LMFDB - Embedded newform 1386.2.bk.b.901.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(703,1386)]

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, 1, 3]))

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

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

chi := DirichletCharacter("1386.703");

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.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.6
Root			$0.500000 - 0.921602i$ of defining polynomial
Character	$\chi$	$=$	1386.901
Dual form			1386.2.bk.b.703.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.54813 - 0.893814i) q^{5} +(-0.165362 + 2.64058i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.54813 - 0.893814i) q^{5} +(-0.165362 + 2.64058i) q^{7} +1.00000i q^{8} +(-0.893814 - 1.54813i) q^{10} +(-2.46279 - 2.22141i) q^{11} -6.37742 q^{13} +(-1.46350 + 2.20413i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0530476 + 0.0918811i) q^{17} +(2.07581 - 3.59541i) q^{19} -1.78763i q^{20} +(-1.02213 - 3.15519i) q^{22} +(3.97933 - 6.89240i) q^{23} +(-0.902194 - 1.56265i) q^{25} +(-5.52301 - 3.18871i) q^{26} +(-2.36949 + 1.17708i) q^{28} -7.65230i q^{29} +(1.10740 - 0.639360i) q^{31} +(-0.866025 + 0.500000i) q^{32} +0.106095i q^{34} +(2.61619 - 3.94016i) q^{35} +(-2.26092 + 3.91603i) q^{37} +(3.59541 - 2.07581i) q^{38} +(0.893814 - 1.54813i) q^{40} +0.0321383 q^{41} +6.87723i q^{43} +(0.692408 - 3.24354i) q^{44} +(6.89240 - 3.97933i) q^{46} +(-8.55805 - 4.94099i) q^{47} +(-6.94531 - 0.873304i) q^{49} -1.80439i q^{50} +(-3.18871 - 5.52301i) q^{52} +(-0.313720 - 0.543380i) q^{53} +(1.82718 + 5.64031i) q^{55} +(-2.64058 - 0.165362i) q^{56} +(3.82615 - 6.62708i) q^{58} +(-10.7863 + 6.22747i) q^{59} +(-4.97512 + 8.61716i) q^{61} +1.27872 q^{62} -1.00000 q^{64} +(9.87308 + 5.70022i) q^{65} +(-5.43609 - 9.41558i) q^{67} +(-0.0530476 + 0.0918811i) q^{68} +(4.23576 - 2.10418i) q^{70} +8.42785 q^{71} +(-0.0625042 - 0.108260i) q^{73} +(-3.91603 + 2.26092i) q^{74} +4.15162 q^{76} +(6.27307 - 6.13584i) q^{77} +(8.80673 + 5.08457i) q^{79} +(1.54813 - 0.893814i) q^{80} +(0.0278326 + 0.0160691i) q^{82} -12.0657 q^{83} -0.189659i q^{85} +(-3.43862 + 5.95586i) q^{86} +(2.22141 - 2.46279i) q^{88} +(4.64198 + 2.68005i) q^{89} +(1.05458 - 16.8401i) q^{91} +7.95866 q^{92} +(-4.94099 - 8.55805i) q^{94} +(-6.42726 + 3.71078i) q^{95} -15.7498i q^{97} +(-5.57816 - 4.22896i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7}+O(q^{10}) $ 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7	$ 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7} - 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} + 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} - 8 q^{35} + 14 q^{37} + 12 q^{38} + 2 q^{40} + 32 q^{41} - 4 q^{44} - 18 q^{46} + 24 q^{47} - 6 q^{49} + 14 q^{55} - 4 q^{56} - 28 q^{61} - 8 q^{62} - 16 q^{64} + 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} + 44 q^{73} + 24 q^{74} + 20 q^{76} + 52 q^{77} + 30 q^{79} + 12 q^{80} - 12 q^{82} + 8 q^{83} + 12 q^{86} - 2 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} - 14 q^{94} + 72 q^{95} - 40 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7 - 2 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^16 + 10 * q^19 + 2 * q^22 + 4 * q^23 + 10 * q^25 - 12 * q^26 + 6 * q^31 - 8 * q^35 + 14 * q^37 + 12 * q^38 + 2 * q^40 + 32 * q^41 - 4 * q^44 - 18 * q^46 + 24 * q^47 - 6 * q^49 + 14 * q^55 - 4 * q^56 - 28 * q^61 - 8 * q^62 - 16 * q^64 + 72 * q^65 - 16 * q^67 - 30 * q^70 + 56 * q^71 + 44 * q^73 + 24 * q^74 + 20 * q^76 + 52 * q^77 + 30 * q^79 + 12 * q^80 - 12 * q^82 + 8 * q^83 + 12 * q^86 - 2 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 - 14 * q^94 + 72 * q^95 - 40 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.54813	−	0.893814i	−0.692345	−	0.399726i	0.112145	−	0.993692i	$-0.464228\pi$
$5$	−1.54813	−	0.893814i	−0.692345	−	0.399726i	−0.804490	+	0.593966i	$0.797561\pi$
$6$		0			0
$7$	−0.165362	+	2.64058i	−0.0625011	+	0.998045i
$7$	−0.165362	+	2.64058i	−0.0625011	+	0.998045i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.893814	−	1.54813i	−0.282649	−	0.489562i
$11$	−2.46279	−	2.22141i	−0.742558	−	0.669782i
$11$	−2.46279	−	2.22141i	−0.742558	−	0.669782i
$12$		0			0
$13$	−6.37742			−1.76878			−0.884389	−	0.466751i	$-0.845424\pi$
$13$	−6.37742			−1.76878			−0.884389	+	0.466751i	$0.845424\pi$
$14$	−1.46350	+	2.20413i	−0.391136	+	0.589078i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0530476	+	0.0918811i	0.0128659	+	0.0222844i	0.872387	−	0.488816i	$-0.162571\pi$
$17$	0.0530476	+	0.0918811i	0.0128659	+	0.0222844i	−0.859521	+	0.511101i	$0.829238\pi$
$18$		0			0
$19$	2.07581	−	3.59541i	0.476224	−	0.824844i	−0.523405	−	0.852084i	$-0.675339\pi$
$19$	2.07581	−	3.59541i	0.476224	−	0.824844i	0.999629	+	0.0272400i	$0.00867184\pi$
$20$		−	1.78763i		−	0.399726i
$21$		0			0
$22$	−1.02213	−	3.15519i	−0.217919	−	0.672690i
$23$	3.97933	−	6.89240i	0.829748	−	1.43717i	−0.0684879	−	0.997652i	$-0.521817\pi$
$23$	3.97933	−	6.89240i	0.829748	−	1.43717i	0.898236	−	0.439514i	$-0.144849\pi$
$24$		0			0
$25$	−0.902194	−	1.56265i	−0.180439	−	0.312529i
$26$	−5.52301	−	3.18871i	−1.08315	−	0.625357i
$27$		0			0
$28$	−2.36949	+	1.17708i	−0.447791	+	0.222447i
$29$		−	7.65230i		−	1.42100i	−0.703699	−	0.710498i	$-0.748470\pi$
$29$		−	7.65230i		−	1.42100i	0.703699	−	0.710498i	$-0.251530\pi$
$30$		0			0
$31$	1.10740	−	0.639360i	0.198896	−	0.114833i	−0.397245	−	0.917713i	$-0.630034\pi$
$31$	1.10740	−	0.639360i	0.198896	−	0.114833i	0.596140	+	0.802880i	$0.296700\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			0.106095i			0.0181952i
$35$	2.61619	−	3.94016i	0.442216	−	0.666008i
$36$		0			0
$37$	−2.26092	+	3.91603i	−0.371693	+	0.643792i	−0.989826	−	0.142282i	$-0.954556\pi$
$37$	−2.26092	+	3.91603i	−0.371693	+	0.643792i	0.618133	+	0.786074i	$0.287889\pi$
$38$	3.59541	−	2.07581i	0.583253	−	0.336741i
$39$		0			0
$40$	0.893814	−	1.54813i	0.141324	−	0.244781i
$41$	0.0321383			0.00501915			0.00250958	−	0.999997i	$-0.499201\pi$
$41$	0.0321383			0.00501915			0.00250958	+	0.999997i	$0.499201\pi$
$42$		0			0
$43$			6.87723i			1.04877i	0.851482	+	0.524384i	$0.175704\pi$
$43$			6.87723i			1.04877i	−0.851482	+	0.524384i	$0.824296\pi$
$44$	0.692408	−	3.24354i	0.104384	−	0.488983i
$45$		0			0
$46$	6.89240	−	3.97933i	1.01623	−	0.586720i
$47$	−8.55805	−	4.94099i	−1.24832	−	0.720718i	−0.277545	−	0.960713i	$-0.589521\pi$
$47$	−8.55805	−	4.94099i	−1.24832	−	0.720718i	−0.970774	+	0.239995i	$0.922854\pi$
$48$		0			0
$49$	−6.94531	−	0.873304i	−0.992187	−	0.124758i
$50$		−	1.80439i		−	0.255179i
$51$		0			0
$52$	−3.18871	−	5.52301i	−0.442194	−	0.765903i
$53$	−0.313720	−	0.543380i	−0.0430928	−	0.0746389i	0.843675	−	0.536855i	$-0.180388\pi$
$53$	−0.313720	−	0.543380i	−0.0430928	−	0.0746389i	−0.886767	+	0.462216i	$0.847054\pi$
$54$		0			0
$55$	1.82718	+	5.64031i	0.246378	+	0.760539i
$56$	−2.64058	−	0.165362i	−0.352862	−	0.0220975i
$57$		0			0
$58$	3.82615	−	6.62708i	0.502398	−	0.870179i
$59$	−10.7863	+	6.22747i	−1.40426	+	0.810748i	−0.994826	−	0.101593i	$-0.967606\pi$
$59$	−10.7863	+	6.22747i	−1.40426	+	0.810748i	−0.409431	+	0.912341i	$0.634273\pi$
$60$		0			0
$61$	−4.97512	+	8.61716i	−0.636999	+	1.10331i	0.349089	+	0.937089i	$0.386491\pi$
$61$	−4.97512	+	8.61716i	−0.636999	+	1.10331i	−0.986088	+	0.166224i	$0.946842\pi$
$62$	1.27872			0.162398
$63$		0			0
$64$	−1.00000			−0.125000
$65$	9.87308	+	5.70022i	1.22460	+	0.707026i
$66$		0			0
