LMFDB - Embedded newform 1386.2.bk.a.901.3

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			901.3
Root			$0.500000 + 0.0286340i$ of defining polynomial
Character	$\chi$	$=$	1386.901
Dual form			1386.2.bk.a.703.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.725202 - 0.418696i) q^{5} +(2.44037 + 1.02205i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.725202 - 0.418696i) q^{5} +(2.44037 + 1.02205i) q^{7} -1.00000i q^{8} +(0.418696 + 0.725202i) q^{10} +(-2.45951 + 2.22504i) q^{11} -2.59370 q^{13} +(-1.60239 - 2.10531i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.98686 - 5.17339i) q^{17} +(-1.55590 + 2.69491i) q^{19} -0.837391i q^{20} +(3.24252 - 0.697189i) q^{22} +(1.43256 - 2.48126i) q^{23} +(-2.14939 - 3.72285i) q^{25} +(2.24621 + 1.29685i) q^{26} +(0.335059 + 2.62445i) q^{28} -5.38769i q^{29} +(-0.913399 + 0.527351i) q^{31} +(0.866025 - 0.500000i) q^{32} +5.97372i q^{34} +(-1.34183 - 1.76297i) q^{35} +(5.49467 - 9.51705i) q^{37} +(2.69491 - 1.55590i) q^{38} +(-0.418696 + 0.725202i) q^{40} -11.2350 q^{41} -1.27527i q^{43} +(-3.15670 - 1.01748i) q^{44} +(-2.48126 + 1.43256i) q^{46} +(10.6034 + 6.12185i) q^{47} +(4.91081 + 4.98838i) q^{49} +4.29878i q^{50} +(-1.29685 - 2.24621i) q^{52} +(2.58730 + 4.48134i) q^{53} +(2.71526 - 0.583820i) q^{55} +(1.02205 - 2.44037i) q^{56} +(-2.69384 + 4.66587i) q^{58} +(8.38751 - 4.84253i) q^{59} +(2.03524 - 3.52514i) q^{61} +1.05470 q^{62} -1.00000 q^{64} +(1.88096 + 1.08597i) q^{65} +(-6.51916 - 11.2915i) q^{67} +(2.98686 - 5.17339i) q^{68} +(0.280576 + 2.19769i) q^{70} -14.0795 q^{71} +(-4.95659 - 8.58507i) q^{73} +(-9.51705 + 5.49467i) q^{74} -3.11181 q^{76} +(-8.27623 + 2.91617i) q^{77} +(-11.7018 - 6.75603i) q^{79} +(0.725202 - 0.418696i) q^{80} +(9.72978 + 5.61749i) q^{82} +2.99287 q^{83} +5.00234i q^{85} +(-0.637637 + 1.10442i) q^{86} +(2.22504 + 2.45951i) q^{88} +(-7.28049 - 4.20339i) q^{89} +(-6.32960 - 2.65091i) q^{91} +2.86511 q^{92} +(-6.12185 - 10.6034i) q^{94} +(2.25669 - 1.30290i) q^{95} -0.786131i q^{97} +(-1.75869 - 6.77547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.725202	−	0.418696i	−0.324320	−	0.187246i	0.328996	−	0.944331i	$-0.393290\pi$
$5$	−0.725202	−	0.418696i	−0.324320	−	0.187246i	−0.653317	+	0.757085i	$0.726623\pi$
$6$		0			0
$7$	2.44037	+	1.02205i	0.922373	+	0.386300i
$7$	2.44037	+	1.02205i	0.922373	+	0.386300i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	0.418696	+	0.725202i	0.132403	+	0.229329i
$11$	−2.45951	+	2.22504i	−0.741570	+	0.670876i
$11$	−2.45951	+	2.22504i	−0.741570	+	0.670876i
$12$		0			0
$13$	−2.59370			−0.719364			−0.359682	−	0.933075i	$-0.617115\pi$
$13$	−2.59370			−0.719364			−0.359682	+	0.933075i	$0.617115\pi$
$14$	−1.60239	−	2.10531i	−0.428258	−	0.562668i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.98686	−	5.17339i	−0.724420	−	1.25473i	−0.959212	−	0.282687i	$-0.908774\pi$
$17$	−2.98686	−	5.17339i	−0.724420	−	1.25473i	0.234792	−	0.972046i	$-0.424559\pi$
$18$		0			0
$19$	−1.55590	+	2.69491i	−0.356949	+	0.618254i	−0.987449	−	0.157935i	$-0.949516\pi$
$19$	−1.55590	+	2.69491i	−0.356949	+	0.618254i	0.630501	+	0.776189i	$0.282850\pi$
$20$		−	0.837391i		−	0.187246i
$21$		0			0
$22$	3.24252	−	0.697189i	0.691307	−	0.148641i
$23$	1.43256	−	2.48126i	0.298709	−	0.517379i	−0.677132	−	0.735862i	$-0.736777\pi$
$23$	1.43256	−	2.48126i	0.298709	−	0.517379i	0.975841	+	0.218483i	$0.0701107\pi$
$24$		0			0
$25$	−2.14939	−	3.72285i	−0.429878	−	0.744570i
$26$	2.24621	+	1.29685i	0.440519	+	0.254334i
$27$		0			0
$28$	0.335059	+	2.62445i	0.0633203	+	0.495974i
$29$		−	5.38769i		−	1.00047i	−0.865890	−	0.500234i	$-0.833247\pi$
$29$		−	5.38769i		−	1.00047i	0.865890	−	0.500234i	$-0.166753\pi$
$30$		0			0
$31$	−0.913399	+	0.527351i	−0.164051	+	0.0947151i	−0.579778	−	0.814775i	$-0.696861\pi$
$31$	−0.913399	+	0.527351i	−0.164051	+	0.0947151i	0.415727	+	0.909490i	$0.363527\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$			5.97372i			1.02448i
$35$	−1.34183	−	1.76297i	−0.226811	−	0.297996i
$36$		0			0
$37$	5.49467	−	9.51705i	0.903319	−	1.56459i	0.0801603	−	0.996782i	$-0.474457\pi$
$37$	5.49467	−	9.51705i	0.903319	−	1.56459i	0.823158	−	0.567812i	$-0.192210\pi$
$38$	2.69491	−	1.55590i	0.437171	−	0.252401i
$39$		0			0
$40$	−0.418696	+	0.725202i	−0.0662016	+	0.114665i
$41$	−11.2350			−1.75461			−0.877304	−	0.479934i	$-0.840661\pi$
$41$	−11.2350			−1.75461			−0.877304	+	0.479934i	$0.840661\pi$
$42$		0			0
$43$		−	1.27527i		−	0.194478i	−0.995261	−	0.0972388i	$-0.968999\pi$
$43$		−	1.27527i		−	0.194478i	0.995261	−	0.0972388i	$-0.0310010\pi$
$44$	−3.15670	−	1.01748i	−0.475890	−	0.153390i
$45$		0			0
$46$	−2.48126	+	1.43256i	−0.365842	+	0.211219i
$47$	10.6034	+	6.12185i	1.54666	+	0.892964i	0.998394	+	0.0566600i	$0.0180451\pi$
$47$	10.6034	+	6.12185i	1.54666	+	0.892964i	0.548266	+	0.836304i	$0.315288\pi$
$48$		0			0
$49$	4.91081	+	4.98838i	0.701544	+	0.712626i
$50$			4.29878i			0.607939i
$51$		0			0
$52$	−1.29685	−	2.24621i	−0.179841	−	0.311494i
$53$	2.58730	+	4.48134i	0.355394	+	0.615560i	0.987185	−	0.159579i	$-0.0510135\pi$
$53$	2.58730	+	4.48134i	0.355394	+	0.615560i	−0.631792	+	0.775138i	$0.717680\pi$
$54$		0			0
$55$	2.71526	−	0.583820i	0.366125	−	0.0787223i
$56$	1.02205	−	2.44037i	0.136578	−	0.326108i
$57$		0			0
$58$	−2.69384	+	4.66587i	−0.353719	+	0.612659i
$59$	8.38751	−	4.84253i	1.09196	−	0.630444i	0.157863	−	0.987461i	$-0.449540\pi$
$59$	8.38751	−	4.84253i	1.09196	−	0.630444i	0.934098	+	0.357017i	$0.116206\pi$
$60$		0			0
$61$	2.03524	−	3.52514i	0.260586	−	0.451348i	−0.705812	−	0.708399i	$-0.749418\pi$
$61$	2.03524	−	3.52514i	0.260586	−	0.451348i	0.966398	+	0.257051i	$0.0827509\pi$
$62$	1.05470			0.133947
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.88096	+	1.08597i	0.233304	+	0.134698i
$66$		0			0
$67$	−6.51916	−	11.2915i	−0.796442	−	1.37948i	−0.921920	−	0.387381i	$-0.873380\pi$
$67$	−6.51916	−	11.2915i	−0.796442	−	1.37948i	0.125478	−	0.992096i	$-0.459954\pi$
$68$	2.98686	−	5.17339i	0.362210	−	0.627366i
$69$		0			0
$70$	0.280576	+	2.19769i	0.0335352	+	0.262674i
$71$	−14.0795			−1.67093			−0.835467	−	0.549541i	$-0.814803\pi$
$71$	−14.0795			−1.67093			−0.835467	+	0.549541i	$0.814803\pi$
$72$		0			0
$73$	−4.95659	−	8.58507i	−0.580125	−	1.00481i	−0.995464	−	0.0951394i	$-0.969670\pi$
$73$	−4.95659	−	8.58507i	−0.580125	−	1.00481i	0.415339	−	0.909667i	$-0.363663\pi$
$74$	−9.51705	+	5.49467i	−1.10633	+	0.638743i
$75$		0			0
$76$	−3.11181			−0.356949
$77$	−8.27623	+	2.91617i	−0.943164	+	0.332329i
$78$		0			0
$79$	−11.7018	−	6.75603i	−1.31655	−	0.760113i	−0.333381	−	0.942792i	$-0.608190\pi$
$79$	−11.7018	−	6.75603i	−1.31655	−	0.760113i	−0.983173	+	0.182680i	$0.941523\pi$
$80$	0.725202	−	0.418696i	0.0810801	−	0.0468116i
$81$		0			0
$82$	9.72978	+	5.61749i	1.07447	+	0.620348i
$83$	2.99287			0.328510			0.164255	−	0.986418i	$-0.447478\pi$
$83$	2.99287			0.328510			0.164255	+	0.986418i	$0.447478\pi$
$84$		0			0
$85$			5.00234i			0.542580i
$86$	−0.637637	+	1.10442i	−0.0687582	+	0.119093i
$87$		0			0
$88$	2.22504	+	2.45951i	0.237190	+	0.262185i
