LMFDB - Embedded newform 1134.2.h.g.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(109,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("1134.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (of order $3$, degree $2$, not 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:	$9.05503558921$
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 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.109
Dual form			1134.2.h.g.541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(2.00000 - 3.46410i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +6.00000 q^{23} +4.00000 q^{25} +(2.00000 + 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{34} +(7.50000 + 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} -4.00000 q^{38} +3.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} -4.00000 q^{52} +(-4.50000 + 7.79423i) q^{53} +(2.50000 + 0.866025i) q^{56} -3.00000 q^{58} +(1.50000 + 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(5.00000 + 8.66025i) q^{67} +6.00000 q^{68} +(-6.00000 + 5.19615i) q^{70} +6.00000 q^{71} +(3.50000 - 6.06218i) q^{73} +8.00000 q^{74} +(2.00000 - 3.46410i) q^{76} +(-8.50000 + 14.7224i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(3.00000 + 5.19615i) q^{82} +(6.00000 + 10.3923i) q^{83} +(-9.00000 + 15.5885i) q^{85} +8.00000 q^{86} +(-3.00000 - 5.19615i) q^{89} +(8.00000 - 6.92820i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(5.00000 + 8.66025i) q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 6 q^{5} + 5 q^{7} + 2 q^{8} - 3 q^{10} + 4 q^{13} - 4 q^{14} - q^{16} - 6 q^{17} + 4 q^{19} - 3 q^{20} + 12 q^{23} + 8 q^{25} + 4 q^{26} - q^{28} + 3 q^{29} - 8 q^{31} - q^{32}+ \cdots - 13 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 6 * q^5 + 5 * q^7 + 2 * q^8 - 3 * q^10 + 4 * q^13 - 4 * q^14 - q^16 - 6 * q^17 + 4 * q^19 - 3 * q^20 + 12 * q^23 + 8 * q^25 + 4 * q^26 - q^28 + 3 * q^29 - 8 * q^31 - q^32 - 6 * q^34 + 15 * q^35 - 8 * q^37 - 8 * q^38 + 6 * q^40 + 6 * q^41 - 8 * q^43 - 6 * q^46 - 6 * q^47 + 11 * q^49 - 4 * q^50 - 8 * q^52 - 9 * q^53 + 5 * q^56 - 6 * q^58 + 3 * q^59 + 10 * q^61 + 16 * q^62 + 2 * q^64 + 12 * q^65 + 10 * q^67 + 12 * q^68 - 12 * q^70 + 12 * q^71 + 7 * q^73 + 16 * q^74 + 4 * q^76 - 17 * q^79 - 3 * q^80 + 6 * q^82 + 12 * q^83 - 18 * q^85 + 16 * q^86 - 6 * q^89 + 16 * q^91 - 6 * q^92 - 6 * q^94 + 12 * q^95 + 10 * q^97 - 13 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−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
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		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
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		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	$0.681602\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$		0			0
$22$		0			0
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$		0			0
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.00000	−	5.19615i	−0.514496	−	0.891133i
$35$	7.50000	+	2.59808i	1.26773	+	0.439155i
$36$		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	$-0.395093\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$	3.00000			0.474342
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$		0			0
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	−4.00000			−0.554700
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		0			0
$55$		0			0
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$		0			0
$58$	−3.00000			−0.393919
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	0.946993	−	0.321253i	$-0.104104\pi$
$59$	1.50000	+	2.59808i	0.195283	+	0.338241i	−0.751710	+	0.659494i	$0.770771\pi$
$60$		0			0
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	8.00000			1.01600
$63$		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	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$	6.00000			0.727607
$69$		0			0
$70$	−6.00000	+	5.19615i	−0.717137	+	0.621059i
$71$	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
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	8.00000			0.929981
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$		0			0
$78$		0			0
$79$	−8.50000	+	14.7224i	−0.956325	+	1.65640i	−0.225018	+	0.974355i	$0.572244\pi$
$79$	−8.50000	+	14.7224i	−0.956325	+	1.65640i	−0.731307	+	0.682048i	$0.761089\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$		0			0
$82$	3.00000	+	5.19615i	0.331295	+	0.573819i
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	−9.00000	+	15.5885i	−0.976187	+	1.69081i
$86$	8.00000			0.862662
$87$		0			0
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	8.00000	−	6.92820i	0.838628	−	0.726273i
$92$	−3.00000	−	5.19615i	−0.312772	−	0.541736i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$		0			0
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	0.999961	+	0.00888289i	$0.00282755\pi$
$97$	5.00000	+	8.66025i	0.507673	+	0.879316i	−0.492287	+	0.870433i	$0.663839\pi$
$98$	−6.50000	+	2.59808i	−0.656599	+	0.262445i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−15.0000			−1.49256			−0.746278	−	0.665635i	$-0.768161\pi$
$101$	−15.0000			−1.49256			−0.746278	+	0.665635i	$0.768161\pi$
$102$		0			0
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$		0			0
$106$	−4.50000	−	7.79423i	−0.437079	−	0.757042i
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$		0			0
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	−0.754204	−	0.656640i	$-0.771977\pi$
$109$	2.00000	−	3.46410i	0.191565	−	0.331801i	0.945769	+	0.324840i	$0.105310\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$	18.0000			1.67851
