LMFDB - Embedded newform 1710.2.p.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(37,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1710.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.2
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1710.37
Dual form			1710.2.p.a.1063.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.12132 + 0.707107i) q^{10} -2.00000 q^{11} +(-4.24264 - 4.24264i) q^{13} -1.41421 q^{14} -1.00000 q^{16} +(-3.00000 - 3.00000i) q^{17} +(4.24264 - 1.00000i) q^{19} +(2.00000 - 1.00000i) q^{20} +(-1.41421 + 1.41421i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} -6.00000 q^{26} +(-1.00000 + 1.00000i) q^{28} -8.48528i q^{31} +(-0.707107 + 0.707107i) q^{32} -4.24264 q^{34} +(1.00000 - 3.00000i) q^{35} +(-4.24264 + 4.24264i) q^{37} +(2.29289 - 3.70711i) q^{38} +(0.707107 - 2.12132i) q^{40} -8.48528i q^{41} +(-5.00000 + 5.00000i) q^{43} +2.00000i q^{44} +1.41421i q^{46} +(-7.00000 - 7.00000i) q^{47} -5.00000i q^{49} +(0.707107 + 4.94975i) q^{50} +(-4.24264 + 4.24264i) q^{52} +(4.24264 + 4.24264i) q^{53} +(-2.00000 - 4.00000i) q^{55} +1.41421i q^{56} +8.00000 q^{61} +(-6.00000 - 6.00000i) q^{62} +1.00000i q^{64} +(4.24264 - 12.7279i) q^{65} +(8.48528 - 8.48528i) q^{67} +(-3.00000 + 3.00000i) q^{68} +(-1.41421 - 2.82843i) q^{70} -8.48528i q^{71} +(-1.00000 + 1.00000i) q^{73} +6.00000i q^{74} +(-1.00000 - 4.24264i) q^{76} +(2.00000 + 2.00000i) q^{77} +8.48528 q^{79} +(-1.00000 - 2.00000i) q^{80} +(-6.00000 - 6.00000i) q^{82} +(-9.00000 + 9.00000i) q^{83} +(3.00000 - 9.00000i) q^{85} +7.07107i q^{86} +(1.41421 + 1.41421i) q^{88} -8.48528 q^{89} +8.48528i q^{91} +(1.00000 + 1.00000i) q^{92} -9.89949 q^{94} +(6.24264 + 7.48528i) q^{95} +(4.24264 - 4.24264i) q^{97} +(-3.53553 - 3.53553i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5} - 4 q^{7} - 8 q^{11} - 4 q^{16} - 12 q^{17} + 8 q^{20} - 4 q^{23} - 12 q^{25} - 24 q^{26} - 4 q^{28} + 4 q^{35} + 12 q^{38} - 20 q^{43} - 28 q^{47} - 8 q^{55} + 32 q^{61} - 24 q^{62} - 12 q^{68}+ \cdots + 8 q^{95}+O(q^{100}) $ 4 * q + 4 * q^5 - 4 * q^7 - 8 * q^11 - 4 * q^16 - 12 * q^17 + 8 * q^20 - 4 * q^23 - 12 * q^25 - 24 * q^26 - 4 * q^28 + 4 * q^35 + 12 * q^38 - 20 * q^43 - 28 * q^47 - 8 * q^55 + 32 * q^61 - 24 * q^62 - 12 * q^68 - 4 * q^73 - 4 * q^76 + 8 * q^77 - 4 * q^80 - 24 * q^82 - 36 * q^83 + 12 * q^85 + 4 * q^92 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$		0			0
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.12132	+	0.707107i	0.670820	+	0.223607i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	−4.24264	−	4.24264i	−1.17670	−	1.17670i	−0.980581	−	0.196116i	$-0.937167\pi$
$13$	−4.24264	−	4.24264i	−1.17670	−	1.17670i	−0.196116	−	0.980581i	$-0.562833\pi$
$14$	−1.41421			−0.377964
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−3.00000	−	3.00000i	−0.727607	−	0.727607i	0.242536	−	0.970143i	$-0.422021\pi$
$17$	−3.00000	−	3.00000i	−0.727607	−	0.727607i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$	4.24264	−	1.00000i	0.973329	−	0.229416i
$19$	4.24264	−	1.00000i	0.973329	−	0.229416i
$20$	2.00000	−	1.00000i	0.447214	−	0.223607i
$21$		0			0
$22$	−1.41421	+	1.41421i	−0.301511	+	0.301511i
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$		0			0
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	−6.00000			−1.17670
$27$		0			0
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$		−	8.48528i		−	1.52400i	−0.647576	−	0.762001i	$-0.724217\pi$
$31$		−	8.48528i		−	1.52400i	0.647576	−	0.762001i	$-0.275783\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	−4.24264			−0.727607
$35$	1.00000	−	3.00000i	0.169031	−	0.507093i
$36$		0			0
$37$	−4.24264	+	4.24264i	−0.697486	+	0.697486i	−0.963868	−	0.266382i	$-0.914172\pi$
$37$	−4.24264	+	4.24264i	−0.697486	+	0.697486i	0.266382	+	0.963868i	$0.414172\pi$
$38$	2.29289	−	3.70711i	0.371956	−	0.601372i
$39$		0			0
$40$	0.707107	−	2.12132i	0.111803	−	0.335410i
$41$		−	8.48528i		−	1.32518i	−0.748983	−	0.662589i	$-0.769458\pi$
$41$		−	8.48528i		−	1.32518i	0.748983	−	0.662589i	$-0.230542\pi$
$42$		0			0
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	−0.976772	−	0.214280i	$-0.931260\pi$
$43$	−5.00000	+	5.00000i	−0.762493	+	0.762493i	0.214280	+	0.976772i	$0.431260\pi$
$44$			2.00000i			0.301511i
$45$		0			0
$46$			1.41421i			0.208514i
$47$	−7.00000	−	7.00000i	−1.02105	−	1.02105i	−0.999774	−	0.0212814i	$-0.993225\pi$
$47$	−7.00000	−	7.00000i	−1.02105	−	1.02105i	−0.0212814	−	0.999774i	$-0.506775\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$	0.707107	+	4.94975i	0.100000	+	0.700000i
$51$		0			0
$52$	−4.24264	+	4.24264i	−0.588348	+	0.588348i
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	0.935664	−	0.352892i	$-0.114802\pi$
$53$	4.24264	+	4.24264i	0.582772	+	0.582772i	−0.352892	+	0.935664i	$0.614802\pi$
$54$		0			0
$55$	−2.00000	−	4.00000i	−0.269680	−	0.539360i
$56$			1.41421i			0.188982i
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	8.00000			1.02430			0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000			1.02430			0.512148	+	0.858898i	$0.328850\pi$
$62$	−6.00000	−	6.00000i	−0.762001	−	0.762001i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	4.24264	−	12.7279i	0.526235	−	1.57870i
$66$		0			0
$67$	8.48528	−	8.48528i	1.03664	−	1.03664i	0.0373395	−	0.999303i	$-0.488112\pi$
$67$	8.48528	−	8.48528i	1.03664	−	1.03664i	0.999303	−	0.0373395i	$-0.0118883\pi$
$68$	−3.00000	+	3.00000i	−0.363803	+	0.363803i
$69$		0			0
$70$	−1.41421	−	2.82843i	−0.169031	−	0.338062i
$71$		−	8.48528i		−	1.00702i	−0.863990	−	0.503509i	$-0.832042\pi$
$71$		−	8.48528i		−	1.00702i	0.863990	−	0.503509i	$-0.167958\pi$
$72$		0			0
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	−0.763202	−	0.646160i	$-0.776374\pi$
$73$	−1.00000	+	1.00000i	−0.117041	+	0.117041i	0.646160	+	0.763202i	$0.276374\pi$
$74$			6.00000i			0.697486i
$75$		0			0
$76$	−1.00000	−	4.24264i	−0.114708	−	0.486664i
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$	8.48528			0.954669			0.477334	−	0.878722i	$-0.341603\pi$
$79$	8.48528			0.954669			0.477334	+	0.878722i	$0.341603\pi$
$80$	−1.00000	−	2.00000i	−0.111803	−	0.223607i
$81$		0			0
$82$	−6.00000	−	6.00000i	−0.662589	−	0.662589i
$83$	−9.00000	+	9.00000i	−0.987878	+	0.987878i	−0.999927	−	0.0120491i	$-0.996165\pi$
$83$	−9.00000	+	9.00000i	−0.987878	+	0.987878i	0.0120491	+	0.999927i	$0.496165\pi$
$84$		0			0
$85$	3.00000	−	9.00000i	0.325396	−	0.976187i
$86$			7.07107i			0.762493i
$87$		0			0
$88$	1.41421	+	1.41421i	0.150756	+	0.150756i
$89$	−8.48528			−0.899438			−0.449719	−	0.893170i	$-0.648476\pi$
