LMFDB - Embedded newform 1386.2.k.v.793.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1386.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (of order $3$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.21870000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 24x^{4} - 43x^{3} + 138x^{2} - 117x + 73 $ x^6 - 3x^5 + 24x^4 - 43x^3 + 138x^2 - 117*x + 73
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.3
Root			$0.500000 - 3.23735i$ of defining polynomial
Character	$\chi$	$=$	1386.793
Dual form			1386.2.k.v.991.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.20942 - 3.82682i) q^{5} +(2.20942 + 1.45550i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.20942 - 3.82682i) q^{5} +(2.20942 + 1.45550i) q^{7} -1.00000 q^{8} +(-2.20942 - 3.82682i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(2.36521 - 1.18566i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.18842 + 2.05840i) q^{17} +(1.84421 - 3.19426i) q^{19} -4.41883 q^{20} -1.00000 q^{22} +(2.36521 - 4.09666i) q^{23} +(-7.26304 - 12.5800i) q^{25} +(0.155792 - 2.64116i) q^{28} +6.52608 q^{29} +(1.68842 + 2.92442i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.37683 q^{34} +(10.4515 - 5.23924i) q^{35} +(-3.84421 + 6.65836i) q^{37} +(-1.84421 - 3.19426i) q^{38} +(-2.20942 + 3.82682i) q^{40} -12.1492 q^{41} +3.06525 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-2.36521 - 4.09666i) q^{46} +(-2.05362 + 3.55698i) q^{47} +(2.76304 + 6.43161i) q^{49} -14.5261 q^{50} +(4.00000 + 6.92820i) q^{53} -4.41883 q^{55} +(-2.20942 - 1.45550i) q^{56} +(3.26304 - 5.65175i) q^{58} +(-6.26304 - 10.8479i) q^{59} +(-1.89783 + 3.28714i) q^{61} +3.37683 q^{62} +1.00000 q^{64} +(-5.07462 - 8.78951i) q^{67} +(1.18842 - 2.05840i) q^{68} +(0.688417 - 11.6708i) q^{70} -0.934749 q^{71} +(3.73042 + 6.46127i) q^{73} +(3.84421 + 6.65836i) q^{74} -3.68842 q^{76} +(0.155792 - 2.64116i) q^{77} +(0.209416 - 0.362720i) q^{79} +(2.20942 + 3.82682i) q^{80} +(-6.07462 + 10.5216i) q^{82} +2.14925 q^{83} +10.5028 q^{85} +(1.53263 - 2.65458i) q^{86} +(0.500000 + 0.866025i) q^{88} +(-6.41883 + 11.1177i) q^{89} -4.73042 q^{92} +(2.05362 + 3.55698i) q^{94} +(-8.14925 - 14.1149i) q^{95} +7.00000 q^{97} +(6.95146 + 0.822941i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8}+O(q^{10}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8} - 3 q^{11} + 3 q^{14} - 3 q^{16} + 3 q^{17} + 9 q^{19} - 6 q^{22} + 3 q^{23} - 15 q^{25} + 3 q^{28} - 18 q^{29} + 6 q^{31} + 3 q^{32} + 6 q^{34} + 30 q^{35} - 21 q^{37} - 9 q^{38} - 24 q^{41} + 6 q^{43} - 3 q^{44} - 3 q^{46} + 3 q^{47} - 12 q^{49} - 30 q^{50} + 24 q^{53} - 9 q^{58} - 9 q^{59} + 6 q^{61} + 12 q^{62} + 6 q^{64} - 6 q^{67} + 3 q^{68} - 18 q^{71} + 21 q^{74} - 18 q^{76} + 3 q^{77} - 12 q^{79} - 12 q^{82} - 36 q^{83} + 3 q^{86} + 3 q^{88} - 12 q^{89} - 6 q^{92} - 3 q^{94} + 42 q^{97} + 9 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8 - 3 * q^11 + 3 * q^14 - 3 * q^16 + 3 * q^17 + 9 * q^19 - 6 * q^22 + 3 * q^23 - 15 * q^25 + 3 * q^28 - 18 * q^29 + 6 * q^31 + 3 * q^32 + 6 * q^34 + 30 * q^35 - 21 * q^37 - 9 * q^38 - 24 * q^41 + 6 * q^43 - 3 * q^44 - 3 * q^46 + 3 * q^47 - 12 * q^49 - 30 * q^50 + 24 * q^53 - 9 * q^58 - 9 * q^59 + 6 * q^61 + 12 * q^62 + 6 * q^64 - 6 * q^67 + 3 * q^68 - 18 * q^71 + 21 * q^74 - 18 * q^76 + 3 * q^77 - 12 * q^79 - 12 * q^82 - 36 * q^83 + 3 * q^86 + 3 * q^88 - 12 * q^89 - 6 * q^92 - 3 * q^94 + 42 * q^97 + 9 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.20942	−	3.82682i	0.988081	−	1.71141i	0.360729	−	0.932671i	$-0.382528\pi$
$5$	2.20942	−	3.82682i	0.988081	−	1.71141i	0.627352	−	0.778736i	$-0.284139\pi$
$6$		0			0
$7$	2.20942	+	1.45550i	0.835081	+	0.550127i
$7$	2.20942	+	1.45550i	0.835081	+	0.550127i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−2.20942	−	3.82682i	−0.698679	−	1.21015i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$	2.36521	−	1.18566i	0.632128	−	0.316881i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.18842	+	2.05840i	0.288233	+	0.499235i	0.973388	−	0.229163i	$-0.0735988\pi$
$17$	1.18842	+	2.05840i	0.288233	+	0.499235i	−0.685155	+	0.728398i	$0.740265\pi$
$18$		0			0
$19$	1.84421	−	3.19426i	0.423090	−	0.732814i	−0.573150	−	0.819451i	$-0.694279\pi$
$19$	1.84421	−	3.19426i	0.423090	−	0.732814i	0.996240	+	0.0866367i	$0.0276119\pi$
$20$	−4.41883			−0.988081
$21$		0			0
$22$	−1.00000			−0.213201
$23$	2.36521	−	4.09666i	0.493180	−	0.854213i	−0.506789	−	0.862070i	$-0.669168\pi$
$23$	2.36521	−	4.09666i	0.493180	−	0.854213i	0.999969	+	0.00785730i	$0.00250108\pi$
$24$		0			0
$25$	−7.26304	−	12.5800i	−1.45261	−	2.51599i
$26$		0			0
$27$		0			0
$28$	0.155792	−	2.64116i	0.0294418	−	0.499132i
$29$	6.52608			1.21186			0.605932	−	0.795517i	$-0.292801\pi$
$29$	6.52608			1.21186			0.605932	+	0.795517i	$0.292801\pi$
$30$		0			0
$31$	1.68842	+	2.92442i	0.303249	+	0.525242i	0.976870	−	0.213835i	$-0.0685954\pi$
$31$	1.68842	+	2.92442i	0.303249	+	0.525242i	−0.673621	+	0.739077i	$0.735262\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	2.37683			0.407624
$35$	10.4515	−	5.23924i	1.76662	−	0.885593i
$36$		0			0
$37$	−3.84421	+	6.65836i	−0.631984	+	1.09463i	0.355162	+	0.934805i	$0.384426\pi$
$37$	−3.84421	+	6.65836i	−0.631984	+	1.09463i	−0.987146	+	0.159823i	$0.948908\pi$
$38$	−1.84421	−	3.19426i	−0.299170	−	0.518178i
$39$		0			0
$40$	−2.20942	+	3.82682i	−0.349339	+	0.605074i
$41$	−12.1492			−1.89739			−0.948697	−	0.316187i	$-0.897597\pi$
$41$	−12.1492			−1.89739			−0.948697	+	0.316187i	$0.897597\pi$
$42$		0			0
$43$	3.06525			0.467446			0.233723	−	0.972303i	$-0.424909\pi$
$43$	3.06525			0.467446			0.233723	+	0.972303i	$0.424909\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$		0			0
$46$	−2.36521	−	4.09666i	−0.348731	−	0.604020i
$47$	−2.05362	+	3.55698i	−0.299552	+	0.518839i	−0.976033	−	0.217620i	$-0.930171\pi$
$47$	−2.05362	+	3.55698i	−0.299552	+	0.518839i	0.676482	+	0.736460i	$0.263504\pi$
$48$		0			0
$49$	2.76304	+	6.43161i	0.394720	+	0.918801i
$50$	−14.5261			−2.05430
$51$		0			0
$52$		0			0
$53$	4.00000	+	6.92820i	0.549442	+	0.951662i	0.998313	+	0.0580651i	$0.0184931\pi$
$53$	4.00000	+	6.92820i	0.549442	+	0.951662i	−0.448871	+	0.893597i	$0.648174\pi$
$54$		0			0
$55$	−4.41883			−0.595835
$56$	−2.20942	−	1.45550i	−0.295246	−	0.194499i
$57$		0			0
$58$	3.26304	−	5.65175i	0.428458	−	0.742112i
$59$	−6.26304	−	10.8479i	−0.815379	−	1.41228i	−0.909056	−	0.416674i	$-0.863196\pi$
$59$	−6.26304	−	10.8479i	−0.815379	−	1.41228i	0.0936773	−	0.995603i	$-0.470138\pi$
$60$		0			0
$61$	−1.89783	+	3.28714i	−0.242993	+	0.420876i	−0.961565	−	0.274576i	$-0.911462\pi$
$61$	−1.89783	+	3.28714i	−0.242993	+	0.420876i	0.718573	+	0.695452i	$0.244796\pi$
$62$	3.37683			0.428858
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−5.07462	−	8.78951i	−0.619964	−	1.07381i	−0.989492	−	0.144589i	$-0.953814\pi$
$67$	−5.07462	−	8.78951i	−0.619964	−	1.07381i	0.369528	−	0.929220i	$-0.379519\pi$
$68$	1.18842	−	2.05840i	0.144117	−	0.249617i
$69$		0			0
