LMFDB - Embedded newform 1152.2.p.e.959.5

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			959.5
Root			$0.500000 + 2.00333i$ of defining polynomial
Character	$\chi$	$=$	1152.959
Dual form			1152.2.p.e.191.5

$q$-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 $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.899371	−	0.437187i	$-0.855975\pi$
$5$	−0.158919	+	0.275255i	−0.0710706	+	0.123098i	0.828300	+	0.560285i	$0.189308\pi$
$6$		0			0
$7$	−2.93038	+	1.69185i	−1.10758	+	0.639461i	−0.938201	−	0.346090i	$-0.887509\pi$
$7$	−2.93038	+	1.69185i	−1.10758	+	0.639461i	−0.169378	+	0.985551i	$0.554176\pi$
$8$		0			0
$9$	−2.44949	+	1.73205i	−0.816497	+	0.577350i
$10$		0			0
$11$	−0.642559	+	0.370982i	−0.193739	+	0.111855i	−0.593732	−	0.804663i	$-0.702346\pi$
$11$	−0.642559	+	0.370982i	−0.193739	+	0.111855i	0.399993	+	0.916518i	$0.369013\pi$
$12$		0			0
$13$	−2.59808	−	1.50000i	−0.720577	−	0.416025i	0.0943882	−	0.995535i	$-0.469911\pi$
$13$	−2.59808	−	1.50000i	−0.720577	−	0.416025i	−0.814965	+	0.579510i	$0.803244\pi$
$14$		0			0
$15$	−0.537734	−	0.117912i	−0.138842	−	0.0304447i
$16$		0			0
$17$		−	4.24264i		−	1.02899i	−0.857493	−	0.514496i	$-0.827979\pi$
$17$		−	4.24264i		−	1.02899i	0.857493	−	0.514496i	$-0.172021\pi$
$18$		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	−0.996091	−	0.0883343i	$-0.971846\pi$
$23$	−2.02166	+	3.50162i	−0.421546	+	0.730139i	0.574545	+	0.818473i	$0.305179\pi$
$24$		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	−0.950165	−	0.311747i	$-0.899086\pi$
$29$	−4.01229	−	6.94949i	−0.745064	−	1.29049i	0.205102	−	0.978741i	$-0.434248\pi$
$30$		0			0
$31$	−4.24755	−	2.45233i	−0.762883	−	0.440451i	0.0674468	−	0.997723i	$-0.478515\pi$
$31$	−4.24755	−	2.45233i	−0.762883	−	0.440451i	−0.830330	+	0.557272i	$0.811848\pi$
$32$		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	$-0.793557\pi$
$37$		−	7.34847i		−	1.20808i	0.796954	−	0.604040i	$-0.206443\pi$
$38$		0			0
$39$	1.11295	−	5.07556i	0.178214	−	0.812741i
$40$		0			0
$41$	−0.825765	−	0.476756i	−0.128963	−	0.0744568i	0.434131	−	0.900850i	$-0.357056\pi$
$41$	−0.825765	−	0.476756i	−0.128963	−	0.0744568i	−0.563094	+	0.826393i	$0.690389\pi$
$42$		0			0
$43$	−3.50162	−	6.06499i	−0.533992	−	0.924902i	−0.999211	−	0.0397062i	$-0.987358\pi$
$43$	−3.50162	−	6.06499i	−0.533992	−	0.924902i	0.465219	−	0.885196i	$-0.345976\pi$
$44$		0			0
$45$	−0.0874863	−	0.949490i	−0.0130417	−	0.141542i
$46$		0			0
$47$	5.15627	+	8.93092i	0.752119	+	1.30271i	0.946794	+	0.321841i	$0.104302\pi$
$47$	5.15627	+	8.93092i	0.752119	+	1.30271i	−0.194675	+	0.980868i	$0.562365\pi$
$48$		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	0.710307	−	0.703892i	$-0.248556\pi$
$59$	3.50162	+	2.02166i	0.455872	+	0.263198i	−0.254435	+	0.967090i	$0.581889\pi$
$60$		0			0
$61$	−7.79423	+	4.50000i	−0.997949	+	0.576166i	−0.907641	−	0.419748i	$-0.862118\pi$
$61$	−7.79423	+	4.50000i	−0.997949	+	0.576166i	−0.0903080	+	0.995914i	$0.528785\pi$
$62$		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	0.156536	+	0.987672i	$0.449967\pi$
$67$	−6.36068	+	11.0170i	−0.777081	+	1.34594i	−0.933617	+	0.358272i	$0.883366\pi$
$68$		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	−0.887695	−	0.460432i	$-0.847694\pi$
$79$	−8.29088	+	4.78674i	−0.932797	+	0.538550i	−0.0451016	+	0.998982i	$0.514361\pi$
$80$		0			0
$81$	3.00000	−	8.48528i	0.333333	−	0.942809i
$82$		0			0
$83$	2.21650	−	1.27970i	0.243293	−	0.140465i	−0.373396	−	0.927672i	$-0.621807\pi$
