LMFDB - Embedded newform 380.2.y.a.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(217,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("380.217");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.y (of order $12$, degree $4$, 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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			373.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	380.373
Dual form			380.2.y.a.217.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.36603 + 0.633975i) q^{3} +(-1.23205 + 1.86603i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(2.59808 + 1.50000i) q^{9} +O(q^{10})$	\(q+(2.36603 + 0.633975i) q^{3} +(-1.23205 + 1.86603i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(2.59808 + 1.50000i) q^{9} +1.00000 q^{11} +(0.633975 + 2.36603i) q^{13} +(-4.09808 + 3.63397i) q^{15} +(1.36603 + 0.366025i) q^{17} +(4.33013 + 0.500000i) q^{19} +(-6.00000 + 3.46410i) q^{21} +(-1.96410 - 4.59808i) q^{25} +(4.33013 - 7.50000i) q^{29} +1.73205i q^{31} +(2.36603 + 0.633975i) q^{33} +(-1.26795 - 6.19615i) q^{35} +(-3.46410 - 3.46410i) q^{37} +6.00000i q^{39} +(3.00000 - 1.73205i) q^{41} +(1.46410 - 5.46410i) q^{43} +(-6.00000 + 3.00000i) q^{45} +(-1.09808 - 4.09808i) q^{47} -1.00000i q^{49} +(3.00000 + 1.73205i) q^{51} +(1.90192 + 7.09808i) q^{53} +(-1.23205 + 1.86603i) q^{55} +(9.92820 + 3.92820i) q^{57} +(-0.866025 - 1.50000i) q^{59} +(-6.50000 + 11.2583i) q^{61} +(-8.19615 + 2.19615i) q^{63} +(-5.19615 - 1.73205i) q^{65} +(11.8301 - 3.16987i) q^{67} +(10.5000 - 6.06218i) q^{71} +(-3.66025 + 13.6603i) q^{73} +(-1.73205 - 12.1244i) q^{75} +(-2.00000 + 2.00000i) q^{77} +(-6.06218 - 10.5000i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.00000 - 4.00000i) q^{83} +(-2.36603 + 2.09808i) q^{85} +(15.0000 - 15.0000i) q^{87} +(7.79423 - 13.5000i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(-1.09808 + 4.09808i) q^{93} +(-6.26795 + 7.46410i) q^{95} +(-5.07180 + 18.9282i) q^{97} +(2.59808 + 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 2 q^{5} - 8 q^{7}+O(q^{10}) $ 4 * q + 6 * q^3 + 2 * q^5 - 8 * q^7	$ 4 q + 6 q^{3} + 2 q^{5} - 8 q^{7} + 4 q^{11} + 6 q^{13} - 6 q^{15} + 2 q^{17} - 24 q^{21} + 6 q^{25} + 6 q^{33} - 12 q^{35} + 12 q^{41} - 8 q^{43} - 24 q^{45} + 6 q^{47} + 12 q^{51} + 18 q^{53} + 2 q^{55} + 12 q^{57} - 26 q^{61} - 12 q^{63} + 30 q^{67} + 42 q^{71} + 20 q^{73} - 8 q^{77} - 18 q^{81} - 16 q^{83} - 6 q^{85} + 60 q^{87} - 24 q^{91} + 6 q^{93} - 32 q^{95} - 48 q^{97}+O(q^{100}) $ 4 * q + 6 * q^3 + 2 * q^5 - 8 * q^7 + 4 * q^11 + 6 * q^13 - 6 * q^15 + 2 * q^17 - 24 * q^21 + 6 * q^25 + 6 * q^33 - 12 * q^35 + 12 * q^41 - 8 * q^43 - 24 * q^45 + 6 * q^47 + 12 * q^51 + 18 * q^53 + 2 * q^55 + 12 * q^57 - 26 * q^61 - 12 * q^63 + 30 * q^67 + 42 * q^71 + 20 * q^73 - 8 * q^77 - 18 * q^81 - 16 * q^83 - 6 * q^85 + 60 * q^87 - 24 * q^91 + 6 * q^93 - 32 * q^95 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.36603	+	0.633975i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$3$	2.36603	+	0.633975i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$4$		0			0
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$5$	−1.23205	+	1.86603i	−0.550990	+	0.834512i
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$		0			0
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$		0			0
$11$	1.00000			0.301511			0.150756	−	0.988571i	$-0.451829\pi$
$11$	1.00000			0.301511			0.150756	+	0.988571i	$0.451829\pi$
$12$		0			0
$13$	0.633975	+	2.36603i	0.175833	+	0.656217i	0.996408	+	0.0846790i	$0.0269865\pi$
$13$	0.633975	+	2.36603i	0.175833	+	0.656217i	−0.820575	+	0.571538i	$0.806347\pi$
$14$		0			0
$15$	−4.09808	+	3.63397i	−1.05812	+	0.938288i
$16$		0			0
$17$	1.36603	+	0.366025i	0.331310	+	0.0887742i	0.420639	−	0.907228i	$-0.361806\pi$
$17$	1.36603	+	0.366025i	0.331310	+	0.0887742i	−0.0893296	+	0.996002i	$0.528472\pi$
$18$		0			0
$19$	4.33013	+	0.500000i	0.993399	+	0.114708i
$19$	4.33013	+	0.500000i	0.993399	+	0.114708i
$20$		0			0
$21$	−6.00000	+	3.46410i	−1.30931	+	0.755929i
$22$		0			0
$23$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$23$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$24$		0			0
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.33013	−	7.50000i	0.804084	−	1.39272i	−0.112823	−	0.993615i	$-0.535989\pi$
$29$	4.33013	−	7.50000i	0.804084	−	1.39272i	0.916907	−	0.399100i	$-0.130677\pi$
$30$		0			0
$31$			1.73205i			0.311086i	0.987829	+	0.155543i	$0.0497126\pi$
$31$			1.73205i			0.311086i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	2.36603	+	0.633975i	0.411872	+	0.110361i
$34$		0			0
$35$	−1.26795	−	6.19615i	−0.214323	−	1.04734i
$36$		0			0
$37$	−3.46410	−	3.46410i	−0.569495	−	0.569495i	0.362492	−	0.931987i	$-0.381926\pi$
$37$	−3.46410	−	3.46410i	−0.569495	−	0.569495i	−0.931987	+	0.362492i	$0.881926\pi$
$38$		0			0
$39$			6.00000i			0.960769i
$40$		0			0
$41$	3.00000	−	1.73205i	0.468521	−	0.270501i	−0.247099	−	0.968990i	$-0.579477\pi$
$41$	3.00000	−	1.73205i	0.468521	−	0.270501i	0.715621	+	0.698489i	$0.246144\pi$
$42$		0			0
$43$	1.46410	−	5.46410i	0.223273	−	0.833268i	−0.759816	−	0.650139i	$-0.774711\pi$
$43$	1.46410	−	5.46410i	0.223273	−	0.833268i	0.983089	−	0.183129i	$-0.0586226\pi$
$44$		0			0
$45$	−6.00000	+	3.00000i	−0.894427	+	0.447214i
$46$		0			0
$47$	−1.09808	−	4.09808i	−0.160171	−	0.597766i	−0.998607	−	0.0527658i	$-0.983196\pi$
$47$	−1.09808	−	4.09808i	−0.160171	−	0.597766i	0.838436	−	0.545000i	$-0.183470\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	3.00000	+	1.73205i	0.420084	+	0.242536i
$52$		0			0
$53$	1.90192	+	7.09808i	0.261249	+	0.974996i	0.964506	+	0.264060i	$0.0850617\pi$
$53$	1.90192	+	7.09808i	0.261249	+	0.974996i	−0.703257	+	0.710936i	$0.748272\pi$
$54$		0			0
$55$	−1.23205	+	1.86603i	−0.166130	+	0.251615i
$56$		0			0
$57$	9.92820	+	3.92820i	1.31502	+	0.520303i
$58$		0			0
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	0.804130	−	0.594454i	$-0.202632\pi$
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	−0.916877	+	0.399170i	$0.869298\pi$
$60$		0			0
$61$	−6.50000	+	11.2583i	−0.832240	+	1.44148i	0.0640184	+	0.997949i	$0.479608\pi$
$61$	−6.50000	+	11.2583i	−0.832240	+	1.44148i	−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$	−8.19615	+	2.19615i	−1.03262	+	0.276689i
$64$		0			0
$65$	−5.19615	−	1.73205i	−0.644503	−	0.214834i
$66$		0			0
$67$	11.8301	−	3.16987i	1.44528	−	0.387262i	0.550901	−	0.834571i	$-0.314284\pi$
$67$	11.8301	−	3.16987i	1.44528	−	0.387262i	0.894379	+	0.447309i	$0.147618\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	10.5000	−	6.06218i	1.24612	−	0.719448i	0.275787	−	0.961219i	$-0.411061\pi$