$70$	0.688417	−	11.6708i	0.0822816	−	1.39493i
$71$	−0.934749			−0.110934			−0.0554672	−	0.998461i	$-0.517665\pi$
$71$	−0.934749			−0.110934			−0.0554672	+	0.998461i	$0.517665\pi$
$72$		0			0
$73$	3.73042	+	6.46127i	0.436612	+	0.756234i	0.997426	−	0.0717077i	$-0.0228449\pi$
$73$	3.73042	+	6.46127i	0.436612	+	0.756234i	−0.560814	+	0.827942i	$0.689512\pi$
$74$	3.84421	+	6.65836i	0.446880	+	0.774019i
$75$		0			0
$76$	−3.68842			−0.423090
$77$	0.155792	−	2.64116i	0.0177541	−	0.300988i
$78$		0			0
$79$	0.209416	−	0.362720i	0.0235612	−	0.0408092i	−0.854004	−	0.520266i	$-0.825833\pi$
$79$	0.209416	−	0.362720i	0.0235612	−	0.0408092i	0.877566	+	0.479457i	$0.159166\pi$
$80$	2.20942	+	3.82682i	0.247020	+	0.427852i
$81$		0			0
$82$	−6.07462	+	10.5216i	−0.670830	+	1.16191i
$83$	2.14925			0.235911			0.117955	−	0.993019i	$-0.462366\pi$
$83$	2.14925			0.235911			0.117955	+	0.993019i	$0.462366\pi$
$84$		0			0
$85$	10.5028			1.13919
$86$	1.53263	−	2.65458i	0.165267	−	0.286251i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−6.41883	+	11.1177i	−0.680395	+	1.17848i	0.294466	+	0.955662i	$0.404858\pi$
$89$	−6.41883	+	11.1177i	−0.680395	+	1.17848i	−0.974860	+	0.222816i	$0.928475\pi$
$90$		0			0
$91$		0			0
$92$	−4.73042			−0.493180
$93$		0			0
$94$	2.05362	+	3.55698i	0.211815	+	0.366875i
$95$	−8.14925	−	14.1149i	−0.836095	−	1.44816i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	6.95146	+	0.822941i	0.702203	+	0.0831296i
$99$		0			0
$100$	−7.26304	+	12.5800i	−0.726304	+	1.25800i
$101$	−7.68187	−	13.3054i	−0.764375	−	1.32394i	−0.940576	−	0.339582i	$-0.889714\pi$
$101$	−7.68187	−	13.3054i	−0.764375	−	1.32394i	0.176201	−	0.984354i	$-0.443619\pi$
$102$		0			0
$103$	1.31158	−	2.27173i	0.129234	−	0.223840i	−0.794146	−	0.607727i	$-0.792081\pi$
$103$	1.31158	−	2.27173i	0.129234	−	0.223840i	0.923380	+	0.383887i	$0.125415\pi$
$104$		0			0
$105$		0			0
$106$	8.00000			0.777029
$107$	5.45146	−	9.44220i	0.527012	−	0.912812i	−0.472492	−	0.881335i	$-0.656645\pi$
$107$	5.45146	−	9.44220i	0.527012	−	0.912812i	0.999504	−	0.0314773i	$-0.0100212\pi$
$108$		0			0
$109$	5.89783	+	10.2153i	0.564910	+	0.978453i	0.997058	+	0.0766501i	$0.0244224\pi$
$109$	5.89783	+	10.2153i	0.564910	+	0.978453i	−0.432148	+	0.901803i	$0.642244\pi$
$110$	−2.20942	+	3.82682i	−0.210660	+	0.364873i
$111$		0			0
$112$	−2.36521	+	1.18566i	−0.223491	+	0.112034i
$113$	−5.37683			−0.505810			−0.252905	−	0.967491i	$-0.581386\pi$
$113$	−5.37683			−0.505810			−0.252905	+	0.967491i	$0.581386\pi$
$114$		0			0
$115$	−10.4515	−	18.1025i	−0.974603	−	1.68806i
$116$	−3.26304	−	5.65175i	−0.302966	−	0.524752i
$117$		0			0
$118$	−12.5261			−1.15312
$119$	−0.370291	+	6.27760i	−0.0339445	+	0.575467i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	1.89783	+	3.28714i	0.171822	+	0.297604i
$123$		0			0
$124$	1.68842	−	2.92442i	0.151624	−	0.262621i
$125$	−42.0942			−3.76502
$126$		0			0
$127$	0.730416			0.0648139			0.0324070	−	0.999475i	$-0.489683\pi$
$127$	0.730416			0.0648139			0.0324070	+	0.999475i	$0.489683\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	3.68842	−	6.38853i	0.322258	−	0.558168i	−0.658695	−	0.752410i	$-0.728891\pi$
$131$	3.68842	−	6.38853i	0.322258	−	0.558168i	0.980954	+	0.194242i	$0.0622246\pi$
$132$		0			0
$133$	8.72387	−	4.37321i	0.756456	−	0.379206i
$134$	−10.1492			−0.876762
$135$		0			0
$136$	−1.18842	−	2.05840i	−0.101906	−	0.176506i
$137$	−4.41883	−	7.65364i	−0.377526	−	0.653895i	0.613175	−	0.789947i	$-0.289892\pi$
$137$	−4.41883	−	7.65364i	−0.377526	−	0.653895i	−0.990702	+	0.136052i	$0.956559\pi$
$138$		0			0
$139$	1.47392			0.125016			0.0625080	−	0.998044i	$-0.480090\pi$
$139$	1.47392			0.125016			0.0625080	+	0.998044i	$0.480090\pi$
$140$	−9.76304	−	6.43161i	−0.825128	−	0.543570i
$141$		0			0
$142$	−0.467375	+	0.809517i	−0.0392212	+	0.0679331i
$143$		0			0
$144$		0			0
$145$	14.4188	−	24.9742i	1.19742	−	2.07399i
$146$	7.46083			0.617463
$147$		0			0
$148$	7.68842			0.631984
$149$	−4.68187	+	8.10924i	−0.383554	+	0.664335i	−0.991567	−	0.129592i	$-0.958633\pi$
$149$	−4.68187	+	8.10924i	−0.383554	+	0.664335i	0.608013	+	0.793927i	$0.291967\pi$
$150$		0			0
$151$	6.78404	+	11.7503i	0.552077	+	0.956226i	0.998125	+	0.0612166i	$0.0194980\pi$
$151$	6.78404	+	11.7503i	0.552077	+	0.956226i	−0.446047	+	0.895009i	$0.647169\pi$
$152$	−1.84421	+	3.19426i	−0.149585	+	0.259089i
$153$		0			0
$154$	−2.20942	−	1.45550i	−0.178040	−	0.117288i
$155$	14.9217			1.19854
$156$		0			0
$157$	9.37029	+	16.2298i	0.747831	+	1.29528i	0.948861	+	0.315696i	$0.102238\pi$
$157$	9.37029	+	16.2298i	0.747831	+	1.29528i	−0.201030	+	0.979585i	$0.564429\pi$
$158$	−0.209416	−	0.362720i	−0.0166603	−	0.0288564i
$159$		0			0
$160$	4.41883			0.349339
$161$	11.1884	−	5.60867i	0.881771	−	0.442025i
$162$		0			0
$163$	−9.38621	+	16.2574i	−0.735185	+	1.27338i	0.219458	+	0.975622i	$0.429571\pi$
$163$	−9.38621	+	16.2574i	−0.735185	+	1.27338i	−0.954642	+	0.297755i	$0.903762\pi$
$164$	6.07462	+	10.5216i	0.474348	+	0.821596i
$165$		0			0
$166$	1.07462	−	1.86130i	0.0834070	−	0.144465i
$167$	23.8898			1.84865			0.924325	−	0.381606i	$-0.124629\pi$
$167$	23.8898			1.84865			0.924325	+	0.381606i	$0.124629\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	5.25142	−	9.09572i	0.402765	−	0.697610i
$171$		0			0
$172$	−1.53263	−	2.65458i	−0.116862	−	0.202410i
$173$	5.68842	−	9.85263i	0.432482	−	0.749081i	−0.564604	−	0.825362i	$-0.690971\pi$
$173$	5.68842	−	9.85263i	0.432482	−	0.749081i	0.997086	+	0.0762805i	$0.0243045\pi$
$174$		0			0
$175$	2.26304	−	38.3657i	0.171070	−	2.90018i
$176$	1.00000			0.0753778
$177$		0			0
$178$	6.41883	+	11.1177i	0.481112	+	0.833310i
$179$	12.3050	+	21.3130i	0.919722	+	1.59301i	0.799837	+	0.600217i	$0.204919\pi$
$179$	12.3050	+	21.3130i	0.919722	+	1.59301i	0.119885	+	0.992788i	$0.461747\pi$
$180$		0			0
$181$	17.4608			1.29785			0.648927	−	0.760851i	$-0.275218\pi$
$181$	17.4608			1.29785			0.648927	+	0.760851i	$0.275218\pi$
$182$		0			0
$183$		0			0
$184$	−2.36521	+	4.09666i	−0.174365	+	0.302010i
$185$	16.9869	+	29.4222i	1.24890	+	2.16316i
$186$		0			0
$187$	1.18842	−	2.05840i	0.0869056	−	0.150525i
$188$	4.10725			0.299552
$189$		0			0
$190$	−16.2985			−1.18242
$191$	−8.41883	+	14.5818i	−0.609165	+	1.05511i	0.382213	+	0.924074i	$0.375162\pi$
$191$	−8.41883	+	14.5818i	−0.609165	+	1.05511i	−0.991378	+	0.131031i	$0.958171\pi$
$192$		0			0
$193$	−2.73042	−	4.72922i	−0.196540	−	0.340417i	0.750865	−	0.660456i	$-0.229637\pi$
$193$	−2.73042	−	4.72922i	−0.196540	−	0.340417i	−0.947404	+	0.320040i	$0.896304\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$		0			0
$196$	4.18842	−	5.60867i	0.299173	−	0.400619i
$197$	9.68842			0.690271			0.345136	−	0.938553i	$-0.387833\pi$
$197$	9.68842			0.690271			0.345136	+	0.938553i	$0.387833\pi$
$198$		0			0
$199$	−10.1492	−	17.5790i	−0.719461	−	1.24614i	−0.961214	−	0.275805i	$-0.911056\pi$
$199$	−10.1492	−	17.5790i	−0.719461	−	1.24614i	0.241752	−	0.970338i	$-0.422278\pi$
$200$	7.26304	+	12.5800i	0.513575	+	0.889537i
$201$		0			0
