LMFDB - Embedded newform 112.3.s.a.17.1

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			17.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	112.17
Dual form			112.3.s.a.33.1

$q$-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 $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

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

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	0.228714	−	0.973494i	$-0.426548\pi$
$3$	−1.50000	−	0.866025i	−0.500000	−	0.288675i	−0.728714	+	0.684819i	$0.759881\pi$
$4$		0			0
$5$	1.50000	−	0.866025i	0.300000	−	0.173205i	−0.342443	−	0.939539i	$-0.611254\pi$
$5$	1.50000	−	0.866025i	0.300000	−	0.173205i	0.642443	+	0.766334i	$0.277921\pi$
$6$		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	−0.292607	−	0.956233i	$-0.594523\pi$
$11$	7.50000	−	12.9904i	0.681818	−	1.18094i	0.974425	−	0.224711i	$-0.0721438\pi$
$12$		0			0
$13$		−	13.8564i		−	1.06588i	−0.846154	−	0.532939i	$-0.821088\pi$
$13$		−	13.8564i		−	1.06588i	0.846154	−	0.532939i	$-0.178912\pi$
$14$		0			0
$15$	−3.00000			−0.200000
$16$		0			0
$17$	25.5000	+	14.7224i	1.50000	+	0.866025i	1.00000			$0$
$17$	25.5000	+	14.7224i	1.50000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$18$		0			0
$19$	−13.5000	+	7.79423i	−0.710526	+	0.410223i	−0.811256	−	0.584691i	$-0.801216\pi$
$19$	−13.5000	+	7.79423i	−0.710526	+	0.410223i	0.100730	+	0.994914i	$0.467882\pi$
$20$		0			0
$21$	−10.5000	−	6.06218i	−0.500000	−	0.288675i
$22$		0			0
$23$	−4.50000	−	7.79423i	−0.195652	−	0.338880i	0.751462	−	0.659776i	$-0.229349\pi$
$23$	−4.50000	−	7.79423i	−0.195652	−	0.338880i	−0.947114	+	0.320897i	$0.896016\pi$
$24$		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	0.659701	−	0.751528i	$-0.270683\pi$
$31$	10.5000	+	6.06218i	0.338710	+	0.195554i	−0.320992	+	0.947082i	$0.604016\pi$
$32$		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	0.576912	−	0.816806i	$-0.304258\pi$
$37$	−15.5000	−	26.8468i	−0.418919	−	0.725589i	−0.995831	+	0.0912174i	$0.970924\pi$
$38$		0			0
$39$	−12.0000	+	20.7846i	−0.307692	+	0.532939i
$40$		0			0
$41$			55.4256i			1.35184i	0.736973	+	0.675922i	$0.236255\pi$
$41$			55.4256i			1.35184i	−0.736973	+	0.675922i	$0.763745\pi$
$42$		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	−0.842727	−	0.538342i	$-0.819051\pi$
$47$	−37.5000	+	21.6506i	−0.797872	+	0.460652i	0.0448543	+	0.998994i	$0.485718\pi$
$48$		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	−0.461290	−	0.887250i	$-0.652613\pi$
$53$	28.5000	−	49.3634i	0.537736	−	0.931386i	0.999026	−	0.0441362i	$-0.0140536\pi$
$54$		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	0.959417	−	0.281990i	$-0.0909946\pi$
$59$	70.5000	+	40.7032i	1.19492	+	0.689885i	0.235498	+	0.971875i	$0.424328\pi$
$60$		0			0
$61$	−70.5000	+	40.7032i	−1.15574	+	0.667265i	−0.950279	−	0.311400i	$-0.899202\pi$
$61$	−70.5000	+	40.7032i	−1.15574	+	0.667265i	−0.205459	+	0.978666i	$0.565869\pi$
$62$		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	−0.988884	−	0.148691i	$-0.952494\pi$
$67$	−24.5000	+	42.4352i	−0.365672	+	0.633362i	0.623212	+	0.782053i	$0.285827\pi$
$68$		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	0.337910	−	0.941178i	$-0.390280\pi$
$73$	−22.5000	−	12.9904i	−0.308219	−	0.177950i	−0.646129	+	0.763228i	$0.723613\pi$
$74$		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	0.537036	−	0.843559i	$-0.319544\pi$
$79$	−36.5000	−	63.2199i	−0.462025	−	0.800251i	−0.999062	+	0.0433077i	$0.986210\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$		0			0
