LMFDB - Embedded newform 380.2.y.a.297.1

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			297.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	380.297
Dual form			380.2.y.a.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.633975 - 2.36603i) q^{3} +(2.23205 - 0.133975i) q^{5} +(-2.00000 - 2.00000i) q^{7} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(0.633975 - 2.36603i) q^{3} +(2.23205 - 0.133975i) q^{5} +(-2.00000 - 2.00000i) q^{7} +(-2.59808 - 1.50000i) q^{9} +1.00000 q^{11} +(2.36603 - 0.633975i) q^{13} +(1.09808 - 5.36603i) q^{15} +(-0.366025 + 1.36603i) q^{17} +(-4.33013 - 0.500000i) q^{19} +(-6.00000 + 3.46410i) q^{21} +(4.96410 - 0.598076i) q^{25} +(-4.33013 + 7.50000i) q^{29} +1.73205i q^{31} +(0.633975 - 2.36603i) q^{33} +(-4.73205 - 4.19615i) q^{35} +(3.46410 - 3.46410i) q^{37} -6.00000i q^{39} +(3.00000 - 1.73205i) q^{41} +(-5.46410 - 1.46410i) q^{43} +(-6.00000 - 3.00000i) q^{45} +(4.09808 - 1.09808i) q^{47} +1.00000i q^{49} +(3.00000 + 1.73205i) q^{51} +(7.09808 - 1.90192i) q^{53} +(2.23205 - 0.133975i) q^{55} +(-3.92820 + 9.92820i) q^{57} +(0.866025 + 1.50000i) q^{59} +(-6.50000 + 11.2583i) q^{61} +(2.19615 + 8.19615i) q^{63} +(5.19615 - 1.73205i) q^{65} +(3.16987 + 11.8301i) q^{67} +(10.5000 - 6.06218i) q^{71} +(13.6603 + 3.66025i) q^{73} +(1.73205 - 12.1244i) q^{75} +(-2.00000 - 2.00000i) q^{77} +(6.06218 + 10.5000i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.00000 + 4.00000i) q^{83} +(-0.633975 + 3.09808i) q^{85} +(15.0000 + 15.0000i) q^{87} +(-7.79423 + 13.5000i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(4.09808 + 1.09808i) q^{93} +(-9.73205 - 0.535898i) q^{95} +(-18.9282 - 5.07180i) q^{97} +(-2.59808 - 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.633975	−	2.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.633975	−	2.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$4$		0			0
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$6$		0			0
$7$	−2.00000	−	2.00000i	−0.755929	−	0.755929i	0.219650	−	0.975579i	$-0.429509\pi$
$7$	−2.00000	−	2.00000i	−0.755929	−	0.755929i	−0.975579	+	0.219650i	$0.929509\pi$
$8$		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
$13$	2.36603	−	0.633975i	0.656217	−	0.175833i	0.0846790	−	0.996408i	$-0.473014\pi$
$13$	2.36603	−	0.633975i	0.656217	−	0.175833i	0.571538	+	0.820575i	$0.306347\pi$
$14$		0			0
$15$	1.09808	−	5.36603i	0.283522	−	1.38550i
$16$		0			0
$17$	−0.366025	+	1.36603i	−0.0887742	+	0.331310i	−0.996002	−	0.0893296i	$-0.971528\pi$
$17$	−0.366025	+	1.36603i	−0.0887742	+	0.331310i	0.907228	+	0.420639i	$0.138194\pi$
$18$		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		0.965926	−	0.258819i	$-0.0833333\pi$
$23$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$24$		0			0
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.33013	+	7.50000i	−0.804084	+	1.39272i	0.112823	+	0.993615i	$0.464011\pi$
$29$	−4.33013	+	7.50000i	−0.804084	+	1.39272i	−0.916907	+	0.399100i	$0.869323\pi$
$30$		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
$33$	0.633975	−	2.36603i	0.110361	−	0.411872i
$34$		0			0
$35$	−4.73205	−	4.19615i	−0.799863	−	0.709279i
$36$		0			0
$37$	3.46410	−	3.46410i	0.569495	−	0.569495i	−0.362492	−	0.931987i	$-0.618074\pi$
$37$	3.46410	−	3.46410i	0.569495	−	0.569495i	0.931987	+	0.362492i	$0.118074\pi$
$38$		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
$43$	−5.46410	−	1.46410i	−0.833268	−	0.223273i	−0.183129	−	0.983089i	$-0.558623\pi$
$43$	−5.46410	−	1.46410i	−0.833268	−	0.223273i	−0.650139	+	0.759816i	$0.725289\pi$
$44$		0			0
$45$	−6.00000	−	3.00000i	−0.894427	−	0.447214i
$46$		0			0
$47$	4.09808	−	1.09808i	0.597766	−	0.160171i	0.0527658	−	0.998607i	$-0.483196\pi$
$47$	4.09808	−	1.09808i	0.597766	−	0.160171i	0.545000	+	0.838436i	$0.316530\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	3.00000	+	1.73205i	0.420084	+	0.242536i
$52$		0			0
$53$	7.09808	−	1.90192i	0.974996	−	0.261249i	0.264060	−	0.964506i	$-0.414938\pi$
$53$	7.09808	−	1.90192i	0.974996	−	0.261249i	0.710936	+	0.703257i	$0.248272\pi$
$54$		0			0
$55$	2.23205	−	0.133975i	0.300970	−	0.0180651i
$56$		0			0
$57$	−3.92820	+	9.92820i	−0.520303	+	1.31502i
$58$		0			0
$59$	0.866025	+	1.50000i	0.112747	+	0.195283i	0.916877	−	0.399170i	$-0.130702\pi$
$59$	0.866025	+	1.50000i	0.112747	+	0.195283i	−0.804130	+	0.594454i	$0.797368\pi$
$60$		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
$63$	2.19615	+	8.19615i	0.276689	+	1.03262i
$64$		0			0
$65$	5.19615	−	1.73205i	0.644503	−	0.214834i
$66$		0			0
$67$	3.16987	+	11.8301i	0.387262	+	1.44528i	0.834571	+	0.550901i	$0.185716\pi$
$67$	3.16987	+	11.8301i	0.387262	+	1.44528i	−0.447309	+	0.894379i	$0.647618\pi$
$68$		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
$73$	13.6603	+	3.66025i	1.59881	+	0.428400i	0.944684	−	0.327983i	$-0.106369\pi$
$73$	13.6603	+	3.66025i	1.59881	+	0.428400i	0.654128	+	0.756384i	$0.273036\pi$
