LMFDB - Embedded newform 387.2.h.a.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,2,Mod(208,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("387.208");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	387.h (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:	$3.09021055822$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	387.307
Dual form			387.2.h.a.208.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(2.50000 + 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{14} -1.00000 q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-3.50000 + 6.06218i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-2.50000 - 4.33013i) q^{26} +(1.50000 + 2.59808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-2.50000 + 4.33013i) q^{31} -5.00000 q^{32} +(-1.50000 - 2.59808i) q^{34} +3.00000 q^{35} +(4.50000 - 7.79423i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-1.50000 + 2.59808i) q^{40} +10.0000 q^{41} +(-4.00000 + 5.19615i) q^{43} +(3.50000 - 6.06218i) q^{46} +8.00000 q^{47} +(-1.00000 + 1.73205i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-2.50000 - 4.33013i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-4.50000 - 7.79423i) q^{56} +(-1.50000 - 2.59808i) q^{58} -12.0000 q^{59} +(6.50000 + 11.2583i) q^{61} +(2.50000 - 4.33013i) q^{62} +7.00000 q^{64} -5.00000 q^{65} +(1.50000 - 2.59808i) q^{67} +(-1.50000 - 2.59808i) q^{68} -3.00000 q^{70} +(-0.500000 - 0.866025i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(-4.50000 + 7.79423i) q^{74} +(0.500000 - 0.866025i) q^{76} +(2.50000 + 4.33013i) q^{79} +(0.500000 - 0.866025i) q^{80} -10.0000 q^{82} +(4.50000 - 7.79423i) q^{83} -3.00000 q^{85} +(4.00000 - 5.19615i) q^{86} +(-0.500000 + 0.866025i) q^{89} +(7.50000 - 12.9904i) q^{91} +(3.50000 - 6.06218i) q^{92} -8.00000 q^{94} +(-0.500000 - 0.866025i) q^{95} -2.00000 q^{97} +(1.00000 - 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^4 - q^5 - 3 * q^7 + 6 * q^8	$ 2 q - 2 q^{2} - 2 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + q^{10} + 5 q^{13} + 3 q^{14} - 2 q^{16} + 3 q^{17} - q^{19} + q^{20} - 7 q^{23} + 4 q^{25} - 5 q^{26} + 3 q^{28} + 3 q^{29} - 5 q^{31} - 10 q^{32} - 3 q^{34} + 6 q^{35} + 9 q^{37} + q^{38} - 3 q^{40} + 20 q^{41} - 8 q^{43} + 7 q^{46} + 16 q^{47} - 2 q^{49} - 4 q^{50} - 5 q^{52} - 5 q^{53} - 9 q^{56} - 3 q^{58} - 24 q^{59} + 13 q^{61} + 5 q^{62} + 14 q^{64} - 10 q^{65} + 3 q^{67} - 3 q^{68} - 6 q^{70} - q^{71} - 11 q^{73} - 9 q^{74} + q^{76} + 5 q^{79} + q^{80} - 20 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - q^{89} + 15 q^{91} + 7 q^{92} - 16 q^{94} - q^{95} - 4 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + q^10 + 5 * q^13 + 3 * q^14 - 2 * q^16 + 3 * q^17 - q^19 + q^20 - 7 * q^23 + 4 * q^25 - 5 * q^26 + 3 * q^28 + 3 * q^29 - 5 * q^31 - 10 * q^32 - 3 * q^34 + 6 * q^35 + 9 * q^37 + q^38 - 3 * q^40 + 20 * q^41 - 8 * q^43 + 7 * q^46 + 16 * q^47 - 2 * q^49 - 4 * q^50 - 5 * q^52 - 5 * q^53 - 9 * q^56 - 3 * q^58 - 24 * q^59 + 13 * q^61 + 5 * q^62 + 14 * q^64 - 10 * q^65 + 3 * q^67 - 3 * q^68 - 6 * q^70 - q^71 - 11 * q^73 - 9 * q^74 + q^76 + 5 * q^79 + q^80 - 20 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - q^89 + 15 * q^91 + 7 * q^92 - 16 * q^94 - q^95 - 4 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/387\mathbb{Z}\right)^\times$.

$n$	$46$	$173$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.00000			−0.707107			−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000			−0.707107			−0.353553	+	0.935414i	$0.615027\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		0			0
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	0.970725	+	0.240192i	$0.0772105\pi$
$13$	2.50000	+	4.33013i	0.693375	+	1.20096i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	1.50000	+	2.59808i	0.400892	+	0.694365i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$		0			0
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	0.227167	+	0.973856i	$0.427054\pi$
$23$	−3.50000	+	6.06218i	−0.729800	+	1.26405i	−0.956967	+	0.290196i	$0.906280\pi$
$24$		0			0
$25$	2.00000	+	3.46410i	0.400000	+	0.692820i
$26$	−2.50000	−	4.33013i	−0.490290	−	0.849208i
$27$		0			0
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	−0.998322	−	0.0579057i	$-0.981558\pi$
$31$	−2.50000	+	4.33013i	−0.449013	+	0.777714i	0.549309	+	0.835619i	$0.314891\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	3.00000			0.507093
$36$		0			0
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	−0.212792	−	0.977098i	$-0.568256\pi$
$37$	4.50000	−	7.79423i	0.739795	−	1.28136i	0.952587	−	0.304266i	$-0.0984111\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$		0			0
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$		0			0
$43$	−4.00000	+	5.19615i	−0.609994	+	0.792406i
$43$	−4.00000	+	5.19615i	−0.609994	+	0.792406i
$44$		0			0
$45$		0			0
$46$	3.50000	−	6.06218i	0.516047	−	0.893819i
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$		0			0
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	−2.50000	−	4.33013i	−0.346688	−	0.600481i
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	−0.985062	−	0.172200i	$-0.944912\pi$
$53$	−2.50000	+	4.33013i	−0.343401	+	0.594789i	0.641661	+	0.766989i	$0.278246\pi$
$54$		0			0
$55$		0			0
$56$	−4.50000	−	7.79423i	−0.601338	−	1.04155i
$57$		0			0
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	−12.0000			−1.56227			−0.781133	−	0.624364i	$-0.785358\pi$
$59$	−12.0000			−1.56227			−0.781133	+	0.624364i	$0.785358\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	2.50000	−	4.33013i	0.317500	−	0.549927i
$63$		0			0
$64$	7.00000			0.875000
$65$	−5.00000			−0.620174
$66$		0			0
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	−0.759733	−	0.650236i	$-0.774670\pi$
$67$	1.50000	−	2.59808i	0.183254	−	0.317406i	0.942987	+	0.332830i	$0.108004\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$		0			0
$70$	−3.00000			−0.358569
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	0.834830	−	0.550508i	$-0.185566\pi$
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	−0.894169	+	0.447730i	$0.852233\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	−4.50000	+	7.79423i	−0.523114	+	0.906061i
$75$		0			0
$76$	0.500000	−	0.866025i	0.0573539	−	0.0993399i
$77$		0			0
$78$		0			0
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	0.971698	−	0.236225i	$-0.0759104\pi$
$79$	2.50000	+	4.33013i	0.281272	+	0.487177i	−0.690426	+	0.723403i	$0.742577\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$		0			0