$202$	−15.3637			−1.08099
$203$	14.4188	+	9.49871i	1.01200	+	0.666679i
$204$		0			0
$205$	−26.8427	+	46.4930i	−1.87478	+	3.24721i
$206$	−1.31158	−	2.27173i	−0.0913823	−	0.158279i
$207$		0			0
$208$		0			0
$209$	−3.68842			−0.255133
$210$		0			0
$211$	22.5130			1.54986			0.774929	−	0.632048i	$-0.217785\pi$
$211$	22.5130			1.54986			0.774929	+	0.632048i	$0.217785\pi$
$212$	4.00000	−	6.92820i	0.274721	−	0.475831i
$213$		0			0
$214$	−5.45146	−	9.44220i	−0.372654	−	0.645456i
$215$	6.77241	−	11.7302i	0.461875	−	0.799991i
$216$		0			0
$217$	−0.526082	+	8.91876i	−0.0357128	+	0.605445i
$218$	11.7957			0.798903
$219$		0			0
$220$	2.20942	+	3.82682i	0.148959	+	0.258004i
$221$		0			0
$222$		0			0
$223$	−7.46083			−0.499614			−0.249807	−	0.968296i	$-0.580367\pi$
$223$	−7.46083			−0.499614			−0.249807	+	0.968296i	$0.580367\pi$
$224$	−0.155792	+	2.64116i	−0.0104093	+	0.176470i
$225$		0			0
$226$	−2.68842	+	4.65647i	−0.178831	+	0.309744i
$227$	−1.38621	−	2.40098i	−0.0920058	−	0.159359i	0.816349	−	0.577559i	$-0.195995\pi$
$227$	−1.38621	−	2.40098i	−0.0920058	−	0.159359i	−0.908355	+	0.418200i	$0.862661\pi$
$228$		0			0
$229$	1.26958	−	2.19898i	0.0838965	−	0.145313i	−0.821024	−	0.570894i	$-0.806597\pi$
$229$	1.26958	−	2.19898i	0.0838965	−	0.145313i	0.904920	+	0.425581i	$0.139930\pi$
$230$	−20.9029			−1.37830
$231$		0			0
$232$	−6.52608			−0.428458
$233$	−12.0261	+	20.8298i	−0.787855	+	1.36460i	0.139424	+	0.990233i	$0.455475\pi$
$233$	−12.0261	+	20.8298i	−0.787855	+	1.36460i	−0.927279	+	0.374372i	$0.877858\pi$
$234$		0			0
$235$	9.07462	+	15.7177i	0.591963	+	1.02531i
$236$	−6.26304	+	10.8479i	−0.407689	+	0.706138i
$237$		0			0
$238$	5.25142	+	3.45948i	0.340399	+	0.224245i
$239$	−7.59133			−0.491042			−0.245521	−	0.969391i	$-0.578959\pi$
$239$	−7.59133			−0.491042			−0.245521	+	0.969391i	$0.578959\pi$
$240$		0			0
$241$	−8.14925	−	14.1149i	−0.524939	−	0.909221i	−0.999578	−	0.0290409i	$-0.990755\pi$
$241$	−8.14925	−	14.1149i	−0.524939	−	0.909221i	0.474639	−	0.880181i	$-0.342579\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$		0			0
$244$	3.79567			0.242993
$245$	30.7173	+	3.63644i	1.96246	+	0.232324i
$246$		0			0
$247$		0			0
$248$	−1.68842	−	2.92442i	−0.107215	−	0.185701i
$249$		0			0
$250$	−21.0471	+	36.4546i	−1.33113	+	2.30559i
$251$	8.61008			0.543463			0.271732	−	0.962373i	$-0.412404\pi$
$251$	8.61008			0.543463			0.271732	+	0.962373i	$0.412404\pi$
$252$		0			0
$253$	−4.73042			−0.297399
$254$	0.365208	−	0.632559i	0.0229152	−	0.0396903i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.418833	−	0.725439i	0.0261261	−	0.0452517i	−0.852667	−	0.522455i	$-0.825016\pi$
$257$	0.418833	−	0.725439i	0.0261261	−	0.0452517i	0.878793	+	0.477203i	$0.158350\pi$
$258$		0			0
$259$	−18.1847	+	9.11585i	−1.12994	+	0.566432i
$260$		0			0
$261$		0			0
$262$	−3.68842	−	6.38853i	−0.227871	−	0.394684i
$263$	5.41883	+	9.38569i	0.334140	+	0.578747i	0.983319	−	0.181888i	$-0.0582210\pi$
$263$	5.41883	+	9.38569i	0.334140	+	0.578747i	−0.649180	+	0.760635i	$0.724888\pi$
$264$		0			0
$265$	35.3507			2.17157
$266$	0.574624	−	9.74170i	0.0352325	−	0.597302i
$267$		0			0
$268$	−5.07462	+	8.78951i	−0.309982	+	0.536905i
$269$	8.93983	+	15.4842i	0.545071	+	0.944091i	0.998602	+	0.0528506i	$0.0168307\pi$
$269$	8.93983	+	15.4842i	0.545071	+	0.944091i	−0.453531	+	0.891240i	$0.649836\pi$
$270$		0			0
$271$	4.41883	−	7.65364i	0.268425	−	0.464926i	−0.700030	−	0.714113i	$-0.746830\pi$
$271$	4.41883	−	7.65364i	0.268425	−	0.464926i	0.968455	+	0.249187i	$0.0801635\pi$
$272$	−2.37683			−0.144117
$273$		0			0
$274$	−8.83767			−0.533903
$275$	−7.26304	+	12.5800i	−0.437978	+	0.758600i
$276$		0			0
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	0.736959	−	1.27645i	0.0441999	−	0.0765564i
$279$		0			0
$280$	−10.4515	+	5.23924i	−0.624594	+	0.313104i
$281$	15.9217			0.949807			0.474903	−	0.880038i	$-0.342483\pi$
$281$	15.9217			0.949807			0.474903	+	0.880038i	$0.342483\pi$
$282$		0			0
$283$	9.04200	+	15.6612i	0.537491	+	0.930962i	0.999038	+	0.0438462i	$0.0139611\pi$
$283$	9.04200	+	15.6612i	0.537491	+	0.930962i	−0.461547	+	0.887116i	$0.652706\pi$
$284$	0.467375	+	0.809517i	0.0277336	+	0.0480360i
$285$		0			0
$286$		0			0
$287$	−26.8427	−	17.6832i	−1.58448	−	1.04381i
$288$		0			0
$289$	5.67533	−	9.82996i	0.333843	−	0.578233i
$290$	−14.4188	−	24.9742i	−0.846703	−	1.46653i
$291$		0			0
$292$	3.73042	−	6.46127i	0.218306	−	0.378117i
$293$	−25.1492			−1.46923			−0.734617	−	0.678482i	$-0.762638\pi$
$293$	−25.1492			−1.46923			−0.734617	+	0.678482i	$0.762638\pi$
$294$		0			0
$295$	−55.3507			−3.22264
$296$	3.84421	−	6.65836i	0.223440	−	0.387010i
$297$		0			0
$298$	4.68187	+	8.10924i	0.271214	+	0.469756i
$299$		0			0
$300$		0			0
$301$	6.77241	+	4.46147i	0.390355	+	0.257155i
$302$	13.5681			0.780755
$303$		0			0
$304$	1.84421	+	3.19426i	0.105773	+	0.183204i
$305$	8.38621	+	14.5253i	0.480193	+	0.831718i
$306$		0			0
$307$	−3.86950			−0.220844			−0.110422	−	0.993885i	$-0.535220\pi$
$307$	−3.86950			−0.220844			−0.110422	+	0.993885i	$0.535220\pi$
$308$	−2.36521	+	1.18566i	−0.134770	+	0.0675593i
$309$		0			0
$310$	7.46083	−	12.9225i	0.423747	−	0.733951i
$311$	−6.78404	−	11.7503i	−0.384688	−	0.666299i	0.607038	−	0.794673i	$-0.292358\pi$
$311$	−6.78404	−	11.7503i	−0.384688	−	0.666299i	−0.991726	+	0.128374i	$0.959024\pi$
$312$		0			0
$313$	−1.26304	+	2.18765i	−0.0713913	+	0.123653i	−0.899511	−	0.436898i	$-0.856077\pi$
$313$	−1.26304	+	2.18765i	−0.0713913	+	0.123653i	0.828120	+	0.560551i	$0.189411\pi$
$314$	18.7406			1.05759
$315$		0			0
$316$	−0.418833			−0.0235612
$317$	−10.0051	+	17.3293i	−0.561941	+	0.973311i	0.435386	+	0.900244i	$0.356612\pi$
$317$	−10.0051	+	17.3293i	−0.561941	+	0.973311i	−0.997327	+	0.0730670i	$0.976721\pi$
$318$		0			0
$319$	−3.26304	−	5.65175i	−0.182695	−	0.316437i
$320$	2.20942	−	3.82682i	0.123510	−	0.213926i
$321$		0			0
$322$	0.736959	−	12.4938i	0.0410691	−	0.696252i
$323$	8.76675			0.487795
$324$		0			0
$325$		0			0
$326$	9.38621	+	16.2574i	0.519854	+	0.900413i
$327$		0			0
$328$	12.1492			0.670830
$329$	−9.71450	+	4.86980i	−0.535578	+	0.268481i
$330$		0			0
$331$	8.07462	−	13.9857i	0.443821	−	0.768721i	−0.554148	−	0.832418i	$-0.686956\pi$
$331$	8.07462	−	13.9857i	0.443821	−	0.768721i	0.997969	+	0.0636969i	$0.0202891\pi$
$332$	−1.07462	−	1.86130i	−0.0589777	−	0.102152i
$333$		0			0
$334$	11.9449	−	20.6892i	0.653597	−	1.13206i
$335$	−44.8478			−2.45030
$336$		0			0
$337$	23.1362			1.26031			0.630154	−	0.776471i	$-0.282992\pi$
$337$	23.1362			1.26031			0.630154	+	0.776471i	$0.282992\pi$
$338$	−6.50000	+	11.2583i	−0.353553	+	0.612372i
$339$		0			0
$340$	−5.25142	−	9.09572i	−0.284798	−	0.493285i
$341$	1.68842	−	2.92442i	0.0914329	−	0.158366i
$342$		0			0
$343$	−3.25650	+	18.2317i	−0.175834	+	0.984420i
$344$	−3.06525			−0.165267
$345$		0			0
$346$	−5.68842	−	9.85263i	−0.305811	−	0.529681i
$347$	7.82829	+	13.5590i	0.420245	+	0.727885i	0.995963	−	0.0897628i	$-0.0286109\pi$
$347$	7.82829	+	13.5590i	0.420245	+	0.727885i	−0.575718	+	0.817648i	$0.695278\pi$