$74$		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	$0.0722440\pi$
$79$	6.06218	+	10.5000i	0.682048	+	1.18134i	−0.292306	+	0.956325i	$0.594423\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	−4.00000	+	4.00000i	−0.439057	+	0.439057i	−0.891695	−	0.452638i	$-0.850483\pi$
$83$	−4.00000	+	4.00000i	−0.439057	+	0.439057i	0.452638	+	0.891695i	$0.350483\pi$
$84$		0			0
$85$	−0.633975	+	3.09808i	−0.0687642	+	0.336034i
$86$		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	$0.476161\pi$
$89$	−7.79423	+	13.5000i	−0.826187	+	1.43100i	−0.901009	+	0.433800i	$0.857172\pi$
$90$		0			0
$91$	−6.00000	−	3.46410i	−0.628971	−	0.363137i
$92$		0			0
$93$	4.09808	+	1.09808i	0.424951	+	0.113865i
$94$		0			0
$95$	−9.73205	−	0.535898i	−0.998487	−	0.0549820i
$96$		0			0
$97$	−18.9282	−	5.07180i	−1.92187	−	0.514963i	−0.987213	−	0.159407i	$-0.949042\pi$
$97$	−18.9282	−	5.07180i	−1.92187	−	0.514963i	−0.934655	−	0.355556i	$-0.884291\pi$
$98$		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	$-0.172408\pi$
$103$	3.46410	+	3.46410i	0.341328	+	0.341328i	−0.515538	+	0.856866i	$0.672408\pi$
$104$		0			0
$105$	−12.9282	+	8.53590i	−1.26166	+	0.833018i
$106$		0			0
$107$	6.92820	−	6.92820i	0.669775	−	0.669775i	−0.287889	−	0.957664i	$-0.592953\pi$
$107$	6.92820	−	6.92820i	0.669775	−	0.669775i	0.957664	+	0.287889i	$0.0929534\pi$
$108$		0			0
$109$	2.59808	+	4.50000i	0.248851	+	0.431022i	0.963207	−	0.268760i	$-0.0866139\pi$
$109$	2.59808	+	4.50000i	0.248851	+	0.431022i	−0.714357	+	0.699782i	$0.753281\pi$
$110$		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	$-0.213245\pi$
$113$	1.73205	+	1.73205i	0.162938	+	0.162938i	−0.620929	+	0.783867i	$0.713245\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−7.09808	−	1.90192i	−0.656217	−	0.175833i
$118$		0			0
$119$	3.46410	−	2.00000i	0.317554	−	0.183340i
$120$		0			0
$121$	−10.0000			−0.909091
$122$		0			0
$123$	−2.19615	−	8.19615i	−0.198020	−	0.739022i
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	4.43782	+	16.5622i	0.393793	+	1.46966i	0.823826	+	0.566843i	$0.191835\pi$
$127$	4.43782	+	16.5622i	0.393793	+	1.46966i	−0.430033	+	0.902813i	$0.641498\pi$
$128$		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
$133$	7.66025	+	9.66025i	0.664228	+	0.837650i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.9282	+	2.92820i	−0.933659	+	0.250173i	−0.693414	−	0.720539i	$-0.743894\pi$
$137$	−10.9282	+	2.92820i	−0.933659	+	0.250173i	−0.240245	+	0.970712i	$0.577228\pi$
$138$		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
$143$	2.36603	−	0.633975i	0.197857	−	0.0530156i
$144$		0			0
$145$	−8.66025	+	17.3205i	−0.719195	+	1.43839i
$146$		0			0
$147$	2.36603	+	0.633975i	0.195146	+	0.0522893i
$148$		0			0
$149$	16.4545	−	9.50000i	1.34800	−	0.778270i	0.360037	−	0.932938i	$-0.382764\pi$
$149$	16.4545	−	9.50000i	1.34800	−	0.778270i	0.987967	+	0.154668i	$0.0494307\pi$
$150$		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
$155$	0.232051	+	3.86603i	0.0186388	+	0.310527i
$156$		0			0
$157$	−0.366025	+	1.36603i	−0.0292120	+	0.109021i	−0.978993	−	0.203896i	$-0.934639\pi$
$157$	−0.366025	+	1.36603i	−0.0292120	+	0.109021i	0.949780	+	0.312917i	$0.101306\pi$
$158$		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	−0.377661	−	0.925944i	$-0.623272\pi$
$163$	7.00000	−	7.00000i	0.548282	−	0.548282i	0.925944	+	0.377661i	$0.123272\pi$
$164$		0			0
$165$	1.09808	−	5.36603i	0.0854851	−	0.417745i
$166$		0			0
$167$	−3.80385	−	14.1962i	−0.294351	−	1.09853i	−0.941732	−	0.336365i	$-0.890802\pi$
$167$	−3.80385	−	14.1962i	−0.294351	−	1.09853i	0.647381	−	0.762166i	$-0.275864\pi$
$168$		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
$173$	2.53590	−	9.46410i	0.192801	−	0.719542i	−0.800024	−	0.599967i	$-0.795180\pi$
$173$	2.53590	−	9.46410i	0.192801	−	0.719542i	0.992825	−	0.119575i	$-0.0381532\pi$
$174$		0			0
$175$	−11.1244	−	8.73205i	−0.840922	−	0.660081i
$176$		0			0
$177$	4.09808	−	1.09808i	0.308030	−	0.0825365i
$178$		0			0
$179$	−1.73205			−0.129460			−0.0647298	−	0.997903i	$-0.520619\pi$
$179$	−1.73205			−0.129460			−0.0647298	+	0.997903i	$0.520619\pi$
$180$		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
$185$	7.26795	−	8.19615i	0.534350	−	0.602593i
$186$		0			0
$187$	−0.366025	+	1.36603i	−0.0267664	+	0.0998937i
$188$		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		−0.965926	−	0.258819i	$-0.916667\pi$
$193$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$194$		0			0
$195$	−0.803848	−	13.3923i	−0.0575647	−	0.959043i
$196$		0			0
$197$	−9.00000	−	9.00000i	−0.641223	−	0.641223i	0.309633	−	0.950856i	$-0.399794\pi$
$197$	−9.00000	−	9.00000i	−0.641223	−	0.641223i	−0.950856	+	0.309633i	$0.899794\pi$
$198$		0			0
$199$	−18.1865	−	10.5000i	−1.28921	−	0.744325i	−0.310696	−	0.950509i	$-0.600562\pi$
$199$	−18.1865	−	10.5000i	−1.28921	−	0.744325i	−0.978513	+	0.206184i	$0.933895\pi$
$200$		0			0
$201$	30.0000			2.11604
$202$		0			0
