LMFDB - Embedded newform 1575.2.m.c.1268.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1575,2,Mod(1268,1575)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1575, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1575.1268"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 $ x^12 + 18x^10 + 107x^8 + 240x^6 + 151x^4 + 30*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1268.4
Root			$2.15459i$ of defining polynomial
Character	$\chi$	$=$	1575.1268
Dual form			1575.2.m.c.1457.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0241053 + 0.0241053i) q^{2} -1.99884i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.0963933 - 0.0963933i) q^{8} -0.390676i q^{11} +(2.20280 + 2.20280i) q^{13} -0.0340901 q^{14} -3.99303 q^{16} +(-4.78742 - 4.78742i) q^{17} -5.50477i q^{19} +(0.00941736 - 0.00941736i) q^{22} +(-2.18868 + 2.18868i) q^{23} +0.106198i q^{26} +(1.41339 + 1.41339i) q^{28} -7.17089 q^{29} +5.38951 q^{31} +(-0.289040 - 0.289040i) q^{32} -0.230805i q^{34} +(2.75668 - 2.75668i) q^{37} +(0.132694 - 0.132694i) q^{38} +2.54112i q^{41} +(-6.99884 - 6.99884i) q^{43} -0.780897 q^{44} -0.105518 q^{46} +(-0.537576 - 0.537576i) q^{47} -1.00000i q^{49} +(4.40304 - 4.40304i) q^{52} +(5.19225 - 5.19225i) q^{53} +0.136321i q^{56} +(-0.172857 - 0.172857i) q^{58} -10.3092 q^{59} -8.12574 q^{61} +(0.129916 + 0.129916i) q^{62} +7.97212i q^{64} +(3.76141 - 3.76141i) q^{67} +(-9.56928 + 9.56928i) q^{68} +16.0785i q^{71} +(-7.17580 - 7.17580i) q^{73} +0.132901 q^{74} -11.0031 q^{76} +(0.276249 + 0.276249i) q^{77} -7.35036i q^{79} +(-0.0612544 + 0.0612544i) q^{82} +(-6.29085 + 6.29085i) q^{83} -0.337418i q^{86} +(-0.0376585 - 0.0376585i) q^{88} -9.94088 q^{89} -3.11523 q^{91} +(4.37481 + 4.37481i) q^{92} -0.0259169i q^{94} +(-2.17456 + 2.17456i) q^{97} +(0.0241053 - 0.0241053i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{8} + 4 q^{13} - 4 q^{14} - 20 q^{16} - 8 q^{17} + 8 q^{22} - 8 q^{23} - 32 q^{29} - 48 q^{32} - 4 q^{37} - 24 q^{38} - 40 q^{43} - 64 q^{44} + 16 q^{46} - 24 q^{47} - 36 q^{52} + 40 q^{53}+ \cdots - 12 q^{97}+O(q^{100}) $ 12 * q - 24 * q^8 + 4 * q^13 - 4 * q^14 - 20 * q^16 - 8 * q^17 + 8 * q^22 - 8 * q^23 - 32 * q^29 - 48 * q^32 - 4 * q^37 - 24 * q^38 - 40 * q^43 - 64 * q^44 + 16 * q^46 - 24 * q^47 - 36 * q^52 + 40 * q^53 + 28 * q^58 - 80 * q^59 - 32 * q^61 - 16 * q^62 + 48 * q^67 - 32 * q^68 + 20 * q^73 - 64 * q^74 + 16 * q^76 - 20 * q^82 - 24 * q^83 - 56 * q^89 - 8 * q^92 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.0241053	+	0.0241053i	0.0170450	+	0.0170450i	0.715578	−	0.698533i	$-0.246163\pi$
$2$	0.0241053	+	0.0241053i	0.0170450	+	0.0170450i	−0.698533	+	0.715578i	$0.746163\pi$
$3$		0			0
$3$		0			0
$4$		−	1.99884i		−	0.999419i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	0.0963933	−	0.0963933i	0.0340802	−	0.0340802i
$9$		0			0
$10$		0			0
$11$		−	0.390676i		−	0.117793i	−0.998264	−	0.0588966i	$-0.981242\pi$
$11$		−	0.390676i		−	0.117793i	0.998264	−	0.0588966i	$-0.0187582\pi$
$12$		0			0
$13$	2.20280	+	2.20280i	0.610947	+	0.610947i	0.943193	−	0.332246i	$-0.107806\pi$
$13$	2.20280	+	2.20280i	0.610947	+	0.610947i	−0.332246	+	0.943193i	$0.607806\pi$
$14$	−0.0340901			−0.00911095
$15$		0			0
$16$	−3.99303			−0.998257
$17$	−4.78742	−	4.78742i	−1.16112	−	1.16112i	−0.984231	−	0.176890i	$-0.943396\pi$
$17$	−4.78742	−	4.78742i	−1.16112	−	1.16112i	−0.176890	−	0.984231i	$-0.556604\pi$
$18$		0			0
$19$		−	5.50477i		−	1.26288i	−0.775424	−	0.631440i	$-0.782464\pi$
$19$		−	5.50477i		−	1.26288i	0.775424	−	0.631440i	$-0.217536\pi$
$20$		0			0
$21$		0			0
$22$	0.00941736	−	0.00941736i	0.00200779	−	0.00200779i
$23$	−2.18868	+	2.18868i	−0.456371	+	0.456371i	−0.897462	−	0.441091i	$-0.854592\pi$
$23$	−2.18868	+	2.18868i	−0.456371	+	0.456371i	0.441091	+	0.897462i	$0.354592\pi$
$24$		0			0
$25$		0			0
$26$			0.106198i			0.0208272i
$27$		0			0
$28$	1.41339	+	1.41339i	0.267106	+	0.267106i
$29$	−7.17089			−1.33160			−0.665801	−	0.746130i	$-0.731910\pi$
$29$	−7.17089			−1.33160			−0.665801	+	0.746130i	$0.731910\pi$
$30$		0			0
$31$	5.38951			0.967985			0.483993	−	0.875072i	$-0.339186\pi$
$31$	5.38951			0.967985			0.483993	+	0.875072i	$0.339186\pi$
$32$	−0.289040	−	0.289040i	−0.0510955	−	0.0510955i
$33$		0			0
$34$		−	0.230805i		−	0.0395827i
$35$		0			0
$36$		0			0
$37$	2.75668	−	2.75668i	0.453195	−	0.453195i	−0.443218	−	0.896414i	$-0.646163\pi$
$37$	2.75668	−	2.75668i	0.453195	−	0.453195i	0.896414	+	0.443218i	$0.146163\pi$
$38$	0.132694	−	0.132694i	0.0215258	−	0.0215258i
$39$		0			0
$40$		0			0
$41$			2.54112i			0.396856i	0.980115	+	0.198428i	$0.0635836\pi$
$41$			2.54112i			0.396856i	−0.980115	+	0.198428i	$0.936416\pi$
$42$		0			0
$43$	−6.99884	−	6.99884i	−1.06731	−	1.06731i	−0.997565	−	0.0697481i	$-0.977780\pi$
$43$	−6.99884	−	6.99884i	−1.06731	−	1.06731i	−0.0697481	−	0.997565i	$-0.522220\pi$
$44$	−0.780897			−0.117725
$45$		0			0
$46$	−0.105518			−0.0155577
$47$	−0.537576	−	0.537576i	−0.0784135	−	0.0784135i	0.666812	−	0.745226i	$-0.267658\pi$
$47$	−0.537576	−	0.537576i	−0.0784135	−	0.0784135i	−0.745226	+	0.666812i	$0.767658\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$		0			0
$52$	4.40304	−	4.40304i	0.610592	−	0.610592i
$53$	5.19225	−	5.19225i	0.713210	−	0.713210i	−0.253995	−	0.967205i	$-0.581745\pi$
$53$	5.19225	−	5.19225i	0.713210	−	0.713210i	0.967205	+	0.253995i	$0.0817448\pi$
$54$		0			0
$55$		0			0
$56$			0.136321i			0.0182166i
$57$		0			0
$58$	−0.172857	−	0.172857i	−0.0226972	−	0.0226972i
$59$	−10.3092			−1.34214			−0.671070	−	0.741394i	$-0.734165\pi$
$59$	−10.3092			−1.34214			−0.671070	+	0.741394i	$0.734165\pi$
$60$		0			0
$61$	−8.12574			−1.04039			−0.520197	−	0.854046i	$-0.674142\pi$
$61$	−8.12574			−1.04039			−0.520197	+	0.854046i	$0.674142\pi$
$62$	0.129916	+	0.129916i	0.0164993	+	0.0164993i
$63$		0			0
$64$			7.97212i			0.996515i
$65$		0			0
$66$		0			0
$67$	3.76141	−	3.76141i	0.459529	−	0.459529i	−0.438972	−	0.898501i	$-0.644657\pi$
$67$	3.76141	−	3.76141i	0.459529	−	0.459529i	0.898501	+	0.438972i	$0.144657\pi$
$68$	−9.56928	+	9.56928i	−1.16045	+	1.16045i
$69$		0			0
$70$		0			0
$71$			16.0785i			1.90816i	0.299550	+	0.954081i	$0.403164\pi$
$71$			16.0785i			1.90816i	−0.299550	+	0.954081i	$0.596836\pi$
$72$		0			0
$73$	−7.17580	−	7.17580i	−0.839864	−	0.839864i	0.148977	−	0.988841i	$-0.452402\pi$