$67$	−5.43609	−	9.41558i	−0.664124	−	1.15030i	−0.979522	−	0.201337i	$-0.935471\pi$
$67$	−5.43609	−	9.41558i	−0.664124	−	1.15030i	0.315398	−	0.948959i	$-0.397862\pi$
$68$	−0.0530476	+	0.0918811i	−0.00643296	+	0.0111422i
$69$		0			0
$70$	4.23576	−	2.10418i	0.506271	−	0.251498i
$71$	8.42785			1.00020			0.500101	−	0.865967i	$-0.333296\pi$
$71$	8.42785			1.00020			0.500101	+	0.865967i	$0.333296\pi$
$72$		0			0
$73$	−0.0625042	−	0.108260i	−0.00731556	−	0.0126709i	0.862344	−	0.506322i	$-0.168995\pi$
$73$	−0.0625042	−	0.108260i	−0.00731556	−	0.0126709i	−0.869660	+	0.493651i	$0.835662\pi$
$74$	−3.91603	+	2.26092i	−0.455229	+	0.262827i
$75$		0			0
$76$	4.15162			0.476224
$77$	6.27307	−	6.13584i	0.714883	−	0.699244i
$78$		0			0
$79$	8.80673	+	5.08457i	0.990835	+	0.572059i	0.905524	−	0.424295i	$-0.139478\pi$
$79$	8.80673	+	5.08457i	0.990835	+	0.572059i	0.0853112	+	0.996354i	$0.472812\pi$
$80$	1.54813	−	0.893814i	0.173086	−	0.0999314i
$81$		0			0
$82$	0.0278326	+	0.0160691i	0.00307359	+	0.00177454i
$83$	−12.0657			−1.32438			−0.662191	−	0.749335i	$-0.730373\pi$
$83$	−12.0657			−1.32438			−0.662191	+	0.749335i	$0.730373\pi$
$84$		0			0
$85$		−	0.189659i		−	0.0205714i
$86$	−3.43862	+	5.95586i	−0.370795	+	0.642237i
$87$		0			0
$88$	2.22141	−	2.46279i	0.236804	−	0.262534i
$89$	4.64198	+	2.68005i	0.492049	+	0.284084i	0.725424	−	0.688302i	$-0.241644\pi$
$89$	4.64198	+	2.68005i	0.492049	+	0.284084i	−0.233375	+	0.972387i	$0.574977\pi$
$90$		0			0
$91$	1.05458	−	16.8401i	0.110550	−	1.76532i
$92$	7.95866			0.829748
$93$		0			0
$94$	−4.94099	−	8.55805i	−0.509624	−	0.882695i
$95$	−6.42726	+	3.71078i	−0.659423	+	0.380718i
$96$		0			0
$97$		−	15.7498i		−	1.59915i	−0.600569	−	0.799573i	$-0.705059\pi$
$97$		−	15.7498i		−	1.59915i	0.600569	−	0.799573i	$-0.294941\pi$
$98$	−5.57816	−	4.22896i	−0.563480	−	0.427189i
$99$		0			0
$100$	0.902194	−	1.56265i	0.0902194	−	0.156265i
$101$	3.78650	+	6.55841i	0.376771	+	0.652586i	0.990590	−	0.136860i	$-0.0437012\pi$
$101$	3.78650	+	6.55841i	0.376771	+	0.652586i	−0.613820	+	0.789446i	$0.710368\pi$
$102$		0			0
$103$	−4.53550	−	2.61857i	−0.446896	−	0.258016i	0.259622	−	0.965710i	$-0.416402\pi$
$103$	−4.53550	−	2.61857i	−0.446896	−	0.258016i	−0.706519	+	0.707695i	$0.749735\pi$
$104$		−	6.37742i		−	0.625357i
$105$		0			0
$106$		−	0.627441i		−	0.0609424i
$107$	−4.12912	−	2.38395i	−0.399177	−	0.230465i	0.286952	−	0.957945i	$-0.407358\pi$
$107$	−4.12912	−	2.38395i	−0.399177	−	0.230465i	−0.686129	+	0.727480i	$0.740691\pi$
$108$		0			0
$109$	7.36585	−	4.25268i	0.705521	−	0.407332i	−0.103880	−	0.994590i	$-0.533126\pi$
$109$	7.36585	−	4.25268i	0.705521	−	0.407332i	0.809400	+	0.587257i	$0.199792\pi$
$110$	−1.23777	+	5.79825i	−0.118016	+	0.552841i
$111$		0			0
$112$	−2.20413	−	1.46350i	−0.208270	−	0.138287i
$113$	−10.3003			−0.968969			−0.484484	−	0.874800i	$-0.660993\pi$
$113$	−10.3003			−0.968969			−0.484484	+	0.874800i	$0.660993\pi$
$114$		0			0
$115$	−12.3210	+	7.11356i	−1.14894	+	0.663343i
$116$	6.62708	−	3.82615i	0.615309	−	0.355249i
$117$		0			0
$118$	−12.4549			−1.14657
$119$	−0.251391	+	0.124883i	−0.0230450	+	0.0114480i
$120$		0			0
$121$	1.13064	+	10.9417i	0.102785	+	0.994704i
$122$	−8.61716	+	4.97512i	−0.780161	+	0.450426i
$123$		0			0
$124$	1.10740	+	0.639360i	0.0994479	+	0.0574163i
$125$			12.1637i			1.08796i
$126$		0			0
$127$		−	3.18422i		−	0.282553i	−0.989970	−	0.141277i	$-0.954879\pi$
$127$		−	3.18422i		−	0.282553i	0.989970	−	0.141277i	$-0.0451207\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	5.70022	+	9.87308i	0.499943	+	0.865926i
$131$	0.543099	−	0.940675i	0.0474508	−	0.0821872i	−0.841324	−	0.540530i	$-0.818224\pi$
$131$	0.543099	−	0.940675i	0.0474508	−	0.0821872i	0.888775	+	0.458343i	$0.151557\pi$
$132$		0			0
$133$	9.15071	+	6.07589i	0.793467	+	0.526846i
$134$		−	10.8722i		−	0.939213i
$135$		0			0
$136$	−0.0918811	+	0.0530476i	−0.00787874	+	0.00454879i
$137$	−3.79098	−	6.56617i	−0.323885	−	0.560986i	0.657401	−	0.753541i	$-0.271656\pi$
$137$	−3.79098	−	6.56617i	−0.323885	−	0.560986i	−0.981286	+	0.192555i	$0.938323\pi$
$138$		0			0
$139$	1.34643			0.114203			0.0571013	−	0.998368i	$-0.481814\pi$
$139$	1.34643			0.114203			0.0571013	+	0.998368i	$0.481814\pi$
$140$	4.72037	+	0.295606i	0.398944	+	0.0249833i
$141$		0			0
$142$	7.29873	+	4.21392i	0.612496	+	0.353625i
$143$	15.7062	+	14.1669i	1.31342	+	1.18469i
$144$		0			0
$145$	−6.83973	+	11.8468i	−0.568008	+	0.983819i
$146$		−	0.125008i		−	0.0103458i
$147$		0			0
$148$	−4.52184			−0.371693
$149$	0.424489	+	0.245079i	0.0347755	+	0.0200776i	0.517287	−	0.855812i	$-0.326942\pi$
$149$	0.424489	+	0.245079i	0.0347755	+	0.0200776i	−0.482511	+	0.875890i	$0.660275\pi$
$150$		0			0
$151$	2.92130	−	1.68661i	0.237732	−	0.137255i	−0.376402	−	0.926456i	$-0.622839\pi$
$151$	2.92130	−	1.68661i	0.237732	−	0.137255i	0.614134	+	0.789202i	$0.289505\pi$
$152$	3.59541	+	2.07581i	0.291626	+	0.168371i
$153$		0			0
$154$	8.50056	−	2.17726i	0.684995	−	0.175449i
$155$	−2.28588			−0.183606
$156$		0			0
$157$	3.51865	−	2.03150i	0.280819	−	0.162131i	−0.352975	−	0.935633i	$-0.614830\pi$
$157$	3.51865	−	2.03150i	0.280819	−	0.162131i	0.633794	+	0.773502i	$0.281497\pi$
$158$	5.08457	+	8.80673i	0.404507	+	0.700626i
$159$		0			0
$160$	1.78763			0.141324
$161$	17.5419	+	11.6475i	1.38250	+	0.917950i
$162$		0			0
$163$	−10.3707	+	17.9626i	−0.812297	+	1.40694i	0.0989554	+	0.995092i	$0.468450\pi$
$163$	−10.3707	+	17.9626i	−0.812297	+	1.40694i	−0.911253	+	0.411848i	$0.864883\pi$
$164$	0.0160691	+	0.0278326i	0.00125479	+	0.00217336i
$165$		0			0
$166$	−10.4492	−	6.03285i	−0.811015	−	0.468240i
$167$	−3.42870			−0.265321			−0.132660	−	0.991162i	$-0.542352\pi$
$167$	−3.42870			−0.265321			−0.132660	+	0.991162i	$0.542352\pi$
$168$		0			0
$169$	27.6715			2.12857
$170$	0.0948293	−	0.164249i	0.00727307	−	0.0125973i
$171$		0			0
$172$	−5.95586	+	3.43862i	−0.454130	+	0.262192i
$173$	−10.5762	+	18.3185i	−0.804094	+	1.39273i	0.112807	+	0.993617i	$0.464016\pi$
$173$	−10.5762	+	18.3185i	−0.804094	+	1.39273i	−0.916901	+	0.399115i	$0.869317\pi$
$174$		0			0
$175$	4.27548	−	2.12391i	0.323196	−	0.160553i
$176$	3.15519	−	1.02213i	0.237832	−	0.0770458i
$177$		0			0
$178$	2.68005	+	4.64198i	0.200878	+	0.347931i
$179$	−7.04330	−	12.1994i	−0.526441	−	0.911822i	−0.999525	−	0.0308052i	$-0.990193\pi$
$179$	−7.04330	−	12.1994i	−0.526441	−	0.911822i	0.473085	−	0.881017i	$-0.343140\pi$
$180$		0			0
$181$			12.4579i			0.925992i	0.886360	+	0.462996i	$0.153225\pi$
$181$			12.4579i			0.925992i	−0.886360	+	0.462996i	$0.846775\pi$
$182$	9.33333	−	14.0566i	0.691833	−	1.04195i
$183$		0			0
$184$	6.89240	+	3.97933i	0.508115	+	0.293360i
$185$	7.00040	−	4.04169i	0.514680	−	0.297151i
$186$		0			0
$187$	0.0734611	−	0.344124i	0.00537201	−	0.0251649i
$188$		−	9.88198i		−	0.720718i
$189$		0			0
$190$	−7.42156			−0.538416
$191$	−13.6147	+	23.5813i	−0.985122	+	1.70628i	−0.343731	+	0.939068i	$0.611691\pi$
$191$	−13.6147	+	23.5813i	−0.985122	+	1.70628i	−0.641391	+	0.767214i	$0.721642\pi$
$192$		0			0
$193$	23.0692	−	13.3190i	1.66056	−	0.958724i	0.688111	−	0.725605i	$-0.258440\pi$
$193$	23.0692	−	13.3190i	1.66056	−	0.958724i	0.972448	−	0.233119i	$-0.0748933\pi$
$194$	7.87488	−	13.6397i	0.565384	−	0.979273i
$195$		0			0
$196$	−2.71635	−	6.45147i	−0.194025	−	0.460819i
$197$		−	11.7764i		−	0.839031i	−0.907748	−	0.419515i	$-0.862200\pi$
$197$		−	11.7764i		−	0.839031i	0.907748	−	0.419515i	$-0.137800\pi$
$198$		0			0
$199$	18.5336	−	10.7004i	1.31381	−	0.758531i	0.331089	−	0.943600i	$-0.392584\pi$
