LMFDB - Embedded newform 1150.2.e.d.1057.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1150,2,Mod(643,1150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1150, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([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("1150.643");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1150 = 2 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1150.e (of order $4$, degree $2$, 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:	$9.18279623245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 40 x^{14} - 116 x^{13} + 800 x^{12} - 2584 x^{11} + 9564 x^{10} - 27124 x^{9} + 33538 x^{8} + \cdots + 2313441 $ x^16 + 40x^14 - 116x^13 + 800x^12 - 2584x^11 + 9564x^10 - 27124x^9 + 33538x^8 + 44880x^7 - 233952x^6 + 263772x^5 + 797544x^4 - 1350648x^3 - 1405404x^2 + 2135484x + 2313441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.8
Root			$1.74711 + 0.723675i$ of defining polynomial
Character	$\chi$	$=$	1150.1057
Dual form			1150.2.e.d.643.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.517638 - 0.517638i) q^{3} +1.00000i q^{4} +0.732051 q^{6} +(2.78710 - 2.78710i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.46410i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.517638 - 0.517638i) q^{3} +1.00000i q^{4} +0.732051 q^{6} +(2.78710 - 2.78710i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.46410i q^{9} +3.94156i q^{11} +(0.517638 + 0.517638i) q^{12} +(-3.15660 + 3.15660i) q^{13} +3.94156 q^{14} -1.00000 q^{16} +(-1.74238 + 1.74238i) q^{18} +3.94156 q^{19} -2.88542i q^{21} +(-2.78710 + 2.78710i) q^{22} +(4.71896 + 0.855252i) q^{23} +0.732051i q^{24} -4.46410 q^{26} +(2.82843 + 2.82843i) q^{27} +(2.78710 + 2.78710i) q^{28} -1.19615i q^{29} -6.92820 q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.04030 + 2.04030i) q^{33} -2.46410 q^{36} +(7.61451 - 7.61451i) q^{37} +(2.78710 + 2.78710i) q^{38} +3.26795i q^{39} +6.46410 q^{41} +(2.04030 - 2.04030i) q^{42} +(4.82741 + 4.82741i) q^{43} -3.94156 q^{44} +(2.73205 + 3.94156i) q^{46} +(6.83083 + 6.83083i) q^{47} +(-0.517638 + 0.517638i) q^{48} -8.53590i q^{49} +(-3.15660 - 3.15660i) q^{52} +(-7.61451 - 7.61451i) q^{53} +4.00000i q^{54} +3.94156i q^{56} +(2.04030 - 2.04030i) q^{57} +(0.845807 - 0.845807i) q^{58} +1.26795i q^{59} -2.88542i q^{61} +(-4.89898 - 4.89898i) q^{62} +(6.86771 + 6.86771i) q^{63} -1.00000i q^{64} +2.88542i q^{66} +(5.57421 - 5.57421i) q^{67} +(2.88542 - 2.00000i) q^{69} -2.53590 q^{71} +(-1.74238 - 1.74238i) q^{72} +(-7.53794 + 7.53794i) q^{73} +10.7685 q^{74} +3.94156i q^{76} +(10.9855 + 10.9855i) q^{77} +(-2.31079 + 2.31079i) q^{78} -14.7101 q^{79} -4.46410 q^{81} +(4.57081 + 4.57081i) q^{82} +(-4.82741 - 4.82741i) q^{83} +2.88542 q^{84} +6.82698i q^{86} +(-0.619174 - 0.619174i) q^{87} +(-2.78710 - 2.78710i) q^{88} +17.5955i q^{91} +(-0.855252 + 4.71896i) q^{92} +(-3.58630 + 3.58630i) q^{93} +9.66025i q^{94} -0.732051 q^{96} +(2.04030 - 2.04030i) q^{97} +(6.03579 - 6.03579i) q^{98} -9.71241 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{6}+O(q^{10}) $ 16 * q - 16 * q^6	$ 16 q - 16 q^{6} - 16 q^{16} - 16 q^{26} + 16 q^{36} + 48 q^{41} + 16 q^{46} - 96 q^{71} - 16 q^{81} + 16 q^{96}+O(q^{100}) $ 16 * q - 16 * q^6 - 16 * q^16 - 16 * q^26 + 16 * q^36 + 48 * q^41 + 16 * q^46 - 96 * q^71 - 16 * q^81 + 16 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.517638	−	0.517638i	0.298858	−	0.298858i	−0.541708	−	0.840567i	$-0.682222\pi$
$3$	0.517638	−	0.517638i	0.298858	−	0.298858i	0.840567	+	0.541708i	$0.182222\pi$
$4$			1.00000i			0.500000i
$5$		0			0
$5$		0			0
$6$	0.732051			0.298858
$7$	2.78710	−	2.78710i	1.05343	−	1.05343i	0.0549365	−	0.998490i	$-0.482504\pi$
$7$	2.78710	−	2.78710i	1.05343	−	1.05343i	0.998490	−	0.0549365i	$-0.0174956\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			2.46410i			0.821367i
$10$		0			0
$11$			3.94156i			1.18843i	0.804308	+	0.594213i	$0.202536\pi$
$11$			3.94156i			1.18843i	−0.804308	+	0.594213i	$0.797464\pi$
$12$	0.517638	+	0.517638i	0.149429	+	0.149429i
$13$	−3.15660	+	3.15660i	−0.875482	+	0.875482i	−0.993063	−	0.117581i	$-0.962486\pi$
$13$	−3.15660	+	3.15660i	−0.875482	+	0.875482i	0.117581	+	0.993063i	$0.462486\pi$
$14$	3.94156			1.05343
$15$		0			0
$16$	−1.00000			−0.250000
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	−1.74238	+	1.74238i	−0.410684	+	0.410684i
$19$	3.94156			0.904256			0.452128	−	0.891953i	$-0.350665\pi$
$19$	3.94156			0.904256			0.452128	+	0.891953i	$0.350665\pi$
$20$		0			0
$21$		−	2.88542i		−	0.629651i
$22$	−2.78710	+	2.78710i	−0.594213	+	0.594213i
$23$	4.71896	+	0.855252i	0.983970	+	0.178332i
$23$	4.71896	+	0.855252i	0.983970	+	0.178332i
$24$			0.732051i			0.149429i
$25$		0			0
$26$	−4.46410			−0.875482
$27$	2.82843	+	2.82843i	0.544331	+	0.544331i
$28$	2.78710	+	2.78710i	0.526713	+	0.526713i
$29$		−	1.19615i		−	0.222120i	−0.993814	−	0.111060i	$-0.964575\pi$
$29$		−	1.19615i		−	0.222120i	0.993814	−	0.111060i	$-0.0354246\pi$
$30$		0			0
$31$	−6.92820			−1.24434			−0.622171	−	0.782881i	$-0.713749\pi$
$31$	−6.92820			−1.24434			−0.622171	+	0.782881i	$0.713749\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	2.04030	+	2.04030i	0.355171	+	0.355171i
$34$		0			0
$35$		0			0
$36$	−2.46410			−0.410684
$37$	7.61451	−	7.61451i	1.25182	−	1.25182i	0.296913	−	0.954904i	$-0.404043\pi$
$37$	7.61451	−	7.61451i	1.25182	−	1.25182i	0.954904	−	0.296913i	$-0.0959572\pi$
$38$	2.78710	+	2.78710i	0.452128	+	0.452128i
$39$			3.26795i			0.523291i
$40$		0			0
$41$	6.46410			1.00952			0.504762	−	0.863259i	$-0.331580\pi$
$41$	6.46410			1.00952			0.504762	+	0.863259i	$0.331580\pi$
$42$	2.04030	−	2.04030i	0.314825	−	0.314825i
$43$	4.82741	+	4.82741i	0.736172	+	0.736172i	0.971835	−	0.235662i	$-0.0757260\pi$
$43$	4.82741	+	4.82741i	0.736172	+	0.736172i	−0.235662	+	0.971835i	$0.575726\pi$
$44$	−3.94156			−0.594213
$45$		0			0
$46$	2.73205	+	3.94156i	0.402819	+	0.581151i
$47$	6.83083	+	6.83083i	0.996379	+	0.996379i	0.999993	−	0.00361434i	$-0.00115048\pi$
$47$	6.83083	+	6.83083i	0.996379	+	0.996379i	−0.00361434	+	0.999993i	$0.501150\pi$
$48$	−0.517638	+	0.517638i	−0.0747146	+	0.0747146i
$49$		−	8.53590i		−	1.21941i
$50$		0			0
$51$		0			0
$52$	−3.15660	−	3.15660i	−0.437741	−	0.437741i
$53$	−7.61451	−	7.61451i	−1.04593	−	1.04593i	−0.998893	−	0.0470404i	$-0.985021\pi$
$53$	−7.61451	−	7.61451i	−1.04593	−	1.04593i	−0.0470404	−	0.998893i	$-0.514979\pi$
$54$			4.00000i			0.544331i
$55$		0			0
$56$			3.94156i			0.526713i
$57$	2.04030	−	2.04030i	0.270245	−	0.270245i
$58$	0.845807	−	0.845807i	0.111060	−	0.111060i
$59$			1.26795i			0.165073i	0.996588	+	0.0825365i	$0.0263021\pi$
$59$			1.26795i			0.165073i	−0.996588	+	0.0825365i	$0.973698\pi$
$60$		0			0
$61$		−	2.88542i		−	0.369440i	−0.982791	−	0.184720i	$-0.940862\pi$
$61$		−	2.88542i		−	0.369440i	0.982791	−	0.184720i	$-0.0591379\pi$
$62$	−4.89898	−	4.89898i	−0.622171	−	0.622171i
$63$	6.86771	+	6.86771i	0.865250	+	0.865250i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$			2.88542i			0.355171i
