LMFDB - Embedded newform 189.2.f.a.64.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(64,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("189.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			64.1
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	189.64
Dual form			189.2.f.a.127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23025 - 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.29679 + 2.24611i) q^{5} +(0.500000 + 0.866025i) q^{7} +5.05408 q^{8} +O(q^{10})$	\(q+(-1.23025 - 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.29679 + 2.24611i) q^{5} +(0.500000 + 0.866025i) q^{7} +5.05408 q^{8} +6.38151 q^{10} +(2.25729 + 3.90975i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(1.23025 - 2.13086i) q^{14} +(-2.16372 - 3.74766i) q^{16} +0.945916 q^{17} -4.05408 q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +(-0.136673 + 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +2.46050 q^{26} -4.05408 q^{28} +(1.23025 + 2.13086i) q^{29} +(-1.16372 + 2.01561i) q^{31} +(-0.269748 + 0.467216i) q^{32} +(-1.16372 - 2.01561i) q^{34} -2.59358 q^{35} +1.78074 q^{37} +(4.98755 + 8.63868i) q^{38} +(-6.55408 + 11.3520i) q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} -18.3025 q^{44} +0.672570 q^{46} +(-6.08113 - 10.5328i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-2.12422 + 3.67926i) q^{50} +(-2.02704 - 3.51094i) q^{52} +6.27335 q^{53} -11.7089 q^{55} +(2.52704 + 4.37697i) q^{56} +(3.02704 - 5.24299i) q^{58} +(-1.36333 + 2.36135i) q^{59} +(1.13667 + 1.96878i) q^{61} +5.72665 q^{62} -7.32743 q^{64} +(-1.29679 - 2.24611i) q^{65} +(7.90856 - 13.6980i) q^{67} +(-1.91741 + 3.32105i) q^{68} +(3.19076 + 5.52655i) q^{70} -3.27335 q^{71} -1.50739 q^{73} +(-2.19076 - 3.79450i) q^{74} +(8.21780 - 14.2336i) q^{76} +(-2.25729 + 3.90975i) q^{77} +(-7.35447 - 12.7383i) q^{79} +11.2235 q^{80} +15.7630 q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(12.8384 - 22.2368i) q^{86} +(11.4086 + 19.7602i) q^{88} +14.3566 q^{89} -1.00000 q^{91} +(-0.554084 - 0.959702i) q^{92} +(-14.9626 + 25.9161i) q^{94} +(5.25729 - 9.10590i) q^{95} +(5.74484 + 9.95036i) q^{97} +2.46050 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) $ 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8	$ 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} - 10 q^{35} - 6 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} - 46 q^{44} + 24 q^{46} - 9 q^{47} - 3 q^{49} + 10 q^{50} - 3 q^{52} + 36 q^{53} - 12 q^{55} + 6 q^{56} + 9 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} + 6 q^{68} - 18 q^{71} + 6 q^{73} + 6 q^{74} + 21 q^{76} + 2 q^{77} - 15 q^{79} - 22 q^{80} + 18 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 4 q^{89} - 6 q^{91} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97} + 2 q^{98}+O(q^{100}) $ 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8 - 2 * q^11 - 3 * q^13 + q^14 - 3 * q^16 + 24 * q^17 - 6 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 + 2 * q^26 - 6 * q^28 + q^29 + 3 * q^31 - 8 * q^32 + 3 * q^34 - 10 * q^35 - 6 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 - 46 * q^44 + 24 * q^46 - 9 * q^47 - 3 * q^49 + 10 * q^50 - 3 * q^52 + 36 * q^53 - 12 * q^55 + 6 * q^56 + 9 * q^58 - 9 * q^59 + 6 * q^61 + 36 * q^62 - 24 * q^64 - 5 * q^65 + 6 * q^68 - 18 * q^71 + 6 * q^73 + 6 * q^74 + 21 * q^76 + 2 * q^77 - 15 * q^79 - 22 * q^80 + 18 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 4 * q^89 - 6 * q^91 + 15 * q^92 - 24 * q^94 + 16 * q^95 - 3 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.23025	−	2.13086i	−0.869920	−	1.50675i	−0.862078	−	0.506776i	$-0.830837\pi$
$2$	−1.23025	−	2.13086i	−0.869920	−	1.50675i	−0.00784213	−	0.999969i	$-0.502496\pi$
$3$		0			0
$3$		0			0
$4$	−2.02704	+	3.51094i	−1.01352	+	1.75547i
$5$	−1.29679	+	2.24611i	−0.579942	+	1.00449i	0.415543	+	0.909573i	$0.363591\pi$
$5$	−1.29679	+	2.24611i	−0.579942	+	1.00449i	−0.995485	+	0.0949156i	$0.969742\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	5.05408			1.78689
$9$		0			0
$10$	6.38151			2.01801
$11$	2.25729	+	3.90975i	0.680600	+	1.17883i	0.974798	+	0.223089i	$0.0716141\pi$
$11$	2.25729	+	3.90975i	0.680600	+	1.17883i	−0.294198	+	0.955744i	$0.595053\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$	1.23025	−	2.13086i	0.328799	−	0.569496i
$15$		0			0
$16$	−2.16372	−	3.74766i	−0.540929	−	0.936916i
$17$	0.945916			0.229418			0.114709	−	0.993399i	$-0.463406\pi$
$17$	0.945916			0.229418			0.114709	+	0.993399i	$0.463406\pi$
$18$		0			0
$19$	−4.05408			−0.930071			−0.465035	−	0.885292i	$-0.653958\pi$
$19$	−4.05408			−0.930071			−0.465035	+	0.885292i	$0.653958\pi$
$20$	−5.25729	−	9.10590i	−1.17557	−	2.03614i
$21$		0			0
$22$	5.55408	−	9.61996i	1.18413	−	2.05098i
$23$	−0.136673	+	0.236725i	−0.0284983	+	0.0493605i	−0.879923	−	0.475117i	$-0.842406\pi$
$23$	−0.136673	+	0.236725i	−0.0284983	+	0.0493605i	0.851425	+	0.524477i	$0.175739\pi$
$24$		0			0
$25$	−0.863327	−	1.49533i	−0.172665	−	0.299065i
$26$	2.46050			0.482545
$27$		0			0
$28$	−4.05408			−0.766150
$29$	1.23025	+	2.13086i	0.228452	+	0.395691i	0.957350	−	0.288932i	$-0.0933002\pi$
$29$	1.23025	+	2.13086i	0.228452	+	0.395691i	−0.728897	+	0.684623i	$0.759967\pi$
$30$		0			0
$31$	−1.16372	+	2.01561i	−0.209009	+	0.362015i	−0.951403	−	0.307949i	$-0.900357\pi$
$31$	−1.16372	+	2.01561i	−0.209009	+	0.362015i	0.742393	+	0.669964i	$0.233691\pi$
$32$	−0.269748	+	0.467216i	−0.0476851	+	0.0825930i
$33$		0			0
$34$	−1.16372	−	2.01561i	−0.199576	−	0.345675i
$35$	−2.59358			−0.438395
$36$		0			0
$37$	1.78074			0.292752			0.146376	−	0.989229i	$-0.453239\pi$
$37$	1.78074			0.292752			0.146376	+	0.989229i	$0.453239\pi$
$38$	4.98755	+	8.63868i	0.809087	+	1.40138i
$39$		0			0
$40$	−6.55408	+	11.3520i	−1.03629	+	1.79491i
$41$	−3.20321	+	5.54812i	−0.500257	+	0.866471i	0.499743	+	0.866174i	$0.333428\pi$
$41$	−3.20321	+	5.54812i	−0.500257	+	0.866471i	−1.00000		0.000297253i	$0.999905\pi$
$42$		0			0
$43$	5.21780	+	9.03749i	0.795707	+	1.37820i	0.922389	+	0.386262i	$0.126234\pi$
$43$	5.21780	+	9.03749i	0.795707	+	1.37820i	−0.126682	+	0.991943i	$0.540433\pi$
$44$	−18.3025			−2.75921
$45$		0			0
$46$	0.672570			0.0991650
$47$	−6.08113	−	10.5328i	−0.887023	−	1.53637i	−0.843377	−	0.537323i	$-0.819436\pi$
$47$	−6.08113	−	10.5328i	−0.887023	−	1.53637i	−0.0436467	−	0.999047i	$-0.513898\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.12422	+	3.67926i	−0.300410	+	0.520326i
$51$		0			0
$52$	−2.02704	−	3.51094i	−0.281100	−	0.486880i
$53$	6.27335			0.861710			0.430855	−	0.902421i	$-0.358212\pi$
$53$	6.27335			0.861710			0.430855	+	0.902421i	$0.358212\pi$
$54$		0			0
$55$	−11.7089			−1.57883
$56$	2.52704	+	4.37697i	0.337690	+	0.584897i
$57$		0			0
$58$	3.02704	−	5.24299i	0.397470	−	0.688438i
$59$	−1.36333	+	2.36135i	−0.177490	+	0.307422i	−0.941020	−	0.338350i	$-0.890131\pi$
$59$	−1.36333	+	2.36135i	−0.177490	+	0.307422i	0.763530	+	0.645772i	$0.223464\pi$
$60$		0			0
$61$	1.13667	+	1.96878i	0.145536	+	0.252076i	0.929573	−	0.368639i	$-0.120176\pi$
$61$	1.13667	+	1.96878i	0.145536	+	0.252076i	−0.784037	+	0.620714i	$0.786843\pi$
$62$	5.72665			0.727286
$63$		0			0
$64$	−7.32743			−0.915929
$65$	−1.29679	−	2.24611i	−0.160847	−	0.278595i
$66$		0			0
$67$	7.90856	−	13.6980i	0.966184	−	1.67348i	0.259784	−	0.965667i	$-0.416349\pi$
$67$	7.90856	−	13.6980i	0.966184	−	1.67348i	0.706400	−	0.707813i	$-0.250318\pi$
$68$	−1.91741	+	3.32105i	−0.232520	+	0.402737i
