145i	$-0.960702\pi$
$599$		−	2.44504e24i		−	0.246289i	0.992389	−	0.123145i	$-0.0392979\pi$
$600$	5.49783e24	+	6.54228e23i	0.545544	+	0.0649184i
$601$	−6.89878e24			−0.674376			−0.337188	−	0.941437i	$-0.609476\pi$
$601$	−6.89878e24			−0.674376			−0.337188	+	0.941437i	$0.609476\pi$
$602$	2.19169e23	−	5.54849e24i	0.0211062	−	0.534326i
$603$			1.96189e24i			0.186131i
$604$	−1.26903e24	+	1.60384e25i	−0.118615	+	1.49909i
$605$	−1.82823e24			−0.168357
$606$	−1.17017e25	−	4.62226e23i	−1.06169	−	0.0419373i
$607$		−	1.58859e25i		−	1.42009i	−0.704158	−	0.710043i	$-0.748675\pi$
$607$		−	1.58859e25i		−	1.42009i	0.704158	−	0.710043i	$-0.251325\pi$
$608$	−9.99486e24	−	1.99903e24i	−0.880328	−	0.176070i
$609$	−1.26967e24			−0.110189
$610$	−1.15712e23	+	2.92937e24i	−0.00989488	+	0.250499i
$611$			3.77282e24i			0.317903i
$612$	4.92594e24	+	3.89764e23i	0.409003	+	0.0323623i
$613$	1.60901e25			1.31648			0.658239	−	0.752809i	$-0.271302\pi$
$613$	1.60901e25			1.31648			0.658239	+	0.752809i	$0.271302\pi$
$614$	2.41222e24	+	9.52843e22i	0.194492	+	0.00768256i
$615$			2.21561e23i			0.0176042i
$616$	−3.72088e23	+	3.12686e24i	−0.0291353	+	0.244839i
$617$	6.42238e24			0.495598			0.247799	−	0.968811i	$-0.420293\pi$
$617$	6.42238e24			0.495598			0.247799	+	0.968811i	$0.420293\pi$
$618$	5.17595e23	−	1.31034e25i	0.0393635	−	0.996527i
$619$			2.76158e24i			0.206986i	0.994630	+	0.103493i	$0.0330020\pi$
$619$			2.76158e24i			0.206986i	−0.994630	+	0.103493i	$0.966998\pi$
$620$	3.20174e23	−	4.04644e24i	0.0236516	−	0.298915i
$621$	−2.82094e24			−0.205386
$622$	−3.18686e24	−	1.25883e23i	−0.228691	−	0.00903346i
$623$		−	1.35097e25i		−	0.955552i
$624$	−3.93177e23	+	2.46898e24i	−0.0274111	+	0.172130i
$625$	1.24721e25			0.857076
$626$	9.04274e23	−	2.28926e25i	0.0612535	−	1.55069i
$627$		−	3.76244e24i		−	0.251224i
$628$	7.39584e24	+	5.85194e23i	0.486800	+	0.0385180i
$629$	9.54165e24			0.619110
$630$	5.82915e23	+	2.30255e22i	0.0372855	+	0.00147280i
$631$		−	8.72241e24i		−	0.550012i	−0.961442	−	0.275006i	$-0.911320\pi$
$631$		−	8.72241e24i		−	0.550012i	0.961442	−	0.275006i	$-0.0886799\pi$
$632$	−1.51889e25	−	1.80744e24i	−0.944217	−	0.112359i
$633$	1.54606e25			0.947531
$634$	−5.86402e23	+	1.48454e25i	−0.0354317	+	0.896990i
$635$		−	1.35037e24i		−	0.0804433i
$636$	1.25115e24	−	1.58124e25i	0.0734847	−	0.928719i
$637$	3.86412e24			0.223767
$638$	−3.18222e24	−	1.25700e23i	−0.181696	−	0.00717710i
$639$			7.51159e24i			0.422887i
$640$	1.08163e24	−	3.81369e24i	0.0600427	−	0.211702i
$641$	1.53205e25			0.838593			0.419296	−	0.907849i	$-0.362277\pi$
$641$	1.53205e25			0.838593			0.419296	+	0.907849i	$0.362277\pi$
$642$	1.48340e23	−	3.75537e24i	0.00800648	−	0.202692i
$643$		−	1.06009e25i		−	0.564216i	−0.959383	−	0.282108i	$-0.908966\pi$
$643$		−	1.06009e25i		−	0.564216i	0.959383	−	0.282108i	$-0.0910336\pi$
$644$	−1.03120e25	−	8.15937e23i	−0.541217	−	0.0428237i
$645$	−2.58031e24			−0.133547
$646$	−2.16331e25	−	8.54521e23i	−1.10414	−	0.0436144i
$647$			2.30140e25i			1.15839i	0.815189	+	0.579194i	$0.196633\pi$
$647$			2.30140e25i			1.15839i	−0.815189	+	0.579194i	$0.803367\pi$
$648$	−2.64495e23	+	2.22269e24i	−0.0131293	+	0.110333i
$649$	1.84205e24			0.0901777
$650$	−2.34847e23	+	5.94540e24i	−0.0113388	+	0.287052i
$651$			8.40466e24i			0.400213i
$652$	−2.18570e24	+	2.76235e25i	−0.102651	+	1.29733i
$653$	−1.95575e25			−0.905930			−0.452965	−	0.891528i	$-0.649634\pi$
$653$	−1.95575e25			−0.905930			−0.452965	+	0.891528i	$0.649634\pi$
$654$	−9.16785e24	−	3.62137e23i	−0.418859	−	0.0165452i
$655$		−	9.02303e23i		−	0.0406613i
$656$	−3.07857e24	−	4.90252e23i	−0.136840	−	0.0217914i
$657$	−1.25868e25			−0.551858
$658$	−4.88893e23	+	1.23768e25i	−0.0211437	+	0.535274i
