LMFDB - Embedded newform 546.2.bk.c.25.1

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			25.1
Root			$-2.38129 - 1.37484i$ of defining polynomial
Character	$\chi$	$=$	546.25
Dual form			546.2.bk.c.415.1

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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	−0.926796	−	0.375566i	$-0.877448\pi$
$5$	−2.38129	+	1.37484i	−1.06494	+	0.614846i	−0.138149	+	0.990412i	$0.544115\pi$
$6$			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	0.406775	−	0.913528i	$-0.366653\pi$
$11$	−0.600231	−	0.346544i	−0.180976	−	0.104487i	−0.587751	+	0.809042i	$0.699987\pi$
$12$	−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	0.164296	+	0.986411i	$0.447465\pi$
$17$	−3.18349	+	5.51396i	−0.772109	+	1.33733i	−0.936405	+	0.350921i	$0.885869\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−1.78106	+	1.02829i	−0.408602	+	0.235907i	−0.690189	−	0.723629i	$-0.742473\pi$
$19$	−1.78106	+	1.02829i	−0.408602	+	0.235907i	0.281587	+	0.959536i	$0.409139\pi$
$20$			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	0.944689	−	0.327968i	$-0.106364\pi$
$23$	0.903131	+	1.56427i	0.188316	+	0.326173i	−0.756373	+	0.654141i	$0.773030\pi$
$24$	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	0.424832	−	0.905272i	$-0.360333\pi$
$31$	−0.817019	−	0.471706i	−0.146741	−	0.0847209i	−0.571573	+	0.820551i	$0.693667\pi$
$32$	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	−0.566940	−	0.823759i	$-0.691873\pi$
$37$	−0.833421	+	0.481176i	−0.137014	+	0.0791048i	0.429926	+	0.902864i	$0.358540\pi$
$38$	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	$0.371169\pi$
$41$			11.7716i			1.83841i	−0.393775	+	0.919207i	$0.628831\pi$
$42$	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	0.193778	−	0.981045i	$-0.437926\pi$
$47$	7.81735	−	4.51335i	1.14028	−	0.658339i	0.946499	+	0.322706i	$0.104593\pi$
$48$	−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	−0.696876	−	0.717191i	$-0.745427\pi$
$53$	1.98505	−	3.43821i	0.272668	−	0.472275i	0.969544	+	0.244917i	$0.0787606\pi$
$54$	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	−0.376915	−	0.926248i	$-0.623015\pi$
$59$	−10.5042	−	6.06459i	−1.36753	−	0.789542i	−0.990612	+	0.136706i	$0.956349\pi$
$60$	2.38129	+	1.37484i	0.307423	+	0.177491i
$61$	5.03217	+	8.71597i	0.644303	+	1.11597i	0.984462	+	0.175598i	$0.0561859\pi$
$61$	5.03217	+	8.71597i	0.644303	+	1.11597i	−0.340159	+	0.940368i	$0.610481\pi$
$62$	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	−0.110908	−	0.993831i	$-0.535376\pi$
$67$	−8.40673	−	4.85363i	−1.02705	−	0.592965i	−0.916137	+	0.400866i	$0.868709\pi$
$68$	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	$0.150665\pi$
$71$			7.68213i			0.911701i	−0.890056	+	0.455851i	$0.849335\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$	−4.89733	−	2.82747i	−0.573189	−	0.330931i	0.185233	−	0.982695i	$-0.440696\pi$
$73$	−4.89733	−	2.82747i	−0.573189	−	0.330931i	−0.758422	+	0.651764i	$0.774029\pi$
$74$	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	0.846305	−	0.532698i	$-0.178822\pi$
$79$	−0.339330	−	0.587736i	−0.0381776	−	0.0661255i	−0.884483	+	0.466573i	$0.845489\pi$
$80$	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	$-0.959257\pi$
