LMFDB - Embedded newform 576.2.bb.b.241.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			241.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	576.241
Dual form			576.2.bb.b.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205i q^{3} +(0.500000 - 1.86603i) q^{5} +(3.86603 + 2.23205i) q^{7} -3.00000 q^{9} +O(q^{10})$	\(q+1.73205i q^{3} +(0.500000 - 1.86603i) q^{5} +(3.86603 + 2.23205i) q^{7} -3.00000 q^{9} +(-1.86603 + 0.500000i) q^{11} +(2.23205 + 0.598076i) q^{13} +(3.23205 + 0.866025i) q^{15} +4.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(-3.86603 + 6.69615i) q^{21} +(-5.59808 + 3.23205i) q^{23} +(1.09808 + 0.633975i) q^{25} -5.19615i q^{27} +(0.232051 + 0.866025i) q^{29} +(4.59808 + 7.96410i) q^{31} +(-0.866025 - 3.23205i) q^{33} +(6.09808 - 6.09808i) q^{35} +(-4.26795 - 4.26795i) q^{37} +(-1.03590 + 3.86603i) q^{39} +(-0.696152 + 0.401924i) q^{41} +(-6.33013 + 1.69615i) q^{43} +(-1.50000 + 5.59808i) q^{45} +(0.598076 - 1.03590i) q^{47} +(6.46410 + 11.1962i) q^{49} +6.92820i q^{51} +(5.73205 + 5.73205i) q^{53} +3.73205i q^{55} +(5.19615 + 5.19615i) q^{57} +(-0.401924 + 1.50000i) q^{59} +(0.571797 + 2.13397i) q^{61} +(-11.5981 - 6.69615i) q^{63} +(2.23205 - 3.86603i) q^{65} +(-8.33013 - 2.23205i) q^{67} +(-5.59808 - 9.69615i) q^{69} -2.92820i q^{71} -7.46410i q^{73} +(-1.09808 + 1.90192i) q^{75} +(-8.33013 - 2.23205i) q^{77} +(0.866025 - 1.50000i) q^{79} +9.00000 q^{81} +(-3.79423 - 14.1603i) q^{83} +(2.00000 - 7.46410i) q^{85} +(-1.50000 + 0.401924i) q^{87} -15.8564i q^{89} +(7.29423 + 7.29423i) q^{91} +(-13.7942 + 7.96410i) q^{93} +(-4.09808 - 7.09808i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(5.59808 - 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} + 12 q^{7} - 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^5 + 12 * q^7 - 12 * q^9	$ 4 q + 2 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{15} + 16 q^{17} + 12 q^{19} - 12 q^{21} - 12 q^{23} - 6 q^{25} - 6 q^{29} + 8 q^{31} + 14 q^{35} - 24 q^{37} - 18 q^{39} + 18 q^{41} - 8 q^{43} - 6 q^{45} - 8 q^{47} + 12 q^{49} + 16 q^{53} - 12 q^{59} + 30 q^{61} - 36 q^{63} + 2 q^{65} - 16 q^{67} - 12 q^{69} + 6 q^{75} - 16 q^{77} + 36 q^{81} + 16 q^{83} + 8 q^{85} - 6 q^{87} - 2 q^{91} - 24 q^{93} - 6 q^{95} - 2 q^{97} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^5 + 12 * q^7 - 12 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^15 + 16 * q^17 + 12 * q^19 - 12 * q^21 - 12 * q^23 - 6 * q^25 - 6 * q^29 + 8 * q^31 + 14 * q^35 - 24 * q^37 - 18 * q^39 + 18 * q^41 - 8 * q^43 - 6 * q^45 - 8 * q^47 + 12 * q^49 + 16 * q^53 - 12 * q^59 + 30 * q^61 - 36 * q^63 + 2 * q^65 - 16 * q^67 - 12 * q^69 + 6 * q^75 - 16 * q^77 + 36 * q^81 + 16 * q^83 + 8 * q^85 - 6 * q^87 - 2 * q^91 - 24 * q^93 - 6 * q^95 - 2 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$			1.73205i			1.00000i
$3$			1.73205i			1.00000i
$4$		0			0
$5$	0.500000	−	1.86603i	0.223607	−	0.834512i	−0.759351	−	0.650681i	$-0.774483\pi$
$5$	0.500000	−	1.86603i	0.223607	−	0.834512i	0.982958	−	0.183831i	$-0.0588499\pi$
$6$		0			0
$7$	3.86603	+	2.23205i	1.46122	+	0.843636i	0.999068	−	0.0431647i	$-0.0137440\pi$
$7$	3.86603	+	2.23205i	1.46122	+	0.843636i	0.462152	+	0.886801i	$0.347077\pi$
$8$		0			0
$9$	−3.00000			−1.00000
$10$		0			0
$11$	−1.86603	+	0.500000i	−0.562628	+	0.150756i	−0.528913	−	0.848676i	$-0.677400\pi$
$11$	−1.86603	+	0.500000i	−0.562628	+	0.150756i	−0.0337145	+	0.999432i	$0.510734\pi$
$12$		0			0
$13$	2.23205	+	0.598076i	0.619060	+	0.165876i	0.554700	−	0.832050i	$-0.312833\pi$
$13$	2.23205	+	0.598076i	0.619060	+	0.165876i	0.0643593	+	0.997927i	$0.479500\pi$
$14$		0			0
$15$	3.23205	+	0.866025i	0.834512	+	0.223607i
$16$		0			0
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		0			0
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$		0			0
$21$	−3.86603	+	6.69615i	−0.843636	+	1.46122i
$22$		0			0
$23$	−5.59808	+	3.23205i	−1.16728	+	0.673929i	−0.953038	−	0.302851i	$-0.902061\pi$
$23$	−5.59808	+	3.23205i	−1.16728	+	0.673929i	−0.214242	+	0.976781i	$0.568728\pi$
$24$		0			0
$25$	1.09808	+	0.633975i	0.219615	+	0.126795i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	0.232051	+	0.866025i	0.0430908	+	0.160817i	0.984119	−	0.177512i	$-0.0568049\pi$
$29$	0.232051	+	0.866025i	0.0430908	+	0.160817i	−0.941028	+	0.338329i	$0.890138\pi$
$30$		0			0
$31$	4.59808	+	7.96410i	0.825839	+	1.43039i	0.901277	+	0.433244i	$0.142631\pi$
$31$	4.59808	+	7.96410i	0.825839	+	1.43039i	−0.0754376	+	0.997151i	$0.524035\pi$
$32$		0			0
$33$	−0.866025	−	3.23205i	−0.150756	−	0.562628i
$34$		0			0
$35$	6.09808	−	6.09808i	1.03076	−	1.03076i
$36$		0			0
$37$	−4.26795	−	4.26795i	−0.701647	−	0.701647i	0.263117	−	0.964764i	$-0.415249\pi$
$37$	−4.26795	−	4.26795i	−0.701647	−	0.701647i	−0.964764	+	0.263117i	$0.915249\pi$
$38$		0			0
$39$	−1.03590	+	3.86603i	−0.165876	+	0.619060i
$40$		0			0
$41$	−0.696152	+	0.401924i	−0.108721	+	0.0627700i	−0.553374	−	0.832933i	$-0.686660\pi$
$41$	−0.696152	+	0.401924i	−0.108721	+	0.0627700i	0.444654	+	0.895703i	$0.353327\pi$
$42$		0			0
$43$	−6.33013	+	1.69615i	−0.965335	+	0.258661i	−0.706857	−	0.707356i	$-0.749888\pi$
$43$	−6.33013	+	1.69615i	−0.965335	+	0.258661i	−0.258478	+	0.966017i	$0.583221\pi$
$44$		0			0
$45$	−1.50000	+	5.59808i	−0.223607	+	0.834512i
$46$		0			0
$47$	0.598076	−	1.03590i	0.0872384	−	0.151101i	−0.819104	−	0.573644i	$-0.805529\pi$
$47$	0.598076	−	1.03590i	0.0872384	−	0.151101i	0.906343	+	0.422543i	$0.138862\pi$
$48$		0			0
$49$	6.46410	+	11.1962i	0.923443	+	1.59945i
$50$		0			0
$51$			6.92820i			0.970143i
$52$		0			0
$53$	5.73205	+	5.73205i	0.787358	+	0.787358i	0.981060	−	0.193703i	$-0.0620497\pi$
$53$	5.73205	+	5.73205i	0.787358	+	0.787358i	−0.193703	+	0.981060i	$0.562050\pi$
$54$		0			0
$55$			3.73205i			0.503230i
$56$		0			0
$57$	5.19615	+	5.19615i	0.688247	+	0.688247i
$58$		0			0
$59$	−0.401924	+	1.50000i	−0.0523260	+	0.195283i	−0.987141	−	0.159852i	$-0.948898\pi$
$59$	−0.401924	+	1.50000i	−0.0523260	+	0.195283i	0.934815	+	0.355135i	$0.115565\pi$
$60$		0			0
$61$	0.571797	+	2.13397i	0.0732111	+	0.273227i	0.992822	−	0.119604i	$-0.0381624\pi$
$61$	0.571797	+	2.13397i	0.0732111	+	0.273227i	−0.919611	+	0.392831i	$0.871496\pi$
$62$		0			0
$63$	−11.5981	−	6.69615i	−1.46122	−	0.843636i
$64$		0			0
$65$	2.23205	−	3.86603i	0.276852	−	0.479521i
$66$		0			0
$67$	−8.33013	−	2.23205i	−1.01769	−	0.272688i	−0.288849	−	0.957375i	$-0.593273\pi$
$67$	−8.33013	−	2.23205i	−1.01769	−	0.272688i	−0.728838	+	0.684686i	$0.759939\pi$
$68$		0			0
$69$	−5.59808	−	9.69615i	−0.673929	−	1.16728i
$70$		0			0
$71$		−	2.92820i		−	0.347514i	−0.984789	−	0.173757i	$-0.944409\pi$
$71$		−	2.92820i		−	0.347514i	0.984789	−	0.173757i	$-0.0555907\pi$
$72$		0			0
$73$		−	7.46410i		−	0.873607i	−0.899557	−	0.436804i	$-0.856111\pi$
$73$		−	7.46410i		−	0.873607i	0.899557	−	0.436804i	$-0.143889\pi$
