LMFDB - Embedded newform 585.2.j.i.406.4

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			406.4
Root			$0.905157 - 1.56778i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.i.451.4

$q$-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	$0.0544167\pi$
$2$	0.905157	+	1.56778i	0.640043	+	1.10859i	−0.345380	+	0.938463i	$0.612250\pi$
$3$		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	0.718261	−	0.695774i	$-0.244938\pi$
$11$	−0.807357	−	1.39838i	−0.243427	−	0.421628i	−0.961688	+	0.274145i	$0.911605\pi$
$12$		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	−0.932070	−	0.362278i	$-0.881999\pi$
$17$	−0.627919	+	1.08759i	−0.152293	+	0.263779i	0.779777	+	0.626057i	$0.215332\pi$
$18$		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	0.926136	−	0.377189i	$-0.123109\pi$
$23$	0.654213	+	1.13313i	0.136413	+	0.236274i	−0.789723	+	0.613463i	$0.789776\pi$
$24$		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	0.914863	−	0.403763i	$-0.132298\pi$
$29$	0.580318	+	1.00514i	0.107762	+	0.186650i	−0.807101	+	0.590413i	$0.798965\pi$
$30$		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	$0.0665368\pi$
$41$	4.28258	+	7.41765i	0.668827	+	1.15844i	−0.309405	+	0.950930i	$0.600130\pi$
$42$		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	$-0.856860\pi$
$47$	−12.3482			−1.80117			−0.900583	+	0.434685i	$0.856860\pi$
$48$		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	$-0.127678\pi$
$53$	13.4045			1.84125			0.920627	+	0.390443i	$0.127678\pi$
$54$		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	−0.692195	−	0.721711i	$-0.743356\pi$
$59$	2.14244	−	3.71082i	0.278922	−	0.483108i	0.971117	+	0.238603i	$0.0766895\pi$
$60$		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	−0.639019	−	0.769191i	$-0.720660\pi$
$71$	2.92075	−	5.05889i	0.346629	−	0.600380i	0.985648	+	0.168811i	$0.0539928\pi$
$72$		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	$-0.707060\pi$
$83$	−11.0342			−1.21116			−0.605582	+	0.795783i	$0.707060\pi$
$84$		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	0.842756	−	0.538296i	$-0.180932\pi$
$89$	−0.422640	−	0.732033i	−0.0447997	−	0.0775954i	−0.887556	+	0.460700i	$0.847598\pi$
$90$		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	$-0.816209\pi$
$101$	−8.96106	−	15.5210i	−0.891659	−	1.54440i	−0.0537731	−	0.998553i	$-0.517125\pi$
$102$		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	0.999426	−	0.0338700i	$-0.0107832\pi$
$107$	4.86566	+	8.42757i	0.470381	+	0.814724i	−0.529045	+	0.848594i	$0.677450\pi$
$108$		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	$0.525121\pi$
$113$	−9.59636	+	16.6214i	−0.902749	+	1.56361i	−0.823910	+	0.566720i	$0.808212\pi$
$114$		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	$-0.736573\pi$
$131$	−15.4894			−1.35332			−0.676659	+	0.736297i	$0.736573\pi$
$132$		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	−0.989808	−	0.142407i	$-0.954516\pi$
$137$	−4.34919	+	7.53302i	−0.371576	+	0.643589i	0.618232	+	0.785996i	$0.287849\pi$
$138$		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	−0.727940	−	0.685641i	$-0.759522\pi$
$149$	2.80522	−	4.85878i	0.229812	−	0.398047i	0.957752	+	0.287594i	$0.0928554\pi$
$150$		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	$-0.878535\pi$
$167$	−10.1644	−	17.6053i	−0.786545	−	1.36234i	0.141527	−	0.989934i	$-0.454799\pi$
$168$		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	$0.425360\pi$
$173$	−9.55106	+	16.5429i	−0.726153	+	1.25773i	−0.958497	+	0.285101i	$0.907973\pi$
$174$		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	0.585818	−	0.810443i	$-0.300773\pi$
$179$	−5.47145	−	9.47683i	−0.408955	−	0.708331i	−0.994773	+	0.102111i	$0.967440\pi$
