LMFDB - Embedded newform 1470.2.n.l.79.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(79,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("1470.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.n (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 $ x^16 - 18x^14 + 227x^12 - 1394x^10 + 6177x^8 - 14768x^6 + 24768x^4 - 11264*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			79.8
Root			$2.73710 + 1.58027i$ of defining polynomial
Character	$\chi$	$=$	1470.79
Dual form			1470.2.n.l.949.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.13945 - 0.650187i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.13945 - 0.650187i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.17791 + 0.506647i) q^{10} +(-2.23483 - 3.87084i) q^{11} +(-0.866025 - 0.500000i) q^{12} +5.88388i q^{13} +(-1.52773 + 1.63280i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.69895 - 3.86764i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.30913 + 5.73159i) q^{19} +(1.63280 + 1.52773i) q^{20} -4.46967i q^{22} +(2.26749 + 1.30913i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.15451 - 2.78209i) q^{25} +(-2.94194 + 5.09559i) q^{26} +1.00000i q^{27} +8.17246 q^{29} +(-2.13945 + 0.650187i) q^{30} +(4.23483 + 7.33495i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.87084 + 2.23483i) q^{33} +7.73528 q^{34} +1.00000 q^{36} +(-2.76019 - 1.59359i) q^{37} +(-5.73159 + 3.30913i) q^{38} +(-2.94194 - 5.09559i) q^{39} +(0.650187 + 2.13945i) q^{40} -3.56282 q^{41} -1.43108i q^{43} +(2.23483 - 3.87084i) q^{44} +(0.506647 - 2.17791i) q^{45} +(1.30913 + 2.26749i) q^{46} +(5.88094 + 3.39536i) q^{47} -1.00000i q^{48} +(4.98896 - 0.332104i) q^{50} +(-3.86764 + 6.69895i) q^{51} +(-5.09559 + 2.94194i) q^{52} +(1.19661 - 0.690865i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-7.29809 - 6.82843i) q^{55} -6.61827i q^{57} +(7.07756 + 4.08623i) q^{58} +(-2.33210 - 4.03932i) q^{59} +(-2.17791 - 0.506647i) q^{60} +(4.89841 - 8.48430i) q^{61} +8.46967i q^{62} -1.00000 q^{64} +(3.82562 + 12.5883i) q^{65} +(2.23483 + 3.87084i) q^{66} +(1.60336 - 0.925698i) q^{67} +(6.69895 + 3.86764i) q^{68} -2.61827 q^{69} +2.02386 q^{71} +(0.866025 + 0.500000i) q^{72} +(3.47871 - 2.00843i) q^{73} +(-1.59359 - 2.76019i) q^{74} +(-2.20687 + 4.48662i) q^{75} -6.61827 q^{76} -5.88388i q^{78} +(-3.49264 + 6.04942i) q^{79} +(-0.506647 + 2.17791i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.08549 - 1.78141i) q^{82} +5.35965i q^{83} +(11.8174 - 12.6302i) q^{85} +(0.715541 - 1.23935i) q^{86} +(-7.07756 + 4.08623i) q^{87} +(3.87084 - 2.23483i) q^{88} +(-7.19562 + 12.4632i) q^{89} +(1.52773 - 1.63280i) q^{90} +2.61827i q^{92} +(-7.33495 - 4.23483i) q^{93} +(3.39536 + 5.88094i) q^{94} +(-3.35313 + 14.4140i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.71966i q^{97} -4.46967 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9	$ 16 q + 8 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{20} - 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} + 32 q^{31} + 16 q^{34} + 16 q^{36} - 48 q^{41} - 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} - 8 q^{54} - 40 q^{59} + 24 q^{61} - 16 q^{64} - 28 q^{65} + 16 q^{69} - 80 q^{71} - 16 q^{74} + 4 q^{75} - 48 q^{76} - 16 q^{79} + 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} - 88 q^{89} - 24 q^{94} - 24 q^{95} + 8 q^{96}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9 - 8 * q^16 - 24 * q^19 + 8 * q^20 - 8 * q^24 - 4 * q^25 + 32 * q^29 - 4 * q^30 + 32 * q^31 + 16 * q^34 + 16 * q^36 - 48 * q^41 - 4 * q^45 - 8 * q^46 - 8 * q^50 - 8 * q^51 - 8 * q^54 - 40 * q^59 + 24 * q^61 - 16 * q^64 - 28 * q^65 + 16 * q^69 - 80 * q^71 - 16 * q^74 + 4 * q^75 - 48 * q^76 - 16 * q^79 + 4 * q^80 - 8 * q^81 + 56 * q^85 - 8 * q^86 - 88 * q^89 - 24 * q^94 - 24 * q^95 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.13945	−	0.650187i	0.956792	−	0.290773i
$5$	2.13945	−	0.650187i	0.956792	−	0.290773i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	2.17791	+	0.506647i	0.688717	+	0.160216i
$11$	−2.23483	−	3.87084i	−0.673828	−	1.16710i	−0.976810	−	0.214107i	$-0.931316\pi$
$11$	−2.23483	−	3.87084i	−0.673828	−	1.16710i	0.302983	−	0.952996i	$-0.402018\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$			5.88388i			1.63189i	0.578126	+	0.815947i	$0.303784\pi$
$13$			5.88388i			1.63189i	−0.578126	+	0.815947i	$0.696216\pi$
$14$		0			0
$15$	−1.52773	+	1.63280i	−0.394457	+	0.421588i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.69895	−	3.86764i	1.62473	−	0.938040i	0.639103	−	0.769121i	$-0.279306\pi$
$17$	6.69895	−	3.86764i	1.62473	−	0.938040i	0.985630	−	0.168919i	$-0.0540276\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−3.30913	+	5.73159i	−0.759168	+	1.31492i	0.184108	+	0.982906i	$0.441060\pi$
$19$	−3.30913	+	5.73159i	−0.759168	+	1.31492i	−0.943276	+	0.332011i	$0.892273\pi$
$20$	1.63280	+	1.52773i	0.365106	+	0.341610i
$21$		0			0
$22$		−	4.46967i		−	0.952936i
$23$	2.26749	+	1.30913i	0.472804	+	0.272974i	0.717413	−	0.696648i	$-0.245326\pi$
$23$	2.26749	+	1.30913i	0.472804	+	0.272974i	−0.244609	+	0.969622i	$0.578660\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.15451	−	2.78209i	0.830903	−	0.556418i
$26$	−2.94194	+	5.09559i	−0.576962	+	0.999327i
$27$			1.00000i			0.192450i
$28$		0			0
$29$	8.17246			1.51759			0.758794	−	0.651331i	$-0.225789\pi$
$29$	8.17246			1.51759			0.758794	+	0.651331i	$0.225789\pi$
$30$	−2.13945	+	0.650187i	−0.390609	+	0.118707i
$31$	4.23483	+	7.33495i	0.760598	+	1.31740i	0.942542	+	0.334086i	$0.108428\pi$
$31$	4.23483	+	7.33495i	0.760598	+	1.31740i	−0.181944	+	0.983309i	$0.558239\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.87084	+	2.23483i	0.673828	+	0.389035i
$34$	7.73528			1.32659
$35$		0			0
$36$	1.00000			0.166667
$37$	−2.76019	−	1.59359i	−0.453772	−	0.261985i	0.255650	−	0.966769i	$-0.417711\pi$
$37$	−2.76019	−	1.59359i	−0.453772	−	0.261985i	−0.709422	+	0.704784i	$0.751044\pi$
$38$	−5.73159	+	3.30913i	−0.929787	+	0.536813i
$39$	−2.94194	−	5.09559i	−0.471087	−	0.815947i
$40$	0.650187	+	2.13945i	0.102804	+	0.338277i
$41$	−3.56282			−0.556419			−0.278209	−	0.960520i	$-0.589741\pi$
$41$	−3.56282			−0.556419			−0.278209	+	0.960520i	$0.589741\pi$
$42$		0			0
$43$		−	1.43108i		−	0.218238i	−0.994029	−	0.109119i	$-0.965197\pi$
$43$		−	1.43108i		−	0.218238i	0.994029	−	0.109119i	$-0.0348029\pi$
$44$	2.23483	−	3.87084i	0.336914	−	0.583552i
$45$	0.506647	−	2.17791i	0.0755265	−	0.324664i
$46$	1.30913	+	2.26749i	0.193021	+	0.334323i
$47$	5.88094	+	3.39536i	0.857824	+	0.495265i	0.863283	−	0.504720i	$-0.168404\pi$
$47$	5.88094	+	3.39536i	0.857824	+	0.495265i	−0.00545912	+	0.999985i	$0.501738\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$	4.98896	−	0.332104i	0.705545	−	0.0469666i
$51$	−3.86764	+	6.69895i	−0.541578	+	0.938040i
$52$	−5.09559	+	2.94194i	−0.706631	+	0.407974i
$53$	1.19661	−	0.690865i	0.164367	−	0.0948976i	−0.415560	−	0.909566i	$-0.636414\pi$
$53$	1.19661	−	0.690865i	0.164367	−	0.0948976i	0.579927	+	0.814668i	$0.303081\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−7.29809	−	6.82843i	−0.984075	−	0.920745i
$56$		0			0
$57$		−	6.61827i		−	0.876611i
$58$	7.07756	+	4.08623i	0.929329	+	0.536548i
$59$	−2.33210	−	4.03932i	−0.303614	−	0.525875i	0.673338	−	0.739335i	$-0.264860\pi$
$59$	−2.33210	−	4.03932i	−0.303614	−	0.525875i	−0.976952	+	0.213460i	$0.931527\pi$
$60$	−2.17791	−	0.506647i	−0.281167	−	0.0654079i
$61$	4.89841	−	8.48430i	0.627178	−	1.08630i	−0.360938	−	0.932590i	$-0.617543\pi$
$61$	4.89841	−	8.48430i	0.627178	−	1.08630i	0.988115	−	0.153714i	$-0.0491234\pi$
$62$			8.46967i			1.07565i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	3.82562	+	12.5883i	0.474510	+	1.56138i
$66$	2.23483	+	3.87084i	0.275089	+	0.476468i
$67$	1.60336	−	0.925698i	0.195881	−	0.113092i	−0.398852	−	0.917015i	$-0.630591\pi$
$67$	1.60336	−	0.925698i	0.195881	−	0.113092i	0.594733	+	0.803923i	$0.297258\pi$
$68$	6.69895	+	3.86764i	0.812366	+	0.469020i
$69$	−2.61827			−0.315203
$70$		0			0
$71$	2.02386			0.240187			0.120094	−	0.992763i	$-0.461680\pi$
$71$	2.02386			0.240187			0.120094	+	0.992763i	$0.461680\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	3.47871	−	2.00843i	0.407152	−	0.235069i	−0.282413	−	0.959293i	$-0.591135\pi$
