LMFDB - Embedded newform 1512.2.j.a.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(323,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("1512.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.j (of order $2$, degree $1$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.56070144.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 16x^{6} - 34x^{5} + 63x^{4} - 74x^{3} + 70x^{2} - 38x + 13 $ x^8 - 4x^7 + 16x^6 - 34x^5 + 63x^4 - 74x^3 + 70x^2 - 38*x + 13
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.4
Root			$0.500000 - 1.56488i$ of defining polynomial
Character	$\chi$	$=$	1512.323
Dual form			1512.2.j.a.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +1.12976 q^{5} +1.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +1.12976 q^{5} +1.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.54329 + 0.413523i) q^{10} +3.86182i q^{11} +5.08658i q^{13} +(-0.366025 - 1.36603i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.00000i q^{17} +7.99158 q^{19} +(1.95681 - 1.12976i) q^{20} +(-1.41352 - 5.27534i) q^{22} -7.68044 q^{23} -3.72363 q^{25} +(-1.86182 - 6.94839i) q^{26} +(1.00000 + 1.73205i) q^{28} -4.73205 q^{29} -4.08658i q^{31} +(-1.46410 + 5.46410i) q^{32} +(-0.732051 - 2.73205i) q^{34} +1.12976i q^{35} -8.28273i q^{37} +(-10.9167 + 2.92512i) q^{38} +(-2.25953 + 2.25953i) q^{40} +8.41249i q^{41} -10.0148 q^{43} +(3.86182 + 6.68886i) q^{44} +(10.4917 - 2.81124i) q^{46} -1.93662 q^{47} -1.00000 q^{49} +(5.08658 - 1.36294i) q^{50} +(5.08658 + 8.81021i) q^{52} -7.72363 q^{53} +4.36294i q^{55} +(-2.00000 - 2.00000i) q^{56} +(6.46410 - 1.73205i) q^{58} -10.9916i q^{59} +11.4641i q^{61} +(1.49579 + 5.58237i) q^{62} -8.00000i q^{64} +5.74663i q^{65} +5.08658 q^{67} +(2.00000 + 3.46410i) q^{68} +(-0.413523 - 1.54329i) q^{70} +13.6804 q^{71} -2.63706 q^{73} +(3.03169 + 11.3144i) q^{74} +(13.8418 - 7.99158i) q^{76} -3.86182 q^{77} +7.17295i q^{79} +(2.25953 - 3.91362i) q^{80} +(-3.07919 - 11.4917i) q^{82} -14.9052i q^{83} +2.25953i q^{85} +(13.6804 - 3.66566i) q^{86} +(-7.72363 - 7.72363i) q^{88} +12.6889i q^{89} -5.08658 q^{91} +(-13.3029 + 7.68044i) q^{92} +(2.64548 - 0.708853i) q^{94} +9.02861 q^{95} +4.17315 q^{97} +(1.36603 - 0.366025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 8 q^{5} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 8 * q^5 - 16 * q^8	$ 8 q - 4 q^{2} - 8 q^{5} - 16 q^{8} + 4 q^{10} + 4 q^{14} + 16 q^{16} + 16 q^{19} - 12 q^{22} + 16 q^{23} + 32 q^{25} + 16 q^{26} + 8 q^{28} - 24 q^{29} + 16 q^{32} + 8 q^{34} - 20 q^{38} + 16 q^{40} + 8 q^{43} + 4 q^{46} - 8 q^{47} - 8 q^{49} + 8 q^{50} + 8 q^{52} - 16 q^{56} + 24 q^{58} - 12 q^{62} + 8 q^{67} + 16 q^{68} - 4 q^{70} + 32 q^{71} + 8 q^{73} + 28 q^{74} + 24 q^{76} - 16 q^{80} - 36 q^{82} + 32 q^{86} - 8 q^{91} - 24 q^{92} + 40 q^{94} + 112 q^{95} - 32 q^{97} + 4 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 8 * q^5 - 16 * q^8 + 4 * q^10 + 4 * q^14 + 16 * q^16 + 16 * q^19 - 12 * q^22 + 16 * q^23 + 32 * q^25 + 16 * q^26 + 8 * q^28 - 24 * q^29 + 16 * q^32 + 8 * q^34 - 20 * q^38 + 16 * q^40 + 8 * q^43 + 4 * q^46 - 8 * q^47 - 8 * q^49 + 8 * q^50 + 8 * q^52 - 16 * q^56 + 24 * q^58 - 12 * q^62 + 8 * q^67 + 16 * q^68 - 4 * q^70 + 32 * q^71 + 8 * q^73 + 28 * q^74 + 24 * q^76 - 16 * q^80 - 36 * q^82 + 32 * q^86 - 8 * q^91 - 24 * q^92 + 40 * q^94 + 112 * q^95 - 32 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

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 $

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	1.12976			0.505246			0.252623	−	0.967565i	$-0.418707\pi$
$5$	1.12976			0.505246			0.252623	+	0.967565i	$0.418707\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	−1.54329	+	0.413523i	−0.488030	+	0.130767i
$11$			3.86182i			1.16438i	0.813052	+	0.582191i	$0.197804\pi$
$11$			3.86182i			1.16438i	−0.813052	+	0.582191i	$0.802196\pi$
$12$		0			0
$13$			5.08658i			1.41076i	0.708828	+	0.705381i	$0.249224\pi$
$13$			5.08658i			1.41076i	−0.708828	+	0.705381i	$0.750776\pi$
$14$	−0.366025	−	1.36603i	−0.0978244	−	0.365086i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$	7.99158			1.83339			0.916697	−	0.399583i	$-0.130845\pi$
$19$	7.99158			1.83339			0.916697	+	0.399583i	$0.130845\pi$
$20$	1.95681	−	1.12976i	0.437556	−	0.252623i
$21$		0			0
$22$	−1.41352	−	5.27534i	−0.301364	−	1.12471i
$23$	−7.68044			−1.60148			−0.800741	−	0.599010i	$-0.795561\pi$
$23$	−7.68044			−1.60148			−0.800741	+	0.599010i	$0.795561\pi$
$24$		0			0
$25$	−3.72363			−0.744726
$26$	−1.86182	−	6.94839i	−0.365132	−	1.36269i
$27$		0			0
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$	−4.73205			−0.878720			−0.439360	−	0.898311i	$-0.644795\pi$
$29$	−4.73205			−0.878720			−0.439360	+	0.898311i	$0.644795\pi$
$30$		0			0
$31$		−	4.08658i		−	0.733971i	−0.930227	−	0.366985i	$-0.880390\pi$
$31$		−	4.08658i		−	0.733971i	0.930227	−	0.366985i	$-0.119610\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$		0			0
$34$	−0.732051	−	2.73205i	−0.125546	−	0.468543i
$35$			1.12976i			0.190965i
$36$		0			0
$37$		−	8.28273i		−	1.36167i	−0.732436	−	0.680836i	$-0.761617\pi$
$37$		−	8.28273i		−	1.36167i	0.732436	−	0.680836i	$-0.238383\pi$
$38$	−10.9167	+	2.92512i	−1.77092	+	0.474517i
$39$		0			0
$40$	−2.25953	+	2.25953i	−0.357263	+	0.357263i
$41$			8.41249i			1.31381i	0.753973	+	0.656905i	$0.228135\pi$
$41$			8.41249i			1.31381i	−0.753973	+	0.656905i	$0.771865\pi$
$42$		0			0
$43$	−10.0148			−1.52724			−0.763620	−	0.645666i	$-0.776580\pi$
$43$	−10.0148			−1.52724			−0.763620	+	0.645666i	$0.776580\pi$
$44$	3.86182	+	6.68886i	0.582191	+	1.00838i
$45$		0			0
$46$	10.4917	−	2.81124i	1.54691	−	0.414494i
$47$	−1.93662			−0.282485			−0.141243	−	0.989975i	$-0.545110\pi$
$47$	−1.93662			−0.282485			−0.141243	+	0.989975i	$0.545110\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	5.08658	−	1.36294i	0.719350	−	0.192749i
$51$		0			0
$52$	5.08658	+	8.81021i	0.705381	+	1.22176i
$53$	−7.72363			−1.06092			−0.530461	−	0.847709i	$-0.677981\pi$
$53$	−7.72363			−1.06092			−0.530461	+	0.847709i	$0.677981\pi$
$54$		0			0
$55$			4.36294i			0.588299i
$56$	−2.00000	−	2.00000i	−0.267261	−	0.267261i
$57$		0			0
$58$	6.46410	−	1.73205i	0.848778	−	0.227429i
$59$		−	10.9916i		−	1.43098i	−0.698622	−	0.715491i	$-0.746203\pi$
$59$		−	10.9916i		−	1.43098i	0.698622	−	0.715491i	$-0.253797\pi$
$60$		0			0
$61$			11.4641i			1.46783i	0.679243	+	0.733914i	$0.262308\pi$
$61$			11.4641i			1.46783i	−0.679243	+	0.733914i	$0.737692\pi$
$62$	1.49579	+	5.58237i	0.189966	+	0.708961i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$			5.74663i			0.712782i
$66$		0			0
$67$	5.08658			0.621424			0.310712	−	0.950504i	$-0.399433\pi$
