LMFDB - Embedded newform 1323.2.s.c.656.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(656,1323)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1323, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1323.656");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.5642081874$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			656.2
Root			$1.29589 + 0.748185i$ of defining polynomial
Character	$\chi$	$=$	1323.656
Dual form			1323.2.s.c.962.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.97141 + 1.13819i) q^{2} +(1.59097 - 2.75564i) q^{4} +1.43429 q^{5} +2.69056i q^{8} +O(q^{10})$	\(q+(-1.97141 + 1.13819i) q^{2} +(1.59097 - 2.75564i) q^{4} +1.43429 q^{5} +2.69056i q^{8} +(-2.82757 + 1.63250i) q^{10} +3.23490i q^{11} +(-4.43334 + 2.55959i) q^{13} +(0.119562 + 0.207087i) q^{16} +(-0.545658 - 0.945107i) q^{17} +(3.88768 + 2.24456i) q^{19} +(2.28191 - 3.95238i) q^{20} +(-3.68194 - 6.37731i) q^{22} -4.00844i q^{23} -2.94282 q^{25} +(5.82662 - 10.0920i) q^{26} +(-1.02859 - 0.593857i) q^{29} +(-3.24275 - 1.87220i) q^{31} +(-5.13160 - 2.96273i) q^{32} +(2.15143 + 1.24213i) q^{34} +(0.119562 - 0.207087i) q^{37} -10.2190 q^{38} +3.85904i q^{40} +(3.71620 + 6.43664i) q^{41} +(-3.82326 + 6.62208i) q^{43} +(8.91423 + 5.14663i) q^{44} +(4.56238 + 7.90228i) q^{46} +(-2.11042 - 3.65536i) q^{47} +(5.80150 - 3.34950i) q^{50} +16.2889i q^{52} +(6.07442 - 3.50707i) q^{53} +4.63977i q^{55} +2.70370 q^{58} +(-4.73531 + 8.20179i) q^{59} +(-2.82757 + 1.63250i) q^{61} +8.52371 q^{62} +13.0104 q^{64} +(-6.35868 + 3.67119i) q^{65} +(-0.330095 + 0.571741i) q^{67} -3.47250 q^{68} +3.82347i q^{71} +(-6.33127 + 3.65536i) q^{73} +0.544337i q^{74} +(12.3704 - 7.14205i) q^{76} +(-1.83009 - 3.16982i) q^{79} +(0.171486 + 0.297022i) q^{80} +(-14.6523 - 8.45951i) q^{82} +(-5.45245 + 9.44392i) q^{83} +(-0.782630 - 1.35556i) q^{85} -17.4064i q^{86} -8.70370 q^{88} +(-6.84573 + 11.8572i) q^{89} +(-11.0458 - 6.37731i) q^{92} +(8.32102 + 4.80415i) q^{94} +(5.57605 + 3.21934i) q^{95} +(-2.69709 - 1.55716i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} + 2 q^{4}+O(q^{10}) $ 12 * q - 6 * q^2 + 2 * q^4	$ 12 q - 6 q^{2} + 2 q^{4} + 2 q^{16} - 10 q^{22} - 30 q^{29} - 12 q^{32} + 2 q^{37} - 10 q^{43} + 54 q^{44} + 20 q^{46} + 36 q^{50} - 12 q^{53} - 4 q^{58} + 16 q^{64} - 78 q^{65} + 12 q^{67} - 6 q^{79} - 6 q^{85} - 68 q^{88} - 30 q^{92} + 72 q^{95}+O(q^{100}) $ 12 * q - 6 * q^2 + 2 * q^4 + 2 * q^16 - 10 * q^22 - 30 * q^29 - 12 * q^32 + 2 * q^37 - 10 * q^43 + 54 * q^44 + 20 * q^46 + 36 * q^50 - 12 * q^53 - 4 * q^58 + 16 * q^64 - 78 * q^65 + 12 * q^67 - 6 * q^79 - 6 * q^85 - 68 * q^88 - 30 * q^92 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.97141	+	1.13819i	−1.39400	+	0.804825i	−0.993755	−	0.111585i	$-0.964407\pi$
$2$	−1.97141	+	1.13819i	−1.39400	+	0.804825i	−0.400242	+	0.916409i	$0.631074\pi$
$3$		0			0
$3$		0			0
$4$	1.59097	−	2.75564i	0.795486	−	1.37782i
$5$	1.43429			0.641433			0.320716	−	0.947175i	$-0.396076\pi$
$5$	1.43429			0.641433			0.320716	+	0.947175i	$0.396076\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.69056i			0.951257i
$9$		0			0
$10$	−2.82757	+	1.63250i	−0.894156	+	0.516241i
$11$			3.23490i			0.975359i	0.873023	+	0.487679i	$0.162157\pi$
$11$			3.23490i			0.975359i	−0.873023	+	0.487679i	$0.837843\pi$
$12$		0			0
$13$	−4.43334	+	2.55959i	−1.22959	+	0.709903i	−0.966944	−	0.254990i	$-0.917928\pi$
$13$	−4.43334	+	2.55959i	−1.22959	+	0.709903i	−0.262644	+	0.964893i	$0.584594\pi$
$14$		0			0
$15$		0			0
$16$	0.119562	+	0.207087i	0.0298904	+	0.0517717i
$17$	−0.545658	−	0.945107i	−0.132341	−	0.229222i	0.792237	−	0.610213i	$-0.208916\pi$
$17$	−0.545658	−	0.945107i	−0.132341	−	0.229222i	−0.924579	+	0.380991i	$0.875583\pi$
$18$		0			0
$19$	3.88768	+	2.24456i	0.891896	+	0.514936i	0.874562	−	0.484914i	$-0.161149\pi$
$19$	3.88768	+	2.24456i	0.891896	+	0.514936i	0.0173336	+	0.999850i	$0.494482\pi$
$20$	2.28191	−	3.95238i	0.510251	−	0.883780i
$21$		0			0
$22$	−3.68194	−	6.37731i	−0.784993	−	1.35965i
$23$		−	4.00844i		−	0.835817i	−0.908489	−	0.417909i	$-0.862763\pi$
$23$		−	4.00844i		−	0.835817i	0.908489	−	0.417909i	$-0.137237\pi$
$24$		0			0
$25$	−2.94282			−0.588564
$26$	5.82662	−	10.0920i	1.14269	−	1.97921i
$27$		0			0
$28$		0			0
$29$	−1.02859	−	0.593857i	−0.191004	−	0.110276i	0.401448	−	0.915882i	$-0.368507\pi$
$29$	−1.02859	−	0.593857i	−0.191004	−	0.110276i	−0.592453	+	0.805605i	$0.701840\pi$
$30$		0			0
$31$	−3.24275	−	1.87220i	−0.582414	−	0.336257i	0.179678	−	0.983726i	$-0.442494\pi$
$31$	−3.24275	−	1.87220i	−0.582414	−	0.336257i	−0.762092	+	0.647468i	$0.775828\pi$
$32$	−5.13160	−	2.96273i	−0.907147	−	0.523742i
$33$		0			0
$34$	2.15143	+	1.24213i	0.368967	+	0.213023i
$35$		0			0
$36$		0			0
$37$	0.119562	−	0.207087i	0.0196558	−	0.0340449i	−0.856030	−	0.516926i	$-0.827076\pi$
$37$	0.119562	−	0.207087i	0.0196558	−	0.0340449i	0.875686	+	0.482881i	$0.160410\pi$
$38$	−10.2190			−1.65773
$39$		0			0
$40$			3.85904i			0.610168i
$41$	3.71620	+	6.43664i	0.580373	+	1.00523i	0.995435	+	0.0954418i	$0.0304264\pi$
$41$	3.71620	+	6.43664i	0.580373	+	1.00523i	−0.415062	+	0.909793i	$0.636240\pi$
$42$		0			0
$43$	−3.82326	+	6.62208i	−0.583041	+	1.00986i	0.412075	+	0.911150i	$0.364804\pi$
$43$	−3.82326	+	6.62208i	−0.583041	+	1.00986i	−0.995116	+	0.0987075i	$0.968529\pi$
$44$	8.91423	+	5.14663i	1.34387	+	0.775884i
$45$		0			0
$46$	4.56238	+	7.90228i	0.672686	+	1.16513i
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	0.670052	−	0.742314i	$-0.266272\pi$
$47$	−2.11042	−	3.65536i	−0.307837	−	0.533189i	−0.977889	+	0.209125i	$0.932939\pi$
$48$		0			0
$49$		0			0
$50$	5.80150	−	3.34950i	0.820457	−	0.473691i
$51$		0			0
$52$			16.2889i			2.25887i
$53$	6.07442	−	3.50707i	0.834386	−	0.481733i	−0.0209662	−	0.999780i	$-0.506674\pi$
$53$	6.07442	−	3.50707i	0.834386	−	0.481733i	0.855352	+	0.518047i	$0.173341\pi$
$54$		0			0
$55$			4.63977i			0.625627i
$56$		0			0
$57$		0			0
$58$	2.70370			0.355013
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	0.373638	+	0.927575i	$0.378110\pi$
$59$	−4.73531	+	8.20179i	−0.616484	+	1.06778i	−0.990122	+	0.140208i	$0.955223\pi$
$60$		0			0
$61$	−2.82757	+	1.63250i	−0.362033	+	0.209020i	−0.669972	−	0.742386i	$-0.733694\pi$
$61$	−2.82757	+	1.63250i	−0.362033	+	0.209020i	0.307939	+	0.951406i	$0.400361\pi$
$62$	8.52371			1.08251
$63$		0			0
$64$	13.0104			1.62630
$65$	−6.35868	+	3.67119i	−0.788698	+	0.455355i
$66$		0			0
$67$	−0.330095	+	0.571741i	−0.0403275	+	0.0698493i	−0.885485	−	0.464669i	$-0.846173\pi$
$67$	−0.330095	+	0.571741i	−0.0403275	+	0.0698493i	0.845157	+	0.534518i	$0.179507\pi$
$68$	−3.47250			−0.421103
$69$		0			0
$70$		0			0
$71$			3.82347i			0.453762i	0.973922	+	0.226881i	$0.0728529\pi$
$71$			3.82347i			0.453762i	−0.973922	+	0.226881i	$0.927147\pi$
$72$		0			0
$73$	−6.33127	+	3.65536i	−0.741020	+	0.427828i	−0.822440	−	0.568852i	$-0.807388\pi$
$73$	−6.33127	+	3.65536i	−0.741020	+	0.427828i	0.0814203	+	0.996680i	$0.474054\pi$
