LMFDB - Embedded newform 735.2.b.a.146.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(146,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("735.146");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.b (of order $2$, degree $1$, 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:	$5.86900454856$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.2
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	735.146
Dual form			735.2.b.a.146.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73205i q^{2} +(-1.50000 + 0.866025i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.50000 - 2.59808i) q^{6} +1.73205i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+1.73205i q^{2} +(-1.50000 + 0.866025i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.50000 - 2.59808i) q^{6} +1.73205i q^{8} +(1.50000 - 2.59808i) q^{9} -1.73205i q^{10} -3.46410i q^{11} +(1.50000 - 0.866025i) q^{12} -3.46410i q^{13} +(1.50000 - 0.866025i) q^{15} -5.00000 q^{16} -6.00000 q^{17} +(4.50000 + 2.59808i) q^{18} -6.92820i q^{19} +1.00000 q^{20} +6.00000 q^{22} -1.73205i q^{23} +(-1.50000 - 2.59808i) q^{24} +1.00000 q^{25} +6.00000 q^{26} +5.19615i q^{27} -1.73205i q^{29} +(1.50000 + 2.59808i) q^{30} +3.46410i q^{31} -5.19615i q^{32} +(3.00000 + 5.19615i) q^{33} -10.3923i q^{34} +(-1.50000 + 2.59808i) q^{36} +4.00000 q^{37} +12.0000 q^{38} +(3.00000 + 5.19615i) q^{39} -1.73205i q^{40} +3.00000 q^{41} +1.00000 q^{43} +3.46410i q^{44} +(-1.50000 + 2.59808i) q^{45} +3.00000 q^{46} +(7.50000 - 4.33013i) q^{48} +1.73205i q^{50} +(9.00000 - 5.19615i) q^{51} +3.46410i q^{52} -9.00000 q^{54} +3.46410i q^{55} +(6.00000 + 10.3923i) q^{57} +3.00000 q^{58} +(-1.50000 + 0.866025i) q^{60} -5.19615i q^{61} -6.00000 q^{62} -1.00000 q^{64} +3.46410i q^{65} +(-9.00000 + 5.19615i) q^{66} -13.0000 q^{67} +6.00000 q^{68} +(1.50000 + 2.59808i) q^{69} -6.92820i q^{71} +(4.50000 + 2.59808i) q^{72} -3.46410i q^{73} +6.92820i q^{74} +(-1.50000 + 0.866025i) q^{75} +6.92820i q^{76} +(-9.00000 + 5.19615i) q^{78} -16.0000 q^{79} +5.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +5.19615i q^{82} +9.00000 q^{83} +6.00000 q^{85} +1.73205i q^{86} +(1.50000 + 2.59808i) q^{87} +6.00000 q^{88} -3.00000 q^{89} +(-4.50000 - 2.59808i) q^{90} +1.73205i q^{92} +(-3.00000 - 5.19615i) q^{93} +6.92820i q^{95} +(4.50000 + 7.79423i) q^{96} +10.3923i q^{97} +(-9.00000 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} - 2 q^{4} - 2 q^{5} - 3 q^{6} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 - 2 * q^4 - 2 * q^5 - 3 * q^6 + 3 * q^9	$ 2 q - 3 q^{3} - 2 q^{4} - 2 q^{5} - 3 q^{6} + 3 q^{9} + 3 q^{12} + 3 q^{15} - 10 q^{16} - 12 q^{17} + 9 q^{18} + 2 q^{20} + 12 q^{22} - 3 q^{24} + 2 q^{25} + 12 q^{26} + 3 q^{30} + 6 q^{33} - 3 q^{36} + 8 q^{37} + 24 q^{38} + 6 q^{39} + 6 q^{41} + 2 q^{43} - 3 q^{45} + 6 q^{46} + 15 q^{48} + 18 q^{51} - 18 q^{54} + 12 q^{57} + 6 q^{58} - 3 q^{60} - 12 q^{62} - 2 q^{64} - 18 q^{66} - 26 q^{67} + 12 q^{68} + 3 q^{69} + 9 q^{72} - 3 q^{75} - 18 q^{78} - 32 q^{79} + 10 q^{80} - 9 q^{81} + 18 q^{83} + 12 q^{85} + 3 q^{87} + 12 q^{88} - 6 q^{89} - 9 q^{90} - 6 q^{93} + 9 q^{96} - 18 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 - 2 * q^4 - 2 * q^5 - 3 * q^6 + 3 * q^9 + 3 * q^12 + 3 * q^15 - 10 * q^16 - 12 * q^17 + 9 * q^18 + 2 * q^20 + 12 * q^22 - 3 * q^24 + 2 * q^25 + 12 * q^26 + 3 * q^30 + 6 * q^33 - 3 * q^36 + 8 * q^37 + 24 * q^38 + 6 * q^39 + 6 * q^41 + 2 * q^43 - 3 * q^45 + 6 * q^46 + 15 * q^48 + 18 * q^51 - 18 * q^54 + 12 * q^57 + 6 * q^58 - 3 * q^60 - 12 * q^62 - 2 * q^64 - 18 * q^66 - 26 * q^67 + 12 * q^68 + 3 * q^69 + 9 * q^72 - 3 * q^75 - 18 * q^78 - 32 * q^79 + 10 * q^80 - 9 * q^81 + 18 * q^83 + 12 * q^85 + 3 * q^87 + 12 * q^88 - 6 * q^89 - 9 * q^90 - 6 * q^93 + 9 * q^96 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			1.73205i			1.22474i	0.790569	+	0.612372i	$0.209785\pi$
$2$			1.73205i			1.22474i	−0.790569	+	0.612372i	$0.790215\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.50000	−	2.59808i	−0.612372	−	1.06066i
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		−	1.73205i		−	0.547723i
$11$		−	3.46410i		−	1.04447i	−0.852803	−	0.522233i	$-0.825099\pi$
$11$		−	3.46410i		−	1.04447i	0.852803	−	0.522233i	$-0.174901\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$		−	3.46410i		−	0.960769i	−0.877058	−	0.480384i	$-0.840497\pi$
$13$		−	3.46410i		−	0.960769i	0.877058	−	0.480384i	$-0.159503\pi$
$14$		0			0
$15$	1.50000	−	0.866025i	0.387298	−	0.223607i
$16$	−5.00000			−1.25000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$	4.50000	+	2.59808i	1.06066	+	0.612372i
$19$		−	6.92820i		−	1.58944i	−0.606977	−	0.794719i	$-0.707618\pi$
$19$		−	6.92820i		−	1.58944i	0.606977	−	0.794719i	$-0.292382\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	6.00000			1.27920
$23$		−	1.73205i		−	0.361158i	−0.983561	−	0.180579i	$-0.942203\pi$
$23$		−	1.73205i		−	0.361158i	0.983561	−	0.180579i	$-0.0577971\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	1.00000			0.200000
$26$	6.00000			1.17670
$27$			5.19615i			1.00000i
$28$		0			0
$29$		−	1.73205i		−	0.321634i	−0.986984	−	0.160817i	$-0.948587\pi$
$29$		−	1.73205i		−	0.321634i	0.986984	−	0.160817i	$-0.0514129\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$			3.46410i			0.622171i	0.950382	+	0.311086i	$0.100693\pi$
$31$			3.46410i			0.622171i	−0.950382	+	0.311086i	$0.899307\pi$
$32$		−	5.19615i		−	0.918559i
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$		−	10.3923i		−	1.78227i
$35$		0			0
$36$	−1.50000	+	2.59808i	−0.250000	+	0.433013i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	12.0000			1.94666
$39$	3.00000	+	5.19615i	0.480384	+	0.832050i
$40$		−	1.73205i		−	0.273861i
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$			3.46410i			0.522233i
$45$	−1.50000	+	2.59808i	−0.223607	+	0.387298i
$46$	3.00000			0.442326
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	7.50000	−	4.33013i	1.08253	−	0.625000i
$49$		0			0
$50$			1.73205i			0.244949i
$51$	9.00000	−	5.19615i	1.26025	−	0.727607i
$52$			3.46410i			0.480384i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−9.00000			−1.22474
$55$			3.46410i			0.467099i
$56$		0			0
$57$	6.00000	+	10.3923i	0.794719	+	1.37649i
$58$	3.00000			0.393919
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$	−1.50000	+	0.866025i	−0.193649	+	0.111803i
$61$		−	5.19615i		−	0.665299i	−0.943051	−	0.332650i	$-0.892057\pi$
$61$		−	5.19615i		−	0.665299i	0.943051	−	0.332650i	$-0.107943\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	−1.00000			−0.125000
