LMFDB - Embedded newform 912.2.bn.o.65.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not 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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 6 x^{14} + 5 x^{13} + 21 x^{12} - 4 x^{11} - 94 x^{10} - 6 x^{9} + 364 x^{8} + \cdots + 6561 $ x^16 - x^15 - 6x^14 + 5x^13 + 21x^12 - 4x^11 - 94x^10 - 6x^9 + 364x^8 - 18x^7 - 846x^6 - 108x^5 + 1701x^4 + 1215x^3 - 4374x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.3
Root			$-0.909329 - 1.47415i$ of defining polynomial
Character	$\chi$	$=$	912.65
Dual form			912.2.bn.o.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909329 + 1.47415i) q^{3} +(2.16072 + 1.24749i) q^{5} -3.30744 q^{7} +(-1.34624 - 2.68098i) q^{9} +O(q^{10})$	\(q+(-0.909329 + 1.47415i) q^{3} +(2.16072 + 1.24749i) q^{5} -3.30744 q^{7} +(-1.34624 - 2.68098i) q^{9} -5.60987i q^{11} +(0.0750107 - 0.0433075i) q^{13} +(-3.80379 + 2.05084i) q^{15} +(-4.69685 - 2.71173i) q^{17} +(-2.61886 - 3.48448i) q^{19} +(3.00755 - 4.87567i) q^{21} +(2.94589 - 1.70081i) q^{23} +(0.612461 + 1.06081i) q^{25} +(5.17634 + 0.453323i) q^{27} +(-1.78928 - 3.09912i) q^{29} +6.88762i q^{31} +(8.26979 + 5.10121i) q^{33} +(-7.14644 - 4.12600i) q^{35} -1.83290i q^{37} +(-0.00436766 + 0.149958i) q^{39} +(1.35094 - 2.33989i) q^{41} +(-4.02978 + 6.97978i) q^{43} +(0.435642 - 7.47225i) q^{45} +(8.16041 - 4.71141i) q^{47} +3.93918 q^{49} +(8.26848 - 4.45802i) q^{51} +(0.741927 + 1.28506i) q^{53} +(6.99825 - 12.1213i) q^{55} +(7.51805 - 0.692053i) q^{57} +(-6.91116 + 11.9705i) q^{59} +(-6.28510 - 10.8861i) q^{61} +(4.45262 + 8.86717i) q^{63} +0.216102 q^{65} +(7.13011 - 4.11657i) q^{67} +(-0.171531 + 5.88929i) q^{69} +(5.20807 - 9.02064i) q^{71} +(-4.19249 + 7.26160i) q^{73} +(-2.12073 - 0.0617681i) q^{75} +18.5543i q^{77} +(-11.1253 - 6.42318i) q^{79} +(-5.37526 + 7.21849i) q^{81} -11.1247i q^{83} +(-6.76571 - 11.7186i) q^{85} +(6.19562 + 0.180453i) q^{87} +(0.0767300 + 0.132900i) q^{89} +(-0.248094 + 0.143237i) q^{91} +(-10.1534 - 6.26311i) q^{93} +(-1.31175 - 10.7960i) q^{95} +(2.41045 + 1.39167i) q^{97} +(-15.0399 + 7.55224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9	$ 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) $ 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.909329	+	1.47415i	−0.525001	+	0.851102i
$3$	−0.909329	+	1.47415i	−0.525001	+	0.851102i
$4$		0			0
$5$	2.16072	+	1.24749i	0.966301	+	0.557894i	0.898107	−	0.439778i	$-0.144943\pi$
$5$	2.16072	+	1.24749i	0.966301	+	0.557894i	0.0681946	+	0.997672i	$0.478276\pi$
$6$		0			0
$7$	−3.30744			−1.25010			−0.625048	−	0.780586i	$-0.714921\pi$
$7$	−3.30744			−1.25010			−0.625048	+	0.780586i	$0.714921\pi$
$8$		0			0
$9$	−1.34624	−	2.68098i	−0.448748	−	0.893659i
$10$		0			0
$11$		−	5.60987i		−	1.69144i	−0.533628	−	0.845719i	$-0.679172\pi$
$11$		−	5.60987i		−	1.69144i	0.533628	−	0.845719i	$-0.320828\pi$
$12$		0			0
$13$	0.0750107	−	0.0433075i	0.0208042	−	0.0120113i	−0.489562	−	0.871969i	$-0.662843\pi$
$13$	0.0750107	−	0.0433075i	0.0208042	−	0.0120113i	0.510366	+	0.859957i	$0.329510\pi$
$14$		0			0
$15$	−3.80379	+	2.05084i	−0.982134	+	0.529525i
$16$		0			0
$17$	−4.69685	−	2.71173i	−1.13915	−	0.657691i	−0.192933	−	0.981212i	$-0.561800\pi$
$17$	−4.69685	−	2.71173i	−1.13915	−	0.657691i	−0.946221	+	0.323521i	$0.895133\pi$
$18$		0			0
$19$	−2.61886	−	3.48448i	−0.600807	−	0.799394i
$19$	−2.61886	−	3.48448i	−0.600807	−	0.799394i
$20$		0			0
$21$	3.00755	−	4.87567i	0.656302	−	1.06396i
$22$		0			0
$23$	2.94589	−	1.70081i	0.614261	−	0.354644i	−0.160370	−	0.987057i	$-0.551269\pi$
$23$	2.94589	−	1.70081i	0.614261	−	0.354644i	0.774631	+	0.632413i	$0.217935\pi$
$24$		0			0
$25$	0.612461	+	1.06081i	0.122492	+	0.212163i
$26$		0			0
$27$	5.17634	+	0.453323i	0.996187	+	0.0872420i
$28$		0			0
$29$	−1.78928	−	3.09912i	−0.332261	−	0.575493i	0.650694	−	0.759340i	$-0.274478\pi$
$29$	−1.78928	−	3.09912i	−0.332261	−	0.575493i	−0.982955	+	0.183847i	$0.941145\pi$
$30$		0			0
$31$			6.88762i			1.23705i	0.785764	+	0.618527i	$0.212270\pi$
$31$			6.88762i			1.23705i	−0.785764	+	0.618527i	$0.787730\pi$
$32$		0			0
$33$	8.26979	+	5.10121i	1.43959	+	0.888007i
$34$		0			0
$35$	−7.14644	−	4.12600i	−1.20797	−	0.697421i
$36$		0			0
$37$		−	1.83290i		−	0.301327i	−0.988585	−	0.150664i	$-0.951859\pi$
$37$		−	1.83290i		−	0.301327i	0.988585	−	0.150664i	$-0.0481411\pi$
$38$		0			0
$39$	−0.00436766	+	0.149958i	−0.000699385	+	0.0240125i
$40$		0			0
$41$	1.35094	−	2.33989i	0.210981	−	0.365430i	−0.741041	−	0.671460i	$-0.765667\pi$
$41$	1.35094	−	2.33989i	0.210981	−	0.365430i	0.952022	+	0.306030i	$0.0990008\pi$
$42$		0			0
$43$	−4.02978	+	6.97978i	−0.614536	+	1.06441i	0.375930	+	0.926648i	$0.377323\pi$
$43$	−4.02978	+	6.97978i	−0.614536	+	1.06441i	−0.990466	+	0.137759i	$0.956010\pi$
$44$		0			0
$45$	0.435642	−	7.47225i	0.0649417	−	1.11390i
$46$		0			0
$47$	8.16041	−	4.71141i	1.19032	−	0.687230i	0.231939	−	0.972730i	$-0.425493\pi$
$47$	8.16041	−	4.71141i	1.19032	−	0.687230i	0.958379	+	0.285500i	$0.0921596\pi$
$48$		0			0
$49$	3.93918			0.562740
$50$		0			0
$51$	8.26848	−	4.45802i	1.15782	−	0.624247i
$52$		0			0
$53$	0.741927	+	1.28506i	0.101912	+	0.176516i	0.912472	−	0.409139i	$-0.134171\pi$
$53$	0.741927	+	1.28506i	0.101912	+	0.176516i	−0.810561	+	0.585655i	$0.800837\pi$
$54$		0			0
$55$	6.99825	−	12.1213i	0.943644	−	1.63444i
$56$		0			0
$57$	7.51805	−	0.692053i	0.995790	−	0.0916646i
$58$		0			0
$59$	−6.91116	+	11.9705i	−0.899757	+	1.55842i	−0.0719523	+	0.997408i	$0.522923\pi$
$59$	−6.91116	+	11.9705i	−0.899757	+	1.55842i	−0.827805	+	0.561017i	$0.810410\pi$
$60$		0			0
$61$	−6.28510	−	10.8861i	−0.804724	−	1.39382i	−0.916477	−	0.400087i	$-0.868980\pi$
$61$	−6.28510	−	10.8861i	−0.804724	−	1.39382i	0.111753	−	0.993736i	$-0.464353\pi$
$62$		0			0
$63$	4.45262	+	8.86717i	0.560978	+	1.11716i
$64$		0			0
$65$	0.216102			0.0268042
$66$		0			0
$67$	7.13011	−	4.11657i	0.871082	−	0.502919i	0.00337429	−	0.999994i	$-0.498926\pi$
$67$	7.13011	−	4.11657i	0.871082	−	0.502919i	0.867708	+	0.497075i	$0.165593\pi$
$68$		0			0
$69$	−0.171531	+	5.88929i	−0.0206499	+	0.708987i
$70$		0			0
$71$	5.20807	−	9.02064i	0.618084	−	1.07055i	−0.371751	−	0.928332i	$-0.621243\pi$
$71$	5.20807	−	9.02064i	0.618084	−	1.07055i	0.989835	−	0.142220i	$-0.0454241\pi$
$72$		0			0
$73$	−4.19249	+	7.26160i	−0.490693	+	0.849906i	−0.999943	−	0.0107133i	$-0.996590\pi$
$73$	−4.19249	+	7.26160i	−0.490693	+	0.849906i	0.509249	+	0.860619i	$0.329923\pi$
$74$		0			0
$75$	−2.12073	−	0.0617681i	−0.244880	−	0.00713237i
$76$		0			0
$77$			18.5543i			2.11446i
$78$		0			0
$79$	−11.1253	−	6.42318i	−1.25169	−	0.722664i	−0.280245	−	0.959928i	$-0.590416\pi$
