LMFDB - Embedded newform 1152.2.p.e.191.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(191,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1152.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.9349208943630483456.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 $ x^16 - 8x^15 + 48x^14 - 196x^13 + 642x^12 - 1668x^11 + 3580x^10 - 6328x^9 + 9297x^8 - 11276x^7 + 11224x^6 - 9024x^5 + 5736x^4 - 2780x^3 + 972x^2 - 220*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.5
Root			$0.500000 - 2.00333i$ of defining polynomial
Character	$\chi$	$=$	1152.191
Dual form			1152.2.p.e.959.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.524648 - 1.65068i) q^{3} +(-0.158919 - 0.275255i) q^{5} +(-2.93038 - 1.69185i) q^{7} +(-2.44949 - 1.73205i) q^{9} +O(q^{10})$	\(q+(0.524648 - 1.65068i) q^{3} +(-0.158919 - 0.275255i) q^{5} +(-2.93038 - 1.69185i) q^{7} +(-2.44949 - 1.73205i) q^{9} +(-0.642559 - 0.370982i) q^{11} +(-2.59808 + 1.50000i) q^{13} +(-0.537734 + 0.117912i) q^{15} +4.24264i q^{17} +2.57024 q^{19} +(-4.33013 + 3.94949i) q^{21} +(-2.02166 - 3.50162i) q^{23} +(2.44949 - 4.24264i) q^{25} +(-4.14418 + 3.13461i) q^{27} +(-4.01229 + 6.94949i) q^{29} +(-4.24755 + 2.45233i) q^{31} +(-0.949490 + 0.866025i) q^{33} +1.07547i q^{35} +7.34847i q^{37} +(1.11295 + 5.07556i) q^{39} +(-0.825765 + 0.476756i) q^{41} +(-3.50162 + 6.06499i) q^{43} +(-0.0874863 + 0.949490i) q^{45} +(5.15627 - 8.93092i) q^{47} +(2.22474 + 3.85337i) q^{49} +(7.00324 + 2.22589i) q^{51} -5.51399 q^{53} +0.235824i q^{55} +(1.34847 - 4.24264i) q^{57} +(3.50162 - 2.02166i) q^{59} +(-7.79423 - 4.50000i) q^{61} +(4.24755 + 9.21975i) q^{63} +(0.825765 + 0.476756i) q^{65} +(-6.36068 - 11.0170i) q^{67} +(-6.84072 + 1.50000i) q^{69} +13.5389 q^{71} -6.44949 q^{73} +(-5.71812 - 6.26922i) q^{75} +(1.25529 + 2.17423i) q^{77} +(-8.29088 - 4.78674i) q^{79} +(3.00000 + 8.48528i) q^{81} +(2.21650 + 1.27970i) q^{83} +(1.16781 - 0.674235i) q^{85} +(9.36635 + 10.2690i) q^{87} -14.6349i q^{89} +10.1511 q^{91} +(1.81954 + 8.29796i) q^{93} +(-0.408459 - 0.707471i) q^{95} +(-5.62372 + 9.74058i) q^{97} +(0.931383 + 2.02166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 24 q^{33} - 72 q^{41} + 16 q^{49} - 96 q^{57} + 72 q^{65} - 64 q^{73} + 48 q^{81} + 8 q^{97}+O(q^{100}) $ 16 * q + 24 * q^33 - 72 * q^41 + 16 * q^49 - 96 * q^57 + 72 * q^65 - 64 * q^73 + 48 * q^81 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	0.524648	−	1.65068i	0.302905	−	0.953021i
$3$	0.524648	−	1.65068i	0.302905	−	0.953021i
$4$		0			0
$5$	−0.158919	−	0.275255i	−0.0710706	−	0.123098i	0.828300	−	0.560285i	$-0.189308\pi$
$5$	−0.158919	−	0.275255i	−0.0710706	−	0.123098i	−0.899371	+	0.437187i	$0.855975\pi$
$6$		0			0
$7$	−2.93038	−	1.69185i	−1.10758	−	0.639461i	−0.169378	−	0.985551i	$-0.554176\pi$
$7$	−2.93038	−	1.69185i	−1.10758	−	0.639461i	−0.938201	+	0.346090i	$0.887509\pi$
$8$		0			0
$9$	−2.44949	−	1.73205i	−0.816497	−	0.577350i
$10$		0			0
$11$	−0.642559	−	0.370982i	−0.193739	−	0.111855i	0.399993	−	0.916518i	$-0.369013\pi$
$11$	−0.642559	−	0.370982i	−0.193739	−	0.111855i	−0.593732	+	0.804663i	$0.702346\pi$
$12$		0			0
$13$	−2.59808	+	1.50000i	−0.720577	+	0.416025i	−0.814965	−	0.579510i	$-0.803244\pi$
$13$	−2.59808	+	1.50000i	−0.720577	+	0.416025i	0.0943882	+	0.995535i	$0.469911\pi$
$14$		0			0
$15$	−0.537734	+	0.117912i	−0.138842	+	0.0304447i
$16$		0			0
$17$			4.24264i			1.02899i	0.857493	+	0.514496i	$0.172021\pi$
$17$			4.24264i			1.02899i	−0.857493	+	0.514496i	$0.827979\pi$
$18$		0			0
$19$	2.57024			0.589653			0.294827	−	0.955551i	$-0.404738\pi$
$19$	2.57024			0.589653			0.294827	+	0.955551i	$0.404738\pi$
$20$		0			0
$21$	−4.33013	+	3.94949i	−0.944911	+	0.861849i
$22$		0			0
$23$	−2.02166	−	3.50162i	−0.421546	−	0.730139i	0.574545	−	0.818473i	$-0.305179\pi$
$23$	−2.02166	−	3.50162i	−0.421546	−	0.730139i	−0.996091	+	0.0883343i	$0.971846\pi$
$24$		0			0
$25$	2.44949	−	4.24264i	0.489898	−	0.848528i
$26$		0			0
$27$	−4.14418	+	3.13461i	−0.797548	+	0.603256i
$28$		0			0
$29$	−4.01229	+	6.94949i	−0.745064	+	1.29049i	0.205102	+	0.978741i	$0.434248\pi$
$29$	−4.01229	+	6.94949i	−0.745064	+	1.29049i	−0.950165	+	0.311747i	$0.899086\pi$
$30$		0			0
$31$	−4.24755	+	2.45233i	−0.762883	+	0.440451i	−0.830330	−	0.557272i	$-0.811848\pi$
$31$	−4.24755	+	2.45233i	−0.762883	+	0.440451i	0.0674468	+	0.997723i	$0.478515\pi$
$32$		0			0
$33$	−0.949490	+	0.866025i	−0.165285	+	0.150756i
$34$		0			0
$35$			1.07547i			0.181787i
$36$		0			0
$37$			7.34847i			1.20808i	0.796954	+	0.604040i	$0.206443\pi$
$37$			7.34847i			1.20808i	−0.796954	+	0.604040i	$0.793557\pi$
$38$		0			0
$39$	1.11295	+	5.07556i	0.178214	+	0.812741i
$40$		0			0
$41$	−0.825765	+	0.476756i	−0.128963	+	0.0744568i	−0.563094	−	0.826393i	$-0.690389\pi$
$41$	−0.825765	+	0.476756i	−0.128963	+	0.0744568i	0.434131	+	0.900850i	$0.357056\pi$
$42$		0			0
$43$	−3.50162	+	6.06499i	−0.533992	+	0.924902i	0.465219	+	0.885196i	$0.345976\pi$
$43$	−3.50162	+	6.06499i	−0.533992	+	0.924902i	−0.999211	+	0.0397062i	$0.987358\pi$
$44$		0			0
$45$	−0.0874863	+	0.949490i	−0.0130417	+	0.141542i
$46$		0			0
$47$	5.15627	−	8.93092i	0.752119	−	1.30271i	−0.194675	−	0.980868i	$-0.562365\pi$
$47$	5.15627	−	8.93092i	0.752119	−	1.30271i	0.946794	−	0.321841i	$-0.104302\pi$
$48$		0			0
$49$	2.22474	+	3.85337i	0.317821	+	0.550482i
$50$		0			0
$51$	7.00324	+	2.22589i	0.980650	+	0.311687i
$52$		0			0
$53$	−5.51399			−0.757405			−0.378702	−	0.925519i	$-0.623630\pi$
$53$	−5.51399			−0.757405			−0.378702	+	0.925519i	$0.623630\pi$
$54$		0			0
$55$			0.235824i			0.0317985i
$56$		0			0
$57$	1.34847	−	4.24264i	0.178609	−	0.561951i
$58$		0			0
$59$	3.50162	−	2.02166i	0.455872	−	0.263198i	−0.254435	−	0.967090i	$-0.581889\pi$
$59$	3.50162	−	2.02166i	0.455872	−	0.263198i	0.710307	+	0.703892i	$0.248556\pi$
$60$		0			0
$61$	−7.79423	−	4.50000i	−0.997949	−	0.576166i	−0.0903080	−	0.995914i	$-0.528785\pi$
$61$	−7.79423	−	4.50000i	−0.997949	−	0.576166i	−0.907641	+	0.419748i	$0.862118\pi$
$62$		0			0
$63$	4.24755	+	9.21975i	0.535141	+	1.16158i
$64$		0			0
$65$	0.825765	+	0.476756i	0.102424	+	0.0591343i
$66$		0			0
$67$	−6.36068	−	11.0170i	−0.777081	−	1.34594i	−0.933617	−	0.358272i	$-0.883366\pi$
$67$	−6.36068	−	11.0170i	−0.777081	−	1.34594i	0.156536	−	0.987672i	$-0.449967\pi$
$68$		0			0
$69$	−6.84072	+	1.50000i	−0.823526	+	0.180579i
$70$		0			0
$71$	13.5389			1.60678			0.803389	−	0.595455i	$-0.203028\pi$
$71$	13.5389			1.60678			0.803389	+	0.595455i	$0.203028\pi$
$72$		0			0
$73$	−6.44949			−0.754856			−0.377428	−	0.926039i	$-0.623191\pi$
$73$	−6.44949			−0.754856			−0.377428	+	0.926039i	$0.623191\pi$
