LMFDB - Embedded newform 1710.2.p.c.37.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(37,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("1710.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.p (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 108x^{16} + 1318x^{12} + 4652x^{8} + 5057x^{4} + 256 $ x^20 + 108x^16 + 1318x^12 + 4652x^8 + 5057x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.9
Root			$2.20512 - 2.20512i$ of defining polynomial
Character	$\chi$	$=$	1710.37
Dual form			1710.2.p.c.1063.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.114611 + 2.23313i) q^{5} +(-1.40368 - 1.40368i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.114611 + 2.23313i) q^{5} +(-1.40368 - 1.40368i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.49802 + 1.66010i) q^{10} +5.29298 q^{11} +(-1.91968 - 1.91968i) q^{13} -1.98511 q^{14} -1.00000 q^{16} +(-0.488117 - 0.488117i) q^{17} +(-2.44789 - 3.60663i) q^{19} +(2.23313 + 0.114611i) q^{20} +(3.74270 - 3.74270i) q^{22} +(3.88930 - 3.88930i) q^{23} +(-4.97373 - 0.511883i) q^{25} -2.71483 q^{26} +(-1.40368 + 1.40368i) q^{28} +6.19060 q^{29} +7.84986i q^{31} +(-0.707107 + 0.707107i) q^{32} -0.690302 q^{34} +(3.29548 - 2.97373i) q^{35} +(5.60602 - 5.60602i) q^{37} +(-4.28120 - 0.819353i) q^{38} +(1.66010 - 1.49802i) q^{40} +1.90599i q^{41} +(7.12884 - 7.12884i) q^{43} -5.29298i q^{44} -5.50029i q^{46} +(7.86994 + 7.86994i) q^{47} -3.05934i q^{49} +(-3.87891 + 3.15500i) q^{50} +(-1.91968 + 1.91968i) q^{52} +(-8.93991 - 8.93991i) q^{53} +(-0.606635 + 11.8199i) q^{55} +1.98511i q^{56} +(4.37741 - 4.37741i) q^{58} +0.611185 q^{59} +8.31021 q^{61} +(5.55069 + 5.55069i) q^{62} +1.00000i q^{64} +(4.50690 - 4.06687i) q^{65} +(10.2011 - 10.2011i) q^{67} +(-0.488117 + 0.488117i) q^{68} +(0.227516 - 4.43300i) q^{70} -3.97022i q^{71} +(7.72265 - 7.72265i) q^{73} -7.92810i q^{74} +(-3.60663 + 2.44789i) q^{76} +(-7.42967 - 7.42967i) q^{77} -17.1528 q^{79} +(0.114611 - 2.23313i) q^{80} +(1.34774 + 1.34774i) q^{82} +(-5.43217 + 5.43217i) q^{83} +(1.14597 - 1.03408i) q^{85} -10.0817i q^{86} +(-3.74270 - 3.74270i) q^{88} -5.42118 q^{89} +5.38924i q^{91} +(-3.88930 - 3.88930i) q^{92} +11.1298 q^{94} +(8.33464 - 5.05310i) q^{95} +(-3.10415 + 3.10415i) q^{97} +(-2.16328 - 2.16328i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) $ 20 * q - 12 * q^5 - 4 * q^7	$ 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) $ 20 * q - 12 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 + 12 * q^17 + 4 * q^23 - 28 * q^25 - 24 * q^26 - 4 * q^28 - 4 * q^35 + 12 * q^38 - 12 * q^43 + 44 * q^47 + 64 * q^55 - 8 * q^58 + 24 * q^62 + 12 * q^68 - 4 * q^73 + 4 * q^76 - 88 * q^77 + 12 * q^80 - 8 * q^82 - 76 * q^83 - 12 * q^85 - 4 * q^92 + 24 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−0.114611	+	2.23313i	−0.0512557	+	0.998686i
$5$	−0.114611	+	2.23313i	−0.0512557	+	0.998686i
$6$		0			0
$7$	−1.40368	−	1.40368i	−0.530543	−	0.530543i	0.390191	−	0.920734i	$-0.372409\pi$
$7$	−1.40368	−	1.40368i	−0.530543	−	0.530543i	−0.920734	+	0.390191i	$0.872409\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	1.49802	+	1.66010i	0.473715	+	0.524971i
$11$	5.29298			1.59589			0.797947	−	0.602728i	$-0.205920\pi$
$11$	5.29298			1.59589			0.797947	+	0.602728i	$0.205920\pi$
$12$		0			0
$13$	−1.91968	−	1.91968i	−0.532423	−	0.532423i	0.388870	−	0.921293i	$-0.372866\pi$
$13$	−1.91968	−	1.91968i	−0.532423	−	0.532423i	−0.921293	+	0.388870i	$0.872866\pi$
$14$	−1.98511			−0.530543
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.488117	−	0.488117i	−0.118386	−	0.118386i	0.645432	−	0.763818i	$-0.276677\pi$
$17$	−0.488117	−	0.488117i	−0.118386	−	0.118386i	−0.763818	+	0.645432i	$0.776677\pi$
$18$		0			0
$19$	−2.44789	−	3.60663i	−0.561585	−	0.827419i
$19$	−2.44789	−	3.60663i	−0.561585	−	0.827419i
$20$	2.23313	+	0.114611i	0.499343	+	0.0256278i
$21$		0			0
$22$	3.74270	−	3.74270i	0.797947	−	0.797947i
$23$	3.88930	−	3.88930i	0.810974	−	0.810974i	−0.173806	−	0.984780i	$-0.555607\pi$
$23$	3.88930	−	3.88930i	0.810974	−	0.810974i	0.984780	+	0.173806i	$0.0556065\pi$
$24$		0			0
$25$	−4.97373	−	0.511883i	−0.994746	−	0.102377i
$26$	−2.71483			−0.532423
$27$		0			0
$28$	−1.40368	+	1.40368i	−0.265271	+	0.265271i
$29$	6.19060			1.14956			0.574782	−	0.818306i	$-0.305087\pi$
$29$	6.19060			1.14956			0.574782	+	0.818306i	$0.305087\pi$
$30$		0			0
$31$			7.84986i			1.40988i	0.709268	+	0.704938i	$0.249025\pi$
$31$			7.84986i			1.40988i	−0.709268	+	0.704938i	$0.750975\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$	−0.690302			−0.118386
$35$	3.29548	−	2.97373i	0.557039	−	0.502652i
$36$		0			0
$37$	5.60602	−	5.60602i	0.921623	−	0.921623i	−0.0755209	−	0.997144i	$-0.524062\pi$
$37$	5.60602	−	5.60602i	0.921623	−	0.921623i	0.997144	+	0.0755209i	$0.0240620\pi$
$38$	−4.28120	−	0.819353i	−0.694502	−	0.132917i
$39$		0			0
$40$	1.66010	−	1.49802i	0.262485	−	0.236857i
$41$			1.90599i			0.297666i	0.988862	+	0.148833i	$0.0475517\pi$
$41$			1.90599i			0.297666i	−0.988862	+	0.148833i	$0.952448\pi$
$42$		0			0
$43$	7.12884	−	7.12884i	1.08714	−	1.08714i	0.0913152	−	0.995822i	$-0.470893\pi$
$43$	7.12884	−	7.12884i	1.08714	−	1.08714i	0.995822	−	0.0913152i	$-0.0291071\pi$
$44$		−	5.29298i		−	0.797947i
$45$		0			0
$46$		−	5.50029i		−	0.810974i
$47$	7.86994	+	7.86994i	1.14795	+	1.14795i	0.986955	+	0.160993i	$0.0514698\pi$
$47$	7.86994	+	7.86994i	1.14795	+	1.14795i	0.160993	+	0.986955i	$0.448530\pi$
$48$		0			0
$49$		−	3.05934i		−	0.437049i
$50$	−3.87891	+	3.15500i	−0.548561	+	0.446185i
$51$		0			0
$52$	−1.91968	+	1.91968i	−0.266211	+	0.266211i
$53$	−8.93991	−	8.93991i	−1.22799	−	1.22799i	−0.964723	−	0.263268i	$-0.915200\pi$
$53$	−8.93991	−	8.93991i	−1.22799	−	1.22799i	−0.263268	−	0.964723i	$-0.584800\pi$
$54$		0			0
$55$	−0.606635	+	11.8199i	−0.0817986	+	1.59380i
$56$			1.98511i			0.265271i
$57$		0			0
$58$	4.37741	−	4.37741i	0.574782	−	0.574782i
$59$	0.611185			0.0795696			0.0397848	−	0.999208i	$-0.487333\pi$
$59$	0.611185			0.0795696			0.0397848	+	0.999208i	$0.487333\pi$
$60$		0			0
$61$	8.31021			1.06401			0.532007	−	0.846740i	$-0.321438\pi$
$61$	8.31021			1.06401			0.532007	+	0.846740i	$0.321438\pi$
$62$	5.55069	+	5.55069i	0.704938	+	0.704938i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	4.50690	−	4.06687i	0.559013	−	0.504433i
$66$		0			0
$67$	10.2011	−	10.2011i	1.24626	−	1.24626i	0.288905	−	0.957358i	$-0.406709\pi$
$67$	10.2011	−	10.2011i	1.24626	−	1.24626i	0.957358	−	0.288905i	$-0.0932913\pi$
$68$	−0.488117	+	0.488117i	−0.0591929	+	0.0591929i
$69$		0			0
$70$	0.227516	−	4.43300i	0.0271933	−	0.529845i
$71$		−	3.97022i		−	0.471178i	−0.971853	−	0.235589i	$-0.924298\pi$
$71$		−	3.97022i		−	0.471178i	0.971853	−	0.235589i	$-0.0757019\pi$
$72$		0			0
$73$	7.72265	−	7.72265i	0.903867	−	0.903867i	−0.0919007	−	0.995768i	$-0.529294\pi$
$73$	7.72265	−	7.72265i	0.903867	−	0.903867i	0.995768	+	0.0919007i	$0.0292942\pi$
$74$		−	7.92810i		−	0.921623i
$75$		0			0
