LMFDB - Embedded newform 1152.2.i.k.769.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(385,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1152.385");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} + \cdots + 729 $ x^12 - 2x^11 + 3x^10 - 8x^9 + 22x^8 - 42x^7 + 51x^6 - 126x^5 + 198x^4 - 216x^3 + 243x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			769.2
Root			$1.19051 + 1.25805i$ of defining polynomial
Character	$\chi$	$=$	1152.769
Dual form			1152.2.i.k.385.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.494250 - 1.66004i) q^{3} +(0.268104 - 0.464369i) q^{5} +(2.35014 + 4.07056i) q^{7} +(-2.51143 + 1.64095i) q^{9} +O(q^{10})$	\(q+(-0.494250 - 1.66004i) q^{3} +(0.268104 - 0.464369i) q^{5} +(2.35014 + 4.07056i) q^{7} +(-2.51143 + 1.64095i) q^{9} +(-2.59922 - 4.50198i) q^{11} +(-0.778295 + 1.34805i) q^{13} +(-0.903379 - 0.215547i) q^{15} +0.695781 q^{17} +5.80593 q^{19} +(5.59572 - 5.91320i) q^{21} +(4.42809 - 7.66967i) q^{23} +(2.35624 + 4.08113i) q^{25} +(3.96530 + 3.35803i) q^{27} +(1.92199 + 3.32898i) q^{29} +(2.77035 - 4.79840i) q^{31} +(-6.18878 + 6.53990i) q^{33} +2.52033 q^{35} +4.09280 q^{37} +(2.62248 + 0.625725i) q^{39} +(1.01019 - 1.74970i) q^{41} +(-3.71522 - 6.43494i) q^{43} +(0.0886801 + 1.60618i) q^{45} +(-0.186066 - 0.322275i) q^{47} +(-7.54633 + 13.0706i) q^{49} +(-0.343890 - 1.15502i) q^{51} +5.30777 q^{53} -2.78744 q^{55} +(-2.86958 - 9.63804i) q^{57} +(-2.57152 + 4.45401i) q^{59} +(-0.921988 - 1.59693i) q^{61} +(-12.5818 - 6.36650i) q^{63} +(0.417328 + 0.722833i) q^{65} +(5.79316 - 10.0340i) q^{67} +(-14.9205 - 3.56004i) q^{69} +10.6289 q^{71} +4.40840 q^{73} +(5.61024 - 5.92854i) q^{75} +(12.2171 - 21.1606i) q^{77} +(3.32244 + 5.75464i) q^{79} +(3.61459 - 8.24225i) q^{81} +(5.28055 + 9.14617i) q^{83} +(0.186541 - 0.323099i) q^{85} +(4.57628 - 4.83592i) q^{87} -7.30777 q^{89} -7.31642 q^{91} +(-9.33475 - 2.22728i) q^{93} +(1.55659 - 2.69609i) q^{95} +(-7.81612 - 13.5379i) q^{97} +(13.9153 + 7.04125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9	$ 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + 4 q^{11} + 10 q^{13} + 4 q^{15} + 4 q^{17} + 4 q^{19} + 2 q^{21} + 8 q^{23} - 14 q^{25} - 14 q^{27} - 2 q^{29} + 8 q^{31} - 10 q^{33} + 8 q^{35} + 22 q^{39} - 2 q^{41} - 2 q^{43} + 10 q^{45} - 14 q^{47} - 18 q^{49} - 38 q^{51} + 24 q^{53} - 16 q^{55} - 38 q^{57} + 6 q^{59} + 14 q^{61} - 16 q^{63} - 8 q^{65} + 4 q^{67} - 50 q^{69} - 28 q^{71} + 60 q^{73} + 50 q^{75} + 2 q^{77} + 16 q^{79} + 22 q^{81} + 24 q^{83} + 16 q^{85} - 36 q^{87} - 48 q^{89} - 52 q^{91} + 42 q^{93} - 20 q^{95} - 14 q^{97} + 68 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9 + 4 * q^11 + 10 * q^13 + 4 * q^15 + 4 * q^17 + 4 * q^19 + 2 * q^21 + 8 * q^23 - 14 * q^25 - 14 * q^27 - 2 * q^29 + 8 * q^31 - 10 * q^33 + 8 * q^35 + 22 * q^39 - 2 * q^41 - 2 * q^43 + 10 * q^45 - 14 * q^47 - 18 * q^49 - 38 * q^51 + 24 * q^53 - 16 * q^55 - 38 * q^57 + 6 * q^59 + 14 * q^61 - 16 * q^63 - 8 * q^65 + 4 * q^67 - 50 * q^69 - 28 * q^71 + 60 * q^73 + 50 * q^75 + 2 * q^77 + 16 * q^79 + 22 * q^81 + 24 * q^83 + 16 * q^85 - 36 * q^87 - 48 * q^89 - 52 * q^91 + 42 * q^93 - 20 * q^95 - 14 * q^97 + 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.494250	−	1.66004i	−0.285356	−	0.958422i
$3$	−0.494250	−	1.66004i	−0.285356	−	0.958422i
$4$		0			0
$5$	0.268104	−	0.464369i	0.119900	−	0.207672i	−0.799828	−	0.600229i	$-0.795076\pi$
$5$	0.268104	−	0.464369i	0.119900	−	0.207672i	0.919728	+	0.392557i	$0.128409\pi$
$6$		0			0
$7$	2.35014	+	4.07056i	0.888270	+	1.53853i	0.841919	+	0.539604i	$0.181426\pi$
$7$	2.35014	+	4.07056i	0.888270	+	1.53853i	0.0463510	+	0.998925i	$0.485241\pi$
$8$		0			0
$9$	−2.51143	+	1.64095i	−0.837144	+	0.546982i
$10$		0			0
$11$	−2.59922	−	4.50198i	−0.783695	−	1.35740i	−0.929776	−	0.368126i	$-0.879999\pi$
$11$	−2.59922	−	4.50198i	−0.783695	−	1.35740i	0.146081	−	0.989273i	$-0.453334\pi$
$12$		0			0
$13$	−0.778295	+	1.34805i	−0.215860	+	0.373881i	−0.953538	−	0.301272i	$-0.902589\pi$
$13$	−0.778295	+	1.34805i	−0.215860	+	0.373881i	0.737678	+	0.675153i	$0.235922\pi$
$14$		0			0
$15$	−0.903379	−	0.215547i	−0.233252	−	0.0556540i
$16$		0			0
$17$	0.695781			0.168752			0.0843759	−	0.996434i	$-0.473110\pi$
$17$	0.695781			0.168752			0.0843759	+	0.996434i	$0.473110\pi$
$18$		0			0
$19$	5.80593			1.33197			0.665986	−	0.745965i	$-0.268011\pi$
$19$	5.80593			1.33197			0.665986	+	0.745965i	$0.268011\pi$
$20$		0			0
$21$	5.59572	−	5.91320i	1.22109	−	1.29037i
$22$		0			0
$23$	4.42809	−	7.66967i	0.923320	−	1.59924i	0.129079	−	0.991634i	$-0.458798\pi$
$23$	4.42809	−	7.66967i	0.923320	−	1.59924i	0.794241	−	0.607603i	$-0.207869\pi$
$24$		0			0
$25$	2.35624	+	4.08113i	0.471248	+	0.816226i
$26$		0			0
$27$	3.96530	+	3.35803i	0.763123	+	0.646253i
$28$		0			0
$29$	1.92199	+	3.32898i	0.356904	+	0.618176i	0.987442	−	0.157982i	$-0.0504989\pi$
$29$	1.92199	+	3.32898i	0.356904	+	0.618176i	−0.630538	+	0.776159i	$0.717166\pi$
$30$		0			0
$31$	2.77035	−	4.79840i	0.497570	−	0.861817i	−0.502426	−	0.864620i	$-0.667559\pi$
$31$	2.77035	−	4.79840i	0.497570	−	0.861817i	0.999996	+	0.00280317i	$0.000892278\pi$
$32$		0			0
$33$	−6.18878	+	6.53990i	−1.07733	+	1.13845i
$34$		0			0
$35$	2.52033			0.426013
$36$		0			0
$37$	4.09280			0.672852			0.336426	−	0.941710i	$-0.390782\pi$
$37$	4.09280			0.672852			0.336426	+	0.941710i	$0.390782\pi$
$38$		0			0
$39$	2.62248	+	0.625725i	0.419933	+	0.100196i
$40$		0			0
$41$	1.01019	−	1.74970i	0.157765	−	0.273258i	−0.776297	−	0.630367i	$-0.782904\pi$
$41$	1.01019	−	1.74970i	0.157765	−	0.273258i	0.934063	+	0.357109i	$0.116238\pi$
$42$		0			0
$43$	−3.71522	−	6.43494i	−0.566565	−	0.981319i	−0.996902	−	0.0786512i	$-0.974939\pi$
$43$	−3.71522	−	6.43494i	−0.566565	−	0.981319i	0.430337	−	0.902668i	$-0.358395\pi$
$44$		0			0
$45$	0.0886801	+	1.60618i	0.0132197	+	0.239435i
$46$		0			0
$47$	−0.186066	−	0.322275i	−0.0271404	−	0.0470086i	0.852136	−	0.523320i	$-0.175307\pi$
$47$	−0.186066	−	0.322275i	−0.0271404	−	0.0470086i	−0.879277	+	0.476311i	$0.841973\pi$
$48$		0			0
$49$	−7.54633	+	13.0706i	−1.07805	+	1.86723i
$50$		0			0
$51$	−0.343890	−	1.15502i	−0.0481542	−	0.161735i
$52$		0			0
$53$	5.30777			0.729078			0.364539	−	0.931188i	$-0.381227\pi$
$53$	5.30777			0.729078			0.364539	+	0.931188i	$0.381227\pi$
$54$		0			0
$55$	−2.78744			−0.375859
$56$		0			0
$57$	−2.86958	−	9.63804i	−0.380085	−	1.27659i
$58$		0			0
$59$	−2.57152	+	4.45401i	−0.334784	+	0.579862i	−0.983443	−	0.181216i	$-0.941997\pi$
$59$	−2.57152	+	4.45401i	−0.334784	+	0.579862i	0.648660	+	0.761079i	$0.275330\pi$
$60$		0			0
$61$	−0.921988	−	1.59693i	−0.118049	−	0.204466i	0.800946	−	0.598737i	$-0.204330\pi$
$61$	−0.921988	−	1.59693i	−0.118049	−	0.204466i	−0.918994	+	0.394271i	$0.870997\pi$
$62$		0			0
