LMFDB - Embedded newform 1638.2.bj.e.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(127,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1638.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.e.1135.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-1.73205 - 3.00000i) q^{10} +(3.46410 - 2.00000i) q^{11} +(-2.59808 - 2.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.232051 - 0.401924i) q^{17} +(-0.464102 - 0.267949i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(2.00000 - 3.46410i) q^{22} +(-1.13397 - 1.96410i) q^{23} -7.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} +(0.866025 - 0.500000i) q^{28} +(4.00000 + 6.92820i) q^{29} +0.464102i q^{31} +(-0.866025 - 0.500000i) q^{32} -0.464102i q^{34} +(1.73205 - 3.00000i) q^{35} +(-7.73205 + 4.46410i) q^{37} -0.535898 q^{38} -3.46410 q^{40} +(6.00000 - 3.46410i) q^{41} +(-1.23205 + 2.13397i) q^{43} -4.00000i q^{44} +(-1.96410 - 1.13397i) q^{46} -7.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(-6.06218 + 3.50000i) q^{50} +(-3.46410 + 1.00000i) q^{52} +11.7321 q^{53} +(-6.92820 - 12.0000i) q^{55} +(0.500000 - 0.866025i) q^{56} +(6.92820 + 4.00000i) q^{58} +(-8.42820 - 4.86603i) q^{59} +(-2.59808 + 4.50000i) q^{61} +(0.232051 + 0.401924i) q^{62} -1.00000 q^{64} +(-8.66025 + 9.00000i) q^{65} +(2.76795 - 1.59808i) q^{67} +(-0.232051 - 0.401924i) q^{68} -3.46410i q^{70} +(-10.3301 - 5.96410i) q^{71} -2.92820i q^{73} +(-4.46410 + 7.73205i) q^{74} +(-0.464102 + 0.267949i) q^{76} +4.00000 q^{77} -2.53590 q^{79} +(-3.00000 + 1.73205i) q^{80} +(3.46410 - 6.00000i) q^{82} +1.73205i q^{83} +(-1.39230 - 0.803848i) q^{85} +2.46410i q^{86} +(-2.00000 - 3.46410i) q^{88} +(-7.16025 + 4.13397i) q^{89} +(-1.00000 - 3.46410i) q^{91} -2.26795 q^{92} +(-3.73205 - 6.46410i) q^{94} +(-0.928203 + 1.60770i) q^{95} +(7.26795 + 4.19615i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4}+O(q^{10}) $ 4 * q + 2 * q^4	$ 4 q + 2 q^{4} + 4 q^{14} - 2 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} + 8 q^{22} - 8 q^{23} - 28 q^{25} - 14 q^{26} + 16 q^{29} - 24 q^{37} - 16 q^{38} + 24 q^{41} + 2 q^{43} + 6 q^{46} + 2 q^{49} + 40 q^{53} + 2 q^{56} - 6 q^{59} - 6 q^{62} - 4 q^{64} + 18 q^{67} + 6 q^{68} - 24 q^{71} - 4 q^{74} + 12 q^{76} + 16 q^{77} - 24 q^{79} - 12 q^{80} + 36 q^{85} - 8 q^{88} + 6 q^{89} - 4 q^{91} - 16 q^{92} - 8 q^{94} + 24 q^{95} + 36 q^{97}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^14 - 2 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 + 8 * q^22 - 8 * q^23 - 28 * q^25 - 14 * q^26 + 16 * q^29 - 24 * q^37 - 16 * q^38 + 24 * q^41 + 2 * q^43 + 6 * q^46 + 2 * q^49 + 40 * q^53 + 2 * q^56 - 6 * q^59 - 6 * q^62 - 4 * q^64 + 18 * q^67 + 6 * q^68 - 24 * q^71 - 4 * q^74 + 12 * q^76 + 16 * q^77 - 24 * q^79 - 12 * q^80 + 36 * q^85 - 8 * q^88 + 6 * q^89 - 4 * q^91 - 16 * q^92 - 8 * q^94 + 24 * q^95 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	3.46410i		−	1.54919i	−0.632456	−	0.774597i	$-0.717953\pi$
$5$		−	3.46410i		−	1.54919i	0.632456	−	0.774597i	$-0.282047\pi$
$6$		0			0
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−1.73205	−	3.00000i	−0.547723	−	0.948683i
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.123371	−	0.992361i	$-0.460630\pi$
$11$	3.46410	−	2.00000i	1.04447	−	0.603023i	0.921095	+	0.389338i	$0.127296\pi$
$12$		0			0
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.232051	−	0.401924i	0.0562806	−	0.0974808i	−0.836512	−	0.547948i	$-0.815409\pi$
$17$	0.232051	−	0.401924i	0.0562806	−	0.0974808i	0.892793	+	0.450467i	$0.148743\pi$
$18$		0			0
$19$	−0.464102	−	0.267949i	−0.106472	−	0.0614718i	0.445818	−	0.895123i	$-0.352913\pi$
$19$	−0.464102	−	0.267949i	−0.106472	−	0.0614718i	−0.552291	+	0.833652i	$0.686246\pi$
$20$	−3.00000	−	1.73205i	−0.670820	−	0.387298i
$21$		0			0
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	−1.13397	−	1.96410i	−0.236450	−	0.409543i	0.723243	−	0.690594i	$-0.242651\pi$
$23$	−1.13397	−	1.96410i	−0.236450	−	0.409543i	−0.959693	+	0.281050i	$0.909317\pi$
$24$		0			0
$25$	−7.00000			−1.40000
$26$	−3.50000	−	0.866025i	−0.686406	−	0.169842i
$27$		0			0
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	4.00000	+	6.92820i	0.742781	+	1.28654i	0.951224	+	0.308500i	$0.0998271\pi$
$29$	4.00000	+	6.92820i	0.742781	+	1.28654i	−0.208443	+	0.978035i	$0.566840\pi$
$30$		0			0
$31$			0.464102i			0.0833551i	0.999131	+	0.0416776i	$0.0132702\pi$
$31$			0.464102i			0.0833551i	−0.999131	+	0.0416776i	$0.986730\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$		−	0.464102i		−	0.0795928i
$35$	1.73205	−	3.00000i	0.292770	−	0.507093i
$36$		0			0
$37$	−7.73205	+	4.46410i	−1.27114	+	0.733894i	−0.975203	−	0.221313i	$-0.928966\pi$
$37$	−7.73205	+	4.46410i	−1.27114	+	0.733894i	−0.295939	+	0.955207i	$0.595632\pi$
$38$	−0.535898			−0.0869342
$39$		0			0
$40$	−3.46410			−0.547723
$41$	6.00000	−	3.46410i	0.937043	−	0.541002i	0.0480106	−	0.998847i	$-0.484712\pi$
$41$	6.00000	−	3.46410i	0.937043	−	0.541002i	0.889032	+	0.457845i	$0.151379\pi$
$42$		0			0
$43$	−1.23205	+	2.13397i	−0.187886	+	0.325428i	−0.944545	−	0.328381i	$-0.893497\pi$
$43$	−1.23205	+	2.13397i	−0.187886	+	0.325428i	0.756659	+	0.653809i	$0.226830\pi$
$44$		−	4.00000i		−	0.603023i
$45$		0			0
$46$	−1.96410	−	1.13397i	−0.289591	−	0.167195i
$47$		−	7.46410i		−	1.08875i	−0.838842	−	0.544376i	$-0.816767\pi$
$47$		−	7.46410i		−	1.08875i	0.838842	−	0.544376i	$-0.183233\pi$
$48$		0			0
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−6.06218	+	3.50000i	−0.857321	+	0.494975i
$51$		0			0
$52$	−3.46410	+	1.00000i	−0.480384	+	0.138675i
$53$	11.7321			1.61152			0.805761	−	0.592241i	$-0.201757\pi$
$53$	11.7321			1.61152			0.805761	+	0.592241i	$0.201757\pi$
$54$		0			0
$55$	−6.92820	−	12.0000i	−0.934199	−	1.61808i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		0			0
$58$	6.92820	+	4.00000i	0.909718	+	0.525226i
$59$	−8.42820	−	4.86603i	−1.09726	−	0.633503i	−0.161759	−	0.986830i	$-0.551717\pi$
$59$	−8.42820	−	4.86603i	−1.09726	−	0.633503i	−0.935500	+	0.353328i	$0.885050\pi$
$60$		0			0
$61$	−2.59808	+	4.50000i	−0.332650	+	0.576166i	−0.983030	−	0.183442i	$-0.941276\pi$
$61$	−2.59808	+	4.50000i	−0.332650	+	0.576166i	0.650381	+	0.759608i	$0.274609\pi$
$62$	0.232051	+	0.401924i	0.0294705	+	0.0510444i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−8.66025	+	9.00000i	−1.07417	+	1.11631i
$66$		0			0
$67$	2.76795	−	1.59808i	0.338159	−	0.195236i	−0.321299	−	0.946978i	$-0.604119\pi$
$67$	2.76795	−	1.59808i	0.338159	−	0.195236i	0.659458	+	0.751742i	$0.270786\pi$
$68$	−0.232051	−	0.401924i	−0.0281403	−	0.0487404i
$69$		0			0
$70$		−	3.46410i		−	0.414039i
$71$	−10.3301	−	5.96410i	−1.22596	−	0.707809i	−0.259778	−	0.965668i	$-0.583649\pi$
$71$	−10.3301	−	5.96410i	−1.22596	−	0.707809i	−0.966182	+	0.257860i	$0.916983\pi$
$72$		0			0
$73$		−	2.92820i		−	0.342720i	−0.985208	−	0.171360i	$-0.945184\pi$
$73$		−	2.92820i		−	0.342720i	0.985208	−	0.171360i	$-0.0548162\pi$
$74$	−4.46410	+	7.73205i	−0.518941	+	0.898833i
$75$		0			0
$76$	−0.464102	+	0.267949i	−0.0532361	+	0.0307359i