$76$	−3.60663	+	2.44789i	−0.413709	+	0.280793i
$77$	−7.42967	−	7.42967i	−0.846689	−	0.846689i
$78$		0			0
$79$	−17.1528			−1.92984			−0.964918	−	0.262550i	$-0.915437\pi$
$79$	−17.1528			−1.92984			−0.964918	+	0.262550i	$0.915437\pi$
$80$	0.114611	−	2.23313i	0.0128139	−	0.249671i
$81$		0			0
$82$	1.34774	+	1.34774i	0.148833	+	0.148833i
$83$	−5.43217	+	5.43217i	−0.596258	+	0.596258i	−0.939315	−	0.343056i	$-0.888538\pi$
$83$	−5.43217	+	5.43217i	−0.596258	+	0.596258i	0.343056	+	0.939315i	$0.388538\pi$
$84$		0			0
$85$	1.14597	−	1.03408i	0.124298	−	0.112162i
$86$		−	10.0817i		−	1.08714i
$87$		0			0
$88$	−3.74270	−	3.74270i	−0.398973	−	0.398973i
$89$	−5.42118			−0.574644			−0.287322	−	0.957834i	$-0.592765\pi$
$89$	−5.42118			−0.574644			−0.287322	+	0.957834i	$0.592765\pi$
$90$		0			0
$91$			5.38924i			0.564946i
$92$	−3.88930	−	3.88930i	−0.405487	−	0.405487i
$93$		0			0
$94$	11.1298			1.14795
$95$	8.33464	−	5.05310i	0.855116	−	0.518437i
$96$		0			0
$97$	−3.10415	+	3.10415i	−0.315178	+	0.315178i	−0.846912	−	0.531734i	$-0.821541\pi$
$97$	−3.10415	+	3.10415i	−0.315178	+	0.315178i	0.531734	+	0.846912i	$0.321541\pi$
$98$	−2.16328	−	2.16328i	−0.218525	−	0.218525i
$99$		0			0
$100$	−0.511883	+	4.97373i	−0.0511883	+	0.497373i
$101$	2.79454			0.278067			0.139034	−	0.990288i	$-0.455600\pi$
$101$	2.79454			0.278067			0.139034	+	0.990288i	$0.455600\pi$
$102$		0			0
$103$	−4.05319	−	4.05319i	−0.399372	−	0.399372i	0.478639	−	0.878012i	$-0.341130\pi$
$103$	−4.05319	−	4.05319i	−0.399372	−	0.399372i	−0.878012	+	0.478639i	$0.841130\pi$
$104$			2.71483i			0.266211i
$105$		0			0
$106$	−12.6429			−1.22799
$107$	7.04015	−	7.04015i	0.680597	−	0.680597i	−0.279537	−	0.960135i	$-0.590181\pi$
$107$	7.04015	−	7.04015i	0.680597	−	0.680597i	0.960135	+	0.279537i	$0.0901811\pi$
$108$		0			0
$109$	−8.64011			−0.827573			−0.413786	−	0.910374i	$-0.635794\pi$
$109$	−8.64011			−0.827573			−0.413786	+	0.910374i	$0.635794\pi$
$110$	7.92898	+	8.78689i	0.755998	+	0.837797i
$111$		0			0
$112$	1.40368	+	1.40368i	0.132636	+	0.132636i
$113$	6.47280	+	6.47280i	0.608910	+	0.608910i	0.942661	−	0.333751i	$-0.108315\pi$
$113$	6.47280	+	6.47280i	0.608910	+	0.608910i	−0.333751	+	0.942661i	$0.608315\pi$
$114$		0			0
$115$	8.23954	+	9.13105i	0.768341	+	0.851475i
$116$		−	6.19060i		−	0.574782i
$117$		0			0
$118$	0.432173	−	0.432173i	0.0397848	−	0.0397848i
$119$			1.37032i			0.125617i
$120$		0			0
$121$	17.0156			1.54688
$122$	5.87621	−	5.87621i	0.532007	−	0.532007i
$123$		0			0
$124$	7.84986			0.704938
$125$	1.71315	−	11.0483i	0.153228	−	0.988191i
$126$		0			0
$127$	−1.33748	+	1.33748i	−0.118683	+	0.118683i	−0.763954	−	0.645271i	$-0.776744\pi$
$127$	−1.33748	+	1.33748i	−0.118683	+	0.118683i	0.645271	+	0.763954i	$0.276744\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$	0.311150	−	6.06257i	0.0272897	−	0.531723i
$131$	−5.33670			−0.466269			−0.233135	−	0.972444i	$-0.574898\pi$
$131$	−5.33670			−0.466269			−0.233135	+	0.972444i	$0.574898\pi$
$132$		0			0
$133$	−1.62650	+	8.49864i	−0.141036	+	0.736926i
$134$		−	14.4265i		−	1.24626i
$135$		0			0
$136$			0.690302i			0.0591929i
$137$	2.97373	+	2.97373i	0.254063	+	0.254063i	0.822634	−	0.568571i	$-0.192504\pi$
$137$	2.97373	+	2.97373i	0.254063	+	0.254063i	−0.568571	+	0.822634i	$0.692504\pi$
$138$		0			0
$139$			13.8993i			1.17892i	0.807796	+	0.589462i	$0.200660\pi$
$139$			13.8993i			1.17892i	−0.807796	+	0.589462i	$0.799340\pi$
$140$	−2.97373	−	3.29548i	−0.251326	−	0.278519i
$141$		0			0
$142$	−2.80737	−	2.80737i	−0.235589	−	0.235589i
$143$	−10.1608	−	10.1608i	−0.849690	−	0.849690i
$144$		0			0
$145$	−0.709511	+	13.8244i	−0.0589217	+	1.14805i
$146$		−	10.9215i		−	0.903867i
$147$		0			0
$148$	−5.60602	−	5.60602i	−0.460812	−	0.460812i
$149$			12.9453i			1.06052i	0.847834	+	0.530262i	$0.177906\pi$
$149$			12.9453i			1.06052i	−0.847834	+	0.530262i	$0.822094\pi$
$150$		0			0
$151$			21.7518i			1.77013i	0.465465	+	0.885066i	$0.345887\pi$
$151$			21.7518i			1.77013i	−0.465465	+	0.885066i	$0.654113\pi$
$152$	−0.819353	+	4.28120i	−0.0664583	+	0.347251i
$153$		0			0
$154$	−10.5071			−0.846689
$155$	−17.5298	−	0.899682i	−1.40802	−	0.0722642i
$156$		0			0
$157$	2.34642	+	2.34642i	0.187264	+	0.187264i	0.794512	−	0.607248i	$-0.207727\pi$
$157$	2.34642	+	2.34642i	0.187264	+	0.187264i	−0.607248	+	0.794512i	$0.707727\pi$
$158$	−12.1288	+	12.1288i	−0.964918	+	0.964918i
$159$		0			0
$160$	−1.49802	−	1.66010i	−0.118429	−	0.131243i
$161$	−10.9187			−0.860513
$162$		0			0
$163$	−14.1411	+	14.1411i	−1.10761	+	1.10761i	−0.114150	+	0.993464i	$0.536414\pi$
$163$	−14.1411	+	14.1411i	−1.10761	+	1.10761i	−0.993464	+	0.114150i	$0.963586\pi$
$164$	1.90599			0.148833
$165$		0			0
$166$			7.68225i			0.596258i
$167$	−9.19018	+	9.19018i	−0.711157	+	0.711157i	−0.966777	−	0.255620i	$-0.917720\pi$
$167$	−9.19018	+	9.19018i	−0.711157	+	0.711157i	0.255620	+	0.966777i	$0.417720\pi$
$168$		0			0
$169$		−	5.62968i		−	0.433052i
$170$	0.0791163	−	1.54153i	0.00606794	−	0.118230i
$171$		0			0
$172$	−7.12884	−	7.12884i	−0.543569	−	0.543569i
$173$	−2.10806	−	2.10806i	−0.160273	−	0.160273i	0.622415	−	0.782688i	$-0.286152\pi$
$173$	−2.10806	−	2.10806i	−0.160273	−	0.160273i	−0.782688	+	0.622415i	$0.786152\pi$
$174$		0			0
$175$	6.26302	+	7.70006i	0.473440	+	0.582070i
$176$	−5.29298			−0.398973
$177$		0			0
$178$	−3.83335	+	3.83335i	−0.287322	+	0.287322i
$179$	7.93836			0.593341			0.296670	−	0.954980i	$-0.404124\pi$
$179$	7.93836			0.593341			0.296670	+	0.954980i	$0.404124\pi$
$180$		0			0
$181$		−	4.77157i		−	0.354668i	−0.984151	−	0.177334i	$-0.943253\pi$
$181$		−	4.77157i		−	0.354668i	0.984151	−	0.177334i	$-0.0567473\pi$
$182$	3.81077	+	3.81077i	0.282473	+	0.282473i
$183$		0			0
$184$	−5.50029			−0.405487
$185$	11.8764	+	13.1615i	0.873173	+	0.967650i
$186$		0			0
$187$	−2.58359	−	2.58359i	−0.188931	−	0.188931i
$188$	7.86994	−	7.86994i	0.573974	−	0.573974i
$189$		0			0
$190$	2.32039	−	9.46656i	0.168339	−	0.686776i
$191$	13.8711			1.00368			0.501840	−	0.864961i	$-0.332657\pi$
$191$	13.8711			1.00368			0.501840	+	0.864961i	$0.332657\pi$
$192$		0			0
$193$	−8.22061	−	8.22061i	−0.591733	−	0.591733i	0.346367	−	0.938099i	$-0.387415\pi$
$193$	−8.22061	−	8.22061i	−0.591733	−	0.591733i	−0.938099	+	0.346367i	$0.887415\pi$
$194$			4.38992i			0.315178i
$195$		0			0
$196$	−3.05934			−0.218525
$197$	0.844893	+	0.844893i	0.0601961	+	0.0601961i	0.736564	−	0.676368i	$-0.236447\pi$
$197$	0.844893	+	0.844893i	0.0601961	+	0.0601961i	−0.676368	+	0.736564i	$0.736447\pi$
$198$		0			0
$199$		−	17.2265i		−	1.22116i	−0.791956	−	0.610578i	$-0.790937\pi$
$199$		−	17.2265i		−	1.22116i	0.791956	−	0.610578i	$-0.209063\pi$
$200$	3.15500	+	3.87891i	0.223092	+	0.274281i
$201$		0			0
$202$	1.97604	−	1.97604i	0.139034	−	0.139034i
$203$	−8.68964	−	8.68964i	−0.609893	−	0.609893i
$204$		0			0
$205$	−4.25633	−	0.218448i	−0.297275	−	0.0152571i
$206$	−5.73207			−0.399372
$207$		0			0
$208$	1.91968	+	1.91968i	0.133106	+	0.133106i
