LMFDB - Embedded newform 1638.2.m.h.289.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(289,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.m (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-8,0,8,-2,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.3
Root			$-0.571299 + 1.29368i$ of defining polynomial
Character	$\chi$	$=$	1638.289
Dual form			1638.2.m.h.1621.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.441221 - 0.764218i) q^{5} +(0.369922 + 2.61976i) q^{7} -1.00000 q^{8} +(-0.441221 + 0.764218i) q^{10} +(0.775934 - 1.34396i) q^{11} +(2.13422 + 2.90605i) q^{13} +(-0.369922 - 2.61976i) q^{14} +1.00000 q^{16} +7.17592 q^{17} +(-2.37080 - 4.10635i) q^{19} +(0.441221 - 0.764218i) q^{20} +(-0.775934 + 1.34396i) q^{22} -5.29348 q^{23} +(2.11065 + 3.65575i) q^{25} +(-2.13422 - 2.90605i) q^{26} +(0.369922 + 2.61976i) q^{28} +(-3.87494 - 6.71160i) q^{29} +(3.24911 + 5.62762i) q^{31} -1.00000 q^{32} -7.17592 q^{34} +(2.16529 + 0.873194i) q^{35} +0.330574 q^{37} +(2.37080 + 4.10635i) q^{38} +(-0.441221 + 0.764218i) q^{40} +(3.02918 + 5.24669i) q^{41} +(3.35975 - 5.81927i) q^{43} +(0.775934 - 1.34396i) q^{44} +5.29348 q^{46} +(-0.976430 + 1.69123i) q^{47} +(-6.72632 + 1.93822i) q^{49} +(-2.11065 - 3.65575i) q^{50} +(2.13422 + 2.90605i) q^{52} +(6.74308 + 11.6794i) q^{53} +(-0.684718 - 1.18597i) q^{55} +(-0.369922 - 2.61976i) q^{56} +(3.87494 + 6.71160i) q^{58} -5.27138 q^{59} +(7.17592 + 12.4291i) q^{61} +(-3.24911 - 5.62762i) q^{62} +1.00000 q^{64} +(3.16252 - 0.348796i) q^{65} +(3.75236 - 6.49929i) q^{67} +7.17592 q^{68} +(-2.16529 - 0.873194i) q^{70} +(-5.00985 + 8.67732i) q^{71} +(-1.93284 - 3.34778i) q^{73} -0.330574 q^{74} +(-2.37080 - 4.10635i) q^{76} +(3.80789 + 1.53560i) q^{77} +(6.67928 - 11.5689i) q^{79} +(0.441221 - 0.764218i) q^{80} +(-3.02918 - 5.24669i) q^{82} +10.5519 q^{83} +(3.16617 - 5.48396i) q^{85} +(-3.35975 + 5.81927i) q^{86} +(-0.775934 + 1.34396i) q^{88} -14.8167 q^{89} +(-6.82366 + 6.66615i) q^{91} -5.29348 q^{92} +(0.976430 - 1.69123i) q^{94} -4.18420 q^{95} +(5.79259 - 10.0331i) q^{97} +(6.72632 - 1.93822i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} + 2 q^{10} - 4 q^{11} + 3 q^{13} - 3 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{25} - 3 q^{26} + 3 q^{28} - 2 q^{29}+ \cdots - 5 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 + 2 * q^10 - 4 * q^11 + 3 * q^13 - 3 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + 2 * q^25 - 3 * q^26 + 3 * q^28 - 2 * q^29 + 14 * q^31 - 8 * q^32 + 4 * q^34 + 22 * q^35 + 12 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 8 * q^46 - 7 * q^47 + 5 * q^49 - 2 * q^50 + 3 * q^52 + q^53 - 25 * q^55 - 3 * q^56 + 2 * q^58 + 32 * q^59 - 4 * q^61 - 14 * q^62 + 8 * q^64 - 10 * q^65 + 19 * q^67 - 4 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 - 12 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 - 2 * q^80 + 12 * q^82 + 64 * q^83 + 15 * q^85 + 4 * q^88 - 22 * q^89 - 38 * q^91 + 8 * q^92 + 7 * q^94 + 56 * q^95 + 11 * q^97 - 5 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.441221	−	0.764218i	0.197320	−	0.341769i	−0.750338	−	0.661054i	$-0.770109\pi$
$5$	0.441221	−	0.764218i	0.197320	−	0.341769i	0.947659	+	0.319285i	$0.103443\pi$
$6$		0			0
$7$	0.369922	+	2.61976i	0.139817	+	0.990177i
$7$	0.369922	+	2.61976i	0.139817	+	0.990177i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.441221	+	0.764218i	−0.139526	+	0.241667i
$11$	0.775934	−	1.34396i	0.233953	−	0.405219i	−0.725015	−	0.688733i	$-0.758167\pi$
$11$	0.775934	−	1.34396i	0.233953	−	0.405219i	0.958968	+	0.283515i	$0.0915005\pi$
$12$		0			0
$13$	2.13422	+	2.90605i	0.591925	+	0.805993i
$13$	2.13422	+	2.90605i	0.591925	+	0.805993i
$14$	−0.369922	−	2.61976i	−0.0988658	−	0.700161i
$15$		0			0
$16$	1.00000			0.250000
$17$	7.17592			1.74042			0.870208	−	0.492685i	$-0.163984\pi$
$17$	7.17592			1.74042			0.870208	+	0.492685i	$0.163984\pi$
$18$		0			0
$19$	−2.37080	−	4.10635i	−0.543900	−	0.942062i	−0.998675	−	0.0514558i	$-0.983614\pi$
$19$	−2.37080	−	4.10635i	−0.543900	−	0.942062i	0.454776	−	0.890606i	$-0.349719\pi$
$20$	0.441221	−	0.764218i	0.0986601	−	0.170884i
$21$		0			0
$22$	−0.775934	+	1.34396i	−0.165430	+	0.286533i
$23$	−5.29348			−1.10377			−0.551883	−	0.833922i	$-0.686091\pi$
$23$	−5.29348			−1.10377			−0.551883	+	0.833922i	$0.686091\pi$
$24$		0			0
$25$	2.11065	+	3.65575i	0.422129	+	0.731150i
$26$	−2.13422	−	2.90605i	−0.418554	−	0.569923i
$27$		0			0
$28$	0.369922	+	2.61976i	0.0699087	+	0.495089i
$29$	−3.87494	−	6.71160i	−0.719559	−	1.24631i	−0.961175	−	0.275940i	$-0.911011\pi$
$29$	−3.87494	−	6.71160i	−0.719559	−	1.24631i	0.241616	−	0.970372i	$-0.422323\pi$
$30$		0			0
$31$	3.24911	+	5.62762i	0.583557	+	1.01075i	0.995054	+	0.0993390i	$0.0316728\pi$
$31$	3.24911	+	5.62762i	0.583557	+	1.01075i	−0.411497	+	0.911411i	$0.634994\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−7.17592			−1.23066
$35$	2.16529	+	0.873194i	0.366000	+	0.147597i
$36$		0			0
$37$	0.330574			0.0543460			0.0271730	−	0.999631i	$-0.491349\pi$
$37$	0.330574			0.0543460			0.0271730	+	0.999631i	$0.491349\pi$
$38$	2.37080	+	4.10635i	0.384595	+	0.666138i
$39$		0			0
$40$	−0.441221	+	0.764218i	−0.0697632	+	0.120833i
$41$	3.02918	+	5.24669i	0.473079	+	0.819396i	0.999525	−	0.0308121i	$-0.00980934\pi$
$41$	3.02918	+	5.24669i	0.473079	+	0.819396i	−0.526447	+	0.850208i	$0.676476\pi$
$42$		0			0
$43$	3.35975	−	5.81927i	0.512358	−	0.887430i	−0.487540	−	0.873101i	$-0.662106\pi$
$43$	3.35975	−	5.81927i	0.512358	−	0.887430i	0.999897	−	0.0143288i	$-0.00456116\pi$
$44$	0.775934	−	1.34396i	0.116977	−	0.202609i
$45$		0			0
$46$	5.29348			0.780480
$47$	−0.976430	+	1.69123i	−0.142427	+	0.246691i	−0.928410	−	0.371557i	$-0.878824\pi$
$47$	−0.976430	+	1.69123i	−0.142427	+	0.246691i	0.785983	+	0.618248i	$0.212157\pi$
$48$		0			0
$49$	−6.72632	+	1.93822i	−0.960902	+	0.276888i
$50$	−2.11065	−	3.65575i	−0.298491	−	0.517001i
$51$		0			0
$52$	2.13422	+	2.90605i	0.295963	+	0.402996i
$53$	6.74308	+	11.6794i	0.926233	+	1.60428i	0.789566	+	0.613666i	$0.210306\pi$
$53$	6.74308	+	11.6794i	0.926233	+	1.60428i	0.136667	+	0.990617i	$0.456361\pi$
$54$		0			0
$55$	−0.684718	−	1.18597i	−0.0923273	−	0.159916i
$56$	−0.369922	−	2.61976i	−0.0494329	−	0.350081i
$57$		0			0
$58$	3.87494	+	6.71160i	0.508805	+	0.881276i
$59$	−5.27138			−0.686275			−0.343137	−	0.939285i	$-0.611490\pi$
$59$	−5.27138			−0.686275			−0.343137	+	0.939285i	$0.611490\pi$
$60$		0			0
$61$	7.17592	+	12.4291i	0.918782	+	1.59138i	0.801267	+	0.598306i	$0.204159\pi$
$61$	7.17592	+	12.4291i	0.918782	+	1.59138i	0.117515	+	0.993071i	$0.462507\pi$
$62$	−3.24911	−	5.62762i	−0.412637	−	0.714708i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.16252	−	0.348796i	0.392262	−	0.0432628i
$66$		0			0
$67$	3.75236	−	6.49929i	0.458424	−	0.794014i	−0.540454	−	0.841374i	$-0.681747\pi$
$67$	3.75236	−	6.49929i	0.458424	−	0.794014i	0.998878	+	0.0473596i	$0.0150807\pi$
$68$	7.17592			0.870208
$69$		0			0
$70$	−2.16529	−	0.873194i	−0.258801	−	0.104367i
$71$	−5.00985	+	8.67732i	−0.594560	+	1.02981i	0.399049	+	0.916930i	$0.369340\pi$
$71$	−5.00985	+	8.67732i	−0.594560	+	1.02981i	−0.993609	+	0.112879i	$0.963993\pi$
$72$		0			0
$73$	−1.93284	−	3.34778i	−0.226222	−	0.391828i	0.730464	−	0.682952i	$-0.239304\pi$
