LMFDB - Embedded newform 459.2.e.b.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [459,2,Mod(154,459)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(459, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("459.154");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.e (of order $3$, 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:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.152695449.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 3x^{5} - 5x^{4} + 6x^{3} - 16x + 16 $ x^8 - 2x^7 + 3x^5 - 5x^4 + 6x^3 - 16*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.3
Root			$1.05924 - 0.937022i$ of defining polynomial
Character	$\chi$	$=$	459.307
Dual form			459.2.e.b.154.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.281864 + 0.488204i) q^{2} +(0.841105 - 1.45684i) q^{4} +(-0.281864 + 0.488204i) q^{5} +(-0.841105 - 1.45684i) q^{7} +2.07577 q^{8} -0.317790 q^{10} +(1.03788 + 1.79767i) q^{11} +(2.59712 - 4.49835i) q^{13} +(0.474155 - 0.821261i) q^{14} +(-1.09712 - 1.90028i) q^{16} +1.00000 q^{17} +1.70629 q^{19} +(0.474155 + 0.821261i) q^{20} +(-0.585085 + 1.01340i) q^{22} +(1.80322 - 3.12327i) q^{23} +(2.34110 + 4.05491i) q^{25} +2.92815 q^{26} -2.82983 q^{28} +(-4.16085 - 7.20681i) q^{29} +(0.658895 - 1.14124i) q^{31} +(2.69425 - 4.66658i) q^{32} +(0.281864 + 0.488204i) q^{34} +0.948310 q^{35} -3.50306 q^{37} +(0.480942 + 0.833016i) q^{38} +(-0.585085 + 1.01340i) q^{40} +(-5.06120 + 8.76625i) q^{41} +(5.20323 + 9.01225i) q^{43} +3.49188 q^{44} +2.03306 q^{46} +(3.12297 + 5.40914i) q^{47} +(2.08509 - 3.61147i) q^{49} +(-1.31975 + 2.28587i) q^{50} +(-4.36891 - 7.56717i) q^{52} -2.47898 q^{53} -1.17017 q^{55} +(-1.74594 - 3.02405i) q^{56} +(2.34559 - 4.06269i) q^{58} +(-2.13052 + 3.69017i) q^{59} +(2.76281 + 4.78532i) q^{61} +0.742877 q^{62} -1.35085 q^{64} +(1.46407 + 2.53585i) q^{65} +(-2.45476 + 4.25176i) q^{67} +(0.841105 - 1.45684i) q^{68} +(0.267295 + 0.462968i) q^{70} -2.07071 q^{71} -9.24986 q^{73} +(-0.987389 - 1.71021i) q^{74} +(1.43517 - 2.48578i) q^{76} +(1.74594 - 3.02405i) q^{77} +(0.735003 + 1.27306i) q^{79} +1.23696 q^{80} -5.70629 q^{82} +(2.22009 + 3.84532i) q^{83} +(-0.281864 + 0.488204i) q^{85} +(-2.93321 + 5.08047i) q^{86} +(2.15441 + 3.73154i) q^{88} -12.6473 q^{89} -8.73782 q^{91} +(-3.03340 - 5.25400i) q^{92} +(-1.76051 + 3.04929i) q^{94} +(-0.480942 + 0.833016i) q^{95} +(7.89747 + 13.6788i) q^{97} +2.35085 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 3 q^{4} + q^{5} + 3 q^{7} + 6 q^{8} - 22 q^{10} + 3 q^{11} + 9 q^{13} + 5 q^{14} + 3 q^{16} + 8 q^{17} - 14 q^{19} + 5 q^{20} + 3 q^{22} + 10 q^{23} + 9 q^{25} - 22 q^{26} - 38 q^{28} - 15 q^{29}+ \cdots + 30 q^{98}+O(q^{100}) $ 8 * q - q^2 - 3 * q^4 + q^5 + 3 * q^7 + 6 * q^8 - 22 * q^10 + 3 * q^11 + 9 * q^13 + 5 * q^14 + 3 * q^16 + 8 * q^17 - 14 * q^19 + 5 * q^20 + 3 * q^22 + 10 * q^23 + 9 * q^25 - 22 * q^26 - 38 * q^28 - 15 * q^29 + 15 * q^31 - 2 * q^32 - q^34 + 10 * q^35 - 24 * q^37 - 20 * q^38 + 3 * q^40 - 6 * q^41 + 18 * q^43 - 24 * q^44 + 8 * q^46 + 12 * q^47 + 9 * q^49 - 2 * q^50 + 4 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^56 + 9 * q^58 - 5 * q^61 - 16 * q^62 - 22 * q^64 - 11 * q^65 + 6 * q^67 - 3 * q^68 - 25 * q^70 + 50 * q^71 + 8 * q^73 + 44 * q^74 - 6 * q^76 - 12 * q^77 + 8 * q^79 - 16 * q^80 - 18 * q^82 - 7 * q^83 + q^85 - 34 * q^86 + 27 * q^88 + 28 * q^89 + 8 * q^91 - 19 * q^92 - 12 * q^94 + 20 * q^95 + 16 * q^97 + 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.281864	+	0.488204i	0.199308	+	0.345212i	0.948304	−	0.317362i	$-0.102797\pi$
$2$	0.281864	+	0.488204i	0.199308	+	0.345212i	−0.748996	+	0.662574i	$0.769464\pi$
$3$		0			0
$3$		0			0
$4$	0.841105	−	1.45684i	0.420552	−	0.728418i
$5$	−0.281864	+	0.488204i	−0.126054	+	0.218331i	−0.922144	−	0.386846i	$-0.873564\pi$
$5$	−0.281864	+	0.488204i	−0.126054	+	0.218331i	0.796091	+	0.605177i	$0.206898\pi$
$6$		0			0
$7$	−0.841105	−	1.45684i	−0.317908	−	0.550632i	0.662144	−	0.749377i	$-0.269647\pi$
$7$	−0.841105	−	1.45684i	−0.317908	−	0.550632i	−0.980051	+	0.198745i	$0.936314\pi$
$8$	2.07577			0.733895
$9$		0			0
$10$	−0.317790			−0.100494
$11$	1.03788	+	1.79767i	0.312934	+	0.542017i	0.978996	−	0.203879i	$-0.0653549\pi$
$11$	1.03788	+	1.79767i	0.312934	+	0.542017i	−0.666062	+	0.745896i	$0.732022\pi$
$12$		0			0
$13$	2.59712	−	4.49835i	0.720313	−	1.24762i	−0.240562	−	0.970634i	$-0.577332\pi$
$13$	2.59712	−	4.49835i	0.720313	−	1.24762i	0.960874	−	0.276984i	$-0.0893350\pi$
$14$	0.474155	−	0.821261i	0.126723	−	0.219491i
$15$		0			0
$16$	−1.09712	−	1.90028i	−0.274281	−	0.475069i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$		0			0
$19$	1.70629			0.391449			0.195725	−	0.980659i	$-0.437294\pi$
$19$	1.70629			0.391449			0.195725	+	0.980659i	$0.437294\pi$
$20$	0.474155	+	0.821261i	0.106024	+	0.183639i
$21$		0			0
$22$	−0.585085	+	1.01340i	−0.124741	+	0.216057i
$23$	1.80322	−	3.12327i	0.375998	−	0.651247i	−0.614478	−	0.788934i	$-0.710633\pi$
$23$	1.80322	−	3.12327i	0.375998	−	0.651247i	0.990476	+	0.137687i	$0.0439668\pi$
$24$		0			0
$25$	2.34110	+	4.05491i	0.468221	+	0.810983i
$26$	2.92815			0.574257
$27$		0			0
$28$	−2.82983			−0.534788
$29$	−4.16085	−	7.20681i	−0.772651	−	1.33827i	−0.936105	−	0.351720i	$-0.885597\pi$
$29$	−4.16085	−	7.20681i	−0.772651	−	1.33827i	0.163454	−	0.986551i	$-0.447736\pi$
$30$		0			0
$31$	0.658895	−	1.14124i	0.118341	−	0.204973i	−0.800769	−	0.598973i	$-0.795576\pi$
$31$	0.658895	−	1.14124i	0.118341	−	0.204973i	0.919110	+	0.394000i	$0.128909\pi$
$32$	2.69425	−	4.66658i	0.476280	−	0.824942i
$33$		0			0
$34$	0.281864	+	0.488204i	0.0483394	+	0.0837262i
$35$	0.948310			0.160294
$36$		0			0
$37$	−3.50306			−0.575900			−0.287950	−	0.957645i	$-0.592974\pi$
$37$	−3.50306			−0.575900			−0.287950	+	0.957645i	$0.592974\pi$
$38$	0.480942	+	0.833016i	0.0780191	+	0.135133i
$39$		0			0
$40$	−0.585085	+	1.01340i	−0.0925101	+	0.160232i
$41$	−5.06120	+	8.76625i	−0.790426	+	1.36906i	0.135277	+	0.990808i	$0.456808\pi$
$41$	−5.06120	+	8.76625i	−0.790426	+	1.36906i	−0.925703	+	0.378251i	$0.876526\pi$
$42$		0			0
$43$	5.20323	+	9.01225i	0.793485	+	1.37436i	0.923797	+	0.382883i	$0.125069\pi$
$43$	5.20323	+	9.01225i	0.793485	+	1.37436i	−0.130313	+	0.991473i	$0.541598\pi$
$44$	3.49188			0.526420
$45$		0			0
$46$	2.03306			0.299758
$47$	3.12297	+	5.40914i	0.455532	+	0.789004i	0.998719	−	0.0506075i	$-0.0161158\pi$
$47$	3.12297	+	5.40914i	0.455532	+	0.789004i	−0.543187	+	0.839612i	$0.682782\pi$
$48$		0			0
$49$	2.08509	−	3.61147i	0.297869	−	0.515925i
$50$	−1.31975	+	2.28587i	−0.186641	+	0.323271i
$51$		0			0
$52$	−4.36891	−	7.56717i	−0.605859	−	1.04938i
$53$	−2.47898			−0.340515			−0.170257	−	0.985400i	$-0.554460\pi$
$53$	−2.47898			−0.340515			−0.170257	+	0.985400i	$0.554460\pi$
$54$		0			0
$55$	−1.17017			−0.157786
$56$	−1.74594	−	3.02405i	−0.233311	−	0.404106i
$57$		0			0
$58$	2.34559	−	4.06269i	0.307992	−	0.533457i
$59$	−2.13052	+	3.69017i	−0.277370	+	0.480419i	−0.970730	−	0.240172i	$-0.922796\pi$
$59$	−2.13052	+	3.69017i	−0.277370	+	0.480419i	0.693360	+	0.720591i	$0.256129\pi$
$60$		0			0
$61$	2.76281	+	4.78532i	0.353741	+	0.612698i	0.986902	−	0.161323i	$-0.0515761\pi$