$199$	18.5336	−	10.7004i	1.31381	−	0.758531i	0.982726	+	0.185069i	$0.0592508\pi$
$200$	1.56265	−	0.902194i	0.110496	−	0.0637948i
$201$		0			0
$202$			7.57300i			0.532834i
$203$	20.2065	+	1.26540i	1.41822	+	0.0888137i
$204$		0			0
$205$	−0.0497542	−	0.0287256i	−0.00347499	−	0.00200628i
$206$	−2.61857	−	4.53550i	−0.182445	−	0.316004i
$207$		0			0
$208$	3.18871	−	5.52301i	0.221097	−	0.382952i
$209$	−13.0992	+	4.24349i	−0.906089	+	0.293529i
$210$		0			0
$211$			25.2654i			1.73934i	0.493630	+	0.869672i	$0.335670\pi$
$211$			25.2654i			1.73934i	−0.493630	+	0.869672i	$0.664330\pi$
$212$	0.313720	−	0.543380i	0.0215464	−	0.0373195i
$213$		0			0
$214$	−2.38395	−	4.12912i	−0.162963	−	0.282261i
$215$	6.14696	−	10.6469i	0.419219	−	0.726109i
$216$		0			0
$217$	1.50516	+	3.02992i	0.102177	+	0.205684i
$218$	8.50535			0.576055
$219$		0			0
$220$	−3.97106	+	4.40254i	−0.267729	+	0.296819i
$221$	−0.338307	−	0.585964i	−0.0227570	−	0.0394162i
$222$		0			0
$223$			9.80133i			0.656346i	0.944618	+	0.328173i	$0.106433\pi$
$223$			9.80133i			0.656346i	−0.944618	+	0.328173i	$0.893567\pi$
$224$	−1.17708	−	2.36949i	−0.0786471	−	0.158318i
$225$		0			0
$226$	−8.92030	−	5.15014i	−0.593370	−	0.342582i
$227$	−11.6454	−	20.1704i	−0.772931	−	1.33875i	−0.935950	−	0.352132i	$-0.885457\pi$
$227$	−11.6454	−	20.1704i	−0.772931	−	1.33875i	0.163020	−	0.986623i	$-0.447877\pi$
$228$		0			0
$229$	−5.65569	−	3.26531i	−0.373739	−	0.215778i	0.301352	−	0.953513i	$-0.402562\pi$
$229$	−5.65569	−	3.26531i	−0.373739	−	0.215778i	−0.675090	+	0.737735i	$0.735895\pi$
$230$	−14.2271			−0.938109
$231$		0			0
$232$	7.65230			0.502398
$233$	9.41166	+	5.43383i	0.616579	+	0.355982i	0.775536	−	0.631304i	$-0.217480\pi$
$233$	9.41166	+	5.43383i	0.616579	+	0.355982i	−0.158957	+	0.987285i	$0.550813\pi$
$234$		0			0
$235$	8.83265	+	15.2986i	0.576179	+	0.997971i
$236$	−10.7863	−	6.22747i	−0.702128	−	0.405374i
$237$		0			0
$238$	−0.280153	−	0.0175441i	−0.0181596	−	0.00113722i
$239$			7.69148i			0.497521i	0.968565	+	0.248760i	$0.0800231\pi$
$239$			7.69148i			0.497521i	−0.968565	+	0.248760i	$0.919977\pi$
$240$		0			0
$241$	−11.4067	−	19.7571i	−0.734773	−	1.27266i	−0.954823	−	0.297176i	$-0.903955\pi$
$241$	−11.4067	−	19.7571i	−0.734773	−	1.27266i	0.220050	−	0.975489i	$-0.429378\pi$
$242$	−4.49171	+	10.0411i	−0.288738	+	0.645469i
$243$		0			0
$244$	−9.95024			−0.636999
$245$	9.97168	+	7.55980i	0.637067	+	0.482978i
$246$		0			0
$247$	−13.2383	+	22.9294i	−0.842334	+	1.45897i
$248$	0.639360	+	1.10740i	0.0405994	+	0.0703203i
$249$		0			0
$250$	−6.08186	+	10.5341i	−0.384650	+	0.666234i
$251$		−	18.1111i		−	1.14317i	−0.820544	−	0.571583i	$-0.806330\pi$
$251$		−	18.1111i		−	1.14317i	0.820544	−	0.571583i	$-0.193670\pi$
$252$		0			0
$253$	−25.1111	+	8.13478i	−1.57872	+	0.511429i
$254$	1.59211	−	2.75761i	0.0998977	−	0.173028i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.41428	+	1.97123i	0.212977	+	0.122962i	0.602694	−	0.797972i	$-0.294094\pi$
$257$	3.41428	+	1.97123i	0.212977	+	0.122962i	−0.389717	+	0.920935i	$0.627427\pi$
$258$		0			0
$259$	−9.96672	−	6.61771i	−0.619302	−	0.411204i
$260$			11.4004i			0.707026i
$261$		0			0
$262$	0.940675	−	0.543099i	0.0581151	−	0.0335528i
$263$	−1.79020	+	1.03357i	−0.110389	+	0.0637329i	−0.554178	−	0.832398i	$-0.686967\pi$
$263$	−1.79020	+	1.03357i	−0.110389	+	0.0637329i	0.443789	+	0.896131i	$0.353634\pi$
$264$		0			0
$265$			1.12163i			0.0689012i
$266$	4.88680	+	9.83723i	0.299629	+	0.603159i
$267$		0			0
$268$	5.43609	−	9.41558i	0.332062	−	0.575148i
$269$	−2.42902	+	1.40240i	−0.148100	+	0.0855057i	−0.572219	−	0.820101i	$-0.693917\pi$
$269$	−2.42902	+	1.40240i	−0.148100	+	0.0855057i	0.424119	+	0.905607i	$0.360584\pi$
$270$		0			0
$271$	−4.64046	+	8.03751i	−0.281888	+	0.488244i	−0.971850	−	0.235602i	$-0.924294\pi$
$271$	−4.64046	+	8.03751i	−0.281888	+	0.488244i	0.689962	+	0.723846i	$0.257627\pi$
$272$	−0.106095			−0.00643296
$273$		0			0
$274$		−	7.58196i		−	0.458043i
$275$	−1.24937	+	5.85261i	−0.0753400	+	0.352926i
$276$		0			0
$277$	−4.53015	+	2.61548i	−0.272190	+	0.157149i	−0.629883	−	0.776690i	$-0.716897\pi$
$277$	−4.53015	+	2.61548i	−0.272190	+	0.157149i	0.357692	+	0.933839i	$0.383564\pi$
$278$	1.16604	+	0.673214i	0.0699345	+	0.0403767i
$279$		0			0
$280$	3.94016	+	2.61619i	0.235469	+	0.156347i
$281$		−	6.87281i		−	0.409998i	−0.978762	−	0.204999i	$-0.934281\pi$
$281$		−	6.87281i		−	0.409998i	0.978762	−	0.204999i	$-0.0657190\pi$
$282$		0			0
$283$	−6.00542	−	10.4017i	−0.356985	−	0.618316i	0.630471	−	0.776213i	$-0.282862\pi$
$283$	−6.00542	−	10.4017i	−0.356985	−	0.618316i	−0.987456	+	0.157897i	$0.949529\pi$
$284$	4.21392	+	7.29873i	0.250050	+	0.433100i
$285$		0			0
$286$	6.51854	+	20.1220i	0.385449	+	1.18984i
$287$	−0.00531446	+	0.0848636i	−0.000313703	+	0.00500934i
$288$		0			0
$289$	8.49437	−	14.7127i	0.499669	−	0.865452i
$290$	−11.8468	+	6.83973i	−0.695665	+	0.401643i
$291$		0			0
$292$	0.0625042	−	0.108260i	0.00365778	−	0.00633546i
$293$	−14.1147			−0.824592			−0.412296	−	0.911050i	$-0.635273\pi$
$293$	−14.1147			−0.824592			−0.412296	+	0.911050i	$0.635273\pi$
$294$		0			0
$295$	22.2648			1.29631
$296$	−3.91603	−	2.26092i	−0.227615	−	0.131413i
$297$		0			0
$298$	0.245079	+	0.424489i	0.0141970	+	0.0245900i
$299$	−25.3779	+	43.9557i	−1.46764	+	2.54203i
$300$		0			0
$301$	−18.1599	−	1.13723i	−1.04672	−	0.0655491i
$302$	3.37323			0.194107
$303$		0			0
$304$	2.07581	+	3.59541i	0.119056	+	0.206211i
$305$	15.4043	−	8.89366i	0.882046	−	0.509249i
$306$		0			0
$307$	−21.0753			−1.20283			−0.601417	−	0.798936i	$-0.705397\pi$
$307$	−21.0753			−1.20283			−0.601417	+	0.798936i	$0.705397\pi$
$308$	8.45033	+	2.36472i	0.481502	+	0.134742i
$309$		0			0
$310$	−1.97963	−	1.14294i	−0.112435	−	0.0649145i
$311$	12.0806	−	6.97475i	0.685029	−	0.395502i	−0.116718	−	0.993165i	$-0.537237\pi$
$311$	12.0806	−	6.97475i	0.685029	−	0.395502i	0.801747	+	0.597663i	$0.203904\pi$
$312$		0			0
$313$	3.45030	+	1.99203i	0.195023	+	0.112596i	0.594332	−	0.804220i	$-0.297417\pi$
$313$	3.45030	+	1.99203i	0.195023	+	0.112596i	−0.399309	+	0.916816i	$0.630750\pi$
$314$	4.06299			0.229288
$315$		0			0
$316$			10.1691i			0.572059i
$317$	6.14927	−	10.6509i	0.345377	−	0.598211i	−0.640045	−	0.768338i	$-0.721084\pi$
$317$	6.14927	−	10.6509i	0.345377	−	0.598211i	0.985422	+	0.170126i	$0.0544175\pi$
$318$		0			0
$319$	−16.9989	+	18.8460i	−0.951757	+	1.05517i
$320$	1.54813	+	0.893814i	0.0865431	+	0.0499657i
$321$		0			0
$322$	9.36799	+	18.8580i	0.522058	+	1.05091i
$323$	0.440467			0.0245082
$324$		0			0
$325$	5.75367	+	9.96565i	0.319156	+	0.552795i
$326$	−17.9626	+	10.3707i	−0.994857	+	0.574381i
$327$		0			0
$328$			0.0321383i			0.00177454i
$329$	14.4623	−	21.7811i	0.797330	−	1.20083i
$330$		0			0
$331$	15.5066	−	26.8582i	0.852319	−	1.47626i	−0.0267909	−	0.999641i	$-0.508529\pi$
$331$	15.5066	−	26.8582i	0.852319	−	1.47626i	0.879110	−	0.476619i	$-0.158138\pi$
$332$	−6.03285	−	10.4492i	−0.331096	−	0.573474i
$333$		0			0
$334$	−2.96934	−	1.71435i	−0.162475	−	0.0938051i
$335$			19.4354i			1.06187i
$336$		0			0
$337$		−	13.6161i		−	0.741718i	−0.928689	−	0.370859i	$-0.879063\pi$
$337$		−	13.6161i		−	0.741718i	0.928689	−	0.370859i	$-0.120937\pi$
$338$	23.9642	+	13.8357i	1.30348	+	0.752565i
$339$		0			0
$340$	0.164249	−	0.0948293i	0.00890766	−	0.00514284i
$341$	−4.14759	−	0.885396i	−0.224604	−	0.0479469i
$342$		0			0
$343$	3.45452	−	18.1952i	0.186527	−	0.982450i
$344$	−6.87723			−0.370795
$345$		0			0
