LMFDB - Embedded newform 1470.2.n.l.79.2

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			79.2
Root			$-2.73710 - 1.58027i$ of defining polynomial
Character	$\chi$	$=$	1470.79
Dual form			1470.2.n.l.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.506647 - 2.17791i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.506647 - 2.17791i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.650187 + 2.13945i) 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} +(-4.48662 + 2.20687i) q^{25} +(-2.94194 + 5.09559i) q^{26} -1.00000i q^{27} +8.17246 q^{29} +(0.506647 + 2.17791i) 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} +(-2.17791 + 0.506647i) q^{40} -3.56282 q^{41} +1.43108i q^{43} +(2.23483 - 3.87084i) q^{44} +(-2.13945 - 0.650187i) 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} +(0.650187 - 2.13945i) q^{60} +(4.89841 - 8.48430i) q^{61} -8.46967i q^{62} -1.00000 q^{64} +(-12.8146 + 2.98105i) 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} +(-2.78209 + 4.15451i) q^{75} -6.61827 q^{76} +5.88388i q^{78} +(-3.49264 + 6.04942i) q^{79} +(2.13945 + 0.650187i) 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} +(14.1595 + 4.30312i) 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
$5$	−0.506647	−	2.17791i	−0.226580	−	0.973993i
$5$	−0.506647	−	2.17791i	−0.226580	−	0.973993i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−0.650187	+	2.13945i	−0.205607	+	0.676554i
$11$	−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	$-0.696216\pi$
$13$		−	5.88388i		−	1.63189i	0.578126	−	0.815947i	$-0.303784\pi$
$14$		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	$0.720694\pi$
$17$	−6.69895	+	3.86764i	−1.62473	+	0.938040i	−0.985630	+	0.168919i	$0.945972\pi$
$18$	−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	0.244609	−	0.969622i	$-0.421340\pi$
$23$	−2.26749	−	1.30913i	−0.472804	−	0.272974i	−0.717413	+	0.696648i	$0.754674\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−4.48662	+	2.20687i	−0.897323	+	0.441374i
$26$	−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	$0.225789\pi$
$30$	0.506647	+	2.17791i	0.0925007	+	0.397631i
$31$	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	0.709422	−	0.704784i	$-0.248956\pi$
$37$	2.76019	+	1.59359i	0.453772	+	0.261985i	−0.255650	+	0.966769i	$0.582289\pi$
$38$	5.73159	−	3.30913i	0.929787	−	0.536813i
$39$	−2.94194	−	5.09559i	−0.471087	−	0.815947i
$40$	−2.17791	+	0.506647i	−0.344358	+	0.0801080i
$41$	−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	$0.0348029\pi$
$43$			1.43108i			0.218238i	−0.994029	+	0.109119i	$0.965197\pi$
$44$	2.23483	−	3.87084i	0.336914	−	0.583552i
$45$	−2.13945	−	0.650187i	−0.318931	−	0.0969242i
$46$	1.30913	+	2.26749i	0.193021	+	0.334323i
$47$	−5.88094	−	3.39536i	−0.857824	−	0.495265i	0.00545912	−	0.999985i	$-0.498262\pi$
$47$	−5.88094	−	3.39536i	−0.857824	−	0.495265i	−0.863283	+	0.504720i	$0.831596\pi$
$48$			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	−0.579927	−	0.814668i	$-0.696919\pi$
$53$	−1.19661	+	0.690865i	−0.164367	+	0.0948976i	0.415560	+	0.909566i	$0.363586\pi$
$54$	−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	$0.931527\pi$
$60$	0.650187	−	2.13945i	0.0839388	−	0.276202i
$61$	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
$65$	−12.8146	+	2.98105i	−1.58945	+	0.369754i
$66$	2.23483	+	3.87084i	0.275089	+	0.476468i
$67$	−1.60336	+	0.925698i	−0.195881	+	0.113092i	−0.594733	−	0.803923i	$-0.702742\pi$
$67$	−1.60336	+	0.925698i	−0.195881	+	0.113092i	0.398852	+	0.917015i	$0.369409\pi$
$68$	−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	−0.689565	−	0.724223i	$-0.742198\pi$
$73$	−3.47871	+	2.00843i	−0.407152	+	0.235069i	0.282413	+	0.959293i	$0.408865\pi$
$74$	−1.59359	−	2.76019i	−0.185252	−	0.320865i
$75$	−2.78209	+	4.15451i	−0.321248	+	0.479722i
$76$	−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	$0.295213\pi$
$80$	2.13945	+	0.650187i	0.239198	+	0.0726932i
$81$	−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	$-0.904964\pi$