$89$	−7.28049	−	4.20339i	−0.771730	−	0.445559i	0.0617614	−	0.998091i	$-0.480328\pi$
$89$	−7.28049	−	4.20339i	−0.771730	−	0.445559i	−0.833491	+	0.552532i	$0.813662\pi$
$90$		0			0
$91$	−6.32960	−	2.65091i	−0.663522	−	0.277891i
$92$	2.86511			0.298709
$93$		0			0
$94$	−6.12185	−	10.6034i	−0.631421	−	1.09365i
$95$	2.25669	−	1.30290i	0.231532	−	0.133675i
$96$		0			0
$97$		−	0.786131i		−	0.0798195i	−0.999203	−	0.0399097i	$-0.987293\pi$
$97$		−	0.786131i		−	0.0798195i	0.999203	−	0.0399097i	$-0.0127070\pi$
$98$	−1.75869	−	6.77547i	−0.177655	−	0.684426i
$99$		0			0
$100$	2.14939	−	3.72285i	0.214939	−	0.372285i
$101$	3.36113	+	5.82166i	0.334445	+	0.579276i	0.983378	−	0.181569i	$-0.0581177\pi$
$101$	3.36113	+	5.82166i	0.334445	+	0.579276i	−0.648933	+	0.760846i	$0.724784\pi$
$102$		0			0
$103$	−3.52596	−	2.03571i	−0.347423	−	0.200585i	0.316127	−	0.948717i	$-0.397618\pi$
$103$	−3.52596	−	2.03571i	−0.347423	−	0.200585i	−0.663550	+	0.748132i	$0.730951\pi$
$104$			2.59370i			0.254334i
$105$		0			0
$106$		−	5.17461i		−	0.502602i
$107$	0.209477	+	0.120942i	0.0202509	+	0.0116919i	0.510091	−	0.860120i	$-0.329612\pi$
$107$	0.209477	+	0.120942i	0.0202509	+	0.0116919i	−0.489840	+	0.871812i	$0.662945\pi$
$108$		0			0
$109$	15.1773	−	8.76259i	1.45372	−	0.839304i	0.455028	−	0.890477i	$-0.349629\pi$
$109$	15.1773	−	8.76259i	1.45372	−	0.839304i	0.998690	+	0.0511733i	$0.0162961\pi$
$110$	−2.64339	−	0.852026i	−0.252038	−	0.0812375i
$111$		0			0
$112$	−2.10531	+	1.60239i	−0.198933	+	0.151412i
$113$	−8.08949			−0.760995			−0.380498	−	0.924782i	$-0.624247\pi$
$113$	−8.08949			−0.760995			−0.380498	+	0.924782i	$0.624247\pi$
$114$		0			0
$115$	−2.07779	+	1.19961i	−0.193755	+	0.111864i
$116$	4.66587	−	2.69384i	0.433216	−	0.250117i
$117$		0			0
$118$	−9.68506			−0.891582
$119$	−2.00155	−	15.6777i	−0.183482	−	1.43717i
$120$		0			0
$121$	1.09837	−	10.9450i	0.0998517	−	0.995002i
$122$	−3.52514	+	2.03524i	−0.319151	+	0.184262i
$123$		0			0
$124$	−0.913399	−	0.527351i	−0.0820257	−	0.0473575i
$125$			7.78672i			0.696465i
$126$		0			0
$127$			12.1313i			1.07648i	0.842791	+	0.538241i	$0.180911\pi$
$127$			12.1313i			1.07648i	−0.842791	+	0.538241i	$0.819089\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−1.08597	−	1.88096i	−0.0952461	−	0.164971i
$131$	−1.02224	+	1.77058i	−0.0893139	+	0.154696i	−0.907221	−	0.420654i	$-0.861801\pi$
$131$	−1.02224	+	1.77058i	−0.0893139	+	0.154696i	0.817907	+	0.575350i	$0.195134\pi$
$132$		0			0
$133$	−6.55132	+	4.98635i	−0.568072	+	0.432371i
$134$			13.0383i			1.12634i
$135$		0			0
$136$	−5.17339	+	2.98686i	−0.443615	+	0.256121i
$137$	−6.60556	−	11.4412i	−0.564351	−	0.977485i	−0.997110	−	0.0759750i	$-0.975793\pi$
$137$	−6.60556	−	11.4412i	−0.564351	−	0.977485i	0.432759	−	0.901510i	$-0.357540\pi$
$138$		0			0
$139$	−6.16293			−0.522733			−0.261367	−	0.965240i	$-0.584173\pi$
$139$	−6.16293			−0.522733			−0.261367	+	0.965240i	$0.584173\pi$
$140$	0.855860	−	2.04354i	0.0723334	−	0.172711i
$141$		0			0
$142$	12.1932	+	7.03977i	1.02323	+	0.590764i
$143$	6.37924	−	5.77110i	0.533459	−	0.482604i
$144$		0			0
$145$	−2.25580	+	3.90716i	−0.187334	+	0.324472i
$146$			9.91318i			0.820421i
$147$		0			0
$148$	10.9893			0.903319
$149$	3.80788	+	2.19848i	0.311954	+	0.180107i	0.647800	−	0.761810i	$-0.275689\pi$
$149$	3.80788	+	2.19848i	0.311954	+	0.180107i	−0.335847	+	0.941917i	$0.609022\pi$
$150$		0			0
$151$	8.86874	−	5.12037i	0.721728	−	0.416690i	−0.0936604	−	0.995604i	$-0.529857\pi$
$151$	8.86874	−	5.12037i	0.721728	−	0.416690i	0.815388	+	0.578914i	$0.196523\pi$
$152$	2.69491	+	1.55590i	0.218586	+	0.126200i
$153$		0			0
$154$	8.62551	+	1.61263i	0.695063	+	0.129950i
$155$	0.883199			0.0709402
$156$		0			0
$157$	−13.8444	+	7.99304i	−1.10490	+	0.637914i	−0.937504	−	0.347975i	$-0.886869\pi$
$157$	−13.8444	+	7.99304i	−1.10490	+	0.637914i	−0.167396	+	0.985890i	$0.553536\pi$
$158$	6.75603	+	11.7018i	0.537481	+	0.930944i
$159$		0			0
$160$	−0.837391			−0.0662016
$161$	6.03195	−	4.59104i	0.475385	−	0.361825i
$162$		0			0
$163$	0.261926	−	0.453669i	0.0205156	−	0.0355341i	−0.855585	−	0.517662i	$-0.826803\pi$
$163$	0.261926	−	0.453669i	0.0205156	−	0.0355341i	0.876101	+	0.482128i	$0.160136\pi$
$164$	−5.61749	−	9.72978i	−0.438652	−	0.759768i
$165$		0			0
$166$	−2.59190	−	1.49643i	−0.201170	−	0.116146i
$167$	−17.0544			−1.31971			−0.659855	−	0.751393i	$-0.729382\pi$
$167$	−17.0544			−1.31971			−0.659855	+	0.751393i	$0.729382\pi$
$168$		0			0
$169$	−6.27269			−0.482515
$170$	2.50117	−	4.33216i	0.191831	−	0.332261i
$171$		0			0
$172$	1.10442	−	0.637637i	0.0842112	−	0.0486194i
$173$	3.61831	−	6.26710i	0.275095	−	0.476479i	−0.695064	−	0.718948i	$-0.744624\pi$
$173$	3.61831	−	6.26710i	0.275095	−	0.476479i	0.970159	+	0.242469i	$0.0779573\pi$
$174$		0			0
$175$	−1.44035	−	11.2819i	−0.108880	−	0.852833i
$176$	−0.697189	−	3.24252i	−0.0525526	−	0.244414i
$177$		0			0
$178$	4.20339	+	7.28049i	0.315057	+	0.545696i
$179$	4.03318	+	6.98568i	0.301454	+	0.522134i	0.976466	−	0.215673i	$-0.0691946\pi$
$179$	4.03318	+	6.98568i	0.301454	+	0.522134i	−0.675011	+	0.737807i	$0.735861\pi$
$180$		0			0
$181$			5.61056i			0.417030i	0.978019	+	0.208515i	$0.0668630\pi$
$181$			5.61056i			0.417030i	−0.978019	+	0.208515i	$0.933137\pi$
$182$	4.15614	+	5.46055i	0.308074	+	0.404763i
$183$		0			0
$184$	−2.48126	−	1.43256i	−0.182921	−	0.105609i
$185$	−7.96950	+	4.60119i	−0.585929	+	0.338286i
$186$		0			0
$187$	18.8572	+	6.07812i	1.37898	+	0.444476i
$188$			12.2437i			0.892964i
$189$		0			0
$190$	−2.60580			−0.189045
$191$	5.89206	−	10.2053i	0.426334	−	0.738433i	−0.570210	−	0.821499i	$-0.693138\pi$
$191$	5.89206	−	10.2053i	0.426334	−	0.738433i	0.996544	+	0.0830666i	$0.0264714\pi$
$192$		0			0
$193$	−15.6730	+	9.04882i	−1.12817	+	0.651348i	−0.943474	−	0.331448i	$-0.892463\pi$
$193$	−15.6730	+	9.04882i	−1.12817	+	0.651348i	−0.184694	+	0.982796i	$0.559130\pi$
$194$	−0.393065	+	0.680809i	−0.0282204	+	0.0488792i
$195$		0			0
$196$	−1.86466	+	6.74708i	−0.133190	+	0.481934i
$197$			6.23110i			0.443948i	0.975053	+	0.221974i	$0.0712500\pi$
$197$			6.23110i			0.443948i	−0.975053	+	0.221974i	$0.928750\pi$
$198$		0			0
$199$	−15.8196	+	9.13344i	−1.12142	+	0.647453i	−0.941763	−	0.336276i	$-0.890832\pi$
$199$	−15.8196	+	9.13344i	−1.12142	+	0.647453i	−0.179658	+	0.983729i	$0.557499\pi$
$200$	−3.72285	+	2.14939i	−0.263245	+	0.151985i
$201$		0			0
$202$		−	6.72227i		−	0.472977i
$203$	5.50651	−	13.1479i	0.386481	−	0.922805i
$204$		0			0
$205$	8.14763	+	4.70404i	0.569055	+	0.328544i
$206$	2.03571	+	3.52596i	0.141835	+	0.245665i
$207$		0			0
$208$	1.29685	−	2.24621i	0.0899205	−	0.155747i
$209$	−2.16952	−	10.0901i	−0.150069	−	0.697947i
$210$		0			0
$211$			10.2446i			0.705269i	0.935761	+	0.352635i	$0.114714\pi$
$211$			10.2446i			0.705269i	−0.935761	+	0.352635i	$0.885286\pi$
$212$	−2.58730	+	4.48134i	−0.177697	+	0.307780i
$213$		0			0
$214$	−0.120942	−	0.209477i	−0.00826740	−	0.0143196i
$215$	−0.533952	+	0.924832i	−0.0364152	+	0.0630730i
$216$		0			0
$217$	−2.76801	+	0.353388i	−0.187905	+	0.0239895i
$218$	−17.5252			−1.18696
$219$		0			0
$220$	1.86323	+	2.05957i	0.125619	+	0.138856i
$221$	7.74703	+	13.4183i	0.521122	+	0.902610i