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$		0			0
$118$	−3.00000			−0.276172
$119$	−12.0000	+	10.3923i	−1.10004	+	0.952661i
$120$		0			0
$121$	−11.0000			−1.00000
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	−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
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$		0			0
$133$	2.00000	+	10.3923i	0.173422	+	0.901127i
$134$	−10.0000			−0.863868
$135$		0			0
$136$	−3.00000	+	5.19615i	−0.257248	+	0.445566i
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$		0			0
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	−0.905314	−	0.424743i	$-0.860365\pi$
$139$	−1.00000	+	1.73205i	−0.0848189	+	0.146911i	0.820495	+	0.571654i	$0.193698\pi$
$140$	−1.50000	−	7.79423i	−0.126773	−	0.658733i
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$		0			0
$144$		0			0
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	3.50000	+	6.06218i	0.289662	+	0.501709i
$147$		0			0
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	−21.0000			−1.72039			−0.860194	−	0.509968i	$-0.829657\pi$
$149$	−21.0000			−1.72039			−0.860194	+	0.509968i	$0.829657\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$		0			0
$154$		0			0
$155$	−12.0000	−	20.7846i	−0.963863	−	1.66946i
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$	−8.50000	−	14.7224i	−0.676224	−	1.17125i
$159$		0			0
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$	15.0000	+	5.19615i	1.18217	+	0.409514i
$162$		0			0
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	0.824202	−	0.566296i	$-0.191624\pi$
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	−0.902528	+	0.430632i	$0.858291\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	−12.0000			−0.931381
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−9.00000	−	15.5885i	−0.690268	−	1.19558i
$171$		0			0
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	−0.642699	−	0.766119i	$-0.722185\pi$
$173$	4.50000	−	7.79423i	0.342129	−	0.592584i	0.984828	+	0.173534i	$0.0555188\pi$
$174$		0			0
$175$	10.0000	+	3.46410i	0.755929	+	0.261861i
$176$		0			0
$177$		0			0
$178$	6.00000			0.449719
$179$	7.50000	−	12.9904i	0.560576	−	0.970947i	−0.436870	−	0.899525i	$-0.643913\pi$
$179$	7.50000	−	12.9904i	0.560576	−	0.970947i	0.997446	−	0.0714220i	$-0.0227537\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	2.00000	+	10.3923i	0.148250	+	0.770329i
$183$		0			0
$184$	6.00000			0.442326
$185$	−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
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$		0			0
$193$	−13.0000	−	22.5167i	−0.935760	−	1.62078i	−0.773272	−	0.634074i	$-0.781381\pi$
$193$	−13.0000	−	22.5167i	−0.935760	−	1.62078i	−0.162488	−	0.986710i	$-0.551952\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−15.0000			−1.06871			−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$		0			0
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	0.602549	+	0.798082i	$0.294152\pi$
$200$	4.00000			0.282843
$201$		0			0
$202$	7.50000	−	12.9904i	0.527698	−	0.914000i
$203$	1.50000	+	7.79423i	0.105279	+	0.547048i
$204$		0			0
$205$	9.00000	−	15.5885i	0.628587	−	1.08875i
$206$	−4.00000	+	6.92820i	−0.278693	+	0.482711i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$		0			0
$210$		0			0
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	9.00000			0.618123
$213$		0			0
$214$	−3.00000			−0.205076
$215$	−12.0000	−	20.7846i	−0.818393	−	1.41750i
$216$		0			0
$217$	−4.00000	−	20.7846i	−0.271538	−	1.41095i
$218$	2.00000	+	3.46410i	0.135457	+	0.234619i
$219$		0			0
$220$		0			0
$221$	12.0000	+	20.7846i	0.807207	+	1.39812i
$222$		0			0
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$	−9.00000	+	15.5885i	−0.593442	+	1.02787i
$231$		0			0
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	−0.994283	−	0.106773i	$-0.965948\pi$
$233$	−9.00000	−	15.5885i	−0.589610	−	1.02123i	0.404674	−	0.914461i	$-0.367385\pi$
$234$		0			0
$235$	−9.00000	+	15.5885i	−0.587095	+	1.01688i
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$		0			0
$238$	−3.00000	−	15.5885i	−0.194461	−	1.01045i
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−1.00000			−0.0644157			−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000			−0.0644157			−0.0322078	+	0.999481i	$0.510254\pi$
$242$	5.50000	−	9.52628i	0.353553	−	0.612372i
$243$		0			0
$244$	−10.0000			−0.640184
$245$	16.5000	+	12.9904i	1.05415	+	0.829925i
$246$		0			0
$247$	16.0000			1.01806
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$		0			0
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$		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
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$		0			0
$259$	−4.00000	−	20.7846i	−0.248548	−	1.29149i
$260$	−12.0000			−0.744208
$261$		0			0
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	−18.0000			−1.10993			−0.554964	−	0.831875i	$-0.687268\pi$
$263$	−18.0000			−1.10993			−0.554964	+	0.831875i	$0.687268\pi$
$264$		0			0
$265$	−13.5000	+	23.3827i	−0.829298	+	1.43639i
$266$	−10.0000	−	3.46410i	−0.613139	−	0.212398i
$267$		0			0
$268$	5.00000	−	8.66025i	0.305424	−	0.529009i
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$		0			0
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	0.943197	+	0.332233i	$0.107802\pi$
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	−0.183876	+	0.982949i	$0.558865\pi$
$272$	−3.00000	−	5.19615i	−0.181902	−	0.315063i
$273$		0			0
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$		0			0