$79$	−11.1253	−	6.42318i	−1.25169	−	0.722664i	−0.971445	+	0.237265i	$0.923749\pi$
$80$		0			0
$81$	−5.37526	+	7.21849i	−0.597251	+	0.802054i
$82$		0			0
$83$		−	11.1247i		−	1.22109i	−0.791981	−	0.610546i	$-0.790950\pi$
$83$		−	11.1247i		−	1.22109i	0.791981	−	0.610546i	$-0.209050\pi$
$84$		0			0
$85$	−6.76571	−	11.7186i	−0.733844	−	1.27106i
$86$		0			0
$87$	6.19562	+	0.180453i	0.664240	+	0.0193466i
$88$		0			0
$89$	0.0767300	+	0.132900i	0.00813336	+	0.0140874i	0.870063	−	0.492940i	$-0.164078\pi$
$89$	0.0767300	+	0.132900i	0.00813336	+	0.0140874i	−0.861930	+	0.507027i	$0.830744\pi$
$90$		0			0
$91$	−0.248094	+	0.143237i	−0.0260073	+	0.0150153i
$92$		0			0
$93$	−10.1534	−	6.26311i	−1.05286	−	0.649455i
$94$		0			0
$95$	−1.31175	−	10.7960i	−0.134583	−	1.10764i
$96$		0			0
$97$	2.41045	+	1.39167i	0.244744	+	0.141303i	0.617355	−	0.786684i	$-0.288204\pi$
$97$	2.41045	+	1.39167i	0.244744	+	0.141303i	−0.372611	+	0.927988i	$0.621537\pi$
$98$		0			0
$99$	−15.0399	+	7.55224i	−1.51157	+	0.759029i
$100$		0			0
$101$	−0.974207	+	0.562459i	−0.0969372	+	0.0559667i	−0.547685	−	0.836685i	$-0.684491\pi$
$101$	−0.974207	+	0.562459i	−0.0969372	+	0.0559667i	0.450748	+	0.892651i	$0.351157\pi$
$102$		0			0
$103$		−	7.08537i		−	0.698142i	−0.937096	−	0.349071i	$-0.886497\pi$
$103$		−	7.08537i		−	0.698142i	0.937096	−	0.349071i	$-0.113503\pi$
$104$		0			0
$105$	12.5808	−	6.78305i	1.22776	−	0.661957i
$106$		0			0
$107$	−2.38288			−0.230362			−0.115181	−	0.993345i	$-0.536745\pi$
$107$	−2.38288			−0.230362			−0.115181	+	0.993345i	$0.536745\pi$
$108$		0			0
$109$	−10.4441	−	6.02988i	−1.00036	−	0.577558i	−0.0920053	−	0.995759i	$-0.529328\pi$
$109$	−10.4441	−	6.02988i	−1.00036	−	0.577558i	−0.908355	+	0.418200i	$0.862661\pi$
$110$		0			0
$111$	2.70198	+	1.66671i	0.256460	+	0.158197i
$112$		0			0
$113$	9.47368			0.891209			0.445605	−	0.895230i	$-0.352989\pi$
$113$	9.47368			0.891209			0.445605	+	0.895230i	$0.352989\pi$
$114$		0			0
$115$	8.48698			0.791415
$116$		0			0
$117$	−0.217089	−	0.142800i	−0.0200699	−	0.0132018i
$118$		0			0
$119$	15.5346	+	8.96889i	1.42405	+	0.822177i
$120$		0			0
$121$	−20.4706			−1.86096
$122$		0			0
$123$	2.22091	+	4.11922i	0.200253	+	0.371418i
$124$		0			0
$125$		−	9.41874i		−	0.842438i
$126$		0			0
$127$	3.48538	−	2.01228i	0.309277	−	0.178561i	−0.337326	−	0.941388i	$-0.609522\pi$
$127$	3.48538	−	2.01228i	0.309277	−	0.178561i	0.646603	+	0.762827i	$0.276189\pi$
$128$		0			0
$129$	−6.62486	−	12.2874i	−0.583286	−	1.08185i
$130$		0			0
$131$	8.42029	+	4.86146i	0.735684	+	0.424748i	0.820498	−	0.571649i	$-0.193696\pi$
$131$	8.42029	+	4.86146i	0.735684	+	0.424748i	−0.0848138	+	0.996397i	$0.527030\pi$
$132$		0			0
$133$	8.66172	+	11.5247i	0.751066	+	0.999320i
$134$		0			0
$135$	10.6191	+	7.43693i	0.913945	+	0.640069i
$136$		0			0
$137$	4.27556	−	2.46849i	0.365286	−	0.210898i	−0.306111	−	0.951996i	$-0.599028\pi$
$137$	4.27556	−	2.46849i	0.365286	−	0.210898i	0.671397	+	0.741098i	$0.265695\pi$
$138$		0			0
$139$	−2.90848	−	5.03764i	−0.246694	−	0.427287i	0.715912	−	0.698190i	$-0.246011\pi$
$139$	−2.90848	−	5.03764i	−0.246694	−	0.427287i	−0.962607	+	0.270903i	$0.912678\pi$
$140$		0			0
$141$	−0.475157	+	16.3139i	−0.0400155	+	1.37388i
$142$		0			0
$143$	−0.242949	−	0.420800i	−0.0203164	−	0.0351891i
$144$		0			0
$145$		−	8.92843i		−	0.741466i
$146$		0			0
$147$	−3.58201	+	5.80695i	−0.295439	+	0.478949i
$148$		0			0
$149$	1.84517	+	1.06531i	0.151162	+	0.0872734i	0.573673	−	0.819084i	$-0.305518\pi$
$149$	1.84517	+	1.06531i	0.151162	+	0.0872734i	−0.422511	+	0.906358i	$0.638851\pi$
$150$		0			0
$151$			2.68931i			0.218853i	0.993995	+	0.109427i	$0.0349015\pi$
$151$			2.68931i			0.218853i	−0.993995	+	0.109427i	$0.965099\pi$
$152$		0			0
$153$	−0.946976	+	16.2428i	−0.0765585	+	1.31315i
$154$		0			0
$155$	−8.59224	+	14.8822i	−0.690145	+	1.19537i
$156$		0			0
$157$	−10.8793	+	18.8435i	−0.868264	+	1.50388i	−0.00449555	+	0.999990i	$0.501431\pi$
$157$	−10.8793	+	18.8435i	−0.868264	+	1.50388i	−0.863769	+	0.503888i	$0.831902\pi$
$158$		0			0
$159$	−2.56902	−	0.0748252i	−0.203737	−	0.00593402i
$160$		0			0
$161$	−9.74338	+	5.62534i	−0.767886	+	0.443339i
$162$		0			0
$163$	−20.7695			−1.62679			−0.813397	−	0.581709i	$-0.802384\pi$
$163$	−20.7695			−1.62679			−0.813397	+	0.581709i	$0.802384\pi$
$164$		0			0
$165$	11.5050	+	21.3387i	0.895659	+	1.66122i
$166$		0			0
$167$	7.07768	+	12.2589i	0.547687	+	0.948622i	0.998432	+	0.0559696i	$0.0178250\pi$
$167$	7.07768	+	12.2589i	0.547687	+	0.948622i	−0.450745	+	0.892653i	$0.648842\pi$
$168$		0			0
$169$	−6.49625	+	11.2518i	−0.499711	+	0.865526i
$170$		0			0
$171$	−5.81619	+	11.7120i	−0.444775	+	0.895642i
$172$		0			0
$173$	−5.06757	+	8.77729i	−0.385280	+	0.667325i	−0.991808	−	0.127737i	$-0.959229\pi$
$173$	−5.06757	+	8.77729i	−0.385280	+	0.667325i	0.606528	+	0.795062i	$0.292562\pi$
$174$		0			0
$175$	−2.02568	−	3.50858i	−0.153127	−	0.265224i
$176$		0			0
$177$	−11.3618	−	21.0732i	−0.854004	−	1.58396i
$178$		0			0
$179$	−21.1785			−1.58295			−0.791477	−	0.611199i	$-0.790688\pi$
$179$	−21.1785			−1.58295			−0.791477	+	0.611199i	$0.790688\pi$
$180$		0			0
$181$	21.4440	−	12.3807i	1.59392	−	0.920248i	0.601291	−	0.799030i	$-0.294653\pi$
$181$	21.4440	−	12.3807i	1.59392	−	0.920248i	0.992626	−	0.121218i	$-0.0386800\pi$
$182$		0			0
$183$	21.7630	+	0.633867i	1.60877	+	0.0468568i
$184$		0			0
$185$	2.28653	−	3.96038i	0.168109	−	0.291173i
$186$		0			0
$187$	−15.2124	+	26.3487i	−1.11244	+	1.92681i
$188$		0			0
$189$	−17.1205	−	1.49934i	−1.24533	−	0.109061i
$190$		0			0
$191$			1.89234i			0.136925i	0.997654	+	0.0684623i	$0.0218093\pi$
$191$			1.89234i			0.136925i	−0.997654	+	0.0684623i	$0.978191\pi$
$192$		0			0
$193$	11.2727	+	6.50832i	0.811430	+	0.468479i	0.847452	−	0.530872i	$-0.178135\pi$
$193$	11.2727	+	6.50832i	0.811430	+	0.468479i	−0.0360221	+	0.999351i	$0.511469\pi$
$194$		0			0
$195$	−0.196508	+	0.318568i	−0.0140722	+	0.0228131i
$196$		0			0
$197$		−	4.29228i		−	0.305812i	−0.988241	−	0.152906i	$-0.951137\pi$
$197$		−	4.29228i		−	0.305812i	0.988241	−	0.152906i	$-0.0488632\pi$
$198$		0			0
$199$	−5.02978	−	8.71183i	−0.356552	−	0.617566i	0.630831	−	0.775921i	$-0.282714\pi$
$199$	−5.02978	−	8.71183i	−0.356552	−	0.617566i	−0.987382	+	0.158355i	$0.949381\pi$
$200$		0			0
$201$	−0.415166	+	14.2542i	−0.0292836	+	1.00541i
$202$		0			0
$203$	5.91794	+	10.2502i	0.415358	+	0.719421i
$204$		0			0
$205$	5.83799	−	3.37056i	0.407743	−	0.235410i
$206$		0			0
$207$	−8.52572	−	5.60816i	−0.592579	−	0.389794i
$208$		0			0
$209$	−19.5475	+	14.6914i	−1.35213	+	1.01623i
$210$		0			0
$211$	−16.4810	−	9.51528i	−1.13460	−	0.655059i	−0.189509	−	0.981879i	$-0.560690\pi$
