LMFDB - Embedded newform 1710.2.t.b.919.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(919,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1710.919");

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.t (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 570)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			919.6
Root			$-0.531325 - 1.98293i$ of defining polynomial
Character	$\chi$	$=$	1710.919
Dual form			1710.2.t.b.1189.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.837733 + 2.07321i) q^{5} +0.785680i q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.837733 + 2.07321i) q^{5} +0.785680i q^{7} -1.00000i q^{8} +(1.76210 + 1.37659i) q^{10} +0.377784 q^{11} +(2.51426 + 1.45161i) q^{13} +(0.392840 + 0.680419i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.45651 - 1.41827i) q^{17} +(-2.82148 - 3.32254i) q^{19} +(2.21432 + 0.311108i) q^{20} +(0.327171 - 0.188892i) q^{22} +(7.86994 + 4.54371i) q^{23} +(-3.59641 + 3.47359i) q^{25} +2.90321 q^{26} +(0.680419 + 0.392840i) q^{28} +(-2.01037 + 3.48207i) q^{29} -4.42864 q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.41827 - 2.45651i) q^{34} +(-1.62888 + 0.658190i) q^{35} -0.0967881i q^{37} +(-4.10474 - 1.46666i) q^{38} +(2.07321 - 0.837733i) q^{40} +(1.43655 + 2.48818i) q^{41} +(0.371213 - 0.214320i) q^{43} +(0.188892 - 0.327171i) q^{44} +9.08742 q^{46} +(10.4680 + 6.04371i) q^{47} +6.38271 q^{49} +(-1.37778 + 4.80642i) q^{50} +(2.51426 - 1.45161i) q^{52} +(6.00443 + 3.46666i) q^{53} +(0.316482 + 0.783227i) q^{55} +0.785680 q^{56} +4.02074i q^{58} +(4.88025 + 8.45283i) q^{59} +(-2.27777 + 3.94521i) q^{61} +(-3.83531 + 2.21432i) q^{62} -1.00000 q^{64} +(-0.903212 + 6.42864i) q^{65} +(-7.31738 - 4.22469i) q^{67} -2.83654i q^{68} +(-1.08156 + 1.38445i) q^{70} +(-5.86987 - 10.1669i) q^{71} +(1.95744 - 1.13013i) q^{73} +(-0.0483940 - 0.0838209i) q^{74} +(-4.28814 + 0.782204i) q^{76} +0.296818i q^{77} +(-0.785680 - 1.36084i) q^{79} +(1.37659 - 1.76210i) q^{80} +(2.48818 + 1.43655i) q^{82} -2.75557i q^{83} +(4.99827 + 3.90474i) q^{85} +(0.214320 - 0.371213i) q^{86} -0.377784i q^{88} +(-5.96912 + 10.3388i) q^{89} +(-1.14050 + 1.97540i) q^{91} +(7.86994 - 4.54371i) q^{92} +12.0874 q^{94} +(4.52468 - 8.63292i) q^{95} +(-2.98299 + 1.72223i) q^{97} +(5.52759 - 3.19135i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4}+O(q^{10}) $ 12 * q + 6 * q^4	$ 12 q + 6 q^{4} - 2 q^{10} + 4 q^{11} + 18 q^{14} - 6 q^{16} + 6 q^{19} - 2 q^{25} + 8 q^{26} + 16 q^{29} + 4 q^{34} - 2 q^{35} + 2 q^{40} - 10 q^{41} + 2 q^{44} + 28 q^{46} - 56 q^{49} - 16 q^{50} - 8 q^{55} + 36 q^{56} - 8 q^{59} - 28 q^{61} - 12 q^{64} + 16 q^{65} + 16 q^{70} - 44 q^{71} - 14 q^{74} - 12 q^{76} - 36 q^{79} - 32 q^{85} - 24 q^{86} - 6 q^{89} + 64 q^{94} + 12 q^{95}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 4 * q^11 + 18 * q^14 - 6 * q^16 + 6 * q^19 - 2 * q^25 + 8 * q^26 + 16 * q^29 + 4 * q^34 - 2 * q^35 + 2 * q^40 - 10 * q^41 + 2 * q^44 + 28 * q^46 - 56 * q^49 - 16 * q^50 - 8 * q^55 + 36 * q^56 - 8 * q^59 - 28 * q^61 - 12 * q^64 + 16 * q^65 + 16 * q^70 - 44 * q^71 - 14 * q^74 - 12 * q^76 - 36 * q^79 - 32 * q^85 - 24 * q^86 - 6 * q^89 + 64 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$1027$	$1351$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.837733	+	2.07321i	0.374645	+	0.927168i
$5$	0.837733	+	2.07321i	0.374645	+	0.927168i
$6$		0			0
$7$			0.785680i			0.296959i	0.988915	+	0.148480i	$0.0474379\pi$
$7$			0.785680i			0.296959i	−0.988915	+	0.148480i	$0.952562\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.76210	+	1.37659i	0.557226	+	0.435315i
$11$	0.377784			0.113906			0.0569531	−	0.998377i	$-0.481861\pi$
$11$	0.377784			0.113906			0.0569531	+	0.998377i	$0.481861\pi$
$12$		0			0
$13$	2.51426	+	1.45161i	0.697329	+	0.402603i	0.806352	−	0.591436i	$-0.201439\pi$
$13$	2.51426	+	1.45161i	0.697329	+	0.402603i	−0.109023	+	0.994039i	$0.534772\pi$
$14$	0.392840	+	0.680419i	0.104991	+	0.181850i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.45651	−	1.41827i	0.595792	−	0.343980i	−0.171593	−	0.985168i	$-0.554891\pi$
$17$	2.45651	−	1.41827i	0.595792	−	0.343980i	0.767384	+	0.641188i	$0.221558\pi$
$18$		0			0
$19$	−2.82148	−	3.32254i	−0.647292	−	0.762242i
$19$	−2.82148	−	3.32254i	−0.647292	−	0.762242i
$20$	2.21432	+	0.311108i	0.495137	+	0.0695658i
$21$		0			0
$22$	0.327171	−	0.188892i	0.0697531	−	0.0402719i
$23$	7.86994	+	4.54371i	1.64100	+	0.947429i	0.980481	+	0.196616i	$0.0629952\pi$
$23$	7.86994	+	4.54371i	1.64100	+	0.947429i	0.660515	+	0.750813i	$0.270338\pi$
$24$		0			0
$25$	−3.59641	+	3.47359i	−0.719282	+	0.694719i
$26$	2.90321			0.569367
$27$		0			0
$28$	0.680419	+	0.392840i	0.128587	+	0.0742398i
$29$	−2.01037	+	3.48207i	−0.373317	+	0.646603i	−0.990074	−	0.140550i	$-0.955113\pi$
$29$	−2.01037	+	3.48207i	−0.373317	+	0.646603i	0.616757	+	0.787154i	$0.288446\pi$
$30$		0			0
$31$	−4.42864			−0.795407			−0.397704	−	0.917514i	$-0.630193\pi$
$31$	−4.42864			−0.795407			−0.397704	+	0.917514i	$0.630193\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	1.41827	−	2.45651i	0.243231	−	0.421288i
$35$	−1.62888	+	0.658190i	−0.275331	+	0.111254i
$36$		0			0
$37$		−	0.0967881i		−	0.0159119i	−0.999968	−	0.00795593i	$-0.997468\pi$
$37$		−	0.0967881i		−	0.0159119i	0.999968	−	0.00795593i	$-0.00253248\pi$
$38$	−4.10474	−	1.46666i	−0.665877	−	0.237924i
$39$		0			0
$40$	2.07321	−	0.837733i	0.327803	−	0.132457i
$41$	1.43655	+	2.48818i	0.224351	+	0.388588i	0.956125	−	0.292960i	$-0.0946403\pi$
$41$	1.43655	+	2.48818i	0.224351	+	0.388588i	−0.731773	+	0.681548i	$0.761307\pi$
$42$		0			0
$43$	0.371213	−	0.214320i	0.0566094	−	0.0326835i	−0.471428	−	0.881904i	$-0.656261\pi$
$43$	0.371213	−	0.214320i	0.0566094	−	0.0326835i	0.528038	+	0.849221i	$0.322928\pi$
$44$	0.188892	−	0.327171i	0.0284766	−	0.0493229i
$45$		0			0
$46$	9.08742			1.33987
$47$	10.4680	+	6.04371i	1.52692	+	0.881566i	0.999489	+	0.0319658i	$0.0101768\pi$
$47$	10.4680	+	6.04371i	1.52692	+	0.881566i	0.527428	+	0.849600i	$0.323157\pi$
$48$		0			0
$49$	6.38271			0.911815
$50$	−1.37778	+	4.80642i	−0.194848	+	0.679731i
$51$		0			0
$52$	2.51426	−	1.45161i	0.348664	−	0.201302i
$53$	6.00443	+	3.46666i	0.824772	+	0.476183i	0.852059	−	0.523445i	$-0.175353\pi$
$53$	6.00443	+	3.46666i	0.824772	+	0.476183i	−0.0272870	+	0.999628i	$0.508687\pi$
$54$		0			0
$55$	0.316482	+	0.783227i	0.0426745	+	0.105610i
$56$	0.785680			0.104991
$57$		0			0
$58$			4.02074i			0.527949i
$59$	4.88025	+	8.45283i	0.635354	+	1.10047i	0.986440	+	0.164122i	$0.0524791\pi$
$59$	4.88025	+	8.45283i	0.635354	+	1.10047i	−0.351086	+	0.936343i	$0.614188\pi$
$60$		0			0
$61$	−2.27777	+	3.94521i	−0.291639	+	0.505133i	−0.974197	−	0.225698i	$-0.927534\pi$
$61$	−2.27777	+	3.94521i	−0.291639	+	0.505133i	0.682559	+	0.730831i	$0.260867\pi$
$62$	−3.83531	+	2.21432i	−0.487085	+	0.281219i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.903212	+	6.42864i	−0.112030	+	0.797375i
$66$		0			0
$67$	−7.31738	−	4.22469i	−0.893960	−	0.516128i	−0.0187245	−	0.999825i	$-0.505961\pi$
$67$	−7.31738	−	4.22469i	−0.893960	−	0.516128i	−0.875236	+	0.483696i	$0.839294\pi$
$68$		−	2.83654i		−	0.343980i
$69$		0			0
$70$	−1.08156	+	1.38445i	−0.129271	+	0.165473i
$71$	−5.86987	−	10.1669i	−0.696626	−	1.20659i	−0.969630	−	0.244578i	$-0.921350\pi$
$71$	−5.86987	−	10.1669i	−0.696626	−	1.20659i	0.273004	−	0.962013i	$-0.411983\pi$