$61$	2.76281	+	4.78532i	0.353741	+	0.612698i	−0.633161	+	0.774020i	$0.718243\pi$
$62$	0.742877			0.0943454
$63$		0			0
$64$	−1.35085			−0.168856
$65$	1.46407	+	2.53585i	0.181596	+	0.314534i
$66$		0			0
$67$	−2.45476	+	4.25176i	−0.299896	+	0.519436i	−0.976112	−	0.217268i	$-0.930285\pi$
$67$	−2.45476	+	4.25176i	−0.299896	+	0.519436i	0.676216	+	0.736704i	$0.263619\pi$
$68$	0.841105	−	1.45684i	0.101999	−	0.176667i
$69$		0			0
$70$	0.267295	+	0.462968i	0.0319479	+	0.0553353i
$71$	−2.07071			−0.245748			−0.122874	−	0.992422i	$-0.539211\pi$
$71$	−2.07071			−0.245748			−0.122874	+	0.992422i	$0.539211\pi$
$72$		0			0
$73$	−9.24986			−1.08261			−0.541307	−	0.840825i	$-0.682070\pi$
$73$	−9.24986			−1.08261			−0.541307	+	0.840825i	$0.682070\pi$
$74$	−0.987389	−	1.71021i	−0.114782	−	0.198808i
$75$		0			0
$76$	1.43517	−	2.48578i	0.164625	−	0.285139i
$77$	1.74594	−	3.02405i	0.198968	−	0.344623i
$78$		0			0
$79$	0.735003	+	1.27306i	0.0826943	+	0.143231i	0.904406	−	0.426672i	$-0.140314\pi$
$79$	0.735003	+	1.27306i	0.0826943	+	0.143231i	−0.821712	+	0.569903i	$0.806981\pi$
$80$	1.23696			0.138297
$81$		0			0
$82$	−5.70629			−0.630154
$83$	2.22009	+	3.84532i	0.243687	+	0.422078i	0.961762	−	0.273888i	$-0.0883097\pi$
$83$	2.22009	+	3.84532i	0.243687	+	0.422078i	−0.718075	+	0.695966i	$0.754976\pi$
$84$		0			0
$85$	−0.281864	+	0.488204i	−0.0305725	+	0.0529531i
$86$	−2.93321	+	5.08047i	−0.316296	+	0.547841i
$87$		0			0
$88$	2.15441	+	3.73154i	0.229661	+	0.397784i
$89$	−12.6473			−1.34061			−0.670307	−	0.742084i	$-0.733838\pi$
$89$	−12.6473			−1.34061			−0.670307	+	0.742084i	$0.733838\pi$
$90$		0			0
$91$	−8.73782			−0.915972
$92$	−3.03340	−	5.25400i	−0.316253	−	0.547767i
$93$		0			0
$94$	−1.76051	+	3.04929i	−0.181583	+	0.314510i
$95$	−0.480942	+	0.833016i	−0.0493436	+	0.0854656i
$96$		0			0
$97$	7.89747	+	13.6788i	0.801867	+	1.38887i	0.918386	+	0.395686i	$0.129493\pi$
$97$	7.89747	+	13.6788i	0.801867	+	1.38887i	−0.116519	+	0.993188i	$0.537174\pi$
$98$	2.35085			0.237471
$99$		0			0
$100$	7.87646			0.787646
$101$	0.758550	+	1.31385i	0.0754785	+	0.130733i	0.901294	−	0.433207i	$-0.142618\pi$
$101$	0.758550	+	1.31385i	0.0754785	+	0.130733i	−0.825816	+	0.563940i	$0.809285\pi$
$102$		0			0
$103$	5.83213	−	10.1015i	0.574657	−	0.995334i	−0.421422	−	0.906865i	$-0.638469\pi$
$103$	5.83213	−	10.1015i	0.574657	−	0.995334i	0.996079	−	0.0884699i	$-0.0281977\pi$
$104$	5.39103	−	9.33753i	0.528634	−	0.915621i
$105$		0			0
$106$	−0.698737	−	1.21025i	−0.0678674	−	0.117550i
$107$	−8.75730			−0.846600			−0.423300	−	0.905990i	$-0.639128\pi$
$107$	−8.75730			−0.846600			−0.423300	+	0.905990i	$0.639128\pi$
$108$		0			0
$109$	−11.6007			−1.11115			−0.555573	−	0.831468i	$-0.687501\pi$
$109$	−11.6007			−1.11115			−0.555573	+	0.831468i	$0.687501\pi$
$110$	−0.329829	−	0.571281i	−0.0314480	−	0.0544695i
$111$		0			0
$112$	−1.84559	+	3.19666i	−0.174392	+	0.302056i
$113$	−7.33604	+	12.7064i	−0.690117	+	1.19532i	0.281682	+	0.959508i	$0.409108\pi$
$113$	−7.33604	+	12.7064i	−0.690117	+	1.19532i	−0.971799	+	0.235810i	$0.924226\pi$
$114$		0			0
$115$	1.01653	+	1.76068i	0.0947917	+	0.164184i
$116$	−13.9989			−1.29976
$117$		0			0
$118$	−2.40207			−0.221129
$119$	−0.841105	−	1.45684i	−0.0771040	−	0.133548i
$120$		0			0
$121$	3.34559	−	5.79474i	0.304145	−	0.526794i
$122$	−1.55747	+	2.69762i	−0.141007	+	0.244231i
$123$		0			0
$124$	−1.10840	−	1.91980i	−0.0995372	−	0.172404i
$125$	−5.45814			−0.488191
$126$		0			0
$127$	−6.87186			−0.609779			−0.304890	−	0.952388i	$-0.598620\pi$
$127$	−6.87186			−0.609779			−0.304890	+	0.952388i	$0.598620\pi$
$128$	−5.76925	−	9.99264i	−0.509935	−	0.883233i
$129$		0			0
$130$	−0.825341	+	1.42953i	−0.0723872	+	0.125378i
$131$	9.63892	−	16.6951i	0.842157	−	1.45866i	−0.0459109	−	0.998946i	$-0.514619\pi$
$131$	9.63892	−	16.6951i	0.842157	−	1.45866i	0.888068	−	0.459713i	$-0.152048\pi$
$132$		0			0
$133$	−1.43517	−	2.48578i	−0.124445	−	0.215545i
$134$	−2.76764			−0.239087
$135$		0			0
$136$	2.07577			0.177996
$137$	−1.99298	−	3.45194i	−0.170272	−	0.294920i	0.768243	−	0.640158i	$-0.221131\pi$
$137$	−1.99298	−	3.45194i	−0.170272	−	0.294920i	−0.938515	+	0.345239i	$0.887798\pi$
$138$		0			0
$139$	−7.47052	+	12.9393i	−0.633641	+	1.09750i	0.353160	+	0.935563i	$0.385107\pi$
$139$	−7.47052	+	12.9393i	−0.633641	+	1.09750i	−0.986801	+	0.161936i	$0.948226\pi$
$140$	0.797628	−	1.38153i	0.0674119	−	0.116761i
$141$		0			0
$142$	−0.583659	−	1.01093i	−0.0489796	−	0.0848351i
$143$	10.7821			0.901641
$144$		0			0
$145$	4.69119			0.389582
$146$	−2.60721	−	4.51581i	−0.215774	−	0.373731i
$147$		0			0
$148$	−2.94644	+	5.10339i	−0.242196	+	0.419496i
$149$	8.04410	−	13.9328i	0.658998	−	1.14142i	−0.321877	−	0.946781i	$-0.604314\pi$
$149$	8.04410	−	13.9328i	0.658998	−	1.14142i	0.980875	−	0.194637i	$-0.0623529\pi$
$150$		0			0
$151$	−0.0850853	−	0.147372i	−0.00692414	−	0.0119930i	0.862543	−	0.505984i	$-0.168871\pi$
$151$	−0.0850853	−	0.147372i	−0.00692414	−	0.0119930i	−0.869467	+	0.493992i	$0.835537\pi$
$152$	3.54186			0.287283
$153$		0			0
$154$	1.96847			0.158624
$155$	0.371438	+	0.643350i	0.0298346	+	0.0516751i
$156$		0			0
$157$	−10.0497	+	17.4066i	−0.802053	+	1.38920i	0.116210	+	0.993225i	$0.462925\pi$
$157$	−10.0497	+	17.4066i	−0.802053	+	1.38920i	−0.918263	+	0.395971i	$0.870408\pi$
$158$	−0.414343	+	0.717663i	−0.0329633	+	0.0570942i
$159$		0			0
$160$	1.51883	+	2.63068i	0.120074	+	0.207974i
$161$	−6.06679			−0.478130
$162$		0			0
$163$	21.4333			1.67879			0.839393	−	0.543525i	$-0.182911\pi$
$163$	21.4333			1.67879			0.839393	+	0.543525i	$0.182911\pi$
$164$	8.51400	+	14.7467i	0.664832	+	1.15152i
$165$		0			0
$166$	−1.25153	+	2.16772i	−0.0971376	+	0.168247i
$167$	−8.99494	+	15.5797i	−0.696049	+	1.20559i	0.273776	+	0.961793i	$0.411727\pi$
$167$	−8.99494	+	15.5797i	−0.696049	+	1.20559i	−0.969826	+	0.243799i	$0.921606\pi$
$168$		0			0
$169$	−6.99011	−	12.1072i	−0.537701	−	0.931325i
$170$	−0.317790			−0.0243734
$171$		0			0
$172$	17.5058			1.33481
$173$	5.48739	+	9.50444i	0.417198	+	0.722609i	0.995656	−	0.0931033i	$-0.0296787\pi$
$173$	5.48739	+	9.50444i	0.417198	+	0.722609i	−0.578458	+	0.815712i	$0.696345\pi$
$174$		0			0
$175$	3.93823	−	6.82121i	0.297702	−	0.515635i
$176$	2.27738	−	3.94453i	0.171664	−	0.297330i
$177$		0			0
$178$	−3.56483	−	6.17447i	−0.267196	−	0.462796i
$179$	23.4021			1.74915			0.874576	−	0.484888i	$-0.161139\pi$
$179$	23.4021			1.74915			0.874576	+	0.484888i	$0.161139\pi$
$180$		0			0
$181$	3.14609			0.233847			0.116924	−	0.993141i	$-0.462697\pi$
$181$	3.14609			0.233847			0.116924	+	0.993141i	$0.462697\pi$
$182$	−2.46288	−	4.26583i	−0.182561	−	0.316205i
$183$		0			0
$184$	3.74307	−	6.48318i	0.275943	−	0.477947i
$185$	0.987389	−	1.71021i	0.0725943	−	0.125737i
$186$		0			0
$187$	1.03788	+	1.79767i	0.0758976	+	0.131458i
$188$	10.5070			0.766300
$189$		0			0
$190$	−0.542242			−0.0393384
$191$	−1.95008	−	3.37763i	−0.141103	−	0.244397i	0.786809	−	0.617196i	$-0.211731\pi$
$191$	−1.95008	−	3.37763i	−0.141103	−	0.244397i	−0.927912	+	0.372799i	$0.878398\pi$
$192$		0			0
$193$	3.17017	−	5.49090i	0.228194	−	0.395243i	−0.729079	−	0.684430i	$-0.760051\pi$
$193$	3.17017	−	5.49090i	0.228194	−	0.395243i	0.957273	+	0.289186i	$0.0933847\pi$