$74$			0.544337i			0.0632779i
$75$		0			0
$76$	12.3704	−	7.14205i	1.41898	−	0.819249i
$77$		0			0
$78$		0			0
$79$	−1.83009	−	3.16982i	−0.205902	−	0.356632i	0.744518	−	0.667602i	$-0.232679\pi$
$79$	−1.83009	−	3.16982i	−0.205902	−	0.356632i	−0.950420	+	0.310970i	$0.899346\pi$
$80$	0.171486	+	0.297022i	0.0191727	+	0.0332081i
$81$		0			0
$82$	−14.6523	−	8.45951i	−1.61808	−	0.934196i
$83$	−5.45245	+	9.44392i	−0.598484	+	1.03660i	0.394561	+	0.918870i	$0.370897\pi$
$83$	−5.45245	+	9.44392i	−0.598484	+	1.03660i	−0.993045	+	0.117735i	$0.962437\pi$
$84$		0			0
$85$	−0.782630	−	1.35556i	−0.0848882	−	0.147031i
$86$		−	17.4064i		−	1.87698i
$87$		0			0
$88$	−8.70370			−0.927817
$89$	−6.84573	+	11.8572i	−0.725646	+	1.25686i	0.233061	+	0.972462i	$0.425126\pi$
$89$	−6.84573	+	11.8572i	−0.725646	+	1.25686i	−0.958708	+	0.284394i	$0.908208\pi$
$90$		0			0
$91$		0			0
$92$	−11.0458	−	6.37731i	−1.15161	−	0.664881i
$93$		0			0
$94$	8.32102	+	4.80415i	0.858248	+	0.495510i
$95$	5.57605	+	3.21934i	0.572091	+	0.330297i
$96$		0			0
$97$	−2.69709	−	1.55716i	−0.273848	−	0.158106i	0.356787	−	0.934186i	$-0.383872\pi$
$97$	−2.69709	−	1.55716i	−0.273848	−	0.158106i	−0.630635	+	0.776080i	$0.717205\pi$
$98$		0			0
$99$		0			0
$100$	−4.68194	+	8.10936i	−0.468194	+	0.810936i
$101$	−7.08942			−0.705424			−0.352712	−	0.935732i	$-0.614740\pi$
$101$	−7.08942			−0.705424			−0.352712	+	0.935732i	$0.614740\pi$
$102$		0			0
$103$		−	1.70352i		−	0.167853i	−0.996472	−	0.0839265i	$-0.973254\pi$
$103$		−	1.70352i		−	0.167853i	0.996472	−	0.0839265i	$-0.0267461\pi$
$104$	−6.88674	−	11.9282i	−0.675300	−	1.16965i
$105$		0			0
$106$	−7.98345	+	13.8277i	−0.775421	+	1.34307i
$107$	4.27455	+	2.46791i	0.413236	+	0.238582i	0.692179	−	0.721726i	$-0.256651\pi$
$107$	4.27455	+	2.46791i	0.413236	+	0.238582i	−0.278943	+	0.960308i	$0.589984\pi$
$108$		0			0
$109$	−4.06922	−	7.04809i	−0.389760	−	0.675085i	0.602657	−	0.798001i	$-0.294109\pi$
$109$	−4.06922	−	7.04809i	−0.389760	−	0.675085i	−0.992417	+	0.122916i	$0.960776\pi$
$110$	−5.28096	−	9.14690i	−0.503520	−	0.872123i
$111$		0			0
$112$		0			0
$113$	3.39699	−	1.96125i	0.319562	−	0.184499i	−0.331635	−	0.943408i	$-0.607600\pi$
$113$	3.39699	−	1.96125i	0.319562	−	0.184499i	0.651197	+	0.758908i	$0.274267\pi$
$114$		0			0
$115$		−	5.74925i		−	0.536121i
$116$	−3.27292	+	1.88962i	−0.303883	+	0.175447i
$117$		0			0
$118$		−	21.5588i		−	1.98465i
$119$		0			0
$120$		0			0
$121$	0.535426			0.0486751
$122$	3.71620	−	6.43664i	0.336449	−	0.582746i
$123$		0			0
$124$	−10.3182	+	5.95724i	−0.926605	+	0.534976i
$125$	−11.3923			−1.01896
$126$		0			0
$127$	6.16827			0.547345			0.273673	−	0.961823i	$-0.411761\pi$
$127$	6.16827			0.547345			0.273673	+	0.961823i	$0.411761\pi$
$128$	−15.3856	+	8.88290i	−1.35991	+	0.785145i
$129$		0			0
$130$	8.35705	−	14.4748i	0.732962	−	1.26953i
$131$	−8.26275			−0.721920			−0.360960	−	0.932581i	$-0.617551\pi$
$131$	−8.26275			−0.721920			−0.360960	+	0.932581i	$0.617551\pi$
$132$		0			0
$133$		0			0
$134$		−	1.50285i		−	0.129826i
$135$		0			0
$136$	2.54287	−	1.46813i	0.218049	−	0.125891i
$137$		−	10.3481i		−	0.884096i	−0.896991	−	0.442048i	$-0.854252\pi$
$137$		−	10.3481i		−	0.884096i	0.896991	−	0.442048i	$-0.145748\pi$
$138$		0			0
$139$	−15.4589	+	8.92521i	−1.31121	+	0.757026i	−0.982296	−	0.187334i	$-0.940015\pi$
$139$	−15.4589	+	8.92521i	−1.31121	+	0.757026i	−0.328912	+	0.944361i	$0.606682\pi$
$140$		0			0
$141$		0			0
$142$	−4.35185	−	7.53762i	−0.365199	−	0.632543i
$143$	−8.28002	−	14.3414i	−0.692410	−	1.19929i
$144$		0			0
$145$	−1.47529	−	0.851761i	−0.122516	−	0.0707349i
$146$	8.32102	−	14.4124i	0.688653	−	1.19278i
$147$		0			0
$148$	−0.380438	−	0.658939i	−0.0312718	−	0.0541644i
$149$			17.5235i			1.43558i	0.696259	+	0.717790i	$0.254846\pi$
$149$			17.5235i			1.43558i	−0.696259	+	0.717790i	$0.745154\pi$
$150$		0			0
$151$	1.10069			0.0895726			0.0447863	−	0.998997i	$-0.485739\pi$
$151$	1.10069			0.0895726			0.0447863	+	0.998997i	$0.485739\pi$
$152$	−6.03911	+	10.4601i	−0.489837	+	0.848422i
$153$		0			0
$154$		0			0
$155$	−4.65103	−	2.68527i	−0.373580	−	0.215686i
$156$		0			0
$157$	−8.45150	−	4.87948i	−0.674503	−	0.389425i	0.123277	−	0.992372i	$-0.460660\pi$
$157$	−8.45150	−	4.87948i	−0.674503	−	0.389425i	−0.797781	+	0.602947i	$0.793993\pi$
$158$	7.21574	+	4.16601i	0.574053	+	0.331430i
$159$		0			0
$160$	−7.36019	−	4.24941i	−0.581874	−	0.335945i
$161$		0			0
$162$		0			0
$163$	3.61273	−	6.25742i	0.282970	−	0.490119i	−0.689145	−	0.724624i	$-0.742013\pi$
$163$	3.61273	−	6.25742i	0.282970	−	0.490119i	0.972115	+	0.234505i	$0.0753468\pi$
$164$	23.6495			1.84671
$165$		0			0
$166$		−	24.8238i		−	1.92670i
$167$	−8.65419	−	14.9895i	−0.669681	−	1.15992i	−0.977993	−	0.208637i	$-0.933097\pi$
$167$	−8.65419	−	14.9895i	−0.669681	−	1.15992i	0.308312	−	0.951285i	$-0.400236\pi$
$168$		0			0
$169$	6.60301	−	11.4367i	0.507924	−	0.879750i
$170$	3.08577	+	1.78157i	0.236668	+	0.136640i
$171$		0			0
$172$	12.1654	+	21.0711i	0.927602	+	1.60665i
$173$	0.978103	+	1.69412i	0.0743638	+	0.128802i	0.900809	−	0.434215i	$-0.142974\pi$
$173$	0.978103	+	1.69412i	0.0743638	+	0.128802i	−0.826446	+	0.563017i	$0.809641\pi$
$174$		0			0
$175$		0			0
$176$	−0.669905	+	0.386770i	−0.0504960	+	0.0291539i
$177$		0			0
$178$		−	31.1671i		−	2.33607i
$179$	−20.0933	+	11.6009i	−1.50184	+	0.867090i	−0.501846	+	0.864957i	$0.667345\pi$
$179$	−20.0933	+	11.6009i	−1.50184	+	0.867090i	−0.999998	+	0.00213247i	$0.999321\pi$
$180$		0			0
$181$			10.2744i			0.763689i	0.924226	+	0.381845i	$0.124711\pi$
$181$			10.2744i			0.763689i	−0.924226	+	0.381845i	$0.875289\pi$
$182$		0			0
$183$		0			0
$184$	10.7850			0.795077
$185$	0.171486	−	0.297022i	0.0126079	−	0.0218375i
$186$		0			0
$187$	3.05733	−	1.76515i	0.223574	−	0.129080i
$188$	−13.4305			−0.979520
$189$		0			0
$190$	−14.6569			−1.06332
$191$	19.6758	−	11.3598i	1.42369	−	0.821968i	0.427079	−	0.904215i	$-0.359543\pi$
$191$	19.6758	−	11.3598i	1.42369	−	0.821968i	0.996612	+	0.0822464i	$0.0262094\pi$
$192$		0			0
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	0.384459	+	0.923142i	$0.374388\pi$
$193$	−8.43598	+	14.6116i	−0.607235	+	1.05176i	−0.991694	+	0.128620i	$0.958945\pi$
$194$	7.08942			0.508991
$195$		0			0
$196$		0			0
$197$			8.94426i			0.637252i	0.947880	+	0.318626i	$0.103221\pi$
$197$			8.94426i			0.637252i	−0.947880	+	0.318626i	$0.896779\pi$
$198$		0			0
$199$	5.01020	−	2.89264i	0.355164	−	0.205054i	−0.311794	−	0.950150i	$-0.600930\pi$
$199$	5.01020	−	2.89264i	0.355164	−	0.205054i	0.666957	+	0.745096i	$0.267596\pi$
$200$		−	7.91784i		−	0.559876i
$201$		0			0
$202$	13.9762	−	8.06914i	0.983359	−	0.567743i
$203$		0			0
$204$		0			0
$205$	5.33009	+	9.23200i	0.372270	+	0.644791i
$206$	1.93894	+	3.35834i	0.135092	+	0.233987i
$207$		0			0
$208$	−1.06012	−	0.612058i	−0.0735058	−	0.0424386i
$209$	−7.26091	+	12.5763i	−0.502248	+	0.869918i
$210$		0			0
$211$	−12.9451	−	22.4216i	−0.891180	−	1.54357i	−0.838462	−	0.544960i	$-0.816545\pi$
