LMFDB - Embedded newform 1176.2.u.a.521.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1176,2,Mod(521,1176)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1176.521"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1176, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.767858691933644783616.8
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} - 3x^{12} + 4x^{10} - 4x^{8} + 16x^{6} - 48x^{4} - 64x^{2} + 256 $ x^16 - x^14 - 3x^12 + 4x^10 - 4x^8 + 16x^6 - 48x^4 - 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.3
Root			$-0.0865986 + 1.41156i$ of defining polynomial
Character	$\chi$	$=$	1176.521
Dual form			1176.2.u.a.1097.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.883857 - 1.48956i) q^{3} +(1.51022 + 2.61578i) q^{5} +(-1.43759 + 2.63312i) q^{9} +(-2.70469 - 1.56155i) q^{11} -1.69614i q^{13} +(2.56155 - 4.56155i) q^{15} +(0.662153 - 1.14688i) q^{17} +(5.55359 - 3.20636i) q^{19} +(1.73205 - 1.00000i) q^{23} +(-2.06155 + 3.57071i) q^{25} +(5.19283 - 0.185917i) q^{27} +9.12311i q^{29} +(6.37845 + 3.68260i) q^{31} +(0.0645276 + 5.40899i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-2.52651 + 1.49915i) q^{39} +10.7575 q^{41} -4.00000 q^{43} +(-9.05876 + 0.216167i) q^{45} +(4.34475 + 7.52534i) q^{47} +(-2.29360 + 0.0273620i) q^{51} +(7.90084 + 4.56155i) q^{53} -9.43318i q^{55} +(-9.68466 - 5.43845i) q^{57} +(2.54421 - 4.40670i) q^{59} +(4.40670 - 2.54421i) q^{61} +(4.43674 - 2.56155i) q^{65} +(3.12311 - 5.40938i) q^{67} +(-3.02045 - 1.69614i) q^{69} +4.87689i q^{71} +(-10.4631 - 6.04090i) q^{73} +(7.14092 - 0.0851890i) q^{75} +(-1.43845 - 2.49146i) q^{79} +(-4.86665 - 7.57071i) q^{81} -1.69614 q^{83} +4.00000 q^{85} +(13.5894 - 8.06352i) q^{87} +(5.75058 + 9.96029i) q^{89} +(-0.152175 - 12.7560i) q^{93} +(16.7743 + 9.68466i) q^{95} +8.68951i q^{97} +(8.00000 - 4.87689i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9} + 8 q^{15} + 16 q^{37} - 4 q^{39} - 64 q^{43} + 24 q^{51} - 56 q^{57} - 16 q^{67} - 56 q^{79} + 64 q^{85} - 56 q^{93} + 128 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 + 8 * q^15 + 16 * q^37 - 4 * q^39 - 64 * q^43 + 24 * q^51 - 56 * q^57 - 16 * q^67 - 56 * q^79 + 64 * q^85 - 56 * q^93 + 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.883857	−	1.48956i	−0.510295	−	0.859999i
$3$	−0.883857	−	1.48956i	−0.510295	−	0.859999i
$4$		0			0
$5$	1.51022	+	2.61578i	0.675393	+	1.16981i	0.976354	+	0.216178i	$0.0693592\pi$
$5$	1.51022	+	2.61578i	0.675393	+	1.16981i	−0.300961	+	0.953636i	$0.597307\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.43759	+	2.63312i	−0.479198	+	0.877707i
$10$		0			0
$11$	−2.70469	−	1.56155i	−0.815494	−	0.470826i	0.0333659	−	0.999443i	$-0.489377\pi$
$11$	−2.70469	−	1.56155i	−0.815494	−	0.470826i	−0.848860	+	0.528617i	$0.822711\pi$
$12$		0			0
$13$		−	1.69614i		−	0.470425i	−0.971944	−	0.235212i	$-0.924421\pi$
$13$		−	1.69614i		−	0.470425i	0.971944	−	0.235212i	$-0.0755786\pi$
$14$		0			0
$15$	2.56155	−	4.56155i	0.661390	−	1.17779i
$16$		0			0
$17$	0.662153	−	1.14688i	0.160596	−	0.278160i	−0.774487	−	0.632590i	$-0.781992\pi$
$17$	0.662153	−	1.14688i	0.160596	−	0.278160i	0.935083	+	0.354430i	$0.115325\pi$
$18$		0			0
$19$	5.55359	−	3.20636i	1.27408	−	0.735591i	0.298327	−	0.954464i	$-0.403571\pi$
$19$	5.55359	−	3.20636i	1.27408	−	0.735591i	0.975753	+	0.218873i	$0.0702381\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	−0.308431	−	0.951247i	$-0.599804\pi$
$23$	1.73205	−	1.00000i	0.361158	−	0.208514i	0.669588	+	0.742732i	$0.266471\pi$
$24$		0			0
$25$	−2.06155	+	3.57071i	−0.412311	+	0.714143i
$26$		0			0
$27$	5.19283	−	0.185917i	0.999360	−	0.0357798i
$28$		0			0
$29$			9.12311i			1.69412i	0.531499	+	0.847059i	$0.321629\pi$
$29$			9.12311i			1.69412i	−0.531499	+	0.847059i	$0.678371\pi$
$30$		0			0
$31$	6.37845	+	3.68260i	1.14560	+	0.661415i	0.947812	−	0.318829i	$-0.103290\pi$
$31$	6.37845	+	3.68260i	1.14560	+	0.661415i	0.197792	+	0.980244i	$0.436623\pi$
$32$		0			0
$33$	0.0645276	+	5.40899i	0.0112328	+	0.941585i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	−2.52651	+	1.49915i	−0.404565	+	0.240056i
$40$		0			0
$41$	10.7575			1.68004			0.840018	−	0.542558i	$-0.182544\pi$
$41$	10.7575			1.68004			0.840018	+	0.542558i	$0.182544\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	−9.05876	+	0.216167i	−1.35040	+	0.0322243i
$46$		0			0
$47$	4.34475	+	7.52534i	0.633748	+	1.09768i	0.986779	+	0.162072i	$0.0518176\pi$
$47$	4.34475	+	7.52534i	0.633748	+	1.09768i	−0.353031	+	0.935611i	$0.614849\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.29360	+	0.0273620i	−0.321169	+	0.00383145i
$52$		0			0
$53$	7.90084	+	4.56155i	1.08526	+	0.626577i	0.932312	−	0.361656i	$-0.117789\pi$
$53$	7.90084	+	4.56155i	1.08526	+	0.626577i	0.152952	+	0.988234i	$0.451122\pi$
$54$		0			0
$55$		−	9.43318i		−	1.27197i
$56$		0			0
$57$	−9.68466	−	5.43845i	−1.28276	−	0.720340i
$58$		0			0
$59$	2.54421	−	4.40670i	0.331228	−	0.573704i	−0.651525	−	0.758627i	$-0.725870\pi$
$59$	2.54421	−	4.40670i	0.331228	−	0.573704i	0.982753	+	0.184923i	$0.0592037\pi$
$60$		0			0
$61$	4.40670	−	2.54421i	0.564221	−	0.325753i	−0.190617	−	0.981664i	$-0.561049\pi$
$61$	4.40670	−	2.54421i	0.564221	−	0.325753i	0.754838	+	0.655912i	$0.227716\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.43674	−	2.56155i	0.550310	−	0.317722i
$66$		0			0
$67$	3.12311	−	5.40938i	0.381548	−	0.660861i	−0.609736	−	0.792605i	$-0.708724\pi$
$67$	3.12311	−	5.40938i	0.381548	−	0.660861i	0.991284	+	0.131744i	$0.0420577\pi$
$68$		0			0
$69$	−3.02045	−	1.69614i	−0.363619	−	0.204191i
$70$		0			0
$71$			4.87689i			0.578781i	0.957211	+	0.289390i	$0.0934526\pi$
$71$			4.87689i			0.578781i	−0.957211	+	0.289390i	$0.906547\pi$
$72$		0			0
$73$	−10.4631	−	6.04090i	−1.22462	−	0.707033i	−0.258719	−	0.965953i	$-0.583300\pi$
$73$	−10.4631	−	6.04090i	−1.22462	−	0.707033i	−0.965899	+	0.258919i	$0.916634\pi$
$74$		0			0
$75$	7.14092	−	0.0851890i	0.824562	−	0.00983678i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.43845	−	2.49146i	−0.161838	−	0.280312i	0.773690	−	0.633564i	$-0.218409\pi$
$79$	−1.43845	−	2.49146i	−0.161838	−	0.280312i	−0.935528	+	0.353253i	$0.885076\pi$
$80$		0			0
$81$	−4.86665	−	7.57071i	−0.540739	−	0.841190i
$82$		0			0
$83$	−1.69614			−0.186176			−0.0930878	−	0.995658i	$-0.529674\pi$
