LMFDB - Embedded newform 592.2.bq.d.65.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(65,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("592.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bq (of order $18$, degree $6$, 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:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 30x^{16} + 333x^{14} + 1826x^{12} + 5490x^{10} + 9432x^{8} + 9385x^{6} + 5316x^{4} + 1584x^{2} + 192 $ x^18 + 30x^16 + 333x^14 + 1826x^12 + 5490x^10 + 9432x^8 + 9385x^6 + 5316x^4 + 1584x^2 + 192
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			65.1
Root			$-0.660907i$ of defining polynomial
Character	$\chi$	$=$	592.65
Dual form			592.2.bq.d.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.354362 + 2.00969i) q^{3} +(0.640888 - 0.763781i) q^{5} +(1.58572 + 1.33057i) q^{7} +(-1.09419 - 0.398252i) q^{9} +O(q^{10})$	\(q+(-0.354362 + 2.00969i) q^{3} +(0.640888 - 0.763781i) q^{5} +(1.58572 + 1.33057i) q^{7} +(-1.09419 - 0.398252i) q^{9} +(-0.884822 - 1.53256i) q^{11} +(1.83841 + 5.05098i) q^{13} +(1.30785 + 1.55864i) q^{15} +(0.448257 - 1.23158i) q^{17} +(4.12204 + 0.726826i) q^{19} +(-3.23595 + 2.71529i) q^{21} +(-3.05179 - 1.76195i) q^{23} +(0.695618 + 3.94504i) q^{25} +(-1.87293 + 3.24402i) q^{27} +(-0.525410 + 0.303345i) q^{29} -1.55107i q^{31} +(3.39351 - 1.23514i) q^{33} +(2.03253 - 0.358390i) q^{35} +(-6.03673 + 0.746918i) q^{37} +(-10.8023 + 1.90475i) q^{39} +(2.15024 - 0.782625i) q^{41} +8.37985i q^{43} +(-1.00543 + 0.580485i) q^{45} +(1.79110 - 3.10228i) q^{47} +(-0.471469 - 2.67384i) q^{49} +(2.31624 + 1.33728i) q^{51} +(-8.47562 + 7.11189i) q^{53} +(-1.73761 - 0.306387i) q^{55} +(-2.92139 + 8.02644i) q^{57} +(6.76937 + 8.06742i) q^{59} +(-1.41913 - 3.89904i) q^{61} +(-1.20517 - 2.08741i) q^{63} +(5.03605 + 1.83297i) q^{65} +(-3.77420 - 3.16693i) q^{67} +(4.62240 - 5.50876i) q^{69} +(1.05928 - 6.00749i) q^{71} +13.5583 q^{73} -8.17480 q^{75} +(0.636103 - 3.60752i) q^{77} +(8.59215 - 10.2397i) q^{79} +(-8.53173 - 7.15897i) q^{81} +(-1.39469 - 0.507624i) q^{83} +(-0.653371 - 1.13167i) q^{85} +(-0.423444 - 1.16340i) q^{87} +(-4.42899 - 5.27827i) q^{89} +(-3.80551 + 10.4556i) q^{91} +(3.11716 + 0.549640i) q^{93} +(3.19690 - 2.68252i) q^{95} +(-6.55603 - 3.78513i) q^{97} +(0.357818 + 2.02929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{3} - 3 q^{5} + 3 q^{7} - 3 q^{9}+O(q^{10}) $ 18 * q + 9 * q^3 - 3 * q^5 + 3 * q^7 - 3 * q^9	$ 18 q + 9 q^{3} - 3 q^{5} + 3 q^{7} - 3 q^{9} - 9 q^{11} + 9 q^{13} + 15 q^{15} - 15 q^{17} - 6 q^{19} - 12 q^{21} + 9 q^{23} + 21 q^{25} - 21 q^{27} - 18 q^{29} + 6 q^{33} + 12 q^{35} + 6 q^{37} + 6 q^{39} - 24 q^{41} + 36 q^{47} + 21 q^{49} - 81 q^{51} - 39 q^{53} - 12 q^{55} + 15 q^{57} + 6 q^{59} + 42 q^{61} + 27 q^{63} + 18 q^{65} - 36 q^{69} + 9 q^{71} - 54 q^{73} - 18 q^{75} + 33 q^{77} + 6 q^{79} - 45 q^{81} + 24 q^{83} + 6 q^{85} - 21 q^{87} + 18 q^{89} + 3 q^{91} + 66 q^{93} + 15 q^{95} - 9 q^{97} - 60 q^{99}+O(q^{100}) $ 18 * q + 9 * q^3 - 3 * q^5 + 3 * q^7 - 3 * q^9 - 9 * q^11 + 9 * q^13 + 15 * q^15 - 15 * q^17 - 6 * q^19 - 12 * q^21 + 9 * q^23 + 21 * q^25 - 21 * q^27 - 18 * q^29 + 6 * q^33 + 12 * q^35 + 6 * q^37 + 6 * q^39 - 24 * q^41 + 36 * q^47 + 21 * q^49 - 81 * q^51 - 39 * q^53 - 12 * q^55 + 15 * q^57 + 6 * q^59 + 42 * q^61 + 27 * q^63 + 18 * q^65 - 36 * q^69 + 9 * q^71 - 54 * q^73 - 18 * q^75 + 33 * q^77 + 6 * q^79 - 45 * q^81 + 24 * q^83 + 6 * q^85 - 21 * q^87 + 18 * q^89 + 3 * q^91 + 66 * q^93 + 15 * q^95 - 9 * q^97 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.354362	+	2.00969i	−0.204591	+	1.16029i	0.693491	+	0.720465i	$0.256072\pi$
$3$	−0.354362	+	2.00969i	−0.204591	+	1.16029i	−0.898082	+	0.439828i	$0.855039\pi$
$4$		0			0
$5$	0.640888	−	0.763781i	0.286614	−	0.341573i	−0.603457	−	0.797396i	$-0.706210\pi$
$5$	0.640888	−	0.763781i	0.286614	−	0.341573i	0.890071	+	0.455823i	$0.150655\pi$
$6$		0			0
$7$	1.58572	+	1.33057i	0.599344	+	0.502909i	0.891235	−	0.453542i	$-0.149840\pi$
$7$	1.58572	+	1.33057i	0.599344	+	0.502909i	−0.291891	+	0.956452i	$0.594284\pi$
$8$		0			0
$9$	−1.09419	−	0.398252i	−0.364729	−	0.132751i
$10$		0			0
$11$	−0.884822	−	1.53256i	−0.266784	−	0.462083i	0.701246	−	0.712920i	$-0.252628\pi$
$11$	−0.884822	−	1.53256i	−0.266784	−	0.462083i	−0.968029	+	0.250837i	$0.919294\pi$
$12$		0			0
$13$	1.83841	+	5.05098i	0.509882	+	1.40089i	0.881359	+	0.472448i	$0.156629\pi$
$13$	1.83841	+	5.05098i	0.509882	+	1.40089i	−0.371476	+	0.928442i	$0.621148\pi$
$14$		0			0
$15$	1.30785	+	1.55864i	0.337686	+	0.402439i
$16$		0			0
$17$	0.448257	−	1.23158i	0.108718	−	0.298701i	−0.873389	−	0.487023i	$-0.838083\pi$
$17$	0.448257	−	1.23158i	0.108718	−	0.298701i	0.982107	+	0.188322i	$0.0603049\pi$
$18$		0			0
$19$	4.12204	+	0.726826i	0.945660	+	0.166745i	0.625154	−	0.780501i	$-0.285036\pi$
$19$	4.12204	+	0.726826i	0.945660	+	0.166745i	0.320506	+	0.947247i	$0.396147\pi$
$20$		0			0
$21$	−3.23595	+	2.71529i	−0.706142	+	0.592524i
$22$		0			0
$23$	−3.05179	−	1.76195i	−0.636341	−	0.367392i	0.146862	−	0.989157i	$-0.453083\pi$
$23$	−3.05179	−	1.76195i	−0.636341	−	0.367392i	−0.783204	+	0.621765i	$0.786416\pi$
$24$		0			0
$25$	0.695618	+	3.94504i	0.139124	+	0.789009i
$26$		0			0
$27$	−1.87293	+	3.24402i	−0.360446	+	0.624311i
$28$		0			0
$29$	−0.525410	+	0.303345i	−0.0975661	+	0.0563298i	−0.547989	−	0.836485i	$-0.684607\pi$
$29$	−0.525410	+	0.303345i	−0.0975661	+	0.0563298i	0.450423	+	0.892815i	$0.351273\pi$
$30$		0			0
$31$		−	1.55107i		−	0.278580i	−0.990252	−	0.139290i	$-0.955518\pi$
$31$		−	1.55107i		−	0.278580i	0.990252	−	0.139290i	$-0.0444821\pi$
$32$		0			0
$33$	3.39351	−	1.23514i	0.590734	−	0.215009i
$34$		0			0
$35$	2.03253	−	0.358390i	0.343560	−	0.0605790i
$36$		0			0
$37$	−6.03673	+	0.746918i	−0.992432	+	0.122792i
$37$	−6.03673	+	0.746918i	−0.992432	+	0.122792i
$38$		0			0
$39$	−10.8023	+	1.90475i	−1.72976	+	0.305003i
$40$		0			0
$41$	2.15024	−	0.782625i	0.335812	−	0.122225i	−0.168610	−	0.985683i	$-0.553928\pi$
$41$	2.15024	−	0.782625i	0.335812	−	0.122225i	0.504422	+	0.863457i	$0.331706\pi$
$42$		0			0
$43$			8.37985i			1.27791i	0.769242	+	0.638957i	$0.220634\pi$
$43$			8.37985i			1.27791i	−0.769242	+	0.638957i	$0.779366\pi$
$44$		0			0
$45$	−1.00543	+	0.580485i	−0.149881	+	0.0865336i
$46$		0			0
$47$	1.79110	−	3.10228i	0.261259	−	0.452514i	−0.705318	−	0.708892i	$-0.749196\pi$
$47$	1.79110	−	3.10228i	0.261259	−	0.452514i	0.966577	+	0.256377i	$0.0825289\pi$
$48$		0			0
$49$	−0.471469	−	2.67384i	−0.0673528	−	0.381977i
$50$		0			0
$51$	2.31624	+	1.33728i	0.324338	+	0.187257i
$52$		0			0
$53$	−8.47562	+	7.11189i	−1.16422	+	0.976893i	−0.999955	−	0.00952421i	$-0.996968\pi$
$53$	−8.47562	+	7.11189i	−1.16422	+	0.976893i	−0.164261	+	0.986417i	$0.552524\pi$
$54$		0			0
$55$	−1.73761	−	0.306387i	−0.234299	−	0.0413133i
$56$		0			0
$57$	−2.92139	+	8.02644i	−0.386947	+	1.06313i
$58$		0			0
$59$	6.76937	+	8.06742i	0.881296	+	1.05029i	0.998365	+	0.0571643i	$0.0182059\pi$
$59$	6.76937	+	8.06742i	0.881296	+	1.05029i	−0.117068	+	0.993124i	$0.537350\pi$
$60$		0			0
$61$	−1.41913	−	3.89904i	−0.181701	−	0.499220i	0.815084	−	0.579343i	$-0.196691\pi$
