LMFDB - Embedded newform 1344.2.s.b.911.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1344,2,Mod(239,1344)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1344, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1344.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1344 = 2^{6} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1344.s (of order $4$, 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:	$10.7318940317$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 336)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			911.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1344.911
Dual form			1344.2.s.b.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.41421i) q^{3} +(-2.41421 + 2.41421i) q^{5} +1.00000 q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.41421i) q^{3} +(-2.41421 + 2.41421i) q^{5} +1.00000 q^{7} +(-1.00000 - 2.82843i) q^{9} +(-1.82843 - 1.82843i) q^{11} +(-1.58579 + 1.58579i) q^{13} +(1.00000 + 5.82843i) q^{15} -6.82843i q^{17} +(2.41421 + 2.41421i) q^{19} +(1.00000 - 1.41421i) q^{21} +3.65685i q^{23} -6.65685i q^{25} +(-5.00000 - 1.41421i) q^{27} +(-3.00000 - 3.00000i) q^{29} -10.4853i q^{31} +(-4.41421 + 0.757359i) q^{33} +(-2.41421 + 2.41421i) q^{35} +(-3.82843 - 3.82843i) q^{37} +(0.656854 + 3.82843i) q^{39} -11.6569 q^{41} +(-1.82843 + 1.82843i) q^{43} +(9.24264 + 4.41421i) q^{45} -5.65685 q^{47} +1.00000 q^{49} +(-9.65685 - 6.82843i) q^{51} +(-0.171573 + 0.171573i) q^{53} +8.82843 q^{55} +(5.82843 - 1.00000i) q^{57} +(-4.07107 - 4.07107i) q^{59} +(-0.414214 + 0.414214i) q^{61} +(-1.00000 - 2.82843i) q^{63} -7.65685i q^{65} +(7.00000 + 7.00000i) q^{67} +(5.17157 + 3.65685i) q^{69} -6.00000i q^{71} -10.8284i q^{73} +(-9.41421 - 6.65685i) q^{75} +(-1.82843 - 1.82843i) q^{77} +2.00000i q^{79} +(-7.00000 + 5.65685i) q^{81} +(10.8995 - 10.8995i) q^{83} +(16.4853 + 16.4853i) q^{85} +(-7.24264 + 1.24264i) q^{87} -4.34315 q^{89} +(-1.58579 + 1.58579i) q^{91} +(-14.8284 - 10.4853i) q^{93} -11.6569 q^{95} -2.00000 q^{97} +(-3.34315 + 7.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 4 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 12 q^{13} + 4 q^{15} + 4 q^{19} + 4 q^{21} - 20 q^{27} - 12 q^{29} - 12 q^{33} - 4 q^{35} - 4 q^{37} - 20 q^{39} - 24 q^{41} + 4 q^{43} + 20 q^{45} + 4 q^{49} - 16 q^{51} - 12 q^{53} + 24 q^{55} + 12 q^{57} + 12 q^{59} + 4 q^{61} - 4 q^{63} + 28 q^{67} + 32 q^{69} - 32 q^{75} + 4 q^{77} - 28 q^{81} + 4 q^{83} + 32 q^{85} - 12 q^{87} - 40 q^{89} - 12 q^{91} - 48 q^{93} - 24 q^{95} - 8 q^{97} - 36 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 12 * q^13 + 4 * q^15 + 4 * q^19 + 4 * q^21 - 20 * q^27 - 12 * q^29 - 12 * q^33 - 4 * q^35 - 4 * q^37 - 20 * q^39 - 24 * q^41 + 4 * q^43 + 20 * q^45 + 4 * q^49 - 16 * q^51 - 12 * q^53 + 24 * q^55 + 12 * q^57 + 12 * q^59 + 4 * q^61 - 4 * q^63 + 28 * q^67 + 32 * q^69 - 32 * q^75 + 4 * q^77 - 28 * q^81 + 4 * q^83 + 32 * q^85 - 12 * q^87 - 40 * q^89 - 12 * q^91 - 48 * q^93 - 24 * q^95 - 8 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times$.

$n$	$127$	$449$	$577$	$1093$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$4$		0			0
$5$	−2.41421	+	2.41421i	−1.07967	+	1.07967i	−0.0831305	+	0.996539i	$0.526492\pi$
$5$	−2.41421	+	2.41421i	−1.07967	+	1.07967i	−0.996539	+	0.0831305i	$0.973508\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		0			0
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$		0			0
$11$	−1.82843	−	1.82843i	−0.551292	−	0.551292i	0.375522	−	0.926813i	$-0.377463\pi$
$11$	−1.82843	−	1.82843i	−0.551292	−	0.551292i	−0.926813	+	0.375522i	$0.877463\pi$
$12$		0			0
$13$	−1.58579	+	1.58579i	−0.439818	+	0.439818i	−0.891951	−	0.452133i	$-0.850663\pi$
$13$	−1.58579	+	1.58579i	−0.439818	+	0.439818i	0.452133	+	0.891951i	$0.350663\pi$
$14$		0			0
$15$	1.00000	+	5.82843i	0.258199	+	1.50489i
$16$		0			0
$17$		−	6.82843i		−	1.65614i	−0.560627	−	0.828068i	$-0.689440\pi$
$17$		−	6.82843i		−	1.65614i	0.560627	−	0.828068i	$-0.310560\pi$
$18$		0			0
$19$	2.41421	+	2.41421i	0.553859	+	0.553859i	0.927552	−	0.373694i	$-0.121909\pi$
$19$	2.41421	+	2.41421i	0.553859	+	0.553859i	−0.373694	+	0.927552i	$0.621909\pi$
$20$		0			0
$21$	1.00000	−	1.41421i	0.218218	−	0.308607i
$22$		0			0
$23$			3.65685i			0.762507i	0.924471	+	0.381253i	$0.124507\pi$
$23$			3.65685i			0.762507i	−0.924471	+	0.381253i	$0.875493\pi$
$24$		0			0
$25$		−	6.65685i		−	1.33137i
$26$		0			0
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$		0			0
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	0.371391	−	0.928477i	$-0.378881\pi$
$29$	−3.00000	−	3.00000i	−0.557086	−	0.557086i	−0.928477	+	0.371391i	$0.878881\pi$
$30$		0			0
$31$		−	10.4853i		−	1.88321i	−0.336717	−	0.941606i	$-0.609316\pi$
$31$		−	10.4853i		−	1.88321i	0.336717	−	0.941606i	$-0.390684\pi$
$32$		0			0
$33$	−4.41421	+	0.757359i	−0.768416	+	0.131839i
$34$		0			0
$35$	−2.41421	+	2.41421i	−0.408077	+	0.408077i
$36$		0			0
$37$	−3.82843	−	3.82843i	−0.629390	−	0.629390i	0.318525	−	0.947914i	$-0.396813\pi$
$37$	−3.82843	−	3.82843i	−0.629390	−	0.629390i	−0.947914	+	0.318525i	$0.896813\pi$
$38$		0			0
$39$	0.656854	+	3.82843i	0.105181	+	0.613039i
$40$		0			0
$41$	−11.6569			−1.82049			−0.910247	−	0.414065i	$-0.864109\pi$
$41$	−11.6569			−1.82049			−0.910247	+	0.414065i	$0.864109\pi$
$42$		0			0
$43$	−1.82843	+	1.82843i	−0.278833	+	0.278833i	−0.832643	−	0.553810i	$-0.813173\pi$
$43$	−1.82843	+	1.82843i	−0.278833	+	0.278833i	0.553810	+	0.832643i	$0.313173\pi$
$44$		0			0
$45$	9.24264	+	4.41421i	1.37781	+	0.658032i
$46$		0			0
$47$	−5.65685			−0.825137			−0.412568	−	0.910927i	$-0.635368\pi$
$47$	−5.65685			−0.825137			−0.412568	+	0.910927i	$0.635368\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$		0			0
$51$	−9.65685	−	6.82843i	−1.35223	−	0.956171i
$52$		0			0
$53$	−0.171573	+	0.171573i	−0.0235673	+	0.0235673i	−0.718792	−	0.695225i	$-0.755305\pi$
$53$	−0.171573	+	0.171573i	−0.0235673	+	0.0235673i	0.695225	+	0.718792i	$0.255305\pi$
$54$		0			0
$55$	8.82843			1.19042
$56$		0			0
$57$	5.82843	−	1.00000i	0.771994	−	0.132453i
$58$		0			0
$59$	−4.07107	−	4.07107i	−0.530008	−	0.530008i	0.390567	−	0.920575i	$-0.372279\pi$
$59$	−4.07107	−	4.07107i	−0.530008	−	0.530008i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		0			0
$61$	−0.414214	+	0.414214i	−0.0530346	+	0.0530346i	−0.733127	−	0.680092i	$-0.761940\pi$
$61$	−0.414214	+	0.414214i	−0.0530346	+	0.0530346i	0.680092	+	0.733127i	$0.261940\pi$