$71$	10.5000	−	6.06218i	1.24612	−	0.719448i	0.970333	+	0.241771i	$0.0777281\pi$
$72$		0			0
$73$	−3.66025	+	13.6603i	−0.428400	+	1.59881i	0.327983	+	0.944684i	$0.393631\pi$
$73$	−3.66025	+	13.6603i	−0.428400	+	1.59881i	−0.756384	+	0.654128i	$0.773036\pi$
$74$		0			0
$75$	−1.73205	−	12.1244i	−0.200000	−	1.40000i
$76$		0			0
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$		0			0
$79$	−6.06218	−	10.5000i	−0.682048	−	1.18134i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$	−6.06218	−	10.5000i	−0.682048	−	1.18134i	0.292306	−	0.956325i	$-0.405577\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−4.00000	−	4.00000i	−0.439057	−	0.439057i	0.452638	−	0.891695i	$-0.350483\pi$
$83$	−4.00000	−	4.00000i	−0.439057	−	0.439057i	−0.891695	+	0.452638i	$0.850483\pi$
$84$		0			0
$85$	−2.36603	+	2.09808i	−0.256631	+	0.227568i
$86$		0			0
$87$	15.0000	−	15.0000i	1.60817	−	1.60817i
$88$		0			0
$89$	7.79423	−	13.5000i	0.826187	−	1.43100i	−0.0748225	−	0.997197i	$-0.523839\pi$
$89$	7.79423	−	13.5000i	0.826187	−	1.43100i	0.901009	−	0.433800i	$-0.142828\pi$
$90$		0			0
$91$	−6.00000	−	3.46410i	−0.628971	−	0.363137i
$92$		0			0
$93$	−1.09808	+	4.09808i	−0.113865	+	0.424951i
$94$		0			0
$95$	−6.26795	+	7.46410i	−0.643078	+	0.765801i
$96$		0			0
$97$	−5.07180	+	18.9282i	−0.514963	+	1.92187i	−0.159407	+	0.987213i	$0.550958\pi$
$97$	−5.07180	+	18.9282i	−0.514963	+	1.92187i	−0.355556	+	0.934655i	$0.615709\pi$
$98$		0			0
$99$	2.59808	+	1.50000i	0.261116	+	0.150756i
$100$		0			0
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	−0.637678	−	0.770303i	$-0.720105\pi$
$101$	3.50000	−	6.06218i	0.348263	−	0.603209i	0.985941	+	0.167094i	$0.0534383\pi$
$102$		0			0
$103$	−3.46410	+	3.46410i	−0.341328	+	0.341328i	−0.856866	−	0.515538i	$-0.827592\pi$
$103$	−3.46410	+	3.46410i	−0.341328	+	0.341328i	0.515538	+	0.856866i	$0.327592\pi$
$104$		0			0
$105$	0.928203	−	15.4641i	0.0905834	−	1.50914i
$106$		0			0
$107$	−6.92820	−	6.92820i	−0.669775	−	0.669775i	0.287889	−	0.957664i	$-0.407047\pi$
$107$	−6.92820	−	6.92820i	−0.669775	−	0.669775i	−0.957664	+	0.287889i	$0.907047\pi$
$108$		0			0
$109$	−2.59808	−	4.50000i	−0.248851	−	0.431022i	0.714357	−	0.699782i	$-0.246719\pi$
$109$	−2.59808	−	4.50000i	−0.248851	−	0.431022i	−0.963207	+	0.268760i	$0.913386\pi$
$110$		0			0
$111$	−6.00000	−	10.3923i	−0.569495	−	0.986394i
$112$		0			0
$113$	−1.73205	+	1.73205i	−0.162938	+	0.162938i	−0.783867	−	0.620929i	$-0.786755\pi$
$113$	−1.73205	+	1.73205i	−0.162938	+	0.162938i	0.620929	+	0.783867i	$0.286755\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.90192	+	7.09808i	−0.175833	+	0.656217i
$118$		0			0
$119$	−3.46410	+	2.00000i	−0.317554	+	0.183340i
$120$		0			0
$121$	−10.0000			−0.909091
$122$		0			0
$123$	8.19615	−	2.19615i	0.739022	−	0.198020i
$124$		0			0
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$		0			0
$127$	16.5622	−	4.43782i	1.46966	−	0.393793i	0.566843	−	0.823826i	$-0.308165\pi$
$127$	16.5622	−	4.43782i	1.46966	−	0.393793i	0.902813	+	0.430033i	$0.141498\pi$
$128$		0			0
$129$	6.92820	−	12.0000i	0.609994	−	1.05654i
$130$		0			0
$131$	−11.0000	−	19.0526i	−0.961074	−	1.66463i	−0.719811	−	0.694170i	$-0.755772\pi$
$131$	−11.0000	−	19.0526i	−0.961074	−	1.66463i	−0.241264	−	0.970460i	$-0.577562\pi$
$132$		0			0
$133$	−9.66025	+	7.66025i	−0.837650	+	0.664228i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.92820	+	10.9282i	0.250173	+	0.933659i	0.970712	+	0.240245i	$0.0772278\pi$
$137$	2.92820	+	10.9282i	0.250173	+	0.933659i	−0.720539	+	0.693414i	$0.756106\pi$
$138$		0			0
$139$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$139$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$140$		0			0
$141$		−	10.3923i		−	0.875190i
$142$		0			0
$143$	0.633975	+	2.36603i	0.0530156	+	0.197857i
$144$		0			0
$145$	8.66025	+	17.3205i	0.719195	+	1.43839i
$146$		0			0
$147$	0.633975	−	2.36603i	0.0522893	−	0.195146i
$148$		0			0
$149$	−16.4545	+	9.50000i	−1.34800	+	0.778270i	−0.987967	−	0.154668i	$-0.950569\pi$
$149$	−16.4545	+	9.50000i	−1.34800	+	0.778270i	−0.360037	+	0.932938i	$0.617236\pi$
$150$		0			0
$151$			5.19615i			0.422857i	0.977393	+	0.211428i	$0.0678115\pi$
$151$			5.19615i			0.422857i	−0.977393	+	0.211428i	$0.932188\pi$
$152$		0			0
$153$	3.00000	+	3.00000i	0.242536	+	0.242536i
$154$		0			0
$155$	−3.23205	−	2.13397i	−0.259605	−	0.171405i
$156$		0			0
$157$	1.36603	+	0.366025i	0.109021	+	0.0292120i	0.312917	−	0.949780i	$-0.398694\pi$
$157$	1.36603	+	0.366025i	0.109021	+	0.0292120i	−0.203896	+	0.978993i	$0.565361\pi$
$158$		0			0
$159$			18.0000i			1.42749i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	7.00000	+	7.00000i	0.548282	+	0.548282i	0.925944	−	0.377661i	$-0.123272\pi$
$163$	7.00000	+	7.00000i	0.548282	+	0.548282i	−0.377661	+	0.925944i	$0.623272\pi$
$164$		0			0
$165$	−4.09808	+	3.63397i	−0.319035	+	0.282905i
$166$		0			0
$167$	−14.1962	+	3.80385i	−1.09853	+	0.294351i	−0.762166	−	0.647381i	$-0.775864\pi$
$167$	−14.1962	+	3.80385i	−1.09853	+	0.294351i	−0.336365	+	0.941732i	$0.609198\pi$
$168$		0			0
$169$	6.06218	−	3.50000i	0.466321	−	0.269231i
$170$		0			0
$171$	10.5000	+	7.79423i	0.802955	+	0.596040i
$172$		0			0
$173$	9.46410	+	2.53590i	0.719542	+	0.192801i	0.599967	−	0.800024i	$-0.295180\pi$
$173$	9.46410	+	2.53590i	0.719542	+	0.192801i	0.119575	+	0.992825i	$0.461847\pi$
$174$		0			0
$175$	13.1244	+	5.26795i	0.992108	+	0.398220i
$176$		0			0
$177$	−1.09808	−	4.09808i	−0.0825365	−	0.308030i
$178$		0			0
$179$	1.73205			0.129460			0.0647298	−	0.997903i	$-0.479381\pi$
$179$	1.73205			0.129460			0.0647298	+	0.997903i	$0.479381\pi$
$180$		0			0
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	0.384345	−	0.923190i	$-0.374427\pi$
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	−0.607333	+	0.794447i	$0.707761\pi$
$182$		0			0
$183$	−22.5167	+	22.5167i	−1.66448	+	1.66448i
$184$		0			0
$185$	10.7321	−	2.19615i	0.789036	−	0.161464i
$186$		0			0
$187$	1.36603	+	0.366025i	0.0998937	+	0.0267664i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.00000			0.361787			0.180894	−	0.983503i	$-0.442101\pi$
$191$	5.00000			0.361787			0.180894	+	0.983503i	$0.442101\pi$
$192$		0			0
$193$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$193$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$194$		0			0
$195$	−11.1962	−	7.39230i	−0.801773	−	0.529374i
$196$		0			0
$197$	−9.00000	+	9.00000i	−0.641223	+	0.641223i	−0.950856	−	0.309633i	$-0.899794\pi$
$197$	−9.00000	+	9.00000i	−0.641223	+	0.641223i	0.309633	+	0.950856i	$0.399794\pi$
