LMFDB - Embedded newform 1764.2.bm.b.1697.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1685,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 5]))

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

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

chi := DirichletCharacter("1764.1685");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.bm (of order $6$, degree $2$, not 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:	$14.0856109166$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1697.5
Root			$0.604587 + 1.62311i$ of defining polynomial
Character	$\chi$	$=$	1764.1697
Dual form			1764.2.bm.b.1685.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.604587 + 1.62311i) q^{3} -0.533560 q^{5} +(-2.26895 + 1.96262i) q^{9} +O(q^{10})$	\(q+(0.604587 + 1.62311i) q^{3} -0.533560 q^{5} +(-2.26895 + 1.96262i) q^{9} -3.92524i q^{11} +(-0.116911 - 0.0674987i) q^{13} +(-0.322584 - 0.866025i) q^{15} +(-2.16266 + 3.74584i) q^{17} +(-1.93067 + 1.11467i) q^{19} +1.96732i q^{23} -4.71531 q^{25} +(-4.55732 - 2.49617i) q^{27} +(-5.16548 + 2.98229i) q^{29} +(0.800341 - 0.462077i) q^{31} +(6.37108 - 2.37315i) q^{33} +(-3.89936 - 6.75388i) q^{37} +(0.0388745 - 0.230568i) q^{39} +(-4.59027 + 7.95059i) q^{41} +(3.24544 + 5.62127i) q^{43} +(1.21062 - 1.04718i) q^{45} +(-3.04329 + 5.27114i) q^{47} +(-7.38742 - 1.24554i) q^{51} +(-9.54072 - 5.50834i) q^{53} +2.09435i q^{55} +(-2.97650 - 2.45977i) q^{57} +(-1.89588 - 3.28377i) q^{59} +(9.35116 + 5.39889i) q^{61} +(0.0623791 + 0.0360146i) q^{65} +(-5.75701 - 9.97144i) q^{67} +(-3.19316 + 1.18941i) q^{69} -3.22884i q^{71} +(0.329991 + 0.190521i) q^{73} +(-2.85082 - 7.65345i) q^{75} +(-4.60310 + 7.97280i) q^{79} +(1.29625 - 8.90616i) q^{81} +(-1.28020 - 2.21737i) q^{83} +(1.15391 - 1.99863i) q^{85} +(-7.96356 - 6.58107i) q^{87} +(-8.56670 - 14.8380i) q^{89} +(1.23388 + 1.01967i) q^{93} +(1.03013 - 0.594746i) q^{95} +(13.6747 - 7.89507i) q^{97} +(7.70375 + 8.90616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{9}+O(q^{10}) $ 16 * q + 6 * q^9	$ 16 q + 6 q^{9} - 12 q^{15} + 16 q^{25} - 12 q^{29} - 2 q^{37} + 18 q^{39} + 4 q^{43} + 6 q^{51} - 36 q^{53} - 42 q^{57} + 24 q^{65} + 14 q^{67} + 20 q^{79} + 54 q^{81} + 6 q^{85} + 30 q^{93} + 60 q^{95} + 90 q^{99}+O(q^{100}) $ 16 * q + 6 * q^9 - 12 * q^15 + 16 * q^25 - 12 * q^29 - 2 * q^37 + 18 * q^39 + 4 * q^43 + 6 * q^51 - 36 * q^53 - 42 * q^57 + 24 * q^65 + 14 * q^67 + 20 * q^79 + 54 * q^81 + 6 * q^85 + 30 * q^93 + 60 * q^95 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.604587	+	1.62311i	0.349059	+	0.937101i
$3$	0.604587	+	1.62311i	0.349059	+	0.937101i
$4$		0			0
$5$	−0.533560			−0.238615			−0.119308	−	0.992857i	$-0.538068\pi$
$5$	−0.533560			−0.238615			−0.119308	+	0.992857i	$0.538068\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.26895	+	1.96262i	−0.756316	+	0.654206i
$10$		0			0
$11$		−	3.92524i		−	1.18350i	−0.806120	−	0.591752i	$-0.798437\pi$
$11$		−	3.92524i		−	1.18350i	0.806120	−	0.591752i	$-0.201563\pi$
$12$		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
$17$	−2.16266	+	3.74584i	−0.524523	+	0.908500i	0.475069	+	0.879948i	$0.342423\pi$
$17$	−2.16266	+	3.74584i	−0.524523	+	0.908500i	−0.999592	+	0.0285519i	$0.990910\pi$
$18$		0			0
$19$	−1.93067	+	1.11467i	−0.442927	+	0.255724i	−0.704838	−	0.709368i	$-0.748980\pi$
$19$	−1.93067	+	1.11467i	−0.442927	+	0.255724i	0.261912	+	0.965092i	$0.415647\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			1.96732i			0.410214i	0.978740	+	0.205107i	$0.0657542\pi$
$23$			1.96732i			0.410214i	−0.978740	+	0.205107i	$0.934246\pi$
$24$		0			0
$25$	−4.71531			−0.943063
$26$		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	$-0.640219\pi$
$31$	0.800341	−	0.462077i	0.143745	−	0.0829915i	0.570148	+	0.821542i	$0.306886\pi$
$32$		0			0
$33$	6.37108	−	2.37315i	1.10906	−	0.413112i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.89936	−	6.75388i	−0.641050	−	1.11033i	−0.985199	−	0.171416i	$-0.945166\pi$
$37$	−3.89936	−	6.75388i	−0.641050	−	1.11033i	0.344149	−	0.938915i	$-0.388168\pi$
$38$		0			0
$39$	0.0388745	−	0.230568i	0.00622491	−	0.0369204i
$40$		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
$45$	1.21062	−	1.04718i	0.180469	−	0.156104i
$46$		0			0
$47$	−3.04329	+	5.27114i	−0.443910	+	0.768874i	−0.997976	−	0.0635985i	$-0.979742\pi$
$47$	−3.04329	+	5.27114i	−0.443910	+	0.768874i	0.554066	+	0.832473i	$0.313076\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−7.38742	−	1.24554i	−1.03445	−	0.174411i
$52$		0			0
$53$	−9.54072	−	5.50834i	−1.31052	−	0.756628i	−0.328337	−	0.944561i	$-0.606488\pi$
$53$	−9.54072	−	5.50834i	−1.31052	−	0.756628i	−0.982182	+	0.187932i	$0.939821\pi$
$54$		0			0
$55$			2.09435i			0.282402i
$56$		0			0
$57$	−2.97650	−	2.45977i	−0.394246	−	0.325804i
$58$		0			0
$59$	−1.89588	−	3.28377i	−0.246823	−	0.427510i	0.715820	−	0.698285i	$-0.246053\pi$
$59$	−1.89588	−	3.28377i	−0.246823	−	0.427510i	−0.962643	+	0.270775i	$0.912720\pi$
$60$		0			0
$61$	9.35116	+	5.39889i	1.19729	+	0.691258i	0.959951	−	0.280168i	$-0.0903903\pi$
