LMFDB - Embedded newform 504.2.q.c.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (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			25.3
Character	$\chi$	$=$	504.25
Dual form			504.2.q.c.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46869 - 0.918117i) q^{3} +(1.89970 - 3.29038i) q^{5} +(-0.841809 - 2.50826i) q^{7} +(1.31412 + 2.69686i) q^{9} +O(q^{10})$	\(q+(-1.46869 - 0.918117i) q^{3} +(1.89970 - 3.29038i) q^{5} +(-0.841809 - 2.50826i) q^{7} +(1.31412 + 2.69686i) q^{9} +(-2.25706 - 3.90934i) q^{11} +(0.588451 + 1.01923i) q^{13} +(-5.81103 + 3.08841i) q^{15} +(-2.95973 + 5.12641i) q^{17} +(2.55676 + 4.42844i) q^{19} +(-1.06651 + 4.45674i) q^{21} +(2.09082 - 3.62140i) q^{23} +(-4.71772 - 8.17134i) q^{25} +(0.545992 - 5.16739i) q^{27} +(2.11164 - 3.65747i) q^{29} -6.24283 q^{31} +(-0.274303 + 7.81387i) q^{33} +(-9.85230 - 1.99507i) q^{35} +(-3.87179 - 6.70614i) q^{37} +(0.0715150 - 2.03720i) q^{39} +(0.754693 + 1.30717i) q^{41} +(-5.01709 + 8.68986i) q^{43} +(11.3701 + 0.799273i) q^{45} -2.23665 q^{47} +(-5.58272 + 4.22295i) q^{49} +(9.05359 - 4.81175i) q^{51} +(6.49368 - 11.2474i) q^{53} -17.1510 q^{55} +(0.310726 - 8.85143i) q^{57} +12.3922 q^{59} +1.45834 q^{61} +(5.65819 - 5.56640i) q^{63} +4.47152 q^{65} +1.62638 q^{67} +(-6.39564 + 3.39912i) q^{69} +8.48517 q^{71} +(3.72984 - 6.46027i) q^{73} +(-0.573349 + 16.3326i) q^{75} +(-7.90563 + 8.95221i) q^{77} -1.84185 q^{79} +(-5.54616 + 7.08803i) q^{81} +(-0.307606 + 0.532789i) q^{83} +(11.2452 + 19.4773i) q^{85} +(-6.45934 + 3.43297i) q^{87} +(-1.25572 - 2.17496i) q^{89} +(2.06112 - 2.33398i) q^{91} +(9.16880 + 5.73164i) q^{93} +19.4283 q^{95} +(2.36751 - 4.10064i) q^{97} +(7.57691 - 11.2243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.46869	−	0.918117i	−0.847951	−	0.530075i
$3$	−1.46869	−	0.918117i	−0.847951	−	0.530075i
$4$		0			0
$5$	1.89970	−	3.29038i	0.849572	−	1.47150i	−0.0320189	−	0.999487i	$-0.510194\pi$
$5$	1.89970	−	3.29038i	0.849572	−	1.47150i	0.881591	−	0.472014i	$-0.156473\pi$
$6$		0			0
$7$	−0.841809	−	2.50826i	−0.318174	−	0.948032i
$7$	−0.841809	−	2.50826i	−0.318174	−	0.948032i
$8$		0			0
$9$	1.31412	+	2.69686i	0.438041	+	0.898955i
$10$		0			0
$11$	−2.25706	−	3.90934i	−0.680529	−	1.17871i	−0.974820	−	0.222995i	$-0.928417\pi$
$11$	−2.25706	−	3.90934i	−0.680529	−	1.17871i	0.294290	−	0.955716i	$-0.404917\pi$
$12$		0			0
$13$	0.588451	+	1.01923i	0.163207	+	0.282683i	0.936017	−	0.351955i	$-0.114483\pi$
$13$	0.588451	+	1.01923i	0.163207	+	0.282683i	−0.772810	+	0.634637i	$0.781150\pi$
$14$		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
$21$	−1.06651	+	4.45674i	−0.232733	+	0.972541i
$22$		0			0
$23$	2.09082	−	3.62140i	0.435966	−	0.755115i	−0.561408	−	0.827539i	$-0.689740\pi$
$23$	2.09082	−	3.62140i	0.435966	−	0.755115i	0.997374	+	0.0724243i	$0.0230736\pi$
$24$		0			0
$25$	−4.71772	−	8.17134i	−0.943545	−	1.63427i
$26$		0			0
$27$	0.545992	−	5.16739i	0.105076	−	0.994464i
$28$		0			0
$29$	2.11164	−	3.65747i	0.392122	−	0.679175i	−0.600607	−	0.799544i	$-0.705075\pi$
$29$	2.11164	−	3.65747i	0.392122	−	0.679175i	0.992729	+	0.120369i	$0.0384078\pi$
$30$		0			0
$31$	−6.24283			−1.12124			−0.560622	−	0.828072i	$-0.689438\pi$
$31$	−6.24283			−1.12124			−0.560622	+	0.828072i	$0.689438\pi$
$32$		0			0
$33$	−0.274303	+	7.81387i	−0.0477500	+	1.36022i
$34$		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
$39$	0.0715150	−	2.03720i	0.0114516	−	0.326213i
$40$		0			0
$41$	0.754693	+	1.30717i	0.117863	+	0.204145i	0.918921	−	0.394442i	$-0.129062\pi$
$41$	0.754693	+	1.30717i	0.117863	+	0.204145i	−0.801057	+	0.598587i	$0.795729\pi$
$42$		0			0
$43$	−5.01709	+	8.68986i	−0.765099	+	1.32519i	0.175095	+	0.984552i	$0.443977\pi$
$43$	−5.01709	+	8.68986i	−0.765099	+	1.32519i	−0.940194	+	0.340639i	$0.889357\pi$
$44$		0			0
$45$	11.3701	+	0.799273i	1.69496	+	0.119149i
$46$		0			0
$47$	−2.23665			−0.326248			−0.163124	−	0.986606i	$-0.552157\pi$
$47$	−2.23665			−0.326248			−0.163124	+	0.986606i	$0.552157\pi$
$48$		0			0
$49$	−5.58272	+	4.22295i	−0.797531	+	0.603278i
$50$		0			0
$51$	9.05359	−	4.81175i	1.26776	−	0.673779i
$52$		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
$59$	12.3922			1.61332			0.806662	−	0.591013i	$-0.201272\pi$
$59$	12.3922			1.61332			0.806662	+	0.591013i	$0.201272\pi$
$60$		0			0
$61$	1.45834			0.186722			0.0933608	−	0.995632i	$-0.470239\pi$
$61$	1.45834			0.186722			0.0933608	+	0.995632i	$0.470239\pi$
$62$		0			0
$63$	5.65819	−	5.56640i	0.712865	−	0.701301i
$64$		0			0
$65$	4.47152			0.554624
$66$		0			0
$67$	1.62638			0.198694			0.0993472	−	0.995053i	$-0.468325\pi$
$67$	1.62638			0.198694			0.0993472	+	0.995053i	$0.468325\pi$
$68$		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
$75$	−0.573349	+	16.3326i	−0.0662047	+	1.88593i
$76$		0			0
$77$	−7.90563	+	8.95221i	−0.900930	+	1.02020i
$78$		0			0
