LMFDB - Embedded newform 1638.2.r.o.1387.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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, 2]))

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

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

chi := DirichletCharacter("1638.757");

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.r (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1387.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1638.1387
Dual form			1638.2.r.o.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(2.00000 - 3.46410i) q^{11} +(3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-2.00000 + 3.46410i) q^{23} +4.00000 q^{25} +(2.50000 - 2.59808i) q^{26} +(0.500000 - 0.866025i) q^{28} +(-4.50000 + 7.79423i) q^{29} +(0.500000 + 0.866025i) q^{32} -5.00000 q^{34} +(-1.50000 - 2.59808i) q^{35} +(-3.50000 + 6.06218i) q^{37} -4.00000 q^{38} +3.00000 q^{40} +(3.50000 - 6.06218i) q^{41} +(-4.00000 - 6.92820i) q^{43} -4.00000 q^{44} +(2.00000 + 3.46410i) q^{46} -12.0000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-1.00000 - 3.46410i) q^{52} -7.00000 q^{53} +(-6.00000 + 10.3923i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(4.50000 + 7.79423i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-3.50000 - 6.06218i) q^{61} +1.00000 q^{64} +(-10.5000 - 2.59808i) q^{65} +(-6.00000 + 10.3923i) q^{67} +(-2.50000 + 4.33013i) q^{68} -3.00000 q^{70} +(6.00000 + 10.3923i) q^{71} -1.00000 q^{73} +(3.50000 + 6.06218i) q^{74} +(-2.00000 + 3.46410i) q^{76} +4.00000 q^{77} -16.0000 q^{79} +(1.50000 - 2.59808i) q^{80} +(-3.50000 - 6.06218i) q^{82} +8.00000 q^{83} +(7.50000 + 12.9904i) q^{85} -8.00000 q^{86} +(-2.00000 + 3.46410i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(1.00000 + 3.46410i) q^{91} +4.00000 q^{92} +(-6.00000 + 10.3923i) q^{94} +(6.00000 + 10.3923i) q^{95} +(-9.00000 - 15.5885i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 6 q^{5} + q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 6 * q^5 + q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 6 q^{5} + q^{7} - 2 q^{8} - 3 q^{10} + 4 q^{11} + 7 q^{13} + 2 q^{14} - q^{16} - 5 q^{17} - 4 q^{19} + 3 q^{20} - 4 q^{22} - 4 q^{23} + 8 q^{25} + 5 q^{26} + q^{28} - 9 q^{29} + q^{32} - 10 q^{34} - 3 q^{35} - 7 q^{37} - 8 q^{38} + 6 q^{40} + 7 q^{41} - 8 q^{43} - 8 q^{44} + 4 q^{46} - 24 q^{47} - q^{49} + 4 q^{50} - 2 q^{52} - 14 q^{53} - 12 q^{55} - q^{56} + 9 q^{58} - 8 q^{59} - 7 q^{61} + 2 q^{64} - 21 q^{65} - 12 q^{67} - 5 q^{68} - 6 q^{70} + 12 q^{71} - 2 q^{73} + 7 q^{74} - 4 q^{76} + 8 q^{77} - 32 q^{79} + 3 q^{80} - 7 q^{82} + 16 q^{83} + 15 q^{85} - 16 q^{86} - 4 q^{88} - 6 q^{89} + 2 q^{91} + 8 q^{92} - 12 q^{94} + 12 q^{95} - 18 q^{97} + q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 6 * q^5 + q^7 - 2 * q^8 - 3 * q^10 + 4 * q^11 + 7 * q^13 + 2 * q^14 - q^16 - 5 * q^17 - 4 * q^19 + 3 * q^20 - 4 * q^22 - 4 * q^23 + 8 * q^25 + 5 * q^26 + q^28 - 9 * q^29 + q^32 - 10 * q^34 - 3 * q^35 - 7 * q^37 - 8 * q^38 + 6 * q^40 + 7 * q^41 - 8 * q^43 - 8 * q^44 + 4 * q^46 - 24 * q^47 - q^49 + 4 * q^50 - 2 * q^52 - 14 * q^53 - 12 * q^55 - q^56 + 9 * q^58 - 8 * q^59 - 7 * q^61 + 2 * q^64 - 21 * q^65 - 12 * q^67 - 5 * q^68 - 6 * q^70 + 12 * q^71 - 2 * q^73 + 7 * q^74 - 4 * q^76 + 8 * q^77 - 32 * q^79 + 3 * q^80 - 7 * q^82 + 16 * q^83 + 15 * q^85 - 16 * q^86 - 4 * q^88 - 6 * q^89 + 2 * q^91 + 8 * q^92 - 12 * q^94 + 12 * q^95 - 18 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$		0			0
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	−0.991838	−	0.127502i	$-0.959304\pi$
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	0.385499	−	0.922708i	$-0.374029\pi$
$18$		0			0
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$		0			0
$22$	−2.00000	−	3.46410i	−0.426401	−	0.738549i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	2.50000	−	2.59808i	0.490290	−	0.509525i
$27$		0			0
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−5.00000			−0.857493
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$		0			0
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$	3.00000			0.474342
$41$	3.50000	−	6.06218i	0.546608	−	0.946753i	−0.451896	−	0.892071i	$-0.649252\pi$
$41$	3.50000	−	6.06218i	0.546608	−	0.946753i	0.998504	−	0.0546823i	$-0.0174146\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	−4.00000			−0.603023
$45$		0			0
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	−12.0000			−1.75038			−0.875190	−	0.483779i	$-0.839264\pi$
$47$	−12.0000			−1.75038			−0.875190	+	0.483779i	$0.839264\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		0			0
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$	−7.00000			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$53$	−7.00000			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$54$		0			0
$55$	−6.00000	+	10.3923i	−0.809040	+	1.40130i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$		0			0
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	−10.5000	−	2.59808i	−1.30236	−	0.322252i
$66$		0			0
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$	−2.50000	+	4.33013i	−0.303170	+	0.525105i
$69$		0			0
$70$	−3.00000			−0.358569
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$		0			0
$73$	−1.00000			−0.117041			−0.0585206	−	0.998286i	$-0.518638\pi$
$73$	−1.00000			−0.117041			−0.0585206	+	0.998286i	$0.518638\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$		0			0
$76$	−2.00000	+	3.46410i	−0.229416	+	0.397360i
$77$	4.00000			0.455842
$78$		0			0
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$	1.50000	−	2.59808i	0.167705	−	0.290474i
$81$		0			0
$82$	−3.50000	−	6.06218i	−0.386510	−	0.669456i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$		0			0
$85$	7.50000	+	12.9904i	0.813489	+	1.40900i
$86$	−8.00000			−0.862662
$87$		0			0
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$		0			0
$91$	1.00000	+	3.46410i	0.104828	+	0.363137i
$92$	4.00000			0.417029
$93$		0			0
$94$	−6.00000	+	10.3923i	−0.618853	+	1.07188i
$95$	6.00000	+	10.3923i	0.615587	+	1.06623i
