LMFDB - Embedded newform 1386.2.k.v.793.1

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			793.1
Root			$0.500000 - 0.679547i$ of defining polynomial
Character	$\chi$	$=$	1386.793
Dual form			1386.2.k.v.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.40280 + 2.42972i) q^{5} +(-1.40280 - 2.24325i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.40280 + 2.42972i) q^{5} +(-1.40280 - 2.24325i) q^{7} -1.00000 q^{8} +(1.40280 + 2.42972i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-2.64411 + 0.0932392i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.98261 + 6.89809i) q^{17} +(3.24131 - 5.61411i) q^{19} +2.80560 q^{20} -1.00000 q^{22} +(-2.64411 + 4.57973i) q^{23} +(-1.43570 - 2.48671i) q^{25} +(-1.24131 + 2.33648i) q^{28} -5.12859 q^{29} +(4.48261 + 7.76411i) q^{31} +(0.500000 + 0.866025i) q^{32} +7.96523 q^{34} +(7.41832 - 0.261592i) q^{35} +(-5.24131 + 9.07821i) q^{37} +(-3.24131 - 5.61411i) q^{38} +(1.40280 - 2.42972i) q^{40} +5.09382 q^{41} +11.4478 q^{43} +(-0.500000 + 0.866025i) q^{44} +(2.64411 + 4.57973i) q^{46} +(0.161495 - 0.279717i) q^{47} +(-3.06430 + 6.29365i) q^{49} -2.87141 q^{50} +(4.00000 + 6.92820i) q^{53} +2.80560 q^{55} +(1.40280 + 2.24325i) q^{56} +(-2.56430 + 4.44149i) q^{58} +(-0.435704 - 0.754661i) q^{59} +(-1.07981 + 1.87029i) q^{61} +8.96523 q^{62} +1.00000 q^{64} +(3.54691 + 6.14343i) q^{67} +(3.98261 - 6.89809i) q^{68} +(3.48261 - 6.55525i) q^{70} +7.44784 q^{71} +(-6.28822 - 10.8915i) q^{73} +(5.24131 + 9.07821i) q^{74} -6.48261 q^{76} +(-1.24131 + 2.33648i) q^{77} +(-3.40280 + 5.89382i) q^{79} +(-1.40280 - 2.42972i) q^{80} +(2.54691 - 4.41138i) q^{82} -15.0938 q^{83} -22.3473 q^{85} +(5.72392 - 9.91412i) q^{86} +(0.500000 + 0.866025i) q^{88} +(0.805603 - 1.39535i) q^{89} +5.28822 q^{92} +(-0.161495 - 0.279717i) q^{94} +(9.09382 + 15.7510i) q^{95} +7.00000 q^{97} +(3.91832 + 5.80059i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.40280	+	2.42972i	−0.627352	+	1.08661i	0.360729	+	0.932671i	$0.382528\pi$
$5$	−1.40280	+	2.42972i	−0.627352	+	1.08661i	−0.988081	+	0.153935i	$0.950805\pi$
$6$		0			0
$7$	−1.40280	−	2.24325i	−0.530209	−	0.847867i
$7$	−1.40280	−	2.24325i	−0.530209	−	0.847867i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.40280	+	2.42972i	0.443605	+	0.768346i
$11$	−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	$0.5\pi$
$14$	−2.64411	+	0.0932392i	−0.706668	+	0.0249192i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.98261	+	6.89809i	0.965926	+	1.67303i	0.707108	+	0.707106i	$0.250000\pi$
$17$	3.98261	+	6.89809i	0.965926	+	1.67303i	0.258818	+	0.965926i	$0.416667\pi$
$18$		0			0
$19$	3.24131	−	5.61411i	0.743607	−	1.28796i	−0.207236	−	0.978291i	$-0.566447\pi$
$19$	3.24131	−	5.61411i	0.743607	−	1.28796i	0.950843	−	0.309674i	$-0.100220\pi$
$20$	2.80560			0.627352
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−2.64411	+	4.57973i	−0.551335	+	0.954940i	0.446844	+	0.894612i	$0.352548\pi$
$23$	−2.64411	+	4.57973i	−0.551335	+	0.954940i	−0.998179	+	0.0603277i	$0.980785\pi$
$24$		0			0
$25$	−1.43570	−	2.48671i	−0.287141	−	0.497342i
$26$		0			0
$27$		0			0
$28$	−1.24131	+	2.33648i	−0.234585	+	0.441554i
$29$	−5.12859			−0.952356			−0.476178	−	0.879349i	$-0.657978\pi$
$29$	−5.12859			−0.952356			−0.476178	+	0.879349i	$0.657978\pi$
$30$		0			0
$31$	4.48261	+	7.76411i	0.805101	+	1.39448i	0.916223	+	0.400669i	$0.131222\pi$
$31$	4.48261	+	7.76411i	0.805101	+	1.39448i	−0.111122	+	0.993807i	$0.535444\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	7.96523			1.36602
$35$	7.41832	−	0.261592i	1.25392	−	0.0442171i
$36$		0			0
$37$	−5.24131	+	9.07821i	−0.861665	+	1.49245i	0.00865499	+	0.999963i	$0.497245\pi$
$37$	−5.24131	+	9.07821i	−0.861665	+	1.49245i	−0.870320	+	0.492486i	$0.836088\pi$
$38$	−3.24131	−	5.61411i	−0.525809	−	0.910728i
$39$		0			0
$40$	1.40280	−	2.42972i	0.221802	−	0.384173i
$41$	5.09382			0.795521			0.397760	−	0.917489i	$-0.369788\pi$
$41$	5.09382			0.795521			0.397760	+	0.917489i	$0.369788\pi$
$42$		0			0
$43$	11.4478			1.74578			0.872890	−	0.487918i	$-0.162243\pi$
$43$	11.4478			1.74578			0.872890	+	0.487918i	$0.162243\pi$
$44$	−0.500000	+	0.866025i	−0.0753778	+	0.130558i
$45$		0			0
$46$	2.64411	+	4.57973i	0.389852	+	0.675244i
$47$	0.161495	−	0.279717i	0.0235565	−	0.0408010i	−0.854007	−	0.520262i	$-0.825834\pi$
$47$	0.161495	−	0.279717i	0.0235565	−	0.0408010i	0.877563	+	0.479461i	$0.159168\pi$
$48$		0			0
$49$	−3.06430	+	6.29365i	−0.437757	+	0.899094i
$50$	−2.87141			−0.406078
$51$		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
$55$	2.80560			0.378307
$56$	1.40280	+	2.24325i	0.187457	+	0.299766i
$57$		0			0
$58$	−2.56430	+	4.44149i	−0.336709	+	0.583196i
$59$	−0.435704	−	0.754661i	−0.0567238	−	0.0982485i	0.836269	−	0.548319i	$-0.184732\pi$
$59$	−0.435704	−	0.754661i	−0.0567238	−	0.0982485i	−0.892993	+	0.450071i	$0.851399\pi$
$60$		0			0
$61$	−1.07981	+	1.87029i	−0.138256	+	0.239466i	−0.926836	−	0.375465i	$-0.877483\pi$
$61$	−1.07981	+	1.87029i	−0.138256	+	0.239466i	0.788581	+	0.614931i	$0.210816\pi$
$62$	8.96523			1.13858
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	3.54691	+	6.14343i	0.433324	+	0.750539i	0.997157	−	0.0753496i	$-0.0240073\pi$
$67$	3.54691	+	6.14343i	0.433324	+	0.750539i	−0.563833	+	0.825889i	$0.690674\pi$
$68$	3.98261	−	6.89809i	0.482963	−	0.836516i
$69$		0			0
$70$	3.48261	−	6.55525i	0.416252	−	0.783502i
$71$	7.44784			0.883896			0.441948	−	0.897041i	$-0.354288\pi$
$71$	7.44784			0.883896			0.441948	+	0.897041i	$0.354288\pi$
$72$		0			0
$73$	−6.28822	−	10.8915i	−0.735980	−	1.27475i	−0.954292	−	0.298876i	$-0.903388\pi$
$73$	−6.28822	−	10.8915i	−0.735980	−	1.27475i	0.218312	−	0.975879i	$-0.429945\pi$
$74$	5.24131	+	9.07821i	0.609289	+	1.05532i
$75$		0			0
$76$	−6.48261			−0.743607
$77$	−1.24131	+	2.33648i	−0.141460	+	0.266267i
$78$		0			0
$79$	−3.40280	+	5.89382i	−0.382845	+	0.663107i	−0.991468	−	0.130353i	$-0.958389\pi$
$79$	−3.40280	+	5.89382i	−0.382845	+	0.663107i	0.608623	+	0.793460i	$0.291722\pi$
$80$	−1.40280	−	2.42972i	−0.156838	−	0.271651i
$81$		0			0
$82$	2.54691	−	4.41138i	0.281259	−	0.487155i
$83$	−15.0938			−1.65676			−0.828381	−	0.560165i	$-0.810738\pi$
$83$	−15.0938			−1.65676			−0.828381	+	0.560165i	$0.810738\pi$
$84$		0			0
$85$	−22.3473			−2.42390
$86$	5.72392	−	9.91412i	0.617226	−	1.06907i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	0.805603	−	1.39535i	0.0853937	−	0.147906i	−0.820165	−	0.572127i	$-0.806119\pi$
$89$	0.805603	−	1.39535i	0.0853937	−	0.147906i	0.905559	+	0.424221i	$0.139452\pi$
$90$		0			0
$91$		0			0
$92$	5.28822			0.551335
$93$		0			0
$94$	−0.161495	−	0.279717i	−0.0166569	−	0.0288507i
