LMFDB - Embedded newform 1206.2.h.e.163.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1206,2,Mod(37,1206)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1206, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1206.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1206 = 2 \cdot 3^{2} \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1206.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.62995848377$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 402)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	1206.163
Dual form			1206.2.h.e.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.69963 q^{5} +(0.555632 + 0.962383i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.69963 q^{5} +(0.555632 + 0.962383i) q^{7} +1.00000 q^{8} +(-1.34981 + 2.33795i) q^{10} +(0.738550 + 1.27921i) q^{11} +(-2.43818 + 4.22305i) q^{13} -1.11126 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.34981 - 2.33795i) q^{17} +(-3.78799 + 6.56099i) q^{19} +(-1.34981 - 2.33795i) q^{20} -1.47710 q^{22} +(0.349814 - 0.605896i) q^{23} +2.28799 q^{25} +(-2.43818 - 4.22305i) q^{26} +(0.555632 - 0.962383i) q^{28} +(1.08836 + 1.88510i) q^{29} +(0.905446 + 1.56828i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.34981 + 2.33795i) q^{34} +(1.50000 + 2.59808i) q^{35} +(1.64400 - 2.84748i) q^{37} +(-3.78799 - 6.56099i) q^{38} +2.69963 q^{40} +(2.89926 + 5.02166i) q^{41} -1.36584 q^{43} +(0.738550 - 1.27921i) q^{44} +(0.349814 + 0.605896i) q^{46} +(2.49381 + 4.31941i) q^{47} +(2.88255 - 4.99272i) q^{49} +(-1.14400 + 1.98146i) q^{50} +4.87636 q^{52} +2.51052 q^{53} +(1.99381 + 3.45338i) q^{55} +(0.555632 + 0.962383i) q^{56} -2.17673 q^{58} +7.32141 q^{59} +(2.93818 - 5.08907i) q^{61} -1.81089 q^{62} +1.00000 q^{64} +(-6.58217 + 11.4007i) q^{65} +(-7.74288 + 2.65477i) q^{67} -2.69963 q^{68} -3.00000 q^{70} +(-0.0716537 - 0.124108i) q^{71} +(-5.78799 + 10.0251i) q^{73} +(1.64400 + 2.84748i) q^{74} +7.57598 q^{76} +(-0.820724 + 1.42154i) q^{77} +(3.88255 + 6.72477i) q^{79} +(-1.34981 + 2.33795i) q^{80} -5.79851 q^{82} +(5.75526 - 9.96840i) q^{83} +(3.64400 - 6.31159i) q^{85} +(0.682918 - 1.18285i) q^{86} +(0.738550 + 1.27921i) q^{88} -5.47710 q^{89} -5.41892 q^{91} -0.699628 q^{92} -4.98762 q^{94} +(-10.2262 + 17.7122i) q^{95} +(5.71634 - 9.90099i) q^{97} +(2.88255 + 4.99272i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 4 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + 4 * q^5 + 3 * q^7 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} + 4 q^{5} + 3 q^{7} + 6 q^{8} - 2 q^{10} - q^{11} + 3 q^{13} - 6 q^{14} - 3 q^{16} + 2 q^{17} + q^{19} - 2 q^{20} + 2 q^{22} - 4 q^{23} - 10 q^{25} + 3 q^{26} + 3 q^{28} - 5 q^{29} - q^{31} - 3 q^{32} + 2 q^{34} + 9 q^{35} - 2 q^{37} + q^{38} + 4 q^{40} - 7 q^{41} + 2 q^{43} - q^{44} - 4 q^{46} - 3 q^{47} + 5 q^{50} - 6 q^{52} - 10 q^{53} - 6 q^{55} + 3 q^{56} + 10 q^{58} + 6 q^{59} + 2 q^{62} + 6 q^{64} - 10 q^{65} + 2 q^{67} - 4 q^{68} - 18 q^{70} + 4 q^{71} - 11 q^{73} - 2 q^{74} - 2 q^{76} + 30 q^{77} + 6 q^{79} - 2 q^{80} + 14 q^{82} + 22 q^{83} + 10 q^{85} - q^{86} - q^{88} - 22 q^{89} + 36 q^{91} + 8 q^{92} + 6 q^{94} - 20 q^{95} + 15 q^{97}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 4 * q^5 + 3 * q^7 + 6 * q^8 - 2 * q^10 - q^11 + 3 * q^13 - 6 * q^14 - 3 * q^16 + 2 * q^17 + q^19 - 2 * q^20 + 2 * q^22 - 4 * q^23 - 10 * q^25 + 3 * q^26 + 3 * q^28 - 5 * q^29 - q^31 - 3 * q^32 + 2 * q^34 + 9 * q^35 - 2 * q^37 + q^38 + 4 * q^40 - 7 * q^41 + 2 * q^43 - q^44 - 4 * q^46 - 3 * q^47 + 5 * q^50 - 6 * q^52 - 10 * q^53 - 6 * q^55 + 3 * q^56 + 10 * q^58 + 6 * q^59 + 2 * q^62 + 6 * q^64 - 10 * q^65 + 2 * q^67 - 4 * q^68 - 18 * q^70 + 4 * q^71 - 11 * q^73 - 2 * q^74 - 2 * q^76 + 30 * q^77 + 6 * q^79 - 2 * q^80 + 14 * q^82 + 22 * q^83 + 10 * q^85 - q^86 - q^88 - 22 * q^89 + 36 * q^91 + 8 * q^92 + 6 * q^94 - 20 * q^95 + 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1206\mathbb{Z}\right)^\times$.

$n$	$739$	$1073$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.69963			1.20731			0.603655	−	0.797246i	$-0.293710\pi$
$5$	2.69963			1.20731			0.603655	+	0.797246i	$0.293710\pi$
$6$		0			0
$7$	0.555632	+	0.962383i	0.210009	+	0.363747i	0.951717	−	0.306976i	$-0.0993173\pi$
$7$	0.555632	+	0.962383i	0.210009	+	0.363747i	−0.741708	+	0.670723i	$0.765984\pi$
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.34981	+	2.33795i	−0.426849	+	0.739324i
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	0.955621	−	0.294598i	$-0.0951858\pi$
$11$	0.738550	+	1.27921i	0.222681	+	0.385695i	−0.732940	+	0.680293i	$0.761852\pi$
$12$		0			0
$13$	−2.43818	+	4.22305i	−0.676229	+	1.17126i	0.299879	+	0.953977i	$0.403054\pi$
$13$	−2.43818	+	4.22305i	−0.676229	+	1.17126i	−0.976108	+	0.217286i	$0.930280\pi$
$14$	−1.11126			−0.296998
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.34981	−	2.33795i	0.327378	−	0.567035i	−0.654613	−	0.755964i	$-0.727168\pi$
$17$	1.34981	−	2.33795i	0.327378	−	0.567035i	0.981991	+	0.188929i	$0.0605016\pi$
$18$		0			0
$19$	−3.78799	+	6.56099i	−0.869025	+	1.50520i	−0.00603068	+	0.999982i	$0.501920\pi$
$19$	−3.78799	+	6.56099i	−0.869025	+	1.50520i	−0.862994	+	0.505214i	$0.831414\pi$
$20$	−1.34981	−	2.33795i	−0.301828	−	0.522781i
$21$		0			0
$22$	−1.47710			−0.314919
$23$	0.349814	−	0.605896i	0.0729413	−	0.126338i	−0.827248	−	0.561837i	$-0.810095\pi$
$23$	0.349814	−	0.605896i	0.0729413	−	0.126338i	0.900189	+	0.435499i	$0.143428\pi$
$24$		0			0
$25$	2.28799			0.457598
$26$	−2.43818	−	4.22305i	−0.478166	−	0.828208i
$27$		0			0
$28$	0.555632	−	0.962383i	0.105005	−	0.181873i
$29$	1.08836	+	1.88510i	0.202104	+	0.350055i	0.949206	−	0.314655i	$-0.101889\pi$
$29$	1.08836	+	1.88510i	0.202104	+	0.350055i	−0.747102	+	0.664709i	$0.768555\pi$
$30$		0			0
$31$	0.905446	+	1.56828i	0.162623	+	0.281671i	0.935809	−	0.352509i	$-0.114671\pi$
$31$	0.905446	+	1.56828i	0.162623	+	0.281671i	−0.773186	+	0.634180i	$0.781338\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.34981	+	2.33795i	0.231491	+	0.400955i
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$		0			0
$37$	1.64400	−	2.84748i	0.270271	−	0.468124i	−0.698660	−	0.715454i	$-0.746220\pi$
$37$	1.64400	−	2.84748i	0.270271	−	0.468124i	0.968931	+	0.247330i	$0.0795533\pi$
$38$	−3.78799	−	6.56099i	−0.614493	−	1.06433i
$39$		0			0
$40$	2.69963			0.426849
$41$	2.89926	+	5.02166i	0.452788	+	0.784251i	0.998558	−	0.0536835i	$-0.0170962\pi$
$41$	2.89926	+	5.02166i	0.452788	+	0.784251i	−0.545770	+	0.837935i	$0.683763\pi$
$42$		0			0
$43$	−1.36584			−0.208288			−0.104144	−	0.994562i	$-0.533210\pi$
$43$	−1.36584			−0.208288			−0.104144	+	0.994562i	$0.533210\pi$
$44$	0.738550	−	1.27921i	0.111341	−	0.192848i
$45$		0			0
$46$	0.349814	+	0.605896i	0.0515773	+	0.0893345i
$47$	2.49381	+	4.31941i	0.363760	+	0.630050i	0.988576	−	0.150721i	$-0.0481596\pi$
$47$	2.49381	+	4.31941i	0.363760	+	0.630050i	−0.624817	+	0.780771i	$0.714826\pi$
$48$		0			0
$49$	2.88255	−	4.99272i	0.411792	−	0.713245i
$50$	−1.14400	+	1.98146i	−0.161785	+	0.280221i
$51$		0			0
$52$	4.87636			0.676229
$53$	2.51052			0.344847			0.172423	−	0.985023i	$-0.444840\pi$
$53$	2.51052			0.344847			0.172423	+	0.985023i	$0.444840\pi$
$54$		0			0
$55$	1.99381	+	3.45338i	0.268845	+	0.465654i
$56$	0.555632	+	0.962383i	0.0742495	+	0.128604i
