LMFDB - Embedded newform 252.2.x.a.209.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.x (of order $6$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.6
Root			$0.604587 - 1.62311i$ of defining polynomial
Character	$\chi$	$=$	252.209
Dual form			252.2.x.a.41.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10336 + 1.33514i) q^{3} +(0.266780 + 0.462077i) q^{5} +(2.54716 + 0.715531i) q^{7} +(-0.565203 + 2.94628i) q^{9} +O(q^{10})$	\(q+(1.10336 + 1.33514i) q^{3} +(0.266780 + 0.462077i) q^{5} +(2.54716 + 0.715531i) q^{7} +(-0.565203 + 2.94628i) q^{9} +(-3.39936 - 1.96262i) q^{11} +(-0.116911 + 0.0674987i) q^{13} +(-0.322584 + 0.866025i) q^{15} +4.32533 q^{17} +2.22935i q^{19} +(1.85509 + 4.19030i) q^{21} +(-1.70375 + 0.983658i) q^{23} +(2.35766 - 4.08358i) q^{25} +(-4.55732 + 2.49617i) q^{27} +(-5.16548 - 2.98229i) q^{29} +(-0.800341 + 0.462077i) q^{31} +(-1.13033 - 6.70409i) q^{33} +(0.348901 + 1.36787i) q^{35} +7.79871 q^{37} +(-0.219115 - 0.0816177i) q^{39} +(-4.59027 - 7.95059i) q^{41} +(3.24544 - 5.62127i) q^{43} +(-1.51219 + 0.524841i) q^{45} +(-3.04329 + 5.27114i) q^{47} +(5.97603 + 3.64514i) q^{49} +(4.77238 + 5.77492i) q^{51} -11.0167i q^{53} -2.09435i q^{55} +(-2.97650 + 2.45977i) q^{57} +(-1.89588 - 3.28377i) q^{59} +(-9.35116 - 5.39889i) q^{61} +(-3.54781 + 7.10021i) q^{63} +(-0.0623791 - 0.0360146i) q^{65} +(-5.75701 - 9.97144i) q^{67} +(-3.19316 - 1.18941i) q^{69} +3.22884i q^{71} +0.381041i q^{73} +(8.05350 - 1.35785i) q^{75} +(-7.25438 - 7.43144i) q^{77} +(-4.60310 + 7.97280i) q^{79} +(-8.36109 - 3.33049i) q^{81} +(-1.28020 + 2.21737i) q^{83} +(1.15391 + 1.99863i) q^{85} +(-1.71759 - 10.1872i) q^{87} +17.1334 q^{89} +(-0.346088 + 0.0882763i) q^{91} +(-1.50000 - 0.558732i) q^{93} +(-1.03013 + 0.594746i) q^{95} +(13.6747 + 7.89507i) q^{97} +(7.70375 - 8.90616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 6 q^{11} - 12 q^{15} + 9 q^{21} + 6 q^{23} - 8 q^{25} - 12 q^{29} + 4 q^{37} + 18 q^{39} + 4 q^{43} - 5 q^{49} - 18 q^{51} - 42 q^{57} - 27 q^{63} - 24 q^{65} + 14 q^{67} - 21 q^{77} + 20 q^{79} - 36 q^{81} + 6 q^{85} - 18 q^{91} - 24 q^{93} - 60 q^{95} + 90 q^{99}+O(q^{100}) $ 16 * q - q^7 + 6 * q^11 - 12 * q^15 + 9 * q^21 + 6 * q^23 - 8 * q^25 - 12 * q^29 + 4 * q^37 + 18 * q^39 + 4 * q^43 - 5 * q^49 - 18 * q^51 - 42 * q^57 - 27 * q^63 - 24 * q^65 + 14 * q^67 - 21 * q^77 + 20 * q^79 - 36 * q^81 + 6 * q^85 - 18 * q^91 - 24 * q^93 - 60 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.10336	+	1.33514i	0.637024	+	0.770844i
$3$	1.10336	+	1.33514i	0.637024	+	0.770844i
$4$		0			0
$5$	0.266780	+	0.462077i	0.119308	+	0.206647i	0.919494	−	0.393105i	$-0.128599\pi$
$5$	0.266780	+	0.462077i	0.119308	+	0.206647i	−0.800186	+	0.599752i	$0.795266\pi$
$6$		0			0
$7$	2.54716	+	0.715531i	0.962735	+	0.270445i
$7$	2.54716	+	0.715531i	0.962735	+	0.270445i
$8$		0			0
$9$	−0.565203	+	2.94628i	−0.188401	+	0.982092i
$10$		0			0
$11$	−3.39936	−	1.96262i	−1.02494	−	0.591752i	−0.109412	−	0.993996i	$-0.534897\pi$
$11$	−3.39936	−	1.96262i	−1.02494	−	0.591752i	−0.915532	+	0.402245i	$0.868230\pi$
$12$		0			0
$13$	−0.116911	+	0.0674987i	−0.0324253	+	0.0187208i	−0.516125	−	0.856513i	$-0.672626\pi$
$13$	−0.116911	+	0.0674987i	−0.0324253	+	0.0187208i	0.483700	+	0.875234i	$0.339293\pi$
$14$		0			0
$15$	−0.322584	+	0.866025i	−0.0832908	+	0.223607i
$16$		0			0
$17$	4.32533			1.04905			0.524523	−	0.851396i	$-0.324244\pi$
$17$	4.32533			1.04905			0.524523	+	0.851396i	$0.324244\pi$
$18$		0			0
$19$			2.22935i			0.511448i	0.966750	+	0.255724i	$0.0823138\pi$
$19$			2.22935i			0.511448i	−0.966750	+	0.255724i	$0.917686\pi$
$20$		0			0
$21$	1.85509	+	4.19030i	0.404814	+	0.914399i
$22$		0			0
$23$	−1.70375	+	0.983658i	−0.355255	+	0.205107i	−0.666998	−	0.745060i	$-0.732421\pi$
$23$	−1.70375	+	0.983658i	−0.355255	+	0.205107i	0.311742	+	0.950167i	$0.399088\pi$
$24$		0			0
$25$	2.35766	−	4.08358i	0.471531	−	0.816716i
$26$		0			0
$27$	−4.55732	+	2.49617i	−0.877056	+	0.480388i
$28$		0			0
$29$	−5.16548	−	2.98229i	−0.959205	−	0.553798i	−0.0632771	−	0.997996i	$-0.520155\pi$
$29$	−5.16548	−	2.98229i	−0.959205	−	0.553798i	−0.895928	+	0.444198i	$0.853489\pi$
$30$		0			0
$31$	−0.800341	+	0.462077i	−0.143745	+	0.0829915i	−0.570148	−	0.821542i	$-0.693114\pi$
$31$	−0.800341	+	0.462077i	−0.143745	+	0.0829915i	0.426402	+	0.904534i	$0.359781\pi$
$32$		0			0
$33$	−1.13033	−	6.70409i	−0.196766	−	1.16703i
$34$		0			0
$35$	0.348901	+	1.36787i	0.0589751	+	0.231213i
$36$		0			0
$37$	7.79871			1.28210			0.641050	−	0.767499i	$-0.278499\pi$
$37$	7.79871			1.28210			0.641050	+	0.767499i	$0.278499\pi$
$38$		0			0
$39$	−0.219115	−	0.0816177i	−0.0350865	−	0.0130693i
$40$		0			0
$41$	−4.59027	−	7.95059i	−0.716880	−	1.24167i	−0.962230	−	0.272239i	$-0.912236\pi$
$41$	−4.59027	−	7.95059i	−0.716880	−	1.24167i	0.245349	−	0.969435i	$-0.421097\pi$
$42$		0			0
$43$	3.24544	−	5.62127i	0.494926	−	0.857236i	−0.505057	−	0.863086i	$-0.668529\pi$
$43$	3.24544	−	5.62127i	0.494926	−	0.857236i	0.999983	+	0.00584958i	$0.00186199\pi$
$44$		0			0
$45$	−1.51219	+	0.524841i	−0.225424	+	0.0782387i
$46$		0			0
$47$	−3.04329	+	5.27114i	−0.443910	+	0.768874i	−0.997976	−	0.0635985i	$-0.979742\pi$
$47$	−3.04329	+	5.27114i	−0.443910	+	0.768874i	0.554066	+	0.832473i	$0.313076\pi$
$48$		0			0
$49$	5.97603	+	3.64514i	0.853719	+	0.520734i
$50$		0			0
$51$	4.77238	+	5.77492i	0.668267	+	0.808651i
$52$		0			0
$53$		−	11.0167i		−	1.51326i	−0.653845	−	0.756628i	$-0.726845\pi$
$53$		−	11.0167i		−	1.51326i	0.653845	−	0.756628i	$-0.273155\pi$
$54$		0			0
$55$		−	2.09435i		−	0.282402i
$56$		0			0
$57$	−2.97650	+	2.45977i	−0.394246	+	0.325804i
$58$		0			0
$59$	−1.89588	−	3.28377i	−0.246823	−	0.427510i	0.715820	−	0.698285i	$-0.246053\pi$
$59$	−1.89588	−	3.28377i	−0.246823	−	0.427510i	−0.962643	+	0.270775i	$0.912720\pi$
$60$		0			0
$61$	−9.35116	−	5.39889i	−1.19729	−	0.691258i	−0.237342	−	0.971426i	$-0.576276\pi$
$61$	−9.35116	−	5.39889i	−1.19729	−	0.691258i	−0.959951	+	0.280168i	$0.909610\pi$
$62$		0			0
$63$	−3.54781	+	7.10021i	−0.446983	+	0.894543i
$64$		0			0
$65$	−0.0623791	−	0.0360146i	−0.00773718	−	0.00446706i
$66$		0			0
$67$	−5.75701	−	9.97144i	−0.703331	−	1.21820i	−0.967291	−	0.253671i	$-0.918362\pi$
$67$	−5.75701	−	9.97144i	−0.703331	−	1.21820i	0.263960	−	0.964534i	$-0.414971\pi$
$68$		0			0
$69$	−3.19316	−	1.18941i	−0.384412	−	0.143189i
$70$		0			0
$71$			3.22884i			0.383192i	0.981474	+	0.191596i	$0.0613664\pi$
$71$			3.22884i			0.383192i	−0.981474	+	0.191596i	$0.938634\pi$
$72$		0			0
$73$			0.381041i			0.0445975i	0.999751	+	0.0222988i	$0.00709850\pi$
$73$			0.381041i			0.0445975i	−0.999751	+	0.0222988i	$0.992901\pi$
$74$		0			0
$75$	8.05350	−	1.35785i	0.929938	−	0.156791i
$76$		0			0
$77$	−7.25438	−	7.43144i	−0.826714	−	0.846892i
$78$		0			0
$79$	−4.60310	+	7.97280i	−0.517889	+	0.897011i	0.481895	+	0.876229i	$0.339949\pi$