$95$	9.09382	+	15.7510i	0.933006	+	1.61601i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	3.91832	+	5.80059i	0.395810	+	0.585948i
$99$		0			0
$100$	−1.43570	+	2.48671i	−0.143570	+	0.248671i
$101$	5.36990	+	9.30094i	0.534325	+	0.925478i	0.999196	+	0.0400994i	$0.0127675\pi$
$101$	5.36990	+	9.30094i	0.534325	+	0.925478i	−0.464871	+	0.885379i	$0.653899\pi$
$102$		0			0
$103$	−1.48261	+	2.56796i	−0.146086	+	0.253029i	−0.929778	−	0.368122i	$-0.880001\pi$
$103$	−1.48261	+	2.56796i	−0.146086	+	0.253029i	0.783691	+	0.621150i	$0.213334\pi$
$104$		0			0
$105$		0			0
$106$	8.00000			0.777029
$107$	2.41832	−	4.18865i	0.233787	−	0.404932i	−0.725132	−	0.688610i	$-0.758221\pi$
$107$	2.41832	−	4.18865i	0.233787	−	0.404932i	0.958920	+	0.283678i	$0.0915547\pi$
$108$		0			0
$109$	5.07981	+	8.79849i	0.486558	+	0.842743i	0.999881	−	0.0154529i	$-0.00491901\pi$
$109$	5.07981	+	8.79849i	0.486558	+	0.842743i	−0.513323	+	0.858196i	$0.671586\pi$
$110$	1.40280	−	2.42972i	0.133752	−	0.231665i
$111$		0			0
$112$	2.64411	−	0.0932392i	0.249845	−	0.00881027i
$113$	−10.9652			−1.03152			−0.515761	−	0.856733i	$-0.672491\pi$
$113$	−10.9652			−1.03152			−0.515761	+	0.856733i	$0.672491\pi$
$114$		0			0
$115$	−7.41832	−	12.8489i	−0.691762	−	1.19817i
$116$	2.56430	+	4.44149i	0.238089	+	0.412382i
$117$		0			0
$118$	−0.871407			−0.0802195
$119$	9.88729	−	18.6106i	0.906366	−	1.70603i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	1.07981	+	1.87029i	0.0977615	+	0.169328i
$123$		0			0
$124$	4.48261	−	7.76411i	0.402551	−	0.697238i
$125$	−5.97199			−0.534151
$126$		0			0
$127$	−9.28822			−0.824196			−0.412098	−	0.911140i	$-0.635204\pi$
$127$	−9.28822			−0.824196			−0.412098	+	0.911140i	$0.635204\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	6.48261	−	11.2282i	0.566389	−	0.981014i	−0.430530	−	0.902576i	$-0.641674\pi$
$131$	6.48261	−	11.2282i	0.566389	−	0.981014i	0.996919	−	0.0784377i	$-0.0249932\pi$
$132$		0			0
$133$	−17.1407	+	0.604433i	−1.48629	+	0.0524110i
$134$	7.09382			0.612813
$135$		0			0
$136$	−3.98261	−	6.89809i	−0.341506	−	0.591506i
$137$	2.80560	+	4.85945i	0.239699	+	0.415171i	0.960628	−	0.277838i	$-0.0896180\pi$
$137$	2.80560	+	4.85945i	0.239699	+	0.415171i	−0.720929	+	0.693009i	$0.756285\pi$
$138$		0			0
$139$	13.1286			1.11355			0.556776	−	0.830662i	$-0.312038\pi$
$139$	13.1286			1.11355			0.556776	+	0.830662i	$0.312038\pi$
$140$	−3.93570	−	6.29365i	−0.332628	−	0.531911i
$141$		0			0
$142$	3.72392	−	6.45002i	0.312504	−	0.541273i
$143$		0			0
$144$		0			0
$145$	7.19440	−	12.4611i	0.597462	−	1.03483i
$146$	−12.5764			−1.04083
$147$		0			0
$148$	10.4826			0.861665
$149$	8.36990	−	14.4971i	0.685689	−	1.18765i	−0.287531	−	0.957771i	$-0.592834\pi$
$149$	8.36990	−	14.4971i	0.685689	−	1.18765i	0.973220	−	0.229877i	$-0.0738323\pi$
$150$		0			0
$151$	−5.44971	−	9.43918i	−0.443491	−	0.768149i	0.554455	−	0.832214i	$-0.312927\pi$
$151$	−5.44971	−	9.43918i	−0.443491	−	0.768149i	−0.997946	+	0.0640648i	$0.979594\pi$
$152$	−3.24131	+	5.61411i	−0.262905	+	0.455364i
$153$		0			0
$154$	1.40280	+	2.24325i	0.113041	+	0.180766i
$155$	−25.1529			−2.02033
$156$		0			0
$157$	−0.887286	−	1.53682i	−0.0708132	−	0.122652i	0.828445	−	0.560071i	$-0.189226\pi$
$157$	−0.887286	−	1.53682i	−0.0708132	−	0.122652i	−0.899258	+	0.437419i	$0.855893\pi$
$158$	3.40280	+	5.89382i	0.270712	+	0.468888i
$159$		0			0
$160$	−2.80560			−0.221802
$161$	13.9826	−	0.493069i	1.10198	−	0.0388593i
$162$		0			0
$163$	2.02952	−	3.51524i	0.158964	−	0.275335i	−0.775531	−	0.631309i	$-0.782518\pi$
$163$	2.02952	−	3.51524i	0.158964	−	0.275335i	0.934496	+	0.355975i	$0.115851\pi$
$164$	−2.54691	−	4.41138i	−0.198880	−	0.344471i
$165$		0			0
$166$	−7.54691	+	13.0716i	−0.585754	+	1.01456i
$167$	−13.8684			−1.07317			−0.536584	−	0.843847i	$-0.680286\pi$
$167$	−13.8684			−1.07317			−0.536584	+	0.843847i	$0.680286\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	−11.1736	+	19.3533i	−0.856978	+	1.48433i
$171$		0			0
$172$	−5.72392	−	9.91412i	−0.436445	−	0.755945i
$173$	8.48261	−	14.6923i	0.644921	−	1.11704i	−0.339399	−	0.940643i	$-0.610224\pi$
$173$	8.48261	−	14.6923i	0.644921	−	1.11704i	0.984320	−	0.176394i	$-0.0564431\pi$
$174$		0			0
$175$	−3.56430	+	6.70900i	−0.269435	+	0.507153i
$176$	1.00000			0.0753778
$177$		0			0
$178$	−0.805603	−	1.39535i	−0.0603825	−	0.104586i
$179$	−6.33513	−	10.9728i	−0.473509	−	0.820142i	0.526031	−	0.850466i	$-0.323680\pi$
$179$	−6.33513	−	10.9728i	−0.473509	−	0.820142i	−0.999540	+	0.0303231i	$0.990346\pi$
$180$		0			0
$181$	−2.57643			−0.191505			−0.0957523	−	0.995405i	$-0.530526\pi$
$181$	−2.57643			−0.191505			−0.0957523	+	0.995405i	$0.530526\pi$
$182$		0			0
$183$		0			0
$184$	2.64411	−	4.57973i	0.194926	−	0.337622i
$185$	−14.7050	−	25.4698i	−1.08113	−	1.87258i
$186$		0			0
$187$	3.98261	−	6.89809i	0.291238	−	0.504438i
$188$	−0.322990			−0.0235565
$189$		0			0
$190$	18.1876			1.31947
$191$	−1.19440	+	2.06876i	−0.0864235	+	0.149690i	−0.905997	−	0.423284i	$-0.860877\pi$
$191$	−1.19440	+	2.06876i	−0.0864235	+	0.149690i	0.819573	+	0.572974i	$0.194210\pi$
$192$		0			0
$193$	7.28822	+	12.6236i	0.524617	+	0.908664i	0.999589	+	0.0286628i	$0.00912489\pi$
$193$	7.28822	+	12.6236i	0.524617	+	0.908664i	−0.474972	+	0.880001i	$0.657542\pi$
$194$	3.50000	−	6.06218i	0.251285	−	0.435239i
$195$		0			0
$196$	6.98261	−	0.493069i	0.498758	−	0.0352192i
$197$	12.4826			0.889349			0.444675	−	0.895692i	$-0.353319\pi$
$197$	12.4826			0.889349			0.444675	+	0.895692i	$0.353319\pi$
$198$		0			0
$199$	7.09382	+	12.2869i	0.502867	+	0.870992i	0.999995	+	0.00331424i	$0.00105496\pi$
$199$	7.09382	+	12.2869i	0.502867	+	0.870992i	−0.497127	+	0.867678i	$0.665612\pi$
$200$	1.43570	+	2.48671i	0.101520	+	0.175837i
$201$		0			0
$202$	10.7398			0.755650
$203$	7.19440	+	11.5047i	0.504948	+	0.807471i
$204$		0			0
$205$	−7.14562	+	12.3766i	−0.499071	+	0.864417i
$206$	1.48261	+	2.56796i	0.103299	+	0.178918i
$207$		0			0
$208$		0			0
$209$	−6.48261			−0.448412
$210$		0			0
$211$	−20.8336			−1.43425			−0.717123	−	0.696947i	$-0.754541\pi$
$211$	−20.8336			−1.43425			−0.717123	+	0.696947i	$0.754541\pi$
$212$	4.00000	−	6.92820i	0.274721	−	0.475831i
$213$		0			0
$214$	−2.41832	−	4.18865i	−0.165313	−	0.286330i
$215$	−16.0590	+	27.8151i	−1.09522	+	1.89697i
$216$		0			0
$217$	11.1286	−	20.9471i	0.755458	−	1.42198i
$218$	10.1596			0.688096
$219$		0			0
$220$	−1.40280	−	2.42972i	−0.0945769	−	0.163812i
$221$		0			0
$222$		0			0
$223$	12.5764			0.842180			0.421090	−	0.907019i	$-0.361648\pi$
$223$	12.5764			0.842180			0.421090	+	0.907019i	$0.361648\pi$
$224$	1.24131	−	2.33648i	0.0829383	−	0.156113i
$225$		0			0
$226$	−5.48261	+	9.49616i	−0.364698	+	0.631675i