$73$	−1.93284	−	3.34778i	−0.226222	−	0.391828i	−0.956685	+	0.291124i	$0.905971\pi$
$74$	−0.330574			−0.0384284
$75$		0			0
$76$	−2.37080	−	4.10635i	−0.271950	−	0.471031i
$77$	3.80789	+	1.53560i	0.433949	+	0.174998i
$78$		0			0
$79$	6.67928	−	11.5689i	0.751478	−	1.30160i	−0.195629	−	0.980678i	$-0.562675\pi$
$79$	6.67928	−	11.5689i	0.751478	−	1.30160i	0.947106	−	0.320920i	$-0.103992\pi$
$80$	0.441221	−	0.764218i	0.0493300	−	0.0854422i
$81$		0			0
$82$	−3.02918	−	5.24669i	−0.334517	−	0.579401i
$83$	10.5519			1.15822			0.579109	−	0.815250i	$-0.303401\pi$
$83$	10.5519			1.15822			0.579109	+	0.815250i	$0.303401\pi$
$84$		0			0
$85$	3.16617	−	5.48396i	0.343419	−	0.594820i
$86$	−3.35975	+	5.81927i	−0.362292	+	0.627508i
$87$		0			0
$88$	−0.775934	+	1.34396i	−0.0827149	+	0.143266i
$89$	−14.8167			−1.57057			−0.785285	−	0.619134i	$-0.787484\pi$
$89$	−14.8167			−1.57057			−0.785285	+	0.619134i	$0.787484\pi$
$90$		0			0
$91$	−6.82366	+	6.66615i	−0.715314	+	0.698803i
$92$	−5.29348			−0.551883
$93$		0			0
$94$	0.976430	−	1.69123i	0.100711	−	0.174437i
$95$	−4.18420			−0.429290
$96$		0			0
$97$	5.79259	−	10.0331i	0.588149	−	1.01870i	−0.406326	−	0.913728i	$-0.633190\pi$
$97$	5.79259	−	10.0331i	0.588149	−	1.01870i	0.994475	−	0.104975i	$-0.0334764\pi$
$98$	6.72632	−	1.93822i	0.679460	−	0.195789i
$99$		0			0
$100$	2.11065	+	3.65575i	0.211065	+	0.365575i
$101$	3.91439	−	6.77993i	0.389497	−	0.674628i	−0.602885	−	0.797828i	$-0.705982\pi$
$101$	3.91439	−	6.77993i	0.389497	−	0.674628i	0.992382	+	0.123200i	$0.0393156\pi$
$102$		0			0
$103$	0.430172	−	0.745081i	0.0423862	−	0.0734150i	−0.844054	−	0.536258i	$-0.819837\pi$
$103$	0.430172	−	0.745081i	0.0423862	−	0.0734150i	0.886440	+	0.462843i	$0.153171\pi$
$104$	−2.13422	−	2.90605i	−0.209277	−	0.284961i
$105$		0			0
$106$	−6.74308	−	11.6794i	−0.654946	−	1.13440i
$107$	8.14260			0.787175			0.393587	−	0.919287i	$-0.371234\pi$
$107$	8.14260			0.787175			0.393587	+	0.919287i	$0.371234\pi$
$108$		0			0
$109$	4.73806	+	8.20656i	0.453824	+	0.786046i	0.998620	−	0.0525229i	$-0.0167263\pi$
$109$	4.73806	+	8.20656i	0.453824	+	0.786046i	−0.544796	+	0.838569i	$0.683393\pi$
$110$	0.684718	+	1.18597i	0.0652853	+	0.113077i
$111$		0			0
$112$	0.369922	+	2.61976i	0.0349543	+	0.247544i
$113$	−5.71537	+	9.89931i	−0.537657	+	0.931249i	0.461373	+	0.887206i	$0.347357\pi$
$113$	−5.71537	+	9.89931i	−0.537657	+	0.931249i	−0.999030	+	0.0440426i	$0.985976\pi$
$114$		0			0
$115$	−2.33559	+	4.04537i	−0.217795	+	0.377233i
$116$	−3.87494	−	6.71160i	−0.359779	−	0.623156i
$117$		0			0
$118$	5.27138			0.485270
$119$	2.65453	+	18.7992i	0.243340	+	1.72332i
$120$		0			0
$121$	4.29585	+	7.44063i	0.390532	+	0.676421i
$122$	−7.17592	−	12.4291i	−0.649677	−	1.12527i
$123$		0			0
$124$	3.24911	+	5.62762i	0.291778	+	0.505375i
$125$	8.13726			0.727819
$126$		0			0
$127$	3.02592	+	5.24105i	0.268507	+	0.465068i	0.968477	−	0.249105i	$-0.0801363\pi$
$127$	3.02592	+	5.24105i	0.268507	+	0.465068i	−0.699969	+	0.714173i	$0.746803\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−3.16252	+	0.348796i	−0.277371	+	0.0305914i
$131$	2.66045	−	4.60804i	0.232445	−	0.402606i	−0.726082	−	0.687608i	$-0.758661\pi$
$131$	2.66045	−	4.60804i	0.232445	−	0.402606i	0.958527	+	0.285002i	$0.0919941\pi$
$132$		0			0
$133$	9.88066	−	7.72997i	0.856762	−	0.670274i
$134$	−3.75236	+	6.49929i	−0.324155	+	0.561453i
$135$		0			0
$136$	−7.17592			−0.615330
$137$	8.01122			0.684445			0.342222	−	0.939619i	$-0.388820\pi$
$137$	8.01122			0.684445			0.342222	+	0.939619i	$0.388820\pi$
$138$		0			0
$139$	8.87582	−	15.3734i	0.752838	−	1.30395i	−0.193605	−	0.981080i	$-0.562018\pi$
$139$	8.87582	−	15.3734i	0.752838	−	1.30395i	0.946442	−	0.322873i	$-0.104649\pi$
$140$	2.16529	+	0.873194i	0.183000	+	0.0737984i
$141$		0			0
$142$	5.00985	−	8.67732i	0.420418	−	0.728185i
$143$	5.56162	−	0.613395i	0.465086	−	0.0512947i
$144$		0			0
$145$	−6.83883			−0.567934
$146$	1.93284	+	3.34778i	0.159963	+	0.277064i
$147$		0			0
$148$	0.330574			0.0271730
$149$	8.66161	+	15.0024i	0.709587	+	1.22904i	0.965010	+	0.262211i	$0.0844518\pi$
$149$	8.66161	+	15.0024i	0.709587	+	1.22904i	−0.255424	+	0.966829i	$0.582215\pi$
$150$		0			0
$151$	−1.40927	−	2.44093i	−0.114685	−	0.198640i	0.802969	−	0.596021i	$-0.203252\pi$
$151$	−1.40927	−	2.44093i	−0.114685	−	0.198640i	−0.917654	+	0.397381i	$0.869919\pi$
$152$	2.37080	+	4.10635i	0.192298	+	0.333069i
$153$		0			0
$154$	−3.80789	−	1.53560i	−0.306848	−	0.123743i
$155$	5.73430			0.460590
$156$		0			0
$157$	6.39822	+	11.0820i	0.510634	+	0.884443i	0.999924	+	0.0123225i	$0.00392247\pi$
$157$	6.39822	+	11.0820i	0.510634	+	0.884443i	−0.489290	+	0.872121i	$0.662744\pi$
$158$	−6.67928	+	11.5689i	−0.531375	+	0.920368i
$159$		0			0
$160$	−0.441221	+	0.764218i	−0.0348816	+	0.0604167i
$161$	−1.95817	−	13.8677i	−0.154326	−	1.09292i
$162$		0			0
$163$	5.34387	+	9.25586i	0.418564	+	0.724975i	0.995795	−	0.0916061i	$-0.0292001\pi$
$163$	5.34387	+	9.25586i	0.418564	+	0.724975i	−0.577231	+	0.816581i	$0.695867\pi$
$164$	3.02918	+	5.24669i	0.236539	+	0.409698i
$165$		0			0
$166$	−10.5519			−0.818984
$167$	9.90412	+	17.1544i	0.766404	+	1.32745i	0.939501	+	0.342546i	$0.111289\pi$
$167$	9.90412	+	17.1544i	0.766404	+	1.32745i	−0.173097	+	0.984905i	$0.555377\pi$
$168$		0			0
$169$	−3.89023	+	12.4043i	−0.299249	+	0.954175i
$170$	−3.16617	+	5.48396i	−0.242834	+	0.420601i
$171$		0			0
$172$	3.35975	−	5.81927i	0.256179	−	0.443715i
$173$	−0.869332	−	1.50573i	−0.0660941	−	0.114478i	0.831085	−	0.556146i	$-0.187720\pi$
$173$	−0.869332	−	1.50573i	−0.0660941	−	0.114478i	−0.897179	+	0.441668i	$0.854387\pi$
$174$		0			0
$175$	−8.79642	+	6.88174i	−0.664947	+	0.520210i
$176$	0.775934	−	1.34396i	0.0584883	−	0.101305i
$177$		0			0
$178$	14.8167			1.11056
$179$	4.89644	−	8.48088i	0.365977	−	0.633890i	−0.622956	−	0.782257i	$-0.714068\pi$
$179$	4.89644	−	8.48088i	0.365977	−	0.633890i	0.988932	+	0.148367i	$0.0474016\pi$
$180$		0			0
$181$	−11.5901			−0.861486			−0.430743	−	0.902475i	$-0.641748\pi$
$181$	−11.5901			−0.861486			−0.430743	+	0.902475i	$0.641748\pi$
$182$	6.82366	−	6.66615i	0.505804	−	0.494128i
$183$		0			0
$184$	5.29348			0.390240
$185$	0.145856	−	0.252631i	0.0107236	−	0.0185738i
$186$		0			0
$187$	5.56804	−	9.64413i	0.407176	−	0.705249i
$188$	−0.976430	+	1.69123i	−0.0712135	+	0.123345i
$189$		0			0
$190$	4.18420			0.303554
$191$	−0.631864	−	1.09442i	−0.0457200	−	0.0791894i	0.842260	−	0.539072i	$-0.181225\pi$
$191$	−0.631864	−	1.09442i	−0.0457200	−	0.0791894i	−0.887980	+	0.459882i	$0.847892\pi$
$192$		0			0
$193$	−9.49130	+	16.4394i	−0.683199	+	1.18334i	0.290800	+	0.956784i	$0.406079\pi$
$193$	−9.49130	+	16.4394i	−0.683199	+	1.18334i	−0.973999	+	0.226552i	$0.927255\pi$
$194$	−5.79259	+	10.0331i	−0.415884	+	0.720332i
$195$		0			0
$196$	−6.72632	+	1.93822i	−0.480451	+	0.138444i
$197$	−12.1786	−	21.0939i	−0.867688	−	1.50288i	−0.864353	−	0.502886i	$-0.832272\pi$
$197$	−12.1786	−	21.0939i	−0.867688	−	1.50288i	−0.00333546	−	0.999994i	$-0.501062\pi$
$198$		0			0
$199$	21.5059			1.52451			0.762255	−	0.647277i	$-0.224092\pi$
$199$	21.5059			1.52451			0.762255	+	0.647277i	$0.224092\pi$
$200$	−2.11065	−	3.65575i	−0.149245	−	0.258500i
$201$		0			0
$202$	−3.91439	+	6.77993i	−0.275416	+	0.477034i
