LMFDB - Embedded newform 252.2.x.a.41.6

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			41.6
Root			$0.604587 + 1.62311i$ of defining polynomial
Character	$\chi$	$=$	252.41
Dual form			252.2.x.a.209.6

$q$-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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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	−0.800186	−	0.599752i	$-0.795266\pi$
$5$	0.266780	−	0.462077i	0.119308	−	0.206647i	0.919494	+	0.393105i	$0.128599\pi$
$6$		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	−0.915532	−	0.402245i	$-0.868230\pi$
$11$	−3.39936	+	1.96262i	−1.02494	+	0.591752i	−0.109412	+	0.993996i	$0.534897\pi$
$12$		0			0
$13$	−0.116911	−	0.0674987i	−0.0324253	−	0.0187208i	0.483700	−	0.875234i	$-0.339293\pi$
$13$	−0.116911	−	0.0674987i	−0.0324253	−	0.0187208i	−0.516125	+	0.856513i	$0.672626\pi$
$14$		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	$-0.917686\pi$
$19$		−	2.22935i		−	0.511448i	0.966750	−	0.255724i	$-0.0823138\pi$
$20$		0			0
$21$	1.85509	−	4.19030i	0.404814	−	0.914399i
$22$		0			0
$23$	−1.70375	−	0.983658i	−0.355255	−	0.205107i	0.311742	−	0.950167i	$-0.399088\pi$
$23$	−1.70375	−	0.983658i	−0.355255	−	0.205107i	−0.666998	+	0.745060i	$0.732421\pi$
$24$		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	−0.895928	−	0.444198i	$-0.853489\pi$
$29$	−5.16548	+	2.98229i	−0.959205	+	0.553798i	−0.0632771	+	0.997996i	$0.520155\pi$
$30$		0			0
$31$	−0.800341	−	0.462077i	−0.143745	−	0.0829915i	0.426402	−	0.904534i	$-0.359781\pi$
$31$	−0.800341	−	0.462077i	−0.143745	−	0.0829915i	−0.570148	+	0.821542i	$0.693114\pi$
$32$		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	0.245349	+	0.969435i	$0.421097\pi$
$41$	−4.59027	+	7.95059i	−0.716880	+	1.24167i	−0.962230	+	0.272239i	$0.912236\pi$
$42$		0			0
$43$	3.24544	+	5.62127i	0.494926	+	0.857236i	0.999983	−	0.00584958i	$-0.00186199\pi$
$43$	3.24544	+	5.62127i	0.494926	+	0.857236i	−0.505057	+	0.863086i	$0.668529\pi$
$44$		0			0
$45$	−1.51219	−	0.524841i	−0.225424	−	0.0782387i
$46$		0			0
$47$	−3.04329	−	5.27114i	−0.443910	−	0.768874i	0.554066	−	0.832473i	$-0.313076\pi$
$47$	−3.04329	−	5.27114i	−0.443910	−	0.768874i	−0.997976	+	0.0635985i	$0.979742\pi$
$48$		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	$0.273155\pi$
$53$			11.0167i			1.51326i	−0.653845	+	0.756628i	$0.726845\pi$
$54$		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	−0.962643	−	0.270775i	$-0.912720\pi$
$59$	−1.89588	+	3.28377i	−0.246823	+	0.427510i	0.715820	+	0.698285i	$0.246053\pi$
$60$		0			0
$61$	−9.35116	+	5.39889i	−1.19729	+	0.691258i	−0.959951	−	0.280168i	$-0.909610\pi$
$61$	−9.35116	+	5.39889i	−1.19729	+	0.691258i	−0.237342	+	0.971426i	$0.576276\pi$
$62$		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	0.263960	+	0.964534i	$0.414971\pi$
$67$	−5.75701	+	9.97144i	−0.703331	+	1.21820i	−0.967291	+	0.253671i	$0.918362\pi$
$68$		0			0
$69$	−3.19316	+	1.18941i	−0.384412	+	0.143189i
$70$		0			0
$71$		−	3.22884i		−	0.383192i	−0.981474	−	0.191596i	$-0.938634\pi$
$71$		−	3.22884i		−	0.383192i	0.981474	−	0.191596i	$-0.0613664\pi$
$72$		0			0
$73$		−	0.381041i		−	0.0445975i	−0.999751	−	0.0222988i	$-0.992901\pi$
$73$		−	0.381041i		−	0.0445975i	0.999751	−	0.0222988i	$-0.00709850\pi$
$74$		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	−0.999784	−	0.0207814i	$-0.993385\pi$
$79$	−4.60310	−	7.97280i	−0.517889	−	0.897011i	0.481895	−	0.876229i	$-0.339949\pi$
$80$		0			0
$81$	−8.36109	+	3.33049i	−0.929010	+	0.370055i
$82$		0			0
$83$	−1.28020	−	2.21737i	−0.140520	−	0.243388i	0.787172	−	0.616733i	$-0.211544\pi$
