LMFDB - Embedded newform 546.2.bk.c.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(25,546)]

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, 4, 3]))

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

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

chi := DirichletCharacter("546.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bk (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 26 x^{18} + 431 x^{16} - 4370 x^{14} + 32381 x^{12} - 160412 x^{10} + 573820 x^{8} + \cdots + 810000 $ x^20 - 26x^18 + 431x^16 - 4370x^14 + 32381x^12 - 160412x^10 + 573820x^8 - 1203000x^6 + 1802736x^4 - 1479600*x^2 + 810000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			415.1
Root			$-2.38129 + 1.37484i$ of defining polynomial
Character	$\chi$	$=$	546.415
Dual form			546.2.bk.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.38129 - 1.37484i) q^{5} -1.00000i q^{6} +(-0.588218 + 2.57953i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.38129 - 1.37484i) q^{5} -1.00000i q^{6} +(-0.588218 + 2.57953i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.37484 + 2.38129i) q^{10} +(-0.600231 + 0.346544i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.924342 - 3.48505i) q^{13} +(1.79918 - 1.93983i) q^{14} -2.74967i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.18349 - 5.51396i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.78106 - 1.02829i) q^{19} -2.74967i q^{20} +(-2.52805 + 0.780355i) q^{21} +0.693087 q^{22} +(0.903131 - 1.56427i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.28036 + 2.21764i) q^{25} +(-2.54303 + 2.55597i) q^{26} -1.00000 q^{27} +(-2.52805 + 0.780355i) q^{28} -8.85216 q^{29} +(-1.37484 + 2.38129i) q^{30} +(-0.817019 + 0.471706i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.600231 - 0.346544i) q^{33} +6.36697i q^{34} +(4.94716 - 5.33391i) q^{35} -1.00000 q^{36} +(-0.833421 - 0.481176i) q^{37} +(1.02829 + 1.78106i) q^{38} +(3.48032 - 0.942023i) q^{39} +(-1.37484 + 2.38129i) q^{40} -11.7716i q^{41} +(2.57953 + 0.588218i) q^{42} -4.97011 q^{43} +(-0.600231 - 0.346544i) q^{44} +(2.38129 - 1.37484i) q^{45} +(-1.56427 + 0.903131i) q^{46} +(7.81735 + 4.51335i) q^{47} -1.00000 q^{48} +(-6.30800 - 3.03466i) q^{49} -2.56071i q^{50} +(3.18349 - 5.51396i) q^{51} +(3.48032 - 0.942023i) q^{52} +(1.98505 + 3.43821i) q^{53} +(0.866025 + 0.500000i) q^{54} +1.90576 q^{55} +(2.57953 + 0.588218i) q^{56} -2.05659i q^{57} +(7.66619 + 4.42608i) q^{58} +(-10.5042 + 6.06459i) q^{59} +(2.38129 - 1.37484i) q^{60} +(5.03217 - 8.71597i) q^{61} +0.943413 q^{62} +(-1.93983 - 1.79918i) q^{63} -1.00000 q^{64} +(-6.99251 + 7.02809i) q^{65} +(0.346544 + 0.600231i) q^{66} +(-8.40673 + 4.85363i) q^{67} +(3.18349 - 5.51396i) q^{68} +1.80626 q^{69} +(-6.95132 + 2.14572i) q^{70} -7.68213i q^{71} +(0.866025 + 0.500000i) q^{72} +(-4.89733 + 2.82747i) q^{73} +(0.481176 + 0.833421i) q^{74} +(-1.28036 + 2.21764i) q^{75} -2.05659i q^{76} +(-0.540854 - 1.75216i) q^{77} +(-3.48505 - 0.924342i) q^{78} +(-0.339330 + 0.587736i) q^{79} +(2.38129 - 1.37484i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.88580 + 10.1945i) q^{82} +2.32585i q^{83} +(-1.93983 - 1.79918i) q^{84} +17.5071i q^{85} +(4.30424 + 2.48505i) q^{86} +(-4.42608 - 7.66619i) q^{87} +(0.346544 + 0.600231i) q^{88} +(11.5995 + 6.69696i) q^{89} -2.74967 q^{90} +(8.44610 + 4.43434i) q^{91} +1.80626 q^{92} +(-0.817019 - 0.471706i) q^{93} +(-4.51335 - 7.81735i) q^{94} +(2.82747 + 4.89733i) q^{95} +(0.866025 + 0.500000i) q^{96} +9.89969i q^{97} +(3.94556 + 5.78209i) q^{98} -0.693087i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9	$ 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9} + 4 q^{10} - 10 q^{12} + 4 q^{13} - 2 q^{14} - 10 q^{16} - 6 q^{17} - 12 q^{22} - 16 q^{23} + 2 q^{25} - 4 q^{26} - 20 q^{27} - 28 q^{29} - 4 q^{30} + 16 q^{35} - 20 q^{36} + 10 q^{38} + 2 q^{39} - 4 q^{40} - 10 q^{42} + 24 q^{43} - 20 q^{48} + 2 q^{49} + 6 q^{51} + 2 q^{52} - 22 q^{53} + 88 q^{55} - 10 q^{56} + 14 q^{61} + 40 q^{62} - 20 q^{64} + 20 q^{65} - 6 q^{66} + 6 q^{68} - 32 q^{69} + 24 q^{74} - 2 q^{75} - 28 q^{77} - 8 q^{78} + 4 q^{79} - 10 q^{81} + 12 q^{82} - 14 q^{87} - 6 q^{88} - 8 q^{90} + 68 q^{91} - 32 q^{92} - 18 q^{94} + 8 q^{95}+O(q^{100}) $ 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9 + 4 * q^10 - 10 * q^12 + 4 * q^13 - 2 * q^14 - 10 * q^16 - 6 * q^17 - 12 * q^22 - 16 * q^23 + 2 * q^25 - 4 * q^26 - 20 * q^27 - 28 * q^29 - 4 * q^30 + 16 * q^35 - 20 * q^36 + 10 * q^38 + 2 * q^39 - 4 * q^40 - 10 * q^42 + 24 * q^43 - 20 * q^48 + 2 * q^49 + 6 * q^51 + 2 * q^52 - 22 * q^53 + 88 * q^55 - 10 * q^56 + 14 * q^61 + 40 * q^62 - 20 * q^64 + 20 * q^65 - 6 * q^66 + 6 * q^68 - 32 * q^69 + 24 * q^74 - 2 * q^75 - 28 * q^77 - 8 * q^78 + 4 * q^79 - 10 * q^81 + 12 * q^82 - 14 * q^87 - 6 * q^88 - 8 * q^90 + 68 * q^91 - 32 * q^92 - 18 * q^94 + 8 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.38129	−	1.37484i	−1.06494	−	0.614846i	−0.138149	−	0.990412i	$-0.544115\pi$
$5$	−2.38129	−	1.37484i	−1.06494	−	0.614846i	−0.926796	+	0.375566i	$0.877448\pi$
$6$		−	1.00000i		−	0.408248i
$7$	−0.588218	+	2.57953i	−0.222326	+	0.974972i
$7$	−0.588218	+	2.57953i	−0.222326	+	0.974972i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.37484	+	2.38129i	0.434762	+	0.753029i
$11$	−0.600231	+	0.346544i	−0.180976	+	0.104487i	−0.587751	−	0.809042i	$-0.699987\pi$
$11$	−0.600231	+	0.346544i	−0.180976	+	0.104487i	0.406775	+	0.913528i	$0.366653\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	0.924342	−	3.48505i	0.256366	−	0.966580i
$13$	0.924342	−	3.48505i	0.256366	−	0.966580i
$14$	1.79918	−	1.93983i	0.480851	−	0.518442i
$15$		−	2.74967i		−	0.709963i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.18349	−	5.51396i	−0.772109	−	1.33733i	−0.936405	−	0.350921i	$-0.885869\pi$
$17$	−3.18349	−	5.51396i	−0.772109	−	1.33733i	0.164296	−	0.986411i	$-0.447465\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−1.78106	−	1.02829i	−0.408602	−	0.235907i	0.281587	−	0.959536i	$-0.409139\pi$
$19$	−1.78106	−	1.02829i	−0.408602	−	0.235907i	−0.690189	+	0.723629i	$0.742473\pi$
$20$		−	2.74967i		−	0.614846i
$21$	−2.52805	+	0.780355i	−0.551666	+	0.170287i
$22$	0.693087			0.147767
$23$	0.903131	−	1.56427i	0.188316	−	0.326173i	−0.756373	−	0.654141i	$-0.773030\pi$
$23$	0.903131	−	1.56427i	0.188316	−	0.326173i	0.944689	+	0.327968i	$0.106364\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	1.28036	+	2.21764i	0.256071	+	0.443528i
$26$	−2.54303	+	2.55597i	−0.498729	+	0.501268i
$27$	−1.00000			−0.192450
$28$	−2.52805	+	0.780355i	−0.477757	+	0.147473i
$29$	−8.85216			−1.64380			−0.821902	−	0.569629i	$-0.807087\pi$
$29$	−8.85216			−1.64380			−0.821902	+	0.569629i	$0.807087\pi$
$30$	−1.37484	+	2.38129i	−0.251010	+	0.434762i
$31$	−0.817019	+	0.471706i	−0.146741	+	0.0847209i	−0.571573	−	0.820551i	$-0.693667\pi$
$31$	−0.817019	+	0.471706i	−0.146741	+	0.0847209i	0.424832	+	0.905272i	$0.360333\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.600231	−	0.346544i	−0.104487	−	0.0603255i
$34$			6.36697i			1.09193i
$35$	4.94716	−	5.33391i	0.836222	−	0.901595i
$36$	−1.00000			−0.166667
$37$	−0.833421	−	0.481176i	−0.137014	−	0.0791048i	0.429926	−	0.902864i	$-0.358540\pi$
$37$	−0.833421	−	0.481176i	−0.137014	−	0.0791048i	−0.566940	+	0.823759i	$0.691873\pi$
$38$	1.02829	+	1.78106i	0.166811	+	0.288926i
$39$	3.48032	−	0.942023i	0.557296	−	0.150844i
$40$	−1.37484	+	2.38129i	−0.217381	+	0.376515i
$41$		−	11.7716i		−	1.83841i	−0.393775	−	0.919207i	$-0.628831\pi$
$41$		−	11.7716i		−	1.83841i	0.393775	−	0.919207i	$-0.371169\pi$
$42$	2.57953	+	0.588218i	0.398031	+	0.0907641i
$43$	−4.97011			−0.757934			−0.378967	−	0.925410i	$-0.623721\pi$
$43$	−4.97011			−0.757934			−0.378967	+	0.925410i	$0.623721\pi$
$44$	−0.600231	−	0.346544i	−0.0904882	−	0.0522434i
$45$	2.38129	−	1.37484i	0.354981	−	0.204949i
$46$	−1.56427	+	0.903131i	−0.230639	+	0.133159i
$47$	7.81735	+	4.51335i	1.14028	+	0.658339i	0.946499	−	0.322706i	$-0.104593\pi$
$47$	7.81735	+	4.51335i	1.14028	+	0.658339i	0.193778	+	0.981045i	$0.437926\pi$
$48$	−1.00000			−0.144338
$49$	−6.30800	−	3.03466i	−0.901143	−	0.433523i
$50$		−	2.56071i		−	0.362139i
$51$	3.18349	−	5.51396i	0.445777	−	0.772109i
$52$	3.48032	−	0.942023i	0.482633	−	0.130635i
$53$	1.98505	+	3.43821i	0.272668	+	0.472275i	0.969544	−	0.244917i	$-0.0787606\pi$
$53$	1.98505	+	3.43821i	0.272668	+	0.472275i	−0.696876	+	0.717191i	$0.745427\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	1.90576			0.256973
$56$	2.57953	+	0.588218i	0.344705	+	0.0786040i
$57$		−	2.05659i		−	0.272402i
$58$	7.66619	+	4.42608i	1.00662	+	0.581173i
$59$	−10.5042	+	6.06459i	−1.36753	+	0.789542i	−0.990612	−	0.136706i	$-0.956349\pi$
$59$	−10.5042	+	6.06459i	−1.36753	+	0.789542i	−0.376915	+	0.926248i	$0.623015\pi$
$60$	2.38129	−	1.37484i	0.307423	−	0.177491i
$61$	5.03217	−	8.71597i	0.644303	−	1.11597i	−0.340159	−	0.940368i	$-0.610481\pi$
