LMFDB - Embedded newform 360.2.bd.a.59.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(59,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5, 3]))

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

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

chi := DirichletCharacter("360.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bd (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	360.59
Dual form			360.2.bd.a.299.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.448288 + 2.19067i) q^{5} +(2.12132 + 1.22474i) q^{6} +(-1.22474 - 2.12132i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.448288 + 2.19067i) q^{5} +(2.12132 + 1.22474i) q^{6} +(-1.22474 - 2.12132i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.00000 - 3.00000i) q^{10} +(4.50000 - 2.59808i) q^{11} -3.46410 q^{12} +(1.22474 - 2.12132i) q^{13} +(3.00000 + 1.73205i) q^{14} +(3.67423 - 1.22474i) q^{15} +(-2.00000 - 3.46410i) q^{16} -5.19615 q^{17} -4.24264i q^{18} -5.00000 q^{19} +(3.34607 + 2.96713i) q^{20} +(-2.12132 + 3.67423i) q^{21} +(-3.67423 + 6.36396i) q^{22} +(-2.44949 - 1.41421i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-4.59808 - 1.96410i) q^{25} +3.46410i q^{26} +5.19615 q^{27} -4.89898 q^{28} +(-4.24264 - 7.34847i) q^{29} +(-3.63397 + 4.09808i) q^{30} +(-6.36396 - 3.67423i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-7.79423 - 4.50000i) q^{33} +(6.36396 - 3.67423i) q^{34} +(5.19615 - 1.73205i) q^{35} +(3.00000 + 5.19615i) q^{36} +(6.12372 - 3.53553i) q^{38} -4.24264 q^{39} +(-6.19615 - 1.26795i) q^{40} +(1.50000 + 0.866025i) q^{41} -6.00000i q^{42} +(7.79423 - 4.50000i) q^{43} -10.3923i q^{44} +(-5.01910 - 4.45069i) q^{45} +4.00000 q^{46} +(-6.12372 + 3.53553i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(0.500000 - 0.866025i) q^{49} +(7.02030 - 0.845807i) q^{50} +(4.50000 + 7.79423i) q^{51} +(-2.44949 - 4.24264i) q^{52} +1.41421i q^{53} +(-6.36396 + 3.67423i) q^{54} +(3.67423 + 11.0227i) q^{55} +(6.00000 - 3.46410i) q^{56} +(4.33013 + 7.50000i) q^{57} +(10.3923 + 6.00000i) q^{58} +(-1.50000 - 0.866025i) q^{59} +(1.55291 - 7.58871i) q^{60} +(6.36396 - 3.67423i) q^{61} +10.3923 q^{62} +7.34847 q^{63} -8.00000 q^{64} +(4.09808 + 3.63397i) q^{65} +12.7279 q^{66} +(-2.59808 - 1.50000i) q^{67} +(-5.19615 + 9.00000i) q^{68} +4.89898i q^{69} +(-5.13922 + 5.79555i) q^{70} -4.24264 q^{71} +(-7.34847 - 4.24264i) q^{72} +3.00000i q^{73} +(1.03590 + 8.59808i) q^{75} +(-5.00000 + 8.66025i) q^{76} +(-11.0227 - 6.36396i) q^{77} +(5.19615 - 3.00000i) q^{78} +(6.36396 - 3.67423i) q^{79} +(8.48528 - 2.82843i) q^{80} +(-4.50000 - 7.79423i) q^{81} -2.44949 q^{82} +(4.24264 + 7.34847i) q^{84} +(2.32937 - 11.3831i) q^{85} +(-6.36396 + 11.0227i) q^{86} +(-7.34847 + 12.7279i) q^{87} +(7.34847 + 12.7279i) q^{88} +10.3923i q^{89} +(9.29423 + 1.90192i) q^{90} -6.00000 q^{91} +(-4.89898 + 2.82843i) q^{92} +12.7279i q^{93} +(5.00000 - 8.66025i) q^{94} +(2.24144 - 10.9534i) q^{95} -9.79796i q^{96} +(-2.59808 + 1.50000i) q^{97} +1.41421i q^{98} +15.5885i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 12 q^{9}+O(q^{10}) $ 8 * q + 8 * q^4 - 12 * q^9	$ 8 q + 8 q^{4} - 12 q^{9} - 8 q^{10} + 36 q^{11} + 24 q^{14} - 16 q^{16} - 40 q^{19} - 16 q^{25} - 36 q^{30} + 24 q^{36} - 8 q^{40} + 12 q^{41} + 32 q^{46} + 4 q^{49} + 36 q^{51} + 48 q^{56} - 12 q^{59} - 64 q^{64} + 12 q^{65} + 36 q^{75} - 40 q^{76} - 36 q^{81} + 12 q^{90} - 48 q^{91} + 40 q^{94}+O(q^{100}) $ 8 * q + 8 * q^4 - 12 * q^9 - 8 * q^10 + 36 * q^11 + 24 * q^14 - 16 * q^16 - 40 * q^19 - 16 * q^25 - 36 * q^30 + 24 * q^36 - 8 * q^40 + 12 * q^41 + 32 * q^46 + 4 * q^49 + 36 * q^51 + 48 * q^56 - 12 * q^59 - 64 * q^64 + 12 * q^65 + 36 * q^75 - 40 * q^76 - 36 * q^81 + 12 * q^90 - 48 * q^91 + 40 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$2$	−1.22474	+	0.707107i	−0.866025	+	0.500000i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−0.448288	+	2.19067i	−0.200480	+	0.979698i
$5$	−0.448288	+	2.19067i	−0.200480	+	0.979698i
$6$	2.12132	+	1.22474i	0.866025	+	0.500000i
$7$	−1.22474	−	2.12132i	−0.462910	−	0.801784i	0.536194	−	0.844094i	$-0.319861\pi$
$7$	−1.22474	−	2.12132i	−0.462910	−	0.801784i	−0.999104	+	0.0423108i	$0.986528\pi$
$8$			2.82843i			1.00000i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	−1.00000	−	3.00000i	−0.316228	−	0.948683i
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.367610	−	0.929980i	$-0.380176\pi$
$11$	4.50000	−	2.59808i	1.35680	−	0.783349i	0.989191	+	0.146631i	$0.0468429\pi$
$12$	−3.46410			−1.00000
$13$	1.22474	−	2.12132i	0.339683	−	0.588348i	−0.644690	−	0.764444i	$-0.723014\pi$
$13$	1.22474	−	2.12132i	0.339683	−	0.588348i	0.984373	+	0.176096i	$0.0563468\pi$
$14$	3.00000	+	1.73205i	0.801784	+	0.462910i
$15$	3.67423	−	1.22474i	0.948683	−	0.316228i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	−5.19615			−1.26025			−0.630126	−	0.776493i	$-0.716997\pi$
$17$	−5.19615			−1.26025			−0.630126	+	0.776493i	$0.716997\pi$
$18$		−	4.24264i		−	1.00000i
$19$	−5.00000			−1.14708			−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−5.00000			−1.14708			−0.573539	+	0.819178i	$0.694430\pi$
$20$	3.34607	+	2.96713i	0.748203	+	0.663470i
$21$	−2.12132	+	3.67423i	−0.462910	+	0.801784i
$22$	−3.67423	+	6.36396i	−0.783349	+	1.35680i
$23$	−2.44949	−	1.41421i	−0.510754	−	0.294884i	0.222390	−	0.974958i	$-0.428614\pi$
$23$	−2.44949	−	1.41421i	−0.510754	−	0.294884i	−0.733144	+	0.680074i	$0.761948\pi$
$24$	4.24264	−	2.44949i	0.866025	−	0.500000i
$25$	−4.59808	−	1.96410i	−0.919615	−	0.392820i
$26$			3.46410i			0.679366i
$27$	5.19615			1.00000
$28$	−4.89898			−0.925820
$29$	−4.24264	−	7.34847i	−0.787839	−	1.36458i	−0.927289	−	0.374347i	$-0.877867\pi$
$29$	−4.24264	−	7.34847i	−0.787839	−	1.36458i	0.139450	−	0.990229i	$-0.455467\pi$
$30$	−3.63397	+	4.09808i	−0.663470	+	0.748203i
$31$	−6.36396	−	3.67423i	−1.14300	−	0.659912i	−0.195829	−	0.980638i	$-0.562740\pi$
$31$	−6.36396	−	3.67423i	−1.14300	−	0.659912i	−0.947172	+	0.320726i	$0.896073\pi$
$32$	4.89898	+	2.82843i	0.866025	+	0.500000i
$33$	−7.79423	−	4.50000i	−1.35680	−	0.783349i
$34$	6.36396	−	3.67423i	1.09141	−	0.630126i
$35$	5.19615	−	1.73205i	0.878310	−	0.292770i
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	6.12372	−	3.53553i	0.993399	−	0.573539i
$39$	−4.24264			−0.679366
$40$	−6.19615	−	1.26795i	−0.979698	−	0.200480i
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	0.612536	−	0.790443i	$-0.290149\pi$
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	−0.378275	+	0.925693i	$0.623483\pi$
$42$		−	6.00000i		−	0.925820i
$43$	7.79423	−	4.50000i	1.18861	−	0.686244i	0.230618	−	0.973044i	$-0.425925\pi$
$43$	7.79423	−	4.50000i	1.18861	−	0.686244i	0.957990	+	0.286801i	$0.0925917\pi$
$44$		−	10.3923i		−	1.56670i
$45$	−5.01910	−	4.45069i	−0.748203	−	0.663470i
$46$	4.00000			0.589768
$47$	−6.12372	+	3.53553i	−0.893237	+	0.515711i	−0.875000	−	0.484123i	$-0.839139\pi$
$47$	−6.12372	+	3.53553i	−0.893237	+	0.515711i	−0.0182371	+	0.999834i	$0.505805\pi$
$48$	−3.46410	+	6.00000i	−0.500000	+	0.866025i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	7.02030	−	0.845807i	0.992820	−	0.119615i
$51$	4.50000	+	7.79423i	0.630126	+	1.09141i
$52$	−2.44949	−	4.24264i	−0.339683	−	0.588348i
$53$			1.41421i			0.194257i	0.995272	+	0.0971286i	$0.0309658\pi$
$53$			1.41421i			0.194257i	−0.995272	+	0.0971286i	$0.969034\pi$
$54$	−6.36396	+	3.67423i	−0.866025	+	0.500000i
$55$	3.67423	+	11.0227i	0.495434	+	1.48630i
$56$	6.00000	−	3.46410i	0.801784	−	0.462910i
$57$	4.33013	+	7.50000i	0.573539	+	0.993399i
$58$	10.3923	+	6.00000i	1.36458	+	0.787839i
$59$	−1.50000	−	0.866025i	−0.195283	−	0.112747i	0.399170	−	0.916877i	$-0.369298\pi$
$59$	−1.50000	−	0.866025i	−0.195283	−	0.112747i	−0.594454	+	0.804130i	$0.702632\pi$
$60$	1.55291	−	7.58871i	0.200480	−	0.979698i
$61$	6.36396	−	3.67423i	0.814822	−	0.470438i	−0.0338058	−	0.999428i	$-0.510763\pi$
$61$	6.36396	−	3.67423i	0.814822	−	0.470438i	0.848628	+	0.528991i	$0.177429\pi$
$62$	10.3923			1.31982
$63$	7.34847			0.925820
$64$	−8.00000			−1.00000
$65$	4.09808	+	3.63397i	0.508304	+	0.450739i
$66$	12.7279			1.56670
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	0.332830	−	0.942987i	$-0.391996\pi$
$67$	−2.59808	−	1.50000i	−0.317406	−	0.183254i	−0.650236	+	0.759733i	$0.725330\pi$
$68$	−5.19615	+	9.00000i	−0.630126	+	1.09141i