$83$	−1.69614			−0.186176			−0.0930878	+	0.995658i	$0.529674\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$		0			0
$87$	13.5894	−	8.06352i	1.45694	−	0.864500i
$88$		0			0
$89$	5.75058	+	9.96029i	0.609560	+	1.05579i	0.991313	+	0.131524i	$0.0419872\pi$
$89$	5.75058	+	9.96029i	0.609560	+	1.05579i	−0.381753	+	0.924264i	$0.624680\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.152175	−	12.7560i	−0.0157798	−	1.32274i
$94$		0			0
$95$	16.7743	+	9.68466i	1.72101	+	0.993625i
$96$		0			0
$97$			8.68951i			0.882286i	0.897437	+	0.441143i	$0.145427\pi$
$97$			8.68951i			0.882286i	−0.897437	+	0.441143i	$0.854573\pi$
$98$		0			0
$99$	8.00000	−	4.87689i	0.804030	−	0.490146i
$100$		0			0
$101$	−1.88206	+	3.25982i	−0.187272	+	0.324364i	−0.944340	−	0.328972i	$-0.893298\pi$
$101$	−1.88206	+	3.25982i	−0.187272	+	0.324364i	0.757068	+	0.653336i	$0.226631\pi$
$102$		0			0
$103$	4.08469	−	2.35829i	0.402476	−	0.232370i	−0.285076	−	0.958505i	$-0.592019\pi$
$103$	4.08469	−	2.35829i	0.402476	−	0.232370i	0.687552	+	0.726135i	$0.258685\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.16879	+	3.56155i	−0.596359	+	0.344308i	−0.767608	−	0.640920i	$-0.778553\pi$
$107$	−6.16879	+	3.56155i	−0.596359	+	0.344308i	0.171249	+	0.985228i	$0.445220\pi$
$108$		0			0
$109$	6.12311	−	10.6055i	0.586487	−	1.01583i	−0.408201	−	0.912892i	$-0.633844\pi$
$109$	6.12311	−	10.6055i	0.586487	−	1.01583i	0.994688	−	0.102934i	$-0.0328229\pi$
$110$		0			0
$111$	1.69614	−	3.02045i	0.160991	−	0.286688i
$112$		0			0
$113$		−	7.36932i		−	0.693247i	−0.938004	−	0.346624i	$-0.887328\pi$
$113$		−	7.36932i		−	0.693247i	0.938004	−	0.346624i	$-0.112672\pi$
$114$		0			0
$115$	5.23157	+	3.02045i	0.487846	+	0.281658i
$116$		0			0
$117$	4.46614	+	2.43836i	0.412895	+	0.225427i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.623106	−	1.07925i	−0.0566460	−	0.0981137i
$122$		0			0
$123$	−9.50808	−	16.0239i	−0.857315	−	1.44483i
$124$		0			0
$125$	2.64861			0.236899
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$		0			0
$129$	3.53543	+	5.95825i	0.311277	+	0.524595i
$130$		0			0
$131$	−6.88897	−	11.9320i	−0.601892	−	1.04251i	−0.992534	−	0.121965i	$-0.961081\pi$
$131$	−6.88897	−	11.9320i	−0.601892	−	1.04251i	0.390643	−	0.920542i	$-0.372253\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	8.32865	+	13.3025i	0.716816	+	1.14490i
$136$		0			0
$137$	−1.94528	−	1.12311i	−0.166196	−	0.0959534i	0.414595	−	0.910006i	$-0.363923\pi$
$137$	−1.94528	−	1.12311i	−0.166196	−	0.0959534i	−0.580791	+	0.814053i	$0.697257\pi$
$138$		0			0
$139$			6.41273i			0.543921i	0.962308	+	0.271960i	$0.0876720\pi$
$139$			6.41273i			0.543921i	−0.962308	+	0.271960i	$0.912328\pi$
$140$		0			0
$141$	7.36932	−	13.1231i	0.620608	−	1.10516i
$142$		0			0
$143$	−2.64861	+	4.58753i	−0.221488	+	0.383629i
$144$		0			0
$145$	−23.8641	+	13.7779i	−1.98180	+	1.14420i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.91791	+	1.68466i	−0.239045	+	0.138013i	−0.614738	−	0.788732i	$-0.710738\pi$
$149$	−2.91791	+	1.68466i	−0.239045	+	0.138013i	0.375693	+	0.926744i	$0.377405\pi$
$150$		0			0
$151$	−6.24621	+	10.8188i	−0.508309	+	0.880418i	0.491644	+	0.870796i	$0.336396\pi$
$151$	−6.24621	+	10.8188i	−0.508309	+	0.880418i	−0.999954	+	0.00962167i	$0.996937\pi$
$152$		0			0
$153$	2.06798	+	3.39228i	0.167186	+	0.274250i
$154$		0			0
$155$			22.2462i			1.78686i
$156$		0			0
$157$	−11.9320	−	6.88897i	−0.952280	−	0.549799i	−0.0584918	−	0.998288i	$-0.518629\pi$
$157$	−11.9320	−	6.88897i	−0.952280	−	0.549799i	−0.893789	+	0.448489i	$0.851962\pi$
$158$		0			0
$159$	−0.188496	−	15.8006i	−0.0149487	−	1.25307i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−7.12311	−	12.3376i	−0.557925	−	0.966354i	−0.997670	−	0.0682312i	$-0.978264\pi$
$163$	−7.12311	−	12.3376i	−0.557925	−	0.966354i	0.439745	−	0.898123i	$-0.355069\pi$
$164$		0			0
$165$	−14.0513	+	8.33758i	−1.09389	+	0.649080i
$166$		0			0
$167$	−3.39228			−0.262503			−0.131251	−	0.991349i	$-0.541899\pi$
$167$	−3.39228			−0.262503			−0.131251	+	0.991349i	$0.541899\pi$
$168$		0			0
$169$	10.1231			0.778700
$170$		0			0
$171$	0.458946	+	19.2327i	0.0350965	+	1.47076i
$172$		0			0
$173$	−7.92295	−	13.7230i	−0.602371	−	1.04334i	−0.992461	−	0.122561i	$-0.960889\pi$
$173$	−7.92295	−	13.7230i	−0.602371	−	1.04334i	0.390090	−	0.920777i	$-0.372444\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.81278	+	0.105134i	−0.662409	+	0.00790234i
$178$		0			0
$179$	4.22351	+	2.43845i	0.315680	+	0.182258i	0.649466	−	0.760391i	$-0.274993\pi$
$179$	4.22351	+	2.43845i	0.315680	+	0.182258i	−0.333785	+	0.942649i	$0.608326\pi$
$180$		0			0
$181$		−	15.6829i		−	1.16570i	−0.812580	−	0.582850i	$-0.801938\pi$
$181$		−	15.6829i		−	1.16570i	0.812580	−	0.582850i	$-0.198062\pi$
$182$		0			0
$183$	−7.68466	−	4.31534i	−0.568066	−	0.318999i
$184$		0			0
$185$	−3.02045	+	5.23157i	−0.222068	+	0.384633i
$186$		0			0
$187$	−3.58184	+	2.06798i	−0.261930	+	0.151225i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	15.0423	−	8.68466i	1.08842	−	0.628400i	0.155265	−	0.987873i	$-0.450377\pi$
$191$	15.0423	−	8.68466i	1.08842	−	0.628400i	0.933155	+	0.359473i	$0.117044\pi$
$192$		0			0
$193$	−3.56155	+	6.16879i	−0.256366	+	0.444039i	−0.965266	−	0.261270i	$-0.915859\pi$
$193$	−3.56155	+	6.16879i	−0.256366	+	0.444039i	0.708900	+	0.705309i	$0.249192\pi$
$194$		0			0
$195$	−7.73704	−	4.34475i	−0.554061	−	0.311134i
$196$		0			0
$197$			17.1231i			1.21997i	0.792413	+	0.609985i	$0.208825\pi$
$197$			17.1231i			1.21997i	−0.792413	+	0.609985i	$0.791175\pi$
$198$		0			0
$199$	−8.67222	−	5.00691i	−0.614757	−	0.354930i	0.160068	−	0.987106i	$-0.448829\pi$
$199$	−8.67222	−	5.00691i	−0.614757	−	0.354930i	−0.774825	+	0.632176i	$0.782162\pi$
$200$		0			0
$201$	−10.8180	+	0.129055i	−0.763042	+	0.00910286i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	16.2462	+	28.1393i	1.13468	+	1.96533i
$206$		0			0
$207$	0.143136	+	5.99829i	0.00994864	+	0.416910i
$208$		0			0
$209$	−20.0276			−1.38534
$210$		0			0
$211$	−22.2462			−1.53149			−0.765746	−	0.643143i	$-0.777630\pi$
$211$	−22.2462			−1.53149			−0.765746	+	0.643143i	$0.777630\pi$
$212$		0			0
$213$	7.26444	−	4.31048i	0.497751	−	0.295349i
$214$		0			0
$215$	−6.04090	−	10.4631i	−0.411986	−	0.713580i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	0.249626	+	20.9248i	0.0168682	+	1.41397i
$220$		0			0