$659$			3.41967e25i			1.45887i	0.684052	+	0.729433i	$0.260216\pi$
$659$			3.41967e25i			1.45887i	−0.684052	+	0.729433i	$0.739784\pi$
$660$	1.45870e24	+	1.15419e23i	0.0613861	+	0.00485716i
$661$	8.22845e24			0.341590			0.170795	−	0.985307i	$-0.445366\pi$
$661$	8.22845e24			0.341590			0.170795	+	0.985307i	$0.445366\pi$
$662$	3.79992e25	+	1.50100e24i	1.55616	+	0.0614692i
$663$			5.31030e24i			0.214535i
$664$	−2.56425e25	−	3.05140e24i	−1.02199	−	0.121615i
$665$	−2.55598e24			−0.100499
$666$	−1.70600e23	+	4.31890e24i	−0.00661774	+	0.167535i
$667$		−	1.04618e25i		−	0.400382i
$668$	1.74602e24	−	2.20666e25i	0.0659265	−	0.833196i
$669$	4.40141e24			0.163967
$670$	3.34042e24	+	1.31949e23i	0.122780	+	0.00484989i
$671$		−	1.52258e25i		−	0.552178i
$672$	−1.60976e24	+	8.04860e24i	−0.0576021	+	0.288003i
$673$	−4.47109e25			−1.57862			−0.789310	−	0.613995i	$-0.789561\pi$
$673$	−4.47109e25			−1.57862			−0.789310	+	0.613995i	$0.789561\pi$
$674$	−1.44542e24	+	3.65922e25i	−0.0503564	+	1.27482i
$675$			5.32716e24i			0.183131i
$676$	2.67093e25	+	2.11337e24i	0.906028	+	0.0716893i
$677$	4.35935e25			1.45923			0.729616	−	0.683857i	$-0.239699\pi$
$677$	4.35935e25			1.45923			0.729616	+	0.683857i	$0.239699\pi$
$678$	−1.00612e25	−	3.97424e23i	−0.332340	−	0.0131277i
$679$			1.39725e24i			0.0455455i
$680$	9.94930e23	−	8.36094e24i	0.0320046	−	0.268952i
$681$	−2.86426e25			−0.909259
$682$	−8.32076e23	+	2.10649e25i	−0.0260678	+	0.659932i
$683$		−	4.74506e24i		−	0.146708i	−0.997306	−	0.0733542i	$-0.976630\pi$
$683$		−	4.74506e24i		−	0.146708i	0.997306	−	0.0733542i	$-0.0233704\pi$
$684$	7.73576e23	−	9.77665e24i	0.0236047	−	0.298322i
$685$	−1.07104e25			−0.322544
$686$	2.97786e25	+	1.17627e24i	0.885089	+	0.0349616i
$687$			1.55557e25i			0.456329i
$688$	5.70950e24	−	3.58532e25i	0.165311	−	1.03808i
$689$	1.70462e25			0.487142
$690$	−1.89725e23	+	4.80309e24i	−0.00535159	+	0.135481i
$691$		−	2.76742e25i		−	0.770500i	−0.922812	−	0.385250i	$-0.874115\pi$
$691$		−	2.76742e25i		−	0.770500i	0.922812	−	0.385250i	$-0.125885\pi$
$692$	4.80560e25	+	3.80242e24i	1.32067	+	0.104497i
$693$	−3.02979e24			−0.0821890
$694$	2.66552e25	+	1.05290e24i	0.713752	+	0.0281937i
$695$			3.64050e24i			0.0962273i
$696$	−8.24312e24	−	9.80911e23i	−0.215084	−	0.0255945i
$697$	−6.62140e24			−0.170551
$698$	1.05285e23	−	2.66539e24i	0.00267711	−	0.0677738i
$699$			1.13749e25i			0.285531i
$700$	−1.54084e24	+	1.94736e25i	−0.0381835	+	0.482573i
$701$	−2.22441e24			−0.0544193			−0.0272097	−	0.999630i	$-0.508662\pi$
$701$	−2.22441e24			−0.0544193			−0.0272097	+	0.999630i	$0.508662\pi$
$702$	−2.40364e24	−	9.49453e22i	−0.0580544	−	0.00229319i
$703$		−	1.89376e25i		−	0.451572i
$704$	−4.83142e24	+	2.00131e25i	−0.113742	+	0.471151i
$705$	5.75582e24			0.133784
$706$	6.12478e23	−	1.55055e25i	0.0140556	−	0.355831i
$707$		−	4.13185e25i		−	0.936203i
$708$	4.78655e24	+	3.78735e23i	0.107084	+	0.00847297i
$709$	−7.75941e25			−1.71401			−0.857004	−	0.515311i	$-0.827677\pi$
$709$	−7.75941e25			−1.71401			−0.857004	+	0.515311i	$0.827677\pi$
$710$	1.27896e25	+	5.05199e23i	0.278954	+	0.0110189i
$711$		−	1.47174e25i		−	0.316960i
$712$	1.04372e25	−	8.77095e25i	0.221955	−	1.86521i
$713$	−6.92525e25			−1.45422
$714$	−6.88123e23	+	1.74205e25i	−0.0142686	+	0.361225i
$715$			1.57252e24i			0.0321989i
$716$	4.41314e24	−	5.57744e25i	0.0892340	−	1.12776i
$717$	−1.91906e24			−0.0383192
$718$	−5.07537e25	−	2.00481e24i	−1.00080	−	0.0395323i
$719$			6.31378e25i			1.22950i	0.788721	+	0.614751i	$0.210744\pi$
$719$			6.31378e25i			1.22950i	−0.788721	+	0.614751i	$0.789256\pi$
$720$	3.76668e24	+	5.99831e23i	0.0724380	+	0.0115355i
$721$	4.62680e25			0.878745
$722$	4.08274e23	−	1.03359e25i	0.00765803	−	0.193871i