$89$	−8.48528			−0.899438			−0.449719	+	0.893170i	$0.648476\pi$
$90$		0			0
$91$			8.48528i			0.889499i
$92$	1.00000	+	1.00000i	0.104257	+	0.104257i
$93$		0			0
$94$	−9.89949			−1.02105
$95$	6.24264	+	7.48528i	0.640481	+	0.767974i
$96$		0			0
$97$	4.24264	−	4.24264i	0.430775	−	0.430775i	−0.458117	−	0.888892i	$-0.651476\pi$
$97$	4.24264	−	4.24264i	0.430775	−	0.430775i	0.888892	+	0.458117i	$0.151476\pi$
$98$	−3.53553	−	3.53553i	−0.357143	−	0.357143i
$99$		0			0
$100$	4.00000	+	3.00000i	0.400000	+	0.300000i
$101$	−4.00000			−0.398015			−0.199007	−	0.979998i	$-0.563772\pi$
$101$	−4.00000			−0.398015			−0.199007	+	0.979998i	$0.563772\pi$
$102$		0			0
$103$	8.48528	+	8.48528i	0.836080	+	0.836080i	0.988340	−	0.152261i	$-0.0486553\pi$
$103$	8.48528	+	8.48528i	0.836080	+	0.836080i	−0.152261	+	0.988340i	$0.548655\pi$
$104$			6.00000i			0.588348i
$105$		0			0
$106$	6.00000			0.582772
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	−0.986151	−	0.165848i	$-0.946964\pi$
$107$	−8.48528	+	8.48528i	−0.820303	+	0.820303i	0.165848	+	0.986151i	$0.446964\pi$
$108$		0			0
$109$	−8.48528			−0.812743			−0.406371	−	0.913708i	$-0.633206\pi$
$109$	−8.48528			−0.812743			−0.406371	+	0.913708i	$0.633206\pi$
$110$	−4.24264	−	1.41421i	−0.404520	−	0.134840i
$111$		0			0
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	0.478806	−	0.877920i	$-0.341070\pi$
$113$	−4.24264	−	4.24264i	−0.399114	−	0.399114i	−0.877920	+	0.478806i	$0.841070\pi$
$114$		0			0
$115$	−3.00000	−	1.00000i	−0.279751	−	0.0932505i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			6.00000i			0.550019i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	5.65685	−	5.65685i	0.512148	−	0.512148i
$123$		0			0
$124$	−8.48528			−0.762001
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$		0			0
$127$	8.48528	−	8.48528i	0.752947	−	0.752947i	−0.222081	−	0.975028i	$-0.571285\pi$
$127$	8.48528	−	8.48528i	0.752947	−	0.752947i	0.975028	+	0.222081i	$0.0712850\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	−6.00000	−	12.0000i	−0.526235	−	1.05247i
$131$	−4.00000			−0.349482			−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000			−0.349482			−0.174741	+	0.984614i	$0.555909\pi$
$132$		0			0
$133$	−5.24264	−	3.24264i	−0.454595	−	0.281173i
$134$		−	12.0000i		−	1.03664i
$135$		0			0
$136$			4.24264i			0.363803i
$137$	3.00000	+	3.00000i	0.256307	+	0.256307i	0.823550	−	0.567243i	$-0.191990\pi$
$137$	3.00000	+	3.00000i	0.256307	+	0.256307i	−0.567243	+	0.823550i	$0.691990\pi$
$138$		0			0
$139$			12.0000i			1.01783i	0.860818	+	0.508913i	$0.169953\pi$
$139$			12.0000i			1.01783i	−0.860818	+	0.508913i	$0.830047\pi$
$140$	−3.00000	−	1.00000i	−0.253546	−	0.0845154i
$141$		0			0
$142$	−6.00000	−	6.00000i	−0.503509	−	0.503509i
$143$	8.48528	+	8.48528i	0.709575	+	0.709575i
$144$		0			0
$145$		0			0
$146$			1.41421i			0.117041i
$147$		0			0
$148$	4.24264	+	4.24264i	0.348743	+	0.348743i
$149$		−	10.0000i		−	0.819232i	−0.912258	−	0.409616i	$-0.865663\pi$
$149$		−	10.0000i		−	0.819232i	0.912258	−	0.409616i	$-0.134337\pi$
$150$		0			0
$151$			16.9706i			1.38104i	0.723311	+	0.690522i	$0.242619\pi$
$151$			16.9706i			1.38104i	−0.723311	+	0.690522i	$0.757381\pi$
$152$	−3.70711	−	2.29289i	−0.300686	−	0.185978i
$153$		0			0
$154$	2.82843			0.227921
$155$	16.9706	−	8.48528i	1.36311	−	0.681554i
$156$		0			0
$157$	−11.0000	−	11.0000i	−0.877896	−	0.877896i	0.115421	−	0.993317i	$-0.463178\pi$
$157$	−11.0000	−	11.0000i	−0.877896	−	0.877896i	−0.993317	+	0.115421i	$0.963178\pi$
$158$	6.00000	−	6.00000i	0.477334	−	0.477334i
$159$		0			0
$160$	−2.12132	−	0.707107i	−0.167705	−	0.0559017i
$161$	2.00000			0.157622
$162$		0			0
$163$	−7.00000	+	7.00000i	−0.548282	+	0.548282i	−0.925944	−	0.377661i	$-0.876728\pi$
$163$	−7.00000	+	7.00000i	−0.548282	+	0.548282i	0.377661	+	0.925944i	$0.376728\pi$
$164$	−8.48528			−0.662589
$165$		0			0
$166$			12.7279i			0.987878i
$167$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$167$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$168$		0			0
$169$			23.0000i			1.76923i
$170$	−4.24264	−	8.48528i	−0.325396	−	0.650791i
$171$		0			0
$172$	5.00000	+	5.00000i	0.381246	+	0.381246i
$173$	12.7279	+	12.7279i	0.967686	+	0.967686i	0.999494	−	0.0318080i	$-0.0101265\pi$
$173$	12.7279	+	12.7279i	0.967686	+	0.967686i	−0.0318080	+	0.999494i	$0.510127\pi$
$174$		0			0
$175$	7.00000	−	1.00000i	0.529150	−	0.0755929i
$176$	2.00000			0.150756
$177$		0			0
$178$	−6.00000	+	6.00000i	−0.449719	+	0.449719i
$179$	16.9706			1.26844			0.634220	−	0.773153i	$-0.281321\pi$
$179$	16.9706			1.26844			0.634220	+	0.773153i	$0.281321\pi$
$180$		0			0
$181$		−	25.4558i		−	1.89212i	−0.323994	−	0.946059i	$-0.605026\pi$
$181$		−	25.4558i		−	1.89212i	0.323994	−	0.946059i	$-0.394974\pi$
$182$	6.00000	+	6.00000i	0.444750	+	0.444750i
$183$		0			0
$184$	1.41421			0.104257
$185$	−12.7279	−	4.24264i	−0.935775	−	0.311925i
$186$		0			0
$187$	6.00000	+	6.00000i	0.438763	+	0.438763i
$188$	−7.00000	+	7.00000i	−0.510527	+	0.510527i
$189$		0			0
$190$	9.70711	+	0.878680i	0.704228	+	0.0637461i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$		0			0
$193$	4.24264	+	4.24264i	0.305392	+	0.305392i	0.843119	−	0.537727i	$-0.180717\pi$
$193$	4.24264	+	4.24264i	0.305392	+	0.305392i	−0.537727	+	0.843119i	$0.680717\pi$
$194$		−	6.00000i		−	0.430775i
$195$		0			0
$196$	−5.00000			−0.357143
$197$	−5.00000	−	5.00000i	−0.356235	−	0.356235i	0.506188	−	0.862423i	$-0.331054\pi$
$197$	−5.00000	−	5.00000i	−0.356235	−	0.356235i	−0.862423	+	0.506188i	$0.831054\pi$
$198$		0			0
$199$			18.0000i			1.27599i	0.770042	+	0.637993i	$0.220235\pi$
$199$			18.0000i			1.27599i	−0.770042	+	0.637993i	$0.779765\pi$
$200$	4.94975	−	0.707107i	0.350000	−	0.0500000i
$201$		0			0
$202$	−2.82843	+	2.82843i	−0.199007	+	0.199007i
$203$		0			0
$204$		0			0
$205$	16.9706	−	8.48528i	1.18528	−	0.592638i
$206$	12.0000			0.836080
$207$		0			0
$208$	4.24264	+	4.24264i	0.294174	+	0.294174i
$209$	−8.48528	+	2.00000i	−0.586939	+	0.138343i
$210$		0			0
$211$			8.48528i			0.584151i	0.956395	+	0.292075i	$0.0943458\pi$
$211$			8.48528i			0.584151i	−0.956395	+	0.292075i	$0.905654\pi$
$212$	4.24264	−	4.24264i	0.291386	−	0.291386i
$213$		0			0
$214$			12.0000i			0.820303i
$215$	−15.0000	−	5.00000i	−1.02299	−	0.340997i
$216$		0			0
$217$	−8.48528	+	8.48528i	−0.576018	+	0.576018i
$218$	−6.00000	+	6.00000i	−0.406371	+	0.406371i
$219$		0			0
$220$	−4.00000	+	2.00000i	−0.269680	+	0.134840i
$221$			25.4558i			1.71235i
$222$		0			0