$69$			4.89898i			0.589768i
$70$	−5.13922	+	5.79555i	−0.614254	+	0.692701i
$71$	−4.24264			−0.503509			−0.251754	−	0.967791i	$-0.581008\pi$
$71$	−4.24264			−0.503509			−0.251754	+	0.967791i	$0.581008\pi$
$72$	−7.34847	−	4.24264i	−0.866025	−	0.500000i
$73$			3.00000i			0.351123i	0.984468	+	0.175562i	$0.0561742\pi$
$73$			3.00000i			0.351123i	−0.984468	+	0.175562i	$0.943826\pi$
$74$		0			0
$75$	1.03590	+	8.59808i	0.119615	+	0.992820i
$76$	−5.00000	+	8.66025i	−0.573539	+	0.993399i
$77$	−11.0227	−	6.36396i	−1.25615	−	0.725241i
$78$	5.19615	−	3.00000i	0.588348	−	0.339683i
$79$	6.36396	−	3.67423i	0.716002	−	0.413384i	−0.0972777	−	0.995257i	$-0.531013\pi$
$79$	6.36396	−	3.67423i	0.716002	−	0.413384i	0.813279	+	0.581874i	$0.197680\pi$
$80$	8.48528	−	2.82843i	0.948683	−	0.316228i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−2.44949			−0.270501
$83$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$83$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$84$	4.24264	+	7.34847i	0.462910	+	0.801784i
$85$	2.32937	−	11.3831i	0.252656	−	1.23467i
$86$	−6.36396	+	11.0227i	−0.686244	+	1.18861i
$87$	−7.34847	+	12.7279i	−0.787839	+	1.36458i
$88$	7.34847	+	12.7279i	0.783349	+	1.35680i
$89$			10.3923i			1.10158i	0.834643	+	0.550791i	$0.185674\pi$
$89$			10.3923i			1.10158i	−0.834643	+	0.550791i	$0.814326\pi$
$90$	9.29423	+	1.90192i	0.979698	+	0.200480i
$91$	−6.00000			−0.628971
$92$	−4.89898	+	2.82843i	−0.510754	+	0.294884i
$93$			12.7279i			1.31982i
$94$	5.00000	−	8.66025i	0.515711	−	0.893237i
$95$	2.24144	−	10.9534i	0.229967	−	1.12379i
$96$		−	9.79796i		−	1.00000i
$97$	−2.59808	+	1.50000i	−0.263795	+	0.152302i	−0.626064	−	0.779771i	$-0.715335\pi$
$97$	−2.59808	+	1.50000i	−0.263795	+	0.152302i	0.362270	+	0.932073i	$0.382002\pi$
$98$			1.41421i			0.142857i
$99$			15.5885i			1.56670i
$100$	−8.00000	+	6.00000i	−0.800000	+	0.600000i
$101$	4.24264	+	7.34847i	0.422159	+	0.731200i	0.996150	−	0.0876610i	$-0.0279392\pi$
$101$	4.24264	+	7.34847i	0.422159	+	0.731200i	−0.573992	+	0.818861i	$0.694606\pi$
$102$	−11.0227	−	6.36396i	−1.09141	−	0.630126i
$103$	8.57321	−	14.8492i	0.844744	−	1.46314i	−0.0410996	−	0.999155i	$-0.513086\pi$
$103$	8.57321	−	14.8492i	0.844744	−	1.46314i	0.885843	−	0.463984i	$-0.153581\pi$
$104$	6.00000	+	3.46410i	0.588348	+	0.339683i
$105$	−7.09808	−	6.29423i	−0.692701	−	0.614254i
$106$	−1.00000	−	1.73205i	−0.0971286	−	0.168232i
$107$	15.5885			1.50699			0.753497	−	0.657452i	$-0.228366\pi$
$107$	15.5885			1.50699			0.753497	+	0.657452i	$0.228366\pi$
$108$	5.19615	−	9.00000i	0.500000	−	0.866025i
$109$			14.6969i			1.40771i	0.710343	+	0.703856i	$0.248540\pi$
$109$			14.6969i			1.40771i	−0.710343	+	0.703856i	$0.751460\pi$
$110$	−12.2942	−	10.9019i	−1.17221	−	1.03946i
$111$		0			0
$112$	−4.89898	+	8.48528i	−0.462910	+	0.801784i
$113$	−5.19615	+	9.00000i	−0.488813	+	0.846649i	−0.999917	−	0.0128699i	$-0.995903\pi$
$113$	−5.19615	+	9.00000i	−0.488813	+	0.846649i	0.511104	+	0.859519i	$0.329237\pi$
$114$	−10.6066	−	6.12372i	−0.993399	−	0.573539i
$115$	4.19615	−	4.73205i	0.391293	−	0.441266i
$116$	−16.9706			−1.57568
$117$	3.67423	+	6.36396i	0.339683	+	0.588348i
$118$	2.44949			0.225494
$119$	6.36396	+	11.0227i	0.583383	+	1.01045i
$120$	3.46410	+	10.3923i	0.316228	+	0.948683i
$121$	8.00000	−	13.8564i	0.727273	−	1.25967i
$122$	−5.19615	+	9.00000i	−0.470438	+	0.814822i
$123$		−	3.00000i		−	0.270501i
$124$	−12.7279	+	7.34847i	−1.14300	+	0.659912i
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$	−9.00000	+	5.19615i	−0.801784	+	0.462910i
$127$	4.89898			0.434714			0.217357	−	0.976092i	$-0.430256\pi$
$127$	4.89898			0.434714			0.217357	+	0.976092i	$0.430256\pi$
$128$	9.79796	−	5.65685i	0.866025	−	0.500000i
$129$	−13.5000	−	7.79423i	−1.18861	−	0.686244i
$130$	−7.58871	−	1.55291i	−0.665574	−	0.136200i
$131$	−6.00000	−	3.46410i	−0.524222	−	0.302660i	0.214438	−	0.976738i	$-0.431208\pi$
$131$	−6.00000	−	3.46410i	−0.524222	−	0.302660i	−0.738661	+	0.674078i	$0.764541\pi$
$132$	−15.5885	+	9.00000i	−1.35680	+	0.783349i
$133$	6.12372	+	10.6066i	0.530994	+	0.919709i
$134$	4.24264			0.366508
$135$	−2.32937	+	11.3831i	−0.200480	+	0.979698i
$136$		−	14.6969i		−	1.26025i
$137$	−7.79423	−	13.5000i	−0.665906	−	1.15338i	−0.979039	−	0.203674i	$-0.934712\pi$
$137$	−7.79423	−	13.5000i	−0.665906	−	1.15338i	0.313133	−	0.949709i	$-0.398621\pi$
$138$	−3.46410	−	6.00000i	−0.294884	−	0.510754i
$139$	−8.50000	+	14.7224i	−0.720961	+	1.24874i	0.239655	+	0.970858i	$0.422966\pi$
$139$	−8.50000	+	14.7224i	−0.720961	+	1.24874i	−0.960615	+	0.277882i	$0.910368\pi$
$140$	2.19615	−	10.7321i	0.185609	−	0.907024i
$141$	10.6066	+	6.12372i	0.893237	+	0.515711i
$142$	5.19615	−	3.00000i	0.436051	−	0.251754i
$143$		−	12.7279i		−	1.06436i
$144$	12.0000			1.00000
$145$	18.0000	−	6.00000i	1.49482	−	0.498273i
$146$	−2.12132	−	3.67423i	−0.175562	−	0.304082i
$147$	−1.73205			−0.142857
$148$		0			0
$149$	6.36396	−	11.0227i	0.521356	−	0.903015i	−0.478335	−	0.878177i	$-0.658760\pi$
$149$	6.36396	−	11.0227i	0.521356	−	0.903015i	0.999691	−	0.0248379i	$-0.00790696\pi$
$150$	−7.34847	−	9.79796i	−0.600000	−	0.800000i
$151$	12.7279	−	7.34847i	1.03578	−	0.598010i	0.117147	−	0.993115i	$-0.462625\pi$
$151$	12.7279	−	7.34847i	1.03578	−	0.598010i	0.918636	+	0.395105i	$0.129292\pi$
$152$		−	14.1421i		−	1.14708i
$153$	7.79423	−	13.5000i	0.630126	−	1.09141i
$154$	18.0000			1.45048
$155$	10.9019	−	12.2942i	0.875664	−	0.987496i
$156$	−4.24264	+	7.34847i	−0.339683	+	0.588348i
$157$	2.44949	−	4.24264i	0.195491	−	0.338600i	−0.751571	−	0.659653i	$-0.770703\pi$
$157$	2.44949	−	4.24264i	0.195491	−	0.338600i	0.947061	+	0.321053i	$0.104037\pi$
$158$	−5.19615	+	9.00000i	−0.413384	+	0.716002i
$159$	2.12132	−	1.22474i	0.168232	−	0.0971286i
$160$	−8.39230	+	9.46410i	−0.663470	+	0.748203i
$161$			6.92820i			0.546019i
$162$	11.0227	+	6.36396i	0.866025	+	0.500000i
$163$		−	6.00000i		−	0.469956i	−0.972001	−	0.234978i	$-0.924498\pi$
$163$		−	6.00000i		−	0.469956i	0.972001	−	0.234978i	$-0.0755019\pi$
$164$	3.00000	−	1.73205i	0.234261	−	0.135250i
$165$	13.3521	−	15.0573i	1.03946	−	1.17221i
$166$		0			0
$167$	1.22474	+	0.707107i	0.0947736	+	0.0547176i	0.546638	−	0.837369i	$-0.315907\pi$
$167$	1.22474	+	0.707107i	0.0947736	+	0.0547176i	−0.451864	+	0.892087i	$0.649241\pi$
$168$	−10.3923	−	6.00000i	−0.801784	−	0.462910i
$169$	3.50000	+	6.06218i	0.269231	+	0.466321i
$170$	5.19615	+	15.5885i	0.398527	+	1.19558i
$171$	7.50000	−	12.9904i	0.573539	−	0.993399i
$172$		−	18.0000i		−	1.37249i
$173$	−17.1464	+	9.89949i	−1.30362	+	0.752645i	−0.981023	−	0.193892i	$-0.937889\pi$
$173$	−17.1464	+	9.89949i	−1.30362	+	0.752645i	−0.322596	+	0.946537i	$0.604555\pi$
$174$		−	20.7846i		−	1.57568i
$175$	1.46498	+	12.1595i	0.110742	+	0.919173i
$176$	−18.0000	−	10.3923i	−1.35680	−	0.783349i
$177$			3.00000i			0.225494i
$178$	−7.34847	−	12.7279i	−0.550791	−	0.953998i
$179$		−	6.92820i		−	0.517838i	−0.965899	−	0.258919i	$-0.916634\pi$
$179$		−	6.92820i		−	0.517838i	0.965899	−	0.258919i	$-0.0833663\pi$
$180$	−12.7279	+	4.24264i	−0.948683	+	0.316228i
$181$		−	7.34847i		−	0.546207i	−0.961985	−	0.273104i	$-0.911950\pi$
$181$		−	7.34847i		−	0.546207i	0.961985	−	0.273104i	$-0.0880502\pi$
$182$	7.34847	−	4.24264i	0.544705	−	0.314485i
$183$	−11.0227	−	6.36396i	−0.814822	−	0.470438i
$184$	4.00000	−	6.92820i	0.294884	−	0.510754i
$185$		0			0
$186$	−9.00000	−	15.5885i	−0.659912	−	1.14300i
$187$	−23.3827	+	13.5000i	−1.70991	+	0.987218i
$188$			14.1421i			1.03142i
$189$	−6.36396	−	11.0227i	−0.462910	−	0.801784i
$190$	5.00000	+	15.0000i	0.362738	+	1.08821i
$191$	−10.6066	−	18.3712i	−0.767467	−	1.32929i	−0.938933	−	0.344101i	$-0.888184\pi$
$191$	−10.6066	−	18.3712i	−0.767467	−	1.32929i	0.171466	−	0.985190i	$-0.445150\pi$
$192$	6.92820	+	12.0000i	0.500000	+	0.866025i
$193$	7.79423	+	4.50000i	0.561041	+	0.323917i	0.753563	−	0.657376i	$-0.228333\pi$
$193$	7.79423	+	4.50000i	0.561041	+	0.323917i	−0.192522	+	0.981293i	$0.561667\pi$
$194$	2.12132	−	3.67423i	0.152302	−	0.263795i
$195$	1.90192	−	9.29423i	0.136200	−	0.665574i
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$			11.3137i			0.806068i	0.915185	+	0.403034i	$0.132044\pi$
$197$			11.3137i			0.806068i	−0.915185	+	0.403034i	$0.867956\pi$
$198$	−11.0227	−	19.0919i	−0.783349	−	1.35680i
$199$			7.34847i			0.520919i	0.965485	+	0.260460i	$0.0838741\pi$