$83$	−1.28020	−	2.21737i	−0.140520	−	0.243388i	−0.927693	+	0.373345i	$0.878211\pi$
$84$		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	0.395310	−	0.918548i	$-0.370637\pi$
$97$	13.6747	−	7.89507i	1.38845	−	0.801622i	0.993141	+	0.116925i	$0.0373038\pi$
$98$		0			0
$99$	7.70375	+	8.90616i	0.774256	+	0.895103i
$100$		0			0
$101$	−7.36862	−	12.7628i	−0.733205	−	1.26995i	−0.955506	−	0.294970i	$-0.904690\pi$
$101$	−7.36862	−	12.7628i	−0.733205	−	1.26995i	0.222301	−	0.974978i	$-0.428643\pi$
$102$		0			0
$103$	−11.1442	−	6.43410i	−1.09807	−	0.633970i	−0.162356	−	0.986732i	$-0.551909\pi$
$103$	−11.1442	−	6.43410i	−1.09807	−	0.633970i	−0.935713	+	0.352762i	$0.885243\pi$
$104$		0			0
$105$	−1.44134	−	1.97509i	−0.140660	−	0.192749i
$106$		0			0
$107$		−	15.7824i		−	1.52574i	−0.646552	−	0.762870i	$-0.723790\pi$
$107$		−	15.7824i		−	1.52574i	0.646552	−	0.762870i	$-0.276210\pi$
$108$		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	0.825324	−	0.564659i	$-0.190992\pi$
$113$	7.96173	+	4.59671i	0.748977	+	0.432422i	−0.0763472	+	0.997081i	$0.524326\pi$
$114$		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	−0.290954	−	0.956737i	$-0.593973\pi$
$131$	7.81823	−	13.5416i	0.683082	−	1.18313i	0.974036	−	0.226395i	$-0.0726940\pi$
$132$		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	−0.405840	−	0.913944i	$-0.633021\pi$
$137$	2.13891	−	1.23490i	0.182739	−	0.105505i	0.588579	+	0.808440i	$0.299688\pi$
$138$		0			0
$139$	16.8526	+	9.72984i	1.42942	+	0.825274i	0.997074	−	0.0764359i	$-0.0243540\pi$
$139$	16.8526	+	9.72984i	1.42942	+	0.825274i	0.432342	+	0.901710i	$0.357687\pi$
$140$		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	0.942630	−	0.333840i	$-0.108344\pi$
$149$	13.7303	+	7.92720i	1.12483	+	0.649422i	0.182201	+	0.983261i	$0.441678\pi$
$150$		0			0
$151$	−4.16548	−	7.21482i	−0.338982	−	0.587134i	0.645260	−	0.763963i	$-0.276749\pi$
$151$	−4.16548	−	7.21482i	−0.338982	−	0.587134i	−0.984242	+	0.176829i	$0.943416\pi$
$152$		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	0.158362	−	0.987381i	$-0.449379\pi$
$157$	−7.73794	−	4.46750i	−0.617555	−	0.356545i	−0.775916	+	0.630836i	$0.782712\pi$
$158$		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	−0.999860	−	0.0167485i	$-0.994669\pi$
$167$	−6.27308	+	10.8653i	−0.485425	+	0.840781i	0.514434	+	0.857530i	$0.328002\pi$
$168$		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	−0.911543	−	0.411206i	$-0.865108\pi$
$173$	−10.6787	−	18.4960i	−0.811886	−	1.40623i	0.0996566	−	0.995022i	$-0.468226\pi$
$174$		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	$-0.930317\pi$
$179$		−	5.81113i		−	0.434344i	0.976133	−	0.217172i	$-0.0696833\pi$
$180$		0			0
$181$		−	7.38877i		−	0.549203i	−0.961558	−	0.274602i	$-0.911454\pi$
$181$		−	7.38877i		−	0.549203i	0.961558	−	0.274602i	$-0.0885460\pi$
$182$		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	−0.230796	−	0.973002i	$-0.574133\pi$
$191$	6.86109	−	3.96125i	0.496451	−	0.286626i	0.727247	+	0.686376i	$0.240800\pi$
$192$		0			0
$193$	3.16548	−	5.48277i	0.227856	−	0.394659i	−0.729316	−	0.684177i	$-0.760162\pi$
$193$	3.16548	−	5.48277i	0.227856	−	0.394659i	0.957173	+	0.289518i	$0.0934951\pi$
$194$		0			0
$195$	−0.0207419	+	0.123022i	−0.00148536	+	0.00880979i
$196$		0			0
$197$		−	15.1580i		−	1.07996i	−0.841677	−	0.539981i	$-0.818431\pi$
$197$		−	15.1580i		−	1.07996i	0.841677	−	0.539981i	$-0.181569\pi$
$198$		0			0
$199$			8.55084i			0.606153i	0.952966	+	0.303076i	$0.0980137\pi$
$199$			8.55084i			0.606153i	−0.952966	+	0.303076i	$0.901986\pi$