$83$		−	13.8564i		−	0.166945i	−0.996510	−	0.0834723i	$-0.973399\pi$
$83$		−	13.8564i		−	0.166945i	0.996510	−	0.0834723i	$-0.0266010\pi$
$84$		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	−0.195431	−	0.980717i	$-0.562611\pi$
$89$	49.5000	−	28.5788i	0.556180	−	0.321111i	0.751611	+	0.659607i	$0.229277\pi$
$90$		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	$-0.954373\pi$
$97$		−	27.7128i		−	0.285699i	0.989744	−	0.142850i	$-0.0456265\pi$
$98$		0			0
$99$	−90.0000			−0.909091
$100$		0			0
$101$	85.5000	+	49.3634i	0.846535	+	0.488747i	0.859480	−	0.511169i	$-0.170787\pi$
$101$	85.5000	+	49.3634i	0.846535	+	0.488747i	−0.0129455	+	0.999916i	$0.504121\pi$
$102$		0			0
$103$	−61.5000	+	35.5070i	−0.597087	+	0.344729i	−0.767895	−	0.640576i	$-0.778696\pi$
$103$	−61.5000	+	35.5070i	−0.597087	+	0.344729i	0.170808	+	0.985304i	$0.445362\pi$
$104$		0			0
$105$	−21.0000			−0.200000
$106$		0			0
$107$	19.5000	+	33.7750i	0.182243	+	0.315654i	0.942644	−	0.333800i	$-0.108331\pi$
$107$	19.5000	+	33.7750i	0.182243	+	0.315654i	−0.760401	+	0.649454i	$0.774998\pi$
$108$		0			0
$109$	−51.5000	+	89.2006i	−0.472477	+	0.818354i	−0.999504	−	0.0314943i	$-0.989973\pi$
$109$	−51.5000	+	89.2006i	−0.472477	+	0.818354i	0.527027	+	0.849849i	$0.323307\pi$
$110$		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	−0.789479	−	0.613777i	$-0.789649\pi$
$131$	−85.5000	+	49.3634i	−0.652672	+	0.376820i	0.136807	+	0.990598i	$0.456316\pi$
$132$		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	−0.957786	−	0.287481i	$-0.907182\pi$
$137$	−31.5000	+	54.5596i	−0.229927	+	0.398245i	0.727859	+	0.685727i	$0.240515\pi$
$138$		0			0
$139$			235.559i			1.69467i	0.531060	+	0.847334i	$0.321794\pi$
$139$			235.559i			1.69467i	−0.531060	+	0.847334i	$0.678206\pi$
$140$		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	0.993693	+	0.112137i	$0.0357695\pi$
$149$	88.5000	+	153.286i	0.593960	+	1.02877i	−0.399733	+	0.916632i	$0.630897\pi$
$150$		0			0
$151$	27.5000	−	47.6314i	0.182119	−	0.315440i	−0.760483	−	0.649358i	$-0.775038\pi$
$151$	27.5000	−	47.6314i	0.182119	−	0.315440i	0.942602	+	0.333918i	$0.108371\pi$
$152$		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	0.746935	−	0.664897i	$-0.231524\pi$
$157$	85.5000	+	49.3634i	0.544586	+	0.314417i	−0.202350	+	0.979313i	$0.564858\pi$
$158$		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	0.899143	−	0.437654i	$-0.144191\pi$
$163$	11.5000	+	19.9186i	0.0705521	+	0.122200i	−0.828591	+	0.559854i	$0.810857\pi$
$164$		0			0
$165$	−22.5000	+	38.9711i	−0.136364	+	0.236189i
$166$		0			0
$167$		−	277.128i		−	1.65945i	−0.558172	−	0.829725i	$-0.688497\pi$
$167$		−	277.128i		−	1.65945i	0.558172	−	0.829725i	$-0.311503\pi$
$168$		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	−0.105896	−	0.994377i	$-0.533771\pi$
$173$	121.500	−	70.1481i	0.702312	−	0.405480i	0.808208	+	0.588897i	$0.200438\pi$
$174$		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	−0.764522	−	0.644598i	$-0.777025\pi$
$179$	31.5000	−	54.5596i	0.175978	−	0.304802i	0.940499	+	0.339796i	$0.110358\pi$
$180$		0			0
$181$		−	124.708i		−	0.688993i	−0.938788	−	0.344496i	$-0.888050\pi$
$181$		−	124.708i		−	0.688993i	0.938788	−	0.344496i	$-0.111950\pi$
$182$		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	0.781723	−	0.623626i	$-0.214341\pi$
$191$	−28.5000	−	49.3634i	−0.149215	−	0.258447i	−0.930937	+	0.365179i	$0.881008\pi$
