LMFDB - Embedded newform 112.3.s.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [112,3,Mod(17,112)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(112, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("112.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.s (of order $6$, 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:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 28)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			33.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	112.33
Dual form			112.3.s.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +(1.50000 + 0.866025i) q^{5} +7.00000 q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +(1.50000 + 0.866025i) q^{5} +7.00000 q^{7} +(-3.00000 + 5.19615i) q^{9} +(7.50000 + 12.9904i) q^{11} +13.8564i q^{13} -3.00000 q^{15} +(25.5000 - 14.7224i) q^{17} +(-13.5000 - 7.79423i) q^{19} +(-10.5000 + 6.06218i) q^{21} +(-4.50000 + 7.79423i) q^{23} +(-11.0000 - 19.0526i) q^{25} -25.9808i q^{27} -6.00000 q^{29} +(10.5000 - 6.06218i) q^{31} +(-22.5000 - 12.9904i) q^{33} +(10.5000 + 6.06218i) q^{35} +(-15.5000 + 26.8468i) q^{37} +(-12.0000 - 20.7846i) q^{39} -55.4256i q^{41} -10.0000 q^{43} +(-9.00000 + 5.19615i) q^{45} +(-37.5000 - 21.6506i) q^{47} +49.0000 q^{49} +(-25.5000 + 44.1673i) q^{51} +(28.5000 + 49.3634i) q^{53} +25.9808i q^{55} +27.0000 q^{57} +(70.5000 - 40.7032i) q^{59} +(-70.5000 - 40.7032i) q^{61} +(-21.0000 + 36.3731i) q^{63} +(-12.0000 + 20.7846i) q^{65} +(-24.5000 - 42.4352i) q^{67} -15.5885i q^{69} +126.000 q^{71} +(-22.5000 + 12.9904i) q^{73} +(33.0000 + 19.0526i) q^{75} +(52.5000 + 90.9327i) q^{77} +(-36.5000 + 63.2199i) q^{79} +(-4.50000 - 7.79423i) q^{81} +13.8564i q^{83} +51.0000 q^{85} +(9.00000 - 5.19615i) q^{87} +(49.5000 + 28.5788i) q^{89} +96.9948i q^{91} +(-10.5000 + 18.1865i) q^{93} +(-13.5000 - 23.3827i) q^{95} +27.7128i q^{97} -90.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 3 q^{5} + 14 q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 3 * q^5 + 14 * q^7 - 6 * q^9	$ 2 q - 3 q^{3} + 3 q^{5} + 14 q^{7} - 6 q^{9} + 15 q^{11} - 6 q^{15} + 51 q^{17} - 27 q^{19} - 21 q^{21} - 9 q^{23} - 22 q^{25} - 12 q^{29} + 21 q^{31} - 45 q^{33} + 21 q^{35} - 31 q^{37} - 24 q^{39} - 20 q^{43} - 18 q^{45} - 75 q^{47} + 98 q^{49} - 51 q^{51} + 57 q^{53} + 54 q^{57} + 141 q^{59} - 141 q^{61} - 42 q^{63} - 24 q^{65} - 49 q^{67} + 252 q^{71} - 45 q^{73} + 66 q^{75} + 105 q^{77} - 73 q^{79} - 9 q^{81} + 102 q^{85} + 18 q^{87} + 99 q^{89} - 21 q^{93} - 27 q^{95} - 180 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 3 * q^5 + 14 * q^7 - 6 * q^9 + 15 * q^11 - 6 * q^15 + 51 * q^17 - 27 * q^19 - 21 * q^21 - 9 * q^23 - 22 * q^25 - 12 * q^29 + 21 * q^31 - 45 * q^33 + 21 * q^35 - 31 * q^37 - 24 * q^39 - 20 * q^43 - 18 * q^45 - 75 * q^47 + 98 * q^49 - 51 * q^51 + 57 * q^53 + 54 * q^57 + 141 * q^59 - 141 * q^61 - 42 * q^63 - 24 * q^65 - 49 * q^67 + 252 * q^71 - 45 * q^73 + 66 * q^75 + 105 * q^77 - 73 * q^79 - 9 * q^81 + 102 * q^85 + 18 * q^87 + 99 * q^89 - 21 * q^93 - 27 * q^95 - 180 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i	−0.728714	−	0.684819i	$-0.759881\pi$
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i	0.228714	+	0.973494i	$0.426548\pi$
$4$		0			0
$5$	1.50000	+	0.866025i	0.300000	+	0.173205i	0.642443	−	0.766334i	$-0.277921\pi$
$5$	1.50000	+	0.866025i	0.300000	+	0.173205i	−0.342443	+	0.939539i	$0.611254\pi$
$6$		0			0
$7$	7.00000			1.00000
$7$	7.00000			1.00000
$8$		0			0
$9$	−3.00000	+	5.19615i	−0.333333	+	0.577350i
$10$		0			0
$11$	7.50000	+	12.9904i	0.681818	+	1.18094i	0.974425	+	0.224711i	$0.0721438\pi$
$11$	7.50000	+	12.9904i	0.681818	+	1.18094i	−0.292607	+	0.956233i	$0.594523\pi$
$12$		0			0
$13$			13.8564i			1.06588i	0.846154	+	0.532939i	$0.178912\pi$
$13$			13.8564i			1.06588i	−0.846154	+	0.532939i	$0.821088\pi$
$14$		0			0
$15$	−3.00000			−0.200000
$16$		0			0
$17$	25.5000	−	14.7224i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$17$	25.5000	−	14.7224i	1.50000	−	0.866025i	1.00000			$0$
$18$		0			0
$19$	−13.5000	−	7.79423i	−0.710526	−	0.410223i	0.100730	−	0.994914i	$-0.467882\pi$
$19$	−13.5000	−	7.79423i	−0.710526	−	0.410223i	−0.811256	+	0.584691i	$0.801216\pi$
$20$		0			0
$21$	−10.5000	+	6.06218i	−0.500000	+	0.288675i
$22$		0			0
$23$	−4.50000	+	7.79423i	−0.195652	+	0.338880i	−0.947114	−	0.320897i	$-0.896016\pi$
$23$	−4.50000	+	7.79423i	−0.195652	+	0.338880i	0.751462	+	0.659776i	$0.229349\pi$
$24$		0			0
$25$	−11.0000	−	19.0526i	−0.440000	−	0.762102i
$26$		0			0
$27$		−	25.9808i		−	0.962250i
$28$		0			0
$29$	−6.00000			−0.206897			−0.103448	−	0.994635i	$-0.532988\pi$
$29$	−6.00000			−0.206897			−0.103448	+	0.994635i	$0.532988\pi$
$30$		0			0
$31$	10.5000	−	6.06218i	0.338710	−	0.195554i	−0.320992	−	0.947082i	$-0.604016\pi$
$31$	10.5000	−	6.06218i	0.338710	−	0.195554i	0.659701	+	0.751528i	$0.270683\pi$
$32$		0			0
$33$	−22.5000	−	12.9904i	−0.681818	−	0.393648i
$34$		0			0
$35$	10.5000	+	6.06218i	0.300000	+	0.173205i
$36$		0			0
$37$	−15.5000	+	26.8468i	−0.418919	+	0.725589i	−0.995831	−	0.0912174i	$-0.970924\pi$
$37$	−15.5000	+	26.8468i	−0.418919	+	0.725589i	0.576912	+	0.816806i	$0.304258\pi$
$38$		0			0
$39$	−12.0000	−	20.7846i	−0.307692	−	0.532939i
$40$		0			0
$41$		−	55.4256i		−	1.35184i	−0.736973	−	0.675922i	$-0.763745\pi$
$41$		−	55.4256i		−	1.35184i	0.736973	−	0.675922i	$-0.236255\pi$
$42$		0			0
$43$	−10.0000			−0.232558			−0.116279	−	0.993217i	$-0.537097\pi$
$43$	−10.0000			−0.232558			−0.116279	+	0.993217i	$0.537097\pi$
$44$		0			0
$45$	−9.00000	+	5.19615i	−0.200000	+	0.115470i
$46$		0			0
$47$	−37.5000	−	21.6506i	−0.797872	−	0.460652i	0.0448543	−	0.998994i	$-0.485718\pi$
$47$	−37.5000	−	21.6506i	−0.797872	−	0.460652i	−0.842727	+	0.538342i	$0.819051\pi$
$48$		0			0
$49$	49.0000			1.00000
$50$		0			0
$51$	−25.5000	+	44.1673i	−0.500000	+	0.866025i
$52$		0			0
$53$	28.5000	+	49.3634i	0.537736	+	0.931386i	0.999026	+	0.0441362i	$0.0140536\pi$
$53$	28.5000	+	49.3634i	0.537736	+	0.931386i	−0.461290	+	0.887250i	$0.652613\pi$
$54$		0			0
$55$			25.9808i			0.472377i
$56$		0			0
$57$	27.0000			0.473684
$58$		0			0
$59$	70.5000	−	40.7032i	1.19492	−	0.689885i	0.235498	−	0.971875i	$-0.424328\pi$
$59$	70.5000	−	40.7032i	1.19492	−	0.689885i	0.959417	+	0.281990i	$0.0909946\pi$
$60$		0			0
$61$	−70.5000	−	40.7032i	−1.15574	−	0.667265i	−0.205459	−	0.978666i	$-0.565869\pi$
$61$	−70.5000	−	40.7032i	−1.15574	−	0.667265i	−0.950279	+	0.311400i	$0.899202\pi$
$62$		0			0
$63$	−21.0000	+	36.3731i	−0.333333	+	0.577350i
$64$		0			0
$65$	−12.0000	+	20.7846i	−0.184615	+	0.319763i
$66$		0			0
$67$	−24.5000	−	42.4352i	−0.365672	−	0.633362i	0.623212	−	0.782053i	$-0.285827\pi$
