LMFDB - Embedded newform 441.2.e.j.361.1

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			361.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	441.361
Dual form			441.2.e.j.226.1

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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	−0.990839	−	0.135045i	$-0.956882\pi$
$2$	−0.866025	−	1.50000i	−0.612372	−	1.06066i	0.378467	−	0.925615i	$-0.376451\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.73205	+	3.00000i	0.774597	+	1.34164i	0.935021	+	0.354593i	$0.115380\pi$
$5$	1.73205	+	3.00000i	0.774597	+	1.34164i	−0.160424	+	0.987048i	$0.551286\pi$
$6$		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	0.477432	+	0.878668i	$0.341568\pi$
$11$	−1.73205	+	3.00000i	−0.522233	+	0.904534i	−0.999665	+	0.0258656i	$0.991766\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		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	$-0.971333\pi$
$17$	−1.73205	+	3.00000i	−0.420084	+	0.727607i	0.575863	+	0.817546i	$0.304666\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	−3.46410			−0.774597
$21$		0			0
$22$	6.00000			1.27920
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	0.988152	−	0.153481i	$-0.0490483\pi$
$23$	1.73205	+	3.00000i	0.361158	+	0.625543i	−0.626994	+	0.779024i	$0.715715\pi$
$24$		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	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	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	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	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	$-0.198650\pi$
$41$	10.3923			1.62301			0.811503	+	0.584349i	$0.198650\pi$
$42$		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	−0.999981	−	0.00612051i	$-0.998052\pi$
$47$	−3.46410	−	6.00000i	−0.505291	−	0.875190i	0.494690	−	0.869069i	$-0.335282\pi$
$48$		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	−0.523786	−	0.851850i	$-0.675481\pi$
$53$	3.46410	−	6.00000i	0.475831	−	0.824163i	0.999617	+	0.0276867i	$0.00881407\pi$
$54$		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	$-0.684405\pi$
$59$	3.46410	−	6.00000i	0.450988	−	0.781133i	0.998448	+	0.0556984i	$0.0177385\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−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	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−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	0.0869195	+	0.996215i	$0.472298\pi$
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	−0.906208	+	0.422833i	$0.861036\pi$
$74$	−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	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$	−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	$-0.107893\pi$
$89$	1.73205	+	3.00000i	0.183597	+	0.317999i	−0.759506	+	0.650500i	$0.774559\pi$
$90$		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	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$		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	$-0.888468\pi$
$101$	−1.73205	+	3.00000i	−0.172345	+	0.298511i	0.766894	+	0.641774i	$0.221801\pi$
$102$		0			0
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−3.46410			−0.339683
$105$		0			0
$106$	−12.0000			−1.16554
$107$	−8.66025	−	15.0000i	−0.837218	−	1.45010i	−0.892211	−	0.451618i	$-0.850847\pi$
$107$	−8.66025	−	15.0000i	−0.837218	−	1.45010i	0.0549930	−	0.998487i	$-0.482486\pi$
$108$		0			0
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−1.00000	+	1.73205i	−0.0957826	+	0.165900i	0.814152	+	0.580651i	$0.197202\pi$
$110$	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	0.992001	+	0.126231i	$0.0402882\pi$
$131$	6.92820	+	12.0000i	0.605320	+	1.04844i	−0.386681	+	0.922214i	$0.626379\pi$
$132$		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	−0.679249	−	0.733908i	$-0.737694\pi$
