LMFDB - Embedded newform 1638.2.y.c.1331.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1638,2,Mod(827,1638)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1638, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1638.827"); 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.y (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 8 x^{15} + 20 x^{14} - 12 x^{13} + 40 x^{12} + 40 x^{11} + 82 x^{10} + 104 x^{9} + 537 x^{8} + \cdots + 16 $ x^16 - 8x^15 + 20x^14 - 12x^13 + 40x^12 + 40x^11 + 82x^10 + 104x^9 + 537x^8 - 2528x^7 + 5494x^6 - 7284x^5 + 6002x^4 - 2984x^3 + 1000x^2 - 192*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1331.5
Root			$0.213522 - 0.0884436i$ of defining polynomial
Character	$\chi$	$=$	1638.1331
Dual form			1638.2.y.c.827.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.98814 - 1.98814i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.81166i q^{10} +(-0.872107 + 0.872107i) q^{11} +(-3.13475 + 1.78139i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +7.84838 q^{17} +(-1.52422 + 1.52422i) q^{19} +(1.98814 - 1.98814i) q^{20} -1.23335 q^{22} +6.35635 q^{23} +2.90541i q^{25} +(-3.47623 - 0.956970i) q^{26} +(0.707107 - 0.707107i) q^{28} +9.83285i q^{29} +(-3.63928 + 3.63928i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.54964 + 5.54964i) q^{34} +2.81166i q^{35} +(-0.000971348 - 0.000971348i) q^{37} -2.15557 q^{38} +2.81166 q^{40} +(0.421121 + 0.421121i) q^{41} +5.21759i q^{43} +(-0.872107 - 0.872107i) q^{44} +(4.49462 + 4.49462i) q^{46} +(-5.01980 + 5.01980i) q^{47} +1.00000i q^{49} +(-2.05444 + 2.05444i) q^{50} +(-1.78139 - 3.13475i) q^{52} +13.7225i q^{53} +3.46775 q^{55} +1.00000 q^{56} +(-6.95287 + 6.95287i) q^{58} +(6.45093 - 6.45093i) q^{59} -3.16463 q^{61} -5.14672 q^{62} -1.00000i q^{64} +(9.77398 + 2.69067i) q^{65} +(0.957291 - 0.957291i) q^{67} +7.84838i q^{68} +(-1.98814 + 1.98814i) q^{70} +(-0.476595 - 0.476595i) q^{71} +(-0.580266 - 0.580266i) q^{73} -0.00137369i q^{74} +(-1.52422 - 1.52422i) q^{76} +1.23335 q^{77} +9.53595 q^{79} +(1.98814 + 1.98814i) q^{80} +0.595555i q^{82} +(6.68556 + 6.68556i) q^{83} +(-15.6037 - 15.6037i) q^{85} +(-3.68939 + 3.68939i) q^{86} -1.23335i q^{88} +(4.11587 - 4.11587i) q^{89} +(3.47623 + 0.956970i) q^{91} +6.35635i q^{92} -7.09906 q^{94} +6.06071 q^{95} +(2.58108 - 2.58108i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{5} + 8 q^{11} + 4 q^{13} - 16 q^{16} + 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} - 24 q^{23} - 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} - 16 q^{38} + 16 q^{41} + 8 q^{44} - 4 q^{47} + 16 q^{50}+ \cdots - 28 q^{97}+O(q^{100}) $ 16 * q - 4 * q^5 + 8 * q^11 + 4 * q^13 - 16 * q^16 + 8 * q^17 + 16 * q^19 + 4 * q^20 - 8 * q^22 - 24 * q^23 - 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 - 16 * q^38 + 16 * q^41 + 8 * q^44 - 4 * q^47 + 16 * q^50 - 16 * q^55 + 16 * q^56 + 4 * q^58 + 8 * q^59 - 40 * q^61 - 24 * q^62 - 56 * q^65 - 4 * q^67 - 4 * q^70 + 24 * q^71 - 12 * q^73 + 16 * q^76 + 8 * q^77 + 16 * q^79 + 4 * q^80 + 8 * q^85 - 24 * q^86 - 16 * q^89 + 8 * q^91 - 8 * q^94 + 40 * q^95 - 28 * q^97

Character values

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

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−1.98814	−	1.98814i	−0.889124	−	0.889124i	0.105315	−	0.994439i	$-0.466415\pi$
$5$	−1.98814	−	1.98814i	−0.889124	−	0.889124i	−0.994439	+	0.105315i	$0.966415\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$		−	2.81166i		−	0.889124i
$11$	−0.872107	+	0.872107i	−0.262950	+	0.262950i	−0.826252	−	0.563301i	$-0.809531\pi$
$11$	−0.872107	+	0.872107i	−0.262950	+	0.262950i	0.563301	+	0.826252i	$0.309531\pi$
$12$		0			0
$13$	−3.13475	+	1.78139i	−0.869423	+	0.494068i
$13$	−3.13475	+	1.78139i	−0.869423	+	0.494068i
$14$		−	1.00000i		−	0.267261i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	7.84838			1.90351			0.951756	−	0.306857i	$-0.0992774\pi$
$17$	7.84838			1.90351			0.951756	+	0.306857i	$0.0992774\pi$
$18$		0			0
$19$	−1.52422	+	1.52422i	−0.349679	+	0.349679i	−0.859990	−	0.510311i	$-0.829530\pi$
$19$	−1.52422	+	1.52422i	−0.349679	+	0.349679i	0.510311	+	0.859990i	$0.329530\pi$
$20$	1.98814	−	1.98814i	0.444562	−	0.444562i
$21$		0			0
$22$	−1.23335			−0.262950
$23$	6.35635			1.32539			0.662695	−	0.748890i	$-0.269413\pi$
$23$	6.35635			1.32539			0.662695	+	0.748890i	$0.269413\pi$
$24$		0			0
$25$			2.90541i			0.581082i
$26$	−3.47623	−	0.956970i	−0.681746	−	0.187677i
$27$		0			0
$28$	0.707107	−	0.707107i	0.133631	−	0.133631i
$29$			9.83285i			1.82591i	0.408056	+	0.912957i	$0.366207\pi$
$29$			9.83285i			1.82591i	−0.408056	+	0.912957i	$0.633793\pi$
$30$		0			0
$31$	−3.63928	+	3.63928i	−0.653634	+	0.653634i	−0.953866	−	0.300232i	$-0.902936\pi$
$31$	−3.63928	+	3.63928i	−0.653634	+	0.653634i	0.300232	+	0.953866i	$0.402936\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	5.54964	+	5.54964i	0.951756	+	0.951756i
$35$			2.81166i			0.475257i
$36$		0			0
$37$	−0.000971348	0	0.000971348i	−0.000159689	0	0.000159689i	0.707027	−	0.707187i	$-0.250036\pi$
$37$	−0.000971348	0	0.000971348i	−0.000159689	0	0.000159689i	−0.707187	+	0.707027i	$0.750036\pi$
$38$	−2.15557			−0.349679
$39$		0			0
$40$	2.81166			0.444562
$41$	0.421121	+	0.421121i	0.0657680	+	0.0657680i	0.739226	−	0.673458i	$-0.235192\pi$
$41$	0.421121	+	0.421121i	0.0657680	+	0.0657680i	−0.673458	+	0.739226i	$0.735192\pi$
$42$		0			0
$43$			5.21759i			0.795675i	0.917456	+	0.397837i	$0.130239\pi$
$43$			5.21759i			0.795675i	−0.917456	+	0.397837i	$0.869761\pi$
$44$	−0.872107	−	0.872107i	−0.131475	−	0.131475i
$45$		0			0
$46$	4.49462	+	4.49462i	0.662695	+	0.662695i
$47$	−5.01980	+	5.01980i	−0.732213	+	0.732213i	−0.971058	−	0.238845i	$-0.923231\pi$
$47$	−5.01980	+	5.01980i	−0.732213	+	0.732213i	0.238845	+	0.971058i	$0.423231\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$	−2.05444	+	2.05444i	−0.290541	+	0.290541i
$51$		0			0
$52$	−1.78139	−	3.13475i	−0.247034	−	0.434712i
$53$			13.7225i			1.88493i	0.334304	+	0.942465i	$0.391499\pi$
$53$			13.7225i			1.88493i	−0.334304	+	0.942465i	$0.608501\pi$
$54$		0			0
$55$	3.46775			0.467591
$56$	1.00000			0.133631
$57$		0			0
$58$	−6.95287	+	6.95287i	−0.912957	+	0.912957i
$59$	6.45093	−	6.45093i	0.839840	−	0.839840i	−0.148997	−	0.988838i	$-0.547605\pi$
$59$	6.45093	−	6.45093i	0.839840	−	0.839840i	0.988838	+	0.148997i	$0.0476046\pi$
$60$		0			0
$61$	−3.16463			−0.405189			−0.202594	−	0.979263i	$-0.564937\pi$
$61$	−3.16463			−0.405189			−0.202594	+	0.979263i	$0.564937\pi$
$62$	−5.14672			−0.653634
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	9.77398	+	2.69067i	1.21231	+	0.333737i
$66$		0			0
$67$	0.957291	−	0.957291i	0.116952	−	0.116952i	−0.646209	−	0.763161i	$-0.723647\pi$
$67$	0.957291	−	0.957291i	0.116952	−	0.116952i	0.763161	+	0.646209i	$0.223647\pi$
$68$			7.84838i			0.951756i