$203$	16.1494	−	12.6342i	1.13346	−	0.886747i
$204$		0			0
$205$	5.34616			0.373392
$206$	−0.430172	+	0.745081i	−0.0299715	+	0.0519122i
$207$		0			0
$208$	2.13422	+	2.90605i	0.147981	+	0.201498i
$209$	−7.35835			−0.508988
$210$		0			0
$211$	3.56775	+	6.17953i	0.245614	+	0.425416i	0.962304	−	0.271976i	$-0.0876771\pi$
$211$	3.56775	+	6.17953i	0.245614	+	0.425416i	−0.716690	+	0.697392i	$0.754344\pi$
$212$	6.74308	+	11.6794i	0.463117	+	0.802141i
$213$		0			0
$214$	−8.14260			−0.556617
$215$	−2.96479	−	5.13517i	−0.202197	−	0.350216i
$216$		0			0
$217$	−13.5411	+	10.5937i	−0.919231	+	0.719145i
$218$	−4.73806	−	8.20656i	−0.320902	−	0.555818i
$219$		0			0
$220$	−0.684718	−	1.18597i	−0.0461637	−	0.0799578i
$221$	15.3150	+	20.8536i	1.03020	+	1.40276i
$222$		0			0
$223$	−12.1673	−	21.0744i	−0.814784	−	1.41125i	−0.909483	−	0.415742i	$-0.863522\pi$
$223$	−12.1673	−	21.0744i	−0.814784	−	1.41125i	0.0946981	−	0.995506i	$-0.469811\pi$
$224$	−0.369922	−	2.61976i	−0.0247164	−	0.175040i
$225$		0			0
$226$	5.71537	−	9.89931i	0.380181	−	0.658492i
$227$	−9.56035			−0.634543			−0.317271	−	0.948335i	$-0.602767\pi$
$227$	−9.56035			−0.634543			−0.317271	+	0.948335i	$0.602767\pi$
$228$		0			0
$229$	−5.40570	+	9.36295i	−0.357219	+	0.618721i	−0.987495	−	0.157650i	$-0.949608\pi$
$229$	−5.40570	+	9.36295i	−0.357219	+	0.618721i	0.630276	+	0.776371i	$0.282942\pi$
$230$	2.33559	−	4.04537i	0.154005	−	0.266744i
$231$		0			0
$232$	3.87494	+	6.71160i	0.254402	+	0.440638i
$233$	5.15806	−	8.93403i	0.337916	−	0.585288i	−0.646125	−	0.763232i	$-0.723611\pi$
$233$	5.15806	−	8.93403i	0.337916	−	0.585288i	0.984041	+	0.177944i	$0.0569447\pi$
$234$		0			0
$235$	0.861644	+	1.49241i	0.0562074	+	0.0973541i
$236$	−5.27138			−0.343137
$237$		0			0
$238$	−2.65453	−	18.7992i	−0.172068	−	1.21857i
$239$	−11.0866			−0.717130			−0.358565	−	0.933505i	$-0.616734\pi$
$239$	−11.0866			−0.717130			−0.358565	+	0.933505i	$0.616734\pi$
$240$		0			0
$241$	−18.6739			−1.20289			−0.601447	−	0.798913i	$-0.705409\pi$
$241$	−18.6739			−1.20289			−0.601447	+	0.798913i	$0.705409\pi$
$242$	−4.29585	−	7.44063i	−0.276148	−	0.478302i
$243$		0			0
$244$	7.17592	+	12.4291i	0.459391	+	0.795689i
$245$	−1.48658	+	5.99555i	−0.0949738	+	0.383042i
$246$		0			0
$247$	6.87345	−	15.6535i	0.437347	−	0.996009i
$248$	−3.24911	−	5.62762i	−0.206319	−	0.357354i
$249$		0			0
$250$	−8.13726			−0.514646
$251$	−0.00354883	+	0.00614676i	−0.000224000	+	0.000387980i	−0.866137	−	0.499806i	$-0.833405\pi$
$251$	−0.00354883	+	0.00614676i	−0.000224000	+	0.000387980i	0.865913	+	0.500194i	$0.166738\pi$
$252$		0			0
$253$	−4.10739	+	7.11421i	−0.258229	+	0.447266i
$254$	−3.02592	−	5.24105i	−0.189863	−	0.328853i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−12.6759			−0.790701			−0.395350	−	0.918530i	$-0.629377\pi$
$257$	−12.6759			−0.790701			−0.395350	+	0.918530i	$0.629377\pi$
$258$		0			0
$259$	0.122287	+	0.866025i	0.00759852	+	0.0538122i
$260$	3.16252	−	0.348796i	0.196131	−	0.0216314i
$261$		0			0
$262$	−2.66045	+	4.60804i	−0.164363	+	0.284686i
$263$	−2.59901	+	4.50161i	−0.160262	+	0.277581i	−0.934963	−	0.354747i	$-0.884567\pi$
$263$	−2.59901	+	4.50161i	−0.160262	+	0.277581i	0.774701	+	0.632328i	$0.217900\pi$
$264$		0			0
$265$	11.9008			0.731058
$266$	−9.88066	+	7.72997i	−0.605822	+	0.473955i
$267$		0			0
$268$	3.75236	−	6.49929i	0.229212	−	0.397007i
$269$	0.685009			0.0417657			0.0208829	−	0.999782i	$-0.493352\pi$
$269$	0.685009			0.0417657			0.0208829	+	0.999782i	$0.493352\pi$
$270$		0			0
$271$	−5.05126			−0.306842			−0.153421	−	0.988161i	$-0.549029\pi$
$271$	−5.05126			−0.306842			−0.153421	+	0.988161i	$0.549029\pi$
$272$	7.17592			0.435104
$273$		0			0
$274$	−8.01122			−0.483976
$275$	6.55090			0.395034
$276$		0			0
$277$	−12.4497			−0.748029			−0.374015	−	0.927423i	$-0.622019\pi$
$277$	−12.4497			−0.748029			−0.374015	+	0.927423i	$0.622019\pi$
$278$	−8.87582	+	15.3734i	−0.532337	+	0.922034i
$279$		0			0
$280$	−2.16529	−	0.873194i	−0.129401	−	0.0521834i
$281$	23.5917			1.40736			0.703680	−	0.710517i	$-0.251539\pi$
$281$	23.5917			1.40736			0.703680	+	0.710517i	$0.251539\pi$
$282$		0			0
$283$	−10.5148	+	18.2121i	−0.625038	+	1.08260i	0.363495	+	0.931596i	$0.381583\pi$
$283$	−10.5148	+	18.2121i	−0.625038	+	1.08260i	−0.988533	+	0.151002i	$0.951750\pi$
$284$	−5.00985	+	8.67732i	−0.297280	+	0.514904i
$285$		0			0
$286$	−5.56162	+	0.613395i	−0.328865	+	0.0362708i
$287$	−12.6245	+	9.87660i	−0.745203	+	0.582997i
$288$		0			0
$289$	34.4938			2.02905
$290$	6.83883			0.401590
$291$		0			0
$292$	−1.93284	−	3.34778i	−0.113111	−	0.195914i
$293$	6.41251	−	11.1068i	0.374623	−	0.648865i	−0.615648	−	0.788021i	$-0.711106\pi$
$293$	6.41251	−	11.1068i	0.374623	−	0.648865i	0.990270	+	0.139156i	$0.0444390\pi$
$294$		0			0
$295$	−2.32584	+	4.02848i	−0.135416	+	0.234547i
$296$	−0.330574			−0.0192142
$297$		0			0
$298$	−8.66161	−	15.0024i	−0.501754	−	0.869063i
$299$	−11.2974	−	15.3831i	−0.653347	−	0.889627i
$300$		0			0
$301$	16.4879	+	6.64909i	0.950349	+	0.383247i
$302$	1.40927	+	2.44093i	0.0810944	+	0.140460i
$303$		0			0
$304$	−2.37080	−	4.10635i	−0.135975	−	0.235515i
$305$	12.6647			0.725177
$306$		0			0
$307$	−20.4988			−1.16993			−0.584963	−	0.811060i	$-0.698891\pi$
$307$	−20.4988			−1.16993			−0.584963	+	0.811060i	$0.698891\pi$
$308$	3.80789	+	1.53560i	0.216974	+	0.0874992i
$309$		0			0
$310$	−5.73430			−0.325686
$311$	−7.06023	−	12.2287i	−0.400349	−	0.693425i	0.593419	−	0.804894i	$-0.297778\pi$
$311$	−7.06023	−	12.2287i	−0.400349	−	0.693425i	−0.993768	+	0.111469i	$0.964444\pi$
$312$		0			0
$313$	14.5296	−	25.1661i	0.821264	−	1.42247i	−0.0834772	−	0.996510i	$-0.526603\pi$
$313$	14.5296	−	25.1661i	0.821264	−	1.42247i	0.904741	−	0.425961i	$-0.140064\pi$
$314$	−6.39822	−	11.0820i	−0.361072	−	0.625396i
$315$		0			0
$316$	6.67928	−	11.5689i	0.375739	−	0.650799i
$317$	6.08027	−	10.5313i	0.341502	−	0.591499i	−0.643210	−	0.765690i	$-0.722398\pi$
$317$	6.08027	−	10.5313i	0.341502	−	0.591499i	0.984712	+	0.174191i	$0.0557310\pi$
$318$		0			0
$319$	−12.0268			−0.673372
$320$	0.441221	−	0.764218i	0.0246650	−	0.0427211i
$321$		0			0
$322$	1.95817	+	13.8677i	0.109125	+	0.772814i
$323$	−17.0127	−	29.4669i	−0.946612	−	1.63958i
$324$		0			0
$325$	−6.11920	+	13.9358i	−0.339432	+	0.773019i
$326$	−5.34387	−	9.25586i	−0.295970	−	0.512635i
$327$		0			0
$328$	−3.02918	−	5.24669i	−0.167259	−	0.289700i
$329$	−4.79182	−	1.93239i	−0.264181	−	0.106536i
$330$		0			0
$331$	−4.96685	−	8.60284i	−0.273003	−	0.472855i	0.696626	−	0.717434i	$-0.254684\pi$
$331$	−4.96685	−	8.60284i	−0.273003	−	0.472855i	−0.969629	+	0.244579i	$0.921350\pi$
$332$	10.5519			0.579109
$333$		0			0
$334$	−9.90412	−	17.1544i	−0.541930	−	0.938649i
$335$	−3.31125	−	5.73525i	−0.180913	−	0.313350i
$336$		0			0
$337$	−3.38360			−0.184316			−0.0921582	−	0.995744i	$-0.529377\pi$
$337$	−3.38360			−0.184316			−0.0921582	+	0.995744i	$0.529377\pi$
$338$	3.89023	−	12.4043i	0.211601	−	0.674704i
$339$		0			0
$340$	3.16617	−	5.48396i	0.171710	−	0.297410i
$341$	10.0844			0.546100
$342$		0			0
$343$	−7.56588	−	16.9044i	−0.408519	−	0.912750i
$344$	−3.35975	+	5.81927i	−0.181146	+	0.313754i
$345$		0			0
$346$	0.869332	+	1.50573i	0.0467356	+	0.0809484i
$347$	−22.2544			−1.19468			−0.597340	−	0.801988i	$-0.703776\pi$
