LMFDB - Embedded newform 1764.2.b.l.1567.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1764,2,Mod(1567,1764)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1764, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1764.1567"); 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.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,-4,0,-4,0,0,0,-4,0,0,0,0,0,0,0,-4,0,0,0,-24,0,0,0,0,-12,24, 0,0,-32,0,-16,-4,0,-32,0,0,32,-24,0,32,0,0,0,24,0,24,0,0,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(50)] == traces)

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

Self dual:	no
Analytic conductor:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.15911316233388032.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 35 x^{8} - 56 x^{7} + 84 x^{6} - 112 x^{5} + 140 x^{4} + \cdots + 64 $ x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 588)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.11
Root			$-0.988865 + 1.01101i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.l.1567.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.988865 - 1.01101i) q^{2} +(-0.0442929 - 1.99951i) q^{4} -1.12886i q^{5} +(-2.06533 - 1.93246i) q^{8} +(-1.14129 - 1.11629i) q^{10} +1.35000i q^{11} -5.58489i q^{13} +(-3.99608 + 0.177128i) q^{16} -3.97347i q^{17} -6.14408 q^{19} +(-2.25717 + 0.0500006i) q^{20} +(1.36487 + 1.33497i) q^{22} +6.61394i q^{23} +3.72567 q^{25} +(-5.64640 - 5.52270i) q^{26} -8.55270 q^{29} +2.92221 q^{31} +(-3.77250 + 4.21524i) q^{32} +(-4.01723 - 3.92923i) q^{34} +6.32497 q^{37} +(-6.07567 + 6.21175i) q^{38} +(-2.18149 + 2.33147i) q^{40} +0.149223i q^{41} -10.6557i q^{43} +(2.69934 - 0.0597956i) q^{44} +(6.68678 + 6.54030i) q^{46} -3.59492 q^{47} +(3.68418 - 3.76670i) q^{50} +(-11.1670 + 0.247371i) q^{52} -0.733587 q^{53} +1.52397 q^{55} +(-8.45746 + 8.64689i) q^{58} -14.4054 q^{59} -9.11488i q^{61} +(2.88967 - 2.95439i) q^{62} +(0.531167 + 7.98235i) q^{64} -6.30457 q^{65} +0.234093i q^{67} +(-7.94500 + 0.175997i) q^{68} -8.74104i q^{71} -1.76546i q^{73} +(6.25454 - 6.39463i) q^{74} +(0.272139 + 12.2852i) q^{76} +8.40771i q^{79} +(0.199953 + 4.51102i) q^{80} +(0.150867 + 0.147562i) q^{82} +9.12928 q^{83} -4.48551 q^{85} +(-10.7731 - 10.5371i) q^{86} +(2.60883 - 2.78820i) q^{88} +7.92746i q^{89} +(13.2246 - 0.292951i) q^{92} +(-3.55489 + 3.63451i) q^{94} +6.93583i q^{95} -6.23063i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} - 24 q^{20} - 12 q^{25} + 24 q^{26} - 32 q^{29} - 16 q^{31} - 4 q^{32} - 32 q^{34} + 32 q^{37} - 24 q^{38} + 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} - 32 q^{52}+ \cdots + 24 q^{88}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 - 24 * q^20 - 12 * q^25 + 24 * q^26 - 32 * q^29 - 16 * q^31 - 4 * q^32 - 32 * q^34 + 32 * q^37 - 24 * q^38 + 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 - 32 * q^52 + 32 * q^53 - 16 * q^55 + 16 * q^58 - 16 * q^59 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 32 * q^74 + 32 * q^76 - 16 * q^80 - 32 * q^82 - 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

Character values

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

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.988865	−	1.01101i	0.699233	−	0.714894i
$2$	0.988865	−	1.01101i	0.699233	−	0.714894i
$3$		0			0
$3$		0			0
$4$	−0.0442929	−	1.99951i	−0.0221465	−	0.999755i
$5$		−	1.12886i		−	0.504843i	−0.967617	−	0.252421i	$-0.918773\pi$
$5$		−	1.12886i		−	0.504843i	0.967617	−	0.252421i	$-0.0812269\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.06533	−	1.93246i	−0.730204	−	0.683229i
$9$		0			0
$10$	−1.14129	−	1.11629i	−0.360909	−	0.353003i
$11$			1.35000i			0.407041i	0.979071	+	0.203521i	$0.0652384\pi$
$11$			1.35000i			0.407041i	−0.979071	+	0.203521i	$0.934762\pi$
$12$		0			0
$13$		−	5.58489i		−	1.54897i	−0.632592	−	0.774485i	$-0.718009\pi$
$13$		−	5.58489i		−	1.54897i	0.632592	−	0.774485i	$-0.281991\pi$
$14$		0			0
$15$		0			0
$16$	−3.99608	+	0.177128i	−0.999019	+	0.0442821i
$17$		−	3.97347i		−	0.963709i	−0.876251	−	0.481855i	$-0.839963\pi$
$17$		−	3.97347i		−	0.963709i	0.876251	−	0.481855i	$-0.160037\pi$
$18$		0			0
$19$	−6.14408			−1.40955			−0.704775	−	0.709431i	$-0.748952\pi$
$19$	−6.14408			−1.40955			−0.704775	+	0.709431i	$0.748952\pi$
$20$	−2.25717	+	0.0500006i	−0.504719	+	0.0111805i
$21$		0			0
$22$	1.36487	+	1.33497i	0.290991	+	0.284617i
$23$			6.61394i			1.37910i	0.724237	+	0.689551i	$0.242192\pi$
$23$			6.61394i			1.37910i	−0.724237	+	0.689551i	$0.757808\pi$
$24$		0			0
$25$	3.72567			0.745134
$26$	−5.64640	−	5.52270i	−1.10735	−	1.08309i
$27$		0			0
$28$		0			0
$29$	−8.55270			−1.58820			−0.794098	−	0.607790i	$-0.792056\pi$
$29$	−8.55270			−1.58820			−0.794098	+	0.607790i	$0.792056\pi$
$30$		0			0
$31$	2.92221			0.524845			0.262422	−	0.964953i	$-0.415479\pi$
$31$	2.92221			0.524845			0.262422	+	0.964953i	$0.415479\pi$
$32$	−3.77250	+	4.21524i	−0.666890	+	0.745156i
$33$		0			0
$34$	−4.01723	−	3.92923i	−0.688950	−	0.673857i
$35$		0			0
$36$		0			0
$37$	6.32497			1.03982			0.519910	−	0.854221i	$-0.325966\pi$
$37$	6.32497			1.03982			0.519910	+	0.854221i	$0.325966\pi$
$38$	−6.07567	+	6.21175i	−0.985603	+	1.00768i
$39$		0			0
$40$	−2.18149	+	2.33147i	−0.344923	+	0.368638i
$41$			0.149223i			0.0233048i	0.999932	+	0.0116524i	$0.00370916\pi$
$41$			0.149223i			0.0233048i	−0.999932	+	0.0116524i	$0.996291\pi$
$42$		0			0
$43$		−	10.6557i		−	1.62498i	−0.582974	−	0.812491i	$-0.698111\pi$
$43$		−	10.6557i		−	1.62498i	0.582974	−	0.812491i	$-0.301889\pi$
$44$	2.69934	−	0.0597956i	0.406942	−	0.00901452i
$45$		0			0
$46$	6.68678	+	6.54030i	0.985912	+	0.964314i
$47$	−3.59492			−0.524373			−0.262186	−	0.965017i	$-0.584444\pi$
$47$	−3.59492			−0.524373			−0.262186	+	0.965017i	$0.584444\pi$
$48$		0			0
$49$		0			0
$50$	3.68418	−	3.76670i	0.521022	−	0.532692i
$51$		0			0
$52$	−11.1670	+	0.247371i	−1.54859	+	0.0343042i
$53$	−0.733587			−0.100766			−0.0503830	−	0.998730i	$-0.516044\pi$
$53$	−0.733587			−0.100766			−0.0503830	+	0.998730i	$0.516044\pi$
$54$		0			0
$55$	1.52397			0.205492
$56$		0			0
$57$		0			0
$58$	−8.45746	+	8.64689i	−1.11052	+	1.13539i
$59$	−14.4054			−1.87542			−0.937712	−	0.347415i	$-0.887060\pi$
$59$	−14.4054			−1.87542			−0.937712	+	0.347415i	$0.887060\pi$
$60$		0			0
$61$		−	9.11488i		−	1.16704i	−0.812098	−	0.583520i	$-0.801675\pi$
$61$		−	9.11488i		−	1.16704i	0.812098	−	0.583520i	$-0.198325\pi$
