LMFDB - Embedded newform 585.2.j.h.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(406,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 8x^{7} + 50x^{6} - 42x^{5} + 124x^{4} - 12x^{3} + 96x^{2} - 36x + 36 $ x^10 - 2x^9 + 10x^8 - 8x^7 + 50x^6 - 42x^5 + 124x^4 - 12x^3 + 96x^2 - 36*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.2
Root			$0.905157 - 1.56778i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.h.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.905157 - 1.56778i) q^{2} +(-0.638619 + 1.10612i) q^{4} +1.00000 q^{5} +(2.21251 - 3.83219i) q^{7} -1.30843 q^{8} +O(q^{10})$	\(q+(-0.905157 - 1.56778i) q^{2} +(-0.638619 + 1.10612i) q^{4} +1.00000 q^{5} +(2.21251 - 3.83219i) q^{7} -1.30843 q^{8} +(-0.905157 - 1.56778i) q^{10} +(0.807357 + 1.39838i) q^{11} +(3.35220 - 1.32768i) q^{13} -8.01069 q^{14} +(2.46157 + 4.26356i) q^{16} +(0.627919 - 1.08759i) q^{17} +(0.361381 - 0.625930i) q^{19} +(-0.638619 + 1.10612i) q^{20} +(1.46157 - 2.53151i) q^{22} +(-0.654213 - 1.13313i) q^{23} +1.00000 q^{25} +(-5.11578 - 4.05375i) q^{26} +(2.82591 + 4.89462i) q^{28} +(-0.580318 - 1.00514i) q^{29} -1.64968 q^{31} +(3.14779 - 5.45213i) q^{32} -2.27346 q^{34} +(2.21251 - 3.83219i) q^{35} +(-2.46157 - 4.26356i) q^{37} -1.30843 q^{38} -1.30843 q^{40} +(-4.28258 - 7.41765i) q^{41} +(-3.57685 + 6.19529i) q^{43} -2.06237 q^{44} +(-1.18433 + 2.05132i) q^{46} +12.3482 q^{47} +(-6.29044 - 10.8954i) q^{49} +(-0.905157 - 1.56778i) q^{50} +(-0.672203 + 4.55582i) q^{52} -13.4045 q^{53} +(0.807357 + 1.39838i) q^{55} +(-2.89491 + 5.01413i) q^{56} +(-1.05056 + 1.81962i) q^{58} +(-2.14244 + 3.71082i) q^{59} +(-2.82484 + 4.89276i) q^{61} +(1.49322 + 2.58633i) q^{62} -1.55070 q^{64} +(3.35220 - 1.32768i) q^{65} +(-0.109367 - 0.189430i) q^{67} +(0.802002 + 1.38911i) q^{68} -8.01069 q^{70} +(-2.92075 + 5.05889i) q^{71} +9.91448 q^{73} +(-4.45621 + 7.71839i) q^{74} +(0.461569 + 0.799462i) q^{76} +7.14515 q^{77} -14.1353 q^{79} +(2.46157 + 4.26356i) q^{80} +(-7.75282 + 13.4283i) q^{82} +11.0342 q^{83} +(0.627919 - 1.08759i) q^{85} +12.9505 q^{86} +(-1.05637 - 1.82968i) q^{88} +(0.422640 + 0.732033i) q^{89} +(2.32887 - 15.7838i) q^{91} +1.67117 q^{92} +(-11.1770 - 19.3592i) q^{94} +(0.361381 - 0.625930i) q^{95} +(-6.77723 + 11.7385i) q^{97} +(-11.3877 + 19.7240i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8}+O(q^{10}) $ 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8	$ 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8} - 2 q^{10} - 8 q^{11} + q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} - 14 q^{22} + 6 q^{23} + 10 q^{25} - 10 q^{26} + 2 q^{28} - 16 q^{29} + 18 q^{31} - 14 q^{32} - q^{35} + 4 q^{37} + 12 q^{38} + 12 q^{40} - 6 q^{41} - 15 q^{43} + 28 q^{44} + 16 q^{46} + 20 q^{47} - 10 q^{49} - 2 q^{50} - 22 q^{52} - 40 q^{53} - 8 q^{55} + 2 q^{56} + 4 q^{58} - 12 q^{59} - 11 q^{61} + 22 q^{62} + 8 q^{64} + q^{65} - 5 q^{67} - 50 q^{68} - 8 q^{70} - 10 q^{71} + 2 q^{73} + 26 q^{74} - 24 q^{76} + 84 q^{77} - 34 q^{79} - 4 q^{80} - 16 q^{82} + 32 q^{83} + 88 q^{86} - 20 q^{88} - 4 q^{89} - q^{91} - 68 q^{92} + 16 q^{94} + 4 q^{95} + 11 q^{97} - 30 q^{98}+O(q^{100}) $ 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8 - 2 * q^10 - 8 * q^11 + q^13 - 8 * q^14 - 4 * q^16 + 4 * q^19 - 6 * q^20 - 14 * q^22 + 6 * q^23 + 10 * q^25 - 10 * q^26 + 2 * q^28 - 16 * q^29 + 18 * q^31 - 14 * q^32 - q^35 + 4 * q^37 + 12 * q^38 + 12 * q^40 - 6 * q^41 - 15 * q^43 + 28 * q^44 + 16 * q^46 + 20 * q^47 - 10 * q^49 - 2 * q^50 - 22 * q^52 - 40 * q^53 - 8 * q^55 + 2 * q^56 + 4 * q^58 - 12 * q^59 - 11 * q^61 + 22 * q^62 + 8 * q^64 + q^65 - 5 * q^67 - 50 * q^68 - 8 * q^70 - 10 * q^71 + 2 * q^73 + 26 * q^74 - 24 * q^76 + 84 * q^77 - 34 * q^79 - 4 * q^80 - 16 * q^82 + 32 * q^83 + 88 * q^86 - 20 * q^88 - 4 * q^89 - q^91 - 68 * q^92 + 16 * q^94 + 4 * q^95 + 11 * q^97 - 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.905157	−	1.56778i	−0.640043	−	1.10859i	−0.985423	−	0.170124i	$-0.945583\pi$
$2$	−0.905157	−	1.56778i	−0.640043	−	1.10859i	0.345380	−	0.938463i	$-0.387750\pi$
$3$		0			0
$3$		0			0
$4$	−0.638619	+	1.10612i	−0.319310	+	0.553061i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.21251	−	3.83219i	0.836252	−	1.44843i	−0.0567556	−	0.998388i	$-0.518076\pi$
$7$	2.21251	−	3.83219i	0.836252	−	1.44843i	0.893007	−	0.450042i	$-0.148591\pi$
$8$	−1.30843			−0.462598
$9$		0			0
$10$	−0.905157	−	1.56778i	−0.286236	−	0.495775i
$11$	0.807357	+	1.39838i	0.243427	+	0.421628i	0.961688	−	0.274145i	$-0.0883950\pi$
$11$	0.807357	+	1.39838i	0.243427	+	0.421628i	−0.718261	+	0.695774i	$0.755062\pi$
$12$		0			0
$13$	3.35220	−	1.32768i	0.929734	−	0.368233i
$13$	3.35220	−	1.32768i	0.929734	−	0.368233i
$14$	−8.01069			−2.14095
$15$		0			0
$16$	2.46157	+	4.26356i	0.615392	+	1.06589i
$17$	0.627919	−	1.08759i	0.152293	−	0.263779i	−0.779777	−	0.626057i	$-0.784668\pi$
$17$	0.627919	−	1.08759i	0.152293	−	0.263779i	0.932070	+	0.362278i	$0.118001\pi$
$18$		0			0
$19$	0.361381	−	0.625930i	0.0829064	−	0.143598i	−0.821591	−	0.570078i	$-0.806913\pi$
$19$	0.361381	−	0.625930i	0.0829064	−	0.143598i	0.904497	+	0.426480i	$0.140246\pi$
$20$	−0.638619	+	1.10612i	−0.142800	+	0.247336i
$21$		0			0
$22$	1.46157	−	2.53151i	0.311608	−	0.539720i
$23$	−0.654213	−	1.13313i	−0.136413	−	0.236274i	0.789723	−	0.613463i	$-0.210224\pi$
$23$	−0.654213	−	1.13313i	−0.136413	−	0.236274i	−0.926136	+	0.377189i	$0.876891\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−5.11578	−	4.05375i	−1.00329	−	0.795005i
$27$		0			0
$28$	2.82591	+	4.89462i	0.534046	+	0.924996i
$29$	−0.580318	−	1.00514i	−0.107762	−	0.186650i	0.807101	−	0.590413i	$-0.201035\pi$
$29$	−0.580318	−	1.00514i	−0.107762	−	0.186650i	−0.914863	+	0.403763i	$0.867702\pi$
$30$		0			0
$31$	−1.64968			−0.296291			−0.148145	−	0.988966i	$-0.547330\pi$
$31$	−1.64968			−0.296291			−0.148145	+	0.988966i	$0.547330\pi$
$32$	3.14779	−	5.45213i	0.556456	−	0.963810i
$33$		0			0
$34$	−2.27346			−0.389895
$35$	2.21251	−	3.83219i	0.373983	−	0.647758i
$36$		0			0
$37$	−2.46157	−	4.26356i	−0.404680	−	0.700925i	0.589605	−	0.807692i	$-0.299284\pi$
$37$	−2.46157	−	4.26356i	−0.404680	−	0.700925i	−0.994284	+	0.106767i	$0.965950\pi$
$38$	−1.30843			−0.212255
$39$		0			0
$40$	−1.30843			−0.206880
$41$	−4.28258	−	7.41765i	−0.668827	−	1.15844i	−0.978232	−	0.207513i	$-0.933463\pi$
$41$	−4.28258	−	7.41765i	−0.668827	−	1.15844i	0.309405	−	0.950930i	$-0.399870\pi$
$42$		0			0
$43$	−3.57685	+	6.19529i	−0.545465	+	0.944773i	0.453113	+	0.891453i	$0.350314\pi$
$43$	−3.57685	+	6.19529i	−0.545465	+	0.944773i	−0.998577	+	0.0533196i	$0.983020\pi$
$44$	−2.06237			−0.310915
$45$		0			0
$46$	−1.18433	+	2.05132i	−0.174620	+	0.302451i
$47$	12.3482			1.80117			0.900583	−	0.434685i	$-0.143140\pi$
$47$	12.3482			1.80117			0.900583	+	0.434685i	$0.143140\pi$
$48$		0			0
$49$	−6.29044	−	10.8954i	−0.898634	−	1.55648i
$50$	−0.905157	−	1.56778i	−0.128009	−	0.221717i
$51$		0			0
$52$	−0.672203	+	4.55582i	−0.0932178	+	0.631779i
$53$	−13.4045			−1.84125			−0.920627	−	0.390443i	$-0.872322\pi$
$53$	−13.4045			−1.84125			−0.920627	+	0.390443i	$0.872322\pi$
$54$		0			0
$55$	0.807357	+	1.39838i	0.108864	+	0.188558i
$56$	−2.89491	+	5.01413i	−0.386849	+	0.670041i
$57$		0			0
$58$	−1.05056	+	1.81962i	−0.137945	+	0.238928i
$59$	−2.14244	+	3.71082i	−0.278922	+	0.483108i	−0.971117	−	0.238603i	$-0.923311\pi$
