LMFDB - Embedded newform 882.2.e.o.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.1
Root			$0.500000 - 1.41036i$ of defining polynomial
Character	$\chi$	$=$	882.373
Dual form			882.2.e.o.655.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-1.71053 + 0.272169i) q^{3} +1.00000 q^{4} +(-1.59097 - 2.75564i) q^{5} +(1.71053 - 0.272169i) q^{6} -1.00000 q^{8} +(2.85185 - 0.931107i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-1.71053 + 0.272169i) q^{3} +1.00000 q^{4} +(-1.59097 - 2.75564i) q^{5} +(1.71053 - 0.272169i) q^{6} -1.00000 q^{8} +(2.85185 - 0.931107i) q^{9} +(1.59097 + 2.75564i) q^{10} +(-1.59097 + 2.75564i) q^{11} +(-1.71053 + 0.272169i) q^{12} +(-2.85185 + 4.93955i) q^{13} +(3.47141 + 4.28061i) q^{15} +1.00000 q^{16} +(0.760877 + 1.31788i) q^{17} +(-2.85185 + 0.931107i) q^{18} +(0.641315 - 1.11079i) q^{19} +(-1.59097 - 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +(-1.11956 - 1.93914i) q^{23} +(1.71053 - 0.272169i) q^{24} +(-2.56238 + 4.43818i) q^{25} +(2.85185 - 4.93955i) q^{26} +(-4.62476 + 2.36887i) q^{27} +(-3.54063 - 6.13255i) q^{29} +(-3.47141 - 4.28061i) q^{30} +9.42107 q^{31} -1.00000 q^{32} +(1.97141 - 5.14663i) q^{33} +(-0.760877 - 1.31788i) q^{34} +(2.85185 - 0.931107i) q^{36} +(0.500000 - 0.866025i) q^{37} +(-0.641315 + 1.11079i) q^{38} +(3.53379 - 9.22544i) q^{39} +(1.59097 + 2.75564i) q^{40} +(2.80150 - 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +(-1.59097 + 2.75564i) q^{44} +(-7.10301 - 6.37731i) q^{45} +(1.11956 + 1.93914i) q^{46} +5.82846 q^{47} +(-1.71053 + 0.272169i) q^{48} +(2.56238 - 4.43818i) q^{50} +(-1.66019 - 2.04719i) q^{51} +(-2.85185 + 4.93955i) q^{52} +(1.02859 + 1.78157i) q^{53} +(4.62476 - 2.36887i) q^{54} +10.1248 q^{55} +(-0.794668 + 2.07459i) q^{57} +(3.54063 + 6.13255i) q^{58} +1.12476 q^{59} +(3.47141 + 4.28061i) q^{60} -3.12476 q^{61} -9.42107 q^{62} +1.00000 q^{64} +18.1488 q^{65} +(-1.97141 + 5.14663i) q^{66} +10.9669 q^{67} +(0.760877 + 1.31788i) q^{68} +(2.44282 + 3.01225i) q^{69} +8.69002 q^{71} +(-2.85185 + 0.931107i) q^{72} +(2.48345 + 4.30146i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(3.17511 - 8.28905i) q^{75} +(0.641315 - 1.11079i) q^{76} +(-3.53379 + 9.22544i) q^{78} -4.13844 q^{79} +(-1.59097 - 2.75564i) q^{80} +(7.26608 - 5.31075i) q^{81} +(-2.80150 + 4.85235i) q^{82} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(-3.41423 - 5.91362i) q^{86} +(7.72545 + 9.52628i) q^{87} +(1.59097 - 2.75564i) q^{88} +(-0.112725 + 0.195246i) q^{89} +(7.10301 + 6.37731i) q^{90} +(-1.11956 - 1.93914i) q^{92} +(-16.1150 + 2.56412i) q^{93} -5.82846 q^{94} -4.08126 q^{95} +(1.71053 - 0.272169i) q^{96} +(-7.42107 - 12.8537i) q^{97} +(-1.97141 + 9.34004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9	$ 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9} + q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} + 6 q^{16} + 4 q^{17} - 8 q^{18} + 3 q^{19} - q^{20} + q^{22} - 7 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} - 12 q^{30} + 40 q^{31} - 6 q^{32} + 3 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} - 3 q^{38} - 5 q^{39} + q^{40} - 6 q^{43} - q^{44} - 9 q^{45} + 7 q^{46} - 18 q^{47} - 2 q^{48} - 2 q^{50} + 6 q^{51} - 8 q^{52} + 15 q^{53} - 7 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} - 28 q^{59} + 12 q^{60} + 16 q^{61} - 40 q^{62} + 6 q^{64} + 24 q^{65} - 3 q^{66} - 2 q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} - 8 q^{72} - 19 q^{73} - 3 q^{74} - 8 q^{75} + 3 q^{76} + 5 q^{78} - 10 q^{79} - q^{80} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} + 27 q^{87} + q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} - 38 q^{93} + 18 q^{94} + 8 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9 + q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 + 6 * q^16 + 4 * q^17 - 8 * q^18 + 3 * q^19 - q^20 + q^22 - 7 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 - 12 * q^30 + 40 * q^31 - 6 * q^32 + 3 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 - 3 * q^38 - 5 * q^39 + q^40 - 6 * q^43 - q^44 - 9 * q^45 + 7 * q^46 - 18 * q^47 - 2 * q^48 - 2 * q^50 + 6 * q^51 - 8 * q^52 + 15 * q^53 - 7 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 - 28 * q^59 + 12 * q^60 + 16 * q^61 - 40 * q^62 + 6 * q^64 + 24 * q^65 - 3 * q^66 - 2 * q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 - 8 * q^72 - 19 * q^73 - 3 * q^74 - 8 * q^75 + 3 * q^76 + 5 * q^78 - 10 * q^79 - q^80 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 + 27 * q^87 + q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 - 38 * q^93 + 18 * q^94 + 8 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.71053	+	0.272169i	−0.987577	+	0.157137i
$3$	−1.71053	+	0.272169i	−0.987577	+	0.157137i
$4$	1.00000			0.500000
$5$	−1.59097	−	2.75564i	−0.711504	−	1.23236i	−0.964292	−	0.264840i	$-0.914681\pi$
$5$	−1.59097	−	2.75564i	−0.711504	−	1.23236i	0.252788	−	0.967522i	$-0.418652\pi$
$6$	1.71053	−	0.272169i	0.698322	−	0.111112i
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	2.85185	−	0.931107i	0.950616	−	0.310369i
$10$	1.59097	+	2.75564i	0.503109	+	0.871411i
$11$	−1.59097	+	2.75564i	−0.479696	+	0.830858i	−0.999729	−	0.0232884i	$-0.992586\pi$
$11$	−1.59097	+	2.75564i	−0.479696	+	0.830858i	0.520033	+	0.854146i	$0.325920\pi$
$12$	−1.71053	+	0.272169i	−0.493788	+	0.0785683i
$13$	−2.85185	+	4.93955i	−0.790960	+	1.36998i	0.134412	+	0.990925i	$0.457085\pi$
$13$	−2.85185	+	4.93955i	−0.790960	+	1.36998i	−0.925373	+	0.379058i	$0.876248\pi$
$14$		0			0
$15$	3.47141	+	4.28061i	0.896314	+	1.10525i
$16$	1.00000			0.250000
$17$	0.760877	+	1.31788i	0.184540	+	0.319632i	0.943421	−	0.331596i	$-0.107587\pi$
$17$	0.760877	+	1.31788i	0.184540	+	0.319632i	−0.758882	+	0.651229i	$0.774254\pi$
$18$	−2.85185	+	0.931107i	−0.672187	+	0.219464i
$19$	0.641315	−	1.11079i	0.147128	−	0.254833i	−0.783037	−	0.621975i	$-0.786330\pi$
$19$	0.641315	−	1.11079i	0.147128	−	0.254833i	0.930165	+	0.367142i	$0.119664\pi$
$20$	−1.59097	−	2.75564i	−0.355752	−	0.616181i
$21$		0			0
$22$	1.59097	−	2.75564i	0.339196	−	0.587505i
$23$	−1.11956	−	1.93914i	−0.233445	−	0.404338i	0.725375	−	0.688354i	$-0.241666\pi$
$23$	−1.11956	−	1.93914i	−0.233445	−	0.404338i	−0.958820	+	0.284016i	$0.908333\pi$
$24$	1.71053	−	0.272169i	0.349161	−	0.0555562i
$25$	−2.56238	+	4.43818i	−0.512476	+	0.887635i
$26$	2.85185	−	4.93955i	0.559293	−	0.968725i
$27$	−4.62476	+	2.36887i	−0.890036	+	0.455890i
$28$		0			0
$29$	−3.54063	−	6.13255i	−0.657478	−	1.13879i	−0.981266	−	0.192656i	$-0.938290\pi$
$29$	−3.54063	−	6.13255i	−0.657478	−	1.13879i	0.323788	−	0.946130i	$-0.395043\pi$
$30$	−3.47141	−	4.28061i	−0.633790	−	0.781528i
$31$	9.42107			1.69207			0.846037	−	0.533125i	$-0.178982\pi$
$31$	9.42107			1.69207			0.846037	+	0.533125i	$0.178982\pi$
$32$	−1.00000			−0.176777
$33$	1.97141	−	5.14663i	0.343178	−	0.895914i
$34$	−0.760877	−	1.31788i	−0.130489	−	0.226014i
$35$		0			0
$36$	2.85185	−	0.931107i	0.475308	−	0.155185i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−0.641315	+	1.11079i	−0.104035	+	0.180194i
$39$	3.53379	−	9.22544i	0.565860	−	1.47725i
$40$	1.59097	+	2.75564i	0.251555	+	0.435706i
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	−0.559976	−	0.828509i	$-0.689190\pi$
$41$	2.80150	−	4.85235i	0.437522	−	0.757810i	0.997498	+	0.0706992i	$0.0225230\pi$
$42$		0			0
$43$	3.41423	+	5.91362i	0.520665	+	0.901819i	0.999711	+	0.0240288i	$0.00764935\pi$
$43$	3.41423	+	5.91362i	0.520665	+	0.901819i	−0.479046	+	0.877790i	$0.659017\pi$
$44$	−1.59097	+	2.75564i	−0.239848	+	0.415429i
$45$	−7.10301	−	6.37731i	−1.05885	−	0.950674i
$46$	1.11956	+	1.93914i	0.165070	+	0.285910i
$47$	5.82846			0.850168			0.425084	−	0.905154i	$-0.360245\pi$
$47$	5.82846			0.850168			0.425084	+	0.905154i	$0.360245\pi$
$48$	−1.71053	+	0.272169i	−0.246894	+	0.0392842i
$49$		0			0
$50$	2.56238	−	4.43818i	0.362375	−	0.627653i
$51$	−1.66019	−	2.04719i	−0.232473	−	0.286663i
$52$	−2.85185	+	4.93955i	−0.395480	+	0.684992i
$53$	1.02859	+	1.78157i	0.141288	+	0.244717i	0.927982	−	0.372626i	$-0.121542\pi$
$53$	1.02859	+	1.78157i	0.141288	+	0.244717i	−0.786694	+	0.617343i	$0.788209\pi$
$54$	4.62476	−	2.36887i	0.629351	−	0.322363i
$55$	10.1248			1.36522
$56$		0			0
$57$	−0.794668	+	2.07459i	−0.105256	+	0.274786i
$58$	3.54063	+	6.13255i	0.464907	+	0.805243i
$59$	1.12476			0.146432			0.0732159	−	0.997316i	$-0.476674\pi$
$59$	1.12476			0.146432			0.0732159	+	0.997316i	$0.476674\pi$
$60$	3.47141	+	4.28061i	0.448157	+	0.552624i
$61$	−3.12476			−0.400085			−0.200042	−	0.979787i	$-0.564108\pi$
$61$	−3.12476			−0.400085			−0.200042	+	0.979787i	$0.564108\pi$
$62$	−9.42107			−1.19648
$63$		0			0
$64$	1.00000			0.125000
$65$	18.1488			2.25109