$79$	−4.60310	+	7.97280i	−0.517889	+	0.897011i	−0.999784	+	0.0207814i	$0.993385\pi$
$80$		0			0
$81$	−8.36109	−	3.33049i	−0.929010	−	0.370055i
$82$		0			0
$83$	−1.28020	+	2.21737i	−0.140520	+	0.243388i	−0.927693	−	0.373345i	$-0.878211\pi$
$83$	−1.28020	+	2.21737i	−0.140520	+	0.243388i	0.787172	+	0.616733i	$0.211544\pi$
$84$		0			0
$85$	1.15391	+	1.99863i	0.125159	+	0.216782i
$86$		0			0
$87$	−1.71759	−	10.1872i	−0.184145	−	1.09218i
$88$		0			0
$89$	17.1334			1.81614			0.908068	−	0.418822i	$-0.137557\pi$
$89$	17.1334			1.81614			0.908068	+	0.418822i	$0.137557\pi$
$90$		0			0
$91$	−0.346088	+	0.0882763i	−0.0362799	+	0.00925387i
$92$		0			0
$93$	−1.50000	−	0.558732i	−0.155543	−	0.0579378i
$94$		0			0
$95$	−1.03013	+	0.594746i	−0.105689	+	0.0610197i
$96$		0			0
$97$	13.6747	+	7.89507i	1.38845	+	0.801622i	0.993141	−	0.116925i	$-0.0373038\pi$
$97$	13.6747	+	7.89507i	1.38845	+	0.801622i	0.395310	+	0.918548i	$0.370637\pi$
$98$		0			0
$99$	7.70375	−	8.90616i	0.774256	−	0.895103i
$100$		0			0
$101$	−7.36862	+	12.7628i	−0.733205	+	1.26995i	0.222301	+	0.974978i	$0.428643\pi$
$101$	−7.36862	+	12.7628i	−0.733205	+	1.26995i	−0.955506	+	0.294970i	$0.904690\pi$
$102$		0			0
$103$	−11.1442	+	6.43410i	−1.09807	+	0.633970i	−0.935713	−	0.352762i	$-0.885243\pi$
$103$	−11.1442	+	6.43410i	−1.09807	+	0.633970i	−0.162356	+	0.986732i	$0.551909\pi$
$104$		0			0
$105$	−1.44134	+	1.97509i	−0.140660	+	0.192749i
$106$		0			0
$107$			15.7824i			1.52574i	0.646552	+	0.762870i	$0.276210\pi$
$107$			15.7824i			1.52574i	−0.646552	+	0.762870i	$0.723790\pi$
$108$		0			0
$109$	−3.08340			−0.295336			−0.147668	−	0.989037i	$-0.547177\pi$
$109$	−3.08340			−0.295336			−0.147668	+	0.989037i	$0.547177\pi$
$110$		0			0
$111$	8.60477	+	10.4124i	0.816728	+	0.988299i
$112$		0			0
$113$	7.96173	−	4.59671i	0.748977	−	0.432422i	−0.0763472	−	0.997081i	$-0.524326\pi$
$113$	7.96173	−	4.59671i	0.748977	−	0.432422i	0.825324	+	0.564659i	$0.190992\pi$
$114$		0			0
$115$	−0.909051	−	0.524841i	−0.0847694	−	0.0489417i
$116$		0			0
$117$	−0.132791	−	0.382603i	−0.0122765	−	0.0353717i
$118$		0			0
$119$	11.0173	+	3.09490i	1.00995	+	0.283709i
$120$		0			0
$121$	2.20375	+	3.81700i	0.200340	+	0.347000i
$122$		0			0
$123$	5.55044	−	14.9010i	0.500467	−	1.34358i
$124$		0			0
$125$	5.18371			0.463645
$126$		0			0
$127$	−10.1065			−0.896810			−0.448405	−	0.893831i	$-0.648008\pi$
$127$	−10.1065			−0.896810			−0.448405	+	0.893831i	$0.648008\pi$
$128$		0			0
$129$	11.0861	−	1.86915i	0.976075	−	0.164570i
$130$		0			0
$131$	7.81823	+	13.5416i	0.683082	+	1.18313i	0.974036	+	0.226395i	$0.0726940\pi$
$131$	7.81823	+	13.5416i	0.683082	+	1.18313i	−0.290954	+	0.956737i	$0.593973\pi$
$132$		0			0
$133$	−1.59517	+	5.67850i	−0.138319	+	0.492389i
$134$		0			0
$135$	−2.36922	−	1.43990i	−0.203910	−	0.123927i
$136$		0			0
$137$	2.13891	+	1.23490i	0.182739	+	0.105505i	0.588579	−	0.808440i	$-0.299688\pi$
$137$	2.13891	+	1.23490i	0.182739	+	0.105505i	−0.405840	+	0.913944i	$0.633021\pi$
$138$		0			0
$139$	16.8526	−	9.72984i	1.42942	−	0.825274i	0.432342	−	0.901710i	$-0.357687\pi$
$139$	16.8526	−	9.72984i	1.42942	−	0.825274i	0.997074	+	0.0764359i	$0.0243540\pi$
$140$		0			0
$141$	−10.3956	+	1.75273i	−0.875464	+	0.147606i
$142$		0			0
$143$	0.529897			0.0443122
$144$		0			0
$145$		−	3.18247i		−	0.264289i
$146$		0			0
$147$	1.72693	+	12.0007i	0.142434	+	0.989804i
$148$		0			0
$149$	13.7303	−	7.92720i	1.12483	−	0.649422i	0.182201	−	0.983261i	$-0.441678\pi$
$149$	13.7303	−	7.92720i	1.12483	−	0.649422i	0.942630	+	0.333840i	$0.108344\pi$
$150$		0			0
$151$	−4.16548	+	7.21482i	−0.338982	+	0.587134i	−0.984242	−	0.176829i	$-0.943416\pi$
$151$	−4.16548	+	7.21482i	−0.338982	+	0.587134i	0.645260	+	0.763963i	$0.276749\pi$
$152$		0			0
$153$	−2.44469	+	12.7436i	−0.197641	+	1.03026i
$154$		0			0
$155$	−0.427030	−	0.246546i	−0.0342999	−	0.0198031i
$156$		0			0
$157$	−7.73794	+	4.46750i	−0.617555	+	0.356545i	−0.775916	−	0.630836i	$-0.782712\pi$
$157$	−7.73794	+	4.46750i	−0.617555	+	0.356545i	0.158362	+	0.987381i	$0.449379\pi$
$158$		0			0
$159$	14.7088	−	12.1553i	1.16649	−	0.963981i
$160$		0			0
$161$	−5.04355	+	1.28645i	−0.397487	+	0.101386i
$162$		0			0
$163$	−14.2062			−1.11272			−0.556358	−	0.830943i	$-0.687802\pi$
$163$	−14.2062			−1.11272			−0.556358	+	0.830943i	$0.687802\pi$
$164$		0			0
$165$	2.79625	−	2.31082i	0.217688	−	0.179897i
$166$		0			0
$167$	−6.27308	−	10.8653i	−0.485425	−	0.840781i	0.514434	−	0.857530i	$-0.328002\pi$
$167$	−6.27308	−	10.8653i	−0.485425	−	0.840781i	−0.999860	+	0.0167485i	$0.994669\pi$
$168$		0			0
$169$	−6.49089	+	11.2425i	−0.499299	+	0.864811i
$170$		0			0
$171$	−6.56828	−	1.26004i	−0.502289	−	0.0963573i
$172$		0			0
$173$	−10.6787	+	18.4960i	−0.811886	+	1.40623i	0.0996566	+	0.995022i	$0.468226\pi$
$173$	−10.6787	+	18.4960i	−0.811886	+	1.40623i	−0.911543	+	0.411206i	$0.865108\pi$
$174$		0			0
$175$	8.92725	−	8.71455i	0.674837	−	0.658758i
$176$		0			0
$177$	2.29245	−	6.15444i	0.172311	−	0.462596i
$178$		0			0
$179$			5.81113i			0.434344i	0.976133	+	0.217172i	$0.0696833\pi$
$179$			5.81113i			0.434344i	−0.976133	+	0.217172i	$0.930317\pi$
$180$		0			0
$181$			7.38877i			0.549203i	0.961558	+	0.274602i	$0.0885460\pi$
$181$			7.38877i			0.549203i	−0.961558	+	0.274602i	$0.911454\pi$
$182$		0			0
$183$	−3.10939	−	18.4420i	−0.229853	−	1.36327i
$184$		0			0
$185$	2.08054	+	3.60360i	0.152964	+	0.264942i
$186$		0			0
$187$	−14.7033	−	8.48897i	−1.07521	−	0.620775i
$188$		0			0
$189$	−13.3943	+	3.09724i	−0.974291	+	0.225291i
$190$		0			0
$191$	6.86109	+	3.96125i	0.496451	+	0.286626i	0.727247	−	0.686376i	$-0.240800\pi$
$191$	6.86109	+	3.96125i	0.496451	+	0.286626i	−0.230796	+	0.973002i	$0.574133\pi$
$192$		0			0
$193$	3.16548	+	5.48277i	0.227856	+	0.394659i	0.957173	−	0.289518i	$-0.0934951\pi$
$193$	3.16548	+	5.48277i	0.227856	+	0.394659i	−0.729316	+	0.684177i	$0.760162\pi$
$194$		0			0
$195$	−0.0207419	−	0.123022i	−0.00148536	−	0.00880979i
$196$		0			0
$197$			15.1580i			1.07996i	0.841677	+	0.539981i	$0.181569\pi$
$197$			15.1580i			1.07996i	−0.841677	+	0.539981i	$0.818431\pi$
$198$		0			0
$199$		−	8.55084i		−	0.606153i	−0.952966	−	0.303076i	$-0.901986\pi$
$199$		−	8.55084i		−	0.606153i	0.952966	−	0.303076i	$-0.0980137\pi$
$200$		0			0
$201$	6.96123	−	18.6885i	0.491007	−	1.31818i
$202$		0			0
$203$	−11.0234	−	11.2924i	−0.773689	−	0.792573i
$204$		0			0
$205$	2.44919	−	4.24212i	0.171059	−	0.296282i
$206$		0			0
$207$	−1.93516	−	5.57567i	−0.134503	−	0.387536i
$208$		0			0
$209$	4.37536	−	7.57835i	0.302650	−	0.524205i
$210$		0			0
$211$	−2.80782	−	4.86329i	−0.193299	−	0.334803i	0.753043	−	0.657971i	$-0.228585\pi$
$211$	−2.80782	−	4.86329i	−0.193299	−	0.334803i	−0.946341	+	0.323169i	$0.895252\pi$
$212$		0			0
$213$	−4.31095	+	3.56256i	−0.295382	+	0.244103i
$214$		0			0
$215$	3.46328			0.236194
$216$		0			0
$217$	−2.36922	+	0.604315i	−0.160833	+	0.0410236i
$218$		0			0