$192$		0			0
$193$	104.500	−	180.999i	0.541451	−	0.937820i	−0.457370	−	0.889276i	$-0.651209\pi$
$193$	104.500	−	180.999i	0.541451	−	0.937820i	0.998821	−	0.0485439i	$-0.0154581\pi$
$194$		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	0.876221	−	0.481910i	$-0.160057\pi$
$199$	178.500	+	103.057i	0.896985	+	0.517874i	0.0207642	+	0.999784i	$0.493390\pi$
$200$		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	$-0.732146\pi$
$223$		−	332.554i		−	1.49127i	0.666353	−	0.745636i	$-0.267854\pi$
$224$		0			0
$225$	132.000			0.586667
$226$		0			0
$227$	−121.500	−	70.1481i	−0.535242	−	0.309022i	0.207906	−	0.978149i	$-0.433335\pi$
$227$	−121.500	−	70.1481i	−0.535242	−	0.309022i	−0.743149	+	0.669126i	$0.766668\pi$
$228$		0			0
$229$	145.500	−	84.0045i	0.635371	−	0.366832i	−0.147458	−	0.989068i	$-0.547109\pi$
$229$	145.500	−	84.0045i	0.635371	−	0.366832i	0.782829	+	0.622237i	$0.213776\pi$
$230$		0			0
$231$	−157.500	+	90.9327i	−0.681818	+	0.393648i
$232$		0			0
$233$	136.500	+	236.425i	0.585837	+	1.01470i	0.994771	+	0.102135i	$0.0325674\pi$
$233$	136.500	+	236.425i	0.585837	+	1.01470i	−0.408934	+	0.912564i	$0.634099\pi$
$234$		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	0.0496668	−	0.998766i	$-0.484184\pi$
$241$	−190.500	−	109.985i	−0.790456	−	0.456370i	−0.840123	+	0.542396i	$0.817517\pi$
$242$		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	$0.0618921\pi$
$251$			96.9948i			0.386434i	−0.981156	+	0.193217i	$0.938108\pi$
$252$		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	−0.787636	−	0.616141i	$-0.788695\pi$
$257$	−166.500	+	96.1288i	−0.647860	+	0.374042i	0.139776	+	0.990183i	$0.455362\pi$
$258$		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	−0.974017	−	0.226476i	$-0.927280\pi$
$263$	−76.5000	+	132.502i	−0.290875	+	0.503809i	0.683142	+	0.730285i	$0.260613\pi$
$264$		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	−0.467243	−	0.884129i	$-0.654753\pi$
$269$	−394.500	−	227.765i	−1.46654	−	0.846709i	−0.999300	+	0.0374200i	$0.988086\pi$
$270$		0			0
$271$	−61.5000	+	35.5070i	−0.226937	+	0.131022i	−0.609158	−	0.793049i	$-0.708493\pi$
$271$	−61.5000	+	35.5070i	−0.226937	+	0.131022i	0.382221	+	0.924071i	$0.375159\pi$
$272$		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	0.335582	+	0.942011i	$0.391067\pi$
$277$	−179.500	+	310.903i	−0.648014	+	1.12239i	−0.983596	+	0.180383i	$0.942266\pi$
$278$		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	0.497347	−	0.867551i	$-0.334307\pi$
$283$	−1.50000	−	0.866025i	−0.00530035	−	0.00306016i	−0.502648	+	0.864491i	$0.667641\pi$
$284$		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	$-0.868323\pi$
$293$		−	235.559i		−	0.803955i	0.915649	−	0.401978i	$-0.131677\pi$
$294$		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	$0.0504956\pi$
$307$			96.9948i			0.315944i	−0.987444	+	0.157972i	$0.949504\pi$
$308$		0			0
$309$	123.000			0.398058
$310$		0			0
$311$	−421.500	−	243.353i	−1.35531	−	0.782486i	−0.366319	−	0.930489i	$-0.619382\pi$
$311$	−421.500	−	243.353i	−1.35531	−	0.782486i	−0.988987	+	0.148003i	$0.952715\pi$
$312$		0			0
$313$	193.500	−	111.717i	0.618211	−	0.356924i	−0.157961	−	0.987445i	$-0.550492\pi$
$313$	193.500	−	111.717i	0.618211	−	0.356924i	0.776172	+	0.630521i	$0.217159\pi$
$314$		0			0
$315$	−63.0000	−	36.3731i	−0.200000	−	0.115470i
$316$		0			0
$317$	−223.500	−	387.113i	−0.705047	−	1.22118i	−0.966674	−	0.256009i	$-0.917592\pi$