$77$	4.00000			0.455842
$78$		0			0
$79$	−2.53590			−0.285311			−0.142655	−	0.989772i	$-0.545564\pi$
$79$	−2.53590			−0.285311			−0.142655	+	0.989772i	$0.545564\pi$
$80$	−3.00000	+	1.73205i	−0.335410	+	0.193649i
$81$		0			0
$82$	3.46410	−	6.00000i	0.382546	−	0.662589i
$83$			1.73205i			0.190117i	0.995472	+	0.0950586i	$0.0303039\pi$
$83$			1.73205i			0.190117i	−0.995472	+	0.0950586i	$0.969696\pi$
$84$		0			0
$85$	−1.39230	−	0.803848i	−0.151017	−	0.0871895i
$86$			2.46410i			0.265711i
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	−7.16025	+	4.13397i	−0.758985	+	0.438200i	−0.828931	−	0.559350i	$-0.811051\pi$
$89$	−7.16025	+	4.13397i	−0.758985	+	0.438200i	0.0699459	+	0.997551i	$0.477717\pi$
$90$		0			0
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	−2.26795			−0.236450
$93$		0			0
$94$	−3.73205	−	6.46410i	−0.384932	−	0.666721i
$95$	−0.928203	+	1.60770i	−0.0952316	+	0.164946i
$96$		0			0
$97$	7.26795	+	4.19615i	0.737948	+	0.426055i	0.821323	−	0.570464i	$-0.193236\pi$
$97$	7.26795	+	4.19615i	0.737948	+	0.426055i	−0.0833745	+	0.996518i	$0.526570\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$		0			0
$100$	−3.50000	+	6.06218i	−0.350000	+	0.606218i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	6.66025			0.656254			0.328127	−	0.944634i	$-0.393583\pi$
$103$	6.66025			0.656254			0.328127	+	0.944634i	$0.393583\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$		0			0
$106$	10.1603	−	5.86603i	0.986851	−	0.569759i
$107$	7.73205	+	13.3923i	0.747486	+	1.29468i	0.949024	+	0.315202i	$0.102072\pi$
$107$	7.73205	+	13.3923i	0.747486	+	1.29468i	−0.201539	+	0.979481i	$0.564594\pi$
$108$		0			0
$109$		−	12.0000i		−	1.14939i	−0.818367	−	0.574696i	$-0.805120\pi$
$109$		−	12.0000i		−	1.14939i	0.818367	−	0.574696i	$-0.194880\pi$
$110$	−12.0000	−	6.92820i	−1.14416	−	0.660578i
$111$		0			0
$112$		−	1.00000i		−	0.0944911i
$113$	8.19615	−	14.1962i	0.771029	−	1.33546i	−0.165970	−	0.986131i	$-0.553076\pi$
$113$	8.19615	−	14.1962i	0.771029	−	1.33546i	0.936999	−	0.349331i	$-0.113591\pi$
$114$		0			0
$115$	−6.80385	+	3.92820i	−0.634462	+	0.366307i
$116$	8.00000			0.742781
$117$		0			0
$118$	−9.73205			−0.895908
$119$	0.401924	−	0.232051i	0.0368443	−	0.0212721i
$120$		0			0
$121$	2.50000	−	4.33013i	0.227273	−	0.393648i
$122$			5.19615i			0.470438i
$123$		0			0
$124$	0.401924	+	0.232051i	0.0360938	+	0.0208388i
$125$			6.92820i			0.619677i
$126$		0			0
$127$	9.46410	+	16.3923i	0.839803	+	1.45458i	0.890059	+	0.455845i	$0.150663\pi$
$127$	9.46410	+	16.3923i	0.839803	+	1.45458i	−0.0502557	+	0.998736i	$0.516004\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.00000	+	12.1244i	−0.263117	+	1.06338i
$131$	−19.0000			−1.66004			−0.830019	−	0.557735i	$-0.811670\pi$
$131$	−19.0000			−1.66004			−0.830019	+	0.557735i	$0.811670\pi$
$132$		0			0
$133$	−0.267949	−	0.464102i	−0.0232341	−	0.0402427i
$134$	1.59808	−	2.76795i	0.138053	−	0.239114i
$135$		0			0
$136$	−0.401924	−	0.232051i	−0.0344647	−	0.0198982i
$137$	12.0000	+	6.92820i	1.02523	+	0.591916i	0.915614	−	0.402058i	$-0.131705\pi$
$137$	12.0000	+	6.92820i	1.02523	+	0.591916i	0.109615	+	0.993974i	$0.465038\pi$
$138$		0			0
$139$	5.46410	−	9.46410i	0.463459	−	0.802735i	−0.535671	−	0.844426i	$-0.679941\pi$
$139$	5.46410	−	9.46410i	0.463459	−	0.802735i	0.999131	+	0.0416919i	$0.0132748\pi$
$140$	−1.73205	−	3.00000i	−0.146385	−	0.253546i
$141$		0			0
$142$	−11.9282			−1.00099
$143$	−14.0000	−	3.46410i	−1.17074	−	0.289683i
$144$		0			0
$145$	24.0000	−	13.8564i	1.99309	−	1.15071i
$146$	−1.46410	−	2.53590i	−0.121170	−	0.209872i
$147$		0			0
$148$			8.92820i			0.733894i
$149$	−15.9904	−	9.23205i	−1.30998	−	0.756319i	−0.327890	−	0.944716i	$-0.606338\pi$
$149$	−15.9904	−	9.23205i	−1.30998	−	0.756319i	−0.982093	+	0.188397i	$0.939671\pi$
$150$		0			0
$151$			12.0000i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$151$			12.0000i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$152$	−0.267949	+	0.464102i	−0.0217335	+	0.0376436i
$153$		0			0
$154$	3.46410	−	2.00000i	0.279145	−	0.161165i
$155$	1.60770			0.129133
$156$		0			0
$157$	10.9282			0.872166			0.436083	−	0.899907i	$-0.356365\pi$
$157$	10.9282			0.872166			0.436083	+	0.899907i	$0.356365\pi$
$158$	−2.19615	+	1.26795i	−0.174717	+	0.100873i
$159$		0			0
$160$	−1.73205	+	3.00000i	−0.136931	+	0.237171i
$161$		−	2.26795i		−	0.178739i
$162$		0			0
$163$	−16.1603	−	9.33013i	−1.26577	−	0.730792i	−0.291584	−	0.956545i	$-0.594182\pi$
$163$	−16.1603	−	9.33013i	−1.26577	−	0.730792i	−0.974185	+	0.225753i	$0.927516\pi$
$164$		−	6.92820i		−	0.541002i
$165$		0			0
$166$	0.866025	+	1.50000i	0.0672166	+	0.116423i
$167$	17.3205	−	10.0000i	1.34030	−	0.773823i	0.353450	−	0.935454i	$-0.385009\pi$
$167$	17.3205	−	10.0000i	1.34030	−	0.773823i	0.986851	+	0.161630i	$0.0516752\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	−1.60770			−0.123305
$171$		0			0
$172$	1.23205	+	2.13397i	0.0939430	+	0.162714i
$173$	−7.46410	+	12.9282i	−0.567485	+	0.982913i	0.429329	+	0.903148i	$0.358750\pi$
$173$	−7.46410	+	12.9282i	−0.567485	+	0.982913i	−0.996814	+	0.0797647i	$0.974583\pi$
$174$		0			0
$175$	−6.06218	−	3.50000i	−0.458258	−	0.264575i
$176$	−3.46410	−	2.00000i	−0.261116	−	0.150756i
$177$		0			0
$178$	−4.13397	+	7.16025i	−0.309854	+	0.536684i
$179$	1.53590	+	2.66025i	0.114798	+	0.198837i	0.917699	−	0.397276i	$-0.130044\pi$
$179$	1.53590	+	2.66025i	0.114798	+	0.198837i	−0.802901	+	0.596113i	$0.796711\pi$
$180$		0			0
$181$	16.7846			1.24759			0.623795	−	0.781588i	$-0.285590\pi$
$181$	16.7846			1.24759			0.623795	+	0.781588i	$0.285590\pi$
$182$	−2.59808	−	2.50000i	−0.192582	−	0.185312i
$183$		0			0
$184$	−1.96410	+	1.13397i	−0.144795	+	0.0835977i
$185$	15.4641	+	26.7846i	1.13694	+	1.96924i
$186$		0			0
$187$		−	1.85641i		−	0.135754i
$188$	−6.46410	−	3.73205i	−0.471443	−	0.272188i
$189$		0			0
$190$			1.85641i			0.134678i
$191$	9.25833	−	16.0359i	0.669909	−	1.16032i	−0.308020	−	0.951380i	$-0.599666\pi$
$191$	9.25833	−	16.0359i	0.669909	−	1.16032i	0.977929	−	0.208937i	$-0.0670003\pi$
$192$		0			0
$193$	8.53590	−	4.92820i	0.614427	−	0.354740i	−0.160269	−	0.987073i	$-0.551236\pi$
$193$	8.53590	−	4.92820i	0.614427	−	0.354740i	0.774696	+	0.632334i	$0.217903\pi$
$194$	8.39230			0.602532
$195$		0			0
$196$	1.00000			0.0714286
$197$	20.2583	−	11.6962i	1.44335	−	0.833316i	0.445275	−	0.895394i	$-0.353106\pi$
$197$	20.2583	−	11.6962i	1.44335	−	0.833316i	0.998071	+	0.0620775i	$0.0197726\pi$
$198$		0			0
$199$	1.06218	−	1.83975i	0.0752958	−	0.130416i	−0.825919	−	0.563789i	$-0.809343\pi$
$199$	1.06218	−	1.83975i	0.0752958	−	0.130416i	0.901215	+	0.433373i	$0.142677\pi$
$200$			7.00000i			0.494975i
$201$		0			0
$202$		0			0
$203$			8.00000i			0.561490i
$204$		0			0
$205$	−12.0000	−	20.7846i	−0.838116	−	1.45166i
$206$	5.76795	−	3.33013i	0.401872	−	0.232021i
$207$		0			0
$208$	−0.866025	+	3.50000i	−0.0600481	+	0.242681i
$209$	−2.14359			−0.148275
$210$		0			0
$211$	11.4641	+	19.8564i	0.789221	+	1.36697i	0.926445	+	0.376431i	$0.122849\pi$
$211$	11.4641	+	19.8564i	0.789221	+	1.36697i	−0.137223	+	0.990540i	$0.543818\pi$