$83$		−	2.32585i		−	0.255295i	0.991820	−	0.127648i	$-0.0407427\pi$
$84$	−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	0.262608	−	0.964903i	$-0.415417\pi$
$89$	11.5995	−	6.69696i	1.22954	−	0.709877i	0.966934	+	0.255026i	$0.0820839\pi$
$90$	−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	$-0.832384\pi$
$97$		−	9.89969i		−	1.00516i	0.864530	−	0.502581i	$-0.167616\pi$
$98$	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	−0.993502	−	0.113811i	$-0.963694\pi$
$101$	−4.00174	+	6.93121i	−0.398188	+	0.689681i	0.595315	+	0.803493i	$0.297027\pi$
$102$	−5.51396	−	3.18349i	−0.545963	−	0.315212i
$103$	6.29145	+	10.8971i	0.619915	+	1.07372i	0.989501	+	0.144527i	$0.0461661\pi$
$103$	6.29145	+	10.8971i	0.619915	+	1.07372i	−0.369586	+	0.929196i	$0.620501\pi$
$104$	−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	0.509806	−	0.860289i	$-0.329717\pi$
$107$	−5.06993	−	8.78138i	−0.490129	−	0.848928i	−0.999935	+	0.0113608i	$0.996384\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	10.7989	+	6.23473i	1.03434	+	0.597179i	0.918226	−	0.396057i	$-0.129622\pi$
$109$	10.7989	+	6.23473i	1.03434	+	0.597179i	0.116118	+	0.993235i	$0.462955\pi$
$110$	−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	0.905339	−	0.424690i	$-0.139617\pi$
$131$	0.971460	+	1.68262i	0.0848769	+	0.147011i	−0.820462	+	0.571701i	$0.806284\pi$
$132$			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	0.498311	−	0.866998i	$-0.333954\pi$
$137$	−0.0395182	−	0.0228159i	−0.00337627	−	0.00194929i	−0.501687	+	0.865049i	$0.667287\pi$
$138$	−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	−0.640340	−	0.768092i	$-0.721206\pi$
$149$	−3.60487	+	2.08127i	−0.295322	+	0.170504i	0.345017	+	0.938596i	$0.387873\pi$
$150$	2.21764	+	1.28036i	0.181070	+	0.104541i
$151$	0.395710	+	0.228464i	0.0322025	+	0.0185921i	0.516015	−	0.856580i	$-0.327415\pi$
$151$	0.395710	+	0.228464i	0.0322025	+	0.0185921i	−0.483812	+	0.875172i	$0.660748\pi$
$152$	−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	−0.833405	−	0.552663i	$-0.813612\pi$
$157$	0.775828	−	1.34377i	0.0619178	−	0.107245i	0.895323	+	0.445418i	$0.146945\pi$
$158$	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	−0.689053	−	0.724711i	$-0.741973\pi$
$163$	−5.18296	+	2.99238i	−0.405961	+	0.234381i	0.283092	+	0.959093i	$0.408640\pi$
$164$	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	$0.0900251\pi$
$167$			7.21268i			0.558134i	−0.960272	+	0.279067i	$0.909975\pi$
$168$	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	−0.866989	−	0.498327i	$-0.833948\pi$
$173$	−11.3781	−	19.7074i	−0.865058	−	1.49832i	0.00193131	−	0.999998i	$-0.499385\pi$
$174$		−	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	−0.423900	−	0.905709i	$-0.639339\pi$
$179$	7.65842	−	13.2648i	0.572417	−	0.991455i	0.996317	−	0.0857464i	$-0.0273275\pi$
$180$	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	0.970722	+	0.240204i	$0.0772144\pi$
$191$	9.58276	+	16.5978i	0.693384	+	1.20098i	−0.277338	+	0.960772i	$0.589452\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−3.22142	−	1.85989i	−0.231883	−	0.133878i	0.379557	−	0.925168i	$-0.376076\pi$
$193$	−3.22142	−	1.85989i	−0.231883	−	0.133878i	−0.611441	+	0.791290i	$0.709410\pi$
$194$	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	$-0.890625\pi$