$346$	−18.3185	+	10.5762i	−0.984810	+	0.568580i
$347$	−24.1708	+	13.9550i	−1.29756	+	0.749144i	−0.979981	−	0.199090i	$-0.936201\pi$
$347$	−24.1708	+	13.9550i	−1.29756	+	0.749144i	−0.317574	+	0.948234i	$0.602868\pi$
$348$		0			0
$349$	27.8147			1.48888			0.744442	−	0.667687i	$-0.232715\pi$
$349$	27.8147			1.48888			0.744442	+	0.667687i	$0.232715\pi$
$350$	4.76463	+	0.298378i	0.254680	+	0.0159490i
$351$		0			0
$352$	3.24354	+	0.692408i	0.172881	+	0.0369055i
$353$	18.6325	−	10.7575i	0.991706	−	0.572562i	0.0859222	−	0.996302i	$-0.472616\pi$
$353$	18.6325	−	10.7575i	0.991706	−	0.572562i	0.905784	+	0.423740i	$0.139283\pi$
$354$		0			0
$355$	−13.0474	−	7.53293i	−0.692485	−	0.399806i
$356$			5.36009i			0.284084i
$357$		0			0
$358$		−	14.0866i		−	0.744500i
$359$	18.0949	+	10.4471i	0.955015	+	0.551378i	0.894635	−	0.446798i	$-0.147436\pi$
$359$	18.0949	+	10.4471i	0.955015	+	0.551378i	0.0603796	+	0.998175i	$0.480769\pi$
$360$		0			0
$361$	0.882009	+	1.52769i	0.0464215	+	0.0804045i
$362$	−6.22897	+	10.7889i	−0.327387	+	0.567052i
$363$		0			0
$364$	15.1112	−	7.50674i	0.792043	−	0.393460i
$365$			0.223468i			0.0116969i
$366$		0			0
$367$	4.62731	−	2.67158i	0.241543	−	0.139455i	−0.374342	−	0.927291i	$-0.622132\pi$
$367$	4.62731	−	2.67158i	0.241543	−	0.139455i	0.615886	+	0.787835i	$0.288798\pi$
$368$	3.97933	+	6.89240i	0.207437	+	0.359291i
$369$		0			0
$370$	8.08337			0.420234
$371$	1.48671	−	0.738549i	0.0771864	−	0.0383435i
$372$		0			0
$373$	−21.9741	−	12.6868i	−1.13778	−	0.656895i	−0.191897	−	0.981415i	$-0.561464\pi$
$373$	−21.9741	−	12.6868i	−1.13778	−	0.656895i	−0.945879	+	0.324520i	$0.894797\pi$
$374$	0.235681	−	0.261290i	0.0121868	−	0.0135110i
$375$		0			0
$376$	4.94099	−	8.55805i	0.254812	−	0.441348i
$377$			48.8019i			2.51343i
$378$		0			0
$379$	22.7532			1.16875			0.584377	−	0.811483i	$-0.301339\pi$
$379$	22.7532			1.16875			0.584377	+	0.811483i	$0.301339\pi$
$380$	−6.42726	−	3.71078i	−0.329711	−	0.190359i
$381$		0			0
$382$	−23.5813	+	13.6147i	−1.20652	+	0.696587i
$383$	14.3310	+	8.27402i	0.732281	+	0.422783i	0.819256	−	0.573428i	$-0.194387\pi$
$383$	14.3310	+	8.27402i	0.732281	+	0.422783i	−0.0869750	+	0.996210i	$0.527720\pi$
$384$		0			0
$385$	−15.1958	+	3.89213i	−0.774451	+	0.198361i
$386$	26.6381			1.35584
$387$		0			0
$388$	13.6397	−	7.87488i	0.692451	−	0.399787i
$389$	3.69906	+	6.40696i	0.187550	+	0.324846i	0.944433	−	0.328705i	$-0.106612\pi$
$389$	3.69906	+	6.40696i	0.187550	+	0.324846i	−0.756883	+	0.653550i	$0.773279\pi$
$390$		0			0
$391$	0.844376			0.0427019
$392$	0.873304	−	6.94531i	0.0441085	−	0.350791i
$393$		0			0
$394$	5.88818	−	10.1986i	0.296642	−	0.513799i
$395$	−9.08932	−	15.7432i	−0.457333	−	0.792124i
$396$		0			0
$397$	3.34925	+	1.93369i	0.168094	+	0.0970492i	0.581687	−	0.813413i	$-0.302393\pi$
$397$	3.34925	+	1.93369i	0.168094	+	0.0970492i	−0.413593	+	0.910462i	$0.635726\pi$
$398$	21.4008			1.07272
$399$		0			0
$400$	1.80439			0.0902194
$401$	1.56681	−	2.71379i	0.0782426	−	0.135520i	−0.824249	−	0.566227i	$-0.808402\pi$
$401$	1.56681	−	2.71379i	0.0782426	−	0.135520i	0.902492	+	0.430707i	$0.141736\pi$
$402$		0			0
$403$	−7.06238	+	4.07747i	−0.351802	+	0.203113i
$404$	−3.78650	+	6.55841i	−0.188385	+	0.326293i
$405$		0			0
$406$	16.8666	+	11.1991i	0.837077	+	0.555803i
$407$	14.2673	−	4.62191i	0.707204	−	0.229099i
$408$		0			0
$409$	−10.0511	−	17.4091i	−0.496996	−	0.860822i	0.502998	−	0.864288i	$-0.332230\pi$
$409$	−10.0511	−	17.4091i	−0.496996	−	0.860822i	−0.999994	+	0.00346526i	$0.998897\pi$
$410$	−0.0287256	−	0.0497542i	−0.00141866	−	0.00245719i
$411$		0			0
$412$		−	5.23715i		−	0.258016i
$413$	−14.6605	−	29.5119i	−0.721395	−	1.45218i
$414$		0			0
$415$	18.6793	+	10.7845i	0.916929	+	0.529389i
$416$	5.52301	−	3.18871i	0.270788	−	0.156339i
$417$		0			0
$418$	−13.4660	−	2.87462i	−0.658642	−	0.140602i
$419$		−	2.63035i		−	0.128501i	−0.997934	−	0.0642506i	$-0.979534\pi$
$419$		−	2.63035i		−	0.128501i	0.997934	−	0.0642506i	$-0.0204657\pi$
$420$		0			0
$421$	24.9232			1.21468			0.607341	−	0.794441i	$-0.292236\pi$
$421$	24.9232			1.21468			0.607341	+	0.794441i	$0.292236\pi$
$422$	−12.6327	+	21.8805i	−0.614951	+	1.06513i
$423$		0			0
$424$	0.543380	−	0.313720i	0.0263888	−	0.0152356i
$425$	0.0957185	−	0.165789i	0.00464303	−	0.00804196i
$426$		0			0
$427$	−21.9316	−	14.5621i	−1.06134	−	0.704712i
$428$		−	4.76790i		−	0.230465i
$429$		0			0
$430$	10.6469	−	6.14696i	0.513437	−	0.296433i
$431$	−11.8175	+	6.82282i	−0.569227	+	0.328644i	−0.756841	−	0.653599i	$-0.773258\pi$
$431$	−11.8175	+	6.82282i	−0.569227	+	0.328644i	0.187613	+	0.982243i	$0.439925\pi$
$432$		0			0
$433$			10.4001i			0.499795i	0.968272	+	0.249897i	$0.0803969\pi$
$433$			10.4001i			0.499795i	−0.968272	+	0.249897i	$0.919603\pi$
$434$	−0.211452	+	3.37656i	−0.0101500	+	0.162080i
$435$		0			0
$436$	7.36585	+	4.25268i	0.352760	+	0.203666i
$437$	−16.5207	−	28.6147i	−0.790292	−	1.36883i
$438$		0			0
$439$	−11.6619	+	20.1991i	−0.556594	+	0.964049i	0.441183	+	0.897417i	$0.354559\pi$
$439$	−11.6619	+	20.1991i	−0.556594	+	0.964049i	−0.997778	+	0.0666324i	$0.978775\pi$
$440$	−5.64031	+	1.82718i	−0.268891	+	0.0871076i
$441$		0			0
$442$		−	0.676613i		−	0.0321832i
$443$	4.91726	−	8.51694i	0.233626	−	0.404652i	−0.725247	−	0.688489i	$-0.758274\pi$
$443$	4.91726	−	8.51694i	0.233626	−	0.404652i	0.958872	+	0.283837i	$0.0916076\pi$
$444$		0			0
$445$	−4.79092	−	8.29813i	−0.227112	−	0.393369i
$446$	−4.90067	+	8.48820i	−0.232053	+	0.401928i
$447$		0			0
$448$	0.165362	−	2.64058i	0.00781263	−	0.124756i
$449$	−9.26223			−0.437112			−0.218556	−	0.975824i	$-0.570135\pi$
$449$	−9.26223			−0.437112			−0.218556	+	0.975824i	$0.570135\pi$
$450$		0			0
$451$	−0.0791497	−	0.0713924i	−0.00372701	−	0.00336174i
$452$	−5.15014	−	8.92030i	−0.242242	−	0.419576i
$453$		0			0
$454$		−	23.2907i		−	1.09309i
$455$	−16.6845	+	25.1280i	−0.782182	+	1.17802i
$456$		0			0
$457$	2.21387	+	1.27818i	0.103560	+	0.0597906i	0.550886	−	0.834581i	$-0.314290\pi$
$457$	2.21387	+	1.27818i	0.103560	+	0.0597906i	−0.447325	+	0.894371i	$0.647623\pi$
$458$	−3.26531	−	5.65569i	−0.152578	−	0.264273i
$459$		0			0
$460$	−12.3210	−	7.11356i	−0.574472	−	0.331672i
$461$	29.5798			1.37767			0.688834	−	0.724919i	$-0.258123\pi$
$461$	29.5798			1.37767			0.688834	+	0.724919i	$0.258123\pi$
$462$		0			0
$463$	−9.24447			−0.429627			−0.214813	−	0.976655i	$-0.568914\pi$
$463$	−9.24447			−0.429627			−0.214813	+	0.976655i	$0.568914\pi$
$464$	6.62708	+	3.82615i	0.307655	+	0.177624i
$465$		0			0
$466$	5.43383	+	9.41166i	0.251717	+	0.435987i
$467$	10.0889	+	5.82484i	0.466859	+	0.269541i	0.714924	−	0.699202i	$-0.246461\pi$
$467$	10.0889	+	5.82484i	0.466859	+	0.269541i	−0.248065	+	0.968743i	$0.579795\pi$
$468$		0			0
$469$	25.7615	−	12.7974i	1.18956	−	0.590931i
$470$			17.6653i			0.814840i
$471$		0			0
$472$	−6.22747	−	10.7863i	−0.286643	−	0.496480i
$473$	15.2772	−	16.9372i	0.702445	−	0.778771i
$474$		0			0
$475$	−7.49114			−0.343717
$476$	−0.233847	−	0.155270i	−0.0107184	−	0.00711679i
$477$		0			0
$478$	−3.84574	+	6.66102i	−0.175900	+	0.304668i
$479$	−5.02758	−	8.70803i	−0.229716	−	0.397880i	0.728008	−	0.685569i	$-0.240446\pi$
$479$	−5.02758	−	8.70803i	−0.229716	−	0.397880i	−0.957724	+	0.287689i	$0.907113\pi$
$480$		0			0
$481$	14.4188	−	24.9742i	0.657443	−	1.13872i
$482$		−	22.8135i		−	1.03913i
$483$		0			0
$484$	−8.91051	+	6.45003i	−0.405023	+	0.293183i
$485$	−14.0774	+	24.3827i	−0.639220	+	1.10716i
$486$		0			0
$487$	−8.65731	−	14.9949i	−0.392300	−	0.679484i	0.600452	−	0.799661i	$-0.294987\pi$
