LMFDB - Embedded newform 126.2.g.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, 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("126.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.g (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.2.g.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} -4.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{19} -3.00000 q^{20} -3.00000 q^{22} +(-2.00000 + 3.46410i) q^{25} +(2.00000 + 3.46410i) q^{26} +(-0.500000 + 2.59808i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.00000 + 5.19615i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(1.50000 + 2.59808i) q^{40} -10.0000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-3.00000 - 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +(4.50000 + 7.79423i) q^{58} +(1.50000 - 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} -1.00000 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(5.00000 - 8.66025i) q^{67} +(1.50000 - 7.79423i) q^{70} +6.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(1.50000 - 7.79423i) q^{77} +(0.500000 + 0.866025i) q^{79} +(1.50000 - 2.59808i) q^{80} +9.00000 q^{83} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{94} +(-6.00000 + 10.3923i) q^{95} -1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 3 * q^5 + 5 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8} + 3 q^{10} + 3 q^{11} - 8 q^{13} - 4 q^{14} - q^{16} + 4 q^{19} - 6 q^{20} - 6 q^{22} - 4 q^{25} + 4 q^{26} - q^{28} - 18 q^{29} + q^{31} - q^{32} + 12 q^{35} - 8 q^{37} + 4 q^{38} + 3 q^{40} - 20 q^{43} + 3 q^{44} - 6 q^{47} + 11 q^{49} + 8 q^{50} + 4 q^{52} - 3 q^{53} + 18 q^{55} + 5 q^{56} + 9 q^{58} + 3 q^{59} + 10 q^{61} - 2 q^{62} + 2 q^{64} - 12 q^{65} + 10 q^{67} + 3 q^{70} + 12 q^{71} - 2 q^{73} - 8 q^{74} - 8 q^{76} + 3 q^{77} + q^{79} + 3 q^{80} + 18 q^{83} + 10 q^{86} + 3 q^{88} + 6 q^{89} - 20 q^{91} - 6 q^{94} - 12 q^{95} - 2 q^{97} - 13 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 3 * q^5 + 5 * q^7 + 2 * q^8 + 3 * q^10 + 3 * q^11 - 8 * q^13 - 4 * q^14 - q^16 + 4 * q^19 - 6 * q^20 - 6 * q^22 - 4 * q^25 + 4 * q^26 - q^28 - 18 * q^29 + q^31 - q^32 + 12 * q^35 - 8 * q^37 + 4 * q^38 + 3 * q^40 - 20 * q^43 + 3 * q^44 - 6 * q^47 + 11 * q^49 + 8 * q^50 + 4 * q^52 - 3 * q^53 + 18 * q^55 + 5 * q^56 + 9 * q^58 + 3 * q^59 + 10 * q^61 - 2 * q^62 + 2 * q^64 - 12 * q^65 + 10 * q^67 + 3 * q^70 + 12 * q^71 - 2 * q^73 - 8 * q^74 - 8 * q^76 + 3 * q^77 + q^79 + 3 * q^80 + 18 * q^83 + 10 * q^86 + 3 * q^88 + 6 * q^89 - 20 * q^91 - 6 * q^94 - 12 * q^95 - 2 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	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
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	0.977672	+	0.210138i	$0.0673912\pi$
$5$	1.50000	+	2.59808i	0.670820	+	1.16190i	−0.306851	+	0.951757i	$0.599275\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.50000	−	2.59808i	0.474342	−	0.821584i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	−3.00000			−0.670820
$21$		0			0
$22$	−3.00000			−0.639602
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$		0			0
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$		0			0
$35$	6.00000	+	5.19615i	1.01419	+	0.878310i
$36$		0			0
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	−0.981236	−	0.192809i	$-0.938240\pi$
$37$	−4.00000	−	6.92820i	−0.657596	−	1.13899i	0.323640	−	0.946180i	$-0.395093\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$		0			0
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$		0			0
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	4.00000			0.565685
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$		0			0
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−1.00000			−0.127000
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000	−	10.3923i	−0.744208	−	1.28901i
$66$		0			0
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$		0			0
$69$		0			0
$70$	1.50000	−	7.79423i	0.179284	−	0.931589i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	−4.00000			−0.458831
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$		0			0
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$		0			0
$86$	5.00000	+	8.66025i	0.539164	+	0.933859i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	−10.0000	+	3.46410i	−1.04828	+	0.363137i
$92$		0			0
$93$		0			0
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.0623905	+	0.998052i	$0.519872\pi$
$101$	−9.00000	+	15.5885i	−0.895533	+	1.55111i	−0.833143	+	0.553058i	$0.813461\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	3.00000			0.291386
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	−4.50000	−	7.79423i	−0.429058	−	0.743151i
$111$		0			0
$112$	−2.00000	−	1.73205i	−0.188982	−	0.163663i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		0			0
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$		0			0
$118$	−3.00000			−0.276172
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	5.00000	−	8.66025i	0.452679	−	0.784063i
$123$		0			0
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$	3.00000			0.268328
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−6.00000	+	10.3923i	−0.526235	+	0.911465i
