LMFDB - Embedded newform 45.9.g.a.28.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,9,Mod(28,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("45.28");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	45.g (of order $4$, degree $2$, 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:	$18.3320374528$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 30x^{3} + 1089x^{2} - 3168x + 4608 $ x^6 - 2x^5 + 2x^4 - 30x^3 + 1089x^2 - 3168*x + 4608
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			28.2
Root			$-4.23471 - 4.23471i$ of defining polynomial
Character	$\chi$	$=$	45.28
Dual form			45.9.g.a.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.39608 - 4.39608i) q^{2} +217.349i q^{4} +(14.1685 + 624.839i) q^{5} +(730.992 - 730.992i) q^{7} +(2080.88 + 2080.88i) q^{8} +O(q^{10})$	\(q+(4.39608 - 4.39608i) q^{2} +217.349i q^{4} +(14.1685 + 624.839i) q^{5} +(730.992 - 730.992i) q^{7} +(2080.88 + 2080.88i) q^{8} +(2809.13 + 2684.56i) q^{10} -19599.8 q^{11} +(-24915.1 - 24915.1i) q^{13} -6426.99i q^{14} -37346.0 q^{16} +(11288.6 - 11288.6i) q^{17} +171525. i q^{19} +(-135808. + 3079.51i) q^{20} +(-86162.2 + 86162.2i) q^{22} +(132074. + 132074. i) q^{23} +(-390224. + 17706.1i) q^{25} -219057. q^{26} +(158880. + 158880. i) q^{28} -127019. i q^{29} -960715. q^{31} +(-696880. + 696880. i) q^{32} -99251.5i q^{34} +(467110. + 446396. i) q^{35} +(-243873. + 243873. i) q^{37} +(754036. + 754036. i) q^{38} +(-1.27073e6 + 1.32970e6i) q^{40} -2.50747e6 q^{41} +(-6763.95 - 6763.95i) q^{43} -4.26000e6i q^{44} +1.16122e6 q^{46} +(1.79394e6 - 1.79394e6i) q^{47} +4.69610e6i q^{49} +(-1.63761e6 + 1.79329e6i) q^{50} +(5.41527e6 - 5.41527e6i) q^{52} +(2.97161e6 + 2.97161e6i) q^{53} +(-277700. - 1.22467e7i) q^{55} +3.04221e6 q^{56} +(-558385. - 558385. i) q^{58} +313805. i q^{59} +1.76977e7 q^{61} +(-4.22338e6 + 4.22338e6i) q^{62} -3.43349e6i q^{64} +(1.52149e7 - 1.59209e7i) q^{65} +(4.41349e6 - 4.41349e6i) q^{67} +(2.45358e6 + 2.45358e6i) q^{68} +(4.01584e6 - 91060.8i) q^{70} +8.89315e6 q^{71} +(1.95076e7 + 1.95076e7i) q^{73} +2.14417e6i q^{74} -3.72808e7 q^{76} +(-1.43273e7 + 1.43273e7i) q^{77} +1.11272e7i q^{79} +(-529136. - 2.33352e7i) q^{80} +(-1.10230e7 + 1.10230e7i) q^{82} +(-1.58712e7 - 1.58712e7i) q^{83} +(7.21353e6 + 6.89365e6i) q^{85} -59469.7 q^{86} +(-4.07848e7 - 4.07848e7i) q^{88} +4.85032e7i q^{89} -3.64255e7 q^{91} +(-2.87062e7 + 2.87062e7i) q^{92} -1.57726e7i q^{94} +(-1.07176e8 + 2.43025e6i) q^{95} +(-1.07411e8 + 1.07411e8i) q^{97} +(2.06444e7 + 2.06444e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8	$ 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8} + 30870 q^{10} - 23192 q^{11} - 119142 q^{13} + 218616 q^{16} + 265502 q^{17} - 412260 q^{20} - 35664 q^{22} - 28888 q^{23} - 340350 q^{25} + 801388 q^{26} + 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} + 4971680 q^{35} - 454002 q^{37} - 1443720 q^{38} + 2683500 q^{40} - 2489432 q^{41} + 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} - 29537650 q^{50} - 735732 q^{52} + 13509122 q^{53} + 4448040 q^{55} + 18454800 q^{56} - 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} + 30943610 q^{65} - 32827752 q^{67} - 8118692 q^{68} - 44156280 q^{70} + 13992928 q^{71} + 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 23045920 q^{80} + 38023056 q^{82} + 14768432 q^{83} - 19713030 q^{85} + 135560008 q^{86} - 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} - 239661000 q^{95} - 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8 + 30870 * q^10 - 23192 * q^11 - 119142 * q^13 + 218616 * q^16 + 265502 * q^17 - 412260 * q^20 - 35664 * q^22 - 28888 * q^23 - 340350 * q^25 + 801388 * q^26 + 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 + 4971680 * q^35 - 454002 * q^37 - 1443720 * q^38 + 2683500 * q^40 - 2489432 * q^41 + 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 - 29537650 * q^50 - 735732 * q^52 + 13509122 * q^53 + 4448040 * q^55 + 18454800 * q^56 - 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 + 30943610 * q^65 - 32827752 * q^67 - 8118692 * q^68 - 44156280 * q^70 + 13992928 * q^71 + 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 23045920 * q^80 + 38023056 * q^82 + 14768432 * q^83 - 19713030 * q^85 + 135560008 * q^86 - 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 - 239661000 * q^95 - 186656202 * q^97 + 345959698 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (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 $

$2$	4.39608	−	4.39608i	0.274755	−	0.274755i	−0.556256	−	0.831011i	$-0.687763\pi$
$2$	4.39608	−	4.39608i	0.274755	−	0.274755i	0.831011	+	0.556256i	$0.187763\pi$
$3$		0			0
$3$		0			0
$4$			217.349i			0.849020i
$5$	14.1685	+	624.839i	0.0226696	+	0.999743i
$5$	14.1685	+	624.839i	0.0226696	+	0.999743i
$6$		0			0
$7$	730.992	−	730.992i	0.304453	−	0.304453i	−0.538300	−	0.842753i	$-0.680933\pi$
$7$	730.992	−	730.992i	0.304453	−	0.304453i	0.842753	+	0.538300i	$0.180933\pi$
$8$	2080.88	+	2080.88i	0.508027	+	0.508027i
$9$		0			0
$10$	2809.13	+	2684.56i	0.280913	+	0.268456i
$11$	−19599.8			−1.33869			−0.669347	−	0.742950i	$-0.733426\pi$
$11$	−19599.8			−1.33869			−0.669347	+	0.742950i	$0.733426\pi$
$12$		0			0
$13$	−24915.1	−	24915.1i	−0.872347	−	0.872347i	0.120381	−	0.992728i	$-0.461588\pi$
$13$	−24915.1	−	24915.1i	−0.872347	−	0.872347i	−0.992728	+	0.120381i	$0.961588\pi$
$14$		−	6426.99i		−	0.167300i
$15$		0			0
$16$	−37346.0			−0.569854
$17$	11288.6	−	11288.6i	0.135159	−	0.135159i	−0.636290	−	0.771450i	$-0.719532\pi$
$17$	11288.6	−	11288.6i	0.135159	−	0.135159i	0.771450	+	0.636290i	$0.219532\pi$
$18$		0			0
$19$			171525.i			1.31617i	0.752943	+	0.658086i	$0.228634\pi$
$19$			171525.i			1.31617i	−0.752943	+	0.658086i	$0.771366\pi$
$20$	−135808.	+	3079.51i	−0.848802	+	0.0192469i
$21$		0			0
$22$	−86162.2	+	86162.2i	−0.367812	+	0.367812i
$23$	132074.	+	132074.i	0.471961	+	0.471961i	0.902549	−	0.430587i	$-0.141694\pi$
$23$	132074.	+	132074.i	0.471961	+	0.471961i	−0.430587	+	0.902549i	$0.641694\pi$
$24$		0			0
$25$	−390224.	+	17706.1i	−0.998972	+	0.0453275i
$26$	−219057.			−0.479363
$27$		0			0
$28$	158880.	+	158880.i	0.258487	+	0.258487i
$29$		−	127019.i		−	0.179588i	−0.995960	−	0.0897939i	$-0.971379\pi$
$29$		−	127019.i		−	0.179588i	0.995960	−	0.0897939i	$-0.0286208\pi$
$30$		0			0
$31$	−960715.			−1.04027			−0.520137	−	0.854083i	$-0.674119\pi$
$31$	−960715.			−1.04027			−0.520137	+	0.854083i	$0.674119\pi$
$32$	−696880.	+	696880.i	−0.664597	+	0.664597i
$33$		0			0
$34$		−	99251.5i		−	0.0742713i
$35$	467110.	+	446396.i	0.311277	+	0.297473i
$36$		0			0
$37$	−243873.	+	243873.i	−0.130124	+	0.130124i	−0.769169	−	0.639045i	$-0.779330\pi$
$37$	−243873.	+	243873.i	−0.130124	+	0.130124i	0.639045	+	0.769169i	$0.279330\pi$
$38$	754036.	+	754036.i	0.361625	+	0.361625i
$39$		0			0
$40$	−1.27073e6	+	1.32970e6i	−0.496380	+	0.519413i
$41$	−2.50747e6			−0.887360			−0.443680	−	0.896185i	$-0.646327\pi$
$41$	−2.50747e6			−0.887360			−0.443680	+	0.896185i	$0.646327\pi$
$42$		0			0
$43$	−6763.95	−	6763.95i	−0.00197846	−	0.00197846i	0.706117	−	0.708095i	$-0.250445\pi$
$43$	−6763.95	−	6763.95i	−0.00197846	−	0.00197846i	−0.708095	+	0.706117i	$0.750445\pi$
$44$		−	4.26000e6i		−	1.13658i
$45$		0			0
$46$	1.16122e6			0.259347
$47$	1.79394e6	−	1.79394e6i	0.367635	−	0.367635i	−0.498979	−	0.866614i	$-0.666291\pi$
$47$	1.79394e6	−	1.79394e6i	0.367635	−	0.367635i	0.866614	+	0.498979i	$0.166291\pi$
$48$		0			0
$49$			4.69610e6i			0.814617i
$50$	−1.63761e6	+	1.79329e6i	−0.262018	+	0.286926i
$51$		0			0
$52$	5.41527e6	−	5.41527e6i	0.740640	−	0.740640i
$53$	2.97161e6	+	2.97161e6i	0.376608	+	0.376608i	0.869877	−	0.493269i	$-0.164198\pi$
$53$	2.97161e6	+	2.97161e6i	0.376608	+	0.376608i	−0.493269	+	0.869877i	$0.664198\pi$