$83$	2.21650	−	1.27970i	0.243293	−	0.140465i	0.616689	+	0.787207i	$0.288474\pi$
$84$		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	$0.282578\pi$
$89$			14.6349i			1.55130i	−0.631163	+	0.775651i	$0.717422\pi$
$90$		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	−0.996463	−	0.0840287i	$-0.973221\pi$
$97$	−5.62372	−	9.74058i	−0.571003	−	0.989006i	0.425461	−	0.904977i	$-0.360112\pi$
$98$		0			0
$99$	0.931383	−	2.02166i	0.0936076	−	0.203185i
$100$		0			0
$101$	0.158919	+	0.275255i	0.0158130	+	0.0273889i	0.873824	−	0.486243i	$-0.161633\pi$
$101$	0.158919	+	0.275255i	0.0158130	+	0.0273889i	−0.858011	+	0.513632i	$0.828300\pi$
$102$		0			0
$103$	−13.2429	−	7.64580i	−1.30486	−	0.753363i	−0.323629	−	0.946184i	$-0.604903\pi$
$103$	−13.2429	−	7.64580i	−1.30486	−	0.753363i	−0.981234	+	0.192821i	$0.938236\pi$
$104$		0			0
$105$	1.77526	−	0.564242i	0.173247	−	0.0550644i
$106$		0			0
$107$			8.75366i			0.846248i	0.906072	+	0.423124i	$0.139067\pi$
$107$			8.75366i			0.846248i	−0.906072	+	0.423124i	$0.860933\pi$
$108$		0			0
$109$		−	13.3485i		−	1.27855i	−0.768978	−	0.639276i	$-0.779234\pi$
$109$		−	13.3485i		−	1.27855i	0.768978	−	0.639276i	$-0.220766\pi$
$110$		0			0
$111$	12.1300	−	3.85536i	1.15133	−	0.365934i
$112$		0			0
$113$	4.50000	+	2.59808i	0.423324	+	0.244406i	0.696499	−	0.717558i	$-0.254740\pi$
$113$	4.50000	+	2.59808i	0.423324	+	0.244406i	−0.273174	+	0.961965i	$0.588074\pi$
$114$		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	$0.0229969\pi$
$127$			1.62694i			0.144368i	−0.997391	+	0.0721839i	$0.977003\pi$
$128$		0			0
$129$	8.17423	−	8.96204i	0.719701	−	0.789063i
$130$		0			0
$131$	−16.2230	−	9.36635i	−1.41741	−	0.818341i	−0.421338	−	0.906904i	$-0.638440\pi$
$131$	−16.2230	−	9.36635i	−1.41741	−	0.818341i	−0.996071	+	0.0885620i	$0.971773\pi$
$132$		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	−0.752050	−	0.659106i	$-0.770935\pi$
$137$	−6.52270	+	3.76588i	−0.557272	+	0.321741i	0.194778	+	0.980847i	$0.437601\pi$
$138$		0			0
$139$	6.64951	−	11.5173i	0.564004	−	0.976883i	−0.433138	−	0.901328i	$-0.642594\pi$
$139$	6.64951	−	11.5173i	0.564004	−	0.976883i	0.997142	−	0.0755556i	$-0.0240730\pi$
$140$		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	−0.721513	−	0.692401i	$-0.756553\pi$
$149$	2.91591	−	5.05051i	0.238881	−	0.413754i	0.960393	+	0.278647i	$0.0898861\pi$
$150$		0			0
$151$	−14.1516	+	8.17045i	−1.15164	+	0.664902i	−0.949287	−	0.314410i	$-0.898193\pi$
$151$	−14.1516	+	8.17045i	−1.15164	+	0.664902i	−0.202356	+	0.979312i	$0.564860\pi$
$152$		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	0.998536	+	0.0540865i	$0.0172247\pi$
$157$	19.3543	+	11.1742i	1.54464	+	0.891801i	0.546108	+	0.837715i	$0.316109\pi$
$158$		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	0.252262	+	0.967659i	$0.418825\pi$
$167$	−9.19959	+	15.9342i	−0.711886	+	1.23302i	−0.964148	+	0.265364i	$0.914508\pi$
$168$		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	0.957010	+	0.290056i	$0.0936738\pi$
$173$	9.59771	+	16.6237i	0.729701	+	1.26388i	−0.227309	+	0.973823i	$0.572993\pi$
$174$		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	$-0.675888\pi$
$179$		−	22.7760i		−	1.70236i	0.524874	−	0.851180i	$-0.324112\pi$
$180$		0			0
$181$			4.65153i			0.345746i	0.984944	+	0.172873i	$0.0553049\pi$
$181$			4.65153i			0.345746i	−0.984944	+	0.172873i	$0.944695\pi$
$182$		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	0.785552	+	0.618796i	$0.212379\pi$