$65$			3.46410i			0.429669i
$66$	−9.00000	+	5.19615i	−1.10782	+	0.639602i
$67$	−13.0000			−1.58820			−0.794101	−	0.607785i	$-0.792058\pi$
$67$	−13.0000			−1.58820			−0.794101	+	0.607785i	$0.792058\pi$
$68$	6.00000			0.727607
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$		0			0
$71$		−	6.92820i		−	0.822226i	−0.911584	−	0.411113i	$-0.865140\pi$
$71$		−	6.92820i		−	0.822226i	0.911584	−	0.411113i	$-0.134860\pi$
$72$	4.50000	+	2.59808i	0.530330	+	0.306186i
$73$		−	3.46410i		−	0.405442i	−0.979236	−	0.202721i	$-0.935021\pi$
$73$		−	3.46410i		−	0.405442i	0.979236	−	0.202721i	$-0.0649785\pi$
$74$			6.92820i			0.805387i
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$			6.92820i			0.794719i
$77$		0			0
$78$	−9.00000	+	5.19615i	−1.01905	+	0.588348i
$79$	−16.0000			−1.80014			−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000			−1.80014			−0.900070	+	0.435745i	$0.856485\pi$
$80$	5.00000			0.559017
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$			5.19615i			0.573819i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$			1.73205i			0.186772i
$87$	1.50000	+	2.59808i	0.160817	+	0.278543i
$88$	6.00000			0.639602
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$	−4.50000	−	2.59808i	−0.474342	−	0.273861i
$91$		0			0
$92$			1.73205i			0.180579i
$93$	−3.00000	−	5.19615i	−0.311086	−	0.538816i
$94$		0			0
$95$			6.92820i			0.710819i
$96$	4.50000	+	7.79423i	0.459279	+	0.795495i
$97$			10.3923i			1.05518i	0.849500	+	0.527589i	$0.176904\pi$
$97$			10.3923i			1.05518i	−0.849500	+	0.527589i	$0.823096\pi$
$98$		0			0
$99$	−9.00000	−	5.19615i	−0.904534	−	0.522233i
$100$	−1.00000			−0.100000
$101$	15.0000			1.49256			0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000			1.49256			0.746278	+	0.665635i	$0.231839\pi$
$102$	9.00000	+	15.5885i	0.891133	+	1.54349i
$103$		−	5.19615i		−	0.511992i	−0.966678	−	0.255996i	$-0.917597\pi$
$103$		−	5.19615i		−	0.511992i	0.966678	−	0.255996i	$-0.0824034\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$		0			0
$107$		−	5.19615i		−	0.502331i	−0.967944	−	0.251166i	$-0.919186\pi$
$107$		−	5.19615i		−	0.502331i	0.967944	−	0.251166i	$-0.0808138\pi$
$108$		−	5.19615i		−	0.500000i
$109$	−5.00000			−0.478913			−0.239457	−	0.970907i	$-0.576969\pi$
$109$	−5.00000			−0.478913			−0.239457	+	0.970907i	$0.576969\pi$
$110$	−6.00000			−0.572078
$111$	−6.00000	+	3.46410i	−0.569495	+	0.328798i
$112$		0			0
$113$		−	6.92820i		−	0.651751i	−0.945413	−	0.325875i	$-0.894341\pi$
$113$		−	6.92820i		−	0.651751i	0.945413	−	0.325875i	$-0.105659\pi$
$114$	−18.0000	+	10.3923i	−1.68585	+	0.973329i
$115$			1.73205i			0.161515i
$116$			1.73205i			0.160817i
$117$	−9.00000	−	5.19615i	−0.832050	−	0.480384i
$118$		0			0
$119$		0			0
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	−1.00000			−0.0909091
$122$	9.00000			0.814822
$123$	−4.50000	+	2.59808i	−0.405751	+	0.234261i
$124$		−	3.46410i		−	0.311086i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		−	12.1244i		−	1.07165i
$129$	−1.50000	+	0.866025i	−0.132068	+	0.0762493i
$130$	−6.00000			−0.526235
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	−3.00000	−	5.19615i	−0.261116	−	0.452267i
$133$		0			0
$134$		−	22.5167i		−	1.94514i
$135$		−	5.19615i		−	0.447214i
$136$		−	10.3923i		−	0.891133i
$137$		−	20.7846i		−	1.77575i	−0.460086	−	0.887875i	$-0.652181\pi$
$137$		−	20.7846i		−	1.77575i	0.460086	−	0.887875i	$-0.347819\pi$
$138$	−4.50000	+	2.59808i	−0.383065	+	0.221163i
$139$		−	10.3923i		−	0.881464i	−0.897639	−	0.440732i	$-0.854719\pi$
$139$		−	10.3923i		−	0.881464i	0.897639	−	0.440732i	$-0.145281\pi$
$140$		0			0
$141$		0			0
$142$	12.0000			1.00702
$143$	−12.0000			−1.00349
$144$	−7.50000	+	12.9904i	−0.625000	+	1.08253i
$145$			1.73205i			0.143839i
$146$	6.00000			0.496564
$147$		0			0
$148$	−4.00000			−0.328798
$149$			22.5167i			1.84464i	0.386431	+	0.922318i	$0.373708\pi$
$149$			22.5167i			1.84464i	−0.386431	+	0.922318i	$0.626292\pi$
$150$	−1.50000	−	2.59808i	−0.122474	−	0.212132i
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	12.0000			0.973329
$153$	−9.00000	+	15.5885i	−0.727607	+	1.26025i
$154$		0			0
$155$		−	3.46410i		−	0.278243i
$156$	−3.00000	−	5.19615i	−0.240192	−	0.416025i
$157$			3.46410i			0.276465i	0.990400	+	0.138233i	$0.0441422\pi$
$157$			3.46410i			0.276465i	−0.990400	+	0.138233i	$0.955858\pi$
$158$		−	27.7128i		−	2.20471i
$159$		0			0
$160$			5.19615i			0.410792i
$161$		0			0
$162$	13.5000	−	7.79423i	1.06066	−	0.612372i
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	−3.00000			−0.234261
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$			15.5885i			1.20990i
$167$	−21.0000			−1.62503			−0.812514	−	0.582941i	$-0.801902\pi$
$167$	−21.0000			−1.62503			−0.812514	+	0.582941i	$0.801902\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$			10.3923i			0.797053i
$171$	−18.0000	−	10.3923i	−1.37649	−	0.794719i
$172$	−1.00000			−0.0762493
$173$	12.0000			0.912343			0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000			0.912343			0.456172	+	0.889892i	$0.349220\pi$
$174$	−4.50000	+	2.59808i	−0.341144	+	0.196960i
$175$		0			0
$176$			17.3205i			1.30558i
$177$		0			0
$178$		−	5.19615i		−	0.389468i
$179$		−	10.3923i		−	0.776757i	−0.921500	−	0.388379i	$-0.873035\pi$
$179$		−	10.3923i		−	0.776757i	0.921500	−	0.388379i	$-0.126965\pi$
$180$	1.50000	−	2.59808i	0.111803	−	0.193649i
$181$		−	5.19615i		−	0.386227i	−0.981176	−	0.193113i	$-0.938141\pi$
$181$		−	5.19615i		−	0.386227i	0.981176	−	0.193113i	$-0.0618586\pi$
$182$		0			0
$183$	4.50000	+	7.79423i	0.332650	+	0.576166i
$184$	3.00000			0.221163
$185$	−4.00000			−0.294086
$186$	9.00000	−	5.19615i	0.659912	−	0.381000i
$187$			20.7846i			1.51992i
$188$		0			0
$189$		0			0
$190$	−12.0000			−0.870572
$191$		−	10.3923i		−	0.751961i	−0.926628	−	0.375980i	$-0.877306\pi$
$191$		−	10.3923i		−	0.751961i	0.926628	−	0.375980i	$-0.122694\pi$
$192$	1.50000	−	0.866025i	0.108253	−	0.0625000i
$193$	22.0000			1.58359			0.791797	−	0.610784i	$-0.209146\pi$
$193$	22.0000			1.58359			0.791797	+	0.610784i	$0.209146\pi$
$194$	−18.0000			−1.29232
$195$	−3.00000	−	5.19615i	−0.214834	−	0.372104i
$196$		0			0
$197$		−	3.46410i		−	0.246807i	−0.992357	−	0.123404i	$-0.960619\pi$
$197$		−	3.46410i		−	0.246807i	0.992357	−	0.123404i	$-0.0393809\pi$
$198$	9.00000	−	15.5885i	0.639602	−	1.10782i
$199$		−	6.92820i		−	0.491127i	−0.969380	−	0.245564i	$-0.921027\pi$
$199$		−	6.92820i		−	0.491127i	0.969380	−	0.245564i	$-0.0789730\pi$