$211$	−16.4810	−	9.51528i	−1.13460	−	0.655059i	−0.945087	+	0.326820i	$0.894023\pi$
$212$		0			0
$213$	8.56194	+	15.8802i	0.586654	+	1.08809i
$214$		0			0
$215$	−17.4144	+	10.0542i	−1.18765	+	0.685692i
$216$		0			0
$217$		−	22.7804i		−	1.54644i
$218$		0			0
$219$	−6.89234	−	12.7835i	−0.465742	−	0.863831i
$220$		0			0
$221$	−0.469752			−0.0315990
$222$		0			0
$223$	21.5194	+	12.4242i	1.44105	+	0.831988i	0.997920	−	0.0644716i	$-0.0205362\pi$
$223$	21.5194	+	12.4242i	1.44105	+	0.831988i	0.443126	+	0.896459i	$0.353870\pi$
$224$		0			0
$225$	2.01949	−	3.07010i	0.134633	−	0.204674i
$226$		0			0
$227$	5.87175			0.389722			0.194861	−	0.980831i	$-0.437574\pi$
$227$	5.87175			0.389722			0.194861	+	0.980831i	$0.437574\pi$
$228$		0			0
$229$	24.1173			1.59372			0.796859	−	0.604166i	$-0.206494\pi$
$229$	24.1173			1.59372			0.796859	+	0.604166i	$0.206494\pi$
$230$		0			0
$231$	−27.3519	−	16.8720i	−1.79962	−	1.11009i
$232$		0			0
$233$	19.4029	+	11.2022i	1.27112	+	0.733883i	0.975199	−	0.221328i	$-0.0710392\pi$
$233$	19.4029	+	11.2022i	1.27112	+	0.733883i	0.295924	+	0.955211i	$0.404372\pi$
$234$		0			0
$235$	23.5098			1.53361
$236$		0			0
$237$	19.5853	−	10.5595i	1.27220	−	0.685916i
$238$		0			0
$239$			9.01601i			0.583197i	0.956541	+	0.291599i	$0.0941872\pi$
$239$			9.01601i			0.583197i	−0.956541	+	0.291599i	$0.905813\pi$
$240$		0			0
$241$	−1.77594	+	1.02534i	−0.114398	+	0.0660480i	−0.556107	−	0.831110i	$-0.687706\pi$
$241$	−1.77594	+	1.02534i	−0.114398	+	0.0660480i	0.441709	+	0.897158i	$0.354372\pi$
$242$		0			0
$243$	−5.75326	−	14.4879i	−0.369072	−	0.929401i
$244$		0			0
$245$	8.51145	+	4.91409i	0.543776	+	0.313949i
$246$		0			0
$247$	−0.347346	−	0.147957i	−0.0221011	−	0.00941429i
$248$		0			0
$249$	16.3994	+	10.1160i	1.03927	+	0.641074i
$250$		0			0
$251$	−12.3766	+	7.14561i	−0.781201	+	0.451027i	−0.836856	−	0.547423i	$-0.815609\pi$
$251$	−12.3766	+	7.14561i	−0.781201	+	0.451027i	0.0556545	+	0.998450i	$0.482275\pi$
$252$		0			0
$253$	−9.54133	−	16.5261i	−0.599858	−	1.03899i
$254$		0			0
$255$	23.4272	+	0.682338i	1.46707	+	0.0427297i
$256$		0			0
$257$	−1.53490	−	2.65853i	−0.0957447	−	0.165835i	0.814174	−	0.580620i	$-0.197190\pi$
$257$	−1.53490	−	2.65853i	−0.0957447	−	0.165835i	−0.909919	+	0.414786i	$0.863857\pi$
$258$		0			0
$259$			6.06222i			0.376688i
$260$		0			0
$261$	−5.89987	+	8.96919i	−0.365193	+	0.555179i
$262$		0			0
$263$	−8.57939	−	4.95331i	−0.529028	−	0.305434i	0.211593	−	0.977358i	$-0.432135\pi$
$263$	−8.57939	−	4.95331i	−0.529028	−	0.305434i	−0.740620	+	0.671924i	$0.765468\pi$
$264$		0			0
$265$			3.70219i			0.227424i
$266$		0			0
$267$	−0.265688	−	0.00773840i	−0.0162598	−	0.000473582i
$268$		0			0
$269$	5.59025	−	9.68260i	0.340844	−	0.590358i	−0.643746	−	0.765239i	$-0.722621\pi$
$269$	5.59025	−	9.68260i	0.340844	−	0.590358i	0.984590	+	0.174881i	$0.0559540\pi$
$270$		0			0
$271$	−1.61953	+	2.80511i	−0.0983794	+	0.170398i	−0.911014	−	0.412375i	$-0.864699\pi$
$271$	−1.61953	+	2.80511i	−0.0983794	+	0.170398i	0.812635	+	0.582774i	$0.198033\pi$
$272$		0			0
$273$	0.0144458	−	0.495977i	0.000874299	−	0.0300179i
$274$		0			0
$275$	5.95102	−	3.43582i	0.358860	−	0.207188i
$276$		0			0
$277$	−14.3892			−0.864566			−0.432283	−	0.901738i	$-0.642292\pi$
$277$	−14.3892			−0.864566			−0.432283	+	0.901738i	$0.642292\pi$
$278$		0			0
$279$	18.4656	−	9.27241i	1.10550	−	0.555125i
$280$		0			0
$281$	−5.94913	−	10.3042i	−0.354895	−	0.614696i	0.632205	−	0.774801i	$-0.282150\pi$
$281$	−5.94913	−	10.3042i	−0.354895	−	0.614696i	−0.987100	+	0.160105i	$0.948817\pi$
$282$		0			0
$283$	12.2041	−	21.1382i	0.725460	−	1.25653i	−0.233325	−	0.972399i	$-0.574960\pi$
$283$	12.2041	−	21.1382i	0.725460	−	1.25653i	0.958784	−	0.284134i	$-0.0917062\pi$
$284$		0			0
$285$	17.1077	+	7.88336i	1.01337	+	0.466970i
$286$		0			0
$287$	−4.46815	+	7.73907i	−0.263747	+	0.456823i
$288$		0			0
$289$	6.20695	+	10.7508i	0.365115	+	0.632398i
$290$		0			0
$291$	−4.24343	+	2.28788i	−0.248754	+	0.134118i
$292$		0			0
$293$	−17.8958			−1.04548			−0.522741	−	0.852492i	$-0.675090\pi$
$293$	−17.8958			−1.04548			−0.522741	+	0.852492i	$0.675090\pi$
$294$		0			0
$295$	−29.8661	+	17.2432i	−1.73887	+	1.00394i
$296$		0			0
$297$	2.54308	−	29.0386i	0.147565	−	1.68499i
$298$		0			0
$299$	0.147316	−	0.255158i	0.00851949	−	0.0147562i
$300$		0			0
$301$	13.3283	−	23.0852i	0.768229	−	1.33061i
$302$		0			0
$303$	0.0567253	−	1.94759i	0.00325878	−	0.111886i
$304$		0			0
$305$		−	31.3624i		−	1.79580i
$306$		0			0
$307$	0.203380	+	0.117422i	0.0116075	+	0.00670161i	0.505793	−	0.862655i	$-0.331200\pi$
$307$	0.203380	+	0.117422i	0.0116075	+	0.00670161i	−0.494185	+	0.869357i	$0.664533\pi$
$308$		0			0
$309$	10.4449	+	6.44293i	0.594190	+	0.366526i
$310$		0			0
$311$		−	15.5000i		−	0.878926i	−0.898261	−	0.439463i	$-0.855169\pi$
$311$		−	15.5000i		−	0.878926i	0.898261	−	0.439463i	$-0.144831\pi$
$312$		0			0
$313$	0.139406	+	0.241458i	0.00787970	+	0.0136480i	0.869938	−	0.493160i	$-0.164158\pi$
$313$	0.139406	+	0.241458i	0.00787970	+	0.0136480i	−0.862059	+	0.506808i	$0.830825\pi$
$314$		0			0
$315$	−1.44086	+	24.7140i	−0.0811833	+	1.39248i
$316$		0			0
$317$	−7.71727	−	13.3667i	−0.433445	−	0.750749i	0.563722	−	0.825964i	$-0.309369\pi$
$317$	−7.71727	−	13.3667i	−0.433445	−	0.750749i	−0.997167	+	0.0752157i	$0.976035\pi$
$318$		0			0
$319$	−17.3857	+	10.0376i	−0.973410	+	0.561999i
$320$		0			0
$321$	2.16683	−	3.51273i	0.120940	−	0.196062i
$322$		0			0
$323$	2.85142	+	23.4677i	0.158657	+	1.30578i
$324$		0			0
$325$	0.0918822	+	0.0530482i	0.00509671	+	0.00294259i
$326$		0			0
$327$	18.3860	−	9.91298i	1.01675	−	0.548189i
$328$		0			0
$329$	−26.9901	+	15.5827i	−1.48801	+	0.859104i
$330$		0			0
$331$		−	33.6114i		−	1.84745i	−0.383058	−	0.923724i	$-0.625129\pi$
$331$		−	33.6114i		−	1.84745i	0.383058	−	0.923724i	$-0.374871\pi$
$332$		0			0
$333$	−4.91397	+	2.46753i	−0.269284	+	0.135220i
$334$		0			0
$335$	20.5415			1.12230
$336$		0			0
$337$	−10.5229	−	6.07543i	−0.573221	−	0.330950i	0.185213	−	0.982698i	$-0.440702\pi$
$337$	−10.5229	−	6.07543i	−0.573221	−	0.330950i	−0.758435	+	0.651749i	$0.774036\pi$
$338$		0			0
$339$	−8.61469	+	13.9656i	−0.467886	+	0.758509i
$340$		0			0
$341$	38.6387			2.09240
$342$		0			0
$343$	10.1235			0.546617
$344$		0			0
$345$	−7.71746	+	12.5111i	−0.415494	+	0.673575i
$346$		0			0
$347$	−2.94061	−	1.69776i	−0.157860	−	0.0911406i	0.418989	−	0.907991i	$-0.362385\pi$
$347$	−2.94061	−	1.69776i	−0.157860	−	0.0911406i	−0.576849	+	0.816851i	$0.695718\pi$
$348$		0			0
$349$	16.2403			0.869324			0.434662	−	0.900594i	$-0.356868\pi$
$349$	16.2403			0.869324			0.434662	+	0.900594i	$0.356868\pi$