$66$	−1.97141	+	5.14663i	−0.242664	+	0.633507i
$67$	10.9669			1.33982			0.669910	−	0.742442i	$-0.266333\pi$
$67$	10.9669			1.33982			0.669910	+	0.742442i	$0.266333\pi$
$68$	0.760877	+	1.31788i	0.0922699	+	0.159816i
$69$	2.44282	+	3.01225i	0.294081	+	0.362632i
$70$		0			0
$71$	8.69002			1.03132			0.515658	−	0.856794i	$-0.327548\pi$
$71$	8.69002			1.03132			0.515658	+	0.856794i	$0.327548\pi$
$72$	−2.85185	+	0.931107i	−0.336094	+	0.109732i
$73$	2.48345	+	4.30146i	0.290666	+	0.503448i	0.973967	−	0.226689i	$-0.0727899\pi$
$73$	2.48345	+	4.30146i	0.290666	+	0.503448i	−0.683302	+	0.730136i	$0.739457\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	3.17511	−	8.28905i	0.366630	−	0.957137i
$76$	0.641315	−	1.11079i	0.0735639	−	0.127416i
$77$		0			0
$78$	−3.53379	+	9.22544i	−0.400123	+	1.04458i
$79$	−4.13844			−0.465610			−0.232805	−	0.972523i	$-0.574790\pi$
$79$	−4.13844			−0.465610			−0.232805	+	0.972523i	$0.574790\pi$
$80$	−1.59097	−	2.75564i	−0.177876	−	0.308090i
$81$	7.26608	−	5.31075i	0.807342	−	0.590084i
$82$	−2.80150	+	4.85235i	−0.309374	+	0.535852i
$83$	4.03379	+	6.98673i	0.442766	+	0.766893i	0.997894	−	0.0648718i	$-0.0206639\pi$
$83$	4.03379	+	6.98673i	0.442766	+	0.766893i	−0.555127	+	0.831765i	$0.687331\pi$
$84$		0			0
$85$	2.42107	−	4.19341i	0.262602	−	0.454839i
$86$	−3.41423	−	5.91362i	−0.368166	−	0.637682i
$87$	7.72545	+	9.52628i	0.828255	+	1.02132i
$88$	1.59097	−	2.75564i	0.169598	−	0.293753i
$89$	−0.112725	+	0.195246i	−0.0119488	+	0.0206960i	−0.871938	−	0.489616i	$-0.837137\pi$
$89$	−0.112725	+	0.195246i	−0.0119488	+	0.0206960i	0.859989	+	0.510312i	$0.170470\pi$
$90$	7.10301	+	6.37731i	0.748723	+	0.672228i
$91$		0			0
$92$	−1.11956	−	1.93914i	−0.116722	−	0.202169i
$93$	−16.1150	+	2.56412i	−1.67105	+	0.265887i
$94$	−5.82846			−0.601160
$95$	−4.08126			−0.418728
$96$	1.71053	−	0.272169i	0.174581	−	0.0277781i
$97$	−7.42107	−	12.8537i	−0.753495	−	1.30509i	−0.946119	−	0.323819i	$-0.895033\pi$
$97$	−7.42107	−	12.8537i	−0.753495	−	1.30509i	0.192624	−	0.981273i	$-0.438300\pi$
$98$		0			0
$99$	−1.97141	+	9.34004i	−0.198134	+	0.938710i
$100$	−2.56238	+	4.43818i	−0.256238	+	0.443818i
$101$	9.29467	−	16.0988i	0.924854	−	1.60189i	0.133058	−	0.991108i	$-0.457520\pi$
$101$	9.29467	−	16.0988i	0.924854	−	1.60189i	0.791796	−	0.610786i	$-0.209146\pi$
$102$	1.66019	+	2.04719i	0.164383	+	0.202702i
$103$	−0.141315	−	0.244765i	−0.0139242	−	0.0241174i	0.858979	−	0.512010i	$-0.171099\pi$
$103$	−0.141315	−	0.244765i	−0.0139242	−	0.0241174i	−0.872904	+	0.487893i	$0.837766\pi$
$104$	2.85185	−	4.93955i	0.279647	−	0.484362i
$105$		0			0
$106$	−1.02859	−	1.78157i	−0.0999055	−	0.173041i
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	−0.448322	−	0.893872i	$-0.647978\pi$
$107$	5.68878	−	9.85326i	0.549955	−	0.952550i	0.998277	−	0.0586780i	$-0.0186885\pi$
$108$	−4.62476	+	2.36887i	−0.445018	+	0.227945i
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	0.740526	−	0.672028i	$-0.234577\pi$
$109$	−2.21053	−	3.82876i	−0.211731	−	0.366728i	−0.952256	+	0.305300i	$0.901243\pi$
$110$	−10.1248			−0.965358
$111$	−0.619562	+	1.61745i	−0.0588062	+	0.153522i
$112$		0			0
$113$	−1.60752	+	2.78431i	−0.151223	+	0.261926i	−0.931677	−	0.363287i	$-0.881655\pi$
$113$	−1.60752	+	2.78431i	−0.151223	+	0.261926i	0.780454	+	0.625213i	$0.214988\pi$
$114$	0.794668	−	2.07459i	0.0744275	−	0.194303i
$115$	−3.56238	+	6.17023i	−0.332194	+	0.575377i
$116$	−3.54063	−	6.13255i	−0.328739	−	0.569393i
$117$	−3.53379	+	16.7422i	−0.326699	+	1.54782i
$118$	−1.12476			−0.103543
$119$		0			0
$120$	−3.47141	−	4.28061i	−0.316895	−	0.390764i
$121$	0.437618	+	0.757977i	0.0397835	+	0.0689070i
$122$	3.12476			0.282903
$123$	−3.47141	+	9.06259i	−0.313007	+	0.817146i
$124$	9.42107			0.846037
$125$	0.396990			0.0355079
$126$		0			0
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	−1.00000			−0.0883883
$129$	−7.44966	−	9.18620i	−0.655906	−	0.808800i
$130$	−18.1488			−1.59176
$131$	3.18194	+	5.51129i	0.278008	+	0.481523i	0.970890	−	0.239528i	$-0.0769926\pi$
$131$	3.18194	+	5.51129i	0.278008	+	0.481523i	−0.692882	+	0.721051i	$0.743659\pi$
$132$	1.97141	−	5.14663i	0.171589	−	0.447957i
$133$		0			0
$134$	−10.9669			−0.947396
$135$	13.8856	+	8.97539i	1.19509	+	0.772479i
$136$	−0.760877	−	1.31788i	−0.0652446	−	0.113007i
$137$	−1.37072	+	2.37416i	−0.117109	+	0.202838i	−0.918621	−	0.395140i	$-0.870696\pi$
$137$	−1.37072	+	2.37416i	−0.117109	+	0.202838i	0.801512	+	0.597979i	$0.204029\pi$
$138$	−2.44282	−	3.01225i	−0.207947	−	0.256420i
$139$	3.98345	−	6.89953i	0.337872	−	0.585211i	−0.646161	−	0.763202i	$-0.723626\pi$
$139$	3.98345	−	6.89953i	0.337872	−	0.585211i	0.984032	+	0.177991i	$0.0569597\pi$
$140$		0			0
$141$	−9.96978	+	1.58632i	−0.839607	+	0.133593i
$142$	−8.69002			−0.729251
$143$	−9.07442	−	15.7174i	−0.758841	−	1.31435i
$144$	2.85185	−	0.931107i	0.237654	−	0.0775923i
$145$	−11.2661	+	19.5134i	−0.935597	+	1.62050i
$146$	−2.48345	−	4.30146i	−0.205532	−	0.355991i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	11.6300	+	20.1437i	0.952764	+	1.65024i	0.739404	+	0.673262i	$0.235107\pi$
$149$	11.6300	+	20.1437i	0.952764	+	1.65024i	0.213360	+	0.976974i	$0.431559\pi$
$150$	−3.17511	+	8.28905i	−0.259246	+	0.676798i
$151$	4.06238	−	7.03625i	0.330592	−	0.572602i	−0.652036	−	0.758188i	$-0.726085\pi$
$151$	4.06238	−	7.03625i	0.330592	−	0.572602i	0.982628	+	0.185586i	$0.0594183\pi$
$152$	−0.641315	+	1.11079i	−0.0520175	+	0.0900970i
$153$	3.39699	+	3.04993i	0.274630	+	0.246572i
$154$		0			0
$155$	−14.9887	−	25.9611i	−1.20392	−	2.08525i
$156$	3.53379	−	9.22544i	0.282930	−	0.738627i
$157$	11.2632			0.898901			0.449451	−	0.893305i	$-0.351620\pi$
$157$	11.2632			0.898901			0.449451	+	0.893305i	$0.351620\pi$
$158$	4.13844			0.329236
$159$	−2.24433	−	2.76748i	−0.177987	−	0.219476i
$160$	1.59097	+	2.75564i	0.125777	+	0.217853i
$161$		0			0
$162$	−7.26608	+	5.31075i	−0.570877	+	0.417252i
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	−0.933383	−	0.358881i	$-0.883158\pi$
$163$	−1.99028	+	3.44727i	−0.155891	+	0.270011i	0.777492	+	0.628893i	$0.216492\pi$
$164$	2.80150	−	4.85235i	0.218761	−	0.378905i
$165$	−17.3187	+	2.75564i	−1.34826	+	0.214527i
$166$	−4.03379	−	6.98673i	−0.313083	−	0.542276i
$167$	−2.61956	+	4.53721i	−0.202708	+	0.351100i	−0.949400	−	0.314070i	$-0.898307\pi$
$167$	−2.61956	+	4.53721i	−0.202708	+	0.351100i	0.746692	+	0.665170i	$0.231641\pi$
$168$		0			0
$169$	−9.76608	−	16.9153i	−0.751237	−	1.30118i
$170$	−2.42107	+	4.19341i	−0.185687	+	0.321620i
$171$	0.794668	−	3.76494i	0.0607698	−	0.287912i
$172$	3.41423	+	5.91362i	0.260333	+	0.450909i
$173$	−2.55159			−0.193994			−0.0969968	−	0.995285i	$-0.530924\pi$
$173$	−2.55159			−0.193994			−0.0969968	+	0.995285i	$0.530924\pi$
$174$	−7.72545	−	9.52628i	−0.585665	−	0.722185i
$175$		0			0
$176$	−1.59097	+	2.75564i	−0.119924	+	0.207714i
$177$	−1.92395	+	0.306125i	−0.144613	+	0.0230098i
$178$	0.112725	−	0.195246i	0.00844910	−	0.0146343i
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	0.967041	−	0.254620i	$-0.0819504\pi$
$179$	3.51887	+	6.09487i	0.263013	+	0.455552i	−0.704028	+	0.710172i	$0.748617\pi$
$180$	−7.10301	−	6.37731i	−0.529427	−	0.475337i
$181$	12.9669			0.963822			0.481911	−	0.876220i	$-0.339943\pi$
$181$	12.9669			0.963822			0.481911	+	0.876220i	$0.339943\pi$
$182$		0			0
$183$	5.34501	−	0.850463i	0.395115	−	0.0628680i
$184$	1.11956	+	1.93914i	0.0825352	+	0.142955i
$185$	−3.18194			−0.233941
$186$	16.1150	−	2.56412i	1.18161	−	0.188010i
$187$	−4.84213			−0.354092
$188$	5.82846			0.425084
$189$		0			0
$190$	4.08126			0.296085
$191$	1.98057			0.143309			0.0716545	−	0.997430i	$-0.477172\pi$
$191$	1.98057			0.143309			0.0716545	+	0.997430i	$0.477172\pi$
$192$	−1.71053	+	0.272169i	−0.123447	+	0.0196421i
$193$	−4.54583			−0.327216			−0.163608	−	0.986525i	$-0.552313\pi$
$193$	−4.54583			−0.327216			−0.163608	+	0.986525i	$0.552313\pi$
$194$	7.42107	+	12.8537i	0.532802	+	0.922839i
$195$	−31.0442	+	4.93955i	−2.22312	+	0.353728i
$196$		0			0
$197$	−21.8148			−1.55424			−0.777120	−	0.629353i	$-0.783320\pi$
$197$	−21.8148			−1.55424			−0.777120	+	0.629353i	$0.783320\pi$
$198$	1.97141	−	9.34004i	0.140102	−	0.663768i
$199$	−6.14132	−	10.6371i	−0.435346	−	0.754042i	0.561978	−	0.827152i	$-0.310041\pi$
$199$	−6.14132	−	10.6371i	−0.435346	−	0.754042i	−0.997324	+	0.0731106i	$0.976707\pi$
$200$	2.56238	−	4.43818i	0.181188	−	0.313826i
$201$	−18.7592	+	2.98485i	−1.32317	+	0.210535i
$202$	−9.29467	+	16.0988i	−0.653971	+	1.13271i
$203$		0			0
$204$	−1.66019	−	2.04719i	−0.116237	−	0.143332i
$205$	−17.8285			−1.24519
$206$	0.141315	+	0.244765i	0.00984589	+	0.0170536i
$207$	−4.99837	−	4.48769i	−0.347410	−	0.311916i
$208$	−2.85185	+	4.93955i	−0.197740	+	0.342496i