$221$	−1.94528	−	1.12311i	−0.130853	−	0.0755483i
$222$		0			0
$223$			20.1907i			1.35207i	0.736871	+	0.676033i	$0.236303\pi$
$223$			20.1907i			1.35207i	−0.736871	+	0.676033i	$0.763697\pi$
$224$		0			0
$225$	−6.43845	−	10.5616i	−0.429230	−	0.704104i
$226$		0			0
$227$	9.53758	−	16.5196i	0.633031	−	1.09644i	−0.353897	−	0.935284i	$-0.615144\pi$
$227$	9.53758	−	16.5196i	0.633031	−	1.09644i	0.986929	−	0.161158i	$-0.0515230\pi$
$228$		0			0
$229$	3.11863	−	1.80054i	0.206085	−	0.118983i	−0.393406	−	0.919365i	$-0.628703\pi$
$229$	3.11863	−	1.80054i	0.206085	−	0.118983i	0.599491	+	0.800382i	$0.295370\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.92820	+	4.00000i	−0.453882	+	0.262049i	−0.709468	−	0.704737i	$-0.751065\pi$
$233$	−6.92820	+	4.00000i	−0.453882	+	0.262049i	0.255586	+	0.966786i	$0.417731\pi$
$234$		0			0
$235$	−13.1231	+	22.7299i	−0.856057	+	1.48273i
$236$		0			0
$237$	−2.43981	+	4.34475i	−0.158483	+	0.282222i
$238$		0			0
$239$			4.24621i			0.274665i	0.990525	+	0.137332i	$0.0438528\pi$
$239$			4.24621i			0.274665i	−0.990525	+	0.137332i	$0.956147\pi$
$240$		0			0
$241$	13.4009	+	7.73704i	0.863230	+	0.498386i	0.865093	−	0.501612i	$-0.167259\pi$
$241$	13.4009	+	7.73704i	0.863230	+	0.498386i	−0.00186227	+	0.999998i	$0.500593\pi$
$242$		0			0
$243$	−6.97563	+	13.9406i	−0.447487	+	0.894291i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−5.43845	−	9.41967i	−0.346040	−	0.599359i
$248$		0			0
$249$	1.49915	+	2.52651i	0.0950045	+	0.160111i
$250$		0			0
$251$	−6.99337			−0.441418			−0.220709	−	0.975340i	$-0.570837\pi$
$251$	−6.99337			−0.441418			−0.220709	+	0.975340i	$0.570837\pi$
$252$		0			0
$253$	−6.24621			−0.392696
$254$		0			0
$255$	−3.53543	−	5.95825i	−0.221397	−	0.373120i
$256$		0			0
$257$	−0.290319	−	0.502848i	−0.0181096	−	0.0313668i	0.856829	−	0.515601i	$-0.172431\pi$
$257$	−0.290319	−	0.502848i	−0.0181096	−	0.0313668i	−0.874938	+	0.484235i	$0.839098\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−24.0222	−	13.1153i	−1.48694	−	0.811818i
$262$		0			0
$263$	−8.11407	−	4.68466i	−0.500335	−	0.288868i	0.228517	−	0.973540i	$-0.426612\pi$
$263$	−8.11407	−	4.68466i	−0.500335	−	0.288868i	−0.728852	+	0.684672i	$0.759946\pi$
$264$		0			0
$265$			27.5559i			1.69274i
$266$		0			0
$267$	9.75379	−	17.3693i	0.596922	−	1.06298i
$268$		0			0
$269$	−4.53067	+	7.84735i	−0.276240	+	0.478462i	−0.970447	−	0.241314i	$-0.922422\pi$
$269$	−4.53067	+	7.84735i	−0.276240	+	0.478462i	0.694207	+	0.719775i	$0.255755\pi$
$270$		0			0
$271$	−4.72872	+	2.73013i	−0.287249	+	0.165844i	−0.636701	−	0.771111i	$-0.719701\pi$
$271$	−4.72872	+	2.73013i	−0.287249	+	0.165844i	0.349451	+	0.936955i	$0.386368\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	11.1517	−	6.43845i	0.672474	−	0.388253i
$276$		0			0
$277$	6.12311	−	10.6055i	0.367902	−	0.637225i	−0.621336	−	0.783545i	$-0.713410\pi$
$277$	6.12311	−	10.6055i	0.367902	−	0.637225i	0.989237	+	0.146320i	$0.0467429\pi$
$278$		0			0
$279$	−18.8664	+	11.5012i	−1.12950	+	0.688556i
$280$		0			0
$281$			28.4924i			1.69972i	0.527012	+	0.849858i	$0.323312\pi$
$281$			28.4924i			1.69972i	−0.527012	+	0.849858i	$0.676688\pi$
$282$		0			0
$283$	10.7852	+	6.22681i	0.641111	+	0.370146i	0.785042	−	0.619442i	$-0.212641\pi$
$283$	10.7852	+	6.22681i	0.641111	+	0.370146i	−0.143931	+	0.989588i	$0.545974\pi$
$284$		0			0
$285$	−0.400197	−	33.5463i	−0.0237056	−	1.98711i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.62311	+	13.2036i	0.448418	+	0.776683i
$290$		0			0
$291$	12.9436	−	7.68028i	0.758765	−	0.450226i
$292$		0			0
$293$	−25.2791			−1.47682			−0.738410	−	0.674352i	$-0.764423\pi$
$293$	−25.2791			−1.47682			−0.738410	+	0.674352i	$0.764423\pi$
$294$		0			0
$295$	15.3693			0.894836
$296$		0			0
$297$	−14.3353	−	7.60602i	−0.831818	−	0.441346i
$298$		0			0
$299$	−1.69614	−	2.93780i	−0.0980904	−	0.169898i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	6.51918	−	0.0777718i	0.374517	−	0.00446787i
$304$		0			0
$305$	13.3102	+	7.68466i	0.762141	+	0.440022i
$306$		0			0
$307$		−	24.5354i		−	1.40031i	−0.713991	−	0.700155i	$-0.753114\pi$
$307$		−	24.5354i		−	1.40031i	0.713991	−	0.700155i	$-0.246886\pi$
$308$		0			0
$309$	−7.12311	−	4.00000i	−0.405219	−	0.227552i
$310$		0			0
$311$	−9.43318	+	16.3387i	−0.534906	+	0.926485i	0.464261	+	0.885698i	$0.346320\pi$
$311$	−9.43318	+	16.3387i	−0.534906	+	0.926485i	−0.999168	+	0.0407869i	$0.987014\pi$
$312$		0			0
$313$	−2.93780	+	1.69614i	−0.166054	+	0.0958716i	−0.580724	−	0.814100i	$-0.697230\pi$
$313$	−2.93780	+	1.69614i	−0.166054	+	0.0958716i	0.414670	+	0.909972i	$0.363897\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.7914	−	6.80776i	0.662271	−	0.382362i	−0.130871	−	0.991399i	$-0.541777\pi$
$317$	11.7914	−	6.80776i	0.662271	−	0.382362i	0.793142	+	0.609037i	$0.208444\pi$
$318$		0			0
$319$	14.2462	−	24.6752i	0.797635	−	1.38154i
$320$		0			0
$321$	10.7575	+	6.04090i	0.600424	+	0.337170i
$322$		0			0
$323$		−	8.49242i		−	0.472531i
$324$		0			0
$325$	6.05643	+	3.49668i	0.335951	+	0.193961i
$326$		0			0
$327$	−21.2096	+	0.253024i	−1.17289	+	0.0139922i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−11.1231	−	19.2658i	−0.611381	−	1.05894i	−0.991008	−	0.133804i	$-0.957281\pi$
$331$	−11.1231	−	19.2658i	−0.611381	−	1.05894i	0.379627	−	0.925140i	$-0.376052\pi$
$332$		0			0
$333$	−5.99829	+	0.143136i	−0.328704	+	0.00784380i
$334$		0			0
$335$	18.8664			1.03078
$336$		0			0
$337$	25.3693			1.38195			0.690977	−	0.722876i	$-0.257180\pi$
$337$	25.3693			1.38195			0.690977	+	0.722876i	$0.257180\pi$
$338$		0			0
$339$	−10.9771	+	6.51342i	−0.596192	+	0.353761i
$340$		0			0
$341$	−11.5012	−	19.9206i	−0.622822	−	1.07876i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−0.124813	−	10.4624i	−0.00671972	−	0.563276i
$346$		0			0
$347$	−7.68762	−	4.43845i	−0.412693	−	0.238268i	0.279253	−	0.960217i	$-0.409913\pi$
$347$	−7.68762	−	4.43845i	−0.412693	−	0.238268i	−0.691946	+	0.721949i	$0.743246\pi$
$348$		0			0
$349$		−	3.60109i		−	0.192762i	−0.995345	−	0.0963809i	$-0.969273\pi$
$349$		−	3.60109i		−	0.192762i	0.995345	−	0.0963809i	$-0.0307267\pi$
$350$		0			0
$351$	−0.315342	−	8.80776i	−0.0168317	−	0.470124i
$352$		0			0
$353$	−0.290319	+	0.502848i	−0.0154521	+	0.0267639i	−0.873648	−	0.486558i	$-0.838252\pi$
$353$	−0.290319	+	0.502848i	−0.0154521	+	0.0267639i	0.858196	+	0.513322i	$0.171585\pi$