$67$	5.08658			0.621424			0.310712	+	0.950504i	$0.399433\pi$
$68$	2.00000	+	3.46410i	0.242536	+	0.420084i
$69$		0			0
$70$	−0.413523	−	1.54329i	−0.0494254	−	0.184458i
$71$	13.6804			1.62357			0.811785	−	0.583957i	$-0.198496\pi$
$71$	13.6804			1.62357			0.811785	+	0.583957i	$0.198496\pi$
$72$		0			0
$73$	−2.63706			−0.308644			−0.154322	−	0.988021i	$-0.549319\pi$
$73$	−2.63706			−0.308644			−0.154322	+	0.988021i	$0.549319\pi$
$74$	3.03169	+	11.3144i	0.352427	+	1.31527i
$75$		0			0
$76$	13.8418	−	7.99158i	1.58777	−	0.916697i
$77$	−3.86182			−0.440095
$78$		0			0
$79$			7.17295i			0.807020i	0.914975	+	0.403510i	$0.132210\pi$
$79$			7.17295i			0.807020i	−0.914975	+	0.403510i	$0.867790\pi$
$80$	2.25953	−	3.91362i	0.252623	−	0.437556i
$81$		0			0
$82$	−3.07919	−	11.4917i	−0.340039	−	1.26904i
$83$		−	14.9052i		−	1.63606i	−0.575177	−	0.818029i	$-0.695067\pi$
$83$		−	14.9052i		−	1.63606i	0.575177	−	0.818029i	$-0.304933\pi$
$84$		0			0
$85$			2.25953i			0.245080i
$86$	13.6804	−	3.66566i	1.47520	−	0.395279i
$87$		0			0
$88$	−7.72363	−	7.72363i	−0.823342	−	0.823342i
$89$			12.6889i			1.34502i	0.740090	+	0.672508i	$0.234783\pi$
$89$			12.6889i			1.34502i	−0.740090	+	0.672508i	$0.765217\pi$
$90$		0			0
$91$	−5.08658			−0.533218
$92$	−13.3029	+	7.68044i	−1.38692	+	0.800741i
$93$		0			0
$94$	2.64548	−	0.708853i	0.272860	−	0.0731126i
$95$	9.02861			0.926316
$96$		0			0
$97$	4.17315			0.423719			0.211860	−	0.977300i	$-0.432048\pi$
$97$	4.17315			0.423719			0.211860	+	0.977300i	$0.432048\pi$
$98$	1.36603	−	0.366025i	0.137989	−	0.0369741i
$99$		0			0
$100$	−6.44952	+	3.72363i	−0.644952	+	0.372363i
$101$	−2.00000			−0.199007			−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	−2.00000			−0.199007			−0.0995037	+	0.995037i	$0.531726\pi$
$102$		0			0
$103$			5.37753i			0.529863i	0.964267	+	0.264932i	$0.0853494\pi$
$103$			5.37753i			0.529863i	−0.964267	+	0.264932i	$0.914651\pi$
$104$	−10.1732	−	10.1732i	−0.997559	−	0.997559i
$105$		0			0
$106$	10.5507	−	2.82705i	1.02477	−	0.274587i
$107$			12.8418i			1.24147i	0.784022	+	0.620733i	$0.213165\pi$
$107$			12.8418i			1.24147i	−0.784022	+	0.620733i	$0.786835\pi$
$108$		0			0
$109$			13.0782i			1.25266i	0.779558	+	0.626330i	$0.215444\pi$
$109$			13.0782i			1.25266i	−0.779558	+	0.626330i	$0.784556\pi$
$110$	−1.59695	−	5.95989i	−0.152263	−	0.568253i
$111$		0			0
$112$	3.46410	+	2.00000i	0.327327	+	0.188982i
$113$		−	7.05496i		−	0.663675i	−0.943337	−	0.331837i	$-0.892331\pi$
$113$		−	7.05496i		−	0.663675i	0.943337	−	0.331837i	$-0.107669\pi$
$114$		0			0
$115$	−8.67709			−0.809143
$116$	−8.19615	+	4.73205i	−0.760994	+	0.439360i
$117$		0			0
$118$	4.02320	+	15.0148i	0.370365	+	1.38222i
$119$	−2.00000			−0.183340
$120$		0			0
$121$	−3.91362			−0.355784
$122$	−4.19615	−	15.6603i	−0.379902	−	1.41781i
$123$		0			0
$124$	−4.08658	−	7.07816i	−0.366985	−	0.635637i
$125$	−9.85565			−0.881516
$126$		0			0
$127$		−	4.63706i		−	0.411472i	−0.978608	−	0.205736i	$-0.934041\pi$
$127$		−	4.63706i		−	0.411472i	0.978608	−	0.205736i	$-0.0659589\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$		0			0
$130$	−2.10341	−	7.85005i	−0.184482	−	0.688495i
$131$			8.36930i			0.731229i	0.930766	+	0.365615i	$0.119141\pi$
$131$			8.36930i			0.731229i	−0.930766	+	0.365615i	$0.880859\pi$
$132$		0			0
$133$			7.99158i			0.692958i
$134$	−6.94839	+	1.86182i	−0.600250	+	0.160836i
$135$		0			0
$136$	−4.00000	−	4.00000i	−0.342997	−	0.342997i
$137$			13.9366i			1.19069i	0.803472	+	0.595343i	$0.202984\pi$
$137$			13.9366i			1.19069i	−0.803472	+	0.595343i	$0.797016\pi$
$138$		0			0
$139$	−13.9832			−1.18604			−0.593018	−	0.805189i	$-0.702064\pi$
$139$	−13.9832			−1.18604			−0.593018	+	0.805189i	$0.702064\pi$
$140$	1.12976	+	1.95681i	0.0954826	+	0.165381i
$141$		0			0
$142$	−18.6878	+	5.00739i	−1.56825	+	0.420211i
$143$	−19.6434			−1.64266
$144$		0			0
$145$	−5.34610			−0.443970
$146$	3.60229	−	0.965230i	0.298127	−	0.0798830i
$147$		0			0
$148$	−8.28273	−	14.3461i	−0.680836	−	1.17924i
$149$	21.7700			1.78347			0.891735	−	0.452558i	$-0.149488\pi$
$149$	21.7700			1.78347			0.891735	+	0.452558i	$0.149488\pi$
$150$		0			0
$151$			16.0464i			1.30584i	0.757428	+	0.652919i	$0.226456\pi$
$151$			16.0464i			1.30584i	−0.757428	+	0.652919i	$0.773544\pi$
$152$	−15.9832	+	15.9832i	−1.29641	+	1.29641i
$153$		0			0
$154$	5.27534	−	1.41352i	0.425099	−	0.113905i
$155$		−	4.61687i		−	0.370836i
$156$		0			0
$157$			5.49572i			0.438606i	0.975657	+	0.219303i	$0.0703783\pi$
$157$			5.49572i			0.438606i	−0.975657	+	0.219303i	$0.929622\pi$
$158$	−2.62548	−	9.79844i	−0.208872	−	0.779522i
$159$		0			0
$160$	−1.65409	+	6.17315i	−0.130767	+	0.488030i
$161$		−	7.68044i		−	0.605304i
$162$		0			0
$163$	1.62247			0.127082			0.0635410	−	0.997979i	$-0.479761\pi$
$163$	1.62247			0.127082			0.0635410	+	0.997979i	$0.479761\pi$
$164$	8.41249	+	14.5709i	0.656905	+	1.13779i
$165$		0			0
$166$	5.45568	+	20.3609i	0.423443	+	1.58031i
$167$	8.70905			0.673926			0.336963	−	0.941518i	$-0.390600\pi$
$167$	8.70905			0.673926			0.336963	+	0.941518i	$0.390600\pi$
$168$		0			0
$169$	−12.8732			−0.990250
$170$	−0.827045	−	3.08658i	−0.0634315	−	0.236729i
$171$		0			0
$172$	−17.3461	+	10.0148i	−1.32263	+	0.763620i
$173$	−1.53891			−0.117001			−0.0585005	−	0.998287i	$-0.518632\pi$
$173$	−1.53891			−0.117001			−0.0585005	+	0.998287i	$0.518632\pi$
$174$		0			0
$175$		−	3.72363i		−	0.281480i
$176$	13.3777	+	7.72363i	1.00838	+	0.582191i
$177$		0			0
$178$	−4.64445	−	17.3333i	−0.348116	−	1.29919i
$179$		−	26.7386i		−	1.99854i	−0.0382400	−	0.999269i	$-0.512175\pi$
$179$		−	26.7386i		−	1.99854i	0.0382400	−	0.999269i	$-0.487825\pi$
$180$		0			0
$181$		−	3.10135i		−	0.230522i	−0.993335	−	0.115261i	$-0.963230\pi$
$181$		−	3.10135i		−	0.230522i	0.993335	−	0.115261i	$-0.0367704\pi$
$182$	6.94839	−	1.86182i	0.515049	−	0.138007i
$183$		0			0
$184$	15.3609	−	15.3609i	1.13242	−	1.13242i
$185$		−	9.35753i		−	0.687980i
$186$		0			0
$187$	−7.72363			−0.564808
$188$	−3.35433	+	1.93662i	−0.244640	+	0.141243i
$189$		0			0
$190$	−12.3333	+	3.30470i	−0.894752	+	0.239748i
$191$	13.8132			0.999489			0.499745	−	0.866173i	$-0.333427\pi$
$191$	13.8132			0.999489			0.499745	+	0.866173i	$0.333427\pi$
$192$		0			0
$193$	7.05496			0.507827			0.253913	−	0.967227i	$-0.418282\pi$
$193$	7.05496			0.507827			0.253913	+	0.967227i	$0.418282\pi$
$194$	−5.70063	+	1.52748i	−0.409281	+	0.109667i
$195$		0			0
$196$	−1.73205	+	1.00000i	−0.123718	+	0.0714286i
$197$	−0.362748			−0.0258448			−0.0129224	−	0.999917i	$-0.504113\pi$
$197$	−0.362748			−0.0258448			−0.0129224	+	0.999917i	$0.504113\pi$
$198$		0			0