$200$		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	−0.946341	−	0.323169i	$-0.895252\pi$
$211$	−2.80782	+	4.86329i	−0.193299	+	0.334803i	0.753043	+	0.657971i	$0.228585\pi$
$212$		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	−0.687403	−	0.726276i	$-0.741249\pi$
$223$	−6.00510	+	3.46705i	−0.402131	+	0.232171i	0.285272	+	0.958447i	$0.407916\pi$
$224$		0			0
$225$	10.6988	−	9.25436i	0.713254	−	0.616957i
$226$		0			0
$227$	7.28833	+	12.6238i	0.483743	+	0.837868i	0.999826	−	0.0186708i	$-0.00594345\pi$
$227$	7.28833	+	12.6238i	0.483743	+	0.837868i	−0.516082	+	0.856539i	$0.672610\pi$
$228$		0			0
$229$	−21.2722	−	12.2815i	−1.40571	−	0.811586i	−0.410738	−	0.911753i	$-0.634729\pi$
$229$	−21.2722	−	12.2815i	−1.40571	−	0.811586i	−0.994971	+	0.100167i	$0.968062\pi$
$230$		0			0
$231$	1.91785	+	17.8852i	0.126185	+	1.17676i
$232$		0			0
$233$			10.5142i			0.688808i	0.938822	+	0.344404i	$0.111919\pi$
$233$			10.5142i			0.688808i	−0.938822	+	0.344404i	$0.888081\pi$
$234$		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	0.934547	−	0.355839i	$-0.115805\pi$
$239$	16.9075	+	9.76154i	1.09365	+	0.631422i	0.159108	+	0.987261i	$0.449138\pi$
$240$		0			0
$241$	−11.3780	+	6.56909i	−0.732922	+	0.423152i	−0.819490	−	0.573093i	$-0.805743\pi$
$241$	−11.3780	+	6.56909i	−0.732922	+	0.423152i	0.0865685	+	0.996246i	$0.472410\pi$
$242$		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	−0.571899	−	0.820324i	$-0.693793\pi$
$257$	6.80481	−	11.7863i	0.424472	−	0.735207i	0.996371	+	0.0851169i	$0.0271264\pi$
$258$		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	0.255468	−	0.966817i	$-0.417770\pi$
$263$	19.7930	−	11.4275i	1.22049	−	0.704651i	0.965023	+	0.262167i	$0.0844371\pi$
$264$		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	$0.0437863\pi$
$271$			4.51473i			0.274251i	−0.990554	+	0.137125i	$0.956214\pi$
$272$		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	0.948932	−	0.315479i	$-0.102165\pi$
$277$	3.34952	+	5.80154i	0.201253	+	0.348581i	−0.747679	+	0.664060i	$0.768832\pi$
$278$		0			0
$279$	−0.909051	+	2.61919i	−0.0544235	+	0.156807i
$280$		0			0
$281$	−15.1414	+	8.74187i	−0.903258	+	0.521496i	−0.878256	−	0.478191i	$-0.841293\pi$
$281$	−15.1414	+	8.74187i	−0.903258	+	0.521496i	−0.0250023	+	0.999687i	$0.507959\pi$
$282$		0			0
$283$	−7.42049	−	4.28422i	−0.441102	−	0.254670i	0.262963	−	0.964806i	$-0.415300\pi$
$283$	−7.42049	−	4.28422i	−0.441102	−	0.254670i	−0.704065	+	0.710135i	$0.748634\pi$
$284$		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	0.255633	+	0.966774i	$0.417716\pi$
$293$	−12.1436	+	21.0333i	−0.709434	+	1.22878i	−0.965067	+	0.262002i	$0.915617\pi$
$294$		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	$0.115883\pi$
$307$			12.4777i			0.712139i	−0.934460	+	0.356069i	$0.884117\pi$
$308$		0			0
$309$	−20.8864	+	7.77994i	−1.18819	+	0.442586i
$310$		0			0
$311$	9.07984	−	15.7267i	0.514871	−	0.891782i	−0.484980	−	0.874525i	$-0.661173\pi$
$311$	9.07984	−	15.7267i	0.514871	−	0.891782i	0.999851	−	0.0172571i	$-0.00549339\pi$
$312$		0			0
$313$	−2.76700	+	1.59753i	−0.156400	+	0.0902977i	−0.576157	−	0.817339i	$-0.695449\pi$
$313$	−2.76700	+	1.59753i	−0.156400	+	0.0902977i	0.419757	+	0.907636i	$0.362115\pi$
$314$		0			0
$315$	−4.22733	−	0.254834i	−0.238183	−	0.0143582i
$316$		0			0
$317$	−22.5893	+	13.0419i	−1.26874	+	0.732508i	−0.974750	−	0.223300i	$-0.928317\pi$
$317$	−22.5893	+	13.0419i	−1.26874	+	0.732508i	−0.293991	+	0.955808i	$0.594984\pi$
$318$		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	0.997931	−	0.0642960i	$-0.0204802\pi$