$61$	9.35116	+	5.39889i	1.19729	+	0.691258i	0.237342	+	0.971426i	$0.423724\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0623791	+	0.0360146i	0.00773718	+	0.00446706i
$66$		0			0
$67$	−5.75701	−	9.97144i	−0.703331	−	1.21820i	−0.967291	−	0.253671i	$-0.918362\pi$
$67$	−5.75701	−	9.97144i	−0.703331	−	1.21820i	0.263960	−	0.964534i	$-0.414971\pi$
$68$		0			0
$69$	−3.19316	+	1.18941i	−0.384412	+	0.143189i
$70$		0			0
$71$		−	3.22884i		−	0.383192i	−0.981474	−	0.191596i	$-0.938634\pi$
$71$		−	3.22884i		−	0.383192i	0.981474	−	0.191596i	$-0.0613664\pi$
$72$		0			0
$73$	0.329991	+	0.190521i	0.0386226	+	0.0222988i	0.519187	−	0.854661i	$-0.326235\pi$
$73$	0.329991	+	0.190521i	0.0386226	+	0.0222988i	−0.480564	+	0.876959i	$0.659568\pi$
$74$		0			0
$75$	−2.85082	−	7.65345i	−0.329184	−	0.883745i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−4.60310	+	7.97280i	−0.517889	+	0.897011i	0.481895	+	0.876229i	$0.339949\pi$
$79$	−4.60310	+	7.97280i	−0.517889	+	0.897011i	−0.999784	+	0.0207814i	$0.993385\pi$
$80$		0			0
$81$	1.29625	−	8.90616i	0.144028	−	0.989574i
$82$		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
$87$	−7.96356	−	6.58107i	−0.853783	−	0.705565i
$88$		0			0
$89$	−8.56670	−	14.8380i	−0.908068	−	1.57282i	−0.816745	−	0.576999i	$-0.804224\pi$
$89$	−8.56670	−	14.8380i	−0.908068	−	1.57282i	−0.0913236	−	0.995821i	$-0.529110\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.23388	+	1.01967i	0.127947	+	0.105735i
$94$		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
$101$	14.7372			1.46641			0.733205	−	0.680008i	$-0.238024\pi$
$101$	14.7372			1.46641			0.733205	+	0.680008i	$0.238024\pi$
$102$		0			0
$103$			12.8682i			1.26794i	0.773357	+	0.633970i	$0.218576\pi$
$103$			12.8682i			1.26794i	−0.773357	+	0.633970i	$0.781424\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.6679	+	7.89119i	−1.32133	+	0.762870i	−0.983941	−	0.178496i	$-0.942877\pi$
$107$	−13.6679	+	7.89119i	−1.32133	+	0.762870i	−0.337389	+	0.941365i	$0.609544\pi$
$108$		0			0
$109$	1.54170	−	2.67030i	0.147668	−	0.255768i	−0.782697	−	0.622403i	$-0.786157\pi$
$109$	1.54170	−	2.67030i	0.147668	−	0.255768i	0.930365	+	0.366634i	$0.119490\pi$
$110$		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
$115$		−	1.04968i		−	0.0978833i
$116$		0			0
$117$	0.397739	−	0.0763010i	0.0367710	−	0.00705403i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.40749			−0.400681
$122$		0			0
$123$	−15.6799	−	2.64368i	−1.41381	−	0.238373i
$124$		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
$129$	−7.16177	+	8.66625i	−0.630559	+	0.763021i
$130$		0			0
$131$	−15.6365			−1.36616			−0.683082	−	0.730342i	$-0.739361\pi$
$131$	−15.6365			−1.36616			−0.683082	+	0.730342i	$0.739361\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.43160	+	1.33186i	0.209279	+	0.114628i
$136$		0			0
$137$			2.46980i			0.211009i	0.994419	+	0.105505i	$0.0336458\pi$
$137$			2.46980i			0.211009i	−0.994419	+	0.105505i	$0.966354\pi$
$138$		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
$143$	−0.264948	+	0.458904i	−0.0221561	+	0.0383755i
$144$		0			0
$145$	2.75610	−	1.59123i	0.228881	−	0.132145i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	15.8544i		−	1.29884i	−0.760429	−	0.649422i	$-0.775011\pi$
$149$		−	15.8544i		−	1.29884i	0.760429	−	0.649422i	$-0.224989\pi$
$150$		0			0
$151$	8.33096			0.677964			0.338982	−	0.940793i	$-0.389917\pi$
$151$	8.33096			0.677964			0.338982	+	0.940793i	$0.389917\pi$
$152$		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	$-0.550621\pi$
$157$	7.73794	−	4.46750i	0.617555	−	0.356545i	0.775916	+	0.630836i	$0.217288\pi$
$158$		0			0
$159$	3.17242	−	18.8159i	0.251589	−	1.49220i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.10310	+	12.3029i	0.556358	+	0.963640i	0.997797	+	0.0663485i	$0.0211349\pi$
$163$	7.10310	+	12.3029i	0.556358	+	0.963640i	−0.441439	+	0.897291i	$0.645532\pi$
$164$		0			0
$165$	−3.39936	+	1.26622i	−0.264639	+	0.0985750i
$166$		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
$171$	2.19292	−	6.31831i	0.167696	−	0.483174i
$172$		0			0
$173$	−10.6787	+	18.4960i	−0.811886	+	1.40623i	0.0996566	+	0.995022i	$0.468226\pi$
$173$	−10.6787	+	18.4960i	−0.811886	+	1.40623i	−0.911543	+	0.411206i	$0.865108\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.18367	−	5.06254i	0.314464	−	0.380524i
$178$		0			0
$179$	5.03259	+	2.90557i	0.376153	+	0.217172i	0.676143	−	0.736770i	$-0.263650\pi$
$179$	5.03259	+	2.90557i	0.376153	+	0.217172i	−0.299990	+	0.953942i	$0.596983\pi$
$180$		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
$189$		0			0
$190$		0			0
$191$	−6.86109	−	3.96125i	−0.496451	−	0.286626i	0.230796	−	0.973002i	$-0.425867\pi$
$191$	−6.86109	−	3.96125i	−0.496451	−	0.286626i	−0.727247	+	0.686376i	$0.759200\pi$
$192$		0			0
$193$	3.16548	+	5.48277i	0.227856	+	0.394659i	0.957173	−	0.289518i	$-0.0934951\pi$
$193$	3.16548	+	5.48277i	0.227856	+	0.394659i	−0.729316	+	0.684177i	$0.760162\pi$
$194$		0			0
$195$	−0.0207419	+	0.123022i	−0.00148536	+	0.00880979i
$196$		0			0
$197$		−	15.1580i		−	1.07996i	−0.841677	−	0.539981i	$-0.818431\pi$
$197$		−	15.1580i		−	1.07996i	0.841677	−	0.539981i	$-0.181569\pi$
