LMFDB - Embedded newform 891.2.e.p.298.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(298,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("891.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.e (of order $3$, degree $2$, not 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			298.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	891.298
Dual form			891.2.e.p.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 + 0.633975i) q^{2} +(0.732051 + 1.26795i) q^{4} +(1.36603 + 2.36603i) q^{5} +(0.133975 - 0.232051i) q^{7} -2.53590 q^{8} +O(q^{10})$	\(q+(-0.366025 + 0.633975i) q^{2} +(0.732051 + 1.26795i) q^{4} +(1.36603 + 2.36603i) q^{5} +(0.133975 - 0.232051i) q^{7} -2.53590 q^{8} -2.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(1.86603 + 3.23205i) q^{13} +(0.0980762 + 0.169873i) q^{14} +(-0.535898 + 0.928203i) q^{16} -6.19615 q^{17} +5.19615 q^{19} +(-2.00000 + 3.46410i) q^{20} +(0.366025 + 0.633975i) q^{22} +(4.00000 + 6.92820i) q^{23} +(-1.23205 + 2.13397i) q^{25} -2.73205 q^{26} +0.392305 q^{28} +(-2.36603 + 4.09808i) q^{29} +(-3.73205 - 6.46410i) q^{31} +(-2.92820 - 5.07180i) q^{32} +(2.26795 - 3.92820i) q^{34} +0.732051 q^{35} +0.464102 q^{37} +(-1.90192 + 3.29423i) q^{38} +(-3.46410 - 6.00000i) q^{40} +(-2.73205 - 4.73205i) q^{41} +(1.73205 - 3.00000i) q^{43} +1.46410 q^{44} -5.85641 q^{46} +(-0.0980762 + 0.169873i) q^{47} +(3.46410 + 6.00000i) q^{49} +(-0.901924 - 1.56218i) q^{50} +(-2.73205 + 4.73205i) q^{52} -1.26795 q^{53} +2.73205 q^{55} +(-0.339746 + 0.588457i) q^{56} +(-1.73205 - 3.00000i) q^{58} +(-0.0980762 - 0.169873i) q^{59} +(3.86603 - 6.69615i) q^{61} +5.46410 q^{62} +2.14359 q^{64} +(-5.09808 + 8.83013i) q^{65} +(3.96410 + 6.86603i) q^{67} +(-4.53590 - 7.85641i) q^{68} +(-0.267949 + 0.464102i) q^{70} -13.8564 q^{71} -7.19615 q^{73} +(-0.169873 + 0.294229i) q^{74} +(3.80385 + 6.58846i) q^{76} +(-0.133975 - 0.232051i) q^{77} +(1.13397 - 1.96410i) q^{79} -2.92820 q^{80} +4.00000 q^{82} +(-8.46410 - 14.6603i) q^{85} +(1.26795 + 2.19615i) q^{86} +(-1.26795 + 2.19615i) q^{88} +17.6603 q^{89} +1.00000 q^{91} +(-5.85641 + 10.1436i) q^{92} +(-0.0717968 - 0.124356i) q^{94} +(7.09808 + 12.2942i) q^{95} +(-7.69615 + 13.3301i) q^{97} -5.07180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{4} + 2 q^{5} + 4 q^{7} - 24 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^4 + 2 * q^5 + 4 * q^7 - 24 * q^8	$ 4 q + 2 q^{2} - 4 q^{4} + 2 q^{5} + 4 q^{7} - 24 q^{8} - 8 q^{10} + 2 q^{11} + 4 q^{13} - 10 q^{14} - 16 q^{16} - 4 q^{17} - 8 q^{20} - 2 q^{22} + 16 q^{23} + 2 q^{25} - 4 q^{26} - 40 q^{28} - 6 q^{29} - 8 q^{31} + 16 q^{32} + 16 q^{34} - 4 q^{35} - 12 q^{37} - 18 q^{38} - 4 q^{41} - 8 q^{44} + 32 q^{46} + 10 q^{47} - 14 q^{50} - 4 q^{52} - 12 q^{53} + 4 q^{55} - 36 q^{56} + 10 q^{59} + 12 q^{61} + 8 q^{62} + 64 q^{64} - 10 q^{65} + 2 q^{67} - 32 q^{68} - 8 q^{70} - 8 q^{73} - 18 q^{74} + 36 q^{76} - 4 q^{77} + 8 q^{79} + 16 q^{80} + 16 q^{82} - 20 q^{85} + 12 q^{86} - 12 q^{88} + 36 q^{89} + 4 q^{91} + 32 q^{92} - 28 q^{94} + 18 q^{95} - 10 q^{97} - 48 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^4 + 2 * q^5 + 4 * q^7 - 24 * q^8 - 8 * q^10 + 2 * q^11 + 4 * q^13 - 10 * q^14 - 16 * q^16 - 4 * q^17 - 8 * q^20 - 2 * q^22 + 16 * q^23 + 2 * q^25 - 4 * q^26 - 40 * q^28 - 6 * q^29 - 8 * q^31 + 16 * q^32 + 16 * q^34 - 4 * q^35 - 12 * q^37 - 18 * q^38 - 4 * q^41 - 8 * q^44 + 32 * q^46 + 10 * q^47 - 14 * q^50 - 4 * q^52 - 12 * q^53 + 4 * q^55 - 36 * q^56 + 10 * q^59 + 12 * q^61 + 8 * q^62 + 64 * q^64 - 10 * q^65 + 2 * q^67 - 32 * q^68 - 8 * q^70 - 8 * q^73 - 18 * q^74 + 36 * q^76 - 4 * q^77 + 8 * q^79 + 16 * q^80 + 16 * q^82 - 20 * q^85 + 12 * q^86 - 12 * q^88 + 36 * q^89 + 4 * q^91 + 32 * q^92 - 28 * q^94 + 18 * q^95 - 10 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.366025	+	0.633975i	−0.258819	+	0.448288i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−0.366025	+	0.633975i	−0.258819	+	0.448288i	0.707107	+	0.707107i	$0.250000\pi$
$3$		0			0
$3$		0			0
$4$	0.732051	+	1.26795i	0.366025	+	0.633975i
$5$	1.36603	+	2.36603i	0.610905	+	1.05812i	0.991088	+	0.133207i	$0.0425277\pi$
$5$	1.36603	+	2.36603i	0.610905	+	1.05812i	−0.380183	+	0.924911i	$0.624139\pi$
$6$		0			0
$7$	0.133975	−	0.232051i	0.0506376	−	0.0877070i	−0.839596	−	0.543212i	$-0.817208\pi$
$7$	0.133975	−	0.232051i	0.0506376	−	0.0877070i	0.890233	+	0.455505i	$0.150541\pi$
$8$	−2.53590			−0.896575
$9$		0			0
$10$	−2.00000			−0.632456
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	1.86603	+	3.23205i	0.517542	+	0.896410i	0.999792	+	0.0203760i	$0.00648633\pi$
$13$	1.86603	+	3.23205i	0.517542	+	0.896410i	−0.482250	+	0.876034i	$0.660180\pi$
$14$	0.0980762	+	0.169873i	0.0262120	+	0.0454005i
$15$		0			0
$16$	−0.535898	+	0.928203i	−0.133975	+	0.232051i
$17$	−6.19615			−1.50279			−0.751394	−	0.659854i	$-0.770618\pi$
$17$	−6.19615			−1.50279			−0.751394	+	0.659854i	$0.770618\pi$
$18$		0			0
$19$	5.19615			1.19208			0.596040	−	0.802955i	$-0.296740\pi$
$19$	5.19615			1.19208			0.596040	+	0.802955i	$0.296740\pi$
$20$	−2.00000	+	3.46410i	−0.447214	+	0.774597i
$21$		0			0
$22$	0.366025	+	0.633975i	0.0780369	+	0.135164i
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$		0			0
$25$	−1.23205	+	2.13397i	−0.246410	+	0.426795i
$26$	−2.73205			−0.535799
$27$		0			0
$28$	0.392305			0.0741386
$29$	−2.36603	+	4.09808i	−0.439360	+	0.760994i	−0.997640	−	0.0686587i	$-0.978128\pi$
$29$	−2.36603	+	4.09808i	−0.439360	+	0.760994i	0.558280	+	0.829652i	$0.311461\pi$
$30$		0			0
$31$	−3.73205	−	6.46410i	−0.670296	−	1.16099i	−0.977820	−	0.209447i	$-0.932834\pi$
$31$	−3.73205	−	6.46410i	−0.670296	−	1.16099i	0.307524	−	0.951540i	$-0.400500\pi$
$32$	−2.92820	−	5.07180i	−0.517638	−	0.896575i
$33$		0			0
$34$	2.26795	−	3.92820i	0.388950	−	0.673681i
$35$	0.732051			0.123739
$36$		0			0
$37$	0.464102			0.0762978			0.0381489	−	0.999272i	$-0.487854\pi$
$37$	0.464102			0.0762978			0.0381489	+	0.999272i	$0.487854\pi$
$38$	−1.90192	+	3.29423i	−0.308533	+	0.534394i
$39$		0			0
$40$	−3.46410	−	6.00000i	−0.547723	−	0.948683i
$41$	−2.73205	−	4.73205i	−0.426675	−	0.739022i	0.569901	−	0.821714i	$-0.306982\pi$
$41$	−2.73205	−	4.73205i	−0.426675	−	0.739022i	−0.996575	+	0.0826915i	$0.973648\pi$
$42$		0			0
$43$	1.73205	−	3.00000i	0.264135	−	0.457496i	−0.703201	−	0.710991i	$-0.748247\pi$
$43$	1.73205	−	3.00000i	0.264135	−	0.457496i	0.967337	+	0.253495i	$0.0815801\pi$
$44$	1.46410			0.220722
$45$		0			0
$46$	−5.85641			−0.863480
$47$	−0.0980762	+	0.169873i	−0.0143059	+	0.0247785i	−0.873090	−	0.487560i	$-0.837887\pi$
$47$	−0.0980762	+	0.169873i	−0.0143059	+	0.0247785i	0.858784	+	0.512338i	$0.171221\pi$
$48$		0			0
$49$	3.46410	+	6.00000i	0.494872	+	0.857143i
$50$	−0.901924	−	1.56218i	−0.127551	−	0.220925i
$51$		0			0
$52$	−2.73205	+	4.73205i	−0.378867	+	0.656217i
$53$	−1.26795			−0.174166			−0.0870831	−	0.996201i	$-0.527755\pi$
$53$	−1.26795			−0.174166			−0.0870831	+	0.996201i	$0.527755\pi$
$54$		0			0
$55$	2.73205			0.368390
$56$	−0.339746	+	0.588457i	−0.0454005	+	0.0786359i
$57$		0			0
$58$	−1.73205	−	3.00000i	−0.227429	−	0.393919i
$59$	−0.0980762	−	0.169873i	−0.0127684	−	0.0221156i	0.859571	−	0.511017i	$-0.170731\pi$
$59$	−0.0980762	−	0.169873i	−0.0127684	−	0.0221156i	−0.872339	+	0.488901i	$0.837398\pi$