$198$		0			0
$199$	18.1865	+	10.5000i	1.28921	+	0.744325i	0.978513	−	0.206184i	$-0.0661046\pi$
$199$	18.1865	+	10.5000i	1.28921	+	0.744325i	0.310696	+	0.950509i	$0.399438\pi$
$200$		0			0
$201$	30.0000			2.11604
$202$		0			0
$203$	6.33975	+	23.6603i	0.444963	+	1.66062i
$204$		0			0
$205$	−0.464102	+	7.73205i	−0.0324143	+	0.540030i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.33013	+	0.500000i	0.299521	+	0.0345857i
$210$		0			0
$211$	−16.5000	+	9.52628i	−1.13591	+	0.655816i	−0.945414	−	0.325872i	$-0.894342\pi$
$211$	−16.5000	+	9.52628i	−1.13591	+	0.655816i	−0.190493	+	0.981689i	$0.561009\pi$
$212$		0			0
$213$	28.6865	−	7.68653i	1.96557	−	0.526673i
$214$		0			0
$215$	8.39230	+	9.46410i	0.572350	+	0.645446i
$216$		0			0
$217$	−3.46410	−	3.46410i	−0.235159	−	0.235159i
$218$		0			0
$219$	−17.3205	+	30.0000i	−1.17041	+	2.02721i
$220$		0			0
$221$			3.46410i			0.233021i
$222$		0			0
$223$	−14.1962	−	3.80385i	−0.950645	−	0.254724i	−0.250009	−	0.968244i	$-0.580434\pi$
$223$	−14.1962	−	3.80385i	−0.950645	−	0.254724i	−0.700636	+	0.713519i	$0.747100\pi$
$224$		0			0
$225$	1.79423	−	14.8923i	0.119615	−	0.992820i
$226$		0			0
$227$	13.8564	+	13.8564i	0.919682	+	0.919682i	0.997006	−	0.0773240i	$-0.0246376\pi$
$227$	13.8564	+	13.8564i	0.919682	+	0.919682i	−0.0773240	+	0.997006i	$0.524638\pi$
$228$		0			0
$229$			21.0000i			1.38772i	0.720110	+	0.693860i	$0.244091\pi$
$229$			21.0000i			1.38772i	−0.720110	+	0.693860i	$0.755909\pi$
$230$		0			0
$231$	−6.00000	+	3.46410i	−0.394771	+	0.227921i
$232$		0			0
$233$	5.49038	−	20.4904i	0.359687	−	1.34237i	−0.514796	−	0.857313i	$-0.672132\pi$
$233$	5.49038	−	20.4904i	0.359687	−	1.34237i	0.874483	−	0.485057i	$-0.161201\pi$
$234$		0			0
$235$	9.00000	+	3.00000i	0.587095	+	0.195698i
$236$		0			0
$237$	−7.68653	−	28.6865i	−0.499294	−	1.86339i
$238$		0			0
$239$		−	19.0000i		−	1.22901i	−0.788914	−	0.614504i	$-0.789356\pi$
$239$		−	19.0000i		−	1.22901i	0.788914	−	0.614504i	$-0.210644\pi$
$240$		0			0
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	0.348013	−	0.937490i	$-0.386857\pi$
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	−0.637883	+	0.770133i	$0.720190\pi$
$242$		0			0
$243$	−5.70577	−	21.2942i	−0.366025	−	1.36603i
$244$		0			0
$245$	1.86603	+	1.23205i	0.119216	+	0.0787128i
$246$		0			0
$247$	1.56218	+	10.5622i	0.0993990	+	0.672055i
$248$		0			0
$249$	−6.92820	−	12.0000i	−0.439057	−	0.760469i
$250$		0			0
$251$	−9.50000	+	16.4545i	−0.599635	+	1.03860i	0.393240	+	0.919436i	$0.371354\pi$
$251$	−9.50000	+	16.4545i	−0.599635	+	1.03860i	−0.992875	+	0.119162i	$0.961979\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−6.92820	+	3.46410i	−0.433861	+	0.216930i
$256$		0			0
$257$	−26.0263	+	6.97372i	−1.62347	+	0.435009i	−0.952020	−	0.306037i	$-0.900997\pi$
$257$	−26.0263	+	6.97372i	−1.62347	+	0.435009i	−0.671455	+	0.741045i	$0.734330\pi$
$258$		0			0
$259$	13.8564			0.860995
$260$		0			0
$261$	22.5000	−	12.9904i	1.39272	−	0.804084i
$262$		0			0
$263$	6.95448	−	25.9545i	0.428832	−	1.60042i	−0.326579	−	0.945170i	$-0.605896\pi$
$263$	6.95448	−	25.9545i	0.428832	−	1.60042i	0.755410	−	0.655252i	$-0.227438\pi$
$264$		0			0
$265$	−15.5885	−	5.19615i	−0.957591	−	0.319197i
$266$		0			0
$267$	27.0000	−	27.0000i	1.65237	−	1.65237i
$268$		0			0
$269$	−9.52628	−	16.5000i	−0.580828	−	1.00602i	−0.995382	−	0.0959980i	$-0.969396\pi$
$269$	−9.52628	−	16.5000i	−0.580828	−	1.00602i	0.414554	−	0.910025i	$-0.363938\pi$
$270$		0			0
$271$	−4.50000	−	7.79423i	−0.273356	−	0.473466i	0.696363	−	0.717689i	$-0.254800\pi$
$271$	−4.50000	−	7.79423i	−0.273356	−	0.473466i	−0.969719	+	0.244224i	$0.921467\pi$
$272$		0			0
$273$	−12.0000	−	12.0000i	−0.726273	−	0.726273i
$274$		0			0
$275$	−1.96410	−	4.59808i	−0.118440	−	0.277274i
$276$		0			0
$277$	−8.00000	+	8.00000i	−0.480673	+	0.480673i	−0.905347	−	0.424673i	$-0.860389\pi$
$277$	−8.00000	+	8.00000i	−0.480673	+	0.480673i	0.424673	+	0.905347i	$0.360389\pi$
$278$		0			0
$279$	−2.59808	+	4.50000i	−0.155543	+	0.269408i
$280$		0			0
$281$	12.0000	+	6.92820i	0.715860	+	0.413302i	0.813227	−	0.581947i	$-0.197709\pi$
$281$	12.0000	+	6.92820i	0.715860	+	0.413302i	−0.0973670	+	0.995249i	$0.531042\pi$
$282$		0			0
$283$	4.75833	−	17.7583i	0.282853	−	1.05562i	−0.667540	−	0.744574i	$-0.732653\pi$
$283$	4.75833	−	17.7583i	0.282853	−	1.05562i	0.950394	−	0.311050i	$-0.100681\pi$
$284$		0			0
$285$	−19.5622	+	13.6865i	−1.15876	+	0.810720i
$286$		0			0
$287$	−2.53590	+	9.46410i	−0.149689	+	0.558648i
$288$		0			0
$289$	−12.9904	−	7.50000i	−0.764140	−	0.441176i
$290$		0			0
$291$	−24.0000	+	41.5692i	−1.40690	+	2.43683i
$292$		0			0
$293$	−3.46410	+	3.46410i	−0.202375	+	0.202375i	−0.801017	−	0.598642i	$-0.795707\pi$
$293$	−3.46410	+	3.46410i	−0.202375	+	0.202375i	0.598642	+	0.801017i	$0.295707\pi$
$294$		0			0
$295$	3.86603	+	0.232051i	0.225089	+	0.0135105i
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	8.00000	+	13.8564i	0.461112	+	0.798670i
$302$		0			0
$303$	12.1244	−	12.1244i	0.696526	−	0.696526i
$304$		0			0
$305$	−13.0000	−	26.0000i	−0.744378	−	1.48876i
$306$		0			0
$307$	−5.70577	+	21.2942i	−0.325646	+	1.21533i	0.588016	+	0.808849i	$0.299909\pi$
$307$	−5.70577	+	21.2942i	−0.325646	+	1.21533i	−0.913661	+	0.406476i	$0.866757\pi$
$308$		0			0
$309$	−10.3923	+	6.00000i	−0.591198	+	0.341328i
$310$		0			0
$311$	22.0000			1.24751			0.623753	−	0.781622i	$-0.285607\pi$
$311$	22.0000			1.24751			0.623753	+	0.781622i	$0.285607\pi$
$312$		0			0
$313$	1.36603	−	0.366025i	0.0772123	−	0.0206890i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	1.36603	−	0.366025i	0.0772123	−	0.0206890i	0.297218	+	0.954810i	$0.403941\pi$
$314$		0			0
$315$	6.00000	−	18.0000i	0.338062	−	1.01419i
$316$		0			0
$317$	4.73205	−	1.26795i	0.265778	−	0.0712151i	−0.123469	−	0.992348i	$-0.539402\pi$
$317$	4.73205	−	1.26795i	0.265778	−	0.0712151i	0.389247	+	0.921133i	$0.372735\pi$
$318$		0			0
$319$	4.33013	−	7.50000i	0.242441	−	0.419919i
$320$		0			0
$321$	−12.0000	−	20.7846i	−0.669775	−	1.16008i
$322$		0			0
$323$	5.73205	+	2.26795i	0.318940	+	0.126192i
$324$		0			0
$325$	9.63397	−	7.56218i	0.534397	−	0.419474i
$326$		0			0
$327$	−3.29423	−	12.2942i	−0.182171	−	0.679872i
$328$		0			0
$329$	10.3923	+	6.00000i	0.572946	+	0.330791i
$330$		0			0
$331$			13.8564i			0.761617i	0.924654	+	0.380808i	$0.124354\pi$
$331$			13.8564i			0.761617i	−0.924654	+	0.380808i	$0.875646\pi$
$332$		0			0
$333$	−3.80385	−	14.1962i	−0.208450	−	0.777944i
$334$		0			0
$335$	−8.66025	+	25.9808i	−0.473160	+	1.41948i
$336$		0			0
$337$	3.80385	−	14.1962i	0.207209	−	0.773314i	−0.781556	−	0.623835i	$-0.785574\pi$