$348$		0			0
$349$	−20.0102			−1.07112			−0.535560	−	0.844497i	$-0.679899\pi$
$349$	−20.0102			−1.07112			−0.535560	+	0.844497i	$0.679899\pi$
$350$	−32.0942	−	21.1427i	−1.71551	−	1.13013i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	3.73042	+	6.46127i	0.198550	+	0.343899i	0.948058	−	0.318096i	$-0.103043\pi$
$353$	3.73042	+	6.46127i	0.198550	+	0.343899i	−0.749508	+	0.661995i	$0.769710\pi$
$354$		0			0
$355$	−2.06525	+	3.57712i	−0.109612	+	0.189854i
$356$	12.8377			0.680395
$357$		0			0
$358$	24.6101			1.30068
$359$	−5.62317	+	9.73961i	−0.296779	+	0.514037i	−0.975397	−	0.220455i	$-0.929246\pi$
$359$	−5.62317	+	9.73961i	−0.296779	+	0.514037i	0.678618	+	0.734492i	$0.262579\pi$
$360$		0			0
$361$	2.69779	+	4.67271i	0.141989	+	0.245932i
$362$	8.73042	−	15.1215i	0.458860	−	0.794770i
$363$		0			0
$364$		0			0
$365$	32.9682			1.72563
$366$		0			0
$367$	2.95800	+	5.12341i	0.154406	+	0.267440i	0.932843	−	0.360284i	$-0.117320\pi$
$367$	2.95800	+	5.12341i	0.154406	+	0.267440i	−0.778436	+	0.627724i	$0.783987\pi$
$368$	2.36521	+	4.09666i	0.123295	+	0.213553i
$369$		0			0
$370$	33.9738			1.76622
$371$	−1.24633	+	21.1293i	−0.0647064	+	1.09698i
$372$		0			0
$373$	11.5630	−	20.0277i	0.598709	−	1.03700i	−0.394303	−	0.918981i	$-0.629014\pi$
$373$	11.5630	−	20.0277i	0.598709	−	1.03700i	0.993012	−	0.118014i	$-0.0376529\pi$
$374$	−1.18842	−	2.05840i	−0.0614516	−	0.106437i
$375$		0			0
$376$	2.05362	−	3.55698i	0.105908	−	0.183437i
$377$		0			0
$378$		0			0
$379$	−6.77241			−0.347876			−0.173938	−	0.984757i	$-0.555649\pi$
$379$	−6.77241			−0.347876			−0.173938	+	0.984757i	$0.555649\pi$
$380$	−8.14925	+	14.1149i	−0.418048	+	0.724080i
$381$		0			0
$382$	8.41883	+	14.5818i	0.430745	+	0.746072i
$383$	12.6819	−	21.9656i	0.648013	−	1.12239i	−0.335583	−	0.942011i	$-0.608933\pi$
$383$	12.6819	−	21.9656i	0.648013	−	1.12239i	0.983597	−	0.180382i	$-0.0577333\pi$
$384$		0			0
$385$	−9.76304	−	6.43161i	−0.497571	−	0.327785i
$386$	−5.46083			−0.277949
$387$		0			0
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	12.6282	+	21.8728i	0.640278	+	1.10899i	0.985371	+	0.170425i	$0.0545140\pi$
$389$	12.6282	+	21.8728i	0.640278	+	1.10899i	−0.345093	+	0.938568i	$0.612153\pi$
$390$		0			0
$391$	11.2434			0.568604
$392$	−2.76304	−	6.43161i	−0.139555	−	0.324845i
$393$		0			0
$394$	4.84421	−	8.39042i	0.244048	−	0.422703i
$395$	−0.925376	−	1.60280i	−0.0465607	−	0.0806455i
$396$		0			0
$397$	6.73696	−	11.6688i	0.338118	−	0.585638i	−0.645961	−	0.763371i	$-0.723543\pi$
$397$	6.73696	−	11.6688i	0.338118	−	0.585638i	0.984079	+	0.177733i	$0.0568763\pi$
$398$	−20.2985			−1.01747
$399$		0			0
$400$	14.5261			0.726304
$401$	16.9449	−	29.3495i	0.846189	−	1.46564i	−0.0383962	−	0.999263i	$-0.512225\pi$
$401$	16.9449	−	29.3495i	0.846189	−	1.46564i	0.884585	−	0.466379i	$-0.154442\pi$
$402$		0			0
$403$		0			0
$404$	−7.68187	+	13.3054i	−0.382188	+	0.661968i
$405$		0			0
$406$	15.4355	−	7.73772i	0.766053	−	0.384017i
$407$	7.68842			0.381101
$408$		0			0
$409$	2.10725	+	3.64986i	0.104197	+	0.180474i	0.913410	−	0.407041i	$-0.133439\pi$
$409$	2.10725	+	3.64986i	0.104197	+	0.180474i	−0.809213	+	0.587515i	$0.800106\pi$
$410$	26.8427	+	46.4930i	1.32567	+	2.29613i
$411$		0			0
$412$	−2.62317			−0.129234
$413$	1.95146	−	33.0834i	0.0960250	−	1.62793i
$414$		0			0
$415$	4.74858	−	8.22479i	0.233099	−	0.403739i
$416$		0			0
$417$		0			0
$418$	−1.84421	+	3.19426i	−0.0902032	+	0.156236i
$419$	22.3116			1.08999			0.544996	−	0.838439i	$-0.316531\pi$
$419$	22.3116			1.08999			0.544996	+	0.838439i	$0.316531\pi$
$420$		0			0
$421$	18.3116			0.892452			0.446226	−	0.894920i	$-0.352768\pi$
$421$	18.3116			0.892452			0.446226	+	0.894920i	$0.352768\pi$
$422$	11.2565	−	19.4968i	0.547958	−	0.949091i
$423$		0			0
$424$	−4.00000	−	6.92820i	−0.194257	−	0.336463i
$425$	17.2630	−	29.9005i	0.837380	−	1.45039i
$426$		0			0
$427$	−8.97754	+	4.50037i	−0.434454	+	0.217788i
$428$	−10.9029			−0.527012
$429$		0			0
$430$	−6.77241	−	11.7302i	−0.326595	−	0.565679i
$431$	−14.4188	−	24.9742i	−0.694531	−	1.20296i	−0.970339	−	0.241750i	$-0.922279\pi$
$431$	−14.4188	−	24.9742i	−0.694531	−	1.20296i	0.275808	−	0.961213i	$-0.411055\pi$
$432$		0			0
$433$	7.62317			0.366346			0.183173	−	0.983081i	$-0.441363\pi$
$433$	7.62317			0.366346			0.183173	+	0.983081i	$0.441363\pi$
$434$	7.46083	+	4.91498i	0.358131	+	0.235927i
$435$		0			0
$436$	5.89783	−	10.2153i	0.282455	−	0.489226i
$437$	−8.72387	−	15.1102i	−0.417319	−	0.722818i
$438$		0			0
$439$	16.6870	−	28.9027i	0.796425	−	1.37945i	−0.125505	−	0.992093i	$-0.540055\pi$
$439$	16.6870	−	28.9027i	0.796425	−	1.37945i	0.921930	−	0.387356i	$-0.126611\pi$
$440$	4.41883			0.210660
$441$		0			0
$442$		0			0
$443$	−2.42538	+	4.20087i	−0.115233	+	0.199590i	−0.917873	−	0.396874i	$-0.870095\pi$
$443$	−2.42538	+	4.20087i	−0.115233	+	0.199590i	0.802640	+	0.596464i	$0.203428\pi$
$444$		0			0
$445$	28.3637	+	49.1275i	1.34457	+	2.32886i
$446$	−3.73042	+	6.46127i	−0.176640	+	0.305950i
$447$		0			0
$448$	2.20942	+	1.45550i	0.104385	+	0.0687659i
$449$	−14.3450			−0.676982			−0.338491	−	0.940970i	$-0.609917\pi$
$449$	−14.3450			−0.676982			−0.338491	+	0.940970i	$0.609917\pi$
$450$		0			0
$451$	6.07462	+	10.5216i	0.286043	+	0.495441i
$452$	2.68842	+	4.65647i	0.126452	+	0.219022i
$453$		0			0
$454$	−2.77241			−0.130116
$455$		0			0
$456$		0			0
$457$	12.5913	−	21.8088i	0.588998	−	1.02017i	−0.405366	−	0.914154i	$-0.632856\pi$
$457$	12.5913	−	21.8088i	0.588998	−	1.02017i	0.994364	−	0.106020i	$-0.0338106\pi$
$458$	−1.26958	−	2.19898i	−0.0593238	−	0.102752i
$459$		0			0
$460$	−10.4515	+	18.1025i	−0.487302	+	0.844031i
$461$	−13.0187			−0.606344			−0.303172	−	0.952936i	$-0.598046\pi$
$461$	−13.0187			−0.606344			−0.303172	+	0.952936i	$0.598046\pi$
$462$		0			0
$463$	−14.2145			−0.660604			−0.330302	−	0.943875i	$-0.607151\pi$
$463$	−14.2145			−0.660604			−0.330302	+	0.943875i	$0.607151\pi$
$464$	−3.26304	+	5.65175i	−0.151483	+	0.262376i
$465$		0			0
$466$	12.0261	+	20.8298i	0.557098	+	0.964921i
$467$	−1.19779	+	2.07463i	−0.0554271	+	0.0960026i	−0.892408	−	0.451230i	$-0.850985\pi$
$467$	−1.19779	+	2.07463i	−0.0554271	+	0.0960026i	0.836981	+	0.547233i	$0.184319\pi$
$468$		0			0
$469$	1.58117	−	26.8058i	0.0730115	−	1.23778i
$470$	18.1492			0.837162
$471$		0			0
$472$	6.26304	+	10.8479i	0.288280	+	0.499315i
$473$	−1.53263	−	2.65458i	−0.0704702	−	0.122058i
$474$		0			0
$475$	−53.5782			−2.45834
$476$	5.62171	−	2.81812i	0.257670	−	0.129168i
$477$		0			0
$478$	−3.79567	+	6.57429i	−0.173610	+	0.300701i
$479$	5.41883	+	9.38569i	0.247593	+	0.428843i	0.962857	−	0.270010i	$-0.0870272\pi$
$479$	5.41883	+	9.38569i	0.247593	+	0.428843i	−0.715265	+	0.698854i	$0.753694\pi$
$480$		0			0
$481$		0			0
$482$	−16.2985			−0.742376
$483$		0			0
$484$	1.00000			0.0454545
$485$	15.4659	−	26.7877i	0.702271	−	1.21637i
$486$		0			0
$487$	17.3217	+	30.0021i	0.784923	+	1.35953i	0.929045	+	0.369967i	$0.120631\pi$
$487$	17.3217	+	30.0021i	0.784923	+	1.35953i	−0.144121	+	0.989560i	$0.546036\pi$