$79$	−1.84185			−0.207224			−0.103612	−	0.994618i	$-0.533040\pi$
$79$	−1.84185			−0.207224			−0.103612	+	0.994618i	$0.533040\pi$
$80$		0			0
$81$	−5.54616	+	7.08803i	−0.616240	+	0.787558i
$82$		0			0
$83$	−0.307606	+	0.532789i	−0.0337641	+	0.0584812i	−0.882414	−	0.470474i	$-0.844083\pi$
$83$	−0.307606	+	0.532789i	−0.0337641	+	0.0584812i	0.848650	+	0.528956i	$0.177416\pi$
$84$		0			0
$85$	11.2452	+	19.4773i	1.21972	+	2.11261i
$86$		0			0
$87$	−6.45934	+	3.43297i	−0.692514	+	0.368053i
$88$		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
$93$	9.16880	+	5.73164i	0.950761	+	0.594344i
$94$		0			0
$95$	19.4283			1.99330
$96$		0			0
$97$	2.36751	−	4.10064i	0.240384	−	0.416357i	−0.720440	−	0.693517i	$-0.756060\pi$
$97$	2.36751	−	4.10064i	0.240384	−	0.416357i	0.960824	+	0.277160i	$0.0893934\pi$
$98$		0			0
$99$	7.57691	−	11.2243i	0.761508	−	1.12809i
$100$		0			0
$101$	5.71081	+	9.89141i	0.568247	+	0.984232i	0.996739	+	0.0806872i	$0.0257115\pi$
$101$	5.71081	+	9.89141i	0.568247	+	0.984232i	−0.428493	+	0.903545i	$0.640955\pi$
$102$		0			0
$103$	3.18752	−	5.52095i	0.314076	−	0.543996i	−0.665165	−	0.746697i	$-0.731639\pi$
$103$	3.18752	−	5.52095i	0.314076	−	0.543996i	0.979241	+	0.202701i	$0.0649720\pi$
$104$		0			0
$105$	12.6383	+	11.9757i	1.23337	+	1.16871i
$106$		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	0.576794	−	0.816890i	$-0.304304\pi$
$113$	−4.45456	−	7.71553i	−0.419050	−	0.725816i	−0.995844	+	0.0910734i	$0.970970\pi$
$114$		0			0
$115$	−7.94386	−	13.7592i	−0.740768	−	1.28305i
$116$		0			0
$117$	−1.97542	+	2.92636i	−0.182628	+	0.270542i
$118$		0			0
$119$	15.3499	+	3.10832i	1.40712	+	0.284939i
$120$		0			0
$121$	−4.68864	+	8.12096i	−0.426240	+	0.738269i
$122$		0			0
$123$	0.0917185	−	2.61272i	0.00826998	−	0.235581i
$124$		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
$129$	15.3469	−	8.15646i	1.35122	−	0.718136i
$130$		0			0
$131$	2.67633	−	4.63553i	0.233832	−	0.405009i	−0.725101	−	0.688643i	$-0.758207\pi$
$131$	2.67633	−	4.63553i	0.233832	−	0.405009i	0.958933	+	0.283634i	$0.0915402\pi$
$132$		0			0
$133$	8.95537	−	10.1409i	0.776529	−	0.879329i
$134$		0			0
$135$	−15.9654	−	11.6130i	−1.37409	−	0.999489i
$136$		0			0
$137$	−2.95121	−	5.11165i	−0.252139	−	0.436718i	0.711976	−	0.702204i	$-0.247801\pi$
$137$	−2.95121	−	5.11165i	−0.252139	−	0.436718i	−0.964115	+	0.265487i	$0.914467\pi$
$138$		0			0
$139$	4.33649	+	7.51102i	0.367816	+	0.637077i	0.989224	−	0.146411i	$-0.0467721\pi$
$139$	4.33649	+	7.51102i	0.367816	+	0.637077i	−0.621407	+	0.783488i	$0.713439\pi$
$140$		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
$147$	12.0765	−	1.07663i	0.996050	−	0.0887989i
$148$		0			0
$149$	5.38860	−	9.33333i	0.441451	−	0.764616i	−0.556346	−	0.830951i	$-0.687797\pi$
$149$	5.38860	−	9.33333i	0.441451	−	0.764616i	0.997797	+	0.0663346i	$0.0211305\pi$
$150$		0			0
$151$	8.41310	+	14.5719i	0.684648	+	1.18585i	0.973547	+	0.228486i	$0.0733776\pi$
$151$	8.41310	+	14.5719i	0.684648	+	1.18585i	−0.288899	+	0.957360i	$0.593289\pi$
$152$		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
$157$	8.96136			0.715194			0.357597	−	0.933876i	$-0.383596\pi$
$157$	8.96136			0.715194			0.357597	+	0.933876i	$0.383596\pi$
$158$		0			0
$159$	−19.8636	+	10.5570i	−1.57529	+	0.837225i
$160$		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
$165$	25.1895	+	15.7466i	1.96100	+	1.22587i
$166$		0			0
$167$	−5.13764	−	8.89866i	−0.397563	−	0.688599i	0.595862	−	0.803087i	$-0.296811\pi$
$167$	−5.13764	−	8.89866i	−0.397563	−	0.688599i	−0.993425	+	0.114488i	$0.963477\pi$
$168$		0			0
$169$	5.80745	−	10.0588i	0.446727	−	0.773754i
$170$		0			0
$171$	−8.58301	+	12.7148i	−0.656359	+	0.972322i
$172$		0			0
$173$	−10.2099			−0.776246			−0.388123	−	0.921608i	$-0.626876\pi$
$173$	−10.2099			−0.776246			−0.388123	+	0.921608i	$0.626876\pi$
$174$		0			0
$175$	−16.5244	+	18.7120i	−1.24913	+	1.41449i
$176$		0			0
$177$	−18.2003	−	11.3775i	−1.36802	−	0.855183i
$178$		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
$185$	−29.4210			−2.16307
$186$		0			0
$187$	26.7212			1.95405
$188$		0			0
$189$	−13.4208	+	2.98046i	−0.976217	+	0.216797i
$190$		0			0
$191$	−2.71483			−0.196438			−0.0982190	−	0.995165i	$-0.531315\pi$
$191$	−2.71483			−0.196438			−0.0982190	+	0.995165i	$0.531315\pi$
$192$		0			0
$193$	1.84169			0.132568			0.0662839	−	0.997801i	$-0.478886\pi$
$193$	1.84169			0.132568			0.0662839	+	0.997801i	$0.478886\pi$
$194$		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
$201$	−2.38866	−	1.49321i	−0.168483	−	0.105323i
$202$		0			0
$203$	−10.9515	−	2.21765i	−0.768643	−	0.155649i
$204$		0			0
$205$	5.73476			0.400533
$206$		0			0
$207$	12.5140	+	0.879683i	0.869785	+	0.0611422i
$208$		0			0
$209$	11.5415	−	19.9905i	0.798344	−	1.38277i
$210$		0			0
$211$	0.771347	+	1.33601i	0.0531017	+	0.0919749i	0.891354	−	0.453307i	$-0.149756\pi$