$317$	−223.500	−	387.113i	−0.705047	−	1.22118i	0.261627	−	0.965169i	$-0.415741\pi$
$318$		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	0.957244	−	0.289282i	$-0.0934164\pi$
$331$	75.5000	+	130.770i	0.228097	+	0.395075i	−0.729147	+	0.684357i	$0.760083\pi$
$332$		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	−0.148107	−	0.988971i	$-0.547318\pi$
$347$	271.500	−	470.252i	0.782421	−	1.35519i	0.930528	−	0.366221i	$-0.119349\pi$
$348$		0			0
$349$		−	180.133i		−	0.516141i	−0.966126	−	0.258071i	$-0.916913\pi$
$349$		−	180.133i		−	0.516141i	0.966126	−	0.258071i	$-0.0830867\pi$
$350$		0			0
$351$	360.000			1.02564
$352$		0			0
$353$	−262.500	−	151.554i	−0.743626	−	0.429333i	0.0797602	−	0.996814i	$-0.474585\pi$
$353$	−262.500	−	151.554i	−0.743626	−	0.429333i	−0.823386	+	0.567481i	$0.807918\pi$
$354$		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	0.891906	−	0.452221i	$-0.149368\pi$
$359$	19.5000	+	33.7750i	0.0543175	+	0.0940808i	−0.837588	+	0.546302i	$0.816035\pi$
$360$		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	0.0294165	−	0.999567i	$-0.490635\pi$
$367$	−301.500	−	174.071i	−0.821526	−	0.474308i	−0.850942	+	0.525259i	$0.823968\pi$
$368$		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	−0.999879	−	0.0155484i	$-0.995051\pi$
$373$	−191.500	−	331.688i	−0.513405	−	0.889243i	0.486474	−	0.873695i	$-0.338283\pi$
$374$		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	−0.816423	−	0.577455i	$-0.804046\pi$
$383$	−277.500	+	160.215i	−0.724543	+	0.418315i	0.0918794	+	0.995770i	$0.470713\pi$
$384$		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	−0.707447	−	0.706767i	$-0.750153\pi$
$389$	100.500	−	174.071i	0.258355	−	0.447484i	0.965801	+	0.259283i	$0.0834863\pi$
$390$		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	−0.557420	−	0.830231i	$-0.688209\pi$
$397$	−46.5000	+	26.8468i	−0.117128	+	0.0676241i	0.440291	+	0.897855i	$0.354875\pi$
$398$		0			0
$399$	189.000			0.473684
$400$		0			0
$401$	88.5000	+	153.286i	0.220698	+	0.382261i	0.955020	−	0.296541i	$-0.0958331\pi$
$401$	88.5000	+	153.286i	0.220698	+	0.382261i	−0.734322	+	0.678801i	$0.762500\pi$
$402$		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	0.810255	−	0.586078i	$-0.199329\pi$
$409$	289.500	+	167.143i	0.707824	+	0.408662i	−0.102431	+	0.994740i	$0.532662\pi$
$410$		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	$0.251761\pi$
$419$			595.825i			1.42202i	−0.703183	+	0.711009i	$0.748239\pi$
$420$		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	−0.611618	−	0.791154i	$-0.709481\pi$
$431$	163.500	−	283.190i	0.379350	−	0.657054i	0.990968	+	0.134100i	$0.0428142\pi$
$432$		0			0
$433$		−	27.7128i		−	0.0640019i	−0.999488	−	0.0320009i	$-0.989812\pi$
$433$		−	27.7128i		−	0.0640019i	0.999488	−	0.0320009i	$-0.0101880\pi$
$434$		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	−0.955740	−	0.294212i	$-0.904943\pi$
$439$	−517.500	+	298.779i	−1.17882	+	0.680589i	−0.223075	+	0.974801i	$0.571610\pi$
$440$		0			0
$441$	−147.000	−	254.611i	−0.333333	−	0.577350i
$442$		0			0
$443$	−364.500	−	631.333i	−0.822799	−	1.42513i	−0.903590	−	0.428399i	$-0.859078\pi$
$443$	−364.500	−	631.333i	−0.822799	−	1.42513i	0.0807907	−	0.996731i	$-0.474255\pi$
$444$		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	−0.857634	−	0.514260i	$-0.828067\pi$
$457$	−399.500	−	691.954i	−0.874179	−	1.51412i	−0.0165451	−	0.999863i	$-0.505267\pi$
$458$		0			0
$459$	−382.500	+	662.509i	−0.833333	+	1.44338i
$460$		0			0