$191$	12.8345	+	22.2299i	0.928669	+	1.60850i	0.143117	+	0.989706i	$0.454287\pi$
$192$		0			0
$193$	1.27526	−	2.20881i	0.0917949	−	0.158993i	−0.816472	−	0.577386i	$-0.804073\pi$
$193$	1.27526	−	2.20881i	0.0917949	−	0.158993i	0.908266	+	0.418392i	$0.137406\pi$
$194$		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	$0.0595383\pi$
$199$			5.24648i			0.371913i	−0.982558	+	0.185956i	$0.940462\pi$
$200$		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	−0.986146	−	0.165880i	$-0.946953\pi$
$211$	−5.07556	+	8.79114i	−0.349416	+	0.605207i	0.636730	+	0.771087i	$0.280287\pi$
$212$		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	−0.936973	−	0.349403i	$-0.886385\pi$
$223$	−16.4693	+	9.50857i	−1.10287	+	0.636741i	−0.165895	+	0.986143i	$0.553051\pi$
$224$		0			0
$225$	−13.3485	−	6.14966i	−0.889898	−	0.409978i
$226$		0			0
$227$	−12.7863	+	7.38216i	−0.848655	+	0.489971i	−0.860197	−	0.509962i	$-0.829659\pi$
$227$	−12.7863	+	7.38216i	−0.848655	+	0.489971i	0.0115418	+	0.999933i	$0.496326\pi$
$228$		0			0
$229$	16.4938	+	9.52270i	1.08994	+	0.629278i	0.933561	−	0.358419i	$-0.116684\pi$
$229$	16.4938	+	9.52270i	1.08994	+	0.629278i	0.156381	+	0.987697i	$0.450017\pi$
$230$		0			0
$231$	4.24755	+	0.931383i	0.279468	+	0.0612805i
$232$		0			0
$233$		−	8.48528i		−	0.555889i	−0.960597	−	0.277945i	$-0.910347\pi$
$233$		−	8.48528i		−	0.555889i	0.960597	−	0.277945i	$-0.0896532\pi$
$234$		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	−0.923974	−	0.382456i	$-0.875078\pi$
$239$	−2.02166	+	3.50162i	−0.130770	+	0.226501i	0.793203	+	0.608957i	$0.208412\pi$
$240$		0			0
$241$	7.84847	+	13.5939i	0.505564	+	0.875663i	0.999979	+	0.00643712i	$0.00204901\pi$
$241$	7.84847	+	13.5939i	0.505564	+	0.875663i	−0.494415	+	0.869226i	$0.664618\pi$
$242$		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	$0.277576\pi$
$251$			24.2599i			1.53127i	−0.643273	+	0.765637i	$0.722424\pi$
$252$		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	0.408521	−	0.912749i	$-0.366045\pi$
$257$	−2.84847	−	1.64456i	−0.177683	−	0.102585i	−0.586203	+	0.810164i	$0.699378\pi$
$258$		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	0.811993	−	0.583667i	$-0.198383\pi$
$263$	−1.61320	−	2.79415i	−0.0994744	−	0.172295i	−0.911467	+	0.411373i	$0.865049\pi$
$264$		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	$-0.959311\pi$
$271$		−	4.19718i		−	0.254961i	0.991841	−	0.127480i	$-0.0406890\pi$
$272$		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	−0.905578	−	0.424180i	$-0.860563\pi$
$277$	−16.4938	+	9.52270i	−0.991017	+	0.572164i	−0.0854387	+	0.996343i	$0.527229\pi$
$278$		0			0
$279$	14.6519	−	1.35003i	0.877186	−	0.0808242i
$280$		0			0
$281$	22.8712	−	13.2047i	1.36438	−	0.787725i	0.374176	−	0.927358i	$-0.377925\pi$
$281$	22.8712	−	13.2047i	1.36438	−	0.787725i	0.990203	+	0.139633i	$0.0445921\pi$
$282$		0			0
$283$	11.7900	−	20.4208i	0.700842	−	1.21389i	−0.267330	−	0.963605i	$-0.586141\pi$
$283$	11.7900	−	20.4208i	0.700842	−	1.21389i	0.968171	−	0.250288i	$-0.0805254\pi$
$284$		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	−0.946273	−	0.323369i	$-0.895185\pi$
$293$	−3.30518	+	5.72474i	−0.193091	+	0.334443i	0.753182	+	0.657812i	$0.228518\pi$
$294$		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	−0.659891	−	0.751361i	$-0.729398\pi$
$311$	5.65653	−	9.79739i	0.320752	−	0.555559i	0.980643	+	0.195802i	$0.0627310\pi$
$312$		0			0