$82$	−10.0000			−1.10432
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$	4.00000	−	5.19615i	0.431331	−	0.560316i
$87$		0			0
$88$		0			0
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	−0.891308	−	0.453398i	$-0.850212\pi$
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	0.838308	+	0.545197i	$0.183545\pi$
$90$		0			0
$91$	7.50000	−	12.9904i	0.786214	−	1.36176i
$92$	3.50000	−	6.06218i	0.364900	−	0.632026i
$93$		0			0
$94$	−8.00000			−0.825137
$95$	−0.500000	−	0.866025i	−0.0512989	−	0.0888523i
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	1.00000	−	1.73205i	0.101015	−	0.174964i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	0.550474	−	0.834853i	$-0.314447\pi$
$101$	−4.50000	−	7.79423i	−0.447767	−	0.775555i	−0.998240	+	0.0592978i	$0.981114\pi$
$102$		0			0
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	0.640464	−	0.767988i	$-0.278742\pi$
$103$	−3.50000	−	6.06218i	−0.344865	−	0.597324i	−0.985329	+	0.170664i	$0.945409\pi$
$104$	7.50000	+	12.9904i	0.735436	+	1.27381i
$105$		0			0
$106$	2.50000	−	4.33013i	0.242821	−	0.420579i
$107$	−12.0000			−1.16008			−0.580042	−	0.814587i	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		0			0
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	−0.983531	−	0.180741i	$-0.942150\pi$
$109$	−3.50000	+	6.06218i	−0.335239	+	0.580651i	0.648292	+	0.761392i	$0.275484\pi$
$110$		0			0
$111$		0			0
$112$	1.50000	+	2.59808i	0.141737	+	0.245495i
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$	−3.50000	−	6.06218i	−0.326377	−	0.565301i
$116$	−1.50000	−	2.59808i	−0.139272	−	0.241225i
$117$		0			0
$118$	12.0000			1.10469
$119$	4.50000	−	7.79423i	0.412514	−	0.714496i
$120$		0			0
$121$	−11.0000			−1.00000
$122$	−6.50000	−	11.2583i	−0.588482	−	1.01928i
$123$		0			0
$124$	2.50000	−	4.33013i	0.224507	−	0.388857i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	3.00000			0.265165
$129$		0			0
$130$	5.00000			0.438529
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$		0			0
$133$	3.00000			0.260133
$134$	−1.50000	+	2.59808i	−0.129580	+	0.224440i
$135$		0			0
$136$	4.50000	+	7.79423i	0.385872	+	0.668350i
$137$	18.0000			1.53784			0.768922	−	0.639343i	$-0.220793\pi$
$137$	18.0000			1.53784			0.768922	+	0.639343i	$0.220793\pi$
$138$		0			0
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	0.446857	+	0.894606i	$0.352543\pi$
$139$	−6.50000	+	11.2583i	−0.551323	+	0.954919i	−0.998179	+	0.0603135i	$0.980790\pi$
$140$	−3.00000			−0.253546
$141$		0			0
$142$	0.500000	+	0.866025i	0.0419591	+	0.0726752i
$143$		0			0
$144$		0			0
$145$	−3.00000			−0.249136
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$		0			0
$148$	−4.50000	+	7.79423i	−0.369898	+	0.640682i
$149$	−10.5000	+	18.1865i	−0.860194	+	1.48990i	0.0115483	+	0.999933i	$0.496324\pi$
$149$	−10.5000	+	18.1865i	−0.860194	+	1.48990i	−0.871742	+	0.489966i	$0.837009\pi$
$150$		0			0
$151$	−8.00000			−0.651031			−0.325515	−	0.945537i	$-0.605538\pi$
$151$	−8.00000			−0.651031			−0.325515	+	0.945537i	$0.605538\pi$
$152$	−1.50000	+	2.59808i	−0.121666	+	0.210732i
$153$		0			0
$154$		0			0
$155$	−2.50000	−	4.33013i	−0.200805	−	0.347804i
$156$		0			0
$157$	0.500000	+	0.866025i	0.0399043	+	0.0691164i	0.885288	−	0.465044i	$-0.153961\pi$
$157$	0.500000	+	0.866025i	0.0399043	+	0.0691164i	−0.845383	+	0.534160i	$0.820628\pi$
$158$	−2.50000	−	4.33013i	−0.198889	−	0.344486i
$159$		0			0
$160$	2.50000	−	4.33013i	0.197642	−	0.342327i
$161$	21.0000			1.65503
$162$		0			0
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	0.884943	−	0.465700i	$-0.154198\pi$
$163$	0.500000	+	0.866025i	0.0391630	+	0.0678323i	−0.845780	+	0.533533i	$0.820864\pi$
$164$	−10.0000			−0.780869
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	−0.918208	−	0.396098i	$-0.870364\pi$
$167$	−1.50000	+	2.59808i	−0.116073	+	0.201045i	0.802135	+	0.597143i	$0.203697\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$	3.00000			0.230089
$171$		0			0
$172$	4.00000	−	5.19615i	0.304997	−	0.396203i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		0			0
$175$	6.00000	−	10.3923i	0.453557	−	0.785584i
$176$		0			0
$177$		0			0
$178$	0.500000	−	0.866025i	0.0374766	−	0.0649113i
$179$	−0.500000	−	0.866025i	−0.0373718	−	0.0647298i	0.846735	−	0.532016i	$-0.178565\pi$
$179$	−0.500000	−	0.866025i	−0.0373718	−	0.0647298i	−0.884106	+	0.467286i	$0.845232\pi$
$180$		0			0
$181$	−3.50000	−	6.06218i	−0.260153	−	0.450598i	0.706129	−	0.708083i	$-0.250440\pi$
$181$	−3.50000	−	6.06218i	−0.260153	−	0.450598i	−0.966282	+	0.257485i	$0.917106\pi$
$182$	−7.50000	+	12.9904i	−0.555937	+	0.962911i
$183$		0			0
$184$	−10.5000	+	18.1865i	−0.774070	+	1.34073i
$185$	4.50000	+	7.79423i	0.330847	+	0.573043i
$186$		0			0
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	0.500000	+	0.866025i	0.0362738	+	0.0628281i
$191$	−9.50000	+	16.4545i	−0.687396	+	1.19060i	0.285282	+	0.958444i	$0.407913\pi$
$191$	−9.50000	+	16.4545i	−0.687396	+	1.19060i	−0.972677	+	0.232161i	$0.925420\pi$
$192$		0			0
$193$	6.00000			0.431889			0.215945	−	0.976406i	$-0.430717\pi$
$193$	6.00000			0.431889			0.215945	+	0.976406i	$0.430717\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	1.00000	−	1.73205i	0.0714286	−	0.123718i
$197$	5.50000	+	9.52628i	0.391859	+	0.678719i	0.992695	−	0.120653i	$-0.0384988\pi$
$197$	5.50000	+	9.52628i	0.391859	+	0.678719i	−0.600836	+	0.799372i	$0.705166\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	6.00000	+	10.3923i	0.424264	+	0.734847i
$201$		0			0
$202$	4.50000	+	7.79423i	0.316619	+	0.548400i
$203$	4.50000	−	7.79423i	0.315838	−	0.547048i
$204$		0			0
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$	3.50000	+	6.06218i	0.243857	+	0.422372i
$207$		0			0
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$		0			0
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	2.50000	−	4.33013i	0.171701	−	0.297394i
$213$		0			0
$214$	12.0000			0.820303
$215$	−2.50000	−	6.06218i	−0.170499	−	0.413437i
$216$		0			0
$217$	15.0000			1.01827
$218$	3.50000	−	6.06218i	0.237050	−	0.410582i
$219$		0			0
$220$		0			0
$221$	−7.50000	+	12.9904i	−0.504505	+	0.873828i
$222$		0			0
$223$	20.0000			1.33930			0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000			1.33930			0.669650	+	0.742677i	$0.266444\pi$
$224$	7.50000	+	12.9904i	0.501115	+	0.867956i
$225$		0			0
$226$	−2.00000			−0.133038
$227$	−3.50000	+	6.06218i	−0.232303	+	0.402361i	−0.958485	−	0.285141i	$-0.907959\pi$
