LMFDB - Embedded newform 572.2.x.a.25.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(25,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 5]))

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

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

chi := DirichletCharacter("572.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.x (of order $10$, degree $4$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			25.13
Character	$\chi$	$=$	572.25
Dual form			572.2.x.a.389.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866400 + 2.66651i) q^{3} +(-0.720035 + 0.991043i) q^{5} +(-1.55809 - 0.506254i) q^{7} +(-3.93255 + 2.85717i) q^{9} +O(q^{10})$	\(q+(0.866400 + 2.66651i) q^{3} +(-0.720035 + 0.991043i) q^{5} +(-1.55809 - 0.506254i) q^{7} +(-3.93255 + 2.85717i) q^{9} +(-3.26664 + 0.573639i) q^{11} +(-3.56896 - 0.512351i) q^{13} +(-3.26646 - 1.06134i) q^{15} +(-0.515960 - 0.374867i) q^{17} +(0.923703 - 0.300129i) q^{19} -4.59327i q^{21} +2.08440 q^{23} +(1.08137 + 3.32811i) q^{25} +(-4.22103 - 3.06675i) q^{27} +(-0.124390 + 0.382834i) q^{29} +(5.69111 + 7.83314i) q^{31} +(-4.35983 - 8.21351i) q^{33} +(1.62360 - 1.17961i) q^{35} +(3.86078 + 1.25444i) q^{37} +(-1.72596 - 9.96056i) q^{39} +(-10.6315 + 3.45439i) q^{41} -0.426591 q^{43} -5.95459i q^{45} +(10.1471 - 3.29700i) q^{47} +(-3.49177 - 2.53692i) q^{49} +(0.552557 - 1.70060i) q^{51} +(-8.42725 + 6.12276i) q^{53} +(1.78359 - 3.65042i) q^{55} +(1.60059 + 2.20303i) q^{57} +(-2.95371 - 0.959719i) q^{59} +(2.29444 + 1.66701i) q^{61} +(7.57372 - 2.46085i) q^{63} +(3.07754 - 3.16809i) q^{65} +4.46823i q^{67} +(1.80592 + 5.55806i) q^{69} +(-1.83029 + 2.51917i) q^{71} +(-2.81684 - 0.915245i) q^{73} +(-7.93753 + 5.76695i) q^{75} +(5.38012 + 0.759968i) q^{77} +(13.6904 - 9.94668i) q^{79} +(0.0141153 - 0.0434424i) q^{81} +(-7.23020 + 9.95151i) q^{83} +(0.743019 - 0.241422i) q^{85} -1.12860 q^{87} +7.83338i q^{89} +(5.30138 + 2.60509i) q^{91} +(-15.9563 + 21.9620i) q^{93} +(-0.367657 + 1.13153i) q^{95} +(1.23704 + 1.70264i) q^{97} +(11.2073 - 11.5892i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{9}+O(q^{10}) $ 56 * q - 2 * q^9	$ 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) $ 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{5}\right)$

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
$3$	0.866400	+	2.66651i	0.500216	+	1.53951i	0.808666	+	0.588267i	$0.200190\pi$
$3$	0.866400	+	2.66651i	0.500216	+	1.53951i	−0.308450	+	0.951241i	$0.599810\pi$
$4$		0			0
$5$	−0.720035	+	0.991043i	−0.322010	+	0.443208i	−0.939079	−	0.343700i	$-0.888320\pi$
$5$	−0.720035	+	0.991043i	−0.322010	+	0.443208i	0.617070	+	0.786908i	$0.288320\pi$
$6$		0			0
$7$	−1.55809	−	0.506254i	−0.588902	−	0.191346i	−0.000617639	−	1.00000i	$-0.500197\pi$
$7$	−1.55809	−	0.506254i	−0.588902	−	0.191346i	−0.588285	+	0.808654i	$0.700197\pi$
$8$		0			0
$9$	−3.93255	+	2.85717i	−1.31085	+	0.952389i
$10$		0			0
$11$	−3.26664	+	0.573639i	−0.984929	+	0.172959i
$11$	−3.26664	+	0.573639i	−0.984929	+	0.172959i
$12$		0			0
$13$	−3.56896	−	0.512351i	−0.989852	−	0.142101i
$13$	−3.56896	−	0.512351i	−0.989852	−	0.142101i
$14$		0			0
$15$	−3.26646	−	1.06134i	−0.843397	−	0.274036i
$16$		0			0
$17$	−0.515960	−	0.374867i	−0.125139	−	0.0909186i	0.523455	−	0.852053i	$-0.324643\pi$
$17$	−0.515960	−	0.374867i	−0.125139	−	0.0909186i	−0.648594	+	0.761134i	$0.724643\pi$
$18$		0			0
$19$	0.923703	−	0.300129i	0.211912	−	0.0688544i	−0.201137	−	0.979563i	$-0.564464\pi$
$19$	0.923703	−	0.300129i	0.211912	−	0.0688544i	0.413049	+	0.910709i	$0.364464\pi$
$20$		0			0
$21$		−	4.59327i		−	1.00233i
$22$		0			0
$23$	2.08440			0.434627			0.217313	−	0.976102i	$-0.430271\pi$
$23$	2.08440			0.434627			0.217313	+	0.976102i	$0.430271\pi$
$24$		0			0
$25$	1.08137	+	3.32811i	0.216274	+	0.665622i
$26$		0			0
$27$	−4.22103	−	3.06675i	−0.812337	−	0.590197i
$28$		0			0
$29$	−0.124390	+	0.382834i	−0.0230987	+	0.0710905i	−0.961941	−	0.273256i	$-0.911899\pi$
$29$	−0.124390	+	0.382834i	−0.0230987	+	0.0710905i	0.938843	+	0.344346i	$0.111899\pi$
$30$		0			0
$31$	5.69111	+	7.83314i	1.02215	+	1.40687i	0.910683	+	0.413105i	$0.135556\pi$
$31$	5.69111	+	7.83314i	1.02215	+	1.40687i	0.111470	+	0.993768i	$0.464444\pi$
$32$		0			0
$33$	−4.35983	−	8.21351i	−0.758949	−	1.42979i
$34$		0			0
$35$	1.62360	−	1.17961i	0.274438	−	0.199391i
$36$		0			0
$37$	3.86078	+	1.25444i	0.634708	+	0.206229i	0.608660	−	0.793431i	$-0.291708\pi$
$37$	3.86078	+	1.25444i	0.634708	+	0.206229i	0.0260486	+	0.999661i	$0.491708\pi$
$38$		0			0
$39$	−1.72596	−	9.96056i	−0.276375	−	1.59497i
$40$		0			0
$41$	−10.6315	+	3.45439i	−1.66036	+	0.539485i	−0.980948	−	0.194269i	$-0.937767\pi$
$41$	−10.6315	+	3.45439i	−1.66036	+	0.539485i	−0.679416	+	0.733754i	$0.737767\pi$
$42$		0			0
$43$	−0.426591			−0.0650545			−0.0325273	−	0.999471i	$-0.510356\pi$
$43$	−0.426591			−0.0650545			−0.0325273	+	0.999471i	$0.510356\pi$
$44$		0			0
$45$		−	5.95459i		−	0.887658i
$46$		0			0
$47$	10.1471	−	3.29700i	1.48011	−	0.480917i	0.545963	−	0.837809i	$-0.316164\pi$
$47$	10.1471	−	3.29700i	1.48011	−	0.480917i	0.934145	+	0.356892i	$0.116164\pi$
$48$		0			0
$49$	−3.49177	−	2.53692i	−0.498824	−	0.362417i
$50$		0			0
$51$	0.552557	−	1.70060i	0.0773735	−	0.238131i
$52$		0			0
$53$	−8.42725	+	6.12276i	−1.15757	+	0.841025i	−0.989469	−	0.144744i	$-0.953764\pi$
$53$	−8.42725	+	6.12276i	−1.15757	+	0.841025i	−0.168103	+	0.985769i	$0.553764\pi$
$54$		0			0
$55$	1.78359	−	3.65042i	0.240500	−	0.492223i
$56$		0			0
$57$	1.60059	+	2.20303i	0.212004	+	0.291798i
$58$		0			0
$59$	−2.95371	−	0.959719i	−0.384541	−	0.124945i	0.110366	−	0.993891i	$-0.464798\pi$
$59$	−2.95371	−	0.959719i	−0.384541	−	0.124945i	−0.494907	+	0.868946i	$0.664798\pi$
$60$		0			0
$61$	2.29444	+	1.66701i	0.293774	+	0.213439i	0.724903	−	0.688851i	$-0.241885\pi$
$61$	2.29444	+	1.66701i	0.293774	+	0.213439i	−0.431129	+	0.902290i	$0.641885\pi$
$62$		0			0
$63$	7.57372	−	2.46085i	0.954200	−	0.310038i
$64$		0			0
$65$	3.07754	−	3.16809i	0.381722	−	0.392953i
$66$		0			0
$67$			4.46823i			0.545881i	0.962031	+	0.272941i	$0.0879963\pi$
$67$			4.46823i			0.545881i	−0.962031	+	0.272941i	$0.912004\pi$
$68$		0			0
$69$	1.80592	+	5.55806i	0.217408	+	0.669112i
$70$		0			0
$71$	−1.83029	+	2.51917i	−0.217215	+	0.298971i	−0.903694	−	0.428179i	$-0.859155\pi$
$71$	−1.83029	+	2.51917i	−0.217215	+	0.298971i	0.686479	+	0.727150i	$0.259155\pi$
$72$		0			0
$73$	−2.81684	−	0.915245i	−0.329686	−	0.107121i	0.139497	−	0.990222i	$-0.455451\pi$
$73$	−2.81684	−	0.915245i	−0.329686	−	0.107121i	−0.469183	+	0.883101i	$0.655451\pi$
$74$		0			0
$75$	−7.93753	+	5.76695i	−0.916547	+	0.665910i
$76$		0			0