$69$		0			0
$70$	−1.98814	+	1.98814i	−0.237628	+	0.237628i
$71$	−0.476595	−	0.476595i	−0.0565614	−	0.0565614i	0.678260	−	0.734822i	$-0.262734\pi$
$71$	−0.476595	−	0.476595i	−0.0565614	−	0.0565614i	−0.734822	+	0.678260i	$0.762734\pi$
$72$		0			0
$73$	−0.580266	−	0.580266i	−0.0679150	−	0.0679150i	0.672333	−	0.740248i	$-0.265292\pi$
$73$	−0.580266	−	0.580266i	−0.0679150	−	0.0679150i	−0.740248	+	0.672333i	$0.765292\pi$
$74$		−	0.00137369i		−	0.000159689i
$75$		0			0
$76$	−1.52422	−	1.52422i	−0.174840	−	0.174840i
$77$	1.23335			0.140553
$78$		0			0
$79$	9.53595			1.07288			0.536439	−	0.843939i	$-0.319769\pi$
$79$	9.53595			1.07288			0.536439	+	0.843939i	$0.319769\pi$
$80$	1.98814	+	1.98814i	0.222281	+	0.222281i
$81$		0			0
$82$			0.595555i			0.0657680i
$83$	6.68556	+	6.68556i	0.733835	+	0.733835i	0.971377	−	0.237542i	$-0.0763417\pi$
$83$	6.68556	+	6.68556i	0.733835	+	0.733835i	−0.237542	+	0.971377i	$0.576342\pi$
$84$		0			0
$85$	−15.6037	−	15.6037i	−1.69246	−	1.69246i
$86$	−3.68939	+	3.68939i	−0.397837	+	0.397837i
$87$		0			0
$88$		−	1.23335i		−	0.131475i
$89$	4.11587	−	4.11587i	0.436282	−	0.436282i	−0.454477	−	0.890759i	$-0.650174\pi$
$89$	4.11587	−	4.11587i	0.436282	−	0.436282i	0.890759	+	0.454477i	$0.150174\pi$
$90$		0			0
$91$	3.47623	+	0.956970i	0.364408	+	0.100318i
$92$			6.35635i			0.662695i
$93$		0			0
$94$	−7.09906			−0.732213
$95$	6.06071			0.621816
$96$		0			0
$97$	2.58108	−	2.58108i	0.262069	−	0.262069i	−0.563825	−	0.825894i	$-0.690671\pi$
$97$	2.58108	−	2.58108i	0.262069	−	0.262069i	0.825894	+	0.563825i	$0.190671\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$		0			0
$100$	−2.90541			−0.290541
$101$	2.51133			0.249887			0.124944	−	0.992164i	$-0.460125\pi$
$101$	2.51133			0.249887			0.124944	+	0.992164i	$0.460125\pi$
$102$		0			0
$103$		−	3.63132i		−	0.357804i	−0.983867	−	0.178902i	$-0.942745\pi$
$103$		−	3.63132i		−	0.357804i	0.983867	−	0.178902i	$-0.0572546\pi$
$104$	0.956970	−	3.47623i	0.0938386	−	0.340873i
$105$		0			0
$106$	−9.70327	+	9.70327i	−0.942465	+	0.942465i
$107$			3.82051i			0.369342i	0.982800	+	0.184671i	$0.0591220\pi$
$107$			3.82051i			0.369342i	−0.982800	+	0.184671i	$0.940878\pi$
$108$		0			0
$109$	−6.45191	+	6.45191i	−0.617981	+	0.617981i	−0.945013	−	0.327033i	$-0.893951\pi$
$109$	−6.45191	+	6.45191i	−0.617981	+	0.617981i	0.327033	+	0.945013i	$0.393951\pi$
$110$	2.45207	+	2.45207i	0.233795	+	0.233795i
$111$		0			0
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$			1.74602i			0.164252i	0.996622	+	0.0821260i	$0.0261710\pi$
$113$			1.74602i			0.164252i	−0.996622	+	0.0821260i	$0.973829\pi$
$114$		0			0
$115$	−12.6373	−	12.6373i	−1.17844	−	1.17844i
$116$	−9.83285			−0.912957
$117$		0			0
$118$	9.12300			0.839840
$119$	−5.54964	−	5.54964i	−0.508735	−	0.508735i
$120$		0			0
$121$			9.47886i			0.861714i
$122$	−2.23773	−	2.23773i	−0.202594	−	0.202594i
$123$		0			0
$124$	−3.63928	−	3.63928i	−0.326817	−	0.326817i
$125$	−4.16434	+	4.16434i	−0.372470	+	0.372470i
$126$		0			0
$127$			19.2104i			1.70465i	0.523011	+	0.852326i	$0.324809\pi$
$127$			19.2104i			1.70465i	−0.523011	+	0.852326i	$0.675191\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	5.00865	+	8.81384i	0.439288	+	0.773025i
$131$		−	19.6194i		−	1.71415i	−0.515190	−	0.857076i	$-0.672279\pi$
$131$		−	19.6194i		−	1.71415i	0.515190	−	0.857076i	$-0.327721\pi$
$132$		0			0
$133$	2.15557			0.186911
$134$	1.35381			0.116952
$135$		0			0
$136$	−5.54964	+	5.54964i	−0.475878	+	0.475878i
$137$	−8.48067	+	8.48067i	−0.724552	+	0.724552i	−0.969529	−	0.244977i	$-0.921220\pi$
$137$	−8.48067	+	8.48067i	−0.724552	+	0.724552i	0.244977	+	0.969529i	$0.421220\pi$
$138$		0			0
$139$	−17.6573			−1.49767			−0.748837	−	0.662755i	$-0.769387\pi$
$139$	−17.6573			−1.49767			−0.748837	+	0.662755i	$0.769387\pi$
$140$	−2.81166			−0.237628
$141$		0			0
$142$		−	0.674007i		−	0.0565614i
$143$	1.18028	−	4.28740i	0.0986996	−	0.358530i
$144$		0			0
$145$	19.5491	−	19.5491i	1.62346	−	1.62346i
$146$		−	0.820620i		−	0.0679150i
$147$		0			0
$148$	0.000971348	0	0.000971348i	7.98443e−5	0	7.98443e-5i
$149$	−5.19872	−	5.19872i	−0.425896	−	0.425896i	0.461332	−	0.887228i	$-0.347372\pi$
$149$	−5.19872	−	5.19872i	−0.425896	−	0.425896i	−0.887228	+	0.461332i	$0.847372\pi$
$150$		0			0
$151$	1.86969	+	1.86969i	0.152153	+	0.152153i	0.779079	−	0.626926i	$-0.215687\pi$
$151$	1.86969	+	1.86969i	0.152153	+	0.152153i	−0.626926	+	0.779079i	$0.715687\pi$
$152$		−	2.15557i		−	0.174840i
$153$		0			0
$154$	0.872107	+	0.872107i	0.0702764	+	0.0702764i
$155$	14.4708			1.16232
$156$		0			0
$157$	−12.2084			−0.974335			−0.487167	−	0.873309i	$-0.661970\pi$
$157$	−12.2084			−0.974335			−0.487167	+	0.873309i	$0.661970\pi$
$158$	6.74294	+	6.74294i	0.536439	+	0.536439i
$159$		0			0
$160$			2.81166i			0.222281i
$161$	−4.49462	−	4.49462i	−0.354225	−	0.354225i
$162$		0			0
$163$	0.218796	+	0.218796i	0.0171374	+	0.0171374i	0.715624	−	0.698486i	$-0.246143\pi$
$163$	0.218796	+	0.218796i	0.0171374	+	0.0171374i	−0.698486	+	0.715624i	$0.746143\pi$
$164$	−0.421121	+	0.421121i	−0.0328840	+	0.0328840i
$165$		0			0
$166$			9.45481i			0.733835i
$167$	15.7026	−	15.7026i	1.21511	−	1.21511i	0.245780	−	0.969326i	$-0.420956\pi$
$167$	15.7026	−	15.7026i	1.21511	−	1.21511i	0.969326	−	0.245780i	$-0.0790440\pi$
$168$		0			0
$169$	6.65331	−	11.1684i	0.511793	−	0.859109i
$170$		−	22.0669i		−	1.69246i
$171$		0			0
$172$	−5.21759			−0.397837
$173$	18.2357			1.38643			0.693217	−	0.720729i	$-0.256193\pi$
$173$	18.2357			1.38643			0.693217	+	0.720729i	$0.256193\pi$
$174$		0			0
$175$	2.05444	−	2.05444i	0.155301	−	0.155301i
$176$	0.872107	−	0.872107i	0.0657376	−	0.0657376i
$177$		0			0
$178$	5.82072			0.436282
$179$	−20.1218			−1.50398			−0.751988	−	0.659176i	$-0.770905\pi$
$179$	−20.1218			−1.50398			−0.751988	+	0.659176i	$0.770905\pi$
$180$		0			0
$181$			4.03633i			0.300018i	0.988685	+	0.150009i	$0.0479303\pi$
$181$			4.03633i			0.300018i	−0.988685	+	0.150009i	$0.952070\pi$
$182$	1.78139	+	3.13475i	0.132045	+	0.232363i
$183$		0			0
$184$	−4.49462	+	4.49462i	−0.331347	+	0.331347i
$185$			0.00386235i			0.000283966i
$186$		0			0
$187$	−6.84463	+	6.84463i	−0.500529	+	0.500529i
$188$	−5.01980	−	5.01980i	−0.366106	−	0.366106i
$189$		0			0
$190$	4.28557	+	4.28557i	0.310908	+	0.310908i
$191$		−	21.2583i		−	1.53820i	−0.639131	−	0.769098i	$-0.720706\pi$
$191$		−	21.2583i		−	1.53820i	0.639131	−	0.769098i	$-0.279294\pi$
$192$		0			0
$193$	−11.8435	−	11.8435i	−0.852514	−	0.852514i	0.137929	−	0.990442i	$-0.455956\pi$
$193$	−11.8435	−	11.8435i	−0.852514	−	0.852514i	−0.990442	+	0.137929i	$0.955956\pi$
$194$	3.65019			0.262069
$195$		0			0
$196$	−1.00000			−0.0714286
$197$	−3.79565	−	3.79565i	−0.270429	−	0.270429i	0.558844	−	0.829273i	$-0.311245\pi$
$197$	−3.79565	−	3.79565i	−0.270429	−	0.270429i	−0.829273	+	0.558844i	$0.811245\pi$
$198$		0			0