$199$			7.34847i			0.520919i	−0.965485	+	0.260460i	$0.916126\pi$
$200$	5.55532	−	13.0053i	0.392820	−	0.919615i
$201$			5.19615i			0.366508i
$202$	−10.3923	−	6.00000i	−0.731200	−	0.422159i
$203$	−10.3923	+	18.0000i	−0.729397	+	1.26335i
$204$	18.0000			1.26025
$205$	−2.56961	+	2.89778i	−0.179469	+	0.202390i
$206$			24.2487i			1.68949i
$207$	7.34847	−	4.24264i	0.510754	−	0.294884i
$208$	−9.79796			−0.679366
$209$	−22.5000	+	12.9904i	−1.55636	+	0.898563i
$210$	13.1440	+	2.68973i	0.907024	+	0.185609i
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	2.44949	+	1.41421i	0.168232	+	0.0971286i
$213$	3.67423	+	6.36396i	0.251754	+	0.436051i
$214$	−19.0919	+	11.0227i	−1.30509	+	0.753497i
$215$	6.36396	+	19.0919i	0.434019	+	1.30206i
$216$			14.6969i			1.00000i
$217$			18.0000i			1.22192i
$218$	−10.3923	−	18.0000i	−0.703856	−	1.21911i
$219$	4.50000	−	2.59808i	0.304082	−	0.175562i
$220$	22.7661	+	4.65874i	1.53489	+	0.314092i
$221$	−6.36396	+	11.0227i	−0.428086	+	0.741467i
$222$		0			0
$223$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$223$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$224$		−	13.8564i		−	0.925820i
$225$	12.0000	−	9.00000i	0.800000	−	0.600000i
$226$		−	14.6969i		−	0.977626i
$227$	−12.9904	−	22.5000i	−0.862202	−	1.49338i	−0.869799	−	0.493406i	$-0.835752\pi$
$227$	−12.9904	−	22.5000i	−0.862202	−	1.49338i	0.00759708	−	0.999971i	$-0.497582\pi$
$228$	17.3205			1.14708
$229$	6.36396	+	3.67423i	0.420542	+	0.242800i	0.695309	−	0.718711i	$-0.255267\pi$
$229$	6.36396	+	3.67423i	0.420542	+	0.242800i	−0.274767	+	0.961511i	$0.588601\pi$
$230$	−1.79315	+	8.76268i	−0.118237	+	0.577794i
$231$			22.0454i			1.45048i
$232$	20.7846	−	12.0000i	1.36458	−	0.787839i
$233$	−5.19615			−0.340411			−0.170206	−	0.985409i	$-0.554443\pi$
$233$	−5.19615			−0.340411			−0.170206	+	0.985409i	$0.554443\pi$
$234$	−9.00000	−	5.19615i	−0.588348	−	0.339683i
$235$	−5.00000	−	15.0000i	−0.326164	−	0.978492i
$236$	−3.00000	+	1.73205i	−0.195283	+	0.112747i
$237$	−11.0227	−	6.36396i	−0.716002	−	0.413384i
$238$	−15.5885	−	9.00000i	−1.01045	−	0.583383i
$239$	−4.24264	+	7.34847i	−0.274434	+	0.475333i	−0.969992	−	0.243137i	$-0.921824\pi$
$239$	−4.24264	+	7.34847i	−0.274434	+	0.475333i	0.695558	+	0.718470i	$0.255157\pi$
$240$	−11.5911	−	10.2784i	−0.748203	−	0.663470i
$241$	8.50000	+	14.7224i	0.547533	+	0.948355i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$	8.50000	+	14.7224i	0.547533	+	0.948355i	−0.450910	+	0.892570i	$0.648900\pi$
$242$			22.6274i			1.45455i
$243$	−7.79423	+	13.5000i	−0.500000	+	0.866025i
$244$		−	14.6969i		−	0.940875i
$245$	1.67303	+	1.48356i	0.106886	+	0.0947814i
$246$	2.12132	+	3.67423i	0.135250	+	0.234261i
$247$	−6.12372	+	10.6066i	−0.389643	+	0.674882i
$248$	10.3923	−	18.0000i	0.659912	−	1.14300i
$249$		0			0
$250$	−1.29423	+	15.7583i	−0.0818542	+	0.996644i
$251$		−	19.0526i		−	1.20259i	−0.799028	−	0.601293i	$-0.794652\pi$
$251$		−	19.0526i		−	1.20259i	0.799028	−	0.601293i	$-0.205348\pi$
$252$	7.34847	−	12.7279i	0.462910	−	0.801784i
$253$	−14.6969			−0.923989
$254$	−6.00000	+	3.46410i	−0.376473	+	0.217357i
$255$	−19.0919	+	6.36396i	−1.19558	+	0.398527i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	12.9904	−	22.5000i	0.810318	−	1.40351i	−0.102324	−	0.994751i	$-0.532628\pi$
$257$	12.9904	−	22.5000i	0.810318	−	1.40351i	0.912642	−	0.408760i	$-0.134039\pi$
$258$	22.0454			1.37249
$259$		0			0
$260$	10.3923	−	3.46410i	0.644503	−	0.214834i
$261$	25.4558			1.57568
$262$	9.79796			0.605320
$263$	6.12372	−	3.53553i	0.377605	−	0.218010i	−0.299171	−	0.954200i	$-0.596710\pi$
$263$	6.12372	−	3.53553i	0.377605	−	0.218010i	0.676776	+	0.736189i	$0.263377\pi$
$264$	12.7279	−	22.0454i	0.783349	−	1.35680i
$265$	−3.09808	−	0.633975i	−0.190313	−	0.0389447i
$266$	−15.0000	−	8.66025i	−0.919709	−	0.530994i
$267$	15.5885	−	9.00000i	0.953998	−	0.550791i
$268$	−5.19615	+	3.00000i	−0.317406	+	0.183254i
$269$	12.7279			0.776035			0.388018	−	0.921652i	$-0.373160\pi$
$269$	12.7279			0.776035			0.388018	+	0.921652i	$0.373160\pi$
$270$	−5.19615	−	15.5885i	−0.316228	−	0.948683i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	10.3923	+	18.0000i	0.630126	+	1.09141i
$273$	5.19615	+	9.00000i	0.314485	+	0.544705i
$274$	19.0919	+	11.0227i	1.15338	+	0.665906i
$275$	−25.7942	+	3.10770i	−1.55545	+	0.187401i
$276$	8.48528	+	4.89898i	0.510754	+	0.294884i
$277$	−9.79796	−	16.9706i	−0.588702	−	1.01966i	−0.994403	−	0.105656i	$-0.966306\pi$
$277$	−9.79796	−	16.9706i	−0.588702	−	1.01966i	0.405700	−	0.914006i	$-0.367028\pi$
$278$		−	24.0416i		−	1.44192i
$279$	19.0919	−	11.0227i	1.14300	−	0.659912i
$280$	4.89898	+	14.6969i	0.292770	+	0.878310i
$281$	−15.0000	+	8.66025i	−0.894825	+	0.516627i	−0.875518	−	0.483186i	$-0.839479\pi$
$281$	−15.0000	+	8.66025i	−0.894825	+	0.516627i	−0.0193073	+	0.999814i	$0.506146\pi$
$282$	−17.3205			−1.03142
$283$	5.19615	+	3.00000i	0.308879	+	0.178331i	0.646425	−	0.762978i	$-0.276263\pi$
$283$	5.19615	+	3.00000i	0.308879	+	0.178331i	−0.337546	+	0.941309i	$0.609597\pi$
$284$	−4.24264	+	7.34847i	−0.251754	+	0.436051i
$285$	−18.3712	+	6.12372i	−1.08821	+	0.362738i
$286$	9.00000	+	15.5885i	0.532181	+	0.921765i
$287$		−	4.24264i		−	0.250435i
$288$	−14.6969	+	8.48528i	−0.866025	+	0.500000i
$289$	10.0000			0.588235
$290$	−17.8028	+	20.0764i	−1.04541	+	1.17893i
$291$	4.50000	+	2.59808i	0.263795	+	0.152302i
$292$	5.19615	+	3.00000i	0.304082	+	0.175562i
$293$	19.5959	+	11.3137i	1.14481	+	0.660954i	0.947616	−	0.319411i	$-0.103485\pi$
$293$	19.5959	+	11.3137i	1.14481	+	0.660954i	0.197190	+	0.980365i	$0.436819\pi$
$294$	2.12132	−	1.22474i	0.123718	−	0.0714286i
$295$	2.56961	−	2.89778i	0.149608	−	0.168715i
$296$		0			0
$297$	23.3827	−	13.5000i	1.35680	−	0.783349i
$298$			18.0000i			1.04271i
$299$	−6.00000	+	3.46410i	−0.346989	+	0.200334i
$300$	15.9282	+	6.80385i	0.919615	+	0.392820i
$301$	−19.0919	−	11.0227i	−1.10044	−	0.635338i
$302$	−10.3923	+	18.0000i	−0.598010	+	1.03578i
$303$	7.34847	−	12.7279i	0.422159	−	0.731200i
$304$	10.0000	+	17.3205i	0.573539	+	0.993399i
$305$	5.19615	+	15.5885i	0.297531	+	0.892592i
$306$			22.0454i			1.26025i
$307$			15.0000i			0.856095i	0.903756	+	0.428048i	$0.140798\pi$
$307$			15.0000i			0.856095i	−0.903756	+	0.428048i	$0.859202\pi$
$308$	−22.0454	+	12.7279i	−1.25615	+	0.725241i
$309$	−29.6985			−1.68949
$310$	−4.65874	+	22.7661i	−0.264599	+	1.29303i
$311$	−8.48528	+	14.6969i	−0.481156	+	0.833387i	−0.999766	−	0.0216240i	$-0.993116\pi$
$311$	−8.48528	+	14.6969i	−0.481156	+	0.833387i	0.518610	+	0.855011i	$0.326450\pi$
$312$		−	12.0000i		−	0.679366i
$313$	12.9904	−	7.50000i	0.734260	−	0.423925i	−0.0857188	−	0.996319i	$-0.527319\pi$
$313$	12.9904	−	7.50000i	0.734260	−	0.423925i	0.819979	+	0.572394i	$0.193985\pi$
$314$			6.92820i			0.390981i
$315$	−3.29423	+	16.0981i	−0.185609	+	0.907024i
$316$		−	14.6969i		−	0.826767i
$317$	28.1691	−	16.2635i	1.58214	−	0.913447i	0.587589	−	0.809160i	$-0.300077\pi$
$317$	28.1691	−	16.2635i	1.58214	−	0.913447i	0.994547	−	0.104287i	$-0.0332561\pi$
$318$	−1.73205	+	3.00000i	−0.0971286	+	0.168232i
$319$	−38.1838	−	22.0454i	−2.13788	−	1.23431i
$320$	3.58630	−	17.5254i	0.200480	−	0.979698i
$321$	−13.5000	−	23.3827i	−0.753497	−	1.30509i
$322$	−4.89898	−	8.48528i	−0.273009	−	0.472866i
$323$	25.9808			1.44561
$324$	−18.0000			−1.00000
$325$	−9.79796	+	7.34847i	−0.543493	+	0.407620i
$326$	4.24264	+	7.34847i	0.234978	+	0.406994i
$327$	22.0454	−	12.7279i	1.21911	−	0.703856i
$328$	−2.44949	+	4.24264i	−0.135250	+	0.234261i
$329$	15.0000	+	8.66025i	0.826977	+	0.477455i
$330$	−5.70577	+	27.8827i	−0.314092	+	1.53489i
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$		0			0
$333$		0			0
$334$	−2.00000			−0.109435
$335$	4.45069	−	5.01910i	0.243167	−	0.274223i
$336$	16.9706			0.925820
$337$	2.59808	+	1.50000i	0.141526	+	0.0817102i	0.569091	−	0.822274i	$-0.307295\pi$
$337$	2.59808	+	1.50000i	0.141526	+	0.0817102i	−0.427565	+	0.903985i	$0.640628\pi$
$338$	−8.57321	−	4.94975i	−0.466321	−	0.269231i
$339$	18.0000			0.977626
$340$	−17.3867	−	15.4176i	−0.942924	−	0.836139i
$341$	−38.1838			−2.06777
$342$			21.2132i			1.14708i
$343$	−19.5959			−1.05808
$344$	12.7279	+	22.0454i	0.686244	+	1.18861i
$345$	−10.7321	−	2.19615i	−0.577794	−	0.118237i
$346$	14.0000	−	24.2487i	0.752645	−	1.30362i
$347$	−2.59808	+	4.50000i	−0.139472	+	0.241573i	−0.927297	−	0.374327i	$-0.877874\pi$
