LMFDB - Embedded newform 1638.2.bj.e.127.1

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			127.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1638.127
Dual form			1638.2.bj.e.1135.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(1.73205 + 3.00000i) q^{10} +(-3.46410 + 2.00000i) q^{11} +(2.59808 + 2.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.23205 + 5.59808i) q^{17} +(6.46410 + 3.73205i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(2.00000 - 3.46410i) q^{22} +(-2.86603 - 4.96410i) q^{23} -7.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(4.00000 + 6.92820i) q^{29} +6.46410i q^{31} +(0.866025 + 0.500000i) q^{32} -6.46410i q^{34} +(-1.73205 + 3.00000i) q^{35} +(-4.26795 + 2.46410i) q^{37} -7.46410 q^{38} +3.46410 q^{40} +(6.00000 - 3.46410i) q^{41} +(2.23205 - 3.86603i) q^{43} +4.00000i q^{44} +(4.96410 + 2.86603i) q^{46} +0.535898i q^{47} +(0.500000 + 0.866025i) q^{49} +(6.06218 - 3.50000i) q^{50} +(3.46410 - 1.00000i) q^{52} +8.26795 q^{53} +(6.92820 + 12.0000i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-6.92820 - 4.00000i) q^{58} +(5.42820 + 3.13397i) q^{59} +(2.59808 - 4.50000i) q^{61} +(-3.23205 - 5.59808i) q^{62} -1.00000 q^{64} +(8.66025 - 9.00000i) q^{65} +(6.23205 - 3.59808i) q^{67} +(3.23205 + 5.59808i) q^{68} -3.46410i q^{70} +(-1.66987 - 0.964102i) q^{71} -10.9282i q^{73} +(2.46410 - 4.26795i) q^{74} +(6.46410 - 3.73205i) q^{76} +4.00000 q^{77} -9.46410 q^{79} +(-3.00000 + 1.73205i) q^{80} +(-3.46410 + 6.00000i) q^{82} +1.73205i q^{83} +(19.3923 + 11.1962i) q^{85} +4.46410i q^{86} +(-2.00000 - 3.46410i) q^{88} +(10.1603 - 5.86603i) q^{89} +(-1.00000 - 3.46410i) q^{91} -5.73205 q^{92} +(-0.267949 - 0.464102i) q^{94} +(12.9282 - 22.3923i) q^{95} +(10.7321 + 6.19615i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.921095	−	0.389338i	$-0.872704\pi$
$11$	−3.46410	+	2.00000i	−1.04447	+	0.603023i	−0.123371	+	0.992361i	$0.539370\pi$
$12$		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
$17$	−3.23205	+	5.59808i	−0.783887	+	1.35773i	0.145774	+	0.989318i	$0.453433\pi$
$17$	−3.23205	+	5.59808i	−0.783887	+	1.35773i	−0.929661	+	0.368415i	$0.879901\pi$
$18$		0			0
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.999813	−	0.0193444i	$-0.00615788\pi$
$19$	6.46410	+	3.73205i	1.48297	+	0.856191i	0.483154	+	0.875536i	$0.339491\pi$
$20$	−3.00000	−	1.73205i	−0.670820	−	0.387298i
$21$		0			0
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	−2.86603	−	4.96410i	−0.597608	−	1.03509i	−0.993173	−	0.116649i	$-0.962785\pi$
$23$	−2.86603	−	4.96410i	−0.597608	−	1.03509i	0.395566	−	0.918438i	$-0.370549\pi$
$24$		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
$31$			6.46410i			1.16099i	0.814265	+	0.580493i	$0.197140\pi$
$31$			6.46410i			1.16099i	−0.814265	+	0.580493i	$0.802860\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$		−	6.46410i		−	1.10858i
$35$	−1.73205	+	3.00000i	−0.292770	+	0.507093i
$36$		0			0
$37$	−4.26795	+	2.46410i	−0.701647	+	0.405096i	−0.807960	−	0.589237i	$-0.799429\pi$
$37$	−4.26795	+	2.46410i	−0.701647	+	0.405096i	0.106314	+	0.994333i	$0.466095\pi$
$38$	−7.46410			−1.21084
$39$		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
$43$	2.23205	−	3.86603i	0.340385	−	0.589563i	−0.644120	−	0.764925i	$-0.722776\pi$
$43$	2.23205	−	3.86603i	0.340385	−	0.589563i	0.984504	+	0.175361i	$0.0561094\pi$
$44$			4.00000i			0.603023i
$45$		0			0
$46$	4.96410	+	2.86603i	0.731917	+	0.422572i
$47$			0.535898i			0.0781688i	0.999236	+	0.0390844i	$0.0124441\pi$
$47$			0.535898i			0.0781688i	−0.999236	+	0.0390844i	$0.987556\pi$
$48$		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
$53$	8.26795			1.13569			0.567845	−	0.823135i	$-0.307777\pi$
$53$	8.26795			1.13569			0.567845	+	0.823135i	$0.307777\pi$
$54$		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
$59$	5.42820	+	3.13397i	0.706692	+	0.408009i	0.809835	−	0.586658i	$-0.199557\pi$
$59$	5.42820	+	3.13397i	0.706692	+	0.408009i	−0.103143	+	0.994667i	$0.532890\pi$
$60$		0			0
$61$	2.59808	−	4.50000i	0.332650	−	0.576166i	−0.650381	−	0.759608i	$-0.725391\pi$
$61$	2.59808	−	4.50000i	0.332650	−	0.576166i	0.983030	+	0.183442i	$0.0587240\pi$
$62$	−3.23205	−	5.59808i	−0.410471	−	0.710956i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	8.66025	−	9.00000i	1.07417	−	1.11631i
$66$		0			0
$67$	6.23205	−	3.59808i	0.761366	−	0.439575i	−0.0684199	−	0.997657i	$-0.521796\pi$
$67$	6.23205	−	3.59808i	0.761366	−	0.439575i	0.829786	+	0.558082i	$0.188462\pi$
$68$	3.23205	+	5.59808i	0.391944	+	0.678866i
$69$		0			0
$70$		−	3.46410i		−	0.414039i
$71$	−1.66987	−	0.964102i	−0.198177	−	0.114418i	0.397628	−	0.917547i	$-0.369834\pi$
$71$	−1.66987	−	0.964102i	−0.198177	−	0.114418i	−0.595805	+	0.803129i	$0.703167\pi$
$72$		0			0
$73$		−	10.9282i		−	1.27905i	−0.768771	−	0.639525i	$-0.779131\pi$
$73$		−	10.9282i		−	1.27905i	0.768771	−	0.639525i	$-0.220869\pi$
$74$	2.46410	−	4.26795i	0.286446	−	0.496139i
$75$		0			0
$76$	6.46410	−	3.73205i	0.741483	−	0.428096i
$77$	4.00000			0.455842
$78$		0			0
$79$	−9.46410			−1.06479			−0.532397	−	0.846495i	$-0.678709\pi$
$79$	−9.46410			−1.06479			−0.532397	+	0.846495i	$0.678709\pi$
$80$	−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
$85$	19.3923	+	11.1962i	2.10339	+	1.21439i
$86$			4.46410i			0.481376i
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	10.1603	−	5.86603i	1.07698	−	0.621797i	0.146903	−	0.989151i	$-0.453069\pi$
$89$	10.1603	−	5.86603i	1.07698	−	0.621797i	0.930081	+	0.367353i	$0.119736\pi$
$90$		0			0
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	−5.73205			−0.597608
$93$		0			0
$94$	−0.267949	−	0.464102i	−0.0276368	−	0.0478684i
$95$	12.9282	−	22.3923i	1.32641	−	2.29740i
$96$		0			0
$97$	10.7321	+	6.19615i	1.08967	+	0.629124i	0.933490	−	0.358604i	$-0.116747\pi$
$97$	10.7321	+	6.19615i	1.08967	+	0.629124i	0.156185	+	0.987728i	$0.450080\pi$
$98$	−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
$103$	−10.6603			−1.05039			−0.525193	−	0.850983i	$-0.676007\pi$
$103$	−10.6603			−1.05039			−0.525193	+	0.850983i	$0.676007\pi$
$104$	−2.50000	+	2.59808i	−0.245145	+	0.254762i
$105$		0			0
$106$	−7.16025	+	4.13397i	−0.695465	+	0.401527i
$107$	4.26795	+	7.39230i	0.412598	+	0.714641i	0.995173	−	0.0981360i	$-0.0312880\pi$
$107$	4.26795	+	7.39230i	0.412598	+	0.714641i	−0.582575	+	0.812777i	$0.697955\pi$
$108$		0			0
$109$			12.0000i			1.14939i	0.818367	+	0.574696i	$0.194880\pi$