$487$	−8.65731	−	14.9949i	−0.392300	−	0.679484i	−0.992753	+	0.120176i	$0.961654\pi$
$488$	−8.61716	−	4.97512i	−0.390080	−	0.225213i
$489$		0			0
$490$	4.85582	+	11.5328i	0.219364	+	0.521000i
$491$			8.44002i			0.380893i	0.981698	+	0.190446i	$0.0609935\pi$
$491$			8.44002i			0.380893i	−0.981698	+	0.190446i	$0.939006\pi$
$492$		0			0
$493$	0.703101	−	0.405936i	0.0316661	−	0.0182824i
$494$	−22.9294	+	13.2383i	−1.03164	+	0.595620i
$495$		0			0
$496$			1.27872i			0.0574163i
$497$	−1.39365	+	22.2544i	−0.0625137	+	0.998246i
$498$		0			0
$499$	−9.53597	+	16.5168i	−0.426889	+	0.739393i	−0.996595	−	0.0824555i	$-0.973724\pi$
$499$	−9.53597	+	16.5168i	−0.426889	+	0.739393i	0.569706	+	0.821849i	$0.307057\pi$
$500$	−10.5341	+	6.08186i	−0.471098	+	0.271989i
$501$		0			0
$502$	9.05557	−	15.6847i	0.404170	−	0.700043i
$503$	3.32018			0.148039			0.0740197	−	0.997257i	$-0.476417\pi$
$503$	3.32018			0.148039			0.0740197	+	0.997257i	$0.476417\pi$
$504$		0			0
$505$		−	13.5377i		−	0.602419i
$506$	−25.8143	−	5.51064i	−1.14758	−	0.244978i
$507$		0			0
$508$	2.75761	−	1.59211i	0.122349	−	0.0706384i
$509$	−3.91339	−	2.25939i	−0.173458	−	0.100146i	0.410758	−	0.911745i	$-0.365264\pi$
$509$	−3.91339	−	2.25939i	−0.173458	−	0.100146i	−0.584215	+	0.811599i	$0.698598\pi$
$510$		0			0
$511$	0.296206	−	0.147145i	0.0131034	−	0.00650931i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	1.97123	+	3.41428i	0.0869474	+	0.150597i
$515$	4.68103	+	8.10779i	0.206271	+	0.357272i
$516$		0			0
$517$	10.1007	+	31.1796i	0.444226	+	1.37128i
$518$	−5.32258	−	10.7145i	−0.233861	−	0.470766i
$519$		0			0
$520$	−5.70022	+	9.87308i	−0.249971	+	0.432963i
$521$	8.10705	−	4.68061i	0.355176	−	0.205061i	−0.311786	−	0.950152i	$-0.600927\pi$
$521$	8.10705	−	4.68061i	0.355176	−	0.205061i	0.666963	+	0.745091i	$0.267594\pi$
$522$		0			0
$523$	−8.70477	+	15.0771i	−0.380633	+	0.659276i	−0.991153	−	0.132725i	$-0.957627\pi$
$523$	−8.70477	+	15.0771i	−0.380633	+	0.659276i	0.610520	+	0.792001i	$0.290961\pi$
$524$	1.08620			0.0474508
$525$		0			0
$526$	−2.06715			−0.0901320
$527$	0.117490	+	0.0678330i	0.00511796	+	0.00295485i
$528$		0			0
$529$	−20.1702	−	34.9357i	−0.876963	−	1.51895i
$530$	−0.560815	+	0.971360i	−0.0243603	+	0.0421932i
$531$		0			0
$532$	−0.686522	+	10.9627i	−0.0297645	+	0.475293i
$533$	−0.204959			−0.00887777
$534$		0			0
$535$	4.26161	+	7.38132i	0.184245	+	0.319122i
$536$	9.41558	−	5.43609i	0.406691	−	0.234803i
$537$		0			0
$538$	−2.80480			−0.120923
$539$	15.1648	+	17.5792i	0.653196	+	0.757189i
$540$		0			0
$541$	34.0973	+	19.6861i	1.46596	+	0.846370i	0.999276	−	0.0380552i	$-0.0121163\pi$
$541$	34.0973	+	19.6861i	1.46596	+	0.846370i	0.466681	+	0.884426i	$0.345450\pi$
$542$	−8.03751	+	4.64046i	−0.345241	+	0.199325i
$543$		0			0
$544$	−0.0918811	−	0.0530476i	−0.00393937	−	0.00227440i
$545$	−15.2044			−0.651285
$546$		0			0
$547$			20.3539i			0.870271i	0.900365	+	0.435135i	$0.143299\pi$
$547$			20.3539i			0.870271i	−0.900365	+	0.435135i	$0.856701\pi$
$548$	3.79098	−	6.56617i	0.161943	−	0.280493i
$549$		0			0
$550$	−4.00830	+	4.44383i	−0.170914	+	0.189485i
$551$	−27.5132	−	15.8847i	−1.17210	−	0.676712i
$552$		0			0
$553$	−14.8825	+	22.4141i	−0.632869	+	0.953144i
$554$	−5.23096			−0.222242
$555$		0			0
$556$	0.673214	+	1.16604i	0.0285506	+	0.0494512i
$557$	11.2830	−	6.51425i	0.478076	−	0.276017i	−0.241538	−	0.970391i	$-0.577652\pi$
$557$	11.2830	−	6.51425i	0.478076	−	0.276017i	0.719614	+	0.694374i	$0.244319\pi$
$558$		0			0
$559$		−	43.8590i		−	1.85504i
$560$	2.10418	+	4.23576i	0.0889179	+	0.178994i
$561$		0			0
$562$	3.43641	−	5.95203i	0.144956	−	0.251071i
$563$	−16.7817	−	29.0667i	−0.707262	−	1.22501i	−0.965869	−	0.259032i	$-0.916597\pi$
$563$	−16.7817	−	29.0667i	−0.707262	−	1.22501i	0.258607	−	0.965983i	$-0.416737\pi$
$564$		0			0
$565$	15.9462	+	9.20653i	0.670861	+	0.387322i
$566$		−	12.0108i		−	0.504853i
$567$		0			0
$568$			8.42785i			0.353625i
$569$	4.80366	+	2.77340i	0.201380	+	0.116267i	0.597299	−	0.802019i	$-0.296241\pi$
$569$	4.80366	+	2.77340i	0.201380	+	0.116267i	−0.395919	+	0.918285i	$0.629574\pi$
$570$		0			0
$571$	−32.1228	+	18.5461i	−1.34430	+	0.776132i	−0.987435	−	0.158025i	$-0.949487\pi$
$571$	−32.1228	+	18.5461i	−1.34430	+	0.776132i	−0.356864	+	0.934156i	$0.616154\pi$
$572$	−4.41578	+	20.6854i	−0.184633	+	0.864901i
$573$		0			0
$574$	−0.0470343	+	0.0708368i	−0.00196317	+	0.00295667i
$575$	−14.3605			−0.598875
$576$		0			0
$577$	2.66926	−	1.54110i	0.111123	−	0.0641567i	−0.443409	−	0.896320i	$-0.646231\pi$
$577$	2.66926	−	1.54110i	0.111123	−	0.0641567i	0.554531	+	0.832163i	$0.312898\pi$
$578$	14.7127	−	8.49437i	0.611967	−	0.353319i
$579$		0			0
$580$	−13.6795			−0.568008
$581$	1.99521	−	31.8604i	0.0827753	−	1.32179i
$582$		0			0
$583$	−0.434445	+	2.03513i	−0.0179929	+	0.0842865i
$584$	0.108260	−	0.0625042i	0.00447985	−	0.00258644i
$585$		0			0
$586$	−12.2237	−	7.05737i	−0.504957	−	0.291537i
$587$		−	46.9255i		−	1.93682i	−0.249356	−	0.968412i	$-0.580219\pi$
$587$		−	46.9255i		−	1.93682i	0.249356	−	0.968412i	$-0.419781\pi$
$588$		0			0
$589$		−	5.30877i		−	0.218744i
$590$	19.2819	+	11.1324i	0.793823	+	0.458314i
$591$		0			0
$592$	−2.26092	−	3.91603i	−0.0929233	−	0.160948i
$593$	2.57479	−	4.45967i	0.105734	−	0.183137i	−0.808304	−	0.588766i	$-0.799614\pi$
$593$	2.57479	−	4.45967i	0.105734	−	0.183137i	0.914038	+	0.405629i	$0.132947\pi$
$594$		0			0
$595$	0.500808	+	0.0313624i	0.0205311	+	0.00128573i
$596$			0.490157i			0.0200776i
$597$		0			0
$598$	−43.9557	+	25.3779i	−1.79748	+	1.03778i
$599$	−17.5731	−	30.4375i	−0.718017	−	1.24364i	−0.961784	−	0.273808i	$-0.911717\pi$
$599$	−17.5731	−	30.4375i	−0.718017	−	1.24364i	0.243768	−	0.969834i	$-0.421616\pi$
$600$		0			0
$601$	−42.8385			−1.74742			−0.873710	−	0.486447i	$-0.838293\pi$
$601$	−42.8385			−1.74742			−0.873710	+	0.486447i	$0.838293\pi$
$602$	−15.1583	−	10.0648i	−0.617806	−	0.410211i
$603$		0			0
$604$	2.92130	+	1.68661i	0.118866	+	0.0686273i
$605$	8.02950	−	17.9498i	0.326446	−	0.729764i
$606$		0			0
$607$	8.33275	−	14.4328i	0.338216	−	0.585807i	−0.645881	−	0.763438i	$-0.723510\pi$
$607$	8.33275	−	14.4328i	0.338216	−	0.585807i	0.984097	+	0.177631i	$0.0568432\pi$
$608$			4.15162i			0.168371i
$609$		0			0
$610$	17.7873			0.720187
$611$	54.5783	+	31.5108i	2.20800	+	1.27479i
$612$		0			0
$613$	10.3018	−	5.94776i	0.416087	−	0.240228i	−0.277315	−	0.960779i	$-0.589445\pi$
$613$	10.3018	−	5.94776i	0.416087	−	0.240228i	0.693402	+	0.720551i	$0.256111\pi$
$614$	−18.2518	−	10.5377i	−0.736582	−	0.425266i
$615$		0			0
$616$	6.13584	+	6.27307i	0.247220	+	0.252749i
$617$	0.0716192			0.00288328			0.00144164	−	0.999999i	$-0.499541\pi$
$617$	0.0716192			0.00288328			0.00144164	+	0.999999i	$0.499541\pi$
$618$		0			0
$619$	25.3042	−	14.6094i	1.01706	−	0.587200i	0.103809	−	0.994597i	$-0.466897\pi$
$619$	25.3042	−	14.6094i	1.01706	−	0.587200i	0.913251	+	0.407397i	$0.133563\pi$
$620$	−1.14294	−	1.97963i	−0.0459015	−	0.0795037i
$621$		0			0
$622$	13.9495			0.559324
$623$	−7.84448	+	11.8143i	−0.314283	+	0.473331i
$624$		0			0
$625$	6.36112	−	11.0178i	0.254445	−	0.440711i
$626$	1.99203	+	3.45030i	0.0796177	+	0.137902i
$627$		0			0
$628$	3.51865	+	2.03150i	0.140410	+	0.0810655i
$629$	−0.479746			−0.0191287
$630$		0			0
$631$	−43.3663			−1.72638			−0.863192	−	0.504876i	$-0.831538\pi$
$631$	−43.3663			−1.72638			−0.863192	+	0.504876i	$0.831538\pi$
$632$	−5.08457	+	8.80673i	−0.202253	+	0.350313i
$633$		0			0
