LMFDB - Embedded newform 441.2.e.i.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:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
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			226.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	441.226
Dual form			441.2.e.i.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} -1.73205 q^{8} +O(q^{10})$	\(q+(-0.866025 + 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} -1.73205 q^{8} +(-3.00000 - 5.19615i) q^{10} +(-1.73205 - 3.00000i) q^{11} -2.00000 q^{13} +(2.50000 - 4.33013i) q^{16} +(1.73205 + 3.00000i) q^{17} +(-2.00000 + 3.46410i) q^{19} +3.46410 q^{20} +6.00000 q^{22} +(1.73205 - 3.00000i) q^{23} +(-3.50000 - 6.06218i) q^{25} +(1.73205 - 3.00000i) q^{26} +(-2.00000 - 3.46410i) q^{31} +(2.59808 + 4.50000i) q^{32} -6.00000 q^{34} +(-1.00000 + 1.73205i) q^{37} +(-3.46410 - 6.00000i) q^{38} +(3.00000 - 5.19615i) q^{40} -10.3923 q^{41} -4.00000 q^{43} +(-1.73205 + 3.00000i) q^{44} +(3.00000 + 5.19615i) q^{46} +(3.46410 - 6.00000i) q^{47} +12.1244 q^{50} +(1.00000 + 1.73205i) q^{52} +(3.46410 + 6.00000i) q^{53} +12.0000 q^{55} +(-3.46410 - 6.00000i) q^{59} +(-5.00000 + 8.66025i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(3.46410 - 6.00000i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.73205 - 3.00000i) q^{68} -10.3923 q^{71} +(7.00000 + 12.1244i) q^{73} +(-1.73205 - 3.00000i) q^{74} +4.00000 q^{76} +(-4.00000 + 6.92820i) q^{79} +(8.66025 + 15.0000i) q^{80} +(9.00000 - 15.5885i) q^{82} -12.0000 q^{85} +(3.46410 - 6.00000i) q^{86} +(3.00000 + 5.19615i) q^{88} +(-1.73205 + 3.00000i) q^{89} -3.46410 q^{92} +(6.00000 + 10.3923i) q^{94} +(-6.92820 - 12.0000i) q^{95} -14.0000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4}+O(q^{10}) $ 4 * q - 2 * q^4	$ 4 q - 2 q^{4} - 12 q^{10} - 8 q^{13} + 10 q^{16} - 8 q^{19} + 24 q^{22} - 14 q^{25} - 8 q^{31} - 24 q^{34} - 4 q^{37} + 12 q^{40} - 16 q^{43} + 12 q^{46} + 4 q^{52} + 48 q^{55} - 20 q^{61} + 4 q^{64} + 8 q^{67} + 28 q^{73} + 16 q^{76} - 16 q^{79} + 36 q^{82} - 48 q^{85} + 12 q^{88} + 24 q^{94} - 56 q^{97}+O(q^{100}) $ 4 * q - 2 * q^4 - 12 * q^10 - 8 * q^13 + 10 * q^16 - 8 * q^19 + 24 * q^22 - 14 * q^25 - 8 * q^31 - 24 * q^34 - 4 * q^37 + 12 * q^40 - 16 * q^43 + 12 * q^46 + 4 * q^52 + 48 * q^55 - 20 * q^61 + 4 * q^64 + 8 * q^67 + 28 * q^73 + 16 * q^76 - 16 * q^79 + 36 * q^82 - 48 * q^85 + 12 * q^88 + 24 * q^94 - 56 * 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 $

$2$	−0.866025	+	1.50000i	−0.612372	+	1.06066i	0.378467	+	0.925615i	$0.376451\pi$
$2$	−0.866025	+	1.50000i	−0.612372	+	1.06066i	−0.990839	+	0.135045i	$0.956882\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.73205	+	3.00000i	−0.774597	+	1.34164i	0.160424	+	0.987048i	$0.448714\pi$
$5$	−1.73205	+	3.00000i	−0.774597	+	1.34164i	−0.935021	+	0.354593i	$0.884620\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.73205			−0.612372
$9$		0			0
$10$	−3.00000	−	5.19615i	−0.948683	−	1.64317i
$11$	−1.73205	−	3.00000i	−0.522233	−	0.904534i	−0.999665	−	0.0258656i	$-0.991766\pi$
$11$	−1.73205	−	3.00000i	−0.522233	−	0.904534i	0.477432	−	0.878668i	$-0.341568\pi$
$12$		0			0
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	1.73205	+	3.00000i	0.420084	+	0.727607i	0.995947	−	0.0899392i	$-0.0286673\pi$
$17$	1.73205	+	3.00000i	0.420084	+	0.727607i	−0.575863	+	0.817546i	$0.695334\pi$
$18$		0			0
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$	3.46410			0.774597
$21$		0			0
$22$	6.00000			1.27920
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	−0.626994	−	0.779024i	$-0.715715\pi$
$23$	1.73205	−	3.00000i	0.361158	−	0.625543i	0.988152	+	0.153481i	$0.0490483\pi$
$24$		0			0
$25$	−3.50000	−	6.06218i	−0.700000	−	1.21244i
$26$	1.73205	−	3.00000i	0.339683	−	0.588348i
$27$		0			0
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	2.59808	+	4.50000i	0.459279	+	0.795495i
$33$		0			0
$34$	−6.00000			−1.02899
$35$		0			0
$36$		0			0
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−3.46410	−	6.00000i	−0.561951	−	0.973329i
$39$		0			0
$40$	3.00000	−	5.19615i	0.474342	−	0.821584i
$41$	−10.3923			−1.62301			−0.811503	−	0.584349i	$-0.801350\pi$
$41$	−10.3923			−1.62301			−0.811503	+	0.584349i	$0.801350\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	−1.73205	+	3.00000i	−0.261116	+	0.452267i
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	3.46410	−	6.00000i	0.505291	−	0.875190i	−0.494690	−	0.869069i	$-0.664718\pi$
$47$	3.46410	−	6.00000i	0.505291	−	0.875190i	0.999981	−	0.00612051i	$-0.00194823\pi$
$48$		0			0
$49$		0			0
$50$	12.1244			1.71464
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	3.46410	+	6.00000i	0.475831	+	0.824163i	0.999617	−	0.0276867i	$-0.00881407\pi$
$53$	3.46410	+	6.00000i	0.475831	+	0.824163i	−0.523786	+	0.851850i	$0.675481\pi$
$54$		0			0
$55$	12.0000			1.61808
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.46410	−	6.00000i	−0.450988	−	0.781133i	0.547460	−	0.836832i	$-0.315595\pi$
$59$	−3.46410	−	6.00000i	−0.450988	−	0.781133i	−0.998448	+	0.0556984i	$0.982261\pi$
$60$		0			0
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	6.92820			0.879883
$63$		0			0
$64$	1.00000			0.125000
$65$	3.46410	−	6.00000i	0.429669	−	0.744208i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.73205	−	3.00000i	0.210042	−	0.363803i
$69$		0			0
$70$		0			0
$71$	−10.3923			−1.23334			−0.616670	−	0.787222i	$-0.711519\pi$
$71$	−10.3923			−1.23334			−0.616670	+	0.787222i	$0.711519\pi$
$72$		0			0
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	0.906208	+	0.422833i	$0.138964\pi$
$73$	7.00000	+	12.1244i	0.819288	+	1.41905i	−0.0869195	+	0.996215i	$0.527702\pi$
$74$	−1.73205	−	3.00000i	−0.201347	−	0.348743i
$75$		0			0
$76$	4.00000			0.458831
$77$		0			0
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	8.66025	+	15.0000i	0.968246	+	1.67705i
$81$		0			0