$96$		0			0
$97$	−9.00000	−	15.5885i	−0.913812	−	1.58277i	−0.808632	−	0.588315i	$-0.799792\pi$
$97$	−9.00000	−	15.5885i	−0.913812	−	1.58277i	−0.105180	−	0.994453i	$-0.533542\pi$
$98$	0.500000	+	0.866025i	0.0505076	+	0.0874818i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$		0			0
$106$	−3.50000	+	6.06218i	−0.339950	+	0.588811i
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$	6.00000	+	10.3923i	0.572078	+	0.990867i
$111$		0			0
$112$	−1.00000			−0.0944911
$113$	−2.50000	−	4.33013i	−0.235180	−	0.407344i	0.724145	−	0.689648i	$-0.242235\pi$
$113$	−2.50000	−	4.33013i	−0.235180	−	0.407344i	−0.959325	+	0.282304i	$0.908901\pi$
$114$		0			0
$115$	6.00000	−	10.3923i	0.559503	−	0.969087i
$116$	9.00000			0.835629
$117$		0			0
$118$	−8.00000			−0.736460
$119$	2.50000	−	4.33013i	0.229175	−	0.396942i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−7.00000			−0.633750
$123$		0			0
$124$		0			0
$125$	3.00000			0.268328
$126$		0			0
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	−0.632166	−	0.774833i	$-0.717834\pi$
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511671\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−7.50000	+	7.79423i	−0.657794	+	0.683599i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	6.00000	+	10.3923i	0.518321	+	0.897758i
$135$		0			0
$136$	2.50000	+	4.33013i	0.214373	+	0.371305i
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	0.922961	−	0.384893i	$-0.125762\pi$
$137$	1.50000	+	2.59808i	0.128154	+	0.221969i	−0.794808	+	0.606861i	$0.792428\pi$
$138$		0			0
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$	−1.50000	+	2.59808i	−0.126773	+	0.219578i
$141$		0			0
$142$	12.0000			1.00702
$143$	10.0000	−	10.3923i	0.836242	−	0.869048i
$144$		0			0
$145$	13.5000	−	23.3827i	1.12111	−	1.94183i
$146$	−0.500000	+	0.866025i	−0.0413803	+	0.0716728i
$147$		0			0
$148$	7.00000			0.575396
$149$	3.50000	+	6.06218i	0.286731	+	0.496633i	0.973028	−	0.230689i	$-0.0740980\pi$
$149$	3.50000	+	6.06218i	0.286731	+	0.496633i	−0.686296	+	0.727322i	$0.740765\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$		0			0
$154$	2.00000	−	3.46410i	0.161165	−	0.279145i
$155$		0			0
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	−8.00000	+	13.8564i	−0.636446	+	1.10236i
$159$		0			0
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$	−4.00000			−0.315244
$162$		0			0
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−7.00000			−0.546608
$165$		0			0
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	−0.978259	−	0.207385i	$-0.933505\pi$
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	0.668730	+	0.743505i	$0.266838\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	15.0000			1.15045
$171$		0			0
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		0			0
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	2.00000	+	3.46410i	0.150756	+	0.261116i
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	−0.201613	−	0.979465i	$-0.564618\pi$
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	0.949048	−	0.315130i	$-0.102048\pi$
$180$		0			0
$181$	−5.00000			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$181$	−5.00000			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$182$	3.50000	+	0.866025i	0.259437	+	0.0641941i
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	10.5000	−	18.1865i	0.771975	−	1.33710i
$186$		0			0
$187$	−20.0000			−1.46254
$188$	6.00000	+	10.3923i	0.437595	+	0.757937i
$189$		0			0
$190$	12.0000			0.870572
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$		0			0
$193$	−9.50000	+	16.4545i	−0.683825	+	1.18442i	0.289980	+	0.957033i	$0.406351\pi$
$193$	−9.50000	+	16.4545i	−0.683825	+	1.18442i	−0.973805	+	0.227387i	$0.926982\pi$
$194$	−18.0000			−1.29232
$195$		0			0
$196$	1.00000			0.0714286
$197$	11.0000	−	19.0526i	0.783718	−	1.35744i	−0.146045	−	0.989278i	$-0.546654\pi$
$197$	11.0000	−	19.0526i	0.783718	−	1.35744i	0.929762	−	0.368161i	$-0.120012\pi$
$198$		0			0
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$	−4.00000			−0.282843
$201$		0			0
$202$	−1.50000	−	2.59808i	−0.105540	−	0.182800i
$203$	−9.00000			−0.631676
$204$		0			0
$205$	−10.5000	+	18.1865i	−0.733352	+	1.27020i
$206$	−2.00000	+	3.46410i	−0.139347	+	0.241355i
$207$		0			0
$208$	−2.50000	+	2.59808i	−0.173344	+	0.180144i
$209$	−16.0000			−1.10674
$210$		0			0
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	3.50000	+	6.06218i	0.240381	+	0.416352i
$213$		0			0
$214$		0			0
$215$	12.0000	+	20.7846i	0.818393	+	1.41750i
$216$		0			0
$217$		0			0
$218$	7.00000	−	12.1244i	0.474100	−	0.821165i
$219$		0			0
$220$	12.0000			0.809040
$221$	−5.00000	−	17.3205i	−0.336336	−	1.16510i
$222$		0			0
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.167412	−	0.985887i	$-0.446459\pi$
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.770097	−	0.637927i	$-0.220208\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$		0			0
$226$	−5.00000			−0.332595
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	0.921903	+	0.387421i	$0.126634\pi$
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	−0.125435	+	0.992102i	$0.540033\pi$
$228$		0			0
$229$	6.00000			0.396491			0.198246	−	0.980152i	$-0.436476\pi$
$229$	6.00000			0.396491			0.198246	+	0.980152i	$0.436476\pi$
$230$	−6.00000	−	10.3923i	−0.395628	−	0.685248i
$231$		0			0
$232$	4.50000	−	7.79423i	0.295439	−	0.511716i
$233$	6.00000			0.393073			0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000			0.393073			0.196537	+	0.980497i	$0.437031\pi$
$234$		0			0
$235$	36.0000			2.34838
$236$	−4.00000	+	6.92820i	−0.260378	+	0.450988i
$237$		0			0
$238$	−2.50000	−	4.33013i	−0.162051	−	0.280680i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$		0			0
$241$	4.50000	+	7.79423i	0.289870	+	0.502070i	0.973779	−	0.227498i	$-0.0730544\pi$
$241$	4.50000	+	7.79423i	0.289870	+	0.502070i	−0.683908	+	0.729568i	$0.739721\pi$
$242$	−5.00000			−0.321412
$243$		0			0
$244$	−3.50000	+	6.06218i	−0.224065	+	0.388091i
$245$	1.50000	−	2.59808i	0.0958315	−	0.165985i
$246$		0			0
$247$	−4.00000	−	13.8564i	−0.254514	−	0.881662i