$209$	−12.9567	−	19.0898i	−0.896230	−	1.32047i
$210$		0			0
$211$		−	7.30842i		−	0.503132i	−0.967840	−	0.251566i	$-0.919054\pi$
$211$		−	7.30842i		−	0.503132i	0.967840	−	0.251566i	$-0.0809456\pi$
$212$	−8.93991	+	8.93991i	−0.613995	+	0.613995i
$213$		0			0
$214$		−	9.95628i		−	0.680597i
$215$	15.1026	+	16.7367i	1.02999	+	1.14143i
$216$		0			0
$217$	11.0187	−	11.0187i	0.748000	−	0.748000i
$218$	−6.10948	+	6.10948i	−0.413786	+	0.413786i
$219$		0			0
$220$	11.8199	+	0.606635i	0.796898	+	0.0408993i
$221$			1.87405i			0.126063i
$222$		0			0
$223$	4.27908	+	4.27908i	0.286548	+	0.286548i	0.835714	−	0.549165i	$-0.185054\pi$
$223$	4.27908	+	4.27908i	0.286548	+	0.286548i	−0.549165	+	0.835714i	$0.685054\pi$
$224$	1.98511			0.132636
$225$		0			0
$226$	9.15392			0.608910
$227$	−13.7190	+	13.7190i	−0.910561	+	0.910561i	−0.996316	−	0.0857552i	$-0.972670\pi$
$227$	−13.7190	+	13.7190i	−0.910561	+	0.910561i	0.0857552	+	0.996316i	$0.472670\pi$
$228$		0			0
$229$			25.2634i			1.66945i	0.550667	+	0.834725i	$0.314373\pi$
$229$			25.2634i			1.66945i	−0.550667	+	0.834725i	$0.685627\pi$
$230$	12.2829	+	0.630395i	0.809908	+	0.0415670i
$231$		0			0
$232$	−4.37741	−	4.37741i	−0.287391	−	0.287391i
$233$	−7.73738	+	7.73738i	−0.506892	+	0.506892i	−0.913571	−	0.406679i	$-0.866687\pi$
$233$	−7.73738	+	7.73738i	−0.506892	+	0.506892i	0.406679	+	0.913571i	$0.366687\pi$
$234$		0			0
$235$	−18.4766	+	16.6726i	−1.20528	+	1.08760i
$236$		−	0.611185i		−	0.0397848i
$237$		0			0
$238$	0.968965	+	0.968965i	0.0628087	+	0.0628087i
$239$		−	11.0820i		−	0.716837i	−0.933561	−	0.358418i	$-0.883316\pi$
$239$		−	11.0820i		−	0.716837i	0.933561	−	0.358418i	$-0.116684\pi$
$240$		0			0
$241$		−	14.5158i		−	0.935043i	−0.883982	−	0.467522i	$-0.845147\pi$
$241$		−	14.5158i		−	0.935043i	0.883982	−	0.467522i	$-0.154853\pi$
$242$	12.0319	−	12.0319i	0.773438	−	0.773438i
$243$		0			0
$244$		−	8.31021i		−	0.532007i
$245$	6.83191	+	0.350635i	0.436475	+	0.0224013i
$246$		0			0
$247$	−2.22441	+	11.6227i	−0.141536	+	0.739537i
$248$	5.55069	−	5.55069i	0.352469	−	0.352469i
$249$		0			0
$250$	−6.60096	−	9.02371i	−0.417481	−	0.570710i
$251$	−6.78199			−0.428075			−0.214038	−	0.976825i	$-0.568662\pi$
$251$	−6.78199			−0.428075			−0.214038	+	0.976825i	$0.568662\pi$
$252$		0			0
$253$	20.5860	−	20.5860i	1.29423	−	1.29423i
$254$			1.89149i			0.118683i
$255$		0			0
$256$	1.00000			0.0625000
$257$	13.1118	−	13.1118i	0.817891	−	0.817891i	−0.167911	−	0.985802i	$-0.553702\pi$
$257$	13.1118	−	13.1118i	0.817891	−	0.817891i	0.985802	+	0.167911i	$0.0537023\pi$
$258$		0			0
$259$	−15.7381			−0.977921
$260$	−4.06687	−	4.50690i	−0.252217	−	0.279506i
$261$		0			0
$262$	−3.77362	+	3.77362i	−0.233135	+	0.233135i
$263$	−8.10698	+	8.10698i	−0.499898	+	0.499898i	−0.911406	−	0.411508i	$-0.865002\pi$
$263$	−8.10698	+	8.10698i	−0.499898	+	0.499898i	0.411508	+	0.911406i	$0.365002\pi$
$264$		0			0
$265$	20.9886	−	18.9393i	1.28932	−	1.16343i
$266$	4.85934	+	7.15956i	0.297945	+	0.438981i
$267$		0			0
$268$	−10.2011	−	10.2011i	−0.623132	−	0.623132i
$269$	16.5207			1.00729			0.503644	−	0.863911i	$-0.331992\pi$
$269$	16.5207			1.00729			0.503644	+	0.863911i	$0.331992\pi$
$270$		0			0
$271$	−1.20001			−0.0728953			−0.0364477	−	0.999336i	$-0.511604\pi$
$271$	−1.20001			−0.0728953			−0.0364477	+	0.999336i	$0.511604\pi$
$272$	0.488117	+	0.488117i	0.0295964	+	0.0295964i
$273$		0			0
$274$	4.20549			0.254063
$275$	−26.3258	−	2.70939i	−1.58751	−	0.163382i
$276$		0			0
$277$	−5.15378	−	5.15378i	−0.309661	−	0.309661i	0.535117	−	0.844778i	$-0.320268\pi$
$277$	−5.15378	−	5.15378i	−0.309661	−	0.309661i	−0.844778	+	0.535117i	$0.820268\pi$
$278$	9.82829	+	9.82829i	0.589462	+	0.589462i
$279$		0			0
$280$	−4.43300	−	0.227516i	−0.264923	−	0.0135967i
$281$			21.1406i			1.26114i	0.776132	+	0.630570i	$0.217179\pi$
$281$			21.1406i			1.26114i	−0.776132	+	0.630570i	$0.782821\pi$
$282$		0			0
$283$	−15.7352	+	15.7352i	−0.935358	+	0.935358i	−0.998034	−	0.0626758i	$-0.980037\pi$
$283$	−15.7352	+	15.7352i	−0.935358	+	0.935358i	0.0626758	+	0.998034i	$0.480037\pi$
$284$	−3.97022			−0.235589
$285$		0			0
$286$	−14.3696			−0.849690
$287$	2.67541	−	2.67541i	0.157924	−	0.157924i
$288$		0			0
$289$		−	16.5235i		−	0.971970i
$290$	9.27362	+	10.2770i	0.544566	+	0.603488i
$291$		0			0
$292$	−7.72265	−	7.72265i	−0.451934	−	0.451934i
$293$	11.6988	+	11.6988i	0.683451	+	0.683451i	0.960776	−	0.277325i	$-0.0894478\pi$
$293$	11.6988	+	11.6988i	0.683451	+	0.683451i	−0.277325	+	0.960776i	$0.589448\pi$
$294$		0			0
$295$	−0.0700487	+	1.36486i	−0.00407839	+	0.0794650i
$296$	−7.92810			−0.460812
$297$		0			0
$298$	9.15374	+	9.15374i	0.530262	+	0.530262i
$299$	−14.9324			−0.863562
$300$		0			0
$301$	−20.0133			−1.15355
$302$	15.3808	+	15.3808i	0.885066	+	0.885066i
$303$		0			0
$304$	2.44789	+	3.60663i	0.140396	+	0.206855i
$305$	−0.952444	+	18.5578i	−0.0545368	+	1.06262i
$306$		0			0
$307$	13.8361	−	13.8361i	0.789668	−	0.789668i	−0.191772	−	0.981440i	$-0.561423\pi$
$307$	13.8361	−	13.8361i	0.789668	−	0.789668i	0.981440	+	0.191772i	$0.0614233\pi$
$308$	−7.42967	+	7.42967i	−0.423345	+	0.423345i
$309$		0			0
$310$	−13.0316	+	11.7592i	−0.740144	+	0.667880i
$311$	0.990577			0.0561705			0.0280852	−	0.999606i	$-0.491059\pi$
$311$	0.990577			0.0561705			0.0280852	+	0.999606i	$0.491059\pi$
$312$		0			0
$313$	5.68394	−	5.68394i	0.321275	−	0.321275i	−0.527981	−	0.849256i	$-0.677051\pi$
$313$	5.68394	−	5.68394i	0.321275	−	0.321275i	0.849256	+	0.527981i	$0.177051\pi$
$314$	3.31834			0.187264
$315$		0			0
$316$			17.1528i			0.964918i
$317$	−9.63331	+	9.63331i	−0.541061	+	0.541061i	−0.923840	−	0.382779i	$-0.874967\pi$
$317$	−9.63331	+	9.63331i	−0.541061	+	0.541061i	0.382779	+	0.923840i	$0.374967\pi$
$318$		0			0
$319$	32.7667			1.83458
$320$	−2.23313	−	0.114611i	−0.124836	−	0.00640696i
$321$		0			0
$322$	−7.72067	+	7.72067i	−0.430256	+	0.430256i
$323$	−0.565601	+	2.95532i	−0.0314709	+	0.164438i
$324$		0			0
$325$	8.56530	+	10.5306i	0.475118	+	0.584133i
$326$			19.9985i			1.10761i
$327$		0			0
$328$	1.34774	−	1.34774i	0.0744165	−	0.0744165i
$329$		−	22.0938i		−	1.21807i
$330$		0			0
$331$			19.9864i			1.09855i	0.835641	+	0.549276i	$0.185096\pi$
$331$			19.9864i			1.09855i	−0.835641	+	0.549276i	$0.814904\pi$
$332$	5.43217	+	5.43217i	0.298129	+	0.298129i
$333$		0			0
$334$			12.9969i			0.711157i
$335$	21.6112	+	23.9495i	1.18075	+	1.30850i
$336$		0			0
$337$	−4.18460	+	4.18460i	−0.227950	+	0.227950i	−0.811836	−	0.583886i	$-0.801532\pi$
$337$	−4.18460	+	4.18460i	−0.227950	+	0.227950i	0.583886	+	0.811836i	$0.301532\pi$
$338$	−3.98078	−	3.98078i	−0.216526	−	0.216526i
$339$		0			0
$340$	−1.03408	−	1.14597i	−0.0560811	−	0.0621490i
$341$			41.5492i			2.25001i
$342$		0			0
$343$	−14.1201	+	14.1201i	−0.762416	+	0.762416i
$344$	−10.0817			−0.543569
$345$		0			0
$346$	−2.98124			−0.160273
$347$	−2.65197	−	2.65197i	−0.142365	−	0.142365i	0.632332	−	0.774697i	$-0.282098\pi$
$347$	−2.65197	−	2.65197i	−0.142365	−	0.142365i	−0.774697	+	0.632332i	$0.782098\pi$