$337$	3.80385	−	14.1962i	0.207209	−	0.773314i	0.988765	−	0.149479i	$-0.0477596\pi$
$338$		0			0
$339$	−5.19615	+	3.00000i	−0.282216	+	0.162938i
$340$		0			0
$341$			1.73205i			0.0937958i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−27.3205	−	7.32051i	−1.46664	−	0.392985i	−0.564863	−	0.825184i	$-0.691071\pi$
$347$	−27.3205	−	7.32051i	−1.46664	−	0.392985i	−0.901778	+	0.432199i	$0.857738\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	18.0000	+	18.0000i	0.958043	+	0.958043i	0.999155	−	0.0411112i	$-0.0130898\pi$
$353$	18.0000	+	18.0000i	0.958043	+	0.958043i	−0.0411112	+	0.999155i	$0.513090\pi$
$354$		0			0
$355$	−1.62436	+	27.0622i	−0.0862118	+	1.43631i
$356$		0			0
$357$	−9.46410	+	2.53590i	−0.500893	+	0.134214i
$358$		0			0
$359$	19.0526	−	11.0000i	1.00556	−	0.580558i	0.0956683	−	0.995413i	$-0.469501\pi$
$359$	19.0526	−	11.0000i	1.00556	−	0.580558i	0.909887	+	0.414855i	$0.136168\pi$
$360$		0			0
$361$	18.5000	+	4.33013i	0.973684	+	0.227901i
$362$		0			0
$363$	−23.6603	−	6.33975i	−1.24184	−	0.332750i
$364$		0			0
$365$	−20.9808	−	23.6603i	−1.09818	−	1.23843i
$366$		0			0
$367$	−1.46410	−	5.46410i	−0.0764255	−	0.285224i	0.917127	−	0.398594i	$-0.130502\pi$
$367$	−1.46410	−	5.46410i	−0.0764255	−	0.285224i	−0.993553	+	0.113371i	$0.963835\pi$
$368$		0			0
$369$	10.3923			0.541002
$370$		0			0
$371$	−18.0000	−	10.3923i	−0.934513	−	0.539542i
$372$		0			0
$373$	3.46410	−	3.46410i	0.179364	−	0.179364i	−0.611714	−	0.791079i	$-0.709520\pi$
$373$	3.46410	−	3.46410i	0.179364	−	0.179364i	0.791079	+	0.611714i	$0.209520\pi$
$374$		0			0
$375$	24.7583	+	11.7058i	1.27851	+	0.604483i
$376$		0			0
$377$	20.4904	+	5.49038i	1.05531	+	0.282769i
$378$		0			0
$379$	−1.73205			−0.0889695			−0.0444847	−	0.999010i	$-0.514165\pi$
$379$	−1.73205			−0.0889695			−0.0444847	+	0.999010i	$0.514165\pi$
$380$		0			0
$381$	42.0000			2.15173
$382$		0			0
$383$	16.5622	+	4.43782i	0.846288	+	0.226762i	0.655807	−	0.754929i	$-0.272329\pi$
$383$	16.5622	+	4.43782i	0.846288	+	0.226762i	0.190481	+	0.981691i	$0.438995\pi$
$384$		0			0
$385$	−1.26795	−	6.19615i	−0.0646207	−	0.315785i
$386$		0			0
$387$	12.0000	−	12.0000i	0.609994	−	0.609994i
$388$		0			0
$389$	−9.52628	−	5.50000i	−0.483002	−	0.278861i	0.238665	−	0.971102i	$-0.423290\pi$
$389$	−9.52628	−	5.50000i	−0.483002	−	0.278861i	−0.721666	+	0.692241i	$0.756624\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−13.9474	−	52.0526i	−0.703555	−	2.62570i
$394$		0			0
$395$	27.0622	+	1.62436i	1.36165	+	0.0817302i
$396$		0			0
$397$	−30.0526	−	8.05256i	−1.50829	−	0.404146i	−0.592426	−	0.805625i	$-0.701830\pi$
$397$	−30.0526	−	8.05256i	−1.50829	−	0.404146i	−0.915868	+	0.401478i	$0.868496\pi$
$398$		0			0
$399$	−27.7128	+	12.0000i	−1.38738	+	0.600751i
$400$		0			0
$401$	−10.5000	+	6.06218i	−0.524345	+	0.302731i	−0.738711	−	0.674023i	$-0.764565\pi$
$401$	−10.5000	+	6.06218i	−0.524345	+	0.302731i	0.214366	+	0.976753i	$0.431232\pi$
$402$		0			0
$403$	−4.09808	+	1.09808i	−0.204140	+	0.0546991i
$404$		0			0
$405$	20.0885	+	1.20577i	0.998203	+	0.0599153i
$406$		0			0
$407$	−3.46410	−	3.46410i	−0.171709	−	0.171709i
$408$		0			0
$409$	7.79423	−	13.5000i	0.385400	−	0.667532i	−0.606425	−	0.795141i	$-0.707397\pi$
$409$	7.79423	−	13.5000i	0.385400	−	0.667532i	0.991825	+	0.127609i	$0.0407302\pi$
$410$		0			0
$411$			27.7128i			1.36697i
$412$		0			0
$413$	4.73205	+	1.26795i	0.232849	+	0.0623917i
$414$		0			0
$415$	12.3923	−	2.53590i	0.608314	−	0.124482i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			1.00000i			0.0488532i	0.999702	+	0.0244266i	$0.00777600\pi$
$419$			1.00000i			0.0488532i	−0.999702	+	0.0244266i	$0.992224\pi$
$420$		0			0
$421$	−19.5000	+	11.2583i	−0.950372	+	0.548697i	−0.893196	−	0.449667i	$-0.851543\pi$
$421$	−19.5000	+	11.2583i	−0.950372	+	0.548697i	−0.0571754	+	0.998364i	$0.518209\pi$
$422$		0			0
$423$	3.29423	−	12.2942i	0.160171	−	0.597766i
$424$		0			0
$425$	−1.00000	−	7.00000i	−0.0485071	−	0.339550i
$426$		0			0
$427$	−9.51666	−	35.5167i	−0.460543	−	1.71877i
$428$		0			0
$429$			6.00000i			0.289683i
$430$		0			0
$431$	4.50000	+	2.59808i	0.216757	+	0.125145i	0.604448	−	0.796645i	$-0.293394\pi$
$431$	4.50000	+	2.59808i	0.216757	+	0.125145i	−0.387691	+	0.921790i	$0.626727\pi$
$432$		0			0
$433$	3.80385	+	14.1962i	0.182801	+	0.682224i	0.995091	+	0.0989688i	$0.0315544\pi$
$433$	3.80385	+	14.1962i	0.182801	+	0.682224i	−0.812289	+	0.583255i	$0.801779\pi$
$434$		0			0
$435$	9.50962	+	46.4711i	0.455951	+	2.22812i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−12.9904	−	22.5000i	−0.619997	−	1.07387i	−0.989486	−	0.144631i	$-0.953800\pi$
$439$	−12.9904	−	22.5000i	−0.619997	−	1.07387i	0.369489	−	0.929235i	$-0.379533\pi$
$440$		0			0
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$		0			0
$443$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$443$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$444$		0			0
$445$	15.5885	+	31.1769i	0.738964	+	1.47793i
$446$		0			0
$447$	−44.9545	+	12.0455i	−2.12627	+	0.569733i
$448$		0			0
$449$	32.9090			1.55307			0.776535	−	0.630074i	$-0.216975\pi$
$449$	32.9090			1.55307			0.776535	+	0.630074i	$0.216975\pi$
$450$		0			0
$451$	3.00000	−	1.73205i	0.141264	−	0.0815591i
$452$		0			0
$453$	−3.29423	+	12.2942i	−0.154776	+	0.577633i
$454$		0			0
$455$	13.8564	−	6.92820i	0.649598	−	0.324799i
$456$		0			0
$457$	11.0000	−	11.0000i	0.514558	−	0.514558i	−0.401361	−	0.915920i	$-0.631463\pi$
$457$	11.0000	−	11.0000i	0.514558	−	0.514558i	0.915920	+	0.401361i	$0.131463\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	5.50000	+	9.52628i	0.256161	+	0.443683i	0.965210	−	0.261476i	$-0.0842091\pi$
$461$	5.50000	+	9.52628i	0.256161	+	0.443683i	−0.709050	+	0.705159i	$0.750876\pi$
$462$		0			0
$463$	−28.0000	−	28.0000i	−1.30127	−	1.30127i	−0.927536	−	0.373735i	$-0.878077\pi$
$463$	−28.0000	−	28.0000i	−1.30127	−	1.30127i	−0.373735	−	0.927536i	$-0.621923\pi$
$464$		0			0
$465$	−6.29423	−	7.09808i	−0.291888	−	0.329165i
$466$		0			0
$467$	−12.0000	+	12.0000i	−0.555294	+	0.555294i	−0.927964	−	0.372670i	$-0.878442\pi$
$467$	−12.0000	+	12.0000i	−0.555294	+	0.555294i	0.372670	+	0.927964i	$0.378442\pi$
$468$		0			0
$469$	−17.3205	+	30.0000i	−0.799787	+	1.38527i
$470$		0			0
$471$	3.00000	+	1.73205i	0.138233	+	0.0798087i
$472$		0			0
$473$	1.46410	−	5.46410i	0.0673195	−	0.251240i
$474$		0			0
$475$	−6.20577	−	20.8923i	−0.284740	−	0.958605i
$476$		0			0
$477$	−5.70577	+	21.2942i	−0.261249	+	0.974996i
$478$		0			0
$479$	−25.1147	−	14.5000i	−1.14752	−	0.662522i	−0.199240	−	0.979951i	$-0.563847\pi$