$54$		0			0
$55$	−277700.	−	1.22467e7i	−0.0303476	−	1.33835i
$56$	3.04221e6			0.309341
$57$		0			0
$58$	−558385.	−	558385.i	−0.0493426	−	0.0493426i
$59$			313805.i			0.0258972i	0.999916	+	0.0129486i	$0.00412178\pi$
$59$			313805.i			0.0258972i	−0.999916	+	0.0129486i	$0.995878\pi$
$60$		0			0
$61$	1.76977e7			1.27820			0.639098	−	0.769125i	$-0.279308\pi$
$61$	1.76977e7			1.27820			0.639098	+	0.769125i	$0.279308\pi$
$62$	−4.22338e6	+	4.22338e6i	−0.285820	+	0.285820i
$63$		0			0
$64$		−	3.43349e6i		−	0.204652i
$65$	1.52149e7	−	1.59209e7i	0.852347	−	0.891899i
$66$		0			0
$67$	4.41349e6	−	4.41349e6i	0.219020	−	0.219020i	−0.589066	−	0.808085i	$-0.700504\pi$
$67$	4.41349e6	−	4.41349e6i	0.219020	−	0.219020i	0.808085	+	0.589066i	$0.200504\pi$
$68$	2.45358e6	+	2.45358e6i	0.114753	+	0.114753i
$69$		0			0
$70$	4.01584e6	−	91060.8i	0.167257	−	0.00379262i
$71$	8.89315e6			0.349963			0.174982	−	0.984572i	$-0.444013\pi$
$71$	8.89315e6			0.349963			0.174982	+	0.984572i	$0.444013\pi$
$72$		0			0
$73$	1.95076e7	+	1.95076e7i	0.686928	+	0.686928i	0.961552	−	0.274624i	$-0.0885532\pi$
$73$	1.95076e7	+	1.95076e7i	0.686928	+	0.686928i	−0.274624	+	0.961552i	$0.588553\pi$
$74$			2.14417e6i			0.0715043i
$75$		0			0
$76$	−3.72808e7			−1.11746
$77$	−1.43273e7	+	1.43273e7i	−0.407569	+	0.407569i
$78$		0			0
$79$			1.11272e7i			0.285680i	0.989746	+	0.142840i	$0.0456234\pi$
$79$			1.11272e7i			0.285680i	−0.989746	+	0.142840i	$0.954377\pi$
$80$	−529136.	−	2.33352e7i	−0.0129184	−	0.569708i
$81$		0			0
$82$	−1.10230e7	+	1.10230e7i	−0.243806	+	0.243806i
$83$	−1.58712e7	−	1.58712e7i	−0.334423	−	0.334423i	0.519840	−	0.854264i	$-0.325992\pi$
$83$	−1.58712e7	−	1.58712e7i	−0.334423	−	0.334423i	−0.854264	+	0.519840i	$0.825992\pi$
$84$		0			0
$85$	7.21353e6	+	6.89365e6i	0.138189	+	0.132061i
$86$	−59469.7			−0.00108718
$87$		0			0
$88$	−4.07848e7	−	4.07848e7i	−0.680092	−	0.680092i
$89$			4.85032e7i			0.773056i	0.922278	+	0.386528i	$0.126326\pi$
$89$			4.85032e7i			0.773056i	−0.922278	+	0.386528i	$0.873674\pi$
$90$		0			0
$91$	−3.64255e7			−0.531178
$92$	−2.87062e7	+	2.87062e7i	−0.400704	+	0.400704i
$93$		0			0
$94$		−	1.57726e7i		−	0.202019i
$95$	−1.07176e8	+	2.43025e6i	−1.31583	+	0.0298371i
$96$		0			0
$97$	−1.07411e8	+	1.07411e8i	−1.21329	+	1.21329i	−0.243348	+	0.969939i	$0.578246\pi$
$97$	−1.07411e8	+	1.07411e8i	−1.21329	+	1.21329i	−0.969939	+	0.243348i	$0.921754\pi$
$98$	2.06444e7	+	2.06444e7i	0.223820	+	0.223820i
$99$		0			0
$100$	−3.84840e6	−	8.48147e7i	−0.0384840	−	0.848147i
$101$	7.16023e7			0.688084			0.344042	−	0.938954i	$-0.388204\pi$
$101$	7.16023e7			0.688084			0.344042	+	0.938954i	$0.388204\pi$
$102$		0			0
$103$	9.89158e7	+	9.89158e7i	0.878854	+	0.878854i	0.993416	−	0.114562i	$-0.0365464\pi$
$103$	9.89158e7	+	9.89158e7i	0.878854	+	0.878854i	−0.114562	+	0.993416i	$0.536546\pi$
$104$		−	1.03691e8i		−	0.886352i
$105$		0			0
$106$	2.61269e7			0.206949
$107$	−4.73497e7	+	4.73497e7i	−0.361228	+	0.361228i	−0.864265	−	0.503037i	$-0.832216\pi$
$107$	−4.73497e7	+	4.73497e7i	−0.361228	+	0.361228i	0.503037	+	0.864265i	$0.332216\pi$
$108$		0			0
$109$		−	2.29072e7i		−	0.162280i	−0.996703	−	0.0811401i	$-0.974144\pi$
$109$		−	2.29072e7i		−	0.162280i	0.996703	−	0.0811401i	$-0.0258561\pi$
$110$	−5.50583e7	−	5.26168e7i	−0.376056	−	0.359380i
$111$		0			0
$112$	−2.72996e7	+	2.72996e7i	−0.173494	+	0.173494i
$113$	1.95361e8	+	1.95361e8i	1.19819	+	1.19819i	0.974709	+	0.223480i	$0.0717416\pi$
$113$	1.95361e8	+	1.95361e8i	1.19819	+	1.19819i	0.223480	+	0.974709i	$0.428258\pi$
$114$		0			0
$115$	−8.06538e7	+	8.43964e7i	−0.461141	+	0.482539i
$116$	2.76075e7			0.152474
$117$		0			0
$118$	1.37951e6	+	1.37951e6i	0.00711537	+	0.00711537i
$119$		−	1.65038e7i		−	0.0822994i
$120$		0			0
$121$	1.69794e8			0.792100
$122$	7.78004e7	−	7.78004e7i	0.351190	−	0.351190i
$123$		0			0
$124$		−	2.08811e8i		−	0.883213i
$125$	−1.65923e7	−	2.43576e8i	−0.0679622	−	0.997688i
$126$		0			0
$127$	1.84792e8	−	1.84792e8i	0.710343	−	0.710343i	−0.256264	−	0.966607i	$-0.582492\pi$
$127$	1.84792e8	−	1.84792e8i	0.710343	−	0.710343i	0.966607	+	0.256264i	$0.0824917\pi$
$128$	−1.93495e8	−	1.93495e8i	−0.720826	−	0.720826i
$129$		0			0
$130$	−3.10371e6	−	1.36876e8i	−0.0108670	−	0.479240i
$131$	3.05076e8			1.03591			0.517956	−	0.855407i	$-0.326693\pi$
$131$	3.05076e8			1.03591			0.517956	+	0.855407i	$0.326693\pi$
$132$		0			0
$133$	1.25383e8	+	1.25383e8i	0.400713	+	0.400713i
$134$		−	3.88041e7i		−	0.120353i
$135$		0			0
$136$	4.69806e7			0.137329
$137$	−3.75735e8	+	3.75735e8i	−1.06659	+	1.06659i	−0.0689766	+	0.997618i	$0.521973\pi$
$137$	−3.75735e8	+	3.75735e8i	−1.06659	+	1.06659i	−0.997618	+	0.0689766i	$0.978027\pi$
$138$		0			0
$139$		−	1.10575e8i		−	0.296208i	−0.988972	−	0.148104i	$-0.952683\pi$
$139$		−	1.10575e8i		−	0.296208i	0.988972	−	0.148104i	$-0.0473171\pi$
$140$	−9.70236e7	+	1.01526e8i	−0.252560	+	0.264280i
$141$		0			0
$142$	3.90950e7	−	3.90950e7i	0.0961540	−	0.0961540i
$143$	4.88331e8	+	4.88331e8i	1.16781	+	1.16781i
$144$		0			0
$145$	7.93665e7	−	1.79967e6i	0.179542	−	0.00407118i
$146$	1.71513e8			0.377474
$147$		0			0
$148$	−5.30056e7	−	5.30056e7i	−0.110478	−	0.110478i
$149$		−	7.23744e8i		−	1.46838i	−0.678942	−	0.734192i	$-0.737561\pi$
$149$		−	7.23744e8i		−	1.46838i	0.678942	−	0.734192i	$-0.262439\pi$
$150$		0			0
$151$	7.67246e8			1.47580			0.737899	−	0.674911i	$-0.235818\pi$
$151$	7.67246e8			1.47580			0.737899	+	0.674911i	$0.235818\pi$
$152$	−3.56922e8	+	3.56922e8i	−0.668651	+	0.668651i
$153$		0			0
$154$			1.25968e8i			0.223963i
$155$	−1.36119e7	−	6.00293e8i	−0.0235826	−	1.04001i
$156$		0			0
$157$	−8.03264e8	+	8.03264e8i	−1.32209	+	1.32209i	−0.410001	+	0.912085i	$0.634472\pi$
$157$	−8.03264e8	+	8.03264e8i	−1.32209	+	1.32209i	−0.912085	+	0.410001i	$0.865528\pi$
$158$	4.89162e7	+	4.89162e7i	0.0784918	+	0.0784918i
$159$		0			0
$160$	−4.45312e8	−	4.25565e8i	−0.679492	−	0.649360i
$161$	1.93090e8			0.287380
$162$		0			0
$163$	−4.34915e8	−	4.34915e8i	−0.616103	−	0.616103i	0.328426	−	0.944530i	$-0.393482\pi$
$163$	−4.34915e8	−	4.34915e8i	−0.616103	−	0.616103i	−0.944530	+	0.328426i	$0.893482\pi$
$164$		−	5.44996e8i		−	0.753386i
$165$		0			0
$166$	−1.39542e8			−0.183769
$167$	−7.16803e8	+	7.16803e8i	−0.921582	+	0.921582i	−0.997141	−	0.0755590i	$-0.975926\pi$
$167$	−7.16803e8	+	7.16803e8i	−0.921582	+	0.921582i	0.0755590	+	0.997141i	$0.475926\pi$
$168$		0			0
$169$			4.25794e8i			0.521979i
$170$	6.20162e7	−	1.40624e6i	0.0742522	−	0.00168370i
$171$		0			0
$172$	1.47014e6	−	1.47014e6i	0.00167975	−	0.00167975i
$173$	−3.40359e8	−	3.40359e8i	−0.379973	−	0.379973i	0.491119	−	0.871092i	$-0.336588\pi$
$173$	−3.40359e8	−	3.40359e8i	−0.379973	−	0.379973i	−0.871092	+	0.491119i	$0.836588\pi$
$174$		0			0
$175$	−2.72307e8	+	2.98193e8i	−0.290340	+	0.317940i
$176$	7.31974e8			0.762860
$177$		0			0
$178$	2.13224e8	+	2.13224e8i	0.212401	+	0.212401i
$179$			1.29181e9i			1.25830i	0.777283	+	0.629151i	$0.216597\pi$
$179$			1.29181e9i			1.25830i	−0.777283	+	0.629151i	$0.783403\pi$
$180$		0			0
$181$	1.92912e8			0.179740			0.0898700	−	0.995954i	$-0.471355\pi$
$181$	1.92912e8			0.179740			0.0898700	+	0.995954i	$0.471355\pi$
$182$	−1.60129e8	+	1.60129e8i	−0.145944	+	0.145944i
$183$		0			0
$184$			5.49660e8i			0.479538i
$185$	−1.55837e8	−	1.48926e8i	−0.133040	−	0.127141i
$186$		0			0
$187$	−2.21255e8	+	2.21255e8i	−0.180937	+	0.180937i
$188$	3.89912e8	+	3.89912e8i	0.312130	+	0.312130i
$189$		0			0
$190$	−4.60468e8	+	4.81835e8i	−0.353334	+	0.369729i
$191$	−7.64646e8			−0.574549			−0.287274	−	0.957848i	$-0.592749\pi$
$191$	−7.64646e8			−0.574549			−0.287274	+	0.957848i	$0.592749\pi$
$192$		0			0
$193$	1.15389e8	+	1.15389e8i	0.0831641	+	0.0831641i	0.747465	−	0.664301i	$-0.231271\pi$