$74$		0			0
$75$	−5.71812	−	6.26922i	−0.660272	−	0.723907i
$76$		0			0
$77$	1.25529	+	2.17423i	0.143054	+	0.247777i
$78$		0			0
$79$	−8.29088	−	4.78674i	−0.932797	−	0.538550i	−0.0451016	−	0.998982i	$-0.514361\pi$
$79$	−8.29088	−	4.78674i	−0.932797	−	0.538550i	−0.887695	+	0.460432i	$0.847694\pi$
$80$		0			0
$81$	3.00000	+	8.48528i	0.333333	+	0.942809i
$82$		0			0
$83$	2.21650	+	1.27970i	0.243293	+	0.140465i	0.616689	−	0.787207i	$-0.288474\pi$
$83$	2.21650	+	1.27970i	0.243293	+	0.140465i	−0.373396	+	0.927672i	$0.621807\pi$
$84$		0			0
$85$	1.16781	−	0.674235i	0.126667	−	0.0731310i
$86$		0			0
$87$	9.36635	+	10.2690i	1.00418	+	1.10096i
$88$		0			0
$89$		−	14.6349i		−	1.55130i	−0.631163	−	0.775651i	$-0.717422\pi$
$89$		−	14.6349i		−	1.55130i	0.631163	−	0.775651i	$-0.282578\pi$
$90$		0			0
$91$	10.1511			1.06413
$92$		0			0
$93$	1.81954	+	8.29796i	0.188677	+	0.860458i
$94$		0			0
$95$	−0.408459	−	0.707471i	−0.0419070	−	0.0725850i
$96$		0			0
$97$	−5.62372	+	9.74058i	−0.571003	+	0.989006i	0.425461	+	0.904977i	$0.360112\pi$
$97$	−5.62372	+	9.74058i	−0.571003	+	0.989006i	−0.996463	+	0.0840287i	$0.973221\pi$
$98$		0			0
$99$	0.931383	+	2.02166i	0.0936076	+	0.203185i
$100$		0			0
$101$	0.158919	−	0.275255i	0.0158130	−	0.0273889i	−0.858011	−	0.513632i	$-0.828300\pi$
$101$	0.158919	−	0.275255i	0.0158130	−	0.0273889i	0.873824	+	0.486243i	$0.161633\pi$
$102$		0			0
$103$	−13.2429	+	7.64580i	−1.30486	+	0.753363i	−0.981234	−	0.192821i	$-0.938236\pi$
$103$	−13.2429	+	7.64580i	−1.30486	+	0.753363i	−0.323629	+	0.946184i	$0.604903\pi$
$104$		0			0
$105$	1.77526	+	0.564242i	0.173247	+	0.0550644i
$106$		0			0
$107$		−	8.75366i		−	0.846248i	−0.906072	−	0.423124i	$-0.860933\pi$
$107$		−	8.75366i		−	0.846248i	0.906072	−	0.423124i	$-0.139067\pi$
$108$		0			0
$109$			13.3485i			1.27855i	0.768978	+	0.639276i	$0.220766\pi$
$109$			13.3485i			1.27855i	−0.768978	+	0.639276i	$0.779234\pi$
$110$		0			0
$111$	12.1300	+	3.85536i	1.15133	+	0.365934i
$112$		0			0
$113$	4.50000	−	2.59808i	0.423324	−	0.244406i	−0.273174	−	0.961965i	$-0.588074\pi$
$113$	4.50000	−	2.59808i	0.423324	−	0.244406i	0.696499	+	0.717558i	$0.254740\pi$
$114$		0			0
$115$	−0.642559	+	1.11295i	−0.0599190	+	0.103783i
$116$		0			0
$117$	8.96204	+	0.825765i	0.828541	+	0.0763420i
$118$		0			0
$119$	7.17793	−	12.4325i	0.658000	−	1.13969i
$120$		0			0
$121$	−5.22474	−	9.04952i	−0.474977	−	0.822684i
$122$		0			0
$123$	0.353736	+	1.61320i	0.0318953	+	0.145458i
$124$		0			0
$125$	−3.14626			−0.281410
$126$		0			0
$127$		−	1.62694i		−	0.144368i	−0.997391	−	0.0721839i	$-0.977003\pi$
$127$		−	1.62694i		−	0.144368i	0.997391	−	0.0721839i	$-0.0229969\pi$
$128$		0			0
$129$	8.17423	+	8.96204i	0.719701	+	0.789063i
$130$		0			0
$131$	−16.2230	+	9.36635i	−1.41741	+	0.818341i	−0.996071	−	0.0885620i	$-0.971773\pi$
$131$	−16.2230	+	9.36635i	−1.41741	+	0.818341i	−0.421338	+	0.906904i	$0.638440\pi$
$132$		0			0
$133$	−7.53177	−	4.34847i	−0.653087	−	0.377060i
$134$		0			0
$135$	1.52140	+	0.642559i	0.130942	+	0.0553027i
$136$		0			0
$137$	−6.52270	−	3.76588i	−0.557272	−	0.321741i	0.194778	−	0.980847i	$-0.437601\pi$
$137$	−6.52270	−	3.76588i	−0.557272	−	0.321741i	−0.752050	+	0.659106i	$0.770935\pi$
$138$		0			0
$139$	6.64951	+	11.5173i	0.564004	+	0.976883i	0.997142	+	0.0755556i	$0.0240730\pi$
$139$	6.64951	+	11.5173i	0.564004	+	0.976883i	−0.433138	+	0.901328i	$0.642594\pi$
$140$		0			0
$141$	−12.0369	−	13.1969i	−1.01369	−	1.11138i
$142$		0			0
$143$	2.22589			0.186138
$144$		0			0
$145$	2.55051			0.211808
$146$		0			0
$147$	7.52789	−	1.65068i	0.620890	−	0.136146i
$148$		0			0
$149$	2.91591	+	5.05051i	0.238881	+	0.413754i	0.960393	−	0.278647i	$-0.0898861\pi$
$149$	2.91591	+	5.05051i	0.238881	+	0.413754i	−0.721513	+	0.692401i	$0.756553\pi$
$150$		0			0
$151$	−14.1516	−	8.17045i	−1.15164	−	0.664902i	−0.202356	−	0.979312i	$-0.564860\pi$
$151$	−14.1516	−	8.17045i	−1.15164	−	0.664902i	−0.949287	+	0.314410i	$0.898193\pi$
$152$		0			0
$153$	7.34847	−	10.3923i	0.594089	−	0.840168i
$154$		0			0
$155$	1.35003	+	0.779441i	0.108437	+	0.0626062i
$156$		0			0
$157$	19.3543	−	11.1742i	1.54464	−	0.891801i	0.546108	−	0.837715i	$-0.316109\pi$
$157$	19.3543	−	11.1742i	1.54464	−	0.891801i	0.998536	−	0.0540865i	$-0.0172247\pi$
$158$		0			0
$159$	−2.89290	+	9.10183i	−0.229422	+	0.721822i
$160$		0			0
$161$			13.6814i			1.07825i
$162$		0			0
$163$	−11.4362			−0.895756			−0.447878	−	0.894095i	$-0.647820\pi$
$163$	−11.4362			−0.895756			−0.447878	+	0.894095i	$0.647820\pi$
$164$		0			0
$165$	0.389270	+	0.123724i	0.0303046	+	0.00963193i
$166$		0			0
$167$	−9.19959	−	15.9342i	−0.711886	−	1.23302i	−0.964148	−	0.265364i	$-0.914508\pi$
$167$	−9.19959	−	15.9342i	−0.711886	−	1.23302i	0.252262	−	0.967659i	$-0.418825\pi$
$168$		0			0
$169$	−2.00000	+	3.46410i	−0.153846	+	0.266469i
$170$		0			0
$171$	−6.29577	−	4.45178i	−0.481450	−	0.340436i
$172$		0			0
$173$	9.59771	−	16.6237i	0.729701	−	1.26388i	−0.227309	−	0.973823i	$-0.572993\pi$
$173$	9.59771	−	16.6237i	0.729701	−	1.26388i	0.957010	−	0.290056i	$-0.0936738\pi$
$174$		0			0
$175$	−14.3559	+	8.28836i	−1.08520	+	0.626541i
$176$		0			0
$177$	−1.50000	−	6.84072i	−0.112747	−	0.514180i
$178$		0			0
$179$			22.7760i			1.70236i	0.524874	+	0.851180i	$0.324112\pi$
$179$			22.7760i			1.70236i	−0.524874	+	0.851180i	$0.675888\pi$
$180$		0			0
$181$		−	4.65153i		−	0.345746i	−0.984944	−	0.172873i	$-0.944695\pi$
$181$		−	4.65153i		−	0.345746i	0.984944	−	0.172873i	$-0.0553049\pi$
$182$		0			0
$183$	−11.5173	+	10.5049i	−0.851382	+	0.776542i
$184$		0			0
$185$	2.02270	−	1.16781i	0.148712	−	0.0858590i
$186$		0			0
$187$	1.57394	−	2.72615i	0.115098	−	0.199356i
$188$		0			0
$189$	17.4473	−	2.17423i	1.26911	−	0.158152i
$190$		0			0
$191$	12.8345	−	22.2299i	0.928669	−	1.60850i	0.143117	−	0.989706i	$-0.454287\pi$
$191$	12.8345	−	22.2299i	0.928669	−	1.60850i	0.785552	−	0.618796i	$-0.212379\pi$
$192$		0			0
$193$	1.27526	+	2.20881i	0.0917949	+	0.158993i	0.908266	−	0.418392i	$-0.137406\pi$
$193$	1.27526	+	2.20881i	0.0917949	+	0.158993i	−0.816472	+	0.577386i	$0.804073\pi$
$194$		0			0
$195$	1.22021	−	1.11295i	0.0873809	−	0.0796997i
$196$		0			0
$197$	11.0280			0.785711			0.392855	−	0.919600i	$-0.371487\pi$
$197$	11.0280			0.785711			0.392855	+	0.919600i	$0.371487\pi$
$198$		0			0
$199$		−	5.24648i		−	0.371913i	−0.982558	−	0.185956i	$-0.940462\pi$
$199$		−	5.24648i		−	0.371913i	0.982558	−	0.185956i	$-0.0595383\pi$
$200$		0			0
$201$	−21.5227	+	4.71940i	−1.51809	+	0.332881i
$202$		0			0
$203$	23.5151	−	13.5764i	1.65043	−	0.952878i
$204$		0			0
$205$	0.262459	+	0.151531i	0.0183309	+	0.0105834i