$203$	23.6603	−	6.33975i	1.66062	−	0.444963i
$204$		0			0
$205$	6.46410	−	4.26795i	0.451472	−	0.298087i
$206$		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
$213$	−7.68653	−	28.6865i	−0.526673	−	1.96557i
$214$		0			0
$215$	−12.3923	−	2.53590i	−0.845148	−	0.172947i
$216$		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
$223$	−3.80385	+	14.1962i	−0.254724	+	0.950645i	0.713519	+	0.700636i	$0.247100\pi$
$223$	−3.80385	+	14.1962i	−0.254724	+	0.950645i	−0.968244	+	0.250009i	$0.919566\pi$
$224$		0			0
$225$	−13.7942	−	5.89230i	−0.919615	−	0.392820i
$226$		0			0
$227$	−13.8564	+	13.8564i	−0.919682	+	0.919682i	−0.997006	−	0.0773240i	$-0.975362\pi$
$227$	−13.8564	+	13.8564i	−0.919682	+	0.919682i	0.0773240	+	0.997006i	$0.475362\pi$
$228$		0			0
$229$		−	21.0000i		−	1.38772i	−0.720110	−	0.693860i	$-0.755909\pi$
$229$		−	21.0000i		−	1.38772i	0.720110	−	0.693860i	$-0.244091\pi$
$230$		0			0
$231$	−6.00000	+	3.46410i	−0.394771	+	0.227921i
$232$		0			0
$233$	−20.4904	−	5.49038i	−1.34237	−	0.359687i	−0.485057	−	0.874483i	$-0.661201\pi$
$233$	−20.4904	−	5.49038i	−1.34237	−	0.359687i	−0.857313	+	0.514796i	$0.827868\pi$
$234$		0			0
$235$	9.00000	−	3.00000i	0.587095	−	0.195698i
$236$		0			0
$237$	28.6865	−	7.68653i	1.86339	−	0.499294i
$238$		0			0
$239$			19.0000i			1.22901i	0.788914	+	0.614504i	$0.210644\pi$
$239$			19.0000i			1.22901i	−0.788914	+	0.614504i	$0.789356\pi$
$240$		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
$243$	−21.2942	+	5.70577i	−1.36603	+	0.366025i
$244$		0			0
$245$	0.133975	+	2.23205i	0.00855932	+	0.142600i
$246$		0			0
$247$	−10.5622	+	1.56218i	−0.672055	+	0.0993990i
$248$		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
$257$	−6.97372	−	26.0263i	−0.435009	−	1.62347i	−0.741045	−	0.671455i	$-0.765670\pi$
$257$	−6.97372	−	26.0263i	−0.435009	−	1.62347i	0.306037	−	0.952020i	$-0.400997\pi$
$258$		0			0
$259$	−13.8564			−0.860995
$260$		0			0
$261$	22.5000	−	12.9904i	1.39272	−	0.804084i
$262$		0			0
$263$	−25.9545	−	6.95448i	−1.60042	−	0.428832i	−0.655252	−	0.755410i	$-0.727438\pi$
$263$	−25.9545	−	6.95448i	−1.60042	−	0.428832i	−0.945170	+	0.326579i	$0.894104\pi$
$264$		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	$0.0306043\pi$
$269$	9.52628	+	16.5000i	0.580828	+	1.00602i	−0.414554	+	0.910025i	$0.636062\pi$
$270$		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
$275$	4.96410	−	0.598076i	0.299347	−	0.0360654i
$276$		0			0
$277$	−8.00000	−	8.00000i	−0.480673	−	0.480673i	0.424673	−	0.905347i	$-0.360389\pi$
$277$	−8.00000	−	8.00000i	−0.480673	−	0.480673i	−0.905347	+	0.424673i	$0.860389\pi$
$278$		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
$283$	−17.7583	−	4.75833i	−1.05562	−	0.282853i	−0.311050	−	0.950394i	$-0.600681\pi$
$283$	−17.7583	−	4.75833i	−1.05562	−	0.282853i	−0.744574	+	0.667540i	$0.767347\pi$
$284$		0			0
$285$	−7.43782	+	22.6865i	−0.440579	+	1.34383i
$286$		0			0
$287$	−9.46410	−	2.53590i	−0.558648	−	0.149689i
$288$		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	$-0.204293\pi$
$293$	3.46410	+	3.46410i	0.202375	+	0.202375i	−0.598642	+	0.801017i	$0.704293\pi$
$294$		0			0
$295$	2.13397	+	3.23205i	0.124245	+	0.188177i
$296$		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
$307$	−21.2942	−	5.70577i	−1.21533	−	0.325646i	−0.406476	−	0.913661i	$-0.633243\pi$
$307$	−21.2942	−	5.70577i	−1.21533	−	0.325646i	−0.808849	+	0.588016i	$0.799909\pi$
$308$		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
$313$	−0.366025	−	1.36603i	−0.0206890	−	0.0772123i	0.954810	−	0.297218i	$-0.0960589\pi$
$313$	−0.366025	−	1.36603i	−0.0206890	−	0.0772123i	−0.975499	+	0.220006i	$0.929392\pi$
$314$		0			0
$315$	6.00000	+	18.0000i	0.338062	+	1.01419i
$316$		0			0
$317$	1.26795	+	4.73205i	0.0712151	+	0.265778i	0.992348	−	0.123469i	$-0.0394019\pi$
$317$	1.26795	+	4.73205i	0.0712151	+	0.265778i	−0.921133	+	0.389247i	$0.872735\pi$
$318$		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
$323$	2.26795	−	5.73205i	0.126192	−	0.318940i
$324$		0			0
$325$	11.3660	−	4.56218i	0.630474	−	0.253064i
$326$		0			0
$327$	12.2942	−	3.29423i	0.679872	−	0.182171i
$328$		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
$333$	−14.1962	+	3.80385i	−0.777944	+	0.208450i
$334$		0			0
$335$	8.66025	+	25.9808i	0.473160	+	1.41948i
$336$		0			0
$337$	14.1962	+	3.80385i	0.773314	+	0.207209i	0.623835	−	0.781556i	$-0.285574\pi$
$337$	14.1962	+	3.80385i	0.773314	+	0.207209i	0.149479	+	0.988765i	$0.452240\pi$
$338$		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
$347$	7.32051	−	27.3205i	0.392985	−	1.46664i	−0.432199	−	0.901778i	$-0.642262\pi$
$347$	7.32051	−	27.3205i	0.392985	−	1.46664i	0.825184	−	0.564863i	$-0.191071\pi$
$348$		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	−0.0411112	−	0.999155i	$-0.513090\pi$
$353$	18.0000	−	18.0000i	0.958043	−	0.958043i	0.999155	+	0.0411112i	$0.0130898\pi$
$354$		0			0
$355$	22.6244	−	14.9378i	1.20078	−	0.792817i
$356$		0			0