$479$	−25.1147	−	14.5000i	−1.14752	−	0.662522i	−0.948282	+	0.317429i	$0.897181\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−29.0718	−	32.7846i	−1.32008	−	1.48867i
$486$		0			0
$487$	12.1244	+	12.1244i	0.549407	+	0.549407i	0.926269	−	0.376862i	$-0.122997\pi$
$487$	12.1244	+	12.1244i	0.549407	+	0.549407i	−0.376862	+	0.926269i	$0.622997\pi$
$488$		0			0
$489$	12.1244	+	21.0000i	0.548282	+	0.949653i
$490$		0			0
$491$	2.50000	+	4.33013i	0.112823	+	0.195416i	0.916908	−	0.399100i	$-0.130677\pi$
$491$	2.50000	+	4.33013i	0.112823	+	0.195416i	−0.804084	+	0.594515i	$0.797344\pi$
$492$		0			0
$493$	8.66025	−	8.66025i	0.390038	−	0.390038i
$494$		0			0
$495$	−6.00000	+	3.00000i	−0.269680	+	0.134840i
$496$		0			0
$497$	−8.87564	+	33.1244i	−0.398127	+	1.48583i
$498$		0			0
$499$	−5.19615	+	3.00000i	−0.232612	+	0.134298i	−0.611776	−	0.791031i	$-0.709545\pi$
$499$	−5.19615	+	3.00000i	−0.232612	+	0.134298i	0.379165	+	0.925329i	$0.376211\pi$
$500$		0			0
$501$	−36.0000			−1.60836
$502$		0			0
$503$	−6.83013	+	1.83013i	−0.304540	+	0.0816013i	−0.407853	−	0.913048i	$-0.633722\pi$
$503$	−6.83013	+	1.83013i	−0.304540	+	0.0816013i	0.103313	+	0.994649i	$0.467056\pi$
$504$		0			0
$505$	7.00000	+	14.0000i	0.311496	+	0.622992i
$506$		0			0
$507$	16.5622	−	4.43782i	0.735552	−	0.197091i
$508$		0			0
$509$	1.73205	−	3.00000i	0.0767718	−	0.132973i	−0.825084	−	0.565011i	$-0.808872\pi$
$509$	1.73205	−	3.00000i	0.0767718	−	0.132973i	0.901855	+	0.432038i	$0.142205\pi$
$510$		0			0
$511$	−20.0000	−	34.6410i	−0.884748	−	1.53243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.19615	−	10.7321i	−0.0967740	−	0.472911i
$516$		0			0
$517$	−1.09808	−	4.09808i	−0.0482933	−	0.180233i
$518$		0			0
$519$	20.7846	+	12.0000i	0.912343	+	0.526742i
$520$		0			0
$521$		−	5.19615i		−	0.227648i	−0.993501	−	0.113824i	$-0.963690\pi$
$521$		−	5.19615i		−	0.227648i	0.993501	−	0.113824i	$-0.0363099\pi$
$522$		0			0
$523$	3.16987	+	11.8301i	0.138609	+	0.517295i	0.999957	+	0.00928008i	$0.00295398\pi$
$523$	3.16987	+	11.8301i	0.138609	+	0.517295i	−0.861348	+	0.508015i	$0.830379\pi$
$524$		0			0
$525$	27.7128	+	20.7846i	1.20949	+	0.907115i
$526$		0			0
$527$	−0.633975	+	2.36603i	−0.0276164	+	0.103066i
$528$		0			0
$529$	−19.9186	+	11.5000i	−0.866025	+	0.500000i
$530$		0			0
$531$		−	5.19615i		−	0.225494i
$532$		0			0
$533$	6.00000	+	6.00000i	0.259889	+	0.259889i
$534$		0			0
$535$	21.4641	−	4.39230i	0.927974	−	0.189896i
$536$		0			0
$537$	4.09808	+	1.09808i	0.176845	+	0.0473855i
$538$		0			0
$539$		−	1.00000i		−	0.0430730i
$540$		0			0
$541$	7.50000	−	12.9904i	0.322450	−	0.558500i	−0.658543	−	0.752543i	$-0.728827\pi$
$541$	7.50000	−	12.9904i	0.322450	−	0.558500i	0.980993	+	0.194043i	$0.0621602\pi$
$542$		0			0
$543$	−6.00000	−	6.00000i	−0.257485	−	0.257485i
$544$		0			0
$545$	11.5981	+	0.696152i	0.496807	+	0.0298199i
$546$		0			0
$547$	−14.1962	+	3.80385i	−0.606984	+	0.162641i	−0.549204	−	0.835689i	$-0.685069\pi$
$547$	−14.1962	+	3.80385i	−0.606984	+	0.162641i	−0.0577800	+	0.998329i	$0.518402\pi$
$548$		0			0
$549$	−33.7750	+	19.5000i	−1.44148	+	0.832240i
$550$		0			0
$551$	22.5000	−	30.3109i	0.958532	−	1.29129i
$552$		0			0
$553$	33.1244	+	8.87564i	1.40859	+	0.377431i
$554$		0			0
$555$	26.7846	+	1.60770i	1.13694	+	0.0682429i
$556$		0			0
$557$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$557$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$558$		0			0
$559$	13.8564			0.586064
$560$		0			0
$561$	3.00000	+	1.73205i	0.126660	+	0.0731272i
$562$		0			0
$563$	−15.5885	+	15.5885i	−0.656975	+	0.656975i	−0.954663	−	0.297688i	$-0.903784\pi$
$563$	−15.5885	+	15.5885i	−0.656975	+	0.656975i	0.297688	+	0.954663i	$0.403784\pi$
$564$		0			0
$565$	−1.09808	−	5.36603i	−0.0461964	−	0.225750i
$566$		0			0
$567$	24.5885	+	6.58846i	1.03262	+	0.276689i
$568$		0			0
$569$	−19.0526			−0.798725			−0.399362	−	0.916793i	$-0.630768\pi$
$569$	−19.0526			−0.798725			−0.399362	+	0.916793i	$0.630768\pi$
$570$		0			0
$571$	15.0000			0.627730			0.313865	−	0.949468i	$-0.398376\pi$
$571$	15.0000			0.627730			0.313865	+	0.949468i	$0.398376\pi$
$572$		0			0
$573$	11.8301	+	3.16987i	0.494211	+	0.132423i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	32.0000	−	32.0000i	1.33218	−	1.33218i	0.428758	−	0.903419i	$-0.358951\pi$
$577$	32.0000	−	32.0000i	1.33218	−	1.33218i	0.903419	−	0.428758i	$-0.141049\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.0000			0.663792
$582$		0			0
$583$	1.90192	+	7.09808i	0.0787696	+	0.293972i
$584$		0			0
$585$	−10.9019	−	12.2942i	−0.450739	−	0.508304i
$586$		0			0
$587$	−8.19615	−	2.19615i	−0.338291	−	0.0906449i	0.0856742	−	0.996323i	$-0.472696\pi$
$587$	−8.19615	−	2.19615i	−0.338291	−	0.0906449i	−0.423966	+	0.905678i	$0.639362\pi$
$588$		0			0
$589$	−0.866025	+	7.50000i	−0.0356840	+	0.309032i
$590$		0			0
$591$	−27.0000	+	15.5885i	−1.11063	+	0.641223i
$592$		0			0
$593$	−21.8564	+	5.85641i	−0.897535	+	0.240494i	−0.677957	−	0.735101i	$-0.737135\pi$
$593$	−21.8564	+	5.85641i	−0.897535	+	0.240494i	−0.219578	+	0.975595i	$0.570468\pi$
$594$		0			0
$595$	0.535898	−	8.92820i	0.0219697	−	0.366021i
$596$		0			0
$597$	36.3731	+	36.3731i	1.48865	+	1.48865i
$598$		0			0
$599$	−20.7846	+	36.0000i	−0.849236	+	1.47092i	0.0326548	+	0.999467i	$0.489604\pi$
$599$	−20.7846	+	36.0000i	−0.849236	+	1.47092i	−0.881891	+	0.471453i	$0.843730\pi$
$600$		0			0
$601$			1.73205i			0.0706518i	0.999376	+	0.0353259i	$0.0112469\pi$
$601$			1.73205i			0.0706518i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	35.4904	+	9.50962i	1.44528	+	0.387262i
$604$		0			0
$605$	12.3205	−	18.6603i	0.500900	−	0.758647i
$606$		0			0
$607$	−22.5167	−	22.5167i	−0.913923	−	0.913923i	0.0826552	−	0.996578i	$-0.473660\pi$
$607$	−22.5167	−	22.5167i	−0.913923	−	0.913923i	−0.996578	+	0.0826552i	$0.973660\pi$
$608$		0			0
$609$			60.0000i			2.43132i
$610$		0			0
$611$	9.00000	−	5.19615i	0.364101	−	0.210214i
$612$		0			0
$613$	6.22243	−	23.2224i	0.251322	−	0.937945i	−0.718778	−	0.695239i	$-0.755298\pi$
$613$	6.22243	−	23.2224i	0.251322	−	0.937945i	0.970100	−	0.242706i	$-0.0780350\pi$
$614$		0			0
$615$	−6.00000	+	18.0000i	−0.241943	+	0.725830i
$616$		0			0
$617$	8.05256	+	30.0526i	0.324184	+	1.20987i	0.915130	+	0.403159i	$0.132088\pi$
$617$	8.05256	+	30.0526i	0.324184	+	1.20987i	−0.590946	+	0.806711i	$0.701245\pi$
$618$		0			0
$619$			6.00000i			0.241160i	0.992704	+	0.120580i	$0.0384755\pi$
$619$			6.00000i			0.241160i	−0.992704	+	0.120580i	$0.961525\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.4115	+	42.5885i	0.457194	+	1.70627i
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$		0			0