$461$			429.549i			0.931776i	0.884844	+	0.465888i	$0.154265\pi$
$461$			429.549i			0.931776i	−0.884844	+	0.465888i	$0.845735\pi$
$462$		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	−0.0808151	−	0.996729i	$-0.525752\pi$
$467$	346.500	−	200.052i	0.741970	−	0.428377i	0.822785	+	0.568353i	$0.192419\pi$
$468$		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	0.900424	−	0.435013i	$-0.143256\pi$
$479$	466.500	+	269.334i	0.973904	+	0.562284i	0.0734798	+	0.997297i	$0.476590\pi$
$480$		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	−0.0284015	+	0.999597i	$0.509042\pi$
$487$	−428.500	+	742.184i	−0.879877	+	1.52399i	−0.851475	+	0.524395i	$0.824292\pi$
$488$		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	0.570648	−	0.821195i	$-0.306692\pi$
$499$	−212.500	−	368.061i	−0.425852	−	0.737597i	−0.996500	+	0.0835981i	$0.973359\pi$
$500$		0			0
$501$	−240.000	+	415.692i	−0.479042	+	0.829725i
$502$		0			0
$503$			193.990i			0.385665i	0.981232	+	0.192833i	$0.0617675\pi$
$503$			193.990i			0.385665i	−0.981232	+	0.192833i	$0.938233\pi$
$504$		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	−0.791198	−	0.611560i	$-0.790542\pi$
$509$	−334.500	+	193.124i	−0.657171	+	0.379418i	0.134027	+	0.990978i	$0.457209\pi$
$510$		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	0.279815	−	0.960054i	$-0.409727\pi$
$521$	−214.500	−	123.842i	−0.411708	−	0.237700i	−0.691523	+	0.722354i	$0.743060\pi$
$522$		0			0
$523$	−685.500	+	395.774i	−1.31071	+	0.756737i	−0.982213	−	0.187769i	$-0.939874\pi$
$523$	−685.500	+	395.774i	−1.31071	+	0.756737i	−0.328494	+	0.944506i	$0.606541\pi$
$524$		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	0.978915	+	0.204268i	$0.0654813\pi$
$541$	360.500	+	624.404i	0.666359	+	1.15417i	−0.312556	+	0.949899i	$0.601185\pi$
$542$		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	−0.428519	−	0.903533i	$-0.640965\pi$
$557$	316.500	−	548.194i	0.568223	−	0.984190i	0.996742	−	0.0806578i	$-0.0257021\pi$
$558$		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	0.696626	−	0.717434i	$-0.254684\pi$
$563$	238.500	+	137.698i	0.423623	+	0.244579i	−0.273003	+	0.962013i	$0.588017\pi$
$564$		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	0.600023	−	0.799983i	$-0.295158\pi$
$569$	−223.500	−	387.113i	−0.392794	−	0.680340i	−0.992817	+	0.119643i	$0.961825\pi$
$570$		0			0
$571$	263.500	−	456.395i	0.461471	−	0.799291i	−0.537563	−	0.843223i	$-0.680655\pi$
$571$	263.500	−	456.395i	0.461471	−	0.799291i	0.999035	+	0.0439319i	$0.0139885\pi$
$572$		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	0.620756	−	0.784004i	$-0.286826\pi$
$577$	145.500	+	84.0045i	0.252166	+	0.145588i	−0.368589	+	0.929592i	$0.620159\pi$
$578$		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	$0.302927\pi$
$587$			956.092i			1.62878i	−0.580320	+	0.814388i	$0.697073\pi$
$588$		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	−0.704727	−	0.709478i	$-0.748931\pi$
$593$	−262.500	+	151.554i	−0.442664	+	0.255572i	0.262063	+	0.965051i	$0.415597\pi$
$594$		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	−0.303247	−	0.952912i	$-0.598071\pi$
$599$	403.500	−	698.883i	0.673623	−	1.16675i	0.976869	−	0.213837i	$-0.0685960\pi$
$600$		0			0
$601$		−	387.979i		−	0.645556i	−0.946475	−	0.322778i	$-0.895383\pi$
$601$		−	387.979i		−	0.645556i	0.946475	−	0.322778i	$-0.104617\pi$
$602$		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	0.123974	−	0.992286i	$-0.460436\pi$