$67$	5.57421	−	5.57421i	0.680998	−	0.680998i	−0.279227	−	0.960225i	$-0.590078\pi$
$67$	5.57421	−	5.57421i	0.680998	−	0.680998i	0.960225	+	0.279227i	$0.0900782\pi$
$68$		0			0
$69$	2.88542	−	2.00000i	0.347364	−	0.240772i
$70$		0			0
$71$	−2.53590			−0.300956			−0.150478	−	0.988613i	$-0.548081\pi$
$71$	−2.53590			−0.300956			−0.150478	+	0.988613i	$0.548081\pi$
$72$	−1.74238	−	1.74238i	−0.205342	−	0.205342i
$73$	−7.53794	+	7.53794i	−0.882249	+	0.882249i	−0.993763	−	0.111514i	$-0.964430\pi$
$73$	−7.53794	+	7.53794i	−0.882249	+	0.882249i	0.111514	+	0.993763i	$0.464430\pi$
$74$	10.7685			1.25182
$75$		0			0
$76$			3.94156i			0.452128i
$77$	10.9855	+	10.9855i	1.25192	+	1.25192i
$78$	−2.31079	+	2.31079i	−0.261645	+	0.261645i
$79$	−14.7101			−1.65502			−0.827508	−	0.561454i	$-0.810242\pi$
$79$	−14.7101			−1.65502			−0.827508	+	0.561454i	$0.810242\pi$
$80$		0			0
$81$	−4.46410			−0.496011
$82$	4.57081	+	4.57081i	0.504762	+	0.504762i
$83$	−4.82741	−	4.82741i	−0.529877	−	0.529877i	0.390659	−	0.920536i	$-0.372247\pi$
$83$	−4.82741	−	4.82741i	−0.529877	−	0.529877i	−0.920536	+	0.390659i	$0.872247\pi$
$84$	2.88542			0.314825
$85$		0			0
$86$			6.82698i			0.736172i
$87$	−0.619174	−	0.619174i	−0.0663824	−	0.0663824i
$88$	−2.78710	−	2.78710i	−0.297106	−	0.297106i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$			17.5955i			1.84451i
$92$	−0.855252	+	4.71896i	−0.0891662	+	0.491985i
$93$	−3.58630	+	3.58630i	−0.371882	+	0.371882i
$94$			9.66025i			0.996379i
$95$		0			0
$96$	−0.732051			−0.0747146
$97$	2.04030	−	2.04030i	0.207161	−	0.207161i	−0.595898	−	0.803060i	$-0.703204\pi$
$97$	2.04030	−	2.04030i	0.207161	−	0.207161i	0.803060	+	0.595898i	$0.203204\pi$
$98$	6.03579	−	6.03579i	0.609707	−	0.609707i
$99$	−9.71241			−0.976133
$100$		0			0
$101$	−3.07180			−0.305655			−0.152828	−	0.988253i	$-0.548838\pi$
$101$	−3.07180			−0.305655			−0.152828	+	0.988253i	$0.548838\pi$
$102$		0			0
$103$	−12.4419	−	12.4419i	−1.22594	−	1.22594i	−0.965487	−	0.260451i	$-0.916129\pi$
$103$	−12.4419	−	12.4419i	−1.22594	−	1.22594i	−0.260451	−	0.965487i	$-0.583871\pi$
$104$		−	4.46410i		−	0.437741i
$105$		0			0
$106$		−	10.7685i		−	1.04593i
$107$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$107$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$108$	−2.82843	+	2.82843i	−0.272166	+	0.272166i
$109$	−18.6517			−1.78651			−0.893253	−	0.449555i	$-0.851583\pi$
$109$	−18.6517			−1.78651			−0.893253	+	0.449555i	$0.851583\pi$
$110$		0			0
$111$		−	7.88312i		−	0.748233i
$112$	−2.78710	+	2.78710i	−0.263357	+	0.263357i
$113$	13.1887	+	13.1887i	1.24069	+	1.24069i	0.959715	+	0.280975i	$0.0906579\pi$
$113$	13.1887	+	13.1887i	1.24069	+	1.24069i	0.280975	+	0.959715i	$0.409342\pi$
$114$	2.88542			0.270245
$115$		0			0
$116$	1.19615			0.111060
$117$	−7.77817	−	7.77817i	−0.719092	−	0.719092i
$118$	−0.896575	+	0.896575i	−0.0825365	+	0.0825365i
$119$		0			0
$120$		0			0
$121$	−4.53590			−0.412354
$122$	2.04030	−	2.04030i	0.184720	−	0.184720i
$123$	3.34607	−	3.34607i	0.301705	−	0.301705i
$124$		−	6.92820i		−	0.622171i
$125$		0			0
$126$			9.71241i			0.865250i
$127$	5.79555	+	5.79555i	0.514272	+	0.514272i	0.915833	−	0.401560i	$-0.131532\pi$
$127$	5.79555	+	5.79555i	0.514272	+	0.514272i	−0.401560	+	0.915833i	$0.631532\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	4.99770			0.440023
$130$		0			0
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$	−2.04030	+	2.04030i	−0.177585	+	0.177585i
$133$	10.9855	−	10.9855i	0.952567	−	0.952567i
$134$	7.88312			0.680998
$135$		0			0
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$	3.45452	+	0.626088i	0.294068	+	0.0532962i
$139$		−	13.4641i		−	1.14201i	−0.820947	−	0.571005i	$-0.806554\pi$
$139$		−	13.4641i		−	1.14201i	0.820947	−	0.571005i	$-0.193446\pi$
$140$		0			0
$141$	7.07180			0.595553
$142$	−1.79315	−	1.79315i	−0.150478	−	0.150478i
$143$	−12.4419	−	12.4419i	−1.04045	−	1.04045i
$144$		−	2.46410i		−	0.205342i
$145$		0			0
$146$	−10.6603			−0.882249
$147$	−4.41851	−	4.41851i	−0.364432	−	0.364432i
$148$	7.61451	+	7.61451i	0.625909	+	0.625909i
$149$	15.7662			1.29162			0.645810	−	0.763498i	$-0.276520\pi$
$149$	15.7662			1.29162			0.645810	+	0.763498i	$0.276520\pi$
$150$		0			0
$151$	−19.3205			−1.57228			−0.786140	−	0.618048i	$-0.787924\pi$
$151$	−19.3205			−1.57228			−0.786140	+	0.618048i	$0.787924\pi$
$152$	−2.78710	+	2.78710i	−0.226064	+	0.226064i
$153$		0			0
$154$			15.5359i			1.25192i
$155$		0			0
$156$	−3.26795			−0.261645
$157$	3.53391	−	3.53391i	0.282036	−	0.282036i	−0.551884	−	0.833921i	$-0.686091\pi$
$157$	3.53391	−	3.53391i	0.282036	−	0.282036i	0.833921	+	0.551884i	$0.186091\pi$
$158$	−10.4016	−	10.4016i	−0.827508	−	0.827508i
$159$	−7.88312			−0.625172
$160$		0			0
$161$	15.5359	−	10.7685i	1.22440	−	0.848680i
$162$	−3.15660	−	3.15660i	−0.248006	−	0.248006i
$163$	9.28032	−	9.28032i	0.726891	−	0.726891i	−0.243108	−	0.969999i	$-0.578167\pi$
$163$	9.28032	−	9.28032i	0.726891	−	0.726891i	0.969999	+	0.243108i	$0.0781670\pi$
$164$			6.46410i			0.504762i
$165$		0			0
$166$		−	6.82698i		−	0.529877i
$167$	−13.3843	−	13.3843i	−1.03571	−	1.03571i	−0.999339	−	0.0363667i	$-0.988422\pi$
$167$	−13.3843	−	13.3843i	−1.03571	−	1.03571i	−0.0363667	−	0.999339i	$-0.511578\pi$
$168$	2.04030	+	2.04030i	0.157413	+	0.157413i
$169$		−	6.92820i		−	0.532939i
$170$		0			0
$171$			9.71241i			0.742726i
$172$	−4.82741	+	4.82741i	−0.368086	+	0.368086i
$173$	15.1266	−	15.1266i	1.15006	−	1.15006i	0.163517	−	0.986541i	$-0.447716\pi$
$173$	15.1266	−	15.1266i	1.15006	−	1.15006i	0.986541	−	0.163517i	$-0.0522838\pi$
$174$		−	0.875644i		−	0.0663824i
$175$		0			0
$176$		−	3.94156i		−	0.297106i
$177$	0.656339	+	0.656339i	0.0493334	+	0.0493334i
$178$		0			0
$179$		−	11.8038i		−	0.882261i	−0.897443	−	0.441130i	$-0.854578\pi$
$179$		−	11.8038i		−	0.882261i	0.897443	−	0.441130i	$-0.145422\pi$
$180$		0			0
$181$		−	5.77084i		−	0.428944i	−0.976730	−	0.214472i	$-0.931197\pi$
$181$		−	5.77084i		−	0.428944i	0.976730	−	0.214472i	$-0.0688030\pi$
$182$	−12.4419	+	12.4419i	−0.922256	+	0.922256i
$183$	−1.49360	−	1.49360i	−0.110410	−	0.110410i
$184$	−3.94156	+	2.73205i	−0.290576	+	0.201409i
$185$		0			0
$186$	−5.07180			−0.371882
$187$		0			0
$188$	−6.83083	+	6.83083i	−0.498190	+	0.498190i
$189$	15.7662			1.14683
$190$		0			0
$191$		−	1.05614i		−	0.0764195i	−0.999270	−	0.0382097i	$-0.987835\pi$
$191$		−	1.05614i		−	0.0764195i	0.999270	−	0.0382097i	$-0.0121655\pi$
$192$	−0.517638	−	0.517638i	−0.0373573	−	0.0373573i
$193$	−7.07107	+	7.07107i	−0.508987	+	0.508987i	−0.914215	−	0.405229i	$-0.867192\pi$
$193$	−7.07107	+	7.07107i	−0.508987	+	0.508987i	0.405229	+	0.914215i	$0.367192\pi$
$194$	2.88542			0.207161
$195$		0			0
$196$	8.53590			0.609707
$197$	−4.94975	−	4.94975i	−0.352655	−	0.352655i	0.508442	−	0.861096i	$-0.330222\pi$
$197$	−4.94975	−	4.94975i	−0.352655	−	0.352655i	−0.861096	+	0.508442i	$0.830222\pi$
$198$	−6.86771	−	6.86771i	−0.488067	−	0.488067i
$199$	1.05614			0.0748676			0.0374338	−	0.999299i	$-0.488082\pi$