$627$	9.92820	+	3.92820i	0.396494	+	0.156877i
$628$		0			0
$629$	−3.46410	−	6.00000i	−0.138123	−	0.239236i
$630$		0			0
$631$	18.5000	−	32.0429i	0.736473	−	1.27561i	−0.217601	−	0.976038i	$-0.569823\pi$
$631$	18.5000	−	32.0429i	0.736473	−	1.27561i	0.954074	−	0.299571i	$-0.0968437\pi$
$632$		0			0
$633$	−45.0788	+	12.0788i	−1.79172	+	0.480091i
$634$		0			0
$635$	−12.1244	+	36.3731i	−0.481140	+	1.44342i
$636$		0			0
$637$	2.36603	−	0.633975i	0.0937453	−	0.0251190i
$638$		0			0
$639$	36.3731			1.43890
$640$		0			0
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	−0.692818	−	0.721113i	$-0.743631\pi$
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	0.278093	+	0.960554i	$0.410298\pi$
$642$		0			0
$643$	1.83013	−	6.83013i	0.0721732	−	0.269354i	−0.920404	−	0.390968i	$-0.872140\pi$
$643$	1.83013	−	6.83013i	0.0721732	−	0.269354i	0.992577	+	0.121614i	$0.0388070\pi$
$644$		0			0
$645$	13.8564	+	27.7128i	0.545595	+	1.09119i
$646$		0			0
$647$	7.00000	−	7.00000i	0.275198	−	0.275198i	−0.555990	−	0.831189i	$-0.687661\pi$
$647$	7.00000	−	7.00000i	0.275198	−	0.275198i	0.831189	+	0.555990i	$0.187661\pi$
$648$		0			0
$649$	−0.866025	−	1.50000i	−0.0339945	−	0.0588802i
$650$		0			0
$651$	−6.00000	−	10.3923i	−0.235159	−	0.407307i
$652$		0			0
$653$	22.0000	+	22.0000i	0.860927	+	0.860927i	0.991446	−	0.130519i	$-0.0416644\pi$
$653$	22.0000	+	22.0000i	0.860927	+	0.860927i	−0.130519	+	0.991446i	$0.541664\pi$
$654$		0			0
$655$	49.1051	+	2.94744i	1.91870	+	0.115166i
$656$		0			0
$657$	−30.0000	+	30.0000i	−1.17041	+	1.17041i
$658$		0			0
$659$	−20.7846	+	36.0000i	−0.809653	+	1.40236i	0.103451	+	0.994635i	$0.467012\pi$
$659$	−20.7846	+	36.0000i	−0.809653	+	1.40236i	−0.913104	+	0.407726i	$0.866322\pi$
$660$		0			0
$661$	−4.50000	−	2.59808i	−0.175030	−	0.101053i	0.409926	−	0.912119i	$-0.365555\pi$
$661$	−4.50000	−	2.59808i	−0.175030	−	0.101053i	−0.584955	+	0.811065i	$0.698888\pi$
$662$		0			0
$663$	−2.19615	+	8.19615i	−0.0852915	+	0.318312i
$664$		0			0
$665$	−2.39230	−	27.4641i	−0.0927696	−	1.06501i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−31.1769	−	18.0000i	−1.20537	−	0.695920i
$670$		0			0
$671$	−6.50000	+	11.2583i	−0.250930	+	0.434623i
$672$		0			0
$673$	6.92820	−	6.92820i	0.267063	−	0.267063i	−0.560853	−	0.827915i	$-0.689527\pi$
$673$	6.92820	−	6.92820i	0.267063	−	0.267063i	0.827915	+	0.560853i	$0.189527\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−31.1769	−	31.1769i	−1.19823	−	1.19823i	−0.974697	−	0.223529i	$-0.928242\pi$
$677$	−31.1769	−	31.1769i	−1.19823	−	1.19823i	−0.223529	−	0.974697i	$-0.571758\pi$
$678$		0			0
$679$	−27.7128	−	48.0000i	−1.06352	−	1.84207i
$680$		0			0
$681$	24.0000	+	41.5692i	0.919682	+	1.59294i
$682$		0			0
$683$	19.0526	−	19.0526i	0.729026	−	0.729026i	−0.241400	−	0.970426i	$-0.577607\pi$
$683$	19.0526	−	19.0526i	0.729026	−	0.729026i	0.970426	+	0.241400i	$0.0776065\pi$
$684$		0			0
$685$	−24.0000	−	8.00000i	−0.916993	−	0.305664i
$686$		0			0
$687$	−13.3135	+	49.6865i	−0.507940	+	1.89566i
$688$		0			0
$689$	−15.5885	+	9.00000i	−0.593873	+	0.342873i
$690$		0			0
$691$	−3.00000			−0.114125			−0.0570627	−	0.998371i	$-0.518173\pi$
$691$	−3.00000			−0.114125			−0.0570627	+	0.998371i	$0.518173\pi$
$692$		0			0
$693$	−8.19615	+	2.19615i	−0.311346	+	0.0834249i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	4.73205	−	1.26795i	0.179239	−	0.0480270i
$698$		0			0
$699$	25.9808	−	45.0000i	0.982683	−	1.70206i
$700$		0			0
$701$	−10.0000	−	17.3205i	−0.377695	−	0.654187i	0.613032	−	0.790058i	$-0.289950\pi$
$701$	−10.0000	−	17.3205i	−0.377695	−	0.654187i	−0.990726	+	0.135872i	$0.956616\pi$
$702$		0			0
$703$	−13.2679	−	16.7321i	−0.500410	−	0.631061i
$704$		0			0
$705$	19.3923	+	12.8038i	0.730356	+	0.482221i
$706$		0			0
$707$	5.12436	+	19.1244i	0.192721	+	0.719245i
$708$		0			0
$709$	−28.5788	−	16.5000i	−1.07330	−	0.619671i	−0.144219	−	0.989546i	$-0.546067\pi$
$709$	−28.5788	−	16.5000i	−1.07330	−	0.619671i	−0.929081	+	0.369875i	$0.879400\pi$
$710$		0			0
$711$		−	36.3731i		−	1.36410i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−5.19615	−	1.73205i	−0.194325	−	0.0647750i
$716$		0			0
$717$	12.0455	−	44.9545i	0.449848	−	1.67886i
$718$		0			0
$719$	14.7224	−	8.50000i	0.549054	−	0.316997i	−0.199686	−	0.979860i	$-0.563992\pi$
$719$	14.7224	−	8.50000i	0.549054	−	0.316997i	0.748740	+	0.662863i	$0.230659\pi$
$720$		0			0
$721$		−	13.8564i		−	0.516040i
$722$		0			0
$723$	−9.00000	−	9.00000i	−0.334714	−	0.334714i
$724$		0			0
$725$	−42.9904	−	5.17949i	−1.59662	−	0.192362i
$726$		0			0
$727$	47.8109	+	12.8109i	1.77321	+	0.475130i	0.989318	−	0.145771i	$-0.0465663\pi$
$727$	47.8109	+	12.8109i	1.77321	+	0.475130i	0.783889	+	0.620901i	$0.213233\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$		0			0
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$		0			0
$733$	10.0000	+	10.0000i	0.369358	+	0.369358i	0.867243	−	0.497885i	$-0.165890\pi$
$733$	10.0000	+	10.0000i	0.369358	+	0.369358i	−0.497885	+	0.867243i	$0.665890\pi$
$734$		0			0
$735$	3.63397	+	4.09808i	0.134041	+	0.151160i
$736$		0			0
$737$	11.8301	−	3.16987i	0.435768	−	0.116764i
$738$		0			0
$739$	19.9186	−	11.5000i	0.732717	−	0.423034i	−0.0866983	−	0.996235i	$-0.527632\pi$
$739$	19.9186	−	11.5000i	0.732717	−	0.423034i	0.819415	+	0.573200i	$0.194298\pi$
$740$		0			0
$741$	−3.00000	+	25.9808i	−0.110208	+	0.954427i
$742$		0			0
$743$	−33.1244	−	8.87564i	−1.21521	−	0.325616i	−0.406409	−	0.913691i	$-0.633219\pi$
$743$	−33.1244	−	8.87564i	−1.21521	−	0.325616i	−0.808806	+	0.588076i	$0.799886\pi$
$744$		0			0
$745$	2.54552	−	42.4090i	0.0932605	−	1.55374i
$746$		0			0
$747$	−4.39230	−	16.3923i	−0.160706	−	0.599763i
$748$		0			0
$749$	27.7128			1.01260
$750$		0			0
$751$	13.5000	+	7.79423i	0.492622	+	0.284415i	0.725662	−	0.688052i	$-0.241534\pi$
$751$	13.5000	+	7.79423i	0.492622	+	0.284415i	−0.233040	+	0.972467i	$0.574867\pi$
$752$		0			0
$753$	−32.9090	+	32.9090i	−1.19927	+	1.19927i
$754$		0			0
$755$	−9.69615	−	6.40192i	−0.352879	−	0.232990i
$756$		0			0
$757$	−31.4186	−	8.41858i	−1.14193	−	0.305979i	−0.362202	−	0.932100i	$-0.617975\pi$
$757$	−31.4186	−	8.41858i	−1.14193	−	0.305979i	−0.779726	+	0.626121i	$0.784642\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.00000			−0.290000			−0.145000	−	0.989432i	$-0.546318\pi$
$761$	−8.00000			−0.290000			−0.145000	+	0.989432i	$0.546318\pi$
$762$		0			0
$763$	14.1962	+	3.80385i	0.513935	+	0.137709i
$764$		0			0
$765$	−9.29423	+	1.90192i	−0.336034	+	0.0687642i
$766$		0			0
$767$	3.00000	−	3.00000i	0.108324	−	0.108324i
$768$		0			0
