LMFDB - Embedded newform 585.2.j.g.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("585.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.591408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 4x^{4} + x^{3} + 10x^{2} - 3x + 1 $ x^6 - x^5 + 4x^4 + x^3 + 10x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.2
Root			$1.08504 - 1.87935i$ of defining polynomial
Character	$\chi$	$=$	585.406
Dual form			585.2.j.g.451.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.269594 - 0.466951i) q^{2} +(0.854638 - 1.48028i) q^{4} +1.00000 q^{5} +(2.40049 - 4.15777i) q^{7} -2.00000 q^{8} +O(q^{10})$	\(q+(-0.269594 - 0.466951i) q^{2} +(0.854638 - 1.48028i) q^{4} +1.00000 q^{5} +(2.40049 - 4.15777i) q^{7} -2.00000 q^{8} +(-0.269594 - 0.466951i) q^{10} +(-1.70928 - 2.96055i) q^{11} +(-2.25513 + 2.81325i) q^{13} -2.58864 q^{14} +(-1.17009 - 2.02665i) q^{16} +(1.43968 - 2.49360i) q^{17} +(-2.48554 + 4.30507i) q^{19} +(0.854638 - 1.48028i) q^{20} +(-0.921622 + 1.59630i) q^{22} +(4.24846 + 7.35856i) q^{23} +1.00000 q^{25} +(1.92162 + 0.294598i) q^{26} +(-4.10310 - 7.10678i) q^{28} +(-1.75513 - 3.03997i) q^{29} +3.04945 q^{31} +(-2.63090 + 4.55685i) q^{32} -1.55252 q^{34} +(2.40049 - 4.15777i) q^{35} +(-1.34017 - 2.32125i) q^{37} +2.68035 q^{38} -2.00000 q^{40} +(-1.87577 - 3.24893i) q^{41} +(-0.794319 + 1.37580i) q^{43} -5.84324 q^{44} +(2.29072 - 3.96765i) q^{46} +0.539189 q^{47} +(-8.02472 - 13.8992i) q^{49} +(-0.269594 - 0.466951i) q^{50} +(2.23707 + 5.74253i) q^{52} +13.7587 q^{53} +(-1.70928 - 2.96055i) q^{55} +(-4.80098 + 8.31555i) q^{56} +(-0.946346 + 1.63912i) q^{58} +(4.20261 - 7.27913i) q^{59} +(1.52472 - 2.64090i) q^{61} +(-0.822114 - 1.42394i) q^{62} -1.84324 q^{64} +(-2.25513 + 2.81325i) q^{65} +(6.42522 + 11.1288i) q^{67} +(-2.46081 - 4.26225i) q^{68} -2.58864 q^{70} +(1.04585 - 1.81147i) q^{71} -5.53919 q^{73} +(-0.722606 + 1.25159i) q^{74} +(4.24846 + 7.35856i) q^{76} -16.4124 q^{77} +2.21235 q^{79} +(-1.17009 - 2.02665i) q^{80} +(-1.01139 + 1.75178i) q^{82} -4.34017 q^{83} +(1.43968 - 2.49360i) q^{85} +0.856576 q^{86} +(3.41855 + 5.92110i) q^{88} +(-3.50667 - 6.07372i) q^{89} +(6.28345 + 16.1295i) q^{91} +14.5236 q^{92} +(-0.145362 - 0.251775i) q^{94} +(-2.48554 + 4.30507i) q^{95} +(7.13449 - 12.3573i) q^{97} +(-4.32684 + 7.49431i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{4} + 6 q^{5} + 5 q^{7} - 12 q^{8}+O(q^{10}) $ 6 * q - 2 * q^4 + 6 * q^5 + 5 * q^7 - 12 * q^8	$ 6 q - 2 q^{4} + 6 q^{5} + 5 q^{7} - 12 q^{8} + 4 q^{11} + 3 q^{13} + 24 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{20} - 12 q^{22} + 8 q^{23} + 6 q^{25} + 18 q^{26} + 6 q^{29} - 18 q^{31} - 8 q^{32} - 8 q^{34} + 5 q^{35} + 14 q^{37} - 28 q^{38} - 12 q^{40} - 20 q^{41} + 15 q^{43} - 48 q^{44} + 28 q^{46} - 30 q^{49} + 16 q^{52} + 32 q^{53} + 4 q^{55} - 10 q^{56} + 6 q^{58} + 10 q^{59} - 9 q^{61} - 2 q^{62} - 24 q^{64} + 3 q^{65} + 11 q^{67} - 18 q^{68} + 24 q^{70} + 4 q^{71} - 30 q^{73} + 8 q^{74} + 8 q^{76} + 34 q^{79} + 4 q^{80} + 14 q^{82} - 4 q^{83} - 4 q^{85} + 20 q^{86} - 8 q^{88} - 22 q^{89} - 31 q^{91} + 56 q^{92} - 8 q^{94} + q^{97} - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^4 + 6 * q^5 + 5 * q^7 - 12 * q^8 + 4 * q^11 + 3 * q^13 + 24 * q^14 + 4 * q^16 - 4 * q^17 - 2 * q^20 - 12 * q^22 + 8 * q^23 + 6 * q^25 + 18 * q^26 + 6 * q^29 - 18 * q^31 - 8 * q^32 - 8 * q^34 + 5 * q^35 + 14 * q^37 - 28 * q^38 - 12 * q^40 - 20 * q^41 + 15 * q^43 - 48 * q^44 + 28 * q^46 - 30 * q^49 + 16 * q^52 + 32 * q^53 + 4 * q^55 - 10 * q^56 + 6 * q^58 + 10 * q^59 - 9 * q^61 - 2 * q^62 - 24 * q^64 + 3 * q^65 + 11 * q^67 - 18 * q^68 + 24 * q^70 + 4 * q^71 - 30 * q^73 + 8 * q^74 + 8 * q^76 + 34 * q^79 + 4 * q^80 + 14 * q^82 - 4 * q^83 - 4 * q^85 + 20 * q^86 - 8 * q^88 - 22 * q^89 - 31 * q^91 + 56 * q^92 - 8 * q^94 + q^97 - 2 * 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 $

$2$	−0.269594	−	0.466951i	−0.190632	−	0.330184i	0.754828	−	0.655923i	$-0.227720\pi$
$2$	−0.269594	−	0.466951i	−0.190632	−	0.330184i	−0.945460	+	0.325739i	$0.894387\pi$
$3$		0			0
$3$		0			0
$4$	0.854638	−	1.48028i	0.427319	−	0.740138i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.40049	−	4.15777i	0.907301	−	1.57149i	0.0895019	−	0.995987i	$-0.471472\pi$
$7$	2.40049	−	4.15777i	0.907301	−	1.57149i	0.817799	−	0.575504i	$-0.195194\pi$
$8$	−2.00000			−0.707107
$9$		0			0
$10$	−0.269594	−	0.466951i	−0.0852532	−	0.147663i
$11$	−1.70928	−	2.96055i	−0.515366	−	0.892640i	−0.999841	−	0.0178349i	$-0.994323\pi$
$11$	−1.70928	−	2.96055i	−0.515366	−	0.892640i	0.484475	−	0.874805i	$-0.339011\pi$
$12$		0			0
$13$	−2.25513	+	2.81325i	−0.625460	+	0.780256i
$13$	−2.25513	+	2.81325i	−0.625460	+	0.780256i
$14$	−2.58864			−0.691842
$15$		0			0
$16$	−1.17009	−	2.02665i	−0.292522	−	0.506662i
$17$	1.43968	−	2.49360i	0.349174	−	0.604787i	−0.636929	−	0.770922i	$-0.719796\pi$
$17$	1.43968	−	2.49360i	0.349174	−	0.604787i	0.986103	+	0.166135i	$0.0531289\pi$
$18$		0			0
$19$	−2.48554	+	4.30507i	−0.570221	+	0.987652i	0.426322	+	0.904571i	$0.359809\pi$
$19$	−2.48554	+	4.30507i	−0.570221	+	0.987652i	−0.996543	+	0.0830801i	$0.973524\pi$
$20$	0.854638	−	1.48028i	0.191103	−	0.331000i
$21$		0			0
$22$	−0.921622	+	1.59630i	−0.196491	+	0.340332i
$23$	4.24846	+	7.35856i	0.885866	+	1.53436i	0.844718	+	0.535212i	$0.179768\pi$
$23$	4.24846	+	7.35856i	0.885866	+	1.53436i	0.0411482	+	0.999153i	$0.486898\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	1.92162	+	0.294598i	0.376861	+	0.0577755i
$27$		0			0
$28$	−4.10310	−	7.10678i	−0.775413	−	1.34306i
$29$	−1.75513	−	3.03997i	−0.325919	−	0.564509i	0.655779	−	0.754953i	$-0.272340\pi$
$29$	−1.75513	−	3.03997i	−0.325919	−	0.564509i	−0.981698	+	0.190444i	$0.939007\pi$
$30$		0			0
$31$	3.04945			0.547697			0.273849	−	0.961773i	$-0.411703\pi$
$31$	3.04945			0.547697			0.273849	+	0.961773i	$0.411703\pi$
$32$	−2.63090	+	4.55685i	−0.465081	+	0.805545i
$33$		0			0
$34$	−1.55252			−0.266255
$35$	2.40049	−	4.15777i	0.405757	−	0.702792i
$36$		0			0
$37$	−1.34017	−	2.32125i	−0.220323	−	0.381611i	0.734583	−	0.678519i	$-0.237378\pi$
$37$	−1.34017	−	2.32125i	−0.220323	−	0.381611i	−0.954906	+	0.296908i	$0.904044\pi$
$38$	2.68035			0.434810
$39$		0			0
$40$	−2.00000			−0.316228
$41$	−1.87577	−	3.24893i	−0.292946	−	0.507397i	0.681559	−	0.731763i	$-0.261302\pi$
$41$	−1.87577	−	3.24893i	−0.292946	−	0.507397i	−0.974505	+	0.224366i	$0.927969\pi$
$42$		0			0
$43$	−0.794319	+	1.37580i	−0.121132	+	0.209808i	−0.920215	−	0.391414i	$-0.871986\pi$
$43$	−0.794319	+	1.37580i	−0.121132	+	0.209808i	0.799082	+	0.601222i	$0.205319\pi$
$44$	−5.84324			−0.880902
$45$		0			0
$46$	2.29072	−	3.96765i	0.337749	−	0.584998i
$47$	0.539189			0.0786488			0.0393244	−	0.999226i	$-0.487479\pi$
$47$	0.539189			0.0786488			0.0393244	+	0.999226i	$0.487479\pi$
$48$		0			0
$49$	−8.02472	−	13.8992i	−1.14639	−	1.98560i
$50$	−0.269594	−	0.466951i	−0.0381264	−	0.0660369i
$51$		0			0
$52$	2.23707	+	5.74253i	0.310226	+	0.796345i
$53$	13.7587			1.88991			0.944953	−	0.327206i	$-0.106107\pi$
$53$	13.7587			1.88991			0.944953	+	0.327206i	$0.106107\pi$
$54$		0			0
$55$	−1.70928	−	2.96055i	−0.230479	−	0.399201i
$56$	−4.80098	+	8.31555i	−0.641558	+	1.11121i
$57$		0			0
$58$	−0.946346	+	1.63912i	−0.124261	+	0.215227i
$59$	4.20261	−	7.27913i	0.547133	−	0.947663i	−0.451336	−	0.892354i	$-0.649052\pi$
$59$	4.20261	−	7.27913i	0.547133	−	0.947663i	0.998469	−	0.0553085i	$-0.0176142\pi$