$194$	−4.45203	+	7.71115i	−0.319637	+	0.553628i
$195$		0			0
$196$	−3.50755	−	6.07526i	−0.250539	−	0.433947i
$197$	−2.03488			−0.144979			−0.0724896	−	0.997369i	$-0.523094\pi$
$197$	−2.03488			−0.144979			−0.0724896	+	0.997369i	$0.523094\pi$
$198$		0			0
$199$	15.8792			1.12565			0.562824	−	0.826576i	$-0.309715\pi$
$199$	15.8792			1.12565			0.562824	+	0.826576i	$0.309715\pi$
$200$	4.85959	+	8.41706i	0.343625	+	0.595176i
$201$		0			0
$202$	−0.427617	+	0.740654i	−0.0300870	+	0.0521122i
$203$	−6.99943	+	12.1234i	−0.491264	+	0.850893i
$204$		0			0
$205$	−2.85314	−	4.94179i	−0.199272	−	0.345150i
$206$	6.57548			0.458135
$207$		0			0
$208$	−11.3975			−0.790273
$209$	1.77093	+	3.06734i	0.122498	+	0.212172i
$210$		0			0
$211$	2.95925	−	5.12556i	0.203723	−	0.352858i	−0.746002	−	0.665943i	$-0.768029\pi$
$211$	2.95925	−	5.12556i	0.203723	−	0.352858i	0.949725	+	0.313085i	$0.101363\pi$
$212$	−2.08509	+	3.61147i	−0.143204	+	0.248037i
$213$		0			0
$214$	−2.46837	−	4.27534i	−0.168734	−	0.292256i
$215$	−5.86642			−0.400086
$216$		0			0
$217$	−2.21680			−0.150486
$218$	−3.26983	−	5.66350i	−0.221461	−	0.383581i
$219$		0			0
$220$	−0.984236	+	1.70475i	−0.0663572	+	0.114934i
$221$	2.59712	−	4.49835i	0.174701	−	0.302592i
$222$		0			0
$223$	8.02995	+	13.9083i	0.537725	+	0.931368i	0.999026	+	0.0441239i	$0.0140496\pi$
$223$	8.02995	+	13.9083i	0.537725	+	0.931368i	−0.461301	+	0.887244i	$0.652617\pi$
$224$	−9.06458			−0.605653
$225$		0			0
$226$	−8.27108			−0.550184
$227$	7.06350	+	12.2343i	0.468821	+	0.812021i	0.999365	−	0.0356360i	$-0.0113457\pi$
$227$	7.06350	+	12.2343i	0.468821	+	0.812021i	−0.530544	+	0.847657i	$0.678012\pi$
$228$		0			0
$229$	−3.05279	+	5.28759i	−0.201734	+	0.349414i	−0.949087	−	0.315013i	$-0.897991\pi$
$229$	−3.05279	+	5.28759i	−0.201734	+	0.349414i	0.747353	+	0.664427i	$0.231324\pi$
$230$	−0.573046	+	0.992545i	−0.0377855	+	0.0654465i
$231$		0			0
$232$	−8.63697	−	14.9597i	−0.567045	−	0.982150i
$233$	13.7798			0.902748			0.451374	−	0.892335i	$-0.350934\pi$
$233$	13.7798			0.902748			0.451374	+	0.892335i	$0.350934\pi$
$234$		0			0
$235$	−3.52102			−0.229686
$236$	3.58398	+	6.20764i	0.233297	+	0.404083i
$237$		0			0
$238$	0.474155	−	0.821261i	0.0307349	−	0.0532344i
$239$	11.6985	−	20.2624i	0.756713	−	1.31067i	−0.187805	−	0.982206i	$-0.560137\pi$
$239$	11.6985	−	20.2624i	0.756713	−	1.31067i	0.944518	−	0.328460i	$-0.106529\pi$
$240$		0			0
$241$	−14.3845	−	24.9147i	−0.926589	−	1.60490i	−0.788986	−	0.614411i	$-0.789394\pi$
$241$	−14.3845	−	24.9147i	−0.926589	−	1.60490i	−0.137602	−	0.990488i	$-0.543940\pi$
$242$	3.77202			0.242474
$243$		0			0
$244$	9.29524			0.595067
$245$	1.17542	+	2.03589i	0.0750950	+	0.130068i
$246$		0			0
$247$	4.43144	−	7.67548i	0.281966	−	0.488379i
$248$	1.36771	−	2.36895i	0.0868499	−	0.150428i
$249$		0			0
$250$	−1.53846	−	2.66468i	−0.0973005	−	0.168529i
$251$	−22.6143			−1.42740			−0.713700	−	0.700451i	$-0.752982\pi$
$251$	−22.6143			−1.42740			−0.713700	+	0.700451i	$0.752982\pi$
$252$		0			0
$253$	7.48614			0.470649
$254$	−1.93693	−	3.35487i	−0.121534	−	0.210503i
$255$		0			0
$256$	1.90145	−	3.29341i	0.118841	−	0.205838i
$257$	12.1795	−	21.0956i	0.759738	−	1.31591i	−0.183246	−	0.983067i	$-0.558660\pi$
$257$	12.1795	−	21.0956i	0.759738	−	1.31591i	0.942984	−	0.332838i	$-0.108006\pi$
$258$		0			0
$259$	2.94644	+	5.10339i	0.183083	+	0.317109i
$260$	4.92576			0.305483
$261$		0			0
$262$	10.8675			0.671395
$263$	15.5016	+	26.8495i	0.955868	+	1.65561i	0.732369	+	0.680908i	$0.238415\pi$
$263$	15.5016	+	26.8495i	0.955868	+	1.65561i	0.223500	+	0.974704i	$0.428252\pi$
$264$		0			0
$265$	0.698737	−	1.21025i	0.0429231	−	0.0743450i
$266$	0.809045	−	1.40131i	0.0496057	−	0.0859197i
$267$		0			0
$268$	4.12942	+	7.15236i	0.252244	+	0.436900i
$269$	31.2060			1.90266			0.951332	−	0.308169i	$-0.0997162\pi$
$269$	31.2060			1.90266			0.951332	+	0.308169i	$0.0997162\pi$
$270$		0			0
$271$	−16.6097			−1.00897			−0.504483	−	0.863422i	$-0.668317\pi$
$271$	−16.6097			−1.00897			−0.504483	+	0.863422i	$0.668317\pi$
$272$	−1.09712	−	1.90028i	−0.0665229	−	0.115221i
$273$		0			0
$274$	1.12350	−	1.94596i	0.0678732	−	0.117560i
$275$	−4.85959	+	8.41706i	−0.293044	+	0.507568i
$276$		0			0
$277$	−3.81469	−	6.60723i	−0.229202	−	0.396990i	0.728370	−	0.685184i	$-0.240278\pi$
$277$	−3.81469	−	6.60723i	−0.229202	−	0.396990i	−0.957572	+	0.288194i	$0.906945\pi$
$278$	−8.42270			−0.505160
$279$		0			0
$280$	1.96847			0.117639
$281$	−13.4470	−	23.2908i	−0.802179	−	1.38942i	−0.918179	−	0.396166i	$-0.870340\pi$
$281$	−13.4470	−	23.2908i	−0.802179	−	1.38942i	0.116000	−	0.993249i	$-0.462993\pi$
$282$		0			0
$283$	0.175423	−	0.303841i	0.0104278	−	0.0180615i	−0.860764	−	0.509004i	$-0.830014\pi$
$283$	0.175423	−	0.303841i	0.0104278	−	0.0180615i	0.871192	+	0.490942i	$0.163347\pi$
$284$	−1.74168	+	3.01668i	−0.103350	+	0.179007i
$285$		0			0
$286$	3.03908	+	5.26384i	0.179704	+	0.311257i
$287$	17.0280			1.00513
$288$		0			0
$289$	1.00000			0.0588235
$290$	1.32228	+	2.29025i	0.0776469	+	0.134488i
$291$		0			0
$292$	−7.78010	+	13.4755i	−0.455296	+	0.788595i
$293$	−8.47969	+	14.6873i	−0.495389	+	0.858039i	−0.999986	−	0.00531644i	$-0.998308\pi$
$293$	−8.47969	+	14.6873i	−0.495389	+	0.858039i	0.504597	+	0.863355i	$0.331641\pi$
$294$		0			0
$295$	−1.20104	−	2.08025i	−0.0699270	−	0.121117i
$296$	−7.27154			−0.422650
$297$		0			0
$298$	9.06938			0.525375
$299$	−9.36638	−	16.2230i	−0.541672	−	0.938203i
$300$		0			0
$301$	8.75292	−	15.1605i	0.504510	−	0.873837i
$302$	0.0479650	−	0.0830779i	0.00276008	−	0.00478059i
$303$		0			0
$304$	−1.87201	−	3.24242i	−0.107367	−	0.185965i
$305$	−3.11495			−0.178361
$306$		0			0
$307$	13.4800			0.769345			0.384672	−	0.923053i	$-0.374314\pi$
$307$	13.4800			0.769345			0.384672	+	0.923053i	$0.374314\pi$
$308$	−2.93703	−	5.08709i	−0.167353	−	0.289864i
$309$		0			0
$310$	−0.209390	+	0.362675i	−0.0118926	+	0.0205986i
$311$	−5.95729	+	10.3183i	−0.337807	+	0.585098i	−0.984020	−	0.178058i	$-0.943018\pi$
$311$	−5.95729	+	10.3183i	−0.337807	+	0.585098i	0.646213	+	0.763157i	$0.276352\pi$
$312$		0			0
$313$	−4.68527	−	8.11513i	−0.264827	−	0.458694i	0.702691	−	0.711495i	$-0.251982\pi$
$313$	−4.68527	−	8.11513i	−0.264827	−	0.458694i	−0.967518	+	0.252801i	$0.918648\pi$
$314$	−11.3306			−0.639423
$315$		0			0
$316$	2.47286			0.139109
$317$	−10.6675	−	18.4766i	−0.599146	−	1.03775i	−0.992947	−	0.118556i	$-0.962174\pi$
$317$	−10.6675	−	18.4766i	−0.599146	−	1.03775i	0.393801	−	0.919196i	$-0.371160\pi$
$318$		0			0
$319$	8.63697	−	14.9597i	0.483577	−	0.837580i
$320$	0.380755	−	0.659488i	0.0212849	−	0.0368665i
$321$		0			0
$322$	−1.71001	−	2.96183i	−0.0952953	−	0.165056i
$323$	1.70629			0.0949404
$324$		0			0
$325$	24.3206			1.34906
$326$	6.04129	+	10.4638i	0.334596	+	0.579537i
$327$		0			0
$328$	−10.5059	+	18.1967i	−0.580090	+	1.00475i
$329$	5.25349	−	9.09931i	0.289634	−	0.501661i
$330$		0			0
$331$	8.77485	+	15.1985i	0.482309	+	0.835384i	0.999794	−	0.0203086i	$-0.00646487\pi$
$331$	8.77485	+	15.1985i	0.482309	+	0.835384i	−0.517485	+	0.855693i	$0.673132\pi$
$332$	7.46933			0.409933
$333$		0			0
$334$	−10.1414			−0.554914
$335$	−1.38382	−	2.39684i	−0.0756060	−	0.130953i
$336$		0			0
