LMFDB - Embedded newform 1344.2.bl.j.1279.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(703,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("1344.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.bl (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1279.1
Root			$-1.33790 + 0.458297i$ of defining polynomial
Character	$\chi$	$=$	1344.1279
Dual form			1344.2.bl.j.703.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-2.12403 - 1.22631i) q^{5} +(2.63169 - 0.272415i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{3} +(-2.12403 - 1.22631i) q^{5} +(2.63169 - 0.272415i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.09586 - 0.632697i) q^{11} +2.99744i q^{13} -2.45262i q^{15} +(1.58759 - 0.916595i) q^{17} +(2.07993 - 3.60254i) q^{19} +(1.55176 + 2.14290i) q^{21} +(-5.83564 - 3.36921i) q^{23} +(0.507662 + 0.879296i) q^{25} -1.00000 q^{27} +9.42323 q^{29} +(4.71989 + 8.17509i) q^{31} +(1.09586 + 0.632697i) q^{33} +(-5.92385 - 2.64865i) q^{35} +(3.75572 - 6.50509i) q^{37} +(-2.59586 + 1.49872i) q^{39} +1.08966i q^{41} +6.27176i q^{43} +(2.12403 - 1.22631i) q^{45} +(3.67579 - 6.36666i) q^{47} +(6.85158 - 1.43382i) q^{49} +(1.58759 + 0.916595i) q^{51} +(-0.0358262 - 0.0620528i) q^{53} -3.10353 q^{55} +4.15985 q^{57} +(-1.68345 - 2.91583i) q^{59} +(9.61496 + 5.55120i) q^{61} +(-1.07993 + 2.41532i) q^{63} +(3.67579 - 6.36666i) q^{65} +(2.43151 - 1.40383i) q^{67} -6.73842i q^{69} -2.92285i q^{71} +(7.01910 - 4.05248i) q^{73} +(-0.507662 + 0.879296i) q^{75} +(2.71162 - 1.96359i) q^{77} +(-1.54471 - 0.891841i) q^{79} +(-0.500000 - 0.866025i) q^{81} +5.33626 q^{83} -4.49611 q^{85} +(4.71162 + 8.16076i) q^{87} +(7.42323 + 4.28581i) q^{89} +(0.816548 + 7.88834i) q^{91} +(-4.71989 + 8.17509i) q^{93} +(-8.83564 + 5.10126i) q^{95} +7.10394i q^{97} +1.26539i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} + 2 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 + 2 * q^7 - 4 * q^9	$ 8 q + 4 q^{3} + 2 q^{7} - 4 q^{9} - 6 q^{11} + 6 q^{19} + 4 q^{21} + 2 q^{25} - 8 q^{27} + 16 q^{29} + 6 q^{31} - 6 q^{33} + 12 q^{35} - 6 q^{37} - 6 q^{39} + 4 q^{47} + 4 q^{49} + 4 q^{53} - 8 q^{55} + 12 q^{57} + 14 q^{59} - 12 q^{61} + 2 q^{63} + 4 q^{65} - 42 q^{67} - 18 q^{73} - 2 q^{75} - 8 q^{77} - 6 q^{79} - 4 q^{81} - 4 q^{83} + 32 q^{85} + 8 q^{87} + 34 q^{91} - 6 q^{93} - 24 q^{95}+O(q^{100}) $ 8 * q + 4 * q^3 + 2 * q^7 - 4 * q^9 - 6 * q^11 + 6 * q^19 + 4 * q^21 + 2 * q^25 - 8 * q^27 + 16 * q^29 + 6 * q^31 - 6 * q^33 + 12 * q^35 - 6 * q^37 - 6 * q^39 + 4 * q^47 + 4 * q^49 + 4 * q^53 - 8 * q^55 + 12 * q^57 + 14 * q^59 - 12 * q^61 + 2 * q^63 + 4 * q^65 - 42 * q^67 - 18 * q^73 - 2 * q^75 - 8 * q^77 - 6 * q^79 - 4 * q^81 - 4 * q^83 + 32 * q^85 + 8 * q^87 + 34 * q^91 - 6 * q^93 - 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$	−2.12403	−	1.22631i	−0.949894	−	0.548422i	−0.0568460	−	0.998383i	$-0.518104\pi$
$5$	−2.12403	−	1.22631i	−0.949894	−	0.548422i	−0.893048	+	0.449961i	$0.851438\pi$
$6$		0			0
$7$	2.63169	−	0.272415i	0.994685	−	0.102963i
$7$	2.63169	−	0.272415i	0.994685	−	0.102963i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.09586	−	0.632697i	0.330415	−	0.190765i	−0.325610	−	0.945504i	$-0.605570\pi$
$11$	1.09586	−	0.632697i	0.330415	−	0.190765i	0.656025	+	0.754739i	$0.272236\pi$
$12$		0			0
$13$			2.99744i			0.831342i	0.909515	+	0.415671i	$0.136453\pi$
$13$			2.99744i			0.831342i	−0.909515	+	0.415671i	$0.863547\pi$
$14$		0			0
$15$		−	2.45262i		−	0.633263i
$16$		0			0
$17$	1.58759	−	0.916595i	0.385047	−	0.222307i	−0.294965	−	0.955508i	$-0.595308\pi$
$17$	1.58759	−	0.916595i	0.385047	−	0.222307i	0.680012	+	0.733201i	$0.261975\pi$
$18$		0			0
$19$	2.07993	−	3.60254i	0.477168	−	0.826479i	−0.522490	−	0.852646i	$-0.674997\pi$
$19$	2.07993	−	3.60254i	0.477168	−	0.826479i	0.999658	+	0.0261665i	$0.00833000\pi$
$20$		0			0
$21$	1.55176	+	2.14290i	0.338622	+	0.467620i
$22$		0			0
$23$	−5.83564	−	3.36921i	−1.21682	−	0.702529i	−0.252580	−	0.967576i	$-0.581279\pi$
$23$	−5.83564	−	3.36921i	−1.21682	−	0.702529i	−0.964236	+	0.265047i	$0.914613\pi$
$24$		0			0
$25$	0.507662	+	0.879296i	0.101532	+	0.175859i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	9.42323			1.74985			0.874925	−	0.484258i	$-0.160910\pi$
$29$	9.42323			1.74985			0.874925	+	0.484258i	$0.160910\pi$
$30$		0			0
$31$	4.71989	+	8.17509i	0.847717	+	1.46829i	0.883240	+	0.468921i	$0.155357\pi$
$31$	4.71989	+	8.17509i	0.847717	+	1.46829i	−0.0355228	+	0.999369i	$0.511310\pi$
$32$		0			0
$33$	1.09586	+	0.632697i	0.190765	+	0.110138i
$34$		0			0
$35$	−5.92385	−	2.64865i	−1.00131	−	0.447703i
$36$		0			0
$37$	3.75572	−	6.50509i	0.617436	−	1.06943i	−0.372516	−	0.928026i	$-0.621505\pi$
$37$	3.75572	−	6.50509i	0.617436	−	1.06943i	0.989952	−	0.141405i	$-0.0451619\pi$
$38$		0			0
$39$	−2.59586	+	1.49872i	−0.415671	+	0.239988i
$40$		0			0
$41$			1.08966i			0.170176i	0.996373	+	0.0850880i	$0.0271171\pi$
$41$			1.08966i			0.170176i	−0.996373	+	0.0850880i	$0.972883\pi$
$42$		0			0
$43$			6.27176i			0.956435i	0.878241	+	0.478218i	$0.158717\pi$
$43$			6.27176i			0.956435i	−0.878241	+	0.478218i	$0.841283\pi$
$44$		0			0
$45$	2.12403	−	1.22631i	0.316631	−	0.182807i
$46$		0			0
$47$	3.67579	−	6.36666i	0.536169	−	0.928672i	−0.462937	−	0.886391i	$-0.653204\pi$
$47$	3.67579	−	6.36666i	0.536169	−	0.928672i	0.999106	−	0.0422808i	$-0.0134624\pi$
$48$		0			0
$49$	6.85158	−	1.43382i	0.978797	−	0.204832i
$50$		0			0
$51$	1.58759	+	0.916595i	0.222307	+	0.128349i
$52$		0			0
$53$	−0.0358262	−	0.0620528i	−0.00492111	−	0.00852361i	0.863554	−	0.504256i	$-0.168233\pi$
$53$	−0.0358262	−	0.0620528i	−0.00492111	−	0.00852361i	−0.868475	+	0.495732i	$0.834900\pi$
$54$		0			0
$55$	−3.10353			−0.418479
$56$		0			0
$57$	4.15985			0.550986
$58$		0			0
$59$	−1.68345	−	2.91583i	−0.219167	−	0.379608i	0.735387	−	0.677648i	$-0.237001\pi$
$59$	−1.68345	−	2.91583i	−0.219167	−	0.379608i	−0.954553	+	0.298040i	$0.903667\pi$
$60$		0			0
$61$	9.61496	+	5.55120i	1.23107	+	0.710758i	0.967253	−	0.253815i	$-0.0816853\pi$
$61$	9.61496	+	5.55120i	1.23107	+	0.710758i	0.263817	+	0.964573i	$0.415019\pi$
$62$		0			0
$63$	−1.07993	+	2.41532i	−0.136058	+	0.304301i
$64$		0			0
$65$	3.67579	−	6.36666i	0.455926	−	0.789686i
$66$		0			0
$67$	2.43151	−	1.40383i	0.297056	−	0.171505i	−0.344064	−	0.938946i	$-0.611804\pi$
$67$	2.43151	−	1.40383i	0.297056	−	0.171505i	0.641120	+	0.767441i	$0.278470\pi$
$68$		0			0
$69$		−	6.73842i		−	0.811211i
$70$		0			0
$71$		−	2.92285i		−	0.346878i	−0.984845	−	0.173439i	$-0.944512\pi$
$71$		−	2.92285i		−	0.346878i	0.984845	−	0.173439i	$-0.0554880\pi$
$72$		0			0
$73$	7.01910	−	4.05248i	0.821523	−	0.474307i	−0.0294183	−	0.999567i	$-0.509365\pi$