$199$	1.05614			0.0748676			0.0374338	+	0.999299i	$0.488082\pi$
$200$		0			0
$201$		−	5.77084i		−	0.407044i
$202$	−2.17209	−	2.17209i	−0.152828	−	0.152828i
$203$	−3.33380	−	3.33380i	−0.233987	−	0.233987i
$204$		0			0
$205$		0			0
$206$		−	17.5955i		−	1.22594i
$207$	−2.10743	+	11.6280i	−0.146476	+	0.808201i
$208$	3.15660	−	3.15660i	0.218871	−	0.218871i
$209$			15.5359i			1.07464i
$210$		0			0
$211$	26.2487			1.80704			0.903518	−	0.428550i	$-0.140976\pi$
$211$	26.2487			1.80704			0.903518	+	0.428550i	$0.140976\pi$
$212$	7.61451	−	7.61451i	0.522967	−	0.522967i
$213$	−1.31268	+	1.31268i	−0.0899432	+	0.0899432i
$214$		0			0
$215$		0			0
$216$	−4.00000			−0.272166
$217$	−19.3096	+	19.3096i	−1.31082	+	1.31082i
$218$	−13.1887	−	13.1887i	−0.893253	−	0.893253i
$219$			7.80385i			0.527335i
$220$		0			0
$221$		0			0
$222$	5.57421	−	5.57421i	0.374116	−	0.374116i
$223$	0.896575	−	0.896575i	0.0600391	−	0.0600391i	−0.676450	−	0.736489i	$-0.736482\pi$
$223$	0.896575	−	0.896575i	0.0600391	−	0.0600391i	0.736489	+	0.676450i	$0.236482\pi$
$224$	−3.94156			−0.263357
$225$		0			0
$226$			18.6517i			1.24069i
$227$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$227$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$228$	2.04030	+	2.04030i	0.135122	+	0.135122i
$229$	−21.5371			−1.42321			−0.711605	−	0.702579i	$-0.752032\pi$
$229$	−21.5371			−1.42321			−0.711605	+	0.702579i	$0.752032\pi$
$230$		0			0
$231$	11.3731			0.748293
$232$	0.845807	+	0.845807i	0.0555300	+	0.0555300i
$233$	−6.88160	+	6.88160i	−0.450829	+	0.450829i	−0.895629	−	0.444801i	$-0.853274\pi$
$233$	−6.88160	+	6.88160i	−0.450829	+	0.450829i	0.444801	+	0.895629i	$0.353274\pi$
$234$		−	11.0000i		−	0.719092i
$235$		0			0
$236$	−1.26795			−0.0825365
$237$	−7.61451	+	7.61451i	−0.494616	+	0.494616i
$238$		0			0
$239$			21.5167i			1.39180i	0.718140	+	0.695899i	$0.244994\pi$
$239$			21.5167i			1.39180i	−0.718140	+	0.695899i	$0.755006\pi$
$240$		0			0
$241$		−	26.5348i		−	1.70926i	−0.519241	−	0.854628i	$-0.673785\pi$
$241$		−	26.5348i		−	1.70926i	0.519241	−	0.854628i	$-0.326215\pi$
$242$	−3.20736	−	3.20736i	−0.206177	−	0.206177i
$243$	−10.7961	+	10.7961i	−0.692568	+	0.692568i
$244$	2.88542			0.184720
$245$		0			0
$246$	4.73205			0.301705
$247$	−12.4419	+	12.4419i	−0.791660	+	0.791660i
$248$	4.89898	−	4.89898i	0.311086	−	0.311086i
$249$	−4.99770			−0.316716
$250$		0			0
$251$		−	7.88312i		−	0.497578i	−0.968558	−	0.248789i	$-0.919967\pi$
$251$		−	7.88312i		−	0.497578i	0.968558	−	0.248789i	$-0.0800326\pi$
$252$	−6.86771	+	6.86771i	−0.432625	+	0.432625i
$253$	−3.37103	+	18.6000i	−0.211935	+	1.16938i
$254$			8.19615i			0.514272i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−9.14162	−	9.14162i	−0.570239	−	0.570239i	0.361956	−	0.932195i	$-0.382109\pi$
$257$	−9.14162	−	9.14162i	−0.570239	−	0.570239i	−0.932195	+	0.361956i	$0.882109\pi$
$258$	3.53391	+	3.53391i	0.220011	+	0.220011i
$259$		−	42.4449i		−	2.63740i
$260$		0			0
$261$	2.94744			0.182442
$262$	5.65685	+	5.65685i	0.349482	+	0.349482i
$263$	−5.57421	−	5.57421i	−0.343720	−	0.343720i	0.514044	−	0.857764i	$-0.328147\pi$
$263$	−5.57421	−	5.57421i	−0.343720	−	0.343720i	−0.857764	+	0.514044i	$0.828147\pi$
$264$	−2.88542			−0.177585
$265$		0			0
$266$	15.5359			0.952567
$267$		0			0
$268$	5.57421	+	5.57421i	0.340499	+	0.340499i
$269$			15.5885i			0.950445i	0.879866	+	0.475223i	$0.157632\pi$
$269$			15.5885i			0.950445i	−0.879866	+	0.475223i	$0.842368\pi$
$270$		0			0
$271$	−6.19615			−0.376389			−0.188195	−	0.982132i	$-0.560264\pi$
$271$	−6.19615			−0.376389			−0.188195	+	0.982132i	$0.560264\pi$
$272$		0			0
$273$	9.10811	+	9.10811i	0.551248	+	0.551248i
$274$		0			0
$275$		0			0
$276$	2.00000	+	2.88542i	0.120386	+	0.173682i
$277$	7.02030	+	7.02030i	0.421809	+	0.421809i	0.885826	−	0.464017i	$-0.153592\pi$
$277$	7.02030	+	7.02030i	0.421809	+	0.421809i	−0.464017	+	0.885826i	$0.653592\pi$
$278$	9.52056	−	9.52056i	0.571005	−	0.571005i
$279$		−	17.0718i		−	1.02206i
$280$		0			0
$281$		−	4.99770i		−	0.298138i	−0.988827	−	0.149069i	$-0.952372\pi$
$281$		−	4.99770i		−	0.298138i	0.988827	−	0.149069i	$-0.0476276\pi$
$282$	5.00052	+	5.00052i	0.297776	+	0.297776i
$283$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$283$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$284$		−	2.53590i		−	0.150478i
$285$		0			0
$286$		−	17.5955i		−	1.04045i
$287$	18.0161	−	18.0161i	1.06346	−	1.06346i
$288$	1.74238	−	1.74238i	0.102671	−	0.102671i
$289$			17.0000i			1.00000i
$290$		0			0
$291$		−	2.11228i		−	0.123824i
$292$	−7.53794	−	7.53794i	−0.441124	−	0.441124i
$293$	−4.08060	−	4.08060i	−0.238391	−	0.238391i	0.577792	−	0.816184i	$-0.303914\pi$
$293$	−4.08060	−	4.08060i	−0.238391	−	0.238391i	−0.816184	+	0.577792i	$0.803914\pi$
$294$		−	6.24871i		−	0.364432i
$295$		0			0
$296$			10.7685i			0.625909i
$297$	−11.1484	+	11.1484i	−0.646897	+	0.646897i
$298$	11.1484	+	11.1484i	0.645810	+	0.645810i
$299$	−17.5955	+	12.1962i	−1.01758	+	0.705322i
$300$		0			0
$301$	26.9090			1.55101
$302$	−13.6617	−	13.6617i	−0.786140	−	0.786140i
$303$	−1.59008	+	1.59008i	−0.0913477	+	0.0913477i
$304$	−3.94156			−0.226064
$305$		0			0
$306$		0			0
$307$	−11.5911	−	11.5911i	−0.661540	−	0.661540i	0.294203	−	0.955743i	$-0.404946\pi$
$307$	−11.5911	−	11.5911i	−0.661540	−	0.661540i	−0.955743	+	0.294203i	$0.904946\pi$
$308$	−10.9855	+	10.9855i	−0.625959	+	0.625959i
$309$	−12.8808			−0.732764
$310$		0			0
$311$	−14.1962			−0.804990			−0.402495	−	0.915422i	$-0.631857\pi$
$311$	−14.1962			−0.804990			−0.402495	+	0.915422i	$0.631857\pi$
$312$	−2.31079	−	2.31079i	−0.130823	−	0.130823i
$313$	−2.04030	−	2.04030i	−0.115325	−	0.115325i	0.647089	−	0.762414i	$-0.275986\pi$
$313$	−2.04030	−	2.04030i	−0.115325	−	0.115325i	−0.762414	+	0.647089i	$0.775986\pi$
$314$	4.99770			0.282036
$315$		0			0
$316$		−	14.7101i		−	0.827508i
$317$	−3.25813	−	3.25813i	−0.182995	−	0.182995i	0.609665	−	0.792660i	$-0.291304\pi$
$317$	−3.25813	−	3.25813i	−0.182995	−	0.182995i	−0.792660	+	0.609665i	$0.791304\pi$
$318$	−5.57421	−	5.57421i	−0.312586	−	0.312586i
$319$	4.71471			0.263973
$320$		0			0
$321$		0			0
$322$	18.6000	+	3.37103i	1.03654	+	0.187860i
$323$		0			0
$324$		−	4.46410i		−	0.248006i
$325$		0			0
$326$	13.1244			0.726891
$327$	−9.65481	+	9.65481i	−0.533912	+	0.533912i
$328$	−4.57081	+	4.57081i	−0.252381	+	0.252381i
$329$	38.0765			2.09922
$330$		0			0
$331$	6.14359			0.337682			0.168841	−	0.985643i	$-0.445997\pi$
$331$	6.14359			0.337682			0.168841	+	0.985643i	$0.445997\pi$
$332$	4.82741	−	4.82741i	0.264938	−	0.264938i
$333$	18.7629	+	18.7629i	1.02820	+	1.02820i
$334$		−	18.9282i		−	1.03571i
$335$		0			0
$336$			2.88542i			0.157413i
$337$	2.04030	−	2.04030i	0.111142	−	0.111142i	−0.649349	−	0.760491i	$-0.724958\pi$
$337$	2.04030	−	2.04030i	0.111142	−	0.111142i	0.760491	+	0.649349i	$0.224958\pi$
$338$	4.89898	−	4.89898i	0.266469	−	0.266469i
$339$	13.6540			0.741582
$340$		0			0
$341$		−	27.3079i		−	1.47881i
$342$	−6.86771	+	6.86771i	−0.371363	+	0.371363i
$343$	−4.28071	−	4.28071i	−0.231137	−	0.231137i