$209$	2.04063	+	3.53447i	0.141153	+	0.244485i
$210$		0			0
$211$	−8.32846	+	14.4253i	−0.573355	+	0.993080i	0.422863	+	0.906193i	$0.361025\pi$
$211$	−8.32846	+	14.4253i	−0.573355	+	0.993080i	−0.996218	+	0.0868863i	$0.972308\pi$
$212$	1.02859	+	1.78157i	0.0706438	+	0.122359i
$213$	−14.8646	+	2.36515i	−1.01850	+	0.162058i
$214$	−5.68878	+	9.85326i	−0.388877	+	0.673555i
$215$	10.8639	−	18.8168i	0.740911	−	1.28330i
$216$	4.62476	−	2.36887i	0.314675	−	0.161181i
$217$		0			0
$218$	2.21053	+	3.82876i	0.149716	+	0.259316i
$219$	−5.41874	−	6.68187i	−0.366165	−	0.451519i
$220$	10.1248			0.682611
$221$	−8.67962			−0.583854
$222$	0.619562	−	1.61745i	0.0415823	−	0.108556i
$223$	5.32846	+	9.22916i	0.356820	+	0.618031i	0.987428	−	0.158071i	$-0.0505276\pi$
$223$	5.32846	+	9.22916i	0.356820	+	0.618031i	−0.630608	+	0.776102i	$0.717194\pi$
$224$		0			0
$225$	−3.17511	+	15.0429i	−0.211674	+	1.00286i
$226$	1.60752	−	2.78431i	0.106931	−	0.185210i
$227$	−7.25404	+	12.5644i	−0.481468	+	0.833926i	−0.999774	−	0.0212688i	$-0.993229\pi$
$227$	−7.25404	+	12.5644i	−0.481468	+	0.833926i	0.518306	+	0.855195i	$0.326563\pi$
$228$	−0.794668	+	2.07459i	−0.0526282	+	0.137393i
$229$	5.12476	+	8.87635i	0.338654	+	0.586566i	0.984180	−	0.177173i	$-0.0566951\pi$
$229$	5.12476	+	8.87635i	0.338654	+	0.586566i	−0.645526	+	0.763738i	$0.723362\pi$
$230$	3.56238	−	6.17023i	0.234896	−	0.406853i
$231$		0			0
$232$	3.54063	+	6.13255i	0.232454	+	0.402622i
$233$	0.540628	−	0.936396i	0.0354177	−	0.0613453i	−0.847773	−	0.530359i	$-0.822057\pi$
$233$	0.540628	−	0.936396i	0.0354177	−	0.0613453i	0.883191	+	0.469014i	$0.155390\pi$
$234$	3.53379	−	16.7422i	0.231011	−	1.09447i
$235$	−9.27292	−	16.0612i	−0.604898	−	1.04771i
$236$	1.12476			0.0732159
$237$	7.07893	−	1.12635i	0.459826	−	0.0731645i
$238$		0			0
$239$	−6.16019	+	10.6698i	−0.398470	+	0.690170i	−0.993537	−	0.113506i	$-0.963792\pi$
$239$	−6.16019	+	10.6698i	−0.398470	+	0.690170i	0.595068	+	0.803676i	$0.297125\pi$
$240$	3.47141	+	4.28061i	0.224079	+	0.276312i
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	−0.995809	−	0.0914555i	$-0.970848\pi$
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	0.577107	+	0.816668i	$0.304181\pi$
$242$	−0.437618	−	0.757977i	−0.0281312	−	0.0487246i
$243$	−10.9834	+	11.0618i	−0.704589	+	0.709616i
$244$	−3.12476			−0.200042
$245$		0			0
$246$	3.47141	−	9.06259i	0.221329	−	0.577809i
$247$	3.65787	+	6.33561i	0.232744	+	0.403125i
$248$	−9.42107			−0.598238
$249$	−8.80150	−	10.8532i	−0.557773	−	0.687791i
$250$	−0.396990			−0.0251079
$251$	−5.11109			−0.322609			−0.161305	−	0.986905i	$-0.551570\pi$
$251$	−5.11109			−0.322609			−0.161305	+	0.986905i	$0.551570\pi$
$252$		0			0
$253$	7.12476			0.447930
$254$	−20.1053			−1.26152
$255$	−3.00000	+	7.83191i	−0.187867	+	0.490453i
$256$	1.00000			0.0625000
$257$	3.83009	+	6.63392i	0.238915	+	0.413813i	0.960403	−	0.278614i	$-0.0898750\pi$
$257$	3.83009	+	6.63392i	0.238915	+	0.413813i	−0.721488	+	0.692427i	$0.756542\pi$
$258$	7.44966	+	9.18620i	0.463795	+	0.571908i
$259$		0			0
$260$	18.1488			1.12554
$261$	−15.8074	−	14.1924i	−0.978453	−	0.878487i
$262$	−3.18194	−	5.51129i	−0.196581	−	0.340488i
$263$	1.54746	−	2.68029i	0.0954208	−	0.165274i	−0.814363	−	0.580355i	$-0.802914\pi$
$263$	1.54746	−	2.68029i	0.0954208	−	0.165274i	0.909784	+	0.415082i	$0.136247\pi$
$264$	−1.97141	+	5.14663i	−0.121332	+	0.316753i
$265$	3.27292	−	5.66886i	0.201054	−	0.348235i
$266$		0			0
$267$	0.139680	−	0.364654i	0.00854830	−	0.0223165i
$268$	10.9669			0.669910
$269$	13.4451	+	23.2877i	0.819765	+	1.41987i	0.905855	+	0.423587i	$0.139229\pi$
$269$	13.4451	+	23.2877i	0.819765	+	1.41987i	−0.0860906	+	0.996287i	$0.527437\pi$
$270$	−13.8856	−	8.97539i	−0.845053	−	0.546225i
$271$	11.1082	−	19.2400i	0.674776	−	1.16875i	−0.301759	−	0.953384i	$-0.597574\pi$
$271$	11.1082	−	19.2400i	0.674776	−	1.16875i	0.976534	−	0.215362i	$-0.0690930\pi$
$272$	0.760877	+	1.31788i	0.0461349	+	0.0799080i
$273$		0			0
$274$	1.37072	−	2.37416i	0.0828084	−	0.143428i
$275$	−8.15335	−	14.1220i	−0.491666	−	0.851590i
$276$	2.44282	+	3.01225i	0.147040	+	0.181316i
$277$	7.31875	−	12.6764i	0.439741	−	0.761653i	−0.557928	−	0.829889i	$-0.688404\pi$
$277$	7.31875	−	12.6764i	0.439741	−	0.761653i	0.997669	+	0.0682357i	$0.0217370\pi$
$278$	−3.98345	+	6.89953i	−0.238911	+	0.413807i
$279$	26.8675	−	8.77202i	1.60851	−	0.525167i
$280$		0			0
$281$	11.6992	+	20.2636i	0.697915	+	1.20882i	0.969188	+	0.246322i	$0.0792219\pi$
$281$	11.6992	+	20.2636i	0.697915	+	1.20882i	−0.271273	+	0.962502i	$0.587445\pi$
$282$	9.96978	−	1.58632i	0.593691	−	0.0944642i
$283$	26.1248			1.55296			0.776478	−	0.630144i	$-0.217004\pi$
$283$	26.1248			1.55296			0.776478	+	0.630144i	$0.217004\pi$
$284$	8.69002			0.515658
$285$	6.98113	−	1.11079i	0.413526	−	0.0657975i
$286$	9.07442	+	15.7174i	0.536582	+	0.929387i
$287$		0			0
$288$	−2.85185	+	0.931107i	−0.168047	+	0.0548660i
$289$	7.34213	−	12.7169i	0.431890	−	0.748056i
$290$	11.2661	−	19.5134i	0.661567	−	1.14587i
$291$	16.1923	+	19.9668i	0.949212	+	1.17048i
$292$	2.48345	+	4.30146i	0.145333	+	0.251724i
$293$	−12.9315	+	22.3980i	−0.755465	+	1.30850i	0.189678	+	0.981846i	$0.439255\pi$
$293$	−12.9315	+	22.3980i	−0.755465	+	1.30850i	−0.945143	+	0.326657i	$0.894078\pi$
$294$		0			0
$295$	−1.78947	−	3.09945i	−0.104187	−	0.180457i
$296$	−0.500000	+	0.866025i	−0.0290619	+	0.0503367i
$297$	0.830095	−	16.5130i	0.0481670	−	0.958182i
$298$	−11.6300	−	20.1437i	−0.673706	−	1.16689i
$299$	12.7713			0.738582
$300$	3.17511	−	8.28905i	0.183315	−	0.478568i
$301$		0			0
$302$	−4.06238	+	7.03625i	−0.233764	+	0.404891i
$303$	−11.5172	+	30.0673i	−0.661648	+	1.72732i
$304$	0.641315	−	1.11079i	0.0367819	−	0.0637082i
$305$	4.97141	+	8.61073i	0.284662	+	0.493049i
$306$	−3.39699	−	3.04993i	−0.194193	−	0.174353i
$307$	−3.53216			−0.201591			−0.100795	−	0.994907i	$-0.532139\pi$
$307$	−3.53216			−0.201591			−0.100795	+	0.994907i	$0.532139\pi$
$308$		0			0
$309$	0.308342	+	0.380217i	0.0175409	+	0.0216298i
$310$	14.9887	+	25.9611i	0.851298	+	1.47449i
$311$	−1.70370			−0.0966078			−0.0483039	−	0.998833i	$-0.515382\pi$
$311$	−1.70370			−0.0966078			−0.0483039	+	0.998833i	$0.515382\pi$
$312$	−3.53379	+	9.22544i	−0.200062	+	0.522288i
$313$	2.84213			0.160647			0.0803234	−	0.996769i	$-0.474405\pi$
$313$	2.84213			0.160647			0.0803234	+	0.996769i	$0.474405\pi$
$314$	−11.2632			−0.635619
$315$		0			0
$316$	−4.13844			−0.232805
$317$	−24.9201			−1.39965			−0.699827	−	0.714313i	$-0.746739\pi$
$317$	−24.9201			−1.39965			−0.699827	+	0.714313i	$0.746739\pi$
$318$	2.24433	+	2.76748i	0.125855	+	0.155193i
$319$	22.5322			1.26156
$320$	−1.59097	−	2.75564i	−0.0889380	−	0.154045i
$321$	−7.04910	+	18.4026i	−0.393442	+	1.02713i
$322$		0			0
$323$	1.95185			0.108604
$324$	7.26608	−	5.31075i	0.403671	−	0.295042i
$325$	−14.6150	−	25.3140i	−0.810697	−	1.40417i
$326$	1.99028	−	3.44727i	0.110232	−	0.190927i
$327$	4.82326	+	5.94758i	0.266727	+	0.328902i
$328$	−2.80150	+	4.85235i	−0.154687	+	0.267926i
$329$		0			0
$330$	17.3187	−	2.75564i	0.953366	−	0.151693i
$331$	−7.17154			−0.394183			−0.197092	−	0.980385i	$-0.563150\pi$
$331$	−7.17154			−0.394183			−0.197092	+	0.980385i	$0.563150\pi$
$332$	4.03379	+	6.98673i	0.221383	+	0.383447i
$333$	0.619562	−	2.93533i	0.0339518	−	0.160855i
$334$	2.61956	−	4.53721i	0.143336	−	0.248265i
$335$	−17.4480	−	30.2209i	−0.953287	−	1.65114i
$336$		0			0
$337$	−10.9211	+	18.9158i	−0.594908	+	1.03041i	0.398651	+	0.917103i	$0.369478\pi$
$337$	−10.9211	+	18.9158i	−0.594908	+	1.03041i	−0.993560	+	0.113309i	$0.963855\pi$
$338$	9.76608	+	16.9153i	0.531205	+	0.920073i
$339$	1.99192	−	5.20018i	0.108186	−	0.282435i
$340$	2.42107	−	4.19341i	0.131301	−	0.227420i
$341$	−14.9887	+	25.9611i	−0.811681	+	1.40587i
$342$	−0.794668	+	3.76494i	−0.0429707	+	0.203585i
$343$		0			0
$344$	−3.41423	−	5.91362i	−0.184083	−	0.318841i
$345$	4.41423	−	11.5239i	0.237654	−	0.620428i
$346$	2.55159			0.137174
$347$	−2.11109			−0.113329			−0.0566646	−	0.998393i	$-0.518047\pi$
$347$	−2.11109			−0.113329			−0.0566646	+	0.998393i	$0.518047\pi$
$348$	7.72545	+	9.52628i	0.414128	+	0.510662i
$349$	−18.1082	−	31.3643i	−0.969310	−	1.67889i	−0.697559	−	0.716527i	$-0.745731\pi$
$349$	−18.1082	−	31.3643i	−0.969310	−	1.67889i	−0.271751	−	0.962368i	$-0.587603\pi$
$350$		0			0
$351$	1.48796	−	29.5999i	0.0794215	−	1.57993i
$352$	1.59097	−	2.75564i	0.0847991	−	0.146876i
$353$	−5.24433	+	9.08344i	−0.279127	+	0.483463i	−0.971168	−	0.238396i	$-0.923378\pi$
$353$	−5.24433	+	9.08344i	−0.279127	+	0.483463i	0.692041	+	0.721858i	$0.256712\pi$
$354$	1.92395	−	0.306125i	0.102257	−	0.0162704i
$355$	−13.8256	−	23.9466i	−0.733786	−	1.27095i
$356$	−0.112725	+	0.195246i	−0.00597442	+	0.0103480i