$83$		−	5.35965i		−	0.588298i	0.955760	−	0.294149i	$-0.0950361\pi$
$84$		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
$95$	14.1595	+	4.30312i	1.45273	+	0.441490i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	7.71966i		−	0.783813i	−0.920005	−	0.391906i	$-0.871816\pi$
$97$		−	7.71966i		−	0.783813i	0.920005	−	0.391906i	$-0.128184\pi$
$98$		0			0
$99$	−4.46967			−0.449218
$100$	−4.15451	−	2.78209i	−0.415451	−	0.278209i
$101$	−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	0.0443310	−	0.999017i	$-0.485884\pi$
$103$	−8.10569	−	4.67982i	−0.798678	−	0.461117i	−0.843009	+	0.537900i	$0.819218\pi$
$104$	−5.88388			−0.576962
$105$		0			0
$106$	1.38173			0.134205
$107$	9.54057	+	5.50825i	0.922322	+	0.532503i	0.884375	−	0.466777i	$-0.154585\pi$
$107$	9.54057	+	5.50825i	0.922322	+	0.532503i	0.0379467	+	0.999280i	$0.487918\pi$
$108$	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	$0.905529\pi$
$110$	9.73455	−	2.26454i	0.928153	−	0.215916i
$111$	3.18719			0.302514
$112$		0			0
$113$		−	12.5723i		−	1.18271i	−0.806413	−	0.591353i	$-0.798594\pi$
$113$		−	12.5723i		−	1.18271i	0.806413	−	0.591353i	$-0.201406\pi$
$114$	3.30913	−	5.73159i	0.309929	−	0.536813i
$115$	−1.70237	+	5.60166i	−0.158746	+	0.522358i
$116$	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	$0.0945399\pi$
$127$			6.59619i			0.585317i	−0.956217	+	0.292658i	$0.905460\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	0.715541	+	1.23935i	0.0629999	+	0.109119i
$130$	12.5883	+	3.82562i	1.10407	+	0.335529i
$131$	−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
$135$	−2.17791	+	0.506647i	−0.187445	+	0.0436053i
$136$	3.86764	+	6.69895i	0.331647	+	0.574430i
$137$	12.3626	−	7.13756i	1.05621	−	0.609803i	0.131828	−	0.991273i	$-0.457915\pi$
$137$	12.3626	−	7.13756i	1.05621	−	0.609803i	0.924381	+	0.381469i	$0.124582\pi$
$138$	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
$145$	−4.14055	−	17.7989i	−0.343854	−	1.47812i
$146$	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	$0.0154687\pi$
$150$	4.48662	−	2.20687i	0.366331	−	0.180190i
$151$	−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	−0.752578	−	0.658503i	$-0.771190\pi$
$157$	−6.99907	+	4.04092i	−0.558587	+	0.322500i	0.193991	+	0.981003i	$0.437857\pi$
$158$	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	0.528108	−	0.849177i	$-0.322902\pi$
$163$	0.724575	+	0.418334i	0.0567531	+	0.0327664i	−0.471355	+	0.881944i	$0.656235\pi$
$164$	−1.78141	−	3.08549i	−0.139105	−	0.240936i
$165$	−2.90612	+	9.56264i	−0.226241	+	0.744450i
$166$	−2.67982	+	4.64159i	−0.207995	+	0.360257i
$167$			2.66762i			0.206427i	0.994659	+	0.103213i	$0.0329125\pi$
$167$			2.66762i			0.206427i	−0.994659	+	0.103213i	$0.967088\pi$
$168$		0			0
$169$	−21.6200			−1.66308
$170$	−3.91906	−	16.8468i	−0.300578	−	1.29209i
$171$	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	0.521160	−	0.853459i	$-0.325500\pi$
$173$	0.560613	+	0.323670i	0.0426226	+	0.0246082i	−0.478537	+	0.878067i	$0.658833\pi$
$174$	−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	$-0.578463\pi$
$180$	−0.506647	−	2.17791i	−0.0377633	−	0.162332i
$181$	−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
$185$	2.07227	−	6.81884i	0.152356	−	0.501331i
$186$	−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	−0.752045	−	0.659112i	$-0.770932\pi$
$193$	−7.74169	+	4.46967i	−0.557259	+	0.321734i	0.194786	+	0.980846i	$0.437599\pi$
$194$	−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	$0.0856071\pi$
$197$			7.45890i			0.531425i	−0.964052	+	0.265712i	$0.914393\pi$
$198$	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	$-0.534868\pi$
$200$	2.20687	+	4.48662i	0.156049	+	0.317252i
$201$	−0.925698	+	1.60336i	−0.0652937	+	0.113092i
$202$			13.3544i			0.939615i
$203$		0			0
$204$	−7.73528			−0.541578
$205$	1.80509	+	7.75951i	0.126073	+	0.541948i
$206$	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
$215$	3.11677	−	0.725054i	0.212562	−	0.0494483i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$			4.69544i			0.318015i