$180$		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	$-0.655114\pi$
$191$	7.33986	−	12.7130i	0.531094	−	0.919881i	0.999342	−	0.0362842i	$-0.0115522\pi$
$192$		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	0.556361	−	0.830941i	$-0.312197\pi$
$197$	−6.19584	−	10.7315i	−0.441436	−	0.764589i	−0.997796	+	0.0663521i	$0.978864\pi$
$198$		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	$-0.581730\pi$
$227$	10.7072	−	18.5453i	0.710659	−	1.23090i	0.964610	−	0.263681i	$-0.0849365\pi$
$228$		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	$-0.644255\pi$
$233$	−13.3665			−0.875670			−0.437835	+	0.899055i	$0.644255\pi$
$234$		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	$-0.545903\pi$
$239$	−4.44339			−0.287419			−0.143709	+	0.989620i	$0.545903\pi$
$240$		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	−0.914232	−	0.405190i	$-0.867205\pi$
$251$	−1.68270	+	2.91452i	−0.106211	+	0.183963i	0.808021	+	0.589153i	$0.200539\pi$
$252$		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	$0.0997712\pi$
$257$	11.9058	+	20.6215i	0.742664	+	1.28633i	−0.208615	+	0.977998i	$0.566895\pi$
$258$		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	$0.0485450\pi$
$263$	10.1481	+	17.5771i	0.625762	+	1.08385i	−0.362631	+	0.931933i	$0.618122\pi$
$264$		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	−0.862875	−	0.505418i	$-0.831338\pi$
$269$	0.102788	−	0.178034i	0.00626711	−	0.0108550i	0.869142	+	0.494563i	$0.164672\pi$
$270$		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	$-0.672222\pi$
$281$	−17.2672			−1.03008			−0.515039	+	0.857167i	$0.672222\pi$
$282$		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	−0.950290	−	0.311367i	$-0.899213\pi$
$293$	−3.51747	+	6.09244i	−0.205493	+	0.355924i	0.744797	+	0.667291i	$0.232546\pi$
$294$		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	$-0.421666\pi$
$311$	8.59247			0.487234			0.243617	+	0.969871i	$0.421666\pi$
$312$		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	$-0.305529\pi$
$317$	20.4269			1.14729			0.573645	+	0.819104i	$0.305529\pi$
$318$		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	$-0.508195\pi$
$347$	15.8872	−	27.5174i	0.852867	−	1.47721i	0.878609	−	0.477541i	$-0.158472\pi$
$348$		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	$0.130567\pi$
$353$	15.1035	+	26.1600i	0.803878	+	1.39236i	−0.113168	+	0.993576i	$0.536100\pi$
$354$		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	$-0.355682\pi$
$359$	16.5984			0.876029			0.438015	+	0.898968i	$0.355682\pi$
$360$		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	−0.827706	−	0.561163i	$-0.810354\pi$
$383$	1.41158	−	2.44493i	0.0721284	−	0.124930i	0.899834	+	0.436233i	$0.143688\pi$
$384$		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	$-0.610768\pi$
$389$	−13.4514			−0.682015			−0.341008	+	0.940061i	$0.610768\pi$
$390$		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	$0.161613\pi$
$401$	17.1810	+	29.7584i	0.857978	+	1.48606i	−0.0158757	+	0.999874i	$0.505054\pi$
$402$		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	$-0.962721\pi$
$419$	−12.2360	−	21.1934i	−0.597768	−	1.03536i	0.395382	−	0.918517i	$-0.370612\pi$
$420$		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	0.808624	−	0.588325i	$-0.200213\pi$
$431$	−2.18386	−	3.78255i	−0.105193	−	0.182199i	−0.913817	+	0.406126i	$0.866879\pi$
$432$		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	$-0.604953\pi$
$443$	−13.6295			−0.647555			−0.323778	+	0.946133i	$0.604953\pi$
$444$		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	−0.705623	−	0.708587i	$-0.749333\pi$
$449$	5.52716	−	9.57332i	0.260843	−	0.451793i	0.966466	+	0.256794i	$0.0826662\pi$