$222$		0			0
$223$		−	15.6665i		−	1.04911i	−0.851377	−	0.524554i	$-0.824232\pi$
$223$		−	15.6665i		−	1.04911i	0.851377	−	0.524554i	$-0.175768\pi$
$224$	2.62445	−	0.335059i	0.175353	−	0.0223871i
$225$		0			0
$226$	7.00571	+	4.04475i	0.466013	+	0.269053i
$227$	7.86025	+	13.6143i	0.521703	+	0.903616i	0.999681	+	0.0252443i	$0.00803637\pi$
$227$	7.86025	+	13.6143i	0.521703	+	0.903616i	−0.477978	+	0.878372i	$0.658630\pi$
$228$		0			0
$229$	−2.16867	−	1.25208i	−0.143310	−	0.0827400i	0.426631	−	0.904426i	$-0.359700\pi$
$229$	−2.16867	−	1.25208i	−0.143310	−	0.0827400i	−0.569940	+	0.821686i	$0.693034\pi$
$230$	2.39922			0.158200
$231$		0			0
$232$	−5.38769			−0.353719
$233$	−0.0479052	−	0.0276581i	−0.00313837	−	0.00181194i	0.498430	−	0.866930i	$-0.333910\pi$
$233$	−0.0479052	−	0.0276581i	−0.00313837	−	0.00181194i	−0.501568	+	0.865118i	$0.667243\pi$
$234$		0			0
$235$	−5.12639	−	8.87916i	−0.334409	−	0.579213i
$236$	8.38751	+	4.84253i	0.545981	+	0.315222i
$237$		0			0
$238$	−6.10547	+	14.5781i	−0.395759	+	0.944957i
$239$		−	5.74465i		−	0.371591i	−0.982588	−	0.185795i	$-0.940514\pi$
$239$		−	5.74465i		−	0.371591i	0.982588	−	0.185795i	$-0.0594861\pi$
$240$		0			0
$241$	3.67123	+	6.35875i	0.236484	+	0.409603i	0.959703	−	0.281016i	$-0.0906714\pi$
$241$	3.67123	+	6.35875i	0.236484	+	0.409603i	−0.723219	+	0.690619i	$0.757338\pi$
$242$	−6.42373	+	8.92949i	−0.412933	+	0.574009i
$243$		0			0
$244$	4.07048			0.260586
$245$	−1.47271	−	5.67372i	−0.0940883	−	0.362481i
$246$		0			0
$247$	4.03556	−	6.98979i	0.256776	−	0.444750i
$248$	0.527351	+	0.913399i	0.0334868	+	0.0580009i
$249$		0			0
$250$	3.89336	−	6.74349i	0.246238	−	0.426496i
$251$			4.20803i			0.265608i	0.991142	+	0.132804i	$0.0423981\pi$
$251$			4.20803i			0.265608i	−0.991142	+	0.132804i	$0.957602\pi$
$252$		0			0
$253$	1.99753	+	9.29019i	0.125583	+	0.584069i
$254$	6.06567	−	10.5060i	0.380594	−	0.659208i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	21.3446	+	12.3233i	1.33144	+	0.768706i	0.985520	−	0.169559i	$-0.0542342\pi$
$257$	21.3446	+	12.3233i	1.33144	+	0.768706i	0.345918	+	0.938265i	$0.387568\pi$
$258$		0			0
$259$	23.1360	−	17.6093i	1.43760	−	1.09419i
$260$			2.17195i			0.134698i
$261$		0			0
$262$	1.77058	−	1.02224i	0.109387	−	0.0631545i
$263$	26.3130	−	15.1918i	1.62253	−	0.936768i	0.636290	−	0.771450i	$-0.280468\pi$
$263$	26.3130	−	15.1918i	1.62253	−	0.936768i	0.986240	−	0.165318i	$-0.0528651\pi$
$264$		0			0
$265$		−	4.33317i		−	0.266185i
$266$	8.16678	−	1.04264i	0.500738	−	0.0639284i
$267$		0			0
$268$	6.51916	−	11.2915i	0.398221	−	0.689739i
$269$	−17.2977	+	9.98686i	−1.05466	+	0.608910i	−0.923951	−	0.382511i	$-0.875059\pi$
$269$	−17.2977	+	9.98686i	−1.05466	+	0.608910i	−0.130711	+	0.991420i	$0.541726\pi$
$270$		0			0
$271$	0.807639	−	1.39887i	0.0490606	−	0.0849754i	−0.840452	−	0.541886i	$-0.817711\pi$
$271$	0.807639	−	1.39887i	0.0490606	−	0.0849754i	0.889513	+	0.456910i	$0.151044\pi$
$272$	5.97372			0.362210
$273$		0			0
$274$			13.2111i			0.798113i
$275$	13.5699	+	4.37390i	0.818298	+	0.263756i
$276$		0			0
$277$	4.48663	−	2.59035i	0.269575	−	0.155639i	−0.359119	−	0.933292i	$-0.616923\pi$
$277$	4.48663	−	2.59035i	0.269575	−	0.155639i	0.628695	+	0.777652i	$0.283590\pi$
$278$	5.33726	+	3.08147i	0.320107	+	0.184814i
$279$		0			0
$280$	−1.76297	+	1.34183i	−0.105358	+	0.0801898i
$281$		−	25.1883i		−	1.50261i	−0.659956	−	0.751304i	$-0.729425\pi$
$281$		−	25.1883i		−	1.50261i	0.659956	−	0.751304i	$-0.270575\pi$
$282$		0			0
$283$	11.5167	+	19.9475i	0.684598	+	1.18576i	0.973563	+	0.228419i	$0.0733556\pi$
$283$	11.5167	+	19.9475i	0.684598	+	1.18576i	−0.288965	+	0.957340i	$0.593311\pi$
$284$	−7.03977	−	12.1932i	−0.417733	−	0.723536i
$285$		0			0
$286$	−8.41014	+	1.80830i	−0.497302	+	0.106927i
$287$	−27.4175	−	11.4828i	−1.61840	−	0.677806i
$288$		0			0
$289$	−9.34267	+	16.1820i	−0.549569	+	0.951881i
$290$	3.90716	−	2.25580i	0.229437	−	0.132465i
$291$		0			0
$292$	4.95659	−	8.58507i	0.290063	−	0.502403i
$293$	−4.18076			−0.244242			−0.122121	−	0.992515i	$-0.538970\pi$
$293$	−4.18076			−0.244242			−0.122121	+	0.992515i	$0.538970\pi$
$294$		0			0
$295$	−8.11019			−0.472194
$296$	−9.51705	−	5.49467i	−0.553167	−	0.319371i
$297$		0			0
$298$	−2.19848	−	3.80788i	−0.127355	−	0.220585i
$299$	−3.71563	+	6.43566i	−0.214880	+	0.372184i
$300$		0			0
$301$	1.30340	−	3.11214i	0.0751267	−	0.179381i
$302$	−10.2407			−0.589288
$303$		0			0
$304$	−1.55590	−	2.69491i	−0.0892372	−	0.154563i
$305$	−2.95192	+	1.70429i	−0.169027	+	0.0975876i
$306$		0			0
$307$	−10.0657			−0.574478			−0.287239	−	0.957859i	$-0.592737\pi$
$307$	−10.0657			−0.574478			−0.287239	+	0.957859i	$0.592737\pi$
$308$	−6.66359	−	5.70934i	−0.379694	−	0.325320i
$309$		0			0
$310$	−0.764873	−	0.441599i	−0.0434418	−	0.0250812i
$311$	−1.23817	+	0.714858i	−0.0702102	+	0.0405359i	−0.534694	−	0.845046i	$-0.679573\pi$
$311$	−1.23817	+	0.714858i	−0.0702102	+	0.0405359i	0.464484	+	0.885582i	$0.346240\pi$
$312$		0			0
$313$	26.3211	+	15.1965i	1.48776	+	0.858958i	0.999902	−	0.0139662i	$-0.00444572\pi$
$313$	26.3211	+	15.1965i	1.48776	+	0.858958i	0.487856	+	0.872924i	$0.337779\pi$
$314$	15.9861			0.902147
$315$		0			0
$316$		−	13.5121i		−	0.760113i
$317$	5.42610	−	9.39829i	0.304760	−	0.527860i	−0.672448	−	0.740145i	$-0.734757\pi$
$317$	5.42610	−	9.39829i	0.304760	−	0.527860i	0.977208	+	0.212284i	$0.0680903\pi$
$318$		0			0
$319$	11.9878	+	13.2511i	0.671190	+	0.741917i
$320$	0.725202	+	0.418696i	0.0405400	+	0.0234058i
$321$		0			0
$322$	−7.51935	+	0.959984i	−0.419037	+	0.0534978i
$323$	18.5891			1.03432
$324$		0			0
$325$	5.57488	+	9.65597i	0.309239	+	0.535617i
$326$	−0.453669	+	0.261926i	−0.0251264	+	0.0145067i
$327$		0			0
$328$			11.2350i			0.620348i
$329$	19.6193	+	25.7768i	1.08164	+	1.42112i
$330$		0			0
$331$	6.45747	−	11.1847i	0.354935	−	0.614765i	−0.632172	−	0.774828i	$-0.717836\pi$
$331$	6.45747	−	11.1847i	0.354935	−	0.614765i	0.987107	+	0.160063i	$0.0511697\pi$
$332$	1.49643	+	2.59190i	0.0821274	+	0.142249i
$333$		0			0
$334$	14.7695	+	8.52720i	0.808154	+	0.466588i
$335$			10.9182i			0.596523i
$336$		0			0
$337$			16.4809i			0.897772i	0.893589	+	0.448886i	$0.148179\pi$
$337$			16.4809i			0.897772i	−0.893589	+	0.448886i	$0.851821\pi$
$338$	5.43231	+	3.13635i	0.295479	+	0.170595i
$339$		0			0
$340$	−4.33216	+	2.50117i	−0.234944	+	0.135645i
$341$	1.07313	−	3.32938i	0.0581135	−	0.180296i
$342$		0			0
$343$	6.88579	+	17.1926i	0.371798	+	0.928314i
$344$	−1.27527			−0.0687582
$345$		0			0
$346$	−6.26710	+	3.61831i	−0.336922	+	0.194522i
$347$	9.92748	−	5.73163i	0.532935	−	0.307690i	−0.209276	−	0.977857i	$-0.567111\pi$
$347$	9.92748	−	5.73163i	0.532935	−	0.307690i	0.742211	+	0.670166i	$0.233777\pi$
$348$		0			0
$349$	20.9561			1.12176			0.560878	−	0.827899i	$-0.310464\pi$
$349$	20.9561			1.12176			0.560878	+	0.827899i	$0.310464\pi$
$350$	−4.39358	+	10.4906i	−0.234847	+	0.560746i
$351$		0			0
$352$	−1.01748	+	3.15670i	−0.0542316	+	0.168253i
$353$	−17.2530	+	9.96104i	−0.918286	+	0.530173i	−0.883088	−	0.469208i	$-0.844540\pi$
$353$	−17.2530	+	9.96104i	−0.918286	+	0.530173i	−0.0351983	+	0.999380i	$0.511206\pi$