$198$		0			0
$199$	−7.40524	−	4.27542i	−0.524944	−	0.303076i	0.214011	−	0.976831i	$-0.431347\pi$
$199$	−7.40524	−	4.27542i	−0.524944	−	0.303076i	−0.738955	+	0.673755i	$0.764680\pi$
$200$		0			0
$201$	12.7041	−	15.3728i	0.896077	−	1.08432i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.44919	−	4.24212i	0.171059	−	0.296282i
$206$		0			0
$207$	−3.86109	−	4.46374i	−0.268364	−	0.310251i
$208$		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
$213$	5.24075	−	1.95211i	0.359090	−	0.133757i
$214$		0			0
$215$	−1.73164	−	2.99929i	−0.118097	−	0.204550i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−0.109727	+	0.650797i	−0.00741464	+	0.0439768i
$220$		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
$227$	−14.5767			−0.967487			−0.483743	−	0.875210i	$-0.660723\pi$
$227$	−14.5767			−0.967487			−0.483743	+	0.875210i	$0.660723\pi$
$228$		0			0
$229$			24.5631i			1.62317i	0.584233	+	0.811586i	$0.301396\pi$
$229$			24.5631i			1.62317i	−0.584233	+	0.811586i	$0.698604\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.10556	−	5.25710i	0.596525	−	0.344404i	−0.171148	−	0.985245i	$-0.554748\pi$
$233$	9.10556	−	5.25710i	0.596525	−	0.344404i	0.767673	+	0.640841i	$0.221414\pi$
$234$		0			0
$235$	1.62378	−	2.81247i	0.105924	−	0.183465i
$236$		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
$241$		−	13.1382i		−	0.846305i	−0.906059	−	0.423152i	$-0.860923\pi$
$241$		−	13.1382i		−	0.846305i	0.906059	−	0.423152i	$-0.139077\pi$
$242$		0			0
$243$	15.2393	−	3.28059i	0.977605	−	0.210450i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.300956			0.0191494
$248$		0			0
$249$	2.82504	−	3.41850i	0.179030	−	0.216639i
$250$		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
$255$	3.94163	+	0.664573i	0.246835	+	0.0416172i
$256$		0			0
$257$	−13.6096			−0.848944			−0.424472	−	0.905441i	$-0.639540\pi$
$257$	−13.6096			−0.848944			−0.424472	+	0.905441i	$0.639540\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	5.86711	−	16.9045i	0.363165	−	1.04636i
$262$		0			0
$263$			22.8550i			1.40930i	0.709554	+	0.704651i	$0.248896\pi$
$263$			22.8550i			1.40930i	−0.709554	+	0.704651i	$0.751104\pi$
$264$		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
$269$	−5.33875	+	9.24698i	−0.325509	+	0.563798i	−0.981615	−	0.190870i	$-0.938869\pi$
$269$	−5.33875	+	9.24698i	−0.325509	+	0.563798i	0.656106	+	0.754669i	$0.272202\pi$
$270$		0			0
$271$	3.90987	−	2.25737i	0.237508	−	0.137125i	−0.376523	−	0.926407i	$-0.622880\pi$
$271$	3.90987	−	2.25737i	0.237508	−	0.137125i	0.614031	+	0.789282i	$0.289547\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			18.5087i			1.11612i
$276$		0			0
$277$	−6.69904			−0.402507			−0.201253	−	0.979539i	$-0.564501\pi$
$277$	−6.69904			−0.402507			−0.201253	+	0.979539i	$0.564501\pi$
$278$		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	$-0.584700\pi$
$283$	7.42049	−	4.28422i	0.441102	−	0.254670i	0.704065	+	0.710135i	$0.251366\pi$
$284$		0			0
$285$	1.58814	+	1.31244i	0.0940733	+	0.0777420i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.854223	−	1.47956i	−0.0502484	−	0.0870328i
$290$		0			0
$291$	21.0821	+	17.4222i	1.23585	+	1.02131i
$292$		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
$297$	−9.79806	+	17.8885i	−0.568541	+	1.03800i
$298$		0			0
$299$	0.132791	−	0.230001i	0.00767951	−	0.0133013i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	8.90995	+	23.9201i	0.511863	+	1.37417i
$304$		0			0
$305$	−4.98941	−	2.88064i	−0.285693	−	0.164945i
$306$		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	0.999851	+	0.0172571i	$0.00549339\pi$
$311$	9.07984	+	15.7267i	0.514871	+	0.891782i	−0.484980	+	0.874525i	$0.661173\pi$
$312$		0			0
$313$	2.76700	+	1.59753i	0.156400	+	0.0902977i	0.576157	−	0.817339i	$-0.304551\pi$
$313$	2.76700	+	1.59753i	0.156400	+	0.0902977i	−0.419757	+	0.907636i	$0.637885\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.5893	+	13.0419i	1.26874	+	0.732508i	0.974750	−	0.223300i	$-0.0716831\pi$
$317$	22.5893	+	13.0419i	1.26874	+	0.732508i	0.293991	+	0.955808i	$0.405016\pi$
$318$		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
$325$	0.551272	+	0.318277i	0.0305791	+	0.0176548i
$326$		0			0
$327$	5.26627	+	0.887911i	0.291226	+	0.0491016i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	8.06484	−	13.9687i	0.443283	−	0.767789i	−0.554647	−	0.832085i	$-0.687147\pi$
$331$	8.06484	−	13.9687i	0.443283	−	0.767789i	0.997931	+	0.0642960i	$0.0204802\pi$
$332$		0			0
$333$	22.1027	+	7.67126i	1.21122	+	0.420383i
$334$		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
$339$	−2.64739	+	15.7019i	−0.143786	+	0.852808i
$340$		0			0
$341$	−1.81376	−	3.14153i	−0.0982207	−	0.170123i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	1.70375	−	0.634624i	0.0917266	−	0.0341670i
$346$		0			0
$347$	30.1403	−	17.4015i	1.61801	−	0.934161i	0.630581	−	0.776124i	$-0.282817\pi$
$347$	30.1403	−	17.4015i	1.61801	−	0.934161i	0.987433	−	0.158037i	$-0.0505166\pi$
$348$		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
$353$	8.05659			0.428809			0.214404	−	0.976745i	$-0.431219\pi$