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	0.599699	−	0.800226i	$-0.295287\pi$
$131$	−4.50000	−	7.79423i	−0.393167	−	0.680985i	−0.992865	+	0.119241i	$0.961954\pi$
$132$		0			0
$133$	8.00000	+	6.92820i	0.693688	+	0.600751i
$134$	−10.0000			−0.863868
$135$		0			0
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$	−7.50000	+	2.59808i	−0.633866	+	0.219578i
$141$		0			0
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	−6.00000	+	10.3923i	−0.501745	+	0.869048i
$144$		0			0
$145$	−13.5000	−	23.3827i	−1.12111	−	1.94183i
$146$	2.00000			0.165521
$147$		0			0
$148$	8.00000			0.657596
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	0.953703	+	0.300750i	$0.0972370\pi$
$149$	9.00000	+	15.5885i	0.737309	+	1.27706i	−0.216394	+	0.976306i	$0.569430\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$		0			0
$154$	−7.50000	+	2.59808i	−0.604367	+	0.209359i
$155$	3.00000			0.240966
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	0.500000	−	0.866025i	0.0397779	−	0.0688973i
$159$		0			0
$160$	−3.00000			−0.237171
$161$		0			0
$162$		0			0
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$		0			0
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	−6.00000			−0.464294			−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000			−0.464294			−0.232147	+	0.972681i	$0.574575\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$		0			0
$172$	5.00000	−	8.66025i	0.381246	−	0.660338i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$		0			0
$175$	−2.00000	+	10.3923i	−0.151186	+	0.785584i
$176$	−3.00000			−0.226134
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	8.00000	+	6.92820i	0.592999	+	0.513553i
$183$		0			0
$184$		0			0
$185$	12.0000	−	20.7846i	0.882258	−	1.52811i
$186$		0			0
$187$		0			0
$188$	6.00000			0.437595
$189$		0			0
$190$	12.0000			0.870572
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	−0.289980	−	0.957033i	$-0.593649\pi$
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	0.973805	−	0.227387i	$-0.0730182\pi$
$194$	0.500000	+	0.866025i	0.0358979	+	0.0621770i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$		0			0
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	18.0000			1.26648
$203$	−22.5000	+	7.79423i	−1.57919	+	0.547048i
$204$		0			0
$205$		0			0
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	12.0000			0.830057
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$		0			0
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	−15.0000	−	25.9808i	−1.02299	−	1.77187i
$216$		0			0
$217$	0.500000	−	2.59808i	0.0339422	−	0.176369i
$218$	14.0000			0.948200
$219$		0			0
$220$	−4.50000	+	7.79423i	−0.303390	+	0.525487i
$221$		0			0
$222$		0			0
$223$	−19.0000			−1.27233			−0.636167	−	0.771551i	$-0.719481\pi$
$223$	−19.0000			−1.27233			−0.636167	+	0.771551i	$0.719481\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$		0			0
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.0634974	+	0.997982i	$0.520225\pi$
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.832529	+	0.553981i	$0.813108\pi$
$228$		0			0
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		0			0
$231$		0			0
$232$	−9.00000			−0.590879
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$		0			0
$235$	9.00000	−	15.5885i	0.587095	−	1.01688i
$236$	1.50000	+	2.59808i	0.0976417	+	0.169120i
$237$		0			0
$238$		0			0
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$		0			0
$244$	−10.0000			−0.640184
$245$	19.5000	+	7.79423i	1.24581	+	0.497955i
$246$		0			0
$247$	−8.00000	−	13.8564i	−0.509028	−	0.881662i
$248$	0.500000	−	0.866025i	0.0317500	−	0.0549927i
$249$		0			0
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	−27.0000			−1.70422			−0.852112	−	0.523359i	$-0.824679\pi$
$251$	−27.0000			−1.70422			−0.852112	+	0.523359i	$0.824679\pi$
$252$		0			0
$253$		0			0
$254$	−2.50000	−	4.33013i	−0.156864	−	0.271696i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	−16.0000	−	13.8564i	−0.994192	−	0.860995i
$260$	12.0000			0.744208
$261$		0			0
$262$	−4.50000	+	7.79423i	−0.278011	+	0.481529i
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$		0			0
$265$	−9.00000			−0.552866
$266$	2.00000	−	10.3923i	0.122628	−	0.637193i
$267$		0			0
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$		0			0
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	0.649211	−	0.760609i	$-0.275099\pi$
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	−0.983312	+	0.181928i	$0.941766\pi$
$272$		0			0
$273$		0			0
$274$	−18.0000			−1.08742
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	−1.00000	−	1.73205i	−0.0599760	−	0.103882i
$279$		0			0
$280$	6.00000	+	5.19615i	0.358569	+	0.310530i
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	−0.995544	−	0.0942988i	$-0.969939\pi$
$283$	−7.00000	+	12.1244i	−0.416107	+	0.720718i	0.579437	+	0.815017i	$0.303272\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	12.0000			0.709575
$287$		0			0
$288$		0			0
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−13.5000	+	23.3827i	−0.792747	+	1.37308i
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−33.0000			−1.92788			−0.963940	−	0.266119i	$-0.914259\pi$