$137$	3.46410	−	6.00000i	0.295958	−	0.512615i	0.975207	+	0.221293i	$0.0710278\pi$
$138$		0			0
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		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	0.688525	−	0.725213i	$-0.258259\pi$
$149$	−3.46410	−	6.00000i	−0.283790	−	0.491539i	−0.972315	+	0.233674i	$0.924925\pi$
$150$		0			0
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	−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	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$	−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	−0.930033	−	0.367477i	$-0.880222\pi$
$163$	−10.0000	−	17.3205i	−0.783260	−	1.35665i	0.146772	−	0.989170i	$-0.453112\pi$
$164$	−5.19615	+	9.00000i	−0.405751	+	0.702782i
$165$		0			0
$166$		0			0
$167$	−20.7846			−1.60836			−0.804181	−	0.594385i	$-0.797396\pi$
$167$	−20.7846			−1.60836			−0.804181	+	0.594385i	$0.797396\pi$
$168$		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	−0.981023	−	0.193892i	$-0.937889\pi$
$173$	−8.66025	−	15.0000i	−0.658427	−	1.14043i	0.322596	−	0.946537i	$-0.395445\pi$
$174$		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	−0.336468	−	0.941695i	$-0.609232\pi$
$179$	8.66025	−	15.0000i	0.647298	−	1.12115i	0.983766	−	0.179458i	$-0.0574343\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$		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	0.854306	+	0.519771i	$0.173983\pi$
$191$	12.1244	+	21.0000i	0.877288	+	1.51951i	0.0229818	+	0.999736i	$0.492684\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	−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	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$	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	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.46410	−	6.00000i	0.229920	−	0.398234i	−0.727864	−	0.685722i	$-0.759487\pi$
$227$	3.46410	−	6.00000i	0.229920	−	0.398234i	0.957784	+	0.287488i	$0.0928200\pi$
$228$		0			0
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	20.7846			1.37050
$231$		0			0
$232$		0			0
$233$	−3.46410	−	6.00000i	−0.226941	−	0.393073i	0.729959	−	0.683491i	$-0.239539\pi$
$233$	−3.46410	−	6.00000i	−0.226941	−	0.393073i	−0.956900	+	0.290418i	$0.906206\pi$
$234$		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	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−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	$-0.272265\pi$
$251$	20.7846			1.31191			0.655956	+	0.754799i	$0.272265\pi$
$252$		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	$-0.132208\pi$
$257$	1.73205	+	3.00000i	0.108042	+	0.187135i	−0.806935	+	0.590641i	$0.798875\pi$
$258$		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	−0.465196	−	0.885208i	$-0.654016\pi$
$263$	8.66025	−	15.0000i	0.534014	−	0.924940i	0.999210	−	0.0397320i	$-0.0126504\pi$
$264$		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	−0.471441	−	0.881897i	$-0.656266\pi$
$269$	8.66025	−	15.0000i	0.528025	−	0.914566i	0.999466	−	0.0326687i	$-0.0104006\pi$
$270$		0			0
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	−0.991658	−	0.128897i	$-0.958856\pi$
$271$	−10.0000	−	17.3205i	−0.607457	−	1.05215i	0.384201	−	0.923249i	$-0.374477\pi$
$272$	−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	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	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	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	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	$-0.598176\pi$
$293$	−10.3923			−0.607125			−0.303562	+	0.952812i	$0.598176\pi$
$294$		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	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$		0			0
$310$	−12.0000	−	20.7846i	−0.681554	−	1.18049i
$311$	−17.3205	+	30.0000i	−0.982156	+	1.70114i	−0.328206	+	0.944606i	$0.606444\pi$
$311$	−17.3205	+	30.0000i	−0.982156	+	1.70114i	−0.653950	+	0.756538i	$0.726889\pi$