$73$	−7.17580	−	7.17580i	−0.839864	−	0.839864i	−0.988841	+	0.148977i	$0.952402\pi$
$74$	0.132901			0.0154495
$75$		0			0
$76$	−11.0031			−1.26215
$77$	0.276249	+	0.276249i	0.0314815	+	0.0314815i
$78$		0			0
$79$		−	7.35036i		−	0.826980i	−0.910509	−	0.413490i	$-0.864310\pi$
$79$		−	7.35036i		−	0.826980i	0.910509	−	0.413490i	$-0.135690\pi$
$80$		0			0
$81$		0			0
$82$	−0.0612544	+	0.0612544i	−0.00676442	+	0.00676442i
$83$	−6.29085	+	6.29085i	−0.690511	+	0.690511i	−0.962344	−	0.271834i	$-0.912370\pi$
$83$	−6.29085	+	6.29085i	−0.690511	+	0.690511i	0.271834	+	0.962344i	$0.412370\pi$
$84$		0			0
$85$		0			0
$86$		−	0.337418i		−	0.0363848i
$87$		0			0
$88$	−0.0376585	−	0.0376585i	−0.00401441	−	0.00401441i
$89$	−9.94088			−1.05373			−0.526865	−	0.849949i	$-0.676633\pi$
$89$	−9.94088			−1.05373			−0.526865	+	0.849949i	$0.676633\pi$
$90$		0			0
$91$	−3.11523			−0.326565
$92$	4.37481	+	4.37481i	0.456106	+	0.456106i
$93$		0			0
$94$		−	0.0259169i		−	0.00267312i
$95$		0			0
$96$		0			0
$97$	−2.17456	+	2.17456i	−0.220793	+	0.220793i	−0.808832	−	0.588039i	$-0.799900\pi$
$97$	−2.17456	+	2.17456i	−0.220793	+	0.220793i	0.588039	+	0.808832i	$0.299900\pi$
$98$	0.0241053	−	0.0241053i	0.00243501	−	0.00243501i
$99$		0			0
$100$		0			0
$101$		−	5.24052i		−	0.521451i	−0.965413	−	0.260725i	$-0.916038\pi$
$101$		−	5.24052i		−	0.521451i	0.965413	−	0.260725i	$-0.0839617\pi$
$102$		0			0
$103$	1.29201	+	1.29201i	0.127306	+	0.127306i	0.767889	−	0.640583i	$-0.221307\pi$
$103$	1.29201	+	1.29201i	0.127306	+	0.127306i	−0.640583	+	0.767889i	$0.721307\pi$
$104$	0.424670			0.0416423
$105$		0			0
$106$	0.250322			0.0243134
$107$	−10.0523	−	10.0523i	−0.971794	−	0.971794i	0.0278187	−	0.999613i	$-0.491144\pi$
$107$	−10.0523	−	10.0523i	−0.971794	−	0.971794i	−0.999613	+	0.0278187i	$0.991144\pi$
$108$		0			0
$109$			13.9522i			1.33638i	0.743991	+	0.668189i	$0.232930\pi$
$109$			13.9522i			1.33638i	−0.743991	+	0.668189i	$0.767070\pi$
$110$		0			0
$111$		0			0
$112$	2.82350	−	2.82350i	0.266795	−	0.266795i
$113$	8.80038	−	8.80038i	0.827870	−	0.827870i	−0.159352	−	0.987222i	$-0.550940\pi$
$113$	8.80038	−	8.80038i	0.827870	−	0.827870i	0.987222	+	0.159352i	$0.0509403\pi$
$114$		0			0
$115$		0			0
$116$			14.3335i			1.33083i
$117$		0			0
$118$	−0.248506	−	0.248506i	−0.0228768	−	0.0228768i
$119$	6.77044			0.620645
$120$		0			0
$121$	10.8474			0.986125
$122$	−0.195874	−	0.195874i	−0.0177336	−	0.0177336i
$123$		0			0
$124$		−	10.7728i		−	0.967423i
$125$		0			0
$126$		0			0
$127$	−4.61675	+	4.61675i	−0.409670	+	0.409670i	−0.881624	−	0.471953i	$-0.843549\pi$
$127$	−4.61675	+	4.61675i	−0.409670	+	0.409670i	0.471953	+	0.881624i	$0.343549\pi$
$128$	−0.770250	+	0.770250i	−0.0680811	+	0.0680811i
$129$		0			0
$130$		0			0
$131$		−	3.44081i		−	0.300625i	−0.988639	−	0.150313i	$-0.951972\pi$
$131$		−	3.44081i		−	0.300625i	0.988639	−	0.150313i	$-0.0480280\pi$
$132$		0			0
$133$	3.89246	+	3.89246i	0.337519	+	0.337519i
$134$	0.181340			0.0156654
$135$		0			0
$136$	−0.922951			−0.0791424
$137$	−1.07863	−	1.07863i	−0.0921540	−	0.0921540i	0.659527	−	0.751681i	$-0.270757\pi$
$137$	−1.07863	−	1.07863i	−0.0921540	−	0.0921540i	−0.751681	+	0.659527i	$0.770757\pi$
$138$		0			0
$139$		−	21.5355i		−	1.82662i	−0.407268	−	0.913309i	$-0.633519\pi$
$139$		−	21.5355i		−	1.82662i	0.407268	−	0.913309i	$-0.366481\pi$
$140$		0			0
$141$		0			0
$142$	−0.387576	+	0.387576i	−0.0325247	+	0.0325247i
$143$	0.860580	−	0.860580i	0.0719653	−	0.0719653i
$144$		0			0
$145$		0			0
$146$		−	0.345950i		−	0.0286310i
$147$		0			0
$148$	−5.51015	−	5.51015i	−0.452932	−	0.452932i
$149$	6.48256			0.531072			0.265536	−	0.964101i	$-0.414451\pi$
$149$	6.48256			0.531072			0.265536	+	0.964101i	$0.414451\pi$
$150$		0			0
$151$	−1.76882			−0.143945			−0.0719724	−	0.997407i	$-0.522929\pi$
$151$	−1.76882			−0.143945			−0.0719724	+	0.997407i	$0.522929\pi$
$152$	−0.530623	−	0.530623i	−0.0430392	−	0.0430392i
$153$		0			0
$154$			0.0133182i			0.00107321i
$155$		0			0
$156$		0			0
$157$	7.49249	−	7.49249i	0.597966	−	0.597966i	−0.341805	−	0.939771i	$-0.611038\pi$
$157$	7.49249	−	7.49249i	0.597966	−	0.597966i	0.939771	+	0.341805i	$0.111038\pi$
$158$	0.177183	−	0.177183i	0.0140959	−	0.0140959i
$159$		0			0
$160$		0			0
$161$		−	3.09526i		−	0.243941i
$162$		0			0
$163$	13.9311	+	13.9311i	1.09117	+	1.09117i	0.995404	+	0.0957639i	$0.0305294\pi$
$163$	13.9311	+	13.9311i	1.09117	+	1.09117i	0.0957639	+	0.995404i	$0.469471\pi$
$164$	5.07928			0.396625
$165$		0			0
$166$	−0.303286			−0.0235396
$167$	0.477182	+	0.477182i	0.0369254	+	0.0369254i	0.725328	−	0.688403i	$-0.241688\pi$
$167$	0.477182	+	0.477182i	0.0369254	+	0.0369254i	−0.688403	+	0.725328i	$0.741688\pi$
$168$		0			0
$169$		−	3.29535i		−	0.253488i
$170$		0			0
$171$		0			0
$172$	−13.9895	+	13.9895i	−1.06669	+	1.06669i
$173$	−14.6395	+	14.6395i	−1.11302	+	1.11302i	−0.120278	+	0.992740i	$0.538379\pi$
$173$	−14.6395	+	14.6395i	−1.11302	+	1.11302i	−0.992740	+	0.120278i	$0.961621\pi$
$174$		0			0
$175$		0			0
$176$			1.55998i			0.117588i
$177$		0			0
$178$	−0.239628	−	0.239628i	−0.0179609	−	0.0179609i
$179$	−3.04789			−0.227810			−0.113905	−	0.993492i	$-0.536336\pi$
$179$	−3.04789			−0.227810			−0.113905	+	0.993492i	$0.536336\pi$
$180$		0			0
$181$	4.12967			0.306956			0.153478	−	0.988152i	$-0.450953\pi$
$181$	4.12967			0.306956			0.153478	+	0.988152i	$0.450953\pi$
$182$	−0.0750936	−	0.0750936i	−0.00556631	−	0.00556631i
$183$		0			0
$184$			0.421948i			0.0311064i
$185$		0			0
$186$		0			0
$187$	−1.87033	+	1.87033i	−0.136772	+	0.136772i
$188$	−1.07453	+	1.07453i	−0.0783679	+	0.0783679i
$189$		0			0
$190$		0			0
$191$		−	21.4943i		−	1.55527i	−0.628714	−	0.777637i	$-0.716418\pi$
$191$		−	21.4943i		−	1.55527i	0.628714	−	0.777637i	$-0.283582\pi$
$192$		0			0
$193$	9.04475	+	9.04475i	0.651055	+	0.651055i	0.953247	−	0.302192i	$-0.0977183\pi$
$193$	9.04475	+	9.04475i	0.651055	+	0.651055i	−0.302192	+	0.953247i	$0.597718\pi$
$194$	−0.104837			−0.00752685
$195$		0			0
$196$	−1.99884			−0.142774
$197$	8.80038	+	8.80038i	0.627001	+	0.627001i	0.947312	−	0.320311i	$-0.103787\pi$
$197$	8.80038	+	8.80038i	0.627001	+	0.627001i	−0.320311	+	0.947312i	$0.603787\pi$
$198$		0			0
$199$			0.816553i			0.0578839i	0.999581	+	0.0289419i	$0.00921379\pi$
$199$			0.816553i			0.0578839i	−0.999581	+	0.0289419i	$0.990786\pi$
$200$		0			0
$201$		0			0