$109$			12.0000i			1.14939i	−0.818367	+	0.574696i	$0.805120\pi$
$110$	−12.0000	−	6.92820i	−1.14416	−	0.660578i
$111$		0			0
$112$			1.00000i			0.0944911i
$113$	−2.19615	+	3.80385i	−0.206597	+	0.357836i	−0.950640	−	0.310295i	$-0.899572\pi$
$113$	−2.19615	+	3.80385i	−0.206597	+	0.357836i	0.744044	+	0.668131i	$0.232905\pi$
$114$		0			0
$115$	−17.1962	+	9.92820i	−1.60355	+	0.925810i
$116$	8.00000			0.742781
$117$		0			0
$118$	−6.26795			−0.577011
$119$	5.59808	−	3.23205i	0.513175	−	0.296282i
$120$		0			0
$121$	2.50000	−	4.33013i	0.227273	−	0.393648i
$122$			5.19615i			0.470438i
$123$		0			0
$124$	5.59808	+	3.23205i	0.502722	+	0.290247i
$125$			6.92820i			0.619677i
$126$		0			0
$127$	2.53590	+	4.39230i	0.225025	+	0.389754i	0.956327	−	0.292300i	$-0.0944204\pi$
$127$	2.53590	+	4.39230i	0.225025	+	0.389754i	−0.731302	+	0.682054i	$0.761087\pi$
$128$	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
$133$	−3.73205	−	6.46410i	−0.323610	−	0.560509i
$134$	−3.59808	+	6.23205i	−0.310826	+	0.538367i
$135$		0			0
$136$	−5.59808	−	3.23205i	−0.480031	−	0.277146i
$137$	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
$139$	−1.46410	+	2.53590i	−0.124183	+	0.215092i	−0.921413	−	0.388584i	$-0.872964\pi$
$139$	−1.46410	+	2.53590i	−0.124183	+	0.215092i	0.797230	+	0.603676i	$0.206298\pi$
$140$	1.73205	+	3.00000i	0.146385	+	0.253546i
$141$		0			0
$142$	1.92820			0.161811
$143$	−14.0000	−	3.46410i	−1.17074	−	0.289683i
$144$		0			0
$145$	24.0000	−	13.8564i	1.99309	−	1.15071i
$146$	5.46410	+	9.46410i	0.452212	+	0.783255i
$147$		0			0
$148$			4.92820i			0.405096i
$149$	9.99038	+	5.76795i	0.818444	+	0.472529i	0.849880	−	0.526977i	$-0.176675\pi$
$149$	9.99038	+	5.76795i	0.818444	+	0.472529i	−0.0314357	+	0.999506i	$0.510008\pi$
$150$		0			0
$151$		−	12.0000i		−	0.976546i	−0.872691	−	0.488273i	$-0.837627\pi$
$151$		−	12.0000i		−	0.976546i	0.872691	−	0.488273i	$-0.162373\pi$
$152$	−3.73205	+	6.46410i	−0.302709	+	0.524308i
$153$		0			0
$154$	−3.46410	+	2.00000i	−0.279145	+	0.161165i
$155$	22.3923			1.79859
$156$		0			0
$157$	−2.92820			−0.233696			−0.116848	−	0.993150i	$-0.537279\pi$
$157$	−2.92820			−0.233696			−0.116848	+	0.993150i	$0.537279\pi$
$158$	8.19615	−	4.73205i	0.652051	−	0.376462i
$159$		0			0
$160$	1.73205	−	3.00000i	0.136931	−	0.237171i
$161$			5.73205i			0.451749i
$162$		0			0
$163$	1.16025	+	0.669873i	0.0908781	+	0.0524685i	0.544750	−	0.838598i	$-0.316624\pi$
$163$	1.16025	+	0.669873i	0.0908781	+	0.0524685i	−0.453872	+	0.891067i	$0.649958\pi$
$164$		−	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	−0.986851	−	0.161630i	$-0.948325\pi$
$167$	−17.3205	+	10.0000i	−1.34030	+	0.773823i	−0.353450	+	0.935454i	$0.614991\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	−22.3923			−1.71741
$171$		0			0
$172$	−2.23205	−	3.86603i	−0.170192	−	0.294782i
$173$	−0.535898	+	0.928203i	−0.0407436	+	0.0705700i	−0.885678	−	0.464300i	$-0.846306\pi$
$173$	−0.535898	+	0.928203i	−0.0407436	+	0.0705700i	0.844934	+	0.534870i	$0.179639\pi$
$174$		0			0
$175$	6.06218	+	3.50000i	0.458258	+	0.264575i
$176$	3.46410	+	2.00000i	0.261116	+	0.150756i
$177$		0			0
$178$	−5.86603	+	10.1603i	−0.439677	+	0.761543i
$179$	8.46410	+	14.6603i	0.632637	+	1.09576i	0.987011	+	0.160655i	$0.0513607\pi$
$179$	8.46410	+	14.6603i	0.632637	+	1.09576i	−0.354374	+	0.935104i	$0.615306\pi$
$180$		0			0
$181$	−24.7846			−1.84223			−0.921113	−	0.389296i	$-0.872718\pi$
$181$	−24.7846			−1.84223			−0.921113	+	0.389296i	$0.872718\pi$
$182$	2.59808	+	2.50000i	0.192582	+	0.185312i
$183$		0			0
$184$	4.96410	−	2.86603i	0.365958	−	0.211286i
$185$	8.53590	+	14.7846i	0.627572	+	1.08699i
$186$		0			0
$187$		−	25.8564i		−	1.89081i
$188$	0.464102	+	0.267949i	0.0338481	+	0.0195422i
$189$		0			0
$190$			25.8564i			1.87582i
$191$	−13.2583	+	22.9641i	−0.959339	+	1.66162i	−0.235229	+	0.971940i	$0.575584\pi$
$191$	−13.2583	+	22.9641i	−0.959339	+	1.66162i	−0.724110	+	0.689684i	$0.757749\pi$
$192$		0			0
$193$	15.4641	−	8.92820i	1.11313	−	0.642666i	0.173492	−	0.984835i	$-0.444495\pi$
$193$	15.4641	−	8.92820i	1.11313	−	0.642666i	0.939638	+	0.342169i	$0.111162\pi$
$194$	−12.3923			−0.889716
$195$		0			0
$196$	1.00000			0.0714286
$197$	−2.25833	+	1.30385i	−0.160899	+	0.0928953i	−0.578288	−	0.815833i	$-0.696279\pi$
$197$	−2.25833	+	1.30385i	−0.160899	+	0.0928953i	0.417388	+	0.908728i	$0.362946\pi$
$198$		0			0
$199$	−11.0622	+	19.1603i	−0.784177	+	1.35823i	0.145312	+	0.989386i	$0.453581\pi$
$199$	−11.0622	+	19.1603i	−0.784177	+	1.35823i	−0.929489	+	0.368849i	$0.879752\pi$
$200$		−	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
$206$	9.23205	−	5.33013i	0.643227	−	0.371368i
$207$		0			0
$208$	0.866025	−	3.50000i	0.0600481	−	0.242681i
$209$	−29.8564			−2.06521
$210$		0			0
$211$	4.53590	+	7.85641i	0.312264	+	0.540857i	0.978852	−	0.204569i	$-0.0655793\pi$
$211$	4.53590	+	7.85641i	0.312264	+	0.540857i	−0.666588	+	0.745426i	$0.732246\pi$
$212$	4.13397	−	7.16025i	0.283923	−	0.491768i
$213$		0			0
$214$	−7.39230	−	4.26795i	−0.505328	−	0.291751i
$215$	−13.3923	−	7.73205i	−0.913348	−	0.527321i
$216$		0			0
$217$	3.23205	−	5.59808i	0.219406	−	0.380022i
$218$	−6.00000	−	10.3923i	−0.406371	−	0.703856i
$219$		0			0
$220$	13.8564			0.934199
$221$	−22.3923	+	6.46410i	−1.50627	+	0.434823i
$222$		0			0
$223$	−6.52628	+	3.76795i	−0.437032	+	0.252321i	−0.702338	−	0.711844i	$-0.747860\pi$
$223$	−6.52628	+	3.76795i	−0.437032	+	0.252321i	0.265306	+	0.964164i	$0.414527\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$		0			0
$226$		−	4.39230i		−	0.292172i
$227$	11.5359	+	6.66025i	0.765664	+	0.442057i	0.831326	−	0.555785i	$-0.187582\pi$
$227$	11.5359	+	6.66025i	0.765664	+	0.442057i	−0.0656613	+	0.997842i	$0.520916\pi$
$228$		0			0
$229$			19.9282i			1.31689i	0.752628	+	0.658446i	$0.228786\pi$
$229$			19.9282i			1.31689i	−0.752628	+	0.658446i	$0.771214\pi$
$230$	9.92820	−	17.1962i	0.654646	−	1.13388i
$231$		0			0
$232$	−6.92820	+	4.00000i	−0.454859	+	0.262613i
$233$	13.4641			0.882063			0.441031	−	0.897492i	$-0.354613\pi$
$233$	13.4641			0.882063			0.441031	+	0.897492i	$0.354613\pi$
$234$		0			0
$235$	1.85641			0.121099
$236$	5.42820	−	3.13397i	0.353346	−	0.204004i
$237$		0			0
$238$	−3.23205	+	5.59808i	−0.209503	+	0.362869i
$239$			12.8564i			0.831612i	0.909453	+	0.415806i	$0.136500\pi$
$239$			12.8564i			0.831612i	−0.909453	+	0.415806i	$0.863500\pi$
$240$		0			0
