LMFDB - Embedded newform 504.2.t.c.193.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.10
Character	$\chi$	$=$	504.193
Dual form			504.2.t.c.457.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52946 + 0.812868i) q^{3} -3.79940 q^{5} +(2.59312 + 0.525101i) q^{7} +(1.67849 + 2.48650i) q^{9} +O(q^{10})$	\(q+(1.52946 + 0.812868i) q^{3} -3.79940 q^{5} +(2.59312 + 0.525101i) q^{7} +(1.67849 + 2.48650i) q^{9} +4.51412 q^{11} +(0.588451 - 1.01923i) q^{13} +(-5.81103 - 3.08841i) q^{15} +(-2.95973 + 5.12641i) q^{17} +(2.55676 + 4.42844i) q^{19} +(3.53923 + 2.91098i) q^{21} -4.18164 q^{23} +9.43545 q^{25} +(0.545992 + 5.16739i) q^{27} +(2.11164 + 3.65747i) q^{29} +(3.12141 + 5.40645i) q^{31} +(6.90416 + 3.66938i) q^{33} +(-9.85230 - 1.99507i) q^{35} +(-3.87179 - 6.70614i) q^{37} +(1.72851 - 1.08053i) q^{39} +(0.754693 - 1.30717i) q^{41} +(-5.01709 - 8.68986i) q^{43} +(-6.37726 - 9.44720i) q^{45} +(1.11832 - 1.93699i) q^{47} +(6.44854 + 2.72330i) q^{49} +(-8.69389 + 5.43476i) q^{51} +(6.49368 - 11.2474i) q^{53} -17.1510 q^{55} +(0.310726 + 8.85143i) q^{57} +(-6.19609 - 10.7319i) q^{59} +(-0.729171 + 1.26296i) q^{61} +(3.04687 + 7.32916i) q^{63} +(-2.23576 + 3.87245i) q^{65} +(-0.813192 - 1.40849i) q^{67} +(-6.39564 - 3.39912i) q^{69} +8.48517 q^{71} +(3.72984 - 6.46027i) q^{73} +(14.4311 + 7.66977i) q^{75} +(11.7057 + 2.37037i) q^{77} +(0.920926 - 1.59509i) q^{79} +(-3.36533 + 8.34713i) q^{81} +(-0.307606 - 0.532789i) q^{83} +(11.2452 - 19.4773i) q^{85} +(0.256630 + 7.31043i) q^{87} +(-1.25572 - 2.17496i) q^{89} +(2.06112 - 2.33398i) q^{91} +(0.379348 + 10.8062i) q^{93} +(-9.71417 - 16.8254i) q^{95} +(2.36751 + 4.10064i) q^{97} +(7.57691 + 11.2243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.52946	+	0.812868i	0.883034	+	0.469309i
$3$	1.52946	+	0.812868i	0.883034	+	0.469309i
$4$		0			0
$5$	−3.79940			−1.69914			−0.849572	−	0.527473i	$-0.823140\pi$
$5$	−3.79940			−1.69914			−0.849572	+	0.527473i	$0.823140\pi$
$6$		0			0
$7$	2.59312	+	0.525101i	0.980107	+	0.198470i
$7$	2.59312	+	0.525101i	0.980107	+	0.198470i
$8$		0			0
$9$	1.67849	+	2.48650i	0.559497	+	0.828832i
$10$		0			0
$11$	4.51412			1.36106			0.680529	−	0.732721i	$-0.261750\pi$
$11$	4.51412			1.36106			0.680529	+	0.732721i	$0.261750\pi$
$12$		0			0
$13$	0.588451	−	1.01923i	0.163207	−	0.282683i	−0.772810	−	0.634637i	$-0.781150\pi$
$13$	0.588451	−	1.01923i	0.163207	−	0.282683i	0.936017	+	0.351955i	$0.114483\pi$
$14$		0			0
$15$	−5.81103	−	3.08841i	−1.50040	−	0.797424i
$16$		0			0
$17$	−2.95973	+	5.12641i	−0.717841	+	1.24334i	0.244012	+	0.969772i	$0.421536\pi$
$17$	−2.95973	+	5.12641i	−0.717841	+	1.24334i	−0.961853	+	0.273565i	$0.911797\pi$
$18$		0			0
$19$	2.55676	+	4.42844i	0.586562	+	1.01595i	0.994679	+	0.103025i	$0.0328521\pi$
$19$	2.55676	+	4.42844i	0.586562	+	1.01595i	−0.408117	+	0.912930i	$0.633815\pi$
$20$		0			0
$21$	3.53923	+	2.91098i	0.772324	+	0.635229i
$22$		0			0
$23$	−4.18164			−0.871931			−0.435966	−	0.899963i	$-0.643593\pi$
$23$	−4.18164			−0.871931			−0.435966	+	0.899963i	$0.643593\pi$
$24$		0			0
$25$	9.43545			1.88709
$26$		0			0
$27$	0.545992	+	5.16739i	0.105076	+	0.994464i
$28$		0			0
$29$	2.11164	+	3.65747i	0.392122	+	0.679175i	0.992729	−	0.120369i	$-0.0384078\pi$
$29$	2.11164	+	3.65747i	0.392122	+	0.679175i	−0.600607	+	0.799544i	$0.705075\pi$
$30$		0			0
$31$	3.12141	+	5.40645i	0.560622	+	0.971027i	0.997442	+	0.0714776i	$0.0227714\pi$
$31$	3.12141	+	5.40645i	0.560622	+	0.971027i	−0.436820	+	0.899549i	$0.643895\pi$
$32$		0			0
$33$	6.90416	+	3.66938i	1.20186	+	0.638758i
$34$		0			0
$35$	−9.85230	−	1.99507i	−1.66534	−	0.337229i
$36$		0			0
$37$	−3.87179	−	6.70614i	−0.636519	−	1.10248i	−0.986191	−	0.165611i	$-0.947040\pi$
$37$	−3.87179	−	6.70614i	−0.636519	−	1.10248i	0.349672	−	0.936872i	$-0.386293\pi$
$38$		0			0
$39$	1.72851	−	1.08053i	0.276783	−	0.173024i
$40$		0			0
$41$	0.754693	−	1.30717i	0.117863	−	0.204145i	−0.801057	−	0.598587i	$-0.795729\pi$
$41$	0.754693	−	1.30717i	0.117863	−	0.204145i	0.918921	+	0.394442i	$0.129062\pi$
$42$		0			0
$43$	−5.01709	−	8.68986i	−0.765099	−	1.32519i	−0.940194	−	0.340639i	$-0.889357\pi$
$43$	−5.01709	−	8.68986i	−0.765099	−	1.32519i	0.175095	−	0.984552i	$-0.443977\pi$
$44$		0			0
$45$	−6.37726	−	9.44720i	−0.950666	−	1.40831i
$46$		0			0
$47$	1.11832	−	1.93699i	0.163124	−	0.282539i	−0.772863	−	0.634572i	$-0.781176\pi$
$47$	1.11832	−	1.93699i	0.163124	−	0.282539i	0.935988	+	0.352033i	$0.114510\pi$
$48$		0			0
$49$	6.44854	+	2.72330i	0.921220	+	0.389043i
$50$		0			0
$51$	−8.69389	+	5.43476i	−1.21739	+	0.761019i
$52$		0			0
$53$	6.49368	−	11.2474i	0.891975	−	1.54495i	0.0544716	−	0.998515i	$-0.482653\pi$
$53$	6.49368	−	11.2474i	0.891975	−	1.54495i	0.837504	−	0.546431i	$-0.184014\pi$
$54$		0			0
$55$	−17.1510			−2.31263
$56$		0			0
$57$	0.310726	+	8.85143i	0.0411566	+	1.17240i
$58$		0			0
$59$	−6.19609	−	10.7319i	−0.806662	−	1.39718i	−0.915163	−	0.403083i	$-0.867939\pi$
$59$	−6.19609	−	10.7319i	−0.806662	−	1.39718i	0.108501	−	0.994096i	$-0.465395\pi$
$60$		0			0
$61$	−0.729171	+	1.26296i	−0.0933608	+	0.161706i	−0.908923	−	0.416963i	$-0.863094\pi$
$61$	−0.729171	+	1.26296i	−0.0933608	+	0.161706i	0.815563	+	0.578669i	$0.196428\pi$
$62$		0			0
$63$	3.04687	+	7.32916i	0.383869	+	0.923388i
$64$		0			0
$65$	−2.23576	+	3.87245i	−0.277312	+	0.480318i
$66$		0			0
$67$	−0.813192	−	1.40849i	−0.0993472	−	0.172074i	0.812067	−	0.583564i	$-0.198342\pi$
$67$	−0.813192	−	1.40849i	−0.0993472	−	0.172074i	−0.911415	+	0.411489i	$0.865009\pi$
$68$		0			0
$69$	−6.39564	−	3.39912i	−0.769945	−	0.409206i
$70$		0			0
$71$	8.48517			1.00700			0.503502	−	0.863994i	$-0.332045\pi$
$71$	8.48517			1.00700			0.503502	+	0.863994i	$0.332045\pi$
$72$		0			0
$73$	3.72984	−	6.46027i	0.436544	−	0.756117i	−0.560876	−	0.827900i	$-0.689535\pi$
$73$	3.72984	−	6.46027i	0.436544	−	0.756117i	0.997420	+	0.0717827i	$0.0228688\pi$
$74$		0			0
$75$	14.4311	+	7.66977i	1.66636	+	0.885629i
$76$		0			0
$77$	11.7057	+	2.37037i	1.33398	+	0.270129i
$78$		0			0
$79$	0.920926	−	1.59509i	0.103612	−	0.179462i	−0.809558	−	0.587040i	$-0.800293\pi$
$79$	0.920926	−	1.59509i	0.103612	−	0.179462i	0.913170	+	0.407578i	$0.133627\pi$
$80$		0			0
$81$	−3.36533	+	8.34713i	−0.373926	+	0.927459i
$82$		0			0
$83$	−0.307606	−	0.532789i	−0.0337641	−	0.0584812i	0.848650	−	0.528956i	$-0.177416\pi$
$83$	−0.307606	−	0.532789i	−0.0337641	−	0.0584812i	−0.882414	+	0.470474i	$0.844083\pi$
$84$		0			0
$85$	11.2452	−	19.4773i	1.21972	−	2.11261i