$57$		0			0
$58$	−2.17673			−0.285818
$59$	7.32141			0.953167			0.476583	−	0.879129i	$-0.341875\pi$
$59$	7.32141			0.953167			0.476583	+	0.879129i	$0.341875\pi$
$60$		0			0
$61$	2.93818	−	5.08907i	0.376195	−	0.651589i	−0.614310	−	0.789065i	$-0.710566\pi$
$61$	2.93818	−	5.08907i	0.376195	−	0.651589i	0.990505	+	0.137476i	$0.0438989\pi$
$62$	−1.81089			−0.229984
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.58217	+	11.4007i	−0.816418	+	1.41408i
$66$		0			0
$67$	−7.74288	+	2.65477i	−0.945943	+	0.324332i
$67$	−7.74288	+	2.65477i	−0.945943	+	0.324332i
$68$	−2.69963			−0.327378
$69$		0			0
$70$	−3.00000			−0.358569
$71$	−0.0716537	−	0.124108i	−0.00850373	−	0.0147289i	0.861742	−	0.507346i	$-0.169374\pi$
$71$	−0.0716537	−	0.124108i	−0.00850373	−	0.0147289i	−0.870246	+	0.492617i	$0.836040\pi$
$72$		0			0
$73$	−5.78799	+	10.0251i	−0.677433	+	1.17335i	0.298318	+	0.954467i	$0.403574\pi$
$73$	−5.78799	+	10.0251i	−0.677433	+	1.17335i	−0.975751	+	0.218882i	$0.929759\pi$
$74$	1.64400	+	2.84748i	0.191111	+	0.331013i
$75$		0			0
$76$	7.57598			0.869025
$77$	−0.820724	+	1.42154i	−0.0935302	+	0.161999i
$78$		0			0
$79$	3.88255	+	6.72477i	0.436821	+	0.756595i	0.997442	−	0.0714766i	$-0.0227711\pi$
$79$	3.88255	+	6.72477i	0.436821	+	0.756595i	−0.560622	+	0.828072i	$0.689438\pi$
$80$	−1.34981	+	2.33795i	−0.150914	+	0.261390i
$81$		0			0
$82$	−5.79851			−0.640339
$83$	5.75526	−	9.96840i	0.631722	−	1.09417i	−0.355478	−	0.934685i	$-0.615682\pi$
$83$	5.75526	−	9.96840i	0.631722	−	1.09417i	0.987200	−	0.159490i	$-0.0509849\pi$
$84$		0			0
$85$	3.64400	−	6.31159i	0.395247	−	0.684588i
$86$	0.682918	−	1.18285i	0.0736409	−	0.127550i
$87$		0			0
$88$	0.738550	+	1.27921i	0.0787297	+	0.136364i
$89$	−5.47710			−0.580571			−0.290286	−	0.956940i	$-0.593750\pi$
$89$	−5.47710			−0.580571			−0.290286	+	0.956940i	$0.593750\pi$
$90$		0			0
$91$	−5.41892			−0.568057
$92$	−0.699628			−0.0729413
$93$		0			0
$94$	−4.98762			−0.514434
$95$	−10.2262	+	17.7122i	−1.04918	+	1.81724i
$96$		0			0
$97$	5.71634	−	9.90099i	0.580406	−	1.00529i	−0.415025	−	0.909810i	$-0.636227\pi$
$97$	5.71634	−	9.90099i	0.580406	−	1.00529i	0.995431	−	0.0954830i	$-0.0304396\pi$
$98$	2.88255	+	4.99272i	0.291181	+	0.504340i
$99$		0			0
$100$	−1.14400	−	1.98146i	−0.114400	−	0.198146i
$101$	−2.64400	−	4.57954i	−0.263087	−	0.455681i	0.703973	−	0.710226i	$-0.251407\pi$
$101$	−2.64400	−	4.57954i	−0.263087	−	0.455681i	−0.967061	+	0.254546i	$0.918074\pi$
$102$		0			0
$103$	7.03706	+	12.1885i	0.693382	+	1.20097i	0.970723	+	0.240202i	$0.0772136\pi$
$103$	7.03706	+	12.1885i	0.693382	+	1.20097i	−0.277341	+	0.960772i	$0.589453\pi$
$104$	−2.43818	+	4.22305i	−0.239083	+	0.414104i
$105$		0			0
$106$	−1.25526	+	2.17417i	−0.121922	+	0.211174i
$107$	−9.57598			−0.925745			−0.462873	−	0.886425i	$-0.653181\pi$
$107$	−9.57598			−0.925745			−0.462873	+	0.886425i	$0.653181\pi$
$108$		0			0
$109$	−13.3214			−1.27596			−0.637980	−	0.770053i	$-0.720230\pi$
$109$	−13.3214			−1.27596			−0.637980	+	0.770053i	$0.720230\pi$
$110$	−3.98762			−0.380205
$111$		0			0
$112$	−1.11126			−0.105005
$113$	7.46108	+	12.9230i	0.701879	+	1.21569i	0.967806	+	0.251697i	$0.0809887\pi$
$113$	7.46108	+	12.9230i	0.701879	+	1.21569i	−0.265927	+	0.963993i	$0.585678\pi$
$114$		0			0
$115$	0.944368	−	1.63569i	0.0880628	−	0.152529i
$116$	1.08836	−	1.88510i	0.101052	−	0.175027i
$117$		0			0
$118$	−3.66071	+	6.34053i	−0.336995	+	0.583693i
$119$	3.00000			0.275010
$120$		0			0
$121$	4.40909	−	7.63676i	0.400826	−	0.694251i
$122$	2.93818	+	5.08907i	0.266010	+	0.460743i
$123$		0			0
$124$	0.905446	−	1.56828i	0.0813115	−	0.140836i
$125$	−7.32141			−0.654847
$126$		0			0
$127$	5.34981	+	9.26615i	0.474719	+	0.822238i	0.999581	−	0.0289497i	$-0.00921627\pi$
$127$	5.34981	+	9.26615i	0.474719	+	0.822238i	−0.524862	+	0.851188i	$0.675883\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−6.58217	−	11.4007i	−0.577295	−	0.999904i
$131$	−2.41164			−0.210706			−0.105353	−	0.994435i	$-0.533597\pi$
$131$	−2.41164			−0.210706			−0.105353	+	0.994435i	$0.533597\pi$
$132$		0			0
$133$	−8.41892			−0.730013
$134$	1.57234	−	8.03292i	0.135830	−	0.693938i
$135$		0			0
$136$	1.34981	−	2.33795i	0.115746	−	0.200477i
$137$	21.9876			1.87853			0.939265	−	0.343194i	$-0.111509\pi$
$137$	21.9876			1.87853			0.939265	+	0.343194i	$0.111509\pi$
$138$		0			0
$139$	−17.9418			−1.52181			−0.760903	−	0.648866i	$-0.775244\pi$
$139$	−17.9418			−1.52181			−0.760903	+	0.648866i	$0.775244\pi$
$140$	1.50000	−	2.59808i	0.126773	−	0.219578i
$141$		0			0
$142$	0.143307			0.0120261
$143$	−7.20286			−0.602334
$144$		0			0
$145$	2.93818	+	5.08907i	0.244002	+	0.422625i
$146$	−5.78799	−	10.0251i	−0.479018	−	0.829683i
$147$		0			0
$148$	−3.28799			−0.270271
$149$	−11.9542			−0.979326			−0.489663	−	0.871912i	$-0.662880\pi$
$149$	−11.9542			−0.979326			−0.489663	+	0.871912i	$0.662880\pi$
$150$		0			0
$151$	−0.323272	+	0.559924i	−0.0263075	+	0.0455659i	−0.878879	−	0.477044i	$-0.841708\pi$
$151$	−0.323272	+	0.559924i	−0.0263075	+	0.0455659i	0.852572	+	0.522610i	$0.175042\pi$
$152$	−3.78799	+	6.56099i	−0.307247	+	0.532167i
$153$		0			0
$154$	−0.820724	−	1.42154i	−0.0661358	−	0.114551i
$155$	2.44437	+	4.23377i	0.196336	+	0.340065i
$156$		0			0
$157$	10.4320	−	18.0687i	0.832563	−	1.44204i	−0.0634357	−	0.997986i	$-0.520206\pi$
$157$	10.4320	−	18.0687i	0.832563	−	1.44204i	0.895999	−	0.444056i	$-0.146461\pi$
$158$	−7.76509			−0.617758
$159$		0			0
$160$	−1.34981	−	2.33795i	−0.106712	−	0.184831i
$161$	0.777472			0.0612734
$162$		0			0
$163$	10.1218	+	17.5314i	0.792799	+	1.37317i	0.924227	+	0.381843i	$0.124711\pi$
$163$	10.1218	+	17.5314i	0.792799	+	1.37317i	−0.131428	+	0.991326i	$0.541956\pi$
$164$	2.89926	−	5.02166i	0.226394	−	0.392126i
$165$		0			0
$166$	5.75526	+	9.96840i	0.446695	+	0.773698i
$167$	−9.20327	−	15.9405i	−0.712170	−	1.23352i	−0.964041	−	0.265754i	$-0.914379\pi$
$167$	−9.20327	−	15.9405i	−0.712170	−	1.23352i	0.251870	−	0.967761i	$-0.418954\pi$
$168$		0			0
$169$	−5.38942	−	9.33476i	−0.414571	−	0.718058i
$170$	3.64400	+	6.31159i	0.279482	+	0.484077i
$171$		0			0
$172$	0.682918	+	1.18285i	0.0520720	+	0.0901913i
$173$	4.32072	−	7.48371i	0.328499	−	0.568976i	−0.653716	−	0.756740i	$-0.726791\pi$
$173$	4.32072	−	7.48371i	0.328499	−	0.568976i	0.982214	+	0.187764i	$0.0601241\pi$
$174$		0			0
$175$	1.27128	+	2.20192i	0.0960999	+	0.166450i
$176$	−1.47710			−0.111341
$177$		0			0
$178$	2.73855	−	4.74331i	0.205263	−	0.355526i
$179$	11.9876			0.895997			0.447998	−	0.894034i	$-0.352137\pi$
$179$	11.9876			0.895997			0.447998	+	0.894034i	$0.352137\pi$
$180$		0			0
$181$	−1.11745	−	1.93549i	−0.0830597	−	0.143864i	0.821503	−	0.570204i	$-0.193136\pi$
$181$	−1.11745	−	1.93549i	−0.0830597	−	0.143864i	−0.904563	+	0.426340i	$0.859803\pi$
$182$	2.70946	−	4.69292i	0.200839	−	0.347863i
$183$		0			0
$184$	0.349814	−	0.605896i	0.0257886	−	0.0446672i
$185$	4.43818	−	7.68715i	0.326301	−	0.565171i
$186$		0			0
$187$	3.98762			0.291604
$188$	2.49381	−	4.31941i	0.181880	−	0.315025i
$189$		0			0
$190$	−10.2262	−	17.7122i	−0.741884	−	1.28498i
$191$	1.86584	−	3.23172i	0.135007	−	0.233839i	−0.790593	−	0.612342i	$-0.790228\pi$
$191$	1.86584	−	3.23172i	0.135007	−	0.233839i	0.925600	+	0.378503i	$0.123561\pi$
$192$		0			0
$193$	11.1643			0.803627			0.401814	−	0.915721i	$-0.368380\pi$
