LMFDB - Embedded newform 252.2.x.a.41.3

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			41.3
Root			$-0.604587 - 1.62311i$ of defining polynomial
Character	$\chi$	$=$	252.41
Dual form			252.2.x.a.209.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10336 + 1.33514i) q^{3} +(-0.266780 + 0.462077i) q^{5} +(-1.89325 + 1.84814i) q^{7} +(-0.565203 - 2.94628i) q^{9} +O(q^{10})$	\(q+(-1.10336 + 1.33514i) q^{3} +(-0.266780 + 0.462077i) q^{5} +(-1.89325 + 1.84814i) q^{7} +(-0.565203 - 2.94628i) q^{9} +(-3.39936 + 1.96262i) q^{11} +(0.116911 + 0.0674987i) q^{13} +(-0.322584 - 0.866025i) q^{15} -4.32533 q^{17} +2.22935i q^{19} +(-0.378597 - 4.56691i) q^{21} +(-1.70375 - 0.983658i) q^{23} +(2.35766 + 4.08358i) q^{25} +(4.55732 + 2.49617i) q^{27} +(-5.16548 + 2.98229i) q^{29} +(0.800341 + 0.462077i) q^{31} +(1.13033 - 6.70409i) q^{33} +(-0.348901 - 1.36787i) q^{35} +7.79871 q^{37} +(-0.219115 + 0.0816177i) q^{39} +(4.59027 - 7.95059i) q^{41} +(3.24544 + 5.62127i) q^{43} +(1.51219 + 0.524841i) q^{45} +(3.04329 + 5.27114i) q^{47} +(0.168767 - 6.99797i) q^{49} +(4.77238 - 5.77492i) q^{51} +11.0167i q^{53} -2.09435i q^{55} +(-2.97650 - 2.45977i) q^{57} +(1.89588 - 3.28377i) q^{59} +(9.35116 - 5.39889i) q^{61} +(6.51520 + 4.53345i) q^{63} +(-0.0623791 + 0.0360146i) q^{65} +(-5.75701 + 9.97144i) q^{67} +(3.19316 - 1.18941i) q^{69} -3.22884i q^{71} +0.381041i q^{73} +(-8.05350 - 1.35785i) q^{75} +(2.80863 - 9.99820i) q^{77} +(-4.60310 - 7.97280i) q^{79} +(-8.36109 + 3.33049i) q^{81} +(1.28020 + 2.21737i) q^{83} +(1.15391 - 1.99863i) q^{85} +(1.71759 - 10.1872i) q^{87} -17.1334 q^{89} +(-0.346088 + 0.0882763i) q^{91} +(-1.50000 + 0.558732i) q^{93} +(-1.03013 - 0.594746i) q^{95} +(-13.6747 + 7.89507i) q^{97} +(7.70375 + 8.90616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.919494	−	0.393105i	$-0.871401\pi$
$5$	−0.266780	+	0.462077i	−0.119308	+	0.206647i	0.800186	+	0.599752i	$0.204734\pi$
$6$		0			0
$7$	−1.89325	+	1.84814i	−0.715580	+	0.698531i
$7$	−1.89325	+	1.84814i	−0.715580	+	0.698531i
$8$		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	0.516125	−	0.856513i	$-0.327374\pi$
$13$	0.116911	+	0.0674987i	0.0324253	+	0.0187208i	−0.483700	+	0.875234i	$0.660707\pi$
$14$		0			0
$15$	−0.322584	−	0.866025i	−0.0832908	−	0.223607i
$16$		0			0
$17$	−4.32533			−1.04905			−0.524523	−	0.851396i	$-0.675756\pi$
$17$	−4.32533			−1.04905			−0.524523	+	0.851396i	$0.675756\pi$
$18$		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
$21$	−0.378597	−	4.56691i	−0.0826167	−	0.996581i
$22$		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	0.570148	−	0.821542i	$-0.306886\pi$
$31$	0.800341	+	0.462077i	0.143745	+	0.0829915i	−0.426402	+	0.904534i	$0.640219\pi$
$32$		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	$-0.578903\pi$
$41$	4.59027	−	7.95059i	0.716880	−	1.24167i	0.962230	−	0.272239i	$-0.0877640\pi$
$42$		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	0.997976	−	0.0635985i	$-0.0202577\pi$
$47$	3.04329	+	5.27114i	0.443910	+	0.768874i	−0.554066	+	0.832473i	$0.686924\pi$
$48$		0			0
$49$	0.168767	−	6.99797i	0.0241096	−	0.999709i
$50$		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	−0.715820	−	0.698285i	$-0.753947\pi$
$59$	1.89588	−	3.28377i	0.246823	−	0.427510i	0.962643	+	0.270775i	$0.0872801\pi$