$82$	9.00000	−	15.5885i	0.993884	−	1.72146i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$	−12.0000			−1.30158
$86$	3.46410	−	6.00000i	0.373544	−	0.646997i
$87$		0			0
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	−1.73205	+	3.00000i	−0.183597	+	0.317999i	−0.943103	−	0.332501i	$-0.892107\pi$
$89$	−1.73205	+	3.00000i	−0.183597	+	0.317999i	0.759506	+	0.650500i	$0.225441\pi$
$90$		0			0
$91$		0			0
$92$	−3.46410			−0.361158
$93$		0			0
$94$	6.00000	+	10.3923i	0.618853	+	1.07188i
$95$	−6.92820	−	12.0000i	−0.710819	−	1.23117i
$96$		0			0
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$		0			0
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$	1.73205	+	3.00000i	0.172345	+	0.298511i	0.939239	−	0.343263i	$-0.111532\pi$
$101$	1.73205	+	3.00000i	0.172345	+	0.298511i	−0.766894	+	0.641774i	$0.778199\pi$
$102$		0			0
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	−0.947576	−	0.319531i	$-0.896475\pi$
$103$	−2.00000	+	3.46410i	−0.197066	+	0.341328i	0.750510	+	0.660859i	$0.229808\pi$
$104$	3.46410			0.339683
$105$		0			0
$106$	−12.0000			−1.16554
$107$	−8.66025	+	15.0000i	−0.837218	+	1.45010i	0.0549930	+	0.998487i	$0.482486\pi$
$107$	−8.66025	+	15.0000i	−0.837218	+	1.45010i	−0.892211	+	0.451618i	$0.850847\pi$
$108$		0			0
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$	−10.3923	+	18.0000i	−0.990867	+	1.71623i
$111$		0			0
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$	6.00000	+	10.3923i	0.559503	+	0.969087i
$116$		0			0
$117$		0			0
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−8.66025	−	15.0000i	−0.784063	−	1.35804i
$123$		0			0
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	6.92820			0.619677
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−6.06218	+	10.5000i	−0.535826	+	0.928078i
$129$		0			0
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$	−6.92820	+	12.0000i	−0.605320	+	1.04844i	0.386681	+	0.922214i	$0.373621\pi$
$131$	−6.92820	+	12.0000i	−0.605320	+	1.04844i	−0.992001	+	0.126231i	$0.959712\pi$
$132$		0			0
$133$		0			0
$134$	−6.92820			−0.598506
$135$		0			0
$136$	−3.00000	−	5.19615i	−0.257248	−	0.445566i
$137$	3.46410	+	6.00000i	0.295958	+	0.512615i	0.975207	−	0.221293i	$-0.0710278\pi$
$137$	3.46410	+	6.00000i	0.295958	+	0.512615i	−0.679249	+	0.733908i	$0.737694\pi$
$138$		0			0
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$		0			0
$142$	9.00000	−	15.5885i	0.755263	−	1.30815i
$143$	3.46410	+	6.00000i	0.289683	+	0.501745i
$144$		0			0
$145$		0			0
$146$	−24.2487			−2.00684
$147$		0			0
$148$	2.00000			0.164399
$149$	−3.46410	+	6.00000i	−0.283790	+	0.491539i	−0.972315	−	0.233674i	$-0.924925\pi$
$149$	−3.46410	+	6.00000i	−0.283790	+	0.491539i	0.688525	+	0.725213i	$0.258259\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	3.46410	−	6.00000i	0.280976	−	0.486664i
$153$		0			0
$154$		0			0
$155$	13.8564			1.11297
$156$		0			0
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	0.594565	−	0.804048i	$-0.297324\pi$
$157$	−5.00000	−	8.66025i	−0.399043	−	0.691164i	−0.993608	+	0.112884i	$0.963991\pi$
$158$	−6.92820	−	12.0000i	−0.551178	−	0.954669i
$159$		0			0
$160$	−18.0000			−1.42302
$161$		0			0
$162$		0			0
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	5.19615	+	9.00000i	0.405751	+	0.702782i
$165$		0			0
$166$		0			0
$167$	20.7846			1.60836			0.804181	−	0.594385i	$-0.202604\pi$
$167$	20.7846			1.60836			0.804181	+	0.594385i	$0.202604\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	10.3923	−	18.0000i	0.797053	−	1.38054i
$171$		0			0
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	8.66025	−	15.0000i	0.658427	−	1.14043i	−0.322596	−	0.946537i	$-0.604555\pi$
$173$	8.66025	−	15.0000i	0.658427	−	1.14043i	0.981023	−	0.193892i	$-0.0621112\pi$
$174$		0			0
$175$		0			0
$176$	−17.3205			−1.30558
$177$		0			0
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	8.66025	+	15.0000i	0.647298	+	1.12115i	0.983766	+	0.179458i	$0.0574343\pi$
$179$	8.66025	+	15.0000i	0.647298	+	1.12115i	−0.336468	+	0.941695i	$0.609232\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$		0			0
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	−3.46410	−	6.00000i	−0.254686	−	0.441129i
$186$		0			0
$187$	6.00000	−	10.3923i	0.438763	−	0.759961i
$188$	−6.92820			−0.505291
$189$		0			0
$190$	24.0000			1.74114
$191$	12.1244	−	21.0000i	0.877288	−	1.51951i	0.0229818	−	0.999736i	$-0.492684\pi$
$191$	12.1244	−	21.0000i	0.877288	−	1.51951i	0.854306	−	0.519771i	$-0.173983\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	12.1244	−	21.0000i	0.870478	−	1.50771i
$195$		0			0
$196$		0			0
$197$	20.7846			1.48084			0.740421	−	0.672143i	$-0.234626\pi$
$197$	20.7846			1.48084			0.740421	+	0.672143i	$0.234626\pi$
$198$		0			0
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$	6.06218	+	10.5000i	0.428661	+	0.742462i
$201$		0			0
$202$	−6.00000			−0.422159
$203$		0			0
$204$		0			0
$205$	18.0000	−	31.1769i	1.25717	−	2.17749i
$206$	−3.46410	−	6.00000i	−0.241355	−	0.418040i
$207$		0			0
$208$	−5.00000	+	8.66025i	−0.346688	+	0.600481i
$209$	13.8564			0.958468
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	3.46410	−	6.00000i	0.237915	−	0.412082i
$213$		0			0
$214$	−15.0000	−	25.9808i	−1.02538	−	1.77601i
$215$	6.92820	−	12.0000i	0.472500	−	0.818393i
$216$		0			0
$217$		0			0
$218$	3.46410			0.234619
$219$		0			0
$220$	−6.00000	−	10.3923i	−0.404520	−	0.700649i
$221$	−3.46410	−	6.00000i	−0.233021	−	0.403604i
$222$		0			0
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.46410	−	6.00000i	−0.229920	−	0.398234i	0.727864	−	0.685722i	$-0.240513\pi$
$227$	−3.46410	−	6.00000i	−0.229920	−	0.398234i	−0.957784	+	0.287488i	$0.907180\pi$
$228$		0			0
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$	−20.7846			−1.37050
$231$		0			0
$232$		0			0
$233$	−3.46410	+	6.00000i	−0.226941	+	0.393073i	−0.956900	−	0.290418i	$-0.906206\pi$
$233$	−3.46410	+	6.00000i	−0.226941	+	0.393073i	0.729959	+	0.683491i	$0.239539\pi$