$354$		0			0
$355$	10.2105	+	5.89504i	0.541918	+	0.312876i
$356$		−	8.40678i		−	0.445559i
$357$		0			0
$358$		−	8.06636i		−	0.426321i
$359$	−3.38989	−	1.95715i	−0.178912	−	0.103295i	0.407870	−	0.913040i	$-0.366272\pi$
$359$	−3.38989	−	1.95715i	−0.178912	−	0.103295i	−0.586781	+	0.809746i	$0.699605\pi$
$360$		0			0
$361$	4.65832	+	8.06845i	0.245175	+	0.424655i
$362$	2.80528	−	4.85889i	0.147442	−	0.255378i
$363$		0			0
$364$	−0.869045	−	6.80705i	−0.0455504	−	0.356786i
$365$			8.30121i			0.434505i
$366$		0			0
$367$	10.4720	−	6.04600i	0.546633	−	0.315599i	−0.201130	−	0.979565i	$-0.564461\pi$
$367$	10.4720	−	6.04600i	0.546633	−	0.315599i	0.747763	+	0.663966i	$0.231128\pi$
$368$	1.43256	+	2.48126i	0.0746772	+	0.129345i
$369$		0			0
$370$	9.20238			0.478409
$371$	1.73380	+	13.5805i	0.0900145	+	0.705064i
$372$		0			0
$373$	−15.3231	−	8.84681i	−0.793401	−	0.458070i	0.0477575	−	0.998859i	$-0.484793\pi$
$373$	−15.3231	−	8.84681i	−0.793401	−	0.458070i	−0.841158	+	0.540789i	$0.818126\pi$
$374$	−13.2918	−	14.6924i	−0.687302	−	0.759727i
$375$		0			0
$376$	6.12185	−	10.6034i	0.315711	−	0.546827i
$377$			13.9741i			0.719701i
$378$		0			0
$379$	19.6577			1.00975			0.504874	−	0.863193i	$-0.331539\pi$
$379$	19.6577			1.00975			0.504874	+	0.863193i	$0.331539\pi$
$380$	2.25669	+	1.30290i	0.115766	+	0.0668374i
$381$		0			0
$382$	−10.2053	+	5.89206i	−0.522151	+	0.301464i
$383$	−1.18944	−	0.686725i	−0.0607777	−	0.0350900i	0.469303	−	0.883037i	$-0.344505\pi$
$383$	−1.18944	−	0.686725i	−0.0607777	−	0.0350900i	−0.530081	+	0.847947i	$0.677838\pi$
$384$		0			0
$385$	7.22293	+	1.35040i	0.368114	+	0.0688230i
$386$	18.0976			0.921145
$387$		0			0
$388$	0.680809	−	0.393065i	0.0345628	−	0.0199549i
$389$	15.6896	+	27.1752i	0.795496	+	1.37784i	0.922524	+	0.385941i	$0.126123\pi$
$389$	15.6896	+	27.1752i	0.795496	+	1.37784i	−0.127027	+	0.991899i	$0.540544\pi$
$390$		0			0
$391$	−17.1154			−0.865562
$392$	4.98838	−	4.91081i	0.251951	−	0.248033i
$393$		0			0
$394$	3.11555	−	5.39629i	0.156959	−	0.271861i
$395$	5.65744	+	9.79897i	0.284657	+	0.493040i
$396$		0			0
$397$	−30.5464	−	17.6360i	−1.53308	−	0.885123i	−0.999218	−	0.0395508i	$-0.987407\pi$
$397$	−30.5464	−	17.6360i	−1.53308	−	0.885123i	−0.533861	−	0.845572i	$-0.679259\pi$
$398$	18.2669			0.915636
$399$		0			0
$400$	4.29878			0.214939
$401$	4.48309	−	7.76494i	0.223875	−	0.387763i	−0.732106	−	0.681190i	$-0.761463\pi$
$401$	4.48309	−	7.76494i	0.223875	−	0.387763i	0.955981	+	0.293428i	$0.0947960\pi$
$402$		0			0
$403$	2.36909	−	1.36779i	0.118013	−	0.0681347i
$404$	−3.36113	+	5.82166i	−0.167223	+	0.289638i
$405$		0			0
$406$	−11.3428	+	8.63320i	−0.562931	+	0.428459i
$407$	7.66165	+	35.6332i	0.379774	+	1.76627i
$408$		0			0
$409$	−17.9762	−	31.1357i	−0.888867	−	1.53956i	−0.841217	−	0.540698i	$-0.818160\pi$
$409$	−17.9762	−	31.1357i	−0.888867	−	1.53956i	−0.0476498	−	0.998864i	$-0.515173\pi$
$410$	−4.70404	−	8.14763i	−0.232316	−	0.402383i
$411$		0			0
$412$		−	4.07143i		−	0.200585i
$413$	25.4180	−	3.24507i	1.25074	−	0.159680i
$414$		0			0
$415$	−2.17043	−	1.25310i	−0.106542	−	0.0615123i
$416$	−2.24621	+	1.29685i	−0.110130	+	0.0635834i
$417$		0			0
$418$	−3.16619	+	9.82304i	−0.154863	+	0.480461i
$419$		−	0.724634i		−	0.0354007i	−0.999843	−	0.0177004i	$-0.994366\pi$
$419$		−	0.724634i		−	0.0354007i	0.999843	−	0.0177004i	$-0.00563449\pi$
$420$		0			0
$421$	3.71423			0.181021			0.0905103	−	0.995896i	$-0.471150\pi$
$421$	3.71423			0.181021			0.0905103	+	0.995896i	$0.471150\pi$
$422$	5.12231	−	8.87211i	0.249350	−	0.431887i
$423$		0			0
$424$	4.48134	−	2.58730i	0.217633	−	0.125651i
$425$	−12.8398	+	22.2393i	−0.622824	+	1.07876i
$426$		0			0
$427$	8.56963	−	6.52252i	0.414714	−	0.315647i
$428$			0.241883i			0.0116919i
$429$		0			0
$430$	0.924832	−	0.533952i	0.0445994	−	0.0257495i
$431$	3.53752	−	2.04239i	0.170396	−	0.0983784i	−0.412376	−	0.911014i	$-0.635301\pi$
$431$	3.53752	−	2.04239i	0.170396	−	0.0983784i	0.582773	+	0.812635i	$0.301968\pi$
$432$		0			0
$433$			30.3109i			1.45665i	0.685232	+	0.728325i	$0.259701\pi$
$433$			30.3109i			1.45665i	−0.685232	+	0.728325i	$0.740299\pi$
$434$	2.57386	+	1.07796i	0.123549	+	0.0517439i
$435$		0			0
$436$	15.1773	+	8.76259i	0.726859	+	0.419652i
$437$	4.45784	+	7.72121i	0.213248	+	0.369356i
$438$		0			0
$439$	6.30512	−	10.9208i	0.300927	−	0.521221i	−0.675419	−	0.737434i	$-0.736037\pi$
$439$	6.30512	−	10.9208i	0.300927	−	0.521221i	0.976346	+	0.216213i	$0.0693707\pi$
$440$	−0.583820	−	2.71526i	−0.0278325	−	0.129445i
$441$		0			0
$442$		−	15.4941i		−	0.736978i
$443$	7.61859	−	13.1958i	0.361970	−	0.626951i	−0.626315	−	0.779570i	$-0.715438\pi$
$443$	7.61859	−	13.1958i	0.361970	−	0.626951i	0.988285	+	0.152619i	$0.0487709\pi$
$444$		0			0
$445$	3.51988	+	6.09662i	0.166858	+	0.289007i
$446$	−7.83326	+	13.5676i	−0.370916	+	0.642445i
$447$		0			0
$448$	−2.44037	−	1.02205i	−0.115297	−	0.0482875i
$449$	−32.2780			−1.52329			−0.761647	−	0.647993i	$-0.775609\pi$
$449$	−32.2780			−1.52329			−0.761647	+	0.647993i	$0.775609\pi$
$450$		0			0
$451$	27.6325	−	24.9983i	1.30117	−	1.17712i
$452$	−4.04475	−	7.00571i	−0.190249	−	0.329521i
$453$		0			0
$454$		−	15.7205i		−	0.737799i
$455$	3.48032	+	4.57262i	0.163160	+	0.214368i
$456$		0			0
$457$	26.2793	+	15.1724i	1.22929	+	0.709733i	0.966882	−	0.255223i	$-0.0821489\pi$
$457$	26.2793	+	15.1724i	1.22929	+	0.709733i	0.262412	+	0.964956i	$0.415482\pi$
$458$	1.25208	+	2.16867i	0.0585060	+	0.101335i
$459$		0			0
$460$	−2.07779	−	1.19961i	−0.0968773	−	0.0559321i
$461$	4.81402			0.224211			0.112106	−	0.993696i	$-0.464240\pi$
$461$	4.81402			0.224211			0.112106	+	0.993696i	$0.464240\pi$
$462$		0			0
$463$	−33.1197			−1.53920			−0.769600	−	0.638526i	$-0.779545\pi$
$463$	−33.1197			−1.53920			−0.769600	+	0.638526i	$0.779545\pi$
$464$	4.66587	+	2.69384i	0.216608	+	0.125059i
$465$		0			0
$466$	0.0276581	+	0.0479052i	0.00128123	+	0.00221916i
$467$	12.4591	+	7.19328i	0.576539	+	0.332865i	0.759757	−	0.650207i	$-0.225318\pi$
$467$	12.4591	+	7.19328i	0.576539	+	0.332865i	−0.183218	+	0.983072i	$0.558651\pi$
$468$		0			0
$469$	−4.36861	−	34.2184i	−0.201724	−	1.58006i
$470$			10.2528i			0.472925i
$471$		0			0
$472$	−4.84253	−	8.38751i	−0.222896	−	0.386067i
$473$	2.83754	+	3.13655i	0.130470	+	0.144219i
$474$		0			0
$475$	13.3770			0.613777
$476$	12.5765	−	9.57226i	0.576445	−	0.438744i
$477$		0			0
$478$	−2.87233	+	4.97501i	−0.131377	+	0.227552i
$479$	−3.23604	−	5.60499i	−0.147859	−	0.256099i	0.782577	−	0.622554i	$-0.213905\pi$
$479$	−3.23604	−	5.60499i	−0.147859	−	0.256099i	−0.930436	+	0.366455i	$0.880571\pi$
$480$		0			0
$481$	−14.2516	+	24.6844i	−0.649815	+	1.12551i
$482$		−	7.34245i		−	0.334440i
$483$		0			0
$484$	10.0279	−	4.52130i	0.455812	−	0.205514i
$485$	−0.329150	+	0.570104i	−0.0149459	+	0.0258871i
$486$		0			0
$487$	2.64048	+	4.57345i	0.119652	+	0.207243i	0.919630	−	0.392787i	$-0.128489\pi$
$487$	2.64048	+	4.57345i	0.119652	+	0.207243i	−0.799978	+	0.600029i	$0.795156\pi$
$488$	−3.52514	−	2.03524i	−0.159576	−	0.0921311i
$489$		0			0
$490$	−1.56145	+	5.64994i	−0.0705392	+	0.255238i