$450$		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	$-0.619786\pi$
$461$	13.3479	−	23.1193i	0.621674	−	1.07677i	0.989174	−	0.146748i	$-0.0468806\pi$
$462$		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	$-0.673987\pi$
$467$	−22.4652			−1.03956			−0.519782	+	0.854299i	$0.673987\pi$
$468$		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	$-0.971674\pi$
$479$	−12.5842	−	21.7964i	−0.574985	−	0.995903i	0.421058	−	0.907034i	$-0.361659\pi$
$480$		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	0.637224	−	0.770679i	$-0.280083\pi$
$491$	−7.72923	−	13.3874i	−0.348815	−	0.604166i	−0.986039	+	0.166513i	$0.946749\pi$
$492$		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	$-0.473239\pi$
$503$	20.2960	−	35.1537i	0.904953	−	1.56742i	0.820980	−	0.570957i	$-0.193428\pi$
$504$		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	0.786746	−	0.617277i	$-0.211764\pi$
$509$	−3.18571	−	5.51781i	−0.141204	−	0.244573i	−0.927950	+	0.372704i	$0.878431\pi$
$510$		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	$-0.510797\pi$
$521$	−1.54817			−0.0678264			−0.0339132	+	0.999425i	$0.510797\pi$
$522$		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	0.829259	−	0.558865i	$-0.188763\pi$
$557$	−1.63700	−	2.83536i	−0.0693617	−	0.120138i	−0.898621	+	0.438727i	$0.855430\pi$
$558$		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	−0.772413	−	0.635121i	$-0.780950\pi$
$563$	3.88716	−	6.73276i	0.163824	−	0.283752i	0.936237	+	0.351369i	$0.114284\pi$
$564$		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	0.936678	−	0.350193i	$-0.113884\pi$
$569$	3.93736	+	6.81970i	0.165063	+	0.285897i	−0.771615	+	0.636090i	$0.780551\pi$
$570$		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	0.608756	−	0.793357i	$-0.291669\pi$
$587$	−9.27183	−	16.0593i	−0.382689	−	0.662837i	−0.991446	+	0.130520i	$0.958335\pi$
$588$		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	$-0.576596\pi$
$593$	−11.6068			−0.476633			−0.238316	+	0.971188i	$0.576596\pi$
$594$		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	$-0.243932\pi$
$599$	35.2656			1.44091			0.720457	+	0.693500i	$0.243932\pi$
$600$		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	−0.914891	−	0.403700i	$-0.867724\pi$
$617$	−2.67847	+	4.63924i	−0.107831	+	0.186769i	0.807060	+	0.590469i	$0.201057\pi$
$618$		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	$-0.478052\pi$
$641$	22.7461	−	39.3974i	0.898416	−	1.55610i	0.829519	−	0.558479i	$-0.188615\pi$
$642$		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	$0.221507\pi$
$647$	23.8826	+	41.3659i	0.938922	+	1.62626i	0.171436	+	0.985195i	$0.445159\pi$
$648$		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	0.763988	−	0.645231i	$-0.223239\pi$
$653$	−4.51773	−	7.82494i	−0.176793	−	0.306214i	−0.940780	+	0.339017i	$0.889905\pi$
$654$		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	$-0.548248\pi$
$659$	20.0387	−	34.7081i	0.780598	−	1.35204i	0.931594	−	0.363501i	$-0.118419\pi$
$660$		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	$-0.211054\pi$
$677$	41.0126			1.57624			0.788121	+	0.615520i	$0.211054\pi$
$678$		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	−0.840847	−	0.541273i	$-0.817943\pi$
$683$	1.26313	−	2.18780i	0.0483322	−	0.0837139i	0.889179	+	0.457559i	$0.151276\pi$
$684$		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	$-0.444899\pi$
$701$	9.12075			0.344486			0.172243	+	0.985054i	$0.444899\pi$
$702$		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	−0.968338	−	0.249642i	$-0.919687\pi$
$719$	−7.18546	+	12.4456i	−0.267973	+	0.464142i	0.700366	+	0.713784i	$0.253020\pi$
$720$		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	$0.0438996\pi$