$193$	1.15389e8	+	1.15389e8i	0.0831641	+	0.0831641i	−0.664301	+	0.747465i	$0.731271\pi$
$194$			9.44378e8i			0.666713i
$195$		0			0
$196$	−1.02069e9			−0.691626
$197$	9.95415e7	−	9.95415e7i	0.0660906	−	0.0660906i	−0.673289	−	0.739379i	$-0.735119\pi$
$197$	9.95415e7	−	9.95415e7i	0.0660906	−	0.0660906i	0.739379	+	0.673289i	$0.235119\pi$
$198$		0			0
$199$		−	1.71187e9i		−	1.09159i	−0.837919	−	0.545795i	$-0.816228\pi$
$199$		−	1.71187e9i		−	1.09159i	0.837919	−	0.545795i	$-0.183772\pi$
$200$	−8.48852e8	−	7.75163e8i	−0.530532	−	0.484477i
$201$		0			0
$202$	3.14769e8	−	3.14769e8i	0.189054	−	0.189054i
$203$	−9.28499e7	−	9.28499e7i	−0.0546761	−	0.0546761i
$204$		0			0
$205$	−3.55271e7	−	1.56676e9i	−0.0201161	−	0.887132i
$206$	8.69683e8			0.482939
$207$		0			0
$208$	9.30479e8	+	9.30479e8i	0.497111	+	0.497111i
$209$		−	3.36185e9i		−	1.76195i
$210$		0			0
$211$	−6.81230e8			−0.343688			−0.171844	−	0.985124i	$-0.554972\pi$
$211$	−6.81230e8			−0.343688			−0.171844	+	0.985124i	$0.554972\pi$
$212$	−6.45878e8	+	6.45878e8i	−0.319747	+	0.319747i
$213$		0			0
$214$			4.16305e8i			0.198498i
$215$	4.13055e6	−	4.32222e6i	0.00193310	−	0.00202280i
$216$		0			0
$217$	−7.02275e8	+	7.02275e8i	−0.316715	+	0.316715i
$218$	−1.00702e8	−	1.00702e8i	−0.0445872	−	0.0445872i
$219$		0			0
$220$	2.66182e9	−	6.03578e7i	1.13628	−	0.0257657i
$221$	−5.62515e8			−0.235812
$222$		0			0
$223$	9.37608e8	+	9.37608e8i	0.379142	+	0.379142i	0.870793	−	0.491651i	$-0.163606\pi$
$223$	9.37608e8	+	9.37608e8i	0.379142	+	0.379142i	−0.491651	+	0.870793i	$0.663606\pi$
$224$			1.01883e9i			0.404677i
$225$		0			0
$226$	1.71765e9			0.658416
$227$	3.47956e9	−	3.47956e9i	1.31045	−	1.31045i	0.389368	−	0.921082i	$-0.372693\pi$
$227$	3.47956e9	−	3.47956e9i	1.31045	−	1.31045i	0.921082	−	0.389368i	$-0.127307\pi$
$228$		0			0
$229$		−	3.67273e9i		−	1.33551i	−0.744382	−	0.667754i	$-0.767256\pi$
$229$		−	3.67273e9i		−	1.33551i	0.744382	−	0.667754i	$-0.232744\pi$
$230$	1.64527e7	+	7.25573e8i	0.00587930	+	0.259281i
$231$		0			0
$232$	2.64311e8	−	2.64311e8i	0.0912354	−	0.0912354i
$233$	3.62893e9	+	3.62893e9i	1.23128	+	1.23128i	0.963474	+	0.267801i	$0.0862970\pi$
$233$	3.62893e9	+	3.62893e9i	1.23128	+	1.23128i	0.267801	+	0.963474i	$0.413703\pi$
$234$		0			0
$235$	1.14634e9	+	1.09551e9i	0.375875	+	0.359207i
$236$	−6.82053e7			−0.0219872
$237$		0			0
$238$	−7.25520e7	−	7.25520e7i	−0.0226121	−	0.0226121i
$239$			2.64336e9i			0.810148i	0.914284	+	0.405074i	$0.132754\pi$
$239$			2.64336e9i			0.810148i	−0.914284	+	0.405074i	$0.867246\pi$
$240$		0			0
$241$	−7.20231e7			−0.0213503			−0.0106751	−	0.999943i	$-0.503398\pi$
$241$	−7.20231e7			−0.0213503			−0.0106751	+	0.999943i	$0.503398\pi$
$242$	7.46425e8	−	7.46425e8i	0.217633	−	0.217633i
$243$		0			0
$244$			3.84658e9i			1.08521i
$245$	−2.93431e9	+	6.65367e7i	−0.814407	+	0.0184670i
$246$		0			0
$247$	4.27356e9	−	4.27356e9i	1.14816	−	1.14816i
$248$	−1.99913e9	−	1.99913e9i	−0.528487	−	0.528487i
$249$		0			0
$250$	−1.14372e9	−	9.97838e8i	−0.292792	−	0.255447i
$251$	−5.78911e7			−0.0145854			−0.00729268	−	0.999973i	$-0.502321\pi$
$251$	−5.78911e7			−0.0145854			−0.00729268	+	0.999973i	$0.502321\pi$
$252$		0			0
$253$	−2.58863e9	−	2.58863e9i	−0.631811	−	0.631811i
$254$		−	1.62472e9i		−	0.390340i
$255$		0			0
$256$	−8.22267e8			−0.191449
$257$	4.73425e8	−	4.73425e8i	0.108522	−	0.108522i	−0.650761	−	0.759283i	$-0.725550\pi$
$257$	4.73425e8	−	4.73425e8i	0.108522	−	0.108522i	0.759283	+	0.650761i	$0.225550\pi$
$258$		0			0
$259$			3.56539e8i			0.0792333i
$260$	3.46040e9	+	3.30695e9i	0.757240	+	0.723660i
$261$		0			0
$262$	1.34114e9	−	1.34114e9i	0.284622	−	0.284622i
$263$	−6.55957e9	−	6.55957e9i	−1.37105	−	1.37105i	−0.858893	−	0.512155i	$-0.828847\pi$
$263$	−6.55957e9	−	6.55957e9i	−1.37105	−	1.37105i	−0.512155	−	0.858893i	$-0.671153\pi$
$264$		0			0
$265$	−1.81468e9	+	1.89889e9i	−0.367973	+	0.385048i
$266$	1.10239e9			0.220195
$267$		0			0
$268$	9.59269e8	+	9.59269e8i	0.185952	+	0.185952i
$269$			5.38818e9i			1.02904i	0.857478	+	0.514521i	$0.172030\pi$
$269$			5.38818e9i			1.02904i	−0.857478	+	0.514521i	$0.827970\pi$
$270$		0			0
$271$	−8.79497e9			−1.63064			−0.815318	−	0.579013i	$-0.803438\pi$
$271$	−8.79497e9			−1.63064			−0.815318	+	0.579013i	$0.803438\pi$
$272$	−4.21585e8	+	4.21585e8i	−0.0770211	+	0.0770211i
$273$		0			0
$274$			3.30352e9i			0.586104i
$275$	7.64831e9	−	3.47036e8i	1.33732	−	0.0606797i
$276$		0			0
$277$	−4.78151e9	+	4.78151e9i	−0.812168	+	0.812168i	−0.984959	−	0.172790i	$-0.944722\pi$
$277$	−4.78151e9	+	4.78151e9i	−0.812168	+	0.812168i	0.172790	+	0.984959i	$0.444722\pi$
$278$	−4.86096e8	−	4.86096e8i	−0.0813846	−	0.0813846i
$279$		0			0
$280$	4.31035e7	+	1.90089e9i	0.00701263	+	0.309261i
$281$	−1.22255e10			−1.96083			−0.980416	−	0.196936i	$-0.936901\pi$
$281$	−1.22255e10			−1.96083			−0.980416	+	0.196936i	$0.936901\pi$
$282$		0			0
$283$	−2.86857e8	−	2.86857e8i	−0.0447219	−	0.0447219i	0.684392	−	0.729114i	$-0.260068\pi$
$283$	−2.86857e8	−	2.86857e8i	−0.0447219	−	0.0447219i	−0.729114	+	0.684392i	$0.760068\pi$
$284$			1.93292e9i			0.297126i
$285$		0			0
$286$	4.29348e9			0.641720
$287$	−1.83294e9	+	1.83294e9i	−0.270160	+	0.270160i
$288$		0			0
$289$			6.72089e9i			0.963464i
$290$	3.40990e8	−	3.56813e8i	0.0482113	−	0.0504485i
$291$		0			0
$292$	−4.23995e9	+	4.23995e9i	−0.583216	+	0.583216i
$293$	1.02814e9	+	1.02814e9i	0.139503	+	0.139503i	0.773410	−	0.633907i	$-0.218550\pi$
$293$	1.02814e9	+	1.02814e9i	0.139503	+	0.139503i	−0.633907	+	0.773410i	$0.718550\pi$
$294$		0			0
$295$	−1.96078e8	+	4.44615e6i	−0.0258905	+	0.000587078i
$296$	−1.01494e9			−0.132213
$297$		0			0
$298$	−3.18163e9	−	3.18163e9i	−0.403445	−	0.403445i
$299$		−	6.58128e9i		−	0.823428i
$300$		0			0
$301$	−9.88879e6			−0.00120469
$302$	3.37287e9	−	3.37287e9i	0.405482	−	0.405482i
$303$		0			0
$304$		−	6.40576e9i		−	0.750026i
$305$	2.50750e8	+	1.10582e10i	0.0289762	+	1.27787i
$306$		0			0
$307$	7.92159e9	−	7.92159e9i	0.891783	−	0.891783i	−0.102908	−	0.994691i	$-0.532815\pi$
$307$	7.92159e9	−	7.92159e9i	0.891783	−	0.891783i	0.994691	+	0.102908i	$0.0328148\pi$
$308$	−3.11403e9	−	3.11403e9i	−0.346034	−	0.346034i
$309$		0			0
$310$	−2.69877e9	−	2.57909e9i	−0.292226	−	0.279267i
$311$	−3.74059e9			−0.399851			−0.199926	−	0.979811i	$-0.564070\pi$
$311$	−3.74059e9			−0.399851			−0.199926	+	0.979811i	$0.564070\pi$
$312$		0			0
$313$	−4.79633e9	−	4.79633e9i	−0.499725	−	0.499725i	0.411627	−	0.911352i	$-0.364961\pi$
$313$	−4.79633e9	−	4.79633e9i	−0.499725	−	0.499725i	−0.911352	+	0.411627i	$0.864961\pi$
$314$			7.06242e9i			0.726499i
$315$		0			0
$316$	−2.41850e9			−0.242548
$317$	5.54903e9	−	5.54903e9i	0.549516	−	0.549516i	−0.376785	−	0.926301i	$-0.622970\pi$
$317$	5.54903e9	−	5.54903e9i	0.549516	−	0.549516i	0.926301	+	0.376785i	$0.122970\pi$
$318$		0			0
$319$			2.48955e9i			0.240413i
$320$	2.14538e9	−	4.86474e7i	0.204599	−	0.00463937i
$321$		0			0
$322$	8.48839e8	−	8.48839e8i	0.0789591	−	0.0789591i
$323$	1.93628e9	+	1.93628e9i	0.177893	+	0.177893i
$324$		0			0
$325$	1.01636e10	+	9.28131e9i	0.910992	+	0.831909i
$326$	−3.82384e9			−0.338555
$327$		0			0
$328$	−5.21774e9	−	5.21774e9i	−0.450803	−	0.450803i
$329$		−	2.62272e9i		−	0.223855i
$330$		0			0
$331$	1.49782e10			1.24780			0.623902	−	0.781503i	$-0.285546\pi$
$331$	1.49782e10			1.24780			0.623902	+	0.781503i	$0.285546\pi$
$332$	3.44958e9	−	3.44958e9i	0.283932	−	0.283932i
$333$		0			0
$334$			6.30224e9i			0.506418i
$335$	2.82026e9	+	2.69519e9i	0.223929	+	0.213998i
$336$		0			0
$337$	6.29203e9	−	6.29203e9i	0.487833	−	0.487833i	−0.419789	−	0.907622i	$-0.637896\pi$
$337$	6.29203e9	−	6.29203e9i	0.487833	−	0.487833i	0.907622	+	0.419789i	$0.137896\pi$
$338$	1.87182e9	+	1.87182e9i	0.143416	+	0.143416i
$339$		0			0