$206$		0			0
$207$	−1.11295	+	12.0788i	−0.0773551	+	0.839535i
$208$		0			0
$209$	−1.65153	−	0.953512i	−0.114239	−	0.0659558i
$210$		0			0
$211$	−5.07556	−	8.79114i	−0.349416	−	0.605207i	0.636730	−	0.771087i	$-0.280287\pi$
$211$	−5.07556	−	8.79114i	−0.349416	−	0.605207i	−0.986146	+	0.165880i	$0.946953\pi$
$212$		0			0
$213$	7.10318	−	22.3485i	0.486702	−	1.53129i
$214$		0			0
$215$	2.22589			0.151805
$216$		0			0
$217$	16.5959			1.12660
$218$		0			0
$219$	−3.38371	+	10.6460i	−0.228650	+	0.719393i
$220$		0			0
$221$	−6.36396	−	11.0227i	−0.428086	−	0.741467i
$222$		0			0
$223$	−16.4693	−	9.50857i	−1.10287	−	0.636741i	−0.165895	−	0.986143i	$-0.553051\pi$
$223$	−16.4693	−	9.50857i	−1.10287	−	0.636741i	−0.936973	+	0.349403i	$0.886385\pi$
$224$		0			0
$225$	−13.3485	+	6.14966i	−0.889898	+	0.409978i
$226$		0			0
$227$	−12.7863	−	7.38216i	−0.848655	−	0.489971i	0.0115418	−	0.999933i	$-0.496326\pi$
$227$	−12.7863	−	7.38216i	−0.848655	−	0.489971i	−0.860197	+	0.509962i	$0.829659\pi$
$228$		0			0
$229$	16.4938	−	9.52270i	1.08994	−	0.629278i	0.156381	−	0.987697i	$-0.450017\pi$
$229$	16.4938	−	9.52270i	1.08994	−	0.629278i	0.933561	+	0.358419i	$0.116684\pi$
$230$		0			0
$231$	4.24755	−	0.931383i	0.279468	−	0.0612805i
$232$		0			0
$233$			8.48528i			0.555889i	0.960597	+	0.277945i	$0.0896532\pi$
$233$			8.48528i			0.555889i	−0.960597	+	0.277945i	$0.910347\pi$
$234$		0			0
$235$	−3.27771			−0.213814
$236$		0			0
$237$	−12.2512	+	11.1742i	−0.795799	+	0.725845i
$238$		0			0
$239$	−2.02166	−	3.50162i	−0.130770	−	0.226501i	0.793203	−	0.608957i	$-0.208412\pi$
$239$	−2.02166	−	3.50162i	−0.130770	−	0.226501i	−0.923974	+	0.382456i	$0.875078\pi$
$240$		0			0
$241$	7.84847	−	13.5939i	0.505564	−	0.875663i	−0.494415	−	0.869226i	$-0.664618\pi$
$241$	7.84847	−	13.5939i	0.505564	−	0.875663i	0.999979	−	0.00643712i	$-0.00204901\pi$
$242$		0			0
$243$	15.5804	−	0.500258i	0.999485	−	0.0320915i
$244$		0			0
$245$	0.707107	−	1.22474i	0.0451754	−	0.0782461i
$246$		0			0
$247$	−6.67767	+	3.85536i	−0.424890	+	0.245310i
$248$		0			0
$249$	3.27526	−	2.98735i	0.207561	−	0.189315i
$250$		0			0
$251$		−	24.2599i		−	1.53127i	−0.643273	−	0.765637i	$-0.722424\pi$
$251$		−	24.2599i		−	1.53127i	0.643273	−	0.765637i	$-0.277576\pi$
$252$		0			0
$253$			3.00000i			0.188608i
$254$		0			0
$255$	−0.500258	−	2.28141i	−0.0313274	−	0.142868i
$256$		0			0
$257$	−2.84847	+	1.64456i	−0.177683	+	0.102585i	−0.586203	−	0.810164i	$-0.699378\pi$
$257$	−2.84847	+	1.64456i	−0.177683	+	0.102585i	0.408521	+	0.912749i	$0.366045\pi$
$258$		0			0
$259$	12.4325	−	21.5338i	0.772521	−	1.33804i
$260$		0			0
$261$	21.8649	−	10.0732i	1.35341	−	0.623516i
$262$		0			0
$263$	−1.61320	+	2.79415i	−0.0994744	+	0.172295i	−0.911467	−	0.411373i	$-0.865049\pi$
$263$	−1.61320	+	2.79415i	−0.0994744	+	0.172295i	0.811993	+	0.583667i	$0.198383\pi$
$264$		0			0
$265$	0.876276	+	1.51775i	0.0538292	+	0.0932349i
$266$		0			0
$267$	−24.1576	−	7.67819i	−1.47842	−	0.469898i
$268$		0			0
$269$	17.4634			1.06476			0.532380	−	0.846505i	$-0.321298\pi$
$269$	17.4634			1.06476			0.532380	+	0.846505i	$0.321298\pi$
$270$		0			0
$271$			4.19718i			0.254961i	0.991841	+	0.127480i	$0.0406890\pi$
$271$			4.19718i			0.254961i	−0.991841	+	0.127480i	$0.959311\pi$
$272$		0			0
$273$	5.32577	−	16.7563i	0.322330	−	1.01414i
$274$		0			0
$275$	−3.14789	+	1.81743i	−0.189825	+	0.109595i
$276$		0			0
$277$	−16.4938	−	9.52270i	−0.991017	−	0.572164i	−0.0854387	−	0.996343i	$-0.527229\pi$
$277$	−16.4938	−	9.52270i	−0.991017	−	0.572164i	−0.905578	+	0.424180i	$0.860563\pi$
$278$		0			0
$279$	14.6519	+	1.35003i	0.877186	+	0.0808242i
$280$		0			0
$281$	22.8712	+	13.2047i	1.36438	+	0.787725i	0.990203	−	0.139633i	$-0.0445921\pi$
$281$	22.8712	+	13.2047i	1.36438	+	0.787725i	0.374176	+	0.927358i	$0.377925\pi$
$282$		0			0
$283$	11.7900	+	20.4208i	0.700842	+	1.21389i	0.968171	+	0.250288i	$0.0805254\pi$
$283$	11.7900	+	20.4208i	0.700842	+	1.21389i	−0.267330	+	0.963605i	$0.586141\pi$
$284$		0			0
$285$	−1.38211	+	0.303062i	−0.0818689	+	0.0179518i
$286$		0			0
$287$	3.22641			0.190449
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$	13.1281	+	14.3933i	0.769583	+	0.843753i
$292$		0			0
$293$	−3.30518	−	5.72474i	−0.193091	−	0.334443i	0.753182	−	0.657812i	$-0.228518\pi$
$293$	−3.30518	−	5.72474i	−0.193091	−	0.334443i	−0.946273	+	0.323369i	$0.895185\pi$
$294$		0			0
$295$	−1.11295	−	0.642559i	−0.0647982	−	0.0374113i
$296$		0			0
$297$	3.82577	−	0.476756i	0.221993	−	0.0276642i
$298$		0			0
$299$	10.5049	+	6.06499i	0.607512	+	0.350747i
$300$		0			0
$301$	20.5222	−	11.8485i	1.18288	−	0.682934i
$302$		0			0
$303$	−0.370982	−	0.406736i	−0.0213124	−	0.0233664i
$304$		0			0
$305$			2.86054i			0.163794i
$306$		0			0
$307$	−17.7320			−1.01202			−0.506010	−	0.862528i	$-0.668880\pi$
$307$	−17.7320			−1.01202			−0.506010	+	0.862528i	$0.668880\pi$
$308$		0			0
$309$	5.67291	+	25.8712i	0.322720	+	1.47176i
$310$		0			0
$311$	5.65653	+	9.79739i	0.320752	+	0.555559i	0.980643	−	0.195802i	$-0.0627310\pi$
$311$	5.65653	+	9.79739i	0.320752	+	0.555559i	−0.659891	+	0.751361i	$0.729398\pi$
$312$		0			0
$313$	4.05051	−	7.01569i	0.228948	−	0.396550i	−0.728548	−	0.684994i	$-0.759805\pi$
$313$	4.05051	−	7.01569i	0.228948	−	0.396550i	0.957497	+	0.288444i	$0.0931380\pi$
$314$		0			0
$315$	1.86277	−	2.63435i	0.104955	−	0.148429i
$316$		0			0
$317$	1.96240	−	3.39898i	0.110219	−	0.190906i	−0.805639	−	0.592406i	$-0.798178\pi$
$317$	1.96240	−	3.39898i	0.110219	−	0.190906i	0.915859	+	0.401501i	$0.131511\pi$
$318$		0			0
$319$	5.15627	−	2.97697i	0.288696	−	0.166679i
$320$		0			0
$321$	−14.4495	−	4.59259i	−0.806492	−	0.256333i
$322$		0			0
$323$			10.9046i			0.606748i
$324$		0			0
$325$			14.6969i			0.815239i
$326$		0			0
$327$	22.0341	+	7.00324i	1.21849	+	0.387280i
$328$		0			0
$329$	−30.2196	+	17.4473i	−1.66606	+	0.961902i
$330$		0			0
$331$	−9.50857	+	16.4693i	−0.522638	+	0.905236i	0.477015	+	0.878895i	$0.341719\pi$
$331$	−9.50857	+	16.4693i	−0.522638	+	0.905236i	−0.999653	+	0.0263407i	$0.991615\pi$
$332$		0			0
$333$	12.7279	−	18.0000i	0.697486	−	0.986394i
$334$		0			0
$335$	−2.02166	+	3.50162i	−0.110455	+	0.191314i
$336$		0			0
$337$	0.848469	+	1.46959i	0.0462191	+	0.0800538i	0.888209	−	0.459439i	$-0.151949\pi$
$337$	0.848469	+	1.46959i	0.0462191	+	0.0800538i	−0.841990	+	0.539493i	$0.818616\pi$
$338$		0			0
$339$	−1.92768	−	8.79114i	−0.104697	−	0.477469i
$340$		0			0
$341$	3.63907			0.197067
$342$		0			0
$343$			8.63019i			0.465986i
$344$		0			0
$345$	1.50000	+	1.64456i	0.0807573	+	0.0885404i
$346$		0			0
$347$	−14.6490	+	8.45763i	−0.786402	+	0.454029i	−0.838694	−	0.544602i	$-0.816681\pi$