$193$	11.1643			0.803627			0.401814	+	0.915721i	$0.368380\pi$
$194$	5.71634	+	9.90099i	0.410409	+	0.710850i
$195$		0			0
$196$	−5.76509			−0.411792
$197$	−11.3374	−	19.6370i	−0.807759	−	1.39908i	−0.914413	−	0.404783i	$-0.867347\pi$
$197$	−11.3374	−	19.6370i	−0.807759	−	1.39908i	0.106654	−	0.994296i	$-0.465986\pi$
$198$		0			0
$199$	4.50000	−	7.79423i	0.318997	−	0.552518i	−0.661282	−	0.750137i	$-0.729987\pi$
$199$	4.50000	−	7.79423i	0.318997	−	0.552518i	0.980279	+	0.197619i	$0.0633208\pi$
$200$	2.28799			0.161785
$201$		0			0
$202$	5.28799			0.372062
$203$	−1.20946	+	2.09485i	−0.0848874	+	0.147029i
$204$		0			0
$205$	7.82691	+	13.5566i	0.546655	+	0.946835i
$206$	−14.0741			−0.980591
$207$		0			0
$208$	−2.43818	−	4.22305i	−0.169057	−	0.292816i
$209$	−11.1905			−0.774062
$210$		0			0
$211$	−9.98762	+	17.2991i	−0.687576	+	1.19092i	0.285044	+	0.958515i	$0.407992\pi$
$211$	−9.98762	+	17.2991i	−0.687576	+	1.19092i	−0.972620	+	0.232402i	$0.925341\pi$
$212$	−1.25526	−	2.17417i	−0.0862116	−	0.149323i
$213$		0			0
$214$	4.78799	−	8.29305i	0.327300	−	0.566901i
$215$	−3.68725			−0.251468
$216$		0			0
$217$	−1.00619	+	1.74277i	−0.0683046	+	0.118307i
$218$	6.66071	−	11.5367i	0.451120	−	0.781363i
$219$		0			0
$220$	1.99381	−	3.45338i	0.134423	−	0.232827i
$221$	6.58217	+	11.4007i	0.442765	+	0.766891i
$222$		0			0
$223$	16.9963			1.13816			0.569078	−	0.822284i	$-0.307300\pi$
$223$	16.9963			1.13816			0.569078	+	0.822284i	$0.307300\pi$
$224$	0.555632	−	0.962383i	0.0371247	−	0.0643019i
$225$		0			0
$226$	−14.9222			−0.992607
$227$	−5.03342	−	8.71814i	−0.334080	−	0.578643i	0.649228	−	0.760594i	$-0.275092\pi$
$227$	−5.03342	−	8.71814i	−0.334080	−	0.578643i	−0.983308	+	0.181951i	$0.941759\pi$
$228$		0			0
$229$	11.4382	−	19.8115i	0.755856	−	1.30918i	−0.189092	−	0.981959i	$-0.560554\pi$
$229$	11.4382	−	19.8115i	0.755856	−	1.30918i	0.944948	−	0.327222i	$-0.106112\pi$
$230$	0.944368	+	1.63569i	0.0622698	+	0.107854i
$231$		0			0
$232$	1.08836	+	1.88510i	0.0714546	+	0.123763i
$233$	−11.4425	−	19.8190i	−0.749624	−	1.29839i	−0.948003	−	0.318261i	$-0.896901\pi$
$233$	−11.4425	−	19.8190i	−0.749624	−	1.29839i	0.198379	−	0.980125i	$-0.436432\pi$
$234$		0			0
$235$	6.73236	+	11.6608i	0.439171	+	0.760666i
$236$	−3.66071	−	6.34053i	−0.238292	−	0.412733i
$237$		0			0
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	9.47524	+	16.4116i	0.612902	+	1.06158i	0.990749	+	0.135710i	$0.0433314\pi$
$239$	9.47524	+	16.4116i	0.612902	+	1.06158i	−0.377846	+	0.925868i	$0.623335\pi$
$240$		0			0
$241$	−11.3745			−0.732696			−0.366348	−	0.930478i	$-0.619392\pi$
$241$	−11.3745			−0.732696			−0.366348	+	0.930478i	$0.619392\pi$
$242$	4.40909	+	7.63676i	0.283427	+	0.490910i
$243$		0			0
$244$	−5.87636			−0.376195
$245$	7.78180	−	13.4785i	0.497161	−	0.861108i
$246$		0			0
$247$	−18.4716	−	31.9937i	−1.17532	−	2.03571i
$248$	0.905446	+	1.56828i	0.0574959	+	0.0995858i
$249$		0			0
$250$	3.66071	−	6.34053i	0.231523	−	0.401010i
$251$	6.17742	−	10.6996i	0.389915	−	0.675353i	−0.602523	−	0.798102i	$-0.705838\pi$
$251$	6.17742	−	10.6996i	0.389915	−	0.675353i	0.992438	+	0.122749i	$0.0391710\pi$
$252$		0			0
$253$	1.03342			0.0649706
$254$	−10.6996			−0.671354
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.117454	+	0.203436i	0.00732658	+	0.0126900i	0.869665	−	0.493642i	$-0.164335\pi$
$257$	0.117454	+	0.203436i	0.00732658	+	0.0126900i	−0.862339	+	0.506332i	$0.831001\pi$
$258$		0			0
$259$	3.65383			0.227038
$260$	13.1643			0.816418
$261$		0			0
$262$	1.20582	−	2.08854i	0.0744957	−	0.129030i
$263$	12.1185			0.747262			0.373631	−	0.927577i	$-0.378113\pi$
$263$	12.1185			0.747262			0.373631	+	0.927577i	$0.378113\pi$
$264$		0			0
$265$	6.77747			0.416337
$266$	4.20946	−	7.29100i	0.258099	−	0.447040i
$267$		0			0
$268$	6.17054	+	5.37815i	0.376926	+	0.328523i
$269$	18.7861			1.14541			0.572705	−	0.819761i	$-0.305894\pi$
$269$	18.7861			1.14541			0.572705	+	0.819761i	$0.305894\pi$
$270$		0			0
$271$	−23.0531			−1.40038			−0.700188	−	0.713959i	$-0.746900\pi$
$271$	−23.0531			−1.40038			−0.700188	+	0.713959i	$0.746900\pi$
$272$	1.34981	+	2.33795i	0.0818445	+	0.141759i
$273$		0			0
$274$	−10.9938	+	19.0418i	−0.664160	+	1.15036i
$275$	1.68980	+	2.92681i	0.101899	+	0.176493i
$276$		0			0
$277$	28.1840			1.69341			0.846707	−	0.532060i	$-0.178582\pi$
$277$	28.1840			1.69341			0.846707	+	0.532060i	$0.178582\pi$
$278$	8.97091	−	15.5381i	0.538039	−	0.931912i
$279$		0			0
$280$	1.50000	+	2.59808i	0.0896421	+	0.155265i
$281$	4.11559	−	7.12842i	0.245516	−	0.425246i	−0.716761	−	0.697319i	$-0.754376\pi$
$281$	4.11559	−	7.12842i	0.245516	−	0.425246i	0.962277	+	0.272073i	$0.0877093\pi$
$282$		0			0
$283$	−4.83922			−0.287662			−0.143831	−	0.989602i	$-0.545942\pi$
$283$	−4.83922			−0.287662			−0.143831	+	0.989602i	$0.545942\pi$
$284$	−0.0716537	+	0.124108i	−0.00425186	+	0.00736444i
$285$		0			0
$286$	3.60143	−	6.23786i	0.212957	−	0.368853i
$287$	−3.22184	+	5.58039i	−0.190179	+	0.329400i
$288$		0			0
$289$	4.85600	+	8.41085i	0.285647	+	0.494756i
$290$	−5.87636			−0.345072
$291$		0			0
$292$	11.5760			0.677433
$293$	17.8960			1.04550			0.522748	−	0.852487i	$-0.324907\pi$
$293$	17.8960			1.04550			0.522748	+	0.852487i	$0.324907\pi$
$294$		0			0
$295$	19.7651			1.15077
$296$	1.64400	−	2.84748i	0.0955553	−	0.165507i
$297$		0			0
$298$	5.97710	−	10.3526i	0.346244	−	0.599712i
$299$	1.70582	+	2.95456i	0.0986500	+	0.170867i
$300$		0			0
$301$	−0.758902	−	1.31446i	−0.0437424	−	0.0757640i
$302$	−0.323272	−	0.559924i	−0.0186022	−	0.0322200i
$303$		0			0
$304$	−3.78799	−	6.56099i	−0.217256	−	0.376299i
$305$	7.93199	−	13.7386i	0.454184	−	0.786670i
$306$		0			0
$307$	8.51671	−	14.7514i	0.486074	−	0.841905i	−0.513798	−	0.857911i	$-0.671762\pi$
$307$	8.51671	−	14.7514i	0.486074	−	0.841905i	0.999872	+	0.0160060i	$0.00509509\pi$
$308$	1.64145			0.0935302
$309$		0			0
$310$	−4.88874			−0.277662
$311$	−11.9294			−0.676456			−0.338228	−	0.941064i	$-0.609828\pi$
$311$	−11.9294			−0.676456			−0.338228	+	0.941064i	$0.609828\pi$
$312$		0			0
$313$	−8.78985			−0.496832			−0.248416	−	0.968653i	$-0.579910\pi$
$313$	−8.78985			−0.496832			−0.248416	+	0.968653i	$0.579910\pi$
$314$	10.4320	+	18.0687i	0.588711	+	1.01968i
$315$		0			0
$316$	3.88255	−	6.72477i	0.218410	−	0.378298i
$317$	14.4462	−	25.0215i	0.811377	−	1.40535i	−0.100524	−	0.994935i	$-0.532052\pi$
$317$	14.4462	−	25.0215i	0.811377	−	1.40535i	0.911901	−	0.410411i	$-0.134615\pi$
$318$		0			0
$319$	−1.60762	+	2.78448i	−0.0900096	+	0.155901i
$320$	2.69963			0.150914
$321$		0			0
$322$	−0.388736	+	0.673310i	−0.0216634	+	0.0375221i
$323$	10.2262	+	17.7122i	0.568999	+	0.985536i
$324$		0			0
$325$	−5.57853	+	9.66230i	−0.309441	+	0.535968i
$326$	−20.2436			−1.12119
$327$		0			0
$328$	2.89926	+	5.02166i	0.160085	+	0.277275i
$329$	−2.77128	+	4.80000i	−0.152786	+	0.264633i
$330$		0			0
$331$	−14.0371	−	24.3129i	−0.771547	−	1.33636i	−0.936715	−	0.350093i	$-0.886150\pi$
$331$	−14.0371	−	24.3129i	−0.771547	−	1.33636i	0.165168	−	0.986265i	$-0.447183\pi$
$332$	−11.5105			−0.631722
$333$		0			0
$334$	18.4065			1.00716
$335$	−20.9029	+	7.16689i	−1.14205	+	0.391569i
$336$		0			0
$337$	−6.25093	+	10.8269i	−0.340510	+	0.589780i	−0.984527	−	0.175230i	$-0.943933\pi$
