LMFDB - Embedded newform 882.2.f.r.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(295,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.f (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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.31116960000.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} - 8x^{4} + 9x^{2} + 81 $ x^8 + x^6 - 8x^4 + 9x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$0.306808 + 1.70466i$ of defining polynomial
Character	$\chi$	$=$	882.295
Dual form			882.2.f.r.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.62968 - 0.586627i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.306808 + 0.531407i) q^{5} +(-1.32288 + 1.11803i) q^{6} -1.00000 q^{8} +(2.31174 + 1.91203i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.62968 - 0.586627i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.306808 + 0.531407i) q^{5} +(-1.32288 + 1.11803i) q^{6} -1.00000 q^{8} +(2.31174 + 1.91203i) q^{9} +0.613616 q^{10} +(2.31174 - 4.00405i) q^{11} +(0.306808 + 1.70466i) q^{12} +(3.25937 + 5.64539i) q^{13} +(-0.188262 - 1.04601i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.03214 q^{17} +(2.81174 - 1.04601i) q^{18} -2.64575 q^{19} +(0.306808 - 0.531407i) q^{20} +(-2.31174 - 4.00405i) q^{22} +(1.81174 + 3.13802i) q^{23} +(1.62968 + 0.586627i) q^{24} +(2.31174 - 4.00405i) q^{25} +6.51873 q^{26} +(-2.64575 - 4.47214i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-1.00000 - 0.359964i) q^{30} +(-3.25937 - 5.64539i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.11628 + 5.16920i) q^{33} +(1.01607 - 1.75988i) q^{34} +(0.500000 - 2.95804i) q^{36} +6.00000 q^{37} +(-1.32288 + 2.29129i) q^{38} +(-2.00000 - 11.1122i) q^{39} +(-0.306808 - 0.531407i) q^{40} +(-1.01607 - 1.75988i) q^{41} +(1.31174 - 2.27200i) q^{43} -4.62348 q^{44} +(-0.306808 + 1.81510i) q^{45} +3.62348 q^{46} +(5.29150 - 9.16515i) q^{47} +(1.32288 - 1.11803i) q^{48} +(-2.31174 - 4.00405i) q^{50} +(-3.31174 - 1.19211i) q^{51} +(3.25937 - 5.64539i) q^{52} -4.00000 q^{53} +(-5.19586 + 0.0552199i) q^{54} +2.83704 q^{55} +(4.31174 + 1.55207i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(6.11628 + 10.5937i) q^{59} +(-0.811738 + 0.686044i) q^{60} +(3.56618 - 6.17680i) q^{61} -6.51873 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(1.41852 + 7.88146i) q^{66} +(-2.31174 - 4.00405i) q^{67} +(-1.01607 - 1.75988i) q^{68} +(-1.11171 - 6.17680i) q^{69} -0.376525 q^{71} +(-2.31174 - 1.91203i) q^{72} -7.32364 q^{73} +(3.00000 - 5.19615i) q^{74} +(-6.11628 + 5.16920i) q^{75} +(1.32288 + 2.29129i) q^{76} +(-10.6235 - 3.82407i) q^{78} +(-6.81174 + 11.7983i) q^{79} -0.613616 q^{80} +(1.68826 + 8.84024i) q^{81} -2.03214 q^{82} +(3.87298 - 6.70820i) q^{83} +(0.623475 + 1.07989i) q^{85} +(-1.31174 - 2.27200i) q^{86} +(-5.29150 + 4.47214i) q^{87} +(-2.31174 + 4.00405i) q^{88} +14.2647 q^{89} +(1.41852 + 1.17325i) q^{90} +(1.81174 - 3.13802i) q^{92} +(2.00000 + 11.1122i) q^{93} +(-5.29150 - 9.16515i) q^{94} +(-0.811738 - 1.40597i) q^{95} +(-0.306808 - 1.70466i) q^{96} +(-8.14842 + 14.1135i) q^{97} +(13.0000 - 4.83619i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 2 * q^9	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 2 q^{9} - 2 q^{11} - 22 q^{15} - 4 q^{16} + 2 q^{18} + 2 q^{22} - 6 q^{23} - 2 q^{25} + 16 q^{29} - 8 q^{30} + 4 q^{32} + 4 q^{36} + 48 q^{37} - 16 q^{39} - 10 q^{43} + 4 q^{44} - 12 q^{46} + 2 q^{50} - 6 q^{51} - 32 q^{53} + 14 q^{57} - 16 q^{58} + 14 q^{60} + 8 q^{64} - 16 q^{65} + 2 q^{67} - 44 q^{71} + 2 q^{72} + 24 q^{74} - 44 q^{78} - 34 q^{79} + 34 q^{81} - 36 q^{85} + 10 q^{86} + 2 q^{88} - 6 q^{92} + 16 q^{93} + 14 q^{95} + 104 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 2 * q^9 - 2 * q^11 - 22 * q^15 - 4 * q^16 + 2 * q^18 + 2 * q^22 - 6 * q^23 - 2 * q^25 + 16 * q^29 - 8 * q^30 + 4 * q^32 + 4 * q^36 + 48 * q^37 - 16 * q^39 - 10 * q^43 + 4 * q^44 - 12 * q^46 + 2 * q^50 - 6 * q^51 - 32 * q^53 + 14 * q^57 - 16 * q^58 + 14 * q^60 + 8 * q^64 - 16 * q^65 + 2 * q^67 - 44 * q^71 + 2 * q^72 + 24 * q^74 - 44 * q^78 - 34 * q^79 + 34 * q^81 - 36 * q^85 + 10 * q^86 + 2 * q^88 - 6 * q^92 + 16 * q^93 + 14 * q^95 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.62968	−	0.586627i	−0.940898	−	0.338689i
$3$	−1.62968	−	0.586627i	−0.940898	−	0.338689i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.306808	+	0.531407i	0.137209	+	0.237652i	0.926439	−	0.376445i	$-0.122854\pi$
$5$	0.306808	+	0.531407i	0.137209	+	0.237652i	−0.789230	+	0.614097i	$0.789520\pi$
$6$	−1.32288	+	1.11803i	−0.540062	+	0.456435i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	2.31174	+	1.91203i	0.770579	+	0.637344i
$10$	0.613616			0.194042
$11$	2.31174	−	4.00405i	0.697015	−	1.20727i	−0.272481	−	0.962161i	$-0.587844\pi$
$11$	2.31174	−	4.00405i	0.697015	−	1.20727i	0.969497	−	0.245105i	$-0.0788223\pi$
$12$	0.306808	+	1.70466i	0.0885678	+	0.492093i
$13$	3.25937	+	5.64539i	0.903986	+	1.56575i	0.822273	+	0.569094i	$0.192706\pi$
$13$	3.25937	+	5.64539i	0.903986	+	1.56575i	0.0817130	+	0.996656i	$0.473961\pi$
$14$		0			0
$15$	−0.188262	−	1.04601i	−0.0486091	−	0.270078i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.03214			0.492865			0.246433	−	0.969160i	$-0.420742\pi$
$17$	2.03214			0.492865			0.246433	+	0.969160i	$0.420742\pi$
$18$	2.81174	−	1.04601i	0.662733	−	0.246546i
$19$	−2.64575			−0.606977			−0.303488	−	0.952835i	$-0.598151\pi$
$19$	−2.64575			−0.606977			−0.303488	+	0.952835i	$0.598151\pi$
$20$	0.306808	−	0.531407i	0.0686044	−	0.118826i
$21$		0			0
$22$	−2.31174	−	4.00405i	−0.492864	−	0.853666i
$23$	1.81174	+	3.13802i	0.377773	+	0.654323i	0.990738	−	0.135788i	$-0.0433565\pi$
$23$	1.81174	+	3.13802i	0.377773	+	0.654323i	−0.612965	+	0.790110i	$0.710023\pi$
$24$	1.62968	+	0.586627i	0.332658	+	0.119745i
$25$	2.31174	−	4.00405i	0.462348	−	0.800809i
$26$	6.51873			1.27843
$27$	−2.64575	−	4.47214i	−0.509175	−	0.860663i
$28$		0			0
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$	−1.00000	−	0.359964i	−0.182574	−	0.0657201i
$31$	−3.25937	−	5.64539i	−0.585400	−	1.01394i	−0.994825	−	0.101599i	$-0.967604\pi$
$31$	−3.25937	−	5.64539i	−0.585400	−	1.01394i	0.409426	−	0.912343i	$-0.365729\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−6.11628	+	5.16920i	−1.06471	+	0.899843i
$34$	1.01607	−	1.75988i	0.174254	−	0.301817i
$35$		0			0
$36$	0.500000	−	2.95804i	0.0833333	−	0.493007i
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$	−1.32288	+	2.29129i	−0.214599	+	0.371696i
$39$	−2.00000	−	11.1122i	−0.320256	−	1.77938i
$40$	−0.306808	−	0.531407i	−0.0485106	−	0.0840228i
$41$	−1.01607	−	1.75988i	−0.158683	−	0.274847i	0.775711	−	0.631088i	$-0.217391\pi$
$41$	−1.01607	−	1.75988i	−0.158683	−	0.274847i	−0.934394	+	0.356241i	$0.884058\pi$
$42$		0			0
$43$	1.31174	−	2.27200i	0.200038	−	0.346476i	−0.748502	−	0.663132i	$-0.769227\pi$
$43$	1.31174	−	2.27200i	0.200038	−	0.346476i	0.948540	+	0.316656i	$0.102560\pi$
$44$	−4.62348			−0.697015
$45$	−0.306808	+	1.81510i	−0.0457362	+	0.270579i
$46$	3.62348			0.534252
$47$	5.29150	−	9.16515i	0.771845	−	1.33687i	−0.164706	−	0.986343i	$-0.552667\pi$
$47$	5.29150	−	9.16515i	0.771845	−	1.33687i	0.936551	−	0.350532i	$-0.113999\pi$
$48$	1.32288	−	1.11803i	0.190941	−	0.161374i
$49$		0			0
$50$	−2.31174	−	4.00405i	−0.326929	−	0.566258i
$51$	−3.31174	−	1.19211i	−0.463736	−	0.166928i
$52$	3.25937	−	5.64539i	0.451993	−	0.782875i
$53$	−4.00000			−0.549442			−0.274721	−	0.961524i	$-0.588586\pi$
$53$	−4.00000			−0.549442			−0.274721	+	0.961524i	$0.588586\pi$
$54$	−5.19586	+	0.0552199i	−0.707067	+	0.00751447i
$55$	2.83704			0.382546
$56$		0			0
$57$	4.31174	+	1.55207i	0.571104	+	0.205577i
$58$	−2.00000	−	3.46410i	−0.262613	−	0.454859i
$59$	6.11628	+	10.5937i	0.796272	+	1.37918i	0.922028	+	0.387123i	$0.126531\pi$
$59$	6.11628	+	10.5937i	0.796272	+	1.37918i	−0.125756	+	0.992061i	$0.540136\pi$
$60$	−0.811738	+	0.686044i	−0.104795	+	0.0885678i
$61$	3.56618	−	6.17680i	0.456602	−	0.790858i	−0.542177	−	0.840264i	$-0.682400\pi$
$61$	3.56618	−	6.17680i	0.456602	−	0.790858i	0.998779	+	0.0494066i	$0.0157330\pi$
$62$	−6.51873			−0.827880
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	1.41852	+	7.88146i	0.174608	+	0.970140i
$67$	−2.31174	−	4.00405i	−0.282424	−	0.489172i	0.689557	−	0.724231i	$-0.257805\pi$
$67$	−2.31174	−	4.00405i	−0.282424	−	0.489172i	−0.971981	+	0.235059i	$0.924472\pi$