$347$	−22.2544			−1.19468			−0.597340	+	0.801988i	$0.703776\pi$
$348$		0			0
$349$	−5.16027	−	8.93784i	−0.276223	−	0.478432i	0.694220	−	0.719763i	$-0.255749\pi$
$349$	−5.16027	−	8.93784i	−0.276223	−	0.478432i	−0.970443	+	0.241331i	$0.922416\pi$
$350$	8.79642	−	6.88174i	0.470188	−	0.367844i
$351$		0			0
$352$	−0.775934	+	1.34396i	−0.0413574	+	0.0716332i
$353$	−0.485103	+	0.840224i	−0.0258195	+	0.0447206i	−0.878646	−	0.477473i	$-0.841553\pi$
$353$	−0.485103	+	0.840224i	−0.0258195	+	0.0447206i	0.852827	+	0.522194i	$0.174886\pi$
$354$		0			0
$355$	4.42091	+	7.65724i	0.234637	+	0.406404i
$356$	−14.8167			−0.785285
$357$		0			0
$358$	−4.89644	+	8.48088i	−0.258785	+	0.448228i
$359$	1.03017	−	1.78430i	0.0543701	−	0.0941717i	−0.837559	−	0.546346i	$-0.816018\pi$
$359$	1.03017	−	1.78430i	0.0543701	−	0.0941717i	0.891929	+	0.452175i	$0.149352\pi$
$360$		0			0
$361$	−1.74142	+	3.01623i	−0.0916537	+	0.158749i
$362$	11.5901			0.609162
$363$		0			0
$364$	−6.82366	+	6.66615i	−0.357657	+	0.349401i
$365$	−3.41124			−0.178552
$366$		0			0
$367$	4.63538	−	8.02871i	0.241965	−	0.419095i	−0.719309	−	0.694690i	$-0.755542\pi$
$367$	4.63538	−	8.02871i	0.241965	−	0.419095i	0.961274	+	0.275595i	$0.0888749\pi$
$368$	−5.29348			−0.275942
$369$		0			0
$370$	−0.145856	+	0.252631i	−0.00758271	+	0.0131336i
$371$	−28.1027	+	21.9857i	−1.45902	+	1.14144i
$372$		0			0
$373$	3.76618	+	6.52322i	0.195006	+	0.337760i	0.946902	−	0.321521i	$-0.104194\pi$
$373$	3.76618	+	6.52322i	0.195006	+	0.337760i	−0.751897	+	0.659281i	$0.770861\pi$
$374$	−5.56804	+	9.64413i	−0.287917	+	0.498686i
$375$		0			0
$376$	0.976430	−	1.69123i	0.0503555	−	0.0872184i
$377$	11.2343	−	25.5848i	0.578594	−	1.31768i
$378$		0			0
$379$	−8.94169	−	15.4875i	−0.459304	−	0.795537i	0.539621	−	0.841908i	$-0.318568\pi$
$379$	−8.94169	−	15.4875i	−0.459304	−	0.795537i	−0.998924	+	0.0463711i	$0.985234\pi$
$380$	−4.18420			−0.214645
$381$		0			0
$382$	0.631864	+	1.09442i	0.0323290	+	0.0559954i
$383$	−9.09536	−	15.7536i	−0.464751	−	0.804972i	0.534439	−	0.845207i	$-0.320523\pi$
$383$	−9.09536	−	15.7536i	−0.464751	−	0.804972i	−0.999190	+	0.0402346i	$0.987189\pi$
$384$		0			0
$385$	2.85366	−	2.23251i	0.145436	−	0.113779i
$386$	9.49130	−	16.4394i	0.483095	−	0.836745i
$387$		0			0
$388$	5.79259	−	10.0331i	0.294074	−	0.509352i
$389$	−8.54918	−	14.8076i	−0.433461	−	0.750776i	0.563708	−	0.825974i	$-0.309374\pi$
$389$	−8.54918	−	14.8076i	−0.433461	−	0.750776i	−0.997169	+	0.0751984i	$0.976041\pi$
$390$		0			0
$391$	−37.9856			−1.92101
$392$	6.72632	−	1.93822i	0.339730	−	0.0978947i
$393$		0			0
$394$	12.1786	+	21.0939i	0.613548	+	1.06270i
$395$	−5.89408	−	10.2088i	−0.296563	−	0.513663i
$396$		0			0
$397$	−13.8385	−	23.9691i	−0.694536	−	1.20297i	−0.970337	−	0.241757i	$-0.922276\pi$
$397$	−13.8385	−	23.9691i	−0.694536	−	1.20297i	0.275800	−	0.961215i	$-0.411057\pi$
$398$	−21.5059			−1.07799
$399$		0			0
$400$	2.11065	+	3.65575i	0.105532	+	0.182787i
$401$	0.784039			0.0391531			0.0195765	−	0.999808i	$-0.493768\pi$
$401$	0.784039			0.0391531			0.0195765	+	0.999808i	$0.493768\pi$
$402$		0			0
$403$	−9.41983	+	21.4526i	−0.469235	+	1.06863i
$404$	3.91439	−	6.77993i	0.194748	−	0.337314i
$405$		0			0
$406$	−16.1494	+	12.6342i	−0.801480	+	0.627025i
$407$	0.256504	−	0.444277i	0.0127144	−	0.0220220i
$408$		0			0
$409$	25.9739			1.28433			0.642164	−	0.766567i	$-0.278037\pi$
$409$	25.9739			1.28433			0.642164	+	0.766567i	$0.278037\pi$
$410$	−5.34616			−0.264028
$411$		0			0
$412$	0.430172	−	0.745081i	0.0211931	−	0.0367075i
$413$	−1.95000	−	13.8098i	−0.0959531	−	0.679534i
$414$		0			0
$415$	4.65571	−	8.06393i	0.228540	−	0.395843i
$416$	−2.13422	−	2.90605i	−0.104639	−	0.142481i
$417$		0			0
$418$	7.35835			0.359909
$419$	−0.207579	−	0.359537i	−0.0101409	−	0.0175645i	0.860910	−	0.508757i	$-0.169895\pi$
$419$	−0.207579	−	0.359537i	−0.0101409	−	0.0175645i	−0.871051	+	0.491192i	$0.836561\pi$
$420$		0			0
$421$	−8.45284			−0.411966			−0.205983	−	0.978556i	$-0.566039\pi$
$421$	−8.45284			−0.411966			−0.205983	+	0.978556i	$0.566039\pi$
$422$	−3.56775	−	6.17953i	−0.173675	−	0.300815i
$423$		0			0
$424$	−6.74308	−	11.6794i	−0.327473	−	0.567200i
$425$	15.1458	+	26.2334i	0.734681	+	1.27250i
$426$		0			0
$427$	−29.9067	+	23.3970i	−1.44728	+	1.13226i
$428$	8.14260			0.393587
$429$		0			0
$430$	2.96479	+	5.13517i	0.142975	+	0.247640i
$431$	−12.3935	+	21.4662i	−0.596973	+	1.03399i	0.396292	+	0.918125i	$0.370297\pi$
$431$	−12.3935	+	21.4662i	−0.596973	+	1.03399i	−0.993265	+	0.115864i	$0.963036\pi$
$432$		0			0
$433$	18.5723	−	32.1682i	0.892529	−	1.54591i	0.0556964	−	0.998448i	$-0.482262\pi$
$433$	18.5723	−	32.1682i	0.892529	−	1.54591i	0.836833	−	0.547458i	$-0.184405\pi$
$434$	13.5411	−	10.5937i	0.649994	−	0.508512i
$435$		0			0
$436$	4.73806	+	8.20656i	0.226912	+	0.393023i
$437$	12.5498	+	21.7369i	0.600338	+	1.03982i
$438$		0			0
$439$	−8.75366			−0.417790			−0.208895	−	0.977938i	$-0.566987\pi$
$439$	−8.75366			−0.417790			−0.208895	+	0.977938i	$0.566987\pi$
$440$	0.684718	+	1.18597i	0.0326426	+	0.0565387i
$441$		0			0
$442$	−15.3150	−	20.8536i	−0.728459	−	0.991903i
$443$	−1.48601	+	2.57384i	−0.0706023	+	0.122287i	−0.899165	−	0.437609i	$-0.855825\pi$
$443$	−1.48601	+	2.57384i	−0.0706023	+	0.122287i	0.828563	+	0.559896i	$0.189159\pi$
$444$		0			0
$445$	−6.53746	+	11.3232i	−0.309905	+	0.536772i
$446$	12.1673	+	21.0744i	0.576140	+	0.997903i
$447$		0			0
$448$	0.369922	+	2.61976i	0.0174772	+	0.123772i
$449$	−2.95700	+	5.12167i	−0.139549	+	0.241707i	−0.927326	−	0.374254i	$-0.877899\pi$
$449$	−2.95700	+	5.12167i	−0.139549	+	0.241707i	0.787777	+	0.615961i	$0.211232\pi$
$450$		0			0
$451$	9.40178			0.442713
$452$	−5.71537	+	9.89931i	−0.268828	+	0.465624i
$453$		0			0
$454$	9.56035			0.448690
$455$	2.08365	+	8.15602i	0.0976829	+	0.382360i
$456$		0			0
$457$	−14.1933			−0.663935			−0.331968	−	0.943291i	$-0.607712\pi$
$457$	−14.1933			−0.663935			−0.331968	+	0.943291i	$0.607712\pi$
$458$	5.40570	−	9.36295i	0.252592	−	0.437502i
$459$		0			0
$460$	−2.33559	+	4.04537i	−0.108898	+	0.188616i
$461$	−15.1395	+	26.2224i	−0.705117	+	1.22130i	0.261532	+	0.965195i	$0.415772\pi$
$461$	−15.1395	+	26.2224i	−0.705117	+	1.22130i	−0.966649	+	0.256104i	$0.917561\pi$
$462$		0			0
$463$	−32.8167			−1.52512			−0.762561	−	0.646916i	$-0.776059\pi$
$463$	−32.8167			−1.52512			−0.762561	+	0.646916i	$0.776059\pi$
$464$	−3.87494	−	6.71160i	−0.179890	−	0.311578i
$465$		0			0
$466$	−5.15806	+	8.93403i	−0.238943	+	0.413861i
$467$	10.4247	−	18.0562i	0.482399	−	0.835540i	−0.517397	−	0.855746i	$-0.673099\pi$
$467$	10.4247	−	18.0562i	0.482399	−	0.835540i	0.999796	+	0.0202058i	$0.00643214\pi$
$468$		0			0
$469$	18.4147	+	7.42608i	0.850310	+	0.342904i
$470$	−0.861644	−	1.49241i	−0.0397447	−	0.0688398i
$471$		0			0
$472$	5.27138			0.242635
$473$	−5.21390	−	9.03074i	−0.239735	−	0.415234i
$474$		0			0
$475$	10.0079	−	17.3341i	0.459192	−	0.795344i
$476$	2.65453	+	18.7992i	0.121670	+	0.861660i
$477$		0			0
$478$	11.0866			0.507087
$479$	−12.0950	+	20.9492i	−0.552637	+	0.957195i	0.445447	+	0.895308i	$0.353045\pi$
$479$	−12.0950	+	20.9492i	−0.552637	+	0.957195i	−0.998083	+	0.0618862i	$0.980288\pi$
$480$		0			0
$481$	0.705517	+	0.960664i	0.0321688	+	0.0438025i
$482$	18.6739			0.850574
$483$		0			0
$484$	4.29585	+	7.44063i	0.195266	+	0.338211i