$60$		0			0
$61$	9.35116	−	5.39889i	1.19729	−	0.691258i	0.237342	−	0.971426i	$-0.423724\pi$
$61$	9.35116	−	5.39889i	1.19729	−	0.691258i	0.959951	+	0.280168i	$0.0903903\pi$
$62$		0			0
$63$	6.51520	+	4.53345i	0.820838	+	0.571162i
$64$		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	$0.00709850\pi$
$73$			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
$77$	2.80863	−	9.99820i	0.320073	−	1.13940i
$78$		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	0.927693	−	0.373345i	$-0.121789\pi$
$83$	1.28020	+	2.21737i	0.140520	+	0.243388i	−0.787172	+	0.616733i	$0.788456\pi$
$84$		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	$-0.862443\pi$
$89$	−17.1334			−1.81614			−0.908068	+	0.418822i	$0.862443\pi$
$90$		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	$-0.962696\pi$
$97$	−13.6747	+	7.89507i	−1.38845	+	0.801622i	−0.395310	+	0.918548i	$0.629363\pi$
$98$		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	$0.0953098\pi$
$101$	7.36862	+	12.7628i	0.733205	+	1.26995i	−0.222301	+	0.974978i	$0.571357\pi$
$102$		0			0
$103$	11.1442	+	6.43410i	1.09807	+	0.633970i	0.935713	−	0.352762i	$-0.114757\pi$
$103$	11.1442	+	6.43410i	1.09807	+	0.633970i	0.162356	+	0.986732i	$0.448091\pi$
$104$		0			0
$105$	2.21127	+	1.04342i	0.215797	+	0.101827i
$106$		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
$119$	8.18891	−	7.99380i	0.750676	−	0.732791i
$120$		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	$0.406027\pi$
$131$	−7.81823	+	13.5416i	−0.683082	+	1.18313i	−0.974036	+	0.226395i	$0.927306\pi$
$132$		0			0
$133$	−4.12015	−	4.22071i	−0.357262	−	0.365982i
$134$		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	−0.432342	−	0.901710i	$-0.642313\pi$
$139$	−16.8526	−	9.72984i	−1.42942	−	0.825274i	−0.997074	+	0.0764359i	$0.975646\pi$
$140$		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
$147$	9.15706	+	7.94659i	0.755262	+	0.655423i
$148$		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	0.775916	−	0.630836i	$-0.217288\pi$
$157$	7.73794	+	4.46750i	0.617555	+	0.356545i	−0.158362	+	0.987381i	$0.550621\pi$
$158$		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	$-0.671998\pi$
$167$	6.27308	−	10.8653i	0.485425	−	0.840781i	0.999860	+	0.0167485i	$0.00533145\pi$
$168$		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	$0.134892\pi$
$173$	10.6787	+	18.4960i	0.811886	+	1.40623i	−0.0996566	+	0.995022i	$0.531774\pi$
$174$		0			0
$175$	−12.0106	−	3.37395i	−0.907920	−	0.255047i
$176$		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	$0.0885460\pi$
$181$			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
$189$	−13.2414	+	3.69669i	−0.963170	+	0.268894i
$190$		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	$-0.901986\pi$
$199$		−	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
$203$	4.26784	−	15.1927i	0.299544	−	1.06632i
$204$		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	−0.285272	−	0.958447i	$-0.592084\pi$
$223$	6.00510	−	3.46705i	0.402131	−	0.232171i	0.687403	+	0.726276i	$0.258751\pi$
$224$		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	$-0.327390\pi$
$227$	−7.28833	−	12.6238i	−0.483743	−	0.837868i	−0.999826	+	0.0186708i	$0.994057\pi$
$228$		0			0
$229$	21.2722	+	12.2815i	1.40571	+	0.811586i	0.994971	−	0.100167i	$-0.0319377\pi$
