LMFDB - Embedded newform 108.2.i.a.85.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(13,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, 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:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			85.1
Root			$-1.29960 + 1.14501i$ of defining polynomial
Character	$\chi$	$=$	108.85
Dual form			108.2.i.a.61.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.829611 + 1.52044i) q^{3} +(-0.399598 + 2.26623i) q^{5} +(-0.715176 + 0.600104i) q^{7} +(-1.62349 - 2.52275i) q^{9} +O(q^{10})$	\(q+(-0.829611 + 1.52044i) q^{3} +(-0.399598 + 2.26623i) q^{5} +(-0.715176 + 0.600104i) q^{7} +(-1.62349 - 2.52275i) q^{9} +(0.843075 + 4.78132i) q^{11} +(5.71397 - 2.07972i) q^{13} +(-3.11417 - 2.48766i) q^{15} +(1.42887 - 2.47487i) q^{17} +(-2.50656 - 4.34148i) q^{19} +(-0.319106 - 1.58524i) q^{21} +(-1.51851 - 1.27419i) q^{23} +(-0.277670 - 0.101064i) q^{25} +(5.18257 - 0.375523i) q^{27} +(1.76640 + 0.642919i) q^{29} +(1.02045 + 0.856259i) q^{31} +(-7.96914 - 2.68479i) q^{33} +(-1.07419 - 1.86056i) q^{35} +(3.00392 - 5.20294i) q^{37} +(-1.57829 + 10.4131i) q^{39} +(-10.5092 + 3.82502i) q^{41} +(1.31468 + 7.45591i) q^{43} +(6.36589 - 2.67112i) q^{45} +(8.37180 - 7.02478i) q^{47} +(-1.06419 + 6.03530i) q^{49} +(2.57750 + 4.22569i) q^{51} +2.60406 q^{53} -11.1725 q^{55} +(8.68044 - 0.209333i) q^{57} +(0.763808 - 4.33177i) q^{59} +(-8.46625 + 7.10403i) q^{61} +(2.67499 + 0.829947i) q^{63} +(2.42983 + 13.7802i) q^{65} +(0.726818 - 0.264540i) q^{67} +(3.19710 - 1.25174i) q^{69} +(4.62509 - 8.01090i) q^{71} +(0.221676 + 0.383954i) q^{73} +(0.384020 - 0.338338i) q^{75} +(-3.47223 - 2.91355i) q^{77} +(-4.92366 - 1.79207i) q^{79} +(-3.72855 + 8.19133i) q^{81} +(-14.8790 - 5.41550i) q^{83} +(5.03766 + 4.22710i) q^{85} +(-2.44295 + 2.15234i) q^{87} +(-7.58162 - 13.1318i) q^{89} +(-2.83845 + 4.91634i) q^{91} +(-2.14847 + 0.841174i) q^{93} +(10.8404 - 3.94559i) q^{95} +(-1.21115 - 6.86875i) q^{97} +(10.6933 - 9.88930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 18 * q + 3 * q^5 + 6 * q^9	$ 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) $ 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.829611	+	1.52044i	−0.478976	+	0.877828i
$3$	−0.829611	+	1.52044i	−0.478976	+	0.877828i
$4$		0			0
$5$	−0.399598	+	2.26623i	−0.178706	+	1.01349i	0.755073	+	0.655640i	$0.227601\pi$
$5$	−0.399598	+	2.26623i	−0.178706	+	1.01349i	−0.933779	+	0.357850i	$0.883510\pi$
$6$		0			0
$7$	−0.715176	+	0.600104i	−0.270311	+	0.226818i	−0.767859	−	0.640618i	$-0.778678\pi$
$7$	−0.715176	+	0.600104i	−0.270311	+	0.226818i	0.497548	+	0.867436i	$0.334234\pi$
$8$		0			0
$9$	−1.62349	−	2.52275i	−0.541164	−	0.840917i
$10$		0			0
$11$	0.843075	+	4.78132i	0.254197	+	1.44162i	0.798126	+	0.602490i	$0.205825\pi$
$11$	0.843075	+	4.78132i	0.254197	+	1.44162i	−0.543929	+	0.839131i	$0.683064\pi$
$12$		0			0
$13$	5.71397	−	2.07972i	1.58477	−	0.576809i	0.608536	−	0.793526i	$-0.291757\pi$
$13$	5.71397	−	2.07972i	1.58477	−	0.576809i	0.976235	+	0.216717i	$0.0695348\pi$
$14$		0			0
$15$	−3.11417	−	2.48766i	−0.804074	−	0.642310i
$16$		0			0
$17$	1.42887	−	2.47487i	0.346551	−	0.600245i	−0.639083	−	0.769138i	$-0.720686\pi$
$17$	1.42887	−	2.47487i	0.346551	−	0.600245i	0.985634	+	0.168893i	$0.0540193\pi$
$18$		0			0
$19$	−2.50656	−	4.34148i	−0.575043	−	0.996004i	−0.996037	−	0.0889406i	$-0.971652\pi$
$19$	−2.50656	−	4.34148i	−0.575043	−	0.996004i	0.420994	−	0.907064i	$-0.361681\pi$
$20$		0			0
$21$	−0.319106	−	1.58524i	−0.0696346	−	0.345927i
$22$		0			0
$23$	−1.51851	−	1.27419i	−0.316632	−	0.265686i	0.470595	−	0.882350i	$-0.344039\pi$
$23$	−1.51851	−	1.27419i	−0.316632	−	0.265686i	−0.787227	+	0.616664i	$0.788484\pi$
$24$		0			0
$25$	−0.277670	−	0.101064i	−0.0555341	−	0.0202127i
$26$		0			0
$27$	5.18257	−	0.375523i	0.997385	−	0.0722695i
$28$		0			0
$29$	1.76640	+	0.642919i	0.328013	+	0.119387i	0.500777	−	0.865576i	$-0.333048\pi$
$29$	1.76640	+	0.642919i	0.328013	+	0.119387i	−0.172764	+	0.984963i	$0.555270\pi$
$30$		0			0
$31$	1.02045	+	0.856259i	0.183278	+	0.153789i	0.729811	−	0.683649i	$-0.239608\pi$
$31$	1.02045	+	0.856259i	0.183278	+	0.153789i	−0.546533	+	0.837438i	$0.684053\pi$
$32$		0			0
$33$	−7.96914	−	2.68479i	−1.38725	−	0.467361i
$34$		0			0
$35$	−1.07419	−	1.86056i	−0.181572	−	0.314491i
$36$		0			0
$37$	3.00392	−	5.20294i	0.493841	−	0.855358i	−0.506134	−	0.862455i	$-0.668926\pi$
$37$	3.00392	−	5.20294i	0.493841	−	0.855358i	0.999975	+	0.00709729i	$0.00225916\pi$
$38$		0			0
$39$	−1.57829	+	10.4131i	−0.252728	+	1.66743i
$40$		0			0
$41$	−10.5092	+	3.82502i	−1.64126	+	0.597368i	−0.987258	−	0.159128i	$-0.949132\pi$
$41$	−10.5092	+	3.82502i	−1.64126	+	0.597368i	−0.653998	+	0.756496i	$0.726910\pi$
$42$		0			0
$43$	1.31468	+	7.45591i	0.200486	+	1.13702i	0.904386	+	0.426715i	$0.140329\pi$
$43$	1.31468	+	7.45591i	0.200486	+	1.13702i	−0.703899	+	0.710300i	$0.748559\pi$
$44$		0			0
$45$	6.36589	−	2.67112i	0.948970	−	0.398188i
$46$		0			0
$47$	8.37180	−	7.02478i	1.22115	−	1.02467i	0.222390	−	0.974958i	$-0.428614\pi$
$47$	8.37180	−	7.02478i	1.22115	−	1.02467i	0.998764	−	0.0497113i	$-0.0158301\pi$
$48$		0			0
$49$	−1.06419	+	6.03530i	−0.152026	+	0.862185i
$50$		0			0
$51$	2.57750	+	4.22569i	0.360922	+	0.591715i
$52$		0			0
$53$	2.60406			0.357696			0.178848	−	0.983877i	$-0.442763\pi$
$53$	2.60406			0.357696			0.178848	+	0.983877i	$0.442763\pi$
$54$		0			0
$55$	−11.1725			−1.50650
$56$		0			0
$57$	8.68044	−	0.209333i	1.14975	−	0.0277269i
$58$		0			0
$59$	0.763808	−	4.33177i	0.0994393	−	0.563949i	−0.893857	−	0.448352i	$-0.852011\pi$
$59$	0.763808	−	4.33177i	0.0994393	−	0.563949i	0.993296	−	0.115596i	$-0.0368779\pi$
$60$		0			0
$61$	−8.46625	+	7.10403i	−1.08399	+	0.909577i	−0.996246	−	0.0865654i	$-0.972411\pi$
$61$	−8.46625	+	7.10403i	−1.08399	+	0.909577i	−0.0877461	+	0.996143i	$0.527966\pi$
$62$		0			0
$63$	2.67499	+	0.829947i	0.337018	+	0.104564i
$64$		0			0
$65$	2.42983	+	13.7802i	0.301383	+	1.70923i
$66$		0			0
$67$	0.726818	−	0.264540i	0.0887949	−	0.0323187i	−0.297241	−	0.954803i	$-0.596066\pi$
$67$	0.726818	−	0.264540i	0.0887949	−	0.0323187i	0.386036	+	0.922484i	$0.373844\pi$
$68$		0			0
$69$	3.19710	−	1.25174i	0.384886	−	0.150691i
$70$		0			0
$71$	4.62509	−	8.01090i	0.548898	−	0.950719i	−0.449453	−	0.893304i	$-0.648381\pi$
$71$	4.62509	−	8.01090i	0.548898	−	0.950719i	0.998350	−	0.0574144i	$-0.0182856\pi$
$72$		0			0
$73$	0.221676	+	0.383954i	0.0259452	+	0.0449384i	0.878706	−	0.477362i	$-0.158407\pi$
$73$	0.221676	+	0.383954i	0.0259452	+	0.0449384i	−0.852761	+	0.522301i	$0.825074\pi$
$74$		0			0
$75$	0.384020	−	0.338338i	0.0443428	−	0.0390679i
$76$		0			0
$77$	−3.47223	−	2.91355i	−0.395698	−	0.332030i
$78$		0			0
$79$	−4.92366	−	1.79207i	−0.553955	−	0.201623i	0.0498479	−	0.998757i	$-0.484126\pi$
$79$	−4.92366	−	1.79207i	−0.553955	−	0.201623i	−0.603803	+	0.797134i	$0.706349\pi$