$212$	5.86603	−	10.1603i	0.402880	−	0.697809i
$213$		0			0
$214$	13.3923	+	7.73205i	0.915479	+	0.528552i
$215$	7.39230	+	4.26795i	0.504151	+	0.291072i
$216$		0			0
$217$	−0.232051	+	0.401924i	−0.0157526	+	0.0272844i
$218$	−6.00000	−	10.3923i	−0.406371	−	0.703856i
$219$		0			0
$220$	−13.8564			−0.934199
$221$	−1.60770	+	0.464102i	−0.108145	+	0.0312189i
$222$		0			0
$223$	12.5263	−	7.23205i	0.838822	−	0.484294i	−0.0180418	−	0.999837i	$-0.505743\pi$
$223$	12.5263	−	7.23205i	0.838822	−	0.484294i	0.856864	+	0.515543i	$0.172410\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$		−	16.3923i		−	1.09040i
$227$	18.4641	+	10.6603i	1.22551	+	0.707546i	0.966086	−	0.258219i	$-0.0831356\pi$
$227$	18.4641	+	10.6603i	1.22551	+	0.707546i	0.259419	+	0.965765i	$0.416469\pi$
$228$		0			0
$229$		−	6.07180i		−	0.401236i	−0.979670	−	0.200618i	$-0.935705\pi$
$229$		−	6.07180i		−	0.401236i	0.979670	−	0.200618i	$-0.0642949\pi$
$230$	−3.92820	+	6.80385i	−0.259018	+	0.448632i
$231$		0			0
$232$	6.92820	−	4.00000i	0.454859	−	0.262613i
$233$	6.53590			0.428181			0.214090	−	0.976814i	$-0.431321\pi$
$233$	6.53590			0.428181			0.214090	+	0.976814i	$0.431321\pi$
$234$		0			0
$235$	−25.8564			−1.68669
$236$	−8.42820	+	4.86603i	−0.548629	+	0.316751i
$237$		0			0
$238$	0.232051	−	0.401924i	0.0150416	−	0.0260528i
$239$			14.8564i			0.960981i	0.877000	+	0.480491i	$0.159541\pi$
$239$			14.8564i			0.960981i	−0.877000	+	0.480491i	$0.840459\pi$
$240$		0			0
$241$	10.2679	+	5.92820i	0.661417	+	0.381869i	0.792817	−	0.609460i	$-0.208614\pi$
$241$	10.2679	+	5.92820i	0.661417	+	0.381869i	−0.131400	+	0.991329i	$0.541947\pi$
$242$		−	5.00000i		−	0.321412i
$243$		0			0
$244$	2.59808	+	4.50000i	0.166325	+	0.288083i
$245$	3.00000	−	1.73205i	0.191663	−	0.110657i
$246$		0			0
$247$	0.535898	+	1.85641i	0.0340984	+	0.118120i
$248$	0.464102			0.0294705
$249$		0			0
$250$	3.46410	+	6.00000i	0.219089	+	0.379473i
$251$	11.9641	−	20.7224i	0.755167	−	1.30799i	−0.190124	−	0.981760i	$-0.560889\pi$
$251$	11.9641	−	20.7224i	0.755167	−	1.30799i	0.945291	−	0.326228i	$-0.105778\pi$
$252$		0			0
$253$	−7.85641	−	4.53590i	−0.493928	−	0.285169i
$254$	16.3923	+	9.46410i	1.02854	+	0.593831i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.23205	+	5.59808i	0.201610	+	0.349198i	0.949047	−	0.315134i	$-0.102049\pi$
$257$	3.23205	+	5.59808i	0.201610	+	0.349198i	−0.747437	+	0.664332i	$0.768716\pi$
$258$		0			0
$259$	−8.92820			−0.554772
$260$	3.46410	+	12.0000i	0.214834	+	0.744208i
$261$		0			0
$262$	−16.4545	+	9.50000i	−1.01656	+	0.586912i
$263$	8.66025	+	15.0000i	0.534014	+	0.924940i	0.999210	+	0.0397320i	$0.0126504\pi$
$263$	8.66025	+	15.0000i	0.534014	+	0.924940i	−0.465196	+	0.885208i	$0.654016\pi$
$264$		0			0
$265$		−	40.6410i		−	2.49656i
$266$	−0.464102	−	0.267949i	−0.0284559	−	0.0164290i
$267$		0			0
$268$		−	3.19615i		−	0.195236i
$269$	0.803848	−	1.39230i	0.0490115	−	0.0848903i	−0.840479	−	0.541844i	$-0.817726\pi$
$269$	0.803848	−	1.39230i	0.0490115	−	0.0848903i	0.889490	+	0.456954i	$0.151060\pi$
$270$		0			0
$271$	−4.79423	+	2.76795i	−0.291229	+	0.168141i	−0.638496	−	0.769625i	$-0.720443\pi$
$271$	−4.79423	+	2.76795i	−0.291229	+	0.168141i	0.347267	+	0.937766i	$0.387110\pi$
$272$	−0.464102			−0.0281403
$273$		0			0
$274$	13.8564			0.837096
$275$	−24.2487	+	14.0000i	−1.46225	+	0.844232i
$276$		0			0
$277$	−13.6603	+	23.6603i	−0.820765	+	1.42161i	0.0843481	+	0.996436i	$0.473119\pi$
$277$	−13.6603	+	23.6603i	−0.820765	+	1.42161i	−0.905113	+	0.425171i	$0.860214\pi$
$278$		−	10.9282i		−	0.655430i
$279$		0			0
$280$	−3.00000	−	1.73205i	−0.179284	−	0.103510i
$281$			18.3923i			1.09719i	0.836087	+	0.548596i	$0.184838\pi$
$281$			18.3923i			1.09719i	−0.836087	+	0.548596i	$0.815162\pi$
$282$		0			0
$283$	−2.26795	−	3.92820i	−0.134816	−	0.233507i	0.790711	−	0.612189i	$-0.209711\pi$
$283$	−2.26795	−	3.92820i	−0.134816	−	0.233507i	−0.925527	+	0.378682i	$0.876378\pi$
$284$	−10.3301	+	5.96410i	−0.612980	+	0.353904i
$285$		0			0
$286$	−13.8564	+	4.00000i	−0.819346	+	0.236525i
$287$	6.92820			0.408959
$288$		0			0
$289$	8.39230	+	14.5359i	0.493665	+	0.855053i
$290$	13.8564	−	24.0000i	0.813676	−	1.40933i
$291$		0			0
$292$	−2.53590	−	1.46410i	−0.148402	−	0.0856801i
$293$	−22.9808	−	13.2679i	−1.34255	−	0.775122i	−0.355369	−	0.934726i	$-0.615645\pi$
$293$	−22.9808	−	13.2679i	−1.34255	−	0.775122i	−0.987181	+	0.159604i	$0.948978\pi$
$294$		0			0
$295$	−16.8564	+	29.1962i	−0.981418	+	1.69987i
$296$	4.46410	+	7.73205i	0.259471	+	0.449416i
$297$		0			0
$298$	−18.4641			−1.06960
$299$	−1.96410	+	7.93782i	−0.113587	+	0.459056i
$300$		0			0
$301$	−2.13397	+	1.23205i	−0.123000	+	0.0710142i
$302$	6.00000	+	10.3923i	0.345261	+	0.598010i
$303$		0			0
$304$			0.535898i			0.0307359i
$305$	15.5885	+	9.00000i	0.892592	+	0.515339i
$306$		0			0
$307$			22.0000i			1.25561i	0.778372	+	0.627803i	$0.216046\pi$
$307$			22.0000i			1.25561i	−0.778372	+	0.627803i	$0.783954\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$		0			0
$310$	1.39230	−	0.803848i	0.0790776	−	0.0456555i
$311$	−21.3205			−1.20898			−0.604488	−	0.796615i	$-0.706622\pi$
$311$	−21.3205			−1.20898			−0.604488	+	0.796615i	$0.706622\pi$
$312$		0			0
$313$	35.3205			1.99643			0.998217	−	0.0596964i	$-0.0190133\pi$
$313$	35.3205			1.99643			0.998217	+	0.0596964i	$0.0190133\pi$
$314$	9.46410	−	5.46410i	0.534090	−	0.308357i
$315$		0			0
$316$	−1.26795	+	2.19615i	−0.0713277	+	0.123543i
$317$		−	9.53590i		−	0.535589i	−0.963476	−	0.267795i	$-0.913705\pi$
$317$		−	9.53590i		−	0.535589i	0.963476	−	0.267795i	$-0.0862949\pi$
$318$		0			0
$319$	27.7128	+	16.0000i	1.55162	+	0.895828i
$320$			3.46410i			0.193649i
$321$		0			0
$322$	−1.13397	−	1.96410i	−0.0631939	−	0.109455i
$323$	−0.215390	+	0.124356i	−0.0119846	+	0.00691933i
$324$		0			0
$325$	18.1865	+	17.5000i	1.00881	+	0.970725i
$326$	−18.6603			−1.03350
$327$		0			0
$328$	−3.46410	−	6.00000i	−0.191273	−	0.331295i
$329$	3.73205	−	6.46410i	0.205755	−	0.356377i
$330$		0			0
$331$	11.5359	+	6.66025i	0.634070	+	0.366081i	0.782327	−	0.622868i	$-0.214033\pi$
$331$	11.5359	+	6.66025i	0.634070	+	0.366081i	−0.148256	+	0.988949i	$0.547366\pi$
$332$	1.50000	+	0.866025i	0.0823232	+	0.0475293i
$333$		0			0
$334$	10.0000	−	17.3205i	0.547176	−	0.947736i
$335$	−5.53590	−	9.58846i	−0.302458	−	0.523873i
$336$		0			0
$337$	−6.00000			−0.326841			−0.163420	−	0.986557i	$-0.552253\pi$
$337$	−6.00000			−0.326841			−0.163420	+	0.986557i	$0.552253\pi$
$338$	6.92820	+	11.0000i	0.376845	+	0.598321i
$339$		0			0
$340$	−1.39230	+	0.803848i	−0.0755083	+	0.0435948i
$341$	0.928203	+	1.60770i	0.0502650	+	0.0870616i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	2.13397	+	1.23205i	0.115056	+	0.0664277i
$345$		0			0
$346$			14.9282i			0.802545i
$347$	−14.8564	+	25.7321i	−0.797534	+	1.38137i	0.123684	+	0.992322i	$0.460529\pi$
$347$	−14.8564	+	25.7321i	−0.797534	+	1.38137i	−0.921218	+	0.389047i	$0.872804\pi$
$348$		0			0
$349$	−29.1340	+	16.8205i	−1.55951	+	0.900381i	−0.562202	+	0.827000i	$0.690046\pi$
$349$	−29.1340	+	16.8205i	−1.55951	+	0.900381i	−0.997304	+	0.0733812i	$0.976621\pi$