$219$	−2.00843	+	3.47871i	−0.135717	+	0.235069i
$220$	−9.56264	−	2.90612i	−0.644713	−	0.195931i
$221$	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	$0.0350548\pi$
$223$			3.28248i			0.219811i	−0.993942	+	0.109906i	$0.964945\pi$
$224$		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	−0.621631	−	0.783310i	$-0.713530\pi$
$227$	−3.82810	+	2.21016i	−0.254080	+	0.146693i	0.367551	+	0.930003i	$0.380196\pi$
$228$	−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	−0.104993	−	0.994473i	$-0.533482\pi$
$233$	−15.5502	−	8.97792i	−1.01873	−	0.588163i	−0.913735	+	0.406310i	$0.866815\pi$
$234$	2.94194	+	5.09559i	0.192321	+	0.333109i
$235$	−4.41525	+	14.5284i	−0.288019	+	0.947731i
$236$	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	$0.556014\pi$
$240$	2.17791	−	0.506647i	0.140584	−	0.0327039i
$241$	−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
$250$	−1.80435	−	11.0338i	−0.114117	−	0.697838i
$251$	−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
$255$	16.5493	+	5.02938i	1.03635	+	0.314952i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.16430	−	0.672210i	−0.0726271	−	0.0419313i	0.463247	−	0.886229i	$-0.346684\pi$
$257$	−1.16430	−	0.672210i	−0.0726271	−	0.0419313i	−0.535874	+	0.844298i	$0.680018\pi$
$258$		−	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	−0.612049	−	0.790820i	$-0.709655\pi$
$263$	−3.78193	+	2.18350i	−0.233204	+	0.134640i	0.378845	+	0.925460i	$0.376321\pi$
$264$	−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	$-0.414919\pi$
$270$	2.13945	+	0.650187i	0.130203	+	0.0395691i
$271$	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
$275$	18.5693	+	12.4350i	1.11977	+	0.749860i
$276$	−1.30913	−	2.26749i	−0.0788007	−	0.136487i
$277$	2.78085	−	1.60552i	0.167085	−	0.0964665i	−0.414126	−	0.910220i	$-0.635913\pi$
$277$	2.78085	−	1.60552i	0.167085	−	0.0964665i	0.581211	+	0.813753i	$0.302579\pi$
$278$	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	$-0.325171\pi$
$283$	25.5992	−	14.7797i	1.52171	−	0.878561i	0.999671	−	0.0256411i	$-0.00816272\pi$
$284$	1.01193	+	1.75271i	0.0600469	+	0.104004i
$285$	14.4140	−	3.35313i	0.853813	−	0.198622i
$286$	26.2990			1.55509
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	21.4172	−	37.0958i	1.25984	−	2.18210i
$290$	−5.31363	+	17.4846i	−0.312027	+	1.02673i
$291$	−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	$-0.989056\pi$
$293$		−	1.17679i		−	0.0687487i	0.999409	−	0.0343743i	$-0.0109438\pi$
$294$		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
$305$	−20.9599	−	6.36978i	−1.20016	−	0.364732i
$306$	3.86764	−	6.69895i	0.221098	−	0.382953i
$307$			20.3761i			1.16293i	0.813572	+	0.581464i	$0.197520\pi$
$307$			20.3761i			1.16293i	−0.813572	+	0.581464i	$0.802480\pi$
$308$		0			0
$309$	−9.35965			−0.532452
$310$	−18.4462	+	4.29113i	−1.04767	+	0.243720i
$311$	−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	0.845894	−	0.533351i	$-0.179067\pi$
$313$	14.2763	+	8.24245i	0.806946	+	0.465891i	−0.0389480	+	0.999241i	$0.512401\pi$
$314$	8.08184			0.456084
$315$		0			0
$316$	−6.98527			−0.392952
$317$	−8.93830	−	5.16053i	−0.502025	−	0.289844i	0.227524	−	0.973772i	$-0.426937\pi$
$317$	−8.93830	−	5.16053i	−0.502025	−	0.289844i	−0.729549	+	0.683928i	$0.760270\pi$
$318$	1.19661	−	0.690865i	0.0671027	−	0.0387418i
$319$	−18.2641	−	31.6343i	−1.02259	−	1.77118i
$320$	0.506647	+	2.17791i	0.0283224	+	0.121749i
$321$	11.0165			0.614881
$322$		0			0
$323$		−	51.1941i		−	2.84852i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	12.9849	+	26.3987i	0.720275	+	1.46434i
$326$	−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	$-0.729171\pi$
$337$		−	27.6035i		−	1.50366i	0.659357	−	0.751830i	$-0.270829\pi$
$338$	18.7235	+	10.8100i	1.01842	+	0.587988i
$339$	−6.28617	−	10.8880i	−0.341418	−	0.591353i
$340$	−5.02938	+	16.5493i	−0.272756	+	0.897509i
$341$	18.9283	−	32.7848i	1.02502	−	1.77539i
$342$		−	6.61827i		−	0.357875i
$343$		0			0
$344$	1.43108			0.0771588
$345$	1.32654	+	5.70237i	0.0714185	+	0.307005i
