LMFDB - Embedded newform 441.2.e.f.226.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(226,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("441.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.e (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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 147)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.2.e.f.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(-0.292893 + 0.507306i) q^{5} +4.41421 q^{8} +O(q^{10})$	\(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(-0.292893 + 0.507306i) q^{5} +4.41421 q^{8} +(-0.707107 - 1.22474i) q^{10} +(-1.00000 - 1.73205i) q^{11} -5.41421 q^{13} +(-1.50000 + 2.59808i) q^{16} +(-3.12132 - 5.40629i) q^{17} +(1.41421 - 2.44949i) q^{19} +2.24264 q^{20} +4.82843 q^{22} +(1.82843 - 3.16693i) q^{23} +(2.32843 + 4.03295i) q^{25} +(6.53553 - 11.3199i) q^{26} +1.17157 q^{29} +(-3.41421 - 5.91359i) q^{31} +(0.792893 + 1.37333i) q^{32} +15.0711 q^{34} +(2.00000 - 3.46410i) q^{37} +(3.41421 + 5.91359i) q^{38} +(-1.29289 + 2.23936i) q^{40} -2.24264 q^{41} -5.65685 q^{43} +(-3.82843 + 6.63103i) q^{44} +(4.41421 + 7.64564i) q^{46} +(-1.41421 + 2.44949i) q^{47} -11.2426 q^{50} +(10.3640 + 17.9509i) q^{52} +(-1.00000 - 1.73205i) q^{53} +1.17157 q^{55} +(-1.41421 + 2.44949i) q^{58} +(3.41421 + 5.91359i) q^{59} +(1.87868 - 3.25397i) q^{61} +16.4853 q^{62} -9.82843 q^{64} +(1.58579 - 2.74666i) q^{65} +(-2.82843 - 4.89898i) q^{67} +(-11.9497 + 20.6976i) q^{68} +13.3137 q^{71} +(-2.94975 - 5.10911i) q^{73} +(4.82843 + 8.36308i) q^{74} -10.8284 q^{76} +(-1.17157 + 2.02922i) q^{79} +(-0.878680 - 1.52192i) q^{80} +(2.70711 - 4.68885i) q^{82} -15.3137 q^{83} +3.65685 q^{85} +(6.82843 - 11.8272i) q^{86} +(-4.41421 - 7.64564i) q^{88} +(2.87868 - 4.98602i) q^{89} -14.0000 q^{92} +(-3.41421 - 5.91359i) q^{94} +(0.828427 + 1.43488i) q^{95} -5.41421 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8} - 4 q^{11} - 16 q^{13} - 6 q^{16} - 4 q^{17} - 8 q^{20} + 8 q^{22} - 4 q^{23} - 2 q^{25} + 12 q^{26} + 16 q^{29} - 8 q^{31} + 6 q^{32} + 32 q^{34} + 8 q^{37} + 8 q^{38} - 8 q^{40} + 8 q^{41} - 4 q^{44} + 12 q^{46} - 28 q^{50} + 16 q^{52} - 4 q^{53} + 16 q^{55} + 8 q^{59} + 16 q^{61} + 32 q^{62} - 28 q^{64} + 12 q^{65} - 28 q^{68} + 8 q^{71} + 8 q^{73} + 8 q^{74} - 32 q^{76} - 16 q^{79} - 12 q^{80} + 8 q^{82} - 16 q^{83} - 8 q^{85} + 16 q^{86} - 12 q^{88} + 20 q^{89} - 56 q^{92} - 8 q^{94} - 8 q^{95} - 16 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8 - 4 * q^11 - 16 * q^13 - 6 * q^16 - 4 * q^17 - 8 * q^20 + 8 * q^22 - 4 * q^23 - 2 * q^25 + 12 * q^26 + 16 * q^29 - 8 * q^31 + 6 * q^32 + 32 * q^34 + 8 * q^37 + 8 * q^38 - 8 * q^40 + 8 * q^41 - 4 * q^44 + 12 * q^46 - 28 * q^50 + 16 * q^52 - 4 * q^53 + 16 * q^55 + 8 * q^59 + 16 * q^61 + 32 * q^62 - 28 * q^64 + 12 * q^65 - 28 * q^68 + 8 * q^71 + 8 * q^73 + 8 * q^74 - 32 * q^76 - 16 * q^79 - 12 * q^80 + 8 * q^82 - 16 * q^83 - 8 * q^85 + 16 * q^86 - 12 * q^88 + 20 * q^89 - 56 * q^92 - 8 * q^94 - 8 * q^95 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	0.0244272	+	0.999702i	$0.492224\pi$
$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	−0.877981	+	0.478696i	$0.841110\pi$
$3$		0			0
$3$		0			0
$4$	−1.91421	−	3.31552i	−0.957107	−	1.65776i
$5$	−0.292893	+	0.507306i	−0.130986	+	0.226874i	−0.924057	−	0.382255i	$-0.875148\pi$
$5$	−0.292893	+	0.507306i	−0.130986	+	0.226874i	0.793071	+	0.609129i	$0.208481\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	4.41421			1.56066
$9$		0			0
$10$	−0.707107	−	1.22474i	−0.223607	−	0.387298i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	−5.41421			−1.50163			−0.750816	−	0.660511i	$-0.770340\pi$
$13$	−5.41421			−1.50163			−0.750816	+	0.660511i	$0.770340\pi$
$14$		0			0
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−3.12132	−	5.40629i	−0.757031	−	1.31122i	−0.944358	−	0.328919i	$-0.893316\pi$
$17$	−3.12132	−	5.40629i	−0.757031	−	1.31122i	0.187327	−	0.982298i	$-0.440018\pi$
$18$		0			0
$19$	1.41421	−	2.44949i	0.324443	−	0.561951i	−0.656957	−	0.753928i	$-0.728157\pi$
$19$	1.41421	−	2.44949i	0.324443	−	0.561951i	0.981399	+	0.191977i	$0.0614899\pi$
$20$	2.24264			0.501470
$21$		0			0
$22$	4.82843			1.02942
$23$	1.82843	−	3.16693i	0.381253	−	0.660350i	−0.609988	−	0.792410i	$-0.708826\pi$
$23$	1.82843	−	3.16693i	0.381253	−	0.660350i	0.991242	+	0.132060i	$0.0421592\pi$
$24$		0			0
$25$	2.32843	+	4.03295i	0.465685	+	0.806591i
$26$	6.53553	−	11.3199i	1.28172	−	2.22001i
$27$		0			0
$28$		0			0
$29$	1.17157			0.217556			0.108778	−	0.994066i	$-0.465306\pi$
$29$	1.17157			0.217556			0.108778	+	0.994066i	$0.465306\pi$
$30$		0			0
$31$	−3.41421	−	5.91359i	−0.613211	−	1.06211i	−0.990696	−	0.136097i	$-0.956544\pi$
$31$	−3.41421	−	5.91359i	−0.613211	−	1.06211i	0.377485	−	0.926016i	$-0.376789\pi$
$32$	0.792893	+	1.37333i	0.140165	+	0.242773i
$33$		0			0
$34$	15.0711			2.58467
$35$		0			0
$36$		0			0
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$	3.41421	+	5.91359i	0.553859	+	0.959311i
$39$		0			0
$40$	−1.29289	+	2.23936i	−0.204424	+	0.354073i
$41$	−2.24264			−0.350242			−0.175121	−	0.984547i	$-0.556032\pi$
$41$	−2.24264			−0.350242			−0.175121	+	0.984547i	$0.556032\pi$
$42$		0			0
$43$	−5.65685			−0.862662			−0.431331	−	0.902194i	$-0.641956\pi$
$43$	−5.65685			−0.862662			−0.431331	+	0.902194i	$0.641956\pi$
$44$	−3.82843	+	6.63103i	−0.577157	+	0.999665i
$45$		0			0
$46$	4.41421	+	7.64564i	0.650840	+	1.12729i
$47$	−1.41421	+	2.44949i	−0.206284	+	0.357295i	−0.950541	−	0.310599i	$-0.899470\pi$
$47$	−1.41421	+	2.44949i	−0.206284	+	0.357295i	0.744257	+	0.667893i	$0.232804\pi$
$48$		0			0
$49$		0			0
$50$	−11.2426			−1.58995
$51$		0			0
$52$	10.3640	+	17.9509i	1.43722	+	2.48934i
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	0.789136	−	0.614218i	$-0.210529\pi$
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	−0.926497	+	0.376303i	$0.877195\pi$
$54$		0			0
$55$	1.17157			0.157975
$56$		0			0
$57$		0			0
$58$	−1.41421	+	2.44949i	−0.185695	+	0.321634i
$59$	3.41421	+	5.91359i	0.444493	+	0.769884i	0.998017	−	0.0629492i	$-0.0200506\pi$
$59$	3.41421	+	5.91359i	0.444493	+	0.769884i	−0.553524	+	0.832833i	$0.686717\pi$
$60$		0			0
$61$	1.87868	−	3.25397i	0.240540	−	0.416628i	−0.720328	−	0.693634i	$-0.756009\pi$
$61$	1.87868	−	3.25397i	0.240540	−	0.416628i	0.960868	+	0.277006i	$0.0893421\pi$
$62$	16.4853			2.09363
$63$		0			0
$64$	−9.82843			−1.22855
$65$	1.58579	−	2.74666i	0.196693	−	0.340682i
$66$		0			0
$67$	−2.82843	−	4.89898i	−0.345547	−	0.598506i	0.639906	−	0.768453i	$-0.278973\pi$
$67$	−2.82843	−	4.89898i	−0.345547	−	0.598506i	−0.985453	+	0.169948i	$0.945640\pi$
$68$	−11.9497	+	20.6976i	−1.44912	+	2.50995i
$69$		0			0
$70$		0			0
$71$	13.3137			1.58005			0.790023	−	0.613077i	$-0.210068\pi$