$199$		−	13.7090i		−	0.971803i	−0.874014	−	0.485902i	$-0.838491\pi$
$199$		−	13.7090i		−	0.971803i	0.874014	−	0.485902i	$-0.161509\pi$
$200$	−2.05444	−	2.05444i	−0.145271	−	0.145271i
$201$		0			0
$202$	1.77578	+	1.77578i	0.124944	+	0.124944i
$203$	6.95287	−	6.95287i	0.487996	−	0.487996i
$204$		0			0
$205$		−	1.67450i		−	0.116952i
$206$	2.56773	−	2.56773i	0.178902	−	0.178902i
$207$		0			0
$208$	3.13475	−	1.78139i	0.217356	−	0.123517i
$209$		−	2.65856i		−	0.183896i
$210$		0			0
$211$	−4.49184			−0.309231			−0.154616	−	0.987975i	$-0.549414\pi$
$211$	−4.49184			−0.309231			−0.154616	+	0.987975i	$0.549414\pi$
$212$	−13.7225			−0.942465
$213$		0			0
$214$	−2.70151	+	2.70151i	−0.184671	+	0.184671i
$215$	10.3733	−	10.3733i	0.707453	−	0.707453i
$216$		0			0
$217$	5.14672			0.349382
$218$	−9.12437			−0.617981
$219$		0			0
$220$			3.46775i			0.233795i
$221$	−24.6027	+	13.9810i	−1.65496	+	0.940465i
$222$		0			0
$223$	−8.59883	+	8.59883i	−0.575820	+	0.575820i	−0.933749	−	0.357929i	$-0.883483\pi$
$223$	−8.59883	+	8.59883i	−0.575820	+	0.575820i	0.357929	+	0.933749i	$0.383483\pi$
$224$			1.00000i			0.0668153i
$225$		0			0
$226$	−1.23462	+	1.23462i	−0.0821260	+	0.0821260i
$227$	−1.53435	−	1.53435i	−0.101839	−	0.101839i	0.654352	−	0.756190i	$-0.272942\pi$
$227$	−1.53435	−	1.53435i	−0.101839	−	0.101839i	−0.756190	+	0.654352i	$0.772942\pi$
$228$		0			0
$229$	17.9893	+	17.9893i	1.18877	+	1.18877i	0.977408	+	0.211360i	$0.0677894\pi$
$229$	17.9893	+	17.9893i	1.18877	+	1.18877i	0.211360	+	0.977408i	$0.432211\pi$
$230$		−	17.8719i		−	1.17844i
$231$		0			0
$232$	−6.95287	−	6.95287i	−0.456478	−	0.456478i
$233$	21.6085			1.41562			0.707811	−	0.706402i	$-0.249683\pi$
$233$	21.6085			1.41562			0.707811	+	0.706402i	$0.249683\pi$
$234$		0			0
$235$	19.9601			1.30206
$236$	6.45093	+	6.45093i	0.419920	+	0.419920i
$237$		0			0
$238$		−	7.84838i		−	0.508735i
$239$	11.2064	+	11.2064i	0.724880	+	0.724880i	0.969595	−	0.244715i	$-0.0786945\pi$
$239$	11.2064	+	11.2064i	0.724880	+	0.724880i	−0.244715	+	0.969595i	$0.578694\pi$
$240$		0			0
$241$	−15.7392	−	15.7392i	−1.01385	−	1.01385i	−0.999903	−	0.0139501i	$-0.995559\pi$
$241$	−15.7392	−	15.7392i	−1.01385	−	1.01385i	−0.0139501	−	0.999903i	$-0.504441\pi$
$242$	−6.70256	+	6.70256i	−0.430857	+	0.430857i
$243$		0			0
$244$		−	3.16463i		−	0.202594i
$245$	1.98814	−	1.98814i	0.127018	−	0.127018i
$246$		0			0
$247$	2.06281	−	7.49326i	0.131254	−	0.476785i
$248$		−	5.14672i		−	0.326817i
$249$		0			0
$250$	−5.88926			−0.372470
$251$	27.1452			1.71339			0.856696	−	0.515822i	$-0.172513\pi$
$251$	27.1452			1.71339			0.856696	+	0.515822i	$0.172513\pi$
$252$		0			0
$253$	−5.54342	+	5.54342i	−0.348512	+	0.348512i
$254$	−13.5838	+	13.5838i	−0.852326	+	0.852326i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−28.5286			−1.77957			−0.889784	−	0.456382i	$-0.849145\pi$
$257$	−28.5286			−1.77957			−0.889784	+	0.456382i	$0.849145\pi$
$258$		0			0
$259$			0.00137369i			8.53572e-5i
$260$	−2.69067	+	9.77398i	−0.166868	+	0.606156i
$261$		0			0
$262$	13.8730	−	13.8730i	0.857076	−	0.857076i
$263$			0.115982i			0.00715176i	0.999994	+	0.00357588i	$0.00113824\pi$
$263$			0.115982i			0.00715176i	−0.999994	+	0.00357588i	$0.998862\pi$
$264$		0			0
$265$	27.2823	−	27.2823i	1.67594	−	1.67594i
$266$	1.52422	+	1.52422i	0.0934557	+	0.0934557i
$267$		0			0
$268$	0.957291	+	0.957291i	0.0584759	+	0.0584759i
$269$			11.1382i			0.679108i	0.940587	+	0.339554i	$0.110276\pi$
$269$			11.1382i			0.679108i	−0.940587	+	0.339554i	$0.889724\pi$
$270$		0			0
$271$	14.5757	+	14.5757i	0.885408	+	0.885408i	0.994078	−	0.108670i	$-0.0346591\pi$
$271$	14.5757	+	14.5757i	0.885408	+	0.885408i	−0.108670	+	0.994078i	$0.534659\pi$
$272$	−7.84838			−0.475878
$273$		0			0
$274$	−11.9935			−0.724552
$275$	−2.53383	−	2.53383i	−0.152796	−	0.152796i
$276$		0			0
$277$			14.5741i			0.875676i	0.899054	+	0.437838i	$0.144256\pi$
$277$			14.5741i			0.875676i	−0.899054	+	0.437838i	$0.855744\pi$
$278$	−12.4856	−	12.4856i	−0.748837	−	0.748837i
$279$		0			0
$280$	−1.98814	−	1.98814i	−0.118814	−	0.118814i
$281$	2.97443	−	2.97443i	0.177440	−	0.177440i	−0.612799	−	0.790239i	$-0.709956\pi$
$281$	2.97443	−	2.97443i	0.177440	−	0.177440i	0.790239	+	0.612799i	$0.209956\pi$
$282$		0			0
$283$			6.71560i			0.399201i	0.979877	+	0.199600i	$0.0639644\pi$
$283$			6.71560i			0.399201i	−0.979877	+	0.199600i	$0.936036\pi$
$284$	0.476595	−	0.476595i	0.0282807	−	0.0282807i
$285$		0			0
$286$	3.86623	−	2.19707i	0.228615	−	0.129915i
$287$		−	0.595555i		−	0.0351545i
$288$		0			0
$289$	44.5970			2.62335
$290$	27.6466			1.62346
$291$		0			0
$292$	0.580266	−	0.580266i	0.0339575	−	0.0339575i
$293$	−9.95137	+	9.95137i	−0.581365	+	0.581365i	−0.935278	−	0.353913i	$-0.884851\pi$
$293$	−9.95137	+	9.95137i	−0.581365	+	0.581365i	0.353913	+	0.935278i	$0.384851\pi$
$294$		0			0
$295$	−25.6507			−1.49344
$296$	0.00137369			7.98443e−5
$297$		0			0
$298$		−	7.35210i		−	0.425896i
$299$	−19.9255	+	11.3231i	−1.15232	+	0.654833i
$300$		0			0
$301$	3.68939	−	3.68939i	0.212653	−	0.212653i
$302$			2.64414i			0.152153i
$303$		0			0
$304$	1.52422	−	1.52422i	0.0874198	−	0.0874198i
$305$	6.29172	+	6.29172i	0.360263	+	0.360263i
$306$		0			0
$307$	−21.7725	−	21.7725i	−1.24262	−	1.24262i	−0.958910	−	0.283710i	$-0.908435\pi$
$307$	−21.7725	−	21.7725i	−1.24262	−	1.24262i	−0.283710	−	0.958910i	$-0.591565\pi$
$308$			1.23335i			0.0702764i
$309$		0			0
$310$	10.2324	+	10.2324i	0.581161	+	0.581161i
$311$	−15.8417			−0.898302			−0.449151	−	0.893456i	$-0.648273\pi$
$311$	−15.8417			−0.898302			−0.449151	+	0.893456i	$0.648273\pi$
$312$		0			0
$313$	17.8183			1.00715			0.503575	−	0.863951i	$-0.332018\pi$
$313$	17.8183			1.00715			0.503575	+	0.863951i	$0.332018\pi$
$314$	−8.63263	−	8.63263i	−0.487167	−	0.487167i
$315$		0			0
$316$			9.53595i			0.536439i
$317$	12.0631	+	12.0631i	0.677531	+	0.677531i	0.959441	−	0.281910i	$-0.0909678\pi$
$317$	12.0631	+	12.0631i	0.677531	+	0.677531i	−0.281910	+	0.959441i	$0.590968\pi$
$318$		0			0
$319$	−8.57530	−	8.57530i	−0.480124	−	0.480124i
$320$	−1.98814	+	1.98814i	−0.111140	+	0.111140i
$321$		0			0
$322$		−	6.35635i		−	0.354225i
$323$	−11.9626	+	11.9626i	−0.665618	+	0.665618i
$324$		0			0
$325$	−5.17567	−	9.10773i	−0.287094	−	0.505206i
$326$			0.309424i			0.0171374i
$327$		0			0
$328$	−0.595555			−0.0328840
$329$	7.09906			0.391384
$330$		0			0
$331$	13.5207	−	13.5207i	0.743167	−	0.743167i	−0.230019	−	0.973186i	$-0.573879\pi$
$331$	13.5207	−	13.5207i	0.743167	−	0.743167i	0.973186	+	0.230019i	$0.0738789\pi$
$332$	−6.68556	+	6.68556i	−0.366918	+	0.366918i
$333$		0			0
$334$	22.2069			1.21511
$335$	−3.80646			−0.207969
$336$		0			0
$337$		−	19.0715i		−	1.03889i	−0.854504	−	0.519446i	$-0.826138\pi$
$337$		−	19.0715i		−	1.03889i	0.854504	−	0.519446i	$-0.173862\pi$
$338$	12.6019	−	3.19267i	0.685451	−	0.173658i
$339$		0			0
$340$	15.6037	−	15.6037i	0.846229	−	0.846229i