$62$	2.88967	−	2.95439i	0.366989	−	0.375208i
$63$		0			0
$64$	0.531167	+	7.98235i	0.0663959	+	0.997793i
$65$	−6.30457			−0.781986
$66$		0			0
$67$			0.234093i			0.0285990i	0.999898	+	0.0142995i	$0.00455182\pi$
$67$			0.234093i			0.0285990i	−0.999898	+	0.0142995i	$0.995448\pi$
$68$	−7.94500	+	0.175997i	−0.963473	+	0.0213427i
$69$		0			0
$70$		0			0
$71$		−	8.74104i		−	1.03737i	−0.854965	−	0.518685i	$-0.826422\pi$
$71$		−	8.74104i		−	1.03737i	0.854965	−	0.518685i	$-0.173578\pi$
$72$		0			0
$73$		−	1.76546i		−	0.206631i	−0.994649	−	0.103316i	$-0.967055\pi$
$73$		−	1.76546i		−	0.206631i	0.994649	−	0.103316i	$-0.0329452\pi$
$74$	6.25454	−	6.39463i	0.727076	−	0.743360i
$75$		0			0
$76$	0.272139	+	12.2852i	0.0312165	+	1.40920i
$77$		0			0
$78$		0			0
$79$			8.40771i			0.945941i	0.881078	+	0.472971i	$0.156818\pi$
$79$			8.40771i			0.945941i	−0.881078	+	0.472971i	$0.843182\pi$
$80$	0.199953	+	4.51102i	0.0223555	+	0.504348i
$81$		0			0
$82$	0.150867	+	0.147562i	0.0166604	+	0.0162955i
$83$	9.12928			1.00207			0.501035	−	0.865427i	$-0.332953\pi$
$83$	9.12928			1.00207			0.501035	+	0.865427i	$0.332953\pi$
$84$		0			0
$85$	−4.48551			−0.486522
$86$	−10.7731	−	10.5371i	−1.16169	−	1.13624i
$87$		0			0
$88$	2.60883	−	2.78820i	0.278102	−	0.297223i
$89$			7.92746i			0.840309i	0.907453	+	0.420155i	$0.138024\pi$
$89$			7.92746i			0.840309i	−0.907453	+	0.420155i	$0.861976\pi$
$90$		0			0
$91$		0			0
$92$	13.2246	−	0.292951i	1.37876	−	0.0305422i
$93$		0			0
$94$	−3.55489	+	3.63451i	−0.366659	+	0.374871i
$95$			6.93583i			0.711601i
$96$		0			0
$97$		−	6.23063i		−	0.632624i	−0.948655	−	0.316312i	$-0.897555\pi$
$97$		−	6.23063i		−	0.632624i	0.948655	−	0.316312i	$-0.102445\pi$
$98$		0			0
$99$		0			0
$100$	−0.165021	−	7.44951i	−0.0165021	−	0.744951i
$101$		−	0.794961i		−	0.0791016i	−0.999218	−	0.0395508i	$-0.987407\pi$
$101$		−	0.794961i		−	0.0791016i	0.999218	−	0.0395508i	$-0.0125927\pi$
$102$		0			0
$103$	−3.35476			−0.330554			−0.165277	−	0.986247i	$-0.552852\pi$
$103$	−3.35476			−0.330554			−0.165277	+	0.986247i	$0.552852\pi$
$104$	−10.7926	+	11.5346i	−1.05830	+	1.13106i
$105$		0			0
$106$	−0.725418	+	0.741666i	−0.0704589	+	0.0720369i
$107$			12.5510i			1.21335i	0.794950	+	0.606675i	$0.207497\pi$
$107$			12.5510i			1.21335i	−0.794950	+	0.606675i	$0.792503\pi$
$108$		0			0
$109$	−15.2532			−1.46099			−0.730496	−	0.682917i	$-0.760711\pi$
$109$	−15.2532			−1.46099			−0.730496	+	0.682917i	$0.760711\pi$
$110$	1.50700	−	1.54075i	0.143687	−	0.146905i
$111$		0			0
$112$		0			0
$113$	11.7783			1.10801			0.554004	−	0.832514i	$-0.313099\pi$
$113$	11.7783			1.10801			0.554004	+	0.832514i	$0.313099\pi$
$114$		0			0
$115$	7.46623			0.696230
$116$	0.378824	+	17.1012i	0.0351729	+	1.58781i
$117$		0			0
$118$	−14.2450	+	14.5640i	−1.31136	+	1.34073i
$119$		0			0
$120$		0			0
$121$	9.17749			0.834317
$122$	−9.21526	−	9.01338i	−0.834310	−	0.816033i
$123$		0			0
$124$	−0.129433	−	5.84299i	−0.0116234	−	0.524716i
$125$		−	9.85008i		−	0.881018i
$126$		0			0
$127$		−	3.52444i		−	0.312743i	−0.987698	−	0.156372i	$-0.950020\pi$
$127$		−	3.52444i		−	0.312743i	0.987698	−	0.156372i	$-0.0499798\pi$
$128$	8.59551	+	7.35644i	0.759743	+	0.650224i
$129$		0			0
$130$	−6.23437	+	6.37400i	−0.546791	+	0.559037i
$131$	−2.37199			−0.207242			−0.103621	−	0.994617i	$-0.533043\pi$
$131$	−2.37199			−0.207242			−0.103621	+	0.994617i	$0.533043\pi$
$132$		0			0
$133$		0			0
$134$	0.236671	+	0.231486i	0.0204452	+	0.0199973i
$135$		0			0
$136$	−7.67860	+	8.20653i	−0.658434	+	0.703704i
$137$	7.17561			0.613054			0.306527	−	0.951862i	$-0.400833\pi$
$137$	7.17561			0.613054			0.306527	+	0.951862i	$0.400833\pi$
$138$		0			0
$139$	22.5888			1.91595			0.957977	−	0.286845i	$-0.0926064\pi$
$139$	22.5888			1.91595			0.957977	+	0.286845i	$0.0926064\pi$
$140$		0			0
$141$		0			0
$142$	−8.83730	−	8.64371i	−0.741610	−	0.725364i
$143$	7.53962			0.630495
$144$		0			0
$145$			9.65482i			0.801789i
$146$	−1.78490	−	1.74580i	−0.147719	−	0.144483i
$147$		0			0
$148$	−0.280151	−	12.6468i	−0.0230283	−	1.03956i
$149$	11.0506			0.905304			0.452652	−	0.891687i	$-0.350478\pi$
$149$	11.0506			0.905304			0.452652	+	0.891687i	$0.350478\pi$
$150$		0			0
$151$		−	1.53950i		−	0.125283i	−0.998036	−	0.0626413i	$-0.980048\pi$
$151$		−	1.53950i		−	0.125283i	0.998036	−	0.0626413i	$-0.0199524\pi$
$152$	12.6896	+	11.8732i	1.02926	+	0.963045i
$153$		0			0
$154$		0			0
$155$		−	3.29878i		−	0.264964i
$156$		0			0
$157$		−	8.55948i		−	0.683121i	−0.939860	−	0.341560i	$-0.889045\pi$
$157$		−	8.55948i		−	0.683121i	0.939860	−	0.341560i	$-0.110955\pi$
$158$	8.50030	+	8.31409i	0.676248	+	0.661433i
$159$		0			0
$160$	4.75843	+	4.25863i	0.376187	+	0.336675i
$161$		0			0
$162$		0			0
$163$		−	5.65996i		−	0.443323i	−0.975124	−	0.221661i	$-0.928852\pi$
$163$		−	5.65996i		−	0.443323i	0.975124	−	0.221661i	$-0.0711479\pi$
$164$	0.298374	−	0.00660954i	0.0232991	−	0.000516118i
$165$		0			0
$166$	9.02763	−	9.22982i	0.700680	−	0.716373i
$167$	4.84357			0.374807			0.187403	−	0.982283i	$-0.439993\pi$
$167$	4.84357			0.374807			0.187403	+	0.982283i	$0.439993\pi$
$168$		0			0
$169$	−18.1910			−1.39931
$170$	−4.43556	+	4.53490i	−0.340192	+	0.347811i
$171$		0			0
$172$	−21.3062	+	0.471973i	−1.62458	+	0.0359876i
$173$			2.10368i			0.159940i	0.996797	+	0.0799701i	$0.0254825\pi$
$173$			2.10368i			0.159940i	−0.996797	+	0.0799701i	$0.974518\pi$
$174$		0			0
$175$		0			0
$176$	−0.239124	−	5.39472i	−0.0180246	−	0.406642i
$177$		0			0
$178$	8.01476	+	7.83919i	0.600732	+	0.587572i
$179$		−	4.00769i		−	0.299549i	−0.988720	−	0.149774i	$-0.952145\pi$
$179$		−	4.00769i		−	0.299549i	0.988720	−	0.149774i	$-0.0478547\pi$
$180$		0			0
$181$		−	5.89663i		−	0.438293i	−0.975692	−	0.219146i	$-0.929673\pi$
$181$		−	5.89663i		−	0.438293i	0.975692	−	0.219146i	$-0.0703272\pi$
$182$		0			0
$183$		0			0
$184$	12.7812	−	13.6600i	0.942243	−	1.00703i
$185$		−	7.14002i		−	0.524945i
$186$		0			0
$187$	5.36420			0.392269
$188$	0.159229	+	7.18808i	0.0116130	+	0.524244i
$189$		0			0
$190$	7.01221	+	6.85859i	0.508719	+	0.497575i
$191$		−	25.3919i		−	1.83729i	−0.395084	−	0.918645i	$-0.629284\pi$
$191$		−	25.3919i		−	1.83729i	0.395084	−	0.918645i	$-0.370716\pi$
$192$		0			0
$193$	0.0733869			0.00528250			0.00264125	−	0.999997i	$-0.499159\pi$
$193$	0.0733869			0.00528250			0.00264125	+	0.999997i	$0.499159\pi$
$194$	−6.29924	−	6.16125i	−0.452259	−	0.442352i