$488$	1.89783	−	3.28714i	0.0859109	−	0.148802i
$489$		0			0
$490$	18.5079	−	24.7838i	0.836102	−	1.11962i
$491$	−38.1492			−1.72165			−0.860826	−	0.508900i	$-0.830052\pi$
$491$	−38.1492			−1.72165			−0.860826	+	0.508900i	$0.830052\pi$
$492$		0			0
$493$	7.75571	+	13.4333i	0.349299	+	0.605004i
$494$		0			0
$495$		0			0
$496$	−3.37683			−0.151624
$497$	−2.06525	−	1.36053i	−0.0926392	−	0.0610280i
$498$		0			0
$499$	0.311583	−	0.539678i	0.0139484	−	0.0241593i	−0.858967	−	0.512031i	$-0.828893\pi$
$499$	0.311583	−	0.539678i	0.0139484	−	0.0241593i	0.872915	+	0.487872i	$0.162227\pi$
$500$	21.0471	+	36.4546i	0.941254	+	1.63030i
$501$		0			0
$502$	4.30504	−	7.45655i	0.192143	−	0.332802i
$503$	−31.1362			−1.38829			−0.694146	−	0.719834i	$-0.744218\pi$
$503$	−31.1362			−1.38829			−0.694146	+	0.719834i	$0.744218\pi$
$504$		0			0
$505$	−67.8898			−3.02106
$506$	−2.36521	+	4.09666i	−0.105146	+	0.182119i
$507$		0			0
$508$	−0.365208	−	0.632559i	−0.0162035	−	0.0280653i
$509$	−21.0522	+	36.4634i	−0.933121	+	1.61621i	−0.155170	+	0.987888i	$0.549592\pi$
$509$	−21.0522	+	36.4634i	−0.933121	+	1.61621i	−0.777951	+	0.628325i	$0.783741\pi$
$510$		0			0
$511$	−1.16233	+	19.7053i	−0.0514187	+	0.871709i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−0.418833	−	0.725439i	−0.0184739	−	0.0319978i
$515$	−5.79567	−	10.0384i	−0.255388	−	0.442344i
$516$		0			0
$517$	4.10725			0.180637
$518$	−1.19779	+	20.3063i	−0.0526279	+	0.892209i
$519$		0			0
$520$		0			0
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$		0			0
$523$	12.6333	−	21.8816i	0.552417	−	0.956814i	−0.445682	−	0.895191i	$-0.647039\pi$
$523$	12.6333	−	21.8816i	0.552417	−	0.956814i	0.998099	−	0.0616232i	$-0.0196277\pi$
$524$	−7.37683			−0.322258
$525$		0			0
$526$	10.8377			0.472545
$527$	−4.01309	+	6.95087i	−0.174813	+	0.302785i
$528$		0			0
$529$	0.311583	+	0.539678i	0.0135471	+	0.0234643i
$530$	17.6753	−	30.6146i	0.767767	−	1.32981i
$531$		0			0
$532$	−8.14925	−	5.36849i	−0.353315	−	0.232754i
$533$		0			0
$534$		0			0
$535$	−24.0891	−	41.7235i	−1.04146	−	1.80386i
$536$	5.07462	+	8.78951i	0.219190	+	0.379649i
$537$		0			0
$538$	17.8797			0.770847
$539$	4.18842	−	5.60867i	0.180408	−	0.241582i
$540$		0			0
$541$	2.20942	−	3.82682i	0.0949902	−	0.164528i	−0.814614	−	0.580003i	$-0.803051\pi$
$541$	2.20942	−	3.82682i	0.0949902	−	0.164528i	0.909605	+	0.415475i	$0.136385\pi$
$542$	−4.41883	−	7.65364i	−0.189805	−	0.328752i
$543$		0			0
$544$	−1.18842	+	2.05840i	−0.0509530	+	0.0882531i
$545$	52.1231			2.23271
$546$		0			0
$547$	−27.6622			−1.18275			−0.591376	−	0.806396i	$-0.701415\pi$
$547$	−27.6622			−1.18275			−0.591376	+	0.806396i	$0.701415\pi$
$548$	−4.41883	+	7.65364i	−0.188763	+	0.326947i
$549$		0			0
$550$	7.26304	+	12.5800i	0.309697	+	0.536411i
$551$	12.0355	−	20.8460i	0.512728	−	0.888070i
$552$		0			0
$553$	0.990626	−	0.496593i	0.0421257	−	0.0211173i
$554$	16.0000			0.679775
$555$		0			0
$556$	−0.736959	−	1.27645i	−0.0312540	−	0.0541335i
$557$	−3.99346	−	6.91687i	−0.169208	−	0.293077i	0.768934	−	0.639329i	$-0.220788\pi$
$557$	−3.99346	−	6.91687i	−0.169208	−	0.293077i	−0.938142	+	0.346252i	$0.887454\pi$
$558$		0			0
$559$		0			0
$560$	−0.688417	+	11.6708i	−0.0290909	+	0.493183i
$561$		0			0
$562$	7.96083	−	13.7886i	0.335807	−	0.581636i
$563$	−13.6753	−	23.6864i	−0.576346	−	0.998261i	−0.995894	−	0.0905280i	$-0.971145\pi$
$563$	−13.6753	−	23.6864i	−0.576346	−	0.998261i	0.419547	−	0.907733i	$-0.362189\pi$
$564$		0			0
$565$	−11.8797	+	20.5762i	−0.499781	+	0.865646i
$566$	18.0840			0.760127
$567$		0			0
$568$	0.934749			0.0392212
$569$	−14.7239	+	25.5025i	−0.617257	+	1.06912i	0.372727	+	0.927941i	$0.378423\pi$
$569$	−14.7239	+	25.5025i	−0.617257	+	1.06912i	−0.989984	+	0.141179i	$0.954911\pi$
$570$		0			0
$571$	7.26304	+	12.5800i	0.303949	+	0.526455i	0.977027	−	0.213117i	$-0.0683615\pi$
$571$	7.26304	+	12.5800i	0.303949	+	0.526455i	−0.673078	+	0.739572i	$0.735028\pi$
$572$		0			0
$573$		0			0
$574$	−28.7355	+	14.4049i	−1.19940	+	0.601248i
$575$	−68.7144			−2.86559
$576$		0			0
$577$	−6.69779	−	11.6009i	−0.278833	−	0.482952i	0.692262	−	0.721646i	$-0.256614\pi$
$577$	−6.69779	−	11.6009i	−0.278833	−	0.482952i	−0.971095	+	0.238694i	$0.923281\pi$
$578$	−5.67533	−	9.82996i	−0.236063	−	0.408872i
$579$		0			0
$580$	−28.8377			−1.19742
$581$	4.74858	+	3.12823i	0.197004	+	0.129781i
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	−3.73042	−	6.46127i	−0.154366	−	0.267369i
$585$		0			0
$586$	−12.5746	+	21.7799i	−0.519453	+	0.899719i
$587$	11.2928			0.466105			0.233053	−	0.972464i	$-0.425129\pi$
$587$	11.2928			0.466105			0.233053	+	0.972464i	$0.425129\pi$
$588$		0			0
$589$	12.4552			0.513206
$590$	−27.6753	+	47.9351i	−1.13938	+	1.97346i
$591$		0			0
$592$	−3.84421	−	6.65836i	−0.157996	−	0.273657i
$593$	−9.78912	+	16.9553i	−0.401991	+	0.696269i	−0.993966	−	0.109687i	$-0.965015\pi$
$593$	−9.78912	+	16.9553i	−0.401991	+	0.696269i	0.591975	+	0.805956i	$0.298348\pi$
$594$		0			0
$595$	23.2051	+	15.2869i	0.951317	+	0.626700i
$596$	9.36375			0.383554
$597$		0			0
$598$		0			0
$599$	5.46591	+	9.46724i	0.223331	+	0.386821i	0.955817	−	0.293961i	$-0.0949735\pi$
$599$	5.46591	+	9.46724i	0.223331	+	0.386821i	−0.732486	+	0.680782i	$0.761640\pi$
$600$		0			0
$601$	−41.2202			−1.68141			−0.840703	−	0.541497i	$-0.817858\pi$
$601$	−41.2202			−1.68141			−0.840703	+	0.541497i	$0.817858\pi$
$602$	7.24995	−	3.63435i	0.295486	−	0.148125i
$603$		0			0
$604$	6.78404	−	11.7503i	0.276039	−	0.478113i
$605$	2.20942	+	3.82682i	0.0898255	+	0.155582i
$606$		0			0
$607$	15.6702	−	27.1417i	0.636036	−	1.10165i	−0.350259	−	0.936653i	$-0.613906\pi$
$607$	15.6702	−	27.1417i	0.636036	−	1.10165i	0.986295	−	0.164993i	$-0.0527603\pi$
$608$	3.68842			0.149585
$609$		0			0
$610$	16.7724			0.679095
$611$		0			0
$612$		0			0
$613$	−8.54425	−	14.7991i	−0.345099	−	0.597729i	0.640273	−	0.768148i	$-0.278821\pi$
$613$	−8.54425	−	14.7991i	−0.345099	−	0.597729i	−0.985372	+	0.170419i	$0.945488\pi$
$614$	−1.93475	+	3.35108i	−0.0780801	+	0.135239i
$615$		0			0
$616$	−0.155792	+	2.64116i	−0.00627702	+	0.106415i
$617$	6.96817			0.280528			0.140264	−	0.990114i	$-0.455205\pi$
$617$	6.96817			0.280528			0.140264	+	0.990114i	$0.455205\pi$
$618$		0			0
$619$	0.00937364	+	0.0162356i	0.000376759	+	0.000652565i	0.866214	−	0.499674i	$-0.166547\pi$
$619$	0.00937364	+	0.0162356i	0.000376759	+	0.000652565i	−0.865837	+	0.500326i	$0.833213\pi$
$620$	−7.46083	−	12.9225i	−0.299634	−	0.518982i
$621$		0			0
$622$	−13.5681			−0.544030
$623$	−30.3637	+	15.2211i	−1.21650	+	0.609821i
$624$		0			0
$625$	−56.6883	+	98.1871i	−2.26753	+	3.92748i
$626$	1.26304	+	2.18765i	0.0504813	+	0.0874361i
$627$		0			0
$628$	9.37029	−	16.2298i	0.373915	−	0.647640i
$629$	−18.2741			−0.728636
$630$		0			0
$631$	−5.78550			−0.230317			−0.115159	−	0.993347i	$-0.536738\pi$
$631$	−5.78550			−0.230317			−0.115159	+	0.993347i	$0.536738\pi$
$632$	−0.209416	+	0.362720i	−0.00833013	+	0.0144282i
$633$		0			0
$634$	10.0051	+	17.3293i	0.397353	+	0.688235i