$227$	−3.50000	+	6.06218i	−0.232303	+	0.402361i	0.726182	+	0.687502i	$0.241293\pi$
$228$		0			0
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	0.975533	−	0.219853i	$-0.0705577\pi$
$229$	4.50000	+	7.79423i	0.297368	+	0.515057i	−0.678165	+	0.734910i	$0.737224\pi$
$230$	3.50000	+	6.06218i	0.230783	+	0.399728i
$231$		0			0
$232$	4.50000	+	7.79423i	0.295439	+	0.511716i
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	0.680135	−	0.733087i	$-0.261921\pi$
$233$	−4.50000	−	7.79423i	−0.294805	−	0.510617i	−0.974939	+	0.222470i	$0.928588\pi$
$234$		0			0
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$	12.0000			0.781133
$237$		0			0
$238$	−4.50000	+	7.79423i	−0.291692	+	0.505225i
$239$	12.5000	−	21.6506i	0.808558	−	1.40046i	−0.105305	−	0.994440i	$-0.533582\pi$
$239$	12.5000	−	21.6506i	0.808558	−	1.40046i	0.913863	−	0.406023i	$-0.133085\pi$
$240$		0			0
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	0.516695	−	0.856170i	$-0.327162\pi$
$241$	−7.50000	−	12.9904i	−0.483117	−	0.836784i	−0.999812	+	0.0193858i	$0.993829\pi$
$242$	11.0000			0.707107
$243$		0			0
$244$	−6.50000	−	11.2583i	−0.416120	−	0.720741i
$245$	−1.00000	−	1.73205i	−0.0638877	−	0.110657i
$246$		0			0
$247$	−5.00000			−0.318142
$248$	−7.50000	+	12.9904i	−0.476250	+	0.824890i
$249$		0			0
$250$	9.00000			0.569210
$251$	3.50000	+	6.06218i	0.220918	+	0.382641i	0.955087	−	0.296326i	$-0.0957613\pi$
$251$	3.50000	+	6.06218i	0.220918	+	0.382641i	−0.734169	+	0.678967i	$0.762428\pi$
$252$		0			0
$253$		0			0
$254$	−16.0000			−1.00393
$255$		0			0
$256$	−17.0000			−1.06250
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$		0			0
$259$	−27.0000			−1.67770
$260$	5.00000			0.310087
$261$		0			0
$262$	−4.00000			−0.247121
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	−0.336270	−	0.941766i	$-0.609166\pi$
$263$	10.5000	−	18.1865i	0.647458	−	1.12143i	0.983728	−	0.179664i	$-0.0575011\pi$
$264$		0			0
$265$	−2.50000	−	4.33013i	−0.153574	−	0.265998i
$266$	−3.00000			−0.183942
$267$		0			0
$268$	−1.50000	+	2.59808i	−0.0916271	+	0.158703i
$269$	−14.0000			−0.853595			−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000			−0.853595			−0.426798	+	0.904347i	$0.640358\pi$
$270$		0			0
$271$	−11.5000	−	19.9186i	−0.698575	−	1.20997i	−0.968960	−	0.247216i	$-0.920484\pi$
$271$	−11.5000	−	19.9186i	−0.698575	−	1.20997i	0.270385	−	0.962752i	$-0.412849\pi$
$272$	−1.50000	−	2.59808i	−0.0909509	−	0.157532i
$273$		0			0
$274$	−18.0000			−1.08742
$275$		0			0
$276$		0			0
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	−0.951807	−	0.306699i	$-0.900776\pi$
$277$	−3.50000	+	6.06218i	−0.210295	+	0.364241i	0.741512	+	0.670940i	$0.234109\pi$
$278$	6.50000	−	11.2583i	0.389844	−	0.675230i
$279$		0			0
$280$	9.00000			0.537853
$281$	−8.50000	+	14.7224i	−0.507067	+	0.878267i	0.492899	+	0.870087i	$0.335937\pi$
$281$	−8.50000	+	14.7224i	−0.507067	+	0.878267i	−0.999967	+	0.00818015i	$0.997396\pi$
$282$		0			0
$283$	−1.50000	−	2.59808i	−0.0891657	−	0.154440i	0.817993	−	0.575228i	$-0.195087\pi$
$283$	−1.50000	−	2.59808i	−0.0891657	−	0.154440i	−0.907159	+	0.420789i	$0.861753\pi$
$284$	0.500000	+	0.866025i	0.0296695	+	0.0513892i
$285$		0			0
$286$		0			0
$287$	−15.0000	−	25.9808i	−0.885422	−	1.53360i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	3.00000			0.176166
$291$		0			0
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$	6.00000	−	10.3923i	0.349334	−	0.605063i
$296$	13.5000	−	23.3827i	0.784672	−	1.35909i
$297$		0			0
$298$	10.5000	−	18.1865i	0.608249	−	1.05352i
$299$	−35.0000			−2.02410
$300$		0			0
$301$	19.5000	+	2.59808i	1.12396	+	0.149751i
$302$	8.00000			0.460348
$303$		0			0
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	−13.0000			−0.744378
$306$		0			0
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	−0.928506	−	0.371318i	$-0.878906\pi$
$307$	−2.50000	+	4.33013i	−0.142683	+	0.247133i	0.785823	+	0.618451i	$0.212239\pi$
$308$		0			0
$309$		0			0
$310$	2.50000	+	4.33013i	0.141990	+	0.245935i
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	−0.905416	−	0.424526i	$-0.860441\pi$
$311$	−1.50000	+	2.59808i	−0.0850572	+	0.147323i	0.820358	+	0.571850i	$0.193774\pi$
$312$		0			0
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	−0.500000	−	0.866025i	−0.0282166	−	0.0488726i
$315$		0			0
$316$	−2.50000	−	4.33013i	−0.140636	−	0.243589i
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$		0			0
$319$		0			0
$320$	−3.50000	+	6.06218i	−0.195656	+	0.338886i
$321$		0			0
$322$	−21.0000			−1.17028
$323$	−3.00000			−0.166924
$324$		0			0
$325$	−10.0000	+	17.3205i	−0.554700	+	0.960769i
$326$	−0.500000	−	0.866025i	−0.0276924	−	0.0479647i
$327$		0			0
$328$	30.0000			1.65647
$329$	−12.0000	−	20.7846i	−0.661581	−	1.14589i
$330$		0			0
$331$	−9.50000	−	16.4545i	−0.522167	−	0.904420i	−0.999667	−	0.0257885i	$-0.991790\pi$
$331$	−9.50000	−	16.4545i	−0.522167	−	0.904420i	0.477500	−	0.878632i	$-0.341543\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$		0			0
$334$	1.50000	−	2.59808i	0.0820763	−	0.142160i
$335$	1.50000	+	2.59808i	0.0819538	+	0.141948i
$336$		0			0
$337$	−1.50000	−	2.59808i	−0.0817102	−	0.141526i	0.822274	−	0.569091i	$-0.192705\pi$
$337$	−1.50000	−	2.59808i	−0.0817102	−	0.141526i	−0.903985	+	0.427565i	$0.859372\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	3.00000			0.162698
$341$		0			0
$342$		0			0
$343$	−15.0000			−0.809924
$344$	−12.0000	+	15.5885i	−0.646997	+	0.840473i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	18.5000	−	32.0429i	0.993132	−	1.72016i	0.395242	−	0.918577i	$-0.370661\pi$
$347$	18.5000	−	32.0429i	0.993132	−	1.72016i	0.597890	−	0.801578i	$-0.296006\pi$
$348$		0			0
$349$	0.500000	−	0.866025i	0.0267644	−	0.0463573i	−0.852333	−	0.523000i	$-0.824813\pi$
$349$	0.500000	−	0.866025i	0.0267644	−	0.0463573i	0.879097	+	0.476642i	$0.158146\pi$
$350$	−6.00000	+	10.3923i	−0.320713	+	0.555492i
$351$		0			0
$352$		0			0
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	−0.979202	−	0.202889i	$-0.934967\pi$
$353$	−12.5000	−	21.6506i	−0.665308	−	1.15235i	0.313894	−	0.949458i	$-0.398366\pi$
$354$		0			0
$355$	1.00000			0.0530745
$356$	0.500000	−	0.866025i	0.0264999	−	0.0458993i
$357$		0			0
$358$	0.500000	+	0.866025i	0.0264258	+	0.0457709i
$359$	9.50000	+	16.4545i	0.501391	+	0.868434i	0.999999	+	0.00160673i	$0.000511438\pi$
$359$	9.50000	+	16.4545i	0.501391	+	0.868434i	−0.498608	+	0.866828i	$0.666155\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$		0			0