$341$		−	6.34768i		−	0.343746i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−3.68939	−	3.68939i	−0.198919	−	0.198919i
$345$		0			0
$346$	12.8946	+	12.8946i	0.693217	+	0.693217i
$347$		−	30.0706i		−	1.61427i	−0.590364	−	0.807137i	$-0.701016\pi$
$347$		−	30.0706i		−	1.61427i	0.590364	−	0.807137i	$-0.298984\pi$
$348$		0			0
$349$	22.5711	+	22.5711i	1.20820	+	1.20820i	0.971609	+	0.236593i	$0.0760308\pi$
$349$	22.5711	+	22.5711i	1.20820	+	1.20820i	0.236593	+	0.971609i	$0.423969\pi$
$350$	2.90541			0.155301
$351$		0			0
$352$	1.23335			0.0657376
$353$	7.04828	+	7.04828i	0.375142	+	0.375142i	0.869346	−	0.494204i	$-0.164540\pi$
$353$	7.04828	+	7.04828i	0.375142	+	0.375142i	−0.494204	+	0.869346i	$0.664540\pi$
$354$		0			0
$355$			1.89508i			0.100580i
$356$	4.11587	+	4.11587i	0.218141	+	0.218141i
$357$		0			0
$358$	−14.2283	−	14.2283i	−0.751988	−	0.751988i
$359$	−22.1617	+	22.1617i	−1.16965	+	1.16965i	−0.187358	+	0.982292i	$0.559992\pi$
$359$	−22.1617	+	22.1617i	−1.16965	+	1.16965i	−0.982292	+	0.187358i	$0.940008\pi$
$360$		0			0
$361$			14.3535i			0.755449i
$362$	−2.85412	+	2.85412i	−0.150009	+	0.150009i
$363$		0			0
$364$	−0.956970	+	3.47623i	−0.0501589	+	0.182204i
$365$			2.30730i			0.120770i
$366$		0			0
$367$	−8.61723			−0.449816			−0.224908	−	0.974380i	$-0.572208\pi$
$367$	−8.61723			−0.449816			−0.224908	+	0.974380i	$0.572208\pi$
$368$	−6.35635			−0.331347
$369$		0			0
$370$	−0.00273110	+	0.00273110i	−0.000141983	+	0.000141983i
$371$	9.70327	−	9.70327i	0.503769	−	0.503769i
$372$		0			0
$373$	−9.70903			−0.502715			−0.251357	−	0.967894i	$-0.580877\pi$
$373$	−9.70903			−0.502715			−0.251357	+	0.967894i	$0.580877\pi$
$374$	−9.67977			−0.500529
$375$		0			0
$376$		−	7.09906i		−	0.366106i
$377$	−17.5161	−	30.8235i	−0.902126	−	1.58749i
$378$		0			0
$379$	−10.4852	+	10.4852i	−0.538588	+	0.538588i	−0.923114	−	0.384526i	$-0.874365\pi$
$379$	−10.4852	+	10.4852i	−0.538588	+	0.538588i	0.384526	+	0.923114i	$0.374365\pi$
$380$			6.06071i			0.310908i
$381$		0			0
$382$	15.0319	−	15.0319i	0.769098	−	0.769098i
$383$	−0.924798	−	0.924798i	−0.0472550	−	0.0472550i	0.683084	−	0.730339i	$-0.260638\pi$
$383$	−0.924798	−	0.924798i	−0.0472550	−	0.0472550i	−0.730339	+	0.683084i	$0.760638\pi$
$384$		0			0
$385$	−2.45207	−	2.45207i	−0.124969	−	0.124969i
$386$		−	16.7492i		−	0.852514i
$387$		0			0
$388$	2.58108	+	2.58108i	0.131034	+	0.131034i
$389$	23.2044			1.17651			0.588256	−	0.808675i	$-0.299815\pi$
$389$	23.2044			1.17651			0.588256	+	0.808675i	$0.299815\pi$
$390$		0			0
$391$	49.8870			2.52289
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$		0			0
$394$		−	5.36786i		−	0.270429i
$395$	−18.9588	−	18.9588i	−0.953922	−	0.953922i
$396$		0			0
$397$	6.31775	+	6.31775i	0.317079	+	0.317079i	0.847644	−	0.530565i	$-0.178020\pi$
$397$	6.31775	+	6.31775i	0.317079	+	0.317079i	−0.530565	+	0.847644i	$0.678020\pi$
$398$	9.69371	−	9.69371i	0.485902	−	0.485902i
$399$		0			0
$400$		−	2.90541i		−	0.145271i
$401$	−9.17426	+	9.17426i	−0.458141	+	0.458141i	−0.898045	−	0.439904i	$-0.855012\pi$
$401$	−9.17426	+	9.17426i	−0.458141	+	0.458141i	0.439904	+	0.898045i	$0.355012\pi$
$402$		0			0
$403$	4.92525	−	17.8912i	0.245344	−	0.891224i
$404$			2.51133i			0.124944i
$405$		0			0
$406$	9.83285			0.487996
$407$	0.00169424			8.39803e−5
$408$		0			0
$409$	−7.98549	+	7.98549i	−0.394857	+	0.394857i	−0.876415	−	0.481557i	$-0.840071\pi$
$409$	−7.98549	+	7.98549i	−0.394857	+	0.394857i	0.481557	+	0.876415i	$0.340071\pi$
$410$	1.18405	−	1.18405i	0.0584759	−	0.0584759i
$411$		0			0
$412$	3.63132			0.178902
$413$	−9.12300			−0.448913
$414$		0			0
$415$		−	26.5837i		−	1.30494i
$416$	3.47623	+	0.956970i	0.170436	+	0.0469193i
$417$		0			0
$418$	1.87989	−	1.87989i	0.0919482	−	0.0919482i
$419$			14.2537i			0.696340i	0.937431	+	0.348170i	$0.113197\pi$
$419$			14.2537i			0.696340i	−0.937431	+	0.348170i	$0.886803\pi$
$420$		0			0
$421$	−1.49790	+	1.49790i	−0.0730032	+	0.0730032i	−0.742666	−	0.669662i	$-0.766439\pi$
$421$	−1.49790	+	1.49790i	−0.0730032	+	0.0730032i	0.669662	+	0.742666i	$0.266439\pi$
$422$	−3.17621	−	3.17621i	−0.154616	−	0.154616i
$423$		0			0
$424$	−9.70327	−	9.70327i	−0.471233	−	0.471233i
$425$			22.8028i			1.10610i
$426$		0			0
$427$	2.23773	+	2.23773i	0.108291	+	0.108291i
$428$	−3.82051			−0.184671
$429$		0			0
$430$	14.6701			0.707453
$431$	18.9615	+	18.9615i	0.913344	+	0.913344i	0.996534	−	0.0831894i	$-0.0265106\pi$
$431$	18.9615	+	18.9615i	0.913344	+	0.913344i	−0.0831894	+	0.996534i	$0.526511\pi$
$432$		0			0
$433$		−	6.53036i		−	0.313829i	−0.987612	−	0.156914i	$-0.949845\pi$
$433$		−	6.53036i		−	0.313829i	0.987612	−	0.156914i	$-0.0501547\pi$
$434$	3.63928	+	3.63928i	0.174691	+	0.174691i
$435$		0			0
$436$	−6.45191	−	6.45191i	−0.308990	−	0.308990i
$437$	−9.68845	+	9.68845i	−0.463461	+	0.463461i
$438$		0			0
$439$		−	10.8428i		−	0.517498i	−0.965945	−	0.258749i	$-0.916690\pi$
$439$		−	10.8428i		−	0.517498i	0.965945	−	0.258749i	$-0.0833103\pi$
$440$	−2.45207	+	2.45207i	−0.116898	+	0.116898i
$441$		0			0
$442$	−27.2828	−	7.51066i	−1.29771	−	0.357246i
$443$		−	30.1273i		−	1.43139i	−0.698413	−	0.715695i	$-0.746110\pi$
$443$		−	30.1273i		−	1.43139i	0.698413	−	0.715695i	$-0.253890\pi$
$444$		0			0
$445$	−16.3659			−0.775817
$446$	−12.1606			−0.575820
$447$		0			0
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$	0.277909	−	0.277909i	0.0131153	−	0.0131153i	−0.700519	−	0.713634i	$-0.747048\pi$
$449$	0.277909	−	0.277909i	0.0131153	−	0.0131153i	0.713634	+	0.700519i	$0.247048\pi$
$450$		0			0
$451$	−0.734525			−0.0345874
$452$	−1.74602			−0.0821260
$453$		0			0
$454$		−	2.16990i		−	0.101839i
$455$	−5.00865	−	8.81384i	−0.234809	−	0.413199i
$456$		0			0
$457$	0.655206	−	0.655206i	0.0306493	−	0.0306493i	−0.691616	−	0.722265i	$-0.743101\pi$
$457$	0.655206	−	0.655206i	0.0306493	−	0.0306493i	0.722265	+	0.691616i	$0.243101\pi$
$458$			25.4408i			1.18877i
$459$		0			0
$460$	12.6373	−	12.6373i	0.589218	−	0.589218i
$461$	12.7087	+	12.7087i	0.591902	+	0.591902i	0.938145	−	0.346243i	$-0.112543\pi$
$461$	12.7087	+	12.7087i	0.591902	+	0.591902i	−0.346243	+	0.938145i	$0.612543\pi$
$462$		0			0
$463$	−25.9370	−	25.9370i	−1.20540	−	1.20540i	−0.972502	−	0.232895i	$-0.925180\pi$
$463$	−25.9370	−	25.9370i	−1.20540	−	1.20540i	−0.232895	−	0.972502i	$-0.574820\pi$
$464$		−	9.83285i		−	0.456478i
$465$		0			0
$466$	15.2795	+	15.2795i	0.707811	+	0.707811i
$467$	0.685678			0.0317294			0.0158647	−	0.999874i	$-0.494950\pi$
$467$	0.685678			0.0317294			0.0158647	+	0.999874i	$0.494950\pi$
$468$		0			0
$469$	−1.35381			−0.0625133
$470$	14.1139	+	14.1139i	0.651028	+	0.651028i
$471$		0			0
$472$			9.12300i			0.419920i
$473$	−4.55030	−	4.55030i	−0.209223	−	0.209223i
$474$		0			0
$475$	−4.42847	−	4.42847i	−0.203192	−	0.203192i
$476$	5.54964	−	5.54964i	0.254367	−	0.254367i
$477$		0			0
$478$			15.8482i			0.724880i