$77$	5.38012	+	0.759968i	0.613122	+	0.0866064i
$78$		0			0
$79$	13.6904	−	9.94668i	1.54029	−	1.11909i	0.590142	−	0.807299i	$-0.299072\pi$
$79$	13.6904	−	9.94668i	1.54029	−	1.11909i	0.950151	−	0.311789i	$-0.100928\pi$
$80$		0			0
$81$	0.0141153	−	0.0434424i	0.00156837	−	0.00482694i
$82$		0			0
$83$	−7.23020	+	9.95151i	−0.793617	+	1.09232i	0.200031	+	0.979790i	$0.435896\pi$
$83$	−7.23020	+	9.95151i	−0.793617	+	1.09232i	−0.993648	+	0.112531i	$0.964104\pi$
$84$		0			0
$85$	0.743019	−	0.241422i	0.0805918	−	0.0261859i
$86$		0			0
$87$	−1.12860			−0.120999
$88$		0			0
$89$			7.83338i			0.830337i	0.909745	+	0.415169i	$0.136277\pi$
$89$			7.83338i			0.830337i	−0.909745	+	0.415169i	$0.863723\pi$
$90$		0			0
$91$	5.30138	+	2.60509i	0.555736	+	0.273088i
$92$		0			0
$93$	−15.9563	+	21.9620i	−1.65459	+	2.27735i
$94$		0			0
$95$	−0.367657	+	1.13153i	−0.0377209	+	0.116093i
$96$		0			0
$97$	1.23704	+	1.70264i	0.125602	+	0.172877i	0.867187	−	0.497982i	$-0.165926\pi$
$97$	1.23704	+	1.70264i	0.125602	+	0.172877i	−0.741585	+	0.670859i	$0.765926\pi$
$98$		0			0
$99$	11.2073	−	11.5892i	1.12637	−	1.16476i
$100$		0			0
$101$	8.17128	−	5.93678i	0.813073	−	0.590732i	−0.101647	−	0.994821i	$-0.532411\pi$
$101$	8.17128	−	5.93678i	0.813073	−	0.590732i	0.914720	+	0.404088i	$0.132411\pi$
$102$		0			0
$103$	3.77804	−	11.6276i	0.372262	−	1.14570i	−0.573046	−	0.819523i	$-0.694238\pi$
$103$	3.77804	−	11.6276i	0.372262	−	1.14570i	0.945308	−	0.326180i	$-0.105762\pi$
$104$		0			0
$105$	4.55213	+	3.30732i	0.444243	+	0.322761i
$106$		0			0
$107$	3.84594	+	11.8366i	0.371801	+	1.14429i	0.945611	+	0.325298i	$0.105465\pi$
$107$	3.84594	+	11.8366i	0.371801	+	1.14429i	−0.573810	+	0.818988i	$0.694535\pi$
$108$		0			0
$109$			9.62287i			0.921704i	0.887477	+	0.460852i	$0.152456\pi$
$109$			9.62287i			0.921704i	−0.887477	+	0.460852i	$0.847544\pi$
$110$		0			0
$111$			11.3816i			1.08030i
$112$		0			0
$113$	2.16665	+	6.66825i	0.203821	+	0.627296i	0.999760	+	0.0219193i	$0.00697769\pi$
$113$	2.16665	+	6.66825i	0.203821	+	0.627296i	−0.795939	+	0.605377i	$0.793022\pi$
$114$		0			0
$115$	−1.50084	+	2.06573i	−0.139954	+	0.192630i
$116$		0			0
$117$	15.4990	−	8.18228i	1.43288	−	0.756452i
$118$		0			0
$119$	0.614135	+	0.845284i	0.0562976	+	0.0774870i
$120$		0			0
$121$	10.3419	−	3.74775i	0.940171	−	0.340704i
$122$		0			0
$123$	−18.4223	−	25.3561i	−1.66108	−	2.28628i
$124$		0			0
$125$	−9.90213	−	3.21740i	−0.885674	−	0.287773i
$126$		0			0
$127$	−6.80825	−	4.94648i	−0.604134	−	0.438929i	0.243210	−	0.969974i	$-0.421800\pi$
$127$	−6.80825	−	4.94648i	−0.604134	−	0.438929i	−0.847344	+	0.531044i	$0.821800\pi$
$128$		0			0
$129$	−0.369599	−	1.13751i	−0.0325414	−	0.100152i
$130$		0			0
$131$	1.19004			0.103975			0.0519873	−	0.998648i	$-0.483444\pi$
$131$	1.19004			0.103975			0.0519873	+	0.998648i	$0.483444\pi$
$132$		0			0
$133$	−1.59115			−0.137970
$134$		0			0
$135$	6.07857	−	1.97505i	0.523160	−	0.169985i
$136$		0			0
$137$	3.92709	−	5.40518i	0.335514	−	0.461795i	−0.607610	−	0.794235i	$-0.707872\pi$
$137$	3.92709	−	5.40518i	0.335514	−	0.461795i	0.943124	+	0.332440i	$0.107872\pi$
$138$		0			0
$139$	−1.38648	+	4.26714i	−0.117599	+	0.361934i	−0.992480	−	0.122404i	$-0.960940\pi$
$139$	−1.38648	+	4.26714i	−0.117599	+	0.361934i	0.874881	+	0.484338i	$0.160940\pi$
$140$		0			0
$141$	17.5829	+	24.2008i	1.48075	+	2.03808i
$142$		0			0
$143$	11.9524	−	0.373630i	0.999512	−	0.0312445i
$144$		0			0
$145$	−0.289840	−	0.398930i	−0.0240699	−	0.0331293i
$146$		0			0
$147$	3.73944	−	11.5088i	0.308424	−	0.949231i
$148$		0			0
$149$	1.59357	−	2.19336i	0.130550	−	0.179687i	−0.738738	−	0.673993i	$-0.764578\pi$
$149$	1.59357	−	2.19336i	0.130550	−	0.179687i	0.869288	+	0.494306i	$0.164578\pi$
$150$		0			0
$151$	16.6163	−	5.39896i	1.35222	−	0.439361i	0.458779	−	0.888551i	$-0.348287\pi$
$151$	16.6163	−	5.39896i	1.35222	−	0.439361i	0.893437	+	0.449189i	$0.148287\pi$
$152$		0			0
$153$	3.10010			0.250628
$154$		0			0
$155$	−11.8608			−0.952681
$156$		0			0
$157$	−2.65499	−	8.17122i	−0.211891	−	0.652135i	−0.999360	−	0.0357795i	$-0.988609\pi$
$157$	−2.65499	−	8.17122i	−0.211891	−	0.652135i	0.787468	−	0.616355i	$-0.211391\pi$
$158$		0			0
$159$	−23.6277	−	17.1666i	−1.87380	−	1.36140i
$160$		0			0
$161$	−3.24768	−	1.05523i	−0.255953	−	0.0831641i
$162$		0			0
$163$	6.65053	+	9.15367i	0.520910	+	0.716971i	0.985711	−	0.168444i	$-0.0538743\pi$
$163$	6.65053	+	9.15367i	0.520910	+	0.716971i	−0.464801	+	0.885415i	$0.653874\pi$
$164$		0			0
$165$	11.2792	+	1.59324i	0.878083	+	0.124033i
$166$		0			0
$167$	0.848134	+	1.16736i	0.0656306	+	0.0903328i	0.840571	−	0.541702i	$-0.182220\pi$
$167$	0.848134	+	1.16736i	0.0656306	+	0.0903328i	−0.774940	+	0.632035i	$0.782220\pi$
$168$		0			0
$169$	12.4750	+	3.65713i	0.959615	+	0.281317i
$170$		0			0
$171$	−2.77499	+	3.81945i	−0.212209	+	0.292081i
$172$		0			0
$173$	2.87523	+	8.84905i	0.218600	+	0.672781i	0.998878	+	0.0473490i	$0.0150773\pi$
$173$	2.87523	+	8.84905i	0.218600	+	0.672781i	−0.780279	+	0.625432i	$0.784923\pi$
$174$		0			0
$175$		−	5.73294i		−	0.433370i
$176$		0			0
$177$		−	8.70759i		−	0.654503i
$178$		0			0
$179$	−3.28273	−	10.1032i	−0.245363	−	0.755149i	−0.995577	−	0.0939539i	$-0.970049\pi$
$179$	−3.28273	−	10.1032i	−0.245363	−	0.755149i	0.750214	−	0.661196i	$-0.229951\pi$
$180$		0			0
$181$	5.41225	+	3.93223i	0.402290	+	0.292281i	0.770473	−	0.637473i	$-0.220020\pi$
$181$	5.41225	+	3.93223i	0.402290	+	0.292281i	−0.368183	+	0.929753i	$0.620020\pi$
$182$		0			0
$183$	−2.45719	+	7.56245i	−0.181641	+	0.559032i
$184$		0			0
$185$	−4.02310	+	2.92296i	−0.295785	+	0.214900i
$186$		0			0
$187$	1.90050	+	0.928581i	0.138978	+	0.0679046i
$188$		0			0
$189$	5.02418	+	6.91519i	0.365455	+	0.503006i
$190$		0			0
$191$	7.20461	−	22.1735i	0.521307	−	1.60442i	−0.250198	−	0.968195i	$-0.580496\pi$
$191$	7.20461	−	22.1735i	0.521307	−	1.60442i	0.771505	−	0.636224i	$-0.219504\pi$
$192$		0			0
$193$	8.55794	−	11.7790i	0.616014	−	0.847870i	−0.381041	−	0.924558i	$-0.624434\pi$
$193$	8.55794	−	11.7790i	0.616014	−	0.847870i	0.997055	+	0.0766876i	$0.0244344\pi$
$194$		0			0
$195$	11.1141	+	5.46145i	0.795898	+	0.391103i
$196$		0			0
$197$			16.0171i			1.14117i	0.821238	+	0.570586i	$0.193284\pi$
$197$			16.0171i			1.14117i	−0.821238	+	0.570586i	$0.806716\pi$
$198$		0			0
$199$	−10.6791			−0.757021			−0.378511	−	0.925597i	$-0.623564\pi$
$199$	−10.6791			−0.757021			−0.378511	+	0.925597i	$0.623564\pi$
$200$		0			0
$201$	−11.9146	+	3.87128i	−0.840389	+	0.273059i
$202$		0			0
$203$	0.387622	−	0.533517i	0.0272058	−	0.0374455i
$204$		0			0
$205$	4.23162	−	13.0236i	0.295549	−	0.909606i
$206$		0			0
$207$	−8.19701	+	5.95547i	−0.569731	+	0.413934i
$208$		0			0