$241$	13.7321	+	7.92820i	0.884559	+	0.510700i	0.872159	−	0.489223i	$-0.162719\pi$
$241$	13.7321	+	7.92820i	0.884559	+	0.510700i	0.0124002	+	0.999923i	$0.496053\pi$
$242$			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
$247$	7.46410	+	25.8564i	0.474929	+	1.64520i
$248$	−6.46410			−0.410471
$249$		0			0
$250$	−3.46410	−	6.00000i	−0.219089	−	0.379473i
$251$	5.03590	−	8.72243i	0.317863	−	0.550555i	−0.662179	−	0.749346i	$-0.730368\pi$
$251$	5.03590	−	8.72243i	0.317863	−	0.550555i	0.980042	+	0.198791i	$0.0637014\pi$
$252$		0			0
$253$	19.8564	+	11.4641i	1.24836	+	0.720742i
$254$	−4.39230	−	2.53590i	−0.275598	−	0.159116i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.232051	−	0.401924i	−0.0144749	−	0.0250713i	0.858697	−	0.512483i	$-0.171274\pi$
$257$	−0.232051	−	0.401924i	−0.0144749	−	0.0250713i	−0.873172	+	0.487412i	$0.837941\pi$
$258$		0			0
$259$	4.92820			0.306224
$260$	−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	$-0.987350\pi$
$263$	−8.66025	−	15.0000i	−0.534014	−	0.924940i	0.465196	−	0.885208i	$-0.345984\pi$
$264$		0			0
$265$		−	28.6410i		−	1.75940i
$266$	6.46410	+	3.73205i	0.396339	+	0.228827i
$267$		0			0
$268$		−	7.19615i		−	0.439575i
$269$	11.1962	−	19.3923i	0.682641	−	1.18237i	−0.291530	−	0.956562i	$-0.594164\pi$
$269$	11.1962	−	19.3923i	0.682641	−	1.18237i	0.974172	−	0.225808i	$-0.0725022\pi$
$270$		0			0
$271$	10.7942	−	6.23205i	0.655703	−	0.378570i	−0.134935	−	0.990854i	$-0.543083\pi$
$271$	10.7942	−	6.23205i	0.655703	−	0.378570i	0.790638	+	0.612284i	$0.209749\pi$
$272$	6.46410			0.391944
$273$		0			0
$274$	−13.8564			−0.837096
$275$	24.2487	−	14.0000i	1.46225	−	0.844232i
$276$		0			0
$277$	3.66025	−	6.33975i	0.219923	−	0.380918i	−0.734861	−	0.678218i	$-0.762753\pi$
$277$	3.66025	−	6.33975i	0.219923	−	0.380918i	0.954784	+	0.297299i	$0.0960859\pi$
$278$		−	2.92820i		−	0.175622i
$279$		0			0
$280$	−3.00000	−	1.73205i	−0.179284	−	0.103510i
$281$			2.39230i			0.142713i	0.997451	+	0.0713565i	$0.0227328\pi$
$281$			2.39230i			0.142713i	−0.997451	+	0.0713565i	$0.977267\pi$
$282$		0			0
$283$	−5.73205	−	9.92820i	−0.340735	−	0.590170i	0.643834	−	0.765165i	$-0.277343\pi$
$283$	−5.73205	−	9.92820i	−0.340735	−	0.590170i	−0.984569	+	0.174994i	$0.944009\pi$
$284$	−1.66987	+	0.964102i	−0.0990887	+	0.0572089i
$285$		0			0
$286$	13.8564	−	4.00000i	0.819346	−	0.236525i
$287$	−6.92820			−0.408959
$288$		0			0
$289$	−12.3923	−	21.4641i	−0.728959	−	1.26259i
$290$	−13.8564	+	24.0000i	−0.813676	+	1.40933i
$291$		0			0
$292$	−9.46410	−	5.46410i	−0.553845	−	0.319762i
$293$	28.9808	+	16.7321i	1.69307	+	0.977497i	0.952012	+	0.306060i	$0.0990109\pi$
$293$	28.9808	+	16.7321i	1.69307	+	0.977497i	0.741062	+	0.671437i	$0.234322\pi$
$294$		0			0
$295$	10.8564	−	18.8038i	0.632084	−	1.09480i
$296$	−2.46410	−	4.26795i	−0.143223	−	0.248070i
$297$		0			0
$298$	−11.5359			−0.668257
$299$	4.96410	−	20.0622i	0.287081	−	1.16023i
$300$		0			0
$301$	−3.86603	+	2.23205i	−0.222834	+	0.128653i
$302$	6.00000	+	10.3923i	0.345261	+	0.598010i
$303$		0			0
$304$		−	7.46410i		−	0.428096i
$305$	−15.5885	−	9.00000i	−0.892592	−	0.515339i
$306$		0			0
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$		0			0
$310$	−19.3923	+	11.1962i	−1.10141	+	0.635899i
$311$	13.3205			0.755337			0.377668	−	0.925941i	$-0.376726\pi$
$311$	13.3205			0.755337			0.377668	+	0.925941i	$0.376726\pi$
$312$		0			0
$313$	0.679492			0.0384072			0.0192036	−	0.999816i	$-0.493887\pi$
$313$	0.679492			0.0384072			0.0192036	+	0.999816i	$0.493887\pi$
$314$	2.53590	−	1.46410i	0.143109	−	0.0826240i
$315$		0			0
$316$	−4.73205	+	8.19615i	−0.266199	+	0.461070i
$317$			16.4641i			0.924716i	0.886693	+	0.462358i	$0.152997\pi$
$317$			16.4641i			0.924716i	−0.886693	+	0.462358i	$0.847003\pi$
$318$		0			0
$319$	−27.7128	−	16.0000i	−1.55162	−	0.895828i
$320$			3.46410i			0.193649i
$321$		0			0
$322$	−2.86603	−	4.96410i	−0.159717	−	0.276639i
$323$	−41.7846	+	24.1244i	−2.32496	+	1.34232i
$324$		0			0
$325$	−18.1865	−	17.5000i	−1.00881	−	0.970725i
$326$	−1.33975			−0.0742017
$327$		0			0
$328$	3.46410	+	6.00000i	0.191273	+	0.331295i
$329$	0.267949	−	0.464102i	0.0147725	−	0.0255868i
$330$		0			0
$331$	18.4641	+	10.6603i	1.01488	+	0.585941i	0.912616	−	0.408817i	$-0.134059\pi$
$331$	18.4641	+	10.6603i	1.01488	+	0.585941i	0.102262	+	0.994757i	$0.467392\pi$
$332$	1.50000	+	0.866025i	0.0823232	+	0.0475293i
$333$		0			0
$334$	10.0000	−	17.3205i	0.547176	−	0.947736i
$335$	−12.4641	−	21.5885i	−0.680987	−	1.17950i
$336$		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
$340$	19.3923	−	11.1962i	1.05170	−	0.607197i
$341$	−12.9282	−	22.3923i	−0.700101	−	1.21261i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	3.86603	+	2.23205i	0.208442	+	0.120344i
$345$		0			0
$346$		−	1.07180i		−	0.0576202i
$347$	12.8564	−	22.2679i	0.690168	−	1.19541i	−0.281614	−	0.959528i	$-0.590870\pi$
$347$	12.8564	−	22.2679i	0.690168	−	1.19541i	0.971783	−	0.235879i	$-0.0757967\pi$
$348$		0			0
$349$	−30.8660	+	17.8205i	−1.65222	+	0.953910i	−0.676064	+	0.736843i	$0.736316\pi$
$349$	−30.8660	+	17.8205i	−1.65222	+	0.953910i	−0.976157	+	0.217067i	$0.930351\pi$
$350$	−7.00000			−0.374166
$351$		0			0
$352$	−4.00000			−0.213201
$353$	−8.08846	+	4.66987i	−0.430505	+	0.248552i	−0.699562	−	0.714572i	$-0.746621\pi$
$353$	−8.08846	+	4.66987i	−0.430505	+	0.248552i	0.269057	+	0.963124i	$0.413288\pi$
$354$		0			0
$355$	−3.33975	+	5.78461i	−0.177255	+	0.307015i
$356$		−	11.7321i		−	0.621797i
$357$		0			0
$358$	−14.6603	−	8.46410i	−0.774819	−	0.447342i
$359$			8.00000i			0.422224i	0.977462	+	0.211112i	$0.0677085\pi$
$359$			8.00000i			0.422224i	−0.977462	+	0.211112i	$0.932292\pi$
$360$		0			0
$361$	18.3564	+	31.7942i	0.966127	+	1.67338i
$362$	21.4641	−	12.3923i	1.12813	−	0.651325i
$363$		0			0
$364$	−3.50000	−	0.866025i	−0.183450	−	0.0453921i
$365$	−37.8564			−1.98149
$366$		0			0
$367$	16.5263	+	28.6244i	0.862665	+	1.49418i	0.869347	+	0.494202i	$0.164540\pi$
$367$	16.5263	+	28.6244i	0.862665	+	1.49418i	−0.00668260	+	0.999978i	$0.502127\pi$
$368$	−2.86603	+	4.96410i	−0.149402	+	0.258772i
$369$		0			0
$370$	−14.7846	−	8.53590i	−0.768615	−	0.443760i
$371$	−7.16025	−	4.13397i	−0.371742	−	0.214625i
$372$		0			0
$373$	13.1244	−	22.7321i	0.679553	−	1.17702i	−0.295562	−	0.955324i	$-0.595507\pi$
$373$	13.1244	−	22.7321i	0.679553	−	1.17702i	0.975116	−	0.221697i	$-0.0711597\pi$
$374$	12.9282	+	22.3923i	0.668501	+	1.15788i
$375$		0			0
$376$	−0.535898			−0.0276368