$227$	10.0295	+	17.3716i	0.665683	+	1.15300i	0.979100	+	0.203381i	$0.0651929\pi$
$227$	10.0295	+	17.3716i	0.665683	+	1.15300i	−0.313417	+	0.949616i	$0.601474\pi$
$228$		0			0
$229$	11.2882	−	19.5518i	0.745946	−	1.29202i	−0.203805	−	0.979011i	$-0.565331\pi$
$229$	11.2882	−	19.5518i	0.745946	−	1.29202i	0.949751	−	0.313005i	$-0.101336\pi$
$230$	−14.8366			−0.978299
$231$		0			0
$232$	5.12859			0.336709
$233$	−0.371407	+	0.643296i	−0.0243317	+	0.0421437i	−0.877935	−	0.478780i	$-0.841079\pi$
$233$	−0.371407	+	0.643296i	−0.0243317	+	0.0421437i	0.853603	+	0.520924i	$0.174412\pi$
$234$		0			0
$235$	0.453091	+	0.784776i	0.0295564	+	0.0511931i
$236$	−0.435704	+	0.754661i	−0.0283619	+	0.0491242i
$237$		0			0
$238$	−11.1736	−	17.8680i	−0.724279	−	1.15821i
$239$	−4.31925			−0.279389			−0.139694	−	0.990195i	$-0.544612\pi$
$239$	−4.31925			−0.279389			−0.139694	+	0.990195i	$0.544612\pi$
$240$		0			0
$241$	9.09382	+	15.7510i	0.585784	+	1.01461i	0.994777	+	0.102071i	$0.0325468\pi$
$241$	9.09382	+	15.7510i	0.585784	+	1.01461i	−0.408993	+	0.912538i	$0.634120\pi$
$242$	0.500000	+	0.866025i	0.0321412	+	0.0556702i
$243$		0			0
$244$	2.15962			0.138256
$245$	−10.9932	−	16.2741i	−0.702332	−	1.03972i
$246$		0			0
$247$		0			0
$248$	−4.48261	−	7.76411i	−0.284646	−	0.493022i
$249$		0			0
$250$	−2.98599	+	5.17189i	−0.188851	+	0.327099i
$251$	−28.6703			−1.80965			−0.904825	−	0.425784i	$-0.859999\pi$
$251$	−28.6703			−1.80965			−0.904825	+	0.425784i	$0.859999\pi$
$252$		0			0
$253$	5.28822			0.332467
$254$	−4.64411	+	8.04383i	−0.291397	+	0.504715i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.80560	+	11.7876i	−0.424522	+	0.735293i	−0.996376	−	0.0850621i	$-0.972891\pi$
$257$	−6.80560	+	11.7876i	−0.424522	+	0.735293i	0.571854	+	0.820356i	$0.306224\pi$
$258$		0			0
$259$	27.7172	−	0.977390i	1.72226	−	0.0607321i
$260$		0			0
$261$		0			0
$262$	−6.48261	−	11.2282i	−0.400497	−	0.693681i
$263$	−1.80560	−	3.12740i	−0.111338	−	0.192843i	0.804972	−	0.593313i	$-0.202180\pi$
$263$	−1.80560	−	3.12740i	−0.111338	−	0.192843i	−0.916310	+	0.400470i	$0.868847\pi$
$264$		0			0
$265$	−22.4448			−1.37877
$266$	−8.04691	+	15.1465i	−0.493388	+	0.928693i
$267$		0			0
$268$	3.54691	−	6.14343i	0.216662	−	0.375270i
$269$	−4.69102	−	8.12508i	−0.286016	−	0.495395i	0.686839	−	0.726810i	$-0.258998\pi$
$269$	−4.69102	−	8.12508i	−0.286016	−	0.495395i	−0.972855	+	0.231415i	$0.925665\pi$
$270$		0			0
$271$	−2.80560	+	4.85945i	−0.170428	+	0.295190i	−0.938570	−	0.345090i	$-0.887848\pi$
$271$	−2.80560	+	4.85945i	−0.170428	+	0.295190i	0.768141	+	0.640280i	$0.221182\pi$
$272$	−7.96523			−0.482963
$273$		0			0
$274$	5.61121			0.338985
$275$	−1.43570	+	2.48671i	−0.0865762	+	0.149954i
$276$		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	$0.673726\pi$
$278$	6.56430	−	11.3697i	0.393700	−	0.681909i
$279$		0			0
$280$	−7.41832	+	0.261592i	−0.443329	+	0.0156331i
$281$	−24.1529			−1.44084			−0.720420	−	0.693539i	$-0.756051\pi$
$281$	−24.1529			−1.44084			−0.720420	+	0.693539i	$0.756051\pi$
$282$		0			0
$283$	−3.77083	−	6.53127i	−0.224152	−	0.388244i	0.731912	−	0.681399i	$-0.238628\pi$
$283$	−3.77083	−	6.53127i	−0.224152	−	0.388244i	−0.956065	+	0.293155i	$0.905295\pi$
$284$	−3.72392	−	6.45002i	−0.220974	−	0.382738i
$285$		0			0
$286$		0			0
$287$	−7.14562	−	11.4267i	−0.421792	−	0.674496i
$288$		0			0
$289$	−23.2224	+	40.2224i	−1.36602	+	2.36602i
$290$	−7.19440	−	12.4611i	−0.422470	−	0.731739i
$291$		0			0
$292$	−6.28822	+	10.8915i	−0.367990	+	0.637377i
$293$	−7.90618			−0.461884			−0.230942	−	0.972968i	$-0.574181\pi$
$293$	−7.90618			−0.461884			−0.230942	+	0.972968i	$0.574181\pi$
$294$		0			0
$295$	2.44482			0.142343
$296$	5.24131	−	9.07821i	0.304645	−	0.527660i
$297$		0			0
$298$	−8.36990	−	14.4971i	−0.484855	−	0.839794i
$299$		0			0
$300$		0			0
$301$	−16.0590	−	25.6803i	−0.925628	−	1.48019i
$302$	−10.8994			−0.627191
$303$		0			0
$304$	3.24131	+	5.61411i	0.185902	+	0.321991i
$305$	−3.02952	−	5.24729i	−0.173470	−	0.300459i
$306$		0			0
$307$	12.8957			0.735995			0.367998	−	0.929827i	$-0.380043\pi$
$307$	12.8957			0.735995			0.367998	+	0.929827i	$0.380043\pi$
$308$	2.64411	−	0.0932392i	0.150662	−	0.00531279i
$309$		0			0
$310$	−12.5764	+	21.7830i	−0.714293	+	1.23719i
$311$	5.44971	+	9.43918i	0.309025	+	0.535247i	0.978149	−	0.207904i	$-0.0666641\pi$
$311$	5.44971	+	9.43918i	0.309025	+	0.535247i	−0.669125	+	0.743150i	$0.733331\pi$
$312$		0			0
$313$	4.56430	−	7.90559i	0.257989	−	0.446851i	−0.707714	−	0.706499i	$-0.750273\pi$
$313$	4.56430	−	7.90559i	0.257989	−	0.446851i	0.965703	+	0.259649i	$0.0836067\pi$
$314$	−1.77457			−0.100145
$315$		0			0
$316$	6.80560			0.382845
$317$	−4.75682	+	8.23906i	−0.267170	+	0.462752i	−0.968130	−	0.250449i	$-0.919422\pi$
$317$	−4.75682	+	8.23906i	−0.267170	+	0.462752i	0.700960	+	0.713201i	$0.252755\pi$
$318$		0			0
$319$	2.56430	+	4.44149i	0.143573	+	0.248676i
$320$	−1.40280	+	2.42972i	−0.0784190	+	0.135826i
$321$		0			0
$322$	6.56430	−	12.3558i	0.365814	−	0.688564i
$323$	51.6355			2.87307
$324$		0			0
$325$		0			0
$326$	−2.02952	−	3.51524i	−0.112405	−	0.194691i
$327$		0			0
$328$	−5.09382			−0.281259
$329$	−0.854020	+	0.0301153i	−0.0470837	+	0.00166031i
$330$		0			0
$331$	−0.546909	+	0.947275i	−0.0300609	+	0.0520669i	−0.880664	−	0.473741i	$-0.842903\pi$
$331$	−0.546909	+	0.947275i	−0.0300609	+	0.0520669i	0.850604	+	0.525807i	$0.176237\pi$
$332$	7.54691	+	13.0716i	0.414190	+	0.717399i
$333$		0			0
$334$	−6.93420	+	12.0104i	−0.379422	+	0.657179i
$335$	−19.9024			−1.08739
$336$		0			0
$337$	−25.7988			−1.40535			−0.702676	−	0.711510i	$-0.748012\pi$
$337$	−25.7988			−1.40535			−0.702676	+	0.711510i	$0.748012\pi$
$338$	−6.50000	+	11.2583i	−0.353553	+	0.612372i
$339$		0			0
$340$	11.1736	+	19.3533i	0.605975	+	1.04958i
$341$	4.48261	−	7.76411i	0.242747	−	0.420450i
$342$		0			0
$343$	18.4168	−	1.95478i	0.994414	−	0.105548i
$344$	−11.4478			−0.617226
$345$		0			0
$346$	−8.48261	−	14.6923i	−0.456028	−	0.789864i
$347$	10.3835	+	17.9848i	0.557418	+	0.965476i	0.997711	+	0.0676219i	$0.0215411\pi$
$347$	10.3835	+	17.9848i	0.557418	+	0.965476i	−0.440293	+	0.897854i	$0.645126\pi$
$348$		0			0
$349$	−9.51364			−0.509254			−0.254627	−	0.967039i	$-0.581953\pi$
$349$	−9.51364			−0.509254			−0.254627	+	0.967039i	$0.581953\pi$
$350$	4.02801	+	6.44127i	0.215306	+	0.344300i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−6.28822	−	10.8915i	−0.334688	−	0.579697i	0.648737	−	0.761013i	$-0.275298\pi$
$353$	−6.28822	−	10.8915i	−0.334688	−	0.579697i	−0.983425	+	0.181316i	$0.941964\pi$
$354$		0			0
$355$	−10.4478	+	18.0962i	−0.554514	+	0.960446i
$356$	−1.61121			−0.0853937
$357$		0			0
$358$	−12.6703			−0.669644