$347$	−14.6490	+	8.45763i	−0.786402	+	0.454029i	0.0522924	+	0.998632i	$0.483347\pi$
$348$		0			0
$349$	−14.1582	−	8.17423i	−0.757871	−	0.437557i	0.0706601	−	0.997500i	$-0.477489\pi$
$349$	−14.1582	−	8.17423i	−0.757871	−	0.437557i	−0.828531	+	0.559944i	$0.810823\pi$
$350$		0			0
$351$	6.06499	−	14.3602i	0.323725	−	0.766492i
$352$		0			0
$353$	−17.1742	−	9.91555i	−0.914092	−	0.527751i	−0.0323467	−	0.999477i	$-0.510298\pi$
$353$	−17.1742	−	9.91555i	−0.914092	−	0.527751i	−0.881746	+	0.471725i	$0.843631\pi$
$354$		0			0
$355$	−2.15159	−	3.72666i	−0.114195	−	0.197791i
$356$		0			0
$357$	−16.7563	−	18.3712i	−0.886836	−	0.972306i
$358$		0			0
$359$	8.08665			0.426797			0.213398	−	0.976965i	$-0.431547\pi$
$359$	8.08665			0.426797			0.213398	+	0.976965i	$0.431547\pi$
$360$		0			0
$361$	−12.3939			−0.652309
$362$		0			0
$363$	−17.6790	+	3.87657i	−0.927908	+	0.203467i
$364$		0			0
$365$	1.02494	+	1.77526i	0.0536480	+	0.0929211i
$366$		0			0
$367$	11.9257	+	6.88533i	0.622519	+	0.359411i	0.777849	−	0.628451i	$-0.216311\pi$
$367$	11.9257	+	6.88533i	0.622519	+	0.359411i	−0.155330	+	0.987863i	$0.549644\pi$
$368$		0			0
$369$	2.84847	+	0.262459i	0.148285	+	0.0136631i
$370$		0			0
$371$	16.1581	+	9.32887i	0.838886	+	0.484331i
$372$		0			0
$373$	25.7183	−	14.8485i	1.33164	−	0.768825i	0.346092	−	0.938201i	$-0.387509\pi$
$373$	25.7183	−	14.8485i	1.33164	−	0.768825i	0.985551	+	0.169376i	$0.0541752\pi$
$374$		0			0
$375$	−1.65068	+	5.19348i	−0.0852408	+	0.268190i
$376$		0			0
$377$		−	24.0737i		−	1.23986i
$378$		0			0
$379$	8.28836			0.425745			0.212872	−	0.977080i	$-0.431718\pi$
$379$	8.28836			0.425745			0.212872	+	0.977080i	$0.431718\pi$
$380$		0			0
$381$	−2.68556	−	0.853572i	−0.137586	−	0.0437298i
$382$		0			0
$383$	5.15627	+	8.93092i	0.263473	+	0.456349i	0.967162	−	0.254159i	$-0.0817987\pi$
$383$	5.15627	+	8.93092i	0.263473	+	0.456349i	−0.703689	+	0.710508i	$0.748465\pi$
$384$		0			0
$385$	0.398979	−	0.691053i	0.0203339	−	0.0352193i
$386$		0			0
$387$	19.0820	−	8.79114i	0.969995	−	0.446879i
$388$		0			0
$389$	−1.11243	+	1.92679i	−0.0564025	+	0.0976919i	−0.892848	−	0.450358i	$-0.851296\pi$
$389$	−1.11243	+	1.92679i	−0.0564025	+	0.0976919i	0.836446	+	0.548050i	$0.184630\pi$
$390$		0			0
$391$	14.8561	−	8.57719i	0.751306	−	0.433767i
$392$		0			0
$393$	6.94949	+	31.6930i	0.350555	+	1.59870i
$394$		0			0
$395$			3.04281i			0.153100i
$396$		0			0
$397$			16.0454i			0.805296i	0.915355	+	0.402648i	$0.131910\pi$
$397$			16.0454i			0.805296i	−0.915355	+	0.402648i	$0.868090\pi$
$398$		0			0
$399$	−11.1295	+	10.1511i	−0.557170	+	0.508192i
$400$		0			0
$401$	33.5227	−	19.3543i	1.67404	−	0.966510i	0.708707	−	0.705503i	$-0.249279\pi$
$401$	33.5227	−	19.3543i	1.67404	−	0.966510i	0.965337	−	0.261007i	$-0.0840545\pi$
$402$		0			0
$403$	7.35698	−	12.7427i	0.366477	−	0.634757i
$404$		0			0
$405$	1.85886	−	2.17423i	0.0923676	−	0.108039i
$406$		0			0
$407$	2.72615	−	4.72183i	0.135130	−	0.234052i
$408$		0			0
$409$	6.29796	+	10.9084i	0.311414	+	0.539385i	0.978669	−	0.205445i	$-0.0658641\pi$
$409$	6.29796	+	10.9084i	0.311414	+	0.539385i	−0.667255	+	0.744830i	$0.732531\pi$
$410$		0			0
$411$	−9.63839	+	8.79114i	−0.475427	+	0.433635i
$412$		0			0
$413$	−13.6814			−0.673219
$414$		0			0
$415$		−	0.813472i		−	0.0399317i
$416$		0			0
$417$	22.5000	−	4.93369i	1.10183	−	0.241604i
$418$		0			0
$419$	−8.22345	+	4.74781i	−0.401742	+	0.231946i	−0.687235	−	0.726435i	$-0.741176\pi$
$419$	−8.22345	+	4.74781i	−0.401742	+	0.231946i	0.285493	+	0.958381i	$0.407843\pi$
$420$		0			0
$421$	−10.1298	−	5.84847i	−0.493698	−	0.285037i	0.232409	−	0.972618i	$-0.425339\pi$
$421$	−10.1298	−	5.84847i	−0.493698	−	0.285037i	−0.726108	+	0.687581i	$0.758673\pi$
$422$		0			0
$423$	−28.0990	+	12.9453i	−1.36622	+	0.629421i
$424$		0			0
$425$	18.0000	+	10.3923i	0.873128	+	0.504101i
$426$		0			0
$427$	15.2267	+	26.3734i	0.736871	+	1.27630i
$428$		0			0
$429$	1.16781	−	3.67423i	0.0563823	−	0.177394i
$430$		0			0
$431$	8.08665			0.389520			0.194760	−	0.980851i	$-0.437607\pi$
$431$	8.08665			0.389520			0.194760	+	0.980851i	$0.437607\pi$
$432$		0			0
$433$	−17.5505			−0.843424			−0.421712	−	0.906730i	$-0.638571\pi$
$433$	−17.5505			−0.843424			−0.421712	+	0.906730i	$0.638571\pi$
$434$		0			0
$435$	1.33812	−	4.21008i	0.0641579	−	0.201858i
$436$		0			0
$437$	−5.19615	−	9.00000i	−0.248566	−	0.430528i
$438$		0			0
$439$	15.5606	+	8.98392i	0.742667	+	0.428779i	0.823038	−	0.567986i	$-0.192277\pi$
$439$	15.5606	+	8.98392i	0.742667	+	0.428779i	−0.0803710	+	0.996765i	$0.525611\pi$
$440$		0			0
$441$	1.22474	−	13.2922i	0.0583212	−	0.632960i
$442$		0			0
$443$	−31.5146	−	18.1950i	−1.49730	−	0.864469i	−0.497308	−	0.867574i	$-0.665678\pi$
$443$	−31.5146	−	18.1950i	−1.49730	−	0.864469i	−0.999995	+	0.00310536i	$0.999012\pi$
$444$		0			0
$445$	−4.02834	+	2.32577i	−0.190962	+	0.110252i
$446$		0			0
$447$	9.86660	−	2.16350i	0.466674	−	0.102330i
$448$		0			0
$449$		−	10.8209i		−	0.510670i	−0.966853	−	0.255335i	$-0.917814\pi$
$449$		−	10.8209i		−	0.510670i	0.966853	−	0.255335i	$-0.0821857\pi$
$450$		0			0
$451$	0.707471			0.0333135
$452$		0			0
$453$	−20.9114	+	19.0732i	−0.982504	+	0.896138i
$454$		0			0
$455$	−1.61320	−	2.79415i	−0.0756281	−	0.130992i
$456$		0			0
$457$	−18.0732	+	31.3037i	−0.845429	+	1.46433i	0.0398186	+	0.999207i	$0.487322\pi$
$457$	−18.0732	+	31.3037i	−0.845429	+	1.46433i	−0.885248	+	0.465120i	$0.846011\pi$
$458$		0			0
$459$	−13.2990	−	17.5823i	−0.620745	−	0.820670i
$460$		0			0
$461$	−10.4477	+	18.0959i	−0.486597	+	0.842811i	−0.999881	−	0.0154078i	$-0.995095\pi$
$461$	−10.4477	+	18.0959i	−0.486597	+	0.842811i	0.513284	+	0.858219i	$0.328429\pi$
$462$		0			0
$463$	8.69934	−	5.02256i	0.404292	−	0.233418i	−0.284042	−	0.958812i	$-0.591676\pi$
$463$	8.69934	−	5.02256i	0.404292	−	0.233418i	0.688334	+	0.725393i	$0.258342\pi$
$464$		0			0
$465$	1.99490	−	1.81954i	0.0925112	−	0.0843790i
$466$		0			0
$467$		−	15.5063i		−	0.717545i	−0.933425	−	0.358773i	$-0.883195\pi$
$467$		−	15.5063i		−	0.717545i	0.933425	−	0.358773i	$-0.116805\pi$
$468$		0			0
$469$			43.0454i			1.98765i
$470$		0			0
$471$	−8.29088	−	37.8104i	−0.382023	−	1.74221i
$472$		0			0
$473$	4.50000	−	2.59808i	0.206910	−	0.119460i
$474$		0			0
$475$	6.29577	−	10.9046i	0.288870	−	0.500337i
$476$		0			0
$477$	13.5065	+	9.55051i	0.618418	+	0.437288i
$478$		0			0
$479$	−15.9691	+	27.6592i	−0.729645	+	1.26378i	0.227388	+	0.973804i	$0.426981\pi$
$479$	−15.9691	+	27.6592i	−0.729645	+	1.26378i	−0.957033	+	0.289978i	$0.906352\pi$
$480$		0			0
$481$	−11.0227	−	19.0919i	−0.502592	−	0.870515i
$482$		0			0