$72$		0			0
$73$	1.95744	−	1.13013i	0.229101	−	0.132271i	−0.381056	−	0.924552i	$-0.624440\pi$
$73$	1.95744	−	1.13013i	0.229101	−	0.132271i	0.610157	+	0.792280i	$0.291106\pi$
$74$	−0.0483940	−	0.0838209i	−0.00562569	−	0.00974399i
$75$		0			0
$76$	−4.28814	+	0.782204i	−0.491884	+	0.0897250i
$77$			0.296818i			0.0338255i
$78$		0			0
$79$	−0.785680	−	1.36084i	−0.0883959	−	0.153106i	0.818437	−	0.574596i	$-0.194841\pi$
$79$	−0.785680	−	1.36084i	−0.0883959	−	0.153106i	−0.906833	+	0.421490i	$0.861507\pi$
$80$	1.37659	−	1.76210i	0.153907	−	0.197009i
$81$		0			0
$82$	2.48818	+	1.43655i	0.274773	+	0.158640i
$83$		−	2.75557i		−	0.302463i	−0.988498	−	0.151231i	$-0.951676\pi$
$83$		−	2.75557i		−	0.302463i	0.988498	−	0.151231i	$-0.0483239\pi$
$84$		0			0
$85$	4.99827	+	3.90474i	0.542138	+	0.423528i
$86$	0.214320	−	0.371213i	0.0231107	−	0.0400289i
$87$		0			0
$88$		−	0.377784i		−	0.0402719i
$89$	−5.96912	+	10.3388i	−0.632726	+	1.09591i	0.354266	+	0.935145i	$0.384731\pi$
$89$	−5.96912	+	10.3388i	−0.632726	+	1.09591i	−0.986992	+	0.160769i	$0.948603\pi$
$90$		0			0
$91$	−1.14050	+	1.97540i	−0.119557	+	0.207078i
$92$	7.86994	−	4.54371i	0.820498	−	0.473715i
$93$		0			0
$94$	12.0874			1.24672
$95$	4.52468	−	8.63292i	0.464222	−	0.885719i
$96$		0			0
$97$	−2.98299	+	1.72223i	−0.302877	+	0.174866i	−0.643735	−	0.765249i	$-0.722616\pi$
$97$	−2.98299	+	1.72223i	−0.302877	+	0.174866i	0.340858	+	0.940115i	$0.389283\pi$
$98$	5.52759	−	3.19135i	0.558371	−	0.322375i
$99$		0			0
$100$	1.21002	+	4.85138i	0.121002	+	0.485138i
$101$	8.54617	−	14.8024i	0.850376	−	1.47289i	−0.0304937	−	0.999535i	$-0.509708\pi$
$101$	8.54617	−	14.8024i	0.850376	−	1.47289i	0.880870	−	0.473359i	$-0.156959\pi$
$102$		0			0
$103$		−	8.11753i		−	0.799844i	−0.916549	−	0.399922i	$-0.869037\pi$
$103$		−	8.11753i		−	0.799844i	0.916549	−	0.399922i	$-0.130963\pi$
$104$	1.45161	−	2.51426i	0.142342	−	0.246543i
$105$		0			0
$106$	6.93332			0.673424
$107$		−	17.7812i		−	1.71898i	−0.511155	−	0.859488i	$-0.670782\pi$
$107$		−	17.7812i		−	1.71898i	0.511155	−	0.859488i	$-0.329218\pi$
$108$		0			0
$109$	0.722230	+	1.25094i	0.0691771	+	0.119818i	0.898539	−	0.438893i	$-0.144629\pi$
$109$	0.722230	+	1.25094i	0.0691771	+	0.119818i	−0.829362	+	0.558711i	$0.811296\pi$
$110$	0.665695	+	0.520053i	0.0634715	+	0.0495851i
$111$		0			0
$112$	0.680419	−	0.392840i	0.0642936	−	0.0371199i
$113$			14.3160i			1.34674i	0.739306	+	0.673369i	$0.235154\pi$
$113$			14.3160i			1.34674i	−0.739306	+	0.673369i	$0.764846\pi$
$114$		0			0
$115$	−2.82717	+	20.1225i	−0.263635	+	1.87643i
$116$	2.01037	+	3.48207i	0.186658	+	0.323302i
$117$		0			0
$118$	8.45283	+	4.88025i	0.778146	+	0.449263i
$119$	1.11430	+	1.93003i	0.102148	+	0.176926i
$120$		0			0
$121$	−10.8573			−0.987025
$122$			4.55554i			0.412439i
$123$		0			0
$124$	−2.21432	+	3.83531i	−0.198852	+	0.344421i
$125$	−10.2143	−	4.54617i	−0.913597	−	0.406622i
$126$		0			0
$127$	3.14252	+	1.81433i	0.278854	+	0.160996i	0.632904	−	0.774230i	$-0.281863\pi$
$127$	3.14252	+	1.81433i	0.278854	+	0.160996i	−0.354051	+	0.935226i	$0.615196\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	2.43212	+	6.01897i	0.213311	+	0.527899i
$131$	−8.40321	−	14.5548i	−0.734192	−	1.27166i	−0.955077	−	0.296358i	$-0.904228\pi$
$131$	−8.40321	−	14.5548i	−0.734192	−	1.27166i	0.220885	−	0.975300i	$-0.429105\pi$
$132$		0			0
$133$	2.61045	−	2.21678i	0.226355	−	0.192219i
$134$	−8.44938			−0.729916
$135$		0			0
$136$	−1.41827	−	2.45651i	−0.121615	−	0.210644i
$137$	−1.89969	−	1.09679i	−0.162302	−	0.0937049i	0.416649	−	0.909067i	$-0.363204\pi$
$137$	−1.89969	−	1.09679i	−0.162302	−	0.0937049i	−0.578951	+	0.815362i	$0.696538\pi$
$138$		0			0
$139$	0.836535	−	1.44892i	0.0709540	−	0.122896i	−0.828366	−	0.560188i	$-0.810729\pi$
$139$	0.836535	−	1.44892i	0.0709540	−	0.122896i	0.899320	+	0.437292i	$0.144062\pi$
$140$	−0.244431	+	1.73975i	−0.0206582	+	0.147035i
$141$		0			0
$142$	−10.1669	−	5.86987i	−0.853189	−	0.492589i
$143$	0.949846	+	0.548394i	0.0794301	+	0.0458590i
$144$		0			0
$145$	−8.90321	−	1.25088i	−0.739372	−	0.103880i
$146$	1.13013	−	1.95744i	0.0935299	−	0.161999i
$147$		0			0
$148$	−0.0838209	−	0.0483940i	−0.00689004	−	0.00397797i
$149$	−2.69926	−	4.67526i	−0.221132	−	0.383012i	0.734020	−	0.679128i	$-0.237642\pi$
$149$	−2.69926	−	4.67526i	−0.221132	−	0.383012i	−0.955152	+	0.296116i	$0.904309\pi$
$150$		0			0
$151$	9.07160			0.738236			0.369118	−	0.929382i	$-0.379660\pi$
$151$	9.07160			0.738236			0.369118	+	0.929382i	$0.379660\pi$
$152$	−3.32254	+	2.82148i	−0.269493	+	0.228852i
$153$		0			0
$154$	0.148409	+	0.257052i	0.0119591	+	0.0207138i
$155$	−3.71002	−	9.18150i	−0.297996	−	0.737476i
$156$		0			0
$157$	13.3094	−	7.68421i	1.06221	−	0.613267i	0.136166	−	0.990686i	$-0.456522\pi$
$157$	13.3094	−	7.68421i	1.06221	−	0.613267i	0.926042	+	0.377419i	$0.123188\pi$
$158$	−1.36084	−	0.785680i	−0.108262	−	0.0625054i
$159$		0			0
$160$	0.311108	−	2.21432i	0.0245952	−	0.175057i
$161$	−3.56990	+	6.18325i	−0.281348	+	0.487309i
$162$		0			0
$163$			7.31756i			0.573156i	0.958057	+	0.286578i	$0.0925177\pi$
$163$			7.31756i			0.573156i	−0.958057	+	0.286578i	$0.907482\pi$
$164$	2.87310			0.224351
$165$		0			0
$166$	−1.37778	−	2.38639i	−0.106937	−	0.185220i
$167$	5.03277	+	2.90567i	0.389448	+	0.224848i	0.681921	−	0.731426i	$-0.261145\pi$
$167$	5.03277	+	2.90567i	0.389448	+	0.224848i	−0.292473	+	0.956274i	$0.594478\pi$
$168$		0			0
$169$	−2.28568	−	3.95891i	−0.175822	−	0.304532i
$170$	6.28100	+	0.882468i	0.481730	+	0.0676822i
$171$		0			0
$172$		−	0.428639i		−	0.0326835i
$173$	−7.55647	+	4.36273i	−0.574508	+	0.331692i	−0.758948	−	0.651152i	$-0.774286\pi$
$173$	−7.55647	+	4.36273i	−0.574508	+	0.331692i	0.184440	+	0.982844i	$0.440953\pi$
$174$		0			0
$175$	−2.72913	−	2.82563i	−0.206303	−	0.213597i
$176$	−0.188892	−	0.327171i	−0.0142383	−	0.0246614i
$177$		0			0
$178$			11.9382i			0.894809i
$179$	−23.2306			−1.73634			−0.868169	−	0.496269i	$-0.834703\pi$
$179$	−23.2306			−1.73634			−0.868169	+	0.496269i	$0.834703\pi$
$180$		0			0
$181$	−3.77309	+	6.53518i	−0.280451	+	0.485756i	−0.971496	−	0.237056i	$-0.923817\pi$
$181$	−3.77309	+	6.53518i	−0.280451	+	0.485756i	0.691045	+	0.722812i	$0.257151\pi$
$182$			2.28100i			0.169079i
$183$		0			0
$184$	4.54371	−	7.86994i	0.334967	−	0.580179i
$185$	0.200662	−	0.0810825i	0.0147530	−	0.00596131i
$186$		0			0
$187$	0.928032	−	0.535799i	0.0678644	−	0.0391815i
$188$	10.4680	−	6.04371i	0.763458	−	0.440783i
$189$		0			0
$190$	−0.397977	−	9.73867i	−0.0288723	−	0.706517i
$191$	20.4701			1.48117			0.740583	−	0.671965i	$-0.234549\pi$
$191$	20.4701			1.48117			0.740583	+	0.671965i	$0.234549\pi$
$192$		0			0
$193$	16.3886	−	9.46198i	1.17968	−	0.681088i	0.223739	−	0.974649i	$-0.428174\pi$
$193$	16.3886	−	9.46198i	1.17968	−	0.681088i	0.955940	+	0.293561i	$0.0948404\pi$
$194$	−1.72223	+	2.98299i	−0.123649	+	0.214166i
$195$		0			0
$196$	3.19135	−	5.52759i	0.227954	−	0.394828i
$197$		−	1.73038i		−	0.123284i	−0.998098	−	0.0616422i	$-0.980366\pi$
$197$		−	1.73038i		−	0.123284i	0.998098	−	0.0616422i	$-0.0196338\pi$
$198$		0			0
$199$	7.53580	−	13.0524i	0.534199	−	0.925259i	−0.465003	−	0.885309i	$-0.653947\pi$
$199$	7.53580	−	13.0524i	0.534199	−	0.925259i	0.999202	−	0.0399501i	$-0.0127199\pi$
$200$	3.47359	+	3.59641i	0.245620	+	0.254304i
$201$		0			0
$202$		−	17.0923i		−	1.20261i
