LMFDB - Embedded newform 1764.2.w.a.509.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(509,1764)]

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, 5, 5]))

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

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

chi := DirichletCharacter("1764.509");

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.w (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			509.1
Root			$-0.604587 + 1.62311i$ of defining polynomial
Character	$\chi$	$=$	1764.509
Dual form			1764.2.w.a.1109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70794 - 0.287965i) q^{3} +(0.266780 + 0.462077i) q^{5} +(2.83415 + 0.983658i) q^{9} +O(q^{10})$	\(q+(-1.70794 - 0.287965i) q^{3} +(0.266780 + 0.462077i) q^{5} +(2.83415 + 0.983658i) q^{9} +(3.39936 + 1.96262i) q^{11} +(-0.116911 - 0.0674987i) q^{13} +(-0.322584 - 0.866025i) q^{15} +(-2.16266 - 3.74584i) q^{17} +(1.93067 + 1.11467i) q^{19} +(1.70375 - 0.983658i) q^{23} +(2.35766 - 4.08358i) q^{25} +(-4.55732 - 2.49617i) q^{27} +(-5.16548 + 2.98229i) q^{29} +0.924154i q^{31} +(-5.24075 - 4.33094i) q^{33} +(-3.89936 + 6.75388i) q^{37} +(0.180240 + 0.148950i) q^{39} +(-4.59027 + 7.95059i) q^{41} +(3.24544 + 5.62127i) q^{43} +(0.301570 + 1.57202i) q^{45} +6.08659 q^{47} +(2.61504 + 7.02046i) q^{51} +(9.54072 - 5.50834i) q^{53} +2.09435i q^{55} +(-2.97650 - 2.45977i) q^{57} +3.79177 q^{59} -10.7978i q^{61} -0.0720292i q^{65} +11.5140 q^{67} +(-3.19316 + 1.18941i) q^{69} -3.22884i q^{71} +(-0.329991 + 0.190521i) q^{73} +(-5.20268 + 6.29561i) q^{75} +9.20620 q^{79} +(7.06484 + 5.57567i) q^{81} +(-1.28020 - 2.21737i) q^{83} +(1.15391 - 1.99863i) q^{85} +(9.68115 - 3.60611i) q^{87} +(-8.56670 + 14.8380i) q^{89} +(0.266124 - 1.57840i) q^{93} +1.18949i q^{95} +(13.6747 - 7.89507i) q^{97} +(7.70375 + 8.90616i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{9}+O(q^{10}) $ 16 * q - 6 * q^9	$ 16 q - 6 q^{9} - 6 q^{11} - 12 q^{15} - 6 q^{23} - 8 q^{25} - 12 q^{29} - 2 q^{37} - 36 q^{39} + 4 q^{43} + 12 q^{51} + 36 q^{53} - 42 q^{57} - 28 q^{67} - 40 q^{79} - 18 q^{81} + 6 q^{85} - 6 q^{93} + 90 q^{99}+O(q^{100}) $ 16 * q - 6 * q^9 - 6 * q^11 - 12 * q^15 - 6 * q^23 - 8 * q^25 - 12 * q^29 - 2 * q^37 - 36 * q^39 + 4 * q^43 + 12 * q^51 + 36 * q^53 - 42 * q^57 - 28 * q^67 - 40 * q^79 - 18 * q^81 + 6 * q^85 - 6 * q^93 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.70794	−	0.287965i	−0.986082	−	0.166257i
$3$	−1.70794	−	0.287965i	−0.986082	−	0.166257i
$4$		0			0
$5$	0.266780	+	0.462077i	0.119308	+	0.206647i	0.919494	−	0.393105i	$-0.128599\pi$
$5$	0.266780	+	0.462077i	0.119308	+	0.206647i	−0.800186	+	0.599752i	$0.795266\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.83415	+	0.983658i	0.944717	+	0.327886i
$10$		0			0
$11$	3.39936	+	1.96262i	1.02494	+	0.591752i	0.915532	−	0.402245i	$-0.131770\pi$
$11$	3.39936	+	1.96262i	1.02494	+	0.591752i	0.109412	+	0.993996i	$0.465103\pi$
$12$		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	−0.999592	−	0.0285519i	$-0.990910\pi$
$17$	−2.16266	−	3.74584i	−0.524523	−	0.908500i	0.475069	−	0.879948i	$-0.342423\pi$
$18$		0			0
$19$	1.93067	+	1.11467i	0.442927	+	0.255724i	0.704838	−	0.709368i	$-0.251020\pi$
$19$	1.93067	+	1.11467i	0.442927	+	0.255724i	−0.261912	+	0.965092i	$0.584353\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.70375	−	0.983658i	0.355255	−	0.205107i	−0.311742	−	0.950167i	$-0.600912\pi$
$23$	1.70375	−	0.983658i	0.355255	−	0.205107i	0.666998	+	0.745060i	$0.267579\pi$
$24$		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
$31$			0.924154i			0.165983i	0.996550	+	0.0829915i	$0.0264474\pi$
$31$			0.924154i			0.165983i	−0.996550	+	0.0829915i	$0.973553\pi$
$32$		0			0
$33$	−5.24075	−	4.33094i	−0.912297	−	0.753920i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.89936	+	6.75388i	−0.641050	+	1.11033i	0.344149	+	0.938915i	$0.388168\pi$
$37$	−3.89936	+	6.75388i	−0.641050	+	1.11033i	−0.985199	+	0.171416i	$0.945166\pi$
$38$		0			0
$39$	0.180240	+	0.148950i	0.0288616	+	0.0238511i
$40$		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
$45$	0.301570	+	1.57202i	0.0449554	+	0.234342i
$46$		0			0
$47$	6.08659			0.887820			0.443910	−	0.896071i	$-0.353591\pi$
$47$	6.08659			0.887820			0.443910	+	0.896071i	$0.353591\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.61504	+	7.02046i	0.366178	+	0.983062i
$52$		0			0
$53$	9.54072	−	5.50834i	1.31052	−	0.756628i	0.328337	−	0.944561i	$-0.393512\pi$
$53$	9.54072	−	5.50834i	1.31052	−	0.756628i	0.982182	+	0.187932i	$0.0601785\pi$
$54$		0			0
$55$			2.09435i			0.282402i
$56$		0			0
$57$	−2.97650	−	2.45977i	−0.394246	−	0.325804i
$58$		0			0
$59$	3.79177			0.493646			0.246823	−	0.969061i	$-0.420613\pi$
$59$	3.79177			0.493646			0.246823	+	0.969061i	$0.420613\pi$
$60$		0			0
$61$		−	10.7978i		−	1.38252i	−0.722608	−	0.691258i	$-0.757057\pi$
$61$		−	10.7978i		−	1.38252i	0.722608	−	0.691258i	$-0.242943\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	0.0720292i		−	0.00893413i
$66$		0			0
$67$	11.5140			1.40666			0.703331	−	0.710863i	$-0.251695\pi$
$67$	11.5140			1.40666			0.703331	+	0.710863i	$0.251695\pi$
$68$		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	$-0.673765\pi$