$219$	−0.508744	+	0.420425i	−0.0343777	+	0.0284097i
$220$		0			0
$221$	−0.505679	+	0.291954i	−0.0340156	+	0.0196389i
$222$		0			0
$223$	−6.00510	−	3.46705i	−0.402131	−	0.232171i	0.285272	−	0.958447i	$-0.407916\pi$
$223$	−6.00510	−	3.46705i	−0.402131	−	0.232171i	−0.687403	+	0.726276i	$0.741249\pi$
$224$		0			0
$225$	10.6988	+	9.25436i	0.713254	+	0.616957i
$226$		0			0
$227$	7.28833	−	12.6238i	0.483743	−	0.837868i	−0.516082	−	0.856539i	$-0.672610\pi$
$227$	7.28833	−	12.6238i	0.483743	−	0.837868i	0.999826	+	0.0186708i	$0.00594345\pi$
$228$		0			0
$229$	−21.2722	+	12.2815i	−1.40571	+	0.811586i	−0.994971	−	0.100167i	$-0.968062\pi$
$229$	−21.2722	+	12.2815i	−1.40571	+	0.811586i	−0.410738	+	0.911753i	$0.634729\pi$
$230$		0			0
$231$	1.91785	−	17.8852i	0.126185	−	1.17676i
$232$		0			0
$233$		−	10.5142i		−	0.688808i	−0.938822	−	0.344404i	$-0.888081\pi$
$233$		−	10.5142i		−	0.688808i	0.938822	−	0.344404i	$-0.111919\pi$
$234$		0			0
$235$	−3.24756			−0.211848
$236$		0			0
$237$	−15.7237	+	2.65107i	−1.02136	+	0.172205i
$238$		0			0
$239$	16.9075	−	9.76154i	1.09365	−	0.631422i	0.159108	−	0.987261i	$-0.449138\pi$
$239$	16.9075	−	9.76154i	1.09365	−	0.631422i	0.934547	+	0.355839i	$0.115805\pi$
$240$		0			0
$241$	−11.3780	−	6.56909i	−0.732922	−	0.423152i	0.0865685	−	0.996246i	$-0.472410\pi$
$241$	−11.3780	−	6.56909i	−0.732922	−	0.423152i	−0.819490	+	0.573093i	$0.805743\pi$
$242$		0			0
$243$	−4.77860	−	14.8380i	−0.306547	−	0.951855i
$244$		0			0
$245$	−0.0900476	+	3.73384i	−0.00575293	+	0.238546i
$246$		0			0
$247$	−0.150478	−	0.260636i	−0.00957469	−	0.0165838i
$248$		0			0
$249$	−4.37303	+	0.737307i	−0.277129	+	0.0467249i
$250$		0			0
$251$	−22.6864			−1.43195			−0.715977	−	0.698124i	$-0.754019\pi$
$251$	−22.6864			−1.43195			−0.715977	+	0.698124i	$0.754019\pi$
$252$		0			0
$253$	7.72218			0.485489
$254$		0			0
$255$	−1.39528	+	3.74584i	−0.0873758	+	0.234574i
$256$		0			0
$257$	6.80481	+	11.7863i	0.424472	+	0.735207i	0.996371	−	0.0851169i	$-0.0271264\pi$
$257$	6.80481	+	11.7863i	0.424472	+	0.735207i	−0.571899	+	0.820324i	$0.693793\pi$
$258$		0			0
$259$	19.8646	+	5.58022i	1.23432	+	0.346738i
$260$		0			0
$261$	11.7062	−	13.5333i	0.724596	−	0.837692i
$262$		0			0
$263$	19.7930	+	11.4275i	1.22049	+	0.704651i	0.965023	−	0.262167i	$-0.0844371\pi$
$263$	19.7930	+	11.4275i	1.22049	+	0.704651i	0.255468	+	0.966817i	$0.417770\pi$
$264$		0			0
$265$	5.09055	−	2.93903i	0.312710	−	0.180543i
$266$		0			0
$267$	18.9043	+	22.8755i	1.15692	+	1.39996i
$268$		0			0
$269$	10.6775			0.651018			0.325509	−	0.945539i	$-0.394464\pi$
$269$	10.6775			0.651018			0.325509	+	0.945539i	$0.394464\pi$
$270$		0			0
$271$		−	4.51473i		−	0.274251i	−0.990554	−	0.137125i	$-0.956214\pi$
$271$		−	4.51473i		−	0.274251i	0.990554	−	0.137125i	$-0.0437863\pi$
$272$		0			0
$273$	−0.499721	−	0.364677i	−0.0302445	−	0.0220712i
$274$		0			0
$275$	−16.0290	+	9.25436i	−0.966587	+	0.558059i
$276$		0			0
$277$	3.34952	−	5.80154i	0.201253	−	0.348581i	−0.747679	−	0.664060i	$-0.768832\pi$
$277$	3.34952	−	5.80154i	0.201253	−	0.348581i	0.948932	+	0.315479i	$0.102165\pi$
$278$		0			0
$279$	−0.909051	−	2.61919i	−0.0544235	−	0.156807i
$280$		0			0
$281$	−15.1414	−	8.74187i	−0.903258	−	0.521496i	−0.0250023	−	0.999687i	$-0.507959\pi$
$281$	−15.1414	−	8.74187i	−0.903258	−	0.521496i	−0.878256	+	0.478191i	$0.841293\pi$
$282$		0			0
$283$	−7.42049	+	4.28422i	−0.441102	+	0.254670i	−0.704065	−	0.710135i	$-0.748634\pi$
$283$	−7.42049	+	4.28422i	−0.441102	+	0.254670i	0.262963	+	0.964806i	$0.415300\pi$
$284$		0			0
$285$	−1.93067	−	0.719152i	−0.114363	−	0.0425989i
$286$		0			0
$287$	−6.00327	−	23.5359i	−0.354362	−	1.38928i
$288$		0			0
$289$	1.70845			0.100497
$290$		0			0
$291$	4.54701	+	26.9687i	0.266550	+	1.58093i
$292$		0			0
$293$	−12.1436	−	21.0333i	−0.709434	−	1.22878i	−0.965067	−	0.262002i	$-0.915617\pi$
$293$	−12.1436	−	21.0333i	−0.709434	−	1.22878i	0.255633	−	0.966774i	$-0.417716\pi$
$294$		0			0
$295$	1.01157	−	1.75209i	0.0588958	−	0.102010i
$296$		0			0
$297$	20.3910	+	0.458904i	1.18320	+	0.0266283i
$298$		0			0
$299$	0.132791	−	0.230001i	0.00767951	−	0.0133013i
$300$		0			0
$301$	12.2889	−	11.9961i	0.708318	−	0.691441i
$302$		0			0
$303$	−25.1704	+	4.24381i	−1.44600	+	0.243801i
$304$		0			0
$305$		−	5.76127i		−	0.329890i
$306$		0			0
$307$		−	12.4777i		−	0.712139i	−0.934460	−	0.356069i	$-0.884117\pi$
$307$		−	12.4777i		−	0.712139i	0.934460	−	0.356069i	$-0.115883\pi$
$308$		0			0
$309$	−20.8864	−	7.77994i	−1.18819	−	0.442586i
$310$		0			0
$311$	9.07984	+	15.7267i	0.514871	+	0.891782i	0.999851	+	0.0172571i	$0.00549339\pi$
$311$	9.07984	+	15.7267i	0.514871	+	0.891782i	−0.484980	+	0.874525i	$0.661173\pi$
$312$		0			0
$313$	−2.76700	−	1.59753i	−0.156400	−	0.0902977i	0.419757	−	0.907636i	$-0.362115\pi$
$313$	−2.76700	−	1.59753i	−0.156400	−	0.0902977i	−0.576157	+	0.817339i	$0.695449\pi$
$314$		0			0
$315$	−4.22733	+	0.254834i	−0.238183	+	0.0143582i
$316$		0			0
$317$	−22.5893	−	13.0419i	−1.26874	−	0.732508i	−0.293991	−	0.955808i	$-0.594984\pi$
$317$	−22.5893	−	13.0419i	−1.26874	−	0.732508i	−0.974750	+	0.223300i	$0.928317\pi$
$318$		0			0
$319$	11.7062	+	20.2757i	0.655421	+	1.13522i
$320$		0			0
$321$	−21.0717	+	17.4136i	−1.17611	+	0.971933i
$322$		0			0
$323$			9.64266i			0.536532i
$324$		0			0
$325$			0.636555i			0.0353097i
$326$		0			0
$327$	−3.40209	−	4.11677i	−0.188136	−	0.227658i
$328$		0			0
$329$	−11.5234	+	11.2489i	−0.635306	+	0.620169i
$330$		0			0
$331$	8.06484	−	13.9687i	0.443283	−	0.767789i	−0.554647	−	0.832085i	$-0.687147\pi$
$331$	8.06484	−	13.9687i	0.443283	−	0.767789i	0.997931	+	0.0642960i	$0.0204802\pi$
$332$		0			0
$333$	−4.40786	+	22.9772i	−0.241549	+	1.25914i
$334$		0			0
$335$	3.07171	−	5.32036i	0.167826	−	0.290683i
$336$		0			0
$337$	−4.16548	−	7.21482i	−0.226908	−	0.393016i	0.729982	−	0.683466i	$-0.239528\pi$
$337$	−4.16548	−	7.21482i	−0.226908	−	0.393016i	−0.956890	+	0.290450i	$0.906195\pi$
$338$		0			0
$339$	14.9219	+	5.55822i	0.810446	+	0.301881i
$340$		0			0
$341$	3.62752			0.196441
$342$		0			0
$343$	12.6137	+	13.5608i	0.681075	+	0.732213i
$344$		0			0
$345$	−0.302272	−	1.79280i	−0.0162738	−	0.0965210i
$346$		0			0
$347$	−30.1403	+	17.4015i	−1.61801	+	0.934161i	−0.630581	+	0.776124i	$0.717183\pi$
$347$	−30.1403	+	17.4015i	−1.61801	+	0.934161i	−0.987433	+	0.158037i	$0.949483\pi$
$348$		0			0
$349$	19.6825	+	11.3637i	1.05358	+	0.608283i	0.923649	−	0.383240i	$-0.125192\pi$
$349$	19.6825	+	11.3637i	1.05358	+	0.608283i	0.129929	+	0.991523i	$0.458525\pi$
$350$		0			0
$351$	0.364313	−	0.599443i	0.0194456	−	0.0319959i
$352$		0			0
$353$	−4.02829	+	6.97721i	−0.214404	+	0.371359i	−0.953088	−	0.302693i	$-0.902114\pi$
$353$	−4.02829	+	6.97721i	−0.214404	+	0.371359i	0.738684	+	0.674052i	$0.235448\pi$
$354$		0			0
$355$	−1.49197	+	0.861390i	−0.0791856	+	0.0457178i
$356$		0			0
$357$	8.02388	+	18.1244i	0.424669	+	0.959246i
$358$		0			0