$69$		0			0
$70$	3.19076	+	5.52655i	0.381368	+	0.660550i
$71$	−3.27335			−0.388475			−0.194237	−	0.980955i	$-0.562223\pi$
$71$	−3.27335			−0.388475			−0.194237	+	0.980955i	$0.562223\pi$
$72$		0			0
$73$	−1.50739			−0.176427			−0.0882134	−	0.996102i	$-0.528116\pi$
$73$	−1.50739			−0.176427			−0.0882134	+	0.996102i	$0.528116\pi$
$74$	−2.19076	−	3.79450i	−0.254670	−	0.441102i
$75$		0			0
$76$	8.21780	−	14.2336i	0.942646	−	1.63271i
$77$	−2.25729	+	3.90975i	−0.257243	+	0.445557i
$78$		0			0
$79$	−7.35447	−	12.7383i	−0.827443	−	1.43317i	−0.900038	−	0.435811i	$-0.856461\pi$
$79$	−7.35447	−	12.7383i	−0.827443	−	1.43317i	0.0725952	−	0.997361i	$-0.476872\pi$
$80$	11.2235			1.25483
$81$		0			0
$82$	15.7630			1.74074
$83$	−0.472958	−	0.819187i	−0.0519139	−	0.0899175i	0.838901	−	0.544285i	$-0.183199\pi$
$83$	−0.472958	−	0.819187i	−0.0519139	−	0.0899175i	−0.890815	+	0.454367i	$0.849865\pi$
$84$		0			0
$85$	−1.22665	+	2.12463i	−0.133049	+	0.230448i
$86$	12.8384	−	22.2368i	1.38440	−	2.39786i
$87$		0			0
$88$	11.4086	+	19.7602i	1.21616	+	2.10644i
$89$	14.3566			1.52180			0.760899	−	0.648871i	$-0.224758\pi$
$89$	14.3566			1.52180			0.760899	+	0.648871i	$0.224758\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$	−0.554084	−	0.959702i	−0.0577673	−	0.100056i
$93$		0			0
$94$	−14.9626	+	25.9161i	−1.54328	+	2.67304i
$95$	5.25729	−	9.10590i	0.539387	−	0.934246i
$96$		0			0
$97$	5.74484	+	9.95036i	0.583300	+	1.01031i	0.995085	+	0.0990246i	$0.0315722\pi$
$97$	5.74484	+	9.95036i	0.583300	+	1.01031i	−0.411785	+	0.911281i	$0.635094\pi$
$98$	2.46050			0.248549
$99$		0			0
$100$	7.00000			0.700000
$101$	−1.83988	−	3.18677i	−0.183075	−	0.317096i	0.759851	−	0.650097i	$-0.225272\pi$
$101$	−1.83988	−	3.18677i	−0.183075	−	0.317096i	−0.942926	+	0.333002i	$0.891939\pi$
$102$		0			0
$103$	4.86333	−	8.42353i	0.479198	−	0.829995i	−0.520518	−	0.853851i	$-0.674261\pi$
$103$	4.86333	−	8.42353i	0.479198	−	0.829995i	0.999715	+	0.0238560i	$0.00759431\pi$
$104$	−2.52704	+	4.37697i	−0.247797	+	0.429197i
$105$		0			0
$106$	−7.71780	−	13.3676i	−0.749619	−	1.29838i
$107$	1.37432			0.132860			0.0664301	−	0.997791i	$-0.478839\pi$
$107$	1.37432			0.132860			0.0664301	+	0.997791i	$0.478839\pi$
$108$		0			0
$109$	−3.39922			−0.325587			−0.162793	−	0.986660i	$-0.552050\pi$
$109$	−3.39922			−0.325587			−0.162793	+	0.986660i	$0.552050\pi$
$110$	14.4050	+	24.9501i	1.37346	+	2.37890i
$111$		0			0
$112$	2.16372	−	3.74766i	0.204452	−	0.354121i
$113$	5.19436	−	8.99689i	0.488644	−	0.846356i	−0.511271	−	0.859420i	$-0.670825\pi$
$113$	5.19436	−	8.99689i	0.488644	−	0.846356i	0.999915	+	0.0130636i	$0.00415840\pi$
$114$		0			0
$115$	−0.354473	−	0.613964i	−0.0330547	−	0.0572525i
$116$	−9.97509			−0.926164
$117$		0			0
$118$	6.70895			0.617608
$119$	0.472958	+	0.819187i	0.0433560	+	0.0750948i
$120$		0			0
$121$	−4.69076	+	8.12463i	−0.426432	+	0.738603i
$122$	2.79679	−	4.84418i	0.253209	−	0.438572i
$123$		0			0
$124$	−4.71780	−	8.17147i	−0.423671	−	0.733820i
$125$	−8.48968			−0.759340
$126$		0			0
$127$	0.672570			0.0596809			0.0298405	−	0.999555i	$-0.490500\pi$
$127$	0.672570			0.0596809			0.0298405	+	0.999555i	$0.490500\pi$
$128$	9.55408	+	16.5482i	0.844470	+	1.46266i
$129$		0			0
$130$	−3.19076	+	5.52655i	−0.279848	+	0.484711i
$131$	3.95691	−	6.85356i	0.345717	−	0.598799i	−0.639767	−	0.768569i	$-0.720969\pi$
$131$	3.95691	−	6.85356i	0.345717	−	0.598799i	0.985484	+	0.169770i	$0.0543026\pi$
$132$		0			0
$133$	−2.02704	−	3.51094i	−0.175767	−	0.304437i
$134$	−38.9181			−3.36201
$135$		0			0
$136$	4.78074			0.409945
$137$	−1.83628	−	3.18054i	−0.156884	−	0.271732i	0.776859	−	0.629674i	$-0.216812\pi$
$137$	−1.83628	−	3.18054i	−0.156884	−	0.271732i	−0.933744	+	0.357943i	$0.883478\pi$
$138$		0			0
$139$	1.02704	−	1.77889i	0.0871126	−	0.150883i	−0.819177	−	0.573541i	$-0.805569\pi$
$139$	1.02704	−	1.77889i	0.0871126	−	0.150883i	0.906289	+	0.422658i	$0.138903\pi$
$140$	5.25729	−	9.10590i	0.444322	−	0.769589i
$141$		0			0
$142$	4.02704	+	6.97504i	0.337942	+	0.585332i
$143$	−4.51459			−0.377529
$144$		0			0
$145$	−6.38151			−0.529956
$146$	1.85447	+	3.21204i	0.153477	+	0.265830i
$147$		0			0
$148$	−3.60963	+	6.25206i	−0.296710	+	0.513917i
$149$	−6.77188	+	11.7292i	−0.554774	+	0.960897i	0.443147	+	0.896449i	$0.353862\pi$
$149$	−6.77188	+	11.7292i	−0.554774	+	0.960897i	−0.997921	+	0.0644482i	$0.979471\pi$
$150$		0			0
$151$	−4.96410	−	8.59808i	−0.403973	−	0.699702i	0.590228	−	0.807236i	$-0.299038\pi$
$151$	−4.96410	−	8.59808i	−0.403973	−	0.699702i	−0.994201	+	0.107535i	$0.965704\pi$
$152$	−20.4897			−1.66193
$153$		0			0
$154$	11.1082			0.895122
$155$	−3.01819	−	5.22765i	−0.242427	−	0.419895i
$156$		0			0
$157$	−3.02704	+	5.24299i	−0.241584	+	0.418436i	−0.961166	−	0.275972i	$-0.911000\pi$
$157$	−3.02704	+	5.24299i	−0.241584	+	0.418436i	0.719581	+	0.694408i	$0.244334\pi$
$158$	−18.0957	+	31.3427i	−1.43962	+	2.49349i
$159$		0			0
$160$	−0.699612	−	1.21176i	−0.0553092	−	0.0957983i
$161$	−0.273346			−0.0215427
$162$		0			0
$163$	17.8171			1.39554			0.697772	−	0.716320i	$-0.254175\pi$
$163$	17.8171			1.39554			0.697772	+	0.716320i	$0.254175\pi$
$164$	−12.9861	−	22.4926i	−1.01404	−	1.75637i
$165$		0			0
$166$	−1.16372	+	2.01561i	−0.0903218	+	0.156442i
$167$	−4.23385	+	7.33325i	−0.327625	+	0.567464i	−0.982040	−	0.188672i	$-0.939582\pi$
$167$	−4.23385	+	7.33325i	−0.327625	+	0.567464i	0.654415	+	0.756136i	$0.272915\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	6.03638			0.462969
$171$		0			0
$172$	−42.3068			−3.22586
$173$	8.67830	+	15.0313i	0.659799	+	1.14281i	0.980667	+	0.195682i	$0.0626920\pi$
$173$	8.67830	+	15.0313i	0.659799	+	1.14281i	−0.320868	+	0.947124i	$0.603975\pi$
$174$		0			0
$175$	0.863327	−	1.49533i	0.0652614	−	0.113036i
$176$	9.76829	−	16.9192i	0.736312	−	1.27533i
$177$		0			0
$178$	−17.6623	−	30.5919i	−1.32384	−	2.29296i
$179$	11.3494			0.848295			0.424147	−	0.905593i	$-0.360574\pi$
$179$	11.3494			0.848295			0.424147	+	0.905593i	$0.360574\pi$
$180$		0			0
$181$	21.8889			1.62699			0.813495	−	0.581572i	$-0.197562\pi$
$181$	21.8889			1.62699			0.813495	+	0.581572i	$0.197562\pi$
$182$	1.23025	+	2.13086i	0.0911924	+	0.157950i
$183$		0			0
$184$	−0.690757	+	1.19643i	−0.0509233	+	0.0882018i
$185$	−2.30924	+	3.99973i	−0.169779	+	0.294066i
$186$		0			0
$187$	2.13521	+	3.69829i	0.156142	+	0.270446i
$188$	49.3068			3.59607
$189$		0			0
$190$	−25.8712			−1.87689
$191$	−0.350874	−	0.607731i	−0.0253883	−	0.0439739i	0.853052	−	0.521826i	$-0.174749\pi$
$191$	−0.350874	−	0.607731i	−0.0253883	−	0.0439739i	−0.878440	+	0.477852i	$0.841416\pi$
$192$		0			0
$193$	−6.07227	+	10.5175i	−0.437092	+	0.757065i	−0.997464	−	0.0711760i	$-0.977325\pi$
$193$	−6.07227	+	10.5175i	−0.437092	+	0.757065i	0.560372	+	0.828241i	$0.310658\pi$
$194$	14.1352	−	24.4829i	1.01485	−	1.75777i
$195$		0			0
$196$	−2.02704	−	3.51094i	−0.144789	−	0.250781i
$197$	16.4107			1.16921			0.584607	−	0.811317i	$-0.301249\pi$
$197$	16.4107			1.16921			0.584607	+	0.811317i	$0.301249\pi$
$198$		0			0
$199$	22.7060			1.60959			0.804794	−	0.593555i	$-0.202276\pi$
$199$	22.7060			1.60959			0.804794	+	0.593555i	$0.202276\pi$
$200$	−4.36333	−	7.55750i	−0.308534	−	0.534396i
$201$		0			0
$202$	−4.52704	+	7.84107i	−0.318522	+	0.551696i
$203$	−1.23025	+	2.13086i	−0.0863468	+	0.149557i
$204$		0			0
$205$	−8.30778	−	14.3895i	−0.580241	−	1.00501i
$206$	−23.9325			−1.66745
$207$		0			0
$208$	4.32743			0.300053
$209$	−9.15126	−	15.8505i	−0.633006	−	1.09640i