$73$	−0.329991	+	0.190521i	−0.0386226	+	0.0222988i	0.480564	+	0.876959i	$0.340432\pi$
$74$		0			0
$75$	−5.20268	+	6.29561i	−0.600753	+	0.726954i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	9.20620			1.03578			0.517889	−	0.855448i	$-0.326718\pi$
$79$	9.20620			1.03578			0.517889	+	0.855448i	$0.326718\pi$
$80$		0			0
$81$	7.06484	+	5.57567i	0.784982	+	0.619519i
$82$		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
$87$	9.68115	−	3.60611i	1.03793	−	0.386616i
$88$		0			0
$89$	−8.56670	+	14.8380i	−0.908068	+	1.57282i	−0.0913236	+	0.995821i	$0.529110\pi$
$89$	−8.56670	+	14.8380i	−0.908068	+	1.57282i	−0.816745	+	0.576999i	$0.804224\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	0.266124	−	1.57840i	0.0275958	−	0.163673i
$94$		0			0
$95$			1.18949i			0.122039i
$96$		0			0
$97$	13.6747	−	7.89507i	1.38845	−	0.801622i	0.395310	−	0.918548i	$-0.370637\pi$
$97$	13.6747	−	7.89507i	1.38845	−	0.801622i	0.993141	+	0.116925i	$0.0373038\pi$
$98$		0			0
$99$	7.70375	+	8.90616i	0.774256	+	0.895103i
$100$		0			0
$101$	−7.36862	+	12.7628i	−0.733205	+	1.26995i	0.222301	+	0.974978i	$0.428643\pi$
$101$	−7.36862	+	12.7628i	−0.733205	+	1.26995i	−0.955506	+	0.294970i	$0.904690\pi$
$102$		0			0
$103$	11.1442	−	6.43410i	1.09807	−	0.633970i	0.162356	−	0.986732i	$-0.448091\pi$
$103$	11.1442	−	6.43410i	1.09807	−	0.633970i	0.935713	+	0.352762i	$0.114757\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.6679	+	7.89119i	1.32133	+	0.762870i	0.983941	−	0.178496i	$-0.0571231\pi$
$107$	13.6679	+	7.89119i	1.32133	+	0.762870i	0.337389	+	0.941365i	$0.390456\pi$
$108$		0			0
$109$	1.54170	+	2.67030i	0.147668	+	0.255768i	0.930365	−	0.366634i	$-0.119490\pi$
$109$	1.54170	+	2.67030i	0.147668	+	0.255768i	−0.782697	+	0.622403i	$0.786157\pi$
$110$		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
$117$	−0.264948	−	0.306302i	−0.0244945	−	0.0283176i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	2.20375	+	3.81700i	0.200340	+	0.347000i
$122$		0			0
$123$	10.1294	−	12.2573i	0.913340	−	1.10521i
$124$		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
$129$	−3.92431	−	10.5354i	−0.345516	−	0.927590i
$130$		0			0
$131$	7.81823	+	13.5416i	0.683082	+	1.18313i	0.974036	+	0.226395i	$0.0726940\pi$
$131$	7.81823	+	13.5416i	0.683082	+	1.18313i	−0.290954	+	0.956737i	$0.593973\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.0623791	−	2.77176i	−0.00536874	−	0.238555i
$136$		0			0
$137$	−2.13891	−	1.23490i	−0.182739	−	0.105505i	0.405840	−	0.913944i	$-0.366979\pi$
$137$	−2.13891	−	1.23490i	−0.182739	−	0.105505i	−0.588579	+	0.808440i	$0.700312\pi$
$138$		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
$149$	−13.7303	+	7.92720i	−1.12483	+	0.649422i	−0.942630	−	0.333840i	$-0.891656\pi$
$149$	−13.7303	+	7.92720i	−1.12483	+	0.649422i	−0.182201	+	0.983261i	$0.558322\pi$
$150$		0			0
$151$	−4.16548	+	7.21482i	−0.338982	+	0.587134i	−0.984242	−	0.176829i	$-0.943416\pi$
$151$	−4.16548	+	7.21482i	−0.338982	+	0.587134i	0.645260	+	0.763963i	$0.276749\pi$
$152$		0			0
$153$	−2.44469	−	12.7436i	−0.197641	−	1.03026i
$154$		0			0
$155$	−0.427030	+	0.246546i	−0.0342999	+	0.0198031i
$156$		0			0
$157$			8.93500i			0.713091i	0.934278	+	0.356545i	$0.116045\pi$
$157$			8.93500i			0.713091i	−0.934278	+	0.356545i	$0.883955\pi$
$158$		0			0
$159$	−17.8812	+	6.66054i	−1.41807	+	0.528215i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.10310	−	12.3029i	0.556358	−	0.963640i	−0.441439	−	0.897291i	$-0.645532\pi$
$163$	7.10310	−	12.3029i	0.556358	−	0.963640i	0.997797	−	0.0663485i	$-0.0211349\pi$
$164$		0			0
$165$	0.603101	−	3.57704i	0.0469513	−	0.278472i
$166$		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
$171$	4.37536	+	5.05828i	0.334592	+	0.386816i
$172$		0			0
$173$	21.3574			1.62377			0.811886	−	0.583816i	$-0.198441\pi$
$173$	21.3574			1.62377			0.811886	+	0.583816i	$0.198441\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.47613	−	1.09190i	−0.486776	−	0.0820720i
$178$		0			0
$179$	−5.03259	+	2.90557i	−0.376153	+	0.217172i	−0.676143	−	0.736770i	$-0.736350\pi$
$179$	−5.03259	+	2.90557i	−0.376153	+	0.217172i	0.299990	+	0.953942i	$0.403017\pi$
$180$		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
$185$	−4.16108			−0.305929
$186$		0			0
$187$		−	16.9779i		−	1.24155i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			7.92250i			0.573252i	0.958043	+	0.286626i	$0.0925338\pi$
$191$			7.92250i			0.573252i	−0.958043	+	0.286626i	$0.907466\pi$
$192$		0			0
$193$	−6.33096			−0.455712			−0.227856	−	0.973695i	$-0.573172\pi$
$193$	−6.33096			−0.455712			−0.227856	+	0.973695i	$0.573172\pi$
$194$		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	$-0.568653\pi$
$199$	7.40524	−	4.27542i	0.524944	−	0.303076i	0.738955	+	0.673755i	$0.235320\pi$
$200$		0			0
$201$	−19.6653	−	3.31564i	−1.38708	−	0.233867i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−4.89838			−0.342118
$206$		0			0
$207$	5.79625	−	1.11193i	0.402868	−	0.0772847i
$208$		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
$213$	−0.929793	+	5.51468i	−0.0637084	+	0.377859i
$214$		0			0
$215$	−1.73164	+	2.99929i	−0.118097	+	0.204550i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	0.618470	−	0.230373i	0.0417924	−	0.0155671i