$346$	−0.323670	−	0.560613i	−0.0174006	−	0.0301387i
$347$	−17.6463	+	10.1881i	−0.947301	+	0.546924i	−0.892241	−	0.451559i	$-0.850868\pi$
$347$	−17.6463	+	10.1881i	−0.947301	+	0.546924i	−0.0550595	+	0.998483i	$0.517535\pi$
$348$	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	−0.578784	−	0.815481i	$-0.696473\pi$
$353$	−3.04275	+	1.75673i	−0.161949	+	0.0935014i	0.416835	+	0.908982i	$0.363139\pi$
$354$	2.33210	+	4.03932i	0.123950	+	0.214688i
$355$	−1.02538	−	4.40778i	−0.0544216	−	0.233941i
$356$	−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	$0.185140\pi$
$360$	−0.650187	+	2.13945i	−0.0342679	+	0.112759i
$361$	−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	0.320155	−	0.947365i	$-0.396265\pi$
$367$	24.9173	−	14.3860i	1.30067	−	0.750945i	0.980520	+	0.196421i	$0.0629318\pi$
$368$	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	0.136428	−	0.990650i	$-0.456438\pi$
$373$	−12.6171	−	7.28446i	−0.653286	−	0.377175i	−0.789714	+	0.613475i	$0.789771\pi$
$374$	−17.2871	−	29.9421i	−0.893892	−	1.54827i
$375$	10.4577	+	3.95428i	0.540034	+	0.204198i
$376$	−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	$0.209714\pi$
$380$	3.35313	+	14.4140i	0.172012	+	0.739424i
$381$	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	0.917809	−	0.397023i	$-0.129957\pi$
$383$	20.2139	+	11.6705i	1.03288	+	0.596334i	0.115072	+	0.993357i	$0.463290\pi$
$384$	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	$0.843167\pi$
$390$	12.8146	−	2.98105i	0.648892	−	0.150951i
$391$	20.2530			1.02424
$392$		0			0
$393$			2.32106i			0.117082i
$394$	3.72945	−	6.45960i	0.187887	−	0.325430i
$395$	14.9447	+	4.54174i	0.751947	+	0.228520i
$396$	−2.23483	−	3.87084i	−0.112305	−	0.194517i
$397$	−7.27977	−	4.20298i	−0.365361	−	0.210941i	0.306069	−	0.952009i	$-0.400986\pi$
$397$	−7.27977	−	4.20298i	−0.365361	−	0.210941i	−0.671430	+	0.741068i	$0.734320\pi$
$398$			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	$0.774890\pi$
$410$	2.31650	−	7.62248i	0.114404	−	0.376447i
$411$	7.13756	−	12.3626i	0.352070	−	0.609803i
$412$		−	9.35965i		−	0.461117i
$413$		0			0
$414$	2.61827			0.128681
$415$	−11.6728	+	2.71545i	−0.572998	+	0.133296i
$416$	−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
$425$	21.5202	−	32.1363i	1.04388	−	1.55884i
$426$	−2.02386			−0.0980561
$427$		0			0
$428$			11.0165i			0.532503i
$429$	−13.1495	+	22.7756i	−0.634863	+	1.09962i
$430$	−3.06173	−	0.930471i	−0.147650	−	0.0448713i
$431$	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	$-0.791827\pi$
$433$		−	25.3184i		−	1.21672i	0.793660	−	0.608362i	$-0.208173\pi$
$434$		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	0.801646	−	0.597800i	$-0.203958\pi$
$443$	14.4125	+	8.32106i	0.684759	+	0.395346i	−0.116887	+	0.993145i	$0.537291\pi$
$444$	1.59359	+	2.76019i	0.0756286	+	0.130993i
$445$	30.7894	+	9.35701i	1.45956	+	0.443565i
$446$	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	$0.657942\pi$
$450$	2.78209	−	4.15451i	0.131149	−	0.195846i
$451$	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	0.997466	−	0.0711396i	$-0.0226636\pi$
$457$	30.6680	+	17.7062i	1.43459	+	0.828261i	0.437124	+	0.899401i	$0.355997\pi$
$458$	−6.90456	+	3.98635i	−0.322629	+	0.186270i
$459$	3.86764	+	6.69895i	0.180526	+	0.312680i
$460$	−5.70237	+	1.32654i	−0.265874	+	0.0618502i
$461$	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	$-0.727470\pi$
$463$		−	32.5061i		−	1.51069i	0.655330	−	0.755343i	$-0.272530\pi$
$464$	−4.08623	+	7.07756i	−0.189698	+	0.328567i
$465$	5.50687	−	18.1204i	0.255375	−	0.840316i
$466$	8.97792	+	15.5502i	0.415894	+	0.720349i
$467$	7.97203	+	4.60265i	0.368902	+	0.212985i	0.672979	−	0.739662i	$-0.265015\pi$
$467$	7.97203	+	4.60265i	0.368902	+	0.212985i	−0.304077	+	0.952648i	$0.598348\pi$
$468$		−	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	$0.475282\pi$
$480$	−2.13945	−	0.650187i	−0.0976522	−	0.0296769i
$481$	9.37652	−	16.2406i	0.427532	−	0.740508i
$482$			4.69669i			0.213928i
$483$		0			0
$484$	−8.97792			−0.408087