$86$		0			0
$87$	0.256630	+	7.31043i	0.0275136	+	0.783761i
$88$		0			0
$89$	−1.25572	−	2.17496i	−0.133106	−	0.230546i	0.791767	−	0.610824i	$-0.209162\pi$
$89$	−1.25572	−	2.17496i	−0.133106	−	0.230546i	−0.924872	+	0.380278i	$0.875828\pi$
$90$		0			0
$91$	2.06112	−	2.33398i	0.216064	−	0.244668i
$92$		0			0
$93$	0.379348	+	10.8062i	0.0393366	+	1.12055i
$94$		0			0
$95$	−9.71417	−	16.8254i	−0.996652	−	1.72625i
$96$		0			0
$97$	2.36751	+	4.10064i	0.240384	+	0.416357i	0.960824	−	0.277160i	$-0.0893934\pi$
$97$	2.36751	+	4.10064i	0.240384	+	0.416357i	−0.720440	+	0.693517i	$0.756060\pi$
$98$		0			0
$99$	7.57691	+	11.2243i	0.761508	+	1.12809i
$100$		0			0
$101$	−11.4216			−1.13649			−0.568247	−	0.822858i	$-0.692378\pi$
$101$	−11.4216			−1.13649			−0.568247	+	0.822858i	$0.692378\pi$
$102$		0			0
$103$	−6.37505			−0.628152			−0.314076	−	0.949398i	$-0.601695\pi$
$103$	−6.37505			−0.628152			−0.314076	+	0.949398i	$0.601695\pi$
$104$		0			0
$105$	−13.4470	−	11.0600i	−1.31229	−	1.07935i
$106$		0			0
$107$	1.11999	+	1.93988i	0.108274	+	0.187536i	0.915071	−	0.403293i	$-0.132134\pi$
$107$	1.11999	+	1.93988i	0.108274	+	0.187536i	−0.806797	+	0.590828i	$0.798801\pi$
$108$		0			0
$109$	−2.73089	+	4.73005i	−0.261572	+	0.453056i	−0.966660	−	0.256064i	$-0.917574\pi$
$109$	−2.73089	+	4.73005i	−0.261572	+	0.453056i	0.705088	+	0.709120i	$0.250908\pi$
$110$		0			0
$111$	−0.470543	−	13.4040i	−0.0446619	−	1.27225i
$112$		0			0
$113$	−4.45456	+	7.71553i	−0.419050	+	0.725816i	−0.995844	−	0.0910734i	$-0.970970\pi$
$113$	−4.45456	+	7.71553i	−0.419050	+	0.725816i	0.576794	+	0.816890i	$0.304304\pi$
$114$		0			0
$115$	15.8877			1.48154
$116$		0			0
$117$	3.52201	−	0.247583i	0.325610	−	0.0228890i
$118$		0			0
$119$	−10.3668	+	11.7392i	−0.950326	+	1.07613i
$120$		0			0
$121$	9.37728			0.852480
$122$		0			0
$123$	2.21683	−	1.38579i	0.199884	−	0.124953i
$124$		0			0
$125$	−16.8520			−1.50729
$126$		0			0
$127$	0.434918			0.0385927			0.0192964	−	0.999814i	$-0.493857\pi$
$127$	0.434918			0.0385927			0.0192964	+	0.999814i	$0.493857\pi$
$128$		0			0
$129$	−0.609732	−	17.3690i	−0.0536839	−	1.52926i
$130$		0			0
$131$	−5.35265			−0.467664			−0.233832	−	0.972277i	$-0.575126\pi$
$131$	−5.35265			−0.467664			−0.233832	+	0.972277i	$0.575126\pi$
$132$		0			0
$133$	4.30461	+	12.8260i	0.373257	+	1.11216i
$134$		0			0
$135$	−2.07444	−	19.6330i	−0.178539	−	1.68974i
$136$		0			0
$137$	5.90242			0.504278			0.252139	−	0.967691i	$-0.418866\pi$
$137$	5.90242			0.504278			0.252139	+	0.967691i	$0.418866\pi$
$138$		0			0
$139$	4.33649	−	7.51102i	0.367816	−	0.637077i	−0.621407	−	0.783488i	$-0.713439\pi$
$139$	4.33649	−	7.51102i	0.367816	−	0.637077i	0.989224	+	0.146411i	$0.0467721\pi$
$140$		0			0
$141$	3.28495	−	2.05350i	0.276643	−	0.172936i
$142$		0			0
$143$	2.65634	−	4.60091i	0.222134	−	0.384747i
$144$		0			0
$145$	−8.02297	−	13.8962i	−0.666271	−	1.15402i
$146$		0			0
$147$	7.64909	+	9.40699i	0.630886	+	0.775875i
$148$		0			0
$149$	−10.7772			−0.882903			−0.441451	−	0.897285i	$-0.645536\pi$
$149$	−10.7772			−0.882903			−0.441451	+	0.897285i	$0.645536\pi$
$150$		0			0
$151$	−16.8262			−1.36930			−0.684648	−	0.728873i	$-0.740044\pi$
$151$	−16.8262			−1.36930			−0.684648	+	0.728873i	$0.740044\pi$
$152$		0			0
$153$	−17.7147	+	1.24527i	−1.43215	+	0.100674i
$154$		0			0
$155$	−11.8595	−	20.5413i	−0.952578	−	1.64991i
$156$		0			0
$157$	−4.48068	−	7.76076i	−0.357597	−	0.619376i	0.629962	−	0.776626i	$-0.283071\pi$
$157$	−4.48068	−	7.76076i	−0.357597	−	0.619376i	−0.987559	+	0.157250i	$0.949737\pi$
$158$		0			0
$159$	19.0745	−	11.9239i	1.51270	−	0.945628i
$160$		0			0
$161$	−10.8435	−	2.19578i	−0.854586	−	0.173052i
$162$		0			0
$163$	−3.71319	−	6.43144i	−0.290840	−	0.503749i	0.683169	−	0.730261i	$-0.260601\pi$
$163$	−3.71319	−	6.43144i	−0.290840	−	0.503749i	−0.974009	+	0.226511i	$0.927268\pi$
$164$		0			0
$165$	−26.2317	−	13.9415i	−2.04213	−	1.08534i
$166$		0			0
$167$	−5.13764	+	8.89866i	−0.397563	+	0.688599i	−0.993425	−	0.114488i	$-0.963477\pi$
$167$	−5.13764	+	8.89866i	−0.397563	+	0.688599i	0.595862	+	0.803087i	$0.296811\pi$
$168$		0			0
$169$	5.80745	+	10.0588i	0.446727	+	0.773754i
$170$		0			0
$171$	−6.71980	+	13.7905i	−0.513876	+	1.05458i
$172$		0			0
$173$	5.10496	−	8.84205i	0.388123	−	0.672249i	−0.604074	−	0.796928i	$-0.706457\pi$
$173$	5.10496	−	8.84205i	0.388123	−	0.672249i	0.992197	+	0.124679i	$0.0397903\pi$
$174$		0			0
$175$	24.4672	+	4.95457i	1.84955	+	0.374530i
$176$		0			0
$177$	−0.753016	−	21.4507i	−0.0566002	−	1.61233i
$178$		0			0
$179$	9.62985	−	16.6794i	0.719769	−	1.24668i	−0.241323	−	0.970445i	$-0.577581\pi$
$179$	9.62985	−	16.6794i	0.719769	−	1.24668i	0.961091	−	0.276231i	$-0.0890854\pi$
$180$		0			0
$181$	−1.39163			−0.103439			−0.0517195	−	0.998662i	$-0.516470\pi$
$181$	−1.39163			−0.103439			−0.0517195	+	0.998662i	$0.516470\pi$
$182$		0			0
$183$	−2.14186	+	1.33893i	−0.158331	+	0.0989764i
$184$		0			0
$185$	14.7105	+	25.4793i	1.08154	+	1.87328i
$186$		0			0
$187$	−13.3606	+	23.1412i	−0.977024	+	1.69225i
$188$		0			0
$189$	−1.29758	+	13.6864i	−0.0943851	+	0.995536i
$190$		0			0
$191$	1.35741	−	2.35111i	0.0982190	−	0.170120i	−0.812728	−	0.582643i	$-0.802019\pi$
$191$	1.35741	−	2.35111i	0.0982190	−	0.170120i	0.910948	+	0.412522i	$0.135352\pi$
$192$		0			0
$193$	−0.920846	−	1.59495i	−0.0662839	−	0.114807i	0.830979	−	0.556304i	$-0.187781\pi$
$193$	−0.920846	−	1.59495i	−0.0662839	−	0.114807i	−0.897263	+	0.441497i	$0.854448\pi$
$194$		0			0
$195$	−6.56729	+	4.10538i	−0.470294	+	0.293992i
$196$		0			0
$197$	21.9198			1.56172			0.780860	−	0.624706i	$-0.214781\pi$
$197$	21.9198			1.56172			0.780860	+	0.624706i	$0.214781\pi$
$198$		0			0
$199$	−0.726101	+	1.25764i	−0.0514719	+	0.0891520i	−0.890613	−	0.454761i	$-0.849725\pi$
$199$	−0.726101	+	1.25764i	−0.0514719	+	0.0891520i	0.839141	+	0.543913i	$0.183058\pi$
$200$		0			0
$201$	−0.0988280	−	2.81524i	−0.00697079	−	0.198572i
$202$		0			0
$203$	3.55519	+	10.5931i	0.249526	+	0.743488i
$204$		0			0
$205$	−2.86738	+	4.96645i	−0.200267	+	0.346872i
$206$		0			0
$207$	−7.01884	−	10.3976i	−0.487843	−	0.722685i
$208$		0			0
$209$	11.5415	+	19.9905i	0.798344	+	1.38277i
$210$		0			0
$211$	0.771347	−	1.33601i	0.0531017	−	0.0919749i	−0.838253	−	0.545282i	$-0.816423\pi$
$211$	0.771347	−	1.33601i	0.0531017	−	0.0919749i	0.891354	+	0.453307i	$0.149756\pi$
$212$		0			0
$213$	12.9777	+	6.89732i	0.889219	+	0.472597i
$214$		0			0
$215$	19.0619	+	33.0162i	1.30001	+	2.25169i
$216$		0			0