$377$	−6.92820	+	28.0000i	−0.356821	+	1.44207i
$378$		0			0
$379$	−8.32051	+	4.80385i	−0.427396	+	0.246757i	−0.698237	−	0.715867i	$-0.746032\pi$
$379$	−8.32051	+	4.80385i	−0.427396	+	0.246757i	0.270841	+	0.962624i	$0.412698\pi$
$380$	−12.9282	−	22.3923i	−0.663203	−	1.14870i
$381$		0			0
$382$		−	26.5167i		−	1.35671i
$383$	−6.33975	−	3.66025i	−0.323946	−	0.187030i	0.329204	−	0.944259i	$-0.393220\pi$
$383$	−6.33975	−	3.66025i	−0.323946	−	0.187030i	−0.653150	+	0.757229i	$0.726553\pi$
$384$		0			0
$385$		−	13.8564i		−	0.706188i
$386$	−8.92820	+	15.4641i	−0.454434	+	0.787102i
$387$		0			0
$388$	10.7321	−	6.19615i	0.544837	−	0.314562i
$389$	−14.6603			−0.743304			−0.371652	−	0.928372i	$-0.621209\pi$
$389$	−14.6603			−0.743304			−0.371652	+	0.928372i	$0.621209\pi$
$390$		0			0
$391$	37.0526			1.87383
$392$	−0.866025	+	0.500000i	−0.0437409	+	0.0252538i
$393$		0			0
$394$	1.30385	−	2.25833i	0.0656869	−	0.113773i
$395$			32.7846i			1.64957i
$396$		0			0
$397$	−25.7942	−	14.8923i	−1.29458	−	0.747423i	−0.315114	−	0.949054i	$-0.602043\pi$
$397$	−25.7942	−	14.8923i	−1.29458	−	0.747423i	−0.979462	+	0.201631i	$0.935376\pi$
$398$		−	22.1244i		−	1.10899i
$399$		0			0
$400$	3.50000	+	6.06218i	0.175000	+	0.303109i
$401$	14.1962	−	8.19615i	0.708922	−	0.409296i	−0.101740	−	0.994811i	$-0.532441\pi$
$401$	14.1962	−	8.19615i	0.708922	−	0.409296i	0.810662	+	0.585515i	$0.199108\pi$
$402$		0			0
$403$	−16.1603	+	16.7942i	−0.805000	+	0.836580i
$404$		0			0
$405$		0			0
$406$	4.00000	+	6.92820i	0.198517	+	0.343841i
$407$	9.85641	−	17.0718i	0.488564	−	0.846218i
$408$		0			0
$409$	5.53590	+	3.19615i	0.273733	+	0.158040i	0.630583	−	0.776122i	$-0.282816\pi$
$409$	5.53590	+	3.19615i	0.273733	+	0.158040i	−0.356850	+	0.934162i	$0.616149\pi$
$410$	20.7846	+	12.0000i	1.02648	+	0.592638i
$411$		0			0
$412$	−5.33013	+	9.23205i	−0.262597	+	0.454830i
$413$	−3.13397	−	5.42820i	−0.154213	−	0.267104i
$414$		0			0
$415$	6.00000			0.294528
$416$	1.00000	+	3.46410i	0.0490290	+	0.169842i
$417$		0			0
$418$	25.8564	−	14.9282i	1.26468	−	0.730162i
$419$	−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
$421$			1.60770i			0.0783543i	0.999232	+	0.0391771i	$0.0124737\pi$
$421$			1.60770i			0.0783543i	−0.999232	+	0.0391771i	$0.987526\pi$
$422$	−7.85641	−	4.53590i	−0.382444	−	0.220804i
$423$		0			0
$424$			8.26795i			0.401527i
$425$	22.6244	−	39.1865i	1.09744	−	1.90083i
$426$		0			0
$427$	−4.50000	+	2.59808i	−0.217770	+	0.125730i
$428$	8.53590			0.412598
$429$		0			0
$430$	15.4641			0.745745
$431$	−4.20577	+	2.42820i	−0.202585	+	0.116962i	−0.597861	−	0.801600i	$-0.703982\pi$
$431$	−4.20577	+	2.42820i	−0.202585	+	0.116962i	0.395276	+	0.918563i	$0.370649\pi$
$432$		0			0
$433$	4.92820	−	8.53590i	0.236834	−	0.410209i	−0.722970	−	0.690880i	$-0.757223\pi$
$433$	4.92820	−	8.53590i	0.236834	−	0.410209i	0.959804	+	0.280670i	$0.0905568\pi$
$434$			6.46410i			0.310287i
$435$		0			0
$436$	10.3923	+	6.00000i	0.497701	+	0.287348i
$437$		−	42.7846i		−	2.04667i
$438$		0			0
$439$	−6.80385	−	11.7846i	−0.324730	−	0.562449i	0.656728	−	0.754128i	$-0.271940\pi$
$439$	−6.80385	−	11.7846i	−0.324730	−	0.562449i	−0.981458	+	0.191679i	$0.938607\pi$
$440$	−12.0000	+	6.92820i	−0.572078	+	0.330289i
$441$		0			0
$442$	16.1603	−	16.7942i	0.768665	−	0.798820i
$443$	22.3923			1.06389			0.531945	−	0.846779i	$-0.321461\pi$
$443$	22.3923			1.06389			0.531945	+	0.846779i	$0.321461\pi$
$444$		0			0
$445$	−20.3205	−	35.1962i	−0.963284	−	1.66846i
$446$	3.76795	−	6.52628i	0.178418	−	0.309028i
$447$		0			0
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	−15.5885	−	9.00000i	−0.735665	−	0.424736i	0.0848262	−	0.996396i	$-0.472967\pi$
$449$	−15.5885	−	9.00000i	−0.735665	−	0.424736i	−0.820491	+	0.571660i	$0.806300\pi$
$450$		0			0
$451$	−13.8564	+	24.0000i	−0.652473	+	1.13012i
$452$	2.19615	+	3.80385i	0.103298	+	0.178918i
$453$		0			0
$454$	−13.3205			−0.625162
$455$	−12.0000	+	3.46410i	−0.562569	+	0.162400i
$456$		0			0
$457$	1.03590	−	0.598076i	0.0484573	−	0.0279768i	−0.475576	−	0.879675i	$-0.657760\pi$
$457$	1.03590	−	0.598076i	0.0484573	−	0.0279768i	0.524033	+	0.851698i	$0.324427\pi$
$458$	−9.96410	−	17.2583i	−0.465592	−	0.806429i
$459$		0			0
$460$			19.8564i			0.925810i
$461$	4.39230	+	2.53590i	0.204570	+	0.118109i	0.598785	−	0.800910i	$-0.295650\pi$
$461$	4.39230	+	2.53590i	0.204570	+	0.118109i	−0.394215	+	0.919018i	$0.628984\pi$
$462$		0			0
$463$			8.24871i			0.383350i	0.981458	+	0.191675i	$0.0613920\pi$
$463$			8.24871i			0.383350i	−0.981458	+	0.191675i	$0.938608\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$		0			0
$466$	−11.6603	+	6.73205i	−0.540151	+	0.311856i
$467$	−39.6410			−1.83437			−0.917184	−	0.398465i	$-0.869543\pi$
$467$	−39.6410			−1.83437			−0.917184	+	0.398465i	$0.869543\pi$
$468$		0			0
$469$	−7.19615			−0.332287
$470$	−1.60770	+	0.928203i	−0.0741574	+	0.0428148i
$471$		0			0
$472$	−3.13397	+	5.42820i	−0.144253	+	0.249853i
$473$			17.8564i			0.821038i
$474$		0			0
$475$	−45.2487	−	26.1244i	−2.07615	−	1.19867i
$476$		−	6.46410i		−	0.296282i
$477$		0			0
$478$	−6.42820	−	11.1340i	−0.294019	−	0.509256i
$479$	3.80385	−	2.19615i	0.173802	−	0.100345i	−0.410575	−	0.911827i	$-0.634672\pi$
$479$	3.80385	−	2.19615i	0.173802	−	0.100345i	0.584377	+	0.811482i	$0.301339\pi$
$480$		0			0
$481$	−17.2487	−	4.26795i	−0.786474	−	0.194602i
$482$	−15.8564			−0.722240
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	21.4641	−	37.1769i	0.974635	−	1.68812i
$486$		0			0
$487$	0.339746	+	0.196152i	0.0153954	+	0.00888851i	0.507678	−	0.861547i	$-0.330504\pi$
$487$	0.339746	+	0.196152i	0.0153954	+	0.00888851i	−0.492283	+	0.870435i	$0.663837\pi$
$488$	4.50000	+	2.59808i	0.203705	+	0.117609i
$489$		0			0
$490$	−1.73205	+	3.00000i	−0.0782461	+	0.135526i
$491$	4.92820	+	8.53590i	0.222407	+	0.385220i	0.955538	−	0.294867i	$-0.0952754\pi$
$491$	4.92820	+	8.53590i	0.222407	+	0.385220i	−0.733132	+	0.680087i	$0.761942\pi$
$492$		0			0
$493$	−51.7128			−2.32903
$494$	−19.3923	−	18.6603i	−0.872501	−	0.839565i
$495$		0			0
$496$	5.59808	−	3.23205i	0.251361	−	0.145123i
$497$	0.964102	+	1.66987i	0.0432459	+	0.0749040i
$498$		0			0
$499$			0.267949i			0.0119951i	0.999982	+	0.00599753i	$0.00190908\pi$
$499$			0.267949i			0.0119951i	−0.999982	+	0.00599753i	$0.998091\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$		0			0
$502$			10.0718i			0.449526i