$293$	−33.0000			−1.92788			−0.963940	+	0.266119i	$0.914259\pi$
$294$		0			0
$295$	9.00000			0.524000
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$		0			0
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$		0			0
$300$		0			0
$301$	−25.0000	+	8.66025i	−1.44098	+	0.499169i
$302$	−1.00000			−0.0575435
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−15.0000	+	25.9808i	−0.858898	+	1.48765i
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	6.00000	+	5.19615i	0.341882	+	0.296078i
$309$		0			0
$310$	−1.50000	−	2.59808i	−0.0851943	−	0.147561i
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	15.5000	+	26.8468i	0.876112	+	1.51747i	0.855574	+	0.517681i	$0.173205\pi$
$313$	15.5000	+	26.8468i	0.876112	+	1.51747i	0.0205381	+	0.999789i	$0.493462\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	0.964281	−	0.264883i	$-0.0853332\pi$
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	−0.711535	+	0.702650i	$0.752000\pi$
$318$		0			0
$319$	−13.5000	+	23.3827i	−0.755855	+	1.30918i
$320$	1.50000	+	2.59808i	0.0838525	+	0.145237i
$321$		0			0
$322$		0			0
$323$		0			0
$324$		0			0
$325$	8.00000	−	13.8564i	0.443760	−	0.768615i
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$		0			0
$329$	−12.0000	−	10.3923i	−0.661581	−	0.572946i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$		0			0
$334$	3.00000	+	5.19615i	0.164153	+	0.284321i
$335$	30.0000			1.63908
$336$		0			0
$337$	−7.00000			−0.381314			−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000			−0.381314			−0.190657	+	0.981657i	$0.561062\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$		0			0
$341$	−1.50000	−	2.59808i	−0.0812296	−	0.140694i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−10.0000			−0.539164
$345$		0			0
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$	10.0000	−	3.46410i	0.534522	−	0.185164i
$351$		0			0
$352$	1.50000	+	2.59808i	0.0799503	+	0.138478i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$		0			0
$355$	9.00000	+	15.5885i	0.477670	+	0.827349i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−12.0000			−0.634220
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	0.924932	+	0.380131i	$0.124121\pi$
$359$	15.0000	+	25.9808i	0.791670	+	1.37121i	−0.133263	+	0.991081i	$0.542545\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−4.00000	−	6.92820i	−0.210235	−	0.364138i
$363$		0			0
$364$	2.00000	−	10.3923i	0.104828	−	0.544705i
$365$	−6.00000			−0.314054
$366$		0			0
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	−0.504093	−	0.863649i	$-0.668173\pi$
$367$	9.50000	−	16.4545i	0.495896	−	0.858917i	0.999989	+	0.00473247i	$0.00150640\pi$
$368$		0			0
$369$		0			0
$370$	−24.0000			−1.24770
$371$	−1.50000	+	7.79423i	−0.0778761	+	0.404656i
$372$		0			0
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	0.743691	−	0.668523i	$-0.233073\pi$
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	−0.950804	+	0.309794i	$0.899740\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	36.0000			1.85409
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$	−6.00000	−	10.3923i	−0.307794	−	0.533114i
$381$		0			0
$382$		0			0
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$		0			0
$385$	22.5000	−	7.79423i	1.14671	−	0.397231i
$386$	−19.0000			−0.967075
$387$		0			0
$388$	0.500000	−	0.866025i	0.0253837	−	0.0439658i
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$		0			0
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$		0			0
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$	−1.50000	+	2.59808i	−0.0754732	+	0.130723i
$396$		0			0
$397$	2.00000	+	3.46410i	0.100377	+	0.173858i	0.911840	−	0.410546i	$-0.134662\pi$
$397$	2.00000	+	3.46410i	0.100377	+	0.173858i	−0.811463	+	0.584404i	$0.801328\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	4.00000			0.200000
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$	−9.00000	−	15.5885i	−0.447767	−	0.775555i
$405$		0			0
$406$	18.0000	+	15.5885i	0.893325	+	0.773642i
$407$	−24.0000			−1.18964
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$		0			0
$412$	8.00000			0.394132
$413$	1.50000	−	7.79423i	0.0738102	−	0.383529i
$414$		0			0
$415$	13.5000	+	23.3827i	0.662689	+	1.14781i
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$		0			0
$418$	−6.00000	−	10.3923i	−0.293470	−	0.508304i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	−7.00000	−	12.1244i	−0.340755	−	0.590204i
$423$		0			0
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$		0			0
$426$		0			0
$427$	20.0000	+	17.3205i	0.967868	+	0.838198i
$428$	3.00000			0.145010
$429$		0			0
$430$	−15.0000	+	25.9808i	−0.723364	+	1.25290i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$	−2.50000	+	0.866025i	−0.120004	+	0.0415705i
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		0			0
$438$		0			0
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$	9.00000			0.429058
$441$		0			0
$442$		0			0
$443$	−16.5000	−	28.5788i	−0.783939	−	1.35782i	−0.929631	−	0.368492i	$-0.879874\pi$
$443$	−16.5000	−	28.5788i	−0.783939	−	1.35782i	0.145692	−	0.989330i	$-0.453459\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	9.50000	+	16.4545i	0.449838	+	0.779142i
$447$		0			0
