LMFDB - Embedded newform 1386.2.bk.a.901.2

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			901.2
Root			$0.500000 - 0.921602i$ of defining polynomial
Character	$\chi$	$=$	1386.901
Dual form			1386.2.bk.a.703.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.54813 - 0.893814i) q^{5} +(0.165362 - 2.64058i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.54813 - 0.893814i) q^{5} +(0.165362 - 2.64058i) q^{7} -1.00000i q^{8} +(0.893814 + 1.54813i) q^{10} +(-0.692408 - 3.24354i) q^{11} +6.37742 q^{13} +(-1.46350 + 2.20413i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.0530476 - 0.0918811i) q^{17} +(-2.07581 + 3.59541i) q^{19} -1.78763i q^{20} +(-1.02213 + 3.15519i) q^{22} +(3.97933 - 6.89240i) q^{23} +(-0.902194 - 1.56265i) q^{25} +(-5.52301 - 3.18871i) q^{26} +(2.36949 - 1.17708i) q^{28} +7.65230i q^{29} +(1.10740 - 0.639360i) q^{31} +(0.866025 - 0.500000i) q^{32} +0.106095i q^{34} +(-2.61619 + 3.94016i) q^{35} +(-2.26092 + 3.91603i) q^{37} +(3.59541 - 2.07581i) q^{38} +(-0.893814 + 1.54813i) q^{40} -0.0321383 q^{41} -6.87723i q^{43} +(2.46279 - 2.22141i) q^{44} +(-6.89240 + 3.97933i) q^{46} +(-8.55805 - 4.94099i) q^{47} +(-6.94531 - 0.873304i) q^{49} +1.80439i q^{50} +(3.18871 + 5.52301i) q^{52} +(-0.313720 - 0.543380i) q^{53} +(-1.82718 + 5.64031i) q^{55} +(-2.64058 - 0.165362i) q^{56} +(3.82615 - 6.62708i) q^{58} +(-10.7863 + 6.22747i) q^{59} +(4.97512 - 8.61716i) q^{61} -1.27872 q^{62} -1.00000 q^{64} +(-9.87308 - 5.70022i) q^{65} +(-5.43609 - 9.41558i) q^{67} +(0.0530476 - 0.0918811i) q^{68} +(4.23576 - 2.10418i) q^{70} +8.42785 q^{71} +(0.0625042 + 0.108260i) q^{73} +(3.91603 - 2.26092i) q^{74} -4.15162 q^{76} +(-8.67933 + 1.29200i) q^{77} +(-8.80673 - 5.08457i) q^{79} +(1.54813 - 0.893814i) q^{80} +(0.0278326 + 0.0160691i) q^{82} +12.0657 q^{83} +0.189659i q^{85} +(-3.43862 + 5.95586i) q^{86} +(-3.24354 + 0.692408i) q^{88} +(4.64198 + 2.68005i) q^{89} +(1.05458 - 16.8401i) q^{91} +7.95866 q^{92} +(4.94099 + 8.55805i) q^{94} +(6.42726 - 3.71078i) q^{95} -15.7498i q^{97} +(5.57816 + 4.22896i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 32 q^{77} - 30 q^{79} + 12 q^{80} - 12 q^{82} - 8 q^{83} + 12 q^{86} + 4 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 - 32 * q^77 - 30 * q^79 + 12 * q^80 - 12 * q^82 - 8 * q^83 + 12 * q^86 + 4 * 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
$11$	−0.692408	−	3.24354i	−0.208769	−	0.977965i
$11$	−0.692408	−	3.24354i	−0.208769	−	0.977965i
$12$		0			0
$13$	6.37742			1.76878			0.884389	−	0.466751i	$-0.154576\pi$
$13$	6.37742			1.76878			0.884389	+	0.466751i	$0.154576\pi$
$14$	−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	0.859521	−	0.511101i	$-0.170762\pi$
$17$	−0.0530476	−	0.0918811i	−0.0128659	−	0.0222844i	−0.872387	+	0.488816i	$0.837429\pi$
$18$		0			0
$19$	−2.07581	+	3.59541i	−0.476224	+	0.824844i	−0.999629	−	0.0272400i	$-0.991328\pi$
$19$	−2.07581	+	3.59541i	−0.476224	+	0.824844i	0.523405	+	0.852084i	$0.324661\pi$
$20$		−	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	$0.251530\pi$
$29$			7.65230i			1.42100i	−0.703699	+	0.710498i	$0.748470\pi$
$30$		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	$-0.500799\pi$
$41$	−0.0321383			−0.00501915			−0.00250958	+	0.999997i	$0.500799\pi$
$42$		0			0
$43$		−	6.87723i		−	1.04877i	−0.851482	−	0.524384i	$-0.824296\pi$