$67$	−24.5000	−	42.4352i	−0.365672	−	0.633362i	−0.988884	+	0.148691i	$0.952494\pi$
$68$		0			0
$69$		−	15.5885i		−	0.225920i
$70$		0			0
$71$	126.000			1.77465			0.887324	−	0.461147i	$-0.152562\pi$
$71$	126.000			1.77465			0.887324	+	0.461147i	$0.152562\pi$
$72$		0			0
$73$	−22.5000	+	12.9904i	−0.308219	+	0.177950i	−0.646129	−	0.763228i	$-0.723613\pi$
$73$	−22.5000	+	12.9904i	−0.308219	+	0.177950i	0.337910	+	0.941178i	$0.390280\pi$
$74$		0			0
$75$	33.0000	+	19.0526i	0.440000	+	0.254034i
$76$		0			0
$77$	52.5000	+	90.9327i	0.681818	+	1.18094i
$78$		0			0
$79$	−36.5000	+	63.2199i	−0.462025	+	0.800251i	−0.999062	−	0.0433077i	$-0.986210\pi$
$79$	−36.5000	+	63.2199i	−0.462025	+	0.800251i	0.537036	+	0.843559i	$0.319544\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$		0			0
$83$			13.8564i			0.166945i	0.996510	+	0.0834723i	$0.0266010\pi$
$83$			13.8564i			0.166945i	−0.996510	+	0.0834723i	$0.973399\pi$
$84$		0			0
$85$	51.0000			0.600000
$86$		0			0
$87$	9.00000	−	5.19615i	0.103448	−	0.0597259i
$88$		0			0
$89$	49.5000	+	28.5788i	0.556180	+	0.321111i	0.751611	−	0.659607i	$-0.229277\pi$
$89$	49.5000	+	28.5788i	0.556180	+	0.321111i	−0.195431	+	0.980717i	$0.562611\pi$
$90$		0			0
$91$			96.9948i			1.06588i
$92$		0			0
$93$	−10.5000	+	18.1865i	−0.112903	+	0.195554i
$94$		0			0
$95$	−13.5000	−	23.3827i	−0.142105	−	0.246134i
$96$		0			0
$97$			27.7128i			0.285699i	0.989744	+	0.142850i	$0.0456265\pi$
$97$			27.7128i			0.285699i	−0.989744	+	0.142850i	$0.954373\pi$
$98$		0			0
$99$	−90.0000			−0.909091
$100$		0			0
$101$	85.5000	−	49.3634i	0.846535	−	0.488747i	−0.0129455	−	0.999916i	$-0.504121\pi$
$101$	85.5000	−	49.3634i	0.846535	−	0.488747i	0.859480	+	0.511169i	$0.170787\pi$
$102$		0			0
$103$	−61.5000	−	35.5070i	−0.597087	−	0.344729i	0.170808	−	0.985304i	$-0.445362\pi$
$103$	−61.5000	−	35.5070i	−0.597087	−	0.344729i	−0.767895	+	0.640576i	$0.778696\pi$
$104$		0			0
$105$	−21.0000			−0.200000
$106$		0			0
$107$	19.5000	−	33.7750i	0.182243	−	0.315654i	−0.760401	−	0.649454i	$-0.774998\pi$
$107$	19.5000	−	33.7750i	0.182243	−	0.315654i	0.942644	+	0.333800i	$0.108331\pi$
$108$		0			0
$109$	−51.5000	−	89.2006i	−0.472477	−	0.818354i	0.527027	−	0.849849i	$-0.323307\pi$
$109$	−51.5000	−	89.2006i	−0.472477	−	0.818354i	−0.999504	+	0.0314943i	$0.989973\pi$
$110$		0			0
$111$		−	53.6936i		−	0.483726i
$112$		0			0
$113$	−78.0000			−0.690265			−0.345133	−	0.938554i	$-0.612166\pi$
$113$	−78.0000			−0.690265			−0.345133	+	0.938554i	$0.612166\pi$
$114$		0			0
$115$	−13.5000	+	7.79423i	−0.117391	+	0.0677759i
$116$		0			0
$117$	−72.0000	−	41.5692i	−0.615385	−	0.355292i
$118$		0			0
$119$	178.500	−	103.057i	1.50000	−	0.866025i
$120$		0			0
$121$	−52.0000	+	90.0666i	−0.429752	+	0.744352i
$122$		0			0
$123$	48.0000	+	83.1384i	0.390244	+	0.675922i
$124$		0			0
$125$		−	81.4064i		−	0.651251i
$126$		0			0
$127$	−50.0000			−0.393701			−0.196850	−	0.980434i	$-0.563071\pi$
$127$	−50.0000			−0.393701			−0.196850	+	0.980434i	$0.563071\pi$
$128$		0			0
$129$	15.0000	−	8.66025i	0.116279	−	0.0671338i
$130$		0			0
$131$	−85.5000	−	49.3634i	−0.652672	−	0.376820i	0.136807	−	0.990598i	$-0.456316\pi$
$131$	−85.5000	−	49.3634i	−0.652672	−	0.376820i	−0.789479	+	0.613777i	$0.789649\pi$
$132$		0			0
$133$	−94.5000	−	54.5596i	−0.710526	−	0.410223i
$134$		0			0
$135$	22.5000	−	38.9711i	0.166667	−	0.288675i
$136$		0			0
$137$	−31.5000	−	54.5596i	−0.229927	−	0.398245i	0.727859	−	0.685727i	$-0.240515\pi$
$137$	−31.5000	−	54.5596i	−0.229927	−	0.398245i	−0.957786	+	0.287481i	$0.907182\pi$
$138$		0			0
$139$		−	235.559i		−	1.69467i	−0.531060	−	0.847334i	$-0.678206\pi$
$139$		−	235.559i		−	1.69467i	0.531060	−	0.847334i	$-0.321794\pi$
$140$		0			0
$141$	75.0000			0.531915
$142$		0			0
$143$	−180.000	+	103.923i	−1.25874	+	0.726735i
$144$		0			0
$145$	−9.00000	−	5.19615i	−0.0620690	−	0.0358355i
$146$		0			0
$147$	−73.5000	+	42.4352i	−0.500000	+	0.288675i
$148$		0			0
$149$	88.5000	−	153.286i	0.593960	−	1.02877i	−0.399733	−	0.916632i	$-0.630897\pi$
$149$	88.5000	−	153.286i	0.593960	−	1.02877i	0.993693	−	0.112137i	$-0.0357695\pi$
$150$		0			0
$151$	27.5000	+	47.6314i	0.182119	+	0.315440i	0.942602	−	0.333918i	$-0.108371\pi$
$151$	27.5000	+	47.6314i	0.182119	+	0.315440i	−0.760483	+	0.649358i	$0.775038\pi$
$152$		0			0
$153$			176.669i			1.15470i
$154$		0			0
$155$	21.0000			0.135484
$156$		0			0
$157$	85.5000	−	49.3634i	0.544586	−	0.314417i	−0.202350	−	0.979313i	$-0.564858\pi$
$157$	85.5000	−	49.3634i	0.544586	−	0.314417i	0.746935	+	0.664897i	$0.231524\pi$
$158$		0			0
$159$	−85.5000	−	49.3634i	−0.537736	−	0.310462i
$160$		0			0
$161$	−31.5000	+	54.5596i	−0.195652	+	0.338880i
$162$		0			0
$163$	11.5000	−	19.9186i	0.0705521	−	0.122200i	−0.828591	−	0.559854i	$-0.810857\pi$
$163$	11.5000	−	19.9186i	0.0705521	−	0.122200i	0.899143	+	0.437654i	$0.144191\pi$
$164$		0			0
$165$	−22.5000	−	38.9711i	−0.136364	−	0.236189i
$166$		0			0
$167$			277.128i			1.65945i	0.558172	+	0.829725i	$0.311503\pi$
$167$			277.128i			1.65945i	−0.558172	+	0.829725i	$0.688497\pi$
$168$		0			0
$169$	−23.0000			−0.136095
$170$		0			0
$171$	81.0000	−	46.7654i	0.473684	−	0.273482i
$172$		0			0
$173$	121.500	+	70.1481i	0.702312	+	0.405480i	0.808208	−	0.588897i	$-0.200438\pi$
$173$	121.500	+	70.1481i	0.702312	+	0.405480i	−0.105896	+	0.994377i	$0.533771\pi$
$174$		0			0
$175$	−77.0000	−	133.368i	−0.440000	−	0.762102i
$176$		0			0
$177$	−70.5000	+	122.110i	−0.398305	+	0.689885i
$178$		0			0
$179$	31.5000	+	54.5596i	0.175978	+	0.304802i	0.940499	−	0.339796i	$-0.110358\pi$
$179$	31.5000	+	54.5596i	0.175978	+	0.304802i	−0.764522	+	0.644598i	$0.777025\pi$
$180$		0			0
$181$			124.708i			0.688993i	0.938788	+	0.344496i	$0.111950\pi$
$181$			124.708i			0.688993i	−0.938788	+	0.344496i	$0.888050\pi$
$182$		0			0
$183$	141.000			0.770492
$184$		0			0
$185$	−46.5000	+	26.8468i	−0.251351	+	0.145118i
$186$		0			0
$187$	382.500	+	220.836i	2.04545	+	1.18094i
$188$		0			0
$189$		−	181.865i		−	0.962250i
$190$		0			0
$191$	−28.5000	+	49.3634i	−0.149215	+	0.258447i	−0.930937	−	0.365179i	$-0.881008\pi$
$191$	−28.5000	+	49.3634i	−0.149215	+	0.258447i	0.781723	+	0.623626i	$0.214341\pi$
$192$		0			0
$193$	104.500	+	180.999i	0.541451	+	0.937820i	0.998821	+	0.0485439i	$0.0154581\pi$
$193$	104.500	+	180.999i	0.541451	+	0.937820i	−0.457370	+	0.889276i	$0.651209\pi$
$194$		0			0
$195$		−	41.5692i		−	0.213175i
$196$		0			0
$197$	−150.000			−0.761421			−0.380711	−	0.924694i	$-0.624321\pi$
$197$	−150.000			−0.761421			−0.380711	+	0.924694i	$0.624321\pi$
$198$		0			0
$199$	178.500	−	103.057i	0.896985	−	0.517874i	0.0207642	−	0.999784i	$-0.493390\pi$
$199$	178.500	−	103.057i	0.896985	−	0.517874i	0.876221	+	0.481910i	$0.160057\pi$
$200$		0			0
$201$	73.5000	+	42.4352i	0.365672	+	0.211121i