$350$	−7.00000			−0.374166
$351$		0			0
$352$	−4.00000			−0.213201
$353$	23.0885	−	13.3301i	1.22887	−	0.709491i	0.262080	−	0.965046i	$-0.415592\pi$
$353$	23.0885	−	13.3301i	1.22887	−	0.709491i	0.966795	+	0.255555i	$0.0822582\pi$
$354$		0			0
$355$	−20.6603	+	35.7846i	−1.09653	+	1.89925i
$356$			8.26795i			0.438200i
$357$		0			0
$358$	2.66025	+	1.53590i	0.140599	+	0.0811748i
$359$		−	8.00000i		−	0.422224i	−0.977462	−	0.211112i	$-0.932292\pi$
$359$		−	8.00000i		−	0.422224i	0.977462	−	0.211112i	$-0.0677085\pi$
$360$		0			0
$361$	−9.35641	−	16.2058i	−0.492442	−	0.852935i
$362$	14.5359	−	8.39230i	0.763990	−	0.441090i
$363$		0			0
$364$	−3.50000	−	0.866025i	−0.183450	−	0.0453921i
$365$	−10.1436			−0.530940
$366$		0			0
$367$	−2.52628	−	4.37564i	−0.131871	−	0.228407i	0.792527	−	0.609837i	$-0.208765\pi$
$367$	−2.52628	−	4.37564i	−0.131871	−	0.228407i	−0.924398	+	0.381430i	$0.875432\pi$
$368$	−1.13397	+	1.96410i	−0.0591125	+	0.102386i
$369$		0			0
$370$	26.7846	+	15.4641i	1.39247	+	0.803940i
$371$	10.1603	+	5.86603i	0.527494	+	0.304549i
$372$		0			0
$373$	−11.1244	+	19.2679i	−0.575997	+	0.997657i	0.419935	+	0.907554i	$0.362053\pi$
$373$	−11.1244	+	19.2679i	−0.575997	+	0.997657i	−0.995932	+	0.0901025i	$0.971281\pi$
$374$	−0.928203	−	1.60770i	−0.0479962	−	0.0831319i
$375$		0			0
$376$	−7.46410			−0.384932
$377$	6.92820	−	28.0000i	0.356821	−	1.44207i
$378$		0			0
$379$	26.3205	−	15.1962i	1.35199	−	0.780574i	0.363465	−	0.931608i	$-0.381594\pi$
$379$	26.3205	−	15.1962i	1.35199	−	0.780574i	0.988529	+	0.151034i	$0.0482603\pi$
$380$	0.928203	+	1.60770i	0.0476158	+	0.0824730i
$381$		0			0
$382$		−	18.5167i		−	0.947395i
$383$	−23.6603	−	13.6603i	−1.20898	−	0.698006i	−0.246445	−	0.969157i	$-0.579263\pi$
$383$	−23.6603	−	13.6603i	−1.20898	−	0.698006i	−0.962537	+	0.271150i	$0.912596\pi$
$384$		0			0
$385$		−	13.8564i		−	0.706188i
$386$	4.92820	−	8.53590i	0.250839	−	0.434466i
$387$		0			0
$388$	7.26795	−	4.19615i	0.368974	−	0.213027i
$389$	2.66025			0.134880			0.0674401	−	0.997723i	$-0.478517\pi$
$389$	2.66025			0.134880			0.0674401	+	0.997723i	$0.478517\pi$
$390$		0			0
$391$	−1.05256			−0.0532302
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$		0			0
$394$	11.6962	−	20.2583i	0.589244	−	1.02060i
$395$			8.78461i			0.442002i
$396$		0			0
$397$	−10.2058	−	5.89230i	−0.512213	−	0.295726i	0.221530	−	0.975154i	$-0.428895\pi$
$397$	−10.2058	−	5.89230i	−0.512213	−	0.295726i	−0.733743	+	0.679427i	$0.762228\pi$
$398$		−	2.12436i		−	0.106484i
$399$		0			0
$400$	3.50000	+	6.06218i	0.175000	+	0.303109i
$401$	3.80385	−	2.19615i	0.189955	−	0.109671i	−0.402006	−	0.915637i	$-0.631687\pi$
$401$	3.80385	−	2.19615i	0.189955	−	0.109671i	0.591962	+	0.805966i	$0.298354\pi$
$402$		0			0
$403$	1.16025	−	1.20577i	0.0577964	−	0.0600637i
$404$		0			0
$405$		0			0
$406$	4.00000	+	6.92820i	0.198517	+	0.343841i
$407$	−17.8564	+	30.9282i	−0.885109	+	1.53305i
$408$		0			0
$409$	12.4641	+	7.19615i	0.616310	+	0.355827i	0.775431	−	0.631432i	$-0.217533\pi$
$409$	12.4641	+	7.19615i	0.616310	+	0.355827i	−0.159121	+	0.987259i	$0.550866\pi$
$410$	−20.7846	−	12.0000i	−1.02648	−	0.592638i
$411$		0			0
$412$	3.33013	−	5.76795i	0.164064	−	0.284166i
$413$	−4.86603	−	8.42820i	−0.239441	−	0.414725i
$414$		0			0
$415$	6.00000			0.294528
$416$	1.00000	+	3.46410i	0.0490290	+	0.169842i
$417$		0			0
$418$	−1.85641	+	1.07180i	−0.0907998	+	0.0524233i
$419$	−2.50000	−	4.33013i	−0.122133	−	0.211541i	0.798476	−	0.602027i	$-0.205640\pi$
$419$	−2.50000	−	4.33013i	−0.122133	−	0.211541i	−0.920609	+	0.390487i	$0.872307\pi$
$420$		0			0
$421$		−	22.3923i		−	1.09133i	−0.838002	−	0.545667i	$-0.816276\pi$
$421$		−	22.3923i		−	1.09133i	0.838002	−	0.545667i	$-0.183724\pi$
$422$	19.8564	+	11.4641i	0.966595	+	0.558064i
$423$		0			0
$424$		−	11.7321i		−	0.569759i
$425$	−1.62436	+	2.81347i	−0.0787928	+	0.136473i
$426$		0			0
$427$	−4.50000	+	2.59808i	−0.217770	+	0.125730i
$428$	15.4641			0.747486
$429$		0			0
$430$	8.53590			0.411638
$431$	−19.7942	+	11.4282i	−0.953454	+	0.550477i	−0.894152	−	0.447763i	$-0.852221\pi$
$431$	−19.7942	+	11.4282i	−0.953454	+	0.550477i	−0.0593021	+	0.998240i	$0.518888\pi$
$432$		0			0
$433$	−8.92820	+	15.4641i	−0.429062	+	0.743157i	−0.996790	−	0.0800589i	$-0.974489\pi$
$433$	−8.92820	+	15.4641i	−0.429062	+	0.743157i	0.567728	+	0.823216i	$0.307823\pi$
$434$			0.464102i			0.0222776i
$435$		0			0
$436$	−10.3923	−	6.00000i	−0.497701	−	0.287348i
$437$			1.21539i			0.0581400i
$438$		0			0
$439$	−17.1962	−	29.7846i	−0.820728	−	1.42154i	−0.905141	−	0.425111i	$-0.860235\pi$
$439$	−17.1962	−	29.7846i	−0.820728	−	1.42154i	0.0844136	−	0.996431i	$-0.473098\pi$
$440$	−12.0000	+	6.92820i	−0.572078	+	0.330289i
$441$		0			0
$442$	−1.16025	+	1.20577i	−0.0551877	+	0.0573527i
$443$	1.60770			0.0763839			0.0381920	−	0.999270i	$-0.487840\pi$
$443$	1.60770			0.0763839			0.0381920	+	0.999270i	$0.487840\pi$
$444$		0			0
$445$	14.3205	+	24.8038i	0.678857	+	1.17582i
$446$	7.23205	−	12.5263i	0.342448	−	0.593137i
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	15.5885	+	9.00000i	0.735665	+	0.424736i	0.820491	−	0.571660i	$-0.193700\pi$
$449$	15.5885	+	9.00000i	0.735665	+	0.424736i	−0.0848262	+	0.996396i	$0.527033\pi$
$450$		0			0
$451$	13.8564	−	24.0000i	0.652473	−	1.13012i
$452$	−8.19615	−	14.1962i	−0.385515	−	0.667731i
$453$		0			0
$454$	21.3205			1.00062
$455$	−12.0000	+	3.46410i	−0.562569	+	0.162400i
$456$		0			0
$457$	7.96410	−	4.59808i	0.372545	−	0.215089i	−0.302025	−	0.953300i	$-0.597663\pi$
$457$	7.96410	−	4.59808i	0.372545	−	0.215089i	0.674570	+	0.738211i	$0.264329\pi$
$458$	−3.03590	−	5.25833i	−0.141858	−	0.245706i
$459$		0			0
$460$			7.85641i			0.366307i
$461$	−16.3923	−	9.46410i	−0.763466	−	0.440787i	0.0670730	−	0.997748i	$-0.478634\pi$
$461$	−16.3923	−	9.46410i	−0.763466	−	0.440787i	−0.830539	+	0.556961i	$0.811967\pi$
$462$		0			0
$463$			40.2487i			1.87052i	0.353966	+	0.935258i	$0.384833\pi$
$463$			40.2487i			1.87052i	−0.353966	+	0.935258i	$0.615167\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$		0			0
$466$	5.66025	−	3.26795i	0.262206	−	0.151385i
$467$	29.6410			1.37162			0.685811	−	0.727779i	$-0.259448\pi$
$467$	29.6410			1.37162			0.685811	+	0.727779i	$0.259448\pi$
$468$		0			0
$469$	3.19615			0.147585
$470$	−22.3923	+	12.9282i	−1.03288	+	0.596334i
$471$		0			0
$472$	−4.86603	+	8.42820i	−0.223977	+	0.387939i
$473$			9.85641i			0.453198i
$474$		0			0
$475$	3.24871	+	1.87564i	0.149061	+	0.0860605i
$476$		−	0.464102i		−	0.0212721i
$477$		0			0
$478$	7.42820	+	12.8660i	0.339758	+	0.588478i
$479$	14.1962	−	8.19615i	0.648639	−	0.374492i	−0.139296	−	0.990251i	$-0.544484\pi$
$479$	14.1962	−	8.19615i	0.648639	−	0.374492i	0.787935	+	0.615759i	$0.211151\pi$
$480$		0			0
$481$	31.2487	+	7.73205i	1.42482	+	0.352551i
$482$	11.8564			0.540045
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	14.5359	−	25.1769i	0.660041	−	1.14322i
$486$		0			0
$487$	17.6603	+	10.1962i	0.800262	+	0.462032i	0.843563	−	0.537030i	$-0.180454\pi$
$487$	17.6603	+	10.1962i	0.800262	+	0.462032i	−0.0433004	+	0.999062i	$0.513787\pi$