$344$	−6.82698			−0.368086
$345$		0			0
$346$	21.3923			1.15006
$347$	−12.0716	−	12.0716i	−0.648037	−	0.648037i	0.304482	−	0.952518i	$-0.401517\pi$
$347$	−12.0716	−	12.0716i	−0.648037	−	0.648037i	−0.952518	+	0.304482i	$0.901517\pi$
$348$	0.619174	−	0.619174i	0.0331912	−	0.0331912i
$349$		−	4.66025i		−	0.249458i	−0.992191	−	0.124729i	$-0.960194\pi$
$349$		−	4.66025i		−	0.249458i	0.992191	−	0.124729i	$-0.0398061\pi$
$350$		0			0
$351$	−17.8564			−0.953104
$352$	2.78710	−	2.78710i	0.148553	−	0.148553i
$353$	21.9575	−	21.9575i	1.16868	−	1.16868i	0.186159	−	0.982520i	$-0.440396\pi$
$353$	21.9575	−	21.9575i	1.16868	−	1.16868i	0.982520	−	0.186159i	$-0.0596039\pi$
$354$			0.928203i			0.0493334i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	8.34658	−	8.34658i	0.441130	−	0.441130i
$359$	20.4809			1.08094			0.540472	−	0.841362i	$-0.318246\pi$
$359$	20.4809			1.08094			0.540472	+	0.841362i	$0.318246\pi$
$360$		0			0
$361$	−3.46410			−0.182321
$362$	4.08060	−	4.08060i	0.214472	−	0.214472i
$363$	−2.34795	+	2.34795i	−0.123236	+	0.123236i
$364$	−17.5955			−0.922256
$365$		0			0
$366$		−	2.11228i		−	0.110410i
$367$	2.78710	−	2.78710i	0.145486	−	0.145486i	−0.630612	−	0.776098i	$-0.717196\pi$
$367$	2.78710	−	2.78710i	0.145486	−	0.145486i	0.776098	+	0.630612i	$0.217196\pi$
$368$	−4.71896	−	0.855252i	−0.245993	−	0.0445831i
$369$			15.9282i			0.829189i
$370$		0			0
$371$	−42.4449			−2.20363
$372$	−3.58630	−	3.58630i	−0.185941	−	0.185941i
$373$	−11.1484	−	11.1484i	−0.577243	−	0.577243i	0.356900	−	0.934143i	$-0.383834\pi$
$373$	−11.1484	−	11.1484i	−0.577243	−	0.577243i	−0.934143	+	0.356900i	$0.883834\pi$
$374$		0			0
$375$		0			0
$376$	−9.66025			−0.498190
$377$	3.77577	+	3.77577i	0.194462	+	0.194462i
$378$	11.1484	+	11.1484i	0.573413	+	0.573413i
$379$	7.88312			0.404929			0.202464	−	0.979290i	$-0.435105\pi$
$379$	7.88312			0.404929			0.202464	+	0.979290i	$0.435105\pi$
$380$		0			0
$381$	6.00000			0.307389
$382$	0.746802	−	0.746802i	0.0382097	−	0.0382097i
$383$	−23.5903	−	23.5903i	−1.20541	−	1.20541i	−0.972498	−	0.232912i	$-0.925175\pi$
$383$	−23.5903	−	23.5903i	−1.20541	−	1.20541i	−0.232912	−	0.972498i	$-0.574825\pi$
$384$		−	0.732051i		−	0.0373573i
$385$		0			0
$386$	−10.0000			−0.508987
$387$	−11.8952	+	11.8952i	−0.604668	+	0.604668i
$388$	2.04030	+	2.04030i	0.103581	+	0.103581i
$389$	24.4225			1.23827			0.619135	−	0.785284i	$-0.287483\pi$
$389$	24.4225			1.23827			0.619135	+	0.785284i	$0.287483\pi$
$390$		0			0
$391$		0			0
$392$	6.03579	+	6.03579i	0.304854	+	0.304854i
$393$	4.14110	−	4.14110i	0.208891	−	0.208891i
$394$		−	7.00000i		−	0.352655i
$395$		0			0
$396$		−	9.71241i		−	0.488067i
$397$	8.00481	+	8.00481i	0.401750	+	0.401750i	0.878849	−	0.477099i	$-0.158312\pi$
$397$	8.00481	+	8.00481i	0.401750	+	0.401750i	−0.477099	+	0.878849i	$0.658312\pi$
$398$	0.746802	+	0.746802i	0.0374338	+	0.0374338i
$399$		−	11.3731i		−	0.569366i
$400$		0			0
$401$			4.99770i			0.249573i	0.992184	+	0.124787i	$0.0398246\pi$
$401$			4.99770i			0.249573i	−0.992184	+	0.124787i	$0.960175\pi$
$402$	4.08060	−	4.08060i	0.203522	−	0.203522i
$403$	21.8695	−	21.8695i	1.08940	−	1.08940i
$404$		−	3.07180i		−	0.152828i
$405$		0			0
$406$		−	4.71471i		−	0.233987i
$407$	30.0131	+	30.0131i	1.48769	+	1.48769i
$408$		0			0
$409$			10.4641i			0.517417i	0.965956	+	0.258708i	$0.0832968\pi$
$409$			10.4641i			0.517417i	−0.965956	+	0.258708i	$0.916703\pi$
$410$		0			0
$411$		0			0
$412$	12.4419	−	12.4419i	0.612969	−	0.612969i
$413$	3.53391	+	3.53391i	0.173892	+	0.173892i
$414$	−9.71241	+	6.73205i	−0.477339	+	0.330862i
$415$		0			0
$416$	4.46410			0.218871
$417$	−6.96953	−	6.96953i	−0.341299	−	0.341299i
$418$	−10.9855	+	10.9855i	−0.537320	+	0.537320i
$419$	−39.1326			−1.91175			−0.955877	−	0.293768i	$-0.905091\pi$
$419$	−39.1326			−1.91175			−0.955877	+	0.293768i	$0.905091\pi$
$420$		0			0
$421$		−	15.7662i		−	0.768400i	−0.923250	−	0.384200i	$-0.874477\pi$
$421$		−	15.7662i		−	0.768400i	0.923250	−	0.384200i	$-0.125523\pi$
$422$	18.5606	+	18.5606i	0.903518	+	0.903518i
$423$	−16.8319	+	16.8319i	−0.818393	+	0.818393i
$424$	10.7685			0.522967
$425$		0			0
$426$	−1.85641			−0.0899432
$427$	−8.04197	−	8.04197i	−0.389178	−	0.389178i
$428$		0			0
$429$	−12.8808			−0.621892
$430$		0			0
$431$			27.3079i			1.31538i	0.753290	+	0.657688i	$0.228466\pi$
$431$			27.3079i			1.31538i	−0.753290	+	0.657688i	$0.771534\pi$
$432$	−2.82843	−	2.82843i	−0.136083	−	0.136083i
$433$	6.12091	+	6.12091i	0.294152	+	0.294152i	0.838718	−	0.544566i	$-0.183306\pi$
$433$	6.12091	+	6.12091i	0.294152	+	0.294152i	−0.544566	+	0.838718i	$0.683306\pi$
$434$	−27.3079			−1.31082
$435$		0			0
$436$		−	18.6517i		−	0.893253i
$437$	18.6000	+	3.37103i	0.889761	+	0.161258i
$438$	−5.51815	+	5.51815i	−0.263668	+	0.263668i
$439$			13.8564i			0.661330i	0.943748	+	0.330665i	$0.107273\pi$
$439$			13.8564i			0.661330i	−0.943748	+	0.330665i	$0.892727\pi$
$440$		0			0
$441$	21.0333			1.00159
$442$		0			0
$443$	17.7284	−	17.7284i	0.842303	−	0.842303i	−0.146855	−	0.989158i	$-0.546915\pi$
$443$	17.7284	−	17.7284i	0.842303	−	0.842303i	0.989158	+	0.146855i	$0.0469149\pi$
$444$	7.88312			0.374116
$445$		0			0
$446$	1.26795			0.0600391
$447$	8.16121	−	8.16121i	0.386012	−	0.386012i
$448$	−2.78710	−	2.78710i	−0.131678	−	0.131678i
$449$			25.4641i			1.20173i	0.799352	+	0.600863i	$0.205176\pi$
$449$			25.4641i			1.20173i	−0.799352	+	0.600863i	$0.794824\pi$
$450$		0			0
$451$			25.4786i			1.19974i
$452$	−13.1887	+	13.1887i	−0.620345	+	0.620345i
$453$	−10.0010	+	10.0010i	−0.469889	+	0.469889i
$454$		0			0
$455$		0			0
$456$			2.88542i			0.135122i
$457$	13.1887	−	13.1887i	0.616942	−	0.616942i	−0.327804	−	0.944746i	$-0.606308\pi$
$457$	13.1887	−	13.1887i	0.616942	−	0.616942i	0.944746	+	0.327804i	$0.106308\pi$
$458$	−15.2290	−	15.2290i	−0.711605	−	0.711605i
$459$		0			0
$460$		0			0
$461$	36.5167			1.70075			0.850375	−	0.526177i	$-0.176375\pi$
$461$	36.5167			1.70075			0.850375	+	0.526177i	$0.176375\pi$
$462$	8.04197	+	8.04197i	0.374146	+	0.374146i
$463$	−4.62158	+	4.62158i	−0.214783	+	0.214783i	−0.806296	−	0.591513i	$-0.798531\pi$
$463$	−4.62158	+	4.62158i	−0.214783	+	0.214783i	0.591513	+	0.806296i	$0.298531\pi$
$464$			1.19615i			0.0555300i
$465$		0			0
$466$	−9.73205			−0.450829
$467$	−6.32101	+	6.32101i	−0.292501	+	0.292501i	−0.838068	−	0.545566i	$-0.816315\pi$
$467$	−6.32101	+	6.32101i	−0.292501	+	0.292501i	0.545566	+	0.838068i	$0.316315\pi$
$468$	7.77817	−	7.77817i	0.359546	−	0.359546i
$469$		−	31.0718i		−	1.43476i
$470$		0			0
$471$		−	3.65857i		−	0.168578i
$472$	−0.896575	−	0.896575i	−0.0412682	−	0.0412682i
$473$	−19.0275	+	19.0275i	−0.874886	+	0.874886i
$474$	−10.7685			−0.494616
$475$		0			0
$476$		0			0
$477$	18.7629	−	18.7629i	0.859095	−	0.859095i
$478$	−15.2146	+	15.2146i	−0.695899	+	0.695899i
$479$	30.4763			1.39250			0.696250	−	0.717799i	$-0.254851\pi$
$479$	30.4763			1.39250			0.696250	+	0.717799i	$0.254851\pi$
$480$		0			0
$481$			48.0719i			2.19189i
$482$	18.7629	−	18.7629i	0.854628	−	0.854628i