$62$		0			0
$63$	−1.00000	−	2.82843i	−0.125988	−	0.356348i
$64$		0			0
$65$		−	7.65685i		−	0.949716i
$66$		0			0
$67$	7.00000	+	7.00000i	0.855186	+	0.855186i	0.990766	−	0.135580i	$-0.0432899\pi$
$67$	7.00000	+	7.00000i	0.855186	+	0.855186i	−0.135580	+	0.990766i	$0.543290\pi$
$68$		0			0
$69$	5.17157	+	3.65685i	0.622584	+	0.440234i
$70$		0			0
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$		0			0
$73$		−	10.8284i		−	1.26737i	−0.773591	−	0.633686i	$-0.781541\pi$
$73$		−	10.8284i		−	1.26737i	0.773591	−	0.633686i	$-0.218459\pi$
$74$		0			0
$75$	−9.41421	−	6.65685i	−1.08706	−	0.768667i
$76$		0			0
$77$	−1.82843	−	1.82843i	−0.208369	−	0.208369i
$78$		0			0
$79$			2.00000i			0.225018i	0.993651	+	0.112509i	$0.0358886\pi$
$79$			2.00000i			0.225018i	−0.993651	+	0.112509i	$0.964111\pi$
$80$		0			0
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$		0			0
$83$	10.8995	−	10.8995i	1.19637	−	1.19637i	0.221131	−	0.975244i	$-0.429025\pi$
$83$	10.8995	−	10.8995i	1.19637	−	1.19637i	0.975244	−	0.221131i	$-0.0709748\pi$
$84$		0			0
$85$	16.4853	+	16.4853i	1.78808	+	1.78808i
$86$		0			0
$87$	−7.24264	+	1.24264i	−0.776493	+	0.133225i
$88$		0			0
$89$	−4.34315			−0.460373			−0.230186	−	0.973147i	$-0.573934\pi$
$89$	−4.34315			−0.460373			−0.230186	+	0.973147i	$0.573934\pi$
$90$		0			0
$91$	−1.58579	+	1.58579i	−0.166236	+	0.166236i
$92$		0			0
$93$	−14.8284	−	10.4853i	−1.53764	−	1.08727i
$94$		0			0
$95$	−11.6569			−1.19597
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−3.34315	+	7.00000i	−0.335999	+	0.703526i
$100$		0			0
$101$	−4.07107	+	4.07107i	−0.405086	+	0.405086i	−0.880021	−	0.474935i	$-0.842472\pi$
$101$	−4.07107	+	4.07107i	−0.405086	+	0.405086i	0.474935	+	0.880021i	$0.342472\pi$
$102$		0			0
$103$	11.3137			1.11477			0.557386	−	0.830253i	$-0.311804\pi$
$103$	11.3137			1.11477			0.557386	+	0.830253i	$0.311804\pi$
$104$		0			0
$105$	1.00000	+	5.82843i	0.0975900	+	0.568796i
$106$		0			0
$107$	5.00000	+	5.00000i	0.483368	+	0.483368i	0.906206	−	0.422837i	$-0.138966\pi$
$107$	5.00000	+	5.00000i	0.483368	+	0.483368i	−0.422837	+	0.906206i	$0.638966\pi$
$108$		0			0
$109$	0.171573	−	0.171573i	0.0164337	−	0.0164337i	−0.698842	−	0.715276i	$-0.746301\pi$
$109$	0.171573	−	0.171573i	0.0164337	−	0.0164337i	0.715276	+	0.698842i	$0.246301\pi$
$110$		0			0
$111$	−9.24264	+	1.58579i	−0.877273	+	0.150516i
$112$		0			0
$113$			9.65685i			0.908440i	0.890889	+	0.454220i	$0.150082\pi$
$113$			9.65685i			0.908440i	−0.890889	+	0.454220i	$0.849918\pi$
$114$		0			0
$115$	−8.82843	−	8.82843i	−0.823255	−	0.823255i
$116$		0			0
$117$	6.07107	+	2.89949i	0.561270	+	0.268058i
$118$		0			0
$119$		−	6.82843i		−	0.625961i
$120$		0			0
$121$		−	4.31371i		−	0.392155i
$122$		0			0
$123$	−11.6569	+	16.4853i	−1.05106	+	1.48643i
$124$		0			0
$125$	4.00000	+	4.00000i	0.357771	+	0.357771i
$126$		0			0
$127$		−	4.34315i		−	0.385392i	−0.981259	−	0.192696i	$-0.938277\pi$
$127$		−	4.34315i		−	0.385392i	0.981259	−	0.192696i	$-0.0617231\pi$
$128$		0			0
$129$	0.757359	+	4.41421i	0.0666818	+	0.388650i
$130$		0			0
$131$	−10.0711	+	10.0711i	−0.879913	+	0.879913i	−0.993525	−	0.113612i	$-0.963758\pi$
$131$	−10.0711	+	10.0711i	−0.879913	+	0.879913i	0.113612	+	0.993525i	$0.463758\pi$
$132$		0			0
$133$	2.41421	+	2.41421i	0.209339	+	0.209339i
$134$		0			0
$135$	15.4853	−	8.65685i	1.33276	−	0.745063i
$136$		0			0
$137$	3.65685			0.312426			0.156213	−	0.987723i	$-0.450071\pi$
$137$	3.65685			0.312426			0.156213	+	0.987723i	$0.450071\pi$
$138$		0			0
$139$	1.58579	−	1.58579i	0.134505	−	0.134505i	−0.636649	−	0.771154i	$-0.719680\pi$
$139$	1.58579	−	1.58579i	0.134505	−	0.134505i	0.771154	+	0.636649i	$0.219680\pi$
$140$		0			0
$141$	−5.65685	+	8.00000i	−0.476393	+	0.673722i
$142$		0			0
$143$	5.79899			0.484936
$144$		0			0
$145$	14.4853			1.20294
$146$		0			0
$147$	1.00000	−	1.41421i	0.0824786	−	0.116642i
$148$		0			0
$149$	−7.48528	+	7.48528i	−0.613218	+	0.613218i	−0.943783	−	0.330565i	$-0.892761\pi$
$149$	−7.48528	+	7.48528i	−0.613218	+	0.613218i	0.330565	+	0.943783i	$0.392761\pi$
$150$		0			0
$151$	6.34315			0.516198			0.258099	−	0.966118i	$-0.416904\pi$
$151$	6.34315			0.516198			0.258099	+	0.966118i	$0.416904\pi$
$152$		0			0
$153$	−19.3137	+	6.82843i	−1.56142	+	0.552046i
$154$		0			0
$155$	25.3137	+	25.3137i	2.03325	+	2.03325i
$156$		0			0
$157$	−16.8995	+	16.8995i	−1.34873	+	1.34873i	−0.461680	+	0.887047i	$0.652753\pi$
$157$	−16.8995	+	16.8995i	−1.34873	+	1.34873i	−0.887047	+	0.461680i	$0.847247\pi$
$158$		0			0
$159$	0.0710678	+	0.414214i	0.00563604	+	0.0328493i
$160$		0			0
$161$			3.65685i			0.288200i
$162$		0			0
$163$	−3.82843	−	3.82843i	−0.299866	−	0.299866i	0.541096	−	0.840961i	$-0.318010\pi$
$163$	−3.82843	−	3.82843i	−0.299866	−	0.299866i	−0.840961	+	0.541096i	$0.818010\pi$
$164$		0			0
$165$	8.82843	−	12.4853i	0.687292	−	0.971978i
$166$		0			0
$167$			12.8284i			0.992693i	0.868124	+	0.496347i	$0.165326\pi$
$167$			12.8284i			0.992693i	−0.868124	+	0.496347i	$0.834674\pi$
$168$		0			0
$169$			7.97056i			0.613120i
$170$		0			0
$171$	4.41421	−	9.24264i	0.337563	−	0.706802i
$172$		0			0
$173$	−14.8995	−	14.8995i	−1.13279	−	1.13279i	−0.989712	−	0.143076i	$-0.954301\pi$
$173$	−14.8995	−	14.8995i	−1.13279	−	1.13279i	−0.143076	−	0.989712i	$-0.545699\pi$
$174$		0			0
$175$		−	6.65685i		−	0.503211i
$176$		0			0
$177$	−9.82843	+	1.68629i	−0.738750	+	0.126749i
$178$		0			0
$179$	15.0000	−	15.0000i	1.12115	−	1.12115i	0.129584	−	0.991568i	$-0.458636\pi$
$179$	15.0000	−	15.0000i	1.12115	−	1.12115i	0.991568	−	0.129584i	$-0.0413643\pi$
$180$		0			0
$181$	12.0711	+	12.0711i	0.897235	+	0.897235i	0.995191	−	0.0979554i	$-0.0312303\pi$
$181$	12.0711	+	12.0711i	0.897235	+	0.897235i	−0.0979554	+	0.995191i	$0.531230\pi$
$182$		0			0
$183$	0.171573	+	1.00000i	0.0126830	+	0.0739221i
$184$		0			0
$185$	18.4853			1.35906
$186$		0			0
$187$	−12.4853	+	12.4853i	−0.913014	+	0.913014i
$188$		0			0
$189$	−5.00000	−	1.41421i	−0.363696	−	0.102869i
$190$		0			0
$191$	17.6569			1.27761			0.638803	−	0.769371i	$-0.279430\pi$
$191$	17.6569			1.27761			0.638803	+	0.769371i	$0.279430\pi$
$192$		0			0
$193$	4.34315			0.312626			0.156313	−	0.987708i	$-0.450039\pi$
$193$	4.34315			0.312626			0.156313	+	0.987708i	$0.450039\pi$
$194$		0			0
$195$	−10.8284	−	7.65685i	−0.775440	−	0.548319i
$196$		0			0
$197$	−0.171573	+	0.171573i	−0.0122241	+	0.0122241i	−0.713192	−	0.700968i	$-0.752751\pi$