$229$	21.2722	+	12.2815i	1.40571	+	0.811586i	0.410738	+	0.911753i	$0.365271\pi$
$230$		0			0
$231$	10.2501	+	14.7815i	0.674406	+	0.972552i
$232$		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	−0.0865685	−	0.996246i	$-0.527590\pi$
$241$	11.3780	−	6.56909i	0.732922	−	0.423152i	0.819490	+	0.573093i	$0.194257\pi$
$242$		0			0
$243$	4.77860	−	14.8380i	0.306547	−	0.951855i
$244$		0			0
$245$	3.18857	+	1.94490i	0.203711	+	0.124255i
$246$		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	$-0.245981\pi$
$251$	22.6864			1.43195			0.715977	+	0.698124i	$0.245981\pi$
$252$		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	$-0.972874\pi$
$257$	−6.80481	+	11.7863i	−0.424472	+	0.735207i	0.571899	+	0.820324i	$0.306207\pi$
$258$		0			0
$259$	−14.7649	+	14.4131i	−0.917445	+	0.895586i
$260$		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	$-0.605536\pi$
$269$	−10.6775			−0.651018			−0.325509	+	0.945539i	$0.605536\pi$
$270$		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
$273$	0.263998	−	0.559477i	0.0159779	−	0.0338611i
$274$		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	0.704065	−	0.710135i	$-0.251366\pi$
$283$	7.42049	+	4.28422i	0.441102	+	0.254670i	−0.262963	+	0.964806i	$0.584700\pi$
$284$		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	$-0.582284\pi$
$293$	12.1436	−	21.0333i	0.709434	−	1.22878i	0.965067	−	0.262002i	$-0.0843826\pi$
$294$		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
$301$	−16.5333	−	4.64443i	−0.952965	−	0.267700i
$302$		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	0.484980	+	0.874525i	$0.338827\pi$
$311$	−9.07984	+	15.7267i	−0.514871	+	0.891782i	−0.999851	+	0.0172571i	$0.994507\pi$
$312$		0			0
$313$	2.76700	−	1.59753i	0.156400	−	0.0902977i	−0.419757	−	0.907636i	$-0.637885\pi$
$313$	2.76700	−	1.59753i	0.156400	−	0.0902977i	0.576157	+	0.817339i	$0.304551\pi$
$314$		0			0
$315$	−3.83293	+	1.80109i	−0.215961	+	0.101480i
$316$		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
$329$	−15.5035	−	4.35514i	−0.854736	−	0.240107i
$330$		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	−0.923649	−	0.383240i	$-0.874808\pi$
$349$	−19.6825	+	11.3637i	−1.05358	+	0.608283i	−0.129929	+	0.991523i	$0.541475\pi$
$350$		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	$-0.0978856\pi$
$353$	4.02829	+	6.97721i	0.214404	+	0.371359i	−0.738684	+	0.674052i	$0.764552\pi$
$354$		0			0
$355$	1.49197	+	0.861390i	0.0791856	+	0.0457178i
$356$		0			0
$357$	1.63756	+	19.7534i	0.0866687	+	1.04546i
$358$		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	−0.929469	−	0.368900i	$-0.879734\pi$
$367$	−20.5888	+	11.8870i	−1.07473	+	0.620494i	−0.145258	+	0.989394i	$0.546401\pi$
$368$		0			0
$369$	−26.0191	−	9.03052i	−1.35450	−	0.470110i
$370$		0			0
$371$	−20.3603	−	20.8573i	−1.05706	−	1.08286i
$372$		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	$0.542404\pi$
$383$	−18.0980	+	31.3466i	−0.924764	+	1.60174i	−0.791941	+	0.610598i	$0.790929\pi$
$384$		0			0
$385$	3.87065	+	3.96512i	0.197267	+	0.202081i
$386$		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	$0.179549\pi$
$397$			21.3049i			1.06926i	−0.845086	+	0.534630i	$0.820451\pi$
$398$		0			0
$399$	10.1812	−	0.844025i	0.509699	−	0.0422541i