$723$		−	4.80484e25i		−	0.890091i
$724$	5.41114e25	+	4.28155e24i	0.990014	+	0.0783347i
$725$	−1.97564e25			−0.356999
$726$	2.47307e25	+	9.76881e23i	0.441375	+	0.0174346i
$727$			6.35475e25i			1.12018i	0.828431	+	0.560092i	$0.189234\pi$
$727$			6.35475e25i			1.12018i	−0.828431	+	0.560092i	$0.810766\pi$
$728$	−8.75909e24	−	1.04231e24i	−0.152502	−	0.0181474i
$729$	−2.15369e24			−0.0370370
$730$	−8.46537e23	+	2.14309e25i	−0.0143794	+	0.364029i
$731$		−	7.71133e25i		−	1.29382i
$732$	3.13051e24	−	3.95642e25i	0.0518819	−	0.655696i
$733$	5.13543e25			0.840700			0.420350	−	0.907362i	$-0.361907\pi$
$733$	5.13543e25			0.840700			0.420350	+	0.907362i	$0.361907\pi$
$734$	−8.22448e25	−	3.24872e24i	−1.32998	−	0.0525350i
$735$		−	5.89511e24i		−	0.0941685i
$736$	−6.63186e25	−	1.32641e25i	−1.04649	−	0.209304i
$737$	−1.73623e25			−0.270645
$738$	1.18387e23	−	2.99709e24i	0.00182304	−	0.0461522i
$739$			7.46529e25i			1.13566i	0.823147	+	0.567828i	$0.192216\pi$
$739$			7.46529e25i			1.13566i	−0.823147	+	0.567828i	$0.807784\pi$
$740$	7.34211e24	+	5.80943e23i	0.110341	+	0.00873068i
$741$	1.05395e25			0.156479
$742$	5.59205e25	+	2.20890e24i	0.820231	+	0.0323997i
$743$		−	4.81104e25i		−	0.697171i	−0.937277	−	0.348586i	$-0.886662\pi$
$743$		−	4.81104e25i		−	0.697171i	0.937277	−	0.348586i	$-0.113338\pi$
$744$	−6.49318e24	+	5.45657e25i	−0.0929611	+	0.781203i
$745$	−1.33757e25			−0.189196
$746$	−1.95309e24	+	4.94444e25i	−0.0272943	+	0.690983i
$747$		−	2.48465e25i		−	0.343068i
$748$	−3.44933e24	+	4.35935e25i	−0.0470566	+	0.594713i
$749$	1.32601e25			0.178736
$750$	1.86022e25	+	7.34798e23i	0.247749	+	0.00978626i
$751$			9.21014e25i			1.21201i	0.795460	+	0.606006i	$0.207229\pi$
$751$			9.21014e25i			1.21201i	−0.795460	+	0.606006i	$0.792771\pi$
$752$	−1.27360e25	+	7.99765e25i	−0.165605	+	1.03992i
$753$	4.05975e25			0.521609
$754$	3.52116e23	−	8.91418e24i	0.00447038	−	0.113172i
$755$			2.63774e25i			0.330909i
$756$	−7.87288e24	−	6.22940e23i	−0.0975972	−	0.00772236i
$757$	1.13544e26			1.39091			0.695456	−	0.718569i	$-0.255202\pi$
$757$	1.13544e26			1.39091			0.695456	+	0.718569i	$0.255202\pi$
$758$	−6.66145e25	−	2.63132e24i	−0.806391	−	0.0318530i
$759$		−	2.49648e25i		−	0.298642i
$760$	−1.65942e25	−	1.97467e24i	−0.196171	−	0.0233438i
$761$	6.05830e25			0.707765			0.353882	−	0.935290i	$-0.384861\pi$
$761$	6.05830e25			0.707765			0.353882	+	0.935290i	$0.384861\pi$
$762$	−7.21547e23	+	1.82667e25i	−0.00833047	+	0.210894i
$763$		−	3.23715e25i		−	0.369353i
$764$	−1.64338e24	+	2.07695e25i	−0.0185310	+	0.234199i
$765$	8.10140e24			0.0902832
$766$	6.11930e25	+	2.41717e24i	0.673974	+	0.0266224i
$767$			5.16003e24i			0.0561687i
$768$	−1.66692e25	+	5.10104e25i	−0.179334	+	0.548792i
$769$	7.81399e25			0.830875			0.415438	−	0.909622i	$-0.363628\pi$
$769$	7.81399e25			0.830875			0.415438	+	0.909622i	$0.363628\pi$
$770$	−2.03771e23	+	5.15868e24i	−0.00214154	+	0.0542153i
$771$		−	3.10976e25i		−	0.323026i
$772$	−1.58251e26	−	1.25216e25i	−1.62476	−	0.128559i
$773$	2.25992e25			0.229339			0.114669	−	0.993404i	$-0.463419\pi$
$773$	2.25992e25			0.229339			0.114669	+	0.993404i	$0.463419\pi$
$774$	3.49043e25	+	1.37874e24i	0.350115	+	0.0138298i
$775$			1.30779e26i			1.29665i
$776$	−1.07947e24	+	9.07138e24i	−0.0105793	+	0.0889033i
$777$	−1.52499e25			−0.147733
$778$	6.80258e24	−	1.72214e26i	0.0651414	−	1.64912i
$779$			1.31417e25i			0.124398i
$780$	−3.23318e23	+	4.08617e24i	−0.00302537	+	0.0382354i
$781$	−6.64760e25			−0.614901
$782$	−1.43541e26	−	5.66998e24i	−1.31255	−	0.0518466i
$783$		−	7.98724e24i		−	0.0722006i
$784$	8.19119e25	+	1.30442e25i	0.731986	+	0.116566i
$785$	1.21635e25			0.107456
$786$	−4.82129e23	+	1.22056e25i	−0.00421076	+	0.106600i