$217$	5.25527	+	15.6586i	0.356751	+	1.06298i
$218$		0			0
$219$	10.9560	−	6.84885i	0.740336	−	0.462803i
$220$		0			0
$221$	3.48332	+	6.03328i	0.234313	+	0.405842i
$222$		0			0
$223$	−0.346045	−	0.599368i	−0.0231729	−	0.0401366i	0.854206	−	0.519934i	$-0.174043\pi$
$223$	−0.346045	−	0.599368i	−0.0231729	−	0.0401366i	−0.877379	+	0.479797i	$0.840710\pi$
$224$		0			0
$225$	15.8373	+	23.4612i	1.05582	+	1.56408i
$226$		0			0
$227$	18.4159			1.22231			0.611155	−	0.791511i	$-0.290705\pi$
$227$	18.4159			1.22231			0.611155	+	0.791511i	$0.290705\pi$
$228$		0			0
$229$	−5.39392			−0.356440			−0.178220	−	0.983991i	$-0.557034\pi$
$229$	−5.39392			−0.356440			−0.178220	+	0.983991i	$0.557034\pi$
$230$		0			0
$231$	15.9765	+	13.1405i	1.05118	+	0.864584i
$232$		0			0
$233$	−8.27352	−	14.3302i	−0.542016	−	0.938800i	−0.998788	−	0.0492161i	$-0.984328\pi$
$233$	−8.27352	−	14.3302i	−0.542016	−	0.938800i	0.456772	−	0.889584i	$-0.349006\pi$
$234$		0			0
$235$	−4.24896	+	7.35941i	−0.277171	+	0.480075i
$236$		0			0
$237$	2.70512	−	1.69103i	0.175716	−	0.109844i
$238$		0			0
$239$	−1.56724	+	2.71454i	−0.101376	+	0.175589i	−0.912252	−	0.409630i	$-0.865658\pi$
$239$	−1.56724	+	2.71454i	−0.101376	+	0.175589i	0.810876	+	0.585219i	$0.198991\pi$
$240$		0			0
$241$	−16.4746			−1.06122			−0.530611	−	0.847615i	$-0.678038\pi$
$241$	−16.4746			−1.06122			−0.530611	+	0.847615i	$0.678038\pi$
$242$		0			0
$243$	−11.9322	+	10.0310i	−0.765454	+	0.643490i
$244$		0			0
$245$	−24.5006	−	10.3469i	−1.56528	−	0.661040i
$246$		0			0
$247$	6.01811			0.382923
$248$		0			0
$249$	−0.0373836	−	1.06492i	−0.00236909	−	0.0674867i
$250$		0			0
$251$	12.8939			0.813858			0.406929	−	0.913460i	$-0.366600\pi$
$251$	12.8939			0.813858			0.406929	+	0.913460i	$0.366600\pi$
$252$		0			0
$253$	−18.8764			−1.18675
$254$		0			0
$255$	33.0316	−	20.6488i	2.06852	−	1.29308i
$256$		0			0
$257$	20.6089			1.28555			0.642774	−	0.766055i	$-0.277783\pi$
$257$	20.6089			1.28555			0.642774	+	0.766055i	$0.277783\pi$
$258$		0			0
$259$	−6.51862	−	19.4229i	−0.405047	−	1.20688i
$260$		0			0
$261$	−5.54991	+	11.3896i	−0.343531	+	0.705000i
$262$		0			0
$263$	9.13233			0.563123			0.281562	−	0.959543i	$-0.409148\pi$
$263$	9.13233			0.563123			0.281562	+	0.959543i	$0.409148\pi$
$264$		0			0
$265$	−24.6721	+	42.7333i	−1.51559	+	2.62509i
$266$		0			0
$267$	−0.152608	−	4.34725i	−0.00933948	−	0.266047i
$268$		0			0
$269$	−12.4387	+	21.5445i	−0.758401	+	1.31359i	0.185265	+	0.982689i	$0.440686\pi$
$269$	−12.4387	+	21.5445i	−0.758401	+	1.31359i	−0.943666	+	0.330900i	$0.892648\pi$
$270$		0			0
$271$	5.70814	+	9.88679i	0.346745	+	0.600580i	0.985669	−	0.168690i	$-0.0539536\pi$
$271$	5.70814	+	9.88679i	0.346745	+	0.600580i	−0.638924	+	0.769270i	$0.720620\pi$
$272$		0			0
$273$	5.04962	−	1.89431i	0.305617	−	0.114649i
$274$		0			0
$275$	42.5927			2.56844
$276$		0			0
$277$	30.9876			1.86186			0.930932	−	0.365192i	$-0.118997\pi$
$277$	30.9876			1.86186			0.930932	+	0.365192i	$0.118997\pi$
$278$		0			0
$279$	−8.20385	+	16.8361i	−0.491151	+	1.00795i
$280$		0			0
$281$	−7.40910	−	12.8329i	−0.441990	−	0.765549i	0.555847	−	0.831285i	$-0.312394\pi$
$281$	−7.40910	−	12.8329i	−0.441990	−	0.765549i	−0.997837	+	0.0657354i	$0.979061\pi$
$282$		0			0
$283$	−12.8715	−	22.2942i	−0.765134	−	1.32525i	−0.940176	−	0.340689i	$-0.889340\pi$
$283$	−12.8715	−	22.2942i	−0.765134	−	1.32525i	0.175042	−	0.984561i	$-0.443994\pi$
$284$		0			0
$285$	−1.18057	−	33.6301i	−0.0699310	−	1.99208i
$286$		0			0
$287$	2.64340	−	2.99335i	0.156035	−	0.176692i
$288$		0			0
$289$	−9.02006	−	15.6232i	−0.530592	−	0.919012i
$290$		0			0
$291$	0.287725	+	8.19623i	0.0168668	+	0.480472i
$292$		0			0
$293$	8.41185	−	14.5697i	0.491425	−	0.851174i	−0.508526	−	0.861047i	$-0.669809\pi$
$293$	8.41185	−	14.5697i	0.491425	−	0.851174i	0.999951	+	0.00987288i	$0.00314269\pi$
$294$		0			0
$295$	23.5414	+	40.7749i	1.37063	+	2.37401i
$296$		0			0
$297$	2.46467	+	23.3262i	0.143015	+	1.35352i
$298$		0			0
$299$	−2.46069	+	4.26203i	−0.142305	+	0.246480i
$300$		0			0
$301$	−8.44686	−	25.1683i	−0.486869	−	1.45068i
$302$		0			0
$303$	−17.4689	−	9.28427i	−1.00356	−	0.533367i
$304$		0			0
$305$	2.77041	−	4.79849i	0.158633	−	0.274761i
$306$		0			0
$307$	−28.2972			−1.61501			−0.807504	−	0.589862i	$-0.799182\pi$
$307$	−28.2972			−1.61501			−0.807504	+	0.589862i	$0.799182\pi$
$308$		0			0
$309$	−9.75037	−	5.18207i	−0.554679	−	0.294798i
$310$		0			0
$311$	−9.93477	−	17.2075i	−0.563349	−	0.975750i	−0.997201	−	0.0747654i	$-0.976179\pi$
$311$	−9.93477	−	17.2075i	−0.563349	−	0.975750i	0.433852	−	0.900984i	$-0.357154\pi$
$312$		0			0
$313$	9.14293	−	15.8360i	0.516789	−	0.895105i	−0.483021	−	0.875609i	$-0.660460\pi$
$313$	9.14293	−	15.8360i	0.516789	−	0.895105i	0.999810	−	0.0194961i	$-0.00620619\pi$
$314$		0			0
$315$	−11.5763	−	27.8464i	−0.652249	−	1.56897i
$316$		0			0
$317$	−6.97401	+	12.0793i	−0.391700	+	0.678444i	−0.992674	−	0.120825i	$-0.961446\pi$
$317$	−6.97401	+	12.0793i	−0.391700	+	0.678444i	0.600974	+	0.799268i	$0.294779\pi$
$318$		0			0
$319$	9.53220	+	16.5103i	0.533701	+	0.924397i
$320$		0			0
$321$	0.136114	+	3.87738i	0.00759713	+	0.216414i
$322$		0			0
$323$	−30.2694			−1.68423
$324$		0			0
$325$	5.55230	−	9.61686i	0.307986	−	0.533447i
$326$		0			0
$327$	−8.02169	+	5.01456i	−0.443601	+	0.277306i
$328$		0			0
$329$	3.91706	−	4.43562i	0.215955	−	0.244544i
$330$		0			0
$331$	−10.4200	+	18.0479i	−0.572733	+	0.992003i	0.423551	+	0.905872i	$0.360783\pi$
$331$	−10.4200	+	18.0479i	−0.572733	+	0.992003i	−0.996284	+	0.0861302i	$0.972550\pi$
$332$		0			0
$333$	10.1760	−	20.8834i	0.557643	−	1.14440i
$334$		0			0
$335$	3.08964	+	5.35142i	0.168805	+	0.292379i
$336$		0			0
$337$	15.4376	−	26.7387i	0.840939	−	1.45655i	−0.0481619	−	0.998840i	$-0.515336\pi$
$337$	15.4376	−	26.7387i	0.840939	−	1.45655i	0.889101	−	0.457710i	$-0.151330\pi$
$338$		0			0
$339$	−13.0848	+	8.17962i	−0.710668	+	0.444256i
$340$		0			0
$341$	14.0904	+	24.4054i	0.763040	+	1.32162i
$342$		0			0
$343$	15.2918	+	10.4480i	0.825681	+	0.564138i
$344$		0			0
$345$	24.2996	+	12.9146i	1.30825	+	0.695299i
$346$		0			0
$347$	5.13427	+	8.89281i	0.275622	+	0.477391i	0.970292	−	0.241938i	$-0.0777829\pi$
$347$	5.13427	+	8.89281i	0.275622	+	0.477391i	−0.694670	+	0.719329i	$0.744450\pi$
$348$		0			0
$349$	4.61262	+	7.98930i	0.246908	+	0.427657i	0.962666	−	0.270691i	$-0.0872521\pi$
$349$	4.61262	+	7.98930i	0.246908	+	0.427657i	−0.715758	+	0.698348i	$0.753919\pi$
$350$		0			0
$351$	5.58803	+	2.48426i	0.298267	+	0.132600i