$210$		0			0
$211$	−2.28074	+	3.95035i	−0.157012	+	0.271954i	−0.933790	−	0.357822i	$-0.883520\pi$
$211$	−2.28074	+	3.95035i	−0.157012	+	0.271954i	0.776778	+	0.629775i	$0.216853\pi$
$212$	−12.7163	+	22.0253i	−0.873362	+	1.51271i
$213$		0			0
$214$	−1.69076	−	2.92848i	−0.115578	−	0.200187i
$215$	−27.0656			−1.84586
$216$		0			0
$217$	−2.32743			−0.157996
$218$	4.18190	+	7.24327i	0.283234	+	0.490576i
$219$		0			0
$220$	23.7345	−	41.1094i	1.60018	−	2.77160i
$221$	−0.472958	+	0.819187i	−0.0318146	+	0.0551045i
$222$		0			0
$223$	−6.66225	−	11.5394i	−0.446137	−	0.772733i	0.551993	−	0.833849i	$-0.313867\pi$
$223$	−6.66225	−	11.5394i	−0.446137	−	0.772733i	−0.998131	+	0.0611159i	$0.980534\pi$
$224$	−0.539495			−0.0360465
$225$		0			0
$226$	−25.5615			−1.70032
$227$	0.690757	+	1.19643i	0.0458472	+	0.0794096i	0.888038	−	0.459769i	$-0.152068\pi$
$227$	0.690757	+	1.19643i	0.0458472	+	0.0794096i	−0.842191	+	0.539179i	$0.818735\pi$
$228$		0			0
$229$	8.98968	−	15.5706i	0.594055	−	1.02893i	−0.399625	−	0.916679i	$-0.630859\pi$
$229$	8.98968	−	15.5706i	0.594055	−	1.02893i	0.993679	−	0.112254i	$-0.0358072\pi$
$230$	−0.872181	+	1.51066i	−0.0575099	+	0.0996101i
$231$		0			0
$232$	6.21780	+	10.7695i	0.408219	+	0.707055i
$233$	18.9823			1.24357			0.621786	−	0.783187i	$-0.286408\pi$
$233$	18.9823			1.24357			0.621786	+	0.783187i	$0.286408\pi$
$234$		0			0
$235$	31.5438			2.05769
$236$	−5.52704	−	9.57312i	−0.359780	−	0.623157i
$237$		0			0
$238$	1.16372	−	2.01561i	0.0754325	−	0.130653i
$239$	2.44592	−	4.23645i	0.158213	−	0.274033i	−0.776011	−	0.630719i	$-0.782760\pi$
$239$	2.44592	−	4.23645i	0.158213	−	0.274033i	0.934224	+	0.356686i	$0.116093\pi$
$240$		0			0
$241$	13.0797	+	22.6546i	0.842535	+	1.45931i	0.887745	+	0.460336i	$0.152271\pi$
$241$	13.0797	+	22.6546i	0.842535	+	1.45931i	−0.0452094	+	0.998978i	$0.514396\pi$
$242$	23.0833			1.48385
$243$		0			0
$244$	−9.21634			−0.590016
$245$	−1.29679	−	2.24611i	−0.0828489	−	0.143498i
$246$		0			0
$247$	2.02704	−	3.51094i	0.128978	−	0.223396i
$248$	−5.88151	+	10.1871i	−0.373477	+	0.646880i
$249$		0			0
$250$	10.4445	+	18.0903i	0.660565	+	1.14413i
$251$	−18.4576			−1.16503			−0.582516	−	0.812819i	$-0.697932\pi$
$251$	−18.4576			−1.16503			−0.582516	+	0.812819i	$0.697932\pi$
$252$		0			0
$253$	−1.23405			−0.0775838
$254$	−0.827430	−	1.43315i	−0.0519176	−	0.0899239i
$255$		0			0
$256$	16.1804	−	28.0253i	1.01128	−	1.75158i
$257$	−5.86693	+	10.1618i	−0.365969	+	0.633876i	−0.988931	−	0.148375i	$-0.952596\pi$
$257$	−5.86693	+	10.1618i	−0.365969	+	0.633876i	0.622962	+	0.782252i	$0.285929\pi$
$258$		0			0
$259$	0.890369	+	1.54216i	0.0553248	+	0.0958254i
$260$	10.5146			0.652087
$261$		0			0
$262$	−19.4720			−1.20298
$263$	−3.76089	−	6.51406i	−0.231907	−	0.401674i	0.726463	−	0.687206i	$-0.241163\pi$
$263$	−3.76089	−	6.51406i	−0.231907	−	0.401674i	−0.958369	+	0.285532i	$0.907830\pi$
$264$		0			0
$265$	−8.13521	+	14.0906i	−0.499742	+	0.865579i
$266$	−4.98755	+	8.63868i	−0.305806	+	0.529672i
$267$		0			0
$268$	32.0620	+	55.5329i	1.95850	+	3.39221i
$269$	18.8348			1.14838			0.574190	−	0.818722i	$-0.305317\pi$
$269$	18.8348			1.14838			0.574190	+	0.818722i	$0.305317\pi$
$270$		0			0
$271$	−23.9823			−1.45682			−0.728410	−	0.685141i	$-0.759740\pi$
$271$	−23.9823			−1.45682			−0.728410	+	0.685141i	$0.759740\pi$
$272$	−2.04669	−	3.54498i	−0.124099	−	0.214946i
$273$		0			0
$274$	−4.51819	+	7.82573i	−0.272954	+	0.472770i
$275$	3.89757	−	6.75078i	0.235032	−	0.407088i
$276$		0			0
$277$	−3.58113	−	6.20269i	−0.215169	−	0.372684i	0.738156	−	0.674630i	$-0.235697\pi$
$277$	−3.58113	−	6.20269i	−0.215169	−	0.372684i	−0.953325	+	0.301947i	$0.902364\pi$
$278$	−5.05408			−0.303124
$279$		0			0
$280$	−13.1082			−0.783363
$281$	7.44085	+	12.8879i	0.443884	+	0.768830i	0.997974	−	0.0636271i	$-0.0202668\pi$
$281$	7.44085	+	12.8879i	0.443884	+	0.768830i	−0.554090	+	0.832457i	$0.686933\pi$
$282$		0			0
$283$	−9.99854	+	17.3180i	−0.594351	+	1.02945i	0.399287	+	0.916826i	$0.369258\pi$
$283$	−9.99854	+	17.3180i	−0.594351	+	1.02945i	−0.993638	+	0.112621i	$0.964076\pi$
$284$	6.63521	−	11.4925i	0.393727	−	0.681956i
$285$		0			0
$286$	5.55408	+	9.61996i	0.328420	+	0.568840i
$287$	−6.40642			−0.378159
$288$		0			0
$289$	−16.1052			−0.947367
$290$	7.85087	+	13.5981i	0.461019	+	0.798509i
$291$		0			0
$292$	3.05555	−	5.29236i	0.178812	−	0.309712i
$293$	7.53278	−	13.0472i	0.440070	−	0.762223i	−0.557625	−	0.830093i	$-0.688287\pi$
$293$	7.53278	−	13.0472i	0.440070	−	0.762223i	0.997694	+	0.0678705i	$0.0216205\pi$
$294$		0			0
$295$	−3.53590	−	6.12435i	−0.205868	−	0.356574i
$296$	9.00000			0.523114
$297$		0			0
$298$	33.3245			1.93044
$299$	−0.136673	−	0.236725i	−0.00790401	−	0.0136901i
$300$		0			0
$301$	−5.21780	+	9.03749i	−0.300749	+	0.520912i
$302$	−12.2142	+	21.1556i	−0.702848	+	1.21737i
$303$		0			0
$304$	8.77188	+	15.1933i	0.503102	+	0.871398i
$305$	−5.89610			−0.337610
$306$		0			0
$307$	−27.2704			−1.55641			−0.778203	−	0.628013i	$-0.783868\pi$
$307$	−27.2704			−1.55641			−0.778203	+	0.628013i	$0.783868\pi$
$308$	−9.15126	−	15.8505i	−0.521442	−	0.903163i
$309$		0			0
$310$	−7.42627	+	12.8627i	−0.421784	+	0.730551i
$311$	−7.99115	+	13.8411i	−0.453136	+	0.784855i	−0.998579	−	0.0532931i	$-0.983028\pi$
$311$	−7.99115	+	13.8411i	−0.453136	+	0.784855i	0.545443	+	0.838148i	$0.316362\pi$
$312$		0			0
$313$	−5.79893	−	10.0440i	−0.327775	−	0.567722i	0.654295	−	0.756239i	$-0.272965\pi$
$313$	−5.79893	−	10.0440i	−0.327775	−	0.567722i	−0.982070	+	0.188517i	$0.939632\pi$
$314$	14.8961			0.840636
$315$		0			0
$316$	59.6313			3.35452
$317$	−1.00885	−	1.74739i	−0.0566629	−	0.0981430i	0.836303	−	0.548268i	$-0.184713\pi$
$317$	−1.00885	−	1.74739i	−0.0566629	−	0.0981430i	−0.892965	+	0.450125i	$0.851379\pi$
$318$		0			0
$319$	−5.55408	+	9.61996i	−0.310969	+	0.538614i
$320$	9.50214	−	16.4582i	0.531186	−	0.920040i
$321$		0			0
$322$	0.336285	+	0.582462i	0.0187404	+	0.0324594i
$323$	−3.83482			−0.213375
$324$		0			0
$325$	1.72665			0.0957775
$326$	−21.9195	−	37.9658i	−1.21401	−	2.10273i
$327$		0			0
$328$	−16.1893	+	28.0407i	−0.893904	+	1.54829i
$329$	6.08113	−	10.5328i	0.335263	−	0.580693i
$330$		0			0
$331$	9.85447	+	17.0684i	0.541651	+	0.938167i	0.998809	+	0.0487815i	$0.0155338\pi$
$331$	9.85447	+	17.0684i	0.541651	+	0.938167i	−0.457159	+	0.889385i	$0.651133\pi$
$332$	3.83482			0.210463
$333$		0			0
$334$	20.8348			1.14003
$335$	20.5115	+	35.5269i	1.12066	+	1.94104i
$336$		0			0
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	−0.133929	−	0.990991i	$-0.542759\pi$
$337$	14.5256	−	25.1590i	0.791259	−	1.37050i	0.925188	−	0.379509i	$-0.123907\pi$
$338$	14.7630	−	25.5703i	0.803003	−	1.39084i
$339$		0			0
$340$	−4.97296	−	8.61342i	−0.269697	−	0.467128i
$341$	−10.5074			−0.569007
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	26.3712	+	45.6763i	1.42184	+	2.46270i
$345$		0			0
$346$	21.3530	−	36.9845i	1.14794	−	1.98830i
$347$	14.5416	−	25.1868i	0.780636	−	1.35210i	−0.150936	−	0.988544i	$-0.548229\pi$
$347$	14.5416	−	25.1868i	0.780636	−	1.35210i	0.931572	−	0.363557i	$-0.118438\pi$
$348$		0			0
$349$	−12.3815	−	21.4454i	−0.662767	−	1.14795i	−0.979885	−	0.199561i	$-0.936049\pi$
$349$	−12.3815	−	21.4454i	−0.662767	−	1.14795i	0.317118	−	0.948386i	$-0.397285\pi$
$350$	−4.24844			−0.227089
$351$		0			0
$352$	−2.43560			−0.129818
$353$	−16.6513	−	28.8408i	−0.886257	−	1.53504i	−0.844266	−	0.535925i	$-0.819963\pi$