$634$	10.6509	−	6.14927i	0.422999	−	0.244219i
$635$	−2.84610	+	4.92958i	−0.112944	+	0.195624i
$636$		0			0
$637$	44.2932	+	5.56943i	1.75496	+	0.220669i
$638$	−24.1445	+	7.82163i	−0.955889	+	0.309661i
$639$		0			0
$640$	0.893814	+	1.54813i	0.0353311	+	0.0611952i
$641$	−2.72745	−	4.72408i	−0.107728	−	0.186590i	0.807122	−	0.590385i	$-0.201024\pi$
$641$	−2.72745	−	4.72408i	−0.107728	−	0.186590i	−0.914849	+	0.403795i	$0.867691\pi$
$642$		0			0
$643$		−	4.26488i		−	0.168190i	−0.996458	−	0.0840952i	$-0.973200\pi$
$643$		−	4.26488i		−	0.168190i	0.996458	−	0.0840952i	$-0.0268000\pi$
$644$	−1.31606	+	21.0155i	−0.0518601	+	0.828126i
$645$		0			0
$646$	0.381456	+	0.220234i	0.0150082	+	0.00866497i
$647$	−20.5525	+	11.8660i	−0.808004	+	0.466501i	−0.846262	−	0.532767i	$-0.821152\pi$
$647$	−20.5525	+	11.8660i	−0.808004	+	0.466501i	0.0382582	+	0.999268i	$0.487819\pi$
$648$		0			0
$649$	40.3982	+	8.62390i	1.58577	+	0.338518i
$650$			11.5073i			0.451355i
$651$		0			0
$652$	−20.7414			−0.812297
$653$	16.8093	−	29.1145i	0.657797	−	1.13934i	−0.323388	−	0.946266i	$-0.604822\pi$
$653$	16.8093	−	29.1145i	0.657797	−	1.13934i	0.981185	−	0.193071i	$-0.0618448\pi$
$654$		0			0
$655$	−1.68158	+	0.970859i	−0.0657047	+	0.0379346i
$656$	−0.0160691	+	0.0278326i	−0.000627394	+	0.00108668i
$657$		0			0
$658$	23.4153	−	11.6319i	0.912822	−	0.453459i
$659$		−	28.9405i		−	1.12736i	−0.825993	−	0.563681i	$-0.809385\pi$
$659$		−	28.9405i		−	1.12736i	0.825993	−	0.563681i	$-0.190615\pi$
$660$		0			0
$661$	−0.518650	+	0.299443i	−0.0201732	+	0.0116470i	−0.510053	−	0.860143i	$-0.670374\pi$
$661$	−0.518650	+	0.299443i	−0.0201732	+	0.0116470i	0.489880	+	0.871790i	$0.337041\pi$
$662$	26.8582	−	15.5066i	1.04387	−	0.602681i
$663$		0			0
$664$		−	12.0657i		−	0.468240i
$665$	−8.73578	−	17.5853i	−0.338759	−	0.681929i
$666$		0			0
$667$	−52.7427	−	30.4510i	−2.04221	−	1.17907i
$668$	−1.71435	−	2.96934i	−0.0663302	−	0.114887i
$669$		0			0
$670$	−9.71770	+	16.8315i	−0.375427	+	0.650259i
$671$	31.3949	−	10.1704i	1.21199	−	0.392625i
$672$		0			0
$673$		−	36.3353i		−	1.40062i	−0.713837	−	0.700312i	$-0.753044\pi$
$673$		−	36.3353i		−	1.40062i	0.713837	−	0.700312i	$-0.246956\pi$
$674$	6.80807	−	11.7919i	0.262237	−	0.454208i
$675$		0			0
$676$	13.8357	+	23.9642i	0.532144	+	0.921700i
$677$	9.99570	−	17.3131i	0.384166	−	0.665395i	−0.607487	−	0.794329i	$-0.707822\pi$
$677$	9.99570	−	17.3131i	0.384166	−	0.665395i	0.991653	+	0.128935i	$0.0411558\pi$
$678$		0			0
$679$	41.5885	+	2.60442i	1.59602	+	0.0999484i
$680$	0.189659			0.00727307
$681$		0			0
$682$	−3.14922	−	2.84057i	−0.120590	−	0.108771i
$683$	−11.0162	−	19.0807i	−0.421524	−	0.730102i	0.574564	−	0.818459i	$-0.305171\pi$
$683$	−11.0162	−	19.0807i	−0.421524	−	0.730102i	−0.996089	+	0.0883577i	$0.971838\pi$
$684$		0			0
$685$			13.5537i			0.517861i
$686$	12.0893	−	14.0303i	0.461572	−	0.535678i
$687$		0			0
$688$	−5.95586	−	3.43862i	−0.227065	−	0.131096i
$689$	2.00073	+	3.46536i	0.0762216	+	0.132020i
$690$		0			0
$691$	9.88161	+	5.70515i	0.375914	+	0.217034i	0.676039	−	0.736866i	$-0.263695\pi$
$691$	9.88161	+	5.70515i	0.375914	+	0.217034i	−0.300125	+	0.953900i	$0.597028\pi$
$692$	−21.1524			−0.804094
$693$		0			0
$694$	−27.9100			−1.05945
$695$	−2.08445	−	1.20346i	−0.0790676	−	0.0456497i
$696$		0			0
$697$	0.00170486	+	0.00295290i	6.45761e−5	+	0.000111849i
$698$	24.0882	+	13.9073i	0.911752	+	0.526400i
$699$		0			0
$700$	3.97710	+	2.64072i	0.150320	+	0.0998098i
$701$		−	1.92874i		−	0.0728474i	−0.999336	−	0.0364237i	$-0.988403\pi$
$701$		−	1.92874i		−	0.0728474i	0.999336	−	0.0364237i	$-0.0115966\pi$
$702$		0			0
$703$	9.38650	+	16.2579i	0.354018	+	0.613178i
$704$	2.46279	+	2.22141i	0.0928198	+	0.0837227i
$705$		0			0
$706$	21.5149			0.809725
$707$	−17.9441	+	8.91403i	−0.674859	+	0.335247i
$708$		0			0
$709$	−9.50162	+	16.4573i	−0.356841	+	0.618066i	−0.987431	−	0.158050i	$-0.949479\pi$
$709$	−9.50162	+	16.4573i	−0.356841	+	0.618066i	0.630590	+	0.776116i	$0.282813\pi$
$710$	−7.53293	−	13.0474i	−0.282706	−	0.489661i
$711$		0			0
$712$	−2.68005	+	4.64198i	−0.100439	+	0.173965i
$713$		−	10.1769i		−	0.381128i
$714$		0			0
$715$	−11.6527	−	35.9706i	−0.435787	−	1.34523i
$716$	7.04330	−	12.1994i	0.263220	−	0.455911i
$717$		0			0
$718$	10.4471	+	18.0949i	0.389883	+	0.675297i
$719$	−17.8998	−	10.3345i	−0.667551	−	0.385411i	0.127597	−	0.991826i	$-0.459274\pi$
$719$	−17.8998	−	10.3345i	−0.667551	−	0.385411i	−0.795148	+	0.606415i	$0.792607\pi$
$720$		0			0
$721$	7.66455	−	11.5433i	0.285443	−	0.429896i
$722$			1.76402i			0.0656500i
$723$		0			0
$724$	−10.7889	+	6.22897i	−0.400966	+	0.231498i
$725$	−11.9578	+	6.90386i	−0.444103	+	0.256403i
$726$		0			0
$727$		−	1.72185i		−	0.0638600i	−0.999490	−	0.0319300i	$-0.989835\pi$
$727$		−	1.72185i		−	0.0638600i	0.999490	−	0.0319300i	$-0.0101654\pi$
$728$	16.8401	+	1.05458i	0.624135	+	0.0390855i
$729$		0			0
$730$	−0.111734	+	0.193529i	−0.00413547	+	0.00716284i
$731$	−0.631887	+	0.364820i	−0.0233712	+	0.0134934i
$732$		0			0
$733$	−0.597125	+	1.03425i	−0.0220553	+	0.0382009i	−0.876842	−	0.480778i	$-0.840354\pi$
$733$	−0.597125	+	1.03425i	−0.0220553	+	0.0382009i	0.854787	+	0.518979i	$0.173688\pi$
$734$	5.34315			0.197219
$735$		0			0
$736$			7.95866i			0.293360i
$737$	−7.52798	+	35.2644i	−0.277297	+	1.29898i
$738$		0			0
$739$	−10.7713	+	6.21881i	−0.396228	+	0.228763i	−0.684855	−	0.728679i	$-0.740135\pi$
$739$	−10.7713	+	6.21881i	−0.396228	+	0.228763i	0.288627	+	0.957442i	$0.406801\pi$
$740$	7.00040	+	4.04169i	0.257340	+	0.148575i
$741$		0			0
$742$	1.65681	+	0.103755i	0.0608233	+	0.00380897i
$743$			19.1754i			0.703479i	0.936098	+	0.351739i	$0.114410\pi$
$743$			19.1754i			0.703479i	−0.936098	+	0.351739i	$0.885590\pi$
$744$		0			0
$745$	−0.438109	−	0.758827i	−0.0160511	−	0.0278013i
$746$	−12.6868	−	21.9741i	−0.464495	−	0.804529i
$747$		0			0
$748$	0.334751	−	0.108443i	0.0122397	−	0.00396506i
$749$	6.97780	−	10.5090i	0.254963	−	0.383992i
$750$		0			0
$751$	−22.9870	+	39.8146i	−0.838807	+	1.45286i	0.0520865	+	0.998643i	$0.483413\pi$
$751$	−22.9870	+	39.8146i	−0.838807	+	1.45286i	−0.890893	+	0.454213i	$0.849921\pi$
$752$	8.55805	−	4.94099i	0.312080	−	0.180179i
$753$		0			0
$754$	−24.4009	+	42.2637i	−0.888630	+	1.53915i
$755$	−6.03007			−0.219457
$756$		0			0
$757$	32.1348			1.16796			0.583979	−	0.811768i	$-0.301495\pi$
$757$	32.1348			1.16796			0.583979	+	0.811768i	$0.301495\pi$
$758$	19.7048	+	11.3766i	0.715712	+	0.413217i
$759$		0			0
$760$	−3.71078	−	6.42726i	−0.134604	−	0.233141i
$761$	−10.2499	+	17.7533i	−0.371558	+	0.643558i	−0.989805	−	0.142426i	$-0.954510\pi$
$761$	−10.2499	+	17.7533i	−0.371558	+	0.643558i	0.618247	+	0.785984i	$0.287843\pi$
$762$		0			0
$763$	10.0115	+	20.1533i	0.362440	+	0.729600i
$764$	−27.2293			−0.985122
$765$		0			0
$766$	8.27402	+	14.3310i	0.298953	+	0.517801i
$767$	68.7888	−	39.7152i	2.48382	−	1.43403i
$768$		0			0
$769$	14.3312			0.516796			0.258398	−	0.966039i	$-0.416805\pi$
$769$	14.3312			0.516796			0.258398	+	0.966039i	$0.416805\pi$
$770$	−15.1060	−	4.22723i	−0.544384	−	0.152339i
$771$		0			0
$772$	23.0692	+	13.3190i	0.830280	+	0.479362i
$773$	25.6118	−	14.7870i	0.921193	−	0.531851i	0.0371778	−	0.999309i	$-0.488163\pi$
$773$	25.6118	−	14.7870i	0.921193	−	0.531851i	0.884016	+	0.467457i	$0.154830\pi$
$774$		0			0
$775$	−1.99819	−	1.15365i	−0.0717771	−	0.0414405i
$776$	15.7498			0.565384
$777$		0			0
$778$			7.39812i			0.265235i
$779$	0.0667130	−	0.115550i	0.00239024	−	0.00414002i
$780$		0			0