$354$		0			0
$355$	−12.7569	+	7.36520i	−0.677066	+	0.390904i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−20.9978	+	12.1231i	−1.10822	+	0.639833i	−0.938369	−	0.345636i	$-0.887663\pi$
$359$	−20.9978	+	12.1231i	−1.10822	+	0.639833i	−0.169855	+	0.985469i	$0.554330\pi$
$360$		0			0
$361$	11.0616	−	19.1592i	0.582187	−	1.00838i
$362$		0			0
$363$	−1.05688	+	1.88206i	−0.0554716	+	0.0987824i
$364$		0			0
$365$		−	36.4924i		−	1.91010i
$366$		0			0
$367$	3.44065	+	1.98646i	0.179600	+	0.103692i	0.587105	−	0.809511i	$-0.300268\pi$
$367$	3.44065	+	1.98646i	0.179600	+	0.103692i	−0.407504	+	0.913203i	$0.633601\pi$
$368$		0			0
$369$	−15.4649	+	28.3258i	−0.805070	+	1.47458i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−5.24621	−	9.08670i	−0.271639	−	0.470492i	0.697643	−	0.716446i	$-0.254232\pi$
$373$	−5.24621	−	9.08670i	−0.271639	−	0.470492i	−0.969282	+	0.245954i	$0.920899\pi$
$374$		0			0
$375$	−2.34100	−	3.94528i	−0.120889	−	0.203733i
$376$		0			0
$377$	15.4741			0.796955
$378$		0			0
$379$	0.492423			0.0252940			0.0126470	−	0.999920i	$-0.495974\pi$
$379$	0.492423			0.0252940			0.0126470	+	0.999920i	$0.495974\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.952473	−	1.64973i	−0.0486691	−	0.0842973i	0.840665	−	0.541556i	$-0.182165\pi$
$383$	−0.952473	−	1.64973i	−0.0486691	−	0.0842973i	−0.889334	+	0.457259i	$0.848831\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.75037	−	10.5325i	0.292308	−	0.535396i
$388$		0			0
$389$	2.91791	+	1.68466i	0.147944	+	0.0854156i	0.572145	−	0.820153i	$-0.306112\pi$
$389$	2.91791	+	1.68466i	0.147944	+	0.0854156i	−0.424201	+	0.905568i	$0.639445\pi$
$390$		0			0
$391$		−	2.64861i		−	0.133946i
$392$		0			0
$393$	−11.6847	+	20.8078i	−0.589413	+	1.04961i
$394$		0			0
$395$	4.34475	−	7.52534i	0.218608	−	0.378641i
$396$		0			0
$397$	32.8583	−	18.9708i	1.64911	−	0.952115i	0.671686	−	0.740836i	$-0.265570\pi$
$397$	32.8583	−	18.9708i	1.64911	−	0.952115i	0.977426	−	0.211279i	$-0.0677628\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	25.2213	−	14.5616i	1.25949	−	0.727169i	0.286518	−	0.958075i	$-0.407502\pi$
$401$	25.2213	−	14.5616i	1.25949	−	0.727169i	0.972976	+	0.230906i	$0.0741689\pi$
$402$		0			0
$403$	6.24621	−	10.8188i	0.311146	−	0.538921i
$404$		0			0
$405$	12.4536	−	24.1636i	0.618826	−	1.20070i
$406$		0			0
$407$		−	6.24621i		−	0.309613i
$408$		0			0
$409$	29.7397	+	17.1702i	1.47053	+	0.849012i	0.999453	−	0.0330780i	$-0.0105310\pi$
$409$	29.7397	+	17.1702i	1.47053	+	0.849012i	0.471080	+	0.882091i	$0.343864\pi$
$410$		0			0
$411$	0.0464098	+	3.89028i	0.00228923	+	0.191893i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.56155	−	4.43674i	−0.125742	−	0.217791i
$416$		0			0
$417$	9.55216	−	5.66794i	0.467771	−	0.277560i
$418$		0			0
$419$	−8.48071			−0.414310			−0.207155	−	0.978308i	$-0.566420\pi$
$419$	−8.48071			−0.414310			−0.207155	+	0.978308i	$0.566420\pi$
$420$		0			0
$421$	−16.7386			−0.815791			−0.407896	−	0.913029i	$-0.633737\pi$
$421$	−16.7386			−0.815791			−0.407896	+	0.913029i	$0.633737\pi$
$422$		0			0
$423$	−26.0611	+	0.621891i	−1.26713	+	0.0302374i
$424$		0			0
$425$	2.73013	+	4.72872i	0.132431	+	0.229377i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	9.17441	−	0.109448i	0.442945	−	0.00528420i
$430$		0			0
$431$	5.19615	+	3.00000i	0.250290	+	0.144505i	0.619897	−	0.784683i	$-0.287174\pi$
$431$	5.19615	+	3.00000i	0.250290	+	0.144505i	−0.369607	+	0.929188i	$0.620508\pi$
$432$		0			0
$433$		−	15.4741i		−	0.743637i	−0.928306	−	0.371818i	$-0.878734\pi$
$433$		−	15.4741i		−	0.743637i	0.928306	−	0.371818i	$-0.121266\pi$
$434$		0			0
$435$	41.6155	+	23.3693i	1.99531	+	1.12047i
$436$		0			0
$437$	6.41273	−	11.1072i	0.306762	−	0.531328i
$438$		0			0
$439$	7.02249	−	4.05444i	0.335165	−	0.193508i	−0.322967	−	0.946410i	$-0.604680\pi$
$439$	7.02249	−	4.05444i	0.335165	−	0.193508i	0.658132	+	0.752903i	$0.271347\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−20.0252	+	11.5616i	−0.951426	+	0.549306i	−0.893524	−	0.449016i	$-0.851775\pi$
$443$	−20.0252	+	11.5616i	−0.951426	+	0.549306i	−0.0579023	+	0.998322i	$0.518441\pi$
$444$		0			0
$445$	−17.3693	+	30.0845i	−0.823385	+	1.42614i
$446$		0			0
$447$	5.08842	+	2.85742i	0.240674	+	0.135151i
$448$		0			0
$449$			10.2462i			0.483549i	0.970333	+	0.241774i	$0.0777294\pi$
$449$			10.2462i			0.483549i	−0.970333	+	0.241774i	$0.922271\pi$
$450$		0			0
$451$	−29.0956	−	16.7984i	−1.37006	−	0.791005i
$452$		0			0
$453$	21.6360	−	0.258111i	1.01655	−	0.0121271i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.80776	−	10.0593i	−0.271676	−	0.470556i	0.697615	−	0.716473i	$-0.254244\pi$
$457$	−5.80776	−	10.0593i	−0.271676	−	0.470556i	−0.969291	+	0.245916i	$0.920911\pi$
$458$		0			0
$459$	3.22522	−	6.07867i	0.150540	−	0.283728i
$460$		0			0
$461$	−13.1973			−0.614659			−0.307330	−	0.951603i	$-0.599435\pi$
$461$	−13.1973			−0.614659			−0.307330	+	0.951603i	$0.599435\pi$
$462$		0			0
$463$	−17.6155			−0.818663			−0.409332	−	0.912386i	$-0.634238\pi$
$463$	−17.6155			−0.818663			−0.409332	+	0.912386i	$0.634238\pi$
$464$		0			0
$465$	33.1371	−	19.6625i	1.53670	−	0.911825i
$466$		0			0
$467$	4.24035	+	7.34451i	0.196220	+	0.339863i	0.947300	−	0.320348i	$-0.103800\pi$
$467$	4.24035	+	7.34451i	0.196220	+	0.339863i	−0.751080	+	0.660212i	$0.770467\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.284671	+	23.8624i	0.0131169	+	1.09952i
$472$		0			0
$473$	10.8188	+	6.24621i	0.497447	+	0.287201i
$474$		0			0
$475$			26.4404i			1.21317i
$476$		0			0
$477$	−23.3693	+	14.2462i	−1.07001	+	0.652289i
$478$		0			0
$479$	−7.73704	+	13.4009i	−0.353514	+	0.612305i	−0.986863	−	0.161562i	$-0.948347\pi$
$479$	−7.73704	+	13.4009i	−0.353514	+	0.612305i	0.633348	+	0.773867i	$0.281680\pi$
$480$		0			0
$481$	2.93780	−	1.69614i	0.133952	−	0.0773374i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−22.7299	+	13.1231i	−1.03211	+	0.595890i
$486$		0			0
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	−0.942309	−	0.334744i	$-0.891350\pi$
$487$	−4.00000	+	6.92820i	−0.181257	+	0.313947i	0.761052	+	0.648691i	$0.224683\pi$
$488$		0			0
$489$	−12.0818	+	21.5150i	−0.546358	+	0.972941i
$490$		0			0
$491$		−	28.8769i		−	1.30320i	−0.758564	−	0.651598i	$-0.774099\pi$
$491$		−	28.8769i		−	1.30320i	0.758564	−	0.651598i	$-0.225901\pi$
$492$		0			0
$493$	10.4631	+	6.04090i	0.471236	+	0.272068i