$348$		0			0
$349$		−	17.8125i		−	0.953481i	−0.879044	−	0.476740i	$-0.841818\pi$
$349$		−	17.8125i		−	0.953481i	0.879044	−	0.476740i	$-0.158182\pi$
$350$	9.87339	+	1.01614i	0.527755	+	0.0543151i
$351$		0			0
$352$	−3.74270	+	3.74270i	−0.199487	+	0.199487i
$353$	11.6167	−	11.6167i	0.618293	−	0.618293i	−0.326801	−	0.945093i	$-0.605971\pi$
$353$	11.6167	−	11.6167i	0.618293	−	0.618293i	0.945093	+	0.326801i	$0.105971\pi$
$354$		0			0
$355$	8.86601	+	0.455031i	0.470559	+	0.0241506i
$356$			5.42118i			0.287322i
$357$		0			0
$358$	5.61326	−	5.61326i	0.296670	−	0.296670i
$359$			4.76092i			0.251272i	0.992076	+	0.125636i	$0.0400971\pi$
$359$			4.76092i			0.251272i	−0.992076	+	0.125636i	$0.959903\pi$
$360$		0			0
$361$	−7.01563	+	17.6573i	−0.369243	+	0.929333i
$362$	−3.37401	−	3.37401i	−0.177334	−	0.177334i
$363$		0			0
$364$	5.38924			0.282473
$365$	16.3606	+	18.1308i	0.856351	+	0.949008i
$366$		0			0
$367$	12.6008	+	12.6008i	0.657754	+	0.657754i	0.954848	−	0.297094i	$-0.0960176\pi$
$367$	12.6008	+	12.6008i	0.657754	+	0.657754i	−0.297094	+	0.954848i	$0.596018\pi$
$368$	−3.88930	+	3.88930i	−0.202744	+	0.202744i
$369$		0			0
$370$	17.7045	+	0.908649i	0.920412	+	0.0472384i
$371$			25.0976i			1.30300i
$372$		0			0
$373$	6.72967	+	6.72967i	0.348449	+	0.348449i	0.859532	−	0.511083i	$-0.170755\pi$
$373$	6.72967	+	6.72967i	0.348449	+	0.348449i	−0.511083	+	0.859532i	$0.670755\pi$
$374$	−3.65375			−0.188931
$375$		0			0
$376$		−	11.1298i		−	0.573974i
$377$	−11.8839	−	11.8839i	−0.612054	−	0.612054i
$378$		0			0
$379$	−10.5434			−0.541578			−0.270789	−	0.962639i	$-0.587285\pi$
$379$	−10.5434			−0.541578			−0.270789	+	0.962639i	$0.587285\pi$
$380$	−5.05310	−	8.33464i	−0.259219	−	0.427558i
$381$		0			0
$382$	9.80837	−	9.80837i	0.501840	−	0.501840i
$383$	−8.53662	−	8.53662i	−0.436201	−	0.436201i	0.454530	−	0.890731i	$-0.349807\pi$
$383$	−8.53662	−	8.53662i	−0.436201	−	0.436201i	−0.890731	+	0.454530i	$0.849807\pi$
$384$		0			0
$385$	17.4429	−	15.7399i	0.888974	−	0.802179i
$386$	−11.6257			−0.591733
$387$		0			0
$388$	3.10415	+	3.10415i	0.157589	+	0.157589i
$389$			25.1180i			1.27353i	0.771056	+	0.636767i	$0.219729\pi$
$389$			25.1180i			1.27353i	−0.771056	+	0.636767i	$0.780271\pi$
$390$		0			0
$391$	−3.79686			−0.192016
$392$	−2.16328	+	2.16328i	−0.109262	+	0.109262i
$393$		0			0
$394$	1.19486			0.0601961
$395$	1.96590	−	38.3043i	0.0989151	−	1.92730i
$396$		0			0
$397$	10.0839	+	10.0839i	0.506098	+	0.506098i	0.913326	−	0.407228i	$-0.133505\pi$
$397$	10.0839	+	10.0839i	0.506098	+	0.506098i	−0.407228	+	0.913326i	$0.633505\pi$
$398$	−12.1810	−	12.1810i	−0.610578	−	0.610578i
$399$		0			0
$400$	4.97373	+	0.511883i	0.248686	+	0.0255942i
$401$			1.57077i			0.0784407i	0.999231	+	0.0392203i	$0.0124874\pi$
$401$			1.57077i			0.0784407i	−0.999231	+	0.0392203i	$0.987513\pi$
$402$		0			0
$403$	15.0692	−	15.0692i	0.750651	−	0.750651i
$404$		−	2.79454i		−	0.139034i
$405$		0			0
$406$	−12.2890			−0.609893
$407$	29.6725	−	29.6725i	1.47081	−	1.47081i
$408$		0			0
$409$	10.9037			0.539153			0.269576	−	0.962979i	$-0.413116\pi$
$409$	10.9037			0.539153			0.269576	+	0.962979i	$0.413116\pi$
$410$	−3.16414	+	2.85521i	−0.156266	+	0.141009i
$411$		0			0
$412$	−4.05319	+	4.05319i	−0.199686	+	0.199686i
$413$	−0.857911	−	0.857911i	−0.0422150	−	0.0422150i
$414$		0			0
$415$	−11.5082	−	12.7533i	−0.564913	−	0.626036i
$416$	2.71483			0.133106
$417$		0			0
$418$	−22.6603	−	4.33682i	−1.10835	−	0.212121i
$419$			6.93967i			0.339025i	0.985528	+	0.169512i	$0.0542193\pi$
$419$			6.93967i			0.339025i	−0.985528	+	0.169512i	$0.945781\pi$
$420$		0			0
$421$			17.7896i			0.867010i	0.901151	+	0.433505i	$0.142723\pi$
$421$			17.7896i			0.867010i	−0.901151	+	0.433505i	$0.857277\pi$
$422$	−5.16783	−	5.16783i	−0.251566	−	0.251566i
$423$		0			0
$424$			12.6429i			0.613995i
$425$	2.17790	+	2.67762i	0.105644	+	0.129884i
$426$		0			0
$427$	−11.6649	−	11.6649i	−0.564505	−	0.564505i
$428$	−7.04015	−	7.04015i	−0.340299	−	0.340299i
$429$		0			0
$430$	22.5137	+	1.15548i	1.08571	+	0.0557220i
$431$			35.0344i			1.68755i	0.536697	+	0.843775i	$0.319672\pi$
$431$			35.0344i			1.68755i	−0.536697	+	0.843775i	$0.680328\pi$
$432$		0			0
$433$	14.6222	+	14.6222i	0.702699	+	0.702699i	0.964989	−	0.262290i	$-0.0844778\pi$
$433$	14.6222	+	14.6222i	0.702699	+	0.702699i	−0.262290	+	0.964989i	$0.584478\pi$
$434$		−	15.5828i		−	0.748000i
$435$		0			0
$436$			8.64011i			0.413786i
$437$	−23.5479	−	4.50668i	−1.12645	−	0.215584i
$438$		0			0
$439$	−25.2333			−1.20432			−0.602160	−	0.798376i	$-0.705693\pi$
$439$	−25.2333			−1.20432			−0.602160	+	0.798376i	$0.705693\pi$
$440$	8.78689	−	7.92898i	0.418899	−	0.377999i
$441$		0			0
$442$	1.32516	+	1.32516i	0.0630313	+	0.0630313i
$443$	17.3294	−	17.3294i	0.823344	−	0.823344i	−0.163242	−	0.986586i	$-0.552195\pi$
$443$	17.3294	−	17.3294i	0.823344	−	0.823344i	0.986586	+	0.163242i	$0.0521952\pi$
$444$		0			0
$445$	0.621328	−	12.1062i	0.0294538	−	0.573888i
$446$	6.05153			0.286548
$447$		0			0
$448$	1.40368	−	1.40368i	0.0663178	−	0.0663178i
$449$	−20.6855			−0.976211			−0.488105	−	0.872785i	$-0.662312\pi$
$449$	−20.6855			−0.976211			−0.488105	+	0.872785i	$0.662312\pi$
$450$		0			0
$451$			10.0884i			0.475043i
$452$	6.47280	−	6.47280i	0.304455	−	0.304455i
$453$		0			0
$454$			19.4016i			0.910561i
$455$	−12.0349	−	0.617667i	−0.564203	−	0.0289567i
$456$		0			0
$457$	−7.86170	−	7.86170i	−0.367755	−	0.367755i	0.498903	−	0.866658i	$-0.333736\pi$
$457$	−7.86170	−	7.86170i	−0.367755	−	0.367755i	−0.866658	+	0.498903i	$0.833736\pi$
$458$	17.8639	+	17.8639i	0.834725	+	0.834725i
$459$		0			0
$460$	9.13105	−	8.23954i	0.425738	−	0.384171i
$461$	−23.8664			−1.11157			−0.555784	−	0.831327i	$-0.687582\pi$
$461$	−23.8664			−1.11157			−0.555784	+	0.831327i	$0.687582\pi$
$462$		0			0
$463$	22.3224	−	22.3224i	1.03741	−	1.03741i	0.0381357	−	0.999273i	$-0.487858\pi$
$463$	22.3224	−	22.3224i	1.03741	−	1.03741i	0.999273	−	0.0381357i	$-0.0121419\pi$
$464$	−6.19060			−0.287391
$465$		0			0
$466$			10.9423i			0.506892i
$467$	−20.6661	−	20.6661i	−0.956312	−	0.956312i	0.0427727	−	0.999085i	$-0.486381\pi$
$467$	−20.6661	−	20.6661i	−0.956312	−	0.956312i	−0.999085	+	0.0427727i	$0.986381\pi$
$468$		0			0
$469$	−28.6382			−1.32239
$470$	−1.27560	+	24.8542i	−0.0588389	+	1.14644i
$471$		0			0
$472$	−0.432173	−	0.432173i	−0.0198924	−	0.0198924i
$473$	37.7328	−	37.7328i	1.73495	−	1.73495i
$474$		0			0
$475$	10.3290	+	19.1915i	0.473926	+	0.880564i
$476$	1.37032			0.0628087
$477$		0			0
$478$	−7.83618	−	7.83618i	−0.358418	−	0.358418i
$479$			15.9212i			0.727459i	0.931505	+	0.363730i	$0.118497\pi$
$479$			15.9212i			0.727459i	−0.931505	+	0.363730i	$0.881503\pi$
$480$		0			0
$481$	−21.5235			−0.981386
$482$	−10.2642	−	10.2642i	−0.467522	−	0.467522i
$483$		0			0
$484$		−	17.0156i		−	0.773438i
$485$	−6.57619	−	7.28773i	−0.298609	−	0.330919i
$486$		0			0
$487$	−10.4874	+	10.4874i	−0.475228	+	0.475228i	−0.903602	−	0.428374i	$-0.859087\pi$