$68$	−1.01607	−	1.75988i	−0.123216	−	0.213417i
$69$	−1.11171	−	6.17680i	−0.133834	−	0.743599i
$70$		0			0
$71$	−0.376525			−0.0446853			−0.0223426	−	0.999750i	$-0.507112\pi$
$71$	−0.376525			−0.0446853			−0.0223426	+	0.999750i	$0.507112\pi$
$72$	−2.31174	−	1.91203i	−0.272441	−	0.225335i
$73$	−7.32364			−0.857167			−0.428583	−	0.903502i	$-0.640987\pi$
$73$	−7.32364			−0.857167			−0.428583	+	0.903502i	$0.640987\pi$
$74$	3.00000	−	5.19615i	0.348743	−	0.604040i
$75$	−6.11628	+	5.16920i	−0.706248	+	0.596888i
$76$	1.32288	+	2.29129i	0.151744	+	0.262829i
$77$		0			0
$78$	−10.6235	−	3.82407i	−1.20287	−	0.432990i
$79$	−6.81174	+	11.7983i	−0.766380	+	1.32741i	0.173133	+	0.984898i	$0.444611\pi$
$79$	−6.81174	+	11.7983i	−0.766380	+	1.32741i	−0.939514	+	0.342511i	$0.888722\pi$
$80$	−0.613616			−0.0686044
$81$	1.68826	+	8.84024i	0.187585	+	0.982248i
$82$	−2.03214			−0.224412
$83$	3.87298	−	6.70820i	0.425115	−	0.736321i	−0.571316	−	0.820730i	$-0.693567\pi$
$83$	3.87298	−	6.70820i	0.425115	−	0.736321i	0.996431	+	0.0844091i	$0.0269003\pi$
$84$		0			0
$85$	0.623475	+	1.07989i	0.0676254	+	0.117131i
$86$	−1.31174	−	2.27200i	−0.141448	−	0.244996i
$87$	−5.29150	+	4.47214i	−0.567309	+	0.479463i
$88$	−2.31174	+	4.00405i	−0.246432	+	0.426833i
$89$	14.2647			1.51206			0.756028	−	0.654540i	$-0.227138\pi$
$89$	14.2647			1.51206			0.756028	+	0.654540i	$0.227138\pi$
$90$	1.41852	+	1.17325i	0.149525	+	0.123672i
$91$		0			0
$92$	1.81174	−	3.13802i	0.188887	−	0.327161i
$93$	2.00000	+	11.1122i	0.207390	+	1.15228i
$94$	−5.29150	−	9.16515i	−0.545777	−	0.945313i
$95$	−0.811738	−	1.40597i	−0.0832825	−	0.144250i
$96$	−0.306808	−	1.70466i	−0.0313135	−	0.173981i
$97$	−8.14842	+	14.1135i	−0.827347	+	1.43301i	0.0727661	+	0.997349i	$0.476817\pi$
$97$	−8.14842	+	14.1135i	−0.827347	+	1.43301i	−0.900113	+	0.435657i	$0.856516\pi$
$98$		0			0
$99$	13.0000	−	4.83619i	1.30655	−	0.486055i
$100$	−4.62348			−0.462348
$101$	8.24406	−	14.2791i	0.820315	−	1.42083i	−0.0851331	−	0.996370i	$-0.527132\pi$
$101$	8.24406	−	14.2791i	0.820315	−	1.42083i	0.905448	−	0.424457i	$-0.139535\pi$
$102$	−2.68826	+	2.27200i	−0.266178	+	0.224961i
$103$	−8.55087	−	14.8105i	−0.842542	−	1.45933i	−0.887739	−	0.460348i	$-0.847725\pi$
$103$	−8.55087	−	14.8105i	−0.842542	−	1.45933i	0.0451964	−	0.998978i	$-0.485609\pi$
$104$	−3.25937	−	5.64539i	−0.319607	−	0.553576i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	10.6235			1.02701			0.513505	−	0.858087i	$-0.328347\pi$
$107$	10.6235			1.02701			0.513505	+	0.858087i	$0.328347\pi$
$108$	−2.55011	+	4.52736i	−0.245384	+	0.435645i
$109$	−9.24695			−0.885697			−0.442849	−	0.896596i	$-0.646032\pi$
$109$	−9.24695			−0.885697			−0.442849	+	0.896596i	$0.646032\pi$
$110$	1.41852	−	2.45695i	0.135251	−	0.234261i
$111$	−9.77810	−	3.51976i	−0.928096	−	0.334081i
$112$		0			0
$113$	8.81174	+	15.2624i	0.828939	+	1.43576i	0.898872	+	0.438212i	$0.144388\pi$
$113$	8.81174	+	15.2624i	0.828939	+	1.43576i	−0.0699331	+	0.997552i	$0.522279\pi$
$114$	3.50000	−	2.95804i	0.327805	−	0.277046i
$115$	−1.11171	+	1.92554i	−0.103668	+	0.179558i
$116$	−4.00000			−0.371391
$117$	−3.25937	+	19.2827i	−0.301329	+	1.78268i
$118$	12.2326			1.12610
$119$		0			0
$120$	0.188262	+	1.04601i	0.0171859	+	0.0954870i
$121$	−5.18826	−	8.98633i	−0.471660	−	0.816939i
$122$	−3.56618	−	6.17680i	−0.322866	−	0.559221i
$123$	0.623475	+	3.46410i	0.0562169	+	0.312348i
$124$	−3.25937	+	5.64539i	−0.292700	+	0.506971i
$125$	5.90512			0.528170
$126$		0			0
$127$	11.6235			1.03142			0.515708	−	0.856764i	$-0.327529\pi$
$127$	11.6235			1.03142			0.515708	+	0.856764i	$0.327529\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−3.47053	+	2.93313i	−0.305563	+	0.258248i
$130$	2.00000	+	3.46410i	0.175412	+	0.303822i
$131$	6.82554	+	11.8222i	0.596350	+	1.03291i	0.993355	+	0.115093i	$0.0367165\pi$
$131$	6.82554	+	11.8222i	0.596350	+	1.03291i	−0.397004	+	0.917817i	$0.629950\pi$
$132$	7.53480	+	2.71226i	0.655820	+	0.236072i
$133$		0			0
$134$	−4.62348			−0.399407
$135$	1.56479	−	2.77806i	0.134675	−	0.239097i
$136$	−2.03214			−0.174254
$137$	−4.93521	+	8.54804i	−0.421644	+	0.730308i	−0.996100	−	0.0882266i	$-0.971880\pi$
$137$	−4.93521	+	8.54804i	−0.421644	+	0.730308i	0.574457	+	0.818535i	$0.305213\pi$
$138$	−5.90512	−	2.12563i	−0.502677	−	0.180945i
$139$	3.96863	+	6.87386i	0.336615	+	0.583033i	0.983794	−	0.179305i	$-0.0573847\pi$
$139$	3.96863	+	6.87386i	0.336615	+	0.583033i	−0.647179	+	0.762338i	$0.724051\pi$
$140$		0			0
$141$	−14.0000	+	11.8322i	−1.17901	+	0.996448i
$142$	−0.188262	+	0.326080i	−0.0157986	+	0.0273640i
$143$	30.1392			2.52037
$144$	−2.81174	+	1.04601i	−0.234311	+	0.0871673i
$145$	2.45446			0.203832
$146$	−3.66182	+	6.34246i	−0.303054	+	0.524905i
$147$		0			0
$148$	−3.00000	−	5.19615i	−0.246598	−	0.427121i
$149$	−7.62348	−	13.2042i	−0.624539	−	1.08173i	−0.988630	−	0.150370i	$-0.951953\pi$
$149$	−7.62348	−	13.2042i	−0.624539	−	1.08173i	0.364090	−	0.931364i	$-0.381380\pi$
$150$	1.41852	+	7.88146i	0.115822	+	0.643518i
$151$	−0.811738	+	1.40597i	−0.0660583	+	0.114416i	−0.897163	−	0.441700i	$-0.854376\pi$
$151$	−0.811738	+	1.40597i	−0.0660583	+	0.114416i	0.831105	+	0.556116i	$0.187709\pi$
$152$	2.64575			0.214599
$153$	4.69776	+	3.88551i	0.379792	+	0.314125i
$154$		0			0
$155$	2.00000	−	3.46410i	0.160644	−	0.278243i
$156$	−8.62348	+	7.28817i	−0.690431	+	0.583520i
$157$	−1.53404	−	2.65704i	−0.122430	−	0.212055i	0.798296	−	0.602266i	$-0.205735\pi$
$157$	−1.53404	−	2.65704i	−0.122430	−	0.212055i	−0.920725	+	0.390211i	$0.872402\pi$
$158$	6.81174	+	11.7983i	0.541913	+	0.938620i
$159$	6.51873	+	2.34651i	0.516969	+	0.186090i
$160$	−0.306808	+	0.531407i	−0.0242553	+	0.0420114i
$161$		0			0
$162$	8.50000	+	2.95804i	0.667823	+	0.232406i
$163$	19.2470			1.50754			0.753769	−	0.657140i	$-0.228234\pi$
$163$	19.2470			1.50754			0.753769	+	0.657140i	$0.228234\pi$
$164$	−1.01607	+	1.75988i	−0.0793416	+	0.137424i
$165$	−4.62348	−	1.66428i	−0.359937	−	0.129564i
$166$	−3.87298	−	6.70820i	−0.300602	−	0.520658i
$167$	0.613616	+	1.06281i	0.0474830	+	0.0822430i	0.888790	−	0.458315i	$-0.151547\pi$
$167$	0.613616	+	1.06281i	0.0474830	+	0.0822430i	−0.841307	+	0.540558i	$0.818213\pi$
$168$		0			0
$169$	−14.7470	+	25.5425i	−1.13438	+	1.96481i
$170$	1.24695			0.0956368
$171$	−6.11628	−	5.05876i	−0.467724	−	0.386853i
$172$	−2.62348			−0.200038
$173$	−3.25937	+	5.64539i	−0.247805	+	0.429211i	−0.962917	−	0.269799i	$-0.913043\pi$
$173$	−3.25937	+	5.64539i	−0.247805	+	0.429211i	0.715111	+	0.699010i	$0.246376\pi$
$174$	1.22723	+	6.81864i	0.0930362	+	0.516920i
$175$		0			0
$176$	2.31174	+	4.00405i	0.174254	+	0.301816i
$177$	−3.75305	−	20.8524i	−0.282096	−	1.56736i
$178$	7.13235	−	12.3536i	0.534592	−	0.925941i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	1.72533	−	0.641847i	0.128598	−	0.0478404i
$181$	−7.13235			−0.530143			−0.265072	−	0.964229i	$-0.585396\pi$
$181$	−7.13235			−0.530143			−0.265072	+	0.964229i	$0.585396\pi$
$182$		0			0
$183$	−9.43521	+	7.97421i	−0.697471	+	0.589471i
$184$	−1.81174	−	3.13802i	−0.133563	−	0.231338i
$185$	1.84085	+	3.18844i	0.135342	+	0.234419i
$186$	10.6235	+	3.82407i	0.778951	+	0.280394i
$187$	4.69776	−	8.13677i	0.343535	−	0.595019i
$188$	−10.5830			−0.771845
$189$		0			0
$190$	−1.62348			−0.117779
$191$	−7.81174	+	13.5303i	−0.565238	+	0.979020i	0.431790	+	0.901974i	$0.357882\pi$
$191$	−7.81174	+	13.5303i	−0.565238	+	0.979020i	−0.997028	+	0.0770459i	$0.975451\pi$
$192$	−1.62968	−	0.586627i	−0.117612	−	0.0423362i
$193$	13.7470	+	23.8104i	0.989527	+	1.71391i	0.619772	+	0.784782i	$0.287225\pi$
$193$	13.7470	+	23.8104i	0.989527	+	1.71391i	0.369756	+	0.929129i	$0.379441\pi$
$194$	8.14842	+	14.1135i	0.585022	+	1.01329i
$195$	5.29150	−	4.47214i	0.378932	−	0.320256i
$196$		0			0
$197$	−13.2470			−0.943806			−0.471903	−	0.881650i	$-0.656433\pi$
$197$	−13.2470			−0.943806			−0.471903	+	0.881650i	$0.656433\pi$
$198$	2.31174	−	13.6764i	0.164288	−	0.971941i
$199$	−20.7834			−1.47330			−0.736649	−	0.676275i	$-0.763593\pi$
$199$	−20.7834			−1.47330			−0.736649	+	0.676275i	$0.763593\pi$
$200$	−2.31174	+	4.00405i	−0.163465	+	0.283129i
$201$	1.41852	+	7.88146i	0.100055	+	0.555915i
$202$	−8.24406	−	14.2791i	−0.580050	−	1.00468i
$203$		0			0
$204$	0.623475	+	3.46410i	0.0436520	+	0.242536i
$205$	0.623475	−	1.07989i	0.0435454	−	0.0754229i