$220$		0			0
$221$			0.583907i			0.0392779i
$222$		0			0
$223$	−6.00510	+	3.46705i	−0.402131	+	0.232171i	−0.687403	−	0.726276i	$-0.741249\pi$
$223$	−6.00510	+	3.46705i	−0.402131	+	0.232171i	0.285272	+	0.958447i	$0.407916\pi$
$224$		0			0
$225$	10.6988	−	9.25436i	0.713254	−	0.616957i
$226$		0			0
$227$	7.28833	−	12.6238i	0.483743	−	0.837868i	−0.516082	−	0.856539i	$-0.672610\pi$
$227$	7.28833	−	12.6238i	0.483743	−	0.837868i	0.999826	+	0.0186708i	$0.00594345\pi$
$228$		0			0
$229$	21.2722	−	12.2815i	1.40571	−	0.811586i	0.410738	−	0.911753i	$-0.365271\pi$
$229$	21.2722	−	12.2815i	1.40571	−	0.811586i	0.994971	+	0.100167i	$0.0319377\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.10556	−	5.25710i	−0.596525	−	0.344404i	0.171148	−	0.985245i	$-0.445252\pi$
$233$	−9.10556	−	5.25710i	−0.596525	−	0.344404i	−0.767673	+	0.640841i	$0.778586\pi$
$234$		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
$241$	11.3780	+	6.56909i	0.732922	+	0.423152i	0.819490	−	0.573093i	$-0.194257\pi$
$241$	11.3780	+	6.56909i	0.732922	+	0.423152i	−0.0865685	+	0.996246i	$0.527590\pi$
$242$		0			0
$243$	−10.4608	−	11.5574i	−0.671057	−	0.741405i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.150478	−	0.260636i	−0.00957469	−	0.0165838i
$248$		0			0
$249$	1.54799	+	4.15581i	0.0980997	+	0.263363i
$250$		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
$255$	−2.54635	+	3.08127i	−0.159459	+	0.192957i
$256$		0			0
$257$	6.80481	+	11.7863i	0.424472	+	0.735207i	0.996371	−	0.0851169i	$-0.0271264\pi$
$257$	6.80481	+	11.7863i	0.424472	+	0.735207i	−0.571899	+	0.820324i	$0.693793\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−17.5733	+	3.37120i	−1.08776	+	0.208672i
$262$		0			0
$263$	−19.7930	−	11.4275i	−1.22049	−	0.704651i	−0.255468	−	0.966817i	$-0.582230\pi$
$263$	−19.7930	−	11.4275i	−1.22049	−	0.704651i	−0.965023	+	0.262167i	$0.915563\pi$
$264$		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	0.656106	−	0.754669i	$-0.272202\pi$
$269$	−5.33875	−	9.24698i	−0.325509	−	0.563798i	−0.981615	+	0.190870i	$0.938869\pi$
$270$		0			0
$271$	−3.90987	−	2.25737i	−0.237508	−	0.137125i	0.376523	−	0.926407i	$-0.377120\pi$
$271$	−3.90987	−	2.25737i	−0.237508	−	0.137125i	−0.614031	+	0.789282i	$0.710453\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	16.0290	−	9.25436i	0.966587	−	0.558059i
$276$		0			0
$277$	3.34952	−	5.80154i	0.201253	−	0.348581i	−0.747679	−	0.664060i	$-0.768832\pi$
$277$	3.34952	−	5.80154i	0.201253	−	0.348581i	0.948932	+	0.315479i	$0.102165\pi$
$278$		0			0
$279$	−0.909051	+	2.61919i	−0.0544235	+	0.156807i
$280$		0			0
$281$	−15.1414	+	8.74187i	−0.903258	+	0.521496i	−0.878256	−	0.478191i	$-0.841293\pi$
$281$	−15.1414	+	8.74187i	−0.903258	+	0.521496i	−0.0250023	+	0.999687i	$0.507959\pi$
$282$		0			0
$283$			8.56844i			0.509341i	0.967028	+	0.254670i	$0.0819670\pi$
$283$			8.56844i			0.509341i	−0.967028	+	0.254670i	$0.918033\pi$
$284$		0			0
$285$	0.342533	−	2.03159i	0.0202899	−	0.120341i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.854223	+	1.47956i	−0.0502484	+	0.0870328i
$290$		0			0
$291$	−25.6291	+	9.54651i	−1.50240	+	0.559626i
$292$		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
$297$	−10.5929	−	17.4296i	−0.614663	−	1.01137i
$298$		0			0
$299$	−0.265582			−0.0153590
$300$		0			0
$301$		0			0
$302$		0			0
$303$	16.2604	−	19.6763i	0.934138	−	1.13037i
$304$		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
$311$	−18.1597			−1.02974			−0.514871	−	0.857268i	$-0.672160\pi$
$311$	−18.1597			−1.02974			−0.514871	+	0.857268i	$0.672160\pi$
$312$		0			0
$313$		−	3.19506i		−	0.180595i	−0.995915	−	0.0902977i	$-0.971218\pi$
$313$		−	3.19506i		−	0.180595i	0.995915	−	0.0902977i	$-0.0287818\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	26.0839i		−	1.46502i	−0.680759	−	0.732508i	$-0.738350\pi$
$317$		−	26.0839i		−	1.46502i	0.680759	−	0.732508i	$-0.261650\pi$
$318$		0			0
$319$	−23.4124			−1.31084
$320$		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
$327$	−1.86418	−	5.00468i	−0.103090	−	0.276760i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−16.1297			−0.886567			−0.443283	−	0.896382i	$-0.646186\pi$
$331$	−16.1297			−0.886567			−0.443283	+	0.896382i	$0.646186\pi$
$332$		0			0
$333$	−17.6949	+	15.3059i	−0.969673	+	0.838758i
$334$		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
$339$	−12.2745	−	10.1436i	−0.666660	−	0.550926i
$340$		0			0
$341$	−1.81376	+	3.14153i	−0.0982207	+	0.170123i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−1.40147	−	1.15817i	−0.0754528	−	0.0623540i
$346$		0			0
$347$			34.8030i			1.86832i	0.356852	+	0.934161i	$0.383850\pi$
$347$			34.8030i			1.86832i	−0.356852	+	0.934161i	$0.616150\pi$
$348$		0			0
$349$	19.6825	−	11.3637i	1.05358	−	0.608283i	0.129929	−	0.991523i	$-0.458525\pi$
$349$	19.6825	−	11.3637i	1.05358	−	0.608283i	0.923649	+	0.383240i	$0.125192\pi$
$350$		0			0
$351$	0.364313	+	0.599443i	0.0194456	+	0.0319959i
$352$		0			0
$353$	−4.02829	+	6.97721i	−0.214404	+	0.371359i	−0.953088	−	0.302693i	$-0.902114\pi$
$353$	−4.02829	+	6.97721i	−0.214404	+	0.371359i	0.738684	+	0.674052i	$0.235448\pi$
$354$		0			0