$350$		0			0
$351$	0.407913	−	0.190170i	0.0217728	−	0.0101505i
$352$		0			0
$353$		−	7.55854i		−	0.402300i	−0.979560	−	0.201150i	$-0.935532\pi$
$353$		−	7.55854i		−	0.402300i	0.979560	−	0.201150i	$-0.0644679\pi$
$354$		0			0
$355$	22.5063	−	12.9940i	1.19451	−	0.689651i
$356$		0			0
$357$	−27.3475	+	14.7446i	−1.44738	+	0.780369i
$358$		0			0
$359$	−3.11783	−	1.80008i	−0.164553	−	0.0950045i	0.415462	−	0.909610i	$-0.363620\pi$
$359$	−3.11783	−	1.80008i	−0.164553	−	0.0950045i	−0.580015	+	0.814606i	$0.696953\pi$
$360$		0			0
$361$	−5.28319	+	18.2507i	−0.278062	+	0.960563i
$362$		0			0
$363$	18.6145	−	30.1768i	0.977008	−	1.58387i
$364$		0			0
$365$	−18.1175	+	10.4602i	−0.948315	+	0.547510i
$366$		0			0
$367$	12.0567	+	20.8828i	0.629354	+	1.09007i	0.987681	+	0.156478i	$0.0500139\pi$
$367$	12.0567	+	20.8828i	0.629354	+	1.09007i	−0.358327	+	0.933596i	$0.616653\pi$
$368$		0			0
$369$	−8.09189	−	0.471768i	−0.421247	−	0.0245593i
$370$		0			0
$371$	−2.45388	−	4.25025i	−0.127399	−	0.220662i
$372$		0			0
$373$		−	7.52606i		−	0.389685i	−0.980835	−	0.194842i	$-0.937580\pi$
$373$		−	7.52606i		−	0.389685i	0.980835	−	0.194842i	$-0.0624195\pi$
$374$		0			0
$375$	13.8846	+	8.56473i	0.717000	+	0.442281i
$376$		0			0
$377$	−0.268430	−	0.154978i	−0.0138249	−	0.00798179i
$378$		0			0
$379$		−	2.92913i		−	0.150459i	−0.997166	−	0.0752297i	$-0.976031\pi$
$379$		−	2.92913i		−	0.150459i	0.997166	−	0.0752297i	$-0.0239690\pi$
$380$		0			0
$381$	−0.202944	+	6.96780i	−0.0103971	+	0.356971i
$382$		0			0
$383$	11.6489	−	20.1764i	0.595229	−	1.03097i	−0.398286	−	0.917261i	$-0.630395\pi$
$383$	11.6489	−	20.1764i	0.595229	−	1.03097i	0.993515	−	0.113705i	$-0.0362719\pi$
$384$		0			0
$385$	−23.1463	+	40.0906i	−1.17965	+	2.04321i
$386$		0			0
$387$	24.1377	+	1.40726i	1.22699	+	0.0715350i
$388$		0			0
$389$	5.90634	−	3.41003i	0.299463	−	0.172895i	−0.342738	−	0.939431i	$-0.611354\pi$
$389$	5.90634	−	3.41003i	0.299463	−	0.172895i	0.642202	+	0.766536i	$0.278021\pi$
$390$		0			0
$391$	−18.4486			−0.932984
$392$		0			0
$393$	−14.8233	+	7.99212i	−0.747738	+	0.403149i
$394$		0			0
$395$	−16.0257	−	27.7573i	−0.806340	−	1.39662i
$396$		0			0
$397$	−11.7214	+	20.3021i	−0.588282	+	1.01893i	0.406176	+	0.913795i	$0.366862\pi$
$397$	−11.7214	+	20.3021i	−0.588282	+	1.01893i	−0.994458	+	0.105139i	$0.966471\pi$
$398$		0			0
$399$	−24.8655	+	2.28892i	−1.24483	+	0.114590i
$400$		0			0
$401$	9.24303	−	16.0094i	0.461575	−	0.799471i	−0.537465	−	0.843286i	$-0.680618\pi$
$401$	9.24303	−	16.0094i	0.461575	−	0.799471i	0.999040	+	0.0438149i	$0.0139512\pi$
$402$		0			0
$403$	0.298285	+	0.516646i	0.0148587	+	0.0257360i
$404$		0			0
$405$	−20.6194	+	8.89152i	−1.02459	+	0.441823i
$406$		0			0
$407$	−10.2823			−0.509677
$408$		0			0
$409$	−2.25799	+	1.30365i	−0.111650	+	0.0644613i	−0.554785	−	0.831994i	$-0.687200\pi$
$409$	−2.25799	+	1.30365i	−0.111650	+	0.0644613i	0.443135	+	0.896455i	$0.353866\pi$
$410$		0			0
$411$	−0.248954	+	8.54749i	−0.0122800	+	0.421617i
$412$		0			0
$413$	22.8583	−	39.5917i	1.12478	−	1.94818i
$414$		0			0
$415$	13.8779	−	24.0372i	0.681240	−	1.17994i
$416$		0			0
$417$	10.0710	+	0.293327i	0.493179	+	0.0143643i
$418$		0			0
$419$			30.2655i			1.47857i	0.673394	+	0.739283i	$0.264836\pi$
$419$			30.2655i			1.47857i	−0.673394	+	0.739283i	$0.735164\pi$
$420$		0			0
$421$	4.65708	+	2.68877i	0.226972	+	0.131042i	0.609174	−	0.793036i	$-0.291501\pi$
$421$	4.65708	+	2.68877i	0.226972	+	0.131042i	−0.382202	+	0.924079i	$0.624834\pi$
$422$		0			0
$423$	−23.6171	−	15.5352i	−1.14830	−	0.755345i
$424$		0			0
$425$		−	6.64331i		−	0.322248i
$426$		0			0
$427$	20.7876	+	36.0052i	1.00598	+	1.74241i
$428$		0			0
$429$	0.841243	+	0.0245020i	0.0406156	+	0.00118297i
$430$		0			0
$431$	11.3963	+	19.7390i	0.548941	+	0.950795i	0.998347	+	0.0574669i	$0.0183024\pi$
$431$	11.3963	+	19.7390i	0.548941	+	0.950795i	−0.449406	+	0.893328i	$0.648364\pi$
$432$		0			0
$433$	18.6538	−	10.7698i	0.896443	−	0.517562i	0.0203985	−	0.999792i	$-0.493506\pi$
$433$	18.6538	−	10.7698i	0.896443	−	0.517562i	0.876044	+	0.482230i	$0.160173\pi$
$434$		0			0
$435$	13.1619	+	8.11888i	0.631063	+	0.389270i
$436$		0			0
$437$	−13.6413	−	5.81072i	−0.652553	−	0.277965i
$438$		0			0
$439$	24.5571	+	14.1780i	1.17204	+	0.676680i	0.954161	−	0.299294i	$-0.0967513\pi$
$439$	24.5571	+	14.1780i	1.17204	+	0.676680i	0.217884	+	0.975975i	$0.430085\pi$
$440$		0			0
$441$	−5.30309	−	10.5608i	−0.252528	−	0.502897i
$442$		0			0
$443$	2.98996	−	1.72625i	0.142057	−	0.0820168i	−0.427287	−	0.904116i	$-0.640531\pi$
$443$	2.98996	−	1.72625i	0.142057	−	0.0820168i	0.569344	+	0.822099i	$0.307197\pi$
$444$		0			0
$445$			0.382879i			0.0181502i
$446$		0			0
$447$	−3.24829	+	1.75134i	−0.153639	+	0.0828355i
$448$		0			0
$449$	26.1195			1.23266			0.616329	−	0.787489i	$-0.288619\pi$
$449$	26.1195			1.23266			0.616329	+	0.787489i	$0.288619\pi$
$450$		0			0
$451$	−13.1265	−	7.57858i	−0.618102	−	0.356862i
$452$		0			0
$453$	−3.96446	−	2.44547i	−0.186266	−	0.114898i
$454$		0			0
$455$	−0.714746			−0.0335078
$456$		0			0
$457$	−10.8975			−0.509765			−0.254882	−	0.966972i	$-0.582037\pi$
$457$	−10.8975			−0.509765			−0.254882	+	0.966972i	$0.582037\pi$
$458$		0			0
$459$	−23.0832	−	16.1660i	−1.07743	−	0.754565i
$460$		0			0
$461$	−13.6381	−	7.87395i	−0.635188	−	0.366726i	0.147570	−	0.989052i	$-0.452855\pi$
$461$	−13.6381	−	7.87395i	−0.635188	−	0.366726i	−0.782759	+	0.622325i	$0.786188\pi$
$462$		0			0
$463$	−5.53876			−0.257408			−0.128704	−	0.991683i	$-0.541082\pi$
$463$	−5.53876			−0.257408			−0.128704	+	0.991683i	$0.541082\pi$
$464$		0			0
$465$	−14.1254	−	26.1991i	−0.655051	−	1.21495i
$466$		0			0
$467$		−	28.9943i		−	1.34170i	−0.741594	−	0.670849i	$-0.765930\pi$
$467$		−	28.9943i		−	1.34170i	0.741594	−	0.670849i	$-0.234070\pi$
$468$		0			0
$469$	−23.5824	+	13.6153i	−1.08894	+	0.628697i
$470$		0			0
$471$	−17.8853	−	33.1727i	−0.824113	−	1.52852i
$472$		0			0
$473$	39.1557	+	22.6065i	1.80038	+	1.03945i
$474$		0			0
$475$	2.09243	−	4.91222i	0.0960075	−	0.225388i
$476$		0			0
$477$	2.44639	−	3.71909i	0.112012	−	0.170285i
$478$		0			0
$479$	13.1643	−	7.60039i	0.601491	−	0.347271i	−0.168137	−	0.985764i	$-0.553775\pi$
$479$	13.1643	−	7.60039i	0.601491	−	0.347271i	0.769628	+	0.638493i	$0.220442\pi$
$480$		0			0
$481$	−0.0793784	−	0.137487i	−0.00361934	−	0.00626888i
$482$		0			0
$483$	0.567329	−	19.4785i	0.0258144	−	0.886302i
$484$		0			0
$485$	3.47220	+	6.01402i	0.157664	+	0.273083i
$486$		0			0
$487$			15.5329i			0.703864i	0.936026	+	0.351932i	$0.114475\pi$
$487$			15.5329i			0.703864i	−0.936026	+	0.351932i	$0.885525\pi$
$488$		0			0
$489$	18.8863	−	30.6174i	0.854068	−	1.38457i