$203$	−2.73579	−	1.57951i	−0.192015	−	0.110860i
$204$		0			0
$205$	−3.95507	+	5.06270i	−0.276234	+	0.353594i
$206$	−4.05877	−	7.02999i	−0.282788	−	0.489803i
$207$		0			0
$208$		−	2.90321i		−	0.201302i
$209$	−1.06591	−	1.25520i	−0.0737306	−	0.0868242i
$210$		0			0
$211$	−6.65801	−	11.5320i	−0.458357	−	0.793897i	0.540518	−	0.841333i	$-0.318228\pi$
$211$	−6.65801	−	11.5320i	−0.458357	−	0.793897i	−0.998874	+	0.0474357i	$0.984895\pi$
$212$	6.00443	−	3.46666i	0.412386	−	0.238091i
$213$		0			0
$214$	−8.89062	−	15.3990i	−0.607750	−	1.05265i
$215$	0.755307	+	0.590060i	0.0515115	+	0.0402417i
$216$		0			0
$217$		−	3.47949i		−	0.236203i
$218$	1.25094	+	0.722230i	0.0847243	+	0.0489156i
$219$		0			0
$220$	0.836535	+	0.117532i	0.0563992	+	0.00792398i
$221$	8.23506			0.553950
$222$		0			0
$223$	−16.6003	+	9.58419i	−1.11164	+	0.641805i	−0.939253	−	0.343224i	$-0.888481\pi$
$223$	−16.6003	+	9.58419i	−1.11164	+	0.641805i	−0.172386	+	0.985030i	$0.555148\pi$
$224$	0.392840	−	0.680419i	0.0262477	−	0.0454624i
$225$		0			0
$226$	7.15801	+	12.3980i	0.476144	+	0.824706i
$227$		−	6.88247i		−	0.456805i	−0.973567	−	0.228403i	$-0.926650\pi$
$227$		−	6.88247i		−	0.456805i	0.973567	−	0.228403i	$-0.0733503\pi$
$228$		0			0
$229$	−13.7462			−0.908375			−0.454187	−	0.890906i	$-0.650070\pi$
$229$	−13.7462			−0.908375			−0.454187	+	0.890906i	$0.650070\pi$
$230$	7.61283	+	18.8401i	0.501975	+	1.24228i
$231$		0			0
$232$	3.48207	+	2.01037i	0.228609	+	0.131987i
$233$	−5.88642	+	3.39853i	−0.385632	+	0.222645i	−0.680266	−	0.732965i	$-0.738136\pi$
$233$	−5.88642	+	3.39853i	−0.385632	+	0.222645i	0.294634	+	0.955610i	$0.404802\pi$
$234$		0			0
$235$	−3.76049	+	26.7654i	−0.245307	+	1.74598i
$236$	9.76049			0.635354
$237$		0			0
$238$	1.93003	+	1.11430i	0.125105	+	0.0722297i
$239$	−10.8573			−0.702299			−0.351149	−	0.936319i	$-0.614209\pi$
$239$	−10.8573			−0.702299			−0.351149	+	0.936319i	$0.614209\pi$
$240$		0			0
$241$	4.84368	−	8.38950i	0.312009	−	0.540415i	−0.666788	−	0.745247i	$-0.732331\pi$
$241$	4.84368	−	8.38950i	0.312009	−	0.540415i	0.978797	+	0.204832i	$0.0656648\pi$
$242$	−9.40268	+	5.42864i	−0.604427	+	0.348966i
$243$		0			0
$244$	2.27777	+	3.94521i	0.145819	+	0.252566i
$245$	5.34700	+	13.2327i	0.341607	+	0.845406i
$246$		0			0
$247$	−2.27091	−	12.4494i	−0.144494	−	0.792135i
$248$			4.42864i			0.281219i
$249$		0			0
$250$	−11.1189	+	1.17006i	−0.703224	+	0.0740011i
$251$	7.54617	−	13.0704i	0.476310	−	0.824993i	−0.523321	−	0.852135i	$-0.675307\pi$
$251$	7.54617	−	13.0704i	0.476310	−	0.824993i	0.999632	+	0.0271420i	$0.00864064\pi$
$252$		0			0
$253$	2.97314	+	1.71654i	0.186920	+	0.107918i
$254$	3.62867			0.227683
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−19.7676	−	11.4128i	−1.23307	−	0.711912i	−0.265400	−	0.964139i	$-0.585504\pi$
$257$	−19.7676	−	11.4128i	−1.23307	−	0.711912i	−0.967668	+	0.252226i	$0.918837\pi$
$258$		0			0
$259$	0.0760445			0.00472517
$260$	5.11576	+	3.99652i	0.317266	+	0.247854i
$261$		0			0
$262$	−14.5548	−	8.40321i	−0.899198	−	0.519152i
$263$	−10.4885	+	6.05554i	−0.646749	+	0.373401i	−0.787209	−	0.616686i	$-0.788475\pi$
$263$	−10.4885	+	6.05554i	−0.646749	+	0.373401i	0.140461	+	0.990086i	$0.455142\pi$
$264$		0			0
$265$	−2.15701	+	15.3526i	−0.132504	+	0.943102i
$266$	1.15233	−	3.22501i	0.0706537	−	0.197738i
$267$		0			0
$268$	−7.31738	+	4.22469i	−0.446980	+	0.258064i
$269$	12.6168	+	21.8529i	0.769258	+	1.33239i	0.937966	+	0.346728i	$0.112707\pi$
$269$	12.6168	+	21.8529i	0.769258	+	1.33239i	−0.168708	+	0.985666i	$0.553960\pi$
$270$		0			0
$271$	−15.4652	−	26.7865i	−0.939444	−	1.62717i	−0.766511	−	0.642232i	$-0.778009\pi$
$271$	−15.4652	−	26.7865i	−0.939444	−	1.62717i	−0.172934	−	0.984933i	$-0.555325\pi$
$272$	−2.45651	−	1.41827i	−0.148948	−	0.0859951i
$273$		0			0
$274$	−2.19358			−0.132519
$275$	−1.35867	+	1.31227i	−0.0819307	+	0.0791328i
$276$		0			0
$277$		−	19.4938i		−	1.17127i	−0.810576	−	0.585634i	$-0.800846\pi$
$277$		−	19.4938i		−	1.17127i	0.810576	−	0.585634i	$-0.199154\pi$
$278$		−	1.67307i		−	0.100344i
$279$		0			0
$280$	0.658190	+	1.62888i	0.0393344	+	0.0973443i
$281$	−3.71755	+	6.43898i	−0.221770	+	0.384117i	−0.955346	−	0.295491i	$-0.904517\pi$
$281$	−3.71755	+	6.43898i	−0.221770	+	0.384117i	0.733575	+	0.679608i	$0.237850\pi$
$282$		0			0
$283$	1.48485	−	0.857279i	0.0882652	−	0.0509599i	−0.455218	−	0.890380i	$-0.650439\pi$
$283$	1.48485	−	0.857279i	0.0882652	−	0.0509599i	0.543483	+	0.839420i	$0.317105\pi$
$284$	−11.7397			−0.696626
$285$		0			0
$286$	1.09679			0.0648544
$287$	−1.95491	+	1.12867i	−0.115395	+	0.0666232i
$288$		0			0
$289$	−4.47703	+	7.75445i	−0.263355	+	0.456144i
$290$	−8.33585	+	3.36831i	−0.489498	+	0.197794i
$291$		0			0
$292$		−	2.26025i		−	0.132271i
$293$			7.93825i			0.463757i	0.972745	+	0.231879i	$0.0744872\pi$
$293$			7.93825i			0.463757i	−0.972745	+	0.231879i	$0.925513\pi$
$294$		0			0
$295$	−13.4362	+	17.1990i	−0.782284	+	1.00136i
$296$	−0.0967881			−0.00562569
$297$		0			0
$298$	−4.67526	−	2.69926i	−0.270831	−	0.156364i
$299$	13.1914	+	22.8481i	0.762876	+	1.32134i
$300$		0			0
$301$	0.168387	+	0.291654i	0.00970565	+	0.0168107i
$302$	7.85623	−	4.53580i	0.452076	−	0.261006i
$303$		0			0
$304$	−1.46666	+	4.10474i	−0.0841188	+	0.235423i
$305$	−10.0874	−	1.41726i	−0.577604	−	0.0811523i
$306$		0			0
$307$	−0.919506	+	0.530877i	−0.0524790	+	0.0302988i	−0.526010	−	0.850478i	$-0.676313\pi$
$307$	−0.919506	+	0.530877i	−0.0524790	+	0.0302988i	0.473531	+	0.880777i	$0.342979\pi$
$308$	0.257052	+	0.148409i	0.0146469	+	0.00845638i
$309$		0			0
$310$	−7.80372	−	6.09641i	−0.443222	−	0.346253i
$311$	−17.5210			−0.993524			−0.496762	−	0.867887i	$-0.665478\pi$
$311$	−17.5210			−0.993524			−0.496762	+	0.867887i	$0.665478\pi$
$312$		0			0
$313$	−10.6480	−	6.14764i	−0.601862	−	0.347485i	0.167912	−	0.985802i	$-0.446298\pi$
$313$	−10.6480	−	6.14764i	−0.601862	−	0.347485i	−0.769774	+	0.638317i	$0.779631\pi$
$314$	7.68421	−	13.3094i	0.433645	−	0.751095i
$315$		0			0
$316$	−1.57136			−0.0883959
$317$	−20.7188	−	11.9620i	−1.16368	−	0.671852i	−0.211498	−	0.977379i	$-0.567834\pi$
$317$	−20.7188	−	11.9620i	−1.16368	−	0.671852i	−0.952183	+	0.305527i	$0.901167\pi$
$318$		0			0
$319$	−0.759487	+	1.31547i	−0.0425231	+	0.0736522i
$320$	−0.837733	−	2.07321i	−0.0468307	−	0.115896i
$321$		0			0
$322$			7.13981i			0.397886i
$323$	−11.6432	−	4.16024i	−0.647847	−	0.231482i
$324$		0			0
$325$	−14.0846	+	3.51293i	−0.781272	+	0.194862i
$326$	3.65878	+	6.33719i	0.202641	+	0.350985i
$327$		0			0
$328$	2.48818	−	1.43655i	0.137387	−	0.0793202i
$329$	−4.74842	+	8.22451i	−0.261789	+	0.453432i
$330$		0			0
$331$	13.0810			0.718995			0.359497	−	0.933146i	$-0.382948\pi$
$331$	13.0810			0.718995			0.359497	+	0.933146i	$0.382948\pi$
$332$	−2.38639	−	1.37778i	−0.130970	−	0.0756157i
$333$		0			0
$334$	5.81135			0.317983
$335$	2.62867	−	18.7096i	0.143620	−	1.02222i
$336$		0			0
$337$	14.3953	−	8.31111i	0.784160	−	0.452735i	−0.0537427	−	0.998555i	$-0.517115\pi$
$337$	14.3953	−	8.31111i	0.784160	−	0.452735i	0.837903	+	0.545820i	$0.183782\pi$
$338$	−3.95891	−	2.28568i	−0.215337	−	0.124325i
$339$		0			0
$340$	5.88074	−	2.37626i	0.318928	−	0.128871i
$341$	−1.67307			−0.0906019
$342$		0			0
$343$			10.5145i			0.567731i
$344$	−0.214320	−	0.371213i	−0.0115553	−	0.0200144i
$345$		0			0
$346$	−4.36273	+	7.55647i	−0.234542	+	0.406238i