$60$		0			0
$61$	3.86603	−	6.69615i	0.494994	−	0.857354i	−0.504990	−	0.863125i	$-0.668504\pi$
$61$	3.86603	−	6.69615i	0.494994	−	0.857354i	0.999983	+	0.00577101i	$0.00183698\pi$
$62$	5.46410			0.693942
$63$		0			0
$64$	2.14359			0.267949
$65$	−5.09808	+	8.83013i	−0.632339	+	1.09524i
$66$		0			0
$67$	3.96410	+	6.86603i	0.484292	+	0.838819i	0.999837	−	0.0180439i	$-0.00574387\pi$
$67$	3.96410	+	6.86603i	0.484292	+	0.838819i	−0.515545	+	0.856862i	$0.672411\pi$
$68$	−4.53590	−	7.85641i	−0.550058	−	0.952729i
$69$		0			0
$70$	−0.267949	+	0.464102i	−0.0320261	+	0.0554708i
$71$	−13.8564			−1.64445			−0.822226	−	0.569160i	$-0.807268\pi$
$71$	−13.8564			−1.64445			−0.822226	+	0.569160i	$0.807268\pi$
$72$		0			0
$73$	−7.19615			−0.842246			−0.421123	−	0.907004i	$-0.638364\pi$
$73$	−7.19615			−0.842246			−0.421123	+	0.907004i	$0.638364\pi$
$74$	−0.169873	+	0.294229i	−0.0197473	+	0.0342034i
$75$		0			0
$76$	3.80385	+	6.58846i	0.436331	+	0.755748i
$77$	−0.133975	−	0.232051i	−0.0152678	−	0.0264446i
$78$		0			0
$79$	1.13397	−	1.96410i	0.127582	−	0.220979i	−0.795157	−	0.606403i	$-0.792612\pi$
$79$	1.13397	−	1.96410i	0.127582	−	0.220979i	0.922739	+	0.385425i	$0.125945\pi$
$80$	−2.92820			−0.327383
$81$		0			0
$82$	4.00000			0.441726
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$		0			0
$85$	−8.46410	−	14.6603i	−0.918061	−	1.59013i
$86$	1.26795	+	2.19615i	0.136726	+	0.236817i
$87$		0			0
$88$	−1.26795	+	2.19615i	−0.135164	+	0.234111i
$89$	17.6603			1.87198			0.935992	−	0.352022i	$-0.114506\pi$
$89$	17.6603			1.87198			0.935992	+	0.352022i	$0.114506\pi$
$90$		0			0
$91$	1.00000			0.104828
$92$	−5.85641	+	10.1436i	−0.610573	+	1.05754i
$93$		0			0
$94$	−0.0717968	−	0.124356i	−0.00740527	−	0.0128263i
$95$	7.09808	+	12.2942i	0.728247	+	1.26136i
$96$		0			0
$97$	−7.69615	+	13.3301i	−0.781426	+	1.35347i	0.149685	+	0.988734i	$0.452174\pi$
$97$	−7.69615	+	13.3301i	−0.781426	+	1.35347i	−0.931111	+	0.364736i	$0.881159\pi$
$98$	−5.07180			−0.512329
$99$		0			0
$100$	−3.60770			−0.360770
$101$	5.09808	−	8.83013i	0.507278	−	0.878630i	−0.492687	−	0.870207i	$-0.663985\pi$
$101$	5.09808	−	8.83013i	0.507278	−	0.878630i	0.999965	−	0.00842387i	$-0.00268143\pi$
$102$		0			0
$103$	7.42820	+	12.8660i	0.731923	+	1.26773i	0.956060	+	0.293170i	$0.0947101\pi$
$103$	7.42820	+	12.8660i	0.731923	+	1.26773i	−0.224138	+	0.974557i	$0.571957\pi$
$104$	−4.73205	−	8.19615i	−0.464016	−	0.803699i
$105$		0			0
$106$	0.464102	−	0.803848i	0.0450775	−	0.0780766i
$107$	11.6603			1.12724			0.563620	−	0.826034i	$-0.309408\pi$
$107$	11.6603			1.12724			0.563620	+	0.826034i	$0.309408\pi$
$108$		0			0
$109$	−15.8564			−1.51877			−0.759384	−	0.650643i	$-0.774500\pi$
$109$	−15.8564			−1.51877			−0.759384	+	0.650643i	$0.774500\pi$
$110$	−1.00000	+	1.73205i	−0.0953463	+	0.165145i
$111$		0			0
$112$	0.143594	+	0.248711i	0.0135683	+	0.0235010i
$113$	2.83013	+	4.90192i	0.266236	+	0.461134i	0.967887	−	0.251387i	$-0.0808866\pi$
$113$	2.83013	+	4.90192i	0.266236	+	0.461134i	−0.701651	+	0.712521i	$0.747553\pi$
$114$		0			0
$115$	−10.9282	+	18.9282i	−1.01906	+	1.76506i
$116$	−6.92820			−0.643268
$117$		0			0
$118$	0.143594			0.0132189
$119$	−0.830127	+	1.43782i	−0.0760976	+	0.131805i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	2.83013	+	4.90192i	0.256228	+	0.443799i
$123$		0			0
$124$	5.46410	−	9.46410i	0.490691	−	0.849901i
$125$	6.92820			0.619677
$126$		0			0
$127$	−1.46410			−0.129918			−0.0649590	−	0.997888i	$-0.520692\pi$
$127$	−1.46410			−0.129918			−0.0649590	+	0.997888i	$0.520692\pi$
$128$	5.07180	−	8.78461i	0.448288	−	0.776457i
$129$		0			0
$130$	−3.73205	−	6.46410i	−0.327323	−	0.566939i
$131$	4.56218	+	7.90192i	0.398599	+	0.690394i	0.993553	−	0.113365i	$-0.0361631\pi$
$131$	4.56218	+	7.90192i	0.398599	+	0.690394i	−0.594954	+	0.803760i	$0.702830\pi$
$132$		0			0
$133$	0.696152	−	1.20577i	0.0603641	−	0.104554i
$134$	−5.80385			−0.501376
$135$		0			0
$136$	15.7128			1.34736
$137$	6.19615	−	10.7321i	0.529373	−	0.916901i	−0.470040	−	0.882645i	$-0.655761\pi$
$137$	6.19615	−	10.7321i	0.529373	−	0.916901i	0.999413	−	0.0342559i	$-0.0109061\pi$
$138$		0			0
$139$	−1.59808	−	2.76795i	−0.135547	−	0.234774i	0.790259	−	0.612773i	$-0.209946\pi$
$139$	−1.59808	−	2.76795i	−0.135547	−	0.234774i	−0.925806	+	0.377998i	$0.876613\pi$
$140$	0.535898	+	0.928203i	0.0452917	+	0.0784475i
$141$		0			0
$142$	5.07180	−	8.78461i	0.425616	−	0.737188i
$143$	3.73205			0.312090
$144$		0			0
$145$	−12.9282			−1.07363
$146$	2.63397	−	4.56218i	0.217989	−	0.377569i
$147$		0			0
$148$	0.339746	+	0.588457i	0.0279269	+	0.0483709i
$149$	−8.92820	−	15.4641i	−0.731427	−	1.26687i	−0.956273	−	0.292474i	$-0.905521\pi$
$149$	−8.92820	−	15.4641i	−0.731427	−	1.26687i	0.224846	−	0.974394i	$-0.427812\pi$
$150$		0			0
$151$	7.59808	−	13.1603i	0.618323	−	1.07097i	−0.371469	−	0.928445i	$-0.621146\pi$
$151$	7.59808	−	13.1603i	0.618323	−	1.07097i	0.989792	−	0.142521i	$-0.0455208\pi$
$152$	−13.1769			−1.06879
$153$		0			0
$154$	0.196152			0.0158064
$155$	10.1962	−	17.6603i	0.818975	−	1.41851i
$156$		0			0
$157$	−8.73205	−	15.1244i	−0.696894	−	1.20705i	−0.969538	−	0.244940i	$-0.921232\pi$
$157$	−8.73205	−	15.1244i	−0.696894	−	1.20705i	0.272645	−	0.962115i	$-0.412102\pi$
$158$	0.830127	+	1.43782i	0.0660414	+	0.114387i
$159$		0			0
$160$	8.00000	−	13.8564i	0.632456	−	1.09545i
$161$	2.14359			0.168939
$162$		0			0
$163$	19.0000			1.48819			0.744097	−	0.668071i	$-0.232880\pi$
$163$	19.0000			1.48819			0.744097	+	0.668071i	$0.232880\pi$
$164$	4.00000	−	6.92820i	0.312348	−	0.541002i
$165$		0			0
$166$		0			0
$167$	9.63397	+	16.6865i	0.745499	+	1.29124i	0.949961	+	0.312368i	$0.101122\pi$
$167$	9.63397	+	16.6865i	0.745499	+	1.29124i	−0.204462	+	0.978875i	$0.565544\pi$
$168$		0			0
$169$	−0.464102	+	0.803848i	−0.0357001	+	0.0618344i
$170$	12.3923			0.950446
$171$		0			0
$172$	5.07180			0.386721
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	−0.365755	−	0.930711i	$-0.619189\pi$
$173$	8.19615	−	14.1962i	0.623142	−	1.07931i	0.988897	−	0.148602i	$-0.0474774\pi$
$174$		0			0
$175$	0.330127	+	0.571797i	0.0249553	+	0.0432238i
$176$	0.535898	+	0.928203i	0.0403949	+	0.0699660i
$177$		0			0
$178$	−6.46410	+	11.1962i	−0.484505	+	0.839187i
$179$	3.80385			0.284313			0.142156	−	0.989844i	$-0.454596\pi$
$179$	3.80385			0.284313			0.142156	+	0.989844i	$0.454596\pi$
$180$		0			0
$181$	18.3205			1.36175			0.680876	−	0.732398i	$-0.261599\pi$
$181$	18.3205			1.36175			0.680876	+	0.732398i	$0.261599\pi$
$182$	−0.366025	+	0.633975i	−0.0271316	+	0.0469933i
$183$		0			0
$184$	−10.1436	−	17.5692i	−0.747796	−	1.29522i
$185$	0.633975	+	1.09808i	0.0466107	+	0.0807322i
$186$		0			0
$187$	−3.09808	+	5.36603i	−0.226554	+	0.392403i
$188$	−0.287187			−0.0209453
$189$		0			0
$190$	−10.3923			−0.753937
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$		0			0
$193$	6.59808	+	11.4282i	0.474940	+	0.822620i	0.999588	−	0.0286991i	$-0.00913645\pi$
$193$	6.59808	+	11.4282i	0.474940	+	0.822620i	−0.524648	+	0.851319i	$0.675803\pi$
$194$	−5.63397	−	9.75833i	−0.404496	−	0.700607i
$195$		0			0
$196$	−5.07180	+	8.78461i	−0.362271	+	0.627472i
$197$	7.66025			0.545771			0.272885	−	0.962047i	$-0.412022\pi$
$197$	7.66025			0.545771			0.272885	+	0.962047i	$0.412022\pi$
$198$		0			0