$234$		0			0
$235$	12.0000	+	20.7846i	0.782794	+	1.35584i
$236$	−3.46410	+	6.00000i	−0.225494	+	0.390567i
$237$		0			0
$238$		0			0
$239$	10.3923			0.672222			0.336111	−	0.941822i	$-0.390888\pi$
$239$	10.3923			0.672222			0.336111	+	0.941822i	$0.390888\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	−0.866025	−	1.50000i	−0.0556702	−	0.0964237i
$243$		0			0
$244$	10.0000			0.640184
$245$		0			0
$246$		0			0
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$	3.46410	+	6.00000i	0.219971	+	0.381000i
$249$		0			0
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	−20.7846			−1.31191			−0.655956	−	0.754799i	$-0.727735\pi$
$251$	−20.7846			−1.31191			−0.655956	+	0.754799i	$0.727735\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	−6.92820	+	12.0000i	−0.434714	+	0.752947i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−1.73205	+	3.00000i	−0.108042	+	0.187135i	−0.914977	−	0.403506i	$-0.867792\pi$
$257$	−1.73205	+	3.00000i	−0.108042	+	0.187135i	0.806935	+	0.590641i	$0.201125\pi$
$258$		0			0
$259$		0			0
$260$	−6.92820			−0.429669
$261$		0			0
$262$	−12.0000	−	20.7846i	−0.741362	−	1.28408i
$263$	8.66025	+	15.0000i	0.534014	+	0.924940i	0.999210	+	0.0397320i	$0.0126504\pi$
$263$	8.66025	+	15.0000i	0.534014	+	0.924940i	−0.465196	+	0.885208i	$0.654016\pi$
$264$		0			0
$265$	−24.0000			−1.47431
$266$		0			0
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	−8.66025	−	15.0000i	−0.528025	−	0.914566i	−0.999466	−	0.0326687i	$-0.989599\pi$
$269$	−8.66025	−	15.0000i	−0.528025	−	0.914566i	0.471441	−	0.881897i	$-0.343734\pi$
$270$		0			0
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	−0.384201	−	0.923249i	$-0.625523\pi$
$271$	10.0000	−	17.3205i	0.607457	−	1.05215i	0.991658	−	0.128897i	$-0.0411435\pi$
$272$	17.3205			1.05021
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−12.1244	+	21.0000i	−0.731126	+	1.26635i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	−13.8564	+	24.0000i	−0.831052	+	1.43942i
$279$		0			0
$280$		0			0
$281$	−20.7846			−1.23991			−0.619953	−	0.784639i	$-0.712848\pi$
$281$	−20.7846			−1.23991			−0.619953	+	0.784639i	$0.712848\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	5.19615	+	9.00000i	0.308335	+	0.534052i
$285$		0			0
$286$	−12.0000			−0.709575
$287$		0			0
$288$		0			0
$289$	2.50000	−	4.33013i	0.147059	−	0.254713i
$290$		0			0
$291$		0			0
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$	10.3923			0.607125			0.303562	−	0.952812i	$-0.401824\pi$
$293$	10.3923			0.607125			0.303562	+	0.952812i	$0.401824\pi$
$294$		0			0
$295$	24.0000			1.39733
$296$	1.73205	−	3.00000i	0.100673	−	0.174371i
$297$		0			0
$298$	−6.00000	−	10.3923i	−0.347571	−	0.602010i
$299$	−3.46410	+	6.00000i	−0.200334	+	0.346989i
$300$		0			0
$301$		0			0
$302$	13.8564			0.797347
$303$		0			0
$304$	10.0000	+	17.3205i	0.573539	+	0.993399i
$305$	−17.3205	−	30.0000i	−0.991769	−	1.71780i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$		0			0
$310$	−12.0000	+	20.7846i	−0.681554	+	1.18049i
$311$	17.3205	+	30.0000i	0.982156	+	1.70114i	0.653950	+	0.756538i	$0.273111\pi$
$311$	17.3205	+	30.0000i	0.982156	+	1.70114i	0.328206	+	0.944606i	$0.393556\pi$
$312$		0			0
$313$	1.00000	−	1.73205i	0.0565233	−	0.0979013i	−0.836379	−	0.548151i	$-0.815332\pi$
$313$	1.00000	−	1.73205i	0.0565233	−	0.0979013i	0.892903	+	0.450250i	$0.148665\pi$
$314$	17.3205			0.977453
$315$		0			0
$316$	8.00000			0.450035
$317$	−3.46410	+	6.00000i	−0.194563	+	0.336994i	−0.946757	−	0.321948i	$-0.895662\pi$
$317$	−3.46410	+	6.00000i	−0.194563	+	0.336994i	0.752194	+	0.658942i	$0.228996\pi$
$318$		0			0
$319$		0			0
$320$	−1.73205	+	3.00000i	−0.0968246	+	0.167705i
$321$		0			0
$322$		0			0
$323$	−13.8564			−0.770991
$324$		0			0
$325$	7.00000	+	12.1244i	0.388290	+	0.672538i
$326$	−17.3205	−	30.0000i	−0.959294	−	1.66155i
$327$		0			0
$328$	18.0000			0.993884
$329$		0			0
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$		0			0
$333$		0			0
$334$	−18.0000	+	31.1769i	−0.984916	+	1.70592i
$335$	−13.8564			−0.757056
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$	7.79423	−	13.5000i	0.423950	−	0.734303i
$339$		0			0
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$	−6.92820	+	12.0000i	−0.375183	+	0.649836i
$342$		0			0
$343$		0			0
$344$	6.92820			0.373544
$345$		0			0
$346$	15.0000	+	25.9808i	0.806405	+	1.39673i
$347$	8.66025	+	15.0000i	0.464907	+	0.805242i	0.999197	−	0.0400587i	$-0.0127545\pi$
$347$	8.66025	+	15.0000i	0.464907	+	0.805242i	−0.534291	+	0.845301i	$0.679421\pi$
$348$		0			0
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$		0			0
$352$	9.00000	−	15.5885i	0.479702	−	0.830868i
$353$	1.73205	+	3.00000i	0.0921878	+	0.159674i	0.908431	−	0.418034i	$-0.137281\pi$
$353$	1.73205	+	3.00000i	0.0921878	+	0.159674i	−0.816244	+	0.577708i	$0.803947\pi$
$354$		0			0
$355$	18.0000	−	31.1769i	0.955341	−	1.65470i
$356$	3.46410			0.183597
$357$		0			0
$358$	−30.0000			−1.58555
$359$	12.1244	−	21.0000i	0.639899	−	1.10834i	−0.345556	−	0.938398i	$-0.612310\pi$
$359$	12.1244	−	21.0000i	0.639899	−	1.10834i	0.985455	−	0.169939i	$-0.0543572\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	1.73205	−	3.00000i	0.0910346	−	0.157676i
$363$		0			0
$364$		0			0
$365$	−48.4974			−2.53847
$366$		0			0
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$	−8.66025	−	15.0000i	−0.451447	−	0.781929i
$369$		0			0
$370$	12.0000			0.623850
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	10.3923	+	18.0000i	0.537373	+	0.930758i
$375$		0			0
$376$	−6.00000	+	10.3923i	−0.309426	+	0.535942i
$377$		0			0
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−6.92820	+	12.0000i	−0.355409	+	0.615587i
$381$		0			0
$382$	21.0000	+	36.3731i	1.07445	+	1.86101i
$383$	−6.92820	+	12.0000i	−0.354015	+	0.613171i	−0.986949	−	0.161034i	$-0.948517\pi$
$383$	−6.92820	+	12.0000i	−0.354015	+	0.613171i	0.632934	+	0.774206i	$0.281850\pi$