$73$	3.47871	−	2.00843i	0.407152	−	0.235069i	0.689565	+	0.724223i	$0.257802\pi$
$74$	−1.59359	−	2.76019i	−0.185252	−	0.320865i
$75$	−2.20687	+	4.48662i	−0.254827	+	0.518070i
$76$	−6.61827			−0.759168
$77$		0			0
$78$		−	5.88388i		−	0.666218i
$79$	−3.49264	+	6.04942i	−0.392952	+	0.680613i	−0.992837	−	0.119473i	$-0.961880\pi$
$79$	−3.49264	+	6.04942i	−0.392952	+	0.680613i	0.599885	+	0.800086i	$0.295213\pi$
$80$	−0.506647	+	2.17791i	−0.0566449	+	0.243498i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.08549	−	1.78141i	−0.340735	−	0.196724i
$83$			5.35965i			0.588298i	0.955760	+	0.294149i	$0.0950361\pi$
$83$			5.35965i			0.588298i	−0.955760	+	0.294149i	$0.904964\pi$
$84$		0			0
$85$	11.8174	−	12.6302i	1.28178	−	1.36994i
$86$	0.715541	−	1.23935i	0.0771588	−	0.133643i
$87$	−7.07756	+	4.08623i	−0.758794	+	0.438090i
$88$	3.87084	−	2.23483i	0.412633	−	0.238234i
$89$	−7.19562	+	12.4632i	−0.762734	+	1.32109i	0.178702	+	0.983903i	$0.442810\pi$
$89$	−7.19562	+	12.4632i	−0.762734	+	1.32109i	−0.941436	+	0.337191i	$0.890523\pi$
$90$	1.52773	−	1.63280i	0.161036	−	0.172113i
$91$		0			0
$92$			2.61827i			0.272974i
$93$	−7.33495	−	4.23483i	−0.760598	−	0.439132i
$94$	3.39536	+	5.88094i	0.350205	+	0.606573i
$95$	−3.35313	+	14.4140i	−0.344024	+	1.47885i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$			7.71966i			0.783813i	0.920005	+	0.391906i	$0.128184\pi$
$97$			7.71966i			0.783813i	−0.920005	+	0.391906i	$0.871816\pi$
$98$		0			0
$99$	−4.46967			−0.449218
$100$	4.48662	+	2.20687i	0.448662	+	0.220687i
$101$	−6.67722	−	11.5653i	−0.664408	−	1.15079i	−0.979446	−	0.201709i	$-0.935350\pi$
$101$	−6.67722	−	11.5653i	−0.664408	−	1.15079i	0.315038	−	0.949079i	$-0.397983\pi$
$102$	−6.69895	+	3.86764i	−0.663294	+	0.382953i
$103$	8.10569	+	4.67982i	0.798678	+	0.461117i	0.843009	−	0.537900i	$-0.180782\pi$
$103$	8.10569	+	4.67982i	0.798678	+	0.461117i	−0.0443310	+	0.999017i	$0.514116\pi$
$104$	−5.88388			−0.576962
$105$		0			0
$106$	1.38173			0.134205
$107$	−9.54057	−	5.50825i	−0.922322	−	0.532503i	−0.0379467	−	0.999280i	$-0.512082\pi$
$107$	−9.54057	−	5.50825i	−0.922322	−	0.532503i	−0.884375	+	0.466777i	$0.845415\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−2.34772	−	4.06637i	−0.224871	−	0.389488i	0.731410	−	0.681938i	$-0.238863\pi$
$109$	−2.34772	−	4.06637i	−0.224871	−	0.389488i	−0.956281	+	0.292451i	$0.905529\pi$
$110$	−2.90612	−	9.56264i	−0.277088	−	0.911762i
$111$	3.18719			0.302514
$112$		0			0
$113$			12.5723i			1.18271i	0.806413	+	0.591353i	$0.201406\pi$
$113$			12.5723i			1.18271i	−0.806413	+	0.591353i	$0.798594\pi$
$114$	3.30913	−	5.73159i	0.309929	−	0.536813i
$115$	5.70237	+	1.32654i	0.531748	+	0.123700i
$116$	4.08623	+	7.07756i	0.379397	+	0.657135i
$117$	5.09559	+	2.94194i	0.471087	+	0.271982i
$118$		−	4.66421i		−	0.429375i
$119$		0			0
$120$	−1.63280	−	1.52773i	−0.149054	−	0.139462i
$121$	−4.48896	+	7.77510i	−0.408087	+	0.706828i
$122$	8.48430	−	4.89841i	0.768133	−	0.443482i
$123$	3.08549	−	1.78141i	0.278209	−	0.160624i
$124$	−4.23483	+	7.33495i	−0.380299	+	0.658698i
$125$	7.07950	−	8.65336i	0.633210	−	0.773980i
$126$		0			0
$127$		−	6.59619i		−	0.585317i	−0.956217	−	0.292658i	$-0.905460\pi$
$127$		−	6.59619i		−	0.585317i	0.956217	−	0.292658i	$-0.0945399\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	0.715541	+	1.23935i	0.0629999	+	0.109119i
$130$	−2.98105	+	12.8146i	−0.261456	+	1.12391i
$131$	−1.16053	+	2.01010i	−0.101396	+	0.175623i	−0.912260	−	0.409611i	$-0.865664\pi$
$131$	−1.16053	+	2.01010i	−0.101396	+	0.175623i	0.810864	+	0.585235i	$0.198998\pi$
$132$			4.46967i			0.389035i
$133$		0			0
$134$	1.85140			0.159936
$135$	0.650187	+	2.13945i	0.0559592	+	0.184135i
$136$	3.86764	+	6.69895i	0.331647	+	0.574430i
$137$	−12.3626	+	7.13756i	−1.05621	+	0.609803i	−0.924381	−	0.381469i	$-0.875418\pi$
$137$	−12.3626	+	7.13756i	−1.05621	+	0.609803i	−0.131828	+	0.991273i	$0.542085\pi$
$138$	−2.26749	−	1.30913i	−0.193021	−	0.111441i
$139$	−14.9632			−1.26916			−0.634581	−	0.772857i	$-0.718827\pi$
$139$	−14.9632			−1.26916			−0.634581	+	0.772857i	$0.718827\pi$
$140$		0			0
$141$	−6.79073			−0.571883
$142$	1.75271	+	1.01193i	0.147084	+	0.0849191i
$143$	22.7756	−	13.1495i	1.90459	−	1.09962i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	17.4846	−	5.31363i	1.45202	−	0.441273i
$146$	4.01687			0.332438
$147$		0			0
$148$		−	3.18719i		−	0.261985i
$149$	5.58255	−	9.66926i	0.457341	−	0.792137i	−0.541479	−	0.840714i	$-0.682135\pi$
$149$	5.58255	−	9.66926i	0.457341	−	0.792137i	0.998819	+	0.0485773i	$0.0154687\pi$
$150$	−4.15451	+	2.78209i	−0.339215	+	0.227157i
$151$	−0.332104	−	0.575221i	−0.0270263	−	0.0468109i	0.852196	−	0.523223i	$-0.175270\pi$
$151$	−0.332104	−	0.575221i	−0.0270263	−	0.0468109i	−0.879222	+	0.476412i	$0.841937\pi$
$152$	−5.73159	−	3.30913i	−0.464893	−	0.268406i
$153$		−	7.73528i		−	0.625360i
$154$		0			0
$155$	13.8293	+	12.9393i	1.11080	+	1.03931i
$156$	2.94194	−	5.09559i	0.235544	−	0.407974i
$157$	6.99907	−	4.04092i	0.558587	−	0.322500i	−0.193991	−	0.981003i	$-0.562143\pi$
$157$	6.99907	−	4.04092i	0.558587	−	0.322500i	0.752578	+	0.658503i	$0.228810\pi$
$158$	−6.04942	+	3.49264i	−0.481266	+	0.277859i
$159$	−0.690865	+	1.19661i	−0.0547892	+	0.0948976i
$160$	−1.52773	+	1.63280i	−0.120777	+	0.129085i
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	−0.724575	−	0.418334i	−0.0567531	−	0.0327664i	0.471355	−	0.881944i	$-0.343765\pi$
$163$	−0.724575	−	0.418334i	−0.0567531	−	0.0327664i	−0.528108	+	0.849177i	$0.677098\pi$
$164$	−1.78141	−	3.08549i	−0.139105	−	0.240936i
$165$	9.73455	+	2.26454i	0.757834	+	0.176295i
$166$	−2.67982	+	4.64159i	−0.207995	+	0.360257i
$167$		−	2.66762i		−	0.206427i	−0.994659	−	0.103213i	$-0.967088\pi$
$167$		−	2.66762i		−	0.206427i	0.994659	−	0.103213i	$-0.0329125\pi$
$168$		0			0
$169$	−21.6200			−1.66308
$170$	16.5493	−	5.02938i	1.26927	−	0.385736i
$171$	3.30913	+	5.73159i	0.253056	+	0.438306i
$172$	1.23935	−	0.715541i	0.0944998	−	0.0545595i
$173$	−0.560613	−	0.323670i	−0.0426226	−	0.0246082i	0.478537	−	0.878067i	$-0.341167\pi$
$173$	−0.560613	−	0.323670i	−0.0426226	−	0.0246082i	−0.521160	+	0.853459i	$0.674500\pi$
$174$	−8.17246			−0.619553
$175$		0			0
$176$	4.46967			0.336914
$177$	4.03932	+	2.33210i	0.303614	+	0.175292i
$178$	−12.4632	+	7.19562i	−0.934155	+	0.539335i
$179$	−12.8687	−	22.2893i	−0.961853	−	1.66598i	−0.717842	−	0.696206i	$-0.754870\pi$
$179$	−12.8687	−	22.2893i	−0.961853	−	1.66598i	−0.244011	−	0.969772i	$-0.578463\pi$
$180$	2.13945	−	0.650187i	0.159465	−	0.0484621i
$181$	−7.42245			−0.551707			−0.275853	−	0.961200i	$-0.588960\pi$
$181$	−7.42245			−0.551707			−0.275853	+	0.961200i	$0.588960\pi$
$182$		0			0
$183$			9.79683i			0.724203i
$184$	−1.30913	+	2.26749i	−0.0965107	+	0.167161i
$185$	−6.94142	−	1.61478i	−0.510343	−	0.118721i
$186$	−4.23483	−	7.33495i	−0.310513	−	0.537824i
$187$	−29.9421	−	17.2871i	−2.18958	−	1.26415i
$188$			6.79073i			0.495265i
$189$		0			0
$190$	−10.1109	+	10.8063i	−0.733522	+	0.783975i
$191$	0.542261	−	0.939224i	0.0392367	−	0.0679599i	−0.845740	−	0.533595i	$-0.820841\pi$
$191$	0.542261	−	0.939224i	0.0392367	−	0.0679599i	0.884977	+	0.465635i	$0.154174\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	7.74169	−	4.46967i	0.557259	−	0.321734i	−0.194786	−	0.980846i	$-0.562401\pi$
$193$	7.74169	−	4.46967i	0.557259	−	0.321734i	0.752045	+	0.659112i	$0.229068\pi$
$194$	−3.85983	+	6.68542i	−0.277120	+	0.479985i
$195$	−9.60723	−	8.98896i	−0.687988	−	0.643713i
$196$		0			0
$197$		−	7.45890i		−	0.531425i	−0.964052	−	0.265712i	$-0.914393\pi$
$197$		−	7.45890i		−	0.531425i	0.964052	−	0.265712i	$-0.0856071\pi$
$198$	−3.87084	−	2.23483i	−0.275089	−	0.158823i
$199$	−12.9147	−	22.3688i	−0.915496	−	1.58569i	−0.806174	−	0.591679i	$-0.798465\pi$
$199$	−12.9147	−	22.3688i	−0.915496	−	1.58569i	−0.109322	−	0.994006i	$-0.534868\pi$
$200$	2.78209	+	4.15451i	0.196723	+	0.293768i
$201$	−0.925698	+	1.60336i	−0.0652937	+	0.113092i
$202$		−	13.3544i		−	0.939615i
$203$		0			0
$204$	−7.73528			−0.541578
$205$	−7.62248	+	2.31650i	−0.532377	+	0.161791i
$206$	4.67982	+	8.10569i	0.326059	+	0.564750i
$207$	2.26749	−	1.30913i	0.157601	−	0.0909912i