$479$	−13.6986	+	13.6986i	−0.625907	+	0.625907i	−0.947035	−	0.321129i	$-0.895938\pi$
$479$	−13.6986	+	13.6986i	−0.625907	+	0.625907i	0.321129	+	0.947035i	$0.395938\pi$
$480$		0			0
$481$	0.00477528	+	0.00131458i	0.000217734	+	5.99398e-5i
$482$		−	22.2586i		−	1.01385i
$483$		0			0
$484$	−9.47886			−0.430857
$485$	−10.2631			−0.466023
$486$		0			0
$487$	−26.0472	+	26.0472i	−1.18031	+	1.18031i	−0.200645	+	0.979664i	$0.564304\pi$
$487$	−26.0472	+	26.0472i	−1.18031	+	1.18031i	−0.979664	+	0.200645i	$0.935696\pi$
$488$	2.23773	−	2.23773i	0.101297	−	0.101297i
$489$		0			0
$490$	2.81166			0.127018
$491$	0.243333			0.0109815			0.00549073	−	0.999985i	$-0.498252\pi$
$491$	0.243333			0.0109815			0.00549073	+	0.999985i	$0.498252\pi$
$492$		0			0
$493$			77.1719i			3.47565i
$494$	6.75716	−	3.83990i	0.304019	−	0.172765i
$495$		0			0
$496$	3.63928	−	3.63928i	0.163408	−	0.163408i
$497$			0.674007i			0.0302334i
$498$		0			0
$499$	24.3025	−	24.3025i	1.08793	−	1.08793i	0.0921854	−	0.995742i	$-0.470615\pi$
$499$	24.3025	−	24.3025i	1.08793	−	1.08793i	0.995742	−	0.0921854i	$-0.0293853\pi$
$500$	−4.16434	−	4.16434i	−0.186235	−	0.186235i
$501$		0			0
$502$	19.1946	+	19.1946i	0.856696	+	0.856696i
$503$		−	43.4003i		−	1.93512i	−0.252636	−	0.967561i	$-0.581298\pi$
$503$		−	43.4003i		−	1.93512i	0.252636	−	0.967561i	$-0.418702\pi$
$504$		0			0
$505$	−4.99289	−	4.99289i	−0.222181	−	0.222181i
$506$	−7.83957			−0.348512
$507$		0			0
$508$	−19.2104			−0.852326
$509$	−27.5992	−	27.5992i	−1.22331	−	1.22331i	−0.966446	−	0.256868i	$-0.917309\pi$
$509$	−27.5992	−	27.5992i	−1.22331	−	1.22331i	−0.256868	−	0.966446i	$-0.582691\pi$
$510$		0			0
$511$			0.820620i			0.0363021i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−20.1728	−	20.1728i	−0.889784	−	0.889784i
$515$	−7.21957	+	7.21957i	−0.318132	+	0.318132i
$516$		0			0
$517$		−	8.75560i		−	0.385071i
$518$	−0.000971348	0	0.000971348i	−4.26786e−5	0	4.26786e-5i
$519$		0			0
$520$	−8.81384	+	5.00865i	−0.386512	+	0.219644i
$521$			24.4167i			1.06972i	0.844942	+	0.534858i	$0.179635\pi$
$521$			24.4167i			1.06972i	−0.844942	+	0.534858i	$0.820365\pi$
$522$		0			0
$523$	12.3719			0.540984			0.270492	−	0.962722i	$-0.412814\pi$
$523$	12.3719			0.540984			0.270492	+	0.962722i	$0.412814\pi$
$524$	19.6194			0.857076
$525$		0			0
$526$	−0.0820117	+	0.0820117i	−0.00357588	+	0.00357588i
$527$	−28.5624	+	28.5624i	−1.24420	+	1.24420i
$528$		0			0
$529$	17.4031			0.756658
$530$	38.5830			1.67594
$531$		0			0
$532$			2.15557i			0.0934557i
$533$	−2.07029	−	0.569928i	−0.0896741	−	0.0246863i
$534$		0			0
$535$	7.59571	−	7.59571i	0.328391	−	0.328391i
$536$			1.35381i			0.0584759i
$537$		0			0
$538$	−7.87590	+	7.87590i	−0.339554	+	0.339554i
$539$	−0.872107	−	0.872107i	−0.0375643	−	0.0375643i
$540$		0			0
$541$	18.7832	+	18.7832i	0.807551	+	0.807551i	0.984263	−	0.176712i	$-0.0565460\pi$
$541$	18.7832	+	18.7832i	0.807551	+	0.807551i	−0.176712	+	0.984263i	$0.556546\pi$
$542$			20.6131i			0.885408i
$543$		0			0
$544$	−5.54964	−	5.54964i	−0.237939	−	0.237939i
$545$	25.6546			1.09892
$546$		0			0
$547$	−0.0847560			−0.00362391			−0.00181195	−	0.999998i	$-0.500577\pi$
$547$	−0.0847560			−0.00362391			−0.00181195	+	0.999998i	$0.500577\pi$
$548$	−8.48067	−	8.48067i	−0.362276	−	0.362276i
$549$		0			0
$550$		−	3.58338i		−	0.152796i
$551$	−14.9874	−	14.9874i	−0.638484	−	0.638484i
$552$		0			0
$553$	−6.74294	−	6.74294i	−0.286739	−	0.286739i
$554$	−10.3055	+	10.3055i	−0.437838	+	0.437838i
$555$		0			0
$556$		−	17.6573i		−	0.748837i
$557$	13.6121	−	13.6121i	0.576762	−	0.576762i	−0.357248	−	0.934010i	$-0.616285\pi$
$557$	13.6121	−	13.6121i	0.576762	−	0.576762i	0.934010	+	0.357248i	$0.116285\pi$
$558$		0			0
$559$	−9.29456	−	16.3558i	−0.393118	−	0.691778i
$560$		−	2.81166i		−	0.118814i
$561$		0			0
$562$	4.20649			0.177440
$563$	−20.1346			−0.848571			−0.424286	−	0.905528i	$-0.639475\pi$
$563$	−20.1346			−0.848571			−0.424286	+	0.905528i	$0.639475\pi$
$564$		0			0
$565$	3.47134	−	3.47134i	0.146040	−	0.146040i
$566$	−4.74864	+	4.74864i	−0.199600	+	0.199600i
$567$		0			0
$568$	0.674007			0.0282807
$569$	18.1813			0.762199			0.381100	−	0.924534i	$-0.375545\pi$
$569$	18.1813			0.762199			0.381100	+	0.924534i	$0.375545\pi$
$570$		0			0
$571$			14.9269i			0.624673i	0.949972	+	0.312337i	$0.101112\pi$
$571$			14.9269i			0.624673i	−0.949972	+	0.312337i	$0.898888\pi$
$572$	4.28740	+	1.18028i	0.179265	+	0.0493498i
$573$		0			0
$574$	0.421121	−	0.421121i	0.0175772	−	0.0175772i
$575$			18.4678i			0.770160i
$576$		0			0
$577$	−7.12081	+	7.12081i	−0.296443	+	0.296443i	−0.839619	−	0.543176i	$-0.817222\pi$
$577$	−7.12081	+	7.12081i	−0.296443	+	0.296443i	0.543176	+	0.839619i	$0.317222\pi$
$578$	31.5349	+	31.5349i	1.31168	+	1.31168i
$579$		0			0
$580$	19.5491	+	19.5491i	0.811732	+	0.811732i
$581$		−	9.45481i		−	0.392252i
$582$		0			0
$583$	−11.9675	−	11.9675i	−0.495643	−	0.495643i
$584$	0.820620			0.0339575
$585$		0			0
$586$	−14.0734			−0.581365
$587$	−7.63001	−	7.63001i	−0.314924	−	0.314924i	0.531890	−	0.846814i	$-0.321482\pi$
$587$	−7.63001	−	7.63001i	−0.314924	−	0.314924i	−0.846814	+	0.531890i	$0.821482\pi$
$588$		0			0
$589$		−	11.0941i		−	0.457124i
$590$	−18.1378	−	18.1378i	−0.746722	−	0.746722i
$591$		0			0
$592$	0.000971348	0	0.000971348i	3.99222e−5	0	3.99222e-5i
$593$	7.01314	−	7.01314i	0.287995	−	0.287995i	−0.548292	−	0.836287i	$-0.684722\pi$
$593$	7.01314	−	7.01314i	0.287995	−	0.287995i	0.836287	+	0.548292i	$0.184722\pi$
$594$		0			0
$595$			22.0669i			0.904656i
$596$	5.19872	−	5.19872i	0.212948	−	0.212948i
$597$		0			0
$598$	−22.0962	−	6.08283i	−0.903579	−	0.248746i
$599$		−	32.7285i		−	1.33725i	−0.743599	−	0.668626i	$-0.766883\pi$
$599$		−	32.7285i		−	1.33725i	0.743599	−	0.668626i	$-0.233117\pi$
$600$		0			0
$601$	11.3105			0.461365			0.230682	−	0.973029i	$-0.425904\pi$
$601$	11.3105			0.461365			0.230682	+	0.973029i	$0.425904\pi$
$602$	5.21759			0.212653
$603$		0			0
$604$	−1.86969	+	1.86969i	−0.0760766	+	0.0760766i
$605$	18.8453	−	18.8453i	0.766171	−	0.766171i
$606$		0			0
$607$	2.60099			0.105571			0.0527854	−	0.998606i	$-0.483190\pi$
$607$	2.60099			0.105571			0.0527854	+	0.998606i	$0.483190\pi$
$608$	2.15557			0.0874198
$609$		0			0
$610$			8.89784i			0.360263i
$611$	6.79359	−	24.6780i	0.274839	−	0.998365i
$612$		0			0
$613$	24.6280	−	24.6280i	0.994715	−	0.994715i	−0.00527094	−	0.999986i	$-0.501678\pi$
$613$	24.6280	−	24.6280i	0.994715	−	0.994715i	0.999986	+	0.00527094i	$0.00167780\pi$
$614$		−	30.7909i		−	1.24262i
$615$		0			0
$616$	−0.872107	+	0.872107i	−0.0351382	+	0.0351382i
$617$	21.4682	+	21.4682i	0.864279	+	0.864279i	0.991832	−	0.127553i	$-0.0407122\pi$
$617$	21.4682	+	21.4682i	0.864279	+	0.864279i	−0.127553	+	0.991832i	$0.540712\pi$
$618$		0			0
$619$	−3.05143	−	3.05143i	−0.122647	−	0.122647i	0.643119	−	0.765766i	$-0.277640\pi$