$74$		0			0
$75$	−1.09808	+	1.90192i	−0.126795	+	0.219615i
$76$		0			0
$77$	−8.33013	−	2.23205i	−0.949306	−	0.254366i
$78$		0			0
$79$	0.866025	−	1.50000i	0.0974355	−	0.168763i	−0.813187	−	0.582003i	$-0.802269\pi$
$79$	0.866025	−	1.50000i	0.0974355	−	0.168763i	0.910622	+	0.413239i	$0.135603\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	−3.79423	−	14.1603i	−0.416471	−	1.55429i	−0.781872	−	0.623440i	$-0.785735\pi$
$83$	−3.79423	−	14.1603i	−0.416471	−	1.55429i	0.365401	−	0.930850i	$-0.380932\pi$
$84$		0			0
$85$	2.00000	−	7.46410i	0.216930	−	0.809595i
$86$		0			0
$87$	−1.50000	+	0.401924i	−0.160817	+	0.0430908i
$88$		0			0
$89$		−	15.8564i		−	1.68078i	−0.541985	−	0.840388i	$-0.682327\pi$
$89$		−	15.8564i		−	1.68078i	0.541985	−	0.840388i	$-0.317673\pi$
$90$		0			0
$91$	7.29423	+	7.29423i	0.764643	+	0.764643i
$92$		0			0
$93$	−13.7942	+	7.96410i	−1.43039	+	0.825839i
$94$		0			0
$95$	−4.09808	−	7.09808i	−0.420454	−	0.728247i
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	−0.890292	−	0.455389i	$-0.849500\pi$
$97$	−0.500000	+	0.866025i	−0.0507673	+	0.0879316i	0.839525	+	0.543321i	$0.182833\pi$
$98$		0			0
$99$	5.59808	−	1.50000i	0.562628	−	0.150756i
$100$		0			0
$101$	0.500000	−	0.133975i	0.0497519	−	0.0133310i	−0.233857	−	0.972271i	$-0.575135\pi$
$101$	0.500000	−	0.133975i	0.0497519	−	0.0133310i	0.283609	+	0.958940i	$0.408468\pi$
$102$		0			0
$103$	13.7942	−	7.96410i	1.35919	−	0.784726i	0.369672	−	0.929162i	$-0.379470\pi$
$103$	13.7942	−	7.96410i	1.35919	−	0.784726i	0.989514	+	0.144436i	$0.0461369\pi$
$104$		0			0
$105$	10.5622	+	10.5622i	1.03076	+	1.03076i
$106$		0			0
$107$	−9.39230	−	9.39230i	−0.907988	−	0.907988i	0.0881214	−	0.996110i	$-0.471914\pi$
$107$	−9.39230	−	9.39230i	−0.907988	−	0.907988i	−0.996110	+	0.0881214i	$0.971914\pi$
$108$		0			0
$109$	−1.73205	+	1.73205i	−0.165900	+	0.165900i	−0.785175	−	0.619274i	$-0.787427\pi$
$109$	−1.73205	+	1.73205i	−0.165900	+	0.165900i	0.619274	+	0.785175i	$0.287427\pi$
$110$		0			0
$111$	7.39230	−	7.39230i	0.701647	−	0.701647i
$112$		0			0
$113$	−6.23205	−	10.7942i	−0.586262	−	1.01544i	−0.994717	−	0.102657i	$-0.967266\pi$
$113$	−6.23205	−	10.7942i	−0.586262	−	1.01544i	0.408455	−	0.912779i	$-0.366068\pi$
$114$		0			0
$115$	3.23205	+	12.0622i	0.301390	+	1.12480i
$116$		0			0
$117$	−6.69615	−	1.79423i	−0.619060	−	0.165876i
$118$		0			0
$119$	15.4641	+	8.92820i	1.41759	+	0.818447i
$120$		0			0
$121$	−6.29423	+	3.63397i	−0.572203	+	0.330361i
$122$		0			0
$123$	−0.696152	−	1.20577i	−0.0627700	−	0.108721i
$124$		0			0
$125$	8.56218	−	8.56218i	0.765824	−	0.765824i
$126$		0			0
$127$	−0.392305			−0.0348114			−0.0174057	−	0.999849i	$-0.505541\pi$
$127$	−0.392305			−0.0348114			−0.0174057	+	0.999849i	$0.505541\pi$
$128$		0			0
$129$	−2.93782	−	10.9641i	−0.258661	−	0.965335i
$130$		0			0
$131$	4.86603	+	1.30385i	0.425147	+	0.113918i	0.465047	−	0.885286i	$-0.346037\pi$
$131$	4.86603	+	1.30385i	0.425147	+	0.113918i	−0.0399004	+	0.999204i	$0.512704\pi$
$132$		0			0
$133$	18.2942	−	4.90192i	1.58631	−	0.425051i
$134$		0			0
$135$	−9.69615	−	2.59808i	−0.834512	−	0.223607i
$136$		0			0
$137$	0.571797	+	0.330127i	0.0488519	+	0.0282047i	0.524227	−	0.851579i	$-0.324354\pi$
$137$	0.571797	+	0.330127i	0.0488519	+	0.0282047i	−0.475375	+	0.879783i	$0.657688\pi$
$138$		0			0
$139$	4.33013	−	16.1603i	0.367277	−	1.37069i	−0.497032	−	0.867732i	$-0.665577\pi$
$139$	4.33013	−	16.1603i	0.367277	−	1.37069i	0.864308	−	0.502962i	$-0.167757\pi$
$140$		0			0
$141$	1.79423	+	1.03590i	0.151101	+	0.0872384i
$142$		0			0
$143$	−4.46410			−0.373307
$144$		0			0
$145$	1.73205			0.143839
$146$		0			0
$147$	−19.3923	+	11.1962i	−1.59945	+	0.923443i
$148$		0			0
$149$	−4.30385	+	16.0622i	−0.352585	+	1.31586i	0.530912	+	0.847427i	$0.321850\pi$
$149$	−4.30385	+	16.0622i	−0.352585	+	1.31586i	−0.883497	+	0.468438i	$0.844817\pi$
$150$		0			0
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	0.232623	−	0.972567i	$-0.425269\pi$
$151$	−6.06218	−	3.50000i	−0.493333	−	0.284826i	−0.725956	+	0.687741i	$0.758602\pi$
$152$		0			0
$153$	−12.0000			−0.970143
$154$		0			0
$155$	17.1603	−	4.59808i	1.37834	−	0.369326i
$156$		0			0
$157$	3.23205	+	0.866025i	0.257946	+	0.0691164i	0.385474	−	0.922719i	$-0.374038\pi$
$157$	3.23205	+	0.866025i	0.257946	+	0.0691164i	−0.127529	+	0.991835i	$0.540704\pi$
$158$		0			0
$159$	−9.92820	+	9.92820i	−0.787358	+	0.787358i
$160$		0			0
$161$	−28.8564			−2.27420
$162$		0			0
$163$	1.92820	−	1.92820i	0.151029	−	0.151029i	−0.627549	−	0.778577i	$-0.715942\pi$
$163$	1.92820	−	1.92820i	0.151029	−	0.151029i	0.778577	+	0.627549i	$0.215942\pi$
$164$		0			0
$165$	−6.46410			−0.503230
$166$		0			0
$167$	−14.2583	+	8.23205i	−1.10334	+	0.637015i	−0.937097	−	0.349069i	$-0.886498\pi$
$167$	−14.2583	+	8.23205i	−1.10334	+	0.637015i	−0.166246	+	0.986084i	$0.553165\pi$
$168$		0			0
$169$	−6.63397	−	3.83013i	−0.510306	−	0.294625i
$170$		0			0
$171$	−9.00000	+	9.00000i	−0.688247	+	0.688247i
$172$		0			0
$173$	−2.03590	−	7.59808i	−0.154786	−	0.577671i	−0.999124	−	0.0418586i	$-0.986672\pi$
$173$	−2.03590	−	7.59808i	−0.154786	−	0.577671i	0.844337	−	0.535812i	$-0.179995\pi$
$174$		0			0
$175$	2.83013	+	4.90192i	0.213937	+	0.370551i
$176$		0			0
$177$	−2.59808	−	0.696152i	−0.195283	−	0.0523260i
$178$		0			0
$179$	5.92820	−	5.92820i	0.443095	−	0.443095i	−0.449956	−	0.893051i	$-0.648560\pi$
$179$	5.92820	−	5.92820i	0.443095	−	0.443095i	0.893051	+	0.449956i	$0.148560\pi$
$180$		0			0
$181$	−7.73205	−	7.73205i	−0.574719	−	0.574719i	0.358725	−	0.933443i	$-0.383212\pi$
$181$	−7.73205	−	7.73205i	−0.574719	−	0.574719i	−0.933443	+	0.358725i	$0.883212\pi$
$182$		0			0
$183$	−3.69615	+	0.990381i	−0.273227	+	0.0732111i
$184$		0			0
$185$	−10.0981	+	5.83013i	−0.742425	+	0.428639i
$186$		0			0
$187$	−7.46410	+	2.00000i	−0.545829	+	0.146254i
$188$		0			0
$189$	11.5981	−	20.0885i	0.843636	−	1.46122i
$190$		0			0
$191$	−1.40192	+	2.42820i	−0.101440	+	0.175699i	−0.912278	−	0.409572i	$-0.865678\pi$
$191$	−1.40192	+	2.42820i	−0.101440	+	0.175699i	0.810838	+	0.585270i	$0.199012\pi$
$192$		0			0
$193$	2.23205	+	3.86603i	0.160667	+	0.278283i	0.935108	−	0.354363i	$-0.115302\pi$
$193$	2.23205	+	3.86603i	0.160667	+	0.278283i	−0.774441	+	0.632646i	$0.781969\pi$
$194$		0			0
$195$	6.69615	+	3.86603i	0.479521	+	0.276852i
$196$		0			0
$197$	3.53590	+	3.53590i	0.251922	+	0.251922i	0.821758	−	0.569836i	$-0.192993\pi$
$197$	3.53590	+	3.53590i	0.251922	+	0.251922i	−0.569836	+	0.821758i	$0.692993\pi$
$198$		0			0
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$		0			0
$201$	3.86603	−	14.4282i	0.272688	−	1.01769i
$202$		0			0
$203$	−1.03590	+	3.86603i	−0.0727058	+	0.271342i
$204$		0			0
$205$	0.401924	+	1.50000i	0.0280716	+	0.104765i
$206$		0			0
$207$	16.7942	−	9.69615i	1.16728	−	0.673929i
$208$		0			0
$209$	−4.09808	+	7.09808i	−0.283470	+	0.490984i