$347$	−2.59808	+	4.50000i	−0.139472	+	0.241573i	0.787825	+	0.615899i	$0.211207\pi$
$348$	14.6969	+	25.4558i	0.787839	+	1.36458i
$349$	12.7279	−	7.34847i	0.681310	−	0.393355i	−0.119038	−	0.992890i	$-0.537981\pi$
$349$	12.7279	−	7.34847i	0.681310	−	0.393355i	0.800348	+	0.599535i	$0.204648\pi$
$350$	−10.3923	−	13.8564i	−0.555492	−	0.740656i
$351$	6.36396	−	11.0227i	0.339683	−	0.588348i
$352$	29.3939			1.56670
$353$	12.9904	+	22.5000i	0.691408	+	1.19755i	0.971377	+	0.237545i	$0.0763427\pi$
$353$	12.9904	+	22.5000i	0.691408	+	1.19755i	−0.279968	+	0.960009i	$0.590324\pi$
$354$	−2.12132	−	3.67423i	−0.112747	−	0.195283i
$355$	1.90192	−	9.29423i	0.100944	−	0.493286i
$356$	18.0000	+	10.3923i	0.953998	+	0.550791i
$357$	11.0227	−	19.0919i	0.583383	−	1.01045i
$358$	4.89898	+	8.48528i	0.258919	+	0.448461i
$359$	4.24264			0.223918			0.111959	−	0.993713i	$-0.464287\pi$
$359$	4.24264			0.223918			0.111959	+	0.993713i	$0.464287\pi$
$360$	12.5885	−	14.1962i	0.663470	−	0.748203i
$361$	6.00000			0.315789
$362$	5.19615	+	9.00000i	0.273104	+	0.473029i
$363$	−27.7128			−1.45455
$364$	−6.00000	+	10.3923i	−0.314485	+	0.544705i
$365$	−6.57201	−	1.34486i	−0.343995	−	0.0703934i
$366$	18.0000			0.940875
$367$	7.34847	+	12.7279i	0.383587	+	0.664392i	0.991572	−	0.129556i	$-0.0413553\pi$
$367$	7.34847	+	12.7279i	0.383587	+	0.664392i	−0.607985	+	0.793948i	$0.708022\pi$
$368$			11.3137i			0.589768i
$369$	−4.50000	+	2.59808i	−0.234261	+	0.135250i
$370$		0			0
$371$	3.00000	−	1.73205i	0.155752	−	0.0899236i
$372$	22.0454	+	12.7279i	1.14300	+	0.659912i
$373$	−7.34847	+	12.7279i	−0.380489	+	0.659027i	−0.991132	−	0.132879i	$-0.957578\pi$
$373$	−7.34847	+	12.7279i	−0.380489	+	0.659027i	0.610643	+	0.791906i	$0.290911\pi$
$374$	19.0919	−	33.0681i	0.987218	−	1.70991i
$375$	−19.2999	−	1.58510i	−0.996644	−	0.0818542i
$376$	−10.0000	−	17.3205i	−0.515711	−	0.893237i
$377$	−20.7846			−1.07046
$378$	15.5885	+	9.00000i	0.801784	+	0.462910i
$379$	−13.0000			−0.667765			−0.333883	−	0.942615i	$-0.608359\pi$
$379$	−13.0000			−0.667765			−0.333883	+	0.942615i	$0.608359\pi$
$380$	−16.7303	−	14.8356i	−0.858248	−	0.761052i
$381$	−4.24264	−	7.34847i	−0.217357	−	0.376473i
$382$	25.9808	+	15.0000i	1.32929	+	0.767467i
$383$	2.44949	+	1.41421i	0.125163	+	0.0722629i	0.561274	−	0.827630i	$-0.310311\pi$
$383$	2.44949	+	1.41421i	0.125163	+	0.0722629i	−0.436111	+	0.899893i	$0.643645\pi$
$384$	−16.9706	−	9.79796i	−0.866025	−	0.500000i
$385$	18.8827	−	21.2942i	0.962351	−	1.08525i
$386$	−12.7279			−0.647834
$387$			27.0000i			1.37249i
$388$			6.00000i			0.304604i
$389$	2.12132	+	3.67423i	0.107555	+	0.186291i	0.914779	−	0.403954i	$-0.132364\pi$
$389$	2.12132	+	3.67423i	0.107555	+	0.186291i	−0.807224	+	0.590245i	$0.799031\pi$
$390$	4.24264	+	12.7279i	0.214834	+	0.644503i
$391$	12.7279	+	7.34847i	0.643679	+	0.371628i
$392$	2.44949	+	1.41421i	0.123718	+	0.0714286i
$393$			12.0000i			0.605320i
$394$	−8.00000	−	13.8564i	−0.403034	−	0.698076i
$395$	5.19615	+	15.5885i	0.261447	+	0.784340i
$396$	27.0000	+	15.5885i	1.35680	+	0.783349i
$397$	29.3939			1.47524			0.737618	−	0.675218i	$-0.235950\pi$
$397$	29.3939			1.47524			0.737618	+	0.675218i	$0.235950\pi$
$398$	−5.19615	−	9.00000i	−0.260460	−	0.451129i
$399$	10.6066	−	18.3712i	0.530994	−	0.919709i
$400$	2.39230	+	19.8564i	0.119615	+	0.992820i
$401$	19.5000	+	11.2583i	0.973784	+	0.562214i	0.900388	−	0.435089i	$-0.143283\pi$
$401$	19.5000	+	11.2583i	0.973784	+	0.562214i	0.0733959	+	0.997303i	$0.476616\pi$
$402$	−3.67423	−	6.36396i	−0.183254	−	0.317406i
$403$	−15.5885	+	9.00000i	−0.776516	+	0.448322i
$404$	16.9706			0.844317
$405$	19.0919	−	6.36396i	0.948683	−	0.316228i
$406$		−	29.3939i		−	1.45879i
$407$		0			0
$408$	−22.0454	+	12.7279i	−1.09141	+	0.630126i
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	−0.853399	−	0.521258i	$-0.825463\pi$
$409$	0.500000	−	0.866025i	0.0247234	−	0.0428222i	0.878122	+	0.478436i	$0.158796\pi$
$410$	1.09808	−	5.36603i	0.0542301	−	0.265009i
$411$	−13.5000	+	23.3827i	−0.665906	+	1.15338i
$412$	−17.1464	−	29.6985i	−0.844744	−	1.46314i
$413$			4.24264i			0.208767i
$414$	−6.00000	+	10.3923i	−0.294884	+	0.510754i
$415$		0			0
$416$	12.0000	−	6.92820i	0.588348	−	0.339683i
$417$	29.4449			1.44192
$418$	18.3712	−	31.8198i	0.898563	−	1.55636i
$419$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$419$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$420$	−18.0000	+	6.00000i	−0.878310	+	0.292770i
$421$	6.36396	−	3.67423i	0.310160	−	0.179071i	−0.336838	−	0.941563i	$-0.609357\pi$
$421$	6.36396	−	3.67423i	0.310160	−	0.179071i	0.646998	+	0.762491i	$0.276024\pi$
$422$		−	11.3137i		−	0.550743i
$423$		−	21.2132i		−	1.03142i
$424$	−4.00000			−0.194257
$425$	23.8923	+	10.2058i	1.15895	+	0.495053i
$426$	−9.00000	−	5.19615i	−0.436051	−	0.251754i
$427$	−15.5885	−	9.00000i	−0.754378	−	0.435541i
$428$	15.5885	−	27.0000i	0.753497	−	1.30509i
$429$	−19.0919	+	11.0227i	−0.921765	+	0.532181i
$430$	−21.2942	−	18.8827i	−1.02690	−	0.910604i
$431$	−4.24264			−0.204361			−0.102180	−	0.994766i	$-0.532582\pi$
$431$	−4.24264			−0.204361			−0.102180	+	0.994766i	$0.532582\pi$
$432$	−10.3923	−	18.0000i	−0.500000	−	0.866025i
$433$		−	15.0000i		−	0.720854i	−0.932787	−	0.360427i	$-0.882631\pi$
$433$		−	15.0000i		−	0.720854i	0.932787	−	0.360427i	$-0.117369\pi$
$434$	−12.7279	−	22.0454i	−0.610960	−	1.05821i
$435$	−24.5885	−	21.8038i	−1.17893	−	1.04541i
$436$	25.4558	+	14.6969i	1.21911	+	0.703856i
$437$	12.2474	+	7.07107i	0.585875	+	0.338255i
$438$	−3.67423	+	6.36396i	−0.175562	+	0.304082i
$439$	−31.8198	+	18.3712i	−1.51868	+	0.876808i	−0.518918	+	0.854824i	$0.673665\pi$
$439$	−31.8198	+	18.3712i	−1.51868	+	0.876808i	−0.999758	+	0.0219843i	$0.993002\pi$
$440$	−31.1769	+	10.3923i	−1.48630	+	0.495434i
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$		−	18.0000i		−	0.856173i
$443$	−7.79423	−	13.5000i	−0.370315	−	0.641404i	0.619299	−	0.785155i	$-0.287417\pi$
$443$	−7.79423	−	13.5000i	−0.370315	−	0.641404i	−0.989614	+	0.143751i	$0.954084\pi$
$444$		0			0
$445$	−22.7661	−	4.65874i	−1.07922	−	0.220846i
$446$		0			0
$447$	−22.0454			−1.04271
$448$	9.79796	+	16.9706i	0.462910	+	0.801784i
$449$		−	19.0526i		−	0.899146i	−0.893244	−	0.449573i	$-0.851576\pi$
$449$		−	19.0526i		−	0.899146i	0.893244	−	0.449573i	$-0.148424\pi$
$450$	−8.33298	+	19.5080i	−0.392820	+	0.919615i
$451$	9.00000			0.423793
$452$	10.3923	+	18.0000i	0.488813	+	0.846649i
$453$	−22.0454	−	12.7279i	−1.03578	−	0.598010i
$454$	31.8198	+	18.3712i	1.49338	+	0.862202i
$455$	2.68973	−	13.1440i	0.126096	−	0.616201i
$456$	−21.2132	+	12.2474i	−0.993399	+	0.573539i
$457$	−23.3827	+	13.5000i	−1.09380	+	0.631503i	−0.934585	−	0.355741i	$-0.884228\pi$
$457$	−23.3827	+	13.5000i	−1.09380	+	0.631503i	−0.159211	+	0.987245i	$0.550895\pi$
$458$	−10.3923			−0.485601
$459$	−27.0000			−1.26025
$460$	−4.00000	−	12.0000i	−0.186501	−	0.559503i
$461$	−6.36396	−	11.0227i	−0.296399	−	0.513378i	0.678910	−	0.734221i	$-0.262453\pi$
$461$	−6.36396	−	11.0227i	−0.296399	−	0.513378i	−0.975309	+	0.220843i	$0.929119\pi$
$462$	−15.5885	−	27.0000i	−0.725241	−	1.25615i
$463$	9.79796	−	16.9706i	0.455350	−	0.788689i	−0.543358	−	0.839501i	$-0.682848\pi$
$463$	9.79796	−	16.9706i	0.455350	−	0.788689i	0.998708	+	0.0508118i	$0.0161809\pi$
$464$	−16.9706	+	29.3939i	−0.787839	+	1.36458i
$465$	−27.8827	−	5.70577i	−1.29303	−	0.264599i
$466$	6.36396	−	3.67423i	0.294805	−	0.170206i
$467$	−25.9808			−1.20225			−0.601123	−	0.799156i	$-0.705280\pi$
$467$	−25.9808			−1.20225			−0.601123	+	0.799156i	$0.705280\pi$
$468$	14.6969			0.679366
$469$			7.34847i			0.339321i
$470$	16.7303	+	14.8356i	0.771712	+	0.684317i
$471$	−8.48528			−0.390981
$472$	2.44949	−	4.24264i	0.112747	−	0.195283i
$473$	23.3827	−	40.5000i	1.07514	−	1.86219i
$474$	18.0000			0.826767
$475$	22.9904	+	9.82051i	1.05487	+	0.450596i
$476$	25.4558			1.16677
$477$	−3.67423	−	2.12132i	−0.168232	−	0.0971286i
$478$		−	12.0000i		−	0.548867i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	21.4641	+	4.39230i	0.979698	+	0.200480i
$481$		0			0
$482$	−20.8207	−	12.0208i	−0.948355	−	0.547533i
$483$	10.3923	−	6.00000i	0.472866	−	0.273009i
$484$	−16.0000	−	27.7128i	−0.727273	−	1.25967i
$485$	−2.12132	−	6.36396i	−0.0963242	−	0.288973i
$486$		−	22.0454i		−	1.00000i
$487$	−19.5959			−0.887976			−0.443988	−	0.896033i	$-0.646437\pi$