$59$	−2.14244	+	3.71082i	−0.278922	+	0.483108i	0.692195	+	0.721711i	$0.256644\pi$
$60$		0			0
$61$	−2.82484	+	4.89276i	−0.361684	+	0.626454i	−0.988238	−	0.152923i	$-0.951131\pi$
$61$	−2.82484	+	4.89276i	−0.361684	+	0.626454i	0.626554	+	0.779378i	$0.284465\pi$
$62$	1.49322	+	2.58633i	0.189639	+	0.328464i
$63$		0			0
$64$	−1.55070			−0.193837
$65$	3.35220	−	1.32768i	0.415789	−	0.164679i
$66$		0			0
$67$	−0.109367	−	0.189430i	−0.0133613	−	0.0231425i	0.859267	−	0.511527i	$-0.170920\pi$
$67$	−0.109367	−	0.189430i	−0.0133613	−	0.0231425i	−0.872629	+	0.488384i	$0.837587\pi$
$68$	0.802002	+	1.38911i	0.0972570	+	0.168454i
$69$		0			0
$70$	−8.01069			−0.957461
$71$	−2.92075	+	5.05889i	−0.346629	+	0.600380i	−0.985648	−	0.168811i	$-0.946007\pi$
$71$	−2.92075	+	5.05889i	−0.346629	+	0.600380i	0.639019	+	0.769191i	$0.279340\pi$
$72$		0			0
$73$	9.91448			1.16040			0.580201	−	0.814473i	$-0.302974\pi$
$73$	9.91448			1.16040			0.580201	+	0.814473i	$0.302974\pi$
$74$	−4.45621	+	7.71839i	−0.518024	+	0.897245i
$75$		0			0
$76$	0.461569	+	0.799462i	0.0529456	+	0.0917045i
$77$	7.14515			0.814266
$78$		0			0
$79$	−14.1353			−1.59035			−0.795175	−	0.606379i	$-0.792621\pi$
$79$	−14.1353			−1.59035			−0.795175	+	0.606379i	$0.792621\pi$
$80$	2.46157	+	4.26356i	0.275212	+	0.476681i
$81$		0			0
$82$	−7.75282	+	13.4283i	−0.856156	+	1.48291i
$83$	11.0342			1.21116			0.605582	−	0.795783i	$-0.292940\pi$
$83$	11.0342			1.21116			0.605582	+	0.795783i	$0.292940\pi$
$84$		0			0
$85$	0.627919	−	1.08759i	0.0681073	−	0.117965i
$86$	12.9505			1.39648
$87$		0			0
$88$	−1.05637	−	1.82968i	−0.112609	−	0.195045i
$89$	0.422640	+	0.732033i	0.0447997	+	0.0775954i	0.887556	−	0.460700i	$-0.152402\pi$
$89$	0.422640	+	0.732033i	0.0447997	+	0.0775954i	−0.842756	+	0.538296i	$0.819068\pi$
$90$		0			0
$91$	2.32887	−	15.7838i	0.244131	−	1.65459i
$92$	1.67117			0.174232
$93$		0			0
$94$	−11.1770	−	19.3592i	−1.15282	−	1.99675i
$95$	0.361381	−	0.625930i	0.0370769	−	0.0642190i
$96$		0			0
$97$	−6.77723	+	11.7385i	−0.688123	+	1.19186i	0.284321	+	0.958729i	$0.408232\pi$
$97$	−6.77723	+	11.7385i	−0.688123	+	1.19186i	−0.972444	+	0.233136i	$0.925101\pi$
$98$	−11.3877	+	19.7240i	−1.15033	+	1.99243i
$99$		0			0
$100$	−0.638619	+	1.10612i	−0.0638619	+	0.110612i
$101$	8.96106	+	15.5210i	0.891659	+	1.54440i	0.837886	+	0.545845i	$0.183791\pi$
$101$	8.96106	+	15.5210i	0.891659	+	1.54440i	0.0537731	+	0.998553i	$0.482875\pi$
$102$		0			0
$103$	13.8134			1.36107			0.680535	−	0.732715i	$-0.261747\pi$
$103$	13.8134			1.36107			0.680535	+	0.732715i	$0.261747\pi$
$104$	−4.38611	+	1.73717i	−0.430093	+	0.170344i
$105$		0			0
$106$	12.1332	+	21.0153i	1.17848	+	2.04119i
$107$	−4.86566	−	8.42757i	−0.470381	−	0.814724i	0.529045	−	0.848594i	$-0.322550\pi$
$107$	−4.86566	−	8.42757i	−0.470381	−	0.814724i	−0.999426	+	0.0338700i	$0.989217\pi$
$108$		0			0
$109$	4.36061			0.417671			0.208835	−	0.977951i	$-0.433033\pi$
$109$	4.36061			0.417671			0.208835	+	0.977951i	$0.433033\pi$
$110$	1.46157	−	2.53151i	0.139355	−	0.241370i
$111$		0			0
$112$	21.7850			2.05849
$113$	9.59636	−	16.6214i	0.902749	−	1.56361i	0.0788389	−	0.996887i	$-0.474879\pi$
$113$	9.59636	−	16.6214i	0.902749	−	1.56361i	0.823910	−	0.566720i	$-0.191788\pi$
$114$		0			0
$115$	−0.654213	−	1.13313i	−0.0610057	−	0.105665i
$116$	1.48241			0.137638
$117$		0			0
$118$	7.75699			0.714089
$119$	−2.77856	−	4.81260i	−0.254710	−	0.441171i
$120$		0			0
$121$	4.19635	−	7.26829i	0.381486	−	0.660754i
$122$	10.2277			0.925972
$123$		0			0
$124$	1.05352	−	1.82474i	0.0946086	−	0.163867i
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.52038	+	2.63337i	0.134912	+	0.233674i	0.925564	−	0.378592i	$-0.123592\pi$
$127$	1.52038	+	2.63337i	0.134912	+	0.233674i	−0.790652	+	0.612266i	$0.790258\pi$
$128$	−4.89195	−	8.47311i	−0.432392	−	0.748924i
$129$		0			0
$130$	−5.11578	−	4.05375i	−0.448684	−	0.355537i
$131$	15.4894			1.35332			0.676659	−	0.736297i	$-0.263427\pi$
$131$	15.4894			1.35332			0.676659	+	0.736297i	$0.263427\pi$
$132$		0			0
$133$	−1.59912	−	2.76976i	−0.138661	−	0.240168i
$134$	−0.197989	+	0.342927i	−0.0171037	+	0.0296244i
$135$		0			0
$136$	−0.821585	+	1.42303i	−0.0704503	+	0.122024i
$137$	4.34919	−	7.53302i	0.371576	−	0.643589i	−0.618232	−	0.785996i	$-0.712151\pi$
$137$	4.34919	−	7.53302i	0.371576	−	0.643589i	0.989808	+	0.142407i	$0.0454841\pi$
$138$		0			0
$139$	−1.01416	+	1.75657i	−0.0860197	+	0.148991i	−0.905825	−	0.423651i	$-0.860748\pi$
$139$	−1.01416	+	1.75657i	−0.0860197	+	0.148991i	0.819806	+	0.572642i	$0.194081\pi$
$140$	2.82591	+	4.89462i	0.238833	+	0.413671i
$141$		0			0
$142$	10.5750			0.887430
$143$	4.56303	+	3.61575i	0.381580	+	0.302364i
$144$		0			0
$145$	−0.580318	−	1.00514i	−0.0481928	−	0.0834724i
$146$	−8.97416	−	15.5437i	−0.742707	−	1.28641i
$147$		0			0
$148$	6.28802			0.516872
$149$	−2.80522	+	4.85878i	−0.229812	+	0.398047i	−0.957752	−	0.287594i	$-0.907145\pi$
$149$	−2.80522	+	4.85878i	−0.229812	+	0.398047i	0.727940	+	0.685641i	$0.240478\pi$
$150$		0			0
$151$	15.5158			1.26266			0.631331	−	0.775514i	$-0.282509\pi$
$151$	15.5158			1.26266			0.631331	+	0.775514i	$0.282509\pi$
$152$	−0.472840	+	0.818983i	−0.0383524	+	0.0664283i
$153$		0			0
$154$	−6.46749	−	11.2020i	−0.521165	−	0.902684i
$155$	−1.64968			−0.132505
$156$		0			0
$157$	−14.4852			−1.15604			−0.578021	−	0.816022i	$-0.696175\pi$
$157$	−14.4852			−1.15604			−0.578021	+	0.816022i	$0.696175\pi$
$158$	12.7947	+	22.1611i	1.01789	+	1.76304i
$159$		0			0
$160$	3.14779	−	5.45213i	0.248855	−	0.431029i
$161$	−5.78982			−0.456302
$162$		0			0
$163$	−7.76699	+	13.4528i	−0.608358	+	1.05371i	0.383153	+	0.923685i	$0.374838\pi$
$163$	−7.76699	+	13.4528i	−0.608358	+	1.05371i	−0.991511	+	0.130022i	$0.958495\pi$
$164$	10.9398			0.854252
$165$		0			0
$166$	−9.98771	−	17.2992i	−0.775197	−	1.34268i
$167$	10.1644	+	17.6053i	0.786545	+	1.36234i	0.928072	+	0.372401i	$0.121465\pi$
$167$	10.1644	+	17.6053i	0.786545	+	1.36234i	−0.141527	+	0.989934i	$0.545201\pi$
$168$		0			0
$169$	9.47452	−	8.90132i	0.728809	−	0.684717i
$170$	−2.27346			−0.174366
$171$		0			0
$172$	−4.56849	−	7.91286i	−0.348344	−	0.603350i
$173$	9.55106	−	16.5429i	0.726153	−	1.25773i	−0.232344	−	0.972634i	$-0.574640\pi$
$173$	9.55106	−	16.5429i	0.726153	−	1.25773i	0.958497	−	0.285101i	$-0.0920271\pi$
$174$		0			0
$175$	2.21251	−	3.83219i	0.167250	−	0.289686i
$176$	−3.97473	+	6.88443i	−0.299606	+	0.518934i
$177$		0			0
$178$	0.765111	−	1.32521i	0.0573475	−	0.0993287i
$179$	5.47145	+	9.47683i	0.408955	+	0.708331i	0.994773	−	0.102111i	$-0.0325598\pi$
$179$	5.47145	+	9.47683i	0.408955	+	0.708331i	−0.585818	+	0.810443i	$0.699227\pi$
$180$		0			0
$181$	−1.45122			−0.107869			−0.0539343	−	0.998544i	$-0.517176\pi$
$181$	−1.45122			−0.107869			−0.0539343	+	0.998544i	$0.517176\pi$
$182$	−26.8535	+	10.6357i	−1.99051	+	0.788367i
$183$		0			0
$184$	0.855989	+	1.48262i	0.0631043	+	0.109300i
$185$	−2.46157	−	4.26356i	−0.180978	−	0.313463i
$186$		0			0
$187$	2.02782			0.148289
$188$	−7.88578	+	13.6586i	−0.575129	+	0.996153i
$189$		0			0
$190$	−1.30843			−0.0949232
$191$	−7.33986	+	12.7130i	−0.531094	+	0.919881i	0.468248	+	0.883597i	$0.344886\pi$
$191$	−7.33986	+	12.7130i	−0.531094	+	0.919881i	−0.999342	+	0.0362842i	$0.988448\pi$
$192$		0			0
$193$	9.91692	+	17.1766i	0.713835	+	1.23640i	0.963407	+	0.268043i	$0.0863769\pi$