$63$	−12.5818	−	6.36650i	−1.58516	−	0.802103i
$64$		0			0
$65$	0.417328	+	0.722833i	0.0517631	+	0.0896564i
$66$		0			0
$67$	5.79316	−	10.0340i	0.707747	−	1.22585i	−0.257944	−	0.966160i	$-0.583045\pi$
$67$	5.79316	−	10.0340i	0.707747	−	1.22585i	0.965691	−	0.259694i	$-0.0836218\pi$
$68$		0			0
$69$	−14.9205	−	3.56004i	−1.79622	−	0.428579i
$70$		0			0
$71$	10.6289			1.26142			0.630708	−	0.776021i	$-0.282765\pi$
$71$	10.6289			1.26142			0.630708	+	0.776021i	$0.282765\pi$
$72$		0			0
$73$	4.40840			0.515964			0.257982	−	0.966150i	$-0.416943\pi$
$73$	4.40840			0.515964			0.257982	+	0.966150i	$0.416943\pi$
$74$		0			0
$75$	5.61024	−	5.92854i	0.647815	−	0.684569i
$76$		0			0
$77$	12.2171	−	21.1606i	1.39227	−	2.41147i
$78$		0			0
$79$	3.32244	+	5.75464i	0.373804	+	0.647448i	0.990147	−	0.140030i	$-0.0447199\pi$
$79$	3.32244	+	5.75464i	0.373804	+	0.647448i	−0.616343	+	0.787478i	$0.711387\pi$
$80$		0			0
$81$	3.61459	−	8.24225i	0.401622	−	0.915806i
$82$		0			0
$83$	5.28055	+	9.14617i	0.579615	+	1.00392i	0.995523	+	0.0945164i	$0.0301305\pi$
$83$	5.28055	+	9.14617i	0.579615	+	1.00392i	−0.415908	+	0.909407i	$0.636536\pi$
$84$		0			0
$85$	0.186541	−	0.323099i	0.0202333	−	0.0350450i
$86$		0			0
$87$	4.57628	−	4.83592i	0.490629	−	0.518465i
$88$		0			0
$89$	−7.30777			−0.774622			−0.387311	−	0.921949i	$-0.626596\pi$
$89$	−7.30777			−0.774622			−0.387311	+	0.921949i	$0.626596\pi$
$90$		0			0
$91$	−7.31642			−0.766969
$92$		0			0
$93$	−9.33475	−	2.22728i	−0.967969	−	0.230958i
$94$		0			0
$95$	1.55659	−	2.69609i	0.159703	−	0.276613i
$96$		0			0
$97$	−7.81612	−	13.5379i	−0.793607	−	1.37457i	−0.923720	−	0.383068i	$-0.874867\pi$
$97$	−7.81612	−	13.5379i	−0.793607	−	1.37457i	0.130113	−	0.991499i	$-0.458466\pi$
$98$		0			0
$99$	13.9153	+	7.04125i	1.39854	+	0.707672i
$100$		0			0
$101$	−4.43218	−	7.67676i	−0.441018	−	0.763866i	0.556747	−	0.830682i	$-0.312049\pi$
$101$	−4.43218	−	7.67676i	−0.441018	−	0.763866i	−0.997765	+	0.0668159i	$0.978716\pi$
$102$		0			0
$103$	1.64986	−	2.85764i	0.162565	−	0.281571i	−0.773223	−	0.634135i	$-0.781356\pi$
$103$	1.64986	−	2.85764i	0.162565	−	0.281571i	0.935788	+	0.352563i	$0.114690\pi$
$104$		0			0
$105$	−1.24567	−	4.18383i	−0.121565	−	0.408300i
$106$		0			0
$107$	−7.12139			−0.688451			−0.344226	−	0.938887i	$-0.611858\pi$
$107$	−7.12139			−0.688451			−0.344226	+	0.938887i	$0.611858\pi$
$108$		0			0
$109$	2.98862			0.286258			0.143129	−	0.989704i	$-0.454284\pi$
$109$	2.98862			0.286258			0.143129	+	0.989704i	$0.454284\pi$
$110$		0			0
$111$	−2.02287	−	6.79419i	−0.192002	−	0.644876i
$112$		0			0
$113$	3.40833	−	5.90340i	0.320629	−	0.555345i	−0.659989	−	0.751275i	$-0.729439\pi$
$113$	3.40833	−	5.90340i	0.320629	−	0.555345i	0.980618	+	0.195930i	$0.0627725\pi$
$114$		0			0
$115$	−2.37437	−	4.11253i	−0.221411	−	0.383496i
$116$		0			0
$117$	−0.257435	−	4.66267i	−0.0237999	−	0.431064i
$118$		0			0
$119$	1.63518	+	2.83222i	0.149897	+	0.259629i
$120$		0			0
$121$	−8.01190	+	13.8770i	−0.728355	+	1.26155i
$122$		0			0
$123$	−3.40386	−	0.812162i	−0.306915	−	0.0732302i
$124$		0			0
$125$	5.20790			0.465809
$126$		0			0
$127$	−17.7567			−1.57565			−0.787826	−	0.615899i	$-0.788793\pi$
$127$	−17.7567			−1.57565			−0.787826	+	0.615899i	$0.788793\pi$
$128$		0			0
$129$	−8.84598	+	9.34786i	−0.778845	+	0.823033i
$130$		0			0
$131$	−3.51253	+	6.08389i	−0.306892	+	0.531552i	−0.977681	−	0.210096i	$-0.932622\pi$
$131$	−3.51253	+	6.08389i	−0.306892	+	0.531552i	0.670789	+	0.741648i	$0.265956\pi$
$132$		0			0
$133$	13.6448	+	23.6334i	1.18315	+	2.04928i
$134$		0			0
$135$	2.62248	−	0.941065i	0.225707	−	0.0809940i
$136$		0			0
$137$	5.71048	+	9.89083i	0.487879	+	0.845031i	0.999903	−	0.0139402i	$-0.00443746\pi$
$137$	5.71048	+	9.89083i	0.487879	+	0.845031i	−0.512024	+	0.858971i	$0.671104\pi$
$138$		0			0
$139$	3.10659	−	5.38078i	0.263498	−	0.456392i	−0.703671	−	0.710526i	$-0.748457\pi$
$139$	3.10659	−	5.38078i	0.263498	−	0.456392i	0.967169	+	0.254134i	$0.0817905\pi$
$140$		0			0
$141$	−0.443025	+	0.468160i	−0.0373094	+	0.0394262i
$142$		0			0
$143$	8.09185			0.676674
$144$		0			0
$145$	2.06117			0.171171
$146$		0			0
$147$	25.4275	+	6.06701i	2.09722	+	0.500399i
$148$		0			0
$149$	−5.47858	+	9.48918i	−0.448823	+	0.777384i	−0.998310	−	0.0581186i	$-0.981490\pi$
$149$	−5.47858	+	9.48918i	−0.448823	+	0.777384i	0.549487	+	0.835502i	$0.314823\pi$
$150$		0			0
$151$	7.28439	+	12.6169i	0.592796	+	1.02675i	0.993854	+	0.110700i	$0.0353091\pi$
$151$	7.28439	+	12.6169i	0.592796	+	1.02675i	−0.401058	+	0.916053i	$0.631358\pi$
$152$		0			0
$153$	−1.74741	+	1.14174i	−0.141270	+	0.0923041i
$154$		0			0
$155$	−1.48548	−	2.57293i	−0.119317	−	0.206663i
$156$		0			0
$157$	−7.66049	+	13.2684i	−0.611373	+	1.05893i	0.379636	+	0.925136i	$0.376049\pi$
$157$	−7.66049	+	13.2684i	−0.611373	+	1.05893i	−0.991009	+	0.133794i	$0.957284\pi$
$158$		0			0
$159$	−2.62337	−	8.81108i	−0.208047	−	0.698764i
$160$		0			0
$161$	41.6265			3.28063
$162$		0			0
$163$	−11.0724			−0.867258			−0.433629	−	0.901091i	$-0.642767\pi$
$163$	−11.0724			−0.867258			−0.433629	+	0.901091i	$0.642767\pi$
$164$		0			0
$165$	1.37769	+	4.62725i	0.107253	+	0.360231i
$166$		0			0
$167$	−4.15607	+	7.19852i	−0.321606	+	0.557039i	−0.980820	−	0.194917i	$-0.937556\pi$
$167$	−4.15607	+	7.19852i	−0.321606	+	0.557039i	0.659213	+	0.751956i	$0.270889\pi$
$168$		0			0
$169$	5.28851	+	9.15997i	0.406809	+	0.704613i
$170$		0			0
$171$	−14.5812	+	9.52721i	−1.11505	+	0.728564i
$172$		0			0
$173$	0.0396656	+	0.0687029i	0.00301572	+	0.00522338i	0.867529	−	0.497386i	$-0.165707\pi$
$173$	0.0396656	+	0.0687029i	0.00301572	+	0.00522338i	−0.864514	+	0.502609i	$0.832373\pi$
$174$		0			0
$175$	−11.0750	+	19.1825i	−0.837191	+	1.45006i
$176$		0			0
$177$	8.66478	+	2.06742i	0.651285	+	0.155397i
$178$		0			0
$179$	−20.8011			−1.55475			−0.777375	−	0.629038i	$-0.783449\pi$
$179$	−20.8011			−1.55475			−0.777375	+	0.629038i	$0.783449\pi$
$180$		0			0
$181$	−5.13118			−0.381397			−0.190699	−	0.981649i	$-0.561075\pi$
$181$	−5.13118			−0.381397			−0.190699	+	0.981649i	$0.561075\pi$
$182$		0			0
$183$	−2.19527	+	2.31982i	−0.162279	+	0.171486i
$184$		0			0
$185$	1.09729	−	1.90057i	0.0806747	−	0.139733i
$186$		0			0
$187$	−1.80849	−	3.13240i	−0.132250	−	0.229063i
$188$		0			0
$189$	−4.35005	+	24.0329i	−0.316420	+	1.74813i
$190$		0			0
$191$	−9.89085	−	17.1315i	−0.715677	−	1.23959i	−0.962698	−	0.270579i	$-0.912785\pi$
$191$	−9.89085	−	17.1315i	−0.715677	−	1.23959i	0.247021	−	0.969010i	$-0.420548\pi$
$192$		0			0
$193$	1.79574	−	3.11031i	0.129260	−	0.223885i	−0.794130	−	0.607748i	$-0.792073\pi$
$193$	1.79574	−	3.11031i	0.129260	−	0.223885i	0.923390	+	0.383863i	$0.125407\pi$
$194$		0			0
$195$	0.993663	−	1.05004i	0.0711577	−	0.0751948i
$196$		0			0
$197$	1.71261			0.122019			0.0610093	−	0.998137i	$-0.480568\pi$