$277$	−28.0000			−1.68236			−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−28.0000			−1.68236			−0.841178	+	0.540758i	$0.818138\pi$
$278$	−1.00000	−	1.73205i	−0.0599760	−	0.103882i
$279$		0			0
$280$	7.50000	+	2.59808i	0.448211	+	0.155265i
$281$	9.00000	+	15.5885i	0.536895	+	0.929929i	0.999069	+	0.0431402i	$0.0137362\pi$
$281$	9.00000	+	15.5885i	0.536895	+	0.929929i	−0.462174	+	0.886789i	$0.652930\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		0			0
$286$		0			0
$287$	12.0000	−	10.3923i	0.708338	−	0.613438i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	−9.00000			−0.528498
$291$		0			0
$292$	−7.00000			−0.409644
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	−0.818878	−	0.573967i	$-0.805404\pi$
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$294$		0			0
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$		0			0
$298$	10.5000	−	18.1865i	0.608249	−	1.05352i
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$		0			0
$301$	−4.00000	−	20.7846i	−0.230556	−	1.19800i
$302$	−4.00000	+	6.92820i	−0.230174	+	0.398673i
$303$		0			0
$304$	−4.00000			−0.229416
$305$	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	$0.426686\pi$
$308$		0			0
$309$		0			0
$310$	24.0000			1.36311
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	−0.927990	−	0.372606i	$-0.878464\pi$
$313$	−2.50000	+	4.33013i	−0.141308	+	0.244753i	0.786681	+	0.617359i	$0.211798\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	17.0000			0.956325
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$		0			0
$320$	3.00000			0.167705
$321$		0			0
$322$	−12.0000	+	10.3923i	−0.668734	+	0.579141i
$323$	−24.0000			−1.33540
$324$		0			0
$325$	8.00000	−	13.8564i	0.443760	−	0.768615i
$326$	2.00000			0.110770
$327$		0			0
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	−12.0000	+	10.3923i	−0.661581	+	0.572946i
$330$		0			0
$331$	−1.00000	+	1.73205i	−0.0549650	+	0.0952021i	−0.892199	−	0.451643i	$-0.850838\pi$
$331$	−1.00000	+	1.73205i	−0.0549650	+	0.0952021i	0.837234	+	0.546845i	$0.184171\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$		0			0
$334$	−3.00000	−	5.19615i	−0.164153	−	0.284321i
$335$	15.0000	+	25.9808i	0.819538	+	1.41948i
$336$		0			0
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$	3.00000			0.163178
$339$		0			0
$340$	18.0000			0.976187
$341$		0			0
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−4.00000	−	6.92820i	−0.215666	−	0.373544i
$345$		0			0
$346$	4.50000	+	7.79423i	0.241921	+	0.419020i
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.844833	−	0.535031i	$-0.820300\pi$
$347$	−16.5000	−	28.5788i	−0.885766	−	1.53419i	−0.0409337	−	0.999162i	$-0.513033\pi$
$348$		0			0
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$	−8.00000	+	6.92820i	−0.427618	+	0.370328i
$351$		0			0
$352$		0			0
$353$	−30.0000			−1.59674			−0.798369	−	0.602168i	$-0.794304\pi$
$353$	−30.0000			−1.59674			−0.798369	+	0.602168i	$0.794304\pi$
$354$		0			0
$355$	18.0000			0.955341
$356$	−3.00000	+	5.19615i	−0.159000	+	0.275396i
$357$		0			0
$358$	7.50000	+	12.9904i	0.396387	+	0.686563i
$359$	−18.0000	−	31.1769i	−0.950004	−	1.64545i	−0.745409	−	0.666608i	$-0.767746\pi$
$359$	−18.0000	−	31.1769i	−0.950004	−	1.64545i	−0.204595	−	0.978847i	$-0.565588\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$		0			0
$364$	−10.0000	−	3.46410i	−0.524142	−	0.181568i
$365$	10.5000	−	18.1865i	0.549595	−	0.951927i
$366$		0			0
$367$	−19.0000			−0.991792			−0.495896	−	0.868382i	$-0.665160\pi$
$367$	−19.0000			−0.991792			−0.495896	+	0.868382i	$0.665160\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$		0			0
$370$	24.0000			1.24770
$371$	−18.0000	+	15.5885i	−0.934513	+	0.809312i
$372$		0			0
$373$	−10.0000			−0.517780			−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000			−0.517780			−0.258890	+	0.965907i	$0.583357\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	12.0000			0.618031
$378$		0			0
$379$	−10.0000			−0.513665			−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000			−0.513665			−0.256833	+	0.966456i	$0.582679\pi$
$380$	6.00000	−	10.3923i	0.307794	−	0.533114i
$381$		0			0
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	6.00000			0.306586			0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000			0.306586			0.153293	+	0.988181i	$0.451012\pi$
$384$		0			0
$385$		0			0
$386$	26.0000			1.32337
$387$		0			0
$388$	5.00000	−	8.66025i	0.253837	−	0.439658i
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$		0			0
$391$	−18.0000	+	31.1769i	−0.910299	+	1.57668i
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$		0			0
$394$	7.50000	−	12.9904i	0.377845	−	0.654446i
$395$	−25.5000	+	44.1673i	−1.28304	+	2.22230i
$396$		0			0
$397$	−16.0000	−	27.7128i	−0.803017	−	1.39087i	−0.917622	−	0.397455i	$-0.869893\pi$
$397$	−16.0000	−	27.7128i	−0.803017	−	1.39087i	0.114605	−	0.993411i	$-0.463440\pi$
$398$	−5.50000	−	9.52628i	−0.275690	−	0.477509i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$	−32.0000			−1.59403
$404$	7.50000	+	12.9904i	0.373139	+	0.646296i
$405$		0			0
$406$	−7.50000	−	2.59808i	−0.372219	−	0.128940i
$407$		0			0
$408$		0			0
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	0.989835	+	0.142222i	$0.0454247\pi$
$409$	12.5000	+	21.6506i	0.618085	+	1.07056i	−0.371750	+	0.928333i	$0.621242\pi$
$410$	9.00000	+	15.5885i	0.444478	+	0.769859i
$411$		0			0
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	1.50000	+	7.79423i	0.0738102	+	0.383529i
$414$		0			0
$415$	18.0000	+	31.1769i	0.883585	+	1.53041i
$416$	−4.00000			−0.196116
$417$		0			0
$418$		0			0