$483$	2.46776	−	13.6162i	0.112287	−	0.619558i
$484$		−	4.53590i		−	0.206177i
$485$		0			0
$486$	−15.2679			−0.692568
$487$	−26.9072	−	26.9072i	−1.21928	−	1.21928i	−0.967884	−	0.251399i	$-0.919109\pi$
$487$	−26.9072	−	26.9072i	−1.21928	−	1.21928i	−0.251399	−	0.967884i	$-0.580891\pi$
$488$	2.04030	+	2.04030i	0.0923601	+	0.0923601i
$489$		−	9.60770i		−	0.434475i
$490$		0			0
$491$	−7.12436			−0.321518			−0.160759	−	0.986994i	$-0.551394\pi$
$491$	−7.12436			−0.321518			−0.160759	+	0.986994i	$0.551394\pi$
$492$	3.34607	+	3.34607i	0.150852	+	0.150852i
$493$		0			0
$494$	−17.5955			−0.791660
$495$		0			0
$496$	6.92820			0.311086
$497$	−7.06781	+	7.06781i	−0.317035	+	0.317035i
$498$	−3.53391	−	3.53391i	−0.158358	−	0.158358i
$499$			26.4449i			1.18383i	0.805999	+	0.591917i	$0.201629\pi$
$499$			26.4449i			1.18383i	−0.805999	+	0.591917i	$0.798371\pi$
$500$		0			0
$501$	−13.8564			−0.619059
$502$	5.57421	−	5.57421i	0.248789	−	0.248789i
$503$	−2.78710	−	2.78710i	−0.124271	−	0.124271i	0.642236	−	0.766507i	$-0.278007\pi$
$503$	−2.78710	−	2.78710i	−0.124271	−	0.124271i	−0.766507	+	0.642236i	$0.778007\pi$
$504$	−9.71241			−0.432625
$505$		0			0
$506$	−15.5359	+	10.7685i	−0.690655	+	0.478720i
$507$	−3.58630	−	3.58630i	−0.159273	−	0.159273i
$508$	−5.79555	+	5.79555i	−0.257136	+	0.257136i
$509$		−	6.92820i		−	0.307087i	−0.988142	−	0.153544i	$-0.950931\pi$
$509$		−	6.92820i		−	0.307087i	0.988142	−	0.153544i	$-0.0490686\pi$
$510$		0			0
$511$			42.0180i			1.85877i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	11.1484	+	11.1484i	0.492215	+	0.492215i
$514$		−	12.9282i		−	0.570239i
$515$		0			0
$516$			4.99770i			0.220011i
$517$	−26.9241	+	26.9241i	−1.18412	+	1.18412i
$518$	30.0131	−	30.0131i	1.31870	−	1.31870i
$519$		−	15.6603i		−	0.687409i
$520$		0			0
$521$			38.0765i			1.66816i	0.551643	+	0.834080i	$0.314001\pi$
$521$			38.0765i			1.66816i	−0.551643	+	0.834080i	$0.685999\pi$
$522$	2.08416	+	2.08416i	0.0912210	+	0.0912210i
$523$	10.4016	+	10.4016i	0.454831	+	0.454831i	0.896954	−	0.442123i	$-0.145775\pi$
$523$	10.4016	+	10.4016i	0.454831	+	0.454831i	−0.442123	+	0.896954i	$0.645775\pi$
$524$			8.00000i			0.349482i
$525$		0			0
$526$		−	7.88312i		−	0.343720i
$527$		0			0
$528$	−2.04030	−	2.04030i	−0.0887927	−	0.0887927i
$529$	21.5371	+	8.07180i	0.936395	+	0.350948i
$530$		0			0
$531$	−3.12436			−0.135585
$532$	10.9855	+	10.9855i	0.476284	+	0.476284i
$533$	−20.4046	+	20.4046i	−0.883820	+	0.883820i
$534$		0			0
$535$		0			0
$536$			7.88312i			0.340499i
$537$	−6.11012	−	6.11012i	−0.263671	−	0.263671i
$538$	−11.0227	+	11.0227i	−0.475223	+	0.475223i
$539$	33.6448			1.44918
$540$		0			0
$541$	−34.1244			−1.46712			−0.733560	−	0.679624i	$-0.762143\pi$
$541$	−34.1244			−1.46712			−0.733560	+	0.679624i	$0.762143\pi$
$542$	−4.38134	−	4.38134i	−0.188195	−	0.188195i
$543$	−2.98721	−	2.98721i	−0.128193	−	0.128193i
$544$		0			0
$545$		0			0
$546$			12.8808i			0.551248i
$547$	−14.1793	−	14.1793i	−0.606263	−	0.606263i	0.335704	−	0.941967i	$-0.391026\pi$
$547$	−14.1793	−	14.1793i	−0.606263	−	0.606263i	−0.941967	+	0.335704i	$0.891026\pi$
$548$		0			0
$549$	7.10997			0.303446
$550$		0			0
$551$		−	4.71471i		−	0.200853i
$552$	−0.626088	+	3.45452i	−0.0266481	+	0.147034i
$553$	−40.9986	+	40.9986i	−1.74344	+	1.74344i
$554$			9.92820i			0.421809i
$555$		0			0
$556$	13.4641			0.571005
$557$	18.7629	−	18.7629i	0.795011	−	0.795011i	−0.187293	−	0.982304i	$-0.559971\pi$
$557$	18.7629	−	18.7629i	0.795011	−	0.795011i	0.982304	+	0.187293i	$0.0599715\pi$
$558$	12.0716	−	12.0716i	0.511031	−	0.511031i
$559$	−30.4763			−1.28901
$560$		0			0
$561$		0			0
$562$	3.53391	−	3.53391i	0.149069	−	0.149069i
$563$	25.6306	+	25.6306i	1.08020	+	1.08020i	0.996490	+	0.0837125i	$0.0266777\pi$
$563$	25.6306	+	25.6306i	1.08020	+	1.08020i	0.0837125	+	0.996490i	$0.473322\pi$
$564$			7.07180i			0.297776i
$565$		0			0
$566$		0			0
$567$	−12.4419	+	12.4419i	−0.522511	+	0.522511i
$568$	1.79315	−	1.79315i	0.0752389	−	0.0752389i
$569$	37.3033			1.56384			0.781918	−	0.623381i	$-0.214241\pi$
$569$	37.3033			1.56384			0.781918	+	0.623381i	$0.214241\pi$
$570$		0			0
$571$			35.1911i			1.47270i	0.676601	+	0.736350i	$0.263452\pi$
$571$			35.1911i			1.47270i	−0.676601	+	0.736350i	$0.736548\pi$
$572$	12.4419	−	12.4419i	0.520223	−	0.520223i
$573$	−0.546697	−	0.546697i	−0.0228386	−	0.0228386i
$574$	25.4786			1.06346
$575$		0			0
$576$	2.46410			0.102671
$577$	−2.08416	−	2.08416i	−0.0867645	−	0.0867645i	0.662392	−	0.749157i	$-0.269541\pi$
$577$	−2.08416	−	2.08416i	−0.0867645	−	0.0867645i	−0.749157	+	0.662392i	$0.769541\pi$
$578$	−12.0208	+	12.0208i	−0.500000	+	0.500000i
$579$			7.32051i			0.304230i
$580$		0			0
$581$	−26.9090			−1.11637
$582$	1.49360	−	1.49360i	0.0619119	−	0.0619119i
$583$	30.0131	−	30.0131i	1.24301	−	1.24301i
$584$		−	10.6603i		−	0.441124i
$585$		0			0
$586$		−	5.77084i		−	0.238391i
$587$	12.1087	+	12.1087i	0.499782	+	0.499782i	0.911370	−	0.411588i	$-0.135026\pi$
$587$	12.1087	+	12.1087i	0.499782	+	0.499782i	−0.411588	+	0.911370i	$0.635026\pi$
$588$	4.41851	−	4.41851i	0.182216	−	0.182216i
$589$	−27.3079			−1.12520
$590$		0			0
$591$	−5.12436			−0.210788
$592$	−7.61451	+	7.61451i	−0.312954	+	0.312954i
$593$	25.5438	−	25.5438i	1.04896	−	1.04896i	0.0502190	−	0.998738i	$-0.484008\pi$
$593$	25.5438	−	25.5438i	1.04896	−	1.04896i	0.998738	−	0.0502190i	$-0.0159919\pi$
$594$	−15.7662			−0.646897
$595$		0			0
$596$			15.7662i			0.645810i
$597$	0.546697	−	0.546697i	0.0223748	−	0.0223748i
$598$	−21.0659	−	3.81793i	−0.861449	−	0.156127i
$599$			44.7846i			1.82985i	0.403624	+	0.914925i	$0.367750\pi$
$599$			44.7846i			1.82985i	−0.403624	+	0.914925i	$0.632250\pi$
$600$		0			0
$601$	−37.1769			−1.51648			−0.758239	−	0.651977i	$-0.773940\pi$
$601$	−37.1769			−1.51648			−0.758239	+	0.651977i	$0.773940\pi$
$602$	19.0275	+	19.0275i	0.775503	+	0.775503i
$603$	13.7354	+	13.7354i	0.559349	+	0.559349i
$604$		−	19.3205i		−	0.786140i
$605$		0			0
$606$	−2.24871			−0.0913477
$607$	18.4219	+	18.4219i	0.747724	+	0.747724i	0.974051	−	0.226328i	$-0.0726720\pi$
$607$	18.4219	+	18.4219i	0.747724	+	0.747724i	−0.226328	+	0.974051i	$0.572672\pi$
$608$	−2.78710	−	2.78710i	−0.113032	−	0.113032i
$609$	−3.45141			−0.139858
$610$		0			0
$611$	−43.1244			−1.74462
$612$		0			0
$613$	26.9241	+	26.9241i	1.08746	+	1.08746i	0.995790	+	0.0916657i	$0.0292191\pi$
$613$	26.9241	+	26.9241i	1.08746	+	1.08746i	0.0916657	+	0.995790i	$0.470781\pi$
$614$		−	16.3923i		−	0.661540i
$615$		0			0
$616$	−15.5359			−0.625959
$617$	11.1484	−	11.1484i	0.448818	−	0.448818i	−0.446143	−	0.894962i	$-0.647203\pi$
$617$	11.1484	−	11.1484i	0.448818	−	0.448818i	0.894962	+	0.446143i	$0.147203\pi$
$618$	−9.10811	−	9.10811i	−0.366382	−	0.366382i
$619$	−19.4248			−0.780749			−0.390375	−	0.920656i	$-0.627654\pi$
$619$	−19.4248			−0.780749			−0.390375	+	0.920656i	$0.627654\pi$
$620$		0			0
$621$	10.9282	+	15.7662i	0.438534	+	0.632677i
$622$	−10.0382	−	10.0382i	−0.402495	−	0.402495i
$623$		0			0
$624$		−	3.26795i		−	0.130823i
$625$		0			0
$626$		−	2.88542i		−	0.115325i