$384$		0			0
$385$		0			0
$386$	24.2487			1.23423
$387$		0			0
$388$	7.00000	+	12.1244i	0.355371	+	0.615521i
$389$	−6.92820	−	12.0000i	−0.351274	−	0.608424i	0.635199	−	0.772348i	$-0.280918\pi$
$389$	−6.92820	−	12.0000i	−0.351274	−	0.608424i	−0.986473	+	0.163924i	$0.947585\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$		0			0
$394$	−18.0000	+	31.1769i	−0.906827	+	1.57067i
$395$	−13.8564	−	24.0000i	−0.697191	−	1.20757i
$396$		0			0
$397$	19.0000	−	32.9090i	0.953583	−	1.65165i	0.216004	−	0.976392i	$-0.430698\pi$
$397$	19.0000	−	32.9090i	0.953583	−	1.65165i	0.737579	−	0.675261i	$-0.235969\pi$
$398$	27.7128			1.38912
$399$		0			0
$400$	−35.0000			−1.75000
$401$	−3.46410	+	6.00000i	−0.172989	+	0.299626i	−0.939463	−	0.342649i	$-0.888676\pi$
$401$	−3.46410	+	6.00000i	−0.172989	+	0.299626i	0.766475	+	0.642275i	$0.222009\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	1.73205	−	3.00000i	0.0861727	−	0.149256i
$405$		0			0
$406$		0			0
$407$	6.92820			0.343418
$408$		0			0
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$	31.1769	+	54.0000i	1.53972	+	2.66687i
$411$		0			0
$412$	4.00000			0.197066
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−5.19615	−	9.00000i	−0.254762	−	0.441261i
$417$		0			0
$418$	−12.0000	+	20.7846i	−0.586939	+	1.01661i
$419$	−20.7846			−1.01539			−0.507697	−	0.861536i	$-0.669503\pi$
$419$	−20.7846			−1.01539			−0.507697	+	0.861536i	$0.669503\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−17.3205	+	30.0000i	−0.843149	+	1.46038i
$423$		0			0
$424$	−6.00000	−	10.3923i	−0.291386	−	0.504695i
$425$	12.1244	−	21.0000i	0.588118	−	1.01865i
$426$		0			0
$427$		0			0
$428$	17.3205			0.837218
$429$		0			0
$430$	12.0000	+	20.7846i	0.578691	+	1.00232i
$431$	−1.73205	−	3.00000i	−0.0834300	−	0.144505i	0.821291	−	0.570509i	$-0.193254\pi$
$431$	−1.73205	−	3.00000i	−0.0834300	−	0.144505i	−0.904721	+	0.426004i	$0.859921\pi$
$432$		0			0
$433$	−26.0000			−1.24948			−0.624740	−	0.780833i	$-0.714795\pi$
$433$	−26.0000			−1.24948			−0.624740	+	0.780833i	$0.714795\pi$
$434$		0			0
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	6.92820	+	12.0000i	0.331421	+	0.574038i
$438$		0			0
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$	−20.7846			−0.990867
$441$		0			0
$442$	12.0000			0.570782
$443$	1.73205	−	3.00000i	0.0822922	−	0.142534i	−0.821942	−	0.569571i	$-0.807109\pi$
$443$	1.73205	−	3.00000i	0.0822922	−	0.142534i	0.904234	+	0.427037i	$0.140443\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	6.92820	−	12.0000i	0.328060	−	0.568216i
$447$		0			0
$448$		0			0
$449$	41.5692			1.96177			0.980886	−	0.194581i	$-0.0623348\pi$
$449$	41.5692			1.96177			0.980886	+	0.194581i	$0.0623348\pi$
$450$		0			0
$451$	18.0000	+	31.1769i	0.847587	+	1.46806i
$452$		0			0
$453$		0			0
$454$	12.0000			0.563188
$455$		0			0
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	−19.0526	−	33.0000i	−0.890268	−	1.54199i
$459$		0			0
$460$	6.00000	−	10.3923i	0.279751	−	0.484544i
$461$	−31.1769			−1.45205			−0.726027	−	0.687666i	$-0.758635\pi$
$461$	−31.1769			−1.45205			−0.726027	+	0.687666i	$0.758635\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$		0			0
$465$		0			0
$466$	−6.00000	−	10.3923i	−0.277945	−	0.481414i
$467$	3.46410	−	6.00000i	0.160300	−	0.277647i	−0.774677	−	0.632358i	$-0.782087\pi$
$467$	3.46410	−	6.00000i	0.160300	−	0.277647i	0.934976	+	0.354711i	$0.115421\pi$
$468$		0			0
$469$		0			0
$470$	−41.5692			−1.91745
$471$		0			0
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	6.92820	+	12.0000i	0.318559	+	0.551761i
$474$		0			0
$475$	28.0000			1.28473
$476$		0			0
$477$		0			0
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	−3.46410	−	6.00000i	−0.158279	−	0.274147i	0.775969	−	0.630771i	$-0.217261\pi$
$479$	−3.46410	−	6.00000i	−0.158279	−	0.274147i	−0.934248	+	0.356624i	$0.883928\pi$
$480$		0			0
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	17.3205			0.788928
$483$		0			0
$484$	1.00000			0.0454545
$485$	24.2487	−	42.0000i	1.10108	−	1.90712i
$486$		0			0
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.819181	+	0.573535i	$0.194428\pi$
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.0871056	+	0.996199i	$0.472238\pi$
$488$	8.66025	−	15.0000i	0.392031	−	0.679018i
$489$		0			0
$490$		0			0
$491$	10.3923			0.468998			0.234499	−	0.972116i	$-0.424655\pi$
$491$	10.3923			0.468998			0.234499	+	0.972116i	$0.424655\pi$
$492$		0			0
$493$		0			0
$494$	6.92820	+	12.0000i	0.311715	+	0.539906i
$495$		0			0
$496$	−20.0000			−0.898027
$497$		0			0
$498$		0			0
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	−0.817781	−	0.575529i	$-0.804796\pi$
$499$	2.00000	−	3.46410i	0.0895323	−	0.155074i	0.907314	+	0.420455i	$0.138129\pi$
$500$	−3.46410	−	6.00000i	−0.154919	−	0.268328i
$501$		0			0
$502$	18.0000	−	31.1769i	0.803379	−	1.39149i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	−12.0000			−0.533993
$506$	10.3923	−	18.0000i	0.461994	−	0.800198i
$507$		0			0
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	−0.901855	−	0.432038i	$-0.857795\pi$
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	0.825084	+	0.565011i	$0.191128\pi$
$510$		0			0
$511$		0			0
$512$	8.66025			0.382733
$513$		0			0
$514$	−3.00000	−	5.19615i	−0.132324	−	0.229192i
$515$	−6.92820	−	12.0000i	−0.305293	−	0.528783i
$516$		0			0
$517$	−24.0000			−1.05552
$518$		0			0
$519$		0			0
$520$	−6.00000	+	10.3923i	−0.263117	+	0.455733i
$521$	1.73205	+	3.00000i	0.0758825	+	0.131432i	0.901470	−	0.432842i	$-0.142489\pi$
$521$	1.73205	+	3.00000i	0.0758825	+	0.131432i	−0.825587	+	0.564275i	$0.809156\pi$
$522$		0			0
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	−0.986216	−	0.165460i	$-0.947089\pi$
$523$	−8.00000	+	13.8564i	−0.349816	+	0.605898i	0.636401	+	0.771358i	$0.280422\pi$
$524$	13.8564			0.605320
$525$		0			0
$526$	−30.0000			−1.30806