$61$	−1.41913	−	3.89904i	−0.181701	−	0.499220i	−0.996785	+	0.0801229i	$0.974469\pi$
$62$		0			0
$63$	−1.20517	−	2.08741i	−0.151837	−	0.262989i
$64$		0			0
$65$	5.03605	+	1.83297i	0.624646	+	0.227352i
$66$		0			0
$67$	−3.77420	−	3.16693i	−0.461091	−	0.386902i	0.382441	−	0.923980i	$-0.375084\pi$
$67$	−3.77420	−	3.16693i	−0.461091	−	0.386902i	−0.843532	+	0.537078i	$0.819528\pi$
$68$		0			0
$69$	4.62240	−	5.50876i	0.556472	−	0.663177i
$70$		0			0
$71$	1.05928	−	6.00749i	0.125714	−	0.712958i	−0.855168	−	0.518351i	$-0.826546\pi$
$71$	1.05928	−	6.00749i	0.125714	−	0.712958i	0.980881	−	0.194606i	$-0.0623429\pi$
$72$		0			0
$73$	13.5583			1.58688			0.793439	−	0.608649i	$-0.208288\pi$
$73$	13.5583			1.58688			0.793439	+	0.608649i	$0.208288\pi$
$74$		0			0
$75$	−8.17480			−0.943945
$76$		0			0
$77$	0.636103	−	3.60752i	0.0724907	−	0.411115i
$78$		0			0
$79$	8.59215	−	10.2397i	0.966692	−	1.15206i	−0.0216434	−	0.999766i	$-0.506890\pi$
$79$	8.59215	−	10.2397i	0.966692	−	1.15206i	0.988335	−	0.152293i	$-0.0486657\pi$
$80$		0			0
$81$	−8.53173	−	7.15897i	−0.947970	−	0.795441i
$82$		0			0
$83$	−1.39469	−	0.507624i	−0.153087	−	0.0557190i	0.264340	−	0.964429i	$-0.414846\pi$
$83$	−1.39469	−	0.507624i	−0.153087	−	0.0557190i	−0.417427	+	0.908710i	$0.637068\pi$
$84$		0			0
$85$	−0.653371	−	1.13167i	−0.0708681	−	0.122747i
$86$		0			0
$87$	−0.423444	−	1.16340i	−0.0453980	−	0.124730i
$88$		0			0
$89$	−4.42899	−	5.27827i	−0.469473	−	0.559496i	0.478401	−	0.878141i	$-0.341216\pi$
$89$	−4.42899	−	5.27827i	−0.469473	−	0.559496i	−0.947874	+	0.318646i	$0.896772\pi$
$90$		0			0
$91$	−3.80551	+	10.4556i	−0.398926	+	1.09604i
$92$		0			0
$93$	3.11716	+	0.549640i	0.323235	+	0.0569950i
$94$		0			0
$95$	3.19690	−	2.68252i	0.327995	−	0.275220i
$96$		0			0
$97$	−6.55603	−	3.78513i	−0.665664	−	0.384321i	0.128768	−	0.991675i	$-0.458898\pi$
$97$	−6.55603	−	3.78513i	−0.665664	−	0.384321i	−0.794432	+	0.607353i	$0.792231\pi$
$98$		0			0
$99$	0.357818	+	2.02929i	0.0359621	+	0.203951i
$100$		0			0
$101$	5.67466	−	9.82879i	0.564649	−	0.978002i	−0.432433	−	0.901666i	$-0.642345\pi$
$101$	5.67466	−	9.82879i	0.564649	−	0.978002i	0.997082	−	0.0763353i	$-0.0243220\pi$
$102$		0			0
$103$	−1.72830	+	0.997837i	−0.170295	+	0.0983198i	−0.582725	−	0.812670i	$-0.698013\pi$
$103$	−1.72830	+	0.997837i	−0.170295	+	0.0983198i	0.412430	+	0.910989i	$0.364680\pi$
$104$		0			0
$105$			4.21175i			0.411025i
$106$		0			0
$107$	17.6836	−	6.43630i	1.70954	−	0.622220i	0.712683	−	0.701486i	$-0.247480\pi$
$107$	17.6836	−	6.43630i	1.70954	−	0.622220i	0.996854	+	0.0792658i	$0.0252576\pi$
$108$		0			0
$109$	7.67973	−	1.35414i	0.735585	−	0.129703i	0.206709	−	0.978403i	$-0.433725\pi$
$109$	7.67973	−	1.35414i	0.735585	−	0.129703i	0.528876	+	0.848699i	$0.322614\pi$
$110$		0			0
$111$	0.638117	−	12.3966i	0.0605674	−	1.17663i
$112$		0			0
$113$	9.87190	−	1.74068i	0.928670	−	0.163750i	0.311200	−	0.950344i	$-0.399269\pi$
$113$	9.87190	−	1.74068i	0.928670	−	0.163750i	0.617470	+	0.786595i	$0.288158\pi$
$114$		0			0
$115$	−3.30160	+	1.20168i	−0.307875	+	0.112057i
$116$		0			0
$117$		−	6.25888i		−	0.578633i
$118$		0			0
$119$	2.34951	−	1.35649i	0.215379	−	0.124349i
$120$		0			0
$121$	3.93418	−	6.81420i	0.357653	−	0.619473i
$122$		0			0
$123$	0.810866	+	4.59865i	0.0731133	+	0.414646i
$124$		0			0
$125$	7.77629	+	4.48964i	0.695533	+	0.401566i
$126$		0			0
$127$	−1.01023	+	0.847688i	−0.0896438	+	0.0752201i	−0.686508	−	0.727122i	$-0.740857\pi$
$127$	−1.01023	+	0.847688i	−0.0896438	+	0.0752201i	0.596864	+	0.802342i	$0.296413\pi$
$128$		0			0
$129$	−16.8409	−	2.96950i	−1.48276	−	0.261450i
$130$		0			0
$131$	3.32807	−	9.14381i	0.290775	−	0.798898i	−0.705178	−	0.709030i	$-0.749133\pi$
$131$	3.32807	−	9.14381i	0.290775	−	0.798898i	0.995954	−	0.0898684i	$-0.0286446\pi$
$132$		0			0
$133$	5.56928	+	6.63721i	0.482918	+	0.575519i
$134$		0			0
$135$	1.27738	+	3.50956i	0.109939	+	0.302055i
$136$		0			0
$137$	3.74079	+	6.47924i	0.319598	+	0.553559i	0.980404	−	0.196997i	$-0.0631189\pi$
$137$	3.74079	+	6.47924i	0.319598	+	0.553559i	−0.660807	+	0.750556i	$0.729786\pi$
$138$		0			0
$139$	−5.21741	−	1.89898i	−0.442535	−	0.161069i	0.111136	−	0.993805i	$-0.464551\pi$
$139$	−5.21741	−	1.89898i	−0.442535	−	0.161069i	−0.553671	+	0.832736i	$0.686773\pi$
$140$		0			0
$141$	5.59992	+	4.69889i	0.471598	+	0.395718i
$142$		0			0
$143$	6.11425	−	7.28668i	0.511300	−	0.609343i
$144$		0			0
$145$	−0.105039	+	0.595708i	−0.00872305	+	0.0494709i
$146$		0			0
$147$	5.54064			0.456984
$148$		0			0
$149$	−7.32465			−0.600059			−0.300029	−	0.953930i	$-0.596997\pi$
$149$	−7.32465			−0.600059			−0.300029	+	0.953930i	$0.596997\pi$
$150$		0			0
$151$	0.793519	−	4.50027i	0.0645757	−	0.366227i	−0.935346	−	0.353733i	$-0.884912\pi$
$151$	0.793519	−	4.50027i	0.0645757	−	0.366227i	0.999922	−	0.0124935i	$-0.00397690\pi$
$152$		0			0
$153$	−0.980956	+	1.16906i	−0.0793056	+	0.0945127i
$154$		0			0
$155$	−1.18468	−	0.994062i	−0.0951556	−	0.0798450i
$156$		0			0
$157$	−11.9534	−	4.35068i	−0.953986	−	0.347222i	−0.182312	−	0.983241i	$-0.558358\pi$
$157$	−11.9534	−	4.35068i	−0.953986	−	0.347222i	−0.771674	+	0.636018i	$0.780580\pi$
$158$		0			0
$159$	−11.2892	−	19.5535i	−0.895294	−	1.55069i
$160$		0			0
$161$	−2.49486	−	6.85457i	−0.196623	−	0.540216i
$162$		0			0
$163$	8.22159	+	9.79811i	0.643965	+	0.767447i	0.984991	−	0.172607i	$-0.0552189\pi$
$163$	8.22159	+	9.79811i	0.643965	+	0.767447i	−0.341026	+	0.940054i	$0.610774\pi$
$164$		0			0
$165$	1.23148	−	3.38348i	0.0958710	−	0.263403i
$166$		0			0
$167$	−23.1506	−	4.08207i	−1.79144	−	0.315880i	−0.823551	−	0.567243i	$-0.808010\pi$
$167$	−23.1506	−	4.08207i	−1.79144	−	0.315880i	−0.967893	+	0.251363i	$0.919121\pi$
$168$		0			0
$169$	−12.1741	+	10.2153i	−0.936469	+	0.785791i
$170$		0			0
$171$	−4.22083	−	2.43689i	−0.322775	−	0.186354i
$172$		0			0
$173$	−0.813008	−	4.61080i	−0.0618118	−	0.350552i	−0.999990	−	0.00440047i	$-0.998599\pi$
$173$	−0.813008	−	4.61080i	−0.0618118	−	0.350552i	0.938178	−	0.346152i	$-0.112512\pi$
$174$		0			0
$175$	−4.14612	+	7.18128i	−0.313417	+	0.542854i
$176$		0			0
$177$	−18.6118	+	10.7455i	−1.39895	+	0.807682i
$178$		0			0
$179$		−	9.73125i		−	0.727348i	−0.931526	−	0.363674i	$-0.881522\pi$
$179$		−	9.73125i		−	0.727348i	0.931526	−	0.363674i	$-0.118478\pi$
$180$		0			0
$181$	8.32509	−	3.03008i	0.618799	−	0.225224i	−0.0135499	−	0.999908i	$-0.504313\pi$
$181$	8.32509	−	3.03008i	0.618799	−	0.225224i	0.632349	+	0.774684i	$0.282091\pi$
$182$		0			0
$183$	8.33873	−	1.47034i	0.616416	−	0.108691i
$184$		0			0
$185$	−3.29839	+	5.08943i	−0.242502	+	0.374182i
$186$		0			0
$187$	−2.28409	+	0.402746i	−0.167029	+	0.0294517i
$188$		0			0
$189$	−7.28634	+	2.65201i	−0.530003	+	0.192905i
$190$		0			0
$191$			6.57730i			0.475917i	0.971275	+	0.237958i	$0.0764782\pi$
$191$			6.57730i			0.475917i	−0.971275	+	0.237958i	$0.923522\pi$
$192$		0			0
$193$	−2.10282	+	1.21406i	−0.151364	+	0.0873902i	−0.573769	−	0.819017i	$-0.694519\pi$
$193$	−2.10282	+	1.21406i	−0.151364	+	0.0873902i	0.422405	+	0.906407i	$0.361186\pi$
$194$		0			0
$195$	−5.46829	+	9.47135i	−0.391592	+	0.678258i
$196$		0			0