$200$			1.73205i			0.122474i
$201$	19.5000	−	11.2583i	1.37542	−	0.794101i
$202$			25.9808i			1.82800i
$203$		0			0
$204$	−9.00000	+	5.19615i	−0.630126	+	0.363803i
$205$	−3.00000			−0.209529
$206$	9.00000			0.627060
$207$	−4.50000	−	2.59808i	−0.312772	−	0.180579i
$208$			17.3205i			1.20096i
$209$	−24.0000			−1.66011
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$	9.00000			0.615227
$215$	−1.00000			−0.0681994
$216$	−9.00000			−0.612372
$217$		0			0
$218$		−	8.66025i		−	0.586546i
$219$	3.00000	+	5.19615i	0.202721	+	0.351123i
$220$		−	3.46410i		−	0.233550i
$221$			20.7846i			1.39812i
$222$	−6.00000	−	10.3923i	−0.402694	−	0.697486i
$223$			3.46410i			0.231973i	0.993251	+	0.115987i	$0.0370030\pi$
$223$			3.46410i			0.231973i	−0.993251	+	0.115987i	$0.962997\pi$
$224$		0			0
$225$	1.50000	−	2.59808i	0.100000	−	0.173205i
$226$	12.0000			0.798228
$227$	−12.0000			−0.796468			−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000			−0.796468			−0.398234	+	0.917284i	$0.630377\pi$
$228$	−6.00000	−	10.3923i	−0.397360	−	0.688247i
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	−3.00000			−0.197814
$231$		0			0
$232$	3.00000			0.196960
$233$		−	3.46410i		−	0.226941i	−0.993541	−	0.113470i	$-0.963803\pi$
$233$		−	3.46410i		−	0.226941i	0.993541	−	0.113470i	$-0.0361967\pi$
$234$	9.00000	−	15.5885i	0.588348	−	1.01905i
$235$		0			0
$236$		0			0
$237$	24.0000	−	13.8564i	1.55897	−	0.900070i
$238$		0			0
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$	−7.50000	+	4.33013i	−0.484123	+	0.279508i
$241$			6.92820i			0.446285i	0.974786	+	0.223142i	$0.0716315\pi$
$241$			6.92820i			0.446285i	−0.974786	+	0.223142i	$0.928369\pi$
$242$		−	1.73205i		−	0.111340i
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$			5.19615i			0.332650i
$245$		0			0
$246$	−4.50000	−	7.79423i	−0.286910	−	0.496942i
$247$	−24.0000			−1.52708
$248$	−6.00000			−0.381000
$249$	−13.5000	+	7.79423i	−0.855528	+	0.493939i
$250$		−	1.73205i		−	0.109545i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$		−	27.7128i		−	1.73886i
$255$	−9.00000	+	5.19615i	−0.563602	+	0.325396i
$256$	19.0000			1.18750
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$	−1.50000	−	2.59808i	−0.0933859	−	0.161749i
$259$		0			0
$260$		−	3.46410i		−	0.214834i
$261$	−4.50000	−	2.59808i	−0.278543	−	0.160817i
$262$		−	20.7846i		−	1.28408i
$263$			1.73205i			0.106803i	0.998573	+	0.0534014i	$0.0170063\pi$
$263$			1.73205i			0.106803i	−0.998573	+	0.0534014i	$0.982994\pi$
$264$	−9.00000	+	5.19615i	−0.553912	+	0.319801i
$265$		0			0
$266$		0			0
$267$	4.50000	−	2.59808i	0.275396	−	0.159000i
$268$	13.0000			0.794101
$269$	3.00000			0.182913			0.0914566	−	0.995809i	$-0.470848\pi$
$269$	3.00000			0.182913			0.0914566	+	0.995809i	$0.470848\pi$
$270$	9.00000			0.547723
$271$			6.92820i			0.420858i	0.977609	+	0.210429i	$0.0674861\pi$
$271$			6.92820i			0.420858i	−0.977609	+	0.210429i	$0.932514\pi$
$272$	30.0000			1.81902
$273$		0			0
$274$	36.0000			2.17484
$275$		−	3.46410i		−	0.208893i
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$	18.0000			1.07957
$279$	9.00000	+	5.19615i	0.538816	+	0.311086i
$280$		0			0
$281$		−	6.92820i		−	0.413302i	−0.978415	−	0.206651i	$-0.933744\pi$
$281$		−	6.92820i		−	0.413302i	0.978415	−	0.206651i	$-0.0662565\pi$
$282$		0			0
$283$			31.1769i			1.85328i	0.375956	+	0.926638i	$0.377314\pi$
$283$			31.1769i			1.85328i	−0.375956	+	0.926638i	$0.622686\pi$
$284$			6.92820i			0.411113i
$285$	−6.00000	−	10.3923i	−0.355409	−	0.615587i
$286$		−	20.7846i		−	1.22902i
$287$		0			0
$288$	−13.5000	−	7.79423i	−0.795495	−	0.459279i
$289$	19.0000			1.11765
$290$	−3.00000			−0.176166
$291$	−9.00000	−	15.5885i	−0.527589	−	0.913812i
$292$			3.46410i			0.202721i
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$		0			0
$295$		0			0
$296$			6.92820i			0.402694i
$297$	18.0000			1.04447
$298$	−39.0000			−2.25921
$299$	−6.00000			−0.346989
$300$	1.50000	−	0.866025i	0.0866025	−	0.0500000i
$301$		0			0
$302$		−	3.46410i		−	0.199337i
$303$	−22.5000	+	12.9904i	−1.29259	+	0.746278i
$304$			34.6410i			1.98680i
$305$			5.19615i			0.297531i
$306$	−27.0000	−	15.5885i	−1.54349	−	0.891133i
$307$		−	22.5167i		−	1.28509i	−0.766246	−	0.642547i	$-0.777878\pi$
$307$		−	22.5167i		−	1.28509i	0.766246	−	0.642547i	$-0.222122\pi$
$308$		0			0
$309$	4.50000	+	7.79423i	0.255996	+	0.443398i
$310$	6.00000			0.340777
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$	−9.00000	+	5.19615i	−0.509525	+	0.294174i
$313$		0			0		1.00000			$0$
$313$		0			0		−1.00000			$\pi$
$314$	−6.00000			−0.338600
$315$		0			0
$316$	16.0000			0.900070
$317$			17.3205i			0.972817i	0.873732	+	0.486408i	$0.161693\pi$
$317$			17.3205i			0.972817i	−0.873732	+	0.486408i	$0.838307\pi$
$318$		0			0
$319$	−6.00000			−0.335936
$320$	1.00000			0.0559017
$321$	4.50000	+	7.79423i	0.251166	+	0.435031i
$322$		0			0
$323$			41.5692i			2.31297i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		−	3.46410i		−	0.192154i
$326$			13.8564i			0.767435i
$327$	7.50000	−	4.33013i	0.414751	−	0.239457i
$328$			5.19615i			0.286910i
$329$		0			0
$330$	9.00000	−	5.19615i	0.495434	−	0.286039i
$331$	10.0000			0.549650			0.274825	−	0.961494i	$-0.411380\pi$
$331$	10.0000			0.549650			0.274825	+	0.961494i	$0.411380\pi$
$332$	−9.00000			−0.493939
$333$	6.00000	−	10.3923i	0.328798	−	0.569495i
$334$		−	36.3731i		−	1.99025i
$335$	13.0000			0.710266
$336$		0			0
$337$	−32.0000			−1.74315			−0.871576	−	0.490261i	$-0.836901\pi$
$337$	−32.0000			−1.74315			−0.871576	+	0.490261i	$0.836901\pi$
$338$			1.73205i			0.0942111i
$339$	6.00000	+	10.3923i	0.325875	+	0.564433i
$340$	−6.00000			−0.325396
$341$	12.0000			0.649836
$342$	18.0000	−	31.1769i	0.973329	−	1.68585i
$343$		0			0
$344$			1.73205i			0.0933859i
$345$	−1.50000	−	2.59808i	−0.0807573	−	0.139876i
$346$			20.7846i			1.11739i
$347$			19.0526i			1.02279i	0.859344	+	0.511397i	$0.170872\pi$
$347$			19.0526i			1.02279i	−0.859344	+	0.511397i	$0.829128\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$			8.66025i			0.463573i	0.972767	+	0.231786i	$0.0744570\pi$
$349$			8.66025i			0.463573i	−0.972767	+	0.231786i	$0.925543\pi$
$350$		0			0
$351$	18.0000			0.960769
$352$	−18.0000			−0.959403
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$		0			0
$355$			6.92820i			0.367711i
$356$	3.00000			0.159000
$357$		0			0
$358$	18.0000			0.951330
$359$			24.2487i			1.27980i	0.768459	+	0.639899i	$0.221024\pi$
$359$			24.2487i			1.27980i	−0.768459	+	0.639899i	$0.778976\pi$
$360$	−4.50000	−	2.59808i	−0.237171	−	0.136931i