$73$	7.01910	−	4.05248i	0.821523	−	0.474307i	0.850941	+	0.525261i	$0.176032\pi$
$74$		0			0
$75$	−0.507662	+	0.879296i	−0.0586198	+	0.101532i
$76$		0			0
$77$	2.71162	−	1.96359i	0.309017	−	0.223772i
$78$		0			0
$79$	−1.54471	−	0.891841i	−0.173794	−	0.100340i	0.410580	−	0.911825i	$-0.365326\pi$
$79$	−1.54471	−	0.891841i	−0.173794	−	0.100340i	−0.584374	+	0.811485i	$0.698660\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	5.33626			0.585730			0.292865	−	0.956154i	$-0.405391\pi$
$83$	5.33626			0.585730			0.292865	+	0.956154i	$0.405391\pi$
$84$		0			0
$85$	−4.49611			−0.487672
$86$		0			0
$87$	4.71162	+	8.16076i	0.505138	+	0.874925i
$88$		0			0
$89$	7.42323	+	4.28581i	0.786861	+	0.454294i	0.838856	−	0.544353i	$-0.183225\pi$
$89$	7.42323	+	4.28581i	0.786861	+	0.454294i	−0.0519952	+	0.998647i	$0.516558\pi$
$90$		0			0
$91$	0.816548	+	7.88834i	0.0855974	+	0.826923i
$92$		0			0
$93$	−4.71989	+	8.17509i	−0.489430	+	0.847717i
$94$		0			0
$95$	−8.83564	+	5.10126i	−0.906518	+	0.523378i
$96$		0			0
$97$			7.10394i			0.721296i	0.932702	+	0.360648i	$0.117444\pi$
$97$			7.10394i			0.721296i	−0.932702	+	0.360648i	$0.882556\pi$
$98$		0			0
$99$			1.26539i			0.127177i
$100$		0			0
$101$	−0.808273	+	0.466657i	−0.0804262	+	0.0464341i	−0.539674	−	0.841874i	$-0.681452\pi$
$101$	−0.808273	+	0.466657i	−0.0804262	+	0.0464341i	0.459248	+	0.888308i	$0.348119\pi$
$102$		0			0
$103$	2.06460	−	3.57600i	0.203431	−	0.352353i	−0.746200	−	0.665721i	$-0.768124\pi$
$103$	2.06460	−	3.57600i	0.203431	−	0.352353i	0.949632	+	0.313368i	$0.101457\pi$
$104$		0			0
$105$	−0.668128	−	6.45452i	−0.0652026	−	0.629897i
$106$		0			0
$107$	−11.9878	−	6.92118i	−1.15891	−	0.669096i	−0.207866	−	0.978157i	$-0.566652\pi$
$107$	−11.9878	−	6.92118i	−1.15891	−	0.669096i	−0.951042	+	0.309062i	$0.899985\pi$
$108$		0			0
$109$	−0.492338	−	0.852754i	−0.0471574	−	0.0816791i	0.841483	−	0.540283i	$-0.181683\pi$
$109$	−0.492338	−	0.852754i	−0.0471574	−	0.0816791i	−0.888641	+	0.458604i	$0.848350\pi$
$110$		0			0
$111$	7.51143			0.712954
$112$		0			0
$113$	5.03187			0.473359			0.236679	−	0.971588i	$-0.423941\pi$
$113$	5.03187			0.473359			0.236679	+	0.971588i	$0.423941\pi$
$114$		0			0
$115$	8.26338	+	14.3126i	0.770564	+	1.33466i
$116$		0			0
$117$	−2.59586	−	1.49872i	−0.239988	−	0.138557i
$118$		0			0
$119$	3.92835	−	2.84468i	0.360111	−	0.260771i
$120$		0			0
$121$	−4.69939	+	8.13958i	−0.427217	+	0.739962i
$122$		0			0
$123$	−0.943672	+	0.544829i	−0.0850880	+	0.0491256i
$124$		0			0
$125$			9.77288i			0.874113i
$126$		0			0
$127$		−	6.38337i		−	0.566433i	−0.959056	−	0.283216i	$-0.908599\pi$
$127$		−	6.38337i		−	0.566433i	0.959056	−	0.283216i	$-0.0914015\pi$
$128$		0			0
$129$	−5.43151	+	3.13588i	−0.478218	+	0.276099i
$130$		0			0
$131$	1.93601	−	3.35327i	0.169150	−	0.292976i	−0.768971	−	0.639283i	$-0.779231\pi$
$131$	1.93601	−	3.35327i	0.169150	−	0.292976i	0.938121	+	0.346307i	$0.112564\pi$
$132$		0			0
$133$	4.49234	−	10.0474i	0.389535	−	0.871217i
$134$		0			0
$135$	2.12403	+	1.22631i	0.182807	+	0.105544i
$136$		0			0
$137$	7.35158	+	12.7333i	0.628088	+	1.08788i	0.987935	+	0.154869i	$0.0494955\pi$
$137$	7.35158	+	12.7333i	0.628088	+	1.08788i	−0.359847	+	0.933011i	$0.617171\pi$
$138$		0			0
$139$	−2.01655			−0.171041			−0.0855207	−	0.996336i	$-0.527255\pi$
$139$	−2.01655			−0.171041			−0.0855207	+	0.996336i	$0.527255\pi$
$140$		0			0
$141$	7.35158			0.619115
$142$		0			0
$143$	1.89647	+	3.28479i	0.158591	+	0.274688i
$144$		0			0
$145$	−20.0152	−	11.5558i	−1.66217	−	0.959656i
$146$		0			0
$147$	4.66752	+	5.21673i	0.384970	+	0.430269i
$148$		0			0
$149$	−0.248055	+	0.429644i	−0.0203215	+	0.0351978i	−0.876007	−	0.482298i	$-0.839802\pi$
$149$	−0.248055	+	0.429644i	−0.0203215	+	0.0351978i	0.855686	+	0.517496i	$0.173136\pi$
$150$		0			0
$151$	−11.4636	+	6.61849i	−0.932891	+	0.538605i	−0.887725	−	0.460374i	$-0.847715\pi$
$151$	−11.4636	+	6.61849i	−0.932891	+	0.538605i	−0.0451665	+	0.998979i	$0.514382\pi$
$152$		0			0
$153$			1.83319i			0.148205i
$154$		0			0
$155$		−	23.1522i		−	1.85963i
$156$		0			0
$157$	−4.38345	+	2.53079i	−0.349838	+	0.201979i	−0.664614	−	0.747187i	$-0.731404\pi$
$157$	−4.38345	+	2.53079i	−0.349838	+	0.201979i	0.314776	+	0.949166i	$0.398071\pi$
$158$		0			0
$159$	0.0358262	−	0.0620528i	0.00284120	−	0.00492111i
$160$		0			0
$161$	−16.2754	−	7.27700i	−1.28268	−	0.573508i
$162$		0			0
$163$	−10.4232	−	6.01786i	−0.816411	−	0.471355i	0.0327665	−	0.999463i	$-0.489568\pi$
$163$	−10.4232	−	6.01786i	−0.816411	−	0.471355i	−0.849177	+	0.528108i	$0.822902\pi$
$164$		0			0
$165$	−1.55176	−	2.68773i	−0.120805	−	0.209240i
$166$		0			0
$167$	−7.46424			−0.577600			−0.288800	−	0.957389i	$-0.593256\pi$
$167$	−7.46424			−0.577600			−0.288800	+	0.957389i	$0.593256\pi$
$168$		0			0
$169$	4.01532			0.308871
$170$		0			0
$171$	2.07993	+	3.60254i	0.159056	+	0.275493i
$172$		0			0
$173$	−3.77932	−	2.18199i	−0.287336	−	0.165894i	0.349404	−	0.936972i	$-0.386384\pi$
$173$	−3.77932	−	2.18199i	−0.287336	−	0.165894i	−0.636740	+	0.771079i	$0.719717\pi$
$174$		0			0
$175$	1.57554	+	2.17574i	0.119100	+	0.164471i
$176$		0			0
$177$	1.68345	−	2.91583i	0.126536	−	0.219167i
$178$		0			0
$179$	−21.2754	+	12.2834i	−1.59020	+	0.918102i	−0.596928	+	0.802295i	$0.703612\pi$
$179$	−21.2754	+	12.2834i	−1.59020	+	0.918102i	−0.993272	+	0.115808i	$0.963054\pi$
$180$		0			0
$181$			11.7182i			0.871011i	0.900186	+	0.435505i	$0.143430\pi$
$181$			11.7182i			0.871011i	−0.900186	+	0.435505i	$0.856570\pi$
$182$		0			0
$183$			11.1024i			0.820713i
$184$		0			0
$185$	−15.9545	+	9.21133i	−1.17300	+	0.677231i
$186$		0			0
$187$	1.15985	−	2.00893i	0.0848169	−	0.146907i
$188$		0			0
$189$	−2.63169	+	0.272415i	−0.191427	+	0.0198152i
$190$		0			0
$191$	−13.7628	−	7.94594i	−0.995839	−	0.574948i	−0.0888244	−	0.996047i	$-0.528311\pi$
$191$	−13.7628	−	7.94594i	−0.995839	−	0.574948i	−0.907014	+	0.421099i	$0.861644\pi$
$192$		0			0
$193$	−9.86690	−	17.0900i	−0.710235	−	1.23016i	−0.964769	−	0.263100i	$-0.915255\pi$
$193$	−9.86690	−	17.0900i	−0.710235	−	1.23016i	0.254533	−	0.967064i	$-0.418078\pi$
$194$		0			0
$195$	7.35158			0.526458
$196$		0			0
$197$	−0.998775			−0.0711598			−0.0355799	−	0.999367i	$-0.511328\pi$
$197$	−0.998775			−0.0711598			−0.0355799	+	0.999367i	$0.511328\pi$
$198$		0			0
$199$	−1.35158	−	2.34101i	−0.0958110	−	0.165950i	0.814136	−	0.580675i	$-0.197211\pi$
$199$	−1.35158	−	2.34101i	−0.0958110	−	0.165950i	−0.909947	+	0.414725i	$0.863878\pi$
$200$		0			0
$201$	2.43151	+	1.40383i	0.171505	+	0.0990186i
$202$		0			0
$203$	24.7990	−	2.56703i	1.74055	−	0.180170i
$204$		0			0
$205$	1.33626	−	2.31446i	0.0933282	−	0.161649i
$206$		0			0
$207$	5.83564	−	3.36921i	0.405605	−	0.234176i
$208$		0			0