$80$		0			0
$81$	−3.72855	+	8.19133i	−0.414283	+	0.910148i
$82$		0			0
$83$	−14.8790	−	5.41550i	−1.63318	−	0.594429i	−0.647352	−	0.762191i	$-0.724124\pi$
$83$	−14.8790	−	5.41550i	−1.63318	−	0.594429i	−0.985827	+	0.167763i	$0.946346\pi$
$84$		0			0
$85$	5.03766	+	4.22710i	0.546411	+	0.458494i
$86$		0			0
$87$	−2.44295	+	2.15234i	−0.261912	+	0.230756i
$88$		0			0
$89$	−7.58162	−	13.1318i	−0.803650	−	1.39196i	−0.917199	−	0.398431i	$-0.869555\pi$
$89$	−7.58162	−	13.1318i	−0.803650	−	1.39196i	0.113548	−	0.993532i	$-0.463778\pi$
$90$		0			0
$91$	−2.83845	+	4.91634i	−0.297550	+	0.515372i
$92$		0			0
$93$	−2.14847	+	0.841174i	−0.222786	+	0.0872257i
$94$		0			0
$95$	10.8404	−	3.94559i	1.11220	−	0.404809i
$96$		0			0
$97$	−1.21115	−	6.86875i	−0.122973	−	0.697416i	−0.982491	−	0.186310i	$-0.940347\pi$
$97$	−1.21115	−	6.86875i	−0.122973	−	0.697416i	0.859518	−	0.511106i	$-0.170764\pi$
$98$		0			0
$99$	10.6933	−	9.88930i	1.07472	−	0.993912i
$100$		0			0
$101$	8.77428	−	7.36249i	0.873073	−	0.732595i	−0.0916699	−	0.995789i	$-0.529220\pi$
$101$	8.77428	−	7.36249i	0.873073	−	0.732595i	0.964743	+	0.263194i	$0.0847760\pi$
$102$		0			0
$103$	2.64756	−	15.0151i	0.260872	−	1.47948i	−0.519665	−	0.854370i	$-0.673943\pi$
$103$	2.64756	−	15.0151i	0.260872	−	1.47948i	0.780537	−	0.625109i	$-0.214946\pi$
$104$		0			0
$105$	3.72003	−	0.0897105i	0.363038	−	0.00875484i
$106$		0			0
$107$	−1.13078			−0.109316			−0.0546582	−	0.998505i	$-0.517407\pi$
$107$	−1.13078			−0.109316			−0.0546582	+	0.998505i	$0.517407\pi$
$108$		0			0
$109$	11.4627			1.09793			0.548963	−	0.835847i	$-0.315023\pi$
$109$	11.4627			1.09793			0.548963	+	0.835847i	$0.315023\pi$
$110$		0			0
$111$	5.41869	+	8.88370i	0.514319	+	0.843203i
$112$		0			0
$113$	−1.55104	+	8.79638i	−0.145909	+	0.827493i	0.820723	+	0.571326i	$0.193571\pi$
$113$	−1.55104	+	8.79638i	−0.145909	+	0.827493i	−0.966632	+	0.256167i	$0.917540\pi$
$114$		0			0
$115$	3.49440	−	2.93215i	0.325854	−	0.273424i
$116$		0			0
$117$	−14.5232	−	11.0385i	−1.34267	−	1.02051i
$118$		0			0
$119$	0.463288	+	2.62744i	0.0424695	+	0.240857i
$120$		0			0
$121$	−11.8136	+	4.29980i	−1.07396	+	0.390891i
$122$		0			0
$123$	2.90279	−	19.1519i	0.261736	−	1.72687i
$124$		0			0
$125$	−5.41299	+	9.37558i	−0.484153	+	0.838577i
$126$		0			0
$127$	0.0199485	+	0.0345518i	0.00177014	+	0.00306598i	0.866909	−	0.498466i	$-0.166103\pi$
$127$	0.0199485	+	0.0345518i	0.00177014	+	0.00306598i	−0.865139	+	0.501532i	$0.832770\pi$
$128$		0			0
$129$	−12.4269	−	4.18661i	−1.09413	−	0.368610i
$130$		0			0
$131$	2.18854	+	1.83640i	0.191214	+	0.160447i	0.733369	−	0.679831i	$-0.237947\pi$
$131$	2.18854	+	1.83640i	0.191214	+	0.160447i	−0.542155	+	0.840279i	$0.682391\pi$
$132$		0			0
$133$	4.39797	+	1.60073i	0.381352	+	0.138801i
$134$		0			0
$135$	−1.21992	+	11.8950i	−0.104994	+	1.02376i
$136$		0			0
$137$	−8.55367	−	3.11328i	−0.730790	−	0.265986i	−0.0502906	−	0.998735i	$-0.516015\pi$
$137$	−8.55367	−	3.11328i	−0.730790	−	0.265986i	−0.680499	+	0.732749i	$0.738237\pi$
$138$		0			0
$139$	−1.65849	−	1.39164i	−0.140671	−	0.118037i	0.569737	−	0.821827i	$-0.307045\pi$
$139$	−1.65849	−	1.39164i	−0.140671	−	0.118037i	−0.710408	+	0.703790i	$0.751490\pi$
$140$		0			0
$141$	3.73543	+	18.5567i	0.314580	+	1.56275i
$142$		0			0
$143$	14.7611	+	25.5670i	1.23438	+	2.13802i
$144$		0			0
$145$	−2.16286	+	3.74618i	−0.179615	+	0.311103i
$146$		0			0
$147$	−8.29346	−	6.62498i	−0.684033	−	0.546419i
$148$		0			0
$149$	3.24975	−	1.18281i	0.266230	−	0.0968999i	−0.205456	−	0.978666i	$-0.565868\pi$
$149$	3.24975	−	1.18281i	0.266230	−	0.0968999i	0.471686	+	0.881766i	$0.343646\pi$
$150$		0			0
$151$	0.850331	+	4.82247i	0.0691989	+	0.392447i	0.999660	+	0.0260571i	$0.00829516\pi$
$151$	0.850331	+	4.82247i	0.0691989	+	0.392447i	−0.930462	+	0.366390i	$0.880594\pi$
$152$		0			0
$153$	−8.56324	+	0.413255i	−0.692297	+	0.0334096i
$154$		0			0
$155$	−2.34825	+	1.97042i	−0.188616	+	0.158268i
$156$		0			0
$157$	−0.210558	+	1.19413i	−0.0168043	+	0.0953021i	−0.992056	−	0.125794i	$-0.959852\pi$
$157$	−0.210558	+	1.19413i	−0.0168043	+	0.0953021i	0.975252	+	0.221096i	$0.0709634\pi$
$158$		0			0
$159$	−2.16036	+	3.95933i	−0.171328	+	0.313995i
$160$		0			0
$161$	1.85065			0.145852
$162$		0			0
$163$	9.21181			0.721525			0.360762	−	0.932658i	$-0.382517\pi$
$163$	9.21181			0.721525			0.360762	+	0.932658i	$0.382517\pi$
$164$		0			0
$165$	9.26880	−	16.9871i	0.721575	−	1.32244i
$166$		0			0
$167$	0.507283	−	2.87695i	0.0392548	−	0.222625i	−0.958869	−	0.283848i	$-0.908389\pi$
$167$	0.507283	−	2.87695i	0.0392548	−	0.222625i	0.998124	+	0.0612230i	$0.0195001\pi$
$168$		0			0
$169$	18.3657	−	15.4106i	1.41274	−	1.18543i
$170$		0			0
$171$	−6.88311	+	13.3718i	−0.526364	+	1.02257i
$172$		0			0
$173$	2.53836	+	14.3958i	0.192988	+	1.09449i	0.915255	+	0.402876i	$0.131989\pi$
$173$	2.53836	+	14.3958i	0.192988	+	1.09449i	−0.722266	+	0.691615i	$0.756900\pi$
$174$		0			0
$175$	0.259232	−	0.0943527i	0.0195961	−	0.00713239i
$176$		0			0
$177$	5.95255	+	4.75501i	0.447421	+	0.357409i
$178$		0			0
$179$	−10.1929	+	17.6546i	−0.761852	+	1.31957i	0.180043	+	0.983659i	$0.442376\pi$
$179$	−10.1929	+	17.6546i	−0.761852	+	1.31957i	−0.941895	+	0.335907i	$0.890957\pi$
$180$		0			0
$181$	1.95796	+	3.39129i	0.145534	+	0.252072i	0.929572	−	0.368640i	$-0.120177\pi$
$181$	1.95796	+	3.39129i	0.145534	+	0.252072i	−0.784038	+	0.620713i	$0.786843\pi$
$182$		0			0
$183$	−3.77757	−	18.7660i	−0.279246	−	1.38722i
$184$		0			0
$185$	10.5907	+	8.88666i	0.778644	+	0.653360i
$186$		0			0
$187$	13.0378	+	4.74537i	0.953418	+	0.347016i
$188$		0			0
$189$	−3.48109	+	3.37864i	−0.253212	+	0.245760i
$190$		0			0
$191$	−15.6790	−	5.70669i	−1.13449	−	0.412922i	−0.294572	−	0.955629i	$-0.595177\pi$
$191$	−15.6790	−	5.70669i	−1.13449	−	0.412922i	−0.839922	+	0.542707i	$0.817399\pi$
$192$		0			0
$193$	−0.141992	−	0.119146i	−0.0102208	−	0.00857629i	0.637663	−	0.770316i	$-0.279901\pi$
$193$	−0.141992	−	0.119146i	−0.0102208	−	0.00857629i	−0.647884	+	0.761739i	$0.724346\pi$
$194$		0			0
$195$	−22.9679	−	7.73782i	−1.64476	−	0.554117i
$196$		0			0
$197$	−0.971346	−	1.68242i	−0.0692055	−	0.119868i	0.829346	−	0.558735i	$-0.188713\pi$
$197$	−0.971346	−	1.68242i	−0.0692055	−	0.119868i	−0.898552	+	0.438867i	$0.855380\pi$
$198$		0			0
$199$	0.601693	−	1.04216i	0.0426529	−	0.0738770i	−0.843911	−	0.536483i	$-0.819752\pi$
$199$	0.601693	−	1.04216i	0.0426529	−	0.0738770i	0.886564	+	0.462606i	$0.153086\pi$
$200$		0			0
$201$	−0.200758	+	1.32455i	−0.0141604	+	0.0934265i
$202$		0			0
$203$	−1.64911	+	0.600226i	−0.115745	+	0.0421276i
$204$		0			0
$205$	−4.46895	−	25.3447i	−0.312125	−	1.77015i
$206$		0			0
$207$	−0.749157	+	5.89946i	−0.0520700	+	0.410041i
$208$		0			0
$209$	18.6448	−	15.6448i	1.28969	−	1.08218i
$210$		0			0
$211$	−1.00749	+	5.71378i	−0.0693587	+	0.393353i	0.930289	+	0.366826i	$0.119556\pi$