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	27.0000			1.26717
$455$	−24.0000	−	20.7846i	−1.12514	−	0.974398i
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$	2.00000	−	3.46410i	0.0934539	−	0.161867i
$459$		0			0
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	18.0000	+	31.1769i	0.832941	+	1.44270i	0.895696	+	0.444667i	$0.146678\pi$
$467$	18.0000	+	31.1769i	0.832941	+	1.44270i	−0.0627555	+	0.998029i	$0.519989\pi$
$468$		0			0
$469$	5.00000	−	25.9808i	0.230879	−	1.19968i
$470$	−18.0000			−0.830278
$471$		0			0
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$		0			0
$475$	−16.0000			−0.734130
$476$		0			0
$477$		0			0
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$	−1.00000			−0.0455488
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−1.50000	−	2.59808i	−0.0681115	−	0.117973i
$486$		0			0
$487$	−20.5000	+	35.5070i	−0.928944	+	1.60898i	−0.143851	+	0.989599i	$0.545949\pi$
$487$	−20.5000	+	35.5070i	−0.928944	+	1.60898i	−0.785093	+	0.619378i	$0.787385\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$		0			0
$490$	−3.00000	−	20.7846i	−0.135526	−	0.938953i
$491$	33.0000			1.48927			0.744635	−	0.667472i	$-0.232624\pi$
$491$	33.0000			1.48927			0.744635	+	0.667472i	$0.232624\pi$
$492$		0			0
$493$		0			0
$494$	−8.00000	+	13.8564i	−0.359937	+	0.623429i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	15.0000	−	5.19615i	0.672842	−	0.233079i
$498$		0			0
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	0.842774	−	0.538267i	$-0.180921\pi$
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	−0.887540	+	0.460730i	$0.847588\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$		0			0
$502$	13.5000	+	23.3827i	0.602534	+	1.04362i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−54.0000			−2.40297
$506$		0			0
$507$		0			0
$508$	−2.50000	+	4.33013i	−0.110920	+	0.192118i
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	0.830866	−	0.556473i	$-0.187846\pi$
$509$	−1.50000	−	2.59808i	−0.0664863	−	0.115158i	−0.897352	+	0.441315i	$0.854512\pi$
$510$		0			0
$511$	−1.00000	+	5.19615i	−0.0442374	+	0.229864i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	12.0000	−	20.7846i	0.528783	−	0.915879i
$516$		0			0
$517$	−18.0000			−0.791639
$518$	−4.00000	+	20.7846i	−0.175750	+	0.913223i
$519$		0			0
$520$	−6.00000	−	10.3923i	−0.263117	−	0.455733i
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	−0.993011	−	0.118020i	$-0.962345\pi$
$521$	−9.00000	+	15.5885i	−0.394297	+	0.682943i	0.598714	+	0.800963i	$0.295679\pi$
$522$		0			0
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$	9.00000			0.393167
$525$		0			0
$526$	6.00000			0.261612
$527$		0			0
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$		0			0
$532$	−10.0000	+	3.46410i	−0.433555	+	0.150188i
$533$		0			0
$534$		0			0
$535$	4.50000	−	7.79423i	0.194552	−	0.336974i
$536$	5.00000	−	8.66025i	0.215967	−	0.374066i
$537$		0			0
$538$	−21.0000			−0.905374
$539$	−3.00000	−	20.7846i	−0.129219	−	0.895257i
$540$		0			0
$541$	−13.0000	−	22.5167i	−0.558914	−	0.968067i	−0.997587	−	0.0694205i	$-0.977885\pi$
$541$	−13.0000	−	22.5167i	−0.558914	−	0.968067i	0.438674	−	0.898646i	$-0.355448\pi$
$542$	−5.50000	+	9.52628i	−0.236245	+	0.409189i
$543$		0			0
$544$		0			0
$545$	−42.0000			−1.79908
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$		0			0
$550$	6.00000	−	10.3923i	0.255841	−	0.443129i
$551$	−18.0000	−	31.1769i	−0.766826	−	1.32818i
$552$		0			0
$553$	2.00000	+	1.73205i	0.0850487	+	0.0736543i
$554$	8.00000			0.339887
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$		0			0
$559$	40.0000			1.69182
$560$	1.50000	−	7.79423i	0.0633866	−	0.329366i
$561$		0			0
$562$	3.00000	+	5.19615i	0.126547	+	0.219186i
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	−0.0824933	−	0.996592i	$-0.526288\pi$
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	0.904320	−	0.426855i	$-0.140378\pi$
$564$		0			0
$565$		0			0
$566$	14.0000			0.588464
$567$		0			0
$568$	6.00000			0.251754
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	−0.945573	−	0.325409i	$-0.894498\pi$
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	0.190974	−	0.981595i	$-0.438835\pi$
$570$		0			0
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	−0.252893	−	0.967494i	$-0.581382\pi$
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	0.964321	−	0.264735i	$-0.0852845\pi$
$572$	−6.00000	−	10.3923i	−0.250873	−	0.434524i
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−11.5000	+	19.9186i	−0.478751	+	0.829222i	−0.999703	−	0.0243645i	$-0.992244\pi$
$577$	−11.5000	+	19.9186i	−0.478751	+	0.829222i	0.520952	+	0.853586i	$0.325577\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$		0			0
$580$	27.0000			1.12111
$581$	22.5000	−	7.79423i	0.933457	−	0.323359i
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	16.5000	+	28.5788i	0.681609	+	1.18058i
$587$	−21.0000			−0.866763			−0.433381	−	0.901211i	$-0.642680\pi$
$587$	−21.0000			−0.866763			−0.433381	+	0.901211i	$0.642680\pi$
$588$		0			0
$589$	4.00000			0.164817
$590$	−4.50000	−	7.79423i	−0.185262	−	0.320883i
$591$		0			0
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	0.999965	−	0.00831589i	$-0.00264706\pi$