$340$	−1.49833e9	+	1.56785e9i	−0.112122	+	0.117325i
$341$	1.88298e10			1.39261
$342$		0			0
$343$	7.64684e9	+	7.64684e9i	0.552466	+	0.552466i
$344$		−	2.81499e7i		−	0.00201022i
$345$		0			0
$346$	−2.99249e9			−0.208799
$347$	8.28230e9	−	8.28230e9i	0.571259	−	0.571259i	−0.361221	−	0.932480i	$-0.617640\pi$
$347$	8.28230e9	−	8.28230e9i	0.571259	−	0.571259i	0.932480	+	0.361221i	$0.117640\pi$
$348$		0			0
$349$		−	1.11611e10i		−	0.752328i	−0.926553	−	0.376164i	$-0.877243\pi$
$349$		−	1.11611e10i		−	0.752328i	0.926553	−	0.376164i	$-0.122757\pi$
$350$	1.13797e8	+	2.50796e9i	0.00758329	+	0.167128i
$351$		0			0
$352$	1.36587e10	−	1.36587e10i	0.889692	−	0.889692i
$353$	−1.05904e10	−	1.05904e10i	−0.682047	−	0.682047i	0.278414	−	0.960461i	$-0.410191\pi$
$353$	−1.05904e10	−	1.05904e10i	−0.682047	−	0.682047i	−0.960461	+	0.278414i	$0.910191\pi$
$354$		0			0
$355$	1.26003e8	+	5.55679e9i	0.00793352	+	0.349873i
$356$	−1.05421e10			−0.656339
$357$		0			0
$358$	5.67888e9	+	5.67888e9i	0.345725	+	0.345725i
$359$		−	9.48530e9i		−	0.571049i	−0.958371	−	0.285524i	$-0.907832\pi$
$359$		−	9.48530e9i		−	0.571049i	0.958371	−	0.285524i	$-0.0921677\pi$
$360$		0			0
$361$	−1.24372e10			−0.732309
$362$	8.48055e8	−	8.48055e8i	0.0493844	−	0.0493844i
$363$		0			0
$364$		−	7.91704e9i		−	0.450980i
$365$	−1.19127e10	+	1.24655e10i	−0.671179	+	0.702324i
$366$		0			0
$367$	−9.59996e9	+	9.59996e9i	−0.529182	+	0.529182i	−0.920329	−	0.391146i	$-0.872079\pi$
$367$	−9.59996e9	+	9.59996e9i	−0.529182	+	0.529182i	0.391146	+	0.920329i	$0.372079\pi$
$368$	−4.93244e9	−	4.93244e9i	−0.268949	−	0.268949i
$369$		0			0
$370$	−1.33976e9	+	3.03797e7i	−0.0714860	+	0.00162097i
$371$	4.34445e9			0.229319
$372$		0			0
$373$	8.48382e9	+	8.48382e9i	0.438285	+	0.438285i	0.891434	−	0.453150i	$-0.149700\pi$
$373$	8.48382e9	+	8.48382e9i	0.438285	+	0.438285i	−0.453150	+	0.891434i	$0.649700\pi$
$374$			1.94531e9i			0.0994265i
$375$		0			0
$376$	7.46595e9			0.373537
$377$	−3.16469e9	+	3.16469e9i	−0.156663	+	0.156663i
$378$		0			0
$379$		−	2.19075e10i		−	1.06178i	−0.847440	−	0.530891i	$-0.821857\pi$
$379$		−	2.19075e10i		−	1.06178i	0.847440	−	0.530891i	$-0.178143\pi$
$380$	−5.28212e8	−	2.32945e10i	−0.0253323	−	1.11717i
$381$		0			0
$382$	−3.36144e9	+	3.36144e9i	−0.157860	+	0.157860i
$383$	2.31285e10	+	2.31285e10i	1.07486	+	1.07486i	0.996961	+	0.0778987i	$0.0248211\pi$
$383$	2.31285e10	+	2.31285e10i	1.07486	+	1.07486i	0.0778987	+	0.996961i	$0.475179\pi$
$384$		0			0
$385$	−9.15526e9	−	8.74927e9i	−0.416704	−	0.398225i
$386$	1.01452e9			0.0456995
$387$		0			0
$388$	−2.33458e10	−	2.33458e10i	−1.03010	−	1.03010i
$389$			2.23175e10i			0.974647i	0.873221	+	0.487324i	$0.162027\pi$
$389$			2.23175e10i			0.974647i	−0.873221	+	0.487324i	$0.837973\pi$
$390$		0			0
$391$	2.98188e9			0.127580
$392$	−9.77202e9	+	9.77202e9i	−0.413847	+	0.413847i
$393$		0			0
$394$		−	8.75184e8i		−	0.0363174i
$395$	−6.95274e9	+	1.57656e8i	−0.285606	+	0.00647624i
$396$		0			0
$397$	−2.26036e10	+	2.26036e10i	−0.909947	+	0.909947i	−0.996267	−	0.0863200i	$-0.972489\pi$
$397$	−2.26036e10	+	2.26036e10i	−0.909947	+	0.909947i	0.0863200	+	0.996267i	$0.472489\pi$
$398$	−7.52553e9	−	7.52553e9i	−0.299919	−	0.299919i
$399$		0			0
$400$	1.45733e10	−	6.61250e8i	0.569268	−	0.0258301i
$401$	−1.77913e10			−0.688064			−0.344032	−	0.938958i	$-0.611793\pi$
$401$	−1.77913e10			−0.688064			−0.344032	+	0.938958i	$0.611793\pi$
$402$		0			0
$403$	2.39363e10	+	2.39363e10i	0.907480	+	0.907480i
$404$			1.55627e10i			0.584197i
$405$		0			0
$406$	−8.16350e8			−0.0300450
$407$	4.77987e9	−	4.77987e9i	0.174196	−	0.174196i
$408$		0			0
$409$			4.37112e10i			1.56206i	0.624490	+	0.781032i	$0.285307\pi$
$409$			4.37112e10i			1.56206i	−0.624490	+	0.781032i	$0.714693\pi$
$410$	−7.04380e9	−	6.73144e9i	−0.249271	−	0.238217i
$411$		0			0
$412$	−2.14993e10	+	2.14993e10i	−0.746165	+	0.746165i
$413$	2.29389e8	+	2.29389e8i	0.00788447	+	0.00788447i
$414$		0			0
$415$	9.69206e9	−	1.01418e10i	0.326756	−	0.341919i
$416$	3.47257e10			1.15952
$417$		0			0
$418$	−1.47790e10	−	1.47790e10i	−0.484104	−	0.484104i
$419$		−	2.98593e10i		−	0.968776i	−0.874853	−	0.484388i	$-0.839042\pi$
$419$		−	2.98593e10i		−	0.968776i	0.874853	−	0.484388i	$-0.160958\pi$
$420$		0			0
$421$	−5.33816e10			−1.69927			−0.849637	−	0.527368i	$-0.823179\pi$
$421$	−5.33816e10			−1.69927			−0.849637	+	0.527368i	$0.823179\pi$
$422$	−2.99474e9	+	2.99474e9i	−0.0944298	+	0.0944298i
$423$		0			0
$424$			1.23671e10i			0.382654i
$425$	−4.20522e9	+	4.60497e9i	−0.128894	+	0.141147i
$426$		0			0
$427$	1.29369e10	−	1.29369e10i	0.389151	−	0.389151i
$428$	−1.02914e10	−	1.02914e10i	−0.306690	−	0.306690i
$429$		0			0
$430$	−842596.	−	3.71590e7i	−2.46459e−5	−	0.00108690i
$431$	−1.68739e10			−0.488997			−0.244499	−	0.969650i	$-0.578623\pi$
$431$	−1.68739e10			−0.488997			−0.244499	+	0.969650i	$0.578623\pi$
$432$		0			0
$433$	7.15187e9	+	7.15187e9i	0.203455	+	0.203455i	0.801478	−	0.598024i	$-0.204047\pi$
$433$	7.15187e9	+	7.15187e9i	0.203455	+	0.203455i	−0.598024	+	0.801478i	$0.704047\pi$
$434$			6.17451e9i			0.174038i
$435$		0			0
$436$	4.97885e9			0.137779
$437$	−2.26540e10	+	2.26540e10i	−0.621182	+	0.621182i
$438$		0			0
$439$		−	2.62124e9i		−	0.0705747i	−0.999377	−	0.0352873i	$-0.988765\pi$
$439$		−	2.62124e9i		−	0.0705747i	0.999377	−	0.0352873i	$-0.0112346\pi$
$440$	2.49061e10	−	2.60618e10i	0.664500	−	0.695335i
$441$		0			0
$442$	−2.47286e9	+	2.47286e9i	−0.0647904	+	0.0647904i
$443$	3.30317e10	+	3.30317e10i	0.857663	+	0.857663i	0.991062	−	0.133400i	$-0.0425894\pi$
$443$	3.30317e10	+	3.30317e10i	0.857663	+	0.857663i	−0.133400	+	0.991062i	$0.542589\pi$
$444$		0			0
$445$	−3.03067e10	+	6.87218e8i	−0.772857	+	0.0175249i
$446$	8.24359e9			0.208342
$447$		0			0
$448$	−2.50985e9	−	2.50985e9i	−0.0623069	−	0.0623069i
$449$		−	2.56081e10i		−	0.630074i	−0.949079	−	0.315037i	$-0.897983\pi$
$449$		−	2.56081e10i		−	0.630074i	0.949079	−	0.315037i	$-0.102017\pi$
$450$		0			0
$451$	4.91459e10			1.18790
$452$	−4.24616e10	+	4.24616e10i	−1.01729	+	1.01729i
$453$		0			0
$454$		−	3.05928e10i		−	0.720105i
$455$	−5.16094e8	−	2.27601e10i	−0.0120416	−	0.531041i
$456$		0			0
$457$	1.31162e10	−	1.31162e10i	0.300707	−	0.300707i	−0.540583	−	0.841290i	$-0.681796\pi$
$457$	1.31162e10	−	1.31162e10i	0.300707	−	0.300707i	0.841290	+	0.540583i	$0.181796\pi$
$458$	−1.61456e10	−	1.61456e10i	−0.366937	−	0.366937i
$459$		0			0
$460$	−1.83435e10	−	1.75300e10i	−0.409685	−	0.391518i
$461$	3.99207e10			0.883883			0.441942	−	0.897044i	$-0.354290\pi$
$461$	3.99207e10			0.883883			0.441942	+	0.897044i	$0.354290\pi$
$462$		0			0
$463$	1.43482e10	+	1.43482e10i	0.312229	+	0.312229i	0.845772	−	0.533544i	$-0.179140\pi$
$463$	1.43482e10	+	1.43482e10i	0.312229	+	0.312229i	−0.533544	+	0.845772i	$0.679140\pi$
$464$			4.74365e9i			0.102339i
$465$		0			0
$466$	3.19061e10			0.676597
$467$	−2.44200e10	+	2.44200e10i	−0.513427	+	0.513427i	−0.915575	−	0.402148i	$-0.868264\pi$
$467$	−2.44200e10	+	2.44200e10i	−0.513427	+	0.513427i	0.402148	+	0.915575i	$0.368264\pi$
$468$		0			0
$469$		−	6.45246e9i		−	0.133363i
$470$	9.85535e9	−	2.23474e8i	0.201967	−	0.00457969i
$471$		0			0
$472$	−6.52990e8	+	6.52990e8i	−0.0131565	+	0.0131565i
$473$	1.32572e8	+	1.32572e8i	0.00264855	+	0.00264855i
$474$		0			0
$475$	−3.03703e9	−	6.69330e10i	−0.0596588	−	1.31482i
$476$	3.58709e9			0.0698738
$477$		0			0
$478$	1.16204e10	+	1.16204e10i	0.222592	+	0.222592i
$479$		−	9.03857e9i		−	0.171695i	−0.996308	−	0.0858475i	$-0.972640\pi$
$479$		−	9.03857e9i		−	0.171695i	0.996308	−	0.0858475i	$-0.0273598\pi$
$480$		0			0
$481$	1.21523e10			0.227026
$482$	−3.16619e8	+	3.16619e8i	−0.00586609	+	0.00586609i
$483$		0			0
$484$			3.69045e10i			0.672508i
$485$	−6.86368e10	−	6.55930e10i	−1.24048	−	1.18547i
$486$		0			0