$208$	−5.09559	−	2.94194i	−0.353316	−	0.203987i
$209$	29.5815			2.04619
$210$		0			0
$211$	5.53375			0.380959			0.190479	−	0.981691i	$-0.438996\pi$
$211$	5.53375			0.380959			0.190479	+	0.981691i	$0.438996\pi$
$212$	1.19661	+	0.690865i	0.0821837	+	0.0474488i
$213$	−1.75271	+	1.01193i	−0.120094	+	0.0693361i
$214$	−5.50825	−	9.54057i	−0.376536	−	0.652180i
$215$	−0.930471	−	3.06173i	−0.0634576	−	0.208808i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$		−	4.69544i		−	0.318015i
$219$	−2.00843	+	3.47871i	−0.135717	+	0.235069i
$220$	2.26454	−	9.73455i	0.152676	−	0.656303i
$221$	22.7567	+	39.4158i	1.53078	+	2.65139i
$222$	2.76019	+	1.59359i	0.185252	+	0.106955i
$223$		−	3.28248i		−	0.219811i	−0.993942	−	0.109906i	$-0.964945\pi$
$223$		−	3.28248i		−	0.219811i	0.993942	−	0.109906i	$-0.0350548\pi$
$224$		0			0
$225$	−0.332104	−	4.98896i	−0.0221403	−	0.332597i
$226$	−6.28617	+	10.8880i	−0.418150	+	0.724256i
$227$	3.82810	−	2.21016i	0.254080	−	0.146693i	−0.367551	−	0.930003i	$-0.619804\pi$
$227$	3.82810	−	2.21016i	0.254080	−	0.146693i	0.621631	+	0.783310i	$0.286470\pi$
$228$	5.73159	−	3.30913i	0.379584	−	0.219153i
$229$	3.98635	−	6.90456i	0.263426	−	0.456266i	−0.703724	−	0.710473i	$-0.748481\pi$
$229$	3.98635	−	6.90456i	0.263426	−	0.456266i	0.967150	+	0.254207i	$0.0818144\pi$
$230$	4.27512	+	4.00000i	0.281893	+	0.263752i
$231$		0			0
$232$			8.17246i			0.536548i
$233$	15.5502	+	8.97792i	1.01873	+	0.588163i	0.913735	−	0.406310i	$-0.133185\pi$
$233$	15.5502	+	8.97792i	1.01873	+	0.588163i	0.104993	+	0.994473i	$0.466518\pi$
$234$	2.94194	+	5.09559i	0.192321	+	0.333109i
$235$	14.7896	+	3.44050i	0.964769	+	0.224434i
$236$	2.33210	−	4.03932i	0.151807	−	0.262938i
$237$		−	6.98527i		−	0.453742i
$238$		0			0
$239$	−5.41296			−0.350135			−0.175068	−	0.984556i	$-0.556014\pi$
$239$	−5.41296			−0.350135			−0.175068	+	0.984556i	$0.556014\pi$
$240$	−0.650187	−	2.13945i	−0.0419694	−	0.138101i
$241$	−2.34835	−	4.06745i	−0.151270	−	0.262008i	0.780424	−	0.625250i	$-0.215003\pi$
$241$	−2.34835	−	4.06745i	−0.151270	−	0.262008i	−0.931695	+	0.363242i	$0.881670\pi$
$242$	−7.77510	+	4.48896i	−0.499803	+	0.288561i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	9.79683			0.627178
$245$		0			0
$246$	3.56282			0.227157
$247$	−33.7240	−	19.4706i	−2.14581	−	1.23888i
$248$	−7.33495	+	4.23483i	−0.465770	+	0.268912i
$249$	−2.67982	−	4.64159i	−0.169827	−	0.294149i
$250$	10.4577	−	3.95428i	0.661404	−	0.250091i
$251$	−7.73402			−0.488167			−0.244084	−	0.969754i	$-0.578487\pi$
$251$	−7.73402			−0.488167			−0.244084	+	0.969754i	$0.578487\pi$
$252$		0			0
$253$		−	11.7028i		−	0.735748i
$254$	3.29809	−	5.71247i	0.206941	−	0.358432i
$255$	−3.91906	+	16.8468i	−0.245421	+	1.05499i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.16430	+	0.672210i	0.0726271	+	0.0419313i	0.535874	−	0.844298i	$-0.319982\pi$
$257$	1.16430	+	0.672210i	0.0726271	+	0.0419313i	−0.463247	+	0.886229i	$0.653316\pi$
$258$			1.43108i			0.0890953i
$259$		0			0
$260$	−8.98896	+	9.60723i	−0.557472	+	0.595815i
$261$	4.08623	−	7.07756i	0.252931	−	0.438090i
$262$	−2.01010	+	1.16053i	−0.124184	+	0.0716979i
$263$	3.78193	−	2.18350i	0.233204	−	0.134640i	−0.378845	−	0.925460i	$-0.623679\pi$
$263$	3.78193	−	2.18350i	0.233204	−	0.134640i	0.612049	+	0.790820i	$0.290345\pi$
$264$	−2.23483	+	3.87084i	−0.137544	+	0.238234i
$265$	2.11091	−	2.25610i	0.129672	−	0.138591i
$266$		0			0
$267$		−	14.3912i		−	0.880730i
$268$	1.60336	+	0.925698i	0.0979406	+	0.0565460i
$269$	−11.5336	−	19.9767i	−0.703213	−	1.21800i	−0.967333	−	0.253511i	$-0.918415\pi$
$269$	−11.5336	−	19.9767i	−0.703213	−	1.21800i	0.264119	−	0.964490i	$-0.414919\pi$
$270$	−0.506647	+	2.17791i	−0.0308336	+	0.132544i
$271$	7.36047	−	12.7487i	0.447117	−	0.774429i	−0.551080	−	0.834452i	$-0.685784\pi$
$271$	7.36047	−	12.7487i	0.447117	−	0.774429i	0.998197	+	0.0600236i	$0.0191176\pi$
$272$			7.73528i			0.469020i
$273$		0			0
$274$	−14.2751			−0.862392
$275$	−20.0537	−	9.86397i	−1.20928	−	0.594820i
$276$	−1.30913	−	2.26749i	−0.0788007	−	0.136487i
$277$	−2.78085	+	1.60552i	−0.167085	+	0.0964665i	−0.581211	−	0.813753i	$-0.697421\pi$
$277$	−2.78085	+	1.60552i	−0.167085	+	0.0964665i	0.414126	+	0.910220i	$0.364087\pi$
$278$	−12.9585	−	7.48159i	−0.777199	−	0.448716i
$279$	8.46967			0.507066
$280$		0			0
$281$	−7.72488			−0.460827			−0.230414	−	0.973093i	$-0.574008\pi$
$281$	−7.72488			−0.460827			−0.230414	+	0.973093i	$0.574008\pi$
$282$	−5.88094	−	3.39536i	−0.350205	−	0.202191i
$283$	−25.5992	+	14.7797i	−1.52171	+	0.878561i	−0.522041	+	0.852920i	$0.674829\pi$
$283$	−25.5992	+	14.7797i	−1.52171	+	0.878561i	−0.999671	+	0.0256411i	$0.991837\pi$
$284$	1.01193	+	1.75271i	0.0600469	+	0.104004i
$285$	−4.30312	−	14.1595i	−0.254895	−	0.838735i
$286$	26.2990			1.55509
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	21.4172	−	37.0958i	1.25984	−	2.18210i
$290$	17.7989	+	4.14055i	1.04519	+	0.243142i
$291$	−3.85983	−	6.68542i	−0.226267	−	0.391906i
$292$	3.47871	+	2.00843i	0.203576	+	0.117535i
$293$			1.17679i			0.0687487i	0.999409	+	0.0343743i	$0.0109438\pi$
$293$			1.17679i			0.0687487i	−0.999409	+	0.0343743i	$0.989056\pi$
$294$		0			0
$295$	−7.61574	−	7.12563i	−0.443406	−	0.414870i
$296$	1.59359	−	2.76019i	0.0926258	−	0.160433i
$297$	3.87084	−	2.23483i	0.224609	−	0.129678i
$298$	9.66926	−	5.58255i	0.560125	−	0.323389i
$299$	−7.70279	+	13.3416i	−0.445464	+	0.771566i
$300$	−4.98896	+	0.332104i	−0.288038	+	0.0191740i
$301$		0			0
$302$		−	0.664208i		−	0.0382209i
$303$	11.5653	+	6.67722i	0.664408	+	0.383596i
$304$	−3.30913	−	5.73159i	−0.189792	−	0.328729i
$305$	4.96354	−	21.3367i	0.284211	−	1.22173i
$306$	3.86764	−	6.69895i	0.221098	−	0.382953i
$307$		−	20.3761i		−	1.16293i	−0.813572	−	0.581464i	$-0.802480\pi$
$307$		−	20.3761i		−	1.16293i	0.813572	−	0.581464i	$-0.197520\pi$
$308$		0			0
$309$	−9.35965			−0.532452
$310$	5.50687	+	18.1204i	0.312769	+	1.02917i
$311$	−9.44670	−	16.3622i	−0.535673	−	0.927813i	−0.999130	−	0.0416937i	$-0.986725\pi$
$311$	−9.44670	−	16.3622i	−0.535673	−	0.927813i	0.463457	−	0.886119i	$-0.346609\pi$
$312$	5.09559	−	2.94194i	0.288481	−	0.166555i
$313$	−14.2763	−	8.24245i	−0.806946	−	0.465891i	0.0389480	−	0.999241i	$-0.487599\pi$
$313$	−14.2763	−	8.24245i	−0.806946	−	0.465891i	−0.845894	+	0.533351i	$0.820933\pi$
$314$	8.08184			0.456084
$315$		0			0
$316$	−6.98527			−0.392952
$317$	8.93830	+	5.16053i	0.502025	+	0.289844i	0.729549	−	0.683928i	$-0.239730\pi$
$317$	8.93830	+	5.16053i	0.502025	+	0.289844i	−0.227524	+	0.973772i	$0.573063\pi$
$318$	−1.19661	+	0.690865i	−0.0671027	+	0.0387418i
$319$	−18.2641	−	31.6343i	−1.02259	−	1.77118i
$320$	−2.13945	+	0.650187i	−0.119599	+	0.0363466i
$321$	11.0165			0.614881
$322$		0			0
$323$			51.1941i			2.84852i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	16.3695	+	24.4447i	0.908016	+	1.35595i
$326$	−0.418334	−	0.724575i	−0.0231694	−	0.0401305i
$327$	4.06637	+	2.34772i	0.224871	+	0.129829i
$328$		−	3.56282i		−	0.196724i
$329$		0			0
$330$	7.29809	+	6.82843i	0.401747	+	0.375893i
$331$	9.59530	−	16.6195i	0.527405	−	0.913493i	−0.472084	−	0.881553i	$-0.656498\pi$
$331$	9.59530	−	16.6195i	0.527405	−	0.913493i	0.999490	−	0.0319396i	$-0.0101684\pi$
$332$	−4.64159	+	2.67982i	−0.254740	+	0.147074i
$333$	−2.76019	+	1.59359i	−0.151257	+	0.0873284i
$334$	1.33381	−	2.31023i	0.0729829	−	0.126410i
$335$	2.82843	−	3.02297i	0.154533	−	0.165162i
$336$		0			0
$337$			27.6035i			1.50366i	0.659357	+	0.751830i	$0.270829\pi$
$337$			27.6035i			1.50366i	−0.659357	+	0.751830i	$0.729171\pi$
$338$	−18.7235	−	10.8100i	−1.01842	−	0.587988i
$339$	−6.28617	−	10.8880i	−0.341418	−	0.591353i
$340$	16.8468	+	3.91906i	0.913644	+	0.212541i
$341$	18.9283	−	32.7848i	1.02502	−	1.77539i
$342$			6.61827i			0.357875i
$343$		0			0
$344$	1.43108			0.0771588
$345$	−5.60166	+	1.70237i	−0.301583	+	0.0916523i
$346$	−0.323670	−	0.560613i	−0.0174006	−	0.0301387i
$347$	17.6463	−	10.1881i	0.947301	−	0.546924i	0.0550595	−	0.998483i	$-0.482465\pi$
$347$	17.6463	−	10.1881i	0.947301	−	0.546924i	0.892241	+	0.451559i	$0.149132\pi$
$348$	−7.07756	−	4.08623i	−0.379397	−	0.219045i
$349$	−17.8281			−0.954314			−0.477157	−	0.878818i	$-0.658333\pi$