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	−0.507184	+	0.861838i	$0.669314\pi$
$594$		0			0
$595$		0			0
$596$	−18.0000			−0.737309
$597$		0			0
$598$		0			0
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$		0			0
$601$	11.0000			0.448699			0.224350	−	0.974509i	$-0.427974\pi$
$601$	11.0000			0.448699			0.224350	+	0.974509i	$0.427974\pi$
$602$	20.0000	+	17.3205i	0.815139	+	0.705931i
$603$		0			0
$604$	0.500000	+	0.866025i	0.0203447	+	0.0352381i
$605$	−3.00000	+	5.19615i	−0.121967	+	0.211254i
$606$		0			0
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	0.928272	−	0.371901i	$-0.121294\pi$
$607$	3.50000	+	6.06218i	0.142061	+	0.246056i	−0.786212	+	0.617957i	$0.787961\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$	30.0000			1.21466
$611$	12.0000	+	20.7846i	0.485468	+	0.840855i
$612$		0			0
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	−4.00000	−	6.92820i	−0.161427	−	0.279600i
$615$		0			0
$616$	1.50000	−	7.79423i	0.0604367	−	0.314038i
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$		0			0
$619$	17.0000	−	29.4449i	0.683288	−	1.18349i	−0.290684	−	0.956819i	$-0.593883\pi$
$619$	17.0000	−	29.4449i	0.683288	−	1.18349i	0.973972	−	0.226670i	$-0.0727838\pi$
$620$	−1.50000	+	2.59808i	−0.0602414	+	0.104341i
$621$		0			0
$622$	−24.0000			−0.962312
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	15.5000	−	26.8468i	0.619505	−	1.07301i
$627$		0			0
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$		0			0
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	0.500000	+	0.866025i	0.0198889	+	0.0344486i
$633$		0			0
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$	7.50000	+	12.9904i	0.297628	+	0.515508i
$636$		0			0
$637$	−22.0000	+	17.3205i	−0.871672	+	0.686264i
$638$	27.0000			1.06894
$639$		0			0
$640$	1.50000	−	2.59808i	0.0592927	−	0.102698i
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	0.401435	+	0.915888i	$0.368512\pi$
$641$	−15.0000	+	25.9808i	−0.592464	+	1.02618i	−0.993899	+	0.110291i	$0.964822\pi$
$642$		0			0
$643$	−34.0000			−1.34083			−0.670415	−	0.741987i	$-0.733884\pi$
$643$	−34.0000			−1.34083			−0.670415	+	0.741987i	$0.733884\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	−0.986916	−	0.161233i	$-0.948453\pi$
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	0.633090	+	0.774078i	$0.281786\pi$
$648$		0			0
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$	−16.0000			−0.627572
$651$		0			0
$652$	−16.0000			−0.626608
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	0.893882	−	0.448303i	$-0.147971\pi$
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	−0.835182	+	0.549973i	$0.814638\pi$
$654$		0			0
$655$	13.5000	−	23.3827i	0.527489	−	0.913637i
$656$		0			0
$657$		0			0
$658$	−3.00000	+	15.5885i	−0.116952	+	0.607701i
$659$	24.0000			0.934907			0.467454	−	0.884018i	$-0.345171\pi$
$659$	24.0000			0.934907			0.467454	+	0.884018i	$0.345171\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	−10.0000	+	17.3205i	−0.388661	+	0.673181i
$663$		0			0
$664$	9.00000			0.349268
$665$	−6.00000	+	31.1769i	−0.232670	+	1.20899i
$666$		0			0
$667$		0			0
$668$	3.00000	−	5.19615i	0.116073	−	0.201045i
$669$		0			0
$670$	−15.0000	−	25.9808i	−0.579501	−	1.00372i
$671$	30.0000			1.15814
$672$		0			0
$673$	29.0000			1.11787			0.558934	−	0.829212i	$-0.311211\pi$
$673$	29.0000			1.11787			0.558934	+	0.829212i	$0.311211\pi$
$674$	3.50000	+	6.06218i	0.134815	+	0.233506i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	−0.986695	−	0.162581i	$-0.948018\pi$
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$678$		0			0
$679$	−2.50000	+	0.866025i	−0.0959412	+	0.0332350i
$680$		0			0
$681$		0			0
$682$	−1.50000	+	2.59808i	−0.0574380	+	0.0994855i
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	−0.355920	−	0.934516i	$-0.615832\pi$
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	0.987275	−	0.159022i	$-0.0508342\pi$
$684$		0			0
$685$	54.0000			2.06323
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$		0			0
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	−12.0000			−0.455514
$695$	3.00000	+	5.19615i	0.113796	+	0.197101i
$696$		0			0
$697$		0			0
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$		0			0
$700$	−8.00000	−	6.92820i	−0.302372	−	0.261861i
$701$	15.0000			0.566542			0.283271	−	0.959040i	$-0.408580\pi$
$701$	15.0000			0.566542			0.283271	+	0.959040i	$0.408580\pi$
$702$		0			0
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	−24.0000			−0.903252
$707$	−9.00000	+	46.7654i	−0.338480	+	1.75879i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$	9.00000	−	15.5885i	0.337764	−	0.585024i
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$		0			0
$714$		0			0
$715$	−36.0000			−1.34632
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	15.0000	−	25.9808i	0.559795	−	0.969593i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$	−16.0000	−	13.8564i	−0.595871	−	0.516040i
$722$	−3.00000			−0.111648
$723$		0			0
$724$	−4.00000	+	6.92820i	−0.148659	+	0.257485i
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$	−10.0000	+	3.46410i	−0.370625	+	0.128388i
$729$		0			0
$730$	3.00000	+	5.19615i	0.111035	+	0.192318i