$248$		0			0
$249$		0			0
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$		0			0
$253$	8.00000	+	13.8564i	0.502956	+	0.871145i
$254$	−4.00000	−	6.92820i	−0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.50000	−	6.06218i	0.218324	−	0.378148i	−0.735972	−	0.677012i	$-0.763274\pi$
$257$	3.50000	−	6.06218i	0.218324	−	0.378148i	0.954296	+	0.298864i	$0.0966077\pi$
$258$		0			0
$259$	−7.00000			−0.434959
$260$	3.00000	+	10.3923i	0.186052	+	0.644503i
$261$		0			0
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	4.00000	−	6.92820i	0.246651	−	0.427211i	−0.715944	−	0.698158i	$-0.754003\pi$
$263$	4.00000	−	6.92820i	0.246651	−	0.427211i	0.962594	+	0.270947i	$0.0873367\pi$
$264$		0			0
$265$	21.0000			1.29002
$266$	−2.00000	−	3.46410i	−0.122628	−	0.212398i
$267$		0			0
$268$	12.0000			0.733017
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$		0			0
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	0.228380	+	0.973572i	$0.426657\pi$
$271$	−12.0000	+	20.7846i	−0.728948	+	1.26258i	−0.957328	+	0.289003i	$0.906676\pi$
$272$	5.00000			0.303170
$273$		0			0
$274$	3.00000			0.181237
$275$	8.00000	−	13.8564i	0.482418	−	0.835573i
$276$		0			0
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	−0.996484	−	0.0837823i	$-0.973300\pi$
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	0.425684	−	0.904872i	$-0.360033\pi$
$278$	−4.00000			−0.239904
$279$		0			0
$280$	1.50000	+	2.59808i	0.0896421	+	0.155265i
$281$	−15.0000			−0.894825			−0.447412	−	0.894328i	$-0.647654\pi$
$281$	−15.0000			−0.894825			−0.447412	+	0.894328i	$0.647654\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$	−4.00000	−	13.8564i	−0.236525	−	0.819346i
$287$	7.00000			0.413197
$288$		0			0
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$	−13.5000	−	23.3827i	−0.792747	−	1.37308i
$291$		0			0
$292$	0.500000	+	0.866025i	0.0292603	+	0.0506803i
$293$	−16.5000	−	28.5788i	−0.963940	−	1.66959i	−0.712436	−	0.701737i	$-0.752408\pi$
$293$	−16.5000	−	28.5788i	−0.963940	−	1.66959i	−0.251505	−	0.967856i	$-0.580925\pi$
$294$		0			0
$295$	12.0000	+	20.7846i	0.698667	+	1.21013i
$296$	3.50000	−	6.06218i	0.203433	−	0.352357i
$297$		0			0
$298$	7.00000			0.405499
$299$	−10.0000	+	10.3923i	−0.578315	+	0.601003i
$300$		0			0
$301$	4.00000	−	6.92820i	0.230556	−	0.399335i
$302$	−4.00000	+	6.92820i	−0.230174	+	0.398673i
$303$		0			0
$304$	4.00000			0.229416
$305$	10.5000	+	18.1865i	0.601228	+	1.04136i
$306$		0			0
$307$	4.00000			0.228292			0.114146	−	0.993464i	$-0.463587\pi$
$307$	4.00000			0.228292			0.114146	+	0.993464i	$0.463587\pi$
$308$	−2.00000	−	3.46410i	−0.113961	−	0.197386i
$309$		0			0
$310$		0			0
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	−6.50000	+	11.2583i	−0.366816	+	0.635344i
$315$		0			0
$316$	8.00000	+	13.8564i	0.450035	+	0.779484i
$317$	−35.0000			−1.96580			−0.982898	−	0.184151i	$-0.941046\pi$
$317$	−35.0000			−1.96580			−0.982898	+	0.184151i	$0.941046\pi$
$318$		0			0
$319$	18.0000	+	31.1769i	1.00781	+	1.74557i
$320$	−3.00000			−0.167705
$321$		0			0
$322$	−2.00000	+	3.46410i	−0.111456	+	0.193047i
$323$	−10.0000	+	17.3205i	−0.556415	+	0.963739i
$324$		0			0
$325$	14.0000	+	3.46410i	0.776580	+	0.192154i
$326$	−4.00000			−0.221540
$327$		0			0
$328$	−3.50000	+	6.06218i	−0.193255	+	0.334728i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$	−4.00000	−	6.92820i	−0.219529	−	0.380235i
$333$		0			0
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	18.0000	−	31.1769i	0.983445	−	1.70338i
$336$		0			0
$337$	−9.00000			−0.490261			−0.245131	−	0.969490i	$-0.578831\pi$
$337$	−9.00000			−0.490261			−0.245131	+	0.969490i	$0.578831\pi$
$338$	11.0000	−	6.92820i	0.598321	−	0.376845i
$339$		0			0
$340$	7.50000	−	12.9904i	0.406745	−	0.704502i
$341$		0			0
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	14.0000			0.752645
$347$	10.0000	+	17.3205i	0.536828	+	0.929814i	0.999072	+	0.0430610i	$0.0137110\pi$
$347$	10.0000	+	17.3205i	0.536828	+	0.929814i	−0.462244	+	0.886753i	$0.652956\pi$
$348$		0			0
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	−0.990282	−	0.139072i	$-0.955588\pi$
$349$	−7.00000	+	12.1244i	−0.374701	+	0.649002i	0.615581	+	0.788074i	$0.288921\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	4.00000			0.213201
$353$	−12.5000	+	21.6506i	−0.665308	+	1.15235i	0.313894	+	0.949458i	$0.398366\pi$
$353$	−12.5000	+	21.6506i	−0.665308	+	1.15235i	−0.979202	+	0.202889i	$0.934967\pi$
$354$		0			0
$355$	−18.0000	−	31.1769i	−0.955341	−	1.65470i
$356$	6.00000			0.317999
$357$		0			0
$358$	−10.0000	−	17.3205i	−0.528516	−	0.915417i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−2.50000	+	4.33013i	−0.131397	+	0.227586i
$363$		0			0
$364$	2.50000	−	2.59808i	0.131036	−	0.136176i
$365$	3.00000			0.157027
$366$		0			0
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$	−2.00000	−	3.46410i	−0.104257	−	0.180579i
$369$		0			0
$370$	−10.5000	−	18.1865i	−0.545869	−	0.945473i
$371$	−3.50000	−	6.06218i	−0.181711	−	0.314733i
$372$		0			0
$373$	−7.50000	−	12.9904i	−0.388335	−	0.672616i	0.603890	−	0.797067i	$-0.293616\pi$
$373$	−7.50000	−	12.9904i	−0.388335	−	0.672616i	−0.992226	+	0.124451i	$0.960283\pi$
$374$	−10.0000	+	17.3205i	−0.517088	+	0.895622i
$375$		0			0
$376$	12.0000			0.618853
$377$	−22.5000	+	23.3827i	−1.15881	+	1.20427i
$378$		0			0
$379$	14.0000	−	24.2487i	0.719132	−	1.24557i	−0.242213	−	0.970223i	$-0.577873\pi$
$379$	14.0000	−	24.2487i	0.719132	−	1.24557i	0.961344	−	0.275349i	$-0.0887935\pi$
$380$	6.00000	−	10.3923i	0.307794	−	0.533114i
$381$		0			0
$382$	−24.0000			−1.22795
$383$	−14.0000	−	24.2487i	−0.715367	−	1.23905i	−0.962818	−	0.270151i	$-0.912926\pi$
$383$	−14.0000	−	24.2487i	−0.715367	−	1.23905i	0.247451	−	0.968900i	$-0.420407\pi$
$384$		0			0
$385$	−12.0000			−0.611577
$386$	9.50000	+	16.4545i	0.483537	+	0.837511i
$387$		0			0
$388$	−9.00000	+	15.5885i	−0.456906	+	0.791384i
$389$	−7.00000			−0.354914			−0.177457	−	0.984129i	$-0.556787\pi$
$389$	−7.00000			−0.354914			−0.177457	+	0.984129i	$0.556787\pi$
$390$		0			0
$391$	20.0000			1.01144