$193$	9.91692	+	17.1766i	0.713835	+	1.23640i	−0.249572	+	0.968356i	$0.580290\pi$
$194$	24.5378			1.76171
$195$		0			0
$196$	16.0688			1.14777
$197$	6.19584	+	10.7315i	0.441436	+	0.764589i	0.997796	−	0.0663521i	$-0.0211361\pi$
$197$	6.19584	+	10.7315i	0.441436	+	0.764589i	−0.556361	+	0.830941i	$0.687803\pi$
$198$		0			0
$199$	−11.5563	+	20.0162i	−0.819208	+	1.41891i	0.0870589	+	0.996203i	$0.472253\pi$
$199$	−11.5563	+	20.0162i	−0.819208	+	1.41891i	−0.906267	+	0.422706i	$0.861080\pi$
$200$	−1.30843			−0.0925197
$201$		0			0
$202$	16.2223	−	28.0979i	1.14140	−	1.97696i
$203$	−5.13585			−0.360466
$204$		0			0
$205$	−4.28258	−	7.41765i	−0.299109	−	0.518071i
$206$	−12.5033	−	21.6563i	−0.871143	−	1.50886i
$207$		0			0
$208$	13.9123	+	11.0241i	0.964647	+	0.764387i
$209$	1.16705			0.0807267
$210$		0			0
$211$	4.42692	+	7.66764i	0.304762	+	0.527862i	0.977208	−	0.212283i	$-0.0680899\pi$
$211$	4.42692	+	7.66764i	0.304762	+	0.527862i	−0.672447	+	0.740146i	$0.734757\pi$
$212$	8.56039	−	14.8270i	0.587930	−	1.01832i
$213$		0			0
$214$	−8.80837	+	15.2565i	−0.602128	+	1.04292i
$215$	−3.57685	+	6.19529i	−0.243939	+	0.422515i
$216$		0			0
$217$	−3.64994	+	6.32187i	−0.247774	+	0.429157i
$218$	−3.94704	−	6.83647i	−0.267327	−	0.463024i
$219$		0			0
$220$	−2.06237			−0.139045
$221$	0.660940	−	4.47949i	0.0444596	−	0.301323i
$222$		0			0
$223$	2.13766	+	3.70253i	0.143148	+	0.247940i	0.928681	−	0.370881i	$-0.120944\pi$
$223$	2.13766	+	3.70253i	0.143148	+	0.247940i	−0.785532	+	0.618821i	$0.787611\pi$
$224$	−13.9291	−	24.1258i	−0.930674	−	1.61197i
$225$		0			0
$226$	−34.7448			−2.31119
$227$	−10.7072	+	18.5453i	−0.710659	+	1.23090i	0.253951	+	0.967217i	$0.418270\pi$
$227$	−10.7072	+	18.5453i	−0.710659	+	1.23090i	−0.964610	+	0.263681i	$0.915064\pi$
$228$		0			0
$229$	0.661510			0.0437138			0.0218569	−	0.999761i	$-0.493042\pi$
$229$	0.661510			0.0437138			0.0218569	+	0.999761i	$0.493042\pi$
$230$	−1.18433	+	2.05132i	−0.0780925	+	0.135260i
$231$		0			0
$232$	0.759303	+	1.31515i	0.0498507	+	0.0863439i
$233$	13.3665			0.875670			0.437835	−	0.899055i	$-0.355745\pi$
$233$	13.3665			0.875670			0.437835	+	0.899055i	$0.355745\pi$
$234$		0			0
$235$	12.3482			0.805506
$236$	−2.73641	−	4.73960i	−0.178125	−	0.308522i
$237$		0			0
$238$	−5.03006	+	8.71233i	−0.326051	+	0.564736i
$239$	4.44339			0.287419			0.143709	−	0.989620i	$-0.454097\pi$
$239$	4.44339			0.287419			0.143709	+	0.989620i	$0.454097\pi$
$240$		0			0
$241$	7.21128	−	12.4903i	0.464519	−	0.804571i	−0.534660	−	0.845067i	$-0.679560\pi$
$241$	7.21128	−	12.4903i	0.464519	−	0.804571i	0.999180	+	0.0404958i	$0.0128938\pi$
$242$	−15.1934			−0.976671
$243$		0			0
$244$	−3.60799	−	6.24923i	−0.230978	−	0.400066i
$245$	−6.29044	−	10.8954i	−0.401881	−	0.696079i
$246$		0			0
$247$	0.380385	−	2.57804i	0.0242033	−	0.164037i
$248$	2.15848			0.137064
$249$		0			0
$250$	−0.905157	−	1.56778i	−0.0572472	−	0.0991550i
$251$	1.68270	−	2.91452i	0.106211	−	0.183963i	−0.808021	−	0.589153i	$-0.799461\pi$
$251$	1.68270	−	2.91452i	0.106211	−	0.183963i	0.914232	+	0.405190i	$0.132795\pi$
$252$		0			0
$253$	1.05637	−	1.82968i	0.0664132	−	0.115031i
$254$	2.75236	−	4.76723i	0.172699	−	0.299123i
$255$		0			0
$256$	−10.4067	+	18.0249i	−0.650417	+	1.12656i
$257$	−11.9058	−	20.6215i	−0.742664	−	1.28633i	−0.951278	−	0.308333i	$-0.900229\pi$
$257$	−11.9058	−	20.6215i	−0.742664	−	1.28633i	0.208615	−	0.977998i	$-0.433105\pi$
$258$		0			0
$259$	−21.7850			−1.35366
$260$	−0.672203	+	4.55582i	−0.0416883	+	0.282540i
$261$		0			0
$262$	−14.0204	−	24.2840i	−0.866181	−	1.50027i
$263$	−10.1481	−	17.5771i	−0.625762	−	1.08385i	−0.988393	−	0.151918i	$-0.951455\pi$
$263$	−10.1481	−	17.5771i	−0.625762	−	1.08385i	0.362631	−	0.931933i	$-0.381878\pi$
$264$		0			0
$265$	−13.4045			−0.823434
$266$	−2.89491	+	5.01413i	−0.177498	+	0.307436i
$267$		0			0
$268$	0.279376			0.0170656
$269$	−0.102788	+	0.178034i	−0.00626711	+	0.0108550i	−0.869142	−	0.494563i	$-0.835328\pi$
$269$	−0.102788	+	0.178034i	−0.00626711	+	0.0108550i	0.862875	+	0.505418i	$0.168662\pi$
$270$		0			0
$271$	5.09923	+	8.83212i	0.309756	+	0.536513i	0.978309	−	0.207151i	$-0.0664193\pi$
$271$	5.09923	+	8.83212i	0.309756	+	0.536513i	−0.668553	+	0.743665i	$0.733086\pi$
$272$	6.18266			0.374879
$273$		0			0
$274$	−15.7468			−0.951299
$275$	0.807357	+	1.39838i	0.0486854	+	0.0843256i
$276$		0			0
$277$	−14.0929	+	24.4096i	−0.846760	+	1.46663i	0.0373245	+	0.999303i	$0.488116\pi$
$277$	−14.0929	+	24.4096i	−0.846760	+	1.46663i	−0.884084	+	0.467328i	$0.845217\pi$
$278$	3.67189			0.220225
$279$		0			0
$280$	−2.89491	+	5.01413i	−0.173004	+	0.299652i
$281$	17.2672			1.03008			0.515039	−	0.857167i	$-0.327778\pi$
$281$	17.2672			1.03008			0.515039	+	0.857167i	$0.327778\pi$
$282$		0			0
$283$	−14.0098	−	24.2657i	−0.832798	−	1.44245i	−0.895811	−	0.444435i	$-0.853404\pi$
$283$	−14.0098	−	24.2657i	−0.832798	−	1.44245i	0.0630133	−	0.998013i	$-0.479929\pi$
$284$	−3.73050	−	6.46141i	−0.221364	−	0.383414i
$285$		0			0
$286$	1.53843	−	10.4266i	0.0909693	−	0.616540i
$287$	−37.9011			−2.23723
$288$		0			0
$289$	7.71144	+	13.3566i	0.453614	+	0.785682i
$290$	−1.05056	+	1.81962i	−0.0616909	+	0.106852i
$291$		0			0
$292$	−6.33157	+	10.9666i	−0.370527	+	0.641772i
$293$	3.51747	−	6.09244i	0.205493	−	0.355924i	−0.744797	−	0.667291i	$-0.767454\pi$
$293$	3.51747	−	6.09244i	0.205493	−	0.355924i	0.950290	+	0.311367i	$0.100787\pi$
$294$		0			0
$295$	−2.14244	+	3.71082i	−0.124738	+	0.216052i
$296$	3.22078	+	5.57856i	0.187204	+	0.324247i
$297$		0			0
$298$	10.1567			0.588359
$299$	−3.69749	−	2.92989i	−0.213831	−	0.169440i
$300$		0			0
$301$	15.8277	+	27.4143i	0.912292	+	1.58014i
$302$	−14.0443	−	24.3254i	−0.808157	−	1.39977i
$303$		0			0
$304$	3.55825			0.204080
$305$	−2.82484	+	4.89276i	−0.161750	+	0.280159i
$306$		0			0
$307$	17.9307			1.02336			0.511679	−	0.859177i	$-0.329024\pi$
$307$	17.9307			1.02336			0.511679	+	0.859177i	$0.329024\pi$
$308$	−4.56303	+	7.90340i	−0.260003	+	0.450338i
$309$		0			0
$310$	1.49322	+	2.58633i	0.0848091	+	0.146894i
$311$	−8.59247			−0.487234			−0.243617	−	0.969871i	$-0.578334\pi$
$311$	−8.59247			−0.487234			−0.243617	+	0.969871i	$0.578334\pi$
$312$		0			0
$313$	−21.8298			−1.23389			−0.616946	−	0.787006i	$-0.711630\pi$
$313$	−21.8298			−1.23389			−0.616946	+	0.787006i	$0.711630\pi$
$314$	13.1113	+	22.7095i	0.739916	+	1.28157i
$315$		0			0
$316$	9.02711	−	15.6354i	0.507814	−	0.879560i
$317$	−20.4269			−1.14729			−0.573645	−	0.819104i	$-0.694471\pi$
$317$	−20.4269			−1.14729			−0.573645	+	0.819104i	$0.694471\pi$
$318$		0			0
$319$	0.937047	−	1.62301i	0.0524646	−	0.0908713i
$320$	−1.55070			−0.0866867
$321$		0			0
$322$	5.24070	+	9.07715i	0.292053	+	0.505850i
$323$	−0.453835	−	0.786066i	−0.0252521	−	0.0437379i
$324$		0			0
$325$	3.35220	−	1.32768i	0.185947	−	0.0736466i
$326$	28.1214			1.55750
$327$		0			0
$328$	5.60344	+	9.70545i	0.309398	+	0.535894i
$329$	27.3205	−	47.3205i	1.50623	−	2.60886i
$330$		0			0
$331$	0.542457	−	0.939564i	0.0298162	−	0.0516431i	−0.850732	−	0.525599i	$-0.823841\pi$
$331$	0.542457	−	0.939564i	0.0298162	−	0.0516431i	0.880548	+	0.473956i	$0.157174\pi$
$332$	−7.04667	+	12.2052i	−0.386736	+	0.669847i
$333$		0			0
$334$	18.4008	−	31.8710i	1.00684	−	1.74391i
$335$	−0.109367	−	0.189430i	−0.00597538	−	0.0103497i
$336$		0			0
$337$	−15.3641			−0.836934			−0.418467	−	0.908232i	$-0.637432\pi$
$337$	−15.3641			−0.836934			−0.418467	+	0.908232i	$0.637432\pi$