$731$		0			0
$732$		0			0
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	0.943468	−	0.331463i	$-0.107542\pi$
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	−0.758789	+	0.651336i	$0.774209\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$		0			0
$737$	−15.0000	−	25.9808i	−0.552532	−	0.957014i
$738$		0			0
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.119677	+	0.992813i	$0.538186\pi$
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.799962	+	0.600050i	$0.795147\pi$
$740$	12.0000	+	20.7846i	0.441129	+	0.764057i
$741$		0			0
$742$	7.50000	−	2.59808i	0.275334	−	0.0953784i
$743$	−42.0000			−1.54083			−0.770415	−	0.637542i	$-0.779951\pi$
$743$	−42.0000			−1.54083			−0.770415	+	0.637542i	$0.779951\pi$
$744$		0			0
$745$	−27.0000	+	46.7654i	−0.989203	+	1.71335i
$746$	−4.00000	+	6.92820i	−0.146450	+	0.253660i
$747$		0			0
$748$		0			0
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$		0			0
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	0.922792	−	0.385299i	$-0.125902\pi$
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	−0.795075	+	0.606511i	$0.792568\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$		0			0
$754$	−18.0000	−	31.1769i	−0.655521	−	1.13540i
$755$	3.00000			0.109181
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	−4.00000	−	6.92820i	−0.145287	−	0.251644i
$759$		0			0
$760$	−6.00000	+	10.3923i	−0.217643	+	0.376969i
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	0.954043	−	0.299670i	$-0.0968765\pi$
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	−0.736543	+	0.676391i	$0.763543\pi$
$762$		0			0
$763$	−7.00000	+	36.3731i	−0.253417	+	1.31679i
$764$		0			0
$765$		0			0
$766$	9.00000	−	15.5885i	0.325183	−	0.563234i
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$		0			0
$769$	−19.0000			−0.685158			−0.342579	−	0.939489i	$-0.611300\pi$
$769$	−19.0000			−0.685158			−0.342579	+	0.939489i	$0.611300\pi$
$770$	−18.0000	−	15.5885i	−0.648675	−	0.561769i
$771$		0			0
$772$	9.50000	+	16.4545i	0.341912	+	0.592210i
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$		0			0
$775$	2.00000	+	3.46410i	0.0718421	+	0.124434i
$776$	−1.00000			−0.0358979
$777$		0			0
$778$	6.00000			0.215110
$779$		0			0
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$		0			0
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$	12.0000			0.428298
$786$		0			0
$787$	−25.0000	+	43.3013i	−0.891154	+	1.54352i	−0.0526599	+	0.998613i	$0.516770\pi$
$787$	−25.0000	+	43.3013i	−0.891154	+	1.54352i	−0.838494	+	0.544911i	$0.816563\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$		0			0
$790$	3.00000			0.106735
$791$		0			0
$792$		0			0
$793$	−20.0000	−	34.6410i	−0.710221	−	1.23014i
$794$	2.00000	−	3.46410i	0.0709773	−	0.122936i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	12.0000	−	20.7846i	0.423735	−	0.733930i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$		0			0
$805$		0			0
$806$	4.00000			0.140894
$807$		0			0
$808$	−9.00000	+	15.5885i	−0.316619	+	0.548400i
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	4.50000	−	23.3827i	0.157919	−	0.820571i
$813$		0			0
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	−24.0000	+	41.5692i	−0.840683	+	1.45611i
$816$		0			0
$817$	−20.0000	−	34.6410i	−0.699711	−	1.21194i
$818$	−25.0000			−0.874105
$819$		0			0
$820$		0			0
$821$	−1.50000	−	2.59808i	−0.0523504	−	0.0906735i	0.838663	−	0.544651i	$-0.183338\pi$
$821$	−1.50000	−	2.59808i	−0.0523504	−	0.0906735i	−0.891013	+	0.453978i	$0.850005\pi$
$822$		0			0
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	−4.00000	−	6.92820i	−0.139347	−	0.241355i
$825$		0			0
$826$	−7.50000	+	2.59808i	−0.260958	+	0.0903986i
$827$	−15.0000			−0.521601			−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000			−0.521601			−0.260801	+	0.965393i	$0.583986\pi$
$828$		0			0
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	−0.829202	−	0.558949i	$-0.811205\pi$
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	0.898665	+	0.438636i	$0.144538\pi$
$830$	13.5000	−	23.3827i	0.468592	−	0.811625i
$831$		0			0
$832$	−4.00000			−0.138675
$833$		0			0
$834$		0			0
$835$	−9.00000	−	15.5885i	−0.311458	−	0.539461i
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$		0			0
$838$		0			0
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	11.0000	+	19.0526i	0.379085	+	0.656595i
$843$		0			0
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$		0			0
$847$	4.00000	+	3.46410i	0.137442	+	0.119028i
$848$	3.00000			0.103020
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−10.0000			−0.342393			−0.171197	−	0.985237i	$-0.554763\pi$
$853$	−10.0000			−0.342393			−0.171197	+	0.985237i	$0.554763\pi$
$854$	5.00000	−	25.9808i	0.171096	−	0.889043i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$		0			0
$859$	−25.0000	−	43.3013i	−0.852989	−	1.47742i	−0.878498	−	0.477746i	$-0.841454\pi$
$859$	−25.0000	−	43.3013i	−0.852989	−	1.47742i	0.0255092	−	0.999675i	$-0.491879\pi$
$860$	30.0000			1.02299
$861$		0			0
$862$	−12.0000			−0.408722
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$		0			0
$865$	−27.0000	+	46.7654i	−0.918028	+	1.59007i
$866$	17.0000	+	29.4449i	0.577684	+	1.00058i