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		0			0
$394$	−11.0000	−	19.0526i	−0.554172	−	0.959854i
$395$	48.0000			2.41514
$396$		0			0
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	0.890028	−	0.455905i	$-0.150684\pi$
$397$	1.00000	+	1.73205i	0.0501886	+	0.0869291i	−0.839840	+	0.542834i	$0.817351\pi$
$398$		0			0
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	−0.996371	−	0.0851195i	$-0.972873\pi$
$401$	−8.50000	+	14.7224i	−0.424470	+	0.735203i	0.571901	+	0.820323i	$0.306206\pi$
$402$		0			0
$403$		0			0
$404$	−3.00000			−0.149256
$405$		0			0
$406$	−4.50000	+	7.79423i	−0.223331	+	0.386821i
$407$	14.0000	+	24.2487i	0.693954	+	1.20196i
$408$		0			0
$409$	6.50000	+	11.2583i	0.321404	+	0.556689i	0.980778	−	0.195127i	$-0.0625118\pi$
$409$	6.50000	+	11.2583i	0.321404	+	0.556689i	−0.659374	+	0.751815i	$0.729178\pi$
$410$	10.5000	+	18.1865i	0.518558	+	0.898169i
$411$		0			0
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$	4.00000	−	6.92820i	0.196827	−	0.340915i
$414$		0			0
$415$	−24.0000			−1.17811
$416$	1.00000	+	3.46410i	0.0490290	+	0.169842i
$417$		0			0
$418$	−8.00000	+	13.8564i	−0.391293	+	0.677739i
$419$	−8.00000	+	13.8564i	−0.390826	+	0.676930i	−0.992559	−	0.121768i	$-0.961144\pi$
$419$	−8.00000	+	13.8564i	−0.390826	+	0.676930i	0.601733	+	0.798697i	$0.294477\pi$
$420$		0			0
$421$	−1.00000			−0.0487370			−0.0243685	−	0.999703i	$-0.507758\pi$
$421$	−1.00000			−0.0487370			−0.0243685	+	0.999703i	$0.507758\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$		0			0
$424$	7.00000			0.339950
$425$	−10.0000	−	17.3205i	−0.485071	−	0.840168i
$426$		0			0
$427$	3.50000	−	6.06218i	0.169377	−	0.293369i
$428$		0			0
$429$		0			0
$430$	24.0000			1.15738
$431$	−2.00000	+	3.46410i	−0.0963366	+	0.166860i	−0.910166	−	0.414244i	$-0.864046\pi$
$431$	−2.00000	+	3.46410i	−0.0963366	+	0.166860i	0.813829	+	0.581104i	$0.197379\pi$
$432$		0			0
$433$	−15.5000	−	26.8468i	−0.744882	−	1.29017i	−0.950250	−	0.311489i	$-0.899172\pi$
$433$	−15.5000	−	26.8468i	−0.744882	−	1.29017i	0.205367	−	0.978685i	$-0.434161\pi$
$434$		0			0
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	16.0000			0.765384
$438$		0			0
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$	6.00000	−	10.3923i	0.286039	−	0.495434i
$441$		0			0
$442$	−17.5000	−	4.33013i	−0.832390	−	0.205963i
$443$	16.0000			0.760183			0.380091	−	0.924949i	$-0.375893\pi$
$443$	16.0000			0.760183			0.380091	+	0.924949i	$0.375893\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−14.0000	−	24.2487i	−0.662919	−	1.14821i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−7.00000	−	12.1244i	−0.330350	−	0.572184i	0.652230	−	0.758021i	$-0.273834\pi$
$449$	−7.00000	−	12.1244i	−0.330350	−	0.572184i	−0.982581	+	0.185837i	$0.940500\pi$
$450$		0			0
$451$	−14.0000	−	24.2487i	−0.659234	−	1.14183i
$452$	−2.50000	+	4.33013i	−0.117590	+	0.203672i
$453$		0			0
$454$	24.0000			1.12638
$455$	−3.00000	−	10.3923i	−0.140642	−	0.487199i
$456$		0			0
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$	3.00000	−	5.19615i	0.140181	−	0.242800i
$459$		0			0
$460$	−12.0000			−0.559503
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	0.997871	−	0.0652135i	$-0.0207728\pi$
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	−0.555412	+	0.831575i	$0.687440\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	−4.50000	−	7.79423i	−0.208907	−	0.361838i
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	−12.0000			−0.554109
$470$	18.0000	−	31.1769i	0.830278	−	1.43808i
$471$		0			0
$472$	4.00000	+	6.92820i	0.184115	+	0.318896i
$473$	−32.0000			−1.47136
$474$		0			0
$475$	−8.00000	−	13.8564i	−0.367065	−	0.635776i
$476$	−5.00000			−0.229175
$477$		0			0
$478$	2.00000	−	3.46410i	0.0914779	−	0.158444i
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	−0.345827	−	0.938298i	$-0.612402\pi$
$479$	14.0000	−	24.2487i	0.639676	−	1.10795i	0.985504	−	0.169654i	$-0.0542649\pi$
$480$		0			0
$481$	−17.5000	+	18.1865i	−0.797931	+	0.829235i
$482$	9.00000			0.409939
$483$		0			0
$484$	−2.50000	+	4.33013i	−0.113636	+	0.196824i
$485$	27.0000	+	46.7654i	1.22601	+	2.12351i
$486$		0			0
$487$	−2.00000	−	3.46410i	−0.0906287	−	0.156973i	0.817147	−	0.576429i	$-0.195554\pi$
$487$	−2.00000	−	3.46410i	−0.0906287	−	0.156973i	−0.907776	+	0.419456i	$0.862221\pi$
$488$	3.50000	+	6.06218i	0.158438	+	0.274422i
$489$		0			0
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	10.0000	−	17.3205i	0.451294	−	0.781664i	−0.547173	−	0.837020i	$-0.684296\pi$
$491$	10.0000	−	17.3205i	0.451294	−	0.781664i	0.998467	+	0.0553560i	$0.0176294\pi$
$492$		0			0
$493$	45.0000			2.02670
$494$	−14.0000	−	3.46410i	−0.629890	−	0.155857i
$495$		0			0
$496$		0			0
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$		0			0
$502$	−12.0000			−0.535586
$503$	−12.0000	−	20.7846i	−0.535054	−	0.926740i	−0.999161	−	0.0409609i	$-0.986958\pi$
$503$	−12.0000	−	20.7846i	−0.535054	−	0.926740i	0.464107	−	0.885779i	$-0.346375\pi$
$504$		0			0
$505$	−4.50000	+	7.79423i	−0.200247	+	0.346839i
$506$	16.0000			0.711287
$507$		0			0
$508$	−8.00000			−0.354943
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	−0.650556	−	0.759458i	$-0.725464\pi$
$509$	7.50000	−	12.9904i	0.332432	−	0.575789i	0.982988	+	0.183669i	$0.0587976\pi$
$510$		0			0
$511$	−0.500000	−	0.866025i	−0.0221187	−	0.0383107i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.50000	−	6.06218i	−0.154378	−	0.267391i
$515$	12.0000			0.528783
$516$		0			0
$517$	−24.0000	+	41.5692i	−1.05552	+	1.82821i
$518$	−3.50000	+	6.06218i	−0.153781	+	0.266357i
$519$		0			0
$520$	10.5000	+	2.59808i	0.460455	+	0.113933i
$521$	17.0000			0.744784			0.372392	−	0.928076i	$-0.378538\pi$
$521$	17.0000			0.744784			0.372392	+	0.928076i	$0.378538\pi$
$522$		0			0
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	−4.00000	−	6.92820i	−0.174408	−	0.302084i
$527$		0			0
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	10.5000	−	18.1865i	0.456091	−	0.789973i
$531$		0			0
$532$	−4.00000			−0.173422
$533$	17.5000	−	18.1865i	0.758009	−	0.787746i
$534$		0			0
$535$		0			0