$364$	−7.50000	+	12.9904i	−0.393107	+	0.680881i
$365$	11.0000			0.575766
$366$		0			0
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	−0.984301	−	0.176500i	$-0.943523\pi$
$367$	−6.50000	+	11.2583i	−0.339297	+	0.587680i	0.645003	+	0.764180i	$0.276856\pi$
$368$	3.50000	−	6.06218i	0.182450	−	0.316013i
$369$		0			0
$370$	−4.50000	−	7.79423i	−0.233944	−	0.405203i
$371$	15.0000			0.778761
$372$		0			0
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	0.687776	−	0.725923i	$-0.258587\pi$
$373$	−5.50000	−	9.52628i	−0.284779	−	0.493252i	−0.972556	+	0.232671i	$0.925254\pi$
$374$		0			0
$375$		0			0
$376$	24.0000			1.23771
$377$	−7.50000	+	12.9904i	−0.386270	+	0.669039i
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	0.500000	+	0.866025i	0.0256495	+	0.0444262i
$381$		0			0
$382$	9.50000	−	16.4545i	0.486062	−	0.841885i
$383$	−8.00000			−0.408781			−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000			−0.408781			−0.204390	+	0.978889i	$0.565521\pi$
$384$		0			0
$385$		0			0
$386$	−6.00000			−0.305392
$387$		0			0
$388$	2.00000			0.101535
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$	−21.0000			−1.06202
$392$	−3.00000	+	5.19615i	−0.151523	+	0.262445i
$393$		0			0
$394$	−5.50000	−	9.52628i	−0.277086	−	0.479927i
$395$	−5.00000			−0.251577
$396$		0			0
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	−0.472526	−	0.881317i	$-0.656658\pi$
$397$	10.5000	−	18.1865i	0.526980	−	0.912756i	0.999506	−	0.0314391i	$-0.0100090\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−18.5000	−	32.0429i	−0.923846	−	1.60015i	−0.793407	−	0.608692i	$-0.791695\pi$
$401$	−18.5000	−	32.0429i	−0.923846	−	1.60015i	−0.130439	−	0.991456i	$-0.541639\pi$
$402$		0			0
$403$	−25.0000			−1.24534
$404$	4.50000	+	7.79423i	0.223883	+	0.387777i
$405$		0			0
$406$	−4.50000	+	7.79423i	−0.223331	+	0.386821i
$407$		0			0
$408$		0			0
$409$	−18.0000			−0.890043			−0.445021	−	0.895520i	$-0.646804\pi$
$409$	−18.0000			−0.890043			−0.445021	+	0.895520i	$0.646804\pi$
$410$	5.00000	−	8.66025i	0.246932	−	0.427699i
$411$		0			0
$412$	3.50000	+	6.06218i	0.172433	+	0.298662i
$413$	18.0000	+	31.1769i	0.885722	+	1.53412i
$414$		0			0
$415$	4.50000	+	7.79423i	0.220896	+	0.382604i
$416$	−12.5000	−	21.6506i	−0.612863	−	1.06151i
$417$		0			0
$418$		0			0
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	18.5000	+	32.0429i	0.901635	+	1.56168i	0.825372	+	0.564590i	$0.190966\pi$
$421$	18.5000	+	32.0429i	0.901635	+	1.56168i	0.0762630	+	0.997088i	$0.475701\pi$
$422$	−8.00000			−0.389434
$423$		0			0
$424$	−7.50000	+	12.9904i	−0.364232	+	0.630869i
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$		0			0
$427$	19.5000	−	33.7750i	0.943671	−	1.63449i
$428$	12.0000			0.580042
$429$		0			0
$430$	2.50000	+	6.06218i	0.120561	+	0.292344i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	−13.5000	+	23.3827i	−0.648769	+	1.12370i	0.334649	+	0.942343i	$0.391382\pi$
$433$	−13.5000	+	23.3827i	−0.648769	+	1.12370i	−0.983417	+	0.181357i	$0.941951\pi$
$434$	−15.0000			−0.720023
$435$		0			0
$436$	3.50000	−	6.06218i	0.167620	−	0.290326i
$437$	−3.50000	−	6.06218i	−0.167428	−	0.289993i
$438$		0			0
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	0.978412	−	0.206666i	$-0.0662612\pi$
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	−0.668184	+	0.743996i	$0.732928\pi$
$440$		0			0
$441$		0			0
$442$	7.50000	−	12.9904i	0.356739	−	0.617889i
$443$	−18.5000	−	32.0429i	−0.878962	−	1.52241i	−0.852482	−	0.522757i	$-0.824904\pi$
$443$	−18.5000	−	32.0429i	−0.878962	−	1.52241i	−0.0264796	−	0.999649i	$-0.508430\pi$
$444$		0			0
$445$	−0.500000	−	0.866025i	−0.0237023	−	0.0410535i
$446$	−20.0000			−0.947027
$447$		0			0
$448$	−10.5000	−	18.1865i	−0.496078	−	0.859233i
$449$	−10.5000	+	18.1865i	−0.495526	+	0.858276i	−0.999987	−	0.00515887i	$-0.998358\pi$
$449$	−10.5000	+	18.1865i	−0.495526	+	0.858276i	0.504461	+	0.863434i	$0.331691\pi$
$450$		0			0
$451$		0			0
$452$	−2.00000			−0.0940721
$453$		0			0
$454$	3.50000	−	6.06218i	0.164263	−	0.284512i
$455$	7.50000	+	12.9904i	0.351605	+	0.608998i
$456$		0			0
$457$	6.00000			0.280668			0.140334	−	0.990104i	$-0.455182\pi$
$457$	6.00000			0.280668			0.140334	+	0.990104i	$0.455182\pi$
$458$	−4.50000	−	7.79423i	−0.210271	−	0.364200i
$459$		0			0
$460$	3.50000	+	6.06218i	0.163188	+	0.282650i
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	−0.828978	−	0.559281i	$-0.811077\pi$
$461$	1.50000	−	2.59808i	0.0698620	−	0.121004i	0.898840	+	0.438276i	$0.144411\pi$
$462$		0			0
$463$	11.5000	−	19.9186i	0.534450	−	0.925695i	−0.464739	−	0.885448i	$-0.653852\pi$
$463$	11.5000	−	19.9186i	0.534450	−	0.925695i	0.999190	−	0.0402476i	$-0.0128147\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	10.5000	−	18.1865i	0.485882	−	0.841572i	−0.513986	−	0.857798i	$-0.671832\pi$
$467$	10.5000	−	18.1865i	0.485882	−	0.841572i	0.999868	+	0.0162260i	$0.00516512\pi$
$468$		0			0
$469$	−9.00000			−0.415581
$470$	4.00000	−	6.92820i	0.184506	−	0.319574i
$471$		0			0
$472$	−36.0000			−1.65703
$473$		0			0
$474$		0			0
$475$	−4.00000			−0.183533
$476$	−4.50000	+	7.79423i	−0.206257	+	0.357248i
$477$		0			0
$478$	−12.5000	+	21.6506i	−0.571737	+	0.990277i
$479$	−7.50000	+	12.9904i	−0.342684	+	0.593546i	−0.984930	−	0.172953i	$-0.944669\pi$
$479$	−7.50000	+	12.9904i	−0.342684	+	0.593546i	0.642246	+	0.766498i	$0.278003\pi$
$480$		0			0
$481$	45.0000			2.05182
$482$	7.50000	+	12.9904i	0.341616	+	0.591696i
$483$		0			0
$484$	11.0000			0.500000
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	4.50000	+	7.79423i	0.203914	+	0.353190i	0.949786	−	0.312899i	$-0.101300\pi$
$487$	4.50000	+	7.79423i	0.203914	+	0.353190i	−0.745872	+	0.666089i	$0.767967\pi$
$488$	19.5000	+	33.7750i	0.882724	+	1.52892i
$489$		0			0
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	0.746438	−	0.665455i	$-0.231763\pi$
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	−0.949520	+	0.313707i	$0.898429\pi$
$492$		0			0
$493$	−4.50000	+	7.79423i	−0.202670	+	0.351034i
$494$	5.00000			0.224961
$495$		0			0
$496$	2.50000	−	4.33013i	0.112253	−	0.194428i
$497$	−1.50000	+	2.59808i	−0.0672842	+	0.116540i
$498$		0			0
$499$	8.50000	+	14.7224i	0.380512	+	0.659067i	0.991136	−	0.132855i	$-0.0424144\pi$
$499$	8.50000	+	14.7224i	0.380512	+	0.659067i	−0.610623	+	0.791921i	$0.709081\pi$
$500$	9.00000			0.402492
$501$		0			0
$502$	−3.50000	−	6.06218i	−0.156213	−	0.270568i