$490$		0			0
$491$	4.40033	+	2.54053i	0.198584	+	0.114652i	0.595995	−	0.802988i	$-0.296758\pi$
$491$	4.40033	+	2.54053i	0.198584	+	0.114652i	−0.397411	+	0.917641i	$0.630091\pi$
$492$		0			0
$493$			19.4082i			0.874100i
$494$		0			0
$495$	−41.9183	−	2.44389i	−1.88409	−	0.109845i
$496$		0			0
$497$	−17.2254	+	29.8352i	−0.772664	+	1.33829i
$498$		0			0
$499$	5.82625	−	10.0914i	0.260819	−	0.451752i	−0.705641	−	0.708570i	$-0.749341\pi$
$499$	5.82625	−	10.0914i	0.260819	−	0.451752i	0.966460	+	0.256818i	$0.0826741\pi$
$500$		0			0
$501$	−24.5074	−	0.713801i	−1.09491	−	0.0318903i
$502$		0			0
$503$	−16.6725	+	9.62586i	−0.743389	+	0.429196i	−0.823300	−	0.567606i	$-0.807870\pi$
$503$	−16.6725	+	9.62586i	−0.743389	+	0.429196i	0.0799113	+	0.996802i	$0.474536\pi$
$504$		0			0
$505$	−2.80665			−0.124894
$506$		0			0
$507$	−10.6797	−	19.8081i	−0.474301	−	0.879707i
$508$		0			0
$509$	−7.32137	−	12.6810i	−0.324514	−	0.562075i	0.656900	−	0.753978i	$-0.271867\pi$
$509$	−7.32137	−	12.6810i	−0.324514	−	0.562075i	−0.981414	+	0.191903i	$0.938534\pi$
$510$		0			0
$511$	13.8664	−	24.0173i	0.613414	−	1.06246i
$512$		0			0
$513$	−11.9765	−	19.2240i	−0.528775	−	0.848762i
$514$		0			0
$515$	8.83893	−	15.3095i	0.389490	−	0.674616i
$516$		0			0
$517$	−26.4304	−	45.7788i	−1.16241	−	2.01335i
$518$		0			0
$519$	−8.33097	−	15.4518i	−0.365689	−	0.678259i
$520$		0			0
$521$	39.9113			1.74855			0.874273	−	0.485435i	$-0.161339\pi$
$521$	39.9113			1.74855			0.874273	+	0.485435i	$0.161339\pi$
$522$		0			0
$523$	−30.2180	+	17.4464i	−1.32134	+	0.762878i	−0.983943	−	0.178484i	$-0.942881\pi$
$523$	−30.2180	+	17.4464i	−1.32134	+	0.762878i	−0.337400	+	0.941361i	$0.609547\pi$
$524$		0			0
$525$	7.01418	+	0.204295i	0.306124	+	0.00891615i
$526$		0			0
$527$	18.6774	−	32.3502i	0.813599	−	1.40920i
$528$		0			0
$529$	−5.71447	+	9.89776i	−0.248455	+	0.430337i
$530$		0			0
$531$	41.3967	+	2.41348i	1.79646	+	0.104736i
$532$		0			0
$533$		−	0.234023i		−	0.0101367i
$534$		0			0
$535$	−5.14874	−	2.97262i	−0.222599	−	0.128518i
$536$		0			0
$537$	19.2582	−	31.2203i	0.831053	−	1.34726i
$538$		0			0
$539$		−	22.0983i		−	0.951840i
$540$		0			0
$541$	−0.127924	−	0.221571i	−0.00549990	−	0.00952610i	0.863262	−	0.504755i	$-0.168417\pi$
$541$	−0.127924	−	0.221571i	−0.00549990	−	0.00952610i	−0.868762	+	0.495229i	$0.835084\pi$
$542$		0			0
$543$	−1.24862	+	42.8697i	−0.0535834	+	1.83972i
$544$		0			0
$545$	−15.0444	−	26.0577i	−0.644433	−	1.11619i
$546$		0			0
$547$	−3.97598	+	2.29554i	−0.170001	+	0.0981500i	−0.582586	−	0.812769i	$-0.697959\pi$
$547$	−3.97598	+	2.29554i	−0.170001	+	0.0981500i	0.412585	+	0.910919i	$0.364626\pi$
$548$		0			0
$549$	−20.7241	+	31.5055i	−0.884484	+	1.34462i
$550$		0			0
$551$	−6.11296	+	14.3509i	−0.260421	+	0.611367i
$552$		0			0
$553$	36.7962	+	21.2443i	1.56473	+	0.903399i
$554$		0			0
$555$	3.75900	+	6.97198i	0.159561	+	0.295944i
$556$		0			0
$557$	−23.8892	+	13.7924i	−1.01222	+	0.584404i	−0.911840	−	0.410546i	$-0.865338\pi$
$557$	−23.8892	+	13.7924i	−1.01222	+	0.584404i	−0.100377	+	0.994949i	$0.532005\pi$
$558$		0			0
$559$			0.698078i			0.0295256i
$560$		0			0
$561$	−25.0089	−	46.3851i	−1.05588	−	1.95838i
$562$		0			0
$563$	39.9327			1.68296			0.841480	−	0.540288i	$-0.181685\pi$
$563$	39.9327			1.68296			0.841480	+	0.540288i	$0.181685\pi$
$564$		0			0
$565$	20.4699	+	11.8183i	0.861177	+	0.497201i
$566$		0			0
$567$	17.7784	−	23.8747i	0.746621	−	1.00264i
$568$		0			0
$569$	−6.50025			−0.272505			−0.136252	−	0.990674i	$-0.543506\pi$
$569$	−6.50025			−0.272505			−0.136252	+	0.990674i	$0.543506\pi$
$570$		0			0
$571$	40.7379			1.70483			0.852414	−	0.522868i	$-0.175138\pi$
$571$	40.7379			1.70483			0.852414	+	0.522868i	$0.175138\pi$
$572$		0			0
$573$	−2.78959	−	1.72075i	−0.116537	−	0.0718856i
$574$		0			0
$575$	3.60849	+	2.08336i	0.150484	+	0.0868822i
$576$		0			0
$577$	−5.10599			−0.212565			−0.106283	−	0.994336i	$-0.533895\pi$
$577$	−5.10599			−0.212565			−0.106283	+	0.994336i	$0.533895\pi$
$578$		0			0
$579$	−19.8449	+	10.6995i	−0.824725	+	0.444657i
$580$		0			0
$581$			36.7942i			1.52648i
$582$		0			0
$583$	7.20899	−	4.16211i	0.298566	−	0.172377i
$584$		0			0
$585$	−0.290926	−	0.579365i	−0.0120283	−	0.0239538i
$586$		0			0
$587$	−10.4549	−	6.03616i	−0.431521	−	0.249139i	0.268473	−	0.963287i	$-0.413481\pi$
$587$	−10.4549	−	6.03616i	−0.431521	−	0.249139i	−0.699995	+	0.714148i	$0.746814\pi$
$588$		0			0
$589$	23.9998	−	18.0377i	0.988894	−	0.743230i
$590$		0			0
$591$	6.32746	+	3.90309i	0.260277	+	0.160552i
$592$		0			0
$593$	19.5316	−	11.2766i	0.802068	−	0.463074i	−0.0421260	−	0.999112i	$-0.513413\pi$
$593$	19.5316	−	11.2766i	0.802068	−	0.463074i	0.844194	+	0.536038i	$0.180080\pi$
$594$		0			0
$595$	22.3772	+	38.7584i	0.917376	+	1.58894i
$596$		0			0
$597$	17.4163	+	0.507265i	0.712801	+	0.0207610i
$598$		0			0
$599$	−11.7498	−	20.3512i	−0.480082	−	0.831526i	0.519657	−	0.854375i	$-0.326060\pi$
$599$	−11.7498	−	20.3512i	−0.480082	−	0.831526i	−0.999739	+	0.0228487i	$0.992726\pi$
$600$		0			0
$601$			10.1425i			0.413720i	0.978371	+	0.206860i	$0.0663245\pi$
$601$			10.1425i			0.413720i	−0.978371	+	0.206860i	$0.933676\pi$
$602$		0			0
$603$	−20.6353	−	13.5738i	−0.840334	−	0.552766i
$604$		0			0
$605$	−44.2311	−	25.5369i	−1.79825	−	1.03822i
$606$		0			0
$607$			15.7277i			0.638368i	0.947693	+	0.319184i	$0.103409\pi$
$607$			15.7277i			0.638368i	−0.947693	+	0.319184i	$0.896591\pi$
$608$		0			0
$609$	−20.4917	−	0.596838i	−0.830364	−	0.0241851i
$610$		0			0
$611$	0.408079	−	0.706813i	0.0165091	−	0.0285946i
$612$		0			0
$613$	21.8135	−	37.7822i	0.881041	−	1.52601i	0.0308549	−	0.999524i	$-0.490177\pi$
$613$	21.8135	−	37.7822i	0.881041	−	1.52601i	0.850186	−	0.526483i	$-0.176490\pi$
$614$		0			0
$615$	−0.339929	+	11.6710i	−0.0137073	+	0.470621i
$616$		0			0
$617$	−30.5063	+	17.6128i	−1.22814	+	0.709065i	−0.966640	−	0.256140i	$-0.917549\pi$
$617$	−30.5063	+	17.6128i	−1.22814	+	0.709065i	−0.261496	+	0.965205i	$0.584216\pi$
$618$		0			0
$619$	−9.52949			−0.383023			−0.191511	−	0.981490i	$-0.561339\pi$
$619$	−9.52949			−0.383023			−0.191511	+	0.981490i	$0.561339\pi$
$620$		0			0
$621$	16.0200	−	7.46854i	0.642859	−	0.299702i
$622$		0			0
$623$	−0.253780	−	0.439560i	−0.0101675	−	0.0176106i
$624$		0			0
$625$	14.8121	−	25.6553i	0.592483	−	1.02621i
$626$		0			0
$627$	−3.88232	−	42.1752i	−0.155045	−	1.68432i
$628$		0			0
$629$	−4.97034	+	8.60888i	−0.198180	+	0.343258i
$630$		0			0
$631$	1.07272	+	1.85801i	0.0427044	+	0.0739662i	0.886588	−	0.462561i	$-0.153069\pi$
$631$	1.07272	+	1.85801i	0.0427044	+	0.0739662i	−0.843883	+	0.536527i	$0.819736\pi$
$632$		0			0