$347$	−4.62989	+	2.67307i	−0.248546	+	0.143498i	−0.619098	−	0.785314i	$-0.712502\pi$
$347$	−4.62989	+	2.67307i	−0.248546	+	0.143498i	0.370552	+	0.928812i	$0.379168\pi$
$348$		0			0
$349$	−0.882468			−0.0472374			−0.0236187	−	0.999721i	$-0.507519\pi$
$349$	−0.882468			−0.0472374			−0.0236187	+	0.999721i	$0.507519\pi$
$350$	−3.77631	−	1.08250i	−0.201852	−	0.0578620i
$351$		0			0
$352$	−0.327171	−	0.188892i	−0.0174383	−	0.0100680i
$353$		−	15.1032i		−	0.803864i	−0.915669	−	0.401932i	$-0.868339\pi$
$353$		−	15.1032i		−	0.803864i	0.915669	−	0.401932i	$-0.131661\pi$
$354$		0			0
$355$	16.1608	−	20.6866i	0.857725	−	1.09793i
$356$	5.96912	+	10.3388i	0.316363	+	0.547957i
$357$		0			0
$358$	−20.1183	+	11.6153i	−1.06329	+	0.613888i
$359$	7.82394	+	13.5515i	0.412932	+	0.715219i	0.995209	−	0.0977715i	$-0.0311714\pi$
$359$	7.82394	+	13.5515i	0.412932	+	0.715219i	−0.582277	+	0.812990i	$0.697838\pi$
$360$		0			0
$361$	−3.07851	+	18.7489i	−0.162027	+	0.986786i
$362$			7.54617i			0.396618i
$363$		0			0
$364$	1.14050	+	1.97540i	0.0597783	+	0.103539i
$365$	3.98280	+	3.11143i	0.208469	+	0.162860i
$366$		0			0
$367$	−27.8642	−	16.0874i	−1.45450	−	0.839756i	−0.455769	−	0.890098i	$-0.650636\pi$
$367$	−27.8642	−	16.0874i	−1.45450	−	0.839756i	−0.998732	+	0.0503417i	$0.983969\pi$
$368$		−	9.08742i		−	0.473715i
$369$		0			0
$370$	0.133237	−	0.170551i	0.00692667	−	0.00886650i
$371$	−2.72369	+	4.71757i	−0.141407	+	0.244924i
$372$		0			0
$373$			15.1160i			0.782677i	0.920247	+	0.391338i	$0.127988\pi$
$373$			15.1160i			0.782677i	−0.920247	+	0.391338i	$0.872012\pi$
$374$	0.535799	−	0.928032i	0.0277055	−	0.0479874i
$375$		0			0
$376$	6.04371	−	10.4680i	0.311681	−	0.539847i
$377$	−10.1092	+	5.83654i	−0.520649	+	0.300597i
$378$		0			0
$379$	0.907658			0.0466232			0.0233116	−	0.999728i	$-0.492579\pi$
$379$	0.907658			0.0466232			0.0233116	+	0.999728i	$0.492579\pi$
$380$	−5.21399	−	8.23494i	−0.267472	−	0.422444i
$381$		0			0
$382$	17.7276	−	10.2351i	0.907025	−	0.523671i
$383$	−0.526479	+	0.303963i	−0.0269018	+	0.0155318i	−0.513391	−	0.858155i	$-0.671611\pi$
$383$	−0.526479	+	0.303963i	−0.0269018	+	0.0155318i	0.486489	+	0.873687i	$0.338277\pi$
$384$		0			0
$385$	−0.615366	+	0.248654i	−0.0313619	+	0.0126726i
$386$	9.46198	−	16.3886i	0.481602	−	0.834159i
$387$		0			0
$388$			3.44446i			0.174866i
$389$	6.04048	−	10.4624i	0.306265	−	0.530466i	−0.671277	−	0.741206i	$-0.734254\pi$
$389$	6.04048	−	10.4624i	0.306265	−	0.530466i	0.977542	+	0.210740i	$0.0675874\pi$
$390$		0			0
$391$	25.7768			1.30359
$392$		−	6.38271i		−	0.322375i
$393$		0			0
$394$	−0.865190	−	1.49855i	−0.0435876	−	0.0754960i
$395$	2.16311	−	2.76890i	0.108838	−	0.139318i
$396$		0			0
$397$	16.3351	−	9.43110i	0.819837	−	0.473333i	−0.0305230	−	0.999534i	$-0.509717\pi$
$397$	16.3351	−	9.43110i	0.819837	−	0.473333i	0.850360	+	0.526201i	$0.176384\pi$
$398$		−	15.0716i		−	0.755471i
$399$		0			0
$400$	4.80642	+	1.37778i	0.240321	+	0.0688892i
$401$	4.88739	+	8.46521i	0.244065	+	0.422732i	0.961868	−	0.273513i	$-0.0881858\pi$
$401$	4.88739	+	8.46521i	0.244065	+	0.422732i	−0.717804	+	0.696246i	$0.754852\pi$
$402$		0			0
$403$	−11.1347	−	6.42864i	−0.554660	−	0.320233i
$404$	−8.54617	−	14.8024i	−0.425188	−	0.736447i
$405$		0			0
$406$	−3.15902			−0.156779
$407$		−	0.0365650i		−	0.00181246i
$408$		0			0
$409$	−19.1916	+	33.2408i	−0.948963	+	1.64365i	−0.201348	+	0.979520i	$0.564532\pi$
$409$	−19.1916	+	33.2408i	−0.948963	+	1.64365i	−0.747615	+	0.664133i	$0.768801\pi$
$410$	−0.893844	+	6.36196i	−0.0441438	+	0.314195i
$411$		0			0
$412$	−7.02999	−	4.05877i	−0.346343	−	0.199961i
$413$	−6.64122	+	3.83431i	−0.326793	+	0.188674i
$414$		0			0
$415$	5.71288	−	2.30843i	0.280434	−	0.113316i
$416$	−1.45161	−	2.51426i	−0.0711708	−	0.123272i
$417$		0			0
$418$	−1.55071	−	0.554082i	−0.0758476	−	0.0271010i
$419$	30.7560			1.50253			0.751266	−	0.660000i	$-0.229444\pi$
$419$	30.7560			1.50253			0.751266	+	0.660000i	$0.229444\pi$
$420$		0			0
$421$	6.31433	+	10.9367i	0.307742	+	0.533024i	0.977868	−	0.209223i	$-0.0670934\pi$
$421$	6.31433	+	10.9367i	0.307742	+	0.533024i	−0.670126	+	0.742247i	$0.733760\pi$
$422$	−11.5320	−	6.65801i	−0.561370	−	0.324107i
$423$		0			0
$424$	3.46666	−	6.00443i	0.168356	−	0.291601i
$425$	−3.90813	+	13.6336i	−0.189572	+	0.661326i
$426$		0			0
$427$	−3.09968	−	1.78960i	−0.150004	−	0.0866047i
$428$	−15.3990	−	8.89062i	−0.744339	−	0.429744i
$429$		0			0
$430$	0.949145	+	0.133353i	0.0457718	+	0.00643086i
$431$	−17.6763	+	30.6162i	−0.851437	+	1.47473i	0.0284739	+	0.999595i	$0.490935\pi$
$431$	−17.6763	+	30.6162i	−0.851437	+	1.47473i	−0.879911	+	0.475138i	$0.842398\pi$
$432$		0			0
$433$	−18.0052	−	10.3953i	−0.865274	−	0.499566i	0.000500727	−	1.00000i	$-0.499841\pi$
$433$	−18.0052	−	10.3953i	−0.865274	−	0.499566i	−0.865775	+	0.500434i	$0.833174\pi$
$434$	−1.73975	−	3.01333i	−0.0835105	−	0.144645i
$435$		0			0
$436$	1.44446			0.0691771
$437$	−7.10822	−	38.9681i	−0.340032	−	1.86410i
$438$		0			0
$439$	−1.96444	−	3.40251i	−0.0937576	−	0.162393i	0.815332	−	0.578994i	$-0.196555\pi$
$439$	−1.96444	−	3.40251i	−0.0937576	−	0.162393i	−0.909089	+	0.416601i	$0.863221\pi$
$440$	0.783227	−	0.316482i	0.0373389	−	0.0150877i
$441$		0			0
$442$	7.13177	−	4.11753i	0.339224	−	0.195851i
$443$	−1.38265	−	0.798275i	−0.0656918	−	0.0379272i	0.466794	−	0.884366i	$-0.345409\pi$
$443$	−1.38265	−	0.798275i	−0.0656918	−	0.0379272i	−0.532486	+	0.846439i	$0.678742\pi$
$444$		0			0
$445$	−26.4351	−	3.71408i	−1.25314	−	0.176064i
$446$	−9.58419	+	16.6003i	−0.453825	+	0.786047i
$447$		0			0
$448$		−	0.785680i		−	0.0371199i
$449$	−14.4588			−0.682351			−0.341175	−	0.940000i	$-0.610825\pi$
$449$	−14.4588			−0.682351			−0.341175	+	0.940000i	$0.610825\pi$
$450$		0			0
$451$	0.542706	+	0.939995i	0.0255550	+	0.0442626i
$452$	12.3980	+	7.15801i	0.583155	+	0.336685i
$453$		0			0
$454$	−3.44123	−	5.96039i	−0.161505	−	0.279735i
$455$	−5.05086	−	0.709636i	−0.236788	−	0.0332682i
$456$		0			0
$457$			28.9052i			1.35213i	0.736842	+	0.676065i	$0.236316\pi$
$457$			28.9052i			1.35213i	−0.736842	+	0.676065i	$0.763684\pi$
$458$	−11.9046	+	6.87310i	−0.556264	+	0.321159i
$459$		0			0
$460$	16.0130	+	12.5096i	0.746609	+	0.583264i
$461$	1.22369	+	2.11949i	0.0569928	+	0.0987145i	0.893114	−	0.449830i	$-0.148515\pi$
$461$	1.22369	+	2.11949i	0.0569928	+	0.0987145i	−0.836121	+	0.548545i	$0.815182\pi$
$462$		0			0
$463$		−	7.67460i		−	0.356669i	−0.983970	−	0.178335i	$-0.942929\pi$
$463$		−	7.67460i		−	0.356669i	0.983970	−	0.178335i	$-0.0570709\pi$
$464$	4.02074			0.186658
$465$		0			0
$466$	−3.39853	+	5.88642i	−0.157434	+	0.272683i
$467$		−	9.78123i		−	0.452622i	−0.974055	−	0.226311i	$-0.927334\pi$
$467$		−	9.78123i		−	0.452622i	0.974055	−	0.226311i	$-0.0726665\pi$
$468$		0			0
$469$	3.31926	−	5.74912i	0.153269	−	0.265470i
$470$	10.1260	+	25.0598i	0.467079	+	1.15592i
$471$		0			0
$472$	8.45283	−	4.88025i	0.389073	−	0.224632i
$473$	0.140238	−	0.0809666i	0.00644817	−	0.00372285i
$474$		0			0
$475$	21.6883	+	2.14853i	0.995129	+	0.0985812i
$476$	2.22861			0.102148
$477$		0			0
$478$	−9.40268	+	5.42864i	−0.430069	+	0.248300i
$479$	16.9716	−	29.3956i	0.775451	−	1.34312i	−0.159089	−	0.987264i	$-0.550856\pi$
$479$	16.9716	−	29.3956i	0.775451	−	1.34312i	0.934540	−	0.355857i	$-0.115811\pi$
$480$		0			0
$481$	0.140498	−	0.243350i	0.00640616	−	0.0110958i
$482$		−	9.68736i		−	0.441247i
$483$		0			0