$195$		0			0
$196$		0			0
$197$	−7.23506			−0.515477			−0.257739	−	0.966215i	$-0.582977\pi$
$197$	−7.23506			−0.515477			−0.257739	+	0.966215i	$0.582977\pi$
$198$		0			0
$199$	−15.3120			−1.08544			−0.542718	−	0.839915i	$-0.682605\pi$
$199$	−15.3120			−1.08544			−0.542718	+	0.839915i	$0.682605\pi$
$200$	−7.69473	−	7.19972i	−0.544100	−	0.509097i
$201$		0			0
$202$	−0.803715	−	0.786109i	−0.0565492	−	0.0553104i
$203$		0			0
$204$		0			0
$205$	0.168453			0.0117653
$206$	−3.31740	+	3.39170i	−0.231134	+	0.236311i
$207$		0			0
$208$	0.989242	+	22.3177i	0.0685916	+	1.54745i
$209$		−	8.29453i		−	0.573745i
$210$		0			0
$211$		−	13.7540i		−	0.946861i	−0.880831	−	0.473431i	$-0.843015\pi$
$211$		−	13.7540i		−	0.946861i	0.880831	−	0.473431i	$-0.156985\pi$
$212$	0.0324927	+	1.46681i	0.00223161	+	0.100741i
$213$		0			0
$214$	12.6892	+	12.4112i	0.867417	+	0.848415i
$215$	−12.0288			−0.820360
$216$		0			0
$217$		0			0
$218$	−15.0833	+	15.4212i	−1.02157	+	1.04445i
$219$		0			0
$220$	−0.0675010	−	3.04719i	−0.00455092	−	0.205441i
$221$	−22.1914			−1.49276
$222$		0			0
$223$	16.4120			1.09903			0.549516	−	0.835483i	$-0.314812\pi$
$223$	16.4120			1.09903			0.549516	+	0.835483i	$0.314812\pi$
$224$		0			0
$225$		0			0
$226$	11.6471	−	11.9080i	0.774756	−	0.792108i
$227$	16.1319			1.07071			0.535356	−	0.844627i	$-0.320178\pi$
$227$	16.1319			1.07071			0.535356	+	0.844627i	$0.320178\pi$
$228$		0			0
$229$			21.6682i			1.43187i	0.698165	+	0.715937i	$0.254000\pi$
$229$			21.6682i			1.43187i	−0.698165	+	0.715937i	$0.746000\pi$
$230$	7.38310	−	7.54846i	0.486827	−	0.497731i
$231$		0			0
$232$	17.6641	+	16.5278i	1.15971	+	1.08510i
$233$	19.0312			1.24678			0.623389	−	0.781912i	$-0.285755\pi$
$233$	19.0312			1.24678			0.623389	+	0.781912i	$0.285755\pi$
$234$		0			0
$235$			4.05817i			0.264726i
$236$	0.638057	+	28.8037i	0.0415340	+	1.87496i
$237$		0			0
$238$		0			0
$239$		−	15.6878i		−	1.01476i	−0.861722	−	0.507381i	$-0.830614\pi$
$239$		−	15.6878i		−	1.01476i	0.861722	−	0.507381i	$-0.169386\pi$
$240$		0			0
$241$		−	11.9011i		−	0.766615i	−0.923621	−	0.383307i	$-0.874785\pi$
$241$		−	11.9011i		−	0.766615i	0.923621	−	0.383307i	$-0.125215\pi$
$242$	9.07530	−	9.27856i	0.583382	−	0.596448i
$243$		0			0
$244$	−18.2253	+	0.403725i	−1.16675	+	0.0258458i
$245$		0			0
$246$		0			0
$247$			34.3140i			2.18335i
$248$	−6.03533	−	5.64707i	−0.383244	−	0.358589i
$249$		0			0
$250$	−9.95856	−	9.74040i	−0.629834	−	0.616037i
$251$	−1.68715			−0.106492			−0.0532459	−	0.998581i	$-0.516957\pi$
$251$	−1.68715			−0.106492			−0.0532459	+	0.998581i	$0.516957\pi$
$252$		0			0
$253$	−8.92885			−0.561352
$254$	−3.56325	−	3.48519i	−0.223578	−	0.218681i
$255$		0			0
$256$	15.9373	−	1.41564i	0.996078	−	0.0884772i
$257$		−	21.3171i		−	1.32972i	−0.746966	−	0.664862i	$-0.768490\pi$
$257$		−	21.3171i		−	1.32972i	0.746966	−	0.664862i	$-0.231510\pi$
$258$		0			0
$259$		0			0
$260$	0.279248	+	12.6061i	0.0173182	+	0.781794i
$261$		0			0
$262$	−2.34558	+	2.39811i	−0.144910	+	0.148156i
$263$		−	11.5846i		−	0.714337i	−0.934040	−	0.357169i	$-0.883742\pi$
$263$		−	11.5846i		−	0.714337i	0.934040	−	0.357169i	$-0.116258\pi$
$264$		0			0
$265$			0.828119i			0.0508709i
$266$		0			0
$267$		0			0
$268$	0.468070	−	0.0103686i	0.0285919	−	0.000633366i
$269$			7.25350i			0.442254i	0.975245	+	0.221127i	$0.0709735\pi$
$269$			7.25350i			0.442254i	−0.975245	+	0.221127i	$0.929027\pi$
$270$		0			0
$271$	29.0144			1.76250			0.881249	−	0.472653i	$-0.156704\pi$
$271$	29.0144			1.76250			0.881249	+	0.472653i	$0.156704\pi$
$272$	0.703814	+	15.8783i	0.0426750	+	0.962764i
$273$		0			0
$274$	7.09571	−	7.25463i	0.428667	−	0.438268i
$275$			5.02967i			0.303300i
$276$		0			0
$277$	−0.345141			−0.0207375			−0.0103688	−	0.999946i	$-0.503301\pi$
$277$	−0.345141			−0.0207375			−0.0103688	+	0.999946i	$0.503301\pi$
$278$	22.3372	−	22.8375i	1.33970	−	1.36970i
$279$		0			0
$280$		0			0
$281$	−6.62734			−0.395354			−0.197677	−	0.980267i	$-0.563340\pi$
$281$	−6.62734			−0.395354			−0.197677	+	0.980267i	$0.563340\pi$
$282$		0			0
$283$	27.7813			1.65143			0.825713	−	0.564090i	$-0.190773\pi$
$283$	27.7813			1.65143			0.825713	+	0.564090i	$0.190773\pi$
$284$	−17.4778	+	0.387166i	−1.03712	+	0.0229741i
$285$		0			0
$286$	7.45567	−	7.62265i	0.440863	−	0.450737i
$287$		0			0
$288$		0			0
$289$	1.21150			0.0712647
$290$	9.76115	+	9.54731i	0.573194	+	0.560638i
$291$		0			0
$292$	−3.53005	+	0.0781973i	−0.206581	+	0.00457615i
$293$		−	7.28491i		−	0.425589i	−0.977097	−	0.212794i	$-0.931744\pi$
$293$		−	7.28491i		−	0.425589i	0.977097	−	0.212794i	$-0.0682565\pi$
$294$		0			0
$295$			16.2617i			0.946794i
$296$	−13.0631	−	12.2228i	−0.759280	−	0.710435i
$297$		0			0
$298$	10.9276	−	11.1723i	0.633018	−	0.647196i
$299$	36.9382			2.13619
$300$		0			0
$301$		0			0
$302$	−1.55645	−	1.52236i	−0.0895638	−	0.0876018i
$303$		0			0
$304$	24.5522	−	1.08829i	1.40817	−	0.0624177i
$305$	−10.2894			−0.589172
$306$		0			0
$307$	−27.1911			−1.55188			−0.775939	−	0.630808i	$-0.782724\pi$
$307$	−27.1911			−1.55188			−0.775939	+	0.630808i	$0.782724\pi$
$308$		0			0
$309$		0			0
$310$	−3.33510	−	3.26204i	−0.189421	−	0.185272i
$311$	20.9218			1.18636			0.593182	−	0.805068i	$-0.297871\pi$
$311$	20.9218			1.18636			0.593182	+	0.805068i	$0.297871\pi$
$312$		0			0
$313$		−	2.61741i		−	0.147945i	−0.997260	−	0.0739724i	$-0.976432\pi$
$313$		−	2.61741i		−	0.147945i	0.997260	−	0.0739724i	$-0.0235677\pi$
$314$	−8.65374	−	8.46417i	−0.488359	−	0.477661i
$315$		0			0
$316$	16.8113	−	0.372402i	0.945709	−	0.0209492i
$317$	12.9486			0.727266			0.363633	−	0.931542i	$-0.381536\pi$
$317$	12.9486			0.727266			0.363633	+	0.931542i	$0.381536\pi$
$318$		0			0
$319$		−	11.5462i		−	0.646461i
$320$	9.01097	−	0.599615i	0.503729	−	0.0335195i
$321$		0			0
$322$		0			0
$323$			24.4134i			1.35840i
$324$		0			0
$325$		−	20.8075i		−	1.15419i
$326$	−5.72229	−	5.59694i	−0.316929	−	0.309986i
$327$		0			0
$328$	0.288369	−	0.308195i	0.0159225	−	0.0170172i
$329$		0			0
$330$		0			0
$331$		−	5.23999i		−	0.288016i	−0.989577	−	0.144008i	$-0.954001\pi$
$331$		−	5.23999i		−	0.288016i	0.989577	−	0.144008i	$-0.0459991\pi$
$332$	−0.404363	−	18.2541i	−0.0221923	−	1.00182i
$333$		0			0
$334$	4.78963	−	4.89691i	0.262077	−	0.267947i
$335$	0.264258			0.0144380
$336$		0			0
$337$	21.6837			1.18119			0.590594	−	0.806969i	$-0.298894\pi$
$337$	21.6837			1.18119			0.590594	+	0.806969i	$0.298894\pi$