$338$	−22.5312	−	6.79685i	−1.22554	−	0.369700i
$339$		0			0
$340$	0.802002	+	1.38911i	0.0434947	+	0.0753350i
$341$	−1.33188	−	2.30688i	−0.0721253	−	0.124925i
$342$		0			0
$343$	−24.6955			−1.33343
$344$	4.68005	−	8.10608i	0.252331	−	0.437050i
$345$		0			0
$346$	−34.5808			−1.85908
$347$	−15.8872	+	27.5174i	−0.852867	+	1.47721i	0.0257422	+	0.999669i	$0.491805\pi$
$347$	−15.8872	+	27.5174i	−0.852867	+	1.47721i	−0.878609	+	0.477541i	$0.841528\pi$
$348$		0			0
$349$	−3.50728	−	6.07479i	−0.187740	−	0.325176i	0.756756	−	0.653697i	$-0.226783\pi$
$349$	−3.50728	−	6.07479i	−0.187740	−	0.325176i	−0.944497	+	0.328521i	$0.893450\pi$
$350$	−8.01069			−0.428189
$351$		0			0
$352$	10.1656			0.541826
$353$	−15.1035	−	26.1600i	−0.803878	−	1.39236i	−0.917046	−	0.398782i	$-0.869433\pi$
$353$	−15.1035	−	26.1600i	−0.803878	−	1.39236i	0.113168	−	0.993576i	$-0.463900\pi$
$354$		0			0
$355$	−2.92075	+	5.05889i	−0.155017	+	0.268498i
$356$	−1.07962			−0.0572199
$357$		0			0
$358$	9.90505	−	17.1560i	0.523498	−	0.906725i
$359$	−16.5984			−0.876029			−0.438015	−	0.898968i	$-0.644318\pi$
$359$	−16.5984			−0.876029			−0.438015	+	0.898968i	$0.644318\pi$
$360$		0			0
$361$	9.23881	+	16.0021i	0.486253	+	0.842215i
$362$	1.31358	+	2.27520i	0.0690405	+	0.119582i
$363$		0			0
$364$	15.9715	+	12.6558i	0.837135	+	0.663346i
$365$	9.91448			0.518947
$366$		0			0
$367$	−10.1642	−	17.6050i	−0.530569	−	0.918973i	−0.999364	−	0.0356659i	$-0.988645\pi$
$367$	−10.1642	−	17.6050i	−0.530569	−	0.918973i	0.468794	−	0.883307i	$-0.344689\pi$
$368$	3.22078	−	5.57856i	0.167895	−	0.290802i
$369$		0			0
$370$	−4.45621	+	7.71839i	−0.231668	+	0.401260i
$371$	−29.6577	+	51.3687i	−1.53975	+	2.66693i
$372$		0			0
$373$	10.3763	−	17.9724i	0.537267	−	0.930574i	−0.461783	−	0.886993i	$-0.652790\pi$
$373$	10.3763	−	17.9724i	0.537267	−	0.930574i	0.999050	−	0.0435808i	$-0.0138766\pi$
$374$	−1.83549	−	3.17917i	−0.0949111	−	0.164391i
$375$		0			0
$376$	−16.1567			−0.833216
$377$	−3.27985	−	2.59896i	−0.168921	−	0.133853i
$378$		0			0
$379$	0.432575	+	0.749242i	0.0222199	+	0.0384860i	0.876922	−	0.480634i	$-0.159593\pi$
$379$	0.432575	+	0.749242i	0.0222199	+	0.0384860i	−0.854702	+	0.519120i	$0.826260\pi$
$380$	0.461569	+	0.799462i	0.0236780	+	0.0410115i
$381$		0			0
$382$	26.5749			1.35969
$383$	−1.41158	+	2.44493i	−0.0721284	+	0.124930i	−0.899834	−	0.436233i	$-0.856312\pi$
$383$	−1.41158	+	2.44493i	−0.0721284	+	0.124930i	0.827706	+	0.561163i	$0.189646\pi$
$384$		0			0
$385$	7.14515			0.364151
$386$	17.9527	−	31.0951i	0.913770	−	1.58270i
$387$		0			0
$388$	−8.65614	−	14.9929i	−0.439449	−	0.761148i
$389$	13.4514			0.682015			0.341008	−	0.940061i	$-0.389232\pi$
$389$	13.4514			0.682015			0.341008	+	0.940061i	$0.389232\pi$
$390$		0			0
$391$	−1.64317			−0.0830987
$392$	8.23057	+	14.2558i	0.415706	+	0.720025i
$393$		0			0
$394$	11.2164	−	19.4274i	0.565075	−	0.978739i
$395$	−14.1353			−0.711227
$396$		0			0
$397$	−4.02006	+	6.96296i	−0.201761	+	0.349461i	−0.949096	−	0.314987i	$-0.898000\pi$
$397$	−4.02006	+	6.96296i	−0.201761	+	0.349461i	0.747335	+	0.664448i	$0.231333\pi$
$398$	41.8413			2.09731
$399$		0			0
$400$	2.46157	+	4.26356i	0.123078	+	0.213178i
$401$	−17.1810	−	29.7584i	−0.857978	−	1.48606i	−0.873854	−	0.486188i	$-0.838387\pi$
$401$	−17.1810	−	29.7584i	−0.857978	−	1.48606i	0.0158757	−	0.999874i	$-0.494946\pi$
$402$		0			0
$403$	−5.53005	+	2.19025i	−0.275472	+	0.109104i
$404$	−22.8908			−1.13886
$405$		0			0
$406$	4.64875	+	8.05187i	0.230714	+	0.399608i
$407$	3.97473	−	6.88443i	0.197020	−	0.341249i
$408$		0			0
$409$	9.73340	−	16.8587i	0.481286	−	0.833611i	−0.518484	−	0.855087i	$-0.673503\pi$
$409$	9.73340	−	16.8587i	0.481286	−	0.833611i	0.999769	+	0.0214764i	$0.00683667\pi$
$410$	−7.75282	+	13.4283i	−0.382885	+	0.663176i
$411$		0			0
$412$	−8.82148	+	15.2792i	−0.434603	+	0.752754i
$413$	9.48037	+	16.4205i	0.466499	+	0.807999i
$414$		0			0
$415$	11.0342			0.541649
$416$	3.31333	−	22.4559i	0.162449	−	1.10099i
$417$		0			0
$418$	−1.05637	−	1.82968i	−0.0516686	−	0.0894926i
$419$	12.2360	+	21.1934i	0.597768	+	1.03536i	0.993150	+	0.116847i	$0.0372788\pi$
$419$	12.2360	+	21.1934i	0.597768	+	1.03536i	−0.395382	+	0.918517i	$0.629388\pi$
$420$		0			0
$421$	27.6979			1.34991			0.674956	−	0.737858i	$-0.264163\pi$
$421$	27.6979			1.34991			0.674956	+	0.737858i	$0.264163\pi$
$422$	8.01411	−	13.8808i	0.390121	−	0.675709i
$423$		0			0
$424$	17.5388			0.851761
$425$	0.627919	−	1.08759i	0.0304585	−	0.0527557i
$426$		0			0
$427$	12.5000	+	21.6506i	0.604917	+	1.04775i
$428$	12.4292			0.600789
$429$		0			0
$430$	12.9505			0.624526
$431$	2.18386	+	3.78255i	0.105193	+	0.182199i	0.913817	−	0.406126i	$-0.133121\pi$
$431$	2.18386	+	3.78255i	0.105193	+	0.182199i	−0.808624	+	0.588325i	$0.799787\pi$
$432$		0			0
$433$	4.52859	−	7.84374i	0.217630	−	0.376946i	−0.736453	−	0.676489i	$-0.763501\pi$
$433$	4.52859	−	7.84374i	0.217630	−	0.376946i	0.954083	+	0.299543i	$0.0968341\pi$
$434$	13.2151			0.634343
$435$		0			0
$436$	−2.78477	+	4.82336i	−0.133366	+	0.230997i
$437$	−0.945680			−0.0452380
$438$		0			0
$439$	8.08964	+	14.0117i	0.386097	+	0.668740i	0.991921	−	0.126859i	$-0.0404896\pi$
$439$	8.08964	+	14.0117i	0.386097	+	0.668740i	−0.605823	+	0.795599i	$0.707156\pi$
$440$	−1.05637	−	1.82968i	−0.0503603	−	0.0872266i
$441$		0			0
$442$	−7.62110	+	3.01843i	−0.362499	+	0.143572i
$443$	13.6295			0.647555			0.323778	−	0.946133i	$-0.395047\pi$
$443$	13.6295			0.647555			0.323778	+	0.946133i	$0.395047\pi$
$444$		0			0
$445$	0.422640	+	0.732033i	0.0200350	+	0.0347017i
$446$	3.86983	−	6.70275i	0.183242	−	0.317384i
$447$		0			0
$448$	−3.43094	+	5.94257i	−0.162097	+	0.280760i
$449$	−5.52716	+	9.57332i	−0.260843	+	0.451793i	−0.966466	−	0.256794i	$-0.917334\pi$
$449$	−5.52716	+	9.57332i	−0.260843	+	0.451793i	0.705623	+	0.708587i	$0.250667\pi$
$450$		0			0
$451$	6.91515	−	11.9774i	0.325622	−	0.563993i
$452$	12.2568	+	21.2295i	0.576513	+	0.998550i
$453$		0			0
$454$	38.7667			1.81941
$455$	2.32887	−	15.7838i	0.109179	−	0.739955i
$456$		0			0
$457$	−12.1176	−	20.9883i	−0.566836	−	0.981789i	−0.996876	−	0.0789794i	$-0.974834\pi$
$457$	−12.1176	−	20.9883i	−0.566836	−	0.981789i	0.430040	−	0.902810i	$-0.358499\pi$
$458$	−0.598770	−	1.03710i	−0.0279787	−	0.0484605i
$459$		0			0
$460$	1.67117			0.0779188
$461$	−13.3479	+	23.1193i	−0.621674	+	1.07677i	0.367499	+	0.930024i	$0.380214\pi$
$461$	−13.3479	+	23.1193i	−0.621674	+	1.07677i	−0.989174	+	0.146748i	$0.953119\pi$
$462$		0			0
$463$	19.8137			0.920819			0.460410	−	0.887707i	$-0.347703\pi$
$463$	19.8137			0.920819			0.460410	+	0.887707i	$0.347703\pi$
$464$	2.85699	−	4.94845i	0.132632	−	0.229726i
$465$		0			0
$466$	−12.0988	−	20.9557i	−0.560466	−	0.970756i
$467$	22.4652			1.03956			0.519782	−	0.854299i	$-0.326013\pi$
$467$	22.4652			1.03956			0.519782	+	0.854299i	$0.326013\pi$
$468$		0			0
$469$	−0.967907			−0.0446938
$470$	−11.1770	−	19.3592i	−0.515558	−	0.892973i
$471$		0			0
$472$	2.80323	−	4.85533i	0.129029	−	0.223485i
$473$	−11.5512			−0.531124
$474$		0			0
$475$	0.361381	−	0.625930i	0.0165813	−	0.0287196i
$476$	7.09776			0.325325
$477$		0			0
$478$	−4.02196	−	6.96624i	−0.183960	−	0.318629i
$479$	12.5842	+	21.7964i	0.574985	+	0.995903i	0.996043	+	0.0888698i	$0.0283255\pi$
$479$	12.5842	+	21.7964i	0.574985	+	0.995903i	−0.421058	+	0.907034i	$0.638341\pi$
$480$		0			0