$211$	0.771347	+	1.33601i	0.0531017	+	0.0919749i	−0.838253	+	0.545282i	$0.816423\pi$
$212$		0			0
$213$	−12.4621	−	7.79037i	−0.853890	−	0.533788i
$214$		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
$219$	−11.4093	+	6.06373i	−0.770967	+	0.409749i
$220$		0			0
$221$	−6.96663			−0.468626
$222$		0			0
$223$	−0.346045	+	0.599368i	−0.0231729	+	0.0401366i	−0.877379	−	0.479797i	$-0.840710\pi$
$223$	−0.346045	+	0.599368i	−0.0231729	+	0.0401366i	0.854206	+	0.519934i	$0.174043\pi$
$224$		0			0
$225$	15.8373	−	23.4612i	1.05582	−	1.56408i
$226$		0			0
$227$	−9.20797	−	15.9487i	−0.611155	−	1.05855i	−0.991046	−	0.133520i	$-0.957372\pi$
$227$	−9.20797	−	15.9487i	−0.611155	−	1.05855i	0.379892	−	0.925031i	$-0.375961\pi$
$228$		0			0
$229$	2.69696	−	4.67127i	0.178220	−	0.308686i	−0.763051	−	0.646338i	$-0.776299\pi$
$229$	2.69696	−	4.67127i	0.178220	−	0.308686i	0.941271	+	0.337652i	$0.109633\pi$
$230$		0			0
$231$	19.8301	−	5.88976i	1.30473	−	0.387518i
$232$		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	0.810876	−	0.585219i	$-0.198991\pi$
$239$	−1.56724	−	2.71454i	−0.101376	−	0.175589i	−0.912252	+	0.409630i	$0.865658\pi$
$240$		0			0
$241$	8.23730	+	14.2674i	0.530611	+	0.919046i	0.999362	+	0.0357151i	$0.0113709\pi$
$241$	8.23730	+	14.2674i	0.530611	+	0.919046i	−0.468751	+	0.883330i	$0.655296\pi$
$242$		0			0
$243$	14.6532	−	5.31812i	0.940006	−	0.341157i
$244$		0			0
$245$	3.28960	+	26.3916i	0.210165	+	1.68610i
$246$		0			0
$247$	−3.00906	+	5.21184i	−0.191462	+	0.331621i
$248$		0			0
$249$	0.940942	−	0.500086i	0.0596298	−	0.0316917i
$250$		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
$255$	1.36664	−	38.9306i	0.0855824	−	2.43793i
$256$		0			0
$257$	−10.3045	+	17.8478i	−0.642774	+	1.11332i	0.342036	+	0.939687i	$0.388883\pi$
$257$	−10.3045	+	17.8478i	−0.642774	+	1.11332i	−0.984811	+	0.173631i	$0.944450\pi$
$258$		0			0
$259$	−13.5614	+	15.3567i	−0.842666	+	0.954222i
$260$		0			0
$261$	12.6387	+	0.888444i	0.782313	+	0.0549933i
$262$		0			0
$263$	−4.56616	−	7.90883i	−0.281562	−	0.487679i	0.690208	−	0.723611i	$-0.257519\pi$
$263$	−4.56616	−	7.90883i	−0.281562	−	0.487679i	−0.971770	+	0.235932i	$0.924186\pi$
$264$		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
$273$	−5.17002	+	1.53555i	−0.312904	+	0.0929359i
$274$		0			0
$275$	−21.2964	+	36.8864i	−1.28422	+	2.22433i
$276$		0			0
$277$	−15.4938	−	26.8360i	−0.930932	−	1.61242i	−0.781732	−	0.623615i	$-0.785663\pi$
$277$	−15.4938	−	26.8360i	−0.930932	−	1.61242i	−0.149200	−	0.988807i	$-0.547670\pi$
$278$		0			0
$279$	−8.20385	−	16.8361i	−0.491151	−	1.00795i
$280$		0			0
$281$	−7.40910	+	12.8329i	−0.441990	+	0.765549i	−0.997837	−	0.0657354i	$-0.979061\pi$
$281$	−7.40910	+	12.8329i	−0.441990	+	0.765549i	0.555847	+	0.831285i	$0.312394\pi$
$282$		0			0
$283$	25.7431			1.53027			0.765134	−	0.643872i	$-0.222673\pi$
$283$	25.7431			1.53027			0.765134	+	0.643872i	$0.222673\pi$
$284$		0			0
$285$	−28.5343	−	17.8375i	−1.69022	−	1.05660i
$286$		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
$291$	−7.24201	+	3.84894i	−0.424534	+	0.225629i
$292$		0			0
$293$	8.41185	+	14.5697i	0.491425	+	0.851174i	0.999951	−	0.00987288i	$-0.00314269\pi$
$293$	8.41185	+	14.5697i	0.491425	+	0.851174i	−0.508526	+	0.861047i	$0.669809\pi$
$294$		0			0
$295$	23.5414	−	40.7749i	1.37063	−	2.37401i
$296$		0			0
$297$	−21.4334	+	9.52863i	−1.24369	+	0.552907i
$298$		0			0
$299$	4.92137			0.284610
$300$		0			0
$301$	26.0198	+	5.26896i	1.49976	+	0.303698i
$302$		0			0
$303$	0.694040	−	19.7706i	0.0398716	−	1.13579i
$304$		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
$311$	19.8695			1.12670			0.563349	−	0.826219i	$-0.309513\pi$
$311$	19.8695			1.12670			0.563349	+	0.826219i	$0.309513\pi$
$312$		0			0
$313$	−18.2859			−1.03358			−0.516789	−	0.856113i	$-0.672873\pi$
$313$	−18.2859			−1.03358			−0.516789	+	0.856113i	$0.672873\pi$
$314$		0			0
$315$	−7.56670	−	29.1921i	−0.426335	−	1.64479i
$316$		0			0
$317$	13.9480			0.783399			0.391700	−	0.920093i	$-0.371887\pi$
$317$	13.9480			0.783399			0.391700	+	0.920093i	$0.371887\pi$
$318$		0			0
$319$	−19.0644			−1.06740
$320$		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
$327$	8.35358	−	4.43971i	0.461954	−	0.245517i
$328$		0			0
$329$	1.88283	+	5.61009i	0.103804	+	0.309294i
$330$		0			0
$331$	20.8399			1.14547			0.572733	−	0.819742i	$-0.305883\pi$
$331$	20.8399			1.14547			0.572733	+	0.819742i	$0.305883\pi$
$332$		0			0
$333$	12.9975	−	19.2544i	0.712261	−	1.05513i
$334$		0			0
$335$	3.08964	−	5.35142i	0.168805	−	0.292379i
$336$		0			0
$337$	15.4376	+	26.7387i	0.840939	+	1.45655i	0.889101	+	0.457710i	$0.151330\pi$
$337$	15.4376	+	26.7387i	0.840939	+	1.45655i	−0.0481619	+	0.998840i	$0.515336\pi$
$338$		0			0
$339$	−0.541367	+	15.4216i	−0.0294030	+	0.837584i
$340$		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
$345$	−0.965424	+	27.5014i	−0.0519767	+	1.48062i