$781$	−20.7560	−	18.7217i	−0.742708	−	0.669917i
$782$	0.731251	+	0.422188i	0.0261495	+	0.0150974i
$783$		0			0
$784$	4.22896	−	5.57816i	0.151034	−	0.199220i
$785$	−7.26311			−0.259232
$786$		0			0
$787$	−13.3487	−	23.1207i	−0.475831	−	0.824164i	0.523786	−	0.851850i	$-0.324519\pi$
$787$	−13.3487	−	23.1207i	−0.475831	−	0.824164i	−0.999617	+	0.0276865i	$0.991186\pi$
$788$	10.1986	−	5.88818i	0.363311	−	0.209758i
$789$		0			0
$790$		−	18.1786i		−	0.646767i
$791$	1.70328	−	27.1987i	0.0605616	−	0.967074i
$792$		0			0
$793$	31.7284	−	54.9552i	1.12671	−	1.95152i
$794$	1.93369	+	3.34925i	0.0686241	+	0.118860i
$795$		0			0
$796$	18.5336	+	10.7004i	0.656907	+	0.379265i
$797$			47.2556i			1.67388i	0.547294	+	0.836940i	$0.315658\pi$
$797$			47.2556i			1.67388i	−0.547294	+	0.836940i	$0.684342\pi$
$798$		0			0
$799$		−	1.04843i		−	0.0370908i
$800$	1.56265	+	0.902194i	0.0552479	+	0.0318974i
$801$		0			0
$802$	2.71379	−	1.56681i	0.0958272	−	0.0553259i
$803$	−0.0865568	+	0.405470i	−0.00305452	+	0.0143087i
$804$		0			0
$805$	−16.7465	−	33.7110i	−0.590236	−	1.18816i
$806$	−8.15494			−0.287245
$807$		0			0
$808$	−6.55841	+	3.78650i	−0.230724	+	0.133209i
$809$	−18.2536	+	10.5387i	−0.641763	+	0.370522i	−0.785293	−	0.619124i	$-0.787488\pi$
$809$	−18.2536	+	10.5387i	−0.641763	+	0.370522i	0.143530	+	0.989646i	$0.454155\pi$
$810$		0			0
$811$	−38.7457			−1.36055			−0.680273	−	0.732959i	$-0.738139\pi$
$811$	−38.7457			−1.36055			−0.680273	+	0.732959i	$0.738139\pi$
$812$	9.00737	+	18.1320i	0.316097	+	0.636310i
$813$		0			0
$814$	14.6668	+	3.13096i	0.514071	+	0.109740i
$815$	32.1104	−	18.5390i	1.12478	−	0.649392i
$816$		0			0
$817$	24.7265	+	14.2758i	0.865070	+	0.499448i
$818$		−	20.1022i		−	0.702858i
$819$		0			0
$820$		−	0.0574512i		−	0.00200628i
$821$	−37.0933	−	21.4158i	−1.29456	−	0.747417i	−0.315105	−	0.949057i	$-0.602040\pi$
$821$	−37.0933	−	21.4158i	−1.29456	−	0.747417i	−0.979460	+	0.201639i	$0.935373\pi$
$822$		0			0
$823$	−16.9309	−	29.3253i	−0.590176	−	1.02221i	−0.994208	−	0.107469i	$-0.965725\pi$
$823$	−16.9309	−	29.3253i	−0.590176	−	1.02221i	0.404033	−	0.914744i	$-0.367608\pi$
$824$	2.61857	−	4.53550i	0.0912224	−	0.158002i
$825$		0			0
$826$	2.05958	−	32.8883i	0.0716619	−	1.14433i
$827$			15.2572i			0.530544i	0.964174	+	0.265272i	$0.0854618\pi$
$827$			15.2572i			0.530544i	−0.964174	+	0.265272i	$0.914538\pi$
$828$		0			0
$829$	−14.9375	+	8.62414i	−0.518799	+	0.299529i	−0.736443	−	0.676499i	$-0.763496\pi$
$829$	−14.9375	+	8.62414i	−0.518799	+	0.299529i	0.217644	+	0.976028i	$0.430163\pi$
$830$	10.7845	+	18.6793i	0.374335	+	0.648367i
$831$		0			0
$832$	6.37742			0.221097
$833$	−0.288192	−	0.684469i	−0.00998525	−	0.0237155i
$834$		0			0
$835$	5.30808	+	3.06462i	0.183694	+	0.106056i
$836$	−10.2246	−	9.22248i	−0.353624	−	0.318966i
$837$		0			0
$838$	1.31518	−	2.27795i	0.0454320	−	0.0786906i
$839$		−	9.80607i		−	0.338543i	−0.985569	−	0.169272i	$-0.945859\pi$
$839$		−	9.80607i		−	0.338543i	0.985569	−	0.169272i	$-0.0541415\pi$
$840$		0			0
$841$	−29.5576			−1.01923
$842$	21.5841	+	12.4616i	0.743838	+	0.429455i
$843$		0			0
$844$	−21.8805	+	12.6327i	−0.753158	+	0.434836i
$845$	−42.8390	−	24.7331i	−1.47371	−	0.850846i
$846$		0			0
$847$	−29.0795	+	1.17618i	−0.999183	+	0.0404141i
$848$	0.627441			0.0215464
$849$		0			0
$850$	0.165789	−	0.0957185i	0.00568652	−	0.00328312i
$851$	17.9939	+	31.1664i	0.616823	+	1.06837i
$852$		0			0
$853$	58.0237			1.98669			0.993346	−	0.115168i	$-0.0367407\pi$
$853$	58.0237			1.98669			0.993346	+	0.115168i	$0.0367407\pi$
$854$	−11.7122	−	23.5770i	−0.400785	−	0.806788i
$855$		0			0
$856$	2.38395	−	4.12912i	0.0814817	−	0.141130i
$857$	20.5434	+	35.5821i	0.701748	+	1.21546i	0.967853	+	0.251518i	$0.0809299\pi$
$857$	20.5434	+	35.5821i	0.701748	+	1.21546i	−0.266105	+	0.963944i	$0.585737\pi$
$858$		0			0
$859$	−23.0028	−	13.2807i	−0.784845	−	0.453130i	0.0532999	−	0.998579i	$-0.483026\pi$
$859$	−23.0028	−	13.2807i	−0.784845	−	0.453130i	−0.838144	+	0.545448i	$0.816359\pi$
$860$	12.2939			0.419219
$861$		0			0
$862$	−13.6456			−0.464772
$863$	4.54395	−	7.87036i	0.154678	−	0.267910i	−0.778264	−	0.627938i	$-0.783899\pi$
$863$	4.54395	−	7.87036i	0.154678	−	0.267910i	0.932942	+	0.360027i	$0.117233\pi$
$864$		0			0
$865$	32.7467	−	18.9063i	1.11342	−	0.642834i
$866$	−5.20003	+	9.00671i	−0.176704	+	0.306061i
$867$		0			0
$868$	−1.87140	+	2.81846i	−0.0635196	+	0.0956649i
$869$	−10.3942	−	32.0856i	−0.352598	−	1.08843i
$870$		0			0
$871$	34.6682	+	60.0471i	1.17469	+	2.03462i
$872$	4.25268	+	7.36585i	0.144014	+	0.249439i
$873$		0			0
$874$		−	33.0414i		−	1.11764i
$875$	−32.1192	−	2.01142i	−1.08583	−	0.0679984i
$876$		0			0
$877$	−3.95476	−	2.28328i	−0.133543	−	0.0771009i	0.431740	−	0.901998i	$-0.357900\pi$
$877$	−3.95476	−	2.28328i	−0.133543	−	0.0771009i	−0.565283	+	0.824897i	$0.691233\pi$
$878$	−20.1991	+	11.6619i	−0.681686	+	0.393572i
$879$		0			0
$880$	−5.79825	−	1.23777i	−0.195459	−	0.0417251i
$881$		−	35.4288i		−	1.19363i	−0.802380	−	0.596813i	$-0.796433\pi$
$881$		−	35.4288i		−	1.19363i	0.802380	−	0.596813i	$-0.203567\pi$
$882$		0			0
$883$	25.2987			0.851368			0.425684	−	0.904872i	$-0.360033\pi$
$883$	25.2987			0.851368			0.425684	+	0.904872i	$0.360033\pi$
$884$	0.338307	−	0.585964i	0.0113785	−	0.0197081i
$885$		0			0
$886$	8.51694	−	4.91726i	0.286132	−	0.165198i
$887$	−22.4831	+	38.9419i	−0.754909	+	1.30754i	0.190511	+	0.981685i	$0.438986\pi$
$887$	−22.4831	+	38.9419i	−0.754909	+	1.30754i	−0.945420	+	0.325855i	$0.894348\pi$
$888$		0			0
$889$	8.40817	+	0.526549i	0.282001	+	0.0176599i
$890$		−	9.58185i		−	0.321184i
$891$		0			0
$892$	−8.48820	+	4.90067i	−0.284206	+	0.164086i
$893$	−35.5298	+	20.5131i	−1.18896	+	0.686446i
$894$		0			0
$895$			25.1816i			0.841727i
$896$	1.46350	−	2.20413i	0.0488920	−	0.0736347i
$897$		0			0
$898$	−8.02133	−	4.63112i	−0.267675	−	0.154542i
$899$	−4.89257	−	8.47419i	−0.163176	−	0.282630i
$900$		0			0
$901$	0.0332842	−	0.0576499i	0.00110886	−	0.00192060i
$902$	−0.0328494	−	0.101403i	−0.00109377	−	0.00337633i
$903$		0			0
$904$		−	10.3003i		−	0.342582i
$905$	11.1351	−	19.2865i	0.370143	−	0.641106i
$906$		0			0
$907$	8.63064	+	14.9487i	0.286576	+	0.496364i	0.972990	−	0.230847i	$-0.0741497\pi$
$907$	8.63064	+	14.9487i	0.286576	+	0.496364i	−0.686414	+	0.727211i	$0.740816\pi$
$908$	11.6454	−	20.1704i	0.386465	−	0.669377i
$909$		0			0
$910$	−27.0132	+	13.4193i	−0.895480	+	0.444844i
$911$	18.9606			0.628194			0.314097	−	0.949391i	$-0.398298\pi$
$911$	18.9606			0.628194			0.314097	+	0.949391i	$0.398298\pi$
$912$		0			0
$913$	29.7152	+	26.8029i	0.983431	+	0.887047i
$914$	1.27818	+	2.21387i	0.0422783	+	0.0732282i
$915$		0			0
$916$		−	6.53063i		−	0.215778i
$917$	2.39412	+	1.58965i	0.0790608	+	0.0524948i
$918$		0			0
$919$	−30.9373	−	17.8617i	−1.02053	−	0.589203i	−0.106272	−	0.994337i	$-0.533891\pi$
$919$	−30.9373	−	17.8617i	−1.02053	−	0.589203i	−0.914257	+	0.405134i	$0.867225\pi$
$920$	−7.11356	−	12.3210i	−0.234527	−	0.406213i
$921$		0			0
$922$	25.6168	+	14.7899i	0.843645	+	0.487079i
$923$	−53.7479			−1.76913
$924$		0			0
$925$	8.15916			0.268272
$926$	−8.00595	−	4.62224i	−0.263092	−	0.151896i
$927$		0			0
$928$	3.82615	+	6.62708i	0.125599	+	0.217545i
$929$	−35.0844	−	20.2560i	−1.15108	−	0.664577i	−0.201930	−	0.979400i	$-0.564721\pi$
$929$	−35.0844	−	20.2560i	−1.15108	−	0.664577i	−0.949150	+	0.314823i	$0.898055\pi$
$930$		0			0
$931$	−17.5570	+	23.1584i	−0.575409	+	0.758987i
$932$			10.8677i			0.355982i
$933$		0			0
$934$	5.82484	+	10.0889i	0.190595	+	0.330119i