$488$	4.50000	+	2.59808i	0.203705	+	0.117609i
$489$		0			0
$490$	1.73205	−	3.00000i	0.0782461	−	0.135526i
$491$	−8.92820	−	15.4641i	−0.402924	−	0.697885i	0.591153	−	0.806559i	$-0.298673\pi$
$491$	−8.92820	−	15.4641i	−0.402924	−	0.697885i	−0.994077	+	0.108674i	$0.965340\pi$
$492$		0			0
$493$	3.71281			0.167217
$494$	1.39230	+	1.33975i	0.0626428	+	0.0602780i
$495$		0			0
$496$	0.401924	−	0.232051i	0.0180469	−	0.0104194i
$497$	−5.96410	−	10.3301i	−0.267527	−	0.463370i
$498$		0			0
$499$		−	3.73205i		−	0.167070i	−0.996505	−	0.0835348i	$-0.973379\pi$
$499$		−	3.73205i		−	0.167070i	0.996505	−	0.0835348i	$-0.0266210\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$		0			0
$502$		−	23.9282i		−	1.06797i
$503$	3.46410	−	6.00000i	0.154457	−	0.267527i	−0.778404	−	0.627763i	$-0.783971\pi$
$503$	3.46410	−	6.00000i	0.154457	−	0.267527i	0.932861	+	0.360236i	$0.117304\pi$
$504$		0			0
$505$		0			0
$506$	−9.07180			−0.403291
$507$		0			0
$508$	18.9282			0.839803
$509$	12.3397	−	7.12436i	0.546950	−	0.315782i	−0.200941	−	0.979603i	$-0.564400\pi$
$509$	12.3397	−	7.12436i	0.546950	−	0.315782i	0.747891	+	0.663822i	$0.231067\pi$
$510$		0			0
$511$	1.46410	−	2.53590i	0.0647680	−	0.112182i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	5.59808	+	3.23205i	0.246921	+	0.142560i
$515$		−	23.0718i		−	1.01666i
$516$		0			0
$517$	−14.9282	−	25.8564i	−0.656542	−	1.13716i
$518$	−7.73205	+	4.46410i	−0.339727	+	0.196141i
$519$		0			0
$520$	9.00000	+	8.66025i	0.394676	+	0.379777i
$521$	30.0000			1.31432			0.657162	−	0.753749i	$-0.271757\pi$
$521$	30.0000			1.31432			0.657162	+	0.753749i	$0.271757\pi$
$522$		0			0
$523$	−0.535898	−	0.928203i	−0.0234332	−	0.0405875i	0.854071	−	0.520156i	$-0.174126\pi$
$523$	−0.535898	−	0.928203i	−0.0234332	−	0.0405875i	−0.877504	+	0.479569i	$0.840793\pi$
$524$	−9.50000	+	16.4545i	−0.415009	+	0.718817i
$525$		0			0
$526$	15.0000	+	8.66025i	0.654031	+	0.377605i
$527$	0.186533	+	0.107695i	0.00812553	+	0.00469127i
$528$		0			0
$529$	8.92820	−	15.4641i	0.388183	−	0.672352i
$530$	−20.3205	−	35.1962i	−0.882666	−	1.52882i
$531$		0			0
$532$	−0.535898			−0.0232341
$533$	−24.2487	−	6.00000i	−1.05033	−	0.259889i
$534$		0			0
$535$	46.3923	−	26.7846i	2.00571	−	1.15800i
$536$	−1.59808	−	2.76795i	−0.0690264	−	0.119557i
$537$		0			0
$538$		−	1.60770i		−	0.0693127i
$539$	3.46410	+	2.00000i	0.149209	+	0.0861461i
$540$		0			0
$541$		−	17.3205i		−	0.744667i	−0.928099	−	0.372333i	$-0.878558\pi$
$541$		−	17.3205i		−	0.744667i	0.928099	−	0.372333i	$-0.121442\pi$
$542$	−2.76795	+	4.79423i	−0.118894	+	0.205930i
$543$		0			0
$544$	−0.401924	+	0.232051i	−0.0172323	+	0.00994910i
$545$	−41.5692			−1.78063
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$	12.0000	−	6.92820i	0.512615	−	0.295958i
$549$		0			0
$550$	−14.0000	+	24.2487i	−0.596962	+	1.03397i
$551$		−	4.28719i		−	0.182640i
$552$		0			0
$553$	−2.19615	−	1.26795i	−0.0933899	−	0.0539187i
$554$			27.3205i			1.16074i
$555$		0			0
$556$	−5.46410	−	9.46410i	−0.231730	−	0.401367i
$557$	39.3109	−	22.6962i	1.66566	−	0.961667i	0.695718	−	0.718315i	$-0.255086\pi$
$557$	39.3109	−	22.6962i	1.66566	−	0.961667i	0.969938	−	0.243351i	$-0.0782469\pi$
$558$		0			0
$559$	8.53590	−	2.46410i	0.361030	−	0.104220i
$560$	−3.46410			−0.146385
$561$		0			0
$562$	9.19615	+	15.9282i	0.387916	+	0.671891i
$563$	−6.92820	+	12.0000i	−0.291989	+	0.505740i	−0.974280	−	0.225341i	$-0.927650\pi$
$563$	−6.92820	+	12.0000i	−0.291989	+	0.505740i	0.682291	+	0.731081i	$0.260984\pi$
$564$		0			0
$565$	−49.1769	−	28.3923i	−2.06889	−	1.19447i
$566$	−3.92820	−	2.26795i	−0.165115	−	0.0953290i
$567$		0			0
$568$	−5.96410	+	10.3301i	−0.250248	+	0.433443i
$569$	−4.26795	−	7.39230i	−0.178922	−	0.309902i	0.762590	−	0.646882i	$-0.223928\pi$
$569$	−4.26795	−	7.39230i	−0.178922	−	0.309902i	−0.941511	+	0.336981i	$0.890594\pi$
$570$		0			0
$571$	−17.3923			−0.727845			−0.363923	−	0.931429i	$-0.618563\pi$
$571$	−17.3923			−0.727845			−0.363923	+	0.931429i	$0.618563\pi$
$572$	−10.0000	+	10.3923i	−0.418121	+	0.434524i
$573$		0			0
$574$	6.00000	−	3.46410i	0.250435	−	0.144589i
$575$	7.93782	+	13.7487i	0.331030	+	0.573361i
$576$		0			0
$577$			42.7846i			1.78115i	0.454840	+	0.890573i	$0.349697\pi$
$577$			42.7846i			1.78115i	−0.454840	+	0.890573i	$0.650303\pi$
$578$	14.5359	+	8.39230i	0.604614	+	0.349074i
$579$		0			0
$580$		−	27.7128i		−	1.15071i
$581$	−0.866025	+	1.50000i	−0.0359288	+	0.0622305i
$582$		0			0
$583$	40.6410	−	23.4641i	1.68318	−	0.971784i
$584$	−2.92820			−0.121170
$585$		0			0
$586$	−26.5359			−1.09619
$587$	−13.9641	+	8.06218i	−0.576360	+	0.332762i	−0.759686	−	0.650291i	$-0.774647\pi$
$587$	−13.9641	+	8.06218i	−0.576360	+	0.332762i	0.183325	+	0.983052i	$0.441314\pi$
$588$		0			0
$589$	0.124356	−	0.215390i	0.00512399	−	0.00887500i
$590$			33.7128i			1.38793i
$591$		0			0
$592$	7.73205	+	4.46410i	0.317785	+	0.183473i
$593$			7.73205i			0.317517i	0.987317	+	0.158759i	$0.0507492\pi$
$593$			7.73205i			0.317517i	−0.987317	+	0.158759i	$0.949251\pi$
$594$		0			0
$595$	−0.803848	−	1.39230i	−0.0329545	−	0.0570789i
$596$	−15.9904	+	9.23205i	−0.654992	+	0.378160i
$597$		0			0
$598$	2.26795	+	7.85641i	0.0927433	+	0.321272i
$599$	−19.0526			−0.778466			−0.389233	−	0.921139i	$-0.627260\pi$
$599$	−19.0526			−0.778466			−0.389233	+	0.921139i	$0.627260\pi$
$600$		0			0
$601$	−12.1244	−	21.0000i	−0.494563	−	0.856608i	0.505418	−	0.862875i	$-0.331338\pi$
$601$	−12.1244	−	21.0000i	−0.494563	−	0.856608i	−0.999980	+	0.00626702i	$0.998005\pi$
$602$	−1.23205	+	2.13397i	−0.0502146	+	0.0869743i
$603$		0			0
$604$	10.3923	+	6.00000i	0.422857	+	0.244137i
$605$	−15.0000	−	8.66025i	−0.609837	−	0.352089i
$606$		0			0
$607$	2.40192	−	4.16025i	0.0974911	−	0.168860i	−0.813154	−	0.582048i	$-0.802252\pi$
$607$	2.40192	−	4.16025i	0.0974911	−	0.168860i	0.910646	+	0.413188i	$0.135585\pi$
$608$	0.267949	+	0.464102i	0.0108668	+	0.0188218i
$609$		0			0
$610$	18.0000			0.728799
$611$	−18.6603	+	19.3923i	−0.754913	+	0.784529i
$612$		0			0
$613$	−11.7846	+	6.80385i	−0.475976	+	0.274805i	−0.718738	−	0.695281i	$-0.755280\pi$
$613$	−11.7846	+	6.80385i	−0.475976	+	0.274805i	0.242762	+	0.970086i	$0.421947\pi$
$614$	11.0000	+	19.0526i	0.443924	+	0.768899i
$615$		0			0
$616$		−	4.00000i		−	0.161165i
$617$	18.9282	+	10.9282i	0.762021	+	0.439953i	0.830021	−	0.557732i	$-0.188328\pi$
$617$	18.9282	+	10.9282i	0.762021	+	0.439953i	−0.0680000	+	0.997685i	$0.521662\pi$
$618$		0			0
$619$			10.7846i			0.433470i	0.976230	+	0.216735i	$0.0695408\pi$
$619$			10.7846i			0.433470i	−0.976230	+	0.216735i	$0.930459\pi$
$620$	0.803848	−	1.39230i	0.0322833	−	0.0559163i
$621$		0			0
$622$	−18.4641	+	10.6603i	−0.740343	+	0.427437i
$623$	−8.26795			−0.331248
$624$		0			0
$625$	−11.0000			−0.440000
$626$	30.5885	−	17.6603i	1.22256	−	0.705846i
$627$		0			0
$628$	5.46410	−	9.46410i	0.218041	−	0.377659i
$629$			4.14359i			0.165216i
$630$		0			0
$631$	−18.2487	−	10.5359i	−0.726470	−	0.419427i	0.0906596	−	0.995882i	$-0.471102\pi$
$631$	−18.2487	−	10.5359i	−0.726470	−	0.419427i	−0.817129	+	0.576454i	$0.804436\pi$
$632$			2.53590i			0.100873i