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$		0			0
$538$	14.0000			0.603583
$539$	2.00000	+	3.46410i	0.0861461	+	0.149209i
$540$		0			0
$541$	43.0000			1.84871			0.924357	−	0.381528i	$-0.124602\pi$
$541$	43.0000			1.84871			0.924357	+	0.381528i	$0.124602\pi$
$542$	12.0000	+	20.7846i	0.515444	+	0.892775i
$543$		0			0
$544$	2.50000	−	4.33013i	0.107187	−	0.185653i
$545$	−42.0000			−1.79908
$546$		0			0
$547$	16.0000			0.684111			0.342055	−	0.939680i	$-0.388877\pi$
$547$	16.0000			0.684111			0.342055	+	0.939680i	$0.388877\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$		0			0
$550$	−8.00000	−	13.8564i	−0.341121	−	0.590839i
$551$	36.0000			1.53365
$552$		0			0
$553$	−8.00000	−	13.8564i	−0.340195	−	0.589234i
$554$	−19.0000			−0.807233
$555$		0			0
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	0.269642	+	0.962961i	$0.413095\pi$
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	−0.968769	+	0.247964i	$0.920239\pi$
$558$		0			0
$559$	−8.00000	−	27.7128i	−0.338364	−	1.17213i
$560$	3.00000			0.126773
$561$		0			0
$562$	−7.50000	+	12.9904i	−0.316368	+	0.547966i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$	7.50000	+	12.9904i	0.315527	+	0.546509i
$566$	−2.00000	−	3.46410i	−0.0840663	−	0.145607i
$567$		0			0
$568$	−6.00000	−	10.3923i	−0.251754	−	0.436051i
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	−0.999018	−	0.0443003i	$-0.985894\pi$
$569$	−11.0000	+	19.0526i	−0.461144	+	0.798725i	0.537874	+	0.843025i	$0.319228\pi$
$570$		0			0
$571$	40.0000			1.67395			0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000			1.67395			0.836974	+	0.547243i	$0.184323\pi$
$572$	−14.0000	−	3.46410i	−0.585369	−	0.144841i
$573$		0			0
$574$	3.50000	−	6.06218i	0.146087	−	0.253030i
$575$	−8.00000	+	13.8564i	−0.333623	+	0.577852i
$576$		0			0
$577$	−5.00000			−0.208153			−0.104076	−	0.994569i	$-0.533189\pi$
$577$	−5.00000			−0.208153			−0.104076	+	0.994569i	$0.533189\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$		0			0
$580$	−27.0000			−1.12111
$581$	4.00000	+	6.92820i	0.165948	+	0.287430i
$582$		0			0
$583$	−14.0000	+	24.2487i	−0.579821	+	1.00428i
$584$	1.00000			0.0413803
$585$		0			0
$586$	−33.0000			−1.36322
$587$	−12.0000	+	20.7846i	−0.495293	+	0.857873i	−0.999985	−	0.00542667i	$-0.998273\pi$
$587$	−12.0000	+	20.7846i	−0.495293	+	0.857873i	0.504692	+	0.863299i	$0.331606\pi$
$588$		0			0
$589$		0			0
$590$	24.0000			0.988064
$591$		0			0
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	33.0000			1.35515			0.677574	−	0.735455i	$-0.263031\pi$
$593$	33.0000			1.35515			0.677574	+	0.735455i	$0.263031\pi$
$594$		0			0
$595$	−7.50000	+	12.9904i	−0.307470	+	0.532554i
$596$	3.50000	−	6.06218i	0.143366	−	0.248316i
$597$		0			0
$598$	4.00000	+	13.8564i	0.163572	+	0.566631i
$599$	4.00000			0.163436			0.0817178	−	0.996656i	$-0.473959\pi$
$599$	4.00000			0.163436			0.0817178	+	0.996656i	$0.473959\pi$
$600$		0			0
$601$	8.50000	−	14.7224i	0.346722	−	0.600541i	−0.638943	−	0.769254i	$-0.720628\pi$
$601$	8.50000	−	14.7224i	0.346722	−	0.600541i	0.985665	+	0.168714i	$0.0539613\pi$
$602$	−4.00000	−	6.92820i	−0.163028	−	0.282372i
$603$		0			0
$604$	4.00000	+	6.92820i	0.162758	+	0.281905i
$605$	7.50000	+	12.9904i	0.304918	+	0.528134i
$606$		0			0
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	0.935713	−	0.352763i	$-0.114758\pi$
$607$	4.00000	+	6.92820i	0.162355	+	0.281207i	−0.773358	+	0.633970i	$0.781424\pi$
$608$	2.00000	−	3.46410i	0.0811107	−	0.140488i
$609$		0			0
$610$	21.0000			0.850265
$611$	−42.0000	−	10.3923i	−1.69914	−	0.420428i
$612$		0			0
$613$	0.500000	−	0.866025i	0.0201948	−	0.0349784i	−0.855751	−	0.517387i	$-0.826905\pi$
$613$	0.500000	−	0.866025i	0.0201948	−	0.0349784i	0.875946	+	0.482409i	$0.160238\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$		0			0
$616$	−4.00000			−0.161165
$617$	−16.5000	−	28.5788i	−0.664265	−	1.15054i	−0.979484	−	0.201522i	$-0.935411\pi$
$617$	−16.5000	−	28.5788i	−0.664265	−	1.15054i	0.315219	−	0.949019i	$-0.397922\pi$
$618$		0			0
$619$	−32.0000			−1.28619			−0.643094	−	0.765787i	$-0.722350\pi$
$619$	−32.0000			−1.28619			−0.643094	+	0.765787i	$0.722350\pi$
$620$		0			0
$621$		0			0
$622$	−4.00000	+	6.92820i	−0.160385	+	0.277796i
$623$	−6.00000			−0.240385
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−3.00000	+	5.19615i	−0.119904	+	0.207680i
$627$		0			0
$628$	6.50000	+	11.2583i	0.259378	+	0.449256i
$629$	35.0000			1.39554
$630$		0			0
$631$	20.0000	+	34.6410i	0.796187	+	1.37904i	0.922082	+	0.386994i	$0.126486\pi$
$631$	20.0000	+	34.6410i	0.796187	+	1.37904i	−0.125895	+	0.992044i	$0.540180\pi$
$632$	16.0000			0.636446
$633$		0			0
$634$	−17.5000	+	30.3109i	−0.695014	+	1.20380i
$635$	−12.0000	+	20.7846i	−0.476205	+	0.824812i
$636$		0			0
$637$	−2.50000	+	2.59808i	−0.0990536	+	0.102940i
$638$	36.0000			1.42525
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		0			0
$643$	−6.00000	−	10.3923i	−0.236617	−	0.409832i	0.723124	−	0.690718i	$-0.242705\pi$
$643$	−6.00000	−	10.3923i	−0.236617	−	0.409832i	−0.959741	+	0.280885i	$0.909372\pi$
$644$	2.00000	+	3.46410i	0.0788110	+	0.136505i
$645$		0			0
$646$	10.0000	+	17.3205i	0.393445	+	0.681466i
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	−0.723645	−	0.690172i	$-0.757535\pi$
$647$	6.00000	−	10.3923i	0.235884	−	0.408564i	0.959529	+	0.281609i	$0.0908680\pi$
$648$		0			0
$649$	−32.0000			−1.25611
$650$	10.0000	−	10.3923i	0.392232	−	0.407620i
$651$		0			0
$652$	−2.00000	+	3.46410i	−0.0783260	+	0.135665i
$653$	−17.0000	+	29.4449i	−0.665261	+	1.15227i	0.313953	+	0.949439i	$0.398347\pi$
$653$	−17.0000	+	29.4449i	−0.665261	+	1.15227i	−0.979214	+	0.202828i	$0.934987\pi$
$654$		0			0
$655$	−36.0000			−1.40664
$656$	3.50000	+	6.06218i	0.136652	+	0.236688i
$657$		0			0
$658$	−12.0000			−0.467809
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	0.500000	−	0.866025i	0.0194477	−	0.0336845i	−0.856138	−	0.516748i	$-0.827143\pi$
$661$	0.500000	−	0.866025i	0.0194477	−	0.0336845i	0.875585	+	0.483063i	$0.160476\pi$
$662$	20.0000			0.777322
$663$		0			0
$664$	−8.00000			−0.310460