$743$	16.7449	+	29.0031i	0.614312	+	1.06402i	−0.376193	+	0.926541i	$0.622767\pi$
$744$		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	−0.730892	−	0.682493i	$-0.760896\pi$
$761$	6.22372	−	10.7798i	0.225610	−	0.390767i	0.956502	+	0.291725i	$0.0942293\pi$
$762$		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	−0.726783	−	0.686868i	$-0.758985\pi$
$773$	6.43507	−	11.1459i	0.231453	−	0.400889i	0.958236	+	0.285978i	$0.0923186\pi$
$774$		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	−0.990197	−	0.139679i	$-0.955393\pi$
$797$	−10.5622	+	18.2943i	−0.374133	+	0.648018i	0.616064	+	0.787696i	$0.288726\pi$
$798$		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	0.749910	−	0.661539i	$-0.230097\pi$
$809$	−5.63041	−	9.75216i	−0.197955	−	0.342868i	−0.947865	+	0.318672i	$0.896763\pi$
$810$		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	$0.110847\pi$
$821$	21.9342	+	37.9912i	0.765510	+	1.32590i	−0.174466	+	0.984663i	$0.555820\pi$
$822$		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	$-0.561531\pi$
$827$	−11.0488			−0.384205			−0.192102	+	0.981375i	$0.561531\pi$
$828$		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	−0.693361	−	0.720591i	$-0.743871\pi$
$839$	8.03414	−	13.9155i	0.277369	−	0.480418i	0.970730	+	0.240173i	$0.0772041\pi$
$840$		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	$-0.870304\pi$
$857$	−53.7559			−1.83627			−0.918134	+	0.396270i	$0.870304\pi$
$858$		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	$-0.688270\pi$
$863$	−32.7600			−1.11516			−0.557581	+	0.830123i	$0.688270\pi$
$864$		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	0.535513	−	0.844527i	$-0.320118\pi$
$881$	−13.7612	−	23.8351i	−0.463626	−	0.803023i	−0.999138	+	0.0415038i	$0.986785\pi$
$882$		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	0.999962	−	0.00871562i	$-0.00277430\pi$
$887$	14.6659	+	25.4021i	0.492433	+	0.852919i	−0.507529	+	0.861635i	$0.669441\pi$
$888$		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	$-0.780812\pi$
$911$	−46.6105			−1.54428			−0.772138	+	0.635455i	$0.780812\pi$
$912$		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	−0.817157	−	0.576415i	$-0.804451\pi$
$929$	2.76179	−	4.78355i	0.0906113	−	0.156943i	0.907768	+	0.419472i	$0.137785\pi$
$930$		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	$-0.604782\pi$
$941$	−19.8331			−0.646541			−0.323271	+	0.946307i	$0.604782\pi$
$942$		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	0.890786	−	0.454424i	$-0.150155\pi$
$947$	1.59561	+	2.76368i	0.0518503	+	0.0898074i	−0.838935	+	0.544231i	$0.816821\pi$
$948$		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	$-0.602313\pi$
$953$	20.4893	−	35.4885i	0.663713	−	1.14958i	0.979633	−	0.200799i	$-0.0643537\pi$
$954$		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	−0.644378	−	0.764707i	$-0.722884\pi$
$971$	10.5968	−	18.3541i	0.340067	−	0.589013i	0.984445	+	0.175694i	$0.0562171\pi$
$972$		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	0.966154	−	0.257965i	$-0.0830519\pi$
$977$	8.11660	+	14.0584i	0.259673	+	0.449767i	−0.706481	+	0.707732i	$0.749719\pi$
$978$		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	$-0.358206\pi$
$983$	27.0181			0.861743			0.430872	+	0.902413i	$0.358206\pi$
$984$		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.i.406.4	yes	10
3.2	odd	2		585.2.j.h.406.2	✓	10
13.3	even	3		7605.2.a.cm.1.2		5
13.9	even	3	inner	585.2.j.i.451.4	yes	10
13.10	even	6		7605.2.a.cn.1.4		5
39.23	odd	6		7605.2.a.cl.1.2		5
39.29	odd	6		7605.2.a.co.1.4		5
39.35	odd	6		585.2.j.h.451.2	yes	10

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
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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