$61$	5.03217	−	8.71597i	0.644303	−	1.11597i	0.984462	−	0.175598i	$-0.0561859\pi$
$62$	0.943413			0.119814
$63$	−1.93983	−	1.79918i	−0.244396	−	0.226675i
$64$	−1.00000			−0.125000
$65$	−6.99251	+	7.02809i	−0.867314	+	0.871728i
$66$	0.346544	+	0.600231i	0.0426566	+	0.0738833i
$67$	−8.40673	+	4.85363i	−1.02705	+	0.592965i	−0.916137	−	0.400866i	$-0.868709\pi$
$67$	−8.40673	+	4.85363i	−1.02705	+	0.592965i	−0.110908	+	0.993831i	$0.535376\pi$
$68$	3.18349	−	5.51396i	0.386054	−	0.668666i
$69$	1.80626			0.217448
$70$	−6.95132	+	2.14572i	−0.830842	+	0.256463i
$71$		−	7.68213i		−	0.911701i	−0.890056	−	0.455851i	$-0.849335\pi$
$71$		−	7.68213i		−	0.911701i	0.890056	−	0.455851i	$-0.150665\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−4.89733	+	2.82747i	−0.573189	+	0.330931i	−0.758422	−	0.651764i	$-0.774029\pi$
$73$	−4.89733	+	2.82747i	−0.573189	+	0.330931i	0.185233	+	0.982695i	$0.440696\pi$
$74$	0.481176	+	0.833421i	0.0559356	+	0.0968832i
$75$	−1.28036	+	2.21764i	−0.147843	+	0.256071i
$76$		−	2.05659i		−	0.235907i
$77$	−0.540854	−	1.75216i	−0.0616361	−	0.199677i
$78$	−3.48505	−	0.924342i	−0.394605	−	0.104661i
$79$	−0.339330	+	0.587736i	−0.0381776	+	0.0661255i	−0.884483	−	0.466573i	$-0.845489\pi$
$79$	−0.339330	+	0.587736i	−0.0381776	+	0.0661255i	0.846305	+	0.532698i	$0.178822\pi$
$80$	2.38129	−	1.37484i	0.266236	−	0.153711i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.88580	+	10.1945i	−0.649978	+	1.12579i
$83$			2.32585i			0.255295i	0.991820	+	0.127648i	$0.0407427\pi$
$83$			2.32585i			0.255295i	−0.991820	+	0.127648i	$0.959257\pi$
$84$	−1.93983	−	1.79918i	−0.211653	−	0.196307i
$85$			17.5071i			1.89891i
$86$	4.30424	+	2.48505i	0.464138	+	0.267970i
$87$	−4.42608	−	7.66619i	−0.474525	−	0.821902i
$88$	0.346544	+	0.600231i	0.0369417	+	0.0639849i
$89$	11.5995	+	6.69696i	1.22954	+	0.709877i	0.966934	−	0.255026i	$-0.0820839\pi$
$89$	11.5995	+	6.69696i	1.22954	+	0.709877i	0.262608	+	0.964903i	$0.415417\pi$
$90$	−2.74967			−0.289841
$91$	8.44610	+	4.43434i	0.885392	+	0.464846i
$92$	1.80626			0.188316
$93$	−0.817019	−	0.471706i	−0.0847209	−	0.0489137i
$94$	−4.51335	−	7.81735i	−0.465516	−	0.806298i
$95$	2.82747	+	4.89733i	0.290093	+	0.502455i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$			9.89969i			1.00516i	0.864530	+	0.502581i	$0.167616\pi$
$97$			9.89969i			1.00516i	−0.864530	+	0.502581i	$0.832384\pi$
$98$	3.94556	+	5.78209i	0.398561	+	0.584079i
$99$		−	0.693087i		−	0.0696579i
$100$	−1.28036	+	2.21764i	−0.128036	+	0.221764i
$101$	−4.00174	−	6.93121i	−0.398188	−	0.689681i	0.595315	−	0.803493i	$-0.297027\pi$
$101$	−4.00174	−	6.93121i	−0.398188	−	0.689681i	−0.993502	+	0.113811i	$0.963694\pi$
$102$	−5.51396	+	3.18349i	−0.545963	+	0.315212i
$103$	6.29145	−	10.8971i	0.619915	−	1.07372i	−0.369586	−	0.929196i	$-0.620501\pi$
$103$	6.29145	−	10.8971i	0.619915	−	1.07372i	0.989501	−	0.144527i	$-0.0461661\pi$
$104$	−3.48505	−	0.924342i	−0.341738	−	0.0906392i
$105$	7.09288	+	1.61741i	0.692194	+	0.157843i
$106$		−	3.97011i		−	0.385611i
$107$	−5.06993	+	8.78138i	−0.490129	+	0.848928i	−0.999935	−	0.0113608i	$-0.996384\pi$
$107$	−5.06993	+	8.78138i	−0.490129	+	0.848928i	0.509806	+	0.860289i	$0.329717\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	10.7989	−	6.23473i	1.03434	−	0.597179i	0.116118	−	0.993235i	$-0.462955\pi$
$109$	10.7989	−	6.23473i	1.03434	−	0.597179i	0.918226	+	0.396057i	$0.129622\pi$
$110$	−1.65044	−	0.952882i	−0.157363	−	0.0908537i
$111$		−	0.962352i		−	0.0913424i
$112$	−1.93983	−	1.79918i	−0.183297	−	0.170006i
$113$	−8.21218			−0.772537			−0.386269	−	0.922386i	$-0.626236\pi$
$113$	−8.21218			−0.772537			−0.386269	+	0.922386i	$0.626236\pi$
$114$	−1.02829	+	1.78106i	−0.0963085	+	0.166811i
$115$	−4.30123	+	2.48332i	−0.401092	+	0.231570i
$116$	−4.42608	−	7.66619i	−0.410951	−	0.711788i
$117$	2.55597	+	2.54303i	0.236300	+	0.235103i
$118$	12.1292			1.11658
$119$	16.0960	−	4.96850i	1.47552	−	0.455462i
$120$	−2.74967			−0.251010
$121$	−5.25982	+	9.11027i	−0.478165	+	0.828206i
$122$	−8.71597	+	5.03217i	−0.789107	+	0.455591i
$123$	10.1945	−	5.88580i	0.919207	−	0.530704i
$124$	−0.817019	−	0.471706i	−0.0733705	−	0.0423605i
$125$			6.70725i			0.599915i
$126$	0.780355	+	2.52805i	0.0695196	+	0.225217i
$127$	6.39687			0.567630			0.283815	−	0.958879i	$-0.408400\pi$
$127$	6.39687			0.567630			0.283815	+	0.958879i	$0.408400\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−2.48505	−	4.30424i	−0.218797	−	0.378967i
$130$	9.56973	−	2.59026i	0.839321	−	0.227180i
$131$	0.971460	−	1.68262i	0.0848769	−	0.147011i	−0.820462	−	0.571701i	$-0.806284\pi$
$131$	0.971460	−	1.68262i	0.0848769	−	0.147011i	0.905339	+	0.424690i	$0.139617\pi$
$132$		−	0.693087i		−	0.0603255i
$133$	3.70017	−	3.98944i	0.320845	−	0.345928i
$134$	9.70725			0.838579
$135$	2.38129	+	1.37484i	0.204949	+	0.118327i
$136$	−5.51396	+	3.18349i	−0.472818	+	0.272982i
$137$	−0.0395182	+	0.0228159i	−0.00337627	+	0.00194929i	−0.501687	−	0.865049i	$-0.667287\pi$
$137$	−0.0395182	+	0.0228159i	−0.00337627	+	0.00194929i	0.498311	+	0.866998i	$0.333954\pi$
$138$	−1.56427	−	0.903131i	−0.133159	−	0.0768796i
$139$	20.8679			1.76999			0.884996	−	0.465599i	$-0.154161\pi$
$139$	20.8679			1.76999			0.884996	+	0.465599i	$0.154161\pi$
$140$	7.09288	+	1.61741i	0.599458	+	0.136696i
$141$			9.02669i			0.760185i
$142$	−3.84107	+	6.65292i	−0.322335	+	0.558301i
$143$	0.652904	+	2.41216i	0.0545986	+	0.201715i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	21.0795	+	12.1703i	1.75056	+	1.01069i
$146$	5.65495			0.468007
$147$	−0.525907	−	6.98022i	−0.0433761	−	0.575719i
$148$		−	0.962352i		−	0.0791048i
$149$	−3.60487	−	2.08127i	−0.295322	−	0.170504i	0.345017	−	0.938596i	$-0.387873\pi$
$149$	−3.60487	−	2.08127i	−0.295322	−	0.170504i	−0.640340	+	0.768092i	$0.721206\pi$
$150$	2.21764	−	1.28036i	0.181070	−	0.104541i
$151$	0.395710	−	0.228464i	0.0322025	−	0.0185921i	−0.483812	−	0.875172i	$-0.660748\pi$
$151$	0.395710	−	0.228464i	0.0322025	−	0.0185921i	0.516015	+	0.856580i	$0.327415\pi$
$152$	−1.02829	+	1.78106i	−0.0834056	+	0.144463i
$153$	6.36697			0.514739
$154$	−0.407687	+	1.78784i	−0.0328523	+	0.144068i
$155$	2.59408			0.208361
$156$	2.55597	+	2.54303i	0.204642	+	0.203605i
$157$	0.775828	+	1.34377i	0.0619178	+	0.107245i	0.895323	−	0.445418i	$-0.146945\pi$
$157$	0.775828	+	1.34377i	0.0619178	+	0.107245i	−0.833405	+	0.552663i	$0.813612\pi$
$158$	0.587736	−	0.339330i	0.0467578	−	0.0269956i
$159$	−1.98505	+	3.43821i	−0.157425	+	0.272668i
$160$	−2.74967			−0.217381
$161$	3.50385	+	3.24979i	0.276142	+	0.256119i
$162$			1.00000i			0.0785674i
$163$	−5.18296	−	2.99238i	−0.405961	−	0.234381i	0.283092	−	0.959093i	$-0.408640\pi$
$163$	−5.18296	−	2.99238i	−0.405961	−	0.234381i	−0.689053	+	0.724711i	$0.741973\pi$
$164$	10.1945	−	5.88580i	0.796057	−	0.459604i
$165$	0.952882	+	1.65044i	0.0741818	+	0.128487i
$166$	1.16293	−	2.01425i	0.0902606	−	0.156336i
$167$		−	7.21268i		−	0.558134i	−0.960272	−	0.279067i	$-0.909975\pi$
$167$		−	7.21268i		−	0.558134i	0.960272	−	0.279067i	$-0.0900251\pi$
$168$	0.780355	+	2.52805i	0.0602057	+	0.195043i
$169$	−11.2912	−	6.44276i	−0.868553	−	0.495597i
$170$	8.75355	−	15.1616i	0.671367	−	1.16284i
$171$	1.78106	−	1.02829i	0.136201	−	0.0786356i
$172$	−2.48505	−	4.30424i	−0.189483	−	0.328195i
$173$	−11.3781	+	19.7074i	−0.865058	+	1.49832i	0.00193131	+	0.999998i	$0.499385\pi$
$173$	−11.3781	+	19.7074i	−0.865058	+	1.49832i	−0.866989	+	0.498327i	$0.833948\pi$
$174$			8.85216i			0.671080i
$175$	−6.47361	+	1.99826i	−0.489359	+	0.151055i
$176$		−	0.693087i		−	0.0522434i
$177$	−10.5042	−	6.06459i	−0.789542	−	0.455842i
$178$	−6.69696	−	11.5995i	−0.501959	−	0.869418i
$179$	7.65842	+	13.2648i	0.572417	+	0.991455i	0.996317	+	0.0857464i	$0.0273275\pi$
$179$	7.65842	+	13.2648i	0.572417	+	0.991455i	−0.423900	+	0.905709i	$0.639339\pi$
$180$	2.38129	+	1.37484i	0.177491	+	0.102474i
$181$	20.1559			1.49817			0.749087	−	0.662472i	$-0.230493\pi$
$181$	20.1559			1.49817			0.749087	+	0.662472i	$0.230493\pi$
$182$	−5.09736	−	8.06330i	−0.377842	−	0.597692i
$183$	10.0643			0.743977
$184$	−1.56427	−	0.903131i	−0.115319	−	0.0665797i
$185$	1.32308	+	2.29164i	0.0972746	+	0.168484i
$186$	0.471706	+	0.817019i	0.0345872	+	0.0599068i
$187$	3.82165	+	2.20643i	0.279467	+	0.161350i
$188$			9.02669i			0.658339i
$189$	0.588218	−	2.57953i	0.0427866	−	0.187634i
$190$		−	5.65495i		−	0.410253i
$191$	9.58276	−	16.5978i	0.693384	−	1.20098i	−0.277338	−	0.960772i	$-0.589452\pi$
$191$	9.58276	−	16.5978i	0.693384	−	1.20098i	0.970722	−	0.240204i	$-0.0772144\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−3.22142	+	1.85989i	−0.231883	+	0.133878i	−0.611441	−	0.791290i	$-0.709410\pi$
$193$	−3.22142	+	1.85989i	−0.231883	+	0.133878i	0.379557	+	0.925168i	$0.376076\pi$
$194$	4.94984	−	8.57338i	0.355378	−	0.615533i
$195$	−9.58276	−	2.54164i	−0.686236	−	0.182011i
$196$	−0.525907	−	6.98022i	−0.0375648	−	0.498587i
$197$			9.45693i			0.673778i	0.941544	+	0.336889i	$0.109375\pi$
$197$			9.45693i			0.673778i	−0.941544	+	0.336889i	$0.890625\pi$