$491$		−	11.3633i		−	0.512820i	−0.966568	−	0.256410i	$-0.917460\pi$
$491$		−	11.3633i		−	0.512820i	0.966568	−	0.256410i	$-0.0825398\pi$
$492$		0			0
$493$	−27.8726	+	16.0923i	−1.25532	+	0.724759i
$494$	−6.98979	+	4.03556i	−0.314485	+	0.181568i
$495$		0			0
$496$		−	1.05470i		−	0.0473575i
$497$	−34.3593	−	14.3901i	−1.54122	−	0.645482i
$498$		0			0
$499$	14.5860	−	25.2638i	0.652961	−	1.13096i	−0.329440	−	0.944176i	$-0.606860\pi$
$499$	14.5860	−	25.2638i	0.652961	−	1.13096i	0.982401	−	0.186785i	$-0.0598066\pi$
$500$	−6.74349	+	3.89336i	−0.301578	+	0.174116i
$501$		0			0
$502$	2.10401	−	3.64426i	0.0939067	−	0.162651i
$503$	22.4317			1.00018			0.500090	−	0.865973i	$-0.333300\pi$
$503$	22.4317			1.00018			0.500090	+	0.865973i	$0.333300\pi$
$504$		0			0
$505$		−	5.62917i		−	0.250495i
$506$	2.91518	−	9.04430i	0.129596	−	0.402068i
$507$		0			0
$508$	−10.5060	+	6.06567i	−0.466130	+	0.269121i
$509$	23.7016	+	13.6841i	1.05055	+	0.606537i	0.922804	−	0.385269i	$-0.125891\pi$
$509$	23.7016	+	13.6841i	1.05055	+	0.606537i	0.127749	+	0.991807i	$0.459225\pi$
$510$		0			0
$511$	−3.32151	−	26.0166i	−0.146935	−	1.15091i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−12.3233	−	21.3446i	−0.543557	−	0.941469i
$515$	1.70469	+	2.95261i	0.0751176	+	0.130107i
$516$		0			0
$517$	−39.7005	+	8.53618i	−1.74602	+	0.375421i
$518$	−28.8410	+	3.68208i	−1.26720	+	0.161782i
$519$		0			0
$520$	1.08597	−	1.88096i	0.0476231	−	0.0824856i
$521$	−30.3032	+	17.4955i	−1.32761	+	0.766493i	−0.984929	−	0.172960i	$-0.944667\pi$
$521$	−30.3032	+	17.4955i	−1.32761	+	0.766493i	−0.342676	+	0.939454i	$0.611333\pi$
$522$		0			0
$523$	19.1224	−	33.1210i	0.836165	−	1.44828i	−0.0569142	−	0.998379i	$-0.518126\pi$
$523$	19.1224	−	33.1210i	0.836165	−	1.44828i	0.893079	−	0.449900i	$-0.148541\pi$
$524$	−2.04449			−0.0893139
$525$		0			0
$526$	−30.3837			−1.32479
$527$	5.45639	+	3.15025i	0.237684	+	0.137227i
$528$		0			0
$529$	7.39556	+	12.8095i	0.321546	+	0.556934i
$530$	−2.16659	+	3.75264i	−0.0941105	+	0.163004i
$531$		0			0
$532$	−7.59396	−	3.18044i	−0.329240	−	0.137889i
$533$	29.1402			1.26220
$534$		0			0
$535$	−0.101275	−	0.175414i	−0.00437852	−	0.00758382i
$536$	−11.2915	+	6.51916i	−0.487719	+	0.281585i
$537$		0			0
$538$	19.9737			0.861128
$539$	−23.1775	−	1.34221i	−0.998327	−	0.0578132i
$540$		0			0
$541$	2.73079	+	1.57662i	0.117406	+	0.0677842i	0.557553	−	0.830141i	$-0.311740\pi$
$541$	2.73079	+	1.57662i	0.117406	+	0.0677842i	−0.440147	+	0.897926i	$0.645074\pi$
$542$	−1.39887	+	0.807639i	−0.0600867	+	0.0346911i
$543$		0			0
$544$	−5.17339	−	2.98686i	−0.221807	−	0.128061i
$545$	−14.6754			−0.628627
$546$		0			0
$547$			20.6313i			0.882131i	0.897475	+	0.441065i	$0.145399\pi$
$547$			20.6313i			0.882131i	−0.897475	+	0.441065i	$0.854601\pi$
$548$	6.60556	−	11.4412i	0.282176	−	0.488742i
$549$		0			0
$550$	−9.56496	−	10.5729i	−0.407851	−	0.450829i
$551$	14.5193	+	8.38273i	0.618543	+	0.357116i
$552$		0			0
$553$	−21.6516	−	28.4471i	−0.920722	−	1.20969i
$554$	−5.18071			−0.220107
$555$		0			0
$556$	−3.08147	−	5.33726i	−0.130683	−	0.226350i
$557$	−1.10046	+	0.635353i	−0.0466281	+	0.0269208i	−0.523133	−	0.852251i	$-0.675237\pi$
$557$	−1.10046	+	0.635353i	−0.0466281	+	0.0269208i	0.476505	+	0.879172i	$0.341904\pi$
$558$		0			0
$559$			3.30769i			0.139900i
$560$	2.19769	−	0.280576i	0.0928694	−	0.0118565i
$561$		0			0
$562$	−12.5942	+	21.8137i	−0.531252	+	0.920156i
$563$	−20.1729	−	34.9405i	−0.850187	−	1.47257i	−0.881039	−	0.473043i	$-0.843155\pi$
$563$	−20.1729	−	34.9405i	−0.850187	−	1.47257i	0.0308519	−	0.999524i	$-0.490178\pi$
$564$		0			0
$565$	5.86652	+	3.38704i	0.246806	+	0.142494i
$566$		−	23.0334i		−	0.968168i
$567$		0			0
$568$			14.0795i			0.590764i
$569$	2.40837	+	1.39047i	0.100964	+	0.0582917i	0.549632	−	0.835407i	$-0.314768\pi$
$569$	2.40837	+	1.39047i	0.100964	+	0.0582917i	−0.448668	+	0.893699i	$0.648101\pi$
$570$		0			0
$571$	−33.0674	+	19.0915i	−1.38383	+	0.798953i	−0.992610	−	0.121346i	$-0.961279\pi$
$571$	−33.0674	+	19.0915i	−1.38383	+	0.798953i	−0.391217	+	0.920299i	$0.627946\pi$
$572$	8.18754	+	2.63903i	0.342338	+	0.110343i
$573$		0			0
$574$	18.0029	+	23.6531i	0.751425	+	0.987262i
$575$	−12.3165			−0.513633
$576$		0			0
$577$	5.92826	−	3.42268i	0.246797	−	0.142488i	−0.371500	−	0.928433i	$-0.621156\pi$
$577$	5.92826	−	3.42268i	0.246797	−	0.142488i	0.618297	+	0.785945i	$0.287823\pi$
$578$	16.1820	−	9.34267i	0.673081	−	0.388604i
$579$		0			0
$580$	−4.51160			−0.187334
$581$	7.30370	+	3.05887i	0.303009	+	0.126903i
$582$		0			0
$583$	−16.3347	−	5.26504i	−0.676513	−	0.218056i
$584$	−8.58507	+	4.95659i	−0.355253	+	0.205105i
$585$		0			0
$586$	3.62064	+	2.09038i	0.149567	+	0.0863527i
$587$		−	22.7050i		−	0.937135i	−0.883428	−	0.468568i	$-0.844770\pi$
$587$		−	22.7050i		−	0.937135i	0.883428	−	0.468568i	$-0.155230\pi$
$588$		0			0
$589$		−	3.28203i		−	0.135234i
$590$	7.02363	+	4.05510i	0.289158	+	0.166946i
$591$		0			0
$592$	5.49467	+	9.51705i	0.225830	+	0.391148i
$593$	−5.05558	+	8.75652i	−0.207608	+	0.359587i	−0.950960	−	0.309313i	$-0.899901\pi$
$593$	−5.05558	+	8.75652i	−0.207608	+	0.359587i	0.743353	+	0.668900i	$0.233234\pi$
$594$		0			0
$595$	−5.11267	+	12.2076i	−0.209599	+	0.500461i
$596$			4.39696i			0.180107i
$597$		0			0
$598$	6.43566	−	3.71563i	0.263174	−	0.151943i
$599$	−1.45219	−	2.51527i	−0.0593349	−	0.102771i	0.834832	−	0.550505i	$-0.185565\pi$
$599$	−1.45219	−	2.51527i	−0.0593349	−	0.102771i	−0.894167	+	0.447734i	$0.852231\pi$
$600$		0			0
$601$	8.68237			0.354161			0.177081	−	0.984196i	$-0.443335\pi$
$601$	8.68237			0.354161			0.177081	+	0.984196i	$0.443335\pi$
$602$	−2.68485	+	2.04349i	−0.109426	+	0.0832866i
$603$		0			0
$604$	8.86874	+	5.12037i	0.360864	+	0.208345i
$605$	−5.37918	+	7.47748i	−0.218695	+	0.304003i
$606$		0			0
$607$	−11.7341	+	20.3240i	−0.476272	+	0.824927i	−0.999630	−	0.0271855i	$-0.991346\pi$
$607$	−11.7341	+	20.3240i	−0.476272	+	0.824927i	0.523359	+	0.852113i	$0.324679\pi$
$608$			3.11181i			0.126200i
$609$		0			0
$610$	3.40859			0.138010
$611$	−27.5020	−	15.8783i	−1.11261	−	0.642367i
$612$		0			0
$613$	26.8294	−	15.4899i	1.08363	−	0.625633i	0.151756	−	0.988418i	$-0.451507\pi$
$613$	26.8294	−	15.4899i	1.08363	−	0.625633i	0.931873	+	0.362785i	$0.118174\pi$
$614$	8.71712	+	5.03283i	0.351794	+	0.203108i
$615$		0			0
$616$	2.91617	+	8.27623i	0.117496	+	0.333459i
$617$	−7.35346			−0.296039			−0.148020	−	0.988984i	$-0.547290\pi$
$617$	−7.35346			−0.296039			−0.148020	+	0.988984i	$0.547290\pi$
$618$		0			0
$619$	−3.16686	+	1.82839i	−0.127287	+	0.0734892i	−0.562292	−	0.826939i	$-0.690080\pi$
$619$	−3.16686	+	1.82839i	−0.127287	+	0.0734892i	0.435005	+	0.900428i	$0.356747\pi$
$620$	0.441599	+	0.764873i	0.0177351	+	0.0307180i
$621$		0			0
$622$	1.42972			0.0573264
$623$	−13.4710	−	17.6989i	−0.539704	−	0.709091i
$624$		0			0
$625$	−7.48667	+	12.9673i	−0.299467	+	0.518692i
$626$	−15.1965	−	26.3211i	−0.607375	−	1.05200i
$627$		0			0
$628$	−13.8444	−	7.99304i	−0.552450	−	0.318957i
$629$	−65.6473			−2.61753
$630$		0			0
$631$	22.5757			0.898724			0.449362	−	0.893350i	$-0.351651\pi$
$631$	22.5757			0.898724			0.449362	+	0.893350i	$0.351651\pi$