$199$		−	7.70029i		−	0.545859i	−0.962034	−	0.272930i	$-0.912007\pi$
$199$		−	7.70029i		−	0.545859i	0.962034	−	0.272930i	$-0.0879926\pi$
$200$	7.44726	−	7.44726i	0.526601	−	0.526601i
$201$		0			0
$202$	2.73205	−	0.732051i	0.192226	−	0.0515069i
$203$		−	4.73205i		−	0.332125i
$204$		0			0
$205$			9.50414i			0.663798i
$206$	−1.96831	−	7.34584i	−0.137139	−	0.511809i
$207$		0			0
$208$	17.6204	+	10.1732i	1.22176	+	0.705381i
$209$			30.8620i			2.13477i
$210$		0			0
$211$	−14.5191			−0.999533			−0.499767	−	0.866160i	$-0.666581\pi$
$211$	−14.5191			−0.999533			−0.499767	+	0.866160i	$0.666581\pi$
$212$	−13.3777	+	7.72363i	−0.918786	+	0.530461i
$213$		0			0
$214$	−4.70043	−	17.5423i	−0.321315	−	1.19916i
$215$	−11.3143			−0.771632
$216$		0			0
$217$	4.08658			0.277415
$218$	−4.78694	−	17.8651i	−0.324212	−	1.20998i
$219$		0			0
$220$	4.36294	+	7.55684i	0.294150	+	0.509482i
$221$	−10.1732			−0.684320
$222$		0			0
$223$			19.2743i			1.29070i	0.763886	+	0.645352i	$0.223289\pi$
$223$			19.2743i			1.29070i	−0.763886	+	0.645352i	$0.776711\pi$
$224$	−5.46410	−	1.46410i	−0.365086	−	0.0978244i
$225$		0			0
$226$	2.58229	+	9.63725i	0.171772	+	0.641060i
$227$		−	23.2341i		−	1.54210i	−0.636773	−	0.771052i	$-0.719731\pi$
$227$		−	23.2341i		−	1.54210i	0.636773	−	0.771052i	$-0.280269\pi$
$228$		0			0
$229$			13.4641i			0.889733i	0.895597	+	0.444866i	$0.146749\pi$
$229$			13.4641i			0.889733i	−0.895597	+	0.444866i	$0.853251\pi$
$230$	11.8531	−	3.17604i	0.781572	−	0.209422i
$231$		0			0
$232$	9.46410	−	9.46410i	0.621349	−	0.621349i
$233$			17.4641i			1.14411i	0.820215	+	0.572056i	$0.193854\pi$
$233$			17.4641i			1.14411i	−0.820215	+	0.572056i	$0.806146\pi$
$234$		0			0
$235$	−2.18793			−0.142725
$236$	−10.9916	−	19.0380i	−0.715491	−	1.23927i
$237$		0			0
$238$	2.73205	−	0.732051i	0.177093	−	0.0474518i
$239$	−1.82724			−0.118194			−0.0590972	−	0.998252i	$-0.518822\pi$
$239$	−1.82724			−0.118194			−0.0590972	+	0.998252i	$0.518822\pi$
$240$		0			0
$241$	−21.5193			−1.38618			−0.693089	−	0.720852i	$-0.743751\pi$
$241$	−21.5193			−1.38618			−0.693089	+	0.720852i	$0.743751\pi$
$242$	5.34610	−	1.43248i	0.343661	−	0.0920836i
$243$		0			0
$244$	11.4641	+	19.8564i	0.733914	+	1.27118i
$245$	−1.12976			−0.0721780
$246$		0			0
$247$			40.6498i			2.58648i
$248$	8.17315	+	8.17315i	0.518996	+	0.518996i
$249$		0			0
$250$	13.4631	−	3.60742i	0.851479	−	0.228153i
$251$		−	1.15818i		−	0.0731035i	−0.999332	−	0.0365517i	$-0.988363\pi$
$251$		−	1.15818i		−	0.0731035i	0.999332	−	0.0365517i	$-0.0116374\pi$
$252$		0			0
$253$		−	29.6604i		−	1.86474i
$254$	1.69728	+	6.33434i	0.106497	+	0.397452i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		−	11.0812i		−	0.691224i	−0.938377	−	0.345612i	$-0.887671\pi$
$257$		−	11.0812i		−	0.691224i	0.938377	−	0.345612i	$-0.112329\pi$
$258$		0			0
$259$	8.28273			0.514664
$260$	5.74663	+	9.95346i	0.356391	+	0.617287i
$261$		0			0
$262$	−3.06338	−	11.4327i	−0.189256	−	0.706313i
$263$	−10.7354			−0.661973			−0.330987	−	0.943635i	$-0.607381\pi$
$263$	−10.7354			−0.661973			−0.330987	+	0.943635i	$0.607381\pi$
$264$		0			0
$265$	−8.72589			−0.536027
$266$	−2.92512	−	10.9167i	−0.179351	−	0.669346i
$267$		0			0
$268$	8.81021	−	5.08658i	0.538169	−	0.310712i
$269$	−5.75204			−0.350708			−0.175354	−	0.984505i	$-0.556107\pi$
$269$	−5.75204			−0.350708			−0.175354	+	0.984505i	$0.556107\pi$
$270$		0			0
$271$		−	1.33735i		−	0.0812380i	−0.999175	−	0.0406190i	$-0.987067\pi$
$271$		−	1.33735i		−	0.0812380i	0.999175	−	0.0406190i	$-0.0129330\pi$
$272$	6.92820	+	4.00000i	0.420084	+	0.242536i
$273$		0			0
$274$	−5.10116	−	19.0378i	−0.308172	−	1.15011i
$275$		−	14.3800i		−	0.867145i
$276$		0			0
$277$		−	3.13537i		−	0.188386i	−0.995554	−	0.0941930i	$-0.969973\pi$
$277$		−	3.13537i		−	0.188386i	0.995554	−	0.0941930i	$-0.0300271\pi$
$278$	19.1014	−	5.11819i	1.14562	−	0.306969i
$279$		0			0
$280$	−2.25953	−	2.25953i	−0.135033	−	0.135033i
$281$			13.3839i			0.798416i	0.916860	+	0.399208i	$0.130715\pi$
$281$			13.3839i			0.798416i	−0.916860	+	0.399208i	$0.869285\pi$
$282$		0			0
$283$	21.8104			1.29649			0.648247	−	0.761430i	$-0.275502\pi$
$283$	21.8104			1.29649			0.648247	+	0.761430i	$0.275502\pi$
$284$	23.6952	−	13.6804i	1.40605	−	0.811785i
$285$		0			0
$286$	26.8334	−	7.18999i	1.58669	−	0.425153i
$287$	−8.41249			−0.496574
$288$		0			0
$289$	13.0000			0.764706
$290$	7.30291	−	1.95681i	0.428842	−	0.114908i
$291$		0			0
$292$	−4.56752	+	2.63706i	−0.267294	+	0.154322i
$293$	30.6982			1.79341			0.896705	−	0.442629i	$-0.145954\pi$
$293$	30.6982			1.79341			0.896705	+	0.442629i	$0.145954\pi$
$294$		0			0
$295$		−	12.4179i		−	0.722998i
$296$	16.5655	+	16.5655i	0.962848	+	0.962848i
$297$		0			0
$298$	−29.7384	+	7.96838i	−1.72270	+	0.461596i
$299$		−	39.0671i		−	2.25931i
$300$		0			0
$301$		−	10.0148i		−	0.577242i
$302$	−5.87339	−	21.9198i	−0.337976	−	1.26134i
$303$		0			0
$304$	15.9832	−	27.6836i	0.916697	−	1.58777i
$305$			12.9517i			0.741614i
$306$		0			0
$307$	9.10977			0.519922			0.259961	−	0.965619i	$-0.416290\pi$
$307$	9.10977			0.519922			0.259961	+	0.965619i	$0.416290\pi$
$308$	−6.68886	+	3.86182i	−0.381133	+	0.220047i
$309$		0			0
$310$	1.68989	+	6.30676i	0.0959794	+	0.358200i
$311$	27.5275			1.56094			0.780470	−	0.625193i	$-0.214980\pi$
$311$	27.5275			1.56094			0.780470	+	0.625193i	$0.214980\pi$
$312$		0			0
$313$	5.36294			0.303131			0.151566	−	0.988447i	$-0.451568\pi$
$313$	5.36294			0.303131			0.151566	+	0.988447i	$0.451568\pi$
$314$	−2.01157	−	7.50729i	−0.113520	−	0.423661i
$315$		0			0
$316$	7.17295	+	12.4239i	0.403510	+	0.698900i
$317$	−7.30832			−0.410476			−0.205238	−	0.978712i	$-0.565797\pi$
$317$	−7.30832			−0.410476			−0.205238	+	0.978712i	$0.565797\pi$
$318$		0			0
$319$		−	18.2743i		−	1.02316i
$320$		−	9.03812i		−	0.505246i
$321$		0			0
$322$	2.81124	+	10.4917i	0.156664	+	0.584678i
$323$			15.9832i			0.889327i
$324$		0			0
$325$		−	18.9405i		−	1.05063i
$326$	−2.21634	+	0.593866i	−0.122752	+	0.0328912i
$327$		0			0
$328$	−16.8250	−	16.8250i	−0.929004	−	0.929004i
$329$		−	1.93662i		−	0.106769i
$330$		0			0
$331$	10.5823			0.581655			0.290828	−	0.956775i	$-0.406069\pi$
$331$	10.5823			0.581655			0.290828	+	0.956775i	$0.406069\pi$
$332$	−14.9052	−	25.8166i	−0.818029	−	1.41687i
$333$		0			0
$334$	−11.8968	+	3.18773i	−0.650963	+	0.174425i
$335$	5.74663			0.313972
$336$		0			0
$337$	−4.29095			−0.233743			−0.116872	−	0.993147i	$-0.537287\pi$
$337$	−4.29095			−0.233743			−0.116872	+	0.993147i	$0.537287\pi$
$338$	17.5852	−	4.71193i	0.956508	−	0.256295i
$339$		0			0
$340$	2.25953	+	3.91362i	0.122540	+	0.212246i
$341$	15.7816			0.854622
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	20.0296	−	20.0296i	1.07992	−	1.07992i