$487$	−10.4874	+	10.4874i	−0.475228	+	0.475228i	0.428374	+	0.903602i	$0.359087\pi$
$488$	−5.87621	−	5.87621i	−0.266003	−	0.266003i
$489$		0			0
$490$	5.07883	−	4.58295i	0.229438	−	0.207037i
$491$	−15.8352			−0.714633			−0.357317	−	0.933983i	$-0.616308\pi$
$491$	−15.8352			−0.714633			−0.357317	+	0.933983i	$0.616308\pi$
$492$		0			0
$493$	−3.02173	−	3.02173i	−0.136092	−	0.136092i
$494$	6.64563	+	9.79141i	0.299001	+	0.440537i
$495$		0			0
$496$		−	7.84986i		−	0.352469i
$497$	−5.57293	+	5.57293i	−0.249980	+	0.249980i
$498$		0			0
$499$		−	21.1108i		−	0.945050i	−0.881317	−	0.472525i	$-0.843343\pi$
$499$		−	21.1108i		−	0.945050i	0.881317	−	0.472525i	$-0.156657\pi$
$500$	−11.0483	−	1.71315i	−0.494095	−	0.0766142i
$501$		0			0
$502$	−4.79559	+	4.79559i	−0.214038	+	0.214038i
$503$	−11.3484	+	11.3484i	−0.506001	+	0.506001i	−0.913297	−	0.407295i	$-0.866472\pi$
$503$	−11.3484	+	11.3484i	−0.506001	+	0.506001i	0.407295	+	0.913297i	$0.366472\pi$
$504$		0			0
$505$	−0.320286	+	6.24058i	−0.0142525	+	0.277702i
$506$		−	29.1129i		−	1.29423i
$507$		0			0
$508$	1.33748	+	1.33748i	0.0593413	+	0.0593413i
$509$	36.8026			1.63125			0.815624	−	0.578582i	$-0.196394\pi$
$509$	36.8026			1.63125			0.815624	+	0.578582i	$0.196394\pi$
$510$		0			0
$511$	−21.6803			−0.959080
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	18.5429i		−	0.817891i
$515$	9.51583	−	8.58674i	0.419317	−	0.378377i
$516$		0			0
$517$	41.6554	+	41.6554i	1.83200	+	1.83200i
$518$	−11.1285	+	11.1285i	−0.488960	+	0.488960i
$519$		0			0
$520$	−6.06257	−	0.311150i	−0.265861	−	0.0136448i
$521$		−	6.00142i		−	0.262927i	−0.991321	−	0.131463i	$-0.958032\pi$
$521$		−	6.00142i		−	0.262927i	0.991321	−	0.131463i	$-0.0419676\pi$
$522$		0			0
$523$	−19.4311	−	19.4311i	−0.849664	−	0.849664i	0.140427	−	0.990091i	$-0.455152\pi$
$523$	−19.4311	−	19.4311i	−0.849664	−	0.849664i	−0.990091	+	0.140427i	$0.955152\pi$
$524$			5.33670i			0.233135i
$525$		0			0
$526$			11.4650i			0.499898i
$527$	3.83165	−	3.83165i	0.166909	−	0.166909i
$528$		0			0
$529$		−	7.25324i		−	0.315358i
$530$	1.44902	−	28.2333i	0.0629415	−	1.22638i
$531$		0			0
$532$	8.49864	+	1.62650i	0.368463	+	0.0705179i
$533$	3.65889	−	3.65889i	0.158484	−	0.158484i
$534$		0			0
$535$	14.9147	+	16.5285i	0.644818	+	0.714587i
$536$	−14.4265			−0.623132
$537$		0			0
$538$	11.6819	−	11.6819i	0.503644	−	0.503644i
$539$		−	16.1930i		−	0.697484i
$540$		0			0
$541$	19.3859			0.833467			0.416734	−	0.909029i	$-0.363175\pi$
$541$	19.3859			0.833467			0.416734	+	0.909029i	$0.363175\pi$
$542$	−0.848534	+	0.848534i	−0.0364477	+	0.0364477i
$543$		0			0
$544$	0.690302			0.0295964
$545$	0.990253	−	19.2945i	0.0424178	−	0.826485i
$546$		0			0
$547$	6.28887	−	6.28887i	0.268893	−	0.268893i	−0.559761	−	0.828654i	$-0.689107\pi$
$547$	6.28887	−	6.28887i	0.268893	−	0.268893i	0.828654	+	0.559761i	$0.189107\pi$
$548$	2.97373	−	2.97373i	0.127031	−	0.127031i
$549$		0			0
$550$	−20.5310	+	16.6994i	−0.875445	+	0.712063i
$551$	−15.1539	−	22.3272i	−0.645579	−	0.951171i
$552$		0			0
$553$	24.0771	+	24.0771i	1.02386	+	1.02386i
$554$	−7.28855			−0.309661
$555$		0			0
$556$	13.8993			0.589462
$557$	−9.88148	−	9.88148i	−0.418692	−	0.418692i	0.466061	−	0.884753i	$-0.345673\pi$
$557$	−9.88148	−	9.88148i	−0.418692	−	0.418692i	−0.884753	+	0.466061i	$0.845673\pi$
$558$		0			0
$559$	−27.3701			−1.15763
$560$	−3.29548	+	2.97373i	−0.139260	+	0.125663i
$561$		0			0
$562$	14.9486	+	14.9486i	0.630570	+	0.630570i
$563$	16.7009	+	16.7009i	0.703858	+	0.703858i	0.965236	−	0.261379i	$-0.0841771\pi$
$563$	16.7009	+	16.7009i	0.703858	+	0.703858i	−0.261379	+	0.965236i	$0.584177\pi$
$564$		0			0
$565$	−15.1965	+	13.7127i	−0.639320	+	0.576900i
$566$			22.2529i			0.935358i
$567$		0			0
$568$	−2.80737	+	2.80737i	−0.117795	+	0.117795i
$569$	−1.12910			−0.0473344			−0.0236672	−	0.999720i	$-0.507534\pi$
$569$	−1.12910			−0.0473344			−0.0236672	+	0.999720i	$0.507534\pi$
$570$		0			0
$571$	−7.89992			−0.330602			−0.165301	−	0.986243i	$-0.552859\pi$
$571$	−7.89992			−0.330602			−0.165301	+	0.986243i	$0.552859\pi$
$572$	−10.1608	+	10.1608i	−0.424845	+	0.424845i
$573$		0			0
$574$		−	3.78360i		−	0.157924i
$575$	−21.3352	+	17.3534i	−0.889738	+	0.723688i
$576$		0			0
$577$	−31.1021	−	31.1021i	−1.29480	−	1.29480i	−0.931785	−	0.363011i	$-0.881749\pi$
$577$	−31.1021	−	31.1021i	−1.29480	−	1.29480i	−0.363011	−	0.931785i	$-0.618251\pi$
$578$	−11.6839	−	11.6839i	−0.485985	−	0.485985i
$579$		0			0
$580$	13.8244	+	0.709511i	0.574027	+	0.0294609i
$581$	15.2501			0.632681
$582$		0			0
$583$	−47.3187	−	47.3187i	−1.95974	−	1.95974i
$584$	−10.9215			−0.451934
$585$		0			0
$586$	16.5446			0.683451
$587$	6.49465	+	6.49465i	0.268063	+	0.268063i	0.828319	−	0.560256i	$-0.189297\pi$
$587$	6.49465	+	6.49465i	0.268063	+	0.268063i	−0.560256	+	0.828319i	$0.689297\pi$
$588$		0			0
$589$	28.3116	−	19.2156i	1.16656	−	0.791766i
$590$	0.915567	+	1.01463i	0.0376933	+	0.0417717i
$591$		0			0
$592$	−5.60602	+	5.60602i	−0.230406	+	0.230406i
$593$	−16.2871	+	16.2871i	−0.668830	+	0.668830i	−0.957445	−	0.288615i	$-0.906805\pi$
$593$	−16.2871	+	16.2871i	−0.668830	+	0.668830i	0.288615	+	0.957445i	$0.406805\pi$
$594$		0			0
$595$	−3.06011	−	0.157054i	−0.125452	−	0.00643860i
$596$	12.9453			0.530262
$597$		0			0
$598$	−10.5588	+	10.5588i	−0.431781	+	0.431781i
$599$	45.2347			1.84824			0.924119	−	0.382104i	$-0.124800\pi$
$599$	45.2347			1.84824			0.924119	+	0.382104i	$0.124800\pi$
$600$		0			0
$601$		−	18.3122i		−	0.746972i	−0.927636	−	0.373486i	$-0.878162\pi$
$601$		−	18.3122i		−	0.746972i	0.927636	−	0.373486i	$-0.121838\pi$
$602$	−14.1515	+	14.1515i	−0.576773	+	0.576773i
$603$		0			0
$604$	21.7518			0.885066
$605$	−1.95018	+	37.9981i	−0.0792861	+	1.54484i
$606$		0			0
$607$	−17.5130	+	17.5130i	−0.710829	+	0.710829i	−0.966709	−	0.255879i	$-0.917635\pi$
$607$	−17.5130	+	17.5130i	−0.710829	+	0.710829i	0.255879	+	0.966709i	$0.417635\pi$
$608$	4.28120	+	0.819353i	0.173626	+	0.0332292i
$609$		0			0
$610$	12.4489	+	13.7958i	0.504039	+	0.558576i
$611$		−	30.2155i		−	1.22239i
$612$		0			0
$613$	2.65427	−	2.65427i	0.107205	−	0.107205i	−0.651470	−	0.758675i	$-0.725847\pi$
$613$	2.65427	−	2.65427i	0.107205	−	0.107205i	0.758675	+	0.651470i	$0.225847\pi$
$614$		−	19.5672i		−	0.789668i
$615$		0			0
$616$			10.5071i			0.423345i
$617$	−6.67261	−	6.67261i	−0.268629	−	0.268629i	0.559919	−	0.828548i	$-0.310832\pi$
$617$	−6.67261	−	6.67261i	−0.268629	−	0.268629i	−0.828548	+	0.559919i	$0.810832\pi$
$618$		0			0
$619$			21.6368i			0.869657i	0.900513	+	0.434829i	$0.143191\pi$
$619$			21.6368i			0.869657i	−0.900513	+	0.434829i	$0.856809\pi$
$620$	−0.899682	+	17.5298i	−0.0361321	+	0.704012i
$621$		0			0
$622$	0.700444	−	0.700444i	0.0280852	−	0.0280852i
$623$	7.60962	+	7.60962i	0.304873	+	0.304873i
$624$		0			0
$625$	24.4760	+	5.09193i	0.979038	+	0.203677i
$626$		−	8.03830i		−	0.321275i
$627$		0			0
$628$	2.34642	−	2.34642i	0.0936322	−	0.0936322i
$629$	−5.47278			−0.218214
$630$		0			0