$357$		0			0
$358$	−3.51887	−	6.09487i	−0.185978	−	0.322124i
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	−0.0195047	−	0.999810i	$-0.506209\pi$
$359$	16.2209	−	28.0955i	0.856108	−	1.48282i	0.875613	−	0.483013i	$-0.160458\pi$
$360$	7.10301	+	6.37731i	0.374361	+	0.336114i
$361$	8.67743	+	15.0297i	0.456707	+	0.791039i
$362$	−12.9669			−0.681525
$363$	−0.954858	−	1.17744i	−0.0501171	−	0.0617995i
$364$		0			0
$365$	7.90219	−	13.6870i	0.413620	−	0.716410i
$366$	−5.34501	+	0.850463i	−0.279388	+	0.0444544i
$367$	−9.05555	+	15.6847i	−0.472696	+	0.818733i	−0.999512	−	0.0312465i	$-0.990052\pi$
$367$	−9.05555	+	15.6847i	−0.472696	+	0.818733i	0.526816	+	0.849979i	$0.323386\pi$
$368$	−1.11956	−	1.93914i	−0.0583612	−	0.101085i
$369$	3.47141	−	16.4467i	0.180714	−	0.856179i
$370$	3.18194			0.165421
$371$		0			0
$372$	−16.1150	+	2.56412i	−0.835526	+	0.132943i
$373$	5.83530	+	10.1070i	0.302140	+	0.523322i	0.976621	−	0.214971i	$-0.0689656\pi$
$373$	5.83530	+	10.1070i	0.302140	+	0.523322i	−0.674480	+	0.738293i	$0.735632\pi$
$374$	4.84213			0.250381
$375$	−0.679065	+	0.108048i	−0.0350668	+	0.00557959i
$376$	−5.82846			−0.300580
$377$	40.3893			2.08016
$378$		0			0
$379$	14.2690			0.732947			0.366474	−	0.930428i	$-0.380565\pi$
$379$	14.2690			0.732947			0.366474	+	0.930428i	$0.380565\pi$
$380$	−4.08126			−0.209364
$381$	−34.3908	+	5.47204i	−1.76190	+	0.280341i
$382$	−1.98057			−0.101335
$383$	−0.824893	−	1.42876i	−0.0421501	−	0.0730061i	0.844181	−	0.536059i	$-0.180087\pi$
$383$	−0.824893	−	1.42876i	−0.0421501	−	0.0730061i	−0.886331	+	0.463053i	$0.846754\pi$
$384$	1.71053	−	0.272169i	0.0872903	−	0.0138891i
$385$		0			0
$386$	4.54583			0.231377
$387$	15.2431	+	13.6857i	0.774849	+	0.695685i
$388$	−7.42107	−	12.8537i	−0.376748	−	0.652546i
$389$	16.0338	−	27.7713i	0.812946	−	1.40806i	−0.0978483	−	0.995201i	$-0.531196\pi$
$389$	16.0338	−	27.7713i	0.812946	−	1.40806i	0.910794	−	0.412862i	$-0.135471\pi$
$390$	31.0442	−	4.93955i	1.57198	−	0.250124i
$391$	1.70370	−	2.95089i	0.0861596	−	0.149233i
$392$		0			0
$393$	−6.94282	−	8.56122i	−0.350219	−	0.431856i
$394$	21.8148			1.09901
$395$	6.58414	+	11.4041i	0.331284	+	0.573800i
$396$	−1.97141	+	9.34004i	−0.0990671	+	0.469355i
$397$	18.9669	−	32.8516i	0.951921	−	1.64878i	0.210660	−	0.977559i	$-0.432439\pi$
$397$	18.9669	−	32.8516i	0.951921	−	1.64878i	0.741261	−	0.671217i	$-0.234228\pi$
$398$	6.14132	+	10.6371i	0.307836	+	0.533188i
$399$		0			0
$400$	−2.56238	+	4.43818i	−0.128119	+	0.221909i
$401$	−5.30959	−	9.19647i	−0.265148	−	0.459250i	0.702454	−	0.711729i	$-0.252087\pi$
$401$	−5.30959	−	9.19647i	−0.265148	−	0.459250i	−0.967602	+	0.252479i	$0.918754\pi$
$402$	18.7592	−	2.98485i	0.935626	−	0.148871i
$403$	−26.8675	+	46.5358i	−1.33836	+	2.31811i
$404$	9.29467	−	16.0988i	0.462427	−	0.800947i
$405$	−26.1947	−	11.5735i	−1.30162	−	0.575090i
$406$		0			0
$407$	1.59097	+	2.75564i	0.0788615	+	0.136592i
$408$	1.66019	+	2.04719i	0.0821916	+	0.101351i
$409$	−5.54583			−0.274224			−0.137112	−	0.990556i	$-0.543782\pi$
$409$	−5.54583			−0.274224			−0.137112	+	0.990556i	$0.543782\pi$
$410$	17.8285			0.880485
$411$	1.69850	−	4.43415i	0.0837806	−	0.218721i
$412$	−0.141315	−	0.244765i	−0.00696209	−	0.0120587i
$413$		0			0
$414$	4.99837	+	4.48769i	0.245656	+	0.220558i
$415$	12.8353	−	22.2314i	0.630060	−	1.09130i
$416$	2.85185	−	4.93955i	0.139823	−	0.242181i
$417$	−4.93598	+	12.8861i	−0.241716	+	0.631033i
$418$	−2.04063	−	3.53447i	−0.0998104	−	0.172877i
$419$	−2.77455	+	4.80566i	−0.135546	+	0.234772i	−0.925806	−	0.378000i	$-0.876612\pi$
$419$	−2.77455	+	4.80566i	−0.135546	+	0.234772i	0.790260	+	0.612772i	$0.209945\pi$
$420$		0			0
$421$	−3.42107	−	5.92546i	−0.166733	−	0.288789i	0.770537	−	0.637396i	$-0.219988\pi$
$421$	−3.42107	−	5.92546i	−0.166733	−	0.288789i	−0.937269	+	0.348606i	$0.886655\pi$
$422$	8.32846	−	14.4253i	0.405423	−	0.702213i
$423$	16.6219	−	5.42692i	0.808184	−	0.263866i
$424$	−1.02859	−	1.78157i	−0.0499527	−	0.0865207i
$425$	−7.79863			−0.378289
$426$	14.8646	−	2.36515i	0.720191	−	0.114592i
$427$		0			0
$428$	5.68878	−	9.85326i	0.274978	−	0.476275i
$429$	19.7999	+	24.4153i	0.955947	+	1.17878i
$430$	−10.8639	+	18.8168i	−0.523903	+	0.907427i
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	0.921321	+	0.388803i	$0.127111\pi$
$431$	16.5539	+	28.6722i	0.797374	+	1.38109i	−0.123947	+	0.992289i	$0.539555\pi$
$432$	−4.62476	+	2.36887i	−0.222509	+	0.113972i
$433$	12.1111			0.582022			0.291011	−	0.956720i	$-0.406008\pi$
$433$	12.1111			0.582022			0.291011	+	0.956720i	$0.406008\pi$
$434$		0			0
$435$	13.9601	−	36.4446i	0.669334	−	1.74739i
$436$	−2.21053	−	3.82876i	−0.105865	−	0.183364i
$437$	−2.87197			−0.137385
$438$	5.41874	+	6.68187i	0.258918	+	0.319272i
$439$	8.83422			0.421634			0.210817	−	0.977526i	$-0.432388\pi$
$439$	8.83422			0.421634			0.210817	+	0.977526i	$0.432388\pi$
$440$	−10.1248			−0.482679
$441$		0			0
$442$	8.67962			0.412847
$443$	17.5185			0.832328			0.416164	−	0.909290i	$-0.363374\pi$
$443$	17.5185			0.832328			0.416164	+	0.909290i	$0.363374\pi$
$444$	−0.619562	+	1.61745i	−0.0294031	+	0.0767608i
$445$	0.717370			0.0340066
$446$	−5.32846	−	9.22916i	−0.252310	−	0.437014i
$447$	−25.3759	−	31.2911i	−1.20024	−	1.48002i
$448$		0			0
$449$	31.2301			1.47384			0.736920	−	0.675980i	$-0.236280\pi$
$449$	31.2301			1.47384			0.736920	+	0.675980i	$0.236280\pi$
$450$	3.17511	−	15.0429i	0.149676	−	0.709127i
$451$	8.91423	+	15.4399i	0.419755	+	0.727036i
$452$	−1.60752	+	2.78431i	−0.0756115	+	0.130963i
$453$	−5.03379	+	13.1414i	−0.236508	+	0.617437i
$454$	7.25404	−	12.5644i	0.340449	−	0.589675i
$455$		0			0
$456$	0.794668	−	2.07459i	0.0372138	−	0.0971516i
$457$	−32.1248			−1.50273			−0.751367	−	0.659885i	$-0.770605\pi$
$457$	−32.1248			−1.50273			−0.751367	+	0.659885i	$0.770605\pi$
$458$	−5.12476	−	8.87635i	−0.239464	−	0.414765i
$459$	−6.64076	−	4.29245i	−0.309964	−	0.200354i
$460$	−3.56238	+	6.17023i	−0.166097	+	0.287688i
$461$	−1.23229	−	2.13438i	−0.0573933	−	0.0994081i	0.835901	−	0.548880i	$-0.184946\pi$
$461$	−1.23229	−	2.13438i	−0.0573933	−	0.0994081i	−0.893295	+	0.449472i	$0.851612\pi$
$462$		0			0
$463$	15.1735	−	26.2812i	0.705171	−	1.22139i	−0.261459	−	0.965215i	$-0.584204\pi$
$463$	15.1735	−	26.2812i	0.705171	−	1.22139i	0.966630	−	0.256177i	$-0.0824631\pi$
$464$	−3.54063	−	6.13255i	−0.164370	−	0.284696i
$465$	32.7044	+	40.3279i	1.51663	+	1.87016i
$466$	−0.540628	+	0.936396i	−0.0250441	+	0.0433777i
$467$	7.98181	−	13.8249i	0.369354	−	0.639740i	−0.620110	−	0.784515i	$-0.712912\pi$
$467$	7.98181	−	13.8249i	0.369354	−	0.639740i	0.989465	+	0.144774i	$0.0462456\pi$
$468$	−3.53379	+	16.7422i	−0.163350	+	0.773909i
$469$		0			0
$470$	9.27292	+	16.0612i	0.427728	+	0.740846i
$471$	−19.2661	+	3.06549i	−0.887734	+	0.141250i
$472$	−1.12476			−0.0517714
$473$	−21.7278			−0.999044
$474$	−7.07893	+	1.12635i	−0.325146	+	0.0517351i
$475$	3.28659	+	5.69254i	0.150799	+	0.261192i
$476$		0			0
$477$	4.59222	+	4.12304i	0.210263	+	0.188781i
$478$	6.16019	−	10.6698i	0.281761	−	0.488024i
$479$	−11.5865	+	20.0683i	−0.529399	+	0.916946i	0.470013	+	0.882659i	$0.344249\pi$
$479$	−11.5865	+	20.0683i	−0.529399	+	0.916946i	−0.999412	+	0.0342863i	$0.989084\pi$
$480$	−3.47141	−	4.28061i	−0.158447	−	0.195382i
$481$	2.85185	+	4.93955i	0.130033	+	0.225224i
$482$	6.50000	−	11.2583i	0.296067	−	0.512803i
$483$		0			0
$484$	0.437618	+	0.757977i	0.0198917	+	0.0344535i
$485$	−23.6134	+	40.8996i	−1.07223	+	1.85716i
$486$	10.9834	−	11.0618i	0.498219	−	0.501774i
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	0.902098	−	0.431531i	$-0.142026\pi$
$487$	1.70658	+	2.95588i	0.0773323	+	0.133943i	−0.824766	+	0.565474i	$0.808693\pi$
$488$	3.12476			0.141451
$489$	2.46621	−	6.43837i	0.111526	−	0.291153i
$490$		0			0
$491$	−9.58414	+	16.6002i	−0.432526	+	0.749157i	−0.997090	−	0.0762323i	$-0.975711\pi$
$491$	−9.58414	+	16.6002i	−0.432526	+	0.749157i	0.564564	+	0.825389i	$0.309044\pi$
$492$	−3.47141	+	9.06259i	−0.156503	+	0.408573i
$493$	5.38796	−	9.33223i	0.242662	−	0.420302i
$494$	−3.65787	−	6.33561i	−0.164575	−	0.285053i
$495$	28.8743	−	9.42724i	1.29780	−	0.423723i
$496$	9.42107			0.423018
$497$		0			0
$498$	8.80150	+	10.8532i	0.394405	+	0.486342i
$499$	−20.5848	−	35.6540i	−0.921503	−	1.59609i	−0.797090	−	0.603860i	$-0.793629\pi$
$499$	−20.5848	−	35.6540i	−0.921503	−	1.59609i	−0.124413	−	0.992231i	$-0.539705\pi$
$500$	0.396990			0.0177539
$501$	3.24596	−	8.47402i	0.145019	−	0.378591i
$502$	5.11109			0.228119
$503$	26.4542			1.17953			0.589767	−	0.807574i	$-0.299220\pi$
$503$	26.4542			1.17953			0.589767	+	0.807574i	$0.299220\pi$
$504$		0			0
$505$	−59.1502			−2.63215
$506$	−7.12476			−0.316734
$507$	21.3090	+	26.2762i	0.946367	+	1.16697i