$632$	−6.75603	+	11.7018i	−0.268740	+	0.465472i
$633$		0			0
$634$	−9.39829	+	5.42610i	−0.373254	+	0.215498i
$635$	5.07934	−	8.79767i	0.201567	−	0.349125i
$636$		0			0
$637$	−12.7372	−	12.9384i	−0.504666	−	0.512638i
$638$	−3.75624	−	17.4697i	−0.148711	−	0.691631i
$639$		0			0
$640$	−0.418696	−	0.725202i	−0.0165504	−	0.0286661i
$641$	−22.2802	−	38.5905i	−0.880017	−	1.52423i	−0.851321	−	0.524646i	$-0.824198\pi$
$641$	−22.2802	−	38.5905i	−0.880017	−	1.52423i	−0.0286961	−	0.999588i	$-0.509136\pi$
$642$		0			0
$643$		−	14.8587i		−	0.585968i	−0.956117	−	0.292984i	$-0.905352\pi$
$643$		−	14.8587i		−	0.585968i	0.956117	−	0.292984i	$-0.0946483\pi$
$644$	6.99194	+	2.92830i	0.275521	+	0.115391i
$645$		0			0
$646$	−16.0986	−	9.29454i	−0.633391	−	0.365689i
$647$	−41.5179	+	23.9704i	−1.63224	+	0.942373i	−0.648836	+	0.760928i	$0.724744\pi$
$647$	−41.5179	+	23.9704i	−1.63224	+	0.942373i	−0.983401	+	0.181445i	$0.941923\pi$
$648$		0			0
$649$	−9.85432	+	30.5728i	−0.386816	+	1.20009i
$650$		−	11.1498i		−	0.437329i
$651$		0			0
$652$	0.523852			0.0205156
$653$	12.9160	−	22.3711i	0.505440	−	0.875448i	−0.494540	−	0.869155i	$-0.664663\pi$
$653$	12.9160	−	22.3711i	0.505440	−	0.875448i	0.999980	−	0.00629344i	$-0.00200328\pi$
$654$		0			0
$655$	1.48267	−	0.856019i	0.0579326	−	0.0334474i
$656$	5.61749	−	9.72978i	0.219326	−	0.379884i
$657$		0			0
$658$	−4.10237	−	32.1330i	−0.159927	−	1.25267i
$659$		−	28.7951i		−	1.12170i	−0.827918	−	0.560850i	$-0.810475\pi$
$659$		−	28.7951i		−	1.12170i	0.827918	−	0.560850i	$-0.189525\pi$
$660$		0			0
$661$	−23.0670	+	13.3177i	−0.897201	+	0.517999i	−0.876291	−	0.481782i	$-0.839990\pi$
$661$	−23.0670	+	13.3177i	−0.897201	+	0.517999i	−0.0209100	+	0.999781i	$0.506656\pi$
$662$	−11.1847	+	6.45747i	−0.434705	+	0.250977i
$663$		0			0
$664$		−	2.99287i		−	0.116146i
$665$	6.83880	−	0.873099i	0.265197	−	0.0338573i
$666$		0			0
$667$	−13.3683	−	7.71817i	−0.517621	−	0.298849i
$668$	−8.52720	−	14.7695i	−0.329927	−	0.571451i
$669$		0			0
$670$	5.45909	−	9.45541i	0.210903	−	0.365295i
$671$	2.83790	+	13.1986i	0.109556	+	0.509527i
$672$		0			0
$673$		−	12.3054i		−	0.474337i	−0.971469	−	0.237168i	$-0.923781\pi$
$673$		−	12.3054i		−	0.474337i	0.971469	−	0.237168i	$-0.0762193\pi$
$674$	8.24045	−	14.2729i	0.317410	−	0.549771i
$675$		0			0
$676$	−3.13635	−	5.43231i	−0.120629	−	0.208935i
$677$	5.73042	−	9.92539i	0.220238	−	0.381464i	−0.734642	−	0.678455i	$-0.762650\pi$
$677$	5.73042	−	9.92539i	0.220238	−	0.381464i	0.954880	+	0.296991i	$0.0959832\pi$
$678$		0			0
$679$	0.803469	−	1.91845i	0.0308343	−	0.0736233i
$680$	5.00234			0.191831
$681$		0			0
$682$	−2.59405	+	2.34676i	−0.0993313	+	0.0898620i
$683$	−3.78001	−	6.54717i	−0.144638	−	0.250520i	0.784600	−	0.620003i	$-0.212868\pi$
$683$	−3.78001	−	6.54717i	−0.144638	−	0.250520i	−0.929238	+	0.369482i	$0.879535\pi$
$684$		0			0
$685$			11.0629i			0.422691i
$686$	2.63304	−	18.3321i	0.100530	−	0.699924i
$687$		0			0
$688$	1.10442	+	0.637637i	0.0421056	+	0.0243097i
$689$	−6.71070	−	11.6233i	−0.255657	−	0.442812i
$690$		0			0
$691$	−16.4626	−	9.50471i	−0.626268	−	0.361576i	0.153037	−	0.988220i	$-0.451095\pi$
$691$	−16.4626	−	9.50471i	−0.626268	−	0.361576i	−0.779305	+	0.626644i	$0.784428\pi$
$692$	7.23663			0.275095
$693$		0			0
$694$	−11.4633			−0.435140
$695$	4.46937	+	2.58039i	0.169533	+	0.0978799i
$696$		0			0
$697$	33.5573	+	58.1230i	1.27107	+	2.20156i
$698$	−18.1485	−	10.4781i	−0.686932	−	0.396600i
$699$		0			0
$700$	9.05026	−	6.88834i	0.342068	−	0.260355i
$701$		−	32.6349i		−	1.23260i	−0.787510	−	0.616302i	$-0.788630\pi$
$701$		−	32.6349i		−	1.23260i	0.787510	−	0.616302i	$-0.211370\pi$
$702$		0			0
$703$	17.0984	+	29.6152i	0.644877	+	1.11696i
$704$	2.45951	−	2.22504i	0.0926962	−	0.0838595i
$705$		0			0
$706$	19.9221			0.749778
$707$	2.25236	+	17.6423i	0.0847087	+	0.663505i
$708$		0			0
$709$	−7.57532	+	13.1208i	−0.284497	+	0.492764i	−0.972487	−	0.232957i	$-0.925160\pi$
$709$	−7.57532	+	13.1208i	−0.284497	+	0.492764i	0.687990	+	0.725720i	$0.258493\pi$
$710$	−5.89504	−	10.2105i	−0.221237	−	0.383194i
$711$		0			0
$712$	−4.20339	+	7.28049i	−0.157529	+	0.272848i
$713$			3.02184i			0.113169i
$714$		0			0
$715$	−7.04258	+	1.51426i	−0.263377	+	0.0566300i
$716$	−4.03318	+	6.98568i	−0.150727	+	0.261067i
$717$		0			0
$718$	1.95715	+	3.38989i	0.0730403	+	0.126510i
$719$	−4.46410	−	2.57735i	−0.166483	−	0.0961189i	0.414444	−	0.910075i	$-0.363976\pi$
$719$	−4.46410	−	2.57735i	−0.166483	−	0.0961189i	−0.580926	+	0.813956i	$0.697310\pi$
$720$		0			0
$721$	−6.52403	−	8.57162i	−0.242968	−	0.319224i
$722$		−	9.31665i		−	0.346730i
$723$		0			0
$724$	−4.85889	+	2.80528i	−0.180579	+	0.104257i
$725$	−20.0575	+	11.5802i	−0.744919	+	0.430079i
$726$		0			0
$727$			24.1329i			0.895041i	0.894274	+	0.447520i	$0.147693\pi$
$727$			24.1329i			0.895041i	−0.894274	+	0.447520i	$0.852307\pi$
$728$	−2.65091	+	6.32960i	−0.0982492	+	0.234591i
$729$		0			0
$730$	4.15061	−	7.18906i	0.153621	−	0.266079i
$731$	−6.59750	+	3.80907i	−0.244017	+	0.140883i
$732$		0			0
$733$	−26.0520	+	45.1235i	−0.962254	+	1.66667i	−0.245436	+	0.969413i	$0.578931\pi$
$733$	−26.0520	+	45.1235i	−0.962254	+	1.66667i	−0.716818	+	0.697260i	$0.754402\pi$
$734$	−12.0920			−0.446324
$735$		0			0
$736$		−	2.86511i		−	0.105609i
$737$	41.1580	+	13.2662i	1.51608	+	0.488666i
$738$		0			0
$739$	4.80361	−	2.77336i	0.176704	−	0.102020i	−0.409039	−	0.912517i	$-0.634136\pi$
$739$	4.80361	−	2.77336i	0.176704	−	0.102020i	0.585743	+	0.810497i	$0.300803\pi$
$740$	−7.96950	−	4.60119i	−0.292965	−	0.169143i
$741$		0			0
$742$	5.28873	−	12.6280i	0.194155	−	0.463587i
$743$			18.2750i			0.670443i	0.942139	+	0.335222i	$0.108811\pi$
$743$			18.2750i			0.670443i	−0.942139	+	0.335222i	$0.891189\pi$
$744$		0			0
$745$	−1.84099	−	3.18869i	−0.0674486	−	0.116824i
$746$	8.84681	+	15.3231i	0.323905	+	0.561019i
$747$		0			0
$748$	4.16481	+	19.3699i	0.152281	+	0.708234i
$749$	0.387592	+	0.509239i	0.0141623	+	0.0186072i
$750$		0			0
$751$	7.35764	−	12.7438i	0.268484	−	0.465028i	−0.699986	−	0.714156i	$-0.746811\pi$
$751$	7.35764	−	12.7438i	0.268484	−	0.465028i	0.968471	+	0.249128i	$0.0801440\pi$
$752$	−10.6034	+	6.12185i	−0.386665	+	0.223241i
$753$		0			0
$754$	6.98704	−	12.1019i	0.254453	−	0.440725i
$755$	−8.57551			−0.312095
$756$		0			0
$757$	−46.8890			−1.70421			−0.852105	−	0.523371i	$-0.824674\pi$
$757$	−46.8890			−1.70421			−0.852105	+	0.523371i	$0.824674\pi$
$758$	−17.0241	−	9.82884i	−0.618342	−	0.357000i
$759$		0			0
$760$	−1.30290	−	2.25669i	−0.0472612	−	0.0818588i
$761$	18.5206	−	32.0787i	0.671373	−	1.16285i	−0.306142	−	0.951986i	$-0.599038\pi$
$761$	18.5206	−	32.0787i	0.671373	−	1.16285i	0.977515	−	0.210866i	$-0.0676283\pi$
$762$		0			0
$763$	45.9940	−	5.87198i	1.66509	−	0.212580i
$764$	11.7841			0.426334
$765$		0			0
$766$	0.686725	+	1.18944i	0.0248124	+	0.0429763i
$767$	−21.7547	+	12.5601i	−0.785518	+	0.453519i
$768$		0			0
$769$	10.3666			0.373830			0.186915	−	0.982376i	$-0.440151\pi$
$769$	10.3666			0.373830			0.186915	+	0.982376i	$0.440151\pi$
$770$	−5.58004	−	4.78095i	−0.201091	−	0.172293i
$771$		0			0