$60$		0			0
$61$	1.52472	−	2.64090i	0.195221	−	0.338133i	−0.751752	−	0.659446i	$-0.770791\pi$
$61$	1.52472	−	2.64090i	0.195221	−	0.338133i	0.946973	+	0.321313i	$0.104124\pi$
$62$	−0.822114	−	1.42394i	−0.104409	−	0.180841i
$63$		0			0
$64$	−1.84324			−0.230406
$65$	−2.25513	+	2.81325i	−0.279714	+	0.348941i
$66$		0			0
$67$	6.42522	+	11.1288i	0.784965	+	1.35960i	0.929020	+	0.370030i	$0.120653\pi$
$67$	6.42522	+	11.1288i	0.784965	+	1.35960i	−0.144055	+	0.989570i	$0.546014\pi$
$68$	−2.46081	−	4.26225i	−0.298417	−	0.516874i
$69$		0			0
$70$	−2.58864			−0.309401
$71$	1.04585	−	1.81147i	0.124120	−	0.214982i	−0.797269	−	0.603625i	$-0.793723\pi$
$71$	1.04585	−	1.81147i	0.124120	−	0.214982i	0.921389	+	0.388642i	$0.127056\pi$
$72$		0			0
$73$	−5.53919			−0.648313			−0.324157	−	0.946003i	$-0.605080\pi$
$73$	−5.53919			−0.648313			−0.324157	+	0.946003i	$0.605080\pi$
$74$	−0.722606	+	1.25159i	−0.0840013	+	0.145494i
$75$		0			0
$76$	4.24846	+	7.35856i	0.487332	+	0.844084i
$77$	−16.4124			−1.87037
$78$		0			0
$79$	2.21235			0.248908			0.124454	−	0.992225i	$-0.460282\pi$
$79$	2.21235			0.248908			0.124454	+	0.992225i	$0.460282\pi$
$80$	−1.17009	−	2.02665i	−0.130820	−	0.226586i
$81$		0			0
$82$	−1.01139	+	1.75178i	−0.111690	+	0.193452i
$83$	−4.34017			−0.476396			−0.238198	−	0.971217i	$-0.576557\pi$
$83$	−4.34017			−0.476396			−0.238198	+	0.971217i	$0.576557\pi$
$84$		0			0
$85$	1.43968	−	2.49360i	0.156155	−	0.270469i
$86$	0.856576			0.0923669
$87$		0			0
$88$	3.41855	+	5.92110i	0.364419	+	0.631192i
$89$	−3.50667	−	6.07372i	−0.371706	−	0.643813i	0.618122	−	0.786082i	$-0.287894\pi$
$89$	−3.50667	−	6.07372i	−0.371706	−	0.643813i	−0.989828	+	0.142269i	$0.954560\pi$
$90$		0			0
$91$	6.28345	+	16.1295i	0.658684	+	1.69083i
$92$	14.5236			1.51419
$93$		0			0
$94$	−0.145362	−	0.251775i	−0.0149930	−	0.0259686i
$95$	−2.48554	+	4.30507i	−0.255011	+	0.441691i
$96$		0			0
$97$	7.13449	−	12.3573i	0.724398	−	1.25469i	−0.234824	−	0.972038i	$-0.575451\pi$
$97$	7.13449	−	12.3573i	0.724398	−	1.25469i	0.959221	−	0.282656i	$-0.0912154\pi$
$98$	−4.32684	+	7.49431i	−0.437077	+	0.757040i
$99$		0			0
$100$	0.854638	−	1.48028i	0.0854638	−	0.148028i
$101$	6.24846	+	10.8227i	0.621745	+	1.07689i	0.989161	+	0.146838i	$0.0469095\pi$
$101$	6.24846	+	10.8227i	0.621745	+	1.07689i	−0.367415	+	0.930057i	$0.619757\pi$
$102$		0			0
$103$	6.85043			0.674993			0.337497	−	0.941327i	$-0.390420\pi$
$103$	6.85043			0.674993			0.337497	+	0.941327i	$0.390420\pi$
$104$	4.51026	−	5.62651i	0.442267	−	0.551724i
$105$		0			0
$106$	−3.70928	−	6.42465i	−0.360277	−	0.624018i
$107$	7.77985	+	13.4751i	0.752107	+	1.30269i	0.946800	+	0.321823i	$0.104296\pi$
$107$	7.77985	+	13.4751i	0.752107	+	1.30269i	−0.194693	+	0.980864i	$0.562371\pi$
$108$		0			0
$109$	15.8371			1.51692			0.758460	−	0.651720i	$-0.225952\pi$
$109$	15.8371			1.51692			0.758460	+	0.651720i	$0.225952\pi$
$110$	−0.921622	+	1.59630i	−0.0878732	+	0.152201i
$111$		0			0
$112$	−11.2351			−1.06162
$113$	−1.53919	+	2.66595i	−0.144795	+	0.250792i	−0.929296	−	0.369335i	$-0.879586\pi$
$113$	−1.53919	+	2.66595i	−0.144795	+	0.250792i	0.784502	+	0.620127i	$0.212919\pi$
$114$		0			0
$115$	4.24846	+	7.35856i	0.396171	+	0.686189i
$116$	−6.00000			−0.557086
$117$		0			0
$118$	−4.53200			−0.417205
$119$	−6.91189	−	11.9717i	−0.633611	−	1.09745i
$120$		0			0
$121$	−0.343245	+	0.594517i	−0.0312040	+	0.0540470i
$122$	−1.64423			−0.148861
$123$		0			0
$124$	2.60617	−	4.51402i	0.234041	−	0.405371i
$125$	1.00000			0.0894427
$126$		0			0
$127$	3.72733	+	6.45593i	0.330747	+	0.572871i	0.982659	−	0.185424i	$-0.0593659\pi$
$127$	3.72733	+	6.45593i	0.330747	+	0.572871i	−0.651911	+	0.758295i	$0.726033\pi$
$128$	5.75872	+	9.97440i	0.509004	+	0.881621i
$129$		0			0
$130$	1.92162	+	0.294598i	0.168537	+	0.0258380i
$131$	−11.6937			−1.02168			−0.510841	−	0.859675i	$-0.670666\pi$
$131$	−11.6937			−1.02168			−0.510841	+	0.859675i	$0.670666\pi$
$132$		0			0
$133$	11.9330	+	20.6686i	1.03472	+	1.79219i
$134$	3.46441	−	6.00053i	0.299279	−	0.518366i
$135$		0			0
$136$	−2.87936	+	4.98720i	−0.246903	+	0.427649i
$137$	−4.63870	+	8.03446i	−0.396311	+	0.686430i	−0.993268	−	0.115843i	$-0.963043\pi$
$137$	−4.63870	+	8.03446i	−0.396311	+	0.686430i	0.596957	+	0.802273i	$0.296376\pi$
$138$		0			0
$139$	−6.45774	+	11.1851i	−0.547738	+	0.948711i	0.450691	+	0.892680i	$0.351178\pi$
$139$	−6.45774	+	11.1851i	−0.547738	+	0.948711i	−0.998429	+	0.0560304i	$0.982156\pi$
$140$	−4.10310	−	7.10678i	−0.346775	−	0.600633i
$141$		0			0
$142$	−1.12783			−0.0946451
$143$	12.1834	+	1.86781i	1.01883	+	0.156194i
$144$		0			0
$145$	−1.75513	−	3.03997i	−0.145756	−	0.252456i
$146$	1.49333	+	2.58653i	0.123589	+	0.214063i
$147$		0			0
$148$	−4.58145			−0.376593
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	−0.904076	−	0.427372i	$-0.859440\pi$
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	0.822153	+	0.569267i	$0.192773\pi$
$150$		0			0
$151$	−8.60424			−0.700203			−0.350101	−	0.936712i	$-0.613853\pi$
$151$	−8.60424			−0.700203			−0.350101	+	0.936712i	$0.613853\pi$
$152$	4.97107	−	8.61015i	0.403207	−	0.698375i
$153$		0			0
$154$	4.42469	+	7.66379i	0.356552	+	0.617566i
$155$	3.04945			0.244938
$156$		0			0
$157$	0.908291			0.0724895			0.0362448	−	0.999343i	$-0.488460\pi$
$157$	0.908291			0.0724895			0.0362448	+	0.999343i	$0.488460\pi$
$158$	−0.596436	−	1.03306i	−0.0474499	−	0.0821857i
$159$		0			0
$160$	−2.63090	+	4.55685i	−0.207991	+	0.360250i
$161$	40.7936			3.21499
$162$		0			0
$163$	7.32211	−	12.6823i	0.573512	−	0.993352i	−0.422689	−	0.906275i	$-0.638914\pi$
$163$	7.32211	−	12.6823i	0.573512	−	0.993352i	0.996202	−	0.0870777i	$-0.0277528\pi$
$164$	−6.41241			−0.500725
$165$		0			0
$166$	1.17009	+	2.02665i	0.0908163	+	0.157298i
$167$	−2.44748	−	4.23916i	−0.189392	−	0.328036i	0.755656	−	0.654969i	$-0.227318\pi$
$167$	−2.44748	−	4.23916i	−0.189392	−	0.328036i	−0.945048	+	0.326933i	$0.893985\pi$
$168$		0			0
$169$	−2.82878	−	12.6885i	−0.217598	−	0.976038i
$170$	−1.55252			−0.119073
$171$		0			0
$172$	1.35771	+	2.35162i	0.103524	+	0.179309i
$173$	−8.77985	+	15.2072i	−0.667520	+	1.15618i	0.311076	+	0.950385i	$0.399311\pi$
$173$	−8.77985	+	15.2072i	−0.667520	+	1.15618i	−0.978595	+	0.205793i	$0.934023\pi$
$174$		0			0
$175$	2.40049	−	4.15777i	0.181460	−	0.314298i
$176$	−4.00000	+	6.92820i	−0.301511	+	0.522233i
$177$		0			0
$178$	−1.89076	+	3.27488i	−0.141718	+	0.245463i
$179$	0.692350	+	1.19919i	0.0517487	+	0.0896314i	0.890739	−	0.454514i	$-0.150187\pi$
$179$	0.692350	+	1.19919i	0.0517487	+	0.0896314i	−0.838991	+	0.544146i	$0.816854\pi$
$180$		0			0
$181$	−7.46800			−0.555092			−0.277546	−	0.960712i	$-0.589521\pi$
$181$	−7.46800			−0.555092			−0.277546	+	0.960712i	$0.589521\pi$
$182$	5.83771	−	7.28249i	0.432720	−	0.539814i
$183$		0			0
$184$	−8.49693	−	14.7171i	−0.626402	−	1.08496i
$185$	−1.34017	−	2.32125i	−0.0985315	−	0.170662i
$186$		0			0
$187$	−9.84324			−0.719809
$188$	0.460811	−	0.798148i	0.0336081	−	0.0582109i
$189$		0			0
$190$	2.68035			0.194453
$191$	−1.20261	+	2.08298i	−0.0870178	+	0.150719i	−0.906249	−	0.422744i	$-0.861067\pi$
$191$	−1.20261	+	2.08298i	−0.0870178	+	0.150719i	0.819231	+	0.573463i	$0.194400\pi$
$192$		0			0
$193$	7.91075	+	13.7018i	0.569428	+	0.986279i	0.996623	+	0.0821189i	$0.0261687\pi$
$193$	7.91075	+	13.7018i	0.569428	+	0.986279i	−0.427194	+	0.904160i	$0.640498\pi$
$194$	−7.69368			−0.552374
$195$		0			0
$196$	−27.4329			−1.95949