$508$	20.1053			0.892030
$509$	6.38564	+	11.0603i	0.283039	+	0.490237i	0.972132	−	0.234436i	$-0.0753242\pi$
$509$	6.38564	+	11.0603i	0.283039	+	0.490237i	−0.689093	+	0.724673i	$0.741991\pi$
$510$	3.00000	−	7.83191i	0.132842	−	0.346803i
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−0.334608	+	6.65634i	−0.0147733	+	0.293884i
$514$	−3.83009	−	6.63392i	−0.168938	−	0.292610i
$515$	−0.449657	+	0.778828i	−0.0198142	+	0.0343193i
$516$	−7.44966	−	9.18620i	−0.327953	−	0.404400i
$517$	−9.27292	+	16.0612i	−0.407822	+	0.706369i
$518$		0			0
$519$	4.36458	−	0.694462i	0.191584	−	0.0304835i
$520$	−18.1488			−0.795879
$521$	3.40615	+	5.89962i	0.149226	+	0.258467i	0.930942	−	0.365168i	$-0.118988\pi$
$521$	3.40615	+	5.89962i	0.149226	+	0.258467i	−0.781716	+	0.623635i	$0.785655\pi$
$522$	15.8074	+	14.1924i	0.691871	+	0.621184i
$523$	−14.7535	+	25.5538i	−0.645125	+	1.11739i	0.339148	+	0.940733i	$0.389861\pi$
$523$	−14.7535	+	25.5538i	−0.645125	+	1.11739i	−0.984273	+	0.176656i	$0.943472\pi$
$524$	3.18194	+	5.51129i	0.139004	+	0.240762i
$525$		0			0
$526$	−1.54746	+	2.68029i	−0.0674727	+	0.116866i
$527$	7.16827	+	12.4158i	0.312255	+	0.540841i
$528$	1.97141	−	5.14663i	0.0857946	−	0.223978i
$529$	8.99316	−	15.5766i	0.391007	−	0.677244i
$530$	−3.27292	+	5.66886i	−0.142166	+	0.246239i
$531$	3.20765	−	1.04728i	0.139200	−	0.0454479i
$532$		0			0
$533$	15.9789	+	27.6763i	0.692125	+	1.19879i
$534$	−0.139680	+	0.364654i	−0.00604456	+	0.0157801i
$535$	−36.2028			−1.56518
$536$	−10.9669			−0.473698
$537$	−7.67799	−	9.46775i	−0.331330	−	0.408564i
$538$	−13.4451	−	23.2877i	−0.579661	−	1.00400i
$539$		0			0
$540$	13.8856	+	8.97539i	0.597543	+	0.386239i
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	−0.355097	−	0.934829i	$-0.615552\pi$
$541$	14.7008	−	25.4626i	0.632038	−	1.09472i	0.987135	−	0.159892i	$-0.0511145\pi$
$542$	−11.1082	+	19.2400i	−0.477139	+	0.826428i
$543$	−22.1803	+	3.52918i	−0.951848	+	0.151452i
$544$	−0.760877	−	1.31788i	−0.0326223	−	0.0565035i
$545$	−7.03379	+	12.1829i	−0.301295	+	0.521857i
$546$		0			0
$547$	17.6150	+	30.5102i	0.753165	+	1.30452i	0.946281	+	0.323344i	$0.104807\pi$
$547$	17.6150	+	30.5102i	0.753165	+	1.30452i	−0.193116	+	0.981176i	$0.561859\pi$
$548$	−1.37072	+	2.37416i	−0.0585544	+	0.101419i
$549$	−8.91135	+	2.90949i	−0.380327	+	0.124174i
$550$	8.15335	+	14.1220i	0.347660	+	0.602165i
$551$	−9.08263			−0.386933
$552$	−2.44282	−	3.01225i	−0.103973	−	0.128210i
$553$		0			0
$554$	−7.31875	+	12.6764i	−0.310944	+	0.538570i
$555$	5.44282	−	0.866025i	0.231035	−	0.0367607i
$556$	3.98345	−	6.89953i	0.168936	−	0.292605i
$557$	−3.36909	−	5.83543i	−0.142753	−	0.247255i	0.785779	−	0.618507i	$-0.212262\pi$
$557$	−3.36909	−	5.83543i	−0.142753	−	0.247255i	−0.928532	+	0.371252i	$0.878929\pi$
$558$	−26.8675	+	8.77202i	−1.13739	+	0.371349i
$559$	−38.9475			−1.64730
$560$		0			0
$561$	8.28263	−	1.31788i	0.349693	−	0.0556408i
$562$	−11.6992	−	20.2636i	−0.493500	−	0.854768i
$563$	1.45993			0.0615286			0.0307643	−	0.999527i	$-0.490206\pi$
$563$	1.45993			0.0615286			0.0307643	+	0.999527i	$0.490206\pi$
$564$	−9.96978	+	1.58632i	−0.419803	+	0.0667963i
$565$	10.2301			0.430383
$566$	−26.1248			−1.09811
$567$		0			0
$568$	−8.69002			−0.364625
$569$	19.5653			0.820218			0.410109	−	0.912036i	$-0.365491\pi$
$569$	19.5653			0.820218			0.410109	+	0.912036i	$0.365491\pi$
$570$	−6.98113	+	1.11079i	−0.292407	+	0.0465259i
$571$	−21.9259			−0.917569			−0.458785	−	0.888547i	$-0.651715\pi$
$571$	−21.9259			−0.917569			−0.458785	+	0.888547i	$0.651715\pi$
$572$	−9.07442	−	15.7174i	−0.379421	−	0.657176i
$573$	−3.38783	+	0.539049i	−0.141529	+	0.0225191i
$574$		0			0
$575$	11.4750			0.478540
$576$	2.85185	−	0.931107i	0.118827	−	0.0387961i
$577$	−12.3655	−	21.4177i	−0.514783	−	0.891631i	−0.999853	−	0.0171554i	$-0.994539\pi$
$577$	−12.3655	−	21.4177i	−0.514783	−	0.891631i	0.485069	−	0.874476i	$-0.338794\pi$
$578$	−7.34213	+	12.7169i	−0.305392	+	0.528955i
$579$	7.77579	−	1.23723i	0.323151	−	0.0514176i
$580$	−11.2661	+	19.5134i	−0.467798	+	0.810251i
$581$		0			0
$582$	−16.1923	−	19.9668i	−0.671194	−	0.827652i
$583$	−6.54583			−0.271101
$584$	−2.48345	−	4.30146i	−0.102766	−	0.177996i
$585$	51.7577	−	16.8985i	2.13992	−	0.698668i
$586$	12.9315	−	22.3980i	0.534194	−	0.925251i
$587$	18.0796	+	31.3148i	0.746226	+	1.29250i	0.949620	+	0.313404i	$0.101469\pi$
$587$	18.0796	+	31.3148i	0.746226	+	1.29250i	−0.203394	+	0.979097i	$0.565197\pi$
$588$		0			0
$589$	6.04187	−	10.4648i	0.248951	−	0.431196i
$590$	1.78947	+	3.09945i	0.0736712	+	0.127602i
$591$	37.3149	−	5.93730i	1.53493	−	0.244228i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	7.55391	−	13.0838i	0.310202	−	0.537285i	−0.668204	−	0.743978i	$-0.732937\pi$
$593$	7.55391	−	13.0838i	0.310202	−	0.537285i	0.978406	+	0.206693i	$0.0662700\pi$
$594$	−0.830095	+	16.5130i	−0.0340592	+	0.677537i
$595$		0			0
$596$	11.6300	+	20.1437i	0.476382	+	0.825118i
$597$	13.4000	+	16.5236i	0.548426	+	0.676265i
$598$	−12.7713			−0.522256
$599$	−5.45417			−0.222851			−0.111426	−	0.993773i	$-0.535542\pi$
$599$	−5.45417			−0.222851			−0.111426	+	0.993773i	$0.535542\pi$
$600$	−3.17511	+	8.28905i	−0.129623	+	0.338399i
$601$	3.36840	+	5.83424i	0.137400	+	0.237984i	0.926512	−	0.376266i	$-0.122792\pi$
$601$	3.36840	+	5.83424i	0.137400	+	0.237984i	−0.789112	+	0.614250i	$0.789459\pi$
$602$		0			0
$603$	31.2759	−	10.2114i	1.27365	−	0.415839i
$604$	4.06238	−	7.03625i	0.165296	−	0.286301i
$605$	1.39248	−	2.41184i	0.0566122	−	0.0980553i
$606$	11.5172	−	30.0673i	0.467856	−	1.22140i
$607$	3.33530	+	5.77690i	0.135376	+	0.234477i	0.925741	−	0.378159i	$-0.123443\pi$
$607$	3.33530	+	5.77690i	0.135376	+	0.234477i	−0.790365	+	0.612636i	$0.790109\pi$
$608$	−0.641315	+	1.11079i	−0.0260088	+	0.0450485i
$609$		0			0
$610$	−4.97141	−	8.61073i	−0.201287	−	0.348638i
$611$	−16.6219	+	28.7899i	−0.672449	+	1.16472i
$612$	3.39699	+	3.04993i	0.137315	+	0.123286i
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	0.878950	−	0.476915i	$-0.158245\pi$
$613$	0.654988	+	1.13447i	0.0264547	+	0.0458209i	−0.852495	+	0.522735i	$0.824912\pi$
$614$	3.53216			0.142546
$615$	30.4962	−	4.85235i	1.22972	−	0.195666i
$616$		0			0
$617$	17.2483	−	29.8749i	0.694390	−	1.20272i	−0.275996	−	0.961159i	$-0.589008\pi$
$617$	17.2483	−	29.8749i	0.694390	−	1.20272i	0.970386	−	0.241560i	$-0.0776589\pi$
$618$	−0.308342	−	0.380217i	−0.0124033	−	0.0152946i
$619$	−8.22421	+	14.2447i	−0.330559	+	0.572545i	−0.982622	−	0.185620i	$-0.940571\pi$
$619$	−8.22421	+	14.2447i	−0.330559	+	0.572545i	0.652063	+	0.758165i	$0.273904\pi$
$620$	−14.9887	−	25.9611i	−0.601959	−	1.04262i
$621$	9.77128	+	6.31595i	0.392108	+	0.253450i
$622$	1.70370			0.0683120
$623$		0			0
$624$	3.53379	−	9.22544i	0.141465	−	0.369313i
$625$	12.1803	+	21.0969i	0.487212	+	0.843877i
$626$	−2.84213			−0.113594
$627$	−4.45254	−	5.49044i	−0.177817	−	0.219267i
$628$	11.2632			0.449451
$629$	1.52175			0.0606763
$630$		0			0
$631$	−30.0118			−1.19475			−0.597375	−	0.801962i	$-0.703790\pi$
$631$	−30.0118			−1.19475			−0.597375	+	0.801962i	$0.703790\pi$
$632$	4.13844			0.164618
$633$	10.3200	−	26.9417i	0.410183	−	1.07084i
$634$	24.9201			0.989704
$635$	−31.9870	−	55.4031i	−1.26937	−	2.19861i
$636$	−2.24433	−	2.76748i	−0.0889933	−	0.109738i
$637$		0			0
$638$	−22.5322			−0.892057
$639$	24.7826	−	8.09134i	0.980386	−	0.320089i
$640$	1.59097	+	2.75564i	0.0628887	+	0.108926i
$641$	−13.9497	+	24.1615i	−0.550978	+	0.954322i	0.447226	+	0.894421i	$0.352412\pi$
$641$	−13.9497	+	24.1615i	−0.550978	+	0.954322i	−0.998204	+	0.0599014i	$0.980921\pi$
$642$	7.04910	−	18.4026i	0.278206	−	0.726294i
$643$	−14.2524	+	24.6859i	−0.562060	+	0.973516i	0.435257	+	0.900306i	$0.356658\pi$
$643$	−14.2524	+	24.6859i	−0.562060	+	0.973516i	−0.997317	+	0.0732100i	$0.976676\pi$
$644$		0			0
$645$	−13.4617	+	35.1436i	−0.530054	+	1.38378i
$646$	−1.95185			−0.0767944
$647$	−8.35705	−	14.4748i	−0.328550	−	0.569065i	0.653675	−	0.756776i	$-0.273226\pi$
$647$	−8.35705	−	14.4748i	−0.328550	−	0.569065i	−0.982224	+	0.187711i	$0.939893\pi$
$648$	−7.26608	+	5.31075i	−0.285439	+	0.208626i
$649$	−1.78947	+	3.09945i	−0.0702427	+	0.121664i
$650$	14.6150	+	25.3140i	0.573249	+	0.992897i
$651$		0			0
$652$	−1.99028	+	3.44727i	−0.0779456	+	0.135006i
$653$	−19.0825	−	33.0519i	−0.746756	−	1.29342i	−0.949370	−	0.314161i	$-0.898277\pi$
$653$	−19.0825	−	33.0519i	−0.746756	−	1.29342i	0.202614	−	0.979259i	$-0.435056\pi$
$654$	−4.82326	−	5.94758i	−0.188604	−	0.232569i
$655$	10.1248	−	17.5366i	0.395607	−	0.685212i
$656$	2.80150	−	4.85235i	0.109380	−	0.189452i
$657$	11.0875	+	9.95475i	0.432566	+	0.388372i
$658$		0			0
$659$	4.37072	+	7.57031i	0.170259	+	0.294898i	0.938510	−	0.345251i	$-0.112206\pi$