$487$	−19.5959			−0.887976			−0.443988	+	0.896033i	$0.646437\pi$
$488$	10.3923	+	18.0000i	0.470438	+	0.814822i
$489$	−9.00000	+	5.19615i	−0.406994	+	0.234978i
$490$	−3.09808	−	0.633975i	−0.139957	−	0.0286401i
$491$	19.5000	+	11.2583i	0.880023	+	0.508081i	0.870666	−	0.491875i	$-0.163688\pi$
$491$	19.5000	+	11.2583i	0.880023	+	0.508081i	0.00935679	+	0.999956i	$0.497022\pi$
$492$	−5.19615	−	3.00000i	−0.234261	−	0.135250i
$493$	22.0454	+	38.1838i	0.992875	+	1.71971i
$494$		−	17.3205i		−	0.779287i
$495$	−34.1492	−	6.98811i	−1.53489	−	0.314092i
$496$			29.3939i			1.31982i
$497$	5.19615	+	9.00000i	0.233079	+	0.403705i
$498$		0			0
$499$	8.50000	−	14.7224i	0.380512	−	0.659067i	−0.610623	−	0.791921i	$-0.709081\pi$
$499$	8.50000	−	14.7224i	0.380512	−	0.659067i	0.991136	+	0.132855i	$0.0424144\pi$
$500$	−9.55772	−	20.2151i	−0.427434	−	0.904046i
$501$		−	2.44949i		−	0.109435i
$502$	13.4722	+	23.3345i	0.601293	+	1.04147i
$503$		−	7.07107i		−	0.315283i	−0.987496	−	0.157642i	$-0.949611\pi$
$503$		−	7.07107i		−	0.315283i	0.987496	−	0.157642i	$-0.0503891\pi$
$504$			20.7846i			0.925820i
$505$	−18.0000	+	6.00000i	−0.800989	+	0.266996i
$506$	18.0000	−	10.3923i	0.800198	−	0.461994i
$507$	6.06218	−	10.5000i	0.269231	−	0.466321i
$508$	4.89898	−	8.48528i	0.217357	−	0.376473i
$509$	8.48528	−	14.6969i	0.376103	−	0.651430i	−0.614388	−	0.789004i	$-0.710597\pi$
$509$	8.48528	−	14.6969i	0.376103	−	0.651430i	0.990492	+	0.137574i	$0.0439304\pi$
$510$	18.8827	−	21.2942i	0.836139	−	0.942924i
$511$	6.36396	−	3.67423i	0.281525	−	0.162539i
$512$		−	22.6274i		−	1.00000i
$513$	−25.9808			−1.14708
$514$			36.7423i			1.62064i
$515$	28.6865	+	25.4378i	1.26408	+	1.12092i
$516$	−27.0000	+	15.5885i	−1.18861	+	0.686244i
$517$	−18.3712	+	31.8198i	−0.807963	+	1.39943i
$518$		0			0
$519$	29.6985	+	17.1464i	1.30362	+	0.752645i
$520$	−10.2784	+	11.5911i	−0.450739	+	0.508304i
$521$		−	29.4449i		−	1.29000i	−0.764181	−	0.645001i	$-0.776857\pi$
$521$		−	29.4449i		−	1.29000i	0.764181	−	0.645001i	$-0.223143\pi$
$522$	−31.1769	+	18.0000i	−1.36458	+	0.787839i
$523$		−	6.00000i		−	0.262362i	−0.991358	−	0.131181i	$-0.958123\pi$
$523$		−	6.00000i		−	0.262362i	0.991358	−	0.131181i	$-0.0418769\pi$
$524$	−12.0000	+	6.92820i	−0.524222	+	0.302660i
$525$	16.9706	−	12.7279i	0.740656	−	0.555492i
$526$	−5.00000	+	8.66025i	−0.218010	+	0.377605i
$527$	33.0681	+	19.0919i	1.44047	+	0.831655i
$528$			36.0000i			1.56670i
$529$	−7.50000	−	12.9904i	−0.326087	−	0.564799i
$530$	4.24264	−	1.41421i	0.184289	−	0.0614295i
$531$	4.50000	−	2.59808i	0.195283	−	0.112747i
$532$	24.4949			1.06199
$533$	3.67423	−	2.12132i	0.159149	−	0.0918846i
$534$	−12.7279	+	22.0454i	−0.550791	+	0.953998i
$535$	−6.98811	+	34.1492i	−0.302123	+	1.47640i
$536$	4.24264	−	7.34847i	0.183254	−	0.317406i
$537$	−10.3923	+	6.00000i	−0.448461	+	0.258919i
$538$	−15.5885	+	9.00000i	−0.672066	+	0.388018i
$539$		−	5.19615i		−	0.223814i
$540$	17.3867	+	15.4176i	0.748203	+	0.663470i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−11.0227	+	6.36396i	−0.473029	+	0.273104i
$544$	−25.4558	−	14.6969i	−1.09141	−	0.630126i
$545$	−32.1962	−	6.58846i	−1.37913	−	0.282219i
$546$	−12.7279	−	7.34847i	−0.544705	−	0.314485i
$547$	28.5788	−	16.5000i	1.22194	−	0.705489i	0.256611	−	0.966515i	$-0.417394\pi$
$547$	28.5788	−	16.5000i	1.22194	−	0.705489i	0.965332	+	0.261026i	$0.0840607\pi$
$548$	−31.1769			−1.33181
$549$			22.0454i			0.940875i
$550$	29.3939	−	22.0454i	1.25336	−	0.940019i
$551$	21.2132	+	36.7423i	0.903713	+	1.56528i
$552$	−13.8564			−0.589768
$553$	−15.5885	−	9.00000i	−0.662889	−	0.382719i
$554$	24.0000	+	13.8564i	1.01966	+	0.588702i
$555$		0			0
$556$	17.0000	+	29.4449i	0.720961	+	1.24874i
$557$		−	24.0416i		−	1.01868i	−0.860566	−	0.509338i	$-0.829890\pi$
$557$		−	24.0416i		−	1.01868i	0.860566	−	0.509338i	$-0.170110\pi$
$558$	−15.5885	+	27.0000i	−0.659912	+	1.14300i
$559$		−	22.0454i		−	0.932421i
$560$	−16.3923	−	14.5359i	−0.692701	−	0.614254i
$561$	40.5000	+	23.3827i	1.70991	+	0.987218i
$562$	12.2474	−	21.2132i	0.516627	−	0.894825i
$563$	2.59808	−	4.50000i	0.109496	−	0.189652i	−0.806070	−	0.591820i	$-0.798410\pi$
$563$	2.59808	−	4.50000i	0.109496	−	0.189652i	0.915566	+	0.402167i	$0.131743\pi$
$564$	21.2132	−	12.2474i	0.893237	−	0.515711i
$565$	−17.3867	−	15.4176i	−0.731462	−	0.648625i
$566$	−8.48528			−0.356663
$567$	−11.0227	+	19.0919i	−0.462910	+	0.801784i
$568$		−	12.0000i		−	0.503509i
$569$	19.5000	−	11.2583i	0.817483	−	0.471974i	−0.0320650	−	0.999486i	$-0.510208\pi$
$569$	19.5000	−	11.2583i	0.817483	−	0.471974i	0.849548	+	0.527512i	$0.176875\pi$
$570$	18.1699	−	20.4904i	0.761052	−	0.858248i
$571$	−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	$0.254357\pi$
$572$	−22.0454	−	12.7279i	−0.921765	−	0.532181i
$573$	−18.3712	+	31.8198i	−0.767467	+	1.32929i
$574$	3.00000	+	5.19615i	0.125218	+	0.216883i
$575$	8.48528	+	11.3137i	0.353861	+	0.471814i
$576$	12.0000	−	20.7846i	0.500000	−	0.866025i
$577$		−	3.00000i		−	0.124892i	−0.998048	−	0.0624458i	$-0.980110\pi$
$577$		−	3.00000i		−	0.124892i	0.998048	−	0.0624458i	$-0.0198901\pi$
$578$	−12.2474	+	7.07107i	−0.509427	+	0.294118i
$579$		−	15.5885i		−	0.647834i
$580$	7.60770	−	37.1769i	0.315892	−	1.54369i
$581$		0			0
$582$	−7.34847			−0.304604
$583$	3.67423	+	6.36396i	0.152171	+	0.263568i
$584$	−8.48528			−0.351123
$585$	−15.5885	+	5.19615i	−0.644503	+	0.214834i
$586$	−32.0000			−1.32191
$587$	−12.9904	−	22.5000i	−0.536170	−	0.928674i	−0.999106	−	0.0422823i	$-0.986537\pi$
$587$	−12.9904	−	22.5000i	−0.536170	−	0.928674i	0.462935	−	0.886392i	$-0.346796\pi$
$588$	−1.73205	+	3.00000i	−0.0714286	+	0.123718i
$589$	31.8198	+	18.3712i	1.31111	+	0.756971i
$590$	−1.09808	+	5.36603i	−0.0452071	+	0.220916i
$591$	16.9706	−	9.79796i	0.698076	−	0.403034i
$592$		0			0
$593$	−31.1769			−1.28028			−0.640141	−	0.768257i	$-0.721124\pi$
$593$	−31.1769			−1.28028			−0.640141	+	0.768257i	$0.721124\pi$
$594$	−19.0919	+	33.0681i	−0.783349	+	1.35680i
$595$	−27.0000	+	9.00000i	−1.10689	+	0.368964i
$596$	−12.7279	−	22.0454i	−0.521356	−	0.903015i
$597$	11.0227	−	6.36396i	0.451129	−	0.260460i
$598$	4.89898	−	8.48528i	0.200334	−	0.346989i
$599$	−16.9706	+	29.3939i	−0.693398	+	1.20100i	0.277319	+	0.960778i	$0.410554\pi$
$599$	−16.9706	+	29.3939i	−0.693398	+	1.20100i	−0.970718	+	0.240223i	$0.922779\pi$
$600$	−24.3190	+	2.92996i	−0.992820	+	0.119615i
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	−0.999934	−	0.0114528i	$-0.996354\pi$
$601$	−12.5000	−	21.6506i	−0.509886	−	0.883148i	0.490049	−	0.871695i	$-0.336979\pi$
$602$	31.1769			1.27068
$603$	7.79423	−	4.50000i	0.317406	−	0.183254i
$604$		−	29.3939i		−	1.19602i
$605$	26.7685	+	23.7370i	1.08830	+	0.965047i
$606$			20.7846i			0.844317i
$607$	14.6969	−	25.4558i	0.596530	−	1.03322i	−0.396799	−	0.917906i	$-0.629879\pi$
$607$	14.6969	−	25.4558i	0.596530	−	1.03322i	0.993329	−	0.115315i	$-0.0367878\pi$
$608$	−24.4949	−	14.1421i	−0.993399	−	0.573539i
$609$	36.0000			1.45879
$610$	−17.3867	−	15.4176i	−0.703965	−	0.624242i
$611$			17.3205i			0.700713i
$612$	−15.5885	−	27.0000i	−0.630126	−	1.09141i
$613$	−41.6413			−1.68188			−0.840939	−	0.541130i	$-0.817997\pi$
$613$	−41.6413			−1.68188			−0.840939	+	0.541130i	$0.817997\pi$
$614$	−10.6066	−	18.3712i	−0.428048	−	0.741400i
$615$	6.57201	+	1.34486i	0.265009	+	0.0542301i
$616$	18.0000	−	31.1769i	0.725241	−	1.25615i
$617$	2.59808	−	4.50000i	0.104595	−	0.181163i	−0.808978	−	0.587839i	$-0.799979\pi$
$617$	2.59808	−	4.50000i	0.104595	−	0.181163i	0.913573	+	0.406676i	$0.133312\pi$
$618$	36.3731	−	21.0000i	1.46314	−	0.844744i
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	0.734068	−	0.679076i	$-0.237620\pi$
$619$	−5.50000	−	9.52628i	−0.221064	−	0.382893i	−0.955131	+	0.296183i	$0.904286\pi$
$620$	−10.3923	−	31.1769i	−0.417365	−	1.25210i
$621$	−12.7279	−	7.34847i	−0.510754	−	0.294884i
$622$		−	24.0000i		−	0.962312i
$623$	22.0454	−	12.7279i	0.883231	−	0.509933i
$624$	8.48528	+	14.6969i	0.339683	+	0.588348i
$625$	17.2846	+	18.0622i	0.691384	+	0.722487i
$626$	−10.6066	+	18.3712i	−0.423925	+	0.734260i
$627$	38.9711	+	22.5000i	1.55636	+	0.898563i
$628$	−4.89898	−	8.48528i	−0.195491	−	0.338600i
$629$		0			0
$630$	−7.34847	−	22.0454i	−0.292770	−	0.878310i
$631$			7.34847i			0.292538i	0.989245	+	0.146269i	$0.0467265\pi$
$631$			7.34847i			0.292538i	−0.989245	+	0.146269i	$0.953274\pi$
