LMFDB - Embedded newform 1323.2.i.c.1097.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1323,2,Mod(521,1323)]

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, 1]))

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

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

chi := DirichletCharacter("1323.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1323 = 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1323.i (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			1097.5
Root			$1.29589 - 0.748185i$ of defining polynomial
Character	$\chi$	$=$	1323.1097
Dual form			1323.2.i.c.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.27639i q^{2} -3.18194 q^{4} +(-0.717144 - 1.24213i) q^{5} -2.69056i q^{8} +O(q^{10})$	\(q+2.27639i q^{2} -3.18194 q^{4} +(-0.717144 - 1.24213i) q^{5} -2.69056i q^{8} +(2.82757 - 1.63250i) q^{10} +(2.80150 + 1.61745i) q^{11} +(-4.43334 - 2.55959i) q^{13} -0.239123 q^{16} +(-0.545658 - 0.945107i) q^{17} +(-3.88768 - 2.24456i) q^{19} +(2.28191 + 3.95238i) q^{20} +(-3.68194 + 6.37731i) q^{22} +(3.47141 - 2.00422i) q^{23} +(1.47141 - 2.54856i) q^{25} +(5.82662 - 10.0920i) q^{26} +(-1.02859 + 0.593857i) q^{29} -3.74440i q^{31} -5.92546i q^{32} +(2.15143 - 1.24213i) q^{34} +(0.119562 - 0.207087i) q^{37} +(5.10948 - 8.84988i) q^{38} +(-3.34203 + 1.92952i) q^{40} +(3.71620 - 6.43664i) q^{41} +(-3.82326 - 6.62208i) q^{43} +(-8.91423 - 5.14663i) q^{44} +(4.56238 + 7.90228i) q^{46} +4.22085 q^{47} +(5.80150 + 3.34950i) q^{50} +(14.1066 + 8.14447i) q^{52} +(-6.07442 + 3.50707i) q^{53} -4.63977i q^{55} +(-1.35185 - 2.34147i) q^{58} +9.47061 q^{59} +3.26499i q^{61} +8.52371 q^{62} +13.0104 q^{64} +7.34238i q^{65} +0.660190 q^{67} +(1.73625 + 3.00728i) q^{68} -3.82347i q^{71} +(6.33127 - 3.65536i) q^{73} +(0.471410 + 0.272169i) q^{74} +(12.3704 + 7.14205i) q^{76} +3.66019 q^{79} +(0.171486 + 0.297022i) q^{80} +(14.6523 + 8.45951i) q^{82} +(-5.45245 - 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} +(15.0744 - 8.70322i) q^{86} +(4.35185 - 7.53762i) q^{88} +(-6.84573 + 11.8572i) q^{89} +(-11.0458 + 6.37731i) q^{92} +9.60829i q^{94} +6.43867i q^{95} +(-2.69709 + 1.55716i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4}+O(q^{10}) $ 12 * q - 4 * q^4	$ 12 q - 4 q^{4} - 4 q^{16} - 10 q^{22} + 24 q^{23} - 30 q^{29} + 2 q^{37} - 10 q^{43} - 54 q^{44} + 20 q^{46} + 36 q^{50} + 12 q^{53} + 2 q^{58} + 16 q^{64} - 24 q^{67} - 12 q^{74} + 12 q^{79} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 30 q^{92}+O(q^{100}) $ 12 * q - 4 * q^4 - 4 * q^16 - 10 * q^22 + 24 * q^23 - 30 * q^29 + 2 * q^37 - 10 * q^43 - 54 * q^44 + 20 * q^46 + 36 * q^50 + 12 * q^53 + 2 * q^58 + 16 * q^64 - 24 * q^67 - 12 * q^74 + 12 * q^79 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 30 * q^92

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			2.27639i			1.60965i	0.593512	+	0.804825i	$0.297741\pi$
$2$			2.27639i			1.60965i	−0.593512	+	0.804825i	$0.702259\pi$
$3$		0			0
$3$		0			0
$4$	−3.18194			−1.59097
$5$	−0.717144	−	1.24213i	−0.320716	−	0.555497i	0.659920	−	0.751336i	$-0.270590\pi$
$5$	−0.717144	−	1.24213i	−0.320716	−	0.555497i	−0.980636	+	0.195839i	$0.937257\pi$
$6$		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
$11$	2.80150	+	1.61745i	0.844686	+	0.487679i	0.858854	−	0.512220i	$-0.171177\pi$
$11$	2.80150	+	1.61745i	0.844686	+	0.487679i	−0.0141686	+	0.999900i	$0.504510\pi$
$12$		0			0
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.262644	−	0.964893i	$-0.584594\pi$
$13$	−4.43334	−	2.55959i	−1.22959	−	0.709903i	−0.966944	+	0.254990i	$0.917928\pi$
$14$		0			0
$15$		0			0
$16$	−0.239123			−0.0597808
$17$	−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	−0.0173336	−	0.999850i	$-0.505518\pi$
$19$	−3.88768	−	2.24456i	−0.891896	−	0.514936i	−0.874562	+	0.484914i	$0.838851\pi$
$20$	2.28191	+	3.95238i	0.510251	+	0.883780i
$21$		0			0
$22$	−3.68194	+	6.37731i	−0.784993	+	1.35965i
$23$	3.47141	−	2.00422i	0.723839	−	0.417909i	−0.0923250	−	0.995729i	$-0.529430\pi$
$23$	3.47141	−	2.00422i	0.723839	−	0.417909i	0.816164	+	0.577820i	$0.196097\pi$
$24$		0			0
$25$	1.47141	−	2.54856i	0.294282	−	0.509711i
$26$	5.82662	−	10.0920i	1.14269	−	1.97921i
$27$		0			0
$28$		0			0
$29$	−1.02859	+	0.593857i	−0.191004	+	0.110276i	−0.592453	−	0.805605i	$-0.701840\pi$
$29$	−1.02859	+	0.593857i	−0.191004	+	0.110276i	0.401448	+	0.915882i	$0.368507\pi$
$30$		0			0
$31$		−	3.74440i		−	0.672514i	−0.941770	−	0.336257i	$-0.890839\pi$
$31$		−	3.74440i		−	0.672514i	0.941770	−	0.336257i	$-0.109161\pi$
$32$		−	5.92546i		−	1.04748i
$33$		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	$0.160410\pi$
$38$	5.10948	−	8.84988i	0.828867	−	1.43564i
$39$		0			0
$40$	−3.34203	+	1.92952i	−0.528421	+	0.305084i
$41$	3.71620	−	6.43664i	0.580373	−	1.00523i	−0.415062	−	0.909793i	$-0.636240\pi$
$41$	3.71620	−	6.43664i	0.580373	−	1.00523i	0.995435	−	0.0954418i	$-0.0304264\pi$
$42$		0			0
$43$	−3.82326	−	6.62208i	−0.583041	−	1.00986i	−0.995116	−	0.0987075i	$-0.968529\pi$
$43$	−3.82326	−	6.62208i	−0.583041	−	1.00986i	0.412075	−	0.911150i	$-0.364804\pi$
$44$	−8.91423	−	5.14663i	−1.34387	−	0.775884i
$45$		0			0
$46$	4.56238	+	7.90228i	0.672686	+	1.16513i
$47$	4.22085			0.615674			0.307837	−	0.951439i	$-0.400395\pi$
$47$	4.22085			0.615674			0.307837	+	0.951439i	$0.400395\pi$
$48$		0			0
$49$		0			0
$50$	5.80150	+	3.34950i	0.820457	+	0.473691i
$51$		0			0
$52$	14.1066	+	8.14447i	1.95624	+	1.12944i
$53$	−6.07442	+	3.50707i	−0.834386	+	0.481733i	−0.855352	−	0.518047i	$-0.826659\pi$
$53$	−6.07442	+	3.50707i	−0.834386	+	0.481733i	0.0209662	+	0.999780i	$0.493326\pi$
$54$		0			0
$55$		−	4.63977i		−	0.625627i
$56$		0			0
$57$		0			0
$58$	−1.35185	−	2.34147i	−0.177506	−	0.307450i
$59$	9.47061			1.23297			0.616484	−	0.787367i	$-0.288556\pi$
$59$	9.47061			1.23297			0.616484	+	0.787367i	$0.288556\pi$
$60$		0			0
$61$			3.26499i			0.418040i	0.977911	+	0.209020i	$0.0670273\pi$
$61$			3.26499i			0.418040i	−0.977911	+	0.209020i	$0.932973\pi$