$635$	1.61379	−	2.79517i	0.0640414	−	0.110923i
$636$		0			0
$637$		0			0
$638$	−6.52608			−0.258370
$639$		0			0
$640$	−2.20942	−	3.82682i	−0.0873348	−	0.151268i
$641$	7.68842	+	13.3167i	0.303674	+	0.525979i	0.976965	−	0.213398i	$-0.0684532\pi$
$641$	7.68842	+	13.3167i	0.303674	+	0.525979i	−0.673291	+	0.739378i	$0.735120\pi$
$642$		0			0
$643$	−35.8058			−1.41204			−0.706022	−	0.708190i	$-0.749512\pi$
$643$	−35.8058			−1.41204			−0.706022	+	0.708190i	$0.749512\pi$
$644$	−10.4515	−	6.88512i	−0.411845	−	0.271312i
$645$		0			0
$646$	4.38338	−	7.59223i	0.172462	−	0.298712i
$647$	4.62825	+	8.01636i	0.181955	+	0.315156i	0.942546	−	0.334076i	$-0.108424\pi$
$647$	4.62825	+	8.01636i	0.181955	+	0.315156i	−0.760591	+	0.649231i	$0.775091\pi$
$648$		0			0
$649$	−6.26304	+	10.8479i	−0.245846	+	0.425818i
$650$		0			0
$651$		0			0
$652$	18.7724			0.735185
$653$	12.4239	−	21.5189i	0.486185	−	0.842098i	−0.513689	−	0.857977i	$-0.671721\pi$
$653$	12.4239	−	21.5189i	0.486185	−	0.842098i	0.999874	+	0.0158790i	$0.00505464\pi$
$654$		0			0
$655$	−16.2985	−	28.2298i	−0.636835	−	1.10303i
$656$	6.07462	−	10.5216i	0.237174	−	0.410798i
$657$		0			0
$658$	−0.639875	+	10.8479i	−0.0249449	+	0.422895i
$659$	6.60442			0.257272			0.128636	−	0.991692i	$-0.458940\pi$
$659$	6.60442			0.257272			0.128636	+	0.991692i	$0.458940\pi$
$660$		0			0
$661$	6.61662	+	11.4603i	0.257357	+	0.445755i	0.965533	−	0.260281i	$-0.0838151\pi$
$661$	6.61662	+	11.4603i	0.257357	+	0.445755i	−0.708176	+	0.706036i	$0.750482\pi$
$662$	−8.07462	−	13.9857i	−0.313829	−	0.543568i
$663$		0			0
$664$	−2.14925			−0.0834070
$665$	2.53917	−	43.0469i	0.0984647	−	1.66929i
$666$		0			0
$667$	15.4355	−	26.7351i	0.597667	−	1.03519i
$668$	−11.9449	−	20.6892i	−0.462163	−	0.800489i
$669$		0			0
$670$	−22.4239	+	38.8394i	−0.866311	+	1.50050i
$671$	3.79567			0.146530
$672$		0			0
$673$	0.130501			0.00503045			0.00251523	−	0.999997i	$-0.499199\pi$
$673$	0.130501			0.00503045			0.00251523	+	0.999997i	$0.499199\pi$
$674$	11.5681	−	20.0365i	0.445586	−	0.771777i
$675$		0			0
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	14.0587	−	24.3504i	0.540320	−	0.935862i	−0.458565	−	0.888661i	$-0.651637\pi$
$677$	14.0587	−	24.3504i	0.540320	−	0.935862i	0.998885	−	0.0472011i	$-0.0150301\pi$
$678$		0			0
$679$	15.4659	+	10.1885i	0.593527	+	0.390999i
$680$	−10.5028			−0.402765
$681$		0			0
$682$	−1.68842	−	2.92442i	−0.0646528	−	0.111982i
$683$	7.95146	+	13.7723i	0.304254	+	0.526984i	0.977095	−	0.212804i	$-0.0682595\pi$
$683$	7.95146	+	13.7723i	0.304254	+	0.526984i	−0.672841	+	0.739787i	$0.734926\pi$
$684$		0			0
$685$	−39.0522			−1.49211
$686$	14.1609	+	11.9361i	0.540665	+	0.455721i
$687$		0			0
$688$	−1.53263	+	2.65458i	−0.0584308	+	0.101205i
$689$		0			0
$690$		0			0
$691$	7.99063	−	13.8402i	0.303978	−	0.526505i	−0.673055	−	0.739592i	$-0.735018\pi$
$691$	7.99063	−	13.8402i	0.303978	−	0.526505i	0.977033	+	0.213087i	$0.0683518\pi$
$692$	−11.3768			−0.432482
$693$		0			0
$694$	15.6566			0.594316
$695$	3.25650	−	5.64042i	0.123526	−	0.213953i
$696$		0			0
$697$	−14.4384	−	25.0080i	−0.546892	−	0.947245i
$698$	−10.0051	+	17.3293i	−0.378698	+	0.655924i
$699$		0			0
$700$	−34.3572	+	17.2230i	−1.29858	+	0.650968i
$701$	−13.9869			−0.528278			−0.264139	−	0.964485i	$-0.585088\pi$
$701$	−13.9869			−0.528278			−0.264139	+	0.964485i	$0.585088\pi$
$702$		0			0
$703$	14.1790	+	24.5588i	0.534773	+	0.926254i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$	7.46083			0.280792
$707$	2.39354	−	40.5781i	0.0900184	−	1.52610i
$708$		0			0
$709$	−3.82096	+	6.61809i	−0.143499	+	0.248548i	−0.928812	−	0.370551i	$-0.879169\pi$
$709$	−3.82096	+	6.61809i	−0.143499	+	0.248548i	0.785313	+	0.619099i	$0.212502\pi$
$710$	2.06525	+	3.57712i	0.0775075	+	0.134247i
$711$		0			0
$712$	6.41883	−	11.1177i	0.240556	−	0.416655i
$713$	15.9738			0.598225
$714$		0			0
$715$		0			0
$716$	12.3050	−	21.3130i	0.459861	−	0.796503i
$717$		0			0
$718$	5.62317	+	9.73961i	0.209855	+	0.363479i
$719$	−9.71879	+	16.8334i	−0.362450	+	0.627781i	−0.988363	−	0.152111i	$-0.951393\pi$
$719$	−9.71879	+	16.8334i	−0.362450	+	0.627781i	0.625914	+	0.779892i	$0.284726\pi$
$720$		0			0
$721$	6.20433	−	3.11019i	0.231061	−	0.115829i
$722$	5.39558			0.200803
$723$		0			0
$724$	−8.73042	−	15.1215i	−0.324463	−	0.561987i
$725$	−47.3992	−	82.0978i	−1.76036	−	3.04904i
$726$		0			0
$727$	−44.9217			−1.66605			−0.833026	−	0.553234i	$-0.813394\pi$
$727$	−44.9217			−1.66605			−0.833026	+	0.553234i	$0.813394\pi$
$728$		0			0
$729$		0			0
$730$	16.4841	−	28.5513i	0.610103	−	1.05673i
$731$	3.64280	+	6.30951i	0.134734	+	0.233366i
$732$		0			0
$733$	−12.5210	+	21.6870i	−0.462474	+	0.801028i	−0.999084	−	0.0428026i	$-0.986371\pi$
$733$	−12.5210	+	21.6870i	−0.462474	+	0.801028i	0.536610	+	0.843830i	$0.319705\pi$
$734$	5.91600			0.218364
$735$		0			0
$736$	4.73042			0.174365
$737$	−5.07462	+	8.78951i	−0.186926	+	0.323766i
$738$		0			0
$739$	3.31158	+	5.73583i	0.121819	+	0.210996i	0.920485	−	0.390778i	$-0.127794\pi$
$739$	3.31158	+	5.73583i	0.121819	+	0.210996i	−0.798666	+	0.601774i	$0.794461\pi$
$740$	16.9869	−	29.4222i	0.624451	−	1.08158i
$741$		0			0
$742$	17.6753	+	11.6440i	0.648882	+	0.427465i
$743$	39.3972			1.44534			0.722671	−	0.691192i	$-0.242914\pi$
$743$	39.3972			1.44534			0.722671	+	0.691192i	$0.242914\pi$
$744$		0			0
$745$	20.6884	+	35.8334i	0.757965	+	1.31283i
$746$	−11.5630	−	20.0277i	−0.423351	−	0.733266i
$747$		0			0
$748$	−2.37683			−0.0869056
$749$	25.7877	−	12.9272i	0.942261	−	0.472348i
$750$		0			0
$751$	5.35358	−	9.27268i	0.195355	−	0.338365i	−0.751662	−	0.659549i	$-0.770747\pi$
$751$	5.35358	−	9.27268i	0.195355	−	0.338365i	0.947017	+	0.321184i	$0.104081\pi$
$752$	−2.05362	−	3.55698i	−0.0748880	−	0.129710i
$753$		0			0
$754$		0			0
$755$	59.9551			2.18199
$756$		0			0
$757$	−17.2797			−0.628043			−0.314022	−	0.949416i	$-0.601676\pi$
$757$	−17.2797			−0.628043			−0.314022	+	0.949416i	$0.601676\pi$
$758$	−3.38621	+	5.86508i	−0.122993	+	0.213029i
$759$		0			0
$760$	8.14925	+	14.1149i	0.295604	+	0.512002i
$761$	−16.3544	+	28.3266i	−0.592846	+	1.02684i	0.401001	+	0.916077i	$0.368662\pi$
$761$	−16.3544	+	28.3266i	−0.592846	+	1.02684i	−0.993847	+	0.110761i	$0.964671\pi$
$762$		0			0
$763$	−1.83767	+	31.1542i	−0.0665280	+	1.12786i
$764$	16.8377			0.609165
$765$		0			0
$766$	−12.6819	−	21.9656i	−0.458215	−	0.793651i
$767$		0			0
$768$		0			0
$769$	12.2145			0.440466			0.220233	−	0.975447i	$-0.429318\pi$
$769$	12.2145			0.440466			0.220233	+	0.975447i	$0.429318\pi$
$770$	−10.4515	+	5.23924i	−0.376644	+	0.188809i
$771$		0			0
$772$	−2.73042	+	4.72922i	−0.0982698	+	0.170208i
$773$	0.102167	+	0.176958i	0.00367468	+	0.00636474i	0.867857	−	0.496814i	$-0.165497\pi$
$773$	0.102167	+	0.176958i	0.00367468	+	0.00636474i	−0.864182	+	0.503179i	$0.832164\pi$
$774$		0			0
$775$	24.5261	−	42.4804i	0.881003	−	1.52594i
$776$	−7.00000			−0.251285
$777$		0			0
$778$	25.2565			0.905489
$779$	−22.4057	+	38.8079i	−0.802769	+	1.39044i
$780$		0			0