$223$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$223$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$224$	1.41421			0.0944911
$225$		0			0
$226$	−6.00000			−0.399114
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$		0			0
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$	−2.82843	+	1.41421i	−0.186501	+	0.0932505i
$231$		0			0
$232$		0			0
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−5.00000	+	5.00000i	−0.327561	+	0.327561i	0.524097	+	0.851658i	$0.324403\pi$
$234$		0			0
$235$	7.00000	−	21.0000i	0.456630	−	1.36989i
$236$		0			0
$237$		0			0
$238$	4.24264	+	4.24264i	0.275010	+	0.275010i
$239$			10.0000i			0.646846i	0.946254	+	0.323423i	$0.104834\pi$
$239$			10.0000i			0.646846i	−0.946254	+	0.323423i	$0.895166\pi$
$240$		0			0
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$	−4.94975	+	4.94975i	−0.318182	+	0.318182i
$243$		0			0
$244$		−	8.00000i		−	0.512148i
$245$	10.0000	−	5.00000i	0.638877	−	0.319438i
$246$		0			0
$247$	−22.2426	−	13.7574i	−1.41527	−	0.875360i
$248$	−6.00000	+	6.00000i	−0.381000	+	0.381000i
$249$		0			0
$250$	−9.19239	+	6.36396i	−0.581378	+	0.402492i
$251$	20.0000			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$251$	20.0000			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$252$		0			0
$253$	2.00000	−	2.00000i	0.125739	−	0.125739i
$254$		−	12.0000i		−	0.752947i
$255$		0			0
$256$	1.00000			0.0625000
$257$	4.24264	−	4.24264i	0.264649	−	0.264649i	−0.562291	−	0.826940i	$-0.690080\pi$
$257$	4.24264	−	4.24264i	0.264649	−	0.264649i	0.826940	+	0.562291i	$0.190080\pi$
$258$		0			0
$259$	8.48528			0.527250
$260$	−12.7279	−	4.24264i	−0.789352	−	0.263117i
$261$		0			0
$262$	−2.82843	+	2.82843i	−0.174741	+	0.174741i
$263$	−3.00000	+	3.00000i	−0.184988	+	0.184988i	−0.793525	−	0.608537i	$-0.791757\pi$
$263$	−3.00000	+	3.00000i	−0.184988	+	0.184988i	0.608537	+	0.793525i	$0.291757\pi$
$264$		0			0
$265$	−4.24264	+	12.7279i	−0.260623	+	0.781870i
$266$	−6.00000	+	1.41421i	−0.367884	+	0.0867110i
$267$		0			0
$268$	−8.48528	−	8.48528i	−0.518321	−	0.518321i
$269$	−8.48528			−0.517357			−0.258678	−	0.965964i	$-0.583287\pi$
$269$	−8.48528			−0.517357			−0.258678	+	0.965964i	$0.583287\pi$
$270$		0			0
$271$	30.0000			1.82237			0.911185	−	0.411997i	$-0.135169\pi$
$271$	30.0000			1.82237			0.911185	+	0.411997i	$0.135169\pi$
$272$	3.00000	+	3.00000i	0.181902	+	0.181902i
$273$		0			0
$274$	4.24264			0.256307
$275$	6.00000	−	8.00000i	0.361814	−	0.482418i
$276$		0			0
$277$	−7.00000	−	7.00000i	−0.420589	−	0.420589i	0.464817	−	0.885407i	$-0.346120\pi$
$277$	−7.00000	−	7.00000i	−0.420589	−	0.420589i	−0.885407	+	0.464817i	$0.846120\pi$
$278$	8.48528	+	8.48528i	0.508913	+	0.508913i
$279$		0			0
$280$	−2.82843	+	1.41421i	−0.169031	+	0.0845154i
$281$		−	25.4558i		−	1.51857i	−0.650759	−	0.759284i	$-0.725549\pi$
$281$		−	25.4558i		−	1.51857i	0.650759	−	0.759284i	$-0.274451\pi$
$282$		0			0
$283$	19.0000	−	19.0000i	1.12943	−	1.12943i	0.139163	−	0.990269i	$-0.455559\pi$
$283$	19.0000	−	19.0000i	1.12943	−	1.12943i	0.990269	−	0.139163i	$-0.0444413\pi$
$284$	−8.48528			−0.503509
$285$		0			0
$286$	12.0000			0.709575
$287$	−8.48528	+	8.48528i	−0.500870	+	0.500870i
$288$		0			0
$289$			1.00000i			0.0588235i
$290$		0			0
$291$		0			0
$292$	1.00000	+	1.00000i	0.0585206	+	0.0585206i
$293$	−4.24264	−	4.24264i	−0.247858	−	0.247858i	0.572233	−	0.820091i	$-0.306077\pi$
$293$	−4.24264	−	4.24264i	−0.247858	−	0.247858i	−0.820091	+	0.572233i	$0.806077\pi$
$294$		0			0
$295$		0			0
$296$	6.00000			0.348743
$297$		0			0
$298$	−7.07107	−	7.07107i	−0.409616	−	0.409616i
$299$	8.48528			0.490716
$300$		0			0
$301$	10.0000			0.576390
$302$	12.0000	+	12.0000i	0.690522	+	0.690522i
$303$		0			0
$304$	−4.24264	+	1.00000i	−0.243332	+	0.0573539i
$305$	8.00000	+	16.0000i	0.458079	+	0.916157i
$306$		0			0
$307$	−8.48528	+	8.48528i	−0.484281	+	0.484281i	−0.906496	−	0.422215i	$-0.861253\pi$
$307$	−8.48528	+	8.48528i	−0.484281	+	0.484281i	0.422215	+	0.906496i	$0.361253\pi$
$308$	2.00000	−	2.00000i	0.113961	−	0.113961i
$309$		0			0
$310$	6.00000	−	18.0000i	0.340777	−	1.02233i
$311$	22.0000			1.24751			0.623753	−	0.781622i	$-0.285607\pi$
$311$	22.0000			1.24751			0.623753	+	0.781622i	$0.285607\pi$
$312$		0			0
$313$	1.00000	−	1.00000i	0.0565233	−	0.0565233i	−0.678280	−	0.734803i	$-0.737274\pi$
$313$	1.00000	−	1.00000i	0.0565233	−	0.0565233i	0.734803	+	0.678280i	$0.237274\pi$
$314$	−15.5563			−0.877896
$315$		0			0
$316$		−	8.48528i		−	0.477334i
$317$	−4.24264	+	4.24264i	−0.238290	+	0.238290i	−0.816142	−	0.577851i	$-0.803891\pi$
$317$	−4.24264	+	4.24264i	−0.238290	+	0.238290i	0.577851	+	0.816142i	$0.303891\pi$
$318$		0			0
$319$		0			0
$320$	−2.00000	+	1.00000i	−0.111803	+	0.0559017i
$321$		0			0
$322$	1.41421	−	1.41421i	0.0788110	−	0.0788110i
$323$	−15.7279	−	9.72792i	−0.875125	−	0.541276i
$324$		0			0
$325$	29.6985	−	4.24264i	1.64738	−	0.235339i
$326$			9.89949i			0.548282i
$327$		0			0
$328$	−6.00000	+	6.00000i	−0.331295	+	0.331295i
$329$			14.0000i			0.771845i
$330$		0			0
$331$			8.48528i			0.466393i	0.972430	+	0.233197i	$0.0749186\pi$
$331$			8.48528i			0.466393i	−0.972430	+	0.233197i	$0.925081\pi$
$332$	9.00000	+	9.00000i	0.493939	+	0.493939i
$333$		0			0
$334$		0			0
$335$	25.4558	+	8.48528i	1.39080	+	0.463600i
$336$		0			0
$337$	−4.24264	+	4.24264i	−0.231111	+	0.231111i	−0.813156	−	0.582045i	$-0.802253\pi$
$337$	−4.24264	+	4.24264i	−0.231111	+	0.231111i	0.582045	+	0.813156i	$0.302253\pi$
$338$	16.2635	+	16.2635i	0.884615	+	0.884615i
$339$		0			0
$340$	−9.00000	−	3.00000i	−0.488094	−	0.162698i
$341$			16.9706i			0.919007i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	7.07107			0.381246
$345$		0			0
$346$	18.0000			0.967686
$347$	15.0000	+	15.0000i	0.805242	+	0.805242i	0.983910	−	0.178667i	$-0.0571786\pi$
$347$	15.0000	+	15.0000i	0.805242	+	0.805242i	−0.178667	+	0.983910i	$0.557179\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$	4.24264	−	5.65685i	0.226779	−	0.302372i
$351$		0			0
$352$	1.41421	−	1.41421i	0.0753778	−	0.0753778i
$353$	25.0000	−	25.0000i	1.33062	−	1.33062i	0.425797	−	0.904819i	$-0.359994\pi$
$353$	25.0000	−	25.0000i	1.33062	−	1.33062i	0.904819	−	0.425797i	$-0.140006\pi$
$354$		0			0
$355$	16.9706	−	8.48528i	0.900704	−	0.450352i
$356$			8.48528i			0.449719i
$357$		0			0
$358$	12.0000	−	12.0000i	0.634220	−	0.634220i
$359$		−	8.00000i		−	0.422224i	−0.977462	−	0.211112i	$-0.932292\pi$
$359$		−	8.00000i		−	0.422224i	0.977462	−	0.211112i	$-0.0677085\pi$
$360$		0			0
$361$	17.0000	−	8.48528i	0.894737	−	0.446594i
$362$	−18.0000	−	18.0000i	−0.946059	−	0.946059i
$363$		0			0
$364$	8.48528			0.444750