$337$	−6.25093	+	10.8269i	−0.340510	+	0.589780i	0.644018	+	0.765011i	$0.277266\pi$
$338$	10.7788			0.586292
$339$		0			0
$340$	−7.28799			−0.395247
$341$	−1.33743	+	2.31650i	−0.0724261	+	0.125446i
$342$		0			0
$343$	14.1854			0.765939
$344$	−1.36584			−0.0736409
$345$		0			0
$346$	4.32072	+	7.48371i	0.232284	+	0.402327i
$347$	11.0247	+	19.0953i	0.591836	+	1.02509i	0.993985	+	0.109516i	$0.0349300\pi$
$347$	11.0247	+	19.0953i	0.591836	+	1.02509i	−0.402149	+	0.915574i	$0.631737\pi$
$348$		0			0
$349$	−7.94692			−0.425389			−0.212694	−	0.977119i	$-0.568224\pi$
$349$	−7.94692			−0.425389			−0.212694	+	0.977119i	$0.568224\pi$
$350$	−2.54256			−0.135906
$351$		0			0
$352$	0.738550	−	1.27921i	0.0393648	−	0.0681819i
$353$	9.64214	−	16.7007i	0.513199	−	0.888887i	−0.486684	−	0.873578i	$-0.661794\pi$
$353$	9.64214	−	16.7007i	0.513199	−	0.888887i	0.999883	−	0.0153087i	$-0.00487311\pi$
$354$		0			0
$355$	−0.193438	−	0.335045i	−0.0102666	−	0.0177823i
$356$	2.73855	+	4.74331i	0.145143	+	0.251395i
$357$		0			0
$358$	−5.99381	+	10.3816i	−0.316783	+	0.548684i
$359$	−1.64145			−0.0866323			−0.0433162	−	0.999061i	$-0.513792\pi$
$359$	−1.64145			−0.0866323			−0.0433162	+	0.999061i	$0.513792\pi$
$360$		0			0
$361$	−19.1978	−	33.2515i	−1.01041	−	1.75008i
$362$	2.23491			0.117464
$363$		0			0
$364$	2.70946	+	4.69292i	0.142014	+	0.245976i
$365$	−15.6254	+	27.0640i	−0.817872	+	1.41660i
$366$		0			0
$367$	−3.11559	−	5.39637i	−0.162633	−	0.281688i	0.773179	−	0.634187i	$-0.218665\pi$
$367$	−3.11559	−	5.39637i	−0.162633	−	0.281688i	−0.935812	+	0.352499i	$0.885332\pi$
$368$	0.349814	+	0.605896i	0.0182353	+	0.0315845i
$369$		0			0
$370$	4.43818	+	7.68715i	0.230730	+	0.399636i
$371$	1.39493	+	2.41608i	0.0724209	+	0.125437i
$372$		0			0
$373$	−10.3214	−	17.8772i	−0.534422	−	0.925647i	−0.999191	−	0.0402147i	$-0.987196\pi$
$373$	−10.3214	−	17.8772i	−0.534422	−	0.925647i	0.464769	−	0.885432i	$-0.346138\pi$
$374$	−1.99381	+	3.45338i	−0.103097	+	0.178570i
$375$		0			0
$376$	2.49381	+	4.31941i	0.128608	+	0.222756i
$377$	−10.6145			−0.546675
$378$		0			0
$379$	17.6804	−	30.6233i	0.908180	−	1.57301i	0.0915883	−	0.995797i	$-0.470806\pi$
$379$	17.6804	−	30.6233i	0.908180	−	1.57301i	0.816591	−	0.577216i	$-0.195861\pi$
$380$	20.4523			1.04918
$381$		0			0
$382$	1.86584	+	3.23172i	0.0954645	+	0.165349i
$383$	−5.63162	+	9.75425i	−0.287762	+	0.498419i	−0.973275	−	0.229642i	$-0.926245\pi$
$383$	−5.63162	+	9.75425i	−0.287762	+	0.498419i	0.685513	+	0.728060i	$0.259578\pi$
$384$		0			0
$385$	−2.21565	+	3.83762i	−0.112920	+	0.195583i
$386$	−5.58217	+	9.66861i	−0.284125	+	0.492119i
$387$		0			0
$388$	−11.4327			−0.580406
$389$	−13.2040	+	22.8699i	−0.669467	+	1.15955i	0.308586	+	0.951196i	$0.400144\pi$
$389$	−13.2040	+	22.8699i	−0.669467	+	1.15955i	−0.978053	+	0.208355i	$0.933189\pi$
$390$		0			0
$391$	−0.944368	−	1.63569i	−0.0477587	−	0.0827206i
$392$	2.88255	−	4.99272i	0.145591	−	0.252170i
$393$		0			0
$394$	22.6749			1.14234
$395$	10.4814	+	18.1544i	0.527378	+	0.913445i
$396$		0			0
$397$	−3.55632			−0.178487			−0.0892433	−	0.996010i	$-0.528445\pi$
$397$	−3.55632			−0.178487			−0.0892433	+	0.996010i	$0.528445\pi$
$398$	4.50000	+	7.79423i	0.225565	+	0.390689i
$399$		0			0
$400$	−1.14400	+	1.98146i	−0.0571998	+	0.0990730i
$401$	−34.5709			−1.72639			−0.863194	−	0.504873i	$-0.831539\pi$
$401$	−34.5709			−1.72639			−0.863194	+	0.504873i	$0.831539\pi$
$402$		0			0
$403$	−8.83056			−0.439881
$404$	−2.64400	+	4.57954i	−0.131544	+	0.227840i
$405$		0			0
$406$	−1.20946	−	2.09485i	−0.0600245	−	0.103965i
$407$	4.85669			0.240737
$408$		0			0
$409$	−1.87017	−	3.23922i	−0.0924738	−	0.160169i	0.816078	−	0.577942i	$-0.196144\pi$
$409$	−1.87017	−	3.23922i	−0.0924738	−	0.160169i	−0.908551	+	0.417773i	$0.862811\pi$
$410$	−15.6538			−0.773087
$411$		0			0
$412$	7.03706	−	12.1885i	0.346691	−	0.600487i
$413$	4.06801	+	7.04600i	0.200174	+	0.346711i
$414$		0			0
$415$	15.5371	−	26.9110i	0.762684	−	1.32101i
$416$	4.87636			0.239083
$417$		0			0
$418$	5.59524	−	9.69124i	0.273672	−	0.474014i
$419$	1.28985	−	2.23409i	0.0630134	−	0.109142i	−0.832798	−	0.553578i	$-0.813262\pi$
$419$	1.28985	−	2.23409i	0.0630134	−	0.109142i	0.895811	+	0.444435i	$0.146596\pi$
$420$		0			0
$421$	−4.74976	+	8.22682i	−0.231489	+	0.400951i	−0.958247	−	0.285943i	$-0.907693\pi$
$421$	−4.74976	+	8.22682i	−0.231489	+	0.400951i	0.726757	+	0.686894i	$0.241026\pi$
$422$	−9.98762	−	17.2991i	−0.486190	−	0.842105i
$423$		0			0
$424$	2.51052			0.121922
$425$	3.08836	−	5.34920i	0.149808	−	0.259474i
$426$		0			0
$427$	6.53018			0.316018
$428$	4.78799	+	8.29305i	0.231436	+	0.400859i
$429$		0			0
$430$	1.84362	−	3.19325i	0.0889075	−	0.153992i
$431$	−0.855315	−	1.48145i	−0.0411991	−	0.0713589i	0.844691	−	0.535255i	$-0.179784\pi$
$431$	−0.855315	−	1.48145i	−0.0411991	−	0.0713589i	−0.885890	+	0.463896i	$0.846451\pi$
$432$		0			0
$433$	9.91961	+	17.1813i	0.476706	+	0.825679i	0.999644	−	0.0266919i	$-0.00849732\pi$
$433$	9.91961	+	17.1813i	0.476706	+	0.825679i	−0.522938	+	0.852371i	$0.675164\pi$
$434$	−1.00619	−	1.74277i	−0.0482987	−	0.0836557i
$435$		0			0
$436$	6.66071	+	11.5367i	0.318990	+	0.552507i
$437$	2.65019	+	4.59026i	0.126776	+	0.219582i
$438$		0			0
$439$	7.53706	−	13.0546i	0.359724	−	0.623061i	−0.628190	−	0.778060i	$-0.716204\pi$
$439$	7.53706	−	13.0546i	0.359724	−	0.623061i	0.987915	+	0.154999i	$0.0495374\pi$
$440$	1.99381	+	3.45338i	0.0950512	+	0.164633i
$441$		0			0
$442$	−13.1643			−0.626164
$443$	−20.7341	−	35.9126i	−0.985109	−	1.70626i	−0.641452	−	0.767163i	$-0.721668\pi$
$443$	−20.7341	−	35.9126i	−0.985109	−	1.70626i	−0.343657	−	0.939095i	$-0.611666\pi$
$444$		0			0
$445$	−14.7861			−0.700930
$446$	−8.49814	+	14.7192i	−0.402399	+	0.696975i
$447$		0			0
$448$	0.555632	+	0.962383i	0.0262511	+	0.0454683i
$449$	−2.11745	−	3.66754i	−0.0999288	−	0.173082i	0.811726	−	0.584038i	$-0.198528\pi$
$449$	−2.11745	−	3.66754i	−0.0999288	−	0.173082i	−0.911655	+	0.410956i	$0.865195\pi$
$450$		0			0
$451$	−4.28249	+	7.41749i	−0.201655	+	0.349276i
$452$	7.46108	−	12.9230i	0.350940	−	0.607845i
$453$		0			0
$454$	10.0668			0.472460
$455$	−14.6291			−0.685821
$456$		0			0
$457$	−7.77197	−	13.4614i	−0.363557	−	0.629700i	0.624986	−	0.780636i	$-0.285105\pi$
$457$	−7.77197	−	13.4614i	−0.363557	−	0.629700i	−0.988544	+	0.150936i	$0.951771\pi$
$458$	11.4382	+	19.8115i	0.534471	+	0.925731i
$459$		0			0
$460$	−1.88874			−0.0880628
$461$	−17.0617			−0.794645			−0.397322	−	0.917679i	$-0.630061\pi$
$461$	−17.0617			−0.794645			−0.397322	+	0.917679i	$0.630061\pi$
$462$		0			0
$463$	−13.9691	+	24.1951i	−0.649197	+	1.12444i	0.334118	+	0.942531i	$0.391562\pi$
$463$	−13.9691	+	24.1951i	−0.649197	+	1.12444i	−0.983315	+	0.181911i	$0.941772\pi$
$464$	−2.17673			−0.101052
$465$		0			0
$466$	22.8850			1.06013
$467$	−12.0167	+	20.8136i	−0.556067	+	0.963136i	0.441753	+	0.897137i	$0.354357\pi$
$467$	−12.0167	+	20.8136i	−0.556067	+	0.963136i	−0.997820	+	0.0659995i	$0.978976\pi$
$468$		0			0
$469$	−6.85710	−	5.97654i	−0.316631	−	0.275971i
$470$	−13.4647			−0.621081
$471$		0			0
$472$	7.32141			0.336995
$473$	−1.00874	−	1.74719i	−0.0463818	−	0.0803357i
$474$		0			0
$475$	−8.66690	+	15.0115i	−0.397664	+	0.688775i
$476$	−1.50000	−	2.59808i	−0.0687524	−	0.119083i
$477$		0			0
$478$	−18.9505			−0.866775
$479$	18.7942	−	32.5525i	0.858728	−	1.48736i	−0.0144147	−	0.999896i	$-0.504588\pi$