$359$		−	17.8217i		−	0.940594i	−0.882508	−	0.470297i	$-0.844147\pi$
$359$		−	17.8217i		−	0.940594i	0.882508	−	0.470297i	$-0.155853\pi$
$360$		0			0
$361$	14.0300			0.738421
$362$		0			0
$363$	−2.66471	+	7.15383i	−0.139861	+	0.375478i
$364$		0			0
$365$	−0.176070	+	0.101654i	−0.00921594	+	0.00532083i
$366$		0			0
$367$	20.5888	+	11.8870i	1.07473	+	0.620494i	0.929469	−	0.368900i	$-0.120266\pi$
$367$	20.5888	+	11.8870i	1.07473	+	0.620494i	0.145258	+	0.989394i	$0.453599\pi$
$368$		0			0
$369$	26.0191	−	9.03052i	1.35450	−	0.470110i
$370$		0			0
$371$	7.88277	−	28.0612i	0.409253	−	1.45687i
$372$		0			0
$373$	−5.26858	−	9.12545i	−0.272797	−	0.472498i	0.696780	−	0.717285i	$-0.254615\pi$
$373$	−5.26858	−	9.12545i	−0.272797	−	0.472498i	−0.969577	+	0.244787i	$0.921282\pi$
$374$		0			0
$375$	5.71948	+	6.92098i	0.295353	+	0.357398i
$376$		0			0
$377$	0.805203			0.0414700
$378$		0			0
$379$	24.0049			1.23305			0.616525	−	0.787336i	$-0.288540\pi$
$379$	24.0049			1.23305			0.616525	+	0.787336i	$0.288540\pi$
$380$		0			0
$381$	−11.1511	−	13.4936i	−0.571289	−	0.691301i
$382$		0			0
$383$	18.0980	+	31.3466i	0.924764	+	1.60174i	0.791941	+	0.610598i	$0.209071\pi$
$383$	18.0980	+	31.3466i	0.924764	+	1.60174i	0.132823	+	0.991140i	$0.457596\pi$
$384$		0			0
$385$	1.49857	−	5.33465i	0.0763743	−	0.271879i
$386$		0			0
$387$	14.7275	+	12.7391i	0.748640	+	0.647567i
$388$		0			0
$389$	18.6031	+	10.7405i	0.943215	+	0.544565i	0.890967	−	0.454069i	$-0.150028\pi$
$389$	18.6031	+	10.7405i	0.943215	+	0.544565i	0.0522481	+	0.998634i	$0.483361\pi$
$390$		0			0
$391$	−7.36925	+	4.25464i	−0.372679	+	0.215166i
$392$		0			0
$393$	−9.45360	+	25.3796i	−0.476871	+	1.28023i
$394$		0			0
$395$	−4.91207			−0.247153
$396$		0			0
$397$			21.3049i			1.06926i	0.845086	+	0.534630i	$0.179549\pi$
$397$			21.3049i			1.06926i	−0.845086	+	0.534630i	$0.820451\pi$
$398$		0			0
$399$	−9.34165	+	4.13565i	−0.467667	+	0.207041i
$400$		0			0
$401$	15.6821	−	9.05406i	0.783126	−	0.452138i	−0.0544110	−	0.998519i	$-0.517328\pi$
$401$	15.6821	−	9.05406i	0.783126	−	0.452138i	0.837537	+	0.546381i	$0.183995\pi$
$402$		0			0
$403$	0.0623791	−	0.108044i	0.00310733	−	0.00538205i
$404$		0			0
$405$	−0.691630	−	4.75198i	−0.0343674	−	0.236128i
$406$		0			0
$407$	−26.5106	−	15.3059i	−1.31408	−	0.758685i
$408$		0			0
$409$	17.6807	−	10.2080i	0.874254	−	0.504751i	0.00549461	−	0.999985i	$-0.498251\pi$
$409$	17.6807	−	10.2080i	0.874254	−	0.504751i	0.868760	+	0.495234i	$0.164918\pi$
$410$		0			0
$411$	0.711217	+	4.21828i	0.0350817	+	0.208073i
$412$		0			0
$413$	−2.47948	−	9.72083i	−0.122007	−	0.478331i
$414$		0			0
$415$	−1.36613			−0.0670607
$416$		0			0
$417$	31.5851	+	11.7651i	1.54673	+	0.576138i
$418$		0			0
$419$	12.6789	+	21.9606i	0.619407	+	1.07284i	0.989594	+	0.143887i	$0.0459602\pi$
$419$	12.6789	+	21.9606i	0.619407	+	1.07284i	−0.370187	+	0.928957i	$0.620706\pi$
$420$		0			0
$421$	−3.21875	+	5.57503i	−0.156872	+	0.271710i	−0.933739	−	0.357954i	$-0.883474\pi$
$421$	−3.21875	+	5.57503i	−0.156872	+	0.271710i	0.776867	+	0.629665i	$0.216808\pi$
$422$		0			0
$423$	−13.8102	−	11.9456i	−0.671472	−	0.580817i
$424$		0			0
$425$	10.1976	−	17.6628i	0.494658	−	0.856773i
$426$		0			0
$427$	−19.9558	−	20.4429i	−0.965729	−	0.989300i
$428$		0			0
$429$	0.584665	+	0.707487i	0.0282279	+	0.0341578i
$430$		0			0
$431$		−	15.1392i		−	0.729230i	−0.931158	−	0.364615i	$-0.881201\pi$
$431$		−	15.1392i		−	0.729230i	0.931158	−	0.364615i	$-0.118799\pi$
$432$		0			0
$433$			8.44792i			0.405981i	0.979181	+	0.202991i	$0.0650661\pi$
$433$			8.44792i			0.405981i	−0.979181	+	0.202991i	$0.934934\pi$
$434$		0			0
$435$	4.24904	−	3.51140i	0.203726	−	0.168359i
$436$		0			0
$437$	−2.19292	−	3.79824i	−0.104901	−	0.181695i
$438$		0			0
$439$	−23.6831	−	13.6734i	−1.13033	−	0.652598i	−0.186314	−	0.982490i	$-0.559654\pi$
$439$	−23.6831	−	13.6734i	−1.13033	−	0.652598i	−0.944018	+	0.329893i	$0.892987\pi$
$440$		0			0
$441$	−14.1173	+	15.5468i	−0.672251	+	0.740324i
$442$		0			0
$443$	−14.6520	−	8.45931i	−0.696135	−	0.401914i	0.109771	−	0.993957i	$-0.464988\pi$
$443$	−14.6520	−	8.45931i	−0.696135	−	0.401914i	−0.805906	+	0.592043i	$0.798322\pi$
$444$		0			0
$445$	4.57085	+	7.91695i	0.216679	+	0.375299i
$446$		0			0
$447$	25.7334	+	9.58537i	1.21715	+	0.453372i
$448$		0			0
$449$			22.5985i			1.06649i	0.845962	+	0.533244i	$0.179027\pi$
$449$			22.5985i			1.06649i	−0.845962	+	0.533244i	$0.820973\pi$
$450$		0			0
$451$			36.0358i			1.69686i
$452$		0			0
$453$	−14.2288	+	2.39903i	−0.668528	+	0.112716i
$454$		0			0
$455$	−0.133120	−	0.136369i	−0.00624076	−	0.00639308i
$456$		0			0
$457$	17.4018	−	30.1408i	0.814022	−	1.40993i	−0.0960053	−	0.995381i	$-0.530607\pi$
$457$	17.4018	−	30.1408i	0.814022	−	1.40993i	0.910028	−	0.414547i	$-0.136060\pi$
$458$		0			0
$459$	−19.7119	+	10.7968i	−0.920072	+	0.503949i
$460$		0			0
$461$	13.8264	−	23.9479i	0.643958	−	1.11537i	−0.340584	−	0.940214i	$-0.610625\pi$
$461$	13.8264	−	23.9479i	0.643958	−	1.11537i	0.984541	−	0.175153i	$-0.0560420\pi$
$462$		0			0
$463$	10.6272	+	18.4069i	0.493889	+	0.855440i	0.999975	−	0.00704260i	$-0.00224175\pi$
$463$	10.6272	+	18.4069i	0.493889	+	0.855440i	−0.506087	+	0.862483i	$0.668908\pi$
$464$		0			0
$465$	−0.141993	−	0.842174i	−0.00658478	−	0.0390549i
$466$		0			0
$467$	−8.80757			−0.407566			−0.203783	−	0.979016i	$-0.565324\pi$
$467$	−8.80757			−0.407566			−0.203783	+	0.979016i	$0.565324\pi$
$468$		0			0
$469$	−7.52915	−	29.5181i	−0.347664	−	1.36302i
$470$		0			0
$471$	−14.5025	−	5.40199i	−0.668238	−	0.248910i
$472$		0			0
$473$	−22.0648	+	12.7391i	−1.01454	+	0.585746i
$474$		0			0
$475$	9.10373	+	5.25604i	0.417708	+	0.241164i
$476$		0			0
$477$	32.4582	+	6.22666i	1.48616	+	0.285099i
$478$		0			0
$479$	6.83139	−	11.8323i	0.312134	−	0.540633i	−0.666690	−	0.745335i	$-0.732289\pi$
$479$	6.83139	−	11.8323i	0.312134	−	0.540633i	0.978824	+	0.204703i	$0.0656227\pi$
$480$		0			0
$481$	−0.911756	+	0.526403i	−0.0415725	+	0.0240019i
$482$		0			0
$483$	−7.28243	−	5.31443i	−0.331362	−	0.241815i
$484$		0			0
$485$			8.42499i			0.382559i
$486$		0			0
$487$	16.6206			0.753149			0.376575	−	0.926386i	$-0.377102\pi$
$487$	16.6206			0.753149			0.376575	+	0.926386i	$0.377102\pi$
$488$		0			0
$489$	−15.6745	−	18.9673i	−0.708826	−	0.857730i
$490$		0			0
$491$	17.8129	−	10.2843i	0.803883	−	0.464122i	−0.0409440	−	0.999161i	$-0.513037\pi$
$491$	17.8129	−	10.2843i	0.803883	−	0.464122i	0.844827	+	0.535039i	$0.179703\pi$
$492$		0			0
$493$	−22.3424	−	12.8994i	−1.00625	−	0.580959i
$494$		0			0
$495$	6.17054	+	1.18373i	0.277345	+	0.0532049i
$496$		0			0
$497$	−2.31033	+	8.22436i	−0.103633	+	0.368913i
$498$		0			0
$499$	1.34609	+	2.33149i	0.0602592	+	0.104372i	0.894581	−	0.446905i	$-0.147474\pi$
$499$	1.34609	+	2.33149i	0.0602592	+	0.104372i	−0.834322	+	0.551277i	$0.814141\pi$
$500$		0			0
$501$	7.58524	−	20.3637i	0.338884	−	0.909785i
$502$		0			0
$503$	−27.3871			−1.22113			−0.610566	−	0.791965i	$-0.709058\pi$