$769$	44.1673	+	25.5000i	1.59271	+	0.919554i	0.992839	+	0.119459i	$0.0381161\pi$
$769$	44.1673	+	25.5000i	1.59271	+	0.919554i	0.599874	+	0.800094i	$0.295217\pi$
$770$		0			0
$771$	−66.0000			−2.37693
$772$		0			0
$773$	−5.70577	−	21.2942i	−0.205222	−	0.765900i	−0.989382	−	0.145341i	$-0.953572\pi$
$773$	−5.70577	−	21.2942i	−0.205222	−	0.765900i	0.784159	−	0.620560i	$-0.213094\pi$
$774$		0			0
$775$	7.96410	−	3.40192i	0.286079	−	0.122201i
$776$		0			0
$777$	32.7846	+	8.78461i	1.17614	+	0.315146i
$778$		0			0
$779$	13.8564	−	6.00000i	0.496457	−	0.214972i
$780$		0			0
$781$	10.5000	−	6.06218i	0.375720	−	0.216922i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.36603	+	2.09808i	−0.0844471	+	0.0748836i
$786$		0			0
$787$	−12.1244	−	12.1244i	−0.432187	−	0.432187i	0.457185	−	0.889372i	$-0.348858\pi$
$787$	−12.1244	−	12.1244i	−0.432187	−	0.432187i	−0.889372	+	0.457185i	$0.848858\pi$
$788$		0			0
$789$	32.9090	−	57.0000i	1.17159	−	2.02925i
$790$		0			0
$791$		−	6.92820i		−	0.246339i
$792$		0			0
$793$	−30.7583	−	8.24167i	−1.09226	−	0.292670i
$794$		0			0
$795$	−33.5885	−	22.1769i	−1.19126	−	0.786534i
$796$		0			0
$797$	−5.19615	−	5.19615i	−0.184057	−	0.184057i	0.609064	−	0.793121i	$-0.291545\pi$
$797$	−5.19615	−	5.19615i	−0.184057	−	0.184057i	−0.793121	+	0.609064i	$0.791545\pi$
$798$		0			0
$799$		−	6.00000i		−	0.212265i
$800$		0			0
$801$	40.5000	−	23.3827i	1.43100	−	0.826187i
$802$		0			0
$803$	−3.66025	+	13.6603i	−0.129168	+	0.482060i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−12.0788	−	45.0788i	−0.425195	−	1.58685i
$808$		0			0
$809$		−	17.0000i		−	0.597688i	−0.954302	−	0.298844i	$-0.903399\pi$
$809$		−	17.0000i		−	0.597688i	0.954302	−	0.298844i	$-0.0966011\pi$
$810$		0			0
$811$	−22.5000	−	12.9904i	−0.790082	−	0.456154i	0.0499095	−	0.998754i	$-0.484107\pi$
$811$	−22.5000	−	12.9904i	−0.790082	−	0.456154i	−0.839991	+	0.542600i	$0.817440\pi$
$812$		0			0
$813$	−5.70577	−	21.2942i	−0.200110	−	0.746821i
$814$		0			0
$815$	−21.6865	+	4.43782i	−0.759646	+	0.155450i
$816$		0			0
$817$	9.07180	−	22.9282i	0.317382	−	0.802156i
$818$		0			0
$819$	−10.3923	−	18.0000i	−0.363137	−	0.628971i
$820$		0			0
$821$	−15.5000	+	26.8468i	−0.540954	+	0.936959i	0.457896	+	0.889006i	$0.348603\pi$
$821$	−15.5000	+	26.8468i	−0.540954	+	0.936959i	−0.998850	+	0.0479535i	$0.984730\pi$
$822$		0			0
$823$	15.0263	−	4.02628i	0.523783	−	0.140347i	0.0127672	−	0.999918i	$-0.495936\pi$
$823$	15.0263	−	4.02628i	0.523783	−	0.140347i	0.511016	+	0.859571i	$0.329269\pi$
$824$		0			0
$825$	−1.73205	−	12.1244i	−0.0603023	−	0.422116i
$826$		0			0
$827$	11.8301	−	3.16987i	0.411374	−	0.110227i	−0.0471960	−	0.998886i	$-0.515029\pi$
$827$	11.8301	−	3.16987i	0.411374	−	0.110227i	0.458570	+	0.888658i	$0.348362\pi$
$828$		0			0
$829$	31.1769			1.08282			0.541409	−	0.840759i	$-0.317891\pi$
$829$	31.1769			1.08282			0.541409	+	0.840759i	$0.317891\pi$
$830$		0			0
$831$	−24.0000	+	13.8564i	−0.832551	+	0.480673i
$832$		0			0
$833$	0.366025	−	1.36603i	0.0126820	−	0.0473300i
$834$		0			0
$835$	10.3923	−	31.1769i	0.359641	−	1.07892i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−17.3205	−	30.0000i	−0.597970	−	1.03572i	−0.993120	−	0.117098i	$-0.962641\pi$
$839$	−17.3205	−	30.0000i	−0.597970	−	1.03572i	0.395150	−	0.918617i	$-0.370693\pi$
$840$		0			0
$841$	−23.0000	−	39.8372i	−0.793103	−	1.37370i
$842$		0			0
$843$	24.0000	+	24.0000i	0.826604	+	0.826604i
$844$		0			0
$845$	−0.937822	+	15.6244i	−0.0322621	+	0.537494i
$846$		0			0
$847$	20.0000	−	20.0000i	0.687208	−	0.687208i
$848$		0			0
$849$	22.5167	−	39.0000i	0.772770	−	1.33848i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.366025	+	1.36603i	−0.0125325	+	0.0467718i	−0.971909	−	0.235357i	$-0.924374\pi$
$853$	−0.366025	+	1.36603i	−0.0125325	+	0.0467718i	0.959376	+	0.282129i	$0.0910406\pi$
$854$		0			0
$855$	−27.4808	+	9.99038i	−0.939822	+	0.341664i
$856$		0			0
$857$	−7.60770	+	28.3923i	−0.259874	+	0.969863i	0.705440	+	0.708770i	$0.250750\pi$
$857$	−7.60770	+	28.3923i	−0.259874	+	0.969863i	−0.965314	+	0.261093i	$0.915917\pi$
$858$		0			0
$859$	35.5070	+	20.5000i	1.21148	+	0.699451i	0.963083	−	0.269206i	$-0.0867613\pi$
$859$	35.5070	+	20.5000i	1.21148	+	0.699451i	0.248402	+	0.968657i	$0.420095\pi$
$860$		0			0
$861$	−12.0000	+	20.7846i	−0.408959	+	0.708338i
$862$		0			0
$863$	1.73205	−	1.73205i	0.0589597	−	0.0589597i	−0.677012	−	0.735972i	$-0.736726\pi$
$863$	1.73205	−	1.73205i	0.0589597	−	0.0589597i	0.735972	+	0.677012i	$0.236726\pi$
$864$		0			0
$865$	−16.3923	+	14.5359i	−0.557355	+	0.494235i
$866$		0			0
$867$	−25.9808	−	25.9808i	−0.882353	−	0.882353i
$868$		0			0
$869$	−6.06218	−	10.5000i	−0.205645	−	0.356188i
$870$		0			0
$871$	15.0000	+	25.9808i	0.508256	+	0.880325i
$872$		0			0
$873$	−41.5692	+	41.5692i	−1.40690	+	1.40690i
$874$		0			0
$875$	−26.0000	+	18.0000i	−0.878960	+	0.608511i
$876$		0			0
$877$	−6.33975	+	23.6603i	−0.214078	+	0.798950i	0.772411	+	0.635123i	$0.219051\pi$
$877$	−6.33975	+	23.6603i	−0.214078	+	0.798950i	−0.986489	+	0.163827i	$0.947616\pi$
$878$		0			0
$879$	−10.3923	+	6.00000i	−0.350524	+	0.202375i
$880$		0			0
$881$	5.00000			0.168454			0.0842271	−	0.996447i	$-0.473158\pi$
$881$	5.00000			0.168454			0.0842271	+	0.996447i	$0.473158\pi$
$882$		0			0
$883$	−27.3205	+	7.32051i	−0.919408	+	0.246355i	−0.687332	−	0.726343i	$-0.741218\pi$
$883$	−27.3205	+	7.32051i	−0.919408	+	0.246355i	−0.232076	+	0.972698i	$0.574552\pi$
$884$		0			0
$885$	9.00000	+	3.00000i	0.302532	+	0.100844i
$886$		0			0
$887$	9.46410	−	2.53590i	0.317773	−	0.0851471i	−0.0964068	−	0.995342i	$-0.530735\pi$
$887$	9.46410	−	2.53590i	0.317773	−	0.0851471i	0.414180	+	0.910195i	$0.364068\pi$
$888$		0			0
$889$	−24.2487	+	42.0000i	−0.813276	+	1.40863i
$890$		0			0
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$		0			0
$893$	−2.70577	−	18.2942i	−0.0905452	−	0.612193i
$894$		0			0
$895$	−2.13397	+	3.23205i	−0.0713309	+	0.108036i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	12.9904	+	7.50000i	0.433253	+	0.250139i
$900$		0			0
$901$			10.3923i			0.346218i
$902$		0			0
$903$	10.1436	+	37.8564i	0.337558	+	1.25978i
$904$		0			0
$905$	6.92820	−	3.46410i	0.230301	−	0.115151i
$906$		0			0
$907$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$907$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$908$		0			0
$909$	18.1865	−	10.5000i	0.603209	−	0.348263i
$910$		0			0
$911$			57.1577i			1.89372i	0.321648	+	0.946859i	$0.395763\pi$
$911$			57.1577i			1.89372i	−0.321648	+	0.946859i	$0.604237\pi$
$912$		0			0
$913$	−4.00000	−	4.00000i	−0.132381	−	0.132381i
$914$		0			0
$915$	−14.2750	−	69.7583i	−0.471917	−	2.30614i
