LMFDB - Embedded newform 546.2.j.d.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(289,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$-1.38232 - 0.298668i$ of defining polynomial
Character	$\chi$	$=$	546.289
Dual form			546.2.j.d.529.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.14553 - 1.98411i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.63641 - 0.222079i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.14553 - 1.98411i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.63641 - 0.222079i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.14553 - 1.98411i) q^{10} +(-0.439279 + 0.760853i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.786978 + 3.51862i) q^{13} +(2.63641 - 0.222079i) q^{14} +(-1.14553 - 1.98411i) q^{15} +1.00000 q^{16} -6.40782 q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.754098 - 1.30614i) q^{19} +(1.14553 - 1.98411i) q^{20} +(1.12588 - 2.39424i) q^{21} +(-0.439279 + 0.760853i) q^{22} +1.31752 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.124459 - 0.215569i) q^{25} +(-0.786978 + 3.51862i) q^{26} -1.00000 q^{27} +(2.63641 - 0.222079i) q^{28} +(-0.669294 - 1.15925i) q^{29} +(-1.14553 - 1.98411i) q^{30} +(-1.94748 - 3.37313i) q^{31} +1.00000 q^{32} +(0.439279 + 0.760853i) q^{33} -6.40782 q^{34} +(2.57945 - 5.48533i) q^{35} +(-0.500000 - 0.866025i) q^{36} +9.38675 q^{37} +(-0.754098 - 1.30614i) q^{38} +(2.65372 + 2.44085i) q^{39} +(1.14553 - 1.98411i) q^{40} +(1.80195 + 3.12107i) q^{41} +(1.12588 - 2.39424i) q^{42} +(-4.95801 + 8.58752i) q^{43} +(-0.439279 + 0.760853i) q^{44} -2.29105 q^{45} +1.31752 q^{46} +(-0.188939 + 0.327251i) q^{47} +(0.500000 - 0.866025i) q^{48} +(6.90136 - 1.17099i) q^{49} +(-0.124459 - 0.215569i) q^{50} +(-3.20391 + 5.54934i) q^{51} +(-0.786978 + 3.51862i) q^{52} +(-1.22356 - 2.11926i) q^{53} -1.00000 q^{54} +(1.00641 + 1.74315i) q^{55} +(2.63641 - 0.222079i) q^{56} -1.50820 q^{57} +(-0.669294 - 1.15925i) q^{58} -5.96823 q^{59} +(-1.14553 - 1.98411i) q^{60} +(-2.40782 - 4.17047i) q^{61} +(-1.94748 - 3.37313i) q^{62} +(-1.51053 - 2.17216i) q^{63} +1.00000 q^{64} +(6.07982 + 5.59212i) q^{65} +(0.439279 + 0.760853i) q^{66} +(-4.87998 + 8.45237i) q^{67} -6.40782 q^{68} +(0.658760 - 1.14101i) q^{69} +(2.57945 - 5.48533i) q^{70} +(1.02408 - 1.77376i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(0.432504 + 0.749119i) q^{73} +9.38675 q^{74} -0.248918 q^{75} +(-0.754098 - 1.30614i) q^{76} +(-0.989151 + 2.10348i) q^{77} +(2.65372 + 2.44085i) q^{78} +(-4.18014 + 7.24022i) q^{79} +(1.14553 - 1.98411i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.80195 + 3.12107i) q^{82} +8.66710 q^{83} +(1.12588 - 2.39424i) q^{84} +(-7.34033 + 12.7138i) q^{85} +(-4.95801 + 8.58752i) q^{86} -1.33859 q^{87} +(-0.439279 + 0.760853i) q^{88} -12.8339 q^{89} -2.29105 q^{90} +(-1.29339 + 9.45130i) q^{91} +1.31752 q^{92} -3.89495 q^{93} +(-0.188939 + 0.327251i) q^{94} -3.45536 q^{95} +(0.500000 - 0.866025i) q^{96} +(4.40338 - 7.62688i) q^{97} +(6.90136 - 1.17099i) q^{98} +0.878558 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 2 * q^5 + 4 * q^6 - 3 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} - 8 q^{17} - 4 q^{18} + 6 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} + 20 q^{23} + 4 q^{24} - 18 q^{25} - 11 q^{26} - 8 q^{27} - 3 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 8 q^{32} + 6 q^{33} - 8 q^{34} - 18 q^{35} - 4 q^{36} + 56 q^{37} + 6 q^{38} - 10 q^{39} + 2 q^{40} - 3 q^{42} - 6 q^{43} - 6 q^{44} - 4 q^{45} + 20 q^{46} + q^{47} + 4 q^{48} + 5 q^{49} - 18 q^{50} - 4 q^{51} - 11 q^{52} + 7 q^{53} - 8 q^{54} + q^{55} - 3 q^{56} + 12 q^{57} + 2 q^{58} - 4 q^{59} - 2 q^{60} + 24 q^{61} + 6 q^{62} + 8 q^{64} + 22 q^{65} + 6 q^{66} - 15 q^{67} - 8 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} - 4 q^{72} + q^{73} + 56 q^{74} - 36 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} + 2 q^{80} - 4 q^{81} - 32 q^{83} - 3 q^{84} - 13 q^{85} - 6 q^{86} + 4 q^{87} - 6 q^{88} - 50 q^{89} - 4 q^{90} - 8 q^{91} + 20 q^{92} + 12 q^{93} + q^{94} + 16 q^{95} + 4 q^{96} - q^{97} + 5 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 2 * q^5 + 4 * q^6 - 3 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 - 8 * q^17 - 4 * q^18 + 6 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 + 20 * q^23 + 4 * q^24 - 18 * q^25 - 11 * q^26 - 8 * q^27 - 3 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 8 * q^32 + 6 * q^33 - 8 * q^34 - 18 * q^35 - 4 * q^36 + 56 * q^37 + 6 * q^38 - 10 * q^39 + 2 * q^40 - 3 * q^42 - 6 * q^43 - 6 * q^44 - 4 * q^45 + 20 * q^46 + q^47 + 4 * q^48 + 5 * q^49 - 18 * q^50 - 4 * q^51 - 11 * q^52 + 7 * q^53 - 8 * q^54 + q^55 - 3 * q^56 + 12 * q^57 + 2 * q^58 - 4 * q^59 - 2 * q^60 + 24 * q^61 + 6 * q^62 + 8 * q^64 + 22 * q^65 + 6 * q^66 - 15 * q^67 - 8 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 - 4 * q^72 + q^73 + 56 * q^74 - 36 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 + 2 * q^80 - 4 * q^81 - 32 * q^83 - 3 * q^84 - 13 * q^85 - 6 * q^86 + 4 * q^87 - 6 * q^88 - 50 * q^89 - 4 * q^90 - 8 * q^91 + 20 * q^92 + 12 * q^93 + q^94 + 16 * q^95 + 4 * q^96 - q^97 + 5 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	1.14553	−	1.98411i	0.512295	−	0.887321i	−0.487604	−	0.873065i	$-0.662129\pi$
$5$	1.14553	−	1.98411i	0.512295	−	0.887321i	0.999898	−	0.0142554i	$-0.00453779\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	2.63641	−	0.222079i	0.996471	−	0.0839380i
$7$	2.63641	−	0.222079i	0.996471	−	0.0839380i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.14553	−	1.98411i	0.362247	−	0.627430i
$11$	−0.439279	+	0.760853i	−0.132448	+	0.229406i	−0.924619	−	0.380892i	$-0.875617\pi$
$11$	−0.439279	+	0.760853i	−0.132448	+	0.229406i	0.792172	+	0.610298i	$0.208950\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.786978	+	3.51862i	−0.218268	+	0.975889i
$13$	−0.786978	+	3.51862i	−0.218268	+	0.975889i
$14$	2.63641	−	0.222079i	0.704611	−	0.0593532i
$15$	−1.14553	−	1.98411i	−0.295774	−	0.512295i
$16$	1.00000			0.250000
$17$	−6.40782			−1.55412			−0.777062	−	0.629423i	$-0.783291\pi$
$17$	−6.40782			−1.55412			−0.777062	+	0.629423i	$0.783291\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.754098	−	1.30614i	−0.173002	−	0.299648i	0.766466	−	0.642285i	$-0.222013\pi$
$19$	−0.754098	−	1.30614i	−0.173002	−	0.299648i	−0.939468	+	0.342637i	$0.888680\pi$
$20$	1.14553	−	1.98411i	0.256147	−	0.443660i
$21$	1.12588	−	2.39424i	0.245687	−	0.522466i
$22$	−0.439279	+	0.760853i	−0.0936545	+	0.162214i
$23$	1.31752			0.274722			0.137361	−	0.990521i	$-0.456138\pi$
$23$	1.31752			0.274722			0.137361	+	0.990521i	$0.456138\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.124459	−	0.215569i	−0.0248918	−	0.0431139i
$26$	−0.786978	+	3.51862i	−0.154339	+	0.690058i
$27$	−1.00000			−0.192450
$28$	2.63641	−	0.222079i	0.498235	−	0.0419690i
$29$	−0.669294	−	1.15925i	−0.124285	−	0.215267i	0.797168	−	0.603757i	$-0.206330\pi$
$29$	−0.669294	−	1.15925i	−0.124285	−	0.215267i	−0.921453	+	0.388490i	$0.872997\pi$
$30$	−1.14553	−	1.98411i	−0.209143	−	0.362247i
$31$	−1.94748	−	3.37313i	−0.349777	−	0.605831i	0.636433	−	0.771332i	$-0.280409\pi$
$31$	−1.94748	−	3.37313i	−0.349777	−	0.605831i	−0.986210	+	0.165501i	$0.947076\pi$
$32$	1.00000			0.176777
$33$	0.439279	+	0.760853i	0.0764686	+	0.132448i
$34$	−6.40782			−1.09893
$35$	2.57945	−	5.48533i	0.436007	−	0.927190i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	9.38675			1.54317			0.771586	−	0.636124i	$-0.219464\pi$
$37$	9.38675			1.54317			0.771586	+	0.636124i	$0.219464\pi$
$38$	−0.754098	−	1.30614i	−0.122331	−	0.211883i
$39$	2.65372	+	2.44085i	0.424936	+	0.390849i
$40$	1.14553	−	1.98411i	0.181124	−	0.313715i
$41$	1.80195	+	3.12107i	0.281417	+	0.487429i	0.971734	−	0.236078i	$-0.0758622\pi$
$41$	1.80195	+	3.12107i	0.281417	+	0.487429i	−0.690317	+	0.723507i	$0.742529\pi$
$42$	1.12588	−	2.39424i	0.173727	−	0.369439i
$43$	−4.95801	+	8.58752i	−0.756089	+	1.30959i	0.188742	+	0.982027i	$0.439559\pi$
$43$	−4.95801	+	8.58752i	−0.756089	+	1.30959i	−0.944831	+	0.327558i	$0.893774\pi$
$44$	−0.439279	+	0.760853i	−0.0662238	+	0.114703i
$45$	−2.29105			−0.341530
$46$	1.31752			0.194258
$47$	−0.188939	+	0.327251i	−0.0275595	+	0.0477345i	−0.879476	−	0.475943i	$-0.842107\pi$
$47$	−0.188939	+	0.327251i	−0.0275595	+	0.0477345i	0.851917	+	0.523677i	$0.175440\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	6.90136	−	1.17099i	0.985909	−	0.167284i
$50$	−0.124459	−	0.215569i	−0.0176012	−	0.0304861i
$51$	−3.20391	+	5.54934i	−0.448637	+	0.777062i
$52$	−0.786978	+	3.51862i	−0.109134	+	0.487944i
$53$	−1.22356	−	2.11926i	−0.168068	−	0.291103i	0.769672	−	0.638439i	$-0.220420\pi$
$53$	−1.22356	−	2.11926i	−0.168068	−	0.291103i	−0.937741	+	0.347336i	$0.887086\pi$
$54$	−1.00000			−0.136083
$55$	1.00641	+	1.74315i	0.135704	+	0.235047i
$56$	2.63641	−	0.222079i	0.352306	−	0.0296766i
$57$	−1.50820			−0.199766
$58$	−0.669294	−	1.15925i	−0.0878826	−	0.152217i
$59$	−5.96823			−0.776997			−0.388498	−	0.921449i	$-0.627006\pi$