$202$	0.126324	−	0.126324i	0.00888815	−	0.00888815i
$203$	5.07059	−	5.07059i	0.355885	−	0.355885i
$204$		0			0
$205$		0			0
$206$			0.0622888i			0.00433987i
$207$		0			0
$208$	−8.79584	−	8.79584i	−0.609882	−	0.609882i
$209$	−2.15058			−0.148759
$210$		0			0
$211$	5.93663			0.408695			0.204347	−	0.978898i	$-0.434493\pi$
$211$	5.93663			0.408695			0.204347	+	0.978898i	$0.434493\pi$
$212$	−10.3785	−	10.3785i	−0.712796	−	0.712796i
$213$		0			0
$214$		−	0.484629i		−	0.0331285i
$215$		0			0
$216$		0			0
$217$	−3.81096	+	3.81096i	−0.258705	+	0.258705i
$218$	−0.336322	+	0.336322i	−0.0227786	+	0.0227786i
$219$		0			0
$220$		0			0
$221$		−	21.0915i		−	1.41877i
$222$		0			0
$223$	2.17086	+	2.17086i	0.145372	+	0.145372i	0.776047	−	0.630675i	$-0.217222\pi$
$223$	2.17086	+	2.17086i	0.145372	+	0.145372i	−0.630675	+	0.776047i	$0.717222\pi$
$224$	0.408764			0.0273117
$225$		0			0
$226$	0.424272			0.0282222
$227$	−17.8822	−	17.8822i	−1.18688	−	1.18688i	−0.977924	−	0.208960i	$-0.932992\pi$
$227$	−17.8822	−	17.8822i	−1.18688	−	1.18688i	−0.208960	−	0.977924i	$-0.567008\pi$
$228$		0			0
$229$		−	2.42623i		−	0.160330i	−0.996782	−	0.0801649i	$-0.974455\pi$
$229$		−	2.42623i		−	0.160330i	0.996782	−	0.0801649i	$-0.0255447\pi$
$230$		0			0
$231$		0			0
$232$	−0.691226	+	0.691226i	−0.0453812	+	0.0453812i
$233$	16.9725	−	16.9725i	1.11191	−	1.11191i	0.119014	−	0.992893i	$-0.462027\pi$
$233$	16.9725	−	16.9725i	1.11191	−	1.11191i	0.992893	−	0.119014i	$-0.0379734\pi$
$234$		0			0
$235$		0			0
$236$			20.6064i			1.34136i
$237$		0			0
$238$	0.163204	+	0.163204i	0.0105789	+	0.0105789i
$239$	−8.48710			−0.548985			−0.274492	−	0.961589i	$-0.588510\pi$
$239$	−8.48710			−0.548985			−0.274492	+	0.961589i	$0.588510\pi$
$240$		0			0
$241$	12.5268			0.806924			0.403462	−	0.914996i	$-0.367807\pi$
$241$	12.5268			0.806924			0.403462	+	0.914996i	$0.367807\pi$
$242$	0.261479	+	0.261479i	0.0168085	+	0.0168085i
$243$		0			0
$244$			16.2420i			1.03979i
$245$		0			0
$246$		0			0
$247$	12.1259	−	12.1259i	0.771553	−	0.771553i
$248$	0.519513	−	0.519513i	0.0329891	−	0.0329891i
$249$		0			0
$250$		0			0
$251$		−	6.60853i		−	0.417127i	−0.978009	−	0.208563i	$-0.933121\pi$
$251$		−	6.60853i		−	0.417127i	0.978009	−	0.208563i	$-0.0668788\pi$
$252$		0			0
$253$	0.855063	+	0.855063i	0.0537574	+	0.0537574i
$254$	−0.222576			−0.0139657
$255$		0			0
$256$	15.9071			0.994194
$257$	20.9703	+	20.9703i	1.30809	+	1.30809i	0.922793	+	0.385296i	$0.125901\pi$
$257$	20.9703	+	20.9703i	1.30809	+	1.30809i	0.385296	+	0.922793i	$0.374099\pi$
$258$		0			0
$259$			3.89853i			0.242243i
$260$		0			0
$261$		0			0
$262$	0.0829419	−	0.0829419i	0.00512417	−	0.00512417i
$263$	16.8546	−	16.8546i	1.03930	−	1.03930i	0.0401013	−	0.999196i	$-0.487232\pi$
$263$	16.8546	−	16.8546i	1.03930	−	1.03930i	0.999196	−	0.0401013i	$-0.0127681\pi$
$264$		0			0
$265$		0			0
$266$			0.187658i			0.0115060i
$267$		0			0
$268$	−7.51845	−	7.51845i	−0.459262	−	0.459262i
$269$	15.6271			0.952798			0.476399	−	0.879229i	$-0.341942\pi$
$269$	15.6271			0.952798			0.476399	+	0.879229i	$0.341942\pi$
$270$		0			0
$271$	−5.42718			−0.329678			−0.164839	−	0.986320i	$-0.552710\pi$
$271$	−5.42718			−0.329678			−0.164839	+	0.986320i	$0.552710\pi$
$272$	19.1163	+	19.1163i	1.15910	+	1.15910i
$273$		0			0
$274$		−	0.0520017i		−	0.00314154i
$275$		0			0
$276$		0			0
$277$	19.7465	−	19.7465i	1.18645	−	1.18645i	0.208411	−	0.978041i	$-0.433171\pi$
$277$	19.7465	−	19.7465i	1.18645	−	1.18645i	0.978041	−	0.208411i	$-0.0668292\pi$
$278$	0.519120	−	0.519120i	0.0311348	−	0.0311348i
$279$		0			0
$280$		0			0
$281$		−	14.3252i		−	0.854572i	−0.904117	−	0.427286i	$-0.859470\pi$
$281$		−	14.3252i		−	0.854572i	0.904117	−	0.427286i	$-0.140530\pi$
$282$		0			0
$283$	11.4260	+	11.4260i	0.679208	+	0.679208i	0.959821	−	0.280613i	$-0.0905377\pi$
$283$	11.4260	+	11.4260i	0.679208	+	0.679208i	−0.280613	+	0.959821i	$0.590538\pi$
$284$	32.1382			1.90705
$285$		0			0
$286$	0.0414891			0.00245330
$287$	−1.79684	−	1.79684i	−0.106064	−	0.106064i
$288$		0			0
$289$			28.8388i			1.69640i
$290$		0			0
$291$		0			0
$292$	−14.3433	+	14.3433i	−0.839376	+	0.839376i
$293$	6.46919	−	6.46919i	0.377934	−	0.377934i	−0.492422	−	0.870356i	$-0.663888\pi$
$293$	6.46919	−	6.46919i	0.377934	−	0.377934i	0.870356	+	0.492422i	$0.163888\pi$
$294$		0			0
$295$		0			0
$296$		−	0.531451i		−	0.0308899i
$297$		0			0
$298$	0.156264	+	0.156264i	0.00905214	+	0.00905214i
$299$	−9.64244			−0.557637
$300$		0			0
$301$	9.89785			0.570503
$302$	−0.0426381	−	0.0426381i	−0.00245354	−	0.00245354i
$303$		0			0
$304$			21.9807i			1.26068i
$305$		0			0
$306$		0			0
$307$	−8.46817	+	8.46817i	−0.483304	+	0.483304i	−0.906185	−	0.422881i	$-0.861019\pi$
$307$	−8.46817	+	8.46817i	−0.483304	+	0.483304i	0.422881	+	0.906185i	$0.361019\pi$
$308$	0.552178	−	0.552178i	0.0314632	−	0.0314632i
$309$		0			0
$310$		0			0
$311$		−	10.3241i		−	0.585425i	−0.956200	−	0.292713i	$-0.905442\pi$
$311$		−	10.3241i		−	0.585425i	0.956200	−	0.292713i	$-0.0945579\pi$
$312$		0			0
$313$	−18.2107	−	18.2107i	−1.02933	−	1.02933i	−0.999557	−	0.0297710i	$-0.990522\pi$
$313$	−18.2107	−	18.2107i	−1.02933	−	1.02933i	−0.0297710	−	0.999557i	$-0.509478\pi$
$314$	0.361218			0.0203847
$315$		0			0
$316$	−14.6922			−0.826500
$317$	24.6528	+	24.6528i	1.38464	+	1.38464i	0.836172	+	0.548467i	$0.184788\pi$
$317$	24.6528	+	24.6528i	1.38464	+	1.38464i	0.548467	+	0.836172i	$0.315212\pi$
$318$		0			0
$319$			2.80149i			0.156853i
$320$		0			0
$321$		0			0
$322$	0.0746122	−	0.0746122i	0.00415798	−	0.00415798i
$323$	−26.3537	+	26.3537i	−1.46636	+	1.46636i
$324$		0			0
$325$		0			0
$326$			0.671627i			0.0371980i
$327$		0			0
$328$	0.244947	+	0.244947i	0.0135249	+	0.0135249i
$329$	0.760247			0.0419138
$330$		0			0
$331$	−13.0815			−0.719025			−0.359513	−	0.933140i	$-0.617057\pi$
$331$	−13.0815			−0.719025			−0.359513	+	0.933140i	$0.617057\pi$
$332$	12.5744	+	12.5744i	0.690109	+	0.690109i
$333$		0			0
$334$			0.0230052i			0.00125879i
$335$		0			0
$336$		0			0
$337$	−6.38566	+	6.38566i	−0.347849	+	0.347849i	−0.859308	−	0.511459i	$-0.829105\pi$
$337$	−6.38566	+	6.38566i	−0.347849	+	0.347849i	0.511459	+	0.859308i	$0.329105\pi$
$338$	0.0794355	−	0.0794355i	0.00432072	−	0.00432072i
$339$		0			0
$340$		0			0
$341$		−	2.10555i		−	0.114022i
$342$		0			0
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	−1.34928			−0.0727484