$355$	1.49197	−	0.861390i	0.0791856	−	0.0457178i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.4341	−	8.91086i	−0.814579	−	0.470297i	0.0339648	−	0.999423i	$-0.489187\pi$
$359$	−15.4341	−	8.91086i	−0.814579	−	0.470297i	−0.848543	+	0.529126i	$0.822520\pi$
$360$		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
$367$	−20.5888	−	11.8870i	−1.07473	−	0.620494i	−0.145258	−	0.989394i	$-0.546401\pi$
$367$	−20.5888	−	11.8870i	−1.07473	−	0.620494i	−0.929469	+	0.368900i	$0.879734\pi$
$368$		0			0
$369$	−20.8302	+	18.0179i	−1.08438	+	0.937975i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.26858	−	9.12545i	−0.272797	−	0.472498i	0.696780	−	0.717285i	$-0.254615\pi$
$373$	−5.26858	−	9.12545i	−0.272797	−	0.472498i	−0.969577	+	0.244787i	$0.921282\pi$
$374$		0			0
$375$	−8.85349	−	1.49273i	−0.457192	−	0.0770841i
$376$		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
$381$	17.2614	+	2.91033i	0.884329	+	0.149101i
$382$		0			0
$383$	18.0980	+	31.3466i	0.924764	+	1.60174i	0.791941	+	0.610598i	$0.209071\pi$
$383$	18.0980	+	31.3466i	0.924764	+	1.60174i	0.132823	+	0.991140i	$0.457596\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.66867	+	19.1240i	0.186489	+	0.972125i
$388$		0			0
$389$	−18.6031	−	10.7405i	−0.943215	−	0.544565i	−0.0522481	−	0.998634i	$-0.516639\pi$
$389$	−18.6031	−	10.7405i	−0.943215	−	0.544565i	−0.890967	+	0.454069i	$0.849972\pi$
$390$		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	$-0.153784\pi$
$397$	18.4505	+	10.6524i	0.926006	+	0.534630i	0.0404601	+	0.999181i	$0.487118\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.6821	+	9.05406i	−0.783126	+	0.452138i	−0.837537	−	0.546381i	$-0.816005\pi$
$401$	−15.6821	+	9.05406i	−0.783126	+	0.452138i	0.0544110	+	0.998519i	$0.482672\pi$
$402$		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
$409$		−	20.4159i		−	1.00950i	−0.863265	−	0.504751i	$-0.831584\pi$
$409$		−	20.4159i		−	1.00950i	0.863265	−	0.504751i	$-0.168416\pi$
$410$		0			0
$411$	3.29753	+	2.72507i	0.162655	+	0.134418i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	0.683065	−	1.18310i	0.0335303	−	0.0580762i
$416$		0			0
$417$	−25.9814	−	21.4710i	−1.27231	−	1.05144i
$418$		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
$423$	17.2503	+	5.98712i	0.838739	+	0.291104i
$424$		0			0
$425$	−20.3953			−0.989316
$426$		0			0
$427$		0			0
$428$		0			0
$429$	0.320369	+	0.860078i	0.0154675	+	0.0415250i
$430$		0			0
$431$	13.1109	−	7.56961i	0.631532	−	0.364615i	−0.149813	−	0.988714i	$-0.547867\pi$
$431$	13.1109	−	7.56961i	0.631532	−	0.364615i	0.781345	+	0.624099i	$0.214534\pi$
$432$		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
$437$	4.38583			0.209803
$438$		0			0
$439$		−	27.3469i		−	1.30520i	−0.757705	−	0.652598i	$-0.773679\pi$
$439$		−	27.3469i		−	1.30520i	0.757705	−	0.652598i	$-0.226321\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	16.9186i		−	0.803828i	−0.915677	−	0.401914i	$-0.868345\pi$
$443$		−	16.9186i		−	0.803828i	0.915677	−	0.401914i	$-0.131655\pi$
$444$		0			0
$445$	−9.14170			−0.433358
$446$		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
$453$	9.19203	−	11.1230i	0.431879	−	0.522604i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−34.8036			−1.62804			−0.814022	−	0.580833i	$-0.802727\pi$
$457$	−34.8036			−1.62804			−0.814022	+	0.580833i	$0.802727\pi$
$458$		0			0
$459$	0.505679	+	22.4694i	0.0236031	+	1.04878i
$460$		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
$465$	0.800341	−	0.298117i	0.0371149	−	0.0138249i
$466$		0			0
$467$	4.40378	−	7.62758i	0.203783	−	0.352962i	−0.745961	−	0.665989i	$-0.768010\pi$
$467$	4.40378	−	7.62758i	0.203783	−	0.352962i	0.949744	+	0.313027i	$0.101343\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	2.57297	−	15.2605i	0.118556	−	0.703166i
$472$		0			0
$473$			25.4783i			1.17149i
$474$		0			0
$475$	9.10373	−	5.25604i	0.417708	−	0.241164i
$476$		0			0
$477$	32.4582	−	6.22666i	1.48616	−	0.285099i
$478$		0			0
$479$	6.83139	−	11.8323i	0.312134	−	0.540633i	−0.666690	−	0.745335i	$-0.732289\pi$
$479$	6.83139	−	11.8323i	0.312134	−	0.540633i	0.978824	+	0.204703i	$0.0656227\pi$
$480$		0			0
$481$	0.911756	−	0.526403i	0.0415725	−	0.0240019i
$482$		0			0
$483$		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	0.613987	−	0.789316i	$-0.289565\pi$
$487$	−8.31028	−	14.3938i	−0.376575	−	0.652246i	−0.990561	+	0.137070i	$0.956232\pi$
$488$		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
$495$	−2.06013	+	5.93571i	−0.0925957	+	0.266790i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.34609	+	2.33149i	0.0602592	+	0.104372i	0.894581	−	0.446905i	$-0.147474\pi$
$499$	1.34609	+	2.33149i	0.0602592	+	0.104372i	−0.834322	+	0.551277i	$0.814141\pi$
$500$		0			0
$501$	13.8429	−	16.7509i	0.618455	−	0.748374i
$502$		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
$507$	7.84862	+	21.0708i	0.348569	+	0.935787i
$508$		0			0
$509$	−2.96117	−	5.12890i	−0.131252	−	0.227334i	0.792908	−	0.609342i	$-0.208566\pi$
$509$	−2.96117	−	5.12890i	−0.131252	−	0.227334i	−0.924159	+	0.382007i	$0.875233\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−6.01627	−	9.89921i	−0.265625	−	0.437061i
$514$		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