$485$	−16.8128	+	3.91115i	−0.763428	+	0.177596i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−25.3466	+	14.6339i	−1.14857	+	0.663125i	−0.948537	−	0.316666i	$-0.897437\pi$
$487$	−25.3466	+	14.6339i	−1.14857	+	0.663125i	−0.200028	+	0.979790i	$0.564103\pi$
$488$	−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
$495$	2.26454	+	9.73455i	0.101784	+	0.437535i
$496$	−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	$0.0145241\pi$
$500$	−3.95428	+	10.4577i	−0.176841	+	0.467683i
$501$	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	$0.150916\pi$
$503$			20.4788i			0.913105i	−0.889696	+	0.456553i	$0.849084\pi$
$504$		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
$515$	−6.08552	+	20.0245i	−0.268160	+	0.882386i
$516$	−0.715541	+	1.23935i	−0.0314999	+	0.0545595i
$517$			30.3523i			1.33489i
$518$		0			0
$519$	0.647340			0.0284151
$520$	2.98105	+	12.8146i	0.130728	+	0.561957i
$521$	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	0.372996	−	0.927833i	$-0.378330\pi$
$523$	−5.58081	−	3.22208i	−0.244032	−	0.140892i	−0.617028	+	0.786941i	$0.711664\pi$
$524$	−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
$530$	−0.700050	−	3.00929i	−0.0304082	−	0.130715i
$531$	−4.66421			−0.202409
$532$		0			0
$533$			20.9632i			0.908016i
$534$	7.19562	−	12.4632i	0.311385	−	0.539335i
$535$	7.16279	−	23.5693i	0.309674	−	1.01899i
$536$	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	$0.135124\pi$
$547$			19.2656i			0.823737i	−0.911243	+	0.411868i	$0.864876\pi$
$548$	12.3626	+	7.13756i	0.528105	+	0.304902i
$549$	−4.89841	−	8.48430i	−0.209059	−	0.362101i
$550$	−9.86397	−	20.0537i	−0.420601	−	0.855092i
$551$	−27.0438	+	46.8412i	−1.15210	+	1.99550i
$552$			2.61827i			0.111441i
$553$		0			0
$554$	−3.21104			−0.136424
$555$	−1.61478	−	6.94142i	−0.0685436	−	0.294647i
$556$	−7.48159	−	12.9585i	−0.317290	−	0.549563i
$557$	18.2215	−	10.5202i	0.772069	−	0.445754i	−0.0615432	−	0.998104i	$-0.519602\pi$
$557$	18.2215	−	10.5202i	0.772069	−	0.445754i	0.833612	+	0.552350i	$0.186269\pi$
$558$	−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	−0.432654	−	0.901560i	$-0.642423\pi$
$563$	3.12714	−	1.80546i	0.131793	−	0.0760910i	0.564447	+	0.825469i	$0.309089\pi$
$564$	−3.39536	−	5.88094i	−0.142971	−	0.247632i
$565$	−27.3815	+	6.36974i	−1.15195	+	0.267977i
$566$	−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	$-0.0784656\pi$
$570$	−14.1595	−	4.30312i	−0.593075	−	0.180238i
$571$	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	0.265080	−	0.964226i	$-0.414602\pi$
$577$	29.6096	−	17.0951i	1.23266	−	0.711679i	0.967585	+	0.252547i	$0.0812684\pi$
$578$	−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
$585$	−3.82562	+	12.5883i	−0.158170	+	0.520461i
$586$	−0.588394	+	1.01913i	−0.0243063	+	0.0420998i
$587$			34.5962i			1.42794i	0.700178	+	0.713969i	$0.253104\pi$
$587$			34.5962i			1.42794i	−0.700178	+	0.713969i	$0.746896\pi$
$588$		0			0
$589$	−56.0545			−2.30969
$590$	10.1582	−	2.36311i	0.418208	−	0.0972877i
$591$	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	−0.221372	−	0.975189i	$-0.571054\pi$
$593$	−28.6520	−	16.5422i	−1.17660	−	0.679309i	−0.955225	+	0.295881i	$0.904387\pi$
$594$	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	$0.793727\pi$
$600$	4.15451	+	2.78209i	0.169607	+	0.113578i
$601$	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
$605$	19.2078	+	5.83733i	0.780909	+	0.237321i
$606$	6.67722	+	11.5653i	0.271243	+	0.469807i
$607$	39.6796	+	22.9090i	1.61054	+	0.929848i	0.989244	+	0.146275i	$0.0467285\pi$
$607$	39.6796	+	22.9090i	1.61054	+	0.929848i	0.621300	+	0.783573i	$0.286605\pi$
$608$			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	0.237938	−	0.971280i	$-0.423528\pi$
$613$	29.6626	−	17.1257i	1.19806	−	0.691701i	0.960122	+	0.279580i	$0.0901952\pi$
$614$	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	$0.285407\pi$
$617$			38.8106i			1.56246i	−0.624245	+	0.781228i	$0.714593\pi$
$618$	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	$0.805952\pi$
$620$	18.1204	+	5.50687i	0.727735	+	0.221161i