$485$	−5.11163	−	8.85361i	−0.232107	−	0.402022i
$486$		0			0
$487$	−40.3065			−1.82646			−0.913230	−	0.407444i	$-0.866420\pi$
$487$	−40.3065			−1.82646			−0.913230	+	0.407444i	$0.866420\pi$
$488$	−7.17592	−	12.4291i	−0.324839	−	0.562637i
$489$		0			0
$490$	1.48658	−	5.99555i	0.0671566	−	0.270851i
$491$	3.58602	+	6.21117i	0.161835	+	0.280306i	0.935527	−	0.353256i	$-0.114925\pi$
$491$	3.58602	+	6.21117i	0.161835	+	0.280306i	−0.773692	+	0.633562i	$0.781592\pi$
$492$		0			0
$493$	−27.8063	−	48.1619i	−1.25233	−	2.16910i
$494$	−6.87345	+	15.6535i	−0.309251	+	0.704285i
$495$		0			0
$496$	3.24911	+	5.62762i	0.145889	+	0.252688i
$497$	−24.5858	−	9.91470i	−1.10282	−	0.444735i
$498$		0			0
$499$	8.24802	−	14.2860i	0.369232	−	0.639528i	−0.620214	−	0.784433i	$-0.712954\pi$
$499$	8.24802	−	14.2860i	0.369232	−	0.639528i	0.989446	+	0.144904i	$0.0462875\pi$
$500$	8.13726			0.363910
$501$		0			0
$502$	0.00354883	−	0.00614676i	0.000158392	−	0.000274343i
$503$	−0.187093	+	0.324055i	−0.00834208	+	0.0144489i	−0.870166	−	0.492758i	$-0.835989\pi$
$503$	−0.187093	+	0.324055i	−0.00834208	+	0.0144489i	0.861824	+	0.507207i	$0.169322\pi$
$504$		0			0
$505$	−3.45423	−	5.98290i	−0.153711	−	0.266236i
$506$	4.10739	−	7.11421i	0.182596	−	0.316265i
$507$		0			0
$508$	3.02592	+	5.24105i	0.134254	+	0.232534i
$509$	−5.26899			−0.233544			−0.116772	−	0.993159i	$-0.537255\pi$
$509$	−5.26899			−0.233544			−0.116772	+	0.993159i	$0.537255\pi$
$510$		0			0
$511$	8.05538	−	6.30200i	0.356349	−	0.278784i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	12.6759			0.559110
$515$	−0.379603	−	0.657491i	−0.0167273	−	0.0289725i
$516$		0			0
$517$	1.51529	+	2.62456i	0.0666424	+	0.115428i
$518$	−0.122287	−	0.866025i	−0.00537296	−	0.0380510i
$519$		0			0
$520$	−3.16252	+	0.348796i	−0.138686	+	0.0152957i
$521$	−3.43343	−	5.94687i	−0.150421	−	0.260537i	0.780961	−	0.624580i	$-0.214730\pi$
$521$	−3.43343	−	5.94687i	−0.150421	−	0.260537i	−0.931382	+	0.364042i	$0.881396\pi$
$522$		0			0
$523$	−2.18445			−0.0955193			−0.0477596	−	0.998859i	$-0.515208\pi$
$523$	−2.18445			−0.0955193			−0.0477596	+	0.998859i	$0.515208\pi$
$524$	2.66045	−	4.60804i	0.116222	−	0.201303i
$525$		0			0
$526$	2.59901	−	4.50161i	0.113322	−	0.196280i
$527$	23.3153	+	40.3833i	1.01563	+	1.75913i
$528$		0			0
$529$	5.02089			0.218299
$530$	−11.9008			−0.516936
$531$		0			0
$532$	9.88066	−	7.72997i	0.428381	−	0.335137i
$533$	−8.78222	+	20.0005i	−0.380400	+	0.866319i
$534$		0			0
$535$	3.59269	−	6.22272i	0.155325	−	0.269032i
$536$	−3.75236	+	6.49929i	−0.162077	+	0.280726i
$537$		0			0
$538$	−0.685009			−0.0295328
$539$	−2.61430	+	10.5438i	−0.112606	+	0.454154i
$540$		0			0
$541$	−18.7629	+	32.4982i	−0.806679	+	1.39721i	0.108473	+	0.994099i	$0.465404\pi$
$541$	−18.7629	+	32.4982i	−0.806679	+	1.39721i	−0.915152	+	0.403109i	$0.867929\pi$
$542$	5.05126			0.216970
$543$		0			0
$544$	−7.17592			−0.307665
$545$	8.36213			0.358194
$546$		0			0
$547$	26.8987			1.15011			0.575054	−	0.818116i	$-0.304981\pi$
$547$	26.8987			1.15011			0.575054	+	0.818116i	$0.304981\pi$
$548$	8.01122			0.342222
$549$		0			0
$550$	−6.55090			−0.279331
$551$	−18.3735	+	31.8238i	−0.782736	+	1.35574i
$552$		0			0
$553$	32.7785	+	13.2186i	1.39388	+	0.562110i
$554$	12.4497			0.528937
$555$		0			0
$556$	8.87582	−	15.3734i	0.376419	−	0.651976i
$557$	1.58336	−	2.74245i	0.0670889	−	0.116201i	−0.830530	−	0.556974i	$-0.811962\pi$
$557$	1.58336	−	2.74245i	0.0670889	−	0.116201i	0.897619	+	0.440773i	$0.145296\pi$
$558$		0			0
$559$	24.0815	−	2.65597i	1.01854	−	0.112335i
$560$	2.16529	+	0.873194i	0.0915001	+	0.0368992i
$561$		0			0
$562$	−23.5917			−0.995154
$563$	−30.8984			−1.30221			−0.651106	−	0.758987i	$-0.725694\pi$
$563$	−30.8984			−1.30221			−0.651106	+	0.758987i	$0.725694\pi$
$564$		0			0
$565$	5.04349	+	8.73558i	0.212181	+	0.367508i
$566$	10.5148	−	18.2121i	0.441969	−	0.765512i
$567$		0			0
$568$	5.00985	−	8.67732i	0.210209	−	0.364092i
$569$	−11.7828			−0.493962			−0.246981	−	0.969020i	$-0.579439\pi$
$569$	−11.7828			−0.493962			−0.246981	+	0.969020i	$0.579439\pi$
$570$		0			0
$571$	−11.9777	−	20.7459i	−0.501250	−	0.868190i	−0.999999	−	0.00144398i	$-0.999540\pi$
$571$	−11.9777	−	20.7459i	−0.501250	−	0.868190i	0.498749	−	0.866746i	$-0.333793\pi$
$572$	5.56162	−	0.613395i	0.232543	−	0.0256473i
$573$		0			0
$574$	12.6245	−	9.87660i	0.526938	−	0.412241i
$575$	−11.1727	−	19.3516i	−0.465932	−	0.807018i
$576$		0			0
$577$	−13.2068	−	22.8748i	−0.549805	−	0.952291i	−0.998287	−	0.0584990i	$-0.981369\pi$
$577$	−13.2068	−	22.8748i	−0.549805	−	0.952291i	0.448482	−	0.893792i	$-0.351965\pi$
$578$	−34.4938			−1.43475
$579$		0			0
$580$	−6.83883			−0.283967
$581$	3.90337	+	27.6434i	0.161939	+	1.14684i
$582$		0			0
$583$	20.9287			0.866780
$584$	1.93284	+	3.34778i	0.0799815	+	0.138532i
$585$		0			0
$586$	−6.41251	+	11.1068i	−0.264898	+	0.458817i
$587$	−15.3403	−	26.5702i	−0.633162	−	1.09667i	−0.986901	−	0.161325i	$-0.948423\pi$
$587$	−15.3403	−	26.5702i	−0.633162	−	1.09667i	0.353739	−	0.935344i	$-0.384910\pi$
$588$		0			0
$589$	15.4060	−	26.6840i	0.634793	−	1.09949i
$590$	2.32584	−	4.02848i	0.0957535	−	0.165850i
$591$		0			0
$592$	0.330574			0.0135865
$593$	−6.14941	+	10.6511i	−0.252526	+	0.437388i	−0.964221	−	0.265101i	$-0.914595\pi$
$593$	−6.14941	+	10.6511i	−0.252526	+	0.437388i	0.711695	+	0.702489i	$0.247928\pi$
$594$		0			0
$595$	15.5379	+	6.26597i	0.636993	+	0.256880i
$596$	8.66161	+	15.0024i	0.354793	+	0.614520i
$597$		0			0
$598$	11.2974	+	15.3831i	0.461986	+	0.629062i
$599$	3.22732	+	5.58989i	0.131865	+	0.228397i	0.924395	−	0.381436i	$-0.124570\pi$
$599$	3.22732	+	5.58989i	0.131865	+	0.228397i	−0.792531	+	0.609832i	$0.791237\pi$
$600$		0			0
$601$	−1.05552	−	1.82822i	−0.0430556	−	0.0745745i	0.843695	−	0.536824i	$-0.180376\pi$
$601$	−1.05552	−	1.82822i	−0.0430556	−	0.0745745i	−0.886750	+	0.462249i	$0.847043\pi$
$602$	−16.4879	−	6.64909i	−0.671998	−	0.270997i
$603$		0			0
$604$	−1.40927	−	2.44093i	−0.0573424	−	0.0993199i
$605$	7.58169			0.308239
$606$		0			0
$607$	−12.5828	−	21.7941i	−0.510722	−	0.884596i	−0.999923	−	0.0124247i	$-0.996045\pi$
$607$	−12.5828	−	21.7941i	−0.510722	−	0.884596i	0.489201	−	0.872171i	$-0.337288\pi$
$608$	2.37080	+	4.10635i	0.0961488	+	0.166535i
$609$		0			0
$610$	−12.6647			−0.512778
$611$	−6.99870	+	0.771892i	−0.283137	+	0.0312274i
$612$		0			0
$613$	12.7273	−	22.0444i	0.514052	−	0.890364i	−0.485815	−	0.874061i	$-0.661477\pi$
$613$	12.7273	−	22.0444i	0.514052	−	0.890364i	0.999867	−	0.0163023i	$-0.00518940\pi$
$614$	20.4988			0.827263
$615$		0			0
$616$	−3.80789	−	1.53560i	−0.153424	−	0.0618713i
$617$	−16.4252	+	28.4493i	−0.661254	+	1.14532i	0.319033	+	0.947744i	$0.396642\pi$
$617$	−16.4252	+	28.4493i	−0.661254	+	1.14532i	−0.980287	+	0.197581i	$0.936691\pi$
$618$		0			0
$619$	0.180058	+	0.311869i	0.00723713	+	0.0125351i	0.869621	−	0.493719i	$-0.164363\pi$
$619$	0.180058	+	0.311869i	0.00723713	+	0.0125351i	−0.862384	+	0.506254i	$0.831030\pi$
$620$	5.73430			0.230295
$621$		0			0
$622$	7.06023	+	12.2287i	0.283089	+	0.490325i
$623$	−5.48103	−	38.8163i	−0.219593	−	1.55514i
$624$		0			0
$625$	−6.96290	+	12.0601i	−0.278516	+	0.482404i
$626$	−14.5296	+	25.1661i	−0.580721	+	1.00584i
$627$		0			0
$628$	6.39822	+	11.0820i	0.255317	+	0.442222i