$633$		0			0
$634$	−4.76795	−	8.25833i	−0.189359	−	0.327980i
$635$	56.7846	−	32.7846i	2.25343	−	1.30102i
$636$		0			0
$637$	0.866025	−	3.50000i	0.0343132	−	0.138675i
$638$	32.0000			1.26689
$639$		0			0
$640$	1.73205	+	3.00000i	0.0684653	+	0.118585i
$641$	−21.3205	+	36.9282i	−0.842109	+	1.45858i	0.0459986	+	0.998942i	$0.485353\pi$
$641$	−21.3205	+	36.9282i	−0.842109	+	1.45858i	−0.888108	+	0.459635i	$0.847980\pi$
$642$		0			0
$643$	−24.4641	−	14.1244i	−0.964770	−	0.557010i	−0.0671322	−	0.997744i	$-0.521385\pi$
$643$	−24.4641	−	14.1244i	−0.964770	−	0.557010i	−0.897638	+	0.440734i	$0.854718\pi$
$644$	−1.96410	−	1.13397i	−0.0773964	−	0.0446849i
$645$		0			0
$646$	−0.124356	+	0.215390i	−0.00489271	+	0.00847442i
$647$	−1.33975	−	2.32051i	−0.0526708	−	0.0912286i	0.838488	−	0.544920i	$-0.183440\pi$
$647$	−1.33975	−	2.32051i	−0.0526708	−	0.0912286i	−0.891159	+	0.453692i	$0.850107\pi$
$648$		0			0
$649$	−38.9282			−1.52807
$650$	24.5000	+	6.06218i	0.960969	+	0.237778i
$651$		0			0
$652$	−16.1603	+	9.33013i	−0.632884	+	0.365396i
$653$	−3.20577	−	5.55256i	−0.125452	−	0.217288i	0.796458	−	0.604694i	$-0.206705\pi$
$653$	−3.20577	−	5.55256i	−0.125452	−	0.217288i	−0.921909	+	0.387406i	$0.873371\pi$
$654$		0			0
$655$			65.8179i			2.57172i
$656$	−6.00000	−	3.46410i	−0.234261	−	0.135250i
$657$		0			0
$658$		−	7.46410i		−	0.290981i
$659$	11.1962	−	19.3923i	0.436140	−	0.755417i	−0.561248	−	0.827648i	$-0.689679\pi$
$659$	11.1962	−	19.3923i	0.436140	−	0.755417i	0.997388	+	0.0722309i	$0.0230118\pi$
$660$		0			0
$661$	4.08142	−	2.35641i	0.158749	−	0.0916536i	−0.418521	−	0.908207i	$-0.637451\pi$
$661$	4.08142	−	2.35641i	0.158749	−	0.0916536i	0.577270	+	0.816553i	$0.304118\pi$
$662$	13.3205			0.517716
$663$		0			0
$664$	1.73205			0.0672166
$665$	−1.60770	+	0.928203i	−0.0623437	+	0.0359942i
$666$		0			0
$667$	9.07180	−	15.7128i	0.351261	−	0.608403i
$668$		−	20.0000i		−	0.773823i
$669$		0			0
$670$	−9.58846	−	5.53590i	−0.370434	−	0.213870i
$671$			20.7846i			0.802381i
$672$		0			0
$673$	−14.8205	−	25.6699i	−0.571289	−	0.989501i	−0.996434	−	0.0843758i	$-0.973110\pi$
$673$	−14.8205	−	25.6699i	−0.571289	−	0.989501i	0.425145	−	0.905125i	$-0.360223\pi$
$674$	−5.19615	+	3.00000i	−0.200148	+	0.115556i
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	−14.9282			−0.573737			−0.286869	−	0.957970i	$-0.592614\pi$
$677$	−14.9282			−0.573737			−0.286869	+	0.957970i	$0.592614\pi$
$678$		0			0
$679$	4.19615	+	7.26795i	0.161034	+	0.278918i
$680$	−0.803848	+	1.39230i	−0.0308261	+	0.0533925i
$681$		0			0
$682$	1.60770	+	0.928203i	0.0615618	+	0.0355427i
$683$	−9.67949	−	5.58846i	−0.370375	−	0.213836i	0.303247	−	0.952912i	$-0.401929\pi$
$683$	−9.67949	−	5.58846i	−0.370375	−	0.213836i	−0.673622	+	0.739076i	$0.735263\pi$
$684$		0			0
$685$	24.0000	−	41.5692i	0.916993	−	1.58828i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	2.46410			0.0939430
$689$	−30.4808	−	29.3301i	−1.16122	−	1.11739i
$690$		0			0
$691$	−18.3397	+	10.5885i	−0.697677	+	0.402804i	−0.806482	−	0.591259i	$-0.798631\pi$
$691$	−18.3397	+	10.5885i	−0.697677	+	0.402804i	0.108805	+	0.994063i	$0.465298\pi$
$692$	7.46410	+	12.9282i	0.283743	+	0.491457i
$693$		0			0
$694$			29.7128i			1.12788i
$695$	−32.7846	−	18.9282i	−1.24359	−	0.717988i
$696$		0			0
$697$		−	3.21539i		−	0.121792i
$698$	−16.8205	+	29.1340i	−0.636666	+	1.10274i
$699$		0			0
$700$	−6.06218	+	3.50000i	−0.229129	+	0.132288i
$701$	22.1244			0.835625			0.417813	−	0.908533i	$-0.362797\pi$
$701$	22.1244			0.835625			0.417813	+	0.908533i	$0.362797\pi$
$702$		0			0
$703$	4.78461			0.180455
$704$	−3.46410	+	2.00000i	−0.130558	+	0.0753778i
$705$		0			0
$706$	13.3301	−	23.0885i	0.501686	−	0.868946i
$707$		0			0
$708$		0			0
$709$	−41.3205	−	23.8564i	−1.55182	−	0.895946i	−0.997993	−	0.0633169i	$-0.979832\pi$
$709$	−41.3205	−	23.8564i	−1.55182	−	0.895946i	−0.553831	−	0.832629i	$-0.686835\pi$
$710$			41.3205i			1.55073i
$711$		0			0
$712$	4.13397	+	7.16025i	0.154927	+	0.268342i
$713$	0.911543	−	0.526279i	0.0341375	−	0.0197093i
$714$		0			0
$715$	−12.0000	+	48.4974i	−0.448775	+	1.81370i
$716$	3.07180			0.114798
$717$		0			0
$718$	−4.00000	−	6.92820i	−0.149279	−	0.258558i
$719$	−20.7321	+	35.9090i	−0.773175	+	1.33918i	0.162639	+	0.986686i	$0.447999\pi$
$719$	−20.7321	+	35.9090i	−0.773175	+	1.33918i	−0.935814	+	0.352493i	$0.885334\pi$
$720$		0			0
$721$	5.76795	+	3.33013i	0.214810	+	0.124020i
$722$	−16.2058	−	9.35641i	−0.603116	−	0.348209i
$723$		0			0
$724$	8.39230	−	14.5359i	0.311898	−	0.540222i
$725$	−28.0000	−	48.4974i	−1.03989	−	1.80115i
$726$		0			0
$727$	−42.9090			−1.59141			−0.795703	−	0.605687i	$-0.792898\pi$
$727$	−42.9090			−1.59141			−0.795703	+	0.605687i	$0.792898\pi$
$728$	−3.46410	+	1.00000i	−0.128388	+	0.0370625i
$729$		0			0
$730$	−8.78461	+	5.07180i	−0.325133	+	0.187716i
$731$	0.571797	+	0.990381i	0.0211487	+	0.0366306i
$732$		0			0
$733$		−	22.8564i		−	0.844221i	−0.906544	−	0.422110i	$-0.861289\pi$
$733$		−	22.8564i		−	0.844221i	0.906544	−	0.422110i	$-0.138711\pi$
$734$	−4.37564	−	2.52628i	−0.161508	−	0.0932467i
$735$		0			0
$736$			2.26795i			0.0835977i
$737$	6.39230	−	11.0718i	0.235464	−	0.407835i
$738$		0			0
$739$	−3.69615	+	2.13397i	−0.135965	+	0.0784995i	−0.566440	−	0.824103i	$-0.691680\pi$
$739$	−3.69615	+	2.13397i	−0.135965	+	0.0784995i	0.430474	+	0.902603i	$0.358346\pi$
$740$	30.9282			1.13694
$741$		0			0
$742$	11.7321			0.430697
$743$	−34.4545	+	19.8923i	−1.26401	+	0.729778i	−0.973848	−	0.227199i	$-0.927043\pi$
$743$	−34.4545	+	19.8923i	−1.26401	+	0.729778i	−0.290164	+	0.956977i	$0.593710\pi$
$744$		0			0
$745$	−31.9808	+	55.3923i	−1.17168	+	2.02942i
$746$			22.2487i			0.814583i
$747$		0			0
$748$	−1.60770	−	0.928203i	−0.0587832	−	0.0339385i
$749$			15.4641i			0.565046i
$750$		0			0
$751$	−2.66025	−	4.60770i	−0.0970740	−	0.168137i	0.813398	−	0.581707i	$-0.197615\pi$
$751$	−2.66025	−	4.60770i	−0.0970740	−	0.168137i	−0.910472	+	0.413570i	$0.864282\pi$
$752$	−6.46410	+	3.73205i	−0.235722	+	0.136094i
$753$		0			0
$754$	−8.00000	−	27.7128i	−0.291343	−	1.00924i
$755$	41.5692			1.51286
$756$		0			0
$757$	3.92820	+	6.80385i	0.142773	+	0.247290i	0.928540	−	0.371233i	$-0.121065\pi$
$757$	3.92820	+	6.80385i	0.142773	+	0.247290i	−0.785767	+	0.618523i	$0.787731\pi$
$758$	15.1962	−	26.3205i	0.551949	−	0.956004i
$759$		0			0
$760$	1.60770	+	0.928203i	0.0583172	+	0.0336695i
$761$	−6.00000	−	3.46410i	−0.217500	−	0.125574i	0.387292	−	0.921957i	$-0.373410\pi$
$761$	−6.00000	−	3.46410i	−0.217500	−	0.125574i	−0.604792	+	0.796383i	$0.706744\pi$
$762$		0			0
$763$	6.00000	−	10.3923i	0.217215	−	0.376227i
$764$	−9.25833	−	16.0359i	−0.334955	−	0.580158i
$765$		0			0
$766$	−27.3205			−0.987130
$767$	9.73205	+	33.7128i	0.351404	+	1.21730i
$768$		0			0
$769$	23.0718	−	13.3205i	0.831990	−	0.480350i	−0.0225434	−	0.999746i	$-0.507176\pi$
$769$	23.0718	−	13.3205i	0.831990	−	0.480350i	0.854534	+	0.519396i	$0.173843\pi$
$770$	−6.92820	−	12.0000i	−0.249675	−	0.432450i
$771$		0			0
$772$		−	9.85641i		−	0.354740i
$773$	−0.803848	−	0.464102i	−0.0289124	−	0.0166926i	0.485474	−	0.874251i	$-0.338647\pi$