$345$		0			0
$346$	2.10219	−	0.563280i	0.113014	−	0.0302821i
$347$		−	10.3405i		−	0.555107i	−0.960710	−	0.277554i	$-0.910476\pi$
$347$		−	10.3405i		−	0.555107i	0.960710	−	0.277554i	$-0.0895236\pi$
$348$		0			0
$349$		−	11.1182i		−	0.595143i	−0.954700	−	0.297572i	$-0.903823\pi$
$349$		−	11.1182i		−	0.595143i	0.954700	−	0.297572i	$-0.0961767\pi$
$350$	1.36294	+	5.08658i	0.0728524	+	0.271889i
$351$		0			0
$352$	−21.1014	−	5.65409i	−1.12471	−	0.301364i
$353$			23.3407i			1.24230i	0.783692	+	0.621150i	$0.213334\pi$
$353$			23.3407i			1.24230i	−0.783692	+	0.621150i	$0.786666\pi$
$354$		0			0
$355$	15.4557			0.820302
$356$	12.6889	+	21.9778i	0.672508	+	1.16482i
$357$		0			0
$358$	9.78701	+	36.5256i	0.517259	+	1.93044i
$359$	22.3923			1.18182			0.590910	−	0.806737i	$-0.298769\pi$
$359$	22.3923			1.18182			0.590910	+	0.806737i	$0.298769\pi$
$360$		0			0
$361$	44.8654			2.36133
$362$	1.13517	+	4.23653i	0.0596634	+	0.222667i
$363$		0			0
$364$	−8.81021	+	5.08658i	−0.461780	+	0.266609i
$365$	−2.97925			−0.155941
$366$		0			0
$367$			1.93696i			0.101109i	0.998721	+	0.0505543i	$0.0160988\pi$
$367$			1.93696i			0.101109i	−0.998721	+	0.0505543i	$0.983901\pi$
$368$	−15.3609	+	26.6058i	−0.800741	+	1.38692i
$369$		0			0
$370$	3.42510	+	12.7826i	0.178062	+	0.664537i
$371$		−	7.72363i		−	0.400991i
$372$		0			0
$373$			15.1246i			0.783120i	0.920153	+	0.391560i	$0.128064\pi$
$373$			15.1246i			0.783120i	−0.920153	+	0.391560i	$0.871936\pi$
$374$	10.5507	−	2.82705i	0.545563	−	0.146183i
$375$		0			0
$376$	3.87325	−	3.87325i	0.199747	−	0.199747i
$377$		−	24.0699i		−	1.23966i
$378$		0			0
$379$	6.15837			0.316334			0.158167	−	0.987412i	$-0.449442\pi$
$379$	6.15837			0.316334			0.158167	+	0.987412i	$0.449442\pi$
$380$	15.6380	−	9.02861i	0.802213	−	0.463158i
$381$		0			0
$382$	−18.8692	+	5.05599i	−0.965433	+	0.258687i
$383$	14.8822			0.760445			0.380222	−	0.924895i	$-0.375847\pi$
$383$	14.8822			0.760445			0.380222	+	0.924895i	$0.375847\pi$
$384$		0			0
$385$	−4.36294			−0.222356
$386$	−9.63725	+	2.58229i	−0.490523	+	0.131435i
$387$		0			0
$388$	7.22811	−	4.17315i	0.366952	−	0.211860i
$389$	−1.82685			−0.0926250			−0.0463125	−	0.998927i	$-0.514747\pi$
$389$	−1.82685			−0.0926250			−0.0463125	+	0.998927i	$0.514747\pi$
$390$		0			0
$391$		−	15.3609i		−	0.776833i
$392$	2.00000	−	2.00000i	0.101015	−	0.101015i
$393$		0			0
$394$	0.495523	−	0.132775i	0.0249641	−	0.00668911i
$395$			8.10375i			0.407744i
$396$		0			0
$397$			2.18999i			0.109912i	0.998489	+	0.0549562i	$0.0175019\pi$
$397$			2.18999i			0.109912i	−0.998489	+	0.0549562i	$0.982498\pi$
$398$	2.81850	+	10.5188i	0.141279	+	0.527259i
$399$		0			0
$400$	−7.44726	+	12.8990i	−0.372363	+	0.644952i
$401$			3.59071i			0.179312i	0.995973	+	0.0896558i	$0.0285767\pi$
$401$			3.59071i			0.179312i	−0.995973	+	0.0896558i	$0.971423\pi$
$402$		0			0
$403$	20.7867			1.03546
$404$	−3.46410	+	2.00000i	−0.172345	+	0.0995037i
$405$		0			0
$406$	1.73205	+	6.46410i	0.0859602	+	0.320808i
$407$	31.9864			1.58551
$408$		0			0
$409$	−35.3588			−1.74838			−0.874191	−	0.485583i	$-0.838607\pi$
$409$	−35.3588			−1.74838			−0.874191	+	0.485583i	$0.838607\pi$
$410$	−3.47876	−	12.9829i	−0.171804	−	0.641179i
$411$		0			0
$412$	5.37753	+	9.31415i	0.264932	+	0.458875i
$413$	10.9916			0.540860
$414$		0			0
$415$		−	16.8394i		−	0.826612i
$416$	−27.7936	−	7.44726i	−1.36269	−	0.365132i
$417$		0			0
$418$	−11.2963	−	42.1583i	−0.552519	−	2.06203i
$419$		−	2.44952i		−	0.119667i	−0.998208	−	0.0598334i	$-0.980943\pi$
$419$		−	2.44952i		−	0.119667i	0.998208	−	0.0598334i	$-0.0190569\pi$
$420$		0			0
$421$			6.26589i			0.305381i	0.988274	+	0.152690i	$0.0487937\pi$
$421$			6.26589i			0.305381i	−0.988274	+	0.152690i	$0.951206\pi$
$422$	19.8334	−	5.31434i	0.965475	−	0.258698i
$423$		0			0
$424$	15.4473	−	15.4473i	0.750185	−	0.750185i
$425$		−	7.44726i		−	0.361245i
$426$		0			0
$427$	−11.4641			−0.554787
$428$	12.8418	+	22.2427i	0.620733	+	1.07514i
$429$		0			0
$430$	15.4557	−	4.14134i	0.745339	−	0.199713i
$431$	3.01177			0.145072			0.0725359	−	0.997366i	$-0.476891\pi$
$431$	3.01177			0.145072			0.0725359	+	0.997366i	$0.476891\pi$
$432$		0			0
$433$	−7.00020			−0.336408			−0.168204	−	0.985752i	$-0.553797\pi$
$433$	−7.00020			−0.336408			−0.168204	+	0.985752i	$0.553797\pi$
$434$	−5.58237	+	1.49579i	−0.267962	+	0.0718002i
$435$		0			0
$436$	13.0782	+	22.6520i	0.626330	+	1.08484i
$437$	−61.3789			−2.93615
$438$		0			0
$439$			1.33735i			0.0638281i	0.999491	+	0.0319140i	$0.0101603\pi$
$439$			1.33735i			0.0638281i	−0.999491	+	0.0319140i	$0.989840\pi$
$440$	−8.72589	−	8.72589i	−0.415990	−	0.415990i
$441$		0			0
$442$	13.8968	−	3.72363i	0.661002	−	0.177115i
$443$			1.90821i			0.0906618i	0.998972	+	0.0453309i	$0.0144342\pi$
$443$			1.90821i			0.0906618i	−0.998972	+	0.0453309i	$0.985566\pi$
$444$		0			0
$445$			14.3354i			0.679565i
$446$	−7.05489	−	26.3292i	−0.334059	−	1.24672i
$447$		0			0
$448$	8.00000			0.377964
$449$			10.0695i			0.475211i	0.971362	+	0.237606i	$0.0763625\pi$
$449$			10.0695i			0.475211i	−0.971362	+	0.237606i	$0.923637\pi$
$450$		0			0
$451$	−32.4875			−1.52978
$452$	−7.05496	−	12.2195i	−0.331837	−	0.574759i
$453$		0			0
$454$	8.50428	+	31.7384i	0.399126	+	1.48956i
$455$	−5.74663			−0.269406
$456$		0			0
$457$	10.3205			0.482773			0.241387	−	0.970429i	$-0.422398\pi$
$457$	10.3205			0.482773			0.241387	+	0.970429i	$0.422398\pi$
$458$	−4.92820	−	18.3923i	−0.230280	−	0.859416i
$459$		0			0
$460$	−15.0292	+	8.67709i	−0.700738	+	0.404572i
$461$	17.9420			0.835644			0.417822	−	0.908529i	$-0.362794\pi$
$461$	17.9420			0.835644			0.417822	+	0.908529i	$0.362794\pi$
$462$		0			0
$463$		−	21.6664i		−	1.00692i	−0.864017	−	0.503462i	$-0.832059\pi$
$463$		−	21.6664i		−	1.00692i	0.864017	−	0.503462i	$-0.167941\pi$
$464$	−9.46410	+	16.3923i	−0.439360	+	0.760994i
$465$		0			0
$466$	−6.39230	−	23.8564i	−0.296118	−	1.10513i
$467$		−	18.3525i		−	0.849251i	−0.905369	−	0.424625i	$-0.860406\pi$
$467$		−	18.3525i		−	0.849251i	0.905369	−	0.424625i	$-0.139594\pi$
$468$		0			0
$469$			5.08658i			0.234876i
$470$	2.98877	−	0.800837i	0.137861	−	0.0369399i
$471$		0			0
$472$	21.9832	+	21.9832i	1.01186	+	1.01186i
$473$		−	38.6752i		−	1.77829i
$474$		0			0
$475$	−29.7577			−1.36538
$476$	−3.46410	+	2.00000i	−0.158777	+	0.0916698i
$477$		0			0
$478$	2.49606	−	0.668816i	0.114167	−	0.0305910i
$479$	14.6518			0.669459			0.334730	−	0.942314i	$-0.391355\pi$
$479$	14.6518			0.669459			0.334730	+	0.942314i	$0.391355\pi$
$480$		0			0
$481$	42.1307			1.92100
$482$	29.3958	−	7.87659i	1.33894	−	0.358769i
$483$		0			0
$484$	−6.77859	+	3.91362i	−0.308118	+	0.177892i