$43$		−	6.87723i		−	1.04877i	0.851482	−	0.524384i	$-0.175704\pi$
$44$	2.46279	−	2.22141i	0.371279	−	0.334891i
$45$		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	$-0.613509\pi$
$61$	4.97512	−	8.61716i	0.636999	−	1.10331i	0.986088	−	0.166224i	$-0.0531576\pi$
$62$	−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	0.869660	−	0.493651i	$-0.164338\pi$
$73$	0.0625042	+	0.108260i	0.00731556	+	0.0126709i	−0.862344	+	0.506322i	$0.831005\pi$
$74$	3.91603	−	2.26092i	0.455229	−	0.262827i
$75$		0			0
$76$	−4.15162			−0.476224
$77$	−8.67933	+	1.29200i	−0.989101	+	0.147237i
$78$		0			0
$79$	−8.80673	−	5.08457i	−0.990835	−	0.572059i	−0.0853112	−	0.996354i	$-0.527188\pi$
$79$	−8.80673	−	5.08457i	−0.990835	−	0.572059i	−0.905524	+	0.424295i	$0.860522\pi$
$80$	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	$-0.269627\pi$
$83$	12.0657			1.32438			0.662191	+	0.749335i	$0.269627\pi$
$84$		0			0
$85$			0.189659i			0.0205714i
$86$	−3.43862	+	5.95586i	−0.370795	+	0.642237i
$87$		0			0
$88$	−3.24354	+	0.692408i	−0.345763	+	0.0738109i
$89$	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	0.613820	−	0.789446i	$-0.289632\pi$
$101$	−3.78650	−	6.55841i	−0.376771	−	0.652586i	−0.990590	+	0.136860i	$0.956299\pi$
$102$		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	0.686129	−	0.727480i	$-0.259309\pi$
$107$	4.12912	+	2.38395i	0.399177	+	0.230465i	−0.286952	+	0.957945i	$0.592642\pi$
$108$		0			0
$109$	−7.36585	+	4.25268i	−0.705521	+	0.407332i	−0.809400	−	0.587257i	$-0.800208\pi$
$109$	−7.36585	+	4.25268i	−0.705521	+	0.407332i	0.103880	+	0.994590i	$0.466874\pi$
$110$	4.40254	−	3.97106i	0.419766	−	0.378626i
$111$		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
$121$	−10.0411	+	4.49171i	−0.912831	+	0.408337i
$122$	−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	$0.0451207\pi$
$127$			3.18422i			0.282553i	−0.989970	+	0.141277i	$0.954879\pi$
$128$	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	−0.888775	−	0.458343i	$-0.848443\pi$
$131$	−0.543099	+	0.940675i	−0.0474508	+	0.0821872i	0.841324	+	0.540530i	$0.181776\pi$
$132$		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	$-0.518186\pi$
$139$	−1.34643			−0.114203			−0.0571013	+	0.998368i	$0.518186\pi$
$140$	−4.72037	−	0.295606i	−0.398944	−	0.0249833i
$141$		0			0
$142$	−7.29873	−	4.21392i	−0.612496	−	0.353625i
$143$	−4.41578	−	20.6854i	−0.369266	−	1.72980i
$144$		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	0.482511	−	0.875890i	$-0.339725\pi$
$149$	−0.424489	−	0.245079i	−0.0347755	−	0.0200776i	−0.517287	+	0.855812i	$0.673058\pi$
$150$		0			0
$151$	−2.92130	+	1.68661i	−0.237732	+	0.137255i	−0.614134	−	0.789202i	$-0.710495\pi$
$151$	−2.92130	+	1.68661i	−0.237732	+	0.137255i	0.376402	+	0.926456i	$0.377161\pi$
$152$	3.59541	+	2.07581i	0.291626	+	0.168371i
$153$		0			0
$154$	8.16252	+	3.22076i	0.657754	+	0.259536i
$155$	−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	$-0.457648\pi$
$167$	3.42870			0.265321			0.132660	+	0.991162i	$0.457648\pi$
$168$		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	$-0.535984\pi$
$173$	10.5762	−	18.3185i	0.804094	−	1.39273i	0.916901	−	0.399115i	$-0.130683\pi$
$174$		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
$187$	−0.261290	+	0.235681i	−0.0191074	+	0.0172347i
$188$		−	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	$0.741560\pi$