$481$	−13.9123	−	11.0241i	−0.634348	−	0.502658i
$482$	−26.1094			−1.18925
$483$		0			0
$484$	5.35974	+	9.28334i	0.243625	+	0.421970i
$485$	−6.77723	+	11.7385i	−0.307738	+	0.533018i
$486$		0			0
$487$	14.7771	−	25.5947i	0.669613	−	1.15980i	−0.308399	−	0.951257i	$-0.599793\pi$
$487$	14.7771	−	25.5947i	0.669613	−	1.15980i	0.978012	−	0.208547i	$-0.0668735\pi$
$488$	3.69609	−	6.40182i	0.167314	−	0.289797i
$489$		0			0
$490$	−11.3877	+	19.7240i	−0.514442	+	0.891040i
$491$	7.72923	+	13.3874i	0.348815	+	0.604166i	0.986039	−	0.166513i	$-0.0532507\pi$
$491$	7.72923	+	13.3874i	0.348815	+	0.604166i	−0.637224	+	0.770679i	$0.719917\pi$
$492$		0			0
$493$	−1.45757			−0.0656457
$494$	−4.38611	+	1.73717i	−0.197340	+	0.0781592i
$495$		0			0
$496$	−4.06080	−	7.03351i	−0.182335	−	0.315814i
$497$	12.9244	+	22.3857i	0.579739	+	1.00414i
$498$		0			0
$499$	−1.38273			−0.0618993			−0.0309497	−	0.999521i	$-0.509853\pi$
$499$	−1.38273			−0.0618993			−0.0309497	+	0.999521i	$0.509853\pi$
$500$	−0.638619	+	1.10612i	−0.0285599	+	0.0494672i
$501$		0			0
$502$	−6.09244			−0.271919
$503$	−20.2960	+	35.1537i	−0.904953	+	1.56742i	−0.0839732	+	0.996468i	$0.526761\pi$
$503$	−20.2960	+	35.1537i	−0.904953	+	1.56742i	−0.820980	+	0.570957i	$0.806572\pi$
$504$		0			0
$505$	8.96106	+	15.5210i	0.398762	+	0.690676i
$506$	−3.82471			−0.170029
$507$		0			0
$508$	−3.88377			−0.172315
$509$	3.18571	+	5.51781i	0.141204	+	0.244573i	0.927950	−	0.372704i	$-0.121569\pi$
$509$	3.18571	+	5.51781i	0.141204	+	0.244573i	−0.786746	+	0.617277i	$0.788236\pi$
$510$		0			0
$511$	21.9359	−	37.9941i	0.970388	−	1.68076i
$512$	18.1109			0.800396
$513$		0			0
$514$	−21.5532	+	37.3313i	−0.950673	+	1.64661i
$515$	13.8134			0.608689
$516$		0			0
$517$	9.96937	+	17.2675i	0.438453	+	0.759422i
$518$	19.7189	+	34.1541i	0.866398	+	1.50064i
$519$		0			0
$520$	−4.38611	+	1.73717i	−0.192344	+	0.0761801i
$521$	1.54817			0.0678264			0.0339132	−	0.999425i	$-0.489203\pi$
$521$	1.54817			0.0678264			0.0339132	+	0.999425i	$0.489203\pi$
$522$		0			0
$523$	−16.5485	−	28.6629i	−0.723617	−	1.25334i	−0.959541	−	0.281570i	$-0.909145\pi$
$523$	−16.5485	−	28.6629i	−0.723617	−	1.25334i	0.235923	−	0.971772i	$-0.424189\pi$
$524$	−9.89185	+	17.1332i	−0.432127	+	0.748467i
$525$		0			0
$526$	−18.3713	+	31.8201i	−0.801028	+	1.38742i
$527$	−1.03586	+	1.79417i	−0.0451229	+	0.0781552i
$528$		0			0
$529$	10.6440	−	18.4360i	0.462783	−	0.801564i
$530$	12.1332	+	21.0153i	0.527033	+	0.912848i
$531$		0			0
$532$	4.08491			0.177104
$533$	−24.2044	−	19.1796i	−1.04841	−	0.830759i
$534$		0			0
$535$	−4.86566	−	8.42757i	−0.210361	−	0.364355i
$536$	0.143099	+	0.247855i	0.00618094	+	0.0107057i
$537$		0			0
$538$	0.372158			0.0160449
$539$	10.1572	−	17.5929i	0.437504	−	0.757779i
$540$		0			0
$541$	−0.149945			−0.00644662			−0.00322331	−	0.999995i	$-0.501026\pi$
$541$	−0.149945			−0.00644662			−0.00322331	+	0.999995i	$0.501026\pi$
$542$	9.23121	−	15.9889i	0.396514	−	0.686783i
$543$		0			0
$544$	−3.95311	−	6.84699i	−0.169488	−	0.293562i
$545$	4.36061			0.186788
$546$		0			0
$547$	−5.12882			−0.219293			−0.109646	−	0.993971i	$-0.534972\pi$
$547$	−5.12882			−0.219293			−0.109646	+	0.993971i	$0.534972\pi$
$548$	5.55495	+	9.62146i	0.237296	+	0.411008i
$549$		0			0
$550$	1.46157	−	2.53151i	0.0623215	−	0.107944i
$551$	−0.838863			−0.0357368
$552$		0			0
$553$	−31.2747	+	54.1693i	−1.32993	+	2.30351i
$554$	51.0251			2.16785
$555$		0			0
$556$	−1.29532	−	2.24356i	−0.0549339	−	0.0951482i
$557$	1.63700	+	2.83536i	0.0693617	+	0.120138i	0.898621	−	0.438727i	$-0.144570\pi$
$557$	1.63700	+	2.83536i	0.0693617	+	0.120138i	−0.829259	+	0.558865i	$0.811237\pi$
$558$		0			0
$559$	−3.76495	+	25.5168i	−0.159241	+	1.07925i
$560$	21.7850			0.920585
$561$		0			0
$562$	−15.6296	−	27.0712i	−0.659294	−	1.14193i
$563$	−3.88716	+	6.73276i	−0.163824	+	0.283752i	−0.936237	−	0.351369i	$-0.885716\pi$
$563$	−3.88716	+	6.73276i	−0.163824	+	0.283752i	0.772413	+	0.635121i	$0.219050\pi$
$564$		0			0
$565$	9.59636	−	16.6214i	0.403722	−	0.699267i
$566$	−25.3622	+	43.9286i	−1.06605	+	1.84646i
$567$		0			0
$568$	3.82158	−	6.61918i	0.160350	−	0.277735i
$569$	−3.93736	−	6.81970i	−0.165063	−	0.285897i	0.771615	−	0.636090i	$-0.219449\pi$
$569$	−3.93736	−	6.81970i	−0.165063	−	0.285897i	−0.936678	+	0.350193i	$0.886116\pi$
$570$		0			0
$571$	−11.4994			−0.481236			−0.240618	−	0.970620i	$-0.577350\pi$
$571$	−11.4994			−0.481236			−0.240618	+	0.970620i	$0.577350\pi$
$572$	−6.91349	+	2.73818i	−0.289068	+	0.114489i
$573$		0			0
$574$	34.3065	+	59.4205i	1.43192	+	2.48017i
$575$	−0.654213	−	1.13313i	−0.0272826	−	0.0472548i
$576$		0			0
$577$	−0.797701			−0.0332087			−0.0166044	−	0.999862i	$-0.505286\pi$
$577$	−0.797701			−0.0332087			−0.0166044	+	0.999862i	$0.505286\pi$
$578$	13.9601	−	24.1796i	0.580665	−	1.00574i
$579$		0			0
$580$	1.48241			0.0615537
$581$	24.4134	−	42.2852i	1.01284	−	1.75429i
$582$		0			0
$583$	−10.8222	−	18.7447i	−0.448211	−	0.776325i
$584$	−12.9724			−0.536800
$585$		0			0
$586$	−12.7355			−0.526097
$587$	9.27183	+	16.0593i	0.382689	+	0.662837i	0.991446	−	0.130520i	$-0.0416647\pi$
$587$	9.27183	+	16.0593i	0.382689	+	0.662837i	−0.608756	+	0.793357i	$0.708331\pi$
$588$		0			0
$589$	−0.596162	+	1.03258i	−0.0245644	+	0.0425468i
$590$	7.75699			0.319350
$591$		0			0
$592$	12.1186	−	20.9901i	0.498073	−	0.862688i
$593$	11.6068			0.476633			0.238316	−	0.971188i	$-0.423404\pi$
$593$	11.6068			0.476633			0.238316	+	0.971188i	$0.423404\pi$
$594$		0			0
$595$	−2.77856	−	4.81260i	−0.113910	−	0.197297i
$596$	−3.58293	−	6.20582i	−0.146763	−	0.254200i
$597$		0			0
$598$	−1.24661	+	8.44886i	−0.0509778	+	0.345500i
$599$	−35.2656			−1.44091			−0.720457	−	0.693500i	$-0.756068\pi$
$599$	−35.2656			−1.44091			−0.720457	+	0.693500i	$0.756068\pi$
$600$		0			0
$601$	0.818735	+	1.41809i	0.0333969	+	0.0578451i	0.882241	−	0.470799i	$-0.156034\pi$
$601$	0.818735	+	1.41809i	0.0333969	+	0.0578451i	−0.848844	+	0.528644i	$0.822701\pi$
$602$	28.6531	−	49.6286i	1.16781	−	2.02271i
$603$		0			0
$604$	−9.90871	+	17.1624i	−0.403180	+	0.698328i
$605$	4.19635	−	7.26829i	0.170606	−	0.295498i
$606$		0			0
$607$	−14.1361	+	24.4844i	−0.573765	+	0.993791i	0.422409	+	0.906405i	$0.361184\pi$
$607$	−14.1361	+	24.4844i	−0.573765	+	0.993791i	−0.996175	+	0.0873853i	$0.972149\pi$
$608$	−2.27510	−	3.94059i	−0.0922675	−	0.159812i
$609$		0			0
$610$	10.2277			0.414107
$611$	41.3935	−	16.3944i	1.67460	−	0.663248i
$612$		0			0
$613$	−10.4972	−	18.1818i	−0.423980	−	0.734354i	0.572345	−	0.820013i	$-0.306034\pi$
$613$	−10.4972	−	18.1818i	−0.423980	−	0.734354i	−0.996325	+	0.0856587i	$0.972701\pi$
$614$	−16.2301	−	28.1113i	−0.654993	−	1.13448i
$615$		0			0
$616$	−9.34890			−0.376678
$617$	2.67847	−	4.63924i	0.107831	−	0.186769i	−0.807060	−	0.590469i	$-0.798943\pi$
$617$	2.67847	−	4.63924i	0.107831	−	0.186769i	0.914891	+	0.403700i	$0.132276\pi$
$618$		0			0
$619$	−38.1621			−1.53386			−0.766931	−	0.641729i	$-0.778217\pi$
$619$	−38.1621			−1.53386			−0.766931	+	0.641729i	$0.778217\pi$
$620$	1.05352	−	1.82474i	0.0423102	−	0.0732835i
$621$		0			0
$622$	7.77753	+	13.4711i	0.311851	+	0.540141i
$623$	3.74038			0.149855
$624$		0			0
$625$	1.00000			0.0400000
$626$	19.7594	+	34.2243i	0.789744	+	1.36788i
$627$		0			0
$628$	9.25050	−	16.0223i	0.369135	−	0.639361i
$629$	−6.18266			−0.246519
$630$		0			0
$631$	−3.74163	+	6.48068i	−0.148952	+	0.257992i	−0.930840	−	0.365426i	$-0.880923\pi$