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	0.748091	−	0.663596i	$-0.230970\pi$
$503$	−4.50000	−	7.79423i	−0.200645	−	0.347527i	−0.948736	+	0.316068i	$0.897637\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$		0			0
$508$	−16.0000			−0.709885
$509$	13.5000	+	23.3827i	0.598377	+	1.03642i	0.993061	+	0.117602i	$0.0375208\pi$
$509$	13.5000	+	23.3827i	0.598377	+	1.03642i	−0.394684	+	0.918817i	$0.629146\pi$
$510$		0			0
$511$	−16.5000	+	28.5788i	−0.729917	+	1.26425i
$512$	11.0000			0.486136
$513$		0			0
$514$	6.00000			0.264649
$515$	7.00000			0.308457
$516$		0			0
$517$		0			0
$518$	27.0000			1.18631
$519$		0			0
$520$	−15.0000			−0.657794
$521$	17.5000	−	30.3109i	0.766689	−	1.32794i	−0.172660	−	0.984981i	$-0.555236\pi$
$521$	17.5000	−	30.3109i	0.766689	−	1.32794i	0.939349	−	0.342963i	$-0.111430\pi$
$522$		0			0
$523$	10.5000	+	18.1865i	0.459133	+	0.795242i	0.998915	−	0.0465630i	$-0.0148268\pi$
$523$	10.5000	+	18.1865i	0.459133	+	0.795242i	−0.539782	+	0.841805i	$0.681493\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−10.5000	+	18.1865i	−0.457822	+	0.792971i
$527$	−15.0000			−0.653410
$528$		0			0
$529$	−13.0000	−	22.5167i	−0.565217	−	0.978985i
$530$	2.50000	+	4.33013i	0.108593	+	0.188089i
$531$		0			0
$532$	−3.00000			−0.130066
$533$	25.0000	+	43.3013i	1.08287	+	1.87559i
$534$		0			0
$535$	6.00000	−	10.3923i	0.259403	−	0.449299i
$536$	4.50000	−	7.79423i	0.194370	−	0.336659i
$537$		0			0
$538$	14.0000			0.603583
$539$		0			0
$540$		0			0
$541$	−15.5000	−	26.8468i	−0.666397	−	1.15423i	−0.978905	−	0.204318i	$-0.934502\pi$
$541$	−15.5000	−	26.8468i	−0.666397	−	1.15423i	0.312507	−	0.949915i	$-0.398831\pi$
$542$	11.5000	+	19.9186i	0.493967	+	0.855576i
$543$		0			0
$544$	−7.50000	−	12.9904i	−0.321560	−	0.556958i
$545$	−3.50000	−	6.06218i	−0.149924	−	0.259675i
$546$		0			0
$547$	−0.500000	+	0.866025i	−0.0213785	+	0.0370286i	−0.876517	−	0.481371i	$-0.840139\pi$
$547$	−0.500000	+	0.866025i	−0.0213785	+	0.0370286i	0.855138	+	0.518400i	$0.173472\pi$
$548$	−18.0000			−0.768922
$549$		0			0
$550$		0			0
$551$	−3.00000			−0.127804
$552$		0			0
$553$	7.50000	−	12.9904i	0.318932	−	0.552407i
$554$	3.50000	−	6.06218i	0.148701	−	0.257557i
$555$		0			0
$556$	6.50000	−	11.2583i	0.275661	−	0.477460i
$557$	6.00000			0.254228			0.127114	−	0.991888i	$-0.459429\pi$
$557$	6.00000			0.254228			0.127114	+	0.991888i	$0.459429\pi$
$558$		0			0
$559$	−32.5000	−	4.33013i	−1.37460	−	0.183145i
$560$	−3.00000			−0.126773
$561$		0			0
$562$	8.50000	−	14.7224i	0.358551	−	0.621028i
$563$	−4.00000			−0.168580			−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000			−0.168580			−0.0842900	+	0.996441i	$0.526862\pi$
$564$		0			0
$565$	−1.00000	+	1.73205i	−0.0420703	+	0.0728679i
$566$	1.50000	+	2.59808i	0.0630497	+	0.109205i
$567$		0			0
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	−8.50000	+	14.7224i	−0.356339	+	0.617196i	−0.987346	−	0.158580i	$-0.949308\pi$
$569$	−8.50000	+	14.7224i	−0.356339	+	0.617196i	0.631008	+	0.775777i	$0.282642\pi$
$570$		0			0
$571$	−6.50000	+	11.2583i	−0.272017	+	0.471146i	−0.969378	−	0.245573i	$-0.921024\pi$
$571$	−6.50000	+	11.2583i	−0.272017	+	0.471146i	0.697362	+	0.716720i	$0.254357\pi$
$572$		0			0
$573$		0			0
$574$	15.0000	+	25.9808i	0.626088	+	1.08442i
$575$	−28.0000			−1.16768
$576$		0			0
$577$	2.50000	+	4.33013i	0.104076	+	0.180266i	0.913360	−	0.407152i	$-0.133478\pi$
$577$	2.50000	+	4.33013i	0.104076	+	0.180266i	−0.809284	+	0.587417i	$0.800145\pi$
$578$	−4.00000	+	6.92820i	−0.166378	+	0.288175i
$579$		0			0
$580$	3.00000			0.124568
$581$	−27.0000			−1.12015
$582$		0			0
$583$		0			0
$584$	−16.5000	−	28.5788i	−0.682775	−	1.18260i
$585$		0			0
$586$	−14.0000			−0.578335
$587$	−6.50000	−	11.2583i	−0.268284	−	0.464681i	0.700135	−	0.714010i	$-0.253123\pi$
$587$	−6.50000	−	11.2583i	−0.268284	−	0.464681i	−0.968419	+	0.249329i	$0.919790\pi$
$588$		0			0
$589$	−2.50000	−	4.33013i	−0.103011	−	0.178420i
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$		0			0
$592$	−4.50000	+	7.79423i	−0.184949	+	0.320341i
$593$	−0.500000	−	0.866025i	−0.0205325	−	0.0355634i	0.855577	−	0.517676i	$-0.173203\pi$
$593$	−0.500000	−	0.866025i	−0.0205325	−	0.0355634i	−0.876109	+	0.482113i	$0.839870\pi$
$594$		0			0
$595$	4.50000	+	7.79423i	0.184482	+	0.319532i
$596$	10.5000	−	18.1865i	0.430097	−	0.744949i
$597$		0			0
$598$	35.0000			1.43126
$599$	−15.5000	+	26.8468i	−0.633313	+	1.09693i	0.353557	+	0.935413i	$0.384972\pi$
$599$	−15.5000	+	26.8468i	−0.633313	+	1.09693i	−0.986870	+	0.161517i	$0.948361\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$	−19.5000	−	2.59808i	−0.794761	−	0.105890i
$603$		0			0
$604$	8.00000			0.325515
$605$	5.50000	−	9.52628i	0.223607	−	0.387298i
$606$		0			0
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	13.0000			0.526355
$611$	20.0000	+	34.6410i	0.809113	+	1.40143i
$612$		0			0
$613$	−30.0000			−1.21169			−0.605844	−	0.795583i	$-0.707165\pi$
$613$	−30.0000			−1.21169			−0.605844	+	0.795583i	$0.707165\pi$
$614$	2.50000	−	4.33013i	0.100892	−	0.174750i
$615$		0			0
$616$		0			0
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	0.996138	−	0.0878015i	$-0.0279841\pi$
$619$	10.5000	+	18.1865i	0.422031	+	0.730978i	−0.574107	+	0.818780i	$0.694651\pi$
$620$	2.50000	+	4.33013i	0.100402	+	0.173902i
$621$		0			0
$622$	1.50000	−	2.59808i	0.0601445	−	0.104173i
$623$	3.00000			0.120192
$624$		0			0
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	−8.50000	+	14.7224i	−0.339728	+	0.588427i
$627$		0			0
$628$	−0.500000	−	0.866025i	−0.0199522	−	0.0345582i
$629$	27.0000			1.07656
$630$		0			0
$631$	4.50000	+	7.79423i	0.179142	+	0.310283i	0.941587	−	0.336770i	$-0.109334\pi$
$631$	4.50000	+	7.79423i	0.179142	+	0.310283i	−0.762445	+	0.647053i	$0.776001\pi$
$632$	7.50000	+	12.9904i	0.298334	+	0.516730i
$633$		0			0
$634$	−18.0000			−0.714871
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$		0			0
$637$	−10.0000			−0.396214
$638$		0			0
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	18.0000			0.710957			0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000			0.710957			0.355479	+	0.934684i	$0.384318\pi$
$642$		0			0
$643$	12.0000			0.473234			0.236617	−	0.971603i	$-0.423961\pi$
$643$	12.0000			0.473234			0.236617	+	0.971603i	$0.423961\pi$
$644$	−21.0000			−0.827516
$645$		0			0
$646$	3.00000			0.118033
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$		0			0
$649$		0			0
$650$	10.0000	−	17.3205i	0.392232	−	0.679366i
$651$		0			0