$337$	−15.1203	+	26.1891i	−0.823655	+	1.42661i	0.0792884	+	0.996852i	$0.474735\pi$
$337$	−15.1203	+	26.1891i	−0.823655	+	1.42661i	−0.902943	+	0.429760i	$0.858598\pi$
$338$	3.94053	−	6.82519i	0.214336	−	0.371242i
$339$		0			0
$340$	0.474155	+	0.821261i	0.0257147	+	0.0445391i
$341$	2.73543			0.148132
$342$		0			0
$343$	−18.7906			−1.01460
$344$	10.8007	+	18.7073i	0.582334	+	1.00863i
$345$		0			0
$346$	−3.09340	+	5.35793i	−0.166302	+	0.288044i
$347$	4.87397	−	8.44196i	0.261648	−	0.453188i	−0.705032	−	0.709176i	$-0.749067\pi$
$347$	4.87397	−	8.44196i	0.261648	−	0.453188i	0.966680	+	0.255988i	$0.0824006\pi$
$348$		0			0
$349$	−1.89084	−	3.27502i	−0.101214	−	0.175308i	0.810971	−	0.585086i	$-0.198939\pi$
$349$	−1.89084	−	3.27502i	−0.101214	−	0.175308i	−0.912185	+	0.409778i	$0.865606\pi$
$350$	4.44019			0.237338
$351$		0			0
$352$	11.1853			0.596177
$353$	−7.12765	−	12.3455i	−0.379367	−	0.657082i	0.611604	−	0.791164i	$-0.290525\pi$
$353$	−7.12765	−	12.3455i	−0.379367	−	0.657082i	−0.990970	+	0.134082i	$0.957191\pi$
$354$		0			0
$355$	0.583659	−	1.01093i	0.0309774	−	0.0536544i
$356$	−10.6377	+	18.4251i	−0.563799	+	0.976528i
$357$		0			0
$358$	6.59621	+	11.4250i	0.348621	+	0.603829i
$359$	12.2391			0.645953			0.322976	−	0.946407i	$-0.395317\pi$
$359$	12.2391			0.645953			0.322976	+	0.946407i	$0.395317\pi$
$360$		0			0
$361$	−16.0886			−0.846767
$362$	0.886772	+	1.53593i	0.0466077	+	0.0807269i
$363$		0			0
$364$	−7.34942	+	12.7296i	−0.385214	+	0.667211i
$365$	2.60721	−	4.51581i	0.136467	−	0.236368i
$366$		0			0
$367$	5.26729	+	9.12322i	0.274951	+	0.476228i	0.970123	−	0.242615i	$-0.0780052\pi$
$367$	5.26729	+	9.12322i	0.274951	+	0.476228i	−0.695172	+	0.718843i	$0.744672\pi$
$368$	−7.91343			−0.412516
$369$		0			0
$370$	1.11324			0.0578745
$371$	2.08509	+	3.61147i	0.108252	+	0.187498i
$372$		0			0
$373$	4.41400	−	7.64528i	0.228548	−	0.395857i	−0.728830	−	0.684695i	$-0.759935\pi$
$373$	4.41400	−	7.64528i	0.228548	−	0.395857i	0.957378	+	0.288838i	$0.0932688\pi$
$374$	−0.585085	+	1.01340i	−0.0302540	+	0.0524015i
$375$		0			0
$376$	6.48256	+	11.2281i	0.334313	+	0.579046i
$377$	−43.2250			−2.22620
$378$		0			0
$379$	7.68221			0.394609			0.197304	−	0.980342i	$-0.436781\pi$
$379$	7.68221			0.394609			0.197304	+	0.980342i	$0.436781\pi$
$380$	0.809045	+	1.40131i	0.0415031	+	0.0718856i
$381$		0			0
$382$	1.09931	−	1.90407i	0.0562458	−	0.0974206i
$383$	−15.0287	+	26.0304i	−0.767929	+	1.33009i	0.170756	+	0.985313i	$0.445379\pi$
$383$	−15.0287	+	26.0304i	−0.767929	+	1.33009i	−0.938684	+	0.344778i	$0.887954\pi$
$384$		0			0
$385$	0.984236	+	1.70475i	0.0501613	+	0.0868819i
$386$	3.57423			0.181924
$387$		0			0
$388$	26.5704			1.34891
$389$	−18.2127	−	31.5454i	−0.923422	−	1.59941i	−0.794079	−	0.607814i	$-0.792046\pi$
$389$	−18.2127	−	31.5454i	−0.923422	−	1.59941i	−0.129343	−	0.991600i	$-0.541287\pi$
$390$		0			0
$391$	1.80322	−	3.12327i	0.0911928	−	0.157951i
$392$	4.32815	−	7.49658i	0.218605	−	0.378635i
$393$		0			0
$394$	−0.573560	−	0.993436i	−0.0288956	−	0.0500486i
$395$	−0.828685			−0.0416957
$396$		0			0
$397$	−13.1637			−0.660670			−0.330335	−	0.943864i	$-0.607162\pi$
$397$	−13.1637			−0.660670			−0.330335	+	0.943864i	$0.607162\pi$
$398$	4.47579	+	7.75230i	0.224351	+	0.388588i
$399$		0			0
$400$	5.13697	−	8.89749i	0.256848	−	0.444874i
$401$	10.1156	−	17.5208i	0.505149	−	0.874945i	−0.494833	−	0.868988i	$-0.664771\pi$
$401$	10.1156	−	17.5208i	0.505149	−	0.874945i	0.999982	−	0.00595634i	$-0.00189597\pi$
$402$		0			0
$403$	−3.42247	−	5.92788i	−0.170485	−	0.295289i
$404$	2.55208			0.126971
$405$		0			0
$406$	−7.89156			−0.391652
$407$	−3.63577	−	6.29734i	−0.180219	−	0.312148i
$408$		0			0
$409$	−18.3515	+	31.7857i	−0.907422	+	1.57170i	−0.0897886	+	0.995961i	$0.528619\pi$
$409$	−18.3515	+	31.7857i	−0.907422	+	1.57170i	−0.817633	+	0.575740i	$0.804714\pi$
$410$	1.60840	−	2.78583i	0.0794332	−	0.137582i
$411$		0			0
$412$	−9.81086	−	16.9929i	−0.483346	−	0.837181i
$413$	7.16796			0.352712
$414$		0			0
$415$	−2.50306			−0.122870
$416$	−13.9946	−	24.2394i	−0.686142	−	1.18843i
$417$		0			0
$418$	−0.998324	+	1.72915i	−0.0488296	+	0.0845754i
$419$	−7.62731	+	13.2109i	−0.372618	+	0.645394i	−0.989967	−	0.141295i	$-0.954873\pi$
$419$	−7.62731	+	13.2109i	−0.372618	+	0.645394i	0.617349	+	0.786689i	$0.288207\pi$
$420$		0			0
$421$	−6.68078	−	11.5715i	−0.325601	−	0.563958i	0.656032	−	0.754733i	$-0.272233\pi$
$421$	−6.68078	−	11.5715i	−0.325601	−	0.563958i	−0.981634	+	0.190774i	$0.938900\pi$
$422$	3.33642			0.162415
$423$		0			0
$424$	−5.14580			−0.249902
$425$	2.34110	+	4.05491i	0.113560	+	0.196692i
$426$		0			0
$427$	4.64762	−	8.04991i	0.224914	−	0.389563i
$428$	−7.36581	+	12.7579i	−0.356040	+	0.616679i
$429$		0			0
$430$	−1.65353	−	2.86401i	−0.0797405	−	0.138115i
$431$	−19.3600			−0.932540			−0.466270	−	0.884642i	$-0.654403\pi$
$431$	−19.3600			−0.932540			−0.466270	+	0.884642i	$0.654403\pi$
$432$		0			0
$433$	−20.9302			−1.00584			−0.502922	−	0.864332i	$-0.667742\pi$
$433$	−20.9302			−1.00584			−0.502922	+	0.864332i	$0.667742\pi$
$434$	−0.624837	−	1.08225i	−0.0299931	−	0.0519496i
$435$		0			0
$436$	−9.75741	+	16.9003i	−0.467295	+	0.809379i
$437$	3.07681	−	5.32920i	0.147184	−	0.254930i
$438$		0			0
$439$	−8.28291	−	14.3464i	−0.395322	−	0.684717i	0.597820	−	0.801630i	$-0.296034\pi$
$439$	−8.28291	−	14.3464i	−0.395322	−	0.684717i	−0.993142	+	0.116913i	$0.962700\pi$
$440$	−2.42900			−0.115798
$441$		0			0
$442$	2.92815			0.139278
$443$	−2.82796	−	4.89817i	−0.134361	−	0.232719i	0.790992	−	0.611826i	$-0.209565\pi$
$443$	−2.82796	−	4.89817i	−0.134361	−	0.232719i	−0.925353	+	0.379107i	$0.876231\pi$
$444$		0			0
$445$	3.56483	−	6.17447i	0.168989	−	0.292698i
$446$	−4.52672	+	7.84050i	−0.214346	+	0.371259i
$447$		0			0
$448$	1.13620	+	1.96796i	0.0536805	+	0.0929774i
$449$	−3.40360			−0.160626			−0.0803129	−	0.996770i	$-0.525592\pi$
$449$	−3.40360			−0.160626			−0.0803129	+	0.996770i	$0.525592\pi$
$450$		0			0
$451$	−21.0117			−0.989405
$452$	12.3408	+	21.3748i	0.580461	+	1.00539i
$453$		0			0
$454$	−3.98190	+	6.89685i	−0.186880	+	0.323685i
$455$	2.46288	−	4.26583i	0.115462	−	0.199985i
$456$		0			0
$457$	4.75832	+	8.24165i	0.222585	+	0.385528i	0.955592	−	0.294693i	$-0.0952173\pi$
$457$	4.75832	+	8.24165i	0.222585	+	0.385528i	−0.733007	+	0.680221i	$0.761884\pi$
$458$	−3.44190			−0.160829
$459$		0			0
$460$	3.42003			0.159460
$461$	0.00253032	+	0.00438263i	0.000117849	+	0.000204120i	0.866084	−	0.499898i	$-0.166629\pi$
$461$	0.00253032	+	0.00438263i	0.000117849	+	0.000204120i	−0.865966	+	0.500102i	$0.833296\pi$
$462$		0			0
$463$	12.1061	−	20.9684i	0.562618	−	0.974483i	−0.434649	−	0.900600i	$-0.643127\pi$
$463$	12.1061	−	20.9684i	0.562618	−	0.974483i	0.997267	−	0.0738833i	$-0.0235392\pi$
$464$	−9.12995	+	15.8135i	−0.423847	+	0.734125i
$465$		0			0
$466$	3.88405	+	6.72737i	0.179925	+	0.311639i
$467$	−9.24373			−0.427749			−0.213874	−	0.976861i	$-0.568608\pi$
$467$	−9.24373			−0.427749			−0.213874	+	0.976861i	$0.568608\pi$
$468$		0			0
$469$	8.25883			0.381357
$470$	−0.992449	−	1.71897i	−0.0457783	−	0.0792903i
$471$		0			0
$472$	−4.42247	+	7.65993i	−0.203560	+	0.352577i
$473$	−10.8007	+	18.7073i	−0.496616	+	0.860165i