$313$	4.05051	+	7.01569i	0.228948	+	0.396550i	0.957497	−	0.288444i	$-0.0931380\pi$
$313$	4.05051	+	7.01569i	0.228948	+	0.396550i	−0.728548	+	0.684994i	$0.759805\pi$
$314$		0			0
$315$	1.86277	+	2.63435i	0.104955	+	0.148429i
$316$		0			0
$317$	1.96240	+	3.39898i	0.110219	+	0.190906i	0.915859	−	0.401501i	$-0.131511\pi$
$317$	1.96240	+	3.39898i	0.110219	+	0.190906i	−0.805639	+	0.592406i	$0.798178\pi$
$318$		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	−0.999653	−	0.0263407i	$-0.991615\pi$
$331$	−9.50857	−	16.4693i	−0.522638	−	0.905236i	0.477015	−	0.878895i	$-0.341719\pi$
$332$		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	−0.841990	−	0.539493i	$-0.818616\pi$
$337$	0.848469	−	1.46959i	0.0462191	−	0.0800538i	0.888209	+	0.459439i	$0.151949\pi$
$338$		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	0.0522924	−	0.998632i	$-0.483347\pi$
$347$	−14.6490	−	8.45763i	−0.786402	−	0.454029i	−0.838694	+	0.544602i	$0.816681\pi$
$348$		0			0
$349$	−14.1582	+	8.17423i	−0.757871	+	0.437557i	−0.828531	−	0.559944i	$-0.810823\pi$
$349$	−14.1582	+	8.17423i	−0.757871	+	0.437557i	0.0706601	+	0.997500i	$0.477489\pi$
$350$		0			0
$351$	6.06499	+	14.3602i	0.323725	+	0.766492i
$352$		0			0
$353$	−17.1742	+	9.91555i	−0.914092	+	0.527751i	−0.881746	−	0.471725i	$-0.843631\pi$
$353$	−17.1742	+	9.91555i	−0.914092	+	0.527751i	−0.0323467	+	0.999477i	$0.510298\pi$
$354$		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	−0.155330	−	0.987863i	$-0.549644\pi$
$367$	11.9257	−	6.88533i	0.622519	−	0.359411i	0.777849	+	0.628451i	$0.216311\pi$
$368$		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	0.985551	−	0.169376i	$-0.0541752\pi$
$373$	25.7183	+	14.8485i	1.33164	+	0.768825i	0.346092	+	0.938201i	$0.387509\pi$
$374$		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	−0.703689	−	0.710508i	$-0.748465\pi$
$383$	5.15627	−	8.93092i	0.263473	−	0.456349i	0.967162	+	0.254159i	$0.0817987\pi$
$384$		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	0.836446	−	0.548050i	$-0.184630\pi$
$389$	−1.11243	−	1.92679i	−0.0564025	−	0.0976919i	−0.892848	+	0.450358i	$0.851296\pi$
$390$		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	$-0.868090\pi$
$397$		−	16.0454i		−	0.805296i	0.915355	−	0.402648i	$-0.131910\pi$
$398$		0			0
$399$	−11.1295	−	10.1511i	−0.557170	−	0.508192i
$400$		0			0
$401$	33.5227	+	19.3543i	1.67404	+	0.966510i	0.965337	+	0.261007i	$0.0840545\pi$
$401$	33.5227	+	19.3543i	1.67404	+	0.966510i	0.708707	+	0.705503i	$0.249279\pi$
$402$		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	−0.667255	−	0.744830i	$-0.732531\pi$
$409$	6.29796	−	10.9084i	0.311414	−	0.539385i	0.978669	+	0.205445i	$0.0658641\pi$
$410$		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	0.285493	−	0.958381i	$-0.407843\pi$
$419$	−8.22345	−	4.74781i	−0.401742	−	0.231946i	−0.687235	+	0.726435i	$0.741176\pi$
$420$		0			0
$421$	−10.1298	+	5.84847i	−0.493698	+	0.285037i	−0.726108	−	0.687581i	$-0.758673\pi$
$421$	−10.1298	+	5.84847i	−0.493698	+	0.285037i	0.232409	+	0.972618i	$0.425339\pi$
$422$		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	−0.0803710	−	0.996765i	$-0.525611\pi$
$439$	15.5606	−	8.98392i	0.742667	−	0.428779i	0.823038	+	0.567986i	$0.192277\pi$
$440$		0			0
$441$	1.22474	+	13.2922i	0.0583212	+	0.632960i
$442$		0			0
$443$	−31.5146	+	18.1950i	−1.49730	+	0.864469i	−0.999995	−	0.00310536i	$-0.999012\pi$
$443$	−31.5146	+	18.1950i	−1.49730	+	0.864469i	−0.497308	+	0.867574i	$0.665678\pi$