$485$	4.71468			0.214083
$486$		0			0
$487$		−	6.60789i		−	0.299432i	−0.988729	−	0.149716i	$-0.952164\pi$
$487$		−	6.60789i		−	0.299432i	0.988729	−	0.149716i	$-0.0478360\pi$
$488$	−22.9282	−	22.9282i	−1.03791	−	1.03791i
$489$		0			0
$490$	1.54329	−	0.413523i	0.0697186	−	0.0186810i
$491$			7.08323i			0.319662i	0.987144	+	0.159831i	$0.0510949\pi$
$491$			7.08323i			0.319662i	−0.987144	+	0.159831i	$0.948905\pi$
$492$		0			0
$493$		−	9.46410i		−	0.426242i
$494$	−14.8788	−	55.5286i	−0.669431	−	2.49835i
$495$		0			0
$496$	−14.1563	−	8.17315i	−0.635637	−	0.366985i
$497$			13.6804i			0.613652i
$498$		0			0
$499$	−7.13297			−0.319316			−0.159658	−	0.987172i	$-0.551039\pi$
$499$	−7.13297			−0.319316			−0.159658	+	0.987172i	$0.551039\pi$
$500$	−17.0705	+	9.85565i	−0.763416	+	0.440758i
$501$		0			0
$502$	0.423922	+	1.58210i	0.0189206	+	0.0706125i
$503$	−14.7321			−0.656870			−0.328435	−	0.944527i	$-0.606521\pi$
$503$	−14.7321			−0.656870			−0.328435	+	0.944527i	$0.606521\pi$
$504$		0			0
$505$	−2.25953			−0.100548
$506$	10.8565	+	40.5169i	0.482629	+	1.80120i
$507$		0			0
$508$	−4.63706	−	8.03162i	−0.205736	−	0.356345i
$509$	6.21955			0.275677			0.137838	−	0.990455i	$-0.455985\pi$
$509$	6.21955			0.275677			0.137838	+	0.990455i	$0.455985\pi$
$510$		0			0
$511$		−	2.63706i		−	0.116657i
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$		0			0
$514$	4.05599	+	15.1372i	0.178902	+	0.667671i
$515$			6.07534i			0.267711i
$516$		0			0
$517$		−	7.47888i		−	0.328921i
$518$	−11.3144	+	3.03169i	−0.497127	+	0.133205i
$519$		0			0
$520$	−11.4933	−	11.4933i	−0.504013	−	0.504013i
$521$		−	20.0897i		−	0.880147i	−0.897962	−	0.440073i	$-0.854952\pi$
$521$		−	20.0897i		−	0.880147i	0.897962	−	0.440073i	$-0.145048\pi$
$522$		0			0
$523$	25.5885			1.11891			0.559453	−	0.828862i	$-0.311011\pi$
$523$	25.5885			1.11891			0.559453	+	0.828862i	$0.311011\pi$
$524$	8.36930	+	14.4961i	0.365615	+	0.633263i
$525$		0			0
$526$	14.6648	−	3.92943i	0.639417	−	0.171331i
$527$	8.17315			0.356028
$528$		0			0
$529$	35.9892			1.56475
$530$	11.9198	−	3.19390i	0.517762	−	0.138734i
$531$		0			0
$532$	7.99158	+	13.8418i	0.346479	+	0.600119i
$533$	−42.7908			−1.85347
$534$		0			0
$535$			14.5082i			0.627246i
$536$	−10.1732	+	10.1732i	−0.439413	+	0.439413i
$537$		0			0
$538$	7.85744	−	2.10539i	0.338758	−	0.0907700i
$539$		−	3.86182i		−	0.166340i
$540$		0			0
$541$		−	25.7932i		−	1.10894i	−0.832205	−	0.554469i	$-0.812922\pi$
$541$		−	25.7932i		−	1.10894i	0.832205	−	0.554469i	$-0.187078\pi$
$542$	0.489503	+	1.82685i	0.0210260	+	0.0784699i
$543$		0			0
$544$	−10.9282	−	2.92820i	−0.468543	−	0.125546i
$545$			14.7752i			0.632902i
$546$		0			0
$547$	−1.41771			−0.0606167			−0.0303084	−	0.999541i	$-0.509649\pi$
$547$	−1.41771			−0.0606167			−0.0303084	+	0.999541i	$0.509649\pi$
$548$	13.9366	+	24.1389i	0.595343	+	1.03116i
$549$		0			0
$550$	5.26344	+	19.6434i	0.224434	+	0.837598i
$551$	−37.8166			−1.61104
$552$		0			0
$553$	−7.17295			−0.305025
$554$	1.14762	+	4.28299i	0.0487579	+	0.181967i
$555$		0			0
$556$	−24.2195	+	13.9832i	−1.02714	+	0.593018i
$557$	−4.36275			−0.184856			−0.0924278	−	0.995719i	$-0.529463\pi$
$557$	−4.36275			−0.184856			−0.0924278	+	0.995719i	$0.529463\pi$
$558$		0			0
$559$		−	50.9409i		−	2.15457i
$560$	3.91362	+	2.25953i	0.165381	+	0.0954826i
$561$		0			0
$562$	−4.89884	−	18.2827i	−0.206645	−	0.771210i
$563$			25.4007i			1.07051i	0.844690	+	0.535256i	$0.179785\pi$
$563$			25.4007i			1.07051i	−0.844690	+	0.535256i	$0.820215\pi$
$564$		0			0
$565$		−	7.97044i		−	0.335319i
$566$	−29.7936	+	7.98316i	−1.25232	+	0.335557i
$567$		0			0
$568$	−27.3609	+	27.3609i	−1.14804	+	1.14804i
$569$			24.9746i			1.04699i	0.852029	+	0.523495i	$0.175372\pi$
$569$			24.9746i			1.04699i	−0.852029	+	0.523495i	$0.824628\pi$
$570$		0			0
$571$	−8.02956			−0.336026			−0.168013	−	0.985785i	$-0.553735\pi$
$571$	−8.02956			−0.336026			−0.168013	+	0.985785i	$0.553735\pi$
$572$	−34.0234	+	19.6434i	−1.42259	+	0.821332i
$573$		0			0
$574$	11.4917	−	3.07919i	0.479653	−	0.128523i
$575$	28.5991			1.19267
$576$		0			0
$577$	−21.7808			−0.906748			−0.453374	−	0.891320i	$-0.649780\pi$
$577$	−21.7808			−0.906748			−0.453374	+	0.891320i	$0.649780\pi$
$578$	−17.7583	+	4.75833i	−0.738649	+	0.197920i
$579$		0			0
$580$	−9.25973	+	5.34610i	−0.384489	+	0.221985i
$581$	14.9052			0.618372
$582$		0			0
$583$		−	29.8272i		−	1.23532i
$584$	5.27411	−	5.27411i	0.218244	−	0.218244i
$585$		0			0
$586$	−41.9346	+	11.2363i	−1.73230	+	0.464169i
$587$			13.2913i			0.548592i	0.961645	+	0.274296i	$0.0884449\pi$
$587$			13.2913i			0.548592i	−0.961645	+	0.274296i	$0.911555\pi$
$588$		0			0
$589$		−	32.6582i		−	1.34566i
$590$	4.54527	+	16.9632i	0.187126	+	0.698363i
$591$		0			0
$592$	−28.6922	−	16.5655i	−1.17924	−	0.680836i
$593$			0.746075i			0.0306376i	0.999883	+	0.0153188i	$0.00487632\pi$
$593$			0.746075i			0.0306376i	−0.999883	+	0.0153188i	$0.995124\pi$
$594$		0			0
$595$	−2.25953			−0.0926317
$596$	37.7068	−	21.7700i	1.54453	−	0.891735i
$597$		0			0
$598$	14.2996	+	53.3667i	0.584753	+	2.18233i
$599$	−42.1595			−1.72259			−0.861296	−	0.508104i	$-0.830346\pi$
$599$	−42.1595			−1.72259			−0.861296	+	0.508104i	$0.830346\pi$
$600$		0			0
$601$	−12.6371			−0.515476			−0.257738	−	0.966215i	$-0.582977\pi$
$601$	−12.6371			−0.515476			−0.257738	+	0.966215i	$0.582977\pi$
$602$	3.66566	+	13.6804i	0.149401	+	0.557573i
$603$		0			0
$604$	16.0464	+	27.7932i	0.652919	+	1.13089i
$605$	−4.42147			−0.179758
$606$		0			0
$607$			44.5950i			1.81006i	0.425352	+	0.905028i	$0.360150\pi$
$607$			44.5950i			1.81006i	−0.425352	+	0.905028i	$0.639850\pi$
$608$	−11.7005	+	43.6668i	−0.474517	+	1.77092i
$609$		0			0
$610$	−4.74067	−	17.6924i	−0.191944	−	0.716345i
$611$		−	9.85078i		−	0.398520i
$612$		0			0
$613$		−	16.6859i		−	0.673935i	−0.941516	−	0.336968i	$-0.890599\pi$
$613$		−	16.6859i		−	0.673935i	0.941516	−	0.336968i	$-0.109401\pi$
$614$	−12.4442	+	3.33441i	−0.502206	+	0.134566i
$615$		0			0
$616$	7.72363	−	7.72363i	0.311194	−	0.311194i
$617$			30.1225i			1.21269i	0.795203	+	0.606343i	$0.207364\pi$
$617$			30.1225i			1.21269i	−0.795203	+	0.606343i	$0.792636\pi$
$618$		0			0
$619$	32.5002			1.30629			0.653147	−	0.757231i	$-0.273448\pi$
$619$	32.5002			1.30629			0.653147	+	0.757231i	$0.273448\pi$
$620$	−4.61687	−	7.99665i	−0.185418	−	0.321153i
$621$		0			0
$622$	−37.6032	+	10.0758i	−1.50775	+	0.404001i
$623$	−12.6889			−0.508368
$624$		0			0
$625$	7.48359			0.299343
$626$	−7.32592	+	1.96297i	−0.292803	+	0.0784562i
$627$		0			0
$628$	5.49572	+	9.51886i	0.219303	+	0.379844i
$629$	16.5655			0.660508
$630$		0			0
$631$			18.8734i			0.751340i	0.926754	+	0.375670i	$0.122587\pi$