$198$	−0.346544	+	0.600231i	−0.0246278	+	0.0426566i
$199$	−1.73497	−	3.00506i	−0.122989	−	0.213023i	0.797956	−	0.602716i	$-0.205915\pi$
$199$	−1.73497	−	3.00506i	−0.122989	−	0.213023i	−0.920945	+	0.389692i	$0.872581\pi$
$200$	2.21764	−	1.28036i	0.156811	−	0.0905348i
$201$	−8.40673	−	4.85363i	−0.592965	−	0.342348i
$202$			8.00347i			0.563122i
$203$	5.20700	−	22.8344i	0.365460	−	1.60266i
$204$	6.36697			0.445777
$205$	−16.1840	+	28.0316i	−1.13034	+	1.95781i
$206$	−10.8971	+	6.29145i	−0.759237	+	0.438346i
$207$	0.903131	+	1.56427i	0.0627719	+	0.108724i
$208$	2.55597	+	2.54303i	0.177225	+	0.176327i
$209$	1.42539			0.0985966
$210$	−5.33391	−	4.94716i	−0.368075	−	0.341386i
$211$	−28.3961			−1.95487			−0.977434	−	0.211241i	$-0.932250\pi$
$211$	−28.3961			−1.95487			−0.977434	+	0.211241i	$0.932250\pi$
$212$	−1.98505	+	3.43821i	−0.136334	+	0.236137i
$213$	6.65292	−	3.84107i	0.455851	−	0.263185i
$214$	8.78138	−	5.06993i	0.600283	−	0.346574i
$215$	11.8353	+	6.83309i	0.807158	+	0.466013i
$216$			1.00000i			0.0680414i
$217$	−0.736197	−	2.38500i	−0.0499763	−	0.161904i
$218$	−12.4695			−0.844538
$219$	−4.89733	−	2.82747i	−0.330931	−	0.191063i
$220$	0.952882	+	1.65044i	0.0642433	+	0.111273i
$221$	−22.1591	+	5.99783i	−1.49058	+	0.403458i
$222$	−0.481176	+	0.833421i	−0.0322944	+	0.0559356i
$223$		−	12.2391i		−	0.819593i	−0.912177	−	0.409797i	$-0.865600\pi$
$223$		−	12.2391i		−	0.819593i	0.912177	−	0.409797i	$-0.134400\pi$
$224$	0.780355	+	2.52805i	0.0521397	+	0.168913i
$225$	−2.56071			−0.170714
$226$	7.11196	+	4.10609i	0.473081	+	0.273133i
$227$	−14.5558	+	8.40380i	−0.966103	+	0.557780i	−0.898046	−	0.439901i	$-0.855013\pi$
$227$	−14.5558	+	8.40380i	−0.966103	+	0.557780i	−0.0680571	+	0.997681i	$0.521680\pi$
$228$	1.78106	−	1.02829i	0.117953	−	0.0681004i
$229$	−19.3011	−	11.1435i	−1.27545	−	0.736381i	−0.299442	−	0.954115i	$-0.596800\pi$
$229$	−19.3011	−	11.1435i	−1.27545	−	0.736381i	−0.976008	+	0.217733i	$0.930134\pi$
$230$	4.96663			0.327490
$231$	1.24699	−	1.34447i	0.0820458	−	0.0884599i
$232$			8.85216i			0.581173i
$233$	−9.06727	+	15.7050i	−0.594017	+	1.02887i	0.399668	+	0.916660i	$0.369125\pi$
$233$	−9.06727	+	15.7050i	−0.594017	+	1.02887i	−0.993685	+	0.112207i	$0.964208\pi$
$234$	−0.942023	−	3.48032i	−0.0615819	−	0.227515i
$235$	−12.4102	−	21.4952i	−0.809554	−	1.40219i
$236$	−10.5042	−	6.06459i	−0.683763	−	0.394771i
$237$	−0.678659			−0.0440837
$238$	−16.4238	−	3.74517i	−1.06460	−	0.242763i
$239$		−	11.2880i		−	0.730158i	−0.930976	−	0.365079i	$-0.881042\pi$
$239$		−	11.2880i		−	0.730158i	0.930976	−	0.365079i	$-0.118958\pi$
$240$	2.38129	+	1.37484i	0.153711	+	0.0887454i
$241$	7.51594	−	4.33933i	0.484144	−	0.279521i	−0.237998	−	0.971266i	$-0.576491\pi$
$241$	7.51594	−	4.33933i	0.484144	−	0.279521i	0.722142	+	0.691745i	$0.243158\pi$
$242$	9.11027	−	5.25982i	0.585630	−	0.338114i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	10.0643			0.644303
$245$	10.8490	+	15.8989i	0.693117	+	1.01574i
$246$	−11.7716			−0.750529
$247$	−5.22996	+	5.25658i	−0.332775	+	0.334468i
$248$	0.471706	+	0.817019i	0.0299534	+	0.0518808i
$249$	−2.01425	+	1.16293i	−0.127648	+	0.0736974i
$250$	3.35363	−	5.80865i	0.212102	−	0.367371i
$251$	−21.8442			−1.37879			−0.689396	−	0.724384i	$-0.742124\pi$
$251$	−21.8442			−1.37879			−0.689396	+	0.724384i	$0.742124\pi$
$252$	0.588218	−	2.57953i	0.0370543	−	0.162495i
$253$			1.25190i			0.0787061i
$254$	−5.53985	−	3.19843i	−0.347601	−	0.200688i
$255$	−15.1616	+	8.75355i	−0.949456	+	0.548169i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.8097	+	22.1871i	−0.799049	+	1.38399i	0.121187	+	0.992630i	$0.461330\pi$
$257$	−12.8097	+	22.1871i	−0.799049	+	1.38399i	−0.920236	+	0.391364i	$0.872003\pi$
$258$			4.97011i			0.309425i
$259$	1.73144	−	1.86680i	0.107587	−	0.115997i
$260$	−9.58276	−	2.54164i	−0.594298	−	0.157626i
$261$	4.42608	−	7.66619i	0.273967	−	0.474525i
$262$	−1.68262	+	0.971460i	−0.103952	+	0.0600170i
$263$	6.43061	+	11.1381i	0.396528	+	0.686807i	0.993295	−	0.115608i	$-0.0368816\pi$
$263$	6.43061	+	11.1381i	0.396528	+	0.686807i	−0.596767	+	0.802415i	$0.703548\pi$
$264$	−0.346544	+	0.600231i	−0.0213283	+	0.0369417i
$265$		−	10.9165i		−	0.670595i
$266$	−5.19916	+	1.60487i	−0.318781	+	0.0984008i
$267$			13.3939i			0.819695i
$268$	−8.40673	−	4.85363i	−0.513523	−	0.296482i
$269$	−4.83200	−	8.36927i	−0.294612	−	0.510283i	0.680282	−	0.732950i	$-0.261857\pi$
$269$	−4.83200	−	8.36927i	−0.294612	−	0.510283i	−0.974895	+	0.222667i	$0.928524\pi$
$270$	−1.37484	−	2.38129i	−0.0836699	−	0.144921i
$271$	−6.33421	−	3.65706i	−0.384776	−	0.222151i	0.295118	−	0.955461i	$-0.404641\pi$
$271$	−6.33421	−	3.65706i	−0.384776	−	0.222151i	−0.679894	+	0.733310i	$0.737974\pi$
$272$	6.36697			0.386054
$273$	0.382794	+	9.53171i	0.0231678	+	0.576885i
$274$	0.0456317			0.00275671
$275$	−1.53702	−	0.887398i	−0.0926857	−	0.0535121i
$276$	0.903131	+	1.56427i	0.0543621	+	0.0941579i
$277$	6.35351	+	11.0046i	0.381745	+	0.661203i	0.991312	−	0.131532i	$-0.0419898\pi$
$277$	6.35351	+	11.0046i	0.381745	+	0.661203i	−0.609566	+	0.792735i	$0.708656\pi$
$278$	−18.0721	−	10.4339i	−1.08389	−	0.625787i
$279$		−	0.943413i		−	0.0564806i
$280$	−5.33391	−	4.94716i	−0.318762	−	0.295649i
$281$		−	23.8172i		−	1.42082i	−0.703790	−	0.710408i	$-0.748510\pi$
$281$		−	23.8172i		−	1.42082i	0.703790	−	0.710408i	$-0.251490\pi$
$282$	4.51335	−	7.81735i	0.268766	−	0.465516i
$283$	−14.5614	−	25.2211i	−0.865586	−	1.49924i	−0.866464	−	0.499240i	$-0.833613\pi$
$283$	−14.5614	−	25.2211i	−0.865586	−	1.49924i	0.000877205	−	1.00000i	$-0.499721\pi$
$284$	6.65292	−	3.84107i	0.394778	−	0.227925i
$285$	−2.82747	+	4.89733i	−0.167485	+	0.290093i
$286$	0.640650	−	2.41545i	0.0378824	−	0.142828i
$287$	30.3652	+	6.92427i	1.79240	+	0.408727i
$288$			1.00000i			0.0589256i
$289$	−11.7692	+	20.3848i	−0.692304	+	1.19911i
$290$	−12.1703	−	21.0795i	−0.714663	−	1.23783i
$291$	−8.57338	+	4.94984i	−0.502581	+	0.290165i
$292$	−4.89733	−	2.82747i	−0.286594	−	0.165465i
$293$		−	6.86285i		−	0.400932i	−0.979701	−	0.200466i	$-0.935754\pi$
$293$		−	6.86285i		−	0.400932i	0.979701	−	0.200466i	$-0.0642456\pi$
$294$	−3.03466	+	6.30800i	−0.176985	+	0.367890i
$295$	33.3513			1.94179
$296$	−0.481176	+	0.833421i	−0.0279678	+	0.0484416i
$297$	0.600231	−	0.346544i	0.0348289	−	0.0201085i
$298$	2.08127	+	3.60487i	0.120565	+	0.208824i
$299$	−4.61676	−	4.59338i	−0.266994	−	0.265642i
$300$	−2.56071			−0.147843
$301$	2.92351	−	12.8206i	0.168508	−	0.738965i
$302$	−0.456927			−0.0262932
$303$	4.00174	−	6.93121i	0.229894	−	0.398188i
$304$	1.78106	−	1.02829i	0.102151	−	0.0589767i
$305$	−23.9661	+	13.8368i	−1.37229	+	0.792295i
$306$	−5.51396	−	3.18349i	−0.315212	−	0.181988i
$307$		−	26.5794i		−	1.51697i	−0.651692	−	0.758484i	$-0.725940\pi$
$307$		−	26.5794i		−	1.51697i	0.651692	−	0.758484i	$-0.274060\pi$
$308$	1.24699	−	1.34447i	0.0710537	−	0.0766085i
$309$	12.5829			0.715816
$310$	−2.24654	−	1.29704i	−0.127595	−	0.0736669i
$311$	−5.31600	−	9.20758i	−0.301443	−	0.522114i	0.675020	−	0.737799i	$-0.264135\pi$
$311$	−5.31600	−	9.20758i	−0.301443	−	0.522114i	−0.976463	+	0.215685i	$0.930801\pi$
$312$	−0.942023	−	3.48032i	−0.0533315	−	0.197034i
$313$	13.4089	−	23.2249i	0.757915	−	1.31275i	−0.185998	−	0.982550i	$-0.559552\pi$
$313$	13.4089	−	23.2249i	0.757915	−	1.31275i	0.943912	−	0.330196i	$-0.107115\pi$
$314$		−	1.55166i		−	0.0875650i
$315$	2.14572	+	6.95132i	0.120898	+	0.391662i
$316$	−0.678659			−0.0381776
$317$	12.8163	+	7.39952i	0.719838	+	0.415598i	0.814693	−	0.579893i	$-0.196905\pi$
$317$	12.8163	+	7.39952i	0.719838	+	0.415598i	−0.0948552	+	0.995491i	$0.530239\pi$
$318$	3.43821	−	1.98505i	0.192805	−	0.111316i
$319$	5.31334	−	3.06766i	0.297490	−	0.171756i
$320$	2.38129	+	1.37484i	0.133118	+	0.0768557i
$321$	−10.1399			−0.565952
$322$	−1.40953	−	4.56632i	−0.0785498	−	0.254471i
$323$			13.0942i			0.728583i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	8.91208	−	2.41225i	0.494353	−	0.133807i
$326$	2.99238	+	5.18296i	0.165733	+	0.287057i
$327$	10.7989	+	6.23473i	0.597179	+	0.344781i
$328$	−11.7716			−0.649978
$329$	−16.2406	+	17.5103i	−0.895375	+	0.965373i
$330$		−	1.90576i		−	0.104909i
$331$	6.00025	+	3.46425i	0.329804	+	0.190412i	0.655754	−	0.754975i	$-0.272351\pi$
$331$	6.00025	+	3.46425i	0.329804	+	0.190412i	−0.325950	+	0.945387i	$0.605684\pi$
$332$	−2.01425	+	1.16293i	−0.110546	+	0.0638239i
$333$	0.833421	−	0.481176i	0.0456712	−	0.0263683i
$334$	−3.60634	+	6.24636i	−0.197330	+	0.341786i
$335$	26.6918			1.45833
$336$	0.588218	−	2.57953i	0.0320899	−	0.140725i
$337$	18.3349			0.998768			0.499384	−	0.866381i	$-0.333560\pi$
$337$	18.3349			0.998768			0.499384	+	0.866381i	$0.333560\pi$
$338$	6.55707	+	11.2252i	0.356658	+	0.610570i
$339$	−4.10609	−	7.11196i	−0.223012	−	0.386269i
$340$	−15.1616	+	8.75355i	−0.822253	+	0.474728i
$341$	0.326934	−	0.566266i	0.0177044	−	0.0306650i
$342$	−2.05659			−0.111208
$343$	11.5385	−	14.4867i	0.623020	−	0.782206i
$344$			4.97011i			0.267970i