$607$	634.500	−	366.329i	1.04530	−	0.603507i	0.921331	+	0.388779i	$0.127103\pi$
$608$		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	−0.994920	−	0.100670i	$-0.967901\pi$
$613$	−251.500	+	435.611i	−0.410277	+	0.710621i	0.584643	+	0.811291i	$0.301235\pi$
$614$		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	0.0826450	−	0.996579i	$-0.473663\pi$
$619$	−457.500	−	264.138i	−0.739095	−	0.426717i	−0.821740	+	0.569862i	$0.806997\pi$
$620$		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	−0.852868	−	0.522127i	$-0.825139\pi$
$641$	16.5000	−	28.5788i	0.0257410	−	0.0445848i	0.878609	+	0.477542i	$0.158472\pi$
$642$		0			0
$643$		−	346.410i		−	0.538741i	−0.963037	−	0.269370i	$-0.913184\pi$
$643$		−	346.410i		−	0.538741i	0.963037	−	0.269370i	$-0.0868155\pi$
$644$		0			0
$645$	30.0000			0.0465116
$646$		0			0
$647$	−661.500	−	381.917i	−1.02241	−	0.590289i	−0.107610	−	0.994193i	$-0.534320\pi$
$647$	−661.500	−	381.917i	−1.02241	−	0.590289i	−0.914801	+	0.403904i	$0.867653\pi$
$648$		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	0.878383	−	0.477958i	$-0.158623\pi$
$653$	16.5000	+	28.5788i	0.0252680	+	0.0437654i	−0.853115	+	0.521723i	$0.825289\pi$
$654$		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	0.984918	−	0.173023i	$-0.0553536\pi$
$661$	877.500	+	506.625i	1.32753	+	0.766452i	0.342616	+	0.939475i	$0.388687\pi$
$662$		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	−0.665693	−	0.746226i	$-0.731864\pi$
$677$	−238.500	+	137.698i	−0.352290	+	0.203394i	0.313404	+	0.949620i	$0.398531\pi$
$678$		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	−0.948481	−	0.316835i	$-0.897380\pi$
$683$	−136.500	+	236.425i	−0.199854	+	0.346157i	0.748627	+	0.662991i	$0.230713\pi$
$684$		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	−0.593479	−	0.804850i	$-0.702246\pi$
$691$	−133.500	+	77.0763i	−0.193198	+	0.111543i	0.400281	+	0.916393i	$0.368913\pi$
$692$		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	0.504219	−	0.863576i	$-0.331780\pi$
$709$	−351.500	−	608.816i	−0.495769	−	0.858697i	−0.999988	+	0.00487903i	$0.998447\pi$
$710$		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	−0.0975455	−	0.995231i	$-0.531099\pi$
$719$	514.500	−	297.047i	0.715577	−	0.413139i	0.813123	+	0.582092i	$0.197766\pi$
$720$		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	$0.00606726\pi$
$727$			27.7128i			0.0381194i	−0.999818	+	0.0190597i	$0.993933\pi$
$728$		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	−0.947401	−	0.320050i	$-0.896300\pi$
$733$	−838.500	+	484.108i	−1.14393	+	0.660448i	−0.196529	+	0.980498i	$0.562967\pi$
$734$		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	−0.992501	−	0.122235i	$-0.960994\pi$
$739$	−288.500	+	499.697i	−0.390392	+	0.676180i	0.602109	+	0.798414i	$0.294327\pi$
$740$		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	0.999828	+	0.0185499i	$0.00590497\pi$
$751$	387.500	+	671.170i	0.515979	+	0.893701i	−0.483849	+	0.875151i	$0.660762\pi$
$752$		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	−0.384482	−	0.923133i	$-0.625620\pi$
$761$	169.500	−	97.8609i	0.222733	−	0.128595i	0.607215	+	0.794537i	$0.292287\pi$
$762$		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	$0.202697\pi$
$769$			914.523i			1.18924i	−0.804008	+	0.594618i	$0.797303\pi$
$770$		0			0
$771$	333.000			0.431907
$772$		0			0
$773$	−154.500	−	89.2006i	−0.199871	−	0.115395i	0.396725	−	0.917938i	$-0.370147\pi$