$357$	−2.53590	−	9.46410i	−0.134214	−	0.500893i
$358$		0			0
$359$	−19.0526	+	11.0000i	−1.00556	+	0.580558i	−0.909887	−	0.414855i	$-0.863832\pi$
$359$	−19.0526	+	11.0000i	−1.00556	+	0.580558i	−0.0956683	+	0.995413i	$0.530499\pi$
$360$		0			0
$361$	18.5000	+	4.33013i	0.973684	+	0.227901i
$362$		0			0
$363$	−6.33975	+	23.6603i	−0.332750	+	1.24184i
$364$		0			0
$365$	30.9808	+	6.33975i	1.62161	+	0.331837i
$366$		0			0
$367$	5.46410	−	1.46410i	0.285224	−	0.0764255i	−0.113371	−	0.993553i	$-0.536165\pi$
$367$	5.46410	−	1.46410i	0.285224	−	0.0764255i	0.398594	+	0.917127i	$0.369498\pi$
$368$		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	$-0.290480\pi$
$373$	−3.46410	−	3.46410i	−0.179364	−	0.179364i	−0.791079	+	0.611714i	$0.790480\pi$
$374$		0			0
$375$	2.24167	−	27.2942i	0.115759	−	1.40947i
$376$		0			0
$377$	−5.49038	+	20.4904i	−0.282769	+	1.05531i
$378$		0			0
$379$	1.73205			0.0889695			0.0444847	−	0.999010i	$-0.485835\pi$
$379$	1.73205			0.0889695			0.0444847	+	0.999010i	$0.485835\pi$
$380$		0			0
$381$	42.0000			2.15173
$382$		0			0
$383$	4.43782	−	16.5622i	0.226762	−	0.846288i	−0.754929	−	0.655807i	$-0.772329\pi$
$383$	4.43782	−	16.5622i	0.226762	−	0.846288i	0.981691	−	0.190481i	$-0.0610047\pi$
$384$		0			0
$385$	−4.73205	−	4.19615i	−0.241168	−	0.213856i
$386$		0			0
$387$	12.0000	+	12.0000i	0.609994	+	0.609994i
$388$		0			0
$389$	9.52628	+	5.50000i	0.483002	+	0.278861i	0.721666	−	0.692241i	$-0.243376\pi$
$389$	9.52628	+	5.50000i	0.483002	+	0.278861i	−0.238665	+	0.971102i	$0.576710\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−52.0526	+	13.9474i	−2.62570	+	0.703555i
$394$		0			0
$395$	14.9378	+	22.6244i	0.751603	+	1.13835i
$396$		0			0
$397$	8.05256	−	30.0526i	0.404146	−	1.50829i	−0.401478	−	0.915868i	$-0.631504\pi$
$397$	8.05256	−	30.0526i	0.404146	−	1.50829i	0.805625	−	0.592426i	$-0.201830\pi$
$398$		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
$403$	1.09808	+	4.09808i	0.0546991	+	0.204140i
$404$		0			0
$405$	−11.0885	−	16.7942i	−0.550990	−	0.834512i
$406$		0			0
$407$	3.46410	−	3.46410i	0.171709	−	0.171709i
$408$		0			0
$409$	−7.79423	+	13.5000i	−0.385400	+	0.667532i	−0.991825	−	0.127609i	$-0.959270\pi$
$409$	−7.79423	+	13.5000i	−0.385400	+	0.667532i	0.606425	+	0.795141i	$0.292603\pi$
$410$		0			0
$411$			27.7128i			1.36697i
$412$		0			0
$413$	1.26795	−	4.73205i	0.0623917	−	0.232849i
$414$		0			0
$415$	−8.39230	+	9.46410i	−0.411962	+	0.464574i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	1.00000i		−	0.0488532i	−0.999702	−	0.0244266i	$-0.992224\pi$
$419$		−	1.00000i		−	0.0488532i	0.999702	−	0.0244266i	$-0.00777600\pi$
$420$		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
$423$	−12.2942	−	3.29423i	−0.597766	−	0.160171i
$424$		0			0
$425$	−1.00000	+	7.00000i	−0.0485071	+	0.339550i
$426$		0			0
$427$	35.5167	−	9.51666i	1.71877	−	0.460543i
$428$		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
$433$	14.1962	−	3.80385i	0.682224	−	0.182801i	0.0989688	−	0.995091i	$-0.468446\pi$
$433$	14.1962	−	3.80385i	0.682224	−	0.182801i	0.583255	+	0.812289i	$0.301779\pi$
$434$		0			0
$435$	35.4904	+	31.4711i	1.70163	+	1.50893i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	12.9904	+	22.5000i	0.619997	+	1.07387i	0.989486	+	0.144631i	$0.0461996\pi$
$439$	12.9904	+	22.5000i	0.619997	+	1.07387i	−0.369489	+	0.929235i	$0.620467\pi$
$440$		0			0
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$		0			0
$443$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$443$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$444$		0			0
$445$	−15.5885	+	31.1769i	−0.738964	+	1.47793i
$446$		0			0
$447$	−12.0455	−	44.9545i	−0.569733	−	2.12627i
$448$		0			0
$449$	−32.9090			−1.55307			−0.776535	−	0.630074i	$-0.783025\pi$
$449$	−32.9090			−1.55307			−0.776535	+	0.630074i	$0.783025\pi$
$450$		0			0
$451$	3.00000	−	1.73205i	0.141264	−	0.0815591i
$452$		0			0
$453$	12.2942	+	3.29423i	0.577633	+	0.154776i
$454$		0			0
$455$	−13.8564	−	6.92820i	−0.649598	−	0.324799i
$456$		0			0
$457$	11.0000	+	11.0000i	0.514558	+	0.514558i	0.915920	−	0.401361i	$-0.131463\pi$
$457$	11.0000	+	11.0000i	0.514558	+	0.514558i	−0.401361	+	0.915920i	$0.631463\pi$
$458$		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	−0.373735	+	0.927536i	$0.621923\pi$
$463$	−28.0000	+	28.0000i	−1.30127	+	1.30127i	−0.927536	+	0.373735i	$0.878077\pi$
$464$		0			0
$465$	9.29423	+	1.90192i	0.431010	+	0.0881996i
$466$		0			0
$467$	−12.0000	−	12.0000i	−0.555294	−	0.555294i	0.372670	−	0.927964i	$-0.378442\pi$
$467$	−12.0000	−	12.0000i	−0.555294	−	0.555294i	−0.927964	+	0.372670i	$0.878442\pi$
$468$		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
$473$	−5.46410	−	1.46410i	−0.251240	−	0.0673195i
$474$		0			0
$475$	−21.7942	+	0.107695i	−0.999988	+	0.00494139i
$476$		0			0
$477$	−21.2942	−	5.70577i	−0.974996	−	0.261249i
$478$		0			0
$479$	25.1147	+	14.5000i	1.14752	+	0.662522i	0.948282	−	0.317429i	$-0.102819\pi$