$197$	−0.171573	+	0.171573i	−0.0122241	+	0.0122241i	0.700968	+	0.713192i	$0.252751\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$	16.8995	−	2.89949i	1.19200	−	0.204515i
$202$		0			0
$203$	−3.00000	−	3.00000i	−0.210559	−	0.210559i
$204$		0			0
$205$	28.1421	−	28.1421i	1.96553	−	1.96553i
$206$		0			0
$207$	10.3431	−	3.65685i	0.718898	−	0.254169i
$208$		0			0
$209$		−	8.82843i		−	0.610675i
$210$		0			0
$211$	−5.00000	−	5.00000i	−0.344214	−	0.344214i	0.513735	−	0.857949i	$-0.328262\pi$
$211$	−5.00000	−	5.00000i	−0.344214	−	0.344214i	−0.857949	+	0.513735i	$0.828262\pi$
$212$		0			0
$213$	−8.48528	−	6.00000i	−0.581402	−	0.411113i
$214$		0			0
$215$		−	8.82843i		−	0.602094i
$216$		0			0
$217$		−	10.4853i		−	0.711787i
$218$		0			0
$219$	−15.3137	−	10.8284i	−1.03480	−	0.731717i
$220$		0			0
$221$	10.8284	+	10.8284i	0.728399	+	0.728399i
$222$		0			0
$223$		−	12.8284i		−	0.859055i	−0.903054	−	0.429528i	$-0.858680\pi$
$223$		−	12.8284i		−	0.859055i	0.903054	−	0.429528i	$-0.141320\pi$
$224$		0			0
$225$	−18.8284	+	6.65685i	−1.25523	+	0.443790i
$226$		0			0
$227$	−6.07107	+	6.07107i	−0.402951	+	0.402951i	−0.879272	−	0.476321i	$-0.841970\pi$
$227$	−6.07107	+	6.07107i	−0.402951	+	0.402951i	0.476321	+	0.879272i	$0.341970\pi$
$228$		0			0
$229$	−8.89949	−	8.89949i	−0.588095	−	0.588095i	0.349020	−	0.937115i	$-0.386515\pi$
$229$	−8.89949	−	8.89949i	−0.588095	−	0.588095i	−0.937115	+	0.349020i	$0.886515\pi$
$230$		0			0
$231$	−4.41421	+	0.757359i	−0.290434	+	0.0498306i
$232$		0			0
$233$	21.3137			1.39631			0.698154	−	0.715948i	$-0.254005\pi$
$233$	21.3137			1.39631			0.698154	+	0.715948i	$0.254005\pi$
$234$		0			0
$235$	13.6569	−	13.6569i	0.890875	−	0.890875i
$236$		0			0
$237$	2.82843	+	2.00000i	0.183726	+	0.129914i
$238$		0			0
$239$	11.3137			0.731823			0.365911	−	0.930650i	$-0.380757\pi$
$239$	11.3137			0.731823			0.365911	+	0.930650i	$0.380757\pi$
$240$		0			0
$241$	11.6569			0.750884			0.375442	−	0.926846i	$-0.377491\pi$
$241$	11.6569			0.750884			0.375442	+	0.926846i	$0.377491\pi$
$242$		0			0
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$		0			0
$245$	−2.41421	+	2.41421i	−0.154238	+	0.154238i
$246$		0			0
$247$	−7.65685			−0.487194
$248$		0			0
$249$	−4.51472	−	26.3137i	−0.286109	−	1.66756i
$250$		0			0
$251$	0.414214	+	0.414214i	0.0261449	+	0.0261449i	0.720058	−	0.693913i	$-0.244115\pi$
$251$	0.414214	+	0.414214i	0.0261449	+	0.0261449i	−0.693913	+	0.720058i	$0.744115\pi$
$252$		0			0
$253$	6.68629	−	6.68629i	0.420364	−	0.420364i
$254$		0			0
$255$	39.7990	−	6.82843i	2.49231	−	0.427613i
$256$		0			0
$257$		−	21.1716i		−	1.32065i	−0.750982	−	0.660323i	$-0.770419\pi$
$257$		−	21.1716i		−	1.32065i	0.750982	−	0.660323i	$-0.229581\pi$
$258$		0			0
$259$	−3.82843	−	3.82843i	−0.237887	−	0.237887i
$260$		0			0
$261$	−5.48528	+	11.4853i	−0.339530	+	0.710921i
$262$		0			0
$263$		−	0.343146i		−	0.0211593i	−0.999944	−	0.0105796i	$-0.996632\pi$
$263$		−	0.343146i		−	0.0211593i	0.999944	−	0.0105796i	$-0.00336767\pi$
$264$		0			0
$265$		−	0.828427i		−	0.0508899i
$266$		0			0
$267$	−4.34315	+	6.14214i	−0.265796	+	0.375893i
$268$		0			0
$269$	8.41421	+	8.41421i	0.513024	+	0.513024i	0.915452	−	0.402428i	$-0.131834\pi$
$269$	8.41421	+	8.41421i	0.513024	+	0.513024i	−0.402428	+	0.915452i	$0.631834\pi$
$270$		0			0
$271$			11.1716i			0.678625i	0.940674	+	0.339312i	$0.110194\pi$
$271$			11.1716i			0.678625i	−0.940674	+	0.339312i	$0.889806\pi$
$272$		0			0
$273$	0.656854	+	3.82843i	0.0397546	+	0.231707i
$274$		0			0
$275$	−12.1716	+	12.1716i	−0.733973	+	0.733973i
$276$		0			0
$277$	−16.3137	−	16.3137i	−0.980196	−	0.980196i	0.0196119	−	0.999808i	$-0.493757\pi$
$277$	−16.3137	−	16.3137i	−0.980196	−	0.980196i	−0.999808	+	0.0196119i	$0.993757\pi$
$278$		0			0
$279$	−29.6569	+	10.4853i	−1.77551	+	0.627737i
$280$		0			0
$281$	29.3137			1.74871			0.874355	−	0.485288i	$-0.161285\pi$
$281$	29.3137			1.74871			0.874355	+	0.485288i	$0.161285\pi$
$282$		0			0
$283$	−6.89949	+	6.89949i	−0.410132	+	0.410132i	−0.881785	−	0.471652i	$-0.843658\pi$
$283$	−6.89949	+	6.89949i	−0.410132	+	0.410132i	0.471652	+	0.881785i	$0.343658\pi$
$284$		0			0
$285$	−11.6569	+	16.4853i	−0.690492	+	0.976504i
$286$		0			0
$287$	−11.6569			−0.688082
$288$		0			0
$289$	−29.6274			−1.74279
$290$		0			0
$291$	−2.00000	+	2.82843i	−0.117242	+	0.165805i
$292$		0			0
$293$	−0.757359	+	0.757359i	−0.0442454	+	0.0442454i	−0.728883	−	0.684638i	$-0.759960\pi$
$293$	−0.757359	+	0.757359i	−0.0442454	+	0.0442454i	0.684638	+	0.728883i	$0.259960\pi$
$294$		0			0
$295$	19.6569			1.14447
$296$		0			0
$297$	6.55635	+	11.7279i	0.380438	+	0.680523i
$298$		0			0
$299$	−5.79899	−	5.79899i	−0.335364	−	0.335364i
$300$		0			0
$301$	−1.82843	+	1.82843i	−0.105389	+	0.105389i
$302$		0			0
$303$	1.68629	+	9.82843i	0.0968749	+	0.564628i
$304$		0			0
$305$		−	2.00000i		−	0.114520i
$306$		0			0
$307$	−4.89949	−	4.89949i	−0.279629	−	0.279629i	0.553332	−	0.832961i	$-0.313356\pi$
$307$	−4.89949	−	4.89949i	−0.279629	−	0.279629i	−0.832961	+	0.553332i	$0.813356\pi$
$308$		0			0
$309$	11.3137	−	16.0000i	0.643614	−	0.910208i
$310$		0			0
$311$			18.4853i			1.04820i	0.851655	+	0.524102i	$0.175599\pi$
$311$			18.4853i			1.04820i	−0.851655	+	0.524102i	$0.824401\pi$
$312$		0			0
$313$		−	3.51472i		−	0.198664i	−0.995054	−	0.0993318i	$-0.968329\pi$
$313$		−	3.51472i		−	0.198664i	0.995054	−	0.0993318i	$-0.0316705\pi$
$314$		0			0
$315$	9.24264	+	4.41421i	0.520764	+	0.248713i
$316$		0			0
$317$	15.1421	+	15.1421i	0.850467	+	0.850467i	0.990191	−	0.139723i	$-0.0446214\pi$
$317$	15.1421	+	15.1421i	0.850467	+	0.850467i	−0.139723	+	0.990191i	$0.544621\pi$
$318$		0			0
$319$			10.9706i			0.614234i
$320$		0			0
$321$	12.0711	−	2.07107i	0.673741	−	0.115596i
$322$		0			0
$323$	16.4853	−	16.4853i	0.917266	−	0.917266i
$324$		0			0
$325$	10.5563	+	10.5563i	0.585561	+	0.585561i
$326$		0			0
$327$	−0.0710678	−	0.414214i	−0.00393006	−	0.0229061i
$328$		0			0
$329$	−5.65685			−0.311872
$330$		0			0
$331$	11.1421	−	11.1421i	0.612427	−	0.612427i	−0.331151	−	0.943578i	$-0.607437\pi$
$331$	11.1421	−	11.1421i	0.612427	−	0.612427i	0.943578	+	0.331151i	$0.107437\pi$
$332$		0			0
$333$	−7.00000	+	14.6569i	−0.383598	+	0.803191i
$334$		0			0
$335$	−33.7990			−1.84664
$336$		0			0
$337$	2.68629			0.146332			0.0731658	−	0.997320i	$-0.476690\pi$
$337$	2.68629			0.146332			0.0731658	+	0.997320i	$0.476690\pi$
$338$		0			0
$339$	13.6569	+	9.65685i	0.741739	+	0.524488i
$340$		0			0
$341$	−19.1716	+	19.1716i	−1.03820	+	1.03820i