$631$	−0.652184			−0.0259631			−0.0129815	−	0.999916i	$-0.504132\pi$
$631$	−0.652184			−0.0259631			−0.0129815	+	0.999916i	$0.504132\pi$
$632$	12.1288	+	12.1288i	0.482459	+	0.482459i
$633$		0			0
$634$			13.6236i			0.541061i
$635$	−2.83349	−	3.14007i	−0.112443	−	0.124610i
$636$		0			0
$637$	−5.87295	+	5.87295i	−0.232695	+	0.232695i
$638$	23.1696	−	23.1696i	0.917291	−	0.917291i
$639$		0			0
$640$	−1.66010	+	1.49802i	−0.0656213	+	0.0592144i
$641$			6.00938i			0.237356i	0.992933	+	0.118678i	$0.0378657\pi$
$641$			6.00938i			0.237356i	−0.992933	+	0.118678i	$0.962134\pi$
$642$		0			0
$643$	−7.37061	+	7.37061i	−0.290669	+	0.290669i	−0.837344	−	0.546676i	$-0.815893\pi$
$643$	−7.37061	+	7.37061i	−0.290669	+	0.290669i	0.546676	+	0.837344i	$0.315893\pi$
$644$			10.9187i			0.430256i
$645$		0			0
$646$	1.68979	+	2.48967i	0.0664837	+	0.0979546i
$647$	−6.73802	−	6.73802i	−0.264899	−	0.264899i	0.562142	−	0.827041i	$-0.309977\pi$
$647$	−6.73802	−	6.73802i	−0.264899	−	0.264899i	−0.827041	+	0.562142i	$0.809977\pi$
$648$		0			0
$649$	3.23499			0.126985
$650$	13.5028	+	1.38968i	0.529625	+	0.0545076i
$651$		0			0
$652$	14.1411	+	14.1411i	0.553807	+	0.553807i
$653$	4.47188	−	4.47188i	0.174998	−	0.174998i	−0.614173	−	0.789171i	$-0.710510\pi$
$653$	4.47188	−	4.47188i	0.174998	−	0.174998i	0.789171	+	0.614173i	$0.210510\pi$
$654$		0			0
$655$	0.611645	−	11.9175i	0.0238990	−	0.465657i
$656$		−	1.90599i		−	0.0744165i
$657$		0			0
$658$	−15.6227	−	15.6227i	−0.609036	−	0.609036i
$659$	−29.4239			−1.14619			−0.573096	−	0.819489i	$-0.694258\pi$
$659$	−29.4239			−1.14619			−0.573096	+	0.819489i	$0.694258\pi$
$660$		0			0
$661$			18.0453i			0.701881i	0.936398	+	0.350941i	$0.114138\pi$
$661$			18.0453i			0.701881i	−0.936398	+	0.350941i	$0.885862\pi$
$662$	14.1325	+	14.1325i	0.549276	+	0.549276i
$663$		0			0
$664$	7.68225			0.298129
$665$	−18.7921	−	4.60623i	−0.728728	−	0.178622i
$666$		0			0
$667$	24.0771	−	24.0771i	0.932267	−	0.932267i
$668$	9.19018	+	9.19018i	0.355579	+	0.355579i
$669$		0			0
$670$	32.2163	+	1.65344i	1.24462	+	0.0638781i
$671$	43.9858			1.69805
$672$		0			0
$673$	−8.20956	−	8.20956i	−0.316455	−	0.316455i	0.530949	−	0.847404i	$-0.321836\pi$
$673$	−8.20956	−	8.20956i	−0.316455	−	0.316455i	−0.847404	+	0.530949i	$0.821836\pi$
$674$			5.91793i			0.227950i
$675$		0			0
$676$	−5.62968			−0.216526
$677$	24.0239	−	24.0239i	0.923313	−	0.923313i	−0.0739493	−	0.997262i	$-0.523560\pi$
$677$	24.0239	−	24.0239i	0.923313	−	0.923313i	0.997262	+	0.0739493i	$0.0235603\pi$
$678$		0			0
$679$	8.71448			0.334431
$680$	−1.54153	−	0.0791163i	−0.0591151	−	0.00303397i
$681$		0			0
$682$	29.3797	+	29.3797i	1.12501	+	1.12501i
$683$	14.5663	+	14.5663i	0.557363	+	0.557363i	0.928556	−	0.371192i	$-0.121051\pi$
$683$	14.5663	+	14.5663i	0.557363	+	0.557363i	−0.371192	+	0.928556i	$0.621051\pi$
$684$		0			0
$685$	−6.98154	+	6.29990i	−0.266751	+	0.240707i
$686$			19.9689i			0.762416i
$687$		0			0
$688$	−7.12884	+	7.12884i	−0.271784	+	0.271784i
$689$			34.3235i			1.30762i
$690$		0			0
$691$	−39.3797			−1.49807			−0.749037	−	0.662528i	$-0.769483\pi$
$691$	−39.3797			−1.49807			−0.749037	+	0.662528i	$0.769483\pi$
$692$	−2.10806	+	2.10806i	−0.0801363	+	0.0801363i
$693$		0			0
$694$	−3.75046			−0.142365
$695$	−31.0389	−	1.59302i	−1.17737	−	0.0604265i
$696$		0			0
$697$	0.930347	−	0.930347i	0.0352394	−	0.0352394i
$698$	−12.5953	−	12.5953i	−0.476740	−	0.476740i
$699$		0			0
$700$	7.70006	−	6.26302i	0.291035	−	0.236720i
$701$	−5.40623			−0.204190			−0.102095	−	0.994775i	$-0.532555\pi$
$701$	−5.40623			−0.204190			−0.102095	+	0.994775i	$0.532555\pi$
$702$		0			0
$703$	−33.9418	−	6.49592i	−1.28014	−	0.244998i
$704$			5.29298i			0.199487i
$705$		0			0
$706$		−	16.4284i		−	0.618293i
$707$	−3.92266	−	3.92266i	−0.147527	−	0.147527i
$708$		0			0
$709$			10.1007i			0.379340i	0.981848	+	0.189670i	$0.0607418\pi$
$709$			10.1007i			0.379340i	−0.981848	+	0.189670i	$0.939258\pi$
$710$	6.59097	−	5.94746i	0.247355	−	0.223204i
$711$		0			0
$712$	3.83335	+	3.83335i	0.143661	+	0.143661i
$713$	30.5304	+	30.5304i	1.14337	+	1.14337i
$714$		0			0
$715$	23.8549	−	21.5259i	0.892124	−	0.805022i
$716$		−	7.93836i		−	0.296670i
$717$		0			0
$718$	3.36648	+	3.36648i	0.125636	+	0.125636i
$719$			41.4079i			1.54425i	0.635469	+	0.772126i	$0.280807\pi$
$719$			41.4079i			1.54425i	−0.635469	+	0.772126i	$0.719193\pi$
$720$		0			0
$721$			11.3788i			0.423768i
$722$	7.52482	+	17.4464i	0.280045	+	0.649288i
$723$		0			0
$724$	−4.77157			−0.177334
$725$	−30.7903	−	3.16886i	−1.14352	−	0.117689i
$726$		0			0
$727$	16.2887	+	16.2887i	0.604113	+	0.604113i	0.941401	−	0.337288i	$-0.109510\pi$
$727$	16.2887	+	16.2887i	0.604113	+	0.604113i	−0.337288	+	0.941401i	$0.609510\pi$
$728$	3.81077	−	3.81077i	0.141236	−	0.141236i
$729$		0			0
$730$	24.3891	+	1.25172i	0.902679	+	0.0463283i
$731$	−6.95941			−0.257403
$732$		0			0
$733$	−8.03197	+	8.03197i	−0.296667	+	0.296667i	−0.839707	−	0.543040i	$-0.817273\pi$
$733$	−8.03197	+	8.03197i	−0.296667	+	0.296667i	0.543040	+	0.839707i	$0.317273\pi$
$734$	17.8202			0.657754
$735$		0			0
$736$			5.50029i			0.202744i
$737$	53.9942	−	53.9942i	1.98890	−	1.98890i
$738$		0			0
$739$			2.95079i			0.108546i	0.998526	+	0.0542732i	$0.0172842\pi$
$739$			2.95079i			0.108546i	−0.998526	+	0.0542732i	$0.982716\pi$
$740$	13.1615	−	11.8764i	0.483825	−	0.436587i
$741$		0			0
$742$	17.7467	+	17.7467i	0.651501	+	0.651501i
$743$	−15.8575	−	15.8575i	−0.581756	−	0.581756i	0.353630	−	0.935386i	$-0.384947\pi$
$743$	−15.8575	−	15.8575i	−0.581756	−	0.581756i	−0.935386	+	0.353630i	$0.884947\pi$
$744$		0			0
$745$	−28.9086	−	1.48368i	−1.05913	−	0.0543579i
$746$	9.51719			0.348449
$747$		0			0
$748$	−2.58359	+	2.58359i	−0.0944655	+	0.0944655i
$749$	−19.7643			−0.722172
$750$		0			0
$751$		−	42.3190i		−	1.54424i	−0.635475	−	0.772121i	$-0.719196\pi$
$751$		−	42.3190i		−	1.54424i	0.635475	−	0.772121i	$-0.280804\pi$
$752$	−7.86994	−	7.86994i	−0.286987	−	0.286987i
$753$		0			0
$754$	−16.8064			−0.612054
$755$	−48.5745	−	2.49299i	−1.76781	−	0.0907294i
$756$		0			0
$757$	6.14572	+	6.14572i	0.223370	+	0.223370i	0.809916	−	0.586546i	$-0.199513\pi$
$757$	6.14572	+	6.14572i	0.223370	+	0.223370i	−0.586546	+	0.809916i	$0.699513\pi$
$758$	−7.45532	+	7.45532i	−0.270789	+	0.270789i
$759$		0			0
$760$	−9.46656	−	2.32039i	−0.343388	−	0.0841695i
$761$	32.5422			1.17966			0.589828	−	0.807529i	$-0.299196\pi$
$761$	32.5422			1.17966			0.589828	+	0.807529i	$0.299196\pi$
$762$		0			0
$763$	12.1280	+	12.1280i	0.439063	+	0.439063i
$764$		−	13.8711i		−	0.501840i
$765$		0			0
$766$	−12.0726			−0.436201
$767$	−1.17328	−	1.17328i	−0.0423646	−	0.0423646i
$768$		0			0
$769$		−	7.15156i		−	0.257892i	−0.991652	−	0.128946i	$-0.958841\pi$
$769$		−	7.15156i		−	0.257892i	0.991652	−	0.128946i	$-0.0411594\pi$
$770$	1.20424	−	23.4638i	0.0433976	−	0.845576i
$771$		0			0
$772$	−8.22061	+	8.22061i	−0.295866	+	0.295866i
$773$	−28.5163	−	28.5163i	−1.02566	−	1.02566i	−0.999662	−	0.0259998i	$-0.991723\pi$