$345$		0			0
$346$	−0.705778			−0.0379429
$347$	−1.89442	−	1.89442i	−0.101698	−	0.101698i	0.654427	−	0.756125i	$-0.272910\pi$
$347$	−1.89442	−	1.89442i	−0.101698	−	0.101698i	−0.756125	+	0.654427i	$0.772910\pi$
$348$		0			0
$349$			27.5744i			1.47602i	0.674789	+	0.738011i	$0.264235\pi$
$349$			27.5744i			1.47602i	−0.674789	+	0.738011i	$0.735765\pi$
$350$		0			0
$351$		0			0
$352$	−0.112921	+	0.112921i	−0.00601870	+	0.00601870i
$353$	10.9194	−	10.9194i	0.581181	−	0.581181i	−0.354047	−	0.935228i	$-0.615195\pi$
$353$	10.9194	−	10.9194i	0.581181	−	0.581181i	0.935228	+	0.354047i	$0.115195\pi$
$354$		0			0
$355$		0			0
$356$			19.8702i			1.05312i
$357$		0			0
$358$	−0.0734704	−	0.0734704i	−0.00388303	−	0.00388303i
$359$	17.0586			0.900318			0.450159	−	0.892948i	$-0.351367\pi$
$359$	17.0586			0.900318			0.450159	+	0.892948i	$0.351367\pi$
$360$		0			0
$361$	−11.3025			−0.594868
$362$	0.0995470	+	0.0995470i	0.00523208	+	0.00523208i
$363$		0			0
$364$			6.22684i			0.326375i
$365$		0			0
$366$		0			0
$367$	−15.2807	+	15.2807i	−0.797645	+	0.797645i	−0.982724	−	0.185079i	$-0.940746\pi$
$367$	−15.2807	+	15.2807i	−0.797645	+	0.797645i	0.185079	+	0.982724i	$0.440746\pi$
$368$	8.73946	−	8.73946i	0.455576	−	0.455576i
$369$		0			0
$370$		0			0
$371$			7.34295i			0.381227i
$372$		0			0
$373$	4.83636	+	4.83636i	0.250417	+	0.250417i	0.821142	−	0.570724i	$-0.193338\pi$
$373$	4.83636	+	4.83636i	0.250417	+	0.250417i	−0.570724	+	0.821142i	$0.693338\pi$
$374$	−0.0901698			−0.00466257
$375$		0			0
$376$	−0.103637			−0.00534469
$377$	−15.7960	−	15.7960i	−0.813537	−	0.813537i
$378$		0			0
$379$		−	15.5588i		−	0.799203i	−0.916689	−	0.399602i	$-0.869148\pi$
$379$		−	15.5588i		−	0.799203i	0.916689	−	0.399602i	$-0.130852\pi$
$380$		0			0
$381$		0			0
$382$	0.518127	−	0.518127i	0.0265097	−	0.0265097i
$383$	−10.6615	+	10.6615i	−0.544777	+	0.544777i	−0.924926	−	0.380148i	$-0.875873\pi$
$383$	−10.6615	+	10.6615i	−0.544777	+	0.544777i	0.380148	+	0.924926i	$0.375873\pi$
$384$		0			0
$385$		0			0
$386$			0.436053i			0.0221945i
$387$		0			0
$388$	4.34659	+	4.34659i	0.220665	+	0.220665i
$389$	22.6658			1.14920			0.574602	−	0.818433i	$-0.305157\pi$
$389$	22.6658			1.14920			0.574602	+	0.818433i	$0.305157\pi$
$390$		0			0
$391$	20.9563			1.05980
$392$	−0.0963933	−	0.0963933i	−0.00486860	−	0.00486860i
$393$		0			0
$394$			0.424272i			0.0213745i
$395$		0			0
$396$		0			0
$397$	−8.59588	+	8.59588i	−0.431415	+	0.431415i	−0.889109	−	0.457695i	$-0.848675\pi$
$397$	−8.59588	+	8.59588i	−0.431415	+	0.431415i	0.457695	+	0.889109i	$0.348675\pi$
$398$	−0.0196833	+	0.0196833i	−0.000986633	+	0.000986633i
$399$		0			0
$400$		0			0
$401$			17.9764i			0.897697i	0.893608	+	0.448848i	$0.148166\pi$
$401$			17.9764i			0.897697i	−0.893608	+	0.448848i	$0.851834\pi$
$402$		0			0
$403$	11.8720	+	11.8720i	0.591387	+	0.591387i
$404$	−10.4749			−0.521148
$405$		0			0
$406$	0.244456			0.0121322
$407$	−1.07697	−	1.07697i	−0.0533833	−	0.0533833i
$408$		0			0
$409$		−	19.3321i		−	0.955908i	−0.878385	−	0.477954i	$-0.841378\pi$
$409$		−	19.3321i		−	0.955908i	0.878385	−	0.477954i	$-0.158622\pi$
$410$		0			0
$411$		0			0
$412$	2.58253	−	2.58253i	0.127232	−	0.127232i
$413$	7.28969	−	7.28969i	0.358702	−	0.358702i
$414$		0			0
$415$		0			0
$416$		−	1.27339i		−	0.0624332i
$417$		0			0
$418$	−0.0518404	−	0.0518404i	−0.00253560	−	0.00253560i
$419$	−0.694391			−0.0339232			−0.0169616	−	0.999856i	$-0.505399\pi$
$419$	−0.694391			−0.0339232			−0.0169616	+	0.999856i	$0.505399\pi$
$420$		0			0
$421$	−13.9451			−0.679641			−0.339821	−	0.940490i	$-0.610366\pi$
$421$	−13.9451			−0.679641			−0.339821	+	0.940490i	$0.610366\pi$
$422$	0.143104	+	0.143104i	0.00696621	+	0.00696621i
$423$		0			0
$424$		−	1.00100i		−	0.0486126i
$425$		0			0
$426$		0			0
$427$	5.74577	−	5.74577i	0.278057	−	0.278057i
$428$	−20.0930	+	20.0930i	−0.971230	+	0.971230i
$429$		0			0
$430$		0			0
$431$		−	31.4909i		−	1.51686i	−0.651754	−	0.758431i	$-0.725966\pi$
$431$		−	31.4909i		−	1.51686i	0.651754	−	0.758431i	$-0.274034\pi$
$432$		0			0
$433$	−21.7296	−	21.7296i	−1.04426	−	1.04426i	−0.998974	−	0.0452816i	$-0.985581\pi$
$433$	−21.7296	−	21.7296i	−1.04426	−	1.04426i	−0.0452816	−	0.998974i	$-0.514419\pi$
$434$	−0.183729			−0.00881927
$435$		0			0
$436$	27.8882			1.33560
$437$	12.0482	+	12.0482i	0.576342	+	0.576342i
$438$		0			0
$439$		−	5.11682i		−	0.244212i	−0.992517	−	0.122106i	$-0.961035\pi$
$439$		−	5.11682i		−	0.244212i	0.992517	−	0.122106i	$-0.0389648\pi$
$440$		0			0
$441$		0			0
$442$	0.508417	−	0.508417i	0.0241829	−	0.0241829i
$443$	16.0066	−	16.0066i	0.760498	−	0.760498i	−0.215914	−	0.976412i	$-0.569273\pi$
$443$	16.0066	−	16.0066i	0.760498	−	0.760498i	0.976412	+	0.215914i	$0.0692731\pi$
$444$		0			0
$445$		0			0
$446$			0.104659i			0.00495574i
$447$		0			0
$448$	−5.63714	−	5.63714i	−0.266330	−	0.266330i
$449$	28.5938			1.34943			0.674713	−	0.738080i	$-0.264267\pi$
$449$	28.5938			1.34943			0.674713	+	0.738080i	$0.264267\pi$
$450$		0			0
$451$	0.992752			0.0467469
$452$	−17.5905	−	17.5905i	−0.827389	−	0.827389i
$453$		0			0
$454$		−	0.862113i		−	0.0404610i
$455$		0			0
$456$		0			0
$457$	−20.1448	+	20.1448i	−0.942336	+	0.942336i	−0.998426	−	0.0560895i	$-0.982137\pi$
$457$	−20.1448	+	20.1448i	−0.942336	+	0.942336i	0.0560895	+	0.998426i	$0.482137\pi$
$458$	0.0584851	−	0.0584851i	0.00273283	−	0.00273283i
$459$		0			0
$460$		0			0
$461$		−	8.52903i		−	0.397236i	−0.980077	−	0.198618i	$-0.936355\pi$
$461$		−	8.52903i		−	0.397236i	0.980077	−	0.198618i	$-0.0636454\pi$
$462$		0			0
$463$	23.3379	+	23.3379i	1.08461	+	1.08461i	0.996073	+	0.0885330i	$0.0282179\pi$
$463$	23.3379	+	23.3379i	1.08461	+	1.08461i	0.0885330	+	0.996073i	$0.471782\pi$
$464$	28.6336			1.32928
$465$		0			0
$466$	0.818256			0.0379050
$467$	26.1758	+	26.1758i	1.21127	+	1.21127i	0.970609	+	0.240660i	$0.0773640\pi$
$467$	26.1758	+	26.1758i	1.21127	+	1.21127i	0.240660	+	0.970609i	$0.422636\pi$
$468$		0			0
$469$			5.31944i			0.245629i
$470$		0			0
$471$		0			0
$472$	−0.993735	+	0.993735i	−0.0457404	+	0.0457404i
$473$	−2.73428	+	2.73428i	−0.125722	+	0.125722i
$474$		0			0
$475$		0			0
$476$		−	13.5330i		−	0.620285i
$477$		0			0
$478$	−0.204584	−	0.204584i	−0.00935746	−	0.00935746i
$479$	29.9325			1.36765			0.683826	−	0.729645i	$-0.260315\pi$
$479$	29.9325			1.36765			0.683826	+	0.729645i	$0.260315\pi$