$199$	−15.0000			−1.06332			−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000			−1.06332			−0.531661	+	0.846957i	$0.678432\pi$
$200$	3.12436	−	5.41154i	0.220925	−	0.382654i
$201$		0			0
$202$	3.73205	+	6.46410i	0.262586	+	0.454813i
$203$	0.633975	+	1.09808i	0.0444963	+	0.0770698i
$204$		0			0
$205$	7.46410	−	12.9282i	0.521315	−	0.902945i
$206$	−10.8756			−0.757742
$207$		0			0
$208$	−4.00000			−0.277350
$209$	2.59808	−	4.50000i	0.179713	−	0.311272i
$210$		0			0
$211$	13.3301	+	23.0885i	0.917684	+	1.58947i	0.802924	+	0.596082i	$0.203277\pi$
$211$	13.3301	+	23.0885i	0.917684	+	1.58947i	0.114760	+	0.993393i	$0.463390\pi$
$212$	−0.928203	−	1.60770i	−0.0637493	−	0.110417i
$213$		0			0
$214$	−4.26795	+	7.39230i	−0.291751	+	0.505328i
$215$	9.46410			0.645446
$216$		0			0
$217$	−2.00000			−0.135769
$218$	5.80385	−	10.0526i	0.393086	−	0.680845i
$219$		0			0
$220$	2.00000	+	3.46410i	0.134840	+	0.233550i
$221$	−11.5622	−	20.0263i	−0.777756	−	1.34711i
$222$		0			0
$223$	4.92820	−	8.53590i	0.330017	−	0.571606i	−0.652498	−	0.757791i	$-0.726279\pi$
$223$	4.92820	−	8.53590i	0.330017	−	0.571606i	0.982515	+	0.186184i	$0.0596122\pi$
$224$	−1.56922			−0.104848
$225$		0			0
$226$	−4.14359			−0.275628
$227$	−6.16987	+	10.6865i	−0.409509	+	0.709290i	−0.994835	−	0.101508i	$-0.967633\pi$
$227$	−6.16987	+	10.6865i	−0.409509	+	0.709290i	0.585326	+	0.810798i	$0.300967\pi$
$228$		0			0
$229$	−2.19615	−	3.80385i	−0.145126	−	0.251365i	0.784294	−	0.620389i	$-0.213025\pi$
$229$	−2.19615	−	3.80385i	−0.145126	−	0.251365i	−0.929420	+	0.369024i	$0.879692\pi$
$230$	−8.00000	−	13.8564i	−0.527504	−	0.913664i
$231$		0			0
$232$	6.00000	−	10.3923i	0.393919	−	0.682288i
$233$	23.6603			1.55003			0.775017	−	0.631940i	$-0.217741\pi$
$233$	23.6603			1.55003			0.775017	+	0.631940i	$0.217741\pi$
$234$		0			0
$235$	−0.535898			−0.0349582
$236$	0.143594	−	0.248711i	0.00934714	−	0.0161897i
$237$		0			0
$238$	−0.607695	−	1.05256i	−0.0393910	−	0.0682273i
$239$	−2.19615	−	3.80385i	−0.142057	−	0.246050i	0.786214	−	0.617954i	$-0.212038\pi$
$239$	−2.19615	−	3.80385i	−0.142057	−	0.246050i	−0.928271	+	0.371904i	$0.878705\pi$
$240$		0			0
$241$	−2.40192	+	4.16025i	−0.154722	+	0.267986i	−0.932958	−	0.359986i	$-0.882781\pi$
$241$	−2.40192	+	4.16025i	−0.154722	+	0.267986i	0.778236	+	0.627972i	$0.216115\pi$
$242$	0.732051			0.0470580
$243$		0			0
$244$	11.3205			0.724721
$245$	−9.46410	+	16.3923i	−0.604639	+	1.04727i
$246$		0			0
$247$	9.69615	+	16.7942i	0.616951	+	1.06859i
$248$	9.46410	+	16.3923i	0.600971	+	1.04091i
$249$		0			0
$250$	−2.53590	+	4.39230i	−0.160384	+	0.277794i
$251$	20.5885			1.29953			0.649766	−	0.760134i	$-0.274867\pi$
$251$	20.5885			1.29953			0.649766	+	0.760134i	$0.274867\pi$
$252$		0			0
$253$	8.00000			0.502956
$254$	0.535898	−	0.928203i	0.0336253	−	0.0582407i
$255$		0			0
$256$	5.85641	+	10.1436i	0.366025	+	0.633975i
$257$	−4.63397	−	8.02628i	−0.289059	−	0.500666i	0.684526	−	0.728988i	$-0.260009\pi$
$257$	−4.63397	−	8.02628i	−0.289059	−	0.500666i	−0.973585	+	0.228323i	$0.926676\pi$
$258$		0			0
$259$	0.0621778	−	0.107695i	0.00386354	−	0.00669185i
$260$	−14.9282			−0.925808
$261$		0			0
$262$	−6.67949			−0.412660
$263$	14.5622	−	25.2224i	0.897942	−	1.55528i	0.0678221	−	0.997697i	$-0.478395\pi$
$263$	14.5622	−	25.2224i	0.897942	−	1.55528i	0.830120	−	0.557584i	$-0.188272\pi$
$264$		0			0
$265$	−1.73205	−	3.00000i	−0.106399	−	0.184289i
$266$	0.509619	+	0.882686i	0.0312467	+	0.0541209i
$267$		0			0
$268$	−5.80385	+	10.0526i	−0.354526	+	0.614058i
$269$	13.0718			0.797002			0.398501	−	0.917168i	$-0.369531\pi$
$269$	13.0718			0.797002			0.398501	+	0.917168i	$0.369531\pi$
$270$		0			0
$271$	−5.73205			−0.348197			−0.174099	−	0.984728i	$-0.555701\pi$
$271$	−5.73205			−0.348197			−0.174099	+	0.984728i	$0.555701\pi$
$272$	3.32051	−	5.75129i	0.201335	−	0.348723i
$273$		0			0
$274$	4.53590	+	7.85641i	0.274024	+	0.474623i
$275$	1.23205	+	2.13397i	0.0742955	+	0.128684i
$276$		0			0
$277$	−8.92820	+	15.4641i	−0.536444	+	0.929148i	0.462648	+	0.886542i	$0.346899\pi$
$277$	−8.92820	+	15.4641i	−0.536444	+	0.929148i	−0.999092	+	0.0426059i	$0.986434\pi$
$278$	2.33975			0.140329
$279$		0			0
$280$	−1.85641			−0.110942
$281$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$281$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$282$		0			0
$283$	−11.1244	−	19.2679i	−0.661274	−	1.14536i	−0.980281	−	0.197608i	$-0.936683\pi$
$283$	−11.1244	−	19.2679i	−0.661274	−	1.14536i	0.319007	−	0.947752i	$-0.396651\pi$
$284$	−10.1436	−	17.5692i	−0.601912	−	1.04254i
$285$		0			0
$286$	−1.36603	+	2.36603i	−0.0807748	+	0.139906i
$287$	−1.46410			−0.0864232
$288$		0			0
$289$	21.3923			1.25837
$290$	4.73205	−	8.19615i	0.277876	−	0.481295i
$291$		0			0
$292$	−5.26795	−	9.12436i	−0.308283	−	0.533963i
$293$	−1.43782	−	2.49038i	−0.0839985	−	0.145490i	0.820966	−	0.570978i	$-0.193436\pi$
$293$	−1.43782	−	2.49038i	−0.0839985	−	0.145490i	−0.904964	+	0.425488i	$0.860102\pi$
$294$		0			0
$295$	0.267949	−	0.464102i	0.0156006	−	0.0270210i
$296$	−1.17691			−0.0684068
$297$		0			0
$298$	13.0718			0.757229
$299$	−14.9282	+	25.8564i	−0.863320	+	1.49531i
$300$		0			0
$301$	−0.464102	−	0.803848i	−0.0267504	−	0.0463330i
$302$	5.56218	+	9.63397i	0.320067	+	0.554373i
$303$		0			0
$304$	−2.78461	+	4.82309i	−0.159708	+	0.276623i
$305$	21.1244			1.20958
$306$		0			0
$307$	7.32051			0.417803			0.208902	−	0.977937i	$-0.433011\pi$
$307$	7.32051			0.417803			0.208902	+	0.977937i	$0.433011\pi$
$308$	0.196152	−	0.339746i	0.0111768	−	0.0193588i
$309$		0			0
$310$	7.46410	+	12.9282i	0.423932	+	0.734273i
$311$	−0.294229	−	0.509619i	−0.0166842	−	0.0288978i	0.857563	−	0.514379i	$-0.171978\pi$
$311$	−0.294229	−	0.509619i	−0.0166842	−	0.0288978i	−0.874247	+	0.485481i	$0.838644\pi$
$312$		0			0
$313$	−5.96410	+	10.3301i	−0.337111	+	0.583893i	−0.983888	−	0.178786i	$-0.942783\pi$
$313$	−5.96410	+	10.3301i	−0.337111	+	0.583893i	0.646777	+	0.762679i	$0.276116\pi$
$314$	12.7846			0.721477
$315$		0			0
$316$	3.32051			0.186793
$317$	−10.2942	+	17.8301i	−0.578181	+	1.00144i	0.417506	+	0.908674i	$0.362904\pi$
$317$	−10.2942	+	17.8301i	−0.578181	+	1.00144i	−0.995688	+	0.0927658i	$0.970429\pi$
$318$		0			0
$319$	2.36603	+	4.09808i	0.132472	+	0.229448i
$320$	2.92820	+	5.07180i	0.163692	+	0.283522i
$321$		0			0
$322$	−0.784610	+	1.35898i	−0.0437246	+	0.0757332i
$323$	−32.1962			−1.79144
$324$		0			0
$325$	−9.19615			−0.510111
$326$	−6.95448	+	12.0455i	−0.385173	+	0.667140i
$327$		0			0
$328$	6.92820	+	12.0000i	0.382546	+	0.662589i
$329$	0.0262794	+	0.0455173i	0.00144883	+	0.00250945i
$330$		0			0
$331$	3.30385	−	5.72243i	0.181596	−	0.314533i	−0.760828	−	0.648953i	$-0.775207\pi$
$331$	3.30385	−	5.72243i	0.181596	−	0.314533i	0.942424	+	0.334420i	$0.108540\pi$
$332$		0			0
$333$		0			0
$334$	−14.1051			−0.771798
$335$	−10.8301	+	18.7583i	−0.591713	+	1.02488i
$336$		0			0
$337$	−10.9904	−	19.0359i	−0.598684	−	1.03695i	−0.993016	−	0.117983i	$-0.962357\pi$
$337$	−10.9904	−	19.0359i	−0.598684	−	1.03695i	0.394331	−	0.918968i	$-0.370976\pi$
$338$	−0.339746	−	0.588457i	−0.0184797	−	0.0320079i
$339$		0			0
$340$	12.3923	−	21.4641i	0.672067	−	1.16405i
$341$	−7.46410			−0.404204
$342$		0			0
$343$	3.73205			0.201512
$344$	−4.39230	+	7.60770i	−0.236817	+	0.410179i
$345$		0			0
