LMFDB - Embedded newform 324.2.l.a.143.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.3
Character	$\chi$	$=$	324.143
Dual form			324.2.l.a.179.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16185 + 0.806289i) q^{2} +(0.699796 - 1.87358i) q^{4} +(-0.297855 + 0.0525198i) q^{5} +(-0.312070 + 0.371910i) q^{7} +(0.697584 + 2.74105i) q^{8} +O(q^{10})$	\(q+(-1.16185 + 0.806289i) q^{2} +(0.699796 - 1.87358i) q^{4} +(-0.297855 + 0.0525198i) q^{5} +(-0.312070 + 0.371910i) q^{7} +(0.697584 + 2.74105i) q^{8} +(0.303717 - 0.301177i) q^{10} +(0.00722947 - 0.0410004i) q^{11} +(4.05761 + 1.47685i) q^{13} +(0.0627115 - 0.683722i) q^{14} +(-3.02057 - 2.62224i) q^{16} +(2.14427 - 1.23800i) q^{17} +(6.55326 + 3.78353i) q^{19} +(-0.110038 + 0.594806i) q^{20} +(0.0246586 + 0.0534654i) q^{22} +(5.03199 - 4.22234i) q^{23} +(-4.61250 + 1.67881i) q^{25} +(-5.90510 + 1.55572i) q^{26} +(0.478416 + 0.844947i) q^{28} +(2.40260 + 6.60109i) q^{29} +(2.30836 + 2.75099i) q^{31} +(5.62374 + 0.611204i) q^{32} +(-1.49314 + 3.16727i) q^{34} +(0.0734187 - 0.127165i) q^{35} +(-3.36015 - 5.81994i) q^{37} +(-10.6645 + 0.887926i) q^{38} +(-0.351738 - 0.779799i) q^{40} +(-2.16312 + 5.94312i) q^{41} +(-2.38200 - 0.420011i) q^{43} +(-0.0717582 - 0.0422369i) q^{44} +(-2.44200 + 8.96296i) q^{46} +(5.51016 + 4.62358i) q^{47} +(1.17461 + 6.66153i) q^{49} +(4.00543 - 5.66954i) q^{50} +(5.60648 - 6.56874i) q^{52} -9.90799i q^{53} +0.0125918i q^{55} +(-1.23712 - 0.595961i) q^{56} +(-8.11385 - 5.73229i) q^{58} +(-0.755918 - 4.28703i) q^{59} +(-5.77142 - 4.84280i) q^{61} +(-4.90006 - 1.33504i) q^{62} +(-7.02675 + 3.82423i) q^{64} +(-1.28614 - 0.226781i) q^{65} +(3.80965 - 10.4669i) q^{67} +(-0.818925 - 4.88380i) q^{68} +(0.0172301 + 0.206943i) q^{70} +(-1.68932 - 2.92598i) q^{71} +(0.315477 - 0.546421i) q^{73} +(8.59654 + 4.05266i) q^{74} +(11.6747 - 9.63033i) q^{76} +(0.0129924 + 0.0154837i) q^{77} +(-1.03548 - 2.84496i) q^{79} +(1.03741 + 0.622407i) q^{80} +(-2.27865 - 8.64913i) q^{82} +(-5.41059 + 1.96930i) q^{83} +(-0.573662 + 0.481360i) q^{85} +(3.10618 - 1.43259i) q^{86} +(0.117427 - 0.00878482i) q^{88} +(-9.00521 - 5.19916i) q^{89} +(-1.81551 + 1.04819i) q^{91} +(-4.38950 - 12.3826i) q^{92} +(-10.1299 - 0.929124i) q^{94} +(-2.15063 - 0.782765i) q^{95} +(-0.578459 + 3.28061i) q^{97} +(-6.73584 - 6.79263i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

Coefficient data

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

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

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

$2$	−1.16185	+	0.806289i	−0.821553	+	0.570132i
$2$	−1.16185	+	0.806289i	−0.821553	+	0.570132i
$3$		0			0
$3$		0			0
$4$	0.699796	−	1.87358i	0.349898	−	0.936788i
$5$	−0.297855	+	0.0525198i	−0.133205	+	0.0234876i	−0.239853	−	0.970809i	$-0.577099\pi$
$5$	−0.297855	+	0.0525198i	−0.133205	+	0.0234876i	0.106648	+	0.994297i	$0.465988\pi$
$6$		0			0
$7$	−0.312070	+	0.371910i	−0.117951	+	0.140569i	−0.821789	−	0.569792i	$-0.807024\pi$
$7$	−0.312070	+	0.371910i	−0.117951	+	0.140569i	0.703838	+	0.710361i	$0.251468\pi$
$8$	0.697584	+	2.74105i	0.246633	+	0.969109i
$9$		0			0
$10$	0.303717	−	0.301177i	0.0960436	−	0.0952405i
$11$	0.00722947	−	0.0410004i	0.00217977	−	0.0123621i	−0.983698	−	0.179826i	$-0.942447\pi$
$11$	0.00722947	−	0.0410004i	0.00217977	−	0.0123621i	0.985878	+	0.167464i	$0.0535577\pi$
$12$		0			0
$13$	4.05761	+	1.47685i	1.12538	+	0.409604i	0.836612	−	0.547796i	$-0.184533\pi$
$13$	4.05761	+	1.47685i	1.12538	+	0.409604i	0.288765	+	0.957400i	$0.406755\pi$
$14$	0.0627115	−	0.683722i	0.0167604	−	0.182733i
$15$		0			0
$16$	−3.02057	−	2.62224i	−0.755142	−	0.655561i
$17$	2.14427	−	1.23800i	0.520062	−	0.300258i	−0.216898	−	0.976194i	$-0.569594\pi$
$17$	2.14427	−	1.23800i	0.520062	−	0.300258i	0.736960	+	0.675936i	$0.236261\pi$
$18$		0			0
$19$	6.55326	+	3.78353i	1.50342	+	0.868001i	0.999992	+	0.00396479i	$0.00126203\pi$
$19$	6.55326	+	3.78353i	1.50342	+	0.868001i	0.503430	+	0.864036i	$0.332071\pi$
$20$	−0.110038	+	0.594806i	−0.0246052	+	0.133003i
$21$		0			0
$22$	0.0246586	+	0.0534654i	0.00525723	+	0.0113989i
$23$	5.03199	−	4.22234i	1.04924	−	0.880418i	0.0562281	−	0.998418i	$-0.482093\pi$
$23$	5.03199	−	4.22234i	1.04924	−	0.880418i	0.993014	+	0.118000i	$0.0376481\pi$
$24$		0			0
$25$	−4.61250	+	1.67881i	−0.922501	+	0.335763i
$26$	−5.90510	+	1.55572i	−1.15809	+	0.305103i
$27$		0			0
$28$	0.478416	+	0.844947i	0.0904122	+	0.159680i
$29$	2.40260	+	6.60109i	0.446152	+	1.22579i	0.935383	+	0.353637i	$0.115055\pi$
$29$	2.40260	+	6.60109i	0.446152	+	1.22579i	−0.489231	+	0.872154i	$0.662722\pi$
$30$		0			0
$31$	2.30836	+	2.75099i	0.414593	+	0.494092i	0.932412	−	0.361398i	$-0.117700\pi$
$31$	2.30836	+	2.75099i	0.414593	+	0.494092i	−0.517819	+	0.855490i	$0.673256\pi$
$32$	5.62374	+	0.611204i	0.994146	+	0.108047i
$33$		0			0
$34$	−1.49314	+	3.16727i	−0.256072	+	0.543182i
$35$	0.0734187	−	0.127165i	0.0124100	−	0.0214948i
$36$		0			0
$37$	−3.36015	−	5.81994i	−0.552405	−	0.956793i	−0.998100	−	0.0616082i	$-0.980377\pi$
$37$	−3.36015	−	5.81994i	−0.552405	−	0.956793i	0.445696	−	0.895184i	$-0.352956\pi$
$38$	−10.6645	+	0.887926i	−1.73002	+	0.144041i
$39$		0			0
$40$	−0.351738	−	0.779799i	−0.0556147	−	0.123297i
$41$	−2.16312	+	5.94312i	−0.337823	+	0.928160i	0.648188	+	0.761480i	$0.275527\pi$
$41$	−2.16312	+	5.94312i	−0.337823	+	0.928160i	−0.986011	+	0.166680i	$0.946695\pi$
$42$		0			0
$43$	−2.38200	−	0.420011i	−0.363252	−	0.0640511i	−0.0109565	−	0.999940i	$-0.503488\pi$
$43$	−2.38200	−	0.420011i	−0.363252	−	0.0640511i	−0.352295	+	0.935889i	$0.614599\pi$
$44$	−0.0717582	−	0.0422369i	−0.0108179	−	0.00636745i
$45$		0			0
$46$	−2.44200	+	8.96296i	−0.360053	+	1.32152i
$47$	5.51016	+	4.62358i	0.803740	+	0.674418i	0.949105	−	0.314960i	$-0.101991\pi$
$47$	5.51016	+	4.62358i	0.803740	+	0.674418i	−0.145365	+	0.989378i	$0.546436\pi$
$48$		0			0
$49$	1.17461	+	6.66153i	0.167801	+	0.951647i
$50$	4.00543	−	5.66954i	0.566454	−	0.801794i
$51$		0			0
$52$	5.60648	−	6.56874i	0.777479	−	0.910920i
$53$		−	9.90799i		−	1.36097i	−0.732763	−	0.680484i	$-0.761770\pi$
$53$		−	9.90799i		−	1.36097i	0.732763	−	0.680484i	$-0.238230\pi$
$54$		0			0
$55$			0.0125918i			0.00169788i
$56$	−1.23712	−	0.595961i	−0.165317	−	0.0796387i
$57$		0			0
$58$	−8.11385	−	5.73229i	−1.06540	−	0.752687i
$59$	−0.755918	−	4.28703i	−0.0984122	−	0.558123i	−0.993648	−	0.112531i	$-0.964104\pi$
$59$	−0.755918	−	4.28703i	−0.0984122	−	0.558123i	0.895236	−	0.445592i	$-0.147007\pi$
$60$		0			0
$61$	−5.77142	−	4.84280i	−0.738955	−	0.620057i	0.193602	−	0.981080i	$-0.437983\pi$
$61$	−5.77142	−	4.84280i	−0.738955	−	0.620057i	−0.932557	+	0.361024i	$0.882427\pi$
$62$	−4.90006	−	1.33504i	−0.622308	−	0.169550i
$63$		0			0
$64$	−7.02675	+	3.82423i	−0.878344	+	0.478029i
$65$	−1.28614	−	0.226781i	−0.159526	−	0.0281287i
$66$		0			0
$67$	3.80965	−	10.4669i	0.465423	−	1.27874i	−0.455932	−	0.890015i	$-0.650694\pi$
$67$	3.80965	−	10.4669i	0.465423	−	1.27874i	0.921354	−	0.388724i	$-0.127084\pi$
$68$	−0.818925	−	4.88380i	−0.0993092	−	0.592248i
$69$		0			0
$70$	0.0172301	+	0.206943i	0.00205939	+	0.0247345i
$71$	−1.68932	−	2.92598i	−0.200485	−	0.347250i	0.748200	−	0.663473i	$-0.230918\pi$
$71$	−1.68932	−	2.92598i	−0.200485	−	0.347250i	−0.948685	+	0.316223i	$0.897585\pi$
$72$		0			0
$73$	0.315477	−	0.546421i	0.0369237	−	0.0639538i	−0.846973	−	0.531636i	$-0.821577\pi$
$73$	0.315477	−	0.546421i	0.0369237	−	0.0639538i	0.883897	+	0.467682i	$0.154911\pi$
$74$	8.59654	+	4.05266i	0.999328	+	0.471112i
$75$		0			0
$76$	11.6747	−	9.63033i	1.33918	−	1.10468i
$77$	0.0129924	+	0.0154837i	0.00148062	+	0.00176453i
$78$		0			0
$79$	−1.03548	−	2.84496i	−0.116501	−	0.320083i	0.867714	−	0.497065i	$-0.165589\pi$
$79$	−1.03548	−	2.84496i	−0.116501	−	0.320083i	−0.984214	+	0.176982i	$0.943367\pi$