$480$		0			0
$481$	12.1448			0.553756
$482$	0.301963	+	0.301963i	0.0137540	+	0.0137540i
$483$		0			0
$484$		−	21.6821i		−	0.985552i
$485$		0			0
$486$		0			0
$487$	9.20330	−	9.20330i	0.417041	−	0.417041i	−0.467141	−	0.884183i	$-0.654716\pi$
$487$	9.20330	−	9.20330i	0.417041	−	0.417041i	0.884183	+	0.467141i	$0.154716\pi$
$488$	−0.783267	+	0.783267i	−0.0354568	+	0.0354568i
$489$		0			0
$490$		0			0
$491$		−	0.109662i		−	0.00494898i	−0.999997	−	0.00247449i	$-0.999212\pi$
$491$		−	0.109662i		−	0.00494898i	0.999997	−	0.00247449i	$-0.000787655\pi$
$492$		0			0
$493$	34.3301	+	34.3301i	1.54615	+	1.54615i
$494$	0.584598			0.0263023
$495$		0			0
$496$	−21.5205			−0.966298
$497$	−11.3692	−	11.3692i	−0.509978	−	0.509978i
$498$		0			0
$499$			4.07430i			0.182391i	0.995833	+	0.0911953i	$0.0290688\pi$
$499$			4.07430i			0.182391i	−0.995833	+	0.0911953i	$0.970931\pi$
$500$		0			0
$501$		0			0
$502$	0.159301	−	0.159301i	0.00710994	−	0.00710994i
$503$	−5.34928	+	5.34928i	−0.238513	+	0.238513i	−0.816234	−	0.577721i	$-0.803942\pi$
$503$	−5.34928	+	5.34928i	−0.238513	+	0.238513i	0.577721	+	0.816234i	$0.303942\pi$
$504$		0			0
$505$		0			0
$506$			0.0412232i			0.00183259i
$507$		0			0
$508$	9.22813	+	9.22813i	0.409432	+	0.409432i
$509$	−38.2954			−1.69742			−0.848708	−	0.528862i	$-0.822619\pi$
$509$	−38.2954			−1.69742			−0.848708	+	0.528862i	$0.822619\pi$
$510$		0			0
$511$	10.1481			0.448926
$512$	1.92395	+	1.92395i	0.0850272	+	0.0850272i
$513$		0			0
$514$			1.01099i			0.0445928i
$515$		0			0
$516$		0			0
$517$	−0.210018	+	0.210018i	−0.00923657	+	0.00923657i
$518$	−0.0939754	+	0.0939754i	−0.00412904	+	0.00412904i
$519$		0			0
$520$		0			0
$521$		−	13.9501i		−	0.611167i	−0.952165	−	0.305583i	$-0.901149\pi$
$521$		−	13.9501i		−	0.611167i	0.952165	−	0.305583i	$-0.0988514\pi$
$522$		0			0
$523$	−30.1757	−	30.1757i	−1.31949	−	1.31949i	−0.914179	−	0.405312i	$-0.867163\pi$
$523$	−30.1757	−	30.1757i	−1.31949	−	1.31949i	−0.405312	−	0.914179i	$-0.632837\pi$
$524$	−6.87762			−0.300450
$525$		0			0
$526$	0.812569			0.0354297
$527$	−25.8019	−	25.8019i	−1.12395	−	1.12395i
$528$		0			0
$529$			13.4194i			0.583451i
$530$		0			0
$531$		0			0
$532$	7.78040	−	7.78040i	0.337323	−	0.337323i
$533$	−5.59757	+	5.59757i	−0.242458	+	0.242458i
$534$		0			0
$535$		0			0
$536$		−	0.725149i		−	0.0313217i
$537$		0			0
$538$	0.376695	+	0.376695i	0.0162405	+	0.0162405i
$539$	−0.390676			−0.0168276
$540$		0			0
$541$	7.24202			0.311359			0.155679	−	0.987808i	$-0.450243\pi$
$541$	7.24202			0.311359			0.155679	+	0.987808i	$0.450243\pi$
$542$	−0.130824	−	0.130824i	−0.00561937	−	0.00561937i
$543$		0			0
$544$			2.76751i			0.118656i
$545$		0			0
$546$		0			0
$547$	−12.9323	+	12.9323i	−0.552944	+	0.552944i	−0.927289	−	0.374346i	$-0.877867\pi$
$547$	−12.9323	+	12.9323i	−0.552944	+	0.552944i	0.374346	+	0.927289i	$0.377867\pi$
$548$	−2.15602	+	2.15602i	−0.0921004	+	0.0921004i
$549$		0			0
$550$		0			0
$551$			39.4741i			1.68165i
$552$		0			0
$553$	5.19749	+	5.19749i	0.221020	+	0.221020i
$554$	0.951992			0.0404462
$555$		0			0
$556$	−43.0460			−1.82556
$557$	−7.14290	−	7.14290i	−0.302654	−	0.302654i	0.539397	−	0.842052i	$-0.318652\pi$
$557$	−7.14290	−	7.14290i	−0.302654	−	0.302654i	−0.842052	+	0.539397i	$0.818652\pi$
$558$		0			0
$559$		−	30.8341i		−	1.30414i
$560$		0			0
$561$		0			0
$562$	0.345314	−	0.345314i	0.0145662	−	0.0145662i
$563$	23.3269	−	23.3269i	0.983111	−	0.983111i	−0.0167491	−	0.999860i	$-0.505332\pi$
$563$	23.3269	−	23.3269i	0.983111	−	0.983111i	0.999860	+	0.0167491i	$0.00533164\pi$
$564$		0			0
$565$		0			0
$566$			0.550857i			0.0231543i
$567$		0			0
$568$	1.54985	+	1.54985i	0.0650305	+	0.0650305i
$569$	−20.2162			−0.847506			−0.423753	−	0.905778i	$-0.639288\pi$
$569$	−20.2162			−0.847506			−0.423753	+	0.905778i	$0.639288\pi$
$570$		0			0
$571$	26.7908			1.12116			0.560581	−	0.828100i	$-0.310578\pi$
$571$	26.7908			1.12116			0.560581	+	0.828100i	$0.310578\pi$
$572$	−1.72016	−	1.72016i	−0.0719235	−	0.0719235i
$573$		0			0
$574$		−	0.0866269i		−	0.00361574i
$575$		0			0
$576$		0			0
$577$	8.31514	−	8.31514i	0.346164	−	0.346164i	−0.512515	−	0.858678i	$-0.671286\pi$
$577$	8.31514	−	8.31514i	0.346164	−	0.346164i	0.858678	+	0.512515i	$0.171286\pi$
$578$	−0.695170	+	0.695170i	−0.0289152	+	0.0289152i
$579$		0			0
$580$		0			0
$581$		−	8.89661i		−	0.369093i
$582$		0			0
$583$	−2.02848	−	2.02848i	−0.0840112	−	0.0840112i
$584$	−1.38340			−0.0572454
$585$		0			0
$586$	0.311884			0.0128838
$587$	−8.18891	−	8.18891i	−0.337993	−	0.337993i	0.517619	−	0.855611i	$-0.326819\pi$
$587$	−8.18891	−	8.18891i	−0.337993	−	0.337993i	−0.855611	+	0.517619i	$0.826819\pi$
$588$		0			0
$589$		−	29.6680i		−	1.22245i
$590$		0			0
$591$		0			0
$592$	−11.0075	+	11.0075i	−0.452405	+	0.452405i
$593$	−17.0635	+	17.0635i	−0.700714	+	0.700714i	−0.964564	−	0.263850i	$-0.915008\pi$
$593$	−17.0635	+	17.0635i	−0.700714	+	0.700714i	0.263850	+	0.964564i	$0.415008\pi$
$594$		0			0
$595$		0			0
$596$		−	12.9576i		−	0.530763i
$597$		0			0
$598$	−0.232434	−	0.232434i	−0.00950494	−	0.00950494i
$599$	−46.8508			−1.91427			−0.957136	−	0.289640i	$-0.906464\pi$
$599$	−46.8508			−1.91427			−0.957136	+	0.289640i	$0.906464\pi$
$600$		0			0
$601$	34.9943			1.42745			0.713723	−	0.700428i	$-0.247008\pi$
$601$	34.9943			1.42745			0.713723	+	0.700428i	$0.247008\pi$
$602$	0.238591	+	0.238591i	0.00972424	+	0.00972424i
$603$		0			0
$604$			3.53559i			0.143861i
$605$		0			0
$606$		0			0
$607$	6.68444	−	6.68444i	0.271313	−	0.271313i	−0.558316	−	0.829629i	$-0.688552\pi$
$607$	6.68444	−	6.68444i	0.271313	−	0.271313i	0.829629	+	0.558316i	$0.188552\pi$
$608$	−1.59110	+	1.59110i	−0.0645275	+	0.0645275i
$609$		0			0
$610$		0			0
$611$		−	2.36834i		−	0.0958129i
$612$		0			0
$613$	10.0152	+	10.0152i	0.404510	+	0.404510i	0.879819	−	0.475309i	$-0.157664\pi$
$613$	10.0152	+	10.0152i	0.404510	+	0.404510i	−0.475309	+	0.879819i	$0.657664\pi$
$614$	−0.408256			−0.0164759
$615$		0			0
$616$	0.0532572			0.00214579
$617$	2.25298	+	2.25298i	0.0907017	+	0.0907017i	0.751002	−	0.660300i	$-0.229571\pi$
$617$	2.25298	+	2.25298i	0.0907017	+	0.0907017i	−0.660300	+	0.751002i	$0.729571\pi$
$618$		0			0
$619$			18.8285i			0.756781i	0.925646	+	0.378390i	$0.123522\pi$
$619$			18.8285i			0.756781i	−0.925646	+	0.378390i	$0.876478\pi$
$620$		0			0
$621$		0			0