$352$		0			0
$353$	8.17321			0.435016			0.217508	−	0.976059i	$-0.430207\pi$
$353$	8.17321			0.435016			0.217508	+	0.976059i	$0.430207\pi$
$354$		0			0
$355$	−32.2386			−1.71104
$356$		0			0
$357$	−25.3981	+	9.52782i	−1.34421	+	0.504266i
$358$		0			0
$359$	6.35957	+	11.0151i	0.335645	+	0.581355i	0.983609	−	0.180317i	$-0.0577123\pi$
$359$	6.35957	+	11.0151i	0.335645	+	0.581355i	−0.647963	+	0.761672i	$0.724379\pi$
$360$		0			0
$361$	−3.57407	+	6.19047i	−0.188109	+	0.325814i
$362$		0			0
$363$	14.3422	+	7.62249i	0.752769	+	0.400077i
$364$		0			0
$365$	−14.1711	+	24.5452i	−0.741752	+	1.28475i
$366$		0			0
$367$	−21.8861			−1.14245			−0.571224	−	0.820794i	$-0.693531\pi$
$367$	−21.8861			−1.14245			−0.571224	+	0.820794i	$0.693531\pi$
$368$		0			0
$369$	4.51701	−	0.317527i	0.235146	−	0.0165298i
$370$		0			0
$371$	22.7449	−	25.7560i	1.18086	−	1.33718i
$372$		0			0
$373$	−13.4625			−0.697063			−0.348531	−	0.937297i	$-0.613320\pi$
$373$	−13.4625			−0.697063			−0.348531	+	0.937297i	$0.613320\pi$
$374$		0			0
$375$	−25.7745	−	13.6985i	−1.33099	−	0.707387i
$376$		0			0
$377$	4.97038			0.255988
$378$		0			0
$379$	−11.2180			−0.576231			−0.288115	−	0.957596i	$-0.593029\pi$
$379$	−11.2180			−0.576231			−0.288115	+	0.957596i	$0.593029\pi$
$380$		0			0
$381$	0.665189	+	0.353531i	0.0340787	+	0.0181119i
$382$		0			0
$383$	−8.00660			−0.409118			−0.204559	−	0.978854i	$-0.565576\pi$
$383$	−8.00660			−0.409118			−0.204559	+	0.978854i	$0.565576\pi$
$384$		0			0
$385$	−44.4745	−	9.00599i	−2.26663	−	0.458988i
$386$		0			0
$387$	13.1862	−	27.0608i	0.670290	−	1.37558i
$388$		0			0
$389$	28.7862			1.45952			0.729759	−	0.683705i	$-0.239632\pi$
$389$	28.7862			1.45952			0.729759	+	0.683705i	$0.239632\pi$
$390$		0			0
$391$	12.3765	−	21.4368i	0.625908	−	1.08410i
$392$		0			0
$393$	−8.18667	−	4.35100i	−0.412963	−	0.219479i
$394$		0			0
$395$	−3.49897	+	6.06039i	−0.176052	+	0.304931i
$396$		0			0
$397$	10.8138	+	18.7301i	0.542731	+	0.940037i	0.998746	+	0.0500651i	$0.0159429\pi$
$397$	10.8138	+	18.7301i	0.542731	+	0.940037i	−0.456015	+	0.889972i	$0.650724\pi$
$398$		0			0
$399$	−3.84215	+	23.1160i	−0.192348	+	1.15725i
$400$		0			0
$401$	26.9932			1.34797			0.673987	−	0.738743i	$-0.264580\pi$
$401$	26.9932			1.34797			0.673987	+	0.738743i	$0.264580\pi$
$402$		0			0
$403$	7.34719			0.365990
$404$		0			0
$405$	12.7862	−	31.7141i	0.635353	−	1.57589i
$406$		0			0
$407$	−17.4777	−	30.2723i	−0.866339	−	1.50054i
$408$		0			0
$409$	10.4737	+	18.1409i	0.517889	+	0.897010i	0.999784	+	0.0207814i	$0.00661539\pi$
$409$	10.4737	+	18.1409i	0.517889	+	0.897010i	−0.481895	+	0.876229i	$0.660051\pi$
$410$		0			0
$411$	9.02752	+	4.79789i	0.445295	+	0.236662i
$412$		0			0
$413$	−10.4318	−	31.0828i	−0.513317	−	1.52948i
$414$		0			0
$415$	1.16872	+	2.02428i	0.0573701	+	0.0993680i
$416$		0			0
$417$	12.7380	−	7.96281i	0.623781	−	0.389941i
$418$		0			0
$419$	6.91450	−	11.9763i	0.337795	−	0.585079i	−0.646222	−	0.763149i	$-0.723652\pi$
$419$	6.91450	−	11.9763i	0.337795	−	0.585079i	0.984018	+	0.178070i	$0.0569855\pi$
$420$		0			0
$421$	−6.86872	−	11.8970i	−0.334761	−	0.579823i	0.648678	−	0.761063i	$-0.275322\pi$
$421$	−6.86872	−	11.8970i	−0.334761	−	0.579823i	−0.983439	+	0.181240i	$0.941989\pi$
$422$		0			0
$423$	6.69342	−	0.470519i	0.325445	−	0.0228774i
$424$		0			0
$425$	−27.9264	+	48.3700i	−1.35463	+	2.34629i
$426$		0			0
$427$	−2.55401	+	2.89212i	−0.123597	+	0.139959i
$428$		0			0
$429$	7.80269	−	4.87765i	0.376717	−	0.235495i
$430$		0			0
$431$	−9.20392	+	15.9417i	−0.443337	+	0.767882i	−0.997935	−	0.0642362i	$-0.979539\pi$
$431$	−9.20392	+	15.9417i	−0.443337	+	0.767882i	0.554598	+	0.832119i	$0.312872\pi$
$432$		0			0
$433$	24.3558			1.17047			0.585233	−	0.810865i	$-0.301003\pi$
$433$	24.3558			1.17047			0.585233	+	0.810865i	$0.301003\pi$
$434$		0			0
$435$	−0.975039	−	27.7753i	−0.0467495	−	1.33172i
$436$		0			0
$437$	−10.6914	−	18.5181i	−0.511441	−	0.885842i
$438$		0			0
$439$	2.91828	−	5.05460i	0.139282	−	0.241243i	−0.787943	−	0.615748i	$-0.788854\pi$
$439$	2.91828	−	5.05460i	0.139282	−	0.241243i	0.927225	+	0.374505i	$0.122187\pi$
$440$		0			0
$441$	4.05234	+	20.6053i	0.192968	+	0.981205i
$442$		0			0
$443$	−7.42002	+	12.8518i	−0.352536	+	0.610610i	−0.986693	−	0.162594i	$-0.948014\pi$
$443$	−7.42002	+	12.8518i	−0.352536	+	0.610610i	0.634157	+	0.773204i	$0.281347\pi$
$444$		0			0
$445$	4.77097	+	8.26356i	0.226166	+	0.391730i
$446$		0			0
$447$	−16.4833	−	8.76044i	−0.779633	−	0.414355i
$448$		0			0
$449$	−4.26289			−0.201178			−0.100589	−	0.994928i	$-0.532073\pi$
$449$	−4.26289			−0.201178			−0.100589	+	0.994928i	$0.532073\pi$
$450$		0			0
$451$	3.40677	−	5.90070i	0.160419	−	0.277853i
$452$		0			0
$453$	−25.7350	−	13.6775i	−1.20914	−	0.642624i
$454$		0			0
$455$	−7.83102	+	8.86772i	−0.367124	+	0.415725i
$456$		0			0
$457$	−19.8730	+	34.4210i	−0.929618	+	1.61015i	−0.145657	+	0.989335i	$0.546530\pi$
$457$	−19.8730	+	34.4210i	−0.929618	+	1.61015i	−0.783961	+	0.620810i	$0.786804\pi$
$458$		0			0
$459$	−28.1061	−	12.4951i	−1.31188	−	0.583222i
$460$		0			0
$461$	−2.68671	−	4.65353i	−0.125133	−	0.216736i	0.796652	−	0.604438i	$-0.206602\pi$
$461$	−2.68671	−	4.65353i	−0.125133	−	0.216736i	−0.921785	+	0.387702i	$0.873269\pi$
$462$		0			0
$463$	19.8205	−	34.3301i	0.921136	−	1.59545i	0.123474	−	0.992348i	$-0.460596\pi$
$463$	19.8205	−	34.3301i	0.921136	−	1.59545i	0.797661	−	0.603106i	$-0.206070\pi$
$464$		0			0
$465$	−1.44130	−	41.0572i	−0.0668385	−	1.90398i
$466$		0			0
$467$	9.43069	+	16.3344i	0.436400	+	0.755867i	0.997409	−	0.0719427i	$-0.0229199\pi$
$467$	9.43069	+	16.3344i	0.436400	+	0.755867i	−0.561009	+	0.827810i	$0.689587\pi$
$468$		0			0
$469$	−1.36910	−	4.07939i	−0.0632193	−	0.188369i
$470$		0			0
$471$	−0.544541	−	15.5120i	−0.0250911	−	0.714754i
$472$		0			0
$473$	−22.6477	−	39.2270i	−1.04134	−	1.80366i
$474$		0			0
$475$	24.1242	+	41.7843i	1.10689	+	1.91720i
$476$		0			0
$477$	38.8662	−	2.73213i	1.77956	−	0.125095i
$478$		0			0
$479$	19.0057			0.868395			0.434197	−	0.900818i	$-0.357032\pi$
$479$	19.0057			0.868395			0.434197	+	0.900818i	$0.357032\pi$
$480$		0			0
$481$	−9.11344			−0.415537
$482$		0			0
$483$	−14.7998	−	12.1727i	−0.673413	−	0.553876i
$484$		0			0
$485$	−8.99511	−	15.5800i	−0.408447	−	0.707451i
$486$		0			0
$487$	−5.21626	+	9.03482i	−0.236371	+	0.409407i	−0.959670	−	0.281128i	$-0.909291\pi$
$487$	−5.21626	+	9.03482i	−0.236371	+	0.409407i	0.723299	+	0.690535i	$0.242625\pi$
$488$		0			0
$489$	−0.451268	−	12.8550i	−0.0204070	−	0.581322i