$503$	−3.46410	+	6.00000i	−0.154457	+	0.267527i	−0.932861	−	0.360236i	$-0.882696\pi$
$503$	−3.46410	+	6.00000i	−0.154457	+	0.267527i	0.778404	+	0.627763i	$0.216029\pi$
$504$		0			0
$505$		0			0
$506$	−22.9282			−1.01928
$507$		0			0
$508$	5.07180			0.225025
$509$	29.6603	−	17.1244i	1.31467	−	0.759024i	0.331802	−	0.943349i	$-0.392343\pi$
$509$	29.6603	−	17.1244i	1.31467	−	0.759024i	0.982865	+	0.184325i	$0.0590100\pi$
$510$		0			0
$511$	−5.46410	+	9.46410i	−0.241718	+	0.418667i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	0.401924	+	0.232051i	0.0177281	+	0.0102353i
$515$			36.9282i			1.62725i
$516$		0			0
$517$	−1.07180	−	1.85641i	−0.0471376	−	0.0816447i
$518$	−4.26795	+	2.46410i	−0.187523	+	0.108266i
$519$		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
$523$	−7.46410	−	12.9282i	−0.326382	−	0.565311i	0.655409	−	0.755274i	$-0.272496\pi$
$523$	−7.46410	−	12.9282i	−0.326382	−	0.565311i	−0.981791	+	0.189963i	$0.939163\pi$
$524$	−9.50000	+	16.4545i	−0.415009	+	0.718817i
$525$		0			0
$526$	15.0000	+	8.66025i	0.654031	+	0.377605i
$527$	−36.1865	−	20.8923i	−1.57631	−	0.910083i
$528$		0			0
$529$	−4.92820	+	8.53590i	−0.214270	+	0.371126i
$530$	14.3205	+	24.8038i	0.622043	+	1.07741i
$531$		0			0
$532$	−7.46410			−0.323610
$533$	24.2487	+	6.00000i	1.05033	+	0.259889i
$534$		0			0
$535$	25.6077	−	14.7846i	1.10712	−	0.639194i
$536$	3.59808	+	6.23205i	0.155413	+	0.269184i
$537$		0			0
$538$			22.3923i			0.965401i
$539$	−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	$-0.121442\pi$
$542$	−6.23205	+	10.7942i	−0.267690	+	0.463652i
$543$		0			0
$544$	−5.59808	+	3.23205i	−0.240016	+	0.138573i
$545$	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
$551$			59.7128i			2.54385i
$552$		0			0
$553$	8.19615	+	4.73205i	0.348536	+	0.201227i
$554$			7.32051i			0.311019i
$555$		0			0
$556$	1.46410	+	2.53590i	0.0620917	+	0.107546i
$557$	−21.3109	+	12.3038i	−0.902971	+	0.521331i	−0.878163	−	0.478361i	$-0.841231\pi$
$557$	−21.3109	+	12.3038i	−0.902971	+	0.521331i	−0.0248083	+	0.999692i	$0.507898\pi$
$558$		0			0
$559$	15.4641	−	4.46410i	0.654062	−	0.188811i
$560$	3.46410			0.146385
$561$		0			0
$562$	−1.19615	−	2.07180i	−0.0504566	−	0.0873935i
$563$	6.92820	−	12.0000i	0.291989	−	0.505740i	−0.682291	−	0.731081i	$-0.739016\pi$
$563$	6.92820	−	12.0000i	0.291989	−	0.505740i	0.974280	+	0.225341i	$0.0723496\pi$
$564$		0			0
$565$	13.1769	+	7.60770i	0.554357	+	0.320058i
$566$	9.92820	+	5.73205i	0.417314	+	0.240936i
$567$		0			0
$568$	0.964102	−	1.66987i	0.0404528	−	0.0700663i
$569$	−7.73205	−	13.3923i	−0.324144	−	0.561435i	0.657194	−	0.753721i	$-0.271743\pi$
$569$	−7.73205	−	13.3923i	−0.324144	−	0.561435i	−0.981339	+	0.192286i	$0.938410\pi$
$570$		0			0
$571$	3.39230			0.141964			0.0709818	−	0.997478i	$-0.477387\pi$
$571$	3.39230			0.141964			0.0709818	+	0.997478i	$0.477387\pi$
$572$	−10.0000	+	10.3923i	−0.418121	+	0.434524i
$573$		0			0
$574$	6.00000	−	3.46410i	0.250435	−	0.144589i
$575$	20.0622	+	34.7487i	0.836651	+	1.44912i
$576$		0			0
$577$		−	1.21539i		−	0.0505974i	−0.999680	−	0.0252987i	$-0.991946\pi$
$577$		−	1.21539i		−	0.0505974i	0.999680	−	0.0252987i	$-0.00805368\pi$
$578$	21.4641	+	12.3923i	0.892789	+	0.515452i
$579$		0			0
$580$		−	27.7128i		−	1.15071i
$581$	0.866025	−	1.50000i	0.0359288	−	0.0622305i
$582$		0			0
$583$	−28.6410	+	16.5359i	−1.18619	+	0.684847i
$584$	10.9282			0.452212
$585$		0			0
$586$	−33.4641			−1.38239
$587$	−7.03590	+	4.06218i	−0.290403	+	0.167664i	−0.638123	−	0.769934i	$-0.720289\pi$
$587$	−7.03590	+	4.06218i	−0.290403	+	0.167664i	0.347721	+	0.937598i	$0.386956\pi$
$588$		0			0
$589$	−24.1244	+	41.7846i	−0.994027	+	1.72170i
$590$			21.7128i			0.893902i
$591$		0			0
$592$	4.26795	+	2.46410i	0.175412	+	0.101274i
$593$		−	4.26795i		−	0.175264i	−0.996153	−	0.0876318i	$-0.972070\pi$
$593$		−	4.26795i		−	0.175264i	0.996153	−	0.0876318i	$-0.0279299\pi$
$594$		0			0
$595$	−11.1962	−	19.3923i	−0.458997	−	0.795007i
$596$	9.99038	−	5.76795i	0.409222	−	0.236264i
$597$		0			0
$598$	5.73205	+	19.8564i	0.234401	+	0.811989i
$599$	19.0526			0.778466			0.389233	−	0.921139i	$-0.372740\pi$
$599$	19.0526			0.778466			0.389233	+	0.921139i	$0.372740\pi$
$600$		0			0
$601$	12.1244	+	21.0000i	0.494563	+	0.856608i	0.999980	−	0.00626702i	$-0.00199487\pi$
$601$	12.1244	+	21.0000i	0.494563	+	0.856608i	−0.505418	+	0.862875i	$0.668662\pi$
$602$	2.23205	−	3.86603i	0.0909716	−	0.157567i
$603$		0			0
$604$	−10.3923	−	6.00000i	−0.422857	−	0.244137i
$605$	−15.0000	−	8.66025i	−0.609837	−	0.352089i
$606$		0			0
$607$	7.59808	−	13.1603i	0.308396	−	0.534158i	−0.669615	−	0.742708i	$-0.733541\pi$
$607$	7.59808	−	13.1603i	0.308396	−	0.534158i	0.978012	+	0.208550i	$0.0668744\pi$
$608$	3.73205	+	6.46410i	0.151355	+	0.262154i
$609$		0			0
$610$	18.0000			0.728799
$611$	−1.33975	+	1.39230i	−0.0542003	+	0.0563266i
$612$		0			0
$613$	29.7846	−	17.1962i	1.20299	−	0.694546i	0.241770	−	0.970333i	$-0.422272\pi$
$613$	29.7846	−	17.1962i	1.20299	−	0.694546i	0.961219	+	0.275787i	$0.0889386\pi$
$614$	11.0000	+	19.0526i	0.443924	+	0.768899i
$615$		0			0
$616$			4.00000i			0.161165i
$617$	5.07180	+	2.92820i	0.204183	+	0.117885i	0.598605	−	0.801044i	$-0.295722\pi$
$617$	5.07180	+	2.92820i	0.204183	+	0.117885i	−0.394422	+	0.918929i	$0.629055\pi$
$618$		0			0
$619$			30.7846i			1.23734i	0.785652	+	0.618669i	$0.212328\pi$
$619$			30.7846i			1.23734i	−0.785652	+	0.618669i	$0.787672\pi$
$620$	11.1962	−	19.3923i	0.449648	−	0.778814i
$621$		0			0
$622$	−11.5359	+	6.66025i	−0.462547	+	0.267052i
$623$	−11.7321			−0.470035
$624$		0			0
$625$	−11.0000			−0.440000
$626$	−0.588457	+	0.339746i	−0.0235195	+	0.0135790i
$627$		0			0
$628$	−1.46410	+	2.53590i	−0.0584240	+	0.101193i
$629$		−	31.8564i		−	1.27020i
$630$		0			0
$631$	30.2487	+	17.4641i	1.20418	+	0.695235i	0.961482	−	0.274867i	$-0.0886337\pi$
$631$	30.2487	+	17.4641i	1.20418	+	0.695235i	0.242700	+	0.970101i	$0.421967\pi$
$632$		−	9.46410i		−	0.376462i
$633$		0			0
$634$	−8.23205	−	14.2583i	−0.326937	−	0.566271i
$635$	15.2154	−	8.78461i	0.603804	−	0.348607i
$636$		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
$641$	13.3205	−	23.0718i	0.526128	−	0.911281i	−0.473408	−	0.880843i	$-0.656976\pi$
$641$	13.3205	−	23.0718i	0.526128	−	0.911281i	0.999537	−	0.0304380i	$-0.00969022\pi$
$642$		0			0
$643$	−17.5359	−	10.1244i	−0.691548	−	0.399266i	0.112643	−	0.993635i	$-0.464068\pi$
$643$	−17.5359	−	10.1244i	−0.691548	−	0.399266i	−0.804192	+	0.594370i	$0.797402\pi$