$209$	−2.84524	+	1.51029i	−0.196809	+	0.104469i
$210$		0			0
$211$	17.7423	−	12.8906i	1.22143	−	0.887423i	0.225214	−	0.974309i	$-0.427692\pi$
$211$	17.7423	−	12.8906i	1.22143	−	0.887423i	0.996218	+	0.0868866i	$0.0276918\pi$
$212$		0			0
$213$	−8.30315	−	2.69786i	−0.568922	−	0.184854i
$214$		0			0
$215$	0.307161	−	0.422770i	0.0209482	−	0.0288327i
$216$		0			0
$217$	−4.90170	−	15.0859i	−0.332749	−	1.02410i
$218$		0			0
$219$		−	8.30408i		−	0.561138i
$220$		0			0
$221$	1.64938	+	1.60224i	0.110949	+	0.107778i
$222$		0			0
$223$	−5.06515	+	1.64577i	−0.339188	+	0.110209i	−0.473658	−	0.880709i	$-0.657067\pi$
$223$	−5.06515	+	1.64577i	−0.339188	+	0.110209i	0.134470	+	0.990918i	$0.457067\pi$
$224$		0			0
$225$	−13.7615	−	9.99832i	−0.917434	−	0.666555i
$226$		0			0
$227$	−18.1942	−	5.91166i	−1.20759	−	0.392371i	−0.365043	−	0.930990i	$-0.618946\pi$
$227$	−18.1942	−	5.91166i	−1.20759	−	0.392371i	−0.842549	+	0.538620i	$0.818946\pi$
$228$		0			0
$229$	−6.38554	−	8.78895i	−0.421969	−	0.580790i	0.544118	−	0.839009i	$-0.316864\pi$
$229$	−6.38554	−	8.78895i	−0.421969	−	0.580790i	−0.966086	+	0.258219i	$0.916864\pi$
$230$		0			0
$231$	2.63488	+	15.0046i	0.173363	+	0.987228i
$232$		0			0
$233$	−18.3134	+	13.3054i	−1.19975	+	0.871669i	−0.994260	−	0.106990i	$-0.965879\pi$
$233$	−18.3134	+	13.3054i	−1.19975	+	0.871669i	−0.205489	+	0.978659i	$0.565879\pi$
$234$		0			0
$235$	−4.03881	+	12.4302i	−0.263463	+	0.810856i
$236$		0			0
$237$	38.3843	+	27.8878i	2.49333	+	1.81151i
$238$		0			0
$239$	14.9562	−	4.85956i	0.967436	−	0.314339i	0.217655	−	0.976026i	$-0.430159\pi$
$239$	14.9562	−	4.85956i	0.967436	−	0.314339i	0.749780	+	0.661687i	$0.230159\pi$
$240$		0			0
$241$		−	14.6842i		−	0.945891i	−0.881092	−	0.472946i	$-0.843191\pi$
$241$		−	14.6842i		−	0.945891i	0.881092	−	0.472946i	$-0.156809\pi$
$242$		0			0
$243$	−15.5244			−0.995888
$244$		0			0
$245$	5.02839	−	1.63382i	0.321252	−	0.104381i
$246$		0			0
$247$	−3.45043	+	0.597890i	−0.219546	+	0.0380428i
$248$		0			0
$249$	−32.8000	−	10.6574i	−2.07862	−	0.675383i
$250$		0			0
$251$	−4.32653	+	3.14340i	−0.273088	+	0.198410i	−0.715897	−	0.698206i	$-0.753982\pi$
$251$	−4.32653	+	3.14340i	−0.273088	+	0.198410i	0.442809	+	0.896616i	$0.353982\pi$
$252$		0			0
$253$	−6.80898	+	1.19569i	−0.428077	+	0.0751725i
$254$		0			0
$255$	1.28750	+	1.77210i	0.0806267	+	0.110973i
$256$		0			0
$257$	−7.30408	+	22.4797i	−0.455616	+	1.40224i	0.414794	+	0.909915i	$0.363854\pi$
$257$	−7.30408	+	22.4797i	−0.455616	+	1.40224i	−0.870410	+	0.492327i	$0.836146\pi$
$258$		0			0
$259$	−5.38037	−	3.90907i	−0.334320	−	0.242898i
$260$		0			0
$261$	−0.604649	−	1.86092i	−0.0374269	−	0.115188i
$262$		0			0
$263$	−13.2062			−0.814327			−0.407163	−	0.913355i	$-0.633482\pi$
$263$	−13.2062			−0.814327			−0.407163	+	0.913355i	$0.633482\pi$
$264$		0			0
$265$		−	12.7604i		−	0.783863i
$266$		0			0
$267$	−20.8878	+	6.78685i	−1.27831	+	0.415348i
$268$		0			0
$269$	13.8462	+	10.0599i	0.844221	+	0.613362i	0.923546	−	0.383487i	$-0.125277\pi$
$269$	13.8462	+	10.0599i	0.844221	+	0.613362i	−0.0793258	+	0.996849i	$0.525277\pi$
$270$		0			0
$271$	21.3643	+	6.94169i	1.29779	+	0.421677i	0.874812	−	0.484463i	$-0.160985\pi$
$271$	21.3643	+	6.94169i	1.29779	+	0.421677i	0.422978	+	0.906140i	$0.360985\pi$
$272$		0			0
$273$	−2.35337	+	16.3932i	−0.142432	+	0.992163i
$274$		0			0
$275$	−5.44158	−	10.2514i	−0.328139	−	0.618184i
$276$		0			0
$277$	−12.3587	+	8.97909i	−0.742559	+	0.539501i	−0.893512	−	0.449040i	$-0.851766\pi$
$277$	−12.3587	+	8.97909i	−0.742559	+	0.539501i	0.150952	+	0.988541i	$0.451766\pi$
$278$		0			0
$279$	−44.7612	−	14.5438i	−2.67978	−	0.870714i
$280$		0			0
$281$	−0.449271	+	0.618369i	−0.0268013	+	0.0368888i	−0.822207	−	0.569188i	$-0.807258\pi$
$281$	−0.449271	+	0.618369i	−0.0268013	+	0.0368888i	0.795406	+	0.606077i	$0.207258\pi$
$282$		0			0
$283$	5.05275	+	15.5508i	0.300355	+	0.924396i	0.981370	+	0.192127i	$0.0615386\pi$
$283$	5.05275	+	15.5508i	0.300355	+	0.924396i	−0.681016	+	0.732269i	$0.738461\pi$
$284$		0			0
$285$	−3.33578			−0.197594
$286$		0			0
$287$	18.3137			1.08102
$288$		0			0
$289$	−5.12760	−	15.7811i	−0.301623	−	0.928302i
$290$		0			0
$291$	−3.46833	+	4.77374i	−0.203317	+	0.279842i
$292$		0			0
$293$	−25.2122	−	8.19195i	−1.47291	−	0.478579i	−0.540926	−	0.841070i	$-0.681926\pi$
$293$	−25.2122	−	8.19195i	−1.47291	−	0.478579i	−0.931987	+	0.362491i	$0.881926\pi$
$294$		0			0
$295$	3.07790	−	2.23623i	0.179202	−	0.130198i
$296$		0			0
$297$	15.5478	+	7.59664i	0.902174	+	0.440802i
$298$		0			0
$299$	−7.43914	−	1.06794i	−0.430216	−	0.0617608i
$300$		0			0
$301$	0.664667	+	0.215963i	0.0383108	+	0.0124479i
$302$		0			0
$303$	22.9101	+	16.6451i	1.31615	+	0.956239i
$304$		0			0
$305$	−3.30416	+	1.07359i	−0.189196	+	0.0614734i
$306$		0			0
$307$			22.3900i			1.27786i	0.769263	+	0.638932i	$0.220624\pi$
$307$			22.3900i			1.27786i	−0.769263	+	0.638932i	$0.779376\pi$
$308$		0			0
$309$	34.2784			1.95003
$310$		0			0
$311$	2.64653	+	8.14518i	0.150071	+	0.461871i	0.997628	−	0.0688331i	$-0.0219276\pi$
$311$	2.64653	+	8.14518i	0.150071	+	0.461871i	−0.847557	+	0.530704i	$0.821928\pi$
$312$		0			0
$313$	−3.73274	−	2.71200i	−0.210987	−	0.153291i	0.477273	−	0.878755i	$-0.341625\pi$
$313$	−3.73274	−	2.71200i	−0.210987	−	0.153291i	−0.688260	+	0.725464i	$0.741625\pi$
$314$		0			0
$315$	−3.01454	+	9.27779i	−0.169850	+	0.522744i
$316$		0			0
$317$	6.72454	+	9.25553i	0.377688	+	0.519843i	0.954970	−	0.296702i	$-0.0958868\pi$
$317$	6.72454	+	9.25553i	0.377688	+	0.519843i	−0.577282	+	0.816545i	$0.695887\pi$
$318$		0			0
$319$	0.186730	−	1.32194i	0.0104549	−	0.0740142i
$320$		0			0
$321$	−28.2302	+	20.5105i	−1.57566	+	1.14478i
$322$		0			0
$323$	−0.589103	−	0.191411i	−0.0327786	−	0.0106504i
$324$		0			0
$325$	−2.15420	−	12.4319i	−0.119494	−	0.689600i
$326$		0			0
$327$	−25.6594	+	8.33726i	−1.41897	+	0.461051i
$328$		0			0
$329$	−17.4792			−0.963661
$330$		0			0
$331$			15.5823i			0.856481i	0.903665	+	0.428240i	$0.140866\pi$
$331$			15.5823i			0.856481i	−0.903665	+	0.428240i	$0.859134\pi$
$332$		0			0
$333$	−18.7669	+	6.09773i	−1.02842	+	0.334153i
$334$		0			0
$335$	−4.42821	−	3.21728i	−0.241939	−	0.175779i
$336$		0			0
$337$	8.05724	−	24.7976i	0.438906	−	1.35081i	−0.450124	−	0.892966i	$-0.648620\pi$
$337$	8.05724	−	24.7976i	0.438906	−	1.35081i	0.889030	−	0.457848i	$-0.151380\pi$
$338$		0			0
$339$	−15.9038	+	11.5548i	−0.863773	+	0.627568i
$340$		0			0
$341$	−23.0842	−	22.3234i	−1.25008	−	1.20888i
$342$		0			0
$343$	10.8968	+	14.9982i	0.588373	+	0.809827i
$344$		0			0
$345$	−6.80861	−	2.21225i	−0.366563	−	0.119104i
$346$		0			0
$347$	13.6286	+	9.90174i	0.731620	+	0.531553i	0.890076	−	0.455813i	$-0.150651\pi$