$621$	−1.30913	+	2.26749i	−0.0525338	+	0.0909912i
$622$			18.8934i			0.757556i
$623$		0			0
$624$	5.88388			0.235544
$625$	15.2595	−	19.8027i	0.610379	−	0.792110i
$626$	−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
$635$	14.3659	−	3.34194i	0.570094	−	0.132621i
$636$	−1.38173			−0.0547892
$637$		0			0
$638$			36.5282i			1.44616i
$639$	1.01193	−	1.75271i	0.0400312	−	0.0693361i
$640$	0.650187	−	2.13945i	0.0257009	−	0.0845693i
$641$	−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	$-0.806166\pi$
$643$		−	29.0091i		−	1.14401i	0.820251	−	0.572004i	$-0.193834\pi$
$644$		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	−0.413482	−	0.910512i	$-0.635687\pi$
$647$	4.28102	−	2.47165i	0.168304	−	0.0971705i	0.581786	+	0.813342i	$0.302354\pi$
$648$	−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	0.332081	−	0.943251i	$-0.392249\pi$
$653$	−8.14548	−	4.70279i	−0.318757	−	0.184035i	−0.650838	+	0.759216i	$0.725582\pi$
$654$	2.34772	+	4.06637i	0.0918031	+	0.159008i
$655$	4.96580	+	1.50913i	0.194030	+	0.0589664i
$656$	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	$0.584108\pi$
$660$	−9.73455	+	2.26454i	−0.378917	+	0.0881473i
$661$	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
$670$	−0.938005	−	4.03218i	−0.0362383	−	0.155777i
$671$	−43.7886			−1.69044
$672$		0			0
$673$			21.8236i			0.841237i	0.907238	+	0.420619i	$0.138187\pi$
$673$			21.8236i			0.841237i	−0.907238	+	0.420619i	$0.861813\pi$
$674$	−13.8018	+	23.9054i	−0.531624	+	0.920800i
$675$	2.20687	+	4.48662i	0.0849424	+	0.172690i
$676$	−10.8100	−	18.7235i	−0.415770	−	0.720135i
$677$	−35.5566	−	20.5286i	−1.36655	−	0.788979i	−0.376065	−	0.926593i	$-0.622723\pi$
$677$	−35.5566	−	20.5286i	−1.36655	−	0.788979i	−0.990486	+	0.137614i	$0.956056\pi$
$678$			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	0.112581	−	0.993643i	$-0.464088\pi$
$683$	26.9024	−	15.5321i	1.02939	−	0.594320i	0.916810	+	0.399323i	$0.130755\pi$
$684$	−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
$690$	1.70237	−	5.60166i	0.0648080	−	0.213252i
$691$	−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
$695$	7.58106	+	32.5885i	0.287566	+	1.23615i
$696$	−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
$705$	3.44050	+	14.7896i	0.129577	+	0.557009i
$706$	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	$0.812534\pi$
$710$	−1.31589	+	4.32994i	−0.0493843	+	0.162500i
$711$	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
$725$	−36.6667	+	18.0355i	−1.36177	+	0.669823i
$726$	4.48896	−	7.77510i	0.166601	−	0.288561i
$727$		−	8.17082i		−	0.303039i	−0.988454	−	0.151519i	$-0.951583\pi$
$727$		−	8.17082i		−	0.303039i	0.988454	−	0.151519i	$-0.0484166\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−2.03514	−	8.74839i	−0.0753238	−	0.323793i
$731$	−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	0.531882	−	0.846818i	$-0.321485\pi$
$733$	1.74512	+	1.00755i	0.0644576	+	0.0372146i	−0.467425	+	0.884033i	$0.654818\pi$
$734$	−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	$0.855751\pi$
$740$	6.94142	−	1.61478i	0.255172	−	0.0593605i
$741$	38.9411			1.43054
$742$		0			0
$743$			36.6654i			1.34512i	0.740041	+	0.672562i	$0.234806\pi$
$743$			36.6654i			1.34512i	−0.740041	+	0.672562i	$0.765194\pi$
$744$	4.23483	−	7.33495i	0.155257	−	0.268912i
$745$	−23.8872	−	7.25941i	−0.875160	−	0.265964i
$746$	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	$-0.757701\pi$
$757$		−	37.9575i		−	1.37959i	0.724006	−	0.689794i	$-0.242299\pi$
$758$	−26.6621	−	15.3934i	−0.968412	−	0.559113i
$759$	5.85140	+	10.1349i	0.212392	+	0.367874i
$760$	4.30312	−	14.1595i	0.156090	−	0.513618i
$761$	−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
$765$	16.8468	−	3.91906i	0.609096	−	0.141694i
$766$	−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	−0.484467	−	0.874810i	$-0.660986\pi$
$773$	0.859321	−	0.496129i	0.0309076	−	0.0178445i	0.515374	+	0.856965i	$0.327653\pi$
$774$	−0.715541	−	1.23935i	−0.0257196	−	0.0445476i
$775$	−35.1873	−	23.5634i	−1.26397	−	0.846421i