$197$	9.23287	+	15.9918i	0.657814	+	1.13937i	0.981180	+	0.193094i	$0.0618522\pi$
$197$	9.23287	+	15.9918i	0.657814	+	1.13937i	−0.323366	+	0.946274i	$0.604814\pi$
$198$		0			0
$199$	−5.47107	+	9.47617i	−0.387834	+	0.671748i	−0.992158	−	0.124991i	$-0.960110\pi$
$199$	−5.47107	+	9.47617i	−0.387834	+	0.671748i	0.604324	+	0.796739i	$0.293443\pi$
$200$	−2.00000			−0.141421
$201$		0			0
$202$	3.36910	−	5.83546i	0.237049	−	0.410581i
$203$	−16.8527			−1.18283
$204$		0			0
$205$	−1.87577	−	3.24893i	−0.131009	−	0.226915i
$206$	−1.84684	−	3.19882i	−0.128675	−	0.222872i
$207$		0			0
$208$	8.34017	+	1.27861i	0.578287	+	0.0886555i
$209$	16.9939			1.17549
$210$		0			0
$211$	7.08864	+	12.2779i	0.488002	+	0.845244i	0.999905	−	0.0137992i	$-0.00439257\pi$
$211$	7.08864	+	12.2779i	0.488002	+	0.845244i	−0.511903	+	0.859043i	$0.671059\pi$
$212$	11.7587	−	20.3667i	0.807592	−	1.39879i
$213$		0			0
$214$	4.19481	−	7.26563i	0.286751	−	0.496668i
$215$	−0.794319	+	1.37580i	−0.0541721	+	0.0938288i
$216$		0			0
$217$	7.32018	−	12.6789i	0.496926	−	0.860701i
$218$	−4.26959	−	7.39515i	−0.289173	−	0.500863i
$219$		0			0
$220$	−5.84324			−0.393951
$221$	3.76846	+	9.67358i	0.253494	+	0.650715i
$222$		0			0
$223$	2.82991	+	4.90155i	0.189505	+	0.328232i	0.945085	−	0.326824i	$-0.105978\pi$
$223$	2.82991	+	4.90155i	0.189505	+	0.328232i	−0.755580	+	0.655056i	$0.772645\pi$
$224$	12.6309	+	21.8774i	0.843937	+	1.46174i
$225$		0			0
$226$	1.65983			0.110410
$227$	10.4397	−	18.0821i	0.692906	−	1.20015i	−0.277976	−	0.960588i	$-0.589663\pi$
$227$	10.4397	−	18.0821i	0.692906	−	1.20015i	0.970882	−	0.239560i	$-0.0770032\pi$
$228$		0			0
$229$	−11.5525			−0.763412			−0.381706	−	0.924284i	$-0.624663\pi$
$229$	−11.5525			−0.763412			−0.381706	+	0.924284i	$0.624663\pi$
$230$	2.29072	−	3.96765i	0.151046	−	0.261619i
$231$		0			0
$232$	3.51026	+	6.07995i	0.230460	+	0.399168i
$233$	3.73206			0.244495			0.122248	−	0.992500i	$-0.460990\pi$
$233$	3.73206			0.244495			0.122248	+	0.992500i	$0.460990\pi$
$234$		0			0
$235$	0.539189			0.0351728
$236$	−7.18342	−	12.4420i	−0.467601	−	0.809908i
$237$		0			0
$238$	−3.72681	+	6.45503i	−0.241573	+	0.418417i
$239$	−27.0928			−1.75248			−0.876242	−	0.481871i	$-0.839957\pi$
$239$	−27.0928			−1.75248			−0.876242	+	0.481871i	$0.839957\pi$
$240$		0			0
$241$	11.7990	−	20.4365i	0.760043	−	1.31643i	−0.182784	−	0.983153i	$-0.558511\pi$
$241$	11.7990	−	20.4365i	0.760043	−	1.31643i	0.942828	−	0.333281i	$-0.108156\pi$
$242$	0.370147			0.0237940
$243$		0			0
$244$	−2.60617	−	4.51402i	−0.166843	−	0.288981i
$245$	−8.02472	−	13.8992i	−0.512681	−	0.887989i
$246$		0			0
$247$	−6.50605	−	16.7009i	−0.413970	−	1.06266i
$248$	−6.09890			−0.387280
$249$		0			0
$250$	−0.269594	−	0.466951i	−0.0170506	−	0.0295326i
$251$	−13.4319	+	23.2647i	−0.847813	+	1.46845i	0.0353430	+	0.999375i	$0.488748\pi$
$251$	−13.4319	+	23.2647i	−0.847813	+	1.46845i	−0.883156	+	0.469080i	$0.844586\pi$
$252$		0			0
$253$	14.5236	−	25.1556i	0.913090	−	1.58152i
$254$	2.00974	−	3.48097i	0.126102	−	0.218415i
$255$		0			0
$256$	1.26180	−	2.18549i	0.0788622	−	0.136593i
$257$	−1.75933	−	3.04726i	−0.109744	−	0.190083i	0.805922	−	0.592021i	$-0.201670\pi$
$257$	−1.75933	−	3.04726i	−0.109744	−	0.190083i	−0.915667	+	0.401939i	$0.868337\pi$
$258$		0			0
$259$	−12.8683			−0.799597
$260$	2.23707	+	5.74253i	0.138737	+	0.356136i
$261$		0			0
$262$	3.15255	+	5.46038i	0.194765	+	0.337343i
$263$	−4.42635	−	7.66666i	−0.272940	−	0.472747i	0.696673	−	0.717389i	$-0.254663\pi$
$263$	−4.42635	−	7.66666i	−0.272940	−	0.472747i	−0.969613	+	0.244642i	$0.921330\pi$
$264$		0			0
$265$	13.7587			0.845192
$266$	6.43415	−	11.1443i	0.394503	−	0.683299i
$267$		0			0
$268$	21.9649			1.34172
$269$	13.6212	−	23.5925i	0.830497	−	1.43846i	−0.0671480	−	0.997743i	$-0.521390\pi$
$269$	13.6212	−	23.5925i	0.830497	−	1.43846i	0.897645	−	0.440720i	$-0.145277\pi$
$270$		0			0
$271$	−6.93188	−	12.0064i	−0.421082	−	0.729335i	0.574964	−	0.818179i	$-0.305016\pi$
$271$	−6.93188	−	12.0064i	−0.421082	−	0.729335i	−0.996046	+	0.0888438i	$0.971683\pi$
$272$	−6.73820			−0.408564
$273$		0			0
$274$	5.00227			0.302198
$275$	−1.70928	−	2.96055i	−0.103073	−	0.178528i
$276$		0			0
$277$	−1.29072	+	2.23560i	−0.0775521	+	0.134324i	−0.902193	−	0.431332i	$-0.858044\pi$
$277$	−1.29072	+	2.23560i	−0.0775521	+	0.134324i	0.824641	+	0.565656i	$0.191377\pi$
$278$	6.96388			0.417666
$279$		0			0
$280$	−4.80098	+	8.31555i	−0.286914	+	0.496949i
$281$	5.35350			0.319363			0.159682	−	0.987169i	$-0.448953\pi$
$281$	5.35350			0.319363			0.159682	+	0.987169i	$0.448953\pi$
$282$		0			0
$283$	−7.94687	−	13.7644i	−0.472392	−	0.818207i	0.527109	−	0.849798i	$-0.323276\pi$
$283$	−7.94687	−	13.7644i	−0.472392	−	0.818207i	−0.999501	+	0.0315904i	$0.989943\pi$
$284$	−1.78765	−	3.09631i	−0.106078	−	0.183732i
$285$		0			0
$286$	−2.41241	−	6.19261i	−0.142649	−	0.366177i
$287$	−18.0111			−1.06316
$288$		0			0
$289$	4.35464	+	7.54245i	0.256155	+	0.443674i
$290$	−0.946346	+	1.63912i	−0.0555714	+	0.0962524i
$291$		0			0
$292$	−4.73400	+	8.19953i	−0.277036	+	0.479841i
$293$	−1.24067	+	2.14889i	−0.0724804	+	0.125540i	−0.899988	−	0.435915i	$-0.856425\pi$
$293$	−1.24067	+	2.14889i	−0.0724804	+	0.125540i	0.827507	+	0.561455i	$0.189758\pi$
$294$		0			0
$295$	4.20261	−	7.27913i	0.244685	−	0.423808i
$296$	2.68035	+	4.64250i	0.155792	+	0.269840i
$297$		0			0
$298$	1.07838			0.0624687
$299$	−30.2823	−	4.64250i	−1.75127	−	0.268482i
$300$		0			0
$301$	3.81351	+	6.60519i	0.219807	+	0.380717i
$302$	2.31965	+	4.01776i	0.133481	+	0.231196i
$303$		0			0
$304$	11.6332			0.667208
$305$	1.52472	−	2.64090i	0.0873055	−	0.151217i
$306$		0			0
$307$	−22.2423			−1.26944			−0.634718	−	0.772744i	$-0.718884\pi$
$307$	−22.2423			−1.26944			−0.634718	+	0.772744i	$0.718884\pi$
$308$	−14.0267	+	24.2949i	−0.799243	+	1.38433i
$309$		0			0
$310$	−0.822114	−	1.42394i	−0.0466930	−	0.0808746i
$311$	0.405220			0.0229779			0.0114890	−	0.999934i	$-0.496343\pi$
$311$	0.405220			0.0229779			0.0114890	+	0.999934i	$0.496343\pi$
$312$		0			0
$313$	−0.353504			−0.0199812			−0.00999061	−	0.999950i	$-0.503180\pi$
$313$	−0.353504			−0.0199812			−0.00999061	+	0.999950i	$0.503180\pi$
$314$	−0.244870	−	0.424128i	−0.0138188	−	0.0239349i
$315$		0			0
$316$	1.89076	−	3.27488i	0.106363	−	0.184227i
$317$	−25.3028			−1.42115			−0.710574	−	0.703622i	$-0.751565\pi$
$317$	−25.3028			−1.42115			−0.710574	+	0.703622i	$0.751565\pi$
$318$		0			0
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$	−1.84324			−0.103041
$321$		0			0
$322$	−10.9977	−	19.0486i	−0.612880	−	1.06154i
$323$	7.15676	+	12.3959i	0.398213	+	0.689724i
$324$		0			0
$325$	−2.25513	+	2.81325i	−0.125092	+	0.156051i
$326$	−7.89601			−0.437319
$327$		0			0
$328$	3.75154	+	6.49785i	0.207144	+	0.358784i
$329$	1.29432	−	2.24183i	0.0713581	−	0.123596i
$330$		0			0
$331$	−2.30098	+	3.98542i	−0.126474	+	0.219059i	−0.922308	−	0.386456i	$-0.873699\pi$
$331$	−2.30098	+	3.98542i	−0.126474	+	0.219059i	0.795834	+	0.605514i	$0.207033\pi$
$332$	−3.70928	+	6.42465i	−0.203573	+	0.352599i
$333$		0			0
$334$	−1.31965	+	2.28571i	−0.0722083	+	0.125068i
$335$	6.42522	+	11.1288i	0.351047	+	0.608031i
$336$		0			0
$337$	−31.0338			−1.69052			−0.845261	−	0.534354i	$-0.820555\pi$
$337$	−31.0338			−1.69052			−0.845261	+	0.534354i	$0.820555\pi$
$338$	−5.16229	+	4.74165i	−0.280791	+	0.257912i
$339$		0			0
$340$	−2.46081	−	4.26225i	−0.133456	−	0.231153i