$773$	−28.5163	−	28.5163i	−1.02566	−	1.02566i	−0.0259998	−	0.999662i	$-0.508277\pi$
$774$		0			0
$775$	4.01821	−	39.0431i	0.144338	−	1.40247i
$776$	4.38992			0.157589
$777$		0			0
$778$	17.7611	+	17.7611i	0.636767	+	0.636767i
$779$	6.87422	−	4.66567i	0.246294	−	0.167165i
$780$		0			0
$781$		−	21.0143i		−	0.751950i
$782$	−2.68479	+	2.68479i	−0.0960078	+	0.0960078i
$783$		0			0
$784$			3.05934i			0.109262i
$785$	−5.50878	+	4.97093i	−0.196617	+	0.177420i
$786$		0			0
$787$	38.7817	−	38.7817i	1.38242	−	1.38242i	0.542110	−	0.840308i	$-0.317626\pi$
$787$	38.7817	−	38.7817i	1.38242	−	1.38242i	0.840308	−	0.542110i	$-0.182374\pi$
$788$	0.844893	−	0.844893i	0.0300981	−	0.0300981i
$789$		0			0
$790$	−25.6952	−	28.4754i	−0.914193	−	1.01311i
$791$		−	18.1715i		−	0.646105i
$792$		0			0
$793$	−15.9529	−	15.9529i	−0.566505	−	0.566505i
$794$	14.2608			0.506098
$795$		0			0
$796$	−17.2265			−0.610578
$797$	2.30137	−	2.30137i	0.0815186	−	0.0815186i	−0.665172	−	0.746690i	$-0.731642\pi$
$797$	2.30137	−	2.30137i	0.0815186	−	0.0815186i	0.746690	+	0.665172i	$0.231642\pi$
$798$		0			0
$799$		−	7.68290i		−	0.271802i
$800$	3.87891	−	3.15500i	0.137140	−	0.111546i
$801$		0			0
$802$	1.11070	+	1.11070i	0.0392203	+	0.0392203i
$803$	40.8758	−	40.8758i	1.44248	−	1.44248i
$804$		0			0
$805$	1.25140	−	24.3828i	0.0441062	−	0.859381i
$806$		−	21.3111i		−	0.750651i
$807$		0			0
$808$	−1.97604	−	1.97604i	−0.0695169	−	0.0695169i
$809$			14.9375i			0.525175i	0.964908	+	0.262588i	$0.0845759\pi$
$809$			14.9375i			0.525175i	−0.964908	+	0.262588i	$0.915424\pi$
$810$		0			0
$811$			4.87288i			0.171110i	0.996333	+	0.0855550i	$0.0272663\pi$
$811$			4.87288i			0.171110i	−0.996333	+	0.0855550i	$0.972734\pi$
$812$	−8.68964	+	8.68964i	−0.304947	+	0.304947i
$813$		0			0
$814$		−	41.9633i		−	1.47081i
$815$	−29.9581	−	33.1995i	−1.04939	−	1.16293i
$816$		0			0
$817$	−43.1617	−	8.26047i	−1.51004	−	0.288997i
$818$	7.71007	−	7.71007i	0.269576	−	0.269576i
$819$		0			0
$820$	−0.218448	+	4.25633i	−0.00762854	+	0.148637i
$821$	56.8328			1.98348			0.991739	−	0.128271i	$-0.0409428\pi$
$821$	56.8328			1.98348			0.991739	+	0.128271i	$0.0409428\pi$
$822$		0			0
$823$	23.0205	−	23.0205i	0.802444	−	0.802444i	−0.181033	−	0.983477i	$-0.557944\pi$
$823$	23.0205	−	23.0205i	0.802444	−	0.802444i	0.983477	+	0.181033i	$0.0579441\pi$
$824$			5.73207i			0.199686i
$825$		0			0
$826$	−1.21327			−0.0422150
$827$	−31.6640	+	31.6640i	−1.10106	+	1.10106i	−0.106782	+	0.994282i	$0.534055\pi$
$827$	−31.6640	+	31.6640i	−1.10106	+	1.10106i	−0.994282	+	0.106782i	$0.965945\pi$
$828$		0			0
$829$	44.3087			1.53891			0.769453	−	0.638704i	$-0.220529\pi$
$829$	44.3087			1.53891			0.769453	+	0.638704i	$0.220529\pi$
$830$	−17.1555	−	0.880472i	−0.595475	−	0.0305616i
$831$		0			0
$832$	1.91968	−	1.91968i	0.0665528	−	0.0665528i
$833$	−1.49332	+	1.49332i	−0.0517404	+	0.0517404i
$834$		0			0
$835$	−19.4695	−	21.5761i	−0.673771	−	0.746673i
$836$	−19.0898	+	12.9567i	−0.660236	+	0.448115i
$837$		0			0
$838$	4.90709	+	4.90709i	0.169512	+	0.169512i
$839$	−1.55759			−0.0537739			−0.0268870	−	0.999638i	$-0.508559\pi$
$839$	−1.55759			−0.0537739			−0.0268870	+	0.999638i	$0.508559\pi$
$840$		0			0
$841$	9.32348			0.321499
$842$	12.5791	+	12.5791i	0.433505	+	0.433505i
$843$		0			0
$844$	−7.30842			−0.251566
$845$	12.5718	+	0.645224i	0.432483	+	0.0221964i
$846$		0			0
$847$	−23.8846	−	23.8846i	−0.820683	−	0.820683i
$848$	8.93991	+	8.93991i	0.306998	+	0.306998i
$849$		0			0
$850$	3.43337	+	0.353354i	0.117764	+	0.0121199i
$851$		−	43.6069i		−	1.49483i
$852$		0			0
$853$	−8.05684	+	8.05684i	−0.275861	+	0.275861i	−0.831454	−	0.555593i	$-0.812491\pi$
$853$	−8.05684	+	8.05684i	−0.275861	+	0.275861i	0.555593	+	0.831454i	$0.312491\pi$
$854$	−16.4967			−0.564505
$855$		0			0
$856$	−9.95628			−0.340299
$857$	35.7901	−	35.7901i	1.22257	−	1.22257i	0.255850	−	0.966716i	$-0.417645\pi$
$857$	35.7901	−	35.7901i	1.22257	−	1.22257i	0.966716	−	0.255850i	$-0.0823553\pi$
$858$		0			0
$859$			49.8517i			1.70092i	0.526042	+	0.850459i	$0.323676\pi$
$859$			49.8517i			1.70092i	−0.526042	+	0.850459i	$0.676324\pi$
$860$	16.7367	−	15.1026i	0.570715	−	0.514993i
$861$		0			0
$862$	24.7731	+	24.7731i	0.843775	+	0.843775i
$863$	37.1291	+	37.1291i	1.26389	+	1.26389i	0.949192	+	0.314698i	$0.101903\pi$
$863$	37.1291	+	37.1291i	1.26389	+	1.26389i	0.314698	+	0.949192i	$0.398097\pi$
$864$		0			0
$865$	4.94917	−	4.46596i	0.168277	−	0.151847i
$866$	20.6789			0.702699
$867$		0			0
$868$	−11.0187	−	11.0187i	−0.374000	−	0.374000i
$869$	−90.7892			−3.07981
$870$		0			0
$871$	−39.1657			−1.32708
$872$	6.10948	+	6.10948i	0.206893	+	0.206893i
$873$		0			0
$874$	−19.8376	+	13.4641i	−0.671015	+	0.455431i
$875$	−17.9130	+	13.1036i	−0.605571	+	0.442983i
$876$		0			0
$877$	9.31345	−	9.31345i	0.314493	−	0.314493i	−0.532154	−	0.846647i	$-0.678617\pi$
$877$	9.31345	−	9.31345i	0.314493	−	0.314493i	0.846647	+	0.532154i	$0.178617\pi$
$878$	−17.8426	+	17.8426i	−0.602160	+	0.602160i
$879$		0			0
$880$	0.606635	−	11.8199i	0.0204496	−	0.398449i
$881$	5.39390			0.181725			0.0908625	−	0.995863i	$-0.471038\pi$
$881$	5.39390			0.181725			0.0908625	+	0.995863i	$0.471038\pi$
$882$		0			0
$883$	35.2377	−	35.2377i	1.18584	−	1.18584i	0.207637	−	0.978206i	$-0.433423\pi$
$883$	35.2377	−	35.2377i	1.18584	−	1.18584i	0.978206	−	0.207637i	$-0.0665774\pi$
$884$	1.87405			0.0630313
$885$		0			0
$886$		−	24.5074i		−	0.823344i
$887$	−21.2160	+	21.2160i	−0.712365	+	0.712365i	−0.967029	−	0.254665i	$-0.918035\pi$
$887$	−21.2160	+	21.2160i	−0.712365	+	0.712365i	0.254665	+	0.967029i	$0.418035\pi$
$888$		0			0
$889$	3.75481			0.125932
$890$	−8.12102	−	8.99971i	−0.272217	−	0.301671i
$891$		0			0
$892$	4.27908	−	4.27908i	0.143274	−	0.143274i
$893$	9.11922	−	47.6488i	0.305163	−	1.59451i
$894$		0			0
$895$	−0.909824	+	17.7274i	−0.0304121	+	0.592561i
$896$		−	1.98511i		−	0.0663178i
$897$		0			0
$898$	−14.6269	+	14.6269i	−0.488105	+	0.488105i
$899$			48.5953i			1.62074i
$900$		0			0
$901$			8.72744i			0.290753i
$902$	7.13356	+	7.13356i	0.237522	+	0.237522i
$903$		0			0
$904$		−	9.15392i		−	0.304455i
$905$	10.6555	+	0.546876i	0.354202	+	0.0181788i
$906$		0			0
$907$	−21.1999	+	21.1999i	−0.703930	+	0.703930i	−0.965252	−	0.261321i	$-0.915842\pi$
$907$	−21.1999	+	21.1999i	−0.703930	+	0.703930i	0.261321	+	0.965252i	$0.415842\pi$
$908$	13.7190	+	13.7190i	0.455281	+	0.455281i
$909$		0			0
$910$	−8.94669	+	8.07318i	−0.296580	+	0.267623i
$911$		−	45.1425i		−	1.49564i	−0.663903	−	0.747819i	$-0.731101\pi$
$911$		−	45.1425i		−	1.49564i	0.663903	−	0.747819i	$-0.268899\pi$
$912$		0			0
$913$	−28.7524	+	28.7524i	−0.951565	+	0.951565i
$914$	−11.1181			−0.367755
$915$		0			0
$916$	25.2634			0.834725
$917$	7.49104	+	7.49104i	0.247376	+	0.247376i
$918$		0			0
$919$			12.1007i			0.399165i	0.979881	+	0.199583i	$0.0639586\pi$
$919$			12.1007i			0.399165i	−0.979881	+	0.199583i	$0.936041\pi$
$920$	0.630395	−	12.2829i	0.0207835	−	0.404954i
$921$		0			0
$922$	−16.8761	+	16.8761i	−0.555784	+	0.555784i