$197$	−4.74016	−	26.8828i	−0.337722	−	1.91532i	−0.398503	−	0.917167i	$-0.630470\pi$
$197$	−4.74016	−	26.8828i	−0.337722	−	1.91532i	0.0607805	−	0.998151i	$-0.480641\pi$
$198$		0			0
$199$	−11.5142	−	6.64774i	−0.816222	−	0.471246i	0.0328902	−	0.999459i	$-0.489529\pi$
$199$	−11.5142	−	6.64774i	−0.816222	−	0.471246i	−0.849112	+	0.528213i	$0.822862\pi$
$200$		0			0
$201$	7.70196	−	6.46271i	0.543254	−	0.455845i
$202$		0			0
$203$	−1.23677	−	0.218076i	−0.0868045	−	0.0153060i
$204$		0			0
$205$	0.780312	−	2.14389i	0.0544993	−	0.149736i
$206$		0			0
$207$	2.63753	+	3.14328i	0.183321	+	0.218473i
$208$		0			0
$209$	−2.53337	−	6.96037i	−0.175237	−	0.481459i
$210$		0			0
$211$	3.16578	+	5.48329i	0.217941	+	0.377485i	0.954178	−	0.299238i	$-0.0967326\pi$
$211$	3.16578	+	5.48329i	0.217941	+	0.377485i	−0.736237	+	0.676724i	$0.763399\pi$
$212$		0			0
$213$	11.6978	+	4.25765i	0.801520	+	0.291729i
$214$		0			0
$215$	6.40036	+	5.37054i	0.436501	+	0.366268i
$216$		0			0
$217$	2.06381	−	2.45956i	0.140101	−	0.166965i
$218$		0			0
$219$	−4.80454	+	27.2479i	−0.324661	+	1.84124i
$220$		0			0
$221$	7.04475			0.473881
$222$		0			0
$223$	−2.43018			−0.162737			−0.0813683	−	0.996684i	$-0.525929\pi$
$223$	−2.43018			−0.162737			−0.0813683	+	0.996684i	$0.525929\pi$
$224$		0			0
$225$	0.809985	−	4.59365i	0.0539990	−	0.306243i
$226$		0			0
$227$	3.25909	−	3.88403i	0.216313	−	0.257792i	−0.646966	−	0.762519i	$-0.723962\pi$
$227$	3.25909	−	3.88403i	0.216313	−	0.257792i	0.863279	+	0.504727i	$0.168407\pi$
$228$		0			0
$229$	7.51681	+	6.30735i	0.496724	+	0.416801i	0.856429	−	0.516265i	$-0.172678\pi$
$229$	7.51681	+	6.30735i	0.496724	+	0.416801i	−0.359704	+	0.933066i	$0.617122\pi$
$230$		0			0
$231$	7.02457	+	2.55673i	0.462183	+	0.168221i
$232$		0			0
$233$	1.38405	+	2.39725i	0.0906722	+	0.157049i	0.907794	−	0.419416i	$-0.137765\pi$
$233$	1.38405	+	2.39725i	0.0906722	+	0.157049i	−0.817122	+	0.576465i	$0.804432\pi$
$234$		0			0
$235$	−1.22157	−	3.35623i	−0.0796862	−	0.218936i
$236$		0			0
$237$	17.5339	+	20.8961i	1.13895	+	1.35735i
$238$		0			0
$239$	−6.50378	+	17.8690i	−0.420694	+	1.15585i	0.530616	+	0.847613i	$0.321961\pi$
$239$	−6.50378	+	17.8690i	−0.420694	+	1.15585i	−0.951310	+	0.308236i	$0.900261\pi$
$240$		0			0
$241$	−1.49887	−	0.264292i	−0.0965509	−	0.0170245i	0.125164	−	0.992136i	$-0.460054\pi$
$241$	−1.49887	−	0.264292i	−0.0965509	−	0.0170245i	−0.221715	+	0.975112i	$0.571165\pi$
$242$		0			0
$243$	8.80210	−	7.38584i	0.564655	−	0.473802i
$244$		0			0
$245$	−2.34438	−	1.35353i	−0.149777	−	0.0864739i
$246$		0			0
$247$	3.90680	+	22.1565i	0.248583	+	1.40979i
$248$		0			0
$249$	1.51439	−	2.62300i	0.0959705	−	0.166226i
$250$		0			0
$251$	−13.8969	+	8.02336i	−0.877163	+	0.506430i	−0.869722	−	0.493542i	$-0.835702\pi$
$251$	−13.8969	+	8.02336i	−0.877163	+	0.506430i	−0.00744072	+	0.999972i	$0.502368\pi$
$252$		0			0
$253$			6.23605i			0.392057i
$254$		0			0
$255$	2.50584	−	0.912050i	0.156922	−	0.0571148i
$256$		0			0
$257$	15.4121	−	2.71756i	0.961378	−	0.169517i	0.329131	−	0.944284i	$-0.393244\pi$
$257$	15.4121	−	2.71756i	0.961378	−	0.169517i	0.632246	+	0.774767i	$0.282133\pi$
$258$		0			0
$259$	−10.5664	−	6.84791i	−0.656562	−	0.425509i
$260$		0			0
$261$	0.695705	−	0.122672i	0.0430631	−	0.00759318i
$262$		0			0
$263$	4.31802	−	1.57163i	0.266260	−	0.0969108i	−0.205440	−	0.978670i	$-0.565863\pi$
$263$	4.31802	−	1.57163i	0.266260	−	0.0969108i	0.471700	+	0.881759i	$0.343640\pi$
$264$		0			0
$265$			11.0314i			0.677656i
$266$		0			0
$267$	12.1771	−	7.03047i	0.745229	−	0.430258i
$268$		0			0
$269$	−8.68426	+	15.0416i	−0.529489	+	0.917102i	0.469919	+	0.882709i	$0.344283\pi$
$269$	−8.68426	+	15.0416i	−0.529489	+	0.917102i	−0.999408	+	0.0343925i	$0.989050\pi$
$270$		0			0
$271$	−2.93250	−	16.6310i	−0.178137	−	1.01026i	−0.934461	−	0.356066i	$-0.884118\pi$
$271$	−2.93250	−	16.6310i	−0.178137	−	1.01026i	0.756324	−	0.654197i	$-0.226993\pi$
$272$		0			0
$273$	−19.6639	−	11.3529i	−1.19011	−	0.687111i
$274$		0			0
$275$	5.43051	−	4.55674i	0.327472	−	0.274781i
$276$		0			0
$277$	−23.5704	−	4.15610i	−1.41621	−	0.249716i	−0.587422	−	0.809281i	$-0.699857\pi$
$277$	−23.5704	−	4.15610i	−1.41621	−	0.249716i	−0.828787	+	0.559565i	$0.810968\pi$
$278$		0			0
$279$	−0.617717	+	1.69716i	−0.0369817	+	0.101607i
$280$		0			0
$281$	9.92422	+	11.8272i	0.592029	+	0.705553i	0.975995	−	0.217795i	$-0.0698863\pi$
$281$	9.92422	+	11.8272i	0.592029	+	0.705553i	−0.383966	+	0.923347i	$0.625442\pi$
$282$		0			0
$283$	−1.03854	−	2.85336i	−0.0617347	−	0.169615i	0.904990	−	0.425432i	$-0.139878\pi$
$283$	−1.03854	−	2.85336i	−0.0617347	−	0.169615i	−0.966725	+	0.255817i	$0.917656\pi$
$284$		0			0
$285$	4.25816	+	7.37535i	0.252232	+	0.436878i
$286$		0			0
$287$	4.45101	+	1.62004i	0.262735	+	0.0956277i
$288$		0			0
$289$	11.7069	+	9.82326i	0.688642	+	0.577839i
$290$		0			0
$291$	9.93012	−	11.8343i	0.582114	−	0.693737i
$292$		0			0
$293$	2.32678	−	13.1958i	0.135932	−	0.770908i	−0.838274	−	0.545249i	$-0.816435\pi$
$293$	2.32678	−	13.1958i	0.135932	−	0.770908i	0.974206	−	0.225660i	$-0.0724537\pi$
$294$		0			0
$295$	10.5001			0.611342
$296$		0			0
$297$	6.62885			0.384645
$298$		0			0
$299$	3.28915	−	18.6537i	0.190216	−	1.07877i
$300$		0			0
$301$	−11.1500	+	13.2880i	−0.642675	+	0.765910i
$302$		0			0
$303$	17.7419	+	14.8872i	1.01925	+	0.855249i
$304$		0			0
$305$	−3.88751	−	1.41494i	−0.222598	−	0.0810192i
$306$		0			0
$307$	17.1776	+	29.7525i	0.980378	+	1.69807i	0.660904	+	0.750470i	$0.270173\pi$
$307$	17.1776	+	29.7525i	0.980378	+	1.69807i	0.319474	+	0.947595i	$0.396494\pi$
$308$		0			0
$309$	−1.39289	−	3.82694i	−0.0792389	−	0.217707i
$310$		0			0
$311$	−2.41229	−	2.87486i	−0.136788	−	0.163018i	0.693301	−	0.720648i	$-0.256155\pi$
$311$	−2.41229	−	2.87486i	−0.136788	−	0.163018i	−0.830090	+	0.557630i	$0.811711\pi$
$312$		0			0
$313$	−5.68575	+	15.6215i	−0.321377	+	0.882977i	0.668835	+	0.743411i	$0.266793\pi$
$313$	−5.68575	+	15.6215i	−0.321377	+	0.882977i	−0.990213	+	0.139566i	$0.955429\pi$
$314$		0			0
$315$	−2.36670	−	0.417313i	−0.133349	−	0.0235129i
$316$		0			0
$317$	17.8110	−	14.9452i	1.00036	−	0.839404i	0.0133284	−	0.999911i	$-0.495757\pi$
$317$	17.8110	−	14.9452i	1.00036	−	0.839404i	0.987035	+	0.160507i	$0.0513129\pi$
$318$		0			0
$319$	0.929788	+	0.536813i	0.0520581	+	0.0300558i
$320$		0			0
$321$	6.66855	+	37.8192i	0.372202	+	2.11086i
$322$		0			0
$323$	2.74287	−	4.75080i	0.152618	−	0.264341i
$324$		0			0
$325$	−18.6475	+	10.7661i	−1.03438	+	0.597198i
$326$		0			0
$327$			15.9137i			0.880030i
$328$		0			0
$329$	6.96799	−	2.53614i	0.384158	−	0.139822i
$330$		0			0
$331$	−13.5378	+	2.38708i	−0.744106	+	0.131206i	−0.532832	−	0.846221i	$-0.678872\pi$
$331$	−13.5378	+	2.38708i	−0.744106	+	0.131206i	−0.211274	+	0.977427i	$0.567761\pi$
$332$		0			0
$333$	6.90278	+	1.58687i	0.378270	+	0.0869600i
$334$		0			0
$335$	−4.83767	+	0.853012i	−0.264310	+	0.0466050i
$336$		0			0
$337$	11.1617	−	4.06251i	0.608015	−	0.221299i	−0.0196197	−	0.999808i	$-0.506246\pi$
$337$	11.1617	−	4.06251i	0.608015	−	0.221299i	0.627634	+	0.778508i	$0.284023\pi$
$338$		0			0
$339$			20.4563i			1.11103i
$340$		0			0