$772$	−15.6730	−	9.04882i	−0.564084	−	0.325674i
$773$	18.7188	−	10.8073i	0.673268	−	0.388712i	−0.124045	−	0.992277i	$-0.539587\pi$
$773$	18.7188	−	10.8073i	0.673268	−	0.388712i	0.797314	+	0.603565i	$0.206254\pi$
$774$		0			0
$775$	3.92650	+	2.26696i	0.141044	+	0.0814318i
$776$	−0.786131			−0.0282204
$777$		0			0
$778$		−	31.3793i		−	1.12500i
$779$	17.4806	−	30.2772i	0.626306	−	1.08479i
$780$		0			0
$781$	34.6288	−	31.3276i	1.23911	−	1.12099i
$782$	14.8224	+	8.55769i	0.530047	+	0.306023i
$783$		0			0
$784$	−6.77547	+	1.75869i	−0.241981	+	0.0628105i
$785$	13.3866			0.477789
$786$		0			0
$787$	24.3455	+	42.1677i	0.867824	+	1.50312i	0.864215	+	0.503122i	$0.167815\pi$
$787$	24.3455	+	42.1677i	0.867824	+	1.50312i	0.00360891	+	0.999993i	$0.498851\pi$
$788$	−5.39629	+	3.11555i	−0.192235	+	0.110987i
$789$		0			0
$790$		−	11.3149i		−	0.402565i
$791$	−19.7414	−	8.26790i	−0.701922	−	0.293973i
$792$		0			0
$793$	−5.27882	+	9.14318i	−0.187456	+	0.324684i
$794$	17.6360	+	30.5464i	0.625877	+	1.08405i
$795$		0			0
$796$	−15.8196	−	9.13344i	−0.560711	−	0.323726i
$797$			36.0374i			1.27651i	0.769825	+	0.638255i	$0.220343\pi$
$797$			36.0374i			1.27651i	−0.769825	+	0.638255i	$0.779657\pi$
$798$		0			0
$799$		−	73.1405i		−	2.58752i
$800$	−3.72285	−	2.14939i	−0.131623	−	0.0759923i
$801$		0			0
$802$	−7.76494	+	4.48309i	−0.274190	+	0.158303i
$803$	31.2929	+	10.0864i	1.10430	+	0.355942i
$804$		0			0
$805$	−6.29664	+	0.803882i	−0.221927	+	0.0283331i
$806$	−2.73559			−0.0963569
$807$		0			0
$808$	5.82166	−	3.36113i	0.204805	−	0.118244i
$809$	25.9030	−	14.9551i	0.910700	−	0.525793i	0.0300439	−	0.999549i	$-0.490435\pi$
$809$	25.9030	−	14.9551i	0.910700	−	0.525793i	0.880656	+	0.473756i	$0.157102\pi$
$810$		0			0
$811$	−18.1295			−0.636611			−0.318306	−	0.947988i	$-0.603114\pi$
$811$	−18.1295			−0.636611			−0.318306	+	0.947988i	$0.603114\pi$
$812$	14.1397	−	1.80520i	0.496207	−	0.0633500i
$813$		0			0
$814$	11.1814	−	34.6900i	0.391908	−	1.21589i
$815$	−0.379899	+	0.219335i	−0.0133073	+	0.00768296i
$816$		0			0
$817$	3.43674	+	1.98420i	0.120236	+	0.0694185i
$818$			35.9524i			1.25705i
$819$		0			0
$820$			9.40808i			0.328544i
$821$	−16.8684	−	9.73899i	−0.588712	−	0.339893i	0.175876	−	0.984412i	$-0.443724\pi$
$821$	−16.8684	−	9.73899i	−0.588712	−	0.339893i	−0.764588	+	0.644519i	$0.777058\pi$
$822$		0			0
$823$	−14.0931	−	24.4100i	−0.491255	−	0.850879i	0.508694	−	0.860947i	$-0.330128\pi$
$823$	−14.0931	−	24.4100i	−0.491255	−	0.850879i	−0.999949	+	0.0100686i	$0.996795\pi$
$824$	−2.03571	+	3.52596i	−0.0709174	+	0.122833i
$825$		0			0
$826$	−23.6351	−	9.89867i	−0.822372	−	0.344419i
$827$			25.7981i			0.897089i	0.893761	+	0.448544i	$0.148057\pi$
$827$			25.7981i			0.897089i	−0.893761	+	0.448544i	$0.851943\pi$
$828$		0			0
$829$	31.9716	−	18.4588i	1.11042	−	0.641100i	0.171480	−	0.985188i	$-0.445145\pi$
$829$	31.9716	−	18.4588i	1.11042	−	0.641100i	0.938938	+	0.344087i	$0.111812\pi$
$830$	1.25310	+	2.17043i	0.0434958	+	0.0753369i
$831$		0			0
$832$	2.59370			0.0899205
$833$	11.1390	−	40.3051i	0.385942	−	1.39649i
$834$		0			0
$835$	12.3679	+	7.14060i	0.428008	+	0.247111i
$836$	7.65352	−	6.92391i	0.264703	−	0.239468i
$837$		0			0
$838$	−0.362317	+	0.627552i	−0.0125160	+	0.0216784i
$839$			6.71611i			0.231866i	0.993257	+	0.115933i	$0.0369858\pi$
$839$			6.71611i			0.231866i	−0.993257	+	0.115933i	$0.963014\pi$
$840$		0			0
$841$	−0.0271771			−0.000937142
$842$	−3.21662	−	1.85712i	−0.110852	−	0.0640005i
$843$		0			0
$844$	−8.87211	+	5.12231i	−0.305390	+	0.176317i
$845$	4.54897	+	2.62635i	0.156489	+	0.0903492i
$846$		0			0
$847$	13.8668	−	25.5873i	0.476470	−	0.879191i
$848$	−5.17461			−0.177697
$849$		0			0
$850$	22.2393	−	12.8398i	0.762800	−	0.440403i
$851$	−15.7429	−	27.2674i	−0.539658	−	0.934716i
$852$		0			0
$853$	−39.8993			−1.36613			−0.683063	−	0.730360i	$-0.739352\pi$
$853$	−39.8993			−1.36613			−0.683063	+	0.730360i	$0.739352\pi$
$854$	−10.6828	+	1.36385i	−0.365557	+	0.0466701i
$855$		0			0
$856$	0.120942	−	0.209477i	0.00413370	−	0.00715978i
$857$	7.85467	+	13.6047i	0.268310	+	0.464727i	0.968426	−	0.249303i	$-0.0802014\pi$
$857$	7.85467	+	13.6047i	0.268310	+	0.464727i	−0.700115	+	0.714030i	$0.746868\pi$
$858$		0			0
$859$	16.6977	+	9.64043i	0.569719	+	0.328927i	0.757037	−	0.653372i	$-0.226646\pi$
$859$	16.6977	+	9.64043i	0.569719	+	0.328927i	−0.187318	+	0.982299i	$0.559980\pi$
$860$	−1.06790			−0.0364152
$861$		0			0
$862$	−4.08478			−0.139128
$863$	19.0761	−	33.0408i	0.649358	−	1.12472i	−0.333918	−	0.942602i	$-0.608371\pi$
$863$	19.0761	−	33.0408i	0.649358	−	1.12472i	0.983276	−	0.182119i	$-0.0582957\pi$
$864$		0			0
$865$	−5.24802	+	3.02995i	−0.178438	+	0.103021i
$866$	15.1555	−	26.2500i	0.515003	−	0.892012i
$867$		0			0
$868$	−1.69005	−	2.22048i	−0.0573640	−	0.0753679i
$869$	43.8131	−	9.42046i	1.48626	−	0.319567i
$870$		0			0
$871$	16.9088	+	29.2868i	0.572932	+	0.992347i
$872$	−8.76259	−	15.1773i	−0.296739	−	0.513967i
$873$		0			0
$874$		−	8.91569i		−	0.301578i
$875$	−7.95845	+	19.0025i	−0.269045	+	0.642401i
$876$		0			0
$877$	−7.92511	−	4.57556i	−0.267612	−	0.154506i	0.360190	−	0.932879i	$-0.382712\pi$
$877$	−7.92511	−	4.57556i	−0.267612	−	0.154506i	−0.627802	+	0.778373i	$0.716045\pi$
$878$	−10.9208	+	6.30512i	−0.368559	+	0.212787i
$879$		0			0
$880$	−0.852026	+	2.64339i	−0.0287218	+	0.0891087i
$881$		−	47.7019i		−	1.60712i	−0.595225	−	0.803559i	$-0.702937\pi$
$881$		−	47.7019i		−	1.60712i	0.595225	−	0.803559i	$-0.297063\pi$
$882$		0			0
$883$	43.7932			1.47376			0.736879	−	0.676025i	$-0.236299\pi$
$883$	43.7932			1.47376			0.736879	+	0.676025i	$0.236299\pi$
$884$	−7.74703	+	13.4183i	−0.260561	+	0.451305i
$885$		0			0
$886$	−13.1958	+	7.61859i	−0.443321	+	0.255952i
$887$	−25.2896	+	43.8029i	−0.849142	+	1.47076i	0.0328338	+	0.999461i	$0.489547\pi$
$887$	−25.2896	+	43.8029i	−0.849142	+	1.47076i	−0.881975	+	0.471296i	$0.843787\pi$
$888$		0			0
$889$	−12.3989	+	29.6049i	−0.415845	+	0.992918i
$890$		−	7.03977i		−	0.235974i
$891$		0			0
$892$	13.5676	−	7.83326i	0.454277	−	0.262277i
$893$	−32.9956	+	19.0500i	−1.10416	+	0.637485i
$894$		0			0
$895$		−	6.75470i		−	0.225785i
$896$	1.60239	+	2.10531i	0.0535323	+	0.0703335i
$897$		0			0
$898$	27.9536	+	16.1390i	0.932823	+	0.538566i
$899$	2.84120	+	4.92111i	0.0947595	+	0.164128i
$900$		0			0
$901$	15.4558	−	26.7703i	0.514908	−	0.891847i
$902$	−36.4296	+	7.83291i	−1.21297	+	0.260807i
$903$		0			0
$904$			8.08949i			0.269053i
$905$	2.34912	−	4.06879i	0.0780873	−	0.135251i
$906$		0			0
$907$	28.9344	+	50.1159i	0.960752	+	1.66407i	0.720620	+	0.693330i	$0.243857\pi$
$907$	28.9344	+	50.1159i	0.960752	+	1.66407i	0.240132	+	0.970740i	$0.422809\pi$
$908$	−7.86025	+	13.6143i	−0.260851	+	0.451808i
$909$		0			0
$910$	−0.727731	−	5.70016i	−0.0241241	−	0.188959i
$911$	−25.4860			−0.844389			−0.422195	−	0.906505i	$-0.638740\pi$
$911$	−25.4860			−0.844389			−0.422195	+	0.906505i	$0.638740\pi$
$912$		0			0
$913$	−7.36098	+	6.65926i	−0.243613	+	0.220389i
$914$	−15.1724	−	26.2793i	−0.501857	−	0.869242i
$915$		0			0
$916$		−	2.50417i		−	0.0827400i
$917$	−4.30428	+	3.27608i	−0.142140	+	0.108186i
$918$		0			0