$71$	13.3137			1.58005			0.790023	+	0.613077i	$0.210068\pi$
$72$		0			0
$73$	−2.94975	−	5.10911i	−0.345242	−	0.597976i	0.640156	−	0.768245i	$-0.278870\pi$
$73$	−2.94975	−	5.10911i	−0.345242	−	0.597976i	−0.985398	+	0.170269i	$0.945536\pi$
$74$	4.82843	+	8.36308i	0.561293	+	0.972188i
$75$		0			0
$76$	−10.8284			−1.24211
$77$		0			0
$78$		0			0
$79$	−1.17157	+	2.02922i	−0.131812	+	0.228306i	−0.924375	−	0.381485i	$-0.875413\pi$
$79$	−1.17157	+	2.02922i	−0.131812	+	0.228306i	0.792563	+	0.609790i	$0.208746\pi$
$80$	−0.878680	−	1.52192i	−0.0982394	−	0.170156i
$81$		0			0
$82$	2.70711	−	4.68885i	0.298950	−	0.517796i
$83$	−15.3137			−1.68090			−0.840449	−	0.541891i	$-0.817709\pi$
$83$	−15.3137			−1.68090			−0.840449	+	0.541891i	$0.817709\pi$
$84$		0			0
$85$	3.65685			0.396642
$86$	6.82843	−	11.8272i	0.736328	−	1.27536i
$87$		0			0
$88$	−4.41421	−	7.64564i	−0.470557	−	0.815028i
$89$	2.87868	−	4.98602i	0.305139	−	0.528517i	−0.672153	−	0.740412i	$-0.734630\pi$
$89$	2.87868	−	4.98602i	0.305139	−	0.528517i	0.977292	+	0.211895i	$0.0679636\pi$
$90$		0			0
$91$		0			0
$92$	−14.0000			−1.45960
$93$		0			0
$94$	−3.41421	−	5.91359i	−0.352149	−	0.609940i
$95$	0.828427	+	1.43488i	0.0849948	+	0.147215i
$96$		0			0
$97$	−5.41421			−0.549730			−0.274865	−	0.961483i	$-0.588633\pi$
$97$	−5.41421			−0.549730			−0.274865	+	0.961483i	$0.588633\pi$
$98$		0			0
$99$		0			0
$100$	8.91421	−	15.4399i	0.891421	−	1.54399i
$101$	−8.53553	−	14.7840i	−0.849317	−	1.47106i	−0.881818	−	0.471589i	$-0.843681\pi$
$101$	−8.53553	−	14.7840i	−0.849317	−	1.47106i	0.0325010	−	0.999472i	$-0.489653\pi$
$102$		0			0
$103$	−6.24264	+	10.8126i	−0.615106	+	1.06539i	0.375260	+	0.926919i	$0.377553\pi$
$103$	−6.24264	+	10.8126i	−0.615106	+	1.06539i	−0.990366	+	0.138475i	$0.955780\pi$
$104$	−23.8995			−2.34354
$105$		0			0
$106$	4.82843			0.468978
$107$	−5.82843	+	10.0951i	−0.563455	+	0.975933i	0.433736	+	0.901040i	$0.357195\pi$
$107$	−5.82843	+	10.0951i	−0.563455	+	0.975933i	−0.997192	+	0.0748933i	$0.976138\pi$
$108$		0			0
$109$	−2.82843	−	4.89898i	−0.270914	−	0.469237i	0.698182	−	0.715920i	$-0.253993\pi$
$109$	−2.82843	−	4.89898i	−0.270914	−	0.469237i	−0.969096	+	0.246683i	$0.920659\pi$
$110$	−1.41421	+	2.44949i	−0.134840	+	0.233550i
$111$		0			0
$112$		0			0
$113$	−17.3137			−1.62874			−0.814368	−	0.580348i	$-0.802916\pi$
$113$	−17.3137			−1.62874			−0.814368	+	0.580348i	$0.802916\pi$
$114$		0			0
$115$	1.07107	+	1.85514i	0.0998776	+	0.172993i
$116$	−2.24264	−	3.88437i	−0.208224	−	0.360654i
$117$		0			0
$118$	−16.4853			−1.51759
$119$		0			0
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	4.53553	+	7.85578i	0.410628	+	0.711228i
$123$		0			0
$124$	−13.0711	+	22.6398i	−1.17382	+	2.03311i
$125$	−5.65685			−0.505964
$126$		0			0
$127$	9.65685			0.856907			0.428454	−	0.903564i	$-0.359059\pi$
$127$	9.65685			0.856907			0.428454	+	0.903564i	$0.359059\pi$
$128$	10.2782	−	17.8023i	0.908471	−	1.57352i
$129$		0			0
$130$	3.82843	+	6.63103i	0.335775	+	0.581580i
$131$	−3.65685	+	6.33386i	−0.319501	+	0.553392i	−0.980384	−	0.197097i	$-0.936849\pi$
$131$	−3.65685	+	6.33386i	−0.319501	+	0.553392i	0.660883	+	0.750489i	$0.270182\pi$
$132$		0			0
$133$		0			0
$134$	13.6569			1.17977
$135$		0			0
$136$	−13.7782	−	23.8645i	−1.18147	−	2.04636i
$137$	−7.07107	−	12.2474i	−0.604122	−	1.04637i	−0.992190	−	0.124739i	$-0.960191\pi$
$137$	−7.07107	−	12.2474i	−0.604122	−	1.04637i	0.388067	−	0.921631i	$-0.373143\pi$
$138$		0			0
$139$	6.34315			0.538019			0.269009	−	0.963138i	$-0.413304\pi$
$139$	6.34315			0.538019			0.269009	+	0.963138i	$0.413304\pi$
$140$		0			0
$141$		0			0
$142$	−16.0711	+	27.8359i	−1.34865	+	2.33594i
$143$	5.41421	+	9.37769i	0.452759	+	0.784202i
$144$		0			0
$145$	−0.343146	+	0.594346i	−0.0284967	+	0.0493577i
$146$	14.2426			1.17873
$147$		0			0
$148$	−15.3137			−1.25878
$149$	−2.65685	+	4.60181i	−0.217658	+	0.376995i	−0.954092	−	0.299515i	$-0.903175\pi$
$149$	−2.65685	+	4.60181i	−0.217658	+	0.376995i	0.736434	+	0.676510i	$0.236508\pi$
$150$		0			0
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	0.511636	−	0.859202i	$-0.329040\pi$
$151$	−6.00000	−	10.3923i	−0.488273	−	0.845714i	−0.999909	+	0.0134886i	$0.995706\pi$
$152$	6.24264	−	10.8126i	0.506345	−	0.877015i
$153$		0			0
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	10.1213	+	17.5306i	0.807769	+	1.39910i	0.914406	+	0.404799i	$0.132659\pi$
$157$	10.1213	+	17.5306i	0.807769	+	1.39910i	−0.106636	+	0.994298i	$0.534008\pi$
$158$	−2.82843	−	4.89898i	−0.225018	−	0.389742i
$159$		0			0
$160$	−0.928932			−0.0734385
$161$		0			0
$162$		0			0
$163$	−5.65685	+	9.79796i	−0.443079	+	0.767435i	−0.997916	−	0.0645236i	$-0.979447\pi$
$163$	−5.65685	+	9.79796i	−0.443079	+	0.767435i	0.554837	+	0.831959i	$0.312781\pi$
$164$	4.29289	+	7.43551i	0.335219	+	0.580616i
$165$		0			0
$166$	18.4853	−	32.0174i	1.43474	−	2.48504i
$167$	19.7990			1.53209			0.766046	−	0.642786i	$-0.222221\pi$
$167$	19.7990			1.53209			0.766046	+	0.642786i	$0.222221\pi$
$168$		0			0
$169$	16.3137			1.25490
$170$	−4.41421	+	7.64564i	−0.338555	+	0.586394i
$171$		0			0
$172$	10.8284	+	18.7554i	0.825660	+	1.43008i
$173$	−3.46447	+	6.00063i	−0.263398	+	0.456220i	−0.967143	−	0.254234i	$-0.918177\pi$
$173$	−3.46447	+	6.00063i	−0.263398	+	0.456220i	0.703744	+	0.710453i	$0.251510\pi$
$174$		0			0
$175$		0			0
$176$	6.00000			0.452267
$177$		0			0
$178$	6.94975	+	12.0373i	0.520906	+	0.902235i
$179$	−4.17157	−	7.22538i	−0.311798	−	0.540050i	0.666954	−	0.745099i	$-0.267598\pi$
$179$	−4.17157	−	7.22538i	−0.311798	−	0.540050i	−0.978752	+	0.205049i	$0.934265\pi$
$180$		0			0
$181$	5.41421			0.402435			0.201218	−	0.979547i	$-0.435510\pi$
$181$	5.41421			0.402435			0.201218	+	0.979547i	$0.435510\pi$
$182$		0			0
$183$		0			0
$184$	8.07107	−	13.9795i	0.595007	−	1.03058i
$185$	1.17157	+	2.02922i	0.0861358	+	0.149191i
$186$		0			0
$187$	−6.24264	+	10.8126i	−0.456507	+	0.790693i
$188$	10.8284			0.789744
$189$		0			0
$190$	−4.00000			−0.290191
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	8.65685	+	14.9941i	0.623134	+	1.07930i	0.988899	+	0.148592i	$0.0474742\pi$
$193$	8.65685	+	14.9941i	0.623134	+	1.07930i	−0.365765	+	0.930707i	$0.619192\pi$
$194$	6.53553	−	11.3199i	0.469224	−	0.812720i
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	5.17157	+	8.95743i	0.366603	+	0.634975i	0.989032	−	0.147701i	$-0.0471874\pi$
$199$	5.17157	+	8.95743i	0.366603	+	0.634975i	−0.622429	+	0.782676i	$0.713854\pi$
$200$	10.2782	+	17.8023i	0.726777	+	1.25881i
$201$		0			0
$202$	41.2132			2.89975
$203$		0			0
$204$		0			0
$205$	0.656854	−	1.13770i	0.0458767	−	0.0794608i
$206$	−15.0711	−	26.1039i	−1.05005	−	1.81874i
$207$		0			0
$208$	8.12132	−	14.0665i	0.563112	−	0.975339i
$209$	−5.65685			−0.391293
$210$		0			0
$211$	−20.9706			−1.44367			−0.721837	−	0.692064i	$-0.756702\pi$