$80$	1.03741	+	0.622407i	0.115986	+	0.0695873i
$81$		0			0
$82$	−2.27865	−	8.64913i	−0.251635	−	0.955136i
$83$	−5.41059	+	1.96930i	−0.593890	+	0.216158i	−0.621439	−	0.783462i	$-0.713452\pi$
$83$	−5.41059	+	1.96930i	−0.593890	+	0.216158i	0.0275495	+	0.999620i	$0.491230\pi$
$84$		0			0
$85$	−0.573662	+	0.481360i	−0.0622224	+	0.0522108i
$86$	3.10618	−	1.43259i	0.334948	−	0.154480i
$87$		0			0
$88$	0.117427	−	0.00878482i	0.0125178	−	0.000936465i
$89$	−9.00521	−	5.19916i	−0.954550	−	0.551110i	−0.0600588	−	0.998195i	$-0.519129\pi$
$89$	−9.00521	−	5.19916i	−0.954550	−	0.551110i	−0.894491	+	0.447085i	$0.852462\pi$
$90$		0			0
$91$	−1.81551	+	1.04819i	−0.190317	+	0.109880i
$92$	−4.38950	−	12.3826i	−0.457637	−	1.29097i
$93$		0			0
$94$	−10.1299	−	0.929124i	−1.04482	−	0.0958318i
$95$	−2.15063	−	0.782765i	−0.220650	−	0.0803100i
$96$		0			0
$97$	−0.578459	+	3.28061i	−0.0587337	+	0.333095i	−0.999989	−	0.00459941i	$-0.998536\pi$
$97$	−0.578459	+	3.28061i	−0.0587337	+	0.333095i	0.941256	+	0.337694i	$0.109647\pi$
$98$	−6.73584	−	6.79263i	−0.680422	−	0.686160i
$99$		0			0
$100$	−0.0824291	+	9.81670i	−0.00824291	+	0.981670i
$101$	10.7344	−	12.7927i	1.06811	−	1.27292i	0.107742	−	0.994179i	$-0.465638\pi$
$101$	10.7344	−	12.7927i	1.06811	−	1.27292i	0.960366	−	0.278743i	$-0.0899177\pi$
$102$		0			0
$103$	−15.6512	+	2.75973i	−1.54216	+	0.271924i	−0.879098	−	0.476640i	$-0.841854\pi$
$103$	−15.6512	+	2.75973i	−1.54216	+	0.271924i	−0.663062	+	0.748565i	$0.730743\pi$
$104$	−1.21760	+	12.1523i	−0.119395	+	1.19163i
$105$		0			0
$106$	7.98871	+	11.5116i	0.775932	+	1.11811i
$107$	1.00162			0.0968302			0.0484151	−	0.998827i	$-0.484583\pi$
$107$	1.00162			0.0968302			0.0484151	+	0.998827i	$0.484583\pi$
$108$		0			0
$109$	7.26618			0.695973			0.347987	−	0.937499i	$-0.386865\pi$
$109$	7.26618			0.695973			0.347987	+	0.937499i	$0.386865\pi$
$110$	−0.0101527	−	0.0146298i	−0.000968019	−	0.00139490i
$111$		0			0
$112$	1.91787	−	0.305058i	0.181221	−	0.0288253i
$113$	−14.2492	+	2.51252i	−1.34045	+	0.236358i	−0.797456	−	0.603377i	$-0.793821\pi$
$113$	−14.2492	+	2.51252i	−1.34045	+	0.236358i	−0.542997	+	0.839735i	$0.682710\pi$
$114$		0			0
$115$	−1.27704	+	1.52192i	−0.119085	+	0.141920i
$116$	14.0490	+	0.117967i	1.30441	+	0.0109529i
$117$		0			0
$118$	4.33485	+	4.37140i	0.399055	+	0.402420i
$119$	−0.208739	+	1.18382i	−0.0191351	+	0.108520i
$120$		0			0
$121$	10.3350	+	3.76163i	0.939545	+	0.341966i
$122$	10.6102	+	0.973177i	0.960605	+	0.0881073i
$123$		0			0
$124$	6.76957	−	2.39974i	0.607925	−	0.215503i
$125$	2.59533	−	1.49841i	0.232133	−	0.134022i
$126$		0			0
$127$	−7.70348	−	4.44760i	−0.683573	−	0.394661i	0.117627	−	0.993058i	$-0.462471\pi$
$127$	−7.70348	−	4.44760i	−0.683573	−	0.394661i	−0.801200	+	0.598397i	$0.795805\pi$
$128$	5.08061	−	10.1088i	0.449067	−	0.893498i
$129$		0			0
$130$	1.67715	−	0.773514i	0.147096	−	0.0678417i
$131$	−14.8870	+	12.4917i	−1.30068	+	1.09140i	−0.310657	+	0.950522i	$0.600549\pi$
$131$	−14.8870	+	12.4917i	−1.30068	+	1.09140i	−0.990027	+	0.140881i	$0.955006\pi$
$132$		0			0
$133$	−3.45221	+	1.25650i	−0.299344	+	0.108952i
$134$	4.01312	+	15.2327i	0.346681	+	1.31590i
$135$		0			0
$136$	4.88922	+	5.01396i	0.419247	+	0.429943i
$137$	5.24564	+	14.4123i	0.448165	+	1.23132i	0.934000	+	0.357274i	$0.116294\pi$
$137$	5.24564	+	14.4123i	0.448165	+	1.23132i	−0.485834	+	0.874051i	$0.661484\pi$
$138$		0			0
$139$	5.74324	+	6.84453i	0.487135	+	0.580545i	0.952486	−	0.304581i	$-0.0985164\pi$
$139$	5.74324	+	6.84453i	0.487135	+	0.580545i	−0.465351	+	0.885126i	$0.654072\pi$
$140$	−0.186875	−	0.226545i	−0.0157938	−	0.0191466i
$141$		0			0
$142$	4.32192	+	2.03748i	0.362688	+	0.170981i
$143$	0.0898857	−	0.155687i	0.00751662	−	0.0130192i
$144$		0			0
$145$	−1.06231	−	1.83998i	−0.0882203	−	0.152802i
$146$	0.0740367	+	0.889226i	0.00612732	+	0.0735928i
$147$		0			0
$148$	−13.2555	+	2.22271i	−1.08960	+	0.182706i
$149$	−0.588938	+	1.61809i	−0.0482477	+	0.132559i	−0.961476	−	0.274889i	$-0.911359\pi$
$149$	−0.588938	+	1.61809i	−0.0482477	+	0.132559i	0.913228	+	0.407448i	$0.133581\pi$
$150$		0			0
$151$	0.593940	+	0.104728i	0.0483342	+	0.00852262i	0.197763	−	0.980250i	$-0.436632\pi$
$151$	0.593940	+	0.104728i	0.0483342	+	0.00852262i	−0.149429	+	0.988772i	$0.547743\pi$
$152$	−5.79941	+	20.6022i	−0.470394	+	1.67106i
$153$		0			0
$154$	−0.0275795	−	0.00751415i	−0.00222242	−	0.000605507i
$155$	−0.832036	−	0.698161i	−0.0668307	−	0.0560776i
$156$		0			0
$157$	−1.80133	−	10.2158i	−0.143762	−	0.815313i	−0.968353	−	0.249584i	$-0.919706\pi$
$157$	−1.80133	−	10.2158i	−0.143762	−	0.815313i	0.824592	−	0.565729i	$-0.191405\pi$
$158$	3.49693	+	2.47052i	0.278201	+	0.196544i
$159$		0			0
$160$	−1.70716	+	0.113308i	−0.134963	+	0.00895775i
$161$			3.18911i			0.251337i
$162$		0			0
$163$		−	5.70430i		−	0.446795i	−0.974727	−	0.223397i	$-0.928285\pi$
$163$		−	5.70430i		−	0.446795i	0.974727	−	0.223397i	$-0.0717148\pi$
$164$	9.62115	+	8.21175i	0.751285	+	0.641230i
$165$		0			0
$166$	4.69849	−	6.65053i	0.364673	−	0.516181i
$167$	0.911752	+	5.17080i	0.0705535	+	0.400129i	0.999549	+	0.0300372i	$0.00956257\pi$
$167$	0.911752	+	5.17080i	0.0705535	+	0.400129i	−0.928995	+	0.370092i	$0.879326\pi$
$168$		0			0
$169$	4.32450	+	3.62869i	0.332654	+	0.279130i
$170$	0.278395	−	1.02181i	0.0213519	−	0.0783689i
$171$		0			0
$172$	−2.45384	+	4.16894i	−0.187104	+	0.317879i
$173$	1.36617	+	0.240893i	0.103868	+	0.0183148i	0.225341	−	0.974280i	$-0.427650\pi$
$173$	1.36617	+	0.240893i	0.103868	+	0.0183148i	−0.121472	+	0.992595i	$0.538762\pi$
$174$		0			0
$175$	0.815054	−	2.23934i	0.0616123	−	0.169278i
$176$	−0.129350	+	0.104887i	−0.00975013	+	0.00790616i
$177$		0			0
$178$	14.6547	−	1.22015i	1.09842	−	0.0914541i
$179$	5.77179	+	9.99703i	0.431403	+	0.747213i	0.996994	−	0.0774732i	$-0.0246852\pi$
$179$	5.77179	+	9.99703i	0.431403	+	0.747213i	−0.565591	+	0.824686i	$0.691352\pi$
$180$		0			0
$181$	8.57298	−	14.8488i	0.637225	−	1.10371i	−0.348814	−	0.937192i	$-0.613416\pi$
$181$	8.57298	−	14.8488i	0.637225	−	1.10371i	0.986039	−	0.166514i	$-0.0532510\pi$
$182$	1.26421	−	2.68166i	0.0937097	−	0.198778i
$183$		0			0
$184$	15.0839	+	10.8475i	1.11200	+	0.799689i
$185$	1.30650	+	1.55702i	0.0960556	+	0.114475i
$186$		0			0
$187$	−0.0352564	−	0.0968660i	−0.00257820	−	0.00708355i
$188$	12.5186	−	7.08814i	0.913014	−	0.516956i
$189$		0			0
$190$	3.12985	−	0.824572i	0.227063	−	0.0598208i
$191$	−15.5567	+	5.66216i	−1.12564	+	0.409699i	−0.836708	−	0.547650i	$-0.815523\pi$
$191$	−15.5567	+	5.66216i	−1.12564	+	0.409699i	−0.288933	+	0.957349i	$0.593300\pi$
$192$		0			0
$193$	−6.74355	+	5.65851i	−0.485411	+	0.407308i	−0.852378	−	0.522925i	$-0.824841\pi$
$193$	−6.74355	+	5.65851i	−0.485411	+	0.407308i	0.366967	+	0.930234i	$0.380396\pi$
$194$	−1.97303	−	4.27798i	−0.141655	−	0.307141i
$195$		0			0
$196$	13.3029	+	2.46100i	0.950205	+	0.175786i
$197$	10.8232	+	6.24879i	0.771122	+	0.445208i	0.833275	−	0.552859i	$-0.186463\pi$
$197$	10.8232	+	6.24879i	0.771122	+	0.445208i	−0.0621526	+	0.998067i	$0.519797\pi$
$198$		0			0
$199$	−3.88531	+	2.24318i	−0.275422	+	0.159015i	−0.631349	−	0.775499i	$-0.717499\pi$
$199$	−3.88531	+	2.24318i	−0.275422	+	0.159015i	0.355927	+	0.934514i	$0.384165\pi$
$200$	−7.81933	−	11.4720i	−0.552910	−	0.811194i
$201$		0			0
$202$	−2.15711	+	23.5182i	−0.151773	+	1.65474i
$203$	−3.20479	−	1.16645i	−0.224932	−	0.0818686i
$204$		0			0
$205$	0.332164	−	1.88379i	0.0231993	−	0.131570i
$206$	15.9592	−	15.8258i	1.11193	−	1.10264i
$207$		0			0
$208$	−8.38363	−	15.1009i	−0.581300	−	1.04706i
$209$	0.202503	−	0.241333i	0.0140074	−	0.0166934i
$210$		0			0
$211$	−22.1033	+	3.89740i	−1.52165	+	0.268308i	−0.871082	−	0.491138i	$-0.836581\pi$
$211$	−22.1033	+	3.89740i	−1.52165	+	0.268308i	−0.650570	+	0.759446i	$0.725470\pi$
$212$	−18.5634	−	6.93358i	−1.27494	−	0.476200i