$444$		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	$0.0821857\pi$
$449$			10.8209i			0.510670i	−0.966853	+	0.255335i	$0.917814\pi$
$450$		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	−0.885248	−	0.465120i	$-0.846011\pi$
$457$	−18.0732	−	31.3037i	−0.845429	−	1.46433i	0.0398186	−	0.999207i	$-0.487322\pi$
$458$		0			0
$459$	−13.2990	+	17.5823i	−0.620745	+	0.820670i
$460$		0			0
$461$	−10.4477	−	18.0959i	−0.486597	−	0.842811i	0.513284	−	0.858219i	$-0.328429\pi$
$461$	−10.4477	−	18.0959i	−0.486597	−	0.842811i	−0.999881	+	0.0154078i	$0.995095\pi$
$462$		0			0
$463$	8.69934	+	5.02256i	0.404292	+	0.233418i	0.688334	−	0.725393i	$-0.258342\pi$
$463$	8.69934	+	5.02256i	0.404292	+	0.233418i	−0.284042	+	0.958812i	$0.591676\pi$
$464$		0			0
$465$	1.99490	+	1.81954i	0.0925112	+	0.0843790i
$466$		0			0
$467$			15.5063i			0.717545i	0.933425	+	0.358773i	$0.116805\pi$
$467$			15.5063i			0.717545i	−0.933425	+	0.358773i	$0.883195\pi$
$468$		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	−0.957033	−	0.289978i	$-0.906352\pi$
$479$	−15.9691	−	27.6592i	−0.729645	−	1.26378i	0.227388	−	0.973804i	$-0.426981\pi$
$480$		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	0.998380	−	0.0568900i	$-0.0181184\pi$
$491$	32.0922	+	18.5285i	1.44830	+	0.836178i	0.449922	+	0.893068i	$0.351452\pi$
$492$		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	−0.969326	−	0.245777i	$-0.920957\pi$
$499$	−6.07186	+	10.5168i	−0.271814	+	0.470795i	0.697513	+	0.716573i	$0.254290\pi$
$500$		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	0.0317262	−	0.999497i	$-0.489900\pi$
$509$	19.8865	−	34.4444i	0.881453	−	1.52672i	0.849726	−	0.527224i	$-0.176767\pi$
$510$		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	$-0.986699\pi$
$521$		−	1.90702i		−	0.0835482i	0.999127	−	0.0417741i	$-0.0133010\pi$
$522$		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	$-0.853234\pi$
$541$		−	20.6969i		−	0.889831i	0.895573	−	0.444915i	$-0.146766\pi$
$542$		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	0.935610	−	0.353035i	$-0.114850\pi$
$547$	3.79045	+	6.56524i	0.162068	+	0.280710i	−0.773542	+	0.633745i	$0.781517\pi$
$548$		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	0.0721633	−	0.997393i	$-0.477010\pi$
$563$	−17.9268	−	10.3500i	−0.755523	−	0.436201i	−0.827686	+	0.561192i	$0.810343\pi$
$564$		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	−0.189580	−	0.981865i	$-0.560713\pi$
$569$	13.5000	−	7.79423i	0.565949	−	0.326751i	0.755530	+	0.655114i	$0.227379\pi$
$570$		0			0
$571$	−14.6490	+	25.3729i	−0.613043	+	1.06182i	0.377681	+	0.925936i	$0.376722\pi$
$571$	−14.6490	+	25.3729i	−0.613043	+	1.06182i	−0.990724	+	0.135887i	$0.956612\pi$
$572$		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	0.663028	−	0.748595i	$-0.269271\pi$
$587$	39.8030	−	22.9802i	1.64284	−	0.948496i	0.979816	−	0.199901i	$-0.0640622\pi$
$588$		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	$-0.889692\pi$
$593$		−	16.5420i		−	0.679297i	0.940552	−	0.339649i	$-0.110308\pi$
$594$		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	−0.124160	−	0.992262i	$-0.539624\pi$
$599$	19.5121	−	33.7960i	0.797244	−	1.38087i	0.921404	−	0.388605i	$-0.127043\pi$
$600$		0			0
$601$	11.6237	+	20.1329i	0.474142	+	0.821237i	0.999562	−	0.0296056i	$-0.00942514\pi$
$601$	11.6237	+	20.1329i	0.474142	+	0.821237i	−0.525420	+	0.850843i	$0.676092\pi$
$602$		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	0.566227	−	0.824249i	$-0.308403\pi$