$59$	−5.96823			−0.776997			−0.388498	+	0.921449i	$0.627006\pi$
$60$	−1.14553	−	1.98411i	−0.147887	−	0.256147i
$61$	−2.40782	−	4.17047i	−0.308290	−	0.533974i	0.669698	−	0.742633i	$-0.266423\pi$
$61$	−2.40782	−	4.17047i	−0.308290	−	0.533974i	−0.977988	+	0.208659i	$0.933090\pi$
$62$	−1.94748	−	3.37313i	−0.247330	−	0.428388i
$63$	−1.51053	−	2.17216i	−0.190309	−	0.273667i
$64$	1.00000			0.125000
$65$	6.07982	+	5.59212i	0.754108	+	0.693617i
$66$	0.439279	+	0.760853i	0.0540715	+	0.0936545i
$67$	−4.87998	+	8.45237i	−0.596184	+	1.03262i	0.397194	+	0.917735i	$0.369984\pi$
$67$	−4.87998	+	8.45237i	−0.596184	+	1.03262i	−0.993379	+	0.114887i	$0.963349\pi$
$68$	−6.40782			−0.777062
$69$	0.658760	−	1.14101i	0.0793054	−	0.137361i
$70$	2.57945	−	5.48533i	0.308303	−	0.655622i
$71$	1.02408	−	1.77376i	0.121536	−	0.210507i	−0.798837	−	0.601547i	$-0.794551\pi$
$71$	1.02408	−	1.77376i	0.121536	−	0.210507i	0.920374	+	0.391040i	$0.127885\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	0.432504	+	0.749119i	0.0506207	+	0.0876777i	0.890225	−	0.455520i	$-0.150547\pi$
$73$	0.432504	+	0.749119i	0.0506207	+	0.0876777i	−0.839605	+	0.543198i	$0.817213\pi$
$74$	9.38675			1.09119
$75$	−0.248918			−0.0287426
$76$	−0.754098	−	1.30614i	−0.0865010	−	0.149824i
$77$	−0.989151	+	2.10348i	−0.112724	+	0.239714i
$78$	2.65372	+	2.44085i	0.300475	+	0.276372i
$79$	−4.18014	+	7.24022i	−0.470303	+	0.814588i	−0.999423	−	0.0339584i	$-0.989189\pi$
$79$	−4.18014	+	7.24022i	−0.470303	+	0.814588i	0.529120	+	0.848547i	$0.322522\pi$
$80$	1.14553	−	1.98411i	0.128074	−	0.221830i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.80195	+	3.12107i	0.198992	+	0.344664i
$83$	8.66710			0.951338			0.475669	−	0.879624i	$-0.342206\pi$
$83$	8.66710			0.951338			0.475669	+	0.879624i	$0.342206\pi$
$84$	1.12588	−	2.39424i	0.122844	−	0.261233i
$85$	−7.34033	+	12.7138i	−0.796170	+	1.37901i
$86$	−4.95801	+	8.58752i	−0.534636	+	0.926016i
$87$	−1.33859			−0.143512
$88$	−0.439279	+	0.760853i	−0.0468273	+	0.0811072i
$89$	−12.8339			−1.36039			−0.680194	−	0.733033i	$-0.738104\pi$
$89$	−12.8339			−1.36039			−0.680194	+	0.733033i	$0.738104\pi$
$90$	−2.29105			−0.241498
$91$	−1.29339	+	9.45130i	−0.135584	+	0.990766i
$92$	1.31752			0.137361
$93$	−3.89495			−0.403888
$94$	−0.188939	+	0.327251i	−0.0194875	+	0.0337534i
$95$	−3.45536			−0.354512
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	4.40338	−	7.62688i	0.447096	−	0.774393i	−0.551100	−	0.834439i	$-0.685792\pi$
$97$	4.40338	−	7.62688i	0.447096	−	0.774393i	0.998196	+	0.0600467i	$0.0191250\pi$
$98$	6.90136	−	1.17099i	0.697143	−	0.118287i
$99$	0.878558			0.0882984
$100$	−0.124459	−	0.215569i	−0.0124459	−	0.0215569i
$101$	5.02693	−	8.70689i	0.500198	−	0.866368i	−0.499802	−	0.866140i	$-0.666594\pi$
$101$	5.02693	−	8.70689i	0.500198	−	0.866368i	1.00000		0.000228594i	$-7.27637e-5\pi$
$102$	−3.20391	+	5.54934i	−0.317234	+	0.549466i
$103$	−6.17983	+	10.7038i	−0.608916	+	1.05467i	0.382503	+	0.923954i	$0.375062\pi$
$103$	−6.17983	+	10.7038i	−0.608916	+	1.05467i	−0.991419	+	0.130720i	$0.958271\pi$
$104$	−0.786978	+	3.51862i	−0.0771695	+	0.345029i
$105$	−3.46071	−	4.97654i	−0.337731	−	0.485660i
$106$	−1.22356	−	2.11926i	−0.118842	−	0.205841i
$107$	−6.80813			−0.658166			−0.329083	−	0.944301i	$-0.606740\pi$
$107$	−6.80813			−0.658166			−0.329083	+	0.944301i	$0.606740\pi$
$108$	−1.00000			−0.0962250
$109$	−0.460710	−	0.797973i	−0.0441280	−	0.0764320i	0.843118	−	0.537729i	$-0.180718\pi$
$109$	−0.460710	−	0.797973i	−0.0441280	−	0.0764320i	−0.887246	+	0.461297i	$0.847384\pi$
$110$	1.00641	+	1.74315i	0.0959575	+	0.166203i
$111$	4.69338	−	8.12917i	0.445476	−	0.771586i
$112$	2.63641	−	0.222079i	0.249118	−	0.0209845i
$113$	5.68802	−	9.85195i	0.535084	−	0.926793i	−0.464075	−	0.885796i	$-0.653613\pi$
$113$	5.68802	−	9.85195i	0.535084	−	0.926793i	0.999159	−	0.0409973i	$-0.0130535\pi$
$114$	−1.50820			−0.141256
$115$	1.50925	−	2.61410i	0.140739	−	0.243767i
$116$	−0.669294	−	1.15925i	−0.0621424	−	0.107634i
$117$	3.44070	−	1.07777i	0.318093	−	0.0996395i
$118$	−5.96823			−0.549420
$119$	−16.8937	+	1.42304i	−1.54864	+	0.130450i
$120$	−1.14553	−	1.98411i	−0.104572	−	0.181124i
$121$	5.11407	+	8.85783i	0.464915	+	0.805257i
$122$	−2.40782	−	4.17047i	−0.217994	−	0.377576i
$123$	3.60390			0.324953
$124$	−1.94748	−	3.37313i	−0.174888	−	0.302916i
$125$	10.8850			0.973582
$126$	−1.51053	−	2.17216i	−0.134569	−	0.193512i
$127$	4.26019	+	7.37887i	0.378031	+	0.654769i	0.990776	−	0.135512i	$-0.0432679\pi$
$127$	4.26019	+	7.37887i	0.378031	+	0.654769i	−0.612745	+	0.790281i	$0.709935\pi$
$128$	1.00000			0.0883883
$129$	4.95801	+	8.58752i	0.436528	+	0.756089i
$130$	6.07982	+	5.59212i	0.533235	+	0.490461i
$131$	2.51964	−	4.36415i	0.220142	−	0.381298i	−0.734709	−	0.678383i	$-0.762681\pi$
$131$	2.51964	−	4.36415i	0.220142	−	0.381298i	0.954851	+	0.297085i	$0.0960145\pi$
$132$	0.439279	+	0.760853i	0.0382343	+	0.0662238i
$133$	−2.27818	−	3.27605i	−0.197543	−	0.284069i
$134$	−4.87998	+	8.45237i	−0.421566	+	0.730174i
$135$	−1.14553	+	1.98411i	−0.0985912	+	0.170765i
$136$	−6.40782			−0.549466
$137$	−18.9452			−1.61860			−0.809300	−	0.587395i	$-0.800153\pi$
$137$	−18.9452			−1.61860			−0.809300	+	0.587395i	$0.800153\pi$
$138$	0.658760	−	1.14101i	0.0560774	−	0.0971289i
$139$	0.565160	−	0.978885i	0.0479362	−	0.0830280i	−0.841062	−	0.540939i	$-0.818069\pi$
$139$	0.565160	−	0.978885i	0.0479362	−	0.0830280i	0.888998	+	0.457911i	$0.151402\pi$
$140$	2.57945	−	5.48533i	0.218003	−	0.463595i
$141$	0.188939	+	0.327251i	0.0159115	+	0.0275595i
$142$	1.02408	−	1.77376i	0.0859392	−	0.148851i
$143$	−2.33145	−	2.14443i	−0.194965	−	0.179326i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−3.06677			−0.254682
$146$	0.432504	+	0.749119i	0.0357943	+	0.0619975i
$147$	2.43658	−	6.56225i	0.200966	−	0.541245i
$148$	9.38675			0.771586
$149$	−0.802500	−	1.38997i	−0.0657433	−	0.113871i	0.831280	−	0.555854i	$-0.187609\pi$
$149$	−0.802500	−	1.38997i	−0.0657433	−	0.113871i	−0.897023	+	0.441983i	$0.854275\pi$
$150$	−0.248918			−0.0203241
$151$	10.2417	+	17.7391i	0.833457	+	1.44359i	0.895281	+	0.445502i	$0.146975\pi$
$151$	10.2417	+	17.7391i	0.833457	+	1.44359i	−0.0618242	+	0.998087i	$0.519692\pi$
$152$	−0.754098	−	1.30614i	−0.0611655	−	0.105942i
$153$	3.20391	+	5.54934i	0.259021	+	0.448637i
$154$	−0.989151	+	2.10348i	−0.0797081	+	0.169503i
$155$	−8.92354			−0.716756
$156$	2.65372	+	2.44085i	0.212468	+	0.195425i
$157$	−5.16462	−	8.94539i	−0.412182	−	0.713919i	0.582946	−	0.812511i	$-0.301900\pi$
$157$	−5.16462	−	8.94539i	−0.412182	−	0.713919i	−0.995128	+	0.0985911i	$0.968566\pi$
$158$	−4.18014	+	7.24022i	−0.332554	+	0.576001i
$159$	−2.44711			−0.194069
$160$	1.14553	−	1.98411i	0.0905618	−	0.156858i
$161$	3.47353	−	0.292594i	0.273753	−	0.0230596i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	3.44890	+	5.97367i	0.270139	+	0.467894i	0.968897	−	0.247464i	$-0.0795972\pi$
$163$	3.44890	+	5.97367i	0.270139	+	0.467894i	−0.698759	+	0.715358i	$0.746264\pi$
$164$	1.80195	+	3.12107i	0.140709	+	0.243715i
$165$	2.01282			0.156698
$166$	8.66710			0.672697
$167$	9.73115	+	16.8549i	0.753019	+	1.30427i	0.946353	+	0.323135i	$0.104737\pi$
$167$	9.73115	+	16.8549i	0.753019	+	1.30427i	−0.193334	+	0.981133i	$0.561930\pi$
$168$	1.12588	−	2.39424i	0.0868636	−	0.184720i
$169$	−11.7613	−	5.53815i	−0.904718	−	0.426011i
$170$	−7.34033	+	12.7138i	−0.562977	+	0.975105i
$171$	−0.754098	+	1.30614i	−0.0576674	+	0.0998828i
$172$	−4.95801	+	8.58752i	−0.378045	+	0.654793i
$173$	−11.0069	−	19.0645i	−0.836840	−	1.44945i	−0.892523	−	0.451002i	$-0.851067\pi$
$173$	−11.0069	−	19.0645i	−0.836840	−	1.44945i	0.0556826	−	0.998449i	$-0.482266\pi$
$174$	−1.33859			−0.101478
$175$	−0.375999	−	0.540690i	−0.0284229	−	0.0408724i
$176$	−0.439279	+	0.760853i	−0.0331119	+	0.0573515i
$177$	−2.98411	+	5.16864i	−0.224300	+	0.388498i
$178$	−12.8339			−0.961939
$179$	4.90819	−	8.50123i	0.366855	−	0.635412i	−0.622217	−	0.782845i	$-0.713768\pi$
$179$	4.90819	−	8.50123i	0.366855	−	0.635412i	0.989072	+	0.147433i	$0.0471012\pi$
$180$	−2.29105			−0.170765
$181$	22.9753			1.70774			0.853869	−	0.520487i	$-0.174250\pi$
$181$	22.9753			1.70774			0.853869	+	0.520487i	$0.174250\pi$
$182$	−1.29339	+	9.45130i	−0.0958723	+	0.700577i
$183$	−4.81564			−0.355983
$184$	1.31752			0.0971289
$185$	10.7528	−	18.6243i	0.790559	−	1.36929i
$186$	−3.89495			−0.285592
$187$	2.81482	−	4.87541i	0.205840	−	0.356525i
$188$	−0.188939	+	0.327251i	−0.0137798	+	0.0238673i
$189$	−2.63641	+	0.222079i	−0.191771	+	0.0161539i
$190$	−3.45536			−0.250678
$191$	4.84536	+	8.39241i	0.350598	+	0.607254i	0.986354	−	0.164636i	$-0.0526450\pi$
$191$	4.84536	+	8.39241i	0.350598	+	0.607254i	−0.635756	+	0.771890i	$0.719312\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	10.5533	−	18.2789i	0.759647	−	1.31575i	−0.183384	−	0.983041i	$-0.558705\pi$
$193$	10.5533	−	18.2789i	0.759647	−	1.31575i	0.943031	−	0.332705i	$-0.107961\pi$
$194$	4.40338	−	7.62688i	0.316144	−	0.547578i
$195$	7.88282	−	2.46922i	0.564501	−	0.176824i
$196$	6.90136	−	1.17099i	0.492954	−	0.0836418i