$631$			18.8734i			0.751340i	−0.926754	+	0.375670i	$0.877413\pi$
$632$	−14.3459	−	14.3459i	−0.570650	−	0.570650i
$633$		0			0
$634$	9.98336	−	2.67503i	0.396490	−	0.106239i
$635$		−	5.23878i		−	0.207895i
$636$		0			0
$637$		−	5.08658i		−	0.201537i
$638$	6.68886	+	24.9632i	0.264815	+	0.988301i
$639$		0			0
$640$	3.30818	+	12.3463i	0.130767	+	0.488030i
$641$		−	13.1417i		−	0.519067i	−0.965734	−	0.259534i	$-0.916431\pi$
$641$		−	13.1417i		−	0.519067i	0.965734	−	0.259534i	$-0.0835688\pi$
$642$		0			0
$643$	11.3121			0.446105			0.223053	−	0.974806i	$-0.428398\pi$
$643$	11.3121			0.446105			0.223053	+	0.974806i	$0.428398\pi$
$644$	−7.68044	−	13.3029i	−0.302652	−	0.524208i
$645$		0			0
$646$	−5.85024	−	21.8334i	−0.230175	−	0.859024i
$647$	10.1038			0.397219			0.198610	−	0.980079i	$-0.436357\pi$
$647$	10.1038			0.397219			0.198610	+	0.980079i	$0.436357\pi$
$648$		0			0
$649$	42.4475			1.66621
$650$	6.93272	+	25.8732i	0.271923	+	1.01483i
$651$		0			0
$652$	2.81021	−	1.62247i	0.110056	−	0.0635410i
$653$	18.2661			0.714807			0.357404	−	0.933950i	$-0.383662\pi$
$653$	18.2661			0.714807			0.357404	+	0.933950i	$0.383662\pi$
$654$		0			0
$655$			9.45534i			0.369451i
$656$	29.1417	+	16.8250i	1.13779	+	0.656905i
$657$		0			0
$658$	0.708853	+	2.64548i	0.0276340	+	0.103131i
$659$		−	37.9781i		−	1.47942i	−0.672927	−	0.739709i	$-0.734963\pi$
$659$		−	37.9781i		−	1.47942i	0.672927	−	0.739709i	$-0.265037\pi$
$660$		0			0
$661$			8.98899i			0.349631i	0.984601	+	0.174816i	$0.0559329\pi$
$661$			8.98899i			0.349631i	−0.984601	+	0.174816i	$0.944067\pi$
$662$	−14.4557	+	3.87339i	−0.561836	+	0.150544i
$663$		0			0
$664$	29.8104	+	29.8104i	1.15687	+	1.15687i
$665$			9.02861i			0.350114i
$666$		0			0
$667$	36.3442			1.40725
$668$	15.0845	−	8.70905i	0.583637	−	0.336963i
$669$		0			0
$670$	−7.85005	+	2.10341i	−0.303274	+	0.0812620i
$671$	−44.2722			−1.70911
$672$		0			0
$673$	21.4937			0.828520			0.414260	−	0.910159i	$-0.364040\pi$
$673$	21.4937			0.828520			0.414260	+	0.910159i	$0.364040\pi$
$674$	5.86155	−	1.57060i	0.225778	−	0.0604971i
$675$		0			0
$676$	−22.2971	+	12.8732i	−0.857581	+	0.495125i
$677$	−13.5920			−0.522383			−0.261192	−	0.965287i	$-0.584115\pi$
$677$	−13.5920			−0.522383			−0.261192	+	0.965287i	$0.584115\pi$
$678$		0			0
$679$			4.17315i			0.160151i
$680$	−4.51906	−	4.51906i	−0.173298	−	0.173298i
$681$		0			0
$682$	−21.5581	+	5.77647i	−0.825501	+	0.221192i
$683$		−	13.0200i		−	0.498196i	−0.968478	−	0.249098i	$-0.919866\pi$
$683$		−	13.0200i		−	0.498196i	0.968478	−	0.249098i	$-0.0801342\pi$
$684$		0			0
$685$			15.7451i			0.601590i
$686$	0.366025	+	1.36603i	0.0139749	+	0.0521551i
$687$		0			0
$688$	−20.0296	+	34.6922i	−0.763620	+	1.32263i
$689$		−	39.2868i		−	1.49671i
$690$		0			0
$691$	−8.07556			−0.307209			−0.153604	−	0.988132i	$-0.549088\pi$
$691$	−8.07556			−0.307209			−0.153604	+	0.988132i	$0.549088\pi$
$692$	−2.66547	+	1.53891i	−0.101326	+	0.0585005i
$693$		0			0
$694$	3.78489	+	14.1254i	0.143672	+	0.536192i
$695$	−15.7977			−0.599240
$696$		0			0
$697$	−16.8250			−0.637292
$698$	4.06954	+	15.1877i	0.154034	+	0.574864i
$699$		0			0
$700$	−3.72363	−	6.44952i	−0.140740	−	0.243769i
$701$	−9.91978			−0.374665			−0.187333	−	0.982297i	$-0.559984\pi$
$701$	−9.91978			−0.374665			−0.187333	+	0.982297i	$0.559984\pi$
$702$		0			0
$703$		−	66.1921i		−	2.49648i
$704$	30.8945			1.16438
$705$		0			0
$706$	−8.54329	−	31.8840i	−0.321531	−	1.19997i
$707$		−	2.00000i		−	0.0752177i
$708$		0			0
$709$			33.4709i			1.25702i	0.777800	+	0.628512i	$0.216336\pi$
$709$			33.4709i			1.25702i	−0.777800	+	0.628512i	$0.783664\pi$
$710$	−21.1129	+	5.65717i	−0.792351	+	0.212310i
$711$		0			0
$712$	−25.3777	−	25.3777i	−0.951070	−	0.951070i
$713$			31.3867i			1.17544i
$714$		0			0
$715$	−22.1924			−0.829950
$716$	−26.7386	−	46.3126i	−0.999269	−	1.73078i
$717$		0			0
$718$	−30.5885	+	8.19615i	−1.14155	+	0.305878i
$719$	−29.1075			−1.08553			−0.542764	−	0.839886i	$-0.682622\pi$
$719$	−29.1075			−1.08553			−0.542764	+	0.839886i	$0.682622\pi$
$720$		0			0
$721$	−5.37753			−0.200270
$722$	−61.2872	+	16.4219i	−2.28087	+	0.611158i
$723$		0			0
$724$	−3.10135	−	5.37170i	−0.115261	−	0.199638i
$725$	17.6204			0.654406
$726$		0			0
$727$			2.39230i			0.0887257i	0.999015	+	0.0443628i	$0.0141258\pi$
$727$			2.39230i			0.0887257i	−0.999015	+	0.0443628i	$0.985874\pi$
$728$	10.1732	−	10.1732i	0.377042	−	0.377042i
$729$		0			0
$730$	4.06974	−	1.09048i	0.150628	−	0.0403606i
$731$		−	20.0296i		−	0.740820i
$732$		0			0
$733$		−	20.3315i		−	0.750962i	−0.926830	−	0.375481i	$-0.877478\pi$
$733$		−	20.3315i		−	0.750962i	0.926830	−	0.375481i	$-0.122522\pi$
$734$	−0.708977	−	2.64594i	−0.0261688	−	0.0976634i
$735$		0			0
$736$	11.2449	−	41.9667i	0.414494	−	1.54691i
$737$			19.6434i			0.723574i
$738$		0			0
$739$	36.5823			1.34570			0.672851	−	0.739778i	$-0.265070\pi$
$739$	36.5823			1.34570			0.672851	+	0.739778i	$0.265070\pi$
$740$	−9.35753	−	16.2077i	−0.343990	−	0.595808i
$741$		0			0
$742$	2.82705	+	10.5507i	0.103784	+	0.387328i
$743$	−13.9864			−0.513110			−0.256555	−	0.966530i	$-0.582587\pi$
$743$	−13.9864			−0.513110			−0.256555	+	0.966530i	$0.582587\pi$
$744$		0			0
$745$	24.5950			0.901091
$746$	−5.53597	−	20.6605i	−0.202686	−	0.756435i
$747$		0			0
$748$	−13.3777	+	7.72363i	−0.489138	+	0.282404i
$749$	−12.8418			−0.469230
$750$		0			0
$751$		−	47.5657i		−	1.73570i	−0.496830	−	0.867848i	$-0.665503\pi$
$751$		−	47.5657i		−	1.73570i	0.496830	−	0.867848i	$-0.334497\pi$
$752$	−3.87325	+	6.70866i	−0.141243	+	0.244640i
$753$		0			0
$754$	8.81021	+	32.8801i	0.320849	+	1.19742i
$755$			18.1287i			0.659769i
$756$		0			0
$757$			41.3844i			1.50414i	0.659082	+	0.752071i	$0.270945\pi$
$757$			41.3844i			1.50414i	−0.659082	+	0.752071i	$0.729055\pi$
$758$	−8.41249	+	2.25412i	−0.305555	+	0.0818733i
$759$		0			0
$760$	−18.0572	+	18.0572i	−0.655004	+	0.655004i
$761$			19.8335i			0.718966i	0.933152	+	0.359483i	$0.117047\pi$
$761$			19.8335i			0.718966i	−0.933152	+	0.359483i	$0.882953\pi$
$762$		0			0
$763$	−13.0782			−0.473461
$764$	23.9252	−	13.8132i	0.865583	−	0.499745i
$765$		0			0
$766$	−20.3295	+	5.44726i	−0.734533	+	0.196818i
$767$	55.9095			2.01878
$768$		0			0
$769$	−20.2739			−0.731096			−0.365548	−	0.930792i	$-0.619118\pi$
$769$	−20.2739			−0.731096			−0.365548	+	0.930792i	$0.619118\pi$
$770$	5.95989	−	1.59695i	0.214780	−	0.0575500i
$771$		0			0
$772$	12.2195	−	7.05496i	0.439791	−	0.253913i
$773$	0.271102			0.00975088			0.00487544	−	0.999988i	$-0.498448\pi$
$773$	0.271102			0.00975088			0.00487544	+	0.999988i	$0.498448\pi$
$774$		0			0
$775$			15.2169i			0.546607i
$776$	−8.34630	+	8.34630i	−0.299615	+	0.299615i