$361$	−29.0000			−1.52632
$362$	9.00000			0.473029
$363$	1.50000	−	0.866025i	0.0787296	−	0.0454545i
$364$		0			0
$365$			3.46410i			0.181319i
$366$	−13.5000	+	7.79423i	−0.705656	+	0.407411i
$367$		−	15.5885i		−	0.813711i	−0.913493	−	0.406855i	$-0.866625\pi$
$367$		−	15.5885i		−	0.813711i	0.913493	−	0.406855i	$-0.133375\pi$
$368$			8.66025i			0.451447i
$369$	4.50000	−	7.79423i	0.234261	−	0.405751i
$370$		−	6.92820i		−	0.360180i
$371$		0			0
$372$	3.00000	+	5.19615i	0.155543	+	0.269408i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$	−36.0000			−1.86152
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$		0			0
$377$	−6.00000			−0.309016
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		−	6.92820i		−	0.355409i
$381$	24.0000	−	13.8564i	1.22956	−	0.709885i
$382$	18.0000			0.920960
$383$	−21.0000			−1.07305			−0.536525	−	0.843884i	$-0.680263\pi$
$383$	−21.0000			−1.07305			−0.536525	+	0.843884i	$0.680263\pi$
$384$	10.5000	+	18.1865i	0.535826	+	0.928078i
$385$		0			0
$386$			38.1051i			1.93950i
$387$	1.50000	−	2.59808i	0.0762493	−	0.132068i
$388$		−	10.3923i		−	0.527589i
$389$			27.7128i			1.40510i	0.711637	+	0.702548i	$0.247954\pi$
$389$			27.7128i			1.40510i	−0.711637	+	0.702548i	$0.752046\pi$
$390$	9.00000	−	5.19615i	0.455733	−	0.263117i
$391$			10.3923i			0.525561i
$392$		0			0
$393$	18.0000	−	10.3923i	0.907980	−	0.524222i
$394$	6.00000			0.302276
$395$	16.0000			0.805047
$396$	9.00000	+	5.19615i	0.452267	+	0.261116i
$397$		−	24.2487i		−	1.21701i	−0.793551	−	0.608504i	$-0.791770\pi$
$397$		−	24.2487i		−	1.21701i	0.793551	−	0.608504i	$-0.208230\pi$
$398$	12.0000			0.601506
$399$		0			0
$400$	−5.00000			−0.250000
$401$			19.0526i			0.951439i	0.879597	+	0.475720i	$0.157812\pi$
$401$			19.0526i			0.951439i	−0.879597	+	0.475720i	$0.842188\pi$
$402$	19.5000	+	33.7750i	0.972572	+	1.68454i
$403$	12.0000			0.597763
$404$	−15.0000			−0.746278
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$		0			0
$407$		−	13.8564i		−	0.686837i
$408$	9.00000	+	15.5885i	0.445566	+	0.771744i
$409$		−	22.5167i		−	1.11338i	−0.830721	−	0.556689i	$-0.812072\pi$
$409$		−	22.5167i		−	1.11338i	0.830721	−	0.556689i	$-0.187928\pi$
$410$		−	5.19615i		−	0.256620i
$411$	18.0000	+	31.1769i	0.887875	+	1.53784i
$412$			5.19615i			0.255996i
$413$		0			0
$414$	4.50000	−	7.79423i	0.221163	−	0.383065i
$415$	−9.00000			−0.441793
$416$	−18.0000			−0.882523
$417$	9.00000	+	15.5885i	0.440732	+	0.763370i
$418$		−	41.5692i		−	2.03322i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	35.0000			1.70580			0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000			1.70580			0.852898	+	0.522078i	$0.174843\pi$
$422$		−	34.6410i		−	1.68630i
$423$		0			0
$424$		0			0
$425$	−6.00000			−0.291043
$426$	−18.0000	+	10.3923i	−0.872103	+	0.503509i
$427$		0			0
$428$			5.19615i			0.251166i
$429$	18.0000	−	10.3923i	0.869048	−	0.501745i
$430$		−	1.73205i		−	0.0835269i
$431$			10.3923i			0.500580i	0.968171	+	0.250290i	$0.0805259\pi$
$431$			10.3923i			0.500580i	−0.968171	+	0.250290i	$0.919474\pi$
$432$		−	25.9808i		−	1.25000i
$433$		−	13.8564i		−	0.665896i	−0.942945	−	0.332948i	$-0.891957\pi$
$433$		−	13.8564i		−	0.665896i	0.942945	−	0.332948i	$-0.108043\pi$
$434$		0			0
$435$	−1.50000	−	2.59808i	−0.0719195	−	0.124568i
$436$	5.00000			0.239457
$437$	−12.0000			−0.574038
$438$	−9.00000	+	5.19615i	−0.430037	+	0.248282i
$439$		−	6.92820i		−	0.330665i	−0.986238	−	0.165333i	$-0.947130\pi$
$439$		−	6.92820i		−	0.330665i	0.986238	−	0.165333i	$-0.0528697\pi$
$440$	−6.00000			−0.286039
$441$		0			0
$442$	−36.0000			−1.71235
$443$		−	15.5885i		−	0.740630i	−0.928906	−	0.370315i	$-0.879250\pi$
$443$		−	15.5885i		−	0.740630i	0.928906	−	0.370315i	$-0.120750\pi$
$444$	6.00000	−	3.46410i	0.284747	−	0.164399i
$445$	3.00000			0.142214
$446$	−6.00000			−0.284108
$447$	−19.5000	−	33.7750i	−0.922318	−	1.59750i
$448$		0			0
$449$			12.1244i			0.572184i	0.958202	+	0.286092i	$0.0923563\pi$
$449$			12.1244i			0.572184i	−0.958202	+	0.286092i	$0.907644\pi$
$450$	4.50000	+	2.59808i	0.212132	+	0.122474i
$451$		−	10.3923i		−	0.489355i
$452$			6.92820i			0.325875i
$453$	3.00000	−	1.73205i	0.140952	−	0.0813788i
$454$		−	20.7846i		−	0.975470i
$455$		0			0
$456$	−18.0000	+	10.3923i	−0.842927	+	0.486664i
$457$	−8.00000			−0.374224			−0.187112	−	0.982339i	$-0.559913\pi$
$457$	−8.00000			−0.374224			−0.187112	+	0.982339i	$0.559913\pi$
$458$		0			0
$459$		−	31.1769i		−	1.45521i
$460$		−	1.73205i		−	0.0807573i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	29.0000			1.34774			0.673872	−	0.738848i	$-0.264630\pi$
$463$	29.0000			1.34774			0.673872	+	0.738848i	$0.264630\pi$
$464$			8.66025i			0.402042i
$465$	3.00000	+	5.19615i	0.139122	+	0.240966i
$466$	6.00000			0.277945
$467$	−21.0000			−0.971764			−0.485882	−	0.874024i	$-0.661502\pi$
$467$	−21.0000			−0.971764			−0.485882	+	0.874024i	$0.661502\pi$
$468$	9.00000	+	5.19615i	0.416025	+	0.240192i
$469$		0			0
$470$		0			0
$471$	−3.00000	−	5.19615i	−0.138233	−	0.239426i
$472$		0			0
$473$		−	3.46410i		−	0.159280i
$474$	24.0000	+	41.5692i	1.10236	+	1.90934i
$475$		−	6.92820i		−	0.317888i
$476$		0			0
$477$		0			0
$478$	−18.0000			−0.823301
$479$	6.00000			0.274147			0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000			0.274147			0.137073	+	0.990561i	$0.456230\pi$
$480$	−4.50000	−	7.79423i	−0.205396	−	0.355756i
$481$		−	13.8564i		−	0.631798i
$482$	−12.0000			−0.546585
$483$		0			0
$484$	1.00000			0.0454545
$485$		−	10.3923i		−	0.471890i
$486$	−13.5000	+	23.3827i	−0.612372	+	1.06066i
$487$	−32.0000			−1.45006			−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000			−1.45006			−0.725029	+	0.688718i	$0.758174\pi$
$488$	9.00000			0.407411
$489$	−12.0000	+	6.92820i	−0.542659	+	0.313304i
$490$		0			0
$491$		−	38.1051i		−	1.71966i	−0.510581	−	0.859830i	$-0.670569\pi$
$491$		−	38.1051i		−	1.71966i	0.510581	−	0.859830i	$-0.329431\pi$
$492$	4.50000	−	2.59808i	0.202876	−	0.117130i
$493$			10.3923i			0.468046i
$494$		−	41.5692i		−	1.87029i
$495$	9.00000	+	5.19615i	0.404520	+	0.233550i
$496$		−	17.3205i		−	0.777714i
$497$		0			0
$498$	−13.5000	−	23.3827i	−0.604949	−	1.04780i
$499$	−14.0000			−0.626726			−0.313363	−	0.949633i	$-0.601456\pi$
$499$	−14.0000			−0.626726			−0.313363	+	0.949633i	$0.601456\pi$
$500$	1.00000			0.0447214
$501$	31.5000	−	18.1865i	1.40732	−	0.812514i
$502$			31.1769i			1.39149i
$503$	15.0000			0.668817			0.334408	−	0.942428i	$-0.391463\pi$
$503$	15.0000			0.668817			0.334408	+	0.942428i	$0.391463\pi$
$504$		0			0