$341$	−2.37710	+	1.37242i	−0.128727	+	0.0743208i
$342$		0			0
$343$	10.0551	−	17.4160i	0.542926	−	0.940375i
$344$		0			0
$345$	−1.24505	−	7.06100i	−0.0670310	−	0.380152i
$346$		0			0
$347$	−25.1199	−	14.5030i	−1.34851	−	0.778560i	−0.360468	−	0.932772i	$-0.617383\pi$
$347$	−25.1199	−	14.5030i	−1.34851	−	0.778560i	−0.988038	+	0.154212i	$0.950716\pi$
$348$		0			0
$349$	−11.1805	+	9.38157i	−0.598480	+	0.502184i	−0.890957	−	0.454088i	$-0.849965\pi$
$349$	−11.1805	+	9.38157i	−0.598480	+	0.502184i	0.292477	+	0.956273i	$0.405521\pi$
$350$		0			0
$351$	−19.8287	−	3.49633i	−1.05838	−	0.186620i
$352$		0			0
$353$	9.35264	−	25.6962i	0.497791	−	1.36767i	−0.395615	−	0.918417i	$-0.629468\pi$
$353$	9.35264	−	25.6962i	0.497791	−	1.36767i	0.893405	−	0.449252i	$-0.148309\pi$
$354$		0			0
$355$	−3.90952	−	4.65919i	−0.207496	−	0.247284i
$356$		0			0
$357$	1.89354	+	5.20247i	0.100217	+	0.275344i
$358$		0			0
$359$	5.37405	+	9.30813i	0.283632	+	0.491264i	0.972276	−	0.233835i	$-0.0751274\pi$
$359$	5.37405	+	9.30813i	0.283632	+	0.491264i	−0.688645	+	0.725099i	$0.741794\pi$
$360$		0			0
$361$	−1.39124	−	0.506372i	−0.0732234	−	0.0266511i
$362$		0			0
$363$	12.3003	+	10.3212i	0.645597	+	0.541720i
$364$		0			0
$365$	8.68935	−	10.3556i	0.454821	−	0.542035i
$366$		0			0
$367$	1.47729	−	8.37816i	0.0771142	−	0.437336i	−0.921667	−	0.387982i	$-0.873172\pi$
$367$	1.47729	−	8.37816i	0.0771142	−	0.437336i	0.998781	−	0.0493547i	$-0.0157165\pi$
$368$		0			0
$369$	−2.66445			−0.138706
$370$		0			0
$371$	−22.9028			−1.18905
$372$		0			0
$373$	−2.57728	+	14.6165i	−0.133447	+	0.756813i	0.842482	+	0.538724i	$0.181093\pi$
$373$	−2.57728	+	14.6165i	−0.133447	+	0.756813i	−0.975929	+	0.218089i	$0.930018\pi$
$374$		0			0
$375$	−11.7784	+	14.0369i	−0.608234	+	0.724865i
$376$		0			0
$377$	−2.49811	−	2.09616i	−0.128659	−	0.107958i
$378$		0			0
$379$	4.61165	+	1.67850i	0.236885	+	0.0862190i	0.457735	−	0.889089i	$-0.348661\pi$
$379$	4.61165	+	1.67850i	0.236885	+	0.0862190i	−0.220850	+	0.975308i	$0.570883\pi$
$380$		0			0
$381$	−1.34560	−	2.33064i	−0.0689371	−	0.119402i
$382$		0			0
$383$	10.4996	+	28.8475i	0.536506	+	1.47404i	0.851198	+	0.524844i	$0.175876\pi$
$383$	10.4996	+	28.8475i	0.536506	+	1.47404i	−0.314692	+	0.949194i	$0.601901\pi$
$384$		0			0
$385$	−2.34768	−	2.79786i	−0.119649	−	0.142592i
$386$		0			0
$387$	3.33729	−	9.16913i	0.169644	−	0.466093i
$388$		0			0
$389$	−38.5245	−	6.79290i	−1.95327	−	0.344414i	−0.998960	−	0.0455870i	$-0.985484\pi$
$389$	−38.5245	−	6.79290i	−1.95327	−	0.344414i	−0.954307	−	0.298827i	$-0.903405\pi$
$390$		0			0
$391$	−3.53796	+	2.96870i	−0.178922	+	0.150134i
$392$		0			0
$393$	17.1968	+	9.92860i	0.867466	+	0.500832i
$394$		0			0
$395$	−2.31430	−	13.1250i	−0.116445	−	0.660392i
$396$		0			0
$397$	4.59778	−	7.96360i	0.230756	−	0.399681i	−0.727275	−	0.686347i	$-0.759213\pi$
$397$	4.59778	−	7.96360i	0.230756	−	0.399681i	0.958031	+	0.286665i	$0.0925467\pi$
$398$		0			0
$399$	−15.3123	+	8.84053i	−0.766571	+	0.442580i
$400$		0			0
$401$		−	2.45751i		−	0.122722i	−0.998116	−	0.0613612i	$-0.980456\pi$
$401$		−	2.45751i		−	0.122722i	0.998116	−	0.0613612i	$-0.0195441\pi$
$402$		0			0
$403$	7.83443	−	2.85150i	0.390261	−	0.142043i
$404$		0			0
$405$	−10.9358	+	1.92827i	−0.543402	+	0.0958165i
$406$		0			0
$407$	6.48613	+	8.59074i	0.321505	+	0.425827i
$408$		0			0
$409$	3.26072	−	0.574953i	0.161232	−	0.0284296i	−0.0924493	−	0.995717i	$-0.529470\pi$
$409$	3.26072	−	0.574953i	0.161232	−	0.0284296i	0.253681	+	0.967288i	$0.418358\pi$
$410$		0			0
$411$	−14.3468	+	5.22182i	−0.707678	+	0.257574i
$412$		0			0
$413$			21.7998i			1.07270i
$414$		0			0
$415$	−1.28155	+	0.739904i	−0.0629089	+	0.0363205i
$416$		0			0
$417$	5.66521	−	9.81243i	0.277426	−	0.480517i
$418$		0			0
$419$	−2.49037	−	14.1236i	−0.121663	−	0.689984i	−0.983234	−	0.182347i	$-0.941630\pi$
$419$	−2.49037	−	14.1236i	−0.121663	−	0.689984i	0.861571	−	0.507636i	$-0.169481\pi$
$420$		0			0
$421$	−8.86400	−	5.11763i	−0.432005	−	0.249418i	0.268196	−	0.963364i	$-0.413573\pi$
$421$	−8.86400	−	5.11763i	−0.432005	−	0.249418i	−0.700200	+	0.713946i	$0.746906\pi$
$422$		0			0
$423$	−3.19530	+	2.68117i	−0.155361	+	0.130363i
$424$		0			0
$425$	5.17044	+	0.911688i	0.250803	+	0.0442233i
$426$		0			0
$427$	2.93761	−	8.07102i	0.142161	−	0.390584i
$428$		0			0
$429$	12.4773	+	14.8699i	0.602409	+	0.717923i
$430$		0			0
$431$	3.97821	+	10.9300i	0.191623	+	0.526481i	0.997880	−	0.0650853i	$-0.0207320\pi$
$431$	3.97821	+	10.9300i	0.191623	+	0.526481i	−0.806256	+	0.591566i	$0.798510\pi$
$432$		0			0
$433$	−18.0948	−	31.3411i	−0.869579	−	1.50616i	−0.862427	−	0.506181i	$-0.831057\pi$
$433$	−18.0948	−	31.3411i	−0.869579	−	1.50616i	−0.00715178	−	0.999974i	$-0.502277\pi$
$434$		0			0
$435$	−1.15996	−	0.422192i	−0.0556160	−	0.0202426i
$436$		0			0
$437$	−11.2989	−	9.48094i	−0.540502	−	0.453535i
$438$		0			0
$439$	−7.71832	+	9.19834i	−0.368376	+	0.439013i	−0.918109	−	0.396327i	$-0.870285\pi$
$439$	−7.71832	+	9.19834i	−0.368376	+	0.439013i	0.549734	+	0.835340i	$0.314729\pi$
$440$		0			0
$441$	−0.548984	+	3.11344i	−0.0261421	+	0.148259i
$442$		0			0
$443$	23.5359			1.11822			0.559112	−	0.829092i	$-0.311142\pi$
$443$	23.5359			1.11822			0.559112	+	0.829092i	$0.311142\pi$
$444$		0			0
$445$	−6.86993			−0.325666
$446$		0			0
$447$	2.59558	−	14.7203i	0.122767	−	0.696244i
$448$		0			0
$449$	−3.20730	+	3.82231i	−0.151362	+	0.180386i	−0.836397	−	0.548124i	$-0.815342\pi$
$449$	−3.20730	+	3.82231i	−0.151362	+	0.180386i	0.685035	+	0.728510i	$0.259787\pi$
$450$		0			0
$451$	−3.10200	−	2.60289i	−0.146068	−	0.122565i
$452$		0			0
$453$	8.76294	+	3.18945i	0.411719	+	0.149853i
$454$		0			0
$455$	5.54684	+	9.60741i	0.260040	+	0.450402i
$456$		0			0
$457$	7.86915	+	21.6203i	0.368103	+	1.01136i	0.976082	+	0.217402i	$0.0697583\pi$
$457$	7.86915	+	21.6203i	0.368103	+	1.01136i	−0.607979	+	0.793953i	$0.708020\pi$
$458$		0			0
$459$	3.15570	+	3.76081i	0.147295	+	0.175540i
$460$		0			0
$461$	−4.42243	+	12.1505i	−0.205973	+	0.565906i	−0.999067	−	0.0431934i	$-0.986247\pi$
$461$	−4.42243	+	12.1505i	−0.205973	+	0.565906i	0.793094	+	0.609100i	$0.208469\pi$
$462$		0			0
$463$	−10.6682	−	1.88110i	−0.495795	−	0.0874220i	−0.0798407	−	0.996808i	$-0.525441\pi$
$463$	−10.6682	−	1.88110i	−0.495795	−	0.0874220i	−0.415954	+	0.909386i	$0.636552\pi$
$464$		0			0
$465$	2.41756	−	2.02857i	0.112112	−	0.0940728i
$466$		0			0
$467$	−30.6966	−	17.7227i	−1.42047	−	0.820109i	−0.424131	−	0.905601i	$-0.639420\pi$
$467$	−30.6966	−	17.7227i	−1.42047	−	0.820109i	−0.996339	+	0.0854922i	$0.972754\pi$
$468$		0			0
$469$	−1.77097	−	10.0437i	−0.0817759	−	0.463774i
$470$		0			0
$471$	12.9793	−	22.4809i	0.598057	−	1.03586i
$472$		0			0
$473$	12.8426	−	7.41467i	0.590503	−	0.340927i
$474$		0			0
$475$			16.7672i			0.769332i
$476$		0			0
$477$	12.1062	−	4.40631i	0.554307	−	0.201751i
$478$		0			0
$479$	8.88677	−	1.56698i	0.406047	−	0.0715970i	0.0331054	−	0.999452i	$-0.489460\pi$
$479$	8.88677	−	1.56698i	0.406047	−	0.0715970i	0.372942	+	0.927855i	$0.378349\pi$
$480$		0			0
$481$	−14.8706	−	29.1183i	−0.678043	−	1.32768i
$482$		0			0
$483$	14.6596	−	2.58489i	0.667036	−	0.117616i