$341$	−5.21235	−	9.02805i	−0.282264	−	0.488896i
$342$		0			0
$343$	−43.4463			−2.34588
$344$	1.58864	−	2.75160i	0.0856536	−	0.148356i
$345$		0			0
$346$	9.46800			0.509003
$347$	−8.97826	+	15.5508i	−0.481978	+	0.834811i	−0.999786	−	0.0206863i	$-0.993415\pi$
$347$	−8.97826	+	15.5508i	−0.481978	+	0.834811i	0.517808	+	0.855497i	$0.326748\pi$
$348$		0			0
$349$	−0.0505820	−	0.0876107i	−0.00270759	−	0.00468969i	0.864668	−	0.502343i	$-0.167529\pi$
$349$	−0.0505820	−	0.0876107i	−0.00270759	−	0.00468969i	−0.867376	+	0.497653i	$0.834195\pi$
$350$	−2.58864			−0.138368
$351$		0			0
$352$	17.9877			0.958748
$353$	−14.6803	−	25.4271i	−0.781356	−	1.35335i	−0.931152	−	0.364631i	$-0.881195\pi$
$353$	−14.6803	−	25.4271i	−0.781356	−	1.35335i	0.149796	−	0.988717i	$-0.452138\pi$
$354$		0			0
$355$	1.04585	−	1.81147i	0.0555082	−	0.0961430i
$356$	−11.9877			−0.635348
$357$		0			0
$358$	0.373308	−	0.646588i	0.0197299	−	0.0341732i
$359$	11.5369			0.608895			0.304448	−	0.952529i	$-0.401528\pi$
$359$	11.5369			0.608895			0.304448	+	0.952529i	$0.401528\pi$
$360$		0			0
$361$	−2.85577	−	4.94634i	−0.150304	−	0.260334i
$362$	2.01333	+	3.48719i	0.105818	+	0.183283i
$363$		0			0
$364$	29.2462	+	4.48365i	1.53292	+	0.235007i
$365$	−5.53919			−0.289934
$366$		0			0
$367$	17.8148	+	30.8562i	0.929927	+	1.61068i	0.783439	+	0.621468i	$0.213464\pi$
$367$	17.8148	+	30.8562i	0.929927	+	1.61068i	0.146488	+	0.989213i	$0.453203\pi$
$368$	9.94214	−	17.2203i	0.518270	−	0.897670i
$369$		0			0
$370$	−0.722606	+	1.25159i	−0.0375665	+	0.0650671i
$371$	33.0277	−	57.2057i	1.71471	−	2.96997i
$372$		0			0
$373$	4.80571	−	8.32374i	0.248830	−	0.430987i	−0.714371	−	0.699767i	$-0.753287\pi$
$373$	4.80571	−	8.32374i	0.248830	−	0.430987i	0.963202	+	0.268780i	$0.0866205\pi$
$374$	2.65368	+	4.59632i	0.137219	+	0.237670i
$375$		0			0
$376$	−1.07838			−0.0556131
$377$	12.5103	+	1.91791i	0.644311	+	0.0987775i
$378$		0			0
$379$	−3.51139	−	6.08191i	−0.180368	−	0.312407i	0.761638	−	0.648003i	$-0.224396\pi$
$379$	−3.51139	−	6.08191i	−0.180368	−	0.312407i	−0.942006	+	0.335596i	$0.891062\pi$
$380$	4.24846	+	7.35856i	0.217942	+	0.377486i
$381$		0			0
$382$	1.29687			0.0663535
$383$	10.1067	−	17.5053i	0.516428	−	0.894480i	−0.483390	−	0.875405i	$-0.660595\pi$
$383$	10.1067	−	17.5053i	0.516428	−	0.894480i	0.999818	−	0.0190745i	$-0.00607197\pi$
$384$		0			0
$385$	−16.4124			−0.836454
$386$	4.26539	−	7.38787i	0.217103	−	0.376033i
$387$		0			0
$388$	−12.1948	−	21.1220i	−0.619098	−	1.07231i
$389$	15.7587			0.798999			0.399500	−	0.916733i	$-0.369184\pi$
$389$	15.7587			0.798999			0.399500	+	0.916733i	$0.369184\pi$
$390$		0			0
$391$	24.4657			1.23729
$392$	16.0494	+	27.7985i	0.810620	+	1.40403i
$393$		0			0
$394$	4.97826	−	8.62260i	0.250801	−	0.434400i
$395$	2.21235			0.111315
$396$		0			0
$397$	−5.67368	+	9.82710i	−0.284754	+	0.493208i	−0.972549	−	0.232696i	$-0.925245\pi$
$397$	−5.67368	+	9.82710i	−0.284754	+	0.493208i	0.687796	+	0.725904i	$0.258579\pi$
$398$	5.89988			0.295734
$399$		0			0
$400$	−1.17009	−	2.02665i	−0.0585043	−	0.101332i
$401$	13.3268	+	23.0828i	0.665511	+	1.15270i	0.979147	+	0.203155i	$0.0651196\pi$
$401$	13.3268	+	23.0828i	0.665511	+	1.15270i	−0.313636	+	0.949543i	$0.601547\pi$
$402$		0			0
$403$	−6.87690	+	8.57887i	−0.342563	+	0.427344i
$404$	21.3607			1.06273
$405$		0			0
$406$	4.54339	+	7.86939i	0.225485	+	0.390551i
$407$	−4.58145	+	7.93530i	−0.227094	+	0.393338i
$408$		0			0
$409$	15.4463	−	26.7539i	0.763773	−	1.32289i	−0.177120	−	0.984189i	$-0.556678\pi$
$409$	15.4463	−	26.7539i	0.763773	−	1.32289i	0.940893	−	0.338704i	$-0.109988\pi$
$410$	−1.01139	+	1.75178i	−0.0499491	+	0.0865145i
$411$		0			0
$412$	5.85464	−	10.1405i	0.288437	−	0.499588i
$413$	−20.1767	−	34.9470i	−0.992829	−	1.71963i
$414$		0			0
$415$	−4.34017			−0.213051
$416$	−6.88655	−	17.6777i	−0.337641	−	0.866719i
$417$		0			0
$418$	−4.58145	−	7.93530i	−0.224086	−	0.388128i
$419$	17.1581	+	29.7187i	0.838227	+	1.45185i	0.891376	+	0.453265i	$0.149741\pi$
$419$	17.1581	+	29.7187i	0.838227	+	1.45185i	−0.0531484	+	0.998587i	$0.516926\pi$
$420$		0			0
$421$	−13.5320			−0.659509			−0.329755	−	0.944067i	$-0.606966\pi$
$421$	−13.5320			−0.659509			−0.329755	+	0.944067i	$0.606966\pi$
$422$	3.82211	−	6.62010i	0.186058	−	0.322261i
$423$		0			0
$424$	−27.5174			−1.33637
$425$	1.43968	−	2.49360i	0.0698348	−	0.120957i
$426$		0			0
$427$	−7.32018	−	12.6789i	−0.354248	−	0.613576i
$428$	26.5958			1.28556
$429$		0			0
$430$	0.856576			0.0413077
$431$	7.63090	+	13.2171i	0.367567	+	0.636645i	0.989185	−	0.146676i	$-0.0468574\pi$
$431$	7.63090	+	13.2171i	0.367567	+	0.636645i	−0.621617	+	0.783321i	$0.713524\pi$
$432$		0			0
$433$	−1.93968	+	3.35963i	−0.0932151	+	0.161453i	−0.908862	−	0.417096i	$-0.863048\pi$
$433$	−1.93968	+	3.35963i	−0.0932151	+	0.161453i	0.815647	+	0.578550i	$0.196381\pi$
$434$	−7.89392			−0.378920
$435$		0			0
$436$	13.5350	−	23.4433i	0.648208	−	1.12273i
$437$	−42.2388			−2.02056
$438$		0			0
$439$	10.1556	+	17.5901i	0.484701	+	0.839527i	0.999846	−	0.0175761i	$-0.00559495\pi$
$439$	10.1556	+	17.5901i	0.484701	+	0.839527i	−0.515144	+	0.857104i	$0.672262\pi$
$440$	3.41855	+	5.92110i	0.162973	+	0.282278i
$441$		0			0
$442$	3.50113	−	4.36763i	0.166532	−	0.207747i
$443$	35.0772			1.66657			0.833283	−	0.552847i	$-0.186458\pi$
$443$	35.0772			1.66657			0.833283	+	0.552847i	$0.186458\pi$
$444$		0			0
$445$	−3.50667	−	6.07372i	−0.166232	−	0.287922i
$446$	1.52586	−	2.64286i	0.0722515	−	0.125143i
$447$		0			0
$448$	−4.42469	+	7.66379i	−0.209047	+	0.362080i
$449$	3.98667	−	6.90511i	0.188143	−	0.325872i	−0.756488	−	0.654007i	$-0.773087\pi$
$449$	3.98667	−	6.90511i	0.188143	−	0.325872i	0.944631	+	0.328135i	$0.106420\pi$
$450$		0			0
$451$	−6.41241	+	11.1066i	−0.301948	+	0.522990i
$452$	2.63090	+	4.55685i	0.123747	+	0.214336i
$453$		0			0
$454$	−11.2579			−0.528360
$455$	6.28345	+	16.1295i	0.294573	+	0.756163i
$456$		0			0
$457$	−1.30458	−	2.25960i	−0.0610256	−	0.105699i	0.833899	−	0.551918i	$-0.186104\pi$
$457$	−1.30458	−	2.25960i	−0.0610256	−	0.105699i	−0.894924	+	0.446218i	$0.852770\pi$
$458$	3.11450	+	5.39446i	0.145531	+	0.252067i
$459$		0			0
$460$	14.5236			0.677166
$461$	−15.0397	+	26.0495i	−0.700469	+	1.21325i	0.267833	+	0.963465i	$0.413693\pi$
$461$	−15.0397	+	26.0495i	−0.700469	+	1.21325i	−0.968302	+	0.249783i	$0.919641\pi$
$462$		0			0
$463$	−6.36788			−0.295940			−0.147970	−	0.988992i	$-0.547274\pi$
$463$	−6.36788			−0.295940			−0.147970	+	0.988992i	$0.547274\pi$
$464$	−4.10731	+	7.11406i	−0.190677	+	0.330262i
$465$		0			0
$466$	−1.00614	−	1.74269i	−0.0466087	−	0.0807286i
$467$	2.06892			0.0957383			0.0478692	−	0.998854i	$-0.484757\pi$
$467$	2.06892			0.0957383			0.0478692	+	0.998854i	$0.484757\pi$
$468$		0			0
$469$	61.6947			2.84880
$470$	−0.145362	−	0.251775i	−0.00670506	−	0.0116135i
$471$		0			0
$472$	−8.40522	+	14.5583i	−0.386882	+	0.670099i
$473$	5.43084			0.249710
$474$		0			0
$475$	−2.48554	+	4.30507i	−0.114044	+	0.197530i
$476$	−23.6286			−1.08302
$477$		0			0
$478$	7.30406	+	12.6510i	0.334080	+	0.578643i
$479$	5.75513	+	9.96818i	0.262959	+	0.455458i	0.967027	−	0.254675i	$-0.0819684\pi$
$479$	5.75513	+	9.96818i	0.262959	+	0.455458i	−0.704068	+	0.710132i	$0.748635\pi$
$480$		0			0
$481$	9.55252	+	1.46447i	0.435557	+	0.0667741i
$482$	−12.7238			−0.579555
$483$		0			0
$484$	0.586699	+	1.01619i	0.0266682	+	0.0461906i
$485$	7.13449	−	12.3573i	0.323961	−	0.561116i
$486$		0			0