$787$		−	8.04579e25i		−	0.694698i	−0.937736	−	0.347349i	$-0.887082\pi$
$787$		−	8.04579e25i		−	0.694698i	0.937736	−	0.347349i	$-0.112918\pi$
$788$	2.96038e25	+	2.34240e24i	0.252704	+	0.0199952i
$789$	6.59920e25			0.556927
$790$	−2.50586e25	−	9.89831e23i	−0.209080	−	0.00825880i
$791$		−	3.55259e25i		−	0.293060i
$792$	−1.96704e25	−	2.34072e24i	−0.160430	−	0.0190908i
$793$	4.26513e25			0.343933
$794$	1.01122e23	−	2.55999e24i	0.000806230	−	0.0204105i
$795$		−	2.60057e25i		−	0.205005i
$796$	−9.91438e24	+	1.25300e26i	−0.0772766	+	0.976641i
$797$	−1.80267e26			−1.38929			−0.694644	−	0.719354i	$-0.744438\pi$
$797$	−1.80267e26			−1.38929			−0.694644	+	0.719354i	$0.744438\pi$
$798$	3.45751e25	+	1.36574e24i	0.263473	+	0.0104074i
$799$			1.72014e26i			1.29611i
$800$	−2.50483e25	+	1.25238e26i	−0.186624	+	0.933097i
$801$	8.49868e25			0.626122
$802$	8.55099e24	−	2.16477e26i	0.0622941	−	1.57704i
$803$		−	1.11391e26i		−	0.802433i
$804$	−4.51158e25	−	3.56978e24i	−0.321384	−	0.0254295i
$805$	−1.69596e25			−0.119468
$806$	−5.90078e25	−	2.33085e24i	−0.411050	−	0.0162367i
$807$			6.20697e25i			0.427581i
$808$	3.19214e25	−	2.68253e26i	0.217460	−	1.82744i
$809$	4.12882e25			0.278156			0.139078	−	0.990281i	$-0.455586\pi$
$809$	4.12882e25			0.278156			0.139078	+	0.990281i	$0.455586\pi$
$810$	−1.44849e23	+	3.66699e24i	−0.000965049	+	0.0244312i
$811$		−	1.66176e26i		−	1.09492i	−0.836833	−	0.547458i	$-0.815596\pi$
$811$		−	1.66176e26i		−	1.09492i	0.836833	−	0.547458i	$-0.184404\pi$
$812$	2.31025e24	−	2.91975e25i	0.0150541	−	0.190258i
$813$	−1.12541e26			−0.725263
$814$	−3.82214e25	−	1.50977e24i	−0.243605	−	0.00962257i
$815$			4.54307e25i			0.286372i
$816$	−1.79261e25	+	1.12568e26i	−0.111757	+	0.701785i
$817$	−1.53049e26			−0.943695
$818$	6.11312e24	−	1.54760e26i	0.0372806	−	0.943797i
$819$		−	8.48719e24i		−	0.0511928i
$820$	−5.09504e24	−	4.03144e23i	−0.0303964	−	0.00240511i
$821$	−1.10018e26			−0.649197			−0.324598	−	0.945852i	$-0.605229\pi$
$821$	−1.10018e26			−0.649197			−0.324598	+	0.945852i	$0.605229\pi$
$822$	1.44881e26	+	5.72289e24i	0.845598	+	0.0334017i
$823$		−	1.56874e26i		−	0.905635i	−0.891603	−	0.452818i	$-0.850419\pi$
$823$		−	1.56874e26i		−	0.905635i	0.891603	−	0.452818i	$-0.149581\pi$
$824$	3.00386e26	+	3.57452e25i	1.71528	+	0.204114i
$825$	−4.71443e25			−0.266283
$826$	−6.68652e23	+	1.69276e25i	−0.00373576	+	0.0945747i
$827$		−	1.55945e26i		−	0.861832i	−0.902392	−	0.430916i	$-0.858190\pi$
$827$		−	1.55945e26i		−	0.861832i	0.902392	−	0.430916i	$-0.141810\pi$
$828$	5.13288e24	−	6.48707e25i	0.0280600	−	0.354630i
$829$	1.68710e26			0.912324			0.456162	−	0.889897i	$-0.349224\pi$
$829$	1.68710e26			0.912324			0.456162	+	0.889897i	$0.349224\pi$
$830$	−4.23050e25	−	1.67108e24i	−0.226302	−	0.00893909i
$831$		−	2.87745e25i		−	0.152265i
$832$	−5.60615e25	−	1.35340e25i	−0.293464	−	0.0708462i
$833$	1.76177e26			0.912312
$834$	1.94524e24	−	4.92456e25i	0.00996502	−	0.252275i
$835$		−	3.62916e25i		−	0.183920i
$836$	8.65213e25	+	6.84598e24i	0.433777	+	0.0343225i
$837$	−5.28719e25			−0.262238
$838$	3.46300e26	+	1.36791e25i	1.69925	+	0.0671214i
$839$			3.60309e26i			1.74911i	0.484926	+	0.874555i	$0.338846\pi$
$839$			3.60309e26i			1.74911i	−0.484926	+	0.874555i	$0.661154\pi$
$840$	−1.59015e24	+	1.33629e25i	−0.00763702	+	0.0641780i
$841$	−1.80836e26			−0.859251
$842$	−1.06750e24	+	2.70248e25i	−0.00501832	+	0.127044i
$843$			1.63427e25i			0.0760109i
$844$	−2.81315e25	+	3.55534e26i	−0.129453	+	1.63606i
$845$	4.39271e25			0.199997
$846$	−7.78598e25	−	3.07552e24i	−0.350736	−	0.0138543i
$847$			8.73237e25i			0.389208i
$848$	3.61347e26	+	5.75433e25i	1.59354	+	0.253765i
$849$	−1.67780e26			−0.732100
$850$	−1.07074e25	+	2.71068e26i	−0.0462288	+	1.17033i
$851$		−	1.25656e26i		−	0.536806i