$474$		0			0
$475$	3.99460	+	6.91885i	0.183285	+	0.317459i
$476$	−2.82983			−0.129705
$477$		0			0
$478$	13.1896			0.603277
$479$	11.9761	+	20.7432i	0.547203	+	0.947783i	0.998465	+	0.0553912i	$0.0176406\pi$
$479$	11.9761	+	20.7432i	0.547203	+	0.947783i	−0.451262	+	0.892391i	$0.649026\pi$
$480$		0			0
$481$	−9.09789	+	15.7580i	−0.414828	+	0.718503i
$482$	8.10897	−	14.0452i	0.369354	−	0.639739i
$483$		0			0
$484$	−5.62799	−	9.74796i	−0.255818	−	0.443089i
$485$	−8.90407			−0.404313
$486$		0			0
$487$	−28.0512			−1.27112			−0.635561	−	0.772051i	$-0.719231\pi$
$487$	−28.0512			−1.27112			−0.635561	+	0.772051i	$0.719231\pi$
$488$	5.73495	+	9.93322i	0.259609	+	0.449656i
$489$		0			0
$490$	−0.662620	+	1.14769i	−0.0299341	+	0.0518474i
$491$	9.70733	−	16.8136i	0.438086	−	0.758787i	−0.559456	−	0.828860i	$-0.688990\pi$
$491$	9.70733	−	16.8136i	0.438086	−	0.758787i	0.997542	+	0.0700731i	$0.0223233\pi$
$492$		0			0
$493$	−4.16085	−	7.20681i	−0.187395	−	0.324578i
$494$	4.99626			0.224793
$495$		0			0
$496$	−2.89156			−0.129835
$497$	1.74168	+	3.01668i	0.0781251	+	0.135317i
$498$		0			0
$499$	−4.96552	+	8.60053i	−0.222287	+	0.385013i	−0.955502	−	0.294984i	$-0.904686\pi$
$499$	−4.96552	+	8.60053i	−0.222287	+	0.385013i	0.733215	+	0.679997i	$0.238019\pi$
$500$	−4.59087	+	7.95162i	−0.205310	+	0.355607i
$501$		0			0
$502$	−6.37416	−	11.0404i	−0.284493	−	0.492756i
$503$	9.73782			0.434188			0.217094	−	0.976151i	$-0.430342\pi$
$503$	9.73782			0.434188			0.217094	+	0.976151i	$0.430342\pi$
$504$		0			0
$505$	−0.855233			−0.0380574
$506$	2.11008	+	3.65476i	0.0938043	+	0.162474i
$507$		0			0
$508$	−5.77996	+	10.0112i	−0.256444	+	0.444174i
$509$	−4.36925	+	7.56776i	−0.193664	+	0.335435i	−0.946462	−	0.322816i	$-0.895370\pi$
$509$	−4.36925	+	7.56776i	−0.193664	+	0.335435i	0.752798	+	0.658252i	$0.228704\pi$
$510$		0			0
$511$	7.78010	+	13.4755i	0.344171	+	0.596122i
$512$	−20.9332			−0.925126
$513$		0			0
$514$	13.7319			0.605688
$515$	3.28774	+	5.69453i	0.144875	+	0.250931i
$516$		0			0
$517$	−6.48256	+	11.2281i	−0.285103	+	0.493812i
$518$	−1.66099	+	2.87693i	−0.0729799	+	0.126405i
$519$		0			0
$520$	3.03908	+	5.26384i	0.133272	+	0.230835i
$521$	−15.7724			−0.691001			−0.345501	−	0.938419i	$-0.612291\pi$
$521$	−15.7724			−0.691001			−0.345501	+	0.938419i	$0.612291\pi$
$522$		0			0
$523$	27.1291			1.18627			0.593136	−	0.805102i	$-0.297890\pi$
$523$	27.1291			1.18627			0.593136	+	0.805102i	$0.297890\pi$
$524$	−16.2147	−	28.0847i	−0.708342	−	1.22688i
$525$		0			0
$526$	−8.73869	+	15.1359i	−0.381025	+	0.659954i
$527$	0.658895	−	1.14124i	0.0287019	−	0.0497132i
$528$		0			0
$529$	4.99679	+	8.65469i	0.217252	+	0.376291i
$530$	0.787797			0.0342197
$531$		0			0
$532$	−4.82850			−0.209342
$533$	26.2891	+	45.5341i	1.13871	+	1.97230i
$534$		0			0
$535$	2.46837	−	4.27534i	0.106717	−	0.184839i
$536$	−5.09551	+	8.82568i	−0.220092	+	0.381211i
$537$		0			0
$538$	8.79586	+	15.2349i	0.379217	+	0.656822i
$539$	8.65631			0.372854
$540$		0			0
$541$	−21.6670			−0.931538			−0.465769	−	0.884906i	$-0.654222\pi$
$541$	−21.6670			−0.931538			−0.465769	+	0.884906i	$0.654222\pi$
$542$	−4.68168	−	8.10890i	−0.201095	−	0.348307i
$543$		0			0
$544$	2.69425	−	4.66658i	0.115515	−	0.200078i
$545$	3.26983	−	5.66350i	0.140064	−	0.242598i
$546$		0			0
$547$	−14.0615	−	24.3552i	−0.601226	−	1.04135i	−0.992636	−	0.121137i	$-0.961346\pi$
$547$	−14.0615	−	24.3552i	−0.601226	−	1.04135i	0.391410	−	0.920216i	$-0.371987\pi$
$548$	−6.70522			−0.286433
$549$		0			0
$550$	−5.47898			−0.233625
$551$	−7.09961	−	12.2969i	−0.302454	−	0.523865i
$552$		0			0
$553$	1.23643	−	2.14156i	0.0525783	−	0.0910684i
$554$	2.15045	−	3.72469i	0.0913639	−	0.158247i
$555$		0			0
$556$	12.5670	+	21.7667i	0.532959	+	0.923112i
$557$	25.4592			1.07874			0.539371	−	0.842069i	$-0.318662\pi$
$557$	25.4592			1.07874			0.539371	+	0.842069i	$0.318662\pi$
$558$		0			0
$559$	54.0537			2.28623
$560$	−1.04041	−	1.80205i	−0.0439655	−	0.0761505i
$561$		0			0
$562$	7.58045	−	13.1297i	0.319762	−	0.553844i
$563$	20.6985	−	35.8509i	0.872338	−	1.51093i	0.0127663	−	0.999919i	$-0.495936\pi$
$563$	20.6985	−	35.8509i	0.872338	−	1.51093i	0.859572	−	0.511015i	$-0.170730\pi$
$564$		0			0
$565$	−4.13554	−	7.16297i	−0.173983	−	0.301348i
$566$	0.197782			0.00831339
$567$		0			0
$568$	−4.29831			−0.180353
$569$	−3.79246	−	6.56873i	−0.158988	−	0.275376i	0.775516	−	0.631328i	$-0.217490\pi$
$569$	−3.79246	−	6.56873i	−0.158988	−	0.275376i	−0.934504	+	0.355952i	$0.884157\pi$
$570$		0			0
$571$	6.45487	−	11.1802i	0.270128	−	0.467875i	−0.698767	−	0.715350i	$-0.746267\pi$
$571$	6.45487	−	11.1802i	0.270128	−	0.467875i	0.968894	+	0.247475i	$0.0796007\pi$
$572$	9.06884	−	15.7077i	0.379187	−	0.656772i
$573$		0			0
$574$	4.79959	+	8.31313i	0.200331	+	0.346983i
$575$	16.8861			0.704200
$576$		0			0
$577$	−28.6186			−1.19141			−0.595703	−	0.803204i	$-0.703127\pi$
$577$	−28.6186			−1.19141			−0.595703	+	0.803204i	$0.703127\pi$
$578$	0.281864	+	0.488204i	0.0117240	+	0.0203066i
$579$		0			0
$580$	3.94578	−	6.83429i	0.163840	−	0.283779i
$581$	3.73466	−	6.46863i	0.154940	−	0.268364i
$582$		0			0
$583$	−2.57290	−	4.45639i	−0.106559	−	0.184565i
$584$	−19.2006			−0.794525
$585$		0			0
$586$	−9.56049			−0.394940
$587$	−3.32964	−	5.76710i	−0.137429	−	0.238034i	0.789094	−	0.614273i	$-0.210551\pi$
$587$	−3.32964	−	5.76710i	−0.137429	−	0.238034i	−0.926523	+	0.376239i	$0.877217\pi$
$588$		0			0
$589$	1.12426	−	1.94728i	0.0463245	−	0.0802364i
$590$	0.677059	−	1.17270i	0.0278741	−	0.0482793i
$591$		0			0
$592$	3.84330	+	6.65678i	0.157958	+	0.273592i
$593$	13.1202			0.538782			0.269391	−	0.963031i	$-0.413178\pi$
$593$	13.1202			0.538782			0.269391	+	0.963031i	$0.413178\pi$
$594$		0			0
$595$	0.948310			0.0388769
$596$	−13.5319	−	23.4379i	−0.554287	−	0.960053i
$597$		0			0
$598$	5.28010	−	9.14540i	0.215919	−	0.373983i
$599$	−13.5595	+	23.4858i	−0.554027	+	0.959603i	0.443951	+	0.896051i	$0.353576\pi$
$599$	−13.5595	+	23.4858i	−0.554027	+	0.959603i	−0.997979	+	0.0635522i	$0.979757\pi$
$600$		0			0
$601$	3.86223	+	6.68958i	0.157544	+	0.272874i	0.933982	−	0.357319i	$-0.116309\pi$
$601$	3.86223	+	6.68958i	0.157544	+	0.272874i	−0.776439	+	0.630193i	$0.782976\pi$
$602$	9.86855			0.402212
$603$		0			0
$604$	−0.286262			−0.0116479
$605$	1.88601	+	3.26666i	0.0766771	+	0.132809i
$606$		0			0
$607$	23.1586	−	40.1119i	0.939979	−	1.62809i	0.174473	−	0.984662i	$-0.444178\pi$
$607$	23.1586	−	40.1119i	0.939979	−	1.62809i	0.765506	−	0.643429i	$-0.222489\pi$
$608$	4.59716	−	7.96252i	0.186440	−	0.322923i
$609$		0			0
$610$	−0.877993	−	1.52073i	−0.0355489	−	0.0615725i
$611$	32.4430			1.31250
$612$		0			0
$613$	34.6545			1.39968			0.699841	−	0.714299i	$-0.253254\pi$
$613$	34.6545			1.39968			0.699841	+	0.714299i	$0.253254\pi$
$614$	3.79954	+	6.58099i	0.153337	+	0.265587i
$615$		0			0
$616$	3.62416	−	6.27724i	0.146022	−	0.252917i
$617$	2.49135	−	4.31514i	0.100298	−	0.173721i	−0.811510	−	0.584339i	$-0.801354\pi$
$617$	2.49135	−	4.31514i	0.100298	−	0.173721i	0.911807	+	0.410618i	$0.134687\pi$
$618$		0			0
$619$	16.8220	+	29.1365i	0.676133	+	1.17110i	0.976136	+	0.217158i	$0.0696788\pi$
$619$	16.8220	+	29.1365i	0.676133	+	1.17110i	−0.300004	+	0.953938i	$0.596988\pi$