$197$		−	9.45693i		−	0.673778i	0.941544	−	0.336889i	$-0.109375\pi$
$198$	−0.346544	−	0.600231i	−0.0246278	−	0.0426566i
$199$	−1.73497	+	3.00506i	−0.122989	+	0.213023i	−0.920945	−	0.389692i	$-0.872581\pi$
$199$	−1.73497	+	3.00506i	−0.122989	+	0.213023i	0.797956	+	0.602716i	$0.205915\pi$
$200$	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	$0.134400\pi$
$223$			12.2391i			0.819593i	−0.912177	+	0.409797i	$0.865600\pi$
$224$	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	−0.0680571	−	0.997681i	$-0.521680\pi$
$227$	−14.5558	−	8.40380i	−0.966103	−	0.557780i	−0.898046	+	0.439901i	$0.855013\pi$
$228$	1.78106	+	1.02829i	0.117953	+	0.0681004i
$229$	−19.3011	+	11.1435i	−1.27545	+	0.736381i	−0.976008	−	0.217733i	$-0.930134\pi$
$229$	−19.3011	+	11.1435i	−1.27545	+	0.736381i	−0.299442	+	0.954115i	$0.596800\pi$
$230$	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	−0.993685	−	0.112207i	$-0.964208\pi$
$233$	−9.06727	−	15.7050i	−0.594017	−	1.02887i	0.399668	−	0.916660i	$-0.369125\pi$
$234$	−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	$0.118958\pi$
$239$			11.2880i			0.730158i	−0.930976	+	0.365079i	$0.881042\pi$
$240$	2.38129	−	1.37484i	0.153711	−	0.0887454i
$241$	7.51594	+	4.33933i	0.484144	+	0.279521i	0.722142	−	0.691745i	$-0.243158\pi$
$241$	7.51594	+	4.33933i	0.484144	+	0.279521i	−0.237998	+	0.971266i	$0.576491\pi$
$242$	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	−0.920236	−	0.391364i	$-0.872003\pi$
$257$	−12.8097	−	22.1871i	−0.799049	−	1.38399i	0.121187	−	0.992630i	$-0.461330\pi$
$258$		−	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	−0.596767	−	0.802415i	$-0.703548\pi$
$263$	6.43061	−	11.1381i	0.396528	−	0.686807i	0.993295	+	0.115608i	$0.0368816\pi$
$264$	−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	−0.974895	−	0.222667i	$-0.928524\pi$
$269$	−4.83200	+	8.36927i	−0.294612	+	0.510283i	0.680282	+	0.732950i	$0.261857\pi$
$270$	−1.37484	+	2.38129i	−0.0836699	+	0.144921i
$271$	−6.33421	+	3.65706i	−0.384776	+	0.222151i	−0.679894	−	0.733310i	$-0.737974\pi$
$271$	−6.33421	+	3.65706i	−0.384776	+	0.222151i	0.295118	+	0.955461i	$0.404641\pi$
$272$	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	−0.609566	−	0.792735i	$-0.708656\pi$
$277$	6.35351	−	11.0046i	0.381745	−	0.661203i	0.991312	+	0.131532i	$0.0419898\pi$
$278$	−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	$0.251490\pi$
$281$			23.8172i			1.42082i	−0.703790	+	0.710408i	$0.748510\pi$
$282$	4.51335	+	7.81735i	0.268766	+	0.465516i
$283$	−14.5614	+	25.2211i	−0.865586	+	1.49924i	0.000877205		1.00000i	$0.499721\pi$
$283$	−14.5614	+	25.2211i	−0.865586	+	1.49924i	−0.866464	+	0.499240i	$0.833613\pi$
$284$	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	$0.0642456\pi$
$293$			6.86285i			0.400932i	−0.979701	+	0.200466i	$0.935754\pi$
$294$	−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	$0.274060\pi$
$307$			26.5794i			1.51697i	−0.651692	+	0.758484i	$0.725940\pi$
$308$	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	−0.976463	−	0.215685i	$-0.930801\pi$
$311$	−5.31600	+	9.20758i	−0.301443	+	0.522114i	0.675020	+	0.737799i	$0.264135\pi$
$312$	−0.942023	+	3.48032i	−0.0533315	+	0.197034i
$313$	13.4089	+	23.2249i	0.757915	+	1.31275i	0.943912	+	0.330196i	$0.107115\pi$