$331$	8.06484	+	13.9687i	0.443283	+	0.767789i	−0.554647	+	0.832085i	$0.687147\pi$
$332$		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	−0.956890	−	0.290450i	$-0.906195\pi$
$337$	−4.16548	+	7.21482i	−0.226908	+	0.393016i	0.729982	+	0.683466i	$0.239528\pi$
$338$		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	−0.987433	−	0.158037i	$-0.949483\pi$
$347$	−30.1403	−	17.4015i	−1.61801	−	0.934161i	−0.630581	−	0.776124i	$-0.717183\pi$
$348$		0			0
$349$	19.6825	−	11.3637i	1.05358	−	0.608283i	0.129929	−	0.991523i	$-0.458525\pi$
$349$	19.6825	−	11.3637i	1.05358	−	0.608283i	0.923649	+	0.383240i	$0.125192\pi$
$350$		0			0
$351$	0.364313	+	0.599443i	0.0194456	+	0.0319959i
$352$		0			0
$353$	−4.02829	−	6.97721i	−0.214404	−	0.371359i	0.738684	−	0.674052i	$-0.235448\pi$
$353$	−4.02829	−	6.97721i	−0.214404	−	0.371359i	−0.953088	+	0.302693i	$0.902114\pi$
$354$		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	$0.155853\pi$
$359$			17.8217i			0.940594i	−0.882508	+	0.470297i	$0.844147\pi$
$360$		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	0.145258	−	0.989394i	$-0.453599\pi$
$367$	20.5888	−	11.8870i	1.07473	−	0.620494i	0.929469	+	0.368900i	$0.120266\pi$
$368$		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	−0.969577	−	0.244787i	$-0.921282\pi$
$373$	−5.26858	+	9.12545i	−0.272797	+	0.472498i	0.696780	+	0.717285i	$0.254615\pi$
$374$		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	0.132823	−	0.991140i	$-0.457596\pi$
$383$	18.0980	−	31.3466i	0.924764	−	1.60174i	0.791941	−	0.610598i	$-0.209071\pi$
$384$		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	0.0522481	−	0.998634i	$-0.483361\pi$
$389$	18.6031	−	10.7405i	0.943215	−	0.544565i	0.890967	+	0.454069i	$0.150028\pi$
$390$		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	$-0.820451\pi$
$397$		−	21.3049i		−	1.06926i	0.845086	−	0.534630i	$-0.179549\pi$
$398$		0			0
$399$	−9.34165	−	4.13565i	−0.467667	−	0.207041i
$400$		0			0
$401$	15.6821	+	9.05406i	0.783126	+	0.452138i	0.837537	−	0.546381i	$-0.183995\pi$
$401$	15.6821	+	9.05406i	0.783126	+	0.452138i	−0.0544110	+	0.998519i	$0.517328\pi$
$402$		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	0.868760	−	0.495234i	$-0.164918\pi$
$409$	17.6807	+	10.2080i	0.874254	+	0.504751i	0.00549461	+	0.999985i	$0.498251\pi$
$410$		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	−0.370187	−	0.928957i	$-0.620706\pi$
$419$	12.6789	−	21.9606i	0.619407	−	1.07284i	0.989594	−	0.143887i	$-0.0459602\pi$
$420$		0			0
$421$	−3.21875	−	5.57503i	−0.156872	−	0.271710i	0.776867	−	0.629665i	$-0.216808\pi$
$421$	−3.21875	−	5.57503i	−0.156872	−	0.271710i	−0.933739	+	0.357954i	$0.883474\pi$
$422$		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	$0.118799\pi$
$431$			15.1392i			0.729230i	−0.931158	+	0.364615i	$0.881201\pi$
$432$		0			0
$433$		−	8.44792i		−	0.405981i	−0.979181	−	0.202991i	$-0.934934\pi$
$433$		−	8.44792i		−	0.405981i	0.979181	−	0.202991i	$-0.0650661\pi$
$434$		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	−0.944018	−	0.329893i	$-0.892987\pi$
$439$	−23.6831	+	13.6734i	−1.13033	+	0.652598i	−0.186314	+	0.982490i	$0.559654\pi$
$440$		0			0
$441$	−14.1173	−	15.5468i	−0.672251	−	0.740324i
$442$		0			0
$443$	−14.6520	+	8.45931i	−0.696135	+	0.401914i	−0.805906	−	0.592043i	$-0.798322\pi$
$443$	−14.6520	+	8.45931i	−0.696135	+	0.401914i	0.109771	+	0.993957i	$0.464988\pi$
$444$		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	$-0.820973\pi$
$449$		−	22.5985i		−	1.06649i	0.845962	−	0.533244i	$-0.179027\pi$