$353$	−16.6513	−	28.8408i	−0.886257	−	1.53504i	−0.0419914	−	0.999118i	$-0.513370\pi$
$354$		0			0
$355$	4.24484	−	7.35228i	0.225293	−	0.390219i
$356$	−29.1015	+	50.4052i	−1.54237	+	2.67147i
$357$		0			0
$358$	−13.9626	−	24.1840i	−0.737949	−	1.27816i
$359$	−25.5366			−1.34777			−0.673884	−	0.738837i	$-0.735375\pi$
$359$	−25.5366			−1.34777			−0.673884	+	0.738837i	$0.735375\pi$
$360$		0			0
$361$	−2.56440			−0.134968
$362$	−26.9289	−	46.6422i	−1.41535	−	2.45146i
$363$		0			0
$364$	2.02704	−	3.51094i	0.106246	−	0.184023i
$365$	1.95477	−	3.38576i	0.102317	−	0.177219i
$366$		0			0
$367$	−13.7252	−	23.7727i	−0.716449	−	1.24093i	−0.962398	−	0.271644i	$-0.912433\pi$
$367$	−13.7252	−	23.7727i	−0.716449	−	1.24093i	0.245949	−	0.969283i	$-0.420900\pi$
$368$	1.18289			0.0616622
$369$		0			0
$370$	11.3638			0.590776
$371$	3.13667	+	5.43288i	0.162848	+	0.282061i
$372$		0			0
$373$	−8.16372	+	14.1400i	−0.422701	+	0.732140i	−0.996203	−	0.0870646i	$-0.972251\pi$
$373$	−8.16372	+	14.1400i	−0.422701	+	0.732140i	0.573502	+	0.819204i	$0.305585\pi$
$374$	5.25370	−	9.09967i	0.271662	−	0.470533i
$375$		0			0
$376$	−30.7345	−	53.2338i	−1.58501	−	2.74532i
$377$	−2.46050			−0.126722
$378$		0			0
$379$	12.0364			0.618267			0.309134	−	0.951019i	$-0.399961\pi$
$379$	12.0364			0.618267			0.309134	+	0.951019i	$0.399961\pi$
$380$	21.3135	+	36.9161i	1.09336	+	1.89376i
$381$		0			0
$382$	−0.863327	+	1.49533i	−0.0441716	+	0.0765075i
$383$	−6.21780	+	10.7695i	−0.317715	+	0.550298i	−0.980011	−	0.198944i	$-0.936249\pi$
$383$	−6.21780	+	10.7695i	−0.317715	+	0.550298i	0.662296	+	0.749242i	$0.269582\pi$
$384$		0			0
$385$	−5.85447	−	10.1402i	−0.298372	−	0.516795i
$386$	29.8817			1.52094
$387$		0			0
$388$	−46.5801			−2.36475
$389$	10.3004	+	17.8408i	0.522250	+	0.904564i	0.999665	+	0.0258860i	$0.00824070\pi$
$389$	10.3004	+	17.8408i	0.522250	+	0.904564i	−0.477414	+	0.878678i	$0.658426\pi$
$390$		0			0
$391$	−0.129281	+	0.223922i	−0.00653803	+	0.0113242i
$392$	−2.52704	+	4.37697i	−0.127635	+	0.221070i
$393$		0			0
$394$	−20.1893	−	34.9689i	−1.01712	−	1.76171i
$395$	38.1488			1.91948
$396$		0			0
$397$	−23.6372			−1.18631			−0.593157	−	0.805087i	$-0.702119\pi$
$397$	−23.6372			−1.18631			−0.593157	+	0.805087i	$0.702119\pi$
$398$	−27.9341	−	48.3833i	−1.40021	−	2.42524i
$399$		0			0
$400$	−3.73599	+	6.47092i	−0.186799	+	0.323546i
$401$	−1.28220	+	2.22084i	−0.0640300	+	0.110903i	−0.896263	−	0.443522i	$-0.853729\pi$
$401$	−1.28220	+	2.22084i	−0.0640300	+	0.110903i	0.832233	+	0.554426i	$0.187062\pi$
$402$		0			0
$403$	−1.16372	−	2.01561i	−0.0579688	−	0.100405i
$404$	14.9181			0.742202
$405$		0			0
$406$	6.05408			0.300459
$407$	4.01965	+	6.96224i	0.199247	+	0.345105i
$408$		0			0
$409$	17.1623	−	29.7259i	0.848619	−	1.46985i	−0.0338223	−	0.999428i	$-0.510768\pi$
$409$	17.1623	−	29.7259i	0.848619	−	1.46985i	0.882441	−	0.470423i	$-0.155899\pi$
$410$	−20.4413	+	35.4054i	−1.00953	+	1.74855i
$411$		0			0
$412$	19.7163	+	34.1497i	0.971354	+	1.68243i
$413$	−2.72665			−0.134170
$414$		0			0
$415$	2.45331			0.120428
$416$	−0.269748	−	0.467216i	−0.0132255	−	0.0229072i
$417$		0			0
$418$	−22.5167	+	39.0001i	−1.10133	+	1.90756i
$419$	2.02850	−	3.51347i	0.0990989	−	0.171644i	−0.812213	−	0.583361i	$-0.801737\pi$
$419$	2.02850	−	3.51347i	0.0990989	−	0.171644i	0.911312	+	0.411717i	$0.135071\pi$
$420$		0			0
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	0.999879	+	0.0155624i	$0.00495387\pi$
$421$	10.5344	+	18.2462i	0.513417	+	0.889264i	−0.486462	+	0.873702i	$0.661713\pi$
$422$	11.2235			0.546353
$423$		0			0
$424$	31.7060			1.53978
$425$	−0.816635	−	1.41445i	−0.0396126	−	0.0686110i
$426$		0			0
$427$	−1.13667	+	1.96878i	−0.0550075	+	0.0952757i
$428$	−2.78580	+	4.82515i	−0.134657	+	0.233232i
$429$		0			0
$430$	33.2975	+	57.6729i	1.60575	+	2.78123i
$431$	−22.6185			−1.08949			−0.544747	−	0.838600i	$-0.683374\pi$
$431$	−22.6185			−1.08949			−0.544747	+	0.838600i	$0.683374\pi$
$432$		0			0
$433$	2.41789			0.116196			0.0580982	−	0.998311i	$-0.481496\pi$
$433$	2.41789			0.116196			0.0580982	+	0.998311i	$0.481496\pi$
$434$	2.86333	+	4.95943i	0.137444	+	0.238060i
$435$		0			0
$436$	6.89037	−	11.9345i	0.329989	−	0.571557i
$437$	0.554084	−	0.959702i	0.0265054	−	0.0459088i
$438$		0			0
$439$	11.7448	+	20.3427i	0.560551	+	0.970902i	0.997448	+	0.0713911i	$0.0227438\pi$
$439$	11.7448	+	20.3427i	0.560551	+	0.970902i	−0.436898	+	0.899511i	$0.643923\pi$
$440$	−59.1780			−2.82120
$441$		0			0
$442$	2.32743			0.110705
$443$	−6.70895	−	11.6202i	−0.318752	−	0.552094i	0.661476	−	0.749966i	$-0.269930\pi$
$443$	−6.70895	−	11.6202i	−0.318752	−	0.552094i	−0.980228	+	0.197872i	$0.936597\pi$
$444$		0			0
$445$	−18.6175	+	32.2465i	−0.882554	+	1.52863i
$446$	−16.3925	+	28.3927i	−0.776208	+	1.34443i
$447$		0			0
$448$	−3.66372	−	6.34574i	−0.173094	−	0.299808i
$449$	9.16225			0.432393			0.216197	−	0.976350i	$-0.430635\pi$
$449$	9.16225			0.432393			0.216197	+	0.976350i	$0.430635\pi$
$450$		0			0
$451$	−28.9224			−1.36190
$452$	21.0584	+	36.4741i	0.990502	+	1.71560i
$453$		0			0
$454$	1.69961	−	2.94381i	0.0797667	−	0.138160i
$455$	1.29679	−	2.24611i	0.0607944	−	0.105299i
$456$		0			0
$457$	−4.40856	−	7.63584i	−0.206224	−	0.357190i	0.744298	−	0.667847i	$-0.232784\pi$
$457$	−4.40856	−	7.63584i	−0.206224	−	0.357190i	−0.950522	+	0.310658i	$0.899451\pi$
$458$	−44.2383			−2.06712
$459$		0			0
$460$	2.87412			0.134007
$461$	−2.82957	−	4.90095i	−0.131786	−	0.228260i	0.792579	−	0.609769i	$-0.208738\pi$
$461$	−2.82957	−	4.90095i	−0.131786	−	0.228260i	−0.924365	+	0.381509i	$0.875405\pi$
$462$		0			0
$463$	−7.86333	+	13.6197i	−0.365440	+	0.632960i	−0.988847	−	0.148937i	$-0.952415\pi$
$463$	−7.86333	+	13.6197i	−0.365440	+	0.632960i	0.623407	+	0.781898i	$0.285748\pi$
$464$	5.32383	−	9.22115i	0.247153	−	0.428081i
$465$		0			0
$466$	−23.3530	−	40.4486i	−1.08181	−	1.87375i
$467$	21.9971			1.01790			0.508952	−	0.860795i	$-0.330033\pi$
$467$	21.9971			1.01790			0.508952	+	0.860795i	$0.330033\pi$
$468$		0			0
$469$	15.8171			0.730366
$470$	−38.8068	−	67.2153i	−1.79002	−	3.10041i
$471$		0			0
$472$	−6.89037	+	11.9345i	−0.317155	+	0.549328i
$473$	−23.5562	+	40.8006i	−1.08312	+	1.87601i
$474$		0			0
$475$	3.50000	+	6.06218i	0.160591	+	0.278152i
$476$	−3.83482			−0.175769
$477$		0			0
$478$	−12.0364			−0.550531
$479$	12.4875	+	21.6291i	0.570571	+	0.988257i	0.996507	+	0.0835043i	$0.0266112\pi$
$479$	12.4875	+	21.6291i	0.570571	+	0.988257i	−0.425937	+	0.904753i	$0.640055\pi$
$480$		0			0
$481$	−0.890369	+	1.54216i	−0.0405973	+	0.0703166i
$482$	32.1826	−	55.7419i	1.46588	−	2.53897i
$483$		0			0
$484$	−19.0167	−	32.9379i	−0.864397	−	1.49718i
$485$	−29.7994			−1.35312
$486$		0			0
$487$	−17.5979			−0.797435			−0.398717	−	0.917074i	$-0.630545\pi$
$487$	−17.5979			−0.797435			−0.398717	+	0.917074i	$0.630545\pi$
$488$	5.74484	+	9.95036i	0.260057	+	0.450432i
$489$		0			0
$490$	−3.19076	+	5.52655i	−0.144144	+	0.249664i
$491$	6.89757	−	11.9469i	0.311283	−	0.539158i	−0.667358	−	0.744737i	$-0.732575\pi$
$491$	6.89757	−	11.9469i	0.311283	−	0.539158i	0.978640	+	0.205580i	$0.0659080\pi$
$492$		0			0
$493$	1.16372	+	2.01561i	0.0524111	+	0.0907787i
$494$	−9.97509			−0.448801
$495$		0			0
$496$	10.0718			0.452237
$497$	−1.63667	−	2.83480i	−0.0734148	−	0.127158i
$498$		0			0
$499$	−6.54377	+	11.3341i	−0.292939	+	0.507386i	−0.974503	−	0.224373i	$-0.927967\pi$
$499$	−6.54377	+	11.3341i	−0.292939	+	0.507386i	0.681564	+	0.731758i	$0.261300\pi$
$500$	17.2089	−	29.8068i	0.769607	−	1.33300i