$345$	−4.30123	−	2.48332i	−0.231570	−	0.133697i
$346$	19.7074	−	11.3781i	1.05948	−	0.611688i
$347$	3.38645	+	5.86550i	0.181794	+	0.314876i	0.942492	−	0.334230i	$-0.108476\pi$
$347$	3.38645	+	5.86550i	0.181794	+	0.314876i	−0.760697	+	0.649107i	$0.775143\pi$
$348$	4.42608	−	7.66619i	0.237263	−	0.410951i
$349$		−	31.1199i		−	1.66581i	−0.553416	−	0.832905i	$-0.686676\pi$
$349$		−	31.1199i		−	1.66581i	0.553416	−	0.832905i	$-0.313324\pi$
$350$	6.60544	+	1.50626i	0.353076	+	0.0805128i
$351$	−0.924342	+	3.48505i	−0.0493377	+	0.186018i
$352$	−0.346544	+	0.600231i	−0.0184708	+	0.0319924i
$353$	8.10390	−	4.67879i	0.431327	−	0.249027i	−0.268585	−	0.963256i	$-0.586556\pi$
$353$	8.10390	−	4.67879i	0.431327	−	0.249027i	0.699912	+	0.714229i	$0.253223\pi$
$354$	6.06459	+	10.5042i	0.322329	+	0.558291i
$355$	−10.5617	+	18.2934i	−0.560556	+	0.970911i
$356$			13.3939i			0.709877i
$357$	12.3509	+	11.4553i	0.653677	+	0.606280i
$358$		−	15.3168i		−	0.809520i
$359$	23.7581	+	13.7167i	1.25390	+	0.723942i	0.971883	−	0.235466i	$-0.0756617\pi$
$359$	23.7581	+	13.7167i	1.25390	+	0.723942i	0.282022	+	0.959408i	$0.408995\pi$
$360$	−1.37484	−	2.38129i	−0.0724603	−	0.125505i
$361$	−7.38522	−	12.7916i	−0.388696	−	0.673241i
$362$	−17.4555	−	10.0779i	−0.917440	−	0.529684i
$363$	−10.5196			−0.552137
$364$	0.382794	+	9.53171i	0.0200639	+	0.499597i
$365$	15.5493			0.813886
$366$	−8.71597	−	5.03217i	−0.455591	−	0.263036i
$367$	8.46693	+	14.6652i	0.441970	+	0.765515i	0.997836	−	0.0657574i	$-0.0209463\pi$
$367$	8.46693	+	14.6652i	0.441970	+	0.765515i	−0.555865	+	0.831272i	$0.687613\pi$
$368$	0.903131	+	1.56427i	0.0470790	+	0.0815431i
$369$	10.1945	+	5.88580i	0.530704	+	0.306402i
$370$		−	2.64615i		−	0.137567i
$371$	−10.0366	+	3.09809i	−0.521076	+	0.160845i
$372$		−	0.943413i		−	0.0489137i
$373$	−10.5004	+	18.1872i	−0.543689	+	0.941697i	0.454999	+	0.890492i	$0.349640\pi$
$373$	−10.5004	+	18.1872i	−0.543689	+	0.941697i	−0.998688	+	0.0512053i	$0.983694\pi$
$374$	−2.20643	−	3.82165i	−0.114092	−	0.197613i
$375$	−5.80865	+	3.35363i	−0.299957	+	0.173181i
$376$	4.51335	−	7.81735i	0.232758	−	0.403149i
$377$	−8.18242	+	30.8502i	−0.421416	+	1.58887i
$378$	−1.79918	+	1.93983i	−0.0925398	+	0.0997743i
$379$		−	8.36838i		−	0.429855i	−0.976630	−	0.214927i	$-0.931049\pi$
$379$		−	8.36838i		−	0.429855i	0.976630	−	0.214927i	$-0.0689515\pi$
$380$	−2.82747	+	4.89733i	−0.145046	+	0.251228i
$381$	3.19843	+	5.53985i	0.163861	+	0.283815i
$382$	−16.5978	+	9.58276i	−0.849219	+	0.490297i
$383$	−19.8299	−	11.4488i	−1.01326	−	0.585005i	−0.101115	−	0.994875i	$-0.532241\pi$
$383$	−19.8299	−	11.4488i	−1.01326	−	0.585005i	−0.912144	+	0.409869i	$0.865574\pi$
$384$			1.00000i			0.0510310i
$385$	−1.12101	+	4.91598i	−0.0571317	+	0.250542i
$386$	3.71978			0.189332
$387$	2.48505	−	4.30424i	0.126322	−	0.218797i
$388$	−8.57338	+	4.94984i	−0.435248	+	0.251290i
$389$	−3.55927	−	6.16484i	−0.180462	−	0.312570i	0.761576	−	0.648076i	$-0.224426\pi$
$389$	−3.55927	−	6.16484i	−0.180462	−	0.312570i	−0.942038	+	0.335506i	$0.891093\pi$
$390$	7.02809	+	6.99251i	0.355881	+	0.354079i
$391$	−11.5004			−0.581601
$392$	−3.03466	+	6.30800i	−0.153273	+	0.318602i
$393$	1.94292			0.0980074
$394$	4.72846	−	8.18994i	0.238217	−	0.412603i
$395$	1.61608	−	0.933046i	0.0813140	−	0.0469466i
$396$	0.600231	−	0.346544i	0.0301627	−	0.0174145i
$397$	−21.0936	−	12.1784i	−1.05866	−	0.611217i	−0.133598	−	0.991036i	$-0.542653\pi$
$397$	−21.0936	−	12.1784i	−1.05866	−	0.611217i	−0.925061	+	0.379819i	$0.875986\pi$
$398$			3.46995i			0.173933i
$399$	5.30504	+	1.20972i	0.265584	+	0.0605619i
$400$	−2.56071			−0.128036
$401$	−6.38990	−	3.68921i	−0.319096	−	0.184230i	0.331893	−	0.943317i	$-0.392313\pi$
$401$	−6.38990	−	3.68921i	−0.319096	−	0.184230i	−0.650990	+	0.759087i	$0.725646\pi$
$402$	4.85363	+	8.40673i	0.242077	+	0.419289i
$403$	0.888716	+	3.28337i	0.0442701	+	0.163556i
$404$	4.00174	−	6.93121i	0.199094	−	0.344841i
$405$			2.74967i			0.136632i
$406$	−15.9266	+	17.1717i	−0.790425	+	0.852218i
$407$	0.666994			0.0330616
$408$	−5.51396	−	3.18349i	−0.272982	−	0.157606i
$409$	22.5412	−	13.0142i	1.11459	−	0.643510i	0.174577	−	0.984643i	$-0.444144\pi$
$409$	22.5412	−	13.0142i	1.11459	−	0.643510i	0.940015	+	0.341133i	$0.110811\pi$
$410$	28.0316	−	16.1840i	1.38438	−	0.799272i
$411$	−0.0395182	−	0.0228159i	−0.00194929	−	0.00112542i
$412$	12.5829			0.619915
$413$	−9.46506	−	30.6632i	−0.465745	−	1.50884i
$414$		−	1.80626i		−	0.0887729i
$415$	3.19767	−	5.53852i	0.156967	−	0.271875i
$416$	−0.942023	−	3.48032i	−0.0461865	−	0.170636i
$417$	10.4339	+	18.0721i	0.510953	+	0.884996i
$418$	−1.23443	−	0.712697i	−0.0603778	−	0.0348592i
$419$	−19.1284			−0.934482			−0.467241	−	0.884130i	$-0.654752\pi$
$419$	−19.1284			−0.934482			−0.467241	+	0.884130i	$0.654752\pi$
$420$	2.14572	+	6.95132i	0.104701	+	0.339190i
$421$		−	10.2725i		−	0.500651i	−0.968162	−	0.250326i	$-0.919462\pi$
$421$		−	10.2725i		−	0.500651i	0.968162	−	0.250326i	$-0.0805377\pi$
$422$	24.5917	+	14.1980i	1.19711	+	0.691150i
$423$	−7.81735	+	4.51335i	−0.380092	+	0.219446i
$424$	3.43821	−	1.98505i	0.166974	−	0.0964027i
$425$	8.15199	−	14.1197i	0.395429	−	0.684904i
$426$	−7.68213			−0.372200
$427$	19.5231	+	18.1076i	0.944791	+	0.876286i
$428$	−10.1399			−0.490129
$429$	−1.76254	+	1.77151i	−0.0850963	+	0.0855294i
$430$	−6.83309	−	11.8353i	−0.329521	−	0.570747i
$431$	0.932887	−	0.538602i	0.0449356	−	0.0259436i	−0.477364	−	0.878706i	$-0.658408\pi$
$431$	0.932887	−	0.538602i	0.0449356	−	0.0259436i	0.522299	+	0.852762i	$0.325074\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	1.44276			0.0693347			0.0346674	−	0.999399i	$-0.488963\pi$
$433$	1.44276			0.0693347			0.0346674	+	0.999399i	$0.488963\pi$
$434$	−0.554933	+	2.43357i	−0.0266376	+	0.116815i
$435$			24.3406i			1.16704i
$436$	10.7989	+	6.23473i	0.517172	+	0.298589i
$437$	−3.21706	+	1.85737i	−0.153893	+	0.0888500i
$438$	2.82747	+	4.89733i	0.135102	+	0.234003i
$439$	−11.2961	+	19.5655i	−0.539135	+	0.933810i	0.459815	+	0.888015i	$0.347916\pi$
$439$	−11.2961	+	19.5655i	−0.539135	+	0.933810i	−0.998951	+	0.0457954i	$0.985418\pi$
$440$		−	1.90576i		−	0.0908537i
$441$	5.78209	−	3.94556i	0.275338	−	0.187884i
$442$	22.1892	+	5.88526i	1.05543	+	0.279933i
$443$	11.7902	−	20.4213i	0.560172	−	0.970246i	−0.437309	−	0.899311i	$-0.644069\pi$
$443$	11.7902	−	20.4213i	0.560172	−	0.970246i	0.997481	−	0.0709346i	$-0.0225982\pi$
$444$	0.833421	−	0.481176i	0.0395524	−	0.0228356i
$445$	−18.4145	−	31.8948i	−0.872930	−	1.51196i
$446$	−6.11957	+	10.5994i	−0.289770	+	0.501896i
$447$		−	4.16254i		−	0.196881i
$448$	0.588218	−	2.57953i	0.0277907	−	0.121872i
$449$			4.09767i			0.193381i	0.995315	+	0.0966904i	$0.0308257\pi$
$449$			4.09767i			0.193381i	−0.995315	+	0.0966904i	$0.969174\pi$
$450$	2.21764	+	1.28036i	0.104541	+	0.0603565i
$451$	4.07937	+	7.06568i	0.192090	+	0.332710i
$452$	−4.10609	−	7.11196i	−0.193134	−	0.334518i
$453$	0.395710	+	0.228464i	0.0185921	+	0.0107342i
$454$	16.8076			0.788820
$455$	−14.0161	−	22.1715i	−0.657085	−	1.03941i
$456$	−2.05659			−0.0963085
$457$	6.40916	+	3.70033i	0.299808	+	0.173094i	0.642356	−	0.766406i	$-0.277957\pi$
$457$	6.40916	+	3.70033i	0.299808	+	0.173094i	−0.342549	+	0.939500i	$0.611290\pi$
$458$	11.1435	+	19.3011i	0.520700	+	0.901879i
$459$	3.18349	+	5.51396i	0.148592	+	0.257370i
$460$	−4.30123	−	2.48332i	−0.200546	−	0.115785i
$461$		−	1.27247i		−	0.0592650i	−0.999561	−	0.0296325i	$-0.990566\pi$
$461$		−	1.27247i		−	0.0592650i	0.999561	−	0.0296325i	$-0.00943370\pi$
$462$	−1.75216	+	0.540854i	−0.0815179	+	0.0251628i
$463$			34.3620i			1.59694i	0.602037	+	0.798468i	$0.294356\pi$
$463$			34.3620i			1.59694i	−0.602037	+	0.798468i	$0.705644\pi$
$464$	4.42608	−	7.66619i	0.205476	−	0.355894i
$465$	1.29704	+	2.24654i	0.0601487	+	0.104181i
$466$	15.7050	−	9.06727i	0.727519	−	0.420033i
$467$	14.7113	−	25.4807i	0.680756	−	1.17910i	−0.293995	−	0.955807i	$-0.594985\pi$
$467$	14.7113	−	25.4807i	0.680756	−	1.17910i	0.974751	−	0.223297i	$-0.0716819\pi$
$468$	−0.924342	+	3.48505i	−0.0427277	+	0.161097i
$469$	−7.57511	−	24.5404i	−0.349786	−	1.13317i
$470$			24.8205i			1.14488i
$471$	−0.775828	+	1.34377i	−0.0357483	+	0.0619178i
$472$	6.06459	+	10.5042i	0.279145	+	0.483494i
$473$	2.98321	−	1.72236i	0.137168	−	0.0791941i
$474$	0.587736	+	0.339330i	0.0269956	+	0.0155859i
$475$		−	5.26633i		−	0.241636i
$476$	12.3509	+	11.4553i	0.566101	+	0.525054i
$477$	−3.97011			−0.181779
$478$	−5.64399	+	9.77567i	−0.258150	+	0.447129i
$479$	−3.36031	+	1.94008i	−0.153536	+	0.0886443i	−0.574800	−	0.818294i	$-0.694920\pi$
$479$	−3.36031	+	1.94008i	−0.153536	+	0.0886443i	0.421263	+	0.906938i	$0.361587\pi$
$480$	−1.37484	−	2.38129i	−0.0627525	−	0.108690i
$481$	−2.44729	+	2.45974i	−0.111587	+	0.112155i
$482$	−8.67866			−0.395302
$483$	−1.06248	+	4.65932i	−0.0483444	+	0.212006i
$484$	−10.5196			−0.478165
$485$	13.6105	−	23.5740i	0.618019	−	1.07044i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−12.6285	+	7.29107i	−0.572252	+	0.330390i	−0.758048	−	0.652198i	$-0.773847\pi$