$312$		0			0
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	0.836379	−	0.548151i	$-0.184668\pi$
$313$	−1.00000	−	1.73205i	−0.0565233	−	0.0979013i	−0.892903	+	0.450250i	$0.851335\pi$
$314$	−17.3205			−0.977453
$315$		0			0
$316$	8.00000			0.450035
$317$	−3.46410	−	6.00000i	−0.194563	−	0.336994i	0.752194	−	0.658942i	$-0.228996\pi$
$317$	−3.46410	−	6.00000i	−0.194563	−	0.336994i	−0.946757	+	0.321948i	$0.895662\pi$
$318$		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	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$		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	−0.534291	−	0.845301i	$-0.679421\pi$
$347$	8.66025	−	15.0000i	0.464907	−	0.805242i	0.999197	+	0.0400587i	$0.0127545\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		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	$-0.862719\pi$
$353$	−1.73205	+	3.00000i	−0.0921878	+	0.159674i	0.816244	+	0.577708i	$0.196053\pi$
$354$		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	0.985455	+	0.169939i	$0.0543572\pi$
$359$	12.1244	+	21.0000i	0.639899	+	1.10834i	−0.345556	+	0.938398i	$0.612310\pi$
$360$		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	$-0.696206\pi$
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	0.995697	+	0.0926670i	$0.0295392\pi$
$368$	−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	0.965945	−	0.258748i	$-0.0833099\pi$
$373$	5.00000	+	8.66025i	0.258890	+	0.448411i	−0.707055	+	0.707159i	$0.749977\pi$
$374$	−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	$-0.0514830\pi$
$383$	6.92820	+	12.0000i	0.354015	+	0.613171i	−0.632934	+	0.774206i	$0.718150\pi$
$384$		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	−0.986473	−	0.163924i	$-0.947585\pi$
$389$	−6.92820	+	12.0000i	−0.351274	+	0.608424i	0.635199	+	0.772348i	$0.280918\pi$
$390$		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	−0.737579	−	0.675261i	$-0.764031\pi$
$397$	−19.0000	−	32.9090i	−0.953583	−	1.65165i	−0.216004	−	0.976392i	$-0.569302\pi$
$398$	−27.7128			−1.38912
$399$		0			0
$400$	−35.0000			−1.75000
$401$	−3.46410	−	6.00000i	−0.172989	−	0.299626i	0.766475	−	0.642275i	$-0.222009\pi$
$401$	−3.46410	−	6.00000i	−0.172989	−	0.299626i	−0.939463	+	0.342649i	$0.888676\pi$
$402$		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	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	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	$-0.330497\pi$
$419$	20.7846			1.01539			0.507697	+	0.861536i	$0.330497\pi$
$420$		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	−0.904721	−	0.426004i	$-0.859921\pi$
$431$	−1.73205	+	3.00000i	−0.0834300	+	0.144505i	0.821291	+	0.570509i	$0.193254\pi$
$432$		0			0
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$		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	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	20.7846			0.990867
$441$		0			0
$442$	12.0000			0.570782
$443$	1.73205	+	3.00000i	0.0822922	+	0.142534i	0.904234	−	0.427037i	$-0.140443\pi$
$443$	1.73205	+	3.00000i	0.0822922	+	0.142534i	−0.821942	+	0.569571i	$0.807109\pi$
$444$		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	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	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	$-0.241365\pi$
$461$	31.1769			1.45205			0.726027	+	0.687666i	$0.241365\pi$
$462$		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	$-0.217913\pi$
$467$	−3.46410	−	6.00000i	−0.160300	−	0.277647i	−0.934976	+	0.354711i	$0.884579\pi$
$468$		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	$-0.782739\pi$
$479$	3.46410	−	6.00000i	0.158279	−	0.274147i	0.934248	+	0.356624i	$0.116072\pi$
$480$		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	0.0871056	−	0.996199i	$-0.472238\pi$
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.819181	−	0.573535i	$-0.194428\pi$