$62$	8.52371			1.08251
$63$		0			0
$64$	13.0104			1.62630
$65$			7.34238i			0.910710i
$66$		0			0
$67$	0.660190			0.0806550			0.0403275	−	0.999187i	$-0.487160\pi$
$67$	0.660190			0.0806550			0.0403275	+	0.999187i	$0.487160\pi$
$68$	1.73625	+	3.00728i	0.210552	+	0.364686i
$69$		0			0
$70$		0			0
$71$		−	3.82347i		−	0.453762i	−0.973922	−	0.226881i	$-0.927147\pi$
$71$		−	3.82347i		−	0.453762i	0.973922	−	0.226881i	$-0.0728529\pi$
$72$		0			0
$73$	6.33127	−	3.65536i	0.741020	−	0.427828i	−0.0814203	−	0.996680i	$-0.525946\pi$
$73$	6.33127	−	3.65536i	0.741020	−	0.427828i	0.822440	+	0.568852i	$0.192612\pi$
$74$	0.471410	+	0.272169i	0.0548003	+	0.0316390i
$75$		0			0
$76$	12.3704	+	7.14205i	1.41898	+	0.819249i
$77$		0			0
$78$		0			0
$79$	3.66019			0.411804			0.205902	−	0.978573i	$-0.433987\pi$
$79$	3.66019			0.411804			0.205902	+	0.978573i	$0.433987\pi$
$80$	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	−0.993045	−	0.117735i	$-0.962437\pi$
$83$	−5.45245	−	9.44392i	−0.598484	−	1.03660i	0.394561	−	0.918870i	$-0.370897\pi$
$84$		0			0
$85$	−0.782630	+	1.35556i	−0.0848882	+	0.147031i
$86$	15.0744	−	8.70322i	1.62552	−	0.938492i
$87$		0			0
$88$	4.35185	−	7.53762i	0.463909	−	0.803513i
$89$	−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
$94$			9.60829i			0.991020i
$95$			6.43867i			0.660594i
$96$		0			0
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	−0.630635	−	0.776080i	$-0.717205\pi$
$97$	−2.69709	+	1.55716i	−0.273848	+	0.158106i	0.356787	+	0.934186i	$0.383872\pi$
$98$		0			0
$99$		0			0
$100$	−4.68194	+	8.10936i	−0.468194	+	0.810936i
$101$	3.54471	−	6.13962i	0.352712	−	0.610915i	−0.634012	−	0.773324i	$-0.718593\pi$
$101$	3.54471	−	6.13962i	0.352712	−	0.610915i	0.986724	+	0.162408i	$0.0519262\pi$
$102$		0			0
$103$	1.47529	−	0.851761i	0.145365	−	0.0839265i	−0.425553	−	0.904933i	$-0.639921\pi$
$103$	1.47529	−	0.851761i	0.145365	−	0.0839265i	0.570918	+	0.821007i	$0.306587\pi$
$104$	−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	0.278943	−	0.960308i	$-0.410016\pi$
$107$	−4.27455	−	2.46791i	−0.413236	−	0.238582i	−0.692179	+	0.721726i	$0.743349\pi$
$108$		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	$0.960776\pi$
$110$	10.5619			1.00704
$111$		0			0
$112$		0			0
$113$	3.39699	+	1.96125i	0.319562	+	0.184499i	0.651197	−	0.758908i	$-0.274267\pi$
$113$	3.39699	+	1.96125i	0.319562	+	0.184499i	−0.331635	+	0.943408i	$0.607600\pi$
$114$		0			0
$115$	−4.97900	−	2.87463i	−0.464294	−	0.268060i
$116$	3.27292	−	1.88962i	0.303883	−	0.175447i
$117$		0			0
$118$			21.5588i			1.98465i
$119$		0			0
$120$		0			0
$121$	−0.267713	−	0.463693i	−0.0243376	−	0.0421539i
$122$	−7.43240			−0.672897
$123$		0			0
$124$			11.9145i			1.06995i
$125$	−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	$0.411761\pi$
$128$			17.7658i			1.57029i
$129$		0			0
$130$	−16.7141			−1.46592
$131$	4.13138	+	7.15575i	0.360960	+	0.625201i	0.988119	−	0.153690i	$-0.0491158\pi$
$131$	4.13138	+	7.15575i	0.360960	+	0.625201i	−0.627159	+	0.778891i	$0.715782\pi$
$132$		0			0
$133$		0			0
$134$			1.50285i			0.129826i
$135$		0			0
$136$	−2.54287	+	1.46813i	−0.218049	+	0.125891i
$137$	−8.96169	−	5.17404i	−0.765649	−	0.442048i	0.0656711	−	0.997841i	$-0.479081\pi$
$137$	−8.96169	−	5.17404i	−0.765649	−	0.442048i	−0.831320	+	0.555794i	$0.812415\pi$
$138$		0			0
$139$	−15.4589	−	8.92521i	−1.31121	−	0.757026i	−0.328912	−	0.944361i	$-0.606682\pi$
$139$	−15.4589	−	8.92521i	−1.31121	−	0.757026i	−0.982296	+	0.187334i	$0.940015\pi$
$140$		0			0
$141$		0			0
$142$	8.70370			0.730398
$143$	−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
$149$	−15.1758	+	8.76175i	−1.24325	+	0.717790i	−0.969754	−	0.244083i	$-0.921513\pi$
$149$	−15.1758	+	8.76175i	−1.24325	+	0.717790i	−0.273495	+	0.961873i	$0.588180\pi$
$150$		0			0
$151$	−0.550343	+	0.953223i	−0.0447863	+	0.0775722i	−0.887550	−	0.460712i	$-0.847594\pi$
$151$	−0.550343	+	0.953223i	−0.0447863	+	0.0775722i	0.842763	+	0.538284i	$0.180927\pi$
$152$	−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
$157$		−	9.75896i		−	0.778850i	−0.921058	−	0.389425i	$-0.872674\pi$
$157$		−	9.75896i		−	0.778850i	0.921058	−	0.389425i	$-0.127326\pi$
$158$			8.33201i			0.662859i
$159$		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	$0.0753468\pi$
$164$	−11.8247	+	20.4810i	−0.923356	+	1.59930i
$165$		0			0
$166$	21.4980	−	12.4119i	1.66857	−	0.963350i
$167$	−8.65419	+	14.9895i	−0.669681	+	1.15992i	0.308312	+	0.951285i	$0.400236\pi$
$167$	−8.65419	+	14.9895i	−0.669681	+	1.15992i	−0.977993	+	0.208637i	$0.933097\pi$
$168$		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
$173$	−1.95621			−0.148728			−0.0743638	−	0.997231i	$-0.523693\pi$
$173$	−1.95621			−0.148728			−0.0743638	+	0.997231i	$0.523693\pi$
$174$		0			0
$175$		0			0
$176$	−0.669905	−	0.386770i	−0.0504960	−	0.0291539i
$177$		0			0
$178$	−26.9915	−	15.5835i	−2.02310	−	1.16804i
$179$	20.0933	−	11.6009i	1.50184	−	0.867090i	0.501846	−	0.864957i	$-0.332655\pi$
$179$	20.0933	−	11.6009i	1.50184	−	0.867090i	0.999998	−	0.00213247i	$-0.000678788\pi$
$180$		0			0
$181$		−	10.2744i		−	0.763689i	−0.924226	−	0.381845i	$-0.875289\pi$
$181$		−	10.2744i		−	0.763689i	0.924226	−	0.381845i	$-0.124711\pi$
$182$		0			0
$183$		0			0
$184$	−5.39248	−	9.34004i	−0.397539	−	0.688557i
$185$	−0.342971			−0.0252158
$186$		0			0
$187$		−	3.53030i		−	0.258161i
$188$	−13.4305			−0.979520
$189$		0			0
$190$	−14.6569			−1.06332
$191$		−	22.7197i		−	1.64394i	−0.569533	−	0.821968i	$-0.692876\pi$
$191$		−	22.7197i		−	1.64394i	0.569533	−	0.821968i	$-0.307124\pi$
$192$		0			0
$193$	16.8720			1.21447			0.607235	−	0.794522i	$-0.292278\pi$
$193$	16.8720			1.21447			0.607235	+	0.794522i	$0.292278\pi$
$194$	−3.54471	−	6.13962i	−0.254495	−	0.440799i
$195$		0			0
$196$		0			0
$197$		−	8.94426i		−	0.637252i	−0.947880	−	0.318626i	$-0.896779\pi$
$197$		−	8.94426i		−	0.637252i	0.947880	−	0.318626i	$-0.103221\pi$
$198$		0			0
$199$	−5.01020	+	2.89264i	−0.355164	+	0.205054i	−0.666957	−	0.745096i	$-0.732404\pi$