$211$	−12.9451	−	22.4216i	−0.891180	−	1.54357i	−0.0527186	−	0.998609i	$-0.516789\pi$
$212$		−	22.3186i		−	1.53285i
$213$		0			0
$214$	−11.2359			−0.768067
$215$	−5.48365	+	9.49796i	−0.373982	+	0.647756i
$216$		0			0
$217$		0			0
$218$	16.0442	+	9.26312i	1.08665	+	0.627378i
$219$		0			0
$220$	12.7856	+	7.38175i	0.862003	+	0.497678i
$221$	4.83818	+	2.79332i	0.325451	+	0.187899i
$222$		0			0
$223$	−15.4827	−	8.93892i	−1.03680	−	0.598594i	−0.117871	−	0.993029i	$-0.537607\pi$
$223$	−15.4827	−	8.93892i	−1.03680	−	0.598594i	−0.918924	+	0.394435i	$0.870940\pi$
$224$		0			0
$225$		0			0
$226$	−4.46457	+	7.73287i	−0.296979	+	0.514383i
$227$	10.9673			0.727925			0.363963	−	0.931414i	$-0.381424\pi$
$227$	10.9673			0.727925			0.363963	+	0.931414i	$0.381424\pi$
$228$		0			0
$229$			19.4393i			1.28459i	0.766459	+	0.642293i	$0.222017\pi$
$229$			19.4393i			1.28459i	−0.766459	+	0.642293i	$0.777983\pi$
$230$	6.54377	+	11.3341i	0.431483	+	0.747351i
$231$		0			0
$232$	1.59781	−	2.76748i	0.104901	−	0.181694i
$233$	2.54639	+	1.47016i	0.166819	+	0.0963131i	0.581085	−	0.813843i	$-0.302628\pi$
$233$	2.54639	+	1.47016i	0.166819	+	0.0963131i	−0.414266	+	0.910156i	$0.635962\pi$
$234$		0			0
$235$	−3.02696	−	5.24284i	−0.197457	−	0.342005i
$236$	15.0675	+	26.0976i	0.980809	+	1.69881i
$237$		0			0
$238$		0			0
$239$	10.7255	−	6.19234i	0.693772	−	0.400549i	−0.111252	−	0.993792i	$-0.535486\pi$
$239$	10.7255	−	6.19234i	0.693772	−	0.400549i	0.805023	+	0.593243i	$0.202153\pi$
$240$		0			0
$241$			13.5034i			0.869828i	0.900472	+	0.434914i	$0.143221\pi$
$241$			13.5034i			0.869828i	−0.900472	+	0.434914i	$0.856779\pi$
$242$	−1.05555	+	0.609419i	−0.0678530	+	0.0391750i
$243$		0			0
$244$			10.3890i			0.665089i
$245$		0			0
$246$		0			0
$247$	−22.9806			−1.46222
$248$	5.03727	−	8.72481i	0.319867	−	0.554026i
$249$		0			0
$250$	22.4589	−	12.9666i	1.42042	−	0.820082i
$251$	7.51441			0.474305			0.237153	−	0.971472i	$-0.423786\pi$
$251$	7.51441			0.474305			0.237153	+	0.971472i	$0.423786\pi$
$252$		0			0
$253$	12.9669			0.815222
$254$	−12.1602	+	7.02069i	−0.762998	+	0.440517i
$255$		0			0
$256$	7.21053	−	12.4890i	0.450658	−	0.780563i
$257$	−7.75576			−0.483791			−0.241895	−	0.970302i	$-0.577769\pi$
$257$	−7.75576			−0.483791			−0.241895	+	0.970302i	$0.577769\pi$
$258$		0			0
$259$		0			0
$260$			23.3630i			1.44891i
$261$		0			0
$262$	16.2893	−	9.40462i	1.00635	−	0.581019i
$263$		−	13.9866i		−	0.862449i	−0.902245	−	0.431224i	$-0.858082\pi$
$263$		−	13.9866i		−	0.862449i	0.902245	−	0.431224i	$-0.141918\pi$
$264$		0			0
$265$	8.71246	−	5.03014i	0.535202	−	0.308999i
$266$		0			0
$267$		0			0
$268$	1.05034	+	1.81925i	0.0641599	+	0.111128i
$269$	12.9160	+	22.3712i	0.787505	+	1.36400i	0.927491	+	0.373846i	$0.121961\pi$
$269$	12.9160	+	22.3712i	0.787505	+	1.36400i	−0.139986	+	0.990154i	$0.544706\pi$
$270$		0			0
$271$	14.4225	+	8.32686i	0.876107	+	0.505821i	0.869373	−	0.494157i	$-0.164523\pi$
$271$	14.4225	+	8.32686i	0.876107	+	0.505821i	0.00673411	+	0.999977i	$0.497856\pi$
$272$	0.130480	−	0.225997i	0.00791148	−	0.0137031i
$273$		0			0
$274$	11.7781	+	20.4003i	0.711542	+	1.23243i
$275$		−	9.51973i		−	0.574061i
$276$		0			0
$277$	31.4088			1.88717			0.943585	−	0.331130i	$-0.107430\pi$
$277$	31.4088			1.88717			0.943585	+	0.331130i	$0.107430\pi$
$278$	20.3172	−	35.1905i	1.21855	−	2.11059i
$279$		0			0
$280$		0			0
$281$	−8.10464	−	4.67922i	−0.483483	−	0.279139i	0.238384	−	0.971171i	$-0.423382\pi$
$281$	−8.10464	−	4.67922i	−0.483483	−	0.279139i	−0.721867	+	0.692032i	$0.756716\pi$
$282$		0			0
$283$	−13.6603	−	7.88676i	−0.812018	−	0.468819i	0.0356380	−	0.999365i	$-0.488654\pi$
$283$	−13.6603	−	7.88676i	−0.812018	−	0.468819i	−0.847656	+	0.530546i	$0.821987\pi$
$284$	10.5361	+	6.08303i	0.625203	+	0.360961i
$285$		0			0
$286$	32.6466	+	18.8485i	1.93044	+	1.11454i
$287$		0			0
$288$		0			0
$289$	7.90451	−	13.6910i	0.464971	−	0.805354i
$290$	3.87788			0.227717
$291$		0			0
$292$			23.2623i			1.36132i
$293$	12.4287	+	21.5271i	0.726090	+	1.25762i	0.958524	+	0.285013i	$0.0919978\pi$
$293$	12.4287	+	21.5271i	0.726090	+	1.25762i	−0.232434	+	0.972612i	$0.574669\pi$
$294$		0			0
$295$	−6.79179	+	11.7637i	−0.395433	+	0.684911i
$296$	0.557180	+	0.321688i	0.0323854	+	0.0186977i
$297$		0			0
$298$	−19.9451	−	34.5460i	−1.15539	−	2.00120i
$299$	10.2600	+	17.7708i	0.593349	+	1.02771i
$300$		0			0
$301$		0			0
$302$	−2.16991	+	1.25280i	−0.124864	+	0.0720903i
$303$		0			0
$304$			1.07345i			0.0615666i
$305$	−4.05555	+	2.34147i	−0.232220	+	0.134072i
$306$		0			0
$307$			18.8878i			1.07799i	0.842310	+	0.538993i	$0.181195\pi$
$307$			18.8878i			1.07799i	−0.842310	+	0.538993i	$0.818805\pi$
$308$		0			0
$309$		0			0
$310$	12.2255			0.694359
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	−0.730953	−	0.682428i	$-0.760924\pi$
$311$	3.97716	−	6.88864i	0.225524	−	0.390619i	0.956476	+	0.291809i	$0.0942573\pi$
$312$		0			0
$313$	9.64210	−	5.56687i	0.545004	−	0.314658i	−0.202101	−	0.979365i	$-0.564777\pi$
$313$	9.64210	−	5.56687i	0.545004	−	0.314658i	0.747104	+	0.664707i	$0.231444\pi$
$314$	22.2152			1.25367
$315$		0			0
$316$	−11.6465			−0.655168
$317$	−20.1380	+	11.6267i	−1.13107	+	0.653021i	−0.944203	−	0.329365i	$-0.893165\pi$
$317$	−20.1380	+	11.6267i	−1.13107	+	0.653021i	−0.186863	+	0.982386i	$0.559832\pi$
$318$		0			0
$319$	1.92107	−	3.32738i	0.107559	−	0.186298i
$320$	18.6607			1.04316
$321$		0			0
$322$		0			0
$323$		−	4.89904i		−	0.272590i
$324$		0			0
$325$	13.0465	−	7.53242i	0.723691	−	0.417823i
$326$			16.4479i			0.910967i
$327$		0			0
$328$	−17.3182	+	9.99866i	−0.956237	+	0.552084i
$329$		0			0
$330$		0			0
$331$	9.57962	+	16.5924i	0.526544	+	0.912000i	0.999522	+	0.0309261i	$0.00984566\pi$
$331$	9.57962	+	16.5924i	0.526544	+	0.912000i	−0.472978	+	0.881074i	$0.656821\pi$
$332$	17.3494	+	30.0500i	0.952171	+	1.64921i
$333$		0			0
$334$	34.1219	+	19.7003i	1.86707	+	1.07795i
$335$	−0.473451	+	0.820041i	−0.0258674	+	0.0448036i
$336$		0			0
$337$	14.2781	+	24.7304i	0.777779	+	1.34715i	0.933219	+	0.359307i	$0.116987\pi$
$337$	14.2781	+	24.7304i	0.777779	+	1.34715i	−0.155441	+	0.987845i	$0.549680\pi$
$338$			30.0620i			1.63516i
$339$		0			0
$340$	−4.98057			−0.270109
$341$	6.05638	−	10.4900i	0.327971	−	0.568063i
$342$		0			0
$343$		0			0
$344$	−17.8171	−	10.2867i	−0.960634	−	0.554622i
$345$		0			0
$346$	−3.85648	−	2.22654i	−0.207326	−	0.119700i
$347$	2.56690	+	1.48200i	0.137798	+	0.0795578i	0.567314	−	0.823501i	$-0.307983\pi$
$347$	2.56690	+	1.48200i	0.137798	+	0.0795578i	−0.429516	+	0.903059i	$0.641316\pi$
$348$		0			0
$349$	23.3885	+	13.5034i	1.25196	+	0.722818i	0.971498	−	0.237048i	$-0.0761797\pi$
$349$	23.3885	+	13.5034i	1.25196	+	0.722818i	0.280460	+	0.959866i	$0.409513\pi$
$350$		0			0
$351$		0			0
$352$	9.58414	−	16.6002i	0.510836	−	0.884794i
$353$	−29.6476			−1.57798			−0.788990	−	0.614405i	$-0.789396\pi$
$353$	−29.6476			−1.57798			−0.788990	+	0.614405i	$0.789396\pi$
$354$		0			0
$355$			5.48395i			0.291058i
$356$	21.7827	+	37.7288i	1.15448	+	1.99962i