$197$	−6.76019	−	11.7090i	−0.481644	−	0.834232i	0.518134	−	0.855299i	$-0.326627\pi$
$197$	−6.76019	−	11.7090i	−0.481644	−	0.834232i	−0.999778	+	0.0210677i	$0.993293\pi$
$198$	0.878558			0.0624364
$199$	−7.58899			−0.537969			−0.268985	−	0.963144i	$-0.586688\pi$
$199$	−7.58899			−0.537969			−0.268985	+	0.963144i	$0.586688\pi$
$200$	−0.124459	−	0.215569i	−0.00880058	−	0.0152431i
$201$	4.87998	+	8.45237i	0.344207	+	0.596184i
$202$	5.02693	−	8.70689i	0.353693	−	0.612615i
$203$	−2.02198	−	2.90763i	−0.141915	−	0.204076i
$204$	−3.20391	+	5.54934i	−0.224319	+	0.388531i
$205$	8.25672			0.576674
$206$	−6.17983	+	10.7038i	−0.430569	+	0.745767i
$207$	−0.658760	−	1.14101i	−0.0457870	−	0.0793054i
$208$	−0.786978	+	3.51862i	−0.0545671	+	0.243972i
$209$	1.32504			0.0916548
$210$	−3.46071	−	4.97654i	−0.238812	−	0.343414i
$211$	−6.06832	−	10.5106i	−0.417760	−	0.723582i	0.577954	−	0.816070i	$-0.303851\pi$
$211$	−6.06832	−	10.5106i	−0.417760	−	0.723582i	−0.995714	+	0.0924876i	$0.970518\pi$
$212$	−1.22356	−	2.11926i	−0.0840341	−	0.145551i
$213$	−1.02408	−	1.77376i	−0.0701690	−	0.121536i
$214$	−6.80813			−0.465394
$215$	11.3591	+	19.6745i	0.774681	+	1.34179i
$216$	−1.00000			−0.0680414
$217$	−5.88345	−	8.46047i	−0.399395	−	0.574334i
$218$	−0.460710	−	0.797973i	−0.0312032	−	0.0540456i
$219$	0.865008			0.0584518
$220$	1.00641	+	1.74315i	0.0678522	+	0.117523i
$221$	5.04281	−	22.5467i	0.339216	−	1.51665i
$222$	4.69338	−	8.12917i	0.314999	−	0.545594i
$223$	−11.0968	−	19.2202i	−0.743094	−	1.28708i	−0.951080	−	0.308945i	$-0.900024\pi$
$223$	−11.0968	−	19.2202i	−0.743094	−	1.28708i	0.207986	−	0.978132i	$-0.433309\pi$
$224$	2.63641	−	0.222079i	0.176153	−	0.0148383i
$225$	−0.124459	+	0.215569i	−0.00829727	+	0.0143713i
$226$	5.68802	−	9.85195i	0.378362	−	0.655342i
$227$	−24.4284			−1.62137			−0.810686	−	0.585482i	$-0.800905\pi$
$227$	−24.4284			−1.62137			−0.810686	+	0.585482i	$0.800905\pi$
$228$	−1.50820			−0.0998828
$229$	−14.9717	+	25.9317i	−0.989358	+	1.71362i	−0.368670	+	0.929560i	$0.620187\pi$
$229$	−14.9717	+	25.9317i	−0.989358	+	1.71362i	−0.620688	+	0.784058i	$0.713147\pi$
$230$	1.50925	−	2.61410i	0.0995173	−	0.172369i
$231$	1.32709	+	1.90837i	0.0873161	+	0.125561i
$232$	−0.669294	−	1.15925i	−0.0439413	−	0.0761086i
$233$	−11.4574	+	19.8448i	−0.750600	+	1.30008i	0.196932	+	0.980417i	$0.436902\pi$
$233$	−11.4574	+	19.8448i	−0.750600	+	1.30008i	−0.947532	+	0.319660i	$0.896431\pi$
$234$	3.44070	−	1.07777i	0.224926	−	0.0704557i
$235$	0.432868	+	0.749750i	0.0282372	+	0.0489083i
$236$	−5.96823			−0.388498
$237$	4.18014	+	7.24022i	0.271529	+	0.470303i
$238$	−16.8937	+	1.42304i	−1.09505	+	0.0922422i
$239$	−1.03992			−0.0672669			−0.0336334	−	0.999434i	$-0.510708\pi$
$239$	−1.03992			−0.0672669			−0.0336334	+	0.999434i	$0.510708\pi$
$240$	−1.14553	−	1.98411i	−0.0739434	−	0.128074i
$241$	6.47888			0.417342			0.208671	−	0.977986i	$-0.433086\pi$
$241$	6.47888			0.417342			0.208671	+	0.977986i	$0.433086\pi$
$242$	5.11407	+	8.85783i	0.328745	+	0.569403i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.40782	−	4.17047i	−0.154145	−	0.266987i
$245$	5.58233	−	15.0344i	0.356642	−	0.960516i
$246$	3.60390			0.229776
$247$	5.18925	−	1.62548i	0.330184	−	0.103427i
$248$	−1.94748	−	3.37313i	−0.123665	−	0.214194i
$249$	4.33355	−	7.50593i	0.274628	−	0.475669i
$250$	10.8850			0.688426
$251$	5.33039	−	9.23251i	0.336451	−	0.582751i	−0.647311	−	0.762226i	$-0.724107\pi$
$251$	5.33039	−	9.23251i	0.336451	−	0.582751i	0.983763	+	0.179475i	$0.0574399\pi$
$252$	−1.51053	−	2.17216i	−0.0951547	−	0.136833i
$253$	−0.578759	+	1.00244i	−0.0363863	+	0.0630229i
$254$	4.26019	+	7.37887i	0.267308	+	0.462992i
$255$	7.34033	+	12.7138i	0.459669	+	0.796170i
$256$	1.00000			0.0625000
$257$	28.0838			1.75182			0.875910	−	0.482475i	$-0.160262\pi$
$257$	28.0838			1.75182			0.875910	+	0.482475i	$0.160262\pi$
$258$	4.95801	+	8.58752i	0.308672	+	0.534636i
$259$	24.7474	−	2.08460i	1.53773	−	0.129531i
$260$	6.07982	+	5.59212i	0.377054	+	0.346808i
$261$	−0.669294	+	1.15925i	−0.0414282	+	0.0717558i
$262$	2.51964	−	4.36415i	0.155664	−	0.269618i
$263$	12.0885	−	20.9378i	0.745407	−	1.29108i	−0.204597	−	0.978846i	$-0.565588\pi$
$263$	12.0885	−	20.9378i	0.745407	−	1.29108i	0.950004	−	0.312237i	$-0.101078\pi$
$264$	0.439279	+	0.760853i	0.0270357	+	0.0468273i
$265$	−5.60646			−0.344402
$266$	−2.27818	−	3.27605i	−0.139684	−	0.200867i
$267$	−6.41693	+	11.1145i	−0.392710	+	0.680194i
$268$	−4.87998	+	8.45237i	−0.298092	+	0.516311i
$269$	−7.93891			−0.484044			−0.242022	−	0.970271i	$-0.577811\pi$
$269$	−7.93891			−0.484044			−0.242022	+	0.970271i	$0.577811\pi$
$270$	−1.14553	+	1.98411i	−0.0697145	+	0.120749i
$271$	−28.6694			−1.74154			−0.870770	−	0.491690i	$-0.836379\pi$
$271$	−28.6694			−1.74154			−0.870770	+	0.491690i	$0.836379\pi$
$272$	−6.40782			−0.388531
$273$	7.53838	+	5.84576i	0.456243	+	0.353801i
$274$	−18.9452			−1.14452
$275$	0.218689			0.0131874
$276$	0.658760	−	1.14101i	0.0396527	−	0.0686805i
$277$	12.4871			0.750279			0.375139	−	0.926968i	$-0.377595\pi$
$277$	12.4871			0.750279			0.375139	+	0.926968i	$0.377595\pi$
$278$	0.565160	−	0.978885i	0.0338960	−	0.0587096i
$279$	−1.94748	+	3.37313i	−0.116592	+	0.201944i
$280$	2.57945	−	5.48533i	0.154152	−	0.327811i
$281$	23.4616			1.39960			0.699800	−	0.714339i	$-0.253272\pi$
$281$	23.4616			1.39960			0.699800	+	0.714339i	$0.253272\pi$
$282$	0.188939	+	0.327251i	0.0112511	+	0.0194875i
$283$	7.89495	−	13.6745i	0.469306	−	0.812862i	−0.530078	−	0.847949i	$-0.677837\pi$
$283$	7.89495	−	13.6745i	0.469306	−	0.812862i	0.999384	+	0.0350867i	$0.0111707\pi$
$284$	1.02408	−	1.77376i	0.0607682	−	0.105254i
$285$	−1.72768	+	2.99243i	−0.102339	+	0.177256i
$286$	−2.33145	−	2.14443i	−0.137861	−	0.126803i
$287$	5.44381	+	7.82825i	0.321338	+	0.462087i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	24.0602			1.41530
$290$	−3.06677			−0.180087
$291$	−4.40338	−	7.62688i	−0.258131	−	0.447096i
$292$	0.432504	+	0.749119i	0.0253104	+	0.0438388i
$293$	3.38969	−	5.87112i	0.198028	−	0.342994i	−0.749861	−	0.661595i	$-0.769880\pi$
$293$	3.38969	−	5.87112i	0.198028	−	0.342994i	0.947889	+	0.318601i	$0.103213\pi$
$294$	2.43658	−	6.56225i	0.142104	−	0.382718i
$295$	−6.83676	+	11.8416i	−0.398051	+	0.689445i
$296$	9.38675			0.545594
$297$	0.439279	−	0.760853i	0.0254895	−	0.0441492i
$298$	−0.802500	−	1.38997i	−0.0464876	−	0.0805188i
$299$	−1.03686	+	4.63585i	−0.0599631	+	0.268098i
$300$	−0.248918			−0.0143713
$301$	−11.1643	+	23.7413i	−0.643497	+	1.36843i
$302$	10.2417	+	17.7391i	0.589343	+	1.02077i
$303$	−5.02693	−	8.70689i	−0.288789	−	0.500198i
$304$	−0.754098	−	1.30614i	−0.0432505	−	0.0749121i
$305$	−11.0329			−0.631741
$306$	3.20391	+	5.54934i	0.183155	+	0.317234i
$307$	−1.27687			−0.0728749			−0.0364374	−	0.999336i	$-0.511601\pi$
$307$	−1.27687			−0.0728749			−0.0364374	+	0.999336i	$0.511601\pi$
$308$	−0.989151	+	2.10348i	−0.0563621	+	0.119857i
$309$	6.17983	+	10.7038i	0.351558	+	0.608916i
$310$	−8.92354			−0.506823
$311$	−12.4336	−	21.5357i	−0.705047	−	1.22118i	−0.966675	−	0.256009i	$-0.917592\pi$
$311$	−12.4336	−	21.5357i	−0.705047	−	1.22118i	0.261627	−	0.965169i	$-0.415741\pi$
$312$	2.65372	+	2.44085i	0.150237	+	0.138186i
$313$	13.1601	−	22.7940i	0.743855	−	1.28839i	−0.206873	−	0.978368i	$-0.566329\pi$
$313$	13.1601	−	22.7940i	0.743855	−	1.28839i	0.950728	−	0.310026i	$-0.100338\pi$
$314$	−5.16462	−	8.94539i	−0.291456	−	0.504817i
$315$	−6.04016	+	0.508795i	−0.340325	+	0.0286673i
$316$	−4.18014	+	7.24022i	−0.235151	+	0.407294i
$317$	9.33620	−	16.1708i	0.524373	−	0.908241i	−0.475224	−	0.879865i	$-0.657633\pi$
$317$	9.33620	−	16.1708i	0.524373	−	0.908241i	0.999597	−	0.0283764i	$-0.00903370\pi$
$318$	−2.44711			−0.137227
$319$	1.17603			0.0658448
$320$	1.14553	−	1.98411i	0.0640368	−	0.110915i
$321$	−3.40406	+	5.89601i	−0.189996	+	0.329083i
$322$	3.47353	−	0.292594i	0.193572	−	0.0163056i
$323$	4.83213	+	8.36949i	0.268867	+	0.465691i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	0.856453	−	0.268275i	0.0475074	−	0.0148812i
$326$	3.44890	+	5.97367i	0.191017	+	0.330851i
$327$	−0.921420			−0.0509547
$328$	1.80195	+	3.12107i	0.0994960	+	0.172332i
$329$	−0.425445	+	0.904730i	−0.0234555	+	0.0498794i
$330$	2.01282			0.110802
$331$	−18.0242	−	31.2189i	−0.990701	−	1.71594i	−0.613179	−	0.789944i	$-0.710110\pi$
$331$	−18.0242	−	31.2189i	−0.990701	−	1.71594i	−0.377522	−	0.926001i	$-0.623224\pi$
$332$	8.66710			0.475669
$333$	−4.69338	−	8.12917i	−0.257195	−	0.445476i
$334$	9.73115	+	16.8549i	0.532465	+	0.922256i
$335$	11.1803	+	19.3648i	0.610844	+	1.05801i
$336$	1.12588	−	2.39424i	0.0614218	−	0.130617i
$337$	16.9888			0.925440			0.462720	−	0.886504i	$-0.346873\pi$
$337$	16.9888			0.925440			0.462720	+	0.886504i	$0.346873\pi$
$338$	−11.7613	−	5.53815i	−0.639732	−	0.301236i
$339$	−5.68802	−	9.85195i	−0.308931	−	0.535084i
$340$	−7.34033	+	12.7138i	−0.398085	+	0.689503i
$341$	3.42194			0.185308
$342$	−0.754098	+	1.30614i	−0.0407770	+	0.0706278i
$343$	17.9348	−	4.61985i	0.968388	−	0.249449i
$344$	−4.95801	+	8.58752i	−0.267318	+	0.463008i