$527$	6.92820	−	12.0000i	0.301797	−	0.522728i
$528$		0			0
$529$	5.50000	+	9.52628i	0.239130	+	0.414186i
$530$	20.7846	−	36.0000i	0.902826	−	1.56374i
$531$		0			0
$532$		0			0
$533$	20.7846			0.900281
$534$		0			0
$535$	−30.0000	−	51.9615i	−1.29701	−	2.24649i
$536$	−3.46410	−	6.00000i	−0.149626	−	0.259161i
$537$		0			0
$538$	30.0000			1.29339
$539$		0			0
$540$		0			0
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	−0.976352	−	0.216186i	$-0.930638\pi$
$541$	−7.00000	+	12.1244i	−0.300954	+	0.521267i	0.675399	+	0.737453i	$0.263972\pi$
$542$	17.3205	+	30.0000i	0.743980	+	1.28861i
$543$		0			0
$544$	−9.00000	+	15.5885i	−0.385872	+	0.668350i
$545$	6.92820			0.296772
$546$		0			0
$547$	−4.00000			−0.171028			−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000			−0.171028			−0.0855138	+	0.996337i	$0.527253\pi$
$548$	3.46410	−	6.00000i	0.147979	−	0.256307i
$549$		0			0
$550$	−21.0000	−	36.3731i	−0.895443	−	1.55095i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−17.3205			−0.735878
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	3.46410	+	6.00000i	0.146779	+	0.254228i	0.930035	−	0.367471i	$-0.119776\pi$
$557$	3.46410	+	6.00000i	0.146779	+	0.254228i	−0.783256	+	0.621699i	$0.786443\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$		0			0
$562$	18.0000	−	31.1769i	0.759284	−	1.31512i
$563$	17.3205	+	30.0000i	0.729972	+	1.26435i	0.956894	+	0.290436i	$0.0938004\pi$
$563$	17.3205	+	30.0000i	0.729972	+	1.26435i	−0.226922	+	0.973913i	$0.572866\pi$
$564$		0			0
$565$		0			0
$566$	6.92820			0.291214
$567$		0			0
$568$	18.0000			0.755263
$569$	−3.46410	+	6.00000i	−0.145223	+	0.251533i	−0.929456	−	0.368933i	$-0.879723\pi$
$569$	−3.46410	+	6.00000i	−0.145223	+	0.251533i	0.784233	+	0.620466i	$0.213057\pi$
$570$		0			0
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	0.994765	+	0.102190i	$0.0325850\pi$
$571$	14.0000	+	24.2487i	0.585882	+	1.01478i	−0.408883	+	0.912587i	$0.634082\pi$
$572$	3.46410	−	6.00000i	0.144841	−	0.250873i
$573$		0			0
$574$		0			0
$575$	−24.2487			−1.01124
$576$		0			0
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	4.33013	+	7.50000i	0.180110	+	0.311959i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$	−12.1244	−	21.0000i	−0.501709	−	0.868986i
$585$		0			0
$586$	−9.00000	+	15.5885i	−0.371787	+	0.643953i
$587$	20.7846			0.857873			0.428936	−	0.903335i	$-0.358888\pi$
$587$	20.7846			0.857873			0.428936	+	0.903335i	$0.358888\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$	−20.7846	+	36.0000i	−0.855689	+	1.48210i
$591$		0			0
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	−12.1244	+	21.0000i	−0.497888	+	0.862367i	−0.999997	−	0.00243746i	$-0.999224\pi$
$593$	−12.1244	+	21.0000i	−0.497888	+	0.862367i	0.502109	+	0.864804i	$0.332557\pi$
$594$		0			0
$595$		0			0
$596$	6.92820			0.283790
$597$		0			0
$598$	−6.00000	−	10.3923i	−0.245358	−	0.424973i
$599$	−22.5167	−	39.0000i	−0.920006	−	1.59350i	−0.799402	−	0.600796i	$-0.794850\pi$
$599$	−22.5167	−	39.0000i	−0.920006	−	1.59350i	−0.120603	−	0.992701i	$-0.538483\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$		0			0
$603$		0			0
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−1.73205	−	3.00000i	−0.0704179	−	0.121967i
$606$		0			0
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	−20.7846			−0.842927
$609$		0			0
$610$	60.0000			2.42933
$611$	−6.92820	+	12.0000i	−0.280285	+	0.485468i
$612$		0			0
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	−0.938967	−	0.344008i	$-0.888215\pi$
$613$	−19.0000	−	32.9090i	−0.767403	−	1.32918i	0.171564	−	0.985173i	$-0.445118\pi$
$614$	−24.2487	+	42.0000i	−0.978598	+	1.69498i
$615$		0			0
$616$		0			0
$617$	−20.7846			−0.836757			−0.418378	−	0.908273i	$-0.637401\pi$
$617$	−20.7846			−0.836757			−0.418378	+	0.908273i	$0.637401\pi$
$618$		0			0
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	0.935146	−	0.354262i	$-0.115268\pi$
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	−0.774373	+	0.632730i	$0.781934\pi$
$620$	−6.92820	−	12.0000i	−0.278243	−	0.481932i
$621$		0			0
$622$	−60.0000			−2.40578
$623$		0			0
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	1.73205	+	3.00000i	0.0692267	+	0.119904i
$627$		0			0
$628$	−5.00000	+	8.66025i	−0.199522	+	0.345582i
$629$	−6.92820			−0.276246
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	6.92820	−	12.0000i	0.275589	−	0.477334i
$633$		0			0
$634$	−6.00000	−	10.3923i	−0.238290	−	0.412731i
$635$	−13.8564	+	24.0000i	−0.549875	+	0.952411i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−21.0000	−	36.3731i	−0.830098	−	1.43777i
$641$	24.2487	+	42.0000i	0.957767	+	1.65890i	0.727906	+	0.685677i	$0.240494\pi$
$641$	24.2487	+	42.0000i	0.957767	+	1.65890i	0.229860	+	0.973224i	$0.426173\pi$
$642$		0			0
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$		0			0
$645$		0			0
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	−3.46410	−	6.00000i	−0.136188	−	0.235884i	0.789863	−	0.613284i	$-0.210152\pi$
$647$	−3.46410	−	6.00000i	−0.136188	−	0.235884i	−0.926051	+	0.377399i	$0.876818\pi$
$648$		0			0
$649$	−12.0000	+	20.7846i	−0.471041	+	0.815867i
$650$	−24.2487			−0.951113
$651$		0			0
$652$	20.0000			0.783260
$653$	−13.8564	+	24.0000i	−0.542243	+	0.939193i	0.456532	+	0.889707i	$0.349091\pi$
$653$	−13.8564	+	24.0000i	−0.542243	+	0.939193i	−0.998775	+	0.0494855i	$0.984242\pi$
$654$		0			0
$655$	−24.0000	−	41.5692i	−0.937758	−	1.62424i
$656$	−25.9808	+	45.0000i	−1.01438	+	1.75695i
$657$		0			0
$658$		0			0
$659$	−10.3923			−0.404827			−0.202413	−	0.979300i	$-0.564878\pi$
$659$	−10.3923			−0.404827			−0.202413	+	0.979300i	$0.564878\pi$
$660$		0			0
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	0.752252	−	0.658876i	$-0.228968\pi$
$661$	−5.00000	−	8.66025i	−0.194477	−	0.336845i	−0.946729	+	0.322031i	$0.895634\pi$
$662$	−17.3205	−	30.0000i	−0.673181	−	1.16598i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−10.3923	−	18.0000i	−0.402090	−	0.696441i