$620$	1.24967			0.0501881
$621$		0			0
$622$	−6.71659			−0.269311
$623$	10.6377	+	18.4251i	0.426192	+	0.738186i
$624$		0			0
$625$	−10.1671	+	17.6099i	−0.406683	+	0.704395i
$626$	2.64122	−	4.57473i	0.105565	−	0.182843i
$627$		0			0
$628$	16.9057	+	29.2815i	0.674610	+	1.16846i
$629$	−3.50306			−0.139676
$630$		0			0
$631$	−27.4426			−1.09247			−0.546236	−	0.837631i	$-0.683940\pi$
$631$	−27.4426			−1.09247			−0.546236	+	0.837631i	$0.683940\pi$
$632$	1.52570	+	2.64258i	0.0606889	+	0.105116i
$633$		0			0
$634$	6.01357	−	10.4158i	0.238830	−	0.413665i
$635$	1.93693	−	3.35487i	0.0768649	−	0.133134i
$636$		0			0
$637$	−10.8305	−	18.7589i	−0.429118	−	0.743254i
$638$	9.73782			0.385524
$639$		0			0
$640$	6.50459			0.257116
$641$	−6.52910	−	11.3087i	−0.257884	−	0.446668i	0.707791	−	0.706422i	$-0.249692\pi$
$641$	−6.52910	−	11.3087i	−0.257884	−	0.446668i	−0.965675	+	0.259754i	$0.916359\pi$
$642$		0			0
$643$	4.96782	−	8.60451i	0.195912	−	0.339329i	−0.751287	−	0.659975i	$-0.770567\pi$
$643$	4.96782	−	8.60451i	0.195912	−	0.339329i	0.947199	+	0.320646i	$0.103900\pi$
$644$	−5.10281	+	8.83832i	−0.201079	+	0.348279i
$645$		0			0
$646$	0.480942	+	0.833016i	0.0189224	+	0.0327746i
$647$	−22.1278			−0.869935			−0.434968	−	0.900446i	$-0.643240\pi$
$647$	−22.1278			−0.869935			−0.434968	+	0.900446i	$0.643240\pi$
$648$		0			0
$649$	−8.84493			−0.347194
$650$	6.85510	+	11.8734i	0.268879	+	0.465712i
$651$		0			0
$652$	18.0277	−	31.2248i	0.706017	−	1.22286i
$653$	6.44631	−	11.1653i	0.252264	−	0.436933i	−0.711885	−	0.702296i	$-0.752158\pi$
$653$	6.44631	−	11.1653i	0.252264	−	0.436933i	0.964149	+	0.265363i	$0.0854916\pi$
$654$		0			0
$655$	5.43374	+	9.41152i	0.212314	+	0.367738i
$656$	22.2111			0.867196
$657$		0			0
$658$	5.92309			0.230906
$659$	−7.19851	−	12.4682i	−0.280414	−	0.485691i	0.691073	−	0.722785i	$-0.257138\pi$
$659$	−7.19851	−	12.4682i	−0.280414	−	0.485691i	−0.971487	+	0.237094i	$0.923805\pi$
$660$		0			0
$661$	6.35902	−	11.0141i	0.247337	−	0.428401i	−0.715449	−	0.698665i	$-0.753778\pi$
$661$	6.35902	−	11.0141i	0.247337	−	0.428401i	0.962786	+	0.270264i	$0.0871111\pi$
$662$	−4.94663	+	8.56782i	−0.192256	+	0.332998i
$663$		0			0
$664$	4.60840	+	7.98198i	0.178841	+	0.309761i
$665$	1.61809			0.0627469
$666$		0			0
$667$	−30.0117			−1.16206
$668$	15.1314	+	26.2083i	0.585450	+	1.01403i
$669$		0			0
$670$	0.780098	−	1.35117i	0.0301378	−	0.0522002i
$671$	−5.73495	+	9.93322i	−0.221395	+	0.383468i
$672$		0			0
$673$	−7.28612	−	12.6199i	−0.280859	−	0.486463i	0.690737	−	0.723106i	$-0.257286\pi$
$673$	−7.28612	−	12.6199i	−0.280859	−	0.486463i	−0.971597	+	0.236643i	$0.923953\pi$
$674$	−17.0475			−0.656645
$675$		0			0
$676$	−23.5177			−0.904526
$677$	−0.789032	−	1.36664i	−0.0303250	−	0.0525244i	0.850465	−	0.526032i	$-0.176321\pi$
$677$	−0.789032	−	1.36664i	−0.0303250	−	0.0525244i	−0.880790	+	0.473508i	$0.842988\pi$
$678$		0			0
$679$	13.2852	−	23.0107i	0.509840	−	0.883068i
$680$	−0.585085	+	1.01340i	−0.0224370	+	0.0388620i
$681$		0			0
$682$	0.771020	+	1.33545i	0.0295239	+	0.0511368i
$683$	−3.39595			−0.129942			−0.0649712	−	0.997887i	$-0.520696\pi$
$683$	−3.39595			−0.129942			−0.0649712	+	0.997887i	$0.520696\pi$
$684$		0			0
$685$	2.24700			0.0858535
$686$	−5.29639	−	9.17362i	−0.202217	−	0.350251i
$687$		0			0
$688$	11.4172	−	19.7751i	0.435276	−	0.753920i
$689$	−6.43823	+	11.1513i	−0.245277	+	0.424832i
$690$		0			0
$691$	−4.75368	−	8.23362i	−0.180839	−	0.313222i	0.761328	−	0.648367i	$-0.224548\pi$
$691$	−4.75368	−	8.23362i	−0.180839	−	0.313222i	−0.942166	+	0.335146i	$0.891214\pi$
$692$	18.4619			0.701815
$693$		0			0
$694$	5.49519			0.208595
$695$	−4.21135	−	7.29427i	−0.159746	−	0.276687i
$696$		0			0
$697$	−5.06120	+	8.76625i	−0.191707	+	0.332046i
$698$	1.06592	−	1.84623i	0.0403456	−	0.0698807i
$699$		0			0
$700$	−6.62493	−	11.4747i	−0.250399	−	0.433703i
$701$	17.4848			0.660392			0.330196	−	0.943912i	$-0.392885\pi$
$701$	17.4848			0.660392			0.330196	+	0.943912i	$0.392885\pi$
$702$		0			0
$703$	−5.97723			−0.225436
$704$	−1.40202	−	2.42837i	−0.0528407	−	0.0915227i
$705$		0			0
$706$	4.01806	−	6.95949i	0.151222	−	0.261924i
$707$	1.27604	−	2.21017i	0.0479904	−	0.0831219i
$708$		0			0
$709$	−14.4481	−	25.0248i	−0.542609	−	0.939826i	−0.998753	−	0.0499204i	$-0.984103\pi$
$709$	−14.4481	−	25.0248i	−0.542609	−	0.939826i	0.456144	−	0.889906i	$-0.349230\pi$
$710$	0.658051			0.0246962
$711$		0			0
$712$	−26.2529			−0.983870
$713$	−2.37627	−	4.11581i	−0.0889919	−	0.154138i
$714$		0			0
$715$	−3.03908	+	5.26384i	−0.113655	+	0.196856i
$716$	19.6836	−	34.0930i	0.735611	−	1.27411i
$717$		0			0
$718$	3.44975	+	5.97515i	0.128744	+	0.222991i
$719$	−12.7032			−0.473751			−0.236875	−	0.971540i	$-0.576123\pi$
$719$	−12.7032			−0.473751			−0.236875	+	0.971540i	$0.576123\pi$
$720$		0			0
$721$	−19.6217			−0.730751
$722$	−4.53480	−	7.85450i	−0.168768	−	0.292314i
$723$		0			0
$724$	2.64619	−	4.58334i	0.0983450	−	0.170339i
$725$	19.4820	−	33.7438i	0.723543	−	1.25321i
$726$		0			0
$727$	11.0459	+	19.1320i	0.409668	+	0.709567i	0.994852	−	0.101334i	$-0.0323111\pi$
$727$	11.0459	+	19.1320i	0.409668	+	0.709567i	−0.585184	+	0.810901i	$0.698978\pi$
$728$	−18.1377			−0.672227
$729$		0			0
$730$	2.93951			0.108796
$731$	5.20323	+	9.01225i	0.192448	+	0.333330i
$732$		0			0
$733$	6.65952	−	11.5346i	0.245975	−	0.426041i	−0.716430	−	0.697659i	$-0.754225\pi$
$733$	6.65952	−	11.5346i	0.245975	−	0.426041i	0.962405	+	0.271618i	$0.0875586\pi$
$734$	−2.96933	+	5.14302i	−0.109600	+	0.189832i
$735$		0			0
$736$	−9.71665	−	16.8297i	−0.358161	−	0.620352i
$737$	−10.1910			−0.375391
$738$		0			0
$739$	15.6507			0.575720			0.287860	−	0.957673i	$-0.407056\pi$
$739$	15.6507			0.575720			0.287860	+	0.957673i	$0.407056\pi$
$740$	−1.66099	−	2.87693i	−0.0610594	−	0.105758i
$741$		0			0
$742$	−1.17542	+	2.03589i	−0.0431511	+	0.0747400i
$743$	−16.5152	+	28.6052i	−0.605884	+	1.04942i	0.386028	+	0.922487i	$0.373847\pi$
$743$	−16.5152	+	28.6052i	−0.605884	+	1.04942i	−0.991911	+	0.126934i	$0.959486\pi$
$744$		0			0
$745$	4.53469	+	7.85432i	0.166138	+	0.287760i
$746$	4.97660			0.182206
$747$		0			0
$748$	3.49188			0.127676
$749$	7.36581	+	12.7579i	0.269141	+	0.466165i
$750$		0			0
$751$	0.486534	−	0.842702i	0.0177539	−	0.0307506i	−0.857012	−	0.515297i	$-0.827682\pi$
$751$	0.486534	−	0.842702i	0.0177539	−	0.0307506i	0.874766	+	0.484546i	$0.161015\pi$
$752$	6.85257	−	11.8690i	0.249888	−	0.432818i
$753$		0			0
$754$	−12.1836	−	21.1026i	−0.443700	−	0.768512i
$755$	0.0959300			0.00349125
$756$		0			0
$757$	39.7406			1.44440			0.722198	−	0.691686i	$-0.243132\pi$
$757$	39.7406			1.44440			0.722198	+	0.691686i	$0.243132\pi$
$758$	2.16534	+	3.75048i	0.0786488	+	0.136224i
$759$		0			0
$760$	−0.998324	+	1.72915i	−0.0362130	+	0.0627228i
$761$	12.2971	−	21.2991i	0.445768	−	0.772093i	−0.552337	−	0.833621i	$-0.686264\pi$
$761$	12.2971	−	21.2991i	0.445768	−	0.772093i	0.998105	+	0.0615279i	$0.0195973\pi$
$762$		0			0
$763$	9.75741	+	16.9003i	0.353242	+	0.611833i
$764$	−6.56088			−0.237364
$765$		0			0
$766$	−16.9442			−0.612218
$767$	11.0665	+	19.1677i	0.399586	+	0.692104i
$768$		0			0
$769$	1.77025	−	3.06616i	0.0638368	−	0.110569i	−0.832341	−	0.554264i	$-0.813000\pi$