$484$	−5.42864	+	9.40268i	−0.246756	+	0.427395i
$485$	−6.06950	−	4.74160i	−0.275602	−	0.215305i
$486$		0			0
$487$		−	33.8780i		−	1.53516i	−0.640953	−	0.767580i	$-0.721461\pi$
$487$		−	33.8780i		−	1.53516i	0.640953	−	0.767580i	$-0.278539\pi$
$488$	3.94521	+	2.27777i	0.178591	+	0.103110i
$489$		0			0
$490$	11.2470	+	8.78635i	0.508087	+	0.396927i
$491$	−20.5622	−	35.6148i	−0.927960	−	1.60727i	−0.786729	−	0.617298i	$-0.788227\pi$
$491$	−20.5622	−	35.6148i	−0.927960	−	1.60727i	−0.141231	−	0.989977i	$-0.545106\pi$
$492$		0			0
$493$			11.4050i			0.513655i
$494$	−8.19135	−	9.64603i	−0.368546	−	0.433995i
$495$		0			0
$496$	2.21432	+	3.83531i	0.0994259	+	0.172211i
$497$	7.98795	−	4.61184i	0.358308	−	0.206869i
$498$		0			0
$499$	9.98987	+	17.3030i	0.447208	+	0.774587i	0.998203	−	0.0599217i	$-0.0190851\pi$
$499$	9.98987	+	17.3030i	0.447208	+	0.774587i	−0.550995	+	0.834508i	$0.685752\pi$
$500$	−9.04426	+	6.57277i	−0.404472	+	0.293943i
$501$		0			0
$502$		−	15.0923i		−	0.673604i
$503$	18.2708	+	10.5486i	0.814653	+	0.470340i	0.848569	−	0.529084i	$-0.177465\pi$
$503$	18.2708	+	10.5486i	0.814653	+	0.470340i	−0.0339160	+	0.999425i	$0.510798\pi$
$504$		0			0
$505$	37.8479	+	5.31756i	1.68421	+	0.236628i
$506$	3.43309			0.152619
$507$		0			0
$508$	3.14252	−	1.81433i	0.139427	−	0.0804981i
$509$	11.3620	−	19.6795i	0.503610	−	0.872278i	−0.496381	−	0.868105i	$-0.665338\pi$
$509$	11.3620	−	19.6795i	0.503610	−	0.872278i	0.999991	−	0.00417367i	$-0.00132853\pi$
$510$		0			0
$511$	0.887918	+	1.53792i	0.0392792	+	0.0680335i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−22.8256			−1.00680
$515$	16.8294	−	6.80032i	0.741590	−	0.299658i
$516$		0			0
$517$	3.95465	+	2.28322i	0.173925	+	0.100416i
$518$	0.0658565	−	0.0380222i	0.00289357	−	0.00167060i
$519$		0			0
$520$	6.42864	+	0.903212i	0.281914	+	0.0396085i
$521$	−29.0923			−1.27456			−0.637279	−	0.770633i	$-0.719940\pi$
$521$	−29.0923			−1.27456			−0.637279	+	0.770633i	$0.719940\pi$
$522$		0			0
$523$	−6.84186	−	3.95015i	−0.299174	−	0.172728i	0.342898	−	0.939373i	$-0.388591\pi$
$523$	−6.84186	−	3.95015i	−0.299174	−	0.172728i	−0.642072	+	0.766645i	$0.721925\pi$
$524$	−16.8064			−0.734192
$525$		0			0
$526$	−6.05554	+	10.4885i	−0.264034	+	0.457320i
$527$	−10.8790	+	6.28100i	−0.473897	+	0.273604i
$528$		0			0
$529$	29.7906	+	51.5988i	1.29524	+	2.24343i
$530$	5.80827	+	14.3742i	0.252295	+	0.624377i
$531$		0			0
$532$	−0.614563	−	3.36911i	−0.0266447	−	0.146069i
$533$			8.34122i			0.361298i
$534$		0			0
$535$	36.8643	−	14.8959i	1.59378	−	0.644007i
$536$	−4.22469	+	7.31738i	−0.182479	+	0.316063i
$537$		0			0
$538$	21.8529	+	12.6168i	0.942145	+	0.543947i
$539$	2.41129			0.103861
$540$		0			0
$541$	10.3160	−	17.8679i	0.443521	−	0.768201i	−0.554427	−	0.832232i	$-0.687063\pi$
$541$	10.3160	−	17.8679i	0.443521	−	0.768201i	0.997948	+	0.0640318i	$0.0203959\pi$
$542$	−26.7865	−	15.4652i	−1.15058	−	0.664287i
$543$		0			0
$544$	−2.83654			−0.121615
$545$	−1.98843	+	2.54529i	−0.0851748	+	0.109028i
$546$		0			0
$547$	−7.43965	−	4.29529i	−0.318097	−	0.183653i	0.332447	−	0.943122i	$-0.392126\pi$
$547$	−7.43965	−	4.29529i	−0.318097	−	0.183653i	−0.650544	+	0.759469i	$0.725459\pi$
$548$	−1.89969	+	1.09679i	−0.0811508	+	0.0468525i
$549$		0			0
$550$	−0.520505	+	1.81579i	−0.0221944	+	0.0774256i
$551$	17.2415	−	3.14504i	0.734513	−	0.133983i
$552$		0			0
$553$	1.06918	−	0.617293i	0.0454663	−	0.0262500i
$554$	−9.74689	−	16.8821i	−0.414106	−	0.717252i
$555$		0			0
$556$	−0.836535	−	1.44892i	−0.0354770	−	0.0614480i
$557$	21.3209	+	12.3097i	0.903397	+	0.521577i	0.878301	−	0.478108i	$-0.158677\pi$
$557$	21.3209	+	12.3097i	0.903397	+	0.521577i	0.0250964	+	0.999685i	$0.492011\pi$
$558$		0			0
$559$	1.24443			0.0526338
$560$	1.38445	+	1.08156i	0.0585037	+	0.0457041i
$561$		0			0
$562$			7.43509i			0.313630i
$563$		−	33.6958i		−	1.42011i	−0.704146	−	0.710055i	$-0.748670\pi$
$563$		−	33.6958i		−	1.42011i	0.704146	−	0.710055i	$-0.251330\pi$
$564$		0			0
$565$	−29.6802	+	11.9930i	−1.24865	+	0.504550i
$566$	0.857279	−	1.48485i	0.0360341	−	0.0624129i
$567$		0			0
$568$	−10.1669	+	5.86987i	−0.426594	+	0.246294i
$569$	−3.59703			−0.150795			−0.0753976	−	0.997154i	$-0.524023\pi$
$569$	−3.59703			−0.150795			−0.0753976	+	0.997154i	$0.524023\pi$
$570$		0			0
$571$	22.2623			0.931647			0.465823	−	0.884878i	$-0.345758\pi$
$571$	22.2623			0.931647			0.465823	+	0.884878i	$0.345758\pi$
$572$	0.949846	−	0.548394i	0.0397151	−	0.0229295i
$573$		0			0
$574$	−1.12867	+	1.95491i	−0.0471097	+	0.0815965i
$575$	−44.0865	+	10.9959i	−1.83853	+	0.458562i
$576$		0			0
$577$		−	34.7719i		−	1.44757i	−0.690025	−	0.723786i	$-0.742400\pi$
$577$		−	34.7719i		−	1.44757i	0.690025	−	0.723786i	$-0.257600\pi$
$578$			8.95407i			0.372440i
$579$		0			0
$580$	−5.53490	+	7.08497i	−0.229824	+	0.294187i
$581$	2.16500			0.0898192
$582$		0			0
$583$	2.26838	+	1.30965i	0.0939468	+	0.0542402i
$584$	−1.13013	−	1.95744i	−0.0467650	−	0.0809993i
$585$		0			0
$586$	3.96912	+	6.87472i	0.163963	+	0.283992i
$587$	21.7306	−	12.5462i	0.896918	−	0.517836i	0.0207191	−	0.999785i	$-0.493404\pi$
$587$	21.7306	−	12.5462i	0.896918	−	0.517836i	0.876199	+	0.481949i	$0.160071\pi$
$588$		0			0
$589$	12.4953	+	14.7143i	0.514861	+	0.606293i
$590$	−3.03657	+	21.6128i	−0.125013	+	0.889787i
$591$		0			0
$592$	−0.0838209	+	0.0483940i	−0.00344502	+	0.00198898i
$593$	36.9025	+	21.3057i	1.51540	+	0.874919i	0.999837	+	0.0180690i	$0.00575185\pi$
$593$	36.9025	+	21.3057i	1.51540	+	0.874919i	0.515567	+	0.856850i	$0.327581\pi$
$594$		0			0
$595$	−3.06788	+	3.92704i	−0.125771	+	0.160993i
$596$	−5.39853			−0.221132
$597$		0			0
$598$	22.8481	+	13.1914i	0.934328	+	0.539435i
$599$	21.3652	−	37.0056i	0.872958	−	1.51201i	0.0140358	−	0.999901i	$-0.495532\pi$
$599$	21.3652	−	37.0056i	0.872958	−	1.51201i	0.858922	−	0.512106i	$-0.171135\pi$
$600$		0			0
$601$	−40.1481			−1.63768			−0.818838	−	0.574025i	$-0.805381\pi$
$601$	−40.1481			−1.63768			−0.818838	+	0.574025i	$0.805381\pi$
$602$	0.291654	+	0.168387i	0.0118869	+	0.00686293i
$603$		0			0
$604$	4.53580	−	7.85623i	0.184559	−	0.319666i
$605$	−9.09550	−	22.5094i	−0.369785	−	0.915138i
$606$		0			0
$607$		−	36.0988i		−	1.46520i	−0.680657	−	0.732602i	$-0.738305\pi$
$607$		−	36.0988i		−	1.46520i	0.680657	−	0.732602i	$-0.261695\pi$
$608$	0.782204	+	4.28814i	0.0317226	+	0.173907i
$609$		0			0
$610$	−9.44459	+	3.81632i	−0.382400	+	0.154518i
$611$	17.5462	+	30.3909i	0.709842	+	1.22948i
$612$		0			0
$613$	−21.8144	+	12.5946i	−0.881076	+	0.508690i	−0.871013	−	0.491260i	$-0.836537\pi$
$613$	−21.8144	+	12.5946i	−0.881076	+	0.508690i	−0.0100632	+	0.999949i	$0.503203\pi$
$614$	−0.530877	+	0.919506i	−0.0214245	+	0.0371083i
$615$		0			0
$616$	0.296818			0.0119591
$617$	2.97740	+	1.71900i	0.119866	+	0.0692045i	0.558734	−	0.829347i	$-0.311287\pi$
$617$	2.97740	+	1.71900i	0.119866	+	0.0692045i	−0.438868	+	0.898551i	$0.644621\pi$
$618$		0			0
$619$	20.7397			0.833601			0.416800	−	0.908998i	$-0.363151\pi$
$619$	20.7397			0.833601			0.416800	+	0.908998i	$0.363151\pi$
$620$	−9.80642	−	1.37778i	−0.393835	−	0.0553332i
$621$		0			0
$622$	−15.1736	+	8.76049i	−0.608407	+	0.351264i
$623$	−8.12301	−	4.68982i	−0.325442	−	0.187894i
$624$		0			0
$625$	0.868304	−	24.9849i	0.0347321	−	0.999397i
$626$	−12.2953			−0.491418
$627$		0			0
$628$		−	15.3684i		−	0.613267i
$629$	−0.137271	−	0.237761i	−0.00547337	−	0.00948015i