$211$	−1.00749	+	5.71378i	−0.0693587	+	0.393353i	−0.999648	+	0.0265264i	$0.991555\pi$
$212$		0			0
$213$	8.34308	+	13.6781i	0.571658	+	0.937209i
$214$		0			0
$215$	−17.4222			−1.18818
$216$		0			0
$217$	−1.24365			−0.0844242
$218$		0			0
$219$	−0.767685	+	0.0185131i	−0.0518754	+	0.00125100i
$220$		0			0
$221$	3.01748	−	17.1130i	0.202978	−	1.15114i
$222$		0			0
$223$	8.82195	−	7.40250i	0.590762	−	0.495708i	−0.297700	−	0.954660i	$-0.596219\pi$
$223$	8.82195	−	7.40250i	0.590762	−	0.495708i	0.888461	+	0.458952i	$0.151775\pi$
$224$		0			0
$225$	0.195837	+	0.864569i	0.0130558	+	0.0576380i
$226$		0			0
$227$	−2.31231	−	13.1138i	−0.153474	−	0.870392i	−0.960168	−	0.279423i	$-0.909857\pi$
$227$	−2.31231	−	13.1138i	−0.153474	−	0.870392i	0.806694	−	0.590969i	$-0.201254\pi$
$228$		0			0
$229$	−18.2916	+	6.65760i	−1.20874	+	0.439946i	−0.866268	−	0.499580i	$-0.833488\pi$
$229$	−18.2916	+	6.65760i	−1.20874	+	0.439946i	−0.342475	+	0.939527i	$0.611265\pi$
$230$		0			0
$231$	7.31049	−	2.86222i	0.480995	−	0.188320i
$232$		0			0
$233$	1.72784	−	2.99271i	0.113195	−	0.196059i	−0.803862	−	0.594816i	$-0.797225\pi$
$233$	1.72784	−	2.99271i	0.113195	−	0.196059i	0.917057	+	0.398757i	$0.130558\pi$
$234$		0			0
$235$	12.5744	+	21.7795i	0.820265	+	1.42074i
$236$		0			0
$237$	6.80945	−	5.99942i	0.442322	−	0.389704i
$238$		0			0
$239$	8.82780	+	7.40741i	0.571023	+	0.479145i	0.881985	−	0.471277i	$-0.156207\pi$
$239$	8.82780	+	7.40741i	0.571023	+	0.479145i	−0.310962	+	0.950422i	$0.600651\pi$
$240$		0			0
$241$	−12.8530	−	4.67811i	−0.827935	−	0.301344i	−0.106924	−	0.994267i	$-0.534100\pi$
$241$	−12.8530	−	4.67811i	−0.827935	−	0.301344i	−0.721011	+	0.692923i	$0.756322\pi$
$242$		0			0
$243$	−9.36120	−	12.4647i	−0.600521	−	0.799609i
$244$		0			0
$245$	−13.2521	−	4.82338i	−0.846648	−	0.308155i
$246$		0			0
$247$	−23.3514	−	19.5942i	−1.48582	−	1.24675i
$248$		0			0
$249$	20.5777	−	18.1299i	1.30406	−	1.14893i
$250$		0			0
$251$	7.32328	+	12.6843i	0.462241	+	0.800626i	0.999072	−	0.0430642i	$-0.0137120\pi$
$251$	7.32328	+	12.6843i	0.462241	+	0.800626i	−0.536831	+	0.843690i	$0.680379\pi$
$252$		0			0
$253$	4.81206	−	8.33473i	0.302532	−	0.524000i
$254$		0			0
$255$	−10.6064	+	4.15263i	−0.664196	+	0.260048i
$256$		0			0
$257$	10.0321	−	3.65138i	0.625784	−	0.227767i	−0.00961103	−	0.999954i	$-0.503059\pi$
$257$	10.0321	−	3.65138i	0.625784	−	0.227767i	0.635395	+	0.772187i	$0.280837\pi$
$258$		0			0
$259$	0.973973	+	5.52368i	0.0605197	+	0.343225i
$260$		0			0
$261$	−1.24582	−	5.49997i	−0.0771142	−	0.340440i
$262$		0			0
$263$	−6.92891	+	5.81404i	−0.427255	+	0.358509i	−0.830915	−	0.556400i	$-0.812182\pi$
$263$	−6.92891	+	5.81404i	−0.427255	+	0.358509i	0.403660	+	0.914909i	$0.367738\pi$
$264$		0			0
$265$	−1.04058	+	5.90142i	−0.0639222	+	0.362521i
$266$		0			0
$267$	26.2559	−	0.633174i	1.60683	−	0.0387496i
$268$		0			0
$269$	15.9649			0.973394			0.486697	−	0.873571i	$-0.338202\pi$
$269$	15.9649			0.973394			0.486697	+	0.873571i	$0.338202\pi$
$270$		0			0
$271$	−12.6954			−0.771193			−0.385596	−	0.922668i	$-0.626004\pi$
$271$	−12.6954			−0.771193			−0.385596	+	0.922668i	$0.626004\pi$
$272$		0			0
$273$	−5.12020	−	8.39435i	−0.309889	−	0.508049i
$274$		0			0
$275$	0.249121	−	1.41283i	0.0150225	−	0.0851971i
$276$		0			0
$277$	−20.8013	+	17.4543i	−1.24983	+	1.04873i	−0.253137	+	0.967430i	$0.581463\pi$
$277$	−20.8013	+	17.4543i	−1.24983	+	1.04873i	−0.996690	+	0.0812992i	$0.974093\pi$
$278$		0			0
$279$	0.503438	−	3.96447i	0.0301400	−	0.237347i
$280$		0			0
$281$	−1.44027	−	8.16819i	−0.0859194	−	0.487273i	−0.997154	−	0.0753864i	$-0.975981\pi$
$281$	−1.44027	−	8.16819i	−0.0859194	−	0.487273i	0.911235	−	0.411887i	$-0.135130\pi$
$282$		0			0
$283$	20.0353	−	7.29225i	1.19097	−	0.433479i	0.330909	−	0.943663i	$-0.392645\pi$
$283$	20.0353	−	7.29225i	1.19097	−	0.433479i	0.860066	+	0.510183i	$0.170422\pi$
$284$		0			0
$285$	−2.99429	+	19.7555i	−0.177366	+	1.17022i
$286$		0			0
$287$	5.22049	−	9.04215i	0.308156	−	0.533741i
$288$		0			0
$289$	4.41667	+	7.64990i	0.259804	+	0.449994i
$290$		0			0
$291$	11.4483	+	3.85691i	0.671112	+	0.226096i
$292$		0			0
$293$	−13.4526	−	11.2881i	−0.785910	−	0.659456i	0.158820	−	0.987308i	$-0.449231\pi$
$293$	−13.4526	−	11.2881i	−0.785910	−	0.659456i	−0.944729	+	0.327851i	$0.893676\pi$
$294$		0			0
$295$	9.51159	+	3.46193i	0.553786	+	0.201562i
$296$		0			0
$297$	6.16479	+	24.4629i	0.357717	+	1.41948i
$298$		0			0
$299$	−11.3267	−	4.12258i	−0.655040	−	0.238415i
$300$		0			0
$301$	−5.41454	−	4.54334i	−0.312089	−	0.261874i
$302$		0			0
$303$	3.91501	+	19.4488i	0.224911	+	1.11730i
$304$		0			0
$305$	−12.7163	−	22.0253i	−0.728132	−	1.26116i
$306$		0			0
$307$	−15.0261	+	26.0260i	−0.857587	+	1.48538i	0.0166369	+	0.999862i	$0.494704\pi$
$307$	−15.0261	+	26.0260i	−0.857587	+	1.48538i	−0.874224	+	0.485523i	$0.838629\pi$
$308$		0			0
$309$	20.6331	+	16.4821i	1.17378	+	0.937636i
$310$		0			0
$311$	19.3160	−	7.03045i	1.09531	−	0.398660i	0.269725	−	0.962937i	$-0.413067\pi$
$311$	19.3160	−	7.03045i	1.09531	−	0.398660i	0.825585	+	0.564277i	$0.190845\pi$
$312$		0			0
$313$	2.37426	+	13.4651i	0.134201	+	0.761093i	0.975413	+	0.220386i	$0.0707319\pi$
$313$	2.37426	+	13.4651i	0.134201	+	0.761093i	−0.841211	+	0.540706i	$0.818157\pi$
$314$		0			0
$315$	−2.94978	+	5.73051i	−0.166201	+	0.322878i
$316$		0			0
$317$	−8.82833	+	7.40785i	−0.495848	+	0.416066i	−0.856117	−	0.516783i	$-0.827130\pi$
$317$	−8.82833	+	7.40785i	−0.495848	+	0.416066i	0.360268	+	0.932849i	$0.382685\pi$
$318$		0			0
$319$	−1.58479	+	8.98777i	−0.0887310	+	0.503218i
$320$		0			0
$321$	0.938105	−	1.71928i	0.0523599	−	0.0959609i
$322$		0			0
$323$	−14.3261			−0.797128
$324$		0			0
$325$	−1.79678			−0.0996677
$326$		0			0
$327$	−9.50957	+	17.4284i	−0.525880	+	0.963790i
$328$		0			0
$329$	−1.77172	+	10.0479i	−0.0976779	+	0.553959i
$330$		0			0
$331$	1.46721	−	1.23114i	0.0806453	−	0.0676694i	−0.601574	−	0.798817i	$-0.705459\pi$
$331$	1.46721	−	1.23114i	0.0806453	−	0.0676694i	0.682219	+	0.731148i	$0.261015\pi$
$332$		0			0
$333$	−18.0026	+	0.868787i	−0.986534	+	0.0476093i
$334$		0			0
$335$	0.309074	+	1.75285i	0.0168865	+	0.0957683i
$336$		0			0
$337$	−0.981575	+	0.357264i	−0.0534698	+	0.0194614i	−0.368617	−	0.929582i	$-0.620168\pi$
$337$	−0.981575	+	0.357264i	−0.0534698	+	0.0194614i	0.315147	+	0.949043i	$0.397946\pi$
$338$		0			0
$339$	−12.0876	−	9.65583i	−0.656510	−	0.524433i
$340$		0			0
$341$	−3.23373	+	5.60099i	−0.175116	+	0.303310i
$342$		0			0
$343$	−6.12831	−	10.6145i	−0.330898	−	0.573131i
$344$		0			0
$345$	1.55917	+	7.74557i	0.0839430	+	0.417007i
$346$		0			0
$347$	−2.42603	−	2.03568i	−0.130236	−	0.109281i	0.575343	−	0.817912i	$-0.304869\pi$
$347$	−2.42603	−	2.03568i	−0.130236	−	0.109281i	−0.705579	+	0.708631i	$0.749313\pi$
$348$		0			0
$349$	−22.1942	−	8.07804i	−1.18803	−	0.432408i	−0.328999	−	0.944330i	$-0.606711\pi$