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	−0.974546	−	0.224189i	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	−0.932061	−	0.362301i	$-0.881991\pi$
$421$	−16.0000	−	27.7128i	−0.779792	−	1.35064i	0.152269	−	0.988339i	$-0.451342\pi$
$422$	2.00000	+	3.46410i	0.0973585	+	0.168630i
$423$		0			0
$424$	−4.50000	+	7.79423i	−0.218539	+	0.378521i
$425$	−12.0000	+	20.7846i	−0.582086	+	1.00820i
$426$		0			0
$427$	20.0000	−	17.3205i	0.967868	−	0.838198i
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$		0			0
$430$	24.0000			1.15738
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$		0			0
$433$	−7.00000			−0.336399			−0.168199	−	0.985753i	$-0.553795\pi$
$433$	−7.00000			−0.336399			−0.168199	+	0.985753i	$0.553795\pi$
$434$	20.0000	+	6.92820i	0.960031	+	0.332564i
$435$		0			0
$436$	−4.00000			−0.191565
$437$	12.0000	+	20.7846i	0.574038	+	0.994263i
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$		0			0
$442$	−24.0000			−1.14156
$443$	19.5000	−	33.7750i	0.926473	−	1.60470i	0.137298	−	0.990530i	$-0.456158\pi$
$443$	19.5000	−	33.7750i	0.926473	−	1.60470i	0.789175	−	0.614168i	$-0.210508\pi$
$444$		0			0
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	−1.00000			−0.0473514
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$		0			0
$451$		0			0
$452$	−6.00000			−0.282216
$453$		0			0
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$	24.0000	−	20.7846i	1.12514	−	0.974398i
$456$		0			0
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$		0			0
$460$	−9.00000	−	15.5885i	−0.419627	−	0.726816i
$461$	16.5000	+	28.5788i	0.768482	+	1.33105i	0.938386	+	0.345589i	$0.112321\pi$
$461$	16.5000	+	28.5788i	0.768482	+	1.33105i	−0.169904	+	0.985461i	$0.554346\pi$
$462$		0			0
$463$	9.50000	−	16.4545i	0.441502	−	0.764705i	−0.556299	−	0.830982i	$-0.687779\pi$
$463$	9.50000	−	16.4545i	0.441502	−	0.764705i	0.997801	+	0.0662777i	$0.0211123\pi$
$464$	−3.00000			−0.139272
$465$		0			0
$466$	18.0000			0.833834
$467$	16.5000	+	28.5788i	0.763529	+	1.32247i	0.941021	+	0.338349i	$0.109868\pi$
$467$	16.5000	+	28.5788i	0.763529	+	1.32247i	−0.177492	+	0.984122i	$0.556798\pi$
$468$		0			0
$469$	5.00000	+	25.9808i	0.230879	+	1.19968i
$470$	−9.00000	−	15.5885i	−0.415139	−	0.719042i
$471$		0			0
$472$	1.50000	+	2.59808i	0.0690431	+	0.119586i
$473$		0			0
$474$		0			0
$475$	8.00000	+	13.8564i	0.367065	+	0.635776i
$476$	15.0000	+	5.19615i	0.687524	+	0.238165i
$477$		0			0
$478$		0			0
$479$	−24.0000			−1.09659			−0.548294	−	0.836286i	$-0.684723\pi$
$479$	−24.0000			−1.09659			−0.548294	+	0.836286i	$0.684723\pi$
$480$		0			0
$481$	−32.0000			−1.45907
$482$	0.500000	−	0.866025i	0.0227744	−	0.0394464i
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	15.0000	+	25.9808i	0.681115	+	1.17973i
$486$		0			0
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	−0.680335	−	0.732901i	$-0.738166\pi$
$487$	6.50000	−	11.2583i	0.294543	−	0.510164i	0.974879	+	0.222737i	$0.0714992\pi$
$488$	5.00000	−	8.66025i	0.226339	−	0.392031i
$489$		0			0
$490$	−19.5000	+	7.79423i	−0.880920	+	0.352107i
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$		0			0
$493$	−18.0000			−0.810679
$494$	−8.00000	+	13.8564i	−0.359937	+	0.623429i
$495$		0			0
$496$	8.00000			0.359211
$497$	15.0000	+	5.19615i	0.672842	+	0.233079i
$498$		0			0
$499$	2.00000			0.0895323			0.0447661	−	0.998997i	$-0.485746\pi$
$499$	2.00000			0.0895323			0.0447661	+	0.998997i	$0.485746\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$	−4.50000	+	7.79423i	−0.200845	+	0.347873i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	−45.0000			−2.00247
$506$		0			0
$507$		0			0
$508$	−2.50000	−	4.33013i	−0.110920	−	0.192118i
$509$	18.0000			0.797836			0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000			0.797836			0.398918	+	0.916987i	$0.369386\pi$
$510$		0			0
$511$	14.0000	−	12.1244i	0.619324	−	0.536350i
$512$	1.00000			0.0441942
$513$		0			0
$514$		0			0
$515$	24.0000			1.05757
$516$		0			0
$517$		0			0
$518$	20.0000	+	6.92820i	0.878750	+	0.304408i
$519$		0			0
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	−0.324185	−	0.945994i	$-0.605090\pi$
$521$	15.0000	−	25.9808i	0.657162	−	1.13824i	0.981347	−	0.192244i	$-0.0615766\pi$
$522$		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	$0.805460\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$		0			0
$526$	9.00000	−	15.5885i	0.392419	−	0.679689i
$527$	48.0000			2.09091
$528$		0			0
$529$	13.0000			0.565217
$530$	−13.5000	−	23.3827i	−0.586403	−	1.01568i
$531$		0			0
$532$	8.00000	−	6.92820i	0.346844	−	0.300376i
$533$	−12.0000	−	20.7846i	−0.519778	−	0.900281i
$534$		0			0
$535$	4.50000	+	7.79423i	0.194552	+	0.336974i
$536$	5.00000	+	8.66025i	0.215967	+	0.374066i
$537$		0			0
$538$	−10.5000	−	18.1865i	−0.452687	−	0.784077i
$539$		0			0
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	−25.0000			−1.07384
$543$		0			0
$544$	6.00000			0.257248
$545$	6.00000	−	10.3923i	0.257012	−	0.445157i
$546$		0			0
$547$	14.0000	+	24.2487i	0.598597	+	1.03680i	0.993028	+	0.117875i	$0.0376081\pi$
$547$	14.0000	+	24.2487i	0.598597	+	1.03680i	−0.394432	+	0.918925i	$0.629059\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$		0			0
$550$		0			0
$551$	−6.00000	+	10.3923i	−0.255609	+	0.442727i
$552$		0			0
$553$	−34.0000	+	29.4449i	−1.44583	+	1.25212i
$554$	14.0000	−	24.2487i	0.594803	−	1.03023i
$555$		0			0
$556$	2.00000			0.0848189
$557$	3.00000	−	5.19615i	0.127114	−	0.220168i	−0.795443	−	0.606028i	$-0.792762\pi$
$557$	3.00000	−	5.19615i	0.127114	−	0.220168i	0.922557	+	0.385860i	$0.126095\pi$