$197$	1.71261			0.122019			0.0610093	+	0.998137i	$0.480568\pi$
$198$		0			0
$199$	18.1299			1.28520			0.642598	−	0.766203i	$-0.277856\pi$
$199$	18.1299			1.28520			0.642598	+	0.766203i	$0.277856\pi$
$200$		0			0
$201$	−19.5201	−	4.65752i	−1.37684	−	0.328516i
$202$		0			0
$203$	−9.03389	+	15.6472i	−0.634055	+	1.09822i
$204$		0			0
$205$	−0.541672	−	0.938204i	−0.0378320	−	0.0655270i
$206$		0			0
$207$	1.46467	+	26.5281i	0.101802	+	1.84383i
$208$		0			0
$209$	−15.0909	−	26.1382i	−1.04386	−	1.80802i
$210$		0			0
$211$	0.734306	−	1.27186i	0.0505517	−	0.0875581i	−0.839642	−	0.543140i	$-0.817235\pi$
$211$	0.734306	−	1.27186i	0.0505517	−	0.0875581i	0.890194	+	0.455582i	$0.150569\pi$
$212$		0			0
$213$	−5.25332	−	17.6443i	−0.359952	−	1.20897i
$214$		0			0
$215$	−3.98425			−0.271724
$216$		0			0
$217$	26.0429			1.76791
$218$		0			0
$219$	−2.17885	−	7.31809i	−0.147233	−	0.494511i
$220$		0			0
$221$	−0.541523	+	0.937946i	−0.0364268	+	0.0630931i
$222$		0			0
$223$	9.57845	+	16.5904i	0.641420	+	1.11097i	0.985116	+	0.171891i	$0.0549878\pi$
$223$	9.57845	+	16.5904i	0.641420	+	1.11097i	−0.343696	+	0.939081i	$0.611679\pi$
$224$		0			0
$225$	−12.6145	−	6.38302i	−0.840964	−	0.425535i
$226$		0			0
$227$	−5.92737	−	10.2665i	−0.393414	−	0.681412i	0.599484	−	0.800387i	$-0.295373\pi$
$227$	−5.92737	−	10.2665i	−0.393414	−	0.681412i	−0.992897	+	0.118975i	$0.962039\pi$
$228$		0			0
$229$	−1.57219	+	2.72311i	−0.103893	+	0.179948i	−0.913285	−	0.407320i	$-0.866463\pi$
$229$	−1.57219	+	2.72311i	−0.103893	+	0.179948i	0.809392	+	0.587268i	$0.199797\pi$
$230$		0			0
$231$	−41.1656	−	9.82214i	−2.70850	−	0.646250i
$232$		0			0
$233$	−2.82935			−0.185357			−0.0926783	−	0.995696i	$-0.529543\pi$
$233$	−2.82935			−0.185357			−0.0926783	+	0.995696i	$0.529543\pi$
$234$		0			0
$235$	−0.199539			−0.0130165
$236$		0			0
$237$	7.91079	−	8.35960i	0.513861	−	0.543015i
$238$		0			0
$239$	1.58766	−	2.74991i	0.102697	−	0.177877i	−0.810098	−	0.586295i	$-0.800586\pi$
$239$	1.58766	−	2.74991i	0.102697	−	0.177877i	0.912795	+	0.408418i	$0.133919\pi$
$240$		0			0
$241$	6.63053	+	11.4844i	0.427110	+	0.739776i	0.996615	−	0.0822117i	$-0.0261984\pi$
$241$	6.63053	+	11.4844i	0.427110	+	0.739776i	−0.569505	+	0.821988i	$0.692865\pi$
$242$		0			0
$243$	−15.4689	−	1.92662i	−0.992333	−	0.123593i
$244$		0			0
$245$	4.04640	+	7.00857i	0.258515	+	0.447761i
$246$		0			0
$247$	−4.51873	+	7.82666i	−0.287520	+	0.497999i
$248$		0			0
$249$	12.5731	−	13.2864i	0.796785	−	0.841991i
$250$		0			0
$251$	−3.06394			−0.193394			−0.0966970	−	0.995314i	$-0.530828\pi$
$251$	−3.06394			−0.193394			−0.0966970	+	0.995314i	$0.530828\pi$
$252$		0			0
$253$	−46.0383			−2.89440
$254$		0			0
$255$	−0.628554	−	0.149973i	−0.0393616	−	0.00939170i
$256$		0			0
$257$	8.14120	−	14.1010i	0.507834	−	0.879595i	−0.492125	−	0.870525i	$-0.663780\pi$
$257$	8.14120	−	14.1010i	0.507834	−	0.879595i	0.999959	−	0.00907003i	$-0.00288712\pi$
$258$		0			0
$259$	9.61866	+	16.6600i	0.597674	+	1.03520i
$260$		0			0
$261$	−10.2896	−	5.20664i	−0.636912	−	0.322283i
$262$		0			0
$263$	11.0730	+	19.1790i	0.682789	+	1.18262i	0.974126	+	0.226005i	$0.0725664\pi$
$263$	11.0730	+	19.1790i	0.682789	+	1.18262i	−0.291337	+	0.956620i	$0.594100\pi$
$264$		0			0
$265$	1.42303	−	2.46476i	0.0874162	−	0.151409i
$266$		0			0
$267$	3.61187	+	12.1312i	0.221043	+	0.742415i
$268$		0			0
$269$	31.7805			1.93769			0.968845	−	0.247667i	$-0.0796639\pi$
$269$	31.7805			1.93769			0.968845	+	0.247667i	$0.0796639\pi$
$270$		0			0
$271$	0.794033			0.0482341			0.0241170	−	0.999709i	$-0.492323\pi$
$271$	0.794033			0.0482341			0.0241170	+	0.999709i	$0.492323\pi$
$272$		0			0
$273$	3.61614	+	12.1455i	0.218859	+	0.735080i
$274$		0			0
$275$	12.2488	−	21.2155i	0.738629	−	1.27934i
$276$		0			0
$277$	12.6085	+	21.8385i	0.757569	+	1.31215i	0.944087	+	0.329696i	$0.106946\pi$
$277$	12.6085	+	21.8385i	0.757569	+	1.31215i	−0.186519	+	0.982451i	$0.559720\pi$
$278$		0			0
$279$	0.916345	+	16.5969i	0.0548601	+	0.993628i
$280$		0			0
$281$	−5.06672	−	8.77581i	−0.302255	−	0.523521i	0.674391	−	0.738374i	$-0.264406\pi$
$281$	−5.06672	−	8.77581i	−0.302255	−	0.523521i	−0.976646	+	0.214853i	$0.931073\pi$
$282$		0			0
$283$	11.6766	−	20.2245i	0.694102	−	1.20222i	−0.276380	−	0.961048i	$-0.589135\pi$
$283$	11.6766	−	20.2245i	0.694102	−	1.20222i	0.970482	−	0.241172i	$-0.0775319\pi$
$284$		0			0
$285$	−5.24496	−	1.25145i	−0.310684	−	0.0741295i
$286$		0			0
$287$	9.49637			0.560553
$288$		0			0
$289$	−16.5159			−0.971523
$290$		0			0
$291$	−18.6103	+	19.6662i	−1.09095	+	1.15285i
$292$		0			0
$293$	−13.1967	+	22.8573i	−0.770959	+	1.33534i	0.166079	+	0.986112i	$0.446889\pi$
$293$	−13.1967	+	22.8573i	−0.770959	+	1.33534i	−0.937038	+	0.349228i	$0.886444\pi$
$294$		0			0
$295$	1.37887	+	2.38827i	0.0802809	+	0.139051i
$296$		0			0
$297$	4.81109	−	26.5800i	0.279168	−	1.54233i
$298$		0			0
$299$	6.89272	+	11.9385i	0.398616	+	0.690424i
$300$		0			0
$301$	17.4626	−	30.2461i	1.00653	−	1.74335i
$302$		0			0
$303$	−10.5531	+	11.1518i	−0.606259	+	0.640655i
$304$		0			0
$305$	−0.988754			−0.0566159
$306$		0			0
$307$	−21.6724			−1.23691			−0.618454	−	0.785821i	$-0.712241\pi$
$307$	−21.6724			−1.23691			−0.618454	+	0.785821i	$0.712241\pi$
$308$		0			0
$309$	−5.55922	−	1.32643i	−0.316253	−	0.0754582i
$310$		0			0
$311$	14.5448	−	25.1924i	0.824761	−	1.42853i	−0.0773408	−	0.997005i	$-0.524643\pi$
$311$	14.5448	−	25.1924i	0.824761	−	1.42853i	0.902102	−	0.431523i	$-0.142024\pi$
$312$		0			0
$313$	3.52393	+	6.10363i	0.199185	+	0.344998i	0.948264	−	0.317482i	$-0.102837\pi$
$313$	3.52393	+	6.10363i	0.199185	+	0.344998i	−0.749080	+	0.662480i	$0.769504\pi$
$314$		0			0
$315$	−6.32963	+	4.13572i	−0.356634	+	0.233021i
$316$		0			0
$317$	0.444372	+	0.769675i	0.0249584	+	0.0432292i	0.878235	−	0.478230i	$-0.158721\pi$
$317$	0.444372	+	0.769675i	0.0249584	+	0.0432292i	−0.853276	+	0.521459i	$0.825388\pi$
$318$		0			0
$319$	9.99135	−	17.3055i	0.559408	−	0.968923i
$320$		0			0
$321$	3.51975	+	11.8218i	0.196453	+	0.659826i
$322$		0			0
$323$	4.03966			0.224772
$324$		0			0
$325$	−7.33540			−0.406895
$326$		0			0
$327$	−1.47713	−	4.96122i	−0.0816853	−	0.274356i
$328$		0			0
$329$	0.874561	−	1.51478i	0.0482161	−	0.0835127i
$330$		0			0
$331$	11.4513	+	19.8342i	0.629420	+	1.09019i	0.987668	+	0.156561i	$0.0500407\pi$
$331$	11.4513	+	19.8342i	0.629420	+	1.09019i	−0.358249	+	0.933626i	$0.616626\pi$
$332$		0			0
$333$	−10.2788	+	6.71606i	−0.563274	+	0.368038i
$334$		0			0
$335$	−3.10634	−	5.38033i	−0.169717	−	0.293959i
$336$		0			0
$337$	0.415255	−	0.719243i	0.0226204	−	0.0391796i	−0.854494	−	0.519462i	$-0.826132\pi$
$337$	0.415255	−	0.719243i	0.0226204	−	0.0391796i	0.877114	+	0.480282i	$0.159466\pi$
$338$		0			0
$339$	−11.4844	−	2.74019i	−0.623748	−	0.148827i
$340$		0			0
$341$	−28.8031			−1.55977