$777$		0			0
$778$	2.49552	−	0.668673i	0.0894689	−	0.0239731i
$779$			67.2291i			2.40873i
$780$		0			0
$781$			52.8313i			1.89045i
$782$	5.62247	+	20.9834i	0.201059	+	0.750363i
$783$		0			0
$784$	−2.00000	+	3.46410i	−0.0714286	+	0.123718i
$785$			6.20887i			0.221604i
$786$		0			0
$787$	−50.0760			−1.78501			−0.892507	−	0.451033i	$-0.851056\pi$
$787$	−50.0760			−1.78501			−0.892507	+	0.451033i	$0.851056\pi$
$788$	−0.628299	+	0.362748i	−0.0223822	+	0.0129224i
$789$		0			0
$790$	−2.96618	−	11.0699i	−0.105532	−	0.393850i
$791$	7.05496			0.250845
$792$		0			0
$793$	−58.3130			−2.07076
$794$	−0.801592	−	2.99158i	−0.0284474	−	0.106167i
$795$		0			0
$796$	−7.70029	−	13.3373i	−0.272930	−	0.472728i
$797$	27.1762			0.962629			0.481314	−	0.876548i	$-0.340160\pi$
$797$	27.1762			0.962629			0.481314	+	0.876548i	$0.340160\pi$
$798$		0			0
$799$		−	3.87325i		−	0.137026i
$800$	5.45177	−	20.3463i	0.192749	−	0.719350i
$801$		0			0
$802$	−1.31429	−	4.90501i	−0.0464093	−	0.173202i
$803$		−	10.1838i		−	0.359379i
$804$		0			0
$805$		−	8.67709i		−	0.305827i
$806$	−28.3951	+	7.60845i	−1.00018	+	0.267996i
$807$		0			0
$808$	4.00000	−	4.00000i	0.140720	−	0.140720i
$809$		−	33.5566i		−	1.17979i	−0.807480	−	0.589894i	$-0.799169\pi$
$809$		−	33.5566i		−	1.17979i	0.807480	−	0.589894i	$-0.200831\pi$
$810$		0			0
$811$	−3.54206			−0.124379			−0.0621893	−	0.998064i	$-0.519808\pi$
$811$	−3.54206			−0.124379			−0.0621893	+	0.998064i	$0.519808\pi$
$812$	−4.73205	−	8.19615i	−0.166062	−	0.287629i
$813$		0			0
$814$	−43.6942	+	11.7078i	−1.53148	+	0.410359i
$815$	1.83301			0.0642077
$816$		0			0
$817$	−80.0339			−2.80003
$818$	48.3010	−	12.9422i	1.68881	−	0.452514i
$819$		0			0
$820$	9.50414	+	16.4617i	0.331899	+	0.574866i
$821$	31.0847			1.08486			0.542431	−	0.840100i	$-0.317504\pi$
$821$	31.0847			1.08486			0.542431	+	0.840100i	$0.317504\pi$
$822$		0			0
$823$			36.2323i			1.26298i	0.775385	+	0.631489i	$0.217556\pi$
$823$			36.2323i			1.26298i	−0.775385	+	0.631489i	$0.782444\pi$
$824$	−10.7551	−	10.7551i	−0.374670	−	0.374670i
$825$		0			0
$826$	−15.0148	+	4.02320i	−0.522431	+	0.139985i
$827$			53.4991i			1.86034i	0.367123	+	0.930172i	$0.380343\pi$
$827$			53.4991i			1.86034i	−0.367123	+	0.930172i	$0.619657\pi$
$828$		0			0
$829$		−	46.2003i		−	1.60460i	−0.596920	−	0.802301i	$-0.703609\pi$
$829$		−	46.2003i		−	1.60460i	0.596920	−	0.802301i	$-0.296391\pi$
$830$	6.16364	+	23.0030i	0.213943	+	0.798446i
$831$		0			0
$832$	40.6926			1.41076
$833$		−	2.00000i		−	0.0692959i
$834$		0			0
$835$	9.83918			0.340499
$836$	30.8620	+	53.4546i	1.06738	+	1.84876i
$837$		0			0
$838$	0.896586	+	3.34610i	0.0309721	+	0.115589i
$839$	29.0211			1.00192			0.500960	−	0.865470i	$-0.332980\pi$
$839$	29.0211			1.00192			0.500960	+	0.865470i	$0.332980\pi$
$840$		0			0
$841$	−6.60770			−0.227852
$842$	−2.29347	−	8.55936i	−0.0790383	−	0.294975i
$843$		0			0
$844$	−25.1477	+	14.5191i	−0.865621	+	0.499767i
$845$	−14.5437			−0.500320
$846$		0			0
$847$		−	3.91362i		−	0.134474i
$848$	−15.4473	+	26.7554i	−0.530461	+	0.918786i
$849$		0			0
$850$	2.72589	+	10.1732i	0.0934972	+	0.348936i
$851$			63.6150i			2.18069i
$852$		0			0
$853$		−	50.8777i		−	1.74202i	−0.491266	−	0.871009i	$-0.663466\pi$
$853$		−	50.8777i		−	1.74202i	0.491266	−	0.871009i	$-0.336534\pi$
$854$	15.6603	−	4.19615i	0.535883	−	0.143589i
$855$		0			0
$856$	−25.6836	−	25.6836i	−0.877849	−	0.877849i
$857$			22.3553i			0.763642i	0.924236	+	0.381821i	$0.124703\pi$
$857$			22.3553i			0.763642i	−0.924236	+	0.381821i	$0.875297\pi$
$858$		0			0
$859$	44.4134			1.51537			0.757684	−	0.652622i	$-0.226331\pi$
$859$	44.4134			1.51537			0.757684	+	0.652622i	$0.226331\pi$
$860$	−19.5970	+	11.3143i	−0.668253	+	0.385816i
$861$		0			0
$862$	−4.11415	+	1.10238i	−0.140129	+	0.0375473i
$863$	−8.80145			−0.299605			−0.149802	−	0.988716i	$-0.547864\pi$
$863$	−8.80145			−0.299605			−0.149802	+	0.988716i	$0.547864\pi$
$864$		0			0
$865$	−1.73860			−0.0591143
$866$	9.56244	−	2.56225i	0.324945	−	0.0870688i
$867$		0			0
$868$	7.07816	−	4.08658i	0.240248	−	0.138707i
$869$	−27.7006			−0.939679
$870$		0			0
$871$			25.8732i			0.876681i
$872$	−26.1563	−	26.1563i	−0.885764	−	0.885764i
$873$		0			0
$874$	83.8451	−	22.4662i	2.83610	−	0.759931i
$875$		−	9.85565i		−	0.333182i
$876$		0			0
$877$		−	25.5280i		−	0.862020i	−0.902347	−	0.431010i	$-0.858157\pi$
$877$		−	25.5280i		−	0.862020i	0.902347	−	0.431010i	$-0.141843\pi$
$878$	−0.489503	−	1.82685i	−0.0165199	−	0.0616532i
$879$		0			0
$880$	15.1137	+	8.72589i	0.509482	+	0.294150i
$881$		−	41.0812i		−	1.38406i	−0.721869	−	0.692030i	$-0.756717\pi$
$881$		−	41.0812i		−	1.38406i	0.721869	−	0.692030i	$-0.243283\pi$
$882$		0			0
$883$	2.80145			0.0942763			0.0471381	−	0.998888i	$-0.484990\pi$
$883$	2.80145			0.0942763			0.0471381	+	0.998888i	$0.484990\pi$
$884$	−17.6204	+	10.1732i	−0.592639	+	0.342160i
$885$		0			0
$886$	−0.698454	−	2.60666i	−0.0234650	−	0.0875726i
$887$	−45.4366			−1.52561			−0.762806	−	0.646628i	$-0.776179\pi$
$887$	−45.4366			−1.52561			−0.762806	+	0.646628i	$0.776179\pi$
$888$		0			0
$889$	4.63706			0.155522
$890$	−5.24713	−	19.5826i	−0.175884	−	0.656409i
$891$		0			0
$892$	19.2743	+	33.3841i	0.645352	+	1.11778i
$893$	−15.4767			−0.517907
$894$		0			0
$895$		−	30.2083i		−	1.00975i
$896$	−10.9282	+	2.92820i	−0.365086	+	0.0978244i
$897$		0			0
$898$	−3.68571	−	13.7552i	−0.122994	−	0.459019i
$899$			19.3379i			0.644954i
$900$		0			0
$901$		−	15.4473i		−	0.514623i
$902$	44.3787	−	11.8912i	1.47765	−	0.395935i
$903$		0			0
$904$	14.1099	+	14.1099i	0.469289	+	0.469289i
$905$		−	3.50380i		−	0.116470i
$906$		0			0
$907$	46.5318			1.54506			0.772531	−	0.634977i	$-0.218990\pi$
$907$	46.5318			1.54506			0.772531	+	0.634977i	$0.218990\pi$
$908$	−23.2341	−	40.2427i	−0.771052	−	1.33550i
$909$		0			0
$910$	7.85005	−	2.10341i	0.260227	−	0.0697275i
$911$	24.9174			0.825550			0.412775	−	0.910833i	$-0.364560\pi$
$911$	24.9174			0.825550			0.412775	+	0.910833i	$0.364560\pi$
$912$		0			0
$913$	57.5611			1.90500
$914$	−14.0981	+	3.77757i	−0.466323	+	0.124951i
$915$		0			0
$916$	13.4641	+	23.3205i	0.444866	+	0.770531i
$917$	−8.36930			−0.276379
$918$		0			0
$919$			8.77228i			0.289371i	0.989478	+	0.144685i	$0.0462170\pi$
$919$			8.77228i			0.289371i	−0.989478	+	0.144685i	$0.953783\pi$
$920$	17.3542	−	17.3542i	0.572151	−	0.572151i
$921$		0			0
$922$	−24.5093	+	6.56724i	−0.807170	+	0.216281i
$923$			69.5866i			2.29047i
$924$		0			0
$925$			30.8418i			1.01407i
$926$	7.93046	+	29.5969i	0.260611	+	0.972614i
$927$		0			0
$928$	6.92820	−	25.8564i	0.227429	−	0.848778i
$929$		−	3.96002i		−	0.129924i	−0.997888	−	0.0649620i	$-0.979307\pi$