$209$		−	5.26385i		−	0.364108i
$210$		0			0
$211$		−	18.1798i		−	1.25155i	−0.780004	−	0.625774i	$-0.784783\pi$
$211$		−	18.1798i		−	1.25155i	0.780004	−	0.625774i	$-0.215217\pi$
$212$		0			0
$213$	2.53126	−	1.46142i	0.173439	−	0.100135i
$214$		0			0
$215$	7.69111	−	13.3214i	0.524530	−	0.908512i
$216$		0			0
$217$	14.6483	+	20.2285i	0.994392	+	1.37320i
$218$		0			0
$219$	7.01910	+	4.05248i	0.474307	+	0.273841i
$220$		0			0
$221$	2.74744	+	4.75871i	0.184813	+	0.320106i
$222$		0			0
$223$	11.5996			0.776769			0.388385	−	0.921497i	$-0.373033\pi$
$223$	11.5996			0.776769			0.388385	+	0.921497i	$0.373033\pi$
$224$		0			0
$225$	−1.01532			−0.0676883
$226$		0			0
$227$	5.08054	+	8.79975i	0.337207	+	0.584060i	0.983906	−	0.178685i	$-0.0571844\pi$
$227$	5.08054	+	8.79975i	0.337207	+	0.584060i	−0.646699	+	0.762745i	$0.723851\pi$
$228$		0			0
$229$	−20.0025	−	11.5485i	−1.32181	−	0.763145i	−0.337789	−	0.941222i	$-0.609679\pi$
$229$	−20.0025	−	11.5485i	−1.32181	−	0.763145i	−0.984017	+	0.178077i	$0.943012\pi$
$230$		0			0
$231$	3.05633	+	1.36653i	0.201092	+	0.0899113i
$232$		0			0
$233$	3.42774	−	5.93701i	0.224558	−	0.388947i	−0.731628	−	0.681704i	$-0.761239\pi$
$233$	3.42774	−	5.93701i	0.224558	−	0.388947i	0.956187	+	0.292757i	$0.0945727\pi$
$234$		0			0
$235$	−15.6150	+	9.01530i	−1.01861	+	0.588093i
$236$		0			0
$237$		−	1.78368i		−	0.115863i
$238$		0			0
$239$		−	22.2257i		−	1.43766i	−0.695184	−	0.718832i	$-0.744677\pi$
$239$		−	22.2257i		−	1.43766i	0.695184	−	0.718832i	$-0.255323\pi$
$240$		0			0
$241$	13.3605	−	7.71367i	0.860623	−	0.496881i	−0.00359762	−	0.999994i	$-0.501145\pi$
$241$	13.3605	−	7.71367i	0.860623	−	0.496881i	0.864221	+	0.503112i	$0.167812\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−16.3113	−	5.35667i	−1.04209	−	0.342225i
$246$		0			0
$247$	10.7984	+	6.23447i	0.687087	+	0.396690i
$248$		0			0
$249$	2.66813	+	4.62133i	0.169086	+	0.292865i
$250$		0			0
$251$	−22.2954			−1.40727			−0.703636	−	0.710561i	$-0.748441\pi$
$251$	−22.2954			−1.40727			−0.703636	+	0.710561i	$0.748441\pi$
$252$		0			0
$253$	−8.52676			−0.536073
$254$		0			0
$255$	−2.24806	−	3.89375i	−0.140779	−	0.243836i
$256$		0			0
$257$	2.48529	+	1.43488i	0.155028	+	0.0895055i	0.575507	−	0.817797i	$-0.304805\pi$
$257$	2.48529	+	1.43488i	0.155028	+	0.0895055i	−0.420479	+	0.907302i	$0.638138\pi$
$258$		0			0
$259$	8.11180	−	18.1425i	0.504043	−	1.12732i
$260$		0			0
$261$	−4.71162	+	8.16076i	−0.291642	+	0.505138i
$262$		0			0
$263$	8.98186	−	5.18568i	0.553845	−	0.319763i	−0.196826	−	0.980438i	$-0.563063\pi$
$263$	8.98186	−	5.18568i	0.553845	−	0.319763i	0.750672	+	0.660676i	$0.229730\pi$
$264$		0			0
$265$			0.175736i			0.0107954i
$266$		0			0
$267$			8.57161i			0.524574i
$268$		0			0
$269$	−4.48011	+	2.58659i	−0.273157	+	0.157707i	−0.630322	−	0.776334i	$-0.717077\pi$
$269$	−4.48011	+	2.58659i	−0.273157	+	0.157707i	0.357164	+	0.934042i	$0.383744\pi$
$270$		0			0
$271$	−12.1195	+	20.9916i	−0.736209	+	1.27515i	0.217982	+	0.975953i	$0.430053\pi$
$271$	−12.1195	+	20.9916i	−0.736209	+	1.27515i	−0.954191	+	0.299198i	$0.903281\pi$
$272$		0			0
$273$	−6.42323	+	4.65132i	−0.388752	+	0.281511i
$274$		0			0
$275$	1.11266	+	0.642393i	0.0670957	+	0.0387377i
$276$		0			0
$277$	−1.50766	−	2.61135i	−0.0905866	−	0.156901i	0.817171	−	0.576395i	$-0.195541\pi$
$277$	−1.50766	−	2.61135i	−0.0905866	−	0.156901i	−0.907758	+	0.419494i	$0.862208\pi$
$278$		0			0
$279$	−9.43978			−0.565145
$280$		0			0
$281$	−6.91922			−0.412766			−0.206383	−	0.978471i	$-0.566169\pi$
$281$	−6.91922			−0.412766			−0.206383	+	0.978471i	$0.566169\pi$
$282$		0			0
$283$	10.2870	+	17.8176i	0.611497	+	1.05914i	0.990988	+	0.133949i	$0.0427658\pi$
$283$	10.2870	+	17.8176i	0.611497	+	1.05914i	−0.379491	+	0.925195i	$0.623901\pi$
$284$		0			0
$285$	−8.83564	−	5.10126i	−0.523378	−	0.302173i
$286$		0			0
$287$	0.296839	+	2.86764i	0.0175218	+	0.169272i
$288$		0			0
$289$	−6.81971	+	11.8121i	−0.401159	+	0.694828i
$290$		0			0
$291$	−6.15219	+	3.55197i	−0.360648	+	0.208220i
$292$		0			0
$293$		−	28.3113i		−	1.65396i	−0.562229	−	0.826982i	$-0.690056\pi$
$293$		−	28.3113i		−	1.65396i	0.562229	−	0.826982i	$-0.309944\pi$
$294$		0			0
$295$			8.25772i			0.480783i
$296$		0			0
$297$	−1.09586	+	0.632697i	−0.0635884	+	0.0367128i
$298$		0			0
$299$	10.0990	−	17.4920i	0.584042	−	1.01159i
$300$		0			0
$301$	1.70852	+	16.5053i	0.0984775	+	0.951352i
$302$		0			0
$303$	−0.808273	−	0.466657i	−0.0464341	−	0.0268087i
$304$		0			0
$305$	−13.6150	−	23.5818i	−0.779590	−	1.35029i
$306$		0			0
$307$	8.65596			0.494022			0.247011	−	0.969013i	$-0.420552\pi$
$307$	8.65596			0.494022			0.247011	+	0.969013i	$0.420552\pi$
$308$		0			0
$309$	4.12921			0.234902
$310$		0			0
$311$	−4.67129	−	8.09091i	−0.264884	−	0.458793i	0.702649	−	0.711537i	$-0.252000\pi$
$311$	−4.67129	−	8.09091i	−0.264884	−	0.458793i	−0.967533	+	0.252743i	$0.918667\pi$
$312$		0			0
$313$	−6.38734	−	3.68773i	−0.361034	−	0.208443i	0.308500	−	0.951224i	$-0.400173\pi$
$313$	−6.38734	−	3.68773i	−0.361034	−	0.208443i	−0.669534	+	0.742781i	$0.733506\pi$
$314$		0			0
$315$	5.25572	−	3.80588i	0.296126	−	0.214437i
$316$		0			0
$317$	−1.81514	+	3.14392i	−0.101949	+	0.176580i	−0.912487	−	0.409105i	$-0.865841\pi$
$317$	−1.81514	+	3.14392i	−0.101949	+	0.176580i	0.810539	+	0.585685i	$0.199174\pi$
$318$		0			0
$319$	10.3266	−	5.96205i	0.578177	−	0.333811i
$320$		0			0
$321$		−	13.8424i		−	0.772605i
$322$		0			0
$323$		−	7.62580i		−	0.424311i
$324$		0			0
$325$	−2.63564	+	1.52169i	−0.146199	+	0.0844081i
$326$		0			0
$327$	0.492338	−	0.852754i	0.0272264	−	0.0471574i
$328$		0			0
$329$	7.93917	−	17.7564i	0.437701	−	0.978942i
$330$		0			0
$331$	0.544164	+	0.314173i	0.0299100	+	0.0172685i	0.514880	−	0.857262i	$-0.327836\pi$
$331$	0.544164	+	0.314173i	0.0299100	+	0.0172685i	−0.484970	+	0.874531i	$0.661170\pi$
$332$		0			0
$333$	3.75572	+	6.50509i	0.205812	+	0.356477i
$334$		0			0
$335$	−6.88612			−0.376229
$336$		0			0
$337$	−22.3119			−1.21541			−0.607704	−	0.794164i	$-0.707909\pi$
$337$	−22.3119			−1.21541			−0.607704	+	0.794164i	$0.707909\pi$
$338$		0			0
$339$	2.51594	+	4.35773i	0.136647	+	0.236679i
$340$		0			0
$341$	10.3447	+	5.97252i	0.560198	+	0.323430i
$342$		0			0
$343$	17.6406	−	5.63984i	0.952505	−	0.304523i
$344$		0			0
$345$	−8.26338	+	14.3126i	−0.444885	+	0.770564i
$346$		0			0
$347$	5.97104	−	3.44738i	0.320542	−	0.185065i	−0.331092	−	0.943598i	$-0.607417\pi$
$347$	5.97104	−	3.44738i	0.320542	−	0.185065i	0.651634	+	0.758533i	$0.274084\pi$
$348$		0			0
$349$			13.4768i			0.721399i	0.932682	+	0.360699i	$0.117462\pi$
$349$			13.4768i			0.721399i	−0.932682	+	0.360699i	$0.882538\pi$
$350$		0			0
$351$		−	2.99744i		−	0.159992i
$352$		0			0