$342$		0			0
$343$	−38.0378			−2.05385
$344$		0			0
$345$	−5.65342	+	5.97416i	−0.304370	+	0.321638i
$346$		0			0
$347$	−8.53131	+	14.7767i	−0.457985	+	0.793253i	−0.998854	−	0.0478537i	$-0.984762\pi$
$347$	−8.53131	+	14.7767i	−0.457985	+	0.793253i	0.540870	+	0.841106i	$0.318095\pi$
$348$		0			0
$349$	10.9443	+	18.9561i	0.585836	+	1.01470i	0.994771	+	0.102134i	$0.0325671\pi$
$349$	10.9443	+	18.9561i	0.585836	+	1.01470i	−0.408935	+	0.912564i	$0.634100\pi$
$350$		0			0
$351$	−7.61296	+	2.73188i	−0.406350	+	0.145817i
$352$		0			0
$353$	9.53407	+	16.5135i	0.507447	+	0.878924i	0.999963	+	0.00862082i	$0.00274413\pi$
$353$	9.53407	+	16.5135i	0.507447	+	0.878924i	−0.492516	+	0.870304i	$0.663923\pi$
$354$		0			0
$355$	2.84964	−	4.93572i	0.151243	−	0.261961i
$356$		0			0
$357$	3.89340	−	4.11429i	0.206061	−	0.217751i
$358$		0			0
$359$	−13.1482			−0.693938			−0.346969	−	0.937877i	$-0.612789\pi$
$359$	−13.1482			−0.693938			−0.346969	+	0.937877i	$0.612789\pi$
$360$		0			0
$361$	14.7088			0.774147
$362$		0			0
$363$	26.9962	+	6.44132i	1.41693	+	0.338081i
$364$		0			0
$365$	1.18191	−	2.04712i	0.0618638	−	0.107151i
$366$		0			0
$367$	−7.79061	−	13.4937i	−0.406666	−	0.704367i	0.587848	−	0.808972i	$-0.299975\pi$
$367$	−7.79061	−	13.4937i	−0.406666	−	0.704367i	−0.994514	+	0.104605i	$0.966642\pi$
$368$		0			0
$369$	0.334139	+	6.05193i	0.0173946	+	0.315051i
$370$		0			0
$371$	12.4740	+	21.6056i	0.647618	+	1.12171i
$372$		0			0
$373$	9.92199	−	17.1854i	0.513741	−	0.889826i	−0.486132	−	0.873885i	$-0.661593\pi$
$373$	9.92199	−	17.1854i	0.513741	−	0.889826i	0.999873	−	0.0159402i	$-0.00507413\pi$
$374$		0			0
$375$	−2.57401	−	8.64530i	−0.132921	−	0.446442i
$376$		0			0
$377$	−5.98350			−0.308166
$378$		0			0
$379$	−15.0470			−0.772914			−0.386457	−	0.922307i	$-0.626301\pi$
$379$	−15.0470			−0.772914			−0.386457	+	0.922307i	$0.626301\pi$
$380$		0			0
$381$	8.77625	+	29.4767i	0.449621	+	1.51014i
$382$		0			0
$383$	−16.4288	+	28.4556i	−0.839474	+	1.45401i	0.0508616	+	0.998706i	$0.483803\pi$
$383$	−16.4288	+	28.4556i	−0.839474	+	1.45401i	−0.890335	+	0.455305i	$0.849530\pi$
$384$		0			0
$385$	−6.55089	−	11.3465i	−0.333864	−	0.578270i
$386$		0			0
$387$	19.8899	+	10.0645i	1.01106	+	0.511605i
$388$		0			0
$389$	−1.87559	−	3.24862i	−0.0950962	−	0.164711i	0.814553	−	0.580090i	$-0.196983\pi$
$389$	−1.87559	−	3.24862i	−0.0950962	−	0.164711i	−0.909649	+	0.415378i	$0.863649\pi$
$390$		0			0
$391$	3.08098	−	5.33641i	0.155812	−	0.269874i
$392$		0			0
$393$	11.8355	+	2.82397i	0.597024	+	0.142450i
$394$		0			0
$395$	3.56304			0.179276
$396$		0			0
$397$	−23.5495			−1.18192			−0.590958	−	0.806702i	$-0.701250\pi$
$397$	−23.5495			−1.18192			−0.590958	+	0.806702i	$0.701250\pi$
$398$		0			0
$399$	32.4884	−	34.3316i	1.62645	−	1.71873i
$400$		0			0
$401$	7.28105	−	12.6111i	0.363598	−	0.629771i	−0.624952	−	0.780663i	$-0.714881\pi$
$401$	7.28105	−	12.6111i	0.363598	−	0.629771i	0.988550	+	0.150893i	$0.0482148\pi$
$402$		0			0
$403$	4.31231	+	7.46914i	0.214811	+	0.372064i
$404$		0			0
$405$	−2.85836	−	3.88828i	−0.142033	−	0.193210i
$406$		0			0
$407$	−10.6381	−	18.4257i	−0.527310	−	0.913328i
$408$		0			0
$409$	3.23655	−	5.60586i	0.160037	−	0.277192i	−0.774845	−	0.632152i	$-0.782172\pi$
$409$	3.23655	−	5.60586i	0.160037	−	0.277192i	0.934882	+	0.354959i	$0.115505\pi$
$410$		0			0
$411$	13.5967	−	14.3681i	0.670677	−	0.708728i
$412$		0			0
$413$	−24.1738			−1.18951
$414$		0			0
$415$	5.66294			0.277983
$416$		0			0
$417$	−10.4677	−	2.49760i	−0.512606	−	0.122308i
$418$		0			0
$419$	−13.4378	+	23.2750i	−0.656481	+	1.13706i	0.325040	+	0.945700i	$0.394622\pi$
$419$	−13.4378	+	23.2750i	−0.656481	+	1.13706i	−0.981520	+	0.191357i	$0.938711\pi$
$420$		0			0
$421$	−3.85521	−	6.67742i	−0.187892	−	0.325438i	0.756656	−	0.653814i	$-0.226832\pi$
$421$	−3.85521	−	6.67742i	−0.187892	−	0.325438i	−0.944547	+	0.328376i	$0.893499\pi$
$422$		0			0
$423$	0.996127	+	0.504049i	0.0484333	+	0.0245077i
$424$		0			0
$425$	1.63943	+	2.83957i	0.0795239	+	0.137740i
$426$		0			0
$427$	4.33361	−	7.50603i	0.209718	−	0.363242i
$428$		0			0
$429$	−3.99940	−	13.4327i	−0.193093	−	0.648539i
$430$		0			0
$431$	3.45993			0.166659			0.0833294	−	0.996522i	$-0.473445\pi$
$431$	3.45993			0.166659			0.0833294	+	0.996522i	$0.473445\pi$
$432$		0			0
$433$	−12.7863			−0.614471			−0.307236	−	0.951633i	$-0.599404\pi$
$433$	−12.7863			−0.614471			−0.307236	+	0.951633i	$0.599404\pi$
$434$		0			0
$435$	−1.01873	−	3.42161i	−0.0488445	−	0.164054i
$436$		0			0
$437$	25.7092	−	44.5296i	1.22984	−	2.13014i
$438$		0			0
$439$	−2.76458	−	4.78840i	−0.131946	−	0.228538i	0.792480	−	0.609897i	$-0.208789\pi$
$439$	−2.76458	−	4.78840i	−0.131946	−	0.228538i	−0.924427	+	0.381359i	$0.875456\pi$
$440$		0			0
$441$	−2.49609	−	45.2091i	−0.118861	−	2.15282i
$442$		0			0
$443$	−13.2718	−	22.9874i	−0.630563	−	1.09217i	−0.987437	−	0.158014i	$-0.949491\pi$
$443$	−13.2718	−	22.9874i	−0.630563	−	1.09217i	0.356874	−	0.934152i	$-0.383842\pi$
$444$		0			0
$445$	−1.95924	+	3.39350i	−0.0928769	+	0.160867i
$446$		0			0
$447$	18.4602	+	4.40460i	0.873135	+	0.208331i
$448$		0			0
$449$	−29.9625			−1.41402			−0.707010	−	0.707204i	$-0.749956\pi$
$449$	−29.9625			−1.41402			−0.707010	+	0.707204i	$0.749956\pi$
$450$		0			0
$451$	−10.5028			−0.494560
$452$		0			0
$453$	17.3443	−	18.3283i	0.814904	−	0.861138i
$454$		0			0
$455$	−1.96156	+	3.39752i	−0.0919593	+	0.159278i
$456$		0			0
$457$	−12.3904	−	21.4608i	−0.579597	−	1.00389i	−0.995525	−	0.0944945i	$-0.969877\pi$
$457$	−12.3904	−	21.4608i	−0.579597	−	1.00389i	0.415928	−	0.909398i	$-0.363457\pi$
$458$		0			0
$459$	2.75898	+	2.33645i	0.128778	+	0.109056i
$460$		0			0
$461$	−5.30632	−	9.19081i	−0.247140	−	0.428059i	0.715591	−	0.698519i	$-0.246157\pi$
$461$	−5.30632	−	9.19081i	−0.247140	−	0.428059i	−0.962731	+	0.270461i	$0.912824\pi$
$462$		0			0
$463$	5.31762	−	9.21040i	0.247131	−	0.428043i	−0.715598	−	0.698513i	$-0.753846\pi$
$463$	5.31762	−	9.21040i	0.247131	−	0.428043i	0.962729	+	0.270469i	$0.0871789\pi$
$464$		0			0
$465$	−3.53696	+	3.73763i	−0.164023	+	0.173328i
$466$		0			0
$467$	−27.3831			−1.26714			−0.633569	−	0.773686i	$-0.718411\pi$
$467$	−27.3831			−1.26714			−0.633569	+	0.773686i	$0.718411\pi$
$468$		0			0
$469$	54.4590			2.51468
$470$		0			0
$471$	25.8121	+	6.15879i	1.18936	+	0.283782i
$472$		0			0
$473$	−19.3133	+	33.4517i	−0.888028	+	1.53811i
$474$		0			0
$475$	13.6802	+	23.6947i	0.627689	+	1.08719i
$476$		0			0
$477$	−13.3301	+	8.70976i	−0.610344	+	0.398793i
$478$		0			0
$479$	20.3026	+	35.1651i	0.927649	+	1.60674i	0.787245	+	0.616641i	$0.211507\pi$
$479$	20.3026	+	35.1651i	0.927649	+	1.60674i	0.140404	+	0.990094i	$0.455160\pi$
$480$		0			0
$481$	−3.18541	+	5.51728i	−0.145242	+	0.251566i
$482$		0			0
$483$	−20.5739	−	69.1015i	−0.936146	−	3.14423i
$484$		0			0