$619$	−3.05143	−	3.05143i	−0.122647	−	0.122647i	−0.765766	+	0.643119i	$0.777640\pi$
$620$			14.4708i			0.581161i
$621$		0			0
$622$	−11.2018	−	11.2018i	−0.449151	−	0.449151i
$623$	−5.82072			−0.233202
$624$		0			0
$625$	31.0856			1.24343
$626$	12.5994	+	12.5994i	0.503575	+	0.503575i
$627$		0			0
$628$		−	12.2084i		−	0.487167i
$629$	−0.00762351	−	0.00762351i	−0.000303969	−	0.000303969i
$630$		0			0
$631$	−9.61661	−	9.61661i	−0.382831	−	0.382831i	0.489290	−	0.872121i	$-0.337256\pi$
$631$	−9.61661	−	9.61661i	−0.382831	−	0.382831i	−0.872121	+	0.489290i	$0.837256\pi$
$632$	−6.74294	+	6.74294i	−0.268220	+	0.268220i
$633$		0			0
$634$			17.0598i			0.677531i
$635$	38.1931	−	38.1931i	1.51565	−	1.51565i
$636$		0			0
$637$	−1.78139	−	3.13475i	−0.0705812	−	0.124203i
$638$		−	12.1273i		−	0.480124i
$639$		0			0
$640$	−2.81166			−0.111140
$641$	−40.2153			−1.58841			−0.794205	−	0.607650i	$-0.792112\pi$
$641$	−40.2153			−1.58841			−0.794205	+	0.607650i	$0.792112\pi$
$642$		0			0
$643$	4.88295	−	4.88295i	0.192565	−	0.192565i	−0.604239	−	0.796803i	$-0.706523\pi$
$643$	4.88295	−	4.88295i	0.192565	−	0.192565i	0.796803	+	0.604239i	$0.206523\pi$
$644$	4.49462	−	4.49462i	0.177113	−	0.177113i
$645$		0			0
$646$	−16.9177			−0.665618
$647$	−13.7605			−0.540980			−0.270490	−	0.962723i	$-0.587186\pi$
$647$	−13.7605			−0.540980			−0.270490	+	0.962723i	$0.587186\pi$
$648$		0			0
$649$			11.2518i			0.441672i
$650$	2.78039	−	10.0999i	0.109056	−	0.396150i
$651$		0			0
$652$	−0.218796	+	0.218796i	−0.00856870	+	0.00856870i
$653$			29.6301i			1.15951i	0.814789	+	0.579757i	$0.196853\pi$
$653$			29.6301i			1.15951i	−0.814789	+	0.579757i	$0.803147\pi$
$654$		0			0
$655$	−39.0061	+	39.0061i	−1.52409	+	1.52409i
$656$	−0.421121	−	0.421121i	−0.0164420	−	0.0164420i
$657$		0			0
$658$	5.01980	+	5.01980i	0.195692	+	0.195692i
$659$			48.8982i			1.90480i	0.304845	+	0.952402i	$0.401395\pi$
$659$			48.8982i			1.90480i	−0.304845	+	0.952402i	$0.598605\pi$
$660$		0			0
$661$	32.8068	+	32.8068i	1.27604	+	1.27604i	0.942868	+	0.333168i	$0.108117\pi$
$661$	32.8068	+	32.8068i	1.27604	+	1.27604i	0.333168	+	0.942868i	$0.391883\pi$
$662$	19.1212			0.743167
$663$		0			0
$664$	−9.45481			−0.366918
$665$	−4.28557	−	4.28557i	−0.166187	−	0.166187i
$666$		0			0
$667$			62.5010i			2.42005i
$668$	15.7026	+	15.7026i	0.607553	+	0.607553i
$669$		0			0
$670$	−2.69157	−	2.69157i	−0.103985	−	0.103985i
$671$	2.75989	−	2.75989i	0.106545	−	0.106545i
$672$		0			0
$673$		−	2.65844i		−	0.102475i	−0.998686	−	0.0512377i	$-0.983683\pi$
$673$		−	2.65844i		−	0.102475i	0.998686	−	0.0512377i	$-0.0163166\pi$
$674$	13.4856	−	13.4856i	0.519446	−	0.519446i
$675$		0			0
$676$	11.1684	+	6.65331i	0.429554	+	0.255896i
$677$			5.85843i			0.225158i	0.993643	+	0.112579i	$0.0359111\pi$
$677$			5.85843i			0.225158i	−0.993643	+	0.112579i	$0.964089\pi$
$678$		0			0
$679$	−3.65019			−0.140082
$680$	22.0669			0.846229
$681$		0			0
$682$	4.48849	−	4.48849i	0.171873	−	0.171873i
$683$	−1.64052	+	1.64052i	−0.0627729	+	0.0627729i	−0.737796	−	0.675023i	$-0.764134\pi$
$683$	−1.64052	+	1.64052i	−0.0627729	+	0.0627729i	0.675023	+	0.737796i	$0.264134\pi$
$684$		0			0
$685$	33.7215			1.28843
$686$	1.00000			0.0381802
$687$		0			0
$688$		−	5.21759i		−	0.198919i
$689$	−24.4451	−	43.0166i	−0.931285	−	1.63880i
$690$		0			0
$691$	−4.12033	+	4.12033i	−0.156745	+	0.156745i	−0.781122	−	0.624378i	$-0.785353\pi$
$691$	−4.12033	+	4.12033i	−0.156745	+	0.156745i	0.624378	+	0.781122i	$0.285353\pi$
$692$			18.2357i			0.693217i
$693$		0			0
$694$	21.2631	−	21.2631i	0.807137	−	0.807137i
$695$	35.1052	+	35.1052i	1.33162	+	1.33162i
$696$		0			0
$697$	3.30512	+	3.30512i	0.125190	+	0.125190i
$698$			31.9203i			1.20820i
$699$		0			0
$700$	2.05444	+	2.05444i	0.0776504	+	0.0776504i
$701$	2.28171			0.0861791			0.0430895	−	0.999071i	$-0.486280\pi$
$701$	2.28171			0.0861791			0.0430895	+	0.999071i	$0.486280\pi$
$702$		0			0
$703$	0.00296109			0.000111680
$704$	0.872107	+	0.872107i	0.0328688	+	0.0328688i
$705$		0			0
$706$			9.96778i			0.375142i
$707$	−1.77578	−	1.77578i	−0.0667851	−	0.0667851i
$708$		0			0
$709$	−13.6589	−	13.6589i	−0.512971	−	0.512971i	0.402465	−	0.915436i	$-0.368154\pi$
$709$	−13.6589	−	13.6589i	−0.512971	−	0.512971i	−0.915436	+	0.402465i	$0.868154\pi$
$710$	−1.34002	+	1.34002i	−0.0502901	+	0.0502901i
$711$		0			0
$712$			5.82072i			0.218141i
$713$	−23.1325	+	23.1325i	−0.866319	+	0.866319i
$714$		0			0
$715$	−10.8705	+	6.17740i	−0.406534	+	0.231022i
$716$		−	20.1218i		−	0.751988i
$717$		0			0
$718$	−31.3414			−1.16965
$719$	−14.1918			−0.529264			−0.264632	−	0.964349i	$-0.585251\pi$
$719$	−14.1918			−0.529264			−0.264632	+	0.964349i	$0.585251\pi$
$720$		0			0
$721$	−2.56773	+	2.56773i	−0.0956273	+	0.0956273i
$722$	−10.1495	+	10.1495i	−0.377724	+	0.377724i
$723$		0			0
$724$	−4.03633			−0.150009
$725$	−28.5685			−1.06101
$726$		0			0
$727$			1.69747i			0.0629555i	0.999504	+	0.0314778i	$0.0100213\pi$
$727$			1.69747i			0.0629555i	−0.999504	+	0.0314778i	$0.989979\pi$
$728$	−3.13475	+	1.78139i	−0.116182	+	0.0660227i
$729$		0			0
$730$	−1.63151	+	1.63151i	−0.0603848	+	0.0603848i
$731$			40.9496i			1.51458i
$732$		0			0
$733$	5.59060	−	5.59060i	0.206494	−	0.206494i	−0.596282	−	0.802775i	$-0.703356\pi$
$733$	5.59060	−	5.59060i	0.206494	−	0.206494i	0.802775	+	0.596282i	$0.203356\pi$
$734$	−6.09330	−	6.09330i	−0.224908	−	0.224908i
$735$		0			0
$736$	−4.49462	−	4.49462i	−0.165674	−	0.165674i
$737$			1.66972i			0.0615050i
$738$		0			0
$739$	−27.2838	−	27.2838i	−1.00365	−	1.00365i	−0.999993	−	0.00365764i	$-0.998836\pi$
$739$	−27.2838	−	27.2838i	−1.00365	−	1.00365i	−0.00365764	−	0.999993i	$-0.501164\pi$
$740$	−0.00386235			−0.000141983
$741$		0			0
$742$	13.7225			0.503769
$743$	−24.2136	−	24.2136i	−0.888309	−	0.888309i	0.106052	−	0.994361i	$-0.466179\pi$
$743$	−24.2136	−	24.2136i	−0.888309	−	0.888309i	−0.994361	+	0.106052i	$0.966179\pi$
$744$		0			0
$745$			20.6716i			0.757348i
$746$	−6.86532	−	6.86532i	−0.251357	−	0.251357i
$747$		0			0
$748$	−6.84463	−	6.84463i	−0.250264	−	0.250264i
$749$	2.70151	−	2.70151i	0.0987109	−	0.0987109i
$750$		0			0
$751$			35.4494i			1.29357i	0.762674	+	0.646783i	$0.223886\pi$
$751$			35.4494i			1.29357i	−0.762674	+	0.646783i	$0.776114\pi$
$752$	5.01980	−	5.01980i	0.183053	−	0.183053i
$753$		0			0
$754$	9.40974	−	34.1813i	0.342682	−	1.24481i
$755$		−	7.43442i		−	0.270566i
$756$		0			0
$757$	−27.6556			−1.00516			−0.502580	−	0.864531i	$-0.667616\pi$
$757$	−27.6556			−1.00516			−0.502580	+	0.864531i	$0.667616\pi$
$758$	−14.8283			−0.538588
$759$		0			0
$760$	−4.28557	+	4.28557i	−0.155454	+	0.155454i
$761$	−13.3104	+	13.3104i	−0.482501	+	0.482501i	−0.905929	−	0.423429i	$-0.860826\pi$
$761$	−13.3104	+	13.3104i	−0.482501	+	0.482501i	0.423429	+	0.905929i	$0.360826\pi$
$762$		0			0
$763$	9.12437			0.330324
$764$	21.2583			0.769098
$765$		0			0
$766$		−	1.30786i		−	0.0472550i