$213$		0			0
$214$	−1.16373	+	0.807595i	−0.0795511	+	0.0552060i
$215$	0.731549			0.0498912
$216$		0			0
$217$	−1.74349			−0.118356
$218$	−8.44222	+	5.85864i	−0.571779	+	0.396797i
$219$		0			0
$220$	0.0235918	+	0.00881173i	0.00159056	+	0.000594087i
$221$	10.5289	−	1.85654i	0.708253	−	0.124884i
$222$		0			0
$223$	11.7737	−	14.0314i	0.788428	−	0.939612i	−0.210854	−	0.977518i	$-0.567624\pi$
$223$	11.7737	−	14.0314i	0.788428	−	0.939612i	0.999281	+	0.0379061i	$0.0120688\pi$
$224$	−1.98231	+	1.90079i	−0.132449	+	0.127002i
$225$		0			0
$226$	14.5296	−	14.4082i	0.966498	−	0.958416i
$227$	3.40406	−	19.3054i	0.225936	−	1.28134i	−0.634953	−	0.772551i	$-0.718980\pi$
$227$	3.40406	−	19.3054i	0.225936	−	1.28134i	0.860888	−	0.508794i	$-0.169908\pi$
$228$		0			0
$229$	−5.32626	−	1.93860i	−0.351969	−	0.128106i	0.159984	−	0.987120i	$-0.448856\pi$
$229$	−5.32626	−	1.93860i	−0.351969	−	0.128106i	−0.511953	+	0.859013i	$0.671078\pi$
$230$	0.256627	−	2.79791i	0.0169215	−	0.184489i
$231$		0			0
$232$	−16.4179	+	11.1905i	−1.07789	+	0.734690i
$233$	−6.50499	+	3.75566i	−0.426156	+	0.246041i	−0.697708	−	0.716383i	$-0.745797\pi$
$233$	−6.50499	+	3.75566i	−0.426156	+	0.246041i	0.271552	+	0.962424i	$0.412463\pi$
$234$		0			0
$235$	−1.88406	−	1.08776i	−0.122902	−	0.0709577i
$236$	−8.56106	−	1.58378i	−0.557277	−	0.103095i
$237$		0			0
$238$	−0.711975	−	1.54372i	−0.0461505	−	0.100065i
$239$	4.95760	−	4.15992i	0.320680	−	0.269083i	−0.468209	−	0.883618i	$-0.655101\pi$
$239$	4.95760	−	4.15992i	0.320680	−	0.269083i	0.788890	+	0.614535i	$0.210656\pi$
$240$		0			0
$241$	0.652071	−	0.237335i	0.0420036	−	0.0152881i	−0.320933	−	0.947102i	$-0.603996\pi$
$241$	0.652071	−	0.237335i	0.0420036	−	0.0152881i	0.362937	+	0.931814i	$0.381774\pi$
$242$	−15.0407	+	3.96253i	−0.966852	+	0.254721i
$243$		0			0
$244$	−13.1122	+	7.42422i	−0.839420	+	0.475287i
$245$	−0.699725	−	1.92248i	−0.0447038	−	0.122823i
$246$		0			0
$247$	21.0029	+	25.0302i	1.33638	+	1.59264i
$248$	−5.93034	+	8.24637i	−0.376577	+	0.523645i
$249$		0			0
$250$	−1.80723	+	3.83352i	−0.114299	+	0.242453i
$251$	−1.09113	+	1.88989i	−0.0688715	+	0.119289i	−0.898405	−	0.439168i	$-0.855273\pi$
$251$	−1.09113	+	1.88989i	−0.0688715	+	0.119289i	0.829533	+	0.558457i	$0.188607\pi$
$252$		0			0
$253$	−0.136739	−	0.236839i	−0.00859670	−	0.0148899i
$254$	12.5363	−	1.04377i	0.786600	−	0.0654921i
$255$		0			0
$256$	2.24768	+	15.8413i	0.140480	+	0.990083i
$257$	4.92162	−	13.5220i	0.307002	−	0.843481i	−0.686235	−	0.727380i	$-0.740738\pi$
$257$	4.92162	−	13.5220i	0.307002	−	0.843481i	0.993237	−	0.116102i	$-0.0370398\pi$
$258$		0			0
$259$	3.21309	+	0.566555i	0.199652	+	0.0352040i
$260$	−1.32493	+	2.25098i	−0.0821686	+	0.139600i
$261$		0			0
$262$	7.22458	−	26.5167i	0.446336	−	1.63821i
$263$	−7.84733	−	6.58469i	−0.483887	−	0.406029i	0.367943	−	0.929849i	$-0.380062\pi$
$263$	−7.84733	−	6.58469i	−0.483887	−	0.406029i	−0.851829	+	0.523819i	$0.824507\pi$
$264$		0			0
$265$	0.520366	+	2.95114i	0.0319658	+	0.181287i
$266$	2.99785	−	4.24334i	0.183810	−	0.260176i
$267$		0			0
$268$	−16.9446	−	14.4624i	−1.03506	−	0.883431i
$269$			3.15222i			0.192194i	0.995372	+	0.0960971i	$0.0306359\pi$
$269$			3.15222i			0.192194i	−0.995372	+	0.0960971i	$0.969364\pi$
$270$		0			0
$271$		−	3.33151i		−	0.202375i	−0.994867	−	0.101188i	$-0.967736\pi$
$271$		−	3.33151i		−	0.202375i	0.994867	−	0.101188i	$-0.0322642\pi$
$272$	−9.72325	−	1.88335i	−0.589559	−	0.114195i
$273$		0			0
$274$	−17.7151	−	12.5154i	−1.07021	−	0.756084i
$275$	0.0354861	+	0.201251i	0.00213989	+	0.0121359i
$276$		0			0
$277$	3.19860	+	2.68395i	0.192186	+	0.161263i	0.733803	−	0.679362i	$-0.237743\pi$
$277$	3.19860	+	2.68395i	0.192186	+	0.161263i	−0.541618	+	0.840625i	$0.682188\pi$
$278$	−12.1915	−	3.32161i	−0.731195	−	0.199217i
$279$		0			0
$280$	0.399782	+	0.112537i	0.0238915	+	0.00672534i
$281$	−19.3295	−	3.40832i	−1.15310	−	0.203323i	−0.435773	−	0.900057i	$-0.643525\pi$
$281$	−19.3295	−	3.40832i	−1.15310	−	0.203323i	−0.717330	+	0.696733i	$0.754636\pi$
$282$		0			0
$283$	5.26641	−	14.4693i	0.313055	−	0.860113i	−0.678980	−	0.734156i	$-0.737578\pi$
$283$	5.26641	−	14.4693i	0.313055	−	0.860113i	0.992036	−	0.125956i	$-0.0401999\pi$
$284$	−6.66423	+	1.11747i	−0.395449	+	0.0663096i
$285$		0			0
$286$	0.0210946	+	0.253358i	0.00124735	+	0.0149814i
$287$	−1.53526	−	2.65916i	−0.0906238	−	0.156965i
$288$		0			0
$289$	−5.43473	+	9.41323i	−0.319690	+	0.553720i
$290$	2.71781	+	1.28125i	0.159595	+	0.0752377i
$291$		0			0
$292$	−0.802992	−	0.973453i	−0.0469916	−	0.0569670i
$293$	−11.9699	−	14.2652i	−0.699290	−	0.833382i	0.293156	−	0.956065i	$-0.405295\pi$
$293$	−11.9699	−	14.2652i	−0.699290	−	0.833382i	−0.992446	+	0.122683i	$0.960850\pi$
$294$		0			0
$295$	0.450307	+	1.23721i	0.0262179	+	0.0720331i
$296$	13.6088	−	13.2702i	0.790995	−	0.771317i
$297$		0			0
$298$	−0.620393	−	2.35484i	−0.0359384	−	0.136412i
$299$	26.6536	−	9.70110i	1.54142	−	0.561029i
$300$		0			0
$301$	0.899557	−	0.754818i	0.0518496	−	0.0435070i
$302$	−0.774511	+	0.357209i	−0.0445681	+	0.0205551i
$303$		0			0
$304$	−9.87326	−	28.6127i	−0.566270	−	1.64105i
$305$	1.97339	+	1.13934i	0.112996	+	0.0652382i
$306$		0			0
$307$	17.7533	−	10.2499i	1.01323	−	0.584990i	0.101096	−	0.994877i	$-0.467765\pi$
$307$	17.7533	−	10.2499i	1.01323	−	0.584990i	0.912136	+	0.409887i	$0.134432\pi$
$308$	0.0381019	−	0.0135067i	0.00217106	−	0.000769617i
$309$		0			0
$310$	1.52962	+	0.140298i	0.0868766	+	0.00796839i
$311$	18.8205	+	6.85012i	1.06722	+	0.388435i	0.815135	−	0.579272i	$-0.196663\pi$
$311$	18.8205	+	6.85012i	1.06722	+	0.388435i	0.252081	+	0.967706i	$0.418885\pi$
$312$		0			0
$313$	−3.06340	+	17.3734i	−0.173154	+	0.982003i	0.767100	+	0.641528i	$0.221699\pi$
$313$	−3.06340	+	17.3734i	−0.173154	+	0.982003i	−0.940253	+	0.340475i	$0.889412\pi$
$314$	10.3298	+	10.4169i	0.582944	+	0.587859i
$315$		0			0
$316$	−6.05487	−	0.0508417i	−0.340613	−	0.00286007i
$317$	−2.76189	+	3.29149i	−0.155123	+	0.184868i	−0.838009	−	0.545657i	$-0.816280\pi$
$317$	−2.76189	+	3.29149i	−0.155123	+	0.184868i	0.682886	+	0.730525i	$0.260725\pi$
$318$		0			0
$319$	0.288017	−	0.0507851i	0.0161258	−	0.00284342i
$320$	1.89210	−	1.50811i	0.105772	−	0.0843058i
$321$		0			0
$322$	−2.57134	−	3.70527i	−0.143295	−	0.206487i
$323$	18.7360			1.04250
$324$		0			0
$325$	−21.1951			−1.17569
$326$	4.59931	+	6.62754i	0.254732	+	0.367066i
$327$		0			0
$328$	−17.7994	−	1.78340i	−0.982807	−	0.0984720i
$329$	−3.43911	+	0.606408i	−0.189604	+	0.0334323i
$330$		0			0
$331$	−12.9390	+	15.4201i	−0.711190	+	0.847563i	−0.993743	−	0.111689i	$-0.964374\pi$
$331$	−12.9390	+	15.4201i	−0.711190	+	0.847563i	0.282554	+	0.959252i	$0.408819\pi$
$332$	−0.0966917	+	11.5153i	−0.00530664	+	0.631982i
$333$		0			0
$334$	−5.22848	−	5.27257i	−0.286090	−	0.288502i
$335$	−0.585001	+	3.31770i	−0.0319620	+	0.181266i
$336$		0			0
$337$	−12.4122	−	4.51765i	−0.676133	−	0.246092i	−0.0189468	−	0.999820i	$-0.506031\pi$
$337$	−12.4122	−	4.51765i	−0.676133	−	0.246092i	−0.657186	+	0.753728i	$0.728254\pi$
$338$	−7.95020	−	0.729198i	−0.432434	−	0.0396631i
$339$		0			0
$340$	0.500417	+	1.41165i	0.0271389	+	0.0765576i
$341$	0.129480	−	0.0747552i	0.00701173	−	0.00404822i
$342$		0			0
$343$	−5.78720	−	3.34124i	−0.312480	−	0.180410i
$344$	−0.510372	−	6.82219i	−0.0275174	−	0.367828i
$345$		0			0
$346$	−1.78152	+	0.821648i	−0.0957751	+	0.0441721i
$347$	13.6769	−	11.4763i	0.734213	−	0.616078i	−0.197064	−	0.980391i	$-0.563141\pi$
$347$	13.6769	−	11.4763i	0.734213	−	0.616078i	0.931277	+	0.364313i	$0.118696\pi$
$348$		0			0
$349$	12.2841	−	4.47105i	0.657554	−	0.239330i	0.00837388	−	0.999965i	$-0.497334\pi$
$349$	12.2841	−	4.47105i	0.657554	−	0.239330i	0.649180	+	0.760635i	$0.275112\pi$
$350$	0.858586	+	3.25895i	0.0458933	+	0.174198i
$351$		0			0
$352$	0.0657163	−	0.226157i	0.00350269	−	0.0120542i