$633$	29.0136	−	15.6429i	1.15319	−	0.621749i
$634$		0			0
$635$	10.0412			0.398473
$636$		0			0
$637$	0.295481	−	0.170596i	0.0117074	−	0.00675925i
$638$		0			0
$639$	−31.1954	−	1.81873i	−1.23407	−	0.0719480i
$640$		0			0
$641$	−15.8676	+	27.4834i	−0.626731	+	1.08553i	0.361473	+	0.932383i	$0.382274\pi$
$641$	−15.8676	+	27.4834i	−0.626731	+	1.08553i	−0.988203	+	0.153147i	$0.951059\pi$
$642$		0			0
$643$	−15.5839	+	26.9922i	−0.614571	+	1.06447i	0.375889	+	0.926665i	$0.377337\pi$
$643$	−15.5839	+	26.9922i	−0.614571	+	1.06447i	−0.990460	+	0.137803i	$0.955996\pi$
$644$		0			0
$645$	1.01399	−	34.8141i	0.0399259	−	1.37080i
$646$		0			0
$647$			34.6595i			1.36260i	0.732002	+	0.681302i	$0.238586\pi$
$647$			34.6595i			1.36260i	−0.732002	+	0.681302i	$0.761414\pi$
$648$		0			0
$649$	67.1528	+	38.7707i	2.63598	+	1.52188i
$650$		0			0
$651$	33.5818	+	20.7149i	1.31617	+	0.811881i
$652$		0			0
$653$		−	30.6175i		−	1.19815i	−0.800691	−	0.599077i	$-0.795534\pi$
$653$		−	30.6175i		−	1.19815i	0.800691	−	0.599077i	$-0.204466\pi$
$654$		0			0
$655$	12.1292	+	21.0085i	0.473928	+	0.820868i
$656$		0			0
$657$	25.1123	+	1.46408i	0.979723	+	0.0571191i
$658$		0			0
$659$	−12.6935	−	21.9858i	−0.494470	−	0.856446i	0.505510	−	0.862821i	$-0.331304\pi$
$659$	−12.6935	−	21.9858i	−0.494470	−	0.856446i	−0.999980	+	0.00637432i	$0.997971\pi$
$660$		0			0
$661$	12.0551	−	6.96001i	0.468889	−	0.270713i	−0.246886	−	0.969045i	$-0.579407\pi$
$661$	12.0551	−	6.96001i	0.468889	−	0.270713i	0.715774	+	0.698332i	$0.246074\pi$
$662$		0			0
$663$	0.427159	−	0.692486i	0.0165895	−	0.0268939i
$664$		0			0
$665$	4.33854	+	35.7070i	0.168241	+	1.38466i
$666$		0			0
$667$	−10.5421	−	6.08646i	−0.408190	−	0.235669i
$668$		0			0
$669$	−37.8834	+	20.4251i	−1.46466	+	0.789681i
$670$		0			0
$671$	−61.0696	+	35.2585i	−2.35757	+	1.36114i
$672$		0			0
$673$			34.2929i			1.32189i	0.750432	+	0.660947i	$0.229845\pi$
$673$			34.2929i			1.32189i	−0.750432	+	0.660947i	$0.770155\pi$
$674$		0			0
$675$	2.68941	+	5.76877i	0.103516	+	0.222040i
$676$		0			0
$677$	45.5709			1.75143			0.875715	−	0.482828i	$-0.160390\pi$
$677$	45.5709			1.75143			0.875715	+	0.482828i	$0.160390\pi$
$678$		0			0
$679$	−7.97243	−	4.60288i	−0.305954	−	0.176642i
$680$		0			0
$681$	−5.33935	+	8.65585i	−0.204605	+	0.331693i
$682$		0			0
$683$	18.8798			0.722417			0.361208	−	0.932485i	$-0.382364\pi$
$683$	18.8798			0.722417			0.361208	+	0.932485i	$0.382364\pi$
$684$		0			0
$685$	12.3177			0.470634
$686$		0			0
$687$	−21.9306	+	35.5526i	−0.836703	+	1.35642i
$688$		0			0
$689$	0.111305	+	0.0642620i	0.00424038	+	0.00244819i
$690$		0			0
$691$	−32.3824			−1.23189			−0.615943	−	0.787791i	$-0.711225\pi$
$691$	−32.3824			−1.23189			−0.615943	+	0.787791i	$0.711225\pi$
$692$		0			0
$693$	49.7437	−	24.9786i	1.88961	−	0.948859i
$694$		0			0
$695$		−	14.5132i		−	0.550517i
$696$		0			0
$697$	−12.6903	+	7.32676i	−0.480680	+	0.277521i
$698$		0			0
$699$	−34.1574	+	18.4162i	−1.29195	+	0.696565i
$700$		0			0
$701$	23.8149	+	13.7495i	0.899477	+	0.519313i	0.877030	−	0.480435i	$-0.159521\pi$
$701$	23.8149	+	13.7495i	0.899477	+	0.519313i	0.0224466	+	0.999748i	$0.492854\pi$
$702$		0			0
$703$	−6.38671	+	4.80011i	−0.240879	+	0.181040i
$704$		0			0
$705$	−21.3781	+	34.6569i	−0.805146	+	1.30526i
$706$		0			0
$707$	3.22213	−	1.86030i	0.121181	−	0.0699638i
$708$		0			0
$709$	−5.50515	−	9.53520i	−0.206750	−	0.358102i	0.743939	−	0.668248i	$-0.232955\pi$
$709$	−5.50515	−	9.53520i	−0.206750	−	0.358102i	−0.950689	+	0.310146i	$0.899622\pi$
$710$		0			0
$711$	−2.24307	+	38.4737i	−0.0841216	+	1.44288i
$712$		0			0
$713$	11.7146	+	20.2902i	0.438714	+	0.759874i
$714$		0			0
$715$		−	1.21231i		−	0.0453377i
$716$		0			0
$717$	−13.2910	−	8.19852i	−0.496360	−	0.306179i
$718$		0			0
$719$	−2.55656	−	1.47603i	−0.0953437	−	0.0550467i	0.451570	−	0.892236i	$-0.350864\pi$
$719$	−2.55656	−	1.47603i	−0.0953437	−	0.0550467i	−0.546914	+	0.837189i	$0.684197\pi$
$720$		0			0
$721$			23.4345i			0.872745i
$722$		0			0
$723$	0.103408	−	3.55038i	0.00384579	−	0.132040i
$724$		0			0
$725$	2.19173	−	3.79618i	0.0813987	−	0.140987i
$726$		0			0
$727$	15.1144	−	26.1789i	0.560562	−	0.970922i	−0.436885	−	0.899517i	$-0.643918\pi$
$727$	15.1144	−	26.1789i	0.560562	−	0.970922i	0.997447	−	0.0714050i	$-0.0227483\pi$
$728$		0			0
$729$	26.5890	+	4.69311i	0.984778	+	0.173819i
$730$		0			0
$731$	37.8546	−	21.8553i	1.40010	−	0.808349i
$732$		0			0
$733$	27.1606			1.00320			0.501599	−	0.865100i	$-0.332745\pi$
$733$	27.1606			1.00320			0.501599	+	0.865100i	$0.332745\pi$
$734$		0			0
$735$	−14.9838	+	8.07864i	−0.552686	+	0.297985i
$736$		0			0
$737$	−23.0934	−	39.9990i	−0.850657	−	1.47338i
$738$		0			0
$739$	4.45902	−	7.72324i	0.164028	−	0.284104i	−0.772282	−	0.635280i	$-0.780885\pi$
$739$	4.45902	−	7.72324i	0.164028	−	0.284104i	0.936310	+	0.351176i	$0.114218\pi$
$740$		0			0
$741$	0.533963	−	0.377499i	0.0196156	−	0.0138678i
$742$		0			0
$743$	12.9057	−	22.3534i	0.473465	−	0.820066i	−0.526073	−	0.850439i	$-0.676336\pi$
$743$	12.9057	−	22.3534i	0.473465	−	0.820066i	0.999539	+	0.0303734i	$0.00966965\pi$
$744$		0			0
$745$	2.65792	+	4.60365i	0.0973786	+	0.168665i
$746$		0			0
$747$	−29.8250	+	14.9765i	−1.09124	+	0.547962i
$748$		0			0
$749$	7.88126			0.287975
$750$		0			0
$751$	39.7293	−	22.9377i	1.44974	−	0.837010i	0.451278	−	0.892383i	$-0.350968\pi$
$751$	39.7293	−	22.9377i	1.44974	−	0.837010i	0.998466	+	0.0553729i	$0.0176348\pi$
$752$		0			0
$753$	0.720652	−	24.7426i	0.0262620	−	0.901671i
$754$		0			0
$755$	−3.35489	+	5.81084i	−0.122097	+	0.211478i
$756$		0			0
$757$	1.48501	−	2.57211i	0.0539735	−	0.0934849i	−0.837776	−	0.546014i	$-0.816145\pi$
$757$	1.48501	−	2.57211i	0.0539735	−	0.0934849i	0.891750	+	0.452529i	$0.149478\pi$
$758$		0			0
$759$	33.0381	+	0.962266i	1.19921	+	0.0349280i
$760$		0			0
$761$		−	14.6431i		−	0.530812i	−0.964137	−	0.265406i	$-0.914494\pi$
$761$		−	14.6431i		−	0.530812i	0.964137	−	0.265406i	$-0.0855060\pi$
$762$		0			0
$763$	34.5432	+	19.9435i	1.25055	+	0.722003i
$764$		0			0
$765$	−22.3089	+	33.9147i	−0.806579	+	1.22619i
$766$		0			0
$767$			1.19722i			0.0432291i
$768$		0			0
$769$	−3.03640	−	5.25920i	−0.109495	−	0.189651i	0.806071	−	0.591819i	$-0.201590\pi$
$769$	−3.03640	−	5.25920i	−0.109495	−	0.189651i	−0.915566	+	0.402168i	$0.868257\pi$
$770$		0			0
$771$	5.31481	+	0.154799i	0.191408	+	0.00557494i
$772$		0			0
$773$	21.3332	+	36.9503i	0.767304	+	1.32901i	0.939020	+	0.343862i	$0.111735\pi$
$773$	21.3332	+	36.9503i	0.767304	+	1.32901i	−0.171716	+	0.985146i	$0.554931\pi$
$774$		0			0
$775$	−7.30648	+	4.21840i	−0.262457	+	0.151529i
$776$		0			0
$777$	−8.93663	−	5.51255i	−0.320600	−	0.197762i
$778$		0			0