$485$	−8.38212			−0.380613
$486$		0			0
$487$	−4.99658			−0.226417			−0.113208	−	0.993571i	$-0.536113\pi$
$487$	−4.99658			−0.226417			−0.113208	+	0.993571i	$0.536113\pi$
$488$		0			0
$489$	5.47254	+	18.3806i	0.247477	+	0.831199i
$490$		0			0
$491$	19.2049	−	33.2639i	0.866705	−	1.50118i	0.00136059	−	0.999999i	$-0.499567\pi$
$491$	19.2049	−	33.2639i	0.866705	−	1.50118i	0.865344	−	0.501178i	$-0.167100\pi$
$492$		0			0
$493$	1.33728	+	2.31624i	0.0602282	+	0.104318i
$494$		0			0
$495$	7.00048	−	4.57404i	0.314648	−	0.205588i
$496$		0			0
$497$	24.9794	+	43.2655i	1.12048	+	1.94072i
$498$		0			0
$499$	11.3616	−	19.6788i	0.508614	−	0.880945i	−0.491337	−	0.870970i	$-0.663491\pi$
$499$	11.3616	−	19.6788i	0.508614	−	0.880945i	0.999950	−	0.00997497i	$-0.00317518\pi$
$500$		0			0
$501$	14.0039	+	3.34135i	0.625650	+	0.149280i
$502$		0			0
$503$	−40.2323			−1.79387			−0.896935	−	0.442161i	$-0.854212\pi$
$503$	−40.2323			−1.79387			−0.896935	+	0.442161i	$0.854212\pi$
$504$		0			0
$505$	−4.75313			−0.211512
$506$		0			0
$507$	12.5920	−	13.3064i	0.559232	−	0.590960i
$508$		0			0
$509$	4.30968	−	7.46459i	0.191023	−	0.330862i	−0.754566	−	0.656224i	$-0.772153\pi$
$509$	4.30968	−	7.46459i	0.191023	−	0.330862i	0.945590	+	0.325362i	$0.105486\pi$
$510$		0			0
$511$	10.3604	+	17.9447i	0.458315	+	0.793825i
$512$		0			0
$513$	23.0223	+	19.4965i	1.01646	+	0.860791i
$514$		0			0
$515$	−0.884666	−	1.53229i	−0.0389830	−	0.0675206i
$516$		0			0
$517$	−0.967251	+	1.67533i	−0.0425396	+	0.0736808i
$518$		0			0
$519$	0.0944444	−	0.0998027i	0.00414565	−	0.00438085i
$520$		0			0
$521$	−20.5770			−0.901496			−0.450748	−	0.892651i	$-0.648843\pi$
$521$	−20.5770			−0.901496			−0.450748	+	0.892651i	$0.648843\pi$
$522$		0			0
$523$	−15.6990			−0.686470			−0.343235	−	0.939250i	$-0.611523\pi$
$523$	−15.6990			−0.686470			−0.343235	+	0.939250i	$0.611523\pi$
$524$		0			0
$525$	37.3174	+	8.90395i	1.62866	+	0.388600i
$526$		0			0
$527$	1.92756	−	3.33863i	0.0839659	−	0.145433i
$528$		0			0
$529$	−27.7159	−	48.0054i	−1.20504	−	2.08719i
$530$		0			0
$531$	−0.850578	−	15.4057i	−0.0369119	−	0.668549i
$532$		0			0
$533$	1.57245	+	2.72357i	0.0681106	+	0.117971i
$534$		0			0
$535$	−1.90927	+	3.30696i	−0.0825450	+	0.142972i
$536$		0			0
$537$	10.2810	+	34.5306i	0.443656	+	1.49011i
$538$		0			0
$539$	78.4584			3.37944
$540$		0			0
$541$	4.79886			0.206319			0.103160	−	0.994665i	$-0.467105\pi$
$541$	4.79886			0.206319			0.103160	+	0.994665i	$0.467105\pi$
$542$		0			0
$543$	2.53609	+	8.51794i	0.108834	+	0.365540i
$544$		0			0
$545$	0.801260	−	1.38782i	0.0343222	−	0.0594478i
$546$		0			0
$547$	−8.26596	−	14.3171i	−0.353427	−	0.612153i	0.633421	−	0.773808i	$-0.281650\pi$
$547$	−8.26596	−	14.3171i	−0.353427	−	0.612153i	−0.986847	+	0.161654i	$0.948317\pi$
$548$		0			0
$549$	4.93599	+	2.49765i	0.210663	+	0.106597i
$550$		0			0
$551$	11.1589	+	19.3278i	0.475386	+	0.823393i
$552$		0			0
$553$	−15.6164	+	27.0484i	−0.664078	+	1.15022i
$554$		0			0
$555$	−3.69735	−	0.882190i	−0.156944	−	0.0374469i
$556$		0			0
$557$	14.2466			0.603649			0.301825	−	0.953363i	$-0.402404\pi$
$557$	14.2466			0.603649			0.301825	+	0.953363i	$0.402404\pi$
$558$		0			0
$559$	11.5661			0.489196
$560$		0			0
$561$	−4.30604	+	4.55034i	−0.181801	+	0.192116i
$562$		0			0
$563$	13.4981	−	23.3794i	0.568876	−	0.985322i	−0.427801	−	0.903873i	$-0.640712\pi$
$563$	13.4981	−	23.3794i	0.568876	−	0.985322i	0.996677	−	0.0814497i	$-0.0259550\pi$
$564$		0			0
$565$	−1.82757	−	3.16545i	−0.0768865	−	0.133171i
$566$		0			0
$567$	42.0454	−	4.65702i	1.76574	−	0.195576i
$568$		0			0
$569$	4.82124	+	8.35063i	0.202117	+	0.350076i	0.949210	−	0.314643i	$-0.101885\pi$
$569$	4.82124	+	8.35063i	0.202117	+	0.350076i	−0.747094	+	0.664719i	$0.768551\pi$
$570$		0			0
$571$	−15.0536	+	26.0736i	−0.629973	+	1.09115i	0.357584	+	0.933881i	$0.383601\pi$
$571$	−15.0536	+	26.0736i	−0.629973	+	1.09115i	−0.987557	+	0.157264i	$0.949733\pi$
$572$		0			0
$573$	−23.5503	+	24.8864i	−0.983826	+	1.03964i
$574$		0			0
$575$	41.7346			1.74045
$576$		0			0
$577$	14.9642			0.622968			0.311484	−	0.950251i	$-0.399174\pi$
$577$	14.9642			0.622968			0.311484	+	0.950251i	$0.399174\pi$
$578$		0			0
$579$	−6.05076	−	1.44372i	−0.251461	−	0.0599988i
$580$		0			0
$581$	−24.8201	+	42.9896i	−1.02971	+	1.78351i
$582$		0			0
$583$	−13.7961	−	23.8955i	−0.571375	−	0.989650i
$584$		0			0
$585$	−2.23422	−	1.13053i	−0.0923736	−	0.0467418i
$586$		0			0
$587$	−12.0511	−	20.8731i	−0.497401	−	0.861523i	0.502595	−	0.864522i	$-0.332379\pi$
$587$	−12.0511	−	20.8731i	−0.497401	−	0.861523i	−0.999996	+	0.00299890i	$0.999045\pi$
$588$		0			0
$589$	16.0845	−	27.8591i	0.662749	−	1.14792i
$590$		0			0
$591$	−0.846460	−	2.84300i	−0.0348187	−	0.116945i
$592$		0			0
$593$	5.62882			0.231148			0.115574	−	0.993299i	$-0.463129\pi$
$593$	5.62882			0.231148			0.115574	+	0.993299i	$0.463129\pi$
$594$		0			0
$595$	1.75360			0.0718904
$596$		0			0
$597$	−8.96073	−	30.0963i	−0.366738	−	1.23176i
$598$		0			0
$599$	9.75087	−	16.8890i	0.398410	−	0.690066i	−0.595120	−	0.803637i	$-0.702896\pi$
$599$	9.75087	−	16.8890i	0.398410	−	0.690066i	0.993530	+	0.113571i	$0.0362289\pi$
$600$		0			0
$601$	−1.36834	−	2.37003i	−0.0558158	−	0.0966757i	0.836767	−	0.547558i	$-0.184443\pi$
$601$	−1.36834	−	2.37003i	−0.0558158	−	0.0966757i	−0.892583	+	0.450883i	$0.851109\pi$
$602$		0			0
$603$	1.91619	+	34.7061i	0.0780334	+	1.41334i
$604$		0			0
$605$	4.29604	+	7.44096i	0.174659	+	0.302518i
$606$		0			0
$607$	23.6876	−	41.0282i	0.961452	−	1.66528i	0.242592	−	0.970128i	$-0.422002\pi$
$607$	23.6876	−	41.0282i	0.961452	−	1.66528i	0.718860	−	0.695155i	$-0.244664\pi$
$608$		0			0
$609$	30.4398	+	7.26296i	1.23348	+	0.294310i
$610$		0			0
$611$	0.579256			0.0234342
$612$		0			0
$613$	−23.1963			−0.936891			−0.468446	−	0.883492i	$-0.655186\pi$
$613$	−23.1963			−0.936891			−0.468446	+	0.883492i	$0.655186\pi$
$614$		0			0
$615$	−1.28973	+	1.36290i	−0.0520069	+	0.0549575i
$616$		0			0
$617$	−19.8253	+	34.3384i	−0.798137	+	1.38241i	0.122691	+	0.992445i	$0.460848\pi$
$617$	−19.8253	+	34.3384i	−0.798137	+	1.38241i	−0.920828	+	0.389969i	$0.872486\pi$
$618$		0			0
$619$	−0.813544	−	1.40910i	−0.0326991	−	0.0566365i	0.849213	−	0.528051i	$-0.177077\pi$
$619$	−0.813544	−	1.40910i	−0.0326991	−	0.0566365i	−0.881912	+	0.471414i	$0.843744\pi$
$620$		0			0
$621$	43.3137	−	15.5429i	1.73812	−	0.623717i
$622$		0			0
$623$	−17.1743	−	29.7467i	−0.688074	−	1.19178i
$624$		0			0
$625$	−10.3849	+	17.9873i	−0.415398	+	0.719490i
$626$		0			0
$627$	−35.9316	+	37.9702i	−1.43497	+	1.51638i
$628$		0			0
$629$	2.84769			0.113545
$630$		0			0
$631$	−30.9685			−1.23283			−0.616417	−	0.787420i	$-0.711417\pi$
$631$	−30.9685			−1.23283			−0.616417	+	0.787420i	$0.711417\pi$
$632$		0			0
$633$	−2.47425	−	0.590359i	−0.0983428	−	0.0234647i