$349$	−17.8281			−0.954314			−0.477157	+	0.878818i	$0.658333\pi$
$350$		0			0
$351$	−5.88388			−0.314058
$352$	3.87084	+	2.23483i	0.206317	+	0.119117i
$353$	3.04275	−	1.75673i	0.161949	−	0.0935014i	−0.416835	−	0.908982i	$-0.636861\pi$
$353$	3.04275	−	1.75673i	0.161949	−	0.0935014i	0.578784	+	0.815481i	$0.303527\pi$
$354$	2.33210	+	4.03932i	0.123950	+	0.214688i
$355$	4.32994	−	1.31589i	0.229809	−	0.0698399i
$356$	−14.3912			−0.762734
$357$		0			0
$358$		−	25.7374i		−	1.36027i
$359$	−1.09898	+	1.90349i	−0.0580018	+	0.100462i	−0.893568	−	0.448927i	$-0.851806\pi$
$359$	−1.09898	+	1.90349i	−0.0580018	+	0.100462i	0.835567	+	0.549389i	$0.185140\pi$
$360$	2.17791	+	0.506647i	0.114786	+	0.0267027i
$361$	−12.4007	−	21.4787i	−0.652671	−	1.13046i
$362$	−6.42803	−	3.71123i	−0.337850	−	0.195058i
$363$		−	8.97792i		−	0.471218i
$364$		0			0
$365$	6.13668	−	6.55876i	0.321208	−	0.343301i
$366$	−4.89841	+	8.48430i	−0.256044	+	0.443482i
$367$	−24.9173	+	14.3860i	−1.30067	+	0.750945i	−0.980520	−	0.196421i	$-0.937068\pi$
$367$	−24.9173	+	14.3860i	−1.30067	+	0.750945i	−0.320155	+	0.947365i	$0.603735\pi$
$368$	−2.26749	+	1.30913i	−0.118201	+	0.0682434i
$369$	−1.78141	+	3.08549i	−0.0927364	+	0.160624i
$370$	−5.20406	−	4.86915i	−0.270546	−	0.253135i
$371$		0			0
$372$		−	8.46967i		−	0.439132i
$373$	12.6171	+	7.28446i	0.653286	+	0.377175i	0.789714	−	0.613475i	$-0.210229\pi$
$373$	12.6171	+	7.28446i	0.653286	+	0.377175i	−0.136428	+	0.990650i	$0.543562\pi$
$374$	−17.2871	−	29.9421i	−0.893892	−	1.54827i
$375$	−1.80435	+	11.0338i	−0.0931761	+	0.569782i
$376$	−3.39536	+	5.88094i	−0.175103	+	0.303287i
$377$			48.0858i			2.47654i
$378$		0			0
$379$	30.7868			1.58141			0.790705	−	0.612197i	$-0.209714\pi$
$379$	30.7868			1.58141			0.790705	+	0.612197i	$0.209714\pi$
$380$	−14.1595	+	4.30312i	−0.726366	+	0.220745i
$381$	3.29809	+	5.71247i	0.168966	+	0.292658i
$382$	0.939224	−	0.542261i	0.0480549	−	0.0277445i
$383$	−20.2139	−	11.6705i	−1.03288	−	0.596334i	−0.115072	−	0.993357i	$-0.536710\pi$
$383$	−20.2139	−	11.6705i	−1.03288	−	0.596334i	−0.917809	+	0.397023i	$0.870043\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	8.93933			0.455000
$387$	−1.23935	−	0.715541i	−0.0629999	−	0.0363730i
$388$	−6.68542	+	3.85983i	−0.339401	+	0.195953i
$389$	−0.609209	−	1.05518i	−0.0308881	−	0.0534998i	0.850168	−	0.526511i	$-0.176500\pi$
$389$	−0.609209	−	1.05518i	−0.0308881	−	0.0534998i	−0.881056	+	0.473012i	$0.843167\pi$
$390$	−3.82562	−	12.5883i	−0.193718	−	0.637432i
$391$	20.2530			1.02424
$392$		0			0
$393$		−	2.32106i		−	0.117082i
$394$	3.72945	−	6.45960i	0.187887	−	0.325430i
$395$	−3.53907	+	15.2133i	−0.178070	+	0.765465i
$396$	−2.23483	−	3.87084i	−0.112305	−	0.194517i
$397$	7.27977	+	4.20298i	0.365361	+	0.210941i	0.671430	−	0.741068i	$-0.265680\pi$
$397$	7.27977	+	4.20298i	0.365361	+	0.210941i	−0.306069	+	0.952009i	$0.599014\pi$
$398$		−	25.8293i		−	1.29471i
$399$		0			0
$400$	0.332104	+	4.98896i	0.0166052	+	0.249448i
$401$	0.332104	−	0.575221i	0.0165845	−	0.0287252i	−0.857614	−	0.514294i	$-0.828054\pi$
$401$	0.332104	−	0.575221i	0.0165845	−	0.0287252i	0.874199	+	0.485569i	$0.161387\pi$
$402$	−1.60336	+	0.925698i	−0.0799681	+	0.0461696i
$403$	−43.1579	+	24.9172i	−2.14985	+	1.24122i
$404$	6.67722	−	11.5653i	0.332204	−	0.575394i
$405$	−1.63280	−	1.52773i	−0.0811347	−	0.0759133i
$406$		0			0
$407$			14.2457i			0.706131i
$408$	−6.69895	−	3.86764i	−0.331647	−	0.191477i
$409$	3.69238	+	6.39539i	0.182576	+	0.316231i	0.942757	−	0.333480i	$-0.108223\pi$
$409$	3.69238	+	6.39539i	0.182576	+	0.316231i	−0.760181	+	0.649712i	$0.774890\pi$
$410$	−7.75951	−	1.80509i	−0.383215	−	0.0891471i
$411$	7.13756	−	12.3626i	0.352070	−	0.609803i
$412$			9.35965i			0.461117i
$413$		0			0
$414$	2.61827			0.128681
$415$	3.48478	+	11.4667i	0.171061	+	0.562879i
$416$	−2.94194	−	5.09559i	−0.144240	−	0.249832i
$417$	12.9585	−	7.48159i	0.634581	−	0.366375i
$418$	25.6183	+	14.7907i	1.25303	+	0.723438i
$419$	18.6274			0.910009			0.455004	−	0.890489i	$-0.349638\pi$
$419$	18.6274			0.910009			0.455004	+	0.890489i	$0.349638\pi$
$420$		0			0
$421$	−13.5043			−0.658159			−0.329079	−	0.944302i	$-0.606738\pi$
$421$	−13.5043			−0.658159			−0.329079	+	0.944302i	$0.606738\pi$
$422$	4.79237	+	2.76687i	0.233289	+	0.134689i
$423$	5.88094	−	3.39536i	0.285941	−	0.165088i
$424$	0.690865	+	1.19661i	0.0335514	+	0.0581127i
$425$	17.0707	−	34.7052i	0.828052	−	1.68345i
$426$	−2.02386			−0.0980561
$427$		0			0
$428$		−	11.0165i		−	0.532503i
$429$	−13.1495	+	22.7756i	−0.634863	+	1.09962i
$430$	0.725054	−	3.11677i	0.0349652	−	0.150304i
$431$	15.8404	+	27.4363i	0.763003	+	1.32156i	0.941296	+	0.337583i	$0.109609\pi$
$431$	15.8404	+	27.4363i	0.763003	+	1.32156i	−0.178293	+	0.983977i	$0.557057\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			25.3184i			1.21672i	0.793660	+	0.608362i	$0.208173\pi$
$433$			25.3184i			1.21672i	−0.793660	+	0.608362i	$0.791827\pi$
$434$		0			0
$435$	−12.4853	+	13.3440i	−0.598623	+	0.639797i
$436$	2.34772	−	4.06637i	0.112435	−	0.194744i
$437$	−15.0068	+	8.66421i	−0.717875	+	0.414465i
$438$	−3.47871	+	2.00843i	−0.166219	+	0.0959667i
$439$	−16.4073	+	28.4183i	−0.783077	+	1.35633i	0.147064	+	0.989127i	$0.453018\pi$
$439$	−16.4073	+	28.4183i	−0.783077	+	1.35633i	−0.930141	+	0.367203i	$0.880316\pi$
$440$	6.82843	−	7.29809i	0.325532	−	0.347923i
$441$		0			0
$442$			45.5134i			2.16485i
$443$	−14.4125	−	8.32106i	−0.684759	−	0.395346i	0.116887	−	0.993145i	$-0.462709\pi$
$443$	−14.4125	−	8.32106i	−0.684759	−	0.395346i	−0.801646	+	0.597800i	$0.796042\pi$
$444$	1.59359	+	2.76019i	0.0756286	+	0.130993i
$445$	−7.29129	+	31.3429i	−0.345640	+	1.48580i
$446$	1.64124	−	2.84271i	0.0777149	−	0.134606i
$447$			11.1651i			0.528091i
$448$		0			0
$449$	−20.1759			−0.952158			−0.476079	−	0.879402i	$-0.657942\pi$
$449$	−20.1759			−0.952158			−0.476079	+	0.879402i	$0.657942\pi$
$450$	2.20687	−	4.48662i	0.104033	−	0.211501i
$451$	7.96230	+	13.7911i	0.374930	+	0.649398i
$452$	−10.8880	+	6.28617i	−0.512126	+	0.295676i
$453$	0.575221	+	0.332104i	0.0270263	+	0.0156036i
$454$	4.42031			0.207456
$455$		0			0
$456$	6.61827			0.309929
$457$	−30.6680	−	17.7062i	−1.43459	−	0.828261i	−0.437124	−	0.899401i	$-0.644003\pi$
$457$	−30.6680	−	17.7062i	−1.43459	−	0.828261i	−0.997466	+	0.0711396i	$0.977336\pi$
$458$	6.90456	−	3.98635i	0.322629	−	0.186270i
$459$	3.86764	+	6.69895i	0.180526	+	0.312680i
$460$	1.70237	+	5.60166i	0.0793732	+	0.261179i
$461$	12.5940			0.586562			0.293281	−	0.956026i	$-0.405253\pi$
$461$	12.5940			0.586562			0.293281	+	0.956026i	$0.405253\pi$
$462$		0			0
$463$			32.5061i			1.51069i	0.655330	+	0.755343i	$0.272530\pi$
$463$			32.5061i			1.51069i	−0.655330	+	0.755343i	$0.727470\pi$
$464$	−4.08623	+	7.07756i	−0.189698	+	0.328567i
$465$	−18.4462	−	4.29113i	−0.855422	−	0.198997i
$466$	8.97792	+	15.5502i	0.415894	+	0.720349i
$467$	−7.97203	−	4.60265i	−0.368902	−	0.212985i	0.304077	−	0.952648i	$-0.401652\pi$
$467$	−7.97203	−	4.60265i	−0.368902	−	0.212985i	−0.672979	+	0.739662i	$0.734985\pi$
$468$			5.88388i			0.271982i
$469$		0			0
$470$	11.0879	+	10.3744i	0.511448	+	0.478534i
$471$	−4.04092	+	6.99907i	−0.186196	+	0.322500i
$472$	4.03932	−	2.33210i	0.185925	−	0.107344i
$473$	−5.53950	+	3.19823i	−0.254706	+	0.147055i
$474$	3.49264	−	6.04942i	0.160422	−	0.277859i
$475$	2.19796	+	33.0183i	0.100849	+	1.51498i
$476$		0			0
$477$		−	1.38173i		−	0.0632651i
$478$	−4.68776	−	2.70648i	−0.214413	−	0.123792i
$479$	19.7457	+	34.2005i	0.902203	+	1.56266i	0.824628	+	0.565675i	$0.191384\pi$
$479$	19.7457	+	34.2005i	0.902203	+	1.56266i	0.0775746	+	0.996987i	$0.475282\pi$
$480$	0.506647	−	2.17791i	0.0231252	−	0.0994077i
$481$	9.37652	−	16.2406i	0.427532	−	0.740508i
$482$		−	4.69669i		−	0.213928i
$483$		0			0
$484$	−8.97792			−0.408087
$485$	5.01923	+	16.5158i	0.227911	+	0.749946i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	25.3466	−	14.6339i	1.14857	−	0.663125i	0.200028	−	0.979790i	$-0.435897\pi$
$487$	25.3466	−	14.6339i	1.14857	−	0.663125i	0.948537	+	0.316666i	$0.102563\pi$
$488$	8.48430	+	4.89841i	0.384066	+	0.221741i
$489$	0.836668			0.0378354
$490$		0			0
$491$	15.3631			0.693325			0.346663	−	0.937990i	$-0.387315\pi$
$491$	15.3631			0.693325			0.346663	+	0.937990i	$0.387315\pi$