$210$		0			0
$211$	−18.5263	−	4.96410i	−1.27540	−	0.341743i	−0.443304	−	0.896371i	$-0.646194\pi$
$211$	−18.5263	−	4.96410i	−1.27540	−	0.341743i	−0.832098	+	0.554629i	$0.812860\pi$
$212$		0			0
$213$	5.07180			0.347514
$214$		0			0
$215$			12.6603i			0.863422i
$216$		0			0
$217$			41.0526i			2.78683i
$218$		0			0
$219$	12.9282			0.873607
$220$		0			0
$221$	8.92820	+	2.39230i	0.600576	+	0.160924i
$222$		0			0
$223$	−7.79423	+	13.5000i	−0.521940	+	0.904027i	0.477734	+	0.878504i	$0.341458\pi$
$223$	−7.79423	+	13.5000i	−0.521940	+	0.904027i	−0.999674	+	0.0255224i	$0.991875\pi$
$224$		0			0
$225$	−3.29423	−	1.90192i	−0.219615	−	0.126795i
$226$		0			0
$227$	5.25833	+	19.6244i	0.349008	+	1.30251i	0.887860	+	0.460114i	$0.152191\pi$
$227$	5.25833	+	19.6244i	0.349008	+	1.30251i	−0.538852	+	0.842400i	$0.681142\pi$
$228$		0			0
$229$	−4.42820	+	16.5263i	−0.292624	+	1.09209i	0.650462	+	0.759539i	$0.274575\pi$
$229$	−4.42820	+	16.5263i	−0.292624	+	1.09209i	−0.943086	+	0.332549i	$0.892091\pi$
$230$		0			0
$231$	3.86603	−	14.4282i	0.254366	−	0.949306i
$232$		0			0
$233$		−	9.07180i		−	0.594313i	−0.954829	−	0.297157i	$-0.903962\pi$
$233$		−	9.07180i		−	0.594313i	0.954829	−	0.297157i	$-0.0960383\pi$
$234$		0			0
$235$	−1.63397	−	1.63397i	−0.106589	−	0.106589i
$236$		0			0
$237$	2.59808	+	1.50000i	0.168763	+	0.0974355i
$238$		0			0
$239$	0.401924	+	0.696152i	0.0259983	+	0.0450304i	0.878732	−	0.477316i	$-0.158390\pi$
$239$	0.401924	+	0.696152i	0.0259983	+	0.0450304i	−0.852734	+	0.522346i	$0.825057\pi$
$240$		0			0
$241$	−2.76795	+	4.79423i	−0.178299	+	0.308823i	−0.941298	−	0.337576i	$-0.890393\pi$
$241$	−2.76795	+	4.79423i	−0.178299	+	0.308823i	0.762999	+	0.646400i	$0.223726\pi$
$242$		0			0
$243$			15.5885i			1.00000i
$244$		0			0
$245$	24.1244	−	6.46410i	1.54125	−	0.412976i
$246$		0			0
$247$	8.49038	−	4.90192i	0.540230	−	0.311902i
$248$		0			0
$249$	24.5263	−	6.57180i	1.55429	−	0.416471i
$250$		0			0
$251$	13.3923	+	13.3923i	0.845315	+	0.845315i	0.989544	−	0.144229i	$-0.0460703\pi$
$251$	13.3923	+	13.3923i	0.845315	+	0.845315i	−0.144229	+	0.989544i	$0.546070\pi$
$252$		0			0
$253$	8.83013	−	8.83013i	0.555145	−	0.555145i
$254$		0			0
$255$	12.9282	+	3.46410i	0.809595	+	0.216930i
$256$		0			0
$257$	12.1603	+	21.0622i	0.758536	+	1.31382i	0.943597	+	0.331096i	$0.107418\pi$
$257$	12.1603	+	21.0622i	0.758536	+	1.31382i	−0.185061	+	0.982727i	$0.559248\pi$
$258$		0			0
$259$	−6.97372	−	26.0263i	−0.433326	−	1.61719i
$260$		0			0
$261$	−0.696152	−	2.59808i	−0.0430908	−	0.160817i
$262$		0			0
$263$	−8.59808	−	4.96410i	−0.530180	−	0.306100i	0.210910	−	0.977506i	$-0.432357\pi$
$263$	−8.59808	−	4.96410i	−0.530180	−	0.306100i	−0.741090	+	0.671406i	$0.765691\pi$
$264$		0			0
$265$	13.5622	−	7.83013i	0.833118	−	0.481001i
$266$		0			0
$267$	27.4641			1.68078
$268$		0			0
$269$	4.26795	−	4.26795i	0.260221	−	0.260221i	−0.564923	−	0.825144i	$-0.691094\pi$
$269$	4.26795	−	4.26795i	0.260221	−	0.260221i	0.825144	+	0.564923i	$0.191094\pi$
$270$		0			0
$271$	1.07180			0.0651070			0.0325535	−	0.999470i	$-0.489636\pi$
$271$	1.07180			0.0651070			0.0325535	+	0.999470i	$0.489636\pi$
$272$		0			0
$273$	−12.6340	+	12.6340i	−0.764643	+	0.764643i
$274$		0			0
$275$	−2.36603	−	0.633975i	−0.142677	−	0.0382301i
$276$		0			0
$277$	6.69615	−	1.79423i	0.402333	−	0.107805i	−0.0519775	−	0.998648i	$-0.516552\pi$
$277$	6.69615	−	1.79423i	0.402333	−	0.107805i	0.454310	+	0.890844i	$0.349886\pi$
$278$		0			0
$279$	−13.7942	−	23.8923i	−0.825839	−	1.43039i
$280$		0			0
$281$	10.0359	+	5.79423i	0.598692	+	0.345655i	0.768527	−	0.639818i	$-0.220990\pi$
$281$	10.0359	+	5.79423i	0.598692	+	0.345655i	−0.169835	+	0.985472i	$0.554324\pi$
$282$		0			0
$283$	−3.52628	+	13.1603i	−0.209616	+	0.782296i	0.778377	+	0.627797i	$0.216043\pi$
$283$	−3.52628	+	13.1603i	−0.209616	+	0.782296i	−0.987993	+	0.154499i	$0.950624\pi$
$284$		0			0
$285$	12.2942	−	7.09808i	0.728247	−	0.420454i
$286$		0			0
$287$	−3.58846			−0.211820
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$	−1.50000	−	0.866025i	−0.0879316	−	0.0507673i
$292$		0			0
$293$	−0.571797	+	2.13397i	−0.0334047	+	0.124668i	−0.980615	−	0.195945i	$-0.937222\pi$
$293$	−0.571797	+	2.13397i	−0.0334047	+	0.124668i	0.947210	+	0.320614i	$0.103889\pi$
$294$		0			0
$295$	2.59808	+	1.50000i	0.151266	+	0.0873334i
$296$		0			0
$297$	2.59808	+	9.69615i	0.150756	+	0.562628i
$298$		0			0
$299$	−14.4282	+	3.86603i	−0.834405	+	0.223578i
$300$		0			0
$301$	−28.2583	−	7.57180i	−1.62878	−	0.436431i
$302$		0			0
$303$	0.232051	+	0.866025i	0.0133310	+	0.0497519i
$304$		0			0
$305$	4.26795			0.244382
$306$		0			0
$307$	−7.92820	+	7.92820i	−0.452486	+	0.452486i	−0.896179	−	0.443693i	$-0.853668\pi$
$307$	−7.92820	+	7.92820i	−0.452486	+	0.452486i	0.443693	+	0.896179i	$0.353668\pi$
$308$		0			0
$309$	13.7942	+	23.8923i	0.784726	+	1.35919i
$310$		0			0
$311$	9.18653	−	5.30385i	0.520921	−	0.300754i	−0.216391	−	0.976307i	$-0.569428\pi$
$311$	9.18653	−	5.30385i	0.520921	−	0.300754i	0.737311	+	0.675553i	$0.236095\pi$
$312$		0			0
$313$	−25.1603	−	14.5263i	−1.42214	−	0.821074i	−0.425660	−	0.904883i	$-0.639958\pi$
$313$	−25.1603	−	14.5263i	−1.42214	−	0.821074i	−0.996482	+	0.0838094i	$0.973291\pi$
$314$		0			0
$315$	−18.2942	+	18.2942i	−1.03076	+	1.03076i
$316$		0			0
$317$	8.96410	+	33.4545i	0.503474	+	1.87899i	0.476150	+	0.879364i	$0.342032\pi$
$317$	8.96410	+	33.4545i	0.503474	+	1.87899i	0.0273246	+	0.999627i	$0.491301\pi$
$318$		0			0
$319$	−0.866025	−	1.50000i	−0.0484881	−	0.0839839i
$320$		0			0
$321$	16.2679	−	16.2679i	0.907988	−	0.907988i
$322$		0			0
$323$	12.0000	−	12.0000i	0.667698	−	0.667698i
$324$		0			0
$325$	2.07180	+	2.07180i	0.114923	+	0.114923i
$326$		0			0
$327$	−3.00000	−	3.00000i	−0.165900	−	0.165900i
$328$		0			0
$329$	4.62436	−	2.66987i	0.254949	−	0.147195i
$330$		0			0
$331$	5.06218	−	1.35641i	0.278242	−	0.0745548i	−0.116999	−	0.993132i	$-0.537328\pi$
$331$	5.06218	−	1.35641i	0.278242	−	0.0745548i	0.395242	+	0.918577i	$0.370661\pi$
$332$		0			0
$333$	12.8038	+	12.8038i	0.701647	+	0.701647i
$334$		0			0
$335$	−8.33013	+	14.4282i	−0.455123	+	0.788297i
$336$		0			0
$337$	−9.69615	−	16.7942i	−0.528183	−	0.914840i	−0.999460	−	0.0328547i	$-0.989540\pi$
$337$	−9.69615	−	16.7942i	−0.528183	−	0.914840i	0.471277	−	0.881985i	$-0.343793\pi$
$338$		0			0
$339$	18.6962	−	10.7942i	1.01544	−	0.586262i
$340$		0			0
$341$	−12.5622	−	12.5622i	−0.680280	−	0.680280i
$342$		0			0
$343$			26.4641i			1.42893i
$344$		0			0
$345$	−20.8923	+	5.59808i	−1.12480	+	0.301390i
$346$		0			0
$347$	−0.473721	+	1.76795i	−0.0254307	+	0.0949085i	−0.977475	−	0.211052i	$-0.932311\pi$
$347$	−0.473721	+	1.76795i	−0.0254307	+	0.0949085i	0.952044	+	0.305961i	$0.0989776\pi$
$348$		0			0
$349$	1.03590	+	3.86603i	0.0554504	+	0.206944i	0.988093	−	0.153858i	$-0.0491698\pi$