$347$	13.6286	+	9.90174i	0.731620	+	0.531553i	−0.158455	+	0.987366i	$0.550651\pi$
$348$		0			0
$349$	4.09509	−	1.33058i	0.219205	−	0.0712242i	−0.197355	−	0.980332i	$-0.563235\pi$
$349$	4.09509	−	1.33058i	0.219205	−	0.0712242i	0.416561	+	0.909108i	$0.363235\pi$
$350$		0			0
$351$	13.4934	+	13.1078i	0.720226	+	0.699642i
$352$		0			0
$353$		−	31.0643i		−	1.65338i	−0.562655	−	0.826692i	$-0.690220\pi$
$353$		−	31.0643i		−	1.65338i	0.562655	−	0.826692i	$-0.309780\pi$
$354$		0			0
$355$	−1.17874	−	3.62778i	−0.0625610	−	0.192543i
$356$		0			0
$357$	−1.72187	+	2.36995i	−0.0911309	+	0.125431i
$358$		0			0
$359$	5.50981	+	1.79024i	0.290796	+	0.0944855i	0.450783	−	0.892634i	$-0.351145\pi$
$359$	5.50981	+	1.79024i	0.290796	+	0.0944855i	−0.159986	+	0.987119i	$0.551145\pi$
$360$		0			0
$361$	−14.6082	+	10.6135i	−0.768851	+	0.558603i
$362$		0			0
$363$	18.9536	+	24.3296i	0.994806	+	1.27697i
$364$		0			0
$365$	2.93527	−	2.13260i	0.153639	−	0.111625i
$366$		0			0
$367$	−2.36900	+	7.29103i	−0.123661	+	0.380589i	−0.993655	−	0.112474i	$-0.964123\pi$
$367$	−2.36900	+	7.29103i	−0.123661	+	0.380589i	0.869994	+	0.493062i	$0.164123\pi$
$368$		0			0
$369$	31.9392	−	43.9606i	1.66269	−	2.28850i
$370$		0			0
$371$	16.2301	−	5.27347i	0.842624	−	0.273785i
$372$		0			0
$373$	−31.8221			−1.64769			−0.823843	−	0.566818i	$-0.808174\pi$
$373$	−31.8221			−1.64769			−0.823843	+	0.566818i	$0.808174\pi$
$374$		0			0
$375$		−	29.1917i		−	1.50745i
$376$		0			0
$377$	0.640090	−	1.30259i	0.0329663	−	0.0670867i
$378$		0			0
$379$	21.6178	−	29.7544i	1.11043	−	1.52838i	0.289656	−	0.957131i	$-0.406459\pi$
$379$	21.6178	−	29.7544i	1.11043	−	1.52838i	0.820777	−	0.571249i	$-0.193541\pi$
$380$		0			0
$381$	7.29116	−	22.4399i	0.373537	−	1.14963i
$382$		0			0
$383$	1.85633	+	2.55502i	0.0948540	+	0.130555i	0.853806	−	0.520591i	$-0.174288\pi$
$383$	1.85633	+	2.55502i	0.0948540	+	0.130555i	−0.758952	+	0.651146i	$0.774288\pi$
$384$		0			0
$385$	−4.62704	+	4.78473i	−0.235816	+	0.243853i
$386$		0			0
$387$	1.67759	−	1.21884i	0.0852768	−	0.0619572i
$388$		0			0
$389$	4.15075	−	12.7747i	0.210451	−	0.647702i	−0.788994	−	0.614401i	$-0.789398\pi$
$389$	4.15075	−	12.7747i	0.210451	−	0.647702i	0.999445	−	0.0333016i	$-0.0106022\pi$
$390$		0			0
$391$	−1.07547	−	0.781372i	−0.0543887	−	0.0395157i
$392$		0			0
$393$	1.03105	+	3.17326i	0.0520098	+	0.160070i
$394$		0			0
$395$			20.7298i			1.04303i
$396$		0			0
$397$		−	34.8565i		−	1.74940i	−0.484666	−	0.874699i	$-0.661059\pi$
$397$		−	34.8565i		−	1.74940i	0.484666	−	0.874699i	$-0.338941\pi$
$398$		0			0
$399$	−1.37858	−	4.24282i	−0.0690151	−	0.212407i
$400$		0			0
$401$	5.90571	−	8.12851i	0.294917	−	0.405918i	−0.635687	−	0.771947i	$-0.719283\pi$
$401$	5.90571	−	8.12851i	0.294917	−	0.405918i	0.930603	+	0.366029i	$0.119283\pi$
$402$		0			0
$403$	−16.2980	−	30.8720i	−0.811863	−	1.53785i
$404$		0			0
$405$	0.0328898	+	0.0452690i	0.00163431	+	0.00224943i
$406$		0			0
$407$	−13.3314	−	1.88312i	−0.660812	−	0.0933428i
$408$		0			0
$409$	16.6506	+	22.9175i	0.823317	+	1.13320i	0.989130	+	0.147042i	$0.0469753\pi$
$409$	16.6506	+	22.9175i	0.823317	+	1.13320i	−0.165813	+	0.986157i	$0.553025\pi$
$410$		0			0
$411$	17.8154	+	5.78856i	0.878767	+	0.285529i
$412$		0			0
$413$	4.11629	+	2.99066i	0.202549	+	0.147161i
$414$		0			0
$415$	−4.65638	−	14.3309i	−0.228573	−	0.703475i
$416$		0			0
$417$	−12.5796			−0.616025
$418$		0			0
$419$	−12.6734			−0.619136			−0.309568	−	0.950877i	$-0.600184\pi$
$419$	−12.6734			−0.619136			−0.309568	+	0.950877i	$0.600184\pi$
$420$		0			0
$421$	27.0807	−	8.79906i	1.31983	−	0.428840i	0.437396	−	0.899269i	$-0.355901\pi$
$421$	27.0807	−	8.79906i	1.31983	−	0.428840i	0.882438	+	0.470429i	$0.155901\pi$
$422$		0			0
$423$	−30.4840	+	41.9576i	−1.48218	+	2.04005i
$424$		0			0
$425$	0.689656	−	2.12254i	0.0334532	−	0.102958i
$426$		0			0
$427$	−2.73102	−	3.75893i	−0.132163	−	0.181907i
$428$		0			0
$429$	11.3519	+	31.5475i	0.548073	+	1.52313i
$430$		0			0
$431$	−15.8211	−	21.7759i	−0.762075	−	1.04891i	−0.997039	−	0.0769026i	$-0.975497\pi$
$431$	−15.8211	−	21.7759i	−0.762075	−	1.04891i	0.234963	−	0.972004i	$-0.424503\pi$
$432$		0			0
$433$	−0.592051	+	1.82215i	−0.0284522	+	0.0875667i	−0.964274	−	0.264906i	$-0.914659\pi$
$433$	−0.592051	+	1.82215i	−0.0284522	+	0.0875667i	0.935822	+	0.352473i	$0.114659\pi$
$434$		0			0
$435$	0.812632	−	1.11849i	0.0389627	−	0.0536276i
$436$		0			0
$437$	1.92536	−	0.625589i	0.0921026	−	0.0299260i
$438$		0			0
$439$	16.2763			0.776825			0.388413	−	0.921486i	$-0.373024\pi$
$439$	16.2763			0.776825			0.388413	+	0.921486i	$0.373024\pi$
$440$		0			0
$441$	20.9800			0.999046
$442$		0			0
$443$	−11.8637	−	36.5128i	−0.563663	−	1.73478i	−0.671890	−	0.740651i	$-0.734517\pi$
$443$	−11.8637	−	36.5128i	−0.563663	−	1.73478i	0.108227	−	0.994126i	$-0.465483\pi$
$444$		0			0
$445$	−7.76322	−	5.64031i	−0.368012	−	0.267376i
$446$		0			0
$447$	7.22928	+	2.34894i	0.341933	+	0.111101i
$448$		0			0
$449$	−14.0969	−	19.4028i	−0.665276	−	0.915674i	0.334366	−	0.942443i	$-0.391478\pi$
$449$	−14.0969	−	19.4028i	−0.665276	−	0.915674i	−0.999642	+	0.0267697i	$0.991478\pi$
$450$		0			0
$451$	32.7478	−	17.3829i	1.54203	−	0.818529i
$452$		0			0
$453$	28.7927	+	39.6298i	1.35280	+	1.86197i
$454$		0			0
$455$	−6.39894	+	3.37814i	−0.299987	+	0.158370i
$456$		0			0
$457$	20.8228	−	28.6602i	0.974052	−	1.34067i	0.0340782	−	0.999419i	$-0.489150\pi$
$457$	20.8228	−	28.6602i	0.974052	−	1.34067i	0.939973	−	0.341248i	$-0.110850\pi$
$458$		0			0
$459$	1.02826	+	3.16465i	0.0479949	+	0.147713i
$460$		0			0
$461$			22.5894i			1.05209i	0.850456	+	0.526046i	$0.176326\pi$
$461$			22.5894i			1.05209i	−0.850456	+	0.526046i	$0.823674\pi$
$462$		0			0
$463$			37.3818i			1.73728i	0.495446	+	0.868639i	$0.335005\pi$
$463$			37.3818i			1.73728i	−0.495446	+	0.868639i	$0.664995\pi$
$464$		0			0
$465$	−10.2762	−	31.6268i	−0.476547	−	1.46666i
$466$		0			0
$467$	26.5286	+	19.2742i	1.22760	+	0.891901i	0.996708	−	0.0810786i	$-0.0258365\pi$
$467$	26.5286	+	19.2742i	1.22760	+	0.891901i	0.230889	+	0.972980i	$0.425836\pi$
$468$		0			0
$469$	2.26206	−	6.96190i	0.104452	−	0.321471i
$470$		0			0
$471$	19.4883	−	14.1591i	0.897975	−	0.652417i
$472$		0			0
$473$	1.39352	−	0.244709i	0.0640741	−	0.0112518i
$474$		0			0
$475$	1.99773	+	2.74963i	0.0916620	+	0.126162i
$476$		0			0
$477$	15.6469	−	48.1561i	0.716421	−	2.20492i
$478$		0			0
$479$	12.4639	−	17.1550i	0.569489	−	0.783834i	−0.423005	−	0.906127i	$-0.639025\pi$
$479$	12.4639	−	17.1550i	0.569489	−	0.783834i	0.992494	+	0.122293i	$0.0390248\pi$
$480$		0			0
$481$	−13.1363	−	6.45514i	−0.598962	−	0.294329i
$482$		0			0
$483$		−	9.57421i		−	0.435642i
$484$		0			0