$338$	−17.9884	+	18.3913i	−0.978443	+	1.00036i
$339$		0			0
$340$	0.198676	+	8.96881i	0.0107747	+	0.486402i
$341$			3.94500i			0.213633i
$342$		0			0
$343$		0			0
$344$	−20.5918	+	22.0076i	−1.11024	+	1.18657i
$345$		0			0
$346$	2.12685	+	2.08026i	0.114340	+	0.111835i
$347$		−	0.655611i		−	0.0351951i	−0.999845	−	0.0175975i	$-0.994398\pi$
$347$		−	0.655611i		−	0.0351951i	0.999845	−	0.0175975i	$-0.00560176\pi$
$348$		0			0
$349$		−	19.4157i		−	1.03930i	−0.854380	−	0.519649i	$-0.826063\pi$
$349$		−	19.4157i		−	1.03930i	0.854380	−	0.519649i	$-0.173937\pi$
$350$		0			0
$351$		0			0
$352$	−5.69059	−	5.09289i	−0.303309	−	0.271452i
$353$			29.8844i			1.59058i	0.606226	+	0.795292i	$0.292683\pi$
$353$			29.8844i			1.59058i	−0.606226	+	0.795292i	$0.707317\pi$
$354$		0			0
$355$	−9.86743			−0.523709
$356$	15.8510	−	0.351130i	0.840103	−	0.0186099i
$357$		0			0
$358$	−4.05182	−	3.96306i	−0.214145	−	0.209454i
$359$		−	12.5933i		−	0.664650i	−0.943165	−	0.332325i	$-0.892167\pi$
$359$		−	12.5933i		−	0.664650i	0.943165	−	0.332325i	$-0.107833\pi$
$360$		0			0
$361$	18.7498			0.986830
$362$	−5.96156	−	5.83097i	−0.313333	−	0.306469i
$363$		0			0
$364$		0			0
$365$	−1.99296			−0.104316
$366$		0			0
$367$	−5.46893			−0.285476			−0.142738	−	0.989761i	$-0.545591\pi$
$367$	−5.46893			−0.285476			−0.142738	+	0.989761i	$0.545591\pi$
$368$	−1.17152	−	26.4298i	−0.0610695	−	1.37775i
$369$		0			0
$370$	−7.21866	−	7.06052i	−0.375280	−	0.367059i
$371$		0			0
$372$		0			0
$373$	−14.8481			−0.768805			−0.384402	−	0.923166i	$-0.625592\pi$
$373$	−14.8481			−0.768805			−0.384402	+	0.923166i	$0.625592\pi$
$374$	5.30447	−	5.42328i	0.274288	−	0.280431i
$375$		0			0
$376$	7.42469	+	6.94705i	0.382899	+	0.358267i
$377$			47.7659i			2.46007i
$378$		0			0
$379$			30.6135i			1.57251i	0.617901	+	0.786256i	$0.287983\pi$
$379$			30.6135i			1.57251i	−0.617901	+	0.786256i	$0.712017\pi$
$380$	13.8683	−	0.307208i	0.711426	−	0.0157594i
$381$		0			0
$382$	−25.6715	−	25.1091i	−1.31347	−	1.28469i
$383$	−23.4784			−1.19969			−0.599844	−	0.800117i	$-0.704771\pi$
$383$	−23.4784			−1.19969			−0.599844	+	0.800117i	$0.704771\pi$
$384$		0			0
$385$		0			0
$386$	0.0725697	−	0.0741951i	0.00369370	−	0.00377643i
$387$		0			0
$388$	−12.4582	+	0.275973i	−0.632469	+	0.0140104i
$389$	36.1774			1.83427			0.917134	−	0.398579i	$-0.130497\pi$
$389$	36.1774			1.83427			0.917134	+	0.398579i	$0.130497\pi$
$390$		0			0
$391$	26.2803			1.32905
$392$		0			0
$393$		0			0
$394$	−7.15450	+	7.31474i	−0.360439	+	0.368511i
$395$	9.49115			0.477552
$396$		0			0
$397$		−	1.33174i		−	0.0668379i	−0.999441	−	0.0334189i	$-0.989360\pi$
$397$		−	1.33174i		−	0.0668379i	0.999441	−	0.0334189i	$-0.0106396\pi$
$398$	−15.1415	+	15.4806i	−0.758973	+	0.775971i
$399$		0			0
$400$	−14.8881	+	0.659921i	−0.744403	+	0.0329961i
$401$	−26.0596			−1.30135			−0.650677	−	0.759355i	$-0.725515\pi$
$401$	−26.0596			−1.30135			−0.650677	+	0.759355i	$0.725515\pi$
$402$		0			0
$403$		−	16.3202i		−	0.812969i
$404$	−1.58953	+	0.0352111i	−0.0790822	+	0.00175182i
$405$		0			0
$406$		0			0
$407$			8.53873i			0.423249i
$408$		0			0
$409$			13.3209i			0.658675i	0.944212	+	0.329337i	$0.106825\pi$
$409$			13.3209i			0.658675i	−0.944212	+	0.329337i	$0.893175\pi$
$410$	0.166577	−	0.170308i	0.00822665	−	0.00841091i
$411$		0			0
$412$	0.148592	+	6.70787i	0.00732060	+	0.330473i
$413$		0			0
$414$		0			0
$415$		−	10.3057i		−	0.505887i
$416$	23.5417	+	21.0690i	1.15422	+	1.03299i
$417$		0			0
$418$	−8.38588	−	8.20217i	−0.410167	−	0.401181i
$419$	−7.54663			−0.368677			−0.184339	−	0.982863i	$-0.559014\pi$
$419$	−7.54663			−0.368677			−0.184339	+	0.982863i	$0.559014\pi$
$420$		0			0
$421$	2.67060			0.130157			0.0650785	−	0.997880i	$-0.479270\pi$
$421$	2.67060			0.130157			0.0650785	+	0.997880i	$0.479270\pi$
$422$	−13.9054	−	13.6008i	−0.676905	−	0.662076i
$423$		0			0
$424$	1.51510	+	1.41763i	0.0735797	+	0.0688462i
$425$		−	14.8039i		−	0.718092i
$426$		0			0
$427$		0			0
$428$	25.0958	−	0.555920i	1.21305	−	0.0268714i
$429$		0			0
$430$	−11.8949	+	12.1613i	−0.573623	+	0.586471i
$431$		−	11.8862i		−	0.572539i	−0.958149	−	0.286269i	$-0.907585\pi$
$431$		−	11.8862i		−	0.572539i	0.958149	−	0.286269i	$-0.0924152\pi$
$432$		0			0
$433$			20.6667i			0.993177i	0.867986	+	0.496589i	$0.165414\pi$
$433$			20.6667i			0.993177i	−0.867986	+	0.496589i	$0.834586\pi$
$434$		0			0
$435$		0			0
$436$	0.675609	+	30.4989i	0.0323558	+	1.46063i
$437$		−	40.6366i		−	1.94391i
$438$		0			0
$439$	−5.42064			−0.258713			−0.129356	−	0.991598i	$-0.541291\pi$
$439$	−5.42064			−0.258713			−0.129356	+	0.991598i	$0.541291\pi$
$440$	−3.14750	−	2.94501i	−0.150051	−	0.140398i
$441$		0			0
$442$	−21.9443	+	22.4358i	−1.04378	+	1.06716i
$443$			22.7038i			1.07869i	0.842085	+	0.539344i	$0.181328\pi$
$443$			22.7038i			1.07869i	−0.842085	+	0.539344i	$0.818672\pi$
$444$		0			0
$445$	8.94902			0.424224
$446$	16.2293	−	16.5928i	0.768479	−	0.785691i
$447$		0			0
$448$		0			0
$449$	15.6516			0.738645			0.369322	−	0.929301i	$-0.379590\pi$
$449$	15.6516			0.738645			0.369322	+	0.929301i	$0.379590\pi$
$450$		0			0
$451$	−0.201452			−0.00948601
$452$	−0.521695	−	23.5508i	−0.0245385	−	1.10774i
$453$		0			0
$454$	15.9523	−	16.3095i	0.748677	−	0.765445i
$455$		0			0
$456$		0			0
$457$	−17.0266			−0.796469			−0.398235	−	0.917284i	$-0.630377\pi$
$457$	−17.0266			−0.796469			−0.398235	+	0.917284i	$0.630377\pi$
$458$	21.9068	+	21.4269i	1.02364	+	1.00121i
$459$		0			0
$460$	−0.330701	−	14.9288i	−0.0154190	−	0.696059i
$461$		−	38.1090i		−	1.77491i	−0.460891	−	0.887457i	$-0.652470\pi$
$461$		−	38.1090i		−	1.77491i	0.460891	−	0.887457i	$-0.347530\pi$
$462$		0			0
$463$		−	1.38958i		−	0.0645794i	−0.999479	−	0.0322897i	$-0.989720\pi$
$463$		−	1.38958i		−	0.0645794i	0.999479	−	0.0322897i	$-0.0102799\pi$
$464$	34.1772	−	1.51492i	1.58664	−	0.0703286i
$465$		0			0
$466$	18.8193	−	19.2408i	0.871788	−	0.891313i
$467$	−3.49381			−0.161674			−0.0808372	−	0.996727i	$-0.525759\pi$
$467$	−3.49381			−0.161674			−0.0808372	+	0.996727i	$0.525759\pi$
$468$		0			0
$469$		0			0
$470$	4.10286	+	4.01298i	0.189251	+	0.185105i
$471$		0			0
$472$	29.7519	+	27.8379i	1.36944	+	1.28134i
$473$	14.3853			0.661435
$474$		0			0
$475$	−22.8908			−1.05030
$476$		0			0
$477$		0			0
$478$	−15.8606	−	15.5132i	−0.725447	−	0.709555i
$479$	13.7216			0.626955			0.313478	−	0.949596i	$-0.398506\pi$
$479$	13.7216			0.626955			0.313478	+	0.949596i	$0.398506\pi$