$629$	2.37217			0.0945847
$630$		0			0
$631$	−7.36478	+	12.7562i	−0.293187	+	0.507815i	−0.974562	−	0.224120i	$-0.928049\pi$
$631$	−7.36478	+	12.7562i	−0.293187	+	0.507815i	0.681374	+	0.731935i	$0.261383\pi$
$632$	−6.67928	+	11.5689i	−0.265687	+	0.460184i
$633$		0			0
$634$	−6.08027	+	10.5313i	−0.241478	+	0.418253i
$635$	5.34041			0.211928
$636$		0			0
$637$	−19.9880	−	15.4104i	−0.791952	−	0.610583i
$638$	12.0268			0.476146
$639$		0			0
$640$	−0.441221	+	0.764218i	−0.0174408	+	0.0302084i
$641$	48.3368			1.90919			0.954595	−	0.297906i	$-0.0962883\pi$
$641$	48.3368			1.90919			0.954595	+	0.297906i	$0.0962883\pi$
$642$		0			0
$643$	−0.0861739	+	0.149258i	−0.00339837	+	0.00588614i	−0.867720	−	0.497054i	$-0.834415\pi$
$643$	−0.0861739	+	0.149258i	−0.00339837	+	0.00588614i	0.864321	+	0.502940i	$0.167748\pi$
$644$	−1.95817	−	13.8677i	−0.0771628	−	0.546462i
$645$		0			0
$646$	17.0127	+	29.4669i	0.669355	+	1.15936i
$647$	13.9682	−	24.1937i	0.549147	−	0.951151i	−0.449186	−	0.893438i	$-0.648286\pi$
$647$	13.9682	−	24.1937i	0.549147	−	0.951151i	0.998333	−	0.0577129i	$-0.0183808\pi$
$648$		0			0
$649$	−4.09024	+	7.08451i	−0.160556	+	0.278091i
$650$	6.11920	−	13.9358i	0.240015	−	0.546607i
$651$		0			0
$652$	5.34387	+	9.25586i	0.209282	+	0.362487i
$653$	41.8489			1.63767			0.818836	−	0.574027i	$-0.194620\pi$
$653$	41.8489			1.63767			0.818836	+	0.574027i	$0.194620\pi$
$654$		0			0
$655$	−2.34770	−	4.06633i	−0.0917322	−	0.158885i
$656$	3.02918	+	5.24669i	0.118270	+	0.204849i
$657$		0			0
$658$	4.79182	+	1.93239i	0.186804	+	0.0753326i
$659$	−3.26341	+	5.65240i	−0.127125	+	0.220186i	−0.922561	−	0.385850i	$-0.873908\pi$
$659$	−3.26341	+	5.65240i	−0.127125	+	0.220186i	0.795437	+	0.606036i	$0.207241\pi$
$660$		0			0
$661$	−0.526326	+	0.911623i	−0.0204717	+	0.0354580i	−0.876080	−	0.482166i	$-0.839850\pi$
$661$	−0.526326	+	0.911623i	−0.0204717	+	0.0354580i	0.855608	+	0.517624i	$0.173183\pi$
$662$	4.96685	+	8.60284i	0.193042	+	0.334359i
$663$		0			0
$664$	−10.5519			−0.409492
$665$	−1.54783	−	10.9616i	−0.0600221	−	0.425073i
$666$		0			0
$667$	20.5119	+	35.5277i	0.794225	+	1.37564i
$668$	9.90412	+	17.1544i	0.383202	+	0.663725i
$669$		0			0
$670$	3.31125	+	5.73525i	0.127925	+	0.221572i
$671$	22.2722			0.859808
$672$		0			0
$673$	−13.1957	−	22.8556i	−0.508655	−	0.881017i	−0.999950	−	0.0100234i	$-0.996809\pi$
$673$	−13.1957	−	22.8556i	−0.508655	−	0.881017i	0.491294	−	0.870994i	$-0.336524\pi$
$674$	3.38360			0.130331
$675$		0			0
$676$	−3.89023	+	12.4043i	−0.149624	+	0.477088i
$677$	10.3481	−	17.9235i	0.397711	−	0.688856i	−0.595732	−	0.803183i	$-0.703138\pi$
$677$	10.3481	−	17.9235i	0.397711	−	0.688856i	0.993443	+	0.114327i	$0.0364713\pi$
$678$		0			0
$679$	28.4271	+	11.4638i	1.09093	+	0.439939i
$680$	−3.16617	+	5.48396i	−0.121417	+	0.210300i
$681$		0			0
$682$	−10.0844			−0.386151
$683$	36.9788			1.41495			0.707477	−	0.706736i	$-0.249833\pi$
$683$	36.9788			1.41495			0.707477	+	0.706736i	$0.249833\pi$
$684$		0			0
$685$	3.53472	−	6.12232i	0.135055	−	0.233922i
$686$	7.56588	+	16.9044i	0.288866	+	0.645412i
$687$		0			0
$688$	3.35975	−	5.81927i	0.128089	−	0.221857i
$689$	−19.5496	+	44.5220i	−0.744780	+	1.69615i
$690$		0			0
$691$	3.51208			0.133606			0.0668029	−	0.997766i	$-0.478720\pi$
$691$	3.51208			0.133606			0.0668029	+	0.997766i	$0.478720\pi$
$692$	−0.869332	−	1.50573i	−0.0330470	−	0.0572391i
$693$		0			0
$694$	22.2544			0.844766
$695$	−7.83241	−	13.5661i	−0.297100	−	0.514593i
$696$		0			0
$697$	21.7372	+	37.6499i	0.823353	+	1.42609i
$698$	5.16027	+	8.93784i	0.195319	+	0.338302i
$699$		0			0
$700$	−8.79642	+	6.88174i	−0.332473	+	0.260105i
$701$	9.53390			0.360090			0.180045	−	0.983658i	$-0.442376\pi$
$701$	9.53390			0.360090			0.180045	+	0.983658i	$0.442376\pi$
$702$		0			0
$703$	−0.783726	−	1.35745i	−0.0295588	−	0.0511973i
$704$	0.775934	−	1.34396i	0.0292441	−	0.0506523i
$705$		0			0
$706$	0.485103	−	0.840224i	0.0182571	−	0.0316222i
$707$	19.2098	+	7.74674i	0.722460	+	0.291346i
$708$		0			0
$709$	−9.56380	−	16.5650i	−0.359176	−	0.622111i	0.628647	−	0.777690i	$-0.283609\pi$
$709$	−9.56380	−	16.5650i	−0.359176	−	0.622111i	−0.987823	+	0.155579i	$0.950276\pi$
$710$	−4.42091	−	7.65724i	−0.165914	−	0.287371i
$711$		0			0
$712$	14.8167			0.555281
$713$	−17.1991	−	29.7897i	−0.644110	−	1.11563i
$714$		0			0
$715$	1.98514	−	4.52093i	0.0742399	−	0.169073i
$716$	4.89644	−	8.48088i	0.182988	−	0.316945i
$717$		0			0
$718$	−1.03017	+	1.78430i	−0.0384455	+	0.0665895i
$719$	−13.8837	−	24.0473i	−0.517775	−	0.896812i	−0.999787	−	0.0206477i	$-0.993427\pi$
$719$	−13.8837	−	24.0473i	−0.517775	−	0.896812i	0.482012	−	0.876165i	$-0.339906\pi$
$720$		0			0
$721$	2.11106	+	0.851328i	0.0786202	+	0.0317051i
$722$	1.74142	−	3.01623i	0.0648089	−	0.112252i
$723$		0			0
$724$	−11.5901			−0.430743
$725$	16.3573	−	28.3316i	0.607494	−	1.05221i
$726$		0			0
$727$	27.4082			1.01651			0.508257	−	0.861205i	$-0.330290\pi$
$727$	27.4082			1.01651			0.508257	+	0.861205i	$0.330290\pi$
$728$	6.82366	−	6.66615i	0.252902	−	0.247064i
$729$		0			0
$730$	3.41124			0.126256
$731$	24.1093	−	41.7586i	0.891716	−	1.54450i
$732$		0			0
$733$	9.70789	−	16.8146i	0.358569	−	0.621060i	−0.629153	−	0.777282i	$-0.716598\pi$
$733$	9.70789	−	16.8146i	0.358569	−	0.621060i	0.987722	+	0.156222i	$0.0499314\pi$
$734$	−4.63538	+	8.02871i	−0.171095	+	0.296345i
$735$		0			0
$736$	5.29348			0.195120
$737$	−5.82318	−	10.0860i	−0.214500	−	0.371524i
$738$		0			0
$739$	−7.58084	+	13.1304i	−0.278866	+	0.483010i	−0.971103	−	0.238660i	$-0.923292\pi$
$739$	−7.58084	+	13.1304i	−0.278866	+	0.483010i	0.692237	+	0.721670i	$0.256625\pi$
$740$	0.145856	−	0.252631i	0.00536178	−	0.00928688i
$741$		0			0
$742$	28.1027	−	21.9857i	1.03168	−	0.807121i
$743$	5.85184	+	10.1357i	0.214683	+	0.371842i	0.953174	−	0.302421i	$-0.0977948\pi$
$743$	5.85184	+	10.1357i	0.214683	+	0.371842i	−0.738491	+	0.674263i	$0.764461\pi$
$744$		0			0
$745$	15.2868			0.560063
$746$	−3.76618	−	6.52322i	−0.137890	−	0.238832i
$747$		0			0
$748$	5.56804	−	9.64413i	0.203588	−	0.352624i
$749$	3.01213	+	21.3317i	0.110061	+	0.779443i
$750$		0			0
$751$	36.7832			1.34224			0.671119	−	0.741350i	$-0.265814\pi$
$751$	36.7832			1.34224			0.671119	+	0.741350i	$0.265814\pi$
$752$	−0.976430	+	1.69123i	−0.0356067	+	0.0616727i
$753$		0			0
$754$	−11.2343	+	25.5848i	−0.409128	+	0.931743i
$755$	−2.48720			−0.0905185
$756$		0			0
$757$	0.469542	+	0.813271i	0.0170658	+	0.0295589i	0.874432	−	0.485148i	$-0.161234\pi$
$757$	0.469542	+	0.813271i	0.0170658	+	0.0295589i	−0.857366	+	0.514707i	$0.827901\pi$
$758$	8.94169	+	15.4875i	0.324777	+	0.562530i
$759$		0			0
$760$	4.18420			0.151777
$761$	−2.83559	−	4.91139i	−0.102790	−	0.178038i	0.810043	−	0.586370i	$-0.199444\pi$
$761$	−2.83559	−	4.91139i	−0.102790	−	0.178038i	−0.912833	+	0.408333i	$0.866110\pi$
$762$		0			0
$763$	−19.7465	+	15.4484i	−0.714872	+	0.559269i
$764$	−0.631864	−	1.09442i	−0.0228600	−	0.0395947i
$765$		0			0
$766$	9.09536	+	15.7536i	0.328629	+	0.569201i
$767$	−11.2503	−	15.3189i	−0.406224	−	0.553133i
$768$		0			0
$769$	0.775934	+	1.34396i	0.0279809	+	0.0484644i	0.879677	−	0.475572i	$-0.157759\pi$
$769$	0.775934	+	1.34396i	0.0279809	+	0.0484644i	−0.851696	+	0.524036i	$0.824426\pi$
$770$	−2.85366	+	2.23251i	−0.102839	+	0.0804542i