$345$	−1.50925	−	2.61410i	−0.0812555	−	0.140739i
$346$	−11.0069	−	19.0645i	−0.591736	−	1.02492i
$347$	12.0361			0.646132			0.323066	−	0.946376i	$-0.395286\pi$
$347$	12.0361			0.646132			0.323066	+	0.946376i	$0.395286\pi$
$348$	−1.33859			−0.0717558
$349$	−11.4544	−	19.8396i	−0.613140	−	1.06199i	−0.990708	−	0.136007i	$-0.956573\pi$
$349$	−11.4544	−	19.8396i	−0.613140	−	1.06199i	0.377568	−	0.925982i	$-0.376760\pi$
$350$	−0.375999	−	0.540690i	−0.0200980	−	0.0289011i
$351$	0.786978	−	3.51862i	0.0420058	−	0.187810i
$352$	−0.439279	+	0.760853i	−0.0234136	+	0.0405536i
$353$	−12.1583	+	21.0588i	−0.647121	+	1.12085i	0.336686	+	0.941617i	$0.390694\pi$
$353$	−12.1583	+	21.0588i	−0.647121	+	1.12085i	−0.983807	+	0.179230i	$0.942639\pi$
$354$	−2.98411	+	5.16864i	−0.158604	+	0.274710i
$355$	−2.34623	−	4.06379i	−0.124525	−	0.215683i
$356$	−12.8339			−0.680194
$357$	−7.21444	+	15.3419i	−0.381829	+	0.811978i
$358$	4.90819	−	8.50123i	0.259406	−	0.449304i
$359$	−14.4734	+	25.0686i	−0.763875	+	1.32307i	0.176965	+	0.984217i	$0.443372\pi$
$359$	−14.4734	+	25.0686i	−0.763875	+	1.32307i	−0.940840	+	0.338853i	$0.889961\pi$
$360$	−2.29105			−0.120749
$361$	8.36267	−	14.4846i	0.440141	−	0.762346i
$362$	22.9753			1.20755
$363$	10.2281			0.536838
$364$	−1.29339	+	9.45130i	−0.0677920	+	0.495383i
$365$	1.98178			0.103731
$366$	−4.81564			−0.251718
$367$	13.5022	−	23.3866i	0.704811	−	1.22077i	−0.261948	−	0.965082i	$-0.584365\pi$
$367$	13.5022	−	23.3866i	0.704811	−	1.22077i	0.966760	−	0.255687i	$-0.0823017\pi$
$368$	1.31752			0.0686805
$369$	1.80195	−	3.12107i	0.0938058	−	0.162476i
$370$	10.7528	−	18.6243i	0.559010	−	0.968234i
$371$	−3.69644	−	5.31552i	−0.191910	−	0.275968i
$372$	−3.89495			−0.201944
$373$	−9.61751	−	16.6580i	−0.497976	−	0.862519i	0.502021	−	0.864855i	$-0.332590\pi$
$373$	−9.61751	−	16.6580i	−0.497976	−	0.862519i	−0.999997	+	0.00233570i	$0.999257\pi$
$374$	2.81482	−	4.87541i	0.145551	−	0.252101i
$375$	5.44249	−	9.42666i	0.281049	−	0.486791i
$376$	−0.188939	+	0.327251i	−0.00974377	+	0.0168767i
$377$	4.60568	−	1.44268i	0.237205	−	0.0743020i
$378$	−2.63641	+	0.222079i	−0.135603	+	0.0114225i
$379$	−16.1551	−	27.9815i	−0.829834	−	1.43731i	−0.898168	−	0.439652i	$-0.855102\pi$
$379$	−16.1551	−	27.9815i	−0.829834	−	1.43731i	0.0683340	−	0.997662i	$-0.478232\pi$
$380$	−3.45536			−0.177256
$381$	8.52039			0.436513
$382$	4.84536	+	8.39241i	0.247910	+	0.429393i
$383$	15.7111	+	27.2125i	0.802802	+	1.39049i	0.917765	+	0.397124i	$0.129992\pi$
$383$	15.7111	+	27.2125i	0.802802	+	1.39049i	−0.114963	+	0.993370i	$0.536675\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	3.04043	+	4.37217i	0.154955	+	0.222827i
$386$	10.5533	−	18.2789i	0.537151	−	0.930373i
$387$	9.91602			0.504060
$388$	4.40338	−	7.62688i	0.223548	−	0.387196i
$389$	2.89119	+	5.00769i	0.146589	+	0.253900i	0.929965	−	0.367649i	$-0.119837\pi$
$389$	2.89119	+	5.00769i	0.146589	+	0.253900i	−0.783375	+	0.621549i	$0.786504\pi$
$390$	7.88282	−	2.46922i	0.399162	−	0.125034i
$391$	−8.44244			−0.426952
$392$	6.90136	−	1.17099i	0.348571	−	0.0591437i
$393$	−2.51964	−	4.36415i	−0.127099	−	0.220142i
$394$	−6.76019	−	11.7090i	−0.340574	−	0.589891i
$395$	9.57692	+	16.5877i	0.481867	+	0.834619i
$396$	0.878558			0.0441492
$397$	−3.49354	−	6.05099i	−0.175336	−	0.303690i	0.764942	−	0.644100i	$-0.222768\pi$
$397$	−3.49354	−	6.05099i	−0.175336	−	0.303690i	−0.940277	+	0.340409i	$0.889434\pi$
$398$	−7.58899			−0.380402
$399$	−3.97623	+	0.334939i	−0.199061	+	0.0167679i
$400$	−0.124459	−	0.215569i	−0.00622295	−	0.0107785i
$401$	−5.93497			−0.296378			−0.148189	−	0.988959i	$-0.547344\pi$
$401$	−5.93497			−0.296378			−0.148189	+	0.988959i	$0.547344\pi$
$402$	4.87998	+	8.45237i	0.243391	+	0.421566i
$403$	13.4014	−	4.19784i	0.667569	−	0.209110i
$404$	5.02693	−	8.70689i	0.250099	−	0.433184i
$405$	1.14553	+	1.98411i	0.0569216	+	0.0985912i
$406$	−2.02198	−	2.90763i	−0.100349	−	0.144303i
$407$	−4.12340	+	7.14194i	−0.204389	+	0.354013i
$408$	−3.20391	+	5.54934i	−0.158617	+	0.274733i
$409$	−14.7785			−0.730748			−0.365374	−	0.930861i	$-0.619059\pi$
$409$	−14.7785			−0.730748			−0.365374	+	0.930861i	$0.619059\pi$
$410$	8.25672			0.407770
$411$	−9.47262	+	16.4071i	−0.467250	+	0.809300i
$412$	−6.17983	+	10.7038i	−0.304458	+	0.527337i
$413$	−15.7347	+	1.32542i	−0.774255	+	0.0652196i
$414$	−0.658760	−	1.14101i	−0.0323763	−	0.0560774i
$415$	9.92839	−	17.1965i	0.487365	−	0.844142i
$416$	−0.786978	+	3.51862i	−0.0385848	+	0.172514i
$417$	−0.565160	−	0.978885i	−0.0276760	−	0.0479362i
$418$	1.32504			0.0648097
$419$	−5.07336	−	8.78731i	−0.247850	−	0.429288i	0.715079	−	0.699043i	$-0.246391\pi$
$419$	−5.07336	−	8.78731i	−0.247850	−	0.429288i	−0.962929	+	0.269755i	$0.913057\pi$
$420$	−3.46071	−	4.97654i	−0.168865	−	0.242830i
$421$	7.70885			0.375706			0.187853	−	0.982197i	$-0.439847\pi$
$421$	7.70885			0.375706			0.187853	+	0.982197i	$0.439847\pi$
$422$	−6.06832	−	10.5106i	−0.295401	−	0.511650i
$423$	0.377877			0.0183730
$424$	−1.22356	−	2.11926i	−0.0594211	−	0.102920i
$425$	0.797511	+	1.38133i	0.0386850	+	0.0670044i
$426$	−1.02408	−	1.77376i	−0.0496170	−	0.0859392i
$427$	−7.27419	−	10.4604i	−0.352023	−	0.506212i
$428$	−6.80813			−0.329083
$429$	−3.02285	+	0.946879i	−0.145945	+	0.0457158i
$430$	11.3591	+	19.6745i	0.547782	+	0.948787i
$431$	−17.8893	+	30.9851i	−0.861696	+	1.49250i	0.00859398	+	0.999963i	$0.497264\pi$
$431$	−17.8893	+	30.9851i	−0.861696	+	1.49250i	−0.870290	+	0.492539i	$0.836069\pi$
$432$	−1.00000			−0.0481125
$433$	−6.32535	+	10.9558i	−0.303977	+	0.526504i	−0.977033	−	0.213088i	$-0.931648\pi$
$433$	−6.32535	+	10.9558i	−0.303977	+	0.526504i	0.673056	+	0.739592i	$0.264981\pi$
$434$	−5.88345	−	8.46047i	−0.282415	−	0.406115i
$435$	−1.53339	+	2.65590i	−0.0735203	+	0.127341i
$436$	−0.460710	−	0.797973i	−0.0220640	−	0.0382160i
$437$	−0.993540	−	1.72086i	−0.0475275	−	0.0823200i
$438$	0.865008			0.0413317
$439$	−27.2045			−1.29840			−0.649200	−	0.760618i	$-0.724896\pi$
$439$	−27.2045			−1.29840			−0.649200	+	0.760618i	$0.724896\pi$
$440$	1.00641	+	1.74315i	0.0479787	+	0.0831016i
$441$	−4.46478	−	5.39126i	−0.212609	−	0.256727i
$442$	5.04281	−	22.5467i	0.239862	−	1.07244i
$443$	−1.74860	+	3.02867i	−0.0830786	+	0.143896i	−0.904571	−	0.426323i	$-0.859809\pi$
$443$	−1.74860	+	3.02867i	−0.0830786	+	0.143896i	0.821492	+	0.570220i	$0.193142\pi$
$444$	4.69338	−	8.12917i	0.222738	−	0.385793i
$445$	−14.7015	+	25.4638i	−0.696919	+	1.20710i
$446$	−11.0968	−	19.2202i	−0.525447	−	0.910101i
$447$	−1.60500			−0.0759139
$448$	2.63641	−	0.222079i	0.124559	−	0.0104923i
$449$	8.08366	−	14.0013i	0.381491	−	0.660762i	−0.609784	−	0.792567i	$-0.708744\pi$
$449$	8.08366	−	14.0013i	0.381491	−	0.660762i	0.991276	+	0.131805i	$0.0420773\pi$
$450$	−0.124459	+	0.215569i	−0.00586706	+	0.0101620i
$451$	−3.16623			−0.149092
$452$	5.68802	−	9.85195i	0.267542	−	0.463397i
$453$	20.4834			0.962393
$454$	−24.4284			−1.14648
$455$	17.2708	+	13.3929i	0.809668	+	0.627871i
$456$	−1.50820			−0.0706278
$457$	26.2609			1.22843			0.614217	−	0.789137i	$-0.289472\pi$
$457$	26.2609			1.22843			0.614217	+	0.789137i	$0.289472\pi$
$458$	−14.9717	+	25.9317i	−0.699582	+	1.21171i
$459$	6.40782			0.299091
$460$	1.50925	−	2.61410i	0.0703693	−	0.121883i
$461$	−4.94386	+	8.56302i	−0.230259	+	0.398819i	−0.957884	−	0.287155i	$-0.907291\pi$
$461$	−4.94386	+	8.56302i	−0.230259	+	0.398819i	0.727626	+	0.685974i	$0.240624\pi$
$462$	1.32709	+	1.90837i	0.0617418	+	0.0887854i
$463$	−14.2082			−0.660310			−0.330155	−	0.943927i	$-0.607101\pi$
$463$	−14.2082			−0.660310			−0.330155	+	0.943927i	$0.607101\pi$
$464$	−0.669294	−	1.15925i	−0.0310712	−	0.0538169i
$465$	−4.46177	+	7.72801i	−0.206910	+	0.358378i
$466$	−11.4574	+	19.8448i	−0.530754	+	0.919293i
$467$	−1.47500	+	2.55478i	−0.0682550	+	0.118221i	−0.898133	−	0.439723i	$-0.855076\pi$
$467$	−1.47500	+	2.55478i	−0.0682550	+	0.118221i	0.829878	+	0.557944i	$0.188410\pi$
$468$	3.44070	−	1.07777i	0.159046	−	0.0498197i
$469$	−10.9886	+	23.3677i	−0.507404	+	1.07902i
$470$	0.432868	+	0.749750i	0.0199667	+	0.0345834i
$471$	−10.3292			−0.475946
$472$	−5.96823			−0.274710
$473$	−4.35590	−	7.54463i	−0.200284	−	0.346903i
$474$	4.18014	+	7.24022i	0.192000	+	0.332554i
$475$	−0.187709	+	0.325121i	−0.00861267	+	0.0149176i
$476$	−16.8937	+	1.42304i	−0.774320	+	0.0652251i
$477$	−1.22356	+	2.11926i	−0.0560228	+	0.0970343i
$478$	−1.03992			−0.0475649
$479$	−9.90480	+	17.1556i	−0.452562	+	0.783861i	−0.998544	−	0.0539362i	$-0.982823\pi$
$479$	−9.90480	+	17.1556i	−0.452562	+	0.783861i	0.545982	+	0.837797i	$0.316157\pi$
$480$	−1.14553	−	1.98411i	−0.0522859	−	0.0905618i
$481$	−7.38717	+	33.0284i	−0.336826	+	1.50597i
$482$	6.47888			0.295105
$483$	1.48337	−	3.15446i	0.0674957	−	0.143533i
$484$	5.11407	+	8.85783i	0.232458	+	0.402628i
$485$	−10.0884	−	17.4736i	−0.458090	−	0.793435i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−12.5946			−0.570714			−0.285357	−	0.958421i	$-0.592112\pi$
$487$	−12.5946			−0.570714			−0.285357	+	0.958421i	$0.592112\pi$
$488$	−2.40782	−	4.17047i	−0.108997	−	0.188788i