$631$	−3.74163	+	6.48068i	−0.148952	+	0.257992i	0.781889	+	0.623418i	$0.214257\pi$
$632$	18.4950			0.735694
$633$		0			0
$634$	18.4896	+	32.0249i	0.734315	+	1.27187i
$635$	1.52038	+	2.63337i	0.0603344	+	0.104502i
$636$		0			0
$637$	−35.5524	−	28.1717i	−1.40864	−	1.11620i
$638$	−3.39270			−0.134318
$639$		0			0
$640$	−4.89195	−	8.47311i	−0.193371	−	0.334929i
$641$	−22.7461	+	39.3974i	−0.898416	+	1.55610i	−0.0688979	+	0.997624i	$0.521948\pi$
$641$	−22.7461	+	39.3974i	−0.898416	+	1.55610i	−0.829519	+	0.558479i	$0.811385\pi$
$642$		0			0
$643$	15.3903	−	26.6568i	0.606935	−	1.05124i	−0.384808	−	0.922997i	$-0.625732\pi$
$643$	15.3903	−	26.6568i	0.606935	−	1.05124i	0.991742	−	0.128245i	$-0.0409345\pi$
$644$	3.69749	−	6.40424i	0.145702	−	0.252362i
$645$		0			0
$646$	−0.821585	+	1.42303i	−0.0323248	+	0.0559882i
$647$	−23.8826	−	41.3659i	−0.938922	−	1.62626i	−0.767486	−	0.641066i	$-0.778493\pi$
$647$	−23.8826	−	41.3659i	−0.938922	−	1.62626i	−0.171436	−	0.985195i	$-0.554841\pi$
$648$		0			0
$649$	−6.91886			−0.271589
$650$	−5.11578	−	4.05375i	−0.200657	−	0.159001i
$651$		0			0
$652$	−9.92030	−	17.1825i	−0.388509	−	0.672917i
$653$	4.51773	+	7.82494i	0.176793	+	0.306214i	0.940780	−	0.339017i	$-0.110095\pi$
$653$	4.51773	+	7.82494i	0.176793	+	0.306214i	−0.763988	+	0.645231i	$0.776761\pi$
$654$		0			0
$655$	15.4894			0.605222
$656$	21.0838	−	36.5181i	0.823182	−	1.42579i
$657$		0			0
$658$	−98.9174			−3.85620
$659$	−20.0387	+	34.7081i	−0.780598	+	1.35204i	0.150996	+	0.988534i	$0.451752\pi$
$659$	−20.0387	+	34.7081i	−0.780598	+	1.35204i	−0.931594	+	0.363501i	$0.881581\pi$
$660$		0			0
$661$	−9.45968	−	16.3846i	−0.367939	−	0.637289i	0.621304	−	0.783569i	$-0.286603\pi$
$661$	−9.45968	−	16.3846i	−0.367939	−	0.637289i	−0.989243	+	0.146281i	$0.953270\pi$
$662$	−1.96404			−0.0763345
$663$		0			0
$664$	−14.4375			−0.560282
$665$	−1.59912	−	2.76976i	−0.0620112	−	0.107407i
$666$		0			0
$667$	−0.759303	+	1.31515i	−0.0294003	+	0.0509229i
$668$	−25.9647			−1.00461
$669$		0			0
$670$	−0.197989	+	0.342927i	−0.00764899	+	0.0132484i
$671$	−9.12261			−0.352174
$672$		0			0
$673$	11.5016	+	19.9213i	0.443353	+	0.767910i	0.997936	−	0.0642188i	$-0.0204556\pi$
$673$	11.5016	+	19.9213i	0.443353	+	0.767910i	−0.554583	+	0.832128i	$0.687122\pi$
$674$	13.9069	+	24.0874i	0.535673	+	0.927813i
$675$		0			0
$676$	3.79533	+	16.1645i	0.145974	+	0.621712i
$677$	−41.0126			−1.57624			−0.788121	−	0.615520i	$-0.788946\pi$
$677$	−41.0126			−1.57624			−0.788121	+	0.615520i	$0.788946\pi$
$678$		0			0
$679$	29.9894	+	51.9432i	1.15089	+	1.99340i
$680$	−0.821585	+	1.42303i	−0.0315063	+	0.0545706i
$681$		0			0
$682$	−2.41112	+	4.17618i	−0.0923265	+	0.159914i
$683$	−1.26313	+	2.18780i	−0.0483322	+	0.0837139i	−0.889179	−	0.457559i	$-0.848724\pi$
$683$	−1.26313	+	2.18780i	−0.0483322	+	0.0837139i	0.840847	+	0.541273i	$0.182057\pi$
$684$		0			0
$685$	4.34919	−	7.53302i	0.166174	−	0.287822i
$686$	22.3533	+	38.7171i	0.853454	+	1.47822i
$687$		0			0
$688$	−35.2187			−1.34270
$689$	−44.9347	+	17.7970i	−1.71188	+	0.678010i
$690$		0			0
$691$	−18.8935	−	32.7244i	−0.718741	−	1.24490i	−0.961499	−	0.274809i	$-0.911385\pi$
$691$	−18.8935	−	32.7244i	−0.718741	−	1.24490i	0.242758	−	0.970087i	$-0.421948\pi$
$692$	12.1990	+	21.1293i	0.463736	+	0.803214i
$693$		0			0
$694$	57.5215			2.18349
$695$	−1.01416	+	1.75657i	−0.0384692	+	0.0666306i
$696$		0			0
$697$	−10.7565			−0.407430
$698$	−6.34928	+	10.9973i	−0.240324	+	0.416253i
$699$		0			0
$700$	2.82591	+	4.89462i	0.106809	+	0.184999i
$701$	−9.12075			−0.344486			−0.172243	−	0.985054i	$-0.555101\pi$
$701$	−9.12075			−0.344486			−0.172243	+	0.985054i	$0.555101\pi$
$702$		0			0
$703$	−3.55825			−0.134202
$704$	−1.25197	−	2.16847i	−0.0471853	−	0.0817273i
$705$		0			0
$706$	−27.3421	+	47.3579i	−1.02903	+	1.78234i
$707$	79.3059			2.98261
$708$		0			0
$709$	10.8701	−	18.8276i	0.408236	−	0.707086i	−0.586456	−	0.809981i	$-0.699477\pi$
$709$	10.8701	−	18.8276i	0.408236	−	0.707086i	0.994692	+	0.102895i	$0.0328106\pi$
$710$	10.5750			0.396871
$711$		0			0
$712$	−0.552993	−	0.957811i	−0.0207243	−	0.0358955i
$713$	1.07924	+	1.86930i	0.0404179	+	0.0700058i
$714$		0			0
$715$	4.56303	+	3.61575i	0.170648	+	0.135221i
$716$	−13.9767			−0.522334
$717$		0			0
$718$	15.0241	+	26.0226i	0.560696	+	0.971154i
$719$	7.18546	−	12.4456i	0.267973	−	0.464142i	−0.700366	−	0.713784i	$-0.746980\pi$
$719$	7.18546	−	12.4456i	0.267973	−	0.464142i	0.968338	+	0.249642i	$0.0803130\pi$
$720$		0			0
$721$	30.5622	−	52.9354i	1.13820	−	1.97142i
$722$	16.7251	−	28.9688i	0.622446	−	1.07811i
$723$		0			0
$724$	0.926779	−	1.60523i	0.0344435	−	0.0596578i
$725$	−0.580318	−	1.00514i	−0.0215525	−	0.0373300i
$726$		0			0
$727$	−38.5088			−1.42821			−0.714106	−	0.700038i	$-0.753166\pi$
$727$	−38.5088			−1.42821			−0.714106	+	0.700038i	$0.753166\pi$
$728$	−3.04715	+	20.6519i	−0.112935	+	0.765410i
$729$		0			0
$730$	−8.97416	−	15.5437i	−0.332149	−	0.575298i
$731$	4.49195	+	7.78028i	0.166141	+	0.287764i
$732$		0			0
$733$	−1.95952			−0.0723767			−0.0361884	−	0.999345i	$-0.511522\pi$
$733$	−1.95952			−0.0723767			−0.0361884	+	0.999345i	$0.511522\pi$
$734$	−18.4005	+	31.8706i	−0.679174	+	1.17636i
$735$		0			0
$736$	−8.23730			−0.303631
$737$	0.176597	−	0.305875i	0.00650503	−	0.0112670i
$738$		0			0
$739$	19.7301	+	34.1736i	0.725784	+	1.25710i	0.958650	+	0.284587i	$0.0918564\pi$
$739$	19.7301	+	34.1736i	0.725784	+	1.25710i	−0.232866	+	0.972509i	$0.574810\pi$
$740$	6.28802			0.231152
$741$		0			0
$742$	107.380			3.94203
$743$	−16.7449	−	29.0031i	−0.614312	−	1.06402i	−0.990505	−	0.137478i	$-0.956100\pi$
$743$	−16.7449	−	29.0031i	−0.614312	−	1.06402i	0.376193	−	0.926541i	$-0.377233\pi$
$744$		0			0
$745$	−2.80522	+	4.85878i	−0.102775	+	0.178012i
$746$	−37.5689			−1.37550
$747$		0			0
$748$	−1.29500	+	2.24301i	−0.0473500	+	0.0820126i
$749$	−43.0613			−1.57343
$750$		0			0
$751$	8.58750	+	14.8740i	0.313362	+	0.542759i	0.979088	−	0.203437i	$-0.0652113\pi$
$751$	8.58750	+	14.8740i	0.313362	+	0.542759i	−0.665726	+	0.746197i	$0.731878\pi$
$752$	30.3959	+	52.6472i	1.10842	+	1.91985i
$753$		0			0
$754$	−1.10581	+	7.49454i	−0.0402711	+	0.272935i
$755$	15.5158			0.564679
$756$		0			0
$757$	21.1595	+	36.6493i	0.769055	+	1.33204i	0.938076	+	0.346430i	$0.112606\pi$
$757$	21.1595	+	36.6493i	0.769055	+	1.33204i	−0.169021	+	0.985612i	$0.554061\pi$
$758$	0.783097	−	1.35636i	0.0284434	−	0.0492653i
$759$		0			0
$760$	−0.472840	+	0.818983i	−0.0171517	+	0.0297076i
$761$	−6.22372	+	10.7798i	−0.225610	+	0.390767i	−0.956502	−	0.291725i	$-0.905771\pi$
$761$	−6.22372	+	10.7798i	−0.225610	+	0.390767i	0.730892	+	0.682493i	$0.239104\pi$
$762$		0			0
$763$	9.64791	−	16.7107i	0.349278	−	0.604967i
$764$	−9.37476	−	16.2376i	−0.339167	−	0.587454i
$765$		0			0
$766$	5.11081			0.184661
$767$	−2.25511	+	15.2839i	−0.0814273	+	0.551870i
$768$		0			0
$769$	3.67747	+	6.36957i	0.132613	+	0.229692i	0.924683	−	0.380738i	$-0.124330\pi$
$769$	3.67747	+	6.36957i	0.132613	+	0.229692i	−0.792070	+	0.610430i	$0.790997\pi$
$770$	−6.46749	−	11.2020i	−0.233072	−	0.403693i
$771$		0			0
$772$	−25.3325			−0.911738
$773$	−6.43507	+	11.1459i	−0.231453	+	0.400889i	−0.958236	−	0.285978i	$-0.907681\pi$
$773$	−6.43507	+	11.1459i	−0.231453	+	0.400889i	0.726783	+	0.686868i	$0.241015\pi$
$774$		0			0
$775$	−1.64968			−0.0592582
$776$	8.86750	−	15.3590i	0.318325	−	0.551355i