$632$	10.3923	+	18.0000i	0.413384	+	0.716002i
$633$	13.8564			0.550743
$634$	−23.0000	+	39.8372i	−0.913447	+	1.58214i
$635$	−2.19615	+	10.7321i	−0.0871517	+	0.425888i
$636$		−	4.89898i		−	0.194257i
$637$	−1.22474	−	2.12132i	−0.0485262	−	0.0840498i
$638$	62.3538			2.46861
$639$	6.36396	−	11.0227i	0.251754	−	0.436051i
$640$	8.00000	+	24.0000i	0.316228	+	0.948683i
$641$	−4.50000	+	2.59808i	−0.177739	+	0.102618i	−0.586230	−	0.810145i	$-0.699389\pi$
$641$	−4.50000	+	2.59808i	−0.177739	+	0.102618i	0.408491	+	0.912762i	$0.366055\pi$
$642$	33.0681	+	19.0919i	1.30509	+	0.753497i
$643$	−18.1865	−	10.5000i	−0.717207	−	0.414080i	0.0965169	−	0.995331i	$-0.469230\pi$
$643$	−18.1865	−	10.5000i	−0.717207	−	0.414080i	−0.813724	+	0.581252i	$0.802563\pi$
$644$	12.0000	+	6.92820i	0.472866	+	0.273009i
$645$	23.1265	−	26.0800i	0.910604	−	1.02690i
$646$	−31.8198	+	18.3712i	−1.25193	+	0.722804i
$647$			5.65685i			0.222394i	0.993798	+	0.111197i	$0.0354684\pi$
$647$			5.65685i			0.222394i	−0.993798	+	0.111197i	$0.964532\pi$
$648$	22.0454	−	12.7279i	0.866025	−	0.500000i
$649$	−9.00000			−0.353281
$650$	6.80385	−	15.9282i	0.266869	−	0.624756i
$651$	27.0000	−	15.5885i	1.05821	−	0.610960i
$652$	−10.3923	−	6.00000i	−0.406994	−	0.234978i
$653$	−9.79796	−	5.65685i	−0.383424	−	0.221370i	0.295883	−	0.955224i	$-0.404386\pi$
$653$	−9.79796	−	5.65685i	−0.383424	−	0.221370i	−0.679307	+	0.733854i	$0.737719\pi$
$654$	−18.0000	+	31.1769i	−0.703856	+	1.21911i
$655$	10.2784	−	11.5911i	0.401612	−	0.452902i
$656$		−	6.92820i		−	0.270501i
$657$	−7.79423	−	4.50000i	−0.304082	−	0.175562i
$658$	−24.4949			−0.954911
$659$	33.0000	−	19.0526i	1.28550	−	0.742182i	0.307650	−	0.951500i	$-0.400458\pi$
$659$	33.0000	−	19.0526i	1.28550	−	0.742182i	0.977848	+	0.209317i	$0.0671242\pi$
$660$	−12.7279	−	38.1838i	−0.495434	−	1.48630i
$661$	−25.4558	−	14.6969i	−0.990118	−	0.571645i	−0.0848081	−	0.996397i	$-0.527028\pi$
$661$	−25.4558	−	14.6969i	−0.990118	−	0.571645i	−0.905309	+	0.424753i	$0.860361\pi$
$662$	12.2474	+	7.07107i	0.476011	+	0.274825i
$663$	22.0454			0.856173
$664$		0			0
$665$	−25.9808	+	8.66025i	−1.00749	+	0.335830i
$666$		0			0
$667$			24.0000i			0.929284i
$668$	2.44949	−	1.41421i	0.0947736	−	0.0547176i
$669$		0			0
$670$	−1.90192	+	9.29423i	−0.0734777	+	0.359067i
$671$	19.0919	−	33.0681i	0.737034	−	1.27658i
$672$	−20.7846	+	12.0000i	−0.801784	+	0.462910i
$673$	−20.7846	+	12.0000i	−0.801188	+	0.462566i	−0.843886	−	0.536522i	$-0.819738\pi$
$673$	−20.7846	+	12.0000i	−0.801188	+	0.462566i	0.0426985	+	0.999088i	$0.486405\pi$
$674$	−4.24264			−0.163420
$675$	−23.8923	−	10.2058i	−0.919615	−	0.392820i
$676$	14.0000			0.538462
$677$	−26.9444	+	15.5563i	−1.03556	+	0.597879i	−0.918572	−	0.395255i	$-0.870656\pi$
$677$	−26.9444	+	15.5563i	−1.03556	+	0.597879i	−0.116985	+	0.993134i	$0.537323\pi$
$678$	−22.0454	+	12.7279i	−0.846649	+	0.488813i
$679$	6.36396	+	3.67423i	0.244226	+	0.141004i
$680$	32.1962	+	6.58846i	1.23467	+	0.252656i
$681$	−22.5000	+	38.9711i	−0.862202	+	1.49338i
$682$	46.7654	−	27.0000i	1.79074	−	1.03388i
$683$	15.5885			0.596476			0.298238	−	0.954492i	$-0.403601\pi$
$683$	15.5885			0.596476			0.298238	+	0.954492i	$0.403601\pi$
$684$	−15.0000	−	25.9808i	−0.573539	−	0.993399i
$685$	33.0681	−	11.0227i	1.26347	−	0.421156i
$686$	24.0000	−	13.8564i	0.916324	−	0.529040i
$687$		−	12.7279i		−	0.485601i
$688$	−31.1769	−	18.0000i	−1.18861	−	0.686244i
$689$	3.00000	+	1.73205i	0.114291	+	0.0659859i
$690$	14.6969	−	4.89898i	0.559503	−	0.186501i
$691$	−8.00000	−	13.8564i	−0.304334	−	0.527123i	0.672779	−	0.739844i	$-0.265101\pi$
$691$	−8.00000	−	13.8564i	−0.304334	−	0.527123i	−0.977113	+	0.212721i	$0.931767\pi$
$692$			39.5980i			1.50529i
$693$	33.0681	−	19.0919i	1.25615	−	0.725241i
$694$		−	7.34847i		−	0.278944i
$695$	−28.4416	−	25.2206i	−1.07885	−	0.956671i
$696$	−36.0000	−	20.7846i	−1.36458	−	0.787839i
$697$	−7.79423	−	4.50000i	−0.295227	−	0.170450i
$698$	−10.3923	+	18.0000i	−0.393355	+	0.681310i
$699$	4.50000	+	7.79423i	0.170206	+	0.294805i
$700$	22.5259	+	9.62209i	0.851398	+	0.363681i
$701$	50.9117			1.92291			0.961454	−	0.274966i	$-0.0886666\pi$
$701$	50.9117			1.92291			0.961454	+	0.274966i	$0.0886666\pi$
$702$			18.0000i			0.679366i
$703$		0			0
$704$	−36.0000	+	20.7846i	−1.35680	+	0.783349i
$705$	−18.1699	+	20.4904i	−0.684317	+	0.771712i
$706$	−31.8198	−	18.3712i	−1.19755	−	0.691408i
$707$	10.3923	−	18.0000i	0.390843	−	0.676960i
$708$	5.19615	+	3.00000i	0.195283	+	0.112747i
$709$	31.8198	−	18.3712i	1.19502	−	0.689944i	0.235578	−	0.971856i	$-0.424302\pi$
$709$	31.8198	−	18.3712i	1.19502	−	0.689944i	0.959440	+	0.281912i	$0.0909685\pi$
$710$	4.24264	+	12.7279i	0.159223	+	0.477670i
$711$			22.0454i			0.826767i
$712$	−29.3939			−1.10158
$713$	10.3923	+	18.0000i	0.389195	+	0.674105i
$714$			31.1769i			1.16677i
$715$	27.8827	+	5.70577i	1.04275	+	0.213384i
$716$	−12.0000	−	6.92820i	−0.448461	−	0.258919i
$717$	14.6969			0.548867
$718$	−5.19615	+	3.00000i	−0.193919	+	0.111959i
$719$	−25.4558			−0.949343			−0.474671	−	0.880163i	$-0.657433\pi$
$719$	−25.4558			−0.949343			−0.474671	+	0.880163i	$0.657433\pi$
$720$	−5.37945	+	26.2880i	−0.200480	+	0.979698i
$721$	−42.0000			−1.56416
$722$	−7.34847	+	4.24264i	−0.273482	+	0.157895i
$723$	14.7224	−	25.5000i	0.547533	−	0.948355i
$724$	−12.7279	−	7.34847i	−0.473029	−	0.273104i
$725$	5.07484	+	42.1218i	0.188475	+	1.56436i
$726$	33.9411	−	19.5959i	1.25967	−	0.727273i
$727$	13.4722	+	23.3345i	0.499656	+	0.865430i	1.00000		0.000397168i	$-0.000126423\pi$
$727$	13.4722	+	23.3345i	0.499656	+	0.865430i	−0.500344	+	0.865827i	$0.666793\pi$
$728$		−	16.9706i		−	0.628971i
$729$	27.0000			1.00000
$730$	9.00000	−	3.00000i	0.333105	−	0.111035i
$731$	−40.5000	+	23.3827i	−1.49795	+	0.864840i
$732$	−22.0454	+	12.7279i	−0.814822	+	0.470438i
$733$	18.3712	−	31.8198i	0.678555	−	1.17529i	−0.296861	−	0.954921i	$-0.595940\pi$
$733$	18.3712	−	31.8198i	0.678555	−	1.17529i	0.975416	−	0.220371i	$-0.0707267\pi$
$734$	−18.0000	−	10.3923i	−0.664392	−	0.383587i
$735$	0.776457	−	3.79435i	0.0286401	−	0.139957i
$736$	−8.00000	−	13.8564i	−0.294884	−	0.510754i
$737$	−15.5885			−0.574208
$738$	3.67423	−	6.36396i	0.135250	−	0.234261i
$739$	43.0000			1.58178			0.790890	−	0.611958i	$-0.209618\pi$
$739$	43.0000			1.58178			0.790890	+	0.611958i	$0.209618\pi$
$740$		0			0
$741$	21.2132			0.779287
$742$	−2.44949	+	4.24264i	−0.0899236	+	0.155752i
$743$	−12.2474	−	7.07107i	−0.449315	−	0.259412i	0.258226	−	0.966085i	$-0.416862\pi$
$743$	−12.2474	−	7.07107i	−0.449315	−	0.259412i	−0.707541	+	0.706672i	$0.750196\pi$
$744$	−36.0000			−1.31982
$745$	21.2942	+	18.8827i	0.780160	+	0.691808i
$746$		−	20.7846i		−	0.760979i
$747$		0			0
$748$			54.0000i			1.97444i
$749$	−19.0919	−	33.0681i	−0.697602	−	1.20828i
$750$	24.7583	−	11.7058i	0.904046	−	0.427434i
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$	24.4949	+	14.1421i	0.893237	+	0.515711i
$753$	−28.5788	+	16.5000i	−1.04147	+	0.601293i
$754$	25.4558	−	14.6969i	0.927047	−	0.535231i
$755$	10.3923	+	31.1769i	0.378215	+	1.13464i
$756$	−25.4558			−0.925820
$757$	−19.5959			−0.712226			−0.356113	−	0.934443i	$-0.615898\pi$
$757$	−19.5959			−0.712226			−0.356113	+	0.934443i	$0.615898\pi$
$758$	15.9217	−	9.19239i	0.578302	−	0.333883i
$759$	12.7279	+	22.0454i	0.461994	+	0.800198i
$760$	30.9808	+	6.33975i	1.12379	+	0.229967i
$761$	3.00000	+	1.73205i	0.108750	+	0.0627868i	0.553388	−	0.832923i	$-0.313335\pi$
$761$	3.00000	+	1.73205i	0.108750	+	0.0627868i	−0.444639	+	0.895710i	$0.646668\pi$
$762$	10.3923	+	6.00000i	0.376473	+	0.217357i
$763$	31.1769	−	18.0000i	1.12868	−	0.651644i
$764$	−42.4264			−1.53493
$765$	26.0800	+	23.1265i	0.942924	+	0.836139i
$766$	−4.00000			−0.144526
$767$	−3.67423	+	2.12132i	−0.132669	+	0.0765964i
$768$	27.7128			1.00000
$769$	−2.00000	+	3.46410i	−0.0721218	+	0.124919i	−0.899831	−	0.436239i	$-0.856310\pi$
$769$	−2.00000	+	3.46410i	−0.0721218	+	0.124919i	0.827709	+	0.561157i	$0.189644\pi$
$770$	−8.06918	+	39.4321i	−0.290793	+	1.42103i
$771$	−45.0000			−1.62064
$772$	15.5885	−	9.00000i	0.561041	−	0.323917i
$773$			45.2548i			1.62770i	0.581073	+	0.813852i	$0.302633\pi$
$773$			45.2548i			1.62770i	−0.581073	+	0.813852i	$0.697367\pi$
$774$	−19.0919	−	33.0681i	−0.686244	−	1.18861i
$775$	22.0454	+	29.3939i	0.791894	+	1.05586i
$776$	−4.24264	−	7.34847i	−0.152302	−	0.263795i
$777$		0			0