$665$	−6.00000	+	10.3923i	−0.232670	+	0.402996i
$666$		0			0
$667$	−18.0000	−	31.1769i	−0.696963	−	1.20717i
$668$	8.00000			0.309529
$669$		0			0
$670$	−18.0000	−	31.1769i	−0.695401	−	1.20447i
$671$	−28.0000			−1.08093
$672$		0			0
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	−0.988968	−	0.148132i	$-0.952674\pi$
$673$	−9.50000	+	16.4545i	−0.366198	+	0.634274i	0.622770	+	0.782405i	$0.286007\pi$
$674$	−4.50000	+	7.79423i	−0.173334	+	0.300222i
$675$		0			0
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$	−22.0000			−0.845529			−0.422764	−	0.906240i	$-0.638940\pi$
$677$	−22.0000			−0.845529			−0.422764	+	0.906240i	$0.638940\pi$
$678$		0			0
$679$	9.00000	−	15.5885i	0.345388	−	0.598230i
$680$	−7.50000	−	12.9904i	−0.287612	−	0.498158i
$681$		0			0
$682$		0			0
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	0.991439	−	0.130573i	$-0.0416818\pi$
$683$	10.0000	+	17.3205i	0.382639	+	0.662751i	−0.608799	+	0.793324i	$0.708349\pi$
$684$		0			0
$685$	−4.50000	−	7.79423i	−0.171936	−	0.297802i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	8.00000			0.304997
$689$	−24.5000	−	6.06218i	−0.933376	−	0.230951i
$690$		0			0
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	−0.181584	−	0.983375i	$-0.558123\pi$
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	0.942420	−	0.334431i	$-0.108544\pi$
$692$	7.00000	−	12.1244i	0.266100	−	0.460899i
$693$		0			0
$694$	20.0000			0.759190
$695$	6.00000	+	10.3923i	0.227593	+	0.394203i
$696$		0			0
$697$	−35.0000			−1.32572
$698$	7.00000	+	12.1244i	0.264954	+	0.458914i
$699$		0			0
$700$	2.00000	−	3.46410i	0.0755929	−	0.130931i
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$		0			0
$703$	28.0000			1.05604
$704$	2.00000	−	3.46410i	0.0753778	−	0.130558i
$705$		0			0
$706$	12.5000	+	21.6506i	0.470444	+	0.814832i
$707$	3.00000			0.112827
$708$		0			0
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	0.875262	−	0.483650i	$-0.160689\pi$
$709$	0.500000	+	0.866025i	0.0187779	+	0.0325243i	−0.856484	+	0.516174i	$0.827356\pi$
$710$	−36.0000			−1.35106
$711$		0			0
$712$	3.00000	−	5.19615i	0.112430	−	0.194734i
$713$		0			0
$714$		0			0
$715$	−30.0000	+	31.1769i	−1.12194	+	1.16595i
$716$	−20.0000			−0.747435
$717$		0			0
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.833744	−	0.552151i	$-0.813807\pi$
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.0613050	−	0.998119i	$-0.519526\pi$
$720$		0			0
$721$	−2.00000	−	3.46410i	−0.0744839	−	0.129010i
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$		0			0
$724$	2.50000	+	4.33013i	0.0929118	+	0.160928i
$725$	−18.0000	+	31.1769i	−0.668503	+	1.15788i
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	−1.00000	−	3.46410i	−0.0370625	−	0.128388i
$729$		0			0
$730$	1.50000	−	2.59808i	0.0555175	−	0.0961591i
$731$	−20.0000	+	34.6410i	−0.739727	+	1.28124i
$732$		0			0
$733$	23.0000			0.849524			0.424762	−	0.905305i	$-0.360358\pi$
$733$	23.0000			0.849524			0.424762	+	0.905305i	$0.360358\pi$
$734$	−2.00000	−	3.46410i	−0.0738213	−	0.127862i
$735$		0			0
$736$	−4.00000			−0.147442
$737$	24.0000	+	41.5692i	0.884051	+	1.53122i
$738$		0			0
$739$	−4.00000	+	6.92820i	−0.147142	+	0.254858i	−0.930170	−	0.367129i	$-0.880341\pi$
$739$	−4.00000	+	6.92820i	−0.147142	+	0.254858i	0.783028	+	0.621987i	$0.213674\pi$
$740$	−21.0000			−0.771975
$741$		0			0
$742$	−7.00000			−0.256978
$743$	8.00000	−	13.8564i	0.293492	−	0.508342i	−0.681141	−	0.732152i	$-0.738516\pi$
$743$	8.00000	−	13.8564i	0.293492	−	0.508342i	0.974633	+	0.223810i	$0.0718494\pi$
$744$		0			0
$745$	−10.5000	−	18.1865i	−0.384690	−	0.666303i
$746$	−15.0000			−0.549189
$747$		0			0
$748$	10.0000	+	17.3205i	0.365636	+	0.633300i
$749$		0			0
$750$		0			0
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$		0			0
$754$	9.00000	+	31.1769i	0.327761	+	1.13540i
$755$	24.0000			0.873449
$756$		0			0
$757$	−19.0000	+	32.9090i	−0.690567	+	1.19610i	0.281086	+	0.959683i	$0.409305\pi$
$757$	−19.0000	+	32.9090i	−0.690567	+	1.19610i	−0.971652	+	0.236414i	$0.924028\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$		0			0
$760$	−6.00000	−	10.3923i	−0.217643	−	0.376969i
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	0.942306	−	0.334752i	$-0.108652\pi$
$761$	5.00000	+	8.66025i	0.181250	+	0.313934i	−0.761057	+	0.648686i	$0.775319\pi$
$762$		0			0
$763$	7.00000	+	12.1244i	0.253417	+	0.438931i
$764$	−12.0000	+	20.7846i	−0.434145	+	0.751961i
$765$		0			0
$766$	−28.0000			−1.01168
$767$	−8.00000	−	27.7128i	−0.288863	−	1.00065i
$768$		0			0
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.0760054	+	0.997107i	$0.524217\pi$
$769$	−25.0000	+	43.3013i	−0.901523	+	1.56148i	−0.825518	+	0.564376i	$0.809117\pi$
$770$	−6.00000	+	10.3923i	−0.216225	+	0.374513i
$771$		0			0
$772$	19.0000			0.683825
$773$	19.0000	+	32.9090i	0.683383	+	1.18365i	0.973942	+	0.226796i	$0.0728252\pi$
$773$	19.0000	+	32.9090i	0.683383	+	1.18365i	−0.290560	+	0.956857i	$0.593841\pi$
$774$		0			0
$775$		0			0
$776$	9.00000	+	15.5885i	0.323081	+	0.559593i
$777$		0			0
$778$	−3.50000	+	6.06218i	−0.125481	+	0.217340i
$779$	−28.0000			−1.00320
$780$		0			0
$781$	48.0000			1.71758
$782$	10.0000	−	17.3205i	0.357599	−	0.619380i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	39.0000			1.39197
$786$		0			0
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	0.963755	+	0.266788i	$0.0859624\pi$
$787$	20.0000	+	34.6410i	0.712923	+	1.23482i	−0.250832	+	0.968031i	$0.580704\pi$
$788$	−22.0000			−0.783718
$789$		0			0
$790$	24.0000	−	41.5692i	0.853882	−	1.47897i
$791$	2.50000	−	4.33013i	0.0888898	−	0.153962i
$792$		0			0
$793$	−7.00000	−	24.2487i	−0.248577	−	0.861097i
$794$	2.00000			0.0709773
$795$		0			0
$796$		0			0
$797$	15.0000	+	25.9808i	0.531327	+	0.920286i	0.999331	+	0.0365596i	$0.0116399\pi$
$797$	15.0000	+	25.9808i	0.531327	+	0.920286i	−0.468004	+	0.883726i	$0.655027\pi$
$798$		0			0
$799$	30.0000	+	51.9615i	1.06132	+	1.83827i
$800$	2.00000	+	3.46410i	0.0707107	+	0.122474i
$801$		0			0
$802$	8.50000	+	14.7224i	0.300145	+	0.519867i
$803$	−2.00000	+	3.46410i	−0.0705785	+	0.122245i