$852$	−1.72737e26	−	1.36678e25i	−0.730179	−	0.0577753i
$853$	−4.08946e26			−1.71051			−0.855254	−	0.518210i	$-0.826599\pi$
$853$	−4.08946e26			−1.71051			−0.855254	+	0.518210i	$0.826599\pi$
$854$	1.39919e26	+	5.52688e24i	0.579101	+	0.0228749i
$855$		−	1.60791e25i		−	0.0658516i
$856$	8.60889e25	+	1.02444e25i	0.348886	+	0.0415165i
$857$	−5.50191e25			−0.220641			−0.110320	−	0.993896i	$-0.535188\pi$
$857$	−5.50191e25			−0.220641			−0.110320	+	0.993896i	$0.535188\pi$
$858$	8.40246e23	−	2.12717e25i	0.00333443	−	0.0844144i
$859$			3.19275e26i			1.25379i	0.779102	+	0.626897i	$0.215675\pi$
$859$			3.19275e26i			1.25379i	−0.779102	+	0.626897i	$0.784325\pi$
$860$	4.69504e24	−	5.93371e25i	0.0182454	−	0.230590i
$861$	1.05826e25			0.0406973
$862$	−2.66258e26	−	1.05174e25i	−1.01330	−	0.0400260i
$863$		−	8.57056e25i		−	0.322784i	−0.986890	−	0.161392i	$-0.948402\pi$
$863$		−	8.57056e25i		−	0.322784i	0.986890	−	0.161392i	$-0.0515983\pi$
$864$	−5.06320e25	−	1.01267e25i	−0.188713	−	0.0377436i
$865$	7.90349e25			0.291524
$866$	3.77911e23	−	9.56719e24i	0.00137952	−	0.0349240i
$867$			8.22993e25i			0.297320i
$868$	−1.93274e26	−	1.52928e25i	−0.691030	−	0.0546776i
$869$	1.30246e26			0.460878
$870$	−1.35995e25	−	5.37189e23i	−0.0476266	−	0.00188128i
$871$		−	4.86361e25i		−	0.168576i
$872$	2.50092e25	−	2.10166e26i	0.0857929	−	0.720964i
$873$	−8.78979e24			−0.0298435
$874$	−1.12534e25	+	2.84890e26i	−0.0378164	+	0.957360i
$875$			6.56838e25i			0.218467i
$876$	2.29025e25	−	2.89447e26i	0.0753955	−	0.952868i
$877$	−8.67226e25			−0.282576			−0.141288	−	0.989968i	$-0.545124\pi$
$877$	−8.67226e25			−0.282576			−0.141288	+	0.989968i	$0.545124\pi$
$878$	−1.78544e26	−	7.05260e24i	−0.575829	−	0.0227457i
$879$			1.55710e26i			0.497070i
$880$	−5.30838e24	+	3.33343e25i	−0.0167733	+	0.105329i
$881$	−3.14533e25			−0.0983746			−0.0491873	−	0.998790i	$-0.515663\pi$
$881$	−3.14533e25			−0.0983746			−0.0491873	+	0.998790i	$0.515663\pi$
$882$	−3.14994e24	+	7.97440e25i	−0.00975182	+	0.246877i
$883$		−	3.04207e26i		−	0.932231i	−0.884724	−	0.466115i	$-0.845653\pi$
$883$		−	3.04207e26i		−	0.932231i	0.884724	−	0.466115i	$-0.154347\pi$
$884$	−1.22116e26	−	9.66242e24i	−0.370427	−	0.0293100i
$885$	7.87215e24			0.0236376
$886$	2.48508e26	+	9.81624e24i	0.738647	+	0.0291771i
$887$			6.10727e26i			1.79695i	0.439029	+	0.898473i	$0.355322\pi$
$887$			6.10727e26i			1.79695i	−0.439029	+	0.898473i	$0.644678\pi$
$888$	−9.90074e25	−	1.17816e25i	−0.288371	−	0.0343154i
$889$	−6.44992e25			−0.185968
$890$	5.71586e24	−	1.44703e26i	0.0163144	−	0.413016i
$891$		−	1.90597e25i		−	0.0538540i
$892$	−8.00864e24	+	1.01215e26i	−0.0224014	+	0.283114i
$893$	3.41401e26			0.945369
$894$	1.80935e26	+	7.14708e24i	0.496005	+	0.0195925i
$895$		−	9.17288e25i		−	0.248942i
$896$	−1.82157e26	−	5.16632e25i	−0.489412	−	0.138806i
$897$	6.99324e25			0.186014
$898$	−1.21911e25	+	3.08630e26i	−0.0321037	+	0.812739i
$899$		−	1.96082e26i		−	0.511211i
$900$	−1.22504e26	−	9.69310e24i	−0.316204	−	0.0250196i
$901$	7.77187e26			1.98611
$902$	2.65236e25	+	1.04770e24i	0.0671079	+	0.00265081i
$903$			1.23246e26i			0.308734i
$904$	2.74462e25	−	2.30645e26i	0.0680716	−	0.572043i
$905$	8.89938e25			0.218536
$906$	1.40943e25	−	3.56811e26i	0.0342680	−	0.867529i
$907$		−	6.00412e26i		−	1.44539i	−0.691170	−	0.722693i	$-0.742904\pi$
$907$		−	6.00412e26i		−	1.44539i	0.691170	−	0.722693i	$-0.257096\pi$
$908$	5.21169e25	−	6.58667e26i	0.124224	−	1.56998i
$909$	2.59926e26			0.613443
$910$	−1.44507e25	−	5.70813e23i	−0.0337689	−	0.00133389i
$911$		−	2.53705e26i		−	0.587036i	−0.955954	−	0.293518i	$-0.905174\pi$
$911$		−	2.53705e26i		−	0.587036i	0.955954	−	0.293518i	$-0.0948260\pi$
$912$	2.23417e26	+	3.55784e25i	0.511874	+	0.0815142i