$202$		0			0
$203$	−42.0000			−0.206897
$204$		0			0
$205$	48.0000	−	83.1384i	0.234146	−	0.405553i
$206$		0			0
$207$	−27.0000	−	46.7654i	−0.130435	−	0.225920i
$208$		0			0
$209$		−	233.827i		−	1.11879i
$210$		0			0
$211$	−346.000			−1.63981			−0.819905	−	0.572499i	$-0.805974\pi$
$211$	−346.000			−1.63981			−0.819905	+	0.572499i	$0.805974\pi$
$212$		0			0
$213$	−189.000	+	109.119i	−0.887324	+	0.512297i
$214$		0			0
$215$	−15.0000	−	8.66025i	−0.0697674	−	0.0402803i
$216$		0			0
$217$	73.5000	−	42.4352i	0.338710	−	0.195554i
$218$		0			0
$219$	22.5000	−	38.9711i	0.102740	−	0.177950i
$220$		0			0
$221$	204.000	+	353.338i	0.923077	+	1.59882i
$222$		0			0
$223$			332.554i			1.49127i	0.666353	+	0.745636i	$0.267854\pi$
$223$			332.554i			1.49127i	−0.666353	+	0.745636i	$0.732146\pi$
$224$		0			0
$225$	132.000			0.586667
$226$		0			0
$227$	−121.500	+	70.1481i	−0.535242	+	0.309022i	−0.743149	−	0.669126i	$-0.766668\pi$
$227$	−121.500	+	70.1481i	−0.535242	+	0.309022i	0.207906	+	0.978149i	$0.433335\pi$
$228$		0			0
$229$	145.500	+	84.0045i	0.635371	+	0.366832i	0.782829	−	0.622237i	$-0.213776\pi$
$229$	145.500	+	84.0045i	0.635371	+	0.366832i	−0.147458	+	0.989068i	$0.547109\pi$
$230$		0			0
$231$	−157.500	−	90.9327i	−0.681818	−	0.393648i
$232$		0			0
$233$	136.500	−	236.425i	0.585837	−	1.01470i	−0.408934	−	0.912564i	$-0.634099\pi$
$233$	136.500	−	236.425i	0.585837	−	1.01470i	0.994771	−	0.102135i	$-0.0325674\pi$
$234$		0			0
$235$	−37.5000	−	64.9519i	−0.159574	−	0.276391i
$236$		0			0
$237$		−	126.440i		−	0.533501i
$238$		0			0
$239$	222.000			0.928870			0.464435	−	0.885607i	$-0.346257\pi$
$239$	222.000			0.928870			0.464435	+	0.885607i	$0.346257\pi$
$240$		0			0
$241$	−190.500	+	109.985i	−0.790456	+	0.456370i	−0.840123	−	0.542396i	$-0.817517\pi$
$241$	−190.500	+	109.985i	−0.790456	+	0.456370i	0.0496668	+	0.998766i	$0.484184\pi$
$242$		0			0
$243$	216.000	+	124.708i	0.888889	+	0.513200i
$244$		0			0
$245$	73.5000	+	42.4352i	0.300000	+	0.173205i
$246$		0			0
$247$	108.000	−	187.061i	0.437247	−	0.757334i
$248$		0			0
$249$	−12.0000	−	20.7846i	−0.0481928	−	0.0834723i
$250$		0			0
$251$		−	96.9948i		−	0.386434i	−0.981156	−	0.193217i	$-0.938108\pi$
$251$		−	96.9948i		−	0.386434i	0.981156	−	0.193217i	$-0.0618921\pi$
$252$		0			0
$253$	−135.000			−0.533597
$254$		0			0
$255$	−76.5000	+	44.1673i	−0.300000	+	0.173205i
$256$		0			0
$257$	−166.500	−	96.1288i	−0.647860	−	0.374042i	0.139776	−	0.990183i	$-0.455362\pi$
$257$	−166.500	−	96.1288i	−0.647860	−	0.374042i	−0.787636	+	0.616141i	$0.788695\pi$
$258$		0			0
$259$	−108.500	+	187.928i	−0.418919	+	0.725589i
$260$		0			0
$261$	18.0000	−	31.1769i	0.0689655	−	0.119452i
$262$		0			0
$263$	−76.5000	−	132.502i	−0.290875	−	0.503809i	0.683142	−	0.730285i	$-0.260613\pi$
$263$	−76.5000	−	132.502i	−0.290875	−	0.503809i	−0.974017	+	0.226476i	$0.927280\pi$
$264$		0			0
$265$			98.7269i			0.372554i
$266$		0			0
$267$	−99.0000			−0.370787
$268$		0			0
$269$	−394.500	+	227.765i	−1.46654	+	0.846709i	−0.999300	−	0.0374200i	$-0.988086\pi$
$269$	−394.500	+	227.765i	−1.46654	+	0.846709i	−0.467243	+	0.884129i	$0.654753\pi$
$270$		0			0
$271$	−61.5000	−	35.5070i	−0.226937	−	0.131022i	0.382221	−	0.924071i	$-0.375159\pi$
$271$	−61.5000	−	35.5070i	−0.226937	−	0.131022i	−0.609158	+	0.793049i	$0.708493\pi$
$272$		0			0
$273$	−84.0000	−	145.492i	−0.307692	−	0.532939i
$274$		0			0
$275$	165.000	−	285.788i	0.600000	−	1.03923i
$276$		0			0
$277$	−179.500	−	310.903i	−0.648014	−	1.12239i	−0.983596	−	0.180383i	$-0.942266\pi$
$277$	−179.500	−	310.903i	−0.648014	−	1.12239i	0.335582	−	0.942011i	$-0.391067\pi$
$278$		0			0
$279$			72.7461i			0.260739i
$280$		0			0
$281$	−222.000			−0.790036			−0.395018	−	0.918673i	$-0.629262\pi$
$281$	−222.000			−0.790036			−0.395018	+	0.918673i	$0.629262\pi$
$282$		0			0
$283$	−1.50000	+	0.866025i	−0.00530035	+	0.00306016i	−0.502648	−	0.864491i	$-0.667641\pi$
$283$	−1.50000	+	0.866025i	−0.00530035	+	0.00306016i	0.497347	+	0.867551i	$0.334307\pi$
$284$		0			0
$285$	40.5000	+	23.3827i	0.142105	+	0.0820445i
$286$		0			0
$287$		−	387.979i		−	1.35184i
$288$		0			0
$289$	289.000	−	500.563i	1.00000	−	1.73205i
$290$		0			0
$291$	−24.0000	−	41.5692i	−0.0824742	−	0.142850i
$292$		0			0
$293$			235.559i			0.803955i	0.915649	+	0.401978i	$0.131677\pi$
$293$			235.559i			0.803955i	−0.915649	+	0.401978i	$0.868323\pi$
$294$		0			0
$295$	141.000			0.477966
$296$		0			0
$297$	337.500	−	194.856i	1.13636	−	0.656080i
$298$		0			0
$299$	−108.000	−	62.3538i	−0.361204	−	0.208541i
$300$		0			0
$301$	−70.0000			−0.232558
$302$		0			0
$303$	−85.5000	+	148.090i	−0.282178	+	0.488747i
$304$		0			0
$305$	−70.5000	−	122.110i	−0.231148	−	0.400359i
$306$		0			0
$307$		−	96.9948i		−	0.315944i	−0.987444	−	0.157972i	$-0.949504\pi$
$307$		−	96.9948i		−	0.315944i	0.987444	−	0.157972i	$-0.0504956\pi$
$308$		0			0
$309$	123.000			0.398058
$310$		0			0
$311$	−421.500	+	243.353i	−1.35531	+	0.782486i	−0.988987	−	0.148003i	$-0.952715\pi$
$311$	−421.500	+	243.353i	−1.35531	+	0.782486i	−0.366319	+	0.930489i	$0.619382\pi$
$312$		0			0
$313$	193.500	+	111.717i	0.618211	+	0.356924i	0.776172	−	0.630521i	$-0.217159\pi$
$313$	193.500	+	111.717i	0.618211	+	0.356924i	−0.157961	+	0.987445i	$0.550492\pi$
$314$		0			0
$315$	−63.0000	+	36.3731i	−0.200000	+	0.115470i
$316$		0			0
$317$	−223.500	+	387.113i	−0.705047	+	1.22118i	0.261627	+	0.965169i	$0.415741\pi$
$317$	−223.500	+	387.113i	−0.705047	+	1.22118i	−0.966674	+	0.256009i	$0.917592\pi$
$318$		0			0
$319$	−45.0000	−	77.9423i	−0.141066	−	0.244333i
$320$		0			0
$321$			67.5500i			0.210436i
$322$		0			0
$323$	−459.000			−1.42105
$324$		0			0
$325$	264.000	−	152.420i	0.812308	−	0.468986i
$326$		0			0
$327$	154.500	+	89.2006i	0.472477	+	0.272785i
$328$		0			0
$329$	−262.500	−	151.554i	−0.797872	−	0.460652i
$330$		0			0
$331$	75.5000	−	130.770i	0.228097	−	0.395075i	−0.729147	−	0.684357i	$-0.760083\pi$
$331$	75.5000	−	130.770i	0.228097	−	0.395075i	0.957244	+	0.289282i	$0.0934164\pi$
$332$		0			0
$333$	−93.0000	−	161.081i	−0.279279	−	0.483726i
$334$		0			0
$335$		−	84.8705i		−	0.253345i
$336$		0			0
$337$	274.000			0.813056			0.406528	−	0.913638i	$-0.366739\pi$
$337$	274.000			0.813056			0.406528	+	0.913638i	$0.366739\pi$
$338$		0			0
$339$	117.000	−	67.5500i	0.345133	−	0.199262i
$340$		0			0
$341$	157.500	+	90.9327i	0.461877	+	0.266665i
$342$		0			0
$343$	343.000			1.00000
$344$		0			0
$345$	13.5000	−	23.3827i	0.0391304	−	0.0677759i
$346$		0			0
$347$	271.500	+	470.252i	0.782421	+	1.35519i	0.930528	+	0.366221i	$0.119349\pi$
$347$	271.500	+	470.252i	0.782421	+	1.35519i	−0.148107	+	0.988971i	$0.547318\pi$
$348$		0			0
$349$			180.133i			0.516141i	0.966126	+	0.258071i	$0.0830867\pi$
$349$			180.133i			0.516141i	−0.966126	+	0.258071i	$0.916913\pi$