$501$		0			0
$502$	22.7075	+	39.3305i	1.01348	+	1.75541i
$503$	22.3068			0.994611			0.497305	−	0.867576i	$-0.334323\pi$
$503$	22.3068			0.994611			0.497305	+	0.867576i	$0.334323\pi$
$504$		0			0
$505$	9.54377			0.424692
$506$	1.51819	+	2.62958i	0.0674917	+	0.116899i
$507$		0			0
$508$	−1.36333	+	2.36135i	−0.0604879	+	0.104768i
$509$	−7.94659	+	13.7639i	−0.352226	+	0.610074i	−0.986639	−	0.162920i	$-0.947909\pi$
$509$	−7.94659	+	13.7639i	−0.352226	+	0.610074i	0.634413	+	0.772994i	$0.281242\pi$
$510$		0			0
$511$	−0.753696	−	1.30544i	−0.0333415	−	0.0577492i
$512$	−41.4078			−1.82998
$513$		0			0
$514$	28.8712			1.27345
$515$	12.6134	+	21.8471i	0.555814	+	0.962698i
$516$		0			0
$517$	27.4538	−	47.5514i	1.20742	−	2.09131i
$518$	2.19076	−	3.79450i	0.0962563	−	0.166721i
$519$		0			0
$520$	−6.55408	−	11.3520i	−0.287416	−	0.497818i
$521$	−4.41789			−0.193551			−0.0967756	−	0.995306i	$-0.530853\pi$
$521$	−4.41789			−0.193551			−0.0967756	+	0.995306i	$0.530853\pi$
$522$		0			0
$523$	25.2733			1.10513			0.552563	−	0.833471i	$-0.313650\pi$
$523$	25.2733			1.10513			0.552563	+	0.833471i	$0.313650\pi$
$524$	16.0416	+	27.7849i	0.700782	+	1.21379i
$525$		0			0
$526$	−9.25370	+	16.0279i	−0.403480	+	0.698848i
$527$	−1.10078	+	1.90660i	−0.0479506	+	0.0830528i
$528$		0			0
$529$	11.4626	+	19.8539i	0.498376	+	0.863212i
$530$	40.0335			1.73894
$531$		0			0
$532$	16.4356			0.712574
$533$	−3.20321	−	5.54812i	−0.138746	−	0.240316i
$534$		0			0
$535$	−1.78220	+	3.08686i	−0.0770513	+	0.133457i
$536$	39.9705	−	69.2310i	1.72646	−	2.99032i
$537$		0			0
$538$	−23.1716	−	40.1344i	−0.998998	−	1.73032i
$539$	−4.51459			−0.194457
$540$		0			0
$541$	−3.43852			−0.147834			−0.0739168	−	0.997264i	$-0.523550\pi$
$541$	−3.43852			−0.147834			−0.0739168	+	0.997264i	$0.523550\pi$
$542$	29.5043	+	51.1029i	1.26732	+	2.19506i
$543$		0			0
$544$	−0.255158	+	0.441947i	−0.0109398	+	0.0189483i
$545$	4.40808	−	7.63501i	0.188821	−	0.327048i
$546$		0			0
$547$	3.46410	+	6.00000i	0.148114	+	0.256542i	0.930531	−	0.366214i	$-0.119346\pi$
$547$	3.46410	+	6.00000i	0.148114	+	0.256542i	−0.782416	+	0.622756i	$0.786013\pi$
$548$	14.8889			0.636023
$549$		0			0
$550$	−19.1800			−0.817836
$551$	−4.98755	−	8.63868i	−0.212477	−	0.368020i
$552$		0			0
$553$	7.35447	−	12.7383i	0.312744	−	0.541688i
$554$	−8.81138	+	15.2618i	−0.374360	+	0.648410i
$555$		0			0
$556$	4.16372	+	7.21177i	0.176581	+	0.305847i
$557$	−33.5835			−1.42298			−0.711488	−	0.702698i	$-0.751979\pi$
$557$	−33.5835			−1.42298			−0.711488	+	0.702698i	$0.751979\pi$
$558$		0			0
$559$	−10.4356			−0.441379
$560$	5.61177	+	9.71987i	0.237140	+	0.410739i
$561$		0			0
$562$	18.3083	−	31.7108i	0.772287	−	1.33764i
$563$	21.2396	−	36.7880i	0.895142	−	1.55043i	0.0615128	−	0.998106i	$-0.480407\pi$
$563$	21.2396	−	36.7880i	0.895142	−	1.55043i	0.833629	−	0.552325i	$-0.186259\pi$
$564$		0			0
$565$	13.4720	+	23.3341i	0.566770	+	0.981675i
$566$	49.2029			2.06815
$567$		0			0
$568$	−16.5438			−0.694161
$569$	5.20175	+	9.00969i	0.218069	+	0.377706i	0.954217	−	0.299114i	$-0.0966910\pi$
$569$	5.20175	+	9.00969i	0.218069	+	0.377706i	−0.736149	+	0.676820i	$0.763358\pi$
$570$		0			0
$571$	−8.92480	+	15.4582i	−0.373491	+	0.646906i	−0.990100	−	0.140364i	$-0.955173\pi$
$571$	−8.92480	+	15.4582i	−0.373491	+	0.646906i	0.616609	+	0.787270i	$0.288506\pi$
$572$	9.15126	−	15.8505i	0.382633	−	0.662741i
$573$		0			0
$574$	7.88151	+	13.6512i	0.328968	+	0.569789i
$575$	0.471974			0.0196827
$576$		0			0
$577$	11.9430			0.497193			0.248597	−	0.968607i	$-0.420031\pi$
$577$	11.9430			0.497193			0.248597	+	0.968607i	$0.420031\pi$
$578$	19.8135	+	34.3180i	0.824134	+	1.42744i
$579$		0			0
$580$	12.9356	−	22.4051i	0.537122	−	0.930322i
$581$	0.472958	−	0.819187i	0.0196216	−	0.0339856i
$582$		0			0
$583$	14.1608	+	24.5272i	0.586480	+	1.01581i
$584$	−7.61849			−0.315255
$585$		0			0
$586$	−37.0689			−1.53130
$587$	11.9299	+	20.6631i	0.492398	+	0.852859i	0.999962	−	0.00875568i	$-0.00278706\pi$
$587$	11.9299	+	20.6631i	0.492398	+	0.852859i	−0.507563	+	0.861614i	$0.669454\pi$
$588$		0			0
$589$	4.71780	−	8.17147i	0.194394	−	0.336699i
$590$	−8.70009	+	15.0690i	−0.358177	+	0.620381i
$591$		0			0
$592$	−3.85301	−	6.67361i	−0.158358	−	0.274284i
$593$	−19.5801			−0.804060			−0.402030	−	0.915626i	$-0.631695\pi$
$593$	−19.5801			−0.804060			−0.402030	+	0.915626i	$0.631695\pi$
$594$		0			0
$595$	−2.45331			−0.100576
$596$	−27.4538	−	47.5514i	−1.12455	−	1.94778i
$597$		0			0
$598$	−0.336285	+	0.582462i	−0.0137517	+	0.0238187i
$599$	9.27335	−	16.0619i	0.378899	−	0.656272i	−0.612004	−	0.790855i	$-0.709636\pi$
$599$	9.27335	−	16.0619i	0.378899	−	0.656272i	0.990902	+	0.134583i	$0.0429696\pi$
$600$		0			0
$601$	9.09931	+	15.7605i	0.371169	+	0.642883i	0.989746	−	0.142841i	$-0.0456238\pi$
$601$	9.09931	+	15.7605i	0.371169	+	0.642883i	−0.618577	+	0.785724i	$0.712290\pi$
$602$	25.6768			1.04651
$603$		0			0
$604$	40.2498			1.63774
$605$	−12.1659	−	21.0719i	−0.494612	−	0.856693i
$606$		0			0
$607$	11.1549	−	19.3208i	0.452762	−	0.784206i	−0.545795	−	0.837919i	$-0.683772\pi$
$607$	11.1549	−	19.3208i	0.452762	−	0.784206i	0.998556	+	0.0537125i	$0.0171055\pi$
$608$	1.09358	−	1.89413i	0.0443505	−	0.0768173i
$609$		0			0
$610$	7.25370	+	12.5638i	0.293694	+	0.508692i
$611$	12.1623			0.492032
$612$		0			0
$613$	10.2370			0.413467			0.206734	−	0.978397i	$-0.433717\pi$
$613$	10.2370			0.413467			0.206734	+	0.978397i	$0.433717\pi$
$614$	33.5495	+	58.1094i	1.35395	+	2.34511i
$615$		0			0
$616$	−11.4086	+	19.7602i	−0.459664	+	0.796161i
$617$	−5.66372	+	9.80984i	−0.228013	+	0.394929i	−0.957219	−	0.289364i	$-0.906556\pi$
$617$	−5.66372	+	9.80984i	−0.228013	+	0.394929i	0.729206	+	0.684294i	$0.239889\pi$
$618$		0			0
$619$	−4.31663	−	7.47663i	−0.173500	−	0.300511i	0.766141	−	0.642672i	$-0.222174\pi$
$619$	−4.31663	−	7.47663i	−0.173500	−	0.300511i	−0.939641	+	0.342161i	$0.888841\pi$
$620$	24.4720			0.982818
$621$		0			0
$622$	39.3245			1.57677
$623$	7.17830	+	12.4332i	0.287593	+	0.498125i
$624$		0			0
$625$	15.3260	−	26.5454i	0.613039	−	1.06181i
$626$	−14.2683	+	24.7134i	−0.570275	+	0.987746i
$627$		0			0
$628$	−12.2719	−	21.2555i	−0.489701	−	0.848188i
$629$	1.68443			0.0671626
$630$		0			0
$631$	−14.8535			−0.591308			−0.295654	−	0.955295i	$-0.595538\pi$
$631$	−14.8535			−0.591308			−0.295654	+	0.955295i	$0.595538\pi$
$632$	−37.1701	−	64.3805i	−1.47855	−	2.56092i
$633$		0			0
$634$	−2.48229	+	4.29945i	−0.0985844	+	0.170753i
$635$	−0.872181	+	1.51066i	−0.0346115	+	0.0599488i
$636$		0			0
$637$	−0.500000	−	0.866025i	−0.0198107	−	0.0343132i
$638$	27.3317			1.08207
$639$		0			0
$640$	−49.5586			−1.95897
$641$	−17.0797	−	29.5828i	−0.674606	−	1.16845i	−0.976584	−	0.215137i	$-0.930980\pi$
$641$	−17.0797	−	29.5828i	−0.674606	−	1.16845i	0.301978	−	0.953315i	$-0.402353\pi$
$642$		0			0
$643$	5.41741	−	9.38323i	0.213642	−	0.370039i	−0.739210	−	0.673475i	$-0.764801\pi$
$643$	5.41741	−	9.38323i	0.213642	−	0.370039i	0.952852	+	0.303437i	$0.0981341\pi$
$644$	0.554084	−	0.959702i	0.0218340	−	0.0378176i
$645$		0			0
$646$	4.71780	+	8.17147i	0.185619	+	0.321502i
$647$	−32.9692			−1.29615			−0.648077	−	0.761575i	$-0.724427\pi$
$647$	−32.9692			−1.29615			−0.648077	+	0.761575i	$0.724427\pi$
$648$		0			0
$649$	−12.3097			−0.483199
$650$	−2.12422	−	3.67926i	−0.0833188	−	0.144312i
$651$		0			0
$652$	−36.1160	+	62.5548i	−1.41441	+	2.44984i
$653$	−1.96557	+	3.40446i	−0.0769185	+	0.133227i	−0.901919	−	0.431905i	$-0.857841\pi$