$346$		0			0
$347$	−10.2685			−0.551244			−0.275622	−	0.961266i	$-0.588884\pi$
$347$	−10.2685			−0.551244			−0.275622	+	0.961266i	$0.588884\pi$
$348$		0			0
$349$	4.61262	−	7.98930i	0.246908	−	0.427657i	−0.715758	−	0.698348i	$-0.753919\pi$
$349$	4.61262	−	7.98930i	0.246908	−	0.427657i	0.962666	+	0.270691i	$0.0872521\pi$
$350$		0			0
$351$	5.58803	−	2.48426i	0.298267	−	0.132600i
$352$		0			0
$353$	−4.08660	−	7.07820i	−0.217508	−	0.376735i	0.736538	−	0.676397i	$-0.236459\pi$
$353$	−4.08660	−	7.07820i	−0.217508	−	0.376735i	−0.954045	+	0.299662i	$0.903126\pi$
$354$		0			0
$355$	16.1193	−	27.9194i	0.855522	−	1.48181i
$356$		0			0
$357$	−19.6905	−	18.6582i	−1.04213	−	0.987495i
$358$		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
$367$	10.9431	+	18.9540i	0.571224	+	0.989388i	0.996441	+	0.0842970i	$0.0268644\pi$
$367$	10.9431	+	18.9540i	0.571224	+	0.989388i	−0.425217	+	0.905091i	$0.639802\pi$
$368$		0			0
$369$	−2.53349	+	3.75308i	−0.131888	+	0.195378i
$370$		0			0
$371$	−33.6778	−	6.81968i	−1.74846	−	0.354060i
$372$		0			0
$373$	6.73126	−	11.6589i	0.348531	−	0.603674i	−0.637457	−	0.770486i	$-0.720014\pi$
$373$	6.73126	−	11.6589i	0.348531	−	0.603674i	0.985989	+	0.166811i	$0.0533471\pi$
$374$		0			0
$375$	24.7505	+	15.4721i	1.27811	+	0.798978i
$376$		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
$381$	−0.638761	−	0.399306i	−0.0327247	−	0.0204570i
$382$		0			0
$383$	4.00330	−	6.93392i	0.204559	−	0.354307i	−0.745433	−	0.666581i	$-0.767757\pi$
$383$	4.00330	−	6.93392i	0.204559	−	0.354307i	0.949992	+	0.312274i	$0.101091\pi$
$384$		0			0
$385$	14.4378	+	43.0190i	0.735819	+	2.19245i
$386$		0			0
$387$	−30.0284	−	2.11087i	−1.52643	−	0.107302i
$388$		0			0
$389$	−14.3931	−	24.9296i	−0.729759	−	1.26398i	−0.956985	−	0.290137i	$-0.906299\pi$
$389$	−14.3931	−	24.9296i	−0.729759	−	1.26398i	0.227226	−	0.973842i	$-0.427034\pi$
$390$		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
$399$	−22.4632	+	6.67183i	−1.12457	+	0.334009i
$400$		0			0
$401$	−13.4966	+	23.3768i	−0.673987	+	1.16738i	0.302777	+	0.953062i	$0.402086\pi$
$401$	−13.4966	+	23.3768i	−0.673987	+	1.16738i	−0.976764	+	0.214318i	$0.931247\pi$
$402$		0			0
$403$	−3.67360	−	6.36285i	−0.182995	−	0.316956i
$404$		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
$409$	−20.9473			−1.03578			−0.517889	−	0.855448i	$-0.673282\pi$
$409$	−20.9473			−1.03578			−0.517889	+	0.855448i	$0.673282\pi$
$410$		0			0
$411$	−0.358663	+	10.2170i	−0.0176916	+	0.503968i
$412$		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
$417$	0.527018	−	15.0128i	0.0258082	−	0.735180i
$418$		0			0
$419$	6.91450	+	11.9763i	0.337795	+	0.585079i	0.984018	−	0.178070i	$-0.0569855\pi$
$419$	6.91450	+	11.9763i	0.337795	+	0.585079i	−0.646222	+	0.763149i	$0.723652\pi$
$420$		0			0
$421$	−6.86872	+	11.8970i	−0.334761	+	0.579823i	−0.983439	−	0.181240i	$-0.941989\pi$
$421$	−6.86872	+	11.8970i	−0.334761	+	0.579823i	0.648678	+	0.761063i	$0.275322\pi$
$422$		0			0
$423$	−2.93923	−	6.03193i	−0.142910	−	0.293283i
$424$		0			0
$425$	55.8529			2.70926
$426$		0			0
$427$	−1.22764	−	3.65790i	−0.0594099	−	0.177018i
$428$		0			0
$429$	−8.12552	+	4.31850i	−0.392304	+	0.208499i
$430$		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
$437$	21.3829			1.02288
$438$		0			0
$439$	−5.83655			−0.278564			−0.139282	−	0.990253i	$-0.544479\pi$
$439$	−5.83655			−0.278564			−0.139282	+	0.990253i	$0.544479\pi$
$440$		0			0
$441$	−18.7251	−	9.50636i	−0.891671	−	0.452684i
$442$		0			0
$443$	14.8400			0.705071			0.352536	−	0.935798i	$-0.385320\pi$
$443$	14.8400			0.705071			0.352536	+	0.935798i	$0.385320\pi$
$444$		0			0
$445$	−9.54194			−0.452331
$446$		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
$453$	1.02245	−	29.1259i	0.0480390	−	1.36845i
$454$		0			0
$455$	−3.76416	−	11.2157i	−0.176467	−	0.525801i
$456$		0			0
$457$	39.7459			1.85924			0.929618	−	0.368525i	$-0.120137\pi$
$457$	39.7459			1.85924			0.929618	+	0.368525i	$0.120137\pi$
$458$		0			0
$459$	24.8742	+	18.0931i	1.16103	+	0.844512i
$460$		0			0
$461$	−2.68671	+	4.65353i	−0.125133	+	0.216736i	−0.921785	−	0.387702i	$-0.873269\pi$
$461$	−2.68671	+	4.65353i	−0.125133	+	0.216736i	0.796652	+	0.604438i	$0.206602\pi$
$462$		0			0
$463$	19.8205	+	34.3301i	0.921136	+	1.59545i	0.797661	+	0.603106i	$0.206070\pi$
$463$	19.8205	+	34.3301i	0.921136	+	1.59545i	0.123474	+	0.992348i	$0.460596\pi$
$464$		0			0
$465$	36.2773	−	19.2804i	1.68232	−	0.894108i
$466$		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
$471$	−13.1615	−	8.22757i	−0.606449	−	0.379106i
$472$		0			0
$473$	45.2955			2.08269
$474$		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
$479$	−9.50287	−	16.4595i	−0.434197	−	0.752052i	0.563032	−	0.826435i	$-0.309635\pi$
$479$	−9.50287	−	16.4595i	−0.434197	−	0.752052i	−0.997230	+	0.0743830i	$0.976301\pi$
$480$		0			0