$492$	3.08549	+	1.78141i	0.139105	+	0.0803121i
$493$	54.7469	−	31.6081i	2.46567	−	1.42356i
$494$	−19.4706	−	33.7240i	−0.876022	−	1.51731i
$495$	−9.56264	+	2.90612i	−0.429809	+	0.130620i
$496$	−8.46967			−0.380299
$497$		0			0
$498$		−	5.35965i		−	0.240172i
$499$	10.2751	−	17.7970i	0.459978	−	0.796705i	−0.538981	−	0.842318i	$-0.681191\pi$
$499$	10.2751	−	17.7970i	0.459978	−	0.796705i	0.998959	+	0.0456128i	$0.0145241\pi$
$500$	11.0338	+	1.80435i	0.493446	+	0.0806929i
$501$	1.33381	+	2.31023i	0.0595903	+	0.103213i
$502$	−6.69786	−	3.86701i	−0.298940	−	0.172593i
$503$		−	20.4788i		−	0.913105i	−0.889696	−	0.456553i	$-0.849084\pi$
$503$		−	20.4788i		−	0.913105i	0.889696	−	0.456553i	$-0.150916\pi$
$504$		0			0
$505$	−21.8052	−	20.4019i	−0.970318	−	0.907873i
$506$	5.85140	−	10.1349i	0.260126	−	0.450552i
$507$	18.7235	−	10.8100i	0.831540	−	0.480090i
$508$	5.71247	−	3.29809i	0.253450	−	0.146329i
$509$	−6.03509	+	10.4531i	−0.267501	+	0.463325i	−0.968216	−	0.250116i	$-0.919531\pi$
$509$	−6.03509	+	10.4531i	−0.267501	+	0.463325i	0.700715	+	0.713441i	$0.252864\pi$
$510$	−11.8174	+	12.6302i	−0.523283	+	0.559275i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−5.73159	−	3.30913i	−0.253056	−	0.146102i
$514$	0.672210	+	1.16430i	0.0296499	+	0.0513551i
$515$	20.3845	+	4.74204i	0.898249	+	0.208959i
$516$	−0.715541	+	1.23935i	−0.0314999	+	0.0545595i
$517$		−	30.3523i		−	1.33489i
$518$		0			0
$519$	0.647340			0.0284151
$520$	−12.5883	+	3.82562i	−0.552033	+	0.167765i
$521$	7.35247	+	12.7348i	0.322117	+	0.557924i	0.980925	−	0.194388i	$-0.0622721\pi$
$521$	7.35247	+	12.7348i	0.322117	+	0.557924i	−0.658807	+	0.752312i	$0.728939\pi$
$522$	7.07756	−	4.08623i	0.309776	−	0.178849i
$523$	5.58081	+	3.22208i	0.244032	+	0.140892i	0.617028	−	0.786941i	$-0.288336\pi$
$523$	5.58081	+	3.22208i	0.244032	+	0.140892i	−0.372996	+	0.927833i	$0.621670\pi$
$524$	−2.32106			−0.101396
$525$		0			0
$526$	4.36700			0.190410
$527$	56.7378	+	32.7576i	2.47154	+	1.42694i
$528$	−3.87084	+	2.23483i	−0.168457	+	0.0972586i
$529$	−8.07233	−	13.9817i	−0.350971	−	0.607899i
$530$	2.95615	−	0.898384i	0.128407	−	0.0390233i
$531$	−4.66421			−0.202409
$532$		0			0
$533$		−	20.9632i		−	0.908016i
$534$	7.19562	−	12.4632i	0.311385	−	0.539335i
$535$	−23.9930	−	5.58148i	−1.03731	−	0.241308i
$536$	0.925698	+	1.60336i	0.0399841	+	0.0692544i
$537$	22.2893	+	12.8687i	0.961853	+	0.555326i
$538$		−	23.0671i		−	0.994494i
$539$		0			0
$540$	−1.52773	+	1.63280i	−0.0657429	+	0.0702647i
$541$	5.79073	−	10.0298i	0.248963	−	0.431216i	−0.714275	−	0.699865i	$-0.753244\pi$
$541$	5.79073	−	10.0298i	0.248963	−	0.431216i	0.963238	+	0.268648i	$0.0865769\pi$
$542$	12.7487	−	7.36047i	0.547604	−	0.316159i
$543$	6.42803	−	3.71123i	0.275853	−	0.159264i
$544$	−3.86764	+	6.69895i	−0.165824	+	0.287215i
$545$	−7.66674	−	7.17335i	−0.328407	−	0.307272i
$546$		0			0
$547$		−	19.2656i		−	0.823737i	−0.911243	−	0.411868i	$-0.864876\pi$
$547$		−	19.2656i		−	0.823737i	0.911243	−	0.411868i	$-0.135124\pi$
$548$	−12.3626	−	7.13756i	−0.528105	−	0.304902i
$549$	−4.89841	−	8.48430i	−0.209059	−	0.362101i
$550$	−12.4350	−	18.5693i	−0.530231	−	0.791797i
$551$	−27.0438	+	46.8412i	−1.15210	+	1.99550i
$552$		−	2.61827i		−	0.111441i
$553$		0			0
$554$	−3.21104			−0.136424
$555$	6.81884	−	2.07227i	0.289443	−	0.0879629i
$556$	−7.48159	−	12.9585i	−0.317290	−	0.549563i
$557$	−18.2215	+	10.5202i	−0.772069	+	0.445754i	−0.833612	−	0.552350i	$-0.813731\pi$
$557$	−18.2215	+	10.5202i	−0.772069	+	0.445754i	0.0615432	+	0.998104i	$0.480398\pi$
$558$	7.33495	+	4.23483i	0.310513	+	0.179275i
$559$	8.42031			0.356141
$560$		0			0
$561$	34.5741			1.45972
$562$	−6.68994	−	3.86244i	−0.282198	−	0.162927i
$563$	−3.12714	+	1.80546i	−0.131793	+	0.0760910i	−0.564447	−	0.825469i	$-0.690911\pi$
$563$	−3.12714	+	1.80546i	−0.131793	+	0.0760910i	0.432654	+	0.901560i	$0.357577\pi$
$564$	−3.39536	−	5.88094i	−0.142971	−	0.247632i
$565$	8.17437	+	26.8979i	0.343898	+	1.13160i
$566$	−29.5594			−1.24247
$567$		0			0
$568$			2.02386i			0.0849191i
$569$	16.6072	−	28.7646i	0.696211	−	1.20587i	−0.273559	−	0.961855i	$-0.588201\pi$
$569$	16.6072	−	28.7646i	0.696211	−	1.20587i	0.969771	−	0.244018i	$-0.0784656\pi$
$570$	3.35313	−	14.4140i	0.140447	−	0.603737i
$571$	16.0888	+	27.8667i	0.673296	+	1.16618i	0.976964	+	0.213405i	$0.0684555\pi$
$571$	16.0888	+	27.8667i	0.673296	+	1.16618i	−0.303667	+	0.952778i	$0.598211\pi$
$572$	22.7756	+	13.1495i	0.952295	+	0.549808i
$573$			1.08452i			0.0453066i
$574$		0			0
$575$	13.0624	−	0.869539i	0.544741	−	0.0362623i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−29.6096	+	17.0951i	−1.23266	+	0.711679i	−0.967585	−	0.252547i	$-0.918732\pi$
$577$	−29.6096	+	17.0951i	−1.23266	+	0.711679i	−0.265080	+	0.964226i	$0.585398\pi$
$578$	37.0958	−	21.4172i	1.54298	−	0.890840i
$579$	−4.46967	+	7.74169i	−0.185753	+	0.321734i
$580$	13.3440	+	12.4853i	0.554081	+	0.518423i
$581$		0			0
$582$		−	7.71966i		−	0.319990i
$583$	−5.34846	−	3.08794i	−0.221511	−	0.127889i
$584$	2.00843	+	3.47871i	0.0831096	+	0.143950i
$585$	12.8146	+	2.98105i	0.529818	+	0.123251i
$586$	−0.588394	+	1.01913i	−0.0243063	+	0.0420998i
$587$		−	34.5962i		−	1.42794i	−0.700178	−	0.713969i	$-0.746896\pi$
$587$		−	34.5962i		−	1.42794i	0.700178	−	0.713969i	$-0.253104\pi$
$588$		0			0
$589$	−56.0545			−2.30969
$590$	−3.03261	−	9.97885i	−0.124851	−	0.410823i
$591$	3.72945	+	6.45960i	0.153409	+	0.265712i
$592$	2.76019	−	1.59359i	0.113443	−	0.0654963i
$593$	28.6520	+	16.5422i	1.17660	+	0.679309i	0.955225	−	0.295881i	$-0.0956131\pi$
$593$	28.6520	+	16.5422i	1.17660	+	0.679309i	0.221372	+	0.975189i	$0.428946\pi$
$594$	4.46967			0.183393
$595$		0			0
$596$	11.1651			0.457341
$597$	22.3688	+	12.9147i	0.915496	+	0.528562i
$598$	−13.3416	+	7.70279i	−0.545580	+	0.314991i
$599$	3.03742	+	5.26097i	0.124106	+	0.214958i	0.921383	−	0.388656i	$-0.127060\pi$
$599$	3.03742	+	5.26097i	0.124106	+	0.214958i	−0.797277	+	0.603613i	$0.793727\pi$
$600$	−4.48662	−	2.20687i	−0.183165	−	0.0900950i
$601$	11.7469			0.479167			0.239584	−	0.970876i	$-0.422989\pi$
$601$	11.7469			0.479167			0.239584	+	0.970876i	$0.422989\pi$
$602$		0			0
$603$		−	1.85140i		−	0.0753947i
$604$	0.332104	−	0.575221i	0.0135131	−	0.0234054i
$605$	−4.54864	+	19.5531i	−0.184928	+	0.794948i
$606$	6.67722	+	11.5653i	0.271243	+	0.469807i
$607$	−39.6796	−	22.9090i	−1.61054	−	0.929848i	−0.989244	−	0.146275i	$-0.953271\pi$
$607$	−39.6796	−	22.9090i	−1.61054	−	0.929848i	−0.621300	−	0.783573i	$-0.713395\pi$
$608$		−	6.61827i		−	0.268406i
$609$		0			0
$610$	14.9669	−	15.9963i	0.605991	−	0.647672i
$611$	−19.9779	+	34.6028i	−0.808220	+	1.39988i
$612$	6.69895	−	3.86764i	0.270789	−	0.156340i
$613$	−29.6626	+	17.1257i	−1.19806	+	0.691701i	−0.960122	−	0.279580i	$-0.909805\pi$
$613$	−29.6626	+	17.1257i	−1.19806	+	0.691701i	−0.237938	+	0.971280i	$0.576472\pi$
$614$	10.1881	−	17.6463i	0.411157	−	0.712145i
$615$	5.44301	−	5.81739i	0.219483	−	0.234580i
$616$		0			0
$617$		−	38.8106i		−	1.56246i	−0.624245	−	0.781228i	$-0.714593\pi$
$617$		−	38.8106i		−	1.56246i	0.624245	−	0.781228i	$-0.285407\pi$
$618$	−8.10569	−	4.67982i	−0.326059	−	0.188250i
$619$	2.13756	+	3.70237i	0.0859159	+	0.148811i	0.905781	−	0.423746i	$-0.139285\pi$
$619$	2.13756	+	3.70237i	0.0859159	+	0.148811i	−0.819865	+	0.572557i	$0.805952\pi$
$620$	−4.29113	+	18.4462i	−0.172336	+	0.740817i
$621$	−1.30913	+	2.26749i	−0.0525338	+	0.0909912i
$622$		−	18.8934i		−	0.757556i
$623$		0			0
$624$	5.88388			0.235544
$625$	9.51995	−	23.1165i	0.380798	−	0.924658i
$626$	−8.24245	−	14.2763i	−0.329434	−	0.570597i
$627$	−25.6183	+	14.7907i	−1.02310	+	0.590685i
$628$	6.99907	+	4.04092i	0.279293	+	0.161250i
$629$	−24.6538			−0.983011
$630$		0			0
$631$	36.8419			1.46665			0.733326	−	0.679878i	$-0.237967\pi$
$631$	36.8419			1.46665			0.733326	+	0.679878i	$0.237967\pi$
$632$	−6.04942	−	3.49264i	−0.240633	−	0.138930i
$633$	−4.79237	+	2.76687i	−0.190479	+	0.109973i
$634$	5.16053	+	8.93830i	0.204951	+	0.354985i
$635$	−4.28876	−	14.1122i	−0.170194	−	0.560027i
$636$	−1.38173			−0.0547892
$637$		0			0
$638$		−	36.5282i		−	1.44616i
$639$	1.01193	−	1.75271i	0.0400312	−	0.0693361i
$640$	−2.17791	−	0.506647i	−0.0860896	−	0.0200270i