$653$	−1.96557	+	3.40446i	−0.0769185	+	0.133227i	0.825000	+	0.565132i	$0.191175\pi$
$654$		0			0
$655$	10.2626	+	17.7753i	0.400991	+	0.694537i
$656$	27.7233			1.08241
$657$		0			0
$658$	−29.9253			−1.16661
$659$	8.40856	+	14.5640i	0.327551	+	0.567335i	0.982025	−	0.188749i	$-0.0604434\pi$
$659$	8.40856	+	14.5640i	0.327551	+	0.567335i	−0.654474	+	0.756084i	$0.727110\pi$
$660$		0			0
$661$	8.51080	−	14.7411i	0.331032	−	0.573364i	−0.651683	−	0.758492i	$-0.725937\pi$
$661$	8.51080	−	14.7411i	0.331032	−	0.573364i	0.982714	+	0.185128i	$0.0592700\pi$
$662$	24.2470	−	41.9970i	0.942386	−	1.63226i
$663$		0			0
$664$	−2.39037	−	4.14024i	−0.0927643	−	0.160672i
$665$	10.5146			0.407738
$666$		0			0
$667$	−0.672570			−0.0260420
$668$	−17.1644	−	29.7296i	−0.664110	−	1.15027i
$669$		0			0
$670$	50.4686	−	87.4141i	1.94977	−	3.37710i
$671$	−5.13161	+	8.88821i	−0.198104	+	0.343126i
$672$		0			0
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	−0.997979	−	0.0635501i	$-0.979758\pi$
$673$	−14.3727	−	24.8942i	−0.554025	−	0.959600i	0.443953	−	0.896050i	$-0.353576\pi$
$674$	−71.4805			−2.75333
$675$		0			0
$676$	−48.6490			−1.87112
$677$	−3.01819	−	5.22765i	−0.115998	−	0.200915i	0.802180	−	0.597082i	$-0.203673\pi$
$677$	−3.01819	−	5.22765i	−0.115998	−	0.200915i	−0.918178	+	0.396167i	$0.870340\pi$
$678$		0			0
$679$	−5.74484	+	9.95036i	−0.220467	+	0.381860i
$680$	−6.19961	+	10.7380i	−0.237744	+	0.411785i
$681$		0			0
$682$	12.9267	+	22.3898i	0.494991	+	0.857349i
$683$	−20.5113			−0.784842			−0.392421	−	0.919786i	$-0.628362\pi$
$683$	−20.5113			−0.784842			−0.392421	+	0.919786i	$0.628362\pi$
$684$		0			0
$685$	9.52510			0.363935
$686$	1.23025	+	2.13086i	0.0469713	+	0.0813566i
$687$		0			0
$688$	22.5797	−	39.1091i	0.860842	−	1.49102i
$689$	−3.13667	+	5.43288i	−0.119498	+	0.206976i
$690$		0			0
$691$	7.50146	+	12.9929i	0.285369	+	0.494274i	0.972699	−	0.232072i	$-0.0745505\pi$
$691$	7.50146	+	12.9929i	0.285369	+	0.494274i	−0.687330	+	0.726346i	$0.741217\pi$
$692$	−70.3652			−2.67488
$693$		0			0
$694$	−71.5595			−2.71636
$695$	2.66372	+	4.61369i	0.101040	+	0.175007i
$696$		0			0
$697$	−3.02997	+	5.24806i	−0.114768	+	0.198784i
$698$	−30.4648	+	52.7665i	−1.15311	+	1.99724i
$699$		0			0
$700$	3.50000	+	6.06218i	0.132288	+	0.229129i
$701$	−38.5113			−1.45455			−0.727275	−	0.686346i	$-0.759214\pi$
$701$	−38.5113			−1.45455			−0.727275	+	0.686346i	$0.759214\pi$
$702$		0			0
$703$	−7.21926			−0.272280
$704$	−16.5402	−	28.6484i	−0.623381	−	1.07973i
$705$		0			0
$706$	−40.9705	+	70.9630i	−1.54195	+	2.67073i
$707$	1.83988	−	3.18677i	0.0691959	−	0.119851i
$708$		0			0
$709$	−3.82004	−	6.61650i	−0.143465	−	0.248488i	0.785334	−	0.619072i	$-0.212491\pi$
$709$	−3.82004	−	6.61650i	−0.143465	−	0.248488i	−0.928799	+	0.370584i	$0.879158\pi$
$710$	−20.8889			−0.783947
$711$		0			0
$712$	72.5595			2.71928
$713$	−0.318097	−	0.550960i	−0.0119128	−	0.0206336i
$714$		0			0
$715$	5.85447	−	10.1402i	0.218945	−	0.379224i
$716$	−23.0057	+	39.8471i	−0.859765	+	1.48916i
$717$		0			0
$718$	31.4164	+	54.4148i	1.17245	+	2.03074i
$719$	30.0364			1.12017			0.560084	−	0.828436i	$-0.310769\pi$
$719$	30.0364			1.12017			0.560084	+	0.828436i	$0.310769\pi$
$720$		0			0
$721$	9.72665			0.362240
$722$	3.15486	+	5.46438i	0.117412	+	0.203363i
$723$		0			0
$724$	−44.3697	+	76.8506i	−1.64899	+	2.85613i
$725$	2.12422	−	3.67926i	0.0788916	−	0.136644i
$726$		0			0
$727$	−1.72812	−	2.99319i	−0.0640923	−	0.111011i	0.832199	−	0.554478i	$-0.187082\pi$
$727$	−1.72812	−	2.99319i	−0.0640923	−	0.111011i	−0.896291	+	0.443466i	$0.853749\pi$
$728$	−5.05408			−0.187317
$729$		0			0
$730$	−9.61944			−0.356032
$731$	4.93560	+	8.54871i	0.182550	+	0.316185i
$732$		0			0
$733$	−19.2630	+	33.3645i	−0.711496	+	1.23235i	0.252799	+	0.967519i	$0.418649\pi$
$733$	−19.2630	+	33.3645i	−0.711496	+	1.23235i	−0.964295	+	0.264829i	$0.914685\pi$
$734$	−33.7709	+	58.4929i	−1.24651	+	2.15901i
$735$		0			0
$736$	−0.0737345	−	0.127712i	−0.00271789	−	0.00470752i
$737$	71.4078			2.63034
$738$		0			0
$739$	45.1239			1.65991			0.829955	−	0.557830i	$-0.188366\pi$
$739$	45.1239			1.65991			0.829955	+	0.557830i	$0.188366\pi$
$740$	−9.36186	−	16.2152i	−0.344149	−	0.596084i
$741$		0			0
$742$	7.71780	−	13.3676i	0.283329	−	0.490741i
$743$	4.74338	−	8.21577i	0.174018	−	0.301407i	−0.765803	−	0.643075i	$-0.777658\pi$
$743$	4.74338	−	8.21577i	0.174018	−	0.301407i	0.939821	+	0.341668i	$0.110992\pi$
$744$		0			0
$745$	−17.5634	−	30.4207i	−0.643474	−	1.11453i
$746$	40.1737			1.47086
$747$		0			0
$748$	−17.3126			−0.633013
$749$	0.687159	+	1.19019i	0.0251082	+	0.0434887i
$750$		0			0
$751$	4.91595	−	8.51467i	0.179386	−	0.310705i	−0.762285	−	0.647242i	$-0.775922\pi$
$751$	4.91595	−	8.51467i	0.179386	−	0.310705i	0.941670	+	0.336537i	$0.109256\pi$
$752$	−26.3157	+	45.5800i	−0.959633	+	1.66213i
$753$		0			0
$754$	3.02704	+	5.24299i	0.110238	+	0.190938i
$755$	25.7496			0.937124
$756$		0			0
$757$	−41.8171			−1.51987			−0.759934	−	0.650000i	$-0.774769\pi$
$757$	−41.8171			−1.51987			−0.759934	+	0.650000i	$0.774769\pi$
$758$	−14.8078	−	25.6478i	−0.537843	−	0.931571i
$759$		0			0
$760$	26.5708	−	46.0220i	0.963825	−	1.66939i
$761$	11.4897	−	19.9007i	0.416501	−	0.721400i	−0.579084	−	0.815268i	$-0.696590\pi$
$761$	11.4897	−	19.9007i	0.416501	−	0.721400i	0.995585	+	0.0938675i	$0.0299230\pi$
$762$		0			0
$763$	−1.69961	−	2.94381i	−0.0615301	−	0.106573i
$764$	2.84494			0.102926
$765$		0			0
$766$	30.5979			1.10555
$767$	−1.36333	−	2.36135i	−0.0492269	−	0.0852635i
$768$		0			0
$769$	−3.04329	+	5.27113i	−0.109744	+	0.190082i	−0.915666	−	0.401939i	$-0.868336\pi$
$769$	−3.04329	+	5.27113i	−0.109744	+	0.190082i	0.805923	+	0.592021i	$0.201670\pi$
$770$	−14.4050	+	24.9501i	−0.519119	+	0.899140i
$771$		0			0
$772$	−24.6175	−	42.6388i	−0.886003	−	1.53460i
$773$	41.8214			1.50421			0.752105	−	0.659043i	$-0.229038\pi$
$773$	41.8214			1.50421			0.752105	+	0.659043i	$0.229038\pi$
$774$		0			0
$775$	4.01867			0.144355
$776$	29.0349	+	50.2899i	1.04229	+	1.80530i
$777$		0			0
$778$	25.3442	−	43.8974i	0.908632	−	1.57380i
$779$	12.9861	−	22.4926i	0.465275	−	0.805880i
$780$		0			0
$781$	−7.38891	−	12.7980i	−0.264396	−	0.457947i
$782$	0.636194			0.0227503
$783$		0			0
$784$	4.32743			0.154551
$785$	−7.85087	−	13.5981i	−0.280210	−	0.485337i
$786$		0			0
$787$	−16.1460	+	27.9657i	−0.575543	+	0.996870i	0.420439	+	0.907321i	$0.361876\pi$
$787$	−16.1460	+	27.9657i	−0.575543	+	0.996870i	−0.995982	+	0.0895491i	$0.971457\pi$
$788$	−33.2652	+	57.6170i	−1.18502	+	2.05252i
$789$		0			0
$790$	−46.9327	−	81.2898i	−1.66979	−	2.89216i
$791$	10.3887			0.369380
$792$		0			0
$793$	−2.27335			−0.0807289
$794$	29.0797	+	50.3675i	1.03200	+	1.78747i
$795$		0			0
$796$	−46.0261	+	79.7195i	−1.63135	+	2.82558i
$797$	23.2829	−	40.3271i	0.824722	−	1.42846i	−0.0774101	−	0.996999i	$-0.524665\pi$
$797$	23.2829	−	40.3271i	0.824722	−	1.42846i	0.902132	−	0.431461i	$-0.142002\pi$
$798$		0			0
$799$	−5.75223	−	9.96316i	−0.203499	−	0.352471i
$800$	0.931521			0.0329343
$801$		0			0
$802$	6.30972			0.222804
$803$	−3.40263	−	5.89352i	−0.120076	−	0.207978i
$804$		0			0
$805$	0.354473	−	0.613964i	0.0124935	−	0.0216394i
$806$	−2.86333	+	4.95943i	−0.100856	+	0.174688i
$807$		0			0
$808$	−9.29893	−	16.1062i	−0.327135	−	0.566615i
$809$	10.8023			0.379790			0.189895	−	0.981804i	$-0.439185\pi$
$809$	10.8023			0.379790			0.189895	+	0.981804i	$0.439185\pi$
$810$		0			0