$767$	−8.73044	+	31.7137i	−0.315238	+	1.14511i
$768$		0			0
$769$	−16.4644	+	16.4644i	−0.593721	+	0.593721i	−0.938635	−	0.344913i	$-0.887908\pi$
$769$	−16.4644	+	16.4644i	−0.593721	+	0.593721i	0.344913	+	0.938635i	$0.387908\pi$
$770$		−	3.46775i		−	0.124969i
$771$		0			0
$772$	11.8435	−	11.8435i	0.426257	−	0.426257i
$773$	33.8374	+	33.8374i	1.21705	+	1.21705i	0.968661	+	0.248387i	$0.0799004\pi$
$773$	33.8374	+	33.8374i	1.21705	+	1.21705i	0.248387	+	0.968661i	$0.420100\pi$
$774$		0			0
$775$	−10.5736	−	10.5736i	−0.379815	−	0.379815i
$776$			3.65019i			0.131034i
$777$		0			0
$778$	16.4080	+	16.4080i	0.588256	+	0.588256i
$779$	−1.28376			−0.0459954
$780$		0			0
$781$	0.831284			0.0297457
$782$	35.2754	+	35.2754i	1.26145	+	1.26145i
$783$		0			0
$784$		−	1.00000i		−	0.0357143i
$785$	24.2720	+	24.2720i	0.866304	+	0.866304i
$786$		0			0
$787$	−30.6237	−	30.6237i	−1.09162	−	1.09162i	−0.995356	−	0.0962614i	$-0.969312\pi$
$787$	−30.6237	−	30.6237i	−1.09162	−	1.09162i	−0.0962614	−	0.995356i	$-0.530688\pi$
$788$	3.79565	−	3.79565i	0.135214	−	0.135214i
$789$		0			0
$790$		−	26.8118i		−	0.953922i
$791$	1.23462	−	1.23462i	0.0438982	−	0.0438982i
$792$		0			0
$793$	9.92031	−	5.63743i	0.352281	−	0.200191i
$794$			8.93464i			0.317079i
$795$		0			0
$796$	13.7090			0.485902
$797$	−37.1725			−1.31672			−0.658358	−	0.752705i	$-0.728749\pi$
$797$	−37.1725			−1.31672			−0.658358	+	0.752705i	$0.728749\pi$
$798$		0			0
$799$	−39.3973	+	39.3973i	−1.39377	+	1.39377i
$800$	2.05444	−	2.05444i	0.0726353	−	0.0726353i
$801$		0			0
$802$	−12.9744			−0.458141
$803$	1.01211			0.0357165
$804$		0			0
$805$			17.8719i			0.629900i
$806$	16.1337	−	9.16831i	0.568284	−	0.322940i
$807$		0			0
$808$	−1.77578	+	1.77578i	−0.0624718	+	0.0624718i
$809$		−	18.6444i		−	0.655501i	−0.944764	−	0.327750i	$-0.893710\pi$
$809$		−	18.6444i		−	0.655501i	0.944764	−	0.327750i	$-0.106290\pi$
$810$		0			0
$811$	0.988016	−	0.988016i	0.0346939	−	0.0346939i	−0.689547	−	0.724241i	$-0.742190\pi$
$811$	0.988016	−	0.988016i	0.0346939	−	0.0346939i	0.724241	+	0.689547i	$0.242190\pi$
$812$	6.95287	+	6.95287i	0.243998	+	0.243998i
$813$		0			0
$814$	0.00119801	+	0.00119801i	4.19902e−5	+	4.19902e-5i
$815$		−	0.869993i		−	0.0304745i
$816$		0			0
$817$	−7.95273	−	7.95273i	−0.278231	−	0.278231i
$818$	−11.2932			−0.394857
$819$		0			0
$820$	1.67450			0.0584759
$821$	7.85970	+	7.85970i	0.274305	+	0.274305i	0.830831	−	0.556525i	$-0.187866\pi$
$821$	7.85970	+	7.85970i	0.274305	+	0.274305i	−0.556525	+	0.830831i	$0.687866\pi$
$822$		0			0
$823$			50.3747i			1.75595i	0.478705	+	0.877976i	$0.341106\pi$
$823$			50.3747i			1.75595i	−0.478705	+	0.877976i	$0.658894\pi$
$824$	2.56773	+	2.56773i	0.0894511	+	0.0894511i
$825$		0			0
$826$	−6.45093	−	6.45093i	−0.224457	−	0.224457i
$827$	1.16220	−	1.16220i	0.0404136	−	0.0404136i	−0.686611	−	0.727025i	$-0.740903\pi$
$827$	1.16220	−	1.16220i	0.0404136	−	0.0404136i	0.727025	+	0.686611i	$0.240903\pi$
$828$		0			0
$829$		−	1.03928i		−	0.0360956i	−0.999837	−	0.0180478i	$-0.994255\pi$
$829$		−	1.03928i		−	0.0360956i	0.999837	−	0.0180478i	$-0.00574510\pi$
$830$	18.7975	−	18.7975i	0.652471	−	0.652471i
$831$		0			0
$832$	1.78139	+	3.13475i	0.0617586	+	0.108678i
$833$			7.84838i			0.271930i
$834$		0			0
$835$	−62.4381			−2.16076
$836$	2.65856			0.0919482
$837$		0			0
$838$	−10.0789	+	10.0789i	−0.348170	+	0.348170i
$839$	29.0485	−	29.0485i	1.00286	−	1.00286i	0.00286874	−	0.999996i	$-0.499087\pi$
$839$	29.0485	−	29.0485i	1.00286	−	1.00286i	0.999996	−	0.00286874i	$-0.000913149\pi$
$840$		0			0
$841$	−67.6849			−2.33396
$842$	−2.11835			−0.0730032
$843$		0			0
$844$		−	4.49184i		−	0.154616i
$845$	−35.4321	+	8.97668i	−1.21890	+	0.308807i
$846$		0			0
$847$	6.70256	−	6.70256i	0.230303	−	0.230303i
$848$		−	13.7225i		−	0.471233i
$849$		0			0
$850$	−16.1240	+	16.1240i	−0.553048	+	0.553048i
$851$	−0.00617422	−	0.00617422i	−0.000211650	−	0.000211650i
$852$		0			0
$853$	−33.0645	−	33.0645i	−1.13211	−	1.13211i	−0.989826	−	0.142281i	$-0.954556\pi$
$853$	−33.0645	−	33.0645i	−1.13211	−	1.13211i	−0.142281	−	0.989826i	$-0.545444\pi$
$854$			3.16463i			0.108291i
$855$		0			0
$856$	−2.70151	−	2.70151i	−0.0923356	−	0.0923356i
$857$	34.9585			1.19416			0.597080	−	0.802182i	$-0.296328\pi$
$857$	34.9585			1.19416			0.597080	+	0.802182i	$0.296328\pi$
$858$		0			0
$859$	−5.39448			−0.184057			−0.0920286	−	0.995756i	$-0.529335\pi$
$859$	−5.39448			−0.184057			−0.0920286	+	0.995756i	$0.529335\pi$
$860$	10.3733	+	10.3733i	0.353727	+	0.353727i
$861$		0			0
$862$			26.8156i			0.913344i
$863$	−8.33914	−	8.33914i	−0.283868	−	0.283868i	0.550782	−	0.834649i	$-0.314330\pi$
$863$	−8.33914	−	8.33914i	−0.283868	−	0.283868i	−0.834649	+	0.550782i	$0.814330\pi$
$864$		0			0
$865$	−36.2551	−	36.2551i	−1.23271	−	1.23271i
$866$	4.61766	−	4.61766i	0.156914	−	0.156914i
$867$		0			0
$868$			5.14672i			0.174691i
$869$	−8.31637	+	8.31637i	−0.282114	+	0.282114i
$870$		0			0
$871$	−1.29556	+	4.70618i	−0.0438984	+	0.159463i
$872$		−	9.12437i		−	0.308990i
$873$		0			0
$874$	−13.7015			−0.463461
$875$	5.88926			0.199093
$876$		0			0
$877$	31.4556	−	31.4556i	1.06218	−	1.06218i	0.0642449	−	0.997934i	$-0.479536\pi$
$877$	31.4556	−	31.4556i	1.06218	−	1.06218i	0.997934	−	0.0642449i	$-0.0204639\pi$
$878$	7.66701	−	7.66701i	0.258749	−	0.258749i
$879$		0			0
$880$	−3.46775			−0.116898
$881$	5.76157			0.194112			0.0970561	−	0.995279i	$-0.469057\pi$
$881$	5.76157			0.194112			0.0970561	+	0.995279i	$0.469057\pi$
$882$		0			0
$883$		−	9.22001i		−	0.310278i	−0.987893	−	0.155139i	$-0.950417\pi$
$883$		−	9.22001i		−	0.310278i	0.987893	−	0.155139i	$-0.0495826\pi$
$884$	−13.9810	−	24.6027i	−0.470232	−	0.827478i
$885$		0			0
$886$	21.3032	−	21.3032i	0.715695	−	0.715695i
$887$		−	50.9594i		−	1.71105i	−0.517762	−	0.855525i	$-0.673235\pi$
$887$		−	50.9594i		−	1.71105i	0.517762	−	0.855525i	$-0.326765\pi$
$888$		0			0
$889$	13.5838	−	13.5838i	0.455587	−	0.455587i
$890$	−11.5724	−	11.5724i	−0.387908	−	0.387908i
$891$		0			0
$892$	−8.59883	−	8.59883i	−0.287910	−	0.287910i
$893$		−	15.3025i		−	0.512079i
$894$		0			0
$895$	40.0051	+	40.0051i	1.33722	+	1.33722i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	0.393023			0.0131153
$899$	−35.7845	−	35.7845i	−1.19348	−	1.19348i
$900$		0			0
$901$			107.699i			3.58799i
$902$	−0.519388	−	0.519388i	−0.0172937	−	0.0172937i
$903$		0			0
$904$	−1.23462	−	1.23462i	−0.0410630	−	0.0410630i
$905$	8.02480	−	8.02480i	0.266753	−	0.266753i
$906$		0			0
$907$			2.53598i			0.0842057i	0.999113	+	0.0421029i	$0.0134057\pi$
$907$			2.53598i			0.0842057i	−0.999113	+	0.0421029i	$0.986594\pi$
$908$	1.53435	−	1.53435i	0.0509193	−	0.0509193i
$909$		0			0
$910$	2.69067	−	9.77398i	0.0891949	−	0.324004i
$911$			0.347480i			0.0115125i	0.999983	+	0.00575626i	$0.00183229\pi$
$911$			0.347480i			0.0115125i	−0.999983	+	0.00575626i	$0.998168\pi$
$912$		0			0