$349$	1.03590	+	3.86603i	0.0554504	+	0.206944i	−0.932643	+	0.360802i	$0.882503\pi$
$350$		0			0
$351$	3.10770	−	11.5981i	0.165876	−	0.619060i
$352$		0			0
$353$	−11.7679	+	20.3827i	−0.626345	+	1.08486i	0.361934	+	0.932204i	$0.382116\pi$
$353$	−11.7679	+	20.3827i	−0.626345	+	1.08486i	−0.988279	+	0.152657i	$0.951217\pi$
$354$		0			0
$355$	−5.46410	−	1.46410i	−0.290004	−	0.0777064i
$356$		0			0
$357$	−15.4641	+	26.7846i	−0.818447	+	1.41759i
$358$		0			0
$359$		−	28.9282i		−	1.52677i	−0.645942	−	0.763386i	$-0.723535\pi$
$359$		−	28.9282i		−	1.52677i	0.645942	−	0.763386i	$-0.276465\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$		0			0
$363$	−6.29423	−	10.9019i	−0.330361	−	0.572203i
$364$		0			0
$365$	−13.9282	−	3.73205i	−0.729035	−	0.195344i
$366$		0			0
$367$	17.4545	−	30.2321i	0.911117	−	1.57810i	0.0986270	−	0.995124i	$-0.468555\pi$
$367$	17.4545	−	30.2321i	0.911117	−	1.57810i	0.812490	−	0.582976i	$-0.198112\pi$
$368$		0			0
$369$	2.08846	−	1.20577i	0.108721	−	0.0627700i
$370$		0			0
$371$	9.36603	+	34.9545i	0.486260	+	1.81475i
$372$		0			0
$373$	0.428203	−	1.59808i	0.0221715	−	0.0827452i	−0.953954	−	0.299954i	$-0.903029\pi$
$373$	0.428203	−	1.59808i	0.0221715	−	0.0827452i	0.976125	+	0.217209i	$0.0696953\pi$
$374$		0			0
$375$	14.8301	+	14.8301i	0.765824	+	0.765824i
$376$		0			0
$377$			2.07180i			0.106703i
$378$		0			0
$379$	15.5885	+	15.5885i	0.800725	+	0.800725i	0.983209	−	0.182484i	$-0.0584137\pi$
$379$	15.5885	+	15.5885i	0.800725	+	0.800725i	−0.182484	+	0.983209i	$0.558414\pi$
$380$		0			0
$381$		−	0.679492i		−	0.0348114i
$382$		0			0
$383$	−3.66987	−	6.35641i	−0.187522	−	0.324797i	0.756902	−	0.653529i	$-0.226712\pi$
$383$	−3.66987	−	6.35641i	−0.187522	−	0.324797i	−0.944423	+	0.328732i	$0.893379\pi$
$384$		0			0
$385$	−8.33013	+	14.4282i	−0.424543	+	0.735329i
$386$		0			0
$387$	18.9904	−	5.08846i	0.965335	−	0.258661i
$388$		0			0
$389$	−8.96410	+	2.40192i	−0.454498	+	0.121782i	−0.478803	−	0.877922i	$-0.658929\pi$
$389$	−8.96410	+	2.40192i	−0.454498	+	0.121782i	0.0243053	+	0.999705i	$0.492263\pi$
$390$		0			0
$391$	−22.3923	+	12.9282i	−1.13243	+	0.653807i
$392$		0			0
$393$	−2.25833	+	8.42820i	−0.113918	+	0.425147i
$394$		0			0
$395$	−2.36603	−	2.36603i	−0.119048	−	0.119048i
$396$		0			0
$397$	17.0526	−	17.0526i	0.855843	−	0.855843i	−0.135002	−	0.990845i	$-0.543104\pi$
$397$	17.0526	−	17.0526i	0.855843	−	0.855843i	0.990845	+	0.135002i	$0.0431041\pi$
$398$		0			0
$399$	8.49038	+	31.6865i	0.425051	+	1.58631i
$400$		0			0
$401$	−16.1603	−	27.9904i	−0.807005	−	1.39777i	−0.914929	−	0.403614i	$-0.867754\pi$
$401$	−16.1603	−	27.9904i	−0.807005	−	1.39777i	0.107925	−	0.994159i	$-0.465579\pi$
$402$		0			0
$403$	5.50000	+	20.5263i	0.273975	+	1.02249i
$404$		0			0
$405$	4.50000	−	16.7942i	0.223607	−	0.834512i
$406$		0			0
$407$	10.0981	+	5.83013i	0.500543	+	0.288989i
$408$		0			0
$409$	19.6244	−	11.3301i	0.970362	−	0.560239i	0.0710154	−	0.997475i	$-0.477376\pi$
$409$	19.6244	−	11.3301i	0.970362	−	0.560239i	0.899347	+	0.437236i	$0.144043\pi$
$410$		0			0
$411$	−0.571797	+	0.990381i	−0.0282047	+	0.0488519i
$412$		0			0
$413$	−4.90192	+	4.90192i	−0.241208	+	0.241208i
$414$		0			0
$415$	−28.3205			−1.39020
$416$		0			0
$417$	27.9904	+	7.50000i	1.37069	+	0.367277i
$418$		0			0
$419$	−18.5263	−	4.96410i	−0.905068	−	0.242512i	−0.223876	−	0.974618i	$-0.571871\pi$
$419$	−18.5263	−	4.96410i	−0.905068	−	0.242512i	−0.681191	+	0.732105i	$0.738538\pi$
$420$		0			0
$421$	17.8923	−	4.79423i	0.872018	−	0.233656i	0.205058	−	0.978750i	$-0.434262\pi$
$421$	17.8923	−	4.79423i	0.872018	−	0.233656i	0.666960	+	0.745094i	$0.267595\pi$
$422$		0			0
$423$	−1.79423	+	3.10770i	−0.0872384	+	0.151101i
$424$		0			0
$425$	4.39230	+	2.53590i	0.213058	+	0.123009i
$426$		0			0
$427$	−2.55256	+	9.52628i	−0.123527	+	0.461009i
$428$		0			0
$429$		−	7.73205i		−	0.373307i
$430$		0			0
$431$	3.32051			0.159943			0.0799716	−	0.996797i	$-0.474517\pi$
$431$	3.32051			0.159943			0.0799716	+	0.996797i	$0.474517\pi$
$432$		0			0
$433$	3.60770			0.173375			0.0866874	−	0.996236i	$-0.472372\pi$
$433$	3.60770			0.173375			0.0866874	+	0.996236i	$0.472372\pi$
$434$		0			0
$435$			3.00000i			0.143839i
$436$		0			0
$437$	−7.09808	+	26.4904i	−0.339547	+	1.26721i
$438$		0			0
$439$	5.93782	+	3.42820i	0.283397	+	0.163619i	0.634960	−	0.772545i	$-0.281016\pi$
$439$	5.93782	+	3.42820i	0.283397	+	0.163619i	−0.351563	+	0.936164i	$0.614350\pi$
$440$		0			0
$441$	−19.3923	−	33.5885i	−0.923443	−	1.59945i
$442$		0			0
$443$	−4.33013	+	1.16025i	−0.205731	+	0.0551253i	−0.360213	−	0.932870i	$-0.617296\pi$
$443$	−4.33013	+	1.16025i	−0.205731	+	0.0551253i	0.154482	+	0.987996i	$0.450629\pi$
$444$		0			0
$445$	−29.5885	−	7.92820i	−1.40263	−	0.375833i
$446$		0			0
$447$	−27.8205	−	7.45448i	−1.31586	−	0.352585i
$448$		0			0
$449$	35.3205			1.66688			0.833439	−	0.552612i	$-0.186369\pi$
$449$	35.3205			1.66688			0.833439	+	0.552612i	$0.186369\pi$
$450$		0			0
$451$	1.09808	−	1.09808i	0.0517064	−	0.0517064i
$452$		0			0
$453$	6.06218	−	10.5000i	0.284826	−	0.493333i
$454$		0			0
$455$	17.2583	−	9.96410i	0.809083	−	0.467124i
$456$		0			0
$457$	−25.9641	−	14.9904i	−1.21455	−	0.701220i	−0.250802	−	0.968038i	$-0.580694\pi$
$457$	−25.9641	−	14.9904i	−1.21455	−	0.701220i	−0.963747	+	0.266818i	$0.914028\pi$
$458$		0			0
$459$		−	20.7846i		−	0.970143i
$460$		0			0
$461$	−1.23205	−	4.59808i	−0.0573823	−	0.214154i	0.931281	−	0.364301i	$-0.118692\pi$
$461$	−1.23205	−	4.59808i	−0.0573823	−	0.214154i	−0.988664	+	0.150147i	$0.952025\pi$
$462$		0			0
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	0.962891	−	0.269892i	$-0.0869880\pi$
$463$	5.33013	+	9.23205i	0.247712	+	0.429050i	−0.715179	+	0.698942i	$0.753655\pi$
$464$		0			0
$465$	7.96410	+	29.7224i	0.369326	+	1.37834i
$466$		0			0
$467$	−21.7846	+	21.7846i	−1.00807	+	1.00807i	−0.00810436	+	0.999967i	$0.502580\pi$
$467$	−21.7846	+	21.7846i	−1.00807	+	1.00807i	−0.999967	+	0.00810436i	$0.997420\pi$
$468$		0			0
$469$	−27.2224	−	27.2224i	−1.25702	−	1.25702i
$470$		0			0
$471$	−1.50000	+	5.59808i	−0.0691164	+	0.257946i
$472$		0			0
$473$	10.9641	−	6.33013i	0.504130	−	0.291060i
$474$		0			0
$475$	5.19615	−	1.39230i	0.238416	−	0.0638833i
$476$		0			0
$477$	−17.1962	−	17.1962i	−0.787358	−	0.787358i
$478$		0			0
$479$	−9.33013	+	16.1603i	−0.426304	+	0.738381i	−0.996541	−	0.0830995i	$-0.973518\pi$
$479$	−9.33013	+	16.1603i	−0.426304	+	0.738381i	0.570237	+	0.821480i	$0.306851\pi$
$480$		0			0
$481$	−6.97372	−	12.0788i	−0.317974	−	0.550748i
$482$		0			0
$483$		−	49.9808i		−	2.27420i
$484$		0			0
$485$	1.36603	+	1.36603i	0.0620280	+	0.0620280i
$486$		0			0
$487$		−	6.78461i		−	0.307440i	−0.988114	−	0.153720i	$-0.950875\pi$
$487$		−	6.78461i		−	0.307440i	0.988114	−	0.153720i	$-0.0491254\pi$
$488$		0			0
$489$	3.33975	+	3.33975i	0.151029	+	0.151029i
$490$		0			0
$491$	0.133975	−	0.500000i	0.00604619	−	0.0225647i	−0.962837	−	0.270084i	$-0.912949\pi$