$627$	8.04197	+	8.04197i	0.321165	+	0.321165i
$628$	3.53391	+	3.53391i	0.141018	+	0.141018i
$629$		0			0
$630$		0			0
$631$		−	8.93926i		−	0.355866i	−0.984043	−	0.177933i	$-0.943059\pi$
$631$		−	8.93926i		−	0.355866i	0.984043	−	0.177933i	$-0.0569411\pi$
$632$	10.4016	−	10.4016i	0.413754	−	0.413754i
$633$	13.5873	−	13.5873i	0.540048	−	0.540048i
$634$		−	4.60770i		−	0.182995i
$635$		0			0
$636$		−	7.88312i		−	0.312586i
$637$	26.9444	+	26.9444i	1.06758	+	1.06758i
$638$	3.33380	+	3.33380i	0.131986	+	0.131986i
$639$		−	6.24871i		−	0.247195i
$640$		0			0
$641$		−	37.3033i		−	1.47339i	−0.676224	−	0.736696i	$-0.736385\pi$
$641$		−	37.3033i		−	1.47339i	0.676224	−	0.736696i	$-0.263615\pi$
$642$		0			0
$643$	−21.5500	−	21.5500i	−0.849850	−	0.849850i	0.140264	−	0.990114i	$-0.455205\pi$
$643$	−21.5500	−	21.5500i	−0.849850	−	0.849850i	−0.990114	+	0.140264i	$0.955205\pi$
$644$	10.7685	+	15.5359i	0.424340	+	0.612200i
$645$		0			0
$646$		0			0
$647$	−7.38563	−	7.38563i	−0.290359	−	0.290359i	0.546863	−	0.837222i	$-0.315822\pi$
$647$	−7.38563	−	7.38563i	−0.290359	−	0.290359i	−0.837222	+	0.546863i	$0.815822\pi$
$648$	3.15660	−	3.15660i	0.124003	−	0.124003i
$649$	−4.99770			−0.196177
$650$		0			0
$651$			19.9908i			0.783501i
$652$	9.28032	+	9.28032i	0.363445	+	0.363445i
$653$	−6.08656	+	6.08656i	−0.238185	+	0.238185i	−0.816098	−	0.577913i	$-0.803867\pi$
$653$	−6.08656	+	6.08656i	−0.238185	+	0.238185i	0.577913	+	0.816098i	$0.303867\pi$
$654$	−13.6540			−0.533912
$655$		0			0
$656$	−6.46410			−0.252381
$657$	−18.5742	−	18.5742i	−0.724650	−	0.724650i
$658$	26.9241	+	26.9241i	1.04961	+	1.04961i
$659$	−9.71241			−0.378342			−0.189171	−	0.981944i	$-0.560580\pi$
$659$	−9.71241			−0.378342			−0.189171	+	0.981944i	$0.560580\pi$
$660$		0			0
$661$		−	34.4179i		−	1.33870i	−0.742947	−	0.669351i	$-0.766572\pi$
$661$		−	34.4179i		−	1.33870i	0.742947	−	0.669351i	$-0.233428\pi$
$662$	4.34418	+	4.34418i	0.168841	+	0.168841i
$663$		0			0
$664$	6.82698			0.264938
$665$		0			0
$666$			26.5348i			1.02820i
$667$	1.02301	−	5.64459i	0.0396112	−	0.218559i
$668$	13.3843	−	13.3843i	0.517853	−	0.517853i
$669$		−	0.928203i		−	0.0358864i
$670$		0			0
$671$	11.3731			0.439052
$672$	−2.04030	+	2.04030i	−0.0787064	+	0.0787064i
$673$	−5.74479	+	5.74479i	−0.221445	+	0.221445i	−0.809107	−	0.587662i	$-0.800049\pi$
$673$	−5.74479	+	5.74479i	−0.221445	+	0.221445i	0.587662	+	0.809107i	$0.300049\pi$
$674$	2.88542			0.111142
$675$		0			0
$676$	6.92820			0.266469
$677$	33.9919	−	33.9919i	1.30642	−	1.30642i	0.382434	−	0.923983i	$-0.375086\pi$
$677$	33.9919	−	33.9919i	1.30642	−	1.30642i	0.923983	−	0.382434i	$-0.124914\pi$
$678$	9.65481	+	9.65481i	0.370791	+	0.370791i
$679$		−	11.3731i		−	0.436458i
$680$		0			0
$681$		0			0
$682$	19.3096	−	19.3096i	0.739404	−	0.739404i
$683$	−14.1421	+	14.1421i	−0.541134	+	0.541134i	−0.923861	−	0.382727i	$-0.874985\pi$
$683$	−14.1421	+	14.1421i	−0.541134	+	0.541134i	0.382727	+	0.923861i	$0.374985\pi$
$684$	−9.71241			−0.371363
$685$		0			0
$686$		−	6.05384i		−	0.231137i
$687$	−11.1484	+	11.1484i	−0.425339	+	0.425339i
$688$	−4.82741	−	4.82741i	−0.184043	−	0.184043i
$689$	48.0719			1.83139
$690$		0			0
$691$	6.24871			0.237712			0.118856	−	0.992911i	$-0.462077\pi$
$691$	6.24871			0.237712			0.118856	+	0.992911i	$0.462077\pi$
$692$	15.1266	+	15.1266i	0.575029	+	0.575029i
$693$	−27.0695	+	27.0695i	−1.02828	+	1.02828i
$694$		−	17.0718i		−	0.648037i
$695$		0			0
$696$	0.875644			0.0331912
$697$		0			0
$698$	3.29530	−	3.29530i	0.124729	−	0.124729i
$699$			7.12436i			0.269468i
$700$		0			0
$701$			37.3033i			1.40893i	0.709740	+	0.704464i	$0.248812\pi$
$701$			37.3033i			1.40893i	−0.709740	+	0.704464i	$0.751188\pi$
$702$	−12.6264	−	12.6264i	−0.476552	−	0.476552i
$703$	30.0131	−	30.0131i	1.13196	−	1.13196i
$704$	3.94156			0.148553
$705$		0			0
$706$	31.0526			1.16868
$707$	−8.56142	+	8.56142i	−0.321985	+	0.321985i
$708$	−0.656339	+	0.656339i	−0.0246667	+	0.0246667i
$709$	−21.5371			−0.808842			−0.404421	−	0.914573i	$-0.632527\pi$
$709$	−21.5371			−0.808842			−0.404421	+	0.914573i	$0.632527\pi$
$710$		0			0
$711$		−	36.2472i		−	1.35938i
$712$		0			0
$713$	−32.6939	−	5.92536i	−1.22440	−	0.221907i
$714$		0			0
$715$		0			0
$716$	11.8038			0.441130
$717$	11.1378	+	11.1378i	0.415950	+	0.415950i
$718$	14.4822	+	14.4822i	0.540472	+	0.540472i
$719$		−	49.5167i		−	1.84666i	−0.384008	−	0.923330i	$-0.625456\pi$
$719$		−	49.5167i		−	1.84666i	0.384008	−	0.923330i	$-0.374544\pi$
$720$		0			0
$721$	−69.3538			−2.58287
$722$	−2.44949	−	2.44949i	−0.0911606	−	0.0911606i
$723$	−13.7354	−	13.7354i	−0.510826	−	0.510826i
$724$	5.77084			0.214472
$725$		0			0
$726$	−3.32051			−0.123236
$727$	−15.2290	+	15.2290i	−0.564813	+	0.564813i	−0.930671	−	0.365858i	$-0.880776\pi$
$727$	−15.2290	+	15.2290i	−0.564813	+	0.564813i	0.365858	+	0.930671i	$0.380776\pi$
$728$	−12.4419	−	12.4419i	−0.461128	−	0.461128i
$729$		−	2.21539i		−	0.0820515i
$730$		0			0
$731$		0			0
$732$	1.49360	−	1.49360i	0.0552052	−	0.0552052i
$733$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$733$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$734$	3.94156			0.145486
$735$		0			0
$736$	−2.73205	−	3.94156i	−0.100705	−	0.145288i
$737$	21.9711	+	21.9711i	0.809315	+	0.809315i
$738$	−11.2629	+	11.2629i	−0.414595	+	0.414595i
$739$			12.0000i			0.441427i	0.975339	+	0.220714i	$0.0708386\pi$
$739$			12.0000i			0.441427i	−0.975339	+	0.220714i	$0.929161\pi$
$740$		0			0
$741$			12.8808i			0.473189i
$742$	−30.0131	−	30.0131i	−1.10181	−	1.10181i
$743$	27.6709	+	27.6709i	1.01515	+	1.01515i	0.999883	+	0.0152647i	$0.00485909\pi$
$743$	27.6709	+	27.6709i	1.01515	+	1.01515i	0.0152647	+	0.999883i	$0.495141\pi$
$744$		−	5.07180i		−	0.185941i
$745$		0			0
$746$		−	15.7662i		−	0.577243i
$747$	11.8952	−	11.8952i	0.435223	−	0.435223i
$748$		0			0
$749$		0			0
$750$		0			0
$751$			24.7055i			0.901517i	0.892646	+	0.450758i	$0.148846\pi$
$751$			24.7055i			0.901517i	−0.892646	+	0.450758i	$0.851154\pi$
$752$	−6.83083	−	6.83083i	−0.249095	−	0.249095i
$753$	−4.08060	−	4.08060i	−0.148705	−	0.148705i
$754$			5.33975i			0.194462i
$755$		0			0
$756$			15.7662i			0.573413i
$757$	11.6951	−	11.6951i	0.425066	−	0.425066i	−0.461878	−	0.886944i	$-0.652824\pi$
$757$	11.6951	−	11.6951i	0.425066	−	0.425066i	0.886944	+	0.461878i	$0.152824\pi$
$758$	5.57421	+	5.57421i	0.202464	+	0.202464i
$759$	7.88312	+	11.3731i	0.286139	+	0.412816i
$760$		0			0
$761$	48.7128			1.76584			0.882919	−	0.469525i	$-0.155575\pi$
$761$	48.7128			1.76584			0.882919	+	0.469525i	$0.155575\pi$
$762$	4.24264	+	4.24264i	0.153695	+	0.153695i
$763$	−51.9841	+	51.9841i	−1.88195	+	1.88195i
$764$	1.05614			0.0382097
$765$		0			0
$766$		−	33.3618i		−	1.20541i
$767$	−4.00240	−	4.00240i	−0.144518	−	0.144518i
$768$	0.517638	−	0.517638i	0.0186787	−	0.0186787i
$769$	10.7685			0.388324			0.194162	−	0.980970i	$-0.437801\pi$
$769$	10.7685			0.388324			0.194162	+	0.980970i	$0.437801\pi$
$770$		0			0
$771$	−9.46410			−0.340841
$772$	−7.07107	−	7.07107i	−0.254493	−	0.254493i