$487$	−12.6285	+	7.29107i	−0.572252	+	0.330390i	0.185796	+	0.982588i	$0.440514\pi$
$488$	−8.71597	−	5.03217i	−0.394554	−	0.227796i
$489$		−	5.98476i		−	0.270640i
$490$	−1.44607	−	19.1933i	−0.0653269	−	0.867066i
$491$	19.2613			0.869250			0.434625	−	0.900612i	$-0.356881\pi$
$491$	19.2613			0.869250			0.434625	+	0.900612i	$0.356881\pi$
$492$	10.1945	+	5.88580i	0.459604	+	0.265352i
$493$	28.1807	+	48.8104i	1.26920	+	2.19831i
$494$	7.15757	−	1.93735i	0.322034	−	0.0871656i
$495$	−0.952882	+	1.65044i	−0.0428289	+	0.0741818i
$496$		−	0.943413i		−	0.0423605i
$497$	19.8163	+	4.51877i	0.888884	+	0.202695i
$498$	2.32585			0.104224
$499$	16.9387	+	9.77954i	0.758278	+	0.437792i	0.828677	−	0.559727i	$-0.189094\pi$
$499$	16.9387	+	9.77954i	0.758278	+	0.437792i	−0.0703990	+	0.997519i	$0.522427\pi$
$500$	−5.80865	+	3.35363i	−0.259771	+	0.149979i
$501$	6.24636	−	3.60634i	0.279067	−	0.161119i
$502$	18.9176	+	10.9221i	0.844334	+	0.487477i
$503$	15.3764			0.685598			0.342799	−	0.939409i	$-0.388625\pi$
$503$	15.3764			0.685598			0.342799	+	0.939409i	$0.388625\pi$
$504$	−1.79918	+	1.93983i	−0.0801418	+	0.0864070i
$505$			22.0069i			0.979296i
$506$	0.625949	−	1.08417i	0.0278268	−	0.0481974i
$507$	−0.0659963	−	12.9998i	−0.00293100	−	0.577343i
$508$	3.19843	+	5.53985i	0.141908	+	0.245791i
$509$	−7.64473	−	4.41369i	−0.338847	−	0.195633i	0.320915	−	0.947108i	$-0.396010\pi$
$509$	−7.64473	−	4.41369i	−0.338847	−	0.195633i	−0.659762	+	0.751475i	$0.729343\pi$
$510$	17.5071			0.775228
$511$	−4.41287	−	14.2960i	−0.195214	−	0.632418i
$512$			1.00000i			0.0441942i
$513$	1.78106	+	1.02829i	0.0786356	+	0.0454003i
$514$	22.1871	−	12.8097i	0.978632	−	0.565013i
$515$	−29.9635	+	17.2994i	−1.32035	+	0.762304i
$516$	2.48505	−	4.30424i	0.109398	−	0.189483i
$517$	−6.25628			−0.275151
$518$	−2.43287	+	0.750976i	−0.106894	+	0.0329960i
$519$	−22.7561			−0.998883
$520$	7.02809	+	6.99251i	0.308202	+	0.306642i
$521$	−14.3434	−	24.8435i	−0.628395	−	1.08841i	−0.987874	−	0.155259i	$-0.950379\pi$
$521$	−14.3434	−	24.8435i	−0.628395	−	1.08841i	0.359478	−	0.933153i	$-0.382955\pi$
$522$	−7.66619	+	4.42608i	−0.335540	+	0.193724i
$523$	13.6397	−	23.6247i	0.596423	−	1.03303i	−0.396922	−	0.917853i	$-0.629921\pi$
$523$	13.6397	−	23.6247i	0.596423	−	1.03303i	0.993344	−	0.115182i	$-0.0367452\pi$
$524$	1.94292			0.0848769
$525$	−4.96735	−	4.60718i	−0.216793	−	0.201074i
$526$		−	12.8612i		−	0.560775i
$527$	5.20194	+	3.00334i	0.226600	+	0.130828i
$528$	0.600231	−	0.346544i	0.0261217	−	0.0150814i
$529$	9.86871	+	17.0931i	0.429074	+	0.743178i
$530$	−5.45825	+	9.45396i	−0.237091	+	0.410654i
$531$		−	12.1292i		−	0.526361i
$532$	5.30504	+	1.20972i	0.230003	+	0.0524481i
$533$	−41.0246	−	10.8810i	−1.77697	−	0.471308i
$534$	6.69696	−	11.5995i	0.289806	−	0.501959i
$535$	24.1459	−	13.9407i	1.04392	−	0.602708i
$536$	4.85363	+	8.40673i	0.209645	+	0.363115i
$537$	−7.65842	+	13.2648i	−0.330485	+	0.572417i
$538$			9.66400i			0.416645i
$539$	4.83790	−	0.364499i	0.208383	−	0.0157001i
$540$			2.74967i			0.118327i
$541$	−4.22098	−	2.43698i	−0.181474	−	0.104774i	0.406511	−	0.913646i	$-0.366745\pi$
$541$	−4.22098	−	2.43698i	−0.181474	−	0.104774i	−0.587985	+	0.808872i	$0.700079\pi$
$542$	3.65706	+	6.33421i	0.157084	+	0.272078i
$543$	10.0779	+	17.4555i	0.432486	+	0.749087i
$544$	−5.51396	−	3.18349i	−0.236409	−	0.136491i
$545$	−34.2869			−1.46869
$546$	4.43434	−	8.44610i	0.189772	−	0.361460i
$547$	−11.3711			−0.486193			−0.243097	−	0.970002i	$-0.578163\pi$
$547$	−11.3711			−0.486193			−0.243097	+	0.970002i	$0.578163\pi$
$548$	−0.0395182	−	0.0228159i	−0.00168814	−	0.000974646i
$549$	5.03217	+	8.71597i	0.214768	+	0.371989i
$550$	0.887398	+	1.53702i	0.0378388	+	0.0655387i
$551$	15.7662	+	9.10262i	0.671662	+	0.387785i
$552$		−	1.80626i		−	0.0768796i
$553$	−1.31649	−	1.22103i	−0.0559827	−	0.0519235i
$554$		−	12.7070i		−	0.539870i
$555$	−1.32308	+	2.29164i	−0.0561615	+	0.0972746i
$556$	10.4339	+	18.0721i	0.442498	+	0.766429i
$557$	1.00500	−	0.580239i	0.0425833	−	0.0245855i	−0.478557	−	0.878056i	$-0.658840\pi$
$557$	1.00500	−	0.580239i	0.0425833	−	0.0245855i	0.521141	+	0.853471i	$0.325507\pi$
$558$	−0.471706	+	0.817019i	−0.0199689	+	0.0345872i
$559$	−4.59408	+	17.3211i	−0.194309	+	0.732604i
$560$	2.14572	+	6.95132i	0.0906733	+	0.293747i
$561$			4.41287i			0.186311i
$562$	−11.9086	+	20.6263i	−0.502335	+	0.870069i
$563$	3.86680	+	6.69750i	0.162966	+	0.282266i	0.935931	−	0.352183i	$-0.114560\pi$
$563$	3.86680	+	6.69750i	0.162966	+	0.282266i	−0.772965	+	0.634449i	$0.781227\pi$
$564$	−7.81735	+	4.51335i	−0.329170	+	0.190046i
$565$	19.5556	+	11.2904i	0.822709	+	0.474991i
$566$			29.1228i			1.22412i
$567$	2.52805	−	0.780355i	0.106168	−	0.0327718i
$568$	−7.68213			−0.322335
$569$	13.2494	−	22.9487i	0.555445	−	0.962059i	−0.442424	−	0.896806i	$-0.645881\pi$
$569$	13.2494	−	22.9487i	0.555445	−	0.962059i	0.997869	−	0.0652529i	$-0.0207854\pi$
$570$	4.89733	−	2.82747i	0.205126	−	0.118430i
$571$	−16.2913	−	28.2174i	−0.681770	−	1.18086i	−0.974440	−	0.224647i	$-0.927877\pi$
$571$	−16.2913	−	28.2174i	−0.681770	−	1.18086i	0.292670	−	0.956214i	$-0.405456\pi$
$572$	−1.76254	+	1.77151i	−0.0736956	+	0.0740706i
$573$	19.1655			0.800651
$574$	−22.8349	−	21.1792i	−0.953112	−	0.884003i
$575$	4.62531			0.192889
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−25.5216	+	14.7349i	−1.06248	+	0.613422i	−0.926117	−	0.377237i	$-0.876874\pi$
$577$	−25.5216	+	14.7349i	−1.06248	+	0.613422i	−0.136361	+	0.990659i	$0.543541\pi$
$578$	20.3848	−	11.7692i	0.847896	−	0.489533i
$579$	−3.22142	−	1.85989i	−0.133878	−	0.0772944i
$580$			24.3406i			1.01069i
$581$	−5.99962	−	1.36811i	−0.248906	−	0.0567587i
$582$	9.89969			0.410355
$583$	−2.38298	−	1.37581i	−0.0986930	−	0.0569804i
$584$	2.82747	+	4.89733i	0.117002	+	0.202653i
$585$	−2.59026	−	9.56973i	−0.107094	−	0.395660i
$586$	−3.43142	+	5.94340i	−0.141751	+	0.245520i
$587$			23.0017i			0.949381i	0.880153	+	0.474690i	$0.157440\pi$
$587$			23.0017i			0.949381i	−0.880153	+	0.474690i	$0.842560\pi$
$588$	5.78209	−	3.94556i	0.238449	−	0.162712i
$589$	1.94021			0.0799450
$590$	−28.8831	−	16.6756i	−1.18910	−	0.686525i
$591$	−8.18994	+	4.72846i	−0.336889	+	0.194503i
$592$	0.833421	−	0.481176i	0.0342534	−	0.0197762i
$593$	38.6090	+	22.2909i	1.58548	+	0.915378i	0.994038	+	0.109031i	$0.0347748\pi$
$593$	38.6090	+	22.2909i	1.58548	+	0.915378i	0.591443	+	0.806347i	$0.298559\pi$
$594$	−0.693087			−0.0284377
$595$	−45.1602	−	10.2980i	−1.85139	−	0.422177i
$596$		−	4.16254i		−	0.170504i
$597$	1.73497	−	3.00506i	0.0710077	−	0.122989i
$598$	1.70154	+	6.28636i	0.0695811	+	0.257068i
$599$	2.90326	+	5.02860i	0.118624	+	0.205463i	0.919223	−	0.393738i	$-0.128818\pi$
$599$	2.90326	+	5.02860i	0.118624	+	0.205463i	−0.800599	+	0.599201i	$0.795485\pi$
$600$	2.21764	+	1.28036i	0.0905348	+	0.0522703i
$601$	−3.28026			−0.133805			−0.0669023	−	0.997760i	$-0.521312\pi$
$601$	−3.28026			−0.133805			−0.0669023	+	0.997760i	$0.521312\pi$
$602$	−8.94211	+	9.64118i	−0.364453	+	0.392945i
$603$		−	9.70725i		−	0.395310i
$604$	0.395710	+	0.228464i	0.0161012	+	0.00929605i
$605$	25.0503	−	14.4628i	1.01844	−	0.587996i
$606$	−6.93121	+	4.00174i	−0.281561	+	0.162559i
$607$	0.434594	−	0.752739i	0.0176396	−	0.0305527i	−0.857071	−	0.515199i	$-0.827718\pi$
$607$	0.434594	−	0.752739i	0.0176396	−	0.0305527i	0.874710	+	0.484646i	$0.161052\pi$
$608$	−2.05659			−0.0834056
$609$	22.3787	−	6.90783i	0.906831	−	0.279919i
$610$	27.6737			1.12047
$611$	22.9552	−	23.0720i	0.928666	−	0.933393i
$612$	3.18349	+	5.51396i	0.128685	+	0.222889i
$613$	−17.2225	+	9.94341i	−0.695610	+	0.401611i	−0.805710	−	0.592310i	$-0.798216\pi$
$613$	−17.2225	+	9.94341i	−0.695610	+	0.401611i	0.110100	+	0.993920i	$0.464883\pi$
$614$	−13.2897	+	23.0185i	−0.536329	+	0.928949i
$615$	−32.3681			−1.30521
$616$	−1.75216	+	0.540854i	−0.0705965	+	0.0217916i
$617$		−	6.32742i		−	0.254732i	−0.991856	−	0.127366i	$-0.959348\pi$
$617$		−	6.32742i		−	0.254732i	0.991856	−	0.127366i	$-0.0406524\pi$
$618$	−10.8971	−	6.29145i	−0.438346	−	0.253079i
$619$	−22.8722	+	13.2053i	−0.919311	+	0.530764i	−0.883415	−	0.468591i	$-0.844762\pi$
$619$	−22.8722	+	13.2053i	−0.919311	+	0.530764i	−0.0358959	+	0.999356i	$0.511428\pi$
$620$	1.29704	+	2.24654i	0.0520903	+	0.0902231i
$621$	−0.903131	+	1.56427i	−0.0362414	+	0.0627719i
$622$			10.6320i			0.426304i
$623$	−24.0981	+	25.9820i	−0.965469	+	1.04095i
$624$	−0.924342	+	3.48505i	−0.0370033	+	0.139514i
$625$	15.6232	−	27.0601i	0.624926	−	1.08240i
$626$	−23.2249	+	13.4089i	−0.928252	+	0.535927i
$627$	0.712697	+	1.23443i	0.0284624	+	0.0492983i
$628$	−0.775828	+	1.34377i	−0.0309589	+	0.0536224i
$629$			6.12727i			0.244310i
$630$	1.61741	−	7.09288i	0.0644391	−	0.282587i
$631$			25.5607i			1.01756i	0.860898	+	0.508778i	$0.169903\pi$
$631$			25.5607i			1.01756i	−0.860898	+	0.508778i	$0.830097\pi$
$632$	0.587736	+	0.339330i	0.0233789	+	0.0134978i
$633$	−14.1980	−	24.5917i	−0.564322	−	0.977434i
$634$	−7.39952	−	12.8163i	−0.293873	−	0.509002i