$913$	2.19887e26			0.498841
$914$	−2.72978e25	+	6.91071e26i	−0.0613213	+	1.55241i
$915$		−	6.50689e25i		−	0.144738i
$916$	−3.57719e26	−	2.83045e25i	−0.787922	−	0.0623442i
$917$	−4.30977e25			−0.0940004
$918$	−1.09589e26	−	4.32883e24i	−0.236691	−	0.00934946i
$919$		−	5.87079e26i		−	1.25562i	−0.778368	−	0.627809i	$-0.783952\pi$
$919$		−	5.87079e26i		−	1.25562i	0.778368	−	0.627809i	$-0.216048\pi$
$920$	−1.10107e26	−	1.31024e25i	−0.233198	−	0.0277499i
$921$	−5.35816e25			−0.112377
$922$	−1.94319e24	+	4.91938e25i	−0.00403587	+	0.102172i
$923$		−	1.86216e26i		−	0.383002i
$924$	5.51289e24	−	6.96733e25i	0.0112288	−	0.141912i
$925$	−2.37293e26			−0.478640
$926$	−8.14693e26	−	3.21809e25i	−1.62740	−	0.0642835i
$927$			2.91062e26i			0.575794i
$928$	3.75560e25	−	1.87775e26i	0.0735779	−	0.367879i
$929$	−1.41038e26			−0.273650			−0.136825	−	0.990595i	$-0.543690\pi$
$929$	−1.41038e26			−0.273650			−0.136825	+	0.990595i	$0.543690\pi$
$930$	−3.55595e24	+	9.00224e25i	−0.00683296	+	0.172983i
$931$		−	3.49663e26i		−	0.665430i
$932$	−2.61578e26	−	2.06973e25i	−0.493013	−	0.0390096i
$933$	7.07885e25			0.132138
$934$	−2.50684e26	−	9.90217e24i	−0.463451	−	0.0183066i
$935$			7.16957e25i			0.131277i
$936$	6.55694e24	−	5.51015e25i	0.0118910	−	0.0999265i
$937$	2.03744e26			0.365955			0.182977	−	0.983117i	$-0.441426\pi$
$937$	2.03744e26			0.365955			0.182977	+	0.983117i	$0.441426\pi$
$938$	6.30240e24	−	1.59552e26i	0.0112119	−	0.283842i
$939$			5.08504e26i			0.895992i
$940$	−1.04731e25	+	1.32361e26i	−0.0182778	+	0.230999i
$941$	−3.52885e26			−0.609995			−0.304997	−	0.952353i	$-0.598656\pi$
$941$	−3.52885e26			−0.609995			−0.304997	+	0.952353i	$0.598656\pi$
$942$	−1.64537e26	−	6.49934e24i	−0.281713	−	0.0111279i
$943$			8.71986e25i			0.147878i
$944$	−1.74188e25	+	1.09383e26i	−0.0292598	+	0.183739i
$945$	−1.29481e25			−0.0215436
$946$	−1.22016e25	+	3.08896e26i	−0.0201093	+	0.509087i
$947$			7.75422e26i			1.26587i	0.774206	+	0.632933i	$0.218149\pi$
$947$			7.75422e26i			1.26587i	−0.774206	+	0.632933i	$0.781851\pi$
$948$	3.38442e26	+	2.67792e25i	0.547280	+	0.0433034i
$949$	3.12032e26			0.499809
$950$	5.37997e26	+	2.12512e25i	0.853625	+	0.0337188i
$951$		−	3.29754e26i		−	0.518281i
$952$	−3.99352e26	−	4.75219e25i	−0.621761	−	0.0739880i
$953$	4.25359e24			0.00656024			0.00328012	−	0.999995i	$-0.498956\pi$
$953$	4.25359e24			0.00656024			0.00328012	+	0.999995i	$0.498956\pi$
$954$	−1.38957e25	+	3.51784e26i	−0.0212297	+	0.537453i
$955$			3.41583e25i			0.0516971i
$956$	3.49185e24	−	4.41309e25i	0.00523522	−	0.0661641i
$957$	7.06854e25			0.104984
$958$	−3.07661e26	−	1.21528e25i	−0.452671	−	0.0178808i
$959$			5.11570e26i			0.745655i
$960$	−2.06475e25	+	8.55275e25i	−0.0298144	+	0.123499i
$961$	−5.98919e26			−0.856757
$962$	4.22924e24	−	1.07067e26i	0.00599358	−	0.151734i
$963$			8.34164e25i			0.117116i
$964$	1.10493e27	+	8.74271e25i	1.53688	+	0.121605i
$965$	−2.60266e26			−0.358650
$966$	2.29415e26	+	9.06204e24i	0.313204	+	0.0123718i
$967$			1.03237e26i			0.139636i	0.997560	+	0.0698181i	$0.0222419\pi$
$967$			1.03237e26i			0.139636i	−0.997560	+	0.0698181i	$0.977758\pi$
$968$	−6.74636e25	+	5.66933e26i	−0.0904047	+	0.759720i
$969$	4.80527e26			0.637975
$970$	−5.91165e23	+	1.49659e25i	−0.000777612	+	0.0196860i
$971$			9.74324e25i			0.126979i	0.997983	+	0.0634893i	$0.0202229\pi$
$971$			9.74324e25i			0.126979i	−0.997983	+	0.0634893i	$0.979777\pi$
$972$	3.91878e24	−	4.95265e25i	0.00506005	−	0.0639502i
$973$	1.73885e26			0.222458
$974$	−1.68546e26	−	6.65768e24i	−0.213643	−	0.00843903i
$975$		−	1.32063e26i		−	0.165859i
$976$	9.04126e26	+	1.43979e26i	1.12507	+	0.179164i
$977$	−1.92666e26			−0.237549			−0.118775	−	0.992921i	$-0.537897\pi$