$521$	19.5943	+	33.9383i	0.858442	+	1.48686i	0.873415	+	0.486976i	$0.161900\pi$
$521$	19.5943	+	33.9383i	0.858442	+	1.48686i	−0.0149735	+	0.999888i	$0.504766\pi$
$522$		0			0
$523$	−19.9496	−	11.5179i	−0.872333	−	0.503642i	−0.00421050	−	0.999991i	$-0.501340\pi$
$523$	−19.9496	−	11.5179i	−0.872333	−	0.503642i	−0.868123	+	0.496349i	$0.834674\pi$
$524$		0			0
$525$		0			0
$526$		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
$535$			8.42085i			0.364065i
$536$		0			0
$537$	9.43208	−	3.51334i	0.407024	−	0.151612i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.66302	−	2.88044i	0.0714990	−	0.123840i	−0.828059	−	0.560640i	$-0.810555\pi$
$541$	1.66302	−	2.88044i	0.0714990	−	0.123840i	0.899558	+	0.436800i	$0.143888\pi$
$542$		0			0
$543$	−2.12771	+	12.6196i	−0.0913088	+	0.541560i
$544$		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
$549$	10.6213	−	30.6026i	0.453307	−	1.30609i
$550$		0			0
$551$	−13.2971			−0.566477
$552$		0			0
$553$		0			0
$554$		0			0
$555$	7.10690	+	1.19825i	0.301671	+	0.0508628i
$556$		0			0
$557$	−3.13213	+	1.80833i	−0.132712	+	0.0766216i	−0.564886	−	0.825169i	$-0.691080\pi$
$557$	−3.13213	+	1.80833i	−0.132712	+	0.0766216i	0.432174	+	0.901790i	$0.357747\pi$
$558$		0			0
$559$		−	0.876252i		−	0.0370615i
$560$		0			0
$561$	−4.88906	+	28.9974i	−0.206416	+	1.22427i
$562$		0			0
$563$	−9.50903			−0.400758			−0.200379	−	0.979718i	$-0.564217\pi$
$563$	−9.50903			−0.400758			−0.200379	+	0.979718i	$0.564217\pi$
$564$		0			0
$565$			4.90525i			0.206365i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			10.5048i			0.440384i	0.975457	+	0.220192i	$0.0706684\pi$
$569$			10.5048i			0.440384i	−0.975457	+	0.220192i	$0.929332\pi$
$570$		0			0
$571$	4.48402			0.187650			0.0938252	−	0.995589i	$-0.470091\pi$
$571$	4.48402			0.187650			0.0938252	+	0.995589i	$0.470091\pi$
$572$		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	0.756310	−	0.654213i	$-0.227000\pi$
$577$	40.8602	−	23.5906i	1.70103	−	0.982090i	0.944720	−	0.327877i	$-0.106333\pi$
$578$		0			0
$579$	10.8129	+	1.82310i	0.449370	+	0.0757653i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	43.2431			1.79095
$584$		0			0
$585$	0.0708521	−	0.204142i	0.00292937	−	0.00844022i
$586$		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
$591$	−4.36498	+	25.8890i	−0.179551	+	1.06493i
$592$		0			0
$593$	4.72490	−	8.18376i	0.194028	−	0.336067i	−0.752553	−	0.658531i	$-0.771178\pi$
$593$	4.72490	−	8.18376i	0.194028	−	0.336067i	0.946582	+	0.322465i	$0.104511\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−13.8789	+	5.16973i	−0.568026	+	0.211583i
$598$		0			0
$599$		−	36.5354i		−	1.49280i	−0.665499	−	0.746398i	$-0.731781\pi$
$599$		−	36.5354i		−	1.49280i	0.665499	−	0.746398i	$-0.268219\pi$
$600$		0			0
$601$	−1.92247	+	1.10994i	−0.0784193	+	0.0452754i	−0.538697	−	0.842500i	$-0.681083\pi$
$601$	−1.92247	+	1.10994i	−0.0784193	+	0.0452754i	0.460278	+	0.887775i	$0.347750\pi$
$602$		0			0
$603$	32.6325	+	11.3259i	1.32890	+	0.461225i
$604$		0			0
$605$	−1.17583	+	2.03660i	−0.0478043	+	0.0827995i
$606$		0			0
$607$	1.71759	−	0.991653i	0.0697149	−	0.0402499i	−0.464737	−	0.885449i	$-0.653851\pi$
$607$	1.71759	−	0.991653i	0.0697149	−	0.0402499i	0.534452	+	0.845199i	$0.320518\pi$
$608$		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	0.999299	−	0.0374258i	$-0.0119158\pi$
$613$	11.5683	+	20.0368i	0.467238	+	0.809280i	−0.532061	+	0.846706i	$0.678582\pi$
$614$		0			0
$615$	8.36616	+	1.41056i	0.337356	+	0.0568794i
$616$		0			0
$617$	−1.19807	−	0.691704i	−0.0482323	−	0.0278470i	0.475690	−	0.879613i	$-0.342198\pi$
$617$	−1.19807	−	0.691704i	−0.0482323	−	0.0278470i	−0.523922	+	0.851766i	$0.675532\pi$
$618$		0			0
$619$	5.22550	+	3.01694i	0.210031	+	0.121261i	0.601326	−	0.799004i	$-0.294639\pi$
$619$	5.22550	+	3.01694i	0.210031	+	0.121261i	−0.391295	+	0.920265i	$0.627973\pi$
$620$		0			0
$621$	−10.2199	+	0.230001i	−0.410110	+	0.00922962i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−10.4054	−	18.0226i	−0.416215	−	0.720905i
$626$		0			0
$627$	−5.29058	−	14.2034i	−0.211285	−	0.567227i
$628$		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
$633$	6.19607	−	7.49768i	0.246272	−	0.298006i
$634$		0			0
$635$	−2.69622	−	4.67000i	−0.106996	−	0.185323i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	3.17607	−	9.15102i	0.125643	−	0.362009i
$640$		0			0
$641$	−40.2246	−	23.2237i	−1.58878	−	0.917281i	−0.993509	−	0.113754i	$-0.963712\pi$
$641$	−40.2246	−	23.2237i	−1.58878	−	0.917281i	−0.595269	−	0.803527i	$-0.702954\pi$
$642$		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	0.816696	−	0.577068i	$-0.195803\pi$
$647$	−2.32507	−	4.02715i	−0.0914081	−	0.158323i	−0.908104	+	0.418745i	$0.862470\pi$
$648$		0			0
$649$	12.8896	+	7.44179i	0.505959	+	0.292116i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.99966	+	1.73186i	−0.117386	+	0.0677727i	−0.557543	−	0.830148i	$-0.688256\pi$
$653$	−2.99966	+	1.73186i	−0.117386	+	0.0677727i	0.440157	+	0.897921i	$0.354923\pi$
$654$		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
$661$			20.2299i			0.786852i	0.919356	+	0.393426i	$0.128710\pi$
$661$			20.2299i			0.786852i	−0.919356	+	0.393426i	$0.871290\pi$
$662$		0			0