$487$	−10.0742	+	17.4490i	−0.456504	+	0.790689i	−0.998773	−	0.0495162i	$-0.984232\pi$
$487$	−10.0742	+	17.4490i	−0.456504	+	0.790689i	0.542269	+	0.840205i	$0.317565\pi$
$488$	−3.04945	+	5.28180i	−0.138042	+	0.239096i
$489$		0			0
$490$	−4.32684	+	7.49431i	−0.195467	+	0.338558i
$491$	−10.9408	−	18.9500i	−0.493752	−	0.855204i	0.506222	−	0.862403i	$-0.331042\pi$
$491$	−10.9408	−	18.9500i	−0.493752	−	0.855204i	−0.999974	+	0.00719955i	$0.997708\pi$
$492$		0			0
$493$	−10.1073			−0.455210
$494$	−6.04453	+	7.54049i	−0.271956	+	0.339263i
$495$		0			0
$496$	−3.56812	−	6.18016i	−0.160213	−	0.277497i
$497$	−5.02113	−	8.69685i	−0.225228	−	0.390107i
$498$		0			0
$499$	−23.8225			−1.06644			−0.533222	−	0.845975i	$-0.679019\pi$
$499$	−23.8225			−1.06644			−0.533222	+	0.845975i	$0.679019\pi$
$500$	0.854638	−	1.48028i	0.0382206	−	0.0662000i
$501$		0			0
$502$	14.4846			0.646481
$503$	2.15449	−	3.73168i	0.0960639	−	0.166388i	−0.813988	−	0.580881i	$-0.802708\pi$
$503$	2.15449	−	3.73168i	0.0960639	−	0.166388i	0.910052	+	0.414494i	$0.136041\pi$
$504$		0			0
$505$	6.24846	+	10.8227i	0.278053	+	0.481602i
$506$	−15.6619			−0.696257
$507$		0			0
$508$	12.7421			0.565338
$509$	0.496928	+	0.860705i	0.0220260	+	0.0381501i	0.876828	−	0.480804i	$-0.159655\pi$
$509$	0.496928	+	0.860705i	0.0220260	+	0.0381501i	−0.854802	+	0.518954i	$0.826322\pi$
$510$		0			0
$511$	−13.2968	+	23.0307i	−0.588215	+	1.01882i
$512$	21.6742			0.957873
$513$		0			0
$514$	−0.948614	+	1.64305i	−0.0418416	+	0.0724717i
$515$	6.85043			0.301866
$516$		0			0
$517$	−0.921622	−	1.59630i	−0.0405329	−	0.0702050i
$518$	3.46922	+	6.00887i	0.152429	+	0.264015i
$519$		0			0
$520$	4.51026	−	5.62651i	0.197788	−	0.246739i
$521$	−9.75154			−0.427223			−0.213611	−	0.976919i	$-0.568523\pi$
$521$	−9.75154			−0.427223			−0.213611	+	0.976919i	$0.568523\pi$
$522$		0			0
$523$	5.51026	+	9.54405i	0.240947	+	0.417332i	0.960984	−	0.276603i	$-0.0892087\pi$
$523$	5.51026	+	9.54405i	0.240947	+	0.417332i	−0.720037	+	0.693935i	$0.755875\pi$
$524$	−9.99386	+	17.3099i	−0.436584	+	0.756185i
$525$		0			0
$526$	−2.38664	+	4.13378i	−0.104062	+	0.180241i
$527$	4.39023	−	7.60411i	0.191242	−	0.331240i
$528$		0			0
$529$	−24.5989	+	42.6065i	−1.06952	+	1.85246i
$530$	−3.70928	−	6.42465i	−0.161121	−	0.279069i
$531$		0			0
$532$	40.7936			1.76863
$533$	13.3701	+	2.04974i	0.579125	+	0.0887841i
$534$		0			0
$535$	7.77985	+	13.4751i	0.336352	+	0.582579i
$536$	−12.8504	−	22.2576i	−0.555054	−	0.961382i
$537$		0			0
$538$	−14.6888			−0.633277
$539$	−27.4329	+	47.5152i	−1.18162	+	2.04663i
$540$		0			0
$541$	−6.28846			−0.270362			−0.135181	−	0.990821i	$-0.543162\pi$
$541$	−6.28846			−0.270362			−0.135181	+	0.990821i	$0.543162\pi$
$542$	−3.73759	+	6.47370i	−0.160543	+	0.278069i
$543$		0			0
$544$	7.57531	+	13.1208i	0.324789	+	0.562550i
$545$	15.8371			0.678387
$546$		0			0
$547$	27.6875			1.18383			0.591917	−	0.805999i	$-0.298371\pi$
$547$	27.6875			1.18383			0.591917	+	0.805999i	$0.298371\pi$
$548$	7.92881	+	13.7331i	0.338702	+	0.586649i
$549$		0			0
$550$	−0.921622	+	1.59630i	−0.0392981	+	0.0680663i
$551$	17.4497			0.743384
$552$		0			0
$553$	5.31072	−	9.19844i	0.225835	−	0.391157i
$554$	1.39189			0.0591357
$555$		0			0
$556$	11.0381	+	19.1185i	0.468118	+	0.810804i
$557$	−10.7321	−	18.5885i	−0.454732	−	0.787619i	0.543941	−	0.839124i	$-0.316932\pi$
$557$	−10.7321	−	18.5885i	−0.454732	−	0.787619i	−0.998673	+	0.0515046i	$0.983598\pi$
$558$		0			0
$559$	−2.07918	−	5.33723i	−0.0879400	−	0.225741i
$560$	−11.2351			−0.474771
$561$		0			0
$562$	−1.44327	−	2.49983i	−0.0608809	−	0.105449i
$563$	−7.83710	+	13.5743i	−0.330294	+	0.572087i	−0.982570	−	0.185896i	$-0.940481\pi$
$563$	−7.83710	+	13.5743i	−0.330294	+	0.572087i	0.652275	+	0.757982i	$0.273815\pi$
$564$		0			0
$565$	−1.53919	+	2.66595i	−0.0647542	+	0.112157i
$566$	−4.28486	+	7.42160i	−0.180106	+	0.311953i
$567$		0			0
$568$	−2.09171	+	3.62295i	−0.0877661	+	0.152015i
$569$	8.21594	+	14.2304i	0.344430	+	0.596571i	0.985250	−	0.171121i	$-0.0547388\pi$
$569$	8.21594	+	14.2304i	0.344430	+	0.596571i	−0.640820	+	0.767691i	$0.721405\pi$
$570$		0			0
$571$	14.6765			0.614191			0.307096	−	0.951679i	$-0.400643\pi$
$571$	14.6765			0.614191			0.307096	+	0.951679i	$0.400643\pi$
$572$	13.1773	−	16.4385i	0.550970	−	0.687329i
$573$		0			0
$574$	4.85568	+	8.41029i	0.202672	+	0.351039i
$575$	4.24846	+	7.35856i	0.177173	+	0.306873i
$576$		0			0
$577$	−17.8622			−0.743611			−0.371806	−	0.928311i	$-0.621261\pi$
$577$	−17.8622			−0.743611			−0.371806	+	0.928311i	$0.621261\pi$
$578$	2.34797	−	4.06681i	0.0976628	−	0.169157i
$579$		0			0
$580$	−6.00000			−0.249136
$581$	−10.4186	+	18.0455i	−0.432234	+	0.748652i
$582$		0			0
$583$	−23.5174	−	40.7334i	−0.973993	−	1.68701i
$584$	11.0784			0.458427
$585$		0			0
$586$	1.33791			0.0552684
$587$	−2.21174	−	3.83084i	−0.0912881	−	0.158116i	0.816765	−	0.576970i	$-0.195765\pi$
$587$	−2.21174	−	3.83084i	−0.0912881	−	0.158116i	−0.908053	+	0.418854i	$0.862432\pi$
$588$		0			0
$589$	−7.57951	+	13.1281i	−0.312308	+	0.540934i
$590$	−4.53200			−0.186580
$591$		0			0
$592$	−3.13624	+	5.43212i	−0.128899	+	0.223259i
$593$	−12.5380			−0.514873			−0.257436	−	0.966295i	$-0.582878\pi$
$593$	−12.5380			−0.514873			−0.257436	+	0.966295i	$0.582878\pi$
$594$		0			0
$595$	−6.91189	−	11.9717i	−0.283360	−	0.490793i
$596$	1.70928	+	2.96055i	0.0700146	+	0.121269i
$597$		0			0
$598$	5.99612	+	15.3920i	0.245200	+	0.629424i
$599$	−23.5825			−0.963555			−0.481777	−	0.876294i	$-0.660009\pi$
$599$	−23.5825			−0.963555			−0.481777	+	0.876294i	$0.660009\pi$
$600$		0			0
$601$	−1.64229	−	2.84453i	−0.0669904	−	0.116031i	0.830585	−	0.556892i	$-0.188006\pi$
$601$	−1.64229	−	2.84453i	−0.0669904	−	0.116031i	−0.897575	+	0.440861i	$0.854673\pi$
$602$	2.05620	−	3.56145i	0.0838046	−	0.145154i
$603$		0			0
$604$	−7.35350	+	12.7366i	−0.299210	+	0.518247i
$605$	−0.343245	+	0.594517i	−0.0139549	+	0.0241706i
$606$		0			0
$607$	3.00421	−	5.20344i	0.121937	−	0.211201i	−0.798595	−	0.601869i	$-0.794423\pi$
$607$	3.00421	−	5.20344i	0.121937	−	0.211201i	0.920531	+	0.390668i	$0.127756\pi$
$608$	−13.0784	−	22.6524i	−0.530398	−	0.918677i
$609$		0			0
$610$	−1.64423			−0.0665729
$611$	−1.21594	+	1.51687i	−0.0491917	+	0.0613662i
$612$		0			0
$613$	2.76539	+	4.78979i	0.111693	+	0.193458i	0.916453	−	0.400142i	$-0.131039\pi$
$613$	2.76539	+	4.78979i	0.111693	+	0.193458i	−0.804760	+	0.593600i	$0.797706\pi$
$614$	5.99641	+	10.3861i	0.241995	+	0.419148i
$615$		0			0
$616$	32.8248			1.32255
$617$	5.94214	−	10.2921i	0.239222	−	0.414344i	−0.721270	−	0.692654i	$-0.756441\pi$
$617$	5.94214	−	10.2921i	0.239222	−	0.414344i	0.960491	+	0.278311i	$0.0897744\pi$
$618$		0			0
$619$	32.2183			1.29496			0.647482	−	0.762081i	$-0.275822\pi$
$619$	32.2183			1.29496			0.647482	+	0.762081i	$0.275822\pi$
$620$	2.60617	−	4.51402i	0.104666	−	0.181288i
$621$		0			0
$622$	−0.109245	−	0.189218i	−0.00438032	−	0.00758695i
$623$	−33.6709			−1.34900
$624$		0			0
$625$	1.00000			0.0400000
$626$	0.0953027	+	0.165069i	0.00380906	+	0.00659749i
$627$		0			0
$628$	0.776260	−	1.34452i	0.0309761	−	0.0536523i
$629$	−7.71769			−0.307724
$630$		0			0
$631$	9.87209	−	17.0990i	0.393002	−	0.680699i	−0.599842	−	0.800118i	$-0.704770\pi$
$631$	9.87209	−	17.0990i	0.393002	−	0.680699i	0.992844	+	0.119420i	$0.0381034\pi$
$632$	−4.42469			−0.176005
$633$		0			0
$634$	6.82150	+	11.8152i	0.270916	+	0.469241i
$635$	3.72733	+	6.45593i	0.147915	+	0.256196i