$488$	−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	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	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	$-0.142205\pi$
$509$	1.73205	+	3.00000i	0.0767718	+	0.132973i	−0.825084	+	0.565011i	$0.808872\pi$
$510$		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	$-0.857511\pi$
$521$	−1.73205	+	3.00000i	−0.0758825	+	0.131432i	0.825587	+	0.564275i	$0.190844\pi$
$522$		0			0
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	0.986216	−	0.165460i	$-0.0529109\pi$
$523$	8.00000	+	13.8564i	0.349816	+	0.605898i	−0.636401	+	0.771358i	$0.719578\pi$
$524$	−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	0.675399	−	0.737453i	$-0.263972\pi$
$541$	−7.00000	−	12.1244i	−0.300954	−	0.521267i	−0.976352	+	0.216186i	$0.930638\pi$
$542$	−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	−0.783256	−	0.621699i	$-0.786443\pi$
$557$	3.46410	−	6.00000i	0.146779	−	0.254228i	0.930035	+	0.367471i	$0.119776\pi$
$558$		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	0.226922	+	0.973913i	$0.427134\pi$
$563$	−17.3205	+	30.0000i	−0.729972	+	1.26435i	−0.956894	+	0.290436i	$0.906200\pi$
$564$		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	0.784233	−	0.620466i	$-0.213057\pi$
$569$	−3.46410	−	6.00000i	−0.145223	−	0.251533i	−0.929456	+	0.368933i	$0.879723\pi$
$570$		0			0
$571$	14.0000	−	24.2487i	0.585882	−	1.01478i	−0.408883	−	0.912587i	$-0.634082\pi$
$571$	14.0000	−	24.2487i	0.585882	−	1.01478i	0.994765	−	0.102190i	$-0.0325850\pi$
$572$	−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	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$	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	$-0.641112\pi$
$587$	−20.7846			−0.857873			−0.428936	+	0.903335i	$0.641112\pi$
$588$		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	$-0.000775869\pi$
$593$	12.1244	+	21.0000i	0.497888	+	0.862367i	−0.502109	+	0.864804i	$0.667443\pi$
$594$		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	−0.120603	+	0.992701i	$0.538483\pi$
$599$	−22.5167	+	39.0000i	−0.920006	+	1.59350i	−0.799402	+	0.600796i	$0.794850\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		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	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	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	0.171564	+	0.985173i	$0.445118\pi$
$613$	−19.0000	+	32.9090i	−0.767403	+	1.32918i	−0.938967	+	0.344008i	$0.888215\pi$
$614$	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	$-0.884732\pi$
$619$	−4.00000	+	6.92820i	−0.160774	+	0.278468i	0.774373	+	0.632730i	$0.218066\pi$
$620$	−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	0.229860	−	0.973224i	$-0.426173\pi$
$641$	24.2487	−	42.0000i	0.957767	−	1.65890i	0.727906	−	0.685677i	$-0.240494\pi$
$642$		0			0
$643$	20.0000			0.788723			0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000			0.788723			0.394362	+	0.918955i	$0.370966\pi$
$644$		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	$-0.789848\pi$
$647$	3.46410	−	6.00000i	0.136188	−	0.235884i	0.926051	+	0.377399i	$0.123182\pi$
$648$		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	−0.998775	−	0.0494855i	$-0.984242\pi$
$653$	−13.8564	−	24.0000i	−0.542243	−	0.939193i	0.456532	−	0.889707i	$-0.349091\pi$
$654$		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	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	−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	$-0.0123697\pi$
$677$	12.1244	+	21.0000i	0.465977	+	0.807096i	−0.533268	+	0.845946i	$0.679036\pi$
$678$		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	−0.999152	−	0.0411658i	$-0.986893\pi$
$683$	−12.1244	+	21.0000i	−0.463926	+	0.803543i	0.535227	+	0.844708i	$0.320226\pi$