$607$	3.33884	+	1.92768i	0.135519	+	0.0782421i	−0.430708	+	0.902492i	$0.641736\pi$
$608$		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	$-0.973966\pi$
$613$		−	4.04541i		−	0.163392i	0.996657	−	0.0816962i	$-0.0260337\pi$
$614$		0			0
$615$	0.387827	+	0.353736i	0.0156387	+	0.0142640i
$616$		0			0
$617$	−22.8712	−	13.2047i	−0.920759	−	0.531600i	−0.0368817	−	0.999320i	$-0.511742\pi$
$617$	−22.8712	−	13.2047i	−0.920759	−	0.531600i	−0.883877	+	0.467719i	$0.845076\pi$
$618$		0			0
$619$	−19.0820	−	33.0511i	−0.766972	−	1.32844i	−0.939197	−	0.343377i	$-0.888429\pi$
$619$	−19.0820	−	33.0511i	−0.766972	−	1.32844i	0.172225	−	0.985058i	$-0.444904\pi$
$620$		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	$0.0595081\pi$
$631$			9.33766i			0.371726i	−0.982576	+	0.185863i	$0.940492\pi$
$632$		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	−0.284917	−	0.958552i	$-0.591966\pi$
$641$	10.1969	−	5.88721i	0.402755	−	0.232531i	0.687672	+	0.726022i	$0.258633\pi$
$642$		0			0
$643$	−6.36068	+	11.0170i	−0.250841	+	0.434469i	−0.963758	−	0.266780i	$-0.914040\pi$
$643$	−6.36068	+	11.0170i	−0.250841	+	0.434469i	0.712917	+	0.701249i	$0.247374\pi$
$644$		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	−0.920751	−	0.390151i	$-0.872423\pi$
$653$	−3.13021	+	5.42168i	−0.122495	+	0.212167i	0.798256	+	0.602318i	$0.205756\pi$
$654$		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	−0.898038	−	0.439917i	$-0.855008\pi$
$659$	−24.8002	+	14.3184i	−0.966078	+	0.557765i	−0.0680394	+	0.997683i	$0.521674\pi$
$660$		0			0
$661$	−3.76588	−	2.17423i	−0.146476	−	0.0845679i	0.424971	−	0.905207i	$-0.360284\pi$
$661$	−3.76588	−	2.17423i	−0.146476	−	0.0845679i	−0.571447	+	0.820639i	$0.693618\pi$
$662$		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	0.912153	−	0.409849i	$-0.134419\pi$
$673$	2.62372	+	4.54442i	0.101137	+	0.175175i	−0.811016	+	0.585024i	$0.801085\pi$
$674$		0			0
$675$	3.14789	−	25.2605i	0.121162	−	0.972276i
$676$		0			0
$677$	−10.3763	−	17.9722i	−0.398792	−	0.690728i	0.594785	−	0.803885i	$-0.297237\pi$
$677$	−10.3763	−	17.9722i	−0.398792	−	0.690728i	−0.993577	+	0.113157i	$0.963904\pi$
$678$		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	$0.118364\pi$
$683$			18.9912i			0.726680i	−0.931657	+	0.363340i	$0.881636\pi$
$684$		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	−0.847347	−	0.531040i	$-0.821801\pi$
$691$	−23.2262	−	40.2290i	−0.883567	−	1.53038i	−0.0362206	−	0.999344i	$-0.511532\pi$
$692$		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	−0.427615	−	0.903961i	$-0.640646\pi$
$709$	3.76588	−	2.17423i	0.141431	−	0.0816551i	0.569046	+	0.822306i	$0.307313\pi$
$710$		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	−0.00728826	−	0.999973i	$-0.502320\pi$
$727$	23.0552	−	13.3109i	0.855070	−	0.493675i	0.862358	+	0.506299i	$0.168987\pi$
$728$		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	0.720338	−	0.693624i	$-0.243987\pi$
$733$	12.9904	+	7.50000i	0.479811	+	0.277019i	−0.240527	+	0.970642i	$0.577320\pi$
$734$		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	−0.634199	−	0.773170i	$-0.718670\pi$
$743$	9.60805	−	16.6416i	0.352485	−	0.610522i	0.986684	+	0.162647i	$0.0520033\pi$
$744$		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	0.997933	+	0.0642608i	$0.0204689\pi$
$751$	42.5467	+	24.5643i	1.55255	+	0.896366i	0.554618	+	0.832105i	$0.312864\pi$
$752$		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	$-0.930023\pi$