$365$	−3.00000	−	1.00000i	−0.157027	−	0.0523424i
$366$		0			0
$367$	17.0000	+	17.0000i	0.887393	+	0.887393i	0.994272	−	0.106879i	$-0.0340858\pi$
$367$	17.0000	+	17.0000i	0.887393	+	0.887393i	−0.106879	+	0.994272i	$0.534086\pi$
$368$	1.00000	−	1.00000i	0.0521286	−	0.0521286i
$369$		0			0
$370$	−12.0000	+	6.00000i	−0.623850	+	0.311925i
$371$		−	8.48528i		−	0.440534i
$372$		0			0
$373$	4.24264	+	4.24264i	0.219676	+	0.219676i	0.808362	−	0.588686i	$-0.200355\pi$
$373$	4.24264	+	4.24264i	0.219676	+	0.219676i	−0.588686	+	0.808362i	$0.700355\pi$
$374$	8.48528			0.438763
$375$		0			0
$376$			9.89949i			0.510527i
$377$		0			0
$378$		0			0
$379$	−25.4558			−1.30758			−0.653789	−	0.756677i	$-0.726822\pi$
$379$	−25.4558			−1.30758			−0.653789	+	0.756677i	$0.726822\pi$
$380$	7.48528	−	6.24264i	0.383987	−	0.320241i
$381$		0			0
$382$	11.3137	−	11.3137i	0.578860	−	0.578860i
$383$	−25.4558	−	25.4558i	−1.30073	−	1.30073i	−0.927898	−	0.372835i	$-0.878386\pi$
$383$	−25.4558	−	25.4558i	−1.30073	−	1.30073i	−0.372835	−	0.927898i	$-0.621614\pi$
$384$		0			0
$385$	−2.00000	+	6.00000i	−0.101929	+	0.305788i
$386$	6.00000			0.305392
$387$		0			0
$388$	−4.24264	−	4.24264i	−0.215387	−	0.215387i
$389$			4.00000i			0.202808i	0.994845	+	0.101404i	$0.0323335\pi$
$389$			4.00000i			0.202808i	−0.994845	+	0.101404i	$0.967667\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	−3.53553	+	3.53553i	−0.178571	+	0.178571i
$393$		0			0
$394$	−7.07107			−0.356235
$395$	8.48528	+	16.9706i	0.426941	+	0.853882i
$396$		0			0
$397$	25.0000	+	25.0000i	1.25471	+	1.25471i	0.953583	+	0.301131i	$0.0973643\pi$
$397$	25.0000	+	25.0000i	1.25471	+	1.25471i	0.301131	+	0.953583i	$0.402636\pi$
$398$	12.7279	+	12.7279i	0.637993	+	0.637993i
$399$		0			0
$400$	3.00000	−	4.00000i	0.150000	−	0.200000i
$401$		−	33.9411i		−	1.69494i	−0.530844	−	0.847469i	$-0.678125\pi$
$401$		−	33.9411i		−	1.69494i	0.530844	−	0.847469i	$-0.321875\pi$
$402$		0			0
$403$	−36.0000	+	36.0000i	−1.79329	+	1.79329i
$404$			4.00000i			0.199007i
$405$		0			0
$406$		0			0
$407$	8.48528	−	8.48528i	0.420600	−	0.420600i
$408$		0			0
$409$	16.9706			0.839140			0.419570	−	0.907723i	$-0.362181\pi$
$409$	16.9706			0.839140			0.419570	+	0.907723i	$0.362181\pi$
$410$	6.00000	−	18.0000i	0.296319	−	0.888957i
$411$		0			0
$412$	8.48528	−	8.48528i	0.418040	−	0.418040i
$413$		0			0
$414$		0			0
$415$	−27.0000	−	9.00000i	−1.32538	−	0.441793i
$416$	6.00000			0.294174
$417$		0			0
$418$	−4.58579	+	7.41421i	−0.224298	+	0.362641i
$419$			2.00000i			0.0977064i	0.998806	+	0.0488532i	$0.0155566\pi$
$419$			2.00000i			0.0977064i	−0.998806	+	0.0488532i	$0.984443\pi$
$420$		0			0
$421$		−	33.9411i		−	1.65419i	−0.562063	−	0.827095i	$-0.689992\pi$
$421$		−	33.9411i		−	1.65419i	0.562063	−	0.827095i	$-0.310008\pi$
$422$	6.00000	+	6.00000i	0.292075	+	0.292075i
$423$		0			0
$424$		−	6.00000i		−	0.291386i
$425$	21.0000	−	3.00000i	1.01865	−	0.145521i
$426$		0			0
$427$	−8.00000	−	8.00000i	−0.387147	−	0.387147i
$428$	8.48528	+	8.48528i	0.410152	+	0.410152i
$429$		0			0
$430$	−14.1421	+	7.07107i	−0.681994	+	0.340997i
$431$		−	16.9706i		−	0.817443i	−0.912659	−	0.408722i	$-0.865975\pi$
$431$		−	16.9706i		−	0.817443i	0.912659	−	0.408722i	$-0.134025\pi$
$432$		0			0
$433$	−21.2132	−	21.2132i	−1.01944	−	1.01944i	−0.999807	−	0.0196343i	$-0.993750\pi$
$433$	−21.2132	−	21.2132i	−1.01944	−	1.01944i	−0.0196343	−	0.999807i	$-0.506250\pi$
$434$			12.0000i			0.576018i
$435$		0			0
$436$			8.48528i			0.406371i
$437$	−3.24264	+	5.24264i	−0.155117	+	0.250790i
$438$		0			0
$439$	−25.4558			−1.21494			−0.607471	−	0.794342i	$-0.707816\pi$
$439$	−25.4558			−1.21494			−0.607471	+	0.794342i	$0.707816\pi$
$440$	−1.41421	+	4.24264i	−0.0674200	+	0.202260i
$441$		0			0
$442$	18.0000	+	18.0000i	0.856173	+	0.856173i
$443$	7.00000	−	7.00000i	0.332580	−	0.332580i	−0.520985	−	0.853566i	$-0.674435\pi$
$443$	7.00000	−	7.00000i	0.332580	−	0.332580i	0.853566	+	0.520985i	$0.174435\pi$
$444$		0			0
$445$	−8.48528	−	16.9706i	−0.402241	−	0.804482i
$446$		0			0
$447$		0			0
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	−16.9706			−0.800890			−0.400445	−	0.916321i	$-0.631145\pi$
$449$	−16.9706			−0.800890			−0.400445	+	0.916321i	$0.631145\pi$
$450$		0			0
$451$			16.9706i			0.799113i
$452$	−4.24264	+	4.24264i	−0.199557	+	0.199557i
$453$		0			0
$454$		0			0
$455$	−16.9706	+	8.48528i	−0.795592	+	0.397796i
$456$		0			0
$457$	−7.00000	−	7.00000i	−0.327446	−	0.327446i	0.524168	−	0.851615i	$-0.324376\pi$
$457$	−7.00000	−	7.00000i	−0.327446	−	0.327446i	−0.851615	+	0.524168i	$0.824376\pi$
$458$	−4.24264	−	4.24264i	−0.198246	−	0.198246i
$459$		0			0
$460$	−1.00000	+	3.00000i	−0.0466252	+	0.139876i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	5.00000	−	5.00000i	0.232370	−	0.232370i	−0.581311	−	0.813681i	$-0.697460\pi$
$463$	5.00000	−	5.00000i	0.232370	−	0.232370i	0.813681	+	0.581311i	$0.197460\pi$
$464$		0			0
$465$		0			0
$466$			7.07107i			0.327561i
$467$	−13.0000	−	13.0000i	−0.601568	−	0.601568i	0.339160	−	0.940729i	$-0.389857\pi$
$467$	−13.0000	−	13.0000i	−0.601568	−	0.601568i	−0.940729	+	0.339160i	$0.889857\pi$
$468$		0			0
$469$	−16.9706			−0.783628
$470$	−9.89949	−	19.7990i	−0.456630	−	0.913259i
$471$		0			0
$472$		0			0
$473$	10.0000	−	10.0000i	0.459800	−	0.459800i
$474$		0			0
$475$	−8.72792	+	19.9706i	−0.400465	+	0.916312i
$476$	6.00000			0.275010
$477$		0			0
$478$	7.07107	+	7.07107i	0.323423	+	0.323423i
$479$			32.0000i			1.46212i	0.682315	+	0.731059i	$0.260973\pi$
$479$			32.0000i			1.46212i	−0.682315	+	0.731059i	$0.739027\pi$
$480$		0			0
$481$	36.0000			1.64146
$482$	−6.00000	−	6.00000i	−0.273293	−	0.273293i
$483$		0			0
$484$			7.00000i			0.318182i
$485$	12.7279	+	4.24264i	0.577945	+	0.192648i
$486$		0			0
$487$	−25.4558	+	25.4558i	−1.15351	+	1.15351i	−0.167671	+	0.985843i	$0.553625\pi$
$487$	−25.4558	+	25.4558i	−1.15351	+	1.15351i	−0.985843	+	0.167671i	$0.946375\pi$
$488$	−5.65685	−	5.65685i	−0.256074	−	0.256074i
$489$		0			0
$490$	3.53553	−	10.6066i	0.159719	−	0.479157i
$491$	−28.0000			−1.26362			−0.631811	−	0.775122i	$-0.717688\pi$
$491$	−28.0000			−1.26362			−0.631811	+	0.775122i	$0.717688\pi$
$492$		0			0
$493$		0			0
$494$	−25.4558	+	6.00000i	−1.14531	+	0.269953i
$495$		0			0
$496$			8.48528i			0.381000i
$497$	−8.48528	+	8.48528i	−0.380617	+	0.380617i
$498$		0			0
$499$		−	36.0000i		−	1.61158i	−0.592200	−	0.805791i	$-0.701741\pi$
$499$		−	36.0000i		−	1.61158i	0.592200	−	0.805791i	$-0.298259\pi$
$500$	−2.00000	+	11.0000i	−0.0894427	+	0.491935i
$501$		0			0