$684$		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	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	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	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$	−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	−0.999811	−	0.0194584i	$-0.993806\pi$
$719$	−13.8564	−	24.0000i	−0.516757	−	0.895049i	0.483054	−	0.875591i	$-0.339528\pi$
$720$		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	$-0.523633\pi$
$727$	−4.00000			−0.148352			−0.0741759	+	0.997245i	$0.523633\pi$
$728$		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	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	−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	−0.989230	−	0.146369i	$-0.953241\pi$
$739$	−10.0000	+	17.3205i	−0.367856	+	0.637145i	0.621374	+	0.783514i	$0.286575\pi$
$740$	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	0.783769	−	0.621052i	$-0.213294\pi$
$751$	−4.00000	−	6.92820i	−0.145962	−	0.252814i	−0.929731	+	0.368238i	$0.879961\pi$
$752$	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	−0.971624	−	0.236532i	$-0.923989\pi$
$761$	−19.0526	−	33.0000i	−0.690655	−	1.19625i	0.280969	−	0.959717i	$-0.409344\pi$
$762$		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	$-0.629834\pi$
$769$	−22.0000			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$770$		0			0
$771$		0			0
$772$	−7.00000	−	12.1244i	−0.251936	−	0.436365i
$773$	−22.5167	+	39.0000i	−0.809868	+	1.40273i	0.103087	+	0.994672i	$0.467128\pi$
$773$	−22.5167	+	39.0000i	−0.809868	+	1.40273i	−0.912955	+	0.408060i	$0.866205\pi$
$774$		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	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$	−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	$-0.313799\pi$
$797$	31.1769			1.10434			0.552171	+	0.833731i	$0.313799\pi$
$798$		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	−0.512726	−	0.858552i	$-0.671364\pi$
$809$	13.8564	−	24.0000i	0.487165	−	0.843795i	0.999891	+	0.0147574i	$0.00469758\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$		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	0.799224	−	0.601033i	$-0.205244\pi$
$821$	−3.46410	−	6.00000i	−0.120898	−	0.209401i	−0.920122	+	0.391632i	$0.871911\pi$
$822$		0			0
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	−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	−0.00453881	+	0.999990i	$0.501445\pi$
$829$	−25.0000	+	43.3013i	−0.868286	+	1.50392i	−0.863747	+	0.503926i	$0.831889\pi$
$830$		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	$-0.383192\pi$
$839$	20.7846			0.717564			0.358782	+	0.933421i	$0.383192\pi$
$840$		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	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$		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	$-0.737738\pi$
$857$	8.66025	−	15.0000i	0.295829	−	0.512390i	0.975177	+	0.221425i	$0.0710709\pi$
$858$		0			0
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$	13.8564			0.472500
$861$		0			0
$862$	6.00000			0.204361
$863$	−19.0526	−	33.0000i	−0.648557	−	1.12333i	−0.983468	−	0.181083i	$-0.942040\pi$
$863$	−19.0526	−	33.0000i	−0.648557	−	1.12333i	0.334911	−	0.942250i	$-0.391294\pi$
$864$		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	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$	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	$-0.839345\pi$
$881$	−51.9615			−1.75063			−0.875314	+	0.483555i	$0.839345\pi$
$882$		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	$-0.203774\pi$
$887$	−3.46410	−	6.00000i	−0.116313	−	0.201460i	−0.918304	+	0.395876i	$0.870441\pi$
$888$		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	−0.534333	−	0.845274i	$-0.679437\pi$
$907$	14.0000	−	24.2487i	0.464862	−	0.805165i	0.999195	+	0.0401089i	$0.0127705\pi$