$977$	−1.92666e26			−0.237549			−0.118775	+	0.992921i	$0.537897\pi$
$978$	2.42751e25	−	6.14548e26i	0.0296559	−	0.750768i
$979$			7.52115e26i			0.910416i
$980$	1.35564e26	+	1.07265e25i	0.162596	+	0.0128654i
$981$	2.03642e26			0.242017
$982$	1.37427e27	+	5.42845e25i	1.61833	+	0.0639253i
$983$		−	5.59929e26i		−	0.653358i	−0.945135	−	0.326679i	$-0.894070\pi$
$983$		−	5.59929e26i		−	0.653358i	0.945135	−	0.326679i	$-0.105930\pi$
$984$	6.87059e25	+	8.17583e24i	0.0794398	+	0.00945313i
$985$	4.86877e25			0.0557819
$986$	1.60540e25	−	4.06424e26i	0.0182260	−	0.461410i
$987$		−	2.74921e26i		−	0.309281i
$988$	−1.91773e25	+	2.42367e26i	−0.0213784	+	0.270185i
$989$	−1.01552e27			−1.12182
$990$	−3.24521e25	−	1.28188e24i	−0.0355243	−	0.00140324i
$991$			9.70725e26i			1.05301i	0.850172	+	0.526506i	$0.176498\pi$
$991$			9.70725e26i			1.05301i	−0.850172	+	0.526506i	$0.823502\pi$
$992$	−1.24298e27	−	2.48604e26i	−1.33617	−	0.267241i
$993$	−8.44062e26			−0.899147
$994$	2.41303e25	−	6.10884e26i	0.0254733	−	0.644883i
$995$			2.06074e26i			0.215584i
$996$	5.71373e26	+	4.52098e25i	0.592360	+	0.0468704i
$997$	−9.36733e26			−0.962409			−0.481204	−	0.876608i	$-0.659800\pi$
$997$	−9.36733e26			−0.962409			−0.481204	+	0.876608i	$0.659800\pi$
$998$	1.83152e27	+	7.23462e25i	1.86482	+	0.0736615i
$999$		−	9.59340e25i		−	0.0968017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	12.19.d.a.7.9	✓	18
3.2	odd	2		36.19.d.e.19.10		18
4.3	odd	2	inner	12.19.d.a.7.10	yes	18
12.11	even	2		36.19.d.e.19.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
12.19.d.a.7.9	✓	18	1.1	even	1	trivial
12.19.d.a.7.10	yes	18	4.3	odd	2	inner
36.19.d.e.19.9		18	12.11	even	2
36.19.d.e.19.10		18	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:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	12.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(20.2086 - 511.601i) q^{2} +11364.0i q^{3} +(-261327. - 20677.5i) q^{4} -429789. q^{5} +(5.81383e6 + 229650. i) q^{6} +2.05285e7i q^{7} +(-1.58597e7 + 1.33277e8i) q^{8} -1.29140e8 q^{9} +O(q^{10})\)	\(q+(20.2086 - 511.601i) q^{2} +11364.0i q^{3} +(-261327. - 20677.5i) q^{4} -429789. q^{5} +(5.81383e6 + 229650. i) q^{6} +2.05285e7i q^{7} +(-1.58597e7 + 1.33277e8i) q^{8} -1.29140e8 q^{9} +(-8.68544e6 + 2.19881e8i) q^{10} -1.14286e9i q^{11} +(2.34978e8 - 2.96972e9i) q^{12} +3.20144e9 q^{13} +(1.05024e10 + 4.14852e8i) q^{14} -4.88412e9i q^{15} +(6.78644e10 + 1.08072e10i) q^{16} +1.45963e11 q^{17} +(-2.60974e9 + 6.60682e10i) q^{18} -2.89697e11i q^{19} +(1.12316e11 + 8.88696e9i) q^{20} -2.33285e11 q^{21} +(-5.84690e11 - 2.30957e10i) q^{22} -1.92222e12i q^{23} +(-1.51456e12 - 1.80229e11i) q^{24} -3.62998e12 q^{25} +(6.46966e10 - 1.63786e12i) q^{26} -1.46755e12i q^{27} +(4.24477e11 - 5.36465e12i) q^{28} +5.44258e12 q^{29} +(-2.49872e12 - 9.87012e10i) q^{30} -3.60274e13i q^{31} +(6.90040e12 - 3.45011e13i) q^{32} +1.29875e13 q^{33} +(2.94971e12 - 7.46748e13i) q^{34} -8.82293e12i q^{35} +(3.37478e13 + 2.67029e12i) q^{36} +6.53703e13 q^{37} +(-1.48209e14 - 5.85437e12i) q^{38} +3.63811e13i q^{39} +(6.81632e12 - 5.72812e13i) q^{40} -4.53635e13 q^{41} +(-4.71437e12 + 1.19349e14i) q^{42} -5.28307e14i q^{43} +(-2.36315e13 + 2.98661e14i) q^{44} +5.55031e13 q^{45} +(-9.83408e14 - 3.88453e13i) q^{46} +1.17848e15i q^{47} +(-1.22813e14 + 7.71210e14i) q^{48} +1.20699e15 q^{49} +(-7.33567e13 + 1.85710e15i) q^{50} +1.65872e15i q^{51} +(-8.36624e14 - 6.61977e13i) q^{52} +5.32455e15 q^{53} +(-7.50799e14 - 2.96571e13i) q^{54} +4.91191e14i q^{55} +(-2.73598e15 - 3.25575e14i) q^{56} +3.29211e15 q^{57} +(1.09987e14 - 2.78443e15i) q^{58} +1.61178e15i q^{59} +(-1.00991e14 + 1.27635e15i) q^{60} +1.33225e16 q^{61} +(-1.84317e16 - 7.28063e14i) q^{62} -2.65105e15i