$313$	13.4089	+	23.2249i	0.757915	+	1.31275i	−0.185998	+	0.982550i	$0.559552\pi$
$314$			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	−0.0948552	−	0.995491i	$-0.530239\pi$
$317$	12.8163	−	7.39952i	0.719838	−	0.415598i	0.814693	+	0.579893i	$0.196905\pi$
$318$	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	−0.325950	−	0.945387i	$-0.605684\pi$
$331$	6.00025	−	3.46425i	0.329804	−	0.190412i	0.655754	+	0.754975i	$0.272351\pi$
$332$	−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	−0.760697	−	0.649107i	$-0.775143\pi$
$347$	3.38645	−	5.86550i	0.181794	−	0.314876i	0.942492	+	0.334230i	$0.108476\pi$
$348$	4.42608	+	7.66619i	0.237263	+	0.410951i
$349$			31.1199i			1.66581i	0.553416	+	0.832905i	$0.313324\pi$
$349$			31.1199i			1.66581i	−0.553416	+	0.832905i	$0.686676\pi$
$350$	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	0.699912	−	0.714229i	$-0.253223\pi$
$353$	8.10390	+	4.67879i	0.431327	+	0.249027i	−0.268585	+	0.963256i	$0.586556\pi$
$354$	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	0.282022	−	0.959408i	$-0.408995\pi$
$359$	23.7581	−	13.7167i	1.25390	−	0.723942i	0.971883	+	0.235466i	$0.0756617\pi$
$360$	−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	−0.555865	−	0.831272i	$-0.687613\pi$
$367$	8.46693	−	14.6652i	0.441970	−	0.765515i	0.997836	+	0.0657574i	$0.0209463\pi$
$368$	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	−0.998688	−	0.0512053i	$-0.983694\pi$
$373$	−10.5004	−	18.1872i	−0.543689	−	0.941697i	0.454999	−	0.890492i	$-0.349640\pi$
$374$	−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	$0.0689515\pi$
$379$			8.36838i			0.429855i	−0.976630	+	0.214927i	$0.931049\pi$
$380$	−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	−0.912144	−	0.409869i	$-0.865574\pi$
$383$	−19.8299	+	11.4488i	−1.01326	+	0.585005i	−0.101115	+	0.994875i	$0.532241\pi$
$384$		−	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	−0.942038	−	0.335506i	$-0.891093\pi$
$389$	−3.55927	+	6.16484i	−0.180462	+	0.312570i	0.761576	+	0.648076i	$0.224426\pi$
$390$	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	−0.925061	−	0.379819i	$-0.875986\pi$
$397$	−21.0936	+	12.1784i	−1.05866	+	0.611217i	−0.133598	+	0.991036i	$0.542653\pi$
$398$		−	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	−0.650990	−	0.759087i	$-0.725646\pi$
$401$	−6.38990	+	3.68921i	−0.319096	+	0.184230i	0.331893	+	0.943317i	$0.392313\pi$
$402$	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	0.940015	−	0.341133i	$-0.110811\pi$
$409$	22.5412	+	13.0142i	1.11459	+	0.643510i	0.174577	+	0.984643i	$0.444144\pi$
$410$	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	$0.0805377\pi$
$421$			10.2725i			0.500651i	−0.968162	+	0.250326i	$0.919462\pi$
$422$	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	0.522299	−	0.852762i	$-0.325074\pi$
$431$	0.932887	+	0.538602i	0.0449356	+	0.0259436i	−0.477364	+	0.878706i	$0.658408\pi$
$432$	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	−0.998951	−	0.0457954i	$-0.985418\pi$
$439$	−11.2961	−	19.5655i	−0.539135	−	0.933810i	0.459815	−	0.888015i	$-0.347916\pi$
$440$			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	0.997481	+	0.0709346i	$0.0225982\pi$
$443$	11.7902	+	20.4213i	0.560172	+	0.970246i	−0.437309	+	0.899311i	$0.644069\pi$