$487$	3.53950e10	−	3.53950e10i	0.629255	−	0.629255i	−0.318626	−	0.947881i	$-0.603221\pi$
$487$	3.53950e10	−	3.53950e10i	0.629255	−	0.629255i	0.947881	+	0.318626i	$0.103221\pi$
$488$	3.68268e10	+	3.68268e10i	0.649358	+	0.649358i
$489$		0			0
$490$	−1.26069e10	+	1.31919e10i	−0.218688	+	0.228836i
$491$	5.87159e10			1.01025			0.505126	−	0.863045i	$-0.331446\pi$
$491$	5.87159e10			1.01025			0.505126	+	0.863045i	$0.331446\pi$
$492$		0			0
$493$	−1.43387e9	−	1.43387e9i	−0.0242730	−	0.0242730i
$494$		−	3.75738e10i		−	0.630924i
$495$		0			0
$496$	3.58788e10			0.592805
$497$	6.50082e9	−	6.50082e9i	0.106547	−	0.106547i
$498$		0			0
$499$		−	2.57394e10i		−	0.415141i	−0.978220	−	0.207571i	$-0.933444\pi$
$499$		−	2.57394e10i		−	0.415141i	0.978220	−	0.207571i	$-0.0665557\pi$
$500$	5.29410e10	−	3.60633e9i	0.847057	−	0.0577012i
$501$		0			0
$502$	−2.54494e8	+	2.54494e8i	−0.00400740	+	0.00400740i
$503$	4.75499e10	+	4.75499e10i	0.742810	+	0.742810i	0.973118	−	0.230308i	$-0.0739733\pi$
$503$	4.75499e10	+	4.75499e10i	0.742810	+	0.742810i	−0.230308	+	0.973118i	$0.573973\pi$
$504$		0			0
$505$	1.01450e9	+	4.47399e10i	0.0155986	+	0.687907i
$506$	−2.27596e10			−0.347186
$507$		0			0
$508$	4.01643e10	+	4.01643e10i	0.603095	+	0.603095i
$509$		−	8.69280e10i		−	1.29506i	−0.762042	−	0.647528i	$-0.775803\pi$
$509$		−	8.69280e10i		−	1.29506i	0.762042	−	0.647528i	$-0.224197\pi$
$510$		0			0
$511$	2.85197e10			0.418275
$512$	4.59200e10	−	4.59200e10i	0.668225	−	0.668225i
$513$		0			0
$514$		−	4.16243e9i		−	0.0596340i
$515$	−6.04050e10	+	6.32080e10i	−0.858705	+	0.898552i
$516$		0			0
$517$	−3.51609e10	+	3.51609e10i	−0.492151	+	0.492151i
$518$	1.56737e9	+	1.56737e9i	0.0217697	+	0.0217697i
$519$		0			0
$520$	6.47900e10	−	1.46914e9i	0.886124	−	0.0200932i
$521$	−6.44123e10			−0.874214			−0.437107	−	0.899409i	$-0.643997\pi$
$521$	−6.44123e10			−0.874214			−0.437107	+	0.899409i	$0.643997\pi$
$522$		0			0
$523$	−5.99903e10	−	5.99903e10i	−0.801815	−	0.801815i	0.181564	−	0.983379i	$-0.441884\pi$
$523$	−5.99903e10	−	5.99903e10i	−0.801815	−	0.801815i	−0.983379	+	0.181564i	$0.941884\pi$
$524$			6.63079e10i			0.879509i
$525$		0			0
$526$	−5.76728e10			−0.753404
$527$	−1.08452e10	+	1.08452e10i	−0.140603	+	0.140603i
$528$		0			0
$529$		−	4.34238e10i		−	0.554505i
$530$	3.70179e8	+	1.63251e10i	0.00469146	+	0.206896i
$531$		0			0
$532$	−2.72519e10	+	2.72519e10i	−0.340213	+	0.340213i
$533$	6.24738e10	+	6.24738e10i	0.774086	+	0.774086i
$534$		0			0
$535$	−3.02568e10	−	2.89151e10i	−0.369324	−	0.352947i
$536$	1.83679e10			0.222536
$537$		0			0
$538$	2.36869e10	+	2.36869e10i	0.282734	+	0.282734i
$539$		−	9.20427e10i		−	1.09052i
$540$		0			0
$541$	−9.38341e10			−1.09540			−0.547698	−	0.836676i	$-0.684496\pi$
$541$	−9.38341e10			−1.09540			−0.547698	+	0.836676i	$0.684496\pi$
$542$	−3.86633e10	+	3.86633e10i	−0.448025	+	0.448025i
$543$		0			0
$544$			1.57337e10i			0.179653i
$545$	1.43133e10	−	3.24560e8i	0.162238	−	0.00367883i
$546$		0			0
$547$	1.86813e10	−	1.86813e10i	0.208669	−	0.208669i	−0.595032	−	0.803702i	$-0.702861\pi$
$547$	1.86813e10	−	1.86813e10i	0.208669	−	0.208669i	0.803702	+	0.595032i	$0.202861\pi$
$548$	−8.16657e10	−	8.16657e10i	−0.905560	−	0.905560i
$549$		0			0
$550$	3.20969e10	−	3.51481e10i	0.350762	−	0.384106i
$551$	2.17869e10			0.236368
$552$		0			0
$553$	8.13393e9	+	8.13393e9i	0.0869761	+	0.0869761i
$554$			4.20398e10i			0.446294i
$555$		0			0
$556$	2.40333e10			0.251487
$557$	4.32331e9	−	4.32331e9i	0.0449154	−	0.0449154i	−0.684292	−	0.729208i	$-0.739889\pi$
$557$	4.32331e9	−	4.32331e9i	0.0449154	−	0.0449154i	0.729208	+	0.684292i	$0.239889\pi$
$558$		0			0
$559$			3.37049e8i			0.00345180i
$560$	−1.74447e10	−	1.66711e10i	−0.177382	−	0.169516i
$561$		0			0
$562$	−5.37441e10	+	5.37441e10i	−0.538748	+	0.538748i
$563$	−5.85471e10	−	5.85471e10i	−0.582736	−	0.582736i	0.352918	−	0.935654i	$-0.385189\pi$
$563$	−5.85471e10	−	5.85471e10i	−0.582736	−	0.582736i	−0.935654	+	0.352918i	$0.885189\pi$
$564$		0			0
$565$	−1.19302e11	+	1.24837e11i	−1.17072	+	1.22504i
$566$	−2.52209e9			−0.0245751
$567$		0			0
$568$	1.85056e10	+	1.85056e10i	0.177791	+	0.177791i
$569$			1.98793e11i			1.89650i	0.317524	+	0.948250i	$0.397149\pi$
$569$			1.98793e11i			1.89650i	−0.317524	+	0.948250i	$0.602851\pi$
$570$		0			0
$571$	6.21842e10			0.584973			0.292487	−	0.956270i	$-0.405517\pi$
$571$	6.21842e10			0.584973			0.292487	+	0.956270i	$0.405517\pi$
$572$	−1.06138e11	+	1.06138e11i	−0.991490	+	0.991490i
$573$		0			0
$574$			1.61155e10i			0.148455i
$575$	−5.38769e10	−	4.91999e10i	−0.492869	−	0.450083i
$576$		0			0
$577$	−1.02056e11	+	1.02056e11i	−0.920739	+	0.920739i	−0.997082	−	0.0763427i	$-0.975676\pi$
$577$	−1.02056e11	+	1.02056e11i	−0.920739	+	0.920739i	0.0763427	+	0.997082i	$0.475676\pi$
$578$	2.95455e10	+	2.95455e10i	0.264716	+	0.264716i
$579$		0			0
$580$	3.91156e8	+	1.72502e10i	0.00345651	+	0.152434i
$581$	−2.32034e10			−0.203633
$582$		0			0
$583$	−5.82431e10	−	5.82431e10i	−0.504162	−	0.504162i
$584$			8.11857e10i			0.697956i
$585$		0			0
$586$	9.03959e9			0.0766581
$587$	1.52761e11	−	1.52761e11i	1.28665	−	1.28665i	0.349837	−	0.936811i	$-0.386237\pi$
$587$	1.52761e11	−	1.52761e11i	1.28665	−	1.28665i	0.936811	−	0.349837i	$-0.113763\pi$
$588$		0			0
$589$		−	1.64787e11i		−	1.36918i
$590$	−8.42427e8	+	8.81518e8i	−0.00695223	+	0.00727484i
$591$		0			0
$592$	9.10768e9	−	9.10768e9i	0.0741517	−	0.0741517i
$593$	−9.35153e10	−	9.35153e10i	−0.756247	−	0.756247i	0.219390	−	0.975637i	$-0.429593\pi$
$593$	−9.35153e10	−	9.35153e10i	−0.756247	−	0.756247i	−0.975637	+	0.219390i	$0.929593\pi$
$594$		0			0
$595$	1.03122e10	−	2.33834e8i	0.0822782	−	0.00186569i
$596$	1.57305e11			1.24669
$597$		0			0
$598$	−2.89318e10	−	2.89318e10i	−0.226241	−	0.226241i
$599$		−	5.65120e10i		−	0.438968i	−0.975616	−	0.219484i	$-0.929563\pi$
$599$		−	5.65120e10i		−	0.438968i	0.975616	−	0.219484i	$-0.0704374\pi$
$600$		0			0
$601$	−9.99220e10			−0.765884			−0.382942	−	0.923772i	$-0.625089\pi$
$601$	−9.99220e10			−0.765884			−0.382942	+	0.923772i	$0.625089\pi$
$602$	−4.34719e7	+	4.34719e7i	−0.000330996	+	0.000330996i
$603$		0			0
$604$			1.66760e11i			1.25298i
$605$	2.40572e9	+	1.06094e11i	0.0179566	+	0.791896i
$606$		0			0
$607$	1.27776e11	−	1.27776e11i	0.941229	−	0.941229i	−0.0571370	−	0.998366i	$-0.518197\pi$
$607$	1.27776e11	−	1.27776e11i	0.941229	−	0.941229i	0.998366	+	0.0571370i	$0.0181972\pi$
$608$	−1.19532e11	−	1.19532e11i	−0.874724	−	0.874724i
$609$		0			0
$610$	4.97151e10	+	4.75105e10i	0.359062	+	0.343139i
$611$	−8.93925e10			−0.641411
$612$		0			0
$613$	6.34636e10	+	6.34636e10i	0.449452	+	0.449452i	0.895172	−	0.445720i	$-0.147052\pi$
$613$	6.34636e10	+	6.34636e10i	0.449452	+	0.449452i	−0.445720	+	0.895172i	$0.647052\pi$
$614$		−	6.96478e10i		−	0.490043i
$615$		0			0
$616$	−5.96267e10			−0.414112
$617$	6.39126e10	−	6.39126e10i	0.441007	−	0.441007i	−0.451343	−	0.892350i	$-0.649055\pi$
$617$	6.39126e10	−	6.39126e10i	0.441007	−	0.441007i	0.892350	+	0.451343i	$0.149055\pi$
$618$		0			0
$619$			5.76225e10i			0.392491i	0.980555	+	0.196245i	$0.0628749\pi$
$619$			5.76225e10i			0.392491i	−0.980555	+	0.196245i	$0.937125\pi$
$620$	1.30473e11	−	2.95853e9i	0.882986	−	0.0200221i
$621$		0			0
$622$	−1.64439e10	+	1.64439e10i	−0.109861	+	0.109861i
$623$	3.54555e10	+	3.54555e10i	0.235359	+	0.235359i
$624$		0			0
$625$	1.51961e11	−	1.38186e10i	0.995891	−	0.0905619i
$626$	−4.21700e10			−0.274604
$627$		0			0
$628$	−1.74589e11	−	1.74589e11i	−1.12248	−	1.12248i
$629$			5.50600e9i			0.0351749i
$630$		0			0
$631$	1.53061e11			0.965486			0.482743	−	0.875762i	$-0.339641\pi$
$631$	1.53061e11			0.965486			0.482743	+	0.875762i	$0.339641\pi$
$632$	−2.31544e10	+	2.31544e10i	−0.145133	+	0.145133i
$633$		0			0
$634$		−	4.87880e10i		−	0.301964i