$652$	−0.500000	−	0.866025i	−0.0195815	−	0.0339162i
$653$	50.0000			1.95665			0.978326	−	0.207072i	$-0.0663936\pi$
$653$	50.0000			1.95665			0.978326	+	0.207072i	$0.0663936\pi$
$654$		0			0
$655$	−2.00000	+	3.46410i	−0.0781465	+	0.135354i
$656$	−10.0000			−0.390434
$657$		0			0
$658$	12.0000	+	20.7846i	0.467809	+	0.810268i
$659$	11.5000	+	19.9186i	0.447976	+	0.775918i	0.998254	−	0.0590638i	$-0.0188115\pi$
$659$	11.5000	+	19.9186i	0.447976	+	0.775918i	−0.550278	+	0.834982i	$0.685478\pi$
$660$		0			0
$661$	−14.0000			−0.544537			−0.272268	−	0.962221i	$-0.587774\pi$
$661$	−14.0000			−0.544537			−0.272268	+	0.962221i	$0.587774\pi$
$662$	9.50000	+	16.4545i	0.369228	+	0.639522i
$663$		0			0
$664$	13.5000	−	23.3827i	0.523902	−	0.907424i
$665$	−1.50000	+	2.59808i	−0.0581675	+	0.100749i
$666$		0			0
$667$	−21.0000			−0.813123
$668$	1.50000	−	2.59808i	0.0580367	−	0.100523i
$669$		0			0
$670$	−1.50000	−	2.59808i	−0.0579501	−	0.100372i
$671$		0			0
$672$		0			0
$673$	−23.5000	−	40.7032i	−0.905858	−	1.56899i	−0.819761	−	0.572706i	$-0.805894\pi$
$673$	−23.5000	−	40.7032i	−0.905858	−	1.56899i	−0.0860977	−	0.996287i	$-0.527440\pi$
$674$	1.50000	+	2.59808i	0.0577778	+	0.100074i
$675$		0			0
$676$	6.00000	−	10.3923i	0.230769	−	0.399704i
$677$	14.0000			0.538064			0.269032	−	0.963131i	$-0.413296\pi$
$677$	14.0000			0.538064			0.269032	+	0.963131i	$0.413296\pi$
$678$		0			0
$679$	3.00000	+	5.19615i	0.115129	+	0.199410i
$680$	−9.00000			−0.345134
$681$		0			0
$682$		0			0
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	−0.766997	−	0.641651i	$-0.778250\pi$
$683$	4.50000	−	7.79423i	0.172188	−	0.298238i	0.939184	+	0.343413i	$0.111583\pi$
$684$		0			0
$685$	−9.00000	+	15.5885i	−0.343872	+	0.595604i
$686$	15.0000			0.572703
$687$		0			0
$688$	4.00000	−	5.19615i	0.152499	−	0.198101i
$689$	−25.0000			−0.952424
$690$		0			0
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	−0.909652	−	0.415371i	$-0.863652\pi$
$691$	−2.50000	+	4.33013i	−0.0951045	+	0.164726i	0.814548	+	0.580097i	$0.196985\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−18.5000	+	32.0429i	−0.702250	+	1.21633i
$695$	−6.50000	−	11.2583i	−0.246559	−	0.427053i
$696$		0			0
$697$	15.0000	+	25.9808i	0.568166	+	0.984092i
$698$	−0.500000	+	0.866025i	−0.0189253	+	0.0327795i
$699$		0			0
$700$	−6.00000	+	10.3923i	−0.226779	+	0.392792i
$701$	3.50000	+	6.06218i	0.132193	+	0.228965i	0.924522	−	0.381129i	$-0.124465\pi$
$701$	3.50000	+	6.06218i	0.132193	+	0.228965i	−0.792329	+	0.610095i	$0.791131\pi$
$702$		0			0
$703$	4.50000	+	7.79423i	0.169721	+	0.293965i
$704$		0			0
$705$		0			0
$706$	12.5000	+	21.6506i	0.470444	+	0.814832i
$707$	−13.5000	+	23.3827i	−0.507720	+	0.879396i
$708$		0			0
$709$	26.0000			0.976450			0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000			0.976450			0.488225	+	0.872718i	$0.337644\pi$
$710$	−1.00000			−0.0375293
$711$		0			0
$712$	−1.50000	+	2.59808i	−0.0562149	+	0.0973670i
$713$	−17.5000	−	30.3109i	−0.655380	−	1.13515i
$714$		0			0
$715$		0			0
$716$	0.500000	+	0.866025i	0.0186859	+	0.0323649i
$717$		0			0
$718$	−9.50000	−	16.4545i	−0.354537	−	0.614076i
$719$	−15.5000	+	26.8468i	−0.578052	+	1.00122i	0.417650	+	0.908608i	$0.362854\pi$
$719$	−15.5000	+	26.8468i	−0.578052	+	1.00122i	−0.995703	+	0.0926083i	$0.970480\pi$
$720$		0			0
$721$	−10.5000	+	18.1865i	−0.391040	+	0.677302i
$722$	−9.00000	−	15.5885i	−0.334945	−	0.580142i
$723$		0			0
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	−32.0000			−1.18681			−0.593407	−	0.804902i	$-0.702218\pi$
$727$	−32.0000			−1.18681			−0.593407	+	0.804902i	$0.702218\pi$
$728$	22.5000	−	38.9711i	0.833905	−	1.44437i
$729$		0			0
$730$	−11.0000			−0.407128
$731$	−19.5000	−	2.59808i	−0.721234	−	0.0960933i
$732$		0			0
$733$	26.0000			0.960332			0.480166	−	0.877178i	$-0.340576\pi$
$733$	26.0000			0.960332			0.480166	+	0.877178i	$0.340576\pi$
$734$	6.50000	−	11.2583i	0.239919	−	0.415553i
$735$		0			0
$736$	17.5000	−	30.3109i	0.645059	−	1.11727i
$737$		0			0
$738$		0			0
$739$	−4.00000			−0.147142			−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000			−0.147142			−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−4.50000	−	7.79423i	−0.165423	−	0.286522i
$741$		0			0
$742$	−15.0000			−0.550667
$743$	10.5000	−	18.1865i	0.385208	−	0.667199i	−0.606590	−	0.795015i	$-0.707463\pi$
$743$	10.5000	−	18.1865i	0.385208	−	0.667199i	0.991798	+	0.127815i	$0.0407965\pi$
$744$		0			0
$745$	−10.5000	−	18.1865i	−0.384690	−	0.666303i
$746$	5.50000	+	9.52628i	0.201369	+	0.348782i
$747$		0			0
$748$		0			0
$749$	18.0000	+	31.1769i	0.657706	+	1.13918i
$750$		0			0
$751$	13.5000	−	23.3827i	0.492622	−	0.853246i	−0.507342	−	0.861745i	$-0.669372\pi$
$751$	13.5000	−	23.3827i	0.492622	−	0.853246i	0.999964	+	0.00849853i	$0.00270520\pi$
$752$	−8.00000			−0.291730
$753$		0			0
$754$	7.50000	−	12.9904i	0.273134	−	0.473082i
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$		0			0
$757$	2.50000	+	4.33013i	0.0908640	+	0.157381i	0.907875	−	0.419241i	$-0.137704\pi$
$757$	2.50000	+	4.33013i	0.0908640	+	0.157381i	−0.817011	+	0.576622i	$0.804370\pi$
$758$	−20.0000			−0.726433
$759$		0			0
$760$	−1.50000	−	2.59808i	−0.0544107	−	0.0942421i
$761$	−18.5000	−	32.0429i	−0.670624	−	1.16156i	−0.977727	−	0.209879i	$-0.932693\pi$
$761$	−18.5000	−	32.0429i	−0.670624	−	1.16156i	0.307103	−	0.951676i	$-0.400640\pi$
$762$		0			0
$763$	21.0000			0.760251
$764$	9.50000	−	16.4545i	0.343698	−	0.595302i
$765$		0			0
$766$	8.00000			0.289052
$767$	−30.0000	−	51.9615i	−1.08324	−	1.87622i
$768$		0			0
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	−0.398541	−	0.917151i	$-0.630483\pi$
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	0.993546	−	0.113429i	$-0.0361834\pi$
$770$		0			0
$771$		0			0
$772$	−6.00000			−0.215945
$773$	−26.0000			−0.935155			−0.467578	−	0.883952i	$-0.654873\pi$
$773$	−26.0000			−0.935155			−0.467578	+	0.883952i	$0.654873\pi$
$774$		0			0
$775$	−20.0000			−0.718421
$776$	−6.00000			−0.215387
$777$		0			0
$778$	−6.00000			−0.215110
$779$	−5.00000	+	8.66025i	−0.179144	+	0.310286i
$780$		0			0
$781$		0			0
$782$	21.0000			0.750958
$783$		0			0
$784$	1.00000	−	1.73205i	0.0357143	−	0.0618590i
$785$	−1.00000			−0.0356915
$786$		0			0
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	0.907137	−	0.420834i	$-0.138263\pi$
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	−0.818022	+	0.575187i	$0.804929\pi$
$788$	−5.50000	−	9.52628i	−0.195929	−	0.339360i