$644$	4.96410	+	2.86603i	0.195613	+	0.112937i
$645$		0			0
$646$	24.1244	−	41.7846i	0.949160	−	1.64399i
$647$	−18.6603	−	32.3205i	−0.733610	−	1.27065i	−0.955330	−	0.295540i	$-0.904500\pi$
$647$	−18.6603	−	32.3205i	−0.733610	−	1.27065i	0.221720	−	0.975110i	$-0.428833\pi$
$648$		0			0
$649$	−25.0718			−0.984154
$650$	24.5000	+	6.06218i	0.960969	+	0.237778i
$651$		0			0
$652$	1.16025	−	0.669873i	0.0454391	−	0.0262343i
$653$	−18.7942	−	32.5526i	−0.735475	−	1.27388i	−0.954515	−	0.298164i	$-0.903626\pi$
$653$	−18.7942	−	32.5526i	−0.735475	−	1.27388i	0.219040	−	0.975716i	$-0.429708\pi$
$654$		0			0
$655$			65.8179i			2.57172i
$656$	−6.00000	−	3.46410i	−0.234261	−	0.135250i
$657$		0			0
$658$			0.535898i			0.0208915i
$659$	0.803848	−	1.39230i	0.0313135	−	0.0542365i	−0.849944	−	0.526873i	$-0.823364\pi$
$659$	0.803848	−	1.39230i	0.0313135	−	0.0542365i	0.881257	+	0.472637i	$0.156698\pi$
$660$		0			0
$661$	43.9186	−	25.3564i	1.70823	−	0.986250i	0.771487	−	0.636245i	$-0.219513\pi$
$661$	43.9186	−	25.3564i	1.70823	−	0.986250i	0.936748	−	0.350005i	$-0.113820\pi$
$662$	−21.3205			−0.828645
$663$		0			0
$664$	−1.73205			−0.0672166
$665$	−22.3923	+	12.9282i	−0.868336	+	0.501334i
$666$		0			0
$667$	22.9282	−	39.7128i	0.887784	−	1.53769i
$668$			20.0000i			0.773823i
$669$		0			0
$670$	21.5885	+	12.4641i	0.834035	+	0.481530i
$671$			20.7846i			0.802381i
$672$		0			0
$673$	19.8205	+	34.3301i	0.764024	+	1.32333i	0.940761	+	0.339071i	$0.110113\pi$
$673$	19.8205	+	34.3301i	0.764024	+	1.32333i	−0.176736	+	0.984258i	$0.556554\pi$
$674$	5.19615	−	3.00000i	0.200148	−	0.115556i
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	−1.07180			−0.0411925			−0.0205962	−	0.999788i	$-0.506556\pi$
$677$	−1.07180			−0.0411925			−0.0205962	+	0.999788i	$0.506556\pi$
$678$		0			0
$679$	−6.19615	−	10.7321i	−0.237787	−	0.411858i
$680$	−11.1962	+	19.3923i	−0.429353	+	0.743661i
$681$		0			0
$682$	22.3923	+	12.9282i	0.857446	+	0.495046i
$683$	−44.3205	−	25.5885i	−1.69588	−	0.979115i	−0.949592	−	0.313489i	$-0.898502\pi$
$683$	−44.3205	−	25.5885i	−1.69588	−	0.979115i	−0.746285	−	0.665626i	$-0.768164\pi$
$684$		0			0
$685$	24.0000	−	41.5692i	0.916993	−	1.58828i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−4.46410			−0.170192
$689$	21.4808	+	20.6699i	0.818352	+	0.787459i
$690$		0			0
$691$	−35.6603	+	20.5885i	−1.35658	+	0.783222i	−0.989161	−	0.146834i	$-0.953092\pi$
$691$	−35.6603	+	20.5885i	−1.35658	+	0.783222i	−0.367419	+	0.930056i	$0.619758\pi$
$692$	0.535898	+	0.928203i	0.0203718	+	0.0352850i
$693$		0			0
$694$			25.7128i			0.976045i
$695$	8.78461	+	5.07180i	0.333219	+	0.192384i
$696$		0			0
$697$			44.7846i			1.69634i
$698$	17.8205	−	30.8660i	0.674516	−	1.16830i
$699$		0			0
$700$	6.06218	−	3.50000i	0.229129	−	0.132288i
$701$	−2.12436			−0.0802358			−0.0401179	−	0.999195i	$-0.512773\pi$
$701$	−2.12436			−0.0802358			−0.0401179	+	0.999195i	$0.512773\pi$
$702$		0			0
$703$	−36.7846			−1.38736
$704$	3.46410	−	2.00000i	0.130558	−	0.0753778i
$705$		0			0
$706$	4.66987	−	8.08846i	0.175753	−	0.304413i
$707$		0			0
$708$		0			0
$709$	−6.67949	−	3.85641i	−0.250854	−	0.144830i	0.369301	−	0.929310i	$-0.379597\pi$
$709$	−6.67949	−	3.85641i	−0.250854	−	0.144830i	−0.620155	+	0.784479i	$0.712930\pi$
$710$		−	6.67949i		−	0.250677i
$711$		0			0
$712$	5.86603	+	10.1603i	0.219839	+	0.380772i
$713$	32.0885	−	18.5263i	1.20172	−	0.693815i
$714$		0			0
$715$	−12.0000	+	48.4974i	−0.448775	+	1.81370i
$716$	16.9282			0.632637
$717$		0			0
$718$	−4.00000	−	6.92820i	−0.149279	−	0.258558i
$719$	−17.2679	+	29.9090i	−0.643986	+	1.11542i	0.340549	+	0.940227i	$0.389387\pi$
$719$	−17.2679	+	29.9090i	−0.643986	+	1.11542i	−0.984535	+	0.175189i	$0.943946\pi$
$720$		0			0
$721$	9.23205	+	5.33013i	0.343820	+	0.198504i
$722$	−31.7942	−	18.3564i	−1.18326	−	0.683155i
$723$		0			0
$724$	−12.3923	+	21.4641i	−0.460556	+	0.797707i
$725$	−28.0000	−	48.4974i	−1.03989	−	1.80115i
$726$		0			0
$727$	22.9090			0.849646			0.424823	−	0.905276i	$-0.360336\pi$
$727$	22.9090			0.849646			0.424823	+	0.905276i	$0.360336\pi$
$728$	3.46410	−	1.00000i	0.128388	−	0.0370625i
$729$		0			0
$730$	32.7846	−	18.9282i	1.21341	−	0.700564i
$731$	14.4282	+	24.9904i	0.533646	+	0.924303i
$732$		0			0
$733$		−	4.85641i		−	0.179375i	−0.995970	−	0.0896877i	$-0.971413\pi$
$733$		−	4.85641i		−	0.179375i	0.995970	−	0.0896877i	$-0.0285869\pi$
$734$	−28.6244	−	16.5263i	−1.05654	−	0.609996i
$735$		0			0
$736$		−	5.73205i		−	0.211286i
$737$	−14.3923	+	24.9282i	−0.530147	+	0.918242i
$738$		0			0
$739$	6.69615	−	3.86603i	0.246322	−	0.142214i	−0.371757	−	0.928330i	$-0.621245\pi$
$739$	6.69615	−	3.86603i	0.246322	−	0.142214i	0.618079	+	0.786116i	$0.287911\pi$
$740$	17.0718			0.627572
$741$		0			0
$742$	8.26795			0.303526
$743$	−1.54552	+	0.892305i	−0.0566995	+	0.0327355i	−0.528082	−	0.849194i	$-0.677089\pi$
$743$	−1.54552	+	0.892305i	−0.0566995	+	0.0327355i	0.471382	+	0.881929i	$0.343755\pi$
$744$		0			0
$745$	19.9808	−	34.6077i	0.732038	−	1.26793i
$746$			26.2487i			0.961034i
$747$		0			0
$748$	−22.3923	−	12.9282i	−0.818744	−	0.472702i
$749$		−	8.53590i		−	0.311895i
$750$		0			0
$751$	14.6603	+	25.3923i	0.534960	+	0.926578i	0.999165	+	0.0408506i	$0.0130068\pi$
$751$	14.6603	+	25.3923i	0.534960	+	0.926578i	−0.464205	+	0.885728i	$0.653660\pi$
$752$	0.464102	−	0.267949i	0.0169240	−	0.00977110i
$753$		0			0
$754$	−8.00000	−	27.7128i	−0.291343	−	1.00924i
$755$	−41.5692			−1.51286
$756$		0			0
$757$	−9.92820	−	17.1962i	−0.360847	−	0.625005i	0.627254	−	0.778815i	$-0.284179\pi$
$757$	−9.92820	−	17.1962i	−0.360847	−	0.625005i	−0.988100	+	0.153810i	$0.950846\pi$
$758$	4.80385	−	8.32051i	0.174484	−	0.302214i
$759$		0			0
$760$	22.3923	+	12.9282i	0.812254	+	0.468955i
$761$	−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
$764$	13.2583	+	22.9641i	0.479670	+	0.830812i
$765$		0			0
$766$	7.32051			0.264501
$767$	6.26795	+	21.7128i	0.226323	+	0.784004i
$768$		0			0
$769$	36.9282	−	21.3205i	1.33167	−	0.768837i	0.346110	−	0.938194i	$-0.387502\pi$
$769$	36.9282	−	21.3205i	1.33167	−	0.768837i	0.985555	+	0.169357i	$0.0541690\pi$
$770$	6.92820	+	12.0000i	0.249675	+	0.432450i
$771$		0			0
$772$		−	17.8564i		−	0.642666i
$773$	−11.1962	−	6.46410i	−0.402698	−	0.232498i	0.284950	−	0.958542i	$-0.408023\pi$
$773$	−11.1962	−	6.46410i	−0.402698	−	0.232498i	−0.687647	+	0.726045i	$0.741356\pi$
$774$		0			0
$775$		−	45.2487i		−	1.62538i