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$	−21.3137	+	3.65685i	−1.14749	+	0.196878i
$346$		0			0
$347$	15.1421	+	15.1421i	0.812872	+	0.812872i	0.985064	−	0.172191i	$-0.0550847\pi$
$347$	15.1421	+	15.1421i	0.812872	+	0.812872i	−0.172191	+	0.985064i	$0.555085\pi$
$348$		0			0
$349$	12.0711	−	12.0711i	0.646149	−	0.646149i	−0.305911	−	0.952060i	$-0.598961\pi$
$349$	12.0711	−	12.0711i	0.646149	−	0.646149i	0.952060	+	0.305911i	$0.0989609\pi$
$350$		0			0
$351$	10.1716	−	5.68629i	0.542918	−	0.303512i
$352$		0			0
$353$		−	8.48528i		−	0.451626i	−0.974171	−	0.225813i	$-0.927496\pi$
$353$		−	8.48528i		−	0.451626i	0.974171	−	0.225813i	$-0.0725038\pi$
$354$		0			0
$355$	14.4853	+	14.4853i	0.768799	+	0.768799i
$356$		0			0
$357$	−9.65685	−	6.82843i	−0.511095	−	0.361399i
$358$		0			0
$359$		−	31.6569i		−	1.67078i	−0.549654	−	0.835392i	$-0.685240\pi$
$359$		−	31.6569i		−	1.67078i	0.549654	−	0.835392i	$-0.314760\pi$
$360$		0			0
$361$		−	7.34315i		−	0.386481i
$362$		0			0
$363$	−6.10051	−	4.31371i	−0.320193	−	0.226411i
$364$		0			0
$365$	26.1421	+	26.1421i	1.36834	+	1.36834i
$366$		0			0
$367$			12.1421i			0.633814i	0.948457	+	0.316907i	$0.102644\pi$
$367$			12.1421i			0.633814i	−0.948457	+	0.316907i	$0.897356\pi$
$368$		0			0
$369$	11.6569	+	32.9706i	0.606832	+	1.71638i
$370$		0			0
$371$	−0.171573	+	0.171573i	−0.00890762	+	0.00890762i
$372$		0			0
$373$	14.3137	+	14.3137i	0.741136	+	0.741136i	0.972797	−	0.231661i	$-0.0744160\pi$
$373$	14.3137	+	14.3137i	0.741136	+	0.741136i	−0.231661	+	0.972797i	$0.574416\pi$
$374$		0			0
$375$	9.65685	−	1.65685i	0.498678	−	0.0855596i
$376$		0			0
$377$	9.51472			0.490033
$378$		0			0
$379$	−1.14214	+	1.14214i	−0.0586676	+	0.0586676i	−0.735832	−	0.677164i	$-0.763209\pi$
$379$	−1.14214	+	1.14214i	−0.0586676	+	0.0586676i	0.677164	+	0.735832i	$0.263209\pi$
$380$		0			0
$381$	−6.14214	−	4.34315i	−0.314671	−	0.222506i
$382$		0			0
$383$	3.31371			0.169323			0.0846613	−	0.996410i	$-0.473019\pi$
$383$	3.31371			0.169323			0.0846613	+	0.996410i	$0.473019\pi$
$384$		0			0
$385$	8.82843			0.449938
$386$		0			0
$387$	7.00000	+	3.34315i	0.355830	+	0.169942i
$388$		0			0
$389$	13.9706	−	13.9706i	0.708336	−	0.708336i	−0.257849	−	0.966185i	$-0.583014\pi$
$389$	13.9706	−	13.9706i	0.708336	−	0.708336i	0.966185	+	0.257849i	$0.0830139\pi$
$390$		0			0
$391$	24.9706			1.26282
$392$		0			0
$393$	4.17157	+	24.3137i	0.210428	+	1.22646i
$394$		0			0
$395$	−4.82843	−	4.82843i	−0.242945	−	0.242945i
$396$		0			0
$397$	1.72792	−	1.72792i	0.0867219	−	0.0867219i	−0.662415	−	0.749137i	$-0.730468\pi$
$397$	1.72792	−	1.72792i	0.0867219	−	0.0867219i	0.749137	+	0.662415i	$0.230468\pi$
$398$		0			0
$399$	5.82843	−	1.00000i	0.291786	−	0.0500626i
$400$		0			0
$401$		−	3.31371i		−	0.165479i	−0.996571	−	0.0827394i	$-0.973633\pi$
$401$		−	3.31371i		−	0.165479i	0.996571	−	0.0827394i	$-0.0263669\pi$
$402$		0			0
$403$	16.6274	+	16.6274i	0.828271	+	0.828271i
$404$		0			0
$405$	3.24264	−	30.5563i	0.161128	−	1.51836i
$406$		0			0
$407$			14.0000i			0.693954i
$408$		0			0
$409$			30.8284i			1.52437i	0.647361	+	0.762184i	$0.275873\pi$
$409$			30.8284i			1.52437i	−0.647361	+	0.762184i	$0.724127\pi$
$410$		0			0
$411$	3.65685	−	5.17157i	0.180379	−	0.255095i
$412$		0			0
$413$	−4.07107	−	4.07107i	−0.200324	−	0.200324i
$414$		0			0
$415$			52.6274i			2.58338i
$416$		0			0
$417$	−0.656854	−	3.82843i	−0.0321663	−	0.187479i
$418$		0			0
$419$	4.75736	−	4.75736i	0.232412	−	0.232412i	−0.581287	−	0.813699i	$-0.697450\pi$
$419$	4.75736	−	4.75736i	0.232412	−	0.232412i	0.813699	+	0.581287i	$0.197450\pi$
$420$		0			0
$421$	−24.3137	−	24.3137i	−1.18498	−	1.18498i	−0.978438	−	0.206539i	$-0.933780\pi$
$421$	−24.3137	−	24.3137i	−1.18498	−	1.18498i	−0.206539	−	0.978438i	$-0.566220\pi$
$422$		0			0
$423$	5.65685	+	16.0000i	0.275046	+	0.777947i
$424$		0			0
$425$	−45.4558			−2.20493
$426$		0			0
$427$	−0.414214	+	0.414214i	−0.0200452	+	0.0200452i
$428$		0			0
$429$	5.79899	−	8.20101i	0.279978	−	0.395949i
$430$		0			0
$431$	−19.3137			−0.930309			−0.465154	−	0.885230i	$-0.654001\pi$
$431$	−19.3137			−0.930309			−0.465154	+	0.885230i	$0.654001\pi$
$432$		0			0
$433$	−37.3137			−1.79318			−0.896591	−	0.442859i	$-0.853964\pi$
$433$	−37.3137			−1.79318			−0.896591	+	0.442859i	$0.853964\pi$
$434$		0			0
$435$	14.4853	−	20.4853i	0.694516	−	0.982194i
$436$		0			0
$437$	−8.82843	+	8.82843i	−0.422321	+	0.422321i
$438$		0			0
$439$	−32.9706			−1.57360			−0.786800	−	0.617209i	$-0.788263\pi$
$439$	−32.9706			−1.57360			−0.786800	+	0.617209i	$0.788263\pi$
$440$		0			0
$441$	−1.00000	−	2.82843i	−0.0476190	−	0.134687i
$442$		0			0
$443$	−5.34315	−	5.34315i	−0.253861	−	0.253861i	0.568691	−	0.822551i	$-0.307450\pi$
$443$	−5.34315	−	5.34315i	−0.253861	−	0.253861i	−0.822551	+	0.568691i	$0.807450\pi$
$444$		0			0
$445$	10.4853	−	10.4853i	0.497050	−	0.497050i
$446$		0			0
$447$	3.10051	+	18.0711i	0.146649	+	0.854732i
$448$		0			0
$449$			20.9706i			0.989662i	0.868989	+	0.494831i	$0.164770\pi$
$449$			20.9706i			0.989662i	−0.868989	+	0.494831i	$0.835230\pi$
$450$		0			0
$451$	21.3137	+	21.3137i	1.00362	+	1.00362i
$452$		0			0
$453$	6.34315	−	8.97056i	0.298027	−	0.421474i
$454$		0			0
$455$		−	7.65685i		−	0.358959i
$456$		0			0
$457$			37.9411i			1.77481i	0.460990	+	0.887405i	$0.347495\pi$
$457$			37.9411i			1.77481i	−0.460990	+	0.887405i	$0.652505\pi$
$458$		0			0
$459$	−9.65685	+	34.1421i	−0.450743	+	1.59362i
$460$		0			0
$461$	−19.5858	−	19.5858i	−0.912201	−	0.912201i	0.0842441	−	0.996445i	$-0.473152\pi$
$461$	−19.5858	−	19.5858i	−0.912201	−	0.912201i	−0.996445	+	0.0842441i	$0.973152\pi$
$462$		0			0
$463$		−	0.343146i		−	0.0159473i	−0.999968	−	0.00797367i	$-0.997462\pi$
$463$		−	0.343146i		−	0.0159473i	0.999968	−	0.00797367i	$-0.00253812\pi$
$464$		0			0
$465$	61.1127	−	10.4853i	2.83403	−	0.486243i
$466$		0			0
$467$	11.5858	−	11.5858i	0.536126	−	0.536126i	−0.386263	−	0.922389i	$-0.626234\pi$
$467$	11.5858	−	11.5858i	0.536126	−	0.536126i	0.922389	+	0.386263i	$0.126234\pi$
$468$		0			0
$469$	7.00000	+	7.00000i	0.323230	+	0.323230i
$470$		0			0
$471$	7.00000	+	40.7990i	0.322543	+	1.87992i
$472$		0			0
$473$	6.68629			0.307436
$474$		0			0
$475$	16.0711	−	16.0711i	0.737391	−	0.737391i
$476$		0			0
$477$	0.656854	+	0.313708i	0.0300753	+	0.0143637i
$478$		0			0
$479$	−4.68629			−0.214122			−0.107061	−	0.994252i	$-0.534144\pi$
$479$	−4.68629			−0.214122			−0.107061	+	0.994252i	$0.534144\pi$
$480$		0			0
$481$	12.1421			0.553634