$211$	−20.9706			−1.44367			−0.721837	+	0.692064i	$0.756702\pi$
$212$	−3.82843	+	6.63103i	−0.262937	+	0.455421i
$213$		0			0
$214$	−14.0711	−	24.3718i	−0.961878	−	1.66602i
$215$	1.65685	−	2.86976i	0.112997	−	0.195716i
$216$		0			0
$217$		0			0
$218$	13.6569			0.924959
$219$		0			0
$220$	−2.24264	−	3.88437i	−0.151199	−	0.261884i
$221$	16.8995	+	29.2708i	1.13678	+	1.96897i
$222$		0			0
$223$	8.97056			0.600713			0.300357	−	0.953827i	$-0.402894\pi$
$223$	8.97056			0.600713			0.300357	+	0.953827i	$0.402894\pi$
$224$		0			0
$225$		0			0
$226$	20.8995	−	36.1990i	1.39021	−	2.40792i
$227$	7.89949	+	13.6823i	0.524308	+	0.908128i	0.999599	+	0.0282996i	$0.00900924\pi$
$227$	7.89949	+	13.6823i	0.524308	+	0.908128i	−0.475292	+	0.879828i	$0.657657\pi$
$228$		0			0
$229$	4.12132	−	7.13834i	0.272345	−	0.471715i	−0.697117	−	0.716957i	$-0.745534\pi$
$229$	4.12132	−	7.13834i	0.272345	−	0.471715i	0.969462	+	0.245243i	$0.0788676\pi$
$230$	−5.17157			−0.341003
$231$		0			0
$232$	5.17157			0.339530
$233$	11.0711	−	19.1757i	0.725290	−	1.25624i	−0.233565	−	0.972341i	$-0.575039\pi$
$233$	11.0711	−	19.1757i	0.725290	−	1.25624i	0.958855	−	0.283898i	$-0.0916275\pi$
$234$		0			0
$235$	−0.828427	−	1.43488i	−0.0540406	−	0.0936011i
$236$	13.0711	−	22.6398i	0.850854	−	1.47372i
$237$		0			0
$238$		0			0
$239$	4.34315			0.280935			0.140467	−	0.990085i	$-0.455139\pi$
$239$	4.34315			0.280935			0.140467	+	0.990085i	$0.455139\pi$
$240$		0			0
$241$	−3.87868	−	6.71807i	−0.249848	−	0.432749i	0.713636	−	0.700517i	$-0.247047\pi$
$241$	−3.87868	−	6.71807i	−0.249848	−	0.432749i	−0.963483	+	0.267768i	$0.913714\pi$
$242$	8.44975	+	14.6354i	0.543170	+	0.940799i
$243$		0			0
$244$	−14.3848			−0.920891
$245$		0			0
$246$		0			0
$247$	−7.65685	+	13.2621i	−0.487194	+	0.843845i
$248$	−15.0711	−	26.1039i	−0.957014	−	1.65760i
$249$		0			0
$250$	6.82843	−	11.8272i	0.431868	−	0.748017i
$251$	4.48528			0.283108			0.141554	−	0.989931i	$-0.454790\pi$
$251$	4.48528			0.283108			0.141554	+	0.989931i	$0.454790\pi$
$252$		0			0
$253$	−7.31371			−0.459809
$254$	−11.6569	+	20.1903i	−0.731416	+	1.26685i
$255$		0			0
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	9.60660	−	16.6391i	0.599243	−	1.03792i	−0.393690	−	0.919243i	$-0.628802\pi$
$257$	9.60660	−	16.6391i	0.599243	−	1.03792i	0.992933	−	0.118677i	$-0.0378651\pi$
$258$		0			0
$259$		0			0
$260$	−12.1421			−0.753023
$261$		0			0
$262$	−8.82843	−	15.2913i	−0.545422	−	0.944699i
$263$	−8.65685	−	14.9941i	−0.533805	−	0.924577i	−0.999220	−	0.0394843i	$-0.987428\pi$
$263$	−8.65685	−	14.9941i	−0.533805	−	0.924577i	0.465416	−	0.885092i	$-0.345905\pi$
$264$		0			0
$265$	1.17157			0.0719691
$266$		0			0
$267$		0			0
$268$	−10.8284	+	18.7554i	−0.661451	+	1.14567i
$269$	−5.36396	−	9.29065i	−0.327046	−	0.566461i	0.654878	−	0.755735i	$-0.272720\pi$
$269$	−5.36396	−	9.29065i	−0.327046	−	0.566461i	−0.981924	+	0.189274i	$0.939387\pi$
$270$		0			0
$271$	9.07107	−	15.7116i	0.551028	−	0.954409i	−0.447173	−	0.894448i	$-0.647569\pi$
$271$	9.07107	−	15.7116i	0.551028	−	0.954409i	0.998201	−	0.0599610i	$-0.0190976\pi$
$272$	18.7279			1.13555
$273$		0			0
$274$	34.1421			2.06260
$275$	4.65685	−	8.06591i	0.280819	−	0.486393i
$276$		0			0
$277$	−6.65685	−	11.5300i	−0.399972	−	0.692771i	0.593750	−	0.804649i	$-0.297647\pi$
$277$	−6.65685	−	11.5300i	−0.399972	−	0.692771i	−0.993722	+	0.111878i	$0.964313\pi$
$278$	−7.65685	+	13.2621i	−0.459228	+	0.795406i
$279$		0			0
$280$		0			0
$281$	16.4853			0.983429			0.491715	−	0.870756i	$-0.336370\pi$
$281$	16.4853			0.983429			0.491715	+	0.870756i	$0.336370\pi$
$282$		0			0
$283$	4.24264	+	7.34847i	0.252199	+	0.436821i	0.964131	−	0.265427i	$-0.0855130\pi$
$283$	4.24264	+	7.34847i	0.252199	+	0.436821i	−0.711932	+	0.702248i	$0.752180\pi$
$284$	−25.4853	−	44.1418i	−1.51227	−	2.61933i
$285$		0			0
$286$	−26.1421			−1.54582
$287$		0			0
$288$		0			0
$289$	−10.9853	+	19.0271i	−0.646193	+	1.11924i
$290$	−0.828427	−	1.43488i	−0.0486469	−	0.0842589i
$291$		0			0
$292$	−11.2929	+	19.5599i	−0.660867	+	1.14465i
$293$	19.4142			1.13419			0.567095	−	0.823652i	$-0.308067\pi$
$293$	19.4142			1.13419			0.567095	+	0.823652i	$0.308067\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	8.82843	−	15.2913i	0.513142	−	0.888788i
$297$		0			0
$298$	−6.41421	−	11.1097i	−0.371565	−	0.643570i
$299$	−9.89949	+	17.1464i	−0.572503	+	0.991604i
$300$		0			0
$301$		0			0
$302$	28.9706			1.66707
$303$		0			0
$304$	4.24264	+	7.34847i	0.243332	+	0.421464i
$305$	1.10051	+	1.90613i	0.0630147	+	0.109145i
$306$		0			0
$307$	−1.85786			−0.106034			−0.0530170	−	0.998594i	$-0.516884\pi$
$307$	−1.85786			−0.106034			−0.0530170	+	0.998594i	$0.516884\pi$
$308$		0			0
$309$		0			0
$310$	−4.82843	+	8.36308i	−0.274236	+	0.474991i
$311$	11.0711	+	19.1757i	0.627783	+	1.08735i	0.987996	+	0.154481i	$0.0493707\pi$
$311$	11.0711	+	19.1757i	0.627783	+	1.08735i	−0.360213	+	0.932870i	$0.617296\pi$
$312$		0			0
$313$	−8.94975	+	15.5014i	−0.505870	+	0.876192i	0.494107	+	0.869401i	$0.335495\pi$
$313$	−8.94975	+	15.5014i	−0.505870	+	0.876192i	−0.999977	+	0.00679098i	$0.997838\pi$
$314$	−48.8701			−2.75790
$315$		0			0
$316$	8.97056			0.504634
$317$	5.00000	−	8.66025i	0.280828	−	0.486408i	−0.690761	−	0.723083i	$-0.742724\pi$
$317$	5.00000	−	8.66025i	0.280828	−	0.486408i	0.971589	+	0.236675i	$0.0760576\pi$
$318$		0			0
$319$	−1.17157	−	2.02922i	−0.0655955	−	0.113615i
$320$	2.87868	−	4.98602i	0.160923	−	0.278727i
$321$		0			0
$322$		0			0
$323$	−17.6569			−0.982454
$324$		0			0
$325$	−12.6066	−	21.8353i	−0.699288	−	1.21120i
$326$	−13.6569	−	23.6544i	−0.756383	−	1.31009i
$327$		0			0
$328$	−9.89949			−0.546608
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	29.3137	+	50.7728i	1.60880	+	2.78652i
$333$		0			0
$334$	−23.8995	+	41.3951i	−1.30772	+	2.26504i
$335$	3.31371			0.181047
$336$		0			0
$337$	−18.3431			−0.999215			−0.499607	−	0.866252i	$-0.666522\pi$
$337$	−18.3431			−0.999215			−0.499607	+	0.866252i	$0.666522\pi$
$338$	−19.6924	+	34.1082i	−1.07112	+	1.85524i
$339$		0			0
$340$	−7.00000	−	12.1244i	−0.379628	−	0.657536i
$341$	−6.82843	+	11.8272i	−0.369780	+	0.640478i
$342$		0			0
$343$		0			0
$344$	−24.9706			−1.34632
$345$		0			0
$346$	−8.36396	−	14.4868i	−0.449649	−	0.778815i
$347$	5.34315	+	9.25460i	0.286835	+	0.496813i	0.973053	−	0.230584i	$-0.0740635\pi$
$347$	5.34315	+	9.25460i	0.286835	+	0.496813i	−0.686217	+	0.727396i	$0.740730\pi$
$348$		0			0
$349$	−9.89949			−0.529908			−0.264954	−	0.964261i	$-0.585357\pi$
$349$	−9.89949			−0.529908			−0.264954	+	0.964261i	$0.585357\pi$
$350$		0			0
$351$		0			0
$352$	1.58579	−	2.74666i	0.0845227	−	0.146398i
$353$	−5.36396	−	9.29065i	−0.285495	−	0.494492i	0.687234	−	0.726436i	$-0.258825\pi$
$353$	−5.36396	−	9.29065i	−0.285495	−	0.494492i	−0.972729	+	0.231944i	$0.925491\pi$
$354$		0			0