q^{63} +(-1.75113e16 - 4.22747e15i) q^{64} -1.37595e15 q^{65} +(2.62459e14 - 6.64441e15i) q^{66} -1.51919e16i q^{67} +(-3.81441e16 - 3.01815e15i) q^{68} +2.18441e16 q^{69} +(-4.51382e15 - 1.78299e14i) q^{70} -5.81662e16i q^{71} +(2.04812e15 - 1.72115e16i) q^{72} +9.74662e16 q^{73} +(1.32104e15 - 3.34435e16i) q^{74} -4.12510e16i q^{75} +(-5.99020e15 + 7.57057e16i) q^{76} +2.34613e16 q^{77} +(1.86126e16 + 7.35211e14i) q^{78} +1.13964e17i q^{79} +(-2.91674e16 - 4.64481e15i) q^{80} +1.66772e16 q^{81} +(-9.16733e14 + 2.32080e16i) q^{82} +1.92400e17i q^{83} +(6.09638e16 + 4.82375e15i) q^{84} -6.27334e16 q^{85} +(-2.70282e17 - 1.06763e16i) q^{86} +6.18494e16i q^{87} +(1.52318e17 + 1.81254e16i) q^{88} -6.58097e17 q^{89} +(1.12164e15 - 2.83954e16i) q^{90} +6.57207e16i q^{91} +(-3.97466e16 + 5.02328e17i) q^{92} +4.09415e17 q^{93} +(6.02909e17 + 2.38153e16i) q^{94} +1.24509e17i q^{95} +(3.92070e17 + 7.84161e16i) q^{96} +6.80639e16 q^{97} +(2.43917e16 - 6.17500e17i) q^{98} +1.47590e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9}+O(q^{10}) \) 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9	\( 18 q - 170 q^{2} - 436932 q^{4} - 1721764 q^{5} - 6731586 q^{6} + 108558736 q^{8} - 2324522934 q^{9} + 1397074644 q^{10} - 6468699852 q^{12} + 1799208612 q^{13} - 48147537912 q^{14} - 119537094672 q^{16} - 282984271180 q^{17} + 21953827710 q^{18} + 491637621128 q^{20} + 254050055640 q^{21} + 272503644408 q^{22} + 4483423343232 q^{24} + 20224739695878 q^{25} - 2765456970196 q^{26} + 27756503338032 q^{28} + 1812741883820 q^{29} - 3579410315772 q^{30} + 216191588070880 q^{32} + 17014318866216 q^{33} - 275796423660708 q^{34} + 56425469699916 q^{36} + 197439381411156 q^{37} - 676030464010008 q^{38} + 19\!\cdots\!68 q^{40}+ \cdots - 37\!\cdots\!22 q^{98}+O(q^{100}) \) 18 * q - 170 * q^2 - 436932 * q^4 - 1721764 * q^5 - 6731586 * q^6 + 108558736 * q^8 - 2324522934 * q^9 + 1397074644 * q^10 - 6468699852 * q^12 + 1799208612 * q^13 - 48147537912 * q^14 - 119537094672 * q^16 - 282984271180 * q^17 + 21953827710 * q^18 + 491637621128 * q^20 + 254050055640 * q^21 + 272503644408 * q^22 + 4483423343232 * q^24 + 20224739695878 * q^25 - 2765456970196 * q^26 + 27756503338032 * q^28 + 1812741883820 * q^29 - 3579410315772 * q^30 + 216191588070880 * q^32 + 17014318866216 * q^33 - 275796423660708 * q^34 + 56425469699916 * q^36 + 197439381411156 * q^37 - 676030464010008 * q^38 + 1941137842438368 * q^40 - 204669372669676 * q^41 - 1059935698181880 * q^42 + 3599128179401424 * q^44 + 222348883607532 * q^45 - 3847169819651040 * q^46 + 1457367907812912 * q^48 - 3424095824368878 * q^49 - 10192520264009358 * q^50 + 4228291003193208 * q^52 - 14112687314785972 * q^53 + 869318113288518 * q^54 - 6591066595001856 * q^56 - 9662233004693640 * q^57 + 17584741731886020 * q^58 + 193536143011224 * q^60 + 4171094773122132 * q^61 + 77227021488187896 * q^62 - 53424456043095936 * q^64 + 35585253307254712 * q^65 + 40644920520184824 * q^66 - 91403316760947112 * q^68 + 26342656148137824 * q^69 + 264958129332427248 * q^70 - 14019292862113968 * q^72 - 83809473755653692 * q^73 + 55949505142092092 * q^74 - 129026923617832848 * q^76 - 354619239852167328 * q^77 - 34535086926497028 * q^78 + 43257628406200352 * q^80 + 300189270593998242 * q^81 - 458290372754774916 * q^82 + 324078384809786832 * q^84 + 166017223439872920 * q^85 - 975848731010420424 * q^86 + 1151342491040801280 * q^88 - 660650117825905468 * q^89 - 180418447249326972 * q^90 + 1359275349780859584 * q^92 - 447365281400937432 * q^93 - 2087066679318498384 * q^94 + 257905715132447136 * q^96 + 2412557706093917220 * q^97 - 3767017570512990122 * q^98

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