$776$	−6.19615	+	10.7321i	−0.222429	+	0.385258i
$777$		0			0
$778$	12.6962	−	7.33013i	0.455179	−	0.262798i
$779$	51.7128			1.85280
$780$		0			0
$781$	7.71281			0.275986
$782$	−32.0885	+	18.5263i	−1.14748	+	0.662498i
$783$		0			0
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$			10.1436i			0.362040i
$786$		0			0
$787$	−7.26795	−	4.19615i	−0.259074	−	0.149577i	0.364838	−	0.931071i	$-0.381124\pi$
$787$	−7.26795	−	4.19615i	−0.259074	−	0.149577i	−0.623912	+	0.781494i	$0.714458\pi$
$788$			2.60770i			0.0928953i
$789$		0			0
$790$	−16.3923	−	28.3923i	−0.583212	−	1.01015i
$791$	3.80385	−	2.19615i	0.135249	−	0.0780862i
$792$		0			0
$793$	18.0000	−	5.19615i	0.639199	−	0.184521i
$794$	29.7846			1.05702
$795$		0			0
$796$	11.0622	+	19.1603i	0.392088	+	0.679117i
$797$	−21.1244	+	36.5885i	−0.748263	+	1.29603i	0.200392	+	0.979716i	$0.435779\pi$
$797$	−21.1244	+	36.5885i	−0.748263	+	1.29603i	−0.948655	+	0.316314i	$0.897555\pi$
$798$		0			0
$799$	−3.00000	−	1.73205i	−0.106132	−	0.0612756i
$800$	−6.06218	−	3.50000i	−0.214330	−	0.123744i
$801$		0			0
$802$	−8.19615	+	14.1962i	−0.289416	+	0.501284i
$803$	21.8564	+	37.8564i	0.771296	+	1.33592i
$804$		0			0
$805$	19.8564			0.699846
$806$	5.59808	−	22.6244i	0.197184	−	0.796909i
$807$		0			0
$808$		0			0
$809$	7.85641	+	13.6077i	0.276217	+	0.478421i	0.970441	−	0.241337i	$-0.0775860\pi$
$809$	7.85641	+	13.6077i	0.276217	+	0.478421i	−0.694225	+	0.719758i	$0.744253\pi$
$810$		0			0
$811$		−	2.14359i		−	0.0752717i	−0.999292	−	0.0376359i	$-0.988017\pi$
$811$		−	2.14359i		−	0.0752717i	0.999292	−	0.0376359i	$-0.0119827\pi$
$812$	−6.92820	−	4.00000i	−0.243132	−	0.140372i
$813$		0			0
$814$			19.7128i			0.690934i
$815$	2.32051	−	4.01924i	0.0812839	−	0.140788i
$816$		0			0
$817$	28.8564	−	16.6603i	1.00956	−	0.582869i
$818$	−6.39230			−0.223502
$819$		0			0
$820$	−24.0000			−0.838116
$821$	−27.0622	+	15.6244i	−0.944477	+	0.545294i	−0.891361	−	0.453295i	$-0.850249\pi$
$821$	−27.0622	+	15.6244i	−0.944477	+	0.545294i	−0.0531158	+	0.998588i	$0.516915\pi$
$822$		0			0
$823$	11.8038	−	20.4449i	0.411456	−	0.712663i	−0.583593	−	0.812046i	$-0.698354\pi$
$823$	11.8038	−	20.4449i	0.411456	−	0.712663i	0.995049	+	0.0993832i	$0.0316870\pi$
$824$		−	10.6603i		−	0.371368i
$825$		0			0
$826$	5.42820	+	3.13397i	0.188871	+	0.109045i
$827$		−	36.3923i		−	1.26548i	−0.774363	−	0.632742i	$-0.781929\pi$
$827$		−	36.3923i		−	1.26548i	0.774363	−	0.632742i	$-0.218071\pi$
$828$		0			0
$829$	3.60770	+	6.24871i	0.125300	+	0.217027i	0.921850	−	0.387546i	$-0.126677\pi$
$829$	3.60770	+	6.24871i	0.125300	+	0.217027i	−0.796550	+	0.604573i	$0.793344\pi$
$830$	−5.19615	+	3.00000i	−0.180361	+	0.104132i
$831$		0			0
$832$	−2.59808	−	2.50000i	−0.0900721	−	0.0866719i
$833$	−6.46410			−0.223968
$834$		0			0
$835$	34.6410	+	60.0000i	1.19880	+	2.07639i
$836$	−14.9282	+	25.8564i	−0.516303	+	0.894263i
$837$		0			0
$838$	4.33013	+	2.50000i	0.149582	+	0.0863611i
$839$	1.39230	+	0.803848i	0.0480677	+	0.0277519i	0.523841	−	0.851816i	$-0.324498\pi$
$839$	1.39230	+	0.803848i	0.0480677	+	0.0277519i	−0.475774	+	0.879568i	$0.657832\pi$
$840$		0			0
$841$	−17.5000	+	30.3109i	−0.603448	+	1.04520i
$842$	−0.803848	−	1.39230i	−0.0277024	−	0.0479820i
$843$		0			0
$844$	9.07180			0.312264
$845$	45.0000	−	1.73205i	1.54805	−	0.0595844i
$846$		0			0
$847$	−4.33013	+	2.50000i	−0.148785	+	0.0859010i
$848$	−4.13397	−	7.16025i	−0.141961	−	0.245884i
$849$		0			0
$850$			45.2487i			1.55202i
$851$	24.4641	+	14.1244i	0.838619	+	0.484177i
$852$		0			0
$853$			47.6410i			1.63120i	0.578618	+	0.815599i	$0.303592\pi$
$853$			47.6410i			1.63120i	−0.578618	+	0.815599i	$0.696408\pi$
$854$	2.59808	−	4.50000i	0.0889043	−	0.153987i
$855$		0			0
$856$	−7.39230	+	4.26795i	−0.252664	+	0.145876i
$857$	−33.7128			−1.15161			−0.575804	−	0.817588i	$-0.695311\pi$
$857$	−33.7128			−1.15161			−0.575804	+	0.817588i	$0.695311\pi$
$858$		0			0
$859$	−15.8564			−0.541014			−0.270507	−	0.962718i	$-0.587191\pi$
$859$	−15.8564			−0.541014			−0.270507	+	0.962718i	$0.587191\pi$
$860$	−13.3923	+	7.73205i	−0.456674	+	0.263661i
$861$		0			0
$862$	2.42820	−	4.20577i	0.0827049	−	0.143249i
$863$			42.9282i			1.46129i	0.682756	+	0.730647i	$0.260781\pi$
$863$			42.9282i			1.46129i	−0.682756	+	0.730647i	$0.739219\pi$
$864$		0			0
$865$	3.21539	+	1.85641i	0.109327	+	0.0631197i
$866$			9.85641i			0.334934i
$867$		0			0
$868$	−3.23205	−	5.59808i	−0.109703	−	0.190011i
$869$	32.7846	−	18.9282i	1.11214	−	0.642095i
$870$		0			0
$871$	25.1865	+	6.23205i	0.853413	+	0.211165i
$872$	−12.0000			−0.406371
$873$		0			0
$874$	21.3923	+	37.0526i	0.723606	+	1.25332i
$875$	3.46410	−	6.00000i	0.117108	−	0.202837i
$876$		0			0
$877$	22.2679	+	12.8564i	0.751935	+	0.434130i	0.826393	−	0.563094i	$-0.190389\pi$
$877$	22.2679	+	12.8564i	0.751935	+	0.434130i	−0.0744575	+	0.997224i	$0.523723\pi$
$878$	11.7846	+	6.80385i	0.397711	+	0.229619i
$879$		0			0
$880$	6.92820	−	12.0000i	0.233550	−	0.404520i
$881$	−16.0167	−	27.7417i	−0.539615	−	0.934641i	−0.998925	−	0.0463644i	$-0.985236\pi$
$881$	−16.0167	−	27.7417i	−0.539615	−	0.934641i	0.459310	−	0.888276i	$-0.348097\pi$
$882$		0			0
$883$	0.320508			0.0107860			0.00539298	−	0.999985i	$-0.498283\pi$
$883$	0.320508			0.0107860			0.00539298	+	0.999985i	$0.498283\pi$
$884$	−5.59808	+	22.6244i	−0.188284	+	0.760939i
$885$		0			0
$886$	−19.3923	+	11.1962i	−0.651497	+	0.376142i
$887$	5.92820	+	10.2679i	0.199050	+	0.344764i	0.948221	−	0.317613i	$-0.102881\pi$
$887$	5.92820	+	10.2679i	0.199050	+	0.344764i	−0.749171	+	0.662377i	$0.769548\pi$
$888$		0			0
$889$		−	5.07180i		−	0.170103i
$890$	35.1962	+	20.3205i	1.17978	+	0.681145i
$891$		0			0
$892$			7.53590i			0.252321i
$893$	−2.00000	+	3.46410i	−0.0669274	+	0.115922i
$894$		0			0
$895$	50.7846	−	29.3205i	1.69754	−	0.980076i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	18.0000			0.600668
$899$	−44.7846	+	25.8564i	−1.49365	+	0.862359i
$900$		0			0
$901$	−26.7224	+	46.2846i	−0.890253	+	1.54196i
$902$		−	27.7128i		−	0.922736i
$903$		0			0
$904$	−3.80385	−	2.19615i	−0.126514	−	0.0730429i
$905$			85.8564i			2.85396i
$906$		0			0
$907$	−9.23205	−	15.9904i	−0.306545	−	0.530952i	0.671059	−	0.741404i	$-0.265840\pi$
$907$	−9.23205	−	15.9904i	−0.306545	−	0.530952i	−0.977604	+	0.210452i	$0.932506\pi$
$908$	11.5359	−	6.66025i	0.382832	−	0.221028i
$909$		0			0
$910$	8.66025	−	9.00000i	0.287085	−	0.298347i
$911$	−27.1769			−0.900411			−0.450206	−	0.892925i	$-0.648649\pi$