$480$		0			0
$481$		−	35.3243i		−	1.61065i
$482$	−12.0321	−	11.7685i	−0.548048	−	0.536042i
$483$		0			0
$484$	−0.406498	−	18.3505i	−0.0184772	−	0.834113i
$485$	−7.03352			−0.319376
$486$		0			0
$487$			3.76034i			0.170397i	0.996364	+	0.0851987i	$0.0271525\pi$
$487$			3.76034i			0.170397i	−0.996364	+	0.0851987i	$0.972847\pi$
$488$	−17.6142	+	18.8252i	−0.797356	+	0.852178i
$489$		0			0
$490$		0			0
$491$			8.60497i			0.388337i	0.980968	+	0.194168i	$0.0622008\pi$
$491$			8.60497i			0.388337i	−0.980968	+	0.194168i	$0.937799\pi$
$492$		0			0
$493$			33.9839i			1.53056i
$494$	34.6919	+	33.9319i	1.56086	+	1.52667i
$495$		0			0
$496$	−11.6774	+	0.517606i	−0.524330	+	0.0232412i
$497$		0			0
$498$		0			0
$499$		−	18.5825i		−	0.831865i	−0.909395	−	0.415933i	$-0.863455\pi$
$499$		−	18.5825i		−	0.831865i	0.909395	−	0.415933i	$-0.136545\pi$
$500$	−19.6953	+	0.436289i	−0.880802	+	0.0195114i
$501$		0			0
$502$	−1.66836	+	1.70573i	−0.0744625	+	0.0761303i
$503$	−33.4544			−1.49166			−0.745828	−	0.666139i	$-0.767946\pi$
$503$	−33.4544			−1.49166			−0.745828	+	0.666139i	$0.767946\pi$
$504$		0			0
$505$	−0.897402			−0.0399338
$506$	−8.82942	+	9.02718i	−0.392516	+	0.401307i
$507$		0			0
$508$	−7.04715	+	0.156108i	−0.312667	+	0.00692616i
$509$			23.9925i			1.06345i	0.846917	+	0.531725i	$0.178456\pi$
$509$			23.9925i			1.06345i	−0.846917	+	0.531725i	$0.821544\pi$
$510$		0			0
$511$		0			0
$512$	14.3286	−	17.5126i	0.633239	−	0.773956i
$513$		0			0
$514$	−21.5519	−	21.0797i	−0.950612	−	0.929787i
$515$			3.78706i			0.166878i
$516$		0			0
$517$		−	4.85315i		−	0.213441i
$518$		0			0
$519$		0			0
$520$	13.0210	+	12.1834i	0.571010	+	0.534276i
$521$			14.0811i			0.616904i	0.951240	+	0.308452i	$0.0998109\pi$
$521$			14.0811i			0.616904i	−0.951240	+	0.308452i	$0.900189\pi$
$522$		0			0
$523$	−35.1452			−1.53679			−0.768396	−	0.639975i	$-0.778945\pi$
$523$	−35.1452			−1.53679			−0.768396	+	0.639975i	$0.778945\pi$
$524$	0.105062	+	4.74282i	0.00458967	+	0.207191i
$525$		0			0
$526$	−11.7122	−	11.4556i	−0.510675	−	0.499488i
$527$		−	11.6113i		−	0.505798i
$528$		0			0
$529$	−20.7443			−0.901924
$530$	0.837239	+	0.818898i	0.0363673	+	0.0355706i
$531$		0			0
$532$		0			0
$533$	0.833397			0.0360984
$534$		0			0
$535$	14.1684			0.612551
$536$	0.452375	−	0.483478i	0.0195396	−	0.0208831i
$537$		0			0
$538$	7.33338	+	7.17273i	0.316164	+	0.309238i
$539$		0			0
$540$		0			0
$541$	12.7152			0.546669			0.273334	−	0.961919i	$-0.411873\pi$
$541$	12.7152			0.546669			0.273334	+	0.961919i	$0.411873\pi$
$542$	28.6913	−	29.3339i	1.23240	−	1.26000i
$543$		0			0
$544$	16.7491	+	14.9899i	0.718114	+	0.642688i
$545$			17.2188i			0.737571i
$546$		0			0
$547$		−	42.0999i		−	1.80006i	−0.435828	−	0.900030i	$-0.643544\pi$
$547$		−	42.0999i		−	1.80006i	0.435828	−	0.900030i	$-0.356456\pi$
$548$	−0.317829	−	14.3477i	−0.0135770	−	0.612903i
$549$		0			0
$550$	5.08506	+	4.97366i	0.216827	+	0.212078i
$551$	52.5485			2.23864
$552$		0			0
$553$		0			0
$554$	−0.341298	+	0.348942i	−0.0145003	+	0.0148251i
$555$		0			0
$556$	−1.00052	−	45.1665i	−0.0424316	−	1.91548i
$557$	−15.8853			−0.673080			−0.336540	−	0.941669i	$-0.609257\pi$
$557$	−15.8853			−0.673080			−0.336540	+	0.941669i	$0.609257\pi$
$558$		0			0
$559$	−59.5110			−2.51705
$560$		0			0
$561$		0			0
$562$	−6.55354	+	6.70032i	−0.276444	+	0.282636i
$563$	−32.9188			−1.38736			−0.693681	−	0.720283i	$-0.744012\pi$
$563$	−32.9188			−1.38736			−0.693681	+	0.720283i	$0.744012\pi$
$564$		0			0
$565$		−	13.2961i		−	0.559370i
$566$	27.4719	−	28.0872i	1.15473	−	1.18059i
$567$		0			0
$568$	−16.8917	+	18.0531i	−0.708762	+	0.757492i
$569$	−34.9841			−1.46661			−0.733304	−	0.679901i	$-0.762023\pi$
$569$	−34.9841			−1.46661			−0.733304	+	0.679901i	$0.762023\pi$
$570$		0			0
$571$			6.50173i			0.272089i	0.990703	+	0.136044i	$0.0434390\pi$
$571$			6.50173i			0.272089i	−0.990703	+	0.136044i	$0.956561\pi$
$572$	−0.333952	−	15.0755i	−0.0139632	−	0.630340i
$573$		0			0
$574$		0			0
$575$			24.6414i			1.02762i
$576$		0			0
$577$			37.2134i			1.54921i	0.632444	+	0.774606i	$0.282052\pi$
$577$			37.2134i			1.54921i	−0.632444	+	0.774606i	$0.717948\pi$
$578$	1.19801	−	1.22484i	0.0498306	−	0.0509467i
$579$		0			0
$580$	19.3049	−	0.427640i	0.801593	−	0.0177568i
$581$		0			0
$582$		0			0
$583$		−	0.990345i		−	0.0410159i
$584$	−3.41168	+	3.64625i	−0.141176	+	0.150883i
$585$		0			0
$586$	−7.36513	−	7.20379i	−0.304251	−	0.297586i
$587$	24.7914			1.02325			0.511625	−	0.859209i	$-0.329044\pi$
$587$	24.7914			1.02325			0.511625	+	0.859209i	$0.329044\pi$
$588$		0			0
$589$	−17.9543			−0.739794
$590$	16.4408	+	16.0806i	0.676857	+	0.662029i
$591$		0			0
$592$	−25.2751	+	1.12033i	−1.03880	+	0.0460453i
$593$			31.0027i			1.27313i	0.771223	+	0.636565i	$0.219645\pi$
$593$			31.0027i			1.27313i	−0.771223	+	0.636565i	$0.780355\pi$
$594$		0			0
$595$		0			0
$596$	−0.489465	−	22.0959i	−0.0200493	−	0.905082i
$597$		0			0
$598$	36.5268	−	37.3449i	1.49369	−	1.52715i
$599$		−	8.22986i		−	0.336263i	−0.985765	−	0.168131i	$-0.946227\pi$
$599$		−	8.22986i		−	0.336263i	0.985765	−	0.168131i	$-0.0537733\pi$
$600$		0			0
$601$			47.6805i			1.94493i	0.233053	+	0.972464i	$0.425128\pi$
$601$			47.6805i			1.94493i	−0.233053	+	0.972464i	$0.574872\pi$
$602$		0			0
$603$		0			0
$604$	−3.07824	+	0.0681889i	−0.125252	+	0.00277457i
$605$		−	10.3601i		−	0.421199i
$606$		0			0
$607$	12.6543			0.513621			0.256810	−	0.966462i	$-0.417328\pi$
$607$	12.6543			0.513621			0.256810	+	0.966462i	$0.417328\pi$
$608$	23.1786	−	25.8988i	0.940015	−	1.05033i
$609$		0			0
$610$	−10.1749	+	10.4028i	−0.411969	+	0.421196i
$611$			20.0772i			0.812238i
$612$		0			0
$613$	0.452915			0.0182930			0.00914652	−	0.999958i	$-0.497089\pi$
$613$	0.452915			0.0182930			0.00914652	+	0.999958i	$0.497089\pi$
$614$	−26.8883	+	27.4905i	−1.08512	+	1.10943i
$615$		0			0
$616$		0			0
$617$	0.575345			0.0231625			0.0115813	−	0.999933i	$-0.496313\pi$
$617$	0.575345			0.0231625			0.0115813	+	0.999933i	$0.496313\pi$
$618$		0			0
$619$	−2.04323			−0.0821243			−0.0410622	−	0.999157i	$-0.513074\pi$
$619$	−2.04323			−0.0821243			−0.0410622	+	0.999157i	$0.513074\pi$
$620$	−6.59593	+	0.146112i	−0.264899	+	0.00586801i
$621$		0			0
$622$	20.6888	−	21.1522i	0.829545	−	0.848125i
$623$		0			0
$624$		0			0
$625$	7.50896			0.300358
$626$	−2.64624	−	2.58827i	−0.105765	−	0.103448i
$627$		0			0
$628$	−17.1148	+	0.379124i	−0.682953	+	0.0151287i