$558$		0			0
$559$	−32.0000			−1.35346
$560$	−6.00000	+	5.19615i	−0.253546	+	0.219578i
$561$		0			0
$562$	−18.0000			−0.759284
$563$	−7.50000	−	12.9904i	−0.316087	−	0.547479i	0.663581	−	0.748105i	$-0.269036\pi$
$563$	−7.50000	−	12.9904i	−0.316087	−	0.547479i	−0.979668	+	0.200625i	$0.935703\pi$
$564$		0			0
$565$	9.00000	−	15.5885i	0.378633	−	0.655811i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	6.00000			0.251754
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$		0			0
$573$		0			0
$574$	3.00000	+	15.5885i	0.125218	+	0.650650i
$575$	24.0000			1.00087
$576$		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	$0.325577\pi$
$578$	19.0000			0.790296
$579$		0			0
$580$	4.50000	−	7.79423i	0.186852	−	0.323638i
$581$	6.00000	+	31.1769i	0.248922	+	1.29344i
$582$		0			0
$583$		0			0
$584$	3.50000	−	6.06218i	0.144831	−	0.250855i
$585$		0			0
$586$	1.50000	+	2.59808i	0.0619644	+	0.107326i
$587$	7.50000	+	12.9904i	0.309558	+	0.536170i	0.978266	−	0.207355i	$-0.0664855\pi$
$587$	7.50000	+	12.9904i	0.309558	+	0.536170i	−0.668708	+	0.743525i	$0.733152\pi$
$588$		0			0
$589$	16.0000	−	27.7128i	0.659269	−	1.14189i
$590$	−9.00000			−0.370524
$591$		0			0
$592$	8.00000			0.328798
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$		0			0
$595$	−36.0000	+	31.1769i	−1.47586	+	1.27813i
$596$	10.5000	+	18.1865i	0.430097	+	0.744949i
$597$		0			0
$598$	12.0000	+	20.7846i	0.490716	+	0.849946i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	0.999934	+	0.0114528i	$0.00364562\pi$
$601$	12.5000	+	21.6506i	0.509886	+	0.883148i	−0.490049	+	0.871695i	$0.663021\pi$
$602$	20.0000	+	6.92820i	0.815139	+	0.282372i
$603$		0			0
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$	−33.0000			−1.34164
$606$		0			0
$607$	11.0000			0.446476			0.223238	−	0.974764i	$-0.428337\pi$
$607$	11.0000			0.446476			0.223238	+	0.974764i	$0.428337\pi$
$608$	2.00000	−	3.46410i	0.0811107	−	0.140488i
$609$		0			0
$610$	15.0000	+	25.9808i	0.607332	+	1.05193i
$611$	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
$616$		0			0
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$		0			0
$619$	−16.0000			−0.643094			−0.321547	−	0.946894i	$-0.604203\pi$
$619$	−16.0000			−0.643094			−0.321547	+	0.946894i	$0.604203\pi$
$620$	−12.0000	+	20.7846i	−0.481932	+	0.834730i
$621$		0			0
$622$	12.0000			0.481156
$623$	−3.00000	−	15.5885i	−0.120192	−	0.624538i
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−2.50000	−	4.33013i	−0.0999201	−	0.173067i
$627$		0			0
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	48.0000			1.91389
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	−8.50000	+	14.7224i	−0.338112	+	0.585627i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	15.0000			0.595257
$636$		0			0
$637$	26.0000	−	10.3923i	1.03016	−	0.411758i
$638$		0			0
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	24.0000			0.947943			0.473972	−	0.880540i	$-0.342820\pi$
$641$	24.0000			0.947943			0.473972	+	0.880540i	$0.342820\pi$
$642$		0			0
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	−0.664052	−	0.747686i	$-0.731165\pi$
$643$	8.00000	−	13.8564i	0.315489	−	0.546443i	0.979541	+	0.201243i	$0.0644981\pi$
$644$	−3.00000	−	15.5885i	−0.118217	−	0.614271i
$645$		0			0
$646$	12.0000	−	20.7846i	0.472134	−	0.817760i
$647$	−21.0000	+	36.3731i	−0.825595	+	1.42997i	0.0758684	+	0.997118i	$0.475827\pi$
$647$	−21.0000	+	36.3731i	−0.825595	+	1.42997i	−0.901464	+	0.432855i	$0.857506\pi$
$648$		0			0
$649$		0			0
$650$	8.00000	+	13.8564i	0.313786	+	0.543493i
$651$		0			0
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$	3.00000			0.117399			0.0586995	−	0.998276i	$-0.481305\pi$
$653$	3.00000			0.117399			0.0586995	+	0.998276i	$0.481305\pi$
$654$		0			0
$655$	−36.0000			−1.40664
$656$	3.00000	+	5.19615i	0.117130	+	0.202876i
$657$		0			0
$658$	−3.00000	−	15.5885i	−0.116952	−	0.607701i
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	0.585758	−	0.810486i	$-0.300797\pi$
$659$	−10.5000	−	18.1865i	−0.409022	−	0.708447i	−0.994780	+	0.102039i	$0.967463\pi$
$660$		0			0
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	−0.989051	−	0.147573i	$-0.952854\pi$
$661$	−16.0000	−	27.7128i	−0.622328	−	1.07790i	0.366723	−	0.930330i	$-0.380480\pi$
$662$	−1.00000	−	1.73205i	−0.0388661	−	0.0673181i
$663$		0			0
$664$	6.00000	+	10.3923i	0.232845	+	0.403300i
$665$	6.00000	+	31.1769i	0.232670	+	1.20899i
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	6.00000			0.232147
$669$		0			0
$670$	−30.0000			−1.15900
$671$		0			0
$672$		0			0
$673$	21.5000	+	37.2391i	0.828764	+	1.43546i	0.899008	+	0.437932i	$0.144289\pi$
$673$	21.5000	+	37.2391i	0.828764	+	1.43546i	−0.0702442	+	0.997530i	$0.522378\pi$
$674$	3.50000	+	6.06218i	0.134815	+	0.233506i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	10.5000	−	18.1865i	0.403548	−	0.698965i	−0.590603	−	0.806962i	$-0.701110\pi$
$677$	10.5000	−	18.1865i	0.403548	−	0.698965i	0.994151	+	0.107997i	$0.0344436\pi$
$678$		0			0
$679$	5.00000	+	25.9808i	0.191882	+	0.997050i
$680$	−9.00000	+	15.5885i	−0.345134	+	0.597790i
$681$		0			0
$682$		0			0
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$		0			0
$685$	36.0000			1.37549
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$		0			0
$688$	8.00000			0.304997
$689$	18.0000	+	31.1769i	0.685745	+	1.18775i
$690$		0			0
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−4.00000	+	6.92820i	−0.152167	+	0.263561i	0.779857	+	0.625958i	$0.215292\pi$
$692$	−9.00000			−0.342129
$693$		0			0
$694$	33.0000			1.25266