$353$	8.05659			0.428809			0.214404	+	0.976745i	$0.431219\pi$
$354$		0			0
$355$			1.72278i			0.0914357i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.4341	−	8.91086i	0.814579	−	0.470297i	−0.0339648	−	0.999423i	$-0.510813\pi$
$359$	15.4341	−	8.91086i	0.814579	−	0.470297i	0.848543	+	0.529126i	$0.177480\pi$
$360$		0			0
$361$	−7.01500	+	12.1503i	−0.369211	+	0.639492i
$362$		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
$367$			23.7739i			1.24099i	0.784211	+	0.620494i	$0.213068\pi$
$367$			23.7739i			1.24099i	−0.784211	+	0.620494i	$0.786932\pi$
$368$		0			0
$369$	−5.18888	−	27.0484i	−0.270122	−	1.40809i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.5372			0.545593			0.272797	−	0.962072i	$-0.412051\pi$
$373$	10.5372			0.545593			0.272797	+	0.962072i	$0.412051\pi$
$374$		0			0
$375$	3.13400	+	8.41371i	0.161839	+	0.434482i
$376$		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
$381$	−6.11028	−	16.4040i	−0.313039	−	0.840401i
$382$		0			0
$383$	−36.1960			−1.84953			−0.924764	−	0.380542i	$-0.875737\pi$
$383$	−36.1960			−1.84953			−0.924764	+	0.380542i	$0.875737\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−18.3962	−	6.38481i	−0.935130	−	0.324558i
$388$		0			0
$389$			21.4810i			1.08913i	0.838718	+	0.544565i	$0.183305\pi$
$389$			21.4810i			1.08913i	−0.838718	+	0.544565i	$0.816695\pi$
$390$		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
$395$	2.45603	−	4.25397i	0.123576	−	0.214041i
$396$		0			0
$397$	−18.4505	+	10.6524i	−0.926006	+	0.534630i	−0.885546	−	0.464551i	$-0.846216\pi$
$397$	−18.4505	+	10.6524i	−0.926006	+	0.534630i	−0.0404601	+	0.999181i	$0.512882\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	18.1081i		−	0.904276i	−0.891948	−	0.452138i	$-0.850661\pi$
$401$		−	18.1081i		−	0.904276i	0.891948	−	0.452138i	$-0.149339\pi$
$402$		0			0
$403$	−0.124758			−0.00621465
$404$		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	$-0.835082\pi$
$409$	−17.6807	+	10.2080i	−0.874254	+	0.504751i	−0.00549461	+	0.999985i	$0.501749\pi$
$410$		0			0
$411$	−4.00875	+	1.49321i	−0.197737	+	0.0736546i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.683065	+	1.18310i	0.0335303	+	0.0580762i
$416$		0			0
$417$	−5.60371	+	33.2360i	−0.274415	+	1.62758i
$418$		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
$423$	−3.44016	−	17.9328i	−0.167266	−	0.871921i
$424$		0			0
$425$	10.1976	−	17.6628i	0.494658	−	0.856773i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.905034	−	0.152592i	−0.0436955	−	0.00736720i
$430$		0			0
$431$	−13.1109	−	7.56961i	−0.631532	−	0.364615i	0.149813	−	0.988714i	$-0.452133\pi$
$431$	−13.1109	−	7.56961i	−0.631532	−	0.364615i	−0.781345	+	0.624099i	$0.785466\pi$
$432$		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	$-0.107013\pi$
$439$	23.6831	+	13.6734i	1.13033	+	0.652598i	0.186314	+	0.982490i	$0.440346\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.6520	+	8.45931i	0.696135	+	0.401914i	0.805906	−	0.592043i	$-0.201678\pi$
$443$	14.6520	+	8.45931i	0.696135	+	0.401914i	−0.109771	+	0.993957i	$0.535012\pi$
$444$		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
$451$	31.2079	+	18.0179i	1.46952	+	0.848431i
$452$		0			0
$453$	5.03679	+	13.5220i	0.236649	+	0.635321i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	17.4018	−	30.1408i	0.814022	−	1.40993i	−0.0960053	−	0.995381i	$-0.530607\pi$
$457$	17.4018	−	30.1408i	0.814022	−	1.40993i	0.910028	−	0.414547i	$-0.136060\pi$
$458$		0			0
$459$	19.2062	−	11.6726i	0.896469	−	0.544831i
$460$		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
$465$	−0.658347	−	0.544057i	−0.0305301	−	0.0252300i
$466$		0			0
$467$	4.40378	+	7.62758i	0.203783	+	0.352962i	0.949744	−	0.313027i	$-0.101343\pi$
$467$	4.40378	+	7.62758i	0.203783	+	0.352962i	−0.745961	+	0.665989i	$0.768010\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	11.9295	+	9.85850i	0.549682	+	0.454256i
$472$		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
$479$	−13.6628			−0.624269			−0.312134	−	0.950038i	$-0.601044\pi$
$479$	−13.6628			−0.624269			−0.312134	+	0.950038i	$0.601044\pi$
$480$		0			0
$481$			1.05281i			0.0480038i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.29625	+	4.21249i	−0.331306	+	0.191280i
$486$		0			0
$487$	−8.31028	+	14.3938i	−0.376575	+	0.652246i	−0.990561	−	0.137070i	$-0.956232\pi$
$487$	−8.31028	+	14.3938i	−0.376575	+	0.652246i	0.613987	+	0.789316i	$0.289565\pi$
$488$		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
$493$		−	25.7988i		−	1.16192i
$494$		0			0
$495$	−4.11041	−	4.75198i	−0.184749	−	0.213585i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.69218			−0.120518			−0.0602592	−	0.998183i	$-0.519193\pi$
$499$	−2.69218			−0.120518			−0.0602592	+	0.998183i	$0.519193\pi$
$500$		0			0
$501$	−21.4281	−	3.61286i	−0.957339	−	0.161411i
$502$		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
$507$	14.3235	−	17.3325i	0.636131	−	0.769763i
$508$		0			0
$509$	5.92234			0.262503			0.131252	−	0.991349i	$-0.458100\pi$
$509$	5.92234			0.262503			0.131252	+	0.991349i	$0.458100\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	11.5811	−	0.260636i	0.511318	−	0.0115073i