$622$	0.248865	−	0.248865i	0.00997859	−	0.00997859i
$623$	7.02926	−	7.02926i	0.281621	−	0.281621i
$624$		0			0
$625$		0			0
$626$		−	0.877948i		−	0.0350899i
$627$		0			0
$628$	−14.9763	−	14.9763i	−0.597618	−	0.597618i
$629$	−26.3948			−1.05243
$630$		0			0
$631$	−18.6473			−0.742338			−0.371169	−	0.928565i	$-0.621043\pi$
$631$	−18.6473			−0.742338			−0.371169	+	0.928565i	$0.621043\pi$
$632$	−0.708525	−	0.708525i	−0.0281836	−	0.0281836i
$633$		0			0
$634$			1.18853i			0.0472025i
$635$		0			0
$636$		0			0
$637$	2.20280	−	2.20280i	0.0872781	−	0.0872781i
$638$	−0.0675309	+	0.0675309i	−0.00267357	+	0.00267357i
$639$		0			0
$640$		0			0
$641$			1.94420i			0.0767912i	0.999263	+	0.0383956i	$0.0122247\pi$
$641$			1.94420i			0.0767912i	−0.999263	+	0.0383956i	$0.987775\pi$
$642$		0			0
$643$	−29.8737	−	29.8737i	−1.17810	−	1.17810i	−0.980227	−	0.197878i	$-0.936595\pi$
$643$	−29.8737	−	29.8737i	−1.17810	−	1.17810i	−0.197878	−	0.980227i	$-0.563405\pi$
$644$	−6.18692			−0.243799
$645$		0			0
$646$	−1.27053			−0.0499882
$647$	5.84909	+	5.84909i	0.229952	+	0.229952i	0.812672	−	0.582721i	$-0.198012\pi$
$647$	5.84909	+	5.84909i	0.229952	+	0.229952i	−0.582721	+	0.812672i	$0.698012\pi$
$648$		0			0
$649$			4.02754i			0.158095i
$650$		0			0
$651$		0			0
$652$	27.8460	−	27.8460i	1.09053	−	1.09053i
$653$	34.0909	−	34.0909i	1.33408	−	1.33408i	0.432396	−	0.901684i	$-0.357668\pi$
$653$	34.0909	−	34.0909i	1.33408	−	1.33408i	0.901684	−	0.432396i	$-0.142332\pi$
$654$		0			0
$655$		0			0
$656$		−	10.1468i		−	0.396164i
$657$		0			0
$658$	0.0183260	+	0.0183260i	0.000714422	+	0.000714422i
$659$	−24.0596			−0.937229			−0.468614	−	0.883403i	$-0.655247\pi$
$659$	−24.0596			−0.937229			−0.468614	+	0.883403i	$0.655247\pi$
$660$		0			0
$661$	−2.95088			−0.114776			−0.0573880	−	0.998352i	$-0.518277\pi$
$661$	−2.95088			−0.114776			−0.0573880	+	0.998352i	$0.518277\pi$
$662$	−0.315334	−	0.315334i	−0.0122558	−	0.0122558i
$663$		0			0
$664$			1.21279i			0.0470654i
$665$		0			0
$666$		0			0
$667$	15.6948	−	15.6948i	0.607704	−	0.607704i
$668$	0.953809	−	0.953809i	0.0369040	−	0.0369040i
$669$		0			0
$670$		0			0
$671$			3.17453i			0.122551i
$672$		0			0
$673$	−18.8062	−	18.8062i	−0.724925	−	0.724925i	0.244679	−	0.969604i	$-0.421317\pi$
$673$	−18.8062	−	18.8062i	−0.724925	−	0.724925i	−0.969604	+	0.244679i	$0.921317\pi$
$674$	−0.307857			−0.0118582
$675$		0			0
$676$	−6.58687			−0.253341
$677$	−4.99857	−	4.99857i	−0.192111	−	0.192111i	0.604497	−	0.796608i	$-0.293374\pi$
$677$	−4.99857	−	4.99857i	−0.192111	−	0.192111i	−0.796608	+	0.604497i	$0.793374\pi$
$678$		0			0
$679$		−	3.07529i		−	0.118019i
$680$		0			0
$681$		0			0
$682$	0.0507550	−	0.0507550i	0.00194351	−	0.00194351i
$683$	−10.0092	+	10.0092i	−0.382990	+	0.382990i	−0.872178	−	0.489188i	$-0.837293\pi$
$683$	−10.0092	+	10.0092i	−0.382990	+	0.382990i	0.489188	+	0.872178i	$0.337293\pi$
$684$		0			0
$685$		0			0
$686$			0.0340901i			0.00130156i
$687$		0			0
$688$	27.9466	+	27.9466i	1.06545	+	1.06545i
$689$	22.8750			0.871466
$690$		0			0
$691$	−19.5494			−0.743696			−0.371848	−	0.928294i	$-0.621276\pi$
$691$	−19.5494			−0.743696			−0.371848	+	0.928294i	$0.621276\pi$
$692$	29.2619	+	29.2619i	1.11237	+	1.11237i
$693$		0			0
$694$		−	0.0913314i		−	0.00346689i
$695$		0			0
$696$		0			0
$697$	12.1654	−	12.1654i	0.460797	−	0.460797i
$698$	−0.664689	+	0.664689i	−0.0251589	+	0.0251589i
$699$		0			0
$700$		0			0
$701$		−	11.8659i		−	0.448171i	−0.974570	−	0.224085i	$-0.928061\pi$
$701$		−	11.8659i		−	0.448171i	0.974570	−	0.224085i	$-0.0719394\pi$
$702$		0			0
$703$	−15.1749	−	15.1749i	−0.572331	−	0.572331i
$704$	3.11451			0.117383
$705$		0			0
$706$	0.526431			0.0198125
$707$	3.70560	+	3.70560i	0.139364	+	0.139364i
$708$		0			0
$709$			29.1357i			1.09421i	0.837063	+	0.547107i	$0.184271\pi$
$709$			29.1357i			1.09421i	−0.837063	+	0.547107i	$0.815729\pi$
$710$		0			0
$711$		0			0
$712$	−0.958234	+	0.958234i	−0.0359113	+	0.0359113i
$713$	−11.7959	+	11.7959i	−0.441760	+	0.441760i
$714$		0			0
$715$		0			0
$716$			6.09224i			0.227678i
$717$		0			0
$718$	0.411203	+	0.411203i	0.0153460	+	0.0153460i
$719$	−33.8893			−1.26386			−0.631928	−	0.775027i	$-0.717736\pi$
$719$	−33.8893			−1.26386			−0.631928	+	0.775027i	$0.717736\pi$
$720$		0			0
$721$	−1.82718			−0.0680478
$722$	−0.272450	−	0.272450i	−0.0101395	−	0.0101395i
$723$		0			0
$724$		−	8.25454i		−	0.306778i
$725$		0			0
$726$		0			0
$727$	26.7239	−	26.7239i	0.991135	−	0.991135i	−0.00882647	−	0.999961i	$-0.502810\pi$
$727$	26.7239	−	26.7239i	0.991135	−	0.991135i	0.999961	+	0.00882647i	$0.00280959\pi$
$728$	−0.300287	+	0.300287i	−0.0111294	+	0.0111294i
$729$		0			0
$730$		0			0
$731$			67.0128i			2.47856i
$732$		0			0
$733$	12.2852	+	12.2852i	0.453763	+	0.453763i	0.896601	−	0.442838i	$-0.146028\pi$
$733$	12.2852	+	12.2852i	0.453763	+	0.453763i	−0.442838	+	0.896601i	$0.646028\pi$
$734$	−0.736691			−0.0271918
$735$		0			0
$736$	1.26523			0.0466370
$737$	−1.46949	−	1.46949i	−0.0541294	−	0.0541294i
$738$		0			0
$739$			3.61431i			0.132955i	0.997788	+	0.0664774i	$0.0211760\pi$
$739$			3.61431i			0.132955i	−0.997788	+	0.0664774i	$0.978824\pi$
$740$		0			0
$741$		0			0
$742$	−0.177004	+	0.177004i	−0.00649802	+	0.00649802i
$743$	−9.96922	+	9.96922i	−0.365735	+	0.365735i	−0.865919	−	0.500184i	$-0.833266\pi$
$743$	−9.96922	+	9.96922i	−0.365735	+	0.365735i	0.500184	+	0.865919i	$0.333266\pi$
$744$		0			0
$745$		0			0
$746$			0.233164i			0.00853674i
$747$		0			0
$748$	3.73849	+	3.73849i	0.136693	+	0.136693i
$749$	14.2161			0.519446
$750$		0			0
$751$	−20.7823			−0.758359			−0.379179	−	0.925323i	$-0.623794\pi$
$751$	−20.7823			−0.758359			−0.379179	+	0.925323i	$0.623794\pi$
$752$	2.14656	+	2.14656i	0.0782768	+	0.0782768i
$753$		0			0
$754$		−	0.761537i		−	0.0277335i
$755$		0			0
$756$		0			0
$757$	−5.61667	+	5.61667i	−0.204141	+	0.204141i	−0.801772	−	0.597630i	$-0.796109\pi$
$757$	−5.61667	+	5.61667i	−0.204141	+	0.204141i	0.597630	+	0.801772i	$0.296109\pi$
$758$	0.375051	−	0.375051i	0.0136224	−	0.0136224i
$759$		0			0
$760$		0			0
$761$			27.7154i			1.00468i	0.864670	+	0.502341i	$0.167528\pi$
$761$			27.7154i			1.00468i	−0.864670	+	0.502341i	$0.832472\pi$
$762$		0			0
$763$	−9.86570	−	9.86570i	−0.357162	−	0.357162i
$764$	−42.9636			−1.55437
$765$		0			0
$766$	−0.513998			−0.0185715
$767$	−22.7090	−	22.7090i	−0.819976	−	0.819976i
$768$		0			0