$630$		0			0
$631$	−17.1629	+	29.7271i	−0.683246	+	1.18342i	0.290739	+	0.956802i	$0.406099\pi$
$631$	−17.1629	+	29.7271i	−0.683246	+	1.18342i	−0.973985	+	0.226614i	$0.927234\pi$
$632$	−1.36084	+	0.785680i	−0.0541312	+	0.0312527i
$633$		0			0
$634$	−23.9240			−0.950142
$635$	−1.12891	+	8.03503i	−0.0447993	+	0.318861i
$636$		0			0
$637$	16.0478	+	9.26517i	0.635835	+	0.367100i
$638$			1.51897i			0.0601368i
$639$		0			0
$640$	−1.76210	−	1.37659i	−0.0696532	−	0.0544144i
$641$	−1.54125	−	2.66952i	−0.0608757	−	0.105440i	0.833981	−	0.551793i	$-0.186056\pi$
$641$	−1.54125	−	2.66952i	−0.0608757	−	0.105440i	−0.894857	+	0.446353i	$0.852723\pi$
$642$		0			0
$643$	27.9069	−	16.1121i	1.10054	−	0.635398i	0.164179	−	0.986431i	$-0.447503\pi$
$643$	27.9069	−	16.1121i	1.10054	−	0.635398i	0.936363	+	0.351032i	$0.114169\pi$
$644$	3.56990	+	6.18325i	0.140674	+	0.243654i
$645$		0			0
$646$	−12.1635	+	2.21875i	−0.478565	+	0.0872956i
$647$			4.90813i			0.192959i	0.995335	+	0.0964793i	$0.0307582\pi$
$647$			4.90813i			0.192959i	−0.995335	+	0.0964793i	$0.969242\pi$
$648$		0			0
$649$	1.84368	+	3.19335i	0.0723708	+	0.125350i
$650$	−10.4411	+	10.0846i	−0.409535	+	0.395550i
$651$		0			0
$652$	6.33719	+	3.65878i	0.248184	+	0.143289i
$653$			41.4405i			1.62169i	0.585260	+	0.810846i	$0.300993\pi$
$653$			41.4405i			1.62169i	−0.585260	+	0.810846i	$0.699007\pi$
$654$		0			0
$655$	23.1355	−	29.6147i	0.903979	−	1.15714i
$656$	1.43655	−	2.48818i	0.0560879	−	0.0971470i
$657$		0			0
$658$			9.49685i			0.370226i
$659$	0.665688	−	1.15300i	0.0259315	−	0.0449147i	−0.852768	−	0.522289i	$-0.825078\pi$
$659$	0.665688	−	1.15300i	0.0259315	−	0.0449147i	0.878700	+	0.477375i	$0.158411\pi$
$660$		0			0
$661$	18.1891	−	31.5045i	0.707475	−	1.22538i	−0.258316	−	0.966061i	$-0.583167\pi$
$661$	18.1891	−	31.5045i	0.707475	−	1.22538i	0.965791	−	0.259322i	$-0.0834992\pi$
$662$	11.3284	−	6.54048i	0.440293	−	0.254203i
$663$		0			0
$664$	−2.75557			−0.106937
$665$	6.78272	+	3.55495i	0.263022	+	0.137855i
$666$		0			0
$667$	−31.6430	+	18.2691i	−1.22522	+	0.707382i
$668$	5.03277	−	2.90567i	0.194724	−	0.112424i
$669$		0			0
$670$	−7.07832	−	17.5174i	−0.273459	−	0.676754i
$671$	−0.860506	+	1.49044i	−0.0332195	+	0.0575378i
$672$		0			0
$673$			38.8069i			1.49590i	0.663757	+	0.747948i	$0.268961\pi$
$673$			38.8069i			1.49590i	−0.663757	+	0.747948i	$0.731039\pi$
$674$	8.31111	−	14.3953i	0.320132	−	0.554485i
$675$		0			0
$676$	−4.57136			−0.175822
$677$			31.6242i			1.21542i	0.794160	+	0.607709i	$0.207911\pi$
$677$			31.6242i			1.21542i	−0.794160	+	0.607709i	$0.792089\pi$
$678$		0			0
$679$	−1.35312	−	2.34368i	−0.0519281	−	0.0899421i
$680$	3.90474	−	4.99827i	0.149740	−	0.191675i
$681$		0			0
$682$	−1.44892	+	0.836535i	−0.0554821	+	0.0320326i
$683$			24.2000i			0.925988i	0.886361	+	0.462994i	$0.153225\pi$
$683$			24.2000i			0.925988i	−0.886361	+	0.462994i	$0.846775\pi$
$684$		0			0
$685$	0.682439	−	4.85728i	0.0260746	−	0.185587i
$686$	5.25726	+	9.10585i	0.200723	+	0.347663i
$687$		0			0
$688$	−0.371213	−	0.214320i	−0.0141524	−	0.00817086i
$689$	10.0645	+	17.4321i	0.383425	+	0.664112i
$690$		0			0
$691$	−21.1782			−0.805658			−0.402829	−	0.915275i	$-0.631973\pi$
$691$	−21.1782			−0.805658			−0.402829	+	0.915275i	$0.631973\pi$
$692$			8.72546i			0.331692i
$693$		0			0
$694$	−2.67307	+	4.62989i	−0.101468	+	0.175748i
$695$	3.70471	+	0.520505i	0.140528	+	0.0197439i
$696$		0			0
$697$	7.05780	+	4.07483i	0.267333	+	0.154345i
$698$	−0.764240	+	0.441234i	−0.0289269	+	0.0167010i
$699$		0			0
$700$	−3.81163	+	0.950685i	−0.144066	+	0.0359325i
$701$	−11.1635	−	19.3357i	−0.421638	−	0.730299i	0.574462	−	0.818531i	$-0.305211\pi$
$701$	−11.1635	−	19.3357i	−0.421638	−	0.730299i	−0.996100	+	0.0882326i	$0.971878\pi$
$702$		0			0
$703$	−0.321582	+	0.273086i	−0.0121287	+	0.0102996i
$704$	−0.377784			−0.0142383
$705$		0			0
$706$	−7.55162	−	13.0798i	−0.284209	−	0.492264i
$707$	11.6300	+	6.71456i	0.437389	+	0.252527i
$708$		0			0
$709$	−11.2733	+	19.5260i	−0.423379	+	0.733313i	−0.996267	−	0.0863198i	$-0.972489\pi$
$709$	−11.2733	+	19.5260i	−0.423379	+	0.733313i	0.572889	+	0.819633i	$0.305823\pi$
$710$	3.65233	−	25.9956i	0.137069	−	0.975596i
$711$		0			0
$712$	10.3388	+	5.96912i	0.387464	+	0.223702i
$713$	−34.8531	−	20.1225i	−1.30526	−	0.753592i
$714$		0			0
$715$	−0.341219	+	2.42864i	−0.0127609	+	0.0908260i
$716$	−11.6153	+	20.1183i	−0.434084	+	0.751856i
$717$		0			0
$718$	13.5515	+	7.82394i	0.505736	+	0.291987i
$719$	16.3111	+	28.2517i	0.608302	+	1.05361i	0.991520	+	0.129952i	$0.0414822\pi$
$719$	16.3111	+	28.2517i	0.608302	+	1.05361i	−0.383219	+	0.923658i	$0.625184\pi$
$720$		0			0
$721$	6.37778			0.237521
$722$	6.70841	+	17.7763i	0.249661	+	0.661566i
$723$		0			0
$724$	3.77309	+	6.53518i	0.140226	+	0.242878i
$725$	−4.86516	−	19.5061i	−0.180688	−	0.724440i
$726$		0			0
$727$	−32.6741	+	18.8644i	−1.21182	+	0.699643i	−0.963155	−	0.268948i	$-0.913324\pi$
$727$	−32.6741	+	18.8644i	−1.21182	+	0.699643i	−0.248662	+	0.968590i	$0.579991\pi$
$728$	1.97540	+	1.14050i	0.0732132	+	0.0422697i
$729$		0			0
$730$	5.00492	+	0.703182i	0.185240	+	0.0260259i
$731$	0.607926	−	1.05296i	0.0224849	−	0.0389451i
$732$		0			0
$733$		−	47.5531i		−	1.75641i	−0.478281	−	0.878207i	$-0.658740\pi$
$733$		−	47.5531i		−	1.75641i	0.478281	−	0.878207i	$-0.341260\pi$
$734$	−32.1748			−1.18760
$735$		0			0
$736$	−4.54371	−	7.86994i	−0.167483	−	0.290090i
$737$	−2.76439	−	1.59602i	−0.101828	−	0.0587902i
$738$		0			0
$739$	−14.6602	−	25.3923i	−0.539286	−	0.934070i	−0.998943	−	0.0459735i	$-0.985361\pi$
$739$	−14.6602	−	25.3923i	−0.539286	−	0.934070i	0.459657	−	0.888096i	$-0.347972\pi$
$740$	0.0301115	−	0.214320i	0.00110692	−	0.00787855i
$741$		0			0
$742$			5.44738i			0.199979i
$743$	7.39176	−	4.26764i	0.271177	−	0.156564i	−0.358245	−	0.933628i	$-0.616625\pi$
$743$	7.39176	−	4.26764i	0.271177	−	0.156564i	0.629423	+	0.777063i	$0.283291\pi$
$744$		0			0
$745$	7.43154	−	9.51276i	0.272271	−	0.348521i
$746$	7.55800	+	13.0908i	0.276718	+	0.479290i
$747$		0			0
$748$		−	1.07160i		−	0.0391815i
$749$	13.9704			0.510466
$750$		0			0
$751$	3.79213	−	6.56817i	0.138377	−	0.239676i	−0.788505	−	0.615028i	$-0.789145\pi$
$751$	3.79213	−	6.56817i	0.138377	−	0.239676i	0.926882	+	0.375352i	$0.122478\pi$
$752$		−	12.0874i		−	0.440783i
$753$		0			0
$754$	−5.83654	+	10.1092i	−0.212554	+	0.368154i
$755$	7.59957	+	18.8073i	0.276577	+	0.684469i
$756$		0			0
$757$	−26.1600	+	15.1035i	−0.950801	+	0.548945i	−0.893330	−	0.449402i	$-0.851637\pi$
$757$	−26.1600	+	15.1035i	−0.950801	+	0.548945i	−0.0574714	+	0.998347i	$0.518304\pi$
$758$	0.786055	−	0.453829i	0.0285508	−	0.0164838i
$759$		0			0
$760$	−8.63292	−	4.52468i	−0.313149	−	0.164127i
$761$	46.3526			1.68028			0.840140	−	0.542369i	$-0.182473\pi$
$761$	46.3526			1.68028			0.840140	+	0.542369i	$0.182473\pi$
$762$		0			0
$763$	−0.982839	+	0.567442i	−0.0355812	+	0.0205428i
$764$	10.2351	−	17.7276i	0.370292	−	0.641364i
$765$		0			0
$766$	−0.303963	+	0.526479i	−0.0109826	+	0.0190225i
$767$			28.3368i			1.02318i
$768$		0			0
$769$	3.85950	−	6.68485i	0.139177	−	0.241062i	−0.788008	−	0.615665i	$-0.788888\pi$
$769$	3.85950	−	6.68485i	0.139177	−	0.241062i	0.927185	+	0.374603i	$0.122221\pi$
$770$	−0.408595	+	0.523023i	−0.0147248	+	0.0188485i
$771$		0			0
$772$		−	18.9240i		−	0.681088i
$773$	18.0095	+	10.3978i	0.647755	+	0.373982i	0.787596	−	0.616193i	$-0.211326\pi$