$781$	0.467375	+	0.809517i	0.0167240	+	0.0289668i
$782$	5.62171	−	9.73708i	0.201032	−	0.348197i
$783$		0			0
$784$	−6.95146	−	0.822941i	−0.248266	−	0.0293908i
$785$	82.8115			2.95567
$786$		0			0
$787$	−12.7790	−	22.1338i	−0.455521	−	0.788985i	0.543197	−	0.839605i	$-0.317214\pi$
$787$	−12.7790	−	22.1338i	−0.455521	−	0.788985i	−0.998718	+	0.0506202i	$0.983880\pi$
$788$	−4.84421	−	8.39042i	−0.172568	−	0.298896i
$789$		0			0
$790$	−1.85075			−0.0658468
$791$	−11.8797	−	7.82598i	−0.422392	−	0.278260i
$792$		0			0
$793$		0			0
$794$	−6.73696	−	11.6688i	−0.239086	−	0.414109i
$795$		0			0
$796$	−10.1492	+	17.5790i	−0.359731	+	0.623072i
$797$	−30.0477			−1.06434			−0.532171	−	0.846637i	$-0.678624\pi$
$797$	−30.0477			−1.06434			−0.532171	+	0.846637i	$0.678624\pi$
$798$		0			0
$799$	−9.76225			−0.345364
$800$	7.26304	−	12.5800i	0.256787	−	0.444769i
$801$		0			0
$802$	−16.9449	−	29.3495i	−0.598346	−	1.03637i
$803$	3.73042	−	6.46127i	0.131644	−	0.228013i
$804$		0			0
$805$	3.25650	−	55.2080i	0.114776	−	1.94582i
$806$		0			0
$807$		0			0
$808$	7.68187	+	13.3054i	0.270247	+	0.468082i
$809$	1.17171	+	2.02946i	0.0411951	+	0.0713520i	0.885888	−	0.463900i	$-0.153550\pi$
$809$	1.17171	+	2.02946i	0.0411951	+	0.0713520i	−0.844693	+	0.535252i	$0.820217\pi$
$810$		0			0
$811$	−11.8695			−0.416794			−0.208397	−	0.978044i	$-0.566825\pi$
$811$	−11.8695			−0.416794			−0.208397	+	0.978044i	$0.566825\pi$
$812$	1.01671	−	17.2364i	0.0356795	−	0.604880i
$813$		0			0
$814$	3.84421	−	6.65836i	0.134739	−	0.233376i
$815$	41.4761	+	71.8387i	1.45284	+	2.51640i
$816$		0			0
$817$	5.65296	−	9.79122i	0.197772	−	0.342551i
$818$	4.21450			0.147357
$819$		0			0
$820$	53.6855			1.87478
$821$	−18.7406	+	32.4596i	−0.654051	+	1.13285i	0.328080	+	0.944650i	$0.393598\pi$
$821$	−18.7406	+	32.4596i	−0.654051	+	1.13285i	−0.982131	+	0.188199i	$0.939735\pi$
$822$		0			0
$823$	−0.646418	−	1.11963i	−0.0225327	−	0.0390278i	0.854539	−	0.519387i	$-0.173840\pi$
$823$	−0.646418	−	1.11963i	−0.0225327	−	0.0390278i	−0.877072	+	0.480359i	$0.840506\pi$
$824$	−1.31158	+	2.27173i	−0.0456912	+	0.0791394i
$825$		0			0
$826$	−27.6753	−	18.2317i	−0.962948	−	0.634362i
$827$	−43.3319			−1.50680			−0.753399	−	0.657563i	$-0.771587\pi$
$827$	−43.3319			−1.50680			−0.753399	+	0.657563i	$0.771587\pi$
$828$		0			0
$829$	−20.0587	−	34.7427i	−0.696668	−	1.20666i	−0.969615	−	0.244635i	$-0.921332\pi$
$829$	−20.0587	−	34.7427i	−0.696668	−	1.20666i	0.272948	−	0.962029i	$-0.412001\pi$
$830$	−4.74858	−	8.22479i	−0.164826	−	0.285487i
$831$		0			0
$832$		0			0
$833$	−9.95517	+	13.3309i	−0.344926	+	0.461887i
$834$		0			0
$835$	52.7826	−	91.4221i	1.82662	−	3.16379i
$836$	1.84421	+	3.19426i	0.0637833	+	0.110476i
$837$		0			0
$838$	11.1558	−	19.3224i	0.385370	−	0.667481i
$839$	−54.6912			−1.88815			−0.944074	−	0.329733i	$-0.893041\pi$
$839$	−54.6912			−1.88815			−0.944074	+	0.329733i	$0.893041\pi$
$840$		0			0
$841$	13.5897			0.468612
$842$	9.15579	−	15.8583i	0.315529	−	0.546513i
$843$		0			0
$844$	−11.2565	−	19.4968i	−0.387465	−	0.671108i
$845$	−28.7224	+	49.7487i	−0.988081	+	1.71141i
$846$		0			0
$847$	−2.36521	+	1.18566i	−0.0812695	+	0.0407398i
$848$	−8.00000			−0.274721
$849$		0			0
$850$	−17.2630	−	29.9005i	−0.592117	−	1.02558i
$851$	18.1847	+	31.4968i	0.623364	+	1.07970i
$852$		0			0
$853$	−20.8275			−0.713120			−0.356560	−	0.934272i	$-0.616050\pi$
$853$	−20.8275			−0.713120			−0.356560	+	0.934272i	$0.616050\pi$
$854$	−0.591333	+	10.0250i	−0.0202350	+	0.343047i
$855$		0			0
$856$	−5.45146	+	9.44220i	−0.186327	+	0.322728i
$857$	−18.4217	−	31.9073i	−0.629272	−	1.08993i	−0.987698	−	0.156373i	$-0.950020\pi$
$857$	−18.4217	−	31.9073i	−0.629272	−	1.08993i	0.358426	−	0.933558i	$-0.383314\pi$
$858$		0			0
$859$	−19.2891	+	33.4097i	−0.658136	+	1.13993i	0.322961	+	0.946412i	$0.395322\pi$
$859$	−19.2891	+	33.4097i	−0.658136	+	1.13993i	−0.981098	+	0.193513i	$0.938012\pi$
$860$	−13.5448			−0.461875
$861$		0			0
$862$	−28.8377			−0.982215
$863$	−8.62825	+	14.9446i	−0.293709	+	0.508719i	−0.974684	−	0.223588i	$-0.928223\pi$
$863$	−8.62825	+	14.9446i	−0.293709	+	0.508719i	0.680975	+	0.732307i	$0.261556\pi$
$864$		0			0
$865$	−25.1362	−	43.5371i	−0.854655	−	1.48031i
$866$	3.81158	−	6.60186i	0.129523	−	0.224340i
$867$		0			0
$868$	7.98691	−	4.00378i	0.271094	−	0.135897i
$869$	−0.418833			−0.0142079
$870$		0			0
$871$		0			0
$872$	−5.89783	−	10.2153i	−0.199726	−	0.345935i
$873$		0			0
$874$	−17.4477			−0.590179
$875$	−93.0035	−	61.2680i	−3.14409	−	2.07124i
$876$		0			0
$877$	−0.125418	+	0.217231i	−0.00423508	+	0.00733537i	−0.868135	−	0.496328i	$-0.834681\pi$
$877$	−0.125418	+	0.217231i	−0.00423508	+	0.00733537i	0.863900	+	0.503663i	$0.168015\pi$
$878$	−16.6870	−	28.9027i	−0.563158	−	0.975417i
$879$		0			0
$880$	2.20942	−	3.82682i	0.0744794	−	0.129002i
$881$	−16.2985			−0.549110			−0.274555	−	0.961571i	$-0.588531\pi$
$881$	−16.2985			−0.549110			−0.274555	+	0.961571i	$0.588531\pi$
$882$		0			0
$883$	−33.9551			−1.14268			−0.571340	−	0.820714i	$-0.693576\pi$
$883$	−33.9551			−1.14268			−0.571340	+	0.820714i	$0.693576\pi$
$884$		0			0
$885$		0			0
$886$	2.42538	+	4.20087i	0.0814821	+	0.141131i
$887$	9.73042	−	16.8536i	0.326715	−	0.565888i	−0.655143	−	0.755505i	$-0.727391\pi$
$887$	9.73042	−	16.8536i	0.326715	−	0.565888i	0.981858	+	0.189618i	$0.0607248\pi$
$888$		0			0
$889$	1.61379	+	1.06312i	0.0541249	+	0.0356559i
$890$	56.7275			1.90151
$891$		0			0
$892$	3.73042	+	6.46127i	0.124904	+	0.216339i
$893$	7.57462	+	13.1196i	0.253475	+	0.439032i
$894$		0			0
$895$	108.748			3.63504
$896$	2.36521	−	1.18566i	0.0790161	−	0.0396101i
$897$		0			0
$898$	−7.17250	+	12.4231i	−0.239349	+	0.414565i
$899$	11.0187	+	19.0850i	0.367496	+	0.636521i
$900$		0			0
$901$	−9.50733	+	16.4672i	−0.316735	+	0.548602i
$902$	12.1492			0.404526
$903$		0			0
$904$	5.37683			0.178831
$905$	38.5782	−	66.8195i	1.28238	−	2.22115i
$906$		0			0
$907$	−0.386207	−	0.668931i	−0.0128238	−	0.0222115i	0.859542	−	0.511065i	$-0.170749\pi$
$907$	−0.386207	−	0.668931i	−0.0128238	−	0.0222115i	−0.872366	+	0.488853i	$0.837415\pi$
$908$	−1.38621	+	2.40098i	−0.0460029	+	0.0796794i
$909$		0			0
$910$		0			0
$911$	8.94491			0.296358			0.148179	−	0.988961i	$-0.452659\pi$
$911$	8.94491			0.296358			0.148179	+	0.988961i	$0.452659\pi$
$912$		0			0
$913$	−1.07462	−	1.86130i	−0.0355649	−	0.0616002i
$914$	−12.5913	−	21.8088i	−0.416484	−	0.721372i
$915$		0			0
$916$	−2.53917			−0.0838965
$917$	17.4477	−	8.74642i	0.576175	−	0.288832i
$918$		0			0
$919$	−29.4406	+	50.9927i	−0.971157	+	1.68209i	−0.279081	+	0.960268i	$0.590030\pi$
$919$	−29.4406	+	50.9927i	−0.971157	+	1.68209i	−0.692076	+	0.721825i	$0.743304\pi$
$920$	10.4515	+	18.1025i	0.344574	+	0.596820i
$921$		0			0
$922$	−6.50937	+	11.2746i	−0.214375	+	0.371308i
$923$		0			0
$924$		0			0
$925$	111.683			3.67210
$926$	−7.10725	+	12.3101i	−0.233559	+	0.404536i
$927$		0			0
$928$	3.26304	+	5.65175i	0.107115	+	0.185528i
$929$	−11.2696	+	19.5195i	−0.369743	+	0.640414i	−0.989525	−	0.144360i	$-0.953888\pi$