$659$	4.37072	+	7.57031i	0.170259	+	0.294898i	−0.768251	+	0.640148i	$0.778873\pi$
$660$	−17.3187	+	2.75564i	−0.674131	+	0.107263i
$661$	20.0837			0.781167			0.390584	−	0.920567i	$-0.372273\pi$
$661$	20.0837			0.781167			0.390584	+	0.920567i	$0.372273\pi$
$662$	7.17154			0.278730
$663$	14.8468	−	2.36232i	0.576601	−	0.0917449i
$664$	−4.03379	−	6.98673i	−0.156541	−	0.271138i
$665$		0			0
$666$	−0.619562	+	2.93533i	−0.0240075	+	0.113742i
$667$	−7.92790	+	13.7315i	−0.306970	+	0.531687i
$668$	−2.61956	+	4.53721i	−0.101354	+	0.175550i
$669$	−11.6264	−	14.3366i	−0.449503	−	0.554283i
$670$	17.4480	+	30.2209i	0.674076	+	1.16753i
$671$	4.97141	−	8.61073i	0.191919	−	0.332414i
$672$		0			0
$673$	−17.0264	−	29.4906i	−0.656319	−	1.13678i	−0.981561	−	0.191148i	$-0.938779\pi$
$673$	−17.0264	−	29.4906i	−0.656319	−	1.13678i	0.325242	−	0.945631i	$-0.394554\pi$
$674$	10.9211	−	18.9158i	0.420664	−	0.728611i
$675$	1.33693	−	26.5955i	0.0514585	−	1.02366i
$676$	−9.76608	−	16.9153i	−0.375618	−	0.650590i
$677$	0.717370			0.0275708			0.0137854	−	0.999905i	$-0.495612\pi$
$677$	0.717370			0.0275708			0.0137854	+	0.999905i	$0.495612\pi$
$678$	−1.99192	+	5.20018i	−0.0764992	+	0.199712i
$679$		0			0
$680$	−2.42107	+	4.19341i	−0.0928437	+	0.160810i
$681$	8.98865	−	23.4661i	0.344446	−	0.899223i
$682$	14.9887	−	25.9611i	0.573945	−	0.994102i
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	0.591260	−	0.806481i	$-0.298631\pi$
$683$	−10.5270	−	18.2332i	−0.402803	−	0.697675i	−0.994063	+	0.108806i	$0.965297\pi$
$684$	0.794668	−	3.76494i	0.0303849	−	0.143956i
$685$	8.72313			0.333294
$686$		0			0
$687$	−11.1819	−	13.7885i	−0.426618	−	0.526064i
$688$	3.41423	+	5.91362i	0.130166	+	0.225455i
$689$	−11.7335			−0.447012
$690$	−4.41423	+	11.5239i	−0.168047	+	0.438709i
$691$	−5.84789			−0.222464			−0.111232	−	0.993794i	$-0.535480\pi$
$691$	−5.84789			−0.222464			−0.111232	+	0.993794i	$0.535480\pi$
$692$	−2.55159			−0.0969968
$693$		0			0
$694$	2.11109			0.0801359
$695$	−25.3502			−0.961588
$696$	−7.72545	−	9.52628i	−0.292832	−	0.361093i
$697$	8.52640			0.322960
$698$	18.1082	+	31.3643i	0.685406	+	1.18716i
$699$	−0.669905	+	1.74888i	−0.0253381	+	0.0661486i
$700$		0			0
$701$	10.2711			0.387935			0.193967	−	0.981008i	$-0.437864\pi$
$701$	10.2711			0.387935			0.193967	+	0.981008i	$0.437864\pi$
$702$	−1.48796	+	29.5999i	−0.0561595	+	1.11718i
$703$	−0.641315	−	1.11079i	−0.0241877	−	0.0418942i
$704$	−1.59097	+	2.75564i	−0.0599620	+	0.103857i
$705$	20.2330	+	24.9494i	0.762018	+	0.939647i
$706$	5.24433	−	9.08344i	0.197373	−	0.341860i
$707$		0			0
$708$	−1.92395	+	0.306125i	−0.0723063	+	0.0115049i
$709$	43.4854			1.63313			0.816564	−	0.577255i	$-0.195876\pi$
$709$	43.4854			1.63313			0.816564	+	0.577255i	$0.195876\pi$
$710$	13.8256	+	23.9466i	0.518865	+	0.898700i
$711$	−11.8022	+	3.85333i	−0.442617	+	0.144511i
$712$	0.112725	−	0.195246i	0.00422455	−	0.00731714i
$713$	−10.5475	−	18.2687i	−0.395006	−	0.684170i
$714$		0			0
$715$	−28.8743	+	50.0117i	−1.07984	+	1.87033i
$716$	3.51887	+	6.09487i	0.131507	+	0.227776i
$717$	7.63323	−	19.9276i	0.285068	−	0.744210i
$718$	−16.2209	+	28.0955i	−0.605360	+	1.04851i
$719$	−25.4412	+	44.0654i	−0.948796	+	1.64336i	−0.200830	+	0.979626i	$0.564364\pi$
$719$	−25.4412	+	44.0654i	−0.948796	+	1.64336i	−0.747966	+	0.663737i	$0.768969\pi$
$720$	−7.10301	−	6.37731i	−0.264714	−	0.237668i
$721$		0			0
$722$	−8.67743	−	15.0297i	−0.322941	−	0.559349i
$723$	8.05430	−	21.0268i	0.299543	−	0.781997i
$724$	12.9669			0.481911
$725$	36.2898			1.34777
$726$	0.954858	+	1.17744i	0.0354381	+	0.0436989i
$727$	−6.07210	−	10.5172i	−0.225202	−	0.390061i	0.731178	−	0.682186i	$-0.238971\pi$
$727$	−6.07210	−	10.5172i	−0.225202	−	0.390061i	−0.956380	+	0.292126i	$0.905637\pi$
$728$		0			0
$729$	15.7769	−	21.9110i	0.584329	−	0.811517i
$730$	−7.90219	+	13.6870i	−0.292473	+	0.506579i
$731$	−5.19562	+	8.99907i	−0.192167	+	0.332843i
$732$	5.34501	−	0.850463i	0.197557	−	0.0314340i
$733$	−23.0848	−	39.9841i	−0.852657	−	1.47685i	−0.878801	−	0.477188i	$-0.841656\pi$
$733$	−23.0848	−	39.9841i	−0.852657	−	1.47685i	0.0261440	−	0.999658i	$-0.491677\pi$
$734$	9.05555	−	15.6847i	0.334246	−	0.578932i
$735$		0			0
$736$	1.11956	+	1.93914i	0.0412676	+	0.0714776i
$737$	−17.4480	+	30.2209i	−0.642706	+	1.11320i
$738$	−3.47141	+	16.4467i	−0.127784	+	0.605410i
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	0.816458	−	0.577405i	$-0.195935\pi$
$739$	−2.49604	−	4.32327i	−0.0918184	−	0.159034i	−0.908276	+	0.418371i	$0.862601\pi$
$740$	−3.18194			−0.116971
$741$	−7.98126	−	9.84172i	−0.293199	−	0.361545i
$742$		0			0
$743$	−15.7060	+	27.2036i	−0.576198	+	0.998004i	0.419712	+	0.907657i	$0.362131\pi$
$743$	−15.7060	+	27.2036i	−0.576198	+	0.998004i	−0.995910	+	0.0903470i	$0.971202\pi$
$744$	16.1150	−	2.56412i	0.590806	−	0.0940052i
$745$	37.0059	−	64.0961i	1.35579	−	2.34830i
$746$	−5.83530	−	10.1070i	−0.213645	−	0.370045i
$747$	18.0092	+	16.1692i	0.658921	+	0.591600i
$748$	−4.84213			−0.177046
$749$		0			0
$750$	0.679065	−	0.108048i	0.0247959	−	0.00394536i
$751$	−1.64815	−	2.85468i	−0.0601419	−	0.104169i	0.834387	−	0.551179i	$-0.185822\pi$
$751$	−1.64815	−	2.85468i	−0.0601419	−	0.104169i	−0.894529	+	0.447010i	$0.852489\pi$
$752$	5.82846			0.212542
$753$	8.74269	−	1.39108i	0.318601	−	0.0506937i
$754$	−40.3893			−1.47089
$755$	−25.8525			−0.940870
$756$		0			0
$757$	−10.1384			−0.368488			−0.184244	−	0.982881i	$-0.558984\pi$
$757$	−10.1384			−0.368488			−0.184244	+	0.982881i	$0.558984\pi$
$758$	−14.2690			−0.518272
$759$	−12.1871	+	1.93914i	−0.442365	+	0.0703862i
$760$	4.08126			0.148043
$761$	7.03379	+	12.1829i	0.254975	+	0.441629i	0.964889	−	0.262659i	$-0.0845995\pi$
$761$	7.03379	+	12.1829i	0.254975	+	0.441629i	−0.709914	+	0.704288i	$0.751266\pi$
$762$	34.3908	−	5.47204i	1.24585	−	0.198231i
$763$		0			0
$764$	1.98057			0.0716545
$765$	3.00000	−	14.2132i	0.108465	−	0.513881i
$766$	0.824893	+	1.42876i	0.0298046	+	0.0516231i
$767$	−3.20765	+	5.55582i	−0.115822	+	0.200609i
$768$	−1.71053	+	0.272169i	−0.0617236	+	0.00982104i
$769$	−11.3461	+	19.6520i	−0.409151	+	0.708669i	−0.994795	−	0.101899i	$-0.967508\pi$
$769$	−11.3461	+	19.6520i	−0.409151	+	0.708669i	0.585644	+	0.810568i	$0.300842\pi$
$770$		0			0
$771$	−8.35705	−	10.3051i	−0.300972	−	0.371129i
$772$	−4.54583			−0.163608
$773$	−0.327772	−	0.567717i	−0.0117891	−	0.0204194i	0.860071	−	0.510175i	$-0.170419\pi$
$773$	−0.327772	−	0.567717i	−0.0117891	−	0.0204194i	−0.871860	+	0.489756i	$0.837086\pi$
$774$	−15.2431	−	13.6857i	−0.547901	−	0.491924i
$775$	−24.1404	+	41.8123i	−0.867148	+	1.50194i
$776$	7.42107	+	12.8537i	0.266401	+	0.461420i
$777$		0			0
$778$	−16.0338	+	27.7713i	−0.574839	+	0.995651i
$779$	−3.59329	−	6.22377i	−0.128743	−	0.222990i
$780$	−31.0442	+	4.93955i	−1.11156	+	0.176864i
$781$	−13.8256	+	23.9466i	−0.494718	+	0.856877i
$782$	−1.70370	+	2.95089i	−0.0609241	+	0.105524i
$783$	30.9018	+	19.9743i	1.10434	+	0.713823i
$784$		0			0
$785$	−17.9194	−	31.0374i	−0.639572	−	1.10777i
$786$	6.94282	+	8.56122i	0.247642	+	0.305368i
$787$	−0.540073			−0.0192515			−0.00962576	−	0.999954i	$-0.503064\pi$
$787$	−0.540073			−0.0192515			−0.00962576	+	0.999954i	$0.503064\pi$
$788$	−21.8148			−0.777120
$789$	−1.91750	+	5.00589i	−0.0682648	+	0.178215i
$790$	−6.58414	−	11.4041i	−0.234253	−	0.405738i
$791$		0			0
$792$	1.97141	−	9.34004i	0.0700510	−	0.331884i
$793$	8.91135	−	15.4349i	0.316451	−	0.548110i
$794$	−18.9669	+	32.8516i	−0.673110	+	1.16586i
$795$	−4.05555	+	10.5876i	−0.143835	+	0.375502i
$796$	−6.14132	−	10.6371i	−0.217673	−	0.377021i
$797$	12.5550	−	21.7459i	0.444721	−	0.770279i	−0.553312	−	0.832974i	$-0.686636\pi$
$797$	12.5550	−	21.7459i	0.444721	−	0.770279i	0.998033	+	0.0626954i	$0.0199697\pi$
$798$		0			0
$799$	4.43474	+	7.68119i	0.156890	+	0.271741i
$800$	2.56238	−	4.43818i	0.0905939	−	0.156913i
$801$	−0.139680	+	0.661770i	−0.00493536	+	0.0233825i
$802$	5.30959	+	9.19647i	0.187488	+	0.324739i
$803$	−15.8044			−0.557725
$804$	−18.7592	+	2.98485i	−0.661587	+	0.105267i
$805$		0			0
$806$	26.8675	−	46.5358i	0.946366	−	1.63915i
$807$	−29.3365	−	36.1750i	−1.03270	−	1.27342i
$808$	−9.29467	+	16.0988i	−0.326985	+	0.566355i
$809$	−14.5865	−	25.2645i	−0.512833	−	0.888252i	−0.999889	−	0.0148817i	$-0.995263\pi$
$809$	−14.5865	−	25.2645i	−0.512833	−	0.888252i	0.487057	−	0.873370i	$-0.338071\pi$
$810$	26.1947	+	11.5735i	0.920387	+	0.406650i
$811$	15.4290			0.541785			0.270892	−	0.962610i	$-0.412681\pi$
$811$	15.4290			0.541785			0.270892	+	0.962610i	$0.412681\pi$
$812$		0			0
$813$	−13.7644	+	35.9339i	−0.482740	+	1.26026i
$814$	−1.59097	−	2.75564i	−0.0557635	−	0.0965853i
$815$	12.6659			0.443669
$816$	−1.66019	−	2.04719i	−0.0581183	−	0.0716658i