$514$		0			0
$515$		−	6.86596i		−	0.302550i
$516$		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
$521$	19.5943	−	33.9383i	0.858442	−	1.48686i	−0.0149735	−	0.999888i	$-0.504766\pi$
$521$	19.5943	−	33.9383i	0.858442	−	1.48686i	0.873415	−	0.486976i	$-0.161900\pi$
$522$		0			0
$523$	19.9496	−	11.5179i	0.872333	−	0.503642i	0.00421050	−	0.999991i	$-0.498660\pi$
$523$	19.9496	−	11.5179i	0.872333	−	0.503642i	0.868123	+	0.496349i	$0.165326\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			3.99727i			0.174124i
$528$		0			0
$529$	19.1297			0.831725
$530$		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
$537$	−1.67340	+	9.92509i	−0.0722127	+	0.428299i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.66302	+	2.88044i	0.0714990	+	0.123840i	0.899558	−	0.436800i	$-0.143888\pi$
$541$	1.66302	+	2.88044i	0.0714990	+	0.123840i	−0.828059	+	0.560640i	$0.810555\pi$
$542$		0			0
$543$	11.9928	−	4.46716i	0.514659	−	0.191704i
$544$		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
$549$	−31.8133	+	6.10295i	−1.35776	+	0.260467i
$550$		0			0
$551$	6.64857	−	11.5157i	0.283238	−	0.490583i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.59116	+	5.55563i	−0.194884	+	0.235824i
$556$		0			0
$557$	3.13213	+	1.80833i	0.132712	+	0.0766216i	0.564886	−	0.825169i	$-0.308920\pi$
$557$	3.13213	+	1.80833i	0.132712	+	0.0766216i	−0.432174	+	0.901790i	$0.642253\pi$
$558$		0			0
$559$		−	0.876252i		−	0.0370615i
$560$		0			0
$561$	−4.88906	+	28.9974i	−0.206416	+	1.22427i
$562$		0			0
$563$	4.75452	+	8.23506i	0.200379	+	0.347067i	0.948651	−	0.316326i	$-0.102449\pi$
$563$	4.75452	+	8.23506i	0.200379	+	0.347067i	−0.748272	+	0.663393i	$0.769116\pi$
$564$		0			0
$565$	−4.24807	−	2.45262i	−0.178718	−	0.103183i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.09742	−	5.25240i	−0.381384	−	0.220192i	0.297036	−	0.954866i	$-0.404002\pi$
$569$	−9.09742	−	5.25240i	−0.381384	−	0.220192i	−0.678420	+	0.734674i	$0.737335\pi$
$570$		0			0
$571$	−2.24201	−	3.88328i	−0.0938252	−	0.162510i	0.815292	−	0.579049i	$-0.196576\pi$
$571$	−2.24201	−	3.88328i	−0.0938252	−	0.162510i	−0.909118	+	0.416539i	$0.863243\pi$
$572$		0			0
$573$	2.28141	−	13.5312i	0.0953071	−	0.565274i
$574$		0			0
$575$		−	9.27651i		−	0.386857i
$576$		0			0
$577$	−40.8602	−	23.5906i	−1.70103	−	0.982090i	−0.944720	−	0.327877i	$-0.893667\pi$
$577$	−40.8602	−	23.5906i	−1.70103	−	0.982090i	−0.756310	−	0.654213i	$-0.773000\pi$
$578$		0			0
$579$	−6.98531	+	8.45272i	−0.290300	+	0.351283i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−21.6215	+	37.4496i	−0.895473	+	1.55100i
$584$		0			0
$585$	−0.212218	+	0.0407112i	−0.00877414	+	0.00168320i
$586$		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
$591$	24.6030	−	9.16433i	1.01203	−	0.376970i
$592$		0			0
$593$	4.72490	+	8.18376i	0.194028	+	0.336067i	0.946582	−	0.322465i	$-0.104511\pi$
$593$	4.72490	+	8.18376i	0.194028	+	0.336067i	−0.752553	+	0.658531i	$0.771178\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.46234	−	14.6044i	0.100777	−	0.597717i
$598$		0			0
$599$	−31.6406	+	18.2677i	−1.29280	+	0.746398i	−0.979150	−	0.203140i	$-0.934885\pi$
$599$	−31.6406	+	18.2677i	−1.29280	+	0.746398i	−0.313650	+	0.949539i	$0.601552\pi$
$600$		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
$605$	2.35166			0.0956087
$606$		0			0
$607$			1.98331i			0.0804999i	0.999190	+	0.0402499i	$0.0128154\pi$
$607$			1.98331i			0.0804999i	−0.999190	+	0.0402499i	$0.987185\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.711589	−	0.410836i	0.0287878	−	0.0166207i
$612$		0			0
$613$	11.5683	−	20.0368i	0.467238	−	0.809280i	−0.532061	−	0.846706i	$-0.678582\pi$
$613$	11.5683	−	20.0368i	0.467238	−	0.809280i	0.999299	+	0.0374258i	$0.0119158\pi$
$614$		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
$619$		−	6.03389i		−	0.242522i	−0.992621	−	0.121261i	$-0.961306\pi$
$619$		−	6.03389i		−	0.242522i	0.992621	−	0.121261i	$-0.0386939\pi$
$620$		0			0
$621$	4.91075	−	8.96568i	0.197062	−	0.359780i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	20.8107			0.832430
$626$		0			0
$627$	−9.65518	+	11.6835i	−0.385591	+	0.466592i
$628$		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
$633$	−9.59121	−	1.61711i	−0.381217	−	0.0642744i
$634$		0			0
$635$	5.39245			0.213993
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6.33698	+	7.32607i	0.250687	+	0.289815i
$640$		0			0
$641$			46.4474i			1.83456i	0.398240	+	0.917281i	$0.369621\pi$
$641$			46.4474i			1.83456i	−0.398240	+	0.917281i	$0.630379\pi$
$642$		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
$647$	−2.32507	+	4.02715i	−0.0914081	+	0.158323i	−0.908104	−	0.418745i	$-0.862470\pi$
$647$	−2.32507	+	4.02715i	−0.0914081	+	0.158323i	0.816696	+	0.577068i	$0.195803\pi$
$648$		0			0
$649$	−12.8896	+	7.44179i	−0.505959	+	0.292116i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	3.46371i		−	0.135545i	−0.997701	−	0.0677727i	$-0.978411\pi$
$653$		−	3.46371i		−	0.135545i	0.997701	−	0.0677727i	$-0.0215893\pi$
$654$		0			0
$655$	8.34299			0.325988