$634$		0			0
$635$	−4.76063	+	8.24566i	−0.188920	+	0.327219i
$636$		0			0
$637$	−11.7466	−	20.3456i	−0.465415	−	0.806123i
$638$		0			0
$639$	−26.6937	+	17.4414i	−1.05599	+	0.689971i
$640$		0			0
$641$	−16.1499	−	27.9725i	−0.637883	−	1.10485i	−0.985897	−	0.167356i	$-0.946477\pi$
$641$	−16.1499	−	27.9725i	−0.637883	−	1.10485i	0.348014	−	0.937489i	$-0.386856\pi$
$642$		0			0
$643$	3.28376	−	5.68763i	0.129499	−	0.224298i	−0.793984	−	0.607939i	$-0.791997\pi$
$643$	3.28376	−	5.68763i	0.129499	−	0.224298i	0.923482	+	0.383641i	$0.125330\pi$
$644$		0			0
$645$	1.96922	+	6.61400i	0.0775379	+	0.260426i
$646$		0			0
$647$	−40.0823			−1.57580			−0.787899	−	0.615805i	$-0.788831\pi$
$647$	−40.0823			−1.57580			−0.787899	+	0.615805i	$0.788831\pi$
$648$		0			0
$649$	26.7358			1.04947
$650$		0			0
$651$	−12.8717	−	43.2321i	−0.504482	−	1.69440i
$652$		0			0
$653$	1.62772	−	2.81929i	0.0636976	−	0.110327i	−0.832418	−	0.554148i	$-0.813044\pi$
$653$	1.62772	−	2.81929i	0.0636976	−	0.110327i	0.896116	+	0.443821i	$0.146377\pi$
$654$		0			0
$655$	1.88345	+	3.26223i	0.0735924	+	0.127466i
$656$		0			0
$657$	−11.0714	+	7.23394i	−0.431936	+	0.282223i
$658$		0			0
$659$	7.58278	+	13.1338i	0.295383	+	0.511619i	0.975074	−	0.221880i	$-0.0712193\pi$
$659$	7.58278	+	13.1338i	0.295383	+	0.511619i	−0.679691	+	0.733499i	$0.737886\pi$
$660$		0			0
$661$	10.1447	−	17.5711i	0.394582	−	0.683435i	−0.598466	−	0.801148i	$-0.704223\pi$
$661$	10.1447	−	17.5711i	0.394582	−	0.683435i	0.993048	+	0.117713i	$0.0375562\pi$
$662$		0			0
$663$	1.82467	+	0.435368i	0.0708643	+	0.0169083i
$664$		0			0
$665$	14.6328			0.567437
$666$		0			0
$667$	34.0429			1.31815
$668$		0			0
$669$	22.8064	−	24.1003i	0.881747	−	0.931773i
$670$		0			0
$671$	−4.79290	+	8.30155i	−0.185028	+	0.320478i
$672$		0			0
$673$	11.6256	+	20.1361i	0.448134	+	0.776191i	0.998265	−	0.0588875i	$-0.0187553\pi$
$673$	11.6256	+	20.1361i	0.448134	+	0.776191i	−0.550130	+	0.835079i	$0.685422\pi$
$674$		0			0
$675$	−4.36134	+	24.0952i	−0.167868	+	0.927426i
$676$		0			0
$677$	15.6380	+	27.0859i	0.601018	+	1.04099i	0.992667	+	0.120879i	$0.0385714\pi$
$677$	15.6380	+	27.0859i	0.601018	+	1.04099i	−0.391649	+	0.920115i	$0.628095\pi$
$678$		0			0
$679$	36.7380	−	63.6320i	1.40987	−	2.44197i
$680$		0			0
$681$	−14.1132	+	14.9139i	−0.540818	+	0.571501i
$682$		0			0
$683$	24.1812			0.925269			0.462635	−	0.886549i	$-0.346904\pi$
$683$	24.1812			0.925269			0.462635	+	0.886549i	$0.346904\pi$
$684$		0			0
$685$	6.12400			0.233986
$686$		0			0
$687$	5.29752	+	1.26399i	0.202113	+	0.0482243i
$688$		0			0
$689$	−4.13101	+	7.15512i	−0.157379	+	0.272588i
$690$		0			0
$691$	9.03942	+	15.6567i	0.343876	+	0.595610i	0.985149	−	0.171702i	$-0.0549268\pi$
$691$	9.03942	+	15.6567i	0.343876	+	0.595610i	−0.641273	+	0.767313i	$0.721593\pi$
$692$		0			0
$693$	4.04102	+	73.1910i	0.153506	+	2.78030i
$694$		0			0
$695$	−1.66578	−	2.88521i	−0.0631866	−	0.109442i
$696$		0			0
$697$	0.702872	−	1.21741i	0.0266232	−	0.0461127i
$698$		0			0
$699$	1.39840	+	4.69681i	0.0528925	+	0.177650i
$700$		0			0
$701$	17.2240			0.650541			0.325271	−	0.945621i	$-0.394545\pi$
$701$	17.2240			0.650541			0.325271	+	0.945621i	$0.394545\pi$
$702$		0			0
$703$	23.7625			0.896219
$704$		0			0
$705$	0.0986224	+	0.331242i	0.00371433	+	0.0124753i
$706$		0			0
$707$	20.8325	−	36.0830i	0.783487	−	1.35704i
$708$		0			0
$709$	−13.3258	−	23.0809i	−0.500459	−	0.866821i	−1.00000		0.000530358i	$-0.999831\pi$
$709$	−13.3258	−	23.0809i	−0.500459	−	0.866821i	0.499541	−	0.866290i	$-0.333502\pi$
$710$		0			0
$711$	−17.7871	−	9.00045i	−0.667070	−	0.337543i
$712$		0			0
$713$	−24.5347	−	42.4954i	−0.918833	−	1.59147i
$714$		0			0
$715$	2.16945	−	3.75760i	0.0811330	−	0.140526i
$716$		0			0
$717$	−5.34965	−	1.27643i	−0.199786	−	0.0476691i
$718$		0			0
$719$	−10.4273			−0.388875			−0.194437	−	0.980915i	$-0.562288\pi$
$719$	−10.4273			−0.388875			−0.194437	+	0.980915i	$0.562288\pi$
$720$		0			0
$721$	15.5096			0.577608
$722$		0			0
$723$	15.7874	−	16.6831i	0.587139	−	0.620451i
$724$		0			0
$725$	−9.05733	+	15.6878i	−0.336381	+	0.582629i
$726$		0			0
$727$	10.5682	+	18.3047i	0.391954	+	0.678884i	0.992707	−	0.120550i	$-0.0384659\pi$
$727$	10.5682	+	18.3047i	0.391954	+	0.678884i	−0.600753	+	0.799434i	$0.705133\pi$
$728$		0			0
$729$	4.44727	+	26.6312i	0.164714	+	0.986341i
$730$		0			0
$731$	−2.58498	−	4.47731i	−0.0956088	−	0.165599i
$732$		0			0
$733$	15.6473	−	27.1020i	0.577948	−	1.00103i	−0.417767	−	0.908554i	$-0.637187\pi$
$733$	15.6473	−	27.1020i	0.577948	−	1.00103i	0.995714	−	0.0924806i	$-0.0294796\pi$
$734$		0			0
$735$	9.63454	−	10.1812i	0.355375	−	0.375537i
$736$		0			0
$737$	−60.2308			−2.21863
$738$		0			0
$739$	31.0455			1.14203			0.571014	−	0.820940i	$-0.306550\pi$
$739$	31.0455			1.14203			0.571014	+	0.820940i	$0.306550\pi$
$740$		0			0
$741$	15.2259	+	3.63291i	0.559338	+	0.133458i
$742$		0			0
$743$	−8.93131	+	15.4695i	−0.327658	+	0.567520i	−0.982047	−	0.188638i	$-0.939593\pi$
$743$	−8.93131	+	15.4695i	−0.327658	+	0.567520i	0.654389	+	0.756158i	$0.272926\pi$
$744$		0			0
$745$	2.93765	+	5.08817i	0.107627	+	0.186416i
$746$		0			0
$747$	−28.2701	−	14.3049i	−1.03435	−	0.523390i
$748$		0			0
$749$	−16.7363	−	28.9881i	−0.611530	−	1.05920i
$750$		0			0
$751$	4.70046	−	8.14144i	0.171522	−	0.297085i	−0.767430	−	0.641133i	$-0.778465\pi$
$751$	4.70046	−	8.14144i	0.171522	−	0.297085i	0.938952	+	0.344047i	$0.111798\pi$
$752$		0			0
$753$	1.51435	+	5.08625i	0.0551861	+	0.185353i
$754$		0			0
$755$	7.81189			0.284304
$756$		0			0
$757$	−49.7959			−1.80986			−0.904931	−	0.425558i	$-0.860078\pi$
$757$	−49.7959			−1.80986			−0.904931	+	0.425558i	$0.860078\pi$
$758$		0			0
$759$	22.7544	+	76.4252i	0.825934	+	2.77406i
$760$		0			0
$761$	5.42633	−	9.39868i	0.196704	−	0.340702i	−0.750754	−	0.660582i	$-0.770309\pi$
$761$	5.42633	−	9.39868i	0.196704	−	0.340702i	0.947458	+	0.319880i	$0.103643\pi$
$762$		0			0
$763$	7.02368	+	12.1654i	0.254274	+	0.440416i
$764$		0			0
$765$	0.0617020	+	1.11755i	0.00223084	+	0.0404050i
$766$		0			0
$767$	−4.00281	−	6.93307i	−0.144533	−	0.250338i
$768$		0			0
$769$	2.93798	−	5.08873i	0.105946	−	0.183504i	−0.808178	−	0.588938i	$-0.799546\pi$
$769$	2.93798	−	5.08873i	0.105946	−	0.183504i	0.914124	+	0.405434i	$0.132880\pi$
$770$		0			0
$771$	−27.4319	−	6.54527i	−0.987936	−	0.235722i
$772$		0			0
$773$	−26.2781			−0.945159			−0.472579	−	0.881288i	$-0.656677\pi$
$773$	−26.2781			−0.945159			−0.472579	+	0.881288i	$0.656677\pi$
$774$		0			0
$775$	26.1105			0.937917
$776$		0			0
$777$	22.9022	−	24.2015i	0.821610	−	0.868225i
$778$		0			0
$779$	5.86510	−	10.1587i	0.210139	−	0.363971i
$780$		0			0
$781$	−27.6268	−	47.8510i	−0.988564	−	1.71224i
$782$		0			0
$783$	−3.55755	+	19.6545i	−0.127136	+	0.702395i
$784$		0			0
$785$	4.10761	+	7.11459i	0.146607	+	0.253930i