$494$		0			0
$495$	24.8387	+	13.5611i	1.11642	+	0.609525i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	18.4924	+	32.0298i	0.827835	+	1.43385i	0.899734	+	0.436440i	$0.143761\pi$
$499$	18.4924	+	32.0298i	0.827835	+	1.43385i	−0.0718991	+	0.997412i	$0.522906\pi$
$500$		0			0
$501$	2.99829	+	5.05302i	0.133954	+	0.225752i
$502$		0			0
$503$	5.29723			0.236192			0.118096	−	0.993002i	$-0.462321\pi$
$503$	5.29723			0.236192			0.118096	+	0.993002i	$0.462321\pi$
$504$		0			0
$505$	−11.3693			−0.505928
$506$		0			0
$507$	−8.94738	−	15.0790i	−0.397367	−	0.669682i
$508$		0			0
$509$	12.8483	+	22.2540i	0.569493	+	0.986391i	0.996616	+	0.0821973i	$0.0261938\pi$
$509$	12.8483	+	22.2540i	0.569493	+	0.986391i	−0.427123	+	0.904193i	$0.640473\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	28.2427	−	17.6826i	1.24695	−	0.780706i
$514$		0			0
$515$	12.3376	+	7.12311i	0.543659	+	0.313882i
$516$		0			0
$517$		−	27.1383i		−	1.19354i
$518$		0			0
$519$	−13.4384	+	23.9309i	−0.589882	+	1.05045i
$520$		0			0
$521$	13.4876	−	23.3612i	0.590903	−	1.02347i	−0.403208	−	0.915108i	$-0.632105\pi$
$521$	13.4876	−	23.3612i	0.590903	−	1.02347i	0.994111	−	0.108366i	$-0.0345618\pi$
$522$		0			0
$523$	−1.97175	+	1.13839i	−0.0862186	+	0.0497783i	−0.542489	−	0.840063i	$-0.682518\pi$
$523$	−1.97175	+	1.13839i	−0.0862186	+	0.0497783i	0.456271	+	0.889841i	$0.349185\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.44703	−	4.87689i	0.367958	−	0.212441i
$528$		0			0
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	7.94584	+	13.0343i	0.344820	+	0.565639i
$532$		0			0
$533$		−	18.2462i		−	0.790331i
$534$		0			0
$535$	−18.6325	−	10.7575i	−0.805554	−	0.465087i
$536$		0			0
$537$	−0.100763	−	8.44643i	−0.00434826	−	0.364490i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.12311	+	3.67733i	0.0912794	+	0.158101i	0.908050	−	0.418862i	$-0.137571\pi$
$541$	2.12311	+	3.67733i	0.0912794	+	0.158101i	−0.816770	+	0.576963i	$0.804238\pi$
$542$		0			0
$543$	−23.3606	+	13.8614i	−1.00250	+	0.594851i
$544$		0			0
$545$	36.9890			1.58444
$546$		0			0
$547$	−38.2462			−1.63529			−0.817645	−	0.575723i	$-0.804721\pi$
$547$	−38.2462			−1.63529			−0.817645	+	0.575723i	$0.804721\pi$
$548$		0			0
$549$	0.364168	+	15.2609i	0.0155423	+	0.651320i
$550$		0			0
$551$	29.2520	+	50.6660i	1.24618	+	2.15844i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	10.4624	−	0.124813i	0.444104	−	0.00529803i
$556$		0			0
$557$	−25.6478	−	14.8078i	−1.08673	−	0.627425i	−0.154028	−	0.988067i	$-0.549224\pi$
$557$	−25.6478	−	14.8078i	−1.08673	−	0.627425i	−0.932705	+	0.360641i	$0.882558\pi$
$558$		0			0
$559$			6.78456i			0.286956i
$560$		0			0
$561$	6.24621	+	3.50758i	0.263715	+	0.148090i
$562$		0			0
$563$	−10.2812	+	17.8076i	−0.433303	+	0.750503i	−0.997155	−	0.0753728i	$-0.975985\pi$
$563$	−10.2812	+	17.8076i	−0.433303	+	0.750503i	0.563852	+	0.825876i	$0.309319\pi$
$564$		0			0
$565$	19.2765	−	11.1293i	0.810970	−	0.468214i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−39.9307	+	23.0540i	−1.67398	+	0.966473i	−0.708606	+	0.705605i	$0.750676\pi$
$569$	−39.9307	+	23.0540i	−1.67398	+	0.966473i	−0.965374	+	0.260868i	$0.915991\pi$
$570$		0			0
$571$	−13.3693	+	23.1563i	−0.559488	+	0.969063i	0.438051	+	0.898950i	$0.355669\pi$
$571$	−13.3693	+	23.1563i	−0.559488	+	0.969063i	−0.997539	+	0.0701122i	$0.977664\pi$
$572$		0			0
$573$	−26.2316	−	14.7304i	−1.09584	−	0.615372i
$574$		0			0
$575$			8.24621i			0.343891i
$576$		0			0
$577$	−11.7512	−	6.78456i	−0.489209	−	0.282445i	0.235037	−	0.971986i	$-0.424479\pi$
$577$	−11.7512	−	6.78456i	−0.489209	−	0.282445i	−0.724246	+	0.689541i	$0.757812\pi$
$578$		0			0
$579$	12.3367	−	0.147173i	0.512696	−	0.00611631i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−14.2462	−	24.6752i	−0.590018	−	1.02194i
$584$		0			0
$585$	0.366650	+	15.3649i	0.0151591	+	0.635262i
$586$		0			0
$587$	48.1184			1.98606			0.993029	−	0.117873i	$-0.0376076\pi$
$587$	48.1184			1.98606			0.993029	+	0.117873i	$0.0376076\pi$
$588$		0			0
$589$	47.2311			1.94612
$590$		0			0
$591$	25.5059	−	15.1344i	1.04917	−	0.622545i
$592$		0			0
$593$	8.39919	+	14.5478i	0.344913	+	0.597408i	0.985338	−	0.170613i	$-0.0545749\pi$
$593$	8.39919	+	14.5478i	0.344913	+	0.597408i	−0.640425	+	0.768021i	$0.721242\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.206899	+	17.3432i	0.00846782	+	0.709810i
$598$		0			0
$599$	−35.8269	−	20.6847i	−1.46385	−	0.845152i	−0.464660	−	0.885489i	$-0.653824\pi$
$599$	−35.8269	−	20.6847i	−1.46385	−	0.845152i	−0.999186	+	0.0403367i	$0.987157\pi$
$600$		0			0
$601$			5.29723i			0.216078i	0.994147	+	0.108039i	$0.0344572\pi$
$601$			5.29723i			0.216078i	−0.994147	+	0.108039i	$0.965543\pi$
$602$		0			0
$603$	9.75379	+	16.0000i	0.397205	+	0.651570i
$604$		0			0
$605$	1.88206	−	3.25982i	0.0765165	−	0.132531i
$606$		0			0
$607$	−12.6157	+	7.28369i	−0.512056	+	0.295636i	−0.733678	−	0.679497i	$-0.762198\pi$
$607$	−12.6157	+	7.28369i	−0.512056	+	0.295636i	0.221622	+	0.975133i	$0.428865\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.7640	−	7.36932i	0.516377	−	0.298131i
$612$		0			0
$613$	2.75379	−	4.76970i	0.111224	−	0.192646i	−0.805040	−	0.593221i	$-0.797856\pi$
$613$	2.75379	−	4.76970i	0.111224	−	0.192646i	0.916264	+	0.400574i	$0.131189\pi$
$614$		0			0
$615$	27.5559	−	49.0708i	1.11116	−	1.97873i
$616$		0			0
$617$		−	16.6307i		−	0.669526i	−0.942302	−	0.334763i	$-0.891344\pi$
$617$		−	16.6307i		−	0.669526i	0.942302	−	0.334763i	$-0.108656\pi$
$618$		0			0
$619$	−13.0789	−	7.55112i	−0.525686	−	0.303505i	0.213572	−	0.976927i	$-0.431490\pi$
$619$	−13.0789	−	7.55112i	−0.525686	−	0.303505i	−0.739258	+	0.673422i	$0.764824\pi$
$620$		0			0
$621$	8.80832	−	5.51484i	0.353466	−	0.221303i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	14.3078	+	24.7818i	0.572311	+	0.991271i
$626$		0			0
$627$	17.7016	+	29.8324i	0.706932	+	1.19139i
$628$		0			0
$629$	2.64861			0.105607
$630$		0			0
$631$	37.1231			1.47785			0.738924	−	0.673789i	$-0.235334\pi$
$631$	37.1231			1.47785			0.738924	+	0.673789i	$0.235334\pi$
$632$		0			0
$633$	19.6625	+	33.1371i	0.781513	+	1.31708i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−12.8415	−	7.01099i	−0.508000	−	0.277351i
$640$		0			0
$641$	−24.1290	−	13.9309i	−0.953037	−	0.550236i	−0.0590141	−	0.998257i	$-0.518796\pi$