$349$	−22.1942	−	8.07804i	−1.18803	−	0.432408i	−0.859032	+	0.511923i	$0.828933\pi$
$350$		0			0
$351$	28.8321	−	12.9240i	1.53894	−	0.689832i
$352$		0			0
$353$	30.0013	+	10.9196i	1.59681	+	0.581190i	0.978770	−	0.204960i	$-0.0657064\pi$
$353$	30.0013	+	10.9196i	1.59681	+	0.581190i	0.618036	+	0.786150i	$0.287929\pi$
$354$		0			0
$355$	16.3064	+	13.6827i	0.865453	+	0.726201i
$356$		0			0
$357$	−4.37922	−	1.47535i	−0.231773	−	0.0780837i
$358$		0			0
$359$	−2.84279	−	4.92386i	−0.150037	−	0.259871i	0.781204	−	0.624276i	$-0.214606\pi$
$359$	−2.84279	−	4.92386i	−0.150037	−	0.259871i	−0.931241	+	0.364404i	$0.881273\pi$
$360$		0			0
$361$	−3.06564	+	5.30985i	−0.161350	+	0.279466i
$362$		0			0
$363$	3.26309	−	21.5291i	0.171268	−	1.12998i
$364$		0			0
$365$	−0.958711	+	0.348942i	−0.0501812	+	0.0182645i
$366$		0			0
$367$	−2.96923	−	16.8393i	−0.154993	−	0.879006i	−0.958793	−	0.284107i	$-0.908303\pi$
$367$	−2.96923	−	16.8393i	−0.154993	−	0.879006i	0.803800	−	0.594900i	$-0.202808\pi$
$368$		0			0
$369$	26.7111	+	20.3021i	1.39053	+	1.05689i
$370$		0			0
$371$	−1.86236	+	1.56271i	−0.0966891	+	0.0811318i
$372$		0			0
$373$	−2.60503	+	14.7739i	−0.134884	+	0.764963i	0.840057	+	0.542498i	$0.182521\pi$
$373$	−2.60503	+	14.7739i	−0.134884	+	0.764963i	−0.974941	+	0.222465i	$0.928590\pi$
$374$		0			0
$375$	−9.76435	−	16.0082i	−0.504229	−	0.826661i
$376$		0			0
$377$	11.4303			0.588689
$378$		0			0
$379$	10.5520			0.542020			0.271010	−	0.962577i	$-0.412642\pi$
$379$	10.5520			0.542020			0.271010	+	0.962577i	$0.412642\pi$
$380$		0			0
$381$	−0.0690835	+	0.00166599i	−0.00353926	+	8.53510e-5i
$382$		0			0
$383$	−0.695233	+	3.94286i	−0.0355248	+	0.201471i	−0.997404	−	0.0720019i	$-0.977061\pi$
$383$	−0.695233	+	3.94286i	−0.0355248	+	0.201471i	0.961880	+	0.273473i	$0.0881724\pi$
$384$		0			0
$385$	7.99028	−	6.70464i	0.407222	−	0.341700i
$386$		0			0
$387$	16.6750	−	15.4212i	0.847640	−	0.783904i
$388$		0			0
$389$	−4.52315	−	25.6520i	−0.229333	−	1.30061i	−0.854227	−	0.519901i	$-0.825969\pi$
$389$	−4.52315	−	25.6520i	−0.229333	−	1.30061i	0.624894	−	0.780710i	$-0.285142\pi$
$390$		0			0
$391$	−5.32320	+	1.93749i	−0.269206	+	0.0979829i
$392$		0			0
$393$	−4.60778	+	1.80405i	−0.232432	+	0.0910022i
$394$		0			0
$395$	6.02872	−	10.4421i	0.303338	−	0.525397i
$396$		0			0
$397$	−11.1476	−	19.3083i	−0.559484	−	0.969055i	−0.997539	−	0.0701069i	$-0.977666\pi$
$397$	−11.1476	−	19.3083i	−0.559484	−	0.969055i	0.438055	−	0.898948i	$-0.355667\pi$
$398$		0			0
$399$	−6.08242	+	5.35887i	−0.304502	+	0.268279i
$400$		0			0
$401$	−8.60036	−	7.21656i	−0.429481	−	0.360378i	0.402275	−	0.915519i	$-0.368220\pi$
$401$	−8.60036	−	7.21656i	−0.429481	−	0.360378i	−0.831756	+	0.555141i	$0.812664\pi$
$402$		0			0
$403$	7.61160	+	2.77040i	0.379161	+	0.138003i
$404$		0			0
$405$	−17.0735	−	11.7230i	−0.848391	−	0.582521i
$406$		0			0
$407$	27.4094	+	9.97621i	1.35863	+	0.494503i
$408$		0			0
$409$	−14.1375	−	11.8628i	−0.699056	−	0.586577i	0.222449	−	0.974944i	$-0.428595\pi$
$409$	−14.1375	−	11.8628i	−0.699056	−	0.586577i	−0.921505	+	0.388367i	$0.873039\pi$
$410$		0			0
$411$	11.8298	−	10.4226i	0.583520	−	0.514107i
$412$		0			0
$413$	2.05325	+	3.55634i	0.101034	+	0.174996i
$414$		0			0
$415$	18.2184	−	31.5552i	0.894306	−	1.54898i
$416$		0			0
$417$	3.49180	−	1.36712i	0.170994	−	0.0669481i
$418$		0			0
$419$	−37.7300	+	13.7326i	−1.84323	+	0.670882i	−0.854855	+	0.518867i	$0.826354\pi$
$419$	−37.7300	+	13.7326i	−1.84323	+	0.670882i	−0.988378	+	0.152015i	$0.951424\pi$
$420$		0			0
$421$	5.75622	+	32.6452i	0.280541	+	1.59103i	0.720791	+	0.693152i	$0.243779\pi$
$421$	5.75622	+	32.6452i	0.280541	+	1.59103i	−0.440250	+	0.897875i	$0.645110\pi$
$422$		0			0
$423$	−31.3133	−	9.71532i	−1.52251	−	0.472375i
$424$		0			0
$425$	−0.646874	+	0.542792i	−0.0313780	+	0.0263293i
$426$		0			0
$427$	1.79170	−	10.1613i	0.0867066	−	0.491738i
$428$		0			0
$429$	−51.1190	+	1.23276i	−2.46805	+	0.0595184i
$430$		0			0
$431$	7.90172			0.380613			0.190306	−	0.981725i	$-0.439052\pi$
$431$	7.90172			0.380613			0.190306	+	0.981725i	$0.439052\pi$
$432$		0			0
$433$	6.54423			0.314496			0.157248	−	0.987559i	$-0.449738\pi$
$433$	6.54423			0.314496			0.157248	+	0.987559i	$0.449738\pi$
$434$		0			0
$435$	−3.90152	−	6.39637i	−0.187063	−	0.306682i
$436$		0			0
$437$	−1.72561	+	9.78642i	−0.0825471	+	0.468148i
$438$		0			0
$439$	−15.3384	+	12.8704i	−0.732060	+	0.614271i	−0.930692	−	0.365803i	$-0.880794\pi$
$439$	−15.3384	+	12.8704i	−0.732060	+	0.614271i	0.198632	+	0.980074i	$0.436350\pi$
$440$		0			0
$441$	16.9532	−	7.11357i	0.807297	−	0.338742i
$442$		0			0
$443$	4.97235	+	28.1996i	0.236243	+	1.33980i	0.839980	+	0.542618i	$0.182567\pi$
$443$	4.97235	+	28.1996i	0.236243	+	1.33980i	−0.603736	+	0.797184i	$0.706322\pi$
$444$		0			0
$445$	32.7892	−	11.9343i	1.55436	−	0.565740i
$446$		0			0
$447$	−0.897631	+	5.92234i	−0.0424565	+	0.280117i
$448$		0			0
$449$	−2.55211	+	4.42039i	−0.120442	+	0.208611i	−0.919942	−	0.392055i	$-0.871764\pi$
$449$	−2.55211	+	4.42039i	−0.120442	+	0.208611i	0.799500	+	0.600666i	$0.205098\pi$
$450$		0			0
$451$	−27.1487	−	47.0229i	−1.27838	−	2.21422i
$452$		0			0
$453$	−8.03773	−	2.70789i	−0.377645	−	0.127228i
$454$		0			0
$455$	−10.0073	−	8.39715i	−0.469151	−	0.393664i
$456$		0			0
$457$	18.3836	+	6.69109i	0.859949	+	0.312996i	0.734090	−	0.679052i	$-0.237609\pi$
$457$	18.3836	+	6.69109i	0.859949	+	0.312996i	0.125859	+	0.992048i	$0.459831\pi$
$458$		0			0
$459$	6.47583	−	13.3628i	0.302266	−	0.623720i
$460$		0			0
$461$	7.87191	+	2.86514i	0.366632	+	0.133443i	0.518765	−	0.854917i	$-0.326392\pi$
$461$	7.87191	+	2.86514i	0.366632	+	0.133443i	−0.152133	+	0.988360i	$0.548614\pi$
$462$		0			0
$463$	25.2770	+	21.2099i	1.17472	+	0.985709i	0.999999	+	0.00109105i	$0.000347291\pi$
$463$	25.2770	+	21.2099i	1.17472	+	0.985709i	0.174723	+	0.984618i	$0.444097\pi$
$464$		0			0
$465$	−1.04777	−	5.20506i	−0.0485892	−	0.241379i
$466$		0			0
$467$	3.70848	+	6.42327i	0.171608	+	0.297234i	0.938982	−	0.343966i	$-0.111770\pi$
$467$	3.70848	+	6.42327i	0.171608	+	0.297234i	−0.767374	+	0.641200i	$0.778437\pi$
$468$		0			0
$469$	−0.361051	+	0.625358i	−0.0166718	+	0.0288764i
$470$		0			0
$471$	−1.64093	−	1.31081i	−0.0756099	−	0.0603987i
$472$		0			0
$473$	−34.5407	+	12.5718i	−1.58818	+	0.578051i
$474$		0			0
$475$	0.257230	+	1.45882i	0.0118025	+	0.0669354i
$476$		0			0
$477$	−4.22768	−	6.56941i	−0.193572	−	0.300792i
$478$		0			0
$479$	1.34791	−	1.13103i	0.0615878	−	0.0516783i	−0.611474	−	0.791264i	$-0.709423\pi$
$479$	1.34791	−	1.13103i	0.0615878	−	0.0516783i	0.673062	+	0.739586i	$0.264979\pi$
$480$		0			0
$481$	6.34367	−	35.9767i	0.289246	−	1.64040i
$482$		0			0
$483$	−1.53532	+	2.81380i	−0.0698594	+	0.128033i
$484$		0			0
$485$	16.0502			0.728800
$486$		0			0
$487$	0.863405			0.0391246			0.0195623	−	0.999809i	$-0.493773\pi$
$487$	0.863405			0.0391246			0.0195623	+	0.999809i	$0.493773\pi$