$199$	−5.01020	+	2.89264i	−0.355164	+	0.205054i	0.311794	+	0.950150i	$0.399070\pi$
$200$	−6.85705	−	3.95892i	−0.484867	−	0.279938i
$201$		0			0
$202$	13.9762	+	8.06914i	0.983359	+	0.567743i
$203$		0			0
$204$		0			0
$205$	−10.6602			−0.744540
$206$	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	−0.0527186	+	0.998609i	$0.516789\pi$
$211$	−12.9451	+	22.4216i	−0.891180	+	1.54357i	−0.838462	+	0.544960i	$0.816545\pi$
$212$	19.3285	−	11.1593i	1.32748	−	0.766423i
$213$		0			0
$214$	5.61793	−	9.73053i	0.384034	−	0.665166i
$215$	−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
$220$			14.7635i			0.995355i
$221$			5.58664i			0.375798i
$222$		0			0
$223$	−15.4827	+	8.93892i	−1.03680	+	0.598594i	−0.918924	−	0.394435i	$-0.870940\pi$
$223$	−15.4827	+	8.93892i	−1.03680	+	0.598594i	−0.117871	+	0.993029i	$0.537607\pi$
$224$		0			0
$225$		0			0
$226$	−4.46457	+	7.73287i	−0.296979	+	0.514383i
$227$	−5.48365	+	9.49796i	−0.363963	+	0.630402i	−0.988609	−	0.150506i	$-0.951910\pi$
$227$	−5.48365	+	9.49796i	−0.363963	+	0.630402i	0.624646	+	0.780908i	$0.285243\pi$
$228$		0			0
$229$	−16.8349	+	9.71965i	−1.11248	+	0.642293i	−0.939471	−	0.342627i	$-0.888683\pi$
$229$	−16.8349	+	9.71965i	−1.11248	+	0.642293i	−0.173012	+	0.984920i	$0.555350\pi$
$230$	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	0.414266	−	0.910156i	$-0.364038\pi$
$233$	−2.54639	−	1.47016i	−0.166819	−	0.0963131i	−0.581085	+	0.813843i	$0.697372\pi$
$234$		0			0
$235$	−3.02696	−	5.24284i	−0.197457	−	0.342005i
$236$	−30.1350			−1.96162
$237$		0			0
$238$		0			0
$239$	10.7255	+	6.19234i	0.693772	+	0.400549i	0.805023	−	0.593243i	$-0.202153\pi$
$239$	10.7255	+	6.19234i	0.693772	+	0.400549i	−0.111252	+	0.993792i	$0.535486\pi$
$240$		0			0
$241$	11.6943	+	6.75168i	0.753293	+	0.434914i	0.826882	−	0.562375i	$-0.190112\pi$
$241$	11.6943	+	6.75168i	0.753293	+	0.434914i	−0.0735896	+	0.997289i	$0.523445\pi$
$242$	1.05555	−	0.609419i	0.0678530	−	0.0391750i
$243$		0			0
$244$		−	10.3890i		−	0.665089i
$245$		0			0
$246$		0			0
$247$	11.4903	+	19.9018i	0.731109	+	1.26632i
$248$	−10.0745			−0.639734
$249$		0			0
$250$		−	25.9333i		−	1.64016i
$251$	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
$254$			14.0414i			0.881034i
$255$		0			0
$256$	−14.4211			−0.901317
$257$	3.87788	+	6.71668i	0.241895	+	0.418975i	0.961254	−	0.275664i	$-0.0888976\pi$
$257$	3.87788	+	6.71668i	0.241895	+	0.418975i	−0.719359	+	0.694639i	$0.755564\pi$
$258$		0			0
$259$		0			0
$260$		−	23.3630i		−	1.44891i
$261$		0			0
$262$	−16.2893	+	9.40462i	−1.00635	+	0.581019i
$263$	−12.1127	−	6.99329i	−0.746903	−	0.431224i	0.0776710	−	0.996979i	$-0.475252\pi$
$263$	−12.1127	−	6.99329i	−0.746903	−	0.431224i	−0.824574	+	0.565755i	$0.808585\pi$
$264$		0			0
$265$	8.71246	+	5.03014i	0.535202	+	0.308999i
$266$		0			0
$267$		0			0
$268$	−2.10069			−0.128320
$269$	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	−0.00673411	−	0.999977i	$-0.502144\pi$
$271$	−14.4225	−	8.32686i	−0.876107	−	0.505821i	−0.869373	+	0.494157i	$0.835477\pi$
$272$	0.130480	+	0.225997i	0.00791148	+	0.0137031i
$273$		0			0
$274$	11.7781	−	20.4003i	0.711542	−	1.23243i
$275$	8.24433	−	4.75986i	0.497152	−	0.287031i
$276$		0			0
$277$	−15.7044	+	27.2008i	−0.943585	+	1.63434i	−0.185025	+	0.982734i	$0.559237\pi$
$277$	−15.7044	+	27.2008i	−0.943585	+	1.63434i	−0.758560	+	0.651603i	$0.774097\pi$
$278$	20.3172	−	35.1905i	1.21855	−	2.11059i
$279$		0			0
$280$		0			0
$281$	−8.10464	+	4.67922i	−0.483483	+	0.279139i	−0.721867	−	0.692032i	$-0.756716\pi$
$281$	−8.10464	+	4.67922i	−0.483483	+	0.279139i	0.238384	+	0.971171i	$0.423382\pi$
$282$		0			0
$283$		−	15.7735i		−	0.937638i	−0.883294	−	0.468819i	$-0.844680\pi$
$283$		−	15.7735i		−	0.937638i	0.883294	−	0.468819i	$-0.155320\pi$
$284$			12.1661i			0.721923i
$285$		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
$290$	−1.93894	+	3.35834i	−0.113858	+	0.197209i
$291$		0			0
$292$	−20.1458	+	11.6312i	−1.17894	+	0.680662i
$293$	12.4287	−	21.5271i	0.726090	−	1.25762i	−0.232434	−	0.972612i	$-0.574669\pi$
$293$	12.4287	−	21.5271i	0.726090	−	1.25762i	0.958524	−	0.285013i	$-0.0919978\pi$
$294$		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
$299$	−20.5199			−1.18670
$300$		0			0
$301$		0			0
$302$	−2.16991	−	1.25280i	−0.124864	−	0.0720903i
$303$		0			0
$304$	0.929636	+	0.536725i	0.0533183	+	0.0307833i
$305$	4.05555	−	2.34147i	0.232220	−	0.134072i
$306$		0			0
$307$		−	18.8878i		−	1.07799i	−0.842310	−	0.538993i	$-0.818805\pi$
$307$		−	18.8878i		−	1.07799i	0.842310	−	0.538993i	$-0.181195\pi$
$308$		0			0
$309$		0			0
$310$	−6.11273	−	10.5876i	−0.347179	−	0.601332i
$311$	−7.95431			−0.451048			−0.225524	−	0.974238i	$-0.572409\pi$
$311$	−7.95431			−0.451048			−0.225524	+	0.974238i	$0.572409\pi$
$312$		0			0
$313$		−	11.1337i		−	0.629316i	−0.949205	−	0.314658i	$-0.898110\pi$
$313$		−	11.1337i		−	0.629316i	0.949205	−	0.314658i	$-0.101890\pi$
$314$	22.2152			1.25367
$315$		0			0
$316$	−11.6465			−0.655168
$317$			23.2534i			1.30604i	0.757340	+	0.653021i	$0.226499\pi$
$317$			23.2534i			1.30604i	−0.757340	+	0.653021i	$0.773501\pi$
$318$		0			0
$319$	−3.84213			−0.215118
$320$	−9.33033	−	16.1606i	−0.521581	−	0.903405i
$321$		0			0
$322$		0			0
$323$			4.89904i			0.272590i
$324$		0			0
$325$	−13.0465	+	7.53242i	−0.723691	+	0.417823i
$326$	14.2443	+	8.22396i	0.788920	+	0.455483i
$327$		0			0
$328$	−17.3182	−	9.99866i	−0.956237	−	0.552084i
$329$		0			0
$330$		0			0
$331$	−19.1592			−1.05309			−0.526544	−	0.850148i	$-0.676512\pi$
$331$	−19.1592			−1.05309			−0.526544	+	0.850148i	$0.676512\pi$
$332$	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	−0.155441	−	0.987845i	$-0.549680\pi$
$337$	14.2781	−	24.7304i	0.777779	−	1.34715i	0.933219	−	0.359307i	$-0.116987\pi$
$338$	−26.0345	+	15.0310i	−1.41609	+	0.817579i
$339$		0			0
$340$	2.49028	−	4.31330i	0.135055	−	0.233922i
$341$	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
$346$		−	4.45308i		−	0.239399i
$347$			2.96400i			0.159116i	0.996830	+	0.0795578i	$0.0253508\pi$