$489$	6.89780			0.311929
$490$	5.58233	−	15.0344i	0.252184	−	0.679187i
$491$	5.81280	+	10.0681i	0.262328	+	0.454365i	0.966860	−	0.255307i	$-0.0821765\pi$
$491$	5.81280	+	10.0681i	0.262328	+	0.454365i	−0.704532	+	0.709672i	$0.748843\pi$
$492$	3.60390			0.162476
$493$	4.28872	+	7.42827i	0.193154	+	0.334553i
$494$	5.18925	−	1.62548i	0.233476	−	0.0731339i
$495$	1.00641	−	1.74315i	0.0452348	−	0.0783489i
$496$	−1.94748	−	3.37313i	−0.0874442	−	0.151458i
$497$	2.30599	−	4.90381i	0.103438	−	0.219966i
$498$	4.33355	−	7.50593i	0.194191	−	0.336349i
$499$	6.22713	−	10.7857i	0.278765	−	0.482834i	−0.692313	−	0.721597i	$-0.743408\pi$
$499$	6.22713	−	10.7857i	0.278765	−	0.482834i	0.971078	+	0.238763i	$0.0767418\pi$
$500$	10.8850			0.486791
$501$	19.4623			0.869512
$502$	5.33039	−	9.23251i	0.237907	−	0.412067i
$503$	−15.7073	+	27.2058i	−0.700354	+	1.21305i	0.267988	+	0.963422i	$0.413641\pi$
$503$	−15.7073	+	27.2058i	−0.700354	+	1.21305i	−0.968342	+	0.249627i	$0.919692\pi$
$504$	−1.51053	−	2.17216i	−0.0672845	−	0.0967558i
$505$	−11.5170	−	19.9479i	−0.512498	−	0.887672i
$506$	−0.578759	+	1.00244i	−0.0257290	+	0.0445639i
$507$	−10.6768	+	7.41654i	−0.474175	+	0.329380i
$508$	4.26019	+	7.37887i	0.189016	+	0.327384i
$509$	7.19772			0.319034			0.159517	−	0.987195i	$-0.449006\pi$
$509$	7.19772			0.319034			0.159517	+	0.987195i	$0.449006\pi$
$510$	7.34033	+	12.7138i	0.325035	+	0.562977i
$511$	1.30662	+	1.87894i	0.0578016	+	0.0831193i
$512$	1.00000			0.0441942
$513$	0.754098	+	1.30614i	0.0332943	+	0.0576674i
$514$	28.0838			1.23872
$515$	14.1583	+	24.5229i	0.623889	+	1.08061i
$516$	4.95801	+	8.58752i	0.218264	+	0.378045i
$517$	−0.165994	−	0.287509i	−0.00730039	−	0.0126446i
$518$	24.7474	−	2.08460i	1.08734	−	0.0915922i
$519$	−22.0138			−0.966300
$520$	6.07982	+	5.59212i	0.266618	+	0.245231i
$521$	11.2983	+	19.5692i	0.494987	+	0.857342i	0.999983	−	0.00577905i	$-0.00183954\pi$
$521$	11.2983	+	19.5692i	0.494987	+	0.857342i	−0.504996	+	0.863121i	$0.668506\pi$
$522$	−0.669294	+	1.15925i	−0.0292942	+	0.0507390i
$523$	−6.07271			−0.265541			−0.132770	−	0.991147i	$-0.542387\pi$
$523$	−6.07271			−0.265541			−0.132770	+	0.991147i	$0.542387\pi$
$524$	2.51964	−	4.36415i	0.110071	−	0.190649i
$525$	−0.656251	+	0.0552795i	−0.0286412	+	0.00241260i
$526$	12.0885	−	20.9378i	0.527082	−	0.912933i
$527$	12.4791	+	21.6144i	0.543597	+	0.941538i
$528$	0.439279	+	0.760853i	0.0191172	+	0.0331119i
$529$	−21.2641			−0.924528
$530$	−5.60646			−0.243529
$531$	2.98411	+	5.16864i	0.129499	+	0.224300i
$532$	−2.27818	−	3.27605i	−0.0987717	−	0.142035i
$533$	−12.3999	+	3.88416i	−0.537101	+	0.168242i
$534$	−6.41693	+	11.1145i	−0.277688	+	0.480969i
$535$	−7.79888	+	13.5081i	−0.337175	+	0.584005i
$536$	−4.87998	+	8.45237i	−0.210783	+	0.365087i
$537$	−4.90819	−	8.50123i	−0.211804	−	0.366855i
$538$	−7.93891			−0.342271
$539$	−2.14067	+	5.76531i	−0.0922053	+	0.248330i
$540$	−1.14553	+	1.98411i	−0.0492956	+	0.0853825i
$541$	3.16494	−	5.48183i	0.136071	−	0.235682i	−0.789935	−	0.613191i	$-0.789886\pi$
$541$	3.16494	−	5.48183i	0.136071	−	0.235682i	0.926006	+	0.377508i	$0.123219\pi$
$542$	−28.6694			−1.23146
$543$	11.4876	−	19.8972i	0.492982	−	0.853869i
$544$	−6.40782			−0.274733
$545$	−2.11102			−0.0904262
$546$	7.53838	+	5.84576i	0.322613	+	0.250175i
$547$	17.3685			0.742625			0.371312	−	0.928508i	$-0.378908\pi$
$547$	17.3685			0.742625			0.371312	+	0.928508i	$0.378908\pi$
$548$	−18.9452			−0.809300
$549$	−2.40782	+	4.17047i	−0.102763	+	0.177991i
$550$	0.218689			0.00932492
$551$	−1.00943	+	1.74838i	−0.0430030	+	0.0744834i
$552$	0.658760	−	1.14101i	0.0280387	−	0.0485645i
$553$	−9.41269	+	20.0165i	−0.400268	+	0.851190i
$554$	12.4871			0.530527
$555$	−10.7528	−	18.6243i	−0.456430	−	0.790559i
$556$	0.565160	−	0.978885i	0.0239681	−	0.0415140i
$557$	−19.9116	+	34.4879i	−0.843681	+	1.46130i	0.0430813	+	0.999072i	$0.486283\pi$
$557$	−19.9116	+	34.4879i	−0.843681	+	1.46130i	−0.886762	+	0.462226i	$0.847051\pi$
$558$	−1.94748	+	3.37313i	−0.0824432	+	0.142796i
$559$	−26.3144	−	24.2035i	−1.11298	−	1.02370i
$560$	2.57945	−	5.48533i	0.109002	−	0.231798i
$561$	−2.81482	−	4.87541i	−0.118842	−	0.205840i
$562$	23.4616			0.989667
$563$	−4.59171			−0.193517			−0.0967587	−	0.995308i	$-0.530848\pi$
$563$	−4.59171			−0.193517			−0.0967587	+	0.995308i	$0.530848\pi$
$564$	0.188939	+	0.327251i	0.00795576	+	0.0137798i
$565$	−13.0316	−	22.5713i	−0.548242	−	0.949583i
$566$	7.89495	−	13.6745i	0.331850	−	0.574780i
$567$	−1.12588	+	2.39424i	−0.0472826	+	0.100549i
$568$	1.02408	−	1.77376i	0.0429696	−	0.0744255i
$569$	−17.4829			−0.732922			−0.366461	−	0.930433i	$-0.619431\pi$
$569$	−17.4829			−0.732922			−0.366461	+	0.930433i	$0.619431\pi$
$570$	−1.72768	+	2.99243i	−0.0723645	+	0.125339i
$571$	8.05500	+	13.9517i	0.337091	+	0.583859i	0.983884	−	0.178806i	$-0.0572235\pi$
$571$	8.05500	+	13.9517i	0.337091	+	0.583859i	−0.646793	+	0.762666i	$0.723890\pi$
$572$	−2.33145	−	2.14443i	−0.0974827	−	0.0896631i
$573$	9.69073			0.404836
$574$	5.44381	+	7.82825i	0.227220	+	0.326745i
$575$	−0.163977	−	0.284017i	−0.00683833	−	0.0118443i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	3.99841	+	6.92544i	0.166456	+	0.288310i	0.937171	−	0.348870i	$-0.113434\pi$
$577$	3.99841	+	6.92544i	0.166456	+	0.288310i	−0.770716	+	0.637179i	$0.780101\pi$
$578$	24.0602			1.00077
$579$	−10.5533	−	18.2789i	−0.438582	−	0.759647i
$580$	−3.06677			−0.127341
$581$	22.8501	−	1.92478i	0.947981	−	0.0798534i
$582$	−4.40338	−	7.62688i	−0.182526	−	0.316144i
$583$	2.14993			0.0890409
$584$	0.432504	+	0.749119i	0.0178971	+	0.0309987i
$585$	1.80301	−	8.06133i	0.0745452	−	0.333295i
$586$	3.38969	−	5.87112i	0.140027	−	0.242534i
$587$	10.4049	+	18.0219i	0.429458	+	0.743842i	0.996825	−	0.0796223i	$-0.0253714\pi$
$587$	10.4049	+	18.0219i	0.429458	+	0.743842i	−0.567367	+	0.823465i	$0.692038\pi$
$588$	2.43658	−	6.56225i	0.100483	−	0.270623i
$589$	−2.93718	+	5.08734i	−0.121024	+	0.209620i
$590$	−6.83676	+	11.8416i	−0.281465	+	0.487511i
$591$	−13.5204			−0.556154
$592$	9.38675			0.385793
$593$	−12.2317	+	21.1859i	−0.502296	+	0.870002i	0.497701	+	0.867349i	$0.334178\pi$
$593$	−12.2317	+	21.1859i	−0.502296	+	0.870002i	−0.999996	+	0.00265305i	$0.999156\pi$
$594$	0.439279	−	0.760853i	0.0180238	−	0.0312182i
$595$	−16.5287	+	35.1490i	−0.677609	+	1.44097i
$596$	−0.802500	−	1.38997i	−0.0328717	−	0.0569354i
$597$	−3.79449	+	6.57226i	−0.155298	+	0.268985i
$598$	−1.03686	+	4.63585i	−0.0424003	+	0.189574i
$599$	−22.4292	−	38.8484i	−0.916431	−	1.58730i	−0.804793	−	0.593555i	$-0.797724\pi$
$599$	−22.4292	−	38.8484i	−0.916431	−	1.58730i	−0.111638	−	0.993749i	$-0.535610\pi$
$600$	−0.248918			−0.0101620
$601$	12.2159	+	21.1585i	0.498296	+	0.863073i	0.999998	−	0.00196699i	$-0.000626114\pi$
$601$	12.2159	+	21.1585i	0.498296	+	0.863073i	−0.501702	+	0.865040i	$0.667293\pi$
$602$	−11.1643	+	23.7413i	−0.455021	+	0.967625i
$603$	9.75996			0.397456
$604$	10.2417	+	17.7391i	0.416728	+	0.721795i
$605$	23.4332			0.952695
$606$	−5.02693	−	8.70689i	−0.204205	−	0.353693i
$607$	18.0911	+	31.3347i	0.734296	+	1.27184i	0.955032	+	0.296504i	$0.0958209\pi$
$607$	18.0911	+	31.3347i	0.734296	+	1.27184i	−0.220735	+	0.975334i	$0.570846\pi$
$608$	−0.754098	−	1.30614i	−0.0305827	−	0.0529708i
$609$	−3.52907	+	0.297272i	−0.143005	+	0.0120461i
$610$	−11.0329			−0.446709
$611$	−1.00278	−	0.922343i	−0.0405682	−	0.0373140i
$612$	3.20391	+	5.54934i	0.129510	+	0.224319i
$613$	−3.10647	+	5.38056i	−0.125469	+	0.217319i	−0.921916	−	0.387389i	$-0.873377\pi$
$613$	−3.10647	+	5.38056i	−0.125469	+	0.217319i	0.796447	+	0.604708i	$0.206710\pi$
$614$	−1.27687			−0.0515303
$615$	4.12836	−	7.15053i	0.166472	−	0.288337i
$616$	−0.989151	+	2.10348i	−0.0398540	+	0.0847516i
$617$	21.8788	−	37.8953i	0.880809	−	1.52561i	0.0303660	−	0.999539i	$-0.490333\pi$
$617$	21.8788	−	37.8953i	0.880809	−	1.52561i	0.850443	−	0.526067i	$-0.176334\pi$
$618$	6.17983	+	10.7038i	0.248589	+	0.430569i
$619$	9.54369	+	16.5301i	0.383593	+	0.664403i	0.991573	−	0.129550i	$-0.0413532\pi$
$619$	9.54369	+	16.5301i	0.383593	+	0.664403i	−0.607980	+	0.793952i	$0.708020\pi$
$620$	−8.92354			−0.358378
$621$	−1.31752			−0.0528703
$622$	−12.4336	−	21.5357i	−0.498544	−	0.863503i
$623$	−33.8354	+	2.85013i	−1.35559	+	0.114188i
$624$	2.65372	+	2.44085i	0.106234	+	0.0977123i
$625$	13.0913	−	22.6748i	0.523653	−	0.906993i
$626$	13.1601	−	22.7940i	0.525985	−	0.911032i
$627$	0.662519	−	1.14752i	0.0264585	−	0.0458274i
$628$	−5.16462	−	8.94539i	−0.206091	−	0.356960i
$629$	−60.1486			−2.39828
$630$	−6.04016	+	0.508795i	−0.240646	+	0.0202709i
$631$	−11.2873	+	19.5502i	−0.449340	+	0.778280i	−0.998343	−	0.0575405i	$-0.981674\pi$
$631$	−11.2873	+	19.5502i	−0.449340	+	0.778280i	0.549003	+	0.835820i	$0.315008\pi$
$632$	−4.18014	+	7.24022i	−0.166277	+	0.288000i
$633$	−12.1366			−0.482388
$634$	9.33620	−	16.1708i	0.370788	−	0.642224i
$635$	19.5206			0.774653
$636$	−2.44711			−0.0970343
$637$	−1.31097	+	25.2048i	−0.0519425	+	0.998650i
$638$	1.17603			0.0465593
$639$	−2.04817			−0.0810242
$640$	1.14553	−	1.98411i	0.0452809	−	0.0784288i