$663$	0.168145	−	0.997282i	0.00653021	−	0.0387312i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.86711	+	10.1621i	−0.227175	+	0.393479i
$668$		0			0
$669$	11.2548	−	4.19226i	0.435134	−	0.162082i
$670$		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
$675$	−20.9379	+	12.7251i	−0.805900	+	0.489788i
$676$		0			0
$677$	15.4290			0.592984			0.296492	−	0.955035i	$-0.404183\pi$
$677$	15.4290			0.592984			0.296492	+	0.955035i	$0.404183\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−16.0833	+	19.4619i	−0.616312	+	0.745782i
$682$		0			0
$683$	13.6137	−	7.85987i	0.520913	−	0.300750i	−0.216395	−	0.976306i	$-0.569430\pi$
$683$	13.6137	−	7.85987i	0.520913	−	0.300750i	0.737308	+	0.675556i	$0.236097\pi$
$684$		0			0
$685$		−	1.31779i		−	0.0503501i
$686$		0			0
$687$	−39.8685	+	14.8505i	−1.52108	+	0.566582i
$688$		0			0
$689$	−1.48722			−0.0566586
$690$		0			0
$691$			48.0214i			1.82682i	0.407039	+	0.913411i	$0.366561\pi$
$691$			48.0214i			1.82682i	−0.407039	+	0.913411i	$0.633439\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			10.3829i			0.393846i
$696$		0			0
$697$	39.7089			1.50408
$698$		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
$705$	−1.96343	−	5.27114i	−0.0739472	−	0.198523i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	34.0864			1.28014			0.640070	−	0.768317i	$-0.278905\pi$
$709$	34.0864			1.28014			0.640070	+	0.768317i	$0.278905\pi$
$710$		0			0
$711$	26.0918	+	9.05575i	0.978518	+	0.339617i
$712$		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
$717$	−26.0661	−	21.5409i	−0.973455	−	0.804462i
$718$		0			0
$719$	9.23791	−	16.0005i	0.344516	−	0.596719i	−0.640750	−	0.767750i	$-0.721376\pi$
$719$	9.23791	−	16.0005i	0.344516	−	0.596719i	0.985266	+	0.171031i	$0.0547097\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−17.5413	−	14.4961i	−0.652369	−	0.539116i
$724$		0			0
$725$			28.1249i			1.04453i
$726$		0			0
$727$	−39.2911	+	22.6847i	−1.45723	+	0.841330i	−0.998874	−	0.0474398i	$-0.984894\pi$
$727$	−39.2911	+	22.6847i	−1.45723	+	0.841330i	−0.458353	+	0.888770i	$0.651560\pi$
$728$		0			0
$729$	14.5383	+	22.7517i	0.538454	+	0.842655i
$730$		0			0
$731$	14.0376	−	24.3138i	0.519200	−	0.899280i
$732$		0			0
$733$	−43.3683	+	25.0387i	−1.60184	+	0.924825i	−0.610724	+	0.791843i	$0.709122\pi$
$733$	−43.3683	+	25.0387i	−1.60184	+	0.924825i	−0.991119	+	0.132981i	$0.957545\pi$
$734$		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	0.978705	−	0.205272i	$-0.0658079\pi$
$739$	8.47021	+	14.6708i	0.311582	+	0.539675i	−0.667123	+	0.744947i	$0.732475\pi$
$740$		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
$747$	−1.44715	−	7.54365i	−0.0529484	−	0.276008i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	14.7028	+	25.4659i	0.536512	+	0.929265i	0.999089	+	0.0426862i	$0.0135916\pi$
$751$	14.7028	+	25.4659i	0.536512	+	0.929265i	−0.462577	+	0.886579i	$0.653075\pi$
$752$		0			0
$753$	38.7472	+	6.53290i	1.41203	+	0.238072i
$754$		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
$759$	−13.1891	−	2.22372i	−0.478733	−	0.0807159i
$760$		0			0
$761$	−6.11067	−	10.5840i	−0.221511	−	0.383669i	0.733756	−	0.679413i	$-0.237766\pi$
$761$	−6.11067	−	10.5840i	−0.221511	−	0.383669i	−0.955267	+	0.295744i	$0.904432\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	5.23633	−	4.52938i	0.189320	−	0.163760i
$766$		0			0
$767$	−0.443300	−	0.255939i	−0.0160066	−	0.00924143i
$768$		0			0
$769$	−29.4039	−	16.9764i	−1.06033	−	0.612184i	−0.134809	−	0.990872i	$-0.543042\pi$
$769$	−29.4039	−	16.9764i	−1.06033	−	0.612184i	−0.925524	+	0.378688i	$0.876375\pi$
$770$		0			0
$771$	−8.22820	−	22.0898i	−0.296331	−	0.795546i
$772$		0			0
$773$	−15.1047	−	26.1622i	−0.543279	−	0.940987i	−0.998713	−	0.0507175i	$-0.983849\pi$
$773$	−15.1047	−	26.1622i	−0.543279	−	0.940987i	0.455434	−	0.890270i	$-0.349484\pi$
$774$		0			0
$775$	3.77386	+	2.17884i	0.135561	+	0.0782662i
$776$		0			0
$777$		0			0
$778$		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
$787$		−	38.4873i		−	1.37192i	−0.727638	−	0.685962i	$-0.759382\pi$
$787$		−	38.4873i		−	1.37192i	0.727638	−	0.685962i	$-0.240618\pi$
$788$		0			0
$789$	30.5147	+	25.2173i	1.08635	+	0.897759i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.728836	+	1.26238i	−0.0258817	+	0.0448285i
$794$		0			0
$795$	−7.84804	−	6.48561i	−0.278341	−	0.230021i
$796$		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
$801$	−38.8748	+	33.6263i	−1.37357	+	1.18813i
$802$		0			0
$803$	−1.49568			−0.0527813
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.45548	+	17.3307i	0.227244	+	0.610070i
$808$		0			0
$809$	44.8465	−	25.8921i	1.57672	−	0.910318i	0.581404	−	0.813615i	$-0.302503\pi$
$809$	44.8465	−	25.8921i	1.57672	−	0.910318i	0.995313	−	0.0967036i	$-0.0308299\pi$
$810$		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
$815$	7.57987			0.265511
$816$		0			0
$817$			14.4705i			0.506257i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			25.8035i			0.900547i	0.892891	+	0.450274i	$0.148674\pi$
$821$			25.8035i			0.900547i	−0.892891	+	0.450274i	$0.851326\pi$
$822$		0			0
$823$	−1.14103			−0.0397737			−0.0198869	−	0.999802i	$-0.506331\pi$
$823$	−1.14103			−0.0397737			−0.0198869	+	0.999802i	$0.506331\pi$