$503$	−27.3871			−1.22113			−0.610566	+	0.791965i	$0.709058\pi$
$504$		0			0
$505$	−7.86321			−0.349908
$506$		0			0
$507$	−22.1722	+	3.73830i	−0.984700	+	0.166024i
$508$		0			0
$509$	−2.96117	−	5.12890i	−0.131252	−	0.227334i	0.792908	−	0.609342i	$-0.208566\pi$
$509$	−2.96117	−	5.12890i	−0.131252	−	0.227334i	−0.924159	+	0.382007i	$0.875233\pi$
$510$		0			0
$511$	−0.272647	+	0.970572i	−0.0120612	+	0.0429356i
$512$		0			0
$513$	−5.56484	−	10.1598i	−0.245693	−	0.448568i
$514$		0			0
$515$	−5.94609	−	3.43298i	−0.262016	−	0.151275i
$516$		0			0
$517$	20.6905	−	11.9456i	0.909966	−	0.525369i
$518$		0			0
$519$	−36.4772	+	6.15019i	−1.60117	+	0.269963i
$520$		0			0
$521$	−39.1886			−1.71688			−0.858442	−	0.512911i	$-0.828567\pi$
$521$	−39.1886			−1.71688			−0.858442	+	0.512911i	$0.828567\pi$
$522$		0			0
$523$		−	23.0358i		−	1.00728i	−0.863912	−	0.503642i	$-0.831993\pi$
$523$		−	23.0358i		−	1.00728i	0.863912	−	0.503642i	$-0.168007\pi$
$524$		0			0
$525$	21.4851	+	2.30387i	0.937687	+	0.100549i
$526$		0			0
$527$	−3.46173	+	1.99863i	−0.150796	+	0.0870618i
$528$		0			0
$529$	−9.56484	+	16.5668i	−0.415862	+	0.720295i
$530$		0			0
$531$	10.7464	−	3.72980i	0.466356	−	0.161860i
$532$		0			0
$533$	1.07331	+	0.619675i	0.0464901	+	0.0268411i
$534$		0			0
$535$	−7.29267	+	4.21043i	−0.315290	+	0.182033i
$536$		0			0
$537$	−7.75868	+	6.41176i	−0.334812	+	0.276688i
$538$		0			0
$539$	−13.1606	−	24.1198i	−0.566869	−	1.03891i
$540$		0			0
$541$	−3.32605			−0.142998			−0.0714990	−	0.997441i	$-0.522778\pi$
$541$	−3.32605			−0.142998			−0.0714990	+	0.997441i	$0.522778\pi$
$542$		0			0
$543$	−9.86505	+	8.15246i	−0.423350	+	0.349856i
$544$		0			0
$545$	−0.822590	−	1.42477i	−0.0352359	−	0.0610303i
$546$		0			0
$547$	13.8937	−	24.0646i	0.594051	−	1.02893i	−0.399629	−	0.916677i	$-0.630861\pi$
$547$	13.8937	−	24.0646i	0.594051	−	1.02893i	0.993680	−	0.112249i	$-0.0358055\pi$
$548$		0			0
$549$	21.1919	−	24.4996i	0.904450	−	1.04562i
$550$		0			0
$551$	6.64857	−	11.5157i	0.283238	−	0.490583i
$552$		0			0
$553$	−17.4296	+	17.0143i	−0.741182	+	0.723523i
$554$		0			0
$555$	−2.51574	+	6.75388i	−0.106787	+	0.286686i
$556$		0			0
$557$			3.61667i			0.153243i	0.997060	+	0.0766216i	$0.0244133\pi$
$557$			3.61667i			0.153243i	−0.997060	+	0.0766216i	$0.975587\pi$
$558$		0			0
$559$			0.876252i			0.0370615i
$560$		0			0
$561$	−4.88906	−	28.9974i	−0.206416	−	1.22427i
$562$		0			0
$563$	4.75452	+	8.23506i	0.200379	+	0.347067i	0.948651	−	0.316326i	$-0.102449\pi$
$563$	4.75452	+	8.23506i	0.200379	+	0.347067i	−0.748272	+	0.663393i	$0.769116\pi$
$564$		0			0
$565$	4.24807	+	2.45262i	0.178718	+	0.103183i
$566$		0			0
$567$	−18.9140	−	14.4659i	−0.794311	−	0.607511i
$568$		0			0
$569$	9.09742	+	5.25240i	0.381384	+	0.220192i	0.678420	−	0.734674i	$-0.262665\pi$
$569$	9.09742	+	5.25240i	0.381384	+	0.220192i	−0.297036	+	0.954866i	$0.595998\pi$
$570$		0			0
$571$	−2.24201	−	3.88328i	−0.0938252	−	0.162510i	0.815292	−	0.579049i	$-0.196576\pi$
$571$	−2.24201	−	3.88328i	−0.0938252	−	0.162510i	−0.909118	+	0.416539i	$0.863243\pi$
$572$		0			0
$573$	2.28141	+	13.5312i	0.0953071	+	0.565274i
$574$		0			0
$575$			9.27651i			0.386857i
$576$		0			0
$577$		−	47.1812i		−	1.96418i	−0.188410	−	0.982090i	$-0.560333\pi$
$577$		−	47.1812i		−	1.96418i	0.188410	−	0.982090i	$-0.439667\pi$
$578$		0			0
$579$	−3.82762	+	10.2758i	−0.159070	+	0.427049i
$580$		0			0
$581$	−4.84747	+	4.73198i	−0.201107	+	0.196316i
$582$		0			0
$583$	−21.6215	+	37.4496i	−0.895473	+	1.55100i
$584$		0			0
$585$	0.141366	−	0.163431i	0.00584476	−	0.00675702i
$586$		0			0
$587$	−5.65373	+	9.79255i	−0.233354	+	0.404182i	−0.958793	−	0.284105i	$-0.908304\pi$
$587$	−5.65373	+	9.79255i	−0.233354	+	0.404182i	0.725439	+	0.688287i	$0.241637\pi$
$588$		0			0
$589$	−1.03013	−	1.78424i	−0.0424458	−	0.0735183i
$590$		0			0
$591$	−20.2381	+	16.7247i	−0.832483	+	0.687962i
$592$		0			0
$593$	−9.44980			−0.388057			−0.194028	−	0.980996i	$-0.562155\pi$
$593$	−9.44980			−0.388057			−0.194028	+	0.980996i	$0.562155\pi$
$594$		0			0
$595$	1.50911	+	5.91649i	0.0618676	+	0.242553i
$596$		0			0
$597$	11.4166	−	9.43463i	0.467249	−	0.386134i
$598$		0			0
$599$	31.6406	−	18.2677i	1.29280	−	0.746398i	0.313650	−	0.949539i	$-0.398448\pi$
$599$	31.6406	−	18.2677i	1.29280	−	0.746398i	0.979150	+	0.203140i	$0.0651147\pi$
$600$		0			0
$601$	−1.92247	−	1.10994i	−0.0784193	−	0.0452754i	0.460278	−	0.887775i	$-0.347750\pi$
$601$	−1.92247	−	1.10994i	−0.0784193	−	0.0452754i	−0.538697	+	0.842500i	$0.681083\pi$
$602$		0			0
$603$	32.6325	−	11.3259i	1.32890	−	0.461225i
$604$		0			0
$605$	−1.17583	+	2.03660i	−0.0478043	+	0.0827995i
$606$		0			0
$607$	−1.71759	+	0.991653i	−0.0697149	+	0.0402499i	−0.534452	−	0.845199i	$-0.679482\pi$
$607$	−1.71759	+	0.991653i	−0.0697149	+	0.0402499i	0.464737	+	0.885449i	$0.346149\pi$
$608$		0			0
$609$	2.91426	−	27.1773i	0.118092	−	1.10128i
$610$		0			0
$611$		−	0.821673i		−	0.0332413i
$612$		0			0
$613$	−23.1365			−0.934476			−0.467238	−	0.884132i	$-0.654751\pi$
$613$	−23.1365			−0.934476			−0.467238	+	0.884132i	$0.654751\pi$
$614$		0			0
$615$	8.36616	−	1.41056i	0.337356	−	0.0568794i
$616$		0			0
$617$	−1.19807	+	0.691704i	−0.0482323	+	0.0278470i	−0.523922	−	0.851766i	$-0.675532\pi$
$617$	−1.19807	+	0.691704i	−0.0482323	+	0.0278470i	0.475690	+	0.879613i	$0.342198\pi$
$618$		0			0
$619$	−5.22550	−	3.01694i	−0.210031	−	0.121261i	0.391295	−	0.920265i	$-0.372027\pi$
$619$	−5.22550	−	3.01694i	−0.210031	−	0.121261i	−0.601326	+	0.799004i	$0.705361\pi$
$620$		0			0
$621$	5.30913	−	8.73568i	0.213048	−	0.350551i
$622$		0			0
$623$	43.6415	+	12.2595i	1.74846	+	0.491165i
$624$		0			0
$625$	−10.4054	−	18.0226i	−0.416215	−	0.720905i
$626$		0			0
$627$	14.9458	−	2.51990i	0.596876	−	0.100635i
$628$		0			0
$629$	33.7320			1.34498
$630$		0			0
$631$	−20.4727			−0.815004			−0.407502	−	0.913204i	$-0.633600\pi$
$631$	−20.4727			−0.815004			−0.407502	+	0.913204i	$0.633600\pi$
$632$		0			0
$633$	3.39515	−	9.11479i	0.134945	−	0.362280i
$634$		0			0
$635$	−2.69622	−	4.67000i	−0.106996	−	0.185323i
$636$		0			0
$637$	−0.944707	−	0.0227832i	−0.0374306	−	0.000902701i
$638$		0			0
$639$	−9.51305	−	1.82495i	−0.376330	−	0.0721939i
$640$		0			0
$641$	40.2246	+	23.2237i	1.58878	+	0.917281i	0.993509	+	0.113754i	$0.0362877\pi$
$641$	40.2246	+	23.2237i	1.58878	+	0.917281i	0.595269	+	0.803527i	$0.297046\pi$
$642$		0			0
$643$	−9.74133	+	5.62416i	−0.384161	+	0.221795i	−0.679627	−	0.733558i	$-0.737858\pi$
$643$	−9.74133	+	5.62416i	−0.384161	+	0.221795i	0.295466	+	0.955353i	$0.404525\pi$
$644$		0			0
$645$	3.82124	+	4.62397i	0.150461	+	0.182069i
$646$		0			0
$647$	4.65015			0.182816			0.0914081	−	0.995814i	$-0.470863\pi$
$647$	4.65015			0.182816			0.0914081	+	0.995814i	$0.470863\pi$
$648$		0			0
$649$			14.8836i			0.584232i
$650$		0			0
$651$	−3.42095	−	2.49647i	−0.134078	−	0.0978445i
$652$		0			0