$629$		−	25.1321i		−	1.00208i
$630$		0			0
$631$			38.8983i			1.54852i	0.632870	+	0.774258i	$0.281877\pi$
$631$			38.8983i			1.54852i	−0.632870	+	0.774258i	$0.718123\pi$
$632$	16.2476	−	17.3647i	0.646295	−	0.690730i
$633$		0			0
$634$	12.8044	−	13.0912i	0.508529	−	0.519918i
$635$	−3.97861			−0.157886
$636$		0			0
$637$		0			0
$638$	−11.6733	−	11.4176i	−0.462151	−	0.452027i
$639$		0			0
$640$	8.30442	−	9.70315i	0.328261	−	0.383551i
$641$	2.06073			0.0813938			0.0406969	−	0.999172i	$-0.487042\pi$
$641$	2.06073			0.0813938			0.0406969	+	0.999172i	$0.487042\pi$
$642$		0			0
$643$	2.86029			0.112799			0.0563994	−	0.998408i	$-0.482038\pi$
$643$	2.86029			0.112799			0.0563994	+	0.998408i	$0.482038\pi$
$644$		0			0
$645$		0			0
$646$	24.6822	+	24.1415i	0.971109	+	0.949835i
$647$	−19.4084			−0.763021			−0.381511	−	0.924364i	$-0.624596\pi$
$647$	−19.4084			−0.763021			−0.381511	+	0.924364i	$0.624596\pi$
$648$		0			0
$649$		−	19.4473i		−	0.763375i
$650$	−21.0366	−	20.5758i	−0.825123	−	0.807048i
$651$		0			0
$652$	−11.3171	+	0.250696i	−0.443214	+	0.00981802i
$653$	0.729729			0.0285565			0.0142783	−	0.999898i	$-0.495455\pi$
$653$	0.729729			0.0285565			0.0142783	+	0.999898i	$0.495455\pi$
$654$		0			0
$655$			2.67765i			0.104625i
$656$	−0.0264317	−	0.596308i	−0.00103198	−	0.0232819i
$657$		0			0
$658$		0			0
$659$			19.6921i			0.767097i	0.923521	+	0.383548i	$0.125298\pi$
$659$			19.6921i			0.767097i	−0.923521	+	0.383548i	$0.874702\pi$
$660$		0			0
$661$		−	9.40545i		−	0.365830i	−0.983129	−	0.182915i	$-0.941447\pi$
$661$		−	9.40545i		−	0.365830i	0.983129	−	0.182915i	$-0.0585533\pi$
$662$	−5.29769	−	5.18164i	−0.205901	−	0.201390i
$663$		0			0
$664$	−18.8550	−	17.6420i	−0.731715	−	0.684643i
$665$		0			0
$666$		0			0
$667$		−	56.5671i		−	2.19029i
$668$	−0.214536	−	9.68476i	−0.00830064	−	0.374715i
$669$		0			0
$670$	0.261316	−	0.267169i	0.0100955	−	0.0103216i
$671$	12.3051			0.475034
$672$		0			0
$673$	30.0031			1.15653			0.578266	−	0.815848i	$-0.303729\pi$
$673$	30.0031			1.15653			0.578266	+	0.815848i	$0.303729\pi$
$674$	21.4423	−	21.9225i	0.825925	−	0.844424i
$675$		0			0
$676$	0.805733	+	36.3731i	0.0309897	+	1.39897i
$677$		−	30.8100i		−	1.18413i	−0.805892	−	0.592063i	$-0.798314\pi$
$677$		−	30.8100i		−	1.18413i	0.805892	−	0.592063i	$-0.201686\pi$
$678$		0			0
$679$		0			0
$680$	9.26405	+	8.66808i	0.355260	+	0.332406i
$681$		0			0
$682$	3.98844	+	3.90107i	0.152725	+	0.149380i
$683$		−	41.6279i		−	1.59285i	−0.604739	−	0.796424i	$-0.706722\pi$
$683$		−	41.6279i		−	1.59285i	0.604739	−	0.796424i	$-0.293278\pi$
$684$		0			0
$685$		−	8.10028i		−	0.309496i
$686$		0			0
$687$		0			0
$688$	1.88743	+	42.5811i	0.0719575	+	1.62339i
$689$			4.09700i			0.156083i
$690$		0			0
$691$	8.78828			0.334322			0.167161	−	0.985930i	$-0.446540\pi$
$691$	8.78828			0.334322			0.167161	+	0.985930i	$0.446540\pi$
$692$	4.20634	−	0.0931783i	0.159901	−	0.00354211i
$693$		0			0
$694$	−0.662831	−	0.648311i	−0.0251607	−	0.0246095i
$695$		−	25.4996i		−	0.967256i
$696$		0			0
$697$	0.592936			0.0224590
$698$	−19.6295	−	19.1995i	−0.742987	−	0.726711i
$699$		0			0
$700$		0			0
$701$	0.0621184			0.00234618			0.00117309	−	0.999999i	$-0.499627\pi$
$701$	0.0621184			0.00234618			0.00117309	+	0.999999i	$0.499627\pi$
$702$		0			0
$703$	−38.8612			−1.46568
$704$	−10.7762	+	0.717078i	−0.406143	+	0.0270259i
$705$		0			0
$706$	30.2135	+	29.5516i	1.13710	+	1.11219i
$707$		0			0
$708$		0			0
$709$	33.2035			1.24698			0.623492	−	0.781830i	$-0.285713\pi$
$709$	33.2035			1.24698			0.623492	+	0.781830i	$0.285713\pi$
$710$	−9.75756	+	9.97610i	−0.366195	+	0.374396i
$711$		0			0
$712$	15.3195	−	16.3728i	0.574124	−	0.613597i
$713$			19.3273i			0.723815i
$714$		0			0
$715$		−	8.51120i		−	0.318301i
$716$	−8.01341	+	0.177512i	−0.299475	+	0.00663394i
$717$		0			0
$718$	−12.7320	−	12.4531i	−0.475154	−	0.464745i
$719$	−31.9070			−1.18993			−0.594966	−	0.803751i	$-0.702834\pi$
$719$	−31.9070			−1.18993			−0.594966	+	0.803751i	$0.702834\pi$
$720$		0			0
$721$		0			0
$722$	18.5410	−	18.9562i	0.690024	−	0.705478i
$723$		0			0
$724$	−11.7904	+	0.261179i	−0.438185	+	0.00970663i
$725$	−31.8645			−1.18342
$726$		0			0
$727$	11.8242			0.438535			0.219268	−	0.975665i	$-0.429633\pi$
$727$	11.8242			0.438535			0.219268	+	0.975665i	$0.429633\pi$
$728$		0			0
$729$		0			0
$730$	−1.97077	+	2.01491i	−0.0729414	+	0.0745751i
$731$	−42.3402			−1.56601
$732$		0			0
$733$			11.8182i			0.436515i	0.975891	+	0.218258i	$0.0700373\pi$
$733$			11.8182i			0.436515i	−0.975891	+	0.218258i	$0.929963\pi$
$734$	−5.40803	+	5.52915i	−0.199614	+	0.204085i
$735$		0			0
$736$	−27.8794	−	24.9511i	−1.02765	−	0.919710i
$737$	−0.316026			−0.0116410
$738$		0			0
$739$			26.5948i			0.978305i	0.872198	+	0.489153i	$0.162694\pi$
$739$			26.5948i			0.978305i	−0.872198	+	0.489153i	$0.837306\pi$
$740$	−14.2765	+	0.316253i	−0.524816	+	0.0116257i
$741$		0			0
$742$		0			0
$743$		−	34.9119i		−	1.28079i	−0.768045	−	0.640396i	$-0.778770\pi$
$743$		−	34.9119i		−	1.28079i	0.768045	−	0.640396i	$-0.221230\pi$
$744$		0			0
$745$		−	12.4747i		−	0.457036i
$746$	−14.6828	+	15.0116i	−0.537574	+	0.549614i
$747$		0			0
$748$	−0.237596	−	10.7258i	−0.00868738	−	0.392173i
$749$		0			0
$750$		0			0
$751$			1.72010i			0.0627672i	0.999507	+	0.0313836i	$0.00999135\pi$
$751$			1.72010i			0.0627672i	−0.999507	+	0.0313836i	$0.990009\pi$
$752$	14.3656	−	0.636762i	0.523859	−	0.0232203i
$753$		0			0
$754$	48.2919	+	47.2340i	1.75869	+	1.72016i
$755$	−1.73788			−0.0632480
$756$		0			0
$757$	33.2057			1.20688			0.603440	−	0.797408i	$-0.293796\pi$
$757$	33.2057			1.20688			0.603440	+	0.797408i	$0.293796\pi$
$758$	30.9507	+	30.2727i	1.12418	+	1.09955i
$759$		0			0
$760$	13.4032	−	14.3248i	0.486186	−	0.519614i
$761$			27.1774i			0.985180i	0.870262	+	0.492590i	$0.163950\pi$
$761$			27.1774i			0.985180i	−0.870262	+	0.492590i	$0.836050\pi$
$762$		0			0
$763$		0			0
$764$	−50.7713	+	1.12468i	−1.83684	+	0.0406895i
$765$		0			0
$766$	−23.2169	+	23.7369i	−0.838862	+	0.857650i
$767$			80.4526i			2.90497i
$768$		0			0
$769$			7.13960i			0.257460i	0.991680	+	0.128730i	$0.0410901\pi$
$769$			7.13960i			0.257460i	−0.991680	+	0.128730i	$0.958910\pi$
$770$		0			0
$771$		0			0
$772$	−0.00325052	−	0.146738i	−0.000116989	−	0.00528121i
$773$		−	26.5575i		−	0.955207i	−0.878575	−	0.477604i	$-0.841506\pi$
$773$		−	26.5575i		−	0.955207i	0.878575	−	0.477604i	$-0.158494\pi$