$817$	8.75839			0.306417
$818$	5.54583			0.193905
$819$		0			0
$820$	−17.8285			−0.622597
$821$	8.48727			0.296208			0.148104	−	0.988972i	$-0.452683\pi$
$821$	8.48727			0.296208			0.148104	+	0.988972i	$0.452683\pi$
$822$	−1.69850	+	4.43415i	−0.0592418	+	0.154659i
$823$	29.0974			1.01427			0.507136	−	0.861866i	$-0.330704\pi$
$823$	29.0974			1.01427			0.507136	+	0.861866i	$0.330704\pi$
$824$	0.141315	+	0.244765i	0.00492294	+	0.00852679i
$825$	17.7902	+	21.9371i	0.619374	+	0.763752i
$826$		0			0
$827$	−25.9396			−0.902007			−0.451003	−	0.892522i	$-0.648934\pi$
$827$	−25.9396			−0.902007			−0.451003	+	0.892522i	$0.648934\pi$
$828$	−4.99837	−	4.48769i	−0.173705	−	0.155958i
$829$	−3.10821	−	5.38358i	−0.107953	−	0.186979i	0.806988	−	0.590568i	$-0.201096\pi$
$829$	−3.10821	−	5.38358i	−0.107953	−	0.186979i	−0.914941	+	0.403588i	$0.867763\pi$
$830$	−12.8353	+	22.2314i	−0.445520	+	0.771663i
$831$	−9.06883	+	23.6754i	−0.314594	+	0.821291i
$832$	−2.85185	+	4.93955i	−0.0988701	+	0.171248i
$833$		0			0
$834$	4.93598	−	12.8861i	0.170919	−	0.446208i
$835$	16.6706			0.576910
$836$	2.04063	+	3.53447i	0.0705766	+	0.122242i
$837$	−43.5702	+	22.3173i	−1.50601	+	0.771399i
$838$	2.77455	−	4.80566i	0.0958452	−	0.166009i
$839$	−21.2947	−	36.8834i	−0.735174	−	1.27336i	−0.954647	−	0.297740i	$-0.903767\pi$
$839$	−21.2947	−	36.8834i	−0.735174	−	1.27336i	0.219474	−	0.975618i	$-0.429566\pi$
$840$		0			0
$841$	−10.5721	+	18.3114i	−0.364555	+	0.631428i
$842$	3.42107	+	5.92546i	0.117898	+	0.204205i
$843$	−25.5270	−	31.4774i	−0.879195	−	1.08414i
$844$	−8.32846	+	14.4253i	−0.286677	+	0.496540i
$845$	−31.0751	+	53.8237i	−1.06902	+	1.85159i
$846$	−16.6219	+	5.42692i	−0.571472	+	0.186581i
$847$		0			0
$848$	1.02859	+	1.78157i	0.0353219	+	0.0611794i
$849$	−44.6873	+	7.11034i	−1.53366	+	0.244026i
$850$	7.79863			0.267491
$851$	−2.23912			−0.0767562
$852$	−14.8646	+	2.36515i	−0.509252	+	0.0810288i
$853$	10.6969	+	18.5275i	0.366254	+	0.634370i	0.988976	−	0.148073i	$-0.0473070\pi$
$853$	10.6969	+	18.5275i	0.366254	+	0.634370i	−0.622723	+	0.782442i	$0.713974\pi$
$854$		0			0
$855$	−11.6391	+	3.80009i	−0.398050	+	0.129960i
$856$	−5.68878	+	9.85326i	−0.194438	+	0.336777i
$857$	−18.4218	+	31.9074i	−0.629275	+	1.08994i	0.358422	+	0.933560i	$0.383315\pi$
$857$	−18.4218	+	31.9074i	−0.629275	+	1.08994i	−0.987697	+	0.156377i	$0.950019\pi$
$858$	−19.7999	−	24.4153i	−0.675956	−	0.833524i
$859$	−8.81875	−	15.2745i	−0.300892	−	0.521160i	0.675446	−	0.737409i	$-0.263951\pi$
$859$	−8.81875	−	15.2745i	−0.300892	−	0.521160i	−0.976338	+	0.216249i	$0.930618\pi$
$860$	10.8639	−	18.8168i	0.370455	−	0.641648i
$861$		0			0
$862$	−16.5539	−	28.6722i	−0.563828	−	0.976579i
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	−0.872428	−	0.488743i	$-0.837456\pi$
$863$	−0.380438	+	0.658939i	−0.0129503	+	0.0224305i	0.859478	+	0.511173i	$0.170789\pi$
$864$	4.62476	−	2.36887i	0.157338	−	0.0805907i
$865$	4.05950	+	7.03127i	0.138027	+	0.239070i
$866$	−12.1111			−0.411552
$867$	−9.09781	+	23.7511i	−0.308978	+	0.806628i
$868$		0			0
$869$	6.58414	−	11.4041i	0.223351	−	0.386856i
$870$	−13.9601	+	36.4446i	−0.473290	+	1.23559i
$871$	−31.2759	+	54.1715i	−1.05974	+	1.83553i
$872$	2.21053	+	3.82876i	0.0748581	+	0.129658i
$873$	−33.1319	−	29.7469i	−1.12134	−	1.00678i
$874$	2.87197			0.0971457
$875$		0			0
$876$	−5.41874	−	6.68187i	−0.183082	−	0.225760i
$877$	20.7495	+	35.9392i	0.700662	+	1.21358i	0.968234	+	0.250044i	$0.0804451\pi$
$877$	20.7495	+	35.9392i	0.700662	+	1.21358i	−0.267573	+	0.963538i	$0.586222\pi$
$878$	−8.83422			−0.298140
$879$	16.0237	−	41.8320i	0.540466	−	1.41096i
$880$	10.1248			0.341306
$881$	−8.35486			−0.281482			−0.140741	−	0.990046i	$-0.544949\pi$
$881$	−8.35486			−0.281482			−0.140741	+	0.990046i	$0.544949\pi$
$882$		0			0
$883$	35.6181			1.19864			0.599322	−	0.800508i	$-0.295437\pi$
$883$	35.6181			1.19864			0.599322	+	0.800508i	$0.295437\pi$
$884$	−8.67962			−0.291927
$885$	3.90451	+	4.81467i	0.131249	+	0.161843i
$886$	−17.5185			−0.588545
$887$	−18.5550	−	32.1382i	−0.623016	−	1.07909i	−0.988921	−	0.148443i	$-0.952574\pi$
$887$	−18.5550	−	32.1382i	−0.623016	−	1.07909i	0.365905	−	0.930652i	$-0.380759\pi$
$888$	0.619562	−	1.61745i	0.0207911	−	0.0542781i
$889$		0			0
$890$	−0.717370			−0.0240463
$891$	3.07442	+	28.4720i	0.102997	+	0.953847i
$892$	5.32846	+	9.22916i	0.178410	+	0.309015i
$893$	3.73788	−	6.47420i	0.125083	−	0.216651i
$894$	25.3759	+	31.2911i	0.848698	+	1.04653i
$895$	11.1969	−	19.3935i	0.374270	−	0.648254i
$896$		0			0
$897$	−21.8457	+	3.47594i	−0.729407	+	0.116058i
$898$	−31.2301			−1.04216
$899$	−33.3565	−	57.7751i	−1.11250	−	1.92691i
$900$	−3.17511	+	15.0429i	−0.105837	+	0.501429i
$901$	−1.56526	+	2.71111i	−0.0521464	+	0.0903202i
$902$	−8.91423	−	15.4399i	−0.296811	−	0.514092i
$903$		0			0
$904$	1.60752	−	2.78431i	0.0534654	−	0.0926048i
$905$	−20.6300	−	35.7321i	−0.685763	−	1.18778i
$906$	5.03379	−	13.1414i	0.167237	−	0.436594i
$907$	24.0751	−	41.6993i	0.799401	−	1.38460i	−0.120606	−	0.992700i	$-0.538484\pi$
$907$	24.0751	−	41.6993i	0.799401	−	1.38460i	0.920007	−	0.391902i	$-0.128183\pi$
$908$	−7.25404	+	12.5644i	−0.240734	+	0.416963i
$909$	11.5172	−	54.5658i	0.382003	−	1.80983i
$910$		0			0
$911$	17.4428	+	30.2119i	0.577906	+	1.00096i	0.995719	+	0.0924301i	$0.0294635\pi$
$911$	17.4428	+	30.2119i	0.577906	+	1.00096i	−0.417813	+	0.908533i	$0.637203\pi$
$912$	−0.794668	+	2.07459i	−0.0263141	+	0.0686965i
$913$	−25.6706			−0.849573
$914$	32.1248			1.06259
$915$	−10.8473	−	13.3759i	−0.358602	−	0.442193i
$916$	5.12476	+	8.87635i	0.169327	+	0.293283i
$917$		0			0
$918$	6.64076	+	4.29245i	0.219178	+	0.141672i
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	0.0249351	+	0.999689i	$0.492062\pi$
$919$	−25.8675	+	44.8037i	−0.853289	+	1.47794i	−0.878224	+	0.478250i	$0.841271\pi$
$920$	3.56238	−	6.17023i	0.117448	−	0.203426i
$921$	6.04187	−	0.961343i	0.199086	−	0.0316773i
$922$	1.23229	+	2.13438i	0.0405832	+	0.0702922i
$923$	−24.7826	+	42.9248i	−0.815730	+	1.41289i
$924$		0			0
$925$	2.56238	+	4.43818i	0.0842506	+	0.145926i
$926$	−15.1735	+	26.2812i	−0.498631	+	0.863655i
$927$	−0.630912	−	0.566453i	−0.0207219	−	0.0186048i
$928$	3.54063	+	6.13255i	0.116227	+	0.201311i
$929$	50.8285			1.66763			0.833814	−	0.552046i	$-0.186153\pi$
$929$	50.8285			1.66763			0.833814	+	0.552046i	$0.186153\pi$
$930$	−32.7044	−	40.3279i	−1.07242	−	1.32240i
$931$		0			0
$932$	0.540628	−	0.936396i	0.0177089	−	0.0306727i
$933$	2.91423	−	0.463693i	0.0954076	−	0.0151806i
$934$	−7.98181	+	13.8249i	−0.261173	+	0.452365i
$935$	7.70370	+	13.3432i	0.251938	+	0.436369i
$936$	3.53379	−	16.7422i	0.115506	−	0.547236i
$937$	−2.54583			−0.0831686			−0.0415843	−	0.999135i	$-0.513241\pi$
$937$	−2.54583			−0.0831686			−0.0415843	+	0.999135i	$0.513241\pi$
$938$		0			0
$939$	−4.86156	+	0.773540i	−0.158651	+	0.0252435i
$940$	−9.27292	−	16.0612i	−0.302449	−	0.523857i
$941$	−1.15787			−0.0377454			−0.0188727	−	0.999822i	$-0.506008\pi$
$941$	−1.15787			−0.0377454			−0.0188727	+	0.999822i	$0.506008\pi$
$942$	19.2661	−	3.06549i	0.627723	−	0.0998791i
$943$	−12.5458			−0.408548
$944$	1.12476			0.0366079
$945$		0			0
$946$	21.7278			0.706431
$947$	9.81479			0.318938			0.159469	−	0.987203i	$-0.449022\pi$
$947$	9.81479			0.318938			0.159469	+	0.987203i	$0.449022\pi$
$948$	7.07893	−	1.12635i	0.229913	−	0.0365822i
$949$	−28.3297			−0.919620
$950$	−3.28659	−	5.69254i	−0.106631	−	0.184690i
$951$	42.6267	−	6.78248i	1.38227	−	0.219937i
$952$		0			0
$953$	6.53791			0.211784			0.105892	−	0.994378i	$-0.466230\pi$
$953$	6.53791			0.211784			0.105892	+	0.994378i	$0.466230\pi$
$954$	−4.59222	−	4.12304i	−0.148678	−	0.133488i
$955$	−3.15103	−	5.45774i	−0.101965	−	0.176608i
$956$	−6.16019	+	10.6698i	−0.199235	+	0.345085i
$957$	−38.5420	+	6.13255i	−1.24589	+	0.198237i
$958$	11.5865	−	20.0683i	0.374341	−	0.648378i
$959$		0			0
$960$	3.47141	+	4.28061i	0.112039	+	0.138156i
$961$	57.7565			1.86311
$962$	−2.85185	−	4.93955i	−0.0919473	−	0.159257i
$963$	7.04910	−	33.3969i	0.227154	−	1.07620i
$964$	−6.50000	+	11.2583i	−0.209351	+	0.362606i
$965$	7.23229	+	12.5267i	0.232816	+	0.403248i
$966$		0			0
$967$	14.4445	−	25.0185i	0.464502	−	0.804542i	−0.534677	−	0.845057i	$-0.679567\pi$
$967$	14.4445	−	25.0185i	0.464502	−	0.804542i	0.999179	+	0.0405151i	$0.0128999\pi$
$968$	−0.437618	−	0.757977i	−0.0140656	−	0.0243623i
$969$	−3.33870	+	0.531232i	−0.107254	+	0.0170656i
$970$	23.6134	−	40.8996i	0.758181	−	1.31321i
$971$	−2.66827	+	4.62158i	−0.0856289	+	0.148314i	−0.905659	−	0.424007i	$-0.860623\pi$
$971$	−2.66827	+	4.62158i	−0.0856289	+	0.148314i	0.820030	+	0.572320i	$0.193957\pi$
$972$	−10.9834	+	11.0618i	−0.352294	+	0.354808i
$973$		0			0