$757$		−	12.0000i		−	0.436147i	0.975932	−	0.218074i	$-0.0699773\pi$
$758$		0			0
$759$	4.95204	−	1.57394i	0.179748	−	0.0571305i
$760$		0			0
$761$	−20.4773	−	11.8226i	−0.742301	−	0.428568i	0.0806041	−	0.996746i	$-0.474315\pi$
$761$	−20.4773	−	11.8226i	−0.742301	−	0.428568i	−0.822905	+	0.568178i	$0.807648\pi$
$762$		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	−0.729840	−	0.683618i	$-0.760406\pi$
$769$	6.29796	−	10.9084i	0.227110	−	0.393366i	0.956950	+	0.290251i	$0.0937389\pi$
$770$		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	−0.913423	−	0.407012i	$-0.866571\pi$
$787$	−2.92397	+	5.06447i	−0.104228	+	0.180529i	0.809194	+	0.587541i	$0.199904\pi$
$788$		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	0.110050	+	0.993926i	$0.464899\pi$
$797$	−22.7470	+	39.3990i	−0.805740	+	1.39558i	−0.915790	+	0.401657i	$0.868434\pi$
$798$		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	$0.0344784\pi$
$809$			6.14966i			0.216211i	−0.994139	+	0.108105i	$0.965522\pi$
$810$		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	0.994073	−	0.108711i	$-0.0346722\pi$
$821$	11.5441	+	19.9949i	0.402890	+	0.697827i	−0.591183	+	0.806537i	$0.701339\pi$
$822$		0			0
$823$	31.7339	+	18.3216i	1.10617	+	0.638650i	0.937836	−	0.347079i	$-0.112826\pi$
$823$	31.7339	+	18.3216i	1.10617	+	0.638650i	0.168339	+	0.985729i	$0.446160\pi$
$824$		0			0
$825$	1.34847	−	6.14966i	0.0469477	−	0.214104i
$826$		0			0
$827$		−	27.0779i		−	0.941591i	−0.882242	−	0.470795i	$-0.843967\pi$
$827$		−	27.0779i		−	0.941591i	0.882242	−	0.470795i	$-0.156033\pi$
$828$		0			0
$829$		−	49.3485i		−	1.71394i	−0.515364	−	0.856972i	$-0.672343\pi$
$829$		−	49.3485i		−	1.71394i	0.515364	−	0.856972i	$-0.327657\pi$
$830$		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	−0.980737	−	0.195333i	$-0.937421\pi$
$839$	−19.1037	−	33.0885i	−0.659532	−	1.14234i	0.321205	−	0.947010i	$-0.395912\pi$
$840$		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	−0.995791	−	0.0916492i	$-0.970786\pi$
$853$	−41.3068	+	23.8485i	−1.41432	+	0.816556i	−0.418525	+	0.908205i	$0.637453\pi$
$854$		0			0
$855$	−0.224861	−	2.44041i	−0.00769007	−	0.0834604i
$856$		0			0
$857$	9.82577	−	5.67291i	0.335642	−	0.193783i	−0.322701	−	0.946501i	$-0.604591\pi$
$857$	9.82577	−	5.67291i	0.335642	−	0.193783i	0.658343	+	0.752718i	$0.271258\pi$
$858$		0			0
$859$	−17.0895	+	29.5998i	−0.583085	+	1.00993i	0.412026	+	0.911172i	$0.364821\pi$
$859$	−17.0895	+	29.5998i	−0.583085	+	1.00993i	−0.995111	+	0.0987606i	$0.968512\pi$
$860$		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	0.980099	−	0.198507i	$-0.0636093\pi$
$877$	38.4462	+	22.1969i	1.29824	+	0.749537i	0.318137	+	0.948045i	$0.396943\pi$
$878$		0			0
$879$	−11.1838	−	2.45233i	−0.377220	−	0.0827149i
$880$		0			0
$881$		−	35.4196i		−	1.19332i	−0.802496	−	0.596658i	$-0.796495\pi$
$881$		−	35.4196i		−	1.19332i	0.802496	−	0.596658i	$-0.203505\pi$
$882$		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	−0.666815	−	0.745223i	$-0.732343\pi$
$887$	9.29139	−	16.0932i	0.311974	−	0.540356i	0.978790	+	0.204867i	$0.0656763\pi$
$888$		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	−0.966673	−	0.256014i	$-0.917591\pi$
$907$	−21.2336	−	36.7777i	−0.705051	−	1.22118i	0.261622	−	0.965171i	$-0.415743\pi$
$908$		0			0
$909$	−0.866025	−	0.398979i	−0.0287242	−	0.0132333i
$910$		0			0
$911$	−4.65601	−	8.06445i	−0.154261	−	0.267187i	0.778529	−	0.627609i	$-0.215966\pi$