$355$	−3.89949	+	6.75412i	−0.206964	+	0.358472i
$356$	−22.0416			−1.16820
$357$		0			0
$358$	20.1421			1.06454
$359$	−5.82843	+	10.0951i	−0.307613	+	0.532801i	−0.977840	−	0.209355i	$-0.932863\pi$
$359$	−5.82843	+	10.0951i	−0.307613	+	0.532801i	0.670227	+	0.742156i	$0.266197\pi$
$360$		0			0
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	−6.53553	+	11.3199i	−0.343500	+	0.594960i
$363$		0			0
$364$		0			0
$365$	3.45584			0.180887
$366$		0			0
$367$	9.65685	+	16.7262i	0.504084	+	0.873099i	0.999989	+	0.00472187i	$0.00150302\pi$
$367$	9.65685	+	16.7262i	0.504084	+	0.873099i	−0.495905	+	0.868377i	$0.665164\pi$
$368$	5.48528	+	9.50079i	0.285940	+	0.495263i
$369$		0			0
$370$	−5.65685			−0.294086
$371$		0			0
$372$		0			0
$373$	16.6569	−	28.8505i	0.862459	−	1.49382i	−0.00708885	−	0.999975i	$-0.502256\pi$
$373$	16.6569	−	28.8505i	0.862459	−	1.49382i	0.869548	−	0.493848i	$-0.164410\pi$
$374$	−15.0711	−	26.1039i	−0.779306	−	1.34980i
$375$		0			0
$376$	−6.24264	+	10.8126i	−0.321940	+	0.557616i
$377$	−6.34315			−0.326689
$378$		0			0
$379$	31.3137			1.60848			0.804239	−	0.594307i	$-0.202573\pi$
$379$	31.3137			1.60848			0.804239	+	0.594307i	$0.202573\pi$
$380$	3.17157	−	5.49333i	0.162698	−	0.281802i
$381$		0			0
$382$	−21.7279	−	37.6339i	−1.11170	−	1.92552i
$383$	14.8284	−	25.6836i	0.757697	−	1.31237i	−0.186325	−	0.982488i	$-0.559658\pi$
$383$	14.8284	−	25.6836i	0.757697	−	1.31237i	0.944022	−	0.329882i	$-0.107009\pi$
$384$		0			0
$385$		0			0
$386$	−41.7990			−2.12751
$387$		0			0
$388$	10.3640	+	17.9509i	0.526150	+	0.911319i
$389$	5.07107	+	8.78335i	0.257113	+	0.445333i	0.965467	−	0.260524i	$-0.0838953\pi$
$389$	5.07107	+	8.78335i	0.257113	+	0.445333i	−0.708354	+	0.705857i	$0.750562\pi$
$390$		0			0
$391$	−22.8284			−1.15448
$392$		0			0
$393$		0			0
$394$	2.41421	−	4.18154i	0.121626	−	0.210663i
$395$	−0.686292	−	1.18869i	−0.0345311	−	0.0598096i
$396$		0			0
$397$	17.1924	−	29.7781i	0.862861	−	1.49452i	−0.00629405	−	0.999980i	$-0.502003\pi$
$397$	17.1924	−	29.7781i	0.862861	−	1.49452i	0.869155	−	0.494539i	$-0.164663\pi$
$398$	−24.9706			−1.25166
$399$		0			0
$400$	−13.9706			−0.698528
$401$	11.0711	−	19.1757i	0.552863	−	0.957586i	−0.445204	−	0.895429i	$-0.646869\pi$
$401$	11.0711	−	19.1757i	0.552863	−	0.957586i	0.998066	−	0.0621570i	$-0.0197980\pi$
$402$		0			0
$403$	18.4853	+	32.0174i	0.920817	+	1.59490i
$404$	−32.6777	+	56.5994i	−1.62577	+	2.81592i
$405$		0			0
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−9.29289	−	16.0958i	−0.459504	−	0.795884i	0.539431	−	0.842030i	$-0.318639\pi$
$409$	−9.29289	−	16.0958i	−0.459504	−	0.795884i	−0.998935	+	0.0461457i	$0.985306\pi$
$410$	1.58579	+	2.74666i	0.0783164	+	0.135648i
$411$		0			0
$412$	47.7990			2.35489
$413$		0			0
$414$		0			0
$415$	4.48528	−	7.76874i	0.220174	−	0.381352i
$416$	−4.29289	−	7.43551i	−0.210476	−	0.364556i
$417$		0			0
$418$	6.82843	−	11.8272i	0.333989	−	0.578486i
$419$	38.8284			1.89689			0.948446	−	0.316938i	$-0.102655\pi$
$419$	38.8284			1.89689			0.948446	+	0.316938i	$0.102655\pi$
$420$		0			0
$421$	−28.6274			−1.39521			−0.697607	−	0.716480i	$-0.745752\pi$
$421$	−28.6274			−1.39521			−0.697607	+	0.716480i	$0.745752\pi$
$422$	25.3137	−	43.8446i	1.23225	−	2.13432i
$423$		0			0
$424$	−4.41421	−	7.64564i	−0.214373	−	0.371305i
$425$	14.5355	−	25.1763i	0.705077	−	1.22123i
$426$		0			0
$427$		0			0
$428$	44.6274			2.15715
$429$		0			0
$430$	4.00000	+	6.92820i	0.192897	+	0.334108i
$431$	3.48528	+	6.03668i	0.167880	+	0.290777i	0.937674	−	0.347515i	$-0.112975\pi$
$431$	3.48528	+	6.03668i	0.167880	+	0.290777i	−0.769794	+	0.638292i	$0.779641\pi$
$432$		0			0
$433$	11.7574			0.565023			0.282511	−	0.959264i	$-0.408833\pi$
$433$	11.7574			0.565023			0.282511	+	0.959264i	$0.408833\pi$
$434$		0			0
$435$		0			0
$436$	−10.8284	+	18.7554i	−0.518588	+	0.898220i
$437$	−5.17157	−	8.95743i	−0.247390	−	0.428492i
$438$		0			0
$439$	17.6569	−	30.5826i	0.842716	−	1.45963i	−0.0448746	−	0.998993i	$-0.514289\pi$
$439$	17.6569	−	30.5826i	0.842716	−	1.45963i	0.887590	−	0.460634i	$-0.152378\pi$
$440$	5.17157			0.246545
$441$		0			0
$442$	−81.5980			−3.88122
$443$	0.514719	−	0.891519i	0.0244550	−	0.0423573i	−0.853539	−	0.521029i	$-0.825548\pi$
$443$	0.514719	−	0.891519i	0.0244550	−	0.0423573i	0.877994	+	0.478672i	$0.158882\pi$
$444$		0			0
$445$	1.68629	+	2.92074i	0.0799379	+	0.138456i
$446$	−10.8284	+	18.7554i	−0.512741	+	0.888093i
$447$		0			0
$448$		0			0
$449$	−17.3137			−0.817084			−0.408542	−	0.912739i	$-0.633963\pi$
$449$	−17.3137			−0.817084			−0.408542	+	0.912739i	$0.633963\pi$
$450$		0			0
$451$	2.24264	+	3.88437i	0.105602	+	0.182908i
$452$	33.1421	+	57.4039i	1.55887	+	2.70005i
$453$		0			0
$454$	−38.1421			−1.79010
$455$		0			0
$456$		0			0
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	−0.575036	−	0.818128i	$-0.695012\pi$
$457$	9.00000	−	15.5885i	0.421002	−	0.729197i	0.996038	+	0.0889312i	$0.0283451\pi$
$458$	9.94975	+	17.2335i	0.464921	+	0.805267i
$459$		0			0
$460$	4.10051	−	7.10228i	0.191187	−	0.331146i
$461$	−19.4142			−0.904210			−0.452105	−	0.891965i	$-0.649327\pi$
$461$	−19.4142			−0.904210			−0.452105	+	0.891965i	$0.649327\pi$
$462$		0			0
$463$	18.6274			0.865689			0.432845	−	0.901468i	$-0.357510\pi$
$463$	18.6274			0.865689			0.432845	+	0.901468i	$0.357510\pi$
$464$	−1.75736	+	3.04384i	−0.0815834	+	0.141307i
$465$		0			0
$466$	26.7279	+	46.2941i	1.23815	+	2.14453i
$467$	−19.8995	+	34.4669i	−0.920839	+	1.59494i	−0.122718	+	0.992442i	$0.539161\pi$
$467$	−19.8995	+	34.4669i	−0.920839	+	1.59494i	−0.798120	+	0.602498i	$0.794172\pi$
$468$		0			0
$469$		0			0
$470$	4.00000			0.184506
$471$		0			0
$472$	15.0711	+	26.1039i	0.693702	+	1.20153i
$473$	5.65685	+	9.79796i	0.260102	+	0.450511i
$474$		0			0
$475$	13.1716			0.604353
$476$		0			0
$477$		0			0
$478$	−5.24264	+	9.08052i	−0.239793	+	0.415333i
$479$	−15.0711	−	26.1039i	−0.688615	−	1.19272i	−0.972286	−	0.233794i	$-0.924886\pi$
$479$	−15.0711	−	26.1039i	−0.688615	−	1.19272i	0.283671	−	0.958922i	$-0.408447\pi$
$480$		0			0
$481$	−10.8284	+	18.7554i	−0.493734	+	0.855172i
$482$	18.7279			0.853033
$483$		0			0
$484$	−26.7990			−1.21814
$485$	1.58579	−	2.74666i	0.0720069	−	0.124720i
$486$		0			0
$487$	9.31371	+	16.1318i	0.422044	+	0.731002i	0.996139	−	0.0877864i	$-0.0279793\pi$
$487$	9.31371	+	16.1318i	0.422044	+	0.731002i	−0.574095	+	0.818789i	$0.694646\pi$
$488$	8.29289	−	14.3637i	0.375402	−	0.650215i
$489$		0			0
$490$		0			0
$491$	−38.9706			−1.75872			−0.879358	−	0.476160i	$-0.842028\pi$
$491$	−38.9706			−1.75872			−0.879358	+	0.476160i	$0.842028\pi$
$492$		0			0
$493$	−3.65685	−	6.33386i	−0.164696	−	0.285263i
$494$	−18.4853	−	32.0174i	−0.831692	−	1.44053i
$495$		0			0
$496$	20.4853			0.919816
$497$		0			0
$498$		0			0
$499$	9.65685	−	16.7262i	0.432300	−	0.748766i	−0.564771	−	0.825248i	$-0.691035\pi$