$347$			2.96400i			0.159116i	−0.996830	+	0.0795578i	$0.974649\pi$
$348$		0			0
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.280460	−	0.959866i	$-0.409513\pi$
$349$	23.3885	−	13.5034i	1.25196	−	0.722818i	0.971498	+	0.237048i	$0.0761797\pi$
$350$		0			0
$351$		0			0
$352$	9.58414	−	16.6002i	0.510836	−	0.884794i
$353$	14.8238	−	25.6755i	0.788990	−	1.36657i	−0.137596	−	0.990488i	$-0.543937\pi$
$353$	14.8238	−	25.6755i	0.788990	−	1.36657i	0.926586	−	0.376083i	$-0.122729\pi$
$354$		0			0
$355$	−4.74924	+	2.74198i	−0.252064	+	0.145529i
$356$	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	0.942821	−	0.333299i	$-0.108162\pi$
$359$	21.3268	+	12.3130i	1.12559	+	0.649858i	0.182766	+	0.983157i	$0.441495\pi$
$360$		0			0
$361$	0.576055	+	0.997756i	0.0303187	+	0.0525135i
$362$	23.3885			1.22927
$363$		0			0
$364$		0			0
$365$	−9.08087	−	5.24284i	−0.475314	−	0.274423i
$366$		0			0
$367$	−4.85598	−	2.80360i	−0.253480	−	0.146347i	0.367877	−	0.929875i	$-0.380085\pi$
$367$	−4.85598	−	2.80360i	−0.253480	−	0.146347i	−0.621357	+	0.783528i	$0.713418\pi$
$368$	−0.830095	+	0.479256i	−0.0432717	+	0.0249829i
$369$		0			0
$370$		−	0.780736i		−	0.0405885i
$371$		0			0
$372$		0			0
$373$	1.86677	+	3.23333i	0.0966574	+	0.167416i	0.910299	−	0.413951i	$-0.135852\pi$
$373$	1.86677	+	3.23333i	0.0966574	+	0.167416i	−0.813642	+	0.581367i	$0.802518\pi$
$374$	8.03633			0.415549
$375$		0			0
$376$		−	11.3565i		−	0.585665i
$377$	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	$0.785722\pi$
$380$		−	20.4875i		−	1.05099i
$381$		0			0
$382$	51.7187			2.64616
$383$	−8.49251	−	14.7095i	−0.433947	−	0.751618i	0.563262	−	0.826278i	$-0.309546\pi$
$383$	−8.49251	−	14.7095i	−0.433947	−	0.751618i	−0.997209	+	0.0746601i	$0.976213\pi$
$384$		0			0
$385$		0			0
$386$			38.4071i			1.95487i
$387$		0			0
$388$	8.58198	−	4.95481i	0.435684	−	0.251542i
$389$	9.43310	+	5.44621i	0.478277	+	0.276134i	0.719698	−	0.694287i	$-0.244280\pi$
$389$	9.43310	+	5.44621i	0.478277	+	0.276134i	−0.241421	+	0.970420i	$0.577613\pi$
$390$		0			0
$391$	−3.78840	−	2.18724i	−0.191588	−	0.110613i
$392$		0			0
$393$		0			0
$394$	20.3606			1.02575
$395$	−2.62488	−	4.54643i	−0.132072	−	0.228756i
$396$		0			0
$397$	−19.3154	−	11.1518i	−0.969412	−	0.559690i	−0.0703551	−	0.997522i	$-0.522413\pi$
$397$	−19.3154	−	11.1518i	−0.969412	−	0.559690i	−0.899057	+	0.437832i	$0.855747\pi$
$398$	−6.58477	−	11.4052i	−0.330065	−	0.571689i
$399$		0			0
$400$	−0.351848	+	0.609419i	−0.0175924	+	0.0304710i
$401$	20.8554	−	12.0409i	1.04147	−	0.601293i	0.121221	−	0.992626i	$-0.461319\pi$
$401$	20.8554	−	12.0409i	1.04147	−	0.601293i	0.920249	+	0.391333i	$0.127986\pi$
$402$		0			0
$403$	−9.58414	+	16.6002i	−0.477420	+	0.826915i
$404$	−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
$409$			26.3492i			1.30289i	0.758698	+	0.651443i	$0.225836\pi$
$409$			26.3492i			1.30289i	−0.758698	+	0.651443i	$0.774164\pi$
$410$		−	24.2667i		−	1.19845i
$411$		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
$416$	−15.1668	+	26.2696i	−0.743611	+	1.28797i
$417$		0			0
$418$	28.6285	−	16.5286i	1.40026	−	0.808443i
$419$	−16.1761	+	28.0178i	−0.790252	+	1.36876i	0.135558	+	0.990769i	$0.456717\pi$
$419$	−16.1761	+	28.0178i	−0.790252	+	1.36876i	−0.925811	+	0.377988i	$0.876616\pi$
$420$		0			0
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	0.698589	−	0.715523i	$-0.253812\pi$
$421$	−5.54746	−	9.60849i	−0.270367	−	0.468289i	−0.968956	+	0.247234i	$0.920478\pi$
$422$	−51.0404	−	29.4682i	−2.48461	−	1.43449i
$423$		0			0
$424$	9.43598	+	16.3436i	0.458252	+	0.793716i
$425$	−3.21155			−0.155783
$426$		0			0
$427$		0			0
$428$	13.6014	+	7.85276i	0.657447	+	0.379577i
$429$		0			0
$430$	−21.6210	−	12.4829i	−1.04266	−	0.601980i
$431$	−14.1202	+	8.15233i	−0.680149	+	0.392684i	−0.799911	−	0.600119i	$-0.795120\pi$
$431$	−14.1202	+	8.15233i	−0.680149	+	0.392684i	0.119762	+	0.992803i	$0.461787\pi$
$432$		0			0
$433$			12.5359i			0.602438i	0.953555	+	0.301219i	$0.0973936\pi$
$433$			12.5359i			0.602438i	−0.953555	+	0.301219i	$0.902606\pi$
$434$		0			0
$435$		0			0
$436$	12.9480	+	22.4266i	0.620098	+	1.07404i
$437$	−17.9943			−0.860785
$438$		0			0
$439$			18.6225i			0.888805i	0.895827	+	0.444403i	$0.146584\pi$
$439$			18.6225i			0.888805i	−0.895827	+	0.444403i	$0.853416\pi$
$440$	−12.4836			−0.595132
$441$		0			0
$442$	−12.7174			−0.604904
$443$		−	4.75085i		−	0.225720i	−0.993611	−	0.112860i	$-0.963999\pi$
$443$		−	4.75085i		−	0.225720i	0.993611	−	0.112860i	$-0.0360011\pi$
$444$		0			0
$445$	19.6375			0.930906
$446$	−20.3484	−	35.2445i	−0.963527	−	1.66888i
$447$		0			0
$448$		0			0
$449$		−	16.2393i		−	0.766379i	−0.923670	−	0.383189i	$-0.874826\pi$
$449$		−	16.2393i		−	0.766379i	0.923670	−	0.383189i	$-0.125174\pi$
$450$		0			0
$451$	20.8219	−	12.0215i	0.980465	−	0.566072i
$452$	−10.8090	−	6.24060i	−0.508414	−	0.293533i
$453$		0			0
$454$	−21.6210	−	12.4829i	−1.01473	−	0.585852i
$455$		0			0
$456$		0			0
$457$	−5.74720			−0.268843			−0.134421	−	0.990924i	$-0.542918\pi$
$457$	−5.74720			−0.268843			−0.134421	+	0.990924i	$0.542918\pi$
$458$	−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	0.885957	+	0.463768i	$0.153503\pi$
$461$	18.1346	+	31.4101i	0.844613	+	1.46291i	−0.0413440	+	0.999145i	$0.513164\pi$
$462$		0			0
$463$	14.6202	−	25.3230i	0.679461	−	1.17686i	−0.295683	−	0.955286i	$-0.595547\pi$
$463$	14.6202	−	25.3230i	0.679461	−	1.17686i	0.975144	−	0.221574i	$-0.0711195\pi$
$464$	0.245960	−	0.142005i	0.0114184	−	0.00659241i
$465$		0			0
$466$	3.34665	−	5.79656i	0.155030	−	0.268521i
$467$	−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
$472$		−	25.4813i		−	1.17287i
$473$		−	24.7357i		−	1.13735i
$474$		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
$479$	−15.5409	+	26.9177i	−0.710083	+	1.22990i	0.254742	+	0.967009i	$0.418009\pi$
$479$	−15.5409	+	26.9177i	−0.710083	+	1.22990i	−0.964826	+	0.262891i	$0.915324\pi$
$480$		0			0
$481$	−1.06012	+	0.612058i	−0.0483371	+	0.0279074i
$482$	−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	$-0.456638\pi$