$653$	2.99966	−	1.73186i	0.117386	−	0.0677727i	−0.440157	−	0.897921i	$-0.645077\pi$
$653$	2.99966	−	1.73186i	0.117386	−	0.0677727i	0.557543	+	0.830148i	$0.311744\pi$
$654$		0			0
$655$	−4.17150	+	7.22524i	−0.162994	+	0.282314i
$656$		0			0
$657$	−1.12265	−	0.215366i	−0.0437989	−	0.00840222i
$658$		0			0
$659$	−1.59819	−	0.922715i	−0.0622566	−	0.0359439i	0.468549	−	0.883438i	$-0.344777\pi$
$659$	−1.59819	−	0.922715i	−0.0622566	−	0.0359439i	−0.530805	+	0.847494i	$0.678110\pi$
$660$		0			0
$661$	−17.5196	+	10.1149i	−0.681433	+	0.393426i	−0.800395	−	0.599473i	$-0.795377\pi$
$661$	−17.5196	+	10.1149i	−0.681433	+	0.393426i	0.118962	+	0.992899i	$0.462043\pi$
$662$		0			0
$663$	−0.947744	−	0.353023i	−0.0368073	−	0.0137103i
$664$		0			0
$665$	−3.04947	+	0.777823i	−0.118253	+	0.0301627i
$666$		0			0
$667$	11.7342			0.454351
$668$		0			0
$669$	−1.99678	−	11.8430i	−0.0771999	−	0.457879i
$670$		0			0
$671$	21.1919	+	36.7055i	0.818106	+	1.41700i
$672$		0			0
$673$	−7.31596	+	12.6716i	−0.282009	+	0.488455i	−0.971880	−	0.235478i	$-0.924334\pi$
$673$	−7.31596	+	12.6716i	−0.282009	+	0.488455i	0.689870	+	0.723933i	$0.257668\pi$
$674$		0			0
$675$	−0.551272	+	24.4953i	−0.0212185	+	0.942824i
$676$		0			0
$677$	−7.71449	+	13.3619i	−0.296492	+	0.513539i	−0.975331	−	0.220748i	$-0.929150\pi$
$677$	−7.71449	+	13.3619i	−0.296492	+	0.513539i	0.678839	+	0.734287i	$0.262483\pi$
$678$		0			0
$679$	29.1823	+	29.8946i	1.11992	+	1.14725i
$680$		0			0
$681$	24.8961	−	4.19757i	0.954022	−	0.160851i
$682$		0			0
$683$		−	15.7197i		−	0.601499i	−0.953703	−	0.300750i	$-0.902763\pi$
$683$		−	15.7197i		−	0.601499i	0.953703	−	0.300750i	$-0.0972368\pi$
$684$		0			0
$685$			1.31779i			0.0503501i
$686$		0			0
$687$	−39.8685	−	14.8505i	−1.52108	−	0.566582i
$688$		0			0
$689$	0.743611	+	1.28797i	0.0283293	+	0.0490678i
$690$		0			0
$691$	41.5878	+	24.0107i	1.58207	+	0.913411i	0.994556	+	0.104199i	$0.0332278\pi$
$691$	41.5878	+	24.0107i	1.58207	+	0.913411i	0.587517	+	0.809212i	$0.300106\pi$
$692$		0			0
$693$	25.9953	−	17.1731i	0.987479	−	0.652354i
$694$		0			0
$695$	8.99187	+	5.19146i	0.341081	+	0.196923i
$696$		0			0
$697$	−19.8544	−	34.3889i	−0.752040	−	1.30257i
$698$		0			0
$699$	14.0379	−	11.6009i	0.530963	−	0.438787i
$700$		0			0
$701$			24.7005i			0.932923i	0.884541	+	0.466462i	$0.154471\pi$
$701$			24.7005i			0.932923i	−0.884541	+	0.466462i	$0.845529\pi$
$702$		0			0
$703$			17.3860i			0.655727i
$704$		0			0
$705$	−3.58322	−	4.33595i	−0.134952	−	0.163301i
$706$		0			0
$707$	−27.9012	+	27.2365i	−1.04933	+	1.02433i
$708$		0			0
$709$	−17.0432	+	29.5196i	−0.640070	+	1.10863i	0.345347	+	0.938475i	$0.387761\pi$
$709$	−17.0432	+	29.5196i	−0.640070	+	1.10863i	−0.985417	+	0.170159i	$0.945572\pi$
$710$		0			0
$711$	−20.8884	−	18.0683i	−0.783376	−	0.677613i
$712$		0			0
$713$	0.909051	−	1.57452i	0.0340442	−	0.0589663i
$714$		0			0
$715$	0.141366	+	0.244853i	0.00528679	+	0.00915698i
$716$		0			0
$717$	31.6880	+	11.8034i	1.18341	+	0.440806i
$718$		0			0
$719$	−18.4758			−0.689032			−0.344516	−	0.938780i	$-0.611957\pi$
$719$	−18.4758			−0.689032			−0.344516	+	0.938780i	$0.611957\pi$
$720$		0			0
$721$	−32.9898	+	8.41466i	−1.22860	+	0.313378i
$722$		0			0
$723$	−3.78334	−	22.4393i	−0.140704	−	0.834526i
$724$		0			0
$725$	−24.3569	+	14.0624i	−0.904591	+	0.522266i
$726$		0			0
$727$	−39.2911	−	22.6847i	−1.45723	−	0.841330i	−0.458353	−	0.888770i	$-0.651560\pi$
$727$	−39.2911	−	22.6847i	−1.45723	−	0.841330i	−0.998874	+	0.0474398i	$0.984894\pi$
$728$		0			0
$729$	14.5383	−	22.7517i	0.538454	−	0.842655i
$730$		0			0
$731$	14.0376	−	24.3138i	0.519200	−	0.899280i
$732$		0			0
$733$	43.3683	−	25.0387i	1.60184	−	0.924825i	0.610724	−	0.791843i	$-0.290878\pi$
$733$	43.3683	−	25.0387i	1.60184	−	0.924825i	0.991119	−	0.132981i	$-0.0424550\pi$
$734$		0			0
$735$	−5.08455	+	3.99953i	−0.187547	+	0.147525i
$736$		0			0
$737$			45.1953i			1.66479i
$738$		0			0
$739$	−16.9404			−0.623163			−0.311582	−	0.950219i	$-0.600859\pi$
$739$	−16.9404			−0.623163			−0.311582	+	0.950219i	$0.600859\pi$
$740$		0			0
$741$	0.181954	−	0.488484i	0.00668426	−	0.0179449i
$742$		0			0
$743$	34.4723	−	19.9026i	1.26467	−	0.730156i	0.290693	−	0.956816i	$-0.406114\pi$
$743$	34.4723	−	19.9026i	1.26467	−	0.730156i	0.973974	+	0.226661i	$0.0727808\pi$
$744$		0			0
$745$	7.32595	+	4.22964i	0.268402	+	0.154962i
$746$		0			0
$747$	−5.80942	−	5.02509i	−0.212556	−	0.183859i
$748$		0			0
$749$	−11.2928	+	40.2002i	−0.412629	+	1.46888i
$750$		0			0
$751$	14.7028	+	25.4659i	0.536512	+	0.929265i	0.999089	+	0.0426862i	$0.0135916\pi$
$751$	14.7028	+	25.4659i	0.536512	+	0.929265i	−0.462577	+	0.886579i	$0.653075\pi$
$752$		0			0
$753$	−25.0312	−	30.2896i	−0.912189	−	1.10381i
$754$		0			0
$755$	−4.44507			−0.161773
$756$		0			0
$757$	−27.4010			−0.995908			−0.497954	−	0.867203i	$-0.665915\pi$
$757$	−27.4010			−0.995908			−0.497954	+	0.867203i	$0.665915\pi$
$758$		0			0
$759$	8.52033	+	10.3102i	0.309268	+	0.374237i
$760$		0			0
$761$	−6.11067	−	10.5840i	−0.221511	−	0.383669i	0.733756	−	0.679413i	$-0.237766\pi$
$761$	−6.11067	−	10.5840i	−0.221511	−	0.383669i	−0.955267	+	0.295744i	$0.904432\pi$
$762$		0			0
$763$	−7.85390	−	2.20627i	−0.284330	−	0.0798722i
$764$		0			0
$765$	−6.54072	+	2.27011i	−0.236480	+	0.0820759i
$766$		0			0
$767$	0.443300	+	0.255939i	0.0160066	+	0.00924143i
$768$		0			0
$769$	−29.4039	+	16.9764i	−1.06033	+	0.612184i	−0.925524	−	0.378688i	$-0.876375\pi$
$769$	−29.4039	+	16.9764i	−1.06033	+	0.612184i	−0.134809	+	0.990872i	$0.543042\pi$
$770$		0			0
$771$	−8.22820	+	22.0898i	−0.296331	+	0.795546i
$772$		0			0
$773$	30.2094			1.08656			0.543279	−	0.839552i	$-0.317183\pi$
$773$	30.2094			1.08656			0.543279	+	0.839552i	$0.317183\pi$
$774$		0			0
$775$			4.35767i			0.156532i
$776$		0			0
$777$	14.4673	+	32.6790i	0.519013	+	1.17235i
$778$		0			0
$779$	17.7246	−	10.2333i	0.635051	−	0.366647i
$780$		0			0
$781$	6.33698	−	10.9760i	0.226755	−	0.392751i
$782$		0			0
$783$	30.9850	+	0.697326i	1.10731	+	0.0249204i
$784$		0			0
$785$	−4.12866	−	2.38368i	−0.147358	−	0.0850772i
$786$		0			0
$787$	33.3310	−	19.2436i	1.18812	−	0.685962i	0.230241	−	0.973134i	$-0.426048\pi$
$787$	33.3310	−	19.2436i	1.18812	−	0.685962i	0.957879	+	0.287172i	$0.0927151\pi$
$788$		0			0
$789$	6.58145	+	39.0351i	0.234306	+	1.38969i
$790$		0			0
$791$	23.5689	−	6.01168i	0.838013	−	0.213751i
$792$		0			0
$793$	1.45767			0.0517635
$794$		0			0
$795$	9.54072	+	3.55380i	0.338375	+	0.126040i
$796$		0			0
$797$	−6.72949	−	11.6558i	−0.238371	−	0.412870i	0.721876	−	0.692022i	$-0.243280\pi$
$797$	−6.72949	−	11.6558i	−0.238371	−	0.412870i	−0.960247	+	0.279152i	$0.909947\pi$
$798$		0			0
$799$	−13.1632	+	22.7994i	−0.465682	+	0.806584i
$800$		0			0
$801$	−9.68386	+	50.4797i	−0.342162	+	1.78361i
$802$		0			0
$803$	0.747839	−	1.29529i	0.0263907	−	0.0457100i
$804$		0			0
$805$	−1.93996	−	1.98731i	−0.0683745	−	0.0700434i
$806$		0			0