$481$	4.55672	−	7.89247i	0.207768	−	0.359866i
$482$		0			0
$483$	13.9098	+	13.1805i	0.632916	+	0.599734i
$484$		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	−0.983894	−	0.178753i	$-0.942794\pi$
$491$	−14.3311	−	24.8221i	−0.646752	−	1.12021i	0.337142	−	0.941454i	$-0.390540\pi$
$492$		0			0
$493$	12.4998	+	21.6503i	0.562962	+	0.975079i
$494$		0			0
$495$	−22.5385	−	46.2538i	−1.01303	−	2.07895i
$496$		0			0
$497$	−7.14289	−	21.2830i	−0.320402	−	0.954673i
$498$		0			0
$499$	16.5396	−	28.6475i	0.740416	−	1.28244i	−0.211890	−	0.977294i	$-0.567962\pi$
$499$	16.5396	−	28.6475i	0.740416	−	1.28244i	0.952306	−	0.305145i	$-0.0987049\pi$
$500$		0			0
$501$	−0.624383	+	17.7864i	−0.0278954	+	0.794636i
$502$		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
$507$	−17.7645	+	9.44138i	−0.788950	+	0.419306i
$508$		0			0
$509$	−15.8820	+	27.5085i	−0.703959	+	1.21929i	0.263107	+	0.964767i	$0.415253\pi$
$509$	−15.8820	+	27.5085i	−0.703959	+	1.21929i	−0.967066	+	0.254526i	$0.918081\pi$
$510$		0			0
$511$	−19.3438	−	3.91709i	−0.855721	−	0.173282i
$512$		0			0
$513$	24.2794	−	10.7939i	1.07196	−	0.476562i
$514$		0			0
$515$	−12.1107	−	20.9763i	−0.533660	−	0.924327i
$516$		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
$525$	41.4491	−	12.3108i	1.80899	−	0.537289i
$526$		0			0
$527$	18.4771	−	32.0033i	0.804876	−	1.39409i
$528$		0			0
$529$	2.75696	+	4.77520i	0.119868	+	0.207617i
$530$		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
$535$	8.51060			0.367945
$536$		0			0
$537$	−29.4569	+	15.6556i	−1.27116	+	0.675588i
$538$		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
$543$	2.04388	+	1.27768i	0.0877112	+	0.0548304i
$544$		0			0
$545$	10.3758	+	17.9713i	0.444449	+	0.769808i
$546$		0			0
$547$	1.37567	−	2.38273i	0.0588195	−	0.101878i	−0.835116	−	0.550073i	$-0.814600\pi$
$547$	1.37567	−	2.38273i	0.0588195	−	0.101878i	0.893936	+	0.448195i	$0.147933\pi$
$548$		0			0
$549$	1.91644	+	3.93295i	0.0817917	+	0.167854i
$550$		0			0
$551$	21.5959			0.920014
$552$		0			0
$553$	1.55049	+	4.61984i	0.0659334	+	0.196455i
$554$		0			0
$555$	43.2104	+	27.0119i	1.83418	+	1.14659i
$556$		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
$563$	15.1001			0.636395			0.318197	−	0.948025i	$-0.396923\pi$
$563$	15.1001			0.636395			0.318197	+	0.948025i	$0.396923\pi$
$564$		0			0
$565$	−33.8494			−1.42405
$566$		0			0
$567$	22.4474	+	7.94444i	0.942702	+	0.333635i
$568$		0			0
$569$	−27.5276			−1.15402			−0.577008	−	0.816738i	$-0.695780\pi$
$569$	−27.5276			−1.15402			−0.577008	+	0.816738i	$0.695780\pi$
$570$		0			0
$571$	−38.8755			−1.62689			−0.813444	−	0.581643i	$-0.802410\pi$
$571$	−38.8755			−1.62689			−0.813444	+	0.581643i	$0.802410\pi$
$572$		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
$579$	−2.70488	−	1.69089i	−0.112411	−	0.0702709i
$580$		0			0
$581$	1.59532	+	0.323049i	0.0661849	+	0.0134023i
$582$		0			0
$583$	−58.6265			−2.42806
$584$		0			0
$585$	5.87613	+	12.0591i	0.242948	+	0.498582i
$586$		0			0
$587$	3.14068	−	5.43982i	0.129630	−	0.224525i	−0.793903	−	0.608044i	$-0.791954\pi$
$587$	3.14068	−	5.43982i	0.129630	−	0.224525i	0.923533	+	0.383519i	$0.125288\pi$
$588$		0			0
$589$	−15.9614	−	27.6460i	−0.657679	−	1.13913i
$590$		0			0
$591$	−32.1935	−	20.1249i	−1.32426	−	0.827829i
$592$		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
$597$	2.22108	−	1.18045i	0.0909029	−	0.0483125i
$598$		0			0
$599$	1.05557			0.0431292			0.0215646	−	0.999767i	$-0.493135\pi$
$599$	1.05557			0.0431292			0.0215646	+	0.999767i	$0.493135\pi$
$600$		0			0
$601$	−12.1622	+	21.0656i	−0.496107	+	0.859283i	−0.999990	−	0.00448941i	$-0.998571\pi$
$601$	−12.1622	+	21.0656i	−0.496107	+	0.859283i	0.503883	+	0.863772i	$0.331904\pi$
$602$		0			0
$603$	2.13727	+	4.38614i	0.0870363	+	0.178617i
$604$		0			0
$605$	17.8140	+	30.8548i	0.724243	+	1.25443i
$606$		0			0
$607$	−2.16502	+	3.74993i	−0.0878756	+	0.152205i	−0.906613	−	0.421963i	$-0.861341\pi$
$607$	−2.16502	+	3.74993i	−0.0878756	+	0.152205i	0.818737	+	0.574168i	$0.194674\pi$
$608$		0			0
$609$	14.0483	+	13.3118i	0.569266	+	0.539421i
$610$		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	0.994331	+	0.106329i	$0.0339096\pi$
$617$	14.6366	+	25.3514i	0.589249	+	1.02061i	−0.405082	+	0.914280i	$0.632757\pi$
$618$		0			0
$619$	18.2381	+	31.5893i	0.733050	+	1.26968i	0.955573	+	0.294753i	$0.0952374\pi$
$619$	18.2381	+	31.5893i	0.733050	+	1.26968i	−0.222523	+	0.974927i	$0.571429\pi$
$620$		0			0
$621$	−17.5716	−	12.7813i	−0.705125	−	0.512897i
$622$		0			0
$623$	−4.39830	+	4.98056i	−0.176214	+	0.199542i
$624$		0			0
$625$	−8.42523	+	14.5929i	−0.337009	+	0.583717i
$626$		0			0
$627$	−35.3046	+	18.7635i	−1.40993	+	0.749341i
$628$		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
$633$	0.0937425	−	2.67038i	0.00372593	−	0.106138i
$634$		0			0
$635$	0.826214	−	1.43104i	0.0327873	−	0.0567893i