$353$	−24.7550	+	14.2923i	−1.31758	+	0.760702i	−0.983338	−	0.181787i	$-0.941812\pi$
$353$	−24.7550	+	14.2923i	−1.31758	+	0.760702i	−0.334237	+	0.942489i	$0.608479\pi$
$354$		0			0
$355$	−3.58431	+	6.20821i	−0.190236	+	0.329498i
$356$		0			0
$357$	4.42774	+	1.97971i	0.234341	+	0.104777i
$358$		0			0
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	0.649906	−	0.760014i	$-0.274808\pi$
$359$	6.00000	+	3.46410i	0.316668	+	0.182828i	−0.333238	+	0.942843i	$0.608141\pi$
$360$		0			0
$361$	0.847808	+	1.46845i	0.0446215	+	0.0772867i
$362$		0			0
$363$	−9.39878			−0.493308
$364$		0			0
$365$	−19.8783			−1.04048
$366$		0			0
$367$	6.47184	+	11.2095i	0.337827	+	0.585134i	0.984024	−	0.178037i	$-0.0569748\pi$
$367$	6.47184	+	11.2095i	0.337827	+	0.585134i	−0.646197	+	0.763171i	$0.723641\pi$
$368$		0			0
$369$	−0.943672	−	0.544829i	−0.0491256	−	0.0283627i
$370$		0			0
$371$	−0.111188	−	0.153544i	−0.00577257	−	0.00797162i
$372$		0			0
$373$	1.53954	−	2.66655i	0.0797141	−	0.138069i	−0.823412	−	0.567443i	$-0.807933\pi$
$373$	1.53954	−	2.66655i	0.0797141	−	0.138069i	0.903127	+	0.429374i	$0.141266\pi$
$374$		0			0
$375$	−8.46356	+	4.88644i	−0.437056	+	0.252335i
$376$		0			0
$377$			28.2456i			1.45472i
$378$		0			0
$379$		−	5.21020i		−	0.267630i	−0.991006	−	0.133815i	$-0.957277\pi$
$379$		−	5.21020i		−	0.267630i	0.991006	−	0.133815i	$-0.0427228\pi$
$380$		0			0
$381$	5.52816	−	3.19169i	0.283216	−	0.163515i
$382$		0			0
$383$	−19.4353	+	33.6629i	−0.993096	+	1.72009i	−0.394963	+	0.918697i	$0.629242\pi$
$383$	−19.4353	+	33.6629i	−0.993096	+	1.72009i	−0.598134	+	0.801396i	$0.704091\pi$
$384$		0			0
$385$	−8.16752	+	0.845446i	−0.416255	+	0.0430879i
$386$		0			0
$387$	−5.43151	−	3.13588i	−0.276099	−	0.159406i
$388$		0			0
$389$	−1.86752	−	3.23463i	−0.0946869	−	0.164002i	0.814791	−	0.579755i	$-0.196852\pi$
$389$	−1.86752	−	3.23463i	−0.0946869	−	0.164002i	−0.909478	+	0.415752i	$0.863518\pi$
$390$		0			0
$391$	−12.3528			−0.624708
$392$		0			0
$393$	3.87202			0.195318
$394$		0			0
$395$	2.18734	+	3.78859i	0.110057	+	0.190625i
$396$		0			0
$397$	5.81082	+	3.35488i	0.291637	+	0.168377i	0.638680	−	0.769473i	$-0.279481\pi$
$397$	5.81082	+	3.35488i	0.291637	+	0.168377i	−0.347043	+	0.937849i	$0.612814\pi$
$398$		0			0
$399$	10.9474	−	1.13320i	0.548058	−	0.0567312i
$400$		0			0
$401$	−2.92385	+	5.06425i	−0.146010	+	0.252897i	−0.929749	−	0.368193i	$-0.879976\pi$
$401$	−2.92385	+	5.06425i	−0.146010	+	0.252897i	0.783739	+	0.621090i	$0.213310\pi$
$402$		0			0
$403$	−24.5044	+	14.1476i	−1.22065	+	0.704743i
$404$		0			0
$405$			2.45262i			0.121871i
$406$		0			0
$407$		−	9.50492i		−	0.471142i
$408$		0			0
$409$	−26.7299	+	15.4325i	−1.32171	+	0.763089i	−0.984001	−	0.178162i	$-0.942985\pi$
$409$	−26.7299	+	15.4325i	−1.32171	+	0.763089i	−0.337708	+	0.941251i	$0.609652\pi$
$410$		0			0
$411$	−7.35158	+	12.7333i	−0.362627	+	0.628088i
$412$		0			0
$413$	−5.22464	−	7.21495i	−0.257088	−	0.355024i
$414$		0			0
$415$	−11.3344	−	6.54389i	−0.556382	−	0.321227i
$416$		0			0
$417$	−1.00827	−	1.74638i	−0.0493754	−	0.0855207i
$418$		0			0
$419$	−29.0866			−1.42097			−0.710487	−	0.703710i	$-0.751525\pi$
$419$	−29.0866			−1.42097			−0.710487	+	0.703710i	$0.751525\pi$
$420$		0			0
$421$	−13.8642			−0.675702			−0.337851	−	0.941200i	$-0.609700\pi$
$421$	−13.8642			−0.675702			−0.337851	+	0.941200i	$0.609700\pi$
$422$		0			0
$423$	3.67579	+	6.36666i	0.178723	+	0.309557i
$424$		0			0
$425$	1.61192	+	0.930641i	0.0781895	+	0.0451427i
$426$		0			0
$427$	26.8158	+	11.9898i	1.29771	+	0.580226i
$428$		0			0
$429$	−1.89647	+	3.28479i	−0.0915627	+	0.158591i
$430$		0			0
$431$	−27.6258	+	15.9498i	−1.33069	+	0.768273i	−0.985405	−	0.170226i	$-0.945550\pi$
$431$	−27.6258	+	15.9498i	−1.33069	+	0.768273i	−0.345282	+	0.938499i	$0.612217\pi$
$432$		0			0
$433$		−	9.82239i		−	0.472034i	−0.971749	−	0.236017i	$-0.924158\pi$
$433$		−	9.82239i		−	0.472034i	0.971749	−	0.236017i	$-0.0758421\pi$
$434$		0			0
$435$		−	23.1116i		−	1.10811i
$436$		0			0
$437$	−24.2754	+	14.0154i	−1.16125	+	0.670449i
$438$		0			0
$439$	8.51989	−	14.7569i	0.406632	−	0.704308i	−0.587878	−	0.808950i	$-0.700036\pi$
$439$	8.51989	−	14.7569i	0.406632	−	0.704308i	0.994510	+	0.104642i	$0.0333697\pi$
$440$		0			0
$441$	−2.18406	+	6.65055i	−0.104003	+	0.316693i
$442$		0			0
$443$	−7.30000	−	4.21466i	−0.346833	−	0.200244i	0.316456	−	0.948607i	$-0.397507\pi$
$443$	−7.30000	−	4.21466i	−0.346833	−	0.200244i	−0.663290	+	0.748363i	$0.730840\pi$
$444$		0			0
$445$	−10.5114	−	18.2063i	−0.498290	−	0.863063i
$446$		0			0
$447$	−0.496110			−0.0234652
$448$		0			0
$449$	9.64064			0.454970			0.227485	−	0.973782i	$-0.426950\pi$
$449$	9.64064			0.454970			0.227485	+	0.973782i	$0.426950\pi$
$450$		0			0
$451$	0.689424	+	1.19412i	0.0324637	+	0.0562288i
$452$		0			0
$453$	−11.4636	−	6.61849i	−0.538605	−	0.310964i
$454$		0			0
$455$	7.93917	−	17.7564i	0.372194	−	0.832433i
$456$		0			0
$457$	14.5229	−	25.1543i	0.679351	−	1.17667i	−0.295825	−	0.955242i	$-0.595595\pi$
$457$	14.5229	−	25.1543i	0.679351	−	1.17667i	0.975177	−	0.221429i	$-0.0710720\pi$
$458$		0			0
$459$	−1.58759	+	0.916595i	−0.0741023	+	0.0427830i
$460$		0			0
$461$			23.9796i			1.11684i	0.829559	+	0.558420i	$0.188592\pi$
$461$			23.9796i			1.11684i	−0.829559	+	0.558420i	$0.811408\pi$
$462$		0			0
$463$		−	28.4975i		−	1.32439i	−0.749331	−	0.662196i	$-0.769625\pi$
$463$		−	28.4975i		−	1.32439i	0.749331	−	0.662196i	$-0.230375\pi$
$464$		0			0
$465$	20.0504	−	11.5761i	0.929813	−	0.536828i
$466$		0			0
$467$	−9.29075	+	16.0921i	−0.429925	+	0.744651i	−0.996866	−	0.0791067i	$-0.974793\pi$
$467$	−9.29075	+	16.0921i	−0.429925	+	0.744651i	0.566942	+	0.823758i	$0.308127\pi$
$468$		0			0
$469$	6.01655	−	4.35683i	0.277818	−	0.201180i
$470$		0			0
$471$	−4.38345	−	2.53079i	−0.201979	−	0.116613i
$472$		0			0
$473$	3.96813	+	6.87300i	0.182455	+	0.316021i
$474$		0			0
$475$	4.22360			0.193792
$476$		0			0
$477$	0.0716524			0.00328074
$478$		0			0
$479$	14.1707	+	24.5443i	0.647475	+	1.12146i	0.983724	+	0.179686i	$0.0575082\pi$
$479$	14.1707	+	24.5443i	0.647475	+	1.12146i	−0.336249	+	0.941773i	$0.609158\pi$
$480$		0			0
$481$	19.4987	+	11.2576i	0.889062	+	0.513300i
$482$		0			0
$483$	−1.83564	−	17.7334i	−0.0835247	−	0.806899i
$484$		0			0
$485$	8.71162	−	15.0890i	0.395574	−	0.685154i
$486$		0			0
$487$	−35.9498	+	20.7556i	−1.62904	+	0.940528i	−0.644662	+	0.764468i	$0.723002\pi$
$487$	−35.9498	+	20.7556i	−1.62904	+	0.940528i	−0.984379	+	0.176060i	$0.943665\pi$
$488$		0			0
$489$		−	12.0357i		−	0.544274i
$490$		0			0
$491$			1.72728i			0.0779509i	0.999240	+	0.0389755i	$0.0124094\pi$
$491$			1.72728i			0.0779509i	−0.999240	+	0.0389755i	$0.987591\pi$
$492$		0			0