$444$	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	$-0.969174\pi$
$449$		−	4.09767i		−	0.193381i	0.995315	−	0.0966904i	$-0.0308257\pi$
$450$	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	−0.342549	−	0.939500i	$-0.611290\pi$
$457$	6.40916	−	3.70033i	0.299808	−	0.173094i	0.642356	+	0.766406i	$0.277957\pi$
$458$	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	$0.00943370\pi$
$461$			1.27247i			0.0592650i	−0.999561	+	0.0296325i	$0.990566\pi$
$462$	−1.75216	−	0.540854i	−0.0815179	−	0.0251628i
$463$		−	34.3620i		−	1.59694i	−0.602037	−	0.798468i	$-0.705644\pi$
$463$		−	34.3620i		−	1.59694i	0.602037	−	0.798468i	$-0.294356\pi$
$464$	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	0.974751	+	0.223297i	$0.0716819\pi$
$467$	14.7113	+	25.4807i	0.680756	+	1.17910i	−0.293995	+	0.955807i	$0.594985\pi$
$468$	−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	0.421263	−	0.906938i	$-0.361587\pi$
$479$	−3.36031	−	1.94008i	−0.153536	−	0.0886443i	−0.574800	+	0.818294i	$0.694920\pi$
$480$	−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	0.185796	−	0.982588i	$-0.440514\pi$
$487$	−12.6285	−	7.29107i	−0.572252	−	0.330390i	−0.758048	+	0.652198i	$0.773847\pi$
$488$	−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	−0.0703990	−	0.997519i	$-0.522427\pi$
$499$	16.9387	−	9.77954i	0.758278	−	0.437792i	0.828677	+	0.559727i	$0.189094\pi$
$500$	−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	−0.659762	−	0.751475i	$-0.729343\pi$
$509$	−7.64473	+	4.41369i	−0.338847	+	0.195633i	0.320915	+	0.947108i	$0.396010\pi$
$510$	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	0.359478	+	0.933153i	$0.382955\pi$
$521$	−14.3434	+	24.8435i	−0.628395	+	1.08841i	−0.987874	+	0.155259i	$0.950379\pi$
$522$	−7.66619	−	4.42608i	−0.335540	−	0.193724i
$523$	13.6397	+	23.6247i	0.596423	+	1.03303i	0.993344	+	0.115182i	$0.0367452\pi$
$523$	13.6397	+	23.6247i	0.596423	+	1.03303i	−0.396922	+	0.917853i	$0.629921\pi$
$524$	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	−0.587985	−	0.808872i	$-0.700079\pi$
$541$	−4.22098	+	2.43698i	−0.181474	+	0.104774i	0.406511	+	0.913646i	$0.366745\pi$
$542$	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	0.521141	−	0.853471i	$-0.325507\pi$
$557$	1.00500	+	0.580239i	0.0425833	+	0.0245855i	−0.478557	+	0.878056i	$0.658840\pi$
$558$	−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	−0.772965	−	0.634449i	$-0.781227\pi$
$563$	3.86680	−	6.69750i	0.162966	−	0.282266i	0.935931	+	0.352183i	$0.114560\pi$
$564$	−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	0.997869	+	0.0652529i	$0.0207854\pi$
$569$	13.2494	+	22.9487i	0.555445	+	0.962059i	−0.442424	+	0.896806i	$0.645881\pi$
$570$	4.89733	+	2.82747i	0.205126	+	0.118430i
$571$	−16.2913	+	28.2174i	−0.681770	+	1.18086i	0.292670	+	0.956214i	$0.405456\pi$
$571$	−16.2913	+	28.2174i	−0.681770	+	1.18086i	−0.974440	+	0.224647i	$0.927877\pi$
$572$	−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	−0.136361	−	0.990659i	$-0.543541\pi$
$577$	−25.5216	−	14.7349i	−1.06248	−	0.613422i	−0.926117	+	0.377237i	$0.876874\pi$
$578$	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	$-0.842560\pi$
$587$		−	23.0017i		−	0.949381i	0.880153	−	0.474690i	$-0.157440\pi$