$773$	18.0095	+	10.3978i	0.647755	+	0.373982i	−0.139841	+	0.990174i	$0.544659\pi$
$774$		0			0
$775$	15.9272	−	15.3833i	0.572122	−	0.552584i
$776$	1.72223	+	2.98299i	0.0618245	+	0.107083i
$777$		0			0
$778$		−	12.0810i		−	0.433124i
$779$	4.21387	−	11.7933i	0.150977	−	0.422540i
$780$		0			0
$781$	−2.21755	−	3.84090i	−0.0793501	−	0.137438i
$782$	22.3234	−	12.8884i	0.798282	−	0.460888i
$783$		0			0
$784$	−3.19135	−	5.52759i	−0.113977	−	0.197414i
$785$	27.0807	+	21.1560i	0.966553	+	0.755089i
$786$		0			0
$787$			31.7255i			1.13089i	0.824786	+	0.565445i	$0.191296\pi$
$787$			31.7255i			1.13089i	−0.824786	+	0.565445i	$0.808704\pi$
$788$	−1.49855	−	0.865190i	−0.0533837	−	0.0308211i
$789$		0			0
$790$	0.488863	−	3.47949i	0.0173929	−	0.123795i
$791$	−11.2478			−0.399927
$792$		0			0
$793$	−11.4538	+	6.61285i	−0.406736	+	0.234829i
$794$	9.43110	−	16.3351i	0.334697	−	0.579713i
$795$		0			0
$796$	−7.53580	−	13.0524i	−0.267099	−	0.462630i
$797$		−	54.5417i		−	1.93197i	−0.258604	−	0.965984i	$-0.583262\pi$
$797$		−	54.5417i		−	1.93197i	0.258604	−	0.965984i	$-0.416738\pi$
$798$		0			0
$799$	34.2864			1.21297
$800$	4.85138	−	1.21002i	0.171522	−	0.0427805i
$801$		0			0
$802$	8.46521	+	4.88739i	0.298917	+	0.172580i
$803$	0.739489	−	0.426944i	0.0260960	−	0.0150665i
$804$		0			0
$805$	−15.8098	−	2.22125i	−0.557223	−	0.0782888i
$806$	−12.8573			−0.452878
$807$		0			0
$808$	−14.8024	−	8.54617i	−0.520747	−	0.300653i
$809$	−14.4429			−0.507786			−0.253893	−	0.967232i	$-0.581711\pi$
$809$	−14.4429			−0.507786			−0.253893	+	0.967232i	$0.581711\pi$
$810$		0			0
$811$	16.0079	−	27.7265i	0.562114	−	0.973610i	−0.435198	−	0.900335i	$-0.643322\pi$
$811$	16.0079	−	27.7265i	0.562114	−	0.973610i	0.997312	−	0.0732748i	$-0.0233450\pi$
$812$	−2.73579	+	1.57951i	−0.0960074	+	0.0554299i
$813$		0			0
$814$	−0.0182825	−	0.0316662i	−0.000640802	−	0.00110990i
$815$	−15.1708	+	6.13016i	−0.531412	+	0.214730i
$816$		0			0
$817$	−1.75945	−	0.628669i	−0.0615555	−	0.0219943i
$818$			38.3832i			1.34204i
$819$		0			0
$820$	2.40689	+	5.95654i	0.0840522	+	0.208012i
$821$	−2.73038	+	4.72916i	−0.0952909	+	0.165049i	−0.909730	−	0.415200i	$-0.863711\pi$
$821$	−2.73038	+	4.72916i	−0.0952909	+	0.165049i	0.814439	+	0.580249i	$0.197045\pi$
$822$		0			0
$823$	45.4901	+	26.2637i	1.58568	+	0.915496i	0.994006	+	0.109322i	$0.0348679\pi$
$823$	45.4901	+	26.2637i	1.58568	+	0.915496i	0.591679	+	0.806174i	$0.298465\pi$
$824$	−8.11753			−0.282788
$825$		0			0
$826$	−3.83431	+	6.64122i	−0.133413	+	0.231078i
$827$	18.7229	+	10.8097i	0.651058	+	0.375888i	0.788861	−	0.614571i	$-0.210671\pi$
$827$	18.7229	+	10.8097i	0.651058	+	0.375888i	−0.137804	+	0.990460i	$0.544004\pi$
$828$		0			0
$829$	−22.1432			−0.769065			−0.384533	−	0.923111i	$-0.625637\pi$
$829$	−22.1432			−0.769065			−0.384533	+	0.923111i	$0.625637\pi$
$830$	3.79328	−	4.85560i	0.131667	−	0.168540i
$831$		0			0
$832$	−2.51426	−	1.45161i	−0.0871661	−	0.0503254i
$833$	15.6792	−	9.05239i	0.543252	−	0.313647i
$834$		0			0
$835$	−1.80796	+	12.8682i	−0.0625669	+	0.445322i
$836$	−1.61999	+	0.295505i	−0.0560286	+	0.0102202i
$837$		0			0
$838$	26.6355	−	15.3780i	0.920109	−	0.531225i
$839$	15.0622	+	26.0885i	0.520006	+	0.900677i	0.999730	+	0.0232570i	$0.00740362\pi$
$839$	15.0622	+	26.0885i	0.520006	+	0.900677i	−0.479724	+	0.877420i	$0.659263\pi$
$840$		0			0
$841$	6.41681	+	11.1142i	0.221269	+	0.383250i
$842$	10.9367	+	6.31433i	0.376905	+	0.217606i
$843$		0			0
$844$	−13.3160			−0.458357
$845$	6.29288	−	8.05521i	0.216482	−	0.277108i
$846$		0			0
$847$		−	8.53035i		−	0.293106i
$848$		−	6.93332i		−	0.238091i
$849$		0			0
$850$	3.43225	+	13.7611i	0.117725	+	0.472002i
$851$	0.439777	−	0.761716i	0.0150754	−	0.0261113i
$852$		0			0
$853$	−20.1303	+	11.6222i	−0.689247	+	0.397937i	−0.803330	−	0.595534i	$-0.796940\pi$
$853$	−20.1303	+	11.6222i	−0.689247	+	0.397937i	0.114083	+	0.993471i	$0.463607\pi$
$854$	−3.57920			−0.122478
$855$		0			0
$856$	−17.7812			−0.607750
$857$	31.9390	−	18.4400i	1.09102	−	0.629899i	0.157170	−	0.987572i	$-0.449763\pi$
$857$	31.9390	−	18.4400i	1.09102	−	0.629899i	0.933847	+	0.357673i	$0.116430\pi$
$858$		0			0
$859$	14.2057	−	24.6050i	0.484693	−	0.839513i	−0.515153	−	0.857099i	$-0.672265\pi$
$859$	14.2057	−	24.6050i	0.484693	−	0.839513i	0.999845	+	0.0175859i	$0.00559806\pi$
$860$	0.888660	−	0.359085i	0.0303031	−	0.0122447i
$861$		0			0
$862$			35.3526i			1.20411i
$863$			15.3082i			0.521097i	0.965461	+	0.260548i	$0.0839034\pi$
$863$			15.3082i			0.521097i	−0.965461	+	0.260548i	$0.916097\pi$
$864$		0			0
$865$	−15.3752	−	12.0114i	−0.522771	−	0.408398i
$866$	−20.7906			−0.706493
$867$		0			0
$868$	−3.01333	−	1.73975i	−0.102279	−	0.0590509i
$869$	−0.296818	−	0.514103i	−0.0100689	−	0.0174398i
$870$		0			0
$871$	−12.2652	−	21.2439i	−0.415590	−	0.719822i
$872$	1.25094	−	0.722230i	0.0423622	−	0.0244578i
$873$		0			0
$874$	−25.6400	−	30.1933i	−0.867285	−	1.02130i
$875$	3.57184	−	8.02519i	0.120750	−	0.271301i
$876$		0			0
$877$	23.8022	−	13.7422i	0.803743	−	0.464041i	−0.0410351	−	0.999158i	$-0.513066\pi$
$877$	23.8022	−	13.7422i	0.803743	−	0.464041i	0.844778	+	0.535116i	$0.179732\pi$
$878$	−3.40251	−	1.96444i	−0.114829	−	0.0662966i
$879$		0			0
$880$	0.520053	−	0.665695i	0.0175310	−	0.0224406i
$881$	20.3210			0.684630			0.342315	−	0.939585i	$-0.388789\pi$
$881$	20.3210			0.684630			0.342315	+	0.939585i	$0.388789\pi$
$882$		0			0
$883$	27.8026	+	16.0519i	0.935633	+	0.540188i	0.888589	−	0.458705i	$-0.151686\pi$
$883$	27.8026	+	16.0519i	0.935633	+	0.540188i	0.0470444	+	0.998893i	$0.485020\pi$
$884$	4.11753	−	7.13177i	0.138488	−	0.239868i
$885$		0			0
$886$	−1.59655			−0.0536371
$887$	21.1520	+	12.2121i	0.710214	+	0.410042i	0.811140	−	0.584852i	$-0.198847\pi$
$887$	21.1520	+	12.2121i	0.710214	+	0.410042i	−0.100926	+	0.994894i	$0.532181\pi$
$888$		0			0
$889$	−1.42549	+	2.46902i	−0.0478093	+	0.0828081i
$890$	−24.7505	+	10.0011i	−0.829639	+	0.335236i
$891$		0			0
$892$			19.1684i			0.641805i
$893$	−9.45483	−	51.8326i	−0.316394	−	1.73451i
$894$		0			0
$895$	−19.4610	−	48.1620i	−0.650511	−	1.60988i
$896$	−0.392840	−	0.680419i	−0.0131239	−	0.0227312i
$897$		0			0
$898$	−12.5216	+	7.22938i	−0.417853	+	0.241247i
$899$	8.90321	−	15.4208i	0.296939	−	0.514313i
$900$		0			0
$901$	19.6666			0.655190
$902$	0.939995	+	0.542706i	0.0312984	+	0.0180701i
$903$		0			0
$904$	14.3160			0.476144
$905$	−16.7096	−	2.34767i	−0.555447	−	0.0780393i
$906$		0			0
$907$	0.681745	−	0.393606i	0.0226370	−	0.0130695i	−0.488639	−	0.872486i	$-0.662506\pi$
$907$	0.681745	−	0.393606i	0.0226370	−	0.0130695i	0.511276	+	0.859417i	$0.329173\pi$
$908$	−5.96039	−	3.44123i	−0.197803	−	0.114201i
$909$		0			0
$910$	−4.72899	+	1.91086i	−0.156764	+	0.0633446i
$911$	−5.93978			−0.196794			−0.0983968	−	0.995147i	$-0.531371\pi$
$911$	−5.93978			−0.196794			−0.0983968	+	0.995147i	$0.531371\pi$
$912$		0			0
$913$		−	1.04101i		−	0.0344524i
$914$	14.4526	+	25.0327i	0.478050	+	0.828007i
$915$		0			0
$916$	−6.87310	+	11.9046i	−0.227094	+	0.393338i
$917$	11.4354	−	6.60224i	0.377631	−	0.218025i
$918$		0			0
$919$	−28.5096			−0.940445			−0.470223	−	0.882548i	$-0.655826\pi$
$919$	−28.5096			−0.940445			−0.470223	+	0.882548i	$0.655826\pi$
$920$	20.1225	+	2.82717i	0.663418	+	0.0932090i
$921$		0			0
$922$	2.11949	+	1.22369i	0.0698017	+	0.0403000i
$923$		−	34.0830i		−	1.12185i
$924$		0			0