$505$	−15.0000			−0.667491
$506$		−	10.3923i		−	0.461994i
$507$	−1.50000	+	0.866025i	−0.0666173	+	0.0384615i
$508$	16.0000			0.709885
$509$	45.0000			1.99459			0.997295	−	0.0735034i	$-0.0234180\pi$
$509$	45.0000			1.99459			0.997295	+	0.0735034i	$0.0234180\pi$
$510$	−9.00000	−	15.5885i	−0.398527	−	0.690268i
$511$		0			0
$512$			8.66025i			0.382733i
$513$	36.0000			1.58944
$514$		0			0
$515$			5.19615i			0.228970i
$516$	1.50000	−	0.866025i	0.0660338	−	0.0381246i
$517$		0			0
$518$		0			0
$519$	−18.0000	+	10.3923i	−0.790112	+	0.456172i
$520$	−6.00000			−0.263117
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$			24.2487i			1.06032i	0.847897	+	0.530161i	$0.177869\pi$
$523$			24.2487i			1.06032i	−0.847897	+	0.530161i	$0.822131\pi$
$524$	12.0000			0.524222
$525$		0			0
$526$	−3.00000			−0.130806
$527$		−	20.7846i		−	0.905392i
$528$	−15.0000	−	25.9808i	−0.652791	−	1.13067i
$529$	20.0000			0.869565
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	10.3923i		−	0.450141i
$534$	4.50000	+	7.79423i	0.194734	+	0.337289i
$535$			5.19615i			0.224649i
$536$		−	22.5167i		−	0.972572i
$537$	9.00000	+	15.5885i	0.388379	+	0.672692i
$538$			5.19615i			0.224022i
$539$		0			0
$540$			5.19615i			0.223607i
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	−12.0000			−0.515444
$543$	4.50000	+	7.79423i	0.193113	+	0.334482i
$544$			31.1769i			1.33670i
$545$	5.00000			0.214176
$546$		0			0
$547$	−1.00000			−0.0427569			−0.0213785	−	0.999771i	$-0.506805\pi$
$547$	−1.00000			−0.0427569			−0.0213785	+	0.999771i	$0.506805\pi$
$548$			20.7846i			0.887875i
$549$	−13.5000	−	7.79423i	−0.576166	−	0.332650i
$550$	6.00000			0.255841
$551$	−12.0000			−0.511217
$552$	−4.50000	+	2.59808i	−0.191533	+	0.110581i
$553$		0			0
$554$			45.0333i			1.91328i
$555$	6.00000	−	3.46410i	0.254686	−	0.147043i
$556$			10.3923i			0.440732i
$557$		−	17.3205i		−	0.733893i	−0.930242	−	0.366947i	$-0.880403\pi$
$557$		−	17.3205i		−	0.733893i	0.930242	−	0.366947i	$-0.119597\pi$
$558$	−9.00000	+	15.5885i	−0.381000	+	0.659912i
$559$		−	3.46410i		−	0.146516i
$560$		0			0
$561$	−18.0000	−	31.1769i	−0.759961	−	1.31629i
$562$	12.0000			0.506189
$563$	−21.0000			−0.885044			−0.442522	−	0.896758i	$-0.645916\pi$
$563$	−21.0000			−0.885044			−0.442522	+	0.896758i	$0.645916\pi$
$564$		0			0
$565$			6.92820i			0.291472i
$566$	−54.0000			−2.26979
$567$		0			0
$568$	12.0000			0.503509
$569$		−	6.92820i		−	0.290445i	−0.989399	−	0.145223i	$-0.953610\pi$
$569$		−	6.92820i		−	0.290445i	0.989399	−	0.145223i	$-0.0463899\pi$
$570$	18.0000	−	10.3923i	0.753937	−	0.435286i
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	12.0000			0.501745
$573$	9.00000	+	15.5885i	0.375980	+	0.651217i
$574$		0			0
$575$		−	1.73205i		−	0.0722315i
$576$	−1.50000	+	2.59808i	−0.0625000	+	0.108253i
$577$		−	24.2487i		−	1.00949i	−0.863269	−	0.504744i	$-0.831587\pi$
$577$		−	24.2487i		−	1.00949i	0.863269	−	0.504744i	$-0.168413\pi$
$578$			32.9090i			1.36883i
$579$	−33.0000	+	19.0526i	−1.37143	+	0.791797i
$580$		−	1.73205i		−	0.0719195i
$581$		0			0
$582$	27.0000	−	15.5885i	1.11919	−	0.646162i
$583$		0			0
$584$	6.00000			0.248282
$585$	9.00000	+	5.19615i	0.372104	+	0.214834i
$586$		−	41.5692i		−	1.71721i
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$		0			0
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$	−20.0000			−0.821995
$593$	−48.0000			−1.97112			−0.985562	−	0.169316i	$-0.945844\pi$
$593$	−48.0000			−1.97112			−0.985562	+	0.169316i	$0.945844\pi$
$594$			31.1769i			1.27920i
$595$		0			0
$596$		−	22.5167i		−	0.922318i
$597$	6.00000	+	10.3923i	0.245564	+	0.425329i
$598$		−	10.3923i		−	0.424973i
$599$		−	13.8564i		−	0.566157i	−0.959097	−	0.283079i	$-0.908644\pi$
$599$		−	13.8564i		−	0.566157i	0.959097	−	0.283079i	$-0.0913558\pi$
$600$	−1.50000	−	2.59808i	−0.0612372	−	0.106066i
$601$			20.7846i			0.847822i	0.905704	+	0.423911i	$0.139343\pi$
$601$			20.7846i			0.847822i	−0.905704	+	0.423911i	$0.860657\pi$
$602$		0			0
$603$	−19.5000	+	33.7750i	−0.794101	+	1.37542i
$604$	2.00000			0.0813788
$605$	1.00000			0.0406558
$606$	−22.5000	−	38.9711i	−0.914000	−	1.58309i
$607$		−	1.73205i		−	0.0703018i	−0.999382	−	0.0351509i	$-0.988809\pi$
$607$		−	1.73205i		−	0.0703018i	0.999382	−	0.0351509i	$-0.0111912\pi$
$608$	−36.0000			−1.45999
$609$		0			0
$610$	−9.00000			−0.364399
$611$		0			0
$612$	9.00000	−	15.5885i	0.363803	−	0.630126i
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	39.0000			1.57391
$615$	4.50000	−	2.59808i	0.181458	−	0.104765i
$616$		0			0
$617$			34.6410i			1.39459i	0.716782	+	0.697297i	$0.245614\pi$
$617$			34.6410i			1.39459i	−0.716782	+	0.697297i	$0.754386\pi$
$618$	−13.5000	+	7.79423i	−0.543050	+	0.313530i
$619$			24.2487i			0.974638i	0.873224	+	0.487319i	$0.162025\pi$
$619$			24.2487i			0.974638i	−0.873224	+	0.487319i	$0.837975\pi$
$620$			3.46410i			0.139122i
$621$	9.00000			0.361158
$622$			41.5692i			1.66677i
$623$		0			0
$624$	−15.0000	−	25.9808i	−0.600481	−	1.04006i
$625$	1.00000			0.0400000
$626$		0			0
$627$	36.0000	−	20.7846i	1.43770	−	0.830057i
$628$		−	3.46410i		−	0.138233i
$629$	−24.0000			−0.956943
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$		−	27.7128i		−	1.10236i
$633$	30.0000	−	17.3205i	1.19239	−	0.688428i
$634$	−30.0000			−1.19145
$635$	16.0000			0.634941
$636$		0			0
$637$		0			0
$638$		−	10.3923i		−	0.411435i
$639$	−18.0000	−	10.3923i	−0.712069	−	0.411113i
$640$			12.1244i			0.479257i
$641$			12.1244i			0.478883i	0.970911	+	0.239442i	$0.0769644\pi$
$641$			12.1244i			0.478883i	−0.970911	+	0.239442i	$0.923036\pi$
$642$	−13.5000	+	7.79423i	−0.532803	+	0.307614i
$643$		−	17.3205i		−	0.683054i	−0.939872	−	0.341527i	$-0.889056\pi$
$643$		−	17.3205i		−	0.683054i	0.939872	−	0.341527i	$-0.110944\pi$
$644$		0			0
$645$	1.50000	−	0.866025i	0.0590624	−	0.0340997i
$646$	−72.0000			−2.83280
$647$	−3.00000			−0.117942			−0.0589711	−	0.998260i	$-0.518782\pi$
$647$	−3.00000			−0.117942			−0.0589711	+	0.998260i	$0.518782\pi$
$648$	13.5000	−	7.79423i	0.530330	−	0.306186i
$649$		0			0
$650$	6.00000			0.235339
$651$		0			0
$652$	−8.00000			−0.313304
$653$			31.1769i			1.22005i	0.792383	+	0.610023i	$0.208840\pi$
$653$			31.1769i			1.22005i	−0.792383	+	0.610023i	$0.791160\pi$
$654$	7.50000	+	12.9904i	0.293273	+	0.507964i
$655$	12.0000			0.468879
$656$	−15.0000			−0.585652
$657$	−9.00000	−	5.19615i	−0.351123	−	0.202721i
$658$		0			0
$659$		−	41.5692i		−	1.61931i	−0.586908	−	0.809653i	$-0.699655\pi$
$659$		−	41.5692i		−	1.61931i	0.586908	−	0.809653i	$-0.300345\pi$