$588$	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	0.591443	−	0.806347i	$-0.298559\pi$
$593$	38.6090	−	22.2909i	1.58548	−	0.915378i	0.994038	−	0.109031i	$-0.0347748\pi$
$594$	−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	−0.800599	−	0.599201i	$-0.795485\pi$
$599$	2.90326	−	5.02860i	0.118624	−	0.205463i	0.919223	+	0.393738i	$0.128818\pi$
$600$	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	0.874710	−	0.484646i	$-0.161052\pi$
$607$	0.434594	+	0.752739i	0.0176396	+	0.0305527i	−0.857071	+	0.515199i	$0.827718\pi$
$608$	−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	0.110100	−	0.993920i	$-0.464883\pi$
$613$	−17.2225	−	9.94341i	−0.695610	−	0.401611i	−0.805710	+	0.592310i	$0.798216\pi$
$614$	−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	$0.0406524\pi$
$617$			6.32742i			0.254732i	−0.991856	+	0.127366i	$0.959348\pi$
$618$	−10.8971	+	6.29145i	−0.438346	+	0.253079i
$619$	−22.8722	−	13.2053i	−0.919311	−	0.530764i	−0.0358959	−	0.999356i	$-0.511428\pi$
$619$	−22.8722	−	13.2053i	−0.919311	−	0.530764i	−0.883415	+	0.468591i	$0.844762\pi$
$620$	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	$-0.830097\pi$
$631$		−	25.5607i		−	1.01756i	0.860898	−	0.508778i	$-0.169903\pi$
$632$	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	−0.790845	−	0.612017i	$-0.790359\pi$
$641$	3.40779	−	5.90247i	0.134600	−	0.233133i	0.925444	+	0.378883i	$0.123692\pi$
$642$	8.78138	−	5.06993i	0.346574	−	0.200094i
$643$			29.4326i			1.16071i	0.814364	+	0.580355i	$0.197086\pi$
$643$			29.4326i			1.16071i	−0.814364	+	0.580355i	$0.802914\pi$
$644$	−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	−0.234532	−	0.972108i	$-0.575356\pi$
$647$	18.4312	−	31.9237i	0.724605	−	1.25505i	0.959137	−	0.282943i	$-0.0913109\pi$
$648$	−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	0.992718	−	0.120461i	$-0.0384372\pi$
$653$	10.0181	+	17.3518i	0.392037	+	0.679028i	−0.600681	+	0.799489i	$0.705104\pi$
$654$	−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	0.918138	−	0.396261i	$-0.129692\pi$
$661$	26.5850	+	15.3488i	1.03404	+	0.597001i	0.115897	+	0.993261i	$0.463026\pi$
$662$	−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	0.996343	+	0.0854400i	$0.0272296\pi$
$677$	14.8873	+	25.7855i	0.572165	+	0.991019i	−0.424178	+	0.905579i	$0.639437\pi$
$678$		−	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	0.937425	+	0.348187i	$0.113203\pi$
$683$	44.6289	+	25.7665i	1.70768	+	0.985927i	0.770251	+	0.637740i	$0.220131\pi$
$684$	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	0.406255	−	0.913760i	$-0.366835\pi$
$691$	36.8206	−	21.2584i	1.40072	−	0.808707i	0.994467	+	0.105053i	$0.0335012\pi$
$692$	−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	−0.727971	−	0.685607i	$-0.759537\pi$
$709$	−13.2657	+	7.65895i	−0.498204	+	0.287638i	0.229768	+	0.973245i	$0.426203\pi$
$710$	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	0.725120	−	0.688622i	$-0.241784\pi$
$719$	−6.26926	−	10.8587i	−0.233804	−	0.404961i	−0.958924	+	0.283662i	$0.908451\pi$
$720$		−	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	−0.872778	−	0.488117i	$-0.837684\pi$
$733$	−23.9996	+	13.8562i	−0.886445	+	0.511789i	−0.0136668	+	0.999907i	$0.504350\pi$
$734$			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	0.877631	−	0.479336i	$-0.159123\pi$