$350$		0			0
$351$	360.000			1.02564
$352$		0			0
$353$	−262.500	+	151.554i	−0.743626	+	0.429333i	−0.823386	−	0.567481i	$-0.807918\pi$
$353$	−262.500	+	151.554i	−0.743626	+	0.429333i	0.0797602	+	0.996814i	$0.474585\pi$
$354$		0			0
$355$	189.000	+	109.119i	0.532394	+	0.307378i
$356$		0			0
$357$	−178.500	+	309.171i	−0.500000	+	0.866025i
$358$		0			0
$359$	19.5000	−	33.7750i	0.0543175	−	0.0940808i	−0.837588	−	0.546302i	$-0.816035\pi$
$359$	19.5000	−	33.7750i	0.0543175	−	0.0940808i	0.891906	+	0.452221i	$0.149368\pi$
$360$		0			0
$361$	−59.0000	−	102.191i	−0.163435	−	0.283078i
$362$		0			0
$363$		−	180.133i		−	0.496235i
$364$		0			0
$365$	−45.0000			−0.123288
$366$		0			0
$367$	−301.500	+	174.071i	−0.821526	+	0.474308i	−0.850942	−	0.525259i	$-0.823968\pi$
$367$	−301.500	+	174.071i	−0.821526	+	0.474308i	0.0294165	+	0.999567i	$0.490635\pi$
$368$		0			0
$369$	288.000	+	166.277i	0.780488	+	0.450615i
$370$		0			0
$371$	199.500	+	345.544i	0.537736	+	0.931386i
$372$		0			0
$373$	−191.500	+	331.688i	−0.513405	+	0.889243i	0.486474	+	0.873695i	$0.338283\pi$
$373$	−191.500	+	331.688i	−0.513405	+	0.889243i	−0.999879	+	0.0155484i	$0.995051\pi$
$374$		0			0
$375$	70.5000	+	122.110i	0.188000	+	0.325626i
$376$		0			0
$377$		−	83.1384i		−	0.220526i
$378$		0			0
$379$	230.000			0.606860			0.303430	−	0.952854i	$-0.401868\pi$
$379$	230.000			0.606860			0.303430	+	0.952854i	$0.401868\pi$
$380$		0			0
$381$	75.0000	−	43.3013i	0.196850	−	0.113652i
$382$		0			0
$383$	−277.500	−	160.215i	−0.724543	−	0.418315i	0.0918794	−	0.995770i	$-0.470713\pi$
$383$	−277.500	−	160.215i	−0.724543	−	0.418315i	−0.816423	+	0.577455i	$0.804046\pi$
$384$		0			0
$385$			181.865i			0.472377i
$386$		0			0
$387$	30.0000	−	51.9615i	0.0775194	−	0.134268i
$388$		0			0
$389$	100.500	+	174.071i	0.258355	+	0.447484i	0.965801	−	0.259283i	$-0.0834863\pi$
$389$	100.500	+	174.071i	0.258355	+	0.447484i	−0.707447	+	0.706767i	$0.750153\pi$
$390$		0			0
$391$			265.004i			0.677759i
$392$		0			0
$393$	171.000			0.435115
$394$		0			0
$395$	−109.500	+	63.2199i	−0.277215	+	0.160050i
$396$		0			0
$397$	−46.5000	−	26.8468i	−0.117128	−	0.0676241i	0.440291	−	0.897855i	$-0.354875\pi$
$397$	−46.5000	−	26.8468i	−0.117128	−	0.0676241i	−0.557420	+	0.830231i	$0.688209\pi$
$398$		0			0
$399$	189.000			0.473684
$400$		0			0
$401$	88.5000	−	153.286i	0.220698	−	0.382261i	−0.734322	−	0.678801i	$-0.762500\pi$
$401$	88.5000	−	153.286i	0.220698	−	0.382261i	0.955020	+	0.296541i	$0.0958331\pi$
$402$		0			0
$403$	84.0000	+	145.492i	0.208437	+	0.361023i
$404$		0			0
$405$		−	15.5885i		−	0.0384900i
$406$		0			0
$407$	−465.000			−1.14251
$408$		0			0
$409$	289.500	−	167.143i	0.707824	−	0.408662i	−0.102431	−	0.994740i	$-0.532662\pi$
$409$	289.500	−	167.143i	0.707824	−	0.408662i	0.810255	+	0.586078i	$0.199329\pi$
$410$		0			0
$411$	94.5000	+	54.5596i	0.229927	+	0.132748i
$412$		0			0
$413$	493.500	−	284.922i	1.19492	−	0.689885i
$414$		0			0
$415$	−12.0000	+	20.7846i	−0.0289157	+	0.0500834i
$416$		0			0
$417$	204.000	+	353.338i	0.489209	+	0.847334i
$418$		0			0
$419$		−	595.825i		−	1.42202i	−0.703183	−	0.711009i	$-0.748239\pi$
$419$		−	595.825i		−	1.42202i	0.703183	−	0.711009i	$-0.251761\pi$
$420$		0			0
$421$	−22.0000			−0.0522565			−0.0261283	−	0.999659i	$-0.508318\pi$
$421$	−22.0000			−0.0522565			−0.0261283	+	0.999659i	$0.508318\pi$
$422$		0			0
$423$	225.000	−	129.904i	0.531915	−	0.307101i
$424$		0			0
$425$	−561.000	−	323.894i	−1.32000	−	0.762102i
$426$		0			0
$427$	−493.500	−	284.922i	−1.15574	−	0.667265i
$428$		0			0
$429$	180.000	−	311.769i	0.419580	−	0.726735i
$430$		0			0
$431$	163.500	+	283.190i	0.379350	+	0.657054i	0.990968	−	0.134100i	$-0.0428142\pi$
$431$	163.500	+	283.190i	0.379350	+	0.657054i	−0.611618	+	0.791154i	$0.709481\pi$
$432$		0			0
$433$			27.7128i			0.0640019i	0.999488	+	0.0320009i	$0.0101880\pi$
$433$			27.7128i			0.0640019i	−0.999488	+	0.0320009i	$0.989812\pi$
$434$		0			0
$435$	18.0000			0.0413793
$436$		0			0
$437$	121.500	−	70.1481i	0.278032	−	0.160522i
$438$		0			0
$439$	−517.500	−	298.779i	−1.17882	−	0.680589i	−0.223075	−	0.974801i	$-0.571610\pi$
$439$	−517.500	−	298.779i	−1.17882	−	0.680589i	−0.955740	+	0.294212i	$0.904943\pi$
$440$		0			0
$441$	−147.000	+	254.611i	−0.333333	+	0.577350i
$442$		0			0
$443$	−364.500	+	631.333i	−0.822799	+	1.42513i	0.0807907	+	0.996731i	$0.474255\pi$
$443$	−364.500	+	631.333i	−0.822799	+	1.42513i	−0.903590	+	0.428399i	$0.859078\pi$
$444$		0			0
$445$	49.5000	+	85.7365i	0.111236	+	0.192666i
$446$		0			0
$447$			306.573i			0.685846i
$448$		0			0
$449$	−270.000			−0.601336			−0.300668	−	0.953729i	$-0.597210\pi$
$449$	−270.000			−0.601336			−0.300668	+	0.953729i	$0.597210\pi$
$450$		0			0
$451$	720.000	−	415.692i	1.59645	−	0.921712i
$452$		0			0
$453$	−82.5000	−	47.6314i	−0.182119	−	0.105147i
$454$		0			0
$455$	−84.0000	+	145.492i	−0.184615	+	0.319763i
$456$		0			0
$457$	−399.500	+	691.954i	−0.874179	+	1.51412i	−0.0165451	+	0.999863i	$0.505267\pi$
$457$	−399.500	+	691.954i	−0.874179	+	1.51412i	−0.857634	+	0.514260i	$0.828067\pi$
$458$		0			0
$459$	−382.500	−	662.509i	−0.833333	−	1.44338i
$460$		0			0
$461$		−	429.549i		−	0.931776i	−0.884844	−	0.465888i	$-0.845735\pi$
$461$		−	429.549i		−	0.931776i	0.884844	−	0.465888i	$-0.154265\pi$
$462$		0			0
$463$	814.000			1.75810			0.879050	−	0.476730i	$-0.158178\pi$
$463$	814.000			1.75810			0.879050	+	0.476730i	$0.158178\pi$
$464$		0			0
$465$	−31.5000	+	18.1865i	−0.0677419	+	0.0391108i
$466$		0			0
$467$	346.500	+	200.052i	0.741970	+	0.428377i	0.822785	−	0.568353i	$-0.192419\pi$
$467$	346.500	+	200.052i	0.741970	+	0.428377i	−0.0808151	+	0.996729i	$0.525752\pi$
$468$		0			0
$469$	−171.500	−	297.047i	−0.365672	−	0.633362i
$470$		0			0
$471$	−85.5000	+	148.090i	−0.181529	+	0.314417i
$472$		0			0
$473$	−75.0000	−	129.904i	−0.158562	−	0.274638i
$474$		0			0
$475$			342.946i			0.721992i
$476$		0			0
$477$	−342.000			−0.716981
$478$		0			0
$479$	466.500	−	269.334i	0.973904	−	0.562284i	0.0734798	−	0.997297i	$-0.476590\pi$
$479$	466.500	−	269.334i	0.973904	−	0.562284i	0.900424	+	0.435013i	$0.143256\pi$
$480$		0			0
$481$	−372.000	−	214.774i	−0.773389	−	0.446516i
$482$		0			0
$483$		−	109.119i		−	0.225920i
$484$		0			0
$485$	−24.0000	+	41.5692i	−0.0494845	+	0.0857097i
$486$		0			0
$487$	−428.500	−	742.184i	−0.879877	−	1.52399i	−0.851475	−	0.524395i	$-0.824292\pi$
$487$	−428.500	−	742.184i	−0.879877	−	1.52399i	−0.0284015	−	0.999597i	$-0.509042\pi$
$488$		0			0
$489$			39.8372i			0.0814666i
$490$		0			0
$491$	−570.000			−1.16090			−0.580448	−	0.814297i	$-0.697123\pi$
$491$	−570.000			−1.16090			−0.580448	+	0.814297i	$0.697123\pi$
$492$		0			0
$493$	−153.000	+	88.3346i	−0.310345	+	0.179178i