$773$	−154.500	−	89.2006i	−0.199871	−	0.115395i	−0.596595	+	0.802542i	$0.703480\pi$
$774$		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	0.304667	−	0.952459i	$-0.401455\pi$
$787$	−289.500	−	167.143i	−0.367853	−	0.212380i	−0.672520	+	0.740079i	$0.734788\pi$
$788$		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	$0.184477\pi$
$797$			872.954i			1.09530i	−0.836708	+	0.547650i	$0.815523\pi$
$798$		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	−0.685795	−	0.727795i	$-0.740545\pi$
$809$	232.500	−	402.702i	0.287392	−	0.497777i	0.973186	+	0.230018i	$0.0738785\pi$
$810$		0			0
$811$			124.708i			0.153770i	0.997040	+	0.0768851i	$0.0244975\pi$
$811$			124.708i			0.153770i	−0.997040	+	0.0768851i	$0.975503\pi$
$812$		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	0.998887	−	0.0471767i	$-0.0150224\pi$
$821$	376.500	+	652.117i	0.458587	+	0.794296i	−0.540299	+	0.841473i	$0.681689\pi$
$822$		0			0
$823$	−12.5000	+	21.6506i	−0.0151883	+	0.0263070i	−0.873520	−	0.486789i	$-0.838168\pi$
$823$	−12.5000	+	21.6506i	−0.0151883	+	0.0263070i	0.858331	+	0.513096i	$0.171501\pi$
$824$		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	−0.998365	−	0.0571537i	$-0.981797\pi$
$829$	−1282.50	−	740.452i	−1.54704	−	0.893187i	−0.548679	−	0.836033i	$-0.684869\pi$
$830$		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	$-0.931123\pi$
$839$		−	360.267i		−	0.429400i	0.976680	−	0.214700i	$-0.0688774\pi$
$840$		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	$-0.750215\pi$
$853$		−	1205.51i		−	1.41326i	0.707585	−	0.706628i	$-0.249785\pi$
$854$		0			0
$855$	162.000			0.189474
$856$		0			0
$857$	169.500	+	97.8609i	0.197783	+	0.114190i	0.595621	−	0.803266i	$-0.296906\pi$
$857$	169.500	+	97.8609i	0.197783	+	0.114190i	−0.397838	+	0.917456i	$0.630239\pi$
$858$		0			0
$859$	1234.50	−	712.739i	1.43714	−	0.829731i	0.439486	−	0.898249i	$-0.355160\pi$
$859$	1234.50	−	712.739i	1.43714	−	0.829731i	0.997650	+	0.0685183i	$0.0218272\pi$
$860$		0			0
$861$	336.000	−	581.969i	0.390244	−	0.675922i
$862$		0			0
$863$	427.500	+	740.452i	0.495365	+	0.857997i	0.999986	−	0.00534379i	$-0.00170099\pi$
$863$	427.500	+	740.452i	0.495365	+	0.857997i	−0.504621	+	0.863341i	$0.668368\pi$
$864$		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	0.926512	−	0.376266i	$-0.122792\pi$
$877$	120.500	+	208.712i	0.137400	+	0.237984i	−0.789112	+	0.614250i	$0.789459\pi$
$878$		0			0
$879$	−204.000	+	353.338i	−0.232082	+	0.401978i
$880$		0			0
$881$			1330.22i			1.50989i	0.655787	+	0.754946i	$0.272337\pi$
$881$			1330.22i			1.50989i	−0.655787	+	0.754946i	$0.727663\pi$
$882$		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	0.284094	−	0.958797i	$-0.408307\pi$
$887$	1114.50	−	643.457i	1.25648	−	0.725431i	0.972389	+	0.233366i	$0.0749740\pi$
$888$		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	−0.994470	−	0.105021i	$-0.966509\pi$
$907$	−368.500	+	638.261i	−0.406284	+	0.703705i	0.588186	+	0.808726i	$0.299842\pi$
$908$		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	0.708185	−	0.706027i	$-0.249514\pi$
$919$	−236.500	−	409.630i	−0.257345	−	0.445735i	−0.965530	+	0.260293i	$0.916181\pi$
$920$		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	−0.336028	−	0.941852i	$-0.609084\pi$
$929$	289.500	−	167.143i	0.311625	−	0.179917i	0.647654	+	0.761935i	$0.275750\pi$
$930$		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	$-0.848412\pi$
$937$		−	859.097i		−	0.916859i	0.888731	−	0.458430i	$-0.151588\pi$
$938$		0			0