$786$		0			0
$787$	−16.3824	+	28.3752i	−0.583970	+	1.01146i	0.411034	+	0.911620i	$0.365168\pi$
$787$	−16.3824	+	28.3752i	−0.583970	+	1.01146i	−0.995003	+	0.0998447i	$0.968165\pi$
$788$		0			0
$789$	26.3649	−	27.8607i	0.938616	−	0.991868i
$790$		0			0
$791$	32.0402			1.13922
$792$		0			0
$793$	2.87032			0.101928
$794$		0			0
$795$	−4.79493	−	1.14407i	−0.170059	−	0.0405761i
$796$		0			0
$797$	−26.8586	+	46.5205i	−0.951382	+	1.64784i	−0.208942	+	0.977928i	$0.567002\pi$
$797$	−26.8586	+	46.5205i	−0.951382	+	1.64784i	−0.742440	+	0.669913i	$0.766331\pi$
$798$		0			0
$799$	−0.129461	−	0.224233i	−0.00458000	−	0.00793279i
$800$		0			0
$801$	18.3530	−	11.9917i	0.648470	−	0.423704i
$802$		0			0
$803$	−11.4584	−	19.8465i	−0.404358	−	0.700368i
$804$		0			0
$805$	11.1602	−	19.3301i	0.393346	−	0.681296i
$806$		0			0
$807$	−15.7075	−	52.7567i	−0.552931	−	1.85712i
$808$		0			0
$809$	−5.82729			−0.204877			−0.102438	−	0.994739i	$-0.532664\pi$
$809$	−5.82729			−0.204877			−0.102438	+	0.994739i	$0.532664\pi$
$810$		0			0
$811$	25.5700			0.897883			0.448942	−	0.893561i	$-0.351801\pi$
$811$	25.5700			0.897883			0.448942	+	0.893561i	$0.351801\pi$
$812$		0			0
$813$	−0.392451	−	1.31812i	−0.0137639	−	0.0462286i
$814$		0			0
$815$	−2.96855	+	5.14169i	−0.103984	+	0.180105i
$816$		0			0
$817$	−21.5703	−	37.3608i	−0.754648	−	1.30709i
$818$		0			0
$819$	18.3747	−	12.0058i	0.642064	−	0.419518i
$820$		0			0
$821$	−6.62309	−	11.4715i	−0.231147	−	0.400359i	0.726999	−	0.686639i	$-0.240915\pi$
$821$	−6.62309	−	11.4715i	−0.231147	−	0.400359i	−0.958146	+	0.286280i	$0.907581\pi$
$822$		0			0
$823$	−5.17425	+	8.96206i	−0.180363	+	0.312398i	−0.942004	−	0.335601i	$-0.891061\pi$
$823$	−5.17425	+	8.96206i	−0.180363	+	0.312398i	0.761641	+	0.647999i	$0.224394\pi$
$824$		0			0
$825$	−41.2725	−	9.84763i	−1.43692	−	0.342851i
$826$		0			0
$827$	−31.2799			−1.08771			−0.543854	−	0.839180i	$-0.683035\pi$
$827$	−31.2799			−1.08771			−0.543854	+	0.839180i	$0.683035\pi$
$828$		0			0
$829$	17.3415			0.602297			0.301148	−	0.953577i	$-0.402630\pi$
$829$	17.3415			0.602297			0.301148	+	0.953577i	$0.402630\pi$
$830$		0			0
$831$	30.0209	−	31.7242i	1.04141	−	1.10050i
$832$		0			0
$833$	−5.25060	+	9.09430i	−0.181922	+	0.315099i
$834$		0			0
$835$	2.22852	+	3.85990i	0.0771209	+	0.133577i
$836$		0			0
$837$	27.0985	−	9.72416i	0.936660	−	0.336116i
$838$		0			0
$839$	11.3050	+	19.5809i	0.390293	+	0.676008i	0.992488	−	0.122341i	$-0.0390402\pi$
$839$	11.3050	+	19.5809i	0.390293	+	0.676008i	−0.602195	+	0.798349i	$0.705707\pi$
$840$		0			0
$841$	7.11192	−	12.3182i	0.245239	−	0.424766i
$842$		0			0
$843$	−12.0639	+	12.7484i	−0.415504	+	0.439077i
$844$		0			0
$845$	5.67148			0.195105
$846$		0			0
$847$	−75.3164			−2.58790
$848$		0			0
$849$	−39.3445	−	9.38763i	−1.35030	−	0.322183i
$850$		0			0
$851$	18.1233	−	31.3904i	0.621258	−	1.07605i
$852$		0			0
$853$	3.98508	+	6.90236i	0.136447	+	0.236332i	0.926149	−	0.377157i	$-0.123098\pi$
$853$	3.98508	+	6.90236i	0.136447	+	0.236332i	−0.789703	+	0.613490i	$0.789765\pi$
$854$		0			0
$855$	0.514870	+	9.32534i	0.0176082	+	0.318920i
$856$		0			0
$857$	−0.886072	−	1.53472i	−0.0302676	−	0.0524251i	0.850495	−	0.525983i	$-0.176303\pi$
$857$	−0.886072	−	1.53472i	−0.0302676	−	0.0524251i	−0.880762	+	0.473558i	$0.842969\pi$
$858$		0			0
$859$	−0.441545	+	0.764779i	−0.0150653	+	0.0260939i	−0.873460	−	0.486896i	$-0.838129\pi$
$859$	−0.441545	+	0.764779i	−0.0150653	+	0.0260939i	0.858394	+	0.512990i	$0.171462\pi$
$860$		0			0
$861$	−4.69359	−	15.7643i	−0.159957	−	0.537246i
$862$		0			0
$863$	−50.3624			−1.71436			−0.857178	−	0.515021i	$-0.827784\pi$
$863$	−50.3624			−1.71436			−0.857178	+	0.515021i	$0.827784\pi$
$864$		0			0
$865$	0.0425380			0.00144633
$866$		0			0
$867$	8.16298	+	27.4170i	0.277229	+	0.931129i
$868$		0			0
$869$	17.2715	−	29.9152i	0.585896	−	1.01480i
$870$		0			0
$871$	9.01758	+	15.6189i	0.305549	+	0.529226i
$872$		0			0
$873$	41.8446	+	21.1737i	1.41623	+	0.716623i
$874$		0			0
$875$	12.2393	+	21.1991i	0.413764	+	0.716661i
$876$		0			0
$877$	−19.6437	+	34.0238i	−0.663319	+	1.14890i	0.316419	+	0.948620i	$0.397520\pi$
$877$	−19.6437	+	34.0238i	−0.663319	+	1.14890i	−0.979738	+	0.200283i	$0.935814\pi$
$878$		0			0
$879$	44.4665	+	10.6097i	1.49982	+	0.357857i
$880$		0			0
$881$	31.7416			1.06940			0.534701	−	0.845041i	$-0.320424\pi$
$881$	31.7416			1.06940			0.534701	+	0.845041i	$0.320424\pi$
$882$		0			0
$883$	−29.5613			−0.994818			−0.497409	−	0.867516i	$-0.665715\pi$
$883$	−29.5613			−0.994818			−0.497409	+	0.867516i	$0.665715\pi$
$884$		0			0
$885$	3.28311	−	3.46938i	0.110360	−	0.116622i
$886$		0			0
$887$	2.39404	−	4.14660i	0.0803839	−	0.139229i	−0.823031	−	0.567997i	$-0.807719\pi$
$887$	2.39404	−	4.14660i	0.0803839	−	0.139229i	0.903415	+	0.428767i	$0.141052\pi$
$888$		0			0
$889$	−41.7307	−	72.2797i	−1.39960	−	2.42418i
$890$		0			0
$891$	−46.5016	+	5.15059i	−1.55786	+	0.172551i
$892$		0			0
$893$	−1.08028	−	1.87111i	−0.0361503	−	0.0626141i
$894$		0			0
$895$	−5.57686	+	9.65941i	−0.186414	+	0.322878i
$896$		0			0
$897$	16.4117	−	17.3428i	0.547970	−	0.579059i
$898$		0			0
$899$	21.2984			0.710340
$900$		0			0
$901$	3.69305			0.123033
$902$		0			0
$903$	−58.8404	−	14.0394i	−1.95809	−	0.467200i
$904$		0			0
$905$	−1.37569	+	2.38276i	−0.0457294	+	0.0792057i
$906$		0			0
$907$	7.27487	+	12.6004i	0.241558	+	0.418391i	0.961158	−	0.275998i	$-0.0890083\pi$
$907$	7.27487	+	12.6004i	0.241558	+	0.418391i	−0.719600	+	0.694389i	$0.755675\pi$
$908$		0			0
$909$	23.7283	+	12.0067i	0.787017	+	0.398237i
$910$		0			0
$911$	−24.3323	−	42.1448i	−0.806166	−	1.39632i	−0.915501	−	0.402315i	$-0.868206\pi$
$911$	−24.3323	−	42.1448i	−0.806166	−	1.39632i	0.109336	−	0.994005i	$-0.465128\pi$
$912$		0			0
$913$	27.4506	−	47.5459i	0.908483	−	1.57354i
$914$		0			0
$915$	0.488692	+	1.64137i	0.0161557	+	0.0542619i
$916$		0			0
$917$	−33.0198			−1.09041
$918$		0			0
$919$	−26.6958			−0.880612			−0.440306	−	0.897848i	$-0.645130\pi$
$919$	−26.6958			−0.880612			−0.440306	+	0.897848i	$0.645130\pi$
$920$		0			0
$921$	10.7116	+	35.9769i	0.352959	+	1.18548i
$922$		0			0
$923$	−8.27240	+	14.3282i	−0.272289	+	0.471619i
$924$		0			0
$925$	9.64362	+	16.7032i	0.317080	+	0.549199i
$926$		0			0
$927$	0.545720	+	9.88410i	0.0179238	+	0.324636i
$928$		0			0
$929$	−5.27705	−	9.14012i	−0.173134	−	0.299878i	0.766380	−	0.642388i	$-0.222056\pi$
$929$	−5.27705	−	9.14012i	−0.173134	−	0.299878i	−0.939514	+	0.342510i	$0.888723\pi$
$930$		0			0
$931$	−43.8135	+	75.8871i	−1.43593	+	2.48710i
$932$		0			0
$933$	−49.0090	−	11.6936i	−1.60448	−	0.382831i
$934$		0			0
$935$	−1.93945			−0.0634268
$936$		0			0
$937$	−17.1990			−0.561866			−0.280933	−	0.959727i	$-0.590644\pi$
$937$	−17.1990			−0.561866			−0.280933	+	0.959727i	$0.590644\pi$
$938$		0			0