$494$		0			0
$495$	−135.000	−	77.9423i	−0.272727	−	0.157459i
$496$		0			0
$497$	882.000			1.77465
$498$		0			0
$499$	−212.500	+	368.061i	−0.425852	+	0.737597i	−0.996500	−	0.0835981i	$-0.973359\pi$
$499$	−212.500	+	368.061i	−0.425852	+	0.737597i	0.570648	+	0.821195i	$0.306692\pi$
$500$		0			0
$501$	−240.000	−	415.692i	−0.479042	−	0.829725i
$502$		0			0
$503$		−	193.990i		−	0.385665i	−0.981232	−	0.192833i	$-0.938233\pi$
$503$		−	193.990i		−	0.385665i	0.981232	−	0.192833i	$-0.0617675\pi$
$504$		0			0
$505$	171.000			0.338614
$506$		0			0
$507$	34.5000	−	19.9186i	0.0680473	−	0.0392871i
$508$		0			0
$509$	−334.500	−	193.124i	−0.657171	−	0.379418i	0.134027	−	0.990978i	$-0.457209\pi$
$509$	−334.500	−	193.124i	−0.657171	−	0.379418i	−0.791198	+	0.611560i	$0.790542\pi$
$510$		0			0
$511$	−157.500	+	90.9327i	−0.308219	+	0.177950i
$512$		0			0
$513$	−202.500	+	350.740i	−0.394737	+	0.683704i
$514$		0			0
$515$	−61.5000	−	106.521i	−0.119417	−	0.206837i
$516$		0			0
$517$		−	649.519i		−	1.25632i
$518$		0			0
$519$	−243.000			−0.468208
$520$		0			0
$521$	−214.500	+	123.842i	−0.411708	+	0.237700i	−0.691523	−	0.722354i	$-0.743060\pi$
$521$	−214.500	+	123.842i	−0.411708	+	0.237700i	0.279815	+	0.960054i	$0.409727\pi$
$522$		0			0
$523$	−685.500	−	395.774i	−1.31071	−	0.756737i	−0.328494	−	0.944506i	$-0.606541\pi$
$523$	−685.500	−	395.774i	−1.31071	−	0.756737i	−0.982213	+	0.187769i	$0.939874\pi$
$524$		0			0
$525$	231.000	+	133.368i	0.440000	+	0.254034i
$526$		0			0
$527$	178.500	−	309.171i	0.338710	−	0.586662i
$528$		0			0
$529$	224.000	+	387.979i	0.423440	+	0.733420i
$530$		0			0
$531$			488.438i			0.919846i
$532$		0			0
$533$	768.000			1.44090
$534$		0			0
$535$	58.5000	−	33.7750i	0.109346	−	0.0631308i
$536$		0			0
$537$	−94.5000	−	54.5596i	−0.175978	−	0.101601i
$538$		0			0
$539$	367.500	+	636.529i	0.681818	+	1.18094i
$540$		0			0
$541$	360.500	−	624.404i	0.666359	−	1.15417i	−0.312556	−	0.949899i	$-0.601185\pi$
$541$	360.500	−	624.404i	0.666359	−	1.15417i	0.978915	−	0.204268i	$-0.0654813\pi$
$542$		0			0
$543$	−108.000	−	187.061i	−0.198895	−	0.344496i
$544$		0			0
$545$		−	178.401i		−	0.327342i
$546$		0			0
$547$	118.000			0.215722			0.107861	−	0.994166i	$-0.465600\pi$
$547$	118.000			0.215722			0.107861	+	0.994166i	$0.465600\pi$
$548$		0			0
$549$	423.000	−	244.219i	0.770492	−	0.444844i
$550$		0			0
$551$	81.0000	+	46.7654i	0.147005	+	0.0848736i
$552$		0			0
$553$	−255.500	+	442.539i	−0.462025	+	0.800251i
$554$		0			0
$555$	46.5000	−	80.5404i	0.0837838	−	0.145118i
$556$		0			0
$557$	316.500	+	548.194i	0.568223	+	0.984190i	0.996742	+	0.0806578i	$0.0257021\pi$
$557$	316.500	+	548.194i	0.568223	+	0.984190i	−0.428519	+	0.903533i	$0.640965\pi$
$558$		0			0
$559$		−	138.564i		−	0.247878i
$560$		0			0
$561$	−765.000			−1.36364
$562$		0			0
$563$	238.500	−	137.698i	0.423623	−	0.244579i	−0.273003	−	0.962013i	$-0.588017\pi$
$563$	238.500	−	137.698i	0.423623	−	0.244579i	0.696626	+	0.717434i	$0.254684\pi$
$564$		0			0
$565$	−117.000	−	67.5500i	−0.207080	−	0.119557i
$566$		0			0
$567$	−31.5000	−	54.5596i	−0.0555556	−	0.0962250i
$568$		0			0
$569$	−223.500	+	387.113i	−0.392794	+	0.680340i	−0.992817	−	0.119643i	$-0.961825\pi$
$569$	−223.500	+	387.113i	−0.392794	+	0.680340i	0.600023	+	0.799983i	$0.295158\pi$
$570$		0			0
$571$	263.500	+	456.395i	0.461471	+	0.799291i	0.999035	−	0.0439319i	$-0.0139885\pi$
$571$	263.500	+	456.395i	0.461471	+	0.799291i	−0.537563	+	0.843223i	$0.680655\pi$
$572$		0			0
$573$		−	98.7269i		−	0.172298i
$574$		0			0
$575$	198.000			0.344348
$576$		0			0
$577$	145.500	−	84.0045i	0.252166	−	0.145588i	−0.368589	−	0.929592i	$-0.620159\pi$
$577$	145.500	−	84.0045i	0.252166	−	0.145588i	0.620756	+	0.784004i	$0.286826\pi$
$578$		0			0
$579$	−313.500	−	180.999i	−0.541451	−	0.312607i
$580$		0			0
$581$			96.9948i			0.166945i
$582$		0			0
$583$	−427.500	+	740.452i	−0.733276	+	1.27007i
$584$		0			0
$585$	−72.0000	−	124.708i	−0.123077	−	0.213175i
$586$		0			0
$587$		−	956.092i		−	1.62878i	−0.580320	−	0.814388i	$-0.697073\pi$
$587$		−	956.092i		−	1.62878i	0.580320	−	0.814388i	$-0.302927\pi$
$588$		0			0
$589$	−189.000			−0.320883
$590$		0			0
$591$	225.000	−	129.904i	0.380711	−	0.219803i
$592$		0			0
$593$	−262.500	−	151.554i	−0.442664	−	0.255572i	0.262063	−	0.965051i	$-0.415597\pi$
$593$	−262.500	−	151.554i	−0.442664	−	0.255572i	−0.704727	+	0.709478i	$0.748931\pi$
$594$		0			0
$595$	357.000			0.600000
$596$		0			0
$597$	−178.500	+	309.171i	−0.298995	+	0.517874i
$598$		0			0
$599$	403.500	+	698.883i	0.673623	+	1.16675i	0.976869	+	0.213837i	$0.0685960\pi$
$599$	403.500	+	698.883i	0.673623	+	1.16675i	−0.303247	+	0.952912i	$0.598071\pi$
$600$		0			0
$601$			387.979i			0.645556i	0.946475	+	0.322778i	$0.104617\pi$
$601$			387.979i			0.645556i	−0.946475	+	0.322778i	$0.895383\pi$
$602$		0			0
$603$	294.000			0.487562
$604$		0			0
$605$	−156.000	+	90.0666i	−0.257851	+	0.148870i
$606$		0			0
$607$	634.500	+	366.329i	1.04530	+	0.603507i	0.921331	−	0.388779i	$-0.127103\pi$
$607$	634.500	+	366.329i	1.04530	+	0.603507i	0.123974	+	0.992286i	$0.460436\pi$
$608$		0			0
$609$	63.0000	−	36.3731i	0.103448	−	0.0597259i
$610$		0			0
$611$	300.000	−	519.615i	0.490998	−	0.850434i
$612$		0			0
$613$	−251.500	−	435.611i	−0.410277	−	0.710621i	0.584643	−	0.811291i	$-0.301235\pi$
$613$	−251.500	−	435.611i	−0.410277	−	0.710621i	−0.994920	+	0.100670i	$0.967901\pi$
$614$		0			0
$615$			166.277i			0.270369i
$616$		0			0
$617$	930.000			1.50729			0.753647	−	0.657280i	$-0.228293\pi$
$617$	930.000			1.50729			0.753647	+	0.657280i	$0.228293\pi$
$618$		0			0
$619$	−457.500	+	264.138i	−0.739095	+	0.426717i	−0.821740	−	0.569862i	$-0.806997\pi$
$619$	−457.500	+	264.138i	−0.739095	+	0.426717i	0.0826450	+	0.996579i	$0.473663\pi$
$620$		0			0
$621$	202.500	+	116.913i	0.326087	+	0.188266i
$622$		0			0
$623$	346.500	+	200.052i	0.556180	+	0.321111i
$624$		0			0
$625$	−204.500	+	354.204i	−0.327200	+	0.566727i
$626$		0			0
$627$	202.500	+	350.740i	0.322967	+	0.559394i
$628$		0			0
$629$			912.791i			1.45118i
$630$		0			0
$631$	−194.000			−0.307448			−0.153724	−	0.988114i	$-0.549127\pi$
$631$	−194.000			−0.307448			−0.153724	+	0.988114i	$0.549127\pi$
$632$		0			0
$633$	519.000	−	299.645i	0.819905	−	0.473372i
$634$		0			0
$635$	−75.0000	−	43.3013i	−0.118110	−	0.0681910i
$636$		0			0
$637$			678.964i			1.06588i
$638$		0			0
$639$	−378.000	+	654.715i	−0.591549	+	1.02459i
$640$		0			0
$641$	16.5000	+	28.5788i	0.0257410	+	0.0445848i	0.878609	−	0.477542i	$-0.158472\pi$
$641$	16.5000	+	28.5788i	0.0257410	+	0.0445848i	−0.852868	+	0.522127i	$0.825139\pi$
$642$		0			0
$643$			346.410i			0.538741i	0.963037	+	0.269370i	$0.0868155\pi$
$643$			346.410i			0.538741i	−0.963037	+	0.269370i	$0.913184\pi$