$488$	8.78467			0.397663
$489$		0			0
$490$		0			0
$491$	22.6758	+	13.0919i	1.02334	+	0.590828i	0.915071	−	0.403293i	$-0.132134\pi$
$491$	22.6758	+	13.0919i	1.02334	+	0.590828i	0.108273	+	0.994121i	$0.465468\pi$
$492$		0			0
$493$	1.12252	+	0.648085i	0.0505556	+	0.0291883i
$494$	−45.3041	+	26.1563i	−2.03833	+	1.17683i
$495$		0			0
$496$			0.895374i			0.0402035i
$497$		0			0
$498$		0			0
$499$	−6.23912	−	10.8065i	−0.279302	−	0.483764i	0.691910	−	0.721984i	$-0.256770\pi$
$499$	−6.23912	−	10.8065i	−0.279302	−	0.483764i	−0.971211	+	0.238220i	$0.923436\pi$
$500$	36.2496			1.62113
$501$		0			0
$502$			17.1057i			0.763465i
$503$	−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
$506$			29.5177i			1.31222i
$507$		0			0
$508$	−19.6271			−0.870811
$509$	17.6924	+	30.6441i	0.784200	+	1.35827i	0.929476	+	0.368883i	$0.120260\pi$
$509$	17.6924	+	30.6441i	0.784200	+	1.35827i	−0.145276	+	0.989391i	$0.546407\pi$
$510$		0			0
$511$		0			0
$512$			2.70367i			0.119486i
$513$		0			0
$514$	−15.2898	+	8.82756i	−0.674403	+	0.389367i
$515$	−2.11599	−	1.22167i	−0.0932419	−	0.0538332i
$516$		0			0
$517$	11.8247	+	6.82701i	0.520051	+	0.300252i
$518$		0			0
$519$		0			0
$520$	19.7551			0.866319
$521$	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	0.830852	−	0.556493i	$-0.187853\pi$
$523$	17.4799	+	10.0920i	0.764341	+	0.441293i	−0.0665110	+	0.997786i	$0.521187\pi$
$524$	−13.1458	−	22.7692i	−0.574277	−	0.994677i
$525$		0			0
$526$	15.9194	−	27.5733i	0.694120	−	1.20225i
$527$	−3.53886	+	2.04316i	−0.154155	+	0.0890015i
$528$		0			0
$529$	−3.46621	+	6.00365i	−0.150705	+	0.261028i
$530$	−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
$535$			7.07939i			0.306069i
$536$		−	1.77628i		−	0.0767237i
$537$		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	$0.00384346\pi$
$542$	18.9552	−	32.8313i	0.814194	−	1.41023i
$543$		0			0
$544$	−5.60020	+	3.23327i	−0.240106	+	0.138626i
$545$	−5.83643	+	10.1090i	−0.250005	+	0.433022i
$546$		0			0
$547$	14.7918	+	25.6201i	0.632451	+	1.09544i	0.987049	+	0.160419i	$0.0512845\pi$
$547$	14.7918	+	25.6201i	0.632451	+	1.09544i	−0.354598	+	0.935019i	$0.615382\pi$
$548$	28.5156	+	16.4635i	1.21813	+	0.703286i
$549$		0			0
$550$	10.8353	+	18.7673i	0.462019	+	0.800240i
$551$	5.33178			0.227141
$552$		0			0
$553$		0			0
$554$	−61.9196	−	35.7493i	−2.63071	−	1.51884i
$555$		0			0
$556$	49.1894	+	28.3995i	2.08609	+	1.20441i
$557$	4.08250	−	2.35703i	0.172981	−	0.0998707i	−0.411010	−	0.911631i	$-0.634824\pi$
$557$	4.08250	−	2.35703i	0.172981	−	0.0998707i	0.583991	+	0.811760i	$0.301490\pi$
$558$		0			0
$559$			39.1439i			1.65561i
$560$		0			0
$561$		0			0
$562$	−10.6517	−	18.4493i	−0.449316	−	0.778238i
$563$	−27.3484			−1.15260			−0.576299	−	0.817239i	$-0.695503\pi$
$563$	−27.3484			−1.15260			−0.576299	+	0.817239i	$0.695503\pi$
$564$		0			0
$565$		−	5.62600i		−	0.236688i
$566$	35.9066			1.50927
$567$		0			0
$568$	−10.2873			−0.431645
$569$		−	23.5580i		−	0.987601i	−0.869575	−	0.493801i	$-0.835607\pi$
$569$		−	23.5580i		−	0.987601i	0.869575	−	0.493801i	$-0.164393\pi$
$570$		0			0
$571$	19.1877			0.802980			0.401490	−	0.915863i	$-0.368492\pi$
$571$	19.1877			0.802980			0.401490	+	0.915863i	$0.368492\pi$
$572$	26.3465	+	45.6336i	1.10160	+	1.90804i
$573$		0			0
$574$		0			0
$575$		−	11.7961i		−	0.491932i
$576$		0			0
$577$	−1.93481	+	1.11706i	−0.0805472	+	0.0465039i	−0.539733	−	0.841836i	$-0.681475\pi$
$577$	−1.93481	+	1.11706i	−0.0805472	+	0.0465039i	0.459185	+	0.888340i	$0.348141\pi$
$578$	31.1661	+	17.9937i	1.29634	+	0.748441i
$579$		0			0
$580$	−4.69430	−	2.71026i	−0.194920	−	0.112537i
$581$		0			0
$582$		0			0
$583$	−22.6900			−0.939725
$584$	−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	0.999110	+	0.0421784i	$0.0134298\pi$
$587$	12.9883	+	22.4963i	0.536083	+	0.928522i	−0.463028	+	0.886344i	$0.653237\pi$
$588$		0			0
$589$	−8.40451	+	14.5570i	−0.346302	+	0.599813i
$590$	26.7788	−	15.4608i	1.10247	−	0.636509i
$591$		0			0
$592$	−0.0285900	+	0.0495193i	−0.00117504	+	0.00203523i
$593$	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
$598$		−	46.7113i		−	1.91017i
$599$			25.2489i			1.03164i	0.856696	+	0.515822i	$0.172513\pi$
$599$			25.2489i			1.03164i	−0.856696	+	0.515822i	$0.827487\pi$
$600$		0			0
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.661907	−	0.749586i	$-0.269748\pi$
$601$	40.2546	−	23.2410i	1.64202	−	0.948021i	0.980114	−	0.198435i	$-0.0635858\pi$
$602$		0			0
$603$		0			0
$604$	1.75116	−	3.03310i	0.0712538	−	0.123415i
$605$	−0.383978	+	0.665069i	−0.0156109	+	0.0270389i
$606$		0			0
$607$	6.09405	−	3.51840i	0.247350	−	0.142808i	−0.371200	−	0.928553i	$-0.621054\pi$
$607$	6.09405	−	3.51840i	0.247350	−	0.142808i	0.618550	+	0.785745i	$0.287720\pi$
$608$	−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	$0.875514\pi$
$614$	42.9961			1.73518
$615$		0			0
$616$		0			0
$617$	30.0043	+	17.3230i	1.20793	+	0.697396i	0.962306	−	0.271970i	$-0.0876751\pi$
$617$	30.0043	+	17.3230i	1.20793	+	0.697396i	0.245620	+	0.969366i	$0.421008\pi$
$618$		0			0
$619$	−14.7072	−	8.49123i	−0.591134	−	0.341291i	0.174412	−	0.984673i	$-0.444198\pi$
$619$	−14.7072	−	8.49123i	−0.591134	−	0.341291i	−0.765546	+	0.643381i	$0.777531\pi$
$620$	14.7993	−	8.54439i	0.594355	−	0.343151i
$621$		0			0
$622$		−	18.1071i		−	0.726029i
$623$		0			0
$624$		0			0
$625$	0.812855	+	1.40791i	0.0325142	+	0.0563162i
$626$	25.3447			1.01298
$627$		0			0
$628$			31.0524i			1.23913i
$629$	−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	$0.325047\pi$
$632$		−	9.84797i		−	0.391731i
$633$		0			0
$634$	−52.9338			−2.10227
$635$	−4.42354	−	7.66179i	−0.175543	−	0.304049i
$636$		0			0
$637$		0			0
$638$		−	8.74619i		−	0.346265i
$639$		0			0
$640$	22.0674	−	12.7406i	0.872292	−	0.503618i
$641$	16.5092	+	9.53157i	0.652073	+	0.376474i	0.789250	−	0.614072i	$-0.210470\pi$
$641$	16.5092	+	9.53157i	0.652073	+	0.376474i	−0.137177	+	0.990547i	$0.543803\pi$
$642$		0			0
$643$	15.3447	+	8.85928i	0.605136	+	0.349376i	0.771060	−	0.636763i	$-0.219727\pi$