$641$	−24.9521	−	43.2184i	−0.985551	−	1.70702i	−0.639464	−	0.768821i	$-0.720844\pi$
$641$	−24.9521	−	43.2184i	−0.985551	−	1.70702i	−0.346086	−	0.938203i	$-0.612490\pi$
$642$	9.54057	+	5.50825i	0.376536	+	0.217393i
$643$			29.0091i			1.14401i	0.820251	+	0.572004i	$0.193834\pi$
$643$			29.0091i			1.14401i	−0.820251	+	0.572004i	$0.806166\pi$
$644$		0			0
$645$	2.33668	+	2.18630i	0.0920066	+	0.0860855i
$646$	−25.5971	+	44.3354i	−1.00710	+	1.74435i
$647$	−4.28102	+	2.47165i	−0.168304	+	0.0971705i	−0.581786	−	0.813342i	$-0.697646\pi$
$647$	−4.28102	+	2.47165i	−0.168304	+	0.0971705i	0.413482	+	0.910512i	$0.364313\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−10.4237	+	18.0544i	−0.409167	+	0.708698i
$650$	1.95406	+	29.3544i	0.0766446	+	1.15138i
$651$		0			0
$652$		−	0.836668i		−	0.0327664i
$653$	8.14548	+	4.70279i	0.318757	+	0.184035i	0.650838	−	0.759216i	$-0.274418\pi$
$653$	8.14548	+	4.70279i	0.318757	+	0.184035i	−0.332081	+	0.943251i	$0.607751\pi$
$654$	2.34772	+	4.06637i	0.0918031	+	0.159008i
$655$	−1.17596	+	5.05507i	−0.0459486	+	0.197518i
$656$	1.78141	−	3.08549i	0.0695523	−	0.120468i
$657$		−	4.01687i		−	0.156713i
$658$		0			0
$659$	−13.4090			−0.522340			−0.261170	−	0.965293i	$-0.584108\pi$
$659$	−13.4090			−0.522340			−0.261170	+	0.965293i	$0.584108\pi$
$660$	2.90612	+	9.56264i	0.113121	+	0.372225i
$661$	6.62545	+	11.4756i	0.257700	+	0.446350i	0.965625	−	0.259938i	$-0.0837020\pi$
$661$	6.62545	+	11.4756i	0.257700	+	0.446350i	−0.707925	+	0.706287i	$0.750369\pi$
$662$	16.6195	−	9.59530i	0.645937	−	0.372932i
$663$	−39.4158	−	22.7567i	−1.53078	−	0.883798i
$664$	−5.35965			−0.207995
$665$		0			0
$666$	−3.18719			−0.123501
$667$	18.5310	+	10.6989i	0.717521	+	0.414261i
$668$	2.31023	−	1.33381i	0.0893854	−	0.0516067i
$669$	1.64124	+	2.84271i	0.0634540	+	0.109906i
$670$	3.96097	−	1.20375i	0.153026	−	0.0465051i
$671$	−43.7886			−1.69044
$672$		0			0
$673$		−	21.8236i		−	0.841237i	−0.907238	−	0.420619i	$-0.861813\pi$
$673$		−	21.8236i		−	0.841237i	0.907238	−	0.420619i	$-0.138187\pi$
$674$	−13.8018	+	23.9054i	−0.531624	+	0.920800i
$675$	2.78209	+	4.15451i	0.107083	+	0.159907i
$676$	−10.8100	−	18.7235i	−0.415770	−	0.720135i
$677$	35.5566	+	20.5286i	1.36655	+	0.788979i	0.990486	−	0.137614i	$-0.0439435\pi$
$677$	35.5566	+	20.5286i	1.36655	+	0.788979i	0.376065	+	0.926593i	$0.377277\pi$
$678$		−	12.5723i		−	0.482837i
$679$		0			0
$680$	12.6302	+	11.8174i	0.484346	+	0.453176i
$681$	−2.21016	+	3.82810i	−0.0846934	+	0.146693i
$682$	32.7848	−	18.9283i	1.25539	−	0.724802i
$683$	−26.9024	+	15.5321i	−1.02939	+	0.594320i	−0.916810	−	0.399323i	$-0.869245\pi$
$683$	−26.9024	+	15.5321i	−1.02939	+	0.594320i	−0.112581	+	0.993643i	$0.535912\pi$
$684$	−3.30913	+	5.73159i	−0.126528	+	0.219153i
$685$	−21.8085	+	23.3085i	−0.833259	+	0.890572i
$686$		0			0
$687$			7.97270i			0.304178i
$688$	1.23935	+	0.715541i	0.0472499	+	0.0272797i
$689$	4.06497	+	7.04073i	0.154863	+	0.268230i
$690$	−5.70237	−	1.32654i	−0.217085	−	0.0505005i
$691$	−16.0006	+	27.7139i	−0.608692	+	1.05429i	0.382764	+	0.923846i	$0.374972\pi$
$691$	−16.0006	+	27.7139i	−0.608692	+	1.05429i	−0.991456	+	0.130439i	$0.958361\pi$
$692$		−	0.647340i		−	0.0246082i
$693$		0			0
$694$	20.3761			0.773468
$695$	−32.0130	+	9.72888i	−1.21432	+	0.369037i
$696$	−4.08623	−	7.07756i	−0.154888	−	0.268274i
$697$	−23.8671	+	13.7797i	−0.904032	+	0.521943i
$698$	−15.4396	−	8.91403i	−0.584396	−	0.337401i
$699$	−17.9558			−0.679152
$700$		0			0
$701$	−45.4635			−1.71713			−0.858567	−	0.512701i	$-0.828645\pi$
$701$	−45.4635			−1.71713			−0.858567	+	0.512701i	$0.828645\pi$
$702$	−5.09559	−	2.94194i	−0.192321	−	0.111036i
$703$	18.2677	−	10.5468i	0.688978	−	0.397781i
$704$	2.23483	+	3.87084i	0.0842284	+	0.145888i
$705$	−14.5284	+	4.41525i	−0.547173	+	0.166288i
$706$	3.51347			0.132231
$707$		0			0
$708$			4.66421i			0.175292i
$709$	−23.8798	+	41.3611i	−0.896826	+	1.55335i	−0.0652969	+	0.997866i	$0.520799\pi$
$709$	−23.8798	+	41.3611i	−0.896826	+	1.55335i	−0.831529	+	0.555482i	$0.812534\pi$
$710$	4.40778	+	1.02538i	0.165421	+	0.0384819i
$711$	3.49264	+	6.04942i	0.130984	+	0.226871i
$712$	−12.4632	−	7.19562i	−0.467078	−	0.269667i
$713$			22.1759i			0.830493i
$714$		0			0
$715$	40.1776	−	42.9411i	1.50256	−	1.60591i
$716$	12.8687	−	22.2893i	0.480927	−	0.832989i
$717$	4.68776	−	2.70648i	0.175068	−	0.101075i
$718$	−1.90349	+	1.09898i	−0.0710374	+	0.0410135i
$719$	−6.58057	+	11.3979i	−0.245414	+	0.425069i	−0.962248	−	0.272175i	$-0.912257\pi$
$719$	−6.58057	+	11.3979i	−0.245414	+	0.425069i	0.716834	+	0.697244i	$0.245591\pi$
$720$	1.63280	+	1.52773i	0.0608510	+	0.0569350i
$721$		0			0
$722$		−	24.8015i		−	0.923016i
$723$	4.06745	+	2.34835i	0.151270	+	0.0873359i
$724$	−3.71123	−	6.42803i	−0.137927	−	0.238896i
$725$	33.9526	−	22.7365i	1.26097	−	0.844413i
$726$	4.48896	−	7.77510i	0.166601	−	0.288561i
$727$			8.17082i			0.303039i	0.988454	+	0.151519i	$0.0484166\pi$
$727$			8.17082i			0.303039i	−0.988454	+	0.151519i	$0.951583\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	8.59390	−	2.61172i	0.318074	−	0.0966640i
$731$	−5.53491	−	9.58674i	−0.204716	−	0.354578i
$732$	−8.48430	+	4.89841i	−0.313589	+	0.181051i
$733$	−1.74512	−	1.00755i	−0.0644576	−	0.0372146i	0.467425	−	0.884033i	$-0.345182\pi$
$733$	−1.74512	−	1.00755i	−0.0644576	−	0.0372146i	−0.531882	+	0.846818i	$0.678515\pi$
$734$	−28.7721			−1.06200
$735$		0			0
$736$	−2.61827			−0.0965107
$737$	−7.16647	−	4.13756i	−0.263980	−	0.152409i
$738$	−3.08549	+	1.78141i	−0.113578	+	0.0655746i
$739$	−1.91295	−	3.31333i	−0.0703690	−	0.121883i	0.828694	−	0.559702i	$-0.189084\pi$
$739$	−1.91295	−	3.31333i	−0.0703690	−	0.121883i	−0.899063	+	0.437819i	$0.855751\pi$
$740$	−2.07227	−	6.81884i	−0.0761781	−	0.250665i
$741$	38.9411			1.43054
$742$		0			0
$743$		−	36.6654i		−	1.34512i	−0.740041	−	0.672562i	$-0.765194\pi$
$743$		−	36.6654i		−	1.34512i	0.740041	−	0.672562i	$-0.234806\pi$
$744$	4.23483	−	7.33495i	0.155257	−	0.268912i
$745$	5.65677	−	24.3166i	0.207248	−	0.890893i
$746$	7.28446	+	12.6171i	0.266703	+	0.461943i
$747$	4.64159	+	2.67982i	0.169827	+	0.0980496i
$748$		−	34.5741i		−	1.26415i
$749$		0			0
$750$	−7.07950	+	8.65336i	−0.258507	+	0.315976i
$751$	10.2329	−	17.7238i	0.373402	−	0.646751i	−0.616684	−	0.787210i	$-0.711525\pi$
$751$	10.2329	−	17.7238i	0.373402	−	0.646751i	0.990086	+	0.140459i	$0.0448579\pi$
$752$	−5.88094	+	3.39536i	−0.214456	+	0.123816i
$753$	6.69786	−	3.86701i	0.244084	−	0.140922i
$754$	−24.0429	+	41.6435i	−0.875590	+	1.51657i
$755$	−1.08452	−	1.01473i	−0.0394698	−	0.0369298i
$756$		0			0
$757$			37.9575i			1.37959i	0.724006	+	0.689794i	$0.242299\pi$
$757$			37.9575i			1.37959i	−0.724006	+	0.689794i	$0.757701\pi$
$758$	26.6621	+	15.3934i	0.968412	+	0.559113i
$759$	5.85140	+	10.1349i	0.212392	+	0.367874i
$760$	−14.4140	−	3.35313i	−0.522852	−	0.121631i
$761$	−17.3065	+	29.9758i	−0.627361	+	1.08662i	0.360718	+	0.932675i	$0.382532\pi$
$761$	−17.3065	+	29.9758i	−0.627361	+	1.08662i	−0.988079	+	0.153946i	$0.950802\pi$
$762$			6.59619i			0.238955i
$763$		0			0
$764$	1.08452			0.0392367
$765$	−5.02938	−	16.5493i	−0.181838	−	0.598340i
$766$	−11.6705	−	20.2139i	−0.421672	−	0.730357i
$767$	23.7669	−	13.7218i	0.858173	−	0.495466i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−1.48961			−0.0537167			−0.0268584	−	0.999639i	$-0.508550\pi$
$769$	−1.48961			−0.0537167			−0.0268584	+	0.999639i	$0.508550\pi$
$770$		0			0
$771$	−1.34442			−0.0484181
$772$	7.74169	+	4.46967i	0.278629	+	0.160867i
$773$	−0.859321	+	0.496129i	−0.0309076	+	0.0178445i	−0.515374	−	0.856965i	$-0.672347\pi$
$773$	−0.859321	+	0.496129i	−0.0309076	+	0.0178445i	0.484467	+	0.874810i	$0.339014\pi$
$774$	−0.715541	−	1.23935i	−0.0257196	−	0.0445476i
$775$	38.0001	+	18.6914i	1.36501	+	0.671416i
$776$	−7.71966			−0.277120
$777$		0			0
$778$		−	1.21842i		−	0.0436824i
$779$	11.7898	−	20.4206i	0.422415	−	0.731644i
$780$	2.98105	−	12.8146i	0.106739	−	0.458836i
$781$	−4.52298	−	7.83403i	−0.161845	−	0.280324i
$782$	17.5396	+	10.1265i	0.627217	+	0.362124i
$783$			8.17246i			0.292060i
$784$		0			0
$785$	12.3468	−	13.1961i	0.440677	−	0.470988i
$786$	1.16053	−	2.01010i	0.0413948	−	0.0716979i
$787$	−8.87786	+	5.12563i	−0.316461	+	0.182709i	−0.649814	−	0.760093i	$-0.725153\pi$