$636$		0			0
$637$	−7.58929	−	3.20506i	−0.300699	−	0.126989i
$638$		0			0
$639$	11.1506	+	22.8834i	0.441109	+	0.905251i
$640$		0			0
$641$	17.5112	+	30.3303i	0.691651	+	1.19797i	0.971297	+	0.237871i	$0.0764495\pi$
$641$	17.5112	+	30.3303i	0.691651	+	1.19797i	−0.279646	+	0.960103i	$0.590217\pi$
$642$		0			0
$643$	7.29049	+	12.6275i	0.287509	+	0.497980i	0.973215	−	0.229899i	$-0.0738396\pi$
$643$	7.29049	+	12.6275i	0.287509	+	0.497980i	−0.685706	+	0.727879i	$0.740506\pi$
$644$		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
$651$	6.65807	−	27.8227i	0.260950	−	1.09046i
$652$		0			0
$653$	4.26780	−	7.39204i	0.167012	−	0.289273i	−0.770356	−	0.637614i	$-0.779922\pi$
$653$	4.26780	−	7.39204i	0.167012	−	0.289273i	0.937368	+	0.348341i	$0.113255\pi$
$654$		0			0
$655$	−10.1684	−	17.6123i	−0.397314	−	0.688168i
$656$		0			0
$657$	22.3239	+	1.56928i	0.870940	+	0.0612234i
$658$		0			0
$659$	−1.81616	+	3.14568i	−0.0707476	+	0.122538i	−0.899229	−	0.437478i	$-0.855872\pi$
$659$	−1.81616	+	3.14568i	−0.0707476	+	0.122538i	0.828482	+	0.560016i	$0.189205\pi$
$660$		0			0
$661$	−31.0231			−1.20666			−0.603330	−	0.797492i	$-0.706160\pi$
$661$	−31.0231			−1.20666			−0.603330	+	0.797492i	$0.706160\pi$
$662$		0			0
$663$	10.2318	+	6.39618i	0.397372	+	0.248407i
$664$		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
$669$	1.05852	−	0.562578i	0.0409249	−	0.0217505i
$670$		0			0
$671$	−3.29156	−	5.70116i	−0.127069	−	0.220091i
$672$		0			0
$673$	0.291838	−	0.505478i	0.0112495	−	0.0194848i	−0.860346	−	0.509711i	$-0.829752\pi$
$673$	0.291838	−	0.505478i	0.0112495	−	0.0194848i	0.871595	+	0.490226i	$0.163086\pi$
$674$		0			0
$675$	−44.8003	+	19.9168i	−1.72436	+	0.766599i
$676$		0			0
$677$	−33.7332			−1.29647			−0.648237	−	0.761439i	$-0.724493\pi$
$677$	−33.7332			−1.29647			−0.648237	+	0.761439i	$0.724493\pi$
$678$		0			0
$679$	−12.2785	−	2.48636i	−0.471204	−	0.0954178i
$680$		0			0
$681$	−1.11905	+	31.8777i	−0.0428822	+	1.22156i
$682$		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
$689$	15.2848			0.582306
$690$		0			0
$691$	−32.3674			−1.23131			−0.615657	−	0.788014i	$-0.711109\pi$
$691$	−32.3674			−1.23131			−0.615657	+	0.788014i	$0.711109\pi$
$692$		0			0
$693$	−34.5319	−	9.55610i	−1.31176	−	0.363006i
$694$		0			0
$695$	32.9521			1.24995
$696$		0			0
$697$	−8.93476			−0.338428
$698$		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
$705$	12.9972	−	6.90768i	0.489504	−	0.260158i
$706$		0			0
$707$	20.0028	−	22.6509i	0.752283	−	0.851873i
$708$		0			0
$709$	31.6544			1.18880			0.594402	−	0.804168i	$-0.297389\pi$
$709$	31.6544			1.18880			0.594402	+	0.804168i	$0.297389\pi$
$710$		0			0
$711$	−2.42042	−	4.96722i	−0.0907728	−	0.186285i
$712$		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
$717$	−0.190468	+	5.42574i	−0.00711316	+	0.202628i
$718$		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
$723$	1.00109	−	28.5173i	0.0372308	−	1.06057i
$724$		0			0
$725$	−39.8486			−1.47994
$726$		0			0
$727$	−13.6310	+	23.6095i	−0.505544	+	0.875629i	0.494435	+	0.869215i	$0.335375\pi$
$727$	−13.6310	+	23.6095i	−0.505544	+	0.875629i	−0.999979	+	0.00641398i	$0.997958\pi$
$728$		0			0
$729$	−26.4038	−	5.64270i	−0.977918	−	0.208989i
$730$		0			0
$731$	−29.6985	−	51.4393i	−1.09844	−	1.90255i
$732$		0			0
$733$	11.2717	−	19.5232i	0.416330	−	0.721105i	−0.579237	−	0.815159i	$-0.696649\pi$
$733$	11.2717	−	19.5232i	0.416330	−	0.721105i	0.995567	+	0.0940545i	$0.0299828\pi$
$734$		0			0
$735$	19.3991	−	41.7814i	0.715548	−	1.54113i
$736$		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	0.798795	−	0.601603i	$-0.205471\pi$
$743$	−3.31474	−	5.74130i	−0.121606	−	0.210628i	−0.920401	+	0.390975i	$0.872138\pi$
$744$		0			0
$745$	−20.4735	−	35.4611i	−0.750089	−	1.29919i
$746$		0			0
$747$	−1.84109	−	0.129421i	−0.0673621	−	0.00473527i
$748$		0			0
$749$	3.92291	−	4.44224i	0.143340	−	0.162316i
$750$		0			0
$751$	−3.93721	+	6.81944i	−0.143671	+	0.248845i	−0.928876	−	0.370390i	$-0.879224\pi$
$751$	−3.93721	+	6.81944i	−0.143671	+	0.248845i	0.785206	+	0.619235i	$0.212557\pi$
$752$		0			0
$753$	−18.9372	−	11.8381i	−0.690111	−	0.431406i
$754$		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
$759$	27.7237	+	17.3307i	1.00631	+	0.629066i
$760$		0			0
$761$	16.2273	−	28.1065i	0.588238	−	1.01886i	−0.406225	−	0.913773i	$-0.633155\pi$
$761$	16.2273	−	28.1065i	0.588238	−	1.01886i	0.994463	−	0.105085i	$-0.0335115\pi$
$762$		0			0
$763$	14.1631	+	2.86799i	0.512737	+	0.103828i
$764$		0			0
$765$	−37.7500	+	55.9224i	−1.36485	+	2.02188i
$766$		0			0
$767$	7.29218	+	12.6304i	0.263305	+	0.456058i
$768$		0			0
$769$	11.4992	+	19.9172i	0.414671	+	0.718232i	0.995394	−	0.0958699i	$-0.0305633\pi$
$769$	11.4992	+	19.9172i	0.414671	+	0.718232i	−0.580723	+	0.814101i	$0.697230\pi$
$770$		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