$450$		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	0.910028	+	0.414547i	$0.136060\pi$
$457$	17.4018	+	30.1408i	0.814022	+	1.40993i	−0.0960053	+	0.995381i	$0.530607\pi$
$458$		0			0
$459$	−19.7119	−	10.7968i	−0.920072	−	0.503949i
$460$		0			0
$461$	13.8264	+	23.9479i	0.643958	+	1.11537i	0.984541	+	0.175153i	$0.0560420\pi$
$461$	13.8264	+	23.9479i	0.643958	+	1.11537i	−0.340584	+	0.940214i	$0.610625\pi$
$462$		0			0
$463$	10.6272	−	18.4069i	0.493889	−	0.855440i	−0.506087	−	0.862483i	$-0.668908\pi$
$463$	10.6272	−	18.4069i	0.493889	−	0.855440i	0.999975	+	0.00704260i	$0.00224175\pi$
$464$		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	0.978824	−	0.204703i	$-0.0656227\pi$
$479$	6.83139	+	11.8323i	0.312134	+	0.540633i	−0.666690	+	0.745335i	$0.732289\pi$
$480$		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	0.844827	−	0.535039i	$-0.179703\pi$
$491$	17.8129	+	10.2843i	0.803883	+	0.464122i	−0.0409440	+	0.999161i	$0.513037\pi$
$492$		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	−0.834322	−	0.551277i	$-0.814141\pi$
$499$	1.34609	−	2.33149i	0.0602592	−	0.104372i	0.894581	+	0.446905i	$0.147474\pi$
$500$		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	−0.924159	−	0.382007i	$-0.875233\pi$
$509$	−2.96117	+	5.12890i	−0.131252	+	0.227334i	0.792908	+	0.609342i	$0.208566\pi$
$510$		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	$0.168007\pi$
$523$			23.0358i			1.00728i	−0.863912	+	0.503642i	$0.831993\pi$
$524$		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	0.993680	+	0.112249i	$0.0358055\pi$
$547$	13.8937	+	24.0646i	0.594051	+	1.02893i	−0.399629	+	0.916677i	$0.630861\pi$
$548$		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	$-0.975587\pi$
$557$		−	3.61667i		−	0.153243i	0.997060	−	0.0766216i	$-0.0244133\pi$
$558$		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	−0.748272	−	0.663393i	$-0.769116\pi$
$563$	4.75452	−	8.23506i	0.200379	−	0.347067i	0.948651	+	0.316326i	$0.102449\pi$
$564$		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	−0.297036	−	0.954866i	$-0.595998\pi$
$569$	9.09742	−	5.25240i	0.381384	−	0.220192i	0.678420	+	0.734674i	$0.262665\pi$
$570$		0			0
$571$	−2.24201	+	3.88328i	−0.0938252	+	0.162510i	−0.909118	−	0.416539i	$-0.863243\pi$
$571$	−2.24201	+	3.88328i	−0.0938252	+	0.162510i	0.815292	+	0.579049i	$0.196576\pi$
$572$		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	$0.439667\pi$
$577$			47.1812i			1.96418i	−0.188410	+	0.982090i	$0.560333\pi$
$578$		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	0.725439	−	0.688287i	$-0.241637\pi$
$587$	−5.65373	−	9.79255i	−0.233354	−	0.404182i	−0.958793	+	0.284105i	$0.908304\pi$
$588$		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	0.979150	−	0.203140i	$-0.0651147\pi$
$599$	31.6406	+	18.2677i	1.29280	+	0.746398i	0.313650	+	0.949539i	$0.398448\pi$
$600$		0			0
$601$	−1.92247	+	1.10994i	−0.0784193	+	0.0452754i	−0.538697	−	0.842500i	$-0.681083\pi$
$601$	−1.92247	+	1.10994i	−0.0784193	+	0.0452754i	0.460278	+	0.887775i	$0.347750\pi$
$602$		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	0.464737	−	0.885449i	$-0.346149\pi$
$607$	−1.71759	−	0.991653i	−0.0697149	−	0.0402499i	−0.534452	+	0.845199i	$0.679482\pi$
$608$		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	0.475690	−	0.879613i	$-0.342198\pi$
$617$	−1.19807	−	0.691704i	−0.0482323	−	0.0278470i	−0.523922	+	0.851766i	$0.675532\pi$
$618$		0			0
$619$	−5.22550	+	3.01694i	−0.210031	+	0.121261i	−0.601326	−	0.799004i	$-0.705361\pi$
$619$	−5.22550	+	3.01694i	−0.210031	+	0.121261i	0.391295	+	0.920265i	$0.372027\pi$