$484$		0			0
$485$	−7.09269	+	2.58153i	−0.322062	+	0.117221i
$486$		0			0
$487$		−	9.71169i		−	0.440079i	−0.975491	−	0.220039i	$-0.929381\pi$
$487$		−	9.71169i		−	0.440079i	0.975491	−	0.220039i	$-0.0706186\pi$
$488$		0			0
$489$	−22.6045	+	13.0507i	−1.02221	+	0.590175i
$490$		0			0
$491$	15.2008	−	26.3286i	0.686003	−	1.18819i	−0.287118	−	0.957895i	$-0.592697\pi$
$491$	15.2008	−	26.3286i	0.686003	−	1.18819i	0.973121	−	0.230296i	$-0.0739695\pi$
$492$		0			0
$493$	0.138074	+	0.783059i	0.00621856	+	0.0352672i
$494$		0			0
$495$	1.77925	+	1.02725i	0.0799714	+	0.0461715i
$496$		0			0
$497$	9.67312	−	8.11671i	0.433899	−	0.364084i
$498$		0			0
$499$	−26.9165	−	4.74611i	−1.20495	−	0.212465i	−0.465112	−	0.885252i	$-0.653986\pi$
$499$	−26.9165	−	4.74611i	−1.20495	−	0.212465i	−0.739836	+	0.672787i	$0.765097\pi$
$500$		0			0
$501$	16.4073	−	45.0788i	0.733026	−	2.01397i
$502$		0			0
$503$	−0.270169	−	0.321975i	−0.0120462	−	0.0143562i	0.759988	−	0.649937i	$-0.225205\pi$
$503$	−0.270169	−	0.321975i	−0.0120462	−	0.0143562i	−0.772034	+	0.635581i	$0.780760\pi$
$504$		0			0
$505$	−3.87022	−	10.6333i	−0.172223	−	0.473178i
$506$		0			0
$507$	−16.2155	−	28.0860i	−0.720154	−	1.24734i
$508$		0			0
$509$	17.6912	+	6.43907i	0.784149	+	0.285407i	0.702902	−	0.711287i	$-0.251887\pi$
$509$	17.6912	+	6.43907i	0.784149	+	0.285407i	0.0812473	+	0.996694i	$0.474110\pi$
$510$		0			0
$511$	21.4996	+	18.0403i	0.951086	+	0.798056i
$512$		0			0
$513$	−10.0781	+	12.0107i	−0.444961	+	0.530283i
$514$		0			0
$515$	−0.345521	+	1.95955i	−0.0152255	+	0.0863479i
$516$		0			0
$517$	−6.33923			−0.278799
$518$		0			0
$519$	9.55435			0.419390
$520$		0			0
$521$	4.62461	−	26.2275i	0.202608	−	1.14905i	−0.698552	−	0.715559i	$-0.746172\pi$
$521$	4.62461	−	26.2275i	0.202608	−	1.14905i	0.901160	−	0.433487i	$-0.142717\pi$
$522$		0			0
$523$	1.75455	−	2.09099i	0.0767210	−	0.0914325i	−0.726319	−	0.687358i	$-0.758770\pi$
$523$	1.75455	−	2.09099i	0.0767210	−	0.0914325i	0.803040	+	0.595926i	$0.203215\pi$
$524$		0			0
$525$	−12.9629	−	10.8772i	−0.565747	−	0.474718i
$526$		0			0
$527$	−1.91026	−	0.695278i	−0.0832123	−	0.0302868i
$528$		0			0
$529$	−5.29107	−	9.16440i	−0.230046	−	0.398452i
$530$		0			0
$531$	−4.19410	−	11.5232i	−0.182008	−	0.500064i
$532$		0			0
$533$	7.90605	+	9.42206i	0.342449	+	0.408115i
$534$		0			0
$535$	6.41728	−	17.6313i	0.277443	−	0.762269i
$536$		0			0
$537$	19.5568	+	3.44839i	0.843937	+	0.148809i
$538$		0			0
$539$	−3.68064	+	3.08842i	−0.158536	+	0.133028i
$540$		0			0
$541$	35.3132	+	20.3881i	1.51823	+	0.876552i	0.999770	+	0.0214527i	$0.00682912\pi$
$541$	35.3132	+	20.3881i	1.51823	+	0.876552i	0.518463	+	0.855100i	$0.326504\pi$
$542$		0			0
$543$	3.13942	+	17.8046i	0.134726	+	0.764067i
$544$		0			0
$545$	3.88758	−	6.73348i	0.166526	−	0.288431i
$546$		0			0
$547$	7.52538	−	4.34478i	0.321762	−	0.185770i	−0.330416	−	0.943836i	$-0.607189\pi$
$547$	7.52538	−	4.34478i	0.321762	−	0.185770i	0.652178	+	0.758066i	$0.273856\pi$
$548$		0			0
$549$			4.83145i			0.206201i
$550$		0			0
$551$	−2.38624	+	0.868519i	−0.101657	+	0.0370002i
$552$		0			0
$553$	27.2494	−	4.80480i	1.15876	−	0.204321i
$554$		0			0
$555$	−9.05933	−	8.43222i	−0.384547	−	0.357928i
$556$		0			0
$557$	−39.5716	+	6.97753i	−1.67670	+	0.295648i	−0.929465	−	0.368911i	$-0.879731\pi$
$557$	−39.5716	+	6.97753i	−1.67670	+	0.295648i	−0.747236	+	0.664558i	$0.768620\pi$
$558$		0			0
$559$	−42.3265	+	15.4056i	−1.79022	+	0.651586i
$560$		0			0
$561$		−	4.73302i		−	0.199828i
$562$		0			0
$563$	−36.2097	+	20.9057i	−1.52606	+	0.881070i	−0.526536	+	0.850153i	$0.676509\pi$
$563$	−36.2097	+	20.9057i	−1.52606	+	0.881070i	−0.999522	+	0.0309168i	$0.990157\pi$
$564$		0			0
$565$	4.99728	−	8.65555i	0.210237	−	0.364142i
$566$		0			0
$567$	−4.00336	−	22.7042i	−0.168125	−	0.953486i
$568$		0			0
$569$	−19.8909	−	11.4840i	−0.833870	−	0.481435i	0.0213056	−	0.999773i	$-0.493218\pi$
$569$	−19.8909	−	11.4840i	−0.833870	−	0.481435i	−0.855176	+	0.518338i	$0.826551\pi$
$570$		0			0
$571$	5.14388	−	4.31623i	0.215265	−	0.180629i	−0.528779	−	0.848760i	$-0.677350\pi$
$571$	5.14388	−	4.31623i	0.215265	−	0.180629i	0.744044	+	0.668131i	$0.232905\pi$
$572$		0			0
$573$	−13.2183	−	2.33075i	−0.552203	−	0.0973683i
$574$		0			0
$575$	4.82809	−	13.2651i	0.201345	−	0.553192i
$576$		0			0
$577$	16.7269	+	19.9344i	0.696351	+	0.829879i	0.992108	−	0.125385i	$-0.0400164\pi$
$577$	16.7269	+	19.9344i	0.696351	+	0.829879i	−0.295757	+	0.955263i	$0.595572\pi$
$578$		0			0
$579$	−1.69473	−	4.65622i	−0.0704304	−	0.193506i
$580$		0			0
$581$	−1.53614	−	2.66068i	−0.0637300	−	0.110384i
$582$		0			0
$583$	18.3988	+	6.69661i	0.762000	+	0.277345i
$584$		0			0
$585$	−4.78041	−	4.01124i	−0.197645	−	0.165844i
$586$		0			0
$587$	23.1752	−	27.6192i	0.956544	−	1.13996i	−0.0335329	−	0.999438i	$-0.510676\pi$
$587$	23.1752	−	27.6192i	0.956544	−	1.13996i	0.990077	−	0.140527i	$-0.0448797\pi$
$588$		0			0
$589$	1.12736	−	6.39357i	0.0464520	−	0.263442i
$590$		0			0
$591$	55.7057			2.29143
$592$		0			0
$593$	−33.1977			−1.36326			−0.681632	−	0.731695i	$-0.738730\pi$
$593$	−33.1977			−1.36326			−0.681632	+	0.731695i	$0.738730\pi$
$594$		0			0
$595$	0.469712	−	2.66387i	0.0192563	−	0.109208i
$596$		0			0
$597$	17.4401	−	20.7843i	0.713775	−	0.850643i
$598$		0			0
$599$	3.49652	+	2.93393i	0.142864	+	0.119877i	0.711419	−	0.702768i	$-0.248053\pi$
$599$	3.49652	+	2.93393i	0.142864	+	0.119877i	−0.568555	+	0.822645i	$0.692497\pi$
$600$		0			0
$601$	5.93036	+	2.15848i	0.241905	+	0.0880460i	0.460127	−	0.887853i	$-0.347804\pi$
$601$	5.93036	+	2.15848i	0.241905	+	0.0880460i	−0.218223	+	0.975899i	$0.570026\pi$
$602$		0			0
$603$	2.86845	+	4.96830i	0.116812	+	0.202325i
$604$		0			0
$605$	−2.68318	−	7.37199i	−0.109087	−	0.299714i
$606$		0			0
$607$	9.16078	+	10.9174i	0.371824	+	0.443123i	0.919216	−	0.393753i	$-0.128824\pi$
$607$	9.16078	+	10.9174i	0.371824	+	0.443123i	−0.547392	+	0.836877i	$0.684379\pi$
$608$		0			0
$609$	0.876531	−	2.40825i	0.0355188	−	0.0975871i
$610$		0			0
$611$	18.9623	+	3.34357i	0.767134	+	0.135267i
$612$		0			0
$613$	17.1875	−	14.4220i	0.694196	−	0.582500i	−0.225920	−	0.974146i	$-0.572539\pi$
$613$	17.1875	−	14.4220i	0.694196	−	0.582500i	0.920116	+	0.391646i	$0.128094\pi$
$614$		0			0
$615$	4.03203	+	2.32789i	0.162587	+	0.0938698i
$616$		0			0
$617$	7.41495	+	42.0523i	0.298515	+	1.69296i	0.652563	+	0.757734i	$0.273694\pi$
$617$	7.41495	+	42.0523i	0.298515	+	1.69296i	−0.354048	+	0.935227i	$0.615195\pi$
$618$		0			0
$619$	16.4533	−	28.4980i	0.661315	−	1.14543i	−0.318956	−	0.947770i	$-0.603332\pi$
$619$	16.4533	−	28.4980i	0.661315	−	1.14543i	0.980270	−	0.197661i	$-0.0633346\pi$
$620$		0			0
$621$	11.4316	−	6.60003i	0.458734	−	0.264850i
$622$		0			0
$623$		−	14.2629i		−	0.571432i
$624$		0			0
$625$	−10.4088	+	3.78848i	−0.416350	+	0.151539i
$626$		0			0
$627$	14.8859	−	2.62478i	0.594485	−	0.104824i
$628$		0			0
$629$	−1.78612	+	7.76951i	−0.0712173	+	0.309790i
$630$		0			0
$631$	−8.99243	+	1.58561i	−0.357983	+	0.0631221i	−0.349747	−	0.936844i	$-0.613733\pi$
$631$	−8.99243	+	1.58561i	−0.357983	+	0.0631221i	−0.00823558	+	0.999966i	$0.502621\pi$
$632$		0			0