$483$	22.5837	+	7.17793i	1.02759	+	0.326607i
$484$		0			0
$485$	3.57486			0.162326
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$	−6.00000	+	18.8776i	−0.271329	+	0.853674i
$490$		0			0
$491$	32.0922	−	18.5285i	1.44830	−	0.836178i	0.449922	−	0.893068i	$-0.351452\pi$
$491$	32.0922	−	18.5285i	1.44830	−	0.836178i	0.998380	+	0.0568900i	$0.0181184\pi$
$492$		0			0
$493$	−29.4842	−	17.0227i	−1.32790	−	0.766664i
$494$		0			0
$495$	0.408459	−	0.577648i	0.0183589	−	0.0259633i
$496$		0			0
$497$	−39.6742	−	22.9059i	−1.77963	−	1.02747i
$498$		0			0
$499$	−6.07186	−	10.5168i	−0.271814	−	0.470795i	0.697513	−	0.716573i	$-0.254290\pi$
$499$	−6.07186	−	10.5168i	−0.271814	−	0.470795i	−0.969326	+	0.245777i	$0.920957\pi$
$500$		0			0
$501$	−31.1288	+	6.82577i	−1.39073	+	0.304953i
$502$		0			0
$503$	−33.3471			−1.48687			−0.743437	−	0.668806i	$-0.766806\pi$
$503$	−33.3471			−1.48687			−0.743437	+	0.668806i	$0.766806\pi$
$504$		0			0
$505$	−0.101021			−0.00449535
$506$		0			0
$507$	4.66883	+	5.11879i	0.207350	+	0.227334i
$508$		0			0
$509$	19.8865	+	34.4444i	0.881453	+	1.52672i	0.849726	+	0.527224i	$0.176767\pi$
$509$	19.8865	+	34.4444i	0.881453	+	1.52672i	0.0317262	+	0.999497i	$0.489900\pi$
$510$		0			0
$511$	18.8994	+	10.9116i	0.836062	+	0.482701i
$512$		0			0
$513$	−10.6515	+	8.05669i	−0.470277	+	0.355711i
$514$		0			0
$515$	4.20909	+	2.43012i	0.185475	+	0.107084i
$516$		0			0
$517$	−6.62642	+	3.82577i	−0.291430	+	0.168257i
$518$		0			0
$519$	−22.4050	−	24.5643i	−0.983472	−	1.07826i
$520$		0			0
$521$			1.90702i			0.0835482i	0.999127	+	0.0417741i	$0.0133010\pi$
$521$			1.90702i			0.0835482i	−0.999127	+	0.0417741i	$0.986699\pi$
$522$		0			0
$523$	−13.4288			−0.587202			−0.293601	−	0.955928i	$-0.594854\pi$
$523$	−13.4288			−0.587202			−0.293601	+	0.955928i	$0.594854\pi$
$524$		0			0
$525$	6.14966	+	28.0454i	0.268393	+	1.22400i
$526$		0			0
$527$	−10.4043	−	18.0208i	−0.453220	−	0.785000i
$528$		0			0
$529$	3.32577	−	5.76039i	0.144598	−	0.250452i
$530$		0			0
$531$	−12.0788	−	1.11295i	−0.524176	−	0.0482977i
$532$		0			0
$533$	1.43027	−	2.47730i	0.0619518	−	0.107304i
$534$		0			0
$535$	−2.40949	+	1.39112i	−0.104171	+	0.0601433i
$536$		0			0
$537$	37.5959	+	11.9494i	1.62238	+	0.515654i
$538$		0			0
$539$		−	3.30136i		−	0.142200i
$540$		0			0
$541$			20.6969i			0.889831i	0.895573	+	0.444915i	$0.146766\pi$
$541$			20.6969i			0.889831i	−0.895573	+	0.444915i	$0.853234\pi$
$542$		0			0
$543$	−7.67819	−	2.44041i	−0.329503	−	0.104728i
$544$		0			0
$545$	3.67423	−	2.12132i	0.157387	−	0.0908674i
$546$		0			0
$547$	3.79045	−	6.56524i	0.162068	−	0.280710i	−0.773542	−	0.633745i	$-0.781517\pi$
$547$	3.79045	−	6.56524i	0.162068	−	0.280710i	0.935610	+	0.353035i	$0.114850\pi$
$548$		0			0
$549$	11.2977	+	24.5227i	0.482172	+	1.04660i
$550$		0			0
$551$	−10.3125	+	17.8618i	−0.439329	+	0.760940i
$552$		0			0
$553$	16.1969	+	28.0539i	0.688764	+	1.19297i
$554$		0			0
$555$	−0.866472	−	3.95153i	−0.0367797	−	0.167733i
$556$		0			0
$557$	−34.7839			−1.47384			−0.736920	−	0.675980i	$-0.763721\pi$
$557$	−34.7839			−1.47384			−0.736920	+	0.675980i	$0.763721\pi$
$558$		0			0
$559$		−	21.0097i		−	0.888617i
$560$		0			0
$561$	−3.67423	−	4.02834i	−0.155126	−	0.170077i
$562$		0			0
$563$	−17.9268	+	10.3500i	−0.755523	+	0.436201i	−0.827686	−	0.561192i	$-0.810343\pi$
$563$	−17.9268	+	10.3500i	−0.755523	+	0.436201i	0.0721633	+	0.997393i	$0.477010\pi$
$564$		0			0
$565$	−1.43027	−	0.825765i	−0.0601718	−	0.0347402i
$566$		0			0
$567$	5.56473	−	29.9406i	0.233697	−	1.25739i
$568$		0			0
$569$	13.5000	+	7.79423i	0.565949	+	0.326751i	0.755530	−	0.655114i	$-0.227379\pi$
$569$	13.5000	+	7.79423i	0.565949	+	0.326751i	−0.189580	+	0.981865i	$0.560713\pi$
$570$		0			0
$571$	−14.6490	−	25.3729i	−0.613043	−	1.06182i	−0.990724	−	0.135887i	$-0.956612\pi$
$571$	−14.6490	−	25.3729i	−0.613043	−	1.06182i	0.377681	−	0.925936i	$-0.376722\pi$
$572$		0			0
$573$	−29.9609	−	32.8485i	−1.25164	−	1.37226i
$574$		0			0
$575$	−19.8082			−0.826057
$576$		0			0
$577$	−5.34847			−0.222660			−0.111330	−	0.993784i	$-0.535511\pi$
$577$	−5.34847			−0.222660			−0.111330	+	0.993784i	$0.535511\pi$
$578$		0			0
$579$	4.31509	−	0.946193i	0.179329	−	0.0393224i
$580$		0			0
$581$	−4.33013	−	7.50000i	−0.179644	−	0.311152i
$582$		0			0
$583$	3.54307	+	2.04559i	0.146739	+	0.0847197i
$584$		0			0
$585$	−1.19694	−	2.59808i	−0.0494873	−	0.107417i
$586$		0			0
$587$	39.8030	+	22.9802i	1.64284	+	0.948496i	0.979816	+	0.199901i	$0.0640622\pi$
$587$	39.8030	+	22.9802i	1.64284	+	0.948496i	0.663028	+	0.748595i	$0.269271\pi$
$588$		0			0
$589$	−10.9172	+	6.30306i	−0.449836	+	0.259713i
$590$		0			0
$591$	5.78580	−	18.2037i	0.237996	−	0.748799i
$592$		0			0
$593$			16.5420i			0.679297i	0.940552	+	0.339649i	$0.110308\pi$
$593$			16.5420i			0.679297i	−0.940552	+	0.339649i	$0.889692\pi$
$594$		0			0
$595$	−4.56283			−0.187058
$596$		0			0
$597$	−8.66025	−	2.75255i	−0.354441	−	0.112654i
$598$		0			0
$599$	19.5121	+	33.7960i	0.797244	+	1.38087i	0.921404	+	0.388605i	$0.127043\pi$
$599$	19.5121	+	33.7960i	0.797244	+	1.38087i	−0.124160	+	0.992262i	$0.539624\pi$
$600$		0			0
$601$	11.6237	−	20.1329i	0.474142	−	0.821237i	−0.525420	−	0.850843i	$-0.676092\pi$
$601$	11.6237	−	20.1329i	0.474142	−	0.821237i	0.999562	+	0.0296056i	$0.00942514\pi$
$602$		0			0
$603$	−3.50162	+	38.0031i	−0.142597	+	1.54761i
$604$		0			0
$605$	−1.66062	+	2.87628i	−0.0675137	+	0.116937i
$606$		0			0
$607$	3.33884	−	1.92768i	0.135519	−	0.0782421i	−0.430708	−	0.902492i	$-0.641736\pi$
$607$	3.33884	−	1.92768i	0.135519	−	0.0782421i	0.566227	+	0.824249i	$0.308403\pi$
$608$		0			0
$609$	−10.0732	−	45.9387i	−0.408187	−	1.86153i
$610$		0			0
$611$			30.9376i			1.25160i
$612$		0			0
$613$			4.04541i			0.163392i	0.996657	+	0.0816962i	$0.0260337\pi$
$613$			4.04541i			0.163392i	−0.996657	+	0.0816962i	$0.973966\pi$
$614$		0			0
$615$	0.387827	−	0.353736i	0.0156387	−	0.0142640i
$616$		0			0
$617$	−22.8712	+	13.2047i	−0.920759	+	0.531600i	−0.883877	−	0.467719i	$-0.845076\pi$
$617$	−22.8712	+	13.2047i	−0.920759	+	0.531600i	−0.0368817	+	0.999320i	$0.511742\pi$
$618$		0			0
$619$	−19.0820	+	33.0511i	−0.766972	+	1.32844i	0.172225	+	0.985058i	$0.444904\pi$
$619$	−19.0820	+	33.0511i	−0.766972	+	1.32844i	−0.939197	+	0.343377i	$0.888429\pi$
$620$		0			0
$621$	19.3543	+	8.17423i	0.776663	+	0.328021i
$622$		0			0
$623$	−24.7602	+	42.8859i	−0.991997	+	1.71819i
$624$		0			0
$625$	−11.7474	−	20.3472i	−0.469898	−	0.813887i
$626$		0			0
$627$	−2.44041	+	2.22589i	−0.0974608	+	0.0888935i
$628$		0			0
$629$	−31.1769			−1.24310
$630$		0			0