$867$		0			0
$868$	2.00000	+	1.73205i	0.0678844	+	0.0587896i
$869$	3.00000			0.101768
$870$		0			0
$871$	−20.0000	+	34.6410i	−0.677674	+	1.17377i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$		0			0
$874$		0			0
$875$	7.50000	−	2.59808i	0.253546	−	0.0878310i
$876$		0			0
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	−0.998888	−	0.0471555i	$-0.984984\pi$
$877$	−16.0000	−	27.7128i	−0.540282	−	0.935795i	0.458606	−	0.888640i	$-0.348349\pi$
$878$	−17.5000	+	30.3109i	−0.590596	+	1.02294i
$879$		0			0
$880$	−4.50000	−	7.79423i	−0.151695	−	0.262743i
$881$	6.00000			0.202145			0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000			0.202145			0.101073	+	0.994879i	$0.467773\pi$
$882$		0			0
$883$	32.0000			1.07689			0.538443	−	0.842662i	$-0.319013\pi$
$883$	32.0000			1.07689			0.538443	+	0.842662i	$0.319013\pi$
$884$		0			0
$885$		0			0
$886$	−16.5000	+	28.5788i	−0.554328	+	0.960125i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$		0			0
$889$	12.5000	−	4.33013i	0.419237	−	0.145228i
$890$	18.0000			0.603361
$891$		0			0
$892$	9.50000	−	16.4545i	0.318084	−	0.550937i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$		0			0
$895$	36.0000			1.20335
$896$	−2.00000	−	1.73205i	−0.0668153	−	0.0578638i
$897$		0			0
$898$	6.00000	+	10.3923i	0.200223	+	0.346796i
$899$	−4.50000	+	7.79423i	−0.150083	+	0.259952i
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.0000	+	20.7846i	0.398893	+	0.690904i
$906$		0			0
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	−13.5000	−	23.3827i	−0.448013	−	0.775982i
$909$		0			0
$910$	−6.00000	+	31.1769i	−0.198898	+	1.03350i
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$		0			0
$913$	13.5000	−	23.3827i	0.446785	−	0.773854i
$914$	0.500000	−	0.866025i	0.0165385	−	0.0286456i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	−18.0000	−	15.5885i	−0.594412	−	0.514776i
$918$		0			0
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$		0			0
$921$		0			0
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$	−24.0000			−0.789970
$924$		0			0
$925$	32.0000			1.05215
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$		0			0
$928$	4.50000	−	7.79423i	0.147720	−	0.255858i
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	0.812607	−	0.582812i	$-0.198048\pi$
$929$	−3.00000	−	5.19615i	−0.0984268	−	0.170480i	−0.911034	+	0.412332i	$0.864714\pi$
$930$		0			0
$931$	26.0000	+	10.3923i	0.852116	+	0.340594i
$932$	24.0000			0.786146
$933$		0			0
$934$	18.0000	−	31.1769i	0.588978	−	1.02014i
$935$		0			0
$936$		0			0
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	−25.0000	+	8.66025i	−0.816279	+	0.282767i
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	−4.50000	+	7.79423i	−0.146696	+	0.254085i	−0.930004	−	0.367549i	$-0.880197\pi$
$941$	−4.50000	+	7.79423i	−0.146696	+	0.254085i	0.783309	+	0.621633i	$0.213531\pi$
$942$		0			0
$943$		0			0
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	30.0000			0.975384
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$		0			0
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	8.00000	+	13.8564i	0.259554	+	0.449561i
$951$		0			0
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	18.0000			0.581554
$959$	9.00000	−	46.7654i	0.290625	−	1.51013i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	16.0000	−	27.7128i	0.515861	−	0.893497i
$963$		0			0
$964$	0.500000	+	0.866025i	0.0161039	+	0.0278928i
$965$	57.0000			1.83489
$966$		0			0
$967$	−1.00000			−0.0321578			−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000			−0.0321578			−0.0160789	+	0.999871i	$0.505118\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$	−1.50000	+	2.59808i	−0.0481621	+	0.0834192i
$971$	−19.5000	−	33.7750i	−0.625785	−	1.08389i	−0.988389	−	0.151948i	$-0.951445\pi$
$971$	−19.5000	−	33.7750i	−0.625785	−	1.08389i	0.362604	−	0.931943i	$-0.381888\pi$
$972$		0			0
$973$	5.00000	−	1.73205i	0.160293	−	0.0555270i
$974$	41.0000			1.31372
$975$		0			0
$976$	5.00000	−	8.66025i	0.160046	−	0.277208i
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$		0			0
$979$	18.0000			0.575282
$980$	−16.5000	+	12.9904i	−0.527073	+	0.414963i
$981$		0			0
$982$	−16.5000	−	28.5788i	−0.526536	−	0.911987i
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		0			0
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$		0			0
$987$		0			0
$988$	16.0000			0.509028
$989$		0			0
$990$		0			0
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	0.500000	+	0.866025i	0.0158750	+	0.0274963i
$993$		0			0
$994$	−12.0000	−	10.3923i	−0.380617	−	0.329624i
$995$	−60.0000			−1.90213
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	−1.00000	+	1.73205i	−0.0316544	+	0.0548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.g.b.109.1		2
3.2	odd	2		42.2.e.b.25.1	✓	2
4.3	odd	2		1008.2.s.n.865.1		2
7.2	even	3	inner	126.2.g.b.37.1		2
7.3	odd	6		882.2.a.k.1.1		1
7.4	even	3		882.2.a.g.1.1		1
7.5	odd	6		882.2.g.b.667.1		2
7.6	odd	2		882.2.g.b.361.1		2
9.2	odd	6		1134.2.h.p.109.1		2
9.4	even	3		1134.2.e.p.865.1		2
9.5	odd	6		1134.2.e.a.865.1		2
9.7	even	3		1134.2.h.a.109.1		2
12.11	even	2		336.2.q.d.193.1		2
15.2	even	4		1050.2.o.b.949.1		4