$485$	−2.57810			−0.117066
$486$		0			0
$487$	−40.3910	+	13.1238i	−1.83029	+	0.594698i	−0.831034	+	0.556222i	$0.812250\pi$
$487$	−40.3910	+	13.1238i	−1.83029	+	0.594698i	−0.999260	+	0.0384762i	$0.987750\pi$
$488$		0			0
$489$	−18.6463	+	25.6644i	−0.843215	+	1.16059i
$490$		0			0
$491$	6.55036	−	20.1599i	0.295613	−	0.909805i	−0.687401	−	0.726278i	$-0.741249\pi$
$491$	6.55036	−	20.1599i	0.295613	−	0.909805i	0.983015	−	0.183527i	$-0.0587514\pi$
$492$		0			0
$493$	0.207692	−	0.150897i	0.00935399	−	0.00679607i
$494$		0			0
$495$	3.41579	+	19.4515i	0.153528	+	0.874281i
$496$		0			0
$497$	4.12709	−	2.99851i	0.185125	−	0.134501i
$498$		0			0
$499$	36.0930	+	11.7273i	1.61574	+	0.524987i	0.970932	−	0.239354i	$-0.0769357\pi$
$499$	36.0930	+	11.7273i	1.61574	+	0.524987i	0.644812	+	0.764341i	$0.276936\pi$
$500$		0			0
$501$	−2.37794	+	3.27295i	−0.106239	+	0.146225i
$502$		0			0
$503$	6.46163	+	19.8869i	0.288110	+	0.886712i	0.985449	+	0.169970i	$0.0543672\pi$
$503$	6.46163	+	19.8869i	0.288110	+	0.886712i	−0.697339	+	0.716741i	$0.745633\pi$
$504$		0			0
$505$			12.3728i			0.550582i
$506$		0			0
$507$	1.05659	+	36.4332i	0.0469249	+	1.61805i
$508$		0			0
$509$	−7.45363	+	2.42183i	−0.330376	+	0.107346i	−0.469508	−	0.882928i	$-0.655569\pi$
$509$	−7.45363	+	2.42183i	−0.330376	+	0.107346i	0.139132	+	0.990274i	$0.455569\pi$
$510$		0			0
$511$	3.92554	+	2.85207i	0.173655	+	0.126168i
$512$		0			0
$513$	−4.81940	−	1.56592i	−0.212782	−	0.0691369i
$514$		0			0
$515$	8.80315	+	12.1165i	0.387913	+	0.533917i
$516$		0			0
$517$	−31.2557	+	16.5909i	−1.37462	+	0.729667i
$518$		0			0
$519$	−21.1050	+	15.3336i	−0.926405	+	0.673072i
$520$		0			0
$521$	−7.70193	+	23.7041i	−0.337428	+	1.03850i	0.628086	+	0.778144i	$0.283839\pi$
$521$	−7.70193	+	23.7041i	−0.337428	+	1.03850i	−0.965514	+	0.260352i	$0.916161\pi$
$522$		0			0
$523$	32.1751	+	23.3766i	1.40692	+	1.02219i	0.993761	+	0.111527i	$0.0355740\pi$
$523$	32.1751	+	23.3766i	1.40692	+	1.02219i	0.413157	+	0.910660i	$0.364426\pi$
$524$		0			0
$525$	15.2869	−	4.96702i	0.667176	−	0.216779i
$526$		0			0
$527$		−	6.17500i		−	0.268987i
$528$		0			0
$529$	−18.6553			−0.811099
$530$		0			0
$531$	14.3577	−	4.66510i	0.623072	−	0.202448i
$532$		0			0
$533$	39.7133	−	6.88152i	1.72018	−	0.298072i
$534$		0			0
$535$	−14.4998	−	4.71127i	−0.626881	−	0.203686i
$536$		0			0
$537$	24.0961	−	17.5069i	1.03982	−	0.755476i
$538$		0			0
$539$	12.8616	+	6.28418i	0.553990	+	0.270679i
$540$		0			0
$541$	−8.50716	−	11.7091i	−0.365751	−	0.503414i	0.585989	−	0.810319i	$-0.300706\pi$
$541$	−8.50716	−	11.7091i	−0.365751	−	0.503414i	−0.951740	+	0.306906i	$0.900706\pi$
$542$		0			0
$543$	−5.79614	+	17.8387i	−0.248736	+	0.765532i
$544$		0			0
$545$	−9.53668	−	6.92880i	−0.408506	−	0.296797i
$546$		0			0
$547$	6.00841	+	18.4920i	0.256901	+	0.790660i	0.993449	+	0.114275i	$0.0364545\pi$
$547$	6.00841	+	18.4920i	0.256901	+	0.790660i	−0.736548	+	0.676385i	$0.763545\pi$
$548$		0			0
$549$	−13.7860			−0.588370
$550$		0			0
$551$			0.390958i			0.0166554i
$552$		0			0
$553$	−26.3665	+	8.56698i	−1.12122	+	0.364305i
$554$		0			0
$555$	−11.2797	−	8.19518i	−0.478797	−	0.347866i
$556$		0			0
$557$	−14.3339	−	4.65736i	−0.607345	−	0.197338i	−0.0108316	−	0.999941i	$-0.503448\pi$
$557$	−14.3339	−	4.65736i	−0.607345	−	0.197338i	−0.596514	+	0.802603i	$0.703448\pi$
$558$		0			0
$559$	1.52249	+	0.218564i	0.0643944	+	0.00924429i
$560$		0			0
$561$	−0.829477	+	5.87221i	−0.0350205	+	0.247925i
$562$		0			0
$563$	17.9996	−	13.0774i	0.758591	−	0.551148i	−0.139887	−	0.990167i	$-0.544674\pi$
$563$	17.9996	−	13.0774i	0.758591	−	0.551148i	0.898478	+	0.439019i	$0.144674\pi$
$564$		0			0
$565$	−8.16859	−	2.65414i	−0.343655	−	0.111660i
$566$		0			0
$567$	−0.0439858	+	0.0605413i	−0.00184723	+	0.00254249i
$568$		0			0
$569$	0.558962	+	1.72031i	0.0234329	+	0.0721191i	0.962089	−	0.272735i	$-0.0879283\pi$
$569$	0.558962	+	1.72031i	0.0234329	+	0.0721191i	−0.938656	+	0.344854i	$0.887928\pi$
$570$		0			0
$571$	−3.66013			−0.153172			−0.0765858	−	0.997063i	$-0.524402\pi$
$571$	−3.66013			−0.153172			−0.0765858	+	0.997063i	$0.524402\pi$
$572$		0			0
$573$	65.3679			2.73078
$574$		0			0
$575$	2.25400	+	6.93711i	0.0939984	+	0.289297i
$576$		0			0
$577$	14.3385	−	19.7353i	0.596921	−	0.821591i	−0.398501	−	0.917168i	$-0.630470\pi$
$577$	14.3385	−	19.7353i	0.596921	−	0.821591i	0.995422	+	0.0955770i	$0.0304696\pi$
$578$		0			0
$579$	38.8234	+	12.6145i	1.61344	+	0.524240i
$580$		0			0
$581$	16.3033	−	11.8450i	0.676374	−	0.491415i
$582$		0			0
$583$	24.0165	−	24.8350i	0.994664	−	1.02856i
$584$		0			0
$585$	−3.05084	+	21.2517i	−0.126137	+	0.878651i
$586$		0			0
$587$	−11.9660	−	3.88797i	−0.493888	−	0.160474i	0.0514745	−	0.998674i	$-0.483608\pi$
$587$	−11.9660	−	3.88797i	−0.493888	−	0.160474i	−0.545362	+	0.838200i	$0.683608\pi$
$588$		0			0
$589$	7.60785	+	5.52742i	0.313476	+	0.227754i
$590$		0			0
$591$	−42.7097	+	13.8772i	−1.75684	+	0.570833i
$592$		0			0
$593$			41.2997i			1.69598i	0.530014	+	0.847989i	$0.322186\pi$
$593$			41.2997i			1.69598i	−0.530014	+	0.847989i	$0.677814\pi$
$594$		0			0
$595$	−1.27991			−0.0524712
$596$		0			0
$597$	−9.25237	−	28.4759i	−0.378674	−	1.16544i
$598$		0			0
$599$	−8.69550	−	6.31765i	−0.355288	−	0.258132i	0.395796	−	0.918339i	$-0.370469\pi$
$599$	−8.69550	−	6.31765i	−0.355288	−	0.258132i	−0.751084	+	0.660206i	$0.770469\pi$
$600$		0			0
$601$	−9.38124	+	28.8725i	−0.382669	+	1.17773i	0.555489	+	0.831524i	$0.312531\pi$
$601$	−9.38124	+	28.8725i	−0.382669	+	1.17773i	−0.938157	+	0.346209i	$0.887469\pi$
$602$		0			0
$603$	−12.7665	−	17.5716i	−0.519892	−	0.715569i
$604$		0			0
$605$	−3.73234	+	12.9478i	−0.151741	+	0.526401i
$606$		0			0
$607$	−20.5750	+	14.9486i	−0.835114	+	0.606746i	−0.921002	−	0.389559i	$-0.872628\pi$
$607$	−20.5750	+	14.9486i	−0.835114	+	0.606746i	0.0858872	+	0.996305i	$0.472628\pi$
$608$		0			0
$609$	1.75846	+	0.571359i	0.0712564	+	0.0231526i
$610$		0			0
$611$	−37.9039	+	6.56798i	−1.53343	+	0.265712i
$612$		0			0
$613$	32.6125	−	10.5965i	1.31721	−	0.427987i	0.435672	−	0.900105i	$-0.356511\pi$
$613$	32.6125	−	10.5965i	1.31721	−	0.427987i	0.881535	+	0.472119i	$0.156511\pi$
$614$		0			0
$615$	38.3937			1.54818
$616$		0			0
$617$			28.1823i			1.13457i	0.823520	+	0.567287i	$0.192007\pi$
$617$			28.1823i			1.13457i	−0.823520	+	0.567287i	$0.807993\pi$
$618$		0			0
$619$	−32.7511	+	10.6415i	−1.31638	+	0.427718i	−0.881250	−	0.472650i	$-0.843297\pi$
$619$	−32.7511	+	10.6415i	−1.31638	+	0.427718i	−0.435129	+	0.900368i	$0.643297\pi$
$620$		0			0
$621$	−8.79830	−	6.39234i	−0.353063	−	0.256516i
$622$		0			0
$623$	3.96568	−	12.2051i	0.158882	−	0.488988i
$624$		0			0
$625$	−3.83683	+	2.78762i	−0.153473	+	0.111505i