$357$		0			0
$358$	26.4081	−	45.7401i	1.39571	−	2.41744i
$359$	−21.3268	−	12.3130i	−1.12559	−	0.649858i	−0.182766	−	0.983157i	$-0.558505\pi$
$359$	−21.3268	−	12.3130i	−1.12559	−	0.649858i	−0.942821	+	0.333299i	$0.891838\pi$
$360$		0			0
$361$	0.576055	+	0.997756i	0.0303187	+	0.0525135i
$362$	−11.6943	−	20.2550i	−0.614636	−	1.06458i
$363$		0			0
$364$		0			0
$365$	−9.08087	+	5.24284i	−0.475314	+	0.274423i
$366$		0			0
$367$		−	5.60720i		−	0.292694i	−0.989233	−	0.146347i	$-0.953248\pi$
$367$		−	5.60720i		−	0.292694i	0.989233	−	0.146347i	$-0.0467515\pi$
$368$	0.830095	−	0.479256i	0.0432717	−	0.0249829i
$369$		0			0
$370$			0.780736i			0.0405885i
$371$		0			0
$372$		0			0
$373$	−3.73353			−0.193315			−0.0966574	−	0.995318i	$-0.530815\pi$
$373$	−3.73353			−0.193315			−0.0966574	+	0.995318i	$0.530815\pi$
$374$	−4.01816	+	6.95966i	−0.207774	+	0.359876i
$375$		0			0
$376$	9.83498	−	5.67823i	0.507200	−	0.292832i
$377$	6.08012			0.313142
$378$		0			0
$379$	−30.4419			−1.56369			−0.781847	−	0.623470i	$-0.785722\pi$
$379$	−30.4419			−1.56369			−0.781847	+	0.623470i	$0.785722\pi$
$380$	17.7427	−	10.2437i	0.910181	−	0.525493i
$381$		0			0
$382$	−25.8594	+	44.7897i	−1.32308	+	2.29164i
$383$	16.9850			0.867894			0.433947	−	0.900938i	$-0.357121\pi$
$383$	16.9850			0.867894			0.433947	+	0.900938i	$0.357121\pi$
$384$		0			0
$385$		0			0
$386$		−	38.4071i		−	1.95487i
$387$		0			0
$388$	−8.58198	+	4.95481i	−0.435684	+	0.251542i
$389$			10.8924i			0.552267i	0.961119	+	0.276134i	$0.0890532\pi$
$389$			10.8924i			0.552267i	−0.961119	+	0.276134i	$0.910947\pi$
$390$		0			0
$391$	−3.78840	+	2.18724i	−0.191588	+	0.110613i
$392$		0			0
$393$		0			0
$394$	−10.1803	−	17.6328i	−0.512877	−	0.888328i
$395$	−2.62488	−	4.54643i	−0.132072	−	0.228756i
$396$		0			0
$397$	19.3154	+	11.1518i	0.969412	+	0.559690i	0.899057	−	0.437832i	$-0.144253\pi$
$397$	19.3154	+	11.1518i	0.969412	+	0.559690i	0.0703551	+	0.997522i	$0.477587\pi$
$398$	−6.58477	+	11.4052i	−0.330065	+	0.571689i
$399$		0			0
$400$	−0.351848	−	0.609419i	−0.0175924	−	0.0304710i
$401$		−	24.0818i		−	1.20259i	−0.799029	−	0.601293i	$-0.794653\pi$
$401$		−	24.0818i		−	1.20259i	0.799029	−	0.601293i	$-0.205347\pi$
$402$		0			0
$403$	19.1683			0.954840
$404$	−11.2791	+	19.5359i	−0.561155	+	0.971949i
$405$		0			0
$406$		0			0
$407$	0.669905	+	0.386770i	0.0332060	+	0.0191715i
$408$		0			0
$409$	22.8191	+	13.1746i	1.12833	+	0.651443i	0.943515	−	0.331330i	$-0.107497\pi$
$409$	22.8191	+	13.1746i	1.12833	+	0.651443i	0.184817	+	0.982773i	$0.440831\pi$
$410$	−21.0156	−	12.1334i	−1.03789	−	0.599224i
$411$		0			0
$412$	−4.69430	−	2.71026i	−0.231272	−	0.133525i
$413$		0			0
$414$		0			0
$415$	−7.82038	+	13.5453i	−0.383887	+	0.664912i
$416$	30.3335			1.48722
$417$		0			0
$418$		−	33.0573i		−	1.61689i
$419$	−16.1761	−	28.0178i	−0.790252	−	1.36876i	−0.925811	−	0.377988i	$-0.876616\pi$
$419$	−16.1761	−	28.0178i	−0.790252	−	1.36876i	0.135558	−	0.990769i	$-0.456717\pi$
$420$		0			0
$421$	−5.54746	+	9.60849i	−0.270367	+	0.468289i	−0.968956	−	0.247234i	$-0.920478\pi$
$421$	−5.54746	+	9.60849i	−0.270367	+	0.468289i	0.698589	+	0.715523i	$0.253812\pi$
$422$	51.0404	+	29.4682i	2.48461	+	1.43449i
$423$		0			0
$424$	9.43598	+	16.3436i	0.458252	+	0.793716i
$425$	1.60577	+	2.78128i	0.0778914	+	0.134912i
$426$		0			0
$427$		0			0
$428$	13.6014	−	7.85276i	0.657447	−	0.379577i
$429$		0			0
$430$		−	24.9658i		−	1.20396i
$431$	14.1202	−	8.15233i	0.680149	−	0.392684i	−0.119762	−	0.992803i	$-0.538213\pi$
$431$	14.1202	−	8.15233i	0.680149	−	0.392684i	0.799911	+	0.600119i	$0.204880\pi$
$432$		0			0
$433$		−	12.5359i		−	0.602438i	−0.953555	−	0.301219i	$-0.902606\pi$
$433$		−	12.5359i		−	0.602438i	0.953555	−	0.301219i	$-0.0973936\pi$
$434$		0			0
$435$		0			0
$436$	−25.8960			−1.24020
$437$	8.99716	−	15.5835i	0.430393	−	0.745462i
$438$		0			0
$439$	−16.1276	+	9.31127i	−0.769728	+	0.444403i	−0.832778	−	0.553608i	$-0.813251\pi$
$439$	−16.1276	+	9.31127i	−0.769728	+	0.444403i	0.0630496	+	0.998010i	$0.479917\pi$
$440$	−12.4836			−0.595132
$441$		0			0
$442$	−12.7174			−0.604904
$443$	4.11436	−	2.37543i	0.195479	−	0.112860i	−0.399066	−	0.916922i	$-0.630666\pi$
$443$	4.11436	−	2.37543i	0.195479	−	0.112860i	0.594545	+	0.804062i	$0.297332\pi$
$444$		0			0
$445$	−9.81875	+	17.0066i	−0.465453	+	0.806189i
$446$	40.6969			1.92705
$447$		0			0
$448$		0			0
$449$			16.2393i			0.766379i	0.923670	+	0.383189i	$0.125174\pi$
$449$			16.2393i			0.766379i	−0.923670	+	0.383189i	$0.874826\pi$
$450$		0			0
$451$	−20.8219	+	12.0215i	−0.980465	+	0.566072i
$452$		−	12.4812i		−	0.587066i
$453$		0			0
$454$	−21.6210	+	12.4829i	−1.01473	+	0.585852i
$455$		0			0
$456$		0			0
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	0.925376	−	0.379050i	$-0.123749\pi$
$457$	2.87360	+	4.97722i	0.134421	+	0.232825i	−0.790955	+	0.611874i	$0.790416\pi$
$458$	−22.1257	−	38.3228i	−1.03387	−	1.79071i
$459$		0			0
$460$	−15.8429	−	9.14690i	−0.738679	−	0.426476i
$461$	18.1346	−	31.4101i	0.844613	−	1.46291i	−0.0413440	−	0.999145i	$-0.513164\pi$
$461$	18.1346	−	31.4101i	0.844613	−	1.46291i	0.885957	−	0.463768i	$-0.153503\pi$
$462$		0			0
$463$	14.6202	+	25.3230i	0.679461	+	1.17686i	0.975144	+	0.221574i	$0.0711195\pi$
$463$	14.6202	+	25.3230i	0.679461	+	1.17686i	−0.295683	+	0.955286i	$0.595547\pi$
$464$		−	0.284010i		−	0.0131848i
$465$		0			0
$466$	−6.69329			−0.310061
$467$	−1.32107	+	2.28817i	−0.0611320	+	0.105884i	−0.894972	−	0.446123i	$-0.852804\pi$
$467$	−1.32107	+	2.28817i	−0.0611320	+	0.105884i	0.833840	+	0.552007i	$0.186138\pi$
$468$		0			0
$469$		0			0
$470$	11.9347	+	6.89053i	0.550508	+	0.317836i
$471$		0			0
$472$	−22.0674	−	12.7406i	−1.01574	−	0.586435i
$473$	−21.4218	−	12.3679i	−0.984973	−	0.568675i
$474$		0			0
$475$	−11.4408	−	6.60532i	−0.524938	−	0.303073i
$476$		0			0
$477$		0			0
$478$	−14.0962	+	24.4153i	−0.644744	+	1.11673i
$479$	31.0819			1.42017			0.710083	−	0.704118i	$-0.248657\pi$
$479$	31.0819			1.42017			0.710083	+	0.704118i	$0.248657\pi$
$480$		0			0
$481$			1.22412i			0.0558149i
$482$	−15.3694	−	26.6207i	−0.700059	−	1.21254i
$483$		0			0
$484$	0.851848	−	1.47544i	0.0387204	−	0.0670657i
$485$	−3.86840	−	2.23342i	−0.175655	−	0.101414i
$486$		0			0
$487$	−17.4360	−	30.2000i	−0.790100	−	1.36849i	−0.925905	−	0.377757i	$-0.876695\pi$
$487$	−17.4360	−	30.2000i	−0.790100	−	1.36849i	0.135805	−	0.990736i	$-0.456638\pi$
$488$	−4.39234	−	7.60775i	−0.198832	−	0.344387i
$489$		0			0
$490$		0			0
$491$	22.6758	−	13.0919i	1.02334	−	0.590828i	0.108273	−	0.994121i	$-0.465468\pi$
$491$	22.6758	−	13.0919i	1.02334	−	0.590828i	0.915071	+	0.403293i	$0.132134\pi$
$492$		0			0
$493$			1.29617i			0.0583766i
$494$	45.3041	−	26.1563i	2.03833	−	1.17683i
$495$		0			0
$496$		−	0.895374i		−	0.0402035i
$497$		0			0
$498$		0			0
$499$	12.4782			0.558603			0.279302	−	0.960203i	$-0.409897\pi$
$499$	12.4782			0.558603			0.279302	+	0.960203i	$0.409897\pi$
$500$	−18.1248	+	31.3931i	−0.810566	+	1.40394i
$501$		0			0