$499$	9.65685	−	16.7262i	0.432300	−	0.748766i	0.997071	+	0.0764820i	$0.0243688\pi$
$500$	10.8284	+	18.7554i	0.484262	+	0.838766i
$501$		0			0
$502$	−5.41421	+	9.37769i	−0.241648	+	0.418547i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	10.0000			0.444994
$506$	8.82843	−	15.2913i	0.392471	−	0.679781i
$507$		0			0
$508$	−18.4853	−	32.0174i	−0.820152	−	1.42054i
$509$	12.7782	−	22.1324i	0.566383	−	0.981003i	−0.430537	−	0.902573i	$-0.641676\pi$
$509$	12.7782	−	22.1324i	0.566383	−	0.981003i	0.996920	−	0.0784305i	$-0.0249909\pi$
$510$		0			0
$511$		0			0
$512$	−31.2426			−1.38074
$513$		0			0
$514$	23.1924	+	40.1704i	1.02297	+	1.77184i
$515$	−3.65685	−	6.33386i	−0.161140	−	0.279103i
$516$		0			0
$517$	5.65685			0.248788
$518$		0			0
$519$		0			0
$520$	7.00000	−	12.1244i	0.306970	−	0.531688i
$521$	16.2929	+	28.2201i	0.713805	+	1.23635i	0.963419	+	0.268000i	$0.0863629\pi$
$521$	16.2929	+	28.2201i	0.713805	+	1.23635i	−0.249614	+	0.968345i	$0.580304\pi$
$522$		0			0
$523$	−7.17157	+	12.4215i	−0.313591	+	0.543156i	−0.979137	−	0.203201i	$-0.934865\pi$
$523$	−7.17157	+	12.4215i	−0.313591	+	0.543156i	0.665546	+	0.746357i	$0.268199\pi$
$524$	28.0000			1.22319
$525$		0			0
$526$	41.7990			1.82252
$527$	−21.3137	+	36.9164i	−0.928440	+	1.60810i
$528$		0			0
$529$	4.81371	+	8.33759i	0.209292	+	0.362504i
$530$	−1.41421	+	2.44949i	−0.0614295	+	0.106399i
$531$		0			0
$532$		0			0
$533$	12.1421			0.525934
$534$		0			0
$535$	−3.41421	−	5.91359i	−0.147609	−	0.255667i
$536$	−12.4853	−	21.6251i	−0.539282	−	0.934064i
$537$		0			0
$538$	25.8995			1.11661
$539$		0			0
$540$		0			0
$541$	2.65685	−	4.60181i	0.114227	−	0.197847i	−0.803243	−	0.595651i	$-0.796894\pi$
$541$	2.65685	−	4.60181i	0.114227	−	0.197847i	0.917471	+	0.397804i	$0.130228\pi$
$542$	21.8995	+	37.9310i	0.940664	+	1.62928i
$543$		0			0
$544$	4.94975	−	8.57321i	0.212219	−	0.367574i
$545$	3.31371			0.141944
$546$		0			0
$547$	−3.02944			−0.129529			−0.0647647	−	0.997901i	$-0.520630\pi$
$547$	−3.02944			−0.129529			−0.0647647	+	0.997901i	$0.520630\pi$
$548$	−27.0711	+	46.8885i	−1.15642	+	2.00298i
$549$		0			0
$550$	11.2426	+	19.4728i	0.479388	+	0.830324i
$551$	1.65685	−	2.86976i	0.0705844	−	0.122256i
$552$		0			0
$553$		0			0
$554$	32.1421			1.36559
$555$		0			0
$556$	−12.1421	−	21.0308i	−0.514941	−	0.891904i
$557$	13.0000	+	22.5167i	0.550828	+	0.954062i	0.998215	+	0.0597213i	$0.0190212\pi$
$557$	13.0000	+	22.5167i	0.550828	+	0.954062i	−0.447387	+	0.894340i	$0.647645\pi$
$558$		0			0
$559$	30.6274			1.29540
$560$		0			0
$561$		0			0
$562$	−19.8995	+	34.4669i	−0.839410	+	1.45390i
$563$	3.41421	+	5.91359i	0.143892	+	0.249228i	0.928959	−	0.370183i	$-0.120705\pi$
$563$	3.41421	+	5.91359i	0.143892	+	0.249228i	−0.785067	+	0.619411i	$0.787372\pi$
$564$		0			0
$565$	5.07107	−	8.78335i	0.213341	−	0.369518i
$566$	−20.4853			−0.861061
$567$		0			0
$568$	58.7696			2.46592
$569$	0.242641	−	0.420266i	0.0101720	−	0.0176185i	−0.860895	−	0.508783i	$-0.830095\pi$
$569$	0.242641	−	0.420266i	0.0101720	−	0.0176185i	0.871067	+	0.491165i	$0.163429\pi$
$570$		0			0
$571$	−16.8284	−	29.1477i	−0.704248	−	1.21979i	−0.966962	−	0.254919i	$-0.917951\pi$
$571$	−16.8284	−	29.1477i	−0.704248	−	1.21979i	0.262715	−	0.964874i	$-0.415382\pi$
$572$	20.7279	−	35.9018i	0.866678	−	1.50113i
$573$		0			0
$574$		0			0
$575$	17.0294			0.710177
$576$		0			0
$577$	−7.05025	−	12.2114i	−0.293506	−	0.508367i	0.681130	−	0.732162i	$-0.261489\pi$
$577$	−7.05025	−	12.2114i	−0.293506	−	0.508367i	−0.974636	+	0.223795i	$0.928155\pi$
$578$	−26.5208	−	45.9354i	−1.10312	−	1.91066i
$579$		0			0
$580$	2.62742			0.109098
$581$		0			0
$582$		0			0
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	−13.0208	−	22.5527i	−0.538805	−	0.933238i
$585$		0			0
$586$	−23.4350	+	40.5907i	−0.968092	+	1.67678i
$587$	−17.1716			−0.708747			−0.354373	−	0.935104i	$-0.615306\pi$
$587$	−17.1716			−0.708747			−0.354373	+	0.935104i	$0.615306\pi$
$588$		0			0
$589$	−19.3137			−0.795807
$590$	4.82843	−	8.36308i	0.198783	−	0.344303i
$591$		0			0
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	10.5355	−	18.2481i	0.432643	−	0.749359i	−0.564457	−	0.825462i	$-0.690915\pi$
$593$	10.5355	−	18.2481i	0.432643	−	0.749359i	0.997100	+	0.0761034i	$0.0242479\pi$
$594$		0			0
$595$		0			0
$596$	20.3431			0.833288
$597$		0			0
$598$	−23.8995	−	41.3951i	−0.977323	−	1.69277i
$599$	−1.00000	−	1.73205i	−0.0408589	−	0.0707697i	0.844873	−	0.534967i	$-0.179676\pi$
$599$	−1.00000	−	1.73205i	−0.0408589	−	0.0707697i	−0.885732	+	0.464198i	$0.846343\pi$
$600$		0			0
$601$	0.928932			0.0378919			0.0189460	−	0.999821i	$-0.493969\pi$
$601$	0.928932			0.0378919			0.0189460	+	0.999821i	$0.493969\pi$
$602$		0			0
$603$		0			0
$604$	−22.9706	+	39.7862i	−0.934659	+	1.61888i
$605$	2.05025	+	3.55114i	0.0833546	+	0.144374i
$606$		0			0
$607$	−14.8284	+	25.6836i	−0.601867	+	1.04246i	0.390671	+	0.920530i	$0.372243\pi$
$607$	−14.8284	+	25.6836i	−0.601867	+	1.04246i	−0.992538	+	0.121934i	$0.961090\pi$
$608$	4.48528			0.181902
$609$		0			0
$610$	−5.31371			−0.215146
$611$	7.65685	−	13.2621i	0.309763	−	0.536526i
$612$		0			0
$613$	−13.6569	−	23.6544i	−0.551595	−	0.955391i	−0.998160	−	0.0606394i	$-0.980686\pi$
$613$	−13.6569	−	23.6544i	−0.551595	−	0.955391i	0.446565	−	0.894751i	$-0.352647\pi$
$614$	2.24264	−	3.88437i	0.0905056	−	0.156760i
$615$		0			0
$616$		0			0
$617$	7.51472			0.302531			0.151266	−	0.988493i	$-0.451665\pi$
$617$	7.51472			0.302531			0.151266	+	0.988493i	$0.451665\pi$
$618$		0			0
$619$	−2.48528	−	4.30463i	−0.0998919	−	0.173018i	0.811748	−	0.584008i	$-0.198516\pi$
$619$	−2.48528	−	4.30463i	−0.0998919	−	0.173018i	−0.911640	+	0.410990i	$0.865183\pi$
$620$	−7.65685	−	13.2621i	−0.307507	−	0.532617i
$621$		0			0
$622$	−53.4558			−2.14338
$623$		0			0
$624$		0			0
$625$	−9.98528	+	17.2950i	−0.399411	+	0.691801i
$626$	−21.6066	−	37.4237i	−0.863573	−	1.49575i
$627$		0			0
$628$	38.7487	−	67.1148i	1.54624	−	2.67817i
$629$	−24.9706			−0.995642
$630$		0			0
$631$	0.686292			0.0273208			0.0136604	−	0.999907i	$-0.495652\pi$
$631$	0.686292			0.0273208			0.0136604	+	0.999907i	$0.495652\pi$
$632$	−5.17157	+	8.95743i	−0.205714	+	0.356307i
$633$		0			0
$634$	12.0711	+	20.9077i	0.479403	+	0.830351i
$635$	−2.82843	+	4.89898i	−0.112243	+	0.194410i
$636$		0			0
$637$		0			0
$638$	5.65685			0.223957
$639$		0			0
$640$	6.02082	+	10.4284i	0.237994	+	0.412217i
$641$	−2.58579	−	4.47871i	−0.102132	−	0.176899i	0.810431	−	0.585835i	$-0.199233\pi$
$641$	−2.58579	−	4.47871i	−0.102132	−	0.176899i	−0.912563	+	0.408936i	$0.865900\pi$
$642$		0			0
$643$	−50.4264			−1.98862			−0.994312	−	0.106510i	$-0.966033\pi$
$643$	−50.4264			−1.98862			−0.994312	+	0.106510i	$0.966033\pi$
$644$		0			0
$645$		0			0
$646$	21.3137	−	36.9164i	0.838577	−	1.45246i