$502$	14.1421	−	14.1421i	0.631194	−	0.631194i
$503$	15.0000	−	15.0000i	0.668817	−	0.668817i	−0.288625	−	0.957442i	$-0.593198\pi$
$503$	15.0000	−	15.0000i	0.668817	−	0.668817i	0.957442	+	0.288625i	$0.0931982\pi$
$504$		0			0
$505$	−4.00000	−	8.00000i	−0.177998	−	0.355995i
$506$		−	2.82843i		−	0.125739i
$507$		0			0
$508$	−8.48528	−	8.48528i	−0.376473	−	0.376473i
$509$	33.9411			1.50441			0.752207	−	0.658927i	$-0.228989\pi$
$509$	33.9411			1.50441			0.752207	+	0.658927i	$0.228989\pi$
$510$		0			0
$511$	2.00000			0.0884748
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	6.00000i		−	0.264649i
$515$	−8.48528	+	25.4558i	−0.373906	+	1.12172i
$516$		0			0
$517$	14.0000	+	14.0000i	0.615719	+	0.615719i
$518$	6.00000	−	6.00000i	0.263625	−	0.263625i
$519$		0			0
$520$	−12.0000	+	6.00000i	−0.526235	+	0.263117i
$521$			33.9411i			1.48699i	0.668743	+	0.743494i	$0.266833\pi$
$521$			33.9411i			1.48699i	−0.668743	+	0.743494i	$0.733167\pi$
$522$		0			0
$523$	16.9706	+	16.9706i	0.742071	+	0.742071i	0.972976	−	0.230905i	$-0.0741688\pi$
$523$	16.9706	+	16.9706i	0.742071	+	0.742071i	−0.230905	+	0.972976i	$0.574169\pi$
$524$			4.00000i			0.174741i
$525$		0			0
$526$			4.24264i			0.184988i
$527$	−25.4558	+	25.4558i	−1.10887	+	1.10887i
$528$		0			0
$529$			21.0000i			0.913043i
$530$	6.00000	+	12.0000i	0.260623	+	0.521247i
$531$		0			0
$532$	−3.24264	+	5.24264i	−0.140586	+	0.227297i
$533$	−36.0000	+	36.0000i	−1.55933	+	1.55933i
$534$		0			0
$535$	−25.4558	−	8.48528i	−1.10055	−	0.366851i
$536$	−12.0000			−0.518321
$537$		0			0
$538$	−6.00000	+	6.00000i	−0.258678	+	0.258678i
$539$			10.0000i			0.430730i
$540$		0			0
$541$	12.0000			0.515920			0.257960	−	0.966156i	$-0.416950\pi$
$541$	12.0000			0.515920			0.257960	+	0.966156i	$0.416950\pi$
$542$	21.2132	−	21.2132i	0.911185	−	0.911185i
$543$		0			0
$544$	4.24264			0.181902
$545$	−8.48528	−	16.9706i	−0.363470	−	0.726939i
$546$		0			0
$547$	8.48528	−	8.48528i	0.362804	−	0.362804i	−0.502040	−	0.864844i	$-0.667417\pi$
$547$	8.48528	−	8.48528i	0.362804	−	0.362804i	0.864844	+	0.502040i	$0.167417\pi$
$548$	3.00000	−	3.00000i	0.128154	−	0.128154i
$549$		0			0
$550$	−1.41421	−	9.89949i	−0.0603023	−	0.422116i
$551$		0			0
$552$		0			0
$553$	−8.48528	−	8.48528i	−0.360831	−	0.360831i
$554$	−9.89949			−0.420589
$555$		0			0
$556$	12.0000			0.508913
$557$	23.0000	+	23.0000i	0.974541	+	0.974541i	0.999684	−	0.0251426i	$-0.00800398\pi$
$557$	23.0000	+	23.0000i	0.974541	+	0.974541i	−0.0251426	+	0.999684i	$0.508004\pi$
$558$		0			0
$559$	42.4264			1.79445
$560$	−1.00000	+	3.00000i	−0.0422577	+	0.126773i
$561$		0			0
$562$	−18.0000	−	18.0000i	−0.759284	−	0.759284i
$563$	−25.4558	−	25.4558i	−1.07284	−	1.07284i	−0.997130	−	0.0757057i	$-0.975879\pi$
$563$	−25.4558	−	25.4558i	−1.07284	−	1.07284i	−0.0757057	−	0.997130i	$-0.524121\pi$
$564$		0			0
$565$	4.24264	−	12.7279i	0.178489	−	0.535468i
$566$		−	26.8701i		−	1.12943i
$567$		0			0
$568$	−6.00000	+	6.00000i	−0.251754	+	0.251754i
$569$	−16.9706			−0.711443			−0.355722	−	0.934592i	$-0.615765\pi$
$569$	−16.9706			−0.711443			−0.355722	+	0.934592i	$0.615765\pi$
$570$		0			0
$571$	−6.00000			−0.251092			−0.125546	−	0.992088i	$-0.540068\pi$
$571$	−6.00000			−0.251092			−0.125546	+	0.992088i	$0.540068\pi$
$572$	8.48528	−	8.48528i	0.354787	−	0.354787i
$573$		0			0
$574$			12.0000i			0.500870i
$575$	−1.00000	−	7.00000i	−0.0417029	−	0.291920i
$576$		0			0
$577$	−23.0000	−	23.0000i	−0.957503	−	0.957503i	0.0416305	−	0.999133i	$-0.486745\pi$
$577$	−23.0000	−	23.0000i	−0.957503	−	0.957503i	−0.999133	+	0.0416305i	$0.986745\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$		0			0
$580$		0			0
$581$	18.0000			0.746766
$582$		0			0
$583$	−8.48528	−	8.48528i	−0.351424	−	0.351424i
$584$	1.41421			0.0585206
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−11.0000	−	11.0000i	−0.454019	−	0.454019i	0.442667	−	0.896686i	$-0.354032\pi$
$587$	−11.0000	−	11.0000i	−0.454019	−	0.454019i	−0.896686	+	0.442667i	$0.854032\pi$
$588$		0			0
$589$	−8.48528	−	36.0000i	−0.349630	−	1.48335i
$590$		0			0
$591$		0			0
$592$	4.24264	−	4.24264i	0.174371	−	0.174371i
$593$	−21.0000	+	21.0000i	−0.862367	+	0.862367i	−0.991613	−	0.129246i	$-0.958744\pi$
$593$	−21.0000	+	21.0000i	−0.862367	+	0.862367i	0.129246	+	0.991613i	$0.458744\pi$
$594$		0			0
$595$	−12.0000	+	6.00000i	−0.491952	+	0.245976i
$596$	−10.0000			−0.409616
$597$		0			0
$598$	6.00000	−	6.00000i	0.245358	−	0.245358i
$599$	25.4558			1.04010			0.520049	−	0.854137i	$-0.325914\pi$
$599$	25.4558			1.04010			0.520049	+	0.854137i	$0.325914\pi$
$600$		0			0
$601$			8.48528i			0.346122i	0.984911	+	0.173061i	$0.0553658\pi$
$601$			8.48528i			0.346122i	−0.984911	+	0.173061i	$0.944634\pi$
$602$	7.07107	−	7.07107i	0.288195	−	0.288195i
$603$		0			0
$604$	16.9706			0.690522
$605$	−7.00000	−	14.0000i	−0.284590	−	0.569181i
$606$		0			0
$607$	25.4558	−	25.4558i	1.03322	−	1.03322i	0.0337920	−	0.999429i	$-0.489242\pi$
$607$	25.4558	−	25.4558i	1.03322	−	1.03322i	0.999429	−	0.0337920i	$-0.0107584\pi$
$608$	−2.29289	+	3.70711i	−0.0929891	+	0.150343i
$609$		0			0
$610$	16.9706	+	5.65685i	0.687118	+	0.229039i
$611$			59.3970i			2.40294i
$612$		0			0
$613$	−17.0000	+	17.0000i	−0.686624	+	0.686624i	−0.961484	−	0.274861i	$-0.911368\pi$
$613$	−17.0000	+	17.0000i	−0.686624	+	0.686624i	0.274861	+	0.961484i	$0.411368\pi$
$614$			12.0000i			0.484281i
$615$		0			0
$616$		−	2.82843i		−	0.113961i
$617$	−27.0000	−	27.0000i	−1.08698	−	1.08698i	−0.995838	−	0.0911411i	$-0.970949\pi$
$617$	−27.0000	−	27.0000i	−1.08698	−	1.08698i	−0.0911411	−	0.995838i	$-0.529051\pi$
$618$		0			0
$619$		−	12.0000i		−	0.482321i	−0.970485	−	0.241160i	$-0.922472\pi$
$619$		−	12.0000i		−	0.482321i	0.970485	−	0.241160i	$-0.0775280\pi$
$620$	−8.48528	−	16.9706i	−0.340777	−	0.681554i
$621$		0			0
$622$	15.5563	−	15.5563i	0.623753	−	0.623753i
$623$	8.48528	+	8.48528i	0.339956	+	0.339956i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$		−	1.41421i		−	0.0565233i
$627$		0			0
$628$	−11.0000	+	11.0000i	−0.438948	+	0.438948i
$629$	25.4558			1.01499
$630$		0			0
$631$	−2.00000			−0.0796187			−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000			−0.0796187			−0.0398094	+	0.999207i	$0.512675\pi$
$632$	−6.00000	−	6.00000i	−0.238667	−	0.238667i
$633$		0			0
$634$			6.00000i			0.238290i
$635$	25.4558	+	8.48528i	1.01018	+	0.336728i
$636$		0			0
$637$	−21.2132	+	21.2132i	−0.840498	+	0.840498i
$638$		0			0
$639$		0			0
$640$	−0.707107	+	2.12132i	−0.0279508	+	0.0838525i
$641$		−	25.4558i		−	1.00545i	−0.864448	−	0.502723i	$-0.832332\pi$