$635$	−15.2328	−	8.79465i	−0.604495	−	0.349005i
$636$	−3.97011			−0.157425
$637$	−16.4067	+	19.1786i	−0.650057	+	0.759885i
$638$	−6.13532			−0.242899
$639$	6.65292	+	3.84107i	0.263185	+	0.151950i
$640$	−1.37484	−	2.38129i	−0.0543452	−	0.0941287i
$641$	3.40779	+	5.90247i	0.134600	+	0.233133i	0.925444	−	0.378883i	$-0.123692\pi$
$641$	3.40779	+	5.90247i	0.134600	+	0.233133i	−0.790845	+	0.612017i	$0.790359\pi$
$642$	8.78138	+	5.06993i	0.346574	+	0.200094i
$643$		−	29.4326i		−	1.16071i	−0.814364	−	0.580355i	$-0.802914\pi$
$643$		−	29.4326i		−	1.16071i	0.814364	−	0.580355i	$-0.197086\pi$
$644$	−1.06248	+	4.65932i	−0.0418674	+	0.183603i
$645$			13.6662i			0.538105i
$646$	6.54712	−	11.3399i	0.257593	−	0.446164i
$647$	18.4312	+	31.9237i	0.724605	+	1.25505i	0.959137	+	0.282943i	$0.0913109\pi$
$647$	18.4312	+	31.9237i	0.724605	+	1.25505i	−0.234532	+	0.972108i	$0.575356\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	4.20329	−	7.28031i	0.164993	−	0.285777i
$650$	−8.92421	−	2.36697i	−0.350036	−	0.0928403i
$651$	1.69737	−	1.83006i	0.0665251	−	0.0717258i
$652$		−	5.98476i		−	0.234381i
$653$	10.0181	−	17.3518i	0.392037	−	0.679028i	−0.600681	−	0.799489i	$-0.705104\pi$
$653$	10.0181	−	17.3518i	0.392037	−	0.679028i	0.992718	+	0.120461i	$0.0384372\pi$
$654$	−6.23473	−	10.7989i	−0.243797	−	0.422269i
$655$	−4.62665	+	2.67120i	−0.180778	+	0.104372i
$656$	10.1945	+	5.88580i	0.398028	+	0.229802i
$657$		−	5.65495i		−	0.220620i
$658$	22.8199	−	7.04403i	0.889614	−	0.274605i
$659$	−30.1565			−1.17473			−0.587365	−	0.809322i	$-0.699835\pi$
$659$	−30.1565			−1.17473			−0.587365	+	0.809322i	$0.699835\pi$
$660$	−0.952882	+	1.65044i	−0.0370909	+	0.0642433i
$661$	26.5850	−	15.3488i	1.03404	−	0.597001i	0.115897	−	0.993261i	$-0.463026\pi$
$661$	26.5850	−	15.3488i	1.03404	−	0.597001i	0.918138	+	0.396261i	$0.129692\pi$
$662$	−3.46425	−	6.00025i	−0.134642	−	0.233206i
$663$	−16.2738	−	16.1914i	−0.632022	−	0.628822i
$664$	2.32585			0.0902606
$665$	−14.2960	+	4.41287i	−0.554375	+	0.171124i
$666$	−0.962352			−0.0372904
$667$	−7.99466	+	13.8472i	−0.309554	+	0.536164i
$668$	6.24636	−	3.60634i	0.241679	−	0.139533i
$669$	10.5994	−	6.11957i	0.409797	−	0.236596i
$670$	−23.1158	−	13.3459i	−0.893040	−	0.515597i
$671$			6.97547i			0.269285i
$672$	−1.79918	+	1.93983i	−0.0694049	+	0.0748307i
$673$	37.5864			1.44885			0.724425	−	0.689353i	$-0.242105\pi$
$673$	37.5864			1.44885			0.724425	+	0.689353i	$0.242105\pi$
$674$	−15.8785	−	9.16747i	−0.611618	−	0.353118i
$675$	−1.28036	−	2.21764i	−0.0492809	−	0.0853570i
$676$	−0.0659963	−	12.9998i	−0.00253832	−	0.499994i
$677$	14.8873	−	25.7855i	0.572165	−	0.991019i	−0.424178	−	0.905579i	$-0.639437\pi$
$677$	14.8873	−	25.7855i	0.572165	−	0.991019i	0.996343	−	0.0854400i	$-0.0272296\pi$
$678$			8.21218i			0.315387i
$679$	−25.5366	−	5.82318i	−0.980004	−	0.223473i
$680$	17.5071			0.671367
$681$	−14.5558	−	8.40380i	−0.557780	−	0.322034i
$682$	−0.566266	+	0.326934i	−0.0216834	+	0.0125189i
$683$	44.6289	−	25.7665i	1.70768	−	0.985927i	0.770251	−	0.637740i	$-0.220131\pi$
$683$	44.6289	−	25.7665i	1.70768	−	0.985927i	0.937425	−	0.348187i	$-0.113203\pi$
$684$	1.78106	+	1.02829i	0.0681004	+	0.0393178i
$685$	0.125472			0.00479406
$686$	−17.2360	+	6.77657i	−0.658072	+	0.258731i
$687$		−	22.2869i		−	0.850300i
$688$	2.48505	−	4.30424i	0.0947417	−	0.164098i
$689$	13.8172	−	3.73993i	0.526394	−	0.142480i
$690$	2.48332	+	4.30123i	0.0945382	+	0.163745i
$691$	36.8206	+	21.2584i	1.40072	+	0.808707i	0.994467	−	0.105053i	$-0.0335012\pi$
$691$	36.8206	+	21.2584i	1.40072	+	0.808707i	0.406255	+	0.913760i	$0.366835\pi$
$692$	−22.7561			−0.865058
$693$	1.78784	+	0.407687i	0.0679145	+	0.0154867i
$694$		−	6.77289i		−	0.257096i
$695$	−49.6925	−	28.6900i	−1.88494	−	1.08827i
$696$	−7.66619	+	4.42608i	−0.290586	+	0.167770i
$697$	−64.9081	+	37.4747i	−2.45857	+	1.41946i
$698$	−15.5599	+	26.9506i	−0.588953	+	1.02010i
$699$	−18.1345			−0.685912
$700$	−4.96735	−	4.60718i	−0.187748	−	0.174135i
$701$	21.9298			0.828278			0.414139	−	0.910214i	$-0.364083\pi$
$701$	21.9298			0.828278			0.414139	+	0.910214i	$0.364083\pi$
$702$	2.54303	−	2.55597i	0.0959805	−	0.0964690i
$703$	0.989580	+	1.71400i	0.0373227	+	0.0646449i
$704$	0.600231	−	0.346544i	0.0226221	−	0.0130609i
$705$	12.4102	−	21.4952i	0.467396	−	0.809554i
$706$	−9.35758			−0.352177
$707$	20.2332	−	6.24555i	0.760948	−	0.234888i
$708$		−	12.1292i		−	0.455842i
$709$	−13.2657	−	7.65895i	−0.498204	−	0.287638i	0.229768	−	0.973245i	$-0.426203\pi$
$709$	−13.2657	−	7.65895i	−0.498204	−	0.287638i	−0.727971	+	0.685607i	$0.759537\pi$
$710$	18.2934	−	10.5617i	0.686538	−	0.396373i
$711$	−0.339330	−	0.587736i	−0.0127259	−	0.0220418i
$712$	6.69696	−	11.5995i	0.250979	−	0.434709i
$713$			1.70405i			0.0638172i
$714$	−4.96850	−	16.0960i	−0.185941	−	0.602379i
$715$	1.76158	−	6.64169i	0.0658793	−	0.248385i
$716$	−7.65842	+	13.2648i	−0.286209	+	0.495728i
$717$	9.77567	−	5.64399i	0.365079	−	0.210779i
$718$	−13.7167	−	23.7581i	−0.511904	−	0.886644i
$719$	−6.26926	+	10.8587i	−0.233804	+	0.404961i	−0.958924	−	0.283662i	$-0.908451\pi$
$719$	−6.26926	+	10.8587i	−0.233804	+	0.404961i	0.725120	+	0.688622i	$0.241784\pi$
$720$			2.74967i			0.102474i
$721$	24.4087	+	22.6389i	0.909028	+	0.843116i
$722$			14.7704i			0.549699i
$723$	7.51594	+	4.33933i	0.279521	+	0.161381i
$724$	10.0779	+	17.4555i	0.374543	+	0.648728i
$725$	−11.3339	−	19.6309i	−0.420931	−	0.729073i
$726$	9.11027	+	5.25982i	0.338114	+	0.195210i
$727$	42.7300			1.58477			0.792383	−	0.610023i	$-0.208840\pi$
$727$	42.7300			1.58477			0.792383	+	0.610023i	$0.208840\pi$
$728$	4.43434	−	8.44610i	0.164348	−	0.313033i
$729$	1.00000			0.0370370
$730$	−13.4661	−	7.77463i	−0.498401	−	0.287752i
$731$	15.8223	+	27.4050i	0.585207	+	1.01361i
$732$	5.03217	+	8.71597i	0.185994	+	0.322152i
$733$	−23.9996	−	13.8562i	−0.886445	−	0.511789i	−0.0136668	−	0.999907i	$-0.504350\pi$
$733$	−23.9996	−	13.8562i	−0.886445	−	0.511789i	−0.872778	+	0.488117i	$0.837684\pi$
$734$		−	16.9339i		−	0.625040i
$735$	−8.34433	+	17.3449i	−0.307785	+	0.639778i
$736$		−	1.80626i		−	0.0665797i
$737$	3.36399	−	5.82659i	0.123914	−	0.214625i
$738$	−5.88580	−	10.1945i	−0.216659	−	0.375265i
$739$	24.5022	−	14.1464i	0.901330	−	0.520383i	0.0236983	−	0.999719i	$-0.492456\pi$
$739$	24.5022	−	14.1464i	0.901330	−	0.520383i	0.877631	+	0.479336i	$0.159123\pi$
$740$	−1.32308	+	2.29164i	−0.0486373	+	0.0842422i
$741$	−7.16732	−	1.90099i	−0.263298	−	0.0698346i
$742$	10.2410	+	2.33529i	0.375960	+	0.0857312i
$743$		−	37.4869i		−	1.37526i	−0.726061	−	0.687630i	$-0.758651\pi$
$743$		−	37.4869i		−	1.37526i	0.726061	−	0.687630i	$-0.241349\pi$
$744$	−0.471706	+	0.817019i	−0.0172936	+	0.0299534i
$745$	5.72282	+	9.91221i	0.209668	+	0.363155i
$746$	18.1872	−	10.5004i	0.665880	−	0.384446i
$747$	−2.01425	−	1.16293i	−0.0736974	−	0.0425492i
$748$			4.41287i			0.161350i
$749$	−19.6697	−	18.2434i	−0.718713	−	0.666601i
$750$	6.70725			0.244914
$751$	1.04017	−	1.80163i	0.0379564	−	0.0657423i	−0.846423	−	0.532511i	$-0.821249\pi$
$751$	1.04017	−	1.80163i	0.0379564	−	0.0657423i	0.884380	+	0.466769i	$0.154582\pi$
$752$	−7.81735	+	4.51335i	−0.285069	+	0.164585i
$753$	−10.9221	−	18.9176i	−0.398023	−	0.689396i
$754$	22.5113	−	22.6259i	0.819813	−	0.823986i
$755$	−1.25640			−0.0457251
$756$	2.52805	−	0.780355i	0.0919444	−	0.0283812i
$757$	−18.0167			−0.654826			−0.327413	−	0.944881i	$-0.606177\pi$
$757$	−18.0167			−0.654826			−0.327413	+	0.944881i	$0.606177\pi$
$758$	−4.18419	+	7.24723i	−0.151977	+	0.263231i
$759$	−1.08417	+	0.625949i	−0.0393530	+	0.0227205i
$760$	4.89733	−	2.82747i	0.177645	−	0.102563i
$761$	−26.7066	−	15.4190i	−0.968113	−	0.558940i	−0.0694523	−	0.997585i	$-0.522125\pi$
$761$	−26.7066	−	15.4190i	−0.968113	−	0.558940i	−0.898660	+	0.438645i	$0.855458\pi$
$762$		−	6.39687i		−	0.231734i
$763$	9.73060	+	31.5234i	0.352272	+	1.14122i
$764$	19.1655			0.693384
$765$	−15.1616	−	8.75355i	−0.548169	−	0.316485i
$766$	11.4488	+	19.8299i	0.413661	+	0.716482i
$767$	11.4260	+	42.2133i	0.412567	+	1.52424i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$			28.1580i			1.01540i	0.861533	+	0.507702i	$0.169505\pi$
$769$			28.1580i			1.01540i	−0.861533	+	0.507702i	$0.830495\pi$
$770$	3.42881	−	3.69686i	0.123566	−	0.133226i
$771$	−25.6195			−0.922663
$772$	−3.22142	−	1.85989i	−0.115942	−	0.0669389i
$773$	6.87642	−	3.97011i	0.247328	−	0.142795i	−0.371212	−	0.928548i	$-0.621058\pi$
$773$	6.87642	−	3.97011i	0.247328	−	0.142795i	0.618540	+	0.785753i	$0.287724\pi$
$774$	−4.30424	+	2.48505i	−0.154713	+	0.0893234i
$775$	−2.09215	−	1.20790i	−0.0751522	−	0.0433892i
$776$	9.89969			0.355378
$777$	2.48242	+	0.566073i	0.0890563	+	0.0203078i
$778$			7.11855i			0.255212i
$779$	−12.1047	+	20.9659i	−0.433694	+	0.751181i
$780$	−2.59026	−	9.56973i	−0.0927460	−	0.342651i
$781$	2.66219	+	4.61105i	0.0952608	+	0.164996i
$782$	9.95966	+	5.75021i	0.356157	+	0.205627i
$783$	8.85216			0.316350
$784$	5.78209	−	3.94556i	0.206503	−	0.140913i