$620$		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	0.595269	−	0.803527i	$-0.297046\pi$
$641$	40.2246	−	23.2237i	1.58878	−	0.917281i	0.993509	−	0.113754i	$-0.0362877\pi$
$642$		0			0
$643$	−9.74133	−	5.62416i	−0.384161	−	0.221795i	0.295466	−	0.955353i	$-0.404525\pi$
$643$	−9.74133	−	5.62416i	−0.384161	−	0.221795i	−0.679627	+	0.733558i	$0.737858\pi$
$644$		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	0.557543	−	0.830148i	$-0.311744\pi$
$653$	2.99966	+	1.73186i	0.117386	+	0.0677727i	−0.440157	+	0.897921i	$0.645077\pi$
$654$		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	−0.530805	−	0.847494i	$-0.678110\pi$
$659$	−1.59819	+	0.922715i	−0.0622566	+	0.0359439i	0.468549	+	0.883438i	$0.344777\pi$
$660$		0			0
$661$	−17.5196	−	10.1149i	−0.681433	−	0.393426i	0.118962	−	0.992899i	$-0.462043\pi$
$661$	−17.5196	−	10.1149i	−0.681433	−	0.393426i	−0.800395	+	0.599473i	$0.795377\pi$
$662$		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	0.689870	−	0.723933i	$-0.257668\pi$
$673$	−7.31596	−	12.6716i	−0.282009	−	0.488455i	−0.971880	+	0.235478i	$0.924334\pi$
$674$		0			0
$675$	−0.551272	−	24.4953i	−0.0212185	−	0.942824i
$676$		0			0
$677$	−7.71449	−	13.3619i	−0.296492	−	0.513539i	0.678839	−	0.734287i	$-0.262483\pi$
$677$	−7.71449	−	13.3619i	−0.296492	−	0.513539i	−0.975331	+	0.220748i	$0.929150\pi$
$678$		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	$0.0972368\pi$
$683$			15.7197i			0.601499i	−0.953703	+	0.300750i	$0.902763\pi$
$684$		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	0.587517	−	0.809212i	$-0.300106\pi$
$691$	41.5878	−	24.0107i	1.58207	−	0.913411i	0.994556	−	0.104199i	$-0.0332278\pi$
$692$		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	$-0.845529\pi$
$701$		−	24.7005i		−	0.932923i	0.884541	−	0.466462i	$-0.154471\pi$
$702$		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	−0.985417	−	0.170159i	$-0.945572\pi$
$709$	−17.0432	−	29.5196i	−0.640070	−	1.10863i	0.345347	−	0.938475i	$-0.387761\pi$
$710$		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	−0.998874	−	0.0474398i	$-0.984894\pi$
$727$	−39.2911	+	22.6847i	−1.45723	+	0.841330i	−0.458353	+	0.888770i	$0.651560\pi$
$728$		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	0.991119	+	0.132981i	$0.0424550\pi$
$733$	43.3683	+	25.0387i	1.60184	+	0.924825i	0.610724	+	0.791843i	$0.290878\pi$
$734$		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	0.973974	−	0.226661i	$-0.0727808\pi$
$743$	34.4723	+	19.9026i	1.26467	+	0.730156i	0.290693	+	0.956816i	$0.406114\pi$
$744$		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	−0.462577	−	0.886579i	$-0.653075\pi$
$751$	14.7028	−	25.4659i	0.536512	−	0.929265i	0.999089	−	0.0426862i	$-0.0135916\pi$
$752$		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	−0.955267	−	0.295744i	$-0.904432\pi$
$761$	−6.11067	+	10.5840i	−0.221511	+	0.383669i	0.733756	+	0.679413i	$0.237766\pi$
$762$		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	−0.134809	−	0.990872i	$-0.543042\pi$
$769$	−29.4039	−	16.9764i	−1.06033	−	0.612184i	−0.925524	+	0.378688i	$0.876375\pi$
$770$		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	0.957879	−	0.287172i	$-0.0927151\pi$
$787$	33.3310	+	19.2436i	1.18812	+	0.685962i	0.230241	+	0.973134i	$0.426048\pi$
$788$		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	−0.960247	−	0.279152i	$-0.909947\pi$
$797$	−6.72949	+	11.6558i	−0.238371	+	0.412870i	0.721876	+	0.692022i	$0.243280\pi$
$798$		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	$0.364163\pi$
$809$			51.7842i			1.82064i	−0.413909	+	0.910318i	$0.635837\pi$