$771$		0			0
$772$	−9.49130	+	16.4394i	−0.341600	+	0.591668i
$773$	29.3595			1.05599			0.527994	−	0.849248i	$-0.322944\pi$
$773$	29.3595			1.05599			0.527994	+	0.849248i	$0.322944\pi$
$774$		0			0
$775$	−13.7154	+	23.7558i	−0.492673	+	0.853335i
$776$	−5.79259	+	10.0331i	−0.207942	+	0.360166i
$777$		0			0
$778$	8.54918	+	14.8076i	0.306503	+	0.530879i
$779$	14.3632	−	24.8778i	0.514615	−	0.891338i
$780$		0			0
$781$	7.77464	+	13.4661i	0.278198	+	0.481854i
$782$	37.9856			1.35836
$783$		0			0
$784$	−6.72632	+	1.93822i	−0.240226	+	0.0692220i
$785$	11.2921			0.403033
$786$		0			0
$787$	−18.3264			−0.653265			−0.326632	−	0.945151i	$-0.605914\pi$
$787$	−18.3264			−0.653265			−0.326632	+	0.945151i	$0.605914\pi$
$788$	−12.1786	−	21.0939i	−0.433844	−	0.751440i
$789$		0			0
$790$	5.89408	+	10.2088i	0.209702	+	0.363215i
$791$	−28.0481	−	11.3109i	−0.997275	−	0.402171i
$792$		0			0
$793$	−20.8045	+	47.3799i	−0.738788	+	1.68251i
$794$	13.8385	+	23.9691i	0.491111	+	0.850630i
$795$		0			0
$796$	21.5059			0.762255
$797$	−6.67504	+	11.5615i	−0.236442	+	0.409529i	−0.959691	−	0.281058i	$-0.909315\pi$
$797$	−6.67504	+	11.5615i	−0.236442	+	0.409529i	0.723249	+	0.690588i	$0.242648\pi$
$798$		0			0
$799$	−7.00678	+	12.1361i	−0.247882	+	0.429345i
$800$	−2.11065	−	3.65575i	−0.0746227	−	0.129250i
$801$		0			0
$802$	−0.784039			−0.0276854
$803$	−5.99903			−0.211701
$804$		0			0
$805$	−11.4619	−	4.62223i	−0.403979	−	0.162912i
$806$	9.41983	−	21.4526i	0.331799	−	0.755636i
$807$		0			0
$808$	−3.91439	+	6.77993i	−0.137708	+	0.238517i
$809$	−16.1928	+	28.0467i	−0.569307	+	0.986069i	0.427327	+	0.904097i	$0.359455\pi$
$809$	−16.1928	+	28.0467i	−0.569307	+	0.986069i	−0.996635	+	0.0819722i	$0.973878\pi$
$810$		0			0
$811$	−11.1640			−0.392022			−0.196011	−	0.980602i	$-0.562799\pi$
$811$	−11.1640			−0.392022			−0.196011	+	0.980602i	$0.562799\pi$
$812$	16.1494	−	12.6342i	0.566732	−	0.443373i
$813$		0			0
$814$	−0.256504	+	0.444277i	−0.00899045	+	0.0155719i
$815$	9.43132			0.330365
$816$		0			0
$817$	−31.8613			−1.11468
$818$	−25.9739			−0.908157
$819$		0			0
$820$	5.34616			0.186696
$821$	31.7025			1.10643			0.553213	−	0.833040i	$-0.313402\pi$
$821$	31.7025			1.10643			0.553213	+	0.833040i	$0.313402\pi$
$822$		0			0
$823$	52.5002			1.83004			0.915022	−	0.403405i	$-0.132173\pi$
$823$	52.5002			1.83004			0.915022	+	0.403405i	$0.132173\pi$
$824$	−0.430172	+	0.745081i	−0.0149858	+	0.0259561i
$825$		0			0
$826$	1.95000	+	13.8098i	0.0678491	+	0.480503i
$827$	−33.4939			−1.16470			−0.582348	−	0.812939i	$-0.697866\pi$
$827$	−33.4939			−1.16470			−0.582348	+	0.812939i	$0.697866\pi$
$828$		0			0
$829$	19.0624	−	33.0170i	0.662064	−	1.14673i	−0.318008	−	0.948088i	$-0.603014\pi$
$829$	19.0624	−	33.0170i	0.662064	−	1.14673i	0.980072	−	0.198641i	$-0.0636528\pi$
$830$	−4.65571	+	8.06393i	−0.161602	+	0.279903i
$831$		0			0
$832$	2.13422	+	2.90605i	0.0739907	+	0.100749i
$833$	−48.2675	+	13.9085i	−1.67237	+	0.481900i
$834$		0			0
$835$	17.4796			0.604908
$836$	−7.35835			−0.254494
$837$		0			0
$838$	0.207579	+	0.359537i	0.00717069	+	0.0124200i
$839$	−12.6246	+	21.8665i	−0.435851	+	0.754916i	−0.997365	−	0.0725514i	$-0.976886\pi$
$839$	−12.6246	+	21.8665i	−0.435851	+	0.754916i	0.561514	+	0.827467i	$0.310219\pi$
$840$		0			0
$841$	−15.5304	+	26.8994i	−0.535530	+	0.927565i
$842$	8.45284			0.291304
$843$		0			0
$844$	3.56775	+	6.17953i	0.122807	+	0.212708i
$845$	7.76311	+	8.44602i	0.267059	+	0.290552i
$846$		0			0
$847$	−17.9036	+	14.0066i	−0.615174	+	0.481271i
$848$	6.74308	+	11.6794i	0.231558	+	0.401071i
$849$		0			0
$850$	−15.1458	−	26.2334i	−0.519498	−	0.899797i
$851$	−1.74989			−0.0599853
$852$		0			0
$853$	30.1001			1.03061			0.515304	−	0.857007i	$-0.327679\pi$
$853$	30.1001			1.03061			0.515304	+	0.857007i	$0.327679\pi$
$854$	29.9067	−	23.3970i	1.02338	−	0.800628i
$855$		0			0
$856$	−8.14260			−0.278308
$857$	11.8157	+	20.4655i	0.403618	+	0.699087i	0.994160	−	0.107920i	$-0.0344191\pi$
$857$	11.8157	+	20.4655i	0.403618	+	0.699087i	−0.590541	+	0.807007i	$0.701086\pi$
$858$		0			0
$859$	−17.7282	+	30.7061i	−0.604878	+	1.04768i	0.387193	+	0.921999i	$0.373445\pi$
$859$	−17.7282	+	30.7061i	−0.604878	+	1.04768i	−0.992071	+	0.125680i	$0.959889\pi$
$860$	−2.96479	−	5.13517i	−0.101099	−	0.175108i
$861$		0			0
$862$	12.3935	−	21.4662i	0.422124	−	0.731140i
$863$	−0.0283138	+	0.0490410i	−0.000963813	+	0.00166937i	−0.866507	−	0.499165i	$-0.833640\pi$
$863$	−0.0283138	+	0.0490410i	−0.000963813	+	0.00166937i	0.865543	+	0.500834i	$0.166973\pi$
$864$		0			0
$865$	−1.53427			−0.0521668
$866$	−18.5723	+	32.1682i	−0.631114	+	1.09312i
$867$		0			0
$868$	−13.5411	+	10.5937i	−0.459615	+	0.359573i
$869$	−10.3654	−	17.9533i	−0.351621	−	0.609025i
$870$		0			0
$871$	26.8956	−	2.96633i	0.911323	−	0.100510i
$872$	−4.73806	−	8.20656i	−0.160451	−	0.277909i
$873$		0			0
$874$	−12.5498	−	21.7369i	−0.424503	−	0.735261i
$875$	3.01015	+	21.3177i	0.101762	+	0.720670i
$876$		0			0
$877$	−17.0082	−	29.4590i	−0.574324	−	0.994759i	−0.996115	−	0.0880657i	$-0.971931\pi$
$877$	−17.0082	−	29.4590i	−0.574324	−	0.994759i	0.421790	−	0.906693i	$-0.361402\pi$
$878$	8.75366			0.295422
$879$		0			0
$880$	−0.684718	−	1.18597i	−0.0230818	−	0.0399789i
$881$	−19.0164	−	32.9374i	−0.640680	−	1.10969i	−0.985281	−	0.170941i	$-0.945319\pi$
$881$	−19.0164	−	32.9374i	−0.640680	−	1.10969i	0.344601	−	0.938749i	$-0.388014\pi$
$882$		0			0
$883$	22.6536			0.762356			0.381178	−	0.924502i	$-0.375519\pi$
$883$	22.6536			0.762356			0.381178	+	0.924502i	$0.375519\pi$
$884$	15.3150	+	20.8536i	0.515098	+	0.701381i
$885$		0			0
$886$	1.48601	−	2.57384i	0.0499234	−	0.0864698i
$887$	−21.3076			−0.715441			−0.357720	−	0.933829i	$-0.616446\pi$
$887$	−21.3076			−0.715441			−0.357720	+	0.933829i	$0.616446\pi$
$888$		0			0
$889$	−12.6110	+	9.86598i	−0.422958	+	0.330894i
$890$	6.53746	−	11.3232i	0.219136	−	0.379555i
$891$		0			0
$892$	−12.1673	−	21.0744i	−0.407392	−	0.705624i
$893$	9.25970			0.309864
$894$		0			0
$895$	−4.32082	−	7.48389i	−0.144429	−	0.250159i
$896$	−0.369922	−	2.61976i	−0.0123582	−	0.0875201i
$897$		0			0
$898$	2.95700	−	5.12167i	0.0986764	−	0.170912i
$899$	25.1802	−	43.6134i	0.839807	−	1.45459i
$900$		0			0
$901$	48.3878	+	83.8101i	1.61203	+	2.79212i
$902$	−9.40178			−0.313045
$903$		0			0
$904$	5.71537	−	9.89931i	0.190090	−	0.329246i
$905$	−5.11380	+	8.85736i	−0.169989	+	0.294429i
$906$		0			0
$907$	−26.7022	+	46.2496i	−0.886632	+	1.53569i	−0.0428006	+	0.999084i	$0.513628\pi$
$907$	−26.7022	+	46.2496i	−0.886632	+	1.53569i	−0.843832	+	0.536608i	$0.819705\pi$
$908$	−9.56035			−0.317271
$909$		0			0
$910$	−2.08365	−	8.15602i	−0.0690722	−	0.270369i
$911$	−5.96942			−0.197776			−0.0988878	−	0.995099i	$-0.531528\pi$
$911$	−5.96942			−0.197776			−0.0988878	+	0.995099i	$0.531528\pi$
$912$		0			0
$913$	8.18756	−	14.1813i	0.270969	−	0.469331i
$914$	14.1933			0.469473
$915$		0			0
$916$	−5.40570	+	9.36295i	−0.178609	+	0.309360i
$917$	13.0561	+	5.26514i	0.431152	+	0.173870i
$918$		0			0
$919$	13.4203	+	23.2446i	0.442695	+	0.766770i	0.997888	−	0.0649513i	$-0.0206892\pi$
$919$	13.4203	+	23.2446i	0.442695	+	0.766770i	−0.555194	+	0.831721i	$0.687356\pi$
$920$	2.33559	−	4.04537i	0.0770023	−	0.133372i
$921$		0			0
$922$	15.1395	−	26.2224i	0.498593	−	0.863589i