$769$	1.77025	−	3.06616i	0.0638368	−	0.110569i	0.896177	+	0.443696i	$0.146333\pi$
$770$	−0.554842	+	0.961015i	−0.0199951	+	0.0346326i
$771$		0			0
$772$	−5.33289	−	9.23684i	−0.191935	−	0.332441i
$773$	42.9261			1.54394			0.771972	−	0.635657i	$-0.219271\pi$
$773$	42.9261			1.54394			0.771972	+	0.635657i	$0.219271\pi$
$774$		0			0
$775$	6.17017			0.221639
$776$	16.3933	+	28.3941i	0.588486	+	1.01929i
$777$		0			0
$778$	10.2670	−	17.7830i	0.368091	−	0.637553i
$779$	−8.63586	+	14.9578i	−0.309412	+	0.535917i
$780$		0			0
$781$	−2.14915	−	3.72244i	−0.0769028	−	0.133200i
$782$	2.03306			0.0727019
$783$		0			0
$784$	−9.15039			−0.326800
$785$	−5.66530	−	9.81259i	−0.202203	−	0.350226i
$786$		0			0
$787$	8.10829	−	14.0440i	0.289029	−	0.500614i	−0.684549	−	0.728967i	$-0.740001\pi$
$787$	8.10829	−	14.0440i	0.289029	−	0.500614i	0.973578	+	0.228353i	$0.0733341\pi$
$788$	−1.71155	+	2.96449i	−0.0609713	+	0.105605i
$789$		0			0
$790$	−0.233577	−	0.404567i	−0.00831029	−	0.0143939i
$791$	24.6815			0.877574
$792$		0			0
$793$	28.7014			1.01922
$794$	−3.71039	−	6.42659i	−0.131677	−	0.228071i
$795$		0			0
$796$	13.3561	−	23.1334i	0.473394	−	0.819943i
$797$	−20.9362	+	36.2626i	−0.741599	+	1.28449i	0.210167	+	0.977665i	$0.432599\pi$
$797$	−20.9362	+	36.2626i	−0.741599	+	1.28449i	−0.951767	+	0.306822i	$0.900734\pi$
$798$		0			0
$799$	3.12297	+	5.40914i	0.110483	+	0.191362i
$800$	25.2301			0.892018
$801$		0			0
$802$	11.4049			0.402722
$803$	−9.60028	−	16.6282i	−0.338786	−	0.586795i
$804$		0			0
$805$	1.71001	−	2.96183i	0.0602700	−	0.104391i
$806$	1.92934	−	3.34172i	0.0679582	−	0.117707i
$807$		0			0
$808$	1.57457	+	2.72724i	0.0553933	+	0.0959440i
$809$	−30.0115			−1.05515			−0.527575	−	0.849509i	$-0.676899\pi$
$809$	−30.0115			−1.05515			−0.527575	+	0.849509i	$0.676899\pi$
$810$		0			0
$811$	13.4654			0.472834			0.236417	−	0.971652i	$-0.424027\pi$
$811$	13.4654			0.472834			0.236417	+	0.971652i	$0.424027\pi$
$812$	11.7745	+	20.3940i	0.413204	+	0.715691i
$813$		0			0
$814$	2.04959	−	3.54999i	0.0718381	−	0.124427i
$815$	−6.04129	+	10.4638i	−0.211617	+	0.366531i
$816$		0			0
$817$	8.87820	+	15.3775i	0.310609	+	0.537991i
$818$	−20.6905			−0.723427
$819$		0			0
$820$	−9.59917			−0.335218
$821$	8.22020	+	14.2378i	0.286887	+	0.496903i	0.973065	−	0.230531i	$-0.0740462\pi$
$821$	8.22020	+	14.2378i	0.286887	+	0.496903i	−0.686178	+	0.727434i	$0.740713\pi$
$822$		0			0
$823$	5.81473	−	10.0714i	0.202689	−	0.351067i	−0.746705	−	0.665155i	$-0.768365\pi$
$823$	5.81473	−	10.0714i	0.202689	−	0.351067i	0.949394	+	0.314088i	$0.101699\pi$
$824$	12.1061	−	20.9685i	0.421738	−	0.730471i
$825$		0			0
$826$	2.02039	+	3.49942i	0.0702985	+	0.121761i
$827$	−12.5268			−0.435601			−0.217801	−	0.975993i	$-0.569888\pi$
$827$	−12.5268			−0.435601			−0.217801	+	0.975993i	$0.569888\pi$
$828$		0			0
$829$	−17.6538			−0.613140			−0.306570	−	0.951848i	$-0.599181\pi$
$829$	−17.6538			−0.613140			−0.306570	+	0.951848i	$0.599181\pi$
$830$	−0.705524	−	1.22200i	−0.0244891	−	0.0424164i
$831$		0			0
$832$	−3.50831	+	6.07658i	−0.121629	+	0.210667i
$833$	2.08509	−	3.61147i	0.0722439	−	0.125130i
$834$		0			0
$835$	−5.07071	−	8.78272i	−0.175479	−	0.303939i
$836$	5.95815			0.206067
$837$		0			0
$838$	−8.59947			−0.297064
$839$	19.9829	+	34.6113i	0.689885	+	1.19492i	0.971875	+	0.235498i	$0.0756722\pi$
$839$	19.9829	+	34.6113i	0.689885	+	1.19492i	−0.281990	+	0.959417i	$0.590994\pi$
$840$		0			0
$841$	−20.1254	+	34.8582i	−0.693979	+	1.20201i
$842$	3.76615	−	6.52316i	0.129790	−	0.224803i
$843$		0			0
$844$	−4.97807	−	8.62227i	−0.171352	−	0.296791i
$845$	7.88106			0.271117
$846$		0			0
$847$	−11.2560			−0.386760
$848$	2.71975	+	4.71075i	0.0933967	+	0.161768i
$849$		0			0
$850$	−1.31975	+	2.28587i	−0.0452670	+	0.0784047i
$851$	−6.31679	+	10.9410i	−0.216537	+	0.375053i
$852$		0			0
$853$	19.8596	+	34.3979i	0.679981	+	1.17776i	0.974986	+	0.222266i	$0.0713454\pi$
$853$	19.8596	+	34.3979i	0.679981	+	1.17776i	−0.295005	+	0.955496i	$0.595321\pi$
$854$	5.24000			0.179309
$855$		0			0
$856$	−18.1781			−0.621315
$857$	−14.2073	−	24.6078i	−0.485313	−	0.840587i	0.514544	−	0.857464i	$-0.327961\pi$
$857$	−14.2073	−	24.6078i	−0.485313	−	0.840587i	−0.999858	+	0.0168765i	$0.994628\pi$
$858$		0			0
$859$	−15.2484	+	26.4111i	−0.520270	+	0.901134i	0.479453	+	0.877568i	$0.340835\pi$
$859$	−15.2484	+	26.4111i	−0.520270	+	0.901134i	−0.999722	+	0.0235657i	$0.992498\pi$
$860$	−4.93427	+	8.54641i	−0.168257	+	0.291430i
$861$		0			0
$862$	−5.45691	−	9.45164i	−0.185863	−	0.321924i
$863$	−55.9758			−1.90544			−0.952719	−	0.303854i	$-0.901726\pi$
$863$	−55.9758			−1.90544			−0.952719	+	0.303854i	$0.901726\pi$
$864$		0			0
$865$	−6.18680			−0.210357
$866$	−5.89949	−	10.2182i	−0.200473	−	0.347229i
$867$		0			0
$868$	−1.86456	+	3.22951i	−0.0632873	+	0.109617i
$869$	−1.52570	+	2.64258i	−0.0517557	+	0.0896435i
$870$		0			0
$871$	12.7506	+	22.0847i	0.432038	+	0.748312i
$872$	−24.0804			−0.815464
$873$		0			0
$874$	3.46898			0.117340
$875$	4.59087	+	7.95162i	0.155200	+	0.268814i
$876$		0			0
$877$	9.39069	−	16.2651i	0.317101	−	0.549235i	−0.662781	−	0.748813i	$-0.730624\pi$
$877$	9.39069	−	16.2651i	0.317101	−	0.549235i	0.979882	+	0.199578i	$0.0639572\pi$
$878$	4.66932	−	8.08749i	0.157582	−	0.272940i
$879$		0			0
$880$	1.28382	+	2.22365i	0.0432777	+	0.0749591i
$881$	16.0574			0.540989			0.270494	−	0.962722i	$-0.412813\pi$
$881$	16.0574			0.540989			0.270494	+	0.962722i	$0.412813\pi$
$882$		0			0
$883$	−7.50162			−0.252449			−0.126225	−	0.992002i	$-0.540286\pi$
$883$	−7.50162			−0.252449			−0.126225	+	0.992002i	$0.540286\pi$
$884$	−4.36891	−	7.56717i	−0.146942	−	0.254511i
$885$		0			0
$886$	1.59420	−	2.76124i	0.0535583	−	0.0927657i
$887$	16.4778	−	28.5405i	0.553272	−	0.958295i	−0.444764	−	0.895648i	$-0.646712\pi$
$887$	16.4778	−	28.5405i	0.553272	−	0.958295i	0.998036	−	0.0626469i	$-0.0199542\pi$
$888$		0			0
$889$	5.77996	+	10.0112i	0.193854	+	0.335764i
$890$	4.01920			0.134724
$891$		0			0
$892$	27.0161			0.904567
$893$	5.32869	+	9.22955i	0.178318	+	0.308855i
$894$		0			0
$895$	−6.59621	+	11.4250i	−0.220487	+	0.381895i
$896$	−9.70509	+	16.8097i	−0.324224	+	0.561573i
$897$		0			0
$898$	−0.959354	−	1.66165i	−0.0320140	−	0.0554500i
$899$	−10.9663			−0.365745
$900$		0			0
$901$	−2.47898			−0.0825869
$902$	−5.92247	−	10.2580i	−0.197197	−	0.341554i
$903$		0			0
$904$	−15.2279	+	26.3755i	−0.506473	+	0.877237i
$905$	−0.886772	+	1.53593i	−0.0294773	+	0.0510562i
$906$		0			0
$907$	23.3642	+	40.4680i	0.775797	+	1.34372i	0.934346	+	0.356368i	$0.115985\pi$
$907$	23.3642	+	40.4680i	0.775797	+	1.34372i	−0.158549	+	0.987351i	$0.550682\pi$
$908$	23.7646			0.788655
$909$		0			0
$910$	2.77679			0.0920498
$911$	−13.6560	−	23.6528i	−0.452442	−	0.783653i	0.546095	−	0.837723i	$-0.316114\pi$
$911$	−13.6560	−	23.6528i	−0.452442	−	0.783653i	−0.998537	+	0.0540702i	$0.982781\pi$
$912$		0			0
$913$	−4.60840	+	7.98198i	−0.152516	+	0.264165i
$914$	−2.68240	+	4.64606i	−0.0887260	+	0.153678i
$915$		0			0
$916$	5.13544	+	8.89484i	0.169680	+	0.293894i
$917$	−32.4294			−1.07091
$918$		0			0
$919$	−34.5935			−1.14113			−0.570567	−	0.821251i	$-0.693276\pi$
$919$	−34.5935			−1.14113			−0.570567	+	0.821251i	$0.693276\pi$