$916$		0			0
$917$	60.1051	+	16.1051i	1.98485	+	0.531838i
$918$		0			0
$919$			10.0000i			0.329870i	0.986304	+	0.164935i	$0.0527414\pi$
$919$			10.0000i			0.329870i	−0.986304	+	0.164935i	$0.947259\pi$
$920$		0			0
$921$	−27.0000	+	46.7654i	−0.889680	+	1.54097i
$922$		0			0
$923$	21.0000	+	21.0000i	0.691223	+	0.691223i
$924$		0			0
$925$	−9.12436	+	22.7321i	−0.300007	+	0.747425i
$926$		0			0
$927$	−14.1962	+	3.80385i	−0.466263	+	0.124935i
$928$		0			0
$929$	30.3109	−	17.5000i	0.994468	−	0.574156i	0.0878612	−	0.996133i	$-0.471997\pi$
$929$	30.3109	−	17.5000i	0.994468	−	0.574156i	0.906607	+	0.421976i	$0.138663\pi$
$930$		0			0
$931$	0.500000	−	4.33013i	0.0163868	−	0.141914i
$932$		0			0
$933$	52.0526	+	13.9474i	1.70412	+	0.456619i
$934$		0			0
$935$	−2.36603	+	2.09808i	−0.0773773	+	0.0686144i
$936$		0			0
$937$	−11.3468	−	42.3468i	−0.370683	−	1.38341i	−0.859550	−	0.511051i	$-0.829256\pi$
$937$	−11.3468	−	42.3468i	−0.370683	−	1.38341i	0.488867	−	0.872358i	$-0.337410\pi$
$938$		0			0
$939$	3.46410			0.113047
$940$		0			0
$941$	49.5000	+	28.5788i	1.61365	+	0.931644i	0.988514	+	0.151131i	$0.0482915\pi$
$941$	49.5000	+	28.5788i	1.61365	+	0.931644i	0.625140	+	0.780513i	$0.285042\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−47.8109	−	12.8109i	−1.55365	−	0.416298i	−0.623000	−	0.782222i	$-0.714086\pi$
$947$	−47.8109	−	12.8109i	−1.55365	−	0.416298i	−0.930645	+	0.365924i	$0.880753\pi$
$948$		0			0
$949$	−34.6410			−1.12449
$950$		0			0
$951$	12.0000			0.389127
$952$		0			0
$953$	9.46410	+	2.53590i	0.306572	+	0.0821458i	0.408825	−	0.912613i	$-0.365938\pi$
$953$	9.46410	+	2.53590i	0.306572	+	0.0821458i	−0.102253	+	0.994758i	$0.532605\pi$
$954$		0			0
$955$	−6.16025	+	9.33013i	−0.199341	+	0.301916i
$956$		0			0
$957$	15.0000	−	15.0000i	0.484881	−	0.484881i
$958$		0			0
$959$	−27.7128	−	16.0000i	−0.894893	−	0.516667i
$960$		0			0
$961$	28.0000			0.903226
$962$		0			0
$963$	−7.60770	−	28.3923i	−0.245155	−	0.914929i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	27.3205	+	7.32051i	0.878568	+	0.235412i	0.669789	−	0.742551i	$-0.266384\pi$
$967$	27.3205	+	7.32051i	0.878568	+	0.235412i	0.208779	+	0.977963i	$0.433051\pi$
$968$		0			0
$969$	12.1244	+	9.00000i	0.389490	+	0.289122i
$970$		0			0
$971$	48.0000	−	27.7128i	1.54039	−	0.889346i	0.541580	−	0.840649i	$-0.317826\pi$
$971$	48.0000	−	27.7128i	1.54039	−	0.889346i	0.998814	−	0.0486971i	$-0.0155069\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	27.5885	−	11.7846i	0.883538	−	0.377410i
$976$		0			0
$977$	3.46410	+	3.46410i	0.110826	+	0.110826i	0.760345	−	0.649519i	$-0.225030\pi$
$977$	3.46410	+	3.46410i	0.110826	+	0.110826i	−0.649519	+	0.760345i	$0.725030\pi$
$978$		0			0
$979$	7.79423	−	13.5000i	0.249105	−	0.431462i
$980$		0			0
$981$		−	15.5885i		−	0.497701i
$982$		0			0
$983$	37.8564	+	10.1436i	1.20743	+	0.323530i	0.805754	−	0.592251i	$-0.201760\pi$
$983$	37.8564	+	10.1436i	1.20743	+	0.323530i	0.401678	+	0.915781i	$0.368427\pi$
$984$		0			0
$985$	−5.70577	−	27.8827i	−0.181801	−	0.888416i
$986$		0			0
$987$	20.7846	+	20.7846i	0.661581	+	0.661581i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−12.0000	+	6.92820i	−0.381193	+	0.220082i	−0.678337	−	0.734751i	$-0.737299\pi$
$991$	−12.0000	+	6.92820i	−0.381193	+	0.220082i	0.297144	+	0.954833i	$0.403966\pi$
$992$		0			0
$993$	−8.78461	+	32.7846i	−0.278771	+	1.04039i
$994$		0			0
$995$	−42.0000	+	21.0000i	−1.33149	+	0.665745i
$996$		0			0
$997$	4.75833	+	17.7583i	0.150698	+	0.562412i	0.999435	+	0.0335977i	$0.0106965\pi$
$997$	4.75833	+	17.7583i	0.150698	+	0.562412i	−0.848738	+	0.528814i	$0.822637\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.y.a.373.1	yes	4
5.2	odd	4	inner	380.2.y.a.297.1	yes	4
19.8	odd	6	inner	380.2.y.a.293.1	yes	4
95.27	even	12	inner	380.2.y.a.217.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.y.a.217.1	✓	4	95.27	even	12	inner
380.2.y.a.293.1	yes	4	19.8	odd	6	inner
380.2.y.a.297.1	yes	4	5.2	odd	4	inner
380.2.y.a.373.1	yes	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:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.36603 + 0.633975i) q^{3} +(-1.23205 + 1.86603i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(2.59808 + 1.50000i) q^{9} +O(q^{10})\)	\(q+(2.36603 + 0.633975i) q^{3} +(-1.23205 + 1.86603i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(2.59808 + 1.50000i) q^{9} +1.00000 q^{11} +(0.633975 + 2.36603i) q^{13} +(-4.09808 + 3.63397i) q^{15} +(1.36603 + 0.366025i) q^{17} +(4.33013 + 0.500000i) q^{19} +(-6.00000 + 3.46410i) q^{21} +(-1.96410 - 4.59808i) q^{25} +(4.33013 - 7.50000i) q^{29} +1.73205i q^{31} +(2.36603 + 0.633975i) q^{33} +(-1.26795 - 6.19615i) q^{35} +(-3.46410 - 3.46410i) q^{37} +6.00000i q^{39} +(3.00000 - 1.73205i) q^{41} +(1.46410 - 5.46410i) q^{43} +(-6.00000 + 3.00000i) q^{45} +(-1.09808 - 4.09808i) q^{47} -1.00000i q^{49} +(3.00000 + 1.73205i) q^{51} +(1.90192 + 7.09808i) q^{53} +(-1.23205 + 1.86603i) q^{55} +(9.92820 + 3.92820i) q^{57} +(-0.866025 - 1.50000i) q^{59} +(-6.50000 + 11.2583i) q^{61} +(-8.19615 + 2.19615i) q^{63} +(-5.19615 - 1.73205i) q^{65} +(11.8301 - 3.16987i) q^{67} +(10.5000 - 6.06218i) q^{71} +(-3.66025 + 13.6603i) q^{73} +(-1.73205 - 12.1244i) q^{75} +(-2.00000 + 2.00000i) q^{77} +(-6.06218 - 10.5000i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.00000 - 4.00000i) q^{83} +(-2.36603 + 2.09808i) q^{85} +(15.0000 - 15.0000i) q^{87} +(7.79423 - 13.5000i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(-1.09808 + 4.09808i) q^{93} +(-6.26795 + 7.46410i) q^{95} +(-5.07180 + 18.9282i) q^{97} +(2.59808 + 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 2 q^{5} - 8 q^{7}+O(q^{10}) \) 4 * q + 6 * q^3 + 2 * q^5 - 8 * q^7	\( 4 q + 6 q^{3} + 2 q^{5} - 8 q^{7} + 4 q^{11} + 6 q^{13} - 6 q^{15} + 2 q^{17} - 24 q^{21} + 6 q^{25} + 6 q^{33} - 12 q^{35} + 12 q^{41} - 8 q^{43} - 24 q^{45} + 6 q^{47} + 12 q^{51} + 18 q^{53} + 2 q^{55} + 12 q^{57} - 26 q^{61} - 12 q^{63} + 30 q^{67} + 42 q^{71} + 20 q^{73} - 8 q^{77} - 18 q^{81} - 16 q^{83} - 6 q^{85} + 60 q^{87} - 24 q^{91} + 6 q^{93} - 32 q^{95} - 48 q^{97}+O(q^{100}) \) 4 * q + 6 * q^3 + 2 * q^5 - 8 * q^7 + 4 * q^11 + 6 * q^13 - 6 * q^15 + 2 * q^17 - 24 * q^21 + 6 * q^25 + 6 * q^33 - 12 * q^35 + 12 * q^41 - 8 * q^43 - 24 * q^45 + 6 * q^47 + 12 * q^51 + 18 * q^53 + 2 * q^55 + 12 * q^57 - 26 * q^61 - 12 * q^63 + 30 * q^67 + 42 * q^71 + 20 * q^73 - 8 * q^77 - 18 * q^81 - 16 * q^83 - 6 * q^85 + 60 * q^87 - 24 * q^91 + 6 * q^93 - 32 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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