$778$	−5.19615	−	3.00000i	−0.186291	−	0.107555i
$779$	−7.50000	−	4.33013i	−0.268715	−	0.155143i
$780$	−14.1962	−	12.5885i	−0.508304	−	0.450739i
$781$	−19.0919	+	11.0227i	−0.683161	+	0.394423i
$782$	−20.7846			−0.743256
$783$	−22.0454	−	38.1838i	−0.787839	−	1.36458i
$784$	−4.00000			−0.142857
$785$	8.19615	+	7.26795i	0.292533	+	0.259404i
$786$	−8.48528	−	14.6969i	−0.302660	−	0.524222i
$787$	41.5692	+	24.0000i	1.48178	+	0.855508i	0.999786	−	0.0206657i	$-0.00657856\pi$
$787$	41.5692	+	24.0000i	1.48178	+	0.855508i	0.481996	+	0.876173i	$0.339912\pi$
$788$	19.5959	+	11.3137i	0.698076	+	0.403034i
$789$	−10.6066	−	6.12372i	−0.377605	−	0.218010i
$790$	−17.3867	−	15.4176i	−0.618590	−	0.548535i
$791$	25.4558			0.905106
$792$	−44.0908			−1.56670
$793$		−	18.0000i		−	0.639199i
$794$	−36.0000	+	20.7846i	−1.27759	+	0.737618i
$795$	1.73205	+	5.19615i	0.0614295	+	0.184289i
$796$	12.7279	+	7.34847i	0.451129	+	0.260460i
$797$	−12.2474	−	7.07107i	−0.433827	−	0.250470i	0.267149	−	0.963655i	$-0.413919\pi$
$797$	−12.2474	−	7.07107i	−0.433827	−	0.250470i	−0.700976	+	0.713185i	$0.747252\pi$
$798$			30.0000i			1.06199i
$799$	31.8198	−	18.3712i	1.12570	−	0.649925i
$800$	−16.9706	−	22.6274i	−0.600000	−	0.800000i
$801$	−27.0000	−	15.5885i	−0.953998	−	0.550791i
$802$	−31.8434			−1.12443
$803$	7.79423	+	13.5000i	0.275052	+	0.476405i
$804$	9.00000	+	5.19615i	0.317406	+	0.183254i
$805$	−15.1774	−	3.10583i	−0.534933	−	0.109466i
$806$	12.7279	−	22.0454i	0.448322	−	0.776516i
$807$	−11.0227	−	19.0919i	−0.388018	−	0.672066i
$808$	−20.7846	+	12.0000i	−0.731200	+	0.422159i
$809$		−	32.9090i		−	1.15702i	−0.815676	−	0.578509i	$-0.803635\pi$
$809$		−	32.9090i		−	1.15702i	0.815676	−	0.578509i	$-0.196365\pi$
$810$	−18.8827	+	21.2942i	−0.663470	+	0.748203i
$811$	47.0000			1.65039			0.825197	−	0.564846i	$-0.191064\pi$
$811$	47.0000			1.65039			0.825197	+	0.564846i	$0.191064\pi$
$812$	20.7846	+	36.0000i	0.729397	+	1.26335i
$813$		0			0
$814$		0			0
$815$	13.1440	+	2.68973i	0.460415	+	0.0942170i
$816$	18.0000	−	31.1769i	0.630126	−	1.09141i
$817$	−38.9711	+	22.5000i	−1.36343	+	0.787175i
$818$			1.41421i			0.0494468i
$819$	9.00000	−	15.5885i	0.314485	−	0.544705i
$820$	2.44949	+	7.34847i	0.0855399	+	0.256620i
$821$	10.6066	+	18.3712i	0.370173	+	0.641158i	0.989592	−	0.143902i	$-0.0459651\pi$
$821$	10.6066	+	18.3712i	0.370173	+	0.641158i	−0.619419	+	0.785061i	$0.712632\pi$
$822$		−	38.1838i		−	1.33181i
$823$	−14.6969	+	25.4558i	−0.512303	+	0.887335i	0.487595	+	0.873070i	$0.337874\pi$
$823$	−14.6969	+	25.4558i	−0.512303	+	0.887335i	−0.999898	+	0.0142651i	$0.995459\pi$
$824$	42.0000	+	24.2487i	1.46314	+	0.844744i
$825$	27.0000	+	36.0000i	0.940019	+	1.25336i
$826$	−3.00000	−	5.19615i	−0.104383	−	0.180797i
$827$	20.7846			0.722752			0.361376	−	0.932420i	$-0.382307\pi$
$827$	20.7846			0.722752			0.361376	+	0.932420i	$0.382307\pi$
$828$		−	16.9706i		−	0.589768i
$829$			51.4393i			1.78656i	0.449500	+	0.893280i	$0.351602\pi$
$829$			51.4393i			1.78656i	−0.449500	+	0.893280i	$0.648398\pi$
$830$		0			0
$831$	−16.9706	+	29.3939i	−0.588702	+	1.01966i
$832$	−9.79796	+	16.9706i	−0.339683	+	0.588348i
$833$	−2.59808	+	4.50000i	−0.0900180	+	0.155916i
$834$	−36.0624	+	20.8207i	−1.24874	+	0.720961i
$835$	−2.09808	+	2.36603i	−0.0726069	+	0.0818797i
$836$			51.9615i			1.79713i
$837$	−33.0681	−	19.0919i	−1.14300	−	0.659912i
$838$		0			0
$839$	14.8492	+	25.7196i	0.512653	+	0.887941i	0.999892	+	0.0146723i	$0.00467051\pi$
$839$	14.8492	+	25.7196i	0.512653	+	0.887941i	−0.487240	+	0.873268i	$0.661996\pi$
$840$	17.8028	−	20.0764i	0.614254	−	0.692701i
$841$	−21.5000	+	37.2391i	−0.741379	+	1.28411i
$842$	−5.19615	+	9.00000i	−0.179071	+	0.310160i
$843$	25.9808	+	15.0000i	0.894825	+	0.516627i
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	−14.8492	+	4.94975i	−0.510829	+	0.170276i
$846$	15.0000	+	25.9808i	0.515711	+	0.893237i
$847$	−39.1918			−1.34665
$848$	4.89898	−	2.82843i	0.168232	−	0.0971286i
$849$		−	10.3923i		−	0.356663i
$850$	−36.4785	+	4.39494i	−1.25120	+	0.150745i
$851$		0			0
$852$	14.6969			0.503509
$853$	−11.0227	−	19.0919i	−0.377410	−	0.653694i	0.613274	−	0.789870i	$-0.289852\pi$
$853$	−11.0227	−	19.0919i	−0.377410	−	0.653694i	−0.990685	+	0.136176i	$0.956519\pi$
$854$	25.4558			0.871081
$855$	25.0955	+	22.2535i	0.858248	+	0.761052i
$856$			44.0908i			1.50699i
$857$	15.5885	+	27.0000i	0.532492	+	0.922302i	0.999280	+	0.0379336i	$0.0120775\pi$
$857$	15.5885	+	27.0000i	0.532492	+	0.922302i	−0.466789	+	0.884369i	$0.654589\pi$
$858$	15.5885	−	27.0000i	0.532181	−	0.921765i
$859$	24.5000	−	42.4352i	0.835929	−	1.44787i	−0.0573424	−	0.998355i	$-0.518263\pi$
$859$	24.5000	−	42.4352i	0.835929	−	1.44787i	0.893272	−	0.449517i	$-0.148404\pi$
$860$	39.4321	+	8.06918i	1.34462	+	0.275157i
$861$	−6.36396	+	3.67423i	−0.216883	+	0.125218i
$862$	5.19615	−	3.00000i	0.176982	−	0.102180i
$863$			24.0416i			0.818387i	0.912448	+	0.409193i	$0.134190\pi$
$863$			24.0416i			0.818387i	−0.912448	+	0.409193i	$0.865810\pi$
$864$	25.4558	+	14.6969i	0.866025	+	0.500000i
$865$	−14.0000	−	42.0000i	−0.476014	−	1.42804i
$866$	10.6066	+	18.3712i	0.360427	+	0.624278i
$867$	−8.66025	−	15.0000i	−0.294118	−	0.509427i
$868$	31.1769	+	18.0000i	1.05821	+	0.610960i
$869$	19.0919	−	33.0681i	0.647648	−	1.12176i
$870$	45.5322	+	9.31749i	1.54369	+	0.315892i
$871$	−6.36396	+	3.67423i	−0.215635	+	0.124497i
$872$	−41.5692			−1.40771
$873$		−	9.00000i		−	0.304604i
$874$	−20.0000			−0.676510
$875$	−27.2942	−	2.24167i	−0.922713	−	0.0757823i
$876$		−	10.3923i		−	0.351123i
$877$	−1.22474	+	2.12132i	−0.0413567	+	0.0716319i	−0.885963	−	0.463756i	$-0.846501\pi$
$877$	−1.22474	+	2.12132i	−0.0413567	+	0.0716319i	0.844606	+	0.535388i	$0.179835\pi$
$878$	25.9808	−	45.0000i	0.876808	−	1.51868i
$879$		−	39.1918i		−	1.32191i
$880$	30.8353	−	34.7733i	1.03946	−	1.17221i
$881$		−	41.5692i		−	1.40050i	−0.713896	−	0.700251i	$-0.753071\pi$
$881$		−	41.5692i		−	1.40050i	0.713896	−	0.700251i	$-0.246929\pi$
$882$	−3.67423	−	2.12132i	−0.123718	−	0.0714286i
$883$		−	9.00000i		−	0.302874i	−0.988467	−	0.151437i	$-0.951610\pi$
$883$		−	9.00000i		−	0.302874i	0.988467	−	0.151437i	$-0.0483901\pi$
$884$	12.7279	+	22.0454i	0.428086	+	0.741467i
$885$	−6.57201	−	1.34486i	−0.220916	−	0.0452071i
$886$	19.0919	+	11.0227i	0.641404	+	0.370315i
$887$	−35.5176	−	20.5061i	−1.19256	−	0.688527i	−0.233677	−	0.972314i	$-0.575076\pi$
$887$	−35.5176	−	20.5061i	−1.19256	−	0.688527i	−0.958887	+	0.283787i	$0.908409\pi$
$888$		0			0
$889$	−6.00000	−	10.3923i	−0.201234	−	0.348547i
$890$	31.1769	−	10.3923i	1.04505	−	0.348351i
$891$	−40.5000	−	23.3827i	−1.35680	−	0.783349i
$892$		0			0
$893$	30.6186	−	17.6777i	1.02461	−	0.591561i
$894$	27.0000	−	15.5885i	0.903015	−	0.521356i
$895$	15.1774	+	3.10583i	0.507325	+	0.103816i
$896$	−24.0000	−	13.8564i	−0.801784	−	0.462910i
$897$	10.3923	+	6.00000i	0.346989	+	0.200334i
$898$	13.4722	+	23.3345i	0.449573	+	0.778683i
$899$			62.3538i			2.07962i
$900$	−3.58846	−	29.7846i	−0.119615	−	0.992820i
$901$		−	7.34847i		−	0.244813i
$902$	−11.0227	+	6.36396i	−0.367016	+	0.211897i
$903$			38.1838i			1.27068i
$904$	−25.4558	−	14.6969i	−0.846649	−	0.488813i
$905$	16.0981	+	3.29423i	0.535118	+	0.109504i
$906$	36.0000			1.19602
$907$	−44.1673	+	25.5000i	−1.46655	+	0.846714i	−0.999300	−	0.0374111i	$-0.988089\pi$
$907$	−44.1673	+	25.5000i	−1.46655	+	0.846714i	−0.467251	+	0.884125i	$0.654756\pi$
$908$	−51.9615			−1.72440
$909$	−25.4558			−0.844317
$910$	6.00000	+	18.0000i	0.198898	+	0.596694i
$911$	−23.3345	−	40.4166i	−0.773107	−	1.33906i	−0.935852	−	0.352393i	$-0.885368\pi$
$911$	−23.3345	−	40.4166i	−0.773107	−	1.33906i	0.162745	−	0.986668i	$-0.447965\pi$
$912$	17.3205	−	30.0000i	0.573539	−	0.993399i
$913$		0			0
$914$	19.0919	−	33.0681i	0.631503	−	1.09380i
$915$	18.8827	−	21.2942i	0.624242	−	0.703965i
$916$	12.7279	−	7.34847i	0.420542	−	0.242800i
$917$			16.9706i			0.560417i
$918$	33.0681	−	19.0919i	1.09141	−	0.630126i
$919$		−	58.7878i		−	1.93923i	−0.244638	−	0.969615i	$-0.578669\pi$
$919$		−	58.7878i		−	1.93923i	0.244638	−	0.969615i	$-0.421331\pi$
$920$	13.3843	+	11.8685i	0.441266	+	0.391293i
$921$	22.5000	−	12.9904i	0.741400	−	0.428048i
$922$	15.5885	+	9.00000i	0.513378	+	0.296399i
$923$	−5.19615	+	9.00000i	−0.171033	+	0.296239i
$924$	38.1838	+	22.0454i	1.25615	+	0.725241i
$925$		0			0
$926$			27.7128i			0.910700i