$660$	3.00000	+	5.19615i	0.116775	+	0.202260i
$661$		−	32.9090i		−	1.28001i	−0.768371	−	0.640005i	$-0.778932\pi$
$661$		−	32.9090i		−	1.28001i	0.768371	−	0.640005i	$-0.221068\pi$
$662$			17.3205i			0.673181i
$663$	−18.0000	−	31.1769i	−0.699062	−	1.21081i
$664$			15.5885i			0.604949i
$665$		0			0
$666$	18.0000	+	10.3923i	0.697486	+	0.402694i
$667$	−3.00000			−0.116160
$668$	21.0000			0.812514
$669$	−3.00000	−	5.19615i	−0.115987	−	0.200895i
$670$			22.5167i			0.869894i
$671$	−18.0000			−0.694882
$672$		0			0
$673$	4.00000			0.154189			0.0770943	−	0.997024i	$-0.475436\pi$
$673$	4.00000			0.154189			0.0770943	+	0.997024i	$0.475436\pi$
$674$		−	55.4256i		−	2.13492i
$675$			5.19615i			0.200000i
$676$	−1.00000			−0.0384615
$677$	−6.00000			−0.230599			−0.115299	−	0.993331i	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$	−18.0000	+	10.3923i	−0.691286	+	0.399114i
$679$		0			0
$680$			10.3923i			0.398527i
$681$	18.0000	−	10.3923i	0.689761	−	0.398234i
$682$			20.7846i			0.795884i
$683$			39.8372i			1.52433i	0.647385	+	0.762163i	$0.275863\pi$
$683$			39.8372i			1.52433i	−0.647385	+	0.762163i	$0.724137\pi$
$684$	18.0000	+	10.3923i	0.688247	+	0.397360i
$685$			20.7846i			0.794139i
$686$		0			0
$687$		0			0
$688$	−5.00000			−0.190623
$689$		0			0
$690$	4.50000	−	2.59808i	0.171312	−	0.0989071i
$691$			3.46410i			0.131781i	0.997827	+	0.0658903i	$0.0209887\pi$
$691$			3.46410i			0.131781i	−0.997827	+	0.0658903i	$0.979011\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	−33.0000			−1.25266
$695$			10.3923i			0.394203i
$696$	−4.50000	+	2.59808i	−0.170572	+	0.0984798i
$697$	−18.0000			−0.681799
$698$	−15.0000			−0.567758
$699$	3.00000	+	5.19615i	0.113470	+	0.196537i
$700$		0			0
$701$			25.9808i			0.981280i	0.871362	+	0.490640i	$0.163237\pi$
$701$			25.9808i			0.981280i	−0.871362	+	0.490640i	$0.836763\pi$
$702$			31.1769i			1.17670i
$703$		−	27.7128i		−	1.04521i
$704$			3.46410i			0.130558i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	19.0000			0.713560			0.356780	−	0.934188i	$-0.383875\pi$
$709$	19.0000			0.713560			0.356780	+	0.934188i	$0.383875\pi$
$710$	−12.0000			−0.450352
$711$	−24.0000	+	41.5692i	−0.900070	+	1.55897i
$712$		−	5.19615i		−	0.194734i
$713$	6.00000			0.224702
$714$		0			0
$715$	12.0000			0.448775
$716$			10.3923i			0.388379i
$717$	−9.00000	−	15.5885i	−0.336111	−	0.582162i
$718$	−42.0000			−1.56743
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$	7.50000	−	12.9904i	0.279508	−	0.484123i
$721$		0			0
$722$		−	50.2295i		−	1.86935i
$723$	−6.00000	−	10.3923i	−0.223142	−	0.386494i
$724$			5.19615i			0.193113i
$725$		−	1.73205i		−	0.0643268i
$726$	1.50000	+	2.59808i	0.0556702	+	0.0964237i
$727$			5.19615i			0.192715i	0.995347	+	0.0963573i	$0.0307191\pi$
$727$			5.19615i			0.192715i	−0.995347	+	0.0963573i	$0.969281\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−6.00000			−0.222070
$731$	−6.00000			−0.221918
$732$	−4.50000	−	7.79423i	−0.166325	−	0.288083i
$733$		−	17.3205i		−	0.639748i	−0.947460	−	0.319874i	$-0.896359\pi$
$733$		−	17.3205i		−	0.639748i	0.947460	−	0.319874i	$-0.103641\pi$
$734$	27.0000			0.996588
$735$		0			0
$736$	−9.00000			−0.331744
$737$			45.0333i			1.65882i
$738$	13.5000	+	7.79423i	0.496942	+	0.286910i
$739$	38.0000			1.39785			0.698926	−	0.715194i	$-0.253662\pi$
$739$	38.0000			1.39785			0.698926	+	0.715194i	$0.253662\pi$
$740$	4.00000			0.147043
$741$	36.0000	−	20.7846i	1.32249	−	0.763542i
$742$		0			0
$743$		−	46.7654i		−	1.71566i	−0.513938	−	0.857828i	$-0.671814\pi$
$743$		−	46.7654i		−	1.71566i	0.513938	−	0.857828i	$-0.328186\pi$
$744$	9.00000	−	5.19615i	0.329956	−	0.190500i
$745$		−	22.5167i		−	0.824947i
$746$		−	6.92820i		−	0.253660i
$747$	13.5000	−	23.3827i	0.493939	−	0.855528i
$748$		−	20.7846i		−	0.759961i
$749$		0			0
$750$	1.50000	+	2.59808i	0.0547723	+	0.0948683i
$751$	−20.0000			−0.729810			−0.364905	−	0.931045i	$-0.618899\pi$
$751$	−20.0000			−0.729810			−0.364905	+	0.931045i	$0.618899\pi$
$752$		0			0
$753$	−27.0000	+	15.5885i	−0.983935	+	0.568075i
$754$		−	10.3923i		−	0.378465i
$755$	2.00000			0.0727875
$756$		0			0
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$			27.7128i			1.00657i
$759$	9.00000	−	5.19615i	0.326679	−	0.188608i
$760$	−12.0000			−0.435286
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$	24.0000	+	41.5692i	0.869428	+	1.50589i
$763$		0			0
$764$			10.3923i			0.375980i
$765$	9.00000	−	15.5885i	0.325396	−	0.563602i
$766$		−	36.3731i		−	1.31421i
$767$		0			0
$768$	−28.5000	+	16.4545i	−1.02841	+	0.593750i
$769$		−	41.5692i		−	1.49902i	−0.661991	−	0.749512i	$-0.730288\pi$
$769$		−	41.5692i		−	1.49902i	0.661991	−	0.749512i	$-0.269712\pi$
$770$		0			0
$771$		0			0
$772$	−22.0000			−0.791797
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$	4.50000	+	2.59808i	0.161749	+	0.0933859i
$775$			3.46410i			0.124434i
$776$	−18.0000			−0.646162
$777$		0			0
$778$	−48.0000			−1.72088
$779$		−	20.7846i		−	0.744686i
$780$	3.00000	+	5.19615i	0.107417	+	0.186052i
$781$	−24.0000			−0.858788
$782$	−18.0000			−0.643679
$783$	9.00000			0.321634
$784$		0			0
$785$		−	3.46410i		−	0.123639i
$786$	18.0000	+	31.1769i	0.642039	+	1.11204i
$787$			25.9808i			0.926114i	0.886328	+	0.463057i	$0.153248\pi$
$787$			25.9808i			0.926114i	−0.886328	+	0.463057i	$0.846752\pi$
$788$			3.46410i			0.123404i
$789$	−1.50000	−	2.59808i	−0.0534014	−	0.0924940i
$790$			27.7128i			0.985978i
$791$		0			0
$792$	9.00000	−	15.5885i	0.319801	−	0.553912i
$793$	−18.0000			−0.639199
$794$	42.0000			1.49052
$795$		0			0
$796$			6.92820i			0.245564i
$797$	−12.0000			−0.425062			−0.212531	−	0.977154i	$-0.568171\pi$
$797$	−12.0000			−0.425062			−0.212531	+	0.977154i	$0.568171\pi$
$798$		0			0
$799$		0			0
$800$		−	5.19615i		−	0.183712i
$801$	−4.50000	+	7.79423i	−0.159000	+	0.275396i
$802$	−33.0000			−1.16527
$803$	−12.0000			−0.423471
$804$	−19.5000	+	11.2583i	−0.687712	+	0.397051i
$805$		0			0
$806$			20.7846i			0.732107i
$807$	−4.50000	+	2.59808i	−0.158408	+	0.0914566i
$808$			25.9808i			0.914000i
$809$			19.0526i			0.669852i	0.942244	+	0.334926i	$0.108711\pi$
$809$			19.0526i			0.669852i	−0.942244	+	0.334926i	$0.891289\pi$
$810$	−13.5000	+	7.79423i	−0.474342	+	0.273861i
$811$			45.0333i			1.58133i	0.612247	+	0.790667i	$0.290266\pi$
$811$			45.0333i			1.58133i	−0.612247	+	0.790667i	$0.709734\pi$
$812$		0			0
$813$	−6.00000	−	10.3923i	−0.210429	−	0.364474i
$814$	24.0000			0.841200
$815$	−8.00000			−0.280228
$816$	−45.0000	+	25.9808i	−1.57532	+	0.909509i
$817$		−	6.92820i		−	0.242387i