$633$	−12.1415	+	4.41915i	−0.482582	+	0.175646i
$634$		0			0
$635$			1.31487i			0.0521790i
$636$		0			0
$637$	12.6387	−	7.29698i	0.500765	−	0.289117i
$638$		0			0
$639$	−3.55155	+	6.15146i	−0.140497	+	0.243348i
$640$		0			0
$641$	3.28290	+	18.6183i	0.129667	+	0.735378i	0.978426	+	0.206598i	$0.0662392\pi$
$641$	3.28290	+	18.6183i	0.129667	+	0.735378i	−0.848759	+	0.528780i	$0.822650\pi$
$642$		0			0
$643$	−4.95729	−	2.86209i	−0.195496	−	0.112870i	0.399057	−	0.916926i	$-0.369338\pi$
$643$	−4.95729	−	2.86209i	−0.195496	−	0.112870i	−0.594553	+	0.804056i	$0.702671\pi$
$644$		0			0
$645$	−13.0612	+	10.9596i	−0.514282	+	0.431534i
$646$		0			0
$647$	8.39393	+	1.48008i	0.330000	+	0.0581878i	0.336193	−	0.941793i	$-0.390860\pi$
$647$	8.39393	+	1.48008i	0.330000	+	0.0581878i	−0.00619377	+	0.999981i	$0.501972\pi$
$648$		0			0
$649$	6.37409	−	17.5127i	0.250205	−	0.687432i
$650$		0			0
$651$	4.21160	+	5.01919i	0.165066	+	0.196717i
$652$		0			0
$653$	8.56441	+	23.5305i	0.335151	+	0.920820i	0.986749	+	0.162255i	$0.0518768\pi$
$653$	8.56441	+	23.5305i	0.335151	+	0.920820i	−0.651598	+	0.758565i	$0.725901\pi$
$654$		0			0
$655$	−4.85094	−	8.40207i	−0.189542	−	0.328296i
$656$		0			0
$657$	−14.8353	−	5.39962i	−0.578781	−	0.210659i
$658$		0			0
$659$	−12.2404	−	10.2709i	−0.476820	−	0.400099i	0.372455	−	0.928050i	$-0.378516\pi$
$659$	−12.2404	−	10.2709i	−0.476820	−	0.400099i	−0.849275	+	0.527951i	$0.822960\pi$
$660$		0			0
$661$	15.1978	−	18.1120i	0.591125	−	0.704476i	−0.384696	−	0.923043i	$-0.625694\pi$
$661$	15.1978	−	18.1120i	0.591125	−	0.704476i	0.975822	+	0.218567i	$0.0701383\pi$
$662$		0			0
$663$	−2.49639	+	14.1577i	−0.0969518	+	0.549841i
$664$		0			0
$665$	8.63866			0.334993
$666$		0			0
$667$	2.13792			0.0827805
$668$		0			0
$669$	0.861162	−	4.88389i	0.0332944	−	0.188822i
$670$		0			0
$671$	−4.71981	+	5.62486i	−0.182206	+	0.217145i
$672$		0			0
$673$	29.9818	+	25.1577i	1.15571	+	0.969758i	0.999838	−	0.0180192i	$-0.00573598\pi$
$673$	29.9818	+	25.1577i	1.15571	+	0.969758i	0.155875	+	0.987777i	$0.450180\pi$
$674$		0			0
$675$	−14.1006	−	5.13221i	−0.542733	−	0.197539i
$676$		0			0
$677$	6.70016	+	11.6050i	0.257508	+	0.446017i	0.965574	−	0.260129i	$-0.0837652\pi$
$677$	6.70016	+	11.6050i	0.257508	+	0.446017i	−0.708066	+	0.706147i	$0.750432\pi$
$678$		0			0
$679$	−5.35961	−	14.7254i	−0.205683	−	0.565109i
$680$		0			0
$681$	6.65079	+	7.92610i	0.254859	+	0.303729i
$682$		0			0
$683$	10.3475	−	28.4296i	0.395938	−	1.08783i	−0.568307	−	0.822817i	$-0.692401\pi$
$683$	10.3475	−	28.4296i	0.395938	−	1.08783i	0.964245	−	0.265013i	$-0.0853764\pi$
$684$		0			0
$685$	7.34615	+	1.29532i	0.280682	+	0.0494918i
$686$		0			0
$687$	−15.3395	+	12.8713i	−0.585237	+	0.491072i
$688$		0			0
$689$	−51.5036	−	29.7356i	−1.96213	−	1.13284i
$690$		0			0
$691$	4.08085	+	23.1436i	0.155243	+	0.880426i	0.958563	+	0.284879i	$0.0919534\pi$
$691$	4.08085	+	23.1436i	0.155243	+	0.880426i	−0.803321	+	0.595547i	$0.796935\pi$
$692$		0			0
$693$	−2.13272	+	3.69398i	−0.0810153	+	0.140323i
$694$		0			0
$695$	−4.79418	+	2.76792i	−0.181854	+	0.104993i
$696$		0			0
$697$		−	2.99901i		−	0.113595i
$698$		0			0
$699$	−5.30817	+	1.93202i	−0.200773	+	0.0730756i
$700$		0			0
$701$	19.5898	−	3.45422i	0.739898	−	0.130464i	0.209019	−	0.977912i	$-0.432973\pi$
$701$	19.5898	−	3.45422i	0.739898	−	0.130464i	0.530879	+	0.847448i	$0.321862\pi$
$702$		0			0
$703$	−25.4265	−	1.30883i	−0.958979	−	0.0493636i
$704$		0			0
$705$	7.17784	−	1.26565i	0.270333	−	0.0476670i
$706$		0			0
$707$	22.0763	−	8.03512i	0.830265	−	0.302192i
$708$		0			0
$709$		−	2.65540i		−	0.0997258i	−0.998756	−	0.0498629i	$-0.984122\pi$
$709$		−	2.65540i		−	0.0997258i	0.998756	−	0.0498629i	$-0.0158784\pi$
$710$		0			0
$711$	−13.4794	+	7.78235i	−0.505518	+	0.291861i
$712$		0			0
$713$	−2.73291	+	4.73353i	−0.102348	+	0.177272i
$714$		0			0
$715$	−1.64688	−	9.33989i	−0.0615897	−	0.349292i
$716$		0			0
$717$	−33.6064	−	19.4026i	−1.25505	−	0.724605i
$718$		0			0
$719$	−33.7594	+	28.3275i	−1.25901	+	1.05644i	−0.263226	+	0.964734i	$0.584787\pi$
$719$	−33.7594	+	28.3275i	−1.25901	+	1.05644i	−0.995786	+	0.0917029i	$0.970769\pi$
$720$		0			0
$721$	−4.06829	−	0.717350i	−0.151511	−	0.0267155i
$722$		0			0
$723$	1.06229	−	2.91861i	0.0395069	−	0.108544i
$724$		0			0
$725$	−1.56219	−	1.86175i	−0.0580185	−	0.0691437i
$726$		0			0
$727$	3.72743	+	10.2410i	0.138243	+	0.379819i	0.989424	−	0.145053i	$-0.0463354\pi$
$727$	3.72743	+	10.2410i	0.138243	+	0.379819i	−0.851181	+	0.524872i	$0.824113\pi$
$728$		0			0
$729$	−4.98198	−	8.62904i	−0.184518	−	0.319594i
$730$		0			0
$731$	10.3204	+	3.75633i	0.381715	+	0.138933i
$732$		0			0
$733$	−24.0430	−	20.1744i	−0.888047	−	0.745160i	0.0797705	−	0.996813i	$-0.474581\pi$
$733$	−24.0430	−	20.1744i	−0.888047	−	0.745160i	−0.967817	+	0.251653i	$0.919026\pi$
$734$		0			0
$735$	3.55093	−	4.23183i	0.130978	−	0.156094i
$736$		0			0
$737$	−1.51400	+	8.58634i	−0.0557690	+	0.316282i
$738$		0			0
$739$	−32.4797			−1.19479			−0.597393	−	0.801949i	$-0.703797\pi$
$739$	−32.4797			−1.19479			−0.597393	+	0.801949i	$0.703797\pi$
$740$		0			0
$741$	−45.9121			−1.68662
$742$		0			0
$743$	3.91602	−	22.2089i	0.143665	−	0.814764i	−0.824764	−	0.565476i	$-0.808692\pi$
$743$	3.91602	−	22.2089i	0.143665	−	0.814764i	0.968429	−	0.249288i	$-0.0801965\pi$
$744$		0			0
$745$	−4.69428	+	5.59443i	−0.171985	+	0.204964i
$746$		0			0
$747$	1.32389	+	1.11087i	0.0484385	+	0.0406447i
$748$		0			0
$749$	36.6051	+	13.3232i	1.33752	+	0.486818i
$750$		0			0
$751$	12.7936	+	22.1592i	0.466845	+	0.808599i	0.999283	−	0.0378699i	$-0.0120573\pi$
$751$	12.7936	+	22.1592i	0.466845	+	0.808599i	−0.532438	+	0.846469i	$0.678724\pi$
$752$		0			0
$753$	−11.1999	−	30.7715i	−0.408148	−	1.12138i
$754$		0			0
$755$	−2.92866	−	3.49024i	−0.106585	−	0.127023i
$756$		0			0
$757$	13.8986	−	38.1860i	0.505152	−	1.38789i	−0.381033	−	0.924562i	$-0.624431\pi$
$757$	13.8986	−	38.1860i	0.505152	−	1.38789i	0.886185	−	0.463332i	$-0.153346\pi$
$758$		0			0
$759$	−12.5325	−	2.20982i	−0.454901	−	0.0802113i
$760$		0			0
$761$	−13.3742	+	11.2223i	−0.484814	+	0.406807i	−0.852163	−	0.523276i	$-0.824710\pi$
$761$	−13.3742	+	11.2223i	−0.484814	+	0.406807i	0.367349	+	0.930083i	$0.380265\pi$
$762$		0			0
$763$	13.9796	+	8.07115i	0.506097	+	0.292195i
$764$		0			0
$765$	0.264221	+	1.49847i	0.00955292	+	0.0541773i
$766$		0			0
$767$	−28.3035	+	49.0231i	−1.02198	+	1.77012i
$768$		0			0
$769$	−17.3511	+	10.0177i	−0.625698	+	0.361247i	−0.779084	−	0.626920i	$-0.784315\pi$
$769$	−17.3511	+	10.0177i	−0.625698	+	0.361247i	0.153386	+	0.988166i	$0.450982\pi$
$770$		0			0
$771$			31.9364i			1.15016i
$772$		0			0
$773$	38.3674	−	13.9646i	1.37998	−	0.502271i	0.457807	−	0.889052i	$-0.348635\pi$
$773$	38.3674	−	13.9646i	1.37998	−	0.502271i	0.922172	+	0.386781i	$0.126413\pi$
$774$		0			0
$775$	6.11904	−	1.07895i	0.219802	−	0.0387571i
$776$		0			0
$777$	17.5065	−	18.8084i	0.628041	−	0.674749i
$778$		0			0
$779$	9.43222	−	1.66315i	0.337944	−	0.0595887i
$780$		0			0
$781$	−10.1441	+	3.69215i	−0.362984	+	0.132115i
$782$		0			0
$783$		−	2.27258i		−	0.0812155i
$784$		0			0
$785$	−10.9838	+	6.34148i	−0.392027	+	0.226337i