$774$		0			0
$775$	10.8872			0.391079
$776$	−12.0405	+	12.8683i	−0.432227	+	0.461945i
$777$		0			0
$778$	35.7746	−	36.5758i	1.28258	−	1.31131i
$779$		−	0.916841i		−	0.0328492i
$780$		0			0
$781$	11.8004			0.422253
$782$	25.9877	−	26.5698i	0.929318	−	0.950132i
$783$		0			0
$784$		0			0
$785$	−9.66247			−0.344869
$786$		0			0
$787$	−24.4670			−0.872153			−0.436077	−	0.899910i	$-0.643632\pi$
$787$	−24.4670			−0.872153			−0.436077	+	0.899910i	$0.643632\pi$
$788$	0.320462	+	14.4666i	0.0114160	+	0.515351i
$789$		0			0
$790$	9.38546	−	9.59567i	0.333920	−	0.341399i
$791$		0			0
$792$		0			0
$793$	−50.9056			−1.80771
$794$	−1.34640	−	1.31691i	−0.0477820	−	0.0467353i
$795$		0			0
$796$	0.678211	+	30.6164i	0.0240386	+	1.08517i
$797$			26.0084i			0.921265i	0.887591	+	0.460632i	$0.152377\pi$
$797$			26.0084i			0.921265i	−0.887591	+	0.460632i	$0.847623\pi$
$798$		0			0
$799$			14.2843i			0.505343i
$800$	−14.0551	+	15.7046i	−0.496922	+	0.555241i
$801$		0			0
$802$	−25.7694	+	26.3466i	−0.909950	+	0.930330i
$803$	2.38337			0.0841075
$804$		0			0
$805$		0			0
$806$	−16.5000	−	16.1385i	−0.581186	−	0.568454i
$807$		0			0
$808$	−1.53623	+	1.64186i	−0.0540445	+	0.0577603i
$809$	13.1975			0.464001			0.232000	−	0.972716i	$-0.425473\pi$
$809$	13.1975			0.464001			0.232000	+	0.972716i	$0.425473\pi$
$810$		0			0
$811$	−4.87597			−0.171219			−0.0856093	−	0.996329i	$-0.527284\pi$
$811$	−4.87597			−0.171219			−0.0856093	+	0.996329i	$0.527284\pi$
$812$		0			0
$813$		0			0
$814$	8.63277	+	8.44365i	0.302578	+	0.295950i
$815$	−6.38932			−0.223808
$816$		0			0
$817$			65.4696i			2.29049i
$818$	13.4676	+	13.1725i	0.470883	+	0.460567i
$819$		0			0
$820$	−0.00746126	−	0.336823i	−0.000260559	−	0.0117624i
$821$	−7.06581			−0.246599			−0.123299	−	0.992370i	$-0.539348\pi$
$821$	−7.06581			−0.246599			−0.123299	+	0.992370i	$0.539348\pi$
$822$		0			0
$823$			21.9614i			0.765528i	0.923846	+	0.382764i	$0.125028\pi$
$823$			21.9614i			0.765528i	−0.923846	+	0.382764i	$0.874972\pi$
$824$	6.92868	+	6.48295i	0.241372	+	0.225844i
$825$		0			0
$826$		0			0
$827$		−	17.4897i		−	0.608175i	−0.952644	−	0.304088i	$-0.901648\pi$
$827$		−	17.4897i		−	0.608175i	0.952644	−	0.304088i	$-0.0983515\pi$
$828$		0			0
$829$			25.6021i			0.889199i	0.895730	+	0.444599i	$0.146654\pi$
$829$			25.6021i			0.889199i	−0.895730	+	0.444599i	$0.853346\pi$
$830$	−10.4192	−	10.1910i	−0.361656	−	0.353733i
$831$		0			0
$832$	44.5805	−	2.96651i	1.54555	−	0.102845i
$833$		0			0
$834$		0			0
$835$		−	5.46772i		−	0.189218i
$836$	−16.5850	+	0.367389i	−0.573604	+	0.0127064i
$837$		0			0
$838$	−7.46260	+	7.62974i	−0.257791	+	0.263565i
$839$	−9.04513			−0.312273			−0.156136	−	0.987736i	$-0.549904\pi$
$839$	−9.04513			−0.312273			−0.156136	+	0.987736i	$0.549904\pi$
$840$		0			0
$841$	44.1486			1.52237
$842$	2.64086	−	2.70001i	0.0910100	−	0.0930484i
$843$		0			0
$844$	−27.5012	+	0.609203i	−0.946629	+	0.0209696i
$845$			20.5351i			0.706431i
$846$		0			0
$847$		0			0
$848$	2.93147	−	0.129939i	0.100667	−	0.00446212i
$849$		0			0
$850$	−14.9669	−	14.6390i	−0.513360	−	0.502114i
$851$			41.8330i			1.43402i
$852$		0			0
$853$			28.8642i			0.988292i	0.869379	+	0.494146i	$0.164519\pi$
$853$			28.8642i			0.988292i	−0.869379	+	0.494146i	$0.835481\pi$
$854$		0			0
$855$		0			0
$856$	24.2543	−	25.9219i	0.828997	−	0.885994i
$857$			48.3887i			1.65293i	0.562992	+	0.826463i	$0.309650\pi$
$857$			48.3887i			1.65293i	−0.562992	+	0.826463i	$0.690350\pi$
$858$		0			0
$859$	−19.8378			−0.676858			−0.338429	−	0.940992i	$-0.609896\pi$
$859$	−19.8378			−0.676858			−0.338429	+	0.940992i	$0.609896\pi$
$860$	0.532793	+	24.0518i	0.0181681	+	0.820159i
$861$		0			0
$862$	−12.0171	−	11.7539i	−0.409304	−	0.400338i
$863$			38.7992i			1.32074i	0.750940	+	0.660370i	$0.229601\pi$
$863$			38.7992i			1.32074i	−0.750940	+	0.660370i	$0.770399\pi$
$864$		0			0
$865$	2.37477			0.0807446
$866$	20.8943	+	20.4365i	0.710016	+	0.694462i
$867$		0			0
$868$		0			0
$869$	−11.3504			−0.385037
$870$		0			0
$871$	1.30738			0.0442989
$872$	31.5029	+	29.4763i	1.06682	+	0.998192i
$873$		0			0
$874$	−41.0841	−	40.1841i	−1.38969	−	1.35925i
$875$		0			0
$876$		0			0
$877$	−14.9697			−0.505492			−0.252746	−	0.967533i	$-0.581334\pi$
$877$	−14.9697			−0.505492			−0.252746	+	0.967533i	$0.581334\pi$
$878$	−5.36028	+	5.48033i	−0.180901	+	0.184952i
$879$		0			0
$880$	−6.08989	+	0.269938i	−0.205290	+	0.00909960i
$881$			44.9991i			1.51606i	0.652221	+	0.758029i	$0.273837\pi$
$881$			44.9991i			1.51606i	−0.652221	+	0.758029i	$0.726163\pi$
$882$		0			0
$883$			20.0940i			0.676217i	0.941107	+	0.338109i	$0.109787\pi$
$883$			20.0940i			0.676217i	−0.941107	+	0.338109i	$0.890213\pi$
$884$	0.982923	+	44.3720i	0.0330593	+	1.49239i
$885$		0			0
$886$	22.9538	+	22.4510i	0.771148	+	0.754255i
$887$	−15.2147			−0.510859			−0.255430	−	0.966828i	$-0.582217\pi$
$887$	−15.2147			−0.510859			−0.255430	+	0.966828i	$0.582217\pi$
$888$		0			0
$889$		0			0
$890$	8.84937	−	9.04757i	0.296631	−	0.303275i
$891$		0			0
$892$	−0.726937	−	32.8160i	−0.0243396	−	1.09876i
$893$	22.0875			0.739130
$894$		0			0
$895$	−4.52413			−0.151225
$896$		0			0
$897$		0			0
$898$	15.4773	−	15.8240i	0.516485	−	0.528052i
$899$	−24.9928			−0.833556
$900$		0			0
$901$			2.91489i			0.0971090i
$902$	−0.199209	+	0.203671i	−0.00663293	+	0.00678149i
$903$		0			0
$904$	−24.3260	−	22.7611i	−0.809072	−	0.757023i
$905$	−6.65648			−0.221269
$906$		0			0
$907$			14.1218i			0.468906i	0.972127	+	0.234453i	$0.0753298\pi$
$907$			14.1218i			0.468906i	−0.972127	+	0.234453i	$0.924670\pi$
$908$	−0.714529	−	32.2559i	−0.0237125	−	1.07045i
$909$		0			0
$910$		0			0
$911$		−	12.5510i		−	0.415832i	−0.978147	−	0.207916i	$-0.933332\pi$
$911$		−	12.5510i		−	0.415832i	0.978147	−	0.207916i	$-0.0666681\pi$
$912$		0			0
$913$			12.3246i			0.407884i
$914$	−16.8370	+	17.2141i	−0.556918	+	0.569391i
$915$		0			0
$916$	43.3257	−	0.959747i	1.43152	−	0.0317109i
$917$		0			0
$918$		0			0
$919$		−	35.4545i		−	1.16954i	−0.811201	−	0.584768i	$-0.801186\pi$
$919$		−	35.4545i		−	1.16954i	0.811201	−	0.584768i	$-0.198814\pi$
$920$	−15.4202	−	14.4282i	−0.508390	−	0.475685i
$921$		0			0
$922$	−38.5287	−	37.6847i	−1.26887	−	1.24108i
$923$	−48.8178			−1.60686
$924$		0			0
$925$	23.5648			0.774804
$926$	−1.40488	−	1.37411i	−0.0461674	−	0.0451560i
$927$		0			0
$928$	32.2651	−	36.0517i	1.05915	−	1.18345i
$929$		−	55.5048i		−	1.82105i	−0.413451	−	0.910526i	$-0.635677\pi$