$811$	5.58307			0.196048			0.0980240	−	0.995184i	$-0.468748\pi$
$811$	5.58307			0.196048			0.0980240	+	0.995184i	$0.468748\pi$
$812$	−4.98755	−	8.63868i	−0.175029	−	0.303158i
$813$		0			0
$814$	9.89037	−	17.1306i	0.346657	−	0.600428i
$815$	−23.1050	+	40.0191i	−0.809335	+	1.40181i
$816$		0			0
$817$	−21.1534	−	36.6388i	−0.740064	−	1.28183i
$818$	−84.4556			−2.95292
$819$		0			0
$820$	67.3609			2.35234
$821$	−15.8940	−	27.5292i	−0.554703	−	0.960774i	−0.997927	−	0.0643630i	$-0.979498\pi$
$821$	−15.8940	−	27.5292i	−0.554703	−	0.960774i	0.443223	−	0.896411i	$-0.353835\pi$
$822$		0			0
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	−0.360623	−	0.932712i	$-0.617436\pi$
$823$	18.0000	−	31.1769i	0.627441	−	1.08676i	0.988063	−	0.154047i	$-0.0492308\pi$
$824$	24.5797	−	42.5732i	0.856273	−	1.48311i
$825$		0			0
$826$	3.35447	+	5.81012i	0.116717	+	0.202160i
$827$	−15.9224			−0.553675			−0.276837	−	0.960917i	$-0.589286\pi$
$827$	−15.9224			−0.553675			−0.276837	+	0.960917i	$0.589286\pi$
$828$		0			0
$829$	35.4720			1.23199			0.615996	−	0.787749i	$-0.288754\pi$
$829$	35.4720			1.23199			0.615996	+	0.787749i	$0.288754\pi$
$830$	−3.01819	−	5.22765i	−0.104763	−	0.181455i
$831$		0			0
$832$	3.66372	−	6.34574i	0.127016	−	0.219999i
$833$	−0.472958	+	0.819187i	−0.0163870	+	0.0283832i
$834$		0			0
$835$	−10.9808	−	19.0194i	−0.380007	−	0.658192i
$836$	74.2000			2.56626
$837$		0			0
$838$	−9.98229			−0.344833
$839$	−27.3391	−	47.3527i	−0.943850	−	1.63480i	−0.758037	−	0.652212i	$-0.773841\pi$
$839$	−27.3391	−	47.3527i	−0.943850	−	1.63480i	−0.185814	−	0.982585i	$-0.559492\pi$
$840$		0			0
$841$	11.4730	−	19.8717i	0.395619	−	0.685233i
$842$	25.9200	−	44.8948i	0.893263	−	1.54718i
$843$		0			0
$844$	−9.24630	−	16.0151i	−0.318271	−	0.551261i
$845$	−31.1230			−1.07066
$846$		0			0
$847$	−9.38151			−0.322353
$848$	−13.5737	−	23.5104i	−0.466124	−	0.807350i
$849$		0			0
$850$	−2.00933	+	3.48027i	−0.0689196	+	0.119372i
$851$	−0.243379	+	0.421545i	−0.00834292	+	0.0144504i
$852$		0			0
$853$	1.09884	+	1.90324i	0.0376234	+	0.0651656i	0.884224	−	0.467063i	$-0.154688\pi$
$853$	1.09884	+	1.90324i	0.0376234	+	0.0651656i	−0.846601	+	0.532229i	$0.821355\pi$
$854$	5.59358			0.191408
$855$		0			0
$856$	6.94592			0.237407
$857$	−7.88823	−	13.6628i	−0.269457	−	0.466713i	0.699265	−	0.714863i	$-0.253511\pi$
$857$	−7.88823	−	13.6628i	−0.269457	−	0.466713i	−0.968722	+	0.248150i	$0.920178\pi$
$858$		0			0
$859$	−2.78813	+	4.82918i	−0.0951298	+	0.164770i	−0.909663	−	0.415348i	$-0.863660\pi$
$859$	−2.78813	+	4.82918i	−0.0951298	+	0.164770i	0.814533	+	0.580117i	$0.196993\pi$
$860$	54.8630	−	95.0255i	1.87081	−	3.24034i
$861$		0			0
$862$	27.8264	+	48.1968i	0.947773	+	1.64159i
$863$	−23.1268			−0.787247			−0.393623	−	0.919272i	$-0.628779\pi$
$863$	−23.1268			−0.787247			−0.393623	+	0.919272i	$0.628779\pi$
$864$		0			0
$865$	−45.0157			−1.53058
$866$	−2.97462	−	5.15218i	−0.101082	−	0.175078i
$867$		0			0
$868$	4.71780	−	8.17147i	0.160133	−	0.277358i
$869$	33.2024	−	57.5083i	1.12631	−	1.95083i
$870$		0			0
$871$	7.90856	+	13.6980i	0.267971	+	0.464140i
$872$	−17.1800			−0.581787
$873$		0			0
$874$	−2.72665			−0.0922304
$875$	−4.24484	−	7.35228i	−0.143502	−	0.248552i
$876$		0			0
$877$	−1.96264	+	3.39939i	−0.0662737	+	0.114789i	−0.897258	−	0.441506i	$-0.854444\pi$
$877$	−1.96264	+	3.39939i	−0.0662737	+	0.114789i	0.830985	+	0.556295i	$0.187778\pi$
$878$	28.8982	−	50.0532i	0.975268	−	1.68921i
$879$		0			0
$880$	25.3348	+	43.8812i	0.854037	+	1.47923i
$881$	−27.1986			−0.916345			−0.458173	−	0.888863i	$-0.651496\pi$
$881$	−27.1986			−0.916345			−0.458173	+	0.888863i	$0.651496\pi$
$882$		0			0
$883$	8.21341			0.276403			0.138202	−	0.990404i	$-0.455868\pi$
$883$	8.21341			0.276403			0.138202	+	0.990404i	$0.455868\pi$
$884$	−1.91741	−	3.32105i	−0.0644895	−	0.111699i
$885$		0			0
$886$	−16.5074	+	28.5916i	−0.554577	+	0.960555i
$887$	−3.24057	+	5.61283i	−0.108808	+	0.188460i	−0.915287	−	0.402801i	$-0.868037\pi$
$887$	−3.24057	+	5.61283i	−0.108808	+	0.188460i	0.806480	+	0.591262i	$0.201370\pi$
$888$		0			0
$889$	0.336285	+	0.582462i	0.0112786	+	0.0195352i
$890$	91.6169			3.07101
$891$		0			0
$892$	54.0187			1.80868
$893$	24.6534	+	42.7009i	0.824995	+	1.42893i
$894$		0			0
$895$	−14.7178	+	25.4920i	−0.491962	+	0.852103i
$896$	−9.55408	+	16.5482i	−0.319180	+	0.552835i
$897$		0			0
$898$	−11.2719	−	19.5235i	−0.376148	−	0.651507i
$899$	−5.72665			−0.190995
$900$		0			0
$901$	5.93406			0.197692
$902$	35.5818	+	61.6295i	1.18474	+	2.05204i
$903$		0			0
$904$	26.2527	−	45.4710i	0.873152	−	1.51234i
$905$	−28.3853	+	49.1648i	−0.943560	+	1.63429i
$906$		0			0
$907$	−5.06440	−	8.77180i	−0.168161	−	0.291263i	0.769613	−	0.638511i	$-0.220449\pi$
$907$	−5.06440	−	8.77180i	−0.168161	−	0.291263i	−0.937773	+	0.347248i	$0.887116\pi$
$908$	−5.60078			−0.185868
$909$		0			0
$910$	−6.38151			−0.211545
$911$	22.9612	+	39.7699i	0.760738	+	1.31764i	0.942471	+	0.334289i	$0.108496\pi$
$911$	22.9612	+	39.7699i	0.760738	+	1.31764i	−0.181733	+	0.983348i	$0.558171\pi$
$912$		0			0
$913$	2.13521	−	3.69829i	0.0706652	−	0.122396i
$914$	−10.8473	+	18.7880i	−0.358796	+	0.621453i
$915$		0			0
$916$	36.4449	+	63.1245i	1.20417	+	2.08569i
$917$	7.91381			0.261337
$918$		0			0
$919$	−4.92432			−0.162438			−0.0812192	−	0.996696i	$-0.525881\pi$
$919$	−4.92432			−0.162438			−0.0812192	+	0.996696i	$0.525881\pi$
$920$	−1.79153	−	3.10303i	−0.0590651	−	0.102304i
$921$		0			0
$922$	−6.96216	+	12.0588i	−0.229287	+	0.397136i
$923$	1.63667	−	2.83480i	0.0538718	−	0.0933086i
$924$		0			0
$925$	−1.53736	−	2.66278i	−0.0505481	−	0.0875518i
$926$	38.6955			1.27161
$927$		0			0
$928$	−1.32743			−0.0435750
$929$	0.00379324	+	0.00657009i	0.000124452	+	0.000215558i	0.866088	−	0.499892i	$-0.166627\pi$
$929$	0.00379324	+	0.00657009i	0.000124452	+	0.000215558i	−0.865963	+	0.500108i	$0.833294\pi$
$930$		0			0
$931$	2.02704	−	3.51094i	0.0664336	−	0.115066i
$932$	−38.4779	+	66.6457i	−1.26039	+	2.18305i
$933$		0			0
$934$	−27.0620	−	46.8727i	−0.885494	−	1.53372i
$935$	−11.0757			−0.362213
$936$		0			0
$937$	21.1623			0.691341			0.345670	−	0.938356i	$-0.387652\pi$
$937$	21.1623			0.691341			0.345670	+	0.938356i	$0.387652\pi$
$938$	−19.4590	−	33.7040i	−0.635360	−	1.10048i
$939$		0			0
$940$	−63.9405	+	110.748i	−2.08551	+	3.61221i
$941$	2.27908	−	3.94748i	0.0742959	−	0.128684i	−0.826484	−	0.562960i	$-0.809662\pi$
$941$	2.27908	−	3.94748i	0.0742959	−	0.128684i	0.900780	+	0.434276i	$0.142996\pi$
$942$		0			0
$943$	−0.875585	−	1.51656i	−0.0285130	−	0.0493859i
$944$	11.7994			0.384038
$945$		0			0
$946$	115.920			3.76890
$947$	6.86760	+	11.8950i	0.223167	+	0.386537i	0.955768	−	0.294122i	$-0.0950271\pi$
$947$	6.86760	+	11.8950i	0.223167	+	0.386537i	−0.732601	+	0.680658i	$0.761694\pi$
$948$		0			0
$949$	0.753696	−	1.30544i	0.0244660	−	0.0423764i
$950$	8.61177	−	14.9160i	0.279403	−	0.483940i
$951$		0			0
$952$	2.39037	+	4.14024i	0.0774723	+	0.134186i
$953$	−8.80699			−0.285286			−0.142643	−	0.989774i	$-0.545560\pi$
$953$	−8.80699			−0.285286			−0.142643	+	0.989774i	$0.545560\pi$
$954$		0			0
$955$	1.82004			0.0588951
$956$	9.91595	+	17.1749i	0.320705	+	0.555477i
$957$		0			0
$958$	30.7257	−	53.2184i	0.992701	−	1.71941i
$959$	1.83628	−	3.18054i	0.0592967	−	0.102705i
$960$		0			0
$961$	12.7915	+	22.1556i	0.412630	+	0.714696i
$962$	4.38151			0.141266
$963$		0			0
$964$	−106.052			−3.41571
$965$	−15.7489	−	27.2779i	−0.506976	−	0.878108i
$966$		0			0