$353$	−7.34903	−	20.1913i	−0.391149	−	1.07467i	−0.966477	−	0.256751i	$-0.917348\pi$
$353$	−7.34903	−	20.1913i	−0.391149	−	1.07467i	0.575328	−	0.817923i	$-0.304874\pi$
$354$		0			0
$355$	0.656843	+	0.782795i	0.0348616	+	0.0415464i
$356$	−16.0428	+	13.2336i	−0.850268	+	0.701379i
$357$		0			0
$358$	−14.7664	−	6.96133i	−0.780431	−	0.367918i
$359$	9.46695	−	16.3972i	0.499647	−	0.865413i	−0.500353	−	0.865821i	$-0.666797\pi$
$359$	9.46695	−	16.3972i	0.499647	−	0.865413i	1.00000		0.000407927i	$0.000129847\pi$
$360$		0			0
$361$	19.1302	+	33.1344i	1.00685	+	1.74392i
$362$	2.01193	+	24.1644i	0.105744	+	1.27005i
$363$		0			0
$364$	0.693366	+	4.13501i	0.0363423	+	0.216733i
$365$	−0.0652682	+	0.179323i	−0.00341629	+	0.00938619i
$366$		0			0
$367$	23.4580	+	4.13627i	1.22450	+	0.215912i	0.748260	−	0.663406i	$-0.230890\pi$
$367$	23.4580	+	4.13627i	1.22450	+	0.215912i	0.476236	+	0.879317i	$0.342001\pi$
$368$	−26.2715	−	0.441225i	−1.36949	−	0.0230004i
$369$		0			0
$370$	−2.77337	−	0.755615i	−0.144180	−	0.0392825i
$371$	3.68488	+	3.09198i	0.191310	+	0.160528i
$372$		0			0
$373$	−3.76380	−	21.3456i	−0.194882	−	1.10523i	−0.912587	−	0.408883i	$-0.865918\pi$
$373$	−3.76380	−	21.3456i	−0.194882	−	1.10523i	0.717705	−	0.696348i	$-0.245193\pi$
$374$	0.119065	+	0.0841171i	0.00615669	+	0.00434959i
$375$		0			0
$376$	−8.82967	+	18.3290i	−0.455356	+	0.945245i
$377$			30.3329i			1.56222i
$378$		0			0
$379$			33.6783i			1.72994i	0.501825	+	0.864969i	$0.332662\pi$
$379$			33.6783i			1.72994i	−0.501825	+	0.864969i	$0.667338\pi$
$380$	−2.97157	+	3.48159i	−0.152438	+	0.178602i
$381$		0			0
$382$	13.5092	−	19.1217i	0.691190	−	0.978354i
$383$	0.261068	+	1.48059i	0.0133400	+	0.0756548i	0.990751	−	0.135693i	$-0.0433260\pi$
$383$	0.261068	+	1.48059i	0.0133400	+	0.0756548i	−0.977411	+	0.211347i	$0.932215\pi$
$384$		0			0
$385$	−0.00468303	−	0.00392953i	−0.000238670	−	0.000200268i
$386$	3.27261	−	12.0116i	0.166571	−	0.611374i
$387$		0			0
$388$	5.74166	+	3.37954i	0.291489	+	0.171570i
$389$	3.80299	+	0.670570i	0.192819	+	0.0339993i	0.269224	−	0.963078i	$-0.413233\pi$
$389$	3.80299	+	0.670570i	0.192819	+	0.0339993i	−0.0764044	+	0.997077i	$0.524344\pi$
$390$		0			0
$391$	5.56271	−	15.2834i	0.281318	−	0.772916i
$392$	−17.4402	+	7.86664i	−0.880865	+	0.397325i
$393$		0			0
$394$	−17.6133	+	1.46648i	−0.887345	+	0.0738801i
$395$	0.457839	+	0.793000i	0.0230364	+	0.0399002i
$396$		0			0
$397$	−9.80431	+	16.9816i	−0.492064	+	0.852280i	−0.999958	−	0.00913954i	$-0.997091\pi$
$397$	−9.80431	+	16.9816i	−0.492064	+	0.852280i	0.507894	+	0.861419i	$0.330424\pi$
$398$	2.70550	−	5.73893i	0.135614	−	0.287666i
$399$		0			0
$400$	18.3346	+	7.02413i	0.916732	+	0.351207i
$401$	13.9437	+	16.6175i	0.696316	+	0.829838i	0.992104	−	0.125416i	$-0.0400266\pi$
$401$	13.9437	+	16.6175i	0.696316	+	0.829838i	−0.295788	+	0.955254i	$0.595582\pi$
$402$		0			0
$403$	5.30360	+	14.5715i	0.264191	+	0.725859i
$404$	−16.4562	−	29.0639i	−0.818728	−	1.44598i
$405$		0			0
$406$	4.66398	−	1.22875i	0.231470	−	0.0609817i
$407$	−0.262912	+	0.0956921i	−0.0130321	+	0.00474328i
$408$		0			0
$409$	−8.42462	+	7.06909i	−0.416570	+	0.349544i	−0.826857	−	0.562413i	$-0.809873\pi$
$409$	−8.42462	+	7.06909i	−0.416570	+	0.349544i	0.410286	+	0.911957i	$0.365429\pi$
$410$	1.13296	+	2.45651i	0.0559528	+	0.121318i
$411$		0			0
$412$	−5.78210	+	31.2550i	−0.284864	+	1.53982i
$413$	1.83029	+	1.05672i	0.0900626	+	0.0519976i
$414$		0			0
$415$	1.50814	−	0.870727i	0.0740319	−	0.0427423i
$416$	21.9163	+	10.7854i	1.07453	+	0.528799i
$417$		0			0
$418$	−0.0406937	+	0.443669i	−0.00199039	+	0.0217006i
$419$	−22.7569	−	8.28284i	−1.11175	−	0.404643i	−0.280114	−	0.959967i	$-0.590372\pi$
$419$	−22.7569	−	8.28284i	−1.11175	−	0.404643i	−0.831635	+	0.555323i	$0.812595\pi$
$420$		0			0
$421$	6.35770	−	36.0563i	0.309855	−	1.75728i	−0.289866	−	0.957067i	$-0.593611\pi$
$421$	6.35770	−	36.0563i	0.309855	−	1.75728i	0.599721	−	0.800209i	$-0.295278\pi$
$422$	22.5383	−	22.3498i	1.09715	−	1.08797i
$423$		0			0
$424$	27.1583	−	6.91165i	1.31893	−	0.335660i
$425$	−7.81210	+	9.31010i	−0.378942	+	0.451606i
$426$		0			0
$427$	3.60217	−	0.635160i	0.174321	−	0.0307375i
$428$	0.700930	−	1.87661i	0.0338807	−	0.0907093i
$429$		0			0
$430$	−0.849951	+	0.589840i	−0.0409883	+	0.0284446i
$431$	−38.5608			−1.85741			−0.928705	−	0.370820i	$-0.879077\pi$
$431$	−38.5608			−1.85741			−0.928705	+	0.370820i	$0.879077\pi$
$432$		0			0
$433$	−6.56251			−0.315374			−0.157687	−	0.987489i	$-0.550404\pi$
$433$	−6.56251			−0.315374			−0.157687	+	0.987489i	$0.550404\pi$
$434$	2.02567	−	1.40576i	0.0972355	−	0.0674784i
$435$		0			0
$436$	5.08484	−	13.6137i	0.243520	−	0.651979i
$437$	48.9513	−	8.63143i	2.34166	−	0.412897i
$438$		0			0
$439$	1.17279	−	1.39768i	0.0559744	−	0.0667077i	−0.737331	−	0.675532i	$-0.763914\pi$
$439$	1.17279	−	1.39768i	0.0559744	−	0.0667077i	0.793305	+	0.608824i	$0.208359\pi$
$440$	−0.0345149	+	0.00878386i	−0.00164543	+	0.000418754i
$441$		0			0
$442$	−10.7362	+	10.6464i	−0.510667	+	0.506397i
$443$	−0.302973	+	1.71824i	−0.0143947	+	0.0816362i	−0.991159	−	0.132681i	$-0.957641\pi$
$443$	−0.302973	+	1.71824i	−0.0143947	+	0.0816362i	0.976764	+	0.214317i	$0.0687526\pi$
$444$		0			0
$445$	2.95530	+	1.07564i	0.140095	+	0.0509903i
$446$	−2.36597	+	25.7954i	−0.112032	+	1.22145i
$447$		0			0
$448$	0.770567	−	3.80675i	0.0364059	−	0.179852i
$449$	−8.00158	+	4.61971i	−0.377618	+	0.218018i	−0.676781	−	0.736184i	$-0.736626\pi$
$449$	−8.00158	+	4.61971i	−0.377618	+	0.218018i	0.299164	+	0.954202i	$0.403292\pi$
$450$		0			0
$451$	0.228032	+	0.131654i	0.0107376	+	0.00619937i
$452$	−5.26415	+	28.4552i	−0.247605	+	1.33842i
$453$		0			0
$454$	11.6107	+	25.1747i	0.544918	+	1.18151i
$455$	0.485708	−	0.407557i	0.0227703	−	0.0191066i
$456$		0			0
$457$	25.9190	−	9.43376i	1.21244	−	0.441293i	0.344891	−	0.938643i	$-0.387916\pi$
$457$	25.9190	−	9.43376i	1.21244	−	0.441293i	0.867550	+	0.497350i	$0.165694\pi$
$458$	7.75140	−	2.04214i	0.362199	−	0.0954229i
$459$		0			0
$460$	1.95776	+	3.45767i	0.0912812	+	0.161215i
$461$	−7.09177	−	19.4845i	−0.330297	−	0.907483i	−0.988034	−	0.154236i	$-0.950709\pi$
$461$	−7.09177	−	19.4845i	−0.330297	−	0.907483i	0.657737	−	0.753247i	$-0.271514\pi$
$462$		0			0
$463$	6.16175	+	7.34328i	0.286361	+	0.341271i	0.889979	−	0.456002i	$-0.150719\pi$
$463$	6.16175	+	7.34328i	0.286361	+	0.341271i	−0.603618	+	0.797274i	$0.706275\pi$
$464$	10.0524	−	26.2393i	0.466673	−	1.21813i
$465$		0			0
$466$	4.52969	−	9.60842i	0.209834	−	0.445101i
$467$	−8.74737	+	15.1509i	−0.404780	+	0.701099i	−0.994296	−	0.106657i	$-0.965985\pi$
$467$	−8.74737	+	15.1509i	−0.404780	+	0.701099i	0.589516	+	0.807757i	$0.299319\pi$
$468$		0			0
$469$	2.70388	+	4.68326i	0.124854	+	0.216253i
$470$	3.06604	−	0.255278i	0.141426	−	0.0117751i
$471$		0			0
$472$	11.2237	−	5.06257i	0.516610	−	0.233024i
$473$	−0.0344412	+	0.0946266i	−0.00158361	+	0.00435093i
$474$		0			0
$475$	−36.5788	−	6.44983i	−1.67835	−	0.295938i
$476$	2.07190	+	1.21952i	0.0949652	+	0.0558966i
$477$		0			0
$478$	−2.40590	+	8.83047i	−0.110043	+	0.403896i
$479$	20.0678	+	16.8388i	0.916919	+	0.769386i	0.973423	−	0.229016i	$-0.0735508\pi$
$479$	20.0678	+	16.8388i	0.916919	+	0.769386i	−0.0565037	+	0.998402i	$0.517995\pi$
$480$		0			0
$481$	−5.03898	−	28.5775i	−0.229758	−	1.30302i
$482$	−0.566250	+	0.801505i	−0.0257920	+	0.0365076i
$483$		0			0
$484$	14.2801	−	16.7310i	0.649095	−	0.760500i
$485$		−	1.00752i		−	0.0457493i
$486$		0			0
$487$		−	7.10957i		−	0.322166i	−0.986941	−	0.161083i	$-0.948501\pi$
$487$		−	7.10957i		−	0.322166i	0.986941	−	0.161083i	$-0.0514986\pi$
$488$	9.24832	−	19.1980i	0.418652	−	0.869054i
$489$		0			0
$490$	2.36305	+	1.66945i	0.106752	+	0.0754182i
$491$	3.43007	+	19.4529i	0.154797	+	0.877897i	0.958971	+	0.283503i	$0.0914967\pi$
$491$	3.43007	+	19.4529i	0.154797	+	0.877897i	−0.804174	+	0.594393i	$0.797392\pi$