$919$	−11.2495	−	6.49491i	−0.371087	−	0.214247i	0.302846	−	0.953039i	$-0.402063\pi$
$919$	−11.2495	−	6.49491i	−0.371087	−	0.214247i	−0.673933	+	0.738792i	$0.735396\pi$
$920$	1.19961	+	2.07779i	0.0395500	+	0.0685026i
$921$		0			0
$922$	−4.16907	−	2.40701i	−0.137301	−	0.0792707i
$923$	36.5182			1.20201
$924$		0			0
$925$	−47.2407			−1.55327
$926$	28.6825	+	16.5598i	0.942564	+	0.544190i
$927$		0			0
$928$	−2.69384	−	4.66587i	−0.0884298	−	0.153165i
$929$	18.8834	+	10.9024i	0.619545	+	0.357695i	0.776692	−	0.629881i	$-0.216896\pi$
$929$	18.8834	+	10.9024i	0.619545	+	0.357695i	−0.157147	+	0.987575i	$0.550230\pi$
$930$		0			0
$931$	−21.0840	+	5.47272i	−0.690999	+	0.179361i
$932$		−	0.0553161i		−	0.00181194i
$933$		0			0
$934$	−7.19328	−	12.4591i	−0.235371	−	0.407675i
$935$	−11.1304	−	12.3033i	−0.364004	−	0.402361i
$936$		0			0
$937$	−31.2647			−1.02137			−0.510686	−	0.859767i	$-0.670609\pi$
$937$	−31.2647			−1.02137			−0.510686	+	0.859767i	$0.670609\pi$
$938$	−13.3259	+	31.8183i	−0.435105	+	1.03890i
$939$		0			0
$940$	5.12639	−	8.87916i	0.167204	−	0.289606i
$941$	9.38779	+	16.2601i	0.306033	+	0.530065i	0.977491	−	0.210978i	$-0.0676648\pi$
$941$	9.38779	+	16.2601i	0.306033	+	0.530065i	−0.671458	+	0.741043i	$0.734332\pi$
$942$		0			0
$943$	−16.0947	+	27.8769i	−0.524117	+	0.907797i
$944$			9.68506i			0.315222i
$945$		0			0
$946$	−0.889107	−	4.13510i	−0.0289074	−	0.134444i
$947$	−19.7729	+	34.2477i	−0.642534	+	1.11290i	0.342331	+	0.939580i	$0.388784\pi$
$947$	−19.7729	+	34.2477i	−0.642534	+	1.11290i	−0.984865	+	0.173323i	$0.944550\pi$
$948$		0			0
$949$	12.8559	+	22.2671i	0.417321	+	0.722822i
$950$	−11.5848	−	6.68848i	−0.375860	−	0.217003i
$951$		0			0
$952$	−15.6777	+	2.00155i	−0.508118	+	0.0648707i
$953$			2.98673i			0.0967495i	0.998829	+	0.0483748i	$0.0154042\pi$
$953$			2.98673i			0.0967495i	−0.998829	+	0.0483748i	$0.984596\pi$
$954$		0			0
$955$	−8.54587	+	4.93396i	−0.276538	+	0.159659i
$956$	4.97501	−	2.87233i	0.160903	−	0.0928976i
$957$		0			0
$958$			6.47208i			0.209104i
$959$	−4.42651	−	34.6719i	−0.142940	−	1.11961i
$960$		0			0
$961$	−14.9438	+	25.8834i	−0.482058	+	0.834949i
$962$	24.6844	−	14.2516i	0.795858	−	0.459489i
$963$		0			0
$964$	−3.67123	+	6.35875i	−0.118242	+	0.204802i
$965$	15.1548			0.487850
$966$		0			0
$967$			3.61655i			0.116300i	0.998308	+	0.0581502i	$0.0185202\pi$
$967$			3.61655i			0.116300i	−0.998308	+	0.0581502i	$0.981480\pi$
$968$	−10.9450	−	1.09837i	−0.351786	−	0.0353029i
$969$		0			0
$970$	0.570104	−	0.329150i	0.0183049	−	0.0105684i
$971$	−23.9499	−	13.8275i	−0.768587	−	0.443744i	0.0637831	−	0.997964i	$-0.479683\pi$
$971$	−23.9499	−	13.8275i	−0.768587	−	0.443744i	−0.832370	+	0.554220i	$0.813017\pi$
$972$		0			0
$973$	−15.0398	−	6.29886i	−0.482155	−	0.201932i
$974$		−	5.28096i		−	0.169213i
$975$		0			0
$976$	2.03524	+	3.52514i	0.0651465	+	0.112837i
$977$	17.4175	+	30.1679i	0.557234	+	0.965158i	0.997726	+	0.0674010i	$0.0214707\pi$
$977$	17.4175	+	30.1679i	0.557234	+	0.965158i	−0.440492	+	0.897757i	$0.645196\pi$
$978$		0			0
$979$	27.2591	−	5.86112i	0.871206	−	0.187322i
$980$	4.17723	−	4.11227i	0.133437	−	0.131362i
$981$		0			0
$982$	−5.68167	+	9.84094i	−0.181309	+	0.314037i
$983$	−19.2919	+	11.1382i	−0.615317	+	0.355254i	−0.775044	−	0.631908i	$-0.782272\pi$
$983$	−19.2919	+	11.1382i	−0.615317	+	0.355254i	0.159726	+	0.987161i	$0.448939\pi$
$984$		0			0
$985$	2.60894	−	4.51881i	0.0831276	−	0.143981i
$986$	32.1845			1.02496
$987$		0			0
$988$	8.07111			0.256776
$989$	−3.16429	−	1.82690i	−0.100619	−	0.0580921i
$990$		0			0
$991$	−27.3088	−	47.3002i	−0.867493	−	1.50254i	−0.864550	−	0.502546i	$-0.832397\pi$
$991$	−27.3088	−	47.3002i	−0.867493	−	1.50254i	−0.00294265	−	0.999996i	$-0.500937\pi$
$992$	−0.527351	+	0.913399i	−0.0167434	+	0.0290005i
$993$		0			0
$994$	22.5610	+	29.6418i	0.715591	+	0.940181i
$995$	15.2965			0.484933
$996$		0			0
$997$	−8.45911	−	14.6516i	−0.267903	−	0.464021i	0.700417	−	0.713734i	$-0.252997\pi$
$997$	−8.45911	−	14.6516i	−0.267903	−	0.464021i	−0.968320	+	0.249712i	$0.919664\pi$
$998$	−25.2638	+	14.5860i	−0.799710	+	0.461713i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bk.a.901.3		16
3.2	odd	2		462.2.p.a.439.6	yes	16
7.3	odd	6		1386.2.bk.b.703.7		16
11.10	odd	2		1386.2.bk.b.901.7		16
21.2	odd	6		3234.2.e.a.2155.4		16
21.5	even	6		3234.2.e.b.2155.5		16
21.17	even	6		462.2.p.b.241.2	yes	16
33.32	even	2		462.2.p.b.439.2	yes	16
77.10	even	6	inner	1386.2.bk.a.703.3		16
231.65	even	6		3234.2.e.b.2155.12		16
231.131	odd	6		3234.2.e.a.2155.13		16
231.164	odd	6		462.2.p.a.241.6	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.6	✓	16	231.164	odd	6
462.2.p.a.439.6	yes	16	3.2	odd	2
462.2.p.b.241.2	yes	16	21.17	even	6
462.2.p.b.439.2	yes	16	33.32	even	2
1386.2.bk.a.703.3		16	77.10	even	6	inner
1386.2.bk.a.901.3		16	1.1	even	1	trivial
1386.2.bk.b.703.7		16	7.3	odd	6
1386.2.bk.b.901.7		16	11.10	odd	2
3234.2.e.a.2155.4		16	21.2	odd	6
3234.2.e.a.2155.13		16	231.131	odd	6
3234.2.e.b.2155.5		16	21.5	even	6
3234.2.e.b.2155.12		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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.725202 - 0.418696i) q^{5} +(2.44037 + 1.02205i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.725202 - 0.418696i) q^{5} +(2.44037 + 1.02205i) q^{7} -1.00000i q^{8} +(0.418696 + 0.725202i) q^{10} +(-2.45951 + 2.22504i) q^{11} -2.59370 q^{13} +(-1.60239 - 2.10531i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.98686 - 5.17339i) q^{17} +(-1.55590 + 2.69491i) q^{19} -0.837391i q^{20} +(3.24252 - 0.697189i) q^{22} +(1.43256 - 2.48126i) q^{23} +(-2.14939 - 3.72285i) q^{25} +(2.24621 + 1.29685i) q^{26} +(0.335059 + 2.62445i) q^{28} -5.38769i q^{29} +(-0.913399 + 0.527351i) q^{31} +(0.866025 - 0.500000i) q^{32} +5.97372i q^{34} +(-1.34183 - 1.76297i) q^{35} +(5.49467 - 9.51705i) q^{37} +(2.69491 - 1.55590i) q^{38} +(-0.418696 + 0.725202i) q^{40} -11.2350 q^{41} -1.27527i q^{43} +(-3.15670 - 1.01748i) q^{44} +(-2.48126 + 1.43256i) q^{46} +(10.6034 + 6.12185i) q^{47} +(4.91081 + 4.98838i) q^{49} +4.29878i q^{50} +(-1.29685 - 2.24621i) q^{52} +(2.58730 + 4.48134i) q^{53} +(2.71526 - 0.583820i) q^{55} +(1.02205 - 2.44037i) q^{56} +(-2.69384 + 4.66587i) q^{58} +(8.38751 - 4.84253i) q^{59} +(2.03524 - 3.52514i) q^{61} +1.05470 q^{62} -1.00000 q^{64} +(1.88096 + 1.08597i) q^{65} +(-6.51916 - 11.2915i) q^{67} +(2.98686 - 5.17339i) q^{68} +(0.280576 + 2.19769i) q^{70} -14.0795 q^{71} +(-4.95659 - 8.58507i) q^{73} +(-9.51705 + 5.49467i) q^{74} -3.11181 q^{76} +(-8.27623 + 2.91617i) q^{77} +(-11.7018 - 6.75603i) q^{79} +(0.725202 - 0.418696i) q^{80} +(9.72978 + 5.61749i) q^{82} +2.99287 q^{83} +5.00234i q^{85} +(-0.637637 + 1.10442i) q^{86} +(2.22504 + 2.45951i) q^{88} +(-7.28049 - 4.20339i) q^{89} +(-6.32960 - 2.65091i) q^{91} +2.86511 q^{92} +(-6.12185 - 10.6034i) q^{94} +(2.25669 - 1.30290i) q^{95} -0.786131i q^{97} +(-1.75869 - 6.77547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 12 q^{5} - 6 q^{7}+O(q^{10}) \) 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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