$786$		0			0
$787$	−26.5477	+	45.9819i	−0.946322	+	1.63908i	−0.193240	+	0.981151i	$0.561900\pi$
$787$	−26.5477	+	45.9819i	−0.946322	+	1.63908i	−0.753082	+	0.657927i	$0.771434\pi$
$788$		0			0
$789$	1.62834	+	9.23478i	0.0579705	+	0.328767i
$790$		0			0
$791$	17.9701	+	10.3751i	0.638944	+	0.368895i
$792$		0			0
$793$	17.0850	−	14.3360i	0.606707	−	0.509087i
$794$		0			0
$795$	−22.1697	−	3.90912i	−0.786279	−	0.138642i
$796$		0			0
$797$	−13.8787	+	38.1313i	−0.491608	+	1.35068i	0.407601	+	0.913160i	$0.366366\pi$
$797$	−13.8787	+	38.1313i	−0.491608	+	1.35068i	−0.899208	+	0.437521i	$0.855857\pi$
$798$		0			0
$799$	−3.01782	−	3.59650i	−0.106763	−	0.127235i
$800$		0			0
$801$	2.74407	+	7.53928i	0.0969571	+	0.266387i
$802$		0			0
$803$	−11.9967	−	20.7789i	−0.423354	−	0.733270i
$804$		0			0
$805$	−6.83432	−	2.48749i	−0.240878	−	0.0876724i
$806$		0			0
$807$	−27.1515	−	22.7828i	−0.955778	−	0.801993i
$808$		0			0
$809$	−10.2354	+	12.1980i	−0.359856	+	0.428860i	−0.915349	−	0.402661i	$-0.868085\pi$
$809$	−10.2354	+	12.1980i	−0.359856	+	0.428860i	0.555493	+	0.831521i	$0.312530\pi$
$810$		0			0
$811$	1.84097	−	10.4407i	0.0646452	−	0.366621i	−0.935274	−	0.353924i	$-0.884847\pi$
$811$	1.84097	−	10.4407i	0.0646452	−	0.366621i	0.999919	−	0.0126972i	$-0.00404175\pi$
$812$		0			0
$813$	34.4623			1.20865
$814$		0			0
$815$	12.7527			0.446708
$816$		0			0
$817$	−6.09069	+	34.5420i	−0.213086	+	1.20847i
$818$		0			0
$819$	8.32789	−	9.92479i	0.291000	−	0.346800i
$820$		0			0
$821$	−1.11689	−	0.937186i	−0.0389799	−	0.0327080i	0.623090	−	0.782150i	$-0.285877\pi$
$821$	−1.11689	−	0.937186i	−0.0389799	−	0.0327080i	−0.662069	+	0.749442i	$0.730322\pi$
$822$		0			0
$823$	28.6794	+	10.4384i	0.999700	+	0.363861i	0.789469	−	0.613790i	$-0.210356\pi$
$823$	28.6794	+	10.4384i	0.999700	+	0.363861i	0.210231	+	0.977652i	$0.432578\pi$
$824$		0			0
$825$	7.23324	+	12.5283i	0.251829	+	0.436181i
$826$		0			0
$827$	7.35407	+	20.2051i	0.255726	+	0.702602i	0.999419	+	0.0340804i	$0.0108502\pi$
$827$	7.35407	+	20.2051i	0.255726	+	0.702602i	−0.743693	+	0.668521i	$0.766928\pi$
$828$		0			0
$829$	−2.16679	−	2.58228i	−0.0752559	−	0.0896865i	0.727103	−	0.686529i	$-0.240866\pi$
$829$	−2.16679	−	2.58228i	−0.0752559	−	0.0896865i	−0.802359	+	0.596842i	$0.796422\pi$
$830$		0			0
$831$	16.7049	−	45.8964i	0.579487	−	1.59213i
$832$		0			0
$833$	−3.50437	−	0.617915i	−0.121419	−	0.0214095i
$834$		0			0
$835$	−17.9547	+	15.0658i	−0.621348	+	0.521373i
$836$		0			0
$837$	5.03170	+	2.90505i	0.173921	+	0.100413i
$838$		0			0
$839$	7.89313	+	44.7641i	0.272501	+	1.54543i	0.746790	+	0.665060i	$0.231594\pi$
$839$	7.89313	+	44.7641i	0.272501	+	1.54543i	−0.474289	+	0.880369i	$0.657295\pi$
$840$		0			0
$841$	−14.3160	+	24.7960i	−0.493654	+	0.855034i
$842$		0			0
$843$	−27.2858	+	15.7534i	−0.939772	+	0.542577i
$844$		0			0
$845$			15.8452i			0.545091i
$846$		0			0
$847$	15.3053	−	5.57066i	0.525896	−	0.191410i
$848$		0			0
$849$	6.10238	−	1.07601i	0.209433	−	0.0369287i
$850$		0			0
$851$	19.7388	+	8.35698i	0.676639	+	0.286474i
$852$		0			0
$853$	−18.9115	+	3.33461i	−0.647518	+	0.114175i	−0.487755	−	0.872981i	$-0.662184\pi$
$853$	−18.9115	+	3.33461i	−0.647518	+	0.114175i	−0.159763	+	0.987155i	$0.551073\pi$
$854$		0			0
$855$	−4.56633	+	1.66201i	−0.156165	+	0.0568395i
$856$		0			0
$857$			53.4371i			1.82538i	0.408655	+	0.912689i	$0.365998\pi$
$857$			53.4371i			1.82538i	−0.408655	+	0.912689i	$0.634002\pi$
$858$		0			0
$859$	10.1449	−	5.85715i	0.346139	−	0.199843i	−0.316845	−	0.948477i	$-0.602623\pi$
$859$	10.1449	−	5.85715i	0.346139	−	0.199843i	0.662983	+	0.748634i	$0.269290\pi$
$860$		0			0
$861$	−4.83303	+	8.37106i	−0.164709	+	0.285285i
$862$		0			0
$863$	2.09213	+	11.8651i	0.0712170	+	0.403891i	0.999488	+	0.0319877i	$0.0101838\pi$
$863$	2.09213	+	11.8651i	0.0712170	+	0.403891i	−0.928271	+	0.371904i	$0.878705\pi$
$864$		0			0
$865$	−4.04268	−	2.33404i	−0.137455	−	0.0793599i
$866$		0			0
$867$	−23.8902	+	20.0462i	−0.811352	+	0.680805i
$868$		0			0
$869$	−23.2955	−	4.10762i	−0.790245	−	0.139342i
$870$		0			0
$871$	9.05758	−	24.8855i	0.306904	−	0.843213i
$872$		0			0
$873$	5.66610	+	6.75259i	0.191768	+	0.228541i
$874$		0			0
$875$	6.35718	+	17.4662i	0.214912	+	0.590466i
$876$		0			0
$877$	11.8245	+	20.4807i	0.399286	+	0.691583i	0.993638	−	0.112622i	$-0.0359248\pi$
$877$	11.8245	+	20.4807i	0.399286	+	0.691583i	−0.594352	+	0.804205i	$0.702591\pi$
$878$		0			0
$879$	25.6949	+	9.35220i	0.866669	+	0.315442i
$880$		0			0
$881$	−5.89364	−	4.94535i	−0.198562	−	0.166613i	0.538086	−	0.842890i	$-0.319148\pi$
$881$	−5.89364	−	4.94535i	−0.198562	−	0.166613i	−0.736647	+	0.676277i	$0.763592\pi$
$882$		0			0
$883$	21.1313	−	25.1833i	0.711126	−	0.847486i	−0.282611	−	0.959235i	$-0.591201\pi$
$883$	21.1313	−	25.1833i	0.711126	−	0.847486i	0.993737	+	0.111748i	$0.0356450\pi$
$884$		0			0
$885$	−3.72085	+	21.1020i	−0.125075	+	0.709336i
$886$		0			0
$887$	−16.4422			−0.552075			−0.276037	−	0.961147i	$-0.589021\pi$
$887$	−16.4422			−0.552075			−0.276037	+	0.961147i	$0.589021\pi$
$888$		0			0
$889$	−2.72985			−0.0915564
$890$		0			0
$891$	−3.42247	+	19.4098i	−0.114657	+	0.650252i
$892$		0			0
$893$	9.63782	−	11.4859i	0.322517	−	0.384361i
$894$		0			0
$895$	−7.43254	−	6.23664i	−0.248442	−	0.208468i
$896$		0			0
$897$	36.3225	+	13.2203i	1.21277	+	0.441414i
$898$		0			0
$899$	0.470510	+	0.814947i	0.0156924	+	0.0271800i
$900$		0			0
$901$	4.95958	+	13.6263i	0.165227	+	0.453959i
$902$		0			0
$903$	−22.7537	−	27.1168i	−0.757195	−	0.902390i
$904$		0			0
$905$	3.02113	−	8.30048i	0.100426	−	0.275917i
$906$		0			0
$907$	9.14252	+	1.61207i	0.303572	+	0.0535280i	0.323359	−	0.946276i	$-0.395188\pi$
$907$	9.14252	+	1.61207i	0.303572	+	0.0535280i	−0.0197871	+	0.999804i	$0.506299\pi$
$908$		0			0
$909$	−10.1235	+	8.49461i	−0.335775	+	0.281748i
$910$		0			0
$911$	12.4920	+	7.21223i	0.413877	+	0.238952i	0.692454	−	0.721462i	$-0.256529\pi$
$911$	12.4920	+	7.21223i	0.413877	+	0.238952i	−0.278577	+	0.960414i	$0.589863\pi$
$912$		0			0
$913$	0.456086	+	2.58659i	0.0150943	+	0.0856037i
$914$		0			0
$915$	4.22117	−	7.31128i	0.139548	−	0.241704i
$916$		0			0
$917$	17.4439	−	10.0712i	0.576048	−	0.332581i
$918$		0			0
$919$		−	35.5649i		−	1.17318i	−0.809885	−	0.586588i	$-0.800471\pi$
$919$		−	35.5649i		−	1.17318i	0.809885	−	0.586588i	$-0.199529\pi$
$920$		0			0
$921$	−65.8803	+	23.9785i	−2.17083	+	0.790117i
$922$		0			0
$923$	32.2911	−	5.69379i	1.06287	−	0.187413i
$924$		0			0
$925$	−7.14588	−	23.2956i	−0.234955	−	0.765954i
$926$		0			0
$927$	2.28848	−	0.403521i	0.0751636	−	0.0132534i
$928$		0			0
$929$	10.3365	−	3.76219i	0.339131	−	0.123434i	−0.166840	−	0.985984i	$-0.553356\pi$
$929$	10.3365	−	3.76219i	0.339131	−	0.123434i	0.505971	+	0.862550i	$0.331134\pi$
$930$		0			0
$931$		−	11.3643i		−	0.372451i
$932$		0			0
$933$	6.63238	−	3.82921i	0.217134	−	0.125363i
$934$		0			0
$935$	−1.15623	+	2.00266i	−0.0378129	+	0.0654939i
$936$		0			0
$937$	−8.45256	−	47.9368i	−0.276133	−	1.56603i	−0.735340	−	0.677699i	$-0.762977\pi$
$937$	−8.45256	−	47.9368i	−0.276133	−	1.56603i	0.459206	−	0.888330i	$-0.348134\pi$
$938$		0			0