$479$	25.1147	+	14.5000i	1.14752	+	0.662522i	0.199240	+	0.979951i	$0.436153\pi$
$480$		0			0
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−42.9282	−	8.78461i	−1.94927	−	0.398889i
$486$		0			0
$487$	−12.1244	+	12.1244i	−0.549407	+	0.549407i	−0.926269	−	0.376862i	$-0.877003\pi$
$487$	−12.1244	+	12.1244i	−0.549407	+	0.549407i	0.376862	+	0.926269i	$0.377003\pi$
$488$		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
$497$	−33.1244	−	8.87564i	−1.48583	−	0.398127i
$498$		0			0
$499$	5.19615	−	3.00000i	0.232612	−	0.134298i	−0.379165	−	0.925329i	$-0.623789\pi$
$499$	5.19615	−	3.00000i	0.232612	−	0.134298i	0.611776	+	0.791031i	$0.290455\pi$
$500$		0			0
$501$	−36.0000			−1.60836
$502$		0			0
$503$	1.83013	+	6.83013i	0.0816013	+	0.304540i	0.994649	−	0.103313i	$-0.0329442\pi$
$503$	1.83013	+	6.83013i	0.0816013	+	0.304540i	−0.913048	+	0.407853i	$0.866278\pi$
$504$		0			0
$505$	7.00000	−	14.0000i	0.311496	−	0.622992i
$506$		0			0
$507$	4.43782	+	16.5622i	0.197091	+	0.735552i
$508$		0			0
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	−0.901855	−	0.432038i	$-0.857795\pi$
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	0.825084	+	0.565011i	$0.191128\pi$
$510$		0			0
$511$	−20.0000	−	34.6410i	−0.884748	−	1.53243i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.19615	+	7.26795i	0.361166	+	0.320264i
$516$		0			0
$517$	4.09808	−	1.09808i	0.180233	−	0.0482933i
$518$		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
$523$	11.8301	−	3.16987i	0.517295	−	0.138609i	0.00928008	−	0.999957i	$-0.497046\pi$
$523$	11.8301	−	3.16987i	0.517295	−	0.138609i	0.508015	+	0.861348i	$0.330379\pi$
$524$		0			0
$525$	−27.7128	+	20.7846i	−1.20949	+	0.907115i
$526$		0			0
$527$	−2.36603	−	0.633975i	−0.103066	−	0.0276164i
$528$		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
$535$	14.5359	−	16.3923i	0.628442	−	0.708701i
$536$		0			0
$537$	−1.09808	+	4.09808i	−0.0473855	+	0.176845i
$538$		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
$545$	6.40192	+	9.69615i	0.274228	+	0.415338i
$546$		0			0
$547$	−3.80385	−	14.1962i	−0.162641	−	0.606984i	−0.998329	−	0.0577800i	$-0.981598\pi$
$547$	−3.80385	−	14.1962i	−0.162641	−	0.606984i	0.835689	−	0.549204i	$-0.185069\pi$
$548$		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
$553$	8.87564	−	33.1244i	0.377431	−	1.40859i
$554$		0			0
$555$	−14.7846	−	22.3923i	−0.627572	−	0.950500i
$556$		0			0
$557$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$557$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$558$		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	$-0.0962155\pi$
$563$	15.5885	+	15.5885i	0.656975	+	0.656975i	−0.297688	+	0.954663i	$0.596216\pi$
$564$		0			0
$565$	4.09808	+	3.63397i	0.172407	+	0.152882i
$566$		0			0
$567$	−6.58846	+	24.5885i	−0.276689	+	1.03262i
$568$		0			0
$569$	19.0526			0.798725			0.399362	−	0.916793i	$-0.369232\pi$
$569$	19.0526			0.798725			0.399362	+	0.916793i	$0.369232\pi$
$570$		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
$573$	3.16987	−	11.8301i	0.132423	−	0.494211i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	32.0000	+	32.0000i	1.33218	+	1.33218i	0.903419	+	0.428758i	$0.141049\pi$
$577$	32.0000	+	32.0000i	1.33218	+	1.33218i	0.428758	+	0.903419i	$0.358951\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.0000			0.663792
$582$		0			0
$583$	7.09808	−	1.90192i	0.293972	−	0.0787696i
$584$		0			0
$585$	−16.0981	−	3.29423i	−0.665574	−	0.136200i
$586$		0			0
$587$	2.19615	−	8.19615i	0.0906449	−	0.338291i	−0.905678	−	0.423966i	$-0.860638\pi$
$587$	2.19615	−	8.19615i	0.0906449	−	0.338291i	0.996323	+	0.0856742i	$0.0273044\pi$
$588$		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
$593$	5.85641	+	21.8564i	0.240494	+	0.897535i	0.975595	+	0.219578i	$0.0704679\pi$
$593$	5.85641	+	21.8564i	0.240494	+	0.897535i	−0.735101	+	0.677957i	$0.762865\pi$
$594$		0			0
$595$	7.46410	−	4.92820i	0.305998	−	0.202037i
$596$		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	$-0.510396\pi$
$599$	20.7846	−	36.0000i	0.849236	−	1.47092i	0.881891	−	0.471453i	$-0.156270\pi$
$600$		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
$603$	9.50962	−	35.4904i	0.387262	−	1.44528i
$604$		0			0
$605$	−22.3205	+	1.33975i	−0.907458	+	0.0544684i
$606$		0			0
$607$	22.5167	−	22.5167i	0.913923	−	0.913923i	−0.0826552	−	0.996578i	$-0.526340\pi$
$607$	22.5167	−	22.5167i	0.913923	−	0.913923i	0.996578	+	0.0826552i	$0.0263400\pi$
$608$		0			0
$609$		−	60.0000i		−	2.43132i
$610$		0			0
$611$	9.00000	−	5.19615i	0.364101	−	0.210214i
$612$		0			0
$613$	−23.2224	−	6.22243i	−0.937945	−	0.251322i	−0.242706	−	0.970100i	$-0.578035\pi$
$613$	−23.2224	−	6.22243i	−0.937945	−	0.251322i	−0.695239	+	0.718778i	$0.744702\pi$
$614$		0			0
$615$	−6.00000	−	18.0000i	−0.241943	−	0.725830i
$616$		0			0
$617$	−30.0526	+	8.05256i	−1.20987	+	0.324184i	−0.806711	−	0.590946i	$-0.798755\pi$