$626$		0			0
$627$	−6.49230	−	6.27833i	−0.259278	−	0.250732i
$628$		0			0
$629$	−1.52176	−	2.09452i	−0.0606765	−	0.0835141i
$630$		0			0
$631$	−1.41150	−	0.458624i	−0.0561909	−	0.0182575i	0.280787	−	0.959770i	$-0.409405\pi$
$631$	−1.41150	−	0.458624i	−0.0561909	−	0.0182575i	−0.336978	+	0.941513i	$0.609405\pi$
$632$		0			0
$633$	49.7447	+	36.1417i	1.97717	+	1.43650i
$634$		0			0
$635$	9.80436	−	3.18563i	0.389074	−	0.126418i
$636$		0			0
$637$	11.1622	+	10.8432i	0.442263	+	0.429622i
$638$		0			0
$639$		−	15.1362i		−	0.598779i
$640$		0			0
$641$	7.18463	+	22.1120i	0.283776	+	0.873372i	0.986763	+	0.162170i	$0.0518492\pi$
$641$	7.18463	+	22.1120i	0.283776	+	0.873372i	−0.702987	+	0.711203i	$0.748151\pi$
$642$		0			0
$643$	2.38903	−	3.28822i	0.0942141	−	0.129675i	−0.759308	−	0.650732i	$-0.774462\pi$
$643$	2.38903	−	3.28822i	0.0942141	−	0.129675i	0.853522	+	0.521057i	$0.174462\pi$
$644$		0			0
$645$	1.39344	+	0.452757i	0.0548668	+	0.0178273i
$646$		0			0
$647$	−3.52006	+	2.55747i	−0.138388	+	0.100545i	−0.654825	−	0.755780i	$-0.727258\pi$
$647$	−3.52006	+	2.55747i	−0.138388	+	0.100545i	0.516438	+	0.856325i	$0.327258\pi$
$648$		0			0
$649$	10.1992	+	1.44069i	0.400356	+	0.0565521i
$650$		0			0
$651$	35.9797	−	26.1408i	1.41016	−	1.02454i
$652$		0			0
$653$	10.9374	−	33.6620i	0.428015	−	1.31729i	−0.472063	−	0.881565i	$-0.656490\pi$
$653$	10.9374	−	33.6620i	0.428015	−	1.31729i	0.900078	−	0.435730i	$-0.143510\pi$
$654$		0			0
$655$	−0.856873	+	1.17938i	−0.0334808	+	0.0460824i
$656$		0			0
$657$	13.6924	−	4.44892i	0.534190	−	0.173569i
$658$		0			0
$659$	−46.7394			−1.82071			−0.910355	−	0.413829i	$-0.864191\pi$
$659$	−46.7394			−1.82071			−0.910355	+	0.413829i	$0.864191\pi$
$660$		0			0
$661$			29.8018i			1.15915i	0.814917	+	0.579577i	$0.196782\pi$
$661$			29.8018i			1.15915i	−0.814917	+	0.579577i	$0.803218\pi$
$662$		0			0
$663$	−2.84336	+	5.78626i	−0.110427	+	0.224720i
$664$		0			0
$665$	1.14569	−	1.57690i	0.0444278	−	0.0611496i
$666$		0			0
$667$	−0.259279	+	0.797978i	−0.0100393	+	0.0308978i
$668$		0			0
$669$	−8.77690	−	12.0804i	−0.339334	−	0.467054i
$670$		0			0
$671$	−8.45139	−	4.12934i	−0.326262	−	0.159412i
$672$		0			0
$673$	28.2142	−	20.4988i	1.08758	−	0.790171i	0.108589	−	0.994087i	$-0.465367\pi$
$673$	28.2142	−	20.4988i	1.08758	−	0.790171i	0.978988	+	0.203915i	$0.0653668\pi$
$674$		0			0
$675$	5.64201	−	17.3643i	0.217161	−	0.668353i
$676$		0			0
$677$	−30.3764	−	22.0697i	−1.16746	−	0.848209i	−0.176757	−	0.984255i	$-0.556561\pi$
$677$	−30.3764	−	22.0697i	−1.16746	−	0.848209i	−0.990703	+	0.136046i	$0.956561\pi$
$678$		0			0
$679$	−1.06545	−	3.27912i	−0.0408882	−	0.125841i
$680$		0			0
$681$		−	53.6368i		−	2.05537i
$682$		0			0
$683$			13.9740i			0.534699i	0.963600	+	0.267349i	$0.0861478\pi$
$683$			13.9740i			0.534699i	−0.963600	+	0.267349i	$0.913852\pi$
$684$		0			0
$685$	2.52912	+	7.78383i	0.0966328	+	0.297405i
$686$		0			0
$687$	17.9033	−	24.6418i	0.683055	−	0.940145i
$688$		0			0
$689$	33.2135	−	17.5342i	1.26534	−	0.667999i
$690$		0			0
$691$	−0.0167320	−	0.0230296i	−0.000636514	−	0.000876086i	0.808699	−	0.588223i	$-0.200172\pi$
$691$	−0.0167320	−	0.0230296i	−0.000636514	−	0.000876086i	−0.809335	+	0.587347i	$0.800172\pi$
$692$		0			0
$693$	−23.3290	+	12.3833i	−0.886195	+	0.470403i
$694$		0			0
$695$	−3.23061	−	4.44655i	−0.122544	−	0.168667i
$696$		0			0
$697$	6.78038	+	2.20308i	0.256825	+	0.0834476i
$698$		0			0
$699$	−51.3458	−	37.3049i	−1.94208	−	1.41100i
$700$		0			0
$701$	9.18430	+	28.2664i	0.346886	+	1.06761i	0.960566	+	0.278051i	$0.0896884\pi$
$701$	9.18430	+	28.2664i	0.346886	+	1.06761i	−0.613680	+	0.789555i	$0.710312\pi$
$702$		0			0
$703$	3.94271			0.148702
$704$		0			0
$705$	−36.6444			−1.38011
$706$		0			0
$707$	−15.7371	+	5.11330i	−0.591855	+	0.192305i
$708$		0			0
$709$	12.7689	−	17.5749i	0.479548	−	0.660041i	−0.498870	−	0.866677i	$-0.666252\pi$
$709$	12.7689	−	17.5749i	0.479548	−	0.660041i	0.978418	+	0.206636i	$0.0662515\pi$
$710$		0			0
$711$	−25.4190	+	78.2317i	−0.953288	+	2.93392i
$712$		0			0
$713$	11.8625	+	16.3274i	0.444255	+	0.611465i
$714$		0			0
$715$	−8.23588	+	12.1144i	−0.308004	+	0.453053i
$716$		0			0
$717$	25.9161	+	35.6705i	0.967855	+	1.33214i
$718$		0			0
$719$	7.63361	−	23.4938i	0.284686	−	0.876173i	−0.701807	−	0.712367i	$-0.747623\pi$
$719$	7.63361	−	23.4938i	0.284686	−	0.876173i	0.986493	−	0.163805i	$-0.0523769\pi$
$720$		0			0
$721$	−11.7731	+	16.2042i	−0.438452	+	0.603477i
$722$		0			0
$723$	39.1555	−	12.7224i	1.45621	−	0.473150i
$724$		0			0
$725$	−1.40863			−0.0523150
$726$		0			0
$727$	−8.29161			−0.307519			−0.153759	−	0.988108i	$-0.549138\pi$
$727$	−8.29161			−0.307519			−0.153759	+	0.988108i	$0.549138\pi$
$728$		0			0
$729$	−13.4927	−	41.5261i	−0.499728	−	1.53800i
$730$		0			0
$731$	0.220104	+	0.159915i	0.00814085	+	0.00591467i
$732$		0			0
$733$	−18.8630	−	6.12895i	−0.696720	−	0.226378i	−0.0608190	−	0.998149i	$-0.519371\pi$
$733$	−18.8630	−	6.12895i	−0.696720	−	0.226378i	−0.635901	+	0.771771i	$0.719371\pi$
$734$		0			0
$735$	8.71320	+	11.9927i	0.321391	+	0.442357i
$736$		0			0
$737$	−2.56315	−	14.5961i	−0.0944150	−	0.537654i
$738$		0			0
$739$	−26.3110	−	36.2140i	−0.967866	−	1.33215i	−0.943117	−	0.332460i	$-0.892121\pi$
$739$	−26.3110	−	36.2140i	−0.967866	−	1.33215i	−0.0247489	−	0.999694i	$-0.507879\pi$
$740$		0			0
$741$	−4.58373	−	8.68259i	−0.168388	−	0.318963i
$742$		0			0
$743$	−1.66791	+	2.29569i	−0.0611898	+	0.0842205i	−0.838515	−	0.544878i	$-0.816576\pi$
$743$	−1.66791	+	2.29569i	−0.0611898	+	0.0842205i	0.777325	+	0.629099i	$0.216576\pi$
$744$		0			0
$745$	1.02629	+	3.15860i	0.0376003	+	0.115722i
$746$		0			0
$747$		−	59.7927i		−	2.18770i
$748$		0			0
$749$		−	20.3895i		−	0.745016i
$750$		0			0
$751$	5.37010	+	16.5275i	0.195958	+	0.603096i	0.999964	+	0.00847539i	$0.00269783\pi$
$751$	5.37010	+	16.5275i	0.195958	+	0.603096i	−0.804006	+	0.594621i	$0.797302\pi$
$752$		0			0
$753$	−12.1304	−	8.81326i	−0.442057	−	0.321173i
$754$		0			0
$755$	−6.61371	+	20.3549i	−0.240698	+	0.740791i
$756$		0			0
$757$	12.8912	−	9.36600i	0.468538	−	0.340413i	−0.328333	−	0.944562i	$-0.606487\pi$
$757$	12.8912	−	9.36600i	0.468538	−	0.340413i	0.796871	+	0.604149i	$0.206487\pi$
$758$		0			0
$759$	−9.08762	−	17.1202i	−0.329860	−	0.621425i
$760$		0			0
$761$	−16.5456	−	22.7730i	−0.599776	−	0.825521i	0.395912	−	0.918289i	$-0.370429\pi$
$761$	−16.5456	−	22.7730i	−0.599776	−	0.825521i	−0.995688	+	0.0927675i	$0.970429\pi$
$762$		0			0
$763$	4.87161	−	14.9933i	0.176364	−	0.542793i
$764$		0			0
$765$	−2.23218	+	3.07233i	−0.0807047	+	0.111080i
$766$		0			0
$767$	10.0500	+	4.93854i	0.362884	+	0.178320i
$768$		0			0