$923$	−7.62154	+	7.62154i	−0.250866	+	0.250866i
$924$		0			0
$925$	−30.7524	+	25.0132i	−1.01113	+	0.822428i
$926$		−	31.5686i		−	1.03741i
$927$		0			0
$928$	−4.37741	+	4.37741i	−0.143696	+	0.143696i
$929$		−	22.0342i		−	0.722920i	−0.932388	−	0.361460i	$-0.882278\pi$
$929$		−	22.0342i		−	0.722920i	0.932388	−	0.361460i	$-0.117722\pi$
$930$		0			0
$931$	−11.0339	+	7.48895i	−0.361623	+	0.245440i
$932$	7.73738	+	7.73738i	0.253446	+	0.253446i
$933$		0			0
$934$	−29.2262			−0.956312
$935$	6.06560	−	5.47339i	0.198366	−	0.178999i
$936$		0			0
$937$	−18.3181	−	18.3181i	−0.598425	−	0.598425i	0.341469	−	0.939893i	$-0.389076\pi$
$937$	−18.3181	−	18.3181i	−0.598425	−	0.598425i	−0.939893	+	0.341469i	$0.889076\pi$
$938$	−20.2503	+	20.2503i	−0.661196	+	0.661196i
$939$		0			0
$940$	16.6726	+	18.4766i	0.543801	+	0.602639i
$941$		−	14.4885i		−	0.472310i	−0.971715	−	0.236155i	$-0.924113\pi$
$941$		−	14.4885i		−	0.472310i	0.971715	−	0.236155i	$-0.0758874\pi$
$942$		0			0
$943$	7.41297	+	7.41297i	0.241399	+	0.241399i
$944$	−0.611185			−0.0198924
$945$		0			0
$946$		−	53.3622i		−	1.73495i
$947$	9.42564	+	9.42564i	0.306292	+	0.306292i	0.843469	−	0.537177i	$-0.180509\pi$
$947$	9.42564	+	9.42564i	0.306292	+	0.306292i	−0.537177	+	0.843469i	$0.680509\pi$
$948$		0			0
$949$	−29.6500			−0.962479
$950$	20.8741	+	6.26671i	0.677245	+	0.203319i
$951$		0			0
$952$	0.968965	−	0.968965i	0.0314043	−	0.0314043i
$953$	−24.3168	−	24.3168i	−0.787700	−	0.787700i	0.193417	−	0.981117i	$-0.438043\pi$
$953$	−24.3168	−	24.3168i	−0.787700	−	0.787700i	−0.981117	+	0.193417i	$0.938043\pi$
$954$		0			0
$955$	−1.58979	+	30.9760i	−0.0514443	+	1.00236i
$956$	−11.0820			−0.358418
$957$		0			0
$958$	11.2580	+	11.2580i	0.363730	+	0.363730i
$959$		−	8.34835i		−	0.269582i
$960$		0			0
$961$	−30.6203			−0.987753
$962$	−15.2194	+	15.2194i	−0.490693	+	0.490693i
$963$		0			0
$964$	−14.5158			−0.467522
$965$	19.2999	−	17.4155i	0.621284	−	0.560625i
$966$		0			0
$967$	−2.49180	−	2.49180i	−0.0801310	−	0.0801310i	0.665905	−	0.746036i	$-0.268045\pi$
$967$	−2.49180	−	2.49180i	−0.0801310	−	0.0801310i	−0.746036	+	0.665905i	$0.768045\pi$
$968$	−12.0319	−	12.0319i	−0.386719	−	0.386719i
$969$		0			0
$970$	−9.80327	−	0.503134i	−0.314764	−	0.0161547i
$971$			55.4935i			1.78087i	0.455110	+	0.890435i	$0.349600\pi$
$971$			55.4935i			1.78087i	−0.455110	+	0.890435i	$0.650400\pi$
$972$		0			0
$973$	19.5102	−	19.5102i	0.625469	−	0.625469i
$974$			14.8314i			0.475228i
$975$		0			0
$976$	−8.31021			−0.266003
$977$	5.49897	−	5.49897i	0.175928	−	0.175928i	−0.613650	−	0.789578i	$-0.710300\pi$
$977$	5.49897	−	5.49897i	0.175928	−	0.175928i	0.789578	+	0.613650i	$0.210300\pi$
$978$		0			0
$979$	−28.6942			−0.917070
$980$	0.350635	−	6.83191i	0.0112006	−	0.218237i
$981$		0			0
$982$	−11.1972	+	11.1972i	−0.357317	+	0.357317i
$983$	21.9026	+	21.9026i	0.698585	+	0.698585i	0.964105	−	0.265520i	$-0.0855437\pi$
$983$	21.9026	+	21.9026i	0.698585	+	0.698585i	−0.265520	+	0.964105i	$0.585544\pi$
$984$		0			0
$985$	−1.98359	+	1.78992i	−0.0632024	+	0.0570316i
$986$	−4.27338			−0.136092
$987$		0			0
$988$	11.6227	+	2.22441i	0.369769	+	0.0707678i
$989$		−	55.4523i		−	1.76328i
$990$		0			0
$991$			37.4884i			1.19086i	0.803408	+	0.595429i	$0.203018\pi$
$991$			37.4884i			1.19086i	−0.803408	+	0.595429i	$0.796982\pi$
$992$	−5.55069	−	5.55069i	−0.176235	−	0.176235i
$993$		0			0
$994$			7.88131i			0.249980i
$995$	38.4691	+	1.97435i	1.21955	+	0.0625912i
$996$		0			0
$997$	−39.6736	−	39.6736i	−1.25648	−	1.25648i	−0.952763	−	0.303714i	$-0.901773\pi$
$997$	−39.6736	−	39.6736i	−1.25648	−	1.25648i	−0.303714	−	0.952763i	$-0.598227\pi$
$998$	−14.9276	−	14.9276i	−0.472525	−	0.472525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.p.c.37.9		20
3.2	odd	2		570.2.m.b.37.2	✓	20
5.3	odd	4	inner	1710.2.p.c.1063.4		20
15.8	even	4		570.2.m.b.493.7	yes	20
19.18	odd	2	inner	1710.2.p.c.37.4		20
57.56	even	2		570.2.m.b.37.7	yes	20
95.18	even	4	inner	1710.2.p.c.1063.9		20
285.113	odd	4		570.2.m.b.493.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.m.b.37.2	✓	20	3.2	odd	2
570.2.m.b.37.7	yes	20	57.56	even	2
570.2.m.b.493.2	yes	20	285.113	odd	4
570.2.m.b.493.7	yes	20	15.8	even	4
1710.2.p.c.37.4		20	19.18	odd	2	inner
1710.2.p.c.37.9		20	1.1	even	1	trivial
1710.2.p.c.1063.4		20	5.3	odd	4	inner
1710.2.p.c.1063.9		20	95.18	even	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.114611 + 2.23313i) q^{5} +(-1.40368 - 1.40368i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(-0.114611 + 2.23313i) q^{5} +(-1.40368 - 1.40368i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(1.49802 + 1.66010i) q^{10} +5.29298 q^{11} +(-1.91968 - 1.91968i) q^{13} -1.98511 q^{14} -1.00000 q^{16} +(-0.488117 - 0.488117i) q^{17} +(-2.44789 - 3.60663i) q^{19} +(2.23313 + 0.114611i) q^{20} +(3.74270 - 3.74270i) q^{22} +(3.88930 - 3.88930i) q^{23} +(-4.97373 - 0.511883i) q^{25} -2.71483 q^{26} +(-1.40368 + 1.40368i) q^{28} +6.19060 q^{29} +7.84986i q^{31} +(-0.707107 + 0.707107i) q^{32} -0.690302 q^{34} +(3.29548 - 2.97373i) q^{35} +(5.60602 - 5.60602i) q^{37} +(-4.28120 - 0.819353i) q^{38} +(1.66010 - 1.49802i) q^{40} +1.90599i q^{41} +(7.12884 - 7.12884i) q^{43} -5.29298i q^{44} -5.50029i q^{46} +(7.86994 + 7.86994i) q^{47} -3.05934i q^{49} +(-3.87891 + 3.15500i) q^{50} +(-1.91968 + 1.91968i) q^{52} +(-8.93991 - 8.93991i) q^{53} +(-0.606635 + 11.8199i) q^{55} +1.98511i q^{56} +(4.37741 - 4.37741i) q^{58} +0.611185 q^{59} +8.31021 q^{61} +(5.55069 + 5.55069i) q^{62} +1.00000i q^{64} +(4.50690 - 4.06687i) q^{65} +(10.2011 - 10.2011i) q^{67} +(-0.488117 + 0.488117i) q^{68} +(0.227516 - 4.43300i) q^{70} -3.97022i q^{71} +(7.72265 - 7.72265i) q^{73} -7.92810i q^{74} +(-3.60663 + 2.44789i) q^{76} +(-7.42967 - 7.42967i) q^{77} -17.1528 q^{79} +(0.114611 - 2.23313i) q^{80} +(1.34774 + 1.34774i) q^{82} +(-5.43217 + 5.43217i) q^{83} +(1.14597 - 1.03408i) q^{85} -10.0817i q^{86} +(-3.74270 - 3.74270i) q^{88} -5.42118 q^{89} +5.38924i q^{91} +(-3.88930 - 3.88930i) q^{92} +11.1298 q^{94} +(8.33464 - 5.05310i) q^{95} +(-3.10415 + 3.10415i) q^{97} +(-2.16328 - 2.16328i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 12 q^{5} - 4 q^{7}+O(q^{10}) \) 20 * q - 12 * q^5 - 4 * q^7	\( 20 q - 12 q^{5} - 4 q^{7} + 8 q^{11} - 20 q^{16} + 12 q^{17} + 4 q^{23} - 28 q^{25} - 24 q^{26} - 4 q^{28} - 4 q^{35} + 12 q^{38} - 12 q^{43} + 44 q^{47} + 64 q^{55} - 8 q^{58} + 24 q^{62} + 12 q^{68} - 4 q^{73} + 4 q^{76} - 88 q^{77} + 12 q^{80} - 8 q^{82} - 76 q^{83} - 12 q^{85} - 4 q^{92} + 24 q^{95}+O(q^{100}) \) 20 * q - 12 * q^5 - 4 * q^7 + 8 * q^11 - 20 * q^16 + 12 * q^17 + 4 * q^23 - 28 * q^25 - 24 * q^26 - 4 * q^28 - 4 * q^35 + 12 * q^38 - 12 * q^43 + 44 * q^47 + 64 * q^55 - 8 * q^58 + 24 * q^62 + 12 * q^68 - 4 * q^73 + 4 * q^76 - 88 * q^77 + 12 * q^80 - 8 * q^82 - 76 * q^83 - 12 * q^85 - 4 * q^92 + 24 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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