$502$	−14.8140	+	8.55285i	−0.661180	+	0.381733i
$503$	−37.8479			−1.68756			−0.843778	−	0.536693i	$-0.819673\pi$
$503$	−37.8479			−1.68756			−0.843778	+	0.536693i	$0.819673\pi$
$504$		0			0
$505$	−10.1683			−0.452482
$506$	−25.5631	+	14.7588i	−1.13642	+	0.656111i
$507$		0			0
$508$	9.81354	−	16.9976i	0.435406	−	0.754145i
$509$	−35.3847			−1.56840			−0.784200	−	0.620508i	$-0.786926\pi$
$509$	−35.3847			−1.56840			−0.784200	+	0.620508i	$0.786926\pi$
$510$		0			0
$511$		0			0
$512$		−	2.70367i		−	0.119486i
$513$		0			0
$514$	15.2898	−	8.82756i	0.674403	−	0.389367i
$515$		−	2.44334i		−	0.107666i
$516$		0			0
$517$	11.8247	−	6.82701i	0.520051	−	0.300252i
$518$		0			0
$519$		0			0
$520$	−9.87756	−	17.1084i	−0.433160	−	0.750255i
$521$	1.15939	+	2.00813i	0.0507940	+	0.0879777i	0.890304	−	0.455366i	$-0.150491\pi$
$521$	1.15939	+	2.00813i	0.0507940	+	0.0879777i	−0.839511	+	0.543343i	$0.817158\pi$
$522$		0			0
$523$	−17.4799	−	10.0920i	−0.764341	−	0.441293i	0.0665110	−	0.997786i	$-0.478813\pi$
$523$	−17.4799	−	10.0920i	−0.764341	−	0.441293i	−0.830852	+	0.556493i	$0.812147\pi$
$524$	−13.1458	+	22.7692i	−0.574277	+	0.994677i
$525$		0			0
$526$	15.9194	+	27.5733i	0.694120	+	1.20225i
$527$			4.08632i			0.178003i
$528$		0			0
$529$	6.93242			0.301409
$530$	−11.4506	+	19.8329i	−0.497380	+	0.861488i
$531$		0			0
$532$		0			0
$533$	−32.9503	−	19.0239i	−1.42724	−	0.824016i
$534$		0			0
$535$	6.13093	+	3.53970i	0.265063	+	0.153034i
$536$	−1.53831	−	0.888141i	−0.0664447	−	0.0383618i
$537$		0			0
$538$	−50.9256	−	29.4019i	−2.19556	−	1.26761i
$539$		0			0
$540$		0			0
$541$	11.3856	−	19.7205i	0.489507	−	0.847851i	−0.510420	−	0.859925i	$-0.670510\pi$
$541$	11.3856	−	19.7205i	0.489507	−	0.847851i	0.999927	+	0.0120743i	$0.00384346\pi$
$542$	−37.9103			−1.62839
$543$		0			0
$544$			6.46655i			0.277251i
$545$	−5.83643	−	10.1090i	−0.250005	−	0.433022i
$546$		0			0
$547$	14.7918	−	25.6201i	0.632451	−	1.09544i	−0.354598	−	0.935019i	$-0.615382\pi$
$547$	14.7918	−	25.6201i	0.632451	−	1.09544i	0.987049	−	0.160419i	$-0.0512845\pi$
$548$	−28.5156	−	16.4635i	−1.21813	−	0.703286i
$549$		0			0
$550$	10.8353	+	18.7673i	0.462019	+	0.800240i
$551$	−2.66589	−	4.61745i	−0.113571	−	0.196710i
$552$		0			0
$553$		0			0
$554$	−61.9196	+	35.7493i	−2.63071	+	1.51884i
$555$		0			0
$556$			56.7990i			2.40881i
$557$	−4.08250	+	2.35703i	−0.172981	+	0.0998707i	−0.583991	−	0.811760i	$-0.698510\pi$
$557$	−4.08250	+	2.35703i	−0.172981	+	0.0998707i	0.411010	+	0.911631i	$0.365176\pi$
$558$		0			0
$559$		−	39.1439i		−	1.65561i
$560$		0			0
$561$		0			0
$562$	21.3034			0.898631
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	−0.419601	−	0.907709i	$-0.637830\pi$
$563$	13.6742	−	23.6844i	0.576299	−	0.998179i	0.995899	−	0.0904697i	$-0.0288368\pi$
$564$		0			0
$565$	4.87226	−	2.81300i	0.204977	−	0.118344i
$566$	35.9066			1.50927
$567$		0			0
$568$	−10.2873			−0.431645
$569$	20.4018	−	11.7790i	0.855288	−	0.493801i	−0.00714355	−	0.999974i	$-0.502274\pi$
$569$	20.4018	−	11.7790i	0.855288	−	0.493801i	0.862432	+	0.506174i	$0.168941\pi$
$570$		0			0
$571$	−9.59385	+	16.6170i	−0.401490	+	0.695401i	−0.993906	−	0.110231i	$-0.964841\pi$
$571$	−9.59385	+	16.6170i	−0.401490	+	0.695401i	0.592416	+	0.805632i	$0.298174\pi$
$572$	−52.6931			−2.20321
$573$		0			0
$574$		0			0
$575$			11.7961i			0.491932i
$576$		0			0
$577$	1.93481	−	1.11706i	0.0805472	−	0.0465039i	−0.459185	−	0.888340i	$-0.651859\pi$
$577$	1.93481	−	1.11706i	0.0805472	−	0.0465039i	0.539733	+	0.841836i	$0.318525\pi$
$578$			35.9875i			1.49688i
$579$		0			0
$580$	−4.69430	+	2.71026i	−0.194920	+	0.112537i
$581$		0			0
$582$		0			0
$583$	11.3450	+	19.6501i	0.469862	+	0.813826i
$584$	−9.83498	−	17.0347i	−0.406974	−	0.704900i
$585$		0			0
$586$	−49.0040	−	28.2925i	−2.02434	−	1.16875i
$587$	12.9883	−	22.4963i	0.536083	−	0.928522i	−0.463028	−	0.886344i	$-0.653237\pi$
$587$	12.9883	−	22.4963i	0.536083	−	0.928522i	0.999110	−	0.0421784i	$-0.0134298\pi$
$588$		0			0
$589$	−8.40451	−	14.5570i	−0.346302	−	0.599813i
$590$		−	30.9215i		−	1.27302i
$591$		0			0
$592$	0.0571799			0.00235008
$593$	2.85877	−	4.95153i	0.117396	−	0.203335i	−0.801339	−	0.598210i	$-0.795879\pi$
$593$	2.85877	−	4.95153i	0.117396	−	0.203335i	0.918735	+	0.394875i	$0.129212\pi$
$594$		0			0
$595$		0			0
$596$	48.2885	+	27.8794i	1.97797	+	1.14198i
$597$		0			0
$598$	−40.4532	−	23.3557i	−1.65425	−	0.955084i
$599$	21.8662	+	12.6245i	0.893429	+	0.515822i	0.875063	−	0.484010i	$-0.160820\pi$
$599$	21.8662	+	12.6245i	0.893429	+	0.515822i	0.0183665	+	0.999831i	$0.494153\pi$
$600$		0			0
$601$	40.2546	+	23.2410i	1.64202	+	0.948021i	0.980114	+	0.198435i	$0.0635858\pi$
$601$	40.2546	+	23.2410i	1.64202	+	0.948021i	0.661907	+	0.749586i	$0.269748\pi$
$602$		0			0
$603$		0			0
$604$	1.75116	−	3.03310i	0.0712538	−	0.123415i
$605$	0.767955			0.0312218
$606$		0			0
$607$		−	7.03681i		−	0.285615i	−0.989750	−	0.142808i	$-0.954387\pi$
$607$		−	7.03681i		−	0.285615i	0.989750	−	0.142808i	$-0.0456130\pi$
$608$	−13.3000	−	23.0363i	−0.539387	−	0.934246i
$609$		0			0
$610$	5.33009	−	9.23200i	0.215809	−	0.373793i
$611$	18.7125	+	10.8036i	0.757025	+	0.437069i
$612$		0			0
$613$	−3.27128	−	5.66602i	−0.132126	−	0.228849i	0.792370	−	0.610041i	$-0.208847\pi$
$613$	−3.27128	−	5.66602i	−0.132126	−	0.228849i	−0.924496	+	0.381192i	$0.875514\pi$
$614$	−21.4980	−	37.2357i	−0.867590	−	1.50271i
$615$		0			0
$616$		0			0
$617$	30.0043	−	17.3230i	1.20793	−	0.697396i	0.245620	−	0.969366i	$-0.421008\pi$
$617$	30.0043	−	17.3230i	1.20793	−	0.697396i	0.962306	+	0.271970i	$0.0876751\pi$
$618$		0			0
$619$		−	16.9825i		−	0.682583i	−0.939958	−	0.341291i	$-0.889136\pi$
$619$		−	16.9825i		−	0.682583i	0.939958	−	0.341291i	$-0.110864\pi$
$620$	−14.7993	+	8.54439i	−0.594355	+	0.343151i
$621$		0			0
$622$			18.1071i			0.726029i
$623$		0			0
$624$		0			0
$625$	−1.62571			−0.0650284
$626$	−12.6724	+	21.9492i	−0.506489	+	0.877265i
$627$		0			0
$628$	−26.8922	+	15.5262i	−1.07312	+	0.619564i
$629$	−0.260959			−0.0104051
$630$		0			0
$631$	26.2438			1.04475			0.522374	−	0.852716i	$-0.325047\pi$
$631$	26.2438			1.04475			0.522374	+	0.852716i	$0.325047\pi$
$632$	8.52859	−	4.92398i	0.339249	−	0.195866i
$633$		0			0
$634$	26.4669	−	45.8420i	1.05113	−	1.82062i
$635$	8.84707			0.351085
$636$		0			0
$637$		0			0
$638$			8.74619i			0.346265i
$639$		0			0
$640$	−22.0674	+	12.7406i	−0.872292	+	0.503618i
$641$			19.0631i			0.752949i	0.926427	+	0.376474i	$0.122864\pi$
$641$			19.0631i			0.752949i	−0.926427	+	0.376474i	$0.877136\pi$
$642$		0			0
$643$	15.3447	−	8.85928i	0.605136	−	0.349376i	−0.165923	−	0.986139i	$-0.553060\pi$
$643$	15.3447	−	8.85928i	0.605136	−	0.349376i	0.771060	+	0.636763i	$0.219727\pi$
$644$		0			0
$645$		0			0
$646$	5.57605	+	9.65801i	0.219387	+	0.379989i
$647$	−10.8951	−	18.8709i	−0.428330	−	0.741890i	0.568395	−	0.822756i	$-0.307565\pi$
$647$	−10.8951	−	18.8709i	−0.428330	−	0.741890i	−0.996725	+	0.0808661i	$0.974231\pi$
$648$		0			0
$649$	−26.5320	−	15.3182i	−1.04147	−	0.601294i