$193$	−23.0692	+	13.3190i	−1.66056	+	0.958724i	−0.972448	+	0.233119i	$0.925107\pi$
$194$	−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	$0.137800\pi$
$197$			11.7764i			0.839031i	−0.907748	+	0.419515i	$0.862200\pi$
$198$		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	$-0.664330\pi$
$211$		−	25.2654i		−	1.73934i	0.493630	−	0.869672i	$-0.335670\pi$
$212$	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
$220$	−5.79825	+	1.23777i	−0.390918	+	0.0834503i
$221$	−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	$0.114543\pi$
$227$	11.6454	+	20.1704i	0.772931	+	1.33875i	−0.163020	+	0.986623i	$0.552123\pi$
$228$		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	0.158957	−	0.987285i	$-0.449187\pi$
$233$	−9.41166	−	5.43383i	−0.616579	−	0.355982i	−0.775536	+	0.631304i	$0.782520\pi$
$234$		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	$-0.919977\pi$
$239$		−	7.69148i		−	0.497521i	0.968565	−	0.248760i	$-0.0800231\pi$
$240$		0			0
$241$	11.4067	+	19.7571i	0.734773	+	1.27266i	0.954823	+	0.297176i	$0.0960447\pi$
$241$	11.4067	+	19.7571i	0.734773	+	1.27266i	−0.220050	+	0.975489i	$0.570622\pi$
$242$	10.9417	+	1.13064i	0.703362	+	0.0726801i
$243$		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	−0.443789	−	0.896131i	$-0.646366\pi$
$263$	1.79020	−	1.03357i	0.110389	−	0.0637329i	0.554178	+	0.832398i	$0.313033\pi$
$264$		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	−0.689962	−	0.723846i	$-0.742373\pi$
$271$	4.64046	−	8.03751i	0.281888	−	0.488244i	0.971850	+	0.235602i	$0.0757061\pi$
$272$	0.106095			0.00643296
$273$		0			0
$274$			7.58196i			0.458043i
$275$	−4.44383	+	4.00830i	−0.267973	+	0.241709i
$276$		0			0
$277$	4.53015	−	2.61548i	0.272190	−	0.157149i	−0.357692	−	0.933839i	$-0.616436\pi$
$277$	4.53015	−	2.61548i	0.272190	−	0.157149i	0.629883	+	0.776690i	$0.283103\pi$
$278$	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	$0.0657190\pi$
$281$			6.87281i			0.409998i	−0.978762	+	0.204999i	$0.934281\pi$
$282$		0			0
$283$	6.00542	+	10.4017i	0.356985	+	0.618316i	0.987456	−	0.157897i	$-0.0504714\pi$
$283$	6.00542	+	10.4017i	0.356985	+	0.618316i	−0.630471	+	0.776213i	$0.717138\pi$
$284$	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	$-0.364727\pi$
$293$	14.1147			0.824592			0.412296	+	0.911050i	$0.364727\pi$
$294$		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	$-0.294603\pi$
$307$	21.0753			1.20283			0.601417	+	0.798936i	$0.294603\pi$
$308$	−5.45857	−	6.87052i	−0.311031	−	0.391484i
$309$		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
$319$	24.8205	−	5.29851i	1.38968	−	0.296660i
$320$	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	$0.120937\pi$
$337$			13.6161i			0.741718i	−0.928689	+	0.370859i	$0.879063\pi$
$338$	−23.9642	−	13.8357i	−1.30348	−	0.752565i
$339$		0			0
$340$	−0.164249	+	0.0948293i	−0.00890766	+	0.00514284i
$341$	−2.84057	−	3.14922i	−0.153825	−	0.170540i
$342$		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	0.317574	−	0.948234i	$-0.397132\pi$
$347$	24.1708	−	13.9550i	1.29756	−	0.749144i	0.979981	+	0.199090i	$0.0637985\pi$
$348$		0			0
$349$	−27.8147			−1.48888			−0.744442	−	0.667687i	$-0.767285\pi$
$349$	−27.8147			−1.48888			−0.744442	+	0.667687i	$0.767285\pi$
$350$	4.76463	+	0.298378i	0.254680	+	0.0159490i
$351$		0			0
$352$	−2.22141	−	2.46279i	−0.118402	−	0.131267i