$492$		0			0
$493$	13.3239	+	11.1801i	0.600081	+	0.503527i
$494$	−44.5838	−	12.1470i	−2.00592	−	0.546521i
$495$		0			0
$496$	0.241218	−	14.3626i	0.0108310	−	0.644901i
$497$	1.61539	+	0.284836i	0.0724600	+	0.0127767i
$498$		0			0
$499$	13.5189	−	37.1430i	0.605191	−	1.66275i	−0.135400	−	0.990791i	$-0.543232\pi$
$499$	13.5189	−	37.1430i	0.605191	−	1.66275i	0.740591	−	0.671956i	$-0.234546\pi$
$500$	−0.991189	−	5.91113i	−0.0443273	−	0.264354i
$501$		0			0
$502$	−0.256069	−	3.07554i	−0.0114289	−	0.137268i
$503$	−19.5426	−	33.8489i	−0.871364	−	1.50925i	−0.860587	−	0.509304i	$-0.829903\pi$
$503$	−19.5426	−	33.8489i	−0.871364	−	1.50925i	−0.0107769	−	0.999942i	$-0.503430\pi$
$504$		0			0
$505$	−2.52541	+	4.37413i	−0.112379	+	0.194646i
$506$	0.349831	+	0.164920i	0.0155519	+	0.00733160i
$507$		0			0
$508$	−13.7238	+	11.3206i	−0.608895	+	0.502271i
$509$	9.47986	+	11.2977i	0.420187	+	0.500760i	0.934065	−	0.357104i	$-0.116236\pi$
$509$	9.47986	+	11.2977i	0.420187	+	0.500760i	−0.513877	+	0.857864i	$0.671791\pi$
$510$		0			0
$511$	0.104769	+	0.287850i	0.00463471	+	0.0127338i
$512$	−15.3842	−	16.5930i	−0.679891	−	0.733314i
$513$		0			0
$514$	5.18448	+	19.6788i	0.228677	+	0.867996i
$515$	4.51685	−	1.64400i	0.199036	−	0.0724432i
$516$		0			0
$517$	0.229404	−	0.192493i	0.0100892	−	0.00846582i
$518$	−4.18995	+	1.93243i	−0.184096	+	0.0849061i
$519$		0			0
$520$	−0.275571	−	3.68358i	−0.0120846	−	0.161536i
$521$	10.1293	+	5.84816i	0.443773	+	0.256213i	0.705197	−	0.709012i	$-0.250859\pi$
$521$	10.1293	+	5.84816i	0.443773	+	0.256213i	−0.261424	+	0.965224i	$0.584192\pi$
$522$		0			0
$523$	−6.89969	+	3.98354i	−0.301702	+	0.174188i	−0.643207	−	0.765692i	$-0.722397\pi$
$523$	−6.89969	+	3.98354i	−0.301702	+	0.174188i	0.341505	+	0.939880i	$0.389063\pi$
$524$	12.9862	+	36.6336i	0.567306	+	1.60034i
$525$		0			0
$526$	14.4266	+	1.32322i	0.629029	+	0.0576950i
$527$	8.35546	+	3.04114i	0.363969	+	0.132474i
$528$		0			0
$529$	3.49884	−	19.8429i	0.152124	−	0.862736i
$530$	−2.98406	−	3.00922i	−0.129619	−	0.130712i
$531$		0			0
$532$	−0.0616937	+	7.34727i	−0.00267476	+	0.318544i
$533$	−17.5542	+	20.9203i	−0.760356	+	0.906157i
$534$		0			0
$535$	−0.298337	+	0.0526049i	−0.0128982	+	0.00227431i
$536$	31.3480	+	3.14090i	1.35403	+	0.135666i
$537$		0			0
$538$	−2.54160	−	3.66241i	−0.109576	−	0.157898i
$539$	0.281617			0.0121301
$540$		0			0
$541$	8.41220			0.361669			0.180834	−	0.983514i	$-0.442120\pi$
$541$	8.41220			0.361669			0.180834	+	0.983514i	$0.442120\pi$
$542$	2.68616	+	3.87072i	0.115381	+	0.166262i
$543$		0			0
$544$	12.8155	−	5.65158i	0.549460	−	0.242309i
$545$	−2.16426	+	0.381618i	−0.0927069	+	0.0163467i
$546$		0			0
$547$	−11.2369	+	13.3916i	−0.480453	+	0.572582i	−0.950763	−	0.309920i	$-0.899698\pi$
$547$	−11.2369	+	13.3916i	−0.480453	+	0.572582i	0.470309	+	0.882502i	$0.344142\pi$
$548$	30.6734	+	0.257559i	1.31030	+	0.0110024i
$549$		0			0
$550$	−0.203496	−	0.205212i	−0.00867711	−	0.00875028i
$551$	−9.23054	+	52.3490i	−0.393234	+	2.23014i
$552$		0			0
$553$	1.38121	+	0.502719i	0.0587350	+	0.0213778i
$554$	−5.88034	−	0.539349i	−0.249832	−	0.0229147i
$555$		0			0
$556$	16.8428	−	5.97062i	0.714295	−	0.253211i
$557$	−0.688812	+	0.397686i	−0.0291859	+	0.0168505i	−0.514522	−	0.857477i	$-0.672031\pi$
$557$	−0.688812	+	0.397686i	−0.0291859	+	0.0168505i	0.485336	+	0.874328i	$0.338697\pi$
$558$		0			0
$559$	−9.04493	−	5.22209i	−0.382560	−	0.220871i
$560$	−0.555224	+	0.191589i	−0.0234625	+	0.00809611i
$561$		0			0
$562$	25.2061	−	11.6252i	1.06326	−	0.490381i
$563$	−4.79979	+	4.02750i	−0.202287	+	0.169739i	−0.738304	−	0.674468i	$-0.764373\pi$
$563$	−4.79979	+	4.02750i	−0.202287	+	0.169739i	0.536017	+	0.844207i	$0.319928\pi$
$564$		0			0
$565$	4.11224	−	1.49673i	0.173003	−	0.0629680i
$566$	5.54768	+	21.0575i	0.233187	+	0.885111i
$567$		0			0
$568$	6.84184	−	6.67163i	0.287077	−	0.279935i
$569$	−1.85350	−	5.09244i	−0.0777027	−	0.213486i	0.894759	−	0.446550i	$-0.147347\pi$
$569$	−1.85350	−	5.09244i	−0.0777027	−	0.213486i	−0.972462	+	0.233063i	$0.925125\pi$
$570$		0			0
$571$	−19.5951	−	23.3525i	−0.820029	−	0.977273i	0.179950	−	0.983676i	$-0.442406\pi$
$571$	−19.5951	−	23.3525i	−0.820029	−	0.977273i	−0.999979	+	0.00640314i	$0.997962\pi$
$572$	−0.228789	−	0.277356i	−0.00956614	−	0.0115969i
$573$		0			0
$574$	3.92780	+	1.85168i	0.163943	+	0.0772875i
$575$	−16.1215	+	27.9233i	−0.672315	+	1.16448i
$576$		0			0
$577$	−9.67484	−	16.7573i	−0.402769	−	0.697616i	0.591290	−	0.806459i	$-0.298619\pi$
$577$	−9.67484	−	16.7573i	−0.402769	−	0.697616i	−0.994059	+	0.108843i	$0.965286\pi$
$578$	−1.27543	−	15.3187i	−0.0530511	−	0.637176i
$579$		0			0
$580$	−4.19075	+	0.702712i	−0.174011	+	0.0291785i
$581$	0.956081	−	2.62681i	0.0396649	−	0.108979i
$582$		0			0
$583$	−0.406232	−	0.0716296i	−0.0168244	−	0.00296659i
$584$	1.71784	+	0.483564i	0.0710848	+	0.0200100i
$585$		0			0
$586$	25.4091	+	6.92282i	1.04964	+	0.285979i
$587$	−33.1376	−	27.8057i	−1.36773	−	1.14767i	−0.973508	−	0.228653i	$-0.926568\pi$
$587$	−33.1376	−	27.8057i	−1.36773	−	1.14767i	−0.394227	−	0.919013i	$-0.628988\pi$
$588$		0			0
$589$	4.71881	+	26.7617i	0.194435	+	1.10270i
$590$	−1.52074	−	1.07438i	−0.0626078	−	0.0442313i
$591$		0			0
$592$	−5.11175	+	26.3907i	−0.210092	+	1.08465i
$593$		−	32.7916i		−	1.34659i	−0.739375	−	0.673294i	$-0.764879\pi$
$593$		−	32.7916i		−	1.34659i	0.739375	−	0.673294i	$-0.235121\pi$
$594$		0			0
$595$		−	0.363568i		−	0.0149048i
$596$	2.61948	+	2.23576i	0.107298	+	0.0915801i
$597$		0			0
$598$	−23.1456	+	32.7617i	−0.946493	+	1.33973i
$599$	−6.52625	−	37.0122i	−0.266655	−	1.51228i	−0.764279	−	0.644885i	$-0.776905\pi$
$599$	−6.52625	−	37.0122i	−0.266655	−	1.51228i	0.497624	−	0.867393i	$-0.334206\pi$
$600$		0			0
$601$	7.65033	+	6.41939i	0.312063	+	0.261852i	0.785344	−	0.619059i	$-0.212486\pi$
$601$	7.65033	+	6.41939i	0.312063	+	0.261852i	−0.473281	+	0.880912i	$0.656930\pi$
$602$	−0.436550	+	1.60229i	−0.0177925	+	0.0653044i
$603$		0			0
$604$	0.611852	−	1.03950i	0.0248959	−	0.0422968i
$605$	−3.27588	−	0.577627i	−0.133184	−	0.0234839i
$606$		0			0
$607$	−9.92909	+	27.2799i	−0.403009	+	1.10726i	0.557783	+	0.829987i	$0.311652\pi$
$607$	−9.92909	+	27.2799i	−0.403009	+	1.10726i	−0.960792	+	0.277271i	$0.910570\pi$
$608$	34.5413	+	25.2830i	1.40084	+	1.02536i
$609$		0			0
$610$	−3.21142	+	0.267382i	−0.130026	+	0.0108260i
$611$	15.5298	+	26.8983i	0.628266	+	1.08819i
$612$		0			0
$613$	−10.6465	+	18.4402i	−0.430007	+	0.744794i	−0.996873	−	0.0790155i	$-0.974822\pi$
$613$	−10.6465	+	18.4402i	−0.430007	+	0.744794i	0.566866	+	0.823810i	$0.308156\pi$
$614$	−12.3623	+	26.2231i	−0.498902	+	1.05828i
$615$		0			0
$616$	−0.0333784	+	0.0464139i	−0.00134485	+	0.00187007i
$617$	−1.59822	−	1.90469i	−0.0643420	−	0.0766798i	0.732913	−	0.680322i	$-0.238160\pi$
$617$	−1.59822	−	1.90469i	−0.0643420	−	0.0766798i	−0.797255	+	0.603642i	$0.793716\pi$
$618$		0			0
$619$	−4.56324	−	12.5374i	−0.183412	−	0.503921i	0.813577	−	0.581457i	$-0.197517\pi$
$619$	−4.56324	−	12.5374i	−0.183412	−	0.503921i	−0.996990	+	0.0775360i	$0.975295\pi$
$620$	−1.89031	+	1.07031i	−0.0759168	+	0.0429847i
$621$		0			0
$622$	−27.3899	+	7.21598i	−1.09823	+	0.289334i
$623$	4.74387	−	1.72663i	0.190059	−	0.0691759i
$624$		0			0
$625$	18.1064	−	15.1931i	0.724256	−	0.607723i
$626$	−10.4488	−	22.6553i	−0.417617	−	0.905488i
$627$		0			0
$628$	−20.4007	−	3.77408i	−0.814077	−	0.150602i
$629$	−14.4101	−	8.31969i	−0.574570	−	0.331728i
$630$		0			0
$631$	−33.1235	+	19.1238i	−1.31862	+	0.761308i	−0.983507	−	0.180868i	$-0.942109\pi$
$631$	−33.1235	+	19.1238i	−1.31862	+	0.761308i	−0.335117	+	0.942176i	$0.608776\pi$
$632$	7.07585	−	4.82290i	0.281462	−	0.191845i
$633$		0			0
$634$	0.555011	−	6.05110i	0.0220423	−	0.240320i
$635$	2.52810	+	0.920154i	0.100325	+	0.0365152i
$636$		0			0