$488$		0			0
$489$	−7.64222	+	14.0060i	−0.345593	+	0.633374i
$490$		0			0
$491$	3.14334	−	17.8268i	0.141857	−	0.804510i	−0.827980	−	0.560757i	$-0.810510\pi$
$491$	3.14334	−	17.8268i	0.141857	−	0.804510i	0.969837	−	0.243753i	$-0.0783787\pi$
$492$		0			0
$493$	4.11510	−	3.45298i	0.185335	−	0.155514i
$494$		0			0
$495$	18.1384	+	28.1854i	0.815261	+	1.26684i
$496$		0			0
$497$	1.49961	+	8.50473i	0.0672669	+	0.381489i
$498$		0			0
$499$	−4.39454	+	1.59948i	−0.196727	+	0.0716027i	−0.438505	−	0.898729i	$-0.644492\pi$
$499$	−4.39454	+	1.59948i	−0.196727	+	0.0716027i	0.241778	+	0.970332i	$0.422269\pi$
$500$		0			0
$501$	3.95338	+	3.15804i	0.176624	+	0.141091i
$502$		0			0
$503$	10.1410	−	17.5648i	0.452166	−	0.783174i	−0.546355	−	0.837554i	$-0.683985\pi$
$503$	10.1410	−	17.5648i	0.452166	−	0.783174i	0.998520	+	0.0543801i	$0.0173183\pi$
$504$		0			0
$505$	13.1789	+	22.8266i	0.586455	+	1.01577i
$506$		0			0
$507$	8.19462	+	40.7088i	0.363936	+	1.80794i
$508$		0			0
$509$	27.4839	+	23.0618i	1.21820	+	1.02219i	0.998917	+	0.0465347i	$0.0148178\pi$
$509$	27.4839	+	23.0618i	1.21820	+	1.02219i	0.219288	+	0.975660i	$0.429627\pi$
$510$		0			0
$511$	−0.388950	−	0.141566i	−0.0172061	−	0.00626251i
$512$		0			0
$513$	−14.6207	−	21.5587i	−0.645520	−	0.951842i
$514$		0			0
$515$	32.9697	+	12.0000i	1.45282	+	0.528783i
$516$		0			0
$517$	40.6457	+	34.1058i	1.78760	+	1.49997i
$518$		0			0
$519$	−23.9938	−	8.08346i	−1.05321	−	0.354824i
$520$		0			0
$521$	−9.97163	−	17.2714i	−0.436865	−	0.756672i	0.560581	−	0.828100i	$-0.310578\pi$
$521$	−9.97163	−	17.2714i	−0.436865	−	0.756672i	−0.997446	+	0.0714274i	$0.977245\pi$
$522$		0			0
$523$	11.7394	−	20.3332i	0.513328	−	0.889111i	−0.486552	−	0.873652i	$-0.661746\pi$
$523$	11.7394	−	20.3332i	0.513328	−	0.889111i	0.999880	−	0.0154593i	$-0.00492105\pi$
$524$		0			0
$525$	−0.0716037	+	0.472423i	−0.00312504	+	0.0206182i
$526$		0			0
$527$	3.57722	−	1.30200i	0.155826	−	0.0567161i
$528$		0			0
$529$	−3.31157	−	18.7808i	−0.143981	−	0.816558i
$530$		0			0
$531$	−12.1680	+	5.10570i	−0.528047	+	0.221568i
$532$		0			0
$533$	−52.0941	+	43.7122i	−2.25645	+	1.89338i
$534$		0			0
$535$	0.451856	−	2.56260i	0.0195354	−	0.110791i
$536$		0			0
$537$	−18.3867	−	30.1441i	−0.793443	−	1.30082i
$538$		0			0
$539$	−29.7538			−1.28159
$540$		0			0
$541$	−33.3333			−1.43311			−0.716555	−	0.697531i	$-0.754282\pi$
$541$	−33.3333			−1.43311			−0.716555	+	0.697531i	$0.754282\pi$
$542$		0			0
$543$	−6.78060	+	0.163518i	−0.290984	+	0.00701722i
$544$		0			0
$545$	−4.58047	+	25.9771i	−0.196206	+	1.11274i
$546$		0			0
$547$	−19.0588	+	15.9922i	−0.814894	+	0.683777i	−0.951770	−	0.306811i	$-0.900738\pi$
$547$	−19.0588	+	15.9922i	−0.814894	+	0.683777i	0.136877	+	0.990588i	$0.456294\pi$
$548$		0			0
$549$	31.6666	+	9.82492i	1.35150	+	0.419317i
$550$		0			0
$551$	−1.63637	−	9.28032i	−0.0697118	−	0.395355i
$552$		0			0
$553$	4.59671	−	1.67306i	0.195472	−	0.0711459i
$554$		0			0
$555$	−22.2978	+	8.73010i	−0.946490	+	0.370572i
$556$		0			0
$557$	−10.0496	+	17.4063i	−0.425813	+	0.737530i	−0.996496	−	0.0836406i	$-0.973345\pi$
$557$	−10.0496	+	17.4063i	−0.425813	+	0.737530i	0.570683	+	0.821171i	$0.306679\pi$
$558$		0			0
$559$	23.0182	+	39.8687i	0.973566	+	1.68627i
$560$		0			0
$561$	−18.0314	+	15.8864i	−0.761284	+	0.670724i
$562$		0			0
$563$	11.4481	+	9.60610i	0.482480	+	0.404849i	0.851322	−	0.524643i	$-0.175801\pi$
$563$	11.4481	+	9.60610i	0.482480	+	0.404849i	−0.368842	+	0.929492i	$0.620246\pi$
$564$		0			0
$565$	−19.3148	−	7.03003i	−0.812582	−	0.295756i
$566$		0			0
$567$	−2.24908	−	8.09576i	−0.0944524	−	0.339990i
$568$		0			0
$569$	36.7616	+	13.3801i	1.54112	+	0.560923i	0.966315	−	0.257363i	$-0.0828538\pi$
$569$	36.7616	+	13.3801i	1.54112	+	0.560923i	0.574810	+	0.818287i	$0.305076\pi$
$570$		0			0
$571$	−1.20038	−	1.00724i	−0.0502342	−	0.0421515i	0.617325	−	0.786708i	$-0.288216\pi$
$571$	−1.20038	−	1.00724i	−0.0502342	−	0.0421515i	−0.667559	+	0.744557i	$0.732661\pi$
$572$		0			0
$573$	21.6842	−	19.1047i	0.905870	−	0.798111i
$574$		0			0
$575$	0.292873	+	0.507270i	0.0122136	+	0.0211546i
$576$		0			0
$577$	2.44151	−	4.22883i	0.101642	−	0.176048i	−0.810720	−	0.585435i	$-0.800924\pi$
$577$	2.44151	−	4.22883i	0.101642	−	0.176048i	0.912361	+	0.409386i	$0.134257\pi$
$578$		0			0
$579$	0.298952	−	0.117046i	0.0124240	−	0.00486428i
$580$		0			0
$581$	13.8909	−	5.05589i	0.576293	−	0.209754i
$582$		0			0
$583$	2.19542	+	12.4509i	0.0909251	+	0.515662i
$584$		0			0
$585$	30.8193	−	28.5020i	1.27422	−	1.17841i
$586$		0			0
$587$	−12.5044	+	10.4925i	−0.516114	+	0.433071i	−0.863274	−	0.504735i	$-0.831590\pi$
$587$	−12.5044	+	10.4925i	−0.516114	+	0.433071i	0.347161	+	0.937806i	$0.387146\pi$
$588$		0			0
$589$	1.15962	−	6.57653i	0.0477813	−	0.270981i
$590$		0			0
$591$	3.36386	−	0.0811213i	0.138371	−	0.00333689i
$592$		0			0
$593$	14.5826			0.598835			0.299418	−	0.954122i	$-0.403208\pi$
$593$	14.5826			0.598835			0.299418	+	0.954122i	$0.403208\pi$
$594$		0			0
$595$	−6.13951			−0.251696
$596$		0			0
$597$	1.08538	+	1.77943i	0.0444216	+	0.0728272i
$598$		0			0
$599$	−4.49878	+	25.5139i	−0.183815	+	1.04247i	0.743653	+	0.668566i	$0.233092\pi$
$599$	−4.49878	+	25.5139i	−0.183815	+	1.04247i	−0.927468	+	0.373902i	$0.878019\pi$
$600$		0			0
$601$	−7.51430	+	6.30525i	−0.306515	+	0.257197i	−0.783050	−	0.621959i	$-0.786337\pi$
$601$	−7.51430	+	6.30525i	−0.306515	+	0.257197i	0.476535	+	0.879156i	$0.341893\pi$
$602$		0			0
$603$	−1.84735	−	1.40410i	−0.0752299	−	0.0571794i
$604$		0			0
$605$	−5.02365	−	28.4906i	−0.204241	−	1.15831i
$606$		0			0
$607$	−9.69750	+	3.52960i	−0.393610	+	0.143262i	−0.531240	−	0.847222i	$-0.678274\pi$
$607$	−9.69750	+	3.52960i	−0.393610	+	0.143262i	0.137630	+	0.990484i	$0.456051\pi$
$608$		0			0
$609$	0.455508	−	3.00533i	0.0184581	−	0.121782i
$610$		0			0
$611$	33.2267	−	57.5504i	1.34421	−	2.32824i
$612$		0			0
$613$	−22.0542	−	38.1990i	−0.890761	−	1.54284i	−0.838965	−	0.544186i	$-0.816839\pi$
$613$	−22.0542	−	38.1990i	−0.890761	−	1.54284i	−0.0517966	−	0.998658i	$-0.516495\pi$
$614$		0			0
$615$	42.2426	+	14.2314i	1.70339	+	0.573867i
$616$		0			0
$617$	−26.5158	−	22.2494i	−1.06749	−	0.895727i	−0.0726635	−	0.997357i	$-0.523150\pi$
$617$	−26.5158	−	22.2494i	−1.06749	−	0.895727i	−0.994822	+	0.101630i	$0.967594\pi$
$618$		0			0
$619$	−18.5907	−	6.76644i	−0.747221	−	0.271966i	−0.0597854	−	0.998211i	$-0.519042\pi$
$619$	−18.5907	−	6.76644i	−0.747221	−	0.271966i	−0.687436	+	0.726245i	$0.741264\pi$
$620$		0			0
$621$	−8.34829	−	6.03331i	−0.335005	−	0.242108i
$622$		0			0
$623$	13.3026	+	4.84175i	0.532958	+	0.193981i
$624$		0			0
$625$	−20.2160	−	16.9633i	−0.808641	−	0.678530i
$626$		0			0
$627$	8.31915	+	41.3274i	0.332235	+	1.65046i
$628$		0			0
$629$	−8.58440	−	14.8686i	−0.342283	−	0.592851i
$630$		0			0
$631$	−8.91382	+	15.4392i	−0.354854	+	0.614624i	−0.987093	−	0.160149i	$-0.948803\pi$