$773$	18.7629	+	18.7629i	0.674856	+	0.674856i	0.958831	−	0.283976i	$-0.0916536\pi$
$773$	18.7629	+	18.7629i	0.674856	+	0.674856i	−0.283976	+	0.958831i	$0.591654\pi$
$774$	−16.8224			−0.604668
$775$		0			0
$776$			2.88542i			0.103581i
$777$	−21.9711	−	21.9711i	−0.788208	−	0.788208i
$778$	17.2693	+	17.2693i	0.619135	+	0.619135i
$779$	25.4786			0.912867
$780$		0			0
$781$		−	9.99540i		−	0.357663i
$782$		0			0
$783$	3.38323	−	3.38323i	0.120907	−	0.120907i
$784$			8.53590i			0.304854i
$785$		0			0
$786$	5.85641			0.208891
$787$	−17.4694	+	17.4694i	−0.622718	+	0.622718i	−0.946226	−	0.323508i	$-0.895138\pi$
$787$	−17.4694	+	17.4694i	−0.622718	+	0.622718i	0.323508	+	0.946226i	$0.395138\pi$
$788$	4.94975	−	4.94975i	0.176327	−	0.176327i
$789$	−5.77084			−0.205448
$790$		0			0
$791$	73.5167			2.61395
$792$	6.86771	−	6.86771i	0.244033	−	0.244033i
$793$	9.10811	+	9.10811i	0.323439	+	0.323439i
$794$			11.3205i			0.401750i
$795$		0			0
$796$			1.05614i			0.0374338i
$797$	−11.6951	+	11.6951i	−0.414262	+	0.414262i	−0.883220	−	0.468958i	$-0.844629\pi$
$797$	−11.6951	+	11.6951i	−0.414262	+	0.414262i	0.468958	+	0.883220i	$0.344629\pi$
$798$	8.04197	−	8.04197i	0.284683	−	0.284683i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	−3.53391	+	3.53391i	−0.124787	+	0.124787i
$803$	−29.7112	−	29.7112i	−1.04849	−	1.04849i
$804$	5.77084			0.203522
$805$		0			0
$806$	30.9282			1.08940
$807$	8.06918	+	8.06918i	0.284049	+	0.284049i
$808$	2.17209	−	2.17209i	0.0764138	−	0.0764138i
$809$			8.85641i			0.311375i	0.987806	+	0.155687i	$0.0497592\pi$
$809$			8.85641i			0.311375i	−0.987806	+	0.155687i	$0.950241\pi$
$810$		0			0
$811$	−32.7846			−1.15122			−0.575612	−	0.817723i	$-0.695236\pi$
$811$	−32.7846			−1.15122			−0.575612	+	0.817723i	$0.695236\pi$
$812$	3.33380	−	3.33380i	0.116993	−	0.116993i
$813$	−3.20736	+	3.20736i	−0.112487	+	0.112487i
$814$			42.4449i			1.48769i
$815$		0			0
$816$		0			0
$817$	19.0275	+	19.0275i	0.665688	+	0.665688i
$818$	−7.39924	+	7.39924i	−0.258708	+	0.258708i
$819$	−43.3572			−1.51502
$820$		0			0
$821$	24.9090			0.869329			0.434664	−	0.900592i	$-0.356867\pi$
$821$	24.9090			0.869329			0.434664	+	0.900592i	$0.356867\pi$
$822$		0			0
$823$	23.7370	−	23.7370i	0.827421	−	0.827421i	−0.159739	−	0.987159i	$-0.551065\pi$
$823$	23.7370	−	23.7370i	0.827421	−	0.827421i	0.987159	+	0.159739i	$0.0510652\pi$
$824$	17.5955			0.612969
$825$		0			0
$826$			4.99770i			0.173892i
$827$	4.82741	−	4.82741i	0.167865	−	0.167865i	−0.618175	−	0.786040i	$-0.712128\pi$
$827$	4.82741	−	4.82741i	0.167865	−	0.167865i	0.786040	+	0.618175i	$0.212128\pi$
$828$	−11.6280	−	2.10743i	−0.404100	−	0.0732382i
$829$			46.1244i			1.60197i	0.598688	+	0.800983i	$0.295689\pi$
$829$			46.1244i			1.60197i	−0.598688	+	0.800983i	$0.704311\pi$
$830$		0			0
$831$	7.26795			0.252122
$832$	3.15660	+	3.15660i	0.109435	+	0.109435i
$833$		0			0
$834$		−	9.85641i		−	0.341299i
$835$		0			0
$836$	−15.5359			−0.537320
$837$	−19.5959	−	19.5959i	−0.677334	−	0.677334i
$838$	−27.6709	−	27.6709i	−0.955877	−	0.955877i
$839$	−49.9012			−1.72278			−0.861390	−	0.507945i	$-0.830405\pi$
$839$	−49.9012			−1.72278			−0.861390	+	0.507945i	$0.830405\pi$
$840$		0			0
$841$	27.5692			0.950663
$842$	11.1484	−	11.1484i	0.384200	−	0.384200i
$843$	−2.58700	−	2.58700i	−0.0891010	−	0.0891010i
$844$			26.2487i			0.903518i
$845$		0			0
$846$	−23.8038			−0.818393
$847$	−12.6420	+	12.6420i	−0.434385	+	0.434385i
$848$	7.61451	+	7.61451i	0.261483	+	0.261483i
$849$		0			0
$850$		0			0
$851$	42.4449	−	29.4202i	1.45499	−	1.00851i
$852$	−1.31268	−	1.31268i	−0.0449716	−	0.0449716i
$853$	34.1678	−	34.1678i	1.16988	−	1.16988i	0.187645	−	0.982237i	$-0.439915\pi$
$853$	34.1678	−	34.1678i	1.16988	−	1.16988i	0.982237	−	0.187645i	$-0.0600854\pi$
$854$		−	11.3731i		−	0.389178i
$855$		0			0
$856$		0			0
$857$	1.41421	+	1.41421i	0.0483086	+	0.0483086i	0.730848	−	0.682540i	$-0.239125\pi$
$857$	1.41421	+	1.41421i	0.0483086	+	0.0483086i	−0.682540	+	0.730848i	$0.739125\pi$
$858$	−9.10811	−	9.10811i	−0.310946	−	0.310946i
$859$			2.73205i			0.0932164i	0.998913	+	0.0466082i	$0.0148412\pi$
$859$			2.73205i			0.0932164i	−0.998913	+	0.0466082i	$0.985159\pi$
$860$		0			0
$861$		−	18.6517i		−	0.635647i
$862$	−19.3096	+	19.3096i	−0.657688	+	0.657688i
$863$	−11.4524	+	11.4524i	−0.389845	+	0.389845i	−0.874632	−	0.484787i	$-0.838897\pi$
$863$	−11.4524	+	11.4524i	−0.389845	+	0.389845i	0.484787	+	0.874632i	$0.338897\pi$
$864$		−	4.00000i		−	0.136083i
$865$		0			0
$866$			8.65627i			0.294152i
$867$	8.79985	+	8.79985i	0.298858	+	0.298858i
$868$	−19.3096	−	19.3096i	−0.655411	−	0.655411i
$869$		−	57.9808i		−	1.96686i
$870$		0			0
$871$			35.1911i			1.19240i
$872$	13.1887	−	13.1887i	0.446626	−	0.446626i
$873$	5.02751	+	5.02751i	0.170155	+	0.170155i
$874$	10.7685	+	15.5359i	0.364251	+	0.525510i
$875$		0			0
$876$	−7.80385			−0.263668
$877$	−20.8343	−	20.8343i	−0.703523	−	0.703523i	0.261642	−	0.965165i	$-0.415736\pi$
$877$	−20.8343	−	20.8343i	−0.703523	−	0.703523i	−0.965165	+	0.261642i	$0.915736\pi$
$878$	−9.79796	+	9.79796i	−0.330665	+	0.330665i
$879$	−4.22455			−0.142491
$880$		0			0
$881$			4.99770i			0.168377i	0.996450	+	0.0841884i	$0.0268297\pi$
$881$			4.99770i			0.168377i	−0.996450	+	0.0841884i	$0.973170\pi$
$882$	14.8728	+	14.8728i	0.500793	+	0.500793i
$883$	−30.4292	+	30.4292i	−1.02402	+	1.02402i	−0.0243183	+	0.999704i	$0.507742\pi$
$883$	−30.4292	+	30.4292i	−1.02402	+	1.02402i	−0.999704	+	0.0243183i	$0.992258\pi$
$884$		0			0
$885$		0			0
$886$	25.0718			0.842303
$887$	35.2538	+	35.2538i	1.18371	+	1.18371i	0.978777	+	0.204930i	$0.0656968\pi$
$887$	35.2538	+	35.2538i	1.18371	+	1.18371i	0.204930	+	0.978777i	$0.434303\pi$
$888$	5.57421	+	5.57421i	0.187058	+	0.187058i
$889$	32.3056			1.08350
$890$		0			0
$891$		−	17.5955i		−	0.589472i
$892$	0.896575	+	0.896575i	0.0300196	+	0.0300196i
$893$	26.9241	+	26.9241i	0.900982	+	0.900982i
$894$	11.5417			0.386012
$895$		0			0
$896$		−	3.94156i		−	0.131678i
$897$	−2.79492	+	15.4213i	−0.0933197	+	0.514902i
$898$	−18.0058	+	18.0058i	−0.600863	+	0.600863i
$899$			8.28719i			0.276393i
$900$		0			0
$901$		0			0
$902$	−18.0161	+	18.0161i	−0.599871	+	0.599871i
$903$	13.9291	−	13.9291i	0.463532	−	0.463532i
$904$	−18.6517			−0.620345
$905$		0			0
$906$	−14.1436			−0.469889
$907$	−10.4016	+	10.4016i	−0.345380	+	0.345380i	−0.858385	−	0.513005i	$-0.828532\pi$
$907$	−10.4016	+	10.4016i	−0.345380	+	0.345380i	0.513005	+	0.858385i	$0.328532\pi$
$908$		0			0
$909$		−	7.56922i		−	0.251055i
$910$		0			0
$911$		−	16.8224i		−	0.557350i	−0.960385	−	0.278675i	$-0.910105\pi$
$911$		−	16.8224i		−	0.557350i	0.960385	−	0.278675i	$-0.0898953\pi$
$912$	−2.04030	+	2.04030i	−0.0675611	+	0.0675611i
$913$	19.0275	−	19.0275i	0.629719	−	0.629719i
$914$	18.6517			0.616942
$915$		0			0
$916$		−	21.5371i		−	0.711605i
$917$	22.2968	−	22.2968i	0.736306	−	0.736306i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$		0			0
$921$	−12.0000			−0.395413
$922$	25.8212	+	25.8212i	0.850375	+	0.850375i
$923$	8.00481	−	8.00481i	0.263481	−	0.263481i