$920$	2.11008	+	3.65476i	0.0695671	+	0.120494i
$921$		0			0
$922$	−0.00142641	+	0.00247062i	−4.69764e−5	+	8.13655e-5i
$923$	−5.37789	+	9.31477i	−0.177015	+	0.306599i
$924$		0			0
$925$	−8.20104	−	14.2046i	−0.269648	−	0.467045i
$926$	13.6491			0.448538
$927$		0			0
$928$	−44.8415			−1.47199
$929$	11.0477	+	19.1352i	0.362464	+	0.627807i	0.988366	−	0.152095i	$-0.0486021\pi$
$929$	11.0477	+	19.1352i	0.362464	+	0.627807i	−0.625901	+	0.779902i	$0.715269\pi$
$930$		0			0
$931$	3.55776	−	6.16221i	0.116601	−	0.201958i
$932$	11.5903	−	20.0750i	0.379653	−	0.657578i
$933$		0			0
$934$	−2.60548	−	4.51282i	−0.0852539	−	0.147664i
$935$	−1.17017			−0.0382687
$936$		0			0
$937$	5.76840			0.188445			0.0942226	−	0.995551i	$-0.469963\pi$
$937$	5.76840			0.188445			0.0942226	+	0.995551i	$0.469963\pi$
$938$	2.32787	+	4.03199i	0.0760077	+	0.131649i
$939$		0			0
$940$	−2.96154	+	5.12954i	−0.0965949	+	0.167307i
$941$	−6.22903	+	10.7890i	−0.203061	+	0.351711i	−0.949513	−	0.313727i	$-0.898422\pi$
$941$	−6.22903	+	10.7890i	−0.203061	+	0.351711i	0.746452	+	0.665439i	$0.231756\pi$
$942$		0			0
$943$	18.2529	+	31.6150i	0.594397	+	1.02953i
$944$	9.34978			0.304309
$945$		0			0
$946$	−12.1773			−0.395919
$947$	−16.9339	−	29.3303i	−0.550277	−	0.953108i	−0.998254	−	0.0590628i	$-0.981189\pi$
$947$	−16.9339	−	29.3303i	−0.550277	−	0.953108i	0.447977	−	0.894045i	$-0.352145\pi$
$948$		0			0
$949$	−24.0230	+	41.6091i	−0.779820	+	1.35069i
$950$	−2.25187	+	3.90036i	−0.0730603	+	0.126544i
$951$		0			0
$952$	−1.74594	−	3.02405i	−0.0565862	−	0.0980102i
$953$	−7.12201			−0.230705			−0.115352	−	0.993325i	$-0.536800\pi$
$953$	−7.12201			−0.230705			−0.115352	+	0.993325i	$0.536800\pi$
$954$		0			0
$955$	2.19863			0.0711460
$956$	−19.6793	−	34.0856i	−0.636475	−	1.10241i
$957$		0			0
$958$	−6.75128	+	11.6936i	−0.218124	+	0.377802i
$959$	−3.35261	+	5.80689i	−0.108261	+	0.187514i
$960$		0			0
$961$	14.6317	+	25.3429i	0.471991	+	0.817512i
$962$	−10.2575			−0.330715
$963$		0			0
$964$	−48.3956			−1.55872
$965$	1.78712	+	3.09538i	0.0575293	+	0.0996437i
$966$		0			0
$967$	−12.8017	+	22.1733i	−0.411676	+	0.713044i	−0.995073	−	0.0991432i	$-0.968390\pi$
$967$	−12.8017	+	22.1733i	−0.411676	+	0.713044i	0.583397	+	0.812187i	$0.301723\pi$
$968$	6.94468	−	12.0285i	0.223210	−	0.386612i
$969$		0			0
$970$	−2.50974	−	4.34700i	−0.0805829	−	0.139574i
$971$	3.26678			0.104836			0.0524180	−	0.998625i	$-0.483307\pi$
$971$	3.26678			0.104836			0.0524180	+	0.998625i	$0.483307\pi$
$972$		0			0
$973$	25.1340			0.805758
$974$	−7.90664	−	13.6947i	−0.253345	−	0.438807i
$975$		0			0
$976$	6.06228	−	10.5002i	0.194049	−	0.336103i
$977$	−29.8689	+	51.7345i	−0.955591	+	1.65513i	−0.222582	+	0.974914i	$0.571448\pi$
$977$	−29.8689	+	51.7345i	−0.955591	+	1.65513i	−0.733010	+	0.680218i	$0.761885\pi$
$978$		0			0
$979$	−13.1265	−	22.7357i	−0.419524	−	0.726636i
$980$	3.95462			0.126326
$981$		0			0
$982$	10.9446			0.349257
$983$	−13.2360	−	22.9255i	−0.422164	−	0.731210i	0.573987	−	0.818865i	$-0.305396\pi$
$983$	−13.2360	−	22.9255i	−0.422164	−	0.731210i	−0.996151	+	0.0876545i	$0.972063\pi$
$984$		0			0
$985$	0.573560	−	0.993436i	0.0182752	−	0.0316535i
$986$	2.34559	−	4.06269i	0.0746989	−	0.129382i
$987$		0			0
$988$	−7.45462	−	12.9118i	−0.237163	−	0.410778i
$989$	37.5303			1.19339
$990$		0			0
$991$	16.1219			0.512130			0.256065	−	0.966660i	$-0.417574\pi$
$991$	16.1219			0.512130			0.256065	+	0.966660i	$0.417574\pi$
$992$	−3.55046	−	6.14957i	−0.112727	−	0.195249i
$993$		0			0
$994$	−0.981837	+	1.70059i	−0.0311420	+	0.0539395i
$995$	−4.47579	+	7.75230i	−0.141892	+	0.245764i
$996$		0			0
$997$	−5.18312	−	8.97743i	−0.164151	−	0.284318i	0.772202	−	0.635377i	$-0.219155\pi$
$997$	−5.18312	−	8.97743i	−0.164151	−	0.284318i	−0.936354	+	0.351059i	$0.885822\pi$
$998$	−5.59841			−0.177215
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.e.b.307.3		8
3.2	odd	2		153.2.e.b.103.2	yes	8
9.2	odd	6		153.2.e.b.52.2	✓	8
9.4	even	3		1377.2.a.f.1.2		4
9.5	odd	6		1377.2.a.e.1.3		4
9.7	even	3	inner	459.2.e.b.154.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.e.b.52.2	✓	8	9.2	odd	6
153.2.e.b.103.2	yes	8	3.2	odd	2
459.2.e.b.154.3		8	9.7	even	3	inner
459.2.e.b.307.3		8	1.1	even	1	trivial
1377.2.a.e.1.3		4	9.5	odd	6
1377.2.a.f.1.2		4	9.4	even	3

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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.281864 + 0.488204i) q^{2} +(0.841105 - 1.45684i) q^{4} +(-0.281864 + 0.488204i) q^{5} +(-0.841105 - 1.45684i) q^{7} +2.07577 q^{8} -0.317790 q^{10} +(1.03788 + 1.79767i) q^{11} +(2.59712 - 4.49835i) q^{13} +(0.474155 - 0.821261i) q^{14} +(-1.09712 - 1.90028i) q^{16} +1.00000 q^{17} +1.70629 q^{19} +(0.474155 + 0.821261i) q^{20} +(-0.585085 + 1.01340i) q^{22} +(1.80322 - 3.12327i) q^{23} +(2.34110 + 4.05491i) q^{25} +2.92815 q^{26} -2.82983 q^{28} +(-4.16085 - 7.20681i) q^{29} +(0.658895 - 1.14124i) q^{31} +(2.69425 - 4.66658i) q^{32} +(0.281864 + 0.488204i) q^{34} +0.948310 q^{35} -3.50306 q^{37} +(0.480942 + 0.833016i) q^{38} +(-0.585085 + 1.01340i) q^{40} +(-5.06120 + 8.76625i) q^{41} +(5.20323 + 9.01225i) q^{43} +3.49188 q^{44} +2.03306 q^{46} +(3.12297 + 5.40914i) q^{47} +(2.08509 - 3.61147i) q^{49} +(-1.31975 + 2.28587i) q^{50} +(-4.36891 - 7.56717i) q^{52} -2.47898 q^{53} -1.17017 q^{55} +(-1.74594 - 3.02405i) q^{56} +(2.34559 - 4.06269i) q^{58} +(-2.13052 + 3.69017i) q^{59} +(2.76281 + 4.78532i) q^{61} +0.742877 q^{62} -1.35085 q^{64} +(1.46407 + 2.53585i) q^{65} +(-2.45476 + 4.25176i) q^{67} +(0.841105 - 1.45684i) q^{68} +(0.267295 + 0.462968i) q^{70} -2.07071 q^{71} -9.24986 q^{73} +(-0.987389 - 1.71021i) q^{74} +(1.43517 - 2.48578i) q^{76} +(1.74594 - 3.02405i) q^{77} +(0.735003 + 1.27306i) q^{79} +1.23696 q^{80} -5.70629 q^{82} +(2.22009 + 3.84532i) q^{83} +(-0.281864 + 0.488204i) q^{85} +(-2.93321 + 5.08047i) q^{86} +(2.15441 + 3.73154i) q^{88} -12.6473 q^{89} -8.73782 q^{91} +(-3.03340 - 5.25400i) q^{92} +(-1.76051 + 3.04929i) q^{94} +(-0.480942 + 0.833016i) q^{95} +(7.89747 + 13.6788i) q^{97} +2.35085 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 3 q^{4} + q^{5} + 3 q^{7} + 6 q^{8} - 22 q^{10} + 3 q^{11} + 9 q^{13} + 5 q^{14} + 3 q^{16} + 8 q^{17} - 14 q^{19} + 5 q^{20} + 3 q^{22} + 10 q^{23} + 9 q^{25} - 22 q^{26} - 38 q^{28} - 15 q^{29}+ \cdots + 30 q^{98}+O(q^{100}) \) 8 * q - q^2 - 3 * q^4 + q^5 + 3 * q^7 + 6 * q^8 - 22 * q^10 + 3 * q^11 + 9 * q^13 + 5 * q^14 + 3 * q^16 + 8 * q^17 - 14 * q^19 + 5 * q^20 + 3 * q^22 + 10 * q^23 + 9 * q^25 - 22 * q^26 - 38 * q^28 - 15 * q^29 + 15 * q^31 - 2 * q^32 - q^34 + 10 * q^35 - 24 * q^37 - 20 * q^38 + 3 * q^40 - 6 * q^41 + 18 * q^43 - 24 * q^44 + 8 * q^46 + 12 * q^47 + 9 * q^49 - 2 * q^50 + 4 * q^52 - 24 * q^53 + 6 * q^55 + 12 * q^56 + 9 * q^58 - 5 * q^61 - 16 * q^62 - 22 * q^64 - 11 * q^65 + 6 * q^67 - 3 * q^68 - 25 * q^70 + 50 * q^71 + 8 * q^73 + 44 * q^74 - 6 * q^76 - 12 * q^77 + 8 * q^79 - 16 * q^80 - 18 * q^82 - 7 * q^83 + q^85 - 34 * q^86 + 27 * q^88 + 28 * q^89 + 8 * q^91 - 19 * q^92 - 12 * q^94 + 20 * q^95 + 16 * q^97 + 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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