$773$	−0.803848	−	0.464102i	−0.0289124	−	0.0166926i	−0.514387	+	0.857558i	$0.671980\pi$
$774$		0			0
$775$		−	3.24871i		−	0.116697i
$776$	4.19615	−	7.26795i	0.150633	−	0.260904i
$777$		0			0
$778$	2.30385	−	1.33013i	0.0825969	−	0.0476874i
$779$	−3.71281			−0.133025
$780$		0			0
$781$	−47.7128			−1.70730
$782$	−0.911543	+	0.526279i	−0.0325967	+	0.0188197i
$783$		0			0
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	37.8564i		−	1.35115i
$786$		0			0
$787$	−10.7321	−	6.19615i	−0.382556	−	0.220869i	0.296374	−	0.955072i	$-0.404223\pi$
$787$	−10.7321	−	6.19615i	−0.382556	−	0.220869i	−0.678930	+	0.734203i	$0.737556\pi$
$788$		−	23.3923i		−	0.833316i
$789$		0			0
$790$	4.39230	+	7.60770i	0.156271	+	0.270670i
$791$	14.1962	−	8.19615i	0.504757	−	0.291422i
$792$		0			0
$793$	18.0000	−	5.19615i	0.639199	−	0.184521i
$794$	−11.7846			−0.418220
$795$		0			0
$796$	−1.06218	−	1.83975i	−0.0376479	−	0.0652081i
$797$	3.12436	−	5.41154i	0.110670	−	0.191687i	−0.805370	−	0.592772i	$-0.798034\pi$
$797$	3.12436	−	5.41154i	0.110670	−	0.191687i	0.916041	+	0.401085i	$0.131367\pi$
$798$		0			0
$799$	−3.00000	−	1.73205i	−0.106132	−	0.0612756i
$800$	6.06218	+	3.50000i	0.214330	+	0.123744i
$801$		0			0
$802$	2.19615	−	3.80385i	0.0775488	−	0.134319i
$803$	−5.85641	−	10.1436i	−0.206668	−	0.357960i
$804$		0			0
$805$	−7.85641			−0.276902
$806$	0.401924	−	1.62436i	0.0141572	−	0.0572155i
$807$		0			0
$808$		0			0
$809$	−19.8564	−	34.3923i	−0.698114	−	1.20917i	−0.969120	−	0.246591i	$-0.920689\pi$
$809$	−19.8564	−	34.3923i	−0.698114	−	1.20917i	0.271006	−	0.962578i	$-0.412644\pi$
$810$		0			0
$811$			29.8564i			1.04840i	0.851595	+	0.524200i	$0.175636\pi$
$811$			29.8564i			1.04840i	−0.851595	+	0.524200i	$0.824364\pi$
$812$	6.92820	+	4.00000i	0.243132	+	0.140372i
$813$		0			0
$814$			35.7128i			1.25173i
$815$	−32.3205	+	55.9808i	−1.13214	+	1.96092i
$816$		0			0
$817$	1.14359	−	0.660254i	0.0400093	−	0.0230994i
$818$	14.3923			0.503215
$819$		0			0
$820$	−24.0000			−0.838116
$821$	−14.9378	+	8.62436i	−0.521334	+	0.300992i	−0.737480	−	0.675369i	$-0.763984\pi$
$821$	−14.9378	+	8.62436i	−0.521334	+	0.300992i	0.216147	+	0.976361i	$0.430651\pi$
$822$		0			0
$823$	22.1962	−	38.4449i	0.773709	−	1.34010i	−0.161808	−	0.986822i	$-0.551732\pi$
$823$	22.1962	−	38.4449i	0.773709	−	1.34010i	0.935517	−	0.353281i	$-0.114934\pi$
$824$		−	6.66025i		−	0.232021i
$825$		0			0
$826$	−8.42820	−	4.86603i	−0.293255	−	0.169311i
$827$			15.6077i			0.542733i	0.962476	+	0.271366i	$0.0874755\pi$
$827$			15.6077i			0.542733i	−0.962476	+	0.271366i	$0.912525\pi$
$828$		0			0
$829$	24.3923	+	42.2487i	0.847180	+	1.46736i	0.883715	+	0.468026i	$0.155035\pi$
$829$	24.3923	+	42.2487i	0.847180	+	1.46736i	−0.0365349	+	0.999332i	$0.511632\pi$
$830$	5.19615	−	3.00000i	0.180361	−	0.104132i
$831$		0			0
$832$	2.59808	+	2.50000i	0.0900721	+	0.0866719i
$833$	0.464102			0.0160802
$834$		0			0
$835$	−34.6410	−	60.0000i	−1.19880	−	2.07639i
$836$	−1.07180	+	1.85641i	−0.0370689	+	0.0642052i
$837$		0			0
$838$	−4.33013	−	2.50000i	−0.149582	−	0.0863611i
$839$	−19.3923	−	11.1962i	−0.669497	−	0.386534i	0.126389	−	0.991981i	$-0.459661\pi$
$839$	−19.3923	−	11.1962i	−0.669497	−	0.386534i	−0.795886	+	0.605447i	$0.792995\pi$
$840$		0			0
$841$	−17.5000	+	30.3109i	−0.603448	+	1.04520i
$842$	−11.1962	−	19.3923i	−0.385845	−	0.668303i
$843$		0			0
$844$	22.9282			0.789221
$845$	45.0000	−	1.73205i	1.54805	−	0.0595844i
$846$		0			0
$847$	4.33013	−	2.50000i	0.148785	−	0.0859010i
$848$	−5.86603	−	10.1603i	−0.201440	−	0.348905i
$849$		0			0
$850$			3.24871i			0.111430i
$851$	17.5359	+	10.1244i	0.601123	+	0.347058i
$852$		0			0
$853$			21.6410i			0.740974i	0.928838	+	0.370487i	$0.120809\pi$
$853$			21.6410i			0.740974i	−0.928838	+	0.370487i	$0.879191\pi$
$854$	−2.59808	+	4.50000i	−0.0889043	+	0.153987i
$855$		0			0
$856$	13.3923	−	7.73205i	0.457740	−	0.264276i
$857$	21.7128			0.741696			0.370848	−	0.928694i	$-0.379067\pi$
$857$	21.7128			0.741696			0.370848	+	0.928694i	$0.379067\pi$
$858$		0			0
$859$	11.8564			0.404535			0.202268	−	0.979330i	$-0.435169\pi$
$859$	11.8564			0.404535			0.202268	+	0.979330i	$0.435169\pi$
$860$	7.39230	−	4.26795i	0.252076	−	0.145536i
$861$		0			0
$862$	−11.4282	+	19.7942i	−0.389246	+	0.674194i
$863$		−	29.0718i		−	0.989615i	−0.869002	−	0.494808i	$-0.835238\pi$
$863$		−	29.0718i		−	0.989615i	0.869002	−	0.494808i	$-0.164762\pi$
$864$		0			0
$865$	44.7846	+	25.8564i	1.52272	+	0.879144i
$866$			17.8564i			0.606785i
$867$		0			0
$868$	0.232051	+	0.401924i	0.00787632	+	0.0136422i
$869$	−8.78461	+	5.07180i	−0.297997	+	0.172049i
$870$		0			0
$871$	−11.1865	−	2.76795i	−0.379041	−	0.0937884i
$872$	−12.0000			−0.406371
$873$		0			0
$874$	0.607695	+	1.05256i	0.0205556	+	0.0356033i
$875$	−3.46410	+	6.00000i	−0.117108	+	0.202837i
$876$		0			0
$877$	25.7321	+	14.8564i	0.868910	+	0.501665i	0.866986	−	0.498333i	$-0.166054\pi$
$877$	25.7321	+	14.8564i	0.868910	+	0.501665i	0.00192388	+	0.999998i	$0.499388\pi$
$878$	−29.7846	−	17.1962i	−1.00518	−	0.580342i
$879$		0			0
$880$	−6.92820	+	12.0000i	−0.233550	+	0.404520i
$881$	29.0167	+	50.2583i	0.977596	+	1.69325i	0.671087	+	0.741378i	$0.265828\pi$
$881$	29.0167	+	50.2583i	0.977596	+	1.69325i	0.306509	+	0.951868i	$0.400839\pi$
$882$		0			0
$883$	−34.3205			−1.15498			−0.577489	−	0.816399i	$-0.695967\pi$
$883$	−34.3205			−1.15498			−0.577489	+	0.816399i	$0.695967\pi$
$884$	−0.401924	+	1.62436i	−0.0135182	+	0.0546330i
$885$		0			0
$886$	1.39230	−	0.803848i	0.0467754	−	0.0270058i
$887$	−7.92820	−	13.7321i	−0.266203	−	0.461077i	0.701675	−	0.712497i	$-0.252436\pi$
$887$	−7.92820	−	13.7321i	−0.266203	−	0.461077i	−0.967878	+	0.251420i	$0.919102\pi$
$888$		0			0
$889$			18.9282i			0.634832i
$890$	24.8038	+	14.3205i	0.831427	+	0.480025i
$891$		0			0
$892$		−	14.4641i		−	0.484294i
$893$	−2.00000	+	3.46410i	−0.0669274	+	0.115922i
$894$		0			0
$895$	9.21539	−	5.32051i	0.308037	−	0.177845i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	18.0000			0.600668
$899$	−3.21539	+	1.85641i	−0.107239	+	0.0619146i
$900$		0			0
$901$	2.72243	−	4.71539i	0.0906974	−	0.157092i
$902$		−	27.7128i		−	0.922736i
$903$		0			0
$904$	−14.1962	−	8.19615i	−0.472157	−	0.272600i
$905$		−	58.1436i		−	1.93276i
$906$		0			0
$907$	−5.76795	−	9.99038i	−0.191522	−	0.331725i	0.754233	−	0.656607i	$-0.228009\pi$
$907$	−5.76795	−	9.99038i	−0.191522	−	0.331725i	−0.945755	+	0.324882i	$0.894676\pi$
$908$	18.4641	−	10.6603i	0.612753	−	0.353773i
$909$		0			0
$910$	−8.66025	+	9.00000i	−0.287085	+	0.298347i
$911$	35.1769			1.16546			0.582732	−	0.812665i	$-0.301984\pi$
$911$	35.1769			1.16546			0.582732	+	0.812665i	$0.301984\pi$
$912$		0			0
$913$	3.46410	+	6.00000i	0.114645	+	0.198571i
$914$	4.59808	−	7.96410i	0.152091	−	0.263429i
$915$		0			0
$916$	−5.25833	−	3.03590i	−0.173740	−	0.100309i
$917$	−16.4545	−	9.50000i	−0.543375	−	0.313718i
$918$		0			0
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	−0.567939	−	0.823071i	$-0.692259\pi$
$919$	13.0000	−	22.5167i	0.428830	−	0.742756i	0.996770	+	0.0803145i	$0.0255924\pi$