$669$		0			0
$670$	12.0000	−	20.7846i	0.463600	−	0.802980i
$671$	34.6410			1.33730
$672$		0			0
$673$	−10.0000			−0.385472			−0.192736	−	0.981251i	$-0.561736\pi$
$673$	−10.0000			−0.385472			−0.192736	+	0.981251i	$0.561736\pi$
$674$	−12.1244	+	21.0000i	−0.467013	+	0.808890i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−12.1244	+	21.0000i	−0.465977	+	0.807096i	−0.999245	−	0.0388507i	$-0.987630\pi$
$677$	−12.1244	+	21.0000i	−0.465977	+	0.807096i	0.533268	+	0.845946i	$0.320964\pi$
$678$		0			0
$679$		0			0
$680$	20.7846			0.797053
$681$		0			0
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	−12.1244	−	21.0000i	−0.463926	−	0.803543i	0.535227	−	0.844708i	$-0.320226\pi$
$683$	−12.1244	−	21.0000i	−0.463926	−	0.803543i	−0.999152	+	0.0411658i	$0.986893\pi$
$684$		0			0
$685$	−24.0000			−0.916993
$686$		0			0
$687$		0			0
$688$	−10.0000	+	17.3205i	−0.381246	+	0.660338i
$689$	−6.92820	−	12.0000i	−0.263944	−	0.457164i
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$	−17.3205			−0.658427
$693$		0			0
$694$	−30.0000			−1.13878
$695$	−27.7128	+	48.0000i	−1.05121	+	1.82074i
$696$		0			0
$697$	−18.0000	−	31.1769i	−0.681799	−	1.18091i
$698$	12.1244	−	21.0000i	0.458914	−	0.794862i
$699$		0			0
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$	−1.73205	−	3.00000i	−0.0652791	−	0.113067i
$705$		0			0
$706$	−6.00000			−0.225813
$707$		0			0
$708$		0			0
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	31.1769	+	54.0000i	1.17005	+	2.02658i
$711$		0			0
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$	−13.8564			−0.518927
$714$		0			0
$715$	−24.0000			−0.897549
$716$	8.66025	−	15.0000i	0.323649	−	0.560576i
$717$		0			0
$718$	21.0000	+	36.3731i	0.783713	+	1.35743i
$719$	13.8564	−	24.0000i	0.516757	−	0.895049i	−0.483054	−	0.875591i	$-0.660472\pi$
$719$	13.8564	−	24.0000i	0.516757	−	0.895049i	0.999811	−	0.0194584i	$-0.00619418\pi$
$720$		0			0
$721$		0			0
$722$	−5.19615			−0.193381
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$		0			0
$727$	4.00000			0.148352			0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000			0.148352			0.0741759	+	0.997245i	$0.476367\pi$
$728$		0			0
$729$		0			0
$730$	42.0000	−	72.7461i	1.55449	−	2.69246i
$731$	−6.92820	−	12.0000i	−0.256249	−	0.443836i
$732$		0			0
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	−0.994471	−	0.105010i	$-0.966513\pi$
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	0.588177	+	0.808732i	$0.299846\pi$
$734$	27.7128			1.02290
$735$		0			0
$736$	18.0000			0.663489
$737$	6.92820	−	12.0000i	0.255204	−	0.442026i
$738$		0			0
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	0.621374	−	0.783514i	$-0.286575\pi$
$739$	−10.0000	−	17.3205i	−0.367856	−	0.637145i	−0.989230	+	0.146369i	$0.953241\pi$
$740$	−3.46410	+	6.00000i	−0.127343	+	0.220564i
$741$		0			0
$742$		0			0
$743$	−10.3923			−0.381257			−0.190628	−	0.981662i	$-0.561053\pi$
$743$	−10.3923			−0.381257			−0.190628	+	0.981662i	$0.561053\pi$
$744$		0			0
$745$	−12.0000	−	20.7846i	−0.439646	−	0.761489i
$746$	8.66025	+	15.0000i	0.317074	+	0.549189i
$747$		0			0
$748$	−12.0000			−0.438763
$749$		0			0
$750$		0			0
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	−0.929731	−	0.368238i	$-0.879961\pi$
$751$	−4.00000	+	6.92820i	−0.145962	+	0.252814i	0.783769	+	0.621052i	$0.213294\pi$
$752$	−17.3205	−	30.0000i	−0.631614	−	1.09399i
$753$		0			0
$754$		0			0
$755$	27.7128			1.00857
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	24.2487	−	42.0000i	0.880753	−	1.52551i
$759$		0			0
$760$	12.0000	+	20.7846i	0.435286	+	0.753937i
$761$	19.0526	−	33.0000i	0.690655	−	1.19625i	−0.280969	−	0.959717i	$-0.590656\pi$
$761$	19.0526	−	33.0000i	0.690655	−	1.19625i	0.971624	−	0.236532i	$-0.0760109\pi$
$762$		0			0
$763$		0			0
$764$	−24.2487			−0.877288
$765$		0			0
$766$	−12.0000	−	20.7846i	−0.433578	−	0.750978i
$767$	6.92820	+	12.0000i	0.250163	+	0.433295i
$768$		0			0
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	22.5167	+	39.0000i	0.809868	+	1.40273i	0.912955	+	0.408060i	$0.133795\pi$
$773$	22.5167	+	39.0000i	0.809868	+	1.40273i	−0.103087	+	0.994672i	$0.532872\pi$
$774$		0			0
$775$	−14.0000	+	24.2487i	−0.502895	+	0.871039i
$776$	24.2487			0.870478
$777$		0			0
$778$	24.0000			0.860442
$779$	20.7846	−	36.0000i	0.744686	−	1.28983i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	−10.3923	+	18.0000i	−0.371628	+	0.643679i
$783$		0			0
$784$		0			0
$785$	34.6410			1.23639
$786$		0			0
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	0.996531	+	0.0832226i	$0.0265213\pi$
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	−0.426193	+	0.904632i	$0.640145\pi$
$788$	−10.3923	−	18.0000i	−0.370211	−	0.641223i
$789$		0			0
$790$	48.0000			1.70776
$791$		0			0
$792$		0			0
$793$	10.0000	−	17.3205i	0.355110	−	0.615069i
$794$	32.9090	+	57.0000i	1.16790	+	2.02285i
$795$		0			0
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	−31.1769			−1.10434			−0.552171	−	0.833731i	$-0.686201\pi$
$797$	−31.1769			−1.10434			−0.552171	+	0.833731i	$0.686201\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$	18.1865	−	31.5000i	0.642991	−	1.11369i
$801$		0			0
$802$	−6.00000	−	10.3923i	−0.211867	−	0.366965i
$803$	24.2487	−	42.0000i	0.855718	−	1.48215i
$804$		0			0
$805$		0			0
$806$	−13.8564			−0.488071
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	13.8564	+	24.0000i	0.487165	+	0.843795i	0.999891	−	0.0147574i	$-0.00469758\pi$
$809$	13.8564	+	24.0000i	0.487165	+	0.843795i	−0.512726	+	0.858552i	$0.671364\pi$
$810$		0			0
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$		0			0
$813$		0			0
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$	−34.6410	−	60.0000i	−1.21342	−	2.10171i
$816$		0			0
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	−24.2487			−0.847836
$819$		0			0
$820$	−36.0000			−1.25717