$647$	−10.5858	−	18.3351i	−0.416170	−	0.720828i	0.579380	−	0.815057i	$-0.303295\pi$
$647$	−10.5858	−	18.3351i	−0.416170	−	0.720828i	−0.995551	+	0.0942294i	$0.969961\pi$
$648$		0			0
$649$	6.82843	−	11.8272i	0.268039	−	0.464258i
$650$	60.8701			2.38752
$651$		0			0
$652$	43.3137			1.69630
$653$	9.75736	−	16.9002i	0.381835	−	0.661358i	−0.609490	−	0.792794i	$-0.708626\pi$
$653$	9.75736	−	16.9002i	0.381835	−	0.661358i	0.991325	+	0.131436i	$0.0419589\pi$
$654$		0			0
$655$	−2.14214	−	3.71029i	−0.0837002	−	0.144973i
$656$	3.36396	−	5.82655i	0.131341	−	0.227489i
$657$		0			0
$658$		0			0
$659$	13.3137			0.518628			0.259314	−	0.965793i	$-0.416503\pi$
$659$	13.3137			0.518628			0.259314	+	0.965793i	$0.416503\pi$
$660$		0			0
$661$	3.77817	+	6.54399i	0.146954	+	0.254532i	0.930100	−	0.367306i	$-0.119720\pi$
$661$	3.77817	+	6.54399i	0.146954	+	0.254532i	−0.783146	+	0.621838i	$0.786386\pi$
$662$	4.82843	+	8.36308i	0.187662	+	0.325040i
$663$		0			0
$664$	−67.5980			−2.62331
$665$		0			0
$666$		0			0
$667$	2.14214	−	3.71029i	0.0829438	−	0.143663i
$668$	−37.8995	−	65.6439i	−1.46638	−	2.53984i
$669$		0			0
$670$	−4.00000	+	6.92820i	−0.154533	+	0.267660i
$671$	−7.51472			−0.290102
$672$		0			0
$673$	0.686292			0.0264546			0.0132273	−	0.999913i	$-0.495789\pi$
$673$	0.686292			0.0264546			0.0132273	+	0.999913i	$0.495789\pi$
$674$	22.1421	−	38.3513i	0.852883	−	1.47724i
$675$		0			0
$676$	−31.2279	−	54.0883i	−1.20107	−	2.08032i
$677$	−14.2929	+	24.7560i	−0.549321	+	0.951451i	0.449001	+	0.893531i	$0.351780\pi$
$677$	−14.2929	+	24.7560i	−0.549321	+	0.951451i	−0.998321	+	0.0579196i	$0.981553\pi$
$678$		0			0
$679$		0			0
$680$	16.1421			0.619023
$681$		0			0
$682$	−16.4853	−	28.5533i	−0.631254	−	1.09336i
$683$	−4.17157	−	7.22538i	−0.159621	−	0.276471i	0.775111	−	0.631825i	$-0.217694\pi$
$683$	−4.17157	−	7.22538i	−0.159621	−	0.276471i	−0.934732	+	0.355354i	$0.884360\pi$
$684$		0			0
$685$	8.28427			0.316526
$686$		0			0
$687$		0			0
$688$	8.48528	−	14.6969i	0.323498	−	0.560316i
$689$	5.41421	+	9.37769i	0.206265	+	0.357262i
$690$		0			0
$691$	−11.6569	+	20.1903i	−0.443448	+	0.768074i	−0.997943	−	0.0641132i	$-0.979578\pi$
$691$	−11.6569	+	20.1903i	−0.443448	+	0.768074i	0.554495	+	0.832187i	$0.312911\pi$
$692$	26.5269			1.00840
$693$		0			0
$694$	−25.7990			−0.979316
$695$	−1.85786	+	3.21792i	−0.0704728	+	0.122062i
$696$		0			0
$697$	7.00000	+	12.1244i	0.265144	+	0.459243i
$698$	11.9497	−	20.6976i	0.452305	−	0.783415i
$699$		0			0
$700$		0			0
$701$	22.8284			0.862218			0.431109	−	0.902300i	$-0.358122\pi$
$701$	22.8284			0.862218			0.431109	+	0.902300i	$0.358122\pi$
$702$		0			0
$703$	−5.65685	−	9.79796i	−0.213352	−	0.369537i
$704$	9.82843	+	17.0233i	0.370423	+	0.641591i
$705$		0			0
$706$	25.8995			0.974740
$707$		0			0
$708$		0			0
$709$	−10.1421	+	17.5667i	−0.380896	+	0.659731i	−0.991191	−	0.132443i	$-0.957718\pi$
$709$	−10.1421	+	17.5667i	−0.380896	+	0.659731i	0.610295	+	0.792174i	$0.291051\pi$
$710$	−9.41421	−	16.3059i	−0.353309	−	0.611949i
$711$		0			0
$712$	12.7071	−	22.0094i	0.476219	−	0.824835i
$713$	−24.9706			−0.935155
$714$		0			0
$715$	−6.34315			−0.237220
$716$	−15.9706	+	27.6618i	−0.596848	+	1.03377i
$717$		0			0
$718$	−14.0711	−	24.3718i	−0.525128	−	0.909548i
$719$	12.9706	−	22.4657i	0.483720	−	0.837828i	−0.516105	−	0.856525i	$-0.672619\pi$
$719$	12.9706	−	22.4657i	0.483720	−	0.837828i	0.999825	+	0.0186972i	$0.00595184\pi$
$720$		0			0
$721$		0			0
$722$	−26.5563			−0.988325
$723$		0			0
$724$	−10.3640	−	17.9509i	−0.385174	−	0.667140i
$725$	2.72792	+	4.72490i	0.101312	+	0.175478i
$726$		0			0
$727$	4.48528			0.166350			0.0831749	−	0.996535i	$-0.473494\pi$
$727$	4.48528			0.166350			0.0831749	+	0.996535i	$0.473494\pi$
$728$		0			0
$729$		0			0
$730$	−4.17157	+	7.22538i	−0.154397	+	0.267423i
$731$	17.6569	+	30.5826i	0.653062	+	1.13114i
$732$		0			0
$733$	−4.84924	+	8.39913i	−0.179111	+	0.310229i	−0.941576	−	0.336800i	$-0.890655\pi$
$733$	−4.84924	+	8.39913i	−0.179111	+	0.310229i	0.762465	+	0.647029i	$0.223989\pi$
$734$	−46.6274			−1.72105
$735$		0			0
$736$	5.79899			0.213754
$737$	−5.65685	+	9.79796i	−0.208373	+	0.360912i
$738$		0			0
$739$	−13.6569	−	23.6544i	−0.502376	−	0.870140i	−0.999996	−	0.00274517i	$-0.999126\pi$
$739$	−13.6569	−	23.6544i	−0.502376	−	0.870140i	0.497621	−	0.867395i	$-0.334207\pi$
$740$	4.48528	−	7.76874i	0.164882	−	0.285584i
$741$		0			0
$742$		0			0
$743$	17.0294			0.624749			0.312375	−	0.949959i	$-0.398876\pi$
$743$	17.0294			0.624749			0.312375	+	0.949959i	$0.398876\pi$
$744$		0			0
$745$	−1.55635	−	2.69568i	−0.0570202	−	0.0987619i
$746$	40.2132	+	69.6513i	1.47231	+	2.55012i
$747$		0			0
$748$	47.7990			1.74770
$749$		0			0
$750$		0			0
$751$	−1.17157	+	2.02922i	−0.0427513	+	0.0740474i	−0.886609	−	0.462519i	$-0.846946\pi$
$751$	−1.17157	+	2.02922i	−0.0427513	+	0.0740474i	0.843858	+	0.536567i	$0.180279\pi$
$752$	−4.24264	−	7.34847i	−0.154713	−	0.267971i
$753$		0			0
$754$	7.65685	−	13.2621i	0.278846	−	0.482976i
$755$	7.02944			0.255827
$756$		0			0
$757$	37.6569			1.36866			0.684331	−	0.729172i	$-0.260094\pi$
$757$	37.6569			1.36866			0.684331	+	0.729172i	$0.260094\pi$
$758$	−37.7990	+	65.4698i	−1.37292	+	2.37797i
$759$		0			0
$760$	3.65685	+	6.33386i	0.132648	+	0.229753i
$761$	−23.2635	+	40.2935i	−0.843300	+	1.46064i	0.0437901	+	0.999041i	$0.486057\pi$
$761$	−23.2635	+	40.2935i	−0.843300	+	1.46064i	−0.887090	+	0.461597i	$0.847277\pi$
$762$		0			0
$763$		0			0
$764$	68.9117			2.49314
$765$		0			0
$766$	35.7990	+	62.0057i	1.29347	+	2.24036i
$767$	−18.4853	−	32.0174i	−0.667465	−	1.15608i
$768$		0			0
$769$	29.6985			1.07095			0.535477	−	0.844550i	$-0.320132\pi$
$769$	29.6985			1.07095			0.535477	+	0.844550i	$0.320132\pi$
$770$		0			0
$771$		0			0
$772$	33.1421	−	57.4039i	1.19281	−	2.06601i
$773$	−10.7782	−	18.6683i	−0.387664	−	0.671454i	0.604471	−	0.796627i	$-0.293385\pi$
$773$	−10.7782	−	18.6683i	−0.387664	−	0.671454i	−0.992135	+	0.125174i	$0.960051\pi$
$774$		0			0
$775$	15.8995	−	27.5387i	0.571127	−	0.989220i
$776$	−23.8995			−0.857942
$777$		0			0
$778$	−24.4853			−0.877840
$779$	−3.17157	+	5.49333i	−0.113633	+	0.196819i
$780$		0			0
$781$	−13.3137	−	23.0600i	−0.476402	−	0.825152i
$782$	27.5563	−	47.7290i	0.985413	−	1.70679i
$783$		0			0
$784$		0			0
$785$	−11.8579			−0.423225
$786$		0			0
$787$	23.6569	+	40.9749i	0.843276	+	1.46060i	0.887110	+	0.461558i	$0.152709\pi$
$787$	23.6569	+	40.9749i	0.843276	+	1.46060i	−0.0438344	+	0.999039i	$0.513957\pi$
$788$	3.82843	+	6.63103i	0.136382	+	0.236221i
$789$		0			0
$790$	3.31371			0.117896
$791$		0			0
$792$		0			0
$793$	−10.1716	+	17.6177i	−0.361203	+	0.625622i
$794$	41.5061	+	71.8907i	1.47300	+	2.55130i
$795$		0			0
$796$	19.7990	−	34.2929i	0.701757	−	1.21548i
$797$	28.3848			1.00544			0.502720	−	0.864449i	$-0.332333\pi$