$643$	15.3447	+	8.85928i	0.605136	+	0.349376i	−0.165923	+	0.986139i	$0.553060\pi$
$644$		0			0
$645$		0			0
$646$	−11.1521			−0.438774
$647$	−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
$653$	−13.0852	+	7.55475i	−0.512064	+	0.295640i	−0.733682	−	0.679493i	$-0.762200\pi$
$653$	−13.0852	+	7.55475i	−0.512064	+	0.295640i	0.221618	+	0.975134i	$0.428866\pi$
$654$		0			0
$655$	5.92558	−	10.2634i	0.231532	−	0.401024i
$656$	−0.888629	+	1.53915i	−0.0346951	+	0.0600938i
$657$		0			0
$658$		0			0
$659$	27.1850	−	15.6952i	1.05898	−	0.611400i	0.133827	−	0.991005i	$-0.457273\pi$
$659$	27.1850	−	15.6952i	1.05898	−	0.611400i	0.925149	+	0.379605i	$0.123940\pi$
$660$		0			0
$661$			43.7116i			1.70019i	0.526633	+	0.850093i	$0.323454\pi$
$661$			43.7116i			1.70019i	−0.526633	+	0.850093i	$0.676546\pi$
$662$		−	43.6139i		−	1.69510i
$663$		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
$668$	27.5371	−	47.6957i	1.06544	−	1.84540i
$669$		0			0
$670$	1.86673	−	1.07776i	0.0721181	−	0.0416374i
$671$	−5.28096	+	9.14690i	−0.203869	+	0.353112i
$672$		0			0
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	0.763495	−	0.645814i	$-0.223482\pi$
$673$	−4.60589	−	7.97763i	−0.177544	−	0.307515i	−0.941039	+	0.338299i	$0.890149\pi$
$674$	56.2960	+	32.5025i	2.16844	+	1.25195i
$675$		0			0
$676$	−21.0104	−	36.3911i	−0.808092	−	1.39966i
$677$	−22.8387			−0.877763			−0.438882	−	0.898545i	$-0.644625\pi$
$677$	−22.8387			−0.877763			−0.438882	+	0.898545i	$0.644625\pi$
$678$		0			0
$679$		0			0
$680$	3.64721	+	2.10571i	0.139864	+	0.0807505i
$681$		0			0
$682$	23.8792	+	13.7867i	0.914383	+	0.527919i
$683$	29.6030	−	17.0913i	1.13273	−	0.653981i	0.188108	−	0.982148i	$-0.439764\pi$
$683$	29.6030	−	17.0913i	1.13273	−	0.653981i	0.944619	+	0.328168i	$0.106431\pi$
$684$		0			0
$685$			14.8421i			0.567088i
$686$		0			0
$687$		0			0
$688$	0.914230	+	1.58349i	0.0348547	+	0.0603701i
$689$	35.9066			1.36793
$690$		0			0
$691$		−	0.258747i		−	0.00984320i	−0.999988	−	0.00492160i	$-0.998433\pi$
$691$		−	0.258747i		−	0.00984320i	0.999988	−	0.00492160i	$-0.00156660\pi$
$692$	6.22453			0.236621
$693$		0			0
$694$	−6.74720			−0.256120
$695$			25.6026i			0.971163i
$696$		0			0
$697$	−8.11109			−0.307229
$698$	30.7389	+	53.2413i	1.16348	+	2.01521i
$699$		0			0
$700$		0			0
$701$			5.16189i			0.194962i	0.995237	+	0.0974810i	$0.0310785\pi$
$701$			5.16189i			0.194962i	−0.995237	+	0.0974810i	$0.968921\pi$
$702$		0			0
$703$	−0.929636	+	0.536725i	−0.0350619	+	0.0202430i
$704$	36.4487	+	21.0437i	1.37371	+	0.793113i
$705$		0			0
$706$	58.4475	+	33.7447i	2.19970	+	1.27000i
$707$		0			0
$708$		0			0
$709$	23.4944			0.882351			0.441175	−	0.897421i	$-0.354562\pi$
$709$	23.4944			0.882351			0.441175	+	0.897421i	$0.354562\pi$
$710$	−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
$716$	−63.9357	+	36.9133i	−2.38939	+	1.37952i
$717$		0			0
$718$	−28.0293	+	48.5481i	−1.04604	+	1.81180i
$719$	−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
$724$			32.6925i			1.21501i
$725$			3.49523i			0.129809i
$726$		0			0
$727$	−5.74874	+	3.31904i	−0.213209	+	0.123096i	−0.602802	−	0.797891i	$-0.705949\pi$
$727$	−5.74874	+	3.31904i	−0.213209	+	0.123096i	0.389593	+	0.920987i	$0.372616\pi$
$728$		0			0
$729$		0			0
$730$	11.9347	−	20.6716i	0.441725	−	0.765089i
$731$	−4.17238	+	7.22678i	−0.154321	+	0.267292i
$732$		0			0
$733$	−5.20130	+	3.00297i	−0.192114	+	0.110917i	−0.592972	−	0.805223i	$-0.702046\pi$
$733$	−5.20130	+	3.00297i	−0.192114	+	0.110917i	0.400858	+	0.916140i	$0.368712\pi$
$734$	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	$0.740463\pi$
$740$	1.09132			0.0401176
$741$		0			0
$742$		0			0
$743$	−27.3807	−	15.8083i	−1.00450	−	0.579949i	−0.0949246	−	0.995484i	$-0.530261\pi$
$743$	−27.3807	−	15.8083i	−1.00450	−	0.579949i	−0.909577	+	0.415535i	$0.863594\pi$
$744$		0			0
$745$	21.7664	+	12.5669i	0.797461	+	0.460414i
$746$	−7.36032	+	4.24948i	−0.269480	+	0.155585i
$747$		0			0
$748$			11.2332i			0.410727i
$749$		0			0
$750$		0			0
$751$	7.13680	+	12.3613i	0.260426	+	0.451070i	0.966355	−	0.257212i	$-0.0828038\pi$
$751$	7.13680	+	12.3613i	0.260426	+	0.451070i	−0.705929	+	0.708282i	$0.749470\pi$
$752$	−1.00930			−0.0368055
$753$		0			0
$754$			13.8407i			0.504049i
$755$	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	$0.563016\pi$
$758$		−	69.2975i		−	2.51700i
$759$		0			0
$760$	17.3236			0.628395
$761$	−2.93098	−	5.07660i	−0.106248	−	0.184027i	0.808000	−	0.589183i	$-0.200550\pi$
$761$	−2.93098	−	5.07660i	−0.106248	−	0.184027i	−0.914247	+	0.405157i	$0.867217\pi$
$762$		0			0
$763$		0			0
$764$			72.2926i			2.61546i
$765$		0			0
$766$	33.4844	−	19.3323i	1.20984	−	0.698503i
$767$	−41.9865	−	24.2409i	−1.51604	−	0.875288i
$768$		0			0
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.906509	−	0.422186i	$-0.138737\pi$
$769$	27.5683	+	15.9166i	0.994140	+	0.573967i	0.0876307	+	0.996153i	$0.472070\pi$
$770$		0			0
$771$		0			0
$772$	−53.6856			−1.93219
$773$	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
$779$	−28.8948	+	16.6824i	−1.03526	+	0.597710i
$780$		0			0
$781$	6.18427	−	10.7115i	0.221290	−	0.383286i
$782$	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
$787$			18.9513i			0.675540i	0.941229	+	0.337770i	$0.109673\pi$
$787$			18.9513i			0.675540i	−0.941229	+	0.337770i	$0.890327\pi$
$788$			28.4601i			1.01385i
$789$		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
$794$	25.3857	−	43.9693i	0.900905	−	1.56041i
$795$		0			0
$796$	15.9422	−	9.20422i	0.565055	−	0.326235i
$797$	26.7207	−	46.2816i	0.946497	−	1.63938i	0.193770	−	0.981047i	$-0.437929\pi$
$797$	26.7207	−	46.2816i	0.946497	−	1.63938i	0.752727	−	0.658333i	$-0.228738\pi$
$798$		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
$803$	23.6495			0.834571
$804$		0			0
$805$		0			0
$806$	−37.7885	−	21.8172i	−1.33104	−	0.768479i
$807$		0			0
$808$	−16.5190	−	9.53727i	−0.581137	−	0.335520i
$809$	−2.23517	+	1.29047i	−0.0785842	+	0.0453706i	−0.538777	−	0.842448i	$-0.681114\pi$