$804$		0			0
$805$	12.0000			0.422944
$806$		0			0
$807$		0			0
$808$	−1.50000	+	2.59808i	−0.0527698	+	0.0914000i
$809$	−2.50000	+	4.33013i	−0.0878953	+	0.152239i	−0.906621	−	0.421945i	$-0.861347\pi$
$809$	−2.50000	+	4.33013i	−0.0878953	+	0.152239i	0.818726	+	0.574184i	$0.194681\pi$
$810$		0			0
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$	4.50000	+	7.79423i	0.157919	+	0.273524i
$813$		0			0
$814$	28.0000			0.981399
$815$	6.00000	+	10.3923i	0.210171	+	0.364027i
$816$		0			0
$817$	−16.0000	+	27.7128i	−0.559769	+	0.969549i
$818$	13.0000			0.454534
$819$		0			0
$820$	21.0000			0.733352
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	−0.607714	−	0.794156i	$-0.707913\pi$
$821$	11.0000	−	19.0526i	0.383903	−	0.664939i	0.991616	+	0.129217i	$0.0412465\pi$
$822$		0			0
$823$	22.0000	+	38.1051i	0.766872	+	1.32826i	0.939251	+	0.343230i	$0.111521\pi$
$823$	22.0000	+	38.1051i	0.766872	+	1.32826i	−0.172379	+	0.985031i	$0.555146\pi$
$824$	4.00000			0.139347
$825$		0			0
$826$	−4.00000	−	6.92820i	−0.139178	−	0.241063i
$827$	24.0000			0.834562			0.417281	−	0.908778i	$-0.362983\pi$
$827$	24.0000			0.834562			0.417281	+	0.908778i	$0.362983\pi$
$828$		0			0
$829$	−15.5000	+	26.8468i	−0.538337	+	0.932427i	0.460657	+	0.887578i	$0.347614\pi$
$829$	−15.5000	+	26.8468i	−0.538337	+	0.932427i	−0.998994	+	0.0448490i	$0.985719\pi$
$830$	−12.0000	+	20.7846i	−0.416526	+	0.721444i
$831$		0			0
$832$	3.50000	+	0.866025i	0.121341	+	0.0300240i
$833$	5.00000			0.173240
$834$		0			0
$835$	12.0000	−	20.7846i	0.415277	−	0.719281i
$836$	8.00000	+	13.8564i	0.276686	+	0.479234i
$837$		0			0
$838$	8.00000	+	13.8564i	0.276355	+	0.478662i
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	−0.971682	−	0.236293i	$-0.924067\pi$
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	0.281205	−	0.959648i	$-0.409266\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	−0.500000	+	0.866025i	−0.0172311	+	0.0298452i
$843$		0			0
$844$	−8.00000			−0.275371
$845$	−34.5000	−	18.1865i	−1.18684	−	0.625636i
$846$		0			0
$847$	2.50000	−	4.33013i	0.0859010	−	0.148785i
$848$	3.50000	−	6.06218i	0.120190	−	0.208176i
$849$		0			0
$850$	−20.0000			−0.685994
$851$	−14.0000	−	24.2487i	−0.479914	−	0.831235i
$852$		0			0
$853$	−49.0000			−1.67773			−0.838864	−	0.544341i	$-0.816780\pi$
$853$	−49.0000			−1.67773			−0.838864	+	0.544341i	$0.816780\pi$
$854$	−3.50000	−	6.06218i	−0.119768	−	0.207443i
$855$		0			0
$856$		0			0
$857$	−31.0000			−1.05894			−0.529470	−	0.848329i	$-0.677609\pi$
$857$	−31.0000			−1.05894			−0.529470	+	0.848329i	$0.677609\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	12.0000	−	20.7846i	0.409197	−	0.708749i
$861$		0			0
$862$	2.00000	+	3.46410i	0.0681203	+	0.117988i
$863$	−12.0000			−0.408485			−0.204242	−	0.978920i	$-0.565473\pi$
$863$	−12.0000			−0.408485			−0.204242	+	0.978920i	$0.565473\pi$
$864$		0			0
$865$	−21.0000	−	36.3731i	−0.714021	−	1.23672i
$866$	−31.0000			−1.05342
$867$		0			0
$868$		0			0
$869$	−32.0000	+	55.4256i	−1.08553	+	1.88019i
$870$		0			0
$871$	−30.0000	+	31.1769i	−1.01651	+	1.05639i
$872$	−14.0000			−0.474100
$873$		0			0
$874$	8.00000	−	13.8564i	0.270604	−	0.468700i
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$		0			0
$877$	−1.50000	−	2.59808i	−0.0506514	−	0.0877308i	0.839588	−	0.543224i	$-0.182796\pi$
$877$	−1.50000	−	2.59808i	−0.0506514	−	0.0877308i	−0.890239	+	0.455493i	$0.849463\pi$
$878$	−8.00000	−	13.8564i	−0.269987	−	0.467631i
$879$		0			0
$880$	−6.00000	−	10.3923i	−0.202260	−	0.350325i
$881$	−20.5000	+	35.5070i	−0.690663	+	1.19626i	0.280959	+	0.959720i	$0.409348\pi$
$881$	−20.5000	+	35.5070i	−0.690663	+	1.19626i	−0.971621	+	0.236543i	$0.923986\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	−12.5000	+	12.9904i	−0.420420	+	0.436914i
$885$		0			0
$886$	8.00000	−	13.8564i	0.268765	−	0.465515i
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	−0.747539	−	0.664218i	$-0.768765\pi$
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	0.948999	+	0.315279i	$0.102098\pi$
$888$		0			0
$889$	8.00000			0.268311
$890$	−9.00000	−	15.5885i	−0.301681	−	0.522526i
$891$		0			0
$892$	−28.0000			−0.937509
$893$	24.0000	+	41.5692i	0.803129	+	1.39106i
$894$		0			0
$895$	−30.0000	+	51.9615i	−1.00279	+	1.73688i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−14.0000			−0.467186
$899$		0			0
$900$		0			0
$901$	17.5000	+	30.3109i	0.583010	+	1.00980i
$902$	−28.0000			−0.932298
$903$		0			0
$904$	2.50000	+	4.33013i	0.0831488	+	0.144018i
$905$	15.0000			0.498617
$906$		0			0
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	12.0000	−	20.7846i	0.398234	−	0.689761i
$909$		0			0
$910$	−10.5000	−	2.59808i	−0.348072	−	0.0861254i
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	16.0000	−	27.7128i	0.529523	−	0.917160i
$914$	−0.500000	−	0.866025i	−0.0165385	−	0.0286456i
$915$		0			0
$916$	−3.00000	−	5.19615i	−0.0991228	−	0.171686i
$917$	6.00000	+	10.3923i	0.198137	+	0.343184i
$918$		0			0
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$	−6.00000	+	10.3923i	−0.197814	+	0.342624i
$921$		0			0
$922$	19.0000			0.625732
$923$	12.0000	+	41.5692i	0.394985	+	1.36827i
$924$		0			0
$925$	−14.0000	+	24.2487i	−0.460317	+	0.797293i
$926$	16.0000	−	27.7128i	0.525793	−	0.910700i
$927$		0			0
$928$	−9.00000			−0.295439
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	0.640768	−	0.767735i	$-0.278616\pi$
$929$	−10.5000	−	18.1865i	−0.344494	−	0.596681i	−0.985262	+	0.171054i	$0.945283\pi$
$930$		0			0
$931$	4.00000			0.131095
$932$	−3.00000	−	5.19615i	−0.0982683	−	0.170206i
$933$		0			0
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$	60.0000			1.96221
$936$		0			0
$937$	−49.0000			−1.60076			−0.800380	−	0.599493i	$-0.795369\pi$
$937$	−49.0000			−1.60076			−0.800380	+	0.599493i	$0.795369\pi$
$938$	−6.00000	+	10.3923i	−0.195907	+	0.339321i
$939$		0			0
$940$	−18.0000	−	31.1769i	−0.587095	−	1.01688i
$941$	50.0000			1.62995			0.814977	−	0.579494i	$-0.196750\pi$
$941$	50.0000			1.62995			0.814977	+	0.579494i	$0.196750\pi$
$942$		0			0
$943$	14.0000	+	24.2487i	0.455903	+	0.789647i