$818$	39.0000			1.36360
$819$		0			0
$820$	3.00000			0.104765
$821$		−	41.5692i		−	1.45078i	−0.688340	−	0.725388i	$-0.741660\pi$
$821$		−	41.5692i		−	1.45078i	0.688340	−	0.725388i	$-0.258340\pi$
$822$	−54.0000	+	31.1769i	−1.88347	+	1.08742i
$823$	23.0000			0.801730			0.400865	−	0.916137i	$-0.368710\pi$
$823$	23.0000			0.801730			0.400865	+	0.916137i	$0.368710\pi$
$824$	9.00000			0.313530
$825$	3.00000	+	5.19615i	0.104447	+	0.180907i
$826$		0			0
$827$			22.5167i			0.782981i	0.920182	+	0.391491i	$0.128040\pi$
$827$			22.5167i			0.782981i	−0.920182	+	0.391491i	$0.871960\pi$
$828$	4.50000	+	2.59808i	0.156386	+	0.0902894i
$829$			13.8564i			0.481253i	0.970618	+	0.240626i	$0.0773529\pi$
$829$			13.8564i			0.481253i	−0.970618	+	0.240626i	$0.922647\pi$
$830$		−	15.5885i		−	0.541083i
$831$	−39.0000	+	22.5167i	−1.35290	+	0.781094i
$832$			3.46410i			0.120096i
$833$		0			0
$834$	−27.0000	+	15.5885i	−0.934934	+	0.539784i
$835$	21.0000			0.726735
$836$	24.0000			0.830057
$837$	−18.0000			−0.622171
$838$		0			0
$839$	30.0000			1.03572			0.517858	−	0.855467i	$-0.326730\pi$
$839$	30.0000			1.03572			0.517858	+	0.855467i	$0.326730\pi$
$840$		0			0
$841$	26.0000			0.896552
$842$			60.6218i			2.08916i
$843$	6.00000	+	10.3923i	0.206651	+	0.357930i
$844$	20.0000			0.688428
$845$	−1.00000			−0.0344010
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−27.0000	−	46.7654i	−0.926638	−	1.60498i
$850$		−	10.3923i		−	0.356453i
$851$		−	6.92820i		−	0.237496i
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$		−	20.7846i		−	0.711651i	−0.934552	−	0.355826i	$-0.884200\pi$
$853$		−	20.7846i		−	0.711651i	0.934552	−	0.355826i	$-0.115800\pi$
$854$		0			0
$855$	18.0000	+	10.3923i	0.615587	+	0.355409i
$856$	9.00000			0.307614
$857$	42.0000			1.43469			0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000			1.43469			0.717346	+	0.696717i	$0.245357\pi$
$858$	18.0000	+	31.1769i	0.614510	+	1.06436i
$859$			27.7128i			0.945549i	0.881183	+	0.472774i	$0.156747\pi$
$859$			27.7128i			0.945549i	−0.881183	+	0.472774i	$0.843253\pi$
$860$	1.00000			0.0340997
$861$		0			0
$862$	−18.0000			−0.613082
$863$		−	8.66025i		−	0.294798i	−0.989077	−	0.147399i	$-0.952910\pi$
$863$		−	8.66025i		−	0.294798i	0.989077	−	0.147399i	$-0.0470902\pi$
$864$	27.0000			0.918559
$865$	−12.0000			−0.408012
$866$	24.0000			0.815553
$867$	−28.5000	+	16.4545i	−0.967911	+	0.558824i
$868$		0			0
$869$			55.4256i			1.88019i
$870$	4.50000	−	2.59808i	0.152564	−	0.0880830i
$871$			45.0333i			1.52590i
$872$		−	8.66025i		−	0.293273i
$873$	27.0000	+	15.5885i	0.913812	+	0.527589i
$874$		−	20.7846i		−	0.703050i
$875$		0			0
$876$	−3.00000	−	5.19615i	−0.101361	−	0.175562i
$877$	32.0000			1.08056			0.540282	−	0.841484i	$-0.318318\pi$
$877$	32.0000			1.08056			0.540282	+	0.841484i	$0.318318\pi$
$878$	12.0000			0.404980
$879$	36.0000	−	20.7846i	1.21425	−	0.701047i
$880$		−	17.3205i		−	0.583874i
$881$	9.00000			0.303218			0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000			0.303218			0.151609	+	0.988441i	$0.451555\pi$
$882$		0			0
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$		−	20.7846i		−	0.699062i
$885$		0			0
$886$	27.0000			0.907083
$887$	−9.00000			−0.302190			−0.151095	−	0.988519i	$-0.548280\pi$
$887$	−9.00000			−0.302190			−0.151095	+	0.988519i	$0.548280\pi$
$888$	−6.00000	−	10.3923i	−0.201347	−	0.348743i
$889$		0			0
$890$			5.19615i			0.174175i
$891$	−27.0000	+	15.5885i	−0.904534	+	0.522233i
$892$		−	3.46410i		−	0.115987i
$893$		0			0
$894$	58.5000	−	33.7750i	1.95653	−	1.12960i
$895$			10.3923i			0.347376i
$896$		0			0
$897$	9.00000	−	5.19615i	0.300501	−	0.173494i
$898$	−21.0000			−0.700779
$899$	6.00000			0.200111
$900$	−1.50000	+	2.59808i	−0.0500000	+	0.0866025i
$901$		0			0
$902$	18.0000			0.599334
$903$		0			0
$904$	12.0000			0.399114
$905$			5.19615i			0.172726i
$906$	3.00000	+	5.19615i	0.0996683	+	0.172631i
$907$	37.0000			1.22856			0.614282	−	0.789086i	$-0.289446\pi$
$907$	37.0000			1.22856			0.614282	+	0.789086i	$0.289446\pi$
$908$	12.0000			0.398234
$909$	22.5000	−	38.9711i	0.746278	−	1.29259i
$910$		0			0
$911$		−	24.2487i		−	0.803396i	−0.915772	−	0.401698i	$-0.868420\pi$
$911$		−	24.2487i		−	0.803396i	0.915772	−	0.401698i	$-0.131580\pi$
$912$	−30.0000	−	51.9615i	−0.993399	−	1.72062i
$913$		−	31.1769i		−	1.03181i
$914$		−	13.8564i		−	0.458329i
$915$	−4.50000	−	7.79423i	−0.148765	−	0.257669i
$916$		0			0
$917$		0			0
$918$	54.0000			1.78227
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$	−3.00000			−0.0989071
$921$	19.5000	+	33.7750i	0.642547	+	1.11292i
$922$			51.9615i			1.71126i
$923$	−24.0000			−0.789970
$924$		0			0
$925$	4.00000			0.131519
$926$			50.2295i			1.65064i
$927$	−13.5000	−	7.79423i	−0.443398	−	0.255996i
$928$	−9.00000			−0.295439
$929$	−21.0000			−0.688988			−0.344494	−	0.938789i	$-0.611949\pi$
$929$	−21.0000			−0.688988			−0.344494	+	0.938789i	$0.611949\pi$
$930$	−9.00000	+	5.19615i	−0.295122	+	0.170389i
$931$		0			0
$932$			3.46410i			0.113470i
$933$	−36.0000	+	20.7846i	−1.17859	+	0.680458i
$934$		−	36.3731i		−	1.19016i
$935$		−	20.7846i		−	0.679729i
$936$	9.00000	−	15.5885i	0.294174	−	0.509525i
$937$			48.4974i			1.58434i	0.610299	+	0.792171i	$0.291049\pi$
$937$			48.4974i			1.58434i	−0.610299	+	0.792171i	$0.708951\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−18.0000			−0.586783			−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000			−0.586783			−0.293392	+	0.955992i	$0.594784\pi$
$942$	9.00000	−	5.19615i	0.293236	−	0.169300i
$943$		−	5.19615i		−	0.169210i
$944$		0			0
$945$		0			0
$946$	6.00000			0.195077
$947$			25.9808i			0.844261i	0.906535	+	0.422131i	$0.138718\pi$
$947$			25.9808i			0.844261i	−0.906535	+	0.422131i	$0.861282\pi$
$948$	−24.0000	+	13.8564i	−0.779484	+	0.450035i
$949$	−12.0000			−0.389536
$950$	12.0000			0.389331
$951$	−15.0000	−	25.9808i	−0.486408	−	0.842484i
$952$		0			0
$953$		−	6.92820i		−	0.224427i	−0.993684	−	0.112213i	$-0.964206\pi$
$953$		−	6.92820i		−	0.224427i	0.993684	−	0.112213i	$-0.0357940\pi$
$954$		0			0
$955$			10.3923i			0.336287i
$956$		−	10.3923i		−	0.336111i
$957$	9.00000	−	5.19615i	0.290929	−	0.167968i
$958$			10.3923i			0.335760i
$959$		0			0
$960$	−1.50000	+	0.866025i	−0.0484123	+	0.0279508i
$961$	19.0000			0.612903
$962$	24.0000			0.773791
$963$	−13.5000	−	7.79423i	−0.435031	−	0.251166i
$964$		−	6.92820i		−	0.223142i
$965$	−22.0000			−0.708205
$966$		0			0
$967$	23.0000			0.739630			0.369815	−	0.929105i	$-0.379421\pi$
$967$	23.0000			0.739630			0.369815	+	0.929105i	$0.379421\pi$