$644$		0			0
$645$	30.0000			0.0465116
$646$		0			0
$647$	−661.500	+	381.917i	−1.02241	+	0.590289i	−0.914801	−	0.403904i	$-0.867653\pi$
$647$	−661.500	+	381.917i	−1.02241	+	0.590289i	−0.107610	+	0.994193i	$0.534320\pi$
$648$		0			0
$649$	1057.50	+	610.548i	1.62943	+	0.940752i
$650$		0			0
$651$	−73.5000	+	127.306i	−0.112903	+	0.195554i
$652$		0			0
$653$	16.5000	−	28.5788i	0.0252680	−	0.0437654i	−0.853115	−	0.521723i	$-0.825289\pi$
$653$	16.5000	−	28.5788i	0.0252680	−	0.0437654i	0.878383	+	0.477958i	$0.158623\pi$
$654$		0			0
$655$	−85.5000	−	148.090i	−0.130534	−	0.226092i
$656$		0			0
$657$		−	155.885i		−	0.237267i
$658$		0			0
$659$	870.000			1.32018			0.660091	−	0.751186i	$-0.270518\pi$
$659$	870.000			1.32018			0.660091	+	0.751186i	$0.270518\pi$
$660$		0			0
$661$	877.500	−	506.625i	1.32753	−	0.766452i	0.342616	−	0.939475i	$-0.388687\pi$
$661$	877.500	−	506.625i	1.32753	−	0.766452i	0.984918	+	0.173023i	$0.0553536\pi$
$662$		0			0
$663$	−612.000	−	353.338i	−0.923077	−	0.532939i
$664$		0			0
$665$	−94.5000	−	163.679i	−0.142105	−	0.246134i
$666$		0			0
$667$	27.0000	−	46.7654i	0.0404798	−	0.0701130i
$668$		0			0
$669$	−288.000	−	498.831i	−0.430493	−	0.745636i
$670$		0			0
$671$		−	1221.10i		−	1.81981i
$672$		0			0
$673$	−14.0000			−0.0208024			−0.0104012	−	0.999946i	$-0.503311\pi$
$673$	−14.0000			−0.0208024			−0.0104012	+	0.999946i	$0.503311\pi$
$674$		0			0
$675$	−495.000	+	285.788i	−0.733333	+	0.423390i
$676$		0			0
$677$	−238.500	−	137.698i	−0.352290	−	0.203394i	0.313404	−	0.949620i	$-0.398531\pi$
$677$	−238.500	−	137.698i	−0.352290	−	0.203394i	−0.665693	+	0.746226i	$0.731864\pi$
$678$		0			0
$679$			193.990i			0.285699i
$680$		0			0
$681$	121.500	−	210.444i	0.178414	−	0.309022i
$682$		0			0
$683$	−136.500	−	236.425i	−0.199854	−	0.346157i	0.748627	−	0.662991i	$-0.230713\pi$
$683$	−136.500	−	236.425i	−0.199854	−	0.346157i	−0.948481	+	0.316835i	$0.897380\pi$
$684$		0			0
$685$		−	109.119i		−	0.159298i
$686$		0			0
$687$	−291.000			−0.423581
$688$		0			0
$689$	−684.000	+	394.908i	−0.992743	+	0.573160i
$690$		0			0
$691$	−133.500	−	77.0763i	−0.193198	−	0.111543i	0.400281	−	0.916393i	$-0.368913\pi$
$691$	−133.500	−	77.0763i	−0.193198	−	0.111543i	−0.593479	+	0.804850i	$0.702246\pi$
$692$		0			0
$693$	−630.000			−0.909091
$694$		0			0
$695$	204.000	−	353.338i	0.293525	−	0.508401i
$696$		0			0
$697$	−816.000	−	1413.35i	−1.17073	−	2.02777i
$698$		0			0
$699$			472.850i			0.676466i
$700$		0			0
$701$	906.000			1.29244			0.646220	−	0.763151i	$-0.276349\pi$
$701$	906.000			1.29244			0.646220	+	0.763151i	$0.276349\pi$
$702$		0			0
$703$	418.500	−	241.621i	0.595306	−	0.343700i
$704$		0			0
$705$	112.500	+	64.9519i	0.159574	+	0.0921304i
$706$		0			0
$707$	598.500	−	345.544i	0.846535	−	0.488747i
$708$		0			0
$709$	−351.500	+	608.816i	−0.495769	+	0.858697i	−0.999988	−	0.00487903i	$-0.998447\pi$
$709$	−351.500	+	608.816i	−0.495769	+	0.858697i	0.504219	+	0.863576i	$0.331780\pi$
$710$		0			0
$711$	−219.000	−	379.319i	−0.308017	−	0.533501i
$712$		0			0
$713$			109.119i			0.153042i
$714$		0			0
$715$	−360.000			−0.503497
$716$		0			0
$717$	−333.000	+	192.258i	−0.464435	+	0.268142i
$718$		0			0
$719$	514.500	+	297.047i	0.715577	+	0.413139i	0.813123	−	0.582092i	$-0.197766\pi$
$719$	514.500	+	297.047i	0.715577	+	0.413139i	−0.0975455	+	0.995231i	$0.531099\pi$
$720$		0			0
$721$	−430.500	−	248.549i	−0.597087	−	0.344729i
$722$		0			0
$723$	190.500	−	329.956i	0.263485	−	0.456370i
$724$		0			0
$725$	66.0000	+	114.315i	0.0910345	+	0.157676i
$726$		0			0
$727$		−	27.7128i		−	0.0381194i	−0.999818	−	0.0190597i	$-0.993933\pi$
$727$		−	27.7128i		−	0.0381194i	0.999818	−	0.0190597i	$-0.00606726\pi$
$728$		0			0
$729$	−351.000			−0.481481
$730$		0			0
$731$	−255.000	+	147.224i	−0.348837	+	0.201401i
$732$		0			0
$733$	−838.500	−	484.108i	−1.14393	−	0.660448i	−0.196529	−	0.980498i	$-0.562967\pi$
$733$	−838.500	−	484.108i	−1.14393	−	0.660448i	−0.947401	+	0.320050i	$0.896300\pi$
$734$		0			0
$735$	−147.000			−0.200000
$736$		0			0
$737$	367.500	−	636.529i	0.498643	−	0.863675i
$738$		0			0
$739$	−288.500	−	499.697i	−0.390392	−	0.676180i	0.602109	−	0.798414i	$-0.294327\pi$
$739$	−288.500	−	499.697i	−0.390392	−	0.676180i	−0.992501	+	0.122235i	$0.960994\pi$
$740$		0			0
$741$			374.123i			0.504889i
$742$		0			0
$743$	−162.000			−0.218035			−0.109017	−	0.994040i	$-0.534770\pi$
$743$	−162.000			−0.218035			−0.109017	+	0.994040i	$0.534770\pi$
$744$		0			0
$745$	265.500	−	153.286i	0.356376	−	0.205754i
$746$		0			0
$747$	−72.0000	−	41.5692i	−0.0963855	−	0.0556482i
$748$		0			0
$749$	136.500	−	236.425i	0.182243	−	0.315654i
$750$		0			0
$751$	387.500	−	671.170i	0.515979	−	0.893701i	−0.483849	−	0.875151i	$-0.660762\pi$
$751$	387.500	−	671.170i	0.515979	−	0.893701i	0.999828	−	0.0185499i	$-0.00590497\pi$
$752$		0			0
$753$	84.0000	+	145.492i	0.111554	+	0.193217i
$754$		0			0
$755$			95.2628i			0.126176i
$756$		0			0
$757$	−950.000			−1.25495			−0.627477	−	0.778635i	$-0.715912\pi$
$757$	−950.000			−1.25495			−0.627477	+	0.778635i	$0.715912\pi$
$758$		0			0
$759$	202.500	−	116.913i	0.266798	−	0.154036i
$760$		0			0
$761$	169.500	+	97.8609i	0.222733	+	0.128595i	0.607215	−	0.794537i	$-0.292287\pi$
$761$	169.500	+	97.8609i	0.222733	+	0.128595i	−0.384482	+	0.923133i	$0.625620\pi$
$762$		0			0
$763$	−360.500	−	624.404i	−0.472477	−	0.818354i
$764$		0			0
$765$	−153.000	+	265.004i	−0.200000	+	0.346410i
$766$		0			0
$767$	564.000	+	976.877i	0.735332	+	1.27363i
$768$		0			0
$769$		−	914.523i		−	1.18924i	−0.804008	−	0.594618i	$-0.797303\pi$
$769$		−	914.523i		−	1.18924i	0.804008	−	0.594618i	$-0.202697\pi$
$770$		0			0
$771$	333.000			0.431907
$772$		0			0
$773$	−154.500	+	89.2006i	−0.199871	+	0.115395i	−0.596595	−	0.802542i	$-0.703480\pi$
$773$	−154.500	+	89.2006i	−0.199871	+	0.115395i	0.396725	+	0.917938i	$0.370147\pi$
$774$		0			0
$775$	−231.000	−	133.368i	−0.298065	−	0.172088i
$776$		0			0
$777$		−	375.855i		−	0.483726i
$778$		0			0
$779$	−432.000	+	748.246i	−0.554557	+	0.960521i
$780$		0			0
$781$	945.000	+	1636.79i	1.20999	+	2.09576i
$782$		0			0
$783$			155.885i			0.199086i
$784$		0			0
$785$	171.000			0.217834
$786$		0			0
$787$	−289.500	+	167.143i	−0.367853	+	0.212380i	−0.672520	−	0.740079i	$-0.734788\pi$
$787$	−289.500	+	167.143i	−0.367853	+	0.212380i	0.304667	+	0.952459i	$0.401455\pi$
$788$		0			0
$789$	229.500	+	132.502i	0.290875	+	0.167936i
$790$		0			0
$791$	−546.000			−0.690265
$792$		0			0
$793$	564.000	−	976.877i	0.711223	−	1.23187i
$794$		0			0
$795$	−85.5000	−	148.090i	−0.107547	−	0.186277i
$796$		0			0
$797$		−	872.954i		−	1.09530i	−0.836708	−	0.547650i	$-0.815523\pi$
$797$		−	872.954i		−	1.09530i	0.836708	−	0.547650i	$-0.184477\pi$
$798$		0			0
$799$	−1275.00			−1.59574