$479$	18.7942	−	32.5525i	0.858728	−	1.48736i	0.873143	−	0.487465i	$-0.162078\pi$
$480$		0			0
$481$	8.01671	+	13.8853i	0.365531	+	0.633117i
$482$	5.68725	−	9.85060i	0.259047	−	0.448683i
$483$		0			0
$484$	−8.81818			−0.400826
$485$	15.4320	−	26.7290i	0.700730	−	1.21370i
$486$		0			0
$487$	3.52723	−	6.10934i	0.159834	−	0.276841i	−0.774975	−	0.631992i	$-0.782237\pi$
$487$	3.52723	−	6.10934i	0.159834	−	0.276841i	0.934809	+	0.355152i	$0.115571\pi$
$488$	2.93818	−	5.08907i	0.133005	−	0.230372i
$489$		0			0
$490$	7.78180	+	13.4785i	0.351546	+	0.608896i
$491$	4.21881			0.190392			0.0951961	−	0.995459i	$-0.469652\pi$
$491$	4.21881			0.190392			0.0951961	+	0.995459i	$0.469652\pi$
$492$		0			0
$493$	5.87636			0.264658
$494$	36.9432			1.66215
$495$		0			0
$496$	−1.81089			−0.0813115
$497$	0.0796262	−	0.137917i	0.00357172	−	0.00618640i
$498$		0			0
$499$	−5.03706	+	8.72445i	−0.225490	+	0.390560i	−0.956466	−	0.291843i	$-0.905732\pi$
$499$	−5.03706	+	8.72445i	−0.225490	+	0.390560i	0.730976	+	0.682403i	$0.239065\pi$
$500$	3.66071	+	6.34053i	0.163712	+	0.283557i
$501$		0			0
$502$	6.17742	+	10.6996i	0.275712	+	0.477546i
$503$	−6.99312	−	12.1124i	−0.311808	−	0.540067i	0.666946	−	0.745106i	$-0.267601\pi$
$503$	−6.99312	−	12.1124i	−0.311808	−	0.540067i	−0.978754	+	0.205039i	$0.934268\pi$
$504$		0			0
$505$	−7.13781	−	12.3630i	−0.317628	−	0.550148i
$506$	−0.516710	+	0.894969i	−0.0229706	+	0.0397862i
$507$		0			0
$508$	5.34981	−	9.26615i	0.237360	−	0.411119i
$509$	−31.4944			−1.39597			−0.697983	−	0.716114i	$-0.745919\pi$
$509$	−31.4944			−1.39597			−0.697983	+	0.716114i	$0.745919\pi$
$510$		0			0
$511$	−12.8640			−0.569069
$512$	1.00000			0.0441942
$513$		0			0
$514$	−0.234908			−0.0103613
$515$	18.9975	+	32.9046i	0.837128	+	1.44995i
$516$		0			0
$517$	−3.68361	+	6.38019i	−0.162005	+	0.280601i
$518$	−1.82691	+	3.16431i	−0.0802700	+	0.139032i
$519$		0			0
$520$	−6.58217	+	11.4007i	−0.288647	+	0.499952i
$521$	40.6822			1.78232			0.891159	−	0.453692i	$-0.149893\pi$
$521$	40.6822			1.78232			0.891159	+	0.453692i	$0.149893\pi$
$522$		0			0
$523$	−18.4010	+	31.8715i	−0.804621	+	1.39364i	0.111925	+	0.993717i	$0.464298\pi$
$523$	−18.4010	+	31.8715i	−0.804621	+	1.39364i	−0.916546	+	0.399928i	$0.869035\pi$
$524$	1.20582	+	2.08854i	0.0526764	+	0.0912382i
$525$		0			0
$526$	−6.05927	+	10.4950i	−0.264197	+	0.457602i
$527$	4.88874			0.212957
$528$		0			0
$529$	11.2553	+	19.4947i	0.489359	+	0.847595i
$530$	−3.38874	+	5.86946i	−0.147197	+	0.254953i
$531$		0			0
$532$	4.20946	+	7.29100i	0.182503	+	0.316105i
$533$	−28.2756			−1.22475
$534$		0			0
$535$	−25.8516			−1.11766
$536$	−7.74288	+	2.65477i	−0.334441	+	0.114669i
$537$		0			0
$538$	−9.39307	+	16.2693i	−0.404964	+	0.701418i
$539$	8.51562			0.366794
$540$		0			0
$541$	2.65521			0.114156			0.0570781	−	0.998370i	$-0.481822\pi$
$541$	2.65521			0.114156			0.0570781	+	0.998370i	$0.481822\pi$
$542$	11.5265	−	19.9646i	0.495107	−	0.857551i
$543$		0			0
$544$	−2.69963			−0.115746
$545$	−35.9629			−1.54048
$546$		0			0
$547$	−15.2651	−	26.4399i	−0.652688	−	1.13049i	−0.982468	−	0.186431i	$-0.940308\pi$
$547$	−15.2651	−	26.4399i	−0.652688	−	1.13049i	0.329780	−	0.944058i	$-0.393025\pi$
$548$	−10.9938	−	19.0418i	−0.469632	−	0.813427i
$549$		0			0
$550$	−3.37959			−0.144106
$551$	−16.4909			−0.702534
$552$		0			0
$553$	−4.31453	+	7.47299i	−0.183473	+	0.317784i
$554$	−14.0920	+	24.4081i	−0.598712	+	1.03700i
$555$		0			0
$556$	8.97091	+	15.5381i	0.380451	+	0.658961i
$557$	−3.90978	−	6.77193i	−0.165663	−	0.286936i	0.771228	−	0.636559i	$-0.219643\pi$
$557$	−3.90978	−	6.77193i	−0.165663	−	0.286936i	−0.936890	+	0.349623i	$0.886310\pi$
$558$		0			0
$559$	3.33015	−	5.76799i	0.140850	−	0.243960i
$560$	−3.00000			−0.126773
$561$		0			0
$562$	4.11559	+	7.12842i	0.173606	+	0.300694i
$563$	−14.3017			−0.602747			−0.301373	−	0.953506i	$-0.597445\pi$
$563$	−14.3017			−0.602747			−0.301373	+	0.953506i	$0.597445\pi$
$564$		0			0
$565$	20.1421	+	34.8872i	0.847386	+	1.46772i
$566$	2.41961	−	4.19088i	0.101704	−	0.176156i
$567$		0			0
$568$	−0.0716537	−	0.124108i	−0.00300652	−	0.00520745i
$569$	6.98074	+	12.0910i	0.292648	+	0.506881i	0.974435	−	0.224670i	$-0.0721303\pi$
$569$	6.98074	+	12.0910i	0.292648	+	0.506881i	−0.681787	+	0.731551i	$0.738797\pi$
$570$		0			0
$571$	1.24543	+	2.15715i	0.0521196	+	0.0902737i	0.890908	−	0.454184i	$-0.150069\pi$
$571$	1.24543	+	2.15715i	0.0521196	+	0.0902737i	−0.838789	+	0.544457i	$0.816736\pi$
$572$	3.60143	+	6.23786i	0.150583	+	0.260818i
$573$		0			0
$574$	−3.22184	−	5.58039i	−0.134477	−	0.232921i
$575$	0.800372	−	1.38628i	0.0333778	−	0.0578121i
$576$		0			0
$577$	−19.1964	−	33.2491i	−0.799156	−	1.38418i	−0.920166	−	0.391528i	$-0.871947\pi$
$577$	−19.1964	−	33.2491i	−0.799156	−	1.38418i	0.121010	−	0.992651i	$-0.461387\pi$
$578$	−9.71201			−0.403966
$579$		0			0
$580$	2.93818	−	5.08907i	0.122001	−	0.211312i
$581$	12.7912			0.530670
$582$		0			0
$583$	1.85414	+	3.21147i	0.0767908	+	0.133006i
$584$	−5.78799	+	10.0251i	−0.239509	+	0.414841i
$585$		0			0
$586$	−8.94801	+	15.4984i	−0.369639	+	0.640233i
$587$	21.7138	−	37.6094i	0.896224	−	1.55231i	0.0639417	−	0.997954i	$-0.479633\pi$
$587$	21.7138	−	37.6094i	0.896224	−	1.55231i	0.832282	−	0.554352i	$-0.187034\pi$
$588$		0			0
$589$	−13.7193			−0.565294
$590$	−9.88255	+	17.1171i	−0.406858	+	0.704699i
$591$		0			0
$592$	1.64400	+	2.84748i	0.0675678	+	0.117031i
$593$	16.7101	−	28.9428i	0.686204	−	1.18854i	−0.286853	−	0.957974i	$-0.592609\pi$
$593$	16.7101	−	28.9428i	0.686204	−	1.18854i	0.973057	−	0.230565i	$-0.0740574\pi$
$594$		0			0
$595$	8.09888			0.332022
$596$	5.97710	+	10.3526i	0.244832	+	0.424061i
$597$		0			0
$598$	−3.41164			−0.139512
$599$	−9.11422	−	15.7863i	−0.372397	−	0.645010i	0.617537	−	0.786542i	$-0.288131\pi$
$599$	−9.11422	−	15.7863i	−0.372397	−	0.645010i	−0.989934	+	0.141532i	$0.954797\pi$
$600$		0			0
$601$	−3.21379	+	5.56645i	−0.131093	+	0.227060i	−0.924098	−	0.382155i	$-0.875182\pi$
$601$	−3.21379	+	5.56645i	−0.131093	+	0.227060i	0.793005	+	0.609215i	$0.208515\pi$
$602$	1.51780			0.0618611
$603$		0			0
$604$	0.646544			0.0263075
$605$	11.9029	−	20.6164i	0.483922	−	0.838177i
$606$		0			0
$607$	17.9876	+	31.1555i	0.730095	+	1.26456i	0.956842	+	0.290608i	$0.0938575\pi$
$607$	17.9876	+	31.1555i	0.730095	+	1.26456i	−0.226747	+	0.973954i	$0.572809\pi$
$608$	7.57598			0.307247
$609$		0			0
$610$	7.93199	+	13.7386i	0.321157	+	0.556260i
$611$	−24.3214			−0.983939
$612$		0			0
$613$	−8.83675	+	15.3057i	−0.356913	+	0.618191i	−0.987443	−	0.157973i	$-0.949504\pi$
$613$	−8.83675	+	15.3057i	−0.356913	+	0.618191i	0.630531	+	0.776164i	$0.282837\pi$
$614$	8.51671	+	14.7514i	0.343706	+	0.595317i
$615$		0			0
$616$	−0.820724	+	1.42154i	−0.0330679	+	0.0572753i
$617$	38.2632			1.54042			0.770210	−	0.637791i	$-0.220151\pi$
$617$	38.2632			1.54042			0.770210	+	0.637791i	$0.220151\pi$
$618$		0			0
$619$	−12.8709	+	22.2930i	−0.517323	+	0.896030i	0.482474	+	0.875910i	$0.339738\pi$
$619$	−12.8709	+	22.2930i	−0.517323	+	0.896030i	−0.999798	+	0.0201201i	$0.993595\pi$
$620$	2.44437	−	4.23377i	0.0981682	−	0.170032i
$621$		0			0
$622$	5.96472	−	10.3312i	0.239163	−	0.414243i
$623$	−3.04325	−	5.27107i	−0.121925	−	0.211181i
$624$		0			0
$625$	−31.2051			−1.24820