$911$	−4.65601	−	8.06445i	−0.154261	−	0.267187i	−0.932790	+	0.360422i	$0.882633\pi$
$912$		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	$0.197506\pi$
$919$			35.2520i			1.16286i	−0.813597	+	0.581429i	$0.802494\pi$
$920$		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	−0.577776	−	0.816195i	$-0.696079\pi$
$929$	−4.87117	+	2.81237i	−0.159818	+	0.0922710i	0.417958	+	0.908466i	$0.362746\pi$
$930$		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	−0.956731	−	0.290972i	$-0.906021\pi$
$941$	−6.94426	+	12.0278i	−0.226376	+	0.392095i	0.730355	+	0.683068i	$0.239355\pi$
$942$		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	0.000269172	−	1.00000i	$-0.499914\pi$
$947$	26.6629	−	15.3939i	0.866429	−	0.500233i	0.866160	+	0.499767i	$0.166581\pi$
$948$		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	$0.251807\pi$
$953$			43.9048i			1.42222i	−0.703082	+	0.711109i	$0.748193\pi$
$954$		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	−0.00755547	−	0.999971i	$-0.502405\pi$
$967$	−27.2821	−	15.7513i	−0.877334	−	0.506529i	−0.869778	+	0.493443i	$0.835738\pi$
$968$		0			0
$969$	18.0000	−	5.72107i	0.578243	−	0.183787i
$970$		0			0
$971$		−	11.2381i		−	0.360648i	−0.983607	−	0.180324i	$-0.942285\pi$
$971$		−	11.2381i		−	0.360648i	0.983607	−	0.180324i	$-0.0577146\pi$
$972$		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	0.999325	+	0.0367438i	$0.0116986\pi$
$977$	47.8485	+	27.6253i	1.53081	+	0.883812i	0.531483	+	0.847069i	$0.321635\pi$
$978$		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	0.702978	−	0.711211i	$-0.251853\pi$
$983$	−8.29088	−	14.3602i	−0.264438	−	0.458020i	−0.967416	+	0.253191i	$0.918520\pi$
$984$		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	$0.158733\pi$
$991$			30.1116i			0.956525i	−0.878217	+	0.478263i	$0.841267\pi$
$992$		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	−0.737901	−	0.674909i	$-0.764183\pi$
$997$	−16.4938	+	9.52270i	−0.522364	+	0.301587i	0.215537	+	0.976496i	$0.430850\pi$
$998$		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.959.5	yes	16
3.2	odd	2		3456.2.p.e.2879.5		16
4.3	odd	2	inner	1152.2.p.e.959.3	yes	16
8.3	odd	2	inner	1152.2.p.e.959.6	yes	16
8.5	even	2	inner	1152.2.p.e.959.4	yes	16
9.2	odd	6	inner	1152.2.p.e.191.6	yes	16
9.7	even	3		3456.2.p.e.575.4		16
12.11	even	2		3456.2.p.e.2879.6		16
24.5	odd	2		3456.2.p.e.2879.3		16
24.11	even	2		3456.2.p.e.2879.4		16
36.7	odd	6		3456.2.p.e.575.3		16
36.11	even	6	inner	1152.2.p.e.191.4	yes	16
72.11	even	6	inner	1152.2.p.e.191.5	yes	16
72.29	odd	6	inner	1152.2.p.e.191.3	✓	16
72.43	odd	6		3456.2.p.e.575.5		16
72.61	even	6		3456.2.p.e.575.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.e.191.3	✓	16	72.29	odd	6	inner
1152.2.p.e.191.4	yes	16	36.11	even	6	inner
1152.2.p.e.191.5	yes	16	72.11	even	6	inner
1152.2.p.e.191.6	yes	16	9.2	odd	6	inner
1152.2.p.e.959.3	yes	16	4.3	odd	2	inner
1152.2.p.e.959.4	yes	16	8.5	even	2	inner
1152.2.p.e.959.5	yes	16	1.1	even	1	trivial
1152.2.p.e.959.6	yes	16	8.3	odd	2	inner
3456.2.p.e.575.3		16	36.7	odd	6
3456.2.p.e.575.4		16	9.7	even	3
3456.2.p.e.575.5		16	72.43	odd	6
3456.2.p.e.575.6		16	72.61	even	6
3456.2.p.e.2879.3		16	24.5	odd	2
3456.2.p.e.2879.4		16	24.11	even	2
3456.2.p.e.2879.5		16	3.2	odd	2
3456.2.p.e.2879.6		16	12.11	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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
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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