$636$		0			0
$637$	57.1988	+	8.76899i	2.26630	+	0.347440i
$638$	6.47027			0.256160
$639$		0			0
$640$	5.75872	+	9.97440i	0.227634	+	0.394273i
$641$	18.0566	−	31.2750i	0.713194	−	1.23529i	−0.250458	−	0.968128i	$-0.580581\pi$
$641$	18.0566	−	31.2750i	0.713194	−	1.23529i	0.963652	−	0.267161i	$-0.0860856\pi$
$642$		0			0
$643$	−19.5911	+	33.9328i	−0.772597	+	1.33818i	0.163537	+	0.986537i	$0.447710\pi$
$643$	−19.5911	+	33.9328i	−0.772597	+	1.33818i	−0.936135	+	0.351641i	$0.885624\pi$
$644$	34.8638	−	60.3858i	1.37382	−	2.37953i
$645$		0			0
$646$	3.85884	−	6.68371i	0.151824	−	0.262967i
$647$	−21.0856	−	36.5213i	−0.828959	−	1.43580i	−0.898856	−	0.438245i	$-0.855600\pi$
$647$	−21.0856	−	36.5213i	−0.828959	−	1.43580i	0.0698964	−	0.997554i	$-0.477733\pi$
$648$		0			0
$649$	−28.7337			−1.12790
$650$	1.92162	+	0.294598i	0.0753722	+	0.0115551i
$651$		0			0
$652$	−12.5155	−	21.6775i	−0.490145	−	0.848956i
$653$	−16.9233	−	29.3120i	−0.662259	−	1.14707i	−0.980021	−	0.198896i	$-0.936265\pi$
$653$	−16.9233	−	29.3120i	−0.662259	−	1.14707i	0.317762	−	0.948171i	$-0.397069\pi$
$654$		0			0
$655$	−11.6937			−0.456910
$656$	−4.38962	+	7.60305i	−0.171386	+	0.296849i
$657$		0			0
$658$	−1.39576			−0.0544126
$659$	−15.7659	+	27.3074i	−0.614153	+	1.06374i	0.376380	+	0.926465i	$0.377169\pi$
$659$	−15.7659	+	27.3074i	−0.614153	+	1.06374i	−0.990533	+	0.137278i	$0.956165\pi$
$660$		0			0
$661$	3.18876	+	5.52309i	0.124028	+	0.214823i	0.921353	−	0.388728i	$-0.127085\pi$
$661$	3.18876	+	5.52309i	0.124028	+	0.214823i	−0.797324	+	0.603551i	$0.793752\pi$
$662$	2.48133			0.0964396
$663$		0			0
$664$	8.68035			0.336863
$665$	11.9330	+	20.6686i	0.462742	+	0.801494i
$666$		0			0
$667$	14.9132	−	25.8304i	0.577442	−	1.00016i
$668$	−8.36683			−0.323723
$669$		0			0
$670$	3.46441	−	6.00053i	0.133842	−	0.231821i
$671$	−10.4247			−0.402441
$672$		0			0
$673$	−4.86130	−	8.42002i	−0.187389	−	0.324568i	0.756990	−	0.653427i	$-0.226669\pi$
$673$	−4.86130	−	8.42002i	−0.187389	−	0.324568i	−0.944379	+	0.328859i	$0.893336\pi$
$674$	8.36655	+	14.4913i	0.322268	+	0.558184i
$675$		0			0
$676$	−21.2001	−	6.65669i	−0.815387	−	0.256027i
$677$	10.0845			0.387580			0.193790	−	0.981043i	$-0.437922\pi$
$677$	10.0845			0.387580			0.193790	+	0.981043i	$0.437922\pi$
$678$		0			0
$679$	−34.2526	−	59.3272i	−1.31449	−	2.27677i
$680$	−2.87936	+	4.98720i	−0.110418	+	0.191250i
$681$		0			0
$682$	−2.81044	+	4.86782i	−0.107617	+	0.186399i
$683$	−3.36849	+	5.83440i	−0.128892	+	0.223247i	−0.923247	−	0.384206i	$-0.874475\pi$
$683$	−3.36849	+	5.83440i	−0.128892	+	0.223247i	0.794356	+	0.607453i	$0.207809\pi$
$684$		0			0
$685$	−4.63870	+	8.03446i	−0.177235	+	0.306981i
$686$	11.7129	+	20.2873i	0.447199	+	0.774572i
$687$		0			0
$688$	3.71769			0.141735
$689$	−31.0277	+	38.7068i	−1.18206	+	1.47461i
$690$		0			0
$691$	8.97220	+	15.5403i	0.341319	+	0.591181i	0.984678	−	0.174383i	$-0.0557931\pi$
$691$	8.97220	+	15.5403i	0.341319	+	0.591181i	−0.643359	+	0.765565i	$0.722460\pi$
$692$	15.0072	+	25.9932i	0.570488	+	0.988114i
$693$		0			0
$694$	9.68195			0.367522
$695$	−6.45774	+	11.1851i	−0.244956	+	0.424276i
$696$		0			0
$697$	−10.8020			−0.409156
$698$	−0.0272733	+	0.0472387i	−0.00103231	+	0.00178801i
$699$		0			0
$700$	−4.10310	−	7.10678i	−0.155083	−	0.268611i
$701$	−41.2762			−1.55898			−0.779490	−	0.626415i	$-0.784522\pi$
$701$	−41.2762			−1.55898			−0.779490	+	0.626415i	$0.784522\pi$
$702$		0			0
$703$	13.3242			0.502531
$704$	3.15061	+	5.45702i	0.118743	+	0.205669i
$705$		0			0
$706$	−7.91548	+	13.7100i	−0.297903	+	0.515983i
$707$	59.9976			2.25644
$708$		0			0
$709$	−0.732866	+	1.26936i	−0.0275234	+	0.0476718i	−0.879459	−	0.475975i	$-0.842095\pi$
$709$	−0.732866	+	1.26936i	−0.0275234	+	0.0476718i	0.851936	+	0.523647i	$0.175429\pi$
$710$	−1.12783			−0.0423266
$711$		0			0
$712$	7.01333	+	12.1474i	0.262836	+	0.455245i
$713$	12.9555	+	22.4395i	0.485186	+	0.840367i
$714$		0			0
$715$	12.1834	+	1.86781i	0.455634	+	0.0698519i
$716$	2.36683			0.0884528
$717$		0			0
$718$	−3.11029	−	5.38718i	−0.116075	−	0.201048i
$719$	−4.80685	+	8.32570i	−0.179265	+	0.310496i	−0.941629	−	0.336652i	$-0.890705\pi$
$719$	−4.80685	+	8.32570i	−0.179265	+	0.310496i	0.762364	+	0.647149i	$0.224039\pi$
$720$		0			0
$721$	16.4444	−	28.4826i	0.612422	−	1.06075i
$722$	−1.53980	+	2.66701i	−0.0573054	+	0.0992559i
$723$		0			0
$724$	−6.38243	+	11.0547i	−0.237201	+	0.410845i
$725$	−1.75513	−	3.03997i	−0.0651839	−	0.112902i
$726$		0			0
$727$	−42.6547			−1.58198			−0.790988	−	0.611831i	$-0.790433\pi$
$727$	−42.6547			−1.58198			−0.790988	+	0.611831i	$0.790433\pi$
$728$	−12.5669	−	32.2590i	−0.465760	−	1.19560i
$729$		0			0
$730$	1.49333	+	2.58653i	0.0552708	+	0.0957318i
$731$	2.28713	+	3.96143i	0.0845926	+	0.146519i
$732$		0			0
$733$	−6.48360			−0.239477			−0.119739	−	0.992805i	$-0.538206\pi$
$733$	−6.48360			−0.239477			−0.119739	+	0.992805i	$0.538206\pi$
$734$	9.60556	−	16.6373i	0.354548	−	0.614095i
$735$		0			0
$736$	−44.7091			−1.64800
$737$	21.9649	−	38.0444i	0.809089	−	1.40138i
$738$		0			0
$739$	21.1845	+	36.6926i	0.779283	+	1.34976i	0.932355	+	0.361543i	$0.117750\pi$
$739$	21.1845	+	36.6926i	0.779283	+	1.34976i	−0.153072	+	0.988215i	$0.548917\pi$
$740$	−4.58145			−0.168417
$741$		0			0
$742$	−35.6163			−1.30752
$743$	−8.71481	−	15.0945i	−0.319715	−	0.553763i	0.660713	−	0.750638i	$-0.270254\pi$
$743$	−8.71481	−	15.0945i	−0.319715	−	0.553763i	−0.980429	+	0.196875i	$0.936921\pi$
$744$		0			0
$745$	−1.00000	+	1.73205i	−0.0366372	+	0.0634574i
$746$	−5.18237			−0.189740
$747$		0			0
$748$	−8.41241	+	14.5707i	−0.307588	+	0.532758i
$749$	74.7019			2.72955
$750$		0			0
$751$	−6.68455	−	11.5780i	−0.243923	−	0.422487i	0.717905	−	0.696141i	$-0.245101\pi$
$751$	−6.68455	−	11.5780i	−0.243923	−	0.422487i	−0.961828	+	0.273654i	$0.911768\pi$
$752$	−0.630898	−	1.09275i	−0.0230065	−	0.0398484i
$753$		0			0
$754$	−2.47712	−	6.35874i	−0.0902116	−	0.231572i
$755$	−8.60424			−0.313140
$756$		0			0
$757$	−13.8462	−	23.9824i	−0.503250	−	0.871654i	−0.999993	−	0.00375649i	$-0.998804\pi$
$757$	−13.8462	−	23.9824i	−0.503250	−	0.871654i	0.496743	−	0.867898i	$-0.334529\pi$
$758$	−1.89330	+	3.27930i	−0.0687679	+	0.119110i
$759$		0			0
$760$	4.97107	−	8.61015i	0.180320	−	0.312323i
$761$	−0.261795	+	0.453443i	−0.00949007	+	0.0164373i	−0.870731	−	0.491759i	$-0.836354\pi$
$761$	−0.261795	+	0.453443i	−0.00949007	+	0.0164373i	0.861241	+	0.508196i	$0.169687\pi$
$762$		0			0
$763$	38.0168	−	65.8471i	1.37630	−	2.38382i
$764$	2.05559	+	3.56039i	0.0743687	+	0.128810i
$765$		0			0
$766$	−10.8988			−0.393791
$767$	11.0006	+	28.2384i	0.397209	+	1.01963i
$768$		0			0
$769$	7.08032	+	12.2635i	0.255323	+	0.442232i	0.964983	−	0.262312i	$-0.0844850\pi$
$769$	7.08032	+	12.2635i	0.255323	+	0.442232i	−0.709660	+	0.704544i	$0.751152\pi$
$770$	4.42469	+	7.66379i	0.159455	+	0.276184i
$771$		0			0
$772$	27.0433			0.973310
$773$	13.7093	−	23.7452i	0.493088	−	0.854054i	−0.506880	−	0.862017i	$-0.669201\pi$
$773$	13.7093	−	23.7452i	0.493088	−	0.854054i	0.999968	+	0.00796257i	$0.00253459\pi$
$774$		0			0
$775$	3.04945			0.109539
$776$	−14.2690	+	24.7146i	−0.512227	+	0.887203i
$777$		0			0
$778$	−4.24846	−	7.35856i	−0.152315	−	0.263817i
$779$	18.6491			0.668175
$780$		0			0
$781$	−7.15061			−0.255869
$782$	−6.59583	−	11.4243i	−0.235866	−	0.408532i
$783$		0			0
$784$	−18.7792	+	32.5266i	−0.670687	+	1.16166i
$785$	0.908291			0.0324183
$786$		0			0