$779$	−11.6912	+	1.42053i	−0.418882	+	0.0508957i
$780$		0			0
$781$	−50.6046	−	29.2166i	−1.81077	−	1.04545i
$782$		0			0
$783$	−7.85702	−	16.8532i	−0.280787	−	0.602286i
$784$		0			0
$785$	−47.0142	+	27.1437i	−1.67801	+	0.968800i
$786$		0			0
$787$			12.8450i			0.457873i	0.973441	+	0.228937i	$0.0735249\pi$
$787$			12.8450i			0.457873i	−0.973441	+	0.228937i	$0.926475\pi$
$788$		0			0
$789$	15.1034	−	8.14313i	0.537696	−	0.289903i
$790$		0			0
$791$	−31.3337			−1.11410
$792$		0			0
$793$	−0.942899	−	0.544383i	−0.0334833	−	0.0193316i
$794$		0			0
$795$	−5.45758	−	3.36650i	−0.193561	−	0.119398i
$796$		0			0
$797$	24.5334			0.869018			0.434509	−	0.900668i	$-0.356922\pi$
$797$	24.5334			0.869018			0.434509	+	0.900668i	$0.356922\pi$
$798$		0			0
$799$	−51.1043			−1.80794
$800$		0			0
$801$	0.253005	−	0.384627i	0.00893949	−	0.0135901i
$802$		0			0
$803$	40.7366	+	23.5193i	1.43756	+	0.829977i
$804$		0			0
$805$	−28.0702			−0.989345
$806$		0			0
$807$	9.19024	+	17.0455i	0.323512	+	0.600031i
$808$		0			0
$809$			44.3313i			1.55861i	0.626647	+	0.779304i	$0.284427\pi$
$809$			44.3313i			1.55861i	−0.626647	+	0.779304i	$0.715573\pi$
$810$		0			0
$811$	−24.9696	+	14.4162i	−0.876800	+	0.506221i	−0.869602	−	0.493753i	$-0.835625\pi$
$811$	−24.9696	+	14.4162i	−0.876800	+	0.506221i	−0.00719832	+	0.999974i	$0.502291\pi$
$812$		0			0
$813$	−2.66247	−	4.93819i	−0.0933768	−	0.173190i
$814$		0			0
$815$	−44.8770	−	25.9097i	−1.57197	−	0.907579i
$816$		0			0
$817$	34.8743	−	4.23736i	1.22010	−	0.148247i
$818$		0			0
$819$	0.718009	+	0.472301i	0.0250893	+	0.0165035i
$820$		0			0
$821$	20.5963	−	11.8913i	0.718815	−	0.415008i	−0.0955012	−	0.995429i	$-0.530445\pi$
$821$	20.5963	−	11.8913i	0.718815	−	0.415008i	0.814317	+	0.580421i	$0.197112\pi$
$822$		0			0
$823$	−16.0364	−	27.7759i	−0.558994	−	0.968206i	−0.997581	−	0.0695173i	$-0.977854\pi$
$823$	−16.0364	−	27.7759i	−0.558994	−	0.968206i	0.438587	−	0.898689i	$-0.355479\pi$
$824$		0			0
$825$	−0.346511	+	11.8970i	−0.0120640	+	0.414200i
$826$		0			0
$827$	6.11874	+	10.5980i	0.212769	+	0.368527i	0.952580	−	0.304288i	$-0.0984184\pi$
$827$	6.11874	+	10.5980i	0.212769	+	0.368527i	−0.739811	+	0.672815i	$0.765085\pi$
$828$		0			0
$829$			5.01804i			0.174284i	0.996196	+	0.0871418i	$0.0277733\pi$
$829$			5.01804i			0.174284i	−0.996196	+	0.0871418i	$0.972227\pi$
$830$		0			0
$831$	13.0846	−	21.2119i	0.453898	−	0.735833i
$832$		0			0
$833$	−18.5017	−	10.6820i	−0.641048	−	0.370109i
$834$		0			0
$835$			35.3173i			1.22221i
$836$		0			0
$837$	−3.12232	+	35.6527i	−0.107923	+	1.23234i
$838$		0			0
$839$	2.27369	−	3.93815i	0.0784965	−	0.135960i	−0.824105	−	0.566437i	$-0.808321\pi$
$839$	2.27369	−	3.93815i	0.0784965	−	0.135960i	0.902601	+	0.430477i	$0.141655\pi$
$840$		0			0
$841$	8.09696	−	14.0243i	0.279205	−	0.483598i
$842$		0			0
$843$	20.5996	+	0.599984i	0.709489	+	0.0206645i
$844$		0			0
$845$	−28.0731	+	16.2080i	−0.965744	+	0.557572i
$846$		0			0
$847$	67.7053			2.32638
$848$		0			0
$849$	20.0633	+	37.2123i	0.688570	+	1.27712i
$850$		0			0
$851$	−3.11742	−	5.39954i	−0.106864	−	0.185094i
$852$		0			0
$853$	−13.1852	+	22.8375i	−0.451454	+	0.781941i	−0.998477	−	0.0551765i	$-0.982428\pi$
$853$	−13.1852	+	22.8375i	−0.451454	+	0.781941i	0.547023	+	0.837118i	$0.315761\pi$
$854$		0			0
$855$	−27.1778	+	18.0508i	−0.929460	+	0.617323i
$856$		0			0
$857$	2.23765	−	3.87573i	0.0764368	−	0.132392i	−0.825273	−	0.564733i	$-0.808979\pi$
$857$	2.23765	−	3.87573i	0.0764368	−	0.132392i	0.901710	+	0.432341i	$0.142312\pi$
$858$		0			0
$859$	−23.6349	−	40.9368i	−0.806411	−	1.39674i	−0.915334	−	0.402695i	$-0.868074\pi$
$859$	−23.6349	−	40.9368i	−0.806411	−	1.39674i	0.108923	−	0.994050i	$-0.465260\pi$
$860$		0			0
$861$	−7.34553	−	13.6241i	−0.250335	−	0.464308i
$862$		0			0
$863$	5.01262			0.170632			0.0853158	−	0.996354i	$-0.472810\pi$
$863$	5.01262			0.170632			0.0853158	+	0.996354i	$0.472810\pi$
$864$		0			0
$865$	−21.8992	+	12.6435i	−0.744594	+	0.429892i
$866$		0			0
$867$	−21.4924	−	0.625986i	−0.729920	−	0.0212596i
$868$		0			0
$869$	−36.0332	+	62.4113i	−1.22234	+	2.11716i
$870$		0			0
$871$	0.356557	−	0.617574i	0.0120815	−	0.0209257i
$872$		0			0
$873$	0.485993	−	8.33589i	0.0164484	−	0.282127i
$874$		0			0
$875$			31.1520i			1.05313i
$876$		0			0
$877$	15.2153	+	8.78456i	0.513784	+	0.296633i	0.734388	−	0.678730i	$-0.237469\pi$
$877$	15.2153	+	8.78456i	0.513784	+	0.296633i	−0.220604	+	0.975364i	$0.570803\pi$
$878$		0			0
$879$	16.2731	−	26.3811i	0.548879	−	0.889811i
$880$		0			0
$881$		−	23.9582i		−	0.807174i	−0.914941	−	0.403587i	$-0.867763\pi$
$881$		−	23.9582i		−	0.807174i	0.914941	−	0.403587i	$-0.132237\pi$
$882$		0			0
$883$	−11.5747	−	20.0479i	−0.389518	−	0.674665i	0.602866	−	0.797842i	$-0.294025\pi$
$883$	−11.5747	−	20.0479i	−0.389518	−	0.674665i	−0.992385	+	0.123177i	$0.960692\pi$
$884$		0			0
$885$	1.73902	−	59.7069i	0.0584565	−	2.00703i
$886$		0			0
$887$	13.3637	+	23.1466i	0.448710	+	0.777188i	0.998302	−	0.0582446i	$-0.0185503\pi$
$887$	13.3637	+	23.1466i	0.448710	+	0.777188i	−0.549592	+	0.835433i	$0.685217\pi$
$888$		0			0
$889$	−11.5277	+	6.65552i	−0.386626	+	0.223219i
$890$		0			0
$891$	40.4948	+	30.1545i	1.35663	+	1.01021i
$892$		0			0
$893$	−37.7878	−	16.0963i	−1.26452	−	0.538641i
$894$		0			0
$895$	−45.7607	−	26.4199i	−1.52961	−	0.883121i
$896$		0			0
$897$	0.242183	+	0.449188i	0.00808627	+	0.0149980i
$898$		0			0
$899$	21.3456	−	12.3239i	0.711915	−	0.411025i
$900$		0			0
$901$		−	8.04763i		−	0.268105i
$902$		0			0
$903$	21.9114	+	40.6399i	0.729164	+	1.35241i
$904$		0			0
$905$	61.7791			2.05361
$906$		0			0
$907$	1.67127	+	0.964909i	0.0554937	+	0.0320393i	0.527490	−	0.849561i	$-0.323133\pi$
$907$	1.67127	+	0.964909i	0.0554937	+	0.0320393i	−0.471996	+	0.881600i	$0.656467\pi$
$908$		0			0
$909$	2.81946	+	1.85462i	0.0935155	+	0.0615138i
$910$		0			0
$911$	−3.65156			−0.120982			−0.0604908	−	0.998169i	$-0.519267\pi$
$911$	−3.65156			−0.120982			−0.0604908	+	0.998169i	$0.519267\pi$
$912$		0			0
$913$	−62.4079			−2.06540
$914$		0			0
$915$	46.2329	+	28.5187i	1.52841	+	0.942799i
$916$		0			0
$917$	−27.8496	−	16.0790i	−0.919676	−	0.530975i
$918$		0			0
$919$	10.1232			0.333934			0.166967	−	0.985962i	$-0.446603\pi$
$919$	10.1232			0.333934			0.166967	+	0.985962i	$0.446603\pi$
$920$		0			0
$921$	−0.358037	+	0.193038i	−0.0117977	+	0.00636083i
$922$		0			0
$923$		−	0.902193i		−	0.0296960i
$924$		0			0
$925$	1.94437	−	1.12258i	0.0639304	−	0.0369102i
$926$		0			0
$927$	−18.9957	+	9.53863i	−0.623901	+	0.313290i
$928$		0			0
$929$	−48.9732	−	28.2747i	−1.60676	−	0.927662i	−0.990089	−	0.140439i	$-0.955149\pi$