$626$	4.39493	−	7.61223i	0.175657	−	0.304246i
$627$		0			0
$628$	−20.8640			−0.832563
$629$	−4.43818	−	7.68715i	−0.176962	−	0.306507i
$630$		0			0
$631$	4.33310	−	7.50516i	0.172498	−	0.298776i	−0.766794	−	0.641893i	$-0.778149\pi$
$631$	4.33310	−	7.50516i	0.172498	−	0.298776i	0.939293	+	0.343117i	$0.111483\pi$
$632$	3.88255	+	6.72477i	0.154439	+	0.267497i
$633$		0			0
$634$	14.4462	+	25.0215i	0.573730	+	0.993729i
$635$	14.4425	+	25.0152i	0.573133	+	0.992696i
$636$		0			0
$637$	14.0563	+	24.3463i	0.556932	+	0.964634i
$638$	−1.60762	−	2.78448i	−0.0636464	−	0.110239i
$639$		0			0
$640$	−1.34981	+	2.33795i	−0.0533561	+	0.0924155i
$641$	−8.87450	−	15.3711i	−0.350522	−	0.607121i	0.635819	−	0.771838i	$-0.280662\pi$
$641$	−8.87450	−	15.3711i	−0.350522	−	0.607121i	−0.986341	+	0.164717i	$0.947329\pi$
$642$		0			0
$643$	13.6181			0.537044			0.268522	−	0.963274i	$-0.413465\pi$
$643$	13.6181			0.537044			0.268522	+	0.963274i	$0.413465\pi$
$644$	−0.388736	−	0.673310i	−0.0153183	−	0.0265321i
$645$		0			0
$646$	−20.4523			−0.804687
$647$	−16.7200	+	28.9599i	−0.657330	+	1.13853i	0.323974	+	0.946066i	$0.394981\pi$
$647$	−16.7200	+	28.9599i	−0.657330	+	1.13853i	−0.981304	+	0.192463i	$0.938352\pi$
$648$		0			0
$649$	5.40723	+	9.36559i	0.212252	+	0.367632i
$650$	−5.57853	−	9.66230i	−0.218808	−	0.378987i
$651$		0			0
$652$	10.1218	−	17.5314i	0.396400	−	0.686584i
$653$	2.27059	−	3.93278i	0.0888552	−	0.153902i	−0.818172	−	0.574973i	$-0.805013\pi$
$653$	2.27059	−	3.93278i	0.0888552	−	0.153902i	0.907027	+	0.421071i	$0.138346\pi$
$654$		0			0
$655$	−6.51052			−0.254387
$656$	−5.79851			−0.226394
$657$		0			0
$658$	−2.77128	−	4.80000i	−0.108036	−	0.187124i
$659$	13.6916	+	23.7145i	0.533348	+	0.923786i	0.999241	+	0.0389452i	$0.0123998\pi$
$659$	13.6916	+	23.7145i	0.533348	+	0.923786i	−0.465893	+	0.884841i	$0.654267\pi$
$660$		0			0
$661$	−33.6515			−1.30889			−0.654446	−	0.756109i	$-0.727098\pi$
$661$	−33.6515			−1.30889			−0.654446	+	0.756109i	$0.727098\pi$
$662$	28.0741			1.09113
$663$		0			0
$664$	5.75526	−	9.96840i	0.223347	−	0.386849i
$665$	−22.7280			−0.881352
$666$		0			0
$667$	1.52290			0.0589669
$668$	−9.20327	+	15.9405i	−0.356085	+	0.616758i
$669$		0			0
$670$	4.24474	−	21.6859i	0.163989	−	0.837799i
$671$	8.67996			0.335086
$672$		0			0
$673$	10.6304			0.409774			0.204887	−	0.978786i	$-0.434317\pi$
$673$	10.6304			0.409774			0.204887	+	0.978786i	$0.434317\pi$
$674$	−6.25093	−	10.8269i	−0.240777	−	0.417038i
$675$		0			0
$676$	−5.38942	+	9.33476i	−0.207286	+	0.359029i
$677$	−5.12543	−	8.87750i	−0.196986	−	0.341190i	0.750564	−	0.660798i	$-0.229782\pi$
$677$	−5.12543	−	8.87750i	−0.196986	−	0.341190i	−0.947550	+	0.319608i	$0.896449\pi$
$678$		0			0
$679$	12.7047			0.487563
$680$	3.64400	−	6.31159i	0.139741	−	0.242038i
$681$		0			0
$682$	−1.33743	−	2.31650i	−0.0512130	−	0.0887035i
$683$	−9.43749	+	16.3462i	−0.361115	+	0.625470i	−0.988145	−	0.153525i	$-0.950937\pi$
$683$	−9.43749	+	16.3462i	−0.361115	+	0.625470i	0.627029	+	0.778996i	$0.284271\pi$
$684$		0			0
$685$	59.3584			2.26797
$686$	−7.09269	+	12.2849i	−0.270800	+	0.469040i
$687$		0			0
$688$	0.682918	−	1.18285i	0.0260360	−	0.0450957i
$689$	−6.12110	+	10.6020i	−0.233195	+	0.403906i
$690$		0			0
$691$	12.7553	+	22.0928i	0.485233	+	0.840448i	0.999856	−	0.0169684i	$-0.00540146\pi$
$691$	12.7553	+	22.0928i	0.485233	+	0.840448i	−0.514623	+	0.857417i	$0.672068\pi$
$692$	−8.64145			−0.328499
$693$		0			0
$694$	−22.0494			−0.836982
$695$	−48.4362			−1.83729
$696$		0			0
$697$	15.6538			0.592931
$698$	3.97346	−	6.88223i	0.150398	−	0.260496i
$699$		0			0
$700$	1.27128	−	2.20192i	0.0480499	−	0.0832249i
$701$	16.5247	+	28.6216i	0.624129	+	1.08102i	0.988709	+	0.149850i	$0.0478792\pi$
$701$	16.5247	+	28.6216i	0.624129	+	1.08102i	−0.364580	+	0.931172i	$0.618787\pi$
$702$		0			0
$703$	12.4549	+	21.5725i	0.469745	+	0.813622i
$704$	0.738550	+	1.27921i	0.0278351	+	0.0482119i
$705$		0			0
$706$	9.64214	+	16.7007i	0.362887	+	0.628538i
$707$	2.93818	−	5.08907i	0.110502	−	0.191394i
$708$		0			0
$709$	8.78180	−	15.2105i	0.329808	−	0.571243i	−0.652666	−	0.757646i	$-0.726349\pi$
$709$	8.78180	−	15.2105i	0.329808	−	0.571243i	0.982473	+	0.186402i	$0.0596828\pi$
$710$	0.386877			0.0145192
$711$		0			0
$712$	−5.47710			−0.205263
$713$	1.26695			0.0474477
$714$		0			0
$715$	−19.4451			−0.727204
$716$	−5.99381	−	10.3816i	−0.223999	−	0.387978i
$717$		0			0
$718$	0.820724	−	1.42154i	0.0306291	−	0.0530512i
$719$	−22.3189	+	38.6574i	−0.832353	+	1.44168i	0.0638141	+	0.997962i	$0.479674\pi$
$719$	−22.3189	+	38.6574i	−0.832353	+	1.44168i	−0.896167	+	0.443716i	$0.853660\pi$
$720$		0			0
$721$	−7.82004	+	13.5447i	−0.291233	+	0.504431i
$722$	38.3955			1.42893
$723$		0			0
$724$	−1.11745	+	1.93549i	−0.0415299	+	0.0719318i
$725$	2.49017	+	4.31310i	0.0924825	+	0.160184i
$726$		0			0
$727$	−9.28002	+	16.0735i	−0.344177	+	0.596132i	−0.985204	−	0.171386i	$-0.945175\pi$
$727$	−9.28002	+	16.0735i	−0.344177	+	0.596132i	0.641027	+	0.767518i	$0.278509\pi$
$728$	−5.41892			−0.200839
$729$		0			0
$730$	−15.6254	−	27.0640i	−0.578323	−	1.00168i
$731$	−1.84362	+	3.19325i	−0.0681889	+	0.118107i
$732$		0			0
$733$	6.44251	+	11.1588i	0.237959	+	0.412158i	0.960129	−	0.279559i	$-0.0901881\pi$
$733$	6.44251	+	11.1588i	0.237959	+	0.412158i	−0.722169	+	0.691717i	$0.756855\pi$
$734$	6.23119			0.229997
$735$		0			0
$736$	−0.699628			−0.0257886
$737$	−9.11450	−	7.94406i	−0.335737	−	0.292623i
$738$		0			0
$739$	−14.0488	+	24.3332i	−0.516792	+	0.895110i	0.483018	+	0.875610i	$0.339541\pi$
$739$	−14.0488	+	24.3332i	−0.516792	+	0.895110i	−0.999810	+	0.0194992i	$0.993793\pi$
$740$	−8.87636			−0.326301
$741$		0			0
$742$	−2.78985			−0.102419
$743$	−12.5185	+	21.6827i	−0.459259	+	0.795460i	−0.998922	−	0.0464213i	$-0.985218\pi$
$743$	−12.5185	+	21.6827i	−0.459259	+	0.795460i	0.539663	+	0.841881i	$0.318552\pi$
$744$		0			0
$745$	−32.2719			−1.18235
$746$	20.6428			0.755788
$747$		0			0
$748$	−1.99381	−	3.45338i	−0.0729009	−	0.126268i
$749$	−5.32072	−	9.21576i	−0.194415	−	0.336737i
$750$		0			0
$751$	−12.4437			−0.454076			−0.227038	−	0.973886i	$-0.572904\pi$
$751$	−12.4437			−0.454076			−0.227038	+	0.973886i	$0.572904\pi$
$752$	−4.98762			−0.181880
$753$		0			0
$754$	5.30725	−	9.19243i	0.193279	−	0.334768i
$755$	−0.872714	+	1.51159i	−0.0317613	+	0.0550122i
$756$		0			0
$757$	15.2200	+	26.3618i	0.553180	+	0.958135i	0.998043	+	0.0625366i	$0.0199190\pi$
$757$	15.2200	+	26.3618i	0.553180	+	0.958135i	−0.444863	+	0.895599i	$0.646748\pi$
$758$	17.6804	+	30.6233i	0.642180	+	1.11229i
$759$		0			0
$760$	−10.2262	+	17.7122i	−0.370942	+	0.642491i
$761$	29.0865			1.05438			0.527192	−	0.849746i	$-0.323245\pi$
$761$	29.0865			1.05438			0.527192	+	0.849746i	$0.323245\pi$
$762$		0			0
$763$	−7.40180	−	12.8203i	−0.267963	−	0.464126i
$764$	−3.73167			−0.135007
$765$		0			0
$766$	−5.63162	−	9.75425i	−0.203479	−	0.352435i
$767$	−17.8509	+	30.9187i	−0.644559	+	1.11641i
$768$		0			0
$769$	8.62041	+	14.9310i	0.310860	+	0.538425i	0.978549	−	0.206015i	$-0.0660497\pi$
$769$	8.62041	+	14.9310i	0.310860	+	0.538425i	−0.667689	+	0.744440i	$0.732716\pi$
$770$	−2.21565	−	3.83762i	−0.0798465	−	0.138298i
$771$		0			0
$772$	−5.58217	−	9.66861i	−0.200907	−	0.347981i
$773$	2.66257	+	4.61170i	0.0957658	+	0.165871i	0.909928	−	0.414766i	$-0.136137\pi$