$776$	−7.71966			−0.277120
$777$		0			0
$778$			1.21842i			0.0436824i
$779$	11.7898	−	20.4206i	0.422415	−	0.731644i
$780$	−12.5883	−	3.82562i	−0.450733	−	0.136979i
$781$	−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	−0.333353	−	0.942802i	$-0.608180\pi$
$787$	8.87786	−	5.12563i	0.316461	−	0.182709i	0.649814	+	0.760093i	$0.274847\pi$
$788$	−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
$795$	2.95615	+	0.898384i	0.104844	+	0.0318624i
$796$	12.9147	−	22.3688i	0.457748	−	0.792843i
$797$			32.6811i			1.15762i	0.815461	+	0.578812i	$0.196483\pi$
$797$			32.6811i			1.15762i	−0.815461	+	0.578812i	$0.803517\pi$
$798$		0			0
$799$	52.5282			1.85831
$800$	−2.78209	+	4.15451i	−0.0983617	+	0.146884i
$801$	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	$0.704190\pi$
$810$	2.17791	−	0.506647i	0.0765241	−	0.0178018i
$811$	−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
$815$	0.543991	−	1.79001i	0.0190552	−	0.0627013i
$816$	−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	−0.753898	−	0.656992i	$-0.771829\pi$
$823$	−16.1190	+	9.30633i	−0.561875	+	0.324398i	0.192023	+	0.981390i	$0.438495\pi$
$824$	−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	$0.103803\pi$
$827$			18.4254i			0.640713i	−0.947297	+	0.320356i	$0.896197\pi$
$828$	−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	$-0.354468\pi$
$830$	11.4667	+	3.48478i	0.398015	+	0.120958i
$831$	1.60552	−	2.78085i	0.0556949	−	0.0964665i
$832$			5.88388i			0.203987i
$833$		0			0
$834$	14.9632			0.518133
$835$	5.80985	−	1.35154i	0.201058	−	0.0467721i
$836$	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
$845$	10.9537	+	47.0866i	0.376820	+	1.61983i
$846$	6.79073			0.233470
$847$		0			0
$848$		−	1.38173i		−	0.0474488i
$849$	14.7797	−	25.5992i	0.507238	−	0.878561i
$850$	−34.7052	+	17.0707i	−1.19038	+	0.585521i
$851$	−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	$-0.666225\pi$
$853$		−	50.6270i		−	1.73344i	0.498798	−	0.866718i	$-0.333775\pi$
$854$		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	−0.311868	−	0.950126i	$-0.600955\pi$
$857$	10.3934	−	6.00063i	0.355031	−	0.204978i	0.666899	+	0.745148i	$0.267621\pi$
$858$	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	0.480951	−	0.876748i	$-0.340292\pi$
$863$	−1.11219	−	0.642125i	−0.0378595	−	0.0218582i	−0.518810	+	0.854889i	$0.673625\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	0.420892	−	1.38495i	0.0143108	−	0.0470898i
$866$	−12.6592	+	21.9264i	−0.430177	+	0.745088i
$867$		−	42.8345i		−	1.45474i
$868$		0			0
$869$	31.2218			1.05913
$870$	4.14055	+	17.7989i	0.140378	+	0.603440i
$871$	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	−0.179713	−	0.983719i	$-0.557517\pi$
$877$	−33.2122	−	19.1751i	−1.12150	−	0.647496i	−0.941782	+	0.336224i	$0.890850\pi$
$878$	28.4183	−	16.4073i	0.959070	−	0.553719i
$879$	−0.588394	−	1.01913i	−0.0198460	−	0.0343743i
$880$	−2.26454	−	9.73455i	−0.0763378	−	0.328152i
$881$	−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	$0.100993\pi$
$883$			18.5412i			0.623962i	−0.950088	+	0.311981i	$0.899007\pi$
$884$	−22.7567	+	39.4158i	−0.765391	+	1.32570i
$885$	−3.03261	+	9.97885i	−0.101940	+	0.335435i
$886$	−8.32106	−	14.4125i	−0.279552	−	0.484198i
$887$	−36.7893	−	21.2403i	−1.23526	−	0.713179i	−0.267140	−	0.963658i	$-0.586079\pi$
$887$	−36.7893	−	21.2403i	−1.23526	−	0.713179i	−0.968122	+	0.250478i	$0.919412\pi$
$888$		−	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
$900$	−4.48662	+	2.20687i	−0.149554	+	0.0735623i
$901$	5.34403	−	9.25613i	0.178036	−	0.308367i
$902$		−	15.9246i		−	0.530231i
$903$		0			0
$904$	−12.5723			−0.418150
$905$	3.76057	+	16.1655i	0.125005	+	0.537358i
$906$	0.332104	+	0.575221i	0.0110334	+	0.0191105i
$907$	−35.6531	+	20.5843i	−1.18384	+	0.683491i	−0.956900	−	0.290417i	$-0.906206\pi$
$907$	−35.6531	+	20.5843i	−1.18384	+	0.683491i	−0.226941	+	0.973908i	$0.572873\pi$
$908$	−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
$915$	−21.3367	+	4.96354i	−0.705368	+	0.164090i