$807$	11.7811	+	14.2560i	0.414714	+	0.501834i
$808$		0			0
$809$		−	51.7842i		−	1.82064i	−0.413909	−	0.910318i	$-0.635837\pi$
$809$		−	51.7842i		−	1.82064i	0.413909	−	0.910318i	$-0.364163\pi$
$810$		0			0
$811$		−	27.2471i		−	0.956775i	−0.878149	−	0.478387i	$-0.841221\pi$
$811$		−	27.2471i		−	0.956775i	0.878149	−	0.478387i	$-0.158779\pi$
$812$		0			0
$813$	6.02781	−	4.98137i	0.211404	−	0.174704i
$814$		0			0
$815$	−3.78993	−	6.56436i	−0.132756	−	0.229939i
$816$		0			0
$817$	12.5318	+	7.23523i	0.438432	+	0.253129i
$818$		0			0
$819$	−0.0644760	−	1.06957i	−0.00225297	−	0.0373737i
$820$		0			0
$821$	22.3465	+	12.9017i	0.779897	+	0.450274i	0.836394	−	0.548129i	$-0.184660\pi$
$821$	22.3465	+	12.9017i	0.779897	+	0.450274i	−0.0564968	+	0.998403i	$0.517993\pi$
$822$		0			0
$823$	0.570514	+	0.988159i	0.0198869	+	0.0344451i	0.875798	−	0.482679i	$-0.160336\pi$
$823$	0.570514	+	0.988159i	0.0198869	+	0.0344451i	−0.855911	+	0.517124i	$0.827003\pi$
$824$		0			0
$825$	−30.0416	−	11.1901i	−1.04592	−	0.389591i
$826$		0			0
$827$			23.1713i			0.805746i	0.915256	+	0.402873i	$0.131988\pi$
$827$			23.1713i			0.805746i	−0.915256	+	0.402873i	$0.868012\pi$
$828$		0			0
$829$			9.60364i			0.333548i	0.985995	+	0.166774i	$0.0533351\pi$
$829$			9.60364i			0.333548i	−0.985995	+	0.166774i	$0.946665\pi$
$830$		0			0
$831$	11.4416	−	1.92909i	0.396905	−	0.0669195i
$832$		0			0
$833$	25.8483	+	15.7664i	0.895590	+	0.546274i
$834$		0			0
$835$	3.34707	−	5.79729i	0.115830	−	0.200623i
$836$		0			0
$837$	2.49398	−	4.10362i	0.0862047	−	0.141842i
$838$		0			0
$839$	−15.7821	+	27.3354i	−0.544859	+	0.943723i	0.453757	+	0.891126i	$0.350083\pi$
$839$	−15.7821	+	27.3354i	−0.544859	+	0.943723i	−0.998616	+	0.0525978i	$0.983250\pi$
$840$		0			0
$841$	3.28812	+	5.69519i	0.113383	+	0.196386i
$842$		0			0
$843$	−5.03471	−	29.8613i	−0.173405	−	1.02848i
$844$		0			0
$845$	−6.92656			−0.238281
$846$		0			0
$847$	2.88211	+	11.2993i	0.0990304	+	0.388250i
$848$		0			0
$849$	−13.9075	−	5.18037i	−0.477304	−	0.177790i
$850$		0			0
$851$	−13.2870	+	7.67126i	−0.455473	+	0.262967i
$852$		0			0
$853$	7.50412	+	4.33250i	0.256936	+	0.148342i	0.622936	−	0.782273i	$-0.285940\pi$
$853$	7.50412	+	4.33250i	0.256936	+	0.148342i	−0.366000	+	0.930615i	$0.619273\pi$
$854$		0			0
$855$	−1.17005	−	3.37120i	−0.0400150	−	0.115293i
$856$		0			0
$857$	−11.4439	+	19.8214i	−0.390917	+	0.677088i	−0.992571	−	0.121669i	$-0.961175\pi$
$857$	−11.4439	+	19.8214i	−0.390917	+	0.677088i	0.601654	+	0.798757i	$0.294509\pi$
$858$		0			0
$859$	−11.4922	+	6.63503i	−0.392109	+	0.226384i	−0.683074	−	0.730350i	$-0.739357\pi$
$859$	−11.4922	+	6.63503i	−0.392109	+	0.226384i	0.290964	+	0.956734i	$0.406024\pi$
$860$		0			0
$861$	24.8000	−	33.9837i	0.845181	−	1.15816i
$862$		0			0
$863$		−	0.746752i		−	0.0254197i	−0.999919	−	0.0127099i	$-0.995954\pi$
$863$		−	0.746752i		−	0.0254197i	0.999919	−	0.0127099i	$-0.00404579\pi$
$864$		0			0
$865$	−11.3955			−0.387457
$866$		0			0
$867$	1.88503	+	2.28102i	0.0640189	+	0.0774674i
$868$		0			0
$869$	31.2951	−	18.0683i	1.06162	−	0.612924i
$870$		0			0
$871$	1.34612	+	0.777181i	0.0456114	+	0.0263338i
$872$		0			0
$873$	−30.9900	+	35.8270i	−1.04885	+	1.21256i
$874$		0			0
$875$	13.2037	+	3.70910i	0.446367	+	0.125391i
$876$		0			0
$877$	−2.18959	−	3.79249i	−0.0739373	−	0.128063i	0.826686	−	0.562663i	$-0.190223\pi$
$877$	−2.18959	−	3.79249i	−0.0739373	−	0.128063i	−0.900624	+	0.434600i	$0.856890\pi$
$878$		0			0
$879$	14.6837	−	39.4206i	0.495268	−	1.32962i
$880$		0			0
$881$	−14.1505			−0.476742			−0.238371	−	0.971174i	$-0.576613\pi$
$881$	−14.1505			−0.476742			−0.238371	+	0.971174i	$0.576613\pi$
$882$		0			0
$883$	23.0261			0.774890			0.387445	−	0.921893i	$-0.373358\pi$
$883$	23.0261			0.774890			0.387445	+	0.921893i	$0.373358\pi$
$884$		0			0
$885$	3.45541	−	0.582593i	0.116152	−	0.0195836i
$886$		0			0
$887$	−26.1812	−	45.3471i	−0.879077	−	1.52261i	−0.852355	−	0.522963i	$-0.824826\pi$
$887$	−26.1812	−	45.3471i	−0.879077	−	1.52261i	−0.0267221	−	0.999643i	$-0.508507\pi$
$888$		0			0
$889$	−25.7429	−	7.23153i	−0.863391	−	0.242538i
$890$		0			0
$891$	21.8858	+	27.7312i	0.733203	+	0.929029i
$892$		0			0
$893$	−11.7512	−	6.78456i	−0.393239	−	0.227037i
$894$		0			0
$895$	−2.68519	+	1.55029i	−0.0897560	+	0.0518206i
$896$		0			0
$897$	0.453600	−	0.0764785i	0.0151453	−	0.00255354i
$898$		0			0
$899$	5.51219			0.183842
$900$		0			0
$901$		−	47.6507i		−	1.58748i
$902$		0			0
$903$	29.5754	+	3.17141i	0.984209	+	0.105538i
$904$		0			0
$905$	−3.41418	+	1.97118i	−0.113491	+	0.0655242i
$906$		0			0
$907$	12.1902	−	21.1141i	0.404770	−	0.701082i	−0.589525	−	0.807750i	$-0.700685\pi$
$907$	12.1902	−	21.1141i	0.404770	−	0.701082i	0.994295	+	0.106669i	$0.0340184\pi$
$908$		0			0
$909$	−33.4380	−	28.9236i	−1.10907	−	0.959335i
$910$		0			0
$911$	−46.8606	−	27.0550i	−1.55256	−	0.896372i	−0.997932	−	0.0642741i	$-0.979527\pi$
$911$	−46.8606	−	27.0550i	−1.55256	−	0.896372i	−0.554629	−	0.832098i	$-0.687140\pi$
$912$		0			0
$913$	8.70372	−	5.02509i	0.288051	−	0.166306i
$914$		0			0
$915$	7.69211	−	6.35675i	0.254293	−	0.210148i
$916$		0			0
$917$	10.2249	+	40.0867i	0.337655	+	1.32378i
$918$		0			0
$919$	6.51894			0.215040			0.107520	−	0.994203i	$-0.465709\pi$
$919$	6.51894			0.215040			0.107520	+	0.994203i	$0.465709\pi$
$920$		0			0
$921$	16.6595	−	13.7673i	0.548948	−	0.453649i
$922$		0			0
$923$	−0.217942	−	0.377487i	−0.00717365	−	0.0124251i
$924$		0			0
$925$	18.3867	−	31.8467i	0.604550	−	1.04711i
$926$		0			0
$927$	−12.6579	−	36.4704i	−0.415740	−	1.19785i
$928$		0			0
$929$	13.9048	−	24.0838i	0.456202	−	0.790165i	−0.542554	−	0.840021i	$-0.682543\pi$
$929$	13.9048	−	24.0838i	0.456202	−	0.790165i	0.998756	+	0.0498555i	$0.0158761\pi$
$930$		0			0
$931$	−8.12629	+	13.3227i	−0.266328	+	0.436633i
$932$		0			0
$933$	−10.9791	+	29.4751i	−0.359440	+	0.964971i
$934$		0			0
$935$		−	9.05875i		−	0.296253i
$936$		0			0
$937$			54.8174i			1.79081i	0.445256	+	0.895403i	$0.353113\pi$
$937$			54.8174i			1.79081i	−0.445256	+	0.895403i	$0.646887\pi$
$938$		0			0
$939$	−0.920066	−	5.45698i	−0.0300252	−	0.178082i
$940$		0			0
$941$	2.56526	+	4.44317i	0.0836252	+	0.144843i	0.904805	−	0.425827i	$-0.140017\pi$
$941$	2.56526	+	4.44317i	0.0836252	+	0.144843i	−0.821179	+	0.570670i	$0.806683\pi$
$942$		0			0
$943$	15.6413	+	9.03052i	0.509351	+	0.294074i
$944$		0			0
$945$	−5.00450	−	5.36291i	−0.162796	−	0.174455i
$946$		0			0
$947$	−0.606033	−	0.349893i	−0.0196934	−	0.0113700i	0.490121	−	0.871654i	$-0.336953\pi$
$947$	−0.606033	−	0.349893i	−0.0196934	−	0.0113700i	−0.509814	+	0.860284i	$0.670286\pi$
$948$		0			0
$949$	−0.0257198	−	0.0445480i	−0.000834899	−	0.00144609i
$950$		0			0
$951$	−7.51125	−	44.5498i	−0.243569	−	1.44463i
$952$		0			0
$953$			0.162845i			0.00527506i	0.999997	+	0.00263753i	$0.000839552\pi$
$953$			0.162845i			0.00527506i	−0.999997	+	0.00263753i	$0.999160\pi$
$954$		0			0