$493$	14.9602	−	8.63729i	0.673774	−	0.389004i
$494$		0			0
$495$	1.55176	−	2.68773i	0.0697465	−	0.120805i
$496$		0			0
$497$	−0.796226	−	7.69203i	−0.0357156	−	0.345035i
$498$		0			0
$499$	36.6216	+	21.1435i	1.63941	+	0.946514i	0.981037	+	0.193822i	$0.0620886\pi$
$499$	36.6216	+	21.1435i	1.63941	+	0.946514i	0.658373	+	0.752691i	$0.271245\pi$
$500$		0			0
$501$	−3.73212	−	6.46422i	−0.166739	−	0.288800i
$502$		0			0
$503$	4.23770			0.188950			0.0944748	−	0.995527i	$-0.469883\pi$
$503$	4.23770			0.188950			0.0944748	+	0.995527i	$0.469883\pi$
$504$		0			0
$505$	2.28906			0.101862
$506$		0			0
$507$	2.00766	+	3.47737i	0.0891634	+	0.154436i
$508$		0			0
$509$	36.1788	+	20.8878i	1.60360	+	0.925836i	0.990760	+	0.135626i	$0.0433046\pi$
$509$	36.1788	+	20.8878i	1.60360	+	0.925836i	0.612836	+	0.790210i	$0.290029\pi$
$510$		0			0
$511$	17.3681	−	12.5770i	0.768321	−	0.556372i
$512$		0			0
$513$	−2.07993	+	3.60254i	−0.0918310	+	0.159056i
$514$		0			0
$515$	−8.77055	+	5.06368i	−0.386476	+	0.223132i
$516$		0			0
$517$		−	9.30265i		−	0.409130i
$518$		0			0
$519$		−	4.36398i		−	0.191557i
$520$		0			0
$521$	30.2681	−	17.4753i	1.32607	−	0.765607i	0.341381	−	0.939925i	$-0.389105\pi$
$521$	30.2681	−	17.4753i	1.32607	−	0.765607i	0.984689	+	0.174318i	$0.0557721\pi$
$522$		0			0
$523$	−6.13503	+	10.6262i	−0.268266	+	0.464651i	−0.968414	−	0.249347i	$-0.919784\pi$
$523$	−6.13503	+	10.6262i	−0.268266	+	0.464651i	0.700148	+	0.713998i	$0.253117\pi$
$524$		0			0
$525$	−1.09648	+	2.45233i	−0.0478541	+	0.107028i
$526$		0			0
$527$	14.9865	+	8.65246i	0.652822	+	0.376907i
$528$		0			0
$529$	11.2032	+	19.4044i	0.487094	+	0.843671i
$530$		0			0
$531$	3.36690			0.146111
$532$		0			0
$533$	−3.26619			−0.141474
$534$		0			0
$535$	16.9750	+	29.4016i	0.733893	+	1.27114i
$536$		0			0
$537$	−21.2754	−	12.2834i	−0.918102	−	0.530067i
$538$		0			0
$539$	6.60122	−	5.90625i	0.284335	−	0.254400i
$540$		0			0
$541$	−0.467883	+	0.810397i	−0.0201158	+	0.0348417i	−0.875908	−	0.482478i	$-0.839737\pi$
$541$	−0.467883	+	0.810397i	−0.0201158	+	0.0348417i	0.855792	+	0.517320i	$0.173070\pi$
$542$		0			0
$543$	−10.1483	+	5.85912i	−0.435505	+	0.251439i
$544$		0			0
$545$			2.41503i			0.103449i
$546$		0			0
$547$		−	7.13048i		−	0.304877i	−0.988313	−	0.152439i	$-0.951287\pi$
$547$		−	7.13048i		−	0.304877i	0.988313	−	0.152439i	$-0.0487127\pi$
$548$		0			0
$549$	−9.61496	+	5.55120i	−0.410356	+	0.236919i
$550$		0			0
$551$	19.5996	−	33.9476i	0.834973	−	1.44621i
$552$		0			0
$553$	−4.30816	−	1.92625i	−0.183201	−	0.0819123i
$554$		0			0
$555$	−15.9545	−	9.21133i	−0.677231	−	0.390999i
$556$		0			0
$557$	4.97622	+	8.61907i	0.210849	+	0.365202i	0.951981	−	0.306159i	$-0.0990438\pi$
$557$	4.97622	+	8.61907i	0.210849	+	0.365202i	−0.741131	+	0.671360i	$0.765710\pi$
$558$		0			0
$559$	−18.7993			−0.795124
$560$		0			0
$561$	2.31971			0.0979381
$562$		0			0
$563$	−0.844531	−	1.46277i	−0.0355927	−	0.0616484i	0.847680	−	0.530507i	$-0.177999\pi$
$563$	−0.844531	−	1.46277i	−0.0355927	−	0.0616484i	−0.883273	+	0.468859i	$0.844665\pi$
$564$		0			0
$565$	−10.6878	−	6.17063i	−0.449641	−	0.259600i
$566$		0			0
$567$	−1.55176	−	2.14290i	−0.0651679	−	0.0899935i
$568$		0			0
$569$	6.96935	−	12.0713i	0.292170	−	0.506054i	−0.682152	−	0.731210i	$-0.738956\pi$
$569$	6.96935	−	12.0713i	0.292170	−	0.506054i	0.974323	+	0.225156i	$0.0722892\pi$
$570$		0			0
$571$	16.1591	−	9.32947i	0.676238	−	0.390426i	−0.122198	−	0.992506i	$-0.538994\pi$
$571$	16.1591	−	9.32947i	0.676238	−	0.390426i	0.798436	+	0.602079i	$0.205661\pi$
$572$		0			0
$573$		−	15.8919i		−	0.663893i
$574$		0			0
$575$		−	6.84168i		−	0.285318i
$576$		0			0
$577$	29.4591	−	17.0082i	1.22640	−	0.708062i	0.260125	−	0.965575i	$-0.416236\pi$
$577$	29.4591	−	17.0082i	1.22640	−	0.708062i	0.966275	+	0.257513i	$0.0829031\pi$
$578$		0			0
$579$	9.86690	−	17.0900i	0.410055	−	0.710235i
$580$		0			0
$581$	14.0434	−	1.45367i	0.582617	−	0.0603086i
$582$		0			0
$583$	−0.0785213	−	0.0453343i	−0.00325202	−	0.00187755i
$584$		0			0
$585$	3.67579	+	6.36666i	0.151975	+	0.263229i
$586$		0			0
$587$	41.9153			1.73003			0.865015	−	0.501746i	$-0.167309\pi$
$587$	41.9153			1.73003			0.865015	+	0.501746i	$0.167309\pi$
$588$		0			0
$589$	39.2681			1.61801
$590$		0			0
$591$	−0.499388	−	0.864965i	−0.0205421	−	0.0355799i
$592$		0			0
$593$	21.1354	+	12.2025i	0.867927	+	0.501098i	0.866659	−	0.498901i	$-0.166263\pi$
$593$	21.1354	+	12.2025i	0.867927	+	0.501098i	0.00126806	+	0.999999i	$0.499596\pi$
$594$		0			0
$595$	−11.8324	+	1.22481i	−0.485080	+	0.0502121i
$596$		0			0
$597$	1.35158	−	2.34101i	0.0553165	−	0.0958110i
$598$		0			0
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	−0.820416	−	0.571767i	$-0.806258\pi$
$599$	−18.0000	+	10.3923i	−0.735460	+	0.424618i	0.0849563	+	0.996385i	$0.472925\pi$
$600$		0			0
$601$			10.6623i			0.434924i	0.976069	+	0.217462i	$0.0697778\pi$
$601$			10.6623i			0.434924i	−0.976069	+	0.217462i	$0.930222\pi$
$602$		0			0
$603$			2.80766i			0.114337i
$604$		0			0
$605$	19.9633	−	11.5258i	0.811622	−	0.468590i
$606$		0			0
$607$	20.0215	−	34.6782i	0.812646	−	1.40754i	−0.0983597	−	0.995151i	$-0.531360\pi$
$607$	20.0215	−	34.6782i	0.812646	−	1.40754i	0.911006	−	0.412393i	$-0.135307\pi$
$608$		0			0
$609$	14.6226	+	20.1931i	0.592539	+	0.818265i
$610$		0			0
$611$	19.0837	+	11.0180i	0.772044	+	0.445740i
$612$		0			0
$613$	11.2481	+	19.4822i	0.454305	+	0.786879i	0.998648	−	0.0519838i	$-0.0165544\pi$
$613$	11.2481	+	19.4822i	0.454305	+	0.786879i	−0.544343	+	0.838863i	$0.683221\pi$
$614$		0			0
$615$	2.67251			0.107766
$616$		0			0
$617$	−18.0820			−0.727954			−0.363977	−	0.931408i	$-0.618581\pi$
$617$	−18.0820			−0.727954			−0.363977	+	0.931408i	$0.618581\pi$
$618$		0			0
$619$	−16.0465	−	27.7933i	−0.644962	−	1.11711i	−0.984310	−	0.176446i	$-0.943540\pi$
$619$	−16.0465	−	27.7933i	−0.644962	−	1.11711i	0.339348	−	0.940661i	$-0.389793\pi$
$620$		0			0
$621$	5.83564	+	3.36921i	0.234176	+	0.135202i
$622$		0			0
$623$	20.7032	+	9.25671i	0.829455	+	0.370862i
$624$		0			0
$625$	14.5229	−	25.1543i	0.580915	−	1.00617i
$626$		0			0
$627$	4.55863	−	2.63193i	0.182054	−	0.105109i
$628$		0			0
$629$		−	13.7699i		−	0.549041i
$630$		0			0
$631$		−	2.95509i		−	0.117640i	−0.998269	−	0.0588201i	$-0.981266\pi$
$631$		−	2.95509i		−	0.117640i	0.998269	−	0.0588201i	$-0.0187338\pi$
$632$		0			0
$633$	15.7442	−	9.08990i	0.625774	−	0.361291i
$634$		0			0
$635$	−7.82798	+	13.5585i	−0.310644	+	0.538051i
$636$		0			0
$637$	4.29780	+	20.5372i	0.170285	+	0.813715i
$638$		0			0
$639$	2.53126	+	1.46142i	0.100135	+	0.0578130i
$640$		0			0
$641$	20.7459	+	35.9329i	0.819412	+	1.41926i	0.906116	+	0.423029i	$0.139033\pi$
$641$	20.7459	+	35.9329i	0.819412	+	1.41926i	−0.0867040	+	0.996234i	$0.527633\pi$