$929$		−	3.96002i		−	0.129924i	0.997888	−	0.0649620i	$-0.0206926\pi$
$930$		0			0
$931$	−7.99158			−0.261913
$932$	17.4641	+	30.2487i	0.572056	+	0.990829i
$933$		0			0
$934$	6.71747	+	25.0699i	0.219802	+	0.820313i
$935$	−8.72589			−0.285367
$936$		0			0
$937$	−11.6077			−0.379207			−0.189603	−	0.981861i	$-0.560720\pi$
$937$	−11.6077			−0.379207			−0.189603	+	0.981861i	$0.560720\pi$
$938$	−1.86182	−	6.94839i	−0.0607904	−	0.226873i
$939$		0			0
$940$	−3.78960	+	2.18793i	−0.123603	+	0.0713624i
$941$	−2.05758			−0.0670751			−0.0335376	−	0.999437i	$-0.510677\pi$
$941$	−2.05758			−0.0670751			−0.0335376	+	0.999437i	$0.510677\pi$
$942$		0			0
$943$		−	64.6117i		−	2.10404i
$944$	−38.0760	−	21.9832i	−1.23927	−	0.715491i
$945$		0			0
$946$	14.1561	+	52.8313i	0.460255	+	1.71770i
$947$		−	53.3723i		−	1.73437i	−0.497989	−	0.867184i	$-0.665928\pi$
$947$		−	53.3723i		−	1.73437i	0.497989	−	0.867184i	$-0.334072\pi$
$948$		0			0
$949$		−	13.4136i		−	0.435423i
$950$	40.6498	−	10.8921i	1.31885	−	0.353386i
$951$		0			0
$952$	4.00000	−	4.00000i	0.129641	−	0.129641i
$953$		−	45.9433i		−	1.48825i	−0.668040	−	0.744125i	$-0.732867\pi$
$953$		−	45.9433i		−	1.48825i	0.668040	−	0.744125i	$-0.267133\pi$
$954$		0			0
$955$	15.6057			0.504988
$956$	−3.16487	+	1.82724i	−0.102359	+	0.0590972i
$957$		0			0
$958$	−20.0148	+	5.36294i	−0.646648	+	0.173269i
$959$	−13.9366			−0.450037
$960$		0			0
$961$	14.2999			0.461287
$962$	−57.5516	+	15.4209i	−1.85554	+	0.497190i
$963$		0			0
$964$	−37.2724	+	21.5193i	−1.20046	+	0.693089i
$965$	7.97044			0.256578
$966$		0			0
$967$			1.43455i			0.0461319i	0.999734	+	0.0230659i	$0.00734276\pi$
$967$			1.43455i			0.0461319i	−0.999734	+	0.0230659i	$0.992657\pi$
$968$	7.82724	−	7.82724i	0.251577	−	0.251577i
$969$		0			0
$970$	−6.44037	+	1.72569i	−0.206788	+	0.0554086i
$971$			13.6030i			0.436542i	0.975888	+	0.218271i	$0.0700417\pi$
$971$			13.6030i			0.436542i	−0.975888	+	0.218271i	$0.929958\pi$
$972$		0			0
$973$		−	13.9832i		−	0.448280i
$974$	2.41866	+	9.02655i	0.0774987	+	0.289229i
$975$		0			0
$976$	39.7128	+	22.9282i	1.27118	+	0.733914i
$977$			10.3860i			0.332278i	0.986102	+	0.166139i	$0.0531300\pi$
$977$			10.3860i			0.332278i	−0.986102	+	0.166139i	$0.946870\pi$
$978$		0			0
$979$	−49.0020			−1.56611
$980$	−1.95681	+	1.12976i	−0.0625080	+	0.0360890i
$981$		0			0
$982$	−2.59264	−	9.67587i	−0.0827345	−	0.308769i
$983$	−20.0062			−0.638098			−0.319049	−	0.947738i	$-0.603363\pi$
$983$	−20.0062			−0.638098			−0.319049	+	0.947738i	$0.603363\pi$
$984$		0			0
$985$	−0.409820			−0.0130580
$986$	3.46410	+	12.9282i	0.110319	+	0.411718i
$987$		0			0
$988$	40.6498	+	70.4075i	1.29324	+	2.23996i
$989$	76.9179			2.44585
$990$		0			0
$991$			45.7220i			1.45241i	0.687480	+	0.726203i	$0.258717\pi$
$991$			45.7220i			1.45241i	−0.687480	+	0.726203i	$0.741283\pi$
$992$	22.3295	+	5.98316i	0.708961	+	0.189966i
$993$		0			0
$994$	−5.00739	−	18.6878i	−0.158825	−	0.592742i
$995$		−	8.69952i		−	0.275793i
$996$		0			0
$997$		−	41.6964i		−	1.32054i	−0.751030	−	0.660269i	$-0.770442\pi$
$997$		−	41.6964i		−	1.32054i	0.751030	−	0.660269i	$-0.229558\pi$
$998$	9.74382	−	2.61085i	0.308435	−	0.0826450i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.j.a.323.4	yes	8
3.2	odd	2		1512.2.j.b.323.5	yes	8
4.3	odd	2		6048.2.j.a.5615.5		8
8.3	odd	2		1512.2.j.b.323.7	yes	8
8.5	even	2		6048.2.j.b.5615.4		8
12.11	even	2		6048.2.j.b.5615.3		8
24.5	odd	2		6048.2.j.a.5615.6		8
24.11	even	2	inner	1512.2.j.a.323.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.j.a.323.2	✓	8	24.11	even	2	inner
1512.2.j.a.323.4	yes	8	1.1	even	1	trivial
1512.2.j.b.323.5	yes	8	3.2	odd	2
1512.2.j.b.323.7	yes	8	8.3	odd	2
6048.2.j.a.5615.5		8	4.3	odd	2
6048.2.j.a.5615.6		8	24.5	odd	2
6048.2.j.b.5615.3		8	12.11	even	2
6048.2.j.b.5615.4		8	8.5	even	2

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:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +1.12976 q^{5} +1.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +1.12976 q^{5} +1.00000i q^{7} +(-2.00000 + 2.00000i) q^{8} +(-1.54329 + 0.413523i) q^{10} +3.86182i q^{11} +5.08658i q^{13} +(-0.366025 - 1.36603i) q^{14} +(2.00000 - 3.46410i) q^{16} +2.00000i q^{17} +7.99158 q^{19} +(1.95681 - 1.12976i) q^{20} +(-1.41352 - 5.27534i) q^{22} -7.68044 q^{23} -3.72363 q^{25} +(-1.86182 - 6.94839i) q^{26} +(1.00000 + 1.73205i) q^{28} -4.73205 q^{29} -4.08658i q^{31} +(-1.46410 + 5.46410i) q^{32} +(-0.732051 - 2.73205i) q^{34} +1.12976i q^{35} -8.28273i q^{37} +(-10.9167 + 2.92512i) q^{38} +(-2.25953 + 2.25953i) q^{40} +8.41249i q^{41} -10.0148 q^{43} +(3.86182 + 6.68886i) q^{44} +(10.4917 - 2.81124i) q^{46} -1.93662 q^{47} -1.00000 q^{49} +(5.08658 - 1.36294i) q^{50} +(5.08658 + 8.81021i) q^{52} -7.72363 q^{53} +4.36294i q^{55} +(-2.00000 - 2.00000i) q^{56} +(6.46410 - 1.73205i) q^{58} -10.9916i q^{59} +11.4641i q^{61} +(1.49579 + 5.58237i) q^{62} -8.00000i q^{64} +5.74663i q^{65} +5.08658 q^{67} +(2.00000 + 3.46410i) q^{68} +(-0.413523 - 1.54329i) q^{70} +13.6804 q^{71} -2.63706 q^{73} +(3.03169 + 11.3144i) q^{74} +(13.8418 - 7.99158i) q^{76} -3.86182 q^{77} +7.17295i q^{79} +(2.25953 - 3.91362i) q^{80} +(-3.07919 - 11.4917i) q^{82} -14.9052i q^{83} +2.25953i q^{85} +(13.6804 - 3.66566i) q^{86} +(-7.72363 - 7.72363i) q^{88} +12.6889i q^{89} -5.08658 q^{91} +(-13.3029 + 7.68044i) q^{92} +(2.64548 - 0.708853i) q^{94} +9.02861 q^{95} +4.17315 q^{97} +(1.36603 - 0.366025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 8 q^{5} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 8 * q^5 - 16 * q^8	\( 8 q - 4 q^{2} - 8 q^{5} - 16 q^{8} + 4 q^{10} + 4 q^{14} + 16 q^{16} + 16 q^{19} - 12 q^{22} + 16 q^{23} + 32 q^{25} + 16 q^{26} + 8 q^{28} - 24 q^{29} + 16 q^{32} + 8 q^{34} - 20 q^{38} + 16 q^{40} + 8 q^{43} + 4 q^{46} - 8 q^{47} - 8 q^{49} + 8 q^{50} + 8 q^{52} - 16 q^{56} + 24 q^{58} - 12 q^{62} + 8 q^{67} + 16 q^{68} - 4 q^{70} + 32 q^{71} + 8 q^{73} + 28 q^{74} + 24 q^{76} - 16 q^{80} - 36 q^{82} + 32 q^{86} - 8 q^{91} - 24 q^{92} + 40 q^{94} + 112 q^{95} - 32 q^{97} + 4 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^5 - 16 * q^8 + 4 * q^10 + 4 * q^14 + 16 * q^16 + 16 * q^19 - 12 * q^22 + 16 * q^23 + 32 * q^25 + 16 * q^26 + 8 * q^28 - 24 * q^29 + 16 * q^32 + 8 * q^34 - 20 * q^38 + 16 * q^40 + 8 * q^43 + 4 * q^46 - 8 * q^47 - 8 * q^49 + 8 * q^50 + 8 * q^52 - 16 * q^56 + 24 * q^58 - 12 * q^62 + 8 * q^67 + 16 * q^68 - 4 * q^70 + 32 * q^71 + 8 * q^73 + 28 * q^74 + 24 * q^76 - 16 * q^80 - 36 * q^82 + 32 * q^86 - 8 * q^91 - 24 * q^92 + 40 * q^94 + 112 * q^95 - 32 * q^97 + 4 * q^98

Introduction

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