$482$		0			0
$483$	5.17157	+	3.65685i	0.235315	+	0.166393i
$484$		0			0
$485$	4.82843	−	4.82843i	0.219248	−	0.219248i
$486$		0			0
$487$	−40.2843			−1.82545			−0.912727	−	0.408569i	$-0.866028\pi$
$487$	−40.2843			−1.82545			−0.912727	+	0.408569i	$0.866028\pi$
$488$		0			0
$489$	−9.24264	+	1.58579i	−0.417967	+	0.0717117i
$490$		0			0
$491$	12.3137	+	12.3137i	0.555710	+	0.555710i	0.928083	−	0.372373i	$-0.121456\pi$
$491$	12.3137	+	12.3137i	0.555710	+	0.555710i	−0.372373	+	0.928083i	$0.621456\pi$
$492$		0			0
$493$	−20.4853	+	20.4853i	−0.922611	+	0.922611i
$494$		0			0
$495$	−8.82843	−	24.9706i	−0.396808	−	1.12234i
$496$		0			0
$497$		−	6.00000i		−	0.269137i
$498$		0			0
$499$	−28.3137	−	28.3137i	−1.26750	−	1.26750i	−0.947378	−	0.320118i	$-0.896277\pi$
$499$	−28.3137	−	28.3137i	−1.26750	−	1.26750i	−0.320118	−	0.947378i	$-0.603723\pi$
$500$		0			0
$501$	18.1421	+	12.8284i	0.810531	+	0.573132i
$502$		0			0
$503$		−	11.1716i		−	0.498116i	−0.968489	−	0.249058i	$-0.919879\pi$
$503$		−	11.1716i		−	0.498116i	0.968489	−	0.249058i	$-0.0801210\pi$
$504$		0			0
$505$		−	19.6569i		−	0.874719i
$506$		0			0
$507$	11.2721	+	7.97056i	0.500611	+	0.353985i
$508$		0			0
$509$	−1.24264	−	1.24264i	−0.0550791	−	0.0550791i	0.679031	−	0.734110i	$-0.262400\pi$
$509$	−1.24264	−	1.24264i	−0.0550791	−	0.0550791i	−0.734110	+	0.679031i	$0.762400\pi$
$510$		0			0
$511$		−	10.8284i		−	0.479021i
$512$		0			0
$513$	−8.65685	−	15.4853i	−0.382209	−	0.683692i
$514$		0			0
$515$	−27.3137	+	27.3137i	−1.20359	+	1.20359i
$516$		0			0
$517$	10.3431	+	10.3431i	0.454891	+	0.454891i
$518$		0			0
$519$	−35.9706	+	6.17157i	−1.57893	+	0.270902i
$520$		0			0
$521$	−9.31371			−0.408041			−0.204020	−	0.978967i	$-0.565401\pi$
$521$	−9.31371			−0.408041			−0.204020	+	0.978967i	$0.565401\pi$
$522$		0			0
$523$	27.0416	−	27.0416i	1.18245	−	1.18245i	0.203340	−	0.979108i	$-0.434820\pi$
$523$	27.0416	−	27.0416i	1.18245	−	1.18245i	0.979108	−	0.203340i	$-0.0651796\pi$
$524$		0			0
$525$	−9.41421	−	6.65685i	−0.410870	−	0.290529i
$526$		0			0
$527$	−71.5980			−3.11886
$528$		0			0
$529$	9.62742			0.418583
$530$		0			0
$531$	−7.44365	+	15.5858i	−0.323027	+	0.676366i
$532$		0			0
$533$	18.4853	−	18.4853i	0.800686	−	0.800686i
$534$		0			0
$535$	−24.1421			−1.04376
$536$		0			0
$537$	−6.21320	−	36.2132i	−0.268120	−	1.56272i
$538$		0			0
$539$	−1.82843	−	1.82843i	−0.0787559	−	0.0787559i
$540$		0			0
$541$	−21.0000	+	21.0000i	−0.902861	+	0.902861i	−0.995683	−	0.0928222i	$-0.970411\pi$
$541$	−21.0000	+	21.0000i	−0.902861	+	0.902861i	0.0928222	+	0.995683i	$0.470411\pi$
$542$		0			0
$543$	29.1421	−	5.00000i	1.25061	−	0.214571i
$544$		0			0
$545$			0.828427i			0.0354859i
$546$		0			0
$547$	−11.1421	−	11.1421i	−0.476403	−	0.476403i	0.427576	−	0.903979i	$-0.359368\pi$
$547$	−11.1421	−	11.1421i	−0.476403	−	0.476403i	−0.903979	+	0.427576i	$0.859368\pi$
$548$		0			0
$549$	1.58579	+	0.757359i	0.0676797	+	0.0323233i
$550$		0			0
$551$		−	14.4853i		−	0.617094i
$552$		0			0
$553$			2.00000i			0.0850487i
$554$		0			0
$555$	18.4853	−	26.1421i	0.784656	−	1.10967i
$556$		0			0
$557$	−13.1421	−	13.1421i	−0.556850	−	0.556850i	0.371559	−	0.928409i	$-0.378823\pi$
$557$	−13.1421	−	13.1421i	−0.556850	−	0.556850i	−0.928409	+	0.371559i	$0.878823\pi$
$558$		0			0
$559$		−	5.79899i		−	0.245271i
$560$		0			0
$561$	5.17157	+	30.1421i	0.218344	+	1.27260i
$562$		0			0
$563$	22.4142	−	22.4142i	0.944646	−	0.944646i	−0.0538999	−	0.998546i	$-0.517165\pi$
$563$	22.4142	−	22.4142i	0.944646	−	0.944646i	0.998546	+	0.0538999i	$0.0171652\pi$
$564$		0			0
$565$	−23.3137	−	23.3137i	−0.980815	−	0.980815i
$566$		0			0
$567$	−7.00000	+	5.65685i	−0.293972	+	0.237566i
$568$		0			0
$569$	−12.6274			−0.529369			−0.264684	−	0.964335i	$-0.585268\pi$
$569$	−12.6274			−0.529369			−0.264684	+	0.964335i	$0.585268\pi$
$570$		0			0
$571$	11.8284	−	11.8284i	0.495004	−	0.495004i	−0.414874	−	0.909879i	$-0.636174\pi$
$571$	11.8284	−	11.8284i	0.495004	−	0.495004i	0.909879	+	0.414874i	$0.136174\pi$
$572$		0			0
$573$	17.6569	−	24.9706i	0.737626	−	1.04316i
$574$		0			0
$575$	24.3431			1.01518
$576$		0			0
$577$	−11.6569			−0.485281			−0.242641	−	0.970116i	$-0.578014\pi$
$577$	−11.6569			−0.485281			−0.242641	+	0.970116i	$0.578014\pi$
$578$		0			0
$579$	4.34315	−	6.14214i	0.180495	−	0.255258i
$580$		0			0
$581$	10.8995	−	10.8995i	0.452187	−	0.452187i
$582$		0			0
$583$	0.627417			0.0259850
$584$		0			0
$585$	−21.6569	+	7.65685i	−0.895401	+	0.316572i
$586$		0			0
$587$	−1.92893	−	1.92893i	−0.0796156	−	0.0796156i	0.666178	−	0.745793i	$-0.267929\pi$
$587$	−1.92893	−	1.92893i	−0.0796156	−	0.0796156i	−0.745793	+	0.666178i	$0.767929\pi$
$588$		0			0
$589$	25.3137	−	25.3137i	1.04303	−	1.04303i
$590$		0			0
$591$	0.0710678	+	0.414214i	0.00292334	+	0.0170385i
$592$		0			0
$593$		−	30.1421i		−	1.23779i	−0.785474	−	0.618895i	$-0.787581\pi$
$593$		−	30.1421i		−	1.23779i	0.785474	−	0.618895i	$-0.212419\pi$
$594$		0			0
$595$	16.4853	+	16.4853i	0.675831	+	0.675831i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			9.02944i			0.368933i	0.982839	+	0.184466i	$0.0590557\pi$
$599$			9.02944i			0.368933i	−0.982839	+	0.184466i	$0.940944\pi$
$600$		0			0
$601$		−	0.485281i		−	0.0197950i	−0.999951	−	0.00989752i	$-0.996849\pi$
$601$		−	0.485281i		−	0.0197950i	0.999951	−	0.00989752i	$-0.00315053\pi$
$602$		0			0
$603$	12.7990	−	26.7990i	0.521215	−	1.09134i
$604$		0			0
$605$	10.4142	+	10.4142i	0.423398	+	0.423398i
$606$		0			0
$607$		−	41.1127i		−	1.66871i	−0.551225	−	0.834356i	$-0.685840\pi$
$607$		−	41.1127i		−	1.66871i	0.551225	−	0.834356i	$-0.314160\pi$
$608$		0			0
$609$	−7.24264	+	1.24264i	−0.293487	+	0.0503543i
$610$		0			0
$611$	8.97056	−	8.97056i	0.362910	−	0.362910i
$612$		0			0
$613$	−19.8284	−	19.8284i	−0.800863	−	0.800863i	0.182368	−	0.983230i	$-0.441624\pi$
$613$	−19.8284	−	19.8284i	−0.800863	−	0.800863i	−0.983230	+	0.182368i	$0.941624\pi$
$614$		0			0
$615$	−11.6569	−	67.9411i	−0.470050	−	2.73965i
$616$		0			0
$617$	−26.0000			−1.04672			−0.523360	−	0.852111i	$-0.675322\pi$
$617$	−26.0000			−1.04672			−0.523360	+	0.852111i	$0.675322\pi$
$618$		0			0
$619$	−23.5858	+	23.5858i	−0.947993	+	0.947993i	−0.998713	−	0.0507201i	$-0.983848\pi$
$619$	−23.5858	+	23.5858i	−0.947993	+	0.947993i	0.0507201	+	0.998713i	$0.483848\pi$
$620$		0			0
$621$	5.17157	−	18.2843i	0.207528	−	0.733723i
$622$		0			0
$623$	−4.34315			−0.174004
$624$		0			0
$625$	13.9706			0.558823
$626$		0			0