$939$	−29.3794	−	16.9622i	−0.958761	−	0.553541i
$940$		0			0
$941$	−15.0774	+	12.6514i	−0.491508	+	0.412424i	−0.854566	−	0.519342i	$-0.826177\pi$
$941$	−15.0774	+	12.6514i	−0.491508	+	0.412424i	0.363058	+	0.931766i	$0.381733\pi$
$942$		0			0
$943$	−7.94103	−	1.40022i	−0.258596	−	0.0455974i
$944$		0			0
$945$	−2.64417	+	7.26480i	−0.0860149	+	0.236324i
$946$		0			0
$947$	12.2906	+	14.6473i	0.399390	+	0.475974i	0.927834	−	0.372994i	$-0.121669\pi$
$947$	12.2906	+	14.6473i	0.399390	+	0.475974i	−0.528444	+	0.848968i	$0.677224\pi$
$948$		0			0
$949$	24.9257	+	68.4827i	0.809121	+	2.22304i
$950$		0			0
$951$	23.7236	+	41.0904i	0.769290	+	1.33245i
$952$		0			0
$953$	43.9106	+	15.9822i	1.42240	+	0.517713i	0.934744	−	0.355321i	$-0.115629\pi$
$953$	43.9106	+	15.9822i	1.42240	+	0.517713i	0.487660	+	0.873034i	$0.337851\pi$
$954$		0			0
$955$	5.02362	+	4.21531i	0.162560	+	0.136404i
$956$		0			0
$957$	−1.40831	+	1.67836i	−0.0455241	+	0.0542536i
$958$		0			0
$959$	−2.68927	+	15.2516i	−0.0868412	+	0.492501i
$960$		0			0
$961$	28.5942			0.922393
$962$		0			0
$963$	−21.9124			−0.706119
$964$		0			0
$965$	−0.420394	+	2.38417i	−0.0135329	+	0.0767491i
$966$		0			0
$967$	5.95207	−	7.09340i	0.191406	−	0.228108i	−0.661803	−	0.749677i	$-0.730209\pi$
$967$	5.95207	−	7.09340i	0.191406	−	0.228108i	0.853209	+	0.521569i	$0.174653\pi$
$968$		0			0
$969$	8.57564	+	7.19582i	0.275489	+	0.231163i
$970$		0			0
$971$	4.93742	+	1.79707i	0.158449	+	0.0576708i	0.420027	−	0.907512i	$-0.362021\pi$
$971$	4.93742	+	1.79707i	0.158449	+	0.0576708i	−0.261578	+	0.965182i	$0.584243\pi$
$972$		0			0
$973$	−5.74659	−	9.95338i	−0.184227	−	0.319091i
$974$		0			0
$975$	−15.0286	−	41.2908i	−0.481301	−	1.32236i
$976$		0			0
$977$	−12.7485	−	15.1930i	−0.407860	−	0.486069i	0.522540	−	0.852615i	$-0.324985\pi$
$977$	−12.7485	−	15.1930i	−0.407860	−	0.486069i	−0.930400	+	0.366546i	$0.880540\pi$
$978$		0			0
$979$	−4.17038	+	11.4580i	−0.133286	+	0.366200i
$980$		0			0
$981$	−8.94236	−	1.57678i	−0.285508	−	0.0503427i
$982$		0			0
$983$	9.79880	−	8.22217i	0.312533	−	0.262246i	−0.473005	−	0.881060i	$-0.656831\pi$
$983$	9.79880	−	8.22217i	0.312533	−	0.262246i	0.785538	+	0.618813i	$0.212386\pi$
$984$		0			0
$985$	−23.5704	−	13.6084i	−0.751017	−	0.433600i
$986$		0			0
$987$	2.62766	+	14.9022i	0.0836393	+	0.474342i
$988$		0			0
$989$	14.7649	−	25.5735i	0.469495	−	0.813190i
$990$		0			0
$991$	31.1868	−	18.0057i	0.990683	−	0.571971i	0.0852045	−	0.996363i	$-0.472846\pi$
$991$	31.1868	−	18.0057i	0.990683	−	0.571971i	0.905478	+	0.424392i	$0.139512\pi$
$992$		0			0
$993$		−	28.0527i		−	0.890224i
$994$		0			0
$995$	−12.4567	+	4.53388i	−0.394905	+	0.143734i
$996$		0			0
$997$	−32.5484	+	5.73917i	−1.03082	+	0.181761i	−0.663377	−	0.748285i	$-0.730878\pi$
$997$	−32.5484	+	5.73917i	−1.03082	+	0.181761i	−0.367442	+	0.930046i	$0.619766\pi$
$998$		0			0
$999$	8.88338	−	20.9822i	0.281058	−	0.663847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bq.d.65.1		18
4.3	odd	2		37.2.h.a.28.1	yes	18
12.11	even	2		333.2.bl.d.28.3		18
20.3	even	4		925.2.ba.a.324.6		36
20.7	even	4		925.2.ba.a.324.1		36
20.19	odd	2		925.2.bb.a.176.3		18
37.4	even	18	inner	592.2.bq.d.337.1		18
148.35	even	36		1369.2.a.m.1.18		18
148.39	even	36		1369.2.a.m.1.1		18
148.99	odd	18		1369.2.b.g.1368.1		18
148.115	odd	18		37.2.h.a.4.1	✓	18
148.123	odd	18		1369.2.b.g.1368.18		18
444.263	even	18		333.2.bl.d.226.3		18
740.263	even	36		925.2.ba.a.374.1		36
740.559	odd	18		925.2.bb.a.226.3		18
740.707	even	36		925.2.ba.a.374.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.h.a.4.1	✓	18	148.115	odd	18
37.2.h.a.28.1	yes	18	4.3	odd	2
333.2.bl.d.28.3		18	12.11	even	2
333.2.bl.d.226.3		18	444.263	even	18
592.2.bq.d.65.1		18	1.1	even	1	trivial
592.2.bq.d.337.1		18	37.4	even	18	inner
925.2.ba.a.324.1		36	20.7	even	4
925.2.ba.a.324.6		36	20.3	even	4
925.2.ba.a.374.1		36	740.263	even	36
925.2.ba.a.374.6		36	740.707	even	36
925.2.bb.a.176.3		18	20.19	odd	2
925.2.bb.a.226.3		18	740.559	odd	18
1369.2.a.m.1.1		18	148.39	even	36
1369.2.a.m.1.18		18	148.35	even	36
1369.2.b.g.1368.1		18	148.99	odd	18
1369.2.b.g.1368.18		18	148.123	odd	18

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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bq (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.354362 + 2.00969i) q^{3} +(0.640888 - 0.763781i) q^{5} +(1.58572 + 1.33057i) q^{7} +(-1.09419 - 0.398252i) q^{9} +O(q^{10})\)	\(q+(-0.354362 + 2.00969i) q^{3} +(0.640888 - 0.763781i) q^{5} +(1.58572 + 1.33057i) q^{7} +(-1.09419 - 0.398252i) q^{9} +(-0.884822 - 1.53256i) q^{11} +(1.83841 + 5.05098i) q^{13} +(1.30785 + 1.55864i) q^{15} +(0.448257 - 1.23158i) q^{17} +(4.12204 + 0.726826i) q^{19} +(-3.23595 + 2.71529i) q^{21} +(-3.05179 - 1.76195i) q^{23} +(0.695618 + 3.94504i) q^{25} +(-1.87293 + 3.24402i) q^{27} +(-0.525410 + 0.303345i) q^{29} -1.55107i q^{31} +(3.39351 - 1.23514i) q^{33} +(2.03253 - 0.358390i) q^{35} +(-6.03673 + 0.746918i) q^{37} +(-10.8023 + 1.90475i) q^{39} +(2.15024 - 0.782625i) q^{41} +8.37985i q^{43} +(-1.00543 + 0.580485i) q^{45} +(1.79110 - 3.10228i) q^{47} +(-0.471469 - 2.67384i) q^{49} +(2.31624 + 1.33728i) q^{51} +(-8.47562 + 7.11189i) q^{53} +(-1.73761 - 0.306387i) q^{55} +(-2.92139 + 8.02644i) q^{57} +(6.76937 + 8.06742i) q^{59} +(-1.41913 - 3.89904i) q^{61} +(-1.20517 - 2.08741i) q^{63} +(5.03605 + 1.83297i) q^{65} +(-3.77420 - 3.16693i) q^{67} +(4.62240 - 5.50876i) q^{69} +(1.05928 - 6.00749i) q^{71} +13.5583 q^{73} -8.17480 q^{75} +(0.636103 - 3.60752i) q^{77} +(8.59215 - 10.2397i) q^{79} +(-8.53173 - 7.15897i) q^{81} +(-1.39469 - 0.507624i) q^{83} +(-0.653371 - 1.13167i) q^{85} +(-0.423444 - 1.16340i) q^{87} +(-4.42899 - 5.27827i) q^{89} +(-3.80551 + 10.4556i) q^{91} +(3.11716 + 0.549640i) q^{93} +(3.19690 - 2.68252i) q^{95} +(-6.55603 - 3.78513i) q^{97} +(0.357818 + 2.02929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{3} - 3 q^{5} + 3 q^{7} - 3 q^{9}+O(q^{10}) \) 18 * q + 9 * q^3 - 3 * q^5 + 3 * q^7 - 3 * q^9	\( 18 q + 9 q^{3} - 3 q^{5} + 3 q^{7} - 3 q^{9} - 9 q^{11} + 9 q^{13} + 15 q^{15} - 15 q^{17} - 6 q^{19} - 12 q^{21} + 9 q^{23} + 21 q^{25} - 21 q^{27} - 18 q^{29} + 6 q^{33} + 12 q^{35} + 6 q^{37} + 6 q^{39} - 24 q^{41} + 36 q^{47} + 21 q^{49} - 81 q^{51} - 39 q^{53} - 12 q^{55} + 15 q^{57} + 6 q^{59} + 42 q^{61} + 27 q^{63} + 18 q^{65} - 36 q^{69} + 9 q^{71} - 54 q^{73} - 18 q^{75} + 33 q^{77} + 6 q^{79} - 45 q^{81} + 24 q^{83} + 6 q^{85} - 21 q^{87} + 18 q^{89} + 3 q^{91} + 66 q^{93} + 15 q^{95} - 9 q^{97} - 60 q^{99}+O(q^{100}) \) 18 * q + 9 * q^3 - 3 * q^5 + 3 * q^7 - 3 * q^9 - 9 * q^11 + 9 * q^13 + 15 * q^15 - 15 * q^17 - 6 * q^19 - 12 * q^21 + 9 * q^23 + 21 * q^25 - 21 * q^27 - 18 * q^29 + 6 * q^33 + 12 * q^35 + 6 * q^37 + 6 * q^39 - 24 * q^41 + 36 * q^47 + 21 * q^49 - 81 * q^51 - 39 * q^53 - 12 * q^55 + 15 * q^57 + 6 * q^59 + 42 * q^61 + 27 * q^63 + 18 * q^65 - 36 * q^69 + 9 * q^71 - 54 * q^73 - 18 * q^75 + 33 * q^77 + 6 * q^79 - 45 * q^81 + 24 * q^83 + 6 * q^85 - 21 * q^87 + 18 * q^89 + 3 * q^91 + 66 * q^93 + 15 * q^95 - 9 * q^97 - 60 * q^99

Introduction

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