$641$	−24.1290	−	13.9309i	−0.953037	−	0.550236i	−0.894023	+	0.448021i	$0.852129\pi$
$642$		0			0
$643$		−	17.7509i		−	0.700025i	−0.936745	−	0.350013i	$-0.886177\pi$
$643$		−	17.7509i		−	0.700025i	0.936745	−	0.350013i	$-0.113823\pi$
$644$		0			0
$645$	−10.2462	+	18.2462i	−0.403444	+	0.718444i
$646$		0			0
$647$	3.60109	−	6.23726i	0.141573	−	0.245212i	−0.786516	−	0.617570i	$-0.788117\pi$
$647$	3.60109	−	6.23726i	0.141573	−	0.245212i	0.928089	+	0.372358i	$0.121451\pi$
$648$		0			0
$649$	−13.7626	+	7.94584i	−0.540229	+	0.311902i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	30.6307	−	17.6847i	1.19867	−	0.692054i	0.238414	−	0.971164i	$-0.423373\pi$
$653$	30.6307	−	17.6847i	1.19867	−	0.692054i	0.960259	+	0.279110i	$0.0900393\pi$
$654$		0			0
$655$	20.8078	−	36.0401i	0.813027	−	1.40820i
$656$		0			0
$657$	30.9481	−	18.8664i	1.20740	−	0.736047i
$658$		0			0
$659$		−	15.1231i		−	0.589113i	−0.955634	−	0.294556i	$-0.904828\pi$
$659$		−	15.1231i		−	0.589113i	0.955634	−	0.294556i	$-0.0951718\pi$
$660$		0			0
$661$	−16.5196	−	9.53758i	−0.642537	−	0.370969i	0.143054	−	0.989715i	$-0.454308\pi$
$661$	−16.5196	−	9.53758i	−0.642537	−	0.370969i	−0.785591	+	0.618746i	$0.787641\pi$
$662$		0			0
$663$	0.0464098	+	3.89028i	0.00180241	+	0.151086i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.12311	+	15.8017i	0.353248	+	0.611844i
$668$		0			0
$669$	30.0753	−	17.8457i	1.16278	−	0.689953i
$670$		0			0
$671$	−15.8917			−0.613492
$672$		0			0
$673$	14.4924			0.558642			0.279321	−	0.960198i	$-0.409891\pi$
$673$	14.4924			0.558642			0.279321	+	0.960198i	$0.409891\pi$
$674$		0			0
$675$	−10.0414	+	18.9254i	−0.386495	+	0.728438i
$676$		0			0
$677$	−21.7009	−	37.5870i	−0.834033	−	1.44459i	−0.894815	−	0.446436i	$-0.852693\pi$
$677$	−21.7009	−	37.5870i	−0.834033	−	1.44459i	0.0607826	−	0.998151i	$-0.480640\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−33.0368	+	0.394119i	−1.26597	+	0.0151027i
$682$		0			0
$683$	1.18586	+	0.684658i	0.0453758	+	0.0261977i	0.522516	−	0.852629i	$-0.324993\pi$
$683$	1.18586	+	0.684658i	0.0453758	+	0.0261977i	−0.477140	+	0.878827i	$0.658327\pi$
$684$		0			0
$685$		−	6.78456i		−	0.259225i
$686$		0			0
$687$	−5.43845	−	3.05398i	−0.207490	−	0.116516i
$688$		0			0
$689$	7.73704	−	13.4009i	0.294758	−	0.510535i
$690$		0			0
$691$	0.966053	−	0.557751i	0.0367504	−	0.0212179i	−0.481512	−	0.876439i	$-0.659912\pi$
$691$	0.966053	−	0.557751i	0.0367504	−	0.0212179i	0.518263	+	0.855222i	$0.326579\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−16.7743	+	9.68466i	−0.636286	+	0.367360i
$696$		0			0
$697$	7.12311	−	12.3376i	0.269807	−	0.467319i
$698$		0			0
$699$	12.0818	+	6.78456i	0.456975	+	0.256616i
$700$		0			0
$701$		−	1.12311i		−	0.0424191i	−0.999775	−	0.0212096i	$-0.993248\pi$
$701$		−	1.12311i		−	0.0424191i	0.999775	−	0.0212096i	$-0.00675172\pi$
$702$		0			0
$703$	11.1072	+	6.41273i	0.418915	+	0.241861i
$704$		0			0
$705$	45.4565	−	0.542283i	1.71199	−	0.0204235i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.123106	−	0.213225i	−0.00462333	−	0.00800784i	0.863704	−	0.503999i	$-0.168138\pi$
$709$	−0.123106	−	0.213225i	−0.00462333	−	0.00800784i	−0.868328	+	0.495991i	$0.834805\pi$
$710$		0			0
$711$	8.62823	−	0.205894i	0.323584	−	0.00772161i
$712$		0			0
$713$	14.7304			0.551658
$714$		0			0
$715$	−16.0000			−0.598366
$716$		0			0
$717$	6.32500	−	3.75304i	0.236211	−	0.140160i
$718$		0			0
$719$	−2.43981	−	4.22587i	−0.0909895	−	0.157598i	0.816938	−	0.576725i	$-0.195670\pi$
$719$	−2.43981	−	4.22587i	−0.0909895	−	0.157598i	−0.907928	+	0.419127i	$0.862336\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−0.319716	−	26.8000i	−0.0118904	−	0.996702i
$724$		0			0
$725$	−32.5760	−	18.8078i	−1.20984	−	0.698503i
$726$		0			0
$727$		−	46.5853i		−	1.72775i	−0.503705	−	0.863876i	$-0.668030\pi$
$727$		−	46.5853i		−	1.72775i	0.503705	−	0.863876i	$-0.331970\pi$
$728$		0			0
$729$	26.9309	−	1.93087i	0.997440	−	0.0715137i
$730$		0			0
$731$	−2.64861	+	4.58753i	−0.0979625	+	0.169676i
$732$		0			0
$733$	26.9827	−	15.5785i	0.996629	−	0.575404i	0.0893800	−	0.995998i	$-0.471511\pi$
$733$	26.9827	−	15.5785i	0.996629	−	0.575404i	0.907249	+	0.420593i	$0.138178\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.8941	+	9.75379i	−0.622301	+	0.359285i
$738$		0			0
$739$	−20.2462	+	35.0675i	−0.744769	+	1.28998i	0.205534	+	0.978650i	$0.434107\pi$
$739$	−20.2462	+	35.0675i	−0.744769	+	1.28998i	−0.950303	+	0.311328i	$0.899226\pi$
$740$		0			0
$741$	−9.22437	+	16.4265i	−0.338866	+	0.603444i
$742$		0			0
$743$		−	30.0000i		−	1.10059i	−0.834969	−	0.550297i	$-0.814515\pi$
$743$		−	30.0000i		−	1.10059i	0.834969	−	0.550297i	$-0.185485\pi$
$744$		0			0
$745$	−8.81341	−	5.08842i	−0.322898	−	0.186425i
$746$		0			0
$747$	2.43836	−	4.46614i	0.0892150	−	0.163408i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	0.682341	−	0.731034i	$-0.260962\pi$
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	−0.974265	+	0.225407i	$0.927629\pi$
$752$		0			0
$753$	6.18114	+	10.4171i	0.225253	+	0.379619i
$754$		0			0
$755$	−37.7327			−1.37323
$756$		0			0
$757$	10.4924			0.381354			0.190677	−	0.981653i	$-0.438932\pi$
$757$	10.4924			0.381354			0.190677	+	0.981653i	$0.438932\pi$
$758$		0			0
$759$	5.52076	+	9.30412i	0.200391	+	0.337718i
$760$		0			0
$761$	18.7848	+	32.5363i	0.680950	+	1.17944i	0.974691	+	0.223555i	$0.0717662\pi$
$761$	18.7848	+	32.5363i	0.680950	+	1.17944i	−0.293741	+	0.955885i	$0.594900\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−5.75037	+	10.5325i	−0.207905	+	0.380803i
$766$		0			0
$767$	−7.47439	−	4.31534i	−0.269885	−	0.155818i
$768$		0			0
$769$			35.8278i			1.29198i	0.763345	+	0.645991i	$0.223556\pi$
$769$			35.8278i			1.29198i	−0.763345	+	0.645991i	$0.776444\pi$
$770$		0			0
$771$	−0.492423	+	0.876894i	−0.0177342	+	0.0315806i
$772$		0			0
$773$	−1.88206	+	3.25982i	−0.0676929	+	0.117248i	−0.897885	−	0.440229i	$-0.854897\pi$
$773$	−1.88206	+	3.25982i	−0.0676929	+	0.117248i	0.830192	+	0.557477i	$0.188230\pi$
$774$		0			0
$775$	−26.2990	+	15.1838i	−0.944689	+	0.545417i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	59.7426	−	34.4924i	2.14050	−	1.23582i
$780$		0			0
$781$	7.61553	−	13.1905i	0.272505	−	0.471993i
$782$		0			0
$783$	1.69614	+	47.3747i	0.0606151	+	1.69303i
$784$		0			0
$785$		−	41.6155i		−	1.48532i
$786$		0			0