$810$		0			0
$811$			27.2471i			0.956775i	0.878149	+	0.478387i	$0.158779\pi$
$811$			27.2471i			0.956775i	−0.878149	+	0.478387i	$0.841221\pi$
$812$		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	−0.0564968	−	0.998403i	$-0.517993\pi$
$821$	22.3465	−	12.9017i	0.779897	−	0.450274i	0.836394	+	0.548129i	$0.184660\pi$
$822$		0			0
$823$	0.570514	−	0.988159i	0.0198869	−	0.0344451i	−0.855911	−	0.517124i	$-0.827003\pi$
$823$	0.570514	−	0.988159i	0.0198869	−	0.0344451i	0.875798	+	0.482679i	$0.160336\pi$
$824$		0			0
$825$	−30.0416	+	11.1901i	−1.04592	+	0.389591i
$826$		0			0
$827$		−	23.1713i		−	0.805746i	−0.915256	−	0.402873i	$-0.868012\pi$
$827$		−	23.1713i		−	0.805746i	0.915256	−	0.402873i	$-0.131988\pi$
$828$		0			0
$829$		−	9.60364i		−	0.333548i	−0.985995	−	0.166774i	$-0.946665\pi$
$829$		−	9.60364i		−	0.333548i	0.985995	−	0.166774i	$-0.0533351\pi$
$830$		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	−0.998616	−	0.0525978i	$-0.983250\pi$
$839$	−15.7821	−	27.3354i	−0.544859	−	0.943723i	0.453757	−	0.891126i	$-0.350083\pi$
$840$		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	−0.366000	−	0.930615i	$-0.619273\pi$
$853$	7.50412	−	4.33250i	0.256936	−	0.148342i	0.622936	+	0.782273i	$0.285940\pi$
$854$		0			0
$855$	−1.17005	+	3.37120i	−0.0400150	+	0.115293i
$856$		0			0
$857$	−11.4439	−	19.8214i	−0.390917	−	0.677088i	0.601654	−	0.798757i	$-0.294509\pi$
$857$	−11.4439	−	19.8214i	−0.390917	−	0.677088i	−0.992571	+	0.121669i	$0.961175\pi$
$858$		0			0
$859$	−11.4922	−	6.63503i	−0.392109	−	0.226384i	0.290964	−	0.956734i	$-0.406024\pi$
$859$	−11.4922	−	6.63503i	−0.392109	−	0.226384i	−0.683074	+	0.730350i	$0.739357\pi$
$860$		0			0
$861$	24.8000	+	33.9837i	0.845181	+	1.15816i
$862$		0			0
$863$			0.746752i			0.0254197i	0.999919	+	0.0127099i	$0.00404579\pi$
$863$			0.746752i			0.0254197i	−0.999919	+	0.0127099i	$0.995954\pi$
$864$		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	−0.900624	−	0.434600i	$-0.856890\pi$
$877$	−2.18959	+	3.79249i	−0.0739373	+	0.128063i	0.826686	+	0.562663i	$0.190223\pi$
$878$		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	−0.0267221	+	0.999643i	$0.508507\pi$
$887$	−26.1812	+	45.3471i	−0.879077	+	1.52261i	−0.852355	+	0.522963i	$0.824826\pi$
$888$		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	0.994295	−	0.106669i	$-0.0340184\pi$
$907$	12.1902	+	21.1141i	0.404770	+	0.701082i	−0.589525	+	0.807750i	$0.700685\pi$
$908$		0			0
$909$	−33.4380	+	28.9236i	−1.10907	+	0.959335i
$910$		0			0
$911$	−46.8606	+	27.0550i	−1.55256	+	0.896372i	−0.554629	+	0.832098i	$0.687140\pi$
$911$	−46.8606	+	27.0550i	−1.55256	+	0.896372i	−0.997932	+	0.0642741i	$0.979527\pi$
$912$		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	0.998756	−	0.0498555i	$-0.0158761\pi$
$929$	13.9048	+	24.0838i	0.456202	+	0.790165i	−0.542554	+	0.840021i	$0.682543\pi$
$930$		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	$-0.646887\pi$
$937$		−	54.8174i		−	1.79081i	0.445256	−	0.895403i	$-0.353113\pi$
$938$		0			0
$939$	−0.920066	+	5.45698i	−0.0300252	+	0.178082i
$940$		0			0
$941$	2.56526	−	4.44317i	0.0836252	−	0.144843i	−0.821179	−	0.570670i	$-0.806683\pi$
$941$	2.56526	−	4.44317i	0.0836252	−	0.144843i	0.904805	+	0.425827i	$0.140017\pi$
$942$		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	−0.509814	−	0.860284i	$-0.670286\pi$
$947$	−0.606033	+	0.349893i	−0.0196934	+	0.0113700i	0.490121	+	0.871654i	$0.336953\pi$
$948$		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	$-0.999160\pi$
$953$		−	0.162845i		−	0.00527506i	0.999997	−	0.00263753i	$-0.000839552\pi$