$939$	8.39054	−	8.86658i	0.273815	−	0.289350i
$940$		0			0
$941$	−19.3051	+	33.4373i	−0.629327	+	1.09003i	0.358360	+	0.933583i	$0.383336\pi$
$941$	−19.3051	+	33.4373i	−0.629327	+	1.09003i	−0.987687	+	0.156443i	$0.949997\pi$
$942$		0			0
$943$	−8.94643	−	15.4957i	−0.291336	−	0.504609i
$944$		0			0
$945$	9.99386	+	8.46333i	0.325100	+	0.275312i
$946$		0			0
$947$	15.2306	+	26.3802i	0.494929	+	0.857243i	0.999983	−	0.00584526i	$-0.00186061\pi$
$947$	15.2306	+	26.3802i	0.494929	+	0.857243i	−0.505054	+	0.863088i	$0.668527\pi$
$948$		0			0
$949$	−3.43103	+	5.94272i	−0.111376	+	0.192909i
$950$		0			0
$951$	1.05806	−	1.11808i	0.0343098	−	0.0362564i
$952$		0			0
$953$	7.78951			0.252327			0.126163	−	0.992009i	$-0.459734\pi$
$953$	7.78951			0.252327			0.126163	+	0.992009i	$0.459734\pi$
$954$		0			0
$955$	−10.6071			−0.343238
$956$		0			0
$957$	−33.6660	−	8.03273i	−1.08827	−	0.259661i
$958$		0			0
$959$	−26.8409	+	46.4897i	−0.866736	+	1.50123i
$960$		0			0
$961$	0.150268	+	0.260272i	0.00484736	+	0.00839587i
$962$		0			0
$963$	17.8849	−	11.6858i	0.576333	−	0.376570i
$964$		0			0
$965$	−0.962887	−	1.66777i	−0.0309964	−	0.0536874i
$966$		0			0
$967$	19.3058	−	33.4386i	0.620832	−	1.07531i	−0.368499	−	0.929628i	$-0.620128\pi$
$967$	19.3058	−	33.4386i	0.620832	−	1.07531i	0.989331	−	0.145685i	$-0.0465385\pi$
$968$		0			0
$969$	−1.99660	−	6.70597i	−0.0641401	−	0.215427i
$970$		0			0
$971$	−15.7257			−0.504661			−0.252331	−	0.967641i	$-0.581197\pi$
$971$	−15.7257			−0.504661			−0.252331	+	0.967641i	$0.581197\pi$
$972$		0			0
$973$	29.2037			0.936229
$974$		0			0
$975$	3.62553	+	12.1770i	0.116110	+	0.389977i
$976$		0			0
$977$	−9.58188	+	16.5963i	−0.306551	+	0.530963i	−0.977606	−	0.210446i	$-0.932508\pi$
$977$	−9.58188	+	16.5963i	−0.306551	+	0.530963i	0.671054	+	0.741408i	$0.265842\pi$
$978$		0			0
$979$	18.9945	+	32.8995i	0.607067	+	1.05147i
$980$		0			0
$981$	−7.50572	+	4.90417i	−0.239639	+	0.156578i
$982$		0			0
$983$	−19.5590	−	33.8772i	−0.623835	−	1.08051i	−0.988765	−	0.149479i	$-0.952240\pi$
$983$	−19.5590	−	33.8772i	−0.623835	−	1.08051i	0.364930	−	0.931035i	$-0.381093\pi$
$984$		0			0
$985$	0.459158	−	0.795285i	0.0146300	−	0.0253399i
$986$		0			0
$987$	−2.94685	−	0.703119i	−0.0937991	−	0.0223805i
$988$		0			0
$989$	−65.8052			−2.09248
$990$		0			0
$991$	−27.5470			−0.875060			−0.437530	−	0.899204i	$-0.644147\pi$
$991$	−27.5470			−0.875060			−0.437530	+	0.899204i	$0.644147\pi$
$992$		0			0
$993$	27.2657	−	28.8126i	0.865251	−	0.914341i
$994$		0			0
$995$	4.86070	−	8.41898i	0.154095	−	0.266900i
$996$		0			0
$997$	15.6863	+	27.1695i	0.496791	+	0.860467i	0.999993	−	0.00370166i	$-0.00117828\pi$
$997$	15.6863	+	27.1695i	0.496791	+	0.860467i	−0.503202	+	0.864169i	$0.667845\pi$
$998$		0			0
$999$	16.2292	+	13.7437i	0.513469	+	0.434833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.i.k.769.2	yes	12
3.2	odd	2		3456.2.i.l.2305.3		12
4.3	odd	2		1152.2.i.i.769.5	yes	12
8.3	odd	2		1152.2.i.l.769.2	yes	12
8.5	even	2		1152.2.i.j.769.5	yes	12
9.2	odd	6		3456.2.i.l.1153.3		12
9.7	even	3	inner	1152.2.i.k.385.2	yes	12
12.11	even	2		3456.2.i.k.2305.3		12
24.5	odd	2		3456.2.i.j.2305.4		12
24.11	even	2		3456.2.i.i.2305.4		12
36.7	odd	6		1152.2.i.i.385.5	✓	12
36.11	even	6		3456.2.i.k.1153.3		12
72.11	even	6		3456.2.i.i.1153.4		12
72.29	odd	6		3456.2.i.j.1153.4		12
72.43	odd	6		1152.2.i.l.385.2	yes	12
72.61	even	6		1152.2.i.j.385.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.i.i.385.5	✓	12	36.7	odd	6
1152.2.i.i.769.5	yes	12	4.3	odd	2
1152.2.i.j.385.5	yes	12	72.61	even	6
1152.2.i.j.769.5	yes	12	8.5	even	2
1152.2.i.k.385.2	yes	12	9.7	even	3	inner
1152.2.i.k.769.2	yes	12	1.1	even	1	trivial
1152.2.i.l.385.2	yes	12	72.43	odd	6
1152.2.i.l.769.2	yes	12	8.3	odd	2
3456.2.i.i.1153.4		12	72.11	even	6
3456.2.i.i.2305.4		12	24.11	even	2
3456.2.i.j.1153.4		12	72.29	odd	6
3456.2.i.j.2305.4		12	24.5	odd	2
3456.2.i.k.1153.3		12	36.11	even	6
3456.2.i.k.2305.3		12	12.11	even	2
3456.2.i.l.1153.3		12	9.2	odd	6
3456.2.i.l.2305.3		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.494250 - 1.66004i) q^{3} +(0.268104 - 0.464369i) q^{5} +(2.35014 + 4.07056i) q^{7} +(-2.51143 + 1.64095i) q^{9} +O(q^{10})\)	\(q+(-0.494250 - 1.66004i) q^{3} +(0.268104 - 0.464369i) q^{5} +(2.35014 + 4.07056i) q^{7} +(-2.51143 + 1.64095i) q^{9} +(-2.59922 - 4.50198i) q^{11} +(-0.778295 + 1.34805i) q^{13} +(-0.903379 - 0.215547i) q^{15} +0.695781 q^{17} +5.80593 q^{19} +(5.59572 - 5.91320i) q^{21} +(4.42809 - 7.66967i) q^{23} +(2.35624 + 4.08113i) q^{25} +(3.96530 + 3.35803i) q^{27} +(1.92199 + 3.32898i) q^{29} +(2.77035 - 4.79840i) q^{31} +(-6.18878 + 6.53990i) q^{33} +2.52033 q^{35} +4.09280 q^{37} +(2.62248 + 0.625725i) q^{39} +(1.01019 - 1.74970i) q^{41} +(-3.71522 - 6.43494i) q^{43} +(0.0886801 + 1.60618i) q^{45} +(-0.186066 - 0.322275i) q^{47} +(-7.54633 + 13.0706i) q^{49} +(-0.343890 - 1.15502i) q^{51} +5.30777 q^{53} -2.78744 q^{55} +(-2.86958 - 9.63804i) q^{57} +(-2.57152 + 4.45401i) q^{59} +(-0.921988 - 1.59693i) q^{61} +(-12.5818 - 6.36650i) q^{63} +(0.417328 + 0.722833i) q^{65} +(5.79316 - 10.0340i) q^{67} +(-14.9205 - 3.56004i) q^{69} +10.6289 q^{71} +4.40840 q^{73} +(5.61024 - 5.92854i) q^{75} +(12.2171 - 21.1606i) q^{77} +(3.32244 + 5.75464i) q^{79} +(3.61459 - 8.24225i) q^{81} +(5.28055 + 9.14617i) q^{83} +(0.186541 - 0.323099i) q^{85} +(4.57628 - 4.83592i) q^{87} -7.30777 q^{89} -7.31642 q^{91} +(-9.33475 - 2.22728i) q^{93} +(1.55659 - 2.69609i) q^{95} +(-7.81612 - 13.5379i) q^{97} +(13.9153 + 7.04125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9	\( 12 q + 4 q^{3} - 2 q^{5} + 6 q^{7} - 2 q^{9} + 4 q^{11} + 10 q^{13} + 4 q^{15} + 4 q^{17} + 4 q^{19} + 2 q^{21} + 8 q^{23} - 14 q^{25} - 14 q^{27} - 2 q^{29} + 8 q^{31} - 10 q^{33} + 8 q^{35} + 22 q^{39} - 2 q^{41} - 2 q^{43} + 10 q^{45} - 14 q^{47} - 18 q^{49} - 38 q^{51} + 24 q^{53} - 16 q^{55} - 38 q^{57} + 6 q^{59} + 14 q^{61} - 16 q^{63} - 8 q^{65} + 4 q^{67} - 50 q^{69} - 28 q^{71} + 60 q^{73} + 50 q^{75} + 2 q^{77} + 16 q^{79} + 22 q^{81} + 24 q^{83} + 16 q^{85} - 36 q^{87} - 48 q^{89} - 52 q^{91} + 42 q^{93} - 20 q^{95} - 14 q^{97} + 68 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 2 * q^5 + 6 * q^7 - 2 * q^9 + 4 * q^11 + 10 * q^13 + 4 * q^15 + 4 * q^17 + 4 * q^19 + 2 * q^21 + 8 * q^23 - 14 * q^25 - 14 * q^27 - 2 * q^29 + 8 * q^31 - 10 * q^33 + 8 * q^35 + 22 * q^39 - 2 * q^41 - 2 * q^43 + 10 * q^45 - 14 * q^47 - 18 * q^49 - 38 * q^51 + 24 * q^53 - 16 * q^55 - 38 * q^57 + 6 * q^59 + 14 * q^61 - 16 * q^63 - 8 * q^65 + 4 * q^67 - 50 * q^69 - 28 * q^71 + 60 * q^73 + 50 * q^75 + 2 * q^77 + 16 * q^79 + 22 * q^81 + 24 * q^83 + 16 * q^85 - 36 * q^87 - 48 * q^89 - 52 * q^91 + 42 * q^93 - 20 * q^95 - 14 * q^97 + 68 * q^99

Introduction

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