$641$		−	25.4558i		−	1.00545i	0.864448	−	0.502723i	$-0.167668\pi$
$642$		0			0
$643$	11.0000	−	11.0000i	0.433798	−	0.433798i	−0.456120	−	0.889918i	$-0.650761\pi$
$643$	11.0000	−	11.0000i	0.433798	−	0.433798i	0.889918	+	0.456120i	$0.150761\pi$
$644$		−	2.00000i		−	0.0788110i
$645$		0			0
$646$	−18.0000	+	4.24264i	−0.708201	+	0.166924i
$647$	−9.00000	−	9.00000i	−0.353827	−	0.353827i	0.507705	−	0.861531i	$-0.330494\pi$
$647$	−9.00000	−	9.00000i	−0.353827	−	0.353827i	−0.861531	+	0.507705i	$0.830494\pi$
$648$		0			0
$649$		0			0
$650$	18.0000	−	24.0000i	0.706018	−	0.941357i
$651$		0			0
$652$	7.00000	+	7.00000i	0.274141	+	0.274141i
$653$	9.00000	−	9.00000i	0.352197	−	0.352197i	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	9.00000	−	9.00000i	0.352197	−	0.352197i	0.860927	+	0.508729i	$0.169885\pi$
$654$		0			0
$655$	−4.00000	−	8.00000i	−0.156293	−	0.312586i
$656$			8.48528i			0.331295i
$657$		0			0
$658$	9.89949	+	9.89949i	0.385922	+	0.385922i
$659$	−16.9706			−0.661079			−0.330540	−	0.943792i	$-0.607231\pi$
$659$	−16.9706			−0.661079			−0.330540	+	0.943792i	$0.607231\pi$
$660$		0			0
$661$			33.9411i			1.32016i	0.751197	+	0.660078i	$0.229477\pi$
$661$			33.9411i			1.32016i	−0.751197	+	0.660078i	$0.770523\pi$
$662$	6.00000	+	6.00000i	0.233197	+	0.233197i
$663$		0			0
$664$	12.7279			0.493939
$665$	1.24264	−	13.7279i	0.0481875	−	0.532346i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	24.0000	−	12.0000i	0.927201	−	0.463600i
$671$	−16.0000			−0.617673
$672$		0			0
$673$	−4.24264	−	4.24264i	−0.163542	−	0.163542i	0.620592	−	0.784134i	$-0.286892\pi$
$673$	−4.24264	−	4.24264i	−0.163542	−	0.163542i	−0.784134	+	0.620592i	$0.786892\pi$
$674$			6.00000i			0.231111i
$675$		0			0
$676$	23.0000			0.884615
$677$	29.6985	−	29.6985i	1.14141	−	1.14141i	0.153212	−	0.988193i	$-0.451038\pi$
$677$	29.6985	−	29.6985i	1.14141	−	1.14141i	0.988193	−	0.153212i	$-0.0489618\pi$
$678$		0			0
$679$	−8.48528			−0.325635
$680$	−8.48528	+	4.24264i	−0.325396	+	0.162698i
$681$		0			0
$682$	12.0000	+	12.0000i	0.459504	+	0.459504i
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	0.850559	−	0.525879i	$-0.176264\pi$
$683$	8.48528	+	8.48528i	0.324680	+	0.324680i	−0.525879	+	0.850559i	$0.676264\pi$
$684$		0			0
$685$	−3.00000	+	9.00000i	−0.114624	+	0.343872i
$686$			16.9706i			0.647939i
$687$		0			0
$688$	5.00000	−	5.00000i	0.190623	−	0.190623i
$689$		−	36.0000i		−	1.37149i
$690$		0			0
$691$	30.0000			1.14125			0.570627	−	0.821209i	$-0.306700\pi$
$691$	30.0000			1.14125			0.570627	+	0.821209i	$0.306700\pi$
$692$	12.7279	−	12.7279i	0.483843	−	0.483843i
$693$		0			0
$694$	21.2132			0.805242
$695$	−24.0000	+	12.0000i	−0.910372	+	0.455186i
$696$		0			0
$697$	−25.4558	+	25.4558i	−0.964209	+	0.964209i
$698$		0			0
$699$		0			0
$700$	−1.00000	−	7.00000i	−0.0377964	−	0.264575i
$701$	32.0000			1.20862			0.604312	−	0.796748i	$-0.293448\pi$
$701$	32.0000			1.20862			0.604312	+	0.796748i	$0.293448\pi$
$702$		0			0
$703$	−13.7574	+	22.2426i	−0.518869	+	0.838897i
$704$		−	2.00000i		−	0.0753778i
$705$		0			0
$706$		−	35.3553i		−	1.33062i
$707$	4.00000	+	4.00000i	0.150435	+	0.150435i
$708$		0			0
$709$			24.0000i			0.901339i	0.892691	+	0.450669i	$0.148815\pi$
$709$			24.0000i			0.901339i	−0.892691	+	0.450669i	$0.851185\pi$
$710$	6.00000	−	18.0000i	0.225176	−	0.675528i
$711$		0			0
$712$	6.00000	+	6.00000i	0.224860	+	0.224860i
$713$	8.48528	+	8.48528i	0.317776	+	0.317776i
$714$		0			0
$715$	−8.48528	+	25.4558i	−0.317332	+	0.951995i
$716$		−	16.9706i		−	0.634220i
$717$		0			0
$718$	−5.65685	−	5.65685i	−0.211112	−	0.211112i
$719$		−	16.0000i		−	0.596699i	−0.954457	−	0.298350i	$-0.903564\pi$
$719$		−	16.0000i		−	0.596699i	0.954457	−	0.298350i	$-0.0964361\pi$
$720$		0			0
$721$		−	16.9706i		−	0.632017i
$722$	6.02082	−	18.0208i	0.224072	−	0.670665i
$723$		0			0
$724$	−25.4558			−0.946059
$725$		0			0
$726$		0			0
$727$	−11.0000	−	11.0000i	−0.407967	−	0.407967i	0.473062	−	0.881029i	$-0.343149\pi$
$727$	−11.0000	−	11.0000i	−0.407967	−	0.407967i	−0.881029	+	0.473062i	$0.843149\pi$
$728$	6.00000	−	6.00000i	0.222375	−	0.222375i
$729$		0			0
$730$	−2.82843	+	1.41421i	−0.104685	+	0.0523424i
$731$	30.0000			1.10959
$732$		0			0
$733$	−17.0000	+	17.0000i	−0.627909	+	0.627909i	−0.947542	−	0.319632i	$-0.896441\pi$
$733$	−17.0000	+	17.0000i	−0.627909	+	0.627909i	0.319632	+	0.947542i	$0.396441\pi$
$734$	24.0416			0.887393
$735$		0			0
$736$		−	1.41421i		−	0.0521286i
$737$	−16.9706	+	16.9706i	−0.625119	+	0.625119i
$738$		0			0
$739$			38.0000i			1.39785i	0.715194	+	0.698926i	$0.246338\pi$
$739$			38.0000i			1.39785i	−0.715194	+	0.698926i	$0.753662\pi$
$740$	−4.24264	+	12.7279i	−0.155963	+	0.467888i
$741$		0			0
$742$	−6.00000	−	6.00000i	−0.220267	−	0.220267i
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$		0			0
$745$	20.0000	−	10.0000i	0.732743	−	0.366372i
$746$	6.00000			0.219676
$747$		0			0
$748$	6.00000	−	6.00000i	0.219382	−	0.219382i
$749$	16.9706			0.620091
$750$		0			0
$751$			16.9706i			0.619265i	0.950856	+	0.309632i	$0.100206\pi$
$751$			16.9706i			0.619265i	−0.950856	+	0.309632i	$0.899794\pi$
$752$	7.00000	+	7.00000i	0.255264	+	0.255264i
$753$		0			0
$754$		0			0
$755$	−33.9411	+	16.9706i	−1.23524	+	0.617622i
$756$		0			0
$757$	−23.0000	−	23.0000i	−0.835949	−	0.835949i	0.152374	−	0.988323i	$-0.451308\pi$
$757$	−23.0000	−	23.0000i	−0.835949	−	0.835949i	−0.988323	+	0.152374i	$0.951308\pi$
$758$	−18.0000	+	18.0000i	−0.653789	+	0.653789i
$759$		0			0
$760$	0.878680	−	9.70711i	0.0318731	−	0.352114i
$761$	−20.0000			−0.724999			−0.362500	−	0.931984i	$-0.618077\pi$
$761$	−20.0000			−0.724999			−0.362500	+	0.931984i	$0.618077\pi$
$762$		0			0
$763$	8.48528	+	8.48528i	0.307188	+	0.307188i
$764$		−	16.0000i		−	0.578860i
$765$		0			0
$766$	−36.0000			−1.30073
$767$		0			0
$768$		0			0
$769$		−	30.0000i		−	1.08183i	−0.841078	−	0.540914i	$-0.818079\pi$
$769$		−	30.0000i		−	1.08183i	0.841078	−	0.540914i	$-0.181921\pi$
$770$	2.82843	+	5.65685i	0.101929	+	0.203859i
$771$		0			0
$772$	4.24264	−	4.24264i	0.152696	−	0.152696i
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.997499	−	0.0706813i	$-0.977483\pi$
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.0706813	−	0.997499i	$-0.522517\pi$
$774$		0			0
$775$	33.9411	+	25.4558i	1.21920	+	0.914401i
$776$	−6.00000			−0.215387
$777$		0			0
$778$	2.82843	+	2.82843i	0.101404	+	0.101404i
$779$	−8.48528	−	36.0000i	−0.304017	−	1.28983i
$780$		0			0
$781$			16.9706i			0.607254i
$782$	4.24264	−	4.24264i	0.151717	−	0.151717i
$783$		0			0
$784$			5.00000i			0.178571i
$785$	11.0000	−	33.0000i	0.392607	−	1.17782i