$789$		0			0
$790$	5.00000			0.177892
$791$	−3.00000	−	5.19615i	−0.106668	−	0.184754i
$792$		0			0
$793$	−32.5000	+	56.2917i	−1.15411	+	1.99898i
$794$	−10.5000	+	18.1865i	−0.372631	+	0.645416i
$795$		0			0
$796$	−8.00000			−0.283552
$797$	−10.5000	+	18.1865i	−0.371929	+	0.644200i	−0.989862	−	0.142031i	$-0.954637\pi$
$797$	−10.5000	+	18.1865i	−0.371929	+	0.644200i	0.617933	+	0.786231i	$0.287970\pi$
$798$		0			0
$799$	12.0000	+	20.7846i	0.424529	+	0.735307i
$800$	−10.0000	−	17.3205i	−0.353553	−	0.612372i
$801$		0			0
$802$	18.5000	+	32.0429i	0.653258	+	1.13148i
$803$		0			0
$804$		0			0
$805$	−10.5000	+	18.1865i	−0.370076	+	0.640991i
$806$	25.0000			0.880587
$807$		0			0
$808$	−13.5000	−	23.3827i	−0.474928	−	0.822600i
$809$	34.0000			1.19538			0.597688	−	0.801729i	$-0.296086\pi$
$809$	34.0000			1.19538			0.597688	+	0.801729i	$0.296086\pi$
$810$		0			0
$811$	23.5000	−	40.7032i	0.825197	−	1.42928i	−0.0765723	−	0.997064i	$-0.524398\pi$
$811$	23.5000	−	40.7032i	0.825197	−	1.42928i	0.901769	−	0.432218i	$-0.142269\pi$
$812$	−4.50000	+	7.79423i	−0.157919	+	0.273524i
$813$		0			0
$814$		0			0
$815$	−1.00000			−0.0350285
$816$		0			0
$817$	−2.50000	−	6.06218i	−0.0874639	−	0.212089i
$818$	18.0000			0.629355
$819$		0			0
$820$	5.00000	−	8.66025i	0.174608	−	0.302429i
$821$	−10.0000			−0.349002			−0.174501	−	0.984657i	$-0.555831\pi$
$821$	−10.0000			−0.349002			−0.174501	+	0.984657i	$0.555831\pi$
$822$		0			0
$823$	15.5000	−	26.8468i	0.540296	−	0.935820i	−0.458591	−	0.888648i	$-0.651646\pi$
$823$	15.5000	−	26.8468i	0.540296	−	0.935820i	0.998887	−	0.0471726i	$-0.0150211\pi$
$824$	−10.5000	−	18.1865i	−0.365785	−	0.633558i
$825$		0			0
$826$	−18.0000	−	31.1769i	−0.626300	−	1.08478i
$827$	16.5000	−	28.5788i	0.573761	−	0.993784i	−0.422414	−	0.906403i	$-0.638817\pi$
$827$	16.5000	−	28.5788i	0.573761	−	0.993784i	0.996175	−	0.0873805i	$-0.0278496\pi$
$828$		0			0
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	−0.945589	−	0.325362i	$-0.894514\pi$
$829$	−5.50000	+	9.52628i	−0.191023	+	0.330861i	0.754567	+	0.656223i	$0.227847\pi$
$830$	−4.50000	−	7.79423i	−0.156197	−	0.270542i
$831$		0			0
$832$	17.5000	+	30.3109i	0.606703	+	1.05084i
$833$	−6.00000			−0.207888
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$		0			0
$837$		0			0
$838$	−28.0000			−0.967244
$839$	52.0000			1.79524			0.897620	−	0.440771i	$-0.145295\pi$
$839$	52.0000			1.79524			0.897620	+	0.440771i	$0.145295\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	−18.5000	−	32.0429i	−0.637552	−	1.10427i
$843$		0			0
$844$	−8.00000			−0.275371
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$	16.5000	+	28.5788i	0.566947	+	0.981981i
$848$	2.50000	−	4.33013i	0.0858504	−	0.148697i
$849$		0			0
$850$	6.00000	−	10.3923i	0.205798	−	0.356453i
$851$	31.5000	+	54.5596i	1.07981	+	1.87028i
$852$		0			0
$853$	2.50000	+	4.33013i	0.0855984	+	0.148261i	0.905646	−	0.424034i	$-0.139386\pi$
$853$	2.50000	+	4.33013i	0.0855984	+	0.148261i	−0.820048	+	0.572295i	$0.806053\pi$
$854$	−19.5000	+	33.7750i	−0.667276	+	1.15576i
$855$		0			0
$856$	−36.0000			−1.23045
$857$	17.5000	−	30.3109i	0.597789	−	1.03540i	−0.395358	−	0.918527i	$-0.629380\pi$
$857$	17.5000	−	30.3109i	0.597789	−	1.03540i	0.993147	−	0.116873i	$-0.0372871\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	2.50000	+	6.06218i	0.0852493	+	0.206719i
$861$		0			0
$862$		0			0
$863$	−13.5000	+	23.3827i	−0.459545	+	0.795956i	−0.998937	−	0.0460992i	$-0.985321\pi$
$863$	−13.5000	+	23.3827i	−0.459545	+	0.795956i	0.539392	+	0.842055i	$0.318654\pi$
$864$		0			0
$865$	−3.00000	+	5.19615i	−0.102003	+	0.176674i
$866$	13.5000	−	23.3827i	0.458749	−	0.794576i
$867$		0			0
$868$	−15.0000			−0.509133
$869$		0			0
$870$		0			0
$871$	15.0000			0.508256
$872$	−10.5000	+	18.1865i	−0.355575	+	0.615874i
$873$		0			0
$874$	3.50000	+	6.06218i	0.118389	+	0.205056i
$875$	13.5000	+	23.3827i	0.456383	+	0.790479i
$876$		0			0
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	0.603897	−	0.797062i	$-0.293614\pi$
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	−0.992225	+	0.124459i	$0.960280\pi$
$878$	−6.50000	−	11.2583i	−0.219364	−	0.379950i
$879$		0			0
$880$		0			0
$881$	−46.0000			−1.54978			−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000			−1.54978			−0.774890	+	0.632096i	$0.782195\pi$
$882$		0			0
$883$	−6.50000	+	11.2583i	−0.218742	+	0.378873i	−0.954424	−	0.298455i	$-0.903529\pi$
$883$	−6.50000	+	11.2583i	−0.218742	+	0.378873i	0.735681	+	0.677328i	$0.236862\pi$
$884$	7.50000	−	12.9904i	0.252252	−	0.436914i
$885$		0			0
$886$	18.5000	+	32.0429i	0.621520	+	1.07650i
$887$	16.0000			0.537227			0.268614	−	0.963248i	$-0.413434\pi$
$887$	16.0000			0.537227			0.268614	+	0.963248i	$0.413434\pi$
$888$		0			0
$889$	−24.0000	−	41.5692i	−0.804934	−	1.39419i
$890$	0.500000	+	0.866025i	0.0167600	+	0.0290292i
$891$		0			0
$892$	−20.0000			−0.669650
$893$	−4.00000	+	6.92820i	−0.133855	+	0.231843i
$894$		0			0
$895$	1.00000			0.0334263
$896$	−4.50000	−	7.79423i	−0.150334	−	0.260387i
$897$		0			0
$898$	10.5000	−	18.1865i	0.350390	−	0.606892i
$899$	−15.0000			−0.500278
$900$		0			0
$901$	−15.0000			−0.499722
$902$		0			0
$903$		0			0
$904$	6.00000			0.199557
$905$	7.00000			0.232688
$906$		0			0
$907$	20.0000			0.664089			0.332045	−	0.943264i	$-0.392262\pi$
$907$	20.0000			0.664089			0.332045	+	0.943264i	$0.392262\pi$
$908$	3.50000	−	6.06218i	0.116152	−	0.201180i
$909$		0			0
$910$	−7.50000	−	12.9904i	−0.248623	−	0.430627i
$911$	52.0000			1.72284			0.861418	−	0.507896i	$-0.169577\pi$
$911$	52.0000			1.72284			0.861418	+	0.507896i	$0.169577\pi$
$912$		0			0
$913$		0			0
$914$	−6.00000			−0.198462
$915$		0			0
$916$	−4.50000	−	7.79423i	−0.148684	−	0.257529i
$917$	−6.00000	−	10.3923i	−0.198137	−	0.343184i
$918$		0			0
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$	−10.5000	−	18.1865i	−0.346175	−	0.599592i
$921$		0			0
$922$	−1.50000	+	2.59808i	−0.0493999	+	0.0855631i
$923$	2.50000	−	4.33013i	0.0822885	−	0.142528i
$924$		0			0
$925$	36.0000			1.18367
$926$	−11.5000	+	19.9186i	−0.377913	+	0.654565i
$927$		0			0
$928$	−7.50000	−	12.9904i	−0.246200	−	0.426430i
$929$	−28.5000	−	49.3634i	−0.935055	−	1.61956i	−0.774536	−	0.632529i	$-0.782017\pi$
$929$	−28.5000	−	49.3634i	−0.935055	−	1.61956i	−0.160518	−	0.987033i	$-0.551317\pi$
$930$		0			0
$931$	−1.00000	−	1.73205i	−0.0327737	−	0.0567657i
$932$	4.50000	+	7.79423i	0.147402	+	0.255308i
$933$		0			0
$934$	−10.5000	+	18.1865i	−0.343570	+	0.595082i