$929$	−11.2696	+	19.5195i	−0.369743	+	0.640414i	0.619782	+	0.784774i	$0.287221\pi$
$930$		0			0
$931$	25.6399	+	3.03535i	0.840313	+	0.0994796i
$932$	24.0522			0.787855
$933$		0			0
$934$	1.19779	+	2.07463i	0.0391929	+	0.0678841i
$935$	−5.25142	−	9.09572i	−0.171740	−	0.297462i
$936$		0			0
$937$	−12.9478			−0.422987			−0.211494	−	0.977379i	$-0.567833\pi$
$937$	−12.9478			−0.422987			−0.211494	+	0.977379i	$0.567833\pi$
$938$	−22.4239	−	14.7722i	−0.732167	−	0.482330i
$939$		0			0
$940$	9.07462	−	15.7177i	0.295982	−	0.512655i
$941$	24.4123	+	42.2833i	0.795818	+	1.37840i	0.922319	+	0.386431i	$0.126292\pi$
$941$	24.4123	+	42.2833i	0.795818	+	1.37840i	−0.126501	+	0.991967i	$0.540375\pi$
$942$		0			0
$943$	−28.7355	+	49.7713i	−0.935757	+	1.62078i
$944$	12.5261			0.407689
$945$		0			0
$946$	−3.06525			−0.0996599
$947$	−15.5615	+	26.9534i	−0.505682	+	0.875867i	0.494296	+	0.869293i	$0.335426\pi$
$947$	−15.5615	+	26.9534i	−0.505682	+	0.875867i	−0.999978	+	0.00657353i	$0.997908\pi$
$948$		0			0
$949$		0			0
$950$	−26.7891	+	46.4001i	−0.869154	+	1.50542i
$951$		0			0
$952$	0.370291	−	6.27760i	0.0120012	−	0.203458i
$953$	−16.2797			−0.527353			−0.263676	−	0.964611i	$-0.584935\pi$
$953$	−16.2797			−0.527353			−0.263676	+	0.964611i	$0.584935\pi$
$954$		0			0
$955$	37.2014	+	64.4347i	1.20381	+	2.08506i
$956$	3.79567	+	6.57429i	0.122761	+	0.212628i
$957$		0			0
$958$	10.8377			0.350149
$959$	1.37683	−	23.3417i	0.0444603	−	0.753743i
$960$		0			0
$961$	9.79850	−	16.9715i	0.316081	−	0.547468i
$962$		0			0
$963$		0			0
$964$	−8.14925	+	14.1149i	−0.262470	+	0.454611i
$965$	−24.1305			−0.776788
$966$		0			0
$967$	3.91308			0.125836			0.0629181	−	0.998019i	$-0.479959\pi$
$967$	3.91308			0.125836			0.0629181	+	0.998019i	$0.479959\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$		0			0
$970$	−15.4659	−	26.7877i	−0.496581	−	0.860103i
$971$	19.6566	−	34.0462i	0.630810	−	1.09259i	−0.356577	−	0.934266i	$-0.616056\pi$
$971$	19.6566	−	34.0462i	0.630810	−	1.09259i	0.987386	−	0.158329i	$-0.0506105\pi$
$972$		0			0
$973$	3.25650	+	2.14529i	0.104399	+	0.0687747i
$974$	34.6435			1.11005
$975$		0			0
$976$	−1.89783	−	3.28714i	−0.0607482	−	0.105219i
$977$	−11.6753	−	20.2223i	−0.373527	−	0.646968i	0.616578	−	0.787293i	$-0.288518\pi$
$977$	−11.6753	−	20.2223i	−0.373527	−	0.646968i	−0.990105	+	0.140326i	$0.955185\pi$
$978$		0			0
$979$	12.8377			0.410294
$980$	−12.2094	−	28.4202i	−0.390015	−	0.907850i
$981$		0			0
$982$	−19.0746	+	33.0382i	−0.608696	+	1.05429i
$983$	−2.25796	−	3.91090i	−0.0720177	−	0.124738i	0.827768	−	0.561071i	$-0.189610\pi$
$983$	−2.25796	−	3.91090i	−0.0720177	−	0.124738i	−0.899785	+	0.436333i	$0.856277\pi$
$984$		0			0
$985$	21.4057	−	37.0758i	0.682044	−	1.18133i
$986$	15.5114			0.493984
$987$		0			0
$988$		0			0
$989$	7.24995	−	12.5573i	0.230535	−	0.399299i
$990$		0			0
$991$	−29.9637	−	51.8986i	−0.951827	−	1.64861i	−0.741467	−	0.670989i	$-0.765870\pi$
$991$	−29.9637	−	51.8986i	−0.951827	−	1.64861i	−0.210360	−	0.977624i	$-0.567463\pi$
$992$	−1.68842	+	2.92442i	−0.0536073	+	0.0928505i
$993$		0			0
$994$	−2.21088	+	1.10830i	−0.0701247	+	0.0351530i
$995$	−89.6957			−2.84354
$996$		0			0
$997$	10.7537	+	18.6259i	0.340572	+	0.589888i	0.984539	−	0.175165i	$-0.0560459\pi$
$997$	10.7537	+	18.6259i	0.340572	+	0.589888i	−0.643967	+	0.765053i	$0.722713\pi$
$998$	−0.311583	−	0.539678i	−0.00986299	−	0.0170832i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.v.793.3		6
3.2	odd	2		462.2.i.g.331.1	yes	6
7.2	even	3		9702.2.a.dv.1.1		3
7.4	even	3	inner	1386.2.k.v.991.3		6
7.5	odd	6		9702.2.a.dw.1.3		3
21.2	odd	6		3234.2.a.bf.1.3		3
21.5	even	6		3234.2.a.bh.1.1		3
21.11	odd	6		462.2.i.g.67.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.g.67.1	✓	6	21.11	odd	6
462.2.i.g.331.1	yes	6	3.2	odd	2
1386.2.k.v.793.3		6	1.1	even	1	trivial
1386.2.k.v.991.3		6	7.4	even	3	inner
3234.2.a.bf.1.3		3	21.2	odd	6
3234.2.a.bh.1.1		3	21.5	even	6
9702.2.a.dv.1.1		3	7.2	even	3
9702.2.a.dw.1.3		3	7.5	odd	6

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.20942 - 3.82682i) q^{5} +(2.20942 + 1.45550i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.20942 - 3.82682i) q^{5} +(2.20942 + 1.45550i) q^{7} -1.00000 q^{8} +(-2.20942 - 3.82682i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(2.36521 - 1.18566i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.18842 + 2.05840i) q^{17} +(1.84421 - 3.19426i) q^{19} -4.41883 q^{20} -1.00000 q^{22} +(2.36521 - 4.09666i) q^{23} +(-7.26304 - 12.5800i) q^{25} +(0.155792 - 2.64116i) q^{28} +6.52608 q^{29} +(1.68842 + 2.92442i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.37683 q^{34} +(10.4515 - 5.23924i) q^{35} +(-3.84421 + 6.65836i) q^{37} +(-1.84421 - 3.19426i) q^{38} +(-2.20942 + 3.82682i) q^{40} -12.1492 q^{41} +3.06525 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-2.36521 - 4.09666i) q^{46} +(-2.05362 + 3.55698i) q^{47} +(2.76304 + 6.43161i) q^{49} -14.5261 q^{50} +(4.00000 + 6.92820i) q^{53} -4.41883 q^{55} +(-2.20942 - 1.45550i) q^{56} +(3.26304 - 5.65175i) q^{58} +(-6.26304 - 10.8479i) q^{59} +(-1.89783 + 3.28714i) q^{61} +3.37683 q^{62} +1.00000 q^{64} +(-5.07462 - 8.78951i) q^{67} +(1.18842 - 2.05840i) q^{68} +(0.688417 - 11.6708i) q^{70} -0.934749 q^{71} +(3.73042 + 6.46127i) q^{73} +(3.84421 + 6.65836i) q^{74} -3.68842 q^{76} +(0.155792 - 2.64116i) q^{77} +(0.209416 - 0.362720i) q^{79} +(2.20942 + 3.82682i) q^{80} +(-6.07462 + 10.5216i) q^{82} +2.14925 q^{83} +10.5028 q^{85} +(1.53263 - 2.65458i) q^{86} +(0.500000 + 0.866025i) q^{88} +(-6.41883 + 11.1177i) q^{89} -4.73042 q^{92} +(2.05362 + 3.55698i) q^{94} +(-8.14925 - 14.1149i) q^{95} +7.00000 q^{97} +(6.95146 + 0.822941i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8}+O(q^{10}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8} - 3 q^{11} + 3 q^{14} - 3 q^{16} + 3 q^{17} + 9 q^{19} - 6 q^{22} + 3 q^{23} - 15 q^{25} + 3 q^{28} - 18 q^{29} + 6 q^{31} + 3 q^{32} + 6 q^{34} + 30 q^{35} - 21 q^{37} - 9 q^{38} - 24 q^{41} + 6 q^{43} - 3 q^{44} - 3 q^{46} + 3 q^{47} - 12 q^{49} - 30 q^{50} + 24 q^{53} - 9 q^{58} - 9 q^{59} + 6 q^{61} + 12 q^{62} + 6 q^{64} - 6 q^{67} + 3 q^{68} - 18 q^{71} + 21 q^{74} - 18 q^{76} + 3 q^{77} - 12 q^{79} - 12 q^{82} - 36 q^{83} + 3 q^{86} + 3 q^{88} - 12 q^{89} - 6 q^{92} - 3 q^{94} + 42 q^{97} + 9 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8 - 3 * q^11 + 3 * q^14 - 3 * q^16 + 3 * q^17 + 9 * q^19 - 6 * q^22 + 3 * q^23 - 15 * q^25 + 3 * q^28 - 18 * q^29 + 6 * q^31 + 3 * q^32 + 6 * q^34 + 30 * q^35 - 21 * q^37 - 9 * q^38 - 24 * q^41 + 6 * q^43 - 3 * q^44 - 3 * q^46 + 3 * q^47 - 12 * q^49 - 30 * q^50 + 24 * q^53 - 9 * q^58 - 9 * q^59 + 6 * q^61 + 12 * q^62 + 6 * q^64 - 6 * q^67 + 3 * q^68 - 18 * q^71 + 21 * q^74 - 18 * q^76 + 3 * q^77 - 12 * q^79 - 12 * q^82 - 36 * q^83 + 3 * q^86 + 3 * q^88 - 12 * q^89 - 6 * q^92 - 3 * q^94 + 42 * q^97 + 9 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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