$787$	−10.6851	+	18.5071i	−0.380882	+	0.659707i	−0.991189	−	0.132459i	$-0.957713\pi$
$787$	−10.6851	+	18.5071i	−0.380882	+	0.659707i	0.610307	+	0.792165i	$0.291046\pi$
$788$	31.5630			1.12439
$789$		0			0
$790$	−0.596436	−	1.03306i	−0.0212203	−	0.0367546i
$791$	7.38962	+	12.7992i	0.262745	+	0.455087i
$792$		0			0
$793$	3.99107	+	10.2450i	0.141727	+	0.363811i
$794$	6.11837			0.217133
$795$		0			0
$796$	9.35157	+	16.1974i	0.331457	+	0.574101i
$797$	1.94275	−	3.36495i	0.0688158	−	0.119193i	−0.829564	−	0.558411i	$-0.811411\pi$
$797$	1.94275	−	3.36495i	0.0688158	−	0.119193i	0.898380	+	0.439218i	$0.144745\pi$
$798$		0			0
$799$	0.776260	−	1.34452i	0.0274621	−	0.0475658i
$800$	−2.63090	+	4.55685i	−0.0930163	+	0.161109i
$801$		0			0
$802$	7.18568	−	12.4460i	0.253735	−	0.439483i
$803$	9.46800	+	16.3991i	0.334118	+	0.578710i
$804$		0			0
$805$	40.7936			1.43779
$806$	5.85989	+	0.898363i	0.206406	+	0.0316435i
$807$		0			0
$808$	−12.4969	−	21.6453i	−0.439640	−	0.761480i
$809$	−25.4524	−	44.0849i	−0.894859	−	1.54994i	−0.833979	−	0.551796i	$-0.813943\pi$
$809$	−25.4524	−	44.0849i	−0.894859	−	1.54994i	−0.0608794	−	0.998145i	$-0.519391\pi$
$810$		0			0
$811$	−42.5174			−1.49299			−0.746495	−	0.665391i	$-0.768265\pi$
$811$	−42.5174			−1.49299			−0.746495	+	0.665391i	$0.768265\pi$
$812$	−14.4030	+	24.9466i	−0.505445	+	0.875456i
$813$		0			0
$814$	4.94053			0.173166
$815$	7.32211	−	12.6823i	0.256482	−	0.444241i
$816$		0			0
$817$	−3.94861	−	6.83920i	−0.138145	−	0.239273i
$818$	−16.6570			−0.582398
$819$		0			0
$820$	−6.41241			−0.223931
$821$	−1.99773	−	3.46017i	−0.0697213	−	0.120761i	0.829057	−	0.559164i	$-0.188878\pi$
$821$	−1.99773	−	3.46017i	−0.0697213	−	0.120761i	−0.898779	+	0.438403i	$0.855544\pi$
$822$		0			0
$823$	0.787653	−	1.36426i	0.0274559	−	0.0475549i	−0.851971	−	0.523589i	$-0.824593\pi$
$823$	0.787653	−	1.36426i	0.0274559	−	0.0475549i	0.879427	+	0.476034i	$0.157926\pi$
$824$	−13.7009			−0.477292
$825$		0			0
$826$	−10.8790	+	18.8430i	−0.378530	+	0.655633i
$827$	−9.17850			−0.319168			−0.159584	−	0.987184i	$-0.551015\pi$
$827$	−9.17850			−0.319168			−0.159584	+	0.987184i	$0.551015\pi$
$828$		0			0
$829$	−24.7358	−	42.8437i	−0.859112	−	1.48802i	−0.872778	−	0.488118i	$-0.837683\pi$
$829$	−24.7358	−	42.8437i	−0.859112	−	1.48802i	0.0136660	−	0.999907i	$-0.495650\pi$
$830$	1.17009	+	2.02665i	0.0406143	+	0.0703460i
$831$		0			0
$832$	4.15676	−	5.18551i	0.144110	−	0.179775i
$833$	−46.2122			−1.60116
$834$		0			0
$835$	−2.44748	−	4.23916i	−0.0846985	−	0.146702i
$836$	14.5236	−	25.1556i	0.502309	−	0.870024i
$837$		0			0
$838$	9.25145	−	16.0240i	0.319586	−	0.553539i
$839$	4.64650	−	8.04797i	0.160415	−	0.277847i	−0.774603	−	0.632448i	$-0.782050\pi$
$839$	4.64650	−	8.04797i	0.160415	−	0.277847i	0.935018	+	0.354601i	$0.115383\pi$
$840$		0			0
$841$	8.33904	−	14.4436i	0.287553	−	0.498057i
$842$	3.64815	+	6.31878i	0.125724	+	0.217760i
$843$		0			0
$844$	24.2329			0.834130
$845$	−2.82878	−	12.6885i	−0.0973130	−	0.436498i
$846$		0			0
$847$	1.64791	+	2.85427i	0.0566229	+	0.0980738i
$848$	−16.0989	−	27.8841i	−0.552838	−	0.957544i
$849$		0			0
$850$	−1.55252			−0.0532510
$851$	11.3874	−	19.7235i	0.390353	−	0.676112i
$852$		0			0
$853$	−11.0423			−0.378080			−0.189040	−	0.981969i	$-0.560538\pi$
$853$	−11.0423			−0.378080			−0.189040	+	0.981969i	$0.560538\pi$
$854$	−3.94696	+	6.83633i	−0.135062	+	0.233934i
$855$		0			0
$856$	−15.5597	−	26.9502i	−0.531820	−	0.921139i
$857$	8.58476			0.293250			0.146625	−	0.989192i	$-0.453159\pi$
$857$	8.58476			0.293250			0.146625	+	0.989192i	$0.453159\pi$
$858$		0			0
$859$	−46.6202			−1.59066			−0.795331	−	0.606176i	$-0.792703\pi$
$859$	−46.6202			−1.59066			−0.795331	+	0.606176i	$0.792703\pi$
$860$	1.35771	+	2.35162i	0.0462975	+	0.0801896i
$861$		0			0
$862$	4.11450	−	7.12651i	0.140140	−	0.242730i
$863$	−10.6947			−0.364053			−0.182026	−	0.983294i	$-0.558266\pi$
$863$	−10.6947			−0.364053			−0.182026	+	0.983294i	$0.558266\pi$
$864$		0			0
$865$	−8.77985	+	15.2072i	−0.298524	+	0.517059i
$866$	2.09171			0.0710792
$867$		0			0
$868$	−12.5122	−	21.6718i	−0.424692	−	0.735588i
$869$	−3.78151	−	6.54977i	−0.128279	−	0.222186i
$870$		0			0
$871$	−45.7978	−	7.02113i	−1.55180	−	0.237902i
$872$	−31.6742			−1.07262
$873$		0			0
$874$	11.3874	+	19.7235i	0.385183	+	0.667157i
$875$	2.40049	−	4.15777i	0.0811514	−	0.140558i
$876$		0			0
$877$	5.29791	−	9.17625i	0.178898	−	0.309860i	−0.762605	−	0.646864i	$-0.776080\pi$
$877$	5.29791	−	9.17625i	0.178898	−	0.309860i	0.941503	+	0.337004i	$0.109414\pi$
$878$	5.47580	−	9.48436i	0.184799	−	0.320082i
$879$		0			0
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	−8.11450	−	14.0547i	−0.273384	−	0.473515i	0.696342	−	0.717710i	$-0.254810\pi$
$881$	−8.11450	−	14.0547i	−0.273384	−	0.473515i	−0.969726	+	0.244195i	$0.921476\pi$
$882$		0			0
$883$	12.6137			0.424484			0.212242	−	0.977217i	$-0.431923\pi$
$883$	12.6137			0.424484			0.212242	+	0.977217i	$0.431923\pi$
$884$	17.5402	+	2.68904i	0.589942	+	0.0904423i
$885$		0			0
$886$	−9.45661	−	16.3793i	−0.317701	−	0.550274i
$887$	−6.69533	−	11.5967i	−0.224807	−	0.389378i	0.731454	−	0.681890i	$-0.238842\pi$
$887$	−6.69533	−	11.5967i	−0.224807	−	0.389378i	−0.956262	+	0.292513i	$0.905509\pi$
$888$		0			0
$889$	35.7897			1.20035
$890$	−1.89076	+	3.27488i	−0.0633783	+	0.109774i
$891$		0			0
$892$	9.67420			0.323916
$893$	−1.34017	+	2.32125i	−0.0448472	+	0.0776776i
$894$		0			0
$895$	0.692350	+	1.19919i	0.0231427	+	0.0400844i
$896$	55.2951			1.84728
$897$		0			0
$898$	−4.29914			−0.143464
$899$	−5.35218	−	9.27024i	−0.178505	−	0.309180i
$900$		0			0
$901$	19.8082	−	34.3088i	0.659906	−	1.14299i
$902$	6.91500			0.230244
$903$		0			0
$904$	3.07838	−	5.33191i	0.102385	−	0.177337i
$905$	−7.46800			−0.248245
$906$		0			0
$907$	23.1526	+	40.1014i	0.768768	+	1.33154i	0.938231	+	0.346008i	$0.112463\pi$
$907$	23.1526	+	40.1014i	0.768768	+	1.33154i	−0.169464	+	0.985536i	$0.554204\pi$
$908$	−17.8443	−	30.9072i	−0.592184	−	1.02569i
$909$		0			0
$910$	5.83771	−	7.28249i	0.193518	−	0.241412i
$911$	40.6947			1.34828			0.674138	−	0.738605i	$-0.264515\pi$
$911$	40.6947			1.34828			0.674138	+	0.738605i	$0.264515\pi$
$912$		0			0
$913$	7.41855	+	12.8493i	0.245518	+	0.425250i
$914$	−0.703414	+	1.21835i	−0.0232669	+	0.0402994i
$915$		0			0
$916$	−9.87322	+	17.1009i	−0.326220	+	0.565030i
$917$	−28.0706	+	48.6197i	−0.926972	+	1.60556i
$918$		0			0
$919$	22.2937	−	38.6138i	0.735402	−	1.27375i	−0.219145	−	0.975692i	$-0.570327\pi$
$919$	22.2937	−	38.6138i	0.735402	−	1.27375i	0.954547	−	0.298061i	$-0.0963398\pi$
$920$	−8.49693	−	14.7171i	−0.280135	−	0.485209i
$921$		0			0
$922$	16.2185			0.534128
$923$	2.73759	+	7.02736i	0.0901090	+	0.231308i
$924$		0			0
$925$	−1.34017	−	2.32125i	−0.0440646	−	0.0763222i
$926$	1.71674	+	2.97349i	0.0564157	+	0.0977149i
$927$		0			0
$928$	18.4703			0.606316
$929$	14.4885	−	25.0948i	0.475353	−	0.823335i	−0.524249	−	0.851565i	$-0.675654\pi$
$929$	14.4885	−	25.0948i	0.475353	−	0.823335i	0.999601	+	0.0282300i	$0.00898707\pi$
$930$		0			0
$931$	79.7829			2.61478
$932$	3.18956	−	5.52448i	0.104478	−	0.180960i
$933$		0			0
$934$	−0.557770	−	0.966086i	−0.0182508	−	0.0316113i
$935$	−9.84324			−0.321909
$936$		0			0
$937$	−53.1871			−1.73755			−0.868774	−	0.495209i	$-0.835091\pi$
$937$	−53.1871			−1.73755			−0.868774	+	0.495209i	$0.835091\pi$
$938$	−16.6326	−	28.8084i	−0.543072	−	0.940629i
$939$		0			0
$940$	0.460811	−	0.798148i	0.0150300	−	0.0260327i