$490$		0			0
$491$	−14.3311	+	24.8221i	−0.646752	+	1.12021i	0.337142	+	0.941454i	$0.390540\pi$
$491$	−14.3311	+	24.8221i	−0.646752	+	1.12021i	−0.983894	+	0.178753i	$0.942794\pi$
$492$		0			0
$493$	−24.9996			−1.12592
$494$		0			0
$495$	−28.7877	−	42.6458i	−1.29391	−	1.91679i
$496$		0			0
$497$	22.0031	+	4.45557i	0.986972	+	0.199860i
$498$		0			0
$499$	−33.0793			−1.48083			−0.740416	−	0.672149i	$-0.765372\pi$
$499$	−33.0793			−1.48083			−0.740416	+	0.672149i	$0.765372\pi$
$500$		0			0
$501$	−15.0913	+	9.43391i	−0.674227	+	0.421476i
$502$		0			0
$503$	−28.9523			−1.29092			−0.645460	−	0.763794i	$-0.723334\pi$
$503$	−28.9523			−1.29092			−0.645460	+	0.763794i	$0.723334\pi$
$504$		0			0
$505$	43.3953			1.93107
$506$		0			0
$507$	0.705785	+	20.1052i	0.0313450	+	0.892904i
$508$		0			0
$509$	31.7641			1.40792			0.703959	−	0.710241i	$-0.251414\pi$
$509$	31.7641			1.40792			0.703959	+	0.710241i	$0.251414\pi$
$510$		0			0
$511$	13.0642	−	14.7937i	0.577927	−	0.654435i
$512$		0			0
$513$	−21.4875	+	15.6297i	−0.948697	+	0.690067i
$514$		0			0
$515$	24.2214			1.06732
$516$		0			0
$517$	5.04825	−	8.74382i	0.222022	−	0.384553i
$518$		0			0
$519$	14.9952	−	9.37390i	0.658218	−	0.411469i
$520$		0			0
$521$	−2.87897	+	4.98652i	−0.126130	+	0.218463i	−0.922174	−	0.386775i	$-0.873589\pi$
$521$	−2.87897	+	4.98652i	−0.126130	+	0.218463i	0.796044	+	0.605239i	$0.206922\pi$
$522$		0			0
$523$	−22.3123	−	38.6461i	−0.975650	−	1.68987i	−0.677774	−	0.735270i	$-0.737055\pi$
$523$	−22.3123	−	38.6461i	−0.975650	−	1.68987i	−0.297875	−	0.954605i	$-0.596278\pi$
$524$		0			0
$525$	33.3942	+	27.4664i	1.45744	+	1.19873i
$526$		0			0
$527$	−36.9542			−1.60975
$528$		0			0
$529$	−5.51392			−0.239736
$530$		0			0
$531$	16.2848	−	33.4200i	0.706702	−	1.45031i
$532$		0			0
$533$	−0.888199	−	1.53841i	−0.0384722	−	0.0666357i
$534$		0			0
$535$	−4.25530	−	7.37040i	−0.183973	−	0.318650i
$536$		0			0
$537$	28.2866	−	17.6826i	1.22066	−	0.763063i
$538$		0			0
$539$	29.1095	+	12.2933i	1.25383	+	0.529510i
$540$		0			0
$541$	15.6719	+	27.1445i	0.673786	+	1.16703i	0.976822	+	0.214053i	$0.0686665\pi$
$541$	15.6719	+	27.1445i	0.673786	+	1.16703i	−0.303036	+	0.952979i	$0.598000\pi$
$542$		0			0
$543$	−2.12844	−	1.13121i	−0.0913401	−	0.0485449i
$544$		0			0
$545$	10.3758	−	17.9713i	0.444449	−	0.769808i
$546$		0			0
$547$	1.37567	+	2.38273i	0.0588195	+	0.101878i	0.893936	−	0.448195i	$-0.147933\pi$
$547$	1.37567	+	2.38273i	0.0588195	+	0.101878i	−0.835116	+	0.550073i	$0.814600\pi$
$548$		0			0
$549$	−4.36426	+	0.306789i	−0.186262	+	0.0130934i
$550$		0			0
$551$	−10.7979	+	18.7026i	−0.460007	+	0.796756i
$552$		0			0
$553$	3.22565	−	3.65268i	0.137169	−	0.155328i
$554$		0			0
$555$	1.78778	+	50.9273i	0.0758870	+	2.16174i
$556$		0			0
$557$	3.42197	−	5.92703i	0.144994	−	0.251136i	−0.784377	−	0.620284i	$-0.787017\pi$
$557$	3.42197	−	5.92703i	0.144994	−	0.251136i	0.929371	+	0.369148i	$0.120350\pi$
$558$		0			0
$559$	−11.8092			−0.499478
$560$		0			0
$561$	−39.2453	+	24.5332i	−1.65694	+	1.03579i
$562$		0			0
$563$	−7.55007	−	13.0771i	−0.318197	−	0.551134i	0.661915	−	0.749579i	$-0.269744\pi$
$563$	−7.55007	−	13.0771i	−0.318197	−	0.551134i	−0.980112	+	0.198445i	$0.936411\pi$
$564$		0			0
$565$	16.9247	−	29.3144i	0.712027	−	1.23327i
$566$		0			0
$567$	−13.1098	+	19.8780i	−0.550560	+	0.834796i
$568$		0			0
$569$	13.7638	−	23.8396i	0.577008	−	0.999408i	−0.418812	−	0.908073i	$-0.637553\pi$
$569$	13.7638	−	23.8396i	0.577008	−	0.999408i	0.995820	−	0.0913346i	$-0.0291133\pi$
$570$		0			0
$571$	19.4377	+	33.6672i	0.813444	+	1.40893i	0.910439	+	0.413642i	$0.135744\pi$
$571$	19.4377	+	33.6672i	0.813444	+	1.40893i	−0.0969950	+	0.995285i	$0.530923\pi$
$572$		0			0
$573$	3.98725	−	2.49253i	0.166570	−	0.104127i
$574$		0			0
$575$	−39.4556			−1.64541
$576$		0			0
$577$	−9.84330	+	17.0491i	−0.409782	+	0.709763i	−0.994865	−	0.101210i	$-0.967729\pi$
$577$	−9.84330	+	17.0491i	−0.409782	+	0.709763i	0.585083	+	0.810973i	$0.301062\pi$
$578$		0			0
$579$	−0.111911	−	3.18794i	−0.00465087	−	0.132486i
$580$		0			0
$581$	−0.517891	−	1.54311i	−0.0214857	−	0.0640190i
$582$		0			0
$583$	29.3132	−	50.7720i	1.21403	−	2.10276i
$584$		0			0
$585$	−13.3815	+	0.940665i	−0.553259	+	0.0388917i
$586$		0			0
$587$	3.14068	+	5.43982i	0.129630	+	0.224525i	0.923533	−	0.383519i	$-0.125288\pi$
$587$	3.14068	+	5.43982i	0.129630	+	0.224525i	−0.793903	+	0.608044i	$0.791954\pi$
$588$		0			0
$589$	−15.9614	+	27.6460i	−0.657679	+	1.13913i
$590$		0			0
$591$	33.5254	+	17.8179i	1.37905	+	0.732930i
$592$		0			0
$593$	7.79280	+	13.4975i	0.320012	+	0.554277i	0.980490	−	0.196568i	$-0.0629798\pi$
$593$	7.79280	+	13.4975i	0.320012	+	0.554277i	−0.660478	+	0.750845i	$0.729646\pi$
$594$		0			0
$595$	39.3877	−	44.6021i	1.61474	−	1.82851i
$596$		0			0
$597$	−2.13284	+	1.33329i	−0.0872913	+	0.0545679i
$598$		0			0
$599$	−0.527783	−	0.914146i	−0.0215646	−	0.0373510i	0.855042	−	0.518559i	$-0.173531\pi$
$599$	−0.527783	−	0.914146i	−0.0215646	−	0.0373510i	−0.876606	+	0.481208i	$0.840198\pi$
$600$		0			0
$601$	−12.1622	−	21.0656i	−0.496107	−	0.859283i	0.503883	−	0.863772i	$-0.331904\pi$
$601$	−12.1622	−	21.0656i	−0.496107	−	0.859283i	−0.999990	+	0.00448941i	$0.998571\pi$
$602$		0			0
$603$	2.13727	−	4.38614i	0.0870363	−	0.178617i
$604$		0			0
$605$	−35.6280			−1.44849
$606$		0			0
$607$	4.33005			0.175751			0.0878756	−	0.996131i	$-0.471992\pi$
$607$	4.33005			0.175751			0.0878756	+	0.996131i	$0.471992\pi$
$608$		0			0
$609$	−3.17325	+	19.0916i	−0.128587	+	0.773630i
$610$		0			0
$611$	−1.31616	−	2.27965i	−0.0532460	−	0.0922247i
$612$		0			0
$613$	−24.3556	+	42.1852i	−0.983714	+	1.70384i	−0.336196	+	0.941792i	$0.609140\pi$
$613$	−24.3556	+	42.1852i	−0.983714	+	1.70384i	−0.647518	+	0.762050i	$0.724193\pi$
$614$		0			0
$615$	−8.42261	+	5.26518i	−0.339632	+	0.212313i
$616$		0			0
$617$	14.6366	−	25.3514i	0.589249	−	1.02061i	−0.405082	−	0.914280i	$-0.632757\pi$
$617$	14.6366	−	25.3514i	0.589249	−	1.02061i	0.994331	−	0.106329i	$-0.0339096\pi$
$618$		0			0
$619$	−36.4762			−1.46610			−0.733050	−	0.680174i	$-0.761904\pi$
$619$	−36.4762			−1.46610			−0.733050	+	0.680174i	$0.761904\pi$
$620$		0			0
$621$	−2.28314	−	21.6081i	−0.0916192	−	0.867105i
$622$		0			0
$623$	−2.11414	−	6.29932i	−0.0847014	−	0.252377i
$624$		0			0
$625$	16.8505			0.674018
$626$		0			0
$627$	1.40265	+	39.9564i	0.0560166	+	1.59571i
$628$		0			0
$629$	45.8379			1.82768
$630$		0			0
$631$	0.501625			0.0199694			0.00998468	−	0.999950i	$-0.496822\pi$