$787$	−20.2426	−	11.6871i	−0.721571	−	0.416599i	0.0937598	−	0.995595i	$-0.470111\pi$
$787$	−20.2426	−	11.6871i	−0.721571	−	0.416599i	−0.815331	+	0.578996i	$0.803445\pi$
$788$		0			0
$789$	0.193583	+	16.2270i	0.00689174	+	0.577696i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−4.31534	−	7.47439i	−0.153242	−	0.265423i
$794$		0			0
$795$	41.0462	−	24.3554i	1.45576	−	0.863799i
$796$		0			0
$797$	48.6990			1.72501			0.862504	−	0.506051i	$-0.168895\pi$
$797$	48.6990			1.72501			0.862504	+	0.506051i	$0.168895\pi$
$798$		0			0
$799$	11.5076			0.407109
$800$		0			0
$801$	−34.4936	+	0.823115i	−1.21877	+	0.0290833i
$802$		0			0
$803$	18.8664	+	32.6775i	0.665779	+	1.15316i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	15.6936	−	0.187220i	0.552441	−	0.00659045i
$808$		0			0
$809$	−9.41967	−	5.43845i	−0.331178	−	0.191206i	0.325186	−	0.945650i	$-0.394573\pi$
$809$	−9.41967	−	5.43845i	−0.331178	−	0.191206i	−0.656364	+	0.754444i	$0.727906\pi$
$810$		0			0
$811$			41.1708i			1.44570i	0.691004	+	0.722851i	$0.257169\pi$
$811$			41.1708i			1.44570i	−0.691004	+	0.722851i	$0.742831\pi$
$812$		0			0
$813$	8.24621	+	4.63068i	0.289207	+	0.162405i
$814$		0			0
$815$	21.5150	−	37.2650i	0.753637	−	1.30534i
$816$		0			0
$817$	−22.2143	+	12.8255i	−0.777182	+	0.448706i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−12.8838	+	7.43845i	−0.449647	+	0.259604i	−0.707681	−	0.706532i	$-0.750259\pi$
$821$	−12.8838	+	7.43845i	−0.449647	+	0.259604i	0.258034	+	0.966136i	$0.416925\pi$
$822$		0			0
$823$	10.5616	−	18.2931i	0.368153	−	0.637659i	−0.621124	−	0.783712i	$-0.713324\pi$
$823$	10.5616	−	18.2931i	0.368153	−	0.637659i	0.989277	+	0.146053i	$0.0466571\pi$
$824$		0			0
$825$	−19.4470	−	10.9205i	−0.677057	−	0.380204i
$826$		0			0
$827$			33.8617i			1.17749i	0.808320	+	0.588744i	$0.200377\pi$
$827$			33.8617i			1.17749i	−0.808320	+	0.588744i	$0.799623\pi$
$828$		0			0
$829$	19.0957	+	11.0249i	0.663222	+	0.382911i	0.793503	−	0.608566i	$-0.208255\pi$
$829$	19.0957	+	11.0249i	0.663222	+	0.382911i	−0.130282	+	0.991477i	$0.541588\pi$
$830$		0			0
$831$	−21.2096	+	0.253024i	−0.735751	+	0.00877729i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−5.12311	−	8.87348i	−0.177292	−	0.307079i
$836$		0			0
$837$	33.8068	+	17.9372i	1.16854	+	0.620002i
$838$		0			0
$839$	−47.9096			−1.65402			−0.827011	−	0.562186i	$-0.809960\pi$
$839$	−47.9096			−1.65402			−0.827011	+	0.562186i	$0.809960\pi$
$840$		0			0
$841$	−54.2311			−1.87004
$842$		0			0
$843$	42.4412	−	25.1832i	1.46175	−	0.867356i
$844$		0			0
$845$	15.2882	+	26.4799i	0.525929	+	0.910935i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.257309	−	21.5688i	−0.00883082	−	0.740239i
$850$		0			0
$851$	3.46410	+	2.00000i	0.118748	+	0.0685591i
$852$		0			0
$853$			6.57576i			0.225150i	0.993643	+	0.112575i	$0.0359098\pi$
$853$			6.57576i			0.225150i	−0.993643	+	0.112575i	$0.964090\pi$
$854$		0			0
$855$	−49.6155	+	30.2462i	−1.69682	+	1.03440i
$856$		0			0
$857$	3.31077	−	5.73442i	0.113094	−	0.195884i	−0.803922	−	0.594734i	$-0.797257\pi$
$857$	3.31077	−	5.73442i	0.113094	−	0.195884i	0.917016	+	0.398850i	$0.130591\pi$
$858$		0			0
$859$	38.5927	−	22.2815i	1.31677	−	0.760236i	0.333560	−	0.942729i	$-0.391750\pi$
$859$	38.5927	−	22.2815i	1.31677	−	0.760236i	0.983207	+	0.182493i	$0.0584167\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−30.4175	+	17.5616i	−1.03542	+	0.597802i	−0.918534	−	0.395343i	$-0.870626\pi$
$863$	−30.4175	+	17.5616i	−1.03542	+	0.597802i	−0.116890	+	0.993145i	$0.537293\pi$
$864$		0			0
$865$	23.9309	−	41.4495i	0.813674	−	1.40932i
$866$		0			0
$867$	12.9299	−	23.0252i	0.439121	−	0.781977i
$868$		0			0
$869$			8.98485i			0.304790i
$870$		0			0
$871$	−9.17507	−	5.29723i	−0.310885	−	0.179490i
$872$		0			0
$873$	−22.8805	−	12.4920i	−0.774389	−	0.422790i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−14.3693	−	24.8884i	−0.485217	−	0.840421i	0.514638	−	0.857407i	$-0.327926\pi$
$877$	−14.3693	−	24.8884i	−0.485217	−	0.840421i	−0.999856	+	0.0169862i	$0.994593\pi$
$878$		0			0
$879$	22.3431	+	37.6548i	0.753614	+	1.27006i
$880$		0			0
$881$	−34.1774			−1.15147			−0.575733	−	0.817638i	$-0.695283\pi$
$881$	−34.1774			−1.15147			−0.575733	+	0.817638i	$0.695283\pi$
$882$		0			0
$883$	−22.2462			−0.748645			−0.374322	−	0.927299i	$-0.622125\pi$
$883$	−22.2462			−0.748645			−0.374322	+	0.927299i	$0.622125\pi$
$884$		0			0
$885$	−13.5843	−	22.8936i	−0.456631	−	0.769559i
$886$		0			0
$887$	−17.1702	−	29.7397i	−0.576519	−	0.998561i	−0.995875	−	0.0907387i	$-0.971077\pi$
$887$	−17.1702	−	29.7397i	−0.576519	−	0.998561i	0.419355	−	0.907822i	$-0.362256\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.34070	+	28.0760i	0.0449153	+	0.940580i
$892$		0			0
$893$	48.2579	+	27.8617i	1.61489	+	0.932358i
$894$		0			0
$895$			14.7304i			0.492383i
$896$		0			0
$897$	−2.87689	+	5.12311i	−0.0960567	+	0.171056i
$898$		0			0
$899$	−33.5968	+	58.1913i	−1.12051	+	1.94079i
$900$		0			0
$901$	10.4631	−	6.04090i	0.348578	−	0.201251i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	41.0230	−	23.6847i	1.36365	−	0.787305i
$906$		0			0
$907$	−8.24621	+	14.2829i	−0.273811	+	0.474254i	−0.969834	−	0.243765i	$-0.921618\pi$
$907$	−8.24621	+	14.2829i	−0.273811	+	0.474254i	0.696023	+	0.718019i	$0.254951\pi$
$908$		0			0
$909$	−5.87787	−	9.64198i	−0.194957	−	0.319804i
$910$		0			0
$911$		−	6.00000i		−	0.198789i	−0.995048	−	0.0993944i	$-0.968309\pi$
$911$		−	6.00000i		−	0.198789i	0.995048	−	0.0993944i	$-0.0316906\pi$
$912$		0			0
$913$	4.58753	+	2.64861i	0.151825	+	0.0876563i
$914$		0			0
$915$	−0.317551	−	26.6185i	−0.0104979	−	0.879982i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	3.19224	+	5.52911i	0.105302	+	0.182389i	0.913862	−	0.406026i	$-0.133086\pi$
$919$	3.19224	+	5.52911i	0.105302	+	0.182389i	−0.808559	+	0.588414i	$0.799752\pi$
$920$		0			0
$921$	−36.5470	+	21.6858i	−1.20427	+	0.714571i
$922$		0			0
$923$	8.27190			0.272273
$924$		0			0
$925$	−8.24621			−0.271134
$926$		0			0
$927$	0.337557	+	14.1457i	0.0110868	+	0.464607i
$928$		0			0
$929$	−25.4064	−	44.0051i	−0.833556	−	1.44376i	−0.895201	−	0.445663i	$-0.852968\pi$
$929$	−25.4064	−	44.0051i	−0.833556	−	1.44376i	0.0616445	−	0.998098i	$-0.480366\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	32.6752	−	0.389805i	1.06974	−	0.0127616i
$934$		0			0
$935$	−10.8188	−	6.24621i	−0.353811	−	0.204273i