$769$		−	31.9673i		−	1.15277i	−0.817178	−	0.576386i	$-0.804463\pi$
$769$		−	31.9673i		−	1.15277i	0.817178	−	0.576386i	$-0.195537\pi$
$770$		0			0
$771$	−66.2704			−2.38667
$772$		0			0
$773$	6.60333	−	2.14555i	0.237505	−	0.0771702i	−0.187846	−	0.982199i	$-0.560151\pi$
$773$	6.60333	−	2.14555i	0.237505	−	0.0771702i	0.425351	+	0.905028i	$0.360151\pi$
$774$		0			0
$775$	−19.9154	+	27.4111i	−0.715381	+	0.984637i
$776$		0			0
$777$	5.76200	−	17.7336i	0.206711	−	0.636190i
$778$		0			0
$779$	−8.78360	+	6.38166i	−0.314705	+	0.228647i
$780$		0			0
$781$	4.53379	−	9.27915i	0.162232	−	0.332034i
$782$		0			0
$783$	1.69911	−	1.23448i	0.0607213	−	0.0441166i
$784$		0			0
$785$	10.0097	+	3.25236i	0.357262	+	0.116082i
$786$		0			0
$787$	0.681205	−	0.937598i	0.0242823	−	0.0334218i	−0.796703	−	0.604371i	$-0.793425\pi$
$787$	0.681205	−	0.937598i	0.0242823	−	0.0334218i	0.820986	+	0.570949i	$0.193425\pi$
$788$		0			0
$789$	−11.4418	−	35.2143i	−0.407340	−	1.25366i
$790$		0			0
$791$		−	11.4866i		−	0.408417i
$792$		0			0
$793$	−7.33469	−	7.12506i	−0.260463	−	0.253018i
$794$		0			0
$795$	34.0256	−	11.0556i	1.20676	−	0.392101i
$796$		0			0
$797$	14.3666	+	10.4379i	0.508891	+	0.369731i	0.812403	−	0.583097i	$-0.198159\pi$
$797$	14.3666	+	10.4379i	0.508891	+	0.369731i	−0.303512	+	0.952828i	$0.598159\pi$
$798$		0			0
$799$	−6.47145	−	2.10270i	−0.228943	−	0.0743882i
$800$		0			0
$801$	−22.3813	−	30.8052i	−0.790804	−	1.08845i
$802$		0			0
$803$	9.72661	+	1.37393i	0.343245	+	0.0484849i
$804$		0			0
$805$	3.38423	−	2.45878i	0.119278	−	0.0866607i
$806$		0			0
$807$	−14.8284	+	45.6370i	−0.521983	+	1.60650i
$808$		0			0
$809$	32.5020	+	23.6141i	1.14271	+	0.830227i	0.987494	−	0.157654i	$-0.0503930\pi$
$809$	32.5020	+	23.6141i	1.14271	+	0.830227i	0.155215	+	0.987881i	$0.450393\pi$
$810$		0			0
$811$	−35.5589	+	11.5538i	−1.24864	+	0.405709i	−0.857434	−	0.514594i	$-0.827943\pi$
$811$	−35.5589	+	11.5538i	−1.24864	+	0.405709i	−0.391208	+	0.920302i	$0.627943\pi$
$812$		0			0
$813$			62.9824i			2.20889i
$814$		0			0
$815$	−13.8603			−0.485505
$816$		0			0
$817$	−0.394043	+	0.128032i	−0.0137858	+	0.00447929i
$818$		0			0
$819$	−28.2912	+	4.90228i	−0.988573	+	0.171300i
$820$		0			0
$821$	17.9109	+	5.81959i	0.625093	+	0.203105i	0.604400	−	0.796681i	$-0.293413\pi$
$821$	17.9109	+	5.81959i	0.625093	+	0.203105i	0.0206930	+	0.999786i	$0.493413\pi$
$822$		0			0
$823$	−16.8575	+	12.2477i	−0.587616	+	0.426928i	−0.841462	−	0.540317i	$-0.818304\pi$
$823$	−16.8575	+	12.2477i	−0.587616	+	0.426928i	0.253846	+	0.967245i	$0.418304\pi$
$824$		0			0
$825$	22.6209	−	23.3918i	0.787559	−	0.814399i
$826$		0			0
$827$	0.410364	+	0.564818i	0.0142698	+	0.0196406i	0.816092	−	0.577922i	$-0.196136\pi$
$827$	0.410364	+	0.564818i	0.0142698	+	0.0196406i	−0.801823	+	0.597562i	$0.796136\pi$
$828$		0			0
$829$	−13.0120	+	40.0467i	−0.451924	+	1.39088i	0.422785	+	0.906230i	$0.361053\pi$
$829$	−13.0120	+	40.0467i	−0.451924	+	1.39088i	−0.874709	+	0.484649i	$0.838947\pi$
$830$		0			0
$831$	−34.6503	−	25.1749i	−1.20201	−	0.873309i
$832$		0			0
$833$	0.850607	+	2.61790i	0.0294718	+	0.0907048i
$834$		0			0
$835$	−1.76759			−0.0611699
$836$		0			0
$837$		−	50.5171i		−	1.74613i
$838$		0			0
$839$	46.6767	−	15.1662i	1.61146	−	0.523595i	0.641554	−	0.767078i	$-0.278290\pi$
$839$	46.6767	−	15.1662i	1.61146	−	0.523595i	0.969905	+	0.243483i	$0.0782900\pi$
$840$		0			0
$841$	23.3304	+	16.9505i	0.804497	+	0.584501i
$842$		0			0
$843$	−2.03813	−	0.662230i	−0.0701971	−	0.0228084i
$844$		0			0
$845$	−12.6068	+	9.73000i	−0.433687	+	0.334722i
$846$		0			0
$847$	−18.0109	+	0.603709i	−0.618861	+	0.0207437i
$848$		0			0
$849$	−37.0885	+	26.9464i	−1.27287	+	0.924796i
$850$		0			0
$851$	8.04740	+	2.61476i	0.275861	+	0.0896328i
$852$		0			0
$853$	−19.6595	+	27.0590i	−0.673129	+	0.926483i	−0.999826	−	0.0186464i	$-0.994064\pi$
$853$	−19.6595	+	27.0590i	−0.673129	+	0.926483i	0.326697	+	0.945129i	$0.394064\pi$
$854$		0			0
$855$	−1.78715	−	5.50027i	−0.0611192	−	0.188105i
$856$		0			0
$857$	−6.72457			−0.229707			−0.114853	−	0.993382i	$-0.536640\pi$
$857$	−6.72457			−0.229707			−0.114853	+	0.993382i	$0.536640\pi$
$858$		0			0
$859$	23.5927			0.804972			0.402486	−	0.915426i	$-0.368146\pi$
$859$	23.5927			0.804972			0.402486	+	0.915426i	$0.368146\pi$
$860$		0			0
$861$	15.8670	+	48.8335i	0.540744	+	1.66424i
$862$		0			0
$863$	−20.0903	+	27.6519i	−0.683882	+	0.941282i	−0.999972	−	0.00744666i	$-0.997630\pi$
$863$	−20.0903	+	27.6519i	−0.683882	+	0.941282i	0.316091	+	0.948729i	$0.397630\pi$
$864$		0			0
$865$	−10.8401	−	3.52215i	−0.368573	−	0.119757i
$866$		0			0
$867$	37.6379	−	27.3455i	1.27825	−	0.928704i
$868$		0			0
$869$	−39.0159	+	40.3456i	−1.32352	+	1.36863i
$870$		0			0
$871$	2.28930	−	15.9470i	0.0775701	−	0.540342i
$872$		0			0
$873$	−9.72945	−	3.16129i	−0.329292	−	0.106993i
$874$		0			0
$875$	13.7996	+	10.0260i	0.466511	+	0.338940i
$876$		0			0
$877$	−22.9387	+	7.45325i	−0.774586	+	0.251678i	−0.669527	−	0.742788i	$-0.733503\pi$
$877$	−22.9387	+	7.45325i	−0.774586	+	0.251678i	−0.105059	+	0.994466i	$0.533503\pi$
$878$		0			0
$879$		−	74.3260i		−	2.50695i
$880$		0			0
$881$	25.2040			0.849145			0.424573	−	0.905394i	$-0.360424\pi$
$881$	25.2040			0.849145			0.424573	+	0.905394i	$0.360424\pi$
$882$		0			0
$883$	5.99237	+	18.4426i	0.201659	+	0.620644i	0.999834	+	0.0182177i	$0.00579918\pi$
$883$	5.99237	+	18.4426i	0.201659	+	0.620644i	−0.798175	+	0.602426i	$0.794201\pi$
$884$		0			0
$885$	8.62960	+	6.26977i	0.290081	+	0.210756i
$886$		0			0
$887$	−4.42542	+	13.6200i	−0.148591	+	0.457316i	−0.997455	−	0.0712949i	$-0.977287\pi$
$887$	−4.42542	+	13.6200i	−0.148591	+	0.457316i	0.848864	+	0.528611i	$0.177287\pi$
$888$		0			0
$889$	8.10369	+	11.1538i	0.271789	+	0.374085i
$890$		0			0
$891$	−0.0211893	+	0.150008i	−0.000709869	+	0.00502545i
$892$		0			0
$893$	8.38339	−	6.09089i	0.280540	−	0.203824i
$894$		0			0
$895$	12.3764	+	4.02134i	0.413698	+	0.134418i
$896$		0			0
$897$	−3.59759	−	20.7618i	−0.120120	−	0.693215i
$898$		0			0
$899$	−3.70671	+	1.20438i	−0.123626	+	0.0401684i
$900$		0			0
$901$	6.64335			0.221322
$902$		0			0
$903$			1.95945i			0.0652064i
$904$		0			0
$905$	−7.79403	+	2.53243i	−0.259082	+	0.0841809i
$906$		0			0
$907$	12.6513	+	9.19168i	0.420078	+	0.305205i	0.777669	−	0.628673i	$-0.216402\pi$
$907$	12.6513	+	9.19168i	0.420078	+	0.305205i	−0.357591	+	0.933878i	$0.616402\pi$
$908$		0			0
$909$	−15.1716	+	46.6935i	−0.503211	+	1.54872i
$910$		0			0
$911$	−20.5490	+	14.9298i	−0.680820	+	0.494645i	−0.873630	−	0.486591i	$-0.838240\pi$
$911$	−20.5490	+	14.9298i	−0.680820	+	0.494645i	0.192809	+	0.981236i	$0.438240\pi$
$912$		0			0
$913$	17.9099	−	36.6555i	0.592730	−	1.21312i