$491$	0.133975	−	0.500000i	0.00604619	−	0.0225647i	0.968883	+	0.247519i	$0.0796153\pi$
$492$		0			0
$493$	0.928203	+	3.46410i	0.0418042	+	0.156015i
$494$		0			0
$495$		−	11.1962i		−	0.503230i
$496$		0			0
$497$	6.53590	−	11.3205i	0.293175	−	0.507794i
$498$		0			0
$499$	−9.33013	−	2.50000i	−0.417674	−	0.111915i	0.0438606	−	0.999038i	$-0.486034\pi$
$499$	−9.33013	−	2.50000i	−0.417674	−	0.111915i	−0.461534	+	0.887122i	$0.652701\pi$
$500$		0			0
$501$	−14.2583	−	24.6962i	−0.637015	−	1.10334i
$502$		0			0
$503$			13.8564i			0.617827i	0.951090	+	0.308913i	$0.0999653\pi$
$503$			13.8564i			0.617827i	−0.951090	+	0.308913i	$0.900035\pi$
$504$		0			0
$505$		−	1.00000i		−	0.0444994i
$506$		0			0
$507$	6.63397	−	11.4904i	0.294625	−	0.510306i
$508$		0			0
$509$	−4.69615	−	1.25833i	−0.208153	−	0.0557745i	0.153236	−	0.988190i	$-0.451031\pi$
$509$	−4.69615	−	1.25833i	−0.208153	−	0.0557745i	−0.361389	+	0.932415i	$0.617697\pi$
$510$		0			0
$511$	16.6603	−	28.8564i	0.737006	−	1.27653i
$512$		0			0
$513$	−15.5885	−	15.5885i	−0.688247	−	0.688247i
$514$		0			0
$515$	−7.96410	−	29.7224i	−0.350940	−	1.30973i
$516$		0			0
$517$	−0.598076	+	2.23205i	−0.0263034	+	0.0981655i
$518$		0			0
$519$	13.1603	−	3.52628i	0.577671	−	0.154786i
$520$		0			0
$521$			41.8564i			1.83376i	0.399160	+	0.916881i	$0.369302\pi$
$521$			41.8564i			1.83376i	−0.399160	+	0.916881i	$0.630698\pi$
$522$		0			0
$523$	−22.1244	−	22.1244i	−0.967431	−	0.967431i	0.0320556	−	0.999486i	$-0.489795\pi$
$523$	−22.1244	−	22.1244i	−0.967431	−	0.967431i	−0.999486	+	0.0320556i	$0.989795\pi$
$524$		0			0
$525$	−8.49038	+	4.90192i	−0.370551	+	0.213937i
$526$		0			0
$527$	18.3923	+	31.8564i	0.801181	+	1.38769i
$528$		0			0
$529$	9.39230	−	16.2679i	0.408361	−	0.707302i
$530$		0			0
$531$	1.20577	−	4.50000i	0.0523260	−	0.195283i
$532$		0			0
$533$	−1.79423	+	0.480762i	−0.0777167	+	0.0208241i
$534$		0			0
$535$	−22.2224	+	12.8301i	−0.960760	+	0.554695i
$536$		0			0
$537$	10.2679	+	10.2679i	0.443095	+	0.443095i
$538$		0			0
$539$	−17.6603	−	17.6603i	−0.760681	−	0.760681i
$540$		0			0
$541$	−15.0000	+	15.0000i	−0.644900	+	0.644900i	−0.951756	−	0.306856i	$-0.900723\pi$
$541$	−15.0000	+	15.0000i	−0.644900	+	0.644900i	0.306856	+	0.951756i	$0.400723\pi$
$542$		0			0
$543$	13.3923	−	13.3923i	0.574719	−	0.574719i
$544$		0			0
$545$	2.36603	+	4.09808i	0.101349	+	0.175542i
$546$		0			0
$547$	5.74167	+	21.4282i	0.245496	+	0.916204i	0.973133	+	0.230242i	$0.0739517\pi$
$547$	5.74167	+	21.4282i	0.245496	+	0.916204i	−0.727637	+	0.685962i	$0.759382\pi$
$548$		0			0
$549$	−1.71539	−	6.40192i	−0.0732111	−	0.273227i
$550$		0			0
$551$	3.29423	+	1.90192i	0.140339	+	0.0810247i
$552$		0			0
$553$	6.69615	−	3.86603i	0.284749	−	0.164400i
$554$		0			0
$555$	−10.0981	−	17.4904i	−0.428639	−	0.742425i
$556$		0			0
$557$	−23.9808	+	23.9808i	−1.01610	+	1.01610i	−0.0162292	+	0.999868i	$0.505166\pi$
$557$	−23.9808	+	23.9808i	−1.01610	+	1.01610i	−0.999868	+	0.0162292i	$0.994834\pi$
$558$		0			0
$559$	−15.1436			−0.640506
$560$		0			0
$561$	−3.46410	−	12.9282i	−0.146254	−	0.545829i
$562$		0			0
$563$	−6.13397	−	1.64359i	−0.258516	−	0.0692692i	0.127233	−	0.991873i	$-0.459390\pi$
$563$	−6.13397	−	1.64359i	−0.258516	−	0.0692692i	−0.385749	+	0.922604i	$0.626057\pi$
$564$		0			0
$565$	−23.2583	+	6.23205i	−0.978485	+	0.262184i
$566$		0			0
$567$	34.7942	+	20.0885i	1.46122	+	0.843636i
$568$		0			0
$569$	27.4808	+	15.8660i	1.15205	+	0.665138i	0.949387	−	0.314109i	$-0.101706\pi$
$569$	27.4808	+	15.8660i	1.15205	+	0.665138i	0.202667	+	0.979248i	$0.435039\pi$
$570$		0			0
$571$	10.5981	−	39.5526i	0.443516	−	1.65522i	−0.276310	−	0.961068i	$-0.589112\pi$
$571$	10.5981	−	39.5526i	0.443516	−	1.65522i	0.719826	−	0.694155i	$-0.244222\pi$
$572$		0			0
$573$	−4.20577	−	2.42820i	−0.175699	−	0.101440i
$574$		0			0
$575$	−8.19615			−0.341803
$576$		0			0
$577$	−25.1769			−1.04813			−0.524064	−	0.851679i	$-0.675585\pi$
$577$	−25.1769			−1.04813			−0.524064	+	0.851679i	$0.675585\pi$
$578$		0			0
$579$	−6.69615	+	3.86603i	−0.278283	+	0.160667i
$580$		0			0
$581$	16.9378	−	63.2128i	0.702699	−	2.62251i
$582$		0			0
$583$	−13.5622	−	7.83013i	−0.561688	−	0.324291i
$584$		0			0
$585$	−6.69615	+	11.5981i	−0.276852	+	0.479521i
$586$		0			0
$587$	14.7942	−	3.96410i	0.610623	−	0.163616i	0.0597617	−	0.998213i	$-0.480966\pi$
$587$	14.7942	−	3.96410i	0.610623	−	0.163616i	0.550861	+	0.834597i	$0.314299\pi$
$588$		0			0
$589$	37.6865	+	10.0981i	1.55285	+	0.416084i
$590$		0			0
$591$	−6.12436	+	6.12436i	−0.251922	+	0.251922i
$592$		0			0
$593$	−5.46410			−0.224384			−0.112192	−	0.993687i	$-0.535787\pi$
$593$	−5.46410			−0.224384			−0.112192	+	0.993687i	$0.535787\pi$
$594$		0			0
$595$	24.3923	−	24.3923i	0.999987	−	0.999987i
$596$		0			0
$597$	37.8564			1.54936
$598$		0			0
$599$	−30.3109	+	17.5000i	−1.23847	+	0.715031i	−0.968781	−	0.247917i	$-0.920254\pi$
$599$	−30.3109	+	17.5000i	−1.23847	+	0.715031i	−0.269688	+	0.962948i	$0.586921\pi$
$600$		0			0
$601$	26.7679	+	15.4545i	1.09189	+	0.630401i	0.934078	−	0.357068i	$-0.116224\pi$
$601$	26.7679	+	15.4545i	1.09189	+	0.630401i	0.157809	+	0.987470i	$0.449557\pi$
$602$		0			0
$603$	24.9904	+	6.69615i	1.01769	+	0.272688i
$604$		0			0
$605$	3.63397	+	13.5622i	0.147742	+	0.551381i
$606$		0			0
$607$	−0.598076	−	1.03590i	−0.0242752	−	0.0420458i	0.853633	−	0.520876i	$-0.174394\pi$
$607$	−0.598076	−	1.03590i	−0.0242752	−	0.0420458i	−0.877908	+	0.478830i	$0.841061\pi$
$608$		0			0
$609$	−6.69615	−	1.79423i	−0.271342	−	0.0727058i
$610$		0			0
$611$	1.95448	−	1.95448i	0.0790699	−	0.0790699i
$612$		0			0
$613$	23.5885	+	23.5885i	0.952729	+	0.952729i	0.998932	−	0.0462032i	$-0.0147122\pi$
$613$	23.5885	+	23.5885i	0.952729	+	0.952729i	−0.0462032	+	0.998932i	$0.514712\pi$
$614$		0			0
$615$	−2.59808	+	0.696152i	−0.104765	+	0.0280716i
$616$		0			0
$617$	−23.0885	+	13.3301i	−0.929506	+	0.536651i	−0.886655	−	0.462431i	$-0.846977\pi$
$617$	−23.0885	+	13.3301i	−0.929506	+	0.536651i	−0.0428509	+	0.999081i	$0.513644\pi$
$618$		0			0
$619$	−7.13397	+	1.91154i	−0.286739	+	0.0768314i	−0.399322	−	0.916811i	$-0.630754\pi$
$619$	−7.13397	+	1.91154i	−0.286739	+	0.0768314i	0.112583	+	0.993642i	$0.464088\pi$
$620$		0			0
$621$	16.7942	+	29.0885i	0.673929	+	1.16728i
$622$		0			0
$623$	35.3923	−	61.3013i	1.41796	−	2.45598i
$624$		0			0
$625$	−8.52628	−	14.7679i	−0.341051	−	0.590718i
$626$		0			0
$627$	−12.2942	−	7.09808i	−0.490984	−	0.283470i
$628$		0			0
$629$	−17.0718	−	17.0718i	−0.680697	−	0.680697i
$630$		0			0
$631$			16.2487i			0.646851i	0.946254	+	0.323425i	$0.104835\pi$
$631$			16.2487i			0.646851i	−0.946254	+	0.323425i	$0.895165\pi$
$632$		0			0
$633$	8.59808	−	32.0885i	0.341743	−	1.27540i
$634$		0			0
$635$	−0.196152	+	0.732051i	−0.00778407	+	0.0290506i
$636$		0			0
$637$	7.73205	+	28.8564i	0.306355	+	1.14333i