$656$		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	$-0.537957\pi$
$661$	17.5196	−	10.1149i	0.681433	−	0.393426i	0.800395	+	0.599473i	$0.204623\pi$
$662$		0			0
$663$	0.779599	+	0.644259i	0.0302771	+	0.0250209i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.86711	−	10.1621i	−0.227175	−	0.393479i
$668$		0			0
$669$	−9.25799	−	7.65078i	−0.357935	−	0.295796i
$670$		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
$675$	21.4892	+	11.7702i	0.827119	+	0.453036i
$676$		0			0
$677$	−7.71449	+	13.3619i	−0.296492	+	0.513539i	−0.975331	−	0.220748i	$-0.929150\pi$
$677$	−7.71449	+	13.3619i	−0.296492	+	0.513539i	0.678839	+	0.734287i	$0.262483\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−8.81286	−	23.6595i	−0.337710	−	0.906633i
$682$		0			0
$683$	−13.6137	−	7.85987i	−0.520913	−	0.300750i	0.216395	−	0.976306i	$-0.430570\pi$
$683$	−13.6137	−	7.85987i	−0.520913	−	0.300750i	−0.737308	+	0.675556i	$0.763903\pi$
$684$		0			0
$685$		−	1.31779i		−	0.0503501i
$686$		0			0
$687$	−39.8685	+	14.8505i	−1.52108	+	0.566582i
$688$		0			0
$689$	0.743611	+	1.28797i	0.0283293	+	0.0490678i
$690$		0			0
$691$	−41.5878	−	24.0107i	−1.58207	−	0.913411i	−0.994556	−	0.104199i	$-0.966772\pi$
$691$	−41.5878	−	24.0107i	−1.58207	−	0.913411i	−0.587517	−	0.809212i	$-0.699894\pi$
$692$		0			0
$693$		0			0
$694$		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
$703$	15.0568	+	8.69302i	0.567876	+	0.327864i
$704$		0			0
$705$	5.54666	+	0.935185i	0.208899	+	0.0352211i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17.0432	+	29.5196i	−0.640070	+	1.10863i	0.345347	+	0.938475i	$0.387761\pi$
$709$	−17.0432	+	29.5196i	−0.640070	+	1.10863i	−0.985417	+	0.170159i	$0.945572\pi$
$710$		0			0
$711$	−5.20338	−	27.1240i	−0.195142	−	1.01723i
$712$		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
$717$	−5.62197	+	33.3444i	−0.209956	+	1.24527i
$718$		0			0
$719$	9.23791	+	16.0005i	0.344516	+	0.596719i	0.985266	−	0.171031i	$-0.0547097\pi$
$719$	9.23791	+	16.0005i	0.344516	+	0.596719i	−0.640750	+	0.767750i	$0.721376\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	21.3247	−	7.94318i	0.793073	−	0.295410i
$724$		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
$731$	−28.0752			−1.03840
$732$		0			0
$733$		−	50.0773i		−	1.84965i	−0.380394	−	0.924825i	$-0.624212\pi$
$733$		−	50.0773i		−	1.84965i	0.380394	−	0.924825i	$-0.375788\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−39.1403	+	22.5976i	−1.44175	+	0.832395i
$738$		0			0
$739$	8.47021	−	14.6708i	0.311582	−	0.539675i	−0.667123	−	0.744947i	$-0.732475\pi$
$739$	8.47021	−	14.6708i	0.311582	−	0.539675i	0.978705	+	0.205272i	$0.0658079\pi$
$740$		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
$745$			8.45928i			0.309924i
$746$		0			0
$747$	7.25657	+	2.51856i	0.265504	+	0.0921493i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−29.4055			−1.07302			−0.536512	−	0.843893i	$-0.680258\pi$
$751$	−29.4055			−1.07302			−0.536512	+	0.843893i	$0.680258\pi$
$752$		0			0
$753$	−13.7159	−	36.8225i	−0.499836	−	1.34189i
$754$		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
$759$	4.66873	+	12.5339i	0.169464	+	0.454952i
$760$		0			0
$761$	12.2213			0.443023			0.221511	−	0.975158i	$-0.428901\pi$
$761$	12.2213			0.443023			0.221511	+	0.975158i	$0.428901\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.30439	+	6.79948i	0.0471603	+	0.245836i
$766$		0			0
$767$			0.511878i			0.0184829i
$768$		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
$773$	−15.1047	+	26.1622i	−0.543279	+	0.940987i	0.455434	+	0.890270i	$0.349484\pi$
$773$	−15.1047	+	26.1622i	−0.543279	+	0.940987i	−0.998713	+	0.0507175i	$0.983849\pi$
$774$		0			0
$775$	−3.77386	+	2.17884i	−0.135561	+	0.0782662i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	20.4666i		−	0.733294i
$780$		0			0
$781$	−12.6740			−0.453510
$782$		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	$-0.907285\pi$
$787$	−33.3310	+	19.2436i	−1.18812	+	0.685962i	−0.230241	+	0.973134i	$0.573952\pi$
$788$		0			0
$789$	−37.0961	+	13.8179i	−1.32066	+	0.491929i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.728836	−	1.26238i	−0.0258817	−	0.0448285i
$794$		0			0
$795$	−1.69268	+	10.0394i	−0.0600331	+	0.356061i
$796$		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
$801$	48.5587	+	16.8534i	1.71574	+	0.595486i
$802$		0			0
$803$	0.747839	−	1.29529i	0.0263907	−	0.0457100i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−18.2366	−	3.07475i	−0.641958	−	0.108236i
$808$		0			0
$809$	−44.8465	−	25.8921i	−1.57672	−	0.910318i	−0.995313	−	0.0967036i	$-0.969170\pi$
$809$	−44.8465	−	25.8921i	−1.57672	−	0.910318i	−0.581404	−	0.813615i	$-0.697497\pi$
$810$		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			0
$820$		0			0
$821$	−22.3465	−	12.9017i	−0.779897	−	0.450274i	0.0564968	−	0.998403i	$-0.482007\pi$
$821$	−22.3465	−	12.9017i	−0.779897	−	0.450274i	−0.836394	+	0.548129i	$0.815340\pi$
$822$		0			0
$823$	0.570514	+	0.988159i	0.0198869	+	0.0344451i	0.875798	−	0.482679i	$-0.160336\pi$
$823$	0.570514	+	0.988159i	0.0198869	+	0.0344451i	−0.855911	+	0.517124i	$0.827003\pi$
$824$		0			0