$400$		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	−0.00549461	−	0.999985i	$-0.501749\pi$
$409$	−17.6807	−	10.2080i	−0.874254	−	0.504751i	−0.868760	+	0.495234i	$0.835082\pi$
$410$		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	$0.379294\pi$
$419$	−12.6789	+	21.9606i	−0.619407	+	1.07284i	−0.989594	+	0.143887i	$0.954040\pi$
$420$		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
$427$	−7.72615	+	27.5037i	−0.373895	+	1.33100i
$428$		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	$0.0650661\pi$
$433$			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	$-0.440346\pi$
$439$	23.6831	−	13.6734i	1.13033	−	0.652598i	0.944018	+	0.329893i	$0.107013\pi$
$440$		0			0
$441$	−20.7133	+	3.45804i	−0.986349	+	0.164669i
$442$		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
$455$	0.0515391	−	0.183470i	0.00241619	−	0.00860120i
$456$		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	$-0.943958\pi$
$461$	−13.8264	−	23.9479i	−0.643958	−	1.11537i	0.340584	−	0.940214i	$-0.389375\pi$
$462$		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	$-0.434676\pi$
$467$	8.80757			0.407566			0.203783	+	0.979016i	$0.434676\pi$
$468$		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	$-0.267711\pi$
$479$	−6.83139	−	11.8323i	−0.312134	−	0.540633i	−0.978824	+	0.204703i	$0.934377\pi$
$480$		0			0
$481$	0.911756	+	0.526403i	0.0415725	+	0.0240019i
$482$		0			0
$483$	−3.84724	+	8.15326i	−0.175056	+	0.370986i
$484$		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
$497$	5.96734	+	6.11299i	0.267672	+	0.274205i
$498$		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	$-0.290942\pi$
$503$	27.3871			1.22113			0.610566	+	0.791965i	$0.290942\pi$
$504$		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	$-0.791434\pi$
$509$	2.96117	−	5.12890i	0.131252	−	0.227334i	0.924159	+	0.382007i	$0.124767\pi$
$510$		0			0
$511$	−0.704217	−	0.721405i	−0.0311527	−	0.0319131i
$512$		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	$-0.171433\pi$
$521$	39.1886			1.71688			0.858442	+	0.512911i	$0.171433\pi$
$522$		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
$525$	17.7567	−	12.3132i	0.774968	−	0.537394i
$526$		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
$553$	23.4497	+	6.58732i	0.997181	+	0.280121i
$554$		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	−0.948651	−	0.316326i	$-0.897551\pi$
$563$	−4.75452	+	8.23506i	−0.200379	+	0.347067i	0.748272	+	0.663393i	$0.230884\pi$
$564$		0			0
$565$	−4.24807	+	2.45262i	−0.178718	+	0.103183i
$566$		0			0
$567$	9.67440	−	21.7579i	0.406287	−	0.913746i
$568$		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	$-0.560333\pi$
$577$		−	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
$581$	−6.52175	−	1.83205i	−0.270568	−	0.0760061i
$582$		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	$-0.0916964\pi$
$587$	5.65373	+	9.79255i	0.233354	+	0.404182i	−0.725439	+	0.688287i	$0.758363\pi$
$588$		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	$-0.437845\pi$
$593$	9.44980			0.388057			0.194028	+	0.980996i	$0.437845\pi$
$594$		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	−0.460278	−	0.887775i	$-0.652250\pi$
$601$	1.92247	−	1.10994i	0.0784193	−	0.0452754i	0.538697	+	0.842500i	$0.318917\pi$