$650$	−17.1467	+	29.6990i	−0.672549	+	1.16489i
$651$		0			0
$652$	−11.4955	−	19.9108i	−0.450198	−	0.779766i
$653$			15.1095i			0.591281i	0.955299	+	0.295640i	$0.0955330\pi$
$653$			15.1095i			0.591281i	−0.955299	+	0.295640i	$0.904467\pi$
$654$		0			0
$655$	−11.8512			−0.463063
$656$	−0.888629	+	1.53915i	−0.0346951	+	0.0600938i
$657$		0			0
$658$		0			0
$659$	27.1850	+	15.6952i	1.05898	+	0.611400i	0.925149	−	0.379605i	$-0.123940\pi$
$659$	27.1850	+	15.6952i	1.05898	+	0.611400i	0.133827	+	0.991005i	$0.457273\pi$
$660$		0			0
$661$	37.8554	+	21.8558i	1.47240	+	0.850093i	0.999518	−	0.0310314i	$-0.00987918\pi$
$661$	37.8554	+	21.8558i	1.47240	+	0.850093i	0.472885	+	0.881124i	$0.343213\pi$
$662$	−37.7707	−	21.8069i	−1.46800	−	0.847551i
$663$		0			0
$664$	−25.4095	−	14.6702i	−0.986078	−	0.569312i
$665$		0			0
$666$		0			0
$667$	−2.38044	+	4.12304i	−0.0921709	+	0.159645i
$668$	−55.0743			−2.13089
$669$		0			0
$670$		−	2.15552i		−	0.0832749i
$671$	−5.28096	−	9.14690i	−0.203869	−	0.353112i
$672$		0			0
$673$	−4.60589	+	7.97763i	−0.177544	+	0.307515i	−0.941039	−	0.338299i	$-0.890149\pi$
$673$	−4.60589	+	7.97763i	−0.177544	+	0.307515i	0.763495	+	0.645814i	$0.223482\pi$
$674$	−56.2960	−	32.5025i	−2.16844	−	1.25195i
$675$		0			0
$676$	−21.0104	−	36.3911i	−0.808092	−	1.39966i
$677$	11.4194	+	19.7789i	0.438882	+	0.760165i	0.997604	−	0.0691899i	$-0.0220414\pi$
$677$	11.4194	+	19.7789i	0.438882	+	0.760165i	−0.558722	+	0.829355i	$0.688708\pi$
$678$		0			0
$679$		0			0
$680$	3.64721	−	2.10571i	0.139864	−	0.0807505i
$681$		0			0
$682$			27.5733i			1.05584i
$683$	−29.6030	+	17.0913i	−1.13273	+	0.653981i	−0.944619	−	0.328168i	$-0.893569\pi$
$683$	−29.6030	+	17.0913i	−1.13273	+	0.653981i	−0.188108	+	0.982148i	$0.560236\pi$
$684$		0			0
$685$		−	14.8421i		−	0.567088i
$686$		0			0
$687$		0			0
$688$	−1.82846			−0.0697094
$689$	−17.9533	+	31.0961i	−0.683967	+	1.18467i
$690$		0			0
$691$	0.224082	−	0.129374i	0.00852446	−	0.00492160i	−0.495732	−	0.868476i	$-0.665100\pi$
$691$	0.224082	−	0.129374i	0.00852446	−	0.00492160i	0.504256	+	0.863554i	$0.331767\pi$
$692$	6.22453			0.236621
$693$		0			0
$694$	−6.74720			−0.256120
$695$	−22.1725	+	12.8013i	−0.841052	+	0.485582i
$696$		0			0
$697$	4.05555	−	7.02441i	0.153615	−	0.266069i
$698$	−61.4778			−2.32697
$699$		0			0
$700$		0			0
$701$		−	5.16189i		−	0.194962i	−0.995237	−	0.0974810i	$-0.968921\pi$
$701$		−	5.16189i		−	0.194962i	0.995237	−	0.0974810i	$-0.0310785\pi$
$702$		0			0
$703$	0.929636	−	0.536725i	0.0350619	−	0.0202430i
$704$			42.0873i			1.58623i
$705$		0			0
$706$	58.4475	−	33.7447i	2.19970	−	1.27000i
$707$		0			0
$708$		0			0
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	0.556602	−	0.830780i	$-0.312105\pi$
$709$	−11.7472	−	20.3468i	−0.441175	−	0.764138i	−0.997777	+	0.0666412i	$0.978772\pi$
$710$	−6.24180	−	10.8111i	−0.234251	−	0.405734i
$711$		0			0
$712$	−31.9024	−	18.4189i	−1.19559	−	0.690276i
$713$	−7.50460	+	12.9984i	−0.281050	+	0.486792i
$714$		0			0
$715$	−11.8759	−	20.5697i	−0.444134	−	0.769263i
$716$			73.8266i			2.75903i
$717$		0			0
$718$	56.0586			2.09209
$719$	−5.07828	+	8.79584i	−0.189388	+	0.328029i	−0.945046	−	0.326937i	$-0.893984\pi$
$719$	−5.07828	+	8.79584i	−0.189388	+	0.328029i	0.755658	+	0.654966i	$0.227317\pi$
$720$		0			0
$721$		0			0
$722$	−2.27128	−	1.31132i	−0.0845283	−	0.0488024i
$723$		0			0
$724$	28.3126	+	16.3463i	1.05223	+	0.607504i
$725$	3.02696	+	1.74761i	0.112418	+	0.0649047i
$726$		0			0
$727$	−5.74874	−	3.31904i	−0.213209	−	0.123096i	0.389593	−	0.920987i	$-0.372616\pi$
$727$	−5.74874	−	3.31904i	−0.213209	−	0.123096i	−0.602802	+	0.797891i	$0.705949\pi$
$728$		0			0
$729$		0			0
$730$	11.9347	−	20.6716i	0.441725	−	0.765089i
$731$	8.34476			0.308642
$732$		0			0
$733$			6.00594i			0.221834i	0.993830	+	0.110917i	$0.0353788\pi$
$733$			6.00594i			0.221834i	−0.993830	+	0.110917i	$0.964621\pi$
$734$	6.38209	+	11.0541i	0.235567	+	0.408014i
$735$		0			0
$736$	−11.8759	+	20.5697i	−0.437752	+	0.758209i
$737$	−1.84953	−	1.06782i	−0.0681281	−	0.0393338i
$738$		0			0
$739$	7.81930	+	13.5434i	0.287638	+	0.498203i	0.973245	−	0.229768i	$-0.0737968\pi$
$739$	7.81930	+	13.5434i	0.287638	+	0.498203i	−0.685608	+	0.727971i	$0.740463\pi$
$740$	−0.545658	−	0.945107i	−0.0200588	−	0.0347428i
$741$		0			0
$742$		0			0
$743$	−27.3807	+	15.8083i	−1.00450	+	0.579949i	−0.909577	−	0.415535i	$-0.863594\pi$
$743$	−27.3807	+	15.8083i	−1.00450	+	0.579949i	−0.0949246	+	0.995484i	$0.530261\pi$
$744$		0			0
$745$			25.1337i			0.920829i
$746$	7.36032	−	4.24948i	0.269480	−	0.155585i
$747$		0			0
$748$		−	11.2332i		−	0.410727i
$749$		0			0
$750$		0			0
$751$	−14.2736			−0.520851			−0.260426	−	0.965494i	$-0.583863\pi$
$751$	−14.2736			−0.520851			−0.260426	+	0.965494i	$0.583863\pi$
$752$	0.504652	−	0.874082i	0.0184028	−	0.0318745i
$753$		0			0
$754$	−11.9864	+	6.92036i	−0.436519	+	0.252025i
$755$	1.57870			0.0574548
$756$		0			0
$757$	−10.8227			−0.393358			−0.196679	−	0.980468i	$-0.563016\pi$
$757$	−10.8227			−0.393358			−0.196679	+	0.980468i	$0.563016\pi$
$758$	60.0134	−	34.6488i	2.17979	−	1.25850i
$759$		0			0
$760$	−8.66182	+	15.0027i	−0.314197	+	0.544206i
$761$	5.86195			0.212496			0.106248	−	0.994340i	$-0.466116\pi$
$761$	5.86195			0.212496			0.106248	+	0.994340i	$0.466116\pi$
$762$		0			0
$763$		0			0
$764$		−	72.2926i		−	2.61546i
$765$		0			0
$766$	−33.4844	+	19.3323i	−1.20984	+	0.698503i
$767$		−	48.4818i		−	1.75058i
$768$		0			0
$769$	27.5683	−	15.9166i	0.994140	−	0.573967i	0.0876307	−	0.996153i	$-0.472070\pi$
$769$	27.5683	−	15.9166i	0.994140	−	0.573967i	0.906509	+	0.422186i	$0.138737\pi$
$770$		0			0
$771$		0			0
$772$	26.8428	+	46.4931i	0.966094	+	1.67332i
$773$	9.51908	+	16.4875i	0.342378	+	0.593015i	0.984874	−	0.173274i	$-0.0554345\pi$
$773$	9.51908	+	16.4875i	0.342378	+	0.593015i	−0.642496	+	0.766289i	$0.722101\pi$
$774$		0			0
$775$	9.54282	+	5.50955i	0.342788	+	0.197909i
$776$	4.18965	−	7.25668i	0.150400	−	0.260500i
$777$		0			0
$778$	−12.3977	−	21.4734i	−0.444478	−	0.769859i
$779$			33.3648i			1.19542i
$780$		0			0
$781$	−12.3685			−0.442581
$782$	4.97900	−	8.62388i	0.178049	−	0.308389i
$783$		0			0
$784$		0			0
$785$	−12.1219	−	6.99857i	−0.432649	−	0.249790i
$786$		0			0
$787$	16.4123	+	9.47564i	0.585035	+	0.337770i	0.763132	−	0.646243i	$-0.223661\pi$
$787$	16.4123	+	9.47564i	0.585035	+	0.337770i	−0.178097	+	0.984013i	$0.556994\pi$
$788$	24.6472	+	14.2301i	0.878020	+	0.506925i
$789$		0			0
$790$	10.3494	+	5.97525i	0.368216	+	0.212590i
$791$		0			0
$792$		0			0
$793$	8.35705	−	14.4748i	0.296768	−	0.514016i
$794$	−50.7714			−1.80181
$795$		0			0
$796$		−	18.4084i		−	0.652470i
$797$	26.7207	+	46.2816i	0.946497	+	1.63938i	0.752727	+	0.658333i	$0.228738\pi$
$797$	26.7207	+	46.2816i	0.946497	+	1.63938i	0.193770	+	0.981047i	$0.437929\pi$
$798$		0			0
$799$	−2.30314	+	3.98916i	−0.0814792	+	0.141126i
$800$	15.1014	+	8.71878i	0.533914	+	0.308256i
$801$		0			0
$802$	27.4097	+	47.4750i	0.967871	+	1.67640i