$920$	3.92820	+	6.80385i	0.129509	+	0.224316i
$921$		0			0
$922$	−18.9282			−0.623367
$923$	11.9282	+	41.3205i	0.392622	+	1.36008i
$924$		0			0
$925$	54.1244	−	31.2487i	1.77960	−	1.02745i
$926$	20.1244	+	34.8564i	0.661327	+	1.14545i
$927$		0			0
$928$		−	8.00000i		−	0.262613i
$929$	26.0885	+	15.0622i	0.855935	+	0.494174i	0.862649	−	0.505803i	$-0.168804\pi$
$929$	26.0885	+	15.0622i	0.855935	+	0.494174i	−0.00671424	+	0.999977i	$0.502137\pi$
$930$		0			0
$931$		−	0.535898i		−	0.0175634i
$932$	3.26795	−	5.66025i	0.107045	−	0.185408i
$933$		0			0
$934$	25.6699	−	14.8205i	0.839944	−	0.484942i
$935$	−6.43078			−0.210309
$936$		0			0
$937$	−31.0718			−1.01507			−0.507536	−	0.861631i	$-0.669443\pi$
$937$	−31.0718			−1.01507			−0.507536	+	0.861631i	$0.669443\pi$
$938$	2.76795	−	1.59808i	0.0903767	−	0.0521790i
$939$		0			0
$940$	−12.9282	+	22.3923i	−0.421671	+	0.730356i
$941$			40.3923i			1.31675i	0.752689	+	0.658376i	$0.228756\pi$
$941$			40.3923i			1.31675i	−0.752689	+	0.658376i	$0.771244\pi$
$942$		0			0
$943$	−13.6077	−	7.85641i	−0.443128	−	0.255840i
$944$			9.73205i			0.316751i
$945$		0			0
$946$	4.92820	+	8.53590i	0.160230	+	0.277526i
$947$	−15.8038	+	9.12436i	−0.513556	+	0.296502i	−0.734294	−	0.678831i	$-0.762487\pi$
$947$	−15.8038	+	9.12436i	−0.513556	+	0.296502i	0.220738	+	0.975333i	$0.429153\pi$
$948$		0			0
$949$	−7.32051	+	7.60770i	−0.237634	+	0.246956i
$950$	3.75129			0.121708
$951$		0			0
$952$	−0.232051	−	0.401924i	−0.00752081	−	0.0130264i
$953$	−15.0000	+	25.9808i	−0.485898	+	0.841599i	−0.999869	−	0.0162081i	$-0.994841\pi$
$953$	−15.0000	+	25.9808i	−0.485898	+	0.841599i	0.513971	+	0.857808i	$0.328174\pi$
$954$		0			0
$955$	−55.5500	−	32.0718i	−1.79756	−	1.03782i
$956$	12.8660	+	7.42820i	0.416117	+	0.240245i
$957$		0			0
$958$	8.19615	−	14.1962i	0.264806	−	0.458657i
$959$	6.92820	+	12.0000i	0.223723	+	0.387500i
$960$		0			0
$961$	30.7846			0.993052
$962$	30.9282	−	8.92820i	0.997165	−	0.287857i
$963$		0			0
$964$	10.2679	−	5.92820i	0.330708	−	0.190935i
$965$	−17.0718	−	29.5692i	−0.549561	−	0.951867i
$966$		0			0
$967$			23.4641i			0.754555i	0.926100	+	0.377277i	$0.123140\pi$
$967$			23.4641i			0.754555i	−0.926100	+	0.377277i	$0.876860\pi$
$968$	−4.33013	−	2.50000i	−0.139176	−	0.0803530i
$969$		0			0
$970$		−	29.0718i		−	0.933439i
$971$	5.03590	−	8.72243i	0.161610	−	0.279916i	−0.773836	−	0.633385i	$-0.781665\pi$
$971$	5.03590	−	8.72243i	0.161610	−	0.279916i	0.935446	+	0.353469i	$0.114998\pi$
$972$		0			0
$973$	9.46410	−	5.46410i	0.303405	−	0.175171i
$974$	20.3923			0.653412
$975$		0			0
$976$	5.19615			0.166325
$977$	1.60770	−	0.928203i	0.0514347	−	0.0296959i	−0.474062	−	0.880491i	$-0.657213\pi$
$977$	1.60770	−	0.928203i	0.0514347	−	0.0296959i	0.525497	+	0.850796i	$0.323879\pi$
$978$		0			0
$979$	−16.5359	+	28.6410i	−0.528490	+	0.915371i
$980$		−	3.46410i		−	0.110657i
$981$		0			0
$982$	−15.4641	−	8.92820i	−0.493479	−	0.284910i
$983$			32.9282i			1.05025i	0.851026	+	0.525123i	$0.175981\pi$
$983$			32.9282i			1.05025i	−0.851026	+	0.525123i	$0.824019\pi$
$984$		0			0
$985$	−40.5167	−	70.1769i	−1.29097	−	2.23602i
$986$	3.21539	−	1.85641i	0.102399	−	0.0591200i
$987$		0			0
$988$	1.87564	+	0.464102i	0.0596722	+	0.0147650i
$989$	5.58846			0.177703
$990$		0			0
$991$	−13.9282	−	24.1244i	−0.442444	−	0.766335i	0.555426	−	0.831566i	$-0.312555\pi$
$991$	−13.9282	−	24.1244i	−0.442444	−	0.766335i	−0.997870	+	0.0652304i	$0.979222\pi$
$992$	0.232051	−	0.401924i	0.00736762	−	0.0127611i
$993$		0			0
$994$	−10.3301	−	5.96410i	−0.327652	−	0.189170i
$995$	−6.37307	−	3.67949i	−0.202040	−	0.116648i
$996$		0			0
$997$	8.99038	−	15.5718i	0.284728	−	0.493164i	−0.687815	−	0.725886i	$-0.741430\pi$
$997$	8.99038	−	15.5718i	0.284728	−	0.493164i	0.972543	+	0.232722i	$0.0747633\pi$
$998$	−1.86603	−	3.23205i	−0.0590680	−	0.102309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.e.127.2		4
3.2	odd	2		546.2.s.c.127.1	yes	4
13.4	even	6	inner	1638.2.bj.e.1135.2		4
39.2	even	12		7098.2.a.bn.1.2		2
39.11	even	12		7098.2.a.bz.1.1		2
39.17	odd	6		546.2.s.c.43.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.c.43.1	✓	4	39.17	odd	6
546.2.s.c.127.1	yes	4	3.2	odd	2
1638.2.bj.e.127.2		4	1.1	even	1	trivial
1638.2.bj.e.1135.2		4	13.4	even	6	inner
7098.2.a.bn.1.2		2	39.2	even	12
7098.2.a.bz.1.1		2	39.11	even	12

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:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-1.73205 - 3.00000i) q^{10} +(3.46410 - 2.00000i) q^{11} +(-2.59808 - 2.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.232051 - 0.401924i) q^{17} +(-0.464102 - 0.267949i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(2.00000 - 3.46410i) q^{22} +(-1.13397 - 1.96410i) q^{23} -7.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} +(0.866025 - 0.500000i) q^{28} +(4.00000 + 6.92820i) q^{29} +0.464102i q^{31} +(-0.866025 - 0.500000i) q^{32} -0.464102i q^{34} +(1.73205 - 3.00000i) q^{35} +(-7.73205 + 4.46410i) q^{37} -0.535898 q^{38} -3.46410 q^{40} +(6.00000 - 3.46410i) q^{41} +(-1.23205 + 2.13397i) q^{43} -4.00000i q^{44} +(-1.96410 - 1.13397i) q^{46} -7.46410i q^{47} +(0.500000 + 0.866025i) q^{49} +(-6.06218 + 3.50000i) q^{50} +(-3.46410 + 1.00000i) q^{52} +11.7321 q^{53} +(-6.92820 - 12.0000i) q^{55} +(0.500000 - 0.866025i) q^{56} +(6.92820 + 4.00000i) q^{58} +(-8.42820 - 4.86603i) q^{59} +(-2.59808 + 4.50000i) q^{61} +(0.232051 + 0.401924i) q^{62} -1.00000 q^{64} +(-8.66025 + 9.00000i) q^{65} +(2.76795 - 1.59808i) q^{67} +(-0.232051 - 0.401924i) q^{68} -3.46410i q^{70} +(-10.3301 - 5.96410i) q^{71} -2.92820i q^{73} +(-4.46410 + 7.73205i) q^{74} +(-0.464102 + 0.267949i) q^{76} +4.00000 q^{77} -2.53590 q^{79} +(-3.00000 + 1.73205i) q^{80} +(3.46410 - 6.00000i) q^{82} +1.73205i q^{83} +(-1.39230 - 0.803848i) q^{85} +2.46410i q^{86} +(-2.00000 - 3.46410i) q^{88} +(-7.16025 + 4.13397i) q^{89} +(-1.00000 - 3.46410i) q^{91} -2.26795 q^{92} +(-3.73205 - 6.46410i) q^{94} +(-0.928203 + 1.60770i) q^{95} +(7.26795 + 4.19615i) q^{97} +(0.866025 + 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 4 * q + 2 * q^4	\( 4 q + 2 q^{4} + 4 q^{14} - 2 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} + 8 q^{22} - 8 q^{23} - 28 q^{25} - 14 q^{26} + 16 q^{29} - 24 q^{37} - 16 q^{38} + 24 q^{41} + 2 q^{43} + 6 q^{46} + 2 q^{49} + 40 q^{53} + 2 q^{56} - 6 q^{59} - 6 q^{62} - 4 q^{64} + 18 q^{67} + 6 q^{68} - 24 q^{71} - 4 q^{74} + 12 q^{76} + 16 q^{77} - 24 q^{79} - 12 q^{80} + 36 q^{85} - 8 q^{88} + 6 q^{89} - 4 q^{91} - 16 q^{92} - 8 q^{94} + 24 q^{95} + 36 q^{97}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^14 - 2 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 + 8 * q^22 - 8 * q^23 - 28 * q^25 - 14 * q^26 + 16 * q^29 - 24 * q^37 - 16 * q^38 + 24 * q^41 + 2 * q^43 + 6 * q^46 + 2 * q^49 + 40 * q^53 + 2 * q^56 - 6 * q^59 - 6 * q^62 - 4 * q^64 + 18 * q^67 + 6 * q^68 - 24 * q^71 - 4 * q^74 + 12 * q^76 + 16 * q^77 - 24 * q^79 - 12 * q^80 + 36 * q^85 - 8 * q^88 + 6 * q^89 - 4 * q^91 - 16 * q^92 - 8 * q^94 + 24 * q^95 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more