$627$	−12.4853	−	8.82843i	−0.498614	−	0.352573i
$628$		0			0
$629$	−26.1421	+	26.1421i	−1.04236	+	1.04236i
$630$		0			0
$631$	2.34315			0.0932792			0.0466396	−	0.998912i	$-0.485149\pi$
$631$	2.34315			0.0932792			0.0466396	+	0.998912i	$0.485149\pi$
$632$		0			0
$633$	−12.0711	+	2.07107i	−0.479782	+	0.0823176i
$634$		0			0
$635$	10.4853	+	10.4853i	0.416096	+	0.416096i
$636$		0			0
$637$	−1.58579	+	1.58579i	−0.0628311	+	0.0628311i
$638$		0			0
$639$	−16.9706	+	6.00000i	−0.671345	+	0.237356i
$640$		0			0
$641$			45.2548i			1.78746i	0.448607	+	0.893729i	$0.351920\pi$
$641$			45.2548i			1.78746i	−0.448607	+	0.893729i	$0.648080\pi$
$642$		0			0
$643$	−27.0416	−	27.0416i	−1.06642	−	1.06642i	−0.997631	−	0.0687864i	$-0.978087\pi$
$643$	−27.0416	−	27.0416i	−1.06642	−	1.06642i	−0.0687864	−	0.997631i	$-0.521913\pi$
$644$		0			0
$645$	−12.4853	−	8.82843i	−0.491607	−	0.347619i
$646$		0			0
$647$		−	12.1421i		−	0.477357i	−0.971099	−	0.238678i	$-0.923286\pi$
$647$		−	12.1421i		−	0.477357i	0.971099	−	0.238678i	$-0.0767141\pi$
$648$		0			0
$649$			14.8873i			0.584378i
$650$		0			0
$651$	−14.8284	−	10.4853i	−0.581172	−	0.410951i
$652$		0			0
$653$	22.6569	+	22.6569i	0.886631	+	0.886631i	0.994198	−	0.107567i	$-0.0343059\pi$
$653$	22.6569	+	22.6569i	0.886631	+	0.886631i	−0.107567	+	0.994198i	$0.534306\pi$
$654$		0			0
$655$		−	48.6274i		−	1.90003i
$656$		0			0
$657$	−30.6274	+	10.8284i	−1.19489	+	0.422457i
$658$		0			0
$659$	−8.51472	+	8.51472i	−0.331686	+	0.331686i	−0.853227	−	0.521540i	$-0.825358\pi$
$659$	−8.51472	+	8.51472i	−0.331686	+	0.331686i	0.521540	+	0.853227i	$0.325358\pi$
$660$		0			0
$661$	−25.3848	−	25.3848i	−0.987353	−	0.987353i	0.0125677	−	0.999921i	$-0.495999\pi$
$661$	−25.3848	−	25.3848i	−0.987353	−	0.987353i	−0.999921	+	0.0125677i	$0.995999\pi$
$662$		0			0
$663$	26.1421	−	4.48528i	1.01528	−	0.174194i
$664$		0			0
$665$	−11.6569			−0.452033
$666$		0			0
$667$	10.9706	−	10.9706i	0.424782	−	0.424782i
$668$		0			0
$669$	−18.1421	−	12.8284i	−0.701415	−	0.495976i
$670$		0			0
$671$	1.51472			0.0584751
$672$		0			0
$673$	−2.00000			−0.0770943			−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000			−0.0770943			−0.0385472	+	0.999257i	$0.512273\pi$
$674$		0			0
$675$	−9.41421	+	33.2843i	−0.362353	+	1.28111i
$676$		0			0
$677$	1.10051	−	1.10051i	0.0422958	−	0.0422958i	−0.685643	−	0.727938i	$-0.740479\pi$
$677$	1.10051	−	1.10051i	0.0422958	−	0.0422958i	0.727938	+	0.685643i	$0.240479\pi$
$678$		0			0
$679$	−2.00000			−0.0767530
$680$		0			0
$681$	2.51472	+	14.6569i	0.0963642	+	0.561652i
$682$		0			0
$683$	−22.3137	−	22.3137i	−0.853810	−	0.853810i	0.136790	−	0.990600i	$-0.456322\pi$
$683$	−22.3137	−	22.3137i	−0.853810	−	0.853810i	−0.990600	+	0.136790i	$0.956322\pi$
$684$		0			0
$685$	−8.82843	+	8.82843i	−0.337317	+	0.337317i
$686$		0			0
$687$	−21.4853	+	3.68629i	−0.819715	+	0.140641i
$688$		0			0
$689$		−	0.544156i		−	0.0207307i
$690$		0			0
$691$	−4.89949	−	4.89949i	−0.186386	−	0.186386i	0.607746	−	0.794132i	$-0.292074\pi$
$691$	−4.89949	−	4.89949i	−0.186386	−	0.186386i	−0.794132	+	0.607746i	$0.792074\pi$
$692$		0			0
$693$	−3.34315	+	7.00000i	−0.126996	+	0.265908i
$694$		0			0
$695$			7.65685i			0.290441i
$696$		0			0
$697$			79.5980i			3.01499i
$698$		0			0
$699$	21.3137	−	30.1421i	0.806158	−	1.14008i
$700$		0			0
$701$	10.6569	+	10.6569i	0.402504	+	0.402504i	0.879114	−	0.476611i	$-0.158135\pi$
$701$	10.6569	+	10.6569i	0.402504	+	0.402504i	−0.476611	+	0.879114i	$0.658135\pi$
$702$		0			0
$703$		−	18.4853i		−	0.697186i
$704$		0			0
$705$	−5.65685	−	32.9706i	−0.213049	−	1.24174i
$706$		0			0
$707$	−4.07107	+	4.07107i	−0.153108	+	0.153108i
$708$		0			0
$709$	−7.82843	−	7.82843i	−0.294003	−	0.294003i	0.544656	−	0.838659i	$-0.316660\pi$
$709$	−7.82843	−	7.82843i	−0.294003	−	0.294003i	−0.838659	+	0.544656i	$0.816660\pi$
$710$		0			0
$711$	5.65685	−	2.00000i	0.212149	−	0.0750059i
$712$		0			0
$713$	38.3431			1.43596
$714$		0			0
$715$	−14.0000	+	14.0000i	−0.523570	+	0.523570i
$716$		0			0
$717$	11.3137	−	16.0000i	0.422518	−	0.597531i
$718$		0			0
$719$	16.0000			0.596699			0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000			0.596699			0.298350	+	0.954457i	$0.403564\pi$
$720$		0			0
$721$	11.3137			0.421345
$722$		0			0
$723$	11.6569	−	16.4853i	0.433523	−	0.613094i
$724$		0			0
$725$	−19.9706	+	19.9706i	−0.741688	+	0.741688i
$726$		0			0
$727$	12.6863			0.470509			0.235254	−	0.971934i	$-0.424408\pi$
$727$	12.6863			0.470509			0.235254	+	0.971934i	$0.424408\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$		0			0
$731$	12.4853	+	12.4853i	0.461785	+	0.461785i
$732$		0			0
$733$	−27.7279	+	27.7279i	−1.02415	+	1.02415i	−0.0244532	+	0.999701i	$0.507784\pi$
$733$	−27.7279	+	27.7279i	−1.02415	+	1.02415i	−0.999701	+	0.0244532i	$0.992216\pi$
$734$		0			0
$735$	1.00000	+	5.82843i	0.0368856	+	0.214985i
$736$		0			0
$737$		−	25.5980i		−	0.942914i
$738$		0			0
$739$	16.1716	+	16.1716i	0.594881	+	0.594881i	0.938946	−	0.344065i	$-0.111804\pi$
$739$	16.1716	+	16.1716i	0.594881	+	0.594881i	−0.344065	+	0.938946i	$0.611804\pi$
$740$		0			0
$741$	−7.65685	+	10.8284i	−0.281282	+	0.397792i
$742$		0			0
$743$		−	15.6569i		−	0.574394i	−0.957871	−	0.287197i	$-0.907277\pi$
$743$		−	15.6569i		−	0.574394i	0.957871	−	0.287197i	$-0.0927235\pi$
$744$		0			0
$745$		−	36.1421i		−	1.32415i
$746$		0			0
$747$	−41.7279	−	19.9289i	−1.52674	−	0.729161i
$748$		0			0
$749$	5.00000	+	5.00000i	0.182696	+	0.182696i
$750$		0			0
$751$			41.3137i			1.50756i	0.657128	+	0.753779i	$0.271771\pi$
$751$			41.3137i			1.50756i	−0.657128	+	0.753779i	$0.728229\pi$
$752$		0			0
$753$	1.00000	−	0.171573i	0.0364420	−	0.00625246i
$754$		0			0
$755$	−15.3137	+	15.3137i	−0.557323	+	0.557323i
$756$		0			0
$757$	31.4853	+	31.4853i	1.14435	+	1.14435i	0.987645	+	0.156707i	$0.0500878\pi$
$757$	31.4853	+	31.4853i	1.14435	+	1.14435i	0.156707	+	0.987645i	$0.449912\pi$
$758$		0			0
$759$	−2.76955	−	16.1421i	−0.100528	−	0.585922i
$760$		0			0
$761$	8.62742			0.312744			0.156372	−	0.987698i	$-0.450020\pi$
$761$	8.62742			0.312744			0.156372	+	0.987698i	$0.450020\pi$
$762$		0			0
$763$	0.171573	−	0.171573i	0.00621136	−	0.00621136i
$764$		0			0
$765$	30.1421	−	63.1127i	1.08979	−	2.28184i
$766$		0			0
$767$	12.9117			0.466214
$768$		0			0
$769$	35.6569			1.28582			0.642910	−	0.765942i	$-0.277727\pi$
$769$	35.6569			1.28582			0.642910	+	0.765942i	$0.277727\pi$
$770$		0			0
$771$	−29.9411	−	21.1716i	−1.07830	−	0.762476i
$772$		0			0