$916$	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	$0.193141\pi$
$920$	5.60166	+	1.70237i	0.184681	+	0.0561253i
$921$	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
$935$	22.4796	−	73.9696i	0.735163	−	2.41907i
$936$	−2.94194	+	5.09559i	−0.0961603	+	0.166555i
$937$			19.8403i			0.648153i	0.946031	+	0.324077i	$0.105054\pi$
$937$			19.8403i			0.648153i	−0.946031	+	0.324077i	$0.894946\pi$
$938$		0			0
$939$	16.4849			0.537964
$940$	−14.7896	+	3.44050i	−0.482384	+	0.112217i
$941$	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	0.359441	−	0.933168i	$-0.382967\pi$
$947$	−8.27760	−	4.77908i	−0.268986	−	0.155299i	−0.628427	+	0.777869i	$0.716301\pi$
$948$	−6.04942	+	3.49264i	−0.196476	+	0.113436i
$949$	11.8174	+	20.4683i	0.383609	+	0.664430i
$950$	−18.4126	+	27.4957i	−0.597384	+	0.892078i
$951$	−10.3211			−0.334683
$952$		0			0
$953$		−	23.7505i		−	0.769354i	−0.923051	−	0.384677i	$-0.874313\pi$
$953$		−	23.7505i		−	0.769354i	0.923051	−	0.384677i	$-0.125687\pi$
$954$	0.690865	−	1.19661i	0.0223676	−	0.0387418i
$955$	−2.32029	−	0.705143i	−0.0750827	−	0.0228179i
$956$	−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	$-0.631379\pi$
$967$		−	56.9706i		−	1.83205i	0.401121	−	0.916025i	$-0.368621\pi$
$968$	7.77510	+	4.48896i	0.249901	+	0.144281i
$969$	−25.5971	−	44.3354i	−0.822296	−	1.42426i
$970$	16.5158	+	5.01923i	0.530292	+	0.161158i
$971$	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
$975$	24.4447	+	16.3695i	0.782855	+	0.524243i
$976$	4.89841	+	8.48430i	0.156794	+	0.271576i
$977$	−21.3152	+	12.3063i	−0.681934	+	0.393715i	−0.800583	−	0.599222i	$-0.795477\pi$
$977$	−21.3152	+	12.3063i	−0.681934	+	0.393715i	0.118650	+	0.992936i	$0.462143\pi$
$978$	−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	0.218918	−	0.975743i	$-0.429747\pi$
$983$	36.7893	−	21.2403i	1.17340	−	0.677460i	0.954477	+	0.298283i	$0.0964140\pi$
$984$	1.78141	+	3.08549i	0.0567892	+	0.0983618i
$985$	16.2448	−	3.77903i	0.517604	−	0.120410i
$986$	63.2162			2.01321
$987$		0			0
$988$			38.9411i			1.23888i
$989$	1.87348	−	3.24496i	0.0595732	−	0.103184i
$990$	2.90612	−	9.56264i	0.0923626	−	0.303921i
$991$	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	0.000342701	−	1.00000i	$-0.499891\pi$
$997$	27.3612	−	15.7970i	0.866539	−	0.500297i	0.866197	+	0.499703i	$0.166558\pi$
$998$	−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.79.2		16
5.4	even	2	inner	1470.2.n.l.79.8		16
7.2	even	3		1470.2.g.j.589.6	yes	8
7.3	odd	6		1470.2.n.k.949.5		16
7.4	even	3	inner	1470.2.n.l.949.8		16
7.5	odd	6		1470.2.g.k.589.7	yes	8
7.6	odd	2		1470.2.n.k.79.3		16
35.2	odd	12		7350.2.a.ds.1.4		4
35.4	even	6	inner	1470.2.n.l.949.2		16
35.9	even	6		1470.2.g.j.589.2	✓	8
35.12	even	12		7350.2.a.dr.1.4		4
35.19	odd	6		1470.2.g.k.589.3	yes	8
35.23	odd	12		7350.2.a.dt.1.4		4
35.24	odd	6		1470.2.n.k.949.3		16
35.33	even	12		7350.2.a.du.1.4		4
35.34	odd	2		1470.2.n.k.79.5		16

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.506647 - 2.17791i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.506647 - 2.17791i) q^{5} -1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.650187 + 2.13945i) 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} +(-4.48662 + 2.20687i) q^{25} +(-2.94194 + 5.09559i) q^{26} -1.00000i q^{27} +8.17246 q^{29} +(0.506647 + 2.17791i) 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} +(-2.17791 + 0.506647i) q^{40} -3.56282 q^{41} +1.43108i q^{43} +(2.23483 - 3.87084i) q^{44} +(-2.13945 - 0.650187i) 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} +(0.650187 - 2.13945i) q^{60} +(4.89841 - 8.48430i) q^{61} -8.46967i q^{62} -1.00000 q^{64} +(-12.8146 + 2.98105i) 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} +(-2.78209 + 4.15451i) q^{75} -6.61827 q^{76} +5.88388i q^{78} +(-3.49264 + 6.04942i) q^{79} +(2.13945 + 0.650187i) 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} +(14.1595 + 4.30312i) 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

Properties

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