$638$		0			0
$639$			8.78461i			0.347514i
$640$		0			0
$641$	9.23205	−	15.9904i	0.364644	−	0.631582i	−0.624075	−	0.781365i	$-0.714524\pi$
$641$	9.23205	−	15.9904i	0.364644	−	0.631582i	0.988719	+	0.149782i	$0.0478573\pi$
$642$		0			0
$643$	29.7224	+	7.96410i	1.17214	+	0.314074i	0.791804	−	0.610776i	$-0.209142\pi$
$643$	29.7224	+	7.96410i	1.17214	+	0.314074i	0.380334	+	0.924849i	$0.375809\pi$
$644$		0			0
$645$	−21.9282			−0.863422
$646$		0			0
$647$			25.6077i			1.00674i	0.864070	+	0.503371i	$0.167907\pi$
$647$			25.6077i			1.00674i	−0.864070	+	0.503371i	$0.832093\pi$
$648$		0			0
$649$		−	3.00000i		−	0.117760i
$650$		0			0
$651$	−71.1051			−2.78683
$652$		0			0
$653$	47.2846	+	12.6699i	1.85039	+	0.495810i	0.999561	−	0.0296324i	$-0.00943367\pi$
$653$	47.2846	+	12.6699i	1.85039	+	0.495810i	0.850829	+	0.525443i	$0.176100\pi$
$654$		0			0
$655$	4.86603	−	8.42820i	0.190131	−	0.329317i
$656$		0			0
$657$			22.3923i			0.873607i
$658$		0			0
$659$	0.330127	+	1.23205i	0.0128599	+	0.0479939i	0.972058	−	0.234742i	$-0.0754246\pi$
$659$	0.330127	+	1.23205i	0.0128599	+	0.0479939i	−0.959198	+	0.282736i	$0.908758\pi$
$660$		0			0
$661$	−5.30385	+	19.7942i	−0.206296	+	0.769906i	0.782755	+	0.622330i	$0.213814\pi$
$661$	−5.30385	+	19.7942i	−0.206296	+	0.769906i	−0.989051	+	0.147576i	$0.952853\pi$
$662$		0			0
$663$	−4.14359	+	15.4641i	−0.160924	+	0.600576i
$664$		0			0
$665$		−	36.5885i		−	1.41884i
$666$		0			0
$667$	−4.09808	−	4.09808i	−0.158678	−	0.158678i
$668$		0			0
$669$	−23.3827	−	13.5000i	−0.904027	−	0.521940i
$670$		0			0
$671$	−2.13397	−	3.69615i	−0.0823812	−	0.142688i
$672$		0			0
$673$	21.1603	−	36.6506i	0.815668	−	1.41278i	−0.0931795	−	0.995649i	$-0.529703\pi$
$673$	21.1603	−	36.6506i	0.815668	−	1.41278i	0.908847	−	0.417129i	$-0.136964\pi$
$674$		0			0
$675$	3.29423	−	5.70577i	0.126795	−	0.219615i
$676$		0			0
$677$	−8.76795	+	2.34936i	−0.336980	+	0.0902934i	−0.423341	−	0.905970i	$-0.639143\pi$
$677$	−8.76795	+	2.34936i	−0.336980	+	0.0902934i	0.0863612	+	0.996264i	$0.472476\pi$
$678$		0			0
$679$	−3.86603	+	2.23205i	−0.148364	+	0.0856582i
$680$		0			0
$681$	−33.9904	+	9.10770i	−1.30251	+	0.349008i
$682$		0			0
$683$	−15.3923	−	15.3923i	−0.588970	−	0.588970i	0.348382	−	0.937353i	$-0.386731\pi$
$683$	−15.3923	−	15.3923i	−0.588970	−	0.588970i	−0.937353	+	0.348382i	$0.886731\pi$
$684$		0			0
$685$	0.901924	−	0.901924i	0.0344607	−	0.0344607i
$686$		0			0
$687$	−28.6244	−	7.66987i	−1.09209	−	0.292624i
$688$		0			0
$689$	9.36603	+	16.2224i	0.356817	+	0.618025i
$690$		0			0
$691$	−0.526279	−	1.96410i	−0.0200206	−	0.0747179i	0.955193	−	0.295984i	$-0.0956476\pi$
$691$	−0.526279	−	1.96410i	−0.0200206	−	0.0747179i	−0.975213	+	0.221266i	$0.928981\pi$
$692$		0			0
$693$	24.9904	+	6.69615i	0.949306	+	0.254366i
$694$		0			0
$695$	−27.9904	−	16.1603i	−1.06174	−	0.612993i
$696$		0			0
$697$	−2.78461	+	1.60770i	−0.105475	+	0.0608958i
$698$		0			0
$699$	15.7128			0.594313
$700$		0			0
$701$	17.0526	−	17.0526i	0.644066	−	0.644066i	−0.307486	−	0.951553i	$-0.599488\pi$
$701$	17.0526	−	17.0526i	0.644066	−	0.644066i	0.951553	+	0.307486i	$0.0994878\pi$
$702$		0			0
$703$	−25.6077			−0.965813
$704$		0			0
$705$	2.83013	−	2.83013i	0.106589	−	0.106589i
$706$		0			0
$707$	2.23205	+	0.598076i	0.0839449	+	0.0224930i
$708$		0			0
$709$	−37.7487	+	10.1147i	−1.41768	+	0.379867i	−0.884661	−	0.466235i	$-0.845610\pi$
$709$	−37.7487	+	10.1147i	−1.41768	+	0.379867i	−0.533022	+	0.846102i	$0.678944\pi$
$710$		0			0
$711$	−2.59808	+	4.50000i	−0.0974355	+	0.168763i
$712$		0			0
$713$	−51.4808	−	29.7224i	−1.92797	−	1.11311i
$714$		0			0
$715$	−2.23205	+	8.33013i	−0.0834740	+	0.311529i
$716$		0			0
$717$	−1.20577	+	0.696152i	−0.0450304	+	0.0259983i
$718$		0			0
$719$	11.3205			0.422184			0.211092	−	0.977466i	$-0.432298\pi$
$719$	11.3205			0.422184			0.211092	+	0.977466i	$0.432298\pi$
$720$		0			0
$721$	71.1051			2.64809
$722$		0			0
$723$	−8.30385	−	4.79423i	−0.308823	−	0.178299i
$724$		0			0
$725$	−0.294229	+	1.09808i	−0.0109274	+	0.0407815i
$726$		0			0
$727$	3.06218	+	1.76795i	0.113570	+	0.0655696i	0.555709	−	0.831377i	$-0.312447\pi$
$727$	3.06218	+	1.76795i	0.113570	+	0.0655696i	−0.442139	+	0.896947i	$0.645780\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−25.3205	+	6.78461i	−0.936513	+	0.250938i
$732$		0			0
$733$	−31.6244	−	8.47372i	−1.16807	−	0.312984i	−0.377887	−	0.925852i	$-0.623349\pi$
$733$	−31.6244	−	8.47372i	−1.16807	−	0.312984i	−0.790185	+	0.612868i	$0.790016\pi$
$734$		0			0
$735$	11.1962	+	41.7846i	0.412976	+	1.54125i
$736$		0			0
$737$	16.6603			0.613688
$738$		0			0
$739$	26.2679	−	26.2679i	0.966282	−	0.966282i	−0.0331677	−	0.999450i	$-0.510560\pi$
$739$	26.2679	−	26.2679i	0.966282	−	0.966282i	0.999450	+	0.0331677i	$0.0105595\pi$
$740$		0			0
$741$	8.49038	+	14.7058i	0.311902	+	0.540230i
$742$		0			0
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.0372984	−	0.999304i	$-0.488125\pi$
$743$	25.1147	−	14.5000i	0.921370	−	0.531953i	0.884072	+	0.467351i	$0.154791\pi$
$744$		0			0
$745$	27.8205	+	16.0622i	1.01926	+	0.588473i
$746$		0			0
$747$	11.3827	+	42.4808i	0.416471	+	1.55429i
$748$		0			0
$749$	−15.3468	−	57.2750i	−0.560759	−	2.09278i
$750$		0			0
$751$	24.7224	+	42.8205i	0.902134	+	1.56254i	0.824718	+	0.565544i	$0.191334\pi$
$751$	24.7224	+	42.8205i	0.902134	+	1.56254i	0.0774160	+	0.996999i	$0.475333\pi$
$752$		0			0
$753$	−23.1962	+	23.1962i	−0.845315	+	0.845315i
$754$		0			0
$755$	−9.56218	+	9.56218i	−0.348003	+	0.348003i
$756$		0			0
$757$	1.53590	+	1.53590i	0.0558232	+	0.0558232i	0.734467	−	0.678644i	$-0.237432\pi$
$757$	1.53590	+	1.53590i	0.0558232	+	0.0558232i	−0.678644	+	0.734467i	$0.737432\pi$
$758$		0			0
$759$	15.2942	+	15.2942i	0.555145	+	0.555145i
$760$		0			0
$761$	16.2846	−	9.40192i	0.590317	−	0.340819i	−0.174906	−	0.984585i	$-0.555962\pi$
$761$	16.2846	−	9.40192i	0.590317	−	0.340819i	0.765223	+	0.643766i	$0.222629\pi$
$762$		0			0
$763$	−10.5622	+	2.83013i	−0.382377	+	0.102457i
$764$		0			0
$765$	−6.00000	+	22.3923i	−0.216930	+	0.809595i
$766$		0			0
$767$	−1.79423	+	3.10770i	−0.0647858	+	0.112212i
$768$		0			0
$769$	−3.50000	−	6.06218i	−0.126213	−	0.218608i	0.795993	−	0.605305i	$-0.206949\pi$
$769$	−3.50000	−	6.06218i	−0.126213	−	0.218608i	−0.922207	+	0.386698i	$0.873616\pi$
$770$		0			0
$771$	−36.4808	+	21.0622i	−1.31382	+	0.758536i
$772$		0			0
$773$	−23.5885	−	23.5885i	−0.848418	−	0.848418i	0.141518	−	0.989936i	$-0.454802\pi$
$773$	−23.5885	−	23.5885i	−0.848418	−	0.848418i	−0.989936	+	0.141518i	$0.954802\pi$
$774$		0			0
$775$			11.6603i			0.418849i
$776$		0			0
$777$	45.0788	−	12.0788i	1.61719	−	0.433326i
$778$		0			0
$779$	−0.882686	+	3.29423i	−0.0316255	+	0.118028i
$780$		0			0
$781$	1.46410	+	5.46410i	0.0523897	+	0.195521i
$782$		0			0
$783$	4.50000	−	1.20577i	0.160817	−	0.0430908i
$784$		0			0
$785$	3.23205	−	5.59808i	0.115357	−	0.199804i