$353$	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	−0.0603796	−	0.998175i	$-0.519231\pi$
$359$	−18.0949	−	10.4471i	−0.955015	−	0.551378i	−0.894635	+	0.446798i	$0.852564\pi$
$360$		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	0.945879	−	0.324520i	$-0.105203\pi$
$373$	21.9741	+	12.6868i	1.13778	+	0.656895i	0.191897	+	0.981415i	$0.438536\pi$
$374$	0.344124	−	0.0734611i	0.0177942	−	0.00379858i
$375$		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
$385$	14.5915	+	5.75752i	0.743654	+	0.293430i
$386$	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	0.999994	−	0.00346526i	$-0.00110303\pi$
$409$	10.0511	+	17.4091i	0.496996	+	0.860822i	−0.502998	+	0.864288i	$0.667770\pi$
$410$	−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
$418$	−9.22248	−	10.2246i	−0.451086	−	0.500100i
$419$		−	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	−0.187613	−	0.982243i	$-0.560075\pi$
$431$	11.8175	−	6.82282i	0.569227	−	0.328644i	0.756841	+	0.653599i	$0.226742\pi$
$432$		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	$-0.645441\pi$
$439$	11.6619	−	20.1991i	0.556594	−	0.964049i	0.997778	−	0.0666324i	$-0.0212255\pi$
$440$	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
$451$	0.0222528	+	0.104242i	0.00104784	+	0.00490856i
$452$	−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	0.447325	−	0.894371i	$-0.352377\pi$
$457$	−2.21387	−	1.27818i	−0.103560	−	0.0597906i	−0.550886	+	0.834581i	$0.685710\pi$
$458$	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	$-0.741877\pi$
$461$	−29.5798			−1.37767			−0.688834	+	0.724919i	$0.741877\pi$
$462$		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
$473$	−22.3066	+	4.76185i	−1.02566	+	0.218950i
$474$		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	0.957724	−	0.287689i	$-0.0928869\pi$
$479$	5.02758	+	8.70803i	0.229716	+	0.397880i	−0.728008	+	0.685569i	$0.759554\pi$
$480$		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	$-0.939006\pi$
$491$		−	8.44002i		−	0.380893i	0.981698	−	0.190446i	$-0.0609935\pi$
$492$		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	$-0.523583\pi$
$503$	−3.32018			−0.148039			−0.0740197	+	0.997257i	$0.523583\pi$
$504$		0			0
$505$			13.5377i			0.602419i
$506$	17.6795	+	19.6005i	0.785949	+	0.871348i
$507$		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	−0.610520	−	0.792001i	$-0.709039\pi$
$523$	8.70477	−	15.0771i	0.380633	−	0.659276i	0.991153	+	0.132725i	$0.0423728\pi$
$524$	−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
$539$	1.97639	+	23.1321i	0.0851291	+	0.996370i
$540$		0			0
$541$	−34.0973	−	19.6861i	−1.46596	−	0.846370i	−0.466681	−	0.884426i	$-0.654550\pi$
$541$	−34.0973	−	19.6861i	−1.46596	−	0.846370i	−0.999276	+	0.0380552i	$0.987884\pi$
$542$	−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	$-0.856701\pi$
$547$		−	20.3539i		−	0.870271i	0.900365	−	0.435135i	$-0.143299\pi$
$548$	3.79098	−	6.56617i	0.161943	−	0.280493i
$549$		0			0
$550$	5.85261	−	1.24937i	0.249556	−	0.0532735i
$551$	−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	−0.719614	−	0.694374i	$-0.755681\pi$
$557$	−11.2830	+	6.51425i	−0.478076	+	0.276017i	0.241538	+	0.970391i	$0.422348\pi$
$558$		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	$0.0834034\pi$
$563$	16.7817	+	29.0667i	0.707262	+	1.22501i	−0.258607	+	0.965983i	$0.583263\pi$