$777$		0			0
$778$	−12.1757	−	21.0889i	−0.436519	−	0.756073i
$779$	−6.19057			−0.221800
$780$		0			0
$781$	−9.43235			−0.337516
$782$	1.48733	+	2.57613i	0.0531867	+	0.0921221i
$783$		0			0
$784$	30.9687	−	53.6393i	1.10602	−	1.91569i
$785$	−14.4852			−0.516997
$786$		0			0
$787$	2.48451	−	4.30329i	0.0885631	−	0.153396i	−0.818341	−	0.574733i	$-0.805106\pi$
$787$	2.48451	−	4.30329i	0.0885631	−	0.153396i	0.906904	+	0.421337i	$0.138439\pi$
$788$	−15.8271			−0.563818
$789$		0			0
$790$	12.7947	+	22.1611i	0.455215	+	0.788456i
$791$	−42.4641	−	73.5500i	−1.50985	−	2.61514i
$792$		0			0
$793$	−2.97339	+	20.1520i	−0.105588	+	0.715619i
$794$	14.5552			0.516543
$795$		0			0
$796$	−14.7602	−	25.5654i	−0.523162	−	0.906143i
$797$	10.5622	−	18.2943i	0.374133	−	0.648018i	−0.616064	−	0.787696i	$-0.711274\pi$
$797$	10.5622	−	18.2943i	0.374133	−	0.648018i	0.990197	+	0.139679i	$0.0446070\pi$
$798$		0			0
$799$	7.75364	−	13.4297i	0.274304	−	0.475109i
$800$	3.14779	−	5.45213i	0.111291	−	0.192762i
$801$		0			0
$802$	−31.1030	+	53.8720i	−1.09829	+	1.90229i
$803$	8.00452	+	13.8642i	0.282473	+	0.489258i
$804$		0			0
$805$	−5.78982			−0.204064
$806$	8.43939	+	6.68738i	0.297265	+	0.235553i
$807$		0			0
$808$	−11.7249	−	20.3081i	−0.412480	−	0.714436i
$809$	5.63041	+	9.75216i	0.197955	+	0.342868i	0.947865	−	0.318672i	$-0.103237\pi$
$809$	5.63041	+	9.75216i	0.197955	+	0.342868i	−0.749910	+	0.661539i	$0.769903\pi$
$810$		0			0
$811$	30.9957			1.08841			0.544203	−	0.838954i	$-0.316832\pi$
$811$	30.9957			1.08841			0.544203	+	0.838954i	$0.316832\pi$
$812$	3.27985	−	5.68087i	0.115100	−	0.199359i
$813$		0			0
$814$	−14.3910			−0.504405
$815$	−7.76699	+	13.4528i	−0.272066	+	0.471232i
$816$		0			0
$817$	2.58521	+	4.47772i	0.0904451	+	0.156655i
$818$	−35.2410			−1.23217
$819$		0			0
$820$	10.9398			0.382033
$821$	−21.9342	−	37.9912i	−0.765510	−	1.32590i	−0.939976	−	0.341239i	$-0.889153\pi$
$821$	−21.9342	−	37.9912i	−0.765510	−	1.32590i	0.174466	−	0.984663i	$-0.444180\pi$
$822$		0			0
$823$	3.04030	−	5.26596i	0.105978	−	0.183560i	−0.808159	−	0.588964i	$-0.799536\pi$
$823$	3.04030	−	5.26596i	0.105978	−	0.183560i	0.914137	+	0.405404i	$0.132869\pi$
$824$	−18.0738			−0.629629
$825$		0			0
$826$	17.1625	−	29.7262i	0.597158	−	1.03431i
$827$	11.0488			0.384205			0.192102	−	0.981375i	$-0.438469\pi$
$827$	11.0488			0.384205			0.192102	+	0.981375i	$0.438469\pi$
$828$		0			0
$829$	−15.7802	−	27.3322i	−0.548070	−	0.949285i	−0.998407	−	0.0564262i	$-0.982029\pi$
$829$	−15.7802	−	27.3322i	−0.548070	−	0.949285i	0.450337	−	0.892859i	$-0.351304\pi$
$830$	−9.98771	−	17.2992i	−0.346679	−	0.600465i
$831$		0			0
$832$	−5.19826	+	2.05884i	−0.180217	+	0.0713773i
$833$	−15.7995			−0.547421
$834$		0			0
$835$	10.1644	+	17.6053i	0.351753	+	0.609255i
$836$	−0.745302	+	1.29090i	−0.0257768	+	0.0446468i
$837$		0			0
$838$	22.1510	−	38.3667i	0.765194	−	1.32535i
$839$	−8.03414	+	13.9155i	−0.277369	+	0.480418i	−0.970730	−	0.240173i	$-0.922796\pi$
$839$	−8.03414	+	13.9155i	−0.277369	+	0.480418i	0.693361	+	0.720591i	$0.256129\pi$
$840$		0			0
$841$	13.8265	−	23.9481i	0.476775	−	0.825798i
$842$	−25.0709	−	43.4241i	−0.864001	−	1.49649i
$843$		0			0
$844$	−11.3085			−0.389253
$845$	9.47452	−	8.90132i	0.325933	−	0.306215i
$846$		0			0
$847$	−18.5690	−	32.1624i	−0.638037	−	1.10511i
$848$	−32.9962	−	57.1511i	−1.13309	−	1.96258i
$849$		0			0
$850$	−2.27346			−0.0779791
$851$	−3.22078	+	5.57856i	−0.110407	+	0.191230i
$852$		0			0
$853$	11.5424			0.395205			0.197602	−	0.980282i	$-0.436685\pi$
$853$	11.5424			0.395205			0.197602	+	0.980282i	$0.436685\pi$
$854$	22.6289	−	39.1944i	0.774346	−	1.34121i
$855$		0			0
$856$	6.36635	+	11.0268i	0.217597	+	0.376890i
$857$	53.7559			1.83627			0.918134	−	0.396270i	$-0.129696\pi$
$857$	53.7559			1.83627			0.918134	+	0.396270i	$0.129696\pi$
$858$		0			0
$859$	3.28910			0.112223			0.0561113	−	0.998425i	$-0.482130\pi$
$859$	3.28910			0.112223			0.0561113	+	0.998425i	$0.482130\pi$
$860$	−4.56849	−	7.91286i	−0.155784	−	0.269826i
$861$		0			0
$862$	3.95347	−	6.84760i	0.134656	−	0.233230i
$863$	32.7600			1.11516			0.557581	−	0.830123i	$-0.311730\pi$
$863$	32.7600			1.11516			0.557581	+	0.830123i	$0.311730\pi$
$864$		0			0
$865$	9.55106	−	16.5429i	0.324746	−	0.562476i
$866$	−16.3963			−0.557170
$867$		0			0
$868$	−4.66184	−	8.07454i	−0.158233	−	0.274068i
$869$	−11.4123	−	19.7666i	−0.387135	−	0.670537i
$870$		0			0
$871$	−0.618124	−	0.489802i	−0.0209443	−	0.0165963i
$872$	−5.70553			−0.193214
$873$		0			0
$874$	0.855989	+	1.48262i	0.0289542	+	0.0501502i
$875$	2.21251	−	3.83219i	0.0747966	−	0.129552i
$876$		0			0
$877$	4.46327	−	7.73061i	0.150714	−	0.261044i	−0.780776	−	0.624811i	$-0.785176\pi$
$877$	4.46327	−	7.73061i	0.150714	−	0.261044i	0.931490	+	0.363767i	$0.118509\pi$
$878$	14.6448	−	25.3655i	0.494238	−	0.856045i
$879$		0			0
$880$	−3.97473	+	6.88443i	−0.133988	+	0.232074i
$881$	13.7612	+	23.8351i	0.463626	+	0.803023i	0.999138	−	0.0415038i	$-0.0132149\pi$
$881$	13.7612	+	23.8351i	0.463626	+	0.803023i	−0.535513	+	0.844527i	$0.679882\pi$
$882$		0			0
$883$	43.2667			1.45604			0.728020	−	0.685555i	$-0.240441\pi$
$883$	43.2667			1.45604			0.728020	+	0.685555i	$0.240441\pi$
$884$	4.53277	+	3.59177i	0.152453	+	0.120804i
$885$		0			0
$886$	−12.3368	−	21.3680i	−0.414463	−	0.717871i
$887$	−14.6659	−	25.4021i	−0.492433	−	0.852919i	0.507529	−	0.861635i	$-0.330559\pi$
$887$	−14.6659	−	25.4021i	−0.492433	−	0.852919i	−0.999962	+	0.00871562i	$0.997226\pi$
$888$		0			0
$889$	13.4554			0.451281
$890$	0.765111	−	1.32521i	0.0256466	−	0.0444212i
$891$		0			0
$892$	−5.46060			−0.182834
$893$	4.46239	−	7.72909i	0.149328	−	0.258644i
$894$		0			0
$895$	5.47145	+	9.47683i	0.182890	+	0.316775i
$896$	−43.2940			−1.44635
$897$		0			0
$898$	20.0118			0.667802
$899$	0.957338	+	1.65816i	0.0319290	+	0.0553027i
$900$		0			0
$901$	−8.41696	+	14.5786i	−0.280409	+	0.485683i
$902$	−25.0372			−0.833647
$903$		0			0
$904$	−12.5561	+	21.7478i	−0.417610	+	0.723322i
$905$	−1.45122			−0.0482403
$906$		0			0
$907$	17.6899	+	30.6399i	0.587385	+	1.01738i	0.994574	+	0.104036i	$0.0331757\pi$
$907$	17.6899	+	30.6399i	0.587385	+	1.01738i	−0.407189	+	0.913344i	$0.633491\pi$
$908$	−13.6756	−	23.6868i	−0.453841	−	0.786075i
$909$		0			0
$910$	−26.8535	+	10.6357i	−0.890183	+	0.352569i
$911$	46.6105			1.54428			0.772138	−	0.635455i	$-0.219188\pi$
$911$	46.6105			1.54428			0.772138	+	0.635455i	$0.219188\pi$
$912$		0			0
$913$	8.90856	+	15.4301i	0.294830	+	0.510661i
$914$	−21.9366	+	37.9953i	−0.725599	+	1.25677i
$915$		0			0
$916$	−0.422453	+	0.731710i	−0.0139582	+	0.0241764i
$917$	34.2706	−	59.3584i	1.13171	−	1.96019i
$918$		0			0
$919$	13.1933	−	22.8514i	0.435205	−	0.753798i	−0.562107	−	0.827064i	$-0.690009\pi$
$919$	13.1933	−	22.8514i	0.435205	−	0.753798i	0.997312	+	0.0732669i	$0.0233425\pi$
$920$	0.855989	+	1.48262i	0.0282211	+	0.0488804i
$921$		0			0
$922$	48.3279			1.59159
$923$	−3.07435	+	20.8362i	−0.101193	+	0.685833i
$924$		0			0
$925$	−2.46157	−	4.26356i	−0.0809359	−	0.140185i
$926$	−17.9345	−	31.0634i	−0.589364	−	1.02081i
$927$		0			0
$928$	−7.30688			−0.239860
$929$	−2.76179	+	4.78355i	−0.0906113	+	0.156943i	−0.907768	−	0.419472i	$-0.862215\pi$
$929$	−2.76179	+	4.78355i	−0.0906113	+	0.156943i	0.817157	+	0.576415i	$0.195549\pi$
$930$		0			0
$931$	−9.09297			−0.298010
$932$	−8.53612	+	14.7850i	−0.279610	+	0.484299i
$933$		0			0