$954$		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	0.495211	+	0.868773i	$0.335091\pi$
$967$	−15.6968	+	27.1876i	−0.504773	+	0.874293i	−0.999985	+	0.00552073i	$0.998243\pi$
$968$		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	0.0497913	−	0.998760i	$-0.484144\pi$
$977$	−24.7013	−	14.2613i	−0.790264	−	0.456259i	−0.840056	+	0.542500i	$0.817478\pi$
$978$		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	0.941722	−	0.336393i	$-0.109207\pi$
$983$	5.62897	+	9.74967i	0.179536	+	0.310966i	−0.762185	+	0.647359i	$0.775874\pi$
$984$		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	−0.249603	−	0.968348i	$-0.580300\pi$
$997$	14.6576	−	8.46256i	0.464210	−	0.268012i	0.713813	+	0.700336i	$0.246967\pi$
$998$		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.41.6	yes	16
3.2	odd	2		756.2.x.a.125.4		16
4.3	odd	2		1008.2.cc.c.545.3		16
7.2	even	3		1764.2.bm.b.1697.5		16
7.3	odd	6		1764.2.w.a.509.8		16
7.4	even	3		1764.2.w.a.509.1		16
7.5	odd	6		1764.2.bm.b.1697.4		16
7.6	odd	2	inner	252.2.x.a.41.3	✓	16
9.2	odd	6	inner	252.2.x.a.209.3	yes	16
9.4	even	3		2268.2.f.b.1133.8		16
9.5	odd	6		2268.2.f.b.1133.10		16
9.7	even	3		756.2.x.a.629.5		16
12.11	even	2		3024.2.cc.c.881.4		16
21.2	odd	6		5292.2.bm.b.2285.5		16
21.5	even	6		5292.2.bm.b.2285.4		16
21.11	odd	6		5292.2.w.a.1097.4		16
21.17	even	6		5292.2.w.a.1097.5		16
21.20	even	2		756.2.x.a.125.5		16
28.27	even	2		1008.2.cc.c.545.6		16
36.7	odd	6		3024.2.cc.c.2897.5		16
36.11	even	6		1008.2.cc.c.209.6		16
63.2	odd	6		1764.2.w.a.1109.8		16
63.11	odd	6		1764.2.bm.b.1685.4		16
63.13	odd	6		2268.2.f.b.1133.9		16
63.16	even	3		5292.2.w.a.521.5		16
63.20	even	6	inner	252.2.x.a.209.6	yes	16
63.25	even	3		5292.2.bm.b.4625.4		16
63.34	odd	6		756.2.x.a.629.4		16
63.38	even	6		1764.2.bm.b.1685.5		16
63.41	even	6		2268.2.f.b.1133.7		16
63.47	even	6		1764.2.w.a.1109.1		16
63.52	odd	6		5292.2.bm.b.4625.5		16
63.61	odd	6		5292.2.w.a.521.4		16
84.83	odd	2		3024.2.cc.c.881.5		16
252.83	odd	6		1008.2.cc.c.209.3		16
252.223	even	6		3024.2.cc.c.2897.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.3	✓	16	7.6	odd	2	inner
252.2.x.a.41.6	yes	16	1.1	even	1	trivial
252.2.x.a.209.3	yes	16	9.2	odd	6	inner
252.2.x.a.209.6	yes	16	63.20	even	6	inner
756.2.x.a.125.4		16	3.2	odd	2
756.2.x.a.125.5		16	21.20	even	2
756.2.x.a.629.4		16	63.34	odd	6
756.2.x.a.629.5		16	9.7	even	3
1008.2.cc.c.209.3		16	252.83	odd	6
1008.2.cc.c.209.6		16	36.11	even	6
1008.2.cc.c.545.3		16	4.3	odd	2
1008.2.cc.c.545.6		16	28.27	even	2
1764.2.w.a.509.1		16	7.4	even	3
1764.2.w.a.509.8		16	7.3	odd	6
1764.2.w.a.1109.1		16	63.47	even	6
1764.2.w.a.1109.8		16	63.2	odd	6
1764.2.bm.b.1685.4		16	63.11	odd	6
1764.2.bm.b.1685.5		16	63.38	even	6
1764.2.bm.b.1697.4		16	7.5	odd	6
1764.2.bm.b.1697.5		16	7.2	even	3
2268.2.f.b.1133.7		16	63.41	even	6
2268.2.f.b.1133.8		16	9.4	even	3
2268.2.f.b.1133.9		16	63.13	odd	6
2268.2.f.b.1133.10		16	9.5	odd	6
3024.2.cc.c.881.4		16	12.11	even	2
3024.2.cc.c.881.5		16	84.83	odd	2
3024.2.cc.c.2897.4		16	252.223	even	6
3024.2.cc.c.2897.5		16	36.7	odd	6
5292.2.w.a.521.4		16	63.61	odd	6
5292.2.w.a.521.5		16	63.16	even	3
5292.2.w.a.1097.4		16	21.11	odd	6
5292.2.w.a.1097.5		16	21.17	even	6
5292.2.bm.b.2285.4		16	21.5	even	6
5292.2.bm.b.2285.5		16	21.2	odd	6
5292.2.bm.b.4625.4		16	63.25	even	3
5292.2.bm.b.4625.5		16	63.52	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

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Representations

Groups

Database

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