$631$	−8.91382	+	15.4392i	−0.354854	+	0.614624i	0.632239	+	0.774773i	$0.282136\pi$
$632$		0			0
$633$	−7.85165	−	6.27205i	−0.312075	−	0.249292i
$634$		0			0
$635$	−0.0862738	+	0.0314011i	−0.00342367	+	0.00124611i
$636$		0			0
$637$	6.47097	+	36.6987i	0.256389	+	1.45406i
$638$		0			0
$639$	−27.7183	+	1.33766i	−1.09652	+	0.0529170i
$640$		0			0
$641$	2.60947	−	2.18961i	0.103068	−	0.0864842i	−0.589798	−	0.807551i	$-0.700792\pi$
$641$	2.60947	−	2.18961i	0.103068	−	0.0864842i	0.692865	+	0.721067i	$0.256348\pi$
$642$		0			0
$643$	2.77990	−	15.7656i	0.109629	−	0.621735i	−0.879641	−	0.475637i	$-0.842217\pi$
$643$	2.77990	−	15.7656i	0.109629	−	0.621735i	0.989270	−	0.146098i	$-0.0466714\pi$
$644$		0			0
$645$	14.4536	−	26.4894i	0.569111	−	1.04302i
$646$		0			0
$647$	−6.63857			−0.260989			−0.130495	−	0.991449i	$-0.541656\pi$
$647$	−6.63857			−0.260989			−0.130495	+	0.991449i	$0.541656\pi$
$648$		0			0
$649$	21.3555			0.838277
$650$		0			0
$651$	1.03174	−	1.89089i	0.0404372	−	0.0741099i
$652$		0			0
$653$	6.75420	−	38.3050i	0.264312	−	1.49899i	−0.506674	−	0.862138i	$-0.669125\pi$
$653$	6.75420	−	38.3050i	0.264312	−	1.49899i	0.770986	−	0.636852i	$-0.219764\pi$
$654$		0			0
$655$	−5.03625	+	4.22592i	−0.196783	+	0.165120i
$656$		0			0
$657$	0.608732	−	1.18258i	0.0237489	−	0.0461368i
$658$		0			0
$659$	−8.22075	−	46.6222i	−0.320235	−	1.81614i	−0.541237	−	0.840870i	$-0.682044\pi$
$659$	−8.22075	−	46.6222i	−0.320235	−	1.81614i	0.221002	−	0.975273i	$-0.429067\pi$
$660$		0			0
$661$	28.7979	−	10.4816i	1.12011	−	0.407686i	0.285417	−	0.958403i	$-0.407868\pi$
$661$	28.7979	−	10.4816i	1.12011	−	0.407686i	0.834692	+	0.550717i	$0.185646\pi$
$662$		0			0
$663$	23.5160	+	18.7850i	0.913285	+	0.729550i
$664$		0			0
$665$	−5.38504	+	9.32717i	−0.208823	+	0.361692i
$666$		0			0
$667$	−1.86311	−	3.22701i	−0.0721401	−	0.124950i
$668$		0			0
$669$	3.93628	+	19.5545i	0.152186	+	0.756019i
$670$		0			0
$671$	−41.1043	−	34.4906i	−1.58681	−	1.33149i
$672$		0			0
$673$	26.2071	+	9.53859i	1.01021	+	0.367686i	0.793513	−	0.608553i	$-0.208250\pi$
$673$	26.2071	+	9.53859i	1.01021	+	0.367686i	0.216696	+	0.976239i	$0.430472\pi$
$674$		0			0
$675$	−1.47700	−	0.419498i	−0.0568496	−	0.0161465i
$676$		0			0
$677$	−20.6944	−	7.53215i	−0.795351	−	0.289484i	−0.0877924	−	0.996139i	$-0.527981\pi$
$677$	−20.6944	−	7.53215i	−0.795351	−	0.289484i	−0.707559	+	0.706655i	$0.750203\pi$
$678$		0			0
$679$	4.98814	+	4.18555i	0.191427	+	0.160627i
$680$		0			0
$681$	21.8571	+	7.36359i	0.837565	+	0.282174i
$682$		0			0
$683$	4.40049	+	7.62187i	0.168380	+	0.291643i	0.937850	−	0.347040i	$-0.112813\pi$
$683$	4.40049	+	7.62187i	0.168380	+	0.291643i	−0.769470	+	0.638682i	$0.779480\pi$
$684$		0			0
$685$	10.4735	−	18.1406i	0.400170	−	0.693115i
$686$		0			0
$687$	5.05242	−	33.3345i	0.192762	−	1.27179i
$688$		0			0
$689$	14.8795	−	5.41571i	0.566866	−	0.206322i
$690$		0			0
$691$	−5.18070	−	29.3812i	−0.197083	−	1.11771i	−0.909421	−	0.415878i	$-0.863474\pi$
$691$	−5.18070	−	29.3812i	−0.197083	−	1.11771i	0.712337	−	0.701837i	$-0.247637\pi$
$692$		0			0
$693$	−1.71302	+	13.4897i	−0.0650723	+	0.512431i
$694$		0			0
$695$	3.81650	−	3.20243i	0.144768	−	0.121475i
$696$		0			0
$697$	−5.54977	+	31.4743i	−0.210212	+	1.19217i
$698$		0			0
$699$	3.11681	+	5.10987i	0.117888	+	0.193273i
$700$		0			0
$701$	12.5757			0.474978			0.237489	−	0.971390i	$-0.423676\pi$
$701$	12.5757			0.474978			0.237489	+	0.971390i	$0.423676\pi$
$702$		0			0
$703$	−30.1179			−1.13592
$704$		0			0
$705$	−43.5464	+	1.05015i	−1.64005	+	0.0395508i
$706$		0			0
$707$	−1.85689	+	10.5309i	−0.0698356	+	0.396057i
$708$		0			0
$709$	17.0741	−	14.3268i	0.641230	−	0.538056i	−0.263165	−	0.964751i	$-0.584767\pi$
$709$	17.0741	−	14.3268i	0.641230	−	0.538056i	0.904396	+	0.426695i	$0.140322\pi$
$710$		0			0
$711$	3.47258	+	15.3306i	0.130232	+	0.574941i
$712$		0			0
$713$	−0.458536	−	2.60049i	−0.0171723	−	0.0973889i
$714$		0			0
$715$	−63.8392	+	23.2356i	−2.38745	+	0.868961i
$716$		0			0
$717$	−18.5862	+	7.27690i	−0.694114	+	0.271761i
$718$		0			0
$719$	−2.65446	+	4.59766i	−0.0989947	+	0.171464i	−0.911269	−	0.411812i	$-0.864896\pi$
$719$	−2.65446	+	4.59766i	−0.0989947	+	0.171464i	0.812274	+	0.583276i	$0.198229\pi$
$720$		0			0
$721$	7.11713	+	12.3272i	0.265056	+	0.459090i
$722$		0			0
$723$	17.7758	−	15.6613i	0.661089	−	0.582448i
$724$		0			0
$725$	−0.425502	−	0.357039i	−0.0158028	−	0.0132601i
$726$		0			0
$727$	−38.0033	−	13.8321i	−1.40946	−	0.513003i	−0.478492	−	0.878092i	$-0.658816\pi$
$727$	−38.0033	−	13.8321i	−1.40946	−	0.513003i	−0.930973	+	0.365089i	$0.881039\pi$
$728$		0			0
$729$	26.7180	−	3.89235i	0.989554	−	0.144161i
$730$		0			0
$731$	20.3309	+	7.39985i	0.751966	+	0.273693i
$732$		0			0
$733$	−3.28038	−	2.75257i	−0.121164	−	0.101668i	0.580193	−	0.814479i	$-0.302977\pi$
$733$	−3.28038	−	2.75257i	−0.121164	−	0.101668i	−0.701356	+	0.712811i	$0.747422\pi$
$734$		0			0
$735$	18.3278	−	16.1476i	0.676031	−	0.595613i
$736$		0			0
$737$	1.87761	+	3.25212i	0.0691627	+	0.119793i
$738$		0			0
$739$	−11.8456	+	20.5172i	−0.435747	+	0.754736i	−0.997356	−	0.0726668i	$-0.976849\pi$
$739$	−11.8456	+	20.5172i	−0.435747	+	0.754736i	0.561609	+	0.827402i	$0.310182\pi$
$740$		0			0
$741$	49.1644	−	19.2490i	1.80610	−	0.707129i
$742$		0			0
$743$	−5.87858	+	2.13963i	−0.215664	+	0.0784953i	−0.447593	−	0.894237i	$-0.647719\pi$
$743$	−5.87858	+	2.13963i	−0.215664	+	0.0784953i	0.231929	+	0.972733i	$0.425496\pi$
$744$		0			0
$745$	1.38194	+	7.83735i	0.0506302	+	0.287138i
$746$		0			0
$747$	10.4939	+	46.3280i	0.383952	+	1.69505i
$748$		0			0
$749$	0.808704	−	0.678583i	0.0295494	−	0.0247949i
$750$		0			0
$751$	−4.77619	+	27.0871i	−0.174286	+	0.988423i	0.764680	+	0.644411i	$0.222897\pi$
$751$	−4.77619	+	27.0871i	−0.174286	+	0.988423i	−0.938965	+	0.344012i	$0.888214\pi$
$752$		0			0
$753$	−25.3612	+	0.611599i	−0.924214	+	0.0222879i
$754$		0			0
$755$	−11.2686			−0.410107
$756$		0			0
$757$	7.48533			0.272059			0.136029	−	0.990705i	$-0.456566\pi$
$757$	7.48533			0.272059			0.136029	+	0.990705i	$0.456566\pi$
$758$		0			0
$759$	8.68035	+	14.2310i	0.315077	+	0.516554i
$760$		0			0
$761$	4.78599	−	27.1427i	0.173492	−	0.983921i	−0.766378	−	0.642389i	$-0.777943\pi$
$761$	4.78599	−	27.1427i	0.173492	−	0.983921i	0.939870	−	0.341532i	$-0.110946\pi$
$762$		0			0
$763$	−8.19783	+	6.87880i	−0.296781	+	0.249029i
$764$		0			0
$765$	2.48532	−	19.5714i	0.0898571	−	0.707607i
$766$		0			0
$767$	−4.64447	−	26.3401i	−0.167702	−	0.951087i
$768$		0			0
$769$	−26.9685	+	9.81572i	−0.972508	+	0.353964i	−0.778923	−	0.627120i	$-0.784234\pi$
$769$	−26.9685	+	9.81572i	−0.972508	+	0.353964i	−0.193585	+	0.981084i	$0.562011\pi$
$770$		0			0
$771$	−2.77101	+	18.2824i	−0.0997956	+	0.658426i
$772$		0			0
$773$	−25.3371	+	43.8851i	−0.911311	+	1.57844i	−0.0990962	+	0.995078i	$0.531595\pi$