$785$		−	4.26655i		−	0.152280i
$786$	−1.68262	−	0.971460i	−0.0600170	−	0.0346508i
$787$	−38.5395	+	22.2508i	−1.37378	+	0.793154i	−0.991402	−	0.130851i	$-0.958229\pi$
$787$	−38.5395	+	22.2508i	−1.37378	+	0.793154i	−0.382381	+	0.924005i	$0.624896\pi$
$788$	−8.18994	+	4.72846i	−0.291754	+	0.168445i
$789$	−6.43061	+	11.1381i	−0.228936	+	0.396528i
$790$	−1.86609			−0.0663926
$791$	4.83056	−	21.1836i	0.171755	−	0.753203i
$792$	−0.693087			−0.0246278
$793$	−25.7242	−	25.5939i	−0.913493	−	0.908867i
$794$	12.1784	+	21.0936i	0.432196	+	0.748585i
$795$	9.45396	−	5.45825i	0.335298	−	0.193584i
$796$	1.73497	−	3.00506i	0.0614945	−	0.106512i
$797$	30.4829			1.07976			0.539879	−	0.841742i	$-0.318470\pi$
$797$	30.4829			1.07976			0.539879	+	0.841742i	$0.318470\pi$
$798$	−3.98944	−	3.70017i	−0.141225	−	0.130985i
$799$		−	57.4727i		−	2.03324i
$800$	2.21764	+	1.28036i	0.0784054	+	0.0452674i
$801$	−11.5995	+	6.69696i	−0.409848	+	0.236626i
$802$	3.68921	+	6.38990i	0.130271	+	0.225635i
$803$	1.95969	−	3.39427i	0.0691558	−	0.119781i
$804$		−	9.70725i		−	0.342348i
$805$	−3.87574	−	12.5559i	−0.136602	−	0.442538i
$806$	0.872036	−	3.28784i	0.0307162	−	0.115809i
$807$	4.83200	−	8.36927i	0.170094	−	0.294612i
$808$	−6.93121	+	4.00174i	−0.243839	+	0.140781i
$809$	3.12627	+	5.41487i	0.109914	+	0.190377i	0.915735	−	0.401782i	$-0.131609\pi$
$809$	3.12627	+	5.41487i	0.109914	+	0.190377i	−0.805821	+	0.592159i	$0.798276\pi$
$810$	1.37484	−	2.38129i	0.0483069	−	0.0836699i
$811$			28.5397i			1.00216i	0.865400	+	0.501082i	$0.167064\pi$
$811$			28.5397i			1.00216i	−0.865400	+	0.501082i	$0.832936\pi$
$812$	22.3787	−	6.90783i	0.785339	−	0.242417i
$813$		−	7.31412i		−	0.256517i
$814$	−0.577633	−	0.333497i	−0.0202460	−	0.0116891i
$815$	8.22808	+	14.2514i	0.288217	+	0.499206i
$816$	3.18349	+	5.51396i	0.111444	+	0.193027i
$817$	8.85204	+	5.11073i	0.309694	+	0.178802i
$818$	−26.0284			−0.910061
$819$	−8.06330	+	5.09736i	−0.281755	+	0.178116i
$820$	−32.3681			−1.13034
$821$	−15.1241	−	8.73193i	−0.527836	−	0.304746i	0.212299	−	0.977205i	$-0.431905\pi$
$821$	−15.1241	−	8.73193i	−0.527836	−	0.304746i	−0.740135	+	0.672459i	$0.765238\pi$
$822$	0.0228159	+	0.0395182i	0.000795795	+	0.00137836i
$823$	7.13184	+	12.3527i	0.248600	+	0.430588i	0.963138	−	0.269009i	$-0.0866961\pi$
$823$	7.13184	+	12.3527i	0.248600	+	0.430588i	−0.714537	+	0.699597i	$0.753363\pi$
$824$	−10.8971	−	6.29145i	−0.379619	−	0.219173i
$825$		−	1.77480i		−	0.0617905i
$826$	−7.13460	+	31.2876i	−0.248245	+	1.08864i
$827$			12.5853i			0.437635i	0.975766	+	0.218818i	$0.0702200\pi$
$827$			12.5853i			0.437635i	−0.975766	+	0.218818i	$0.929780\pi$
$828$	−0.903131	+	1.56427i	−0.0313860	+	0.0543621i
$829$	5.13167	+	8.88832i	0.178230	+	0.308704i	0.941274	−	0.337642i	$-0.109629\pi$
$829$	5.13167	+	8.88832i	0.178230	+	0.308704i	−0.763044	+	0.646346i	$0.776296\pi$
$830$	−5.53852	+	3.19767i	−0.192245	+	0.110993i
$831$	−6.35351	+	11.0046i	−0.220401	+	0.381745i
$832$	−0.924342	+	3.48505i	−0.0320458	+	0.120822i
$833$	3.34843	+	44.4428i	0.116016	+	1.53985i
$834$		−	20.8679i		−	0.722596i
$835$	−9.91626	+	17.1755i	−0.343166	+	0.594381i
$836$	0.712697	+	1.23443i	0.0246491	+	0.0426936i
$837$	0.817019	−	0.471706i	0.0282403	−	0.0163046i
$838$	16.5657	+	9.56418i	0.572251	+	0.330389i
$839$		−	32.1258i		−	1.10911i	−0.832148	−	0.554553i	$-0.812889\pi$
$839$		−	32.1258i		−	1.10911i	0.832148	−	0.554553i	$-0.187111\pi$
$840$	1.61741	−	7.09288i	0.0558059	−	0.244728i
$841$	49.3607			1.70209
$842$	−5.13625	+	8.89625i	−0.177007	+	0.306585i
$843$	20.6263	−	11.9086i	0.710408	−	0.410154i
$844$	−14.1980	−	24.5917i	−0.488717	−	0.846483i
$845$	18.0298	+	30.8656i	0.620244	+	1.06181i
$846$	9.02669			0.310344
$847$	−20.4063	−	18.9267i	−0.701170	−	0.650329i
$848$	−3.97011			−0.136334
$849$	14.5614	−	25.2211i	0.499747	−	0.865586i
$850$	−14.1197	+	8.15199i	−0.484300	+	0.279611i
$851$	−1.50538	+	0.869130i	−0.0516036	+	0.0297934i
$852$	6.65292	+	3.84107i	0.227925	+	0.131593i
$853$			6.55511i			0.224443i	0.993683	+	0.112221i	$0.0357966\pi$
$853$			6.55511i			0.224443i	−0.993683	+	0.112221i	$0.964203\pi$
$854$	−7.85376	−	25.4432i	−0.268750	−	0.870648i
$855$	−5.65495			−0.193395
$856$	8.78138	+	5.06993i	0.300141	+	0.173287i
$857$	−8.45109	−	14.6377i	−0.288684	−	0.500015i	0.684812	−	0.728720i	$-0.259884\pi$
$857$	−8.45109	−	14.6377i	−0.288684	−	0.500015i	−0.973496	+	0.228705i	$0.926551\pi$
$858$	2.41216	−	0.652904i	0.0823498	−	0.0222898i
$859$	−25.6471	+	44.4221i	−0.875068	+	1.51566i	−0.0183773	+	0.999831i	$0.505850\pi$
$859$	−25.6471	+	44.4221i	−0.875068	+	1.51566i	−0.856690	+	0.515831i	$0.827483\pi$
$860$			13.6662i			0.466013i
$861$	9.18602	+	29.7592i	0.313059	+	1.01419i
$862$	−1.07720			−0.0366897
$863$	36.2199	+	20.9116i	1.23294	+	0.711839i	0.967642	−	0.252327i	$-0.0811959\pi$
$863$	36.2199	+	20.9116i	1.23294	+	0.711839i	0.265299	+	0.964166i	$0.414529\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	54.1889	−	31.2860i	1.84248	−	1.06375i
$866$	−1.24947	−	0.721381i	−0.0424587	−	0.0245135i
$867$	−23.5383			−0.799404
$868$	1.69737	−	1.83006i	0.0576124	−	0.0621164i
$869$		−	0.470370i		−	0.0159562i
$870$	12.1703	−	21.0795i	0.412611	−	0.714663i
$871$	9.14445	+	33.7843i	0.309848	+	1.14474i
$872$	−6.23473	−	10.7989i	−0.211135	−	0.365696i
$873$	−8.57338	−	4.94984i	−0.290165	−	0.167527i
$874$	3.71474			0.125653
$875$	−17.3016	−	3.94533i	−0.584901	−	0.133376i
$876$		−	5.65495i		−	0.191063i
$877$	−32.7437	−	18.9046i	−1.10568	−	0.638363i	−0.167971	−	0.985792i	$-0.553722\pi$
$877$	−32.7437	−	18.9046i	−1.10568	−	0.638363i	−0.937706	+	0.347429i	$0.887055\pi$
$878$	19.5655	−	11.2961i	0.660303	−	0.381226i
$879$	5.94340	−	3.43142i	0.200466	−	0.115739i
$880$	−0.952882	+	1.65044i	−0.0321216	+	0.0556363i
$881$	20.8312			0.701819			0.350910	−	0.936409i	$-0.385872\pi$
$881$	20.8312			0.701819			0.350910	+	0.936409i	$0.385872\pi$
$882$	−6.98022	+	0.525907i	−0.235036	+	0.0177082i
$883$	−28.4623			−0.957833			−0.478916	−	0.877860i	$-0.658970\pi$
$883$	−28.4623			−0.957833			−0.478916	+	0.877860i	$0.658970\pi$
$884$	−16.2738	−	16.1914i	−0.547347	−	0.544576i
$885$	16.6756	+	28.8831i	0.560546	+	0.970893i
$886$	−20.4213	+	11.7902i	−0.686067	+	0.396101i
$887$	22.3022	−	38.6285i	0.748834	−	1.29702i	−0.199548	−	0.979888i	$-0.563947\pi$
$887$	22.3022	−	38.6285i	0.748834	−	1.29702i	0.948382	−	0.317130i	$-0.102719\pi$
$888$	−0.962352			−0.0322944
$889$	−3.76276	+	16.5009i	−0.126199	+	0.553424i
$890$			36.8289i			1.23451i
$891$	0.600231	+	0.346544i	0.0201085	+	0.0116096i
$892$	10.5994	−	6.11957i	0.354894	−	0.204898i
$893$	−9.28209	−	16.0771i	−0.310613	−	0.537998i
$894$	−2.08127	+	3.60487i	−0.0696081	+	0.120565i
$895$		−	42.1163i		−	1.40779i
$896$	−1.79918	+	1.93983i	−0.0601064	+	0.0648053i
$897$	1.66960	−	6.29492i	0.0557465	−	0.210181i
$898$	2.04883	−	3.54868i	0.0683705	−	0.118421i
$899$	7.23238	−	4.17562i	0.241213	−	0.139265i
$900$	−1.28036	−	2.21764i	−0.0426785	−	0.0739213i
$901$	12.6388	−	21.8910i	0.421059	−	0.729295i
$902$		−	8.15874i		−	0.271656i
$903$	12.5647	−	3.87845i	0.418126	−	0.129067i
$904$			8.21218i			0.273133i
$905$	−47.9969	−	27.7110i	−1.59547	−	0.921146i
$906$	−0.228464	−	0.395710i	−0.00759019	−	0.0131466i
$907$	−25.3044	−	43.8285i	−0.840219	−	1.45530i	−0.889709	−	0.456528i	$-0.849093\pi$
$907$	−25.3044	−	43.8285i	−0.840219	−	1.45530i	0.0494896	−	0.998775i	$-0.484241\pi$
$908$	−14.5558	−	8.40380i	−0.483052	−	0.278890i
$909$	8.00347			0.265458
$910$	1.05256	+	26.2091i	0.0348920	+	0.868823i
$911$	34.6935			1.14945			0.574723	−	0.818348i	$-0.305110\pi$
$911$	34.6935			1.14945			0.574723	+	0.818348i	$0.305110\pi$
$912$	1.78106	+	1.02829i	0.0589767	+	0.0340502i
$913$	−0.806009	−	1.39605i	−0.0266750	−	0.0462025i
$914$	−3.70033	−	6.40916i	−0.122396	−	0.211996i
$915$	−23.9661	−	13.8368i	−0.792295	−	0.457432i
$916$		−	22.2869i		−	0.736381i
$917$	3.76894	+	3.49566i	0.124461	+	0.115437i
$918$		−	6.36697i		−	0.210141i
$919$	7.62505	−	13.2070i	0.251527	−	0.435658i	−0.712419	−	0.701754i	$-0.752401\pi$
$919$	7.62505	−	13.2070i	0.251527	−	0.435658i	0.963946	+	0.266096i	$0.0857339\pi$
$920$	2.48332	+	4.30123i	0.0818725	+	0.141807i
$921$	23.0185	−	13.2897i	0.758484	−	0.437911i
$922$	−0.636237	+	1.10199i	−0.0209534	+	0.0362923i
$923$	−26.7726	−	7.10092i	−0.881232	−	0.233730i
$924$	1.78784	+	0.407687i	0.0588157	+	0.0134119i
$925$		−	2.46430i		−	0.0810258i
$926$	17.1810	−	29.7583i	0.564602	−	0.977920i
$927$	6.29145	+	10.8971i	0.206638	+	0.357908i
$928$	−7.66619	+	4.42608i	−0.251655	+	0.145293i
$929$	−31.1416	−	17.9796i	−1.02172	−	0.589892i	−0.107121	−	0.994246i	$-0.534163\pi$
$929$	−31.1416	−	17.9796i	−1.02172	−	0.589892i	−0.914603	+	0.404354i	$0.867497\pi$
$930$		−	2.59408i		−	0.0850632i
$931$	8.11438	+	11.8914i	0.265938	+	0.389724i
$932$	−18.1345			−0.594017
$933$	5.31600	−	9.20758i	0.174038	−	0.301443i
$934$	−25.4807	+	14.7113i	−0.833752	+	0.481367i
$935$	−6.06697	−	10.5083i	−0.198411	−	0.343658i
$936$	2.54303	−	2.55597i	0.0831215	−	0.0835446i