$206$	−17.1017			−1.19153
$207$	−1.81174	+	10.7184i	−0.125924	+	0.744979i
$208$	−6.51873			−0.451993
$209$	−6.11628	+	10.5937i	−0.423072	+	0.732782i
$210$		0			0
$211$	−7.62348	−	13.2042i	−0.524822	−	0.909018i	−0.999582	−	0.0289028i	$-0.990799\pi$
$211$	−7.62348	−	13.2042i	−0.524822	−	0.909018i	0.474761	−	0.880115i	$-0.342535\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$	0.613616	+	0.220879i	0.0420443	+	0.0151344i
$214$	5.31174	−	9.20020i	0.363103	−	0.628913i
$215$	1.60981			0.109788
$216$	2.64575	+	4.47214i	0.180021	+	0.304290i
$217$		0			0
$218$	−4.62348	+	8.00809i	−0.313141	+	0.542377i
$219$	11.9352	+	4.29624i	0.806507	+	0.290313i
$220$	−1.41852	−	2.45695i	−0.0956366	−	0.165647i
$221$	6.62348	+	11.4722i	0.445543	+	0.771703i
$222$	−7.93725	+	6.70820i	−0.532714	+	0.450225i
$223$	0.613616	−	1.06281i	0.0410908	−	0.0711713i	−0.844749	−	0.535163i	$-0.820250\pi$
$223$	0.613616	−	1.06281i	0.0410908	−	0.0711713i	0.885839	+	0.463992i	$0.153583\pi$
$224$		0			0
$225$	13.0000	−	4.83619i	0.866667	−	0.322413i
$226$	17.6235			1.17230
$227$	−1.13159	+	1.95997i	−0.0751062	+	0.130088i	−0.901132	−	0.433544i	$-0.857263\pi$
$227$	−1.13159	+	1.95997i	−0.0751062	+	0.130088i	0.826026	+	0.563632i	$0.190596\pi$
$228$	−0.811738	−	4.51011i	−0.0537586	−	0.298689i
$229$	−3.75746	−	6.50812i	−0.248300	−	0.430068i	0.714754	−	0.699376i	$-0.246539\pi$
$229$	−3.75746	−	6.50812i	−0.248300	−	0.430068i	−0.963054	+	0.269307i	$0.913205\pi$
$230$	1.11171	+	1.92554i	0.0733041	+	0.126966i
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	17.0000			1.11371			0.556854	−	0.830611i	$-0.312008\pi$
$233$	17.0000			1.11371			0.556854	+	0.830611i	$0.312008\pi$
$234$	15.0696	+	12.4640i	0.985131	+	0.814799i
$235$	6.49390			0.423615
$236$	6.11628	−	10.5937i	0.398136	−	0.689592i
$237$	18.0222	−	15.2315i	1.17067	−	0.989393i
$238$		0			0
$239$	−1.18826	−	2.05813i	−0.0768623	−	0.133129i	0.825032	−	0.565086i	$-0.191157\pi$
$239$	−1.18826	−	2.05813i	−0.0768623	−	0.133129i	−0.901895	+	0.431956i	$0.857824\pi$
$240$	1.00000	+	0.359964i	0.0645497	+	0.0232356i
$241$	−4.08415	+	7.07395i	−0.263083	+	0.455673i	−0.967060	−	0.254550i	$-0.918073\pi$
$241$	−4.08415	+	7.07395i	−0.263083	+	0.455673i	0.703977	+	0.710223i	$0.251406\pi$
$242$	−10.3765			−0.667028
$243$	2.43459	−	15.3972i	0.156179	−	0.987729i
$244$	−7.13235			−0.456602
$245$		0			0
$246$	3.31174	+	1.19211i	0.211149	+	0.0760059i
$247$	−8.62348	−	14.9363i	−0.548699	−	0.950374i
$248$	3.25937	+	5.64539i	0.206970	+	0.358483i
$249$	−10.2470	+	8.66025i	−0.649374	+	0.548821i
$250$	2.95256	−	5.11398i	0.186736	−	0.323437i
$251$	−10.3917			−0.655919			−0.327960	−	0.944692i	$-0.606361\pi$
$251$	−10.3917			−0.655919			−0.327960	+	0.944692i	$0.606361\pi$
$252$		0			0
$253$	16.7530			1.05326
$254$	5.81174	−	10.0662i	0.364661	−	0.631611i
$255$	−0.382574	−	2.12563i	−0.0239577	−	0.133112i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.0535	−	24.3414i	−0.876636	−	1.51838i	−0.855010	−	0.518611i	$-0.826449\pi$
$257$	−14.0535	−	24.3414i	−0.876636	−	1.51838i	−0.0216253	−	0.999766i	$-0.506884\pi$
$258$	0.804903	+	4.47214i	0.0501111	+	0.278423i
$259$		0			0
$260$	4.00000			0.248069
$261$	11.2470	−	4.18403i	0.696169	−	0.258985i
$262$	13.6511			0.843367
$263$	6.81174	−	11.7983i	0.420030	−	0.727513i	−0.575912	−	0.817512i	$-0.695353\pi$
$263$	6.81174	−	11.7983i	0.420030	−	0.727513i	0.995942	+	0.0899987i	$0.0286863\pi$
$264$	6.11628	−	5.16920i	0.376431	−	0.318142i
$265$	−1.22723	−	2.12563i	−0.0753883	−	0.130576i
$266$		0			0
$267$	−23.2470	−	8.36806i	−1.42269	−	0.512117i
$268$	−2.31174	+	4.00405i	−0.141212	+	0.244586i
$269$	10.8140			0.659344			0.329672	−	0.944096i	$-0.393062\pi$
$269$	10.8140			0.659344			0.329672	+	0.944096i	$0.393062\pi$
$270$	−1.62348	−	2.74417i	−0.0988016	−	0.167005i
$271$	−18.3290			−1.11341			−0.556703	−	0.830712i	$-0.687934\pi$
$271$	−18.3290			−1.11341			−0.556703	+	0.830712i	$0.687934\pi$
$272$	−1.01607	+	1.75988i	−0.0616082	+	0.106708i
$273$		0			0
$274$	4.93521	+	8.54804i	0.298147	+	0.516406i
$275$	−10.6883	−	18.5126i	−0.644526	−	1.11635i
$276$	−4.79341	+	4.05117i	−0.288529	+	0.243852i
$277$	−6.24695	+	10.8200i	−0.375343	+	0.650113i	−0.990378	−	0.138387i	$-0.955808\pi$
$277$	−6.24695	+	10.8200i	−0.375343	+	0.650113i	0.615035	+	0.788499i	$0.289142\pi$
$278$	7.93725			0.476045
$279$	3.25937	−	19.2827i	0.195133	−	1.15442i
$280$		0			0
$281$	−2.43521	+	4.21791i	−0.145273	+	0.251620i	−0.929475	−	0.368886i	$-0.879739\pi$
$281$	−2.43521	+	4.21791i	−0.145273	+	0.251620i	0.784202	+	0.620506i	$0.213073\pi$
$282$	3.24695	+	18.0404i	0.193353	+	1.07429i
$283$	5.59831	+	9.69656i	0.332785	+	0.576401i	0.983057	−	0.183301i	$-0.0586783\pi$
$283$	5.59831	+	9.69656i	0.332785	+	0.576401i	−0.650272	+	0.759702i	$0.725345\pi$
$284$	0.188262	+	0.326080i	0.0111713	+	0.0193493i
$285$	0.498095	+	2.76748i	0.0295046	+	0.163931i
$286$	15.0696	−	26.1013i	0.891084	−	1.54340i
$287$		0			0
$288$	−0.500000	+	2.95804i	−0.0294628	+	0.174304i
$289$	−12.8704			−0.757084
$290$	1.22723	−	2.12563i	0.0720655	−	0.124821i
$291$	21.5587	−	18.2204i	1.26379	−	1.06810i
$292$	3.66182	+	6.34246i	0.214292	+	0.371164i
$293$	7.01683	+	12.1535i	0.409928	+	0.710015i	0.994881	−	0.101051i	$-0.0322206\pi$
$293$	7.01683	+	12.1535i	0.409928	+	0.710015i	−0.584954	+	0.811067i	$0.698887\pi$
$294$		0			0
$295$	−3.75305	+	6.50047i	−0.218511	+	0.378472i
$296$	−6.00000			−0.348743
$297$	−24.0229	+	0.255308i	−1.39395	+	0.0148145i
$298$	−15.2470			−0.883232
$299$	−11.8102	+	20.4559i	−0.683004	+	1.18300i
$300$	7.53480	+	2.71226i	0.435022	+	0.156592i
$301$		0			0
$302$	0.811738	+	1.40597i	0.0467103	+	0.0809045i
$303$	−21.8117	+	18.4343i	−1.25305	+	1.05902i
$304$	1.32288	−	2.29129i	0.0758721	−	0.131414i
$305$	4.37652			0.250599
$306$	5.71383	−	2.12563i	0.326638	−	0.121514i
$307$	−13.2288			−0.755005			−0.377503	−	0.926009i	$-0.623217\pi$
$307$	−13.2288			−0.755005			−0.377503	+	0.926009i	$0.623217\pi$
$308$		0			0
$309$	5.24695	+	29.1527i	0.298489	+	1.65844i
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−5.10022	−	8.83383i	−0.289207	−	0.500921i	0.684414	−	0.729094i	$-0.260058\pi$
$311$	−5.10022	−	8.83383i	−0.289207	−	0.500921i	−0.973621	+	0.228173i	$0.926725\pi$
$312$	2.00000	+	11.1122i	0.113228	+	0.629106i
$313$	8.95332	−	15.5076i	0.506072	−	0.876542i	−0.493904	−	0.869517i	$-0.664430\pi$
$313$	8.95332	−	15.5076i	0.506072	−	0.876542i	0.999975	−	0.00702519i	$-0.00223621\pi$
$314$	−3.06808			−0.173142
$315$		0			0
$316$	13.6235			0.766380
$317$	6.62348	−	11.4722i	0.372011	−	0.644343i	−0.617863	−	0.786285i	$-0.712002\pi$
$317$	6.62348	−	11.4722i	0.372011	−	0.644343i	0.989875	+	0.141943i	$0.0453349\pi$
$318$	5.29150	−	4.47214i	0.296733	−	0.250785i
$319$	−9.24695	−	16.0162i	−0.517730	−	0.896734i
$320$	0.306808	+	0.531407i	0.0171511	+	0.0297066i
$321$	−17.3129	−	6.23202i	−0.966312	−	0.347837i
$322$		0			0
$323$	−5.37652			−0.299158
$324$	6.81174	−	5.88220i	0.378430	−	0.326789i
$325$	30.1392			1.67182
$326$	9.62348	−	16.6683i	0.532995	−	0.923174i
$327$	15.0696	+	5.42451i	0.833351	+	0.299976i
$328$	1.01607	+	1.75988i	0.0561030	+	0.0971732i
$329$		0			0
$330$	−3.75305	+	3.17191i	−0.206599	+	0.174608i
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−7.74597			−0.425115
$333$	13.8704	+	11.4722i	0.760095	+	0.628672i
$334$	1.22723			0.0671511
$335$	1.41852	−	2.45695i	0.0775020	−	0.134237i
$336$		0			0
$337$	−16.9352	−	29.3326i	−0.922520	−	1.59785i	−0.795502	−	0.605951i	$-0.792793\pi$
$337$	−16.9352	−	29.3326i	−0.922520	−	1.59785i	−0.127018	−	0.991900i	$-0.540541\pi$
$338$	14.7470	+	25.5425i	0.802128	+	1.38933i
$339$	−5.40702	−	30.0420i	−0.293669	−	1.63166i
$340$	0.623475	−	1.07989i	0.0338127	−	0.0585653i
$341$	−30.1392			−1.63213
$342$	−7.43916	+	2.76748i	−0.402264	+	0.149648i
$343$		0			0
$344$	−1.31174	+	2.27200i	−0.0707242	+	0.122498i
$345$	2.94131	−	2.48586i	0.158355	−	0.133834i
$346$	3.25937	+	5.64539i	0.175225	+	0.303498i
$347$	−3.31174	−	5.73610i	−0.177783	−	0.307930i	0.763338	−	0.646000i	$-0.223559\pi$
$347$	−3.31174	−	5.73610i	−0.177783	−	0.307930i	−0.941121	+	0.338070i	$0.890226\pi$
$348$	6.51873	+	2.34651i	0.349441	+	0.125786i
$349$	5.71383	−	9.89665i	0.305854	−	0.529755i	−0.671597	−	0.740917i	$-0.734391\pi$
$349$	5.71383	−	9.89665i	0.305854	−	0.529755i	0.977451	+	0.211161i	$0.0677246\pi$
$350$		0			0
$351$	16.6235	−	29.5126i	0.887295	−	1.57527i