$346$	6.00000	+	10.3923i	0.322562	+	0.558694i
$347$	13.8301	+	23.9545i	0.742440	+	1.28594i	0.951381	+	0.308016i	$0.0996650\pi$
$347$	13.8301	+	23.9545i	0.742440	+	1.28594i	−0.208941	+	0.977928i	$0.567002\pi$
$348$		0			0
$349$	15.0622	−	26.0885i	0.806260	−	1.39648i	−0.109177	−	0.994022i	$-0.534822\pi$
$349$	15.0622	−	26.0885i	0.806260	−	1.39648i	0.915437	−	0.402461i	$-0.131845\pi$
$350$	−0.483340			−0.0258356
$351$		0			0
$352$	−5.85641			−0.312148
$353$	−1.56218	+	2.70577i	−0.0831463	+	0.144014i	−0.904600	−	0.426262i	$-0.859830\pi$
$353$	−1.56218	+	2.70577i	−0.0831463	+	0.144014i	0.821453	+	0.570276i	$0.193164\pi$
$354$		0			0
$355$	−18.9282	−	32.7846i	−1.00460	−	1.74003i
$356$	12.9282	+	22.3923i	0.685193	+	1.18679i
$357$		0			0
$358$	−1.39230	+	2.41154i	−0.0735856	+	0.127454i
$359$	−13.4641			−0.710608			−0.355304	−	0.934751i	$-0.615623\pi$
$359$	−13.4641			−0.710608			−0.355304	+	0.934751i	$0.615623\pi$
$360$		0			0
$361$	8.00000			0.421053
$362$	−6.70577	+	11.6147i	−0.352448	+	0.610457i
$363$		0			0
$364$	0.732051	+	1.26795i	0.0383699	+	0.0664586i
$365$	−9.83013	−	17.0263i	−0.514532	−	0.891196i
$366$		0			0
$367$	−0.0358984	+	0.0621778i	−0.00187388	+	0.00324566i	−0.866961	−	0.498376i	$-0.833930\pi$
$367$	−0.0358984	+	0.0621778i	−0.00187388	+	0.00324566i	0.865087	+	0.501622i	$0.167263\pi$
$368$	−8.57437			−0.446970
$369$		0			0
$370$	−0.928203			−0.0482550
$371$	−0.169873	+	0.294229i	−0.00881937	+	0.0152756i
$372$		0			0
$373$	−2.06218	−	3.57180i	−0.106776	−	0.184941i	0.807687	−	0.589612i	$-0.200719\pi$
$373$	−2.06218	−	3.57180i	−0.106776	−	0.184941i	−0.914462	+	0.404671i	$0.867386\pi$
$374$	−2.26795	−	3.92820i	−0.117273	−	0.203123i
$375$		0			0
$376$	0.248711	−	0.430781i	0.0128263	−	0.0222158i
$377$	−17.6603			−0.909549
$378$		0			0
$379$	−12.8564			−0.660389			−0.330195	−	0.943913i	$-0.607114\pi$
$379$	−12.8564			−0.660389			−0.330195	+	0.943913i	$0.607114\pi$
$380$	−10.3923	+	18.0000i	−0.533114	+	0.923381i
$381$		0			0
$382$	−1.46410	−	2.53590i	−0.0749100	−	0.129748i
$383$	10.6340	+	18.4186i	0.543371	+	0.941146i	0.998708	+	0.0508264i	$0.0161855\pi$
$383$	10.6340	+	18.4186i	0.543371	+	0.941146i	−0.455337	+	0.890319i	$0.650481\pi$
$384$		0			0
$385$	0.366025	−	0.633975i	0.0186544	−	0.0323103i
$386$	−9.66025			−0.491694
$387$		0			0
$388$	−22.5359			−1.14409
$389$	7.26795	−	12.5885i	0.368500	−	0.638260i	−0.620832	−	0.783944i	$-0.713205\pi$
$389$	7.26795	−	12.5885i	0.368500	−	0.638260i	0.989331	+	0.145684i	$0.0465382\pi$
$390$		0			0
$391$	−24.7846	−	42.9282i	−1.25341	−	2.17097i
$392$	−8.78461	−	15.2154i	−0.443690	−	0.768493i
$393$		0			0
$394$	−2.80385	+	4.85641i	−0.141256	+	0.244662i
$395$	6.19615			0.311762
$396$		0			0
$397$	−0.392305			−0.0196892			−0.00984461	−	0.999952i	$-0.503134\pi$
$397$	−0.392305			−0.0196892			−0.00984461	+	0.999952i	$0.503134\pi$
$398$	5.49038	−	9.50962i	0.275208	−	0.476674i
$399$		0			0
$400$	−1.32051	−	2.28719i	−0.0660254	−	0.114359i
$401$	−6.73205	−	11.6603i	−0.336183	−	0.582285i	0.647529	−	0.762041i	$-0.275803\pi$
$401$	−6.73205	−	11.6603i	−0.336183	−	0.582285i	−0.983711	+	0.179756i	$0.942469\pi$
$402$		0			0
$403$	13.9282	−	24.1244i	0.693813	−	1.20172i
$404$	14.9282			0.742706
$405$		0			0
$406$	−0.928203			−0.0460660
$407$	0.232051	−	0.401924i	0.0115023	−	0.0199226i
$408$		0			0
$409$	16.4545	+	28.5000i	0.813622	+	1.40923i	0.910313	+	0.413920i	$0.135841\pi$
$409$	16.4545	+	28.5000i	0.813622	+	1.40923i	−0.0966915	+	0.995314i	$0.530826\pi$
$410$	5.46410	+	9.46410i	0.269853	+	0.467399i
$411$		0			0
$412$	−10.8756	+	18.8372i	−0.535805	+	0.928041i
$413$	−0.0525589			−0.00258625
$414$		0			0
$415$		0			0
$416$	10.9282	−	18.9282i	0.535799	−	0.928032i
$417$		0			0
$418$	1.90192	+	3.29423i	0.0930261	+	0.161126i
$419$	−15.8564	−	27.4641i	−0.774636	−	1.34171i	−0.934999	−	0.354651i	$-0.884600\pi$
$419$	−15.8564	−	27.4641i	−0.774636	−	1.34171i	0.160363	−	0.987058i	$-0.448734\pi$
$420$		0			0
$421$	3.42820	−	5.93782i	0.167080	−	0.289392i	−0.770312	−	0.637668i	$-0.779899\pi$
$421$	3.42820	−	5.93782i	0.167080	−	0.289392i	0.937392	+	0.348276i	$0.113233\pi$
$422$	−19.5167			−0.950056
$423$		0			0
$424$	3.21539			0.156153
$425$	7.63397	−	13.2224i	0.370302	−	0.641382i
$426$		0			0
$427$	−1.03590	−	1.79423i	−0.0501306	−	0.0868288i
$428$	8.53590	+	14.7846i	0.412598	+	0.714641i
$429$		0			0
$430$	−3.46410	+	6.00000i	−0.167054	+	0.289346i
$431$	−21.4641			−1.03389			−0.516945	−	0.856019i	$-0.672931\pi$
$431$	−21.4641			−1.03389			−0.516945	+	0.856019i	$0.672931\pi$
$432$		0			0
$433$	−24.3923			−1.17222			−0.586110	−	0.810232i	$-0.699341\pi$
$433$	−24.3923			−1.17222			−0.586110	+	0.810232i	$0.699341\pi$
$434$	0.732051	−	1.26795i	0.0351396	−	0.0608635i
$435$		0			0
$436$	−11.6077	−	20.1051i	−0.555908	−	0.962861i
$437$	20.7846	+	36.0000i	0.994263	+	1.72211i
$438$		0			0
$439$	−18.7321	+	32.4449i	−0.894032	+	1.54851i	−0.0590339	+	0.998256i	$0.518802\pi$
$439$	−18.7321	+	32.4449i	−0.894032	+	1.54851i	−0.834998	+	0.550253i	$0.814531\pi$
$440$	−6.92820			−0.330289
$441$		0			0
$442$	16.9282			0.805193
$443$	−3.36603	+	5.83013i	−0.159925	+	0.276998i	−0.934841	−	0.355066i	$-0.884458\pi$
$443$	−3.36603	+	5.83013i	−0.159925	+	0.276998i	0.774917	+	0.632063i	$0.217792\pi$
$444$		0			0
$445$	24.1244	+	41.7846i	1.14360	+	1.98078i
$446$	3.60770	+	6.24871i	0.170829	+	0.295885i
$447$		0			0
$448$	0.287187	−	0.497423i	0.0135683	−	0.0235010i
$449$	−38.2487			−1.80507			−0.902534	−	0.430618i	$-0.858296\pi$
$449$	−38.2487			−1.80507			−0.902534	+	0.430618i	$0.858296\pi$
$450$		0			0
$451$	−5.46410			−0.257294
$452$	−4.14359	+	7.17691i	−0.194898	+	0.337574i
$453$		0			0
$454$	−4.51666	−	7.82309i	−0.211977	−	0.367156i
$455$	1.36603	+	2.36603i	0.0640403	+	0.110921i
$456$		0			0
$457$	12.4641	−	21.5885i	0.583046	−	1.00987i	−0.412070	−	0.911152i	$-0.635194\pi$
$457$	12.4641	−	21.5885i	0.583046	−	1.00987i	0.995116	−	0.0987132i	$-0.0314726\pi$
$458$	3.21539			0.150245
$459$		0			0
$460$	−32.0000			−1.49201
$461$	−6.16987	+	10.6865i	−0.287360	+	0.497721i	−0.973179	−	0.230051i	$-0.926111\pi$
$461$	−6.16987	+	10.6865i	−0.287360	+	0.497721i	0.685819	+	0.727772i	$0.259444\pi$
$462$		0			0
$463$	−7.89230	−	13.6699i	−0.366787	−	0.635293i	0.622275	−	0.782799i	$-0.286209\pi$
$463$	−7.89230	−	13.6699i	−0.366787	−	0.635293i	−0.989061	+	0.147506i	$0.952875\pi$
$464$	−2.53590	−	4.39230i	−0.117726	−	0.203908i
$465$		0			0
$466$	−8.66025	+	15.0000i	−0.401179	+	0.694862i
$467$	5.07180			0.234695			0.117347	−	0.993091i	$-0.462561\pi$
$467$	5.07180			0.234695			0.117347	+	0.993091i	$0.462561\pi$
$468$		0			0
$469$	2.12436			0.0980936
$470$	0.196152	−	0.339746i	0.00904784	−	0.0156713i
$471$		0			0
$472$	0.248711	+	0.430781i	0.0114479	+	0.0198283i
$473$	−1.73205	−	3.00000i	−0.0796398	−	0.137940i
$474$		0			0
$475$	−6.40192	+	11.0885i	−0.293740	+	0.508773i
$476$	−2.43078			−0.111415
$477$		0			0
$478$	3.21539			0.147069
$479$	16.7583	−	29.0263i	0.765708	−	1.32624i	−0.174164	−	0.984717i	$-0.555722\pi$
$479$	16.7583	−	29.0263i	0.765708	−	1.32624i	0.939872	−	0.341528i	$-0.110944\pi$
$480$		0			0
$481$	0.866025	+	1.50000i	0.0394874	+	0.0683941i
$482$	−1.75833	−	3.04552i	−0.0800897	−	0.138720i
$483$		0			0
$484$	0.732051	−	1.26795i	0.0332750	−	0.0576341i
$485$	−42.0526			−1.90951
$486$		0			0