$695$	−3.00000	+	5.19615i	−0.113796	+	0.197101i
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	−10.0000			−0.378506
$699$		0			0
$700$	−2.00000	−	10.3923i	−0.0755929	−	0.392792i
$701$	−39.0000			−1.47301			−0.736505	−	0.676432i	$-0.763525\pi$
$701$	−39.0000			−1.47301			−0.736505	+	0.676432i	$0.763525\pi$
$702$		0			0
$703$	16.0000	−	27.7128i	0.603451	−	1.04521i
$704$		0			0
$705$		0			0
$706$	15.0000	−	25.9808i	0.564532	−	0.977799i
$707$	−37.5000	−	12.9904i	−1.41033	−	0.488554i
$708$		0			0
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	−0.931309	−	0.364229i	$-0.881333\pi$
$709$	−4.00000	+	6.92820i	−0.150223	+	0.260194i	0.781086	+	0.624423i	$0.214666\pi$
$710$	−9.00000	+	15.5885i	−0.337764	+	0.585024i
$711$		0			0
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−24.0000	−	41.5692i	−0.898807	−	1.55678i
$714$		0			0
$715$		0			0
$716$	−15.0000			−0.560576
$717$		0			0
$718$	36.0000			1.34351
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	0.998224	−	0.0595683i	$-0.0189724\pi$
$719$	12.0000	+	20.7846i	0.447524	+	0.775135i	−0.550700	+	0.834703i	$0.685639\pi$
$720$		0			0
$721$	20.0000	+	6.92820i	0.744839	+	0.258020i
$722$	1.50000	+	2.59808i	0.0558242	+	0.0966904i
$723$		0			0
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$		0			0
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	0.570049	−	0.821611i	$-0.306924\pi$
$727$	−11.5000	−	19.9186i	−0.426511	−	0.738739i	−0.996560	+	0.0828714i	$0.973591\pi$
$728$	8.00000	−	6.92820i	0.296500	−	0.256776i
$729$		0			0
$730$	10.5000	+	18.1865i	0.388622	+	0.673114i
$731$	48.0000			1.77534
$732$		0			0
$733$	44.0000			1.62518			0.812589	−	0.582838i	$-0.198058\pi$
$733$	44.0000			1.62518			0.812589	+	0.582838i	$0.198058\pi$
$734$	9.50000	−	16.4545i	0.350651	−	0.607346i
$735$		0			0
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$		0			0
$738$		0			0
$739$	−7.00000	+	12.1244i	−0.257499	+	0.446002i	−0.965571	−	0.260138i	$-0.916232\pi$
$739$	−7.00000	+	12.1244i	−0.257499	+	0.446002i	0.708072	+	0.706140i	$0.249565\pi$
$740$	−12.0000	+	20.7846i	−0.441129	+	0.764057i
$741$		0			0
$742$	−4.50000	−	23.3827i	−0.165200	−	0.858405i
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	−0.997707	−	0.0676840i	$-0.978439\pi$
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	0.557470	+	0.830197i	$0.311772\pi$
$744$		0			0
$745$	−63.0000			−2.30814
$746$	5.00000	−	8.66025i	0.183063	−	0.317074i
$747$		0			0
$748$		0			0
$749$	1.50000	+	7.79423i	0.0548088	+	0.284795i
$750$		0			0
$751$	−43.0000			−1.56909			−0.784546	−	0.620070i	$-0.787104\pi$
$751$	−43.0000			−1.56909			−0.784546	+	0.620070i	$0.787104\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$		0			0
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$	24.0000			0.873449
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	5.00000	−	8.66025i	0.181608	−	0.314555i
$759$		0			0
$760$	6.00000	+	10.3923i	0.217643	+	0.376969i
$761$	48.0000			1.74000			0.869999	−	0.493053i	$-0.164119\pi$
$761$	48.0000			1.74000			0.869999	+	0.493053i	$0.164119\pi$
$762$		0			0
$763$	8.00000	−	6.92820i	0.289619	−	0.250818i
$764$	−18.0000			−0.651217
$765$		0			0
$766$	−3.00000	+	5.19615i	−0.108394	+	0.187745i
$767$	12.0000			0.433295
$768$		0			0
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	−0.999364	−	0.0356685i	$-0.988644\pi$
$769$	−13.0000	+	22.5167i	−0.468792	+	0.811972i	0.530572	+	0.847640i	$0.321977\pi$
$770$		0			0
$771$		0			0
$772$	−13.0000	+	22.5167i	−0.467880	+	0.810392i
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$		0			0
$775$	−16.0000	−	27.7128i	−0.574737	−	0.995474i
$776$	5.00000	+	8.66025i	0.179490	+	0.310885i
$777$		0			0
$778$	4.50000	−	7.79423i	0.161333	−	0.279437i
$779$	24.0000			0.859889
$780$		0			0
$781$		0			0
$782$	−18.0000	−	31.1769i	−0.643679	−	1.11488i
$783$		0			0
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$	−21.0000	−	36.3731i	−0.749522	−	1.29821i
$786$		0			0
$787$	11.0000	+	19.0526i	0.392108	+	0.679150i	0.992727	−	0.120384i	$-0.0384127\pi$
$787$	11.0000	+	19.0526i	0.392108	+	0.679150i	−0.600620	+	0.799535i	$0.705079\pi$
$788$	7.50000	+	12.9904i	0.267176	+	0.462763i
$789$		0			0
$790$	−25.5000	−	44.1673i	−0.907249	−	1.57140i
$791$	12.0000	−	10.3923i	0.426671	−	0.369508i
$792$		0			0
$793$	−20.0000	−	34.6410i	−0.710221	−	1.23014i
$794$	32.0000			1.13564
$795$		0			0
$796$	11.0000			0.389885
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	−0.980237	−	0.197826i	$-0.936612\pi$
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	0.661441	+	0.749997i	$0.269945\pi$
$798$		0			0
$799$	−18.0000	−	31.1769i	−0.636794	−	1.10296i
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$		0			0
$804$		0			0
$805$	45.0000	+	15.5885i	1.58604	+	0.549421i
$806$	16.0000	−	27.7128i	0.563576	−	0.976142i
$807$		0			0
$808$	−15.0000			−0.527698
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	−0.996125	−	0.0879478i	$-0.971969\pi$
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	0.574228	+	0.818696i	$0.305302\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	6.00000	−	5.19615i	0.210559	−	0.182349i
$813$		0			0
$814$		0			0
$815$	−3.00000	−	5.19615i	−0.105085	−	0.182013i
$816$		0			0
$817$	16.0000	−	27.7128i	0.559769	−	0.969549i
$818$	−25.0000			−0.874105
$819$		0			0
$820$	−18.0000			−0.628587
$821$	−10.5000	+	18.1865i	−0.366453	+	0.634714i	−0.989008	−	0.147861i	$-0.952761\pi$
$821$	−10.5000	+	18.1865i	−0.366453	+	0.634714i	0.622556	+	0.782576i	$0.286094\pi$
$822$		0			0
$823$	−11.5000	−	19.9186i	−0.400865	−	0.694318i	0.592966	−	0.805228i	$-0.297957\pi$