$641$	21.8244			0.862010			0.431005	−	0.902349i	$-0.358159\pi$
$641$	21.8244			0.862010			0.431005	+	0.902349i	$0.358159\pi$
$642$	−3.40406	+	5.89601i	−0.134348	+	0.232697i
$643$	7.72503	−	13.3801i	0.304645	−	0.527661i	−0.672537	−	0.740064i	$-0.734795\pi$
$643$	7.72503	−	13.3801i	0.304645	−	0.527661i	0.977182	+	0.212402i	$0.0681287\pi$
$644$	3.47353	−	0.292594i	0.136876	−	0.0115298i
$645$	22.7181			0.894525
$646$	4.83213	+	8.36949i	0.190118	+	0.329293i
$647$	−5.39230	+	9.33974i	−0.211993	+	0.367183i	−0.952338	−	0.305044i	$-0.901329\pi$
$647$	−5.39230	+	9.33974i	−0.211993	+	0.367183i	0.740345	+	0.672227i	$0.234662\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	2.62172	−	4.54094i	0.102911	−	0.178248i
$650$	0.856453	−	0.268275i	0.0335928	−	0.0105226i
$651$	−10.2687	+	0.864988i	−0.402462	+	0.0339015i
$652$	3.44890	+	5.97367i	0.135069	+	0.233947i
$653$	−20.3332			−0.795699			−0.397850	−	0.917451i	$-0.630243\pi$
$653$	−20.3332			−0.795699			−0.397850	+	0.917451i	$0.630243\pi$
$654$	−0.921420			−0.0360304
$655$	−5.77264	−	9.99850i	−0.225556	−	0.390674i
$656$	1.80195	+	3.12107i	0.0703543	+	0.121857i
$657$	0.432504	−	0.749119i	0.0168736	−	0.0292259i
$658$	−0.425445	+	0.904730i	−0.0165856	+	0.0352700i
$659$	15.1395	−	26.2224i	0.589752	−	1.02148i	−0.404512	−	0.914532i	$-0.632559\pi$
$659$	15.1395	−	26.2224i	0.589752	−	1.02148i	0.994265	−	0.106948i	$-0.0341079\pi$
$660$	2.01282			0.0783489
$661$	−4.94372	+	8.56277i	−0.192288	+	0.333053i	−0.946008	−	0.324143i	$-0.894924\pi$
$661$	−4.94372	+	8.56277i	−0.192288	+	0.333053i	0.753720	+	0.657196i	$0.228258\pi$
$662$	−18.0242	−	31.2189i	−0.700531	−	1.21336i
$663$	−17.0046	−	15.6405i	−0.660403	−	0.607428i
$664$	8.66710			0.336349
$665$	−9.10975	+	0.767363i	−0.353261	+	0.0297571i
$666$	−4.69338	−	8.12917i	−0.181865	−	0.314999i
$667$	−0.881809	−	1.52734i	−0.0341438	−	0.0591387i
$668$	9.73115	+	16.8549i	0.376510	+	0.652134i
$669$	−22.1935			−0.858051
$670$	11.1803	+	19.3648i	0.431932	+	0.748128i
$671$	4.23082			0.163329
$672$	1.12588	−	2.39424i	0.0434318	−	0.0923599i
$673$	−7.13518	−	12.3585i	−0.275041	−	0.476385i	0.695104	−	0.718909i	$-0.255358\pi$
$673$	−7.13518	−	12.3585i	−0.275041	−	0.476385i	−0.970146	+	0.242524i	$0.922025\pi$
$674$	16.9888			0.654385
$675$	0.124459	+	0.215569i	0.00479043	+	0.00829727i
$676$	−11.7613	−	5.53815i	−0.452359	−	0.213006i
$677$	16.7860	−	29.0742i	0.645139	−	1.11741i	−0.339130	−	0.940739i	$-0.610133\pi$
$677$	16.7860	−	29.0742i	0.645139	−	1.11741i	0.984269	−	0.176674i	$-0.0565338\pi$
$678$	−5.68802	−	9.85195i	−0.218447	−	0.378362i
$679$	9.91537	−	21.0855i	0.380517	−	0.809188i
$680$	−7.34033	+	12.7138i	−0.281489	+	0.487553i
$681$	−12.2142	+	21.1556i	−0.468050	+	0.810686i
$682$	3.42194			0.131033
$683$	−17.6901			−0.676893			−0.338446	−	0.940986i	$-0.609901\pi$
$683$	−17.6901			−0.676893			−0.338446	+	0.940986i	$0.609901\pi$
$684$	−0.754098	+	1.30614i	−0.0288337	+	0.0499414i
$685$	−21.7023	+	37.5894i	−0.829201	+	1.43622i
$686$	17.9348	−	4.61985i	0.684754	−	0.176387i
$687$	14.9717	+	25.9317i	0.571206	+	0.989358i
$688$	−4.95801	+	8.58752i	−0.189022	+	0.327396i
$689$	8.41978	−	2.63741i	0.320768	−	0.100477i
$690$	−1.50925	−	2.61410i	−0.0574563	−	0.0995173i
$691$	38.2717			1.45593			0.727963	−	0.685617i	$-0.240467\pi$
$691$	38.2717			1.45593			0.727963	+	0.685617i	$0.240467\pi$
$692$	−11.0069	−	19.0645i	−0.418420	−	0.724725i
$693$	2.31624	−	0.195109i	0.0879867	−	0.00741159i
$694$	12.0361			0.456884
$695$	−1.29481	−	2.24268i	−0.0491149	−	0.0850696i
$696$	−1.33859			−0.0507390
$697$	−11.5466	−	19.9992i	−0.437358	−	0.757526i
$698$	−11.4544	−	19.8396i	−0.433555	−	0.750940i
$699$	11.4574	+	19.8448i	0.433359	+	0.750600i
$700$	−0.375999	−	0.540690i	−0.0142114	−	0.0204362i
$701$	−29.3574			−1.10882			−0.554408	−	0.832245i	$-0.687055\pi$
$701$	−29.3574			−1.10882			−0.554408	+	0.832245i	$0.687055\pi$
$702$	0.786978	−	3.51862i	0.0297026	−	0.132802i
$703$	−7.07854	−	12.2604i	−0.266972	−	0.462409i
$704$	−0.439279	+	0.760853i	−0.0165559	+	0.0286757i
$705$	0.865737			0.0326055
$706$	−12.1583	+	21.0588i	−0.457584	+	0.792558i
$707$	11.3194	−	24.0714i	0.425711	−	0.905296i
$708$	−2.98411	+	5.16864i	−0.112150	+	0.194249i
$709$	0.660813	+	1.14456i	0.0248174	+	0.0429849i	0.878167	−	0.478354i	$-0.158766\pi$
$709$	0.660813	+	1.14456i	0.0248174	+	0.0429849i	−0.853350	+	0.521338i	$0.825433\pi$
$710$	−2.34623	−	4.06379i	−0.0880524	−	0.152511i
$711$	8.36029			0.313535
$712$	−12.8339			−0.480969
$713$	−2.56584	−	4.44416i	−0.0960915	−	0.166435i
$714$	−7.21444	+	15.3419i	−0.269994	+	0.574155i
$715$	−6.92551	+	2.16935i	−0.259000	+	0.0811291i
$716$	4.90819	−	8.50123i	0.183428	−	0.317706i
$717$	−0.519960	+	0.900598i	−0.0194183	+	0.0336334i
$718$	−14.4734	+	25.0686i	−0.540141	+	0.935552i
$719$	−12.3591	−	21.4065i	−0.460915	−	0.798328i	0.538092	−	0.842886i	$-0.319145\pi$
$719$	−12.3591	−	21.4065i	−0.460915	−	0.798328i	−0.999007	+	0.0445581i	$0.985812\pi$
$720$	−2.29105			−0.0853825
$721$	−13.9155	+	29.5920i	−0.518240	+	1.10206i
$722$	8.36267	−	14.4846i	0.311226	−	0.539060i
$723$	3.23944	−	5.61088i	0.120476	−	0.208671i
$724$	22.9753			0.853869
$725$	−0.166599	+	0.288559i	−0.00618734	+	0.0107168i
$726$	10.2281			0.379602
$727$	8.76033			0.324903			0.162451	−	0.986717i	$-0.448060\pi$
$727$	8.76033			0.324903			0.162451	+	0.986717i	$0.448060\pi$
$728$	−1.29339	+	9.45130i	−0.0479362	+	0.350289i
$729$	1.00000			0.0370370
$730$	1.98178			0.0733489
$731$	31.7700	−	55.0273i	1.17506	−	2.03526i
$732$	−4.81564			−0.177991
$733$	−6.38026	+	11.0509i	−0.235660	+	0.408176i	−0.959464	−	0.281830i	$-0.909059\pi$
$733$	−6.38026	+	11.0509i	−0.235660	+	0.408176i	0.723804	+	0.690006i	$0.242392\pi$
$734$	13.5022	−	23.3866i	0.498377	−	0.863214i
$735$	−10.2291	−	12.3517i	−0.377304	−	0.455598i
$736$	1.31752			0.0485645
$737$	−4.28734	−	7.42590i	−0.157926	−	0.273536i
$738$	1.80195	−	3.12107i	0.0663307	−	0.114888i
$739$	−10.8324	+	18.7623i	−0.398476	+	0.690181i	−0.993538	−	0.113499i	$-0.963794\pi$
$739$	−10.8324	+	18.7623i	−0.398476	+	0.690181i	0.595062	+	0.803680i	$0.297128\pi$
$740$	10.7528	−	18.6243i	0.395280	−	0.684645i
$741$	1.18692	−	5.30677i	0.0436025	−	0.194949i
$742$	−3.69644	−	5.31552i	−0.135701	−	0.195139i
$743$	6.46703	+	11.2012i	0.237252	+	0.410933i	0.959925	−	0.280258i	$-0.0904199\pi$
$743$	6.46703	+	11.2012i	0.237252	+	0.410933i	−0.722673	+	0.691191i	$0.757087\pi$
$744$	−3.89495			−0.142796
$745$	−3.67714			−0.134720
$746$	−9.61751	−	16.6580i	−0.352122	−	0.609893i
$747$	−4.33355	−	7.50593i	−0.158556	−	0.274628i
$748$	2.81482	−	4.87541i	0.102920	−	0.178263i
$749$	−17.9490	+	1.51194i	−0.655844	+	0.0552452i
$750$	5.44249	−	9.42666i	0.198732	−	0.344213i
$751$	8.60728			0.314084			0.157042	−	0.987592i	$-0.449804\pi$
$751$	8.60728			0.314084			0.157042	+	0.987592i	$0.449804\pi$
$752$	−0.188939	+	0.327251i	−0.00688989	+	0.0119336i
$753$	−5.33039	−	9.23251i	−0.194250	−	0.336451i
$754$	4.60568	−	1.44268i	0.167729	−	0.0525394i
$755$	46.9285			1.70790
$756$	−2.63641	+	0.222079i	−0.0958855	+	0.00807694i
$757$	7.93369	+	13.7416i	0.288355	+	0.499445i	0.973417	−	0.229039i	$-0.0735584\pi$
$757$	7.93369	+	13.7416i	0.288355	+	0.499445i	−0.685062	+	0.728484i	$0.740225\pi$
$758$	−16.1551	−	27.9815i	−0.586781	−	1.01633i
$759$	0.578759	+	1.00244i	0.0210076	+	0.0363863i
$760$	−3.45536			−0.125339
$761$	−13.0174	−	22.5468i	−0.471880	−	0.817321i	0.527602	−	0.849492i	$-0.323091\pi$
$761$	−13.0174	−	22.5468i	−0.471880	−	0.817321i	−0.999482	+	0.0321708i	$0.989758\pi$
$762$	8.52039			0.308661
$763$	−1.39184	−	2.00147i	−0.0503879	−	0.0724582i
$764$	4.84536	+	8.39241i	0.175299	+	0.303627i
$765$	14.6807			0.530780
$766$	15.7111	+	27.2125i	0.567667	+	0.983228i
$767$	4.69686	−	20.9999i	0.169594	−	0.758263i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	18.9239	+	32.7772i	0.682415	+	1.18198i	0.974242	+	0.225506i	$0.0724036\pi$
$769$	18.9239	+	32.7772i	0.682415	+	1.18198i	−0.291827	+	0.956471i	$0.594263\pi$
$770$	3.04043	+	4.37217i	0.109570	+	0.157562i
$771$	14.0419	−	24.3213i	0.505707	−	0.875910i
$772$	10.5533	−	18.2789i	0.379823	−	0.657873i
$773$	42.7258			1.53674			0.768370	−	0.640006i	$-0.221068\pi$
$773$	42.7258			1.53674			0.768370	+	0.640006i	$0.221068\pi$
$774$	9.91602			0.356424
$775$	−0.484762	+	0.839632i	−0.0174132	+	0.0301605i
$776$	4.40338	−	7.62688i	0.158072	−	0.273789i
$777$	10.5684	−	22.4742i	0.379138	−	0.806256i
$778$	2.89119	+	5.00769i	0.103654	+	0.179534i
$779$	2.71770	−	4.70719i	0.0973715	−	0.168652i
$780$	7.88282	−	2.46922i	0.282250	−	0.0884121i
$781$	0.899716	+	1.55835i	0.0321944	+	0.0557623i
$782$	−8.44244			−0.301901
$783$	0.669294	+	1.15925i	0.0239186	+	0.0414282i
$784$	6.90136	−	1.17099i	0.246477	−	0.0418209i
$785$	−23.6648			−0.844634
$786$	−2.51964	−	4.36415i	−0.0898728	−	0.155664i
$787$	7.03691			0.250839			0.125419	−	0.992104i	$-0.459972\pi$
$787$	7.03691			0.250839			0.125419	+	0.992104i	$0.459972\pi$
$788$	−6.76019	−	11.7090i	−0.240822	−	0.417116i
$789$	−12.0885	−	20.9378i	−0.430361	−	0.745407i
$790$	9.57692	+	16.5877i	0.340732	+	0.590165i