$924$			11.3731i			0.374146i
$925$		0			0
$926$	−6.53590			−0.214783
$927$	30.6581	−	30.6581i	1.00695	−	1.00695i
$928$	−0.845807	+	0.845807i	−0.0277650	+	0.0277650i
$929$			0.320508i			0.0105155i	0.999986	+	0.00525776i	$0.00167361\pi$
$929$			0.320508i			0.0105155i	−0.999986	+	0.00525776i	$0.998326\pi$
$930$		0			0
$931$		−	33.6448i		−	1.10266i
$932$	−6.88160	−	6.88160i	−0.225414	−	0.225414i
$933$	−7.34847	+	7.34847i	−0.240578	+	0.240578i
$934$	−8.93926			−0.292501
$935$		0			0
$936$	11.0000			0.359546
$937$	24.3371	−	24.3371i	0.795060	−	0.795060i	−0.187252	−	0.982312i	$-0.559958\pi$
$937$	24.3371	−	24.3371i	0.795060	−	0.795060i	0.982312	+	0.187252i	$0.0599582\pi$
$938$	21.9711	−	21.9711i	0.717381	−	0.717381i
$939$	−2.11228			−0.0689315
$940$		0			0
$941$		−	50.1841i		−	1.63596i	−0.575249	−	0.817978i	$-0.695095\pi$
$941$		−	50.1841i		−	1.63596i	0.575249	−	0.817978i	$-0.304905\pi$
$942$	2.58700	−	2.58700i	0.0842890	−	0.0842890i
$943$	30.5038	+	5.52844i	0.993341	+	0.180031i
$944$		−	1.26795i		−	0.0412682i
$945$		0			0
$946$	−26.9090			−0.874886
$947$	2.82843	+	2.82843i	0.0919115	+	0.0919115i	0.751568	−	0.659656i	$-0.229298\pi$
$947$	2.82843	+	2.82843i	0.0919115	+	0.0919115i	−0.659656	+	0.751568i	$0.729298\pi$
$948$	−7.61451	−	7.61451i	−0.247308	−	0.247308i
$949$		−	47.5885i		−	1.54479i
$950$		0			0
$951$	−3.37307			−0.109379
$952$		0			0
$953$	−2.04030	−	2.04030i	−0.0660919	−	0.0660919i	0.673288	−	0.739380i	$-0.264881\pi$
$953$	−2.04030	−	2.04030i	−0.0660919	−	0.0660919i	−0.739380	+	0.673288i	$0.764881\pi$
$954$	26.5348			0.859095
$955$		0			0
$956$	−21.5167			−0.695899
$957$	2.44051	−	2.44051i	0.0788905	−	0.0788905i
$958$	21.5500	+	21.5500i	0.696250	+	0.696250i
$959$		0			0
$960$		0			0
$961$	17.0000			0.548387
$962$	−33.9919	+	33.9919i	−1.09594	+	1.09594i
$963$		0			0
$964$	26.5348			0.854628
$965$		0			0
$966$	11.3731	−	7.88312i	0.365922	−	0.253635i
$967$	−15.7322	−	15.7322i	−0.505914	−	0.505914i	0.407356	−	0.913270i	$-0.366451\pi$
$967$	−15.7322	−	15.7322i	−0.505914	−	0.505914i	−0.913270	+	0.407356i	$0.866451\pi$
$968$	3.20736	−	3.20736i	0.103089	−	0.103089i
$969$		0			0
$970$		0			0
$971$		−	47.0157i		−	1.50881i	−0.656411	−	0.754403i	$-0.727926\pi$
$971$		−	47.0157i		−	1.50881i	0.656411	−	0.754403i	$-0.272074\pi$
$972$	−10.7961	−	10.7961i	−0.346284	−	0.346284i
$973$	−37.5259	−	37.5259i	−1.20302	−	1.20302i
$974$		−	38.0526i		−	1.21928i
$975$		0			0
$976$			2.88542i			0.0923601i
$977$	−35.4856	+	35.4856i	−1.13528	+	1.13528i	−0.145999	+	0.989285i	$0.546639\pi$
$977$	−35.4856	+	35.4856i	−1.13528	+	1.13528i	−0.989285	+	0.145999i	$0.953361\pi$
$978$	6.79367	−	6.79367i	0.217237	−	0.217237i
$979$		0			0
$980$		0			0
$981$		−	45.9596i		−	1.46738i
$982$	−5.03768	−	5.03768i	−0.160759	−	0.160759i
$983$	−37.3257	−	37.3257i	−1.19051	−	1.19051i	−0.976925	−	0.213581i	$-0.931487\pi$
$983$	−37.3257	−	37.3257i	−1.19051	−	1.19051i	−0.213581	−	0.976925i	$-0.568513\pi$
$984$			4.73205i			0.150852i
$985$		0			0
$986$		0			0
$987$	19.7098	−	19.7098i	0.627371	−	0.627371i
$988$	−12.4419	−	12.4419i	−0.395830	−	0.395830i
$989$	18.6517	+	26.9090i	0.593088	+	0.855655i
$990$		0			0
$991$	13.8038			0.438494			0.219247	−	0.975669i	$-0.429640\pi$
$991$	13.8038			0.438494			0.219247	+	0.975669i	$0.429640\pi$
$992$	4.89898	+	4.89898i	0.155543	+	0.155543i
$993$	3.18016	−	3.18016i	0.100919	−	0.100919i
$994$	−9.99540			−0.317035
$995$		0			0
$996$		−	4.99770i		−	0.158358i
$997$	−34.3436	−	34.3436i	−1.08767	−	1.08767i	−0.995768	−	0.0919058i	$-0.970704\pi$
$997$	−34.3436	−	34.3436i	−1.08767	−	1.08767i	−0.0919058	−	0.995768i	$-0.529296\pi$
$998$	−18.6993	+	18.6993i	−0.591917	+	0.591917i
$999$	43.0742			1.36281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1150.2.e.d.1057.8	yes	16
5.2	odd	4	inner	1150.2.e.d.643.2	yes	16
5.3	odd	4	inner	1150.2.e.d.643.7	yes	16
5.4	even	2	inner	1150.2.e.d.1057.1	yes	16
23.22	odd	2	inner	1150.2.e.d.1057.7	yes	16
115.22	even	4	inner	1150.2.e.d.643.1	✓	16
115.68	even	4	inner	1150.2.e.d.643.8	yes	16
115.114	odd	2	inner	1150.2.e.d.1057.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1150.2.e.d.643.1	✓	16	115.22	even	4	inner
1150.2.e.d.643.2	yes	16	5.2	odd	4	inner
1150.2.e.d.643.7	yes	16	5.3	odd	4	inner
1150.2.e.d.643.8	yes	16	115.68	even	4	inner
1150.2.e.d.1057.1	yes	16	5.4	even	2	inner
1150.2.e.d.1057.2	yes	16	115.114	odd	2	inner
1150.2.e.d.1057.7	yes	16	23.22	odd	2	inner
1150.2.e.d.1057.8	yes	16	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:	\( N \)	\(=\)	\( 1150 = 2 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1150.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.517638 - 0.517638i) q^{3} +1.00000i q^{4} +0.732051 q^{6} +(2.78710 - 2.78710i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.46410i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.517638 - 0.517638i) q^{3} +1.00000i q^{4} +0.732051 q^{6} +(2.78710 - 2.78710i) q^{7} +(-0.707107 + 0.707107i) q^{8} +2.46410i q^{9} +3.94156i q^{11} +(0.517638 + 0.517638i) q^{12} +(-3.15660 + 3.15660i) q^{13} +3.94156 q^{14} -1.00000 q^{16} +(-1.74238 + 1.74238i) q^{18} +3.94156 q^{19} -2.88542i q^{21} +(-2.78710 + 2.78710i) q^{22} +(4.71896 + 0.855252i) q^{23} +0.732051i q^{24} -4.46410 q^{26} +(2.82843 + 2.82843i) q^{27} +(2.78710 + 2.78710i) q^{28} -1.19615i q^{29} -6.92820 q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.04030 + 2.04030i) q^{33} -2.46410 q^{36} +(7.61451 - 7.61451i) q^{37} +(2.78710 + 2.78710i) q^{38} +3.26795i q^{39} +6.46410 q^{41} +(2.04030 - 2.04030i) q^{42} +(4.82741 + 4.82741i) q^{43} -3.94156 q^{44} +(2.73205 + 3.94156i) q^{46} +(6.83083 + 6.83083i) q^{47} +(-0.517638 + 0.517638i) q^{48} -8.53590i q^{49} +(-3.15660 - 3.15660i) q^{52} +(-7.61451 - 7.61451i) q^{53} +4.00000i q^{54} +3.94156i q^{56} +(2.04030 - 2.04030i) q^{57} +(0.845807 - 0.845807i) q^{58} +1.26795i q^{59} -2.88542i q^{61} +(-4.89898 - 4.89898i) q^{62} +(6.86771 + 6.86771i) q^{63} -1.00000i q^{64} +2.88542i q^{66} +(5.57421 - 5.57421i) q^{67} +(2.88542 - 2.00000i) q^{69} -2.53590 q^{71} +(-1.74238 - 1.74238i) q^{72} +(-7.53794 + 7.53794i) q^{73} +10.7685 q^{74} +3.94156i q^{76} +(10.9855 + 10.9855i) q^{77} +(-2.31079 + 2.31079i) q^{78} -14.7101 q^{79} -4.46410 q^{81} +(4.57081 + 4.57081i) q^{82} +(-4.82741 - 4.82741i) q^{83} +2.88542 q^{84} +6.82698i q^{86} +(-0.619174 - 0.619174i) q^{87} +(-2.78710 - 2.78710i) q^{88} +17.5955i q^{91} +(-0.855252 + 4.71896i) q^{92} +(-3.58630 + 3.58630i) q^{93} +9.66025i q^{94} -0.732051 q^{96} +(2.04030 - 2.04030i) q^{97} +(6.03579 - 6.03579i) q^{98} -9.71241 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{6}+O(q^{10}) \) 16 * q - 16 * q^6	\( 16 q - 16 q^{6} - 16 q^{16} - 16 q^{26} + 16 q^{36} + 48 q^{41} + 16 q^{46} - 96 q^{71} - 16 q^{81} + 16 q^{96}+O(q^{100}) \) 16 * q - 16 * q^6 - 16 * q^16 - 16 * q^26 + 16 * q^36 + 48 * q^41 + 16 * q^46 - 96 * q^71 - 16 * q^81 + 16 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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