$642$		0			0
$643$	−16.7686			−0.661290			−0.330645	−	0.943755i	$-0.607266\pi$
$643$	−16.7686			−0.661290			−0.330645	+	0.943755i	$0.607266\pi$
$644$		0			0
$645$	15.3822			0.605675
$646$		0			0
$647$	9.31180	+	16.1285i	0.366085	+	0.634077i	0.988950	−	0.148252i	$-0.0473647\pi$
$647$	9.31180	+	16.1285i	0.366085	+	0.634077i	−0.622865	+	0.782329i	$0.714031\pi$
$648$		0			0
$649$	−3.68967	−	2.13023i	−0.144832	−	0.0836189i
$650$		0			0
$651$	−10.1943	+	22.8001i	−0.399545	+	0.893605i
$652$		0			0
$653$	12.8305	−	22.2230i	0.502095	−	0.869654i	−0.497902	−	0.867233i	$-0.665896\pi$
$653$	12.8305	−	22.2230i	0.502095	−	0.869654i	0.999997	−	0.00242072i	$-0.000770540\pi$
$654$		0			0
$655$	−8.22428	+	4.74829i	−0.321349	+	0.185531i
$656$		0			0
$657$			8.10495i			0.316204i
$658$		0			0
$659$			27.7044i			1.07921i	0.841919	+	0.539604i	$0.181426\pi$
$659$			27.7044i			1.07921i	−0.841919	+	0.539604i	$0.818574\pi$
$660$		0			0
$661$	29.5472	−	17.0591i	1.14925	−	0.663522i	0.200548	−	0.979684i	$-0.435728\pi$
$661$	29.5472	−	17.0591i	1.14925	−	0.663522i	0.948705	+	0.316162i	$0.102394\pi$
$662$		0			0
$663$	−2.74744	+	4.75871i	−0.106702	+	0.184813i
$664$		0			0
$665$	−21.8630	+	15.8319i	−0.847811	+	0.613935i
$666$		0			0
$667$	−54.9906	−	31.7489i	−2.12925	−	1.22932i
$668$		0			0
$669$	5.79982	+	10.0456i	0.224234	+	0.388385i
$670$		0			0
$671$	14.0489			0.542352
$672$		0			0
$673$	−17.7032			−0.682407			−0.341203	−	0.939990i	$-0.610834\pi$
$673$	−17.7032			−0.682407			−0.341203	+	0.939990i	$0.610834\pi$
$674$		0			0
$675$	−0.507662	−	0.879296i	−0.0195399	−	0.0338441i
$676$		0			0
$677$	35.5808	+	20.5426i	1.36748	+	0.789516i	0.990606	−	0.136747i	$-0.0436649\pi$
$677$	35.5808	+	20.5426i	1.36748	+	0.789516i	0.376876	+	0.926264i	$0.376998\pi$
$678$		0			0
$679$	1.93522	+	18.6954i	0.0742668	+	0.717462i
$680$		0			0
$681$	−5.08054	+	8.79975i	−0.194687	+	0.337207i
$682$		0			0
$683$	18.3842	−	10.6141i	0.703450	−	0.406137i	−0.105181	−	0.994453i	$-0.533542\pi$
$683$	18.3842	−	10.6141i	0.703450	−	0.406137i	0.808631	+	0.588316i	$0.200209\pi$
$684$		0			0
$685$		−	36.0612i		−	1.37783i
$686$		0			0
$687$		−	23.0970i		−	0.881204i
$688$		0			0
$689$	0.186000	−	0.107387i	0.00708603	−	0.00409112i
$690$		0			0
$691$	19.4878	−	33.7539i	0.741352	−	1.28406i	−0.210528	−	0.977588i	$-0.567518\pi$
$691$	19.4878	−	33.7539i	0.741352	−	1.28406i	0.951880	−	0.306472i	$-0.0991485\pi$
$692$		0			0
$693$	0.344712	+	3.33012i	0.0130945	+	0.126501i
$694$		0			0
$695$	4.28321	+	2.47291i	0.162471	+	0.0938028i
$696$		0			0
$697$	0.998775	+	1.72993i	0.0378313	+	0.0655257i
$698$		0			0
$699$	6.85547			0.259298
$700$		0			0
$701$	−4.28115			−0.161697			−0.0808485	−	0.996726i	$-0.525763\pi$
$701$	−4.28115			−0.161697			−0.0808485	+	0.996726i	$0.525763\pi$
$702$		0			0
$703$	−15.6232	−	27.0602i	−0.589241	−	1.02060i
$704$		0			0
$705$	−15.6150	−	9.01530i	−0.588093	−	0.339536i
$706$		0			0
$707$	−2.00000	+	1.44828i	−0.0752177	+	0.0544682i
$708$		0			0
$709$	−21.8796	+	37.8965i	−0.821704	+	1.42323i	0.0827080	+	0.996574i	$0.473643\pi$
$709$	−21.8796	+	37.8965i	−0.821704	+	1.42323i	−0.904412	+	0.426660i	$0.859690\pi$
$710$		0			0
$711$	1.54471	−	0.891841i	0.0579313	−	0.0334466i
$712$		0			0
$713$		−	63.6092i		−	2.38218i
$714$		0			0
$715$		−	9.30265i		−	0.347899i
$716$		0			0
$717$	19.2481	−	11.1129i	0.718832	−	0.415018i
$718$		0			0
$719$	−20.7657	+	35.9672i	−0.774429	+	1.34135i	0.160685	+	0.987006i	$0.448630\pi$
$719$	−20.7657	+	35.9672i	−0.774429	+	1.34135i	−0.935115	+	0.354345i	$0.884704\pi$
$720$		0			0
$721$	4.45924	−	9.97334i	0.166071	−	0.371427i
$722$		0			0
$723$	13.3605	+	7.71367i	0.496881	+	0.286874i
$724$		0			0
$725$	4.78382	+	8.28582i	0.177667	+	0.307727i
$726$		0			0
$727$	−7.19963			−0.267020			−0.133510	−	0.991047i	$-0.542625\pi$
$727$	−7.19963			−0.267020			−0.133510	+	0.991047i	$0.542625\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	5.74867	+	9.95698i	0.212622	+	0.368272i
$732$		0			0
$733$	−20.9219	−	12.0793i	−0.772768	−	0.446158i	0.0610934	−	0.998132i	$-0.480541\pi$
$733$	−20.9219	−	12.0793i	−0.772768	−	0.446158i	−0.833861	+	0.551974i	$0.813875\pi$
$734$		0			0
$735$	−3.51661	−	16.8043i	−0.129712	−	0.619836i
$736$		0			0
$737$	1.77640	−	3.07682i	0.0654345	−	0.113336i
$738$		0			0
$739$	−8.16690	+	4.71516i	−0.300424	+	0.173450i	−0.642634	−	0.766174i	$-0.722158\pi$
$739$	−8.16690	+	4.71516i	−0.300424	+	0.173450i	0.342209	+	0.939624i	$0.388825\pi$
$740$		0			0
$741$			12.4689i			0.458058i
$742$		0			0
$743$			2.32851i			0.0854248i	0.999087	+	0.0427124i	$0.0135999\pi$
$743$			2.32851i			0.0854248i	−0.999087	+	0.0427124i	$0.986400\pi$
$744$		0			0
$745$	1.05375	−	0.608384i	0.0386065	−	0.0222895i
$746$		0			0
$747$	−2.66813	+	4.62133i	−0.0976217	+	0.169086i
$748$		0			0
$749$	−33.4337	−	14.9487i	−1.22164	−	0.546215i
$750$		0			0
$751$	−26.9834	−	15.5789i	−0.984638	−	0.568481i	−0.0809709	−	0.996716i	$-0.525802\pi$
$751$	−26.9834	−	15.5789i	−0.984638	−	0.568481i	−0.903667	+	0.428235i	$0.859135\pi$
$752$		0			0
$753$	−11.1477	−	19.3084i	−0.406244	−	0.703636i
$754$		0			0
$755$	32.4652			1.18153
$756$		0			0
$757$	0.559856			0.0203483			0.0101742	−	0.999948i	$-0.496761\pi$
$757$	0.559856			0.0203483			0.0101742	+	0.999948i	$0.496761\pi$
$758$		0			0
$759$	−4.26338	−	7.38439i	−0.154751	−	0.268036i
$760$		0			0
$761$	39.6196	+	22.8744i	1.43621	+	0.829196i	0.997584	−	0.0694744i	$-0.0221322\pi$
$761$	39.6196	+	22.8744i	1.43621	+	0.829196i	0.438625	+	0.898670i	$0.355466\pi$
$762$		0			0
$763$	−1.52798	−	2.11006i	−0.0553167	−	0.0763895i
$764$		0			0
$765$	2.24806	−	3.89375i	0.0812786	−	0.140779i
$766$		0			0
$767$	8.74002	−	5.04606i	0.315584	−	0.182203i
$768$		0			0
$769$			8.33377i			0.300524i	0.988646	+	0.150262i	$0.0480117\pi$
$769$			8.33377i			0.300524i	−0.988646	+	0.150262i	$0.951988\pi$
$770$		0			0
$771$			2.86976i			0.103352i
$772$		0			0
$773$	−26.5674	+	15.3387i	−0.955563	+	0.551695i	−0.894805	−	0.446458i	$-0.852685\pi$
$773$	−26.5674	+	15.3387i	−0.955563	+	0.551695i	−0.0607584	+	0.998153i	$0.519352\pi$
$774$		0			0
$775$	−4.79222	+	8.30037i	−0.172142	+	0.298158i
$776$		0			0
$777$	19.7678	−	2.04622i	0.709165	−	0.0734079i
$778$		0			0
$779$	3.92554	+	2.26641i	0.140647	+	0.0812025i
$780$		0			0
$781$	−1.84928	−	3.20304i	−0.0661723	−	0.114614i
$782$		0			0
$783$	−9.42323			−0.336759
$784$		0			0
$785$	12.4141			0.443078
$786$		0			0
$787$	−11.0792	−	19.1897i	−0.394931	−	0.684040i	0.598162	−	0.801375i	$-0.295898\pi$
$787$	−11.0792	−	19.1897i	−0.394931	−	0.684040i	−0.993092	+	0.117335i	$0.962565\pi$
$788$		0			0
$789$	8.98186	+	5.18568i	0.319763	+	0.184615i
$790$		0			0
$791$	13.2423	−	1.37076i	0.470843	−	0.0487385i