$564$		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	0.395919	−	0.918285i	$-0.370426\pi$
$569$	−4.80366	−	2.77340i	−0.201380	−	0.116267i	−0.597299	+	0.802019i	$0.703759\pi$
$570$		0			0
$571$	32.1228	−	18.5461i	1.34430	−	0.776132i	0.356864	−	0.934156i	$-0.383846\pi$
$571$	32.1228	−	18.5461i	1.34430	−	0.776132i	0.987435	+	0.158025i	$0.0505126\pi$
$572$	15.7062	−	14.1669i	0.656710	−	0.592347i
$573$		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
$583$	−1.54525	+	1.39381i	−0.0639978	+	0.0577255i
$584$	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	−0.914038	−	0.405629i	$-0.867053\pi$
$593$	−2.57479	+	4.45967i	−0.105734	+	0.183137i	0.808304	+	0.588766i	$0.200386\pi$
$594$		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	$-0.161707\pi$
$601$	42.8385			1.74742			0.873710	+	0.486447i	$0.161707\pi$
$602$	15.1583	+	10.0648i	0.617806	+	0.410211i
$603$		0			0
$604$	−2.92130	−	1.68661i	−0.118866	−	0.0686273i
$605$	19.5598	+	2.02116i	0.795217	+	0.0821717i
$606$		0			0
$607$	−8.33275	+	14.4328i	−0.338216	+	0.585807i	−0.984097	−	0.177631i	$-0.943157\pi$
$607$	−8.33275	+	14.4328i	−0.338216	+	0.585807i	0.645881	+	0.763438i	$0.276490\pi$
$608$			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	−0.693402	−	0.720551i	$-0.743889\pi$
$613$	−10.3018	+	5.94776i	−0.416087	+	0.240228i	0.277315	+	0.960779i	$0.410555\pi$
$614$	−18.2518	−	10.5377i	−0.736582	−	0.425266i
$615$		0			0
$616$	1.29200	+	8.67933i	0.0520561	+	0.349700i
$617$	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
$649$	27.6676	+	30.6739i	1.08605	+	1.20406i
$650$			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	$0.190615\pi$
$659$			28.9405i			1.12736i	−0.825993	+	0.563681i	$0.809385\pi$
$660$		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	$0.246956\pi$
$673$			36.3353i			1.40062i	−0.713837	+	0.700312i	$0.753044\pi$
$674$	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	−0.991653	−	0.128935i	$-0.958844\pi$
$677$	−9.99570	+	17.3131i	−0.384166	+	0.665395i	0.607487	+	0.794329i	$0.292178\pi$
$678$		0			0
$679$	−41.5885	−	2.60442i	−1.59602	−	0.0999484i
$680$	0.189659			0.00727307
$681$		0			0
$682$	0.885396	+	4.14759i	0.0339036	+	0.158819i
$683$	−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	$0.0115966\pi$
$701$			1.92874i			0.0728474i	−0.999336	+	0.0364237i	$0.988403\pi$
$702$		0			0
$703$	−9.38650	−	16.2579i	−0.354018	−	0.613178i
$704$	0.692408	+	3.24354i	0.0260961	+	0.122246i
$705$		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	−0.854787	−	0.518979i	$-0.826312\pi$
$733$	0.597125	−	1.03425i	0.0220553	−	0.0382009i	0.876842	+	0.480778i	$0.159646\pi$
$734$	−5.34315			−0.197219
$735$		0			0
$736$		−	7.95866i		−	0.293360i
$737$	−26.7758	+	24.1516i	−0.986301	+	0.889636i
$738$		0			0
$739$	10.7713	−	6.21881i	0.396228	−	0.228763i	−0.288627	−	0.957442i	$-0.593199\pi$
$739$	10.7713	−	6.21881i	0.396228	−	0.228763i	0.684855	+	0.728679i	$0.259865\pi$
$740$	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	$-0.885590\pi$
$743$		−	19.1754i		−	0.703479i	0.936098	−	0.351739i	$-0.114410\pi$
$744$		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	−0.618247	−	0.785984i	$-0.712157\pi$
$761$	10.2499	−	17.7533i	0.371558	−	0.643558i	0.989805	+	0.142426i	$0.0454903\pi$
$762$		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	$-0.583195\pi$
$769$	−14.3312			−0.516796			−0.258398	+	0.966039i	$0.583195\pi$