$773$	2.66257	+	4.61170i	0.0957658	+	0.165871i	−0.814162	+	0.580638i	$0.802803\pi$
$774$		0			0
$775$	2.07165	+	3.58821i	0.0744160	+	0.128892i
$776$	5.71634	−	9.90099i	0.205205	−	0.355425i
$777$		0			0
$778$	−13.2040	−	22.8699i	−0.473385	−	0.819927i
$779$	−43.9294			−1.57394
$780$		0			0
$781$	0.105840	−	0.183320i	0.00378724	−	0.00655969i
$782$	1.88874			0.0675411
$783$		0			0
$784$	2.88255	+	4.99272i	0.102948	+	0.178311i
$785$	28.1625	−	48.7789i	1.00516	−	1.74099i
$786$		0			0
$787$	8.63712	−	14.9599i	0.307880	−	0.533264i	−0.670018	−	0.742344i	$-0.733714\pi$
$787$	8.63712	−	14.9599i	0.307880	−	0.533264i	0.977898	+	0.209081i	$0.0670471\pi$
$788$	−11.3374	+	19.6370i	−0.403879	+	0.699540i
$789$		0			0
$790$	−20.9629			−0.745825
$791$	−8.29123	+	14.3608i	−0.294802	+	0.510612i
$792$		0			0
$793$	14.3276	+	24.8161i	0.508788	+	0.881247i
$794$	1.77816	−	3.07986i	0.0631046	−	0.109300i
$795$		0			0
$796$	−9.00000			−0.318997
$797$	2.45489	+	4.25199i	0.0869566	+	0.150613i	0.906223	−	0.422799i	$-0.138953\pi$
$797$	2.45489	+	4.25199i	0.0869566	+	0.150613i	−0.819267	+	0.573413i	$0.805619\pi$
$798$		0			0
$799$	13.4647			0.476348
$800$	−1.14400	−	1.98146i	−0.0404464	−	0.0700552i
$801$		0			0
$802$	17.2854	−	29.9393i	0.610370	−	1.05719i
$803$	−17.0989			−0.603407
$804$		0			0
$805$	2.09888			0.0739760
$806$	4.41528	−	7.64749i	0.155522	−	0.269371i
$807$		0			0
$808$	−2.64400	−	4.57954i	−0.0930155	−	0.161107i
$809$	−10.9666			−0.385564			−0.192782	−	0.981242i	$-0.561751\pi$
$809$	−10.9666			−0.385564			−0.192782	+	0.981242i	$0.561751\pi$
$810$		0			0
$811$	20.1971	+	34.9824i	0.709215	+	1.22840i	0.965149	+	0.261703i	$0.0842840\pi$
$811$	20.1971	+	34.9824i	0.709215	+	1.22840i	−0.255933	+	0.966694i	$0.582383\pi$
$812$	2.41892			0.0848874
$813$		0			0
$814$	−2.42835	+	4.20602i	−0.0851135	+	0.147421i
$815$	27.3251	+	47.3284i	0.957155	+	1.65784i
$816$		0			0
$817$	5.17377	−	8.96124i	0.181007	−	0.313514i
$818$	3.74033			0.130778
$819$		0			0
$820$	7.82691	−	13.5566i	0.273328	−	0.473417i
$821$	−11.3621	+	19.6798i	−0.396541	+	0.686829i	−0.993297	−	0.115594i	$-0.963123\pi$
$821$	−11.3621	+	19.6798i	−0.396541	+	0.686829i	0.596756	+	0.802423i	$0.296456\pi$
$822$		0			0
$823$	7.01121	−	12.1438i	0.244395	−	0.423305i	−0.717566	−	0.696490i	$-0.754744\pi$
$823$	7.01121	−	12.1438i	0.244395	−	0.423305i	0.961961	+	0.273185i	$0.0880772\pi$
$824$	7.03706	+	12.1885i	0.245148	+	0.424608i
$825$		0			0
$826$	−8.13602			−0.283088
$827$	8.88323	−	15.3862i	0.308900	−	0.535031i	−0.669222	−	0.743063i	$-0.733372\pi$
$827$	8.88323	−	15.3862i	0.308900	−	0.535031i	0.978122	+	0.208032i	$0.0667057\pi$
$828$		0			0
$829$	11.5178			0.400030			0.200015	−	0.979793i	$-0.435901\pi$
$829$	11.5178			0.400030			0.200015	+	0.979793i	$0.435901\pi$
$830$	15.5371	+	26.9110i	0.539299	+	0.934094i
$831$		0			0
$832$	−2.43818	+	4.22305i	−0.0845286	+	0.146408i
$833$	−7.78180	−	13.4785i	−0.269623	−	0.467002i
$834$		0			0
$835$	−24.8454	−	43.0335i	−0.859811	−	1.48924i
$836$	5.59524	+	9.69124i	0.193516	+	0.335179i
$837$		0			0
$838$	1.28985	+	2.23409i	0.0445572	+	0.0771753i
$839$	−24.6396	−	42.6770i	−0.850653	−	1.47337i	−0.880620	−	0.473823i	$-0.842873\pi$
$839$	−24.6396	−	42.6770i	−0.850653	−	1.47337i	0.0299668	−	0.999551i	$-0.490460\pi$
$840$		0			0
$841$	12.1309	−	21.0114i	0.418308	−	0.724530i
$842$	−4.74976	−	8.22682i	−0.163688	−	0.283515i
$843$		0			0
$844$	19.9752			0.687576
$845$	−14.5494	−	25.2004i	−0.500516	−	0.866919i
$846$		0			0
$847$	9.79932			0.336709
$848$	−1.25526	+	2.17417i	−0.0431058	+	0.0746615i
$849$		0			0
$850$	3.08836	+	5.34920i	0.105930	+	0.183476i
$851$	−1.15019	−	1.99218i	−0.0394279	−	0.0682911i
$852$		0			0
$853$	7.50000	−	12.9904i	0.256795	−	0.444782i	−0.708586	−	0.705624i	$-0.750667\pi$
$853$	7.50000	−	12.9904i	0.256795	−	0.444782i	0.965382	+	0.260842i	$0.0840001\pi$
$854$	−3.26509	+	5.65531i	−0.111729	+	0.193521i
$855$		0			0
$856$	−9.57598			−0.327300
$857$	38.0480			1.29969			0.649847	−	0.760065i	$-0.274833\pi$
$857$	38.0480			1.29969			0.649847	+	0.760065i	$0.274833\pi$
$858$		0			0
$859$	−20.1964	−	34.9812i	−0.689092	−	1.19354i	−0.972132	−	0.234434i	$-0.924676\pi$
$859$	−20.1964	−	34.9812i	−0.689092	−	1.19354i	0.283040	−	0.959108i	$-0.408657\pi$
$860$	1.84362	+	3.19325i	0.0628671	+	0.108889i
$861$		0			0
$862$	1.71063			0.0582643
$863$	46.3570			1.57801			0.789006	−	0.614386i	$-0.210596\pi$
$863$	46.3570			1.57801			0.789006	+	0.614386i	$0.210596\pi$
$864$		0			0
$865$	11.6643	−	20.2032i	0.396600	−	0.686931i
$866$	−19.8392			−0.674164
$867$		0			0
$868$	2.01238			0.0683046
$869$	−5.73491	+	9.93315i	−0.194543	+	0.336959i
$870$		0			0
$871$	7.66730	−	39.1714i	0.259797	−	1.32727i
$872$	−13.3214			−0.451120
$873$		0			0
$874$	−5.30037			−0.179288
$875$	−4.06801	−	7.04600i	−0.137524	−	0.238198i
$876$		0			0
$877$	2.78180	−	4.81822i	0.0939348	−	0.162700i	−0.815229	−	0.579139i	$-0.803389\pi$
$877$	2.78180	−	4.81822i	0.0939348	−	0.162700i	0.909164	+	0.416439i	$0.136722\pi$
$878$	7.53706	+	13.0546i	0.254364	+	0.440571i
$879$		0			0
$880$	−3.98762			−0.134423
$881$	11.1342	−	19.2849i	0.375120	−	0.649726i	−0.615225	−	0.788351i	$-0.710935\pi$
$881$	11.1342	−	19.2849i	0.375120	−	0.649726i	0.990345	+	0.138625i	$0.0442683\pi$
$882$		0			0
$883$	18.2687	+	31.6424i	0.614792	+	1.06485i	0.990421	+	0.138081i	$0.0440933\pi$
$883$	18.2687	+	31.6424i	0.614792	+	1.06485i	−0.375629	+	0.926770i	$0.622573\pi$
$884$	6.58217	−	11.4007i	0.221382	−	0.383446i
$885$		0			0
$886$	41.4683			1.39315
$887$	15.4938	−	26.8361i	0.520231	−	0.901067i	−0.479492	−	0.877546i	$-0.659179\pi$
$887$	15.4938	−	26.8361i	0.520231	−	0.901067i	0.999723	−	0.0235207i	$-0.00748757\pi$
$888$		0			0
$889$	−5.94506	+	10.2971i	−0.199391	+	0.345355i
$890$	7.39307	−	12.8052i	0.247816	−	0.429230i
$891$		0			0
$892$	−8.49814	−	14.7192i	−0.284539	−	0.492836i
$893$	−37.7861			−1.26446
$894$		0			0
$895$	32.3621			1.08175
$896$	−1.11126			−0.0371247
$897$		0			0
$898$	4.23491			0.141321
$899$	−1.97091	+	3.41372i	−0.0657335	+	0.113854i
$900$		0			0
$901$	3.38874	−	5.86946i	0.112895	−	0.195540i
$902$	−4.28249	−	7.41749i	−0.142591	−	0.246975i
$903$		0			0
$904$	7.46108	+	12.9230i	0.248152	+	0.429811i
$905$	−3.01671	−	5.22510i	−0.100279	−	0.173688i
$906$		0			0
$907$	−24.8559	−	43.0517i	−0.825328	−	1.42951i	−0.901669	−	0.432427i	$-0.857657\pi$
$907$	−24.8559	−	43.0517i	−0.825328	−	1.42951i	0.0763412	−	0.997082i	$-0.475676\pi$
$908$	−5.03342	+	8.71814i	−0.167040	+	0.289322i
$909$		0			0
$910$	7.31453	−	12.6691i	0.242474	−	0.419978i
$911$	10.6232			0.351961			0.175981	−	0.984394i	$-0.443690\pi$
$911$	10.6232			0.351961			0.175981	+	0.984394i	$0.443690\pi$
$912$		0			0
$913$	17.0022			0.562690
$914$	15.5439			0.514148
$915$		0			0
$916$	−22.8764			−0.755856
$917$	−1.33998	−	2.32092i	−0.0442501	−	0.0766434i
$918$		0			0
$919$	0.644685	−	1.11663i	0.0212662	−	0.0368341i	−0.855196	−	0.518304i	$-0.826564\pi$
$919$	0.644685	−	1.11663i	0.0212662	−	0.0368341i	0.876463	+	0.481470i	$0.159897\pi$
$920$	0.944368	−	1.63569i	0.0311349	−	0.0539272i
$921$		0			0
$922$	8.53087	−	14.7759i	0.280949	−	0.486619i
$923$	0.698818			0.0230019
$924$		0			0
$925$	3.76145	−	6.51502i	0.123676	−	0.214213i
$926$	−13.9691	−	24.1951i	−0.459051	−	0.795101i
$927$		0			0
$928$	1.08836	−	1.88510i	0.0357273	−	0.0618815i