$936$		0			0
$937$		−	18.8664i		−	0.616337i	−0.951332	−	0.308168i	$-0.900284\pi$
$937$		−	18.8664i		−	0.616337i	0.951332	−	0.308168i	$-0.0997161\pi$
$938$		0			0
$939$	5.12311	+	2.87689i	0.167186	+	0.0938839i
$940$		0			0
$941$	5.11131	−	8.85305i	0.166624	−	0.288601i	−0.770607	−	0.637311i	$-0.780047\pi$
$941$	5.11131	−	8.85305i	0.166624	−	0.288601i	0.937231	+	0.348710i	$0.113380\pi$
$942$		0			0
$943$	18.6325	−	10.7575i	0.606758	−	0.350312i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−44.7004	+	25.8078i	−1.45257	+	0.838640i	−0.998627	−	0.0523926i	$-0.983315\pi$
$947$	−44.7004	+	25.8078i	−1.45257	+	0.838640i	−0.453940	+	0.891032i	$0.649982\pi$
$948$		0			0
$949$	−10.2462	+	17.7470i	−0.332606	+	0.576091i
$950$		0			0
$951$	−20.5625	−	11.5469i	−0.666785	−	0.374435i
$952$		0			0
$953$		−	22.7386i		−	0.736577i	−0.929712	−	0.368288i	$-0.879944\pi$
$953$		−	22.7386i		−	0.736577i	0.929712	−	0.368288i	$-0.120056\pi$
$954$		0			0
$955$	45.4344	+	26.2316i	1.47022	+	0.848833i
$956$		0			0
$957$	−49.3468	+	0.588693i	−1.59516	+	0.0190297i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	11.6231	+	20.1318i	0.374939	+	0.649413i
$962$		0			0
$963$	−0.509786	−	21.3632i	−0.0164276	−	0.688421i
$964$		0			0
$965$	−21.5150			−0.692591
$966$		0			0
$967$	28.4924			0.916255			0.458127	−	0.888887i	$-0.348520\pi$
$967$	28.4924			0.916255			0.458127	+	0.888887i	$0.348520\pi$
$968$		0			0
$969$	−12.6500	+	7.50609i	−0.406376	+	0.241130i
$970$		0			0
$971$	−12.9299	−	22.3952i	−0.414939	−	0.718695i	0.580483	−	0.814272i	$-0.302864\pi$
$971$	−12.9299	−	22.3952i	−0.414939	−	0.718695i	−0.995422	+	0.0955769i	$0.969530\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.144493	−	12.1120i	−0.00462747	−	0.387895i
$976$		0			0
$977$	−32.6957	−	18.8769i	−1.04603	−	0.603925i	−0.124494	−	0.992220i	$-0.539731\pi$
$977$	−32.6957	−	18.8769i	−1.04603	−	0.603925i	−0.921535	+	0.388295i	$0.873064\pi$
$978$		0			0
$979$		−	35.9193i		−	1.14799i
$980$		0			0
$981$	19.1231	+	31.3693i	0.610554	+	1.00155i
$982$		0			0
$983$	−3.60109	+	6.23726i	−0.114857	+	0.198938i	−0.917723	−	0.397222i	$-0.869974\pi$
$983$	−3.60109	+	6.23726i	−0.114857	+	0.198938i	0.802866	+	0.596160i	$0.203308\pi$
$984$		0			0
$985$	−44.7904	+	25.8597i	−1.42714	+	0.823959i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.92820	+	4.00000i	−0.220304	+	0.127193i
$990$		0			0
$991$	−6.56155	+	11.3649i	−0.208435	+	0.361019i	−0.951222	−	0.308509i	$-0.900170\pi$
$991$	−6.56155	+	11.3649i	−0.208435	+	0.361019i	0.742787	+	0.669528i	$0.233504\pi$
$992$		0			0
$993$	−18.8664	+	33.5968i	−0.598706	+	1.06616i
$994$		0			0
$995$		−	30.2462i		−	0.958869i
$996$		0			0
$997$	−7.34451	−	4.24035i	−0.232603	−	0.134293i	0.379169	−	0.925327i	$-0.376210\pi$
$997$	−7.34451	−	4.24035i	−0.232603	−	0.134293i	−0.611772	+	0.791034i	$0.709543\pi$
$998$		0			0
$999$	5.51484	+	8.80832i	0.174482	+	0.278683i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.u.a.521.3		16
3.2	odd	2	inner	1176.2.u.a.521.1		16
7.2	even	3	inner	1176.2.u.a.1097.8		16
7.3	odd	6		168.2.k.a.41.5	yes	8
7.4	even	3		168.2.k.a.41.4	yes	8
7.5	odd	6	inner	1176.2.u.a.1097.1		16
7.6	odd	2	inner	1176.2.u.a.521.6		16
21.2	odd	6	inner	1176.2.u.a.1097.6		16
21.5	even	6	inner	1176.2.u.a.1097.3		16
21.11	odd	6		168.2.k.a.41.6	yes	8
21.17	even	6		168.2.k.a.41.3	✓	8
21.20	even	2	inner	1176.2.u.a.521.8		16
28.3	even	6		336.2.k.c.209.4		8
28.11	odd	6		336.2.k.c.209.5		8
56.3	even	6		1344.2.k.i.1217.5		8
56.11	odd	6		1344.2.k.i.1217.4		8
56.45	odd	6		1344.2.k.f.1217.4		8
56.53	even	6		1344.2.k.f.1217.5		8
84.11	even	6		336.2.k.c.209.3		8
84.59	odd	6		336.2.k.c.209.6		8
168.11	even	6		1344.2.k.i.1217.6		8
168.53	odd	6		1344.2.k.f.1217.3		8
168.59	odd	6		1344.2.k.i.1217.3		8
168.101	even	6		1344.2.k.f.1217.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.k.a.41.3	✓	8	21.17	even	6
168.2.k.a.41.4	yes	8	7.4	even	3
168.2.k.a.41.5	yes	8	7.3	odd	6
168.2.k.a.41.6	yes	8	21.11	odd	6
336.2.k.c.209.3		8	84.11	even	6
336.2.k.c.209.4		8	28.3	even	6
336.2.k.c.209.5		8	28.11	odd	6
336.2.k.c.209.6		8	84.59	odd	6
1176.2.u.a.521.1		16	3.2	odd	2	inner
1176.2.u.a.521.3		16	1.1	even	1	trivial
1176.2.u.a.521.6		16	7.6	odd	2	inner
1176.2.u.a.521.8		16	21.20	even	2	inner
1176.2.u.a.1097.1		16	7.5	odd	6	inner
1176.2.u.a.1097.3		16	21.5	even	6	inner
1176.2.u.a.1097.6		16	21.2	odd	6	inner
1176.2.u.a.1097.8		16	7.2	even	3	inner
1344.2.k.f.1217.3		8	168.53	odd	6
1344.2.k.f.1217.4		8	56.45	odd	6
1344.2.k.f.1217.5		8	56.53	even	6
1344.2.k.f.1217.6		8	168.101	even	6
1344.2.k.i.1217.3		8	168.59	odd	6
1344.2.k.i.1217.4		8	56.11	odd	6
1344.2.k.i.1217.5		8	56.3	even	6
1344.2.k.i.1217.6		8	168.11	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.883857 - 1.48956i) q^{3} +(1.51022 + 2.61578i) q^{5} +(-1.43759 + 2.63312i) q^{9} +(-2.70469 - 1.56155i) q^{11} -1.69614i q^{13} +(2.56155 - 4.56155i) q^{15} +(0.662153 - 1.14688i) q^{17} +(5.55359 - 3.20636i) q^{19} +(1.73205 - 1.00000i) q^{23} +(-2.06155 + 3.57071i) q^{25} +(5.19283 - 0.185917i) q^{27} +9.12311i q^{29} +(6.37845 + 3.68260i) q^{31} +(0.0645276 + 5.40899i) q^{33} +(1.00000 + 1.73205i) q^{37} +(-2.52651 + 1.49915i) q^{39} +10.7575 q^{41} -4.00000 q^{43} +(-9.05876 + 0.216167i) q^{45} +(4.34475 + 7.52534i) q^{47} +(-2.29360 + 0.0273620i) q^{51} +(7.90084 + 4.56155i) q^{53} -9.43318i q^{55} +(-9.68466 - 5.43845i) q^{57} +(2.54421 - 4.40670i) q^{59} +(4.40670 - 2.54421i) q^{61} +(4.43674 - 2.56155i) q^{65} +(3.12311 - 5.40938i) q^{67} +(-3.02045 - 1.69614i) q^{69} +4.87689i q^{71} +(-10.4631 - 6.04090i) q^{73} +(7.14092 - 0.0851890i) q^{75} +(-1.43845 - 2.49146i) q^{79} +(-4.86665 - 7.57071i) q^{81} -1.69614 q^{83} +4.00000 q^{85} +(13.5894 - 8.06352i) q^{87} +(5.75058 + 9.96029i) q^{89} +(-0.152175 - 12.7560i) q^{93} +(16.7743 + 9.68466i) q^{95} +8.68951i q^{97} +(8.00000 - 4.87689i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9} + 8 q^{15} + 16 q^{37} - 4 q^{39} - 64 q^{43} + 24 q^{51} - 56 q^{57} - 16 q^{67} - 56 q^{79} + 64 q^{85} - 56 q^{93} + 128 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 + 8 * q^15 + 16 * q^37 - 4 * q^39 - 64 * q^43 + 24 * q^51 - 56 * q^57 - 16 * q^67 - 56 * q^79 + 64 * q^85 - 56 * q^93 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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