$786$		0			0
$787$	25.4558	−	25.4558i	0.907403	−	0.907403i	−0.0886592	−	0.996062i	$-0.528258\pi$
$787$	25.4558	−	25.4558i	0.907403	−	0.907403i	0.996062	+	0.0886592i	$0.0282582\pi$
$788$	−5.00000	+	5.00000i	−0.178118	+	0.178118i
$789$		0			0
$790$	18.0000	+	6.00000i	0.640411	+	0.213470i
$791$			8.48528i			0.301702i
$792$		0			0
$793$	−33.9411	−	33.9411i	−1.20528	−	1.20528i
$794$	35.3553			1.25471
$795$		0			0
$796$	18.0000			0.637993
$797$	4.24264	−	4.24264i	0.150282	−	0.150282i	−0.627962	−	0.778244i	$-0.716111\pi$
$797$	4.24264	−	4.24264i	0.150282	−	0.150282i	0.778244	+	0.627962i	$0.216111\pi$
$798$		0			0
$799$			42.0000i			1.48585i
$800$	−0.707107	−	4.94975i	−0.0250000	−	0.175000i
$801$		0			0
$802$	−24.0000	−	24.0000i	−0.847469	−	0.847469i
$803$	2.00000	−	2.00000i	0.0705785	−	0.0705785i
$804$		0			0
$805$	2.00000	+	4.00000i	0.0704907	+	0.140981i
$806$			50.9117i			1.79329i
$807$		0			0
$808$	2.82843	+	2.82843i	0.0995037	+	0.0995037i
$809$			8.00000i			0.281265i	0.990062	+	0.140633i	$0.0449136\pi$
$809$			8.00000i			0.281265i	−0.990062	+	0.140633i	$0.955086\pi$
$810$		0			0
$811$			50.9117i			1.78775i	0.448315	+	0.893876i	$0.352024\pi$
$811$			50.9117i			1.78775i	−0.448315	+	0.893876i	$0.647976\pi$
$812$		0			0
$813$		0			0
$814$		−	12.0000i		−	0.420600i
$815$	−21.0000	−	7.00000i	−0.735598	−	0.245199i
$816$		0			0
$817$	−16.2132	+	26.2132i	−0.567228	+	0.917084i
$818$	12.0000	−	12.0000i	0.419570	−	0.419570i
$819$		0			0
$820$	−8.48528	−	16.9706i	−0.296319	−	0.592638i
$821$	−34.0000			−1.18661			−0.593304	−	0.804978i	$-0.702177\pi$
$821$	−34.0000			−1.18661			−0.593304	+	0.804978i	$0.702177\pi$
$822$		0			0
$823$	23.0000	−	23.0000i	0.801730	−	0.801730i	−0.181636	−	0.983366i	$-0.558139\pi$
$823$	23.0000	−	23.0000i	0.801730	−	0.801730i	0.983366	+	0.181636i	$0.0581393\pi$
$824$		−	12.0000i		−	0.418040i
$825$		0			0
$826$		0			0
$827$	8.48528	−	8.48528i	0.295062	−	0.295062i	−0.544014	−	0.839076i	$-0.683096\pi$
$827$	8.48528	−	8.48528i	0.295062	−	0.295062i	0.839076	+	0.544014i	$0.183096\pi$
$828$		0			0
$829$	8.48528			0.294706			0.147353	−	0.989084i	$-0.452925\pi$
$829$	8.48528			0.294706			0.147353	+	0.989084i	$0.452925\pi$
$830$	−25.4558	+	12.7279i	−0.883585	+	0.441793i
$831$		0			0
$832$	4.24264	−	4.24264i	0.147087	−	0.147087i
$833$	−15.0000	+	15.0000i	−0.519719	+	0.519719i
$834$		0			0
$835$		0			0
$836$	2.00000	+	8.48528i	0.0691714	+	0.293470i
$837$		0			0
$838$	1.41421	+	1.41421i	0.0488532	+	0.0488532i
$839$	−42.4264			−1.46472			−0.732361	−	0.680916i	$-0.761582\pi$
$839$	−42.4264			−1.46472			−0.732361	+	0.680916i	$0.761582\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	−24.0000	−	24.0000i	−0.827095	−	0.827095i
$843$		0			0
$844$	8.48528			0.292075
$845$	−46.0000	+	23.0000i	−1.58245	+	0.791224i
$846$		0			0
$847$	7.00000	+	7.00000i	0.240523	+	0.240523i
$848$	−4.24264	−	4.24264i	−0.145693	−	0.145693i
$849$		0			0
$850$	12.7279	−	16.9706i	0.436564	−	0.582086i
$851$		−	8.48528i		−	0.290872i
$852$		0			0
$853$	−1.00000	+	1.00000i	−0.0342393	+	0.0342393i	−0.724019	−	0.689780i	$-0.757707\pi$
$853$	−1.00000	+	1.00000i	−0.0342393	+	0.0342393i	0.689780	+	0.724019i	$0.257707\pi$
$854$	−11.3137			−0.387147
$855$		0			0
$856$	12.0000			0.410152
$857$	−29.6985	+	29.6985i	−1.01448	+	1.01448i	−0.0145873	+	0.999894i	$0.504643\pi$
$857$	−29.6985	+	29.6985i	−1.01448	+	1.01448i	−0.999894	+	0.0145873i	$0.995357\pi$
$858$		0			0
$859$			22.0000i			0.750630i	0.926897	+	0.375315i	$0.122466\pi$
$859$			22.0000i			0.750630i	−0.926897	+	0.375315i	$0.877534\pi$
$860$	−5.00000	+	15.0000i	−0.170499	+	0.511496i
$861$		0			0
$862$	−12.0000	−	12.0000i	−0.408722	−	0.408722i
$863$	16.9706	+	16.9706i	0.577685	+	0.577685i	0.934265	−	0.356580i	$-0.116057\pi$
$863$	16.9706	+	16.9706i	0.577685	+	0.577685i	−0.356580	+	0.934265i	$0.616057\pi$
$864$		0			0
$865$	−12.7279	+	38.1838i	−0.432762	+	1.29829i
$866$	−30.0000			−1.01944
$867$		0			0
$868$	8.48528	+	8.48528i	0.288009	+	0.288009i
$869$	−16.9706			−0.575687
$870$		0			0
$871$	−72.0000			−2.43963
$872$	6.00000	+	6.00000i	0.203186	+	0.203186i
$873$		0			0
$874$	1.41421	+	6.00000i	0.0478365	+	0.202953i
$875$	9.00000	+	13.0000i	0.304256	+	0.439480i
$876$		0			0
$877$	12.7279	−	12.7279i	0.429791	−	0.429791i	−0.458766	−	0.888557i	$-0.651708\pi$
$877$	12.7279	−	12.7279i	0.429791	−	0.429791i	0.888557	+	0.458766i	$0.151708\pi$
$878$	−18.0000	+	18.0000i	−0.607471	+	0.607471i
$879$		0			0
$880$	2.00000	+	4.00000i	0.0674200	+	0.134840i
$881$	8.00000			0.269527			0.134763	−	0.990878i	$-0.456973\pi$
$881$	8.00000			0.269527			0.134763	+	0.990878i	$0.456973\pi$
$882$		0			0
$883$	13.0000	−	13.0000i	0.437485	−	0.437485i	−0.453680	−	0.891165i	$-0.649889\pi$
$883$	13.0000	−	13.0000i	0.437485	−	0.437485i	0.891165	+	0.453680i	$0.149889\pi$
$884$	25.4558			0.856173
$885$		0			0
$886$		−	9.89949i		−	0.332580i
$887$	−8.48528	+	8.48528i	−0.284908	+	0.284908i	−0.835063	−	0.550155i	$-0.814569\pi$
$887$	−8.48528	+	8.48528i	−0.284908	+	0.284908i	0.550155	+	0.835063i	$0.314569\pi$
$888$		0			0
$889$	−16.9706			−0.569174
$890$	−18.0000	−	6.00000i	−0.603361	−	0.201120i
$891$		0			0
$892$		0			0
$893$	−36.6985	−	22.6985i	−1.22807	−	0.759576i
$894$		0			0
$895$	16.9706	+	33.9411i	0.567263	+	1.13453i
$896$		−	1.41421i		−	0.0472456i
$897$		0			0
$898$	−12.0000	+	12.0000i	−0.400445	+	0.400445i
$899$		0			0
$900$		0			0
$901$		−	25.4558i		−	0.848057i
$902$	12.0000	+	12.0000i	0.399556	+	0.399556i
$903$		0			0
$904$			6.00000i			0.199557i
$905$	50.9117	−	25.4558i	1.69236	−	0.846181i
$906$		0			0
$907$	−8.48528	+	8.48528i	−0.281749	+	0.281749i	−0.833806	−	0.552057i	$-0.813843\pi$
$907$	−8.48528	+	8.48528i	−0.281749	+	0.281749i	0.552057	+	0.833806i	$0.313843\pi$
$908$		0			0
$909$		0			0
$910$	−6.00000	+	18.0000i	−0.198898	+	0.596694i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$	18.0000	−	18.0000i	0.595713	−	0.595713i
$914$	−9.89949			−0.327446
$915$		0			0
$916$	−6.00000			−0.198246
$917$	4.00000	+	4.00000i	0.132092	+	0.132092i
$918$		0			0
$919$		−	38.0000i		−	1.25350i	−0.779219	−	0.626752i	$-0.784384\pi$
$919$		−	38.0000i		−	1.25350i	0.779219	−	0.626752i	$-0.215616\pi$
$920$	1.41421	+	2.82843i	0.0466252	+	0.0932505i
$921$		0			0
$922$	9.89949	−	9.89949i	0.326023	−	0.326023i
$923$	−36.0000	+	36.0000i	−1.18495	+	1.18495i
$924$		0			0
$925$	−4.24264	−	29.6985i	−0.139497	−	0.976480i
$926$		−	7.07107i		−	0.232370i
$927$		0			0
$928$		0			0
$929$			28.0000i			0.918650i	0.888268	+	0.459325i	$0.151909\pi$
$929$			28.0000i			0.918650i	−0.888268	+	0.459325i	$0.848091\pi$