$803$	−11.8247	−	20.4810i	−0.417286	−	0.722760i
$804$		0			0
$805$		0			0
$806$	−37.7885	+	21.8172i	−1.33104	+	0.768479i
$807$		0			0
$808$		−	19.0745i		−	0.671040i
$809$	2.23517	−	1.29047i	0.0785842	−	0.0453706i	−0.460193	−	0.887819i	$-0.652220\pi$
$809$	2.23517	−	1.29047i	0.0785842	−	0.0453706i	0.538777	+	0.842448i	$0.318886\pi$
$810$		0			0
$811$			6.06938i			0.213125i	0.994306	+	0.106562i	$0.0339844\pi$
$811$			6.06938i			0.213125i	−0.994306	+	0.106562i	$0.966016\pi$
$812$		0			0
$813$		0			0
$814$	−1.76088			−0.0617187
$815$	5.18169	−	8.97494i	0.181507	−	0.314379i
$816$		0			0
$817$	−29.7272	+	17.1630i	−1.04002	+	0.600458i
$818$	−59.9811			−2.09719
$819$		0			0
$820$	33.9201			1.18454
$821$	8.03938	−	4.64154i	0.280576	−	0.161991i	−0.353108	−	0.935583i	$-0.614875\pi$
$821$	8.03938	−	4.64154i	0.280576	−	0.161991i	0.633684	+	0.773592i	$0.281542\pi$
$822$		0			0
$823$	−9.03448	+	15.6482i	−0.314922	+	0.545461i	−0.979421	−	0.201828i	$-0.935312\pi$
$823$	−9.03448	+	15.6482i	−0.314922	+	0.545461i	0.664499	+	0.747289i	$0.268645\pi$
$824$	4.58343			0.159671
$825$		0			0
$826$		0			0
$827$			48.5440i			1.68804i	0.536310	+	0.844021i	$0.319818\pi$
$827$			48.5440i			1.68804i	−0.536310	+	0.844021i	$0.680182\pi$
$828$		0			0
$829$	−4.71804	+	2.72396i	−0.163864	+	0.0946071i	−0.579689	−	0.814837i	$-0.696826\pi$
$829$	−4.71804	+	2.72396i	−0.163864	+	0.0946071i	0.415825	+	0.909445i	$0.363493\pi$
$830$		−	35.6044i		−	1.23585i
$831$		0			0
$832$	−57.6796	+	33.3013i	−1.99968	+	1.15452i
$833$		0			0
$834$		0			0
$835$	−12.4126	−	21.4992i	−0.429556	−	0.744012i
$836$	23.1038	+	40.0170i	0.799062	+	1.38402i
$837$		0			0
$838$	63.7793	+	36.8230i	2.20322	+	1.27203i
$839$	24.2673	−	42.0322i	0.837801	−	1.45111i	−0.0539281	−	0.998545i	$-0.517174\pi$
$839$	24.2673	−	42.0322i	0.837801	−	1.45111i	0.891729	−	0.452569i	$-0.149492\pi$
$840$		0			0
$841$	−13.7947	−	23.8931i	−0.475678	−	0.823899i
$842$		−	25.2564i		−	0.870392i
$843$		0			0
$844$	−82.3814			−2.83569
$845$	9.47061	−	16.4036i	0.325799	−	0.564300i
$846$		0			0
$847$		0			0
$848$	1.45254	+	0.838622i	0.0498803	+	0.0287984i
$849$		0			0
$850$	−6.33127	−	3.65536i	−0.217161	−	0.125378i
$851$	−0.830095	−	0.479256i	−0.0284553	−	0.0164287i
$852$		0			0
$853$	−10.7703	−	6.21823i	−0.368768	−	0.212908i	0.304152	−	0.952623i	$-0.401627\pi$
$853$	−10.7703	−	6.21823i	−0.368768	−	0.212908i	−0.672920	+	0.739715i	$0.734960\pi$
$854$		0			0
$855$		0			0
$856$	−6.64007	+	11.5009i	−0.226953	+	0.393094i
$857$	10.5815			0.361459			0.180729	−	0.983533i	$-0.442154\pi$
$857$	10.5815			0.361459			0.180729	+	0.983533i	$0.442154\pi$
$858$		0			0
$859$		−	32.4993i		−	1.10886i	−0.832230	−	0.554431i	$-0.812936\pi$
$859$		−	32.4993i		−	1.10886i	0.832230	−	0.554431i	$-0.187064\pi$
$860$	17.4487	+	30.2220i	0.594995	+	1.03056i
$861$		0			0
$862$	−18.5579	+	32.1432i	−0.632084	+	1.09480i
$863$	−21.8414	−	12.6102i	−0.743491	−	0.429255i	0.0798460	−	0.996807i	$-0.474557\pi$
$863$	−21.8414	−	12.6102i	−0.743491	−	0.429255i	−0.823337	+	0.567552i	$0.807890\pi$
$864$		0			0
$865$	1.40288	+	2.42986i	0.0476994	+	0.0826177i
$866$	14.2683	+	24.7135i	0.484857	+	0.839797i
$867$		0			0
$868$		0			0
$869$	10.2540	−	5.92017i	0.347844	−	0.200828i
$870$		0			0
$871$		−	3.37963i		−	0.114514i
$872$	18.9633	−	10.9485i	0.642179	−	0.370762i
$873$		0			0
$874$			40.9621i			1.38556i
$875$		0			0
$876$		0			0
$877$	−14.9579			−0.505091			−0.252546	−	0.967585i	$-0.581268\pi$
$877$	−14.9579			−0.505091			−0.252546	+	0.967585i	$0.581268\pi$
$878$	21.1961	−	36.7127i	0.715333	−	1.23899i
$879$		0			0
$880$	−0.960836	+	0.554739i	−0.0323898	+	0.0187003i
$881$	36.4482			1.22797			0.613985	−	0.789318i	$-0.289566\pi$
$881$	36.4482			1.22797			0.613985	+	0.789318i	$0.289566\pi$
$882$		0			0
$883$	15.9831			0.537873			0.268936	−	0.963158i	$-0.413328\pi$
$883$	15.9831			0.537873			0.268936	+	0.963158i	$0.413328\pi$
$884$	15.3948	−	8.88819i	0.517783	−	0.298942i
$885$		0			0
$886$	−5.40739	+	9.36588i	−0.181665	+	0.314653i
$887$	49.0416			1.64666			0.823329	−	0.567565i	$-0.192114\pi$
$887$	49.0416			1.64666			0.823329	+	0.567565i	$0.192114\pi$
$888$		0			0
$889$		0			0
$890$		−	44.7026i		−	1.49843i
$891$		0			0
$892$	−49.2649	+	28.4431i	−1.64951	+	0.952346i
$893$		−	18.9479i		−	0.634066i
$894$		0			0
$895$	−28.8196	+	16.6390i	−0.963332	+	0.556180i
$896$		0			0
$897$		0			0
$898$	−18.4834	−	32.0143i	−0.616801	−	1.06833i
$899$	2.22364	+	3.85145i	0.0741625	+	0.128453i
$900$		0			0
$901$	−6.62911	−	3.82732i	−0.220848	−	0.127506i
$902$	27.3657	−	47.3987i	0.911177	−	1.57820i
$903$		0			0
$904$	5.27687	+	9.13981i	0.175506	+	0.303986i
$905$			14.7364i			0.489855i
$906$		0			0
$907$	−4.85829			−0.161317			−0.0806585	−	0.996742i	$-0.525702\pi$
$907$	−4.85829			−0.161317			−0.0806585	+	0.996742i	$0.525702\pi$
$908$	17.4487	−	30.2220i	0.579054	−	1.00295i
$909$		0			0
$910$		0			0
$911$	−14.4945	−	8.36843i	−0.480226	−	0.277258i	0.240285	−	0.970702i	$-0.422759\pi$
$911$	−14.4945	−	8.36843i	−0.480226	−	0.277258i	−0.720510	+	0.693444i	$0.756092\pi$
$912$		0			0
$913$	−30.5501	−	17.6381i	−1.01106	−	0.583737i
$914$	−11.3301	−	6.54143i	−0.374766	−	0.216371i
$915$		0			0
$916$	53.5678	+	30.9274i	1.76993	+	1.02187i
$917$		0			0
$918$		0			0
$919$	−15.3200	+	26.5350i	−0.505360	+	0.875309i	0.494621	+	0.869109i	$0.335307\pi$
$919$	−15.3200	+	26.5350i	−0.505360	+	0.875309i	−0.999981	+	0.00620006i	$0.998026\pi$
$920$	15.4687			0.509989
$921$		0			0
$922$			82.5628i			2.71906i
$923$	−9.78651	−	16.9507i	−0.322127	−	0.557940i
$924$		0			0
$925$	−0.351848	+	0.609419i	−0.0115687	+	0.0200376i
$926$	−57.6450	−	33.2814i	−1.89433	−	1.09369i
$927$		0			0
$928$	3.51887	+	6.09487i	0.115513	+	0.200074i
$929$	−14.8723	−	25.7595i	−0.487943	−	0.845142i	0.511961	−	0.859009i	$-0.328919\pi$
$929$	−14.8723	−	25.7595i	−0.487943	−	0.845142i	−0.999904	+	0.0138670i	$0.995586\pi$
$930$		0			0
$931$		0			0
$932$	8.10245	−	4.67795i	0.265405	−	0.153231i
$933$		0			0
$934$		−	6.01456i		−	0.196802i
$935$	4.38508	−	2.53173i	0.143408	−	0.0827964i
$936$		0			0
$937$			4.03712i			0.131887i	0.997823	+	0.0659434i	$0.0210057\pi$
$937$			4.03712i			0.131887i	−0.997823	+	0.0659434i	$0.978994\pi$
$938$		0			0
$939$		0			0
$940$	−19.2632			−0.628296
$941$	−7.20264	+	12.4753i	−0.234799	+	0.406684i	−0.959214	−	0.282680i	$-0.908777\pi$
$941$	−7.20264	+	12.4753i	−0.234799	+	0.406684i	0.724415	+	0.689364i	$0.242110\pi$
$942$		0			0
$943$	25.8009	−	14.8962i	0.840193	−	0.485085i
$944$	−2.26464			−0.0737079
$945$		0			0
$946$	56.3081			1.83073
$947$	27.0334	−	15.6077i	0.878467	−	0.507183i	0.00831468	−	0.999965i	$-0.497353\pi$
$947$	27.0334	−	15.6077i	0.878467	−	0.507183i	0.870153	+	0.492782i	$0.164020\pi$
$948$		0			0
$949$	18.7125	−	32.4109i	0.607432	−	1.05210i
$950$	30.0726			0.975682
$951$		0			0
$952$		0			0
$953$		−	8.55869i		−	0.277243i	−0.990345	−	0.138622i	$-0.955733\pi$
$953$		−	8.55869i		−	0.277243i	0.990345	−	0.138622i	$-0.0442672\pi$
$954$		0			0
$955$	28.2207	−	16.2933i	0.913202	−	0.527237i