$635$	1.18083e11	+	1.12847e11i	0.726263	+	0.694057i
$636$		0			0
$637$	1.17004e11	−	1.17004e11i	0.710628	−	0.710628i
$638$	1.09442e10	+	1.09442e10i	0.0660546	+	0.0660546i
$639$		0			0
$640$	1.18162e11	−	1.23645e11i	0.704300	−	0.736982i
$641$	−1.10388e11			−0.653867			−0.326934	−	0.945047i	$-0.606015\pi$
$641$	−1.10388e11			−0.653867			−0.326934	+	0.945047i	$0.606015\pi$
$642$		0			0
$643$	4.62452e10	+	4.62452e10i	0.270535	+	0.270535i	0.829315	−	0.558781i	$-0.188731\pi$
$643$	4.62452e10	+	4.62452e10i	0.270535	+	0.270535i	−0.558781	+	0.829315i	$0.688731\pi$
$644$			4.19680e10i			0.243991i
$645$		0			0
$646$	1.70241e10			0.0977539
$647$	9.64071e10	−	9.64071e10i	0.550164	−	0.550164i	−0.376324	−	0.926488i	$-0.622812\pi$
$647$	9.64071e10	−	9.64071e10i	0.550164	−	0.550164i	0.926488	+	0.376324i	$0.122812\pi$
$648$		0			0
$649$		−	6.15052e9i		−	0.0346683i
$650$	8.54813e10	−	3.87864e9i	0.478870	−	0.0217283i
$651$		0			0
$652$	9.45283e10	−	9.45283e10i	0.523084	−	0.523084i
$653$	2.02786e11	+	2.02786e11i	1.11528	+	1.11528i	0.992424	+	0.122857i	$0.0392057\pi$
$653$	2.02786e11	+	2.02786e11i	1.11528	+	1.11528i	0.122857	+	0.992424i	$0.460794\pi$
$654$		0			0
$655$	4.32247e9	+	1.90623e11i	0.0234837	+	1.03565i
$656$	9.36438e10			0.505666
$657$		0			0
$658$	−1.15297e10	−	1.15297e10i	−0.0615053	−	0.0615053i
$659$			5.78139e10i			0.306542i	0.988184	+	0.153271i	$0.0489808\pi$
$659$			5.78139e10i			0.306542i	−0.988184	+	0.153271i	$0.951019\pi$
$660$		0			0
$661$	3.80376e10			0.199254			0.0996271	−	0.995025i	$-0.468235\pi$
$661$	3.80376e10			0.199254			0.0996271	+	0.995025i	$0.468235\pi$
$662$	6.58451e10	−	6.58451e10i	0.342840	−	0.342840i
$663$		0			0
$664$		−	6.60520e10i		−	0.339792i
$665$	−7.65679e10	+	8.01209e10i	−0.391526	+	0.409694i
$666$		0			0
$667$	1.67759e10	−	1.67759e10i	0.0847585	−	0.0847585i
$668$	−1.55797e11	−	1.55797e11i	−0.782442	−	0.782442i
$669$		0			0
$670$	2.42463e10	−	5.49796e8i	0.120323	−	0.00272836i
$671$	−3.46872e11			−1.71111
$672$		0			0
$673$	1.23735e11	+	1.23735e11i	0.603158	+	0.603158i	0.941149	−	0.337991i	$-0.109747\pi$
$673$	1.23735e11	+	1.23735e11i	0.603158	+	0.603158i	−0.337991	+	0.941149i	$0.609747\pi$
$674$		−	5.53205e10i		−	0.268069i
$675$		0			0
$676$	−9.25460e10			−0.443170
$677$	8.44279e10	−	8.44279e10i	0.401912	−	0.401912i	−0.476994	−	0.878906i	$-0.658274\pi$
$677$	8.44279e10	−	8.44279e10i	0.401912	−	0.401912i	0.878906	+	0.476994i	$0.158274\pi$
$678$		0			0
$679$			1.57034e11i			0.738778i
$680$	6.65644e8	+	2.93553e10i	0.00311320	+	0.137294i
$681$		0			0
$682$	8.27774e10	−	8.27774e10i	0.382626	−	0.382626i
$683$	2.87370e10	+	2.87370e10i	0.132056	+	0.132056i	0.770045	−	0.637989i	$-0.220234\pi$
$683$	2.87370e10	+	2.87370e10i	0.132056	+	0.132056i	−0.637989	+	0.770045i	$0.720234\pi$
$684$		0			0
$685$	−2.40098e11	−	2.29450e11i	−1.09050	−	1.04214i
$686$	6.72321e10			0.303585
$687$		0			0
$688$	2.52606e8	+	2.52606e8i	0.00112743	+	0.00112743i
$689$		−	1.48076e11i		−	0.657065i
$690$		0			0
$691$	−8.87703e10			−0.389364			−0.194682	−	0.980866i	$-0.562367\pi$
$691$	−8.87703e10			−0.389364			−0.194682	+	0.980866i	$0.562367\pi$
$692$	7.39768e10	−	7.39768e10i	0.322605	−	0.322605i
$693$		0			0
$694$		−	7.28192e10i		−	0.313912i
$695$	6.90915e10	−	1.56668e9i	0.296132	−	0.00671492i
$696$		0			0
$697$	−2.83059e10	+	2.83059e10i	−0.119935	+	0.119935i
$698$	−4.90652e10	−	4.90652e10i	−0.206706	−	0.206706i
$699$		0			0
$700$	−6.48120e10	−	5.91857e10i	−0.269938	−	0.246504i
$701$	−1.22790e11			−0.508499			−0.254249	−	0.967139i	$-0.581828\pi$
$701$	−1.22790e11			−0.508499			−0.254249	+	0.967139i	$0.581828\pi$
$702$		0			0
$703$	−4.18303e10	−	4.18303e10i	−0.171266	−	0.171266i
$704$			6.72957e10i			0.273966i
$705$		0			0
$706$	−9.31125e10			−0.374791
$707$	5.23407e10	−	5.23407e10i	0.209489	−	0.209489i
$708$		0			0
$709$			2.07670e11i			0.821842i	0.911671	+	0.410921i	$0.134793\pi$
$709$			2.07670e11i			0.821842i	−0.911671	+	0.410921i	$0.865207\pi$
$710$	2.49820e10	+	2.38742e10i	0.0983091	+	0.0939495i
$711$		0			0
$712$	−1.00929e11	+	1.00929e11i	−0.392733	+	0.392733i
$713$	−1.26886e11	−	1.26886e11i	−0.490969	−	0.490969i
$714$		0			0
$715$	−2.98210e11	+	3.12048e11i	−1.14103	+	1.19398i
$716$	−2.80773e11			−1.06832
$717$		0			0
$718$	−4.16981e10	−	4.16981e10i	−0.156898	−	0.156898i
$719$			1.66571e11i			0.623281i	0.950200	+	0.311640i	$0.100878\pi$
$719$			1.66571e11i			0.623281i	−0.950200	+	0.311640i	$0.899122\pi$
$720$		0			0
$721$	1.44613e11			0.535140
$722$	−5.46750e10	+	5.46750e10i	−0.201205	+	0.201205i
$723$		0			0
$724$			4.19292e10i			0.152603i
$725$	2.24901e9	+	4.95658e10i	0.00814027	+	0.179403i
$726$		0			0
$727$	1.61369e11	−	1.61369e11i	0.577673	−	0.577673i	−0.356588	−	0.934262i	$-0.616060\pi$
$727$	1.61369e11	−	1.61369e11i	0.577673	−	0.577673i	0.934262	+	0.356588i	$0.116060\pi$
$728$	−7.57970e10	−	7.57970e10i	−0.269853	−	0.269853i
$729$		0			0
$730$	2.43009e9	+	1.07168e11i	0.00855717	+	0.377377i
$731$	−1.52712e8			−0.000534814
$732$		0			0
$733$	4.72057e10	+	4.72057e10i	0.163523	+	0.163523i	0.784125	−	0.620603i	$-0.213112\pi$
$733$	4.72057e10	+	4.72057e10i	0.163523	+	0.163523i	−0.620603	+	0.784125i	$0.713112\pi$
$734$			8.44043e10i			0.290791i
$735$		0			0
$736$	−1.84080e11			−0.627328
$737$	−8.65036e10	+	8.65036e10i	−0.293200	+	0.293200i
$738$		0			0
$739$			2.13693e11i			0.716494i	0.933627	+	0.358247i	$0.116625\pi$
$739$			2.13693e11i			0.716494i	−0.933627	+	0.358247i	$0.883375\pi$
$740$	3.23690e10	−	3.38710e10i	0.107945	−	0.112954i
$741$		0			0
$742$	1.90985e10	−	1.90985e10i	0.0630064	−	0.0630064i
$743$	3.10741e11	+	3.10741e11i	1.01963	+	1.01963i	0.999803	+	0.0198284i	$0.00631198\pi$
$743$	3.10741e11	+	3.10741e11i	1.01963	+	1.01963i	0.0198284	+	0.999803i	$0.493688\pi$
$744$		0			0
$745$	4.52224e11	−	1.02544e10i	1.46801	−	0.0332877i
$746$	7.45910e10			0.240841
$747$		0			0
$748$	−4.80896e10	−	4.80896e10i	−0.153619	−	0.153619i
$749$			6.92245e10i			0.219954i
$750$		0			0
$751$	−5.29510e11			−1.66462			−0.832308	−	0.554313i	$-0.812981\pi$
$751$	−5.29510e11			−1.66462			−0.832308	+	0.554313i	$0.812981\pi$
$752$	−6.69965e10	+	6.69965e10i	−0.209498	+	0.209498i
$753$		0			0
$754$			2.78245e10i			0.0860877i
$755$	1.08707e10	+	4.79405e11i	0.0334557	+	1.47542i
$756$		0			0
$757$	−1.66172e11	+	1.66172e11i	−0.506029	+	0.506029i	−0.913305	−	0.407276i	$-0.866479\pi$
$757$	−1.66172e11	+	1.66172e11i	−0.506029	+	0.506029i	0.407276	+	0.913305i	$0.366479\pi$
$758$	−9.63068e10	−	9.63068e10i	−0.291729	−	0.291729i
$759$		0			0
$760$	−2.28076e11	−	2.17962e11i	−0.683637	−	0.653321i
$761$	3.61095e11			1.07667			0.538335	−	0.842731i	$-0.319054\pi$
$761$	3.61095e11			1.07667			0.538335	+	0.842731i	$0.319054\pi$
$762$		0			0
$763$	−1.67450e10	−	1.67450e10i	−0.0494067	−	0.0494067i
$764$		−	1.66195e11i		−	0.487803i
$765$		0			0
$766$	2.03349e11			0.590646
$767$	7.81849e9	−	7.81849e9i	0.0225913	−	0.0225913i
$768$		0			0
$769$		−	2.04700e11i		−	0.585345i	−0.956213	−	0.292672i	$-0.905455\pi$
$769$		−	2.04700e11i		−	0.585345i	0.956213	−	0.292672i	$-0.0945446\pi$
$770$	−7.87096e10	+	1.78477e9i	−0.223906	+	0.00507716i
$771$		0			0
$772$	−2.50797e10	+	2.50797e10i	−0.0706080	+	0.0706080i
$773$	8.07889e10	+	8.07889e10i	0.226274	+	0.226274i	0.811134	−	0.584860i	$-0.198851\pi$
$773$	8.07889e10	+	8.07889e10i	0.226274	+	0.226274i	−0.584860	+	0.811134i	$0.698851\pi$
$774$		0			0
$775$	3.74894e11	−	1.70105e10i	1.03921	−	0.0471531i
$776$	−4.47020e11			−1.23276
$777$		0			0
$778$	9.81095e10	+	9.81095e10i	0.267789	+	0.267789i
$779$		−	4.30093e11i		−	1.16792i
$780$		0			0
$781$	−1.74304e11			−0.468493
$782$	1.31086e10	−	1.31086e10i	0.0350532	−	0.0350532i
$783$		0			0
$784$		−	1.75380e11i		−	0.464213i
$785$	−5.13292e11	−	4.90530e11i	−1.35172	−	1.29177i