$739$	24.5022	+	14.1464i	0.901330	+	0.520383i	0.0236983	+	0.999719i	$0.492456\pi$
$740$	−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	$0.241349\pi$
$743$			37.4869i			1.37526i	−0.726061	+	0.687630i	$0.758651\pi$
$744$	−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	0.884380	−	0.466769i	$-0.154582\pi$
$751$	1.04017	+	1.80163i	0.0379564	+	0.0657423i	−0.846423	+	0.532511i	$0.821249\pi$
$752$	−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	−0.898660	−	0.438645i	$-0.855458\pi$
$761$	−26.7066	+	15.4190i	−0.968113	+	0.558940i	−0.0694523	+	0.997585i	$0.522125\pi$
$762$			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	$-0.830495\pi$
$769$		−	28.1580i		−	1.01540i	0.861533	−	0.507702i	$-0.169505\pi$
$770$	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	0.618540	−	0.785753i	$-0.287724\pi$
$773$	6.87642	+	3.97011i	0.247328	+	0.142795i	−0.371212	+	0.928548i	$0.621058\pi$
$774$	−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	−0.382381	−	0.924005i	$-0.624896\pi$
$787$	−38.5395	−	22.2508i	−1.37378	−	0.793154i	−0.991402	+	0.130851i	$0.958229\pi$
$788$	−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	−0.805821	−	0.592159i	$-0.798276\pi$
$809$	3.12627	−	5.41487i	0.109914	−	0.190377i	0.915735	+	0.401782i	$0.131609\pi$
$810$	1.37484	+	2.38129i	0.0483069	+	0.0836699i
$811$		−	28.5397i		−	1.00216i	−0.865400	−	0.501082i	$-0.832936\pi$
$811$		−	28.5397i		−	1.00216i	0.865400	−	0.501082i	$-0.167064\pi$
$812$	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	−0.740135	−	0.672459i	$-0.765238\pi$
$821$	−15.1241	+	8.73193i	−0.527836	+	0.304746i	0.212299	+	0.977205i	$0.431905\pi$
$822$	0.0228159	−	0.0395182i	0.000795795	−	0.00137836i
$823$	7.13184	−	12.3527i	0.248600	−	0.430588i	−0.714537	−	0.699597i	$-0.753363\pi$
$823$	7.13184	−	12.3527i	0.248600	−	0.430588i	0.963138	+	0.269009i	$0.0866961\pi$
$824$	−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	$-0.929780\pi$
$827$		−	12.5853i		−	0.437635i	0.975766	−	0.218818i	$-0.0702200\pi$
$828$	−0.903131	−	1.56427i	−0.0313860	−	0.0543621i
$829$	5.13167	−	8.88832i	0.178230	−	0.308704i	−0.763044	−	0.646346i	$-0.776296\pi$
$829$	5.13167	−	8.88832i	0.178230	−	0.308704i	0.941274	+	0.337642i	$0.109629\pi$
$830$	−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	$0.187111\pi$
$839$			32.1258i			1.10911i	−0.832148	+	0.554553i	$0.812889\pi$
$840$	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	$-0.964203\pi$
$853$		−	6.55511i		−	0.224443i	0.993683	−	0.112221i	$-0.0357966\pi$
$854$	−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	−0.973496	−	0.228705i	$-0.926551\pi$
$857$	−8.45109	+	14.6377i	−0.288684	+	0.500015i	0.684812	+	0.728720i	$0.259884\pi$
$858$	2.41216	+	0.652904i	0.0823498	+	0.0222898i
$859$	−25.6471	−	44.4221i	−0.875068	−	1.51566i	−0.856690	−	0.515831i	$-0.827483\pi$
$859$	−25.6471	−	44.4221i	−0.875068	−	1.51566i	−0.0183773	−	0.999831i	$-0.505850\pi$
$860$		−	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	0.265299	−	0.964166i	$-0.414529\pi$
$863$	36.2199	−	20.9116i	1.23294	−	0.711839i	0.967642	+	0.252327i	$0.0811959\pi$
$864$	−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	−0.937706	−	0.347429i	$-0.887055\pi$