$777$	34.0169	−	10.1034i	1.22035	−	0.362457i
$778$		0			0
$779$	−3.85914	+	6.68423i	−0.138268	+	0.239487i
$780$		0			0
$781$	−19.1515	−	33.1714i	−0.685296	−	1.18697i
$782$		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
$787$	−9.11300			−0.324843			−0.162422	−	0.986721i	$-0.551931\pi$
$787$	−9.11300			−0.324843			−0.162422	+	0.986721i	$0.551931\pi$
$788$		0			0
$789$	−0.554930	+	15.8079i	−0.0197560	+	0.562777i
$790$		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
$795$	−2.99842	+	85.4140i	−0.106343	+	3.02932i
$796$		0			0
$797$	−27.5330	−	47.6886i	−0.975270	−	1.68922i	−0.679042	−	0.734099i	$-0.737605\pi$
$797$	−27.5330	−	47.6886i	−0.975270	−	1.68922i	−0.296228	−	0.955117i	$-0.595729\pi$
$798$		0			0
$799$	6.61988	−	11.4660i	0.234195	−	0.405637i
$800$		0			0
$801$	4.21542	−	6.24467i	0.148944	−	0.220644i
$802$		0			0
$803$	−33.6739			−1.18833
$804$		0			0
$805$	−27.8243	+	31.5078i	−0.980679	+	1.11050i
$806$		0			0
$807$	38.0490	−	20.2220i	1.33939	−	0.711849i
$808$		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
$815$	−28.2158			−0.988357
$816$		0			0
$817$	−51.3100			−1.79511
$818$		0			0
$819$	9.00299	+	2.49142i	0.314590	+	0.0870574i
$820$		0			0
$821$	39.6107			1.38242			0.691212	−	0.722652i	$-0.257077\pi$
$821$	39.6107			1.38242			0.691212	+	0.722652i	$0.257077\pi$
$822$		0			0
$823$	−32.3470			−1.12755			−0.563773	−	0.825930i	$-0.690651\pi$
$823$	−32.3470			−1.12755			−0.563773	+	0.825930i	$0.690651\pi$
$824$		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
$831$	−1.88298	+	53.6390i	−0.0653197	+	1.86072i
$832$		0			0
$833$	−5.12520	−	41.1181i	−0.177578	−	1.42466i
$834$		0			0
$835$	−39.0399			−1.35103
$836$		0			0
$837$	−3.40853	+	32.2591i	−0.117816	+	1.11504i
$838$		0			0
$839$	2.35256	−	4.07475i	0.0812193	−	0.140676i	−0.822555	−	0.568686i	$-0.807452\pi$
$839$	2.35256	−	4.07475i	0.0812193	−	0.140676i	0.903774	+	0.428010i	$0.140785\pi$
$840$		0			0
$841$	5.58195	+	9.66822i	0.192481	+	0.333387i
$842$		0			0
$843$	22.6638	−	12.0452i	0.780584	−	0.414860i
$844$		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
$849$	−37.8087	−	23.6351i	−1.29759	−	0.811156i
$850$		0			0
$851$	−32.3809			−1.11000
$852$		0			0
$853$	1.87889	−	3.25434i	0.0643321	−	0.111426i	−0.832065	−	0.554678i	$-0.812842\pi$
$853$	1.87889	−	3.25434i	0.0643321	−	0.111426i	0.896398	+	0.443251i	$0.146175\pi$
$854$		0			0
$855$	25.5312	+	52.3956i	0.873149	+	1.79189i
$856$		0			0
$857$	26.5780	+	46.0345i	0.907888	+	1.57251i	0.816993	+	0.576648i	$0.195640\pi$
$857$	26.5780	+	46.0345i	0.907888	+	1.57251i	0.0908957	+	0.995860i	$0.471027\pi$
$858$		0			0
$859$	26.4888	−	45.8799i	0.903786	−	1.56540i	0.0812476	−	0.996694i	$-0.474110\pi$
$859$	26.4888	−	45.8799i	0.903786	−	1.56540i	0.822538	−	0.568709i	$-0.192557\pi$
$860$		0			0
$861$	−6.63059	+	1.96936i	−0.225970	+	0.0671156i
$862$		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
$871$	0.957046	+	1.65765i	0.0324283	+	0.0561674i
$872$		0			0
$873$	14.1701	+	0.996096i	0.479584	+	0.0337127i
$874$		0			0
$875$	14.1862	+	42.2693i	0.479581	+	1.42896i
$876$		0			0
$877$	−1.83865	+	3.18463i	−0.0620868	+	0.107537i	−0.895398	−	0.445267i	$-0.853109\pi$
$877$	−1.83865	+	3.18463i	−0.0620868	+	0.107537i	0.833311	+	0.552804i	$0.186442\pi$
$878$		0			0
$879$	1.02230	−	29.1216i	0.0344813	−	0.982246i
$880$		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
$885$	−72.0113	+	38.2721i	−2.42063	+	1.28650i
$886$		0			0
$887$	4.25124	−	7.36336i	0.142743	−	0.247237i	−0.785786	−	0.618499i	$-0.787741\pi$
$887$	4.25124	−	7.36336i	0.142743	−	0.247237i	0.928528	+	0.371261i	$0.121075\pi$
$888$		0			0
$889$	−0.366118	−	1.09089i	−0.0122792	−	0.0365872i
$890$		0			0
$891$	40.2275	+	5.68374i	1.34767	+	0.190412i
$892$		0			0
$893$	−5.71857	−	9.90486i	−0.191365	−	0.331453i
$894$		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
$903$	−33.3776	−	31.6277i	−1.11074	−	1.05251i
$904$		0			0
$905$	−2.64368	+	4.57899i	−0.0878789	+	0.152211i
$906$		0			0
$907$	1.59544	+	2.76339i	0.0529758	+	0.0917568i	0.891297	−	0.453419i	$-0.149796\pi$
$907$	1.59544	+	2.76339i	0.0529758	+	0.0917568i	−0.838321	+	0.545176i	$0.816463\pi$
$908$		0			0
$909$	−19.1711	+	28.3998i	−0.635865	+	0.941963i
$910$		0			0
$911$	7.63889	−	13.2309i	0.253088	−	0.438361i	−0.711287	−	0.702902i	$-0.751887\pi$
$911$	7.63889	−	13.2309i	0.253088	−	0.438361i	0.964374	+	0.264541i	$0.0852206\pi$
$912$		0			0
$913$	2.77714			0.0919099
$914$		0			0
$915$	−8.47447	+	4.50396i	−0.280157	+	0.148896i
$916$		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
$921$	41.5600	+	25.9801i	1.36945	+	0.856075i
$922$		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
$927$	19.0781	+	1.34111i	0.626606	+	0.0440477i
$928$		0			0
$929$	47.9781			1.57411			0.787055	−	0.616883i	$-0.211605\pi$
$929$	47.9781			1.57411			0.787055	+	0.616883i	$0.211605\pi$
$930$		0			0