$487$	−8.85641			−0.401322			−0.200661	−	0.979661i	$-0.564309\pi$
$487$	−8.85641			−0.401322			−0.200661	+	0.979661i	$0.564309\pi$
$488$	−9.80385	+	16.9808i	−0.443799	+	0.768683i
$489$		0			0
$490$	−6.92820	−	12.0000i	−0.312984	−	0.542105i
$491$	4.02628	+	6.97372i	0.181703	+	0.314720i	0.942461	−	0.334317i	$-0.108506\pi$
$491$	4.02628	+	6.97372i	0.181703	+	0.314720i	−0.760757	+	0.649036i	$0.775172\pi$
$492$		0			0
$493$	14.6603	−	25.3923i	0.660265	−	1.14361i
$494$	−14.1962			−0.638715
$495$		0			0
$496$	8.00000			0.359211
$497$	−1.85641	+	3.21539i	−0.0832712	+	0.144230i
$498$		0			0
$499$	6.26795	+	10.8564i	0.280592	+	0.485999i	0.971531	−	0.236914i	$-0.0761359\pi$
$499$	6.26795	+	10.8564i	0.280592	+	0.485999i	−0.690939	+	0.722913i	$0.742803\pi$
$500$	5.07180	+	8.78461i	0.226818	+	0.392860i
$501$		0			0
$502$	−7.53590	+	13.0526i	−0.336344	+	0.582564i
$503$	−9.07180			−0.404491			−0.202246	−	0.979335i	$-0.564824\pi$
$503$	−9.07180			−0.404491			−0.202246	+	0.979335i	$0.564824\pi$
$504$		0			0
$505$	27.8564			1.23959
$506$	−2.92820	+	5.07180i	−0.130175	+	0.225469i
$507$		0			0
$508$	−1.07180	−	1.85641i	−0.0475533	−	0.0823647i
$509$	−11.0263	−	19.0981i	−0.488731	−	0.846507i	0.511185	−	0.859471i	$-0.329207\pi$
$509$	−11.0263	−	19.0981i	−0.488731	−	0.846507i	−0.999916	+	0.0129635i	$0.995873\pi$
$510$		0			0
$511$	−0.964102	+	1.66987i	−0.0426493	+	0.0738708i
$512$	11.7128			0.517638
$513$		0			0
$514$	6.78461			0.299256
$515$	−20.2942	+	35.1506i	−0.894271	+	1.54892i
$516$		0			0
$517$	0.0980762	+	0.169873i	0.00431339	+	0.00747101i
$518$	0.0455173	+	0.0788383i	0.00199992	+	0.00346396i
$519$		0			0
$520$	12.9282	−	22.3923i	0.566939	−	0.981968i
$521$	20.7846			0.910590			0.455295	−	0.890341i	$-0.349534\pi$
$521$	20.7846			0.910590			0.455295	+	0.890341i	$0.349534\pi$
$522$		0			0
$523$	−11.9808			−0.523882			−0.261941	−	0.965084i	$-0.584363\pi$
$523$	−11.9808			−0.523882			−0.261941	+	0.965084i	$0.584363\pi$
$524$	−6.67949	+	11.5692i	−0.291795	+	0.505404i
$525$		0			0
$526$	10.6603	+	18.4641i	0.464809	+	0.805073i
$527$	23.1244	+	40.0526i	1.00731	+	1.74472i
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	2.53590			0.110152
$531$		0			0
$532$	2.03848			0.0883791
$533$	10.1962	−	17.6603i	0.441644	−	0.764951i
$534$		0			0
$535$	15.9282	+	27.5885i	0.688636	+	1.19275i
$536$	−10.0526	−	17.4115i	−0.434204	−	0.752064i
$537$		0			0
$538$	−4.78461	+	8.28719i	−0.206279	+	0.357286i
$539$	6.92820			0.298419
$540$		0			0
$541$	7.58846			0.326253			0.163127	−	0.986605i	$-0.447842\pi$
$541$	7.58846			0.326253			0.163127	+	0.986605i	$0.447842\pi$
$542$	2.09808	−	3.63397i	0.0901201	−	0.156093i
$543$		0			0
$544$	18.1436	+	31.4256i	0.777900	+	1.34736i
$545$	−21.6603	−	37.5167i	−0.927823	−	1.60704i
$546$		0			0
$547$	13.5981	−	23.5526i	0.581412	−	1.00703i	−0.413901	−	0.910322i	$-0.635834\pi$
$547$	13.5981	−	23.5526i	0.581412	−	1.00703i	0.995312	−	0.0967126i	$-0.0308328\pi$
$548$	18.1436			0.775056
$549$		0			0
$550$	−1.80385			−0.0769163
$551$	−12.2942	+	21.2942i	−0.523752	+	0.907165i
$552$		0			0
$553$	−0.303848	−	0.526279i	−0.0129209	−	0.0223797i
$554$	−6.53590	−	11.3205i	−0.277684	−	0.480962i
$555$		0			0
$556$	2.33975	−	4.05256i	0.0992273	−	0.171867i
$557$	−32.7321			−1.38690			−0.693451	−	0.720504i	$-0.743911\pi$
$557$	−32.7321			−1.38690			−0.693451	+	0.720504i	$0.743911\pi$
$558$		0			0
$559$	12.9282			0.546805
$560$	−0.392305	+	0.679492i	−0.0165779	+	0.0287138i
$561$		0			0
$562$		0			0
$563$	9.85641	+	17.0718i	0.415398	+	0.719490i	0.995470	−	0.0950747i	$-0.0303090\pi$
$563$	9.85641	+	17.0718i	0.415398	+	0.719490i	−0.580072	+	0.814565i	$0.696976\pi$
$564$		0			0
$565$	−7.73205	+	13.3923i	−0.325290	+	0.563418i
$566$	16.2872			0.684602
$567$		0			0
$568$	35.1384			1.47438
$569$	0.339746	−	0.588457i	0.0142429	−	0.0246694i	−0.858816	−	0.512284i	$-0.828800\pi$
$569$	0.339746	−	0.588457i	0.0142429	−	0.0246694i	0.873059	+	0.487615i	$0.162133\pi$
$570$		0			0
$571$	−3.93782	−	6.82051i	−0.164793	−	0.285429i	0.771789	−	0.635879i	$-0.219362\pi$
$571$	−3.93782	−	6.82051i	−0.164793	−	0.285429i	−0.936582	+	0.350449i	$0.886029\pi$
$572$	2.73205	+	4.73205i	0.114233	+	0.197857i
$573$		0			0
$574$	0.535898	−	0.928203i	0.0223680	−	0.0387425i
$575$	−19.7128			−0.822081
$576$		0			0
$577$	−3.00000			−0.124892			−0.0624458	−	0.998048i	$-0.519890\pi$
$577$	−3.00000			−0.124892			−0.0624458	+	0.998048i	$0.519890\pi$
$578$	−7.83013	+	13.5622i	−0.325690	+	0.564112i
$579$		0			0
$580$	−9.46410	−	16.3923i	−0.392975	−	0.680653i
$581$		0			0
$582$		0			0
$583$	−0.633975	+	1.09808i	−0.0262565	+	0.0454777i
$584$	18.2487			0.755137
$585$		0			0
$586$	2.10512			0.0869616
$587$	−16.2942	+	28.2224i	−0.672535	+	1.16486i	0.304648	+	0.952465i	$0.401461\pi$
$587$	−16.2942	+	28.2224i	−0.672535	+	1.16486i	−0.977183	+	0.212399i	$0.931872\pi$
$588$		0			0
$589$	−19.3923	−	33.5885i	−0.799046	−	1.38399i
$590$	0.196152	+	0.339746i	0.00807547	+	0.0139871i
$591$		0			0
$592$	−0.248711	+	0.430781i	−0.0102220	+	0.0177050i
$593$	7.71281			0.316727			0.158364	−	0.987381i	$-0.449378\pi$
$593$	7.71281			0.316727			0.158364	+	0.987381i	$0.449378\pi$
$594$		0			0
$595$	−4.53590			−0.185954
$596$	13.0718	−	22.6410i	0.535442	−	0.927412i
$597$		0			0
$598$	−10.9282	−	18.9282i	−0.446887	−	0.774032i
$599$	−1.12436	−	1.94744i	−0.0459399	−	0.0795703i	0.842141	−	0.539257i	$-0.181295\pi$
$599$	−1.12436	−	1.94744i	−0.0459399	−	0.0795703i	−0.888081	+	0.459687i	$0.847962\pi$
$600$		0			0
$601$	11.9282	−	20.6603i	0.486562	−	0.842749i	−0.513319	−	0.858198i	$-0.671584\pi$
$601$	11.9282	−	20.6603i	0.486562	−	0.842749i	0.999881	+	0.0154485i	$0.00491760\pi$
$602$	0.679492			0.0276940
$603$		0			0
$604$	22.2487			0.905287
$605$	1.36603	−	2.36603i	0.0555368	−	0.0961926i
$606$		0			0
$607$	3.20577	+	5.55256i	0.130118	+	0.225371i	0.923722	−	0.383064i	$-0.125131\pi$
$607$	3.20577	+	5.55256i	0.130118	+	0.225371i	−0.793604	+	0.608435i	$0.791798\pi$
$608$	−15.2154	−	26.3538i	−0.617066	−	1.06879i
$609$		0			0
$610$	−7.73205	+	13.3923i	−0.313062	+	0.542239i
$611$	−0.732051			−0.0296156
$612$		0			0
$613$	−42.9090			−1.73308			−0.866538	−	0.499110i	$-0.833660\pi$
$613$	−42.9090			−1.73308			−0.866538	+	0.499110i	$0.833660\pi$
$614$	−2.67949	+	4.64102i	−0.108135	+	0.187296i
$615$		0			0
$616$	0.339746	+	0.588457i	0.0136888	+	0.0237096i
$617$	5.07180	+	8.78461i	0.204183	+	0.353655i	0.949872	−	0.312639i	$-0.101213\pi$
$617$	5.07180	+	8.78461i	0.204183	+	0.353655i	−0.745689	+	0.666294i	$0.767880\pi$
$618$		0			0
$619$	−6.76795	+	11.7224i	−0.272027	+	0.471164i	−0.969381	−	0.245563i	$-0.921027\pi$
$619$	−6.76795	+	11.7224i	−0.272027	+	0.471164i	0.697354	+	0.716727i	$0.254361\pi$
$620$	29.8564			1.19906
$621$		0			0
$622$	0.430781			0.0172727
$623$	2.36603	−	4.09808i	0.0947928	−	0.164186i
$624$		0			0
$625$	15.6244	+	27.0622i	0.624974	+	1.08249i
$626$	−4.36603	−	7.56218i	−0.174501	−	0.302245i
$627$		0			0
$628$	12.7846	−	22.1436i	0.510161	−	0.883626i
$629$	−2.87564			−0.114659
$630$		0			0
$631$	17.3923			0.692377			0.346188	−	0.938165i	$-0.387476\pi$
$631$	17.3923			0.692377			0.346188	+	0.938165i	$0.387476\pi$
$632$	−2.87564	+	4.98076i	−0.114387	+	0.198124i
$633$		0			0
$634$	−7.53590	−	13.0526i	−0.299289	−	0.518383i
$635$	−2.00000	−	3.46410i	−0.0793676	−	0.137469i