$787$	−8.87786	+	5.12563i	−0.316461	+	0.182709i	0.333353	+	0.942802i	$0.391820\pi$
$788$	6.45960	−	3.72945i	0.230114	−	0.132856i
$789$	−2.18350	+	3.78193i	−0.0777347	+	0.134640i
$790$	−10.6716	+	11.4056i	−0.379678	+	0.405793i
$791$		0			0
$792$		−	4.46967i		−	0.158823i
$793$	49.9206	+	28.8217i	1.77273	+	1.02349i
$794$	4.20298	+	7.27977i	0.149158	+	0.258349i
$795$	−0.700050	+	3.00929i	−0.0248282	+	0.106728i
$796$	12.9147	−	22.3688i	0.457748	−	0.792843i
$797$		−	32.6811i		−	1.15762i	−0.815461	−	0.578812i	$-0.803517\pi$
$797$		−	32.6811i		−	1.15762i	0.815461	−	0.578812i	$-0.196483\pi$
$798$		0			0
$799$	52.5282			1.85831
$800$	−2.20687	+	4.48662i	−0.0780246	+	0.158626i
$801$	7.19562	+	12.4632i	0.254245	+	0.440365i
$802$	0.575221	−	0.332104i	0.0203118	−	0.0117270i
$803$	−15.5487	−	8.97703i	−0.548701	−	0.316793i
$804$	−1.85140			−0.0652937
$805$		0			0
$806$	−49.8345			−1.75535
$807$	19.9767	+	11.5336i	0.703213	+	0.406000i
$808$	11.5653	−	6.67722i	0.406865	−	0.234904i
$809$	11.2258	+	19.4436i	0.394677	+	0.683601i	0.993060	−	0.117610i	$-0.0375231\pi$
$809$	11.2258	+	19.4436i	0.394677	+	0.683601i	−0.598383	+	0.801210i	$0.704190\pi$
$810$	−0.650187	−	2.13945i	−0.0228453	−	0.0751727i
$811$	−37.6581			−1.32235			−0.661177	−	0.750230i	$-0.729943\pi$
$811$	−37.6581			−1.32235			−0.661177	+	0.750230i	$0.729943\pi$
$812$		0			0
$813$			14.7209i			0.516286i
$814$	−7.12283	+	12.3371i	−0.249655	+	0.432415i
$815$	−1.82219	−	0.423895i	−0.0638285	−	0.0148484i
$816$	−3.86764	−	6.69895i	−0.135394	−	0.234510i
$817$	8.20237	+	4.73564i	0.286965	+	0.165679i
$818$			7.38476i			0.258202i
$819$		0			0
$820$	−5.81739	−	5.44301i	−0.203152	−	0.190078i
$821$	10.7419	−	18.6056i	0.374896	−	0.649338i	−0.615416	−	0.788203i	$-0.711012\pi$
$821$	10.7419	−	18.6056i	0.374896	−	0.649338i	0.990311	+	0.138864i	$0.0443452\pi$
$822$	12.3626	−	7.13756i	0.431196	−	0.248951i
$823$	16.1190	−	9.30633i	0.561875	−	0.324398i	−0.192023	−	0.981390i	$-0.561505\pi$
$823$	16.1190	−	9.30633i	0.561875	−	0.324398i	0.753898	+	0.656992i	$0.228171\pi$
$824$	−4.67982	+	8.10569i	−0.163029	+	0.282375i
$825$	22.2990	−	1.48440i	0.776351	−	0.0516800i
$826$		0			0
$827$		−	18.4254i		−	0.640713i	−0.947297	−	0.320356i	$-0.896197\pi$
$827$		−	18.4254i		−	0.640713i	0.947297	−	0.320356i	$-0.103803\pi$
$828$	2.26749	+	1.30913i	0.0788007	+	0.0454956i
$829$	−16.0188	−	27.7454i	−0.556357	−	0.963639i	−0.997797	−	0.0663478i	$-0.978865\pi$
$829$	−16.0188	−	27.7454i	−0.556357	−	0.963639i	0.441439	−	0.897291i	$-0.354468\pi$
$830$	−2.71545	+	11.6728i	−0.0942547	+	0.405171i
$831$	1.60552	−	2.78085i	0.0556949	−	0.0964665i
$832$		−	5.88388i		−	0.203987i
$833$		0			0
$834$	14.9632			0.518133
$835$	−1.73445	−	5.70725i	−0.0600233	−	0.197508i
$836$	14.7907	+	25.6183i	0.511548	+	0.886027i
$837$	−7.33495	+	4.23483i	−0.253533	+	0.146377i
$838$	16.1318	+	9.31371i	0.557264	+	0.321737i
$839$	8.45154			0.291780			0.145890	−	0.989301i	$-0.453395\pi$
$839$	8.45154			0.291780			0.145890	+	0.989301i	$0.453395\pi$
$840$		0			0
$841$	37.7891			1.30307
$842$	−11.6951	−	6.75214i	−0.403038	−	0.232694i
$843$	6.68994	−	3.86244i	0.230414	−	0.133029i
$844$	2.76687	+	4.79237i	0.0952397	+	0.164960i
$845$	−46.2551	+	14.0571i	−1.59122	+	0.483578i
$846$	6.79073			0.233470
$847$		0			0
$848$			1.38173i			0.0474488i
$849$	14.7797	−	25.5992i	0.507238	−	0.878561i
$850$	32.1363	−	21.5202i	1.10227	−	0.738138i
$851$	−4.17246	−	7.22691i	−0.143030	−	0.247735i
$852$	−1.75271	−	1.01193i	−0.0600469	−	0.0346681i
$853$			50.6270i			1.73344i	0.498798	+	0.866718i	$0.333775\pi$
$853$			50.6270i			1.73344i	−0.498798	+	0.866718i	$0.666225\pi$
$854$		0			0
$855$	10.8063	+	10.1109i	0.369569	+	0.345786i
$856$	5.50825	−	9.54057i	0.188268	−	0.326090i
$857$	−10.3934	+	6.00063i	−0.355031	+	0.204978i	−0.666899	−	0.745148i	$-0.732379\pi$
$857$	−10.3934	+	6.00063i	−0.355031	+	0.204978i	0.311868	+	0.950126i	$0.399045\pi$
$858$	−22.7756	+	13.1495i	−0.777546	+	0.448916i
$859$	17.8560	−	30.9274i	0.609238	−	1.05523i	−0.382128	−	0.924109i	$-0.624809\pi$
$859$	17.8560	−	30.9274i	0.609238	−	1.05523i	0.991366	−	0.131122i	$-0.0418579\pi$
$860$	2.18630	−	2.33668i	0.0745523	−	0.0796801i
$861$		0			0
$862$			31.6807i			1.07905i
$863$	1.11219	+	0.642125i	0.0378595	+	0.0218582i	0.518810	−	0.854889i	$-0.326375\pi$
$863$	1.11219	+	0.642125i	0.0378595	+	0.0218582i	−0.480951	+	0.876748i	$0.659708\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−1.40985	−	0.327973i	−0.0479364	−	0.0111514i
$866$	−12.6592	+	21.9264i	−0.430177	+	0.745088i
$867$			42.8345i			1.45474i
$868$		0			0
$869$	31.2218			1.05913
$870$	−17.4846	+	5.31363i	−0.592783	+	0.180149i
$871$	5.44670	+	9.43396i	0.184554	+	0.319657i
$872$	4.06637	−	2.34772i	0.137705	−	0.0795038i
$873$	6.68542	+	3.85983i	0.226267	+	0.130635i
$874$	−17.3284			−0.586142
$875$		0			0
$876$	−4.01687			−0.135717
$877$	33.2122	+	19.1751i	1.12150	+	0.647496i	0.941782	−	0.336224i	$-0.109150\pi$
$877$	33.2122	+	19.1751i	1.12150	+	0.647496i	0.179713	+	0.983719i	$0.442483\pi$
$878$	−28.4183	+	16.4073i	−0.959070	+	0.553719i
$879$	−0.588394	−	1.01913i	−0.0198460	−	0.0343743i
$880$	9.56264	−	2.90612i	0.322356	−	0.0979653i
$881$	−0.389472			−0.0131216			−0.00656082	−	0.999978i	$-0.502088\pi$
$881$	−0.389472			−0.0131216			−0.00656082	+	0.999978i	$0.502088\pi$
$882$		0			0
$883$		−	18.5412i		−	0.623962i	−0.950088	−	0.311981i	$-0.899007\pi$
$883$		−	18.5412i		−	0.623962i	0.950088	−	0.311981i	$-0.100993\pi$
$884$	−22.7567	+	39.4158i	−0.765391	+	1.32570i
$885$	10.1582	+	2.36311i	0.341466	+	0.0794350i
$886$	−8.32106	−	14.4125i	−0.279552	−	0.484198i
$887$	36.7893	+	21.2403i	1.23526	+	0.713179i	0.968122	−	0.250478i	$-0.0805879\pi$
$887$	36.7893	+	21.2403i	1.23526	+	0.713179i	0.267140	+	0.963658i	$0.413921\pi$
$888$			3.18719i			0.106955i
$889$		0			0
$890$	−21.9859	+	23.4981i	−0.736968	+	0.787658i
$891$	−2.23483	+	3.87084i	−0.0748697	+	0.129678i
$892$	2.84271	−	1.64124i	0.0951810	−	0.0549528i
$893$	−38.9217	+	22.4714i	−1.30246	+	0.751978i
$894$	−5.58255	+	9.66926i	−0.186708	+	0.323389i
$895$	−42.0242	−	39.3198i	−1.40471	−	1.31431i
$896$		0			0
$897$		−	15.4056i		−	0.514378i
$898$	−17.4728	−	10.0879i	−0.583075	−	0.336639i
$899$	34.6090	+	59.9445i	1.15427	+	1.99926i
$900$	4.15451	−	2.78209i	0.138484	−	0.0927363i
$901$	5.34403	−	9.25613i	0.178036	−	0.308367i
$902$			15.9246i			0.530231i
$903$		0			0
$904$	−12.5723			−0.418150
$905$	−15.8800	+	4.82599i	−0.527869	+	0.160421i
$906$	0.332104	+	0.575221i	0.0110334	+	0.0191105i
$907$	35.6531	−	20.5843i	1.18384	−	0.683491i	0.226941	−	0.973908i	$-0.427127\pi$
$907$	35.6531	−	20.5843i	1.18384	−	0.683491i	0.956900	+	0.290417i	$0.0937940\pi$
$908$	3.82810	+	2.21016i	0.127040	+	0.0733466i
$909$	−13.3544			−0.442939
$910$		0			0
$911$	−25.1703			−0.833929			−0.416964	−	0.908923i	$-0.636906\pi$
$911$	−25.1703			−0.833929			−0.416964	+	0.908923i	$0.636906\pi$
$912$	5.73159	+	3.30913i	0.189792	+	0.109576i
$913$	20.7464	−	11.9779i	0.686604	−	0.396411i
$914$	−17.7062	−	30.6680i	−0.585669	−	1.01441i
$915$	6.36978	+	20.9599i	0.210578	+	0.692911i
$916$	7.97270			0.263426
$917$		0			0
$918$			7.73528i			0.255302i
$919$	−2.51841	+	4.36201i	−0.0830745	+	0.143889i	−0.904569	−	0.426327i	$-0.859807\pi$
$919$	−2.51841	+	4.36201i	−0.0830745	+	0.143889i	0.821495	+	0.570216i	$0.193141\pi$
$920$	−1.32654	+	5.70237i	−0.0437347	+	0.188001i
$921$	10.1881	+	17.6463i	0.335708	+	0.581464i
$922$	10.9067	+	6.29701i	0.359195	+	0.207381i
$923$			11.9081i			0.391961i
$924$		0			0
$925$	−15.9007	+	1.05848i	−0.522813	+	0.0348026i
$926$	−16.2530	+	28.1511i	−0.534108	+	0.925102i
$927$	8.10569	−	4.67982i	0.266226	−	0.153706i
$928$	−7.07756	+	4.08623i	−0.232332	+	0.134137i
$929$	7.14231	−	12.3708i	0.234332	−	0.405874i	−0.724747	−	0.689015i	$-0.758043\pi$
$929$	7.14231	−	12.3708i	0.234332	−	0.405874i	0.959078	+	0.283141i	$0.0913765\pi$
$930$	−13.8293	−	12.9393i	−0.453481	−	0.424297i
$931$		0			0
$932$			17.9558i			0.588163i
$933$	16.3622	+	9.44670i	0.535673	+	0.309271i
$934$	−4.60265	−	7.97203i	−0.150603	−	0.260853i
$935$	−75.2994	−	17.5169i	−2.46255	−	0.572863i
$936$	−2.94194	+	5.09559i	−0.0961603	+	0.166555i