$823$	−11.5000	−	19.9186i	−0.400865	−	0.694318i	−0.993831	+	0.110910i	$0.964624\pi$
$824$	8.00000			0.278693
$825$		0			0
$826$	−7.50000	−	2.59808i	−0.260958	−	0.0903986i
$827$	21.0000			0.730242			0.365121	−	0.930960i	$-0.381028\pi$
$827$	21.0000			0.730242			0.365121	+	0.930960i	$0.381028\pi$
$828$		0			0
$829$	−16.0000	+	27.7128i	−0.555703	+	0.962506i	0.442145	+	0.896943i	$0.354217\pi$
$829$	−16.0000	+	27.7128i	−0.555703	+	0.962506i	−0.997848	+	0.0655624i	$0.979116\pi$
$830$	−36.0000			−1.24958
$831$		0			0
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	−39.0000	+	15.5885i	−1.35127	+	0.540108i
$834$		0			0
$835$	−9.00000	+	15.5885i	−0.311458	+	0.539461i
$836$		0			0
$837$		0			0
$838$	−6.00000	−	10.3923i	−0.207267	−	0.358996i
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	0.995353	−	0.0962912i	$-0.0306980\pi$
$839$	12.0000	+	20.7846i	0.414286	+	0.717564i	−0.581067	+	0.813856i	$0.697365\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	32.0000			1.10279
$843$		0			0
$844$	−4.00000			−0.137686
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	−27.5000	−	9.52628i	−0.944911	−	0.327327i
$848$	−4.50000	−	7.79423i	−0.154531	−	0.267655i
$849$		0			0
$850$	−12.0000	−	20.7846i	−0.411597	−	0.712906i
$851$	−24.0000	−	41.5692i	−0.822709	−	1.42497i
$852$		0			0
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	−0.946232	−	0.323489i	$-0.895144\pi$
$853$	−22.0000	−	38.1051i	−0.753266	−	1.30469i	0.192966	−	0.981205i	$-0.438189\pi$
$854$	5.00000	+	25.9808i	0.171096	+	0.889043i
$855$		0			0
$856$	1.50000	+	2.59808i	0.0512689	+	0.0888004i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	−12.0000	+	20.7846i	−0.409197	+	0.708749i
$861$		0			0
$862$	−6.00000	−	10.3923i	−0.204361	−	0.353963i
$863$	−21.0000	−	36.3731i	−0.714848	−	1.23815i	−0.963018	−	0.269437i	$-0.913162\pi$
$863$	−21.0000	−	36.3731i	−0.714848	−	1.23815i	0.248170	−	0.968717i	$-0.420171\pi$
$864$		0			0
$865$	13.5000	−	23.3827i	0.459014	−	0.795035i
$866$	3.50000	−	6.06218i	0.118935	−	0.206001i
$867$		0			0
$868$	−16.0000	+	13.8564i	−0.543075	+	0.470317i
$869$		0			0
$870$		0			0
$871$	40.0000			1.35535
$872$	2.00000	−	3.46410i	0.0677285	−	0.117309i
$873$		0			0
$874$	−24.0000			−0.811812
$875$	−7.50000	−	2.59808i	−0.253546	−	0.0878310i
$876$		0			0
$877$	14.0000			0.472746			0.236373	−	0.971662i	$-0.424041\pi$
$877$	14.0000			0.472746			0.236373	+	0.971662i	$0.424041\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$		0			0
$880$		0			0
$881$	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	$0.319013\pi$
$884$	12.0000	−	20.7846i	0.403604	−	0.699062i
$885$		0			0
$886$	19.5000	+	33.7750i	0.655115	+	1.13469i
$887$	−42.0000			−1.41022			−0.705111	−	0.709097i	$-0.749103\pi$
$887$	−42.0000			−1.41022			−0.705111	+	0.709097i	$0.749103\pi$
$888$		0			0
$889$	12.5000	+	4.33013i	0.419237	+	0.145228i
$890$	18.0000			0.603361
$891$		0			0
$892$	0.500000	−	0.866025i	0.0167412	−	0.0289967i
$893$	−24.0000			−0.803129
$894$		0			0
$895$	22.5000	−	38.9711i	0.752092	−	1.30266i
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$		0			0
$898$	−3.00000	+	5.19615i	−0.100111	+	0.173398i
$899$	12.0000	−	20.7846i	0.400222	−	0.693206i
$900$		0			0
$901$	−27.0000	−	46.7654i	−0.899500	−	1.55798i
$902$		0			0
$903$		0			0
$904$	3.00000	−	5.19615i	0.0997785	−	0.172821i
$905$	−30.0000			−0.997234
$906$		0			0
$907$	8.00000			0.265636			0.132818	−	0.991140i	$-0.457597\pi$
$907$	8.00000			0.265636			0.132818	+	0.991140i	$0.457597\pi$
$908$	−1.50000	−	2.59808i	−0.0497792	−	0.0862202i
$909$		0			0
$910$	6.00000	+	31.1769i	0.198898	+	1.03350i
$911$	27.0000	+	46.7654i	0.894550	+	1.54941i	0.834361	+	0.551219i	$0.185837\pi$
$911$	27.0000	+	46.7654i	0.894550	+	1.54941i	0.0601892	+	0.998187i	$0.480830\pi$
$912$		0			0
$913$		0			0
$914$	0.500000	+	0.866025i	0.0165385	+	0.0286456i
$915$		0			0
$916$	−7.00000	−	12.1244i	−0.231287	−	0.400600i
$917$	−30.0000	−	10.3923i	−0.990687	−	0.343184i
$918$		0			0
$919$	18.5000	+	32.0429i	0.610259	+	1.05700i	0.991197	+	0.132398i	$0.0422678\pi$
$919$	18.5000	+	32.0429i	0.610259	+	1.05700i	−0.380938	+	0.924601i	$0.624399\pi$
$920$	18.0000			0.593442
$921$		0			0
$922$	−33.0000			−1.08680
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$		0			0
$925$	−16.0000	−	27.7128i	−0.526077	−	0.911192i
$926$	9.50000	+	16.4545i	0.312189	+	0.540728i
$927$		0			0
$928$	1.50000	−	2.59808i	0.0492399	−	0.0852860i
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	−0.911034	−	0.412332i	$-0.864714\pi$
$929$	−3.00000	+	5.19615i	−0.0984268	+	0.170480i	0.812607	+	0.582812i	$0.198048\pi$
$930$		0			0
$931$	−4.00000	+	27.7128i	−0.131095	+	0.908251i
$932$	−9.00000	+	15.5885i	−0.294805	+	0.510617i
$933$		0			0
$934$	−33.0000			−1.07979
$935$		0			0
$936$		0			0
$937$	−1.00000			−0.0326686			−0.0163343	−	0.999867i	$-0.505200\pi$
$937$	−1.00000			−0.0326686			−0.0163343	+	0.999867i	$0.505200\pi$
$938$	−25.0000	−	8.66025i	−0.816279	−	0.282767i
$939$		0			0
$940$	18.0000			0.587095
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$		0			0
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$		0			0
$947$	−22.5000	+	38.9711i	−0.731152	+	1.26639i	0.225240	+	0.974303i	$0.427684\pi$
$947$	−22.5000	+	38.9711i	−0.731152	+	1.26639i	−0.956391	+	0.292089i	$0.905650\pi$
$948$		0			0
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$	−16.0000			−0.519109
$951$		0			0
$952$	−12.0000	+	10.3923i	−0.388922	+	0.336817i
$953$	−48.0000			−1.55487			−0.777436	−	0.628962i	$-0.783480\pi$