$821$	−3.46410	+	6.00000i	−0.120898	+	0.209401i	−0.920122	−	0.391632i	$-0.871911\pi$
$821$	−3.46410	+	6.00000i	−0.120898	+	0.209401i	0.799224	+	0.601033i	$0.205244\pi$
$822$		0			0
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	−0.997686	−	0.0679910i	$-0.978341\pi$
$823$	−16.0000	−	27.7128i	−0.557725	−	0.966008i	0.439961	−	0.898017i	$-0.354992\pi$
$824$	3.46410	−	6.00000i	0.120678	−	0.209020i
$825$		0			0
$826$		0			0
$827$	−10.3923			−0.361376			−0.180688	−	0.983540i	$-0.557832\pi$
$827$	−10.3923			−0.361376			−0.180688	+	0.983540i	$0.557832\pi$
$828$		0			0
$829$	25.0000	+	43.3013i	0.868286	+	1.50392i	0.863747	+	0.503926i	$0.168111\pi$
$829$	25.0000	+	43.3013i	0.868286	+	1.50392i	0.00453881	+	0.999990i	$0.498555\pi$
$830$		0			0
$831$		0			0
$832$	−2.00000			−0.0693375
$833$		0			0
$834$		0			0
$835$	−36.0000	+	62.3538i	−1.24583	+	2.15784i
$836$	−6.92820	−	12.0000i	−0.239617	−	0.415029i
$837$		0			0
$838$	18.0000	−	31.1769i	0.621800	−	1.07699i
$839$	−20.7846			−0.717564			−0.358782	−	0.933421i	$-0.616808\pi$
$839$	−20.7846			−0.717564			−0.358782	+	0.933421i	$0.616808\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	8.66025	−	15.0000i	0.298452	−	0.516934i
$843$		0			0
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	15.5885	−	27.0000i	0.536259	−	0.928828i
$846$		0			0
$847$		0			0
$848$	34.6410			1.18958
$849$		0			0
$850$	21.0000	+	36.3731i	0.720294	+	1.24759i
$851$	3.46410	+	6.00000i	0.118748	+	0.205677i
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$		0			0
$856$	15.0000	−	25.9808i	0.512689	−	0.888004i
$857$	−8.66025	−	15.0000i	−0.295829	−	0.512390i	0.679349	−	0.733816i	$-0.262262\pi$
$857$	−8.66025	−	15.0000i	−0.295829	−	0.512390i	−0.975177	+	0.221425i	$0.928929\pi$
$858$		0			0
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$	−13.8564			−0.472500
$861$		0			0
$862$	6.00000			0.204361
$863$	−19.0526	+	33.0000i	−0.648557	+	1.12333i	0.334911	+	0.942250i	$0.391294\pi$
$863$	−19.0526	+	33.0000i	−0.648557	+	1.12333i	−0.983468	+	0.181083i	$0.942040\pi$
$864$		0			0
$865$	30.0000	+	51.9615i	1.02003	+	1.76674i
$866$	22.5167	−	39.0000i	0.765147	−	1.32527i
$867$		0			0
$868$		0			0
$869$	27.7128			0.940093
$870$		0			0
$871$	−4.00000	−	6.92820i	−0.135535	−	0.234753i
$872$	1.73205	+	3.00000i	0.0586546	+	0.101593i
$873$		0			0
$874$	−24.0000			−0.811812
$875$		0			0
$876$		0			0
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$	−13.8564	−	24.0000i	−0.467631	−	0.809961i
$879$		0			0
$880$	30.0000	−	51.9615i	1.01130	−	1.75162i
$881$	51.9615			1.75063			0.875314	−	0.483555i	$-0.160655\pi$
$881$	51.9615			1.75063			0.875314	+	0.483555i	$0.160655\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	−3.46410	+	6.00000i	−0.116510	+	0.201802i
$885$		0			0
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	3.46410	−	6.00000i	0.116313	−	0.201460i	−0.801991	−	0.597336i	$-0.796226\pi$
$887$	3.46410	−	6.00000i	0.116313	−	0.201460i	0.918304	+	0.395876i	$0.129559\pi$
$888$		0			0
$889$		0			0
$890$	20.7846			0.696702
$891$		0			0
$892$	4.00000	+	6.92820i	0.133930	+	0.231973i
$893$	13.8564	+	24.0000i	0.463687	+	0.803129i
$894$		0			0
$895$	−60.0000			−2.00558
$896$		0			0
$897$		0			0
$898$	−36.0000	+	62.3538i	−1.20134	+	2.08077i
$899$		0			0
$900$		0			0
$901$	−12.0000	+	20.7846i	−0.399778	+	0.692436i
$902$	−62.3538			−2.07616
$903$		0			0
$904$		0			0
$905$	3.46410	−	6.00000i	0.115151	−	0.199447i
$906$		0			0
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	0.999195	−	0.0401089i	$-0.0127705\pi$
$907$	14.0000	+	24.2487i	0.464862	+	0.805165i	−0.534333	+	0.845274i	$0.679437\pi$
$908$	−3.46410	+	6.00000i	−0.114960	+	0.199117i
$909$		0			0
$910$		0			0
$911$	31.1769			1.03294			0.516469	−	0.856306i	$-0.327246\pi$
$911$	31.1769			1.03294			0.516469	+	0.856306i	$0.327246\pi$
$912$		0			0
$913$		0			0
$914$	8.66025	+	15.0000i	0.286456	+	0.496156i
$915$		0			0
$916$	22.0000			0.726900
$917$		0			0
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$	−10.3923	−	18.0000i	−0.342624	−	0.593442i
$921$		0			0
$922$	27.0000	−	46.7654i	0.889198	−	1.54014i
$923$	20.7846			0.684134
$924$		0			0
$925$	14.0000			0.460317
$926$	−27.7128	+	48.0000i	−0.910700	+	1.57738i
$927$		0			0
$928$		0			0
$929$	−22.5167	+	39.0000i	−0.738748	+	1.27955i	0.214312	+	0.976765i	$0.431249\pi$
$929$	−22.5167	+	39.0000i	−0.738748	+	1.27955i	−0.953059	+	0.302783i	$0.902084\pi$
$930$		0			0
$931$		0			0
$932$	6.92820			0.226941
$933$		0			0
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	20.7846	+	36.0000i	0.679729	+	1.17733i
$936$		0			0
$937$	46.0000			1.50275			0.751377	−	0.659873i	$-0.229390\pi$
$937$	46.0000			1.50275			0.751377	+	0.659873i	$0.229390\pi$
$938$		0			0
$939$		0			0
$940$	12.0000	−	20.7846i	0.391397	−	0.677919i
$941$	−8.66025	−	15.0000i	−0.282316	−	0.488986i	0.689639	−	0.724154i	$-0.257769\pi$
$941$	−8.66025	−	15.0000i	−0.282316	−	0.488986i	−0.971955	+	0.235168i	$0.924436\pi$
$942$		0			0
$943$	−18.0000	+	31.1769i	−0.586161	+	1.01526i
$944$	−34.6410			−1.12747
$945$		0			0
$946$	−24.0000			−0.780307
$947$	12.1244	−	21.0000i	0.393989	−	0.682408i	−0.598983	−	0.800762i	$-0.704428\pi$
$947$	12.1244	−	21.0000i	0.393989	−	0.682408i	0.992972	+	0.118354i	$0.0377616\pi$
$948$		0			0
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$	−24.2487	+	42.0000i	−0.786732	+	1.36266i
$951$		0			0
$952$		0			0
$953$	−41.5692			−1.34656			−0.673280	−	0.739388i	$-0.735115\pi$
$953$	−41.5692			−1.34656			−0.673280	+	0.739388i	$0.735115\pi$
$954$		0			0
$955$	42.0000	+	72.7461i	1.35909	+	2.35401i
$956$	−5.19615	−	9.00000i	−0.168056	−	0.291081i
$957$		0			0
$958$	12.0000			0.387702
$959$		0			0
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	3.46410	+	6.00000i	0.111687	+	0.193448i
$963$		0			0
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$	48.4974			1.56119
$966$		0			0
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	0.866025	−	1.50000i	0.0278351	−	0.0482118i