$931$	−32.9748	−	13.9257i	−1.08070	−	0.456395i
$932$		0			0
$933$	−29.1823	−	18.2426i	−0.955385	−	0.597235i
$934$		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
$941$	−9.95586			−0.324552			−0.162276	−	0.986745i	$-0.551883\pi$
$941$	−9.95586			−0.324552			−0.162276	+	0.986745i	$0.551883\pi$
$942$		0			0
$943$	6.31170			0.205537
$944$		0			0
$945$	−15.6886	+	49.8214i	−0.510350	+	1.62069i
$946$		0			0
$947$	−21.2213			−0.689601			−0.344800	−	0.938676i	$-0.612053\pi$
$947$	−21.2213			−0.689601			−0.344800	+	0.938676i	$0.612053\pi$
$948$		0			0
$949$	8.77930			0.284988
$950$		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
$957$	27.9998	+	17.5033i	0.905104	+	0.565803i
$958$		0			0
$959$	−10.3370	+	11.7054i	−0.333798	+	0.377988i
$960$		0			0
$961$	7.97290			0.257190
$962$		0			0
$963$	−3.75980	+	5.56972i	−0.121158	+	0.179482i
$964$		0			0
$965$	3.49866	−	6.05986i	0.112626	−	0.195074i
$966$		0			0
$967$	15.9559	+	27.6365i	0.513108	+	0.888729i	0.999884	+	0.0152023i	$0.00483924\pi$
$967$	15.9559	+	27.6365i	0.513108	+	0.888729i	−0.486777	+	0.873526i	$0.661827\pi$
$968$		0			0
$969$	44.4564	+	27.7908i	1.42815	+	0.892769i
$970$		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
$975$	−16.9840	+	9.02657i	−0.543924	+	0.289081i
$976$		0			0
$977$	8.58455			0.274644			0.137322	−	0.990526i	$-0.456150\pi$
$977$	8.58455			0.274644			0.137322	+	0.990526i	$0.456150\pi$
$978$		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
$983$	11.2504	+	19.4863i	0.358834	+	0.621518i	0.987766	−	0.155942i	$-0.0498412\pi$
$983$	11.2504	+	19.4863i	0.358834	+	0.621518i	−0.628933	+	0.777460i	$0.716508\pi$
$984$		0			0
$985$	41.6411	−	72.1244i	1.32679	−	2.29807i
$986$		0			0
$987$	2.38542	−	9.96816i	0.0759286	−	0.317290i
$988$		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
$997$	−18.3955	−	31.8619i	−0.582590	−	1.00908i	−0.995171	−	0.0981549i	$-0.968706\pi$
$997$	−18.3955	−	31.8619i	−0.582590	−	1.00908i	0.412581	−	0.910921i	$-0.364627\pi$
$998$		0			0
$999$	−36.7672	+	16.3456i	−1.16326	+	0.517151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.c.25.3	✓	22
3.2	odd	2		1512.2.q.d.1369.2		22
4.3	odd	2		1008.2.q.l.529.9		22
7.2	even	3		504.2.t.c.457.10	yes	22
9.4	even	3		504.2.t.c.193.10	yes	22
9.5	odd	6		1512.2.t.c.361.10		22
12.11	even	2		3024.2.q.l.2881.2		22
21.2	odd	6		1512.2.t.c.289.10		22
28.23	odd	6		1008.2.t.l.961.2		22
36.23	even	6		3024.2.t.k.1873.10		22
36.31	odd	6		1008.2.t.l.193.2		22
63.23	odd	6		1512.2.q.d.793.2		22
63.58	even	3	inner	504.2.q.c.121.3	yes	22
84.23	even	6		3024.2.t.k.289.10		22
252.23	even	6		3024.2.q.l.2305.2		22
252.247	odd	6		1008.2.q.l.625.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.3	✓	22	1.1	even	1	trivial
504.2.q.c.121.3	yes	22	63.58	even	3	inner
504.2.t.c.193.10	yes	22	9.4	even	3
504.2.t.c.457.10	yes	22	7.2	even	3
1008.2.q.l.529.9		22	4.3	odd	2
1008.2.q.l.625.9		22	252.247	odd	6
1008.2.t.l.193.2		22	36.31	odd	6
1008.2.t.l.961.2		22	28.23	odd	6
1512.2.q.d.793.2		22	63.23	odd	6
1512.2.q.d.1369.2		22	3.2	odd	2
1512.2.t.c.289.10		22	21.2	odd	6
1512.2.t.c.361.10		22	9.5	odd	6
3024.2.q.l.2305.2		22	252.23	even	6
3024.2.q.l.2881.2		22	12.11	even	2
3024.2.t.k.289.10		22	84.23	even	6
3024.2.t.k.1873.10		22	36.23	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46869 - 0.918117i) q^{3} +(1.89970 - 3.29038i) q^{5} +(-0.841809 - 2.50826i) q^{7} +(1.31412 + 2.69686i) q^{9} +O(q^{10})\)	\(q+(-1.46869 - 0.918117i) q^{3} +(1.89970 - 3.29038i) q^{5} +(-0.841809 - 2.50826i) q^{7} +(1.31412 + 2.69686i) q^{9} +(-2.25706 - 3.90934i) q^{11} +(0.588451 + 1.01923i) q^{13} +(-5.81103 + 3.08841i) q^{15} +(-2.95973 + 5.12641i) q^{17} +(2.55676 + 4.42844i) q^{19} +(-1.06651 + 4.45674i) q^{21} +(2.09082 - 3.62140i) q^{23} +(-4.71772 - 8.17134i) q^{25} +(0.545992 - 5.16739i) q^{27} +(2.11164 - 3.65747i) q^{29} -6.24283 q^{31} +(-0.274303 + 7.81387i) q^{33} +(-9.85230 - 1.99507i) q^{35} +(-3.87179 - 6.70614i) q^{37} +(0.0715150 - 2.03720i) q^{39} +(0.754693 + 1.30717i) q^{41} +(-5.01709 + 8.68986i) q^{43} +(11.3701 + 0.799273i) q^{45} -2.23665 q^{47} +(-5.58272 + 4.22295i) q^{49} +(9.05359 - 4.81175i) q^{51} +(6.49368 - 11.2474i) q^{53} -17.1510 q^{55} +(0.310726 - 8.85143i) q^{57} +12.3922 q^{59} +1.45834 q^{61} +(5.65819 - 5.56640i) q^{63} +4.47152 q^{65} +1.62638 q^{67} +(-6.39564 + 3.39912i) q^{69} +8.48517 q^{71} +(3.72984 - 6.46027i) q^{73} +(-0.573349 + 16.3326i) q^{75} +(-7.90563 + 8.95221i) q^{77} -1.84185 q^{79} +(-5.54616 + 7.08803i) q^{81} +(-0.307606 + 0.532789i) q^{83} +(11.2452 + 19.4773i) q^{85} +(-6.45934 + 3.43297i) q^{87} +(-1.25572 - 2.17496i) q^{89} +(2.06112 - 2.33398i) q^{91} +(9.16880 + 5.73164i) q^{93} +19.4283 q^{95} +(2.36751 - 4.10064i) q^{97} +(7.57691 - 11.2243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

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