$352$	4.62348			0.246432
$353$	−1.01607	+	1.75988i	−0.0540798	+	0.0936690i	−0.891798	−	0.452434i	$-0.850556\pi$
$353$	−1.01607	+	1.75988i	−0.0540798	+	0.0936690i	0.837718	+	0.546103i	$0.183889\pi$
$354$	−19.9352	−	7.17595i	−1.05954	−	0.381398i
$355$	−0.115521	−	0.200088i	−0.00613121	−	0.0106196i
$356$	−7.13235	−	12.3536i	−0.378014	−	0.654739i
$357$		0			0
$358$		0			0
$359$	−20.1174			−1.06175			−0.530877	−	0.847449i	$-0.678137\pi$
$359$	−20.1174			−1.06175			−0.530877	+	0.847449i	$0.678137\pi$
$360$	0.306808	−	1.81510i	0.0161702	−	0.0956642i
$361$	−12.0000			−0.631579
$362$	−3.56618	+	6.17680i	−0.187434	+	0.324645i
$363$	3.18360	+	17.6885i	0.167096	+	0.928403i
$364$		0			0
$365$	−2.24695	−	3.89183i	−0.117611	−	0.203708i
$366$	2.18826	+	12.1582i	0.114382	+	0.635521i
$367$	−15.0696	+	26.1013i	−0.786627	+	1.36248i	0.141395	+	0.989953i	$0.454841\pi$
$367$	−15.0696	+	26.1013i	−0.786627	+	1.36248i	−0.928022	+	0.372525i	$0.878492\pi$
$368$	−3.62348			−0.188887
$369$	1.01607	−	6.01114i	0.0528944	−	0.312927i
$370$	3.68170			0.191402
$371$		0			0
$372$	8.62348	−	7.28817i	0.447106	−	0.377874i
$373$	4.62348	+	8.00809i	0.239394	+	0.414643i	0.960541	−	0.278139i	$-0.0897178\pi$
$373$	4.62348	+	8.00809i	0.239394	+	0.414643i	−0.721146	+	0.692783i	$0.756384\pi$
$374$	−4.69776	−	8.13677i	−0.242916	−	0.420742i
$375$	−9.62348	−	3.46410i	−0.496954	−	0.178885i
$376$	−5.29150	+	9.16515i	−0.272888	+	0.472657i
$377$	26.0749			1.34293
$378$		0			0
$379$	5.37652			0.276174			0.138087	−	0.990420i	$-0.455905\pi$
$379$	5.37652			0.276174			0.138087	+	0.990420i	$0.455905\pi$
$380$	−0.811738	+	1.40597i	−0.0416413	+	0.0721248i
$381$	−18.9426	−	6.81864i	−0.970458	−	0.349330i
$382$	7.81174	+	13.5303i	0.399683	+	0.692272i
$383$	9.96939	+	17.2675i	0.509412	+	0.882327i	0.999941	+	0.0109023i	$0.00347039\pi$
$383$	9.96939	+	17.2675i	0.509412	+	0.882327i	−0.490529	+	0.871425i	$0.663196\pi$
$384$	−1.32288	+	1.11803i	−0.0675077	+	0.0570544i
$385$		0			0
$386$	27.4939			1.39940
$387$	7.37652	−	2.74417i	0.374970	−	0.139494i
$388$	16.2968			0.827347
$389$	−8.37652	+	14.5086i	−0.424707	+	0.735614i	−0.996393	−	0.0848588i	$-0.972956\pi$
$389$	−8.37652	+	14.5086i	−0.424707	+	0.735614i	0.571686	+	0.820472i	$0.306289\pi$
$390$	−1.22723	−	6.81864i	−0.0621433	−	0.345275i
$391$	3.68170	+	6.37688i	0.186191	+	0.322493i
$392$		0			0
$393$	−4.18826	−	23.2705i	−0.211270	−	1.17384i
$394$	−6.62348	+	11.4722i	−0.333686	+	0.577961i
$395$	−8.35958			−0.420616
$396$	−10.6883	−	8.84024i	−0.537105	−	0.444239i
$397$	17.1017			0.858312			0.429156	−	0.903230i	$-0.358811\pi$
$397$	17.1017			0.858312			0.429156	+	0.903230i	$0.358811\pi$
$398$	−10.3917	+	17.9990i	−0.520890	+	0.902208i
$399$		0			0
$400$	2.31174	+	4.00405i	0.115587	+	0.200202i
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$	7.53480	+	2.71226i	0.375802	+	0.135275i
$403$	21.2470	−	36.8008i	1.05839	−	1.83318i
$404$	−16.4881			−0.820315
$405$	−4.17979	+	3.60941i	−0.207696	+	0.179353i
$406$		0			0
$407$	13.8704	−	24.0243i	0.687531	−	1.19084i
$408$	3.31174	+	1.19211i	0.163955	+	0.0590180i
$409$	10.7942	+	18.6961i	0.533737	+	0.924460i	0.999223	+	0.0394049i	$0.0125462\pi$
$409$	10.7942	+	18.6961i	0.533737	+	0.924460i	−0.465486	+	0.885055i	$0.654120\pi$
$410$	−0.623475	−	1.07989i	−0.0307913	−	0.0533320i
$411$	13.0573	−	11.0355i	0.644071	−	0.544340i
$412$	−8.55087	+	14.8105i	−0.421271	+	0.729663i
$413$		0			0
$414$	8.37652	+	6.92820i	0.411684	+	0.340503i
$415$	4.75305			0.233318
$416$	−3.25937	+	5.64539i	−0.159804	+	0.276788i
$417$	−2.43521	−	13.5303i	−0.119253	−	0.662583i
$418$	6.11628	+	10.5937i	0.299157	+	0.518155i
$419$	6.21193	+	10.7594i	0.303472	+	0.525630i	0.976920	−	0.213605i	$-0.0685206\pi$
$419$	6.21193	+	10.7594i	0.303472	+	0.525630i	−0.673448	+	0.739235i	$0.735187\pi$
$420$		0			0
$421$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$421$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$422$	−15.2470			−0.742210
$423$	29.7566	−	11.0699i	1.44682	−	0.538237i
$424$	4.00000			0.194257
$425$	4.69776	−	8.13677i	0.227875	−	0.394691i
$426$	0.498095	−	0.420967i	0.0241328	−	0.0203959i
$427$		0			0
$428$	−5.31174	−	9.20020i	−0.256753	−	0.444708i
$429$	−49.1174	−	17.6805i	−2.37141	−	0.853621i
$430$	0.804903	−	1.39413i	0.0388159	−	0.0672311i
$431$	−8.00000			−0.385346			−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000			−0.385346			−0.192673	+	0.981263i	$0.561716\pi$
$432$	5.19586	−	0.0552199i	0.249986	−	0.00265677i
$433$	−4.48660			−0.215612			−0.107806	−	0.994172i	$-0.534383\pi$
$433$	−4.48660			−0.215612			−0.107806	+	0.994172i	$0.534383\pi$
$434$		0			0
$435$	−4.00000	−	1.43985i	−0.191785	−	0.0690357i
$436$	4.62348	+	8.00809i	0.221424	+	0.383518i
$437$	−4.79341	−	8.30243i	−0.229300	−	0.397159i
$438$	9.68826	−	8.18808i	0.462923	−	0.391241i
$439$	−15.4919	+	26.8328i	−0.739390	+	1.28066i	0.213381	+	0.976969i	$0.431552\pi$
$439$	−15.4919	+	26.8328i	−0.739390	+	1.28066i	−0.952770	+	0.303691i	$0.901781\pi$
$440$	−2.83704			−0.135251
$441$		0			0
$442$	13.2470			0.630093
$443$	−15.3117	+	26.5207i	−0.727483	+	1.26004i	0.230461	+	0.973081i	$0.425976\pi$
$443$	−15.3117	+	26.5207i	−0.727483	+	1.26004i	−0.957944	+	0.286955i	$0.907357\pi$
$444$	1.84085	+	10.2280i	0.0873628	+	0.485398i
$445$	4.37652	+	7.58036i	0.207467	+	0.359344i
$446$	−0.613616	−	1.06281i	−0.0290556	−	0.0503257i
$447$	4.67789	+	25.9909i	0.221256	+	1.22933i
$448$		0			0
$449$	−15.0000			−0.707894			−0.353947	−	0.935266i	$-0.615161\pi$
$449$	−15.0000			−0.707894			−0.353947	+	0.935266i	$0.615161\pi$
$450$	2.31174	−	13.6764i	0.108976	−	0.644713i
$451$	−9.39553			−0.442418
$452$	8.81174	−	15.2624i	0.414469	−	0.717882i
$453$	2.14766	−	1.81510i	0.100906	−	0.0852809i
$454$	1.13159	+	1.95997i	0.0531081	+	0.0919859i
$455$		0			0
$456$	−4.31174	−	1.55207i	−0.201916	−	0.0726823i
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	−0.965512	−	0.260358i	$-0.916159\pi$
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	0.708233	+	0.705979i	$0.249493\pi$
$458$	−7.51493			−0.351149
$459$	−5.37652	−	9.08799i	−0.250955	−	0.424191i
$460$	2.22342			0.103668
$461$	−0.920424	+	1.59422i	−0.0428684	+	0.0742503i	−0.886664	−	0.462415i	$-0.846983\pi$
$461$	−0.920424	+	1.59422i	−0.0428684	+	0.0742503i	0.843795	+	0.536666i	$0.180316\pi$
$462$		0			0
$463$	−17.8117	−	30.8508i	−0.827782	−	1.43376i	−0.899775	−	0.436355i	$-0.856269\pi$
$463$	−17.8117	−	30.8508i	−0.827782	−	1.43376i	0.0719931	−	0.997405i	$-0.477064\pi$
$464$	2.00000	+	3.46410i	0.0928477	+	0.160817i
$465$	−5.29150	+	4.47214i	−0.245388	+	0.207390i
$466$	8.50000	−	14.7224i	0.393755	−	0.682003i
$467$	−7.32364			−0.338898			−0.169449	−	0.985539i	$-0.554199\pi$
$467$	−7.32364			−0.338898			−0.169449	+	0.985539i	$0.554199\pi$
$468$	18.3290	−	6.81864i	0.847257	−	0.315192i
$469$		0			0
$470$	3.24695	−	5.62388i	0.149771	−	0.259410i
$471$	0.941312	+	5.23004i	0.0433733	+	0.240987i
$472$	−6.11628	−	10.5937i	−0.281525	−	0.487615i
$473$	−6.06479	−	10.5045i	−0.278859	−	0.482998i
$474$	−4.17979	−	23.2234i	−0.191984	−	1.06669i
$475$	−6.11628	+	10.5937i	−0.280634	+	0.486073i
$476$		0			0
$477$	−9.24695	−	7.64813i	−0.423389	−	0.350184i
$478$	−2.37652			−0.108700
$479$	−7.74597	+	13.4164i	−0.353922	+	0.613011i	−0.986933	−	0.161132i	$-0.948486\pi$
$479$	−7.74597	+	13.4164i	−0.353922	+	0.613011i	0.633011	+	0.774143i	$0.281819\pi$
$480$	0.811738	−	0.686044i	0.0370506	−	0.0313135i
$481$	19.5562	+	33.8723i	0.891686	+	1.54445i
$482$	4.08415	+	7.07395i	0.186028	+	0.322210i
$483$		0			0
$484$	−5.18826	+	8.98633i	−0.235830	+	0.408470i
$485$	−10.0000			−0.454077
$486$	−12.1170	−	9.80700i	−0.549640	−	0.444854i
$487$	−5.62348			−0.254824			−0.127412	−	0.991850i	$-0.540667\pi$
$487$	−5.62348			−0.254824			−0.127412	+	0.991850i	$0.540667\pi$
$488$	−3.56618	+	6.17680i	−0.161433	+	0.279610i
$489$	−31.3664	−	11.2908i	−1.41844	−	0.510587i
$490$		0			0
$491$	−7.55869	−	13.0920i	−0.341119	−	0.590835i	0.643522	−	0.765428i	$-0.277473\pi$
$491$	−7.55869	−	13.0920i	−0.341119	−	0.590835i	−0.984641	+	0.174593i	$0.944139\pi$
$492$	2.68826	−	2.27200i	0.121196	−	0.102430i
$493$	4.06427	−	7.03952i	0.183046	−	0.317044i
$494$	−17.2470			−0.775977
$495$	6.55849	+	5.42451i	0.294782	+	0.243814i
$496$	6.51873			0.292700
$497$		0			0
$498$	2.37652	+	13.2042i	0.106495	+	0.591696i