$769$		−	16.1150i		−	0.581123i	−0.956856	−	0.290561i	$-0.906158\pi$
$769$		−	16.1150i		−	0.581123i	0.956856	−	0.290561i	$-0.0938421\pi$
$770$		0			0
$771$		0			0
$772$	18.0790	−	18.0790i	0.650677	−	0.650677i
$773$	−15.2927	+	15.2927i	−0.550041	+	0.550041i	−0.926452	−	0.376412i	$-0.877158\pi$
$773$	−15.2927	+	15.2927i	−0.550041	+	0.550041i	0.376412	+	0.926452i	$0.377158\pi$
$774$		0			0
$775$		0			0
$776$			0.419226i			0.0150493i
$777$		0			0
$778$	0.546367	+	0.546367i	0.0195882	+	0.0195882i
$779$	13.9883			0.501182
$780$		0			0
$781$	6.28146			0.224768
$782$	0.505157	+	0.505157i	0.0180644	+	0.0180644i
$783$		0			0
$784$			3.99303i			0.142608i
$785$		0			0
$786$		0			0
$787$	−5.60346	+	5.60346i	−0.199742	+	0.199742i	−0.799889	−	0.600148i	$-0.795109\pi$
$787$	−5.60346	+	5.60346i	−0.199742	+	0.199742i	0.600148	+	0.799889i	$0.295109\pi$
$788$	17.5905	−	17.5905i	0.626637	−	0.626637i
$789$		0			0
$790$		0			0
$791$			12.4456i			0.442515i
$792$		0			0
$793$	−17.8994	−	17.8994i	−0.635626	−	0.635626i
$794$	−0.414413			−0.0147070
$795$		0			0
$796$	1.63216			0.0578502
$797$	−20.1318	−	20.1318i	−0.713105	−	0.713105i	0.254079	−	0.967184i	$-0.418228\pi$
$797$	−20.1318	−	20.1318i	−0.713105	−	0.713105i	−0.967184	+	0.254079i	$0.918228\pi$
$798$		0			0
$799$			5.14721i			0.182095i
$800$		0			0
$801$		0			0
$802$	−0.433326	+	0.433326i	−0.0153013	+	0.0153013i
$803$	−2.80341	+	2.80341i	−0.0989302	+	0.0989302i
$804$		0			0
$805$		0			0
$806$			0.572358i			0.0201604i
$807$		0			0
$808$	−0.505150	−	0.505150i	−0.0177711	−	0.0177711i
$809$	39.2478			1.37988			0.689939	−	0.723868i	$-0.257637\pi$
$809$	39.2478			1.37988			0.689939	+	0.723868i	$0.257637\pi$
$810$		0			0
$811$	−50.5122			−1.77372			−0.886861	−	0.462036i	$-0.847119\pi$
$811$	−50.5122			−1.77372			−0.886861	+	0.462036i	$0.847119\pi$
$812$	−10.1353	−	10.1353i	−0.355679	−	0.355679i
$813$		0			0
$814$		−	0.0519213i		−	0.00181984i
$815$		0			0
$816$		0			0
$817$	−38.5270	+	38.5270i	−1.34789	+	1.34789i
$818$	0.466005	−	0.466005i	0.0162935	−	0.0162935i
$819$		0			0
$820$		0			0
$821$		−	22.3236i		−	0.779097i	−0.921006	−	0.389549i	$-0.872631\pi$
$821$		−	22.3236i		−	0.779097i	0.921006	−	0.389549i	$-0.127369\pi$
$822$		0			0
$823$	−23.8490	−	23.8490i	−0.831323	−	0.831323i	0.156375	−	0.987698i	$-0.450019\pi$
$823$	−23.8490	−	23.8490i	−0.831323	−	0.831323i	−0.987698	+	0.156375i	$0.950019\pi$
$824$	0.249083			0.00867721
$825$		0			0
$826$	0.351441			0.0122282
$827$	−17.6588	−	17.6588i	−0.614057	−	0.614057i	0.329944	−	0.944001i	$-0.392970\pi$
$827$	−17.6588	−	17.6588i	−0.614057	−	0.614057i	−0.944001	+	0.329944i	$0.892970\pi$
$828$		0			0
$829$		−	17.1138i		−	0.594388i	−0.954817	−	0.297194i	$-0.903949\pi$
$829$		−	17.1138i		−	0.594388i	0.954817	−	0.297194i	$-0.0960509\pi$
$830$		0			0
$831$		0			0
$832$	−17.5610	+	17.5610i	−0.608818	+	0.608818i
$833$	−4.78742	+	4.78742i	−0.165874	+	0.165874i
$834$		0			0
$835$		0			0
$836$			4.29866i			0.148672i
$837$		0			0
$838$	−0.0167385	−	0.0167385i	−0.000578223	−	0.000578223i
$839$	−43.4377			−1.49964			−0.749818	−	0.661644i	$-0.769859\pi$
$839$	−43.4377			−1.49964			−0.749818	+	0.661644i	$0.769859\pi$
$840$		0			0
$841$	22.4217			0.773162
$842$	−0.336150	−	0.336150i	−0.0115845	−	0.0115845i
$843$		0			0
$844$		−	11.8664i		−	0.408457i
$845$		0			0
$846$		0			0
$847$	−7.67025	+	7.67025i	−0.263553	+	0.263553i
$848$	−20.7328	+	20.7328i	−0.711967	+	0.711967i
$849$		0			0
$850$		0			0
$851$			12.0670i			0.413650i
$852$		0			0
$853$	27.5983	+	27.5983i	0.944949	+	0.944949i	0.998562	−	0.0536129i	$-0.0170737\pi$
$853$	27.5983	+	27.5983i	0.944949	+	0.944949i	−0.0536129	+	0.998562i	$0.517074\pi$
$854$	0.277007			0.00947899
$855$		0			0
$856$	−1.93795			−0.0662378
$857$	−19.1806	−	19.1806i	−0.655198	−	0.655198i	0.299042	−	0.954240i	$-0.403333\pi$
$857$	−19.1806	−	19.1806i	−0.655198	−	0.655198i	−0.954240	+	0.299042i	$0.903333\pi$
$858$		0			0
$859$		−	37.8659i		−	1.29197i	−0.763351	−	0.645984i	$-0.776447\pi$
$859$		−	37.8659i		−	1.29197i	0.763351	−	0.645984i	$-0.223553\pi$
$860$		0			0
$861$		0			0
$862$	0.759097	−	0.759097i	0.0258550	−	0.0258550i
$863$	−14.5099	+	14.5099i	−0.493924	+	0.493924i	−0.909540	−	0.415616i	$-0.863566\pi$
$863$	−14.5099	+	14.5099i	−0.493924	+	0.493924i	0.415616	+	0.909540i	$0.363566\pi$
$864$		0			0
$865$		0			0
$866$		−	1.04760i		−	0.0355988i
$867$		0			0
$868$	7.61749	+	7.61749i	0.258555	+	0.258555i
$869$	−2.87161			−0.0974126
$870$		0			0
$871$	16.5713			0.561496
$872$	1.34490	+	1.34490i	0.0455440	+	0.0455440i
$873$		0			0
$874$			0.580850i			0.0196475i
$875$		0			0
$876$		0			0
$877$	2.22943	−	2.22943i	0.0752826	−	0.0752826i	−0.668463	−	0.743745i	$-0.733047\pi$
$877$	2.22943	−	2.22943i	0.0752826	−	0.0752826i	0.743745	+	0.668463i	$0.233047\pi$
$878$	0.123343	−	0.123343i	0.00416261	−	0.00416261i
$879$		0			0
$880$		0			0
$881$			13.5419i			0.456238i	0.973633	+	0.228119i	$0.0732575\pi$
$881$			13.5419i			0.456238i	−0.973633	+	0.228119i	$0.926742\pi$
$882$		0			0
$883$	−23.3601	−	23.3601i	−0.786129	−	0.786129i	0.194728	−	0.980857i	$-0.437617\pi$
$883$	−23.3601	−	23.3601i	−0.786129	−	0.786129i	−0.980857	+	0.194728i	$0.937617\pi$
$884$	−42.1584			−1.41794
$885$		0			0
$886$	0.771690			0.0259254
$887$	12.4892	+	12.4892i	0.419346	+	0.419346i	0.884978	−	0.465632i	$-0.154173\pi$
$887$	12.4892	+	12.4892i	0.419346	+	0.419346i	−0.465632	+	0.884978i	$0.654173\pi$
$888$		0			0
$889$		−	6.52907i		−	0.218978i
$890$		0			0
$891$		0			0
$892$	4.33921	−	4.33921i	0.145287	−	0.145287i
$893$	−2.95923	+	2.95923i	−0.0990269	+	0.0990269i
$894$		0			0
$895$		0			0
$896$		−	1.08930i		−	0.0363909i
$897$		0			0
$898$	0.689263	+	0.689263i	0.0230010	+	0.0230010i
$899$	−38.6476			−1.28897
$900$		0			0
$901$	−49.7150			−1.65625
$902$	0.0239306	+	0.0239306i	0.000796802	+	0.000796802i
$903$		0			0
$904$		−	1.69660i		−	0.0564279i
$905$		0			0
$906$		0			0
$907$	30.6351	−	30.6351i	1.01722	−	1.01722i	0.0173730	−	0.999849i	$-0.494470\pi$
$907$	30.6351	−	30.6351i	1.01722	−	1.01722i	0.999849	−	0.0173730i	$-0.00553028\pi$
$908$	−35.7436	+	35.7436i	−1.18619	+	1.18619i
$909$		0			0
$910$		0			0
$911$			39.0547i			1.29394i	0.762516	+	0.646969i	$0.223964\pi$
$911$			39.0547i			1.29394i	−0.762516	+	0.646969i	$0.776036\pi$
$912$		0			0
$913$	2.45768	+	2.45768i	0.0813374	+	0.0813374i
$914$	−0.971196			−0.0321243