$786$		0			0
$787$	3.06218	+	0.820508i	0.109155	+	0.0292480i	0.312983	−	0.949759i	$-0.398672\pi$
$787$	3.06218	+	0.820508i	0.109155	+	0.0292480i	−0.203828	+	0.979007i	$0.565338\pi$
$788$		0			0
$789$	8.59808	−	14.8923i	0.306100	−	0.530180i
$790$		0			0
$791$		−	55.6410i		−	1.97837i
$792$		0			0
$793$			5.10512i			0.181288i
$794$		0			0
$795$	13.5622	+	23.4904i	0.481001	+	0.833118i
$796$		0			0
$797$	−41.2846	−	11.0622i	−1.46238	−	0.391842i	−0.562066	−	0.827092i	$-0.689993\pi$
$797$	−41.2846	−	11.0622i	−1.46238	−	0.391842i	−0.900310	+	0.435250i	$0.856660\pi$
$798$		0			0
$799$	2.39230	−	4.14359i	0.0846337	−	0.146590i
$800$		0			0
$801$			47.5692i			1.68078i
$802$		0			0
$803$	3.73205	+	13.9282i	0.131701	+	0.491516i
$804$		0			0
$805$	−14.4282	+	53.8468i	−0.508527	+	1.89785i
$806$		0			0
$807$	7.39230	+	7.39230i	0.260221	+	0.260221i
$808$		0			0
$809$			36.6410i			1.28823i	0.764929	+	0.644115i	$0.222774\pi$
$809$			36.6410i			1.28823i	−0.764929	+	0.644115i	$0.777226\pi$
$810$		0			0
$811$	18.4641	+	18.4641i	0.648362	+	0.648362i	0.952597	−	0.304235i	$-0.0984007\pi$
$811$	18.4641	+	18.4641i	0.648362	+	0.648362i	−0.304235	+	0.952597i	$0.598401\pi$
$812$		0			0
$813$			1.85641i			0.0651070i
$814$		0			0
$815$	−2.63397	−	4.56218i	−0.0922641	−	0.159806i
$816$		0			0
$817$	−13.9019	+	24.0788i	−0.486367	+	0.842412i
$818$		0			0
$819$	−21.8827	−	21.8827i	−0.764643	−	0.764643i
$820$		0			0
$821$	−40.0167	+	10.7224i	−1.39659	+	0.374215i	−0.877119	−	0.480272i	$-0.840538\pi$
$821$	−40.0167	+	10.7224i	−1.39659	+	0.374215i	−0.519472	+	0.854488i	$0.673871\pi$
$822$		0			0
$823$	36.6506	−	21.1603i	1.27756	−	0.737600i	0.301162	−	0.953573i	$-0.402626\pi$
$823$	36.6506	−	21.1603i	1.27756	−	0.737600i	0.976399	+	0.215973i	$0.0692923\pi$
$824$		0			0
$825$	1.09808	−	4.09808i	0.0382301	−	0.142677i
$826$		0			0
$827$	31.3923	+	31.3923i	1.09162	+	1.09162i	0.995356	+	0.0962613i	$0.0306884\pi$
$827$	31.3923	+	31.3923i	1.09162	+	1.09162i	0.0962613	+	0.995356i	$0.469312\pi$
$828$		0			0
$829$	−14.2679	+	14.2679i	−0.495546	+	0.495546i	−0.910048	−	0.414502i	$-0.863956\pi$
$829$	−14.2679	+	14.2679i	−0.495546	+	0.495546i	0.414502	+	0.910048i	$0.363956\pi$
$830$		0			0
$831$	3.10770	+	11.5981i	0.107805	+	0.402333i
$832$		0			0
$833$	25.8564	+	44.7846i	0.895871	+	1.55169i
$834$		0			0
$835$	8.23205	+	30.7224i	0.284882	+	1.06319i
$836$		0			0
$837$	41.3827	−	23.8923i	1.43039	−	0.825839i
$838$		0			0
$839$	6.74167	+	3.89230i	0.232748	+	0.134377i	0.611839	−	0.790982i	$-0.290430\pi$
$839$	6.74167	+	3.89230i	0.232748	+	0.134377i	−0.379091	+	0.925359i	$0.623763\pi$
$840$		0			0
$841$	24.4186	−	14.0981i	0.842020	−	0.486141i
$842$		0			0
$843$	−10.0359	+	17.3827i	−0.345655	+	0.598692i
$844$		0			0
$845$	−10.4641	+	10.4641i	−0.359976	+	0.359976i
$846$		0			0
$847$	−32.4449			−1.11482
$848$		0			0
$849$	−22.7942	−	6.10770i	−0.782296	−	0.209616i
$850$		0			0
$851$	37.6865	+	10.0981i	1.29188	+	0.346158i
$852$		0			0
$853$	7.69615	−	2.06218i	0.263511	−	0.0706076i	−0.124644	−	0.992201i	$-0.539779\pi$
$853$	7.69615	−	2.06218i	0.263511	−	0.0706076i	0.388156	+	0.921594i	$0.373112\pi$
$854$		0			0
$855$	12.2942	+	21.2942i	0.420454	+	0.728247i
$856$		0			0
$857$	−14.6436	−	8.45448i	−0.500216	−	0.288800i	0.228587	−	0.973523i	$-0.426589\pi$
$857$	−14.6436	−	8.45448i	−0.500216	−	0.288800i	−0.728803	+	0.684724i	$0.759923\pi$
$858$		0			0
$859$	−1.20577	+	4.50000i	−0.0411404	+	0.153538i	−0.983440	−	0.181231i	$-0.941992\pi$
$859$	−1.20577	+	4.50000i	−0.0411404	+	0.153538i	0.942300	+	0.334769i	$0.108658\pi$
$860$		0			0
$861$		−	6.21539i		−	0.211820i
$862$		0			0
$863$	26.5359			0.903292			0.451646	−	0.892197i	$-0.350837\pi$
$863$	26.5359			0.903292			0.451646	+	0.892197i	$0.350837\pi$
$864$		0			0
$865$	−15.1962			−0.516685
$866$		0			0
$867$		−	1.73205i		−	0.0588235i
$868$		0			0
$869$	−0.866025	+	3.23205i	−0.0293779	+	0.109640i
$870$		0			0
$871$	−17.2583	−	9.96410i	−0.584776	−	0.337621i
$872$		0			0
$873$	1.50000	−	2.59808i	0.0507673	−	0.0879316i
$874$		0			0
$875$	52.2128	−	13.9904i	1.76512	−	0.472961i
$876$		0			0
$877$	49.9449	+	13.3827i	1.68652	+	0.451901i	0.969488	−	0.245140i	$-0.0788341\pi$
$877$	49.9449	+	13.3827i	1.68652	+	0.451901i	0.717031	+	0.697042i	$0.245501\pi$
$878$		0			0
$879$	−3.69615	−	0.990381i	−0.124668	−	0.0334047i
$880$		0			0
$881$	31.3205			1.05521			0.527607	−	0.849488i	$-0.323089\pi$
$881$	31.3205			1.05521			0.527607	+	0.849488i	$0.323089\pi$
$882$		0			0
$883$	3.00000	−	3.00000i	0.100958	−	0.100958i	−0.654824	−	0.755782i	$-0.727257\pi$
$883$	3.00000	−	3.00000i	0.100958	−	0.100958i	0.755782	+	0.654824i	$0.227257\pi$
$884$		0			0
$885$	−2.59808	+	4.50000i	−0.0873334	+	0.151266i
$886$		0			0
$887$	8.93782	−	5.16025i	0.300103	−	0.173264i	−0.342386	−	0.939559i	$-0.611235\pi$
$887$	8.93782	−	5.16025i	0.300103	−	0.173264i	0.642489	+	0.766295i	$0.277902\pi$
$888$		0			0
$889$	−1.51666	−	0.875644i	−0.0508672	−	0.0293682i
$890$		0			0
$891$	−16.7942	+	4.50000i	−0.562628	+	0.150756i
$892$		0			0
$893$	−1.31347	−	4.90192i	−0.0439535	−	0.164037i
$894$		0			0
$895$	−8.09808	−	14.0263i	−0.270689	−	0.468847i
$896$		0			0
$897$	−6.69615	−	24.9904i	−0.223578	−	0.834405i
$898$		0			0
$899$	−5.83013	+	5.83013i	−0.194446	+	0.194446i
$900$		0			0
$901$	22.9282	+	22.9282i	0.763849	+	0.763849i
$902$		0			0
$903$	13.1147	−	48.9449i	0.436431	−	1.62878i
$904$		0			0
$905$	−18.2942	+	10.5622i	−0.608121	+	0.351099i
$906$		0			0
$907$	−9.06218	+	2.42820i	−0.300905	+	0.0806272i	−0.406112	−	0.913823i	$-0.633116\pi$
$907$	−9.06218	+	2.42820i	−0.300905	+	0.0806272i	0.105208	+	0.994450i	$0.466449\pi$
$908$		0			0
$909$	−1.50000	+	0.401924i	−0.0497519	+	0.0133310i
$910$		0			0
$911$	4.13397	−	7.16025i	0.136965	−	0.237230i	−0.789382	−	0.613903i	$-0.789599\pi$
$911$	4.13397	−	7.16025i	0.136965	−	0.237230i	0.926346	+	0.376673i	$0.122932\pi$
$912$		0			0
$913$	14.1603	+	24.5263i	0.468636	+	0.811701i
$914$		0			0
$915$			7.39230i			0.244382i
$916$		0			0
$917$	15.9019	+	15.9019i	0.525128	+	0.525128i
$918$		0			0
$919$		−	36.5359i		−	1.20521i	−0.798040	−	0.602604i	$-0.794130\pi$
$919$		−	36.5359i		−	1.20521i	0.798040	−	0.602604i	$-0.205870\pi$
$920$		0			0
$921$	−13.7321	−	13.7321i	−0.452486	−	0.452486i
$922$		0			0
$923$	1.75129	−	6.53590i	0.0576444	−	0.215132i
$924$		0			0
$925$	−1.98076	−	7.39230i	−0.0651271	−	0.243057i
$926$		0			0
$927$	−41.3827	+	23.8923i	−1.35919	+	0.784726i
$928$		0			0
$929$	9.35641	−	16.2058i	0.306974	−	0.531694i	−0.670725	−	0.741706i	$-0.734017\pi$
$929$	9.35641	−	16.2058i	0.306974	−	0.531694i	0.977699	+	0.210012i	$0.0673503\pi$
$930$		0			0
$931$	52.9808	+	14.1962i	1.73637	+	0.465260i
$932$		0			0
$933$	9.18653	+	15.9115i	0.300754	+	0.520921i
$934$		0			0
$935$			14.9282i			0.488204i
$936$		0			0
$937$		−	19.0718i		−	0.623048i	−0.950238	−	0.311524i	$-0.899160\pi$