$359$	−0.0347742	+	0.0602306i	−0.00183531	+	0.00317885i	−0.866942	−	0.498410i	$-0.833918\pi$
$359$	−0.0347742	+	0.0602306i	−0.00183531	+	0.00317885i	0.865106	+	0.501589i	$0.167251\pi$
$360$		0			0
$361$	−11.5121	−	19.9396i	−0.605902	−	1.04945i
$362$	−1.28822	+	2.23126i	−0.0677071	+	0.117272i
$363$		0			0
$364$		0			0
$365$	35.2845			1.84687
$366$		0			0
$367$	15.7708	+	27.3159i	0.823231	+	1.42588i	0.903264	+	0.429085i	$0.141164\pi$
$367$	15.7708	+	27.3159i	0.823231	+	1.42588i	−0.0800336	+	0.996792i	$0.525503\pi$
$368$	−2.64411	−	4.57973i	−0.137834	−	0.238735i
$369$		0			0
$370$	−29.4100			−1.52896
$371$	9.93045	−	18.6919i	0.515563	−	0.970434i
$372$		0			0
$373$	−7.65624	+	13.2610i	−0.396425	+	0.686629i	−0.993282	−	0.115719i	$-0.963083\pi$
$373$	−7.65624	+	13.2610i	−0.396425	+	0.686629i	0.596857	+	0.802348i	$0.296416\pi$
$374$	−3.98261	−	6.89809i	−0.205936	−	0.356692i
$375$		0			0
$376$	−0.161495	+	0.279717i	−0.00832847	+	0.0144253i
$377$		0			0
$378$		0			0
$379$	16.0590			0.824898			0.412449	−	0.910981i	$-0.364674\pi$
$379$	16.0590			0.824898			0.412449	+	0.910981i	$0.364674\pi$
$380$	9.09382	−	15.7510i	0.466503	−	0.808007i
$381$		0			0
$382$	1.19440	+	2.06876i	0.0611107	+	0.105847i
$383$	−0.369899	+	0.640684i	−0.0189010	+	0.0327374i	−0.875321	−	0.483542i	$-0.839350\pi$
$383$	−0.369899	+	0.640684i	−0.0189010	+	0.0327374i	0.856420	+	0.516279i	$0.172683\pi$
$384$		0			0
$385$	−3.93570	−	6.29365i	−0.200582	−	0.320754i
$386$	14.5764			0.741921
$387$		0			0
$388$	−3.50000	−	6.06218i	−0.177686	−	0.307760i
$389$	1.79160	+	3.10313i	0.0908375	+	0.157335i	0.907864	−	0.419265i	$-0.137712\pi$
$389$	1.79160	+	3.10313i	0.0908375	+	0.157335i	−0.817026	+	0.576600i	$0.804379\pi$
$390$		0			0
$391$	−42.1218			−2.13019
$392$	3.06430	−	6.29365i	0.154770	−	0.317878i
$393$		0			0
$394$	6.24131	−	10.8103i	0.314432	−	0.544613i
$395$	−9.54691	−	16.5357i	−0.480357	−	0.832003i
$396$		0			0
$397$	12.5643	−	21.7620i	0.630584	−	1.09220i	−0.356849	−	0.934162i	$-0.616149\pi$
$397$	12.5643	−	21.7620i	0.630584	−	1.09220i	0.987433	−	0.158041i	$-0.0505179\pi$
$398$	14.1876			0.711162
$399$		0			0
$400$	2.87141			0.143570
$401$	−1.93420	+	3.35013i	−0.0965891	+	0.167297i	−0.910271	−	0.414014i	$-0.864127\pi$
$401$	−1.93420	+	3.35013i	−0.0965891	+	0.167297i	0.813682	+	0.581311i	$0.197460\pi$
$402$		0			0
$403$		0			0
$404$	5.36990	−	9.30094i	0.267162	−	0.462739i
$405$		0			0
$406$	13.5606	−	0.478186i	0.672999	−	0.0237320i
$407$	10.4826			0.519604
$408$		0			0
$409$	−2.32299	−	4.02354i	−0.114864	−	0.198951i	0.802861	−	0.596166i	$-0.203310\pi$
$409$	−2.32299	−	4.02354i	−0.114864	−	0.198951i	−0.917726	+	0.397215i	$0.869977\pi$
$410$	7.14562	+	12.3766i	0.352897	+	0.611235i
$411$		0			0
$412$	2.96523			0.146086
$413$	−1.08168	+	2.03603i	−0.0532262	+	0.100186i
$414$		0			0
$415$	21.1736	−	36.6738i	1.03937	−	1.80025i
$416$		0			0
$417$		0			0
$418$	−3.24131	+	5.61411i	−0.158537	+	0.274595i
$419$	19.5174			0.953487			0.476743	−	0.879043i	$-0.341817\pi$
$419$	19.5174			0.953487			0.476743	+	0.879043i	$0.341817\pi$
$420$		0			0
$421$	15.5174			0.756271			0.378136	−	0.925750i	$-0.376565\pi$
$421$	15.5174			0.756271			0.378136	+	0.925750i	$0.376565\pi$
$422$	−10.4168	+	18.0424i	−0.507082	+	0.878292i
$423$		0			0
$424$	−4.00000	−	6.92820i	−0.194257	−	0.336463i
$425$	11.4357	−	19.8072i	0.554713	−	0.960791i
$426$		0			0
$427$	5.71028	−	0.201361i	0.276340	−	0.00974456i
$428$	−4.83663			−0.233787
$429$		0			0
$430$	16.0590	+	27.8151i	0.774436	+	1.34136i
$431$	−7.19440	−	12.4611i	−0.346542	−	0.600228i	0.639091	−	0.769131i	$-0.279311\pi$
$431$	−7.19440	−	12.4611i	−0.346542	−	0.600228i	−0.985633	+	0.168903i	$0.945977\pi$
$432$		0			0
$433$	2.03477			0.0977850			0.0488925	−	0.998804i	$-0.484431\pi$
$433$	2.03477			0.0977850			0.0488925	+	0.998804i	$0.484431\pi$
$434$	−12.5764	−	20.1112i	−0.603688	−	0.965368i
$435$		0			0
$436$	5.07981	−	8.79849i	0.243279	−	0.421371i
$437$	17.1407	+	29.6886i	0.819952	+	1.42020i
$438$		0			0
$439$	−1.61308	+	2.79393i	−0.0769880	+	0.133347i	−0.901949	−	0.431842i	$-0.857864\pi$
$439$	−1.61308	+	2.79393i	−0.0769880	+	0.133347i	0.824961	+	0.565190i	$0.191197\pi$
$440$	−2.80560			−0.133752
$441$		0			0
$442$		0			0
$443$	−11.0469	+	19.1338i	−0.524854	+	0.909075i	0.474727	+	0.880133i	$0.342547\pi$
$443$	−11.0469	+	19.1338i	−0.524854	+	0.909075i	−0.999581	+	0.0289413i	$0.990786\pi$
$444$		0			0
$445$	2.26020	+	3.91478i	0.107144	+	0.185579i
$446$	6.28822	−	10.8915i	0.297756	−	0.515728i
$447$		0			0
$448$	−1.40280	−	2.24325i	−0.0662761	−	0.105983i
$449$	−22.2497			−1.05003			−0.525014	−	0.851094i	$-0.675940\pi$
$449$	−22.2497			−1.05003			−0.525014	+	0.851094i	$0.675940\pi$
$450$		0			0
$451$	−2.54691	−	4.41138i	−0.119929	−	0.207724i
$452$	5.48261	+	9.49616i	0.257880	+	0.446662i
$453$		0			0
$454$	20.0590			0.941418
$455$		0			0
$456$		0			0
$457$	9.31925	−	16.1414i	0.435936	−	0.755063i	−0.561436	−	0.827520i	$-0.689751\pi$
$457$	9.31925	−	16.1414i	0.435936	−	0.755063i	0.997372	+	0.0724572i	$0.0230841\pi$
$458$	−11.2882	−	19.5518i	−0.527464	−	0.913594i
$459$		0			0
$460$	−7.41832	+	12.8489i	−0.345881	+	0.599083i
$461$	20.9895			0.977578			0.488789	−	0.872402i	$-0.337439\pi$
$461$	20.9895			0.977578			0.488789	+	0.872402i	$0.337439\pi$
$462$		0			0
$463$	−5.35402			−0.248822			−0.124411	−	0.992231i	$-0.539704\pi$
$463$	−5.35402			−0.248822			−0.124411	+	0.992231i	$0.539704\pi$
$464$	2.56430	−	4.44149i	0.119044	−	0.206191i
$465$		0			0
$466$	0.371407	+	0.643296i	0.0172051	+	0.0298001i
$467$	13.0121	−	22.5377i	0.602130	−	1.04292i	−0.390368	−	0.920659i	$-0.627652\pi$
$467$	13.0121	−	22.5377i	0.602130	−	1.04292i	0.992498	−	0.122261i	$-0.0390144\pi$
$468$		0			0
$469$	8.80560	−	16.5746i	0.406605	−	0.765344i
$470$	0.906181			0.0417990
$471$		0			0
$472$	0.435704	+	0.754661i	0.0200549	+	0.0347361i
$473$	−5.72392	−	9.91412i	−0.263186	−	0.455852i
$474$		0			0
$475$	−18.6142			−0.854079
$476$	−21.0609	+	0.742671i	−0.965326	+	0.0340403i
$477$		0			0
$478$	−2.15962	+	3.74058i	−0.0987789	+	0.171090i
$479$	−1.80560	−	3.12740i	−0.0825001	−	0.142894i	0.821823	−	0.569743i	$-0.192957\pi$
$479$	−1.80560	−	3.12740i	−0.0825001	−	0.142894i	−0.904323	+	0.426848i	$0.859624\pi$
$480$		0			0
$481$		0			0
$482$	18.1876			0.828424
$483$		0			0
$484$	1.00000			0.0454545
$485$	−9.81961	+	17.0081i	−0.445886	+	0.772296i
$486$		0			0
$487$	4.03103	+	6.98195i	0.182663	+	0.316382i	0.942787	−	0.333397i	$-0.108195\pi$
$487$	4.03103	+	6.98195i	0.182663	+	0.316382i	−0.760123	+	0.649779i	$0.774861\pi$
$488$	1.07981	−	1.87029i	0.0488808	−	0.0846640i
$489$		0			0
$490$	−19.5904	+	1.38336i	−0.885006	+	0.0624936i
$491$	−20.9062			−0.943483			−0.471741	−	0.881737i	$-0.656374\pi$
$491$	−20.9062			−0.943483			−0.471741	+	0.881737i	$0.656374\pi$
$492$		0			0
$493$	−20.4252	−	35.3775i	−0.919905	−	1.59332i
$494$		0			0
$495$		0			0
$496$	−8.96523			−0.402551
$497$	−10.4478	−	16.7073i	−0.468650	−	0.749426i
$498$		0			0
$499$	−2.48261	+	4.30001i	−0.111137	+	0.192495i	−0.916229	−	0.400655i	$-0.868783\pi$
$499$	−2.48261	+	4.30001i	−0.111137	+	0.192495i	0.805092	+	0.593150i	$0.202116\pi$
$500$	2.98599	+	5.17189i	0.133538	+	0.231294i
$501$		0			0
$502$	−14.3351	+	24.8292i	−0.639808	+	1.10818i
$503$	17.7988			0.793611			0.396806	−	0.917903i	$-0.370119\pi$
$503$	17.7988			0.793611			0.396806	+	0.917903i	$0.370119\pi$
$504$		0			0
$505$	−30.1316			−1.34084
$506$	2.64411	−	4.57973i	0.117545	−	0.203594i
$507$		0			0
$508$	4.64411	+	8.04383i	0.206049	+	0.356887i
$509$	2.25719	−	3.90956i	0.100048	−	0.173288i	−0.811656	−	0.584135i	$-0.801434\pi$
$509$	2.25719	−	3.90956i	0.100048	−	0.173288i	0.911704	+	0.410847i	$0.134767\pi$
$510$		0			0
$511$	−15.6112	+	29.3846i	−0.690599	+	1.29990i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	6.80560	+	11.7876i	0.300182	+	0.519931i
$515$	−4.15962	−	7.20468i	−0.183295	−	0.317476i
$516$		0			0
$517$	−0.322990			−0.0142051
$518$	13.0121	−	24.4925i	0.571720	−	1.07614i
$519$		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
$523$	−3.45158	+	5.97832i	−0.150927	+	0.261414i	−0.931569	−	0.363566i	$-0.881559\pi$
$523$	−3.45158	+	5.97832i	−0.150927	+	0.261414i	0.780641	+	0.624979i	$0.214893\pi$
$524$	−12.9652			−0.566389
$525$		0			0
$526$	−3.61121			−0.157456
$527$	−35.7050	+	61.8429i	−1.55534	+	2.69392i
$528$		0			0
$529$	−2.48261	−	4.30001i	−0.107940	−	0.186957i
$530$	−11.2224	+	19.4378i	−0.487470	+	0.844323i
$531$		0			0
$532$	9.09382	+	14.5421i	0.394267	+	0.630480i
$533$		0			0
$534$		0			0
$535$	6.78484	+	11.7517i	0.293334	+	0.508069i
$536$	−3.54691	−	6.14343i	−0.153203	−	0.265356i
$537$		0			0
$538$	−9.38203			−0.404488
$539$	6.98261	−	0.493069i	0.300762	−	0.0212380i
$540$		0			0
$541$	−1.40280	+	2.42972i	−0.0603111	+	0.104462i	−0.894604	−	0.446859i	$-0.852543\pi$
$541$	−1.40280	+	2.42972i	−0.0603111	+	0.104462i	0.834293	+	0.551321i	$0.185876\pi$
$542$	2.80560	+	4.85945i	0.120511	+	0.208731i
$543$		0			0
$544$	−3.98261	+	6.89809i	−0.170753	+	0.295753i
$545$	−28.5039			−1.22097
$546$		0			0
$547$	32.9274			1.40788			0.703938	−	0.710262i	$-0.251423\pi$
$547$	32.9274			1.40788			0.703938	+	0.710262i	$0.251423\pi$
$548$	2.80560	−	4.85945i	0.119849	−	0.207585i
$549$		0			0
$550$	1.43570	+	2.48671i	0.0612186	+	0.106034i
$551$	−16.6233	+	28.7925i	−0.708178	+	1.22660i
$552$		0			0
$553$	17.9947	−	0.634549i	0.765215	−	0.0269838i
$554$	16.0000			0.679775
$555$		0			0
$556$	−6.56430	−	11.3697i	−0.278388	−	0.482182i
$557$	11.8525	+	20.5292i	0.502207	+	0.869848i	0.999997	+	0.00255037i	$0.000811808\pi$
$557$	11.8525	+	20.5292i	0.502207	+	0.869848i	−0.497790	+	0.867298i	$0.665855\pi$
$558$		0			0
$559$		0			0
$560$	−3.48261	+	6.55525i	−0.147167	+	0.277010i
$561$		0			0
$562$	−12.0764	+	20.9170i	−0.509414	+	0.882330i
$563$	15.2224	+	26.3660i	0.641548	+	1.11119i	0.985087	+	0.172056i	$0.0550409\pi$
$563$	15.2224	+	26.3660i	0.641548	+	1.11119i	−0.343539	+	0.939138i	$0.611626\pi$
$564$		0			0
$565$	15.3820	−	26.6425i	0.647127	−	1.12086i
$566$	−7.54166			−0.317000
$567$		0			0
$568$	−7.44784			−0.312504
$569$	11.1407	−	19.2963i	0.467044	−	0.808943i	−0.532248	−	0.846589i	$-0.678652\pi$
$569$	11.1407	−	19.2963i	0.467044	−	0.808943i	0.999291	+	0.0376455i	$0.0119858\pi$
$570$		0			0
$571$	1.43570	+	2.48671i	0.0600823	+	0.104066i	0.894502	−	0.447064i	$-0.147530\pi$
$571$	1.43570	+	2.48671i	0.0600823	+	0.104066i	−0.834420	+	0.551130i	$0.814197\pi$
$572$		0			0
$573$		0			0
$574$	−13.4686	+	0.474943i	−0.562169	+	0.0198238i
$575$	15.1846			0.633242
$576$		0			0
$577$	7.51214	+	13.0114i	0.312734	+	0.541672i	0.978953	−	0.204084i	$-0.0654217\pi$
$577$	7.51214	+	13.0114i	0.312734	+	0.541672i	−0.666219	+	0.745756i	$0.732088\pi$
$578$	23.2224	+	40.2224i	0.965925	+	1.67303i
$579$		0			0
$580$	−14.3888			−0.597462
$581$	21.1736	+	33.8591i	0.878430	+	1.40471i
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	6.28822	+	10.8915i	0.260208	+	0.450694i
$585$		0			0
$586$	−3.95309	+	6.84695i	−0.163301	+	0.282845i
$587$	42.5069			1.75445			0.877223	−	0.480082i	$-0.159393\pi$
$587$	42.5069			1.75445			0.877223	+	0.480082i	$0.159393\pi$
$588$		0			0
$589$	58.1181			2.39471
$590$	1.22241	−	2.11728i	0.0503259	−	0.0871670i
$591$		0			0
$592$	−5.24131	−	9.07821i	−0.215416	−	0.373112i
$593$	7.69289	−	13.3245i	0.315909	−	0.547171i	−0.663721	−	0.747980i	$-0.731024\pi$
$593$	7.69289	−	13.3245i	0.315909	−	0.547171i	0.979630	+	0.200809i	$0.0643572\pi$
$594$		0			0
$595$	31.3488	+	50.1304i	1.28517	+	2.05515i
$596$	−16.7398			−0.685689
$597$		0			0
$598$		0			0
$599$	−19.8196	−	34.3286i	−0.809807	−	1.40263i	−0.912997	−	0.407966i	$-0.866238\pi$
$599$	−19.8196	−	34.3286i	−0.809807	−	1.40263i	0.103190	−	0.994662i	$-0.467095\pi$
$600$		0			0
$601$	33.3405			1.35999			0.679994	−	0.733218i	$-0.261983\pi$
$601$	33.3405			1.35999			0.679994	+	0.733218i	$0.261983\pi$
$602$	−30.2693	+	1.06739i	−1.23369	+	0.0435034i
$603$		0			0
$604$	−5.44971	+	9.43918i	−0.221746	+	0.384075i
$605$	−1.40280	−	2.42972i	−0.0570320	−	0.0987823i
$606$		0			0
$607$	−7.97923	+	13.8204i	−0.323867	+	0.560954i	−0.981282	−	0.192574i	$-0.938316\pi$
$607$	−7.97923	+	13.8204i	−0.323867	+	0.560954i	0.657415	+	0.753528i	$0.271650\pi$
$608$	6.48261			0.262905
$609$		0			0
$610$	−6.05904			−0.245324
$611$		0			0
$612$		0			0
$613$	−23.3333	−	40.4144i	−0.942421	−	1.63232i	−0.760834	−	0.648947i	$-0.775210\pi$
$613$	−23.3333	−	40.4144i	−0.942421	−	1.63232i	−0.181587	−	0.983375i	$-0.558123\pi$
$614$	6.44784	−	11.1680i	0.260214	−	0.450703i
$615$		0			0
$616$	1.24131	−	2.33648i	0.0500137	−	0.0941396i
$617$	9.28447			0.373779			0.186889	−	0.982381i	$-0.440159\pi$
$617$	9.28447			0.373779			0.186889	+	0.982381i	$0.440159\pi$
$618$		0			0
$619$	−16.9947	−	29.4358i	−0.683077	−	1.18312i	−0.974037	−	0.226388i	$-0.927308\pi$
$619$	−16.9947	−	29.4358i	−0.683077	−	1.18312i	0.290961	−	0.956735i	$-0.406025\pi$
$620$	12.5764	+	21.7830i	0.505082	+	0.874827i
$621$		0			0
$622$	10.8994			0.437027
$623$	−4.26020	+	0.150227i	−0.170681	+	0.00601874i
$624$		0			0
$625$	15.5560	−	26.9438i	0.622241	−	1.07775i
$626$	−4.56430	−	7.90559i	−0.182426	−	0.315971i
$627$		0			0
$628$	−0.887286	+	1.53682i	−0.0354066	+	0.0613260i
$629$	−83.4964			−3.32922
$630$		0			0
$631$	−14.6460			−0.583047			−0.291524	−	0.956564i	$-0.594162\pi$
$631$	−14.6460			−0.583047			−0.291524	+	0.956564i	$0.594162\pi$
$632$	3.40280	−	5.89382i	0.135356	−	0.234444i
$633$		0			0
$634$	4.75682	+	8.23906i	0.188918	+	0.327215i
$635$	13.0295	−	22.5678i	0.517061	−	0.895576i
$636$		0			0
$637$		0			0
$638$	5.12859			0.203043
$639$		0			0
$640$	1.40280	+	2.42972i	0.0554506	+	0.0960432i
$641$	10.4826	+	18.1564i	0.414038	+	0.717135i	0.995327	−	0.0965620i	$-0.0307846\pi$
$641$	10.4826	+	18.1564i	0.414038	+	0.717135i	−0.581289	+	0.813697i	$0.697451\pi$
$642$		0			0
$643$	−23.6733			−0.933582			−0.466791	−	0.884368i	$-0.654590\pi$
$643$	−23.6733			−0.933582			−0.466791	+	0.884368i	$0.654590\pi$
$644$	−7.41832	−	11.8628i	−0.292323	−	0.467458i
$645$		0			0
$646$	25.8177	−	44.7176i	1.01579	−	1.75939i
$647$	−6.20840	−	10.7533i	−0.244078	−	0.422755i	0.717794	−	0.696255i	$-0.245152\pi$
$647$	−6.20840	−	10.7533i	−0.244078	−	0.422755i	−0.961872	+	0.273500i	$0.911818\pi$
$648$		0			0
$649$	−0.435704	+	0.754661i	−0.0171029	+	0.0296230i
$650$		0			0
$651$		0			0
$652$	−4.05904			−0.158964
$653$	−0.0487812	+	0.0844916i	−0.00190896	+	0.00330641i	−0.866978	−	0.498346i	$-0.833941\pi$
$653$	−0.0487812	+	0.0844916i	−0.00190896	+	0.00330641i	0.865069	+	0.501652i	$0.167274\pi$
$654$		0			0
$655$	18.1876	+	31.5019i	0.710650	+	1.23088i
$656$	−2.54691	+	4.41138i	−0.0994401	+	0.172235i
$657$		0			0
$658$	−0.400929	+	0.754661i	−0.0156299	+	0.0294197i
$659$	35.0243			1.36435			0.682176	−	0.731188i	$-0.261034\pi$
$659$	35.0243			1.36435			0.682176	+	0.731188i	$0.261034\pi$
$660$		0			0
$661$	−14.8177	−	25.6651i	−0.576343	−	0.998256i	−0.995894	−	0.0905240i	$-0.971146\pi$
$661$	−14.8177	−	25.6651i	−0.576343	−	0.998256i	0.419551	−	0.907732i	$-0.362188\pi$
$662$	0.546909	+	0.947275i	0.0212562	+	0.0368169i
$663$		0			0
$664$	15.0938			0.585754
$665$	22.5764	−	42.4951i	0.875476	−	1.64789i
$666$		0			0
$667$	13.5606	−	23.4876i	0.525067	−	0.909442i
$668$	6.93420	+	12.0104i	0.268292	+	0.464696i
$669$		0			0
$670$	−9.95122	+	17.2360i	−0.384449	+	0.665885i
$671$	2.15962			0.0833713
$672$		0			0
$673$	16.8957			0.651281			0.325640	−	0.945494i	$-0.394420\pi$
$673$	16.8957			0.651281			0.325640	+	0.945494i	$0.394420\pi$
$674$	−12.8994	+	22.3425i	−0.496867	+	0.860599i
$675$		0			0
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	6.59533	−	11.4234i	0.253479	−	0.439038i	−0.711002	−	0.703190i	$-0.751758\pi$
$677$	6.59533	−	11.4234i	0.253479	−	0.439038i	0.964481	+	0.264151i	$0.0850918\pi$
$678$		0			0
$679$	−9.81961	−	15.7027i	−0.376842	−	0.602615i
$680$	22.3473			0.856978
$681$		0			0
$682$	−4.48261	−	7.76411i	−0.171648	−	0.297303i
$683$	4.91832	+	8.51877i	0.188194	+	0.325962i	0.944648	−	0.328085i	$-0.106403\pi$
$683$	4.91832	+	8.51877i	0.188194	+	0.325962i	−0.756454	+	0.654047i	$0.773070\pi$
$684$		0			0
$685$	−15.7428			−0.601502
$686$	7.51552	−	16.9268i	0.286944	−	0.646269i
$687$		0			0
$688$	−5.72392	+	9.91412i	−0.218222	+	0.377972i
$689$		0			0
$690$		0			0
$691$	24.9947	−	43.2922i	0.950845	−	1.64691i	0.207243	−	0.978290i	$-0.433551\pi$
$691$	24.9947	−	43.2922i	0.950845	−	1.64691i	0.743602	−	0.668622i	$-0.233116\pi$
$692$	−16.9652			−0.644921
$693$		0			0
$694$	20.7671			0.788308
$695$	−18.4168	+	31.8988i	−0.698589	+	1.20999i
$696$		0			0
$697$	20.2867	+	35.1376i	0.768414	+	1.33093i
$698$	−4.75682	+	8.23906i	−0.180048	+	0.311853i
$699$		0			0
$700$	7.59231	−	0.267728i	0.286962	−	0.0101192i
$701$	17.7050			0.668710			0.334355	−	0.942447i	$-0.391482\pi$
$701$	17.7050			0.668710			0.334355	+	0.942447i	$0.391482\pi$
$702$		0			0
$703$	33.9774	+	58.8505i	1.28148	+	2.21959i
$704$	−0.500000	−	0.866025i	−0.0188445	−	0.0326396i
$705$		0			0
$706$	−12.5764			−0.473320
$707$	13.3314	−	25.0934i	0.501378	−	0.943733i
$708$		0			0
$709$	15.9774	−	27.6736i	0.600042	−	1.03930i	−0.392772	−	0.919636i	$-0.628484\pi$
$709$	15.9774	−	27.6736i	0.600042	−	1.03930i	0.992814	−	0.119668i	$-0.0381830\pi$
$710$	10.4478	+	18.0962i	0.392100	+	0.679138i
$711$		0			0
$712$	−0.805603	+	1.39535i	−0.0301912	+	0.0522928i
$713$	−47.4100			−1.77552
$714$		0			0
$715$		0			0
$716$	−6.33513	+	10.9728i	−0.236755	+	0.410071i
$717$		0			0
$718$	0.0347742	+	0.0602306i	0.00129776	+	0.00224779i
$719$	10.8975	−	18.8751i	0.406410	−	0.703923i	−0.588074	−	0.808807i	$-0.700114\pi$
$719$	10.8975	−	18.8751i	0.406410	−	0.703923i	0.994484	+	0.104884i	$0.0334471\pi$
$720$		0			0
$721$	7.84038	−	0.276475i	0.291991	−	0.0102965i
$722$	−23.0243			−0.856875
$723$		0			0
$724$	1.28822	+	2.23126i	0.0478762	+	0.0829239i
$725$	7.36314	+	12.7533i	0.273460	+	0.473647i
$726$		0			0
$727$	−4.84714			−0.179770			−0.0898852	−	0.995952i	$-0.528650\pi$
$727$	−4.84714			−0.179770			−0.0898852	+	0.995952i	$0.528650\pi$
$728$		0			0
$729$		0			0
$730$	17.6422	−	30.5572i	0.652968	−	1.13097i
$731$	45.5923	+	78.9682i	1.68629	+	2.92074i
$732$		0			0
$733$	−6.11459	+	10.5908i	−0.225847	+	0.391179i	−0.956573	−	0.291492i	$-0.905848\pi$
$733$	−6.11459	+	10.5908i	−0.225847	+	0.391179i	0.730726	+	0.682671i	$0.239182\pi$
$734$	31.5417			1.16422
$735$		0			0
$736$	−5.28822			−0.194926
$737$	3.54691	−	6.14343i	0.130652	−	0.226296i
$738$		0			0
$739$	0.517387	+	0.896141i	0.0190324	+	0.0329651i	0.875385	−	0.483427i	$-0.160608\pi$
$739$	0.517387	+	0.896141i	0.0190324	+	0.0329651i	−0.856352	+	0.516392i	$0.827275\pi$
$740$	−14.7050	+	25.4698i	−0.540567	+	0.936290i
$741$		0			0
$742$	−11.2224	−	17.9460i	−0.411988	−	0.658817i
$743$	23.9925			0.880200			0.440100	−	0.897949i	$-0.354943\pi$
$743$	23.9925			0.880200			0.440100	+	0.897949i	$0.354943\pi$
$744$		0			0
$745$	23.4826	+	40.6731i	0.860336	+	1.49015i
$746$	7.65624	+	13.2610i	0.280315	+	0.485520i
$747$		0			0
$748$	−7.96523			−0.291238
$749$	−12.7886	+	0.450964i	−0.467285	+	0.0164779i
$750$		0			0
$751$	−10.2534	+	17.7595i	−0.374153	+	0.648053i	−0.990200	−	0.139657i	$-0.955400\pi$
$751$	−10.2534	+	17.7595i	−0.374153	+	0.648053i	0.616047	+	0.787710i	$0.288733\pi$
$752$	0.161495	+	0.279717i	0.00588912	+	0.0102002i
$753$		0			0
$754$		0			0
$755$	30.5794			1.11290
$756$		0			0
$757$	−16.8019			−0.610674			−0.305337	−	0.952244i	$-0.598769\pi$
$757$	−16.8019			−0.610674			−0.305337	+	0.952244i	$0.598769\pi$
$758$	8.02952	−	13.9075i	0.291645	−	0.505145i
$759$		0			0
$760$	−9.09382	−	15.7510i	−0.329867	−	0.571347i
$761$	−7.25495	+	12.5659i	−0.262992	+	0.455515i	−0.967036	−	0.254642i	$-0.918043\pi$
$761$	−7.25495	+	12.5659i	−0.262992	+	0.455515i	0.704044	+	0.710157i	$0.251376\pi$
$762$		0			0
$763$	12.6112	−	23.7378i	0.456556	−	0.859366i
$764$	2.38879			0.0864235
$765$		0			0
$766$	0.369899	+	0.640684i	0.0133650	+	0.0231489i
$767$		0			0
$768$		0			0
$769$	3.35402			0.120949			0.0604745	−	0.998170i	$-0.480739\pi$
$769$	3.35402			0.120949			0.0604745	+	0.998170i	$0.480739\pi$
$770$	−7.41832	+	0.261592i	−0.267338	+	0.00942712i
$771$		0			0
$772$	7.28822	−	12.6236i	0.262309	−	0.454332i
$773$	0.920188	+	1.59381i	0.0330969	+	0.0573255i	0.882099	−	0.471063i	$-0.156130\pi$
$773$	0.920188	+	1.59381i	0.0330969	+	0.0573255i	−0.849003	+	0.528389i	$0.822796\pi$
$774$		0			0
$775$	12.8714	−	22.2939i	0.462355	−	0.800822i
$776$	−7.00000			−0.251285
$777$		0			0
$778$	3.58319			0.128464
$779$	16.5106	−	28.5972i	0.591555	−	1.02460i
$780$		0			0
$781$	−3.72392	−	6.45002i	−0.133252	−	0.230800i
$782$	−21.0609	+	36.4786i	−0.753137	+	1.30447i
$783$		0			0
$784$	−3.91832	−	5.80059i	−0.139940	−	0.207164i
$785$	4.97875			0.177699
$786$		0			0
$787$	−5.79347	−	10.0346i	−0.206515	−	0.357694i	0.744099	−	0.668069i	$-0.232879\pi$
$787$	−5.79347	−	10.0346i	−0.206515	−	0.357694i	−0.950614	+	0.310375i	$0.899545\pi$
$788$	−6.24131	−	10.8103i	−0.222337	−	0.385100i
$789$		0			0
$790$	−19.0938			−0.679328
$791$	15.3820	+	24.5977i	0.546922	+	0.874593i
$792$		0			0
$793$		0			0
$794$	−12.5643	−	21.7620i	−0.445890	−	0.772304i
$795$		0			0
$796$	7.09382	−	12.2869i	0.251434	−	0.435496i
$797$	48.4653			1.71673			0.858365	−	0.513039i	$-0.171480\pi$
$797$	48.4653			1.71673			0.858365	+	0.513039i	$0.171480\pi$
$798$		0			0
$799$	2.57269			0.0910151
$800$	1.43570	−	2.48671i	0.0507598	−	0.0879185i
$801$		0			0
$802$	1.93420	+	3.35013i	0.0682988	+	0.118297i
$803$	−6.28822	+	10.8915i	−0.221906	+	0.384353i
$804$		0			0
$805$	−18.4168	+	34.6656i	−0.649107	+	1.22180i
$806$		0			0
$807$		0			0
$808$	−5.36990	−	9.30094i	−0.188912	−	0.327206i
$809$	−1.38354	−	2.39637i	−0.0486428	−	0.0842517i	0.840679	−	0.541534i	$-0.182156\pi$
$809$	−1.38354	−	2.39637i	−0.0486428	−	0.0842517i	−0.889322	+	0.457282i	$0.848823\pi$
$810$		0			0
$811$	4.89568			0.171910			0.0859552	−	0.996299i	$-0.472606\pi$
$811$	4.89568			0.171910			0.0859552	+	0.996299i	$0.472606\pi$
$812$	6.36616	−	11.9829i	0.223408	−	0.420517i
$813$		0			0
$814$	5.24131	−	9.07821i	0.183708	−	0.318191i
$815$	5.69403	+	9.86235i	0.199453	+	0.345463i
$816$		0			0
$817$	37.1060	−	64.2694i	1.29817	−	2.24850i
$818$	−4.64598			−0.162443
$819$		0			0
$820$	14.2912			0.499071
$821$	1.77457	−	3.07365i	0.0619330	−	0.107271i	−0.833396	−	0.552676i	$-0.813607\pi$
$821$	1.77457	−	3.07365i	0.0619330	−	0.107271i	0.895329	+	0.445405i	$0.146940\pi$
$822$		0			0
$823$	−16.2534	−	28.1518i	−0.566559	−	0.981310i	−0.996903	−	0.0786443i	$-0.974941\pi$
$823$	−16.2534	−	28.1518i	−0.566559	−	0.981310i	0.430343	−	0.902665i	$-0.358392\pi$
$824$	1.48261	−	2.56796i	0.0516493	−	0.0894592i
$825$		0			0
$826$	1.22241	+	1.95478i	0.0425331	+	0.0680155i
$827$	−19.5447			−0.679635			−0.339817	−	0.940491i	$-0.610365\pi$
$827$	−19.5447			−0.679635			−0.339817	+	0.940491i	$0.610365\pi$
$828$		0			0
$829$	−12.5953	−	21.8157i	−0.437454	−	0.757692i	0.560039	−	0.828467i	$-0.310786\pi$
$829$	−12.5953	−	21.8157i	−0.437454	−	0.757692i	−0.997492	+	0.0707744i	$0.977453\pi$
$830$	−21.1736	−	36.6738i	−0.734947	−	1.27297i
$831$		0			0
$832$		0			0
$833$	−55.6181	+	3.92740i	−1.92705	+	0.136076i
$834$		0			0
$835$	19.4546	−	33.6964i	0.673254	−	1.16611i
$836$	3.24131	+	5.61411i	0.112103	+	0.194168i
$837$		0			0
$838$	9.75869	−	16.9026i	0.337108	−	0.583889i
$839$	50.4033			1.74011			0.870057	−	0.492950i	$-0.164082\pi$
$839$	50.4033			1.74011			0.870057	+	0.492950i	$0.164082\pi$
$840$		0			0
$841$	−2.69754			−0.0930185
$842$	7.75869	−	13.4385i	0.267382	−	0.463120i
$843$		0			0
$844$	10.4168	+	18.0424i	0.358561	+	0.621046i
$845$	18.2364	−	31.5864i	0.627352	−	1.08661i
$846$		0			0
$847$	2.64411	−	0.0932392i	0.0908526	−	0.00320374i
$848$	−8.00000			−0.274721
$849$		0			0
$850$	−11.4357	−	19.8072i	−0.392241	−	0.679382i
$851$	−27.7172	−	48.0075i	−0.950132	−	1.64568i
$852$		0			0
$853$	−16.8752			−0.577794			−0.288897	−	0.957360i	$-0.593289\pi$
$853$	−16.8752			−0.577794			−0.288897	+	0.957360i	$0.593289\pi$
$854$	2.68075	−	5.04592i	0.0917335	−	0.172668i
$855$		0			0
$856$	−2.41832	+	4.18865i	−0.0826564	+	0.143165i
$857$	21.6529	+	37.5039i	0.739648	+	1.28111i	0.952654	+	0.304057i	$0.0983412\pi$
$857$	21.6529	+	37.5039i	0.739648	+	1.28111i	−0.213006	+	0.977051i	$0.568325\pi$
$858$		0			0
$859$	−1.80711	+	3.13001i	−0.0616578	+	0.106794i	−0.895207	−	0.445651i	$-0.852972\pi$
$859$	−1.80711	+	3.13001i	−0.0616578	+	0.106794i	0.833549	+	0.552446i	$0.186305\pi$
$860$	32.1181			1.09522
$861$		0			0
$862$	−14.3888			−0.490084
$863$	2.20840	−	3.82507i	0.0751750	−	0.130207i	−0.825987	−	0.563689i	$-0.809382\pi$
$863$	2.20840	−	3.82507i	0.0751750	−	0.130207i	0.901162	+	0.433482i	$0.142715\pi$
$864$		0			0
$865$	23.7988	+	41.2208i	0.809185	+	1.40155i
$866$	1.01739	−	1.76217i	0.0345722	−	0.0598808i
$867$		0			0
$868$	−23.7050	+	0.835910i	−0.804601	+	0.0283726i
$869$	6.80560			0.230864
$870$		0			0
$871$		0			0
$872$	−5.07981	−	8.79849i	−0.172024	−	0.297955i
$873$		0			0
$874$	34.2815			1.15959
$875$	8.37751	+	13.3966i	0.283212	+	0.452889i
$876$		0			0
$877$	−22.1389	+	38.3456i	−0.747576	+	1.29484i	0.201405	+	0.979508i	$0.435449\pi$
$877$	−22.1389	+	38.3456i	−0.747576	+	1.29484i	−0.948982	+	0.315332i	$0.897884\pi$
$878$	1.61308	+	2.79393i	0.0544387	+	0.0942907i
$879$		0			0
$880$	−1.40280	+	2.42972i	−0.0472884	+	0.0819060i
$881$	18.1876			0.612757			0.306379	−	0.951910i	$-0.400883\pi$
$881$	18.1876			0.612757			0.306379	+	0.951910i	$0.400883\pi$
$882$		0			0
$883$	−4.57945			−0.154111			−0.0770553	−	0.997027i	$-0.524552\pi$
$883$	−4.57945			−0.154111			−0.0770553	+	0.997027i	$0.524552\pi$
$884$		0			0
$885$		0			0
$886$	11.0469	+	19.1338i	0.371128	+	0.642813i
$887$	−0.288216	+	0.499204i	−0.00967734	+	0.0167616i	−0.870824	−	0.491596i	$-0.836414\pi$
$887$	−0.288216	+	0.499204i	−0.00967734	+	0.0167616i	0.861146	+	0.508357i	$0.169747\pi$
$888$		0			0
$889$	13.0295	+	20.8357i	0.436996	+	0.698808i
$890$	4.52040			0.151524
$891$		0			0
$892$	−6.28822	−	10.8915i	−0.210545	−	0.364675i
$893$	−1.04691	−	1.81330i	−0.0350335	−	0.0606798i
$894$		0			0
$895$	35.5477			1.18823
$896$	−2.64411	+	0.0932392i	−0.0883334	+	0.00311490i
$897$		0			0
$898$	−11.1248	+	19.2688i	−0.371241	+	0.643008i
$899$	−22.9895	−	39.8190i	−0.766743	−	1.32804i
$900$		0			0
$901$	−31.8609	+	55.1847i	−1.06144	+	1.83847i
$902$	−5.09382			−0.169606
$903$		0			0
$904$	10.9652			0.364698
$905$	3.61422	−	6.26002i	0.120141	−	0.208090i
$906$		0			0
$907$	11.0295	+	19.1037i	0.366229	+	0.634328i	0.988973	−	0.148098i	$-0.0473153\pi$
$907$	11.0295	+	19.1037i	0.366229	+	0.634328i	−0.622743	+	0.782426i	$0.713982\pi$
$908$	10.0295	−	17.3716i	0.332841	−	0.576498i
$909$		0			0
$910$		0			0
$911$	−9.93420			−0.329135			−0.164567	−	0.986366i	$-0.552623\pi$
$911$	−9.93420			−0.329135			−0.164567	+	0.986366i	$0.552623\pi$
$912$		0			0
$913$	7.54691	+	13.0716i	0.249766	+	0.432608i
$914$	−9.31925	−	16.1414i	−0.308253	−	0.533910i
$915$		0			0
$916$	−22.5764			−0.745946
$917$	−34.2815	+	1.20887i	−1.13207	+	0.0399203i
$918$		0			0
$919$	−22.3174	+	38.6548i	−0.736182	+	1.27511i	0.218020	+	0.975944i	$0.430040\pi$
$919$	−22.3174	+	38.6548i	−0.736182	+	1.27511i	−0.954203	+	0.299161i	$0.903293\pi$
$920$	7.41832	+	12.8489i	0.244575	+	0.423616i
$921$		0			0
$922$	10.4947	−	18.1774i	0.345626	−	0.598642i
$923$		0			0
$924$		0			0
$925$	30.0999			0.989677
$926$	−2.67701	+	4.63672i	−0.0879720	+	0.152372i
$927$		0			0
$928$	−2.56430	−	4.44149i	−0.0841772	−	0.145799i
$929$	−21.2882	+	36.8723i	−0.698444	+	1.20974i	0.270562	+	0.962702i	$0.412790\pi$
$929$	−21.2882	+	36.8723i	−0.698444	+	1.20974i	−0.969006	+	0.247037i	$0.920543\pi$
$930$		0			0
$931$	25.4009	+	37.6030i	0.832482	+	1.23239i
$932$	0.742815			0.0243317
$933$		0			0
$934$	−13.0121	−	22.5377i	−0.425770	−	0.737455i
$935$	11.1736	+	19.3533i	0.365417	+	0.632920i
$936$		0			0
$937$	−36.2572			−1.18447			−0.592235	−	0.805765i	$-0.701754\pi$
$937$	−36.2572			−1.18447			−0.592235	+	0.805765i	$0.701754\pi$
$938$	−9.95122	−	15.9132i	−0.324919	−	0.519584i
$939$		0			0
$940$	0.453091	−	0.784776i	0.0147782	−	0.0255966i
$941$	1.34189	+	2.32421i	0.0437442	+	0.0757672i	0.887069	−	0.461638i	$-0.152738\pi$
$941$	1.34189	+	2.32421i	0.0437442	+	0.0757672i	−0.843324	+	0.537405i	$0.819405\pi$
$942$		0			0
$943$	−13.4686	+	23.3283i	−0.438598	+	0.759674i
$944$	0.871407			0.0283619
$945$		0			0
$946$	−11.4478			−0.372201
$947$	24.7519	−	42.8716i	0.804330	−	1.39314i	−0.112413	−	0.993662i	$-0.535858\pi$
$947$	24.7519	−	42.8716i	0.804330	−	1.39314i	0.916743	−	0.399478i	$-0.130809\pi$
$948$		0			0
$949$		0			0
$950$	−9.30711	+	16.1204i	−0.301963	+	0.523014i
$951$		0			0
$952$	−9.88729	+	18.6106i	−0.320449	+	0.603174i
$953$	−15.8019			−0.511872			−0.255936	−	0.966694i	$-0.582384\pi$
$953$	−15.8019			−0.511872			−0.255936	+	0.966694i	$0.582384\pi$
$954$		0			0
$955$	−3.35100	−	5.80411i	−0.108436	−	0.187817i
$956$	2.15962	+	3.74058i	0.0698472	+	0.120979i
$957$		0			0
$958$	−3.61121			−0.116673
$959$	6.96523	−	13.1105i	0.224919	−	0.423360i
$960$		0			0
$961$	−24.6876	+	42.7602i	−0.796375	+	1.37936i
$962$		0			0
$963$		0			0
$964$	9.09382	−	15.7510i	0.292892	−	0.507304i
$965$	−40.8957			−1.31648
$966$		0			0
$967$	−12.6497			−0.406788			−0.203394	−	0.979097i	$-0.565197\pi$
$967$	−12.6497			−0.406788			−0.203394	+	0.979097i	$0.565197\pi$
$968$	0.500000	−	0.866025i	0.0160706	−	0.0278351i
$969$		0			0
$970$	9.81961	+	17.0081i	0.315289	+	0.546096i
$971$	24.7671	−	42.8978i	0.794814	−	1.37666i	−0.128144	−	0.991756i	$-0.540902\pi$
$971$	24.7671	−	42.8978i	0.794814	−	1.37666i	0.922957	−	0.384902i	$-0.125765\pi$
$972$		0			0
$973$	−18.4168	−	29.4507i	−0.590416	−	0.944144i
$974$	8.06206			0.258325
$975$		0			0
$976$	−1.07981	−	1.87029i	−0.0345639	−	0.0598665i
$977$	17.2224	+	29.8301i	0.550994	+	0.954349i	0.998203	+	0.0599199i	$0.0190845\pi$
$977$	17.2224	+	29.8301i	0.550994	+	0.954349i	−0.447209	+	0.894429i	$0.647582\pi$
$978$		0			0
$979$	−1.61121			−0.0514944
$980$	−8.59720	+	17.6575i	−0.274627	+	0.564048i
$981$		0			0
$982$	−10.4531	+	18.1053i	−0.333572	+	0.577763i
$983$	−1.67888	−	2.90791i	−0.0535480	−	0.0927479i	0.838009	−	0.545657i	$-0.183720\pi$
$983$	−1.67888	−	2.90791i	−0.0535480	−	0.0927479i	−0.891557	+	0.452909i	$0.850386\pi$
$984$		0			0
$985$	−17.5106	+	30.3293i	−0.557935	+	0.966372i
$986$	−40.8504			−1.30094
$987$		0			0
$988$		0			0
$989$	−30.2693	+	52.4280i	−0.962508	+	1.66711i
$990$		0			0
$991$	22.9237	+	39.7050i	0.728195	+	1.26127i	0.957645	+	0.287950i	$0.0929738\pi$
$991$	22.9237	+	39.7050i	0.728195	+	1.26127i	−0.229450	+	0.973320i	$0.573693\pi$
$992$	−4.48261	+	7.76411i	−0.142323	+	0.246511i
$993$		0			0
$994$	−19.6929	+	0.694430i	−0.624621	+	0.0220260i
$995$	−39.8049			−1.26190
$996$		0			0
$997$	21.9305	+	37.9847i	0.694544	+	1.20299i	0.970334	+	0.241768i	$0.0777273\pi$
$997$	21.9305	+	37.9847i	0.694544	+	1.20299i	−0.275790	+	0.961218i	$0.588939\pi$
$998$	2.48261	+	4.30001i	0.0785857	+	0.136114i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.v.793.1		6
3.2	odd	2		462.2.i.g.331.3	yes	6
7.2	even	3		9702.2.a.dv.1.3		3
7.4	even	3	inner	1386.2.k.v.991.1		6
7.5	odd	6		9702.2.a.dw.1.1		3
21.2	odd	6		3234.2.a.bf.1.1		3
21.5	even	6		3234.2.a.bh.1.3		3
21.11	odd	6		462.2.i.g.67.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.g.67.3	✓	6	21.11	odd	6
462.2.i.g.331.3	yes	6	3.2	odd	2
1386.2.k.v.793.1		6	1.1	even	1	trivial
1386.2.k.v.991.1		6	7.4	even	3	inner
3234.2.a.bf.1.1		3	21.2	odd	6
3234.2.a.bh.1.3		3	21.5	even	6
9702.2.a.dv.1.3		3	7.2	even	3
9702.2.a.dw.1.1		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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.40280 + 2.42972i) q^{5} +(-1.40280 - 2.24325i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.40280 + 2.42972i) q^{5} +(-1.40280 - 2.24325i) q^{7} -1.00000 q^{8} +(1.40280 + 2.42972i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(-2.64411 + 0.0932392i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.98261 + 6.89809i) q^{17} +(3.24131 - 5.61411i) q^{19} +2.80560 q^{20} -1.00000 q^{22} +(-2.64411 + 4.57973i) q^{23} +(-1.43570 - 2.48671i) q^{25} +(-1.24131 + 2.33648i) q^{28} -5.12859 q^{29} +(4.48261 + 7.76411i) q^{31} +(0.500000 + 0.866025i) q^{32} +7.96523 q^{34} +(7.41832 - 0.261592i) q^{35} +(-5.24131 + 9.07821i) q^{37} +(-3.24131 - 5.61411i) q^{38} +(1.40280 - 2.42972i) q^{40} +5.09382 q^{41} +11.4478 q^{43} +(-0.500000 + 0.866025i) q^{44} +(2.64411 + 4.57973i) q^{46} +(0.161495 - 0.279717i) q^{47} +(-3.06430 + 6.29365i) q^{49} -2.87141 q^{50} +(4.00000 + 6.92820i) q^{53} +2.80560 q^{55} +(1.40280 + 2.24325i) q^{56} +(-2.56430 + 4.44149i) q^{58} +(-0.435704 - 0.754661i) q^{59} +(-1.07981 + 1.87029i) q^{61} +8.96523 q^{62} +1.00000 q^{64} +(3.54691 + 6.14343i) q^{67} +(3.98261 - 6.89809i) q^{68} +(3.48261 - 6.55525i) q^{70} +7.44784 q^{71} +(-6.28822 - 10.8915i) q^{73} +(5.24131 + 9.07821i) q^{74} -6.48261 q^{76} +(-1.24131 + 2.33648i) q^{77} +(-3.40280 + 5.89382i) q^{79} +(-1.40280 - 2.42972i) q^{80} +(2.54691 - 4.41138i) q^{82} -15.0938 q^{83} -22.3473 q^{85} +(5.72392 - 9.91412i) q^{86} +(0.500000 + 0.866025i) q^{88} +(0.805603 - 1.39535i) q^{89} +5.28822 q^{92} +(-0.161495 - 0.279717i) q^{94} +(9.09382 + 15.7510i) q^{95} +7.00000 q^{97} +(3.91832 + 5.80059i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8}+O(q^{10}) \) 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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Representations

Groups

Database

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