$944$	8.00000			0.260378
$945$		0			0
$946$	−16.0000	+	27.7128i	−0.520205	+	0.901021i
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$		0			0
$949$	−3.50000	−	0.866025i	−0.113615	−	0.0281124i
$950$	−16.0000			−0.519109
$951$		0			0
$952$	−2.50000	+	4.33013i	−0.0810255	+	0.140340i
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	0.813337	−	0.581793i	$-0.197649\pi$
$953$	−3.00000	−	5.19615i	−0.0971795	−	0.168320i	−0.910516	+	0.413473i	$0.864315\pi$
$954$		0			0
$955$	36.0000	+	62.3538i	1.16493	+	2.01772i
$956$	−2.00000	−	3.46410i	−0.0646846	−	0.112037i
$957$		0			0
$958$	−14.0000	−	24.2487i	−0.452319	−	0.783440i
$959$	−1.50000	+	2.59808i	−0.0484375	+	0.0838963i
$960$		0			0
$961$	−31.0000			−1.00000
$962$	7.00000	+	24.2487i	0.225689	+	0.781810i
$963$		0			0
$964$	4.50000	−	7.79423i	0.144935	−	0.251035i
$965$	28.5000	−	49.3634i	0.917447	−	1.58907i
$966$		0			0
$967$	40.0000			1.28631			0.643157	−	0.765735i	$-0.277624\pi$
$967$	40.0000			1.28631			0.643157	+	0.765735i	$0.277624\pi$
$968$	2.50000	+	4.33013i	0.0803530	+	0.139176i
$969$		0			0
$970$	54.0000			1.73384
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$	2.00000	−	3.46410i	0.0641171	−	0.111054i
$974$	−4.00000			−0.128168
$975$		0			0
$976$	7.00000			0.224065
$977$	23.5000	−	40.7032i	0.751832	−	1.30221i	−0.195103	−	0.980783i	$-0.562504\pi$
$977$	23.5000	−	40.7032i	0.751832	−	1.30221i	0.946934	−	0.321428i	$-0.104163\pi$
$978$		0			0
$979$	12.0000	+	20.7846i	0.383522	+	0.664279i
$980$	−3.00000			−0.0958315
$981$		0			0
$982$	−10.0000	−	17.3205i	−0.319113	−	0.552720i
$983$	28.0000			0.893061			0.446531	−	0.894768i	$-0.352659\pi$
$983$	28.0000			0.893061			0.446531	+	0.894768i	$0.352659\pi$
$984$		0			0
$985$	−33.0000	+	57.1577i	−1.05147	+	1.82120i
$986$	22.5000	−	38.9711i	0.716546	−	1.24109i
$987$		0			0
$988$	−10.0000	+	10.3923i	−0.318142	+	0.330623i
$989$	32.0000			1.01754
$990$		0			0
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	−0.491698	−	0.870766i	$-0.663623\pi$
$991$	16.0000	−	27.7128i	0.508257	−	0.880327i	0.999954	−	0.00956046i	$-0.00304324\pi$
$992$		0			0
$993$		0			0
$994$	6.00000	+	10.3923i	0.190308	+	0.329624i
$995$		0			0
$996$		0			0
$997$	−19.5000	−	33.7750i	−0.617571	−	1.06966i	−0.989928	−	0.141575i	$-0.954783\pi$
$997$	−19.5000	−	33.7750i	−0.617571	−	1.06966i	0.372356	−	0.928090i	$-0.378550\pi$
$998$	2.00000	−	3.46410i	0.0633089	−	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.o.1387.1		2
3.2	odd	2		546.2.l.b.295.1	yes	2
13.3	even	3	inner	1638.2.r.o.757.1		2
39.17	odd	6		7098.2.a.a.1.1		1
39.29	odd	6		546.2.l.b.211.1	✓	2
39.35	odd	6		7098.2.a.v.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.b.211.1	✓	2	39.29	odd	6
546.2.l.b.295.1	yes	2	3.2	odd	2
1638.2.r.o.757.1		2	13.3	even	3	inner
1638.2.r.o.1387.1		2	1.1	even	1	trivial
7098.2.a.a.1.1		1	39.17	odd	6
7098.2.a.v.1.1		1	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.00000 q^{5} +(0.500000 + 0.866025i) q^{7} -1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(2.00000 - 3.46410i) q^{11} +(3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(-2.00000 - 3.46410i) q^{19} +(1.50000 + 2.59808i) q^{20} +(-2.00000 - 3.46410i) q^{22} +(-2.00000 + 3.46410i) q^{23} +4.00000 q^{25} +(2.50000 - 2.59808i) q^{26} +(0.500000 - 0.866025i) q^{28} +(-4.50000 + 7.79423i) q^{29} +(0.500000 + 0.866025i) q^{32} -5.00000 q^{34} +(-1.50000 - 2.59808i) q^{35} +(-3.50000 + 6.06218i) q^{37} -4.00000 q^{38} +3.00000 q^{40} +(3.50000 - 6.06218i) q^{41} +(-4.00000 - 6.92820i) q^{43} -4.00000 q^{44} +(2.00000 + 3.46410i) q^{46} -12.0000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-1.00000 - 3.46410i) q^{52} -7.00000 q^{53} +(-6.00000 + 10.3923i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(4.50000 + 7.79423i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-3.50000 - 6.06218i) q^{61} +1.00000 q^{64} +(-10.5000 - 2.59808i) q^{65} +(-6.00000 + 10.3923i) q^{67} +(-2.50000 + 4.33013i) q^{68} -3.00000 q^{70} +(6.00000 + 10.3923i) q^{71} -1.00000 q^{73} +(3.50000 + 6.06218i) q^{74} +(-2.00000 + 3.46410i) q^{76} +4.00000 q^{77} -16.0000 q^{79} +(1.50000 - 2.59808i) q^{80} +(-3.50000 - 6.06218i) q^{82} +8.00000 q^{83} +(7.50000 + 12.9904i) q^{85} -8.00000 q^{86} +(-2.00000 + 3.46410i) q^{88} +(-3.00000 + 5.19615i) q^{89} +(1.00000 + 3.46410i) q^{91} +4.00000 q^{92} +(-6.00000 + 10.3923i) q^{94} +(6.00000 + 10.3923i) q^{95} +(-9.00000 - 15.5885i) q^{97} +(0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 6 q^{5} + q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 6 * q^5 + q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 6 q^{5} + q^{7} - 2 q^{8} - 3 q^{10} + 4 q^{11} + 7 q^{13} + 2 q^{14} - q^{16} - 5 q^{17} - 4 q^{19} + 3 q^{20} - 4 q^{22} - 4 q^{23} + 8 q^{25} + 5 q^{26} + q^{28} - 9 q^{29} + q^{32} - 10 q^{34} - 3 q^{35} - 7 q^{37} - 8 q^{38} + 6 q^{40} + 7 q^{41} - 8 q^{43} - 8 q^{44} + 4 q^{46} - 24 q^{47} - q^{49} + 4 q^{50} - 2 q^{52} - 14 q^{53} - 12 q^{55} - q^{56} + 9 q^{58} - 8 q^{59} - 7 q^{61} + 2 q^{64} - 21 q^{65} - 12 q^{67} - 5 q^{68} - 6 q^{70} + 12 q^{71} - 2 q^{73} + 7 q^{74} - 4 q^{76} + 8 q^{77} - 32 q^{79} + 3 q^{80} - 7 q^{82} + 16 q^{83} + 15 q^{85} - 16 q^{86} - 4 q^{88} - 6 q^{89} + 2 q^{91} + 8 q^{92} - 12 q^{94} + 12 q^{95} - 18 q^{97} + q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 6 * q^5 + q^7 - 2 * q^8 - 3 * q^10 + 4 * q^11 + 7 * q^13 + 2 * q^14 - q^16 - 5 * q^17 - 4 * q^19 + 3 * q^20 - 4 * q^22 - 4 * q^23 + 8 * q^25 + 5 * q^26 + q^28 - 9 * q^29 + q^32 - 10 * q^34 - 3 * q^35 - 7 * q^37 - 8 * q^38 + 6 * q^40 + 7 * q^41 - 8 * q^43 - 8 * q^44 + 4 * q^46 - 24 * q^47 - q^49 + 4 * q^50 - 2 * q^52 - 14 * q^53 - 12 * q^55 - q^56 + 9 * q^58 - 8 * q^59 - 7 * q^61 + 2 * q^64 - 21 * q^65 - 12 * q^67 - 5 * q^68 - 6 * q^70 + 12 * q^71 - 2 * q^73 + 7 * q^74 - 4 * q^76 + 8 * q^77 - 32 * q^79 + 3 * q^80 - 7 * q^82 + 16 * q^83 + 15 * q^85 - 16 * q^86 - 4 * q^88 - 6 * q^89 + 2 * q^91 + 8 * q^92 - 12 * q^94 + 12 * q^95 - 18 * q^97 + q^98

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