$602$		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	$-0.320518\pi$
$607$	1.71759	+	0.991653i	0.0697149	+	0.0402499i	−0.464737	+	0.885449i	$0.653851\pi$
$608$		0			0
$609$	15.5755	+	22.4612i	0.631151	+	0.910173i
$610$		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	−0.391295	−	0.920265i	$-0.627973\pi$
$619$	5.22550	−	3.01694i	0.210031	−	0.121261i	0.601326	+	0.799004i	$0.294639\pi$
$620$		0			0
$621$	−5.30913	−	8.73568i	−0.213048	−	0.350551i
$622$		0			0
$623$	32.4378	−	31.6649i	1.29959	−	1.26863i
$624$		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
$637$	0.492084	−	0.806748i	0.0194971	−	0.0319645i
$638$		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	0.679627	−	0.733558i	$-0.262142\pi$
$643$	9.74133	+	5.62416i	0.384161	+	0.221795i	−0.295466	+	0.955353i	$0.595475\pi$
$644$		0			0
$645$	3.82124	−	4.62397i	0.150461	−	0.182069i
$646$		0			0
$647$	−4.65015			−0.182816			−0.0914081	−	0.995814i	$-0.529137\pi$
$647$	−4.65015			−0.182816			−0.0914081	+	0.995814i	$0.529137\pi$
$648$		0			0
$649$			14.8836i			0.584232i
$650$		0			0
$651$	1.80726	−	3.83002i	0.0708320	−	0.150111i
$652$		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	0.800395	−	0.599473i	$-0.204623\pi$
$661$	17.5196	+	10.1149i	0.681433	+	0.393426i	−0.118962	+	0.992899i	$0.537957\pi$
$662$		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	0.975331	−	0.220748i	$-0.0708499\pi$
$677$	7.71449	+	13.3619i	0.296492	+	0.513539i	−0.678839	+	0.734287i	$0.737517\pi$
$678$		0			0
$679$	11.2983	−	40.2200i	0.433590	−	1.54350i
$680$		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	$0.699894\pi$
$691$	−41.5878	+	24.0107i	−1.58207	+	0.913411i	−0.994556	+	0.104199i	$0.966772\pi$
$692$		0			0
$693$	−31.0449	−	2.62397i	−1.17930	−	0.0996766i
$694$		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
$707$	−37.5381	−	10.5449i	−1.41176	−	0.396583i
$708$		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	$-0.388043\pi$
$719$	18.4758			0.689032			0.344516	+	0.938780i	$0.388043\pi$
$720$		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	$-0.348440\pi$
$727$	39.2911	−	22.6847i	1.45723	−	0.841330i	0.998874	+	0.0474398i	$0.0151062\pi$
$728$		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	$-0.957545\pi$
$733$	−43.3683	−	25.0387i	−1.60184	−	0.924825i	−0.610724	−	0.791843i	$-0.709122\pi$
$734$		0			0
$735$	−6.11486	+	2.11127i	−0.225550	+	0.0778755i
$736$		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
$749$	29.1680	+	29.8799i	1.06578	+	1.09179i
$750$		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	−0.733756	−	0.679413i	$-0.762234\pi$
$761$	6.11067	−	10.5840i	0.221511	−	0.383669i	0.955267	+	0.295744i	$0.0955676\pi$
$762$		0			0
$763$	5.83763	−	5.69855i	0.211337	−	0.206301i
$764$		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	$-0.123625\pi$
$769$	29.4039	+	16.9764i	1.06033	+	0.612184i	0.134809	+	0.990872i	$0.456958\pi$
$770$		0			0
$771$	−8.22820	−	22.0898i	−0.296331	−	0.795546i
$772$		0			0
$773$	−30.2094			−1.08656			−0.543279	−	0.839552i	$-0.682817\pi$
$773$	−30.2094			−1.08656			−0.543279	+	0.839552i	$0.682817\pi$
$774$		0			0
$775$			4.35767i			0.156532i
$776$		0			0
$777$	−2.95257	−	35.6160i	−0.105923	−	1.27772i
$778$		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	$-0.573952\pi$