$937$		−	19.8403i		−	0.648153i	−0.946031	−	0.324077i	$-0.894946\pi$
$937$		−	19.8403i		−	0.648153i	0.946031	−	0.324077i	$-0.105054\pi$
$938$		0			0
$939$	16.4849			0.537964
$940$	4.41525	+	14.5284i	0.144009	+	0.473866i
$941$	7.95271	+	13.7745i	0.259251	+	0.449036i	0.966041	−	0.258387i	$-0.0831910\pi$
$941$	7.95271	+	13.7745i	0.259251	+	0.449036i	−0.706791	+	0.707423i	$0.749858\pi$
$942$	−6.99907	+	4.04092i	−0.228042	+	0.131660i
$943$	−8.07865	−	4.66421i	−0.263077	−	0.151888i
$944$	4.66421			0.151807
$945$		0			0
$946$	−6.39646			−0.207967
$947$	8.27760	+	4.77908i	0.268986	+	0.155299i	0.628427	−	0.777869i	$-0.283699\pi$
$947$	8.27760	+	4.77908i	0.268986	+	0.155299i	−0.359441	+	0.933168i	$0.617033\pi$
$948$	6.04942	−	3.49264i	0.196476	−	0.113436i
$949$	11.8174	+	20.4683i	0.383609	+	0.664430i
$950$	−14.6057	+	29.6936i	−0.473870	+	0.963389i
$951$	−10.3211			−0.334683
$952$		0			0
$953$			23.7505i			0.769354i	0.923051	+	0.384677i	$0.125687\pi$
$953$			23.7505i			0.769354i	−0.923051	+	0.384677i	$0.874313\pi$
$954$	0.690865	−	1.19661i	0.0223676	−	0.0387418i
$955$	0.549471	−	2.36200i	0.0177805	−	0.0764324i
$956$	−2.70648	−	4.68776i	−0.0875338	−	0.151613i
$957$	31.6343	+	18.2641i	1.02259	+	0.590394i
$958$			39.4914i			1.27591i
$959$		0			0
$960$	1.52773	−	1.63280i	0.0493072	−	0.0526986i
$961$	−20.3676	+	35.2778i	−0.657020	+	1.13799i
$962$	16.2406	−	9.37652i	0.523618	−	0.302311i
$963$	−9.54057	+	5.50825i	−0.307441	+	0.177501i
$964$	2.34835	−	4.06745i	0.0756351	−	0.131004i
$965$	13.6569	−	14.5962i	0.439630	−	0.469868i
$966$		0			0
$967$			56.9706i			1.83205i	0.401121	+	0.916025i	$0.368621\pi$
$967$			56.9706i			1.83205i	−0.401121	+	0.916025i	$0.631379\pi$
$968$	−7.77510	−	4.48896i	−0.249901	−	0.144281i
$969$	−25.5971	−	44.3354i	−0.822296	−	1.42426i
$970$	−3.91115	+	16.8128i	−0.125579	+	0.539825i
$971$	16.5429	−	28.6531i	0.530886	−	0.919522i	−0.468464	−	0.883482i	$-0.655193\pi$
$971$	16.5429	−	28.6531i	0.530886	−	0.919522i	0.999350	−	0.0360392i	$-0.0114741\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$	29.2678			0.937800
$975$	−26.3987	−	12.9849i	−0.845435	−	0.415851i
$976$	4.89841	+	8.48430i	0.156794	+	0.271576i
$977$	21.3152	−	12.3063i	0.681934	−	0.393715i	−0.118650	−	0.992936i	$-0.537857\pi$
$977$	21.3152	−	12.3063i	0.681934	−	0.393715i	0.800583	+	0.599222i	$0.204523\pi$
$978$	0.724575	+	0.418334i	0.0231694	+	0.0133768i
$979$	64.3241			2.05581
$980$		0			0
$981$	−4.69544			−0.149914
$982$	13.3048	+	7.68153i	0.424573	+	0.245127i
$983$	−36.7893	+	21.2403i	−1.17340	+	0.677460i	−0.954477	−	0.298283i	$-0.903586\pi$
$983$	−36.7893	+	21.2403i	−1.17340	+	0.677460i	−0.218918	+	0.975743i	$0.570253\pi$
$984$	1.78141	+	3.08549i	0.0567892	+	0.0983618i
$985$	−4.84968	−	15.9580i	−0.154524	−	0.508463i
$986$	63.2162			2.01321
$987$		0			0
$988$		−	38.9411i		−	1.23888i
$989$	1.87348	−	3.24496i	0.0595732	−	0.103184i
$990$	−9.73455	−	2.26454i	−0.309384	−	0.0719720i
$991$	0.419154	+	0.725996i	0.0133149	+	0.0230620i	0.872606	−	0.488425i	$-0.162428\pi$
$991$	0.419154	+	0.725996i	0.0133149	+	0.0230620i	−0.859291	+	0.511487i	$0.829095\pi$
$992$	−7.33495	−	4.23483i	−0.232885	−	0.134456i
$993$			19.1906i			0.608995i
$994$		0			0
$995$	−42.1742	−	39.4601i	−1.33701	−	1.25097i
$996$	2.67982	−	4.64159i	0.0849135	−	0.147074i
$997$	−27.3612	+	15.7970i	−0.866539	+	0.500297i	−0.866197	−	0.499703i	$-0.833442\pi$
$997$	−27.3612	+	15.7970i	−0.866539	+	0.500297i	−0.000342701		1.00000i	$0.500109\pi$
$998$	17.7970	−	10.2751i	0.563355	−	0.325253i
$999$	1.59359	−	2.76019i	0.0504191	−	0.0873284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.n.l.79.8		16
5.4	even	2	inner	1470.2.n.l.79.2		16
7.2	even	3		1470.2.g.j.589.2	✓	8
7.3	odd	6		1470.2.n.k.949.3		16
7.4	even	3	inner	1470.2.n.l.949.2		16
7.5	odd	6		1470.2.g.k.589.3	yes	8
7.6	odd	2		1470.2.n.k.79.5		16
35.2	odd	12		7350.2.a.dt.1.4		4
35.4	even	6	inner	1470.2.n.l.949.8		16
35.9	even	6		1470.2.g.j.589.6	yes	8
35.12	even	12		7350.2.a.du.1.4		4
35.19	odd	6		1470.2.g.k.589.7	yes	8
35.23	odd	12		7350.2.a.ds.1.4		4
35.24	odd	6		1470.2.n.k.949.5		16
35.33	even	12		7350.2.a.dr.1.4		4
35.34	odd	2		1470.2.n.k.79.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1470.2.g.j.589.2	✓	8	7.2	even	3
1470.2.g.j.589.6	yes	8	35.9	even	6
1470.2.g.k.589.3	yes	8	7.5	odd	6
1470.2.g.k.589.7	yes	8	35.19	odd	6
1470.2.n.k.79.3		16	35.34	odd	2
1470.2.n.k.79.5		16	7.6	odd	2
1470.2.n.k.949.3		16	7.3	odd	6
1470.2.n.k.949.5		16	35.24	odd	6
1470.2.n.l.79.2		16	5.4	even	2	inner
1470.2.n.l.79.8		16	1.1	even	1	trivial
1470.2.n.l.949.2		16	7.4	even	3	inner
1470.2.n.l.949.8		16	35.4	even	6	inner
7350.2.a.dr.1.4		4	35.33	even	12
7350.2.a.ds.1.4		4	35.23	odd	12
7350.2.a.dt.1.4		4	35.2	odd	12
7350.2.a.du.1.4		4	35.12	even	12

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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.13945 - 0.650187i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.13945 - 0.650187i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(2.17791 + 0.506647i) q^{10} +(-2.23483 - 3.87084i) q^{11} +(-0.866025 - 0.500000i) q^{12} +5.88388i q^{13} +(-1.52773 + 1.63280i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.69895 - 3.86764i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.30913 + 5.73159i) q^{19} +(1.63280 + 1.52773i) q^{20} -4.46967i q^{22} +(2.26749 + 1.30913i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.15451 - 2.78209i) q^{25} +(-2.94194 + 5.09559i) q^{26} +1.00000i q^{27} +8.17246 q^{29} +(-2.13945 + 0.650187i) q^{30} +(4.23483 + 7.33495i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.87084 + 2.23483i) q^{33} +7.73528 q^{34} +1.00000 q^{36} +(-2.76019 - 1.59359i) q^{37} +(-5.73159 + 3.30913i) q^{38} +(-2.94194 - 5.09559i) q^{39} +(0.650187 + 2.13945i) q^{40} -3.56282 q^{41} -1.43108i q^{43} +(2.23483 - 3.87084i) q^{44} +(0.506647 - 2.17791i) q^{45} +(1.30913 + 2.26749i) q^{46} +(5.88094 + 3.39536i) q^{47} -1.00000i q^{48} +(4.98896 - 0.332104i) q^{50} +(-3.86764 + 6.69895i) q^{51} +(-5.09559 + 2.94194i) q^{52} +(1.19661 - 0.690865i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-7.29809 - 6.82843i) q^{55} -6.61827i q^{57} +(7.07756 + 4.08623i) q^{58} +(-2.33210 - 4.03932i) q^{59} +(-2.17791 - 0.506647i) q^{60} +(4.89841 - 8.48430i) q^{61} +8.46967i q^{62} -1.00000 q^{64} +(3.82562 + 12.5883i) q^{65} +(2.23483 + 3.87084i) q^{66} +(1.60336 - 0.925698i) q^{67} +(6.69895 + 3.86764i) q^{68} -2.61827 q^{69} +2.02386 q^{71} +(0.866025 + 0.500000i) q^{72} +(3.47871 - 2.00843i) q^{73} +(-1.59359 - 2.76019i) q^{74} +(-2.20687 + 4.48662i) q^{75} -6.61827 q^{76} -5.88388i q^{78} +(-3.49264 + 6.04942i) q^{79} +(-0.506647 + 2.17791i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.08549 - 1.78141i) q^{82} +5.35965i q^{83} +(11.8174 - 12.6302i) q^{85} +(0.715541 - 1.23935i) q^{86} +(-7.07756 + 4.08623i) q^{87} +(3.87084 - 2.23483i) q^{88} +(-7.19562 + 12.4632i) q^{89} +(1.52773 - 1.63280i) q^{90} +2.61827i q^{92} +(-7.33495 - 4.23483i) q^{93} +(3.39536 + 5.88094i) q^{94} +(-3.35313 + 14.4140i) q^{95} +(0.500000 - 0.866025i) q^{96} +7.71966i q^{97} -4.46967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9	\( 16 q + 8 q^{4} + 4 q^{5} - 16 q^{6} + 8 q^{9} - 8 q^{16} - 24 q^{19} + 8 q^{20} - 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} + 32 q^{31} + 16 q^{34} + 16 q^{36} - 48 q^{41} - 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} - 8 q^{54} - 40 q^{59} + 24 q^{61} - 16 q^{64} - 28 q^{65} + 16 q^{69} - 80 q^{71} - 16 q^{74} + 4 q^{75} - 48 q^{76} - 16 q^{79} + 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} - 88 q^{89} - 24 q^{94} - 24 q^{95} + 8 q^{96}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^5 - 16 * q^6 + 8 * q^9 - 8 * q^16 - 24 * q^19 + 8 * q^20 - 8 * q^24 - 4 * q^25 + 32 * q^29 - 4 * q^30 + 32 * q^31 + 16 * q^34 + 16 * q^36 - 48 * q^41 - 4 * q^45 - 8 * q^46 - 8 * q^50 - 8 * q^51 - 8 * q^54 - 40 * q^59 + 24 * q^61 - 16 * q^64 - 28 * q^65 + 16 * q^69 - 80 * q^71 - 16 * q^74 + 4 * q^75 - 48 * q^76 - 16 * q^79 + 4 * q^80 - 8 * q^81 + 56 * q^85 - 8 * q^86 - 88 * q^89 - 24 * q^94 - 24 * q^95 + 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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