$800$		0			0
$801$	−297.000	+	171.473i	−0.370787	+	0.214074i
$802$		0			0
$803$	−337.500	−	194.856i	−0.420299	−	0.242660i
$804$		0			0
$805$	−94.5000	+	54.5596i	−0.117391	+	0.0677759i
$806$		0			0
$807$	394.500	−	683.294i	0.488848	−	0.846709i
$808$		0			0
$809$	232.500	+	402.702i	0.287392	+	0.497777i	0.973186	−	0.230018i	$-0.0738785\pi$
$809$	232.500	+	402.702i	0.287392	+	0.497777i	−0.685795	+	0.727795i	$0.740545\pi$
$810$		0			0
$811$		−	124.708i		−	0.153770i	−0.997040	−	0.0768851i	$-0.975503\pi$
$811$		−	124.708i		−	0.153770i	0.997040	−	0.0768851i	$-0.0244975\pi$
$812$		0			0
$813$	123.000			0.151292
$814$		0			0
$815$	34.5000	−	19.9186i	0.0423313	−	0.0244400i
$816$		0			0
$817$	135.000	+	77.9423i	0.165239	+	0.0954006i
$818$		0			0
$819$	−504.000	−	290.985i	−0.615385	−	0.355292i
$820$		0			0
$821$	376.500	−	652.117i	0.458587	−	0.794296i	−0.540299	−	0.841473i	$-0.681689\pi$
$821$	376.500	−	652.117i	0.458587	−	0.794296i	0.998887	+	0.0471767i	$0.0150224\pi$
$822$		0			0
$823$	−12.5000	−	21.6506i	−0.0151883	−	0.0263070i	0.858331	−	0.513096i	$-0.171501\pi$
$823$	−12.5000	−	21.6506i	−0.0151883	−	0.0263070i	−0.873520	+	0.486789i	$0.838168\pi$
$824$		0			0
$825$			571.577i			0.692820i
$826$		0			0
$827$	246.000			0.297461			0.148730	−	0.988878i	$-0.452481\pi$
$827$	246.000			0.297461			0.148730	+	0.988878i	$0.452481\pi$
$828$		0			0
$829$	−1282.50	+	740.452i	−1.54704	+	0.893187i	−0.548679	+	0.836033i	$0.684869\pi$
$829$	−1282.50	+	740.452i	−1.54704	+	0.893187i	−0.998365	+	0.0571537i	$0.981797\pi$
$830$		0			0
$831$	538.500	+	310.903i	0.648014	+	0.374131i
$832$		0			0
$833$	1249.50	−	721.399i	1.50000	−	0.866025i
$834$		0			0
$835$	−240.000	+	415.692i	−0.287425	+	0.497835i
$836$		0			0
$837$	−157.500	−	272.798i	−0.188172	−	0.325924i
$838$		0			0
$839$			360.267i			0.429400i	0.976680	+	0.214700i	$0.0688774\pi$
$839$			360.267i			0.429400i	−0.976680	+	0.214700i	$0.931123\pi$
$840$		0			0
$841$	−805.000			−0.957194
$842$		0			0
$843$	333.000	−	192.258i	0.395018	−	0.228064i
$844$		0			0
$845$	−34.5000	−	19.9186i	−0.0408284	−	0.0235723i
$846$		0			0
$847$	−364.000	+	630.466i	−0.429752	+	0.744352i
$848$		0			0
$849$	1.50000	−	2.59808i	0.00176678	−	0.00306016i
$850$		0			0
$851$	−139.500	−	241.621i	−0.163925	−	0.283926i
$852$		0			0
$853$			1205.51i			1.41326i	0.707585	+	0.706628i	$0.249785\pi$
$853$			1205.51i			1.41326i	−0.707585	+	0.706628i	$0.750215\pi$
$854$		0			0
$855$	162.000			0.189474
$856$		0			0
$857$	169.500	−	97.8609i	0.197783	−	0.114190i	−0.397838	−	0.917456i	$-0.630239\pi$
$857$	169.500	−	97.8609i	0.197783	−	0.114190i	0.595621	+	0.803266i	$0.296906\pi$
$858$		0			0
$859$	1234.50	+	712.739i	1.43714	+	0.829731i	0.997650	−	0.0685183i	$-0.0218272\pi$
$859$	1234.50	+	712.739i	1.43714	+	0.829731i	0.439486	+	0.898249i	$0.355160\pi$
$860$		0			0
$861$	336.000	+	581.969i	0.390244	+	0.675922i
$862$		0			0
$863$	427.500	−	740.452i	0.495365	−	0.857997i	−0.504621	−	0.863341i	$-0.668368\pi$
$863$	427.500	−	740.452i	0.495365	−	0.857997i	0.999986	+	0.00534379i	$0.00170099\pi$
$864$		0			0
$865$	121.500	+	210.444i	0.140462	+	0.243288i
$866$		0			0
$867$			1001.13i			1.15470i
$868$		0			0
$869$	−1095.00			−1.26007
$870$		0			0
$871$	588.000	−	339.482i	0.675086	−	0.389761i
$872$		0			0
$873$	−144.000	−	83.1384i	−0.164948	−	0.0952330i
$874$		0			0
$875$		−	569.845i		−	0.651251i
$876$		0			0
$877$	120.500	−	208.712i	0.137400	−	0.237984i	−0.789112	−	0.614250i	$-0.789459\pi$
$877$	120.500	−	208.712i	0.137400	−	0.237984i	0.926512	+	0.376266i	$0.122792\pi$
$878$		0			0
$879$	−204.000	−	353.338i	−0.232082	−	0.401978i
$880$		0			0
$881$		−	1330.22i		−	1.50989i	−0.655787	−	0.754946i	$-0.727663\pi$
$881$		−	1330.22i		−	1.50989i	0.655787	−	0.754946i	$-0.272337\pi$
$882$		0			0
$883$	1286.00			1.45640			0.728199	−	0.685365i	$-0.240358\pi$
$883$	1286.00			1.45640			0.728199	+	0.685365i	$0.240358\pi$
$884$		0			0
$885$	−211.500	+	122.110i	−0.238983	+	0.137977i
$886$		0			0
$887$	1114.50	+	643.457i	1.25648	+	0.725431i	0.972389	−	0.233366i	$-0.0749740\pi$
$887$	1114.50	+	643.457i	1.25648	+	0.725431i	0.284094	+	0.958797i	$0.408307\pi$
$888$		0			0
$889$	−350.000			−0.393701
$890$		0			0
$891$	67.5000	−	116.913i	0.0757576	−	0.131216i
$892$		0			0
$893$	337.500	+	584.567i	0.377940	+	0.654610i
$894$		0			0
$895$			109.119i			0.121921i
$896$		0			0
$897$	216.000			0.240803
$898$		0			0
$899$	−63.0000	+	36.3731i	−0.0700779	+	0.0404595i
$900$		0			0
$901$	1453.50	+	839.179i	1.61321	+	0.931386i
$902$		0			0
$903$	105.000	−	60.6218i	0.116279	−	0.0671338i
$904$		0			0
$905$	−108.000	+	187.061i	−0.119337	+	0.206698i
$906$		0			0
$907$	−368.500	−	638.261i	−0.406284	−	0.703705i	0.588186	−	0.808726i	$-0.299842\pi$
$907$	−368.500	−	638.261i	−0.406284	−	0.703705i	−0.994470	+	0.105021i	$0.966509\pi$
$908$		0			0
$909$			592.361i			0.651663i
$910$		0			0
$911$	−1266.00			−1.38968			−0.694841	−	0.719164i	$-0.744525\pi$
$911$	−1266.00			−1.38968			−0.694841	+	0.719164i	$0.744525\pi$
$912$		0			0
$913$	−180.000	+	103.923i	−0.197152	+	0.113826i
$914$		0			0
$915$	211.500	+	122.110i	0.231148	+	0.133453i
$916$		0			0
$917$	−598.500	−	345.544i	−0.652672	−	0.376820i
$918$		0			0
$919$	−236.500	+	409.630i	−0.257345	+	0.445735i	−0.965530	−	0.260293i	$-0.916181\pi$
$919$	−236.500	+	409.630i	−0.257345	+	0.445735i	0.708185	+	0.706027i	$0.249514\pi$
$920$		0			0
$921$	84.0000	+	145.492i	0.0912052	+	0.157972i
$922$		0			0
$923$			1745.91i			1.89156i
$924$		0			0
$925$	682.000			0.737297
$926$		0			0
$927$	369.000	−	213.042i	0.398058	−	0.229819i
$928$		0			0
$929$	289.500	+	167.143i	0.311625	+	0.179917i	0.647654	−	0.761935i	$-0.275750\pi$
$929$	289.500	+	167.143i	0.311625	+	0.179917i	−0.336028	+	0.941852i	$0.609084\pi$
$930$		0			0
$931$	−661.500	−	381.917i	−0.710526	−	0.410223i
$932$		0			0
$933$	421.500	−	730.059i	0.451768	−	0.782486i
$934$		0			0
$935$	382.500	+	662.509i	0.409091	+	0.708566i
$936$		0			0
$937$			859.097i			0.916859i	0.888731	+	0.458430i	$0.151588\pi$
$937$			859.097i			0.916859i	−0.888731	+	0.458430i	$0.848412\pi$
$938$		0			0
$939$	−387.000			−0.412141
$940$		0			0
$941$	−106.500	+	61.4878i	−0.113177	+	0.0653430i	−0.555520	−	0.831503i	$-0.687481\pi$
$941$	−106.500	+	61.4878i	−0.113177	+	0.0653430i	0.442343	+	0.896846i	$0.354147\pi$
$942$		0			0
$943$	432.000	+	249.415i	0.458112	+	0.264491i
$944$		0			0
$945$	157.500	−	272.798i	0.166667	−	0.288675i
$946$		0			0
$947$	−100.500	+	174.071i	−0.106125	+	0.183813i	−0.914197	−	0.405270i	$-0.867178\pi$
$947$	−100.500	+	174.071i	−0.106125	+	0.183813i	0.808073	+	0.589083i	$0.200511\pi$
$948$		0			0
$949$	−180.000	−	311.769i	−0.189673	−	0.328524i
$950$		0			0
$951$		−	774.227i		−	0.814119i
$952$		0			0