$935$		0			0
$936$		0			0
$937$	−17.5000	−	30.3109i	−0.571700	−	0.990214i	−0.996392	−	0.0848755i	$-0.972951\pi$
$937$	−17.5000	−	30.3109i	−0.571700	−	0.990214i	0.424691	−	0.905338i	$-0.360383\pi$
$938$	9.00000			0.293860
$939$		0			0
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	−4.50000	+	7.79423i	−0.146696	+	0.254085i	−0.930004	−	0.367549i	$-0.880197\pi$
$941$	−4.50000	+	7.79423i	−0.146696	+	0.254085i	0.783309	+	0.621633i	$0.213531\pi$
$942$		0			0
$943$	−35.0000	+	60.6218i	−1.13976	+	1.97412i
$944$	12.0000			0.390567
$945$		0			0
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	27.5000	−	47.6314i	0.892688	−	1.54618i
$950$	4.00000			0.129777
$951$		0			0
$952$	13.5000	−	23.3827i	0.437538	−	0.757837i
$953$	−20.5000	−	35.5070i	−0.664060	−	1.15019i	−0.979539	−	0.201253i	$-0.935499\pi$
$953$	−20.5000	−	35.5070i	−0.664060	−	1.15019i	0.315479	−	0.948933i	$-0.397835\pi$
$954$		0			0
$955$	−9.50000	−	16.4545i	−0.307413	−	0.532455i
$956$	−12.5000	+	21.6506i	−0.404279	+	0.700232i
$957$		0			0
$958$	7.50000	−	12.9904i	0.242314	−	0.419700i
$959$	−27.0000	−	46.7654i	−0.871875	−	1.51013i
$960$		0			0
$961$	3.00000	+	5.19615i	0.0967742	+	0.167618i
$962$	−45.0000			−1.45086
$963$		0			0
$964$	7.50000	+	12.9904i	0.241559	+	0.418392i
$965$	−3.00000	+	5.19615i	−0.0965734	+	0.167270i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−33.0000			−1.06066
$969$		0			0
$970$	−1.00000	+	1.73205i	−0.0321081	+	0.0556128i
$971$	17.5000	+	30.3109i	0.561602	+	0.972723i	0.997357	+	0.0726575i	$0.0231480\pi$
$971$	17.5000	+	30.3109i	0.561602	+	0.972723i	−0.435755	+	0.900065i	$0.643519\pi$
$972$		0			0
$973$	39.0000			1.25028
$974$	−4.50000	−	7.79423i	−0.144189	−	0.249743i
$975$		0			0
$976$	−6.50000	−	11.2583i	−0.208060	−	0.360370i
$977$	−20.5000	+	35.5070i	−0.655853	+	1.13597i	0.325826	+	0.945430i	$0.394358\pi$
$977$	−20.5000	+	35.5070i	−0.655853	+	1.13597i	−0.981679	+	0.190541i	$0.938976\pi$
$978$		0			0
$979$		0			0
$980$	1.00000	+	1.73205i	0.0319438	+	0.0553283i
$981$		0			0
$982$	4.50000	+	7.79423i	0.143601	+	0.248724i
$983$	−25.5000	+	44.1673i	−0.813324	+	1.40872i	0.0972017	+	0.995265i	$0.469011\pi$
$983$	−25.5000	+	44.1673i	−0.813324	+	1.40872i	−0.910525	+	0.413453i	$0.864323\pi$
$984$		0			0
$985$	−11.0000			−0.350489
$986$	4.50000	−	7.79423i	0.143309	−	0.248219i
$987$		0			0
$988$	5.00000			0.159071
$989$	−17.5000	−	42.4352i	−0.556468	−	1.34936i
$990$		0			0
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$	12.5000	−	21.6506i	0.396875	−	0.687408i
$993$		0			0
$994$	1.50000	−	2.59808i	0.0475771	−	0.0824060i
$995$	−4.00000	+	6.92820i	−0.126809	+	0.219639i
$996$		0			0
$997$	−14.0000			−0.443384			−0.221692	−	0.975117i	$-0.571158\pi$
$997$	−14.0000			−0.443384			−0.221692	+	0.975117i	$0.571158\pi$
$998$	−8.50000	−	14.7224i	−0.269063	−	0.466030i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.2.h.a.307.1		2
3.2	odd	2		43.2.c.a.6.1	✓	2
12.11	even	2		688.2.i.d.49.1		2
43.36	even	3	inner	387.2.h.a.208.1		2
129.80	even	6		1849.2.a.a.1.1		1
129.92	odd	6		1849.2.a.c.1.1		1
129.122	odd	6		43.2.c.a.36.1	yes	2
516.251	even	6		688.2.i.d.337.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.a.6.1	✓	2	3.2	odd	2
43.2.c.a.36.1	yes	2	129.122	odd	6
387.2.h.a.208.1		2	43.36	even	3	inner
387.2.h.a.307.1		2	1.1	even	1	trivial
688.2.i.d.49.1		2	12.11	even	2
688.2.i.d.337.1		2	516.251	even	6
1849.2.a.a.1.1		1	129.80	even	6
1849.2.a.c.1.1		1	129.92	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:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	387.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(2.50000 + 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{14} -1.00000 q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-3.50000 + 6.06218i) q^{23} +(2.00000 + 3.46410i) q^{25} +(-2.50000 - 4.33013i) q^{26} +(1.50000 + 2.59808i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-2.50000 + 4.33013i) q^{31} -5.00000 q^{32} +(-1.50000 - 2.59808i) q^{34} +3.00000 q^{35} +(4.50000 - 7.79423i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-1.50000 + 2.59808i) q^{40} +10.0000 q^{41} +(-4.00000 + 5.19615i) q^{43} +(3.50000 - 6.06218i) q^{46} +8.00000 q^{47} +(-1.00000 + 1.73205i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-2.50000 - 4.33013i) q^{52} +(-2.50000 + 4.33013i) q^{53} +(-4.50000 - 7.79423i) q^{56} +(-1.50000 - 2.59808i) q^{58} -12.0000 q^{59} +(6.50000 + 11.2583i) q^{61} +(2.50000 - 4.33013i) q^{62} +7.00000 q^{64} -5.00000 q^{65} +(1.50000 - 2.59808i) q^{67} +(-1.50000 - 2.59808i) q^{68} -3.00000 q^{70} +(-0.500000 - 0.866025i) q^{71} +(-5.50000 - 9.52628i) q^{73} +(-4.50000 + 7.79423i) q^{74} +(0.500000 - 0.866025i) q^{76} +(2.50000 + 4.33013i) q^{79} +(0.500000 - 0.866025i) q^{80} -10.0000 q^{82} +(4.50000 - 7.79423i) q^{83} -3.00000 q^{85} +(4.00000 - 5.19615i) q^{86} +(-0.500000 + 0.866025i) q^{89} +(7.50000 - 12.9904i) q^{91} +(3.50000 - 6.06218i) q^{92} -8.00000 q^{94} +(-0.500000 - 0.866025i) q^{95} -2.00000 q^{97} +(1.00000 - 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^4 - q^5 - 3 * q^7 + 6 * q^8	\( 2 q - 2 q^{2} - 2 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + q^{10} + 5 q^{13} + 3 q^{14} - 2 q^{16} + 3 q^{17} - q^{19} + q^{20} - 7 q^{23} + 4 q^{25} - 5 q^{26} + 3 q^{28} + 3 q^{29} - 5 q^{31} - 10 q^{32} - 3 q^{34} + 6 q^{35} + 9 q^{37} + q^{38} - 3 q^{40} + 20 q^{41} - 8 q^{43} + 7 q^{46} + 16 q^{47} - 2 q^{49} - 4 q^{50} - 5 q^{52} - 5 q^{53} - 9 q^{56} - 3 q^{58} - 24 q^{59} + 13 q^{61} + 5 q^{62} + 14 q^{64} - 10 q^{65} + 3 q^{67} - 3 q^{68} - 6 q^{70} - q^{71} - 11 q^{73} - 9 q^{74} + q^{76} + 5 q^{79} + q^{80} - 20 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - q^{89} + 15 q^{91} + 7 q^{92} - 16 q^{94} - q^{95} - 4 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + q^10 + 5 * q^13 + 3 * q^14 - 2 * q^16 + 3 * q^17 - q^19 + q^20 - 7 * q^23 + 4 * q^25 - 5 * q^26 + 3 * q^28 + 3 * q^29 - 5 * q^31 - 10 * q^32 - 3 * q^34 + 6 * q^35 + 9 * q^37 + q^38 - 3 * q^40 + 20 * q^41 - 8 * q^43 + 7 * q^46 + 16 * q^47 - 2 * q^49 - 4 * q^50 - 5 * q^52 - 5 * q^53 - 9 * q^56 - 3 * q^58 - 24 * q^59 + 13 * q^61 + 5 * q^62 + 14 * q^64 - 10 * q^65 + 3 * q^67 - 3 * q^68 - 6 * q^70 - q^71 - 11 * q^73 - 9 * q^74 + q^76 + 5 * q^79 + q^80 - 20 * q^82 + 9 * q^83 - 6 * q^85 + 8 * q^86 - q^89 + 15 * q^91 + 7 * q^92 - 16 * q^94 - q^95 - 4 * q^97 + 2 * q^98

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