$499$	−9.31174	−	16.1284i	−0.416851	−	0.722006i	0.578770	−	0.815491i	$-0.303533\pi$
$499$	−9.31174	−	16.1284i	−0.416851	−	0.722006i	−0.995621	+	0.0934843i	$0.970200\pi$
$500$	−2.95256	−	5.11398i	−0.132042	−	0.228704i
$501$	−0.376525	−	2.09201i	−0.0168219	−	0.0934643i
$502$	−5.19586	+	8.99949i	−0.231903	+	0.401667i
$503$	10.2004			0.454815			0.227407	−	0.973800i	$-0.426975\pi$
$503$	10.2004			0.454815			0.227407	+	0.973800i	$0.426975\pi$
$504$		0			0
$505$	10.1174			0.450217
$506$	8.37652	−	14.5086i	0.372382	−	0.644984i
$507$	39.0168	−	32.9752i	1.73280	−	1.46448i
$508$	−5.81174	−	10.0662i	−0.257854	−	0.446617i
$509$	−11.0053	−	19.0618i	−0.487803	−	0.844899i	0.512099	−	0.858927i	$-0.328868\pi$
$509$	−11.0053	−	19.0618i	−0.487803	−	0.844899i	−0.999902	+	0.0140272i	$0.995535\pi$
$510$	−2.03214	−	0.731495i	−0.0899845	−	0.0323911i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	7.00000	+	11.8322i	0.309058	+	0.522403i
$514$	−28.1071			−1.23975
$515$	5.24695	−	9.08799i	0.231208	−	0.400464i
$516$	4.27543	+	1.53900i	0.188216	+	0.0677508i
$517$	−24.4651	−	42.3749i	−1.07598	−	1.86364i
$518$		0			0
$519$	8.62348	−	7.28817i	0.378529	−	0.319915i
$520$	2.00000	−	3.46410i	0.0877058	−	0.151911i
$521$	−35.0084			−1.53375			−0.766873	−	0.641799i	$-0.778188\pi$
$521$	−35.0084			−1.53375			−0.766873	+	0.641799i	$0.778188\pi$
$522$	2.00000	−	11.8322i	0.0875376	−	0.517880i
$523$	14.8783			0.650583			0.325292	−	0.945614i	$-0.394538\pi$
$523$	14.8783			0.650583			0.325292	+	0.945614i	$0.394538\pi$
$524$	6.82554	−	11.8222i	0.298175	−	0.516455i
$525$		0			0
$526$	−6.81174	−	11.7983i	−0.297006	−	0.514429i
$527$	−6.62348	−	11.4722i	−0.288523	−	0.499737i
$528$	−1.41852	−	7.88146i	−0.0617331	−	0.342996i
$529$	4.93521	−	8.54804i	0.214574	−	0.371654i
$530$	−2.45446			−0.106615
$531$	−6.11628	+	36.1844i	−0.265424	+	1.57027i
$532$		0			0
$533$	6.62348	−	11.4722i	0.286895	−	0.496916i
$534$	−18.8704	+	15.9484i	−0.816603	+	0.690156i
$535$	3.25937	+	5.64539i	0.140915	+	0.244071i
$536$	2.31174	+	4.00405i	0.0998519	+	0.172948i
$537$		0			0
$538$	5.40702	−	9.36524i	0.233113	−	0.403764i
$539$		0			0
$540$	−3.18826	+	0.0338838i	−0.137201	+	0.00145813i
$541$	4.00000			0.171973			0.0859867	−	0.996296i	$-0.472596\pi$
$541$	4.00000			0.171973			0.0859867	+	0.996296i	$0.472596\pi$
$542$	−9.16449	+	15.8734i	−0.393648	+	0.681819i
$543$	11.6235	+	4.18403i	0.498811	+	0.179554i
$544$	1.01607	+	1.75988i	0.0435635	+	0.0754543i
$545$	−2.83704	−	4.91389i	−0.121525	−	0.210488i
$546$		0			0
$547$	−4.68826	+	8.12031i	−0.200456	+	0.347199i	−0.948675	−	0.316252i	$-0.897576\pi$
$547$	−4.68826	+	8.12031i	−0.200456	+	0.347199i	0.748220	+	0.663451i	$0.230909\pi$
$548$	9.87043			0.421644
$549$	20.0543	−	7.46049i	0.855897	−	0.318406i
$550$	−21.3765			−0.911498
$551$	−5.29150	+	9.16515i	−0.225426	+	0.390449i
$552$	1.11171	+	6.17680i	0.0473176	+	0.262902i
$553$		0			0
$554$	6.24695	+	10.8200i	0.265408	+	0.459699i
$555$	−1.12957	−	6.27604i	−0.0479477	−	0.266403i
$556$	3.96863	−	6.87386i	0.168307	−	0.291517i
$557$	43.2470			1.83243			0.916216	−	0.400685i	$-0.131228\pi$
$557$	43.2470			1.83243			0.916216	+	0.400685i	$0.131228\pi$
$558$	−15.0696	−	12.4640i	−0.637947	−	0.527645i
$559$	17.1017			0.723327
$560$		0			0
$561$	−12.4291	+	10.5045i	−0.524758	+	0.443501i
$562$	2.43521	+	4.21791i	0.102723	+	0.177922i
$563$	10.4874	+	18.1646i	0.441990	+	0.765548i	0.997837	−	0.0657359i	$-0.0209395\pi$
$563$	10.4874	+	18.1646i	0.441990	+	0.765548i	−0.555847	+	0.831284i	$0.687606\pi$
$564$	17.2470	+	6.20828i	0.726228	+	0.261416i
$565$	−5.40702	+	9.36524i	−0.227475	+	0.393999i
$566$	11.1966			0.470629
$567$		0			0
$568$	0.376525			0.0157986
$569$	0.935213	−	1.61984i	0.0392062	−	0.0679071i	−0.845756	−	0.533569i	$-0.820850\pi$
$569$	0.935213	−	1.61984i	0.0392062	−	0.0679071i	0.884963	+	0.465662i	$0.154184\pi$
$570$	2.64575	+	0.952374i	0.110818	+	0.0398906i
$571$	9.31174	+	16.1284i	0.389684	+	0.674953i	0.992407	−	0.122998i	$-0.0392509\pi$
$571$	9.31174	+	16.1284i	0.389684	+	0.674953i	−0.602723	+	0.797951i	$0.705918\pi$
$572$	−15.0696	−	26.1013i	−0.630092	−	1.09135i
$573$	20.6679	−	17.4676i	0.863415	−	0.729718i
$574$		0			0
$575$	16.7530			0.698650
$576$	2.31174	+	1.91203i	0.0963224	+	0.0796680i
$577$	12.6151			0.525175			0.262588	−	0.964908i	$-0.415424\pi$
$577$	12.6151			0.525175			0.262588	+	0.964908i	$0.415424\pi$
$578$	−6.43521	+	11.1461i	−0.267670	+	0.463617i
$579$	−8.43535	−	46.8678i	−0.350561	−	1.94776i
$580$	−1.22723	−	2.12563i	−0.0509580	−	0.0882619i
$581$		0			0
$582$	−5.00000	−	27.7806i	−0.207257	−	1.15154i
$583$	−9.24695	+	16.0162i	−0.382970	+	0.663323i
$584$	7.32364			0.303054
$585$	−11.2470	+	4.18403i	−0.465004	+	0.172988i
$586$	14.0337			0.579725
$587$	17.0061	−	29.4554i	0.701917	−	1.21576i	−0.265876	−	0.964007i	$-0.585661\pi$
$587$	17.0061	−	29.4554i	0.701917	−	1.21576i	0.967793	−	0.251748i	$-0.0810055\pi$
$588$		0			0
$589$	8.62348	+	14.9363i	0.355324	+	0.615439i
$590$	3.75305	+	6.50047i	0.154511	+	0.267620i
$591$	21.5883	+	7.77102i	0.888026	+	0.319657i
$592$	−3.00000	+	5.19615i	−0.123299	+	0.213561i
$593$	−35.4307			−1.45496			−0.727482	−	0.686126i	$-0.759310\pi$
$593$	−35.4307			−1.45496			−0.727482	+	0.686126i	$0.759310\pi$
$594$	−11.7904	+	20.9321i	−0.483764	+	0.858855i
$595$		0			0
$596$	−7.62348	+	13.2042i	−0.312270	+	0.540867i
$597$	33.8704	+	12.1921i	1.38622	+	0.498990i
$598$	11.8102	+	20.4559i	0.482957	+	0.836505i
$599$	−19.2470	−	33.3367i	−0.786409	−	1.36210i	−0.928154	−	0.372197i	$-0.878604\pi$
$599$	−19.2470	−	33.3367i	−0.786409	−	1.36210i	0.141745	−	0.989903i	$-0.454729\pi$
$600$	6.11628	−	5.16920i	0.249696	−	0.211032i
$601$	−5.31138	+	9.19958i	−0.216656	+	0.375259i	−0.953783	−	0.300495i	$-0.902848\pi$
$601$	−5.31138	+	9.19958i	−0.216656	+	0.375259i	0.737128	+	0.675753i	$0.236182\pi$
$602$		0			0
$603$	2.31174	−	13.6764i	0.0941412	−	0.556947i
$604$	1.62348			0.0660583
$605$	3.18360	−	5.51416i	0.129432	−	0.224182i
$606$	5.05869	+	28.1067i	0.205495	+	1.14176i
$607$	9.96939	+	17.2675i	0.404645	+	0.700866i	0.994280	−	0.106804i	$-0.0340618\pi$
$607$	9.96939	+	17.2675i	0.404645	+	0.700866i	−0.589635	+	0.807670i	$0.700728\pi$
$608$	−1.32288	−	2.29129i	−0.0536497	−	0.0929240i
$609$		0			0
$610$	2.18826	−	3.79018i	0.0886002	−	0.153460i
$611$	68.9878			2.79095
$612$	1.01607	−	6.01114i	0.0410721	−	0.242986i
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	−6.61438	+	11.4564i	−0.266935	+	0.462344i
$615$	−1.64956	+	1.39413i	−0.0665167	+	0.0562169i
$616$		0			0
$617$	5.55869	+	9.62793i	0.223784	+	0.387606i	0.955954	−	0.293516i	$-0.0948255\pi$
$617$	5.55869	+	9.62793i	0.223784	+	0.387606i	−0.732170	+	0.681122i	$0.761492\pi$
$618$	27.8704	+	10.0323i	1.12111	+	0.403560i
$619$	−1.51416	+	2.62261i	−0.0608593	+	0.105411i	−0.894850	−	0.446367i	$-0.852717\pi$
$619$	−1.51416	+	2.62261i	−0.0608593	+	0.105411i	0.833990	+	0.551779i	$0.186051\pi$
$620$	−4.00000			−0.160644
$621$	9.24025	−	16.4048i	0.370799	−	0.658300i
$622$	−10.2004			−0.409000
$623$		0			0
$624$	10.6235	+	3.82407i	0.425279	+	0.153085i
$625$	−9.74695	−	16.8822i	−0.389878	−	0.675289i
$626$	−8.95332	−	15.5076i	−0.357847	−	0.619809i
$627$	16.1822	−	13.6764i	0.646253	−	0.546184i
$628$	−1.53404	+	2.65704i	−0.0612149	+	0.106027i
$629$	12.1928			0.486159
$630$		0			0
$631$	20.3765			0.811177			0.405588	−	0.914056i	$-0.367067\pi$
$631$	20.3765			0.811177			0.405588	+	0.914056i	$0.367067\pi$
$632$	6.81174	−	11.7983i	0.270956	−	0.469310i
$633$	4.67789	+	25.9909i	0.185929	+	1.03304i
$634$	−6.62348	−	11.4722i	−0.263052	−	0.455619i
$635$	3.56618	+	6.17680i	0.141519	+	0.245119i
$636$	−1.22723	−	6.81864i	−0.0486629	−	0.270377i
$637$		0			0
$638$	−18.4939			−0.732181
$639$	−0.870426	−	0.719927i	−0.0344335	−	0.0284799i
$640$	0.613616			0.0242553
$641$	−7.74695	+	13.4181i	−0.305986	+	0.529984i	−0.977480	−	0.211026i	$-0.932319\pi$
$641$	−7.74695	+	13.4181i	−0.305986	+	0.529984i	0.671494	+	0.741010i	$0.265653\pi$
$642$	−14.0535	+	11.8774i	−0.554649	+	0.468764i
$643$	2.85692	+	4.94832i	0.112666	+	0.195143i	0.916844	−	0.399245i	$-0.130728\pi$
$643$	2.85692	+	4.94832i	0.112666	+	0.195143i	−0.804178	+	0.594388i	$0.797394\pi$
$644$		0			0
$645$	−2.62348	−	0.944356i	−0.103299	−	0.0371840i
$646$	−2.68826	+	4.65621i	−0.105768	+	0.183196i
$647$	−19.1736			−0.753793			−0.376897	−	0.926255i	$-0.623009\pi$
$647$	−19.1736			−0.753793			−0.376897	+	0.926255i	$0.623009\pi$