$934$	−20.3345	−	35.2204i	−0.665366	−	1.15245i
$935$	2.02782			0.0663167
$936$		0			0
$937$	7.15026			0.233589			0.116794	−	0.993156i	$-0.462738\pi$
$937$	7.15026			0.233589			0.116794	+	0.993156i	$0.462738\pi$
$938$	0.876108	+	1.51746i	0.0286059	+	0.0495469i
$939$		0			0
$940$	−7.88578	+	13.6586i	−0.257206	+	0.445493i
$941$	19.8331			0.646541			0.323271	−	0.946307i	$-0.395218\pi$
$941$	19.8331			0.646541			0.323271	+	0.946307i	$0.395218\pi$
$942$		0			0
$943$	−5.60344	+	9.70545i	−0.182473	+	0.316053i
$944$	−21.0951			−0.686587
$945$		0			0
$946$	10.4556	+	18.1097i	0.339942	+	0.588797i
$947$	−1.59561	−	2.76368i	−0.0518503	−	0.0898074i	0.838935	−	0.544231i	$-0.183179\pi$
$947$	−1.59561	−	2.76368i	−0.0518503	−	0.0898074i	−0.890786	+	0.454424i	$0.849845\pi$
$948$		0			0
$949$	33.2353	−	13.1633i	1.07886	−	0.427298i
$950$	−1.30843			−0.0424509
$951$		0			0
$952$	3.63554	+	6.29693i	0.117828	+	0.204085i
$953$	−20.4893	+	35.4885i	−0.663713	+	1.14958i	0.315920	+	0.948786i	$0.397687\pi$
$953$	−20.4893	+	35.4885i	−0.663713	+	1.14958i	−0.979633	+	0.200799i	$0.935646\pi$
$954$		0			0
$955$	−7.33986	+	12.7130i	−0.237512	+	0.411384i
$956$	−2.83763	+	4.91492i	−0.0917756	+	0.158960i
$957$		0			0
$958$	22.7813	−	39.4584i	0.736030	−	1.27484i
$959$	−19.2453	−	33.3338i	−0.621463	−	1.07640i
$960$		0			0
$961$	−28.2786			−0.912212
$962$	−4.69056	+	31.7900i	−0.151230	+	1.02495i
$963$		0			0
$964$	9.21053	+	15.9531i	0.296651	+	0.513815i
$965$	9.91692	+	17.1766i	0.319237	+	0.552935i
$966$		0			0
$967$	−41.6355			−1.33891			−0.669453	−	0.742854i	$-0.733471\pi$
$967$	−41.6355			−1.33891			−0.669453	+	0.742854i	$0.733471\pi$
$968$	−5.49061	+	9.51002i	−0.176475	+	0.305664i
$969$		0			0
$970$	24.5378			0.787862
$971$	−10.5968	+	18.3541i	−0.340067	+	0.589013i	−0.984445	−	0.175694i	$-0.943783\pi$
$971$	−10.5968	+	18.3541i	−0.340067	+	0.589013i	0.644378	+	0.764707i	$0.277116\pi$
$972$		0			0
$973$	4.48768	+	7.77288i	0.143868	+	0.249187i
$974$	−53.5023			−1.71433
$975$		0			0
$976$	−27.8141			−0.890309
$977$	−8.11660	−	14.0584i	−0.259673	−	0.449767i	0.706481	−	0.707732i	$-0.250281\pi$
$977$	−8.11660	−	14.0584i	−0.259673	−	0.449767i	−0.966154	+	0.257965i	$0.916948\pi$
$978$		0			0
$979$	−0.682442	+	1.18202i	−0.0218109	+	0.0377777i
$980$	16.0688			0.513298
$981$		0			0
$982$	13.9923	−	24.2354i	0.446513	−	0.773384i
$983$	−27.0181			−0.861743			−0.430872	−	0.902413i	$-0.641794\pi$
$983$	−27.0181			−0.861743			−0.430872	+	0.902413i	$0.641794\pi$
$984$		0			0
$985$	6.19584	+	10.7315i	0.197416	+	0.341934i
$986$	1.31933	+	2.28515i	0.0420160	+	0.0727739i
$987$		0			0
$988$	2.60871	+	2.06714i	0.0829940	+	0.0657645i
$989$	9.36009			0.297634
$990$		0			0
$991$	8.49526	+	14.7142i	0.269861	+	0.467413i	0.968826	−	0.247743i	$-0.0796890\pi$
$991$	8.49526	+	14.7142i	0.269861	+	0.467413i	−0.698965	+	0.715156i	$0.746356\pi$
$992$	−5.19284	+	8.99426i	−0.164873	+	0.285568i
$993$		0			0
$994$	23.3972	−	40.5252i	0.742115	−	1.28538i
$995$	−11.5563	+	20.0162i	−0.366361	+	0.634556i
$996$		0			0
$997$	−19.7128	+	34.1435i	−0.624309	+	1.08134i	0.364365	+	0.931256i	$0.381286\pi$
$997$	−19.7128	+	34.1435i	−0.624309	+	1.08134i	−0.988674	+	0.150079i	$0.952047\pi$
$998$	1.25158	+	2.16781i	0.0396182	+	0.0686208i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.h.406.2	✓	10
3.2	odd	2		585.2.j.i.406.4	yes	10
13.3	even	3		7605.2.a.co.1.4		5
13.9	even	3	inner	585.2.j.h.451.2	yes	10
13.10	even	6		7605.2.a.cl.1.2		5
39.23	odd	6		7605.2.a.cn.1.4		5
39.29	odd	6		7605.2.a.cm.1.2		5
39.35	odd	6		585.2.j.i.451.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.j.h.406.2	✓	10	1.1	even	1	trivial
585.2.j.h.451.2	yes	10	13.9	even	3	inner
585.2.j.i.406.4	yes	10	3.2	odd	2
585.2.j.i.451.4	yes	10	39.35	odd	6
7605.2.a.cl.1.2		5	13.10	even	6
7605.2.a.cm.1.2		5	39.29	odd	6
7605.2.a.cn.1.4		5	39.23	odd	6
7605.2.a.co.1.4		5	13.3	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.905157 - 1.56778i) q^{2} +(-0.638619 + 1.10612i) q^{4} +1.00000 q^{5} +(2.21251 - 3.83219i) q^{7} -1.30843 q^{8} +O(q^{10})\)	\(q+(-0.905157 - 1.56778i) q^{2} +(-0.638619 + 1.10612i) q^{4} +1.00000 q^{5} +(2.21251 - 3.83219i) q^{7} -1.30843 q^{8} +(-0.905157 - 1.56778i) q^{10} +(0.807357 + 1.39838i) q^{11} +(3.35220 - 1.32768i) q^{13} -8.01069 q^{14} +(2.46157 + 4.26356i) q^{16} +(0.627919 - 1.08759i) q^{17} +(0.361381 - 0.625930i) q^{19} +(-0.638619 + 1.10612i) q^{20} +(1.46157 - 2.53151i) q^{22} +(-0.654213 - 1.13313i) q^{23} +1.00000 q^{25} +(-5.11578 - 4.05375i) q^{26} +(2.82591 + 4.89462i) q^{28} +(-0.580318 - 1.00514i) q^{29} -1.64968 q^{31} +(3.14779 - 5.45213i) q^{32} -2.27346 q^{34} +(2.21251 - 3.83219i) q^{35} +(-2.46157 - 4.26356i) q^{37} -1.30843 q^{38} -1.30843 q^{40} +(-4.28258 - 7.41765i) q^{41} +(-3.57685 + 6.19529i) q^{43} -2.06237 q^{44} +(-1.18433 + 2.05132i) q^{46} +12.3482 q^{47} +(-6.29044 - 10.8954i) q^{49} +(-0.905157 - 1.56778i) q^{50} +(-0.672203 + 4.55582i) q^{52} -13.4045 q^{53} +(0.807357 + 1.39838i) q^{55} +(-2.89491 + 5.01413i) q^{56} +(-1.05056 + 1.81962i) q^{58} +(-2.14244 + 3.71082i) q^{59} +(-2.82484 + 4.89276i) q^{61} +(1.49322 + 2.58633i) q^{62} -1.55070 q^{64} +(3.35220 - 1.32768i) q^{65} +(-0.109367 - 0.189430i) q^{67} +(0.802002 + 1.38911i) q^{68} -8.01069 q^{70} +(-2.92075 + 5.05889i) q^{71} +9.91448 q^{73} +(-4.45621 + 7.71839i) q^{74} +(0.461569 + 0.799462i) q^{76} +7.14515 q^{77} -14.1353 q^{79} +(2.46157 + 4.26356i) q^{80} +(-7.75282 + 13.4283i) q^{82} +11.0342 q^{83} +(0.627919 - 1.08759i) q^{85} +12.9505 q^{86} +(-1.05637 - 1.82968i) q^{88} +(0.422640 + 0.732033i) q^{89} +(2.32887 - 15.7838i) q^{91} +1.67117 q^{92} +(-11.1770 - 19.3592i) q^{94} +(0.361381 - 0.625930i) q^{95} +(-6.77723 + 11.7385i) q^{97} +(-11.3877 + 19.7240i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8}+O(q^{10}) \) 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8	\( 10 q - 2 q^{2} - 6 q^{4} + 10 q^{5} - q^{7} + 12 q^{8} - 2 q^{10} - 8 q^{11} + q^{13} - 8 q^{14} - 4 q^{16} + 4 q^{19} - 6 q^{20} - 14 q^{22} + 6 q^{23} + 10 q^{25} - 10 q^{26} + 2 q^{28} - 16 q^{29} + 18 q^{31} - 14 q^{32} - q^{35} + 4 q^{37} + 12 q^{38} + 12 q^{40} - 6 q^{41} - 15 q^{43} + 28 q^{44} + 16 q^{46} + 20 q^{47} - 10 q^{49} - 2 q^{50} - 22 q^{52} - 40 q^{53} - 8 q^{55} + 2 q^{56} + 4 q^{58} - 12 q^{59} - 11 q^{61} + 22 q^{62} + 8 q^{64} + q^{65} - 5 q^{67} - 50 q^{68} - 8 q^{70} - 10 q^{71} + 2 q^{73} + 26 q^{74} - 24 q^{76} + 84 q^{77} - 34 q^{79} - 4 q^{80} - 16 q^{82} + 32 q^{83} + 88 q^{86} - 20 q^{88} - 4 q^{89} - q^{91} - 68 q^{92} + 16 q^{94} + 4 q^{95} + 11 q^{97} - 30 q^{98}+O(q^{100}) \) 10 * q - 2 * q^2 - 6 * q^4 + 10 * q^5 - q^7 + 12 * q^8 - 2 * q^10 - 8 * q^11 + q^13 - 8 * q^14 - 4 * q^16 + 4 * q^19 - 6 * q^20 - 14 * q^22 + 6 * q^23 + 10 * q^25 - 10 * q^26 + 2 * q^28 - 16 * q^29 + 18 * q^31 - 14 * q^32 - q^35 + 4 * q^37 + 12 * q^38 + 12 * q^40 - 6 * q^41 - 15 * q^43 + 28 * q^44 + 16 * q^46 + 20 * q^47 - 10 * q^49 - 2 * q^50 - 22 * q^52 - 40 * q^53 - 8 * q^55 + 2 * q^56 + 4 * q^58 - 12 * q^59 - 11 * q^61 + 22 * q^62 + 8 * q^64 + q^65 - 5 * q^67 - 50 * q^68 - 8 * q^70 - 10 * q^71 + 2 * q^73 + 26 * q^74 - 24 * q^76 + 84 * q^77 - 34 * q^79 - 4 * q^80 - 16 * q^82 + 32 * q^83 + 88 * q^86 - 20 * q^88 - 4 * q^89 - q^91 - 68 * q^92 + 16 * q^94 + 4 * q^95 + 11 * q^97 - 30 * q^98

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