$923$	−35.9088	+	3.96041i	−1.18195	+	0.130358i
$924$		0			0
$925$	0.697725	+	1.20850i	0.0229411	+	0.0397351i
$926$	32.8167			1.07842
$927$		0			0
$928$	3.87494	+	6.71160i	0.127201	+	0.220319i
$929$	−4.10661	−	7.11286i	−0.134734	−	0.233365i	0.790762	−	0.612124i	$-0.209685\pi$
$929$	−4.10661	−	7.11286i	−0.134734	−	0.233365i	−0.925496	+	0.378758i	$0.876351\pi$
$930$		0			0
$931$	23.9058	+	23.0255i	0.783480	+	0.754630i
$932$	5.15806	−	8.93403i	0.168958	−	0.292644i
$933$		0			0
$934$	−10.4247	+	18.0562i	−0.341108	+	0.590816i
$935$	−4.91348	−	8.51039i	−0.160688	−	0.278320i
$936$		0			0
$937$	−22.5249			−0.735855			−0.367927	−	0.929854i	$-0.619933\pi$
$937$	−22.5249			−0.735855			−0.367927	+	0.929854i	$0.619933\pi$
$938$	−18.4147	−	7.42608i	−0.601260	−	0.242470i
$939$		0			0
$940$	0.861644	+	1.49241i	0.0281037	+	0.0486771i
$941$	7.98410	+	13.8289i	0.260274	+	0.450808i	0.966315	−	0.257363i	$-0.0828537\pi$
$941$	7.98410	+	13.8289i	0.260274	+	0.450808i	−0.706040	+	0.708172i	$0.749520\pi$
$942$		0			0
$943$	−16.0349	−	27.7733i	−0.522168	−	0.904422i
$944$	−5.27138			−0.171569
$945$		0			0
$946$	5.21390	+	9.03074i	0.169518	+	0.293615i
$947$	1.35007			0.0438715			0.0219358	−	0.999759i	$-0.493017\pi$
$947$	1.35007			0.0438715			0.0219358	+	0.999759i	$0.493017\pi$
$948$		0			0
$949$	5.60370	−	12.7618i	0.181904	−	0.414266i
$950$	−10.0079	+	17.3341i	−0.324698	+	0.562393i
$951$		0			0
$952$	−2.65453	−	18.7992i	−0.0860338	−	0.609286i
$953$	21.1684	−	36.6647i	0.685711	−	1.18769i	−0.287502	−	0.957780i	$-0.592825\pi$
$953$	21.1684	−	36.6647i	0.685711	−	1.18769i	0.973213	−	0.229906i	$-0.0738420\pi$
$954$		0			0
$955$	−1.11517			−0.0360860
$956$	−11.0866			−0.358565
$957$		0			0
$958$	12.0950	−	20.9492i	0.390773	−	0.676839i
$959$	2.96353	+	20.9875i	0.0956973	+	0.677722i
$960$		0			0
$961$	−5.61340	+	9.72269i	−0.181077	+	0.313635i
$962$	−0.705517	−	0.960664i	−0.0227468	−	0.0309730i
$963$		0			0
$964$	−18.6739			−0.601447
$965$	8.37553	+	14.5068i	0.269618	+	0.466992i
$966$		0			0
$967$	−24.2814			−0.780838			−0.390419	−	0.920637i	$-0.627670\pi$
$967$	−24.2814			−0.780838			−0.390419	+	0.920637i	$0.627670\pi$
$968$	−4.29585	−	7.44063i	−0.138074	−	0.239151i
$969$		0			0
$970$	5.11163	+	8.85361i	0.164125	+	0.284272i
$971$	−12.3692	−	21.4241i	−0.396946	−	0.687531i	0.596401	−	0.802686i	$-0.296597\pi$
$971$	−12.3692	−	21.4241i	−0.396946	−	0.687531i	−0.993347	+	0.115155i	$0.963263\pi$
$972$		0			0
$973$	43.5580	+	17.5656i	1.39640	+	0.563127i
$974$	40.3065			1.29150
$975$		0			0
$976$	7.17592	+	12.4291i	0.229696	+	0.397844i
$977$	−2.83780	+	4.91521i	−0.0907892	+	0.157251i	−0.907843	−	0.419309i	$-0.862272\pi$
$977$	−2.83780	+	4.91521i	−0.0907892	+	0.157251i	0.817054	+	0.576561i	$0.195606\pi$
$978$		0			0
$979$	−11.4968	+	19.9131i	−0.367440	+	0.636424i
$980$	−1.48658	+	5.99555i	−0.0474869	+	0.191521i
$981$		0			0
$982$	−3.58602	−	6.21117i	−0.114435	−	0.198207i
$983$	14.6863	+	25.4374i	0.468419	+	0.811326i	0.999349	−	0.0360900i	$-0.0114903\pi$
$983$	14.6863	+	25.4374i	0.468419	+	0.811326i	−0.530929	+	0.847416i	$0.678157\pi$
$984$		0			0
$985$	−21.4938			−0.684850
$986$	27.8063	+	48.1619i	0.885532	+	1.53379i
$987$		0			0
$988$	6.87345	−	15.6535i	0.218674	−	0.498005i
$989$	−17.7848	+	30.8041i	−0.565523	+	0.979515i
$990$		0			0
$991$	−2.80304	+	4.85500i	−0.0890414	+	0.154224i	−0.907106	−	0.420902i	$-0.861714\pi$
$991$	−2.80304	+	4.85500i	−0.0890414	+	0.154224i	0.818065	+	0.575126i	$0.195047\pi$
$992$	−3.24911	−	5.62762i	−0.103159	−	0.178677i
$993$		0			0
$994$	24.5858	+	9.91470i	0.779814	+	0.314475i
$995$	9.48885	−	16.4352i	0.300817	−	0.521030i
$996$		0			0
$997$	52.0689			1.64904			0.824520	−	0.565833i	$-0.191445\pi$
$997$	52.0689			1.64904			0.824520	+	0.565833i	$0.191445\pi$
$998$	−8.24802	+	14.2860i	−0.261086	+	0.452215i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.m.h.289.3		8
3.2	odd	2		546.2.j.c.289.2	✓	8
7.4	even	3		1638.2.p.h.991.3		8
13.9	even	3		1638.2.p.h.919.3		8
21.11	odd	6		546.2.k.c.445.2	yes	8
39.35	odd	6		546.2.k.c.373.2	yes	8
91.74	even	3	inner	1638.2.m.h.1621.3		8
273.74	odd	6		546.2.j.c.529.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.c.289.2	✓	8	3.2	odd	2
546.2.j.c.529.2	yes	8	273.74	odd	6
546.2.k.c.373.2	yes	8	39.35	odd	6
546.2.k.c.445.2	yes	8	21.11	odd	6
1638.2.m.h.289.3		8	1.1	even	1	trivial
1638.2.m.h.1621.3		8	91.74	even	3	inner
1638.2.p.h.919.3		8	13.9	even	3
1638.2.p.h.991.3		8	7.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.m (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.441221 - 0.764218i) q^{5} +(0.369922 + 2.61976i) q^{7} -1.00000 q^{8} +(-0.441221 + 0.764218i) q^{10} +(0.775934 - 1.34396i) q^{11} +(2.13422 + 2.90605i) q^{13} +(-0.369922 - 2.61976i) q^{14} +1.00000 q^{16} +7.17592 q^{17} +(-2.37080 - 4.10635i) q^{19} +(0.441221 - 0.764218i) q^{20} +(-0.775934 + 1.34396i) q^{22} -5.29348 q^{23} +(2.11065 + 3.65575i) q^{25} +(-2.13422 - 2.90605i) q^{26} +(0.369922 + 2.61976i) q^{28} +(-3.87494 - 6.71160i) q^{29} +(3.24911 + 5.62762i) q^{31} -1.00000 q^{32} -7.17592 q^{34} +(2.16529 + 0.873194i) q^{35} +0.330574 q^{37} +(2.37080 + 4.10635i) q^{38} +(-0.441221 + 0.764218i) q^{40} +(3.02918 + 5.24669i) q^{41} +(3.35975 - 5.81927i) q^{43} +(0.775934 - 1.34396i) q^{44} +5.29348 q^{46} +(-0.976430 + 1.69123i) q^{47} +(-6.72632 + 1.93822i) q^{49} +(-2.11065 - 3.65575i) q^{50} +(2.13422 + 2.90605i) q^{52} +(6.74308 + 11.6794i) q^{53} +(-0.684718 - 1.18597i) q^{55} +(-0.369922 - 2.61976i) q^{56} +(3.87494 + 6.71160i) q^{58} -5.27138 q^{59} +(7.17592 + 12.4291i) q^{61} +(-3.24911 - 5.62762i) q^{62} +1.00000 q^{64} +(3.16252 - 0.348796i) q^{65} +(3.75236 - 6.49929i) q^{67} +7.17592 q^{68} +(-2.16529 - 0.873194i) q^{70} +(-5.00985 + 8.67732i) q^{71} +(-1.93284 - 3.34778i) q^{73} -0.330574 q^{74} +(-2.37080 - 4.10635i) q^{76} +(3.80789 + 1.53560i) q^{77} +(6.67928 - 11.5689i) q^{79} +(0.441221 - 0.764218i) q^{80} +(-3.02918 - 5.24669i) q^{82} +10.5519 q^{83} +(3.16617 - 5.48396i) q^{85} +(-3.35975 + 5.81927i) q^{86} +(-0.775934 + 1.34396i) q^{88} -14.8167 q^{89} +(-6.82366 + 6.66615i) q^{91} -5.29348 q^{92} +(0.976430 - 1.69123i) q^{94} -4.18420 q^{95} +(5.79259 - 10.0331i) q^{97} +(6.72632 - 1.93822i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} - 2 q^{5} + 3 q^{7} - 8 q^{8} + 2 q^{10} - 4 q^{11} + 3 q^{13} - 3 q^{14} + 8 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + 2 q^{25} - 3 q^{26} + 3 q^{28} - 2 q^{29}+ \cdots - 5 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 - 2 * q^5 + 3 * q^7 - 8 * q^8 + 2 * q^10 - 4 * q^11 + 3 * q^13 - 3 * q^14 + 8 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + 2 * q^25 - 3 * q^26 + 3 * q^28 - 2 * q^29 + 14 * q^31 - 8 * q^32 + 4 * q^34 + 22 * q^35 + 12 * q^37 + 4 * q^38 + 2 * q^40 - 12 * q^41 - 4 * q^44 - 8 * q^46 - 7 * q^47 + 5 * q^49 - 2 * q^50 + 3 * q^52 + q^53 - 25 * q^55 - 3 * q^56 + 2 * q^58 + 32 * q^59 - 4 * q^61 - 14 * q^62 + 8 * q^64 - 10 * q^65 + 19 * q^67 - 4 * q^68 - 22 * q^70 - 20 * q^71 - 7 * q^73 - 12 * q^74 - 4 * q^76 + 24 * q^77 + 24 * q^79 - 2 * q^80 + 12 * q^82 + 64 * q^83 + 15 * q^85 + 4 * q^88 - 22 * q^89 - 38 * q^91 + 8 * q^92 + 7 * q^94 + 56 * q^95 + 11 * q^97 - 5 * q^98

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