$825$	−30.0416	+	11.1901i	−1.04592	+	0.389591i
$826$		0			0
$827$		−	23.1713i		−	0.805746i	−0.915256	−	0.402873i	$-0.868012\pi$
$827$		−	23.1713i		−	0.805746i	0.915256	−	0.402873i	$-0.131988\pi$
$828$		0			0
$829$	8.31700	+	4.80182i	0.288861	+	0.166774i	0.637428	−	0.770510i	$-0.279998\pi$
$829$	8.31700	+	4.80182i	0.288861	+	0.166774i	−0.348567	+	0.937284i	$0.613332\pi$
$830$		0			0
$831$	−4.05016	−	10.8733i	−0.140498	−	0.377189i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	3.34707	−	5.79729i	0.115830	−	0.200623i
$836$		0			0
$837$	−4.80083	+	0.108044i	−0.165941	+	0.00373454i
$838$		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
$843$	−23.3433	−	19.2908i	−0.803985	−	0.664411i
$844$		0			0
$845$	3.46328	+	5.99858i	0.119140	+	0.206357i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	11.4401	+	9.45405i	0.392622	+	0.324462i
$850$		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
$857$	22.8878			0.781834			0.390917	−	0.920426i	$-0.372158\pi$
$857$	22.8878			0.781834			0.390917	+	0.920426i	$0.372158\pi$
$858$		0			0
$859$			13.2701i			0.452769i	0.974038	+	0.226384i	$0.0726905\pi$
$859$			13.2701i			0.452769i	−0.974038	+	0.226384i	$0.927309\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.646706	−	0.373376i	0.0220141	−	0.0127099i	−0.488953	−	0.872310i	$-0.662621\pi$
$863$	0.646706	−	0.373376i	0.0220141	−	0.0127099i	0.510967	+	0.859601i	$0.329288\pi$
$864$		0			0
$865$	5.69773	−	9.86875i	0.193729	−	0.335548i
$866$		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
$871$			1.55436i			0.0526676i
$872$		0			0
$873$	−15.5321	+	44.7516i	−0.525681	+	1.51461i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.37919			0.147875			0.0739373	−	0.997263i	$-0.476444\pi$
$877$	4.37919			0.147875			0.0739373	+	0.997263i	$0.476444\pi$
$878$		0			0
$879$	−41.4810	−	6.99384i	−1.39912	−	0.235896i
$880$		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
$885$	−2.23224	+	2.70117i	−0.0750360	+	0.0907989i
$886$		0			0
$887$	52.3623			1.75815			0.879077	−	0.476679i	$-0.158160\pi$
$887$	52.3623			1.75815			0.879077	+	0.476679i	$0.158160\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−34.9588	−	5.08811i	−1.17116	−	0.170458i
$892$		0			0
$893$		−	13.5691i		−	0.454073i
$894$		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
$899$	−2.75610	+	4.77370i	−0.0919209	+	0.159212i
$900$		0			0
$901$	41.2667	−	23.8254i	1.37479	−	0.793738i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			3.94236i			0.131048i
$906$		0			0
$907$	−24.3804			−0.809539			−0.404770	−	0.914419i	$-0.632648\pi$
$907$	−24.3804			−0.809539			−0.404770	+	0.914419i	$0.632648\pi$
$908$		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
$915$	1.65905	−	9.83994i	0.0548464	−	0.325298i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.25947	−	5.64556i	−0.107520	−	0.186230i	0.807245	−	0.590216i	$-0.200958\pi$
$919$	−3.25947	−	5.64556i	−0.107520	−	0.186230i	−0.914765	+	0.403986i	$0.867624\pi$
$920$		0			0
$921$	−20.2526	+	7.54385i	−0.667346	+	0.248578i
$922$		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
$927$	−25.2554	−	29.1973i	−0.829495	−	0.958964i
$928$		0			0
$929$	13.9048	−	24.0838i	0.456202	−	0.790165i	−0.542554	−	0.840021i	$-0.682543\pi$
$929$	13.9048	−	24.0838i	0.456202	−	0.790165i	0.998756	+	0.0498555i	$0.0158761\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−20.0366	+	24.2457i	−0.655970	+	0.793770i
$934$		0			0
$935$	−7.84511	−	4.52938i	−0.256563	−	0.148126i
$936$		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	0.904805	−	0.425827i	$-0.140017\pi$
$941$	2.56526	+	4.44317i	0.0836252	+	0.144843i	−0.821179	+	0.570670i	$0.806683\pi$
$942$		0			0
$943$	−15.6413	−	9.03052i	−0.509351	−	0.294074i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.606033	+	0.349893i	0.0196934	+	0.0113700i	0.509814	−	0.860284i	$-0.329714\pi$
$947$	0.606033	+	0.349893i	0.0196934	+	0.0113700i	−0.490121	+	0.871654i	$0.663047\pi$
$948$		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
$955$	3.66081	+	2.11357i	0.118461	+	0.0683934i
$956$		0			0
$957$	−25.8323	+	31.2589i	−0.835038	+	1.01046i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.0730	+	26.1071i	−0.486225	+	0.842166i
$962$		0			0
$963$	15.5245	−	44.7296i	0.500268	−	1.44139i
$964$		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
$969$	15.6511	−	5.82983i	0.502785	−	0.187281i
$970$		0			0
$971$	1.46120	+	2.53087i	0.0468920	+	0.0812194i	0.888519	−	0.458840i	$-0.151735\pi$
$971$	1.46120	+	2.53087i	0.0468920	+	0.0812194i	−0.841627	+	0.540060i	$0.818402\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.183306	+	1.08720i	−0.00587048	+	0.0348183i
$976$		0			0
$977$	24.7013	−	14.2613i	0.790264	−	0.456259i	−0.0497913	−	0.998760i	$-0.515856\pi$
$977$	24.7013	−	14.2613i	0.790264	−	0.456259i	0.840056	+	0.542500i	$0.182522\pi$
$978$		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
$983$	−11.2579			−0.359073			−0.179536	−	0.983751i	$-0.557460\pi$
$983$	−11.2579			−0.359073			−0.179536	+	0.983751i	$0.557460\pi$
$984$		0			0
$985$			8.08771i			0.257696i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−11.0588	+	6.38481i	−0.351650	+	0.203025i