$969$		0			0
$970$	42.0000	+	72.7461i	1.34854	+	2.33574i
$971$	13.8564	−	24.0000i	0.444673	−	0.770197i	−0.553356	−	0.832945i	$-0.686653\pi$
$971$	13.8564	−	24.0000i	0.444673	−	0.770197i	0.998029	+	0.0627481i	$0.0199865\pi$
$972$		0			0
$973$		0			0
$974$	−69.2820			−2.21994
$975$		0			0
$976$	25.0000	+	43.3013i	0.800230	+	1.38604i
$977$	−17.3205	−	30.0000i	−0.554132	−	0.959785i	−0.997970	−	0.0636782i	$-0.979717\pi$
$977$	−17.3205	−	30.0000i	−0.554132	−	0.959785i	0.443838	−	0.896107i	$-0.353616\pi$
$978$		0			0
$979$	12.0000			0.383522
$980$		0			0
$981$		0			0
$982$	−9.00000	+	15.5885i	−0.287202	+	0.497448i
$983$	6.92820	+	12.0000i	0.220975	+	0.382741i	0.955104	−	0.296269i	$-0.0957426\pi$
$983$	6.92820	+	12.0000i	0.220975	+	0.382741i	−0.734129	+	0.679010i	$0.762409\pi$
$984$		0			0
$985$	−36.0000	+	62.3538i	−1.14706	+	1.98676i
$986$		0			0
$987$		0			0
$988$	−8.00000			−0.254514
$989$	−6.92820	+	12.0000i	−0.220304	+	0.381578i
$990$		0			0
$991$	−28.0000	−	48.4974i	−0.889449	−	1.54057i	−0.840528	−	0.541769i	$-0.817755\pi$
$991$	−28.0000	−	48.4974i	−0.889449	−	1.54057i	−0.0489218	−	0.998803i	$-0.515578\pi$
$992$	10.3923	−	18.0000i	0.329956	−	0.571501i
$993$		0			0
$994$		0			0
$995$	55.4256			1.75711
$996$		0			0
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	0.775923	−	0.630828i	$-0.217285\pi$
$997$	−5.00000	−	8.66025i	−0.158352	−	0.274273i	−0.934274	+	0.356555i	$0.883951\pi$
$998$	3.46410	+	6.00000i	0.109654	+	0.189927i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.e.i.226.1		4
3.2	odd	2	inner	441.2.e.i.226.2		4
7.2	even	3		441.2.a.g.1.2		2
7.3	odd	6		441.2.e.j.361.1		4
7.4	even	3	inner	441.2.e.i.361.1		4
7.5	odd	6		63.2.a.b.1.2	yes	2
7.6	odd	2		441.2.e.j.226.1		4
21.2	odd	6		441.2.a.g.1.1		2
21.5	even	6		63.2.a.b.1.1	✓	2
21.11	odd	6	inner	441.2.e.i.361.2		4
21.17	even	6		441.2.e.j.361.2		4
21.20	even	2		441.2.e.j.226.2		4
28.19	even	6		1008.2.a.n.1.1		2
28.23	odd	6		7056.2.a.cm.1.2		2
35.12	even	12		1575.2.d.i.1324.4		4
35.19	odd	6		1575.2.a.q.1.1		2
35.33	even	12		1575.2.d.i.1324.1		4
56.5	odd	6		4032.2.a.bt.1.2		2
56.19	even	6		4032.2.a.bq.1.2		2
63.5	even	6		567.2.f.j.379.2		4
63.40	odd	6		567.2.f.j.379.1		4
63.47	even	6		567.2.f.j.190.2		4
63.61	odd	6		567.2.f.j.190.1		4
77.54	even	6		7623.2.a.bi.1.1		2
84.23	even	6		7056.2.a.cm.1.1		2
84.47	odd	6		1008.2.a.n.1.2		2
105.47	odd	12		1575.2.d.i.1324.2		4
105.68	odd	12		1575.2.d.i.1324.3		4
105.89	even	6		1575.2.a.q.1.2		2
168.5	even	6		4032.2.a.bt.1.1		2
168.131	odd	6		4032.2.a.bq.1.1		2
231.131	odd	6		7623.2.a.bi.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.a.b.1.1	✓	2	21.5	even	6
63.2.a.b.1.2	yes	2	7.5	odd	6
441.2.a.g.1.1		2	21.2	odd	6
441.2.a.g.1.2		2	7.2	even	3
441.2.e.i.226.1		4	1.1	even	1	trivial
441.2.e.i.226.2		4	3.2	odd	2	inner
441.2.e.i.361.1		4	7.4	even	3	inner
441.2.e.i.361.2		4	21.11	odd	6	inner
441.2.e.j.226.1		4	7.6	odd	2
441.2.e.j.226.2		4	21.20	even	2
441.2.e.j.361.1		4	7.3	odd	6
441.2.e.j.361.2		4	21.17	even	6
567.2.f.j.190.1		4	63.61	odd	6
567.2.f.j.190.2		4	63.47	even	6
567.2.f.j.379.1		4	63.40	odd	6
567.2.f.j.379.2		4	63.5	even	6
1008.2.a.n.1.1		2	28.19	even	6
1008.2.a.n.1.2		2	84.47	odd	6
1575.2.a.q.1.1		2	35.19	odd	6
1575.2.a.q.1.2		2	105.89	even	6
1575.2.d.i.1324.1		4	35.33	even	12
1575.2.d.i.1324.2		4	105.47	odd	12
1575.2.d.i.1324.3		4	105.68	odd	12
1575.2.d.i.1324.4		4	35.12	even	12
4032.2.a.bq.1.1		2	168.131	odd	6
4032.2.a.bq.1.2		2	56.19	even	6
4032.2.a.bt.1.1		2	168.5	even	6
4032.2.a.bt.1.2		2	56.5	odd	6
7056.2.a.cm.1.1		2	84.23	even	6
7056.2.a.cm.1.2		2	28.23	odd	6
7623.2.a.bi.1.1		2	77.54	even	6
7623.2.a.bi.1.2		2	231.131	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} -1.73205 q^{8} +O(q^{10})\)	\(q+(-0.866025 + 1.50000i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.73205 + 3.00000i) q^{5} -1.73205 q^{8} +(-3.00000 - 5.19615i) q^{10} +(-1.73205 - 3.00000i) q^{11} -2.00000 q^{13} +(2.50000 - 4.33013i) q^{16} +(1.73205 + 3.00000i) q^{17} +(-2.00000 + 3.46410i) q^{19} +3.46410 q^{20} +6.00000 q^{22} +(1.73205 - 3.00000i) q^{23} +(-3.50000 - 6.06218i) q^{25} +(1.73205 - 3.00000i) q^{26} +(-2.00000 - 3.46410i) q^{31} +(2.59808 + 4.50000i) q^{32} -6.00000 q^{34} +(-1.00000 + 1.73205i) q^{37} +(-3.46410 - 6.00000i) q^{38} +(3.00000 - 5.19615i) q^{40} -10.3923 q^{41} -4.00000 q^{43} +(-1.73205 + 3.00000i) q^{44} +(3.00000 + 5.19615i) q^{46} +(3.46410 - 6.00000i) q^{47} +12.1244 q^{50} +(1.00000 + 1.73205i) q^{52} +(3.46410 + 6.00000i) q^{53} +12.0000 q^{55} +(-3.46410 - 6.00000i) q^{59} +(-5.00000 + 8.66025i) q^{61} +6.92820 q^{62} +1.00000 q^{64} +(3.46410 - 6.00000i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.73205 - 3.00000i) q^{68} -10.3923 q^{71} +(7.00000 + 12.1244i) q^{73} +(-1.73205 - 3.00000i) q^{74} +4.00000 q^{76} +(-4.00000 + 6.92820i) q^{79} +(8.66025 + 15.0000i) q^{80} +(9.00000 - 15.5885i) q^{82} -12.0000 q^{85} +(3.46410 - 6.00000i) q^{86} +(3.00000 + 5.19615i) q^{88} +(-1.73205 + 3.00000i) q^{89} -3.46410 q^{92} +(6.00000 + 10.3923i) q^{94} +(-6.92820 - 12.0000i) q^{95} -14.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4}+O(q^{10}) \) 4 * q - 2 * q^4	\( 4 q - 2 q^{4} - 12 q^{10} - 8 q^{13} + 10 q^{16} - 8 q^{19} + 24 q^{22} - 14 q^{25} - 8 q^{31} - 24 q^{34} - 4 q^{37} + 12 q^{40} - 16 q^{43} + 12 q^{46} + 4 q^{52} + 48 q^{55} - 20 q^{61} + 4 q^{64} + 8 q^{67} + 28 q^{73} + 16 q^{76} - 16 q^{79} + 36 q^{82} - 48 q^{85} + 12 q^{88} + 24 q^{94} - 56 q^{97}+O(q^{100}) \) 4 * q - 2 * q^4 - 12 * q^10 - 8 * q^13 + 10 * q^16 - 8 * q^19 + 24 * q^22 - 14 * q^25 - 8 * q^31 - 24 * q^34 - 4 * q^37 + 12 * q^40 - 16 * q^43 + 12 * q^46 + 4 * q^52 + 48 * q^55 - 20 * q^61 + 4 * q^64 + 8 * q^67 + 28 * q^73 + 16 * q^76 - 16 * q^79 + 36 * q^82 - 48 * q^85 + 12 * q^88 + 24 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more