$648$	−1.68826	−	8.84024i	−0.0663212	−	0.347277i
$649$	56.5570			2.22006
$650$	15.0696	−	26.1013i	0.591079	−	1.02378i
$651$		0			0
$652$	−9.62348	−	16.6683i	−0.376884	−	0.652783i
$653$	−9.37652	−	16.2406i	−0.366932	−	0.635544i	0.622152	−	0.782896i	$-0.286258\pi$
$653$	−9.37652	−	16.2406i	−0.366932	−	0.635544i	−0.989084	+	0.147352i	$0.952925\pi$
$654$	12.2326	−	10.3384i	0.478331	−	0.404264i
$655$	−4.18826	+	7.25428i	−0.163649	+	0.283448i
$656$	2.03214			0.0793416
$657$	−16.9303	−	14.0030i	−0.660515	−	0.546310i
$658$		0			0
$659$	−15.2470	+	26.4085i	−0.593937	+	1.02873i	0.399759	+	0.916620i	$0.369094\pi$
$659$	−15.2470	+	26.4085i	−0.593937	+	1.02873i	−0.993696	+	0.112109i	$0.964240\pi$
$660$	0.870426	+	4.83619i	0.0338813	+	0.188248i
$661$	15.9900	+	27.6955i	0.621940	+	1.07723i	0.989124	+	0.147083i	$0.0469886\pi$
$661$	15.9900	+	27.6955i	0.621940	+	1.07723i	−0.367184	+	0.930148i	$0.619678\pi$
$662$	4.00000	+	6.92820i	0.155464	+	0.269272i
$663$	−4.06427	−	22.5816i	−0.157843	−	0.876995i
$664$	−3.87298	+	6.70820i	−0.150301	+	0.260329i
$665$		0			0
$666$	16.8704	−	6.27604i	0.653716	−	0.243192i
$667$	14.4939			0.561206
$668$	0.613616	−	1.06281i	0.0237415	−	0.0411215i
$669$	−1.62348	+	1.37209i	−0.0627672	+	0.0530480i
$670$	−1.41852	−	2.45695i	−0.0548022	−	0.0949202i
$671$	−16.4881	−	28.5583i	−0.636517	−	1.10248i
$672$		0			0
$673$	−14.8117	+	25.6547i	−0.570951	+	0.988915i	0.425518	+	0.904950i	$0.360092\pi$
$673$	−14.8117	+	25.6547i	−0.570951	+	0.988915i	−0.996469	+	0.0839654i	$0.973241\pi$
$674$	−33.8704			−1.30464
$675$	−24.0229	+	0.255308i	−0.924643	+	0.00982680i
$676$	29.4939			1.13438
$677$	13.4598	−	23.3131i	0.517302	−	0.895993i	−0.482496	−	0.875898i	$-0.660270\pi$
$677$	13.4598	−	23.3131i	0.517302	−	0.895993i	0.999798	−	0.0200953i	$-0.00639696\pi$
$678$	−28.7207	−	10.3384i	−1.10301	−	0.397044i
$679$		0			0
$680$	−0.623475	−	1.07989i	−0.0239092	−	0.0414119i
$681$	2.99390	−	2.53031i	0.114727	−	0.0969616i
$682$	−15.0696	+	26.1013i	−0.577045	+	0.999471i
$683$	44.3643			1.69755			0.848777	−	0.528751i	$-0.177340\pi$
$683$	44.3643			1.69755			0.848777	+	0.528751i	$0.177340\pi$
$684$	−1.32288	+	7.82624i	−0.0505814	+	0.299244i
$685$	−6.05665			−0.231413
$686$		0			0
$687$	2.30564	+	12.8104i	0.0879656	+	0.488747i
$688$	1.31174	+	2.27200i	0.0500095	+	0.0866190i
$689$	−13.0375	−	22.5816i	−0.496688	−	0.860289i
$690$	−0.682164	−	3.79018i	−0.0259695	−	0.144290i
$691$	−13.9579	+	24.1758i	−0.530983	+	0.919690i	0.468363	+	0.883536i	$0.344844\pi$
$691$	−13.9579	+	24.1758i	−0.530983	+	0.919690i	−0.999346	+	0.0361539i	$0.988489\pi$
$692$	6.51873			0.247805
$693$		0			0
$694$	−6.62348			−0.251424
$695$	−2.43521	+	4.21791i	−0.0923729	+	0.159995i
$696$	5.29150	−	4.47214i	0.200574	−	0.169516i
$697$	−2.06479	−	3.57632i	−0.0782094	−	0.135463i
$698$	−5.71383	−	9.89665i	−0.216272	−	0.374594i
$699$	−27.7046	−	9.97266i	−1.04789	−	0.377201i
$700$		0			0
$701$	−0.753049			−0.0284423			−0.0142211	−	0.999899i	$-0.504527\pi$
$701$	−0.753049			−0.0284423			−0.0142211	+	0.999899i	$0.504527\pi$
$702$	−17.2470	−	29.1527i	−0.650944	−	1.10030i
$703$	−15.8745			−0.598718
$704$	2.31174	−	4.00405i	0.0871269	−	0.150908i
$705$	−10.5830	−	3.80950i	−0.398579	−	0.143474i
$706$	1.01607	+	1.75988i	0.0382402	+	0.0662340i
$707$		0			0
$708$	−16.1822	+	13.6764i	−0.608163	+	0.513992i
$709$	11.2470	−	19.4803i	0.422388	−	0.731598i	−0.573784	−	0.819006i	$-0.694525\pi$
$709$	11.2470	−	19.4803i	0.422388	−	0.731598i	0.996173	+	0.0874087i	$0.0278586\pi$
$710$	−0.231042			−0.00867083
$711$	−38.3056	+	14.2503i	−1.43657	+	0.534426i
$712$	−14.2647			−0.534592
$713$	11.8102	−	20.4559i	0.442297	−	0.766081i
$714$		0			0
$715$	9.24695	+	16.0162i	0.345816	+	0.598971i
$716$		0			0
$717$	0.729137	+	4.05117i	0.0272301	+	0.151294i
$718$	−10.0587	+	17.4222i	−0.375387	+	0.650189i
$719$	4.06427			0.151572			0.0757859	−	0.997124i	$-0.475853\pi$
$719$	4.06427			0.151572			0.0757859	+	0.997124i	$0.475853\pi$
$720$	−1.41852	−	1.17325i	−0.0528651	−	0.0437246i
$721$		0			0
$722$	−6.00000	+	10.3923i	−0.223297	+	0.386762i
$723$	10.8056	−	9.13243i	0.401866	−	0.339639i
$724$	3.56618	+	6.17680i	0.132536	+	0.229559i
$725$	−9.24695	−	16.0162i	−0.343423	−	0.594826i
$726$	16.9105	+	6.08715i	0.627606	+	0.225915i
$727$	1.03594	−	1.79431i	0.0384211	−	0.0665472i	−0.846175	−	0.532904i	$-0.821101\pi$
$727$	1.03594	−	1.79431i	0.0384211	−	0.0665472i	0.884596	+	0.466357i	$0.154434\pi$
$728$		0			0
$729$	−13.0000	+	23.6643i	−0.481481	+	0.876456i
$730$	−4.49390			−0.166327
$731$	2.66563	−	4.61700i	0.0985918	−	0.170766i
$732$	11.6235	+	4.18403i	0.429616	+	0.154646i
$733$	13.3443	+	23.1130i	0.492882	+	0.853697i	0.999966	−	0.00819960i	$-0.00261004\pi$
$733$	13.3443	+	23.1130i	0.492882	+	0.853697i	−0.507084	+	0.861896i	$0.669277\pi$
$734$	15.0696	+	26.1013i	0.556229	+	0.963417i
$735$		0			0
$736$	−1.81174	+	3.13802i	−0.0667815	+	0.115669i
$737$	−21.3765			−0.787414
$738$	−4.69776	−	3.88551i	−0.172927	−	0.143028i
$739$	−9.87043			−0.363089			−0.181545	−	0.983383i	$-0.558110\pi$
$739$	−9.87043			−0.363089			−0.181545	+	0.983383i	$0.558110\pi$
$740$	1.84085	−	3.18844i	0.0676709	−	0.117209i
$741$	5.29150	+	29.4002i	0.194388	+	1.08004i
$742$		0			0
$743$	−5.37652	−	9.31241i	−0.197246	−	0.341639i	0.750389	−	0.660997i	$-0.229866\pi$
$743$	−5.37652	−	9.31241i	−0.197246	−	0.341639i	−0.947634	+	0.319357i	$0.896533\pi$
$744$	−2.00000	−	11.1122i	−0.0733236	−	0.407394i
$745$	4.67789	−	8.10234i	0.171385	−	0.296847i
$746$	9.24695			0.338555
$747$	21.7796	−	8.10234i	0.796875	−	0.296449i
$748$	−9.39553			−0.343535
$749$		0			0
$750$	−7.81174	+	6.60212i	−0.285244	+	0.241075i
$751$	10.8117	+	18.7265i	0.394526	+	0.683339i	0.993041	−	0.117773i	$-0.0375755\pi$
$751$	10.8117	+	18.7265i	0.394526	+	0.683339i	−0.598515	+	0.801112i	$0.704242\pi$
$752$	5.29150	+	9.16515i	0.192961	+	0.334219i
$753$	16.9352	+	6.09606i	0.617153	+	0.222153i
$754$	13.0375	−	22.5816i	0.474797	−	0.822372i
$755$	−0.996190			−0.0362551
$756$		0			0
$757$	−17.7409			−0.644802			−0.322401	−	0.946603i	$-0.604490\pi$
$757$	−17.7409			−0.644802			−0.322401	+	0.946603i	$0.604490\pi$
$758$	2.68826	−	4.65621i	0.0976421	−	0.169121i
$759$	−27.3022	−	9.82779i	−0.991006	−	0.356726i
$760$	0.811738	+	1.40597i	0.0294448	+	0.0509999i
$761$	−18.3290	−	31.7467i	−0.664425	−	1.15082i	−0.979441	−	0.201731i	$-0.935343\pi$
$761$	−18.3290	−	31.7467i	−0.664425	−	1.15082i	0.315016	−	0.949086i	$-0.397990\pi$
$762$	−15.3764	+	12.9954i	−0.557029	+	0.470775i
$763$		0			0
$764$	15.6235			0.565238
$765$	−0.623475	+	3.68853i	−0.0225418	+	0.133359i
$766$	19.9388			0.720417
$767$	−39.8704	+	69.0576i	−1.43964	+	2.49353i
$768$	0.306808	+	1.70466i	0.0110710	+	0.0615117i
$769$	18.9426	+	32.8095i	0.683087	+	1.18314i	0.974034	+	0.226402i	$0.0726964\pi$
$769$	18.9426	+	32.8095i	0.683087	+	1.18314i	−0.290947	+	0.956739i	$0.593970\pi$
$770$		0			0
$771$	8.62348	+	47.9130i	0.310567	+	1.72555i
$772$	13.7470	−	23.8104i	0.494764	−	0.856956i
$773$	−21.3971			−0.769598			−0.384799	−	0.923000i	$-0.625729\pi$
$773$	−21.3971			−0.769598			−0.384799	+	0.923000i	$0.625729\pi$
$774$	1.31174	−	7.76034i	0.0471494	−	0.278940i
$775$	−30.1392			−1.08263
$776$	8.14842	−	14.1135i	0.292511	−	0.506644i
$777$		0			0
$778$	8.37652	+	14.5086i	0.300313	+	0.520157i
$779$	2.68826	+	4.65621i	0.0963170	+	0.166826i
$780$	−6.51873	−	2.34651i	−0.233408	−	0.0840185i
$781$	−0.870426	+	1.50762i	−0.0311463	+	0.0539470i
$782$	7.36339			0.263314
$783$	−20.7834	+	0.220879i	−0.742739	+	0.00789359i
$784$		0			0
$785$	0.941312	−	1.63040i	0.0335968	−	0.0581915i
$786$	−22.2470	−	8.00809i	−0.793522	−	0.285639i
$787$	−13.2288	−	22.9129i	−0.471554	−	0.816756i	0.527916	−	0.849296i	$-0.322974\pi$
$787$	−13.2288	−	22.9129i	−0.471554	−	0.816756i	−0.999470	+	0.0325406i	$0.989640\pi$
$788$	6.62348	+	11.4722i	0.235952	+	0.408680i
$789$	−18.0222	+	15.2315i	−0.641606	+	0.542256i
$790$	−4.17979	+	7.23961i	−0.148710	+	0.257574i
$791$		0			0
$792$	−13.0000	+	4.83619i	−0.461935	+	0.171846i
$793$	46.4939			1.65105
$794$	8.55087	−	14.8105i	0.303459	−	0.525606i
$795$	0.753049	+	4.18403i	0.0267079	+	0.148392i
$796$	10.3917	+	17.9990i	0.368325	+	0.637957i
$797$	4.79341	+	8.30243i	0.169791	+	0.294087i	0.938346	−	0.345697i	$-0.112357\pi$
$797$	4.79341	+	8.30243i	0.169791	+	0.294087i	−0.768555	+	0.639784i	$0.779024\pi$