$631$	0.501625			0.0199694			0.00998468	+	0.999950i	$0.496822\pi$
$632$		0			0
$633$	2.26575	−	1.41637i	0.0900553	−	0.0562958i
$634$		0			0
$635$	−1.65243			−0.0655746
$636$		0			0
$637$	6.57031	−	4.96999i	0.260325	−	0.196918i
$638$		0			0
$639$	14.2423	+	21.0983i	0.563416	+	0.834637i
$640$		0			0
$641$	−35.0224			−1.38330			−0.691651	−	0.722232i	$-0.743116\pi$
$641$	−35.0224			−1.38330			−0.691651	+	0.722232i	$0.743116\pi$
$642$		0			0
$643$	7.29049	−	12.6275i	0.287509	−	0.497980i	−0.685706	−	0.727879i	$-0.740506\pi$
$643$	7.29049	−	12.6275i	0.287509	−	0.497980i	0.973215	+	0.229899i	$0.0738396\pi$
$644$		0			0
$645$	2.31662	+	65.9918i	0.0912166	+	2.59843i
$646$		0			0
$647$	−11.6503	+	20.1790i	−0.458022	+	0.793318i	−0.998856	−	0.0478116i	$-0.984775\pi$
$647$	−11.6503	+	20.1790i	−0.458022	+	0.793318i	0.540834	+	0.841129i	$0.318109\pi$
$648$		0			0
$649$	−27.9699	−	48.4453i	−1.09791	−	1.90164i
$650$		0			0
$651$	−4.69068	+	28.2211i	−0.183842	+	1.10607i
$652$		0			0
$653$	−8.53559			−0.334023			−0.167012	−	0.985955i	$-0.553412\pi$
$653$	−8.53559			−0.334023			−0.167012	+	0.985955i	$0.553412\pi$
$654$		0			0
$655$	20.3369			0.794628
$656$		0			0
$657$	22.3239	−	1.56928i	0.870940	−	0.0612234i
$658$		0			0
$659$	−1.81616	−	3.14568i	−0.0707476	−	0.122538i	0.828482	−	0.560016i	$-0.189205\pi$
$659$	−1.81616	−	3.14568i	−0.0707476	−	0.122538i	−0.899229	+	0.437478i	$0.855872\pi$
$660$		0			0
$661$	15.5116	+	26.8668i	0.603330	+	1.04500i	0.992313	+	0.123753i	$0.0394932\pi$
$661$	15.5116	+	26.8668i	0.603330	+	1.04500i	−0.388983	+	0.921245i	$0.627173\pi$
$662$		0			0
$663$	0.423331	+	12.0591i	0.0164408	+	0.468338i
$664$		0			0
$665$	−16.3549	−	48.7313i	−0.634217	−	1.88972i
$666$		0			0
$667$	−8.83011	−	15.2942i	−0.341903	−	0.592194i
$668$		0			0
$669$	−0.0420552	−	1.19800i	−0.00162595	−	0.0463173i
$670$		0			0
$671$	−3.29156	+	5.70116i	−0.127069	+	0.220091i
$672$		0			0
$673$	0.291838	+	0.505478i	0.0112495	+	0.0194848i	0.871595	−	0.490226i	$-0.163086\pi$
$673$	0.291838	+	0.505478i	0.0112495	+	0.0194848i	−0.860346	+	0.509711i	$0.829752\pi$
$674$		0			0
$675$	5.15168	+	48.7566i	0.198288	+	1.87664i
$676$		0			0
$677$	16.8666	−	29.2138i	0.648237	−	1.12278i	−0.335307	−	0.942109i	$-0.608840\pi$
$677$	16.8666	−	29.2138i	0.648237	−	1.12278i	0.983544	−	0.180670i	$-0.0578265\pi$
$678$		0			0
$679$	3.98597	+	11.8766i	0.152968	+	0.455783i
$680$		0			0
$681$	28.1664	+	14.9697i	1.07934	+	0.573641i
$682$		0			0
$683$	−1.60312	+	2.77668i	−0.0613417	+	0.106247i	−0.895065	−	0.445935i	$-0.852871\pi$
$683$	−1.60312	+	2.77668i	−0.0613417	+	0.106247i	0.833724	+	0.552182i	$0.186205\pi$
$684$		0			0
$685$	−22.4257			−0.856841
$686$		0			0
$687$	−8.24978	−	4.38454i	−0.314749	−	0.167281i
$688$		0			0
$689$	−7.64242	−	13.2371i	−0.291153	−	0.504292i
$690$		0			0
$691$	16.1837	−	28.0310i	0.615657	−	1.06635i	−0.374611	−	0.927182i	$-0.622224\pi$
$691$	16.1837	−	28.0310i	0.615657	−	1.06635i	0.990269	−	0.139168i	$-0.0444428\pi$
$692$		0			0
$693$	13.7539	+	33.0847i	0.522468	+	1.25678i
$694$		0			0
$695$	−16.4761	+	28.5374i	−0.624973	+	1.08249i
$696$		0			0
$697$	4.46738	+	7.73773i	0.169214	+	0.293087i
$698$		0			0
$699$	−1.00549	−	28.6427i	−0.0380311	−	1.08337i
$700$		0			0
$701$	21.2591			0.802943			0.401472	−	0.915871i	$-0.368499\pi$
$701$	21.2591			0.802943			0.401472	+	0.915871i	$0.368499\pi$
$702$		0			0
$703$	19.7985	−	34.2920i	0.746715	−	1.29335i
$704$		0			0
$705$	−12.4808	+	7.80208i	−0.470056	+	0.293843i
$706$		0			0
$707$	−29.6176	−	5.99751i	−1.11389	−	0.225560i
$708$		0			0
$709$	−15.8272	+	27.4135i	−0.594402	+	1.02953i	0.399229	+	0.916851i	$0.369278\pi$
$709$	−15.8272	+	27.4135i	−0.594402	+	1.02953i	−0.993631	+	0.112684i	$0.964055\pi$
$710$		0			0
$711$	5.51195	−	0.387467i	0.206714	−	0.0145311i
$712$		0			0
$713$	−13.0526	−	22.6078i	−0.488824	−	0.846669i
$714$		0			0
$715$	−10.0925	+	17.4807i	−0.377438	+	0.653741i
$716$		0			0
$717$	−4.60359	+	2.87782i	−0.171924	+	0.107474i
$718$		0			0
$719$	−14.9776	−	25.9420i	−0.558571	−	0.967473i	−0.997616	−	0.0690079i	$-0.978017\pi$
$719$	−14.9776	−	25.9420i	−0.558571	−	0.967473i	0.439045	−	0.898465i	$-0.355317\pi$
$720$		0			0
$721$	−16.5313	−	3.34755i	−0.615656	−	0.124669i
$722$		0			0
$723$	−25.1972	−	13.3917i	−0.937095	−	0.498042i
$724$		0			0
$725$	19.9243	+	34.5099i	0.739969	+	1.28166i
$726$		0			0
$727$	−13.6310	−	23.6095i	−0.505544	−	0.875629i	−0.999979	−	0.00641398i	$-0.997958\pi$
$727$	−13.6310	−	23.6095i	−0.505544	−	0.875629i	0.494435	−	0.869215i	$-0.335375\pi$
$728$		0			0
$729$	−26.4038	+	5.64270i	−0.977918	+	0.208989i
$730$		0			0
$731$	59.3970			2.19688
$732$		0			0
$733$	−22.5434			−0.832660			−0.416330	−	0.909214i	$-0.636684\pi$
$733$	−22.5434			−0.832660			−0.416330	+	0.909214i	$0.636684\pi$
$734$		0			0
$735$	−29.0620	−	35.7409i	−1.07197	−	1.31832i
$736$		0			0
$737$	−3.67085	−	6.35809i	−0.135217	−	0.234203i
$738$		0			0
$739$	−8.82742	+	15.2895i	−0.324722	+	0.562435i	−0.981456	−	0.191687i	$-0.938604\pi$
$739$	−8.82742	+	15.2895i	−0.324722	+	0.562435i	0.656734	+	0.754122i	$0.271937\pi$
$740$		0			0
$741$	9.20446	+	4.89193i	0.338134	+	0.179710i
$742$		0			0
$743$	−3.31474	+	5.74130i	−0.121606	+	0.210628i	−0.920401	−	0.390975i	$-0.872138\pi$
$743$	−3.31474	+	5.74130i	−0.121606	+	0.210628i	0.798795	+	0.601603i	$0.205471\pi$
$744$		0			0
$745$	40.9469			1.50018
$746$		0			0
$747$	0.808464	−	1.65914i	0.0295802	−	0.0607049i
$748$		0			0
$749$	1.88564	+	5.61846i	0.0688997	+	0.205294i
$750$		0			0
$751$	7.87441			0.287341			0.143671	−	0.989626i	$-0.454109\pi$
$751$	7.87441			0.287341			0.143671	+	0.989626i	$0.454109\pi$
$752$		0			0
$753$	19.7207	+	10.4811i	0.718664	+	0.381951i
$754$		0			0
$755$	63.9295			2.32663
$756$		0			0
$757$	−37.1503			−1.35025			−0.675125	−	0.737703i	$-0.735910\pi$
$757$	−37.1503			−1.35025			−0.675125	+	0.737703i	$0.735910\pi$
$758$		0			0
$759$	−28.8707	−	15.3440i	−1.04794	−	0.556953i
$760$		0			0
$761$	−32.4545			−1.17648			−0.588238	−	0.808688i	$-0.700178\pi$
$761$	−32.4545			−1.17648			−0.588238	+	0.808688i	$0.700178\pi$
$762$		0			0
$763$	−9.56529	+	10.8316i	−0.346287	+	0.392129i
$764$		0			0
$765$	67.3052	−	4.73127i	2.43343	−	0.171060i
$766$		0			0
$767$	−14.5844			−0.526611
$768$		0			0
$769$	11.4992	−	19.9172i	0.414671	−	0.718232i	−0.580723	−	0.814101i	$-0.697230\pi$
$769$	11.4992	−	19.9172i	0.414671	−	0.718232i	0.995394	+	0.0958699i	$0.0305633\pi$
$770$		0			0
$771$	31.5205	+	16.7523i	1.13518	+	0.603320i