$990$		0			0
$991$	−10.5811	+	18.3270i	−0.336120	+	0.582177i	−0.983699	−	0.179821i	$-0.942448\pi$
$991$	−10.5811	+	18.3270i	−0.336120	+	0.582177i	0.647579	+	0.761998i	$0.275781\pi$
$992$		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
$997$			16.9251i			0.536024i	0.963416	+	0.268012i	$0.0863667\pi$
$997$			16.9251i			0.536024i	−0.963416	+	0.268012i	$0.913633\pi$
$998$		0			0
$999$	0.911756	+	40.5130i	0.0288467	+	1.28178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.bm.b.1697.5		16
3.2	odd	2		5292.2.bm.b.2285.5		16
7.2	even	3		1764.2.w.a.509.1		16
7.3	odd	6		252.2.x.a.41.3	✓	16
7.4	even	3		252.2.x.a.41.6	yes	16
7.5	odd	6		1764.2.w.a.509.8		16
7.6	odd	2	inner	1764.2.bm.b.1697.4		16
9.2	odd	6		1764.2.w.a.1109.8		16
9.7	even	3		5292.2.w.a.521.5		16
21.2	odd	6		5292.2.w.a.1097.4		16
21.5	even	6		5292.2.w.a.1097.5		16
21.11	odd	6		756.2.x.a.125.4		16
21.17	even	6		756.2.x.a.125.5		16
21.20	even	2		5292.2.bm.b.2285.4		16
28.3	even	6		1008.2.cc.c.545.6		16
28.11	odd	6		1008.2.cc.c.545.3		16
63.2	odd	6	inner	1764.2.bm.b.1685.4		16
63.4	even	3		2268.2.f.b.1133.8		16
63.11	odd	6		252.2.x.a.209.3	yes	16
63.16	even	3		5292.2.bm.b.4625.4		16
63.20	even	6		1764.2.w.a.1109.1		16
63.25	even	3		756.2.x.a.629.5		16
63.31	odd	6		2268.2.f.b.1133.9		16
63.32	odd	6		2268.2.f.b.1133.10		16
63.34	odd	6		5292.2.w.a.521.4		16
63.38	even	6		252.2.x.a.209.6	yes	16
63.47	even	6	inner	1764.2.bm.b.1685.5		16
63.52	odd	6		756.2.x.a.629.4		16
63.59	even	6		2268.2.f.b.1133.7		16
63.61	odd	6		5292.2.bm.b.4625.5		16
84.11	even	6		3024.2.cc.c.881.4		16
84.59	odd	6		3024.2.cc.c.881.5		16
252.11	even	6		1008.2.cc.c.209.6		16
252.115	even	6		3024.2.cc.c.2897.4		16
252.151	odd	6		3024.2.cc.c.2897.5		16
252.227	odd	6		1008.2.cc.c.209.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.3	✓	16	7.3	odd	6
252.2.x.a.41.6	yes	16	7.4	even	3
252.2.x.a.209.3	yes	16	63.11	odd	6
252.2.x.a.209.6	yes	16	63.38	even	6
756.2.x.a.125.4		16	21.11	odd	6
756.2.x.a.125.5		16	21.17	even	6
756.2.x.a.629.4		16	63.52	odd	6
756.2.x.a.629.5		16	63.25	even	3
1008.2.cc.c.209.3		16	252.227	odd	6
1008.2.cc.c.209.6		16	252.11	even	6
1008.2.cc.c.545.3		16	28.11	odd	6
1008.2.cc.c.545.6		16	28.3	even	6
1764.2.w.a.509.1		16	7.2	even	3
1764.2.w.a.509.8		16	7.5	odd	6
1764.2.w.a.1109.1		16	63.20	even	6
1764.2.w.a.1109.8		16	9.2	odd	6
1764.2.bm.b.1685.4		16	63.2	odd	6	inner
1764.2.bm.b.1685.5		16	63.47	even	6	inner
1764.2.bm.b.1697.4		16	7.6	odd	2	inner
1764.2.bm.b.1697.5		16	1.1	even	1	trivial
2268.2.f.b.1133.7		16	63.59	even	6
2268.2.f.b.1133.8		16	63.4	even	3
2268.2.f.b.1133.9		16	63.31	odd	6
2268.2.f.b.1133.10		16	63.32	odd	6
3024.2.cc.c.881.4		16	84.11	even	6
3024.2.cc.c.881.5		16	84.59	odd	6
3024.2.cc.c.2897.4		16	252.115	even	6
3024.2.cc.c.2897.5		16	252.151	odd	6
5292.2.w.a.521.4		16	63.34	odd	6
5292.2.w.a.521.5		16	9.7	even	3
5292.2.w.a.1097.4		16	21.2	odd	6
5292.2.w.a.1097.5		16	21.5	even	6
5292.2.bm.b.2285.4		16	21.20	even	2
5292.2.bm.b.2285.5		16	3.2	odd	2
5292.2.bm.b.4625.4		16	63.16	even	3
5292.2.bm.b.4625.5		16	63.61	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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.604587 + 1.62311i) q^{3} -0.533560 q^{5} +(-2.26895 + 1.96262i) q^{9} +O(q^{10})\)	\(q+(0.604587 + 1.62311i) q^{3} -0.533560 q^{5} +(-2.26895 + 1.96262i) q^{9} -3.92524i q^{11} +(-0.116911 - 0.0674987i) q^{13} +(-0.322584 - 0.866025i) q^{15} +(-2.16266 + 3.74584i) q^{17} +(-1.93067 + 1.11467i) q^{19} +1.96732i q^{23} -4.71531 q^{25} +(-4.55732 - 2.49617i) q^{27} +(-5.16548 + 2.98229i) q^{29} +(0.800341 - 0.462077i) q^{31} +(6.37108 - 2.37315i) q^{33} +(-3.89936 - 6.75388i) q^{37} +(0.0388745 - 0.230568i) q^{39} +(-4.59027 + 7.95059i) q^{41} +(3.24544 + 5.62127i) q^{43} +(1.21062 - 1.04718i) q^{45} +(-3.04329 + 5.27114i) q^{47} +(-7.38742 - 1.24554i) q^{51} +(-9.54072 - 5.50834i) q^{53} +2.09435i q^{55} +(-2.97650 - 2.45977i) q^{57} +(-1.89588 - 3.28377i) q^{59} +(9.35116 + 5.39889i) q^{61} +(0.0623791 + 0.0360146i) q^{65} +(-5.75701 - 9.97144i) q^{67} +(-3.19316 + 1.18941i) q^{69} -3.22884i q^{71} +(0.329991 + 0.190521i) q^{73} +(-2.85082 - 7.65345i) q^{75} +(-4.60310 + 7.97280i) q^{79} +(1.29625 - 8.90616i) q^{81} +(-1.28020 - 2.21737i) q^{83} +(1.15391 - 1.99863i) q^{85} +(-7.96356 - 6.58107i) q^{87} +(-8.56670 - 14.8380i) q^{89} +(1.23388 + 1.01967i) q^{93} +(1.03013 - 0.594746i) q^{95} +(13.6747 - 7.89507i) q^{97} +(7.70375 + 8.90616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{9}+O(q^{10}) \) 16 * q + 6 * q^9	\( 16 q + 6 q^{9} - 12 q^{15} + 16 q^{25} - 12 q^{29} - 2 q^{37} + 18 q^{39} + 4 q^{43} + 6 q^{51} - 36 q^{53} - 42 q^{57} + 24 q^{65} + 14 q^{67} + 20 q^{79} + 54 q^{81} + 6 q^{85} + 30 q^{93} + 60 q^{95} + 90 q^{99}+O(q^{100}) \) 16 * q + 6 * q^9 - 12 * q^15 + 16 * q^25 - 12 * q^29 - 2 * q^37 + 18 * q^39 + 4 * q^43 + 6 * q^51 - 36 * q^53 - 42 * q^57 + 24 * q^65 + 14 * q^67 + 20 * q^79 + 54 * q^81 + 6 * q^85 + 30 * q^93 + 60 * q^95 + 90 * q^99

Introduction

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