$941$	−26.3617			−0.859368			−0.429684	−	0.902979i	$-0.641375\pi$
$941$	−26.3617			−0.859368			−0.429684	+	0.902979i	$0.641375\pi$
$942$		0			0
$943$	15.9383	−	27.6059i	0.519021	−	0.898971i
$944$	−19.6697			−0.640193
$945$		0			0
$946$	−1.46412	−	2.53594i	−0.0476028	−	0.0824504i
$947$	−25.3890	−	43.9751i	−0.825032	−	1.42900i	−0.901895	−	0.431956i	$-0.857824\pi$
$947$	−25.3890	−	43.9751i	−0.825032	−	1.42900i	0.0768629	−	0.997042i	$-0.475510\pi$
$948$		0			0
$949$	12.4916	−	15.5831i	0.405494	−	0.505850i
$950$	2.68035			0.0869619
$951$		0			0
$952$	13.8238	+	23.9435i	0.448031	+	0.776012i
$953$	−10.4163	+	18.0415i	−0.337417	+	0.584423i	−0.983946	−	0.178466i	$-0.942886\pi$
$953$	−10.4163	+	18.0415i	−0.337417	+	0.584423i	0.646529	+	0.762889i	$0.276220\pi$
$954$		0			0
$955$	−1.20261	+	2.08298i	−0.0389155	+	0.0674037i
$956$	−23.1545	+	40.1047i	−0.748870	+	1.29708i
$957$		0			0
$958$	3.10310	−	5.37473i	0.100257	−	0.173650i
$959$	22.2703	+	38.5733i	0.719146	+	1.24560i
$960$		0			0
$961$	−21.7009			−0.700028
$962$	−1.89147	−	4.85537i	−0.0609834	−	0.156544i
$963$		0			0
$964$	−20.1678	−	34.9317i	−0.649562	−	1.12507i
$965$	7.91075	+	13.7018i	0.254656	+	0.441077i
$966$		0			0
$967$	−5.92777			−0.190624			−0.0953120	−	0.995447i	$-0.530385\pi$
$967$	−5.92777			−0.190624			−0.0953120	+	0.995447i	$0.530385\pi$
$968$	0.686489	−	1.18903i	0.0220646	−	0.0382170i
$969$		0			0
$970$	−7.69368			−0.247029
$971$	5.24846	−	9.09061i	0.168431	−	0.291731i	−0.769437	−	0.638722i	$-0.779463\pi$
$971$	5.24846	−	9.09061i	0.168431	−	0.291731i	0.937868	+	0.346991i	$0.112797\pi$
$972$		0			0
$973$	31.0035	+	53.6996i	0.993927	+	1.72153i
$974$	10.8638			0.348097
$975$		0			0
$976$	−7.13624			−0.228425
$977$	26.6609	+	46.1780i	0.852957	+	1.47736i	0.878528	+	0.477692i	$0.158526\pi$
$977$	26.6609	+	46.1780i	0.852957	+	1.47736i	−0.0255707	+	0.999673i	$0.508140\pi$
$978$		0			0
$979$	−11.9877	+	20.7633i	−0.383129	+	0.663599i
$980$	−27.4329			−0.876313
$981$		0			0
$982$	−5.89917	+	10.2177i	−0.188250	+	0.326058i
$983$	−21.7275			−0.693000			−0.346500	−	0.938050i	$-0.612630\pi$
$983$	−21.7275			−0.693000			−0.346500	+	0.938050i	$0.612630\pi$
$984$		0			0
$985$	9.23287	+	15.9918i	0.294184	+	0.509541i
$986$	2.72487	+	4.71962i	0.0867777	+	0.150303i
$987$		0			0
$988$	−30.2823	−	4.64250i	−0.963409	−	0.147697i
$989$	−13.4985			−0.429228
$990$		0			0
$991$	4.37823	+	7.58331i	0.139079	+	0.240892i	0.927148	−	0.374695i	$-0.122252\pi$
$991$	4.37823	+	7.58331i	0.139079	+	0.240892i	−0.788069	+	0.615587i	$0.788919\pi$
$992$	−8.02279	+	13.8959i	−0.254724	+	0.441194i
$993$		0			0
$994$	−2.70734	+	4.68925i	−0.0858715	+	0.148734i
$995$	−5.47107	+	9.47617i	−0.173445	+	0.300415i
$996$		0			0
$997$	−1.72960	+	2.99576i	−0.0547770	+	0.0948766i	−0.892114	−	0.451811i	$-0.850778\pi$
$997$	−1.72960	+	2.99576i	−0.0547770	+	0.0948766i	0.837337	+	0.546688i	$0.184111\pi$
$998$	6.42243	+	11.1240i	0.203298	+	0.352123i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.j.g.406.2		6
3.2	odd	2		195.2.i.e.16.2	✓	6
13.3	even	3		7605.2.a.bu.1.2		3
13.9	even	3	inner	585.2.j.g.451.2		6
13.10	even	6		7605.2.a.bt.1.2		3
15.2	even	4		975.2.bb.j.874.3		12
15.8	even	4		975.2.bb.j.874.4		12
15.14	odd	2		975.2.i.m.601.2		6
39.23	odd	6		2535.2.a.z.1.2		3
39.29	odd	6		2535.2.a.y.1.2		3
39.35	odd	6		195.2.i.e.61.2	yes	6
195.74	odd	6		975.2.i.m.451.2		6
195.113	even	12		975.2.bb.j.724.3		12
195.152	even	12		975.2.bb.j.724.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.i.e.16.2	✓	6	3.2	odd	2
195.2.i.e.61.2	yes	6	39.35	odd	6
585.2.j.g.406.2		6	1.1	even	1	trivial
585.2.j.g.451.2		6	13.9	even	3	inner
975.2.i.m.451.2		6	195.74	odd	6
975.2.i.m.601.2		6	15.14	odd	2
975.2.bb.j.724.3		12	195.113	even	12
975.2.bb.j.724.4		12	195.152	even	12
975.2.bb.j.874.3		12	15.2	even	4
975.2.bb.j.874.4		12	15.8	even	4
2535.2.a.y.1.2		3	39.29	odd	6
2535.2.a.z.1.2		3	39.23	odd	6
7605.2.a.bt.1.2		3	13.10	even	6
7605.2.a.bu.1.2		3	13.3	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.269594 - 0.466951i) q^{2} +(0.854638 - 1.48028i) q^{4} +1.00000 q^{5} +(2.40049 - 4.15777i) q^{7} -2.00000 q^{8} +O(q^{10})\)	\(q+(-0.269594 - 0.466951i) q^{2} +(0.854638 - 1.48028i) q^{4} +1.00000 q^{5} +(2.40049 - 4.15777i) q^{7} -2.00000 q^{8} +(-0.269594 - 0.466951i) q^{10} +(-1.70928 - 2.96055i) q^{11} +(-2.25513 + 2.81325i) q^{13} -2.58864 q^{14} +(-1.17009 - 2.02665i) q^{16} +(1.43968 - 2.49360i) q^{17} +(-2.48554 + 4.30507i) q^{19} +(0.854638 - 1.48028i) q^{20} +(-0.921622 + 1.59630i) q^{22} +(4.24846 + 7.35856i) q^{23} +1.00000 q^{25} +(1.92162 + 0.294598i) q^{26} +(-4.10310 - 7.10678i) q^{28} +(-1.75513 - 3.03997i) q^{29} +3.04945 q^{31} +(-2.63090 + 4.55685i) q^{32} -1.55252 q^{34} +(2.40049 - 4.15777i) q^{35} +(-1.34017 - 2.32125i) q^{37} +2.68035 q^{38} -2.00000 q^{40} +(-1.87577 - 3.24893i) q^{41} +(-0.794319 + 1.37580i) q^{43} -5.84324 q^{44} +(2.29072 - 3.96765i) q^{46} +0.539189 q^{47} +(-8.02472 - 13.8992i) q^{49} +(-0.269594 - 0.466951i) q^{50} +(2.23707 + 5.74253i) q^{52} +13.7587 q^{53} +(-1.70928 - 2.96055i) q^{55} +(-4.80098 + 8.31555i) q^{56} +(-0.946346 + 1.63912i) q^{58} +(4.20261 - 7.27913i) q^{59} +(1.52472 - 2.64090i) q^{61} +(-0.822114 - 1.42394i) q^{62} -1.84324 q^{64} +(-2.25513 + 2.81325i) q^{65} +(6.42522 + 11.1288i) q^{67} +(-2.46081 - 4.26225i) q^{68} -2.58864 q^{70} +(1.04585 - 1.81147i) q^{71} -5.53919 q^{73} +(-0.722606 + 1.25159i) q^{74} +(4.24846 + 7.35856i) q^{76} -16.4124 q^{77} +2.21235 q^{79} +(-1.17009 - 2.02665i) q^{80} +(-1.01139 + 1.75178i) q^{82} -4.34017 q^{83} +(1.43968 - 2.49360i) q^{85} +0.856576 q^{86} +(3.41855 + 5.92110i) q^{88} +(-3.50667 - 6.07372i) q^{89} +(6.28345 + 16.1295i) q^{91} +14.5236 q^{92} +(-0.145362 - 0.251775i) q^{94} +(-2.48554 + 4.30507i) q^{95} +(7.13449 - 12.3573i) q^{97} +(-4.32684 + 7.49431i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{4} + 6 q^{5} + 5 q^{7} - 12 q^{8}+O(q^{10}) \) 6 * q - 2 * q^4 + 6 * q^5 + 5 * q^7 - 12 * q^8	\( 6 q - 2 q^{4} + 6 q^{5} + 5 q^{7} - 12 q^{8} + 4 q^{11} + 3 q^{13} + 24 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{20} - 12 q^{22} + 8 q^{23} + 6 q^{25} + 18 q^{26} + 6 q^{29} - 18 q^{31} - 8 q^{32} - 8 q^{34} + 5 q^{35} + 14 q^{37} - 28 q^{38} - 12 q^{40} - 20 q^{41} + 15 q^{43} - 48 q^{44} + 28 q^{46} - 30 q^{49} + 16 q^{52} + 32 q^{53} + 4 q^{55} - 10 q^{56} + 6 q^{58} + 10 q^{59} - 9 q^{61} - 2 q^{62} - 24 q^{64} + 3 q^{65} + 11 q^{67} - 18 q^{68} + 24 q^{70} + 4 q^{71} - 30 q^{73} + 8 q^{74} + 8 q^{76} + 34 q^{79} + 4 q^{80} + 14 q^{82} - 4 q^{83} - 4 q^{85} + 20 q^{86} - 8 q^{88} - 22 q^{89} - 31 q^{91} + 56 q^{92} - 8 q^{94} + q^{97} - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^4 + 6 * q^5 + 5 * q^7 - 12 * q^8 + 4 * q^11 + 3 * q^13 + 24 * q^14 + 4 * q^16 - 4 * q^17 - 2 * q^20 - 12 * q^22 + 8 * q^23 + 6 * q^25 + 18 * q^26 + 6 * q^29 - 18 * q^31 - 8 * q^32 - 8 * q^34 + 5 * q^35 + 14 * q^37 - 28 * q^38 - 12 * q^40 - 20 * q^41 + 15 * q^43 - 48 * q^44 + 28 * q^46 - 30 * q^49 + 16 * q^52 + 32 * q^53 + 4 * q^55 - 10 * q^56 + 6 * q^58 + 10 * q^59 - 9 * q^61 - 2 * q^62 - 24 * q^64 + 3 * q^65 + 11 * q^67 - 18 * q^68 + 24 * q^70 + 4 * q^71 - 30 * q^73 + 8 * q^74 + 8 * q^76 + 34 * q^79 + 4 * q^80 + 14 * q^82 - 4 * q^83 - 4 * q^85 + 20 * q^86 - 8 * q^88 - 22 * q^89 - 31 * q^91 + 56 * q^92 - 8 * q^94 + q^97 - 2 * q^98

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