$772$		0			0
$773$	13.2117	−	22.8834i	0.475194	−	0.823059i	−0.524403	−	0.851470i	$-0.675711\pi$
$773$	13.2117	−	22.8834i	0.475194	−	0.823059i	0.999596	+	0.0284109i	$0.00904469\pi$
$774$		0			0
$775$	29.4519	+	51.0123i	1.05794	+	1.83241i
$776$		0			0
$777$	5.81830	−	35.0053i	0.208730	−	1.25581i
$778$		0			0
$779$	7.71828			0.276536
$780$		0			0
$781$	38.3031			1.37059
$782$		0			0
$783$	−17.7466	+	12.9086i	−0.634212	+	0.461316i
$784$		0			0
$785$	17.0239	+	29.4862i	0.607609	+	1.05241i
$786$		0			0
$787$	4.55650	+	7.89209i	0.162422	+	0.281323i	0.935737	−	0.352699i	$-0.114736\pi$
$787$	4.55650	+	7.89209i	0.162422	+	0.281323i	−0.773315	+	0.634022i	$0.781403\pi$
$788$		0			0
$789$	13.9675	+	7.42337i	0.497257	+	0.264279i
$790$		0			0
$791$	−15.6027	+	17.6682i	−0.554767	+	0.628209i
$792$		0			0
$793$	0.858162	+	1.48638i	0.0304742	+	0.0527829i
$794$		0			0
$795$	−72.4715	+	45.3037i	−2.57030	+	1.60676i
$796$		0			0
$797$	−27.5330	+	47.6886i	−0.975270	+	1.68922i	−0.296228	+	0.955117i	$0.595729\pi$
$797$	−27.5330	+	47.6886i	−0.975270	+	1.68922i	−0.679042	+	0.734099i	$0.737605\pi$
$798$		0			0
$799$	6.61988	+	11.4660i	0.234195	+	0.405637i
$800$		0			0
$801$	3.30033	−	6.77299i	0.116611	−	0.239312i
$802$		0			0
$803$	16.8369	−	29.1624i	0.594163	−	1.02912i
$804$		0			0
$805$	41.1987	+	8.34266i	1.45206	+	0.294040i
$806$		0			0
$807$	−36.5373	+	22.8404i	−1.28617	+	0.804019i
$808$		0			0
$809$	11.0961	−	19.2191i	0.390119	−	0.675707i	−0.602346	−	0.798235i	$-0.705767\pi$
$809$	11.0961	−	19.2191i	0.390119	−	0.675707i	0.992465	+	0.122529i	$0.0391004\pi$
$810$		0			0
$811$	52.0941			1.82927			0.914636	−	0.404279i	$-0.132478\pi$
$811$	52.0941			1.82927			0.914636	+	0.404279i	$0.132478\pi$
$812$		0			0
$813$	0.693716	+	19.7614i	0.0243297	+	0.693063i
$814$		0			0
$815$	14.1079	+	24.4356i	0.494179	+	0.855943i
$816$		0			0
$817$	25.6550	−	44.4358i	0.897555	−	1.55461i
$818$		0			0
$819$	9.26301	+	1.20740i	0.323676	+	0.0421901i
$820$		0			0
$821$	−19.8054	+	34.3039i	−0.691212	+	1.19721i	0.280229	+	0.959933i	$0.409590\pi$
$821$	−19.8054	+	34.3039i	−0.691212	+	1.19721i	−0.971441	+	0.237282i	$0.923744\pi$
$822$		0			0
$823$	16.1735	+	28.0134i	0.563773	+	0.976484i	0.997163	+	0.0752773i	$0.0239842\pi$
$823$	16.1735	+	28.0134i	0.563773	+	0.976484i	−0.433389	+	0.901207i	$0.642682\pi$
$824$		0			0
$825$	65.1439	+	34.6223i	2.26802	+	1.20539i
$826$		0			0
$827$	−38.1724			−1.32738			−0.663692	−	0.748006i	$-0.731012\pi$
$827$	−38.1724			−1.32738			−0.663692	+	0.748006i	$0.731012\pi$
$828$		0			0
$829$	27.7372	−	48.0422i	0.963353	−	1.66858i	0.249375	−	0.968407i	$-0.419775\pi$
$829$	27.7372	−	48.0422i	0.963353	−	1.66858i	0.713977	−	0.700169i	$-0.246892\pi$
$830$		0			0
$831$	47.3943	+	25.1888i	1.64409	+	0.873790i
$832$		0			0
$833$	−33.0467	+	24.9976i	−1.14500	+	0.866116i
$834$		0			0
$835$	19.5200	−	33.8096i	0.675516	−	1.17003i
$836$		0			0
$837$	−26.2329	+	19.0814i	−0.906743	+	0.659551i
$838$		0			0
$839$	2.35256	+	4.07475i	0.0812193	+	0.140676i	0.903774	−	0.428010i	$-0.140785\pi$
$839$	2.35256	+	4.07475i	0.0812193	+	0.140676i	−0.822555	+	0.568686i	$0.807452\pi$
$840$		0			0
$841$	5.58195	−	9.66822i	0.192481	−	0.333387i
$842$		0			0
$843$	−0.900435	−	25.6501i	−0.0310126	−	0.883436i
$844$		0			0
$845$	−22.0648	−	38.2174i	−0.759054	−	1.31472i
$846$		0			0
$847$	24.3164	+	4.92402i	0.835522	+	0.169191i
$848$		0			0
$849$	−1.56429	−	44.5609i	−0.0536863	−	1.52933i
$850$		0			0
$851$	16.1904	+	28.0426i	0.555001	+	0.961289i
$852$		0			0
$853$	1.87889	+	3.25434i	0.0643321	+	0.111426i	0.896398	−	0.443251i	$-0.146175\pi$
$853$	1.87889	+	3.25434i	0.0643321	+	0.111426i	−0.832065	+	0.554678i	$0.812842\pi$
$854$		0			0
$855$	25.5312	−	52.3956i	0.873149	−	1.79189i
$856$		0			0
$857$	−53.1561			−1.81578			−0.907888	−	0.419212i	$-0.862306\pi$
$857$	−53.1561			−1.81578			−0.907888	+	0.419212i	$0.862306\pi$
$858$		0			0
$859$	−52.9776			−1.80757			−0.903786	−	0.427985i	$-0.859224\pi$
$859$	−52.9776			−1.80757			−0.903786	+	0.427985i	$0.859224\pi$
$860$		0			0
$861$	6.47617	−	2.42947i	0.220707	−	0.0827960i
$862$		0			0
$863$	9.57834	+	16.5902i	0.326051	+	0.564736i	0.981724	−	0.190308i	$-0.0609487\pi$
$863$	9.57834	+	16.5902i	0.326051	+	0.564736i	−0.655674	+	0.755044i	$0.727615\pi$
$864$		0			0
$865$	−19.3958	+	33.5945i	−0.659477	+	1.14225i
$866$		0			0
$867$	−1.09622	−	31.2272i	−0.0372295	−	1.06053i
$868$		0			0
$869$	4.15717	−	7.20043i	0.141022	−	0.244258i
$870$		0			0
$871$	−1.91409			−0.0648566
$872$		0			0
$873$	−6.22239	+	12.7697i	−0.210596	+	0.432189i
$874$		0			0
$875$	−43.6994	−	8.84904i	−1.47731	−	0.299152i
$876$		0			0
$877$	3.67730			0.124174			0.0620868	−	0.998071i	$-0.480224\pi$
$877$	3.67730			0.124174			0.0620868	+	0.998071i	$0.480224\pi$
$878$		0			0
$879$	24.7089	−	15.4461i	0.833409	−	0.520985i
$880$		0			0
$881$	−14.8862			−0.501529			−0.250765	−	0.968048i	$-0.580682\pi$
$881$	−14.8862			−0.501529			−0.250765	+	0.968048i	$0.580682\pi$
$882$		0			0
$883$	39.9262			1.34362			0.671811	−	0.740722i	$-0.265517\pi$
$883$	39.9262			1.34362			0.671811	+	0.740722i	$0.265517\pi$
$884$		0			0
$885$	2.86101	+	81.4997i	0.0961718	+	2.73958i
$886$		0			0
$887$	−8.50247			−0.285485			−0.142743	−	0.989760i	$-0.545592\pi$
$887$	−8.50247			−0.285485			−0.142743	+	0.989760i	$0.545592\pi$
$888$		0			0
$889$	1.12779	+	0.228376i	0.0378250	+	0.00765949i
$890$		0			0
$891$	−15.1915	+	37.6799i	−0.508935	+	1.26233i
$892$		0			0
$893$	11.4371			0.382730
$894$		0			0
$895$	−36.5877	+	63.3717i	−1.22299	+	2.11828i
$896$		0			0
$897$	−7.22799	+	4.51839i	−0.241336	+	0.150865i
$898$		0			0
$899$	−13.1826	+	22.8329i	−0.439665	+	0.761521i
$900$		0			0
$901$	38.4391	+	66.5785i	1.28059	+	2.21805i
$902$		0			0
$903$	7.53939	−	45.3601i	0.250895	−	1.50949i
$904$		0			0
$905$	5.28736			0.175758
$906$		0			0
$907$	−3.19089			−0.105952			−0.0529758	−	0.998596i	$-0.516871\pi$
$907$	−3.19089			−0.105952			−0.0529758	+	0.998596i	$0.516871\pi$
$908$		0			0
$909$	−19.1711	−	28.3998i	−0.635865	−	0.941963i
$910$		0			0
$911$	7.63889	+	13.2309i	0.253088	+	0.438361i	0.964374	−	0.264541i	$-0.0852206\pi$
$911$	7.63889	+	13.2309i	0.253088	+	0.438361i	−0.711287	+	0.702902i	$0.751887\pi$
$912$		0			0
$913$	−1.38857	−	2.40507i	−0.0459550	−	0.0795963i
$914$		0			0
$915$	8.13778	−	5.08712i	0.269027	−	0.168175i
$916$		0			0
$917$	−13.8801	−	2.81069i	−0.458360	−	0.0928170i
$918$		0			0
$919$	25.2681	+	43.7656i	0.833516	+	1.44369i	0.895233	+	0.445599i	$0.147009\pi$