$787$	−33.3310	−	19.2436i	−1.18812	−	0.685962i	−0.957879	+	0.287172i	$0.907285\pi$
$788$		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	$-0.756720\pi$
$797$	6.72949	−	11.6558i	0.238371	−	0.412870i	0.960247	+	0.279152i	$0.0900533\pi$
$798$		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
$805$	−0.751079	+	2.67371i	−0.0264721	+	0.0942357i
$806$		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	$-0.841221\pi$
$811$		−	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
$819$	0.455697	+	0.969778i	0.0159233	+	0.0338868i
$820$		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	$0.0533351\pi$
$829$			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
$833$	−0.729974	+	30.2685i	−0.0252921	+	1.04874i
$834$		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	$0.0167501\pi$
$839$	15.7821	+	27.3354i	0.544859	+	0.943723i	−0.453757	+	0.891126i	$0.649917\pi$
$840$		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	$-0.714060\pi$
$853$	−7.50412	+	4.33250i	−0.256936	+	0.148342i	0.366000	+	0.930615i	$0.380727\pi$
$854$		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	$-0.0388247\pi$
$857$	11.4439	+	19.8214i	0.390917	+	0.677088i	−0.601654	+	0.798757i	$0.705491\pi$
$858$		0			0
$859$	11.4922	+	6.63503i	0.392109	+	0.226384i	0.683074	−	0.730350i	$-0.260643\pi$
$859$	11.4922	+	6.63503i	0.392109	+	0.226384i	−0.290964	+	0.956734i	$0.593976\pi$
$860$		0			0
$861$	−38.0475	−	17.9533i	−1.29665	−	0.611847i
$862$		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
$875$	9.81404	−	9.58021i	0.331775	−	0.323870i
$876$		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	$-0.423387\pi$
$881$	14.1505			0.476742			0.238371	+	0.971174i	$0.423387\pi$
$882$		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	$-0.491493\pi$
$887$	26.1812	−	45.3471i	0.879077	−	1.52261i	0.852355	−	0.522963i	$-0.175174\pi$
$888$		0			0
$889$	19.1342	−	18.6783i	0.641739	−	0.626449i
$890$		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
$903$	24.4431	−	16.9498i	0.813417	−	0.564056i
$904$		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	0.542554	−	0.840021i	$-0.317457\pi$
$929$	−13.9048	−	24.0838i	−0.456202	−	0.790165i	−0.998756	+	0.0498555i	$0.984124\pi$
$930$		0			0
$931$	15.6009	+	0.376242i	0.511299	+	0.0123308i
$932$		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	$-0.859983\pi$
$941$	−2.56526	+	4.44317i	−0.0836252	+	0.144843i	0.821179	+	0.570670i	$0.193317\pi$
$942$		0			0
$943$	−15.6413	+	9.03052i	−0.509351	+	0.294074i
$944$		0			0
$945$	1.82439	−	7.10475i	0.0593474	−	0.231117i
$946$		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
$959$	−1.76722	+	6.29097i	−0.0570664	+	0.203146i
$960$		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	$-0.485068\pi$
$971$	2.92239			0.0937841			0.0468920	+	0.998900i	$0.485068\pi$
$972$		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	0.762185	−	0.647359i	$-0.224126\pi$
$983$	−5.62897	−	9.74967i	−0.179536	−	0.310966i	−0.941722	+	0.336393i	$0.890793\pi$
$984$		0			0
$985$	7.00416	+	4.04386i	0.223171	+	0.128848i
$986$		0			0
$987$	22.9206	−	15.8941i	0.729572	−	0.505914i
$988$		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	$-0.753033\pi$
$997$	−14.6576	+	8.46256i	−0.464210	+	0.268012i	0.249603	+	0.968348i	$0.419700\pi$