$927$	25.7196	+	44.5477i	0.844744	+	1.46314i
$928$		−	48.0000i		−	1.57568i
$929$	27.0000	−	15.5885i	0.885841	−	0.511441i	0.0132613	−	0.999912i	$-0.495779\pi$
$929$	27.0000	−	15.5885i	0.885841	−	0.511441i	0.872580	+	0.488471i	$0.162445\pi$
$930$	38.1838	−	12.7279i	1.25210	−	0.417365i
$931$	−2.50000	+	4.33013i	−0.0819342	+	0.141914i
$932$	−5.19615	+	9.00000i	−0.170206	+	0.294805i
$933$	29.3939			0.962312
$934$	31.8198	−	18.3712i	1.04118	−	0.601123i
$935$	−19.0919	−	57.2756i	−0.624371	−	1.87311i
$936$	−18.0000	+	10.3923i	−0.588348	+	0.339683i
$937$			36.0000i			1.17607i	0.808836	+	0.588034i	$0.200098\pi$
$937$			36.0000i			1.17607i	−0.808836	+	0.588034i	$0.799902\pi$
$938$	−5.19615	−	9.00000i	−0.169660	−	0.293860i
$939$	−22.5000	−	12.9904i	−0.734260	−	0.423925i
$940$	−30.9808	−	6.33975i	−1.01048	−	0.206780i
$941$	−16.9706	+	29.3939i	−0.553225	+	0.958213i	0.444815	+	0.895623i	$0.353270\pi$
$941$	−16.9706	+	29.3939i	−0.553225	+	0.958213i	−0.998039	+	0.0625904i	$0.980064\pi$
$942$	10.3923	−	6.00000i	0.338600	−	0.195491i
$943$	−2.44949	−	4.24264i	−0.0797664	−	0.138159i
$944$			6.92820i			0.225494i
$945$	27.0000	−	9.00000i	0.878310	−	0.292770i
$946$			66.1362i			2.15027i
$947$	−18.1865	−	31.5000i	−0.590983	−	1.02361i	−0.994100	−	0.108464i	$-0.965407\pi$
$947$	−18.1865	−	31.5000i	−0.590983	−	1.02361i	0.403117	−	0.915148i	$-0.367927\pi$
$948$	−22.0454	+	12.7279i	−0.716002	+	0.413384i
$949$	6.36396	+	3.67423i	0.206583	+	0.119271i
$950$	−35.1015	+	4.22904i	−1.13884	+	0.137208i
$951$	−48.7904	−	28.1691i	−1.58214	−	0.913447i
$952$	−31.1769	+	18.0000i	−1.01045	+	0.583383i
$953$	15.5885			0.504960			0.252480	−	0.967602i	$-0.418754\pi$
$953$	15.5885			0.504960			0.252480	+	0.967602i	$0.418754\pi$
$954$	6.00000			0.194257
$955$	45.0000	−	15.0000i	1.45617	−	0.485389i
$956$	8.48528	+	14.6969i	0.274434	+	0.475333i
$957$			76.3675i			2.46861i
$958$		0			0
$959$	−19.0919	+	33.0681i	−0.616509	+	1.06783i
$960$	−29.3939	+	9.79796i	−0.948683	+	0.316228i
$961$	11.5000	+	19.9186i	0.370968	+	0.642535i
$962$		0			0
$963$	−23.3827	+	40.5000i	−0.753497	+	1.30509i
$964$	34.0000			1.09507
$965$	−13.3521	+	15.0573i	−0.429819	+	0.484711i
$966$	−8.48528	+	14.6969i	−0.273009	+	0.472866i
$967$	14.6969	−	25.4558i	0.472622	−	0.818605i	−0.526887	−	0.849935i	$-0.676641\pi$
$967$	14.6969	−	25.4558i	0.472622	−	0.818605i	0.999509	+	0.0313303i	$0.00997439\pi$
$968$	39.1918	+	22.6274i	1.25967	+	0.727273i
$969$	−22.5000	−	38.9711i	−0.722804	−	1.25193i
$970$	7.09808	+	6.29423i	0.227905	+	0.202096i
$971$			3.46410i			0.111168i	0.998454	+	0.0555842i	$0.0177021\pi$
$971$			3.46410i			0.111168i	−0.998454	+	0.0555842i	$0.982298\pi$
$972$	15.5885	+	27.0000i	0.500000	+	0.866025i
$973$	41.6413			1.33496
$974$	24.0000	−	13.8564i	0.769010	−	0.443988i
$975$	19.5080	+	8.33298i	0.624756	+	0.266869i
$976$	−25.4558	−	14.6969i	−0.814822	−	0.470438i
$977$	28.5788	−	49.5000i	0.914318	−	1.58365i	0.106421	−	0.994321i	$-0.466061\pi$
$977$	28.5788	−	49.5000i	0.914318	−	1.58365i	0.807897	−	0.589324i	$-0.200606\pi$
$978$	7.34847	−	12.7279i	0.234978	−	0.406994i
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$	4.24264	−	1.41421i	0.135526	−	0.0451754i
$981$	−38.1838	−	22.0454i	−1.21911	−	0.703856i
$982$	−31.8434			−1.01616
$983$	−24.4949	+	14.1421i	−0.781266	+	0.451064i	−0.836879	−	0.547388i	$-0.815622\pi$
$983$	−24.4949	+	14.1421i	−0.781266	+	0.451064i	0.0556128	+	0.998452i	$0.482289\pi$
$984$	8.48528			0.270501
$985$	−24.7846	−	5.07180i	−0.789703	−	0.161601i
$986$	−54.0000	−	31.1769i	−1.71971	−	0.992875i
$987$		−	30.0000i		−	0.954911i
$988$	12.2474	+	21.2132i	0.389643	+	0.674882i
$989$	−25.4558			−0.809449
$990$	46.7654	−	15.5885i	1.48630	−	0.495434i
$991$			44.0908i			1.40059i	0.713853	+	0.700295i	$0.246948\pi$
$991$			44.0908i			1.40059i	−0.713853	+	0.700295i	$0.753052\pi$
$992$	−20.7846	−	36.0000i	−0.659912	−	1.14300i
$993$	−8.66025	+	15.0000i	−0.274825	+	0.476011i
$994$	−12.7279	−	7.34847i	−0.403705	−	0.233079i
$995$	−16.0981	−	3.29423i	−0.510343	−	0.104434i
$996$		0			0
$997$	−20.8207	−	36.0624i	−0.659397	−	1.14211i	−0.980772	−	0.195157i	$-0.937478\pi$
$997$	−20.8207	−	36.0624i	−0.659397	−	1.14211i	0.321375	−	0.946952i	$-0.395855\pi$
$998$			24.0416i			0.761025i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bd.a.59.1	✓	8
5.4	even	2	inner	360.2.bd.a.59.4	yes	8
8.3	odd	2	inner	360.2.bd.a.59.3	yes	8
9.2	odd	6	inner	360.2.bd.a.299.2	yes	8
40.19	odd	2	inner	360.2.bd.a.59.2	yes	8
45.29	odd	6	inner	360.2.bd.a.299.3	yes	8
72.11	even	6	inner	360.2.bd.a.299.4	yes	8
360.299	even	6	inner	360.2.bd.a.299.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bd.a.59.1	✓	8	1.1	even	1	trivial
360.2.bd.a.59.2	yes	8	40.19	odd	2	inner
360.2.bd.a.59.3	yes	8	8.3	odd	2	inner
360.2.bd.a.59.4	yes	8	5.4	even	2	inner
360.2.bd.a.299.1	yes	8	360.299	even	6	inner
360.2.bd.a.299.2	yes	8	9.2	odd	6	inner
360.2.bd.a.299.3	yes	8	45.29	odd	6	inner
360.2.bd.a.299.4	yes	8	72.11	even	6	inner

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.448288 + 2.19067i) q^{5} +(2.12132 + 1.22474i) q^{6} +(-1.22474 - 2.12132i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.448288 + 2.19067i) q^{5} +(2.12132 + 1.22474i) q^{6} +(-1.22474 - 2.12132i) q^{7} +2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-1.00000 - 3.00000i) q^{10} +(4.50000 - 2.59808i) q^{11} -3.46410 q^{12} +(1.22474 - 2.12132i) q^{13} +(3.00000 + 1.73205i) q^{14} +(3.67423 - 1.22474i) q^{15} +(-2.00000 - 3.46410i) q^{16} -5.19615 q^{17} -4.24264i q^{18} -5.00000 q^{19} +(3.34607 + 2.96713i) q^{20} +(-2.12132 + 3.67423i) q^{21} +(-3.67423 + 6.36396i) q^{22} +(-2.44949 - 1.41421i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-4.59808 - 1.96410i) q^{25} +3.46410i q^{26} +5.19615 q^{27} -4.89898 q^{28} +(-4.24264 - 7.34847i) q^{29} +(-3.63397 + 4.09808i) q^{30} +(-6.36396 - 3.67423i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-7.79423 - 4.50000i) q^{33} +(6.36396 - 3.67423i) q^{34} +(5.19615 - 1.73205i) q^{35} +(3.00000 + 5.19615i) q^{36} +(6.12372 - 3.53553i) q^{38} -4.24264 q^{39} +(-6.19615 - 1.26795i) q^{40} +(1.50000 + 0.866025i) q^{41} -6.00000i q^{42} +(7.79423 - 4.50000i) q^{43} -10.3923i q^{44} +(-5.01910 - 4.45069i) q^{45} +4.00000 q^{46} +(-6.12372 + 3.53553i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(0.500000 - 0.866025i) q^{49} +(7.02030 - 0.845807i) q^{50} +(4.50000 + 7.79423i) q^{51} +(-2.44949 - 4.24264i) q^{52} +1.41421i q^{53} +(-6.36396 + 3.67423i) q^{54} +(3.67423 + 11.0227i) q^{55} +(6.00000 - 3.46410i) q^{56} +(4.33013 + 7.50000i) q^{57} +(10.3923 + 6.00000i) q^{58} +(-1.50000 - 0.866025i) q^{59} +(1.55291 - 7.58871i) q^{60} +(6.36396 - 3.67423i) q^{61} +10.3923 q^{62} +7.34847 q^{63} -8.00000 q^{64} +(4.09808 + 3.63397i) q^{65} +12.7279 q^{66} +(-2.59808 - 1.50000i) q^{67} +(-5.19615 + 9.00000i) q^{68} +4.89898i q^{69} +(-5.13922 + 5.79555i) q^{70} -4.24264 q^{71} +(-7.34847 - 4.24264i) q^{72} +3.00000i q^{73} +(1.03590 + 8.59808i) q^{75} +(-5.00000 + 8.66025i) q^{76} +(-11.0227 - 6.36396i) q^{77} +(5.19615 - 3.00000i) q^{78} +(6.36396 - 3.67423i) q^{79} +(8.48528 - 2.82843i) q^{80} +(-4.50000 - 7.79423i) q^{81} -2.44949 q^{82} +(4.24264 + 7.34847i) q^{84} +(2.32937 - 11.3831i) q^{85} +(-6.36396 + 11.0227i) q^{86} +(-7.34847 + 12.7279i) q^{87} +(7.34847 + 12.7279i) q^{88} +10.3923i q^{89} +(9.29423 + 1.90192i) q^{90} -6.00000 q^{91} +(-4.89898 + 2.82843i) q^{92} +12.7279i q^{93} +(5.00000 - 8.66025i) q^{94} +(2.24144 - 10.9534i) q^{95} -9.79796i q^{96} +(-2.59808 + 1.50000i) q^{97} +1.41421i q^{98} +15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) 8 * q + 8 * q^4 - 12 * q^9	\( 8 q + 8 q^{4} - 12 q^{9} - 8 q^{10} + 36 q^{11} + 24 q^{14} - 16 q^{16} - 40 q^{19} - 16 q^{25} - 36 q^{30} + 24 q^{36} - 8 q^{40} + 12 q^{41} + 32 q^{46} + 4 q^{49} + 36 q^{51} + 48 q^{56} - 12 q^{59} - 64 q^{64} + 12 q^{65} + 36 q^{75} - 40 q^{76} - 36 q^{81} + 12 q^{90} - 48 q^{91} + 40 q^{94}+O(q^{100}) \) 8 * q + 8 * q^4 - 12 * q^9 - 8 * q^10 + 36 * q^11 + 24 * q^14 - 16 * q^16 - 40 * q^19 - 16 * q^25 - 36 * q^30 + 24 * q^36 - 8 * q^40 + 12 * q^41 + 32 * q^46 + 4 * q^49 + 36 * q^51 + 48 * q^56 - 12 * q^59 - 64 * q^64 + 12 * q^65 + 36 * q^75 - 40 * q^76 - 36 * q^81 + 12 * q^90 - 48 * q^91 + 40 * q^94

Introduction

L-functions

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