$631$		−	9.33766i		−	0.371726i	−0.982576	−	0.185863i	$-0.940492\pi$
$631$		−	9.33766i		−	0.371726i	0.982576	−	0.185863i	$-0.0595081\pi$
$632$		0			0
$633$	−17.1742	+	3.76588i	−0.682615	+	0.149680i
$634$		0			0
$635$	−0.447824	+	0.258552i	−0.0177714	+	0.0102603i
$636$		0			0
$637$	−11.5601	−	6.67423i	−0.458028	−	0.264443i
$638$		0			0
$639$	−33.1635	−	23.4501i	−1.31193	−	0.927673i
$640$		0			0
$641$	10.1969	+	5.88721i	0.402755	+	0.232531i	0.687672	−	0.726022i	$-0.258633\pi$
$641$	10.1969	+	5.88721i	0.402755	+	0.232531i	−0.284917	+	0.958552i	$0.591966\pi$
$642$		0			0
$643$	−6.36068	−	11.0170i	−0.250841	−	0.434469i	0.712917	−	0.701249i	$-0.247374\pi$
$643$	−6.36068	−	11.0170i	−0.250841	−	0.434469i	−0.963758	+	0.266780i	$0.914040\pi$
$644$		0			0
$645$	1.16781	−	3.67423i	0.0459824	−	0.144673i
$646$		0			0
$647$	−20.6251			−0.810856			−0.405428	−	0.914127i	$-0.632877\pi$
$647$	−20.6251			−0.810856			−0.405428	+	0.914127i	$0.632877\pi$
$648$		0			0
$649$	−3.00000			−0.117760
$650$		0			0
$651$	8.70701	−	27.3946i	0.341255	−	1.07368i
$652$		0			0
$653$	−3.13021	−	5.42168i	−0.122495	−	0.212167i	0.798256	−	0.602318i	$-0.205756\pi$
$653$	−3.13021	−	5.42168i	−0.122495	−	0.212167i	−0.920751	+	0.390151i	$0.872423\pi$
$654$		0			0
$655$	5.15627	+	2.97697i	0.201472	+	0.116320i
$656$		0			0
$657$	15.7980	+	11.1708i	0.616337	+	0.435816i
$658$		0			0
$659$	−24.8002	−	14.3184i	−0.966078	−	0.557765i	−0.0680394	−	0.997683i	$-0.521674\pi$
$659$	−24.8002	−	14.3184i	−0.966078	−	0.557765i	−0.898038	+	0.439917i	$0.855008\pi$
$660$		0			0
$661$	−3.76588	+	2.17423i	−0.146476	+	0.0845679i	−0.571447	−	0.820639i	$-0.693618\pi$
$661$	−3.76588	+	2.17423i	−0.146476	+	0.0845679i	0.424971	+	0.905207i	$0.360284\pi$
$662$		0			0
$663$	−21.5338	+	4.72183i	−0.836303	+	0.183381i
$664$		0			0
$665$			2.76421i			0.107192i
$666$		0			0
$667$	32.4460			1.25631
$668$		0			0
$669$	−24.3362	+	22.1969i	−0.940892	+	0.858183i
$670$		0			0
$671$	3.33884	+	5.78304i	0.128894	+	0.223252i
$672$		0			0
$673$	2.62372	−	4.54442i	0.101137	−	0.175175i	−0.811016	−	0.585024i	$-0.801085\pi$
$673$	2.62372	−	4.54442i	0.101137	−	0.175175i	0.912153	+	0.409849i	$0.134419\pi$
$674$		0			0
$675$	3.14789	+	25.2605i	0.121162	+	0.972276i
$676$		0			0
$677$	−10.3763	+	17.9722i	−0.398792	+	0.690728i	−0.993577	−	0.113157i	$-0.963904\pi$
$677$	−10.3763	+	17.9722i	−0.398792	+	0.690728i	0.594785	+	0.803885i	$0.297237\pi$
$678$		0			0
$679$	32.9593	−	19.0290i	1.26486	−	0.730268i
$680$		0			0
$681$	−18.8939	+	17.2330i	−0.724015	+	0.660371i
$682$		0			0
$683$		−	18.9912i		−	0.726680i	−0.931657	−	0.363340i	$-0.881636\pi$
$683$		−	18.9912i		−	0.726680i	0.931657	−	0.363340i	$-0.118364\pi$
$684$		0			0
$685$			2.39388i			0.0914653i
$686$		0			0
$687$	−7.06550	−	32.2221i	−0.269566	−	1.22935i
$688$		0			0
$689$	14.3258	−	8.27098i	0.545768	−	0.315099i
$690$		0			0
$691$	−23.2262	+	40.2290i	−0.883567	+	1.53038i	−0.0362206	+	0.999344i	$0.511532\pi$
$691$	−23.2262	+	40.2290i	−0.883567	+	1.53038i	−0.847347	+	0.531040i	$0.821801\pi$
$692$		0			0
$693$	0.691053	−	7.50000i	0.0262509	−	0.284901i
$694$		0			0
$695$	2.11346	−	3.66062i	0.0801681	−	0.138855i
$696$		0			0
$697$	−2.02270	−	3.50343i	−0.0766154	−	0.132702i
$698$		0			0
$699$	14.0065	+	4.45178i	0.529774	+	0.168382i
$700$		0			0
$701$	32.8769			1.24174			0.620871	−	0.783913i	$-0.286779\pi$
$701$	32.8769			1.24174			0.620871	+	0.783913i	$0.286779\pi$
$702$		0			0
$703$			18.8873i			0.712349i
$704$		0			0
$705$	−1.71964	+	5.41045i	−0.0647655	+	0.203769i
$706$		0			0
$707$	−0.931383	+	0.537734i	−0.0350283	+	0.0202236i
$708$		0			0
$709$	3.76588	+	2.17423i	0.141431	+	0.0816551i	0.569046	−	0.822306i	$-0.307313\pi$
$709$	3.76588	+	2.17423i	0.141431	+	0.0816551i	−0.427615	+	0.903961i	$0.640646\pi$
$710$		0			0
$711$	12.0175	+	26.0853i	0.450693	+	0.978275i
$712$		0			0
$713$	17.1742	+	9.91555i	0.643180	+	0.371340i
$714$		0			0
$715$	−0.353736	−	0.612688i	−0.0132290	−	0.0229132i
$716$		0			0
$717$	−6.84072	+	1.50000i	−0.255471	+	0.0560185i
$718$		0			0
$719$	8.90357			0.332047			0.166023	−	0.986122i	$-0.446907\pi$
$719$	8.90357			0.332047			0.166023	+	0.986122i	$0.446907\pi$
$720$		0			0
$721$	51.7423			1.92699
$722$		0			0
$723$	−18.3216	−	20.0873i	−0.681387	−	0.747056i
$724$		0			0
$725$	19.6561	+	34.0454i	0.730010	+	1.26441i
$726$		0			0
$727$	23.0552	+	13.3109i	0.855070	+	0.493675i	0.862358	−	0.506299i	$-0.168987\pi$
$727$	23.0552	+	13.3109i	0.855070	+	0.493675i	−0.00728826	+	0.999973i	$0.502320\pi$
$728$		0			0
$729$	7.34847	−	25.9808i	0.272166	−	0.962250i
$730$		0			0
$731$	−25.7316	−	14.8561i	−0.951716	−	0.549473i
$732$		0			0
$733$	12.9904	−	7.50000i	0.479811	−	0.277019i	−0.240527	−	0.970642i	$-0.577320\pi$
$733$	12.9904	−	7.50000i	0.479811	−	0.277019i	0.720338	+	0.693624i	$0.243987\pi$
$734$		0			0
$735$	−1.65068	−	1.80977i	−0.0608863	−	0.0667542i
$736$		0			0
$737$			9.43879i			0.347682i
$738$		0			0
$739$	31.1609			1.14627			0.573135	−	0.819461i	$-0.305727\pi$
$739$	31.1609			1.14627			0.573135	+	0.819461i	$0.305727\pi$
$740$		0			0
$741$	2.86054	+	13.0454i	0.105084	+	0.479235i
$742$		0			0
$743$	9.60805	+	16.6416i	0.352485	+	0.610522i	0.986684	−	0.162647i	$-0.0520033\pi$
$743$	9.60805	+	16.6416i	0.352485	+	0.610522i	−0.634199	+	0.773170i	$0.718670\pi$
$744$		0			0
$745$	0.926786	−	1.60524i	0.0339548	−	0.0588115i
$746$		0			0
$747$	−3.21280	−	6.97370i	−0.117550	−	0.255154i
$748$		0			0
$749$	−14.8099	+	25.6515i	−0.541143	+	0.937287i
$750$		0			0
$751$	42.5467	−	24.5643i	1.55255	−	0.896366i	0.554618	−	0.832105i	$-0.312864\pi$
$751$	42.5467	−	24.5643i	1.55255	−	0.896366i	0.997933	−	0.0642608i	$-0.0204689\pi$
$752$		0			0
$753$	−40.0454	−	12.7279i	−1.45934	−	0.463831i
$754$		0			0
$755$			5.19375i			0.189020i
$756$		0			0
$757$			12.0000i			0.436147i	0.975932	+	0.218074i	$0.0699773\pi$
$757$			12.0000i			0.436147i	−0.975932	+	0.218074i	$0.930023\pi$
$758$		0			0
$759$	4.95204	+	1.57394i	0.179748	+	0.0571305i
$760$		0			0
$761$	−20.4773	+	11.8226i	−0.742301	+	0.428568i	−0.822905	−	0.568178i	$-0.807648\pi$
$761$	−20.4773	+	11.8226i	−0.742301	+	0.428568i	0.0806041	+	0.996746i	$0.474315\pi$
$762$		0			0
$763$	22.5837	−	39.1161i	0.817584	−	1.41610i
$764$		0			0
$765$	−4.02834	−	0.371173i	−0.145645	−	0.0134198i
$766$		0			0
$767$	−6.06499	+	10.5049i	−0.218994	+	0.379309i
$768$		0			0
$769$	6.29796	+	10.9084i	0.227110	+	0.393366i	0.956950	−	0.290251i	$-0.0937389\pi$
$769$	6.29796	+	10.9084i	0.227110	+	0.393366i	−0.729840	+	0.683618i	$0.760406\pi$
$770$		0			0
$771$	1.22021	+	5.56473i	0.0439447	+	0.200409i
$772$		0			0
$773$	−22.1346			−0.796126			−0.398063	−	0.917358i	$-0.630318\pi$