$937$		−	19.0718i		−	0.623048i	0.950238	−	0.311524i	$-0.100840\pi$
$938$		0			0
$939$	25.1603	−	43.5788i	0.821074	−	1.42214i
$940$		0			0
$941$	−34.0885	−	9.13397i	−1.11125	−	0.297759i	−0.343913	−	0.939001i	$-0.611753\pi$
$941$	−34.0885	−	9.13397i	−1.11125	−	0.297759i	−0.767338	+	0.641242i	$0.778419\pi$
$942$		0			0
$943$	2.59808	−	4.50000i	0.0846050	−	0.146540i
$944$		0			0
$945$	−31.6865	−	31.6865i	−1.03076	−	1.03076i
$946$		0			0
$947$	−10.9904	−	41.0167i	−0.357139	−	1.33286i	−0.877771	−	0.479081i	$-0.840970\pi$
$947$	−10.9904	−	41.0167i	−0.357139	−	1.33286i	0.520631	−	0.853782i	$-0.325697\pi$
$948$		0			0
$949$	4.46410	−	16.6603i	0.144911	−	0.540815i
$950$		0			0
$951$	−57.9449	+	15.5263i	−1.87899	+	0.503474i
$952$		0			0
$953$			32.5359i			1.05394i	0.849884	+	0.526971i	$0.176672\pi$
$953$			32.5359i			1.05394i	−0.849884	+	0.526971i	$0.823328\pi$
$954$		0			0
$955$	3.83013	+	3.83013i	0.123940	+	0.123940i
$956$		0			0
$957$	2.59808	−	1.50000i	0.0839839	−	0.0484881i
$958$		0			0
$959$	1.47372	+	2.55256i	0.0475889	+	0.0824264i
$960$		0			0
$961$	−26.7846	+	46.3923i	−0.864020	+	1.49653i
$962$		0			0
$963$	28.1769	+	28.1769i	0.907988	+	0.907988i
$964$		0			0
$965$	8.33013	−	2.23205i	0.268156	−	0.0718523i
$966$		0			0
$967$	−27.0622	+	15.6244i	−0.870261	+	0.502445i	−0.867435	−	0.497551i	$-0.834233\pi$
$967$	−27.0622	+	15.6244i	−0.870261	+	0.502445i	−0.00282602	+	0.999996i	$0.500900\pi$
$968$		0			0
$969$	20.7846	+	20.7846i	0.667698	+	0.667698i
$970$		0			0
$971$	23.9808	+	23.9808i	0.769579	+	0.769579i	0.978032	−	0.208453i	$-0.0668429\pi$
$971$	23.9808	+	23.9808i	0.769579	+	0.769579i	−0.208453	+	0.978032i	$0.566843\pi$
$972$		0			0
$973$	52.8109	−	52.8109i	1.69304	−	1.69304i
$974$		0			0
$975$	−3.58846	+	3.58846i	−0.114923	+	0.114923i
$976$		0			0
$977$	−24.2846	−	42.0622i	−0.776933	−	1.34569i	−0.933701	−	0.358053i	$-0.883441\pi$
$977$	−24.2846	−	42.0622i	−0.776933	−	1.34569i	0.156768	−	0.987635i	$-0.449893\pi$
$978$		0			0
$979$	7.92820	+	29.5885i	0.253386	+	0.945651i
$980$		0			0
$981$	5.19615	−	5.19615i	0.165900	−	0.165900i
$982$		0			0
$983$	−1.08142	−	0.624356i	−0.0344918	−	0.0199139i	0.482655	−	0.875811i	$-0.339673\pi$
$983$	−1.08142	−	0.624356i	−0.0344918	−	0.0199139i	−0.517147	+	0.855897i	$0.673006\pi$
$984$		0			0
$985$	8.36603	−	4.83013i	0.266564	−	0.153901i
$986$		0			0
$987$	4.62436	+	8.00962i	0.147195	+	0.254949i
$988$		0			0
$989$	29.9545	−	29.9545i	0.952497	−	0.952497i
$990$		0			0
$991$	44.3923			1.41017			0.705084	−	0.709124i	$-0.250909\pi$
$991$	44.3923			1.41017			0.705084	+	0.709124i	$0.250909\pi$
$992$		0			0
$993$	2.34936	+	8.76795i	0.0745548	+	0.278242i
$994$		0			0
$995$	−40.7846	−	10.9282i	−1.29296	−	0.346447i
$996$		0			0
$997$	3.96410	−	1.06218i	0.125544	−	0.0336395i	−0.195500	−	0.980704i	$-0.562633\pi$
$997$	3.96410	−	1.06218i	0.125544	−	0.0336395i	0.321044	+	0.947064i	$0.395966\pi$
$998$		0			0
$999$	−22.1769	+	22.1769i	−0.701647	+	0.701647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.b.241.1		4
3.2	odd	2		1728.2.bc.b.1585.1		4
4.3	odd	2		144.2.x.d.133.1	yes	4
9.4	even	3		576.2.bb.a.49.1		4
9.5	odd	6		1728.2.bc.c.1009.1		4
12.11	even	2		432.2.y.a.181.1		4
16.3	odd	4		144.2.x.a.61.1	✓	4
16.13	even	4		576.2.bb.a.529.1		4
36.23	even	6		432.2.y.d.37.1		4
36.31	odd	6		144.2.x.a.85.1	yes	4
48.29	odd	4		1728.2.bc.c.721.1		4
48.35	even	4		432.2.y.d.397.1		4
144.13	even	12	inner	576.2.bb.b.337.1		4
144.67	odd	12		144.2.x.d.13.1	yes	4
144.77	odd	12		1728.2.bc.b.145.1		4
144.131	even	12		432.2.y.a.253.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.a.61.1	✓	4	16.3	odd	4
144.2.x.a.85.1	yes	4	36.31	odd	6
144.2.x.d.13.1	yes	4	144.67	odd	12
144.2.x.d.133.1	yes	4	4.3	odd	2
432.2.y.a.181.1		4	12.11	even	2
432.2.y.a.253.1		4	144.131	even	12
432.2.y.d.37.1		4	36.23	even	6
432.2.y.d.397.1		4	48.35	even	4
576.2.bb.a.49.1		4	9.4	even	3
576.2.bb.a.529.1		4	16.13	even	4
576.2.bb.b.241.1		4	1.1	even	1	trivial
576.2.bb.b.337.1		4	144.13	even	12	inner
1728.2.bc.b.145.1		4	144.77	odd	12
1728.2.bc.b.1585.1		4	3.2	odd	2
1728.2.bc.c.721.1		4	48.29	odd	4
1728.2.bc.c.1009.1		4	9.5	odd	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{3} +(0.500000 - 1.86603i) q^{5} +(3.86603 + 2.23205i) q^{7} -3.00000 q^{9} +O(q^{10})\)	\(q+1.73205i q^{3} +(0.500000 - 1.86603i) q^{5} +(3.86603 + 2.23205i) q^{7} -3.00000 q^{9} +(-1.86603 + 0.500000i) q^{11} +(2.23205 + 0.598076i) q^{13} +(3.23205 + 0.866025i) q^{15} +4.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(-3.86603 + 6.69615i) q^{21} +(-5.59808 + 3.23205i) q^{23} +(1.09808 + 0.633975i) q^{25} -5.19615i q^{27} +(0.232051 + 0.866025i) q^{29} +(4.59808 + 7.96410i) q^{31} +(-0.866025 - 3.23205i) q^{33} +(6.09808 - 6.09808i) q^{35} +(-4.26795 - 4.26795i) q^{37} +(-1.03590 + 3.86603i) q^{39} +(-0.696152 + 0.401924i) q^{41} +(-6.33013 + 1.69615i) q^{43} +(-1.50000 + 5.59808i) q^{45} +(0.598076 - 1.03590i) q^{47} +(6.46410 + 11.1962i) q^{49} +6.92820i q^{51} +(5.73205 + 5.73205i) q^{53} +3.73205i q^{55} +(5.19615 + 5.19615i) q^{57} +(-0.401924 + 1.50000i) q^{59} +(0.571797 + 2.13397i) q^{61} +(-11.5981 - 6.69615i) q^{63} +(2.23205 - 3.86603i) q^{65} +(-8.33013 - 2.23205i) q^{67} +(-5.59808 - 9.69615i) q^{69} -2.92820i q^{71} -7.46410i q^{73} +(-1.09808 + 1.90192i) q^{75} +(-8.33013 - 2.23205i) q^{77} +(0.866025 - 1.50000i) q^{79} +9.00000 q^{81} +(-3.79423 - 14.1603i) q^{83} +(2.00000 - 7.46410i) q^{85} +(-1.50000 + 0.401924i) q^{87} -15.8564i q^{89} +(7.29423 + 7.29423i) q^{91} +(-13.7942 + 7.96410i) q^{93} +(-4.09808 - 7.09808i) q^{95} +(-0.500000 + 0.866025i) q^{97} +(5.59808 - 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} + 12 q^{7} - 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^5 + 12 * q^7 - 12 * q^9	\( 4 q + 2 q^{5} + 12 q^{7} - 12 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{15} + 16 q^{17} + 12 q^{19} - 12 q^{21} - 12 q^{23} - 6 q^{25} - 6 q^{29} + 8 q^{31} + 14 q^{35} - 24 q^{37} - 18 q^{39} + 18 q^{41} - 8 q^{43} - 6 q^{45} - 8 q^{47} + 12 q^{49} + 16 q^{53} - 12 q^{59} + 30 q^{61} - 36 q^{63} + 2 q^{65} - 16 q^{67} - 12 q^{69} + 6 q^{75} - 16 q^{77} + 36 q^{81} + 16 q^{83} + 8 q^{85} - 6 q^{87} - 2 q^{91} - 24 q^{93} - 6 q^{95} - 2 q^{97} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^5 + 12 * q^7 - 12 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^15 + 16 * q^17 + 12 * q^19 - 12 * q^21 - 12 * q^23 - 6 * q^25 - 6 * q^29 + 8 * q^31 + 14 * q^35 - 24 * q^37 - 18 * q^39 + 18 * q^41 - 8 * q^43 - 6 * q^45 - 8 * q^47 + 12 * q^49 + 16 * q^53 - 12 * q^59 + 30 * q^61 - 36 * q^63 + 2 * q^65 - 16 * q^67 - 12 * q^69 + 6 * q^75 - 16 * q^77 + 36 * q^81 + 16 * q^83 + 8 * q^85 - 6 * q^87 - 2 * q^91 - 24 * q^93 - 6 * q^95 - 2 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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