15.8	even	4		1050.2.o.b.949.2		4
15.14	odd	2		1050.2.i.e.151.1		2
21.2	odd	6		42.2.e.b.37.1	yes	2
21.5	even	6		294.2.e.f.79.1		2
21.11	odd	6		294.2.a.d.1.1		1
21.17	even	6		294.2.a.a.1.1		1
21.20	even	2		294.2.e.f.67.1		2
24.5	odd	2		1344.2.q.v.193.1		2
24.11	even	2		1344.2.q.j.193.1		2
28.3	even	6		7056.2.a.bz.1.1		1
28.11	odd	6		7056.2.a.g.1.1		1
28.23	odd	6		1008.2.s.n.289.1		2
63.2	odd	6		1134.2.e.a.919.1		2
63.16	even	3		1134.2.e.p.919.1		2
63.23	odd	6		1134.2.h.p.541.1		2
63.58	even	3		1134.2.h.a.541.1		2
84.11	even	6		2352.2.a.m.1.1		1
84.23	even	6		336.2.q.d.289.1		2
84.47	odd	6		2352.2.q.m.961.1		2
84.59	odd	6		2352.2.a.n.1.1		1
84.83	odd	2		2352.2.q.m.1537.1		2
105.2	even	12		1050.2.o.b.499.2		4
105.23	even	12		1050.2.o.b.499.1		4
105.44	odd	6		1050.2.i.e.751.1		2
105.59	even	6		7350.2.a.cw.1.1		1
105.74	odd	6		7350.2.a.ce.1.1		1
168.11	even	6		9408.2.a.bu.1.1		1
168.53	odd	6		9408.2.a.d.1.1		1
168.59	odd	6		9408.2.a.bm.1.1		1
168.101	even	6		9408.2.a.db.1.1		1
168.107	even	6		1344.2.q.j.961.1		2
168.149	odd	6		1344.2.q.v.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.b.25.1	✓	2	3.2	odd	2
42.2.e.b.37.1	yes	2	21.2	odd	6
126.2.g.b.37.1		2	7.2	even	3	inner
126.2.g.b.109.1		2	1.1	even	1	trivial
294.2.a.a.1.1		1	21.17	even	6
294.2.a.d.1.1		1	21.11	odd	6
294.2.e.f.67.1		2	21.20	even	2
294.2.e.f.79.1		2	21.5	even	6
336.2.q.d.193.1		2	12.11	even	2
336.2.q.d.289.1		2	84.23	even	6
882.2.a.g.1.1		1	7.4	even	3
882.2.a.k.1.1		1	7.3	odd	6
882.2.g.b.361.1		2	7.6	odd	2
882.2.g.b.667.1		2	7.5	odd	6
1008.2.s.n.289.1		2	28.23	odd	6
1008.2.s.n.865.1		2	4.3	odd	2
1050.2.i.e.151.1		2	15.14	odd	2
1050.2.i.e.751.1		2	105.44	odd	6
1050.2.o.b.499.1		4	105.23	even	12
1050.2.o.b.499.2		4	105.2	even	12
1050.2.o.b.949.1		4	15.2	even	4
1050.2.o.b.949.2		4	15.8	even	4
1134.2.e.a.865.1		2	9.5	odd	6
1134.2.e.a.919.1		2	63.2	odd	6
1134.2.e.p.865.1		2	9.4	even	3
1134.2.e.p.919.1		2	63.16	even	3
1134.2.h.a.109.1		2	9.7	even	3
1134.2.h.a.541.1		2	63.58	even	3
1134.2.h.p.109.1		2	9.2	odd	6
1134.2.h.p.541.1		2	63.23	odd	6
1344.2.q.j.193.1		2	24.11	even	2
1344.2.q.j.961.1		2	168.107	even	6
1344.2.q.v.193.1		2	24.5	odd	2
1344.2.q.v.961.1		2	168.149	odd	6
2352.2.a.m.1.1		1	84.11	even	6
2352.2.a.n.1.1		1	84.59	odd	6
2352.2.q.m.961.1		2	84.47	odd	6
2352.2.q.m.1537.1		2	84.83	odd	2
7056.2.a.g.1.1		1	28.11	odd	6
7056.2.a.bz.1.1		1	28.3	even	6
7350.2.a.ce.1.1		1	105.74	odd	6
7350.2.a.cw.1.1		1	105.59	even	6
9408.2.a.d.1.1		1	168.53	odd	6
9408.2.a.bm.1.1		1	168.59	odd	6
9408.2.a.bu.1.1		1	168.11	even	6
9408.2.a.db.1.1		1	168.101	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{10} +(1.50000 - 2.59808i) q^{11} -4.00000 q^{13} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{19} -3.00000 q^{20} -3.00000 q^{22} +(-2.00000 + 3.46410i) q^{25} +(2.00000 + 3.46410i) q^{26} +(-0.500000 + 2.59808i) q^{28} -9.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(6.00000 + 5.19615i) q^{35} +(-4.00000 - 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(1.50000 + 2.59808i) q^{40} -10.0000 q^{43} +(1.50000 + 2.59808i) q^{44} +(-3.00000 - 5.19615i) q^{47} +(5.50000 - 4.33013i) q^{49} +4.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +9.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +(4.50000 + 7.79423i) q^{58} +(1.50000 - 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} -1.00000 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(5.00000 - 8.66025i) q^{67} +(1.50000 - 7.79423i) q^{70} +6.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(1.50000 - 7.79423i) q^{77} +(0.500000 + 0.866025i) q^{79} +(1.50000 - 2.59808i) q^{80} +9.00000 q^{83} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-3.00000 + 5.19615i) q^{94} +(-6.00000 + 10.3923i) q^{95} -1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 3 * q^5 + 5 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 3 q^{5} + 5 q^{7} + 2 q^{8} + 3 q^{10} + 3 q^{11} - 8 q^{13} - 4 q^{14} - q^{16} + 4 q^{19} - 6 q^{20} - 6 q^{22} - 4 q^{25} + 4 q^{26} - q^{28} - 18 q^{29} + q^{31} - q^{32} + 12 q^{35} - 8 q^{37} + 4 q^{38} + 3 q^{40} - 20 q^{43} + 3 q^{44} - 6 q^{47} + 11 q^{49} + 8 q^{50} + 4 q^{52} - 3 q^{53} + 18 q^{55} + 5 q^{56} + 9 q^{58} + 3 q^{59} + 10 q^{61} - 2 q^{62} + 2 q^{64} - 12 q^{65} + 10 q^{67} + 3 q^{70} + 12 q^{71} - 2 q^{73} - 8 q^{74} - 8 q^{76} + 3 q^{77} + q^{79} + 3 q^{80} + 18 q^{83} + 10 q^{86} + 3 q^{88} + 6 q^{89} - 20 q^{91} - 6 q^{94} - 12 q^{95} - 2 q^{97} - 13 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 3 * q^5 + 5 * q^7 + 2 * q^8 + 3 * q^10 + 3 * q^11 - 8 * q^13 - 4 * q^14 - q^16 + 4 * q^19 - 6 * q^20 - 6 * q^22 - 4 * q^25 + 4 * q^26 - q^28 - 18 * q^29 + q^31 - q^32 + 12 * q^35 - 8 * q^37 + 4 * q^38 + 3 * q^40 - 20 * q^43 + 3 * q^44 - 6 * q^47 + 11 * q^49 + 8 * q^50 + 4 * q^52 - 3 * q^53 + 18 * q^55 + 5 * q^56 + 9 * q^58 + 3 * q^59 + 10 * q^61 - 2 * q^62 + 2 * q^64 - 12 * q^65 + 10 * q^67 + 3 * q^70 + 12 * q^71 - 2 * q^73 - 8 * q^74 - 8 * q^76 + 3 * q^77 + q^79 + 3 * q^80 + 18 * q^83 + 10 * q^86 + 3 * q^88 + 6 * q^89 - 20 * q^91 - 6 * q^94 - 12 * q^95 - 2 * q^97 - 13 * q^98

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