$770$	−9.75788	−	12.2819i	−0.351650	−	0.442610i
$771$		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
$781$	−5.83551	−	27.3361i	−0.208811	−	0.978162i
$782$	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	0.999617	−	0.0276865i	$-0.00881401\pi$
$787$	13.3487	+	23.1207i	0.475831	+	0.824164i	−0.523786	+	0.851850i	$0.675481\pi$
$788$	−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
$803$	0.307869	−	0.277695i	0.0108645	−	0.00979965i
$804$		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	−0.143530	−	0.989646i	$-0.545845\pi$
$809$	18.2536	−	10.5387i	0.641763	−	0.370522i	0.785293	+	0.619124i	$0.212512\pi$
$810$		0			0
$811$	38.7457			1.36055			0.680273	−	0.732959i	$-0.261861\pi$
$811$	38.7457			1.36055			0.680273	+	0.732959i	$0.261861\pi$
$812$	9.00737	+	18.1320i	0.316097	+	0.636310i
$813$		0			0
$814$	−10.0449	−	11.1363i	−0.352073	−	0.390328i
$815$	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	0.979460	−	0.201639i	$-0.0646269\pi$
$821$	37.0933	+	21.4158i	1.29456	+	0.747417i	0.315105	+	0.949057i	$0.397960\pi$
$822$		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	$-0.914538\pi$
$827$		−	15.2572i		−	0.530544i	0.964174	−	0.265272i	$-0.0854618\pi$
$828$		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
$836$	2.87462	+	13.4660i	0.0994207	+	0.465730i
$837$		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
$847$	10.2003	+	27.2572i	0.350486	+	0.936568i
$848$	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	$-0.963259\pi$
$853$	−58.0237			−1.98669			−0.993346	+	0.115168i	$0.963259\pi$
$854$	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	$-0.919070\pi$
$857$	−20.5434	−	35.5821i	−0.701748	−	1.21546i	0.266105	−	0.963944i	$-0.414263\pi$
$858$		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	0.565283	−	0.824897i	$-0.308767\pi$
$877$	3.95476	+	2.28328i	0.133543	+	0.0771009i	−0.431740	+	0.901998i	$0.642100\pi$
$878$	−20.1991	+	11.6619i	−0.681686	+	0.393572i
$879$		0			0
$880$	−3.97106	−	4.40254i	−0.133864	−	0.148410i
$881$		−	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	$-0.561014\pi$
$887$	22.4831	−	38.9419i	0.754909	−	1.30754i	0.945420	−	0.325855i	$-0.105652\pi$
$888$		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
$913$	−8.35438	−	39.1356i	−0.276490	−	1.29520i
$914$	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	0.914257	−	0.405134i	$-0.132775\pi$
$919$	30.9373	+	17.8617i	1.02053	+	0.589203i	0.106272	+	0.994337i	$0.466109\pi$
$920$	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
$935$	0.615166	−	0.131321i	0.0201181	−	0.00429466i
$936$		0			0
$937$	36.2513			1.18428			0.592140	−	0.805835i	$-0.298283\pi$
$937$	36.2513			1.18428			0.592140	+	0.805835i	$0.298283\pi$
$938$	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	$0.0937605\pi$
$941$	22.3898	+	38.7803i	0.729887	+	1.26420i	−0.227044	+	0.973884i	$0.572906\pi$
$942$		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	$-0.875926\pi$
$953$		−	23.4615i		−	0.759991i	0.924988	−	0.379996i	$-0.124074\pi$
$954$		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	$0.373308\pi$
$967$			57.3317i			1.84366i	−0.387589	+	0.921832i	$0.626692\pi$
$968$	4.49171	+	10.0411i	0.144369	+	0.322735i
$969$		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	0.633128	−	0.774047i	$-0.281771\pi$