$773$	−25.3371	+	43.8851i	−0.911311	+	1.57844i	−0.812215	+	0.583359i	$0.801738\pi$
$774$		0			0
$775$	−0.196812	−	0.340888i	−0.00706969	−	0.0122451i
$776$		0			0
$777$	−9.20645	−	3.10163i	−0.330280	−	0.111270i
$778$		0			0
$779$	42.9481	+	36.0377i	1.53877	+	1.29119i
$780$		0			0
$781$	42.2019	+	15.3602i	1.51010	+	0.549633i
$782$		0			0
$783$	9.39594	+	2.66864i	0.335783	+	0.0953695i
$784$		0			0
$785$	−2.62204	−	0.954345i	−0.0935847	−	0.0340620i
$786$		0			0
$787$	−16.4304	−	13.7868i	−0.585682	−	0.491445i	0.301126	−	0.953584i	$-0.402638\pi$
$787$	−16.4304	−	13.7868i	−0.585682	−	0.491445i	−0.886807	+	0.462139i	$0.847082\pi$
$788$		0			0
$789$	−3.09162	−	15.3584i	−0.110065	−	0.546774i
$790$		0			0
$791$	−4.16947	−	7.22174i	−0.148249	−	0.256775i
$792$		0			0
$793$	−33.6016	+	58.1996i	−1.19323	+	2.06673i
$794$		0			0
$795$	−8.10949	−	6.47802i	−0.287614	−	0.229752i
$796$		0			0
$797$	33.1545	−	12.0672i	1.17439	−	0.427444i	0.320174	−	0.947359i	$-0.396259\pi$
$797$	33.1545	−	12.0672i	1.17439	−	0.427444i	0.854218	+	0.519915i	$0.174036\pi$
$798$		0			0
$799$	−5.42322	−	30.7566i	−0.191860	−	1.08809i
$800$		0			0
$801$	−20.8195	+	40.4458i	−0.735619	+	1.42908i
$802$		0			0
$803$	−1.64892	+	1.38361i	−0.0581890	+	0.0488264i
$804$		0			0
$805$	−0.739515	+	4.19400i	−0.0260645	+	0.147819i
$806$		0			0
$807$	−13.2446	+	24.2736i	−0.466233	+	0.854473i
$808$		0			0
$809$	−35.2973			−1.24099			−0.620493	−	0.784212i	$-0.713068\pi$
$809$	−35.2973			−1.24099			−0.620493	+	0.784212i	$0.713068\pi$
$810$		0			0
$811$	52.0319			1.82709			0.913544	−	0.406741i	$-0.133335\pi$
$811$	52.0319			1.82709			0.913544	+	0.406741i	$0.133335\pi$
$812$		0			0
$813$	10.5323	−	19.3027i	0.369383	−	0.676975i
$814$		0			0
$815$	−3.68102	+	20.8761i	−0.128941	+	0.731258i
$816$		0			0
$817$	29.0744	−	24.3963i	1.01718	−	0.853518i
$818$		0			0
$819$	17.0109	−	0.820931i	0.594409	−	0.0286857i
$820$		0			0
$821$	−1.07166	−	6.07770i	−0.0374013	−	0.212113i	0.960380	−	0.278695i	$-0.0899018\pi$
$821$	−1.07166	−	6.07770i	−0.0374013	−	0.212113i	−0.997781	+	0.0665818i	$0.978791\pi$
$822$		0			0
$823$	49.4317	−	17.9917i	1.72308	−	0.627150i	0.724981	−	0.688769i	$-0.241849\pi$
$823$	49.4317	−	17.9917i	1.72308	−	0.627150i	0.998100	+	0.0616193i	$0.0196265\pi$
$824$		0			0
$825$	1.94146	+	1.55088i	0.0675930	+	0.0539946i
$826$		0			0
$827$	8.02687	−	13.9029i	0.279121	−	0.483453i	−0.692045	−	0.721854i	$-0.743290\pi$
$827$	8.02687	−	13.9029i	0.279121	−	0.483453i	0.971167	+	0.238402i	$0.0766235\pi$
$828$		0			0
$829$	−4.85932	−	8.41658i	−0.168771	−	0.292320i	0.769217	−	0.638988i	$-0.220647\pi$
$829$	−4.85932	−	8.41658i	−0.168771	−	0.292320i	−0.937988	+	0.346668i	$0.887313\pi$
$830$		0			0
$831$	−9.28136	−	46.1074i	−0.321967	−	1.59945i
$832$		0			0
$833$	13.4160	+	11.2574i	0.464837	+	0.390044i
$834$		0			0
$835$	6.31712	+	2.29924i	0.218613	+	0.0795686i
$836$		0			0
$837$	5.61010	+	4.05442i	0.193913	+	0.140141i
$838$		0			0
$839$	3.50811	+	1.27685i	0.121114	+	0.0440817i	0.401866	−	0.915698i	$-0.368362\pi$
$839$	3.50811	+	1.27685i	0.121114	+	0.0440817i	−0.280752	+	0.959780i	$0.590584\pi$
$840$		0			0
$841$	−19.5084	−	16.3695i	−0.672705	−	0.564467i
$842$		0			0
$843$	13.6141	+	4.58657i	0.468896	+	0.157970i
$844$		0			0
$845$	27.5852	+	47.7790i	0.948960	+	1.64365i
$846$		0			0
$847$	5.86847	−	10.1645i	0.201643	−	0.349256i
$848$		0			0
$849$	−5.53405	+	36.5123i	−0.189928	+	1.25310i
$850$		0			0
$851$	−11.1910	+	4.07319i	−0.383623	+	0.139627i
$852$		0			0
$853$	1.25348	+	7.10882i	0.0429182	+	0.243401i	0.998718	−	0.0506165i	$-0.0161186\pi$
$853$	1.25348	+	7.10882i	0.0429182	+	0.243401i	−0.955800	+	0.294018i	$0.905008\pi$
$854$		0			0
$855$	−27.5531	−	20.9421i	−0.942296	−	0.716203i
$856$		0			0
$857$	−16.6370	+	13.9601i	−0.568309	+	0.476868i	−0.881084	−	0.472959i	$-0.843186\pi$
$857$	−16.6370	+	13.9601i	−0.568309	+	0.476868i	0.312775	+	0.949827i	$0.398741\pi$
$858$		0			0
$859$	−8.73108	+	49.5164i	−0.297901	+	1.68948i	0.357273	+	0.934000i	$0.383707\pi$
$859$	−8.73108	+	49.5164i	−0.297901	+	1.68948i	−0.655173	+	0.755479i	$0.727404\pi$
$860$		0			0
$861$	9.41710	+	15.4389i	0.320934	+	0.526157i
$862$		0			0
$863$	40.5856			1.38155			0.690776	−	0.723069i	$-0.257269\pi$
$863$	40.5856			1.38155			0.690776	+	0.723069i	$0.257269\pi$
$864$		0			0
$865$	−33.6385			−1.14374
$866$		0			0
$867$	−15.2954	+	0.368856i	−0.519458	+	0.0125270i
$868$		0			0
$869$	4.41742	−	25.0524i	0.149851	−	0.849845i
$870$		0			0
$871$	3.60285	−	3.02315i	0.122078	−	0.102435i
$872$		0			0
$873$	−15.3619	+	14.2068i	−0.519920	+	0.480826i
$874$		0			0
$875$	−1.75508	−	9.95354i	−0.0593325	−	0.336491i
$876$		0			0
$877$	−7.95738	+	2.89625i	−0.268701	+	0.0977993i	−0.472857	−	0.881139i	$-0.656777\pi$
$877$	−7.95738	+	2.89625i	−0.268701	+	0.0977993i	0.204156	+	0.978938i	$0.434555\pi$
$878$		0			0
$879$	28.3233	−	11.0892i	0.955321	−	0.374030i
$880$		0			0
$881$	−21.5635	+	37.3491i	−0.726493	+	1.25832i	0.231863	+	0.972748i	$0.425518\pi$
$881$	−21.5635	+	37.3491i	−0.726493	+	1.25832i	−0.958356	+	0.285575i	$0.907815\pi$
$882$		0			0
$883$	12.9872	+	22.4945i	0.437054	+	0.757000i	0.997461	−	0.0712176i	$-0.0226885\pi$
$883$	12.9872	+	22.4945i	0.437054	+	0.757000i	−0.560407	+	0.828218i	$0.689355\pi$
$884$		0			0
$885$	−13.1546	+	11.5898i	−0.442187	+	0.389586i
$886$		0			0
$887$	−8.00642	−	6.71819i	−0.268829	−	0.225575i	0.498400	−	0.866947i	$-0.333921\pi$
$887$	−8.00642	−	6.71819i	−0.268829	−	0.225575i	−0.767230	+	0.641372i	$0.778365\pi$
$888$		0			0
$889$	−0.0350013	−	0.0127394i	−0.00117391	−	0.000427267i
$890$		0			0
$891$	−42.3088	−	10.9215i	−1.41740	−	0.365883i
$892$		0			0
$893$	−51.4823	−	18.7380i	−1.72279	−	0.627045i
$894$		0			0
$895$	−35.9364	−	30.1542i	−1.20122	−	1.00794i
$896$		0			0
$897$	15.6649	−	13.8015i	0.523036	−	0.460817i
$898$		0			0
$899$	1.25202	+	2.16857i	0.0417573	+	0.0723258i
$900$		0			0
$901$	3.72086	−	6.44472i	0.123960	−	0.214705i
$902$		0			0
$903$	11.3999	−	4.46330i	0.379363	−	0.148529i
$904$		0			0
$905$	−8.46785	+	3.08204i	−0.281481	+	0.102451i
$906$		0			0
$907$	−2.72906	−	15.4772i	−0.0906168	−	0.513914i	−0.996003	−	0.0893238i	$-0.971529\pi$
$907$	−2.72906	−	15.4772i	−0.0906168	−	0.513914i	0.905386	−	0.424590i	$-0.139582\pi$
$908$		0			0
$909$	−32.8187	−	10.1824i	−1.08853	−	0.337728i
$910$		0			0
$911$	−31.8864	+	26.7558i	−1.05644	+	0.886460i	−0.993756	−	0.111573i	$-0.964411\pi$
$911$	−31.8864	+	26.7558i	−1.05644	+	0.886460i	−0.0626861	+	0.998033i	$0.519967\pi$
$912$		0			0
$913$	13.3491	−	75.7068i	0.441792	−	2.50553i
$914$		0			0
$915$	44.0377	−	1.06199i	1.45584	−	0.0351084i
$916$		0			0
$917$	−2.66722			−0.0880794
$918$		0			0
$919$	59.0705			1.94856			0.974278	−	0.225348i	$-0.0723520\pi$
$919$	59.0705			1.94856			0.974278	+	0.225348i	$0.0723520\pi$
$920$		0			0
$921$	−27.1052	−	44.4379i	−0.893148	−	1.46428i
$922$		0			0
$923$	9.76727	−	55.3929i	0.321493	−	1.82328i