$773$	−5.44365	+	5.44365i	−0.195795	+	0.195795i	−0.798194	−	0.602400i	$-0.794211\pi$
$773$	−5.44365	+	5.44365i	−0.195795	+	0.195795i	0.602400	+	0.798194i	$0.294211\pi$
$774$		0			0
$775$	−69.7990			−2.50725
$776$		0			0
$777$	−9.24264	+	1.58579i	−0.331578	+	0.0568898i
$778$		0			0
$779$	−28.1421	−	28.1421i	−1.00830	−	1.00830i
$780$		0			0
$781$	−10.9706	+	10.9706i	−0.392558	+	0.392558i
$782$		0			0
$783$	10.7574	+	19.2426i	0.384437	+	0.687676i
$784$		0			0
$785$		−	81.5980i		−	2.91236i
$786$		0			0
$787$	25.0416	+	25.0416i	0.892638	+	0.892638i	0.994771	−	0.102133i	$-0.0325667\pi$
$787$	25.0416	+	25.0416i	0.892638	+	0.892638i	−0.102133	+	0.994771i	$0.532567\pi$
$788$		0			0
$789$	−0.485281	−	0.343146i	−0.0172765	−	0.0122163i
$790$		0			0
$791$			9.65685i			0.343358i
$792$		0			0
$793$		−	1.31371i		−	0.0466512i
$794$		0			0
$795$	−1.17157	−	0.828427i	−0.0415514	−	0.0293813i
$796$		0			0
$797$	−31.5858	−	31.5858i	−1.11883	−	1.11883i	−0.991914	−	0.126912i	$-0.959493\pi$
$797$	−31.5858	−	31.5858i	−1.11883	−	1.11883i	−0.126912	−	0.991914i	$-0.540507\pi$
$798$		0			0
$799$			38.6274i			1.36654i
$800$		0			0
$801$	4.34315	+	12.2843i	0.153458	+	0.434043i
$802$		0			0
$803$	−19.7990	+	19.7990i	−0.698691	+	0.698691i
$804$		0			0
$805$	−8.82843	−	8.82843i	−0.311161	−	0.311161i
$806$		0			0
$807$	20.3137	−	3.48528i	0.715076	−	0.122688i
$808$		0			0
$809$	45.3137			1.59315			0.796573	−	0.604543i	$-0.206644\pi$
$809$	45.3137			1.59315			0.796573	+	0.604543i	$0.206644\pi$
$810$		0			0
$811$	−1.92893	+	1.92893i	−0.0677340	+	0.0677340i	−0.740162	−	0.672428i	$-0.765251\pi$
$811$	−1.92893	+	1.92893i	−0.0677340	+	0.0677340i	0.672428	+	0.740162i	$0.265251\pi$
$812$		0			0
$813$	15.7990	+	11.1716i	0.554095	+	0.391804i
$814$		0			0
$815$	18.4853			0.647511
$816$		0			0
$817$	−8.82843			−0.308868
$818$		0			0
$819$	6.07107	+	2.89949i	0.212140	+	0.101317i
$820$		0			0
$821$	1.48528	−	1.48528i	0.0518367	−	0.0518367i	−0.680713	−	0.732550i	$-0.738330\pi$
$821$	1.48528	−	1.48528i	0.0518367	−	0.0518367i	0.732550	+	0.680713i	$0.238330\pi$
$822$		0			0
$823$	8.97056			0.312694			0.156347	−	0.987702i	$-0.450028\pi$
$823$	8.97056			0.312694			0.156347	+	0.987702i	$0.450028\pi$
$824$		0			0
$825$	5.04163	+	29.3848i	0.175527	+	1.02305i
$826$		0			0
$827$	9.00000	+	9.00000i	0.312961	+	0.312961i	0.846055	−	0.533095i	$-0.178971\pi$
$827$	9.00000	+	9.00000i	0.312961	+	0.312961i	−0.533095	+	0.846055i	$0.678971\pi$
$828$		0			0
$829$	−5.10051	+	5.10051i	−0.177148	+	0.177148i	−0.790111	−	0.612963i	$-0.789977\pi$
$829$	−5.10051	+	5.10051i	−0.177148	+	0.177148i	0.612963	+	0.790111i	$0.289977\pi$
$830$		0			0
$831$	−39.3848	+	6.75736i	−1.36624	+	0.234410i
$832$		0			0
$833$		−	6.82843i		−	0.236591i
$834$		0			0
$835$	−30.9706	−	30.9706i	−1.07178	−	1.07178i
$836$		0			0
$837$	−14.8284	+	52.4264i	−0.512545	+	1.81212i
$838$		0			0
$839$			0.544156i			0.0187863i	0.999956	+	0.00939317i	$0.00298998\pi$
$839$			0.544156i			0.0187863i	−0.999956	+	0.00939317i	$0.997010\pi$
$840$		0			0
$841$		−	11.0000i		−	0.379310i
$842$		0			0
$843$	29.3137	−	41.4558i	1.00962	−	1.42782i
$844$		0			0
$845$	−19.2426	−	19.2426i	−0.661967	−	0.661967i
$846$		0			0
$847$		−	4.31371i		−	0.148221i
$848$		0			0
$849$	2.85786	+	16.6569i	0.0980817	+	0.571662i
$850$		0			0
$851$	14.0000	−	14.0000i	0.479914	−	0.479914i
$852$		0			0
$853$	−25.5858	−	25.5858i	−0.876041	−	0.876041i	0.117082	−	0.993122i	$-0.462646\pi$
$853$	−25.5858	−	25.5858i	−0.876041	−	0.876041i	−0.993122	+	0.117082i	$0.962646\pi$
$854$		0			0
$855$	11.6569	+	32.9706i	0.398656	+	1.12757i
$856$		0			0
$857$	35.9411			1.22773			0.613863	−	0.789413i	$-0.289615\pi$
$857$	35.9411			1.22773			0.613863	+	0.789413i	$0.289615\pi$
$858$		0			0
$859$	−3.10051	+	3.10051i	−0.105788	+	0.105788i	−0.758020	−	0.652232i	$-0.773833\pi$
$859$	−3.10051	+	3.10051i	−0.105788	+	0.105788i	0.652232	+	0.758020i	$0.273833\pi$
$860$		0			0
$861$	−11.6569	+	16.4853i	−0.397265	+	0.561817i
$862$		0			0
$863$	16.6863			0.568008			0.284004	−	0.958823i	$-0.408337\pi$
$863$	16.6863			0.568008			0.284004	+	0.958823i	$0.408337\pi$
$864$		0			0
$865$	71.9411			2.44607
$866$		0			0
$867$	−29.6274	+	41.8995i	−1.00620	+	1.42298i
$868$		0			0
$869$	3.65685	−	3.65685i	0.124050	−	0.124050i
$870$		0			0
$871$	−22.2010			−0.752253
$872$		0			0
$873$	2.00000	+	5.65685i	0.0676897	+	0.191456i
$874$		0			0
$875$	4.00000	+	4.00000i	0.135225	+	0.135225i
$876$		0			0
$877$	23.4853	−	23.4853i	0.793042	−	0.793042i	−0.188946	−	0.981987i	$-0.560507\pi$
$877$	23.4853	−	23.4853i	0.793042	−	0.793042i	0.981987	+	0.188946i	$0.0605071\pi$
$878$		0			0
$879$	0.313708	+	1.82843i	0.0105811	+	0.0616713i
$880$		0			0
$881$			31.5147i			1.06176i	0.847448	+	0.530879i	$0.178138\pi$
$881$			31.5147i			1.06176i	−0.847448	+	0.530879i	$0.821862\pi$
$882$		0			0
$883$	28.9411	+	28.9411i	0.973946	+	0.973946i	0.999669	−	0.0257227i	$-0.00818869\pi$
$883$	28.9411	+	28.9411i	0.973946	+	0.973946i	−0.0257227	+	0.999669i	$0.508189\pi$
$884$		0			0
$885$	19.6569	−	27.7990i	0.660758	−	0.934453i
$886$		0			0
$887$			44.8284i			1.50519i	0.658483	+	0.752596i	$0.271198\pi$
$887$			44.8284i			1.50519i	−0.658483	+	0.752596i	$0.728802\pi$
$888$		0			0
$889$		−	4.34315i		−	0.145664i
$890$		0			0
$891$	23.1421	+	2.45584i	0.775291	+	0.0822739i
$892$		0			0
$893$	−13.6569	−	13.6569i	−0.457009	−	0.457009i
$894$		0			0
$895$			72.4264i			2.42095i
$896$		0			0
$897$	−14.0000	+	2.40202i	−0.467446	+	0.0802011i
$898$		0			0
$899$	−31.4558	+	31.4558i	−1.04911	+	1.04911i
$900$		0			0
$901$	1.17157	+	1.17157i	0.0390308	+	0.0390308i
$902$		0			0
$903$	0.757359	+	4.41421i	0.0252033	+	0.146896i
$904$		0			0
$905$	−58.2843			−1.93743
$906$		0			0
$907$	−2.31371	+	2.31371i	−0.0768254	+	0.0768254i	−0.744475	−	0.667650i	$-0.767300\pi$
$907$	−2.31371	+	2.31371i	−0.0768254	+	0.0768254i	0.667650	+	0.744475i	$0.267300\pi$
$908$		0			0
$909$	15.5858	+	7.44365i	0.516948	+	0.246890i
$910$		0			0
$911$	−12.2843			−0.406996			−0.203498	−	0.979075i	$-0.565231\pi$
$911$	−12.2843			−0.406996			−0.203498	+	0.979075i	$0.565231\pi$
$912$		0			0
$913$	−39.8579			−1.31910
$914$		0			0
$915$	−2.82843	−	2.00000i	−0.0935049	−	0.0661180i
$916$		0			0
$917$	−10.0711	+	10.0711i	−0.332576	+	0.332576i
$918$		0			0
$919$	13.6569			0.450498			0.225249	−	0.974301i	$-0.427680\pi$
$919$	13.6569			0.450498			0.225249	+	0.974301i	$0.427680\pi$
$920$		0			0
$921$	−11.8284	+	2.02944i	−0.389760	+	0.0668722i
$922$		0			0