$998$		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.41.3	✓	16
3.2	odd	2		756.2.x.a.125.5		16
4.3	odd	2		1008.2.cc.c.545.6		16
7.2	even	3		1764.2.bm.b.1697.4		16
7.3	odd	6		1764.2.w.a.509.1		16
7.4	even	3		1764.2.w.a.509.8		16
7.5	odd	6		1764.2.bm.b.1697.5		16
7.6	odd	2	inner	252.2.x.a.41.6	yes	16
9.2	odd	6	inner	252.2.x.a.209.6	yes	16
9.4	even	3		2268.2.f.b.1133.9		16
9.5	odd	6		2268.2.f.b.1133.7		16
9.7	even	3		756.2.x.a.629.4		16
12.11	even	2		3024.2.cc.c.881.5		16
21.2	odd	6		5292.2.bm.b.2285.4		16
21.5	even	6		5292.2.bm.b.2285.5		16
21.11	odd	6		5292.2.w.a.1097.5		16
21.17	even	6		5292.2.w.a.1097.4		16
21.20	even	2		756.2.x.a.125.4		16
28.27	even	2		1008.2.cc.c.545.3		16
36.7	odd	6		3024.2.cc.c.2897.4		16
36.11	even	6		1008.2.cc.c.209.3		16
63.2	odd	6		1764.2.w.a.1109.1		16
63.11	odd	6		1764.2.bm.b.1685.5		16
63.13	odd	6		2268.2.f.b.1133.8		16
63.16	even	3		5292.2.w.a.521.4		16
63.20	even	6	inner	252.2.x.a.209.3	yes	16
63.25	even	3		5292.2.bm.b.4625.5		16
63.34	odd	6		756.2.x.a.629.5		16
63.38	even	6		1764.2.bm.b.1685.4		16
63.41	even	6		2268.2.f.b.1133.10		16
63.47	even	6		1764.2.w.a.1109.8		16
63.52	odd	6		5292.2.bm.b.4625.4		16
63.61	odd	6		5292.2.w.a.521.5		16
84.83	odd	2		3024.2.cc.c.881.4		16
252.83	odd	6		1008.2.cc.c.209.6		16
252.223	even	6		3024.2.cc.c.2897.5		16

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

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)

\(f(q)\)	\(=\)	\(q+(-1.10336 + 1.33514i) q^{3} +(-0.266780 + 0.462077i) q^{5} +(-1.89325 + 1.84814i) q^{7} +(-0.565203 - 2.94628i) q^{9} +O(q^{10})\)	\(q+(-1.10336 + 1.33514i) q^{3} +(-0.266780 + 0.462077i) q^{5} +(-1.89325 + 1.84814i) q^{7} +(-0.565203 - 2.94628i) q^{9} +(-3.39936 + 1.96262i) q^{11} +(0.116911 + 0.0674987i) q^{13} +(-0.322584 - 0.866025i) q^{15} -4.32533 q^{17} +2.22935i q^{19} +(-0.378597 - 4.56691i) q^{21} +(-1.70375 - 0.983658i) q^{23} +(2.35766 + 4.08358i) q^{25} +(4.55732 + 2.49617i) q^{27} +(-5.16548 + 2.98229i) q^{29} +(0.800341 + 0.462077i) q^{31} +(1.13033 - 6.70409i) q^{33} +(-0.348901 - 1.36787i) q^{35} +7.79871 q^{37} +(-0.219115 + 0.0816177i) q^{39} +(4.59027 - 7.95059i) q^{41} +(3.24544 + 5.62127i) q^{43} +(1.51219 + 0.524841i) q^{45} +(3.04329 + 5.27114i) q^{47} +(0.168767 - 6.99797i) q^{49} +(4.77238 - 5.77492i) q^{51} +11.0167i q^{53} -2.09435i q^{55} +(-2.97650 - 2.45977i) q^{57} +(1.89588 - 3.28377i) q^{59} +(9.35116 - 5.39889i) q^{61} +(6.51520 + 4.53345i) q^{63} +(-0.0623791 + 0.0360146i) q^{65} +(-5.75701 + 9.97144i) q^{67} +(3.19316 - 1.18941i) q^{69} -3.22884i q^{71} +0.381041i q^{73} +(-8.05350 - 1.35785i) q^{75} +(2.80863 - 9.99820i) q^{77} +(-4.60310 - 7.97280i) q^{79} +(-8.36109 + 3.33049i) q^{81} +(1.28020 + 2.21737i) q^{83} +(1.15391 - 1.99863i) q^{85} +(1.71759 - 10.1872i) q^{87} -17.1334 q^{89} +(-0.346088 + 0.0882763i) q^{91} +(-1.50000 + 0.558732i) q^{93} +(-1.03013 - 0.594746i) q^{95} +(-13.6747 + 7.89507i) q^{97} +(7.70375 + 8.90616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 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

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Representations

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Database

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