$636$		0			0
$637$	−12.9282	+	22.3923i	−0.512234	+	0.887215i
$638$	−3.46410			−0.137145
$639$		0			0
$640$	27.7128			1.09545
$641$	13.5622	−	23.4904i	0.535674	−	0.927814i	−0.463457	−	0.886120i	$-0.653391\pi$
$641$	13.5622	−	23.4904i	0.535674	−	0.927814i	0.999130	−	0.0416946i	$-0.0132757\pi$
$642$		0			0
$643$	−4.80385	−	8.32051i	−0.189445	−	0.328129i	0.755620	−	0.655010i	$-0.227336\pi$
$643$	−4.80385	−	8.32051i	−0.189445	−	0.328129i	−0.945065	+	0.326881i	$0.894002\pi$
$644$	1.56922	+	2.71797i	0.0618359	+	0.107103i
$645$		0			0
$646$	11.7846	−	20.4115i	0.463659	−	0.803081i
$647$	22.2487			0.874687			0.437344	−	0.899295i	$-0.355919\pi$
$647$	22.2487			0.874687			0.437344	+	0.899295i	$0.355919\pi$
$648$		0			0
$649$	−0.196152			−0.00769966
$650$	3.36603	−	5.83013i	0.132026	−	0.228676i
$651$		0			0
$652$	13.9090	+	24.0910i	0.544717	+	0.943478i
$653$	−11.2679	−	19.5167i	−0.440949	−	0.763746i	0.556811	−	0.830639i	$-0.312025\pi$
$653$	−11.2679	−	19.5167i	−0.440949	−	0.763746i	−0.997760	+	0.0668931i	$0.978691\pi$
$654$		0			0
$655$	−12.4641	+	21.5885i	−0.487013	+	0.843531i
$656$	5.85641			0.228654
$657$		0			0
$658$	−0.0384758			−0.00149994
$659$	−10.1699	+	17.6147i	−0.396162	+	0.686173i	−0.993249	−	0.116004i	$-0.962991\pi$
$659$	−10.1699	+	17.6147i	−0.396162	+	0.686173i	0.597087	+	0.802177i	$0.296325\pi$
$660$		0			0
$661$	−11.6962	−	20.2583i	−0.454928	−	0.787958i	0.543756	−	0.839243i	$-0.317002\pi$
$661$	−11.6962	−	20.2583i	−0.454928	−	0.787958i	−0.998684	+	0.0512854i	$0.983668\pi$
$662$	2.41858	+	4.18911i	0.0940009	+	0.162814i
$663$		0			0
$664$		0			0
$665$	3.80385			0.147507
$666$		0			0
$667$	−37.8564			−1.46581
$668$	−14.1051	+	24.4308i	−0.545743	+	0.945255i
$669$		0			0
$670$	−7.92820	−	13.7321i	−0.306293	−	0.530515i
$671$	−3.86603	−	6.69615i	−0.149246	−	0.258502i
$672$		0			0
$673$	−24.7224	+	42.8205i	−0.952980	+	1.65061i	−0.214055	+	0.976822i	$0.568667\pi$
$673$	−24.7224	+	42.8205i	−0.952980	+	1.65061i	−0.738925	+	0.673788i	$0.764666\pi$
$674$	16.0910			0.619803
$675$		0			0
$676$	−1.35898			−0.0522686
$677$	−9.12436	+	15.8038i	−0.350677	+	0.607391i	−0.986368	−	0.164553i	$-0.947382\pi$
$677$	−9.12436	+	15.8038i	−0.350677	+	0.607391i	0.635691	+	0.771944i	$0.280715\pi$
$678$		0			0
$679$	2.06218	+	3.57180i	0.0791391	+	0.137073i
$680$	21.4641	+	37.1769i	0.823111	+	1.42567i
$681$		0			0
$682$	2.73205	−	4.73205i	0.104616	−	0.181200i
$683$	−8.58846			−0.328628			−0.164314	−	0.986408i	$-0.552541\pi$
$683$	−8.58846			−0.328628			−0.164314	+	0.986408i	$0.552541\pi$
$684$		0			0
$685$	33.8564			1.29359
$686$	−1.36603	+	2.36603i	−0.0521551	+	0.0903353i
$687$		0			0
$688$	1.85641	+	3.21539i	0.0707748	+	0.122586i
$689$	−2.36603	−	4.09808i	−0.0901384	−	0.156124i
$690$		0			0
$691$	24.3923	−	42.2487i	0.927927	−	1.60722i	0.141142	−	0.989989i	$-0.454923\pi$
$691$	24.3923	−	42.2487i	0.927927	−	1.60722i	0.786785	−	0.617227i	$-0.211744\pi$
$692$	24.0000			0.912343
$693$		0			0
$694$	−20.2487			−0.768631
$695$	4.36603	−	7.56218i	0.165613	−	0.286850i
$696$		0			0
$697$	16.9282	+	29.3205i	0.641201	+	1.11059i
$698$	11.0263	+	19.0981i	0.417351	+	0.722873i
$699$		0			0
$700$	−0.483340	+	0.837169i	−0.0182685	+	0.0316420i
$701$	−48.0526			−1.81492			−0.907460	−	0.420138i	$-0.861982\pi$
$701$	−48.0526			−1.81492			−0.907460	+	0.420138i	$0.861982\pi$
$702$		0			0
$703$	2.41154			0.0909531
$704$	1.07180	−	1.85641i	0.0403949	−	0.0699660i
$705$		0			0
$706$	−1.14359	−	1.98076i	−0.0430397	−	0.0745470i
$707$	−1.36603	−	2.36603i	−0.0513747	−	0.0889835i
$708$		0			0
$709$	7.30385	−	12.6506i	0.274302	−	0.475105i	−0.695657	−	0.718374i	$-0.744887\pi$
$709$	7.30385	−	12.6506i	0.274302	−	0.475105i	0.969959	+	0.243270i	$0.0782200\pi$
$710$	27.7128			1.04004
$711$		0			0
$712$	−44.7846			−1.67837
$713$	29.8564	−	51.7128i	1.11813	−	1.93666i
$714$		0			0
$715$	5.09808	+	8.83013i	0.190657	+	0.330228i
$716$	2.78461	+	4.82309i	0.104066	+	0.180247i
$717$		0			0
$718$	4.92820	−	8.53590i	0.183919	−	0.318557i
$719$	28.9808			1.08080			0.540400	−	0.841408i	$-0.318273\pi$
$719$	28.9808			1.08080			0.540400	+	0.841408i	$0.318273\pi$
$720$		0			0
$721$	3.98076			0.148251
$722$	−2.92820	+	5.07180i	−0.108976	+	0.188753i
$723$		0			0
$724$	13.4115	+	23.2295i	0.498436	+	0.863317i
$725$	−5.83013	−	10.0981i	−0.216525	−	0.375033i
$726$		0			0
$727$	−2.66025	+	4.60770i	−0.0986634	+	0.170890i	−0.911132	−	0.412115i	$-0.864790\pi$
$727$	−2.66025	+	4.60770i	−0.0986634	+	0.170890i	0.812468	+	0.583005i	$0.198123\pi$
$728$	−2.53590			−0.0939866
$729$		0			0
$730$	14.3923			0.532683
$731$	−10.7321	+	18.5885i	−0.396939	+	0.687519i
$732$		0			0
$733$	−5.53590	−	9.58846i	−0.204473	−	0.354158i	0.745492	−	0.666515i	$-0.232215\pi$
$733$	−5.53590	−	9.58846i	−0.204473	−	0.354158i	−0.949965	+	0.312357i	$0.898881\pi$
$734$	−0.0262794	−	0.0455173i	−0.000969992	−	0.00168008i
$735$		0			0
$736$	23.4256	−	40.5744i	0.863480	−	1.49559i
$737$	7.92820			0.292039
$738$		0			0
$739$	14.2487			0.524147			0.262074	−	0.965048i	$-0.415594\pi$
$739$	14.2487			0.524147			0.262074	+	0.965048i	$0.415594\pi$
$740$	−0.928203	+	1.60770i	−0.0341214	+	0.0591000i
$741$		0			0
$742$	−0.124356	−	0.215390i	−0.00456524	−	0.00790723i
$743$	−1.29423	−	2.24167i	−0.0474806	−	0.0822389i	0.841308	−	0.540556i	$-0.181786\pi$
$743$	−1.29423	−	2.24167i	−0.0474806	−	0.0822389i	−0.888789	+	0.458317i	$0.848453\pi$
$744$		0			0
$745$	24.3923	−	42.2487i	0.893665	−	1.54787i
$746$	3.01924			0.110542
$747$		0			0
$748$	−9.07180			−0.331698
$749$	1.56218	−	2.70577i	0.0570807	−	0.0988667i
$750$		0			0
$751$	−6.16025	−	10.6699i	−0.224791	−	0.389349i	0.731466	−	0.681878i	$-0.238837\pi$
$751$	−6.16025	−	10.6699i	−0.224791	−	0.389349i	−0.956257	+	0.292529i	$0.905503\pi$
$752$	−0.105118	−	0.182069i	−0.00383325	−	0.00663938i
$753$		0			0
$754$	6.46410	−	11.1962i	0.235409	−	0.407740i
$755$	41.5167			1.51095
$756$		0			0
$757$	−6.32051			−0.229723			−0.114861	−	0.993382i	$-0.536642\pi$
$757$	−6.32051			−0.229723			−0.114861	+	0.993382i	$0.536642\pi$
$758$	4.70577	−	8.15064i	0.170921	−	0.296044i
$759$		0			0
$760$	−18.0000	−	31.1769i	−0.652929	−	1.13091i
$761$	−17.6603	−	30.5885i	−0.640184	−	1.10883i	−0.985391	−	0.170304i	$-0.945525\pi$
$761$	−17.6603	−	30.5885i	−0.640184	−	1.10883i	0.345208	−	0.938526i	$-0.387808\pi$
$762$		0			0
$763$	−2.12436	+	3.67949i	−0.0769068	+	0.133207i
$764$	−5.85641			−0.211877
$765$		0			0
$766$	−15.5692			−0.562539
$767$	0.366025	−	0.633975i	0.0132164	−	0.0228915i
$768$		0			0
$769$	−2.79423	−	4.83975i	−0.100762	−	0.174526i	0.811237	−	0.584718i	$-0.198795\pi$
$769$	−2.79423	−	4.83975i	−0.100762	−	0.174526i	−0.911999	+	0.410192i	$0.865462\pi$
$770$	0.267949	+	0.464102i	0.00965622	+	0.0167251i
$771$		0			0
$772$	−9.66025	+	16.7321i	−0.347680	+	0.602200i
$773$	3.12436			0.112375			0.0561876	−	0.998420i	$-0.482105\pi$
$773$	3.12436			0.112375			0.0561876	+	0.998420i	$0.482105\pi$
$774$		0			0
$775$	18.3923			0.660671
$776$	19.5167	−	33.8038i	0.700607	−	1.21349i
$777$		0			0
$778$	5.32051	+	9.21539i	0.190749	+	0.330388i
$779$	−14.1962	−	24.5885i	−0.508630	−	0.880973i
$780$		0			0
$781$	−6.92820	+	12.0000i	−0.247911	+	0.429394i
$782$	36.2872			1.29763
$783$		0			0
$784$	−7.42563			−0.265201
$785$	23.8564	−	41.3205i	0.851472	−	1.47479i
$786$		0			0