$798$		0			0
$799$	10.7530	−	18.6248i	0.380416	−	0.658899i
$800$	4.62348			0.163465
$801$	32.9762	+	27.2746i	1.16516	+	0.963700i
$802$	15.0000			0.529668
$803$	−16.9303	+	29.3242i	−0.597458	+	1.03483i
$804$	6.11628	−	5.16920i	0.215705	−	0.182304i
$805$		0			0
$806$	−21.2470	−	36.8008i	−0.748392	−	1.29625i
$807$	−17.6235	−	6.34381i	−0.620376	−	0.223313i
$808$	−8.24406	+	14.2791i	−0.290025	+	0.502338i
$809$	−27.1174			−0.953396			−0.476698	−	0.879067i	$-0.658167\pi$
$809$	−27.1174			−0.953396			−0.476698	+	0.879067i	$0.658167\pi$
$810$	1.03594	+	5.42451i	0.0363994	+	0.190598i
$811$	26.8798			0.943879			0.471939	−	0.881631i	$-0.343554\pi$
$811$	26.8798			0.943879			0.471939	+	0.881631i	$0.343554\pi$
$812$		0			0
$813$	29.8704	+	10.7523i	1.04760	+	0.377099i
$814$	−13.8704	−	24.0243i	−0.486158	−	0.842051i
$815$	5.90512	+	10.2280i	0.206847	+	0.358270i
$816$	2.68826	−	2.27200i	0.0941080	−	0.0795358i
$817$	−3.47053	+	6.01114i	−0.121419	+	0.210303i
$818$	21.5883			0.754819
$819$		0			0
$820$	−1.24695			−0.0435454
$821$	−11.8704	+	20.5602i	−0.414281	+	0.717555i	−0.995353	−	0.0962969i	$-0.969300\pi$
$821$	−11.8704	+	20.5602i	−0.414281	+	0.717555i	0.581072	+	0.813852i	$0.302633\pi$
$822$	−3.02833	−	16.8257i	−0.105625	−	0.586865i
$823$	17.8704	+	30.9525i	0.622924	+	1.07894i	0.988938	+	0.148327i	$0.0473887\pi$
$823$	17.8704	+	30.9525i	0.622924	+	1.07894i	−0.366015	+	0.930609i	$0.619278\pi$
$824$	8.55087	+	14.8105i	0.297884	+	0.515950i
$825$	6.55849	+	36.4397i	0.228337	+	1.26867i
$826$		0			0
$827$	4.75305			0.165280			0.0826399	−	0.996579i	$-0.473665\pi$
$827$	4.75305			0.165280			0.0826399	+	0.996579i	$0.473665\pi$
$828$	10.1883	−	3.79018i	0.354067	−	0.131718i
$829$	26.0749			0.905620			0.452810	−	0.891607i	$-0.350422\pi$
$829$	26.0749			0.905620			0.452810	+	0.891607i	$0.350422\pi$
$830$	2.37652	−	4.11626i	0.0824904	−	0.142878i
$831$	16.5279	−	13.9686i	0.573346	−	0.484566i
$832$	3.25937	+	5.64539i	0.112998	+	0.195719i
$833$		0			0
$834$	−12.9352	−	4.65621i	−0.447910	−	0.161231i
$835$	−0.376525	+	0.652160i	−0.0130302	+	0.0225689i
$836$	12.2326			0.423072
$837$	−16.6235	+	29.5126i	−0.574591	+	1.02011i
$838$	12.4239			0.429175
$839$	−21.7796	+	37.7234i	−0.751916	+	1.30236i	0.194977	+	0.980808i	$0.437537\pi$
$839$	−21.7796	+	37.7234i	−0.751916	+	1.30236i	−0.946893	+	0.321549i	$0.895796\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$		0			0
$843$	6.44297	−	5.44530i	0.221908	−	0.187546i
$844$	−7.62348	+	13.2042i	−0.262411	+	0.454509i
$845$	−18.0979			−0.622588
$846$	5.29150	−	31.3050i	0.181926	−	1.07629i
$847$		0			0
$848$	2.00000	−	3.46410i	0.0686803	−	0.118958i
$849$	−3.43521	−	19.0864i	−0.117896	−	0.655045i
$850$	−4.69776	−	8.13677i	−0.161132	−	0.279089i
$851$	10.8704	+	18.8281i	0.372633	+	0.645420i
$852$	−0.115521	−	0.641847i	−0.00395768	−	0.0219893i
$853$	6.40321	−	11.0907i	0.219242	−	0.379738i	−0.735335	−	0.677704i	$-0.762975\pi$
$853$	6.40321	−	11.0907i	0.219242	−	0.379738i	0.954576	+	0.297966i	$0.0963083\pi$
$854$		0			0
$855$	0.811738	−	4.80230i	0.0277608	−	0.164235i
$856$	−10.6235			−0.363103
$857$	−17.7154	+	30.6839i	−0.605145	+	1.04814i	0.386884	+	0.922129i	$0.373552\pi$
$857$	−17.7154	+	30.6839i	−0.605145	+	1.04814i	−0.992029	+	0.126013i	$0.959782\pi$
$858$	−39.8704	+	33.6967i	−1.36115	+	1.15039i
$859$	6.92119	+	11.9878i	0.236148	+	0.409020i	0.959606	−	0.281349i	$-0.0907817\pi$
$859$	6.92119	+	11.9878i	0.236148	+	0.409020i	−0.723458	+	0.690369i	$0.757448\pi$
$860$	−0.804903	−	1.39413i	−0.0274470	−	0.0475396i
$861$		0			0
$862$	−4.00000	+	6.92820i	−0.136241	+	0.235976i
$863$	7.12957			0.242694			0.121347	−	0.992610i	$-0.461279\pi$
$863$	7.12957			0.242694			0.121347	+	0.992610i	$0.461279\pi$
$864$	2.55011	−	4.52736i	0.0867564	−	0.154024i
$865$	−4.00000			−0.136004
$866$	−2.24330	+	3.88551i	−0.0762304	+	0.132035i
$867$	20.9747	+	7.55014i	0.712339	+	0.256416i
$868$		0			0
$869$	31.4939	+	54.5490i	1.06836	+	1.85045i
$870$	−3.24695	+	2.74417i	−0.110082	+	0.0930362i
$871$	15.0696	−	26.1013i	0.510614	−	0.884410i
$872$	9.24695			0.313141
$873$	−45.8224	+	17.0466i	−1.55085	+	0.576940i
$874$	−9.58681			−0.324279
$875$		0			0
$876$	−2.24695	−	12.4843i	−0.0759174	−	0.421806i
$877$	−6.00000	−	10.3923i	−0.202606	−	0.350923i	0.746762	−	0.665092i	$-0.231608\pi$
$877$	−6.00000	−	10.3923i	−0.202606	−	0.350923i	−0.949367	+	0.314169i	$0.898274\pi$
$878$	15.4919	+	26.8328i	0.522827	+	0.905564i
$879$	−4.30564	−	23.9226i	−0.145226	−	0.806890i
$880$	−1.41852	+	2.45695i	−0.0478183	+	0.0828237i
$881$	−26.0749			−0.878487			−0.439244	−	0.898368i	$-0.644753\pi$
$881$	−26.0749			−0.878487			−0.439244	+	0.898368i	$0.644753\pi$
$882$		0			0
$883$	−33.8704			−1.13983			−0.569915	−	0.821703i	$-0.693024\pi$
$883$	−33.8704			−1.13983			−0.569915	+	0.821703i	$0.693024\pi$
$884$	6.62348	−	11.4722i	0.222772	−	0.385852i
$885$	9.92963	−	8.39207i	0.333781	−	0.282096i
$886$	15.3117	+	26.5207i	0.514408	+	0.890981i
$887$	5.71383	+	9.89665i	0.191852	+	0.332297i	0.945864	−	0.324564i	$-0.105217\pi$
$887$	5.71383	+	9.89665i	0.191852	+	0.332297i	−0.754012	+	0.656860i	$0.771884\pi$
$888$	9.77810	+	3.51976i	0.328132	+	0.118115i
$889$		0			0
$890$	8.75305			0.293403
$891$	39.2995	+	13.6764i	1.31658	+	0.458177i
$892$	−1.22723			−0.0410908
$893$	−14.0000	+	24.2487i	−0.468492	+	0.811452i
$894$	24.8477	+	8.94427i	0.831032	+	0.299141i
$895$		0			0
$896$		0			0
$897$	31.2470	−	26.4085i	1.04331	−	0.881754i
$898$	−7.50000	+	12.9904i	−0.250278	+	0.433495i
$899$	−26.0749			−0.869648
$900$	−10.6883	−	8.84024i	−0.356275	−	0.294675i
$901$	−8.12854			−0.270801
$902$	−4.69776	+	8.13677i	−0.156418	+	0.270925i
$903$		0			0
$904$	−8.81174	−	15.2624i	−0.293074	−	0.507619i
$905$	−2.18826	−	3.79018i	−0.0727403	−	0.125990i
$906$	−0.498095	−	2.76748i	−0.0165481	−	0.0919432i
$907$	−14.3117	+	24.7887i	−0.475213	+	0.823094i	−0.999597	−	0.0283884i	$-0.990962\pi$
$907$	−14.3117	+	24.7887i	−0.475213	+	0.823094i	0.524384	+	0.851482i	$0.324296\pi$
$908$	2.26318			0.0751062
$909$	46.3603	−	17.2467i	1.53767	−	0.572037i
$910$		0			0
$911$	−25.4352	+	44.0551i	−0.842706	+	1.45961i	0.0448922	+	0.998992i	$0.485706\pi$
$911$	−25.4352	+	44.0551i	−0.842706	+	1.45961i	−0.887598	+	0.460618i	$0.847628\pi$
$912$	−3.50000	+	2.95804i	−0.115897	+	0.0979505i
$913$	−17.9066	−	31.0152i	−0.592623	−	1.02645i
$914$	5.50000	+	9.52628i	0.181924	+	0.315101i
$915$	−7.13235	−	2.56739i	−0.235788	−	0.0848752i
$916$	−3.75746	+	6.50812i	−0.124150	+	0.215034i
$917$		0			0
$918$	−10.5587	+	0.112214i	−0.348489	+	0.00370362i
$919$	−49.3643			−1.62838			−0.814189	−	0.580599i	$-0.802818\pi$
$919$	−49.3643			−1.62838			−0.814189	+	0.580599i	$0.802818\pi$
$920$	1.11171	−	1.92554i	0.0366520	−	0.0634832i
$921$	21.5587	+	7.76034i	0.710383	+	0.255712i
$922$	0.920424	+	1.59422i	0.0303126	+	0.0525029i
$923$	−1.22723	−	2.12563i	−0.0403948	−	0.0699659i
$924$		0			0
$925$	13.8704	−	24.0243i	0.456057	−	0.789914i
$926$	−35.6235			−1.17066
$927$	8.55087	−	50.5876i	0.280847	−	1.66152i
$928$	4.00000			0.131306
$929$	17.7154	−	30.6839i	0.581222	−	1.00671i	−0.414113	−	0.910226i	$-0.635908\pi$
$929$	17.7154	−	30.6839i	0.581222	−	1.00671i	0.995335	−	0.0964805i	$-0.0307585\pi$
$930$	1.22723	+	6.81864i	0.0402425	+	0.223592i
$931$		0			0
$932$	−8.50000	−	14.7224i	−0.278427	−	0.482249i
$933$	3.12957	+	17.3883i	0.102458	+	0.569267i
$934$	−3.66182	+	6.34246i	−0.119818	+	0.207532i
$935$	5.76525			0.188544
$936$	3.25937	−	19.2827i	0.106536	−	0.630274i
$937$	−23.6205			−0.771647			−0.385824	−	0.922573i	$-0.626083\pi$
$937$	−23.6205			−0.771647			−0.385824	+	0.922573i	$0.626083\pi$
$938$		0			0
$939$	−23.6883	+	20.0202i	−0.773037	+	0.653336i
$940$	−3.24695	−	5.62388i	−0.105904	−	0.183431i
$941$	−26.5730	−	46.0258i	−0.866256	−	1.50040i	−0.865794	−	0.500400i	$-0.833186\pi$
$941$	−26.5730	−	46.0258i	−0.866256	−	1.50040i	−0.000461671	−	1.00000i	$-0.500147\pi$
$942$	5.00000	+	1.79982i	0.162909	+	0.0586413i
$943$	3.68170	−	6.37688i	0.119893	−	0.207660i
$944$	−12.2326			−0.398136
$945$		0			0
$946$	−12.1296			−0.394366
$947$	10.1822	−	17.6360i	0.330876	−	0.573094i	−0.651808	−	0.758384i	$-0.725989\pi$
$947$	10.1822	−	17.6360i	0.330876	−	0.573094i	0.982684	+	0.185290i	$0.0593225\pi$
$948$	−22.2020	−	7.99190i	−0.721086	−	0.259565i
$949$	−23.8704	−	41.3448i	−0.774867	−	1.34211i
$950$	6.11628	+	10.5937i	0.198438	+	0.343705i