$792$		0			0
$793$	−16.6394	+	28.8203i	−0.590883	+	1.02344i
$794$		0			0
$795$	−0.152192	+	0.0878679i	−0.00539768	+	0.00311635i
$796$		0			0
$797$			24.1705i			0.856164i	0.903740	+	0.428082i	$0.140811\pi$
$797$			24.1705i			0.856164i	−0.903740	+	0.428082i	$0.859189\pi$
$798$		0			0
$799$		−	13.4768i		−	0.476776i
$800$		0			0
$801$	−7.42323	+	4.28581i	−0.262287	+	0.151431i
$802$		0			0
$803$	5.12798	−	8.88192i	0.180963	−	0.313436i
$804$		0			0
$805$	25.6456	+	35.4152i	0.903889	+	1.24822i
$806$		0			0
$807$	−4.48011	−	2.58659i	−0.157707	−	0.0910524i
$808$		0			0
$809$	−7.61046	−	13.1817i	−0.267569	−	0.463444i	0.700664	−	0.713491i	$-0.252887\pi$
$809$	−7.61046	−	13.1817i	−0.267569	−	0.463444i	−0.968234	+	0.250047i	$0.919554\pi$
$810$		0			0
$811$	−48.4574			−1.70157			−0.850785	−	0.525515i	$-0.823873\pi$
$811$	−48.4574			−1.70157			−0.850785	+	0.525515i	$0.823873\pi$
$812$		0			0
$813$	−24.2391			−0.850101
$814$		0			0
$815$	14.7595	+	25.5642i	0.517002	+	0.895474i
$816$		0			0
$817$	22.5943	+	13.0448i	0.790474	+	0.456380i
$818$		0			0
$819$	−7.23978	−	3.23702i	−0.252978	−	0.113111i
$820$		0			0
$821$	25.7647	−	44.6257i	0.899193	−	1.55745i	0.0706654	−	0.997500i	$-0.477488\pi$
$821$	25.7647	−	44.6257i	0.899193	−	1.55745i	0.828528	−	0.559948i	$-0.189179\pi$
$822$		0			0
$823$	1.90279	−	1.09858i	0.0663272	−	0.0382941i	−0.466470	−	0.884537i	$-0.654474\pi$
$823$	1.90279	−	1.09858i	0.0663272	−	0.0382941i	0.532797	+	0.846243i	$0.321141\pi$
$824$		0			0
$825$			1.28479i			0.0447305i
$826$		0			0
$827$		−	10.2864i		−	0.357693i	−0.983877	−	0.178846i	$-0.942763\pi$
$827$		−	10.2864i		−	0.357693i	0.983877	−	0.178846i	$-0.0572365\pi$
$828$		0			0
$829$	−0.662548	+	0.382522i	−0.0230112	+	0.0132855i	−0.511461	−	0.859306i	$-0.670896\pi$
$829$	−0.662548	+	0.382522i	−0.0230112	+	0.0132855i	0.488450	+	0.872592i	$0.337562\pi$
$830$		0			0
$831$	1.50766	−	2.61135i	0.0523002	−	0.0905866i
$832$		0			0
$833$	9.56326	−	8.55644i	0.331347	−	0.296463i
$834$		0			0
$835$	15.8542	+	9.15345i	0.548659	+	0.316768i
$836$		0			0
$837$	−4.71989	−	8.17509i	−0.163143	−	0.282572i
$838$		0			0
$839$	−3.50389			−0.120968			−0.0604839	−	0.998169i	$-0.519264\pi$
$839$	−3.50389			−0.120968			−0.0604839	+	0.998169i	$0.519264\pi$
$840$		0			0
$841$	59.7973			2.06198
$842$		0			0
$843$	−3.45961	−	5.99222i	−0.119155	−	0.206383i
$844$		0			0
$845$	−8.52866	−	4.92402i	−0.293395	−	0.169392i
$846$		0			0
$847$	−10.1500	+	22.7010i	−0.348758	+	0.780017i
$848$		0			0
$849$	−10.2870	+	17.8176i	−0.353048	+	0.611497i
$850$		0			0
$851$	−43.8341	+	25.3076i	−1.50261	+	0.867534i
$852$		0			0
$853$		−	25.3974i		−	0.869589i	−0.900530	−	0.434795i	$-0.856821\pi$
$853$		−	25.3974i		−	0.869589i	0.900530	−	0.434795i	$-0.143179\pi$
$854$		0			0
$855$		−	10.2025i		−	0.348919i
$856$		0			0
$857$	−25.0609	+	14.4689i	−0.856065	+	0.494249i	−0.862693	−	0.505729i	$-0.831224\pi$
$857$	−25.0609	+	14.4689i	−0.856065	+	0.494249i	0.00662744	+	0.999978i	$0.497890\pi$
$858$		0			0
$859$	−2.34404	+	4.05999i	−0.0799775	+	0.138525i	−0.903240	−	0.429136i	$-0.858818\pi$
$859$	−2.34404	+	4.05999i	−0.0799775	+	0.138525i	0.823263	+	0.567661i	$0.192152\pi$
$860$		0			0
$861$	−2.33503	+	1.69089i	−0.0795777	+	0.0576254i
$862$		0			0
$863$	−37.6419	−	21.7325i	−1.28134	−	0.739784i	−0.304250	−	0.952592i	$-0.598406\pi$
$863$	−37.6419	−	21.7325i	−1.28134	−	0.739784i	−0.977094	+	0.212808i	$0.931739\pi$
$864$		0			0
$865$	5.35158	+	9.26921i	0.181959	+	0.315163i
$866$		0			0
$867$	−13.6394			−0.463219
$868$		0			0
$869$	−2.25706			−0.0765655
$870$		0			0
$871$	4.20791	+	7.28831i	0.142580	+	0.246955i
$872$		0			0
$873$	−6.15219	−	3.55197i	−0.208220	−	0.120216i
$874$		0			0
$875$	2.66227	+	25.7192i	0.0900013	+	0.869467i
$876$		0			0
$877$	−23.0063	+	39.8481i	−0.776868	+	1.34558i	0.156870	+	0.987619i	$0.449860\pi$
$877$	−23.0063	+	39.8481i	−0.776868	+	1.34558i	−0.933738	+	0.357956i	$0.883474\pi$
$878$		0			0
$879$	24.5183	−	14.1556i	0.826982	−	0.477458i
$880$		0			0
$881$			40.8047i			1.37475i	0.726304	+	0.687373i	$0.241236\pi$
$881$			40.8047i			1.37475i	−0.726304	+	0.687373i	$0.758764\pi$
$882$		0			0
$883$			6.06234i			0.204014i	0.994784	+	0.102007i	$0.0325264\pi$
$883$			6.06234i			0.204014i	−0.994784	+	0.102007i	$0.967474\pi$
$884$		0			0
$885$	−7.15140	+	4.12886i	−0.240392	+	0.138790i
$886$		0			0
$887$	22.1276	−	38.3262i	0.742973	−	1.28687i	−0.208163	−	0.978094i	$-0.566749\pi$
$887$	22.1276	−	38.3262i	0.742973	−	1.28687i	0.951136	−	0.308772i	$-0.0999181\pi$
$888$		0			0
$889$	−1.73892	−	16.7991i	−0.0583216	−	0.563422i
$890$		0			0
$891$	−1.09586	−	0.632697i	−0.0367128	−	0.0211961i
$892$		0			0
$893$	−15.2908	−	26.4844i	−0.511685	−	0.886265i
$894$		0			0
$895$	60.2528			2.01403
$896$		0			0
$897$	20.1980			0.674393
$898$		0			0
$899$	44.4766	+	77.0358i	1.48338	+	2.56929i
$900$		0			0
$901$	−0.113755	−	0.0656762i	−0.00378971	−	0.00218799i
$902$		0			0
$903$	−13.4398	+	9.73229i	−0.447248	+	0.323870i
$904$		0			0
$905$	14.3702	−	24.8899i	0.477681	−	0.827368i
$906$		0			0
$907$	5.54526	−	3.20156i	0.184127	−	0.106306i	−0.405103	−	0.914271i	$-0.632764\pi$
$907$	5.54526	−	3.20156i	0.184127	−	0.106306i	0.589230	+	0.807965i	$0.299431\pi$
$908$		0			0
$909$		−	0.933313i		−	0.0309561i
$910$		0			0
$911$			48.9687i			1.62241i	0.584765	+	0.811203i	$0.301187\pi$
$911$			48.9687i			1.62241i	−0.584765	+	0.811203i	$0.698813\pi$
$912$		0			0
$913$	5.84781	−	3.37623i	0.193534	−	0.111737i
$914$		0			0
$915$	13.6150	−	23.5818i	0.450097	−	0.779590i
$916$		0			0
$917$	4.18150	−	9.35216i	0.138085	−	0.308835i
$918$		0			0
$919$	−21.2676	−	12.2789i	−0.701554	−	0.405042i	0.106372	−	0.994326i	$-0.466077\pi$
$919$	−21.2676	−	12.2789i	−0.701554	−	0.405042i	−0.807926	+	0.589284i	$0.799410\pi$
$920$		0			0
$921$	4.32798	+	7.49628i	0.142612	+	0.247011i
$922$		0			0
$923$	8.76108			0.288374
$924$		0			0
$925$	7.62654			0.250759
$926$		0			0
$927$	2.06460	+	3.57600i	0.0678105	+	0.117451i
$928$		0			0
$929$	−8.51680	−	4.91718i	−0.279427	−	0.161327i	0.353737	−	0.935345i	$-0.384911\pi$
$929$	−8.51680	−	4.91718i	−0.279427	−	0.161327i	−0.633164	+	0.774018i	$0.718244\pi$
$930$		0			0
$931$	9.08539	−	27.6653i	0.297762	−	0.906695i
$932$		0			0
$933$	4.67129	−	8.09091i	0.152931	−	0.264884i
$934$		0			0
$935$	−4.92712	+	2.84468i	−0.161134	+	0.0930308i
$936$		0			0
$937$		−	38.1447i		−	1.24613i	−0.782168	−	0.623067i	$-0.785886\pi$
$937$		−	38.1447i		−	1.24613i	0.782168	−	0.623067i	$-0.214114\pi$
$938$		0			0
$939$		−	7.37547i		−	0.240689i
$940$		0			0
$941$	−29.7788	+	17.1928i	−0.970760	+	0.560469i	−0.899468	−	0.436987i	$-0.856046\pi$
$941$	−29.7788	+	17.1928i	−0.970760	+	0.560469i	−0.0712922	+	0.997455i	$0.522712\pi$