$997$	−11.1707	−	19.3483i	−0.353781	−	0.612766i	−0.986909	+	0.161281i	$0.948437\pi$
$998$	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.a.901.2		16
3.2	odd	2		462.2.p.a.439.7	yes	16
7.3	odd	6		1386.2.bk.b.703.6		16
11.10	odd	2		1386.2.bk.b.901.6		16
21.2	odd	6		3234.2.e.a.2155.3		16
21.5	even	6		3234.2.e.b.2155.6		16
21.17	even	6		462.2.p.b.241.3	yes	16
33.32	even	2		462.2.p.b.439.3	yes	16
77.10	even	6	inner	1386.2.bk.a.703.2		16
231.65	even	6		3234.2.e.b.2155.11		16
231.131	odd	6		3234.2.e.a.2155.14		16
231.164	odd	6		462.2.p.a.241.7	✓	16

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.54813 - 0.893814i) q^{5} +(0.165362 - 2.64058i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.54813 - 0.893814i) q^{5} +(0.165362 - 2.64058i) q^{7} -1.00000i q^{8} +(0.893814 + 1.54813i) q^{10} +(-0.692408 - 3.24354i) q^{11} +6.37742 q^{13} +(-1.46350 + 2.20413i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.0530476 - 0.0918811i) q^{17} +(-2.07581 + 3.59541i) q^{19} -1.78763i q^{20} +(-1.02213 + 3.15519i) q^{22} +(3.97933 - 6.89240i) q^{23} +(-0.902194 - 1.56265i) q^{25} +(-5.52301 - 3.18871i) q^{26} +(2.36949 - 1.17708i) q^{28} +7.65230i q^{29} +(1.10740 - 0.639360i) q^{31} +(0.866025 - 0.500000i) q^{32} +0.106095i q^{34} +(-2.61619 + 3.94016i) q^{35} +(-2.26092 + 3.91603i) q^{37} +(3.59541 - 2.07581i) q^{38} +(-0.893814 + 1.54813i) q^{40} -0.0321383 q^{41} -6.87723i q^{43} +(2.46279 - 2.22141i) q^{44} +(-6.89240 + 3.97933i) q^{46} +(-8.55805 - 4.94099i) q^{47} +(-6.94531 - 0.873304i) q^{49} +1.80439i q^{50} +(3.18871 + 5.52301i) q^{52} +(-0.313720 - 0.543380i) q^{53} +(-1.82718 + 5.64031i) q^{55} +(-2.64058 - 0.165362i) q^{56} +(3.82615 - 6.62708i) q^{58} +(-10.7863 + 6.22747i) q^{59} +(4.97512 - 8.61716i) q^{61} -1.27872 q^{62} -1.00000 q^{64} +(-9.87308 - 5.70022i) q^{65} +(-5.43609 - 9.41558i) q^{67} +(0.0530476 - 0.0918811i) q^{68} +(4.23576 - 2.10418i) q^{70} +8.42785 q^{71} +(0.0625042 + 0.108260i) q^{73} +(3.91603 - 2.26092i) q^{74} -4.15162 q^{76} +(-8.67933 + 1.29200i) q^{77} +(-8.80673 - 5.08457i) q^{79} +(1.54813 - 0.893814i) q^{80} +(0.0278326 + 0.0160691i) q^{82} +12.0657 q^{83} +0.189659i q^{85} +(-3.43862 + 5.95586i) q^{86} +(-3.24354 + 0.692408i) q^{88} +(4.64198 + 2.68005i) q^{89} +(1.05458 - 16.8401i) q^{91} +7.95866 q^{92} +(4.94099 + 8.55805i) q^{94} +(6.42726 - 3.71078i) q^{95} -15.7498i q^{97} +(5.57816 + 4.22896i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7}+O(q^{10}) \) 16 * q + 8 * q^4 - 12 * q^5 - 6 * q^7	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7} + 2 q^{10} + 4 q^{11} - 8 q^{14} - 8 q^{16} - 10 q^{19} + 2 q^{22} + 4 q^{23} + 10 q^{25} - 12 q^{26} + 6 q^{31} + 8 q^{35} + 14 q^{37} + 12 q^{38} - 2 q^{40} - 32 q^{41} - 4 q^{44} + 18 q^{46} + 24 q^{47} - 6 q^{49} - 14 q^{55} - 4 q^{56} + 28 q^{61} + 8 q^{62} - 16 q^{64} - 72 q^{65} - 16 q^{67} - 30 q^{70} + 56 q^{71} - 44 q^{73} - 24 q^{74} - 20 q^{76} - 32 q^{77} - 30 q^{79} + 12 q^{80} - 12 q^{82} - 8 q^{83} + 12 q^{86} + 4 q^{88} + 36 q^{89} - 8 q^{91} + 8 q^{92} + 14 q^{94} - 72 q^{95} + 40 q^{98}+O(q^{100}) \) 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 - 32 * q^77 - 30 * q^79 + 12 * q^80 - 12 * q^82 - 8 * q^83 + 12 * q^86 + 4 * q^88 + 36 * q^89 - 8 * q^91 + 8 * q^92 + 14 * q^94 - 72 * q^95 + 40 * q^98

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