$791$	12.8081	−	27.2370i	0.455403	−	0.968436i
$792$	0.878558			0.0312182
$793$	16.5692	−	5.19013i	0.588389	−	0.184307i
$794$	−3.49354	−	6.05099i	−0.123981	−	0.214742i
$795$	−2.80323	+	4.85534i	−0.0994203	+	0.172201i
$796$	−7.58899			−0.268985
$797$	6.48013	−	11.2239i	0.229538	−	0.397572i	−0.728133	−	0.685436i	$-0.759612\pi$
$797$	6.48013	−	11.2239i	0.229538	−	0.397572i	0.957671	+	0.287864i	$0.0929451\pi$
$798$	−3.97623	+	0.334939i	−0.140757	+	0.0118567i
$799$	1.21069	−	2.09697i	0.0428310	−	0.0741854i
$800$	−0.124459	−	0.215569i	−0.00440029	−	0.00762153i
$801$	6.41693	+	11.1145i	0.226731	+	0.392710i
$802$	−5.93497			−0.209571
$803$	−0.759959			−0.0268184
$804$	4.87998	+	8.45237i	0.172104	+	0.298092i
$805$	3.39848	−	7.22704i	0.119781	−	0.254720i
$806$	13.4014	−	4.19784i	0.472043	−	0.147863i
$807$	−3.96946	+	6.87530i	−0.139732	+	0.242022i
$808$	5.02693	−	8.70689i	0.176847	−	0.306307i
$809$	−12.0464	+	20.8650i	−0.423530	+	0.733575i	−0.996282	−	0.0861534i	$-0.972542\pi$
$809$	−12.0464	+	20.8650i	−0.423530	+	0.733575i	0.572752	+	0.819729i	$0.305876\pi$
$810$	1.14553	+	1.98411i	0.0402497	+	0.0697145i
$811$	−0.569121			−0.0199845			−0.00999227	−	0.999950i	$-0.503181\pi$
$811$	−0.569121			−0.0199845			−0.00999227	+	0.999950i	$0.503181\pi$
$812$	−2.02198	−	2.90763i	−0.0709576	−	0.102038i
$813$	−14.3347	+	24.8284i	−0.502739	+	0.870770i
$814$	−4.12340	+	7.14194i	−0.144525	+	0.250325i
$815$	15.8032			0.553562
$816$	−3.20391	+	5.54934i	−0.112159	+	0.194266i
$817$	14.9553			0.523220
$818$	−14.7785			−0.516717
$819$	8.83176	−	3.60554i	0.308607	−	0.125988i
$820$	8.25672			0.288337
$821$	51.4686			1.79627			0.898134	−	0.439722i	$-0.144923\pi$
$821$	51.4686			1.79627			0.898134	+	0.439722i	$0.144923\pi$
$822$	−9.47262	+	16.4071i	−0.330395	+	0.572262i
$823$	38.8653			1.35476			0.677379	−	0.735634i	$-0.263116\pi$
$823$	38.8653			1.35476			0.677379	+	0.735634i	$0.263116\pi$
$824$	−6.17983	+	10.7038i	−0.215284	+	0.372884i
$825$	0.109344	−	0.189390i	0.00380688	−	0.00659372i
$826$	−15.7347	+	1.32542i	−0.547481	+	0.0461172i
$827$	28.2170			0.981203			0.490601	−	0.871384i	$-0.336777\pi$
$827$	28.2170			0.981203			0.490601	+	0.871384i	$0.336777\pi$
$828$	−0.658760	−	1.14101i	−0.0228935	−	0.0396527i
$829$	5.78905	−	10.0269i	0.201062	−	0.348250i	−0.747809	−	0.663914i	$-0.768894\pi$
$829$	5.78905	−	10.0269i	0.201062	−	0.348250i	0.948871	+	0.315665i	$0.102227\pi$
$830$	9.92839	−	17.1965i	0.344619	−	0.596898i
$831$	6.24357	−	10.8142i	0.216587	−	0.375139i
$832$	−0.786978	+	3.51862i	−0.0272835	+	0.121986i
$833$	−44.2227	+	7.50347i	−1.53223	+	0.259980i
$834$	−0.565160	−	0.978885i	−0.0195699	−	0.0338960i
$835$	44.5892			1.54307
$836$	1.32504			0.0458274
$837$	1.94748	+	3.37313i	0.0673146	+	0.116592i
$838$	−5.07336	−	8.78731i	−0.175256	−	0.303553i
$839$	−15.9568	+	27.6379i	−0.550889	+	0.954167i	0.447322	+	0.894373i	$0.352378\pi$
$839$	−15.9568	+	27.6379i	−0.550889	+	0.954167i	−0.998211	+	0.0597941i	$0.980956\pi$
$840$	−3.46071	−	4.97654i	−0.119406	−	0.171707i
$841$	13.6041	−	23.5630i	0.469107	−	0.812516i
$842$	7.70885			0.265665
$843$	11.7308	−	20.3183i	0.404030	−	0.699800i
$844$	−6.06832	−	10.5106i	−0.208880	−	0.361791i
$845$	−24.4612	+	16.9917i	−0.841491	+	0.584531i
$846$	0.377877			0.0129917
$847$	15.4499	+	22.2172i	0.530866	+	0.763391i
$848$	−1.22356	−	2.11926i	−0.0420171	−	0.0727757i
$849$	−7.89495	−	13.6745i	−0.270954	−	0.469306i
$850$	0.797511	+	1.38133i	0.0273544	+	0.0473792i
$851$	12.3672			0.423944
$852$	−1.02408	−	1.77376i	−0.0350845	−	0.0607682i
$853$	6.06219			0.207565			0.103783	−	0.994600i	$-0.466905\pi$
$853$	6.06219			0.207565			0.103783	+	0.994600i	$0.466905\pi$
$854$	−7.27419	−	10.4604i	−0.248918	−	0.357946i
$855$	1.72768	+	2.99243i	0.0590854	+	0.102339i
$856$	−6.80813			−0.232697
$857$	27.2702	+	47.2333i	0.931531	+	1.61346i	0.780706	+	0.624899i	$0.214860\pi$
$857$	27.2702	+	47.2333i	0.931531	+	1.61346i	0.150825	+	0.988560i	$0.451807\pi$
$858$	−3.02285	+	0.946879i	−0.103199	+	0.0323259i
$859$	27.3472	−	47.3667i	0.933074	−	1.61613i	0.155042	−	0.987908i	$-0.450449\pi$
$859$	27.3472	−	47.3667i	0.933074	−	1.61613i	0.778033	−	0.628224i	$-0.216218\pi$
$860$	11.3591	+	19.6745i	0.387341	+	0.670894i
$861$	9.50137	−	0.800351i	0.323806	−	0.0272759i
$862$	−17.8893	+	30.9851i	−0.609311	+	1.05536i
$863$	−2.28666	+	3.96062i	−0.0778389	+	0.134821i	−0.902317	−	0.431073i	$-0.858135\pi$
$863$	−2.28666	+	3.96062i	−0.0778389	+	0.134821i	0.824478	+	0.565893i	$0.191469\pi$
$864$	−1.00000			−0.0340207
$865$	−50.4348			−1.71484
$866$	−6.32535	+	10.9558i	−0.214944	+	0.372294i
$867$	12.0301	−	20.8367i	0.408563	−	0.707652i
$868$	−5.88345	−	8.46047i	−0.199697	−	0.287167i
$869$	−3.67250	−	6.36095i	−0.124581	−	0.215780i
$870$	−1.53339	+	2.65590i	−0.0519867	+	0.0900436i
$871$	−25.9002	−	23.8226i	−0.877596	−	0.807198i
$872$	−0.460710	−	0.797973i	−0.0156016	−	0.0270228i
$873$	−8.80677			−0.298064
$874$	−0.993540	−	1.72086i	−0.0336070	−	0.0582090i
$875$	28.6973	−	2.41733i	0.970146	−	0.0817205i
$876$	0.865008			0.0292259
$877$	−29.3607	−	50.8542i	−0.991440	−	1.71723i	−0.608788	−	0.793333i	$-0.708344\pi$
$877$	−29.3607	−	50.8542i	−0.991440	−	1.71723i	−0.382652	−	0.923893i	$-0.624989\pi$
$878$	−27.2045			−0.918108
$879$	−3.38969	−	5.87112i	−0.114331	−	0.198028i
$880$	1.00641	+	1.74315i	0.0339261	+	0.0587617i
$881$	6.95948	+	12.0542i	0.234471	+	0.406115i	0.959119	−	0.283004i	$-0.0913309\pi$
$881$	6.95948	+	12.0542i	0.234471	+	0.406115i	−0.724648	+	0.689119i	$0.757998\pi$
$882$	−4.46478	−	5.39126i	−0.150337	−	0.181533i
$883$	40.5135			1.36339			0.681695	−	0.731637i	$-0.261243\pi$
$883$	40.5135			1.36339			0.681695	+	0.731637i	$0.261243\pi$
$884$	5.04281	−	22.5467i	0.169608	−	0.758327i
$885$	6.83676	+	11.8416i	0.229815	+	0.398051i
$886$	−1.74860	+	3.02867i	−0.0587455	+	0.101750i
$887$	47.9785			1.61096			0.805480	−	0.592623i	$-0.201908\pi$
$887$	47.9785			1.61096			0.805480	+	0.592623i	$0.201908\pi$
$888$	4.69338	−	8.12917i	0.157499	−	0.272797i
$889$	12.8703	+	18.5077i	0.431657	+	0.620727i
$890$	−14.7015	+	25.4638i	−0.492796	+	0.853548i
$891$	−0.439279	−	0.760853i	−0.0147164	−	0.0254895i
$892$	−11.0968	−	19.2202i	−0.371547	−	0.643538i
$893$	0.569914			0.0190714
$894$	−1.60500			−0.0536792
$895$	−11.2449	−	19.4768i	−0.375876	−	0.651036i
$896$	2.63641	−	0.222079i	0.0880764	−	0.00741914i
$897$	3.49634	+	3.21587i	0.116739	+	0.107375i
$898$	8.08366	−	14.0013i	0.269755	−	0.467230i
$899$	−2.60687	+	4.51523i	−0.0869439	+	0.150591i
$900$	−0.124459	+	0.215569i	−0.00414863	+	0.00718565i
$901$	7.84033	+	13.5798i	0.261199	+	0.452410i
$902$	−3.16623			−0.105424
$903$	14.9785	+	21.5392i	0.498452	+	0.716780i
$904$	5.68802	−	9.85195i	0.189181	−	0.327671i
$905$	26.3188	−	45.5854i	0.874866	−	1.51531i
$906$	20.4834			0.680514
$907$	12.6807	−	21.9637i	0.421057	−	0.729292i	−0.574986	−	0.818163i	$-0.694993\pi$
$907$	12.6807	−	21.9637i	0.421057	−	0.729292i	0.996043	+	0.0888709i	$0.0283259\pi$
$908$	−24.4284			−0.810686
$909$	−10.0539			−0.333465
$910$	17.2708	+	13.3929i	0.572522	+	0.443972i
$911$	−50.6581			−1.67838			−0.839189	−	0.543840i	$-0.816970\pi$
$911$	−50.6581			−1.67838			−0.839189	+	0.543840i	$0.816970\pi$
$912$	−1.50820			−0.0499414
$913$	−3.80727	+	6.59439i	−0.126002	+	0.218242i
$914$	26.2609			0.868634
$915$	−5.51644	+	9.55476i	−0.182368	+	0.315871i
$916$	−14.9717	+	25.9317i	−0.494679	+	0.856809i
$917$	5.67364	−	12.0653i	0.187360	−	0.398431i
$918$	6.40782			0.211490
$919$	12.5781	+	21.7859i	0.414913	+	0.718650i	0.995419	−	0.0956058i	$-0.0304788\pi$
$919$	12.5781	+	21.7859i	0.414913	+	0.718650i	−0.580507	+	0.814255i	$0.697145\pi$
$920$	1.50925	−	2.61410i	0.0497586	−	0.0861845i
$921$	−0.638435	+	1.10580i	−0.0210372	+	0.0364374i
$922$	−4.94386	+	8.56302i	−0.162817	+	0.282008i
$923$	5.43527	+	4.99927i	0.178904	+	0.164553i
$924$	1.32709	+	1.90837i	0.0436581	+	0.0627807i
$925$	−1.16827	−	2.02350i	−0.0384124	−	0.0665322i
$926$	−14.2082			−0.466909
$927$	12.3597			0.405944
$928$	−0.669294	−	1.15925i	−0.0219706	−	0.0380543i
$929$	−15.1105	−	26.1722i	−0.495759	−	0.858681i	0.504229	−	0.863570i	$-0.331777\pi$
$929$	−15.1105	−	26.1722i	−0.495759	−	0.858681i	−0.999988	+	0.00488962i	$0.998444\pi$
$930$	−4.46177	+	7.72801i	−0.146307	+	0.253411i
$931$	−6.73377	−	8.13108i	−0.220691	−	0.266486i
$932$	−11.4574	+	19.8448i	−0.375300	+	0.650039i
$933$	−24.8673			−0.814118
$934$	−1.47500	+	2.55478i	−0.0482635	+	0.0835949i
$935$	−6.44890	−	11.1698i	−0.210902	−	0.365292i
$936$	3.44070	−	1.07777i	0.112463	−	0.0352279i
$937$	−33.2013			−1.08464			−0.542320	−	0.840172i	$-0.682454\pi$
$937$	−33.2013			−1.08464			−0.542320	+	0.840172i	$0.682454\pi$
$938$	−10.9886	+	23.3677i	−0.358789	+	0.762982i
$939$	−13.1601	−	22.7940i	−0.429465	−	0.743855i
$940$	0.432868	+	0.749750i	0.0141186	+	0.0244542i
$941$	10.3309	+	17.8937i	0.336779	+	0.583318i	0.983825	−	0.179133i	$-0.0573292\pi$
$941$	10.3309	+	17.8937i	0.336779	+	0.583318i	−0.647046	+	0.762451i	$0.723996\pi$
$942$	−10.3292			−0.336545
$943$	2.37411	+	4.11207i	0.0773115	+	0.133908i
$944$	−5.96823			−0.194249