$967$	−19.1642	+	33.1934i	−0.616279	+	1.06743i	0.373880	+	0.927477i	$0.378027\pi$
$967$	−19.1642	+	33.1934i	−0.616279	+	1.06743i	−0.990159	+	0.139949i	$0.955306\pi$
$968$	−23.7075	+	41.0626i	−0.761987	+	1.31980i
$969$		0			0
$970$	36.6608	+	63.4984i	1.17711	+	2.03881i
$971$	31.0187			0.995436			0.497718	−	0.867339i	$-0.334171\pi$
$971$	31.0187			0.995436			0.497718	+	0.867339i	$0.334171\pi$
$972$		0			0
$973$	2.05408			0.0658509
$974$	21.6498	+	37.4986i	0.693704	+	1.20153i
$975$		0			0
$976$	4.91887	−	8.51974i	0.157449	−	0.272710i
$977$	−26.3712	+	45.6763i	−0.843689	+	1.46131i	0.0430652	+	0.999072i	$0.486288\pi$
$977$	−26.3712	+	45.6763i	−0.843689	+	1.46131i	−0.886755	+	0.462241i	$0.847046\pi$
$978$		0			0
$979$	32.4071	+	56.1307i	1.03574	+	1.79395i
$980$	10.5146			0.335876
$981$		0			0
$982$	−33.9430			−1.08316
$983$	−9.15146	−	15.8508i	−0.291886	−	0.505562i	0.682370	−	0.731007i	$-0.260950\pi$
$983$	−9.15146	−	15.8508i	−0.291886	−	0.505562i	−0.974256	+	0.225446i	$0.927616\pi$
$984$		0			0
$985$	−21.2812	+	36.8601i	−0.678076	+	1.17446i
$986$	2.86333	−	4.95943i	0.0911869	−	0.157940i
$987$		0			0
$988$	8.21780	+	14.2336i	0.261443	+	0.452833i
$989$	−2.85253			−0.0907052
$990$		0			0
$991$	−12.6008			−0.400277			−0.200138	−	0.979768i	$-0.564139\pi$
$991$	−12.6008			−0.400277			−0.200138	+	0.979768i	$0.564139\pi$
$992$	−0.627819	−	1.08741i	−0.0199333	−	0.0345254i
$993$		0			0
$994$	−4.02704	+	6.97504i	−0.127730	+	0.221235i
$995$	−29.4449	+	51.0001i	−0.933467	+	1.61681i
$996$		0			0
$997$	−5.87120	−	10.1692i	−0.185943	−	0.322062i	0.757951	−	0.652311i	$-0.226201\pi$
$997$	−5.87120	−	10.1692i	−0.185943	−	0.322062i	−0.943894	+	0.330249i	$0.892867\pi$
$998$	32.2019			1.01933
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.f.a.64.1		6
3.2	odd	2		63.2.f.b.22.3	✓	6
4.3	odd	2		3024.2.r.g.1009.2		6
7.2	even	3		1323.2.g.c.361.1		6
7.3	odd	6		1323.2.h.e.226.3		6
7.4	even	3		1323.2.h.d.226.3		6
7.5	odd	6		1323.2.g.b.361.1		6
7.6	odd	2		1323.2.f.c.442.1		6
9.2	odd	6		63.2.f.b.43.3	yes	6
9.4	even	3		567.2.a.g.1.3		3
9.5	odd	6		567.2.a.d.1.1		3
9.7	even	3	inner	189.2.f.a.127.1		6
12.11	even	2		1008.2.r.k.337.3		6
21.2	odd	6		441.2.g.e.67.3		6
21.5	even	6		441.2.g.d.67.3		6
21.11	odd	6		441.2.h.c.373.1		6
21.17	even	6		441.2.h.b.373.1		6
21.20	even	2		441.2.f.d.148.3		6
36.7	odd	6		3024.2.r.g.2017.2		6
36.11	even	6		1008.2.r.k.673.3		6
36.23	even	6		9072.2.a.bq.1.2		3
36.31	odd	6		9072.2.a.cd.1.2		3
63.2	odd	6		441.2.h.c.214.1		6
63.11	odd	6		441.2.g.e.79.3		6
63.13	odd	6		3969.2.a.p.1.3		3
63.16	even	3		1323.2.h.d.802.3		6
63.20	even	6		441.2.f.d.295.3		6
63.25	even	3		1323.2.g.c.667.1		6
63.34	odd	6		1323.2.f.c.883.1		6
63.38	even	6		441.2.g.d.79.3		6
63.41	even	6		3969.2.a.m.1.1		3
63.47	even	6		441.2.h.b.214.1		6
63.52	odd	6		1323.2.g.b.667.1		6
63.61	odd	6		1323.2.h.e.802.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.b.22.3	✓	6	3.2	odd	2
63.2.f.b.43.3	yes	6	9.2	odd	6
189.2.f.a.64.1		6	1.1	even	1	trivial
189.2.f.a.127.1		6	9.7	even	3	inner
441.2.f.d.148.3		6	21.20	even	2
441.2.f.d.295.3		6	63.20	even	6
441.2.g.d.67.3		6	21.5	even	6
441.2.g.d.79.3		6	63.38	even	6
441.2.g.e.67.3		6	21.2	odd	6
441.2.g.e.79.3		6	63.11	odd	6
441.2.h.b.214.1		6	63.47	even	6
441.2.h.b.373.1		6	21.17	even	6
441.2.h.c.214.1		6	63.2	odd	6
441.2.h.c.373.1		6	21.11	odd	6
567.2.a.d.1.1		3	9.5	odd	6
567.2.a.g.1.3		3	9.4	even	3
1008.2.r.k.337.3		6	12.11	even	2
1008.2.r.k.673.3		6	36.11	even	6
1323.2.f.c.442.1		6	7.6	odd	2
1323.2.f.c.883.1		6	63.34	odd	6
1323.2.g.b.361.1		6	7.5	odd	6
1323.2.g.b.667.1		6	63.52	odd	6
1323.2.g.c.361.1		6	7.2	even	3
1323.2.g.c.667.1		6	63.25	even	3
1323.2.h.d.226.3		6	7.4	even	3
1323.2.h.d.802.3		6	63.16	even	3
1323.2.h.e.226.3		6	7.3	odd	6
1323.2.h.e.802.3		6	63.61	odd	6
3024.2.r.g.1009.2		6	4.3	odd	2
3024.2.r.g.2017.2		6	36.7	odd	6
3969.2.a.m.1.1		3	63.41	even	6
3969.2.a.p.1.3		3	63.13	odd	6
9072.2.a.bq.1.2		3	36.23	even	6
9072.2.a.cd.1.2		3	36.31	odd	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23025 - 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.29679 + 2.24611i) q^{5} +(0.500000 + 0.866025i) q^{7} +5.05408 q^{8} +O(q^{10})\)	\(q+(-1.23025 - 2.13086i) q^{2} +(-2.02704 + 3.51094i) q^{4} +(-1.29679 + 2.24611i) q^{5} +(0.500000 + 0.866025i) q^{7} +5.05408 q^{8} +6.38151 q^{10} +(2.25729 + 3.90975i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(1.23025 - 2.13086i) q^{14} +(-2.16372 - 3.74766i) q^{16} +0.945916 q^{17} -4.05408 q^{19} +(-5.25729 - 9.10590i) q^{20} +(5.55408 - 9.61996i) q^{22} +(-0.136673 + 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +2.46050 q^{26} -4.05408 q^{28} +(1.23025 + 2.13086i) q^{29} +(-1.16372 + 2.01561i) q^{31} +(-0.269748 + 0.467216i) q^{32} +(-1.16372 - 2.01561i) q^{34} -2.59358 q^{35} +1.78074 q^{37} +(4.98755 + 8.63868i) q^{38} +(-6.55408 + 11.3520i) q^{40} +(-3.20321 + 5.54812i) q^{41} +(5.21780 + 9.03749i) q^{43} -18.3025 q^{44} +0.672570 q^{46} +(-6.08113 - 10.5328i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-2.12422 + 3.67926i) q^{50} +(-2.02704 - 3.51094i) q^{52} +6.27335 q^{53} -11.7089 q^{55} +(2.52704 + 4.37697i) q^{56} +(3.02704 - 5.24299i) q^{58} +(-1.36333 + 2.36135i) q^{59} +(1.13667 + 1.96878i) q^{61} +5.72665 q^{62} -7.32743 q^{64} +(-1.29679 - 2.24611i) q^{65} +(7.90856 - 13.6980i) q^{67} +(-1.91741 + 3.32105i) q^{68} +(3.19076 + 5.52655i) q^{70} -3.27335 q^{71} -1.50739 q^{73} +(-2.19076 - 3.79450i) q^{74} +(8.21780 - 14.2336i) q^{76} +(-2.25729 + 3.90975i) q^{77} +(-7.35447 - 12.7383i) q^{79} +11.2235 q^{80} +15.7630 q^{82} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(12.8384 - 22.2368i) q^{86} +(11.4086 + 19.7602i) q^{88} +14.3566 q^{89} -1.00000 q^{91} +(-0.554084 - 0.959702i) q^{92} +(-14.9626 + 25.9161i) q^{94} +(5.25729 - 9.10590i) q^{95} +(5.74484 + 9.95036i) q^{97} +2.46050 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8}+O(q^{10}) \) 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8	\( 6 q - q^{2} - 3 q^{4} - 5 q^{5} + 3 q^{7} + 12 q^{8} - 2 q^{11} - 3 q^{13} + q^{14} - 3 q^{16} + 24 q^{17} - 6 q^{19} - 16 q^{20} + 15 q^{22} - 6 q^{25} + 2 q^{26} - 6 q^{28} + q^{29} + 3 q^{31} - 8 q^{32} + 3 q^{34} - 10 q^{35} - 6 q^{37} + 8 q^{38} - 21 q^{40} - 22 q^{41} + 3 q^{43} - 46 q^{44} + 24 q^{46} - 9 q^{47} - 3 q^{49} + 10 q^{50} - 3 q^{52} + 36 q^{53} - 12 q^{55} + 6 q^{56} + 9 q^{58} - 9 q^{59} + 6 q^{61} + 36 q^{62} - 24 q^{64} - 5 q^{65} + 6 q^{68} - 18 q^{71} + 6 q^{73} + 6 q^{74} + 21 q^{76} + 2 q^{77} - 15 q^{79} - 22 q^{80} + 18 q^{82} - 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 4 q^{89} - 6 q^{91} + 15 q^{92} - 24 q^{94} + 16 q^{95} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) 6 * q - q^2 - 3 * q^4 - 5 * q^5 + 3 * q^7 + 12 * q^8 - 2 * q^11 - 3 * q^13 + q^14 - 3 * q^16 + 24 * q^17 - 6 * q^19 - 16 * q^20 + 15 * q^22 - 6 * q^25 + 2 * q^26 - 6 * q^28 + q^29 + 3 * q^31 - 8 * q^32 + 3 * q^34 - 10 * q^35 - 6 * q^37 + 8 * q^38 - 21 * q^40 - 22 * q^41 + 3 * q^43 - 46 * q^44 + 24 * q^46 - 9 * q^47 - 3 * q^49 + 10 * q^50 - 3 * q^52 + 36 * q^53 - 12 * q^55 + 6 * q^56 + 9 * q^58 - 9 * q^59 + 6 * q^61 + 36 * q^62 - 24 * q^64 - 5 * q^65 + 6 * q^68 - 18 * q^71 + 6 * q^73 + 6 * q^74 + 21 * q^76 + 2 * q^77 - 15 * q^79 - 22 * q^80 + 18 * q^82 - 12 * q^83 - 9 * q^85 + 34 * q^86 + 21 * q^88 + 4 * q^89 - 6 * q^91 + 15 * q^92 - 24 * q^94 + 16 * q^95 - 3 * q^97 + 2 * q^98

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