$809$	−2.23517	+	1.29047i	−0.0785842	+	0.0453706i	0.460193	+	0.887819i	$0.347780\pi$
$810$		0			0
$811$		−	6.06938i		−	0.213125i	−0.994306	−	0.106562i	$-0.966016\pi$
$811$		−	6.06938i		−	0.213125i	0.994306	−	0.106562i	$-0.0339844\pi$
$812$		0			0
$813$		0			0
$814$	0.880438	+	1.52496i	0.0308593	+	0.0534500i
$815$	−10.3634			−0.363013
$816$		0			0
$817$			34.3261i			1.20092i
$818$	−59.9811			−2.09719
$819$		0			0
$820$	33.9201			1.18454
$821$		−	9.28308i		−	0.323982i	−0.986792	−	0.161991i	$-0.948208\pi$
$821$		−	9.28308i		−	0.323982i	0.986792	−	0.161991i	$-0.0517915\pi$
$822$		0			0
$823$	18.0690			0.629844			0.314922	−	0.949117i	$-0.398022\pi$
$823$	18.0690			0.629844			0.314922	+	0.949117i	$0.398022\pi$
$824$	−2.29172	−	3.96937i	−0.0798357	−	0.138280i
$825$		0			0
$826$		0			0
$827$		−	48.5440i		−	1.68804i	−0.536310	−	0.844021i	$-0.680182\pi$
$827$		−	48.5440i		−	1.68804i	0.536310	−	0.844021i	$-0.319818\pi$
$828$		0			0
$829$	4.71804	−	2.72396i	0.163864	−	0.0946071i	−0.415825	−	0.909445i	$-0.636507\pi$
$829$	4.71804	−	2.72396i	0.163864	−	0.0946071i	0.579689	+	0.814837i	$0.303174\pi$
$830$	−30.8344	−	17.8022i	−1.07028	−	0.617924i
$831$		0			0
$832$	−57.6796	−	33.3013i	−1.99968	−	1.15452i
$833$		0			0
$834$		0			0
$835$	24.8252			0.859111
$836$	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	0.891729	+	0.452569i	$0.149492\pi$
$839$	24.2673	+	42.0322i	0.837801	+	1.45111i	−0.0539281	+	0.998545i	$0.517174\pi$
$840$		0			0
$841$	−13.7947	+	23.8931i	−0.475678	+	0.823899i
$842$	21.8727	−	12.6282i	0.753781	−	0.435196i
$843$		0			0
$844$	41.1907	−	71.3444i	1.41784	−	2.45578i
$845$	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
$850$		−	7.31073i		−	0.250756i
$851$		−	0.958511i		−	0.0328573i
$852$		0			0
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	−0.672920	−	0.739715i	$-0.734960\pi$
$853$	−10.7703	+	6.21823i	−0.368768	+	0.212908i	0.304152	+	0.952623i	$0.401627\pi$
$854$		0			0
$855$		0			0
$856$	−6.64007	+	11.5009i	−0.226953	+	0.393094i
$857$	−5.29077	+	9.16388i	−0.180729	+	0.313032i	−0.942129	−	0.335250i	$-0.891179\pi$
$857$	−5.29077	+	9.16388i	−0.180729	+	0.313032i	0.761400	+	0.648283i	$0.224512\pi$
$858$		0			0
$859$	28.1452	−	16.2496i	0.960302	−	0.554431i	0.0640360	−	0.997948i	$-0.479603\pi$
$859$	28.1452	−	16.2496i	0.960302	−	0.554431i	0.896266	+	0.443517i	$0.146269\pi$
$860$	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	0.823337	−	0.567552i	$-0.192110\pi$
$863$	21.8414	+	12.6102i	0.743491	+	0.429255i	−0.0798460	+	0.996807i	$0.525443\pi$
$864$		0			0
$865$	1.40288	+	2.42986i	0.0476994	+	0.0826177i
$866$	−28.5366			−0.969715
$867$		0			0
$868$		0			0
$869$	10.2540	+	5.92017i	0.347844	+	0.200828i
$870$		0			0
$871$	−2.92685	−	1.68982i	−0.0991724	−	0.0572572i
$872$	−18.9633	+	10.9485i	−0.642179	+	0.370762i
$873$		0			0
$874$		−	40.9621i		−	1.38556i
$875$		0			0
$876$		0			0
$877$	7.47893	+	12.9539i	0.252546	+	0.437422i	0.964226	−	0.265082i	$-0.0853989\pi$
$877$	7.47893	+	12.9539i	0.252546	+	0.437422i	−0.711680	+	0.702503i	$0.752066\pi$
$878$	−42.3921			−1.43067
$879$		0			0
$880$			1.10948i			0.0374005i
$881$	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	$0.413328\pi$
$884$		−	17.7764i		−	0.597884i
$885$		0			0
$886$	10.8148			0.363330
$887$	−24.5208	−	42.4713i	−0.823329	−	1.42605i	−0.903190	−	0.429241i	$-0.858781\pi$
$887$	−24.5208	−	42.4713i	−0.823329	−	1.42605i	0.0798613	−	0.996806i	$-0.474552\pi$
$888$		0			0
$889$		0			0
$890$			44.7026i			1.49843i
$891$		0			0
$892$	49.2649	−	28.4431i	1.64951	−	0.952346i
$893$	−16.4093	−	9.47393i	−0.549117	−	0.317033i
$894$		0			0
$895$	−28.8196	−	16.6390i	−0.963332	−	0.556180i
$896$		0			0
$897$		0			0
$898$	36.9669			1.23360
$899$	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
$905$	−12.7621	+	7.36821i	−0.424227	+	0.244928i
$906$		0			0
$907$	2.42915	−	4.20741i	0.0806585	−	0.139705i	−0.822874	−	0.568223i	$-0.807631\pi$
$907$	2.42915	−	4.20741i	0.0806585	−	0.139705i	0.903533	+	0.428519i	$0.140964\pi$
$908$	17.4487	−	30.2220i	0.579054	−	1.00295i
$909$		0			0
$910$		0			0
$911$	−14.4945	+	8.36843i	−0.480226	+	0.277258i	−0.720510	−	0.693444i	$-0.756092\pi$
$911$	−14.4945	+	8.36843i	−0.480226	+	0.277258i	0.240285	+	0.970702i	$0.422759\pi$
$912$		0			0
$913$		−	35.2763i		−	1.16747i
$914$		−	13.0829i		−	0.432743i
$915$		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	$0.998026\pi$
$920$	−7.73436	+	13.3963i	−0.254994	+	0.441663i
$921$		0			0
$922$	−71.5015	+	41.2814i	−2.35478	+	1.35953i
$923$	−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
$929$	29.7445			0.975885			0.487943	−	0.872876i	$-0.337747\pi$
$929$	29.7445			0.975885			0.487943	+	0.872876i	$0.337747\pi$
$930$		0			0
$931$		0			0
$932$	8.10245	+	4.67795i	0.265405	+	0.153231i
$933$		0			0
$934$	−5.20876	−	3.00728i	−0.170436	−	0.0984011i
$935$	−4.38508	+	2.53173i	−0.143408	+	0.0827964i
$936$		0			0
$937$		−	4.03712i		−	0.131887i	−0.997823	−	0.0659434i	$-0.978994\pi$
$937$		−	4.03712i		−	0.131887i	0.997823	−	0.0659434i	$-0.0210057\pi$
$938$		0			0
$939$		0			0
$940$	9.63160	+	16.6824i	0.314148	+	0.544121i
$941$	14.4053			0.469599			0.234799	−	0.972044i	$-0.424557\pi$
$941$	14.4053			0.469599			0.234799	+	0.972044i	$0.424557\pi$
$942$		0			0
$943$		−	29.7923i		−	0.970171i
$944$	−2.26464			−0.0737079
$945$		0			0
$946$	56.3081			1.83073
$947$		−	31.2155i		−	1.01437i	−0.861838	−	0.507183i	$-0.830687\pi$
$947$		−	31.2155i		−	1.01437i	0.861838	−	0.507183i	$-0.169313\pi$
$948$		0			0
$949$	−37.4249			−1.21486
$950$	−15.0363	−	26.0436i	−0.487841	−	0.844966i
$951$		0			0
$952$		0			0
$953$			8.55869i			0.277243i	0.990345	+	0.138622i	$0.0442672\pi$
$953$			8.55869i			0.277243i	−0.990345	+	0.138622i	$0.955733\pi$
$954$		0			0
$955$	−28.2207	+	16.2933i	−0.913202	+	0.527237i
$956$	−34.1278	−	19.7037i	−1.10377	−	0.637263i
$957$		0			0
$958$	−61.2751	−	35.3772i	−1.97971	−	1.14298i
$959$		0			0
$960$		0			0
$961$	16.9795			0.547724
$962$	−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	−0.484413	−	0.874840i	$-0.660967\pi$