$974$	−1.70658	−	2.95588i	−0.0546822	−	0.0947124i
$975$	31.8892	+	39.3227i	1.02127	+	1.25933i
$976$	−3.12476			−0.100021
$977$	−48.0722			−1.53797			−0.768983	−	0.639269i	$-0.779237\pi$
$977$	−48.0722			−1.53797			−0.768983	+	0.639269i	$0.779237\pi$
$978$	−2.46621	+	6.43837i	−0.0788606	+	0.205876i
$979$	−0.358685	−	0.621261i	−0.0114636	−	0.0198556i
$980$		0			0
$981$	−9.86909	−	8.86079i	−0.315096	−	0.282903i
$982$	9.58414	−	16.6002i	0.305842	−	0.529734i
$983$	14.7313	−	25.5154i	0.469857	−	0.813816i	−0.529549	−	0.848279i	$-0.677639\pi$
$983$	14.7313	−	25.5154i	0.469857	−	0.813816i	0.999406	+	0.0344634i	$0.0109722\pi$
$984$	3.47141	−	9.06259i	0.110665	−	0.288905i
$985$	34.7067	+	60.1138i	1.10585	+	1.91538i
$986$	−5.38796	+	9.33223i	−0.171588	+	0.297199i
$987$		0			0
$988$	3.65787	+	6.33561i	0.116372	+	0.201563i
$989$	7.64488	−	13.2413i	0.243093	−	0.421050i
$990$	−28.8743	+	9.42724i	−0.917685	+	0.299617i
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	0.999929	−	0.0119112i	$-0.00379153\pi$
$991$	15.4142	+	26.6982i	0.489649	+	0.848097i	−0.510280	+	0.860008i	$0.670458\pi$
$992$	−9.42107			−0.299119
$993$	12.2672	−	1.95187i	0.389286	−	0.0619407i
$994$		0			0
$995$	−19.5413	+	33.8466i	−0.619501	+	1.07301i
$996$	−8.80150	−	10.8532i	−0.278886	−	0.343896i
$997$	2.77292	−	4.80283i	0.0878191	−	0.152107i	−0.818770	−	0.574122i	$-0.805344\pi$
$997$	2.77292	−	4.80283i	0.0878191	−	0.152107i	0.906589	+	0.422015i	$0.138677\pi$
$998$	20.5848	+	35.6540i	0.651601	+	1.12861i
$999$	−0.260877	+	5.18960i	−0.00825377	+	0.164192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.e.o.373.1		6
3.2	odd	2		2646.2.e.p.1549.3		6
7.2	even	3		882.2.f.o.589.2		6
7.3	odd	6		126.2.h.d.67.1	yes	6
7.4	even	3		882.2.h.p.67.3		6
7.5	odd	6		882.2.f.n.589.2		6
7.6	odd	2		126.2.e.c.121.3	yes	6
9.2	odd	6		2646.2.h.o.667.1		6
9.7	even	3		882.2.h.p.79.3		6
21.2	odd	6		2646.2.f.m.1765.3		6
21.5	even	6		2646.2.f.l.1765.1		6
21.11	odd	6		2646.2.h.o.361.1		6
21.17	even	6		378.2.h.c.361.3		6
21.20	even	2		378.2.e.d.37.1		6
28.3	even	6		1008.2.t.h.193.3		6
28.27	even	2		1008.2.q.g.625.1		6
63.2	odd	6		2646.2.f.m.883.3		6
63.5	even	6		7938.2.a.ca.1.3		3
63.11	odd	6		2646.2.e.p.2125.3		6
63.13	odd	6		1134.2.g.m.163.3		6
63.16	even	3		882.2.f.o.295.2		6
63.20	even	6		378.2.h.c.289.3		6
63.23	odd	6		7938.2.a.bz.1.1		3
63.25	even	3	inner	882.2.e.o.655.1		6
63.31	odd	6		1134.2.g.m.487.3		6
63.34	odd	6		126.2.h.d.79.1	yes	6
63.38	even	6		378.2.e.d.235.1		6
63.40	odd	6		7938.2.a.bv.1.1		3
63.41	even	6		1134.2.g.l.163.1		6
63.47	even	6		2646.2.f.l.883.1		6
63.52	odd	6		126.2.e.c.25.3	✓	6
63.58	even	3		7938.2.a.bw.1.3		3
63.59	even	6		1134.2.g.l.487.1		6
63.61	odd	6		882.2.f.n.295.2		6
84.59	odd	6		3024.2.t.h.1873.3		6
84.83	odd	2		3024.2.q.g.2305.1		6
252.83	odd	6		3024.2.t.h.289.3		6
252.115	even	6		1008.2.q.g.529.1		6
252.223	even	6		1008.2.t.h.961.3		6
252.227	odd	6		3024.2.q.g.2881.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.3	✓	6	63.52	odd	6
126.2.e.c.121.3	yes	6	7.6	odd	2
126.2.h.d.67.1	yes	6	7.3	odd	6
126.2.h.d.79.1	yes	6	63.34	odd	6
378.2.e.d.37.1		6	21.20	even	2
378.2.e.d.235.1		6	63.38	even	6
378.2.h.c.289.3		6	63.20	even	6
378.2.h.c.361.3		6	21.17	even	6
882.2.e.o.373.1		6	1.1	even	1	trivial
882.2.e.o.655.1		6	63.25	even	3	inner
882.2.f.n.295.2		6	63.61	odd	6
882.2.f.n.589.2		6	7.5	odd	6
882.2.f.o.295.2		6	63.16	even	3
882.2.f.o.589.2		6	7.2	even	3
882.2.h.p.67.3		6	7.4	even	3
882.2.h.p.79.3		6	9.7	even	3
1008.2.q.g.529.1		6	252.115	even	6
1008.2.q.g.625.1		6	28.27	even	2
1008.2.t.h.193.3		6	28.3	even	6
1008.2.t.h.961.3		6	252.223	even	6
1134.2.g.l.163.1		6	63.41	even	6
1134.2.g.l.487.1		6	63.59	even	6
1134.2.g.m.163.3		6	63.13	odd	6
1134.2.g.m.487.3		6	63.31	odd	6
2646.2.e.p.1549.3		6	3.2	odd	2
2646.2.e.p.2125.3		6	63.11	odd	6
2646.2.f.l.883.1		6	63.47	even	6
2646.2.f.l.1765.1		6	21.5	even	6
2646.2.f.m.883.3		6	63.2	odd	6
2646.2.f.m.1765.3		6	21.2	odd	6
2646.2.h.o.361.1		6	21.11	odd	6
2646.2.h.o.667.1		6	9.2	odd	6
3024.2.q.g.2305.1		6	84.83	odd	2
3024.2.q.g.2881.1		6	252.227	odd	6
3024.2.t.h.289.3		6	252.83	odd	6
3024.2.t.h.1873.3		6	84.59	odd	6
7938.2.a.bv.1.1		3	63.40	odd	6
7938.2.a.bw.1.3		3	63.58	even	3
7938.2.a.bz.1.1		3	63.23	odd	6
7938.2.a.ca.1.3		3	63.5	even	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-1.71053 + 0.272169i) q^{3} +1.00000 q^{4} +(-1.59097 - 2.75564i) q^{5} +(1.71053 - 0.272169i) q^{6} -1.00000 q^{8} +(2.85185 - 0.931107i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-1.71053 + 0.272169i) q^{3} +1.00000 q^{4} +(-1.59097 - 2.75564i) q^{5} +(1.71053 - 0.272169i) q^{6} -1.00000 q^{8} +(2.85185 - 0.931107i) q^{9} +(1.59097 + 2.75564i) q^{10} +(-1.59097 + 2.75564i) q^{11} +(-1.71053 + 0.272169i) q^{12} +(-2.85185 + 4.93955i) q^{13} +(3.47141 + 4.28061i) q^{15} +1.00000 q^{16} +(0.760877 + 1.31788i) q^{17} +(-2.85185 + 0.931107i) q^{18} +(0.641315 - 1.11079i) q^{19} +(-1.59097 - 2.75564i) q^{20} +(1.59097 - 2.75564i) q^{22} +(-1.11956 - 1.93914i) q^{23} +(1.71053 - 0.272169i) q^{24} +(-2.56238 + 4.43818i) q^{25} +(2.85185 - 4.93955i) q^{26} +(-4.62476 + 2.36887i) q^{27} +(-3.54063 - 6.13255i) q^{29} +(-3.47141 - 4.28061i) q^{30} +9.42107 q^{31} -1.00000 q^{32} +(1.97141 - 5.14663i) q^{33} +(-0.760877 - 1.31788i) q^{34} +(2.85185 - 0.931107i) q^{36} +(0.500000 - 0.866025i) q^{37} +(-0.641315 + 1.11079i) q^{38} +(3.53379 - 9.22544i) q^{39} +(1.59097 + 2.75564i) q^{40} +(2.80150 - 4.85235i) q^{41} +(3.41423 + 5.91362i) q^{43} +(-1.59097 + 2.75564i) q^{44} +(-7.10301 - 6.37731i) q^{45} +(1.11956 + 1.93914i) q^{46} +5.82846 q^{47} +(-1.71053 + 0.272169i) q^{48} +(2.56238 - 4.43818i) q^{50} +(-1.66019 - 2.04719i) q^{51} +(-2.85185 + 4.93955i) q^{52} +(1.02859 + 1.78157i) q^{53} +(4.62476 - 2.36887i) q^{54} +10.1248 q^{55} +(-0.794668 + 2.07459i) q^{57} +(3.54063 + 6.13255i) q^{58} +1.12476 q^{59} +(3.47141 + 4.28061i) q^{60} -3.12476 q^{61} -9.42107 q^{62} +1.00000 q^{64} +18.1488 q^{65} +(-1.97141 + 5.14663i) q^{66} +10.9669 q^{67} +(0.760877 + 1.31788i) q^{68} +(2.44282 + 3.01225i) q^{69} +8.69002 q^{71} +(-2.85185 + 0.931107i) q^{72} +(2.48345 + 4.30146i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(3.17511 - 8.28905i) q^{75} +(0.641315 - 1.11079i) q^{76} +(-3.53379 + 9.22544i) q^{78} -4.13844 q^{79} +(-1.59097 - 2.75564i) q^{80} +(7.26608 - 5.31075i) q^{81} +(-2.80150 + 4.85235i) q^{82} +(4.03379 + 6.98673i) q^{83} +(2.42107 - 4.19341i) q^{85} +(-3.41423 - 5.91362i) q^{86} +(7.72545 + 9.52628i) q^{87} +(1.59097 - 2.75564i) q^{88} +(-0.112725 + 0.195246i) q^{89} +(7.10301 + 6.37731i) q^{90} +(-1.11956 - 1.93914i) q^{92} +(-16.1150 + 2.56412i) q^{93} -5.82846 q^{94} -4.08126 q^{95} +(1.71053 - 0.272169i) q^{96} +(-7.42107 - 12.8537i) q^{97} +(-1.97141 + 9.34004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9	\( 6 q - 6 q^{2} - 2 q^{3} + 6 q^{4} - q^{5} + 2 q^{6} - 6 q^{8} + 8 q^{9} + q^{10} - q^{11} - 2 q^{12} - 8 q^{13} + 12 q^{15} + 6 q^{16} + 4 q^{17} - 8 q^{18} + 3 q^{19} - q^{20} + q^{22} - 7 q^{23} + 2 q^{24} + 2 q^{25} + 8 q^{26} + 7 q^{27} - 5 q^{29} - 12 q^{30} + 40 q^{31} - 6 q^{32} + 3 q^{33} - 4 q^{34} + 8 q^{36} + 3 q^{37} - 3 q^{38} - 5 q^{39} + q^{40} - 6 q^{43} - q^{44} - 9 q^{45} + 7 q^{46} - 18 q^{47} - 2 q^{48} - 2 q^{50} + 6 q^{51} - 8 q^{52} + 15 q^{53} - 7 q^{54} + 26 q^{55} + 22 q^{57} + 5 q^{58} - 28 q^{59} + 12 q^{60} + 16 q^{61} - 40 q^{62} + 6 q^{64} + 24 q^{65} - 3 q^{66} - 2 q^{67} + 4 q^{68} - 3 q^{69} + 14 q^{71} - 8 q^{72} - 19 q^{73} - 3 q^{74} - 8 q^{75} + 3 q^{76} + 5 q^{78} - 10 q^{79} - q^{80} + 8 q^{81} - 2 q^{83} - 2 q^{85} + 6 q^{86} + 27 q^{87} + q^{88} + 9 q^{89} + 9 q^{90} - 7 q^{92} - 38 q^{93} + 18 q^{94} + 8 q^{95} + 2 q^{96} - 28 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 2 * q^3 + 6 * q^4 - q^5 + 2 * q^6 - 6 * q^8 + 8 * q^9 + q^10 - q^11 - 2 * q^12 - 8 * q^13 + 12 * q^15 + 6 * q^16 + 4 * q^17 - 8 * q^18 + 3 * q^19 - q^20 + q^22 - 7 * q^23 + 2 * q^24 + 2 * q^25 + 8 * q^26 + 7 * q^27 - 5 * q^29 - 12 * q^30 + 40 * q^31 - 6 * q^32 + 3 * q^33 - 4 * q^34 + 8 * q^36 + 3 * q^37 - 3 * q^38 - 5 * q^39 + q^40 - 6 * q^43 - q^44 - 9 * q^45 + 7 * q^46 - 18 * q^47 - 2 * q^48 - 2 * q^50 + 6 * q^51 - 8 * q^52 + 15 * q^53 - 7 * q^54 + 26 * q^55 + 22 * q^57 + 5 * q^58 - 28 * q^59 + 12 * q^60 + 16 * q^61 - 40 * q^62 + 6 * q^64 + 24 * q^65 - 3 * q^66 - 2 * q^67 + 4 * q^68 - 3 * q^69 + 14 * q^71 - 8 * q^72 - 19 * q^73 - 3 * q^74 - 8 * q^75 + 3 * q^76 + 5 * q^78 - 10 * q^79 - q^80 + 8 * q^81 - 2 * q^83 - 2 * q^85 + 6 * q^86 + 27 * q^87 + q^88 + 9 * q^89 + 9 * q^90 - 7 * q^92 - 38 * q^93 + 18 * q^94 + 8 * q^95 + 2 * q^96 - 28 * q^97 - 3 * q^99

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