$951$	−17.5241	+	14.8105i	−0.568257	+	0.480265i
$952$		0			0
$953$	0.623475			0.0201963			0.0100982	−	0.999949i	$-0.496786\pi$
$953$	0.623475			0.0201963			0.0100982	+	0.999949i	$0.496786\pi$
$954$	−11.2470	+	4.18403i	−0.364133	+	0.135463i
$955$	−9.58681			−0.310222
$956$	−1.18826	+	2.05813i	−0.0384311	+	0.0665647i
$957$	5.67408	+	31.5258i	0.183417	+	1.01909i
$958$	7.74597	+	13.4164i	0.250261	+	0.433464i
$959$		0			0
$960$	−0.188262	−	1.04601i	−0.00607614	−	0.0337597i
$961$	−5.74695	+	9.95401i	−0.185386	+	0.321097i
$962$	39.1124			1.26103
$963$	24.5587	+	20.3124i	0.791393	+	0.654559i
$964$	8.16830			0.263083
$965$	−8.43535	+	14.6105i	−0.271543	+	0.470327i
$966$		0			0
$967$	22.0587	+	38.2068i	0.709360	+	1.22865i	0.965095	+	0.261900i	$0.0843491\pi$
$967$	22.0587	+	38.2068i	0.709360	+	1.22865i	−0.255735	+	0.966747i	$0.582318\pi$
$968$	5.18826	+	8.98633i	0.166757	+	0.288832i
$969$	8.76203	+	3.15401i	0.281477	+	0.101322i
$970$	−5.00000	+	8.66025i	−0.160540	+	0.278064i
$971$	54.7559			1.75720			0.878600	−	0.477559i	$-0.158478\pi$
$971$	54.7559			1.75720			0.878600	+	0.477559i	$0.158478\pi$
$972$	−14.5516	+	5.59017i	−0.466744	+	0.179305i
$973$		0			0
$974$	−2.81174	+	4.87007i	−0.0900939	+	0.156047i
$975$	−49.1174	−	17.6805i	−1.57301	−	0.566228i
$976$	3.56618	+	6.17680i	0.114150	+	0.197714i
$977$	−15.6883	−	27.1729i	−0.501912	−	0.869337i	−0.999998	−	0.00220917i	$-0.999297\pi$
$977$	−15.6883	−	27.1729i	−0.501912	−	0.869337i	0.498086	−	0.867128i	$-0.334037\pi$
$978$	−25.4613	+	21.5187i	−0.814163	+	0.688094i
$979$	32.9762	−	57.1165i	1.05393	−	1.82545i
$980$		0			0
$981$	−21.3765	−	17.6805i	−0.682500	−	0.564494i
$982$	−15.1174			−0.482415
$983$	−14.2647	+	24.7072i	−0.454973	+	0.788037i	−0.998687	−	0.0512341i	$-0.983685\pi$
$983$	−14.2647	+	24.7072i	−0.454973	+	0.788037i	0.543713	+	0.839271i	$0.317018\pi$
$984$	−0.623475	−	3.46410i	−0.0198757	−	0.110432i
$985$	−4.06427	−	7.03952i	−0.129498	−	0.224298i
$986$	−4.06427	−	7.03952i	−0.129433	−	0.224184i
$987$		0			0
$988$	−8.62348	+	14.9363i	−0.274349	+	0.475187i
$989$	9.50610			0.302276
$990$	7.97701	−	2.96756i	0.253526	−	0.0943153i
$991$	−44.9878			−1.42908			−0.714542	−	0.699592i	$-0.753365\pi$
$991$	−44.9878			−1.42908			−0.714542	+	0.699592i	$0.753365\pi$
$992$	3.25937	−	5.64539i	0.103485	−	0.179241i
$993$	10.5830	−	8.94427i	0.335842	−	0.283838i
$994$		0			0
$995$	−6.37652	−	11.0445i	−0.202149	−	0.350133i
$996$	12.6235	+	4.54399i	0.399990	+	0.143982i
$997$	2.53023	−	4.38249i	0.0801332	−	0.138795i	−0.823174	−	0.567789i	$-0.807799\pi$
$997$	2.53023	−	4.38249i	0.0801332	−	0.138795i	0.903307	+	0.428995i	$0.141132\pi$
$998$	−18.6235			−0.589516
$999$	−15.8745	−	26.8328i	−0.502247	−	0.848953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.f.r.295.1	✓	8
3.2	odd	2		2646.2.f.p.883.2		8
7.2	even	3		882.2.e.r.655.3		8
7.3	odd	6		882.2.h.s.79.2		8
7.4	even	3		882.2.h.s.79.3		8
7.5	odd	6		882.2.e.r.655.2		8
7.6	odd	2	inner	882.2.f.r.295.4	yes	8
9.2	odd	6		7938.2.a.cq.1.3		4
9.4	even	3	inner	882.2.f.r.589.1	yes	8
9.5	odd	6		2646.2.f.p.1765.2		8
9.7	even	3		7938.2.a.ch.1.2		4
21.2	odd	6		2646.2.e.s.2125.2		8
21.5	even	6		2646.2.e.s.2125.3		8
21.11	odd	6		2646.2.h.r.667.3		8
21.17	even	6		2646.2.h.r.667.2		8
21.20	even	2		2646.2.f.p.883.3		8
63.4	even	3		882.2.e.r.373.4		8
63.5	even	6		2646.2.h.r.361.2		8
63.13	odd	6	inner	882.2.f.r.589.4	yes	8
63.20	even	6		7938.2.a.cq.1.2		4
63.23	odd	6		2646.2.h.r.361.3		8
63.31	odd	6		882.2.e.r.373.1		8
63.32	odd	6		2646.2.e.s.1549.2		8
63.34	odd	6		7938.2.a.ch.1.3		4
63.40	odd	6		882.2.h.s.67.2		8
63.41	even	6		2646.2.f.p.1765.3		8
63.58	even	3		882.2.h.s.67.3		8
63.59	even	6		2646.2.e.s.1549.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.r.373.1		8	63.31	odd	6
882.2.e.r.373.4		8	63.4	even	3
882.2.e.r.655.2		8	7.5	odd	6
882.2.e.r.655.3		8	7.2	even	3
882.2.f.r.295.1	✓	8	1.1	even	1	trivial
882.2.f.r.295.4	yes	8	7.6	odd	2	inner
882.2.f.r.589.1	yes	8	9.4	even	3	inner
882.2.f.r.589.4	yes	8	63.13	odd	6	inner
882.2.h.s.67.2		8	63.40	odd	6
882.2.h.s.67.3		8	63.58	even	3
882.2.h.s.79.2		8	7.3	odd	6
882.2.h.s.79.3		8	7.4	even	3
2646.2.e.s.1549.2		8	63.32	odd	6
2646.2.e.s.1549.3		8	63.59	even	6
2646.2.e.s.2125.2		8	21.2	odd	6
2646.2.e.s.2125.3		8	21.5	even	6
2646.2.f.p.883.2		8	3.2	odd	2
2646.2.f.p.883.3		8	21.20	even	2
2646.2.f.p.1765.2		8	9.5	odd	6
2646.2.f.p.1765.3		8	63.41	even	6
2646.2.h.r.361.2		8	63.5	even	6
2646.2.h.r.361.3		8	63.23	odd	6
2646.2.h.r.667.2		8	21.17	even	6
2646.2.h.r.667.3		8	21.11	odd	6
7938.2.a.ch.1.2		4	9.7	even	3
7938.2.a.ch.1.3		4	63.34	odd	6
7938.2.a.cq.1.2		4	63.20	even	6
7938.2.a.cq.1.3		4	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.62968 - 0.586627i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.306808 + 0.531407i) q^{5} +(-1.32288 + 1.11803i) q^{6} -1.00000 q^{8} +(2.31174 + 1.91203i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.62968 - 0.586627i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.306808 + 0.531407i) q^{5} +(-1.32288 + 1.11803i) q^{6} -1.00000 q^{8} +(2.31174 + 1.91203i) q^{9} +0.613616 q^{10} +(2.31174 - 4.00405i) q^{11} +(0.306808 + 1.70466i) q^{12} +(3.25937 + 5.64539i) q^{13} +(-0.188262 - 1.04601i) q^{15} +(-0.500000 + 0.866025i) q^{16} +2.03214 q^{17} +(2.81174 - 1.04601i) q^{18} -2.64575 q^{19} +(0.306808 - 0.531407i) q^{20} +(-2.31174 - 4.00405i) q^{22} +(1.81174 + 3.13802i) q^{23} +(1.62968 + 0.586627i) q^{24} +(2.31174 - 4.00405i) q^{25} +6.51873 q^{26} +(-2.64575 - 4.47214i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-1.00000 - 0.359964i) q^{30} +(-3.25937 - 5.64539i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-6.11628 + 5.16920i) q^{33} +(1.01607 - 1.75988i) q^{34} +(0.500000 - 2.95804i) q^{36} +6.00000 q^{37} +(-1.32288 + 2.29129i) q^{38} +(-2.00000 - 11.1122i) q^{39} +(-0.306808 - 0.531407i) q^{40} +(-1.01607 - 1.75988i) q^{41} +(1.31174 - 2.27200i) q^{43} -4.62348 q^{44} +(-0.306808 + 1.81510i) q^{45} +3.62348 q^{46} +(5.29150 - 9.16515i) q^{47} +(1.32288 - 1.11803i) q^{48} +(-2.31174 - 4.00405i) q^{50} +(-3.31174 - 1.19211i) q^{51} +(3.25937 - 5.64539i) q^{52} -4.00000 q^{53} +(-5.19586 + 0.0552199i) q^{54} +2.83704 q^{55} +(4.31174 + 1.55207i) q^{57} +(-2.00000 - 3.46410i) q^{58} +(6.11628 + 10.5937i) q^{59} +(-0.811738 + 0.686044i) q^{60} +(3.56618 - 6.17680i) q^{61} -6.51873 q^{62} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} +(1.41852 + 7.88146i) q^{66} +(-2.31174 - 4.00405i) q^{67} +(-1.01607 - 1.75988i) q^{68} +(-1.11171 - 6.17680i) q^{69} -0.376525 q^{71} +(-2.31174 - 1.91203i) q^{72} -7.32364 q^{73} +(3.00000 - 5.19615i) q^{74} +(-6.11628 + 5.16920i) q^{75} +(1.32288 + 2.29129i) q^{76} +(-10.6235 - 3.82407i) q^{78} +(-6.81174 + 11.7983i) q^{79} -0.613616 q^{80} +(1.68826 + 8.84024i) q^{81} -2.03214 q^{82} +(3.87298 - 6.70820i) q^{83} +(0.623475 + 1.07989i) q^{85} +(-1.31174 - 2.27200i) q^{86} +(-5.29150 + 4.47214i) q^{87} +(-2.31174 + 4.00405i) q^{88} +14.2647 q^{89} +(1.41852 + 1.17325i) q^{90} +(1.81174 - 3.13802i) q^{92} +(2.00000 + 11.1122i) q^{93} +(-5.29150 - 9.16515i) q^{94} +(-0.811738 - 1.40597i) q^{95} +(-0.306808 - 1.70466i) q^{96} +(-8.14842 + 14.1135i) q^{97} +(13.0000 - 4.83619i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 2 * q^9	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 2 q^{9} - 2 q^{11} - 22 q^{15} - 4 q^{16} + 2 q^{18} + 2 q^{22} - 6 q^{23} - 2 q^{25} + 16 q^{29} - 8 q^{30} + 4 q^{32} + 4 q^{36} + 48 q^{37} - 16 q^{39} - 10 q^{43} + 4 q^{44} - 12 q^{46} + 2 q^{50} - 6 q^{51} - 32 q^{53} + 14 q^{57} - 16 q^{58} + 14 q^{60} + 8 q^{64} - 16 q^{65} + 2 q^{67} - 44 q^{71} + 2 q^{72} + 24 q^{74} - 44 q^{78} - 34 q^{79} + 34 q^{81} - 36 q^{85} + 10 q^{86} + 2 q^{88} - 6 q^{92} + 16 q^{93} + 14 q^{95} + 104 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 - 2 * q^9 - 2 * q^11 - 22 * q^15 - 4 * q^16 + 2 * q^18 + 2 * q^22 - 6 * q^23 - 2 * q^25 + 16 * q^29 - 8 * q^30 + 4 * q^32 + 4 * q^36 + 48 * q^37 - 16 * q^39 - 10 * q^43 + 4 * q^44 - 12 * q^46 + 2 * q^50 - 6 * q^51 - 32 * q^53 + 14 * q^57 - 16 * q^58 + 14 * q^60 + 8 * q^64 - 16 * q^65 + 2 * q^67 - 44 * q^71 + 2 * q^72 + 24 * q^74 - 44 * q^78 - 34 * q^79 + 34 * q^81 - 36 * q^85 + 10 * q^86 + 2 * q^88 - 6 * q^92 + 16 * q^93 + 14 * q^95 + 104 * q^99

Introduction

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