$929$	35.6291			1.16895			0.584476	−	0.811411i	$-0.301300\pi$
$929$	35.6291			1.16895			0.584476	+	0.811411i	$0.301300\pi$
$930$		0			0
$931$	21.8381	+	37.8247i	0.715716	+	1.23966i
$932$	−11.4425	+	19.8190i	−0.374812	+	0.649193i
$933$		0			0
$934$	−12.0167	−	20.8136i	−0.393199	−	0.681040i
$935$	10.7651			0.352056
$936$		0			0
$937$	6.07413			0.198433			0.0992165	−	0.995066i	$-0.468366\pi$
$937$	6.07413			0.198433			0.0992165	+	0.995066i	$0.468366\pi$
$938$	8.60439	−	2.95015i	0.280943	−	0.0963258i
$939$		0			0
$940$	6.73236	−	11.6608i	0.219585	−	0.380333i
$941$	40.4582			1.31890			0.659451	−	0.751748i	$-0.270789\pi$
$941$	40.4582			1.31890			0.659451	+	0.751748i	$0.270789\pi$
$942$		0			0
$943$	4.05680			0.132108
$944$	−3.66071	+	6.34053i	−0.119146	+	0.206367i
$945$		0			0
$946$	2.01748			0.0655938
$947$	−2.69606			−0.0876103			−0.0438051	−	0.999040i	$-0.513948\pi$
$947$	−2.69606			−0.0876103			−0.0438051	+	0.999040i	$0.513948\pi$
$948$		0			0
$949$	−28.2243	−	48.8859i	−0.916200	−	1.58690i
$950$	−8.66690	−	15.0115i	−0.281191	−	0.487038i
$951$		0			0
$952$	3.00000			0.0972306
$953$	−4.20149			−0.136100			−0.0680498	−	0.997682i	$-0.521678\pi$
$953$	−4.20149			−0.136100			−0.0680498	+	0.997682i	$0.521678\pi$
$954$		0			0
$955$	5.03706	−	8.72445i	0.162996	−	0.282317i
$956$	9.47524	−	16.4116i	0.306451	−	0.530789i
$957$		0			0
$958$	18.7942	+	32.5525i	0.607212	+	1.05172i
$959$	12.2170	+	21.1605i	0.394508	+	0.683309i
$960$		0			0
$961$	13.8603	−	24.0068i	0.447108	−	0.774413i
$962$	−16.0334			−0.516938
$963$		0			0
$964$	5.68725	+	9.85060i	0.183174	+	0.317267i
$965$	30.1396			0.970228
$966$		0			0
$967$	−20.3763	−	35.2928i	−0.655257	−	1.13494i	−0.981829	−	0.189766i	$-0.939227\pi$
$967$	−20.3763	−	35.2928i	−0.655257	−	1.13494i	0.326572	−	0.945172i	$-0.394106\pi$
$968$	4.40909	−	7.63676i	0.141713	−	0.245455i
$969$		0			0
$970$	15.4320	+	26.7290i	0.495491	+	0.858216i
$971$	−4.84362	−	8.38940i	−0.155439	−	0.269229i	0.777780	−	0.628537i	$-0.216346\pi$
$971$	−4.84362	−	8.38940i	−0.155439	−	0.269229i	−0.933219	+	0.359308i	$0.883013\pi$
$972$		0			0
$973$	−9.96905	−	17.2669i	−0.319593	−	0.553551i
$974$	3.52723	+	6.10934i	0.113020	+	0.195756i
$975$		0			0
$976$	2.93818	+	5.08907i	0.0940488	+	0.162897i
$977$	26.5192	−	45.9326i	0.848424	−	1.46951i	−0.0341906	−	0.999415i	$-0.510885\pi$
$977$	26.5192	−	45.9326i	0.848424	−	1.46951i	0.882614	−	0.470098i	$-0.155781\pi$
$978$		0			0
$979$	−4.04511	−	7.00634i	−0.129282	−	0.223924i
$980$	−15.5636			−0.497161
$981$		0			0
$982$	−2.10940	+	3.65360i	−0.0673138	+	0.116591i
$983$	38.8443			1.23894			0.619471	−	0.785020i	$-0.287347\pi$
$983$	38.8443			1.23894			0.619471	+	0.785020i	$0.287347\pi$
$984$		0			0
$985$	−30.6069	−	53.0126i	−0.975216	−	1.68912i
$986$	−2.93818	+	5.08907i	−0.0935707	+	0.162069i
$987$		0			0
$988$	−18.4716	+	31.9937i	−0.587660	+	1.01786i
$989$	−0.477789	+	0.827554i	−0.0151928	+	0.0263147i
$990$		0			0
$991$	18.7280			0.594913			0.297457	−	0.954735i	$-0.403862\pi$
$991$	18.7280			0.594913			0.297457	+	0.954735i	$0.403862\pi$
$992$	0.905446	−	1.56828i	0.0287479	−	0.0497929i
$993$		0			0
$994$	0.0796262	+	0.137917i	0.00252559	+	0.00437445i
$995$	12.1483	−	21.0415i	0.385128	−	0.667061i
$996$		0			0
$997$	−55.5300			−1.75865			−0.879327	−	0.476219i	$-0.842007\pi$
$997$	−55.5300			−1.75865			−0.879327	+	0.476219i	$0.842007\pi$
$998$	−5.03706	−	8.72445i	−0.159445	−	0.276168i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1206.2.h.e.163.3		6
3.2	odd	2		402.2.e.c.163.1	yes	6
67.37	even	3	inner	1206.2.h.e.37.3		6
201.104	odd	6		402.2.e.c.37.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
402.2.e.c.37.1	✓	6	201.104	odd	6
402.2.e.c.163.1	yes	6	3.2	odd	2
1206.2.h.e.37.3		6	67.37	even	3	inner
1206.2.h.e.163.3		6	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1206 = 2 \cdot 3^{2} \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1206.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.69963 q^{5} +(0.555632 + 0.962383i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.69963 q^{5} +(0.555632 + 0.962383i) q^{7} +1.00000 q^{8} +(-1.34981 + 2.33795i) q^{10} +(0.738550 + 1.27921i) q^{11} +(-2.43818 + 4.22305i) q^{13} -1.11126 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.34981 - 2.33795i) q^{17} +(-3.78799 + 6.56099i) q^{19} +(-1.34981 - 2.33795i) q^{20} -1.47710 q^{22} +(0.349814 - 0.605896i) q^{23} +2.28799 q^{25} +(-2.43818 - 4.22305i) q^{26} +(0.555632 - 0.962383i) q^{28} +(1.08836 + 1.88510i) q^{29} +(0.905446 + 1.56828i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.34981 + 2.33795i) q^{34} +(1.50000 + 2.59808i) q^{35} +(1.64400 - 2.84748i) q^{37} +(-3.78799 - 6.56099i) q^{38} +2.69963 q^{40} +(2.89926 + 5.02166i) q^{41} -1.36584 q^{43} +(0.738550 - 1.27921i) q^{44} +(0.349814 + 0.605896i) q^{46} +(2.49381 + 4.31941i) q^{47} +(2.88255 - 4.99272i) q^{49} +(-1.14400 + 1.98146i) q^{50} +4.87636 q^{52} +2.51052 q^{53} +(1.99381 + 3.45338i) q^{55} +(0.555632 + 0.962383i) q^{56} -2.17673 q^{58} +7.32141 q^{59} +(2.93818 - 5.08907i) q^{61} -1.81089 q^{62} +1.00000 q^{64} +(-6.58217 + 11.4007i) q^{65} +(-7.74288 + 2.65477i) q^{67} -2.69963 q^{68} -3.00000 q^{70} +(-0.0716537 - 0.124108i) q^{71} +(-5.78799 + 10.0251i) q^{73} +(1.64400 + 2.84748i) q^{74} +7.57598 q^{76} +(-0.820724 + 1.42154i) q^{77} +(3.88255 + 6.72477i) q^{79} +(-1.34981 + 2.33795i) q^{80} -5.79851 q^{82} +(5.75526 - 9.96840i) q^{83} +(3.64400 - 6.31159i) q^{85} +(0.682918 - 1.18285i) q^{86} +(0.738550 + 1.27921i) q^{88} -5.47710 q^{89} -5.41892 q^{91} -0.699628 q^{92} -4.98762 q^{94} +(-10.2262 + 17.7122i) q^{95} +(5.71634 - 9.90099i) q^{97} +(2.88255 + 4.99272i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 4 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + 4 * q^5 + 3 * q^7 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} + 4 q^{5} + 3 q^{7} + 6 q^{8} - 2 q^{10} - q^{11} + 3 q^{13} - 6 q^{14} - 3 q^{16} + 2 q^{17} + q^{19} - 2 q^{20} + 2 q^{22} - 4 q^{23} - 10 q^{25} + 3 q^{26} + 3 q^{28} - 5 q^{29} - q^{31} - 3 q^{32} + 2 q^{34} + 9 q^{35} - 2 q^{37} + q^{38} + 4 q^{40} - 7 q^{41} + 2 q^{43} - q^{44} - 4 q^{46} - 3 q^{47} + 5 q^{50} - 6 q^{52} - 10 q^{53} - 6 q^{55} + 3 q^{56} + 10 q^{58} + 6 q^{59} + 2 q^{62} + 6 q^{64} - 10 q^{65} + 2 q^{67} - 4 q^{68} - 18 q^{70} + 4 q^{71} - 11 q^{73} - 2 q^{74} - 2 q^{76} + 30 q^{77} + 6 q^{79} - 2 q^{80} + 14 q^{82} + 22 q^{83} + 10 q^{85} - q^{86} - q^{88} - 22 q^{89} + 36 q^{91} + 8 q^{92} + 6 q^{94} - 20 q^{95} + 15 q^{97}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 4 * q^5 + 3 * q^7 + 6 * q^8 - 2 * q^10 - q^11 + 3 * q^13 - 6 * q^14 - 3 * q^16 + 2 * q^17 + q^19 - 2 * q^20 + 2 * q^22 - 4 * q^23 - 10 * q^25 + 3 * q^26 + 3 * q^28 - 5 * q^29 - q^31 - 3 * q^32 + 2 * q^34 + 9 * q^35 - 2 * q^37 + q^38 + 4 * q^40 - 7 * q^41 + 2 * q^43 - q^44 - 4 * q^46 - 3 * q^47 + 5 * q^50 - 6 * q^52 - 10 * q^53 - 6 * q^55 + 3 * q^56 + 10 * q^58 + 6 * q^59 + 2 * q^62 + 6 * q^64 - 10 * q^65 + 2 * q^67 - 4 * q^68 - 18 * q^70 + 4 * q^71 - 11 * q^73 - 2 * q^74 - 2 * q^76 + 30 * q^77 + 6 * q^79 - 2 * q^80 + 14 * q^82 + 22 * q^83 + 10 * q^85 - q^86 - q^88 - 22 * q^89 + 36 * q^91 + 8 * q^92 + 6 * q^94 - 20 * q^95 + 15 * q^97

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