$786$		0			0
$787$	−1.41727e11	+	1.41727e11i	−0.369448	+	0.369448i	−0.867276	−	0.497828i	$-0.834131\pi$
$787$	−1.41727e11	+	1.41727e11i	−0.369448	+	0.369448i	0.497828	+	0.867276i	$0.334131\pi$
$788$	2.16353e10	+	2.16353e10i	0.0561122	+	0.0561122i
$789$		0			0
$790$	−2.98717e10	+	3.12578e10i	−0.0766923	+	0.0802510i
$791$	2.85615e11			0.729584
$792$		0			0
$793$	−4.40940e11	−	4.40940e11i	−1.11503	−	1.11503i
$794$			1.98735e11i			0.500025i
$795$		0			0
$796$	3.72074e11			0.926781
$797$	2.66505e11	−	2.66505e11i	0.660499	−	0.660499i	−0.294998	−	0.955498i	$-0.595319\pi$
$797$	2.66505e11	−	2.66505e11i	0.660499	−	0.660499i	0.955498	+	0.294998i	$0.0953191\pi$
$798$		0			0
$799$		−	4.05024e10i		−	0.0993787i
$800$	2.59600e11	−	2.84278e11i	0.633789	−	0.694038i
$801$		0			0
$802$	−7.82117e10	+	7.82117e10i	−0.189049	+	0.189049i
$803$	−3.82344e11	−	3.82344e11i	−0.919586	−	0.919586i
$804$		0			0
$805$	2.73580e9	+	1.20650e11i	0.00651479	+	0.287306i
$806$	2.10452e11			0.498669
$807$		0			0
$808$	1.48996e11	+	1.48996e11i	0.349565	+	0.349565i
$809$			6.78011e11i			1.58286i	0.611259	+	0.791431i	$0.290663\pi$
$809$			6.78011e11i			1.58286i	−0.611259	+	0.791431i	$0.709337\pi$
$810$		0			0
$811$	4.62623e11			1.06941			0.534704	−	0.845039i	$-0.320423\pi$
$811$	4.62623e11			1.06941			0.534704	+	0.845039i	$0.320423\pi$
$812$	2.01808e10	−	2.01808e10i	0.0464211	−	0.0464211i
$813$		0			0
$814$		−	4.20253e10i		−	0.0957224i
$815$	2.65590e11	−	2.77914e11i	0.601978	−	0.629912i
$816$		0			0
$817$	1.16019e9	−	1.16019e9i	0.00260399	−	0.00260399i
$818$	1.92158e11	+	1.92158e11i	0.429185	+	0.429185i
$819$		0			0
$820$	3.40535e11	−	7.72177e9i	0.753193	−	0.0170790i
$821$	2.02486e11			0.445678			0.222839	−	0.974855i	$-0.428468\pi$
$821$	2.02486e11			0.445678			0.222839	+	0.974855i	$0.428468\pi$
$822$		0			0
$823$	5.67731e11	+	5.67731e11i	1.23749	+	1.23749i	0.961022	+	0.276473i	$0.0891657\pi$
$823$	5.67731e11	+	5.67731e11i	1.23749	+	1.23749i	0.276473	+	0.961022i	$0.410834\pi$
$824$			4.11664e11i			0.892963i
$825$		0			0
$826$	2.01682e9			0.00433259
$827$	−5.76065e11	+	5.76065e11i	−1.23154	+	1.23154i	−0.268173	+	0.963371i	$0.586420\pi$
$827$	−5.76065e11	+	5.76065e11i	−1.23154	+	1.23154i	−0.963371	+	0.268173i	$0.913580\pi$
$828$		0			0
$829$		−	2.12691e11i		−	0.450330i	−0.974321	−	0.225165i	$-0.927708\pi$
$829$		−	2.12691e11i		−	0.450330i	0.974321	−	0.225165i	$-0.0722922\pi$
$830$	−1.97710e9	−	8.71912e10i	−0.00416596	−	0.183722i
$831$		0			0
$832$	−8.55457e10	+	8.55457e10i	−0.178527	+	0.178527i
$833$	5.30126e10	+	5.30126e10i	0.110103	+	0.110103i
$834$		0			0
$835$	−4.58043e11	−	4.37731e11i	−0.942237	−	0.900454i
$836$	7.30696e11			1.49593
$837$		0			0
$838$	−1.31264e11	−	1.31264e11i	−0.266176	−	0.266176i
$839$		−	8.36816e11i		−	1.68881i	−0.535701	−	0.844407i	$-0.679953\pi$
$839$		−	8.36816e11i		−	1.68881i	0.535701	−	0.844407i	$-0.320047\pi$
$840$		0			0
$841$	4.84113e11			0.967748
$842$	−2.34670e11	+	2.34670e11i	−0.466883	+	0.466883i
$843$		0			0
$844$		−	1.48065e11i		−	0.291797i
$845$	−2.66053e11	+	6.03286e9i	−0.521845	+	0.0118331i
$846$		0			0
$847$	1.24118e11	−	1.24118e11i	0.241157	−	0.241157i
$848$	−1.10978e11	−	1.10978e11i	−0.214611	−	0.214611i
$849$		0			0
$850$	1.75735e9	+	3.87303e10i	0.00336654	+	0.0741950i
$851$	−6.44187e10			−0.122827
$852$		0			0
$853$	2.74662e11	+	2.74662e11i	0.518803	+	0.518803i	0.917209	−	0.398406i	$-0.130436\pi$
$853$	2.74662e11	+	2.74662e11i	0.518803	+	0.518803i	−0.398406	+	0.917209i	$0.630436\pi$
$854$		−	1.13743e11i		−	0.213842i
$855$		0			0
$856$	−1.97058e11			−0.367027
$857$	9.65564e10	−	9.65564e10i	0.179002	−	0.179002i	−0.611919	−	0.790921i	$-0.709602\pi$
$857$	9.65564e10	−	9.65564e10i	0.179002	−	0.179002i	0.790921	+	0.611919i	$0.209602\pi$
$858$		0			0
$859$		−	7.22383e11i		−	1.32677i	−0.748280	−	0.663383i	$-0.769120\pi$
$859$		−	7.22383e11i		−	1.32677i	0.748280	−	0.663383i	$-0.230880\pi$
$860$	9.39430e8	+	8.97771e8i	0.00171740	+	0.00164124i
$861$		0			0
$862$	−7.41790e10	+	7.41790e10i	−0.134354	+	0.134354i
$863$	9.33124e10	+	9.33124e10i	0.168227	+	0.168227i	0.786200	−	0.617973i	$-0.212046\pi$
$863$	9.33124e10	+	9.33124e10i	0.168227	+	0.168227i	−0.617973	+	0.786200i	$0.712046\pi$
$864$		0			0
$865$	2.07848e11	−	2.17492e11i	0.371262	−	0.388490i
$866$	6.28803e10			0.111800
$867$		0			0
$868$	−1.52639e11	−	1.52639e11i	−0.268897	−	0.268897i
$869$		−	2.18092e11i		−	0.382437i
$870$		0			0
$871$	−2.19925e11			−0.382123
$872$	4.76670e10	−	4.76670e10i	0.0824427	−	0.0824427i
$873$		0			0
$874$			1.99177e11i			0.341346i
$875$	−1.90181e11	−	1.65923e11i	−0.324441	−	0.283058i
$876$		0			0
$877$	5.23388e11	−	5.23388e11i	0.884760	−	0.884760i	−0.109254	−	0.994014i	$-0.534846\pi$
$877$	5.23388e11	−	5.23388e11i	0.884760	−	0.884760i	0.994014	+	0.109254i	$0.0348463\pi$
$878$	−1.15232e10	−	1.15232e10i	−0.0193907	−	0.0193907i
$879$		0			0
$880$	1.03710e10	+	4.57366e11i	0.0172937	+	0.762664i
$881$	8.15621e10			0.135389			0.0676947	−	0.997706i	$-0.478436\pi$
$881$	8.15621e10			0.135389			0.0676947	+	0.997706i	$0.478436\pi$
$882$		0			0
$883$	−3.22895e11	−	3.22895e11i	−0.531151	−	0.531151i	0.389764	−	0.920915i	$-0.372557\pi$
$883$	−3.22895e11	−	3.22895e11i	−0.531151	−	0.531151i	−0.920915	+	0.389764i	$0.872557\pi$
$884$		−	1.22262e11i		−	0.200209i
$885$		0			0
$886$	2.90420e11			0.471294
$887$	−4.59932e11	+	4.59932e11i	−0.743018	+	0.743018i	−0.973158	−	0.230140i	$-0.926082\pi$
$887$	−4.59932e11	+	4.59932e11i	−0.743018	+	0.743018i	0.230140	+	0.973158i	$0.426082\pi$
$888$		0			0
$889$		−	2.70163e11i		−	0.432532i
$890$	−1.30210e11	+	1.36252e11i	−0.207531	+	0.217161i
$891$		0			0
$892$	−2.03788e11	+	2.03788e11i	−0.321899	+	0.321899i
$893$	3.07706e11	+	3.07706e11i	0.483871	+	0.483871i
$894$		0			0
$895$	−8.07171e11	+	1.83029e10i	−1.25798	+	0.0285252i
$896$	−2.82887e11			−0.438915
$897$		0			0
$898$	−1.12575e11	−	1.12575e11i	−0.173116	−	0.173116i
$899$			1.22029e11i			0.186821i
$900$		0			0
$901$	6.70910e10			0.101804
$902$	2.16049e11	−	2.16049e11i	0.326382	−	0.326382i
$903$		0			0
$904$			8.13047e11i			1.21742i
$905$	2.73327e9	+	1.20539e11i	0.00407463	+	0.179694i
$906$		0			0
$907$	−7.98076e11	+	7.98076e11i	−1.17928	+	1.17928i	−0.199347	+	0.979929i	$0.563882\pi$
$907$	−7.98076e11	+	7.98076e11i	−1.17928	+	1.17928i	−0.979929	+	0.199347i	$0.936118\pi$
$908$	7.56278e11	+	7.56278e11i	1.11260	+	1.11260i
$909$		0			0
$910$	−1.02324e11	−	9.77862e10i	−0.149215	−	0.142598i
$911$	1.50243e11			0.218132			0.109066	−	0.994034i	$-0.465214\pi$
$911$	1.50243e11			0.218132			0.109066	+	0.994034i	$0.465214\pi$
$912$		0			0
$913$	3.11072e11	+	3.11072e11i	0.447690	+	0.447690i
$914$		−	1.15320e11i		−	0.165241i
$915$		0			0
$916$	7.98264e11			1.13387
$917$	2.23008e11	−	2.23008e11i	0.315387	−	0.315387i
$918$		0			0
$919$			1.02471e12i			1.43662i	0.695725	+	0.718308i	$0.255083\pi$
$919$			1.02471e12i			1.43662i	−0.695725	+	0.718308i	$0.744917\pi$
$920$	−3.43449e11	+	7.78786e9i	−0.479415	+	0.0108709i
$921$		0			0
$922$	1.75495e11	−	1.75495e11i	0.242851	−	0.242851i
$923$	−2.21574e11	−	2.21574e11i	−0.305289	−	0.305289i
$924$		0			0
$925$	9.08470e10	−	9.94831e10i	0.124092	−	0.135888i
$926$	1.26151e11			0.171573
$927$		0			0
$928$	8.85171e10	+	8.85171e10i	0.119353	+	0.119353i
$929$		−	1.38553e12i		−	1.86017i	−0.367346	−	0.930084i	$-0.619734\pi$
$929$		−	1.38553e12i		−	1.86017i	0.367346	−	0.930084i	$-0.380266\pi$
$930$		0			0
$931$	−8.05498e11			−1.07218
$932$	−7.88745e11	+	7.88745e11i	−1.04538	+	1.04538i
$933$		0			0
$934$			2.14705e11i			0.282133i
$935$	−1.41384e11	−	1.35114e11i	−0.184992	−	0.176789i
$936$		0			0
$937$	−7.72786e11	+	7.72786e11i	−1.00254	+	1.00254i	−0.00254091	+	0.999997i	$0.500809\pi$
$937$	−7.72786e11	+	7.72786e11i	−1.00254	+	1.00254i	−0.999997	+	0.00254091i	$0.999191\pi$