$968$		−	1.73205i		−	0.0556702i
$969$	−36.0000	−	62.3538i	−1.15649	−	2.00309i
$970$	18.0000			0.577945
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	−13.5000	−	7.79423i	−0.433013	−	0.250000i
$973$		0			0
$974$		−	55.4256i		−	1.77595i
$975$	3.00000	+	5.19615i	0.0960769	+	0.166410i
$976$			25.9808i			0.831624i
$977$		−	24.2487i		−	0.775785i	−0.921705	−	0.387893i	$-0.873203\pi$
$977$		−	24.2487i		−	0.775785i	0.921705	−	0.387893i	$-0.126797\pi$
$978$	−12.0000	−	20.7846i	−0.383718	−	0.664619i
$979$			10.3923i			0.332140i
$980$		0			0
$981$	−7.50000	+	12.9904i	−0.239457	+	0.414751i
$982$	66.0000			2.10614
$983$	−57.0000			−1.81802			−0.909009	−	0.416777i	$-0.863160\pi$
$983$	−57.0000			−1.81802			−0.909009	+	0.416777i	$0.863160\pi$
$984$	−4.50000	−	7.79423i	−0.143455	−	0.248471i
$985$			3.46410i			0.110375i
$986$	−18.0000			−0.573237
$987$		0			0
$988$	24.0000			0.763542
$989$		−	1.73205i		−	0.0550760i
$990$	−9.00000	+	15.5885i	−0.286039	+	0.495434i
$991$	34.0000			1.08005			0.540023	−	0.841650i	$-0.318416\pi$
$991$	34.0000			1.08005			0.540023	+	0.841650i	$0.318416\pi$
$992$	18.0000			0.571501
$993$	−15.0000	+	8.66025i	−0.476011	+	0.274825i
$994$		0			0
$995$			6.92820i			0.219639i
$996$	13.5000	−	7.79423i	0.427764	−	0.246970i
$997$		−	6.92820i		−	0.219418i	−0.993964	−	0.109709i	$-0.965008\pi$
$997$		−	6.92820i		−	0.219418i	0.993964	−	0.109709i	$-0.0349920\pi$
$998$		−	24.2487i		−	0.767580i
$999$			20.7846i			0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.b.a.146.2		2
3.2	odd	2		735.2.b.b.146.1		2
7.2	even	3		105.2.s.b.101.1	yes	2
7.3	odd	6		105.2.s.a.26.1	✓	2
7.4	even	3		735.2.s.c.656.1		2
7.5	odd	6		735.2.s.e.521.1		2
7.6	odd	2		735.2.b.b.146.2		2
21.2	odd	6		105.2.s.a.101.1	yes	2
21.5	even	6		735.2.s.c.521.1		2
21.11	odd	6		735.2.s.e.656.1		2
21.17	even	6		105.2.s.b.26.1	yes	2
21.20	even	2	inner	735.2.b.a.146.1		2
35.2	odd	12		525.2.q.a.374.2		4
35.3	even	12		525.2.q.b.299.1		4
35.9	even	6		525.2.t.a.101.1		2
35.17	even	12		525.2.q.b.299.2		4
35.23	odd	12		525.2.q.a.374.1		4
35.24	odd	6		525.2.t.e.26.1		2
105.2	even	12		525.2.q.b.374.1		4
105.17	odd	12		525.2.q.a.299.1		4
105.23	even	12		525.2.q.b.374.2		4
105.38	odd	12		525.2.q.a.299.2		4
105.44	odd	6		525.2.t.e.101.1		2
105.59	even	6		525.2.t.a.26.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.s.a.26.1	✓	2	7.3	odd	6
105.2.s.a.101.1	yes	2	21.2	odd	6
105.2.s.b.26.1	yes	2	21.17	even	6
105.2.s.b.101.1	yes	2	7.2	even	3
525.2.q.a.299.1		4	105.17	odd	12
525.2.q.a.299.2		4	105.38	odd	12
525.2.q.a.374.1		4	35.23	odd	12
525.2.q.a.374.2		4	35.2	odd	12
525.2.q.b.299.1		4	35.3	even	12
525.2.q.b.299.2		4	35.17	even	12
525.2.q.b.374.1		4	105.2	even	12
525.2.q.b.374.2		4	105.23	even	12
525.2.t.a.26.1		2	105.59	even	6
525.2.t.a.101.1		2	35.9	even	6
525.2.t.e.26.1		2	35.24	odd	6
525.2.t.e.101.1		2	105.44	odd	6
735.2.b.a.146.1		2	21.20	even	2	inner
735.2.b.a.146.2		2	1.1	even	1	trivial
735.2.b.b.146.1		2	3.2	odd	2
735.2.b.b.146.2		2	7.6	odd	2
735.2.s.c.521.1		2	21.5	even	6
735.2.s.c.656.1		2	7.4	even	3
735.2.s.e.521.1		2	7.5	odd	6
735.2.s.e.656.1		2	21.11	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.73205i q^{2} +(-1.50000 + 0.866025i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.50000 - 2.59808i) q^{6} +1.73205i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+1.73205i q^{2} +(-1.50000 + 0.866025i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(-1.50000 - 2.59808i) q^{6} +1.73205i q^{8} +(1.50000 - 2.59808i) q^{9} -1.73205i q^{10} -3.46410i q^{11} +(1.50000 - 0.866025i) q^{12} -3.46410i q^{13} +(1.50000 - 0.866025i) q^{15} -5.00000 q^{16} -6.00000 q^{17} +(4.50000 + 2.59808i) q^{18} -6.92820i q^{19} +1.00000 q^{20} +6.00000 q^{22} -1.73205i q^{23} +(-1.50000 - 2.59808i) q^{24} +1.00000 q^{25} +6.00000 q^{26} +5.19615i q^{27} -1.73205i q^{29} +(1.50000 + 2.59808i) q^{30} +3.46410i q^{31} -5.19615i q^{32} +(3.00000 + 5.19615i) q^{33} -10.3923i q^{34} +(-1.50000 + 2.59808i) q^{36} +4.00000 q^{37} +12.0000 q^{38} +(3.00000 + 5.19615i) q^{39} -1.73205i q^{40} +3.00000 q^{41} +1.00000 q^{43} +3.46410i q^{44} +(-1.50000 + 2.59808i) q^{45} +3.00000 q^{46} +(7.50000 - 4.33013i) q^{48} +1.73205i q^{50} +(9.00000 - 5.19615i) q^{51} +3.46410i q^{52} -9.00000 q^{54} +3.46410i q^{55} +(6.00000 + 10.3923i) q^{57} +3.00000 q^{58} +(-1.50000 + 0.866025i) q^{60} -5.19615i q^{61} -6.00000 q^{62} -1.00000 q^{64} +3.46410i q^{65} +(-9.00000 + 5.19615i) q^{66} -13.0000 q^{67} +6.00000 q^{68} +(1.50000 + 2.59808i) q^{69} -6.92820i q^{71} +(4.50000 + 2.59808i) q^{72} -3.46410i q^{73} +6.92820i q^{74} +(-1.50000 + 0.866025i) q^{75} +6.92820i q^{76} +(-9.00000 + 5.19615i) q^{78} -16.0000 q^{79} +5.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +5.19615i q^{82} +9.00000 q^{83} +6.00000 q^{85} +1.73205i q^{86} +(1.50000 + 2.59808i) q^{87} +6.00000 q^{88} -3.00000 q^{89} +(-4.50000 - 2.59808i) q^{90} +1.73205i q^{92} +(-3.00000 - 5.19615i) q^{93} +6.92820i q^{95} +(4.50000 + 7.79423i) q^{96} +10.3923i q^{97} +(-9.00000 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} - 2 q^{4} - 2 q^{5} - 3 q^{6} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 - 2 * q^4 - 2 * q^5 - 3 * q^6 + 3 * q^9	\( 2 q - 3 q^{3} - 2 q^{4} - 2 q^{5} - 3 q^{6} + 3 q^{9} + 3 q^{12} + 3 q^{15} - 10 q^{16} - 12 q^{17} + 9 q^{18} + 2 q^{20} + 12 q^{22} - 3 q^{24} + 2 q^{25} + 12 q^{26} + 3 q^{30} + 6 q^{33} - 3 q^{36} + 8 q^{37} + 24 q^{38} + 6 q^{39} + 6 q^{41} + 2 q^{43} - 3 q^{45} + 6 q^{46} + 15 q^{48} + 18 q^{51} - 18 q^{54} + 12 q^{57} + 6 q^{58} - 3 q^{60} - 12 q^{62} - 2 q^{64} - 18 q^{66} - 26 q^{67} + 12 q^{68} + 3 q^{69} + 9 q^{72} - 3 q^{75} - 18 q^{78} - 32 q^{79} + 10 q^{80} - 9 q^{81} + 18 q^{83} + 12 q^{85} + 3 q^{87} + 12 q^{88} - 6 q^{89} - 9 q^{90} - 6 q^{93} + 9 q^{96} - 18 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 - 2 * q^4 - 2 * q^5 - 3 * q^6 + 3 * q^9 + 3 * q^12 + 3 * q^15 - 10 * q^16 - 12 * q^17 + 9 * q^18 + 2 * q^20 + 12 * q^22 - 3 * q^24 + 2 * q^25 + 12 * q^26 + 3 * q^30 + 6 * q^33 - 3 * q^36 + 8 * q^37 + 24 * q^38 + 6 * q^39 + 6 * q^41 + 2 * q^43 - 3 * q^45 + 6 * q^46 + 15 * q^48 + 18 * q^51 - 18 * q^54 + 12 * q^57 + 6 * q^58 - 3 * q^60 - 12 * q^62 - 2 * q^64 - 18 * q^66 - 26 * q^67 + 12 * q^68 + 3 * q^69 + 9 * q^72 - 3 * q^75 - 18 * q^78 - 32 * q^79 + 10 * q^80 - 9 * q^81 + 18 * q^83 + 12 * q^85 + 3 * q^87 + 12 * q^88 - 6 * q^89 - 9 * q^90 - 6 * q^93 + 9 * q^96 - 18 * q^99

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