$617$	−30.0526	+	8.05256i	−1.20987	+	0.324184i	−0.403159	+	0.915130i	$0.632088\pi$
$618$		0			0
$619$		−	6.00000i		−	0.241160i	−0.992704	−	0.120580i	$-0.961525\pi$
$619$		−	6.00000i		−	0.241160i	0.992704	−	0.120580i	$-0.0384755\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	42.5885	−	11.4115i	1.70627	−	0.457194i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$		0			0
$627$	−3.92820	+	9.92820i	−0.156877	+	0.396494i
$628$		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
$633$	12.0788	+	45.0788i	0.480091	+	1.79172i
$634$		0			0
$635$	12.1244	+	36.3731i	0.481140	+	1.44342i
$636$		0			0
$637$	0.633975	+	2.36603i	0.0251190	+	0.0937453i
$638$		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
$643$	−6.83013	−	1.83013i	−0.269354	−	0.0721732i	0.121614	−	0.992577i	$-0.461193\pi$
$643$	−6.83013	−	1.83013i	−0.269354	−	0.0721732i	−0.390968	+	0.920404i	$0.627860\pi$
$644$		0			0
$645$	−13.8564	+	27.7128i	−0.545595	+	1.09119i
$646$		0			0
$647$	7.00000	+	7.00000i	0.275198	+	0.275198i	0.831189	−	0.555990i	$-0.187661\pi$
$647$	7.00000	+	7.00000i	0.275198	+	0.275198i	−0.555990	+	0.831189i	$0.687661\pi$
$648$		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	−0.130519	−	0.991446i	$-0.541664\pi$
$653$	22.0000	−	22.0000i	0.860927	−	0.860927i	0.991446	+	0.130519i	$0.0416644\pi$
$654$		0			0
$655$	−27.1051	−	41.0526i	−1.05908	−	1.60406i
$656$		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	$-0.532988\pi$
$659$	20.7846	−	36.0000i	0.809653	−	1.40236i	0.913104	−	0.407726i	$-0.133678\pi$
$660$		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
$663$	8.19615	+	2.19615i	0.318312	+	0.0852915i
$664$		0			0
$665$	18.3923	+	20.5359i	0.713223	+	0.796348i
$666$		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	$-0.310473\pi$
$673$	−6.92820	−	6.92820i	−0.267063	−	0.267063i	−0.827915	+	0.560853i	$0.810473\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	31.1769	−	31.1769i	1.19823	−	1.19823i	0.223529	−	0.974697i	$-0.428242\pi$
$677$	31.1769	−	31.1769i	1.19823	−	1.19823i	0.974697	−	0.223529i	$-0.0717577\pi$
$678$		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	$-0.422393\pi$
$683$	−19.0526	−	19.0526i	−0.729026	−	0.729026i	−0.970426	+	0.241400i	$0.922393\pi$
$684$		0			0
$685$	−24.0000	+	8.00000i	−0.916993	+	0.305664i
$686$		0			0
$687$	−49.6865	−	13.3135i	−1.89566	−	0.507940i
$688$		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
$693$	2.19615	+	8.19615i	0.0834249	+	0.311346i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.26795	+	4.73205i	0.0480270	+	0.179239i
$698$		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
$703$	−16.7321	+	13.2679i	−0.631061	+	0.500410i
$704$		0			0
$705$	−1.39230	−	23.1962i	−0.0524372	−	0.873618i
$706$		0			0
$707$	−19.1244	+	5.12436i	−0.719245	+	0.192721i
$708$		0			0
$709$	28.5788	+	16.5000i	1.07330	+	0.619671i	0.929081	−	0.369875i	$-0.120600\pi$
$709$	28.5788	+	16.5000i	1.07330	+	0.619671i	0.144219	+	0.989546i	$0.453933\pi$
$710$		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
$717$	44.9545	+	12.0455i	1.67886	+	0.449848i
$718$		0			0
$719$	−14.7224	+	8.50000i	−0.549054	+	0.316997i	−0.748740	−	0.662863i	$-0.769341\pi$
$719$	−14.7224	+	8.50000i	−0.549054	+	0.316997i	0.199686	+	0.979860i	$0.436008\pi$
$720$		0			0
$721$		−	13.8564i		−	0.516040i
$722$		0			0
$723$	−9.00000	+	9.00000i	−0.334714	+	0.334714i
$724$		0			0
$725$	−17.0096	+	39.8205i	−0.631721	+	1.47890i
$726$		0			0
$727$	−12.8109	+	47.8109i	−0.475130	+	1.77321i	0.145771	+	0.989318i	$0.453434\pi$
$727$	−12.8109	+	47.8109i	−0.475130	+	1.77321i	−0.620901	+	0.783889i	$0.713233\pi$
$728$		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	−0.497885	−	0.867243i	$-0.665890\pi$
$733$	10.0000	−	10.0000i	0.369358	−	0.369358i	0.867243	+	0.497885i	$0.165890\pi$
$734$		0			0
$735$	5.36603	+	1.09808i	0.197929	+	0.0405032i
$736$		0			0
$737$	3.16987	+	11.8301i	0.116764	+	0.435768i
$738$		0			0
$739$	−19.9186	+	11.5000i	−0.732717	+	0.423034i	−0.819415	−	0.573200i	$-0.805702\pi$
$739$	−19.9186	+	11.5000i	−0.732717	+	0.423034i	0.0866983	+	0.996235i	$0.472368\pi$
$740$		0			0
$741$	−3.00000	+	25.9808i	−0.110208	+	0.954427i
$742$		0			0
$743$	−8.87564	+	33.1244i	−0.325616	+	1.21521i	0.588076	+	0.808806i	$0.299886\pi$
$743$	−8.87564	+	33.1244i	−0.325616	+	1.21521i	−0.913691	+	0.406409i	$0.866781\pi$
$744$		0			0
$745$	35.4545	−	23.4090i	1.29895	−	0.857638i
$746$		0			0
$747$	16.3923	−	4.39230i	0.599763	−	0.160706i
$748$		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
$755$	0.696152	+	11.5981i	0.0253356	+	0.422097i
$756$		0			0
$757$	8.41858	−	31.4186i	0.305979	−	1.14193i	−0.626121	−	0.779726i	$-0.715358\pi$
$757$	8.41858	−	31.4186i	0.305979	−	1.14193i	0.932100	−	0.362202i	$-0.117975\pi$
$758$		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
$763$	3.80385	−	14.1962i	0.137709	−	0.513935i
$764$		0			0
$765$	6.29423	−	7.09808i	0.227568	−	0.256631i
$766$		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	$-0.961884\pi$