$953$	−48.0000			−1.55487			−0.777436	+	0.628962i	$0.783480\pi$
$954$		0			0
$955$	27.0000	−	46.7654i	0.873699	−	1.51329i
$956$		0			0
$957$		0			0
$958$	12.0000	−	20.7846i	0.387702	−	0.671520i
$959$	30.0000	+	10.3923i	0.968751	+	0.335585i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	16.0000	−	27.7128i	0.515861	−	0.893497i
$963$		0			0
$964$	0.500000	+	0.866025i	0.0161039	+	0.0278928i
$965$	−39.0000	−	67.5500i	−1.25545	−	2.17451i
$966$		0			0
$967$	18.5000	−	32.0429i	0.594920	−	1.03043i	−0.398638	−	0.917108i	$-0.630517\pi$
$967$	18.5000	−	32.0429i	0.594920	−	1.03043i	0.993558	−	0.113323i	$-0.0361496\pi$
$968$	−11.0000			−0.353553
$969$		0			0
$970$	−30.0000			−0.963242
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	0.889090	−	0.457732i	$-0.151338\pi$
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	−0.840953	+	0.541108i	$0.818005\pi$
$972$		0			0
$973$	−4.00000	+	3.46410i	−0.128234	+	0.111054i
$974$	6.50000	+	11.2583i	0.208273	+	0.360740i
$975$		0			0
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	−6.00000	−	10.3923i	−0.191957	−	0.332479i	0.753942	−	0.656941i	$-0.228150\pi$
$977$	−6.00000	−	10.3923i	−0.191957	−	0.332479i	−0.945899	+	0.324462i	$0.894817\pi$
$978$		0			0
$979$		0			0
$980$	3.00000	−	20.7846i	0.0958315	−	0.663940i
$981$		0			0
$982$	−13.5000	−	23.3827i	−0.430802	−	0.746171i
$983$	−24.0000			−0.765481			−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000			−0.765481			−0.382741	+	0.923856i	$0.625020\pi$
$984$		0			0
$985$	−45.0000			−1.43382
$986$	9.00000	−	15.5885i	0.286618	−	0.496438i
$987$		0			0
$988$	−8.00000	−	13.8564i	−0.254514	−	0.440831i
$989$	−24.0000	−	41.5692i	−0.763156	−	1.32182i
$990$		0			0
$991$	−11.5000	+	19.9186i	−0.365310	+	0.632735i	−0.988826	−	0.149076i	$-0.952370\pi$
$991$	−11.5000	+	19.9186i	−0.365310	+	0.632735i	0.623516	+	0.781810i	$0.285704\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$		0			0
$994$	−12.0000	+	10.3923i	−0.380617	+	0.329624i
$995$	−16.5000	+	28.5788i	−0.523085	+	0.906010i
$996$		0			0
$997$	32.0000			1.01345			0.506725	−	0.862108i	$-0.330856\pi$
$997$	32.0000			1.01345			0.506725	+	0.862108i	$0.330856\pi$
$998$	−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	1134.2.h.g.109.1		2
3.2	odd	2		1134.2.h.k.109.1		2
7.2	even	3		1134.2.e.j.919.1		2
9.2	odd	6		1134.2.e.f.865.1		2
9.4	even	3		378.2.g.a.109.1	✓	2
9.5	odd	6		378.2.g.f.109.1	yes	2
9.7	even	3		1134.2.e.j.865.1		2
21.2	odd	6		1134.2.e.f.919.1		2
63.2	odd	6		1134.2.h.k.541.1		2
63.4	even	3		2646.2.a.bc.1.1		1
63.16	even	3	inner	1134.2.h.g.541.1		2
63.23	odd	6		378.2.g.f.163.1	yes	2
63.31	odd	6		2646.2.a.r.1.1		1
63.32	odd	6		2646.2.a.b.1.1		1
63.58	even	3		378.2.g.a.163.1	yes	2
63.59	even	6		2646.2.a.m.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.a.109.1	✓	2	9.4	even	3
378.2.g.a.163.1	yes	2	63.58	even	3
378.2.g.f.109.1	yes	2	9.5	odd	6
378.2.g.f.163.1	yes	2	63.23	odd	6
1134.2.e.f.865.1		2	9.2	odd	6
1134.2.e.f.919.1		2	21.2	odd	6
1134.2.e.j.865.1		2	9.7	even	3
1134.2.e.j.919.1		2	7.2	even	3
1134.2.h.g.109.1		2	1.1	even	1	trivial
1134.2.h.g.541.1		2	63.16	even	3	inner
1134.2.h.k.109.1		2	3.2	odd	2
1134.2.h.k.541.1		2	63.2	odd	6
2646.2.a.b.1.1		1	63.32	odd	6
2646.2.a.m.1.1		1	63.59	even	6
2646.2.a.r.1.1		1	63.31	odd	6
2646.2.a.bc.1.1		1	63.4	even	3

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(2.00000 - 3.46410i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +(-1.50000 - 2.59808i) q^{20} +6.00000 q^{23} +4.00000 q^{25} +(2.00000 + 3.46410i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{34} +(7.50000 + 2.59808i) q^{35} +(-4.00000 - 6.92820i) q^{37} -4.00000 q^{38} +3.00000 q^{40} +(3.00000 - 5.19615i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(-3.00000 + 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{50} -4.00000 q^{52} +(-4.50000 + 7.79423i) q^{53} +(2.50000 + 0.866025i) q^{56} -3.00000 q^{58} +(1.50000 + 2.59808i) q^{59} +(5.00000 - 8.66025i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(5.00000 + 8.66025i) q^{67} +6.00000 q^{68} +(-6.00000 + 5.19615i) q^{70} +6.00000 q^{71} +(3.50000 - 6.06218i) q^{73} +8.00000 q^{74} +(2.00000 - 3.46410i) q^{76} +(-8.50000 + 14.7224i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(3.00000 + 5.19615i) q^{82} +(6.00000 + 10.3923i) q^{83} +(-9.00000 + 15.5885i) q^{85} +8.00000 q^{86} +(-3.00000 - 5.19615i) q^{89} +(8.00000 - 6.92820i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(6.00000 + 10.3923i) q^{95} +(5.00000 + 8.66025i) q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 6 q^{5} + 5 q^{7} + 2 q^{8} - 3 q^{10} + 4 q^{13} - 4 q^{14} - q^{16} - 6 q^{17} + 4 q^{19} - 3 q^{20} + 12 q^{23} + 8 q^{25} + 4 q^{26} - q^{28} + 3 q^{29} - 8 q^{31} - q^{32}+ \cdots - 13 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 6 * q^5 + 5 * q^7 + 2 * q^8 - 3 * q^10 + 4 * q^13 - 4 * q^14 - q^16 - 6 * q^17 + 4 * q^19 - 3 * q^20 + 12 * q^23 + 8 * q^25 + 4 * q^26 - q^28 + 3 * q^29 - 8 * q^31 - q^32 - 6 * q^34 + 15 * q^35 - 8 * q^37 - 8 * q^38 + 6 * q^40 + 6 * q^41 - 8 * q^43 - 6 * q^46 - 6 * q^47 + 11 * q^49 - 4 * q^50 - 8 * q^52 - 9 * q^53 + 5 * q^56 - 6 * q^58 + 3 * q^59 + 10 * q^61 + 16 * q^62 + 2 * q^64 + 12 * q^65 + 10 * q^67 + 12 * q^68 - 12 * q^70 + 12 * q^71 + 7 * q^73 + 16 * q^74 + 4 * q^76 - 17 * q^79 - 3 * q^80 + 6 * q^82 + 12 * q^83 - 18 * q^85 + 16 * q^86 - 6 * q^89 + 16 * q^91 - 6 * q^92 - 6 * q^94 + 12 * q^95 + 10 * q^97 - 13 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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