$929$	−48.9732	−	28.2747i	−1.60676	−	0.927662i	−0.616668	−	0.787223i	$-0.711518\pi$
$930$		0			0
$931$	−10.3161	−	13.7260i	−0.338098	−	0.449851i
$932$		0			0
$933$	22.8494	+	14.0946i	0.748055	+	0.461437i
$934$		0			0
$935$	−65.7395	+	37.9547i	−2.14991	+	1.24125i
$936$		0			0
$937$	−14.9702	−	25.9292i	−0.489056	−	0.847069i	0.510865	−	0.859661i	$-0.329325\pi$
$937$	−14.9702	−	25.9292i	−0.489056	−	0.847069i	−0.999921	+	0.0125917i	$0.995992\pi$
$938$		0			0
$939$	−0.482712	−	0.0140594i	−0.0157527	−	0.000458812i
$940$		0			0
$941$	−0.746226	−	1.29250i	−0.0243263	−	0.0421343i	0.853606	−	0.520919i	$-0.174411\pi$
$941$	−0.746226	−	1.29250i	−0.0243263	−	0.0421343i	−0.877932	+	0.478785i	$0.841077\pi$
$942$		0			0
$943$		−	9.19077i		−	0.299293i
$944$		0			0
$945$	−35.1220	−	24.5972i	−1.14252	−	0.800148i
$946$		0			0
$947$	−7.72511	−	4.46009i	−0.251032	−	0.144934i	0.369205	−	0.929348i	$-0.379630\pi$
$947$	−7.72511	−	4.46009i	−0.251032	−	0.144934i	−0.620237	+	0.784415i	$0.712964\pi$
$948$		0			0
$949$			0.726263i			0.0235755i
$950$		0			0
$951$	26.7221	+	0.778305i	0.866522	+	0.0252383i
$952$		0			0
$953$	−6.87726	+	11.9118i	−0.222776	+	0.385860i	−0.955650	−	0.294505i	$-0.904845\pi$
$953$	−6.87726	+	11.9118i	−0.222776	+	0.385860i	0.732874	+	0.680365i	$0.238179\pi$
$954$		0			0
$955$	−2.36067	+	4.08880i	−0.0763894	+	0.132310i
$956$		0			0
$957$	1.01232	−	34.7566i	0.0327236	−	1.12352i
$958$		0			0
$959$	−14.1412	+	8.16440i	−0.456642	+	0.263642i
$960$		0			0
$961$	−16.4394			−0.530302
$962$		0			0
$963$	3.20794	+	6.38846i	0.103374	+	0.205865i
$964$		0			0
$965$	16.2381	+	28.1253i	0.522724	+	0.905385i
$966$		0			0
$967$	−21.7214	+	37.6226i	−0.698513	+	1.20986i	0.270469	+	0.962729i	$0.412821\pi$
$967$	−21.7214	+	37.6226i	−0.698513	+	1.20986i	−0.968982	+	0.247131i	$0.920512\pi$
$968$		0			0
$969$	−37.1878	−	17.1364i	−1.19465	−	0.550502i
$970$		0			0
$971$	−27.3032	+	47.2906i	−0.876203	+	1.51763i	−0.0207268	+	0.999785i	$0.506598\pi$
$971$	−27.3032	+	47.2906i	−0.876203	+	1.51763i	−0.855476	+	0.517843i	$0.826735\pi$
$972$		0			0
$973$	9.61963	+	16.6617i	0.308391	+	0.534149i
$974$		0			0
$975$	−0.161752	+	0.0872100i	−0.00518022	+	0.00279296i
$976$		0			0
$977$	5.08365			0.162640			0.0813202	−	0.996688i	$-0.474086\pi$
$977$	5.08365			0.162640			0.0813202	+	0.996688i	$0.474086\pi$
$978$		0			0
$979$	0.745552	−	0.430445i	0.0238280	−	0.0137571i
$980$		0			0
$981$	−2.10573	+	36.1180i	−0.0672306	+	1.15316i
$982$		0			0
$983$	−9.44498	+	16.3592i	−0.301248	+	0.521777i	−0.976419	−	0.215884i	$-0.930737\pi$
$983$	−9.44498	+	16.3592i	−0.301248	+	0.521777i	0.675171	+	0.737661i	$0.264070\pi$
$984$		0			0
$985$	5.35457	−	9.27439i	0.170611	−	0.295507i
$986$		0			0
$987$	1.57156	−	53.9573i	0.0500232	−	1.71748i
$988$		0			0
$989$			27.4156i			0.871765i
$990$		0			0
$991$	−2.57283	−	1.48543i	−0.0817287	−	0.0471861i	0.458579	−	0.888654i	$-0.348359\pi$
$991$	−2.57283	−	1.48543i	−0.0817287	−	0.0471861i	−0.540307	+	0.841468i	$0.681692\pi$
$992$		0			0
$993$	49.5482	+	30.5638i	1.57237	+	0.969913i
$994$		0			0
$995$		−	25.0984i		−	0.795673i
$996$		0			0
$997$	26.5333	+	45.9570i	0.840317	+	1.45547i	0.889627	+	0.456688i	$0.150964\pi$
$997$	26.5333	+	45.9570i	0.840317	+	1.45547i	−0.0493104	+	0.998784i	$0.515702\pi$
$998$		0			0
$999$	0.830897	−	9.48773i	0.0262884	−	0.300179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.o.65.3		16
3.2	odd	2		912.2.bn.n.65.6		16
4.3	odd	2		456.2.bf.c.65.6	✓	16
12.11	even	2		456.2.bf.d.65.3	yes	16
19.12	odd	6		912.2.bn.n.449.6		16
57.50	even	6	inner	912.2.bn.o.449.3		16
76.31	even	6		456.2.bf.d.449.3	yes	16
228.107	odd	6		456.2.bf.c.449.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bf.c.65.6	✓	16	4.3	odd	2
456.2.bf.c.449.6	yes	16	228.107	odd	6
456.2.bf.d.65.3	yes	16	12.11	even	2
456.2.bf.d.449.3	yes	16	76.31	even	6
912.2.bn.n.65.6		16	3.2	odd	2
912.2.bn.n.449.6		16	19.12	odd	6
912.2.bn.o.65.3		16	1.1	even	1	trivial
912.2.bn.o.449.3		16	57.50	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.909329 + 1.47415i) q^{3} +(2.16072 + 1.24749i) q^{5} -3.30744 q^{7} +(-1.34624 - 2.68098i) q^{9} +O(q^{10})\)	\(q+(-0.909329 + 1.47415i) q^{3} +(2.16072 + 1.24749i) q^{5} -3.30744 q^{7} +(-1.34624 - 2.68098i) q^{9} -5.60987i q^{11} +(0.0750107 - 0.0433075i) q^{13} +(-3.80379 + 2.05084i) q^{15} +(-4.69685 - 2.71173i) q^{17} +(-2.61886 - 3.48448i) q^{19} +(3.00755 - 4.87567i) q^{21} +(2.94589 - 1.70081i) q^{23} +(0.612461 + 1.06081i) q^{25} +(5.17634 + 0.453323i) q^{27} +(-1.78928 - 3.09912i) q^{29} +6.88762i q^{31} +(8.26979 + 5.10121i) q^{33} +(-7.14644 - 4.12600i) q^{35} -1.83290i q^{37} +(-0.00436766 + 0.149958i) q^{39} +(1.35094 - 2.33989i) q^{41} +(-4.02978 + 6.97978i) q^{43} +(0.435642 - 7.47225i) q^{45} +(8.16041 - 4.71141i) q^{47} +3.93918 q^{49} +(8.26848 - 4.45802i) q^{51} +(0.741927 + 1.28506i) q^{53} +(6.99825 - 12.1213i) q^{55} +(7.51805 - 0.692053i) q^{57} +(-6.91116 + 11.9705i) q^{59} +(-6.28510 - 10.8861i) q^{61} +(4.45262 + 8.86717i) q^{63} +0.216102 q^{65} +(7.13011 - 4.11657i) q^{67} +(-0.171531 + 5.88929i) q^{69} +(5.20807 - 9.02064i) q^{71} +(-4.19249 + 7.26160i) q^{73} +(-2.12073 - 0.0617681i) q^{75} +18.5543i q^{77} +(-11.1253 - 6.42318i) q^{79} +(-5.37526 + 7.21849i) q^{81} -11.1247i q^{83} +(-6.76571 - 11.7186i) q^{85} +(6.19562 + 0.180453i) q^{87} +(0.0767300 + 0.132900i) q^{89} +(-0.248094 + 0.143237i) q^{91} +(-10.1534 - 6.26311i) q^{93} +(-1.31175 - 10.7960i) q^{95} +(2.41045 + 1.39167i) q^{97} +(-15.0399 + 7.55224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9}+O(q^{10}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9	\( 16 q + q^{3} - 3 q^{5} + 13 q^{9} - 3 q^{13} - 15 q^{15} + 3 q^{17} - 11 q^{19} - 6 q^{21} - 3 q^{23} + 11 q^{25} + 4 q^{27} - 5 q^{29} + q^{33} + 24 q^{35} + 9 q^{39} - 6 q^{41} - 13 q^{43} + 33 q^{45} + 27 q^{47} + 8 q^{49} - 15 q^{51} + 7 q^{53} + 12 q^{55} + 23 q^{57} - 10 q^{59} - q^{61} + 8 q^{63} + 30 q^{65} + 24 q^{67} + 41 q^{69} + 27 q^{71} + 2 q^{73} + 21 q^{75} + 21 q^{79} - 7 q^{81} - 5 q^{85} + 23 q^{87} - 25 q^{89} + 78 q^{91} - 56 q^{93} + 13 q^{95} - 60 q^{97} + 35 q^{99}+O(q^{100}) \) 16 * q + q^3 - 3 * q^5 + 13 * q^9 - 3 * q^13 - 15 * q^15 + 3 * q^17 - 11 * q^19 - 6 * q^21 - 3 * q^23 + 11 * q^25 + 4 * q^27 - 5 * q^29 + q^33 + 24 * q^35 + 9 * q^39 - 6 * q^41 - 13 * q^43 + 33 * q^45 + 27 * q^47 + 8 * q^49 - 15 * q^51 + 7 * q^53 + 12 * q^55 + 23 * q^57 - 10 * q^59 - q^61 + 8 * q^63 + 30 * q^65 + 24 * q^67 + 41 * q^69 + 27 * q^71 + 2 * q^73 + 21 * q^75 + 21 * q^79 - 7 * q^81 - 5 * q^85 + 23 * q^87 - 25 * q^89 + 78 * q^91 - 56 * q^93 + 13 * q^95 - 60 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more