$914$		0			0
$915$	−5.72545	−	7.88041i	−0.189278	−	0.260518i
$916$		0			0
$917$	−1.85419	−	0.602464i	−0.0612309	−	0.0198951i
$918$		0			0
$919$	13.4476	+	9.77029i	0.443597	+	0.322292i	0.787063	−	0.616873i	$-0.211601\pi$
$919$	13.4476	+	9.77029i	0.443597	+	0.322292i	−0.343466	+	0.939165i	$0.611601\pi$
$920$		0			0
$921$	−59.7031	+	19.3987i	−1.96728	+	0.639209i
$922$		0			0
$923$	7.82292	−	8.05308i	0.257495	−	0.265070i
$924$		0			0
$925$			14.2056i			0.467078i
$926$		0			0
$927$	18.3647	+	56.5207i	0.603176	+	1.85638i
$928$		0			0
$929$	10.8838	−	14.9803i	0.357088	−	0.491489i	−0.592247	−	0.805757i	$-0.701759\pi$
$929$	10.8838	−	14.9803i	0.357088	−	0.491489i	0.949334	+	0.314268i	$0.101759\pi$
$930$		0			0
$931$	−3.98676	−	1.29538i	−0.130661	−	0.0424543i
$932$		0			0
$933$	−19.4262	+	14.1140i	−0.635986	+	0.462071i
$934$		0			0
$935$	−2.28869	+	1.21486i	−0.0748481	+	0.0397303i
$936$		0			0
$937$	−16.2302	+	11.7920i	−0.530219	+	0.385227i	−0.820440	−	0.571733i	$-0.806271\pi$
$937$	−16.2302	+	11.7920i	−0.530219	+	0.385227i	0.290221	+	0.956960i	$0.406271\pi$
$938$		0			0
$939$	3.99751	−	12.3031i	0.130454	−	0.401495i
$940$		0			0
$941$	−18.5615	+	25.5478i	−0.605089	+	0.832834i	−0.996162	−	0.0875260i	$-0.972104\pi$
$941$	−18.5615	+	25.5478i	−0.605089	+	0.832834i	0.391073	+	0.920360i	$0.372104\pi$
$942$		0			0
$943$	−22.1603	+	7.20032i	−0.721639	+	0.234475i
$944$		0			0
$945$	−10.4708			−0.340616
$946$		0			0
$947$		−	2.08682i		−	0.0678126i	−0.999425	−	0.0339063i	$-0.989205\pi$
$947$		−	2.08682i		−	0.0678126i	0.999425	−	0.0339063i	$-0.0107948\pi$
$948$		0			0
$949$	9.58425	+	4.70969i	0.311118	+	0.152883i
$950$		0			0
$951$	−18.8538	+	25.9500i	−0.611376	+	0.841487i
$952$		0			0
$953$	13.3166	−	40.9843i	0.431367	−	1.32761i	−0.465397	−	0.885102i	$-0.654089\pi$
$953$	13.3166	−	40.9843i	0.431367	−	1.32761i	0.896764	−	0.442509i	$-0.145911\pi$
$954$		0			0
$955$	16.7873	+	23.1058i	0.543225	+	0.747686i
$956$		0			0
$957$	3.68673	−	0.647410i	0.119175	−	0.0209278i
$958$		0			0
$959$	−8.85515	+	6.43364i	−0.285948	+	0.207753i
$960$		0			0
$961$	−19.3898	+	59.6757i	−0.625478	+	1.92502i
$962$		0			0
$963$	−48.9435	−	35.5595i	−1.57718	−	1.14589i
$964$		0			0
$965$	5.51148	+	16.9626i	0.177421	+	0.546045i
$966$		0			0
$967$			1.80424i			0.0580204i	0.999579	+	0.0290102i	$0.00923554\pi$
$967$			1.80424i			0.0580204i	−0.999579	+	0.0290102i	$0.990764\pi$
$968$		0			0
$969$		−	1.73668i		−	0.0557903i
$970$		0			0
$971$	15.0473	+	46.3107i	0.482890	+	1.48618i	0.835014	+	0.550229i	$0.185459\pi$
$971$	15.0473	+	46.3107i	0.482890	+	1.48618i	−0.352124	+	0.935953i	$0.614541\pi$
$972$		0			0
$973$	4.32051	−	5.94667i	0.138509	−	0.190642i
$974$		0			0
$975$	31.2834	−	16.5152i	1.00187	−	0.528911i
$976$		0			0
$977$	−6.52382	−	8.97927i	−0.208715	−	0.287272i	0.691806	−	0.722083i	$-0.256815\pi$
$977$	−6.52382	−	8.97927i	−0.208715	−	0.287272i	−0.900522	+	0.434811i	$0.856815\pi$
$978$		0			0
$979$	−4.49354	−	25.5888i	−0.143614	−	0.817823i
$980$		0			0
$981$	−27.4941	−	37.8424i	−0.877821	−	1.20822i
$982$		0			0
$983$	21.9926	+	7.14583i	0.701455	+	0.227917i	0.637964	−	0.770066i	$-0.279777\pi$
$983$	21.9926	+	7.14583i	0.701455	+	0.227917i	0.0634906	+	0.997982i	$0.479777\pi$
$984$		0			0
$985$	−15.8737	−	11.5329i	−0.505777	−	0.367468i
$986$		0			0
$987$	−15.1440	−	46.6085i	−0.482039	−	1.48356i
$988$		0			0
$989$	−0.889186			−0.0282745
$990$		0			0
$991$	−27.3342			−0.868299			−0.434149	−	0.900841i	$-0.642951\pi$
$991$	−27.3342			−0.868299			−0.434149	+	0.900841i	$0.642951\pi$
$992$		0			0
$993$	−41.5503	+	13.5005i	−1.31856	+	0.428426i
$994$		0			0
$995$	7.68933	−	10.5835i	0.243768	−	0.335518i
$996$		0			0
$997$	−17.9642	+	55.2881i	−0.568932	+	1.75099i	0.0870390	+	0.996205i	$0.472260\pi$
$997$	−17.9642	+	55.2881i	−0.568932	+	1.75099i	−0.655971	+	0.754786i	$0.727740\pi$
$998$		0			0
$999$	−12.4494	−	17.1351i	−0.393881	−	0.542131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.x.a.25.13	✓	56
11.4	even	5	inner	572.2.x.a.389.14	yes	56
13.12	even	2	inner	572.2.x.a.25.14	yes	56
143.103	even	10	inner	572.2.x.a.389.13	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.x.a.25.13	✓	56	1.1	even	1	trivial
572.2.x.a.25.14	yes	56	13.12	even	2	inner
572.2.x.a.389.13	yes	56	143.103	even	10	inner
572.2.x.a.389.14	yes	56	11.4	even	5	inner

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.x (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866400 + 2.66651i) q^{3} +(-0.720035 + 0.991043i) q^{5} +(-1.55809 - 0.506254i) q^{7} +(-3.93255 + 2.85717i) q^{9} +O(q^{10})\)	\(q+(0.866400 + 2.66651i) q^{3} +(-0.720035 + 0.991043i) q^{5} +(-1.55809 - 0.506254i) q^{7} +(-3.93255 + 2.85717i) q^{9} +(-3.26664 + 0.573639i) q^{11} +(-3.56896 - 0.512351i) q^{13} +(-3.26646 - 1.06134i) q^{15} +(-0.515960 - 0.374867i) q^{17} +(0.923703 - 0.300129i) q^{19} -4.59327i q^{21} +2.08440 q^{23} +(1.08137 + 3.32811i) q^{25} +(-4.22103 - 3.06675i) q^{27} +(-0.124390 + 0.382834i) q^{29} +(5.69111 + 7.83314i) q^{31} +(-4.35983 - 8.21351i) q^{33} +(1.62360 - 1.17961i) q^{35} +(3.86078 + 1.25444i) q^{37} +(-1.72596 - 9.96056i) q^{39} +(-10.6315 + 3.45439i) q^{41} -0.426591 q^{43} -5.95459i q^{45} +(10.1471 - 3.29700i) q^{47} +(-3.49177 - 2.53692i) q^{49} +(0.552557 - 1.70060i) q^{51} +(-8.42725 + 6.12276i) q^{53} +(1.78359 - 3.65042i) q^{55} +(1.60059 + 2.20303i) q^{57} +(-2.95371 - 0.959719i) q^{59} +(2.29444 + 1.66701i) q^{61} +(7.57372 - 2.46085i) q^{63} +(3.07754 - 3.16809i) q^{65} +4.46823i q^{67} +(1.80592 + 5.55806i) q^{69} +(-1.83029 + 2.51917i) q^{71} +(-2.81684 - 0.915245i) q^{73} +(-7.93753 + 5.76695i) q^{75} +(5.38012 + 0.759968i) q^{77} +(13.6904 - 9.94668i) q^{79} +(0.0141153 - 0.0434424i) q^{81} +(-7.23020 + 9.95151i) q^{83} +(0.743019 - 0.241422i) q^{85} -1.12860 q^{87} +7.83338i q^{89} +(5.30138 + 2.60509i) q^{91} +(-15.9563 + 21.9620i) q^{93} +(-0.367657 + 1.13153i) q^{95} +(1.23704 + 1.70264i) q^{97} +(11.2073 - 11.5892i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{9}+O(q^{10}) \) 56 * q - 2 * q^9	\( 56 q - 2 q^{9} + q^{13} - 10 q^{17} + 12 q^{23} + 2 q^{25} + 12 q^{27} + 44 q^{29} - 42 q^{35} + 15 q^{39} + 48 q^{43} - 2 q^{49} - 12 q^{51} - 22 q^{53} - 40 q^{55} - 4 q^{61} - 6 q^{65} + 8 q^{69} + 20 q^{75} - 2 q^{77} + 48 q^{79} - 130 q^{81} - 20 q^{87} + 47 q^{91} + 12 q^{95}+O(q^{100}) \) 56 * q - 2 * q^9 + q^13 - 10 * q^17 + 12 * q^23 + 2 * q^25 + 12 * q^27 + 44 * q^29 - 42 * q^35 + 15 * q^39 + 48 * q^43 - 2 * q^49 - 12 * q^51 - 22 * q^53 - 40 * q^55 - 4 * q^61 - 6 * q^65 + 8 * q^69 + 20 * q^75 - 2 * q^77 + 48 * q^79 - 130 * q^81 - 20 * q^87 + 47 * q^91 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more