$913$	−11.6611			−0.385924
$914$	0.926602			0.0306493
$915$		0			0
$916$	−17.9893	+	17.9893i	−0.594384	+	0.594384i
$917$	−13.8730	+	13.8730i	−0.458127	+	0.458127i
$918$		0			0
$919$	−2.62522			−0.0865982			−0.0432991	−	0.999062i	$-0.513787\pi$
$919$	−2.62522			−0.0865982			−0.0432991	+	0.999062i	$0.513787\pi$
$920$	17.8719			0.589218
$921$		0			0
$922$			17.9728i			0.591902i
$923$	2.34301	+	0.645005i	0.0771210	+	0.0212306i
$924$		0			0
$925$	0.00282216	−	0.00282216i	9.27922e−5	−	9.27922e-5i
$926$		−	36.6805i		−	1.20540i
$927$		0			0
$928$	6.95287	−	6.95287i	0.228239	−	0.228239i
$929$	18.5436	+	18.5436i	0.608396	+	0.608396i	0.942527	−	0.334131i	$-0.108443\pi$
$929$	18.5436	+	18.5436i	0.608396	+	0.608396i	−0.334131	+	0.942527i	$0.608443\pi$
$930$		0			0
$931$	−1.52422	−	1.52422i	−0.0499542	−	0.0499542i
$932$			21.6085i			0.707811i
$933$		0			0
$934$	0.484847	+	0.484847i	0.0158647	+	0.0158647i
$935$	27.2162			0.890064
$936$		0			0
$937$	−25.5510			−0.834713			−0.417357	−	0.908743i	$-0.637043\pi$
$937$	−25.5510			−0.834713			−0.417357	+	0.908743i	$0.637043\pi$
$938$	−0.957291	−	0.957291i	−0.0312567	−	0.0312567i
$939$		0			0
$940$			19.9601i			0.651028i
$941$	−18.7699	−	18.7699i	−0.611881	−	0.611881i	0.331555	−	0.943436i	$-0.392427\pi$
$941$	−18.7699	−	18.7699i	−0.611881	−	0.611881i	−0.943436	+	0.331555i	$0.892427\pi$
$942$		0			0
$943$	2.67679	+	2.67679i	0.0871683	+	0.0871683i
$944$	−6.45093	+	6.45093i	−0.209960	+	0.209960i
$945$		0			0
$946$		−	6.43509i		−	0.209223i
$947$	21.5262	−	21.5262i	0.699507	−	0.699507i	−0.264797	−	0.964304i	$-0.585305\pi$
$947$	21.5262	−	21.5262i	0.699507	−	0.699507i	0.964304	+	0.264797i	$0.0853050\pi$
$948$		0			0
$949$	2.85267	+	0.785309i	0.0926015	+	0.0254922i
$950$		−	6.26281i		−	0.203192i
$951$		0			0
$952$	7.84838			0.254367
$953$	8.94992			0.289916			0.144958	−	0.989438i	$-0.453695\pi$
$953$	8.94992			0.289916			0.144958	+	0.989438i	$0.453695\pi$
$954$		0			0
$955$	−42.2645	+	42.2645i	−1.36765	+	1.36765i
$956$	−11.2064	+	11.2064i	−0.362440	+	0.362440i
$957$		0			0
$958$	−19.3728			−0.625907
$959$	11.9935			0.387289
$960$		0			0
$961$			4.51130i			0.145526i
$962$	0.00244708	+	0.00430618i	7.88971e−5	+	0.000138837i
$963$		0			0
$964$	15.7392	−	15.7392i	0.506926	−	0.506926i
$965$			47.0931i			1.51598i
$966$		0			0
$967$	24.9789	−	24.9789i	0.803266	−	0.803266i	−0.180339	−	0.983605i	$-0.557719\pi$
$967$	24.9789	−	24.9789i	0.803266	−	0.803266i	0.983605	+	0.180339i	$0.0577194\pi$
$968$	−6.70256	−	6.70256i	−0.215429	−	0.215429i
$969$		0			0
$970$	−7.25710	−	7.25710i	−0.233012	−	0.233012i
$971$		−	44.9405i		−	1.44221i	−0.692827	−	0.721104i	$-0.743635\pi$
$971$		−	44.9405i		−	1.44221i	0.692827	−	0.721104i	$-0.256365\pi$
$972$		0			0
$973$	12.4856	+	12.4856i	0.400270	+	0.400270i
$974$	−36.8362			−1.18031
$975$		0			0
$976$	3.16463			0.101297
$977$	38.8342	+	38.8342i	1.24242	+	1.24242i	0.958995	+	0.283422i	$0.0914698\pi$
$977$	38.8342	+	38.8342i	1.24242	+	1.24242i	0.283422	+	0.958995i	$0.408530\pi$
$978$		0			0
$979$			7.17897i			0.229441i
$980$	1.98814	+	1.98814i	0.0635088	+	0.0635088i
$981$		0			0
$982$	0.172062	+	0.172062i	0.00549073	+	0.00549073i
$983$	10.9153	−	10.9153i	0.348145	−	0.348145i	−0.511273	−	0.859418i	$-0.670826\pi$
$983$	10.9153	−	10.9153i	0.348145	−	0.348145i	0.859418	+	0.511273i	$0.170826\pi$
$984$		0			0
$985$			15.0926i			0.480890i
$986$	−54.5688	+	54.5688i	−1.73782	+	1.73782i
$987$		0			0
$988$	7.49326	+	2.06281i	0.238392	+	0.0656268i
$989$			33.1648i			1.05458i
$990$		0			0
$991$	−10.5793			−0.336064			−0.168032	−	0.985782i	$-0.553741\pi$
$991$	−10.5793			−0.336064			−0.168032	+	0.985782i	$0.553741\pi$
$992$	5.14672			0.163408
$993$		0			0
$994$	−0.476595	+	0.476595i	−0.0151167	+	0.0151167i
$995$	−27.2554	+	27.2554i	−0.864053	+	0.864053i
$996$		0			0
$997$	5.09165			0.161254			0.0806270	−	0.996744i	$-0.474308\pi$
$997$	5.09165			0.161254			0.0806270	+	0.996744i	$0.474308\pi$
$998$	34.3689			1.08793
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.y.c.1331.5	yes	16
3.2	odd	2		1638.2.y.d.1331.4	yes	16
13.8	odd	4		1638.2.y.d.827.4	yes	16
39.8	even	4	inner	1638.2.y.c.827.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.y.c.827.5	✓	16	39.8	even	4	inner
1638.2.y.c.1331.5	yes	16	1.1	even	1	trivial
1638.2.y.d.827.4	yes	16	13.8	odd	4
1638.2.y.d.1331.4	yes	16	3.2	odd	2

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.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.98814 - 1.98814i) q^{5} +(-0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -2.81166i q^{10} +(-0.872107 + 0.872107i) q^{11} +(-3.13475 + 1.78139i) q^{13} -1.00000i q^{14} -1.00000 q^{16} +7.84838 q^{17} +(-1.52422 + 1.52422i) q^{19} +(1.98814 - 1.98814i) q^{20} -1.23335 q^{22} +6.35635 q^{23} +2.90541i q^{25} +(-3.47623 - 0.956970i) q^{26} +(0.707107 - 0.707107i) q^{28} +9.83285i q^{29} +(-3.63928 + 3.63928i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.54964 + 5.54964i) q^{34} +2.81166i q^{35} +(-0.000971348 - 0.000971348i) q^{37} -2.15557 q^{38} +2.81166 q^{40} +(0.421121 + 0.421121i) q^{41} +5.21759i q^{43} +(-0.872107 - 0.872107i) q^{44} +(4.49462 + 4.49462i) q^{46} +(-5.01980 + 5.01980i) q^{47} +1.00000i q^{49} +(-2.05444 + 2.05444i) q^{50} +(-1.78139 - 3.13475i) q^{52} +13.7225i q^{53} +3.46775 q^{55} +1.00000 q^{56} +(-6.95287 + 6.95287i) q^{58} +(6.45093 - 6.45093i) q^{59} -3.16463 q^{61} -5.14672 q^{62} -1.00000i q^{64} +(9.77398 + 2.69067i) q^{65} +(0.957291 - 0.957291i) q^{67} +7.84838i q^{68} +(-1.98814 + 1.98814i) q^{70} +(-0.476595 - 0.476595i) q^{71} +(-0.580266 - 0.580266i) q^{73} -0.00137369i q^{74} +(-1.52422 - 1.52422i) q^{76} +1.23335 q^{77} +9.53595 q^{79} +(1.98814 + 1.98814i) q^{80} +0.595555i q^{82} +(6.68556 + 6.68556i) q^{83} +(-15.6037 - 15.6037i) q^{85} +(-3.68939 + 3.68939i) q^{86} -1.23335i q^{88} +(4.11587 - 4.11587i) q^{89} +(3.47623 + 0.956970i) q^{91} +6.35635i q^{92} -7.09906 q^{94} +6.06071 q^{95} +(2.58108 - 2.58108i) q^{97} +(-0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{5} + 8 q^{11} + 4 q^{13} - 16 q^{16} + 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} - 24 q^{23} - 8 q^{26} - 8 q^{31} + 4 q^{34} - 4 q^{37} - 16 q^{38} + 16 q^{41} + 8 q^{44} - 4 q^{47} + 16 q^{50}+ \cdots - 28 q^{97}+O(q^{100}) \) 16 * q - 4 * q^5 + 8 * q^11 + 4 * q^13 - 16 * q^16 + 8 * q^17 + 16 * q^19 + 4 * q^20 - 8 * q^22 - 24 * q^23 - 8 * q^26 - 8 * q^31 + 4 * q^34 - 4 * q^37 - 16 * q^38 + 16 * q^41 + 8 * q^44 - 4 * q^47 + 16 * q^50 - 16 * q^55 + 16 * q^56 + 4 * q^58 + 8 * q^59 - 40 * q^61 - 24 * q^62 - 56 * q^65 - 4 * q^67 - 4 * q^70 + 24 * q^71 - 12 * q^73 + 16 * q^76 + 8 * q^77 + 16 * q^79 + 4 * q^80 + 8 * q^85 - 24 * q^86 - 16 * q^89 + 8 * q^91 - 8 * q^94 + 40 * q^95 - 28 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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