$787$	7.52628	+	13.0359i	0.268283	+	0.464680i	0.968419	−	0.249330i	$-0.0802105\pi$
$787$	7.52628	+	13.0359i	0.268283	+	0.464680i	−0.700136	+	0.714010i	$0.746877\pi$
$788$	5.60770	+	9.71281i	0.199766	+	0.346005i
$789$		0			0
$790$	−2.26795	+	3.92820i	−0.0806900	+	0.139759i
$791$	1.51666			0.0539262
$792$		0			0
$793$	28.8564			1.02472
$794$	0.143594	−	0.248711i	0.00509594	−	0.00882643i
$795$		0			0
$796$	−10.9808	−	19.0192i	−0.389203	−	0.674119i
$797$	4.00000	+	6.92820i	0.141687	+	0.245410i	0.928132	−	0.372251i	$-0.121414\pi$
$797$	4.00000	+	6.92820i	0.141687	+	0.245410i	−0.786445	+	0.617661i	$0.788081\pi$
$798$		0			0
$799$	0.607695	−	1.05256i	0.0214987	−	0.0372369i
$800$	14.4308			0.510205
$801$		0			0
$802$	9.85641			0.348042
$803$	−3.59808	+	6.23205i	−0.126973	+	0.219924i
$804$		0			0
$805$	2.92820	+	5.07180i	0.103206	+	0.178757i
$806$	10.1962	+	17.6603i	0.359144	+	0.622056i
$807$		0			0
$808$	−12.9282	+	22.3923i	−0.454813	+	0.787759i
$809$	−54.5885			−1.91923			−0.959614	−	0.281320i	$-0.909228\pi$
$809$	−54.5885			−1.91923			−0.959614	+	0.281320i	$0.909228\pi$
$810$		0			0
$811$	−0.392305			−0.0137757			−0.00688784	−	0.999976i	$-0.502192\pi$
$811$	−0.392305			−0.0137757			−0.00688784	+	0.999976i	$0.502192\pi$
$812$	−0.928203	+	1.60770i	−0.0325735	+	0.0564190i
$813$		0			0
$814$	0.169873	+	0.294229i	0.00595404	+	0.0103127i
$815$	25.9545	+	44.9545i	0.909146	+	1.57469i
$816$		0			0
$817$	9.00000	−	15.5885i	0.314870	−	0.545371i
$818$	−24.0910			−0.842323
$819$		0			0
$820$	21.8564			0.763259
$821$	4.19615	−	7.26795i	0.146447	−	0.253653i	−0.783465	−	0.621436i	$-0.786550\pi$
$821$	4.19615	−	7.26795i	0.146447	−	0.253653i	0.929912	+	0.367783i	$0.119883\pi$
$822$		0			0
$823$	3.35641	+	5.81347i	0.116997	+	0.202645i	0.918576	−	0.395244i	$-0.129340\pi$
$823$	3.35641	+	5.81347i	0.116997	+	0.202645i	−0.801579	+	0.597888i	$0.796007\pi$
$824$	−18.8372	−	32.6269i	−0.656224	−	1.13661i
$825$		0			0
$826$	0.0192379	−	0.0333210i	0.000669372	−	0.00115939i
$827$	−6.98076			−0.242745			−0.121372	−	0.992607i	$-0.538730\pi$
$827$	−6.98076			−0.242745			−0.121372	+	0.992607i	$0.538730\pi$
$828$		0			0
$829$	−21.3923			−0.742985			−0.371493	−	0.928436i	$-0.621154\pi$
$829$	−21.3923			−0.742985			−0.371493	+	0.928436i	$0.621154\pi$
$830$		0			0
$831$		0			0
$832$	4.00000	+	6.92820i	0.138675	+	0.240192i
$833$	−21.4641	−	37.1769i	−0.743687	−	1.28810i
$834$		0			0
$835$	−26.3205	+	45.5885i	−0.910859	+	1.57765i
$836$	7.60770			0.263118
$837$		0			0
$838$	23.2154			0.801962
$839$	27.5167	−	47.6603i	0.949981	−	1.64541i	0.204523	−	0.978862i	$-0.434436\pi$
$839$	27.5167	−	47.6603i	0.949981	−	1.64541i	0.745458	−	0.666553i	$-0.232231\pi$
$840$		0			0
$841$	3.30385	+	5.72243i	0.113926	+	0.197325i
$842$	2.50962	+	4.34679i	0.0864872	+	0.149800i
$843$		0			0
$844$	−19.5167	+	33.8038i	−0.671791	+	1.16358i
$845$	−2.53590			−0.0872376
$846$		0			0
$847$	−0.267949			−0.00920684
$848$	0.679492	−	1.17691i	0.0233338	−	0.0404154i
$849$		0			0
$850$	5.58846	+	9.67949i	0.191683	+	0.332004i
$851$	1.85641	+	3.21539i	0.0636368	+	0.110222i
$852$		0			0
$853$	−7.86603	+	13.6244i	−0.269328	+	0.466489i	−0.968688	−	0.248280i	$-0.920135\pi$
$853$	−7.86603	+	13.6244i	−0.269328	+	0.466489i	0.699361	+	0.714769i	$0.253468\pi$
$854$	1.51666			0.0518991
$855$		0			0
$856$	−29.5692			−1.01066
$857$	17.0981	−	29.6147i	0.584059	−	1.01162i	−0.410933	−	0.911666i	$-0.634797\pi$
$857$	17.0981	−	29.6147i	0.584059	−	1.01162i	0.994992	−	0.0999545i	$-0.0318697\pi$
$858$		0			0
$859$	−0.571797	−	0.990381i	−0.0195095	−	0.0337914i	0.856106	−	0.516801i	$-0.172877\pi$
$859$	−0.571797	−	0.990381i	−0.0195095	−	0.0337914i	−0.875615	+	0.483009i	$0.839544\pi$
$860$	6.92820	+	12.0000i	0.236250	+	0.409197i
$861$		0			0
$862$	7.85641	−	13.6077i	0.267590	−	0.463480i
$863$	−47.9090			−1.63084			−0.815420	−	0.578870i	$-0.803494\pi$
$863$	−47.9090			−1.63084			−0.815420	+	0.578870i	$0.803494\pi$
$864$		0			0
$865$	44.7846			1.52272
$866$	8.92820	−	15.4641i	0.303393	−	0.525492i
$867$		0			0
$868$	−1.46410	−	2.53590i	−0.0496948	−	0.0860740i
$869$	−1.13397	−	1.96410i	−0.0384675	−	0.0666276i
$870$		0			0
$871$	−14.7942	+	25.6244i	−0.501283	+	0.868248i
$872$	40.2102			1.36169
$873$		0			0
$874$	−30.4308			−1.02934
$875$	0.928203	−	1.60770i	0.0313790	−	0.0543500i
$876$		0			0
$877$	0.401924	+	0.696152i	0.0135720	+	0.0235074i	0.872732	−	0.488200i	$-0.162346\pi$
$877$	0.401924	+	0.696152i	0.0135720	+	0.0235074i	−0.859160	+	0.511708i	$0.829013\pi$
$878$	−13.7128	−	23.7513i	−0.462785	−	0.801567i
$879$		0			0
$880$	−1.46410	+	2.53590i	−0.0493549	+	0.0854851i
$881$	16.6795			0.561946			0.280973	−	0.959716i	$-0.409343\pi$
$881$	16.6795			0.561946			0.280973	+	0.959716i	$0.409343\pi$
$882$		0			0
$883$	−40.3205			−1.35689			−0.678447	−	0.734650i	$-0.737347\pi$
$883$	−40.3205			−1.35689			−0.678447	+	0.734650i	$0.737347\pi$
$884$	16.9282	−	29.3205i	0.569357	−	0.986155i
$885$		0			0
$886$	−2.46410	−	4.26795i	−0.0827831	−	0.143385i
$887$	1.63397	+	2.83013i	0.0548635	+	0.0950264i	0.892153	−	0.451734i	$-0.149194\pi$
$887$	1.63397	+	2.83013i	0.0548635	+	0.0950264i	−0.837289	+	0.546760i	$0.815861\pi$
$888$		0			0
$889$	−0.196152	+	0.339746i	−0.00657874	+	0.0113947i
$890$	−35.3205			−1.18395
$891$		0			0
$892$	14.4308			0.483178
$893$	−0.509619	+	0.882686i	−0.0170537	+	0.0295380i
$894$		0			0
$895$	5.19615	+	9.00000i	0.173688	+	0.300837i
$896$	−1.35898	−	2.35383i	−0.0454005	−	0.0786359i
$897$		0			0
$898$	14.0000	−	24.2487i	0.467186	−	0.809190i
$899$	35.3205			1.17800
$900$		0			0
$901$	7.85641			0.261735
$902$	2.00000	−	3.46410i	0.0665927	−	0.115342i
$903$		0			0
$904$	−7.17691	−	12.4308i	−0.238701	−	0.413442i
$905$	25.0263	+	43.3468i	0.831902	+	1.44090i
$906$		0			0
$907$	−2.76795	+	4.79423i	−0.0919082	+	0.159190i	−0.908314	−	0.418289i	$-0.862630\pi$
$907$	−2.76795	+	4.79423i	−0.0919082	+	0.159190i	0.816406	+	0.577479i	$0.195963\pi$
$908$	−18.0666			−0.599563
$909$		0			0
$910$	−2.00000			−0.0662994
$911$	−1.26795	+	2.19615i	−0.0420090	+	0.0727618i	−0.886265	−	0.463178i	$-0.846709\pi$
$911$	−1.26795	+	2.19615i	−0.0420090	+	0.0727618i	0.844256	+	0.535940i	$0.180042\pi$
$912$		0			0
$913$		0			0
$914$	9.12436	+	15.8038i	0.301807	+	0.522745i
$915$		0			0
$916$	3.21539	−	5.56922i	0.106239	−	0.184012i
$917$	2.44486			0.0807365
$918$		0			0
$919$	−8.67949			−0.286310			−0.143155	−	0.989700i	$-0.545725\pi$
$919$	−8.67949			−0.286310			−0.143155	+	0.989700i	$0.545725\pi$
$920$	27.7128	−	48.0000i	0.913664	−	1.58251i
$921$		0			0
$922$	−4.51666	−	7.82309i	−0.148748	−	0.257640i
$923$	−25.8564	−	44.7846i	−0.851074	−	1.47410i
$924$		0			0
$925$	−0.571797	+	0.990381i	−0.0188006	+	0.0325635i
$926$	11.5551			0.379725
$927$		0			0
$928$	27.7128			0.909718
$929$	23.3660	−	40.4711i	0.766614	−	1.32782i	−0.172774	−	0.984961i	$-0.555273\pi$
$929$	23.3660	−	40.4711i	0.766614	−	1.32782i	0.939389	−	0.342854i	$-0.111394\pi$
$930$		0			0
$931$	18.0000	+	31.1769i	0.589926	+	1.02178i
$932$	17.3205	+	30.0000i	0.567352	+	0.982683i
$933$		0			0
$934$	−1.85641	+	3.21539i	−0.0607435	+	0.105211i
$935$	−16.9282			−0.553611
$936$		0			0
$937$	−34.8038			−1.13699			−0.568496	−	0.822686i	$-0.692475\pi$
$937$	−34.8038			−1.13699			−0.568496	+	0.822686i	$0.692475\pi$
$938$	−0.777568	+	1.34679i	−0.0253885	+	0.0439742i