$919$	25.2681	+	43.7656i	0.833516	+	1.44369i	−0.0617164	+	0.998094i	$0.519657\pi$
$920$		0			0
$921$	−43.2794	−	23.0019i	−1.42611	−	0.757938i
$922$		0			0
$923$	4.99310	−	8.64831i	0.164350	−	0.284662i
$924$		0			0
$925$	−36.5321	−	63.2755i	−1.20117	−	2.08048i
$926$		0			0
$927$	−10.7005	−	15.8515i	−0.351449	−	0.520633i
$928$		0			0
$929$	−23.9890	+	41.5502i	−0.787055	+	1.36322i	0.140709	+	0.990051i	$0.455062\pi$
$929$	−23.9890	+	41.5502i	−0.787055	+	1.36322i	−0.927764	+	0.373168i	$0.878271\pi$
$930$		0			0
$931$	4.42739	+	35.5198i	0.145102	+	1.16411i
$932$		0			0
$933$	−1.20738	−	34.3939i	−0.0395279	−	1.12601i
$934$		0			0
$935$	50.7623	−	87.9228i	1.66010	−	2.87538i
$936$		0			0
$937$	20.5226			0.670443			0.335222	−	0.942139i	$-0.391189\pi$
$937$	20.5226			0.670443			0.335222	+	0.942139i	$0.391189\pi$
$938$		0			0
$939$	26.8563	−	16.7886i	0.876423	−	0.547874i
$940$		0			0
$941$	4.97793	+	8.62203i	0.162276	+	0.281070i	0.935685	−	0.352838i	$-0.114783\pi$
$941$	4.97793	+	8.62203i	0.162276	+	0.281070i	−0.773409	+	0.633908i	$0.781450\pi$
$942$		0			0
$943$	−3.15585	+	5.46609i	−0.102769	+	0.178000i
$944$		0			0
$945$	4.93003	−	51.9999i	0.160374	−	1.69156i
$946$		0			0
$947$	10.6107	−	18.3782i	0.344800	−	0.597212i	−0.640517	−	0.767944i	$-0.721280\pi$
$947$	10.6107	−	18.3782i	0.344800	−	0.597212i	0.985317	+	0.170732i	$0.0546133\pi$
$948$		0			0
$949$	−4.38965	−	7.60310i	−0.142494	−	0.246807i
$950$		0			0
$951$	−20.4854	+	12.8059i	−0.664284	+	0.415260i
$952$		0			0
$953$	−35.9191			−1.16353			−0.581767	−	0.813355i	$-0.697639\pi$
$953$	−35.9191			−1.16353			−0.581767	+	0.813355i	$0.697639\pi$
$954$		0			0
$955$	−5.15736	+	8.93281i	−0.166888	+	0.289059i
$956$		0			0
$957$	1.15846	+	33.0002i	0.0374476	+	1.06674i
$958$		0			0
$959$	15.3057	+	3.09937i	0.494246	+	0.100084i
$960$		0			0
$961$	−3.98645	+	6.90473i	−0.128595	+	0.222733i
$962$		0			0
$963$	−2.94362	+	6.04094i	−0.0948567	+	0.194666i
$964$		0			0
$965$	3.49866	+	6.05986i	0.112626	+	0.195074i
$966$		0			0
$967$	15.9559	−	27.6365i	0.513108	−	0.888729i	−0.486777	−	0.873526i	$-0.661827\pi$
$967$	15.9559	−	27.6365i	0.513108	−	0.888729i	0.999884	−	0.0152023i	$-0.00483924\pi$
$968$		0			0
$969$	−46.2957	−	24.6050i	−1.48723	−	0.790426i
$970$		0			0
$971$	−28.6645	−	49.6483i	−0.919886	−	1.59329i	−0.799585	−	0.600553i	$-0.794947\pi$
$971$	−28.6645	−	49.6483i	−0.919886	−	1.59329i	−0.120301	−	0.992737i	$-0.538386\pi$
$972$		0			0
$973$	15.1891	−	17.1999i	0.486940	−	0.551403i
$974$		0			0
$975$	16.3092	−	10.1953i	0.522314	−	0.326511i
$976$		0			0
$977$	−4.29227	−	7.43444i	−0.137322	−	0.237849i	0.789160	−	0.614188i	$-0.210516\pi$
$977$	−4.29227	−	7.43444i	−0.137322	−	0.237849i	−0.926482	+	0.376339i	$0.877183\pi$
$978$		0			0
$979$	−5.66845	−	9.81805i	−0.181164	−	0.313786i
$980$		0			0
$981$	−16.3450	+	1.14899i	−0.521856	+	0.0366843i
$982$		0			0
$983$	−22.5009			−0.717667			−0.358834	−	0.933402i	$-0.616825\pi$
$983$	−22.5009			−0.717667			−0.358834	+	0.933402i	$0.616825\pi$
$984$		0			0
$985$	−83.2821			−2.65359
$986$		0			0
$987$	9.59656	−	3.60005i	0.305462	−	0.114591i
$988$		0			0
$989$	20.9796	+	36.3378i	0.667114	+	1.15548i
$990$		0			0
$991$	19.3652	−	33.5415i	0.615156	−	1.06548i	−0.375201	−	0.926944i	$-0.622426\pi$
$991$	19.3652	−	33.5415i	0.615156	−	1.06548i	0.990357	−	0.138538i	$-0.0442405\pi$
$992$		0			0
$993$	−30.6075	+	19.1335i	−0.971299	+	0.607183i
$994$		0			0
$995$	2.75875	−	4.77829i	0.0874582	−	0.151482i
$996$		0			0
$997$	36.7909			1.16518			0.582590	−	0.812766i	$-0.302039\pi$
$997$	36.7909			1.16518			0.582590	+	0.812766i	$0.302039\pi$
$998$		0			0
$999$	32.5393	−	23.6686i	1.02950	−	0.748840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.193.10	yes	22
3.2	odd	2		1512.2.t.c.361.10		22
4.3	odd	2		1008.2.t.l.193.2		22
7.2	even	3		504.2.q.c.121.3	yes	22
9.2	odd	6		1512.2.q.d.1369.2		22
9.7	even	3		504.2.q.c.25.3	✓	22
12.11	even	2		3024.2.t.k.1873.10		22
21.2	odd	6		1512.2.q.d.793.2		22
28.23	odd	6		1008.2.q.l.625.9		22
36.7	odd	6		1008.2.q.l.529.9		22
36.11	even	6		3024.2.q.l.2881.2		22
63.2	odd	6		1512.2.t.c.289.10		22
63.16	even	3	inner	504.2.t.c.457.10	yes	22
84.23	even	6		3024.2.q.l.2305.2		22
252.79	odd	6		1008.2.t.l.961.2		22
252.191	even	6		3024.2.t.k.289.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.3	✓	22	9.7	even	3
504.2.q.c.121.3	yes	22	7.2	even	3
504.2.t.c.193.10	yes	22	1.1	even	1	trivial
504.2.t.c.457.10	yes	22	63.16	even	3	inner
1008.2.q.l.529.9		22	36.7	odd	6
1008.2.q.l.625.9		22	28.23	odd	6
1008.2.t.l.193.2		22	4.3	odd	2
1008.2.t.l.961.2		22	252.79	odd	6
1512.2.q.d.793.2		22	21.2	odd	6
1512.2.q.d.1369.2		22	9.2	odd	6
1512.2.t.c.289.10		22	63.2	odd	6
1512.2.t.c.361.10		22	3.2	odd	2
3024.2.q.l.2305.2		22	84.23	even	6
3024.2.q.l.2881.2		22	36.11	even	6
3024.2.t.k.289.10		22	252.191	even	6
3024.2.t.k.1873.10		22	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.52946 + 0.812868i) q^{3} -3.79940 q^{5} +(2.59312 + 0.525101i) q^{7} +(1.67849 + 2.48650i) q^{9} +O(q^{10})\)	\(q+(1.52946 + 0.812868i) q^{3} -3.79940 q^{5} +(2.59312 + 0.525101i) q^{7} +(1.67849 + 2.48650i) q^{9} +4.51412 q^{11} +(0.588451 - 1.01923i) q^{13} +(-5.81103 - 3.08841i) q^{15} +(-2.95973 + 5.12641i) q^{17} +(2.55676 + 4.42844i) q^{19} +(3.53923 + 2.91098i) q^{21} -4.18164 q^{23} +9.43545 q^{25} +(0.545992 + 5.16739i) q^{27} +(2.11164 + 3.65747i) q^{29} +(3.12141 + 5.40645i) q^{31} +(6.90416 + 3.66938i) q^{33} +(-9.85230 - 1.99507i) q^{35} +(-3.87179 - 6.70614i) q^{37} +(1.72851 - 1.08053i) q^{39} +(0.754693 - 1.30717i) q^{41} +(-5.01709 - 8.68986i) q^{43} +(-6.37726 - 9.44720i) q^{45} +(1.11832 - 1.93699i) q^{47} +(6.44854 + 2.72330i) q^{49} +(-8.69389 + 5.43476i) q^{51} +(6.49368 - 11.2474i) q^{53} -17.1510 q^{55} +(0.310726 + 8.85143i) q^{57} +(-6.19609 - 10.7319i) q^{59} +(-0.729171 + 1.26296i) q^{61} +(3.04687 + 7.32916i) q^{63} +(-2.23576 + 3.87245i) q^{65} +(-0.813192 - 1.40849i) q^{67} +(-6.39564 - 3.39912i) q^{69} +8.48517 q^{71} +(3.72984 - 6.46027i) q^{73} +(14.4311 + 7.66977i) q^{75} +(11.7057 + 2.37037i) q^{77} +(0.920926 - 1.59509i) q^{79} +(-3.36533 + 8.34713i) q^{81} +(-0.307606 - 0.532789i) q^{83} +(11.2452 - 19.4773i) q^{85} +(0.256630 + 7.31043i) q^{87} +(-1.25572 - 2.17496i) q^{89} +(2.06112 - 2.33398i) q^{91} +(0.379348 + 10.8062i) q^{93} +(-9.71417 - 16.8254i) q^{95} +(2.36751 + 4.10064i) q^{97} +(7.57691 + 11.2243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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