$824$		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	$-0.720002\pi$
$829$	−8.31700	+	4.80182i	−0.288861	+	0.166774i	0.348567	+	0.937284i	$0.386668\pi$
$830$		0			0
$831$	−7.39144	+	8.94417i	−0.256406	+	0.310270i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−6.69413			−0.231660
$836$		0			0
$837$	2.30685	−	4.21166i	0.0797362	−	0.145576i
$838$		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
$843$	28.3780	−	10.5704i	0.977389	−	0.364066i
$844$		0			0
$845$	3.46328	−	5.99858i	0.119140	−	0.206357i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2.46741	−	14.6344i	0.0846814	−	0.502252i
$850$		0			0
$851$			15.3425i			0.525935i
$852$		0			0
$853$	7.50412	−	4.33250i	0.256936	−	0.148342i	−0.366000	−	0.930615i	$-0.619273\pi$
$853$	7.50412	−	4.33250i	0.256936	−	0.148342i	0.622936	+	0.782273i	$0.285940\pi$
$854$		0			0
$855$	−1.17005	+	3.37120i	−0.0400150	+	0.115293i
$856$		0			0
$857$	−11.4439	+	19.8214i	−0.390917	+	0.677088i	−0.992571	−	0.121669i	$-0.961175\pi$
$857$	−11.4439	+	19.8214i	−0.390917	+	0.677088i	0.601654	+	0.798757i	$0.294509\pi$
$858$		0			0
$859$	11.4922	−	6.63503i	0.392109	−	0.226384i	−0.290964	−	0.956734i	$-0.593976\pi$
$859$	11.4922	−	6.63503i	0.392109	−	0.226384i	0.683074	+	0.730350i	$0.260643\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.646706	−	0.373376i	−0.0220141	−	0.0127099i	0.488953	−	0.872310i	$-0.337379\pi$
$863$	−0.646706	−	0.373376i	−0.0220141	−	0.0127099i	−0.510967	+	0.859601i	$0.670712\pi$
$864$		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
$871$	−1.34612	−	0.777181i	−0.0456114	−	0.0263338i
$872$		0			0
$873$	46.5221	−	8.92464i	1.57453	−	0.302053i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−2.18959	−	3.79249i	−0.0739373	−	0.128063i	0.826686	−	0.562663i	$-0.190223\pi$
$877$	−2.18959	−	3.79249i	−0.0739373	−	0.128063i	−0.900624	+	0.434600i	$0.856890\pi$
$878$		0			0
$879$	26.7974	−	32.4267i	0.903853	−	1.09373i
$880$		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
$885$	−1.22316	−	3.28377i	−0.0411162	−	0.110383i
$886$		0			0
$887$	−26.1812	−	45.3471i	−0.879077	−	1.52261i	−0.852355	−	0.522963i	$-0.824826\pi$
$887$	−26.1812	−	45.3471i	−0.879077	−	1.52261i	−0.0267221	−	0.999643i	$-0.508507\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	13.0730	+	32.8193i	0.437961	+	1.09949i
$892$		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
$899$	−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
$905$	3.41418	−	1.97118i	0.113491	−	0.0655242i
$906$		0			0
$907$	12.1902	−	21.1141i	0.404770	−	0.701082i	−0.589525	−	0.807750i	$-0.700685\pi$
$907$	12.1902	−	21.1141i	0.404770	−	0.701082i	0.994295	+	0.106669i	$0.0340184\pi$
$908$		0			0
$909$	−33.4380	+	28.9236i	−1.10907	+	0.959335i
$910$		0			0
$911$	−46.8606	+	27.0550i	−1.55256	+	0.896372i	−0.554629	+	0.832098i	$0.687140\pi$
$911$	−46.8606	+	27.0550i	−1.55256	+	0.896372i	−0.997932	+	0.0642741i	$0.979527\pi$
$912$		0			0
$913$		−	10.0502i		−	0.332613i
$914$		0			0
$915$	−9.35116	+	3.48319i	−0.309140	+	0.115151i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−3.25947	+	5.64556i	−0.107520	+	0.186230i	−0.914765	−	0.403986i	$-0.867624\pi$
$919$	−3.25947	+	5.64556i	−0.107520	+	0.186230i	0.807245	+	0.590216i	$0.200958\pi$
$920$		0			0
$921$	3.59314	−	21.3112i	0.118398	−	0.702228i
$922$		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
$927$	37.9132	−	7.27315i	1.24523	−	0.238881i
$928$		0			0
$929$	−27.8096			−0.912404			−0.456202	−	0.889876i	$-0.650791\pi$
$929$	−27.8096			−0.912404			−0.456202	+	0.889876i	$0.650791\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	31.0157	+	5.22936i	1.01541	+	0.171202i
$934$		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
$941$	−5.13053			−0.167250			−0.0836252	−	0.996497i	$-0.526650\pi$
$941$	−5.13053			−0.167250			−0.0836252	+	0.996497i	$0.526650\pi$
$942$		0			0
$943$			18.0610i			0.588148i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	0.699787i		−	0.0227400i	−0.999935	−	0.0113700i	$-0.996381\pi$
$947$		−	0.699787i		−	0.0227400i	0.999935	−	0.0113700i	$-0.00361926\pi$
$948$		0			0
$949$	0.0514395			0.00166980
$950$		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
$957$	39.9871	+	6.74196i	1.29260	+	0.217937i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	30.1459			0.972450
$962$		0			0
$963$	30.9748	+	35.8094i	0.998148	+	1.15394i
$964$		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
$969$	−2.77675	+	16.4691i	−0.0892021	+	0.529065i
$970$		0			0
$971$	1.46120	−	2.53087i	0.0468920	−	0.0812194i	−0.841627	−	0.540060i	$-0.818402\pi$
$971$	1.46120	−	2.53087i	0.0468920	−	0.0812194i	0.888519	+	0.458840i	$0.151735\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.03320	−	0.384853i	0.0330887	−	0.0123252i
$976$		0			0
$977$			28.5226i			0.912519i	0.889847	+	0.456259i	$0.150811\pi$
$977$			28.5226i			0.912519i	−0.889847	+	0.456259i	$0.849189\pi$
$978$		0			0
$979$	−58.2425	+	33.6263i	−1.86144	+	1.07470i
$980$		0			0
$981$	1.74275	+	9.08454i	0.0556416	+	0.290047i
$982$		0			0
$983$	5.62897	−	9.74967i	0.179536	−	0.310966i	−0.762185	−	0.647359i	$-0.775874\pi$
$983$	5.62897	−	9.74967i	0.179536	−	0.310966i	0.941722	+	0.336393i	$0.109207\pi$