$953$	66.0000			0.0692550			0.0346275	−	0.999400i	$-0.488976\pi$
$953$	66.0000			0.0692550			0.0346275	+	0.999400i	$0.488976\pi$
$954$		0			0
$955$	−85.5000	+	49.3634i	−0.0895288	+	0.0516895i
$956$		0			0
$957$	135.000	+	77.9423i	0.141066	+	0.0814444i
$958$		0			0
$959$	−220.500	−	381.917i	−0.229927	−	0.398245i
$960$		0			0
$961$	−407.000	+	704.945i	−0.423517	+	0.733553i
$962$		0			0
$963$	117.000	+	202.650i	0.121495	+	0.210436i
$964$		0			0
$965$			361.999i			0.375128i
$966$		0			0
$967$	−194.000			−0.200620			−0.100310	−	0.994956i	$-0.531984\pi$
$967$	−194.000			−0.200620			−0.100310	+	0.994956i	$0.531984\pi$
$968$		0			0
$969$	688.500	−	397.506i	0.710526	−	0.410223i
$970$		0			0
$971$	−1285.50	−	742.184i	−1.32389	−	0.764350i	−0.339546	−	0.940590i	$-0.610273\pi$
$971$	−1285.50	−	742.184i	−1.32389	−	0.764350i	−0.984347	+	0.176240i	$0.943607\pi$
$972$		0			0
$973$		−	1648.91i		−	1.69467i
$974$		0			0
$975$	−264.000	+	457.261i	−0.270769	+	0.468986i
$976$		0			0
$977$	760.500	+	1317.22i	0.778403	+	1.34823i	0.932862	+	0.360235i	$0.117303\pi$
$977$	760.500	+	1317.22i	0.778403	+	1.34823i	−0.154458	+	0.987999i	$0.549363\pi$
$978$		0			0
$979$			857.365i			0.875756i
$980$		0			0
$981$	618.000			0.629969
$982$		0			0
$983$	−973.500	+	562.050i	−0.990336	+	0.571771i	−0.905375	−	0.424614i	$-0.860410\pi$
$983$	−973.500	+	562.050i	−0.990336	+	0.571771i	−0.0849611	+	0.996384i	$0.527077\pi$
$984$		0			0
$985$	−225.000	−	129.904i	−0.228426	−	0.131882i
$986$		0			0
$987$	525.000			0.531915
$988$		0			0
$989$	45.0000	−	77.9423i	0.0455005	−	0.0788092i
$990$		0			0
$991$	411.500	+	712.739i	0.415237	+	0.719212i	0.995453	−	0.0952507i	$-0.0303653\pi$
$991$	411.500	+	712.739i	0.415237	+	0.719212i	−0.580216	+	0.814463i	$0.697032\pi$
$992$		0			0
$993$			261.540i			0.263383i
$994$		0			0
$995$	357.000			0.358794
$996$		0			0
$997$	109.500	−	63.2199i	0.109829	−	0.0634101i	−0.444079	−	0.895988i	$-0.646469\pi$
$997$	109.500	−	63.2199i	0.109829	−	0.0634101i	0.553909	+	0.832578i	$0.313136\pi$
$998$		0			0
$999$	697.500	+	402.702i	0.698198	+	0.403105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.s.a.33.1		2
3.2	odd	2		1008.3.cg.c.145.1		2
4.3	odd	2		28.3.h.a.5.1	✓	2
7.2	even	3		784.3.c.a.97.1		2
7.3	odd	6	inner	112.3.s.a.17.1		2
7.4	even	3		784.3.s.b.129.1		2
7.5	odd	6		784.3.c.a.97.2		2
7.6	odd	2		784.3.s.b.705.1		2
8.3	odd	2		448.3.s.a.257.1		2
8.5	even	2		448.3.s.b.257.1		2
12.11	even	2		252.3.z.a.145.1		2
20.3	even	4		700.3.o.a.649.2		4
20.7	even	4		700.3.o.a.649.1		4
20.19	odd	2		700.3.s.a.201.1		2
21.17	even	6		1008.3.cg.c.577.1		2
28.3	even	6		28.3.h.a.17.1	yes	2
28.11	odd	6		196.3.h.a.129.1		2
28.19	even	6		196.3.b.a.97.1		2
28.23	odd	6		196.3.b.a.97.2		2
28.27	even	2		196.3.h.a.117.1		2
56.3	even	6		448.3.s.a.129.1		2
56.45	odd	6		448.3.s.b.129.1		2
84.11	even	6		1764.3.z.f.325.1		2
84.23	even	6		1764.3.d.a.685.2		2
84.47	odd	6		1764.3.d.a.685.1		2
84.59	odd	6		252.3.z.a.73.1		2
84.83	odd	2		1764.3.z.f.901.1		2
140.3	odd	12		700.3.o.a.549.1		4
140.59	even	6		700.3.s.a.101.1		2
140.87	odd	12		700.3.o.a.549.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.h.a.5.1	✓	2	4.3	odd	2
28.3.h.a.17.1	yes	2	28.3	even	6
112.3.s.a.17.1		2	7.3	odd	6	inner
112.3.s.a.33.1		2	1.1	even	1	trivial
196.3.b.a.97.1		2	28.19	even	6
196.3.b.a.97.2		2	28.23	odd	6
196.3.h.a.117.1		2	28.27	even	2
196.3.h.a.129.1		2	28.11	odd	6
252.3.z.a.73.1		2	84.59	odd	6
252.3.z.a.145.1		2	12.11	even	2
448.3.s.a.129.1		2	56.3	even	6
448.3.s.a.257.1		2	8.3	odd	2
448.3.s.b.129.1		2	56.45	odd	6
448.3.s.b.257.1		2	8.5	even	2
700.3.o.a.549.1		4	140.3	odd	12
700.3.o.a.549.2		4	140.87	odd	12
700.3.o.a.649.1		4	20.7	even	4
700.3.o.a.649.2		4	20.3	even	4
700.3.s.a.101.1		2	140.59	even	6
700.3.s.a.201.1		2	20.19	odd	2
784.3.c.a.97.1		2	7.2	even	3
784.3.c.a.97.2		2	7.5	odd	6
784.3.s.b.129.1		2	7.4	even	3
784.3.s.b.705.1		2	7.6	odd	2
1008.3.cg.c.145.1		2	3.2	odd	2
1008.3.cg.c.577.1		2	21.17	even	6
1764.3.d.a.685.1		2	84.47	odd	6
1764.3.d.a.685.2		2	84.23	even	6
1764.3.z.f.325.1		2	84.11	even	6
1764.3.z.f.901.1		2	84.83	odd	2

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:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +(1.50000 + 0.866025i) q^{5} +7.00000 q^{7} +(-3.00000 + 5.19615i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +(1.50000 + 0.866025i) q^{5} +7.00000 q^{7} +(-3.00000 + 5.19615i) q^{9} +(7.50000 + 12.9904i) q^{11} +13.8564i q^{13} -3.00000 q^{15} +(25.5000 - 14.7224i) q^{17} +(-13.5000 - 7.79423i) q^{19} +(-10.5000 + 6.06218i) q^{21} +(-4.50000 + 7.79423i) q^{23} +(-11.0000 - 19.0526i) q^{25} -25.9808i q^{27} -6.00000 q^{29} +(10.5000 - 6.06218i) q^{31} +(-22.5000 - 12.9904i) q^{33} +(10.5000 + 6.06218i) q^{35} +(-15.5000 + 26.8468i) q^{37} +(-12.0000 - 20.7846i) q^{39} -55.4256i q^{41} -10.0000 q^{43} +(-9.00000 + 5.19615i) q^{45} +(-37.5000 - 21.6506i) q^{47} +49.0000 q^{49} +(-25.5000 + 44.1673i) q^{51} +(28.5000 + 49.3634i) q^{53} +25.9808i q^{55} +27.0000 q^{57} +(70.5000 - 40.7032i) q^{59} +(-70.5000 - 40.7032i) q^{61} +(-21.0000 + 36.3731i) q^{63} +(-12.0000 + 20.7846i) q^{65} +(-24.5000 - 42.4352i) q^{67} -15.5885i q^{69} +126.000 q^{71} +(-22.5000 + 12.9904i) q^{73} +(33.0000 + 19.0526i) q^{75} +(52.5000 + 90.9327i) q^{77} +(-36.5000 + 63.2199i) q^{79} +(-4.50000 - 7.79423i) q^{81} +13.8564i q^{83} +51.0000 q^{85} +(9.00000 - 5.19615i) q^{87} +(49.5000 + 28.5788i) q^{89} +96.9948i q^{91} +(-10.5000 + 18.1865i) q^{93} +(-13.5000 - 23.3827i) q^{95} +27.7128i q^{97} -90.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 3 q^{5} + 14 q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 3 * q^5 + 14 * q^7 - 6 * q^9	\( 2 q - 3 q^{3} + 3 q^{5} + 14 q^{7} - 6 q^{9} + 15 q^{11} - 6 q^{15} + 51 q^{17} - 27 q^{19} - 21 q^{21} - 9 q^{23} - 22 q^{25} - 12 q^{29} + 21 q^{31} - 45 q^{33} + 21 q^{35} - 31 q^{37} - 24 q^{39} - 20 q^{43} - 18 q^{45} - 75 q^{47} + 98 q^{49} - 51 q^{51} + 57 q^{53} + 54 q^{57} + 141 q^{59} - 141 q^{61} - 42 q^{63} - 24 q^{65} - 49 q^{67} + 252 q^{71} - 45 q^{73} + 66 q^{75} + 105 q^{77} - 73 q^{79} - 9 q^{81} + 102 q^{85} + 18 q^{87} + 99 q^{89} - 21 q^{93} - 27 q^{95} - 180 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 3 * q^5 + 14 * q^7 - 6 * q^9 + 15 * q^11 - 6 * q^15 + 51 * q^17 - 27 * q^19 - 21 * q^21 - 9 * q^23 - 22 * q^25 - 12 * q^29 + 21 * q^31 - 45 * q^33 + 21 * q^35 - 31 * q^37 - 24 * q^39 - 20 * q^43 - 18 * q^45 - 75 * q^47 + 98 * q^49 - 51 * q^51 + 57 * q^53 + 54 * q^57 + 141 * q^59 - 141 * q^61 - 42 * q^63 - 24 * q^65 - 49 * q^67 + 252 * q^71 - 45 * q^73 + 66 * q^75 + 105 * q^77 - 73 * q^79 - 9 * q^81 + 102 * q^85 + 18 * q^87 + 99 * q^89 - 21 * q^93 - 27 * q^95 - 180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more