$939$		0			0
$940$	−0.392305	−	0.679492i	−0.0127956	−	0.0221626i
$941$	16.7321	+	28.9808i	0.545449	+	0.944746i	0.998578	+	0.0533010i	$0.0169743\pi$
$941$	16.7321	+	28.9808i	0.545449	+	0.944746i	−0.453129	+	0.891445i	$0.649692\pi$
$942$		0			0
$943$	21.8564	−	37.8564i	0.711743	−	1.23277i
$944$	0.210236			0.00684258
$945$		0			0
$946$	2.53590			0.0824492
$947$	−3.16987	+	5.49038i	−0.103007	+	0.178413i	−0.912922	−	0.408134i	$-0.866180\pi$
$947$	−3.16987	+	5.49038i	−0.103007	+	0.178413i	0.809915	+	0.586547i	$0.199513\pi$
$948$		0			0
$949$	−13.4282	−	23.2583i	−0.435898	−	0.754997i
$950$	−4.68653	−	8.11731i	−0.152051	−	0.263360i
$951$		0			0
$952$	2.10512	−	3.64617i	0.0682273	−	0.118173i
$953$	33.8564			1.09672			0.548358	−	0.836243i	$-0.315253\pi$
$953$	33.8564			1.09672			0.548358	+	0.836243i	$0.315253\pi$
$954$		0			0
$955$	−10.9282			−0.353628
$956$	3.21539	−	5.56922i	0.103993	−	0.180121i
$957$		0			0
$958$	12.2679	+	21.2487i	0.396359	+	0.686515i
$959$	−1.66025	−	2.87564i	−0.0536124	−	0.0928594i
$960$		0			0
$961$	−12.3564	+	21.4019i	−0.398594	+	0.690385i
$962$	−1.26795			−0.0408803
$963$		0			0
$964$	−7.03332			−0.226528
$965$	−18.0263	+	31.2224i	−0.580286	+	1.00509i
$966$		0			0
$967$	−30.7942	−	53.3372i	−0.990276	−	1.71521i	−0.615619	−	0.788044i	$-0.711094\pi$
$967$	−30.7942	−	53.3372i	−0.990276	−	1.71521i	−0.374657	−	0.927163i	$-0.622240\pi$
$968$	1.26795	+	2.19615i	0.0407534	+	0.0705870i
$969$		0			0
$970$	15.3923	−	26.6603i	0.494217	−	0.856009i
$971$	28.5885			0.917447			0.458724	−	0.888579i	$-0.348307\pi$
$971$	28.5885			0.917447			0.458724	+	0.888579i	$0.348307\pi$
$972$		0			0
$973$	−0.856406			−0.0274551
$974$	3.24167	−	5.61474i	0.103870	−	0.179908i
$975$		0			0
$976$	4.14359	+	7.17691i	0.132633	+	0.229727i
$977$	−9.16987	−	15.8827i	−0.293370	−	0.508132i	0.681234	−	0.732066i	$-0.261444\pi$
$977$	−9.16987	−	15.8827i	−0.293370	−	0.508132i	−0.974604	+	0.223933i	$0.928110\pi$
$978$		0			0
$979$	8.83013	−	15.2942i	0.282212	−	0.488806i
$980$	−27.7128			−0.885253
$981$		0			0
$982$	−5.89488			−0.188113
$983$	11.0263	−	19.0981i	0.351684	−	0.609134i	−0.634861	−	0.772626i	$-0.718943\pi$
$983$	11.0263	−	19.0981i	0.351684	−	0.609134i	0.986545	+	0.163492i	$0.0522759\pi$
$984$		0			0
$985$	10.4641	+	18.1244i	0.333414	+	0.577490i
$986$	10.7321	+	18.5885i	0.341778	+	0.591977i
$987$		0			0
$988$	−14.1962	+	24.5885i	−0.451640	+	0.782263i
$989$	27.7128			0.881216
$990$		0			0
$991$	−19.5359			−0.620578			−0.310289	−	0.950642i	$-0.600426\pi$
$991$	−19.5359			−0.620578			−0.310289	+	0.950642i	$0.600426\pi$
$992$	−21.8564	+	37.8564i	−0.693942	+	1.20194i
$993$		0			0
$994$	−1.35898	−	2.35383i	−0.0431044	−	0.0746589i
$995$	−20.4904	−	35.4904i	−0.649589	−	1.12512i
$996$		0			0
$997$	−13.9282	+	24.1244i	−0.441111	+	0.764026i	−0.997772	−	0.0667134i	$-0.978749\pi$
$997$	−13.9282	+	24.1244i	−0.441111	+	0.764026i	0.556662	+	0.830739i	$0.312082\pi$
$998$	−9.17691			−0.290490
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.e.p.298.1		4
3.2	odd	2		891.2.e.m.298.2		4
9.2	odd	6		297.2.a.f.1.1	yes	2
9.4	even	3	inner	891.2.e.p.595.1		4
9.5	odd	6		891.2.e.m.595.2		4
9.7	even	3		297.2.a.e.1.2	✓	2
36.7	odd	6		4752.2.a.w.1.1		2
36.11	even	6		4752.2.a.bf.1.2		2
45.29	odd	6		7425.2.a.z.1.2		2
45.34	even	6		7425.2.a.bl.1.1		2
99.43	odd	6		3267.2.a.q.1.1		2
99.65	even	6		3267.2.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.a.e.1.2	✓	2	9.7	even	3
297.2.a.f.1.1	yes	2	9.2	odd	6
891.2.e.m.298.2		4	3.2	odd	2
891.2.e.m.595.2		4	9.5	odd	6
891.2.e.p.298.1		4	1.1	even	1	trivial
891.2.e.p.595.1		4	9.4	even	3	inner
3267.2.a.l.1.2		2	99.65	even	6
3267.2.a.q.1.1		2	99.43	odd	6
4752.2.a.w.1.1		2	36.7	odd	6
4752.2.a.bf.1.2		2	36.11	even	6
7425.2.a.z.1.2		2	45.29	odd	6
7425.2.a.bl.1.1		2	45.34	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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 0.633975i) q^{2} +(0.732051 + 1.26795i) q^{4} +(1.36603 + 2.36603i) q^{5} +(0.133975 - 0.232051i) q^{7} -2.53590 q^{8} +O(q^{10})\)	\(q+(-0.366025 + 0.633975i) q^{2} +(0.732051 + 1.26795i) q^{4} +(1.36603 + 2.36603i) q^{5} +(0.133975 - 0.232051i) q^{7} -2.53590 q^{8} -2.00000 q^{10} +(0.500000 - 0.866025i) q^{11} +(1.86603 + 3.23205i) q^{13} +(0.0980762 + 0.169873i) q^{14} +(-0.535898 + 0.928203i) q^{16} -6.19615 q^{17} +5.19615 q^{19} +(-2.00000 + 3.46410i) q^{20} +(0.366025 + 0.633975i) q^{22} +(4.00000 + 6.92820i) q^{23} +(-1.23205 + 2.13397i) q^{25} -2.73205 q^{26} +0.392305 q^{28} +(-2.36603 + 4.09808i) q^{29} +(-3.73205 - 6.46410i) q^{31} +(-2.92820 - 5.07180i) q^{32} +(2.26795 - 3.92820i) q^{34} +0.732051 q^{35} +0.464102 q^{37} +(-1.90192 + 3.29423i) q^{38} +(-3.46410 - 6.00000i) q^{40} +(-2.73205 - 4.73205i) q^{41} +(1.73205 - 3.00000i) q^{43} +1.46410 q^{44} -5.85641 q^{46} +(-0.0980762 + 0.169873i) q^{47} +(3.46410 + 6.00000i) q^{49} +(-0.901924 - 1.56218i) q^{50} +(-2.73205 + 4.73205i) q^{52} -1.26795 q^{53} +2.73205 q^{55} +(-0.339746 + 0.588457i) q^{56} +(-1.73205 - 3.00000i) q^{58} +(-0.0980762 - 0.169873i) q^{59} +(3.86603 - 6.69615i) q^{61} +5.46410 q^{62} +2.14359 q^{64} +(-5.09808 + 8.83013i) q^{65} +(3.96410 + 6.86603i) q^{67} +(-4.53590 - 7.85641i) q^{68} +(-0.267949 + 0.464102i) q^{70} -13.8564 q^{71} -7.19615 q^{73} +(-0.169873 + 0.294229i) q^{74} +(3.80385 + 6.58846i) q^{76} +(-0.133975 - 0.232051i) q^{77} +(1.13397 - 1.96410i) q^{79} -2.92820 q^{80} +4.00000 q^{82} +(-8.46410 - 14.6603i) q^{85} +(1.26795 + 2.19615i) q^{86} +(-1.26795 + 2.19615i) q^{88} +17.6603 q^{89} +1.00000 q^{91} +(-5.85641 + 10.1436i) q^{92} +(-0.0717968 - 0.124356i) q^{94} +(7.09808 + 12.2942i) q^{95} +(-7.69615 + 13.3301i) q^{97} -5.07180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{4} + 2 q^{5} + 4 q^{7} - 24 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^4 + 2 * q^5 + 4 * q^7 - 24 * q^8	\( 4 q + 2 q^{2} - 4 q^{4} + 2 q^{5} + 4 q^{7} - 24 q^{8} - 8 q^{10} + 2 q^{11} + 4 q^{13} - 10 q^{14} - 16 q^{16} - 4 q^{17} - 8 q^{20} - 2 q^{22} + 16 q^{23} + 2 q^{25} - 4 q^{26} - 40 q^{28} - 6 q^{29} - 8 q^{31} + 16 q^{32} + 16 q^{34} - 4 q^{35} - 12 q^{37} - 18 q^{38} - 4 q^{41} - 8 q^{44} + 32 q^{46} + 10 q^{47} - 14 q^{50} - 4 q^{52} - 12 q^{53} + 4 q^{55} - 36 q^{56} + 10 q^{59} + 12 q^{61} + 8 q^{62} + 64 q^{64} - 10 q^{65} + 2 q^{67} - 32 q^{68} - 8 q^{70} - 8 q^{73} - 18 q^{74} + 36 q^{76} - 4 q^{77} + 8 q^{79} + 16 q^{80} + 16 q^{82} - 20 q^{85} + 12 q^{86} - 12 q^{88} + 36 q^{89} + 4 q^{91} + 32 q^{92} - 28 q^{94} + 18 q^{95} - 10 q^{97} - 48 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^4 + 2 * q^5 + 4 * q^7 - 24 * q^8 - 8 * q^10 + 2 * q^11 + 4 * q^13 - 10 * q^14 - 16 * q^16 - 4 * q^17 - 8 * q^20 - 2 * q^22 + 16 * q^23 + 2 * q^25 - 4 * q^26 - 40 * q^28 - 6 * q^29 - 8 * q^31 + 16 * q^32 + 16 * q^34 - 4 * q^35 - 12 * q^37 - 18 * q^38 - 4 * q^41 - 8 * q^44 + 32 * q^46 + 10 * q^47 - 14 * q^50 - 4 * q^52 - 12 * q^53 + 4 * q^55 - 36 * q^56 + 10 * q^59 + 12 * q^61 + 8 * q^62 + 64 * q^64 - 10 * q^65 + 2 * q^67 - 32 * q^68 - 8 * q^70 - 8 * q^73 - 18 * q^74 + 36 * q^76 - 4 * q^77 + 8 * q^79 + 16 * q^80 + 16 * q^82 - 20 * q^85 + 12 * q^86 - 12 * q^88 + 36 * q^89 + 4 * q^91 + 32 * q^92 - 28 * q^94 + 18 * q^95 - 10 * q^97 - 48 * q^98

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