$797$	28.3848			1.00544			0.502720	+	0.864449i	$0.332333\pi$
$798$		0			0
$799$	17.6569			0.624655
$800$	−3.69239	+	6.39540i	−0.130546	+	0.226112i
$801$		0			0
$802$	26.7279	+	46.2941i	0.943796	+	1.63470i
$803$	−5.89949	+	10.2182i	−0.208189	+	0.360593i
$804$		0			0
$805$		0			0
$806$	−89.2548			−3.14387
$807$		0			0
$808$	−37.6777	−	65.2596i	−1.32550	−	2.29583i
$809$	−23.9706	−	41.5182i	−0.842760	−	1.45970i	−0.887552	−	0.460707i	$-0.847596\pi$
$809$	−23.9706	−	41.5182i	−0.842760	−	1.45970i	0.0447922	−	0.998996i	$-0.485737\pi$
$810$		0			0
$811$	6.34315			0.222738			0.111369	−	0.993779i	$-0.464476\pi$
$811$	6.34315			0.222738			0.111369	+	0.993779i	$0.464476\pi$
$812$		0			0
$813$		0			0
$814$	9.65685	−	16.7262i	0.338473	−	0.586252i
$815$	−3.31371	−	5.73951i	−0.116074	−	0.201046i
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	44.8701			1.56884
$819$		0			0
$820$	−5.02944			−0.175636
$821$	−16.6569	+	28.8505i	−0.581328	+	1.00689i	0.413994	+	0.910280i	$0.364133\pi$
$821$	−16.6569	+	28.8505i	−0.581328	+	1.00689i	−0.995322	+	0.0966104i	$0.969200\pi$
$822$		0			0
$823$	12.4853	+	21.6251i	0.435210	+	0.753805i	0.997313	−	0.0732621i	$-0.0233410\pi$
$823$	12.4853	+	21.6251i	0.435210	+	0.753805i	−0.562103	+	0.827067i	$0.690008\pi$
$824$	−27.5563	+	47.7290i	−0.959971	+	1.66272i
$825$		0			0
$826$		0			0
$827$	−36.3431			−1.26378			−0.631888	−	0.775060i	$-0.717720\pi$
$827$	−36.3431			−1.26378			−0.631888	+	0.775060i	$0.717720\pi$
$828$		0			0
$829$	12.3640	+	21.4150i	0.429418	+	0.743774i	0.996822	−	0.0796659i	$-0.0253853\pi$
$829$	12.3640	+	21.4150i	0.429418	+	0.743774i	−0.567404	+	0.823440i	$0.692052\pi$
$830$	10.8284	+	18.7554i	0.375860	+	0.651009i
$831$		0			0
$832$	53.2132			1.84484
$833$		0			0
$834$		0			0
$835$	−5.79899	+	10.0441i	−0.200682	+	0.347592i
$836$	10.8284	+	18.7554i	0.374509	+	0.648669i
$837$		0			0
$838$	−46.8701	+	81.1813i	−1.61910	+	2.80436i
$839$	45.1716			1.55950			0.779748	−	0.626094i	$-0.215347\pi$
$839$	45.1716			1.55950			0.779748	+	0.626094i	$0.215347\pi$
$840$		0			0
$841$	−27.6274			−0.952670
$842$	34.5563	−	59.8534i	1.19089	−	2.06268i
$843$		0			0
$844$	40.1421	+	69.5282i	1.38175	+	2.39326i
$845$	−4.77817	+	8.27604i	−0.164374	+	0.284704i
$846$		0			0
$847$		0			0
$848$	6.00000			0.206041
$849$		0			0
$850$	35.0919	+	60.7809i	1.20364	+	2.08477i
$851$	−7.31371	−	12.6677i	−0.250711	−	0.434244i
$852$		0			0
$853$	−49.4975			−1.69476			−0.847381	−	0.530986i	$-0.821822\pi$
$853$	−49.4975			−1.69476			−0.847381	+	0.530986i	$0.821822\pi$
$854$		0			0
$855$		0			0
$856$	−25.7279	+	44.5621i	−0.879362	+	1.52310i
$857$	−6.29289	−	10.8996i	−0.214961	−	0.372324i	0.738299	−	0.674473i	$-0.235629\pi$
$857$	−6.29289	−	10.8996i	−0.214961	−	0.372324i	−0.953261	+	0.302149i	$0.902296\pi$
$858$		0			0
$859$	3.27208	−	5.66741i	0.111642	−	0.193369i	−0.804791	−	0.593559i	$-0.797722\pi$
$859$	3.27208	−	5.66741i	0.111642	−	0.193369i	0.916432	+	0.400190i	$0.131056\pi$
$860$	−12.6863			−0.432599
$861$		0			0
$862$	−16.8284			−0.573179
$863$	−2.65685	+	4.60181i	−0.0904404	+	0.156647i	−0.907697	−	0.419627i	$-0.862161\pi$
$863$	−2.65685	+	4.60181i	−0.0904404	+	0.156647i	0.817256	+	0.576275i	$0.195494\pi$
$864$		0			0
$865$	−2.02944	−	3.51509i	−0.0690029	−	0.119517i
$866$	−14.1924	+	24.5819i	−0.482277	+	0.835328i
$867$		0			0
$868$		0			0
$869$	4.68629			0.158972
$870$		0			0
$871$	15.3137	+	26.5241i	0.518885	+	0.898736i
$872$	−12.4853	−	21.6251i	−0.422805	−	0.732320i
$873$		0			0
$874$	24.9706			0.844642
$875$		0			0
$876$		0			0
$877$	−5.65685	+	9.79796i	−0.191018	+	0.330854i	−0.945588	−	0.325366i	$-0.894512\pi$
$877$	−5.65685	+	9.79796i	−0.191018	+	0.330854i	0.754570	+	0.656220i	$0.227846\pi$
$878$	42.6274	+	73.8329i	1.43861	+	2.49174i
$879$		0			0
$880$	−1.75736	+	3.04384i	−0.0592406	+	0.102608i
$881$	30.2426			1.01890			0.509450	−	0.860500i	$-0.329849\pi$
$881$	30.2426			1.01890			0.509450	+	0.860500i	$0.329849\pi$
$882$		0			0
$883$	−27.3137			−0.919179			−0.459590	−	0.888131i	$-0.652004\pi$
$883$	−27.3137			−0.919179			−0.459590	+	0.888131i	$0.652004\pi$
$884$	64.6985	−	112.061i	2.17605	−	3.76902i
$885$		0			0
$886$	1.24264	+	2.15232i	0.0417473	+	0.0723085i
$887$	−1.41421	+	2.44949i	−0.0474846	+	0.0822458i	−0.888791	−	0.458313i	$-0.848454\pi$
$887$	−1.41421	+	2.44949i	−0.0474846	+	0.0822458i	0.841306	+	0.540559i	$0.181787\pi$
$888$		0			0
$889$		0			0
$890$	−8.14214			−0.272925
$891$		0			0
$892$	−17.1716	−	29.7420i	−0.574947	−	0.995837i
$893$	4.00000	+	6.92820i	0.133855	+	0.231843i
$894$		0			0
$895$	4.88730			0.163364
$896$		0			0
$897$		0			0
$898$	20.8995	−	36.1990i	0.697425	−	1.20798i
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$		0			0
$901$	−6.24264	+	10.8126i	−0.207973	+	0.360219i
$902$	−10.8284			−0.360547
$903$		0			0
$904$	−76.4264			−2.54190
$905$	−1.58579	+	2.74666i	−0.0527133	+	0.0913022i
$906$		0			0
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	0.967730	−	0.251990i	$-0.0810849\pi$
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	−0.702094	+	0.712084i	$0.747752\pi$
$908$	30.2426	−	52.3818i	1.00364	−	1.73835i
$909$		0			0
$910$		0			0
$911$	34.9706			1.15863			0.579313	−	0.815105i	$-0.303321\pi$
$911$	34.9706			1.15863			0.579313	+	0.815105i	$0.303321\pi$
$912$		0			0
$913$	15.3137	+	26.5241i	0.506810	+	0.877820i
$914$	21.7279	+	37.6339i	0.718696	+	1.24482i
$915$		0			0
$916$	−31.5563			−1.04265
$917$		0			0
$918$		0			0
$919$	−24.1421	+	41.8154i	−0.796376	+	1.37936i	0.125586	+	0.992083i	$0.459919\pi$
$919$	−24.1421	+	41.8154i	−0.796376	+	1.37936i	−0.921962	+	0.387280i	$0.873415\pi$
$920$	4.72792	+	8.18900i	0.155875	+	0.269983i
$921$		0			0
$922$	23.4350	−	40.5907i	0.771792	−	1.33678i
$923$	−72.0833			−2.37265
$924$		0			0
$925$	18.6274			0.612466
$926$	−22.4853	+	38.9456i	−0.738912	+	1.27983i
$927$		0			0
$928$	0.928932	+	1.60896i	0.0304937	+	0.0528166i
$929$	−1.60660	+	2.78272i	−0.0527109	+	0.0912979i	−0.891177	−	0.453656i	$-0.850120\pi$
$929$	−1.60660	+	2.78272i	−0.0527109	+	0.0912979i	0.838466	+	0.544954i	$0.183453\pi$
$930$		0			0
$931$		0			0
$932$	−84.7696			−2.77672
$933$		0			0
$934$	−48.0416	−	83.2105i	−1.57197	−	2.72273i
$935$	−3.65685	−	6.33386i	−0.119592	−	0.207139i
$936$		0			0
$937$	−33.4142			−1.09159			−0.545797	−	0.837917i	$-0.683773\pi$
$937$	−33.4142			−1.09159			−0.545797	+	0.837917i	$0.683773\pi$
$938$		0			0
$939$		0			0
$940$	−3.17157	+	5.49333i	−0.103445	+	0.179173i
$941$	3.60660	+	6.24682i	0.117572	+	0.203640i	0.918805	−	0.394712i	$-0.129156\pi$
$941$	3.60660	+	6.24682i	0.117572	+	0.203640i	−0.801233	+	0.598352i	$0.795822\pi$
$942$		0			0
$943$	−4.10051	+	7.10228i	−0.133531	+	0.231282i
$944$	−20.4853			−0.666739
$945$		0			0
$946$	−27.3137			−0.888045
$947$	26.6569	−	46.1710i	0.866231	−	1.50036i	0.000412082	−	1.00000i	$-0.499869\pi$