$773$	−22.1346			−0.796126			−0.398063	+	0.917358i	$0.630318\pi$
$774$		0			0
$775$			24.0278i			0.863104i
$776$		0			0
$777$	−29.0227	−	31.8198i	−1.04118	−	1.14153i
$778$		0			0
$779$	−2.12241	+	1.22538i	−0.0760434	+	0.0439037i
$780$		0			0
$781$	−8.69958	−	5.02270i	−0.311295	−	0.179726i
$782$		0			0
$783$	−5.15627	−	41.3769i	−0.184270	−	1.47869i
$784$		0			0
$785$	−6.15153	−	3.55159i	−0.219558	−	0.126762i
$786$		0			0
$787$	−2.92397	−	5.06447i	−0.104228	−	0.180529i	0.809194	−	0.587541i	$-0.199904\pi$
$787$	−2.92397	−	5.06447i	−0.104228	−	0.180529i	−0.913423	+	0.407012i	$0.866571\pi$
$788$		0			0
$789$	3.76588	+	4.12883i	0.134069	+	0.146990i
$790$		0			0
$791$	−17.5823			−0.625154
$792$		0			0
$793$	27.0000			0.958798
$794$		0			0
$795$	2.96506	−	0.650165i	0.105160	−	0.0230590i
$796$		0			0
$797$	−22.7470	−	39.3990i	−0.805740	−	1.39558i	−0.915790	−	0.401657i	$-0.868434\pi$
$797$	−22.7470	−	39.3990i	−0.805740	−	1.39558i	0.110050	−	0.993926i	$-0.464899\pi$
$798$		0			0
$799$	37.8907	+	21.8762i	1.34048	+	0.773924i
$800$		0			0
$801$	−25.3485	+	35.8481i	−0.895644	+	1.26663i
$802$		0			0
$803$	4.14418	+	2.39264i	0.146245	+	0.0844346i
$804$		0			0
$805$	3.76588	−	2.17423i	0.132730	−	0.0766317i
$806$		0			0
$807$	9.16212	−	28.8264i	0.322522	−	1.01474i
$808$		0			0
$809$		−	6.14966i		−	0.216211i	−0.994139	−	0.108105i	$-0.965522\pi$
$809$		−	6.14966i		−	0.216211i	0.994139	−	0.108105i	$-0.0344784\pi$
$810$		0			0
$811$	19.1470			0.672341			0.336170	−	0.941801i	$-0.390868\pi$
$811$	19.1470			0.672341			0.336170	+	0.941801i	$0.390868\pi$
$812$		0			0
$813$	6.92820	+	2.20204i	0.242983	+	0.0772290i
$814$		0			0
$815$	1.81743	+	3.14789i	0.0636619	+	0.110266i
$816$		0			0
$817$	−9.00000	+	15.5885i	−0.314870	+	0.545371i
$818$		0			0
$819$	−24.8651	−	17.5823i	−0.868856	−	0.614374i
$820$		0			0
$821$	11.5441	−	19.9949i	0.402890	−	0.697827i	−0.591183	−	0.806537i	$-0.701339\pi$
$821$	11.5441	−	19.9949i	0.402890	−	0.697827i	0.994073	+	0.108711i	$0.0346722\pi$
$822$		0			0
$823$	31.7339	−	18.3216i	1.10617	−	0.638650i	0.168339	−	0.985729i	$-0.446160\pi$
$823$	31.7339	−	18.3216i	1.10617	−	0.638650i	0.937836	+	0.347079i	$0.112826\pi$
$824$		0			0
$825$	1.34847	+	6.14966i	0.0469477	+	0.214104i
$826$		0			0
$827$			27.0779i			0.941591i	0.882242	+	0.470795i	$0.156033\pi$
$827$			27.0779i			0.941591i	−0.882242	+	0.470795i	$0.843967\pi$
$828$		0			0
$829$			49.3485i			1.71394i	0.515364	+	0.856972i	$0.327657\pi$
$829$			49.3485i			1.71394i	−0.515364	+	0.856972i	$0.672343\pi$
$830$		0			0
$831$	−24.3724	+	22.2299i	−0.845468	+	0.771148i
$832$		0			0
$833$	−16.3485	+	9.43879i	−0.566441	+	0.327035i
$834$		0			0
$835$	−2.92397	+	5.06447i	−0.101188	+	0.175263i
$836$		0			0
$837$	9.91555	−	23.4773i	0.342732	−	0.811494i
$838$		0			0
$839$	−19.1037	+	33.0885i	−0.659532	+	1.14234i	0.321205	+	0.947010i	$0.395912\pi$
$839$	−19.1037	+	33.0885i	−0.659532	+	1.14234i	−0.980737	+	0.195333i	$0.937421\pi$
$840$		0			0
$841$	−17.6969	−	30.6520i	−0.610239	−	1.05697i
$842$		0			0
$843$	33.7960	−	30.8252i	1.16400	−	1.06168i
$844$		0			0
$845$	1.27135			0.0437357
$846$		0			0
$847$			35.3580i			1.21492i
$848$		0			0
$849$	39.8939	−	8.74774i	1.36915	−	0.300222i
$850$		0			0
$851$	25.7316	−	14.8561i	0.882066	−	0.509261i
$852$		0			0
$853$	−41.3068	−	23.8485i	−1.41432	−	0.816556i	−0.418525	−	0.908205i	$-0.637453\pi$
$853$	−41.3068	−	23.8485i	−1.41432	−	0.816556i	−0.995791	+	0.0916492i	$0.970786\pi$
$854$		0			0
$855$	−0.224861	+	2.44041i	−0.00769007	+	0.0834604i
$856$		0			0
$857$	9.82577	+	5.67291i	0.335642	+	0.193783i	0.658343	−	0.752718i	$-0.271258\pi$
$857$	9.82577	+	5.67291i	0.335642	+	0.193783i	−0.322701	+	0.946501i	$0.604591\pi$
$858$		0			0
$859$	−17.0895	−	29.5998i	−0.583085	−	1.00993i	−0.995111	−	0.0987606i	$-0.968512\pi$
$859$	−17.0895	−	29.5998i	−0.583085	−	1.00993i	0.412026	−	0.911172i	$-0.364821\pi$
$860$		0			0
$861$	1.69273	−	5.32577i	0.0576880	−	0.181502i
$862$		0			0
$863$	0.816917			0.0278082			0.0139041	−	0.999903i	$-0.495574\pi$
$863$	0.816917			0.0278082			0.0139041	+	0.999903i	$0.495574\pi$
$864$		0			0
$865$	−6.10102			−0.207441
$866$		0			0
$867$	−0.524648	+	1.65068i	−0.0178180	+	0.0560600i
$868$		0			0
$869$	3.55159	+	6.15153i	0.120479	+	0.208676i
$870$		0			0
$871$	33.0511	+	19.0820i	1.11989	+	0.646571i
$872$		0			0
$873$	30.6464	−	14.1189i	1.03722	−	0.477851i
$874$		0			0
$875$	9.21975	+	5.32302i	0.311684	+	0.179951i
$876$		0			0
$877$	38.4462	−	22.1969i	1.29824	−	0.749537i	0.318137	−	0.948045i	$-0.396943\pi$
$877$	38.4462	−	22.1969i	1.29824	−	0.749537i	0.980099	+	0.198507i	$0.0636093\pi$
$878$		0			0
$879$	−11.1838	+	2.45233i	−0.377220	+	0.0827149i
$880$		0			0
$881$			35.4196i			1.19332i	0.802496	+	0.596658i	$0.203505\pi$
$881$			35.4196i			1.19332i	−0.802496	+	0.596658i	$0.796495\pi$
$882$		0			0
$883$	−20.3023			−0.683225			−0.341613	−	0.939841i	$-0.610973\pi$
$883$	−20.3023			−0.683225			−0.341613	+	0.939841i	$0.610973\pi$
$884$		0			0
$885$	−1.64456	+	1.50000i	−0.0552814	+	0.0504219i
$886$		0			0
$887$	9.29139	+	16.0932i	0.311974	+	0.540356i	0.978790	−	0.204867i	$-0.0656763\pi$
$887$	9.29139	+	16.0932i	0.311974	+	0.540356i	−0.666815	+	0.745223i	$0.732343\pi$
$888$		0			0
$889$	−2.75255	+	4.76756i	−0.0923176	+	0.159899i
$890$		0			0
$891$	1.22021	−	6.56524i	0.0408785	−	0.219944i
$892$		0			0
$893$	13.2528	−	22.9546i	0.443489	−	0.768146i
$894$		0			0
$895$	6.26922	−	3.61953i	0.209557	−	0.120988i
$896$		0			0
$897$	15.5227	−	14.1582i	0.518288	−	0.472728i
$898$		0			0
$899$		−	39.3578i		−	1.31266i
$900$		0			0
$901$		−	23.3939i		−	0.779363i
$902$		0			0
$903$	−8.79114	−	40.0918i	−0.292551	−	1.33417i
$904$		0			0
$905$	−1.28036	+	0.739215i	−0.0425605	+	0.0245723i
$906$		0			0
$907$	−21.2336	+	36.7777i	−0.705051	+	1.22118i	0.261622	+	0.965171i	$0.415743\pi$
$907$	−21.2336	+	36.7777i	−0.705051	+	1.22118i	−0.966673	+	0.256014i	$0.917591\pi$
$908$		0			0
$909$	−0.866025	+	0.398979i	−0.0287242	+	0.0132333i
$910$		0			0
$911$	−4.65601	+	8.06445i	−0.154261	+	0.267187i	−0.932790	−	0.360422i	$-0.882633\pi$
$911$	−4.65601	+	8.06445i	−0.154261	+	0.267187i	0.778529	+	0.627609i	$0.215966\pi$
$912$		0			0
$913$	−0.949490	−	1.64456i	−0.0314235	−	0.0544271i
$914$		0			0
$915$	4.72183	+	1.50077i	0.156099	+	0.0496140i
$916$		0			0
$917$	63.3860			2.09319
$918$		0			0
$919$		−	35.2520i		−	1.16286i	−0.813597	−	0.581429i	$-0.802494\pi$
$919$		−	35.2520i		−	1.16286i	0.813597	−	0.581429i	$-0.197506\pi$
$920$		0			0
$921$	−9.30306	+	29.2699i	−0.306546	+	0.964476i
$922$		0			0
$923$	−35.1752	+	20.3084i	−1.15781	+	0.668460i
$924$		0			0