$942$		0			0
$943$	3.67129	−	6.35886i	0.119554	−	0.207073i
$944$		0			0
$945$	5.92385	+	2.64865i	0.192703	+	0.0861605i
$946$		0			0
$947$	−14.2630	−	8.23476i	−0.463486	−	0.267594i	0.250023	−	0.968240i	$-0.419562\pi$
$947$	−14.2630	−	8.23476i	−0.463486	−	0.267594i	−0.713509	+	0.700646i	$0.752895\pi$
$948$		0			0
$949$	12.1471	+	21.0394i	0.394311	+	0.682966i
$950$		0			0
$951$	−3.63028			−0.117720
$952$		0			0
$953$	−52.4540			−1.69915			−0.849576	−	0.527466i	$-0.823142\pi$
$953$	−52.4540			−1.69915			−0.849576	+	0.527466i	$0.823142\pi$
$954$		0			0
$955$	19.4883	+	33.7548i	0.630628	+	1.09228i
$956$		0			0
$957$	10.3266	+	5.96205i	0.333811	+	0.192726i
$958$		0			0
$959$	22.8158	+	31.5074i	0.736761	+	1.01743i
$960$		0			0
$961$	−29.0547	+	50.3243i	−0.937250	+	1.62336i
$962$		0			0
$963$	11.9878	−	6.92118i	0.386303	−	0.223032i
$964$		0			0
$965$			48.3995i			1.55803i
$966$		0			0
$967$			16.3573i			0.526016i	0.964794	+	0.263008i	$0.0847146\pi$
$967$			16.3573i			0.526016i	−0.964794	+	0.263008i	$0.915285\pi$
$968$		0			0
$969$	6.60414	−	3.81290i	0.212155	−	0.122488i
$970$		0			0
$971$	11.6591	−	20.1942i	0.374159	−	0.648063i	−0.616042	−	0.787714i	$-0.711265\pi$
$971$	11.6591	−	20.1942i	0.374159	−	0.648063i	0.990201	+	0.139651i	$0.0445981\pi$
$972$		0			0
$973$	−5.30693	+	0.549337i	−0.170132	+	0.0176109i
$974$		0			0
$975$	−2.63564	−	1.52169i	−0.0844081	−	0.0487331i
$976$		0			0
$977$	−19.9922	−	34.6275i	−0.639608	−	1.10783i	−0.985519	−	0.169566i	$-0.945763\pi$
$977$	−19.9922	−	34.6275i	−0.639608	−	1.10783i	0.345911	−	0.938267i	$-0.387570\pi$
$978$		0			0
$979$	10.8465			0.346655
$980$		0			0
$981$	0.984676			0.0314383
$982$		0			0
$983$	10.7628	+	18.6417i	0.343279	+	0.594577i	0.985040	−	0.172328i	$-0.0551290\pi$
$983$	10.7628	+	18.6417i	0.343279	+	0.594577i	−0.641761	+	0.766905i	$0.721796\pi$
$984$		0			0
$985$	2.12143	+	1.22481i	0.0675943	+	0.0390256i
$986$		0			0
$987$	19.3471	−	2.00268i	0.615824	−	0.0637459i
$988$		0			0
$989$	21.1309	−	36.5998i	0.671923	−	1.16381i
$990$		0			0
$991$	9.69666	−	5.59837i	0.308025	−	0.177838i	−0.338018	−	0.941140i	$-0.609756\pi$
$991$	9.69666	−	5.59837i	0.308025	−	0.177838i	0.646042	+	0.763302i	$0.276423\pi$
$992$		0			0
$993$			0.628347i			0.0199400i
$994$		0			0
$995$			6.62982i			0.210179i
$996$		0			0
$997$	49.1699	−	28.3883i	1.55723	−	0.899066i	0.559707	−	0.828690i	$-0.310914\pi$
$997$	49.1699	−	28.3883i	1.55723	−	0.899066i	0.997521	−	0.0703755i	$-0.0224197\pi$
$998$		0			0
$999$	−3.75572	+	6.50509i	−0.118826	+	0.205812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.bl.j.1279.1		8
4.3	odd	2		1344.2.bl.i.1279.1		8
7.3	odd	6		1344.2.bl.i.703.1		8
8.3	odd	2		84.2.o.b.19.2	yes	8
8.5	even	2		84.2.o.a.19.1	✓	8
24.5	odd	2		252.2.bf.g.19.4		8
24.11	even	2		252.2.bf.f.19.3		8
28.3	even	6	inner	1344.2.bl.j.703.1		8
56.3	even	6		84.2.o.a.31.1	yes	8
56.5	odd	6		588.2.b.a.391.8		8
56.11	odd	6		588.2.o.d.31.1		8
56.13	odd	2		588.2.o.d.19.1		8
56.19	even	6		588.2.b.b.391.7		8
56.27	even	2		588.2.o.b.19.2		8
56.37	even	6		588.2.b.b.391.8		8
56.45	odd	6		84.2.o.b.31.2	yes	8
56.51	odd	6		588.2.b.a.391.7		8
56.53	even	6		588.2.o.b.31.2		8
168.5	even	6		1764.2.b.j.1567.1		8
168.59	odd	6		252.2.bf.g.199.4		8
168.101	even	6		252.2.bf.f.199.3		8
168.107	even	6		1764.2.b.j.1567.2		8
168.131	odd	6		1764.2.b.i.1567.2		8
168.149	odd	6		1764.2.b.i.1567.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.1	✓	8	8.5	even	2
84.2.o.a.31.1	yes	8	56.3	even	6
84.2.o.b.19.2	yes	8	8.3	odd	2
84.2.o.b.31.2	yes	8	56.45	odd	6
252.2.bf.f.19.3		8	24.11	even	2
252.2.bf.f.199.3		8	168.101	even	6
252.2.bf.g.19.4		8	24.5	odd	2
252.2.bf.g.199.4		8	168.59	odd	6
588.2.b.a.391.7		8	56.51	odd	6
588.2.b.a.391.8		8	56.5	odd	6
588.2.b.b.391.7		8	56.19	even	6
588.2.b.b.391.8		8	56.37	even	6
588.2.o.b.19.2		8	56.27	even	2
588.2.o.b.31.2		8	56.53	even	6
588.2.o.d.19.1		8	56.13	odd	2
588.2.o.d.31.1		8	56.11	odd	6
1344.2.bl.i.703.1		8	7.3	odd	6
1344.2.bl.i.1279.1		8	4.3	odd	2
1344.2.bl.j.703.1		8	28.3	even	6	inner
1344.2.bl.j.1279.1		8	1.1	even	1	trivial
1764.2.b.i.1567.1		8	168.149	odd	6
1764.2.b.i.1567.2		8	168.131	odd	6
1764.2.b.j.1567.1		8	168.5	even	6
1764.2.b.j.1567.2		8	168.107	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-2.12403 - 1.22631i) q^{5} +(2.63169 - 0.272415i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-2.12403 - 1.22631i) q^{5} +(2.63169 - 0.272415i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.09586 - 0.632697i) q^{11} +2.99744i q^{13} -2.45262i q^{15} +(1.58759 - 0.916595i) q^{17} +(2.07993 - 3.60254i) q^{19} +(1.55176 + 2.14290i) q^{21} +(-5.83564 - 3.36921i) q^{23} +(0.507662 + 0.879296i) q^{25} -1.00000 q^{27} +9.42323 q^{29} +(4.71989 + 8.17509i) q^{31} +(1.09586 + 0.632697i) q^{33} +(-5.92385 - 2.64865i) q^{35} +(3.75572 - 6.50509i) q^{37} +(-2.59586 + 1.49872i) q^{39} +1.08966i q^{41} +6.27176i q^{43} +(2.12403 - 1.22631i) q^{45} +(3.67579 - 6.36666i) q^{47} +(6.85158 - 1.43382i) q^{49} +(1.58759 + 0.916595i) q^{51} +(-0.0358262 - 0.0620528i) q^{53} -3.10353 q^{55} +4.15985 q^{57} +(-1.68345 - 2.91583i) q^{59} +(9.61496 + 5.55120i) q^{61} +(-1.07993 + 2.41532i) q^{63} +(3.67579 - 6.36666i) q^{65} +(2.43151 - 1.40383i) q^{67} -6.73842i q^{69} -2.92285i q^{71} +(7.01910 - 4.05248i) q^{73} +(-0.507662 + 0.879296i) q^{75} +(2.71162 - 1.96359i) q^{77} +(-1.54471 - 0.891841i) q^{79} +(-0.500000 - 0.866025i) q^{81} +5.33626 q^{83} -4.49611 q^{85} +(4.71162 + 8.16076i) q^{87} +(7.42323 + 4.28581i) q^{89} +(0.816548 + 7.88834i) q^{91} +(-4.71989 + 8.17509i) q^{93} +(-8.83564 + 5.10126i) q^{95} +7.10394i q^{97} +1.26539i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} + 2 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 + 2 * q^7 - 4 * q^9	\( 8 q + 4 q^{3} + 2 q^{7} - 4 q^{9} - 6 q^{11} + 6 q^{19} + 4 q^{21} + 2 q^{25} - 8 q^{27} + 16 q^{29} + 6 q^{31} - 6 q^{33} + 12 q^{35} - 6 q^{37} - 6 q^{39} + 4 q^{47} + 4 q^{49} + 4 q^{53} - 8 q^{55} + 12 q^{57} + 14 q^{59} - 12 q^{61} + 2 q^{63} + 4 q^{65} - 42 q^{67} - 18 q^{73} - 2 q^{75} - 8 q^{77} - 6 q^{79} - 4 q^{81} - 4 q^{83} + 32 q^{85} + 8 q^{87} + 34 q^{91} - 6 q^{93} - 24 q^{95}+O(q^{100}) \) 8 * q + 4 * q^3 + 2 * q^7 - 4 * q^9 - 6 * q^11 + 6 * q^19 + 4 * q^21 + 2 * q^25 - 8 * q^27 + 16 * q^29 + 6 * q^31 - 6 * q^33 + 12 * q^35 - 6 * q^37 - 6 * q^39 + 4 * q^47 + 4 * q^49 + 4 * q^53 - 8 * q^55 + 12 * q^57 + 14 * q^59 - 12 * q^61 + 2 * q^63 + 4 * q^65 - 42 * q^67 - 18 * q^73 - 2 * q^75 - 8 * q^77 - 6 * q^79 - 4 * q^81 - 4 * q^83 + 32 * q^85 + 8 * q^87 + 34 * q^91 - 6 * q^93 - 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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