$769$	−44.1673	−	25.5000i	−1.59271	−	0.919554i	−0.599874	−	0.800094i	$-0.704783\pi$
$770$		0			0
$771$	−66.0000			−2.37693
$772$		0			0
$773$	−21.2942	+	5.70577i	−0.765900	+	0.205222i	−0.620560	−	0.784159i	$-0.713094\pi$
$773$	−21.2942	+	5.70577i	−0.765900	+	0.205222i	−0.145341	+	0.989382i	$0.546428\pi$
$774$		0			0
$775$	1.03590	+	8.59808i	0.0372106	+	0.308852i
$776$		0			0
$777$	−8.78461	+	32.7846i	−0.315146	+	1.17614i
$778$		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
$785$	−0.633975	+	3.09808i	−0.0226275	+	0.110575i
$786$		0			0
$787$	12.1244	−	12.1244i	0.432187	−	0.432187i	−0.457185	−	0.889372i	$-0.651142\pi$
$787$	12.1244	−	12.1244i	0.432187	−	0.432187i	0.889372	+	0.457185i	$0.151142\pi$
$788$		0			0
$789$	−32.9090	+	57.0000i	−1.17159	+	2.02925i
$790$		0			0
$791$		−	6.92820i		−	0.246339i
$792$		0			0
$793$	−8.24167	+	30.7583i	−0.292670	+	1.09226i
$794$		0			0
$795$	−2.41154	−	40.1769i	−0.0855286	−	1.42493i
$796$		0			0
$797$	5.19615	−	5.19615i	0.184057	−	0.184057i	−0.609064	−	0.793121i	$-0.708455\pi$
$797$	5.19615	−	5.19615i	0.184057	−	0.184057i	0.793121	+	0.609064i	$0.208455\pi$
$798$		0			0
$799$			6.00000i			0.212265i
$800$		0			0
$801$	40.5000	−	23.3827i	1.43100	−	0.826187i
$802$		0			0
$803$	13.6603	+	3.66025i	0.482060	+	0.129168i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	45.0788	−	12.0788i	1.58685	−	0.425195i
$808$		0			0
$809$			17.0000i			0.597688i	0.954302	+	0.298844i	$0.0966011\pi$
$809$			17.0000i			0.597688i	−0.954302	+	0.298844i	$0.903399\pi$
$810$		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
$813$	−21.2942	+	5.70577i	−0.746821	+	0.200110i
$814$		0			0
$815$	14.6865	−	16.5622i	0.514447	−	0.580148i
$816$		0			0
$817$	22.9282	+	9.07180i	0.802156	+	0.317382i
$818$		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
$823$	−4.02628	−	15.0263i	−0.140347	−	0.523783i	−0.999918	−	0.0127672i	$-0.995936\pi$
$823$	−4.02628	−	15.0263i	−0.140347	−	0.523783i	0.859571	−	0.511016i	$-0.170731\pi$
$824$		0			0
$825$	1.73205	−	12.1244i	0.0603023	−	0.422116i
$826$		0			0
$827$	3.16987	+	11.8301i	0.110227	+	0.411374i	0.998886	−	0.0471960i	$-0.0150285\pi$
$827$	3.16987	+	11.8301i	0.110227	+	0.411374i	−0.888658	+	0.458570i	$0.848362\pi$
$828$		0			0
$829$	−31.1769			−1.08282			−0.541409	−	0.840759i	$-0.682109\pi$
$829$	−31.1769			−1.08282			−0.541409	+	0.840759i	$0.682109\pi$
$830$		0			0
$831$	−24.0000	+	13.8564i	−0.832551	+	0.480673i
$832$		0			0
$833$	−1.36603	−	0.366025i	−0.0473300	−	0.0126820i
$834$		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	$0.0373593\pi$
$839$	17.3205	+	30.0000i	0.597970	+	1.03572i	−0.395150	+	0.918617i	$0.629307\pi$
$840$		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
$845$	−13.0622	+	8.62436i	−0.449353	+	0.296687i
$846$		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
$853$	1.36603	+	0.366025i	0.0467718	+	0.0125325i	0.282129	−	0.959376i	$-0.408959\pi$
$853$	1.36603	+	0.366025i	0.0467718	+	0.0125325i	−0.235357	+	0.971909i	$0.575626\pi$
$854$		0			0
$855$	24.4808	+	15.9904i	0.837224	+	0.546859i
$856$		0			0
$857$	−28.3923	−	7.60770i	−0.969863	−	0.259874i	−0.261093	−	0.965314i	$-0.584083\pi$
$857$	−28.3923	−	7.60770i	−0.969863	−	0.259874i	−0.708770	+	0.705440i	$0.750750\pi$
$858$		0			0
$859$	−35.5070	−	20.5000i	−1.21148	−	0.699451i	−0.248402	−	0.968657i	$-0.579905\pi$
$859$	−35.5070	−	20.5000i	−1.21148	−	0.699451i	−0.963083	+	0.269206i	$0.913239\pi$
$860$		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	$-0.263274\pi$
$863$	−1.73205	−	1.73205i	−0.0589597	−	0.0589597i	−0.735972	+	0.677012i	$0.763274\pi$
$864$		0			0
$865$	4.39230	−	21.4641i	0.149343	−	0.729801i
$866$		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
$877$	−23.6603	−	6.33975i	−0.798950	−	0.214078i	−0.163827	−	0.986489i	$-0.552384\pi$
$877$	−23.6603	−	6.33975i	−0.798950	−	0.214078i	−0.635123	+	0.772411i	$0.719051\pi$
$878$		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
$883$	7.32051	+	27.3205i	0.246355	+	0.919408i	0.972698	+	0.232076i	$0.0745518\pi$
$883$	7.32051	+	27.3205i	0.246355	+	0.919408i	−0.726343	+	0.687332i	$0.758782\pi$
$884$		0			0
$885$	9.00000	−	3.00000i	0.302532	−	0.100844i
$886$		0			0
$887$	2.53590	+	9.46410i	0.0851471	+	0.317773i	0.995342	−	0.0964068i	$-0.0307350\pi$
$887$	2.53590	+	9.46410i	0.0851471	+	0.317773i	−0.910195	+	0.414180i	$0.864068\pi$
$888$		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
$893$	−18.2942	+	2.70577i	−0.612193	+	0.0905452i
$894$		0			0
$895$	−3.86603	+	0.232051i	−0.129227	+	0.00775660i
$896$		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
$903$	37.8564	−	10.1436i	1.25978	−	0.337558i
$904$		0			0
$905$	−6.92820	−	3.46410i	−0.230301	−	0.115151i
$906$		0			0
$907$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$907$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$908$		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