$929$		−	55.5048i		−	1.82105i	0.413451	−	0.910526i	$-0.364323\pi$
$930$		0			0
$931$		0			0
$932$	−0.842949	−	38.0531i	−0.0276117	−	1.24647i
$933$		0			0
$934$	−3.45491	+	3.53229i	−0.113048	+	0.115580i
$935$		−	6.05545i		−	0.198034i
$936$		0			0
$937$		−	18.8683i		−	0.616400i	−0.951322	−	0.308200i	$-0.900273\pi$
$937$		−	18.8683i		−	0.616400i	0.951322	−	0.308200i	$-0.0997265\pi$
$938$		0			0
$939$		0			0
$940$	8.11435	−	0.179748i	0.264661	−	0.00586274i
$941$			40.2290i			1.31143i	0.755009	+	0.655715i	$0.227633\pi$
$941$			40.2290i			1.31143i	−0.755009	+	0.655715i	$0.772367\pi$
$942$		0			0
$943$	−0.986956			−0.0321397
$944$	57.5651	−	2.55160i	1.87358	−	0.0830476i
$945$		0			0
$946$	14.2251	−	14.5437i	0.462497	−	0.472856i
$947$		−	49.5808i		−	1.61116i	−0.592488	−	0.805579i	$-0.701854\pi$
$947$		−	49.5808i		−	1.61116i	0.592488	−	0.805579i	$-0.298146\pi$
$948$		0			0
$949$	−9.85989			−0.320066
$950$	−22.6359	+	23.1429i	−0.734406	+	0.750855i
$951$		0			0
$952$		0			0
$953$	35.9273			1.16380			0.581900	−	0.813260i	$-0.302309\pi$
$953$	35.9273			1.16380			0.581900	+	0.813260i	$0.302309\pi$
$954$		0			0
$955$	−28.6639			−0.927543
$956$	−31.3680	+	0.694860i	−1.01451	+	0.0224734i
$957$		0			0
$958$	13.5688	−	13.8727i	0.438388	−	0.448206i
$959$		0			0
$960$		0			0
$961$	−22.4607			−0.724538
$962$	−35.7133	−	34.9309i	−1.15144	−	1.12622i
$963$		0			0
$964$	−23.7963	+	0.527133i	−0.766427	+	0.0169778i
$965$		−	0.0828437i		−	0.00266683i
$966$		0			0
$967$		−	33.5277i		−	1.07818i	−0.842249	−	0.539089i	$-0.818769\pi$
$967$		−	33.5277i		−	1.07818i	0.842249	−	0.539089i	$-0.181231\pi$
$968$	−18.9545	−	17.7352i	−0.609222	−	0.570030i
$969$		0			0
$970$	−6.95520	+	7.11098i	−0.223318	+	0.228320i
$971$	−14.7198			−0.472381			−0.236191	−	0.971707i	$-0.575899\pi$
$971$	−14.7198			−0.472381			−0.236191	+	0.971707i	$0.575899\pi$
$972$		0			0
$973$		0			0
$974$	3.80175	+	3.71847i	0.121816	+	0.119148i
$975$		0			0
$976$	1.61450	+	36.4238i	0.0516790	+	1.16590i
$977$	8.97289			0.287068			0.143534	−	0.989645i	$-0.454153\pi$
$977$	8.97289			0.287068			0.143534	+	0.989645i	$0.454153\pi$
$978$		0			0
$979$	−10.7021			−0.342041
$980$		0			0
$981$		0			0
$982$	8.69973	+	8.50915i	0.277620	+	0.271538i
$983$	−1.86632			−0.0595265			−0.0297633	−	0.999557i	$-0.509475\pi$
$983$	−1.86632			−0.0595265			−0.0297633	+	0.999557i	$0.509475\pi$
$984$		0			0
$985$			8.16739i			0.260235i
$986$	34.3582	+	33.6055i	1.09419	+	1.07022i
$987$		0			0
$988$	68.6112	−	1.51987i	2.18281	−	0.0483535i
$989$	70.4763			2.24102
$990$		0			0
$991$		−	6.49237i		−	0.206237i	−0.994669	−	0.103119i	$-0.967118\pi$
$991$		−	6.49237i		−	0.206237i	0.994669	−	0.103119i	$-0.0328821\pi$
$992$	−11.0240	+	12.3178i	−0.350014	+	0.391091i
$993$		0			0
$994$		0			0
$995$			17.2851i			0.547974i
$996$		0			0
$997$		−	12.3327i		−	0.390582i	−0.980745	−	0.195291i	$-0.937435\pi$
$997$		−	12.3327i		−	0.390582i	0.980745	−	0.195291i	$-0.0625651\pi$
$998$	−18.7871	−	18.3755i	−0.594695	−	0.581667i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.l.1567.11		12
3.2	odd	2		588.2.b.c.391.2	yes	12
4.3	odd	2		1764.2.b.m.1567.12		12
7.6	odd	2		1764.2.b.m.1567.11		12
12.11	even	2		588.2.b.d.391.1	yes	12
21.2	odd	6		588.2.o.f.31.11		24
21.5	even	6		588.2.o.e.31.11		24
21.11	odd	6		588.2.o.f.19.6		24
21.17	even	6		588.2.o.e.19.6		24
21.20	even	2		588.2.b.d.391.2	yes	12
28.27	even	2	inner	1764.2.b.l.1567.12		12
84.11	even	6		588.2.o.e.19.11		24
84.23	even	6		588.2.o.e.31.6		24
84.47	odd	6		588.2.o.f.31.6		24
84.59	odd	6		588.2.o.f.19.11		24
84.83	odd	2		588.2.b.c.391.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.1	✓	12	84.83	odd	2
588.2.b.c.391.2	yes	12	3.2	odd	2
588.2.b.d.391.1	yes	12	12.11	even	2
588.2.b.d.391.2	yes	12	21.20	even	2
588.2.o.e.19.6		24	21.17	even	6
588.2.o.e.19.11		24	84.11	even	6
588.2.o.e.31.6		24	84.23	even	6
588.2.o.e.31.11		24	21.5	even	6
588.2.o.f.19.6		24	21.11	odd	6
588.2.o.f.19.11		24	84.59	odd	6
588.2.o.f.31.6		24	84.47	odd	6
588.2.o.f.31.11		24	21.2	odd	6
1764.2.b.l.1567.11		12	1.1	even	1	trivial
1764.2.b.l.1567.12		12	28.27	even	2	inner
1764.2.b.m.1567.11		12	7.6	odd	2
1764.2.b.m.1567.12		12	4.3	odd	2

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988865 - 1.01101i) q^{2} +(-0.0442929 - 1.99951i) q^{4} -1.12886i q^{5} +(-2.06533 - 1.93246i) q^{8} +(-1.14129 - 1.11629i) q^{10} +1.35000i q^{11} -5.58489i q^{13} +(-3.99608 + 0.177128i) q^{16} -3.97347i q^{17} -6.14408 q^{19} +(-2.25717 + 0.0500006i) q^{20} +(1.36487 + 1.33497i) q^{22} +6.61394i q^{23} +3.72567 q^{25} +(-5.64640 - 5.52270i) q^{26} -8.55270 q^{29} +2.92221 q^{31} +(-3.77250 + 4.21524i) q^{32} +(-4.01723 - 3.92923i) q^{34} +6.32497 q^{37} +(-6.07567 + 6.21175i) q^{38} +(-2.18149 + 2.33147i) q^{40} +0.149223i q^{41} -10.6557i q^{43} +(2.69934 - 0.0597956i) q^{44} +(6.68678 + 6.54030i) q^{46} -3.59492 q^{47} +(3.68418 - 3.76670i) q^{50} +(-11.1670 + 0.247371i) q^{52} -0.733587 q^{53} +1.52397 q^{55} +(-8.45746 + 8.64689i) q^{58} -14.4054 q^{59} -9.11488i q^{61} +(2.88967 - 2.95439i) q^{62} +(0.531167 + 7.98235i) q^{64} -6.30457 q^{65} +0.234093i q^{67} +(-7.94500 + 0.175997i) q^{68} -8.74104i q^{71} -1.76546i q^{73} +(6.25454 - 6.39463i) q^{74} +(0.272139 + 12.2852i) q^{76} +8.40771i q^{79} +(0.199953 + 4.51102i) q^{80} +(0.150867 + 0.147562i) q^{82} +9.12928 q^{83} -4.48551 q^{85} +(-10.7731 - 10.5371i) q^{86} +(2.60883 - 2.78820i) q^{88} +7.92746i q^{89} +(13.2246 - 0.292951i) q^{92} +(-3.55489 + 3.63451i) q^{94} +6.93583i q^{95} -6.23063i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} - 24 q^{20} - 12 q^{25} + 24 q^{26} - 32 q^{29} - 16 q^{31} - 4 q^{32} - 32 q^{34} + 32 q^{37} - 24 q^{38} + 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} - 32 q^{52}+ \cdots + 24 q^{88}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 - 24 * q^20 - 12 * q^25 + 24 * q^26 - 32 * q^29 - 16 * q^31 - 4 * q^32 - 32 * q^34 + 32 * q^37 - 24 * q^38 + 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 - 32 * q^52 + 32 * q^53 - 16 * q^55 + 16 * q^58 - 16 * q^59 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 32 * q^74 + 32 * q^76 - 16 * q^80 - 32 * q^82 - 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

Introduction

L-functions

Modular forms

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Database

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