$938$	−2.83655e10	−	2.83655e10i	−0.0366420	−	0.0366420i
$939$		0			0
$940$	−2.38108e11	+	2.49157e11i	−0.304973	+	0.319125i
$941$	6.91185e11			0.881528			0.440764	−	0.897623i	$-0.354708\pi$
$941$	6.91185e11			0.881528			0.440764	+	0.897623i	$0.354708\pi$
$942$		0			0
$943$	−3.31172e11	−	3.31172e11i	−0.418800	−	0.418800i
$944$		−	1.17194e10i		−	0.0147576i
$945$		0			0
$946$	1.16559e9			0.00145540
$947$	−6.05426e11	+	6.05426e11i	−0.752768	+	0.752768i	−0.974995	−	0.222227i	$-0.928667\pi$
$947$	−6.05426e11	+	6.05426e11i	−0.752768	+	0.752768i	0.222227	+	0.974995i	$0.428667\pi$
$948$		0			0
$949$		−	9.72066e11i		−	1.19848i
$950$	−3.07594e11	−	2.80892e11i	−0.377644	−	0.344861i
$951$		0			0
$952$	3.43424e10	−	3.43424e10i	0.0418103	−	0.0418103i
$953$	3.45330e11	+	3.45330e11i	0.418661	+	0.418661i	0.884742	−	0.466081i	$-0.154335\pi$
$953$	3.45330e11	+	3.45330e11i	0.418661	+	0.418661i	−0.466081	+	0.884742i	$0.654335\pi$
$954$		0			0
$955$	−1.08339e10	−	4.77781e11i	−0.0130248	−	0.574401i
$956$	−5.74532e11			−0.687832
$957$		0			0
$958$	−3.97343e10	−	3.97343e10i	−0.0471740	−	0.0471740i
$959$			5.49319e11i			0.649456i
$960$		0			0
$961$	7.00825e10			0.0821705
$962$	5.34222e10	−	5.34222e10i	0.0623766	−	0.0623766i
$963$		0			0
$964$		−	1.56542e10i		−	0.0181268i
$965$	−7.04648e10	+	7.37346e10i	−0.0812575	+	0.0850281i
$966$		0			0
$967$	−1.77273e10	+	1.77273e10i	−0.0202739	+	0.0202739i	−0.717171	−	0.696897i	$-0.754563\pi$
$967$	−1.77273e10	+	1.77273e10i	−0.0202739	+	0.0202739i	0.696897	+	0.717171i	$0.254563\pi$
$968$	3.53320e11	+	3.53320e11i	0.402408	+	0.402408i
$969$		0			0
$970$	−5.90084e11	+	1.33804e10i	−0.666541	+	0.0151141i
$971$	−1.52187e12			−1.71199			−0.855994	−	0.516986i	$-0.827054\pi$
$971$	−1.52187e12			−1.71199			−0.855994	+	0.516986i	$0.827054\pi$
$972$		0			0
$973$	−8.08294e10	−	8.08294e10i	−0.0901816	−	0.0901816i
$974$		−	3.11199e11i		−	0.345782i
$975$		0			0
$976$	−6.60938e11			−0.728385
$977$	−2.88131e11	+	2.88131e11i	−0.316237	+	0.316237i	−0.847320	−	0.531083i	$-0.821785\pi$
$977$	−2.88131e11	+	2.88131e11i	−0.316237	+	0.316237i	0.531083	+	0.847320i	$0.321785\pi$
$978$		0			0
$979$		−	9.50654e11i		−	1.03488i
$980$	−1.44617e10	−	6.37769e11i	−0.0156789	−	0.691448i
$981$		0			0
$982$	2.58120e11	−	2.58120e11i	0.277572	−	0.277572i
$983$	2.15222e9	+	2.15222e9i	0.00230501	+	0.00230501i	0.708258	−	0.705953i	$-0.249481\pi$
$983$	2.15222e9	+	2.15222e9i	0.00230501	+	0.00230501i	−0.705953	+	0.708258i	$0.749481\pi$
$984$		0			0
$985$	6.36078e10	+	6.07871e10i	0.0675718	+	0.0645753i
$986$	−1.26068e10			−0.0133382
$987$		0			0
$988$	9.28854e11	+	9.28854e11i	0.974810	+	0.974810i
$989$		−	1.78669e9i		−	0.00186751i
$990$		0			0
$991$	1.40286e10			0.0145452			0.00727261	−	0.999974i	$-0.497685\pi$
$991$	1.40286e10			0.0145452			0.00727261	+	0.999974i	$0.497685\pi$
$992$	6.69504e11	−	6.69504e11i	0.691363	−	0.691363i
$993$		0			0
$994$		−	5.71562e10i		−	0.0585488i
$995$	1.06965e12	−	2.42547e10i	1.09131	−	0.0247459i
$996$		0			0
$997$	7.09850e11	−	7.09850e11i	0.718433	−	0.718433i	−0.249851	−	0.968284i	$-0.580382\pi$
$997$	7.09850e11	−	7.09850e11i	0.718433	−	0.718433i	0.968284	+	0.249851i	$0.0803818\pi$
$998$	−1.13152e11	−	1.13152e11i	−0.114062	−	0.114062i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.9.g.a.28.2		6
3.2	odd	2		5.9.c.a.3.2	yes	6
5.2	odd	4	inner	45.9.g.a.37.2		6
12.11	even	2		80.9.p.c.33.1		6
15.2	even	4		5.9.c.a.2.2	✓	6
15.8	even	4		25.9.c.b.7.2		6
15.14	odd	2		25.9.c.b.18.2		6
60.47	odd	4		80.9.p.c.17.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.9.c.a.2.2	✓	6	15.2	even	4
5.9.c.a.3.2	yes	6	3.2	odd	2
25.9.c.b.7.2		6	15.8	even	4
25.9.c.b.18.2		6	15.14	odd	2
45.9.g.a.28.2		6	1.1	even	1	trivial
45.9.g.a.37.2		6	5.2	odd	4	inner
80.9.p.c.17.1		6	60.47	odd	4
80.9.p.c.33.1		6	12.11	even	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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.39608 - 4.39608i) q^{2} +217.349i q^{4} +(14.1685 + 624.839i) q^{5} +(730.992 - 730.992i) q^{7} +(2080.88 + 2080.88i) q^{8} +O(q^{10})\)	\(q+(4.39608 - 4.39608i) q^{2} +217.349i q^{4} +(14.1685 + 624.839i) q^{5} +(730.992 - 730.992i) q^{7} +(2080.88 + 2080.88i) q^{8} +(2809.13 + 2684.56i) q^{10} -19599.8 q^{11} +(-24915.1 - 24915.1i) q^{13} -6426.99i q^{14} -37346.0 q^{16} +(11288.6 - 11288.6i) q^{17} +171525. i q^{19} +(-135808. + 3079.51i) q^{20} +(-86162.2 + 86162.2i) q^{22} +(132074. + 132074. i) q^{23} +(-390224. + 17706.1i) q^{25} -219057. q^{26} +(158880. + 158880. i) q^{28} -127019. i q^{29} -960715. q^{31} +(-696880. + 696880. i) q^{32} -99251.5i q^{34} +(467110. + 446396. i) q^{35} +(-243873. + 243873. i) q^{37} +(754036. + 754036. i) q^{38} +(-1.27073e6 + 1.32970e6i) q^{40} -2.50747e6 q^{41} +(-6763.95 - 6763.95i) q^{43} -4.26000e6i q^{44} +1.16122e6 q^{46} +(1.79394e6 - 1.79394e6i) q^{47} +4.69610e6i q^{49} +(-1.63761e6 + 1.79329e6i) q^{50} +(5.41527e6 - 5.41527e6i) q^{52} +(2.97161e6 + 2.97161e6i) q^{53} +(-277700. - 1.22467e7i) q^{55} +3.04221e6 q^{56} +(-558385. - 558385. i) q^{58} +313805. i q^{59} +1.76977e7 q^{61} +(-4.22338e6 + 4.22338e6i) q^{62} -3.43349e6i q^{64} +(1.52149e7 - 1.59209e7i) q^{65} +(4.41349e6 - 4.41349e6i) q^{67} +(2.45358e6 + 2.45358e6i) q^{68} +(4.01584e6 - 91060.8i) q^{70} +8.89315e6 q^{71} +(1.95076e7 + 1.95076e7i) q^{73} +2.14417e6i q^{74} -3.72808e7 q^{76} +(-1.43273e7 + 1.43273e7i) q^{77} +1.11272e7i q^{79} +(-529136. - 2.33352e7i) q^{80} +(-1.10230e7 + 1.10230e7i) q^{82} +(-1.58712e7 - 1.58712e7i) q^{83} +(7.21353e6 + 6.89365e6i) q^{85} -59469.7 q^{86} +(-4.07848e7 - 4.07848e7i) q^{88} +4.85032e7i q^{89} -3.64255e7 q^{91} +(-2.87062e7 + 2.87062e7i) q^{92} -1.57726e7i q^{94} +(-1.07176e8 + 2.43025e6i) q^{95} +(-1.07411e8 + 1.07411e8i) q^{97} +(2.06444e7 + 2.06444e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8	\( 6 q + 2 q^{2} - 220 q^{5} - 2352 q^{7} + 8220 q^{8} + 30870 q^{10} - 23192 q^{11} - 119142 q^{13} + 218616 q^{16} + 265502 q^{17} - 412260 q^{20} - 35664 q^{22} - 28888 q^{23} - 340350 q^{25} + 801388 q^{26} + 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} + 4971680 q^{35} - 454002 q^{37} - 1443720 q^{38} + 2683500 q^{40} - 2489432 q^{41} + 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} - 29537650 q^{50} - 735732 q^{52} + 13509122 q^{53} + 4448040 q^{55} + 18454800 q^{56} - 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} + 30943610 q^{65} - 32827752 q^{67} - 8118692 q^{68} - 44156280 q^{70} + 13992928 q^{71} + 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 23045920 q^{80} + 38023056 q^{82} + 14768432 q^{83} - 19713030 q^{85} + 135560008 q^{86} - 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} - 239661000 q^{95} - 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 220 * q^5 - 2352 * q^7 + 8220 * q^8 + 30870 * q^10 - 23192 * q^11 - 119142 * q^13 + 218616 * q^16 + 265502 * q^17 - 412260 * q^20 - 35664 * q^22 - 28888 * q^23 - 340350 * q^25 + 801388 * q^26 + 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 + 4971680 * q^35 - 454002 * q^37 - 1443720 * q^38 + 2683500 * q^40 - 2489432 * q^41 + 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 - 29537650 * q^50 - 735732 * q^52 + 13509122 * q^53 + 4448040 * q^55 + 18454800 * q^56 - 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 + 30943610 * q^65 - 32827752 * q^67 - 8118692 * q^68 - 44156280 * q^70 + 13992928 * q^71 + 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 23045920 * q^80 + 38023056 * q^82 + 14768432 * q^83 - 19713030 * q^85 + 135560008 * q^86 - 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 - 239661000 * q^95 - 186656202 * q^97 + 345959698 * q^98

Introduction

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