$877$	−32.7437	+	18.9046i	−1.10568	+	0.638363i	−0.167971	+	0.985792i	$0.553722\pi$
$878$	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	0.948382	+	0.317130i	$0.102719\pi$
$887$	22.3022	+	38.6285i	0.748834	+	1.29702i	−0.199548	+	0.979888i	$0.563947\pi$
$888$	−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	0.0494896	+	0.998775i	$0.484241\pi$
$907$	−25.3044	+	43.8285i	−0.840219	+	1.45530i	−0.889709	+	0.456528i	$0.849093\pi$
$908$	−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	0.963946	−	0.266096i	$-0.0857339\pi$
$919$	7.62505	+	13.2070i	0.251527	+	0.435658i	−0.712419	+	0.701754i	$0.752401\pi$
$920$	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	−0.914603	−	0.404354i	$-0.867497\pi$
$929$	−31.1416	+	17.9796i	−1.02172	+	0.589892i	−0.107121	+	0.994246i	$0.534163\pi$
$930$			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	0.803190	−	0.595722i	$-0.203134\pi$
$941$	21.1317	+	12.2004i	0.688875	+	0.397722i	−0.114316	+	0.993444i	$0.536468\pi$
$942$	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	−0.594126	−	0.804372i	$-0.702502\pi$
$947$	−5.98798	+	3.45716i	−0.194583	+	0.112343i	0.399543	+	0.916714i	$0.369169\pi$
$948$	−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	$-0.652215\pi$
$967$		−	55.2168i		−	1.77565i	0.460179	−	0.887826i	$-0.347785\pi$
$968$	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	0.528028	−	0.849227i	$-0.322932\pi$
$971$	−14.6904	−	25.4446i	−0.471438	−	0.816555i	−0.999466	+	0.0326719i	$0.989598\pi$
$972$	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	0.0637191	−	0.997968i	$-0.479704\pi$
$977$	−24.0268	−	13.8719i	−0.768687	−	0.443802i	−0.832406	+	0.554166i	$0.813037\pi$
$978$	−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	−0.356906	−	0.934140i	$-0.616168\pi$
$983$	−42.1491	−	24.3348i	−1.34435	−	0.776160i	−0.987442	+	0.157981i	$0.949502\pi$
$984$	−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	0.392335	+	0.919822i	$0.371667\pi$
$991$	−18.9014	+	32.7382i	−0.600422	+	1.03996i	−0.992757	+	0.120139i	$0.961666\pi$
$992$	−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	−0.979741	−	0.200268i	$-0.935819\pi$
$997$	−9.99148	+	17.3058i	−0.316433	+	0.548079i	0.663308	+	0.748347i	$0.269152\pi$
$998$	−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.25.1	✓	20
3.2	odd	2		1638.2.dm.e.1117.10		20
7.2	even	3	inner	546.2.bk.c.415.10	yes	20
7.3	odd	6		3822.2.c.n.883.5		10
7.4	even	3		3822.2.c.m.883.1		10
13.12	even	2	inner	546.2.bk.c.25.10	yes	20
21.2	odd	6		1638.2.dm.e.415.1		20
39.38	odd	2		1638.2.dm.e.1117.1		20
91.25	even	6		3822.2.c.m.883.10		10
91.38	odd	6		3822.2.c.n.883.6		10
91.51	even	6	inner	546.2.bk.c.415.1	yes	20
273.233	odd	6		1638.2.dm.e.415.10		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bk.c.25.1	✓	20	1.1	even	1	trivial
546.2.bk.c.25.10	yes	20	13.12	even	2	inner
546.2.bk.c.415.1	yes	20	91.51	even	6	inner
546.2.bk.c.415.10	yes	20	7.2	even	3	inner
1638.2.dm.e.415.1		20	21.2	odd	6
1638.2.dm.e.415.10		20	273.233	odd	6
1638.2.dm.e.1117.1		20	39.38	odd	2
1638.2.dm.e.1117.10		20	3.2	odd	2
3822.2.c.m.883.1		10	7.4	even	3
3822.2.c.m.883.10		10	91.25	even	6
3822.2.c.n.883.5		10	7.3	odd	6
3822.2.c.n.883.6		10	91.38	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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