$637$	−5.07197	+	28.7646i	−0.200959	+	1.13969i
$638$	−0.293685	+	0.291229i	−0.0116271	+	0.0115299i
$639$		0			0
$640$	−0.982372	+	3.27778i	−0.0388317	+	0.129566i
$641$	−9.13644	+	10.8884i	−0.360868	+	0.430065i	−0.915679	−	0.401911i	$-0.868346\pi$
$641$	−9.13644	+	10.8884i	−0.360868	+	0.430065i	0.554811	+	0.831976i	$0.312791\pi$
$642$		0			0
$643$	−0.627325	+	0.110614i	−0.0247393	+	0.00436221i	−0.186004	−	0.982549i	$-0.559554\pi$
$643$	−0.627325	+	0.110614i	−0.0247393	+	0.00436221i	0.161265	+	0.986911i	$0.448443\pi$
$644$	5.97504	+	2.23173i	0.235450	+	0.0879424i
$645$		0			0
$646$	−21.7684	+	15.1066i	−0.856467	+	0.594361i
$647$	−7.26586			−0.285650			−0.142825	−	0.989748i	$-0.545619\pi$
$647$	−7.26586			−0.285650			−0.142825	+	0.989748i	$0.545619\pi$
$648$		0			0
$649$	−0.181235			−0.00711408
$650$	24.6255	−	17.0894i	0.965892	−	0.670300i
$651$		0			0
$652$	−10.6874	−	3.99185i	−0.418552	−	0.156333i
$653$	−31.3669	+	5.53083i	−1.22748	+	0.216438i	−0.749543	−	0.661955i	$-0.769727\pi$
$653$	−31.3669	+	5.53083i	−1.22748	+	0.216438i	−0.477938	+	0.878393i	$0.658616\pi$
$654$		0			0
$655$	3.77810	−	4.50257i	0.147623	−	0.175930i
$656$	22.1182	−	12.2794i	0.863570	−	0.479430i
$657$		0			0
$658$	3.50679	−	3.47747i	0.136709	−	0.135566i
$659$	2.56367	−	14.5393i	0.0998663	−	0.566370i	−0.893281	−	0.449499i	$-0.851603\pi$
$659$	2.56367	−	14.5393i	0.0998663	−	0.566370i	0.993147	−	0.116871i	$-0.0372864\pi$
$660$		0			0
$661$	−18.8308	−	6.85385i	−0.732433	−	0.266584i	−0.0512388	−	0.998686i	$-0.516317\pi$
$661$	−18.8308	−	6.85385i	−0.732433	−	0.266584i	−0.681194	+	0.732103i	$0.738539\pi$
$662$	2.60013	−	28.3484i	0.101057	−	1.10179i
$663$		0			0
$664$	−9.17229	−	13.4570i	−0.355954	−	0.522232i
$665$	0.962265	−	0.555564i	0.0373150	−	0.0215438i
$666$		0			0
$667$	39.9619	+	23.0720i	1.54733	+	0.893352i
$668$	10.3259	+	1.91027i	0.399522	+	0.0739107i
$669$		0			0
$670$	−1.99534	−	4.32636i	−0.0770869	−	0.167142i
$671$	−0.240281	+	0.201620i	−0.00927594	+	0.00778344i
$672$		0			0
$673$	−32.6670	+	11.8898i	−1.25922	+	0.458319i	−0.883508	−	0.468417i	$-0.844825\pi$
$673$	−32.6670	+	11.8898i	−1.25922	+	0.458319i	−0.375713	+	0.926736i	$0.622602\pi$
$674$	18.0636	−	4.75894i	0.695784	−	0.183307i
$675$		0			0
$676$	9.82490	−	5.56294i	0.377881	−	0.213959i
$677$	−11.4934	−	31.5778i	−0.441726	−	1.21363i	−0.938356	−	0.345670i	$-0.887652\pi$
$677$	−11.4934	−	31.5778i	−0.441726	−	1.21363i	0.496630	−	0.867962i	$-0.334571\pi$
$678$		0			0
$679$	−1.03957	−	1.23891i	−0.0398951	−	0.0475451i
$680$	−1.71961	−	1.23665i	−0.0659440	−	0.0474234i
$681$		0			0
$682$	−0.0901620	+	0.191253i	−0.00345248	+	0.00732344i
$683$	12.3153	−	21.3308i	0.471233	−	0.816200i	−0.528225	−	0.849104i	$-0.677142\pi$
$683$	12.3153	−	21.3308i	0.471233	−	0.816200i	0.999459	+	0.0329044i	$0.0104757\pi$
$684$		0			0
$685$	−2.31937	−	4.01726i	−0.0886185	−	0.153492i
$686$	9.41787	−	0.784130i	0.359576	−	0.0299382i
$687$		0			0
$688$	6.09363	+	7.51486i	0.232318	+	0.286501i
$689$	14.6326	−	40.2027i	0.557458	−	1.53160i
$690$		0			0
$691$	−14.4784	−	2.55293i	−0.550784	−	0.0971181i	−0.108672	−	0.994078i	$-0.534660\pi$
$691$	−14.4784	−	2.55293i	−0.550784	−	0.0971181i	−0.442113	+	0.896960i	$0.645771\pi$
$692$	1.40737	−	2.39105i	0.0535003	−	0.0908942i
$693$		0			0
$694$	−6.63731	+	24.3612i	−0.251949	+	0.924739i
$695$	−2.07012	−	1.73704i	−0.0785243	−	0.0658897i
$696$		0			0
$697$	2.71925	+	15.4216i	0.102999	+	0.584135i
$698$	−10.6674	+	15.0992i	−0.403765	+	0.571515i
$699$		0			0
$700$	−3.62521	−	3.09415i	−0.137020	−	0.116948i
$701$			32.3443i			1.22163i	0.791775	+	0.610813i	$0.209157\pi$
$701$			32.3443i			1.22163i	−0.791775	+	0.610813i	$0.790843\pi$
$702$		0			0
$703$		−	50.8528i		−	1.91795i
$704$	0.105995	+	0.315747i	0.00399484	+	0.0119002i
$705$		0			0
$706$	24.8185	+	17.5338i	0.934056	+	0.659895i
$707$	1.40787	+	7.98443i	0.0529484	+	0.300285i
$708$		0			0
$709$	−30.0746	−	25.2356i	−1.12947	−	0.947741i	−0.130430	−	0.991458i	$-0.541636\pi$
$709$	−30.0746	−	25.2356i	−1.12947	−	0.947741i	−0.999044	+	0.0437162i	$0.986080\pi$
$710$	−1.39431	−	0.379886i	−0.0523276	−	0.0142569i
$711$		0			0
$712$	7.96929	−	28.3106i	0.298662	−	1.06099i
$713$	23.2312	+	4.09629i	0.870016	+	0.153407i
$714$		0			0
$715$	−0.0185962	+	0.0510927i	−0.000695460	+	0.00191076i
$716$	22.7693	−	3.81799i	0.850927	−	0.142685i
$717$		0			0
$718$	2.22172	+	26.6843i	0.0829140	+	0.995848i
$719$	−0.482259	−	0.835298i	−0.0179852	−	0.0311514i	0.856893	−	0.515495i	$-0.172392\pi$
$719$	−0.482259	−	0.835298i	−0.0179852	−	0.0311514i	−0.874878	+	0.484343i	$0.839059\pi$
$720$		0			0
$721$	3.85790	−	6.68207i	0.143676	−	0.248853i
$722$	−48.9423	−	23.0728i	−1.82145	−	0.858682i
$723$		0			0
$724$	−21.8211	−	26.4533i	−0.810974	−	0.983129i
$725$	−22.1640	−	26.4140i	−0.823151	−	0.980993i
$726$		0			0
$727$	−7.16819	−	19.6944i	−0.265854	−	0.730427i	−0.998745	−	0.0500812i	$-0.984052\pi$
$727$	−7.16819	−	19.6944i	−0.265854	−	0.730427i	0.732892	−	0.680345i	$-0.238170\pi$
$728$	−4.13960	−	4.24521i	−0.153424	−	0.157338i
$729$		0			0
$730$	−0.0687541	−	0.260972i	−0.00254470	−	0.00965899i
$731$	−5.62763	+	2.04829i	−0.208146	+	0.0757588i
$732$		0			0
$733$	1.37507	−	1.15382i	0.0507892	−	0.0426172i	−0.617040	−	0.786932i	$-0.711668\pi$
$733$	1.37507	−	1.15382i	0.0507892	−	0.0426172i	0.667829	+	0.744315i	$0.267224\pi$
$734$	−30.5897	+	14.1082i	−1.12909	+	0.520742i
$735$		0			0
$736$	30.8793	−	20.6698i	1.13823	−	0.761897i
$737$	−0.401606	−	0.231867i	−0.0147934	−	0.00854095i
$738$		0			0
$739$	17.1448	−	9.89858i	0.630683	−	0.364125i	−0.150333	−	0.988635i	$-0.548035\pi$
$739$	17.1448	−	9.89858i	0.630683	−	0.364125i	0.781017	+	0.624510i	$0.214701\pi$
$740$	3.83148	−	1.35822i	0.140848	−	0.0499292i
$741$		0			0
$742$	−6.77432	−	0.621345i	−0.248693	−	0.0228103i
$743$	36.3877	+	13.2440i	1.33494	+	0.485877i	0.908214	−	0.418507i	$-0.137446\pi$
$743$	36.3877	+	13.2440i	1.33494	+	0.485877i	0.426721	+	0.904383i	$0.359669\pi$
$744$		0			0
$745$	0.0904359	−	0.512888i	0.00331332	−	0.0187907i
$746$	21.5837	+	21.7656i	0.790234	+	0.796897i
$747$		0			0
$748$	−0.206158	−	0.00173107i	−0.00753789	−	6.32943e-5i
$749$	−0.312575	+	0.372512i	−0.0114212	+	0.0136113i
$750$		0			0
$751$	−22.7048	+	4.00346i	−0.828508	+	0.146088i	−0.571792	−	0.820398i	$-0.693752\pi$
$751$	−22.7048	+	4.00346i	−0.828508	+	0.146088i	−0.256716	+	0.966487i	$0.582641\pi$
$752$	−4.51969	−	28.4148i	−0.164816	−	1.03618i
$753$		0			0
$754$	−24.4571	−	35.2423i	−0.890674	−	1.28345i
$755$	−0.182408			−0.00663851
$756$		0			0
$757$	33.3070			1.21056			0.605281	−	0.796012i	$-0.293061\pi$
$757$	33.3070			1.21056			0.605281	+	0.796012i	$0.293061\pi$
$758$	−27.1544	−	39.1292i	−0.986294	−	1.42124i
$759$		0			0
$760$	0.645358	−	6.44104i	0.0234096	−	0.233641i
$761$	−15.6353	+	2.75693i	−0.566780	+	0.0999386i	−0.449693	−	0.893183i	$-0.648467\pi$
$761$	−15.6353	+	2.75693i	−0.566780	+	0.0999386i	−0.117087	+	0.993122i	$0.537356\pi$
$762$		0			0
$763$	−2.26755	+	2.70236i	−0.0820909	+	0.0978322i
$764$	−0.278010	+	33.1089i	−0.0100580	+	1.19784i
$765$		0			0
$766$	−1.49711	−	1.50973i	−0.0540927	−	0.0545488i
$767$	3.26407	−	18.5114i	0.117859	−	0.668409i
$768$		0			0
$769$	20.7088	+	7.53738i	0.746777	+	0.271805i	0.687249	−	0.726422i	$-0.258818\pi$
$769$	20.7088	+	7.53738i	0.746777	+	0.271805i	0.0595284	+	0.998227i	$0.481040\pi$
$770$	0.00860933		0.000789653i	0.000310259		2.84571e-5i
$771$		0			0
$772$	5.88253	+	16.5944i	0.211717	+	0.597244i
$773$	18.9410	−	10.9356i	0.681261	−	0.393326i	−0.119069	−	0.992886i	$-0.537991\pi$
$773$	18.9410	−	10.9356i	0.681261	−	0.393326i	0.800330	+	0.599560i	$0.204658\pi$
$774$		0			0
$775$	−15.2657	−	8.81366i	−0.548360	−	0.316596i
$776$	−9.39584	+	0.702909i	−0.337291	+	0.0252330i
$777$		0			0
$778$	−4.95918	+	2.28721i	−0.177795	+	0.0820004i
$779$	−36.6615	+	30.7626i	−1.31353	+	1.10219i