$956$		−	39.4074i		−	1.27453i
$957$		0			0
$958$	−61.2751	+	35.3772i	−1.97971	+	1.14298i
$959$		0			0
$960$		0			0
$961$	−8.48973	−	14.7046i	−0.273862	−	0.474343i
$962$	−1.39328	−	2.41323i	−0.0449212	−	0.0778058i
$963$		0			0
$964$	37.2104	+	21.4835i	1.19847	+	0.691936i
$965$	−12.0996	+	20.9572i	−0.389501	+	0.674635i
$966$		0			0
$967$	16.0280	+	27.7614i	0.515427	+	0.892745i	0.999840	+	0.0179059i	$0.00569994\pi$
$967$	16.0280	+	27.7614i	0.515427	+	0.892745i	−0.484413	+	0.874840i	$0.660967\pi$
$968$			1.44060i			0.0463026i
$969$		0			0
$970$	10.1683			0.326483
$971$	16.6183	−	28.7838i	0.533307	−	0.923715i	−0.465936	−	0.884818i	$-0.654282\pi$
$971$	16.6183	−	28.7838i	0.533307	−	0.923715i	0.999243	−	0.0388964i	$-0.0123842\pi$
$972$		0			0
$973$		0			0
$974$	68.7469	+	39.6911i	2.20279	+	1.27178i
$975$		0			0
$976$	−0.676137	−	0.390368i	−0.0216426	−	0.0124954i
$977$	45.1558	+	26.0707i	1.44466	+	0.834076i	0.998156	−	0.0607042i	$-0.0193346\pi$
$977$	45.1558	+	26.0707i	1.44466	+	0.834076i	0.446507	+	0.894780i	$0.352668\pi$
$978$		0			0
$979$	−38.3567	−	22.1453i	−1.22589	−	0.707765i
$980$		0			0
$981$		0			0
$982$	−29.8022	+	51.6189i	−0.951026	+	1.64723i
$983$	−24.2385			−0.773087			−0.386544	−	0.922271i	$-0.626331\pi$
$983$	−24.2385			−0.773087			−0.386544	+	0.922271i	$0.626331\pi$
$984$		0			0
$985$			12.8286i			0.408755i
$986$	−1.47529	−	2.55528i	−0.0469829	−	0.0813768i
$987$		0			0
$988$	−36.5614	+	63.3263i	−1.16317	+	2.01468i
$989$	26.5442	+	15.3253i	0.844056	+	0.487316i
$990$		0			0
$991$	12.0991	+	20.9562i	0.384339	+	0.665695i	0.991677	−	0.128749i	$-0.0410960\pi$
$991$	12.0991	+	20.9562i	0.384339	+	0.665695i	−0.607338	+	0.794443i	$0.707763\pi$
$992$	11.0937	+	19.2148i	0.352224	+	0.610070i
$993$		0			0
$994$		0			0
$995$	7.18607	−	4.14888i	0.227814	−	0.131528i
$996$		0			0
$997$		−	10.1835i		−	0.322516i	−0.986912	−	0.161258i	$-0.948445\pi$
$997$		−	10.1835i		−	0.322516i	0.986912	−	0.161258i	$-0.0515551\pi$
$998$	−24.5997	+	14.2027i	−0.778691	+	0.449578i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1323.2.s.c.656.2		12
3.2	odd	2		441.2.s.c.362.6		12
7.2	even	3		189.2.o.a.62.5		12
7.3	odd	6		1323.2.i.c.521.2		12
7.4	even	3		1323.2.i.c.521.1		12
7.5	odd	6		189.2.o.a.62.6		12
7.6	odd	2	inner	1323.2.s.c.656.1		12
9.4	even	3		441.2.i.c.68.2		12
9.5	odd	6		1323.2.i.c.1097.6		12
21.2	odd	6		63.2.o.a.20.1	✓	12
21.5	even	6		63.2.o.a.20.2	yes	12
21.11	odd	6		441.2.i.c.227.5		12
21.17	even	6		441.2.i.c.227.6		12
21.20	even	2		441.2.s.c.362.5		12
28.19	even	6		3024.2.cc.a.2897.4		12
28.23	odd	6		3024.2.cc.a.2897.3		12
63.2	odd	6		567.2.c.c.566.11		12
63.4	even	3		441.2.s.c.374.5		12
63.5	even	6		189.2.o.a.125.5		12
63.13	odd	6		441.2.i.c.68.1		12
63.16	even	3		567.2.c.c.566.2		12
63.23	odd	6		189.2.o.a.125.6		12
63.31	odd	6		441.2.s.c.374.6		12
63.32	odd	6	inner	1323.2.s.c.962.1		12
63.40	odd	6		63.2.o.a.41.1	yes	12
63.41	even	6		1323.2.i.c.1097.5		12
63.47	even	6		567.2.c.c.566.12		12
63.58	even	3		63.2.o.a.41.2	yes	12
63.59	even	6	inner	1323.2.s.c.962.2		12
63.61	odd	6		567.2.c.c.566.1		12
84.23	even	6		1008.2.cc.a.209.5		12
84.47	odd	6		1008.2.cc.a.209.2		12
252.23	even	6		3024.2.cc.a.881.4		12
252.103	even	6		1008.2.cc.a.545.5		12
252.131	odd	6		3024.2.cc.a.881.3		12
252.247	odd	6		1008.2.cc.a.545.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.1	✓	12	21.2	odd	6
63.2.o.a.20.2	yes	12	21.5	even	6
63.2.o.a.41.1	yes	12	63.40	odd	6
63.2.o.a.41.2	yes	12	63.58	even	3
189.2.o.a.62.5		12	7.2	even	3
189.2.o.a.62.6		12	7.5	odd	6
189.2.o.a.125.5		12	63.5	even	6
189.2.o.a.125.6		12	63.23	odd	6
441.2.i.c.68.1		12	63.13	odd	6
441.2.i.c.68.2		12	9.4	even	3
441.2.i.c.227.5		12	21.11	odd	6
441.2.i.c.227.6		12	21.17	even	6
441.2.s.c.362.5		12	21.20	even	2
441.2.s.c.362.6		12	3.2	odd	2
441.2.s.c.374.5		12	63.4	even	3
441.2.s.c.374.6		12	63.31	odd	6
567.2.c.c.566.1		12	63.61	odd	6
567.2.c.c.566.2		12	63.16	even	3
567.2.c.c.566.11		12	63.2	odd	6
567.2.c.c.566.12		12	63.47	even	6
1008.2.cc.a.209.2		12	84.47	odd	6
1008.2.cc.a.209.5		12	84.23	even	6
1008.2.cc.a.545.2		12	252.247	odd	6
1008.2.cc.a.545.5		12	252.103	even	6
1323.2.i.c.521.1		12	7.4	even	3
1323.2.i.c.521.2		12	7.3	odd	6
1323.2.i.c.1097.5		12	63.41	even	6
1323.2.i.c.1097.6		12	9.5	odd	6
1323.2.s.c.656.1		12	7.6	odd	2	inner
1323.2.s.c.656.2		12	1.1	even	1	trivial
1323.2.s.c.962.1		12	63.32	odd	6	inner
1323.2.s.c.962.2		12	63.59	even	6	inner
3024.2.cc.a.881.3		12	252.131	odd	6
3024.2.cc.a.881.4		12	252.23	even	6
3024.2.cc.a.2897.3		12	28.23	odd	6
3024.2.cc.a.2897.4		12	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1323 = 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1323.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.97141 + 1.13819i) q^{2} +(1.59097 - 2.75564i) q^{4} +1.43429 q^{5} +2.69056i q^{8} +O(q^{10})\)	\(q+(-1.97141 + 1.13819i) q^{2} +(1.59097 - 2.75564i) q^{4} +1.43429 q^{5} +2.69056i q^{8} +(-2.82757 + 1.63250i) q^{10} +3.23490i q^{11} +(-4.43334 + 2.55959i) q^{13} +(0.119562 + 0.207087i) q^{16} +(-0.545658 - 0.945107i) q^{17} +(3.88768 + 2.24456i) q^{19} +(2.28191 - 3.95238i) q^{20} +(-3.68194 - 6.37731i) q^{22} -4.00844i q^{23} -2.94282 q^{25} +(5.82662 - 10.0920i) q^{26} +(-1.02859 - 0.593857i) q^{29} +(-3.24275 - 1.87220i) q^{31} +(-5.13160 - 2.96273i) q^{32} +(2.15143 + 1.24213i) q^{34} +(0.119562 - 0.207087i) q^{37} -10.2190 q^{38} +3.85904i q^{40} +(3.71620 + 6.43664i) q^{41} +(-3.82326 + 6.62208i) q^{43} +(8.91423 + 5.14663i) q^{44} +(4.56238 + 7.90228i) q^{46} +(-2.11042 - 3.65536i) q^{47} +(5.80150 - 3.34950i) q^{50} +16.2889i q^{52} +(6.07442 - 3.50707i) q^{53} +4.63977i q^{55} +2.70370 q^{58} +(-4.73531 + 8.20179i) q^{59} +(-2.82757 + 1.63250i) q^{61} +8.52371 q^{62} +13.0104 q^{64} +(-6.35868 + 3.67119i) q^{65} +(-0.330095 + 0.571741i) q^{67} -3.47250 q^{68} +3.82347i q^{71} +(-6.33127 + 3.65536i) q^{73} +0.544337i q^{74} +(12.3704 - 7.14205i) q^{76} +(-1.83009 - 3.16982i) q^{79} +(0.171486 + 0.297022i) q^{80} +(-14.6523 - 8.45951i) q^{82} +(-5.45245 + 9.44392i) q^{83} +(-0.782630 - 1.35556i) q^{85} -17.4064i q^{86} -8.70370 q^{88} +(-6.84573 + 11.8572i) q^{89} +(-11.0458 - 6.37731i) q^{92} +(8.32102 + 4.80415i) q^{94} +(5.57605 + 3.21934i) q^{95} +(-2.69709 - 1.55716i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} + 2 q^{4}+O(q^{10}) \) 12 * q - 6 * q^2 + 2 * q^4	\( 12 q - 6 q^{2} + 2 q^{4} + 2 q^{16} - 10 q^{22} - 30 q^{29} - 12 q^{32} + 2 q^{37} - 10 q^{43} + 54 q^{44} + 20 q^{46} + 36 q^{50} - 12 q^{53} - 4 q^{58} + 16 q^{64} - 78 q^{65} + 12 q^{67} - 6 q^{79} - 6 q^{85} - 68 q^{88} - 30 q^{92} + 72 q^{95}+O(q^{100}) \) 12 * q - 6 * q^2 + 2 * q^4 + 2 * q^16 - 10 * q^22 - 30 * q^29 - 12 * q^32 + 2 * q^37 - 10 * q^43 + 54 * q^44 + 20 * q^46 + 36 * q^50 - 12 * q^53 - 4 * q^58 + 16 * q^64 - 78 * q^65 + 12 * q^67 - 6 * q^79 - 6 * q^85 - 68 * q^88 - 30 * q^92 + 72 * q^95

Introduction

L-functions

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