$925$	31.1769	+	18.0000i	1.02509	+	0.591836i
$926$		0			0
$927$	45.6813	+	4.20909i	1.50037	+	0.138245i
$928$		0			0
$929$	−4.87117	−	2.81237i	−0.159818	−	0.0922710i	0.417958	−	0.908466i	$-0.362746\pi$
$929$	−4.87117	−	2.81237i	−0.159818	−	0.0922710i	−0.577776	+	0.816195i	$0.696079\pi$
$930$		0			0
$931$	5.71812	+	9.90408i	0.187404	+	0.324593i
$932$		0			0
$933$	19.1400	−	4.19694i	0.626617	−	0.137402i
$934$		0			0
$935$	−1.00052			−0.0327204
$936$		0			0
$937$	−8.85357			−0.289234			−0.144617	−	0.989488i	$-0.546195\pi$
$937$	−8.85357			−0.289234			−0.144617	+	0.989488i	$0.546195\pi$
$938$		0			0
$939$	−9.45557	−	10.3669i	−0.308571	−	0.338310i
$940$		0			0
$941$	−6.94426	−	12.0278i	−0.226376	−	0.392095i	0.730355	−	0.683068i	$-0.239355\pi$
$941$	−6.94426	−	12.0278i	−0.226376	−	0.392095i	−0.956731	+	0.290972i	$0.906021\pi$
$942$		0			0
$943$	3.33884	+	1.92768i	0.108727	+	0.0627738i
$944$		0			0
$945$	−3.37117	−	4.45694i	−0.109664	−	0.144984i
$946$		0			0
$947$	26.6629	+	15.3939i	0.866429	+	0.500233i	0.866160	−	0.499767i	$-0.166581\pi$
$947$	26.6629	+	15.3939i	0.866429	+	0.500233i	0.000269172		1.00000i	$0.499914\pi$
$948$		0			0
$949$	16.7563	−	9.67423i	0.543931	−	0.314039i
$950$		0			0
$951$	−4.58106	−	5.02256i	−0.148551	−	0.162868i
$952$		0			0
$953$		−	43.9048i		−	1.42222i	−0.703082	−	0.711109i	$-0.748193\pi$
$953$		−	43.9048i		−	1.42222i	0.703082	−	0.711109i	$-0.251807\pi$
$954$		0			0
$955$	−8.15854			−0.264004
$956$		0			0
$957$	−2.20881	−	10.0732i	−0.0714006	−	0.325621i
$958$		0			0
$959$	12.7427	+	22.0709i	0.411482	+	0.712708i
$960$		0			0
$961$	−3.47219	+	6.01402i	−0.112006	+	0.194001i
$962$		0			0
$963$	−15.1618	+	21.4420i	−0.488582	+	0.690959i
$964$		0			0
$965$	0.405324	−	0.702041i	0.0130478	−	0.0225995i
$966$		0			0
$967$	−27.2821	+	15.7513i	−0.877334	+	0.506529i	−0.869778	−	0.493443i	$-0.835738\pi$
$967$	−27.2821	+	15.7513i	−0.877334	+	0.506529i	−0.00755547	+	0.999971i	$0.502405\pi$
$968$		0			0
$969$	18.0000	+	5.72107i	0.578243	+	0.183787i
$970$		0			0
$971$			11.2381i			0.360648i	0.983607	+	0.180324i	$0.0577146\pi$
$971$			11.2381i			0.360648i	−0.983607	+	0.180324i	$0.942285\pi$
$972$		0			0
$973$		−	45.0000i		−	1.44263i
$974$		0			0
$975$	24.2599	+	7.71071i	0.776940	+	0.246940i
$976$		0			0
$977$	47.8485	−	27.6253i	1.53081	−	0.883812i	0.531483	−	0.847069i	$-0.321635\pi$
$977$	47.8485	−	27.6253i	1.53081	−	0.883812i	0.999325	−	0.0367438i	$-0.0116986\pi$
$978$		0			0
$979$	−5.42930	+	9.40382i	−0.173521	+	0.300547i
$980$		0			0
$981$	23.1202	−	32.6969i	0.738172	−	1.04393i
$982$		0			0
$983$	−8.29088	+	14.3602i	−0.264438	+	0.458020i	−0.967416	−	0.253191i	$-0.918520\pi$
$983$	−8.29088	+	14.3602i	−0.264438	+	0.458020i	0.702978	+	0.711211i	$0.251853\pi$
$984$		0			0
$985$	−1.75255	−	3.03551i	−0.0558409	−	0.0967193i
$986$		0			0
$987$	12.9453	+	59.0367i	0.412053	+	1.87916i
$988$		0			0
$989$	28.3164			0.900408
$990$		0			0
$991$		−	30.1116i		−	0.956525i	−0.878217	−	0.478263i	$-0.841267\pi$
$991$		−	30.1116i		−	0.956525i	0.878217	−	0.478263i	$-0.158733\pi$
$992$		0			0
$993$	22.1969	+	24.3362i	0.704399	+	0.772286i
$994$		0			0
$995$	−1.44412	+	0.833763i	−0.0457817	+	0.0264321i
$996$		0			0
$997$	−16.4938	−	9.52270i	−0.522364	−	0.301587i	0.215537	−	0.976496i	$-0.430850\pi$
$997$	−16.4938	−	9.52270i	−0.522364	−	0.301587i	−0.737901	+	0.674909i	$0.764183\pi$
$998$		0			0
$999$	−23.0346	−	30.4534i	−0.728781	−	0.963502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.p.e.191.5	yes	16
3.2	odd	2		3456.2.p.e.575.5		16
4.3	odd	2	inner	1152.2.p.e.191.3	✓	16
8.3	odd	2	inner	1152.2.p.e.191.6	yes	16
8.5	even	2	inner	1152.2.p.e.191.4	yes	16
9.4	even	3		3456.2.p.e.2879.4		16
9.5	odd	6	inner	1152.2.p.e.959.6	yes	16
12.11	even	2		3456.2.p.e.575.6		16
24.5	odd	2		3456.2.p.e.575.3		16
24.11	even	2		3456.2.p.e.575.4		16
36.23	even	6	inner	1152.2.p.e.959.4	yes	16
36.31	odd	6		3456.2.p.e.2879.3		16
72.5	odd	6	inner	1152.2.p.e.959.3	yes	16
72.13	even	6		3456.2.p.e.2879.6		16
72.59	even	6	inner	1152.2.p.e.959.5	yes	16
72.67	odd	6		3456.2.p.e.2879.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.e.191.3	✓	16	4.3	odd	2	inner
1152.2.p.e.191.4	yes	16	8.5	even	2	inner
1152.2.p.e.191.5	yes	16	1.1	even	1	trivial
1152.2.p.e.191.6	yes	16	8.3	odd	2	inner
1152.2.p.e.959.3	yes	16	72.5	odd	6	inner
1152.2.p.e.959.4	yes	16	36.23	even	6	inner
1152.2.p.e.959.5	yes	16	72.59	even	6	inner
1152.2.p.e.959.6	yes	16	9.5	odd	6	inner
3456.2.p.e.575.3		16	24.5	odd	2
3456.2.p.e.575.4		16	24.11	even	2
3456.2.p.e.575.5		16	3.2	odd	2
3456.2.p.e.575.6		16	12.11	even	2
3456.2.p.e.2879.3		16	36.31	odd	6
3456.2.p.e.2879.4		16	9.4	even	3
3456.2.p.e.2879.5		16	72.67	odd	6
3456.2.p.e.2879.6		16	72.13	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.524648 - 1.65068i) q^{3} +(-0.158919 - 0.275255i) q^{5} +(-2.93038 - 1.69185i) q^{7} +(-2.44949 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.524648 - 1.65068i) q^{3} +(-0.158919 - 0.275255i) q^{5} +(-2.93038 - 1.69185i) q^{7} +(-2.44949 - 1.73205i) q^{9} +(-0.642559 - 0.370982i) q^{11} +(-2.59808 + 1.50000i) q^{13} +(-0.537734 + 0.117912i) q^{15} +4.24264i q^{17} +2.57024 q^{19} +(-4.33013 + 3.94949i) q^{21} +(-2.02166 - 3.50162i) q^{23} +(2.44949 - 4.24264i) q^{25} +(-4.14418 + 3.13461i) q^{27} +(-4.01229 + 6.94949i) q^{29} +(-4.24755 + 2.45233i) q^{31} +(-0.949490 + 0.866025i) q^{33} +1.07547i q^{35} +7.34847i q^{37} +(1.11295 + 5.07556i) q^{39} +(-0.825765 + 0.476756i) q^{41} +(-3.50162 + 6.06499i) q^{43} +(-0.0874863 + 0.949490i) q^{45} +(5.15627 - 8.93092i) q^{47} +(2.22474 + 3.85337i) q^{49} +(7.00324 + 2.22589i) q^{51} -5.51399 q^{53} +0.235824i q^{55} +(1.34847 - 4.24264i) q^{57} +(3.50162 - 2.02166i) q^{59} +(-7.79423 - 4.50000i) q^{61} +(4.24755 + 9.21975i) q^{63} +(0.825765 + 0.476756i) q^{65} +(-6.36068 - 11.0170i) q^{67} +(-6.84072 + 1.50000i) q^{69} +13.5389 q^{71} -6.44949 q^{73} +(-5.71812 - 6.26922i) q^{75} +(1.25529 + 2.17423i) q^{77} +(-8.29088 - 4.78674i) q^{79} +(3.00000 + 8.48528i) q^{81} +(2.21650 + 1.27970i) q^{83} +(1.16781 - 0.674235i) q^{85} +(9.36635 + 10.2690i) q^{87} -14.6349i q^{89} +10.1511 q^{91} +(1.81954 + 8.29796i) q^{93} +(-0.408459 - 0.707471i) q^{95} +(-5.62372 + 9.74058i) q^{97} +(0.931383 + 2.02166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 24 q^{33} - 72 q^{41} + 16 q^{49} - 96 q^{57} + 72 q^{65} - 64 q^{73} + 48 q^{81} + 8 q^{97}+O(q^{100}) \) 16 * q + 24 * q^33 - 72 * q^41 + 16 * q^49 - 96 * q^57 + 72 * q^65 - 64 * q^73 + 48 * q^81 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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