$780$		0			0
$781$	−0.132179	+	0.0481093i	−0.00472975	+	0.00172149i
$782$	5.85981	+	22.2422i	0.209546	+	0.795380i
$783$		0			0
$784$	13.9202	−	23.2017i	0.497149	−	0.828633i
$785$	1.07307	+	2.94823i	0.0382994	+	0.105227i
$786$		0			0
$787$	−2.17335	−	2.59010i	−0.0774716	−	0.0923271i	0.725916	−	0.687783i	$-0.241416\pi$
$787$	−2.17335	−	2.59010i	−0.0774716	−	0.0923271i	−0.803388	+	0.595456i	$0.796971\pi$
$788$	19.2816	−	15.9052i	0.686879	−	0.566600i
$789$		0			0
$790$	−1.17133	−	0.552198i	−0.0416740	−	0.0196463i
$791$	3.51231	−	6.08351i	0.124884	−	0.216305i
$792$		0			0
$793$	−16.2661	−	28.1737i	−0.577625	−	1.00048i
$794$	−2.30090	−	27.6351i	−0.0816557	−	0.980735i
$795$		0			0
$796$	1.48385	+	8.84919i	0.0525936	+	0.313651i
$797$	−16.3658	+	44.9646i	−0.579705	+	1.59273i	0.208974	+	0.977921i	$0.432988\pi$
$797$	−16.3658	+	44.9646i	−0.579705	+	1.59273i	−0.788679	+	0.614805i	$0.789235\pi$
$798$		0			0
$799$	17.5393	+	3.09264i	0.620494	+	0.109410i
$800$	−26.9656	+	6.62203i	−0.953378	+	0.234124i
$801$		0			0
$802$	−29.5990	−	8.06437i	−1.04518	−	0.284763i
$803$	−0.0201228	−	0.0168850i	−0.000710117	−	0.000595859i
$804$		0			0
$805$	−0.167491	−	0.949891i	−0.00590330	−	0.0334793i
$806$	−17.9109	−	12.6537i	−0.630883	−	0.445708i
$807$		0			0
$808$	42.5536	+	20.4995i	1.49703	+	0.721169i
$809$		−	17.3637i		−	0.610473i	−0.952277	−	0.305237i	$-0.901264\pi$
$809$		−	17.3637i		−	0.610473i	0.952277	−	0.305237i	$-0.0987356\pi$
$810$		0			0
$811$		−	13.7618i		−	0.483242i	−0.970371	−	0.241621i	$-0.922321\pi$
$811$		−	13.7618i		−	0.483242i	0.970371	−	0.241621i	$-0.0776791\pi$
$812$	−4.42813	+	5.18814i	−0.155397	+	0.182068i
$813$		0			0
$814$	0.228309	−	0.323163i	0.00800223	−	0.0113269i
$815$	0.299589	+	1.69905i	0.0104941	+	0.0595152i
$816$		0			0
$817$	−14.0208	−	11.7648i	−0.490524	−	0.411599i
$818$	4.08842	−	15.0059i	0.142948	−	0.524669i
$819$		0			0
$820$	−3.29698	−	1.94061i	−0.115136	−	0.0677689i
$821$	26.2703	+	4.63216i	0.916840	+	0.161664i	0.612108	−	0.790774i	$-0.290322\pi$
$821$	26.2703	+	4.63216i	0.916840	+	0.161664i	0.304732	+	0.952438i	$0.401433\pi$
$822$		0			0
$823$	−15.0879	+	41.4538i	−0.525932	+	1.44499i	0.337888	+	0.941186i	$0.390288\pi$
$823$	−15.0879	+	41.4538i	−0.525932	+	1.44499i	−0.863820	+	0.503801i	$0.831935\pi$
$824$	−18.4826	−	40.9757i	−0.643872	−	1.42746i
$825$		0			0
$826$	−2.97854	+	0.247993i	−0.103637	+	0.00862876i
$827$	5.67028	+	9.82121i	0.197175	+	0.341517i	0.947611	−	0.319426i	$-0.103490\pi$
$827$	5.67028	+	9.82121i	0.197175	+	0.341517i	−0.750436	+	0.660943i	$0.770157\pi$
$828$		0			0
$829$	14.5329	−	25.1717i	0.504747	−	0.874248i	−0.495238	−	0.868757i	$-0.664919\pi$
$829$	14.5329	−	25.1717i	0.504747	−	0.874248i	0.999985	−	0.00549015i	$-0.00174758\pi$
$830$	−1.05018	+	2.22765i	−0.0364523	+	0.0773230i
$831$		0			0
$832$	−34.1596	+	5.13977i	−1.18427	+	0.178189i
$833$	10.7656	+	12.8300i	0.373007	+	0.444532i
$834$		0			0
$835$	−0.543139	−	1.49226i	−0.0187961	−	0.0516419i
$836$	−0.310446	−	0.548289i	−0.0107370	−	0.0189630i
$837$		0			0
$838$	33.1185	−	8.72523i	1.14406	−	0.301408i
$839$	−11.0585	+	4.02496i	−0.381781	+	0.138957i	−0.525779	−	0.850621i	$-0.676226\pi$
$839$	−11.0585	+	4.02496i	−0.381781	+	0.138957i	0.143998	+	0.989578i	$0.454004\pi$
$840$		0			0
$841$	−15.5866	+	13.0787i	−0.537469	+	0.450990i
$842$	21.6851	+	47.0182i	0.747318	+	1.62035i
$843$		0			0
$844$	−8.16571	+	44.1395i	−0.281075	+	1.51935i
$845$	−1.47865	−	0.853700i	−0.0508672	−	0.0293682i
$846$		0			0
$847$	−4.62422	+	2.66980i	−0.158890	+	0.0917353i
$848$	−25.9812	+	29.9278i	−0.892197	+	1.02772i
$849$		0			0
$850$	1.56987	−	17.1158i	0.0538461	−	0.587065i
$851$	−41.4820	−	15.0982i	−1.42198	−	0.517560i
$852$		0			0
$853$	−7.59288	+	43.0614i	−0.259975	+	1.47439i	0.522996	+	0.852335i	$0.324814\pi$
$853$	−7.59288	+	43.0614i	−0.259975	+	1.47439i	−0.782971	+	0.622058i	$0.786297\pi$
$854$	−3.67306	+	3.64235i	−0.125690	+	0.124639i
$855$		0			0
$856$	0.698713	+	2.74549i	0.0238815	+	0.0938390i
$857$	2.62091	−	3.12348i	0.0895287	−	0.106696i	−0.719420	−	0.694575i	$-0.755592\pi$
$857$	2.62091	−	3.12348i	0.0895287	−	0.106696i	0.808949	+	0.587879i	$0.200037\pi$
$858$		0			0
$859$	38.3251	−	6.75775i	1.30764	−	0.230571i	0.523961	−	0.851743i	$-0.324454\pi$
$859$	38.3251	−	6.75775i	1.30764	−	0.230571i	0.783675	+	0.621171i	$0.213343\pi$
$860$	0.511936	−	1.37061i	0.0174569	−	0.0467375i
$861$		0			0
$862$	44.8019	−	31.0912i	1.52596	−	1.05897i
$863$	48.5663			1.65322			0.826608	−	0.562778i	$-0.190268\pi$
$863$	48.5663			1.65322			0.826608	+	0.562778i	$0.190268\pi$
$864$		0			0
$865$	−0.419573			−0.0142659
$866$	7.62466	−	5.29128i	0.259097	−	0.179805i
$867$		0			0
$868$	−1.22009	+	3.26656i	−0.0414125	+	0.110874i
$869$	−0.124130	+	0.0218875i	−0.00421083	+	0.000742483i
$870$		0			0
$871$	30.9161	−	36.8444i	1.04755	−	1.24842i
$872$	5.06877	+	19.9170i	0.171650	+	0.674474i
$873$		0			0
$874$	−49.9147	+	49.4973i	−1.68839	+	1.67427i
$875$	−0.252648	+	1.43284i	−0.00854107	+	0.0484388i
$876$		0			0
$877$	15.9919	+	5.82058i	0.540008	+	0.196547i	0.597602	−	0.801793i	$-0.296120\pi$
$877$	15.9919	+	5.82058i	0.540008	+	0.196547i	−0.0575935	+	0.998340i	$0.518343\pi$
$878$	−0.235677	+	2.56951i	−0.00795371	+	0.0867167i
$879$		0			0
$880$	0.0330189	−	0.0380345i	0.00111307	−	0.00128214i
$881$	2.59611	−	1.49886i	0.0874651	−	0.0504980i	−0.455630	−	0.890169i	$-0.650586\pi$
$881$	2.59611	−	1.49886i	0.0874651	−	0.0504980i	0.543095	+	0.839672i	$0.317252\pi$
$882$		0			0
$883$	17.0858	+	9.86450i	0.574984	+	0.331967i	0.759137	−	0.650931i	$-0.225621\pi$
$883$	17.0858	+	9.86450i	0.574984	+	0.331967i	−0.184154	+	0.982897i	$0.558954\pi$
$884$	3.88975	−	21.0260i	0.130827	−	0.707180i
$885$		0			0
$886$	−1.03339	−	2.24063i	−0.0347175	−	0.0752754i
$887$	35.6487	−	29.9128i	1.19697	−	1.00437i	0.197254	−	0.980352i	$-0.436798\pi$
$887$	35.6487	−	29.9128i	1.19697	−	1.00437i	0.999711	−	0.0240206i	$-0.00764673\pi$
$888$		0			0
$889$	4.05813	−	1.47704i	0.136105	−	0.0495383i
$890$	−4.30090	+	1.13309i	−0.144166	+	0.0379813i
$891$		0			0
$892$	−18.0497	−	31.8781i	−0.604347	−	1.06736i
$893$	18.6161	+	51.1474i	0.622965	+	1.71158i
$894$		0			0
$895$	−2.24419	−	2.67453i	−0.0750152	−	0.0893996i
$896$	2.17405	+	5.04417i	0.0726300	+	0.168514i
$897$		0			0
$898$	5.57182	−	11.8190i	0.185934	−	0.394405i
$899$	−12.6135	+	21.8472i	−0.420683	+	0.728645i
$900$		0			0
$901$	−12.2661	−	21.2454i	−0.408642	−	0.707788i
$902$	−0.371091	+	0.0308969i	−0.0123560	+	0.00102876i
$903$		0			0
$904$	−16.8270	−	37.3052i	−0.559657	−	1.24075i
$905$	−1.77364	+	4.87305i	−0.0589579	+	0.161986i
$906$		0			0
$907$	34.2556	+	6.04019i	1.13744	+	0.200561i	0.710485	−	0.703712i	$-0.248476\pi$
$907$	34.2556	+	6.04019i	1.13744	+	0.200561i	0.426954	+	0.904273i	$0.359587\pi$
$908$	−33.7880	−	19.8876i	−1.12129	−	0.659994i
$909$		0			0
$910$	−0.235711	+	0.865141i	−0.00781375	+	0.0286791i
$911$	−22.9255	−	19.2368i	−0.759557	−	0.637344i	0.178454	−	0.983948i	$-0.442890\pi$
$911$	−22.9255	−	19.2368i	−0.759557	−	0.637344i	−0.938012	+	0.346604i	$0.887335\pi$
$912$		0			0
$913$	0.0416261	+	0.236073i	0.00137762	+	0.00781289i
$914$	−22.5077	+	31.8589i	−0.744489	+	1.05380i
$915$		0			0
$916$	−7.35942	+	8.62253i	−0.243162	+	0.284896i
$917$		−	9.43490i		−	0.311568i
$918$		0			0
$919$			52.7647i			1.74055i	0.492569	+	0.870273i	$0.336058\pi$
$919$			52.7647i			1.74055i	−0.492569	+	0.870273i	$0.663942\pi$
$920$	−5.06252	−	2.43878i	−0.166906	−	0.0804042i
$921$		0			0
$922$	23.9497	+	16.9201i	0.788742	+	0.557232i
$923$	−2.53335	−	14.3673i	−0.0833862	−	0.472907i
$924$		0			0
$925$	25.2693	+	21.2034i	0.830849	+	0.697165i
$926$	−13.0798	−	3.56365i	−0.429830	−	0.117109i
$927$		0			0
$928$	9.47698	+	38.5913i	0.311097	+	1.26682i
$929$	54.7677	+	9.65703i	1.79687	+	0.316837i	0.969550	−	0.244892i	$-0.0787526\pi$