$923$	9.51472	+	9.51472i	0.313181	+	0.313181i
$924$		0			0
$925$	−25.4853	+	25.4853i	−0.837951	+	0.837951i
$926$		0			0
$927$	−11.3137	−	32.0000i	−0.371591	−	1.05102i
$928$		0			0
$929$			43.1127i			1.41448i	0.706973	+	0.707241i	$0.250060\pi$
$929$			43.1127i			1.41448i	−0.706973	+	0.707241i	$0.749940\pi$
$930$		0			0
$931$	2.41421	+	2.41421i	0.0791227	+	0.0791227i
$932$		0			0
$933$	26.1421	+	18.4853i	0.855855	+	0.605181i
$934$		0			0
$935$		−	60.2843i		−	1.97151i
$936$		0			0
$937$		−	30.1421i		−	0.984701i	−0.870397	−	0.492350i	$-0.836138\pi$
$937$		−	30.1421i		−	0.984701i	0.870397	−	0.492350i	$-0.163862\pi$
$938$		0			0
$939$	−4.97056	−	3.51472i	−0.162208	−	0.114699i
$940$		0			0
$941$	−28.3553	−	28.3553i	−0.924358	−	0.924358i	0.0729761	−	0.997334i	$-0.476750\pi$
$941$	−28.3553	−	28.3553i	−0.924358	−	0.924358i	−0.997334	+	0.0729761i	$0.976750\pi$
$942$		0			0
$943$		−	42.6274i		−	1.38814i
$944$		0			0
$945$	15.4853	−	8.65685i	0.503736	−	0.281607i
$946$		0			0
$947$	9.14214	−	9.14214i	0.297079	−	0.297079i	−0.542789	−	0.839869i	$-0.682632\pi$
$947$	9.14214	−	9.14214i	0.297079	−	0.297079i	0.839869	+	0.542789i	$0.182632\pi$
$948$		0			0
$949$	17.1716	+	17.1716i	0.557413	+	0.557413i
$950$		0			0
$951$	36.5563	−	6.27208i	1.18542	−	0.203386i
$952$		0			0
$953$	−31.6569			−1.02547			−0.512733	−	0.858548i	$-0.671367\pi$
$953$	−31.6569			−1.02547			−0.512733	+	0.858548i	$0.671367\pi$
$954$		0			0
$955$	−42.6274	+	42.6274i	−1.37939	+	1.37939i
$956$		0			0
$957$	15.5147	+	10.9706i	0.501520	+	0.354628i
$958$		0			0
$959$	3.65685			0.118086
$960$		0			0
$961$	−78.9411			−2.54649
$962$		0			0
$963$	9.14214	−	19.1421i	0.294601	−	0.616847i
$964$		0			0
$965$	−10.4853	+	10.4853i	−0.337533	+	0.337533i
$966$		0			0
$967$	0.686292			0.0220696			0.0110348	−	0.999939i	$-0.496487\pi$
$967$	0.686292			0.0220696			0.0110348	+	0.999939i	$0.496487\pi$
$968$		0			0
$969$	−6.82843	−	39.7990i	−0.219361	−	1.27853i
$970$		0			0
$971$	16.8995	+	16.8995i	0.542331	+	0.542331i	0.924212	−	0.381881i	$-0.124724\pi$
$971$	16.8995	+	16.8995i	0.542331	+	0.542331i	−0.381881	+	0.924212i	$0.624724\pi$
$972$		0			0
$973$	1.58579	−	1.58579i	0.0508380	−	0.0508380i
$974$		0			0
$975$	25.4853	−	4.37258i	0.816182	−	0.140035i
$976$		0			0
$977$		−	31.3137i		−	1.00181i	−0.865501	−	0.500907i	$-0.833000\pi$
$977$		−	31.3137i		−	1.00181i	0.865501	−	0.500907i	$-0.167000\pi$
$978$		0			0
$979$	7.94113	+	7.94113i	0.253799	+	0.253799i
$980$		0			0
$981$	−0.656854	−	0.313708i	−0.0209717	−	0.0100159i
$982$		0			0
$983$		−	54.4853i		−	1.73781i	−0.494978	−	0.868905i	$-0.664824\pi$
$983$		−	54.4853i		−	1.73781i	0.494978	−	0.868905i	$-0.335176\pi$
$984$		0			0
$985$		−	0.828427i		−	0.0263959i
$986$		0			0
$987$	−5.65685	+	8.00000i	−0.180060	+	0.254643i
$988$		0			0
$989$	−6.68629	−	6.68629i	−0.212612	−	0.212612i
$990$		0			0
$991$			45.3137i			1.43944i	0.694266	+	0.719719i	$0.255729\pi$
$991$			45.3137i			1.43944i	−0.694266	+	0.719719i	$0.744271\pi$
$992$		0			0
$993$	−4.61522	−	26.8995i	−0.146460	−	0.853630i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−34.0711	−	34.0711i	−1.07904	−	1.07904i	−0.996596	−	0.0824460i	$-0.973727\pi$
$997$	−34.0711	−	34.0711i	−1.07904	−	1.07904i	−0.0824460	−	0.996596i	$-0.526273\pi$
$998$		0			0
$999$	13.7279	+	24.5563i	0.434332	+	0.776929i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1344.2.s.b.911.1		4
3.2	odd	2		1344.2.s.a.911.1		4
4.3	odd	2		336.2.s.a.155.2	✓	4
12.11	even	2		336.2.s.b.155.2	yes	4
16.3	odd	4		1344.2.s.a.239.1		4
16.13	even	4		336.2.s.b.323.2	yes	4
48.29	odd	4		336.2.s.a.323.1	yes	4
48.35	even	4	inner	1344.2.s.b.239.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.a.155.2	✓	4	4.3	odd	2
336.2.s.a.323.1	yes	4	48.29	odd	4
336.2.s.b.155.2	yes	4	12.11	even	2
336.2.s.b.323.2	yes	4	16.13	even	4
1344.2.s.a.239.1		4	16.3	odd	4
1344.2.s.a.911.1		4	3.2	odd	2
1344.2.s.b.239.2		4	48.35	even	4	inner
1344.2.s.b.911.1		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1344.s (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.41421i) q^{3} +(-2.41421 + 2.41421i) q^{5} +1.00000 q^{7} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.41421i) q^{3} +(-2.41421 + 2.41421i) q^{5} +1.00000 q^{7} +(-1.00000 - 2.82843i) q^{9} +(-1.82843 - 1.82843i) q^{11} +(-1.58579 + 1.58579i) q^{13} +(1.00000 + 5.82843i) q^{15} -6.82843i q^{17} +(2.41421 + 2.41421i) q^{19} +(1.00000 - 1.41421i) q^{21} +3.65685i q^{23} -6.65685i q^{25} +(-5.00000 - 1.41421i) q^{27} +(-3.00000 - 3.00000i) q^{29} -10.4853i q^{31} +(-4.41421 + 0.757359i) q^{33} +(-2.41421 + 2.41421i) q^{35} +(-3.82843 - 3.82843i) q^{37} +(0.656854 + 3.82843i) q^{39} -11.6569 q^{41} +(-1.82843 + 1.82843i) q^{43} +(9.24264 + 4.41421i) q^{45} -5.65685 q^{47} +1.00000 q^{49} +(-9.65685 - 6.82843i) q^{51} +(-0.171573 + 0.171573i) q^{53} +8.82843 q^{55} +(5.82843 - 1.00000i) q^{57} +(-4.07107 - 4.07107i) q^{59} +(-0.414214 + 0.414214i) q^{61} +(-1.00000 - 2.82843i) q^{63} -7.65685i q^{65} +(7.00000 + 7.00000i) q^{67} +(5.17157 + 3.65685i) q^{69} -6.00000i q^{71} -10.8284i q^{73} +(-9.41421 - 6.65685i) q^{75} +(-1.82843 - 1.82843i) q^{77} +2.00000i q^{79} +(-7.00000 + 5.65685i) q^{81} +(10.8995 - 10.8995i) q^{83} +(16.4853 + 16.4853i) q^{85} +(-7.24264 + 1.24264i) q^{87} -4.34315 q^{89} +(-1.58579 + 1.58579i) q^{91} +(-14.8284 - 10.4853i) q^{93} -11.6569 q^{95} -2.00000 q^{97} +(-3.34315 + 7.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 4 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 12 q^{13} + 4 q^{15} + 4 q^{19} + 4 q^{21} - 20 q^{27} - 12 q^{29} - 12 q^{33} - 4 q^{35} - 4 q^{37} - 20 q^{39} - 24 q^{41} + 4 q^{43} + 20 q^{45} + 4 q^{49} - 16 q^{51} - 12 q^{53} + 24 q^{55} + 12 q^{57} + 12 q^{59} + 4 q^{61} - 4 q^{63} + 28 q^{67} + 32 q^{69} - 32 q^{75} + 4 q^{77} - 28 q^{81} + 4 q^{83} + 32 q^{85} - 12 q^{87} - 40 q^{89} - 12 q^{91} - 48 q^{93} - 24 q^{95} - 8 q^{97} - 36 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 12 * q^13 + 4 * q^15 + 4 * q^19 + 4 * q^21 - 20 * q^27 - 12 * q^29 - 12 * q^33 - 4 * q^35 - 4 * q^37 - 20 * q^39 - 24 * q^41 + 4 * q^43 + 20 * q^45 + 4 * q^49 - 16 * q^51 - 12 * q^53 + 24 * q^55 + 12 * q^57 + 12 * q^59 + 4 * q^61 - 4 * q^63 + 28 * q^67 + 32 * q^69 - 32 * q^75 + 4 * q^77 - 28 * q^81 + 4 * q^83 + 32 * q^85 - 12 * q^87 - 40 * q^89 - 12 * q^91 - 48 * q^93 - 24 * q^95 - 8 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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