$930$		0			0
$931$	−5.00000	−	21.2132i	−0.163868	−	0.695235i
$932$	5.00000	+	5.00000i	0.163780	+	0.163780i
$933$		0			0
$934$	−18.3848			−0.601568
$935$	−6.00000	+	18.0000i	−0.196221	+	0.588663i
$936$		0			0
$937$	−25.0000	−	25.0000i	−0.816714	−	0.816714i	0.168916	−	0.985630i	$-0.445973\pi$
$937$	−25.0000	−	25.0000i	−0.816714	−	0.816714i	−0.985630	+	0.168916i	$0.945973\pi$
$938$	−12.0000	+	12.0000i	−0.391814	+	0.391814i
$939$		0			0
$940$	−21.0000	−	7.00000i	−0.684944	−	0.228315i
$941$		−	25.4558i		−	0.829837i	−0.909859	−	0.414918i	$-0.863810\pi$
$941$		−	25.4558i		−	0.829837i	0.909859	−	0.414918i	$-0.136190\pi$
$942$		0			0
$943$	8.48528	+	8.48528i	0.276319	+	0.276319i
$944$		0			0
$945$		0			0
$946$		−	14.1421i		−	0.459800i
$947$	−15.0000	−	15.0000i	−0.487435	−	0.487435i	0.420061	−	0.907496i	$-0.362009\pi$
$947$	−15.0000	−	15.0000i	−0.487435	−	0.487435i	−0.907496	+	0.420061i	$0.862009\pi$
$948$		0			0
$949$	8.48528			0.275444
$950$	7.94975	+	20.2929i	0.257924	+	0.658388i
$951$		0			0
$952$	4.24264	−	4.24264i	0.137505	−	0.137505i
$953$	12.7279	+	12.7279i	0.412298	+	0.412298i	0.882538	−	0.470240i	$-0.155833\pi$
$953$	12.7279	+	12.7279i	0.412298	+	0.412298i	−0.470240	+	0.882538i	$0.655833\pi$
$954$		0			0
$955$	16.0000	+	32.0000i	0.517748	+	1.03550i
$956$	10.0000			0.323423
$957$		0			0
$958$	22.6274	+	22.6274i	0.731059	+	0.731059i
$959$		−	6.00000i		−	0.193750i
$960$		0			0
$961$	−41.0000			−1.32258
$962$	25.4558	−	25.4558i	0.820729	−	0.820729i
$963$		0			0
$964$	−8.48528			−0.273293
$965$	−4.24264	+	12.7279i	−0.136575	+	0.409726i
$966$		0			0
$967$	−13.0000	−	13.0000i	−0.418052	−	0.418052i	0.466480	−	0.884532i	$-0.345522\pi$
$967$	−13.0000	−	13.0000i	−0.418052	−	0.418052i	−0.884532	+	0.466480i	$0.845522\pi$
$968$	4.94975	+	4.94975i	0.159091	+	0.159091i
$969$		0			0
$970$	12.0000	−	6.00000i	0.385297	−	0.192648i
$971$		−	50.9117i		−	1.63383i	−0.576755	−	0.816917i	$-0.695681\pi$
$971$		−	50.9117i		−	1.63383i	0.576755	−	0.816917i	$-0.304319\pi$
$972$		0			0
$973$	12.0000	−	12.0000i	0.384702	−	0.384702i
$974$			36.0000i			1.15351i
$975$		0			0
$976$	−8.00000			−0.256074
$977$	4.24264	−	4.24264i	0.135734	−	0.135734i	−0.635975	−	0.771709i	$-0.719402\pi$
$977$	4.24264	−	4.24264i	0.135734	−	0.135734i	0.771709	+	0.635975i	$0.219402\pi$
$978$		0			0
$979$	16.9706			0.542382
$980$	−5.00000	−	10.0000i	−0.159719	−	0.319438i
$981$		0			0
$982$	−19.7990	+	19.7990i	−0.631811	+	0.631811i
$983$	−16.9706	−	16.9706i	−0.541277	−	0.541277i	0.382626	−	0.923903i	$-0.375020\pi$
$983$	−16.9706	−	16.9706i	−0.541277	−	0.541277i	−0.923903	+	0.382626i	$0.875020\pi$
$984$		0			0
$985$	5.00000	−	15.0000i	0.159313	−	0.477940i
$986$		0			0
$987$		0			0
$988$	−13.7574	+	22.2426i	−0.437680	+	0.707633i
$989$		−	10.0000i		−	0.317982i
$990$		0			0
$991$		−	33.9411i		−	1.07818i	−0.842250	−	0.539088i	$-0.818769\pi$
$991$		−	33.9411i		−	1.07818i	0.842250	−	0.539088i	$-0.181231\pi$
$992$	6.00000	+	6.00000i	0.190500	+	0.190500i
$993$		0			0
$994$			12.0000i			0.380617i
$995$	−36.0000	+	18.0000i	−1.14128	+	0.570638i
$996$		0			0
$997$	11.0000	+	11.0000i	0.348373	+	0.348373i	0.859503	−	0.511130i	$-0.170773\pi$
$997$	11.0000	+	11.0000i	0.348373	+	0.348373i	−0.511130	+	0.859503i	$0.670773\pi$
$998$	−25.4558	−	25.4558i	−0.805791	−	0.805791i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.a.37.2		4
3.2	odd	2		190.2.f.a.37.1	✓	4
5.3	odd	4	inner	1710.2.p.a.1063.1		4
15.2	even	4		950.2.f.a.493.1		4
15.8	even	4		190.2.f.a.113.2	yes	4
15.14	odd	2		950.2.f.a.607.2		4
19.18	odd	2	inner	1710.2.p.a.37.1		4
57.56	even	2		190.2.f.a.37.2	yes	4
95.18	even	4	inner	1710.2.p.a.1063.2		4
285.113	odd	4		190.2.f.a.113.1	yes	4
285.227	odd	4		950.2.f.a.493.2		4
285.284	even	2		950.2.f.a.607.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.f.a.37.1	✓	4	3.2	odd	2
190.2.f.a.37.2	yes	4	57.56	even	2
190.2.f.a.113.1	yes	4	285.113	odd	4
190.2.f.a.113.2	yes	4	15.8	even	4
950.2.f.a.493.1		4	15.2	even	4
950.2.f.a.493.2		4	285.227	odd	4
950.2.f.a.607.1		4	285.284	even	2
950.2.f.a.607.2		4	15.14	odd	2
1710.2.p.a.37.1		4	19.18	odd	2	inner
1710.2.p.a.37.2		4	1.1	even	1	trivial
1710.2.p.a.1063.1		4	5.3	odd	4	inner
1710.2.p.a.1063.2		4	95.18	even	4	inner

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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(1.00000 + 2.00000i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.12132 + 0.707107i) q^{10} -2.00000 q^{11} +(-4.24264 - 4.24264i) q^{13} -1.41421 q^{14} -1.00000 q^{16} +(-3.00000 - 3.00000i) q^{17} +(4.24264 - 1.00000i) q^{19} +(2.00000 - 1.00000i) q^{20} +(-1.41421 + 1.41421i) q^{22} +(-1.00000 + 1.00000i) q^{23} +(-3.00000 + 4.00000i) q^{25} -6.00000 q^{26} +(-1.00000 + 1.00000i) q^{28} -8.48528i q^{31} +(-0.707107 + 0.707107i) q^{32} -4.24264 q^{34} +(1.00000 - 3.00000i) q^{35} +(-4.24264 + 4.24264i) q^{37} +(2.29289 - 3.70711i) q^{38} +(0.707107 - 2.12132i) q^{40} -8.48528i q^{41} +(-5.00000 + 5.00000i) q^{43} +2.00000i q^{44} +1.41421i q^{46} +(-7.00000 - 7.00000i) q^{47} -5.00000i q^{49} +(0.707107 + 4.94975i) q^{50} +(-4.24264 + 4.24264i) q^{52} +(4.24264 + 4.24264i) q^{53} +(-2.00000 - 4.00000i) q^{55} +1.41421i q^{56} +8.00000 q^{61} +(-6.00000 - 6.00000i) q^{62} +1.00000i q^{64} +(4.24264 - 12.7279i) q^{65} +(8.48528 - 8.48528i) q^{67} +(-3.00000 + 3.00000i) q^{68} +(-1.41421 - 2.82843i) q^{70} -8.48528i q^{71} +(-1.00000 + 1.00000i) q^{73} +6.00000i q^{74} +(-1.00000 - 4.24264i) q^{76} +(2.00000 + 2.00000i) q^{77} +8.48528 q^{79} +(-1.00000 - 2.00000i) q^{80} +(-6.00000 - 6.00000i) q^{82} +(-9.00000 + 9.00000i) q^{83} +(3.00000 - 9.00000i) q^{85} +7.07107i q^{86} +(1.41421 + 1.41421i) q^{88} -8.48528 q^{89} +8.48528i q^{91} +(1.00000 + 1.00000i) q^{92} -9.89949 q^{94} +(6.24264 + 7.48528i) q^{95} +(4.24264 - 4.24264i) q^{97} +(-3.53553 - 3.53553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5} - 4 q^{7} - 8 q^{11} - 4 q^{16} - 12 q^{17} + 8 q^{20} - 4 q^{23} - 12 q^{25} - 24 q^{26} - 4 q^{28} + 4 q^{35} + 12 q^{38} - 20 q^{43} - 28 q^{47} - 8 q^{55} + 32 q^{61} - 24 q^{62} - 12 q^{68}+ \cdots + 8 q^{95}+O(q^{100}) \) 4 * q + 4 * q^5 - 4 * q^7 - 8 * q^11 - 4 * q^16 - 12 * q^17 + 8 * q^20 - 4 * q^23 - 12 * q^25 - 24 * q^26 - 4 * q^28 + 4 * q^35 + 12 * q^38 - 20 * q^43 - 28 * q^47 - 8 * q^55 + 32 * q^61 - 24 * q^62 - 12 * q^68 - 4 * q^73 - 4 * q^76 + 8 * q^77 - 4 * q^80 - 24 * q^82 - 36 * q^83 + 12 * q^85 + 4 * q^92 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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