$925$	0.336202	+	0.348089i	0.0110543	+	0.0114451i
$926$	−3.83730	−	6.64640i	−0.126102	−	0.218414i
$927$		0			0
$928$	3.48207	−	2.01037i	0.114304	−	0.0659937i
$929$	1.34199	+	2.32439i	0.0440291	+	0.0762606i	0.887200	−	0.461385i	$-0.152647\pi$
$929$	1.34199	+	2.32439i	0.0440291	+	0.0762606i	−0.843171	+	0.537645i	$0.819314\pi$
$930$		0			0
$931$	−18.0087	−	21.2068i	−0.590211	−	0.695024i
$932$			6.79706i			0.222645i
$933$		0			0
$934$	−4.89062	−	8.47080i	−0.160026	−	0.277173i
$935$	1.88827	+	1.47515i	0.0617530	+	0.0482425i
$936$		0			0
$937$	42.3258	+	24.4368i	1.38272	+	0.798315i	0.992481	−	0.122398i	$-0.0390583\pi$
$937$	42.3258	+	24.4368i	1.38272	+	0.798315i	0.390241	+	0.920713i	$0.372392\pi$
$938$		−	6.63851i		−	0.216755i
$939$		0			0
$940$	21.2993	+	16.6394i	0.694706	+	0.542717i
$941$	−28.7961	+	49.8762i	−0.938724	+	1.62592i	−0.170871	+	0.985293i	$0.554658\pi$
$941$	−28.7961	+	49.8762i	−0.938724	+	1.62592i	−0.767854	+	0.640625i	$0.778675\pi$
$942$		0			0
$943$			26.1091i			0.850228i
$944$	4.88025	−	8.45283i	0.158838	−	0.275116i
$945$		0			0
$946$	0.0809666	−	0.140238i	0.00263245	−	0.00455954i
$947$	−24.0430	+	13.8812i	−0.781293	+	0.451080i	−0.836888	−	0.547373i	$-0.815628\pi$
$947$	−24.0430	+	13.8812i	−0.781293	+	0.451080i	0.0555950	+	0.998453i	$0.482294\pi$
$948$		0			0
$949$	6.56199			0.213011
$950$	19.8569	−	8.98349i	0.644243	−	0.291463i
$951$		0			0
$952$	1.93003	−	1.11430i	0.0625527	−	0.0361148i
$953$	23.3993	−	13.5096i	0.757978	−	0.437619i	−0.0705910	−	0.997505i	$-0.522489\pi$
$953$	23.3993	−	13.5096i	0.757978	−	0.437619i	0.828569	+	0.559886i	$0.189155\pi$
$954$		0			0
$955$	17.1485	+	42.4389i	0.554912	+	1.37329i
$956$	−5.42864	+	9.40268i	−0.175575	+	0.304104i
$957$		0			0
$958$		−	33.9432i		−	1.09665i
$959$	0.861725	−	1.49255i	0.0278265	−	0.0481970i
$960$		0			0
$961$	−11.3872			−0.367327
$962$		−	0.280996i		−	0.00905968i
$963$		0			0
$964$	−4.84368	−	8.38950i	−0.156004	−	0.270208i
$965$	33.3460	+	26.0505i	1.07344	+	0.838594i
$966$		0			0
$967$	47.4916	−	27.4193i	1.52723	−	0.881744i	0.527749	−	0.849400i	$-0.323036\pi$
$967$	47.4916	−	27.4193i	1.52723	−	0.881744i	0.999477	−	0.0323441i	$-0.0102972\pi$
$968$			10.8573i			0.348966i
$969$		0			0
$970$	−7.62714	−	1.07160i	−0.244893	−	0.0344070i
$971$	−9.23575	−	15.9968i	−0.296389	−	0.513362i	0.678918	−	0.734214i	$-0.262449\pi$
$971$	−9.23575	−	15.9968i	−0.296389	−	0.513362i	−0.975307	+	0.220853i	$0.929116\pi$
$972$		0			0
$973$	1.13839	+	0.657249i	0.0364951	+	0.0210704i
$974$	−16.9390	−	29.3392i	−0.542761	−	0.940090i
$975$		0			0
$976$	4.55554			0.145819
$977$		−	21.1131i		−	0.675467i	−0.941242	−	0.337734i	$-0.890340\pi$
$977$		−	21.1131i		−	0.675467i	0.941242	−	0.337734i	$-0.109660\pi$
$978$		0			0
$979$	−2.25504	+	3.90585i	−0.0720714	+	0.124831i
$980$	14.1334	+	1.98571i	0.451473	+	0.0634312i
$981$		0			0
$982$	−35.6148	−	20.5622i	−1.13651	−	0.656167i
$983$	−29.0617	+	16.7788i	−0.926924	+	0.535160i	−0.885837	−	0.463996i	$-0.846415\pi$
$983$	−29.0617	+	16.7788i	−0.926924	+	0.535160i	−0.0410865	+	0.999156i	$0.513082\pi$
$984$		0			0
$985$	3.58744	−	1.44960i	0.114305	−	0.0461879i
$986$	5.70249	+	9.87700i	0.181604	+	0.314548i
$987$		0			0
$988$	−11.9169	−	4.25803i	−0.379128	−	0.135466i
$989$	3.89523			0.123861
$990$		0			0
$991$	7.88347	+	13.6546i	0.250427	+	0.433752i	0.963643	−	0.267192i	$-0.0860957\pi$
$991$	7.88347	+	13.6546i	0.250427	+	0.433752i	−0.713217	+	0.700944i	$0.752762\pi$
$992$	3.83531	+	2.21432i	0.121771	+	0.0703047i
$993$		0			0
$994$	4.61184	−	7.98795i	0.146279	−	0.253362i
$995$	33.3733	+	4.68889i	1.05801	+	0.148648i
$996$		0			0
$997$	−29.9992	−	17.3200i	−0.950083	−	0.548531i	−0.0569762	−	0.998376i	$-0.518146\pi$
$997$	−29.9992	−	17.3200i	−0.950083	−	0.548531i	−0.893107	+	0.449845i	$0.851479\pi$
$998$	17.3030	+	9.98987i	0.547716	+	0.316224i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.t.b.919.6		12
3.2	odd	2		570.2.q.b.349.1	yes	12
5.4	even	2	inner	1710.2.t.b.919.2		12
15.14	odd	2		570.2.q.b.349.5	yes	12
19.11	even	3	inner	1710.2.t.b.1189.2		12
57.11	odd	6		570.2.q.b.49.5	yes	12
95.49	even	6	inner	1710.2.t.b.1189.6		12
285.239	odd	6		570.2.q.b.49.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.q.b.49.1	✓	12	285.239	odd	6
570.2.q.b.49.5	yes	12	57.11	odd	6
570.2.q.b.349.1	yes	12	3.2	odd	2
570.2.q.b.349.5	yes	12	15.14	odd	2
1710.2.t.b.919.2		12	5.4	even	2	inner
1710.2.t.b.919.6		12	1.1	even	1	trivial
1710.2.t.b.1189.2		12	19.11	even	3	inner
1710.2.t.b.1189.6		12	95.49	even	6	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.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.837733 + 2.07321i) q^{5} +0.785680i q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.837733 + 2.07321i) q^{5} +0.785680i q^{7} -1.00000i q^{8} +(1.76210 + 1.37659i) q^{10} +0.377784 q^{11} +(2.51426 + 1.45161i) q^{13} +(0.392840 + 0.680419i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.45651 - 1.41827i) q^{17} +(-2.82148 - 3.32254i) q^{19} +(2.21432 + 0.311108i) q^{20} +(0.327171 - 0.188892i) q^{22} +(7.86994 + 4.54371i) q^{23} +(-3.59641 + 3.47359i) q^{25} +2.90321 q^{26} +(0.680419 + 0.392840i) q^{28} +(-2.01037 + 3.48207i) q^{29} -4.42864 q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.41827 - 2.45651i) q^{34} +(-1.62888 + 0.658190i) q^{35} -0.0967881i q^{37} +(-4.10474 - 1.46666i) q^{38} +(2.07321 - 0.837733i) q^{40} +(1.43655 + 2.48818i) q^{41} +(0.371213 - 0.214320i) q^{43} +(0.188892 - 0.327171i) q^{44} +9.08742 q^{46} +(10.4680 + 6.04371i) q^{47} +6.38271 q^{49} +(-1.37778 + 4.80642i) q^{50} +(2.51426 - 1.45161i) q^{52} +(6.00443 + 3.46666i) q^{53} +(0.316482 + 0.783227i) q^{55} +0.785680 q^{56} +4.02074i q^{58} +(4.88025 + 8.45283i) q^{59} +(-2.27777 + 3.94521i) q^{61} +(-3.83531 + 2.21432i) q^{62} -1.00000 q^{64} +(-0.903212 + 6.42864i) q^{65} +(-7.31738 - 4.22469i) q^{67} -2.83654i q^{68} +(-1.08156 + 1.38445i) q^{70} +(-5.86987 - 10.1669i) q^{71} +(1.95744 - 1.13013i) q^{73} +(-0.0483940 - 0.0838209i) q^{74} +(-4.28814 + 0.782204i) q^{76} +0.296818i q^{77} +(-0.785680 - 1.36084i) q^{79} +(1.37659 - 1.76210i) q^{80} +(2.48818 + 1.43655i) q^{82} -2.75557i q^{83} +(4.99827 + 3.90474i) q^{85} +(0.214320 - 0.371213i) q^{86} -0.377784i q^{88} +(-5.96912 + 10.3388i) q^{89} +(-1.14050 + 1.97540i) q^{91} +(7.86994 - 4.54371i) q^{92} +12.0874 q^{94} +(4.52468 - 8.63292i) q^{95} +(-2.98299 + 1.72223i) q^{97} +(5.52759 - 3.19135i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4}+O(q^{10}) \) 12 * q + 6 * q^4	\( 12 q + 6 q^{4} - 2 q^{10} + 4 q^{11} + 18 q^{14} - 6 q^{16} + 6 q^{19} - 2 q^{25} + 8 q^{26} + 16 q^{29} + 4 q^{34} - 2 q^{35} + 2 q^{40} - 10 q^{41} + 2 q^{44} + 28 q^{46} - 56 q^{49} - 16 q^{50} - 8 q^{55} + 36 q^{56} - 8 q^{59} - 28 q^{61} - 12 q^{64} + 16 q^{65} + 16 q^{70} - 44 q^{71} - 14 q^{74} - 12 q^{76} - 36 q^{79} - 32 q^{85} - 24 q^{86} - 6 q^{89} + 64 q^{94} + 12 q^{95}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 4 * q^11 + 18 * q^14 - 6 * q^16 + 6 * q^19 - 2 * q^25 + 8 * q^26 + 16 * q^29 + 4 * q^34 - 2 * q^35 + 2 * q^40 - 10 * q^41 + 2 * q^44 + 28 * q^46 - 56 * q^49 - 16 * q^50 - 8 * q^55 + 36 * q^56 - 8 * q^59 - 28 * q^61 - 12 * q^64 + 16 * q^65 + 16 * q^70 - 44 * q^71 - 14 * q^74 - 12 * q^76 - 36 * q^79 - 32 * q^85 - 24 * q^86 - 6 * q^89 + 64 * q^94 + 12 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more