$937$	−55.4856			−1.81263			−0.906317	−	0.422598i	$-0.861118\pi$
$937$	−55.4856			−1.81263			−0.906317	+	0.422598i	$0.861118\pi$
$938$	−5.70998	+	25.0402i	−0.186438	+	0.817591i
$939$	26.8178			0.875164
$940$	12.4102	−	21.4952i	0.404777	−	0.701095i
$941$	21.1317	−	12.2004i	0.688875	−	0.397722i	−0.114316	−	0.993444i	$-0.536468\pi$
$941$	21.1317	−	12.2004i	0.688875	−	0.397722i	0.803190	+	0.595722i	$0.203134\pi$
$942$	1.34377	−	0.775828i	0.0437825	−	0.0252778i
$943$	−18.4139	−	10.6313i	−0.599640	−	0.346202i
$944$		−	12.1292i		−	0.394771i
$945$	−4.94716	+	5.33391i	−0.160931	+	0.173512i
$946$	−3.44472			−0.111997
$947$	−5.98798	−	3.45716i	−0.194583	−	0.112343i	0.399543	−	0.916714i	$-0.369169\pi$
$947$	−5.98798	−	3.45716i	−0.194583	−	0.112343i	−0.594126	+	0.804372i	$0.702502\pi$
$948$	−0.339330	−	0.587736i	−0.0110209	−	0.0190888i
$949$	5.32709	+	19.6810i	0.172925	+	0.638872i
$950$	−2.63316	+	4.56077i	−0.0854311	+	0.147971i
$951$			14.7990i			0.479892i
$952$	−4.96850	−	16.0960i	−0.161030	−	0.521676i
$953$	11.5990			0.375727			0.187864	−	0.982195i	$-0.439844\pi$
$953$	11.5990			0.375727			0.187864	+	0.982195i	$0.439844\pi$
$954$	3.43821	+	1.98505i	0.111316	+	0.0642685i
$955$	−45.6386	+	26.3495i	−1.47683	+	0.852649i
$956$	9.77567	−	5.64399i	0.316168	−	0.182540i
$957$	5.31334	+	3.06766i	0.171756	+	0.0991633i
$958$	3.88015			0.125362
$959$	−0.0356090	−	0.115359i	−0.00114987	−	0.00372515i
$960$			2.74967i			0.0887454i
$961$	−15.0550	+	26.0760i	−0.485645	+	0.841161i
$962$	3.34929	−	0.906557i	0.107985	−	0.0292286i
$963$	−5.06993	−	8.78138i	−0.163376	−	0.282976i
$964$	7.51594	+	4.33933i	0.242072	+	0.139760i
$965$	10.2282			0.329257
$966$	3.24979	−	3.50385i	0.104560	−	0.112734i
$967$			55.2168i			1.77565i	0.460179	+	0.887826i	$0.347785\pi$
$967$			55.2168i			1.77565i	−0.460179	+	0.887826i	$0.652215\pi$
$968$	9.11027	+	5.25982i	0.292815	+	0.169057i
$969$	−11.3399	+	6.54712i	−0.364291	+	0.210324i
$970$	−23.5740	+	13.6105i	−0.756916	+	0.437006i
$971$	−14.6904	+	25.4446i	−0.471438	+	0.816555i	−0.999466	−	0.0326719i	$-0.989598\pi$
$971$	−14.6904	+	25.4446i	−0.471438	+	0.816555i	0.528028	+	0.849227i	$0.322932\pi$
$972$	1.00000			0.0320750
$973$	−12.2749	+	53.8295i	−0.393515	+	1.72569i
$974$	14.5821			0.467242
$975$	6.54511	+	6.51196i	0.209611	+	0.208550i
$976$	5.03217	+	8.71597i	0.161076	+	0.278992i
$977$	−24.0268	+	13.8719i	−0.768687	+	0.443802i	−0.832406	−	0.554166i	$-0.813037\pi$
$977$	−24.0268	+	13.8719i	−0.768687	+	0.443802i	0.0637191	+	0.997968i	$0.479704\pi$
$978$	−2.99238	+	5.18296i	−0.0956858	+	0.165733i
$979$	−9.28316			−0.296691
$980$	−8.34433	+	17.3449i	−0.266550	+	0.554064i
$981$			12.4695i			0.398119i
$982$	−16.6808	−	9.63064i	−0.532305	−	0.307326i
$983$	−42.1491	+	24.3348i	−1.34435	+	0.776160i	−0.987442	−	0.157981i	$-0.949502\pi$
$983$	−42.1491	+	24.3348i	−1.34435	+	0.776160i	−0.356906	+	0.934140i	$0.616168\pi$
$984$	−5.88580	−	10.1945i	−0.187632	−	0.324989i
$985$	13.0017	−	22.5197i	0.414270	−	0.717536i
$986$		−	56.3614i		−	1.79491i
$987$	−23.2847	−	5.30967i	−0.741159	−	0.169009i
$988$	−7.16732	−	1.90099i	−0.228023	−	0.0604786i
$989$	−4.48866	+	7.77458i	−0.142731	+	0.247217i
$990$	1.65044	−	0.952882i	0.0524544	−	0.0302846i
$991$	−18.9014	−	32.7382i	−0.600422	−	1.03996i	−0.992757	−	0.120139i	$-0.961666\pi$
$991$	−18.9014	−	32.7382i	−0.600422	−	1.03996i	0.392335	−	0.919822i	$-0.371667\pi$
$992$	−0.471706	+	0.817019i	−0.0149767	+	0.0259404i
$993$			6.92849i			0.219869i
$994$	−14.9021	−	13.8215i	−0.472664	−	0.438392i
$995$			9.54123i			0.302477i
$996$	−2.01425	−	1.16293i	−0.0638239	−	0.0368487i
$997$	−9.99148	−	17.3058i	−0.316433	−	0.548079i	0.663308	−	0.748347i	$-0.269152\pi$
$997$	−9.99148	−	17.3058i	−0.316433	−	0.548079i	−0.979741	+	0.200268i	$0.935819\pi$
$998$	−9.77954	−	16.9387i	−0.309566	−	0.536184i
$999$	0.833421	+	0.481176i	0.0263683	+	0.0152237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bk.c.415.1	yes	20
3.2	odd	2		1638.2.dm.e.415.10		20
7.2	even	3		3822.2.c.m.883.10		10
7.4	even	3	inner	546.2.bk.c.25.10	yes	20
7.5	odd	6		3822.2.c.n.883.6		10
13.12	even	2	inner	546.2.bk.c.415.10	yes	20
21.11	odd	6		1638.2.dm.e.1117.1		20
39.38	odd	2		1638.2.dm.e.415.1		20
91.12	odd	6		3822.2.c.n.883.5		10
91.25	even	6	inner	546.2.bk.c.25.1	✓	20
91.51	even	6		3822.2.c.m.883.1		10
273.116	odd	6		1638.2.dm.e.1117.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.c.25.1	✓	20	91.25	even	6	inner
546.2.bk.c.25.10	yes	20	7.4	even	3	inner
546.2.bk.c.415.1	yes	20	1.1	even	1	trivial
546.2.bk.c.415.10	yes	20	13.12	even	2	inner
1638.2.dm.e.415.1		20	39.38	odd	2
1638.2.dm.e.415.10		20	3.2	odd	2
1638.2.dm.e.1117.1		20	21.11	odd	6
1638.2.dm.e.1117.10		20	273.116	odd	6
3822.2.c.m.883.1		10	91.51	even	6
3822.2.c.m.883.10		10	7.2	even	3
3822.2.c.n.883.5		10	91.12	odd	6
3822.2.c.n.883.6		10	7.5	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.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.38129 - 1.37484i) q^{5} -1.00000i q^{6} +(-0.588218 + 2.57953i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.38129 - 1.37484i) q^{5} -1.00000i q^{6} +(-0.588218 + 2.57953i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.37484 + 2.38129i) q^{10} +(-0.600231 + 0.346544i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(0.924342 - 3.48505i) q^{13} +(1.79918 - 1.93983i) q^{14} -2.74967i q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.18349 - 5.51396i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-1.78106 - 1.02829i) q^{19} -2.74967i q^{20} +(-2.52805 + 0.780355i) q^{21} +0.693087 q^{22} +(0.903131 - 1.56427i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.28036 + 2.21764i) q^{25} +(-2.54303 + 2.55597i) q^{26} -1.00000 q^{27} +(-2.52805 + 0.780355i) q^{28} -8.85216 q^{29} +(-1.37484 + 2.38129i) q^{30} +(-0.817019 + 0.471706i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.600231 - 0.346544i) q^{33} +6.36697i q^{34} +(4.94716 - 5.33391i) q^{35} -1.00000 q^{36} +(-0.833421 - 0.481176i) q^{37} +(1.02829 + 1.78106i) q^{38} +(3.48032 - 0.942023i) q^{39} +(-1.37484 + 2.38129i) q^{40} -11.7716i q^{41} +(2.57953 + 0.588218i) q^{42} -4.97011 q^{43} +(-0.600231 - 0.346544i) q^{44} +(2.38129 - 1.37484i) q^{45} +(-1.56427 + 0.903131i) q^{46} +(7.81735 + 4.51335i) q^{47} -1.00000 q^{48} +(-6.30800 - 3.03466i) q^{49} -2.56071i q^{50} +(3.18349 - 5.51396i) q^{51} +(3.48032 - 0.942023i) q^{52} +(1.98505 + 3.43821i) q^{53} +(0.866025 + 0.500000i) q^{54} +1.90576 q^{55} +(2.57953 + 0.588218i) q^{56} -2.05659i q^{57} +(7.66619 + 4.42608i) q^{58} +(-10.5042 + 6.06459i) q^{59} +(2.38129 - 1.37484i) q^{60} +(5.03217 - 8.71597i) q^{61} +0.943413 q^{62} +(-1.93983 - 1.79918i) q^{63} -1.00000 q^{64} +(-6.99251 + 7.02809i) q^{65} +(0.346544 + 0.600231i) q^{66} +(-8.40673 + 4.85363i) q^{67} +(3.18349 - 5.51396i) q^{68} +1.80626 q^{69} +(-6.95132 + 2.14572i) q^{70} -7.68213i q^{71} +(0.866025 + 0.500000i) q^{72} +(-4.89733 + 2.82747i) q^{73} +(0.481176 + 0.833421i) q^{74} +(-1.28036 + 2.21764i) q^{75} -2.05659i q^{76} +(-0.540854 - 1.75216i) q^{77} +(-3.48505 - 0.924342i) q^{78} +(-0.339330 + 0.587736i) q^{79} +(2.38129 - 1.37484i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.88580 + 10.1945i) q^{82} +2.32585i q^{83} +(-1.93983 - 1.79918i) q^{84} +17.5071i q^{85} +(4.30424 + 2.48505i) q^{86} +(-4.42608 - 7.66619i) q^{87} +(0.346544 + 0.600231i) q^{88} +(11.5995 + 6.69696i) q^{89} -2.74967 q^{90} +(8.44610 + 4.43434i) q^{91} +1.80626 q^{92} +(-0.817019 - 0.471706i) q^{93} +(-4.51335 - 7.81735i) q^{94} +(2.82747 + 4.89733i) q^{95} +(0.866025 + 0.500000i) q^{96} +9.89969i q^{97} +(3.94556 + 5.78209i) q^{98} -0.693087i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9	\( 20 q + 10 q^{3} + 10 q^{4} - 10 q^{9} + 4 q^{10} - 10 q^{12} + 4 q^{13} - 2 q^{14} - 10 q^{16} - 6 q^{17} - 12 q^{22} - 16 q^{23} + 2 q^{25} - 4 q^{26} - 20 q^{27} - 28 q^{29} - 4 q^{30} + 16 q^{35} - 20 q^{36} + 10 q^{38} + 2 q^{39} - 4 q^{40} - 10 q^{42} + 24 q^{43} - 20 q^{48} + 2 q^{49} + 6 q^{51} + 2 q^{52} - 22 q^{53} + 88 q^{55} - 10 q^{56} + 14 q^{61} + 40 q^{62} - 20 q^{64} + 20 q^{65} - 6 q^{66} + 6 q^{68} - 32 q^{69} + 24 q^{74} - 2 q^{75} - 28 q^{77} - 8 q^{78} + 4 q^{79} - 10 q^{81} + 12 q^{82} - 14 q^{87} - 6 q^{88} - 8 q^{90} + 68 q^{91} - 32 q^{92} - 18 q^{94} + 8 q^{95}+O(q^{100}) \) 20 * q + 10 * q^3 + 10 * q^4 - 10 * q^9 + 4 * q^10 - 10 * q^12 + 4 * q^13 - 2 * q^14 - 10 * q^16 - 6 * q^17 - 12 * q^22 - 16 * q^23 + 2 * q^25 - 4 * q^26 - 20 * q^27 - 28 * q^29 - 4 * q^30 + 16 * q^35 - 20 * q^36 + 10 * q^38 + 2 * q^39 - 4 * q^40 - 10 * q^42 + 24 * q^43 - 20 * q^48 + 2 * q^49 + 6 * q^51 + 2 * q^52 - 22 * q^53 + 88 * q^55 - 10 * q^56 + 14 * q^61 + 40 * q^62 - 20 * q^64 + 20 * q^65 - 6 * q^66 + 6 * q^68 - 32 * q^69 + 24 * q^74 - 2 * q^75 - 28 * q^77 - 8 * q^78 + 4 * q^79 - 10 * q^81 + 12 * q^82 - 14 * q^87 - 6 * q^88 - 8 * q^90 + 68 * q^91 - 32 * q^92 - 18 * q^94 + 8 * q^95

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