$967$	16.0280	−	27.7614i	0.515427	−	0.892745i	0.999840	−	0.0179059i	$-0.00569994\pi$
$968$	−1.24759	+	0.720299i	−0.0400992	+	0.0231513i
$969$		0			0
$970$	−5.08414	+	8.80598i	−0.163242	+	0.282743i
$971$	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
$976$		−	0.780736i		−	0.0249908i
$977$			52.1414i			1.66815i	0.551649	+	0.834076i	$0.313999\pi$
$977$			52.1414i			1.66815i	−0.551649	+	0.834076i	$0.686001\pi$
$978$		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
$983$	12.1192	−	20.9911i	0.386544	−	0.669513i	−0.605438	−	0.795892i	$-0.707002\pi$
$983$	12.1192	−	20.9911i	0.386544	−	0.669513i	0.991982	+	0.126379i	$0.0403356\pi$
$984$		0			0
$985$	−11.1099	+	6.41432i	−0.353992	+	0.204377i
$986$	−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	$0.707763\pi$
$992$	−22.1873			−0.704448
$993$		0			0
$994$		0			0
$995$	7.18607	+	4.14888i	0.227814	+	0.131528i
$996$		0			0
$997$	−8.81920	−	5.09177i	−0.279307	−	0.161258i	0.353803	−	0.935320i	$-0.384888\pi$
$997$	−8.81920	−	5.09177i	−0.279307	−	0.161258i	−0.633110	+	0.774062i	$0.718222\pi$
$998$	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.i.c.1097.5		12
3.2	odd	2		441.2.i.c.68.1		12
7.2	even	3		189.2.o.a.125.5		12
7.3	odd	6		1323.2.s.c.962.1		12
7.4	even	3		1323.2.s.c.962.2		12
7.5	odd	6		189.2.o.a.125.6		12
7.6	odd	2	inner	1323.2.i.c.1097.6		12
9.2	odd	6		1323.2.s.c.656.1		12
9.7	even	3		441.2.s.c.362.5		12
21.2	odd	6		63.2.o.a.41.1	yes	12
21.5	even	6		63.2.o.a.41.2	yes	12
21.11	odd	6		441.2.s.c.374.6		12
21.17	even	6		441.2.s.c.374.5		12
21.20	even	2		441.2.i.c.68.2		12
28.19	even	6		3024.2.cc.a.881.4		12
28.23	odd	6		3024.2.cc.a.881.3		12
63.2	odd	6		189.2.o.a.62.6		12
63.5	even	6		567.2.c.c.566.2		12
63.11	odd	6	inner	1323.2.i.c.521.2		12
63.16	even	3		63.2.o.a.20.2	yes	12
63.20	even	6		1323.2.s.c.656.2		12
63.23	odd	6		567.2.c.c.566.1		12
63.25	even	3		441.2.i.c.227.6		12
63.34	odd	6		441.2.s.c.362.6		12
63.38	even	6	inner	1323.2.i.c.521.1		12
63.40	odd	6		567.2.c.c.566.11		12
63.47	even	6		189.2.o.a.62.5		12
63.52	odd	6		441.2.i.c.227.5		12
63.58	even	3		567.2.c.c.566.12		12
63.61	odd	6		63.2.o.a.20.1	✓	12
84.23	even	6		1008.2.cc.a.545.5		12
84.47	odd	6		1008.2.cc.a.545.2		12
252.47	odd	6		3024.2.cc.a.2897.3		12
252.79	odd	6		1008.2.cc.a.209.2		12
252.187	even	6		1008.2.cc.a.209.5		12
252.191	even	6		3024.2.cc.a.2897.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.1	✓	12	63.61	odd	6
63.2.o.a.20.2	yes	12	63.16	even	3
63.2.o.a.41.1	yes	12	21.2	odd	6
63.2.o.a.41.2	yes	12	21.5	even	6
189.2.o.a.62.5		12	63.47	even	6
189.2.o.a.62.6		12	63.2	odd	6
189.2.o.a.125.5		12	7.2	even	3
189.2.o.a.125.6		12	7.5	odd	6
441.2.i.c.68.1		12	3.2	odd	2
441.2.i.c.68.2		12	21.20	even	2
441.2.i.c.227.5		12	63.52	odd	6
441.2.i.c.227.6		12	63.25	even	3
441.2.s.c.362.5		12	9.7	even	3
441.2.s.c.362.6		12	63.34	odd	6
441.2.s.c.374.5		12	21.17	even	6
441.2.s.c.374.6		12	21.11	odd	6
567.2.c.c.566.1		12	63.23	odd	6
567.2.c.c.566.2		12	63.5	even	6
567.2.c.c.566.11		12	63.40	odd	6
567.2.c.c.566.12		12	63.58	even	3
1008.2.cc.a.209.2		12	252.79	odd	6
1008.2.cc.a.209.5		12	252.187	even	6
1008.2.cc.a.545.2		12	84.47	odd	6
1008.2.cc.a.545.5		12	84.23	even	6
1323.2.i.c.521.1		12	63.38	even	6	inner
1323.2.i.c.521.2		12	63.11	odd	6	inner
1323.2.i.c.1097.5		12	1.1	even	1	trivial
1323.2.i.c.1097.6		12	7.6	odd	2	inner
1323.2.s.c.656.1		12	9.2	odd	6
1323.2.s.c.656.2		12	63.20	even	6
1323.2.s.c.962.1		12	7.3	odd	6
1323.2.s.c.962.2		12	7.4	even	3
3024.2.cc.a.881.3		12	28.23	odd	6
3024.2.cc.a.881.4		12	28.19	even	6
3024.2.cc.a.2897.3		12	252.47	odd	6
3024.2.cc.a.2897.4		12	252.191	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.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.27639i q^{2} -3.18194 q^{4} +(-0.717144 - 1.24213i) q^{5} -2.69056i q^{8} +O(q^{10})\)	\(q+2.27639i q^{2} -3.18194 q^{4} +(-0.717144 - 1.24213i) q^{5} -2.69056i q^{8} +(2.82757 - 1.63250i) q^{10} +(2.80150 + 1.61745i) q^{11} +(-4.43334 - 2.55959i) q^{13} -0.239123 q^{16} +(-0.545658 - 0.945107i) q^{17} +(-3.88768 - 2.24456i) q^{19} +(2.28191 + 3.95238i) q^{20} +(-3.68194 + 6.37731i) q^{22} +(3.47141 - 2.00422i) q^{23} +(1.47141 - 2.54856i) q^{25} +(5.82662 - 10.0920i) q^{26} +(-1.02859 + 0.593857i) q^{29} -3.74440i q^{31} -5.92546i q^{32} +(2.15143 - 1.24213i) q^{34} +(0.119562 - 0.207087i) q^{37} +(5.10948 - 8.84988i) q^{38} +(-3.34203 + 1.92952i) q^{40} +(3.71620 - 6.43664i) q^{41} +(-3.82326 - 6.62208i) q^{43} +(-8.91423 - 5.14663i) q^{44} +(4.56238 + 7.90228i) q^{46} +4.22085 q^{47} +(5.80150 + 3.34950i) q^{50} +(14.1066 + 8.14447i) q^{52} +(-6.07442 + 3.50707i) q^{53} -4.63977i q^{55} +(-1.35185 - 2.34147i) q^{58} +9.47061 q^{59} +3.26499i q^{61} +8.52371 q^{62} +13.0104 q^{64} +7.34238i q^{65} +0.660190 q^{67} +(1.73625 + 3.00728i) q^{68} -3.82347i q^{71} +(6.33127 - 3.65536i) q^{73} +(0.471410 + 0.272169i) q^{74} +(12.3704 + 7.14205i) q^{76} +3.66019 q^{79} +(0.171486 + 0.297022i) q^{80} +(14.6523 + 8.45951i) q^{82} +(-5.45245 - 9.44392i) q^{83} +(-0.782630 + 1.35556i) q^{85} +(15.0744 - 8.70322i) q^{86} +(4.35185 - 7.53762i) q^{88} +(-6.84573 + 11.8572i) q^{89} +(-11.0458 + 6.37731i) q^{92} +9.60829i q^{94} +6.43867i q^{95} +(-2.69709 + 1.55716i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4}+O(q^{10}) \) 12 * q - 4 * q^4	\( 12 q - 4 q^{4} - 4 q^{16} - 10 q^{22} + 24 q^{23} - 30 q^{29} + 2 q^{37} - 10 q^{43} - 54 q^{44} + 20 q^{46} + 36 q^{50} + 12 q^{53} + 2 q^{58} + 16 q^{64} - 24 q^{67} - 12 q^{74} + 12 q^{79} - 6 q^{85} + 96 q^{86} + 34 q^{88} - 30 q^{92}+O(q^{100}) \) 12 * q - 4 * q^4 - 4 * q^16 - 10 * q^22 + 24 * q^23 - 30 * q^29 + 2 * q^37 - 10 * q^43 - 54 * q^44 + 20 * q^46 + 36 * q^50 + 12 * q^53 + 2 * q^58 + 16 * q^64 - 24 * q^67 - 12 * q^74 + 12 * q^79 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 30 * q^92

Introduction

L-functions

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Database

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