$945$	−2.57945	+	5.48533i	−0.0839096	+	0.178438i
$946$	−4.35590	−	7.54463i	−0.141622	−	0.245297i
$947$	5.01447			0.162948			0.0814741	−	0.996675i	$-0.474037\pi$
$947$	5.01447			0.162948			0.0814741	+	0.996675i	$0.474037\pi$
$948$	4.18014	+	7.24022i	0.135765	+	0.235151i
$949$	−2.97623	+	0.932275i	−0.0966126	+	0.0302629i
$950$	−0.187709	+	0.325121i	−0.00609008	+	0.0105483i
$951$	−9.33620	−	16.1708i	−0.302747	−	0.524373i
$952$	−16.8937	+	1.42304i	−0.547527	+	0.0461211i
$953$	20.4600	−	35.4378i	0.662765	−	1.14794i	−0.317121	−	0.948385i	$-0.602716\pi$
$953$	20.4600	−	35.4378i	0.662765	−	1.14794i	0.979886	−	0.199558i	$-0.0639505\pi$
$954$	−1.22356	+	2.11926i	−0.0396141	+	0.0686136i
$955$	22.2020			0.718438
$956$	−1.03992			−0.0336334
$957$	0.588013	−	1.01847i	0.0190078	−	0.0329224i
$958$	−9.90480	+	17.1556i	−0.320010	+	0.554273i
$959$	−49.9475	+	4.20734i	−1.61289	+	0.135862i
$960$	−1.14553	−	1.98411i	−0.0369717	−	0.0640368i
$961$	7.91468	−	13.7086i	0.255312	−	0.442214i
$962$	−7.38717	+	33.0284i	−0.238172	+	1.06488i
$963$	3.40406	+	5.89601i	0.109694	+	0.189996i
$964$	6.47888			0.208671
$965$	−24.1783	−	41.8780i	−0.778326	−	1.34810i
$966$	1.48337	−	3.15446i	0.0477267	−	0.101493i
$967$	48.1932			1.54979			0.774894	−	0.632091i	$-0.217803\pi$
$967$	48.1932			1.54979			0.774894	+	0.632091i	$0.217803\pi$
$968$	5.11407	+	8.85783i	0.164372	+	0.284701i
$969$	9.66426			0.310461
$970$	−10.0884	−	17.4736i	−0.323918	−	0.561043i
$971$	16.0612	+	27.8188i	0.515428	+	0.892747i	0.999840	+	0.0179070i	$0.00570029\pi$
$971$	16.0612	+	27.8188i	0.515428	+	0.892747i	−0.484412	+	0.874840i	$0.660966\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	1.27261	−	2.70626i	0.0407978	−	0.0867586i
$974$	−12.5946			−0.403556
$975$	0.195893	−	0.875847i	0.00627360	−	0.0280496i
$976$	−2.40782	−	4.17047i	−0.0770725	−	0.133493i
$977$	−9.97418	+	17.2758i	−0.319102	+	0.552701i	−0.980301	−	0.197509i	$-0.936715\pi$
$977$	−9.97418	+	17.2758i	−0.319102	+	0.552701i	0.661199	+	0.750211i	$0.270048\pi$
$978$	6.89780			0.220567
$979$	5.63764	−	9.76469i	0.180180	−	0.312081i
$980$	5.58233	−	15.0344i	0.178321	−	0.480258i
$981$	−0.460710	+	0.797973i	−0.0147093	+	0.0254773i
$982$	5.81280	+	10.0681i	0.185494	+	0.321285i
$983$	4.74110	+	8.21182i	0.151218	+	0.261916i	0.931675	−	0.363292i	$-0.118347\pi$
$983$	4.74110	+	8.21182i	0.151218	+	0.261916i	−0.780458	+	0.625208i	$0.785014\pi$
$984$	3.60390			0.114888
$985$	−30.9759			−0.986974
$986$	4.28872	+	7.42827i	0.136581	+	0.236564i
$987$	0.570797	+	0.820811i	0.0181687	+	0.0261267i
$988$	5.18925	−	1.62548i	0.165092	−	0.0517135i
$989$	−6.53228	+	11.3142i	−0.207714	+	0.359772i
$990$	1.00641	−	1.74315i	0.0319858	−	0.0554011i
$991$	−12.7652	+	22.1100i	−0.405501	+	0.702348i	−0.994380	−	0.105873i	$-0.966236\pi$
$991$	−12.7652	+	22.1100i	−0.405501	+	0.702348i	0.588879	+	0.808221i	$0.299570\pi$
$992$	−1.94748	−	3.37313i	−0.0618324	−	0.107097i
$993$	−36.0485			−1.14396
$994$	2.30599	−	4.90381i	0.0731416	−	0.155539i
$995$	−8.69338	+	15.0574i	−0.275599	+	0.477351i
$996$	4.33355	−	7.50593i	0.137314	−	0.237834i
$997$	52.1407			1.65131			0.825657	−	0.564172i	$-0.190805\pi$
$997$	52.1407			1.65131			0.825657	+	0.564172i	$0.190805\pi$
$998$	6.22713	−	10.7857i	0.197116	−	0.341415i
$999$	−9.38675			−0.296984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.j.d.289.3	✓	8
3.2	odd	2		1638.2.m.g.289.2		8
7.4	even	3		546.2.k.b.445.3	yes	8
13.9	even	3		546.2.k.b.373.3	yes	8
21.11	odd	6		1638.2.p.i.991.2		8
39.35	odd	6		1638.2.p.i.919.2		8
91.74	even	3	inner	546.2.j.d.529.3	yes	8
273.74	odd	6		1638.2.m.g.1621.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.3	✓	8	1.1	even	1	trivial
546.2.j.d.529.3	yes	8	91.74	even	3	inner
546.2.k.b.373.3	yes	8	13.9	even	3
546.2.k.b.445.3	yes	8	7.4	even	3
1638.2.m.g.289.2		8	3.2	odd	2
1638.2.m.g.1621.2		8	273.74	odd	6
1638.2.p.i.919.2		8	39.35	odd	6
1638.2.p.i.991.2		8	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.14553 - 1.98411i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.63641 - 0.222079i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(1.14553 - 1.98411i) q^{5} +(0.500000 - 0.866025i) q^{6} +(2.63641 - 0.222079i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.14553 - 1.98411i) q^{10} +(-0.439279 + 0.760853i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.786978 + 3.51862i) q^{13} +(2.63641 - 0.222079i) q^{14} +(-1.14553 - 1.98411i) q^{15} +1.00000 q^{16} -6.40782 q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.754098 - 1.30614i) q^{19} +(1.14553 - 1.98411i) q^{20} +(1.12588 - 2.39424i) q^{21} +(-0.439279 + 0.760853i) q^{22} +1.31752 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.124459 - 0.215569i) q^{25} +(-0.786978 + 3.51862i) q^{26} -1.00000 q^{27} +(2.63641 - 0.222079i) q^{28} +(-0.669294 - 1.15925i) q^{29} +(-1.14553 - 1.98411i) q^{30} +(-1.94748 - 3.37313i) q^{31} +1.00000 q^{32} +(0.439279 + 0.760853i) q^{33} -6.40782 q^{34} +(2.57945 - 5.48533i) q^{35} +(-0.500000 - 0.866025i) q^{36} +9.38675 q^{37} +(-0.754098 - 1.30614i) q^{38} +(2.65372 + 2.44085i) q^{39} +(1.14553 - 1.98411i) q^{40} +(1.80195 + 3.12107i) q^{41} +(1.12588 - 2.39424i) q^{42} +(-4.95801 + 8.58752i) q^{43} +(-0.439279 + 0.760853i) q^{44} -2.29105 q^{45} +1.31752 q^{46} +(-0.188939 + 0.327251i) q^{47} +(0.500000 - 0.866025i) q^{48} +(6.90136 - 1.17099i) q^{49} +(-0.124459 - 0.215569i) q^{50} +(-3.20391 + 5.54934i) q^{51} +(-0.786978 + 3.51862i) q^{52} +(-1.22356 - 2.11926i) q^{53} -1.00000 q^{54} +(1.00641 + 1.74315i) q^{55} +(2.63641 - 0.222079i) q^{56} -1.50820 q^{57} +(-0.669294 - 1.15925i) q^{58} -5.96823 q^{59} +(-1.14553 - 1.98411i) q^{60} +(-2.40782 - 4.17047i) q^{61} +(-1.94748 - 3.37313i) q^{62} +(-1.51053 - 2.17216i) q^{63} +1.00000 q^{64} +(6.07982 + 5.59212i) q^{65} +(0.439279 + 0.760853i) q^{66} +(-4.87998 + 8.45237i) q^{67} -6.40782 q^{68} +(0.658760 - 1.14101i) q^{69} +(2.57945 - 5.48533i) q^{70} +(1.02408 - 1.77376i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(0.432504 + 0.749119i) q^{73} +9.38675 q^{74} -0.248918 q^{75} +(-0.754098 - 1.30614i) q^{76} +(-0.989151 + 2.10348i) q^{77} +(2.65372 + 2.44085i) q^{78} +(-4.18014 + 7.24022i) q^{79} +(1.14553 - 1.98411i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.80195 + 3.12107i) q^{82} +8.66710 q^{83} +(1.12588 - 2.39424i) q^{84} +(-7.34033 + 12.7138i) q^{85} +(-4.95801 + 8.58752i) q^{86} -1.33859 q^{87} +(-0.439279 + 0.760853i) q^{88} -12.8339 q^{89} -2.29105 q^{90} +(-1.29339 + 9.45130i) q^{91} +1.31752 q^{92} -3.89495 q^{93} +(-0.188939 + 0.327251i) q^{94} -3.45536 q^{95} +(0.500000 - 0.866025i) q^{96} +(4.40338 - 7.62688i) q^{97} +(6.90136 - 1.17099i) q^{98} +0.878558 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 2 * q^5 + 4 * q^6 - 3 * q^7 + 8 * q^8 - 4 * q^9	\( 8 q + 8 q^{2} + 4 q^{3} + 8 q^{4} + 2 q^{5} + 4 q^{6} - 3 q^{7} + 8 q^{8} - 4 q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} + 8 q^{16} - 8 q^{17} - 4 q^{18} + 6 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} + 20 q^{23} + 4 q^{24} - 18 q^{25} - 11 q^{26} - 8 q^{27} - 3 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 8 q^{32} + 6 q^{33} - 8 q^{34} - 18 q^{35} - 4 q^{36} + 56 q^{37} + 6 q^{38} - 10 q^{39} + 2 q^{40} - 3 q^{42} - 6 q^{43} - 6 q^{44} - 4 q^{45} + 20 q^{46} + q^{47} + 4 q^{48} + 5 q^{49} - 18 q^{50} - 4 q^{51} - 11 q^{52} + 7 q^{53} - 8 q^{54} + q^{55} - 3 q^{56} + 12 q^{57} + 2 q^{58} - 4 q^{59} - 2 q^{60} + 24 q^{61} + 6 q^{62} + 8 q^{64} + 22 q^{65} + 6 q^{66} - 15 q^{67} - 8 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} - 4 q^{72} + q^{73} + 56 q^{74} - 36 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} + 2 q^{80} - 4 q^{81} - 32 q^{83} - 3 q^{84} - 13 q^{85} - 6 q^{86} + 4 q^{87} - 6 q^{88} - 50 q^{89} - 4 q^{90} - 8 q^{91} + 20 q^{92} + 12 q^{93} + q^{94} + 16 q^{95} + 4 q^{96} - q^{97} + 5 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 4 * q^3 + 8 * q^4 + 2 * q^5 + 4 * q^6 - 3 * q^7 + 8 * q^8 - 4 * q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 + 8 * q^16 - 8 * q^17 - 4 * q^18 + 6 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 + 20 * q^23 + 4 * q^24 - 18 * q^25 - 11 * q^26 - 8 * q^27 - 3 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 8 * q^32 + 6 * q^33 - 8 * q^34 - 18 * q^35 - 4 * q^36 + 56 * q^37 + 6 * q^38 - 10 * q^39 + 2 * q^40 - 3 * q^42 - 6 * q^43 - 6 * q^44 - 4 * q^45 + 20 * q^46 + q^47 + 4 * q^48 + 5 * q^49 - 18 * q^50 - 4 * q^51 - 11 * q^52 + 7 * q^53 - 8 * q^54 + q^55 - 3 * q^56 + 12 * q^57 + 2 * q^58 - 4 * q^59 - 2 * q^60 + 24 * q^61 + 6 * q^62 + 8 * q^64 + 22 * q^65 + 6 * q^66 - 15 * q^67 - 8 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 - 4 * q^72 + q^73 + 56 * q^74 - 36 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 + 2 * q^80 - 4 * q^81 - 32 * q^83 - 3 * q^84 - 13 * q^85 - 6 * q^86 + 4 * q^87 - 6 * q^88 - 50 * q^89 - 4 * q^90 - 8 * q^91 + 20 * q^92 + 12 * q^93 + q^94 + 16 * q^95 + 4 * q^96 - q^97 + 5 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more