$915$		0			0
$916$	−4.84964			−0.160237
$917$	2.43302	+	2.43302i	0.0803454	+	0.0803454i
$918$		0			0
$919$		−	44.2050i		−	1.45819i	−0.684413	−	0.729095i	$-0.739941\pi$
$919$		−	44.2050i		−	1.45819i	0.684413	−	0.729095i	$-0.260059\pi$
$920$		0			0
$921$		0			0
$922$	0.205595	−	0.205595i	0.00677091	−	0.00677091i
$923$	−35.4176	+	35.4176i	−1.16578	+	1.16578i
$924$		0			0
$925$		0			0
$926$			1.12514i			0.0369743i
$927$		0			0
$928$	2.07267	+	2.07267i	0.0680388	+	0.0680388i
$929$	44.4925			1.45975			0.729875	−	0.683580i	$-0.239578\pi$
$929$	44.4925			1.45975			0.729875	+	0.683580i	$0.239578\pi$
$930$		0			0
$931$	−5.50477			−0.180412
$932$	−33.9253	−	33.9253i	−1.11126	−	1.11126i
$933$		0			0
$934$			1.26195i			0.0412923i
$935$		0			0
$936$		0			0
$937$	−7.24786	+	7.24786i	−0.236777	+	0.236777i	−0.815514	−	0.578737i	$-0.803546\pi$
$937$	−7.24786	+	7.24786i	−0.236777	+	0.236777i	0.578737	+	0.815514i	$0.303546\pi$
$938$	−0.128227	+	0.128227i	−0.00418675	+	0.00418675i
$939$		0			0
$940$		0			0
$941$		−	29.6137i		−	0.965380i	−0.875791	−	0.482690i	$-0.839660\pi$
$941$		−	29.6137i		−	0.965380i	0.875791	−	0.482690i	$-0.160340\pi$
$942$		0			0
$943$	−5.56169	−	5.56169i	−0.181113	−	0.181113i
$944$	41.1648			1.33980
$945$		0			0
$946$	−0.131821			−0.00428588
$947$	35.1629	+	35.1629i	1.14264	+	1.14264i	0.987965	+	0.154676i	$0.0494332\pi$
$947$	35.1629	+	35.1629i	1.14264	+	1.14264i	0.154676	+	0.987965i	$0.450567\pi$
$948$		0			0
$949$		−	31.6137i		−	1.02622i
$950$		0			0
$951$		0			0
$952$	0.652625	−	0.652625i	0.0211517	−	0.0211517i
$953$	23.2547	−	23.2547i	0.753295	−	0.753295i	−0.221798	−	0.975093i	$-0.571192\pi$
$953$	23.2547	−	23.2547i	0.753295	−	0.753295i	0.975093	+	0.221798i	$0.0711925\pi$
$954$		0			0
$955$		0			0
$956$			16.9643i			0.548666i
$957$		0			0
$958$	0.721533	+	0.721533i	0.0233117	+	0.0233117i
$959$	1.52542			0.0492584
$960$		0			0
$961$	−1.95314			−0.0630047
$962$	0.292755	+	0.292755i	0.00943879	+	0.00943879i
$963$		0			0
$964$		−	25.0391i		−	0.806455i
$965$		0			0
$966$		0			0
$967$	9.48404	−	9.48404i	0.304986	−	0.304986i	−0.537975	−	0.842961i	$-0.680810\pi$
$967$	9.48404	−	9.48404i	0.304986	−	0.304986i	0.842961	+	0.537975i	$0.180810\pi$
$968$	1.04561	−	1.04561i	0.0336073	−	0.0336073i
$969$		0			0
$970$		0			0
$971$			27.4171i			0.879858i	0.898033	+	0.439929i	$0.144996\pi$
$971$			27.4171i			0.879858i	−0.898033	+	0.439929i	$0.855004\pi$
$972$		0			0
$973$	15.2279	+	15.2279i	0.488184	+	0.488184i
$974$	0.443697			0.0142170
$975$		0			0
$976$	32.4463			1.03858
$977$	−0.810961	−	0.810961i	−0.0259449	−	0.0259449i	0.694015	−	0.719960i	$-0.255840\pi$
$977$	−0.810961	−	0.810961i	−0.0259449	−	0.0259449i	−0.719960	+	0.694015i	$0.755840\pi$
$978$		0			0
$979$			3.88366i			0.124122i
$980$		0			0
$981$		0			0
$982$	0.00264344	−	0.00264344i	8.43555e−5	−	8.43555e-5i
$983$	1.20950	−	1.20950i	0.0385771	−	0.0385771i	−0.687555	−	0.726132i	$-0.741316\pi$
$983$	1.20950	−	1.20950i	0.0385771	−	0.0385771i	0.726132	+	0.687555i	$0.241316\pi$
$984$		0			0
$985$		0			0
$986$			1.65508i			0.0527084i
$987$		0			0
$988$	−24.2377	−	24.2377i	−0.771104	−	0.771104i
$989$	30.6364			0.974181
$990$		0			0
$991$	−28.2009			−0.895832			−0.447916	−	0.894076i	$-0.647834\pi$
$991$	−28.2009			−0.895832			−0.447916	+	0.894076i	$0.647834\pi$
$992$	−1.55778	−	1.55778i	−0.0494597	−	0.0494597i
$993$		0			0
$994$		−	0.548116i		−	0.0173852i
$995$		0			0
$996$		0			0
$997$	−23.4397	+	23.4397i	−0.742342	+	0.742342i	−0.973028	−	0.230687i	$-0.925903\pi$
$997$	−23.4397	+	23.4397i	−0.742342	+	0.742342i	0.230687	+	0.973028i	$0.425903\pi$
$998$	−0.0982123	+	0.0982123i	−0.00310886	+	0.00310886i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.m.c.1268.4		12
3.2	odd	2		1575.2.m.d.1268.3		12
5.2	odd	4		1575.2.m.d.1457.3		12
5.3	odd	4		315.2.m.b.197.4	yes	12
5.4	even	2		315.2.m.a.8.3	✓	12
15.2	even	4	inner	1575.2.m.c.1457.4		12
15.8	even	4		315.2.m.a.197.3	yes	12
15.14	odd	2		315.2.m.b.8.4	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.3	✓	12	5.4	even	2
315.2.m.a.197.3	yes	12	15.8	even	4
315.2.m.b.8.4	yes	12	15.14	odd	2
315.2.m.b.197.4	yes	12	5.3	odd	4
1575.2.m.c.1268.4		12	1.1	even	1	trivial
1575.2.m.c.1457.4		12	15.2	even	4	inner
1575.2.m.d.1268.3		12	3.2	odd	2
1575.2.m.d.1457.3		12	5.2	odd	4

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0241053 + 0.0241053i) q^{2} -1.99884i q^{4} +(-0.707107 + 0.707107i) q^{7} +(0.0963933 - 0.0963933i) q^{8} -0.390676i q^{11} +(2.20280 + 2.20280i) q^{13} -0.0340901 q^{14} -3.99303 q^{16} +(-4.78742 - 4.78742i) q^{17} -5.50477i q^{19} +(0.00941736 - 0.00941736i) q^{22} +(-2.18868 + 2.18868i) q^{23} +0.106198i q^{26} +(1.41339 + 1.41339i) q^{28} -7.17089 q^{29} +5.38951 q^{31} +(-0.289040 - 0.289040i) q^{32} -0.230805i q^{34} +(2.75668 - 2.75668i) q^{37} +(0.132694 - 0.132694i) q^{38} +2.54112i q^{41} +(-6.99884 - 6.99884i) q^{43} -0.780897 q^{44} -0.105518 q^{46} +(-0.537576 - 0.537576i) q^{47} -1.00000i q^{49} +(4.40304 - 4.40304i) q^{52} +(5.19225 - 5.19225i) q^{53} +0.136321i q^{56} +(-0.172857 - 0.172857i) q^{58} -10.3092 q^{59} -8.12574 q^{61} +(0.129916 + 0.129916i) q^{62} +7.97212i q^{64} +(3.76141 - 3.76141i) q^{67} +(-9.56928 + 9.56928i) q^{68} +16.0785i q^{71} +(-7.17580 - 7.17580i) q^{73} +0.132901 q^{74} -11.0031 q^{76} +(0.276249 + 0.276249i) q^{77} -7.35036i q^{79} +(-0.0612544 + 0.0612544i) q^{82} +(-6.29085 + 6.29085i) q^{83} -0.337418i q^{86} +(-0.0376585 - 0.0376585i) q^{88} -9.94088 q^{89} -3.11523 q^{91} +(4.37481 + 4.37481i) q^{92} -0.0259169i q^{94} +(-2.17456 + 2.17456i) q^{97} +(0.0241053 - 0.0241053i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{8} + 4 q^{13} - 4 q^{14} - 20 q^{16} - 8 q^{17} + 8 q^{22} - 8 q^{23} - 32 q^{29} - 48 q^{32} - 4 q^{37} - 24 q^{38} - 40 q^{43} - 64 q^{44} + 16 q^{46} - 24 q^{47} - 36 q^{52} + 40 q^{53}+ \cdots - 12 q^{97}+O(q^{100}) \) 12 * q - 24 * q^8 + 4 * q^13 - 4 * q^14 - 20 * q^16 - 8 * q^17 + 8 * q^22 - 8 * q^23 - 32 * q^29 - 48 * q^32 - 4 * q^37 - 24 * q^38 - 40 * q^43 - 64 * q^44 + 16 * q^46 - 24 * q^47 - 36 * q^52 + 40 * q^53 + 28 * q^58 - 80 * q^59 - 32 * q^61 - 16 * q^62 + 48 * q^67 - 32 * q^68 + 20 * q^73 - 64 * q^74 + 16 * q^76 - 20 * q^82 - 24 * q^83 - 56 * q^89 - 8 * q^92 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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