$955$			4.22714i			0.136787i
$956$		0			0
$957$	−14.1548	+	38.0008i	−0.457561	+	1.22839i
$958$		0			0
$959$	4.56453	+	4.67594i	0.147396	+	0.150994i
$960$		0			0
$961$	−15.0730	+	26.1071i	−0.486225	+	0.842166i
$962$		0			0
$963$	−46.4992	−	8.92025i	−1.49842	−	0.287451i
$964$		0			0
$965$	−1.68897	+	2.92539i	−0.0543700	+	0.0941716i
$966$		0			0
$967$	−15.6968	−	27.1876i	−0.504773	−	0.874293i	−0.999985	−	0.00552073i	$-0.998243\pi$
$967$	−15.6968	−	27.1876i	−0.504773	−	0.874293i	0.495211	−	0.868773i	$-0.335091\pi$
$968$		0			0
$969$	−12.8743	+	10.6393i	−0.413583	+	0.341784i
$970$		0			0
$971$	−2.92239			−0.0937841			−0.0468920	−	0.998900i	$-0.514932\pi$
$971$	−2.92239			−0.0937841			−0.0468920	+	0.998900i	$0.514932\pi$
$972$		0			0
$973$	49.8882	−	12.7249i	1.59934	−	0.407942i
$974$		0			0
$975$	−0.849890	+	0.702347i	−0.0272183	+	0.0224931i
$976$		0			0
$977$	−24.7013	+	14.2613i	−0.790264	+	0.456259i	−0.840056	−	0.542500i	$-0.817478\pi$
$977$	−24.7013	+	14.2613i	−0.790264	+	0.456259i	0.0497913	+	0.998760i	$0.484144\pi$
$978$		0			0
$979$	−58.2425	−	33.6263i	−1.86144	−	1.07470i
$980$		0			0
$981$	1.74275	−	9.08454i	0.0556416	−	0.290047i
$982$		0			0
$983$	5.62897	−	9.74967i	0.179536	−	0.310966i	−0.762185	−	0.647359i	$-0.775874\pi$
$983$	5.62897	−	9.74967i	0.179536	−	0.310966i	0.941722	+	0.336393i	$0.109207\pi$
$984$		0			0
$985$	−7.00416	+	4.04386i	−0.223171	+	0.128848i
$986$		0			0
$987$	−27.7333	−	2.97387i	−0.882759	−	0.0946592i
$988$		0			0
$989$			12.7696i			0.406050i
$990$		0			0
$991$	21.1622			0.672240			0.336120	−	0.941819i	$-0.390885\pi$
$991$	21.1622			0.672240			0.336120	+	0.941819i	$0.390885\pi$
$992$		0			0
$993$	27.5486	−	4.64478i	0.874228	−	0.147398i
$994$		0			0
$995$	3.95114	−	2.28119i	0.125260	−	0.0723187i
$996$		0			0
$997$	14.6576	+	8.46256i	0.464210	+	0.268012i	0.713813	−	0.700336i	$-0.246967\pi$
$997$	14.6576	+	8.46256i	0.464210	+	0.268012i	−0.249603	+	0.968348i	$0.580300\pi$
$998$		0			0
$999$	−35.5412	+	19.4669i	−1.12447	+	0.615906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.x.a.209.6	yes	16
3.2	odd	2		756.2.x.a.629.4		16
4.3	odd	2		1008.2.cc.c.209.3		16
7.2	even	3		1764.2.w.a.1109.1		16
7.3	odd	6		1764.2.bm.b.1685.4		16
7.4	even	3		1764.2.bm.b.1685.5		16
7.5	odd	6		1764.2.w.a.1109.8		16
7.6	odd	2	inner	252.2.x.a.209.3	yes	16
9.2	odd	6		2268.2.f.b.1133.9		16
9.4	even	3		756.2.x.a.125.5		16
9.5	odd	6	inner	252.2.x.a.41.3	✓	16
9.7	even	3		2268.2.f.b.1133.7		16
12.11	even	2		3024.2.cc.c.2897.4		16
21.2	odd	6		5292.2.w.a.521.4		16
21.5	even	6		5292.2.w.a.521.5		16
21.11	odd	6		5292.2.bm.b.4625.5		16
21.17	even	6		5292.2.bm.b.4625.4		16
21.20	even	2		756.2.x.a.629.5		16
28.27	even	2		1008.2.cc.c.209.6		16
36.23	even	6		1008.2.cc.c.545.6		16
36.31	odd	6		3024.2.cc.c.881.5		16
63.4	even	3		5292.2.w.a.1097.5		16
63.5	even	6		1764.2.bm.b.1697.5		16
63.13	odd	6		756.2.x.a.125.4		16
63.20	even	6		2268.2.f.b.1133.8		16
63.23	odd	6		1764.2.bm.b.1697.4		16
63.31	odd	6		5292.2.w.a.1097.4		16
63.32	odd	6		1764.2.w.a.509.8		16
63.34	odd	6		2268.2.f.b.1133.10		16
63.40	odd	6		5292.2.bm.b.2285.5		16
63.41	even	6	inner	252.2.x.a.41.6	yes	16
63.58	even	3		5292.2.bm.b.2285.4		16
63.59	even	6		1764.2.w.a.509.1		16
84.83	odd	2		3024.2.cc.c.2897.5		16
252.139	even	6		3024.2.cc.c.881.4		16
252.167	odd	6		1008.2.cc.c.545.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.3	✓	16	9.5	odd	6	inner
252.2.x.a.41.6	yes	16	63.41	even	6	inner
252.2.x.a.209.3	yes	16	7.6	odd	2	inner
252.2.x.a.209.6	yes	16	1.1	even	1	trivial
756.2.x.a.125.4		16	63.13	odd	6
756.2.x.a.125.5		16	9.4	even	3
756.2.x.a.629.4		16	3.2	odd	2
756.2.x.a.629.5		16	21.20	even	2
1008.2.cc.c.209.3		16	4.3	odd	2
1008.2.cc.c.209.6		16	28.27	even	2
1008.2.cc.c.545.3		16	252.167	odd	6
1008.2.cc.c.545.6		16	36.23	even	6
1764.2.w.a.509.1		16	63.59	even	6
1764.2.w.a.509.8		16	63.32	odd	6
1764.2.w.a.1109.1		16	7.2	even	3
1764.2.w.a.1109.8		16	7.5	odd	6
1764.2.bm.b.1685.4		16	7.3	odd	6
1764.2.bm.b.1685.5		16	7.4	even	3
1764.2.bm.b.1697.4		16	63.23	odd	6
1764.2.bm.b.1697.5		16	63.5	even	6
2268.2.f.b.1133.7		16	9.7	even	3
2268.2.f.b.1133.8		16	63.20	even	6
2268.2.f.b.1133.9		16	9.2	odd	6
2268.2.f.b.1133.10		16	63.34	odd	6
3024.2.cc.c.881.4		16	252.139	even	6
3024.2.cc.c.881.5		16	36.31	odd	6
3024.2.cc.c.2897.4		16	12.11	even	2
3024.2.cc.c.2897.5		16	84.83	odd	2
5292.2.w.a.521.4		16	21.2	odd	6
5292.2.w.a.521.5		16	21.5	even	6
5292.2.w.a.1097.4		16	63.31	odd	6
5292.2.w.a.1097.5		16	63.4	even	3
5292.2.bm.b.2285.4		16	63.58	even	3
5292.2.bm.b.2285.5		16	63.40	odd	6
5292.2.bm.b.4625.4		16	21.17	even	6
5292.2.bm.b.4625.5		16	21.11	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.10336 + 1.33514i) q^{3} +(0.266780 + 0.462077i) q^{5} +(2.54716 + 0.715531i) q^{7} +(-0.565203 + 2.94628i) q^{9} +O(q^{10})\)	\(q+(1.10336 + 1.33514i) q^{3} +(0.266780 + 0.462077i) q^{5} +(2.54716 + 0.715531i) q^{7} +(-0.565203 + 2.94628i) q^{9} +(-3.39936 - 1.96262i) q^{11} +(-0.116911 + 0.0674987i) q^{13} +(-0.322584 + 0.866025i) q^{15} +4.32533 q^{17} +2.22935i q^{19} +(1.85509 + 4.19030i) q^{21} +(-1.70375 + 0.983658i) q^{23} +(2.35766 - 4.08358i) q^{25} +(-4.55732 + 2.49617i) q^{27} +(-5.16548 - 2.98229i) q^{29} +(-0.800341 + 0.462077i) q^{31} +(-1.13033 - 6.70409i) q^{33} +(0.348901 + 1.36787i) q^{35} +7.79871 q^{37} +(-0.219115 - 0.0816177i) q^{39} +(-4.59027 - 7.95059i) q^{41} +(3.24544 - 5.62127i) q^{43} +(-1.51219 + 0.524841i) q^{45} +(-3.04329 + 5.27114i) q^{47} +(5.97603 + 3.64514i) q^{49} +(4.77238 + 5.77492i) q^{51} -11.0167i q^{53} -2.09435i q^{55} +(-2.97650 + 2.45977i) q^{57} +(-1.89588 - 3.28377i) q^{59} +(-9.35116 - 5.39889i) q^{61} +(-3.54781 + 7.10021i) q^{63} +(-0.0623791 - 0.0360146i) q^{65} +(-5.75701 - 9.97144i) q^{67} +(-3.19316 - 1.18941i) q^{69} +3.22884i q^{71} +0.381041i q^{73} +(8.05350 - 1.35785i) q^{75} +(-7.25438 - 7.43144i) q^{77} +(-4.60310 + 7.97280i) q^{79} +(-8.36109 - 3.33049i) q^{81} +(-1.28020 + 2.21737i) q^{83} +(1.15391 + 1.99863i) q^{85} +(-1.71759 - 10.1872i) q^{87} +17.1334 q^{89} +(-0.346088 + 0.0882763i) q^{91} +(-1.50000 - 0.558732i) q^{93} +(-1.03013 + 0.594746i) q^{95} +(13.6747 + 7.89507i) q^{97} +(7.70375 - 8.90616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 6 q^{11} - 12 q^{15} + 9 q^{21} + 6 q^{23} - 8 q^{25} - 12 q^{29} + 4 q^{37} + 18 q^{39} + 4 q^{43} - 5 q^{49} - 18 q^{51} - 42 q^{57} - 27 q^{63} - 24 q^{65} + 14 q^{67} - 21 q^{77} + 20 q^{79} - 36 q^{81} + 6 q^{85} - 18 q^{91} - 24 q^{93} - 60 q^{95} + 90 q^{99}+O(q^{100}) \) 16 * q - q^7 + 6 * q^11 - 12 * q^15 + 9 * q^21 + 6 * q^23 - 8 * q^25 - 12 * q^29 + 4 * q^37 + 18 * q^39 + 4 * q^43 - 5 * q^49 - 18 * q^51 - 42 * q^57 - 27 * q^63 - 24 * q^65 + 14 * q^67 - 21 * q^77 + 20 * q^79 - 36 * q^81 + 6 * q^85 - 18 * q^91 - 24 * q^93 - 60 * q^95 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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