$911$	−27.1769			−0.900411			−0.450206	+	0.892925i	$0.648649\pi$
$912$		0			0
$913$	−3.46410	−	6.00000i	−0.114645	−	0.198571i
$914$	−0.598076	+	1.03590i	−0.0197826	+	0.0342645i
$915$		0			0
$916$	17.2583	+	9.96410i	0.570231	+	0.329223i
$917$	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	$0.0255924\pi$
$920$	−9.92820	−	17.1962i	−0.327323	−	0.566940i
$921$		0			0
$922$	−5.07180			−0.167031
$923$	−1.92820	−	6.67949i	−0.0634676	−	0.219858i
$924$		0			0
$925$	29.8756	−	17.2487i	0.982305	−	0.567134i
$926$	−4.12436	−	7.14359i	−0.135535	−	0.234753i
$927$		0			0
$928$			8.00000i			0.262613i
$929$	−5.08846	−	2.93782i	−0.166947	−	0.0963868i	0.414199	−	0.910187i	$-0.364062\pi$
$929$	−5.08846	−	2.93782i	−0.166947	−	0.0963868i	−0.581145	+	0.813800i	$0.697395\pi$
$930$		0			0
$931$			7.46410i			0.244626i
$932$	6.73205	−	11.6603i	0.220516	−	0.381944i
$933$		0			0
$934$	34.3301	−	19.8205i	1.12332	−	0.648547i
$935$	−89.5692			−2.92923
$936$		0			0
$937$	−44.9282			−1.46774			−0.733870	−	0.679290i	$-0.762288\pi$
$937$	−44.9282			−1.46774			−0.733870	+	0.679290i	$0.762288\pi$
$938$	6.23205	−	3.59808i	0.203484	−	0.117481i
$939$		0			0
$940$	0.928203	−	1.60770i	0.0302747	−	0.0524372i
$941$		−	19.6077i		−	0.639193i	−0.947554	−	0.319596i	$-0.896453\pi$
$941$		−	19.6077i		−	0.639193i	0.947554	−	0.319596i	$-0.103547\pi$
$942$		0			0
$943$	−34.3923	−	19.8564i	−1.11997	−	0.646614i
$944$		−	6.26795i		−	0.204004i
$945$		0			0
$946$	−8.92820	−	15.4641i	−0.290281	−	0.502781i
$947$	−26.1962	+	15.1244i	−0.851261	+	0.491476i	−0.861076	−	0.508476i	$-0.830209\pi$
$947$	−26.1962	+	15.1244i	−0.851261	+	0.491476i	0.00981541	+	0.999952i	$0.496876\pi$
$948$		0			0
$949$	27.3205	−	28.3923i	0.886861	−	0.921653i
$950$	52.2487			1.69517
$951$		0			0
$952$	3.23205	+	5.59808i	0.104751	+	0.181435i
$953$	−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
$955$	79.5500	+	45.9282i	2.57418	+	1.48620i
$956$	11.1340	+	6.42820i	0.360098	+	0.207903i
$957$		0			0
$958$	−2.19615	+	3.80385i	−0.0709545	+	0.122897i
$959$	−6.92820	−	12.0000i	−0.223723	−	0.387500i
$960$		0			0
$961$	−10.7846			−0.347891
$962$	17.0718	−	4.92820i	0.550417	−	0.158892i
$963$		0			0
$964$	13.7321	−	7.92820i	0.442280	−	0.255350i
$965$	−30.9282	−	53.5692i	−0.995614	−	1.72445i
$966$		0			0
$967$		−	16.5359i		−	0.531759i	−0.964006	−	0.265879i	$-0.914338\pi$
$967$		−	16.5359i		−	0.531759i	0.964006	−	0.265879i	$-0.0856623\pi$
$968$	4.33013	+	2.50000i	0.139176	+	0.0803530i
$969$		0			0
$970$			42.9282i			1.37834i
$971$	11.9641	−	20.7224i	0.383946	−	0.665014i	−0.607676	−	0.794185i	$-0.707898\pi$
$971$	11.9641	−	20.7224i	0.383946	−	0.665014i	0.991622	+	0.129170i	$0.0412314\pi$
$972$		0			0
$973$	2.53590	−	1.46410i	0.0812972	−	0.0469369i
$974$	−0.392305			−0.0125703
$975$		0			0
$976$	−5.19615			−0.166325
$977$	22.3923	−	12.9282i	0.716393	−	0.413610i	−0.0970305	−	0.995281i	$-0.530934\pi$
$977$	22.3923	−	12.9282i	0.716393	−	0.413610i	0.813424	+	0.581672i	$0.197601\pi$
$978$		0			0
$979$	−23.4641	+	40.6410i	−0.749916	+	1.29889i
$980$		−	3.46410i		−	0.110657i
$981$		0			0
$982$	−8.53590	−	4.92820i	−0.272391	−	0.157265i
$983$		−	19.0718i		−	0.608296i	−0.952625	−	0.304148i	$-0.901628\pi$
$983$		−	19.0718i		−	0.608296i	0.952625	−	0.304148i	$-0.0983717\pi$
$984$		0			0
$985$	4.51666	+	7.82309i	0.143913	+	0.249264i
$986$	44.7846	−	25.8564i	1.42623	−	0.823436i
$987$		0			0
$988$	26.1244	+	6.46410i	0.831126	+	0.205650i
$989$	−25.5885			−0.813666
$990$		0			0
$991$	−0.0717968	−	0.124356i	−0.00228070	−	0.00395029i	0.864883	−	0.501974i	$-0.167393\pi$
$991$	−0.0717968	−	0.124356i	−0.00228070	−	0.00395029i	−0.867164	+	0.498024i	$0.834059\pi$
$992$	−3.23205	+	5.59808i	−0.102618	+	0.177739i
$993$		0			0
$994$	−1.66987	−	0.964102i	−0.0529652	−	0.0305794i
$995$	66.3731	+	38.3205i	2.10417	+	1.21484i
$996$		0			0
$997$	−16.9904	+	29.4282i	−0.538091	+	0.932001i	0.460916	+	0.887444i	$0.347521\pi$
$997$	−16.9904	+	29.4282i	−0.538091	+	0.932001i	−0.999007	+	0.0445568i	$0.985812\pi$
$998$	−0.133975	−	0.232051i	−0.00424089	−	0.00734544i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.bj.e.127.1		4
3.2	odd	2		546.2.s.c.127.2	yes	4
13.4	even	6	inner	1638.2.bj.e.1135.1		4
39.2	even	12		7098.2.a.bz.1.2		2
39.11	even	12		7098.2.a.bn.1.1		2
39.17	odd	6		546.2.s.c.43.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.s.c.43.2	✓	4	39.17	odd	6
546.2.s.c.127.2	yes	4	3.2	odd	2
1638.2.bj.e.127.1		4	1.1	even	1	trivial
1638.2.bj.e.1135.1		4	13.4	even	6	inner
7098.2.a.bn.1.1		2	39.11	even	12
7098.2.a.bz.1.2		2	39.2	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} -3.46410i q^{5} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(1.73205 + 3.00000i) q^{10} +(-3.46410 + 2.00000i) q^{11} +(2.59808 + 2.50000i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.23205 + 5.59808i) q^{17} +(6.46410 + 3.73205i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(2.00000 - 3.46410i) q^{22} +(-2.86603 - 4.96410i) q^{23} -7.00000 q^{25} +(-3.50000 - 0.866025i) q^{26} +(-0.866025 + 0.500000i) q^{28} +(4.00000 + 6.92820i) q^{29} +6.46410i q^{31} +(0.866025 + 0.500000i) q^{32} -6.46410i q^{34} +(-1.73205 + 3.00000i) q^{35} +(-4.26795 + 2.46410i) q^{37} -7.46410 q^{38} +3.46410 q^{40} +(6.00000 - 3.46410i) q^{41} +(2.23205 - 3.86603i) q^{43} +4.00000i q^{44} +(4.96410 + 2.86603i) q^{46} +0.535898i q^{47} +(0.500000 + 0.866025i) q^{49} +(6.06218 - 3.50000i) q^{50} +(3.46410 - 1.00000i) q^{52} +8.26795 q^{53} +(6.92820 + 12.0000i) q^{55} +(0.500000 - 0.866025i) q^{56} +(-6.92820 - 4.00000i) q^{58} +(5.42820 + 3.13397i) q^{59} +(2.59808 - 4.50000i) q^{61} +(-3.23205 - 5.59808i) q^{62} -1.00000 q^{64} +(8.66025 - 9.00000i) q^{65} +(6.23205 - 3.59808i) q^{67} +(3.23205 + 5.59808i) q^{68} -3.46410i q^{70} +(-1.66987 - 0.964102i) q^{71} -10.9282i q^{73} +(2.46410 - 4.26795i) q^{74} +(6.46410 - 3.73205i) q^{76} +4.00000 q^{77} -9.46410 q^{79} +(-3.00000 + 1.73205i) q^{80} +(-3.46410 + 6.00000i) q^{82} +1.73205i q^{83} +(19.3923 + 11.1962i) q^{85} +4.46410i q^{86} +(-2.00000 - 3.46410i) q^{88} +(10.1603 - 5.86603i) q^{89} +(-1.00000 - 3.46410i) q^{91} -5.73205 q^{92} +(-0.267949 - 0.464102i) q^{94} +(12.9282 - 22.3923i) q^{95} +(10.7321 + 6.19615i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4}+O(q^{10}) \) 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

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