$929$	54.7677	+	9.65703i	1.79687	+	0.316837i	0.827321	+	0.561729i	$0.189864\pi$
$930$		0			0
$931$	−17.5066	+	48.0989i	−0.573755	+	1.57638i
$932$	2.48434	+	14.8158i	0.0813772	+	0.485307i
$933$		0			0
$934$	−2.05285	−	24.6560i	−0.0671713	−	0.806768i
$935$	0.0155887	+	0.0270003i	0.000509803	+	0.000883005i
$936$		0			0
$937$	9.12048	−	15.7971i	0.297953	−	0.516070i	−0.677715	−	0.735325i	$-0.737029\pi$
$937$	9.12048	−	15.7971i	0.297953	−	0.516070i	0.975667	+	0.219255i	$0.0703628\pi$
$938$	−6.91756	−	3.26114i	−0.225866	−	0.106480i
$939$		0			0
$940$	−3.35646	+	2.76871i	−0.109476	+	0.0903054i
$941$	−11.2021	−	13.3502i	−0.365179	−	0.435204i	0.551899	−	0.833911i	$-0.313903\pi$
$941$	−11.2021	−	13.3502i	−0.365179	−	0.435204i	−0.917078	+	0.398707i	$0.869459\pi$
$942$		0			0
$943$	14.2091	+	39.0392i	0.462712	+	1.27129i
$944$	−8.95832	+	14.9315i	−0.291568	+	0.485978i
$945$		0			0
$946$	−0.0362807	−	0.137712i	−0.00117959	−	0.00447739i
$947$	40.4292	−	14.7150i	1.31377	−	0.478174i	0.412315	−	0.911042i	$-0.364720\pi$
$947$	40.4292	−	14.7150i	1.31377	−	0.478174i	0.901458	+	0.432868i	$0.142498\pi$
$948$		0			0
$949$	2.08706	−	1.75125i	0.0677488	−	0.0568480i
$950$	47.6995	−	21.9993i	1.54758	−	0.713753i
$951$		0			0
$952$	−3.39052	+	0.253647i	−0.109887	+	0.00822074i
$953$	17.5809	+	10.1503i	0.569502	+	0.328802i	0.756950	−	0.653472i	$-0.226688\pi$
$953$	17.5809	+	10.1503i	0.569502	+	0.328802i	−0.187449	+	0.982274i	$0.560022\pi$
$954$		0			0
$955$	4.33625	−	2.50353i	0.140318	−	0.0810124i
$956$	−4.32461	−	12.1995i	−0.139868	−	0.394561i
$957$		0			0
$958$	−36.8927	−	3.38383i	−1.19195	−	0.109326i
$959$	−6.99708	−	2.54673i	−0.225947	−	0.0822382i
$960$		0			0
$961$	3.14365	−	17.8285i	0.101408	−	0.575113i
$962$	28.8962	+	29.1399i	0.931652	+	0.939507i
$963$		0			0
$964$	0.0116530	−	1.38779i	0.000375319	−	0.0446977i
$965$	1.71141	−	2.03958i	0.0550923	−	0.0656565i
$966$		0			0
$967$	46.0060	−	8.11209i	1.47945	−	0.260867i	0.625093	−	0.780550i	$-0.285061\pi$
$967$	46.0060	−	8.11209i	1.47945	−	0.260867i	0.854359	+	0.519683i	$0.173950\pi$
$968$	−3.10131	+	30.9528i	−0.0996798	+	0.994861i
$969$		0			0
$970$	0.812356	+	1.17059i	0.0260832	+	0.0375855i
$971$	29.3788			0.942809			0.471405	−	0.881917i	$-0.343747\pi$
$971$	29.3788			0.942809			0.471405	+	0.881917i	$0.343747\pi$
$972$		0			0
$973$	−4.33784			−0.139065
$974$	5.73237	+	8.26027i	0.183677	+	0.264676i
$975$		0			0
$976$	4.73399	+	29.7621i	0.151531	+	0.952661i
$977$	−18.3908	+	3.24280i	−0.588375	+	0.103746i	−0.459907	−	0.887967i	$-0.652117\pi$
$977$	−18.3908	+	3.24280i	−0.588375	+	0.103746i	−0.128468	+	0.991714i	$0.541006\pi$
$978$		0			0
$979$	−0.278270	+	0.331630i	−0.00889356	+	0.0105989i
$980$	−4.09157	−	0.0343562i	−0.130700	−	0.00109747i
$981$		0			0
$982$	−19.6699	−	19.8357i	−0.627691	−	0.632984i
$983$	−4.54380	+	25.7692i	−0.144925	+	0.821909i	0.822503	+	0.568761i	$0.192577\pi$
$983$	−4.54380	+	25.7692i	−0.144925	+	0.821909i	−0.967428	+	0.253148i	$0.918534\pi$
$984$		0			0
$985$	−3.55193	−	1.29280i	−0.113174	−	0.0411919i
$986$	−24.4949	−	2.24669i	−0.780075	−	0.0715490i
$987$		0			0
$988$	61.5938	−	21.8344i	1.95956	−	0.694644i
$989$	−13.7596	+	7.94413i	−0.437531	+	0.252609i
$990$		0			0
$991$	−25.5875	−	14.7730i	−0.812815	−	0.469279i	0.0351178	−	0.999383i	$-0.488819\pi$
$991$	−25.5875	−	14.7730i	−0.812815	−	0.469279i	−0.847932	+	0.530105i	$0.822153\pi$
$992$	11.3002	+	16.8817i	0.358781	+	0.535995i
$993$		0			0
$994$	−2.10650	+	0.971531i	−0.0668141	+	0.0308151i
$995$	1.03945	−	0.872198i	0.0329526	−	0.0276505i
$996$		0			0
$997$	−37.2095	+	13.5431i	−1.17844	+	0.428916i	−0.855649	−	0.517556i	$-0.826842\pi$
$997$	−37.2095	+	13.5431i	−1.17844	+	0.428916i	−0.322787	+	0.946472i	$0.604620\pi$
$998$	14.2410	+	54.0548i	0.450790	+	1.71107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.143.3		96
3.2	odd	2		108.2.l.a.47.14	yes	96
4.3	odd	2	inner	324.2.l.a.143.16		96
9.2	odd	6		972.2.l.d.107.3		96
9.4	even	3		972.2.l.b.755.9		96
9.5	odd	6		972.2.l.c.755.8		96
9.7	even	3		972.2.l.a.107.14		96
12.11	even	2		108.2.l.a.47.1	yes	96
27.4	even	9		108.2.l.a.23.1	✓	96
27.5	odd	18		972.2.l.b.215.7		96
27.13	even	9		972.2.l.d.863.12		96
27.14	odd	18		972.2.l.a.863.5		96
27.22	even	9		972.2.l.c.215.10		96
27.23	odd	18	inner	324.2.l.a.179.16		96
36.7	odd	6		972.2.l.a.107.5		96
36.11	even	6		972.2.l.d.107.12		96
36.23	even	6		972.2.l.c.755.10		96
36.31	odd	6		972.2.l.b.755.7		96
108.23	even	18	inner	324.2.l.a.179.3		96
108.31	odd	18		108.2.l.a.23.14	yes	96
108.59	even	18		972.2.l.b.215.9		96
108.67	odd	18		972.2.l.d.863.3		96
108.95	even	18		972.2.l.a.863.14		96
108.103	odd	18		972.2.l.c.215.8		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.1	✓	96	27.4	even	9
108.2.l.a.23.14	yes	96	108.31	odd	18
108.2.l.a.47.1	yes	96	12.11	even	2
108.2.l.a.47.14	yes	96	3.2	odd	2
324.2.l.a.143.3		96	1.1	even	1	trivial
324.2.l.a.143.16		96	4.3	odd	2	inner
324.2.l.a.179.3		96	108.23	even	18	inner
324.2.l.a.179.16		96	27.23	odd	18	inner
972.2.l.a.107.5		96	36.7	odd	6
972.2.l.a.107.14		96	9.7	even	3
972.2.l.a.863.5		96	27.14	odd	18
972.2.l.a.863.14		96	108.95	even	18
972.2.l.b.215.7		96	27.5	odd	18
972.2.l.b.215.9		96	108.59	even	18
972.2.l.b.755.7		96	36.31	odd	6
972.2.l.b.755.9		96	9.4	even	3
972.2.l.c.215.8		96	108.103	odd	18
972.2.l.c.215.10		96	27.22	even	9
972.2.l.c.755.8		96	9.5	odd	6
972.2.l.c.755.10		96	36.23	even	6
972.2.l.d.107.3		96	9.2	odd	6
972.2.l.d.107.12		96	36.11	even	6
972.2.l.d.863.3		96	108.67	odd	18
972.2.l.d.863.12		96	27.13	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.16185 + 0.806289i) q^{2} +(0.699796 - 1.87358i) q^{4} +(-0.297855 + 0.0525198i) q^{5} +(-0.312070 + 0.371910i) q^{7} +(0.697584 + 2.74105i) q^{8} +O(q^{10})\)	\(q+(-1.16185 + 0.806289i) q^{2} +(0.699796 - 1.87358i) q^{4} +(-0.297855 + 0.0525198i) q^{5} +(-0.312070 + 0.371910i) q^{7} +(0.697584 + 2.74105i) q^{8} +(0.303717 - 0.301177i) q^{10} +(0.00722947 - 0.0410004i) q^{11} +(4.05761 + 1.47685i) q^{13} +(0.0627115 - 0.683722i) q^{14} +(-3.02057 - 2.62224i) q^{16} +(2.14427 - 1.23800i) q^{17} +(6.55326 + 3.78353i) q^{19} +(-0.110038 + 0.594806i) q^{20} +(0.0246586 + 0.0534654i) q^{22} +(5.03199 - 4.22234i) q^{23} +(-4.61250 + 1.67881i) q^{25} +(-5.90510 + 1.55572i) q^{26} +(0.478416 + 0.844947i) q^{28} +(2.40260 + 6.60109i) q^{29} +(2.30836 + 2.75099i) q^{31} +(5.62374 + 0.611204i) q^{32} +(-1.49314 + 3.16727i) q^{34} +(0.0734187 - 0.127165i) q^{35} +(-3.36015 - 5.81994i) q^{37} +(-10.6645 + 0.887926i) q^{38} +(-0.351738 - 0.779799i) q^{40} +(-2.16312 + 5.94312i) q^{41} +(-2.38200 - 0.420011i) q^{43} +(-0.0717582 - 0.0422369i) q^{44} +(-2.44200 + 8.96296i) q^{46} +(5.51016 + 4.62358i) q^{47} +(1.17461 + 6.66153i) q^{49} +(4.00543 - 5.66954i) q^{50} +(5.60648 - 6.56874i) q^{52} -9.90799i q^{53} +0.0125918i q^{55} +(-1.23712 - 0.595961i) q^{56} +(-8.11385 - 5.73229i) q^{58} +(-0.755918 - 4.28703i) q^{59} +(-5.77142 - 4.84280i) q^{61} +(-4.90006 - 1.33504i) q^{62} +(-7.02675 + 3.82423i) q^{64} +(-1.28614 - 0.226781i) q^{65} +(3.80965 - 10.4669i) q^{67} +(-0.818925 - 4.88380i) q^{68} +(0.0172301 + 0.206943i) q^{70} +(-1.68932 - 2.92598i) q^{71} +(0.315477 - 0.546421i) q^{73} +(8.59654 + 4.05266i) q^{74} +(11.6747 - 9.63033i) q^{76} +(0.0129924 + 0.0154837i) q^{77} +(-1.03548 - 2.84496i) q^{79} +(1.03741 + 0.622407i) q^{80} +(-2.27865 - 8.64913i) q^{82} +(-5.41059 + 1.96930i) q^{83} +(-0.573662 + 0.481360i) q^{85} +(3.10618 - 1.43259i) q^{86} +(0.117427 - 0.00878482i) q^{88} +(-9.00521 - 5.19916i) q^{89} +(-1.81551 + 1.04819i) q^{91} +(-4.38950 - 12.3826i) q^{92} +(-10.1299 - 0.929124i) q^{94} +(-2.15063 - 0.782765i) q^{95} +(-0.578459 + 3.28061i) q^{97} +(-6.73584 - 6.79263i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

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