$984$		0			0
$985$	7.00416	−	4.04386i	0.223171	−	0.128848i
$986$		0			0
$987$		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	0.647579	−	0.761998i	$-0.275781\pi$
$991$	−10.5811	−	18.3270i	−0.336120	−	0.582177i	−0.983699	+	0.179821i	$0.942448\pi$
$992$		0			0
$993$	27.5486	+	4.64478i	0.874228	+	0.147398i
$994$		0			0
$995$	3.95114	+	2.28119i	0.125260	+	0.0723187i
$996$		0			0
$997$	−14.6576	−	8.46256i	−0.464210	−	0.268012i	0.249603	−	0.968348i	$-0.419700\pi$
$997$	−14.6576	−	8.46256i	−0.464210	−	0.268012i	−0.713813	+	0.700336i	$0.753033\pi$
$998$		0			0
$999$	34.6294	−	21.0461i	1.09563	−	0.665870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.w.a.509.1		16
3.2	odd	2		5292.2.w.a.1097.4		16
7.2	even	3		252.2.x.a.41.6	yes	16
7.3	odd	6		1764.2.bm.b.1697.4		16
7.4	even	3		1764.2.bm.b.1697.5		16
7.5	odd	6		252.2.x.a.41.3	✓	16
7.6	odd	2	inner	1764.2.w.a.509.8		16
9.2	odd	6		1764.2.bm.b.1685.4		16
9.7	even	3		5292.2.bm.b.4625.4		16
21.2	odd	6		756.2.x.a.125.4		16
21.5	even	6		756.2.x.a.125.5		16
21.11	odd	6		5292.2.bm.b.2285.5		16
21.17	even	6		5292.2.bm.b.2285.4		16
21.20	even	2		5292.2.w.a.1097.5		16
28.19	even	6		1008.2.cc.c.545.6		16
28.23	odd	6		1008.2.cc.c.545.3		16
63.2	odd	6		252.2.x.a.209.3	yes	16
63.5	even	6		2268.2.f.b.1133.7		16
63.11	odd	6	inner	1764.2.w.a.1109.8		16
63.16	even	3		756.2.x.a.629.5		16
63.20	even	6		1764.2.bm.b.1685.5		16
63.23	odd	6		2268.2.f.b.1133.10		16
63.25	even	3		5292.2.w.a.521.5		16
63.34	odd	6		5292.2.bm.b.4625.5		16
63.38	even	6	inner	1764.2.w.a.1109.1		16
63.40	odd	6		2268.2.f.b.1133.9		16
63.47	even	6		252.2.x.a.209.6	yes	16
63.52	odd	6		5292.2.w.a.521.4		16
63.58	even	3		2268.2.f.b.1133.8		16
63.61	odd	6		756.2.x.a.629.4		16
84.23	even	6		3024.2.cc.c.881.4		16
84.47	odd	6		3024.2.cc.c.881.5		16
252.47	odd	6		1008.2.cc.c.209.3		16
252.79	odd	6		3024.2.cc.c.2897.5		16
252.187	even	6		3024.2.cc.c.2897.4		16
252.191	even	6		1008.2.cc.c.209.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.3	✓	16	7.5	odd	6
252.2.x.a.41.6	yes	16	7.2	even	3
252.2.x.a.209.3	yes	16	63.2	odd	6
252.2.x.a.209.6	yes	16	63.47	even	6
756.2.x.a.125.4		16	21.2	odd	6
756.2.x.a.125.5		16	21.5	even	6
756.2.x.a.629.4		16	63.61	odd	6
756.2.x.a.629.5		16	63.16	even	3
1008.2.cc.c.209.3		16	252.47	odd	6
1008.2.cc.c.209.6		16	252.191	even	6
1008.2.cc.c.545.3		16	28.23	odd	6
1008.2.cc.c.545.6		16	28.19	even	6
1764.2.w.a.509.1		16	1.1	even	1	trivial
1764.2.w.a.509.8		16	7.6	odd	2	inner
1764.2.w.a.1109.1		16	63.38	even	6	inner
1764.2.w.a.1109.8		16	63.11	odd	6	inner
1764.2.bm.b.1685.4		16	9.2	odd	6
1764.2.bm.b.1685.5		16	63.20	even	6
1764.2.bm.b.1697.4		16	7.3	odd	6
1764.2.bm.b.1697.5		16	7.4	even	3
2268.2.f.b.1133.7		16	63.5	even	6
2268.2.f.b.1133.8		16	63.58	even	3
2268.2.f.b.1133.9		16	63.40	odd	6
2268.2.f.b.1133.10		16	63.23	odd	6
3024.2.cc.c.881.4		16	84.23	even	6
3024.2.cc.c.881.5		16	84.47	odd	6
3024.2.cc.c.2897.4		16	252.187	even	6
3024.2.cc.c.2897.5		16	252.79	odd	6
5292.2.w.a.521.4		16	63.52	odd	6
5292.2.w.a.521.5		16	63.25	even	3
5292.2.w.a.1097.4		16	3.2	odd	2
5292.2.w.a.1097.5		16	21.20	even	2
5292.2.bm.b.2285.4		16	21.17	even	6
5292.2.bm.b.2285.5		16	21.11	odd	6
5292.2.bm.b.4625.4		16	9.7	even	3
5292.2.bm.b.4625.5		16	63.34	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.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.70794 - 0.287965i) q^{3} +(0.266780 + 0.462077i) q^{5} +(2.83415 + 0.983658i) q^{9} +O(q^{10})\)	\(q+(-1.70794 - 0.287965i) q^{3} +(0.266780 + 0.462077i) q^{5} +(2.83415 + 0.983658i) q^{9} +(3.39936 + 1.96262i) q^{11} +(-0.116911 - 0.0674987i) q^{13} +(-0.322584 - 0.866025i) q^{15} +(-2.16266 - 3.74584i) q^{17} +(1.93067 + 1.11467i) q^{19} +(1.70375 - 0.983658i) q^{23} +(2.35766 - 4.08358i) q^{25} +(-4.55732 - 2.49617i) q^{27} +(-5.16548 + 2.98229i) q^{29} +0.924154i q^{31} +(-5.24075 - 4.33094i) q^{33} +(-3.89936 + 6.75388i) q^{37} +(0.180240 + 0.148950i) q^{39} +(-4.59027 + 7.95059i) q^{41} +(3.24544 + 5.62127i) q^{43} +(0.301570 + 1.57202i) q^{45} +6.08659 q^{47} +(2.61504 + 7.02046i) q^{51} +(9.54072 - 5.50834i) q^{53} +2.09435i q^{55} +(-2.97650 - 2.45977i) q^{57} +3.79177 q^{59} -10.7978i q^{61} -0.0720292i q^{65} +11.5140 q^{67} +(-3.19316 + 1.18941i) q^{69} -3.22884i q^{71} +(-0.329991 + 0.190521i) q^{73} +(-5.20268 + 6.29561i) q^{75} +9.20620 q^{79} +(7.06484 + 5.57567i) q^{81} +(-1.28020 - 2.21737i) q^{83} +(1.15391 - 1.99863i) q^{85} +(9.68115 - 3.60611i) q^{87} +(-8.56670 + 14.8380i) q^{89} +(0.266124 - 1.57840i) q^{93} +1.18949i q^{95} +(13.6747 - 7.89507i) q^{97} +(7.70375 + 8.90616i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{9}+O(q^{10}) \) 16 * q - 6 * q^9	\( 16 q - 6 q^{9} - 6 q^{11} - 12 q^{15} - 6 q^{23} - 8 q^{25} - 12 q^{29} - 2 q^{37} - 36 q^{39} + 4 q^{43} + 12 q^{51} + 36 q^{53} - 42 q^{57} - 28 q^{67} - 40 q^{79} - 18 q^{81} + 6 q^{85} - 6 q^{93} + 90 q^{99}+O(q^{100}) \) 16 * q - 6 * q^9 - 6 * q^11 - 12 * q^15 - 6 * q^23 - 8 * q^25 - 12 * q^29 - 2 * q^37 - 36 * q^39 + 4 * q^43 + 12 * q^51 + 36 * q^53 - 42 * q^57 - 28 * q^67 - 40 * q^79 - 18 * q^81 + 6 * q^85 - 6 * q^93 + 90 * q^99

Introduction

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