$947$	26.6569	−	46.1710i	0.866231	−	1.50036i	0.865819	−	0.500357i	$-0.166798\pi$
$948$		0			0
$949$	15.9706	+	27.6618i	0.518426	+	0.897941i
$950$	−15.8995	+	27.5387i	−0.515848	+	0.893474i
$951$		0			0
$952$		0			0
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$		0			0
$955$	−5.27208	−	9.13151i	−0.170600	−	0.295489i
$956$	−8.31371	−	14.3998i	−0.268885	−	0.465722i
$957$		0			0
$958$	72.7696			2.35108
$959$		0			0
$960$		0			0
$961$	−7.81371	+	13.5337i	−0.252055	+	0.436572i
$962$	−26.1421	−	45.2795i	−0.842856	−	1.45987i
$963$		0			0
$964$	−14.8492	+	25.7196i	−0.478262	+	0.828374i
$965$	−10.1421			−0.326487
$966$		0			0
$967$	22.3431			0.718507			0.359254	−	0.933240i	$-0.383031\pi$
$967$	22.3431			0.718507			0.359254	+	0.933240i	$0.383031\pi$
$968$	15.4497	−	26.7597i	0.496574	−	0.860091i
$969$		0			0
$970$	3.82843	+	6.63103i	0.122923	+	0.212910i
$971$	2.68629	−	4.65279i	0.0862072	−	0.149315i	−0.819698	−	0.572796i	$-0.805859\pi$
$971$	2.68629	−	4.65279i	0.0862072	−	0.149315i	0.905905	+	0.423481i	$0.139192\pi$
$972$		0			0
$973$		0			0
$974$	−44.9706			−1.44095
$975$		0			0
$976$	5.63604	+	9.76191i	0.180405	+	0.312471i
$977$	−13.4142	−	23.2341i	−0.429159	−	0.743325i	0.567640	−	0.823277i	$-0.307857\pi$
$977$	−13.4142	−	23.2341i	−0.429159	−	0.743325i	−0.996799	+	0.0799522i	$0.974523\pi$
$978$		0			0
$979$	−11.5147			−0.368012
$980$		0			0
$981$		0			0
$982$	47.0416	−	81.4785i	1.50116	−	2.60008i
$983$	−18.6274	−	32.2636i	−0.594122	−	1.02905i	−0.993670	−	0.112338i	$-0.964166\pi$
$983$	−18.6274	−	32.2636i	−0.594122	−	1.02905i	0.399548	−	0.916712i	$-0.369167\pi$
$984$		0			0
$985$	0.585786	−	1.01461i	0.0186647	−	0.0323282i
$986$	17.6569			0.562309
$987$		0			0
$988$	58.6274			1.86519
$989$	−10.3431	+	17.9149i	−0.328893	+	0.569659i
$990$		0			0
$991$	−10.4853	−	18.1610i	−0.333076	−	0.576904i	0.650037	−	0.759902i	$-0.274753\pi$
$991$	−10.4853	−	18.1610i	−0.333076	−	0.576904i	−0.983113	+	0.182998i	$0.941420\pi$
$992$	5.41421	−	9.37769i	0.171901	−	0.297742i
$993$		0			0
$994$		0			0
$995$	−6.05887			−0.192079
$996$		0			0
$997$	−5.19239	−	8.99348i	−0.164445	−	0.284826i	0.772013	−	0.635606i	$-0.219250\pi$
$997$	−5.19239	−	8.99348i	−0.164445	−	0.284826i	−0.936458	+	0.350780i	$0.885917\pi$
$998$	23.3137	+	40.3805i	0.737983	+	1.27822i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.e.f.226.1		4
3.2	odd	2		147.2.e.e.79.2		4
7.2	even	3		441.2.a.j.1.2		2
7.3	odd	6		441.2.e.g.361.1		4
7.4	even	3	inner	441.2.e.f.361.1		4
7.5	odd	6		441.2.a.i.1.2		2
7.6	odd	2		441.2.e.g.226.1		4
12.11	even	2		2352.2.q.bb.961.1		4
21.2	odd	6		147.2.a.d.1.1	✓	2
21.5	even	6		147.2.a.e.1.1	yes	2
21.11	odd	6		147.2.e.e.67.2		4
21.17	even	6		147.2.e.d.67.2		4
21.20	even	2		147.2.e.d.79.2		4
28.19	even	6		7056.2.a.cf.1.2		2
28.23	odd	6		7056.2.a.cv.1.1		2
84.11	even	6		2352.2.q.bb.1537.1		4
84.23	even	6		2352.2.a.be.1.2		2
84.47	odd	6		2352.2.a.bc.1.1		2
84.59	odd	6		2352.2.q.bd.1537.2		4
84.83	odd	2		2352.2.q.bd.961.2		4
105.44	odd	6		3675.2.a.bf.1.2		2
105.89	even	6		3675.2.a.bd.1.2		2
168.5	even	6		9408.2.a.di.1.2		2
168.107	even	6		9408.2.a.dq.1.1		2
168.131	odd	6		9408.2.a.dt.1.2		2
168.149	odd	6		9408.2.a.ef.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.a.d.1.1	✓	2	21.2	odd	6
147.2.a.e.1.1	yes	2	21.5	even	6
147.2.e.d.67.2		4	21.17	even	6
147.2.e.d.79.2		4	21.20	even	2
147.2.e.e.67.2		4	21.11	odd	6
147.2.e.e.79.2		4	3.2	odd	2
441.2.a.i.1.2		2	7.5	odd	6
441.2.a.j.1.2		2	7.2	even	3
441.2.e.f.226.1		4	1.1	even	1	trivial
441.2.e.f.361.1		4	7.4	even	3	inner
441.2.e.g.226.1		4	7.6	odd	2
441.2.e.g.361.1		4	7.3	odd	6
2352.2.a.bc.1.1		2	84.47	odd	6
2352.2.a.be.1.2		2	84.23	even	6
2352.2.q.bb.961.1		4	12.11	even	2
2352.2.q.bb.1537.1		4	84.11	even	6
2352.2.q.bd.961.2		4	84.83	odd	2
2352.2.q.bd.1537.2		4	84.59	odd	6
3675.2.a.bd.1.2		2	105.89	even	6
3675.2.a.bf.1.2		2	105.44	odd	6
7056.2.a.cf.1.2		2	28.19	even	6
7056.2.a.cv.1.1		2	28.23	odd	6
9408.2.a.di.1.2		2	168.5	even	6
9408.2.a.dq.1.1		2	168.107	even	6
9408.2.a.dt.1.2		2	168.131	odd	6
9408.2.a.ef.1.1		2	168.149	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(-0.292893 + 0.507306i) q^{5} +4.41421 q^{8} +O(q^{10})\)	\(q+(-1.20711 + 2.09077i) q^{2} +(-1.91421 - 3.31552i) q^{4} +(-0.292893 + 0.507306i) q^{5} +4.41421 q^{8} +(-0.707107 - 1.22474i) q^{10} +(-1.00000 - 1.73205i) q^{11} -5.41421 q^{13} +(-1.50000 + 2.59808i) q^{16} +(-3.12132 - 5.40629i) q^{17} +(1.41421 - 2.44949i) q^{19} +2.24264 q^{20} +4.82843 q^{22} +(1.82843 - 3.16693i) q^{23} +(2.32843 + 4.03295i) q^{25} +(6.53553 - 11.3199i) q^{26} +1.17157 q^{29} +(-3.41421 - 5.91359i) q^{31} +(0.792893 + 1.37333i) q^{32} +15.0711 q^{34} +(2.00000 - 3.46410i) q^{37} +(3.41421 + 5.91359i) q^{38} +(-1.29289 + 2.23936i) q^{40} -2.24264 q^{41} -5.65685 q^{43} +(-3.82843 + 6.63103i) q^{44} +(4.41421 + 7.64564i) q^{46} +(-1.41421 + 2.44949i) q^{47} -11.2426 q^{50} +(10.3640 + 17.9509i) q^{52} +(-1.00000 - 1.73205i) q^{53} +1.17157 q^{55} +(-1.41421 + 2.44949i) q^{58} +(3.41421 + 5.91359i) q^{59} +(1.87868 - 3.25397i) q^{61} +16.4853 q^{62} -9.82843 q^{64} +(1.58579 - 2.74666i) q^{65} +(-2.82843 - 4.89898i) q^{67} +(-11.9497 + 20.6976i) q^{68} +13.3137 q^{71} +(-2.94975 - 5.10911i) q^{73} +(4.82843 + 8.36308i) q^{74} -10.8284 q^{76} +(-1.17157 + 2.02922i) q^{79} +(-0.878680 - 1.52192i) q^{80} +(2.70711 - 4.68885i) q^{82} -15.3137 q^{83} +3.65685 q^{85} +(6.82843 - 11.8272i) q^{86} +(-4.41421 - 7.64564i) q^{88} +(2.87868 - 4.98602i) q^{89} -14.0000 q^{92} +(-3.41421 - 5.91359i) q^{94} +(0.828427 + 1.43488i) q^{95} -5.41421 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} - 4 q^{5} + 12 q^{8} - 4 q^{11} - 16 q^{13} - 6 q^{16} - 4 q^{17} - 8 q^{20} + 8 q^{22} - 4 q^{23} - 2 q^{25} + 12 q^{26} + 16 q^{29} - 8 q^{31} + 6 q^{32} + 32 q^{34} + 8 q^{37} + 8 q^{38} - 8 q^{40} + 8 q^{41} - 4 q^{44} + 12 q^{46} - 28 q^{50} + 16 q^{52} - 4 q^{53} + 16 q^{55} + 8 q^{59} + 16 q^{61} + 32 q^{62} - 28 q^{64} + 12 q^{65} - 28 q^{68} + 8 q^{71} + 8 q^{73} + 8 q^{74} - 32 q^{76} - 16 q^{79} - 12 q^{80} + 8 q^{82} - 16 q^{83} - 8 q^{85} + 16 q^{86} - 12 q^{88} + 20 q^{89} - 56 q^{92} - 8 q^{94} - 8 q^{95} - 16 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 - 4 * q^5 + 12 * q^8 - 4 * q^11 - 16 * q^13 - 6 * q^16 - 4 * q^17 - 8 * q^20 + 8 * q^22 - 4 * q^23 - 2 * q^25 + 12 * q^26 + 16 * q^29 - 8 * q^31 + 6 * q^32 + 32 * q^34 + 8 * q^37 + 8 * q^38 - 8 * q^40 + 8 * q^41 - 4 * q^44 + 12 * q^46 - 28 * q^50 + 16 * q^52 - 4 * q^53 + 16 * q^55 + 8 * q^59 + 16 * q^61 + 32 * q^62 - 28 * q^64 + 12 * q^65 - 28 * q^68 + 8 * q^71 + 8 * q^73 + 8 * q^74 - 32 * q^76 - 16 * q^79 - 12 * q^80 + 8 * q^82 - 16 * q^83 - 8 * q^85 + 16 * q^86 - 12 * q^88 + 20 * q^89 - 56 * q^92 - 8 * q^94 - 8 * q^95 - 16 * q^97

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