$915$	53.2750	+	47.2417i	1.76122	+	1.56176i
$916$		0			0
$917$	−16.1051	+	60.1051i	−0.531838	+	1.98485i
$918$		0			0
$919$		−	10.0000i		−	0.329870i	−0.986304	−	0.164935i	$-0.947259\pi$
$919$		−	10.0000i		−	0.329870i	0.986304	−	0.164935i	$-0.0527414\pi$
$920$		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
$925$	15.1244	−	19.2679i	0.497286	−	0.633526i
$926$		0			0
$927$	−3.80385	−	14.1962i	−0.124935	−	0.466263i
$928$		0			0
$929$	−30.3109	+	17.5000i	−0.994468	+	0.574156i	−0.906607	−	0.421976i	$-0.861337\pi$
$929$	−30.3109	+	17.5000i	−0.994468	+	0.574156i	−0.0878612	+	0.996133i	$0.528003\pi$
$930$		0			0
$931$	0.500000	−	4.33013i	0.0163868	−	0.141914i
$932$		0			0
$933$	13.9474	−	52.0526i	0.456619	−	1.70412i
$934$		0			0
$935$	−0.633975	+	3.09808i	−0.0207332	+	0.101318i
$936$		0			0
$937$	42.3468	−	11.3468i	1.38341	−	0.370683i	0.511051	−	0.859550i	$-0.329256\pi$
$937$	42.3468	−	11.3468i	1.38341	−	0.370683i	0.872358	+	0.488867i	$0.162590\pi$
$938$		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
$947$	12.8109	−	47.8109i	0.416298	−	1.55365i	−0.365924	−	0.930645i	$-0.619247\pi$
$947$	12.8109	−	47.8109i	0.416298	−	1.55365i	0.782222	−	0.623000i	$-0.214086\pi$
$948$		0			0
$949$	34.6410			1.12449
$950$		0			0
$951$	12.0000			0.389127
$952$		0			0
$953$	2.53590	−	9.46410i	0.0821458	−	0.306572i	−0.912613	−	0.408825i	$-0.865938\pi$
$953$	2.53590	−	9.46410i	0.0821458	−	0.306572i	0.994758	+	0.102253i	$0.0326052\pi$
$954$		0			0
$955$	11.1603	−	0.669873i	0.361137	−	0.0216766i
$956$		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
$963$	−28.3923	+	7.60770i	−0.914929	+	0.245155i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−7.32051	+	27.3205i	−0.235412	+	0.878568i	0.742551	+	0.669789i	$0.233616\pi$
$967$	−7.32051	+	27.3205i	−0.235412	+	0.878568i	−0.977963	+	0.208779i	$0.933051\pi$
$968$		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
$975$	−3.58846	−	29.7846i	−0.114923	−	0.953871i
$976$		0			0
$977$	−3.46410	+	3.46410i	−0.110826	+	0.110826i	−0.760345	−	0.649519i	$-0.774970\pi$
$977$	−3.46410	+	3.46410i	−0.110826	+	0.110826i	0.649519	+	0.760345i	$0.274970\pi$
$978$		0			0
$979$	−7.79423	+	13.5000i	−0.249105	+	0.431462i
$980$		0			0
$981$		−	15.5885i		−	0.497701i
$982$		0			0
$983$	10.1436	−	37.8564i	0.323530	−	1.20743i	−0.592251	−	0.805754i	$-0.701760\pi$
$983$	10.1436	−	37.8564i	0.323530	−	1.20743i	0.915781	−	0.401678i	$-0.131573\pi$
$984$		0			0
$985$	−21.2942	−	18.8827i	−0.678491	−	0.601652i
$986$		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
$993$	32.7846	+	8.78461i	1.04039	+	0.278771i
$994$		0			0
$995$	−42.0000	−	21.0000i	−1.33149	−	0.665745i
$996$		0			0
$997$	−17.7583	+	4.75833i	−0.562412	+	0.150698i	−0.528814	−	0.848738i	$-0.677363\pi$
$997$	−17.7583	+	4.75833i	−0.562412	+	0.150698i	−0.0335977	+	0.999435i	$0.510697\pi$
$998$		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.297.1	yes	4
5.3	odd	4	inner	380.2.y.a.373.1	yes	4
19.8	odd	6	inner	380.2.y.a.217.1	✓	4
95.8	even	12	inner	380.2.y.a.293.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.y.a.217.1	✓	4	19.8	odd	6	inner
380.2.y.a.293.1	yes	4	95.8	even	12	inner
380.2.y.a.297.1	yes	4	1.1	even	1	trivial
380.2.y.a.373.1	yes	4	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.633975 - 2.36603i) q^{3} +(2.23205 - 0.133975i) q^{5} +(-2.00000 - 2.00000i) q^{7} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(0.633975 - 2.36603i) q^{3} +(2.23205 - 0.133975i) q^{5} +(-2.00000 - 2.00000i) q^{7} +(-2.59808 - 1.50000i) q^{9} +1.00000 q^{11} +(2.36603 - 0.633975i) q^{13} +(1.09808 - 5.36603i) q^{15} +(-0.366025 + 1.36603i) q^{17} +(-4.33013 - 0.500000i) q^{19} +(-6.00000 + 3.46410i) q^{21} +(4.96410 - 0.598076i) q^{25} +(-4.33013 + 7.50000i) q^{29} +1.73205i q^{31} +(0.633975 - 2.36603i) q^{33} +(-4.73205 - 4.19615i) q^{35} +(3.46410 - 3.46410i) q^{37} -6.00000i q^{39} +(3.00000 - 1.73205i) q^{41} +(-5.46410 - 1.46410i) q^{43} +(-6.00000 - 3.00000i) q^{45} +(4.09808 - 1.09808i) q^{47} +1.00000i q^{49} +(3.00000 + 1.73205i) q^{51} +(7.09808 - 1.90192i) q^{53} +(2.23205 - 0.133975i) q^{55} +(-3.92820 + 9.92820i) q^{57} +(0.866025 + 1.50000i) q^{59} +(-6.50000 + 11.2583i) q^{61} +(2.19615 + 8.19615i) q^{63} +(5.19615 - 1.73205i) q^{65} +(3.16987 + 11.8301i) q^{67} +(10.5000 - 6.06218i) q^{71} +(13.6603 + 3.66025i) q^{73} +(1.73205 - 12.1244i) q^{75} +(-2.00000 - 2.00000i) q^{77} +(6.06218 + 10.5000i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(-4.00000 + 4.00000i) q^{83} +(-0.633975 + 3.09808i) q^{85} +(15.0000 + 15.0000i) q^{87} +(-7.79423 + 13.5000i) q^{89} +(-6.00000 - 3.46410i) q^{91} +(4.09808 + 1.09808i) q^{93} +(-9.73205 - 0.535898i) q^{95} +(-18.9282 - 5.07180i) q^{97} +(-2.59808 - 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 2 q^{5} - 8 q^{7}+O(q^{10}) \) 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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