$924$		0			0
$925$	−1.35993	+	1.14111i	−0.0447141	+	0.0375196i
$926$		0			0
$927$	−42.1776	+	17.6977i	−1.38529	+	0.581269i
$928$		0			0
$929$	−4.03698	−	22.8948i	−0.132449	−	0.751155i	−0.976602	−	0.215053i	$-0.931007\pi$
$929$	−4.03698	−	22.8948i	−0.132449	−	0.751155i	0.844153	−	0.536102i	$-0.180104\pi$
$930$		0			0
$931$	28.8696	−	10.5077i	0.946162	−	0.344375i
$932$		0			0
$933$	−5.33537	+	35.2014i	−0.174672	+	1.15244i
$934$		0			0
$935$	−15.9640	+	27.6504i	−0.522078	+	0.904266i
$936$		0			0
$937$	16.3639	+	28.3431i	0.534586	+	0.925930i	0.999183	+	0.0404081i	$0.0128658\pi$
$937$	16.3639	+	28.3431i	0.534586	+	0.925930i	−0.464597	+	0.885522i	$0.653801\pi$
$938$		0			0
$939$	−22.4426	−	7.56087i	−0.732388	−	0.246740i
$940$		0			0
$941$	40.4606	+	33.9505i	1.31898	+	1.10675i	0.986521	+	0.163636i	$0.0523222\pi$
$941$	40.4606	+	33.9505i	1.31898	+	1.10675i	0.332457	+	0.943118i	$0.392122\pi$
$942$		0			0
$943$	20.8321	+	7.58227i	0.678387	+	0.246913i
$944$		0			0
$945$	−6.26575	−	9.23906i	−0.203825	−	0.300547i
$946$		0			0
$947$	30.8614	+	11.2326i	1.00286	+	0.365012i	0.790687	−	0.612220i	$-0.209723\pi$
$947$	30.8614	+	11.2326i	1.00286	+	0.365012i	0.212174	+	0.977232i	$0.431946\pi$
$948$		0			0
$949$	2.06517	+	1.73288i	0.0670381	+	0.0562517i
$950$		0			0
$951$	−3.93913	−	19.5686i	−0.127735	−	0.634555i
$952$		0			0
$953$	−1.92754	−	3.33860i	−0.0624391	−	0.108148i	0.833116	−	0.553098i	$-0.186555\pi$
$953$	−1.92754	−	3.33860i	−0.0624391	−	0.108148i	−0.895555	+	0.444951i	$0.853221\pi$
$954$		0			0
$955$	19.1980	−	33.2519i	0.621233	−	1.07601i
$956$		0			0
$957$	−12.3506	−	9.86593i	−0.399239	−	0.318920i
$958$		0			0
$959$	7.98567	−	2.90655i	0.257871	−	0.0938573i
$960$		0			0
$961$	−5.07496	−	28.7815i	−0.163708	−	0.928435i
$962$		0			0
$963$	1.83581	+	2.85267i	0.0591580	+	0.0919260i
$964$		0			0
$965$	0.326751	−	0.274177i	0.0105185	−	0.00882607i
$966$		0			0
$967$	−0.438417	+	2.48638i	−0.0140985	+	0.0799567i	−0.991045	−	0.133527i	$-0.957370\pi$
$967$	−0.438417	+	2.48638i	−0.0140985	+	0.0799567i	0.976947	+	0.213483i	$0.0684809\pi$
$968$		0			0
$969$	11.8851	−	21.7821i	0.381805	−	0.699741i
$970$		0			0
$971$	8.91263			0.286020			0.143010	−	0.989721i	$-0.454322\pi$
$971$	8.91263			0.286020			0.143010	+	0.989721i	$0.454322\pi$
$972$		0			0
$973$	2.02124			0.0647979
$974$		0			0
$975$	1.49063	−	2.73191i	0.0477384	−	0.0874911i
$976$		0			0
$977$	−8.20448	+	46.5299i	−0.262485	+	1.48862i	0.513619	+	0.858018i	$0.328304\pi$
$977$	−8.20448	+	46.5299i	−0.262485	+	1.48862i	−0.776104	+	0.630605i	$0.782807\pi$
$978$		0			0
$979$	56.3952	−	47.3212i	1.80240	−	1.51239i
$980$		0			0
$981$	−18.6096	−	28.9175i	−0.594158	−	0.923265i
$982$		0			0
$983$	−0.324382	−	1.83966i	−0.0103462	−	0.0586761i	0.979198	−	0.202909i	$-0.0650396\pi$
$983$	−0.324382	−	1.83966i	−0.0103462	−	0.0586761i	−0.989544	+	0.144233i	$0.953929\pi$
$984$		0			0
$985$	4.20091	−	1.52900i	0.133852	−	0.0487181i
$986$		0			0
$987$	−13.8074	−	11.0296i	−0.439495	−	0.351077i
$988$		0			0
$989$	7.50385	−	12.9970i	0.238609	−	0.413282i
$990$		0			0
$991$	8.11469	+	14.0551i	0.257772	+	0.446473i	0.965645	−	0.259866i	$-0.0836785\pi$
$991$	8.11469	+	14.0551i	0.257772	+	0.446473i	−0.707873	+	0.706340i	$0.750345\pi$
$992$		0			0
$993$	0.654658	+	3.25218i	0.0207749	+	0.103205i
$994$		0			0
$995$	2.12135	+	1.78002i	0.0672513	+	0.0564305i
$996$		0			0
$997$	−12.6043	−	4.58759i	−0.399182	−	0.145290i	0.134625	−	0.990897i	$-0.457017\pi$
$997$	−12.6043	−	4.58759i	−0.399182	−	0.145290i	−0.533807	+	0.845606i	$0.679239\pi$
$998$		0			0
$999$	13.6142	−	28.0926i	0.430733	−	0.888811i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.i.a.85.1	yes	18
3.2	odd	2		324.2.i.a.145.3		18
4.3	odd	2		432.2.u.d.193.3		18
9.2	odd	6		972.2.i.d.757.3		18
9.4	even	3		972.2.i.c.109.3		18
9.5	odd	6		972.2.i.b.109.1		18
9.7	even	3		972.2.i.a.757.1		18
27.2	odd	18		972.2.i.b.865.1		18
27.4	even	9		2916.2.e.c.973.8		18
27.5	odd	18		2916.2.e.d.1945.2		18
27.7	even	9	inner	108.2.i.a.61.1	✓	18
27.11	odd	18		972.2.i.d.217.3		18
27.13	even	9		2916.2.a.d.1.2		9
27.14	odd	18		2916.2.a.c.1.8		9
27.16	even	9		972.2.i.a.217.1		18
27.20	odd	18		324.2.i.a.181.3		18
27.22	even	9		2916.2.e.c.1945.8		18
27.23	odd	18		2916.2.e.d.973.2		18
27.25	even	9		972.2.i.c.865.3		18
108.7	odd	18		432.2.u.d.385.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.61.1	✓	18	27.7	even	9	inner
108.2.i.a.85.1	yes	18	1.1	even	1	trivial
324.2.i.a.145.3		18	3.2	odd	2
324.2.i.a.181.3		18	27.20	odd	18
432.2.u.d.193.3		18	4.3	odd	2
432.2.u.d.385.3		18	108.7	odd	18
972.2.i.a.217.1		18	27.16	even	9
972.2.i.a.757.1		18	9.7	even	3
972.2.i.b.109.1		18	9.5	odd	6
972.2.i.b.865.1		18	27.2	odd	18
972.2.i.c.109.3		18	9.4	even	3
972.2.i.c.865.3		18	27.25	even	9
972.2.i.d.217.3		18	27.11	odd	18
972.2.i.d.757.3		18	9.2	odd	6
2916.2.a.c.1.8		9	27.14	odd	18
2916.2.a.d.1.2		9	27.13	even	9
2916.2.e.c.973.8		18	27.4	even	9
2916.2.e.c.1945.8		18	27.22	even	9
2916.2.e.d.973.2		18	27.23	odd	18
2916.2.e.d.1945.2		18	27.5	odd	18

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.829611 + 1.52044i) q^{3} +(-0.399598 + 2.26623i) q^{5} +(-0.715176 + 0.600104i) q^{7} +(-1.62349 - 2.52275i) q^{9} +O(q^{10})\)	\(q+(-0.829611 + 1.52044i) q^{3} +(-0.399598 + 2.26623i) q^{5} +(-0.715176 + 0.600104i) q^{7} +(-1.62349 - 2.52275i) q^{9} +(0.843075 + 4.78132i) q^{11} +(5.71397 - 2.07972i) q^{13} +(-3.11417 - 2.48766i) q^{15} +(1.42887 - 2.47487i) q^{17} +(-2.50656 - 4.34148i) q^{19} +(-0.319106 - 1.58524i) q^{21} +(-1.51851 - 1.27419i) q^{23} +(-0.277670 - 0.101064i) q^{25} +(5.18257 - 0.375523i) q^{27} +(1.76640 + 0.642919i) q^{29} +(1.02045 + 0.856259i) q^{31} +(-7.96914 - 2.68479i) q^{33} +(-1.07419 - 1.86056i) q^{35} +(3.00392 - 5.20294i) q^{37} +(-1.57829 + 10.4131i) q^{39} +(-10.5092 + 3.82502i) q^{41} +(1.31468 + 7.45591i) q^{43} +(6.36589 - 2.67112i) q^{45} +(8.37180 - 7.02478i) q^{47} +(-1.06419 + 6.03530i) q^{49} +(2.57750 + 4.22569i) q^{51} +2.60406 q^{53} -11.1725 q^{55} +(8.68044 - 0.209333i) q^{57} +(0.763808 - 4.33177i) q^{59} +(-8.46625 + 7.10403i) q^{61} +(2.67499 + 0.829947i) q^{63} +(2.42983 + 13.7802i) q^{65} +(0.726818 - 0.264540i) q^{67} +(3.19710 - 1.25174i) q^{69} +(4.62509 - 8.01090i) q^{71} +(0.221676 + 0.383954i) q^{73} +(0.384020 - 0.338338i) q^{75} +(-3.47223 - 2.91355i) q^{77} +(-4.92366 - 1.79207i) q^{79} +(-3.72855 + 8.19133i) q^{81} +(-14.8790 - 5.41550i) q^{83} +(5.03766 + 4.22710i) q^{85} +(-2.44295 + 2.15234i) q^{87} +(-7.58162 - 13.1318i) q^{89} +(-2.83845 + 4.91634i) q^{91} +(-2.14847 + 0.841174i) q^{93} +(10.8404 - 3.94559i) q^{95} +(-1.21115 - 6.86875i) q^{97} +(10.6933 - 9.88930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 18 * q + 3 * q^5 + 6 * q^9	\( 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

Introduction

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