$939$	−387.000			−0.412141
$940$		0			0
$941$	−106.500	−	61.4878i	−0.113177	−	0.0653430i	0.442343	−	0.896846i	$-0.354147\pi$
$941$	−106.500	−	61.4878i	−0.113177	−	0.0653430i	−0.555520	+	0.831503i	$0.687481\pi$
$942$		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	0.808073	−	0.589083i	$-0.200511\pi$
$947$	−100.500	−	174.071i	−0.106125	−	0.183813i	−0.914197	+	0.405270i	$0.867178\pi$
$948$		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	−0.984347	−	0.176240i	$-0.943607\pi$
$971$	−1285.50	+	742.184i	−1.32389	+	0.764350i	−0.339546	+	0.940590i	$0.610273\pi$
$972$		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	−0.154458	−	0.987999i	$-0.549363\pi$
$977$	760.500	−	1317.22i	0.778403	−	1.34823i	0.932862	−	0.360235i	$-0.117303\pi$
$978$		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	−0.0849611	−	0.996384i	$-0.527077\pi$
$983$	−973.500	−	562.050i	−0.990336	−	0.571771i	−0.905375	+	0.424614i	$0.860410\pi$
$984$		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	−0.580216	−	0.814463i	$-0.697032\pi$
$991$	411.500	−	712.739i	0.415237	−	0.719212i	0.995453	+	0.0952507i	$0.0303653\pi$
$992$		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	0.553909	−	0.832578i	$-0.313136\pi$
$997$	109.500	+	63.2199i	0.109829	+	0.0634101i	−0.444079	+	0.895988i	$0.646469\pi$
$998$		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.17.1		2
3.2	odd	2		1008.3.cg.c.577.1		2
4.3	odd	2		28.3.h.a.17.1	yes	2
7.2	even	3		784.3.s.b.705.1		2
7.3	odd	6		784.3.c.a.97.1		2
7.4	even	3		784.3.c.a.97.2		2
7.5	odd	6	inner	112.3.s.a.33.1		2
7.6	odd	2		784.3.s.b.129.1		2
8.3	odd	2		448.3.s.a.129.1		2
8.5	even	2		448.3.s.b.129.1		2
12.11	even	2		252.3.z.a.73.1		2
20.3	even	4		700.3.o.a.549.1		4
20.7	even	4		700.3.o.a.549.2		4
20.19	odd	2		700.3.s.a.101.1		2
21.5	even	6		1008.3.cg.c.145.1		2
28.3	even	6		196.3.b.a.97.2		2
28.11	odd	6		196.3.b.a.97.1		2
28.19	even	6		28.3.h.a.5.1	✓	2
28.23	odd	6		196.3.h.a.117.1		2
28.27	even	2		196.3.h.a.129.1		2
56.5	odd	6		448.3.s.b.257.1		2
56.19	even	6		448.3.s.a.257.1		2
84.11	even	6		1764.3.d.a.685.1		2
84.23	even	6		1764.3.z.f.901.1		2
84.47	odd	6		252.3.z.a.145.1		2
84.59	odd	6		1764.3.d.a.685.2		2
84.83	odd	2		1764.3.z.f.325.1		2
140.19	even	6		700.3.s.a.201.1		2
140.47	odd	12		700.3.o.a.649.1		4
140.103	odd	12		700.3.o.a.649.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
28.3.h.a.5.1	✓	2	28.19	even	6
28.3.h.a.17.1	yes	2	4.3	odd	2
112.3.s.a.17.1		2	1.1	even	1	trivial
112.3.s.a.33.1		2	7.5	odd	6	inner
196.3.b.a.97.1		2	28.11	odd	6
196.3.b.a.97.2		2	28.3	even	6
196.3.h.a.117.1		2	28.23	odd	6
196.3.h.a.129.1		2	28.27	even	2
252.3.z.a.73.1		2	12.11	even	2
252.3.z.a.145.1		2	84.47	odd	6
448.3.s.a.129.1		2	8.3	odd	2
448.3.s.a.257.1		2	56.19	even	6
448.3.s.b.129.1		2	8.5	even	2
448.3.s.b.257.1		2	56.5	odd	6
700.3.o.a.549.1		4	20.3	even	4
700.3.o.a.549.2		4	20.7	even	4
700.3.o.a.649.1		4	140.47	odd	12
700.3.o.a.649.2		4	140.103	odd	12
700.3.s.a.101.1		2	20.19	odd	2
700.3.s.a.201.1		2	140.19	even	6
784.3.c.a.97.1		2	7.3	odd	6
784.3.c.a.97.2		2	7.4	even	3
784.3.s.b.129.1		2	7.6	odd	2
784.3.s.b.705.1		2	7.2	even	3
1008.3.cg.c.145.1		2	21.5	even	6
1008.3.cg.c.577.1		2	3.2	odd	2
1764.3.d.a.685.1		2	84.11	even	6
1764.3.d.a.685.2		2	84.59	odd	6
1764.3.z.f.325.1		2	84.83	odd	2
1764.3.z.f.901.1		2	84.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
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

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