$908$	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	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$	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	0.953059	+	0.302783i	$0.0979158\pi$
$929$	22.5167	+	39.0000i	0.738748	+	1.27955i	−0.214312	+	0.976765i	$0.568751\pi$
$930$		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	$-0.770610\pi$
$937$	−46.0000			−1.50275			−0.751377	+	0.659873i	$0.770610\pi$
$938$		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	$-0.742231\pi$
$941$	8.66025	−	15.0000i	0.282316	−	0.488986i	0.971955	+	0.235168i	$0.0755639\pi$
$942$		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	0.992972	−	0.118354i	$-0.0377616\pi$
$947$	12.1244	+	21.0000i	0.393989	+	0.682408i	−0.598983	+	0.800762i	$0.704428\pi$
$948$		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	$-0.313347\pi$
$971$	−13.8564	−	24.0000i	−0.444673	−	0.770197i	−0.998029	+	0.0627481i	$0.980014\pi$
$972$		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	0.443838	+	0.896107i	$0.353616\pi$
$977$	−17.3205	+	30.0000i	−0.554132	+	0.959785i	−0.997970	+	0.0636782i	$0.979717\pi$
$978$		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	$-0.904257\pi$
$983$	−6.92820	+	12.0000i	−0.220975	+	0.382741i	0.734129	+	0.679010i	$0.237591\pi$
$984$		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	−0.0489218	+	0.998803i	$0.515578\pi$
$991$	−28.0000	+	48.4974i	−0.889449	+	1.54057i	−0.840528	+	0.541769i	$0.817755\pi$
$992$	−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	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$	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.j.361.1		4
3.2	odd	2	inner	441.2.e.j.361.2		4
7.2	even	3	inner	441.2.e.j.226.1		4
7.3	odd	6		441.2.a.g.1.2		2
7.4	even	3		63.2.a.b.1.2	yes	2
7.5	odd	6		441.2.e.i.226.1		4
7.6	odd	2		441.2.e.i.361.1		4
21.2	odd	6	inner	441.2.e.j.226.2		4
21.5	even	6		441.2.e.i.226.2		4
21.11	odd	6		63.2.a.b.1.1	✓	2
21.17	even	6		441.2.a.g.1.1		2
21.20	even	2		441.2.e.i.361.2		4
28.3	even	6		7056.2.a.cm.1.2		2
28.11	odd	6		1008.2.a.n.1.1		2
35.4	even	6		1575.2.a.q.1.1		2
35.18	odd	12		1575.2.d.i.1324.1		4
35.32	odd	12		1575.2.d.i.1324.4		4
56.11	odd	6		4032.2.a.bq.1.2		2
56.53	even	6		4032.2.a.bt.1.2		2
63.4	even	3		567.2.f.j.379.1		4
63.11	odd	6		567.2.f.j.190.2		4
63.25	even	3		567.2.f.j.190.1		4
63.32	odd	6		567.2.f.j.379.2		4
77.32	odd	6		7623.2.a.bi.1.1		2
84.11	even	6		1008.2.a.n.1.2		2
84.59	odd	6		7056.2.a.cm.1.1		2
105.32	even	12		1575.2.d.i.1324.2		4
105.53	even	12		1575.2.d.i.1324.3		4
105.74	odd	6		1575.2.a.q.1.2		2
168.11	even	6		4032.2.a.bq.1.1		2
168.53	odd	6		4032.2.a.bt.1.1		2
231.32	even	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	21.11	odd	6
63.2.a.b.1.2	yes	2	7.4	even	3
441.2.a.g.1.1		2	21.17	even	6
441.2.a.g.1.2		2	7.3	odd	6
441.2.e.i.226.1		4	7.5	odd	6
441.2.e.i.226.2		4	21.5	even	6
441.2.e.i.361.1		4	7.6	odd	2
441.2.e.i.361.2		4	21.20	even	2
441.2.e.j.226.1		4	7.2	even	3	inner
441.2.e.j.226.2		4	21.2	odd	6	inner
441.2.e.j.361.1		4	1.1	even	1	trivial
441.2.e.j.361.2		4	3.2	odd	2	inner
567.2.f.j.190.1		4	63.25	even	3
567.2.f.j.190.2		4	63.11	odd	6
567.2.f.j.379.1		4	63.4	even	3
567.2.f.j.379.2		4	63.32	odd	6
1008.2.a.n.1.1		2	28.11	odd	6
1008.2.a.n.1.2		2	84.11	even	6
1575.2.a.q.1.1		2	35.4	even	6
1575.2.a.q.1.2		2	105.74	odd	6
1575.2.d.i.1324.1		4	35.18	odd	12
1575.2.d.i.1324.2		4	105.32	even	12
1575.2.d.i.1324.3		4	105.53	even	12
1575.2.d.i.1324.4		4	35.32	odd	12
4032.2.a.bq.1.1		2	168.11	even	6
4032.2.a.bq.1.2		2	56.11	odd	6
4032.2.a.bt.1.1		2	168.53	odd	6
4032.2.a.bt.1.2		2	56.53	even	6
7056.2.a.cm.1.1		2	84.59	odd	6
7056.2.a.cm.1.2		2	28.3	even	6
7623.2.a.bi.1.1		2	77.32	odd	6
7623.2.a.bi.1.2		2	231.32	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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

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