$935$	−0.421310	+	0.467089i	−0.0137783	+	0.0152754i
$936$		0			0
$937$	−36.2513			−1.18428			−0.592140	−	0.805835i	$-0.701717\pi$
$937$	−36.2513			−1.18428			−0.592140	+	0.805835i	$0.701717\pi$
$938$	28.7088	+	1.79785i	0.937376	+	0.0587018i
$939$		0			0
$940$	−8.83265	+	15.2986i	−0.288089	+	0.498985i
$941$	−22.3898	−	38.7803i	−0.729887	−	1.26420i	−0.956931	−	0.290316i	$-0.906239\pi$
$941$	−22.3898	−	38.7803i	−0.729887	−	1.26420i	0.227044	−	0.973884i	$-0.427094\pi$
$942$		0			0
$943$	0.127889	−	0.221510i	0.00416463	−	0.00721336i
$944$		−	12.4549i		−	0.405374i
$945$		0			0
$946$	21.6990	−	7.02941i	0.705495	−	0.228546i
$947$	−7.35348	+	12.7366i	−0.238956	+	0.413884i	−0.960415	−	0.278573i	$-0.910138\pi$
$947$	−7.35348	+	12.7366i	−0.238956	+	0.413884i	0.721459	+	0.692457i	$0.243472\pi$
$948$		0			0
$949$	0.398615	+	0.690422i	0.0129396	+	0.0224120i
$950$	−6.48752	−	3.74557i	−0.210483	−	0.121522i
$951$		0			0
$952$	−0.124883	−	0.251391i	−0.00404747	−	0.00814764i
$953$			23.4615i			0.759991i	0.924988	+	0.379996i	$0.124074\pi$
$953$			23.4615i			0.759991i	−0.924988	+	0.379996i	$0.875926\pi$
$954$		0			0
$955$	42.1546	−	24.3379i	1.36409	−	0.787557i
$956$	−6.66102	+	3.84574i	−0.215433	+	0.124380i
$957$		0			0
$958$		−	10.0552i		−	0.324868i
$959$	17.9654	−	8.92459i	0.580133	−	0.288190i
$960$		0			0
$961$	−14.6824	+	25.4307i	−0.473627	+	0.820346i
$962$	24.9742	−	14.4188i	0.805200	−	0.464882i
$963$		0			0
$964$	11.4067	−	19.7571i	0.367387	−	0.636332i
$965$	−47.6189			−1.53291
$966$		0			0
$967$		−	57.3317i		−	1.84366i	−0.387589	−	0.921832i	$-0.626692\pi$
$967$		−	57.3317i		−	1.84366i	0.387589	−	0.921832i	$-0.373308\pi$
$968$	−10.9417	+	1.13064i	−0.351681	+	0.0363400i
$969$		0			0
$970$	−24.3827	+	14.0774i	−0.782881	+	0.451997i
$971$	42.1712	+	24.3476i	1.35334	+	0.781351i	0.988716	−	0.149805i	$-0.0478644\pi$
$971$	42.1712	+	24.3476i	1.35334	+	0.781351i	0.364623	+	0.931155i	$0.381198\pi$
$972$		0			0
$973$	−0.222649	+	3.55535i	−0.00713778	+	0.113979i
$974$		−	17.3146i		−	0.554797i
$975$		0			0
$976$	−4.97512	−	8.61716i	−0.159250	−	0.275828i
$977$	21.1278	+	36.5945i	0.675939	+	1.17076i	0.976193	+	0.216902i	$0.0695950\pi$
$977$	21.1278	+	36.5945i	0.675939	+	1.17076i	−0.300255	+	0.953859i	$0.597072\pi$
$978$		0			0
$979$	−5.47871	−	16.9121i	−0.175100	−	0.540514i
$980$	−1.56114	+	12.4156i	−0.0498689	+	0.396603i
$981$		0			0
$982$	−4.22001	+	7.30927i	−0.134666	+	0.233248i
$983$	−20.4533	+	11.8087i	−0.652359	+	0.376639i	−0.789359	−	0.613931i	$-0.789587\pi$
$983$	−20.4533	+	11.8087i	−0.652359	+	0.376639i	0.137001	+	0.990571i	$0.456254\pi$
$984$		0			0
$985$	−10.5259	+	18.2313i	−0.335382	+	0.580899i
$986$	0.811871			0.0258553
$987$		0			0
$988$	−26.4766			−0.842334
$989$	47.4007	+	27.3668i	1.50725	+	0.870213i
$990$		0			0
$991$	−13.4870	−	23.3602i	−0.428429	−	0.742060i	0.568305	−	0.822818i	$-0.307599\pi$
$991$	−13.4870	−	23.3602i	−0.428429	−	0.742060i	−0.996734	+	0.0807577i	$0.974266\pi$
$992$	−0.639360	+	1.10740i	−0.0202997	+	0.0351601i
$993$		0			0
$994$	−12.3341	+	18.5760i	−0.391215	+	0.589196i
$995$	−38.2566			−1.21282
$996$		0			0
$997$	11.1707	+	19.3483i	0.353781	+	0.612766i	0.986909	−	0.161281i	$-0.0515626\pi$
$997$	11.1707	+	19.3483i	0.353781	+	0.612766i	−0.633128	+	0.774047i	$0.718229\pi$
$998$	−16.5168	+	9.53597i	−0.522830	+	0.301856i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.b.901.6		16
3.2	odd	2		462.2.p.b.439.3	yes	16
7.3	odd	6		1386.2.bk.a.703.2		16
11.10	odd	2		1386.2.bk.a.901.2		16
21.2	odd	6		3234.2.e.b.2155.11		16
21.5	even	6		3234.2.e.a.2155.14		16
21.17	even	6		462.2.p.a.241.7	✓	16
33.32	even	2		462.2.p.a.439.7	yes	16
77.10	even	6	inner	1386.2.bk.b.703.6		16
231.65	even	6		3234.2.e.a.2155.3		16
231.131	odd	6		3234.2.e.b.2155.6		16
231.164	odd	6		462.2.p.b.241.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.7	✓	16	21.17	even	6
462.2.p.a.439.7	yes	16	33.32	even	2
462.2.p.b.241.3	yes	16	231.164	odd	6
462.2.p.b.439.3	yes	16	3.2	odd	2
1386.2.bk.a.703.2		16	7.3	odd	6
1386.2.bk.a.901.2		16	11.10	odd	2
1386.2.bk.b.703.6		16	77.10	even	6	inner
1386.2.bk.b.901.6		16	1.1	even	1	trivial
3234.2.e.a.2155.3		16	231.65	even	6
3234.2.e.a.2155.14		16	21.5	even	6
3234.2.e.b.2155.6		16	231.131	odd	6
3234.2.e.b.2155.11		16	21.2	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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.54813 - 0.893814i) q^{5} +(-0.165362 + 2.64058i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.54813 - 0.893814i) q^{5} +(-0.165362 + 2.64058i) q^{7} +1.00000i q^{8} +(-0.893814 - 1.54813i) q^{10} +(-2.46279 - 2.22141i) q^{11} -6.37742 q^{13} +(-1.46350 + 2.20413i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0530476 + 0.0918811i) q^{17} +(2.07581 - 3.59541i) q^{19} -1.78763i q^{20} +(-1.02213 - 3.15519i) q^{22} +(3.97933 - 6.89240i) q^{23} +(-0.902194 - 1.56265i) q^{25} +(-5.52301 - 3.18871i) q^{26} +(-2.36949 + 1.17708i) q^{28} -7.65230i q^{29} +(1.10740 - 0.639360i) q^{31} +(-0.866025 + 0.500000i) q^{32} +0.106095i q^{34} +(2.61619 - 3.94016i) q^{35} +(-2.26092 + 3.91603i) q^{37} +(3.59541 - 2.07581i) q^{38} +(0.893814 - 1.54813i) q^{40} +0.0321383 q^{41} +6.87723i q^{43} +(0.692408 - 3.24354i) q^{44} +(6.89240 - 3.97933i) q^{46} +(-8.55805 - 4.94099i) q^{47} +(-6.94531 - 0.873304i) q^{49} -1.80439i q^{50} +(-3.18871 - 5.52301i) q^{52} +(-0.313720 - 0.543380i) q^{53} +(1.82718 + 5.64031i) q^{55} +(-2.64058 - 0.165362i) q^{56} +(3.82615 - 6.62708i) q^{58} +(-10.7863 + 6.22747i) q^{59} +(-4.97512 + 8.61716i) q^{61} +1.27872 q^{62} -1.00000 q^{64} +(9.87308 + 5.70022i) q^{65} +(-5.43609 - 9.41558i) q^{67} +(-0.0530476 + 0.0918811i) q^{68} +(4.23576 - 2.10418i) q^{70} +8.42785 q^{71} +(-0.0625042 - 0.108260i) q^{73} +(-3.91603 + 2.26092i) q^{74} +4.15162 q^{76} +(6.27307 - 6.13584i) q^{77} +(8.80673 + 5.08457i) q^{79} +(1.54813 - 0.893814i) q^{80} +(0.0278326 + 0.0160691i) q^{82} -12.0657 q^{83} -0.189659i q^{85} +(-3.43862 + 5.95586i) q^{86} +(2.22141 - 2.46279i) q^{88} +(4.64198 + 2.68005i) q^{89} +(1.05458 - 16.8401i) q^{91} +7.95866 q^{92} +(-4.94099 - 8.55805i) q^{94} +(-6.42726 + 3.71078i) q^{95} -15.7498i q^{97} +(-5.57816 - 4.22896i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7	\( 16 q + 8 q^{4} - 12 q^{5} + 6 q^{7} - 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} + 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} - 8 q^{35} + 14 q^{37} + 12 q^{38} + 2 q^{40} + 32 q^{41} - 4 q^{44} - 18 q^{46} + 24 q^{47} - 6 q^{49} + 14 q^{55} - 4 q^{56} - 28 q^{61} - 8 q^{62} - 16 q^{64} + 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} + 44 q^{73} + 24 q^{74} + 20 q^{76} + 52 q^{77} + 30 q^{79} + 12 q^{80} - 12 q^{82} + 8 q^{83} + 12 q^{86} - 2 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} - 14 q^{94} + 72 q^{95} - 40 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 12 * q^5 + 6 * q^7 - 2 * q^10 + 4 * q^11 - 8 * q^14 - 8 * q^16 + 10 * q^19 + 2 * q^22 + 4 * q^23 + 10 * q^25 - 12 * q^26 + 6 * q^31 - 8 * q^35 + 14 * q^37 + 12 * q^38 + 2 * q^40 + 32 * q^41 - 4 * q^44 - 18 * q^46 + 24 * q^47 - 6 * q^49 + 14 * q^55 - 4 * q^56 - 28 * q^61 - 8 * q^62 - 16 * q^64 + 72 * q^65 - 16 * q^67 - 30 * q^70 + 56 * q^71 + 44 * q^73 + 24 * q^74 + 20 * q^76 + 52 * q^77 + 30 * q^79 